LMFDB - Embedded newform 9.10.c.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,10,Mod(4,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	9.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.63532252547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 $ x^16 - 8x^15 + 1984x^14 - 13748x^13 + 1552498x^12 - 9136628x^11 + 609566956x^10 - 2964409064x^9 + 126210674407x^8 - 487156186164x^7 + 13162328064828x^6 - 37794288146040x^5 + 578928267028062x^4 - 1095428523832956x^3 + 5807598664427172x^2 - 5266103139591300*x + 1336504689748125
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{28}\cdot 17^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.5
Root			$0.500000 - 3.55897i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.10.c.a.7.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.83216 + 6.63749i) q^{2} +(58.6695 + 127.440i) q^{3} +(226.629 - 392.533i) q^{4} +(-1105.48 + 1914.74i) q^{5} +(-621.050 + 877.788i) q^{6} +(3116.58 + 5398.07i) q^{7} +7398.05 q^{8} +(-12798.8 + 14953.6i) q^{9} +O(q^{10})$	\(q+(3.83216 + 6.63749i) q^{2} +(58.6695 + 127.440i) q^{3} +(226.629 - 392.533i) q^{4} +(-1105.48 + 1914.74i) q^{5} +(-621.050 + 877.788i) q^{6} +(3116.58 + 5398.07i) q^{7} +7398.05 q^{8} +(-12798.8 + 14953.6i) q^{9} -16945.4 q^{10} +(-9312.12 - 16129.1i) q^{11} +(63320.5 + 5851.85i) q^{12} +(84699.6 - 146704. i) q^{13} +(-23886.4 + 41372.5i) q^{14} +(-308872. - 28544.8i) q^{15} +(-87683.6 - 151872. i) q^{16} +433113. q^{17} +(-148302. - 27647.1i) q^{18} +51200.2 q^{19} +(501066. + 867871. i) q^{20} +(-505081. + 713877. i) q^{21} +(71371.1 - 123618. i) q^{22} +(-152281. + 263759. i) q^{23} +(434039. + 942805. i) q^{24} +(-1.46759e6 - 2.54194e6i) q^{25} +1.29833e6 q^{26} +(-2.65659e6 - 753752. i) q^{27} +2.82523e6 q^{28} +(568995. + 985528. i) q^{29} +(-994179. - 2.15952e6i) q^{30} +(389293. - 674275. i) q^{31} +(2.56594e6 - 4.44433e6i) q^{32} +(1.50915e6 - 2.13302e6i) q^{33} +(1.65976e6 + 2.87479e6i) q^{34} -1.37812e7 q^{35} +(2.96922e6 + 8.41288e6i) q^{36} -6.32050e6 q^{37} +(196207. + 339841. i) q^{38} +(2.36652e7 + 2.18705e6i) q^{39} +(-8.17836e6 + 1.41653e7i) q^{40} +(1.23991e6 - 2.14759e6i) q^{41} +(-6.67391e6 - 616778. i) q^{42} +(1.56300e7 + 2.70719e7i) q^{43} -8.44159e6 q^{44} +(-1.44836e7 - 4.10372e7i) q^{45} -2.33427e6 q^{46} +(-5.07040e6 - 8.78219e6i) q^{47} +(1.42102e7 - 2.00847e7i) q^{48} +(750710. - 1.30027e6i) q^{49} +(1.12481e7 - 1.94822e7i) q^{50} +(2.54105e7 + 5.51958e7i) q^{51} +(-3.83908e7 - 6.64948e7i) q^{52} -3.32278e7 q^{53} +(-5.17744e6 - 2.05216e7i) q^{54} +4.11773e7 q^{55} +(2.30566e7 + 3.99352e7i) q^{56} +(3.00389e6 + 6.52494e6i) q^{57} +(-4.36096e6 + 7.55340e6i) q^{58} +(2.33603e7 - 4.04612e7i) q^{59} +(-8.12041e7 + 1.14773e8i) q^{60} +(3.06902e7 + 5.31570e7i) q^{61} +5.96733e6 q^{62} +(-1.20609e8 - 2.24846e7i) q^{63} -5.04557e7 q^{64} +(1.87267e8 + 3.24355e8i) q^{65} +(1.99412e7 + 1.84289e6i) q^{66} +(1.37409e8 - 2.37999e8i) q^{67} +(9.81560e7 - 1.70011e8i) q^{68} +(-4.25477e7 - 3.93210e6i) q^{69} +(-5.28117e7 - 9.14726e7i) q^{70} -2.93935e8 q^{71} +(-9.46860e7 + 1.10628e8i) q^{72} -1.55084e8 q^{73} +(-2.42212e7 - 4.19523e7i) q^{74} +(2.37841e8 - 3.36163e8i) q^{75} +(1.16034e7 - 2.00978e7i) q^{76} +(5.80439e7 - 1.00535e8i) q^{77} +(7.61723e7 + 1.65459e8i) q^{78} +(1.17883e8 + 2.04180e8i) q^{79} +3.87728e8 q^{80} +(-5.98026e7 - 3.82777e8i) q^{81} +1.90061e7 q^{82} +(-1.68070e8 - 2.91106e8i) q^{83} +(1.65755e8 + 3.60046e8i) q^{84} +(-4.78796e8 + 8.29299e8i) q^{85} +(-1.19793e8 + 2.07488e8i) q^{86} +(-9.22129e7 + 1.30333e8i) q^{87} +(-6.88915e7 - 1.19324e8i) q^{88} -1.03812e9 q^{89} +(2.16881e8 - 2.53396e8i) q^{90} +1.05589e9 q^{91} +(6.90228e7 + 1.19551e8i) q^{92} +(1.08769e8 + 1.00520e7i) q^{93} +(3.88611e7 - 6.73095e7i) q^{94} +(-5.66005e7 + 9.80350e7i) q^{95} +(7.16926e8 + 6.62557e7i) q^{96} +(1.34786e8 + 2.33457e8i) q^{97} +1.15074e7 q^{98} +(3.60372e8 + 6.71823e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9}+O(q^{10}) $ 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16} - 831078 q^{17} - 1039500 q^{18} - 170554 q^{19} + 1855164 q^{20} - 503475 q^{21} + 529359 q^{22} + 1064559 q^{23} - 2686059 q^{24} - 2293229 q^{25} + 2436312 q^{26} - 6176520 q^{27} + 1225724 q^{28} - 1309053 q^{29} + 30713544 q^{30} - 2359819 q^{31} + 5760063 q^{32} - 19931472 q^{33} + 981801 q^{34} - 31066554 q^{35} - 48894093 q^{36} + 16391516 q^{37} + 39490203 q^{38} + 74528535 q^{39} - 16760496 q^{40} + 54747318 q^{41} + 25242354 q^{42} + 15249608 q^{43} - 332509926 q^{44} - 139865967 q^{45} + 2390520 q^{46} + 156295545 q^{47} + 312045027 q^{48} + 15239583 q^{49} + 315590163 q^{50} + 3098385 q^{51} - 19773358 q^{52} - 525516228 q^{53} - 591710103 q^{54} - 7579770 q^{55} + 470339790 q^{56} + 581271465 q^{57} + 55408560 q^{58} + 307774074 q^{59} - 430082172 q^{60} + 69192125 q^{61} - 914436924 q^{62} - 693544725 q^{63} - 403588478 q^{64} + 482470359 q^{65} + 1912534074 q^{66} + 14328044 q^{67} + 915409575 q^{68} - 724756329 q^{69} - 229271934 q^{70} - 1239601392 q^{71} - 1729340037 q^{72} + 598613198 q^{73} + 1022736000 q^{74} + 1477690413 q^{75} + 119954093 q^{76} + 717995541 q^{77} + 243023958 q^{78} + 30257531 q^{79} - 2927826528 q^{80} - 1055378241 q^{81} - 202376022 q^{82} + 1176168291 q^{83} + 1383634866 q^{84} + 4818366 q^{85} + 1426944009 q^{86} + 617958567 q^{87} + 911312427 q^{88} - 3317041296 q^{89} - 981417492 q^{90} - 739230122 q^{91} - 76813998 q^{92} - 552731577 q^{93} - 1954316784 q^{94} - 391400652 q^{95} + 1854064512 q^{96} - 267311278 q^{97} + 4827300318 q^{98} + 1672014609 q^{99}+O(q^{100}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9 + 1020 * q^10 + 99150 * q^11 - 241212 * q^12 + 32435 * q^13 + 394824 * q^14 + 723843 * q^15 - 328193 * q^16 - 831078 * q^17 - 1039500 * q^18 - 170554 * q^19 + 1855164 * q^20 - 503475 * q^21 + 529359 * q^22 + 1064559 * q^23 - 2686059 * q^24 - 2293229 * q^25 + 2436312 * q^26 - 6176520 * q^27 + 1225724 * q^28 - 1309053 * q^29 + 30713544 * q^30 - 2359819 * q^31 + 5760063 * q^32 - 19931472 * q^33 + 981801 * q^34 - 31066554 * q^35 - 48894093 * q^36 + 16391516 * q^37 + 39490203 * q^38 + 74528535 * q^39 - 16760496 * q^40 + 54747318 * q^41 + 25242354 * q^42 + 15249608 * q^43 - 332509926 * q^44 - 139865967 * q^45 + 2390520 * q^46 + 156295545 * q^47 + 312045027 * q^48 + 15239583 * q^49 + 315590163 * q^50 + 3098385 * q^51 - 19773358 * q^52 - 525516228 * q^53 - 591710103 * q^54 - 7579770 * q^55 + 470339790 * q^56 + 581271465 * q^57 + 55408560 * q^58 + 307774074 * q^59 - 430082172 * q^60 + 69192125 * q^61 - 914436924 * q^62 - 693544725 * q^63 - 403588478 * q^64 + 482470359 * q^65 + 1912534074 * q^66 + 14328044 * q^67 + 915409575 * q^68 - 724756329 * q^69 - 229271934 * q^70 - 1239601392 * q^71 - 1729340037 * q^72 + 598613198 * q^73 + 1022736000 * q^74 + 1477690413 * q^75 + 119954093 * q^76 + 717995541 * q^77 + 243023958 * q^78 + 30257531 * q^79 - 2927826528 * q^80 - 1055378241 * q^81 - 202376022 * q^82 + 1176168291 * q^83 + 1383634866 * q^84 + 4818366 * q^85 + 1426944009 * q^86 + 617958567 * q^87 + 911312427 * q^88 - 3317041296 * q^89 - 981417492 * q^90 - 739230122 * q^91 - 76813998 * q^92 - 552731577 * q^93 - 1954316784 * q^94 - 391400652 * q^95 + 1854064512 * q^96 - 267311278 * q^97 + 4827300318 * q^98 + 1672014609 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.83216	+	6.63749i	0.169359	+	0.293339i	0.938195	−	0.346108i	$-0.112497\pi$
$2$	3.83216	+	6.63749i	0.169359	+	0.293339i	−0.768836	+	0.639447i	$0.779164\pi$
$3$	58.6695	+	127.440i	0.418183	+	0.908363i
$3$	58.6695	+	127.440i	0.418183	+	0.908363i
$4$	226.629	−	392.533i	0.442635	−	0.766666i
$5$	−1105.48	+	1914.74i	−0.791014	+	1.37008i	0.134326	+	0.990937i	$0.457113\pi$
$5$	−1105.48	+	1914.74i	−0.791014	+	1.37008i	−0.925340	+	0.379139i	$0.876220\pi$
$6$	−621.050	+	877.788i	−0.195635	+	0.276509i
$7$	3116.58	+	5398.07i	0.490610	+	0.849762i	0.999942	−	0.0108087i	$-0.00344058\pi$
$7$	3116.58	+	5398.07i	0.490610	+	0.849762i	−0.509331	+	0.860570i	$0.670107\pi$
$8$	7398.05			0.638575
$9$	−12798.8	+	14953.6i	−0.650246	+	0.759724i
$10$	−16945.4			−0.535862
$11$	−9312.12	−	16129.1i	−0.191770	−	0.332156i	0.754067	−	0.656798i	$-0.228090\pi$
$11$	−9312.12	−	16129.1i	−0.191770	−	0.332156i	−0.945837	+	0.324642i	$0.894756\pi$
$12$	63320.5	+	5851.85i	0.881514	+	0.0814662i
$13$	84699.6	−	146704.i	0.822501	−	1.42461i	−0.0813133	−	0.996689i	$-0.525911\pi$
$13$	84699.6	−	146704.i	0.822501	−	1.42461i	0.903814	−	0.427925i	$-0.140755\pi$
$14$	−23886.4	+	41372.5i	−0.166179	+	0.287830i
$15$	−308872.	−	28544.8i	−1.57531	−	0.145585i
$16$	−87683.6	−	151872.i	−0.334486	−	0.579347i
$17$	433113.			1.25771			0.628856	−	0.777522i	$-0.283524\pi$
$17$	433113.			1.25771			0.628856	+	0.777522i	$0.283524\pi$
$18$	−148302.	−	27647.1i	−0.332981	−	0.0620760i
$19$	51200.2			0.0901322			0.0450661	−	0.998984i	$-0.485650\pi$
$19$	51200.2			0.0901322			0.0450661	+	0.998984i	$0.485650\pi$
$20$	501066.	+	867871.i	0.700261	+	1.21289i
$21$	−505081.	+	713877.i	−0.566727	+	0.801008i
$22$	71371.1	−	123618.i	0.0649561	−	0.112507i
$23$	−152281.	+	263759.i	−0.113468	+	0.196532i	−0.917166	−	0.398505i	$-0.869529\pi$
$23$	−152281.	+	263759.i	−0.113468	+	0.196532i	0.803699	+	0.595037i	$0.202862\pi$
$24$	434039.	+	942805.i	0.267041	+	0.580058i
$25$	−1.46759e6	−	2.54194e6i	−0.751406	−	1.30147i
$26$	1.29833e6			0.557192
$27$	−2.65659e6	−	753752.i	−0.962027	−	0.272955i
$28$	2.82523e6			0.868645
$29$	568995.	+	985528.i	0.149389	+	0.258749i	0.931002	−	0.365015i	$-0.118936\pi$
$29$	568995.	+	985528.i	0.149389	+	0.258749i	−0.781613	+	0.623764i	$0.785603\pi$
$30$	−994179.	−	2.15952e6i	−0.224088	−	0.486757i
$31$	389293.	−	674275.i	0.0757092	−	0.131132i	−0.825685	−	0.564131i	$-0.809211\pi$
$31$	389293.	−	674275.i	0.0757092	−	0.131132i	0.901394	+	0.432999i	$0.142545\pi$
$32$	2.56594e6	−	4.44433e6i	0.432584	−	0.749258i
$33$	1.50915e6	−	2.13302e6i	0.221523	−	0.313099i
$34$	1.65976e6	+	2.87479e6i	0.213005	+	0.368935i
$35$	−1.37812e7			−1.55232
$36$	2.96922e6	+	8.41288e6i	0.294633	+	0.834802i
$37$	−6.32050e6			−0.554426			−0.277213	−	0.960808i	$-0.589411\pi$
$37$	−6.32050e6			−0.554426			−0.277213	+	0.960808i	$0.589411\pi$
$38$	196207.	+	339841.i	0.0152647	+	0.0264393i
$39$	2.36652e7	+	2.18705e6i	1.63802	+	0.151380i
$40$	−8.17836e6	+	1.41653e7i	−0.505122	+	0.874897i
$41$	1.23991e6	−	2.14759e6i	0.0685271	−	0.118692i	−0.829726	−	0.558171i	$-0.811503\pi$
$41$	1.23991e6	−	2.14759e6i	0.0685271	−	0.118692i	0.898253	+	0.439478i	$0.144837\pi$
$42$	−6.67391e6	−	616778.i	−0.330947	−	0.0305849i
$43$	1.56300e7	+	2.70719e7i	0.697189	+	1.20757i	0.969437	+	0.245339i	$0.0788993\pi$
$43$	1.56300e7	+	2.70719e7i	0.697189	+	1.20757i	−0.272249	+	0.962227i	$0.587767\pi$
$44$	−8.44159e6			−0.339537
$45$	−1.44836e7	−	4.10372e7i	−0.526526	−	1.49184i
$46$	−2.33427e6			−0.0768671
$47$	−5.07040e6	−	8.78219e6i	−0.151566	−	0.262520i	0.780237	−	0.625484i	$-0.215098\pi$
$47$	−5.07040e6	−	8.78219e6i	−0.151566	−	0.262520i	−0.931803	+	0.362964i	$0.881765\pi$
$48$	1.42102e7	−	2.00847e7i	0.386381	−	0.546108i
$49$	750710.	−	1.30027e6i	0.0186033	−	0.0322219i
$50$	1.12481e7	−	1.94822e7i	0.254515	−	0.440832i
$51$	2.54105e7	+	5.51958e7i	0.525954	+	1.14246i
$52$	−3.83908e7	−	6.64948e7i	−0.728135	−	1.26117i
$53$	−3.32278e7			−0.578442			−0.289221	−	0.957262i	$-0.593396\pi$
$53$	−3.32278e7			−0.578442			−0.289221	+	0.957262i	$0.593396\pi$
$54$	−5.17744e6	−	2.05216e7i	−0.0828597	−	0.328427i
$55$	4.11773e7			0.606772
$56$	2.30566e7	+	3.99352e7i	0.313292	+	0.542637i
$57$	3.00389e6	+	6.52494e6i	0.0376918	+	0.0818727i
$58$	−4.36096e6	+	7.55340e6i	−0.0506007	+	0.0876429i
$59$	2.33603e7	−	4.04612e7i	0.250983	−	0.434715i	−0.712814	−	0.701353i	$-0.752580\pi$
$59$	2.33603e7	−	4.04612e7i	0.250983	−	0.434715i	0.963797	+	0.266639i	$0.0859130\pi$
$60$	−8.12041e7	+	1.14773e8i	−0.808904	+	1.14330i
$61$	3.06902e7	+	5.31570e7i	0.283802	+	0.491560i	0.972318	−	0.233662i	$-0.0750708\pi$
$61$	3.06902e7	+	5.31570e7i	0.283802	+	0.491560i	−0.688516	+	0.725221i	$0.741737\pi$
$62$	5.96733e6			0.0512882
$63$	−1.20609e8	−	2.24846e7i	−0.964602	−	0.179826i
$64$	−5.04557e7			−0.375924
$65$	1.87267e8	+	3.24355e8i	1.30122	+	2.25378i
$66$	1.99412e7	+	1.84289e6i	0.129361	+	0.0119551i
$67$	1.37409e8	−	2.37999e8i	0.833062	−	1.44291i	−0.0625367	−	0.998043i	$-0.519919\pi$
$67$	1.37409e8	−	2.37999e8i	0.833062	−	1.44291i	0.895599	−	0.444863i	$-0.146748\pi$
$68$	9.81560e7	−	1.70011e8i	0.556707	−	0.964245i
$69$	−4.25477e7	−	3.93210e6i	−0.225972	−	0.0208835i
$70$	−5.28117e7	−	9.14726e7i	−0.262899	−	0.455355i
$71$	−2.93935e8			−1.37274			−0.686372	−	0.727251i	$-0.740798\pi$
$71$	−2.93935e8			−1.37274			−0.686372	+	0.727251i	$0.740798\pi$
$72$	−9.46860e7	+	1.10628e8i	−0.415231	+	0.485141i
$73$	−1.55084e8			−0.639168			−0.319584	−	0.947558i	$-0.603543\pi$
$73$	−1.55084e8			−0.639168			−0.319584	+	0.947558i	$0.603543\pi$
$74$	−2.42212e7	−	4.19523e7i	−0.0938971	−	0.162635i
$75$	2.37841e8	−	3.36163e8i	0.867984	−	1.22680i
$76$	1.16034e7	−	2.00978e7i	0.0398957	−	0.0691013i
$77$	5.80439e7	−	1.00535e8i	0.188169	−	0.325918i
$78$	7.61723e7	+	1.65459e8i	0.233008	+	0.506133i
$79$	1.17883e8	+	2.04180e8i	0.340511	+	0.589782i	0.984528	−	0.175230i	$-0.0560668\pi$
$79$	1.17883e8	+	2.04180e8i	0.340511	+	0.589782i	−0.644017	+	0.765011i	$0.722733\pi$
$80$	3.87728e8			1.05833
$81$	−5.98026e7	−	3.82777e8i	−0.154361	−	0.988015i
$82$	1.90061e7			0.0464228
$83$	−1.68070e8	−	2.91106e8i	−0.388722	−	0.673287i	0.603556	−	0.797321i	$-0.293750\pi$
$83$	−1.68070e8	−	2.91106e8i	−0.388722	−	0.673287i	−0.992278	+	0.124034i	$0.960417\pi$
$84$	1.65755e8	+	3.60046e8i	0.363253	+	0.789045i
$85$	−4.78796e8	+	8.29299e8i	−0.994867	+	1.72316i
$86$	−1.19793e8	+	2.07488e8i	−0.236150	+	0.409025i
$87$	−9.22129e7	+	1.30333e8i	−0.172566	+	0.243903i
$88$	−6.88915e7	−	1.19324e8i	−0.122460	−	0.212107i
$89$	−1.03812e9			−1.75384			−0.876922	−	0.480633i	$-0.840407\pi$
$89$	−1.03812e9			−1.75384			−0.876922	+	0.480633i	$0.840407\pi$
$90$	2.16881e8	−	2.53396e8i	0.348442	−	0.407107i
$91$	1.05589e9			1.61411
$92$	6.90228e7	+	1.19551e8i	0.100449	+	0.173983i
$93$	1.08769e8	+	1.00520e7i	0.150776	+	0.0139342i
$94$	3.88611e7	−	6.73095e7i	0.0513382	−	0.0889203i
$95$	−5.66005e7	+	9.80350e7i	−0.0712958	+	0.123488i
$96$	7.16926e8	+	6.62557e7i	0.861498	+	0.0796164i
$97$	1.34786e8	+	2.33457e8i	0.154587	+	0.267753i	0.932909	−	0.360113i	$-0.117262\pi$
$97$	1.34786e8	+	2.33457e8i	0.154587	+	0.267753i	−0.778321	+	0.627866i	$0.783929\pi$
$98$	1.15074e7			0.0126026
$99$	3.60372e8	+	6.71823e7i	0.377045	+	0.0702905i
$100$	−1.33039e9			−1.33039
$101$	−4.90047e8	−	8.48786e8i	−0.468588	−	0.811618i	0.530767	−	0.847518i	$-0.321904\pi$
$101$	−4.90047e8	−	8.48786e8i	−0.468588	−	0.811618i	−0.999355	+	0.0358992i	$0.988570\pi$
$102$	−2.68985e8	+	3.80181e8i	−0.246052	+	0.347768i
$103$	8.36838e7	−	1.44945e8i	0.0732611	−	0.126892i	−0.827068	−	0.562102i	$-0.809993\pi$
$103$	8.36838e7	−	1.44945e8i	0.0732611	−	0.126892i	0.900329	+	0.435210i	$0.143326\pi$
$104$	6.26612e8	−	1.08532e9i	0.525229	−	0.909723i
$105$	−8.08535e8	−	1.75627e9i	−0.649153	−	1.41007i
$106$	−1.27334e8	−	2.20549e8i	−0.0979644	−	0.169679i
$107$	1.91944e9			1.41563			0.707813	−	0.706400i	$-0.249682\pi$
$107$	1.91944e9			1.41563			0.707813	+	0.706400i	$0.249682\pi$
$108$	−8.97933e8	+	8.71976e8i	−0.635092	+	0.616734i
$109$	2.60871e8			0.177013			0.0885066	−	0.996076i	$-0.471791\pi$
$109$	2.60871e8			0.177013			0.0885066	+	0.996076i	$0.471791\pi$
$110$	1.57798e8	+	2.73314e8i	0.102762	+	0.177990i
$111$	−3.70820e8	−	8.05483e8i	−0.231852	−	0.503620i
$112$	5.46545e8	−	9.46644e8i	0.328205	−	0.568468i
$113$	−1.63303e9	+	2.82850e9i	−0.942197	+	1.63193i	−0.180929	+	0.983496i	$0.557911\pi$
$113$	−1.63303e9	+	2.82850e9i	−0.942197	+	1.63193i	−0.761268	+	0.648438i	$0.775423\pi$
$114$	−3.17979e7	+	4.49429e7i	−0.0176330	+	0.0249223i
$115$	−3.36687e8	−	5.83159e8i	−0.179509	−	0.310918i
$116$	5.15803e8			0.264499
$117$	1.10971e9	+	3.14420e9i	0.547485	+	1.55122i
$118$	3.58081e8			0.170025
$119$	1.34983e9	+	2.33797e9i	0.617046	+	1.06876i
$120$	−2.28505e9	−	2.11176e8i	−1.00596	−	0.0929668i
$121$	1.00554e9	−	1.74165e9i	0.426448	−	0.738630i
$122$	−2.35220e8	+	4.07412e8i	−0.0961290	+	0.166500i
$123$	3.46433e8	+	3.20160e7i	0.136473	+	0.0126123i
$124$	−1.76450e8	−	3.05621e8i	−0.0670231	−	0.116087i
$125$	2.17127e9			0.795461
$126$	−3.12953e8	−	8.86707e8i	−0.110614	−	0.313410i
$127$	−1.25753e9			−0.428944			−0.214472	−	0.976730i	$-0.568803\pi$
$127$	−1.25753e9			−0.428944			−0.214472	+	0.976730i	$0.568803\pi$
$128$	−1.50711e9	−	2.61040e9i	−0.496251	−	0.859531i
$129$	−2.53304e9	+	3.58018e9i	−0.805355	+	1.13828i
$130$	−1.43527e9	+	2.48596e9i	−0.440747	+	0.763396i
$131$	9.06758e8	−	1.57055e9i	0.269011	−	0.465941i	−0.699596	−	0.714539i	$-0.746636\pi$
$131$	9.06758e8	−	1.57055e9i	0.269011	−	0.465941i	0.968607	+	0.248598i	$0.0799698\pi$
$132$	−4.95264e8	−	1.07579e9i	−0.141989	−	0.308423i
$133$	1.59569e8	+	2.76382e8i	0.0442198	+	0.0765909i
$134$	2.10629e9			0.564347
$135$	4.38003e9	−	4.25342e9i	1.13495	−	1.10214i
$136$	3.20419e9			0.803144
$137$	−3.25621e9	−	5.63992e9i	−0.789714	−	1.36783i	−0.926142	−	0.377175i	$-0.876896\pi$
$137$	−3.25621e9	−	5.63992e9i	−0.789714	−	1.36783i	0.136428	−	0.990650i	$-0.456438\pi$
$138$	−1.36950e8	−	2.97478e8i	−0.0321445	−	0.0698232i
$139$	9.16659e8	−	1.58770e9i	0.208277	−	0.360746i	−0.742895	−	0.669408i	$-0.766548\pi$
$139$	9.16659e8	−	1.58770e9i	0.208277	−	0.360746i	0.951172	+	0.308662i	$0.0998811\pi$
$140$	−3.12322e9	+	5.40957e9i	−0.687110	+	1.19011i
$141$	8.21722e8	−	1.16142e9i	0.175081	−	0.247458i
$142$	−1.12641e9	−	1.95099e9i	−0.232487	−	0.402679i
$143$	−3.15493e9			−0.630925
$144$	3.39329e9	+	6.32594e8i	0.657643	+	0.122601i
$145$	−2.51604e9			−0.472674
$146$	−5.94308e8	−	1.02937e9i	−0.108249	−	0.187493i
$147$	2.09750e8	+	1.93843e7i	0.0370487	+	0.00342391i
$148$	−1.43241e9	+	2.48101e9i	−0.245408	+	0.425060i
$149$	5.34302e8	−	9.25439e8i	0.0888074	−	0.153819i	−0.818200	−	0.574934i	$-0.805028\pi$
$149$	5.34302e8	−	9.25439e8i	0.0888074	−	0.153819i	0.907007	+	0.421115i	$0.138361\pi$
$150$	3.14273e9	+	2.90439e8i	0.506870	+	0.0468430i
$151$	4.03980e9	+	6.99713e9i	0.632358	+	1.09528i	0.987068	+	0.160300i	$0.0512463\pi$
$151$	4.03980e9	+	6.99713e9i	0.632358	+	1.09528i	−0.354710	+	0.934976i	$0.615420\pi$
$152$	3.78781e8			0.0575562
$153$	−5.54332e9	+	6.47662e9i	−0.817822	+	0.955514i
$154$	8.89733e8			0.127473
$155$	8.60707e8	+	1.49079e9i	0.119774	+	0.207455i
$156$	6.22172e9	−	8.79373e9i	0.841104	−	1.18881i
$157$	−3.62446e9	+	6.27775e9i	−0.476096	+	0.824623i	−0.999625	−	0.0273849i	$-0.991282\pi$
$157$	−3.62446e9	+	6.27775e9i	−0.476096	+	0.824623i	0.523528	+	0.852008i	$0.324615\pi$
$158$	−9.03496e8	+	1.56490e9i	−0.115337	+	0.199770i
$159$	−1.94946e9	−	4.23454e9i	−0.241895	−	0.525435i
$160$	5.67316e9	+	9.82619e9i	0.684360	+	1.18535i
$161$	−1.89839e9			−0.222673
$162$	2.31151e9	−	1.86380e9i	0.263680	−	0.212609i
$163$	−1.25726e10			−1.39502			−0.697511	−	0.716574i	$-0.745709\pi$
$163$	−1.25726e10			−1.39502			−0.697511	+	0.716574i	$0.745709\pi$
$164$	−5.61999e8	−	9.73411e8i	−0.0606650	−	0.105075i
$165$	2.41585e9	+	5.24762e9i	0.253742	+	0.551169i
$166$	1.28814e9	−	2.23113e9i	0.131667	−	0.228054i
$167$	7.07474e9	−	1.22538e10i	0.703860	−	1.21912i	−0.263241	−	0.964730i	$-0.584791\pi$
$167$	7.07474e9	−	1.22538e10i	0.703860	−	1.21912i	0.967101	−	0.254392i	$-0.0818752\pi$
$168$	−3.73661e9	+	5.28130e9i	−0.361898	+	0.511504i
$169$	−9.04581e9	−	1.56678e10i	−0.853016	−	1.47747i
$170$	−7.33929e9			−0.673959
$171$	−6.55300e8	+	7.65629e8i	−0.0586081	+	0.0684756i
$172$	1.41688e10			1.23440
$173$	6.14075e9	+	1.06361e10i	0.521211	+	0.902764i	0.999696	+	0.0246683i	$0.00785297\pi$
$173$	6.14075e9	+	1.06361e10i	0.521211	+	0.902764i	−0.478484	+	0.878096i	$0.658814\pi$
$174$	−1.21846e9	−	1.12606e8i	−0.100772	−	0.00931297i
$175$	9.14771e9	−	1.58443e10i	0.737294	−	1.27703i
$176$	−1.63304e9	+	2.82851e9i	−0.128289	+	0.222203i
$177$	6.52689e9	+	6.03191e8i	0.499835	+	0.0461929i
$178$	−3.97823e9	−	6.89049e9i	−0.297030	−	0.514470i
$179$	−5.47007e8			−0.0398249			−0.0199124	−	0.999802i	$-0.506339\pi$
$179$	−5.47007e8			−0.0398249			−0.0199124	+	0.999802i	$0.506339\pi$
$180$	−1.93909e10	−	3.61494e9i	−1.37680	−	0.256670i
$181$	8.46578e9			0.586291			0.293146	−	0.956068i	$-0.405298\pi$
$181$	8.46578e9			0.586291			0.293146	+	0.956068i	$0.405298\pi$
$182$	4.04634e9	+	7.00847e9i	0.273364	+	0.473481i
$183$	−4.97374e9	+	7.02985e9i	−0.327833	+	0.463357i
$184$	−1.12659e9	+	1.95130e9i	−0.0724576	+	0.125500i
$185$	6.98716e9	−	1.21021e10i	0.438559	−	0.759606i
$186$	3.50100e8	+	7.60475e8i	0.0214479	+	0.0465883i
$187$	−4.03320e9	−	6.98571e9i	−0.241192	−	0.417757i
$188$	−4.59640e9			−0.268354
$189$	−4.21065e9	−	1.66896e10i	−0.240033	−	0.951408i
$190$	−8.67609e8			−0.0482984
$191$	1.45905e10	+	2.52716e10i	0.793271	+	1.37399i	0.923932	+	0.382558i	$0.124957\pi$
$191$	1.45905e10	+	2.52716e10i	0.793271	+	1.37399i	−0.130661	+	0.991427i	$0.541710\pi$
$192$	−2.96021e9	−	6.43007e9i	−0.157205	−	0.341476i
$193$	−1.06260e10	+	1.84048e10i	−0.551268	+	0.954824i	0.446915	+	0.894576i	$0.352522\pi$
$193$	−1.06260e10	+	1.84048e10i	−0.551268	+	0.954824i	−0.998183	+	0.0602479i	$0.980811\pi$
$194$	−1.03305e9	+	1.78929e9i	−0.0523615	+	0.0906928i
$195$	−3.03489e10	+	4.28950e10i	−1.50310	+	2.12447i
$196$	−3.40266e8	−	5.89357e8i	−0.0164689	−	0.0285251i
$197$	1.91891e10			0.907728			0.453864	−	0.891071i	$-0.350045\pi$
$197$	1.91891e10			0.907728			0.453864	+	0.891071i	$0.350045\pi$
$198$	9.35081e8	+	2.64942e9i	0.0432370	+	0.122506i
$199$	6.01109e9			0.271716			0.135858	−	0.990728i	$-0.456621\pi$
$199$	6.01109e9			0.271716			0.135858	+	0.990728i	$0.456621\pi$
$200$	−1.08573e10	−	1.88054e10i	−0.479829	−	0.831088i
$201$	3.83922e10	+	3.54806e9i	1.65905	+	0.153324i
$202$	3.75587e9	−	6.50536e9i	0.158719	−	0.274910i
$203$	−3.54663e9	+	6.14295e9i	−0.146583	+	0.253889i
$204$	2.74250e10	+	2.53451e9i	1.10869	+	0.102461i
$205$	2.74138e9	+	4.74821e9i	0.108412	+	0.187775i
$206$	1.28276e9			0.0496298
$207$	−1.99514e9	−	5.65296e9i	−0.0755279	−	0.213998i
$208$	−2.97071e10			−1.10046
$209$	−4.76782e8	−	8.25811e8i	−0.0172847	−	0.0299380i
$210$	8.55881e9	−	1.20970e10i	0.303687	−	0.429229i
$211$	6.05024e9	−	1.04793e10i	0.210137	−	0.363967i	−0.741621	−	0.670820i	$-0.765942\pi$
$211$	6.05024e9	−	1.04793e10i	0.210137	−	0.363967i	0.951757	+	0.306852i	$0.0992758\pi$
$212$	−7.53038e9	+	1.30430e10i	−0.256039	+	0.443472i
$213$	−1.72450e10	−	3.74591e10i	−0.574058	−	1.24695i
$214$	7.35562e9	+	1.27403e10i	0.239749	+	0.415258i
$215$	−6.91142e10			−2.20594
$216$	−1.96536e10	−	5.57629e9i	−0.614327	−	0.174303i
$217$	4.85304e9			0.148575
$218$	9.99697e8	+	1.73153e9i	0.0299788	+	0.0519248i
$219$	−9.09871e9	−	1.97639e10i	−0.267289	−	0.580596i
$220$	9.33197e9	−	1.61634e10i	0.268579	−	0.465192i
$221$	3.66845e10	−	6.35395e10i	1.03447	−	1.79175i
$222$	3.92535e9	−	5.54806e9i	0.108465	−	0.153304i
$223$	2.63189e10	+	4.55857e10i	0.712682	+	1.23440i	0.963847	+	0.266457i	$0.0858530\pi$
$223$	2.63189e10	+	4.55857e10i	0.712682	+	1.23440i	−0.251165	+	0.967944i	$0.580814\pi$
$224$	3.19877e10			0.848921
$225$	5.67946e10	+	1.05879e10i	1.47736	+	0.275416i
$226$	−2.50322e10			−0.638279
$227$	−6.19793e9	−	1.07351e10i	−0.154928	−	0.268343i	0.778105	−	0.628135i	$-0.216181\pi$
$227$	−6.19793e9	−	1.07351e10i	−0.154928	−	0.268343i	−0.933033	+	0.359791i	$0.882848\pi$
$228$	3.24202e9	+	2.99616e8i	0.0794528	+	0.00734273i
$229$	−2.20676e10	+	3.82222e10i	−0.530268	+	0.918451i	0.469108	+	0.883141i	$0.344575\pi$
$229$	−2.20676e10	+	3.82222e10i	−0.530268	+	0.918451i	−0.999376	+	0.0353106i	$0.988758\pi$
$230$	2.58047e9	−	4.46951e9i	0.0608029	−	0.105314i
$231$	1.62176e10	+	1.49877e9i	0.374741	+	0.0346322i
$232$	4.20945e9	+	7.29099e9i	0.0953959	+	0.165231i
$233$	−5.44229e10			−1.20971			−0.604853	−	0.796337i	$-0.706768\pi$
$233$	−5.44229e10			−1.20971			−0.604853	+	0.796337i	$0.706768\pi$
$234$	−1.66170e10	+	1.94148e10i	−0.362312	+	0.423312i
$235$	2.24208e10			0.479563
$236$	−1.05882e10	−	1.83393e10i	−0.222187	−	0.384840i
$237$	−1.91045e10	+	2.70022e10i	−0.393340	+	0.555944i
$238$	−1.03455e10	+	1.79190e10i	−0.209005	+	0.362007i
$239$	−4.21933e10	+	7.30809e10i	−0.836474	+	1.44882i	0.0563504	+	0.998411i	$0.482054\pi$
$239$	−4.21933e10	+	7.30809e10i	−0.836474	+	1.44882i	−0.892825	+	0.450405i	$0.851280\pi$
$240$	2.27478e10	+	4.94120e10i	0.442577	+	0.961351i
$241$	−3.24645e10	−	5.62302e10i	−0.619916	−	1.07373i	−0.989501	−	0.144528i	$-0.953833\pi$
$241$	−3.24645e10	−	5.62302e10i	−0.619916	−	1.07373i	0.369585	−	0.929197i	$-0.379500\pi$
$242$	1.54136e10			0.288892
$243$	4.52724e10	−	3.00786e10i	0.832924	−	0.553387i
$244$	2.78212e10			0.502483
$245$	1.65978e9	+	2.87483e9i	0.0294309	+	0.0509759i
$246$	1.11508e9	+	2.42213e9i	0.0194132	+	0.0421687i
$247$	4.33663e9	−	7.51127e9i	0.0741338	−	0.128404i
$248$	2.88001e9	−	4.98832e9i	0.0483460	−	0.0837378i
$249$	2.72379e10	−	3.84979e10i	0.449031	−	0.634658i
$250$	8.32065e9	+	1.44118e10i	0.134719	+	0.233339i
$251$	4.84990e10			0.771260			0.385630	−	0.922654i	$-0.373984\pi$
$251$	4.84990e10			0.771260			0.385630	+	0.922654i	$0.373984\pi$
$252$	−3.61595e10	+	4.22475e10i	−0.564833	+	0.659930i
$253$	5.67225e9			0.0870389
$254$	−4.81904e9	−	8.34682e9i	−0.0726455	−	0.125826i
$255$	−1.33776e11	−	1.23631e10i	−1.98129	−	0.183104i
$256$	−1.36567e9	+	2.36541e9i	−0.0198731	+	0.0344213i
$257$	−1.82031e10	+	3.15287e10i	−0.260284	+	0.450824i	−0.966317	−	0.257354i	$-0.917149\pi$
$257$	−1.82031e10	+	3.15287e10i	−0.260284	+	0.450824i	0.706034	+	0.708178i	$0.250483\pi$
$258$	−3.34704e10	−	3.09321e9i	−0.470297	−	0.0434631i
$259$	−1.96983e10	−	3.41185e10i	−0.272007	−	0.471130i
$260$	1.69760e11			2.30386
$261$	−2.20197e10	−	4.10502e9i	−0.293717	−	0.0547561i
$262$	1.38994e10			0.182238
$263$	1.36692e10	+	2.36758e10i	0.176174	+	0.305143i	0.940567	−	0.339608i	$-0.110294\pi$
$263$	1.36692e10	+	2.36758e10i	0.176174	+	0.305143i	−0.764393	+	0.644751i	$0.776961\pi$
$264$	1.11647e10	−	1.57802e10i	0.141459	−	0.199937i
$265$	3.67325e10	−	6.36225e10i	0.457556	−	0.792509i
$266$	−1.22299e9	+	2.11828e9i	−0.0149780	+	0.0259427i
$267$	−6.09057e10	−	1.32297e11i	−0.733428	−	1.59313i
$268$	−6.22816e10	−	1.07875e11i	−0.737485	−	1.27736i
$269$	1.34342e9			0.0156432			0.00782159	−	0.999969i	$-0.497510\pi$
$269$	1.34342e9			0.0156432			0.00782159	+	0.999969i	$0.497510\pi$
$270$	4.50170e10	+	1.27727e10i	0.515513	+	0.146266i
$271$	−1.98471e10			−0.223530			−0.111765	−	0.993735i	$-0.535650\pi$
$271$	−1.98471e10			−0.223530			−0.111765	+	0.993735i	$0.535650\pi$
$272$	−3.79769e10	−	6.57780e10i	−0.420688	−	0.728652i
$273$	6.19486e10	+	1.34563e11i	0.674993	+	1.46620i
$274$	2.49566e10	−	4.32262e10i	0.267491	−	0.463307i
$275$	−2.73327e10	+	4.73417e10i	−0.288195	+	0.499168i
$276$	−1.11860e10	+	1.58102e10i	−0.116034	+	0.164001i
$277$	6.66879e10	+	1.15507e11i	0.680594	+	1.17882i	0.974800	+	0.223081i	$0.0716113\pi$
$277$	6.66879e10	+	1.15507e11i	0.680594	+	1.17882i	−0.294206	+	0.955742i	$0.595055\pi$
$278$	1.40511e10			0.141094
$279$	5.10039e9	+	1.44512e10i	0.0503947	+	0.142786i
$280$	−1.01954e11			−0.991272
$281$	−3.21667e9	−	5.57144e9i	−0.0307772	−	0.0533076i	0.850227	−	0.526417i	$-0.176465\pi$
$281$	−3.21667e9	−	5.57144e9i	−0.0307772	−	0.0533076i	−0.881004	+	0.473109i	$0.843132\pi$
$282$	1.08579e10	+	1.00344e9i	0.102241	+	0.00944870i
$283$	1.92398e10	−	3.33244e10i	0.178305	−	0.308833i	−0.762995	−	0.646404i	$-0.776272\pi$
$283$	1.92398e10	−	3.33244e10i	0.178305	−	0.308833i	0.941300	+	0.337571i	$0.109605\pi$
$284$	−6.66143e10	+	1.15379e11i	−0.607624	+	1.05244i
$285$	−1.58143e10	−	1.46150e9i	−0.141987	−	0.0131219i
$286$	−1.20902e10	−	2.09408e10i	−0.106853	−	0.185075i
$287$	1.54571e10			0.134480
$288$	3.36181e10	+	9.52521e10i	0.287943	+	0.815846i
$289$	6.89991e10			0.581839
$290$	−9.64187e9	−	1.67002e10i	−0.0800516	−	0.138653i
$291$	−2.18439e10	+	3.08740e10i	−0.178571	+	0.252391i
$292$	−3.51466e10	+	6.08757e10i	−0.282918	+	0.490028i
$293$	9.29644e10	−	1.61019e11i	0.736906	−	1.27636i	−0.216976	−	0.976177i	$-0.569619\pi$
$293$	9.29644e10	−	1.61019e11i	0.736906	−	1.27636i	0.953882	−	0.300182i	$-0.0970475\pi$
$294$	6.75131e8	+	1.46650e9i	0.00527018	+	0.0114477i
$295$	5.16484e10	+	8.94576e10i	0.397061	+	0.687730i
$296$	−4.67594e10			−0.354043
$297$	1.25811e10	+	4.98673e10i	0.0938245	+	0.371888i
$298$	8.19013e9			0.0601613
$299$	2.57964e10	+	4.46806e10i	0.186654	+	0.323295i
$300$	−7.80535e10	−	1.69545e11i	−0.556348	−	1.20848i
$301$	−9.74240e10	+	1.68743e11i	−0.684096	+	1.18489i
$302$	−3.09623e10	+	5.36283e10i	−0.214191	+	0.370990i
$303$	7.94183e10	−	1.12249e11i	0.541288	−	0.765053i
$304$	−4.48941e9	−	7.77589e9i	−0.0301480	−	0.0522179i
$305$	−1.35709e11			−0.897966
$306$	−6.42314e10	−	1.19743e10i	−0.418795	−	0.0780737i
$307$	1.44816e11			0.930450			0.465225	−	0.885192i	$-0.345973\pi$
$307$	1.44816e11			0.930450			0.465225	+	0.885192i	$0.345973\pi$
$308$	−2.63089e10	−	4.55683e10i	−0.166580	−	0.288526i
$309$	2.33814e10	+	2.16082e9i	0.145901	+	0.0134836i
$310$	−6.59673e9	+	1.14259e10i	−0.0405697	+	0.0702687i
$311$	−8.64353e9	+	1.49710e10i	−0.0523925	+	0.0907465i	−0.891032	−	0.453940i	$-0.850018\pi$
$311$	−8.64353e9	+	1.49710e10i	−0.0523925	+	0.0907465i	0.838640	+	0.544687i	$0.183351\pi$
$312$	1.75076e11	+	1.61799e10i	1.04600	+	0.0966675i
$313$	−3.03029e10	−	5.24862e10i	−0.178457	−	0.309097i	0.762895	−	0.646522i	$-0.223777\pi$
$313$	−3.03029e10	−	5.24862e10i	−0.178457	−	0.309097i	−0.941352	+	0.337425i	$0.890444\pi$
$314$	−5.55580e10			−0.322525
$315$	1.76383e11	−	2.06079e11i	1.00939	−	1.17933i
$316$	1.06863e11			0.602887
$317$	−1.23929e11	−	2.14652e11i	−0.689298	−	1.19390i	−0.972065	−	0.234710i	$-0.924586\pi$
$317$	−1.23929e11	−	2.14652e11i	−0.689298	−	1.19390i	0.282768	−	0.959188i	$-0.408747\pi$
$318$	2.06361e10	−	2.91669e10i	0.113163	−	0.159944i
$319$	1.05971e10	−	1.83547e10i	0.0572966	−	0.0992407i
$320$	5.57776e10	−	9.66096e10i	0.297361	−	0.515045i
$321$	1.12613e11	+	2.44614e11i	0.591991	+	1.28590i
$322$	−7.27492e9	−	1.26005e10i	−0.0377118	−	0.0653187i
$323$	2.21755e10			0.113360
$324$	−1.63806e11	−	6.32739e10i	−0.825803	−	0.318987i
$325$	−4.97217e11			−2.47213
$326$	−4.81803e10	−	8.34507e10i	−0.236260	−	0.409214i
$327$	1.53051e10	+	3.32453e10i	0.0740239	+	0.160792i
$328$	9.17290e9	−	1.58879e10i	0.0437597	−	0.0757941i
$329$	3.16046e10	−	5.47407e10i	0.148720	−	0.257590i
$330$	−2.55732e10	+	3.61449e10i	−0.118706	+	0.167778i
$331$	−1.52348e10	−	2.63875e10i	−0.0697607	−	0.120829i	0.829035	−	0.559196i	$-0.188890\pi$
$331$	−1.52348e10	−	2.63875e10i	−0.0697607	−	0.120829i	−0.898796	+	0.438367i	$0.855557\pi$
$332$	−1.52358e11			−0.688248
$333$	8.08947e10	−	9.45145e10i	0.360513	−	0.421211i
$334$	1.08446e11			0.476821
$335$	3.03804e11	+	5.26203e11i	1.31793	+	2.28272i
$336$	1.52706e11	+	1.41125e10i	0.653624	+	0.0604056i
$337$	−2.66771e10	+	4.62062e10i	−0.112669	+	0.195149i	−0.916846	−	0.399242i	$-0.869273\pi$
$337$	−2.66771e10	+	4.62062e10i	−0.112669	+	0.195149i	0.804177	+	0.594391i	$0.202607\pi$
$338$	6.93299e10	−	1.20083e11i	0.288932	−	0.500445i
$339$	−4.56272e11	−	4.21670e10i	−1.87640	−	0.173410i
$340$	2.17018e11	+	3.75886e11i	0.880726	+	1.52546i
$341$	−1.45006e10			−0.0580751
$342$	−7.59307e9	−	1.41554e9i	−0.0300124	−	0.00559505i
$343$	2.60889e11			1.01773
$344$	1.15631e11	+	2.00279e11i	0.445207	+	0.771122i
$345$	5.45644e10	−	7.71209e10i	0.207359	−	0.293080i
$346$	−4.70646e10	+	8.15184e10i	−0.176544	+	0.305783i
$347$	6.25615e10	−	1.08360e11i	0.231646	−	0.401222i	−0.726647	−	0.687011i	$-0.758922\pi$
$347$	6.25615e10	−	1.08360e11i	0.231646	−	0.401222i	0.958293	+	0.285789i	$0.0922557\pi$
$348$	3.02619e10	+	6.57339e10i	0.110609	+	0.240261i
$349$	−1.27508e11	−	2.20851e11i	−0.460070	−	0.796865i	0.538894	−	0.842374i	$-0.318842\pi$
$349$	−1.27508e11	−	2.20851e11i	−0.460070	−	0.796865i	−0.998964	+	0.0455090i	$0.985509\pi$
$350$	1.40222e11			0.499470
$351$	−3.35590e11	+	3.25890e11i	−1.18012	+	1.14601i
$352$	−9.55772e10			−0.331827
$353$	−1.66531e10	−	2.88441e10i	−0.0570834	−	0.0988713i	0.836072	−	0.548620i	$-0.184847\pi$
$353$	−1.66531e10	−	2.88441e10i	−0.0570834	−	0.0988713i	−0.893155	+	0.449749i	$0.851513\pi$
$354$	2.10084e10	+	4.56337e10i	0.0711015	+	0.154444i
$355$	3.24938e11	−	5.62810e11i	1.08586	−	1.88076i
$356$	−2.35267e11	+	4.07495e11i	−0.776313	+	1.34461i
$357$	−2.18757e11	+	3.09190e11i	−0.712779	+	1.00744i
$358$	−2.09622e9	−	3.63076e9i	−0.00674471	−	0.0116822i
$359$	−8.10854e10			−0.257643			−0.128821	−	0.991668i	$-0.541119\pi$
$359$	−8.10854e10			−0.257643			−0.128821	+	0.991668i	$0.541119\pi$
$360$	−1.07150e11	−	3.03595e11i	−0.336227	−	0.952651i
$361$	−3.20066e11			−0.991876
$362$	3.24422e10	+	5.61916e10i	0.0992938	+	0.171982i
$363$	2.80950e11	+	2.59644e10i	0.849277	+	0.0784871i
$364$	2.39296e11	−	4.14472e11i	0.714461	−	1.23748i
$365$	1.71442e11	−	2.96946e11i	0.505590	−	0.875708i
$366$	−6.57207e10	−	6.07367e9i	−0.191442	−	0.0176924i
$367$	−2.35647e11	−	4.08152e11i	−0.678054	−	1.17442i	−0.975566	−	0.219706i	$-0.929490\pi$
$367$	−2.35647e11	−	4.08152e11i	−0.678054	−	1.17442i	0.297512	−	0.954718i	$-0.403843\pi$
$368$	5.34103e10			0.151813
$369$	1.62449e10	+	4.60277e10i	0.0456140	+	0.129241i
$370$	1.07104e11			0.297096
$371$	−1.03557e11	−	1.79366e11i	−0.283790	−	0.491538i
$372$	2.85960e10	−	4.04174e10i	0.0774215	−	0.109427i
$373$	−2.53168e11	+	4.38500e11i	−0.677204	+	1.17295i	0.298616	+	0.954373i	$0.403475\pi$
$373$	−2.53168e11	+	4.38500e11i	−0.677204	+	1.17295i	−0.975819	+	0.218578i	$0.929858\pi$
$374$	3.09117e10	−	5.35407e10i	0.0816961	−	0.141502i
$375$	1.27387e11	+	2.76706e11i	0.332648	+	0.722567i
$376$	−3.75110e10	−	6.49710e10i	−0.0967863	−	0.167639i
$377$	1.92775e11			0.491489
$378$	9.46410e10	−	9.19052e10i	0.238433	−	0.231541i
$379$	3.43255e11			0.854557			0.427278	−	0.904120i	$-0.359472\pi$
$379$	3.43255e11			0.854557			0.427278	+	0.904120i	$0.359472\pi$
$380$	2.56546e10	+	4.44351e10i	0.0631161	+	0.109320i
$381$	−7.37784e10	−	1.60259e11i	−0.179377	−	0.389637i
$382$	−1.11827e11	+	1.93689e11i	−0.268695	+	0.465394i
$383$	2.19794e11	−	3.80695e11i	0.521942	−	0.904030i	−0.477732	−	0.878506i	$-0.658541\pi$
$383$	2.19794e11	−	3.80695e11i	0.521942	−	0.904030i	0.999674	−	0.0255246i	$-0.00812562\pi$
$384$	2.44247e11	−	3.45217e11i	0.573242	−	0.810217i
$385$	1.28332e11	+	2.22278e11i	0.297689	+	0.515612i
$386$	−1.62882e11			−0.373449
$387$	−6.04869e11	−	1.12763e11i	−1.37076	−	0.255544i
$388$	1.22186e11			0.273703
$389$	2.52265e11	+	4.36935e11i	0.558577	+	0.967484i	0.997616	+	0.0690158i	$0.0219859\pi$
$389$	2.52265e11	+	4.36935e11i	0.558577	+	0.967484i	−0.439038	+	0.898468i	$0.644681\pi$
$390$	−4.01017e11	−	3.70605e10i	−0.877753	−	0.0811187i
$391$	−6.59551e10	+	1.14238e11i	−0.142709	+	0.247180i
$392$	5.55379e9	−	9.61945e9i	0.0118796	−	0.0205761i
$393$	2.53350e11	+	2.34136e10i	0.535740	+	0.0495111i
$394$	7.35356e10	+	1.27367e11i	0.153732	+	0.266272i
$395$	−5.21269e11			−1.07739
$396$	1.08042e11	−	1.26233e11i	0.220783	−	0.257954i
$397$	−2.62244e11			−0.529844			−0.264922	−	0.964270i	$-0.585346\pi$
$397$	−2.62244e11			−0.529844			−0.264922	+	0.964270i	$0.585346\pi$
$398$	2.30355e10	+	3.98986e10i	0.0460175	+	0.0797047i
$399$	−2.58602e10	+	3.65506e10i	−0.0510804	+	0.0721966i
$400$	−2.57367e11	+	4.45773e11i	−0.502670	+	0.870650i
$401$	−1.23763e11	+	2.14363e11i	−0.239023	+	0.414000i	−0.960434	−	0.278507i	$-0.910160\pi$
$401$	−1.23763e11	+	2.14363e11i	−0.239023	+	0.414000i	0.721411	+	0.692507i	$0.243494\pi$
$402$	1.23575e11	+	2.68425e11i	0.236000	+	0.512631i
$403$	−6.59459e10	−	1.14222e11i	−0.124542	−	0.215713i
$404$	−4.44235e11			−0.829654
$405$	7.99029e11	+	3.08644e11i	1.47576	+	0.570047i
$406$	−5.43651e10			−0.0993008
$407$	5.88573e10	+	1.01944e11i	0.106323	+	0.184156i
$408$	1.87988e11	+	4.08341e11i	0.335861	+	0.729546i
$409$	−7.78721e10	+	1.34878e11i	−0.137603	+	0.238335i	−0.926589	−	0.376076i	$-0.877273\pi$
$409$	−7.78721e10	+	1.34878e11i	−0.137603	+	0.238335i	0.788986	+	0.614411i	$0.210606\pi$
$410$	−2.10108e10	+	3.63918e10i	−0.0367210	+	0.0636027i
$411$	5.27710e11	−	7.45862e11i	0.912236	−	1.28935i
$412$	−3.79304e10	−	6.56973e10i	−0.0648559	−	0.112334i
$413$	2.91216e11			0.492538
$414$	2.98758e10	−	3.49058e10i	0.0499825	−	0.0583977i
$415$	7.43190e11			1.22994
$416$	−4.34668e11	−	7.52866e11i	−0.711602	−	1.23253i
$417$	2.56116e11	+	2.36693e10i	0.414786	+	0.0383330i
$418$	3.65421e9	−	6.32928e9i	0.00585464	−	0.0101405i
$419$	−4.60177e11	+	7.97051e11i	−0.729394	+	1.26335i	0.227746	+	0.973721i	$0.426865\pi$
$419$	−4.60177e11	+	7.97051e11i	−0.729394	+	1.26335i	−0.957140	+	0.289627i	$0.906469\pi$
$420$	−8.72633e11	−	8.06455e10i	−1.36839	−	0.126461i
$421$	4.28419e11	+	7.42043e11i	0.664660	+	1.15122i	0.979377	+	0.202039i	$0.0647567\pi$
$421$	4.28419e11	+	7.42043e11i	0.664660	+	1.15122i	−0.314718	+	0.949185i	$0.601910\pi$
$422$	9.27419e10			0.142354
$423$	1.96221e11	+	3.65804e10i	0.297998	+	0.0555542i
$424$	−2.45821e11			−0.369379
$425$	−6.35632e11	−	1.10095e12i	−0.945052	−	1.63688i
$426$	1.82549e11	−	2.58013e11i	0.268556	−	0.379576i
$427$	−1.91297e11	+	3.31336e11i	−0.278472	+	0.482328i
$428$	4.35002e11	−	7.53446e11i	0.626606	−	1.08531i
$429$	−1.85098e11	−	4.02064e11i	−0.263842	−	0.573109i
$430$	−2.64857e11	−	4.58745e11i	−0.373597	−	0.647088i
$431$	5.94731e11			0.830181			0.415090	−	0.909780i	$-0.363750\pi$
$431$	5.94731e11			0.830181			0.415090	+	0.909780i	$0.363750\pi$
$432$	1.18465e11	+	4.69554e11i	0.163649	+	0.648648i
$433$	−1.28268e12			−1.75357			−0.876787	−	0.480880i	$-0.840317\pi$
$433$	−1.28268e12			−1.75357			−0.876787	+	0.480880i	$0.840317\pi$
$434$	1.85976e10	+	3.22120e10i	0.0251625	+	0.0435827i
$435$	−1.47615e11	−	3.20644e11i	−0.197664	−	0.429359i
$436$	5.91209e10	−	1.02400e11i	0.0783522	−	0.135710i
$437$	−7.79683e9	+	1.35045e10i	−0.0102271	+	0.0177138i
$438$	9.63151e10	−	1.36131e11i	0.125043	−	0.176735i
$439$	4.00633e11	+	6.93916e11i	0.514821	+	0.891696i	0.999852	+	0.0171991i	$0.00547493\pi$
$439$	4.00633e11	+	6.93916e11i	0.514821	+	0.891696i	−0.485031	+	0.874497i	$0.661192\pi$
$440$	3.04631e11			0.387470
$441$	9.83557e9	+	2.78677e10i	0.0123830	+	0.0350855i
$442$	5.62324e11			0.700787
$443$	−3.57521e11	−	6.19245e11i	−0.441047	−	0.763916i	0.556720	−	0.830700i	$-0.312059\pi$
$443$	−3.57521e11	−	6.19245e11i	−0.441047	−	0.763916i	−0.997767	+	0.0667840i	$0.978726\pi$
$444$	−4.00217e11	−	3.69866e10i	−0.488734	−	0.0451670i
$445$	1.14761e12	−	1.98772e12i	1.38731	−	2.40290i
$446$	−2.01716e11	+	3.49383e11i	−0.241398	+	0.418114i
$447$	1.49285e11	+	1.37964e10i	0.176861	+	0.0163448i
$448$	−1.57249e11	−	2.72363e11i	−0.184432	−	0.319446i
$449$	8.30808e11			0.964700			0.482350	−	0.875979i	$-0.339783\pi$
$449$	8.30808e11			0.964700			0.482350	+	0.875979i	$0.339783\pi$
$450$	1.47369e11	+	4.17549e11i	0.169414	+	0.480010i
$451$	−4.61847e10			−0.0525659
$452$	7.40185e11	+	1.28204e12i	0.834099	+	1.44470i
$453$	−6.54700e11	+	9.25349e11i	−0.730467	+	1.03244i
$454$	4.75029e10	−	8.22774e10i	0.0524770	−	0.0908928i
$455$	−1.16726e12	+	2.02176e12i	−1.27678	+	2.21145i
$456$	2.22229e10	+	4.82718e10i	0.0240690	+	0.0522819i
$457$	−2.80720e11	−	4.86221e11i	−0.301058	−	0.521447i	0.675318	−	0.737527i	$-0.264006\pi$
$457$	−2.80720e11	−	4.86221e11i	−0.301058	−	0.521447i	−0.976376	+	0.216079i	$0.930673\pi$
$458$	−3.38266e11			−0.359223
$459$	−1.15060e12	−	3.26460e11i	−1.20995	−	0.343299i
$460$	−3.05212e11			−0.317827
$461$	−2.67794e11	−	4.63834e11i	−0.276151	−	0.478308i	0.694274	−	0.719711i	$-0.255726\pi$
$461$	−2.67794e11	−	4.63834e11i	−0.276151	−	0.478308i	−0.970425	+	0.241403i	$0.922392\pi$
$462$	5.22002e10	+	1.13387e11i	0.0533069	+	0.115791i
$463$	−6.33673e11	+	1.09755e12i	−0.640841	+	1.10997i	0.344404	+	0.938822i	$0.388081\pi$
$463$	−6.33673e11	+	1.09755e12i	−0.640841	+	1.10997i	−0.985245	+	0.171148i	$0.945252\pi$
$464$	9.97831e10	−	1.72829e11i	0.0999369	−	0.173096i
$465$	−1.39489e11	+	1.97152e11i	−0.138357	+	0.195552i
$466$	−2.08557e11	−	3.61231e11i	−0.204875	−	0.354853i
$467$	9.53957e11			0.928117			0.464059	−	0.885804i	$-0.346393\pi$
$467$	9.53957e11			0.928117			0.464059	+	0.885804i	$0.346393\pi$
$468$	1.48570e12	+	2.76971e11i	1.43161	+	0.266887i
$469$	1.71298e12			1.63483
$470$	8.59201e10	+	1.48818e11i	0.0812184	+	0.140674i
$471$	−1.01268e12	−	9.35882e10i	−0.948153	−	0.0876248i
$472$	1.72820e11	−	2.99333e11i	0.160271	−	0.277598i
$473$	2.91096e11	−	5.04194e11i	0.267400	−	0.463151i
$474$	−2.52438e11	−	2.33294e10i	−0.229695	−	0.0212276i
$475$	−7.51408e10	−	1.30148e11i	−0.0677258	−	0.117305i
$476$	1.22364e12			1.09251
$477$	4.25275e11	−	4.96876e11i	0.376129	−	0.439456i
$478$	−6.46765e11			−0.566658
$479$	6.43441e11	+	1.11447e12i	0.558469	+	0.967297i	0.997625	+	0.0688858i	$0.0219444\pi$
$479$	6.43441e11	+	1.11447e12i	0.558469	+	0.967297i	−0.439155	+	0.898411i	$0.644722\pi$
$480$	−9.19407e11	+	1.29948e12i	−0.790537	+	1.11734i
$481$	−5.35344e11	+	9.27243e11i	−0.456016	+	0.789843i
$482$	2.48819e11	−	4.30966e11i	0.209977	−	0.363690i
$483$	−1.11377e11	−	2.41930e11i	−0.0931182	−	0.202268i
$484$	−4.55770e11	−	7.89418e11i	−0.377522	−	0.653887i
$485$	−5.96012e11			−0.489122
$486$	3.73137e11	+	1.85230e11i	0.303393	+	0.150608i
$487$	−1.22356e12			−0.985704			−0.492852	−	0.870113i	$-0.664046\pi$
$487$	−1.22356e12			−0.985704			−0.492852	+	0.870113i	$0.664046\pi$
$488$	2.27048e11	+	3.93258e11i	0.181229	+	0.313898i
$489$	−7.37628e11	−	1.60225e12i	−0.583375	−	1.26719i
$490$	−1.27211e10	+	2.20336e10i	−0.00996880	+	0.0172665i
$491$	5.85291e11	−	1.01375e12i	0.454470	−	0.787165i	−0.544188	−	0.838963i	$-0.683162\pi$
$491$	5.85291e11	−	1.01375e12i	0.454470	−	0.787165i	0.998658	+	0.0517987i	$0.0164954\pi$
$492$	9.10791e10	−	1.28731e11i	0.0700770	−	0.0990464i
$493$	2.46439e11	+	4.26845e11i	0.187888	+	0.325431i
$494$	6.64747e10			0.0502210
$495$	−5.27019e11	+	6.15750e11i	−0.394551	+	0.460979i
$496$	−1.36538e11			−0.101295
$497$	−9.16072e11	−	1.58668e12i	−0.673482	−	1.16650i
$498$	3.59909e11	+	3.32615e10i	0.262217	+	0.0242332i
$499$	1.10884e12	−	1.92057e12i	0.800602	−	1.38668i	−0.118619	−	0.992940i	$-0.537847\pi$
$499$	1.10884e12	−	1.92057e12i	0.800602	−	1.38668i	0.919221	−	0.393743i	$-0.128820\pi$
$500$	4.92073e11	−	8.52296e11i	0.352099	−	0.609853i
$501$	1.97669e12	+	1.82679e11i	1.40175	+	0.129544i
$502$	1.85856e11	+	3.21912e11i	0.130620	+	0.226240i
$503$	−2.31868e12			−1.61505			−0.807524	−	0.589834i	$-0.799193\pi$
$503$	−2.31868e12			−1.61505			−0.807524	+	0.589834i	$0.799193\pi$
$504$	−8.92272e11	−	1.66342e11i	−0.615971	−	0.114832i
$505$	2.16694e12			1.48264
$506$	2.17370e10	+	3.76495e10i	0.0147408	+	0.0255319i
$507$	1.46599e12	−	2.07202e12i	0.985359	−	1.39270i
$508$	−2.84992e11	+	4.93621e11i	−0.189866	+	0.328857i
$509$	−1.26661e12	+	2.19383e12i	−0.836396	+	1.44868i	0.0564927	+	0.998403i	$0.482008\pi$
$509$	−1.26661e12	+	2.19383e12i	−0.836396	+	1.44868i	−0.892889	+	0.450277i	$0.851325\pi$
$510$	−4.30592e11	−	9.35317e11i	−0.281838	−	0.612200i
$511$	−4.83332e11	−	8.37155e11i	−0.313582	−	0.543140i
$512$	−1.56422e12			−1.00596
$513$	−1.36018e11	−	3.85922e10i	−0.0867096	−	0.0246021i
$514$	−2.79029e11			−0.176326
$515$	1.85021e11	+	3.20465e11i	0.115901	+	0.200747i
$516$	8.31278e11	+	1.80567e12i	0.516205	+	1.12128i
$517$	−9.44323e10	+	1.63562e11i	−0.0581317	+	0.100687i
$518$	1.50974e11	−	2.61495e11i	0.0921338	−	0.159580i
$519$	−9.95186e11	+	1.40659e12i	−0.602076	+	0.850970i
$520$	1.38541e12	+	2.39960e12i	0.830926	+	1.43921i
$521$	9.44125e11			0.561384			0.280692	−	0.959798i	$-0.409436\pi$
$521$	9.44125e11			0.561384			0.280692	+	0.959798i	$0.409436\pi$
$522$	−5.71359e10	−	1.61887e11i	−0.0336815	−	0.0954320i
$523$	−1.67874e12			−0.981128			−0.490564	−	0.871405i	$-0.663209\pi$
$523$	−1.67874e12			−0.981128			−0.490564	+	0.871405i	$0.663209\pi$
$524$	−4.10995e11	−	7.11865e11i	−0.238148	−	0.412484i
$525$	2.55588e12	+	2.36205e11i	1.46833	+	0.135698i
$526$	−1.04765e11	+	1.81459e11i	−0.0596735	+	0.103358i
$527$	1.68608e11	−	2.92037e11i	0.0952204	−	0.164927i
$528$	−4.56274e11	−	4.21672e10i	−0.255490	−	0.0236114i
$529$	8.54197e11	+	1.47951e12i	0.474250	+	0.821425i
$530$	5.63059e11			0.309965
$531$	3.06059e11	+	8.67175e11i	0.167063	+	0.473349i
$532$	1.44652e11			0.0782929
$533$	−2.10040e11	−	3.63799e11i	−0.112727	−	0.195249i
$534$	6.44722e11	−	9.11246e11i	0.343113	−	0.484953i
$535$	−2.12190e12	+	3.67524e12i	−1.11978	+	1.93952i
$536$	1.01656e12	−	1.76073e12i	0.531973	−	0.921404i
$537$	−3.20926e10	−	6.97105e10i	−0.0166541	−	0.0361754i
$538$	5.14818e9	+	8.91691e9i	0.00264932	+	0.00458875i
$539$	−2.79628e10			−0.0142703
$540$	−6.76965e11	−	2.68326e12i	−0.342606	−	1.35797i
$541$	−1.34365e12			−0.674372			−0.337186	−	0.941438i	$-0.609475\pi$
$541$	−1.34365e12			−0.674372			−0.337186	+	0.941438i	$0.609475\pi$
$542$	−7.60574e10	−	1.31735e11i	−0.0378569	−	0.0655700i
$543$	4.96683e11	+	1.07888e12i	0.245177	+	0.532565i
$544$	1.11134e12	−	1.92490e12i	0.544066	−	0.942351i
$545$	−2.88386e11	+	4.99499e11i	−0.140020	+	0.242522i
$546$	−6.55761e11	+	9.26849e11i	−0.315776	+	0.446315i
$547$	3.04392e11	+	5.27222e11i	0.145375	+	0.251797i	0.929513	−	0.368790i	$-0.120228\pi$
$547$	3.04392e11	+	5.27222e11i	0.145375	+	0.251797i	−0.784138	+	0.620587i	$0.786894\pi$
$548$	−2.95181e12			−1.39822
$549$	−1.18769e12	−	2.21415e11i	−0.557991	−	0.104023i
$550$	−4.18974e11			−0.195234
$551$	2.91326e10	+	5.04592e10i	0.0134647	+	0.0233216i
$552$	−3.14770e11	−	2.90899e10i	−0.144300	−	0.0133357i
$553$	−7.34785e11	+	1.27268e12i	−0.334116	+	0.578706i
$554$	−5.11117e11	+	8.85281e11i	−0.230529	+	0.399289i
$555$	1.95222e12	+	1.80417e11i	0.873396	+	0.0807160i
$556$	−4.15483e11	−	7.19638e11i	−0.184381	−	0.319358i
$557$	−6.12226e11			−0.269503			−0.134751	−	0.990879i	$-0.543024\pi$
$557$	−6.12226e11			−0.269503			−0.134751	+	0.990879i	$0.543024\pi$
$558$	−7.63746e10	+	8.92333e10i	−0.0333499	+	0.0389649i
$559$	5.29541e12			2.29375
$560$	1.20838e12	+	2.09298e12i	0.519229	+	0.899331i
$561$	6.53631e11	−	9.23838e11i	0.278612	−	0.393788i
$562$	2.46536e10	−	4.27013e10i	0.0104248	−	0.0180563i
$563$	2.12194e12	−	3.67531e12i	0.890114	−	1.54172i	0.0503772	−	0.998730i	$-0.483958\pi$
$563$	2.12194e12	−	3.67531e12i	0.890114	−	1.54172i	0.839737	−	0.542993i	$-0.182709\pi$
$564$	−2.69668e11	−	5.85764e11i	−0.112221	−	0.243762i
$565$	−3.61055e12	−	6.25366e12i	−1.49058	−	2.58176i
$566$	2.94921e11			0.120790
$567$	1.87988e12	−	1.51577e12i	0.763846	−	0.615900i
$568$	−2.17455e12			−0.876600
$569$	2.05395e12	+	3.55754e12i	0.821456	+	1.42280i	0.904598	+	0.426265i	$0.140171\pi$
$569$	2.05395e12	+	3.55754e12i	0.821456	+	1.42280i	−0.0831427	+	0.996538i	$0.526496\pi$
$570$	−5.09021e10	−	1.10568e11i	−0.0201976	−	0.0438725i
$571$	1.90871e12	−	3.30597e12i	0.751409	−	1.30148i	−0.195731	−	0.980658i	$-0.562708\pi$
$571$	1.90871e12	−	3.30597e12i	0.751409	−	1.30148i	0.947140	−	0.320821i	$-0.103959\pi$
$572$	−7.15000e11	+	1.23842e12i	−0.279270	+	0.483709i
$573$	−2.36458e12	+	3.34209e12i	−0.916344	+	1.29515i
$574$	5.92340e10	+	1.02596e11i	0.0227755	+	0.0394483i
$575$	8.93946e11			0.341041
$576$	6.45772e11	−	7.54497e11i	0.244443	−	0.285599i
$577$	1.58536e12			0.595440			0.297720	−	0.954653i	$-0.403774\pi$
$577$	1.58536e12			0.595440			0.297720	+	0.954653i	$0.403774\pi$
$578$	2.64415e11	+	4.57981e11i	0.0985398	+	0.170676i
$579$	−2.96893e12	−	2.74377e11i	−1.09786	−	0.101460i
$580$	−5.70208e11	+	9.87629e11i	−0.209222	+	0.362383i
$581$	1.04761e12	−	1.81451e12i	0.381422	−	0.660643i
$582$	−2.88635e11	−	2.66746e10i	−0.104279	−	0.00963705i
$583$	3.09421e11	+	5.35933e11i	0.110928	+	0.192133i
$584$	−1.14732e12			−0.408157
$585$	−7.24708e12	−	1.35104e12i	−2.55836	−	0.476942i
$586$	1.42502e12			0.499207
$587$	−7.16024e11	−	1.24019e12i	−0.248918	−	0.431139i	0.714308	−	0.699832i	$-0.246742\pi$
$587$	−7.16024e11	−	1.24019e12i	−0.248918	−	0.431139i	−0.963226	+	0.268693i	$0.913408\pi$
$588$	5.51444e10	−	7.79407e10i	0.0190241	−	0.0268885i
$589$	1.99318e10	−	3.45230e10i	0.00682384	−	0.0118192i
$590$	−3.95850e11	+	6.85632e11i	−0.134492	+	0.232947i
$591$	1.12581e12	+	2.44545e12i	0.379597	+	0.824546i
$592$	5.54204e11	+	9.59910e11i	0.185448	+	0.321205i
$593$	4.74549e12			1.57592			0.787961	−	0.615725i	$-0.211137\pi$
$593$	4.74549e12			1.57592			0.787961	+	0.615725i	$0.211137\pi$
$594$	−2.82781e11	+	2.74607e11i	−0.0931990	+	0.0905049i
$595$	−5.96881e12			−1.95237
$596$	−2.42177e11	−	4.19463e11i	−0.0786185	−	0.136171i
$597$	3.52668e11	+	7.66052e11i	0.113627	+	0.246816i
$598$	−1.97712e11	+	3.42446e11i	−0.0632232	+	0.109506i
$599$	−7.86184e10	+	1.36171e11i	−0.0249519	+	0.0432179i	−0.878232	−	0.478235i	$-0.841277\pi$
$599$	−7.86184e10	+	1.36171e11i	−0.0249519	+	0.0432179i	0.853280	+	0.521453i	$0.174610\pi$
$600$	1.75956e12	−	2.48695e12i	0.554273	−	0.783406i
$601$	1.65008e12	+	2.85803e12i	0.515906	+	0.893576i	0.999830	+	0.0184653i	$0.00587803\pi$
$601$	1.65008e12	+	2.85803e12i	0.515906	+	0.893576i	−0.483923	+	0.875110i	$0.660789\pi$
$602$	−1.49338e12			−0.463431
$603$	1.80028e12	+	5.10085e12i	0.554515	+	1.57114i
$604$	3.66214e12			1.11962
$605$	2.22321e12	+	3.85070e12i	0.674653	+	1.16853i
$606$	1.04940e12	+	9.69814e10i	0.316092	+	0.0292120i
$607$	1.95171e12	−	3.38046e12i	0.583534	−	1.01071i	−0.411522	−	0.911400i	$-0.635003\pi$
$607$	1.95171e12	−	3.38046e12i	0.583534	−	1.01071i	0.995056	−	0.0993113i	$-0.0316640\pi$
$608$	1.31376e11	−	2.27550e11i	0.0389898	−	0.0675323i
$609$	−9.90935e11	−	9.15786e10i	−0.291922	−	0.0269784i
$610$	−5.20059e11	−	9.00768e11i	−0.152079	−	0.263408i
$611$	−1.71784e12			−0.498653
$612$	1.28601e12	+	3.64373e12i	0.370564	+	1.04994i
$613$	−2.67659e12			−0.765615			−0.382807	−	0.923828i	$-0.625043\pi$
$613$	−2.67659e12			−0.765615			−0.382807	+	0.923828i	$0.625043\pi$
$614$	5.54957e11	+	9.61214e11i	0.157580	+	0.272937i
$615$	−4.44275e11	+	6.27935e11i	−0.125232	+	0.177001i
$616$	4.29411e11	−	7.43762e11i	0.120160	−	0.208123i
$617$	−1.82429e12	+	3.15976e12i	−0.506769	+	0.877750i	0.493200	+	0.869916i	$0.335827\pi$
$617$	−1.82429e12	+	3.15976e12i	−0.506769	+	0.877750i	−0.999969	+	0.00783384i	$0.997506\pi$
$618$	7.52587e10	+	1.63474e11i	0.0207543	+	0.0450818i
$619$	−4.83256e11	−	8.37024e11i	−0.132303	−	0.229155i	0.792261	−	0.610182i	$-0.208904\pi$
$619$	−4.83256e11	−	8.37024e11i	−0.132303	−	0.229155i	−0.924564	+	0.381027i	$0.875571\pi$
$620$	7.80245e11			0.212065
$621$	6.03358e11	−	5.85917e11i	0.162803	−	0.158097i
$622$	−1.32493e11			−0.0354926
$623$	−3.23537e12	−	5.60382e12i	−0.860454	−	1.49035i
$624$	−1.74290e12	−	3.78586e12i	−0.460194	−	0.999618i
$625$	4.66099e11	−	8.07307e11i	0.122185	−	0.211631i
$626$	2.32251e11	−	4.02271e11i	0.0604468	−	0.104697i
$627$	7.72686e10	−	1.09211e11i	0.0199664	−	0.0282203i
$628$	1.64282e12	+	2.84544e12i	0.421474	+	0.730014i
$629$	−2.73749e12			−0.697308
$630$	2.04377e12	+	3.81010e11i	0.516893	+	0.0963617i
$631$	−4.92249e12			−1.23610			−0.618049	−	0.786139i	$-0.712077\pi$
$631$	−4.92249e12			−1.23610			−0.618049	+	0.786139i	$0.712077\pi$
$632$	8.72106e11	+	1.51053e12i	0.217442	+	0.376620i
$633$	1.69045e12	+	1.56225e11i	0.418490	+	0.0386753i
$634$	9.49832e11	−	1.64516e12i	0.233478	−	0.404395i
$635$	1.39016e12	−	2.40784e12i	0.339300	−	0.587686i
$636$	−2.10400e12	−	1.94444e11i	−0.509904	−	0.0471235i
$637$	−1.27170e11	−	2.20265e11i	−0.0306025	−	0.0530050i
$638$	1.62439e11			0.0388148
$639$	3.76202e12	−	4.39541e12i	0.892621	−	1.04291i
$640$	6.66431e12			1.57016
$641$	−2.40584e12	−	4.16704e12i	−0.562866	−	0.974913i	−0.997245	−	0.0741828i	$-0.976365\pi$
$641$	−2.40584e12	−	4.16704e12i	−0.562866	−	0.974913i	0.434378	−	0.900731i	$-0.356968\pi$
$642$	−1.19207e12	+	1.68486e12i	−0.276946	+	0.391433i
$643$	−2.66650e12	+	4.61852e12i	−0.615167	+	1.06550i	0.375189	+	0.926948i	$0.377578\pi$
$643$	−2.66650e12	+	4.61852e12i	−0.615167	+	1.06550i	−0.990355	+	0.138551i	$0.955755\pi$
$644$	−4.30230e11	+	7.45180e11i	−0.0985630	+	0.170716i
$645$	−4.05489e12	−	8.80790e12i	−0.922488	−	2.00380i
$646$	8.49799e10	+	1.47189e11i	0.0191986	+	0.0332530i
$647$	6.50961e12			1.46045			0.730223	−	0.683209i	$-0.239416\pi$
$647$	6.50961e12			1.46045			0.730223	+	0.683209i	$0.239416\pi$
$648$	−4.42422e11	−	2.83180e12i	−0.0985710	−	0.630922i
$649$	−8.70134e11			−0.192524
$650$	−1.90541e12	−	3.30028e12i	−0.418677	−	0.725170i
$651$	2.84725e11	+	6.18471e11i	0.0621315	+	0.134960i
$652$	−2.84932e12	+	4.93517e12i	−0.617486	+	1.06952i
$653$	−2.67842e12	+	4.63916e12i	−0.576460	+	0.998458i	0.419421	+	0.907792i	$0.362233\pi$
$653$	−2.67842e12	+	4.63916e12i	−0.576460	+	0.998458i	−0.995881	+	0.0906665i	$0.971100\pi$
$654$	−1.62014e11	+	2.28989e11i	−0.0346299	+	0.0489457i
$655$	2.00480e12	+	3.47241e12i	0.425583	+	0.737132i
$656$	−4.34879e11			−0.0916856
$657$	1.98489e12	−	2.31908e12i	0.415616	−	0.485591i
$658$	4.84455e11			0.100748
$659$	−6.53510e11	−	1.13191e12i	−0.134980	−	0.233791i	0.790610	−	0.612320i	$-0.209764\pi$
$659$	−6.53510e11	−	1.13191e12i	−0.134980	−	0.233791i	−0.925590	+	0.378529i	$0.876430\pi$
$660$	2.60737e12	+	2.40963e11i	0.534878	+	0.0494314i
$661$	−6.08403e10	+	1.05379e11i	−0.0123961	+	0.0214707i	−0.872157	−	0.489226i	$-0.837279\pi$
$661$	−6.08403e10	+	1.05379e11i	−0.0123961	+	0.0214707i	0.859761	+	0.510697i	$0.170613\pi$
$662$	1.16764e11	−	2.02242e11i	0.0236292	−	0.0409270i
$663$	1.02497e13	+	9.47241e11i	2.06016	+	0.190392i
$664$	−1.24339e12	−	2.15362e12i	−0.248228	−	0.429944i
$665$	−7.05599e11			−0.139914
$666$	9.37341e11	+	1.74744e11i	0.184614	+	0.0344166i
$667$	−3.46590e11			−0.0678030
$668$	−3.20668e12	−	5.55414e12i	−0.623106	−	1.07925i
$669$	−4.26531e12	+	6.02856e12i	−0.823252	+	1.16358i
$670$	−2.32845e12	+	4.03299e12i	−0.446406	+	0.773198i
$671$	5.71582e11	−	9.90009e11i	0.108850	−	0.188533i
$672$	1.87670e12	+	4.07651e12i	0.355004	+	0.771128i
$673$	−1.64753e12	−	2.85361e12i	−0.309575	−	0.536200i	0.668694	−	0.743538i	$-0.266854\pi$
$673$	−1.64753e12	−	2.85361e12i	−0.309575	−	0.536200i	−0.978269	+	0.207337i	$0.933520\pi$
$674$	−4.08924e11			−0.0763261
$675$	1.98279e12	+	7.85908e12i	0.367628	+	1.45715i
$676$	−8.20017e12			−1.51030
$677$	−5.84161e11	−	1.01180e12i	−0.106877	−	0.185116i	0.807627	−	0.589694i	$-0.200752\pi$
$677$	−5.84161e11	−	1.01180e12i	−0.106877	−	0.185116i	−0.914503	+	0.404578i	$0.867418\pi$
$678$	−1.46862e12	−	3.19009e12i	−0.266917	−	0.579789i
$679$	−8.40145e11	+	1.45517e12i	−0.151684	+	0.262725i
$680$	−3.54215e12	+	6.13519e12i	−0.635298	+	1.10037i
$681$	1.00445e12	−	1.41969e12i	0.178965	−	0.252947i
$682$	−5.55685e10	−	9.62474e10i	−0.00983555	−	0.0170357i
$683$	7.05520e11			0.124055			0.0620277	−	0.998074i	$-0.480243\pi$
$683$	7.05520e11			0.124055			0.0620277	+	0.998074i	$0.480243\pi$
$684$	1.52025e11	+	4.30741e11i	0.0265559	+	0.0752425i
$685$	1.43986e13			2.49870
$686$	9.99767e11	+	1.73165e12i	0.172362	+	0.298539i
$687$	−6.16572e12	−	5.69814e11i	−1.05604	−	0.0975950i
$688$	2.74099e12	−	4.74753e12i	0.466400	−	0.807829i
$689$	−2.81438e12	+	4.87465e12i	−0.475769	+	0.824056i
$690$	7.20989e11	+	6.66311e10i	0.121090	+	0.0111907i
$691$	2.84563e12	+	4.92877e12i	0.474817	+	0.822408i	0.999584	−	0.0288384i	$-0.00918082\pi$
$691$	2.84563e12	+	4.92877e12i	0.474817	+	0.822408i	−0.524767	+	0.851246i	$0.675847\pi$
$692$	5.56669e12			0.922825
$693$	7.60473e11	+	2.15469e12i	0.125252	+	0.354883i
$694$	9.58982e11			0.156925
$695$	2.02669e12	+	3.51033e12i	0.329500	+	0.570711i
$696$	−6.82195e11	+	9.64210e11i	−0.110196	+	0.155751i
$697$	5.37021e11	−	9.30147e11i	0.0861874	−	0.149281i
$698$	9.77264e11	−	1.69267e12i	0.155834	−	0.269913i
$699$	−3.19296e12	−	6.93564e12i	−0.505878	−	1.09885i
$700$	−4.14627e12	−	7.18155e12i	−0.652705	−	1.13052i
$701$	−3.75961e12			−0.588046			−0.294023	−	0.955798i	$-0.594994\pi$
$701$	−3.75961e12			−0.588046			−0.294023	+	0.955798i	$0.594994\pi$
$702$	−3.44913e12	−	9.78619e11i	−0.536034	−	0.152089i
$703$	−3.23611e11			−0.0499717
$704$	4.69850e11	+	8.13804e11i	0.0720912	+	0.124866i
$705$	1.31542e12	+	2.85730e12i	0.200545	+	0.435617i
$706$	1.27635e11	−	2.21070e11i	0.0193352	−	0.0334895i
$707$	3.05454e12	−	5.29061e12i	0.459788	−	0.796376i
$708$	1.71596e12	−	2.42532e12i	0.256659	−	0.362760i
$709$	1.85253e12	+	3.20868e12i	0.275333	+	0.476890i	0.970219	−	0.242229i	$-0.0778787\pi$
$709$	1.85253e12	+	3.20868e12i	0.275333	+	0.476890i	−0.694886	+	0.719120i	$0.744545\pi$
$710$	4.98086e12			0.735600
$711$	−4.56200e12	−	8.50470e11i	−0.669487	−	0.124809i
$712$	−7.68003e12			−1.11996
$713$	1.18564e11	+	2.05359e11i	0.0171811	+	0.0297585i
$714$	−2.89056e12	−	2.67135e11i	−0.416236	−	0.0384670i
$715$	3.48770e12	−	6.04087e12i	0.499071	−	0.864416i
$716$	−1.23968e11	+	2.14718e11i	−0.0176279	+	0.0305324i
$717$	−1.17889e13	−	1.08948e12i	−1.66585	−	0.153952i
$718$	−3.10732e11	−	5.38204e11i	−0.0436341	−	0.0755765i
$719$	−1.23468e11			−0.0172296			−0.00861478	−	0.999963i	$-0.502742\pi$
$719$	−1.23468e11			−0.0172296			−0.00861478	+	0.999963i	$0.502742\pi$
$720$	−4.96245e12	+	5.79795e12i	−0.688177	+	0.804041i
$721$	1.04323e12			0.143771
$722$	−1.22654e12	−	2.12444e12i	−0.167983	−	0.290956i
$723$	5.26129e12	−	7.43627e12i	0.716094	−	1.01212i
$724$	1.91859e12	−	3.32310e12i	0.259513	−	0.449490i
$725$	1.67010e12	−	2.89270e12i	0.224503	−	0.388850i
$726$	9.04308e11	+	1.96431e12i	0.120810	+	0.262418i
$727$	−5.89947e12	−	1.02182e13i	−0.783264	−	1.35665i	−0.930031	−	0.367482i	$-0.880220\pi$
$727$	−5.89947e12	−	1.02182e13i	−0.783264	−	1.35665i	0.146766	−	0.989171i	$-0.453113\pi$
$728$	7.81153e12			1.03073
$729$	6.48931e12	+	4.00482e12i	0.850991	+	0.525181i
$730$	2.62797e12			0.342505
$731$	6.76955e12	+	1.17252e13i	0.876862	+	1.51877i
$732$	1.63225e12	+	3.54553e12i	0.210130	+	0.456437i
$733$	3.53411e12	−	6.12126e12i	0.452181	−	0.783200i	−0.546341	−	0.837563i	$-0.683980\pi$
$733$	3.53411e12	−	6.12126e12i	0.452181	−	0.783200i	0.998521	+	0.0543633i	$0.0173129\pi$
$734$	1.80607e12	−	3.12821e12i	0.229669	−	0.397799i
$735$	−2.68989e11	+	3.80187e11i	−0.0339971	+	0.0480512i
$736$	7.81489e11	+	1.35358e12i	0.0981686	+	0.170033i
$737$	−5.11826e12			−0.639026
$738$	−2.43255e11	+	2.84211e11i	−0.0301862	+	0.0352685i
$739$	−4.61726e12			−0.569488			−0.284744	−	0.958604i	$-0.591909\pi$
$739$	−4.61726e12			−0.569488			−0.284744	+	0.958604i	$0.591909\pi$
$740$	−3.16699e12	−	5.48538e12i	−0.388243	−	0.672456i
$741$	1.21166e12	+	1.11977e11i	0.147639	+	0.0136442i
$742$	7.93693e11	−	1.37472e12i	0.0961247	−	0.166493i
$743$	7.55678e11	−	1.30887e12i	0.0909677	−	0.157561i	−0.816951	−	0.576707i	$-0.804337\pi$
$743$	7.55678e11	−	1.30887e12i	0.0909677	−	0.157561i	0.907919	+	0.419147i	$0.137671\pi$
$744$	8.04678e11	+	7.43654e10i	0.0962818	+	0.00889801i
$745$	1.18132e12	+	2.04610e12i	0.140496	+	0.243346i
$746$	−3.88072e12			−0.458763
$747$	6.50419e12	+	1.21254e12i	0.764277	+	0.142480i
$748$	−3.65616e12			−0.427040
$749$	5.98209e12	+	1.03613e13i	0.694521	+	1.20294i
$750$	−1.34847e12	+	1.90591e12i	−0.155620	+	0.219952i
$751$	−7.49028e12	+	1.29735e13i	−0.859247	+	1.48826i	0.0134003	+	0.999910i	$0.495734\pi$
$751$	−7.49028e12	+	1.29735e13i	−0.859247	+	1.48826i	−0.872648	+	0.488350i	$0.837599\pi$
$752$	−8.89182e11	+	1.54011e12i	−0.101394	+	0.175619i
$753$	2.84541e12	+	6.18069e12i	0.322528	+	0.700584i
$754$	7.38743e11	+	1.27954e12i	0.0832382	+	0.144173i
$755$	−1.78636e13			−2.00082
$756$	−7.50546e12	−	2.12952e12i	−0.835660	−	0.237101i
$757$	3.27715e12			0.362714			0.181357	−	0.983417i	$-0.441951\pi$
$757$	3.27715e12			0.362714			0.181357	+	0.983417i	$0.441951\pi$
$758$	1.31541e12	+	2.27836e12i	0.144727	+	0.250674i
$759$	3.32788e11	+	7.22870e11i	0.0363982	+	0.0790629i
$760$	−4.18733e11	+	7.25267e11i	−0.0455278	+	0.0788564i
$761$	−2.91809e12	+	5.05428e12i	−0.315404	+	0.546296i	−0.979523	−	0.201331i	$-0.935473\pi$
$761$	−2.91809e12	+	5.05428e12i	−0.315404	+	0.546296i	0.664119	+	0.747627i	$0.268807\pi$
$762$	7.80987e11	−	1.10384e12i	0.0839163	−	0.118607i
$763$	8.13023e11	+	1.40820e12i	0.0868445	+	0.150419i
$764$	1.32266e13			1.40452
$765$	−6.27303e12	−	1.77738e13i	−0.662218	−	1.87630i
$766$	3.36915e12			0.353583
$767$	−3.95721e12	−	6.85409e12i	−0.412867	−	0.715106i
$768$	−3.81571e11	−	3.52634e10i	−0.0395776	−	0.00365762i
$769$	7.88296e11	−	1.36537e12i	0.0812870	−	0.140793i	−0.822516	−	0.568742i	$-0.807430\pi$
$769$	7.88296e11	−	1.36537e12i	0.0812870	−	0.140793i	0.903803	+	0.427949i	$0.140764\pi$
$770$	−9.83578e11	+	1.70361e12i	−0.100833	+	0.174647i
$771$	−5.08598e12	−	4.70028e11i	−0.518358	−	0.0479048i
$772$	4.81633e12	+	8.34213e12i	0.488021	+	0.845277i
$773$	1.49007e13			1.50106			0.750529	−	0.660837i	$-0.229799\pi$
$773$	1.49007e13			1.50106			0.750529	+	0.660837i	$0.229799\pi$
$774$	−1.56949e12	−	4.44694e12i	−0.157190	−	0.445376i
$775$	−2.28529e12			−0.227553
$776$	9.97157e11	+	1.72713e12i	0.0987156	+	0.170980i
$777$	3.19236e12	−	4.51206e12i	0.314208	−	0.444100i
$778$	−1.93344e12	+	3.34881e12i	−0.189200	+	0.327705i
$779$	6.34835e10	−	1.09957e11i	0.00617650	−	0.0106980i
$780$	9.95975e12	+	2.16342e13i	0.963436	+	2.09274i
$781$	2.73716e12	+	4.74090e12i	0.263251	+	0.455965i
$782$	−1.01100e12			−0.0966766
$783$	−7.68741e11	−	3.04702e12i	−0.0730890	−	0.289700i
$784$	−2.63300e11			−0.0248902
$785$	−8.01350e12	−	1.38798e13i	−0.753198	−	1.30458i
$786$	8.15468e11	+	1.77133e12i	0.0762089	+	0.165538i
$787$	−4.94718e12	+	8.56877e12i	−0.459697	+	0.796219i	−0.998945	−	0.0459287i	$-0.985375\pi$
$787$	−4.94718e12	+	8.56877e12i	−0.459697	+	0.796219i	0.539248	+	0.842147i	$0.318709\pi$
$788$	4.34880e12	−	7.53234e12i	0.401792	−	0.695925i
$789$	−2.21527e12	+	3.13105e12i	−0.203507	+	0.287636i
$790$	−1.99758e12	−	3.45992e12i	−0.182466	−	0.316041i
$791$	−2.03579e13			−1.84901
$792$	2.66605e12	+	4.97018e11i	0.240771	+	0.0448858i
$793$	1.03978e13			0.933710
$794$	−1.00496e12	−	1.74064e12i	−0.0897339	−	0.155424i
$795$	1.02631e13	+	9.48479e11i	0.911228	+	0.0842123i
$796$	1.36229e12	−	2.35955e12i	0.120271	−	0.208315i
$797$	−1.27503e11	+	2.20842e11i	−0.0111933	+	0.0193874i	−0.871568	−	0.490275i	$-0.836896\pi$
$797$	−1.27503e11	+	2.20842e11i	−0.0111933	+	0.0193874i	0.860374	+	0.509662i	$0.170230\pi$
$798$	−3.41705e11	−	3.15791e10i	−0.0298290	−	0.00275668i
$799$	−2.19606e12	−	3.80368e12i	−0.190626	−	0.330174i
$800$	−1.50630e13			−1.30018
$801$	1.32866e13	−	1.55236e13i	1.14043	−	1.33244i
$802$	−1.89711e12			−0.161923
$803$	1.44416e12	+	2.50136e12i	0.122573	+	0.212303i
$804$	1.00935e13	−	1.42661e13i	0.851904	−	1.20407i
$805$	2.09862e12	−	3.63492e12i	0.176138	−	0.305079i
$806$	5.05430e11	−	8.75431e11i	0.0421846	−	0.0730658i
$807$	7.88175e10	+	1.71205e11i	0.00654171	+	0.0142097i
$808$	−3.62539e12	−	6.27936e12i	−0.299229	−	0.518279i
$809$	−1.62301e13			−1.33215			−0.666075	−	0.745885i	$-0.732027\pi$
$809$	−1.62301e13			−1.33215			−0.666075	+	0.745885i	$0.732027\pi$
$810$	1.01338e12	+	6.48632e12i	0.0827161	+	0.529439i
$811$	−4.16753e12			−0.338287			−0.169143	−	0.985591i	$-0.554100\pi$
$811$	−4.16753e12			−0.338287			−0.169143	+	0.985591i	$0.554100\pi$
$812$	1.60754e12	+	2.78434e12i	0.129766	+	0.224761i
$813$	−1.16442e12	−	2.52931e12i	−0.0934765	−	0.203046i
$814$	−4.51101e11	+	7.81330e11i	−0.0360134	+	0.0623770i
$815$	1.38987e13	−	2.40733e13i	1.10348	−	1.91129i
$816$	6.15464e12	−	8.69893e12i	0.485956	−	0.686847i
$817$	8.00257e11	+	1.38609e12i	0.0628392	+	0.108841i
$818$	−1.19367e12			−0.0932171
$819$	−1.35141e13	+	1.57894e13i	−1.04957	+	1.22628i
$820$	2.48510e12			0.191947
$821$	1.10895e12	+	1.92075e12i	0.0851855	+	0.147546i	0.905470	−	0.424410i	$-0.139518\pi$
$821$	1.10895e12	+	1.92075e12i	0.0851855	+	0.147546i	−0.820285	+	0.571955i	$0.806185\pi$
$822$	6.97292e12	+	6.44412e11i	0.532711	+	0.0492312i
$823$	2.36686e11	−	4.09953e11i	0.0179835	−	0.0311483i	−0.856894	−	0.515493i	$-0.827609\pi$
$823$	2.36686e11	−	4.09953e11i	0.0179835	−	0.0311483i	0.874877	+	0.484345i	$0.160942\pi$
$824$	6.19096e11	−	1.07231e12i	0.0467828	−	0.0810301i
$825$	−7.63681e12	−	7.05766e11i	−0.573944	−	0.0530418i
$826$	1.11599e12	+	1.93295e12i	0.0834159	+	0.144481i
$827$	−3.43656e12			−0.255475			−0.127738	−	0.991808i	$-0.540772\pi$
$827$	−3.43656e12			−0.255475			−0.127738	+	0.991808i	$0.540772\pi$
$828$	−2.67113e12	−	4.97965e11i	−0.197496	−	0.0368182i
$829$	−1.73227e13			−1.27386			−0.636929	−	0.770922i	$-0.719796\pi$
$829$	−1.73227e13			−1.27386			−0.636929	+	0.770922i	$0.719796\pi$
$830$	2.84802e12	+	4.93292e12i	0.208301	+	0.360788i
$831$	−1.08076e13	+	1.52754e13i	−0.786186	+	1.11119i
$832$	−4.27358e12	+	7.40206e12i	−0.309198	+	0.535547i
$833$	3.25143e11	−	5.63163e11i	0.0233976	−	0.0405258i
$834$	8.24373e11	+	1.79067e12i	0.0590033	+	0.128165i
$835$	1.56419e13	+	2.70926e13i	1.11353	+	1.92868i
$836$	−4.32211e11			−0.0306032
$837$	−1.54243e12	+	1.49784e12i	−0.108628	+	0.105487i
$838$	−7.05389e12			−0.494118
$839$	1.22497e13	+	2.12171e13i	0.853486	+	1.47828i	0.878043	+	0.478583i	$0.158849\pi$
$839$	1.22497e13	+	2.12171e13i	0.853486	+	1.47828i	−0.0245567	+	0.999698i	$0.507817\pi$
$840$	−5.98158e12	−	1.29930e13i	−0.414533	−	0.900434i
$841$	6.60606e12	−	1.14420e13i	0.455366	−	0.788717i
$842$	−3.28354e12	+	5.68726e12i	−0.225132	+	0.389941i
$843$	5.21303e11	−	7.36806e11i	0.0355522	−	0.0502492i
$844$	−2.74232e12	−	4.74984e12i	−0.186028	−	0.322209i
$845$	3.99997e13			2.69899
$846$	5.09147e11	+	1.44260e12i	0.0341725	+	0.0968229i
$847$	1.25354e13			0.836879
$848$	2.91353e12	+	5.04638e12i	0.193481	+	0.335119i
$849$	5.37564e12	+	4.96797e11i	0.355096	+	0.0328167i
$850$	4.87169e12	−	8.43801e12i	0.320106	−	0.554440i
$851$	9.62495e11	−	1.66709e12i	0.0629094	−	0.108962i
$852$	−1.86121e13	−	1.72007e12i	−1.21009	−	0.111832i
$853$	−1.92703e12	−	3.33772e12i	−0.124629	−	0.215863i	0.796959	−	0.604033i	$-0.206441\pi$
$853$	−1.92703e12	−	3.33772e12i	−0.124629	−	0.215863i	−0.921588	+	0.388170i	$0.873107\pi$
$854$	−2.93232e12			−0.188647
$855$	−7.41562e11	−	2.10111e12i	−0.0474570	−	0.134463i
$856$	1.42001e13			0.903984
$857$	1.88200e12	+	3.25971e12i	0.119181	+	0.206427i	0.919443	−	0.393223i	$-0.128640\pi$
$857$	1.88200e12	+	3.25971e12i	0.119181	+	0.206427i	−0.800263	+	0.599650i	$0.795307\pi$
$858$	1.95937e12	−	2.76936e12i	0.123431	−	0.174456i
$859$	1.17704e12	−	2.03869e12i	0.0737599	−	0.127756i	−0.826786	−	0.562516i	$-0.809833\pi$
$859$	1.17704e12	−	2.03869e12i	0.0737599	−	0.127756i	0.900546	+	0.434760i	$0.143167\pi$
$860$	−1.56633e13	+	2.71296e13i	−0.976428	+	1.69122i
$861$	9.06859e11	+	1.96985e12i	0.0562374	+	0.122157i
$862$	2.27910e12	+	3.94752e12i	0.140599	+	0.243524i
$863$	−1.83375e13			−1.12536			−0.562680	−	0.826675i	$-0.690230\pi$
$863$	−1.83375e13			−1.12536			−0.562680	+	0.826675i	$0.690230\pi$
$864$	−1.01666e13	+	9.87267e12i	−0.620672	+	0.602730i
$865$	−2.71538e13			−1.64914
$866$	−4.91545e12	−	8.51380e12i	−0.296984	−	0.514391i
$867$	4.04814e12	+	8.79323e12i	0.243315	+	0.528521i
$868$	1.09984e12	−	1.90498e12i	0.0657644	−	0.113907i
$869$	2.19549e12	−	3.80270e12i	0.130600	−	0.226205i
$870$	1.56259e12	−	2.20855e12i	0.0924714	−	0.130698i
$871$	−2.32769e13	−	4.03168e13i	−1.37039	−	2.37358i
$872$	1.92993e12			0.113036
$873$	−5.21614e12	−	9.72418e11i	−0.303938	−	0.0566616i
$874$	−1.19515e11			−0.00692820
$875$	6.76693e12	+	1.17207e13i	0.390261	+	0.675952i
$876$	−9.82002e12	−	9.07530e11i	−0.563435	−	0.0520706i
$877$	−5.75313e11	+	9.96472e11i	−0.0328402	+	0.0568809i	−0.881978	−	0.471290i	$-0.843789\pi$
$877$	−5.75313e11	+	9.96472e11i	−0.0328402	+	0.0568809i	0.849138	+	0.528171i	$0.177122\pi$
$878$	−3.07058e12	+	5.31840e12i	−0.174379	+	0.302034i
$879$	2.59744e13	+	2.40046e12i	1.46756	+	0.135626i
$880$	−3.61057e12	−	6.25370e12i	−0.202957	−	0.351532i
$881$	2.37153e13			1.32628			0.663142	−	0.748494i	$-0.269223\pi$
$881$	2.37153e13			1.32628			0.663142	+	0.748494i	$0.269223\pi$
$882$	−1.47280e11	+	1.72077e11i	−0.00819476	+	0.00957446i
$883$	2.59683e13			1.43754			0.718771	−	0.695247i	$-0.244705\pi$
$883$	2.59683e13			1.43754			0.718771	+	0.695247i	$0.244705\pi$
$884$	−1.66276e13	−	2.87998e13i	−0.915785	−	1.58619i
$885$	−8.37027e12	+	1.18305e13i	−0.458664	+	0.648273i
$886$	2.74016e12	−	4.74609e12i	0.149391	−	0.258752i
$887$	7.91049e12	−	1.37014e13i	0.429089	−	0.743204i	−0.567704	−	0.823233i	$-0.692168\pi$
$887$	7.91049e12	−	1.37014e13i	0.429089	−	0.743204i	0.996793	+	0.0800293i	$0.0255014\pi$
$888$	−2.74335e12	−	5.95900e12i	−0.148055	−	0.321599i
$889$	−3.91918e12	−	6.78821e12i	−0.210444	−	0.364500i
$890$	1.75913e13			0.939818
$891$	−5.61695e12	+	4.52903e12i	−0.298573	+	0.240744i
$892$	2.38585e13			1.26183
$893$	−2.59605e11	−	4.49649e11i	−0.0136610	−	0.0236615i
$894$	4.80510e11	+	1.04375e12i	0.0251585	+	0.0546483i
$895$	6.04703e11	−	1.04738e12i	0.0315020	−	0.0545631i
$896$	9.39407e12	−	1.62710e13i	0.486931	−	0.843389i
$897$	−4.18063e12	+	5.90887e12i	−0.215613	+	0.304746i
$898$	3.18379e12	+	5.51449e12i	0.163381	+	0.282984i
$899$	8.86023e11			0.0452404
$900$	1.70274e13	−	1.98942e13i	0.865083	−	1.01073i
$901$	−1.43914e13			−0.727513
$902$	−1.76987e11	−	3.06551e11i	−0.00890251	−	0.0154196i
$903$	−2.72204e13	−	2.51561e12i	−1.36239	−	0.125907i
$904$	−1.20813e13	+	2.09253e13i	−0.601664	+	1.04211i
$905$	−9.35871e12	+	1.62098e13i	−0.463765	+	0.803264i
$906$	−8.65091e12	−	7.99486e11i	−0.426565	−	0.0394216i
$907$	−7.76777e12	−	1.34542e13i	−0.381122	−	0.660122i	0.610101	−	0.792323i	$-0.291129\pi$
$907$	−7.76777e12	−	1.34542e13i	−0.381122	−	0.660122i	−0.991223	+	0.132202i	$0.957795\pi$
$908$	−5.61852e12			−0.274306
$909$	1.89644e13	+	3.53544e12i	0.921303	+	0.171754i
$910$	−1.78925e13			−0.864939
$911$	−2.56238e12	−	4.43818e12i	−0.123257	−	0.213487i	0.797793	−	0.602931i	$-0.206001\pi$
$911$	−2.56238e12	−	4.43818e12i	−0.123257	−	0.213487i	−0.921050	+	0.389444i	$0.872667\pi$
$912$	7.27567e11	−	1.02834e12i	0.0348254	−	0.0492220i
$913$	−3.13018e12	+	5.42163e12i	−0.149091	+	0.258233i
$914$	2.15152e12	−	3.72655e12i	0.101974	−	0.176624i
$915$	−7.96198e12	−	1.72947e13i	−0.375514	−	0.815679i
$916$	1.00023e13	+	1.73245e13i	0.469430	+	0.813077i
$917$	1.13039e13			0.527919
$918$	−2.24242e12	−	8.88817e12i	−0.104214	−	0.413067i
$919$	2.60261e13			1.20362			0.601810	−	0.798639i	$-0.294446\pi$
$919$	2.60261e13			1.20362			0.601810	+	0.798639i	$0.294446\pi$
$920$	−2.49082e12	−	4.31423e12i	−0.114630	−	0.198545i
$921$	8.49626e12	+	1.84553e13i	0.389098	+	0.845186i
$922$	2.05246e12	−	3.55497e12i	0.0935375	−	0.162012i
$923$	−2.48962e13	+	4.31215e13i	−1.12908	+	1.95563i
$924$	4.26368e12	−	6.02626e12i	0.192425	−	0.271972i
$925$	9.27590e12	+	1.60663e13i	0.416599	+	0.721570i
$926$	−9.71334e12			−0.434129
$927$	1.09640e12	+	3.10649e12i	0.0487652	+	0.138169i
$928$	5.84002e12			0.258493
$929$	−2.01836e13	−	3.49590e13i	−0.889052	−	1.53988i	−0.840998	−	0.541039i	$-0.818031\pi$
$929$	−2.01836e13	−	3.49590e13i	−0.889052	−	1.53988i	−0.0480546	−	0.998845i	$-0.515302\pi$
$930$	−1.84314e12	−	1.70336e11i	−0.0807950	−	0.00746678i
$931$	3.84365e10	−	6.65740e10i	0.00167676	−	0.00290423i
$932$	−1.23338e13	+	2.13628e13i	−0.535458	+	0.927440i
$933$	−2.41502e12	−	2.23187e11i	−0.104340	−	0.00964276i
$934$	3.65572e12	+	6.33188e12i	0.157185	+	0.272253i
$935$	1.78344e13			0.763144
$936$	8.20967e12	+	2.32610e13i	0.349611	+	0.990572i
$937$	−1.54039e12			−0.0652835			−0.0326418	−	0.999467i	$-0.510392\pi$
$937$	−1.54039e12			−0.0652835			−0.0326418	+	0.999467i	$0.510392\pi$
$938$	6.56440e12	+	1.13699e13i	0.276874	+	0.479560i
$939$	4.91097e12	−	6.94113e12i	0.206145	−	0.291363i
$940$	5.08121e12	−	8.80091e12i	0.212271	−	0.367665i
$941$	2.77277e12	−	4.80258e12i	0.115282	−	0.199674i	−0.802611	−	0.596503i	$-0.796556\pi$
$941$	2.77277e12	−	4.80258e12i	0.115282	−	0.199674i	0.917892	+	0.396829i	$0.129890\pi$
$942$	−3.25956e12	−	7.08030e12i	−0.134875	−	0.292970i
$943$	3.77630e11	+	6.54075e11i	0.0155512	+	0.0269355i
$944$	−8.19325e12			−0.335801
$945$	3.66109e13	+	1.03876e13i	1.49337	+	0.423713i
$946$	4.46211e12			0.181147
$947$	−8.80699e12	−	1.52542e13i	−0.355838	−	0.616330i	0.631423	−	0.775439i	$-0.282471\pi$
$947$	−8.80699e12	−	1.52542e13i	−0.355838	−	0.616330i	−0.987261	+	0.159109i	$0.949138\pi$
$948$	6.26961e12	+	1.36186e13i	0.252117	+	0.547641i
$949$	−1.31356e13	+	2.27515e13i	−0.525716	+	0.910567i
$950$	5.75903e11	−	9.97493e11i	0.0229400	−	0.0397332i
$951$	2.00843e13	−	2.83870e13i	0.796240	−	1.12540i
$952$	9.98610e12	+	1.72964e13i	0.394031	+	0.682481i
$953$	−4.21531e13			−1.65543			−0.827717	−	0.561146i	$-0.810361\pi$
$953$	−4.21531e13			−1.65543			−0.827717	+	0.561146i	$0.810361\pi$
$954$	4.92774e12	+	9.18652e11i	0.192610	+	0.0359074i
$955$	−6.45180e13			−2.50995
$956$	1.91244e13	+	3.31245e13i	0.740505	+	1.28259i
$957$	2.96085e12	+	2.73631e11i	0.114107	+	0.0105453i
$958$	−4.93154e12	+	8.54168e12i	−0.189164	+	0.327641i
$959$	2.02965e13	−	3.51545e13i	0.774884	−	1.34214i
$960$	1.55843e13	+	1.44025e12i	0.592199	+	0.0547289i
$961$	1.29167e13	+	2.23724e13i	0.488536	+	0.846170i
$962$	−8.20609e12			−0.308922
$963$	−2.45666e13	+	2.87027e13i	−0.920505	+	1.07548i
$964$	−2.94296e13			−1.09759
$965$	−2.34936e13	−	4.06921e13i	−0.872121	−	1.51056i
$966$	1.17899e12	−	1.66638e12i	0.0435626	−	0.0615711i
$967$	1.62577e13	−	2.81592e13i	0.597918	−	1.03562i	−0.395210	−	0.918591i	$-0.629328\pi$
$967$	1.62577e13	−	2.81592e13i	0.597918	−	1.03562i	0.993128	−	0.117033i	$-0.0373383\pi$
$968$	7.43905e12	−	1.28848e13i	0.272319	−	0.471671i
$969$	1.30102e12	+	2.82604e12i	0.0474054	+	0.102972i
$970$	−2.28401e12	−	3.95603e12i	−0.0828373	−	0.143478i
$971$	4.38405e13			1.58266			0.791332	−	0.611386i	$-0.209388\pi$
$971$	4.38405e13			1.58266			0.791332	+	0.611386i	$0.209388\pi$
$972$	−1.54678e12	−	2.45876e13i	−0.0555814	−	0.883523i
$973$	1.14274e13			0.408731
$974$	−4.68889e12	−	8.12140e12i	−0.166938	−	0.289145i
$975$	−2.91715e13	−	6.33652e13i	−1.03380	−	2.24559i
$976$	5.38206e12	−	9.32200e12i	0.189856	−	0.328840i
$977$	−6.56481e12	+	1.13706e13i	−0.230514	+	0.399261i	−0.957959	−	0.286904i	$-0.907374\pi$
$977$	−6.56481e12	+	1.13706e13i	−0.230514	+	0.399261i	0.727446	+	0.686165i	$0.240707\pi$
$978$	7.80822e12	−	1.10361e13i	0.272915	−	0.385736i
$979$	9.66707e12	+	1.67438e13i	0.336335	+	0.582550i
$980$	1.50462e12			0.0521087
$981$	−3.33883e12	+	3.90097e12i	−0.115102	+	0.134481i
$982$	8.97171e12			0.307874
$983$	9.26273e12	+	1.60435e13i	0.316408	+	0.548035i	0.979736	−	0.200294i	$-0.0641897\pi$
$983$	9.26273e12	+	1.60435e13i	0.316408	+	0.548035i	−0.663328	+	0.748329i	$0.730856\pi$
$984$	2.56292e12	+	2.36856e11i	0.0871481	+	0.00805391i
$985$	−2.12130e13	+	3.67421e13i	−0.718025	+	1.24366i
$986$	−1.88879e12	+	3.27148e12i	−0.0636410	+	0.110230i
$987$	8.83036e12	+	8.16070e11i	0.296177	+	0.0273716i
$988$	−1.96562e12	−	3.40455e12i	−0.0656285	−	0.113672i
$989$	−9.52062e12			−0.316433
$990$	−6.10666e12	−	1.13843e12i	−0.202044	−	0.0376660i
$991$	3.95986e13			1.30421			0.652106	−	0.758127i	$-0.273885\pi$
$991$	3.95986e13			1.30421			0.652106	+	0.758127i	$0.273885\pi$
$992$	−1.99780e12	−	3.46029e12i	−0.0655012	−	0.113451i
$993$	2.46899e12	−	3.48966e12i	0.0805839	−	0.113897i
$994$	7.02107e12	−	1.21608e13i	0.228121	−	0.395116i
$995$	−6.64512e12	+	1.15097e13i	−0.214931	+	0.372271i
$996$	−8.93879e12	−	1.94165e13i	−0.287814	−	0.625179i
$997$	−2.39753e13	−	4.15264e13i	−0.768485	−	1.33105i	−0.938385	−	0.345593i	$-0.887678\pi$
$997$	−2.39753e13	−	4.15264e13i	−0.768485	−	1.33105i	0.169900	−	0.985461i	$-0.445656\pi$
$998$	1.69970e13			0.542357
$999$	1.67910e13	+	4.76409e12i	0.533373	+	0.151334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.10.c.a.4.5	✓	16
3.2	odd	2		27.10.c.a.10.4		16
9.2	odd	6		27.10.c.a.19.4		16
9.4	even	3		81.10.a.c.1.4		8
9.5	odd	6		81.10.a.d.1.5		8
9.7	even	3	inner	9.10.c.a.7.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.5	✓	16	1.1	even	1	trivial
9.10.c.a.7.5	yes	16	9.7	even	3	inner
27.10.c.a.10.4		16	3.2	odd	2
27.10.c.a.19.4		16	9.2	odd	6
81.10.a.c.1.4		8	9.4	even	3
81.10.a.d.1.5		8	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.83216 + 6.63749i) q^{2} +(58.6695 + 127.440i) q^{3} +(226.629 - 392.533i) q^{4} +(-1105.48 + 1914.74i) q^{5} +(-621.050 + 877.788i) q^{6} +(3116.58 + 5398.07i) q^{7} +7398.05 q^{8} +(-12798.8 + 14953.6i) q^{9} +O(q^{10})\)	\(q+(3.83216 + 6.63749i) q^{2} +(58.6695 + 127.440i) q^{3} +(226.629 - 392.533i) q^{4} +(-1105.48 + 1914.74i) q^{5} +(-621.050 + 877.788i) q^{6} +(3116.58 + 5398.07i) q^{7} +7398.05 q^{8} +(-12798.8 + 14953.6i) q^{9} -16945.4 q^{10} +(-9312.12 - 16129.1i) q^{11} +(63320.5 + 5851.85i) q^{12} +(84699.6 - 146704. i) q^{13} +(-23886.4 + 41372.5i) q^{14} +(-308872. - 28544.8i) q^{15} +(-87683.6 - 151872. i) q^{16} +433113. q^{17} +(-148302. - 27647.1i) q^{18} +51200.2 q^{19} +(501066. + 867871. i) q^{20} +(-505081. + 713877. i) q^{21} +(71371.1 - 123618. i) q^{22} +(-152281. + 263759. i) q^{23} +(434039. + 942805. i) q^{24} +(-1.46759e6 - 2.54194e6i) q^{25} +1.29833e6 q^{26} +(-2.65659e6 - 753752. i) q^{27} +2.82523e6 q^{28} +(568995. + 985528. i) q^{29} +(-994179. - 2.15952e6i) q^{30} +(389293. - 674275. i) q^{31} +(2.56594e6 - 4.44433e6i) q^{32} +(1.50915e6 - 2.13302e6i) q^{33} +(1.65976e6 + 2.87479e6i) q^{34} -1.37812e7 q^{35} +(2.96922e6 + 8.41288e6i) q^{36} -6.32050e6 q^{37} +(196207. + 339841. i) q^{38} +(2.36652e7 + 2.18705e6i) q^{39} +(-8.17836e6 + 1.41653e7i) q^{40} +(1.23991e6 - 2.14759e6i) q^{41} +(-6.67391e6 - 616778. i) q^{42} +(1.56300e7 + 2.70719e7i) q^{43} -8.44159e6 q^{44} +(-1.44836e7 - 4.10372e7i) q^{45} -2.33427e6 q^{46} +(-5.07040e6 - 8.78219e6i) q^{47} +(1.42102e7 - 2.00847e7i) q^{48} +(750710. - 1.30027e6i) q^{49} +(1.12481e7 - 1.94822e7i) q^{50} +(2.54105e7 + 5.51958e7i) q^{51} +(-3.83908e7 - 6.64948e7i) q^{52} -3.32278e7 q^{53} +(-5.17744e6 - 2.05216e7i) q^{54} +4.11773e7 q^{55} +(2.30566e7 + 3.99352e7i) q^{56} +(3.00389e6 + 6.52494e6i) q^{57} +(-4.36096e6 + 7.55340e6i) q^{58} +(2.33603e7 - 4.04612e7i) q^{59} +(-8.12041e7 + 1.14773e8i) q^{60} +(3.06902e7 + 5.31570e7i) q^{61} +5.96733e6 q^{62} +(-1.20609e8 - 2.24846e7i) q^{63} -5.04557e7 q^{64} +(1.87267e8 + 3.24355e8i) q^{65} +(1.99412e7 + 1.84289e6i) q^{66} +(1.37409e8 - 2.37999e8i) q^{67} +(9.81560e7 - 1.70011e8i) q^{68} +(-4.25477e7 - 3.93210e6i) q^{69} +(-5.28117e7 - 9.14726e7i) q^{70} -2.93935e8 q^{71} +(-9.46860e7 + 1.10628e8i) q^{72} -1.55084e8 q^{73} +(-2.42212e7 - 4.19523e7i) q^{74} +(2.37841e8 - 3.36163e8i) q^{75} +(1.16034e7 - 2.00978e7i) q^{76} +(5.80439e7 - 1.00535e8i) q^{77} +(7.61723e7 + 1.65459e8i) q^{78} +(1.17883e8 + 2.04180e8i) q^{79} +3.87728e8 q^{80} +(-5.98026e7 - 3.82777e8i) q^{81} +1.90061e7 q^{82} +(-1.68070e8 - 2.91106e8i) q^{83} +(1.65755e8 + 3.60046e8i) q^{84} +(-4.78796e8 + 8.29299e8i) q^{85} +(-1.19793e8 + 2.07488e8i) q^{86} +(-9.22129e7 + 1.30333e8i) q^{87} +(-6.88915e7 - 1.19324e8i) q^{88} -1.03812e9 q^{89} +(2.16881e8 - 2.53396e8i) q^{90} +1.05589e9 q^{91} +(6.90228e7 + 1.19551e8i) q^{92} +(1.08769e8 + 1.00520e7i) q^{93} +(3.88611e7 - 6.73095e7i) q^{94} +(-5.66005e7 + 9.80350e7i) q^{95} +(7.16926e8 + 6.62557e7i) q^{96} +(1.34786e8 + 2.33457e8i) q^{97} +1.15074e7 q^{98} +(3.60372e8 + 6.71823e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9}+O(q^{10}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16} - 831078 q^{17} - 1039500 q^{18} - 170554 q^{19} + 1855164 q^{20} - 503475 q^{21} + 529359 q^{22} + 1064559 q^{23} - 2686059 q^{24} - 2293229 q^{25} + 2436312 q^{26} - 6176520 q^{27} + 1225724 q^{28} - 1309053 q^{29} + 30713544 q^{30} - 2359819 q^{31} + 5760063 q^{32} - 19931472 q^{33} + 981801 q^{34} - 31066554 q^{35} - 48894093 q^{36} + 16391516 q^{37} + 39490203 q^{38} + 74528535 q^{39} - 16760496 q^{40} + 54747318 q^{41} + 25242354 q^{42} + 15249608 q^{43} - 332509926 q^{44} - 139865967 q^{45} + 2390520 q^{46} + 156295545 q^{47} + 312045027 q^{48} + 15239583 q^{49} + 315590163 q^{50} + 3098385 q^{51} - 19773358 q^{52} - 525516228 q^{53} - 591710103 q^{54} - 7579770 q^{55} + 470339790 q^{56} + 581271465 q^{57} + 55408560 q^{58} + 307774074 q^{59} - 430082172 q^{60} + 69192125 q^{61} - 914436924 q^{62} - 693544725 q^{63} - 403588478 q^{64} + 482470359 q^{65} + 1912534074 q^{66} + 14328044 q^{67} + 915409575 q^{68} - 724756329 q^{69} - 229271934 q^{70} - 1239601392 q^{71} - 1729340037 q^{72} + 598613198 q^{73} + 1022736000 q^{74} + 1477690413 q^{75} + 119954093 q^{76} + 717995541 q^{77} + 243023958 q^{78} + 30257531 q^{79} - 2927826528 q^{80} - 1055378241 q^{81} - 202376022 q^{82} + 1176168291 q^{83} + 1383634866 q^{84} + 4818366 q^{85} + 1426944009 q^{86} + 617958567 q^{87} + 911312427 q^{88} - 3317041296 q^{89} - 981417492 q^{90} - 739230122 q^{91} - 76813998 q^{92} - 552731577 q^{93} - 1954316784 q^{94} - 391400652 q^{95} + 1854064512 q^{96} - 267311278 q^{97} + 4827300318 q^{98} + 1672014609 q^{99}+O(q^{100}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9 + 1020 * q^10 + 99150 * q^11 - 241212 * q^12 + 32435 * q^13 + 394824 * q^14 + 723843 * q^15 - 328193 * q^16 - 831078 * q^17 - 1039500 * q^18 - 170554 * q^19 + 1855164 * q^20 - 503475 * q^21 + 529359 * q^22 + 1064559 * q^23 - 2686059 * q^24 - 2293229 * q^25 + 2436312 * q^26 - 6176520 * q^27 + 1225724 * q^28 - 1309053 * q^29 + 30713544 * q^30 - 2359819 * q^31 + 5760063 * q^32 - 19931472 * q^33 + 981801 * q^34 - 31066554 * q^35 - 48894093 * q^36 + 16391516 * q^37 + 39490203 * q^38 + 74528535 * q^39 - 16760496 * q^40 + 54747318 * q^41 + 25242354 * q^42 + 15249608 * q^43 - 332509926 * q^44 - 139865967 * q^45 + 2390520 * q^46 + 156295545 * q^47 + 312045027 * q^48 + 15239583 * q^49 + 315590163 * q^50 + 3098385 * q^51 - 19773358 * q^52 - 525516228 * q^53 - 591710103 * q^54 - 7579770 * q^55 + 470339790 * q^56 + 581271465 * q^57 + 55408560 * q^58 + 307774074 * q^59 - 430082172 * q^60 + 69192125 * q^61 - 914436924 * q^62 - 693544725 * q^63 - 403588478 * q^64 + 482470359 * q^65 + 1912534074 * q^66 + 14328044 * q^67 + 915409575 * q^68 - 724756329 * q^69 - 229271934 * q^70 - 1239601392 * q^71 - 1729340037 * q^72 + 598613198 * q^73 + 1022736000 * q^74 + 1477690413 * q^75 + 119954093 * q^76 + 717995541 * q^77 + 243023958 * q^78 + 30257531 * q^79 - 2927826528 * q^80 - 1055378241 * q^81 - 202376022 * q^82 + 1176168291 * q^83 + 1383634866 * q^84 + 4818366 * q^85 + 1426944009 * q^86 + 617958567 * q^87 + 911312427 * q^88 - 3317041296 * q^89 - 981417492 * q^90 - 739230122 * q^91 - 76813998 * q^92 - 552731577 * q^93 - 1954316784 * q^94 - 391400652 * q^95 + 1854064512 * q^96 - 267311278 * q^97 + 4827300318 * q^98 + 1672014609 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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