LMFDB - Embedded newform 9.10.c.a.4.2

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			4.2
Root			$0.500000 + 15.6774i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.10.c.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.8270 - 22.2170i) q^{2} +(-90.7998 - 106.950i) q^{3} +(-73.0637 + 126.550i) q^{4} +(-353.226 + 611.805i) q^{5} +(-1211.43 + 3389.15i) q^{6} +(2284.21 + 3956.36i) q^{7} -9386.09 q^{8} +(-3193.79 + 19422.2i) q^{9} +18123.3 q^{10} +(-35716.7 - 61863.1i) q^{11} +(20168.8 - 3676.53i) q^{12} +(13201.0 - 22864.9i) q^{13} +(58599.1 - 101497. i) q^{14} +(97505.6 - 17774.1i) q^{15} +(157804. + 273325. i) q^{16} -314759. q^{17} +(472469. - 178171. i) q^{18} -904019. q^{19} +(-51616.0 - 89401.5i) q^{20} +(215729. - 603534. i) q^{21} +(-916276. + 1.58704e6i) q^{22} +(55921.2 - 96858.3i) q^{23} +(852255. + 1.00385e6i) q^{24} +(727026. + 1.25925e6i) q^{25} -677318. q^{26} +(2.36720e6 - 1.42195e6i) q^{27} -667571. q^{28} +(-2.19402e6 - 3.80015e6i) q^{29} +(-1.64559e6 - 1.93829e6i) q^{30} +(4.94392e6 - 8.56313e6i) q^{31} +(1.64546e6 - 2.85003e6i) q^{32} +(-3.37322e6 + 9.43708e6i) q^{33} +(4.03742e6 + 6.99301e6i) q^{34} -3.22736e6 q^{35} +(-2.22452e6 - 1.82323e6i) q^{36} -6.32122e6 q^{37} +(1.15959e7 + 2.00846e7i) q^{38} +(-3.64406e6 + 664268. i) q^{39} +(3.31541e6 - 5.74246e6i) q^{40} +(-2.68019e6 + 4.64223e6i) q^{41} +(-1.61759e7 + 2.94867e6i) q^{42} +(-1.12275e7 - 1.94466e7i) q^{43} +1.04384e7 q^{44} +(-1.07544e7 - 8.81438e6i) q^{45} -2.86920e6 q^{46} +(2.23644e7 + 3.87363e7i) q^{47} +(1.49036e7 - 4.16950e7i) q^{48} +(9.74159e6 - 1.68729e7i) q^{49} +(1.86511e7 - 3.23047e7i) q^{50} +(2.85801e7 + 3.36636e7i) q^{51} +(1.92903e6 + 3.34118e6i) q^{52} -4.00972e7 q^{53} +(-6.19556e7 - 3.43528e7i) q^{54} +5.04642e7 q^{55} +(-2.14398e7 - 3.71348e7i) q^{56} +(8.20848e7 + 9.66852e7i) q^{57} +(-5.62853e7 + 9.74890e7i) q^{58} +(4.79118e7 - 8.29857e7i) q^{59} +(-4.87481e6 + 1.36380e7i) q^{60} +(-1.01113e7 - 1.75132e7i) q^{61} -2.53663e8 q^{62} +(-8.41364e7 + 3.17284e7i) q^{63} +7.71659e7 q^{64} +(9.32588e6 + 1.61529e7i) q^{65} +(2.52932e8 - 4.61065e7i) q^{66} +(-9.12489e7 + 1.58048e8i) q^{67} +(2.29975e7 - 3.98328e7i) q^{68} +(-1.54367e7 + 2.81392e6i) q^{69} +(4.13974e7 + 7.17024e7i) q^{70} +1.38543e8 q^{71} +(2.99772e7 - 1.82298e8i) q^{72} -2.17970e8 q^{73} +(8.10823e7 + 1.40439e8i) q^{74} +(6.86631e7 - 1.92095e8i) q^{75} +(6.60510e7 - 1.14404e8i) q^{76} +(1.63169e8 - 2.82617e8i) q^{77} +(6.15004e7 + 7.24395e7i) q^{78} +(-1.97294e8 - 3.41722e8i) q^{79} -2.22962e8 q^{80} +(-3.67020e8 - 1.24061e8i) q^{81} +1.37515e8 q^{82} +(2.36638e8 + 4.09870e8i) q^{83} +(6.06153e7 + 7.13970e7i) q^{84} +(1.11181e8 - 1.92571e8i) q^{85} +(-2.88030e8 + 4.98883e8i) q^{86} +(-2.07211e8 + 5.79704e8i) q^{87} +(3.35240e8 + 5.80653e8i) q^{88} +2.60507e8 q^{89} +(-5.78820e7 + 3.51994e8i) q^{90} +1.20616e8 q^{91} +(8.17161e6 + 1.41537e7i) q^{92} +(-1.36474e9 + 2.48775e8i) q^{93} +(5.73736e8 - 9.93741e8i) q^{94} +(3.19323e8 - 5.53083e8i) q^{95} +(-4.54219e8 + 8.27988e7i) q^{96} +(-2.87421e8 - 4.97828e8i) q^{97} -4.99822e8 q^{98} +(1.31559e9 - 4.96118e8i) 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} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16}+ \cdots + 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

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 $

$2$	−12.8270	−	22.2170i	−0.566879	−	0.981862i	−0.996872	−	0.0790305i	$-0.974818\pi$
$2$	−12.8270	−	22.2170i	−0.566879	−	0.981862i	0.429994	−	0.902832i	$-0.358516\pi$
$3$	−90.7998	−	106.950i	−0.647201	−	0.762319i
$3$	−90.7998	−	106.950i	−0.647201	−	0.762319i
$4$	−73.0637	+	126.550i	−0.142703	+	0.247168i
$5$	−353.226	+	611.805i	−0.252748	+	0.437772i	−0.964281	−	0.264880i	$-0.914668\pi$
$5$	−353.226	+	611.805i	−0.252748	+	0.437772i	0.711534	+	0.702652i	$0.248001\pi$
$6$	−1211.43	+	3389.15i	−0.381608	+	1.06760i
$7$	2284.21	+	3956.36i	0.359579	+	0.622809i	0.987891	−	0.155153i	$-0.0495870\pi$
$7$	2284.21	+	3956.36i	0.359579	+	0.622809i	−0.628311	+	0.777962i	$0.716254\pi$
$8$	−9386.09			−0.810177
$9$	−3193.79	+	19422.2i	−0.162261	+	0.986748i
$10$	18123.3			0.573109
$11$	−35716.7	−	61863.1i	−0.735537	−	1.27399i	−0.954487	−	0.298251i	$-0.903597\pi$
$11$	−35716.7	−	61863.1i	−0.735537	−	1.27399i	0.218951	−	0.975736i	$-0.429737\pi$
$12$	20168.8	−	3676.53i	0.280778	−	0.0511826i
$13$	13201.0	−	22864.9i	0.128193	−	0.222036i	−0.794784	−	0.606893i	$-0.792416\pi$
$13$	13201.0	−	22864.9i	0.128193	−	0.222036i	0.922976	+	0.384857i	$0.125749\pi$
$14$	58599.1	−	101497.i	0.407675	−	0.706114i
$15$	97505.6	−	17774.1i	0.497301	−	0.0906520i
$16$	157804.	+	273325.i	0.601975	+	1.04265i
$17$	−314759.			−0.914026			−0.457013	−	0.889460i	$-0.651081\pi$
$17$	−314759.			−0.914026			−0.457013	+	0.889460i	$0.651081\pi$
$18$	472469.	−	178171.i	1.06083	−	0.400048i
$19$	−904019.			−1.59143			−0.795713	−	0.605674i	$-0.792904\pi$
$19$	−904019.			−1.59143			−0.795713	+	0.605674i	$0.792904\pi$
$20$	−51616.0	−	89401.5i	−0.0721355	−	0.124942i
$21$	215729.	−	603534.i	0.242059	−	0.677197i
$22$	−916276.	+	1.58704e6i	−0.833920	+	1.44439i
$23$	55921.2	−	96858.3i	0.0416678	−	0.0721708i	−0.844439	−	0.535651i	$-0.820066\pi$
$23$	55921.2	−	96858.3i	0.0416678	−	0.0721708i	0.886107	+	0.463480i	$0.153400\pi$
$24$	852255.	+	1.00385e6i	0.524347	+	0.617614i
$25$	727026.	+	1.25925e6i	0.372237	+	0.644734i
$26$	−677318.			−0.290678
$27$	2.36720e6	−	1.42195e6i	0.857233	−	0.514929i
$28$	−667571.			−0.205251
$29$	−2.19402e6	−	3.80015e6i	−0.576035	−	0.997722i	−0.995928	−	0.0901485i	$-0.971266\pi$
$29$	−2.19402e6	−	3.80015e6i	−0.576035	−	0.997722i	0.419893	−	0.907573i	$-0.362067\pi$
$30$	−1.64559e6	−	1.93829e6i	−0.370917	−	0.436892i
$31$	4.94392e6	−	8.56313e6i	0.961488	−	1.66535i	0.242721	−	0.970096i	$-0.421960\pi$
$31$	4.94392e6	−	8.56313e6i	0.961488	−	1.66535i	0.718767	−	0.695251i	$-0.244707\pi$
$32$	1.64546e6	−	2.85003e6i	0.277404	−	0.480478i
$33$	−3.37322e6	+	9.43708e6i	−0.495145	+	1.38524i
$34$	4.03742e6	+	6.99301e6i	0.518142	+	0.897448i
$35$	−3.22736e6			−0.363531
$36$	−2.22452e6	−	1.82323e6i	−0.220737	−	0.180917i
$37$	−6.32122e6			−0.554489			−0.277245	−	0.960799i	$-0.589421\pi$
$37$	−6.32122e6			−0.554489			−0.277245	+	0.960799i	$0.589421\pi$
$38$	1.15959e7	+	2.00846e7i	0.902145	+	1.56256i
$39$	−3.64406e6	+	664268.i	−0.252229	+	0.0459783i
$40$	3.31541e6	−	5.74246e6i	0.204770	−	0.354673i
$41$	−2.68019e6	+	4.64223e6i	−0.148128	+	0.256566i	−0.930536	−	0.366201i	$-0.880658\pi$
$41$	−2.68019e6	+	4.64223e6i	−0.148128	+	0.256566i	0.782407	+	0.622767i	$0.213992\pi$
$42$	−1.61759e7	+	2.94867e6i	−0.802133	+	0.146219i
$43$	−1.12275e7	−	1.94466e7i	−0.500812	−	0.867432i	−1.00000		0.000938191i	$-0.999701\pi$
$43$	−1.12275e7	−	1.94466e7i	−0.500812	−	0.867432i	0.499187	−	0.866494i	$-0.333632\pi$
$44$	1.04384e7			0.419852
$45$	−1.07544e7	−	8.81438e6i	−0.390959	−	0.320432i
$46$	−2.86920e6			−0.0944824
$47$	2.23644e7	+	3.87363e7i	0.668524	+	1.15792i	0.978317	+	0.207114i	$0.0664069\pi$
$47$	2.23644e7	+	3.87363e7i	0.668524	+	1.15792i	−0.309793	+	0.950804i	$0.600260\pi$
$48$	1.49036e7	−	4.16950e7i	0.405234	−	1.13370i
$49$	9.74159e6	−	1.68729e7i	0.241406	−	0.418127i
$50$	1.86511e7	−	3.23047e7i	0.422027	−	0.730971i
$51$	2.85801e7	+	3.36636e7i	0.591559	+	0.696779i
$52$	1.92903e6	+	3.34118e6i	0.0365868	+	0.0633702i
$53$	−4.00972e7			−0.698027			−0.349013	−	0.937118i	$-0.613483\pi$
$53$	−4.00972e7			−0.698027			−0.349013	+	0.937118i	$0.613483\pi$
$54$	−6.19556e7	−	3.43528e7i	−0.991537	−	0.549782i
$55$	5.04642e7			0.743621
$56$	−2.14398e7	−	3.71348e7i	−0.291323	−	0.504586i
$57$	8.20848e7	+	9.66852e7i	1.02997	+	1.21317i
$58$	−5.62853e7	+	9.74890e7i	−0.653084	+	1.13117i
$59$	4.79118e7	−	8.29857e7i	0.514764	−	0.891598i	−0.485089	−	0.874465i	$-0.661213\pi$
$59$	4.79118e7	−	8.29857e7i	0.514764	−	0.891598i	0.999853	−	0.0171331i	$-0.00545391\pi$
$60$	−4.87481e6	+	1.36380e7i	−0.0485598	+	0.135853i
$61$	−1.01113e7	−	1.75132e7i	−0.0935020	−	0.161950i	0.815480	−	0.578785i	$-0.196473\pi$
$61$	−1.01113e7	−	1.75132e7i	−0.0935020	−	0.161950i	−0.908982	+	0.416834i	$0.863139\pi$
$62$	−2.53663e8			−2.18019
$63$	−8.41364e7	+	3.17284e7i	−0.672901	+	0.253756i
$64$	7.71659e7			0.574931
$65$	9.32588e6	+	1.61529e7i	0.0648007	+	0.112238i
$66$	2.52932e8	−	4.61065e7i	1.64080	−	0.299099i
$67$	−9.12489e7	+	1.58048e8i	−0.553211	+	0.958190i	0.444829	+	0.895615i	$0.353264\pi$
$67$	−9.12489e7	+	1.58048e8i	−0.553211	+	0.958190i	−0.998040	+	0.0625744i	$0.980069\pi$
$68$	2.29975e7	−	3.98328e7i	0.130434	−	0.225918i
$69$	−1.54367e7	+	2.81392e6i	−0.0819847	+	0.0149448i
$70$	4.13974e7	+	7.17024e7i	0.206078	+	0.356938i
$71$	1.38543e8			0.647025			0.323512	−	0.946224i	$-0.395136\pi$
$71$	1.38543e8			0.647025			0.323512	+	0.946224i	$0.395136\pi$
$72$	2.99772e7	−	1.82298e8i	0.131460	−	0.799440i
$73$	−2.17970e8			−0.898347			−0.449173	−	0.893445i	$-0.648281\pi$
$73$	−2.17970e8			−0.898347			−0.449173	+	0.893445i	$0.648281\pi$
$74$	8.10823e7	+	1.40439e8i	0.314328	+	0.544432i
$75$	6.86631e7	−	1.92095e8i	0.250581	−	0.701036i
$76$	6.60510e7	−	1.14404e8i	0.227101	−	0.393350i
$77$	1.63169e8	−	2.82617e8i	0.528967	−	0.916198i
$78$	6.15004e7	+	7.24395e7i	0.188127	+	0.221590i
$79$	−1.97294e8	−	3.41722e8i	−0.569890	−	0.987078i	−0.996576	−	0.0826785i	$-0.973653\pi$
$79$	−1.97294e8	−	3.41722e8i	−0.569890	−	0.987078i	0.426686	−	0.904400i	$-0.359681\pi$
$80$	−2.22962e8			−0.608591
$81$	−3.67020e8	−	1.24061e8i	−0.947343	−	0.320222i
$82$	1.37515e8			0.335883
$83$	2.36638e8	+	4.09870e8i	0.547310	+	0.947969i	0.998458	+	0.0555197i	$0.0176816\pi$
$83$	2.36638e8	+	4.09870e8i	0.547310	+	0.947969i	−0.451147	+	0.892450i	$0.648985\pi$
$84$	6.06153e7	+	7.13970e7i	0.132839	+	0.156467i
$85$	1.11181e8	−	1.92571e8i	0.231018	−	0.400135i
$86$	−2.88030e8	+	4.98883e8i	−0.567799	+	0.983458i
$87$	−2.07211e8	+	5.79704e8i	−0.387772	+	1.08485i
$88$	3.35240e8	+	5.80653e8i	0.595915	+	1.03215i
$89$	2.60507e8			0.440113			0.220057	−	0.975487i	$-0.429376\pi$
$89$	2.60507e8			0.440113			0.220057	+	0.975487i	$0.429376\pi$
$90$	−5.78820e7	+	3.51994e8i	−0.0929934	+	0.565514i
$91$	1.20616e8			0.184381
$92$	8.17161e6	+	1.41537e7i	0.0118922	+	0.0205979i
$93$	−1.36474e9	+	2.48775e8i	−1.89180	+	0.344853i
$94$	5.73736e8	−	9.93741e8i	0.757944	−	1.31280i
$95$	3.19323e8	−	5.53083e8i	0.402229	−	0.696682i
$96$	−4.54219e8	+	8.27988e7i	−0.545814	+	0.0994955i
$97$	−2.87421e8	−	4.97828e8i	−0.329644	−	0.570961i	0.652797	−	0.757533i	$-0.273595\pi$
$97$	−2.87421e8	−	4.97828e8i	−0.329644	−	0.570961i	−0.982441	+	0.186572i	$0.940262\pi$
$98$	−4.99822e8			−0.547391
$99$	1.31559e9	−	4.96118e8i	1.37645	−	0.519070i
$100$	−2.12477e8			−0.212477
$101$	−7.03860e7	−	1.21912e8i	−0.0673039	−	0.116574i	0.830410	−	0.557153i	$-0.188106\pi$
$101$	−7.03860e7	−	1.21912e8i	−0.0673039	−	0.116574i	−0.897714	+	0.440579i	$0.854773\pi$
$102$	3.81309e8	−	1.06677e9i	0.348800	−	0.975818i
$103$	1.70819e7	−	2.95867e7i	0.0149544	−	0.0259017i	−0.858451	−	0.512895i	$-0.828573\pi$
$103$	1.70819e7	−	2.95867e7i	0.0149544	−	0.0259017i	0.873406	+	0.486993i	$0.161906\pi$
$104$	−1.23906e8	+	2.14612e8i	−0.103859	+	0.179888i
$105$	2.93044e8	+	3.45168e8i	0.235278	+	0.277127i
$106$	5.14326e8	+	8.90839e8i	0.395696	+	0.685366i
$107$	1.61837e9			1.19358			0.596790	−	0.802397i	$-0.296443\pi$
$107$	1.61837e9			1.19358			0.596790	+	0.802397i	$0.296443\pi$
$108$	6.99129e6	+	4.03463e8i	0.00494482	+	0.285362i
$109$	−8.56262e8			−0.581015			−0.290508	−	0.956873i	$-0.593824\pi$
$109$	−8.56262e8			−0.581015			−0.290508	+	0.956873i	$0.593824\pi$
$110$	−6.47305e8	−	1.12116e9i	−0.421543	−	0.730133i
$111$	5.73966e8	+	6.76057e8i	0.358866	+	0.422698i
$112$	−7.20914e8	+	1.24866e9i	−0.432915	+	0.749831i
$113$	−9.66311e8	+	1.67370e9i	−0.557524	+	0.965661i	0.440178	+	0.897911i	$0.354915\pi$
$113$	−9.66311e8	+	1.67370e9i	−0.557524	+	0.965661i	−0.997702	+	0.0677501i	$0.978418\pi$
$114$	1.09516e9	−	3.06386e9i	0.607301	−	1.69901i
$115$	3.95056e7	+	6.84257e7i	0.0210629	+	0.0364820i
$116$	6.41212e8			0.328807
$117$	4.01923e8	+	3.29418e8i	0.198293	+	0.162522i
$118$	−2.45826e9			−1.16724
$119$	−7.18976e8	−	1.24530e9i	−0.328665	−	0.569264i
$120$	−9.15197e8	+	1.66830e8i	−0.402901	+	0.0734442i
$121$	−1.37239e9	+	2.37705e9i	−0.582028	+	1.00810i
$122$	−2.59394e8	+	4.49284e8i	−0.106009	+	0.183612i
$123$	7.39849e8	−	1.34866e8i	0.291454	−	0.0531287i
$124$	7.22443e8	+	1.25131e9i	0.274414	+	0.475298i
$125$	−2.40700e9			−0.881824
$126$	1.78413e9	+	1.46228e9i	0.630607	+	0.516848i
$127$	4.98705e9			1.70109			0.850545	−	0.525903i	$-0.176272\pi$
$127$	4.98705e9			1.70109			0.850545	+	0.525903i	$0.176272\pi$
$128$	−1.83228e9	−	3.17361e9i	−0.603320	−	1.04498i
$129$	−1.06037e9	+	2.96653e9i	−0.337134	+	0.943182i
$130$	2.39246e8	−	4.14387e8i	0.0734683	−	0.127251i
$131$	9.58360e7	−	1.65993e8i	0.0284320	−	0.0492457i	−0.851459	−	0.524421i	$-0.824282\pi$
$131$	9.58360e7	−	1.65993e8i	0.0284320	−	0.0492457i	0.879891	+	0.475175i	$0.157615\pi$
$132$	−9.47803e8	−	1.11639e9i	−0.271729	−	0.320061i
$133$	−2.06497e9	−	3.57663e9i	−0.572243	−	0.991155i
$134$	4.68180e9			1.25441
$135$	3.37993e7	+	1.95054e9i	0.00875802	+	0.505420i
$136$	2.95436e9			0.740523
$137$	−5.00385e8	−	8.66692e8i	−0.121356	−	0.210195i	0.798947	−	0.601402i	$-0.205391\pi$
$137$	−5.00385e8	−	8.66692e8i	−0.121356	−	0.210195i	−0.920303	+	0.391207i	$0.872058\pi$
$138$	2.60523e8	+	3.06862e8i	0.0611491	+	0.0720257i
$139$	6.75119e8	−	1.16934e9i	0.153396	−	0.265689i	−0.779078	−	0.626927i	$-0.784312\pi$
$139$	6.75119e8	−	1.16934e9i	0.153396	−	0.265689i	0.932474	+	0.361238i	$0.117646\pi$
$140$	2.35803e8	−	4.08423e8i	0.0518768	−	0.0898533i
$141$	2.11218e9	−	5.90913e9i	0.450033	−	1.25903i
$142$	−1.77709e9	−	3.07800e9i	−0.366785	−	0.635290i
$143$	−1.88599e9			−0.377161
$144$	−5.81255e9	+	2.19195e9i	−1.12651	+	0.424815i
$145$	3.09993e9			0.582366
$146$	2.79590e9	+	4.84264e9i	0.509253	+	0.882053i
$147$	−2.68910e9	+	4.90192e8i	−0.474984	+	0.0865840i
$148$	4.61852e8	−	7.99951e8i	0.0791270	−	0.137052i
$149$	−1.76496e9	+	3.05700e9i	−0.293357	+	0.508110i	−0.974601	−	0.223947i	$-0.928106\pi$
$149$	−1.76496e9	+	3.05700e9i	−0.293357	+	0.508110i	0.681244	+	0.732056i	$0.261439\pi$
$150$	−5.14852e9	+	9.38514e8i	−0.830370	+	0.151367i
$151$	−2.86323e8	−	4.95926e8i	−0.0448188	−	0.0776284i	0.842746	−	0.538312i	$-0.180938\pi$
$151$	−2.86323e8	−	4.95926e8i	−0.0448188	−	0.0776284i	−0.887565	+	0.460683i	$0.847604\pi$
$152$	8.48521e9			1.28934
$153$	1.00528e9	−	6.11330e9i	0.148311	−	0.901913i
$154$	−8.37186e9			−1.19944
$155$	3.49264e9	+	6.04943e9i	0.486028	+	0.841825i
$156$	1.82185e8	−	5.09689e8i	0.0246293	−	0.0689041i
$157$	−4.20086e8	+	7.27610e8i	−0.0551810	+	0.0955763i	−0.892296	−	0.451450i	$-0.850907\pi$
$157$	−4.20086e8	+	7.27610e8i	−0.0551810	+	0.0955763i	0.837115	+	0.547026i	$0.184240\pi$
$158$	−5.06137e9	+	8.76654e9i	−0.646117	+	1.11911i
$159$	3.64081e9	+	4.28841e9i	0.451764	+	0.532119i
$160$	1.16244e9	+	2.01340e9i	0.140227	+	0.242880i
$161$	5.10942e8			0.0599315
$162$	1.95151e9	+	9.74541e9i	0.222614	+	1.11169i
$163$	−7.00425e9			−0.777173			−0.388586	−	0.921412i	$-0.627037\pi$
$163$	−7.00425e9			−0.777173			−0.388586	+	0.921412i	$0.627037\pi$
$164$	−3.91650e8	−	6.78357e8i	−0.0422766	−	0.0732253i
$165$	−4.58214e9	−	5.39717e9i	−0.481272	−	0.566876i
$166$	6.07072e9	−	1.05148e10i	0.620517	−	1.07477i
$167$	4.63508e9	−	8.02820e9i	0.461141	−	0.798719i	−0.537877	−	0.843023i	$-0.680774\pi$
$167$	4.63508e9	−	8.02820e9i	0.461141	−	0.798719i	0.999018	+	0.0443040i	$0.0141070\pi$
$168$	−2.02485e9	+	5.66483e9i	−0.196111	+	0.548649i
$169$	4.95372e9	+	8.58009e9i	0.467133	+	0.809099i
$170$	−5.70448e9			−0.523836
$171$	2.88725e9	−	1.75580e10i	0.258227	−	1.57034i
$172$	3.28129e9			0.285869
$173$	−4.13667e9	−	7.16492e9i	−0.351110	−	0.608141i	0.635334	−	0.772237i	$-0.280862\pi$
$173$	−4.13667e9	−	7.16492e9i	−0.351110	−	0.608141i	−0.986444	+	0.164097i	$0.947529\pi$
$174$	1.55372e10	−	2.83224e9i	1.28499	−	0.234239i
$175$	−3.32136e9	+	5.75276e9i	−0.267697	+	0.463665i
$176$	1.12725e10	−	1.95245e10i	0.885549	−	1.53382i
$177$	−1.32257e10	+	2.41090e9i	−1.01284	+	0.184628i
$178$	−3.34152e9	−	5.78769e9i	−0.249491	−	0.432131i
$179$	−2.36310e10			−1.72046			−0.860229	−	0.509907i	$-0.829680\pi$
$179$	−2.36310e10			−1.72046			−0.860229	+	0.509907i	$0.829680\pi$
$180$	1.90122e9	−	7.16964e8i	0.134991	−	0.0509062i
$181$	1.40618e10			0.973841			0.486921	−	0.873446i	$-0.338120\pi$
$181$	1.40618e10			0.973841			0.486921	+	0.873446i	$0.338120\pi$
$182$	−1.54714e9	−	2.67972e9i	−0.104522	−	0.181037i
$183$	−9.54946e8	+	2.67160e9i	−0.0629432	+	0.176093i
$184$	−5.24881e8	+	9.09121e8i	−0.0337583	+	0.0584711i
$185$	2.23282e9	−	3.86735e9i	0.140146	−	0.242740i
$186$	2.30325e10	+	2.71293e10i	1.41102	+	1.66200i
$187$	1.12422e10	+	1.94720e10i	0.672299	+	1.16446i
$188$	−6.53611e9			−0.381600
$189$	1.10329e10	+	6.11749e9i	0.628946	+	0.348735i
$190$	−1.63838e10			−0.912061
$191$	4.87596e9	+	8.44541e9i	0.265100	+	0.459167i	0.967590	−	0.252527i	$-0.0812616\pi$
$191$	4.87596e9	+	8.44541e9i	0.265100	+	0.459167i	−0.702490	+	0.711694i	$0.747928\pi$
$192$	−7.00665e9	−	8.25293e9i	−0.372096	−	0.438281i
$193$	−4.97588e9	+	8.61847e9i	−0.258144	+	0.447118i	−0.965745	−	0.259494i	$-0.916444\pi$
$193$	−4.97588e9	+	8.61847e9i	−0.258144	+	0.447118i	0.707601	+	0.706612i	$0.249778\pi$
$194$	−7.37349e9	+	1.27713e10i	−0.373737	+	0.647331i
$195$	8.80772e8	−	2.46409e9i	0.0436222	−	0.122040i
$196$	1.42351e9	+	2.46560e9i	0.0688984	+	0.119336i
$197$	−3.23117e9			−0.152849			−0.0764244	−	0.997075i	$-0.524350\pi$
$197$	−3.23117e9			−0.152849			−0.0764244	+	0.997075i	$0.524350\pi$
$198$	−2.78973e10	−	2.28647e10i	−1.28994	−	1.05724i
$199$	−2.90155e10			−1.31157			−0.655785	−	0.754947i	$-0.727662\pi$
$199$	−2.90155e10			−1.31157			−0.655785	+	0.754947i	$0.727662\pi$
$200$	−6.82393e9	−	1.18194e10i	−0.301578	−	0.522348i
$201$	2.51887e10	−	4.59159e9i	1.08849	−	0.198418i
$202$	−1.80568e9	+	3.12754e9i	−0.0763063	+	0.132166i
$203$	1.00232e10	−	1.73607e10i	0.414260	−	0.717520i
$204$	−6.34830e9	+	1.15722e9i	−0.256639	+	0.0467822i
$205$	−1.89343e9	−	3.27951e9i	−0.0748783	−	0.129693i
$206$	−8.76437e8			−0.0339092
$207$	1.70260e9	+	1.39545e9i	0.0644533	+	0.0528262i
$208$	8.33270e9			0.308675
$209$	3.22886e10	+	5.59255e10i	1.17055	+	2.02746i
$210$	3.90972e9	−	1.09380e10i	0.138726	−	0.388108i
$211$	2.12768e9	−	3.68525e9i	0.0738985	−	0.127996i	−0.826708	−	0.562631i	$-0.809789\pi$
$211$	2.12768e9	−	3.68525e9i	0.0738985	−	0.127996i	0.900607	+	0.434635i	$0.143123\pi$
$212$	2.92965e9	−	5.07430e9i	0.0996102	−	0.172530i
$213$	−1.25796e10	−	1.48172e10i	−0.418755	−	0.493240i
$214$	−2.07589e10	−	3.59554e10i	−0.676615	−	1.17193i
$215$	1.58634e10			0.506317
$216$	−2.22188e10	+	1.33466e10i	−0.694510	+	0.417184i
$217$	4.51718e10			1.38292
$218$	1.09833e10	+	1.90236e10i	0.329365	+	0.570477i
$219$	1.97916e10	+	2.33120e10i	0.581411	+	0.684827i
$220$	−3.68710e9	+	6.38625e9i	−0.106117	+	0.183799i
$221$	−4.15515e9	+	7.19692e9i	−0.117171	+	0.202947i
$222$	7.65772e9	−	2.14236e10i	0.211598	−	0.591975i
$223$	−2.11759e10	−	3.66777e10i	−0.573416	−	0.993185i	−0.996212	−	0.0869601i	$-0.972285\pi$
$223$	−2.11759e10	−	3.66777e10i	−0.573416	−	0.993185i	0.422796	−	0.906225i	$-0.361049\pi$
$224$	1.50343e10			0.398995
$225$	−2.67792e10	+	1.00986e10i	−0.696589	+	0.262689i
$226$	4.95795e10			1.26419
$227$	−2.96301e10	−	5.13208e10i	−0.740656	−	1.28285i	−0.952197	−	0.305485i	$-0.901181\pi$
$227$	−2.96301e10	−	5.13208e10i	−0.740656	−	1.28285i	0.211541	−	0.977369i	$-0.432152\pi$
$228$	−1.82329e10	+	3.32365e9i	−0.446838	+	0.0814532i
$229$	3.07523e10	−	5.32645e10i	0.738954	−	1.27991i	−0.214013	−	0.976831i	$-0.568653\pi$
$229$	3.07523e10	−	5.32645e10i	0.738954	−	1.27991i	0.952967	−	0.303075i	$-0.0980133\pi$
$230$	1.01348e9	−	1.75539e9i	0.0238802	−	0.0413617i
$231$	−4.50417e10	+	8.21056e9i	−1.04078	+	0.189723i
$232$	2.05932e10	+	3.56685e10i	0.466690	+	0.808331i
$233$	−4.69389e10			−1.04335			−0.521677	−	0.853143i	$-0.674693\pi$
$233$	−4.69389e10			−1.04335			−0.521677	+	0.853143i	$0.674693\pi$
$234$	2.16321e9	−	1.31550e10i	0.0471659	−	0.286826i
$235$	−3.15987e10			−0.675872
$236$	7.00123e9	+	1.21265e10i	0.146916	+	0.254467i
$237$	−1.86331e10	+	5.21290e10i	−0.383635	+	1.07328i
$238$	−1.84446e10	+	3.19470e10i	−0.372626	+	0.645407i
$239$	−5.22440e9	+	9.04892e9i	−0.103573	+	0.179393i	−0.913154	−	0.407614i	$-0.866361\pi$
$239$	−5.22440e9	+	9.04892e9i	−0.103573	+	0.179393i	0.809581	+	0.587008i	$0.199694\pi$
$240$	2.02449e10	+	2.38459e10i	0.393881	+	0.463940i
$241$	−1.49700e10	−	2.59288e10i	−0.285854	−	0.495114i	0.686962	−	0.726693i	$-0.258944\pi$
$241$	−1.49700e10	−	2.59288e10i	−0.285854	−	0.495114i	−0.972816	+	0.231580i	$0.925611\pi$
$242$	7.04147e10			1.31976
$243$	2.00570e10	+	5.05176e10i	0.369010	+	0.929426i
$244$	2.95507e9			0.0533719
$245$	6.88196e9	+	1.19199e10i	0.122030	+	0.211361i
$246$	−1.24864e10	−	1.47073e10i	−0.217384	−	0.256050i
$247$	−1.19340e10	+	2.06703e10i	−0.204009	+	0.353354i
$248$	−4.64041e10	+	8.03743e10i	−0.778976	+	1.34923i
$249$	2.23490e10	−	6.25246e10i	0.368435	−	1.03075i
$250$	3.08746e10	+	5.34764e10i	0.499887	+	0.865830i
$251$	−1.50652e9			−0.0239576			−0.0119788	−	0.999928i	$-0.503813\pi$
$251$	−1.50652e9			−0.0239576			−0.0119788	+	0.999928i	$0.503813\pi$
$252$	2.13208e9	−	1.29657e10i	0.0333044	−	0.202531i
$253$	−7.98928e9			−0.122593
$254$	−6.39689e10	−	1.10797e11i	−0.964311	−	1.67024i
$255$	−3.06908e10	+	5.59457e9i	−0.454546	+	0.0828583i
$256$	−2.72509e10	+	4.72000e10i	−0.396553	+	0.686850i
$257$	4.35790e10	−	7.54811e10i	0.623130	−	1.07929i	−0.365770	−	0.930705i	$-0.619194\pi$
$257$	4.35790e10	−	7.54811e10i	0.623130	−	1.07929i	0.988899	−	0.148587i	$-0.0474725\pi$
$258$	7.95088e10	−	1.44935e10i	1.11719	−	0.203650i
$259$	−1.44390e10	−	2.50090e10i	−0.199383	−	0.345341i
$260$	−2.72553e9			−0.0369889
$261$	8.08143e10	−	3.04757e10i	1.07797	−	0.406510i
$262$	−4.91715e9			−0.0644700
$263$	2.10643e10	+	3.64844e10i	0.271485	+	0.470226i	0.969242	−	0.246108i	$-0.0791519\pi$
$263$	2.10643e10	+	3.64844e10i	0.271485	+	0.470226i	−0.697757	+	0.716334i	$0.745819\pi$
$264$	3.16614e10	−	8.85773e10i	0.401155	−	1.12229i
$265$	1.41633e10	−	2.45316e10i	0.176425	−	0.305577i
$266$	−5.29747e10	+	9.17548e10i	−0.648785	+	1.12373i
$267$	−2.36540e10	−	2.78613e10i	−0.284842	−	0.335507i
$268$	−1.33340e10	−	2.30951e10i	−0.157889	−	0.273472i
$269$	6.32241e10			0.736202			0.368101	−	0.929786i	$-0.380008\pi$
$269$	6.32241e10			0.736202			0.368101	+	0.929786i	$0.380008\pi$
$270$	4.29015e10	−	2.57704e10i	0.491288	−	0.295111i
$271$	−1.63811e11			−1.84493			−0.922467	−	0.386075i	$-0.873831\pi$
$271$	−1.63811e11			−1.84493			−0.922467	+	0.386075i	$0.873831\pi$
$272$	−4.96703e10	−	8.60314e10i	−0.550220	−	0.953009i
$273$	−1.09519e10	−	1.28999e10i	−0.119332	−	0.140557i
$274$	−1.28369e10	+	2.22341e10i	−0.137588	+	0.238310i
$275$	5.19339e10	−	8.99522e10i	0.547588	−	0.948451i
$276$	7.71758e8	−	2.15911e9i	0.00800553	−	0.0223967i
$277$	8.63022e10	+	1.49480e11i	0.880771	+	1.52554i	0.850485	+	0.525999i	$0.176308\pi$
$277$	8.63022e10	+	1.49480e11i	0.880771	+	1.52554i	0.0302857	+	0.999541i	$0.490358\pi$
$278$	−3.46390e10			−0.347827
$279$	1.50525e11	+	1.23370e11i	1.48726	+	1.21897i
$280$	3.02923e10			0.294525
$281$	1.27714e10	+	2.21208e10i	0.122197	+	0.211652i	0.920634	−	0.390427i	$-0.127673\pi$
$281$	1.27714e10	+	2.21208e10i	0.122197	+	0.211652i	−0.798437	+	0.602079i	$0.794339\pi$
$282$	−1.58376e11	+	2.88701e10i	−1.49131	+	0.271849i
$283$	3.69467e10	−	6.39936e10i	0.342402	−	0.593058i	−0.642476	−	0.766306i	$-0.722093\pi$
$283$	3.69467e10	−	6.39936e10i	0.342402	−	0.593058i	0.984878	+	0.173248i	$0.0554261\pi$
$284$	−1.01224e10	+	1.75326e10i	−0.0923321	+	0.159924i
$285$	−8.81469e10	+	1.60681e10i	−0.791417	+	0.144266i
$286$	2.41916e10	+	4.19010e10i	0.213805	+	0.370320i
$287$	−2.44885e10			−0.213056
$288$	5.00984e10	+	4.10608e10i	0.429099	+	0.351691i
$289$	−1.95145e10			−0.164557
$290$	−3.97628e10	−	6.88712e10i	−0.330131	−	0.571803i
$291$	−2.71451e10	+	7.59424e10i	−0.221908	+	0.620821i
$292$	1.59257e10	−	2.75841e10i	0.128196	−	0.222043i
$293$	−1.01768e11	+	1.76267e11i	−0.806687	+	1.39722i	0.108459	+	0.994101i	$0.465408\pi$
$293$	−1.01768e11	+	1.76267e11i	−0.806687	+	1.39722i	−0.915146	+	0.403122i	$0.867925\pi$
$294$	4.53837e10	+	5.34561e10i	0.354272	+	0.417287i
$295$	3.38474e10	+	5.86253e10i	0.260211	+	0.450699i
$296$	5.93316e10			0.449234
$297$	−1.72515e11	−	9.56553e10i	−1.28654	−	0.713354i
$298$	9.05566e10			0.665192
$299$	−1.47643e9	−	2.55726e9i	−0.0106830	−	0.0185035i
$300$	1.92929e10	+	2.27245e10i	0.137515	+	0.161975i
$301$	5.12919e10	−	8.88401e10i	0.360163	−	0.623821i
$302$	−7.34533e9	+	1.27225e10i	−0.0508136	+	0.0880118i
$303$	−6.64752e9	+	1.85974e10i	−0.0453073	+	0.126754i
$304$	−1.42658e11	−	2.47091e11i	−0.957998	−	1.65930i
$305$	1.42862e10			0.0945297
$306$	−1.48714e11	+	5.60811e10i	−0.969629	+	0.365654i
$307$	8.22523e10			0.528476			0.264238	−	0.964457i	$-0.414880\pi$
$307$	8.22523e10			0.528476			0.264238	+	0.964457i	$0.414880\pi$
$308$	2.38434e10	+	4.12980e10i	0.150970	+	0.261488i
$309$	−4.71534e9	+	8.59550e8i	−0.0294239	+	0.00536362i
$310$	8.96002e10	−	1.55192e11i	0.551038	−	0.954425i
$311$	1.16047e11	−	2.00999e11i	0.703415	−	1.21835i	−0.263846	−	0.964565i	$-0.584991\pi$
$311$	1.16047e11	−	2.00999e11i	0.703415	−	1.21835i	0.967261	−	0.253785i	$-0.0816756\pi$
$312$	3.42035e10	−	6.23489e9i	0.204350	−	0.0372506i
$313$	−3.15040e10	−	5.45665e10i	−0.185531	−	0.321349i	0.758224	−	0.651994i	$-0.226067\pi$
$313$	−3.15040e10	−	5.45665e10i	−0.185531	−	0.321349i	−0.943755	+	0.330645i	$0.892734\pi$
$314$	2.15537e10			0.125124
$315$	1.03075e10	−	6.26824e10i	0.0589871	−	0.358714i
$316$	5.76600e10			0.325299
$317$	1.15735e11	+	2.00459e11i	0.643722	+	1.11496i	0.984595	+	0.174850i	$0.0559439\pi$
$317$	1.15735e11	+	2.00459e11i	0.643722	+	1.11496i	−0.340873	+	0.940109i	$0.610723\pi$
$318$	4.85749e10	−	1.35895e11i	0.266373	−	0.745217i
$319$	−1.56726e11	+	2.71458e11i	−0.847390	+	1.46772i
$320$	−2.72570e10	+	4.72105e10i	−0.145312	+	0.251689i
$321$	−1.46948e11	−	1.73086e11i	−0.772486	−	0.909889i
$322$	−6.55385e9	−	1.13516e10i	−0.0339739	−	0.0588445i
$323$	2.84548e11			1.45460
$324$	4.25157e10	−	3.73821e10i	0.214337	−	0.188456i
$325$	3.83899e10			0.190872
$326$	8.98436e10	+	1.55614e11i	0.440563	+	0.763077i
$327$	7.77484e10	+	9.15776e10i	0.376034	+	0.442919i
$328$	2.51565e10	−	4.35724e10i	0.120010	−	0.207864i
$329$	−1.02170e11	+	1.76963e11i	−0.480775	+	0.832726i
$330$	−6.11339e10	+	1.71031e11i	−0.283772	+	0.793893i
$331$	−7.72274e10	−	1.33762e11i	−0.353627	−	0.612500i	0.633255	−	0.773943i	$-0.281718\pi$
$331$	−7.72274e10	−	1.33762e11i	−0.353627	−	0.612500i	−0.986882	+	0.161443i	$0.948385\pi$
$332$	−6.91587e10			−0.312410
$333$	2.01886e10	−	1.22772e11i	0.0899722	−	0.547141i
$334$	−2.37817e11			−1.04564
$335$	−6.44629e10	−	1.11653e11i	−0.279646	−	0.484361i
$336$	1.99004e11	−	3.62760e10i	0.851793	−	0.155272i
$337$	−6.76249e10	+	1.17130e11i	−0.285609	+	0.494690i	−0.972757	−	0.231828i	$-0.925529\pi$
$337$	−6.76249e10	+	1.17130e11i	−0.285609	+	0.494690i	0.687148	+	0.726518i	$0.258863\pi$
$338$	1.27083e11	−	2.20113e11i	0.529616	−	0.917321i
$339$	2.66744e11	−	4.86242e10i	1.09697	−	0.199965i
$340$	1.62466e10	+	2.81399e10i	0.0659337	+	0.114201i
$341$	−7.06323e11			−2.82884
$342$	−4.27121e11	+	1.61070e11i	−1.68824	+	0.636647i
$343$	2.73359e11			1.06638
$344$	1.05382e11	+	1.82528e11i	0.405747	+	0.702774i
$345$	3.73106e9	−	1.04382e10i	0.0141790	−	0.0396679i
$346$	−1.06122e11	+	1.83809e11i	−0.398074	+	0.689484i
$347$	1.41753e11	−	2.45523e11i	0.524867	−	0.909096i	−0.474714	−	0.880140i	$-0.657449\pi$
$347$	1.41753e11	−	2.45523e11i	0.524867	−	0.909096i	0.999581	−	0.0289556i	$-0.00921813\pi$
$348$	−5.82219e10	−	6.85779e10i	−0.212804	−	0.250656i
$349$	−4.86799e10	−	8.43160e10i	−0.175645	−	0.304225i	0.764740	−	0.644340i	$-0.222868\pi$
$349$	−4.86799e10	−	8.43160e10i	−0.175645	−	0.304225i	−0.940384	+	0.340114i	$0.889534\pi$
$350$	1.70412e11			0.607008
$351$	−1.26318e9	−	7.28970e10i	−0.00444203	−	0.256347i
$352$	−2.35082e11			−0.816164
$353$	−1.91861e10	−	3.32314e10i	−0.0657660	−	0.113910i	0.831268	−	0.555873i	$-0.187616\pi$
$353$	−1.91861e10	−	3.32314e10i	−0.0657660	−	0.113910i	−0.897034	+	0.441962i	$0.854282\pi$
$354$	2.23209e11	+	2.62912e11i	0.755436	+	0.889806i
$355$	−4.89368e10	+	8.47611e10i	−0.163534	+	0.283249i
$356$	−1.90336e10	+	3.29672e10i	−0.0628053	+	0.108782i
$357$	−6.79028e10	+	1.89968e11i	−0.221249	+	0.618975i
$358$	3.03115e11	+	5.25011e11i	0.975291	+	1.68925i
$359$	−4.48036e11			−1.42360			−0.711800	−	0.702383i	$-0.752120\pi$
$359$	−4.48036e11			−1.42360			−0.711800	+	0.702383i	$0.752120\pi$
$360$	1.00942e11	+	8.27326e10i	0.316746	+	0.259606i
$361$	4.94563e11			1.53264
$362$	−1.80371e11	−	3.12412e11i	−0.552050	−	0.956178i
$363$	3.78840e11	−	6.90580e10i	1.14519	−	0.208754i
$364$	−8.81262e9	+	1.52639e10i	−0.0263117	+	0.0455732i
$365$	7.69926e10	−	1.33355e11i	0.227055	−	0.393271i
$366$	7.16041e10	−	1.30526e10i	0.208580	−	0.0380217i
$367$	3.74037e10	+	6.47850e10i	0.107626	+	0.186414i	0.914808	−	0.403889i	$-0.132342\pi$
$367$	3.74037e10	+	6.47850e10i	0.107626	+	0.186414i	−0.807182	+	0.590302i	$0.799008\pi$
$368$	3.52983e10			0.100332
$369$	−8.16021e10	−	6.68814e10i	−0.229130	−	0.187796i
$370$	−1.14561e11			−0.317783
$371$	−9.15902e10	−	1.58639e11i	−0.250996	−	0.434738i
$372$	6.82302e10	−	1.90884e11i	0.184728	−	0.516805i
$373$	1.39696e11	−	2.41961e11i	0.373675	−	0.647225i	−0.616452	−	0.787392i	$-0.711431\pi$
$373$	1.39696e11	−	2.41961e11i	0.373675	−	0.647225i	0.990128	+	0.140167i	$0.0447641\pi$
$374$	2.88406e11	−	4.99535e11i	0.762224	−	1.32021i
$375$	2.18556e11	+	2.57430e11i	0.570717	+	0.672231i
$376$	−2.09914e11	−	3.63582e11i	−0.541623	−	0.938118i
$377$	−1.15853e11			−0.295374
$378$	−5.60720e9	−	3.23588e11i	−0.0141265	−	0.815228i
$379$	−6.40616e11			−1.59485			−0.797427	−	0.603415i	$-0.793806\pi$
$379$	−6.40616e11			−1.59485			−0.797427	+	0.603415i	$0.793806\pi$
$380$	4.66618e10	+	8.08206e10i	0.114798	+	0.198836i
$381$	−4.52823e11	−	5.33367e11i	−1.10095	−	1.29677i
$382$	1.25088e11	−	2.16659e11i	0.300559	−	0.520584i
$383$	−1.66528e11	+	2.88435e11i	−0.395451	+	0.684942i	−0.993159	−	0.116772i	$-0.962745\pi$
$383$	−1.66528e11	+	2.88435e11i	−0.395451	+	0.684942i	0.597707	+	0.801714i	$0.296079\pi$
$384$	−1.73048e11	+	4.84127e11i	−0.406140	+	1.13624i
$385$	1.15271e11	+	1.99655e11i	0.267390	+	0.463134i
$386$	2.55302e11			0.585345
$387$	4.13553e11	−	1.55954e11i	0.937199	−	0.353425i
$388$	8.40002e10			0.188164
$389$	8.15796e10	+	1.41300e11i	0.180638	+	0.312873i	0.942098	−	0.335338i	$-0.108851\pi$
$389$	8.15796e10	+	1.41300e11i	0.180638	+	0.312873i	−0.761460	+	0.648212i	$0.775517\pi$
$390$	−6.60423e10	+	1.20387e10i	−0.144555	+	0.0263506i
$391$	−1.76017e10	+	3.04870e10i	−0.0380855	+	0.0659660i
$392$	−9.14355e10	+	1.58371e11i	−0.195581	+	0.338757i
$393$	−2.64549e10	+	4.82241e9i	−0.0559422	+	0.0101976i
$394$	4.14462e10	+	7.17870e10i	0.0866467	+	0.150076i
$395$	2.78757e11			0.576153
$396$	−3.33380e10	+	2.02736e11i	−0.0681257	+	0.414288i
$397$	2.79119e11			0.563939			0.281969	−	0.959423i	$-0.409012\pi$
$397$	2.79119e11			0.563939			0.281969	+	0.959423i	$0.409012\pi$
$398$	3.72182e11	+	6.44638e11i	0.743501	+	1.28778i
$399$	−1.95023e11	+	5.45606e11i	−0.385220	+	1.07771i
$400$	−2.29455e11	+	3.97428e11i	−0.448155	+	0.776227i
$401$	−3.79966e11	+	6.58121e11i	−0.733830	+	1.27103i	0.221405	+	0.975182i	$0.428936\pi$
$401$	−3.79966e11	+	6.58121e11i	−0.733830	+	1.27103i	−0.955235	+	0.295848i	$0.904398\pi$
$402$	−4.25106e11	−	5.00720e11i	−0.811858	−	0.956264i
$403$	−1.30530e11	−	2.26084e11i	−0.246511	−	0.426970i
$404$	2.05707e10			0.0384178
$405$	2.05542e11	−	1.80723e11i	0.379623	−	0.333785i
$406$	−5.14269e11			−0.939341
$407$	2.25773e11	+	3.91051e11i	0.407847	+	0.706412i
$408$	−2.68255e11	−	3.15970e11i	−0.479267	−	0.564515i
$409$	1.89971e10	−	3.29039e10i	0.0335685	−	0.0581423i	−0.848753	−	0.528789i	$-0.822646\pi$
$409$	1.89971e10	−	3.29039e10i	0.0335685	−	0.0581423i	0.882322	+	0.470647i	$0.155979\pi$
$410$	−4.85739e10	+	8.41325e10i	−0.0848938	+	0.147040i
$411$	−4.72583e10	+	1.32212e11i	−0.0816939	+	0.228551i
$412$	2.49613e9	+	4.32342e9i	0.00426805	+	0.00739248i
$413$	4.37762e11			0.740394
$414$	9.16363e9	−	5.57261e10i	0.0153308	−	0.0932303i
$415$	−3.34347e11			−0.553326
$416$	−4.34436e10	−	7.52465e10i	−0.0711223	−	0.123187i
$417$	−1.86362e11	+	3.39716e10i	−0.301818	+	0.0550179i
$418$	8.28331e11	−	1.43471e12i	1.32712	−	2.29864i
$419$	3.66823e11	−	6.35355e11i	0.581424	−	1.00706i	−0.413887	−	0.910328i	$-0.635829\pi$
$419$	3.66823e11	−	6.35355e11i	0.581424	−	1.00706i	0.995311	−	0.0967277i	$-0.0308376\pi$
$420$	−6.50919e10	+	1.18655e10i	−0.102072	+	0.0186065i
$421$	1.60716e11	+	2.78368e11i	0.249339	+	0.431867i	0.963342	−	0.268275i	$-0.0864535\pi$
$421$	1.60716e11	+	2.78368e11i	0.249339	+	0.431867i	−0.714004	+	0.700142i	$0.753120\pi$
$422$	−1.09167e11			−0.167566
$423$	−8.23770e11	+	3.10649e11i	−1.25105	+	0.471779i
$424$	3.76356e11			0.565525
$425$	−2.28838e11	−	3.96359e11i	−0.340234	−	0.589303i
$426$	−1.67835e11	+	4.69542e11i	−0.246910	+	0.690767i
$427$	4.61924e10	−	8.00077e10i	0.0672428	−	0.116468i
$428$	−1.18244e11	+	2.04805e11i	−0.170327	+	0.295015i
$429$	1.71247e11	+	2.01707e11i	0.244099	+	0.287517i
$430$	−2.03479e11	−	3.52437e11i	−0.287020	−	0.497133i
$431$	3.86098e11			0.538952			0.269476	−	0.963007i	$-0.413150\pi$
$431$	3.86098e11			0.538952			0.269476	+	0.963007i	$0.413150\pi$
$432$	7.62208e11	+	4.22625e11i	1.05292	+	0.583820i
$433$	5.48808e11			0.750282			0.375141	−	0.926968i	$-0.377594\pi$
$433$	5.48808e11			0.750282			0.375141	+	0.926968i	$0.377594\pi$
$434$	−5.79418e11	−	1.00358e12i	−0.783950	−	1.35784i
$435$	−2.81473e11	−	3.31539e11i	−0.376908	−	0.443949i
$436$	6.25617e10	−	1.08360e11i	0.0829123	−	0.143608i
$437$	−5.05538e10	+	8.75617e10i	−0.0663113	+	0.114854i
$438$	2.64055e11	−	7.38734e11i	0.342816	−	0.959079i
$439$	1.50050e11	+	2.59895e11i	0.192817	+	0.333969i	0.946183	−	0.323633i	$-0.104904\pi$
$439$	1.50050e11	+	2.59895e11i	0.192817	+	0.333969i	−0.753365	+	0.657602i	$0.771571\pi$
$440$	−4.73662e11			−0.602465
$441$	2.96596e11	+	2.43091e11i	0.373415	+	0.306052i
$442$	2.13192e11			0.265687
$443$	−2.11330e11	−	3.66034e11i	−0.260702	−	0.451549i	0.705727	−	0.708484i	$-0.250621\pi$
$443$	−2.11330e11	−	3.66034e11i	−0.260702	−	0.451549i	−0.966429	+	0.256935i	$0.917287\pi$
$444$	−1.27491e11	+	2.32401e10i	−0.155689	+	0.0283802i
$445$	−9.20178e10	+	1.59379e11i	−0.111238	+	0.192669i
$446$	−5.43246e11	+	9.40929e11i	−0.650114	+	1.12603i
$447$	4.87206e11	−	8.88118e10i	0.577203	−	0.105217i
$448$	1.76263e11	+	3.05296e11i	0.206733	+	0.358072i
$449$	1.63406e12			1.89741			0.948704	−	0.316165i	$-0.102395\pi$
$449$	1.63406e12			1.89741			0.948704	+	0.316165i	$0.102395\pi$
$450$	5.67859e11	+	4.65419e11i	0.652806	+	0.535042i
$451$	3.82911e11			0.435816
$452$	−1.41205e11	−	2.44573e11i	−0.159120	−	0.275605i
$453$	−2.70414e10	+	7.56524e10i	−0.0301709	+	0.0844074i
$454$	−7.60130e11	+	1.31658e12i	−0.839724	+	1.45445i
$455$	−4.26045e10	+	7.37932e10i	−0.0466020	+	0.0807170i
$456$	−7.70455e11	−	9.07497e11i	−0.834460	−	0.982886i
$457$	−6.23184e11	−	1.07939e12i	−0.668334	−	1.15759i	−0.978370	−	0.206863i	$-0.933675\pi$
$457$	−6.23184e11	−	1.07939e12i	−0.668334	−	1.15759i	0.310036	−	0.950725i	$-0.399659\pi$
$458$	−1.57784e12			−1.67559
$459$	−7.45099e11	+	4.47572e11i	−0.783533	+	0.470659i
$460$	−1.15457e10			−0.0120229
$461$	−1.44026e11	−	2.49459e11i	−0.148520	−	0.257244i	0.782161	−	0.623077i	$-0.214118\pi$
$461$	−1.44026e11	−	2.49459e11i	−0.148520	−	0.257244i	−0.930681	+	0.365833i	$0.880784\pi$
$462$	7.60163e11	+	8.95374e11i	0.776279	+	0.914357i
$463$	−7.86329e11	+	1.36196e12i	−0.795225	+	1.37737i	0.127472	+	0.991842i	$0.459314\pi$
$463$	−7.86329e11	+	1.36196e12i	−0.795225	+	1.37737i	−0.922696	+	0.385527i	$0.874020\pi$
$464$	6.92449e11	−	1.19936e12i	0.693517	−	1.20121i
$465$	3.29858e11	−	9.22827e11i	0.327182	−	0.915339i
$466$	6.02085e11	+	1.04284e12i	0.591454	+	1.02443i
$467$	2.12882e11			0.207116			0.103558	−	0.994623i	$-0.466977\pi$
$467$	2.12882e11			0.207116			0.103558	+	0.994623i	$0.466977\pi$
$468$	−7.10539e10	+	2.67949e10i	−0.0684670	+	0.0258194i
$469$	−8.33726e11			−0.795693
$470$	4.05317e11	+	7.02029e11i	0.383137	+	0.663613i
$471$	1.15962e11	−	2.11385e10i	0.108573	−	0.0197915i
$472$	−4.49705e11	+	7.78911e11i	−0.417050	+	0.722352i
$473$	−8.02019e11	+	1.38914e12i	−0.736732	+	1.27606i
$474$	1.39716e12	−	2.54685e11i	1.27128	−	0.231740i
$475$	−6.57245e11	−	1.13838e12i	−0.592388	−	1.02605i
$476$	2.10124e11			0.187605
$477$	1.28062e11	−	7.78773e11i	0.113263	−	0.688777i
$478$	2.68053e11			0.234853
$479$	−7.62418e11	−	1.32055e12i	−0.661733	−	1.14616i	−0.980160	−	0.198208i	$-0.936488\pi$
$479$	−7.62418e11	−	1.32055e12i	−0.661733	−	1.14616i	0.318426	−	0.947948i	$-0.396846\pi$
$480$	1.09785e11	−	3.07140e11i	0.0943970	−	0.264089i
$481$	−8.34466e10	+	1.44534e11i	−0.0710814	+	0.123117i
$482$	−3.84040e11	+	6.65176e11i	−0.324089	+	0.561339i
$483$	−4.63934e10	−	5.46455e10i	−0.0387877	−	0.0456869i
$484$	−2.00544e11	−	3.47353e11i	−0.166114	−	0.287718i
$485$	4.06098e11			0.333267
$486$	8.65079e11	−	1.09360e12i	0.703384	−	0.889188i
$487$	−1.81008e12			−1.45820			−0.729101	−	0.684406i	$-0.760062\pi$
$487$	−1.81008e12			−1.45820			−0.729101	+	0.684406i	$0.760062\pi$
$488$	9.49052e10	+	1.64381e11i	0.0757532	+	0.131208i
$489$	6.35985e11	+	7.49108e11i	0.502987	+	0.592454i
$490$	1.76550e11	−	3.05793e11i	0.138352	−	0.239632i
$491$	5.76915e11	−	9.99245e11i	0.447966	−	0.775899i	−0.550288	−	0.834975i	$-0.685482\pi$
$491$	5.76915e11	−	9.99245e11i	0.447966	−	0.775899i	0.998254	+	0.0590757i	$0.0188153\pi$
$492$	−3.69889e10	+	1.03482e11i	−0.0284595	+	0.0796198i
$493$	6.90587e11	+	1.19613e12i	0.526511	+	0.911944i
$494$	6.12309e11			0.462593
$495$	−1.61172e11	+	9.80124e11i	−0.120661	+	0.733766i
$496$	3.12068e12			2.31517
$497$	3.16460e11	+	5.48125e11i	0.232657	+	0.402973i
$498$	−1.67578e12	+	3.05475e11i	−1.22091	+	0.222558i
$499$	1.00972e12	−	1.74888e12i	0.729032	−	1.26272i	−0.228260	−	0.973600i	$-0.573304\pi$
$499$	1.00972e12	−	1.74888e12i	0.729032	−	1.26272i	0.957293	−	0.289121i	$-0.0933629\pi$
$500$	1.75865e11	−	3.04607e11i	0.125839	−	0.217959i
$501$	−1.27948e12	+	2.33235e11i	−0.907330	+	0.165395i
$502$	1.93241e10	+	3.34703e10i	0.0135810	+	0.0235230i
$503$	−7.16624e11			−0.499155			−0.249578	−	0.968355i	$-0.580292\pi$
$503$	−7.16624e11			−0.499155			−0.249578	+	0.968355i	$0.580292\pi$
$504$	7.89712e11	−	2.97806e11i	0.545169	−	0.205587i
$505$	9.94486e10			0.0680437
$506$	1.02478e11	+	1.77498e11i	0.0694953	+	0.120369i
$507$	4.67848e11	−	1.30887e12i	0.314462	−	0.879754i
$508$	−3.64372e11	+	6.31112e11i	−0.242750	+	0.420455i
$509$	7.90670e11	−	1.36948e12i	0.522114	−	0.904327i	−0.477555	−	0.878602i	$-0.658477\pi$
$509$	7.90670e11	−	1.36948e12i	0.522114	−	0.904327i	0.999669	−	0.0257257i	$-0.00818966\pi$
$510$	5.17965e11	+	6.10096e11i	0.339028	+	0.399331i
$511$	−4.97889e11	−	8.62369e11i	−0.323027	−	0.559499i
$512$	−4.78068e11			−0.307450
$513$	−2.14000e12	+	1.28547e12i	−1.36422	+	0.819472i
$514$	−2.23595e12			−1.41296
$515$	1.20675e10	+	2.09015e10i	0.00755936	+	0.0130932i
$516$	−2.97941e11	−	3.50935e11i	−0.185015	−	0.217923i
$517$	1.59757e12	−	2.76707e12i	0.983448	−	1.70338i
$518$	−3.70417e11	+	6.41582e11i	−0.226052	+	0.391533i
$519$	−3.90683e11	+	1.09299e12i	−0.236358	+	0.661247i
$520$	−8.75336e10	−	1.51613e11i	−0.0525001	−	0.0909328i
$521$	1.03065e12			0.612834			0.306417	−	0.951897i	$-0.400870\pi$
$521$	1.03065e12			0.612834			0.306417	+	0.951897i	$0.400870\pi$
$522$	−1.71368e12	−	1.40454e12i	−1.01021	−	0.827975i
$523$	2.03811e12			1.19116			0.595579	−	0.803297i	$-0.296923\pi$
$523$	2.03811e12			1.19116			0.595579	+	0.803297i	$0.296923\pi$
$524$	1.40043e10	+	2.42561e10i	0.00811465	+	0.0140550i
$525$	9.16838e11	−	1.67129e11i	0.526715	−	0.0960140i
$526$	5.40383e11	−	9.35971e11i	0.307798	−	0.533122i
$527$	−1.55615e12	+	2.69532e12i	−0.878825	+	1.52217i
$528$	−3.11169e12	+	5.67225e11i	−1.74238	+	0.317616i
$529$	8.94322e11	+	1.54901e12i	0.496528	+	0.860011i
$530$	−7.26693e11			−0.400046
$531$	1.45874e12	+	1.19559e12i	0.796256	+	0.652614i
$532$	6.03497e11			0.326642
$533$	7.07626e10	+	1.22564e11i	0.0379779	+	0.0657797i
$534$	−3.15586e11	+	8.82898e11i	−0.167951	+	0.469867i
$535$	−5.71651e11	+	9.90128e11i	−0.301675	+	0.522516i
$536$	8.56471e11	−	1.48345e12i	0.448199	−	0.776303i
$537$	2.14569e12	+	2.52735e12i	1.11348	+	1.31154i
$538$	−8.10975e11	−	1.40465e12i	−0.417337	−	0.722849i
$539$	−1.39175e12			−0.710251
$540$	−2.49310e11	−	1.38236e11i	−0.126173	−	0.0699600i
$541$	−1.53998e12			−0.772905			−0.386453	−	0.922309i	$-0.626300\pi$
$541$	−1.53998e12			−0.772905			−0.386453	+	0.922309i	$0.626300\pi$
$542$	2.10120e12	+	3.63939e12i	1.04585	+	1.81147i
$543$	−1.27681e12	−	1.50392e12i	−0.630271	−	0.742378i
$544$	−5.17925e11	+	8.97072e11i	−0.253555	+	0.439170i
$545$	3.02454e11	−	5.23865e11i	0.146850	−	0.254352i
$546$	−1.46117e11	+	4.08785e11i	−0.0703615	+	0.196846i
$547$	9.59604e11	+	1.66208e12i	0.458299	+	0.793797i	0.998871	−	0.0475005i	$-0.0151256\pi$
$547$	9.59604e11	+	1.66208e12i	0.458299	+	0.793797i	−0.540572	+	0.841298i	$0.681792\pi$
$548$	1.46240e11			0.0692713
$549$	3.72438e11	−	1.40449e11i	0.174976	−	0.0659847i
$550$	−2.66463e12			−1.24166
$551$	1.98343e12	+	3.43541e12i	0.916717	+	1.58780i
$552$	1.44890e11	−	2.64117e10i	0.0664221	−	0.0121080i
$553$	9.01319e11	−	1.56113e12i	0.409841	−	0.709865i
$554$	2.21400e12	−	3.83475e12i	0.998580	−	1.72959i
$555$	−6.16354e11	+	1.12354e11i	−0.275748	+	0.0502656i
$556$	9.86533e10	+	1.70873e11i	0.0437799	+	0.0758291i
$557$	−2.71058e11			−0.119320			−0.0596601	−	0.998219i	$-0.519002\pi$
$557$	−2.71058e11			−0.119320			−0.0596601	+	0.998219i	$0.519002\pi$
$558$	8.10146e11	−	4.92668e12i	0.353760	−	2.15130i
$559$	−5.92858e11			−0.256802
$560$	−5.09291e11	−	8.82118e11i	−0.218836	−	0.379036i
$561$	1.06175e12	−	2.97041e12i	0.452575	−	1.26614i
$562$	3.27638e11	−	5.67486e11i	0.138542	−	0.239962i
$563$	−1.54117e11	+	2.66939e11i	−0.0646492	+	0.111976i	−0.896538	−	0.442966i	$-0.853926\pi$
$563$	−1.54117e11	+	2.66939e11i	−0.0646492	+	0.111976i	0.831889	+	0.554942i	$0.187260\pi$
$564$	5.93477e11	+	6.99039e11i	0.246972	+	0.290901i
$565$	−6.82652e11	−	1.18239e12i	−0.281826	−	0.488137i
$566$	−1.89566e12			−0.776402
$567$	−3.47521e11	−	1.73544e12i	−0.141207	−	0.705159i
$568$	−1.30037e12			−0.524205
$569$	−1.79082e12	−	3.10180e12i	−0.716222	−	1.24053i	−0.962486	−	0.271330i	$-0.912536\pi$
$569$	−1.79082e12	−	3.10180e12i	−0.716222	−	1.24053i	0.246264	−	0.969203i	$-0.420797\pi$
$570$	1.48765e12	+	1.75226e12i	0.590287	+	0.695281i
$571$	4.45411e10	−	7.71475e10i	0.0175347	−	0.0303710i	−0.857125	−	0.515109i	$-0.827752\pi$
$571$	4.45411e10	−	7.71475e10i	0.0175347	−	0.0303710i	0.874660	+	0.484738i	$0.161085\pi$
$572$	1.37797e11	−	2.38672e11i	0.0538219	−	0.0932222i
$573$	4.60504e11	−	1.28833e12i	0.178459	−	0.499265i
$574$	3.14113e11	+	5.44060e11i	0.120777	+	0.209191i
$575$	1.62624e11			0.0620413
$576$	−2.46452e11	+	1.49873e12i	−0.0932890	+	0.567312i
$577$	−4.29975e11			−0.161492			−0.0807462	−	0.996735i	$-0.525730\pi$
$577$	−4.29975e11			−0.161492			−0.0807462	+	0.996735i	$0.525730\pi$
$578$	2.50312e11	+	4.33553e11i	0.0932838	+	0.161572i
$579$	1.37356e12	−	2.50383e11i	0.507918	−	0.0925874i
$580$	−2.26493e11	+	3.92297e11i	−0.0831051	+	0.143942i
$581$	−1.08106e12	+	1.87245e12i	−0.393603	+	0.681740i
$582$	2.03540e12	−	3.71030e11i	0.735355	−	0.134047i
$583$	1.43214e12	+	2.48054e12i	0.513424	+	0.889277i
$584$	2.04589e12			0.727820
$585$	−3.43509e11	+	1.29540e11i	−0.121265	+	0.0457301i
$586$	5.22149e12			1.82917
$587$	−1.13503e12	−	1.96594e12i	−0.394582	−	0.683436i	0.598466	−	0.801148i	$-0.295777\pi$
$587$	−1.13503e12	−	1.96594e12i	−0.394582	−	0.683436i	−0.993048	+	0.117712i	$0.962444\pi$
$588$	1.34442e11	−	3.76121e11i	0.0463807	−	0.129757i
$589$	−4.46940e12	+	7.74123e12i	−1.53014	+	2.65028i
$590$	8.68320e11	−	1.50397e12i	0.295016	−	0.510983i
$591$	2.93390e11	+	3.45575e11i	0.0989239	+	0.116520i
$592$	−9.97514e11	−	1.72774e12i	−0.333788	−	0.578138i
$593$	−4.09944e12			−1.36138			−0.680688	−	0.732573i	$-0.738319\pi$
$593$	−4.09944e12			−1.36138			−0.680688	+	0.732573i	$0.738319\pi$
$594$	8.76763e10	+	5.05974e12i	0.0288964	+	1.66759i
$595$	1.01584e12			0.332277
$596$	−2.57909e11	−	4.46712e11i	−0.0837256	−	0.145017i
$597$	2.63460e12	+	3.10322e12i	0.848850	+	0.999836i
$598$	−3.78764e10	+	6.56039e10i	−0.0121119	+	0.0209785i
$599$	8.09154e11	−	1.40150e12i	0.256809	−	0.444806i	−0.708576	−	0.705634i	$-0.750662\pi$
$599$	8.09154e11	−	1.40150e12i	0.256809	−	0.444806i	0.965385	+	0.260828i	$0.0839955\pi$
$600$	−6.44478e11	+	1.80302e12i	−0.203015	+	0.567963i
$601$	−8.60804e11	−	1.49096e12i	−0.269134	−	0.466155i	0.699504	−	0.714629i	$-0.253404\pi$
$601$	−8.60804e11	−	1.49096e12i	−0.269134	−	0.466155i	−0.968639	+	0.248474i	$0.920071\pi$
$602$	−2.63168e12			−0.816675
$603$	−2.77820e12	−	2.27702e12i	−0.855727	−	0.701357i
$604$	8.36793e10			0.0255830
$605$	−9.69528e11	−	1.67927e12i	−0.294213	−	0.509591i
$606$	4.98447e11	−	9.08610e10i	0.150139	−	0.0273685i
$607$	2.07028e12	−	3.58583e12i	0.618985	−	1.07211i	−0.370686	−	0.928758i	$-0.620877\pi$
$607$	2.07028e12	−	3.58583e12i	0.618985	−	1.07211i	0.989671	−	0.143356i	$-0.0457894\pi$
$608$	−1.48753e12	+	2.57648e12i	−0.441468	+	0.764646i
$609$	−2.76683e12	+	5.04361e11i	−0.815089	+	0.148581i
$610$	−1.83249e11	−	3.17397e11i	−0.0535869	−	0.0928152i
$611$	1.18093e12			0.342799
$612$	7.00190e11	+	5.73878e11i	0.201760	+	0.165363i
$613$	1.88290e12			0.538585			0.269292	−	0.963058i	$-0.413210\pi$
$613$	1.88290e12			0.538585			0.269292	+	0.963058i	$0.413210\pi$
$614$	−1.05505e12	−	1.82740e12i	−0.299582	−	0.518891i
$615$	−1.78822e11	+	5.00281e11i	−0.0504061	+	0.141019i
$616$	−1.53152e12	+	2.65267e12i	−0.428557	+	0.742283i
$617$	1.45653e12	−	2.52278e12i	0.404609	−	0.700803i	−0.589667	−	0.807646i	$-0.700741\pi$
$617$	1.45653e12	−	2.52278e12i	0.404609	−	0.700803i	0.994276	+	0.106844i	$0.0340744\pi$
$618$	7.95803e10	+	9.37353e10i	0.0219461	+	0.0258497i
$619$	1.23748e12	+	2.14337e12i	0.338789	+	0.586799i	0.984205	−	0.177032i	$-0.0566495\pi$
$619$	1.23748e12	+	2.14337e12i	0.338789	+	0.586799i	−0.645417	+	0.763831i	$0.723316\pi$
$620$	−1.02074e12			−0.277430
$621$	−5.35096e9	−	3.08800e11i	−0.00144384	−	0.0833231i
$622$	−5.95413e12			−1.59500
$623$	5.95052e11	+	1.03066e12i	0.158255	+	0.274107i
$624$	−7.56608e11	−	8.91186e11i	−0.199775	−	0.235309i
$625$	−5.69756e11	+	9.86847e11i	−0.149358	+	0.258696i
$626$	−8.08203e11	+	1.39985e12i	−0.210347	+	0.364331i
$627$	3.04946e12	−	8.53130e12i	0.787986	−	2.20451i
$628$	−6.13860e10	−	1.06324e11i	−0.0157489	−	0.0272780i
$629$	1.98966e12			0.506817
$630$	−1.52483e12	+	5.75024e11i	−0.385646	+	0.145430i
$631$	5.10645e12			1.28229			0.641146	−	0.767419i	$-0.278459\pi$
$631$	5.10645e12			1.28229			0.641146	+	0.767419i	$0.278459\pi$
$632$	1.85182e12	+	3.20744e12i	0.461712	+	0.799708i
$633$	−5.87333e11	+	1.07064e11i	−0.145401	+	0.0265049i
$634$	2.96907e12	−	5.14257e12i	0.729824	−	1.26409i
$635$	−1.76155e12	+	3.05110e12i	−0.429946	+	0.744689i
$636$	−8.08710e11	+	1.47418e11i	−0.195991	+	0.0357268i
$637$	−2.57198e11	−	4.45480e11i	−0.0618928	−	0.107202i
$638$	8.04130e12			1.92147
$639$	−4.42476e11	+	2.69080e12i	−0.104987	+	0.638450i
$640$	2.58884e12			0.609951
$641$	3.03247e11	+	5.25239e11i	0.0709472	+	0.122884i	0.899317	−	0.437298i	$-0.144064\pi$
$641$	3.03247e11	+	5.25239e11i	0.0709472	+	0.122884i	−0.828370	+	0.560182i	$0.810731\pi$
$642$	−1.96055e12	+	5.48491e12i	−0.455480	+	1.27427i
$643$	1.25492e12	−	2.17359e12i	0.289512	−	0.501450i	−0.684181	−	0.729312i	$-0.739840\pi$
$643$	1.25492e12	−	2.17359e12i	0.289512	−	0.501450i	0.973693	+	0.227862i	$0.0731736\pi$
$644$	−3.73313e10	+	6.46598e10i	−0.00855238	+	0.0148132i
$645$	−1.44039e12	−	1.69659e12i	−0.327689	−	0.385975i
$646$	−3.64990e12	−	6.32182e12i	−0.824584	−	1.42822i
$647$	2.81592e12			0.631758			0.315879	−	0.948799i	$-0.397701\pi$
$647$	2.81592e12			0.631758			0.315879	+	0.948799i	$0.397701\pi$
$648$	3.44488e12	+	1.16444e12i	0.767515	+	0.259437i
$649$	−6.84501e12			−1.51451
$650$	−4.92428e11	−	8.52910e11i	−0.108201	−	0.187410i
$651$	−4.10159e12	−	4.83114e12i	−0.895030	−	1.05423i
$652$	5.11757e11	−	8.86389e11i	0.110905	−	0.192092i
$653$	−5.41859e10	+	9.38527e10i	−0.0116621	+	0.0201994i	−0.871798	−	0.489866i	$-0.837046\pi$
$653$	−5.41859e10	+	9.38527e10i	−0.0116621	+	0.0201994i	0.860135	+	0.510066i	$0.170379\pi$
$654$	1.03730e12	−	2.90200e12i	0.221720	−	0.620295i
$655$	6.77035e10	+	1.17266e11i	0.0143723	+	0.0248935i
$656$	−1.69178e12			−0.356678
$657$	6.96150e11	−	4.23345e12i	0.145767	−	0.886441i
$658$	5.24213e12			1.09016
$659$	3.26356e12	+	5.65265e12i	0.674073	+	1.16753i	0.976739	+	0.214432i	$0.0687901\pi$
$659$	3.26356e12	+	5.65265e12i	0.674073	+	1.16753i	−0.302666	+	0.953097i	$0.597877\pi$
$660$	1.01780e12	−	1.85533e11i	0.208793	−	0.0380604i
$661$	−2.14242e12	+	3.71079e12i	−0.436515	+	0.756066i	−0.997418	−	0.0718158i	$-0.977121\pi$
$661$	−2.14242e12	+	3.71079e12i	−0.436515	+	0.756066i	0.560903	+	0.827881i	$0.310454\pi$
$662$	−1.98119e12	+	3.43153e12i	−0.400927	+	0.694426i
$663$	1.14700e12	−	2.09085e11i	0.230543	−	0.0420253i
$664$	−2.22111e12	−	3.84707e12i	−0.443418	−	0.768023i
$665$	2.91760e12			0.578533
$666$	−2.98658e12	+	1.12626e12i	−0.588221	+	0.221822i
$667$	−4.90768e11			−0.0960085
$668$	6.77313e11	+	1.17314e12i	0.131612	+	0.227959i
$669$	−1.99993e12	+	5.59510e12i	−0.386009	+	1.07992i
$670$	−1.65373e12	+	2.86435e12i	−0.317050	+	0.549147i
$671$	−7.22282e11	+	1.25103e12i	−0.137548	+	0.238241i
$672$	−1.36511e12	−	1.60793e12i	−0.258230	−	0.304162i
$673$	−2.48556e12	−	4.30512e12i	−0.467043	−	0.808942i	0.532248	−	0.846588i	$-0.321347\pi$
$673$	−2.48556e12	−	4.30512e12i	−0.467043	−	0.808942i	−0.999291	+	0.0376463i	$0.988014\pi$
$674$	3.46970e12			0.647623
$675$	3.51160e12	+	1.94710e12i	0.651086	+	0.361011i
$676$	−1.44775e12			−0.266644
$677$	−3.82144e12	−	6.61893e12i	−0.699163	−	1.21099i	−0.968757	−	0.248011i	$-0.920223\pi$
$677$	−3.82144e12	−	6.61893e12i	−0.699163	−	1.21099i	0.269595	−	0.962974i	$-0.413110\pi$
$678$	−4.50181e12	−	5.30255e12i	−0.818188	−	0.963720i
$679$	1.31306e12	−	2.27428e12i	0.237066	−	0.410611i
$680$	−1.04356e12	+	1.80749e12i	−0.187165	+	0.324180i
$681$	−2.79838e12	+	7.82887e12i	−0.498591	+	1.39488i
$682$	9.06000e12	+	1.56924e13i	1.60361	+	2.77753i
$683$	−4.20646e12			−0.739646			−0.369823	−	0.929102i	$-0.620582\pi$
$683$	−4.20646e12			−0.739646			−0.369823	+	0.929102i	$0.620582\pi$
$684$	2.01101e12	+	1.64823e12i	0.351287	+	0.287916i
$685$	7.06995e11			0.122690
$686$	−3.50638e12	−	6.07323e12i	−0.604506	−	1.04703i
$687$	−8.48896e12	+	1.54744e12i	−1.45395	+	0.265038i
$688$	3.54349e12	−	6.13750e12i	0.602952	−	1.04434i
$689$	−5.29324e11	+	9.16816e11i	−0.0894818	+	0.154987i
$690$	−2.79763e11	+	5.09975e10i	−0.0469861	+	0.00856502i
$691$	1.16845e12	+	2.02381e12i	0.194966	+	0.337690i	0.946889	−	0.321560i	$-0.104207\pi$
$691$	1.16845e12	+	2.02381e12i	0.194966	+	0.337690i	−0.751924	+	0.659250i	$0.770874\pi$
$692$	1.20896e12			0.200417
$693$	4.96790e12	+	4.07171e12i	0.818225	+	0.670621i
$694$	−7.27305e12			−1.19014
$695$	4.76938e11	+	8.26082e11i	0.0775409	+	0.134305i
$696$	1.94490e12	−	5.44115e12i	0.314164	−	0.878920i
$697$	8.43615e11	−	1.46118e12i	0.135393	−	0.234508i
$698$	−1.24883e12	+	2.16304e12i	−0.199138	+	0.344918i
$699$	4.26204e12	+	5.02014e12i	0.675259	+	0.795368i
$700$	−4.85341e11	−	8.40635e11i	−0.0764022	−	0.132333i
$701$	1.10126e12			0.172250			0.0861251	−	0.996284i	$-0.472552\pi$
$701$	1.10126e12			0.172250			0.0861251	+	0.996284i	$0.472552\pi$
$702$	−1.60335e12	+	9.63113e11i	−0.249179	+	0.149679i
$703$	5.71450e12			0.882429
$704$	−2.75611e12	−	4.77373e12i	−0.422883	−	0.732454i
$705$	2.86916e12	+	3.37950e12i	0.437425	+	0.515230i
$706$	−4.92201e11	+	8.52518e11i	−0.0745627	+	0.129146i
$707$	3.21553e11	−	5.56946e11i	0.0484022	−	0.0838350i
$708$	6.61222e11	−	1.84987e12i	0.0989004	−	0.276688i
$709$	−6.57748e11	−	1.13925e12i	−0.0977578	−	0.169322i	0.812998	−	0.582266i	$-0.197834\pi$
$709$	−6.57748e11	−	1.13925e12i	−0.0977578	−	0.169322i	−0.910756	+	0.412944i	$0.864500\pi$
$710$	2.51085e12			0.370816
$711$	7.26710e12	−	2.74048e12i	1.06647	−	0.402173i
$712$	−2.44514e12			−0.356570
$713$	−5.52940e11	−	9.57720e11i	−0.0801263	−	0.138783i
$714$	5.09151e12	−	9.28122e11i	0.733170	−	0.133648i
$715$	6.66180e11	−	1.15386e12i	0.0953266	−	0.165111i
$716$	1.72657e12	−	2.99051e12i	0.245514	−	0.425243i
$717$	1.44216e12	−	2.62889e11i	0.203787	−	0.0371480i
$718$	5.74695e12	+	9.95402e12i	0.807008	+	1.39778i
$719$	−1.32450e13			−1.84830			−0.924151	−	0.382027i	$-0.875226\pi$
$719$	−1.32450e13			−1.84830			−0.924151	+	0.382027i	$0.875226\pi$
$720$	7.12093e11	−	4.33040e12i	0.0987507	−	0.600526i
$721$	1.56074e11			0.0215091
$722$	−6.34376e12	−	1.09877e13i	−0.868819	−	1.50484i
$723$	−1.41382e12	+	3.95537e12i	−0.192430	+	0.538350i
$724$	−1.02741e12	+	1.77952e12i	−0.138970	+	0.240702i
$725$	3.19021e12	−	5.52561e12i	0.428843	−	0.742778i
$726$	−6.39364e12	−	7.53088e12i	−0.854149	−	1.00608i
$727$	−2.35848e12	−	4.08501e12i	−0.313132	−	0.542360i	0.665907	−	0.746035i	$-0.268045\pi$
$727$	−2.35848e12	−	4.08501e12i	−0.313132	−	0.542360i	−0.979039	+	0.203675i	$0.934712\pi$
$728$	−1.13211e12			−0.149382
$729$	3.58171e12	−	6.73209e12i	0.469695	−	0.882829i
$730$	−3.95034e12			−0.514851
$731$	3.53396e12	+	6.12100e12i	0.457755	+	0.792855i
$732$	−2.68319e11	−	3.16045e11i	−0.0345424	−	0.0406864i
$733$	−8.29559e11	+	1.43684e12i	−0.106140	+	0.183840i	−0.914203	−	0.405256i	$-0.867183\pi$
$733$	−8.29559e11	+	1.43684e12i	−0.106140	+	0.183840i	0.808063	+	0.589096i	$0.200516\pi$
$734$	9.59553e11	−	1.66199e12i	0.122022	−	0.211348i
$735$	6.49959e11	−	1.81835e12i	0.0821472	−	0.229819i
$736$	−1.84032e11	−	3.18753e11i	−0.0231177	−	0.0400410i
$737$	1.30364e13			1.62763
$738$	−4.39195e11	+	2.67084e12i	−0.0545009	+	0.331432i
$739$	−5.72028e12			−0.705533			−0.352767	−	0.935711i	$-0.614759\pi$
$739$	−5.72028e12			−0.705533			−0.352767	+	0.935711i	$0.614759\pi$
$740$	3.26276e11	+	5.65126e11i	0.0399984	+	0.0692792i
$741$	3.29430e12	−	6.00511e11i	0.401403	−	0.0731711i
$742$	−2.34966e12	+	4.06972e12i	−0.284568	+	0.492887i
$743$	3.35872e12	−	5.81747e12i	0.404318	−	0.700300i	−0.589923	−	0.807459i	$-0.700842\pi$
$743$	3.35872e12	−	5.81747e12i	0.404318	−	0.700300i	0.994242	+	0.107159i	$0.0341754\pi$
$744$	1.28096e13	−	2.33503e12i	1.53269	−	0.279392i
$745$	−1.24686e12	−	2.15962e12i	−0.148291	−	0.256847i
$746$	−7.16752e12			−0.847314
$747$	−8.71632e12	+	3.28699e12i	−1.02421	+	0.386238i
$748$	−3.28558e12			−0.383755
$749$	3.69670e12	+	6.40287e12i	0.429186	+	0.743373i
$750$	2.91592e12	−	8.15771e12i	0.336511	−	0.941439i
$751$	−4.55508e12	+	7.88962e12i	−0.522536	+	0.905058i	0.477121	+	0.878838i	$0.341680\pi$
$751$	−4.55508e12	+	7.88962e12i	−0.522536	+	0.905058i	−0.999656	+	0.0262203i	$0.991653\pi$
$752$	−7.05839e12	+	1.22255e13i	−0.804869	+	1.39407i
$753$	1.36792e11	+	1.61123e11i	0.0155054	+	0.0182633i
$754$	1.48605e12	+	2.57391e12i	0.167441	+	0.290016i
$755$	4.04547e11			0.0453114
$756$	−1.58028e12	+	9.49253e11i	−0.175948	+	0.105690i
$757$	−4.86606e12			−0.538575			−0.269288	−	0.963060i	$-0.586788\pi$
$757$	−4.86606e12			−0.538575			−0.269288	+	0.963060i	$0.586788\pi$
$758$	8.21717e12	+	1.42326e13i	0.904089	+	1.56593i
$759$	7.25425e11	+	8.54457e11i	0.0793422	+	0.0934549i
$760$	−2.99719e12	+	5.19129e12i	−0.325877	+	0.564435i
$761$	−1.85589e12	+	3.21450e12i	−0.200596	+	0.347442i	−0.948720	−	0.316116i	$-0.897621\pi$
$761$	−1.85589e12	+	3.21450e12i	−0.200596	+	0.347442i	0.748125	+	0.663558i	$0.230954\pi$
$762$	−6.04146e12	+	1.69019e13i	−0.649150	+	1.81609i
$763$	−1.95588e12	−	3.38768e12i	−0.208921	−	0.361862i
$764$	−1.42502e12			−0.151322
$765$	3.38506e12	+	2.77441e12i	0.357347	+	0.292883i
$766$	8.54423e12			0.896692
$767$	−1.26497e12	−	2.19099e12i	−0.131978	−	0.228592i
$768$	7.52244e12	−	1.37125e12i	0.780249	−	0.142230i
$769$	3.31651e12	−	5.74436e12i	0.341989	−	0.592343i	−0.642813	−	0.766023i	$-0.722233\pi$
$769$	3.31651e12	−	5.74436e12i	0.341989	−	0.592343i	0.984802	+	0.173681i	$0.0555660\pi$
$770$	2.95716e12	−	5.12194e12i	0.303156	−	0.525081i
$771$	−1.20297e13	+	2.19287e12i	−1.22606	+	0.223495i
$772$	−7.27112e11	−	1.25940e12i	−0.0736756	−	0.127610i
$773$	−7.34772e12			−0.740193			−0.370096	−	0.928993i	$-0.620675\pi$
$773$	−7.34772e12			−0.740193			−0.370096	+	0.928993i	$0.620675\pi$
$774$	−8.76947e12	−	7.18749e12i	−0.878293	−	0.719852i
$775$	1.43774e13			1.43161
$776$	2.69776e12	+	4.67266e12i	0.267070	+	0.462579i
$777$	−1.36367e12	+	3.81507e12i	−0.134219	+	0.375498i
$778$	2.09284e12	−	3.62491e12i	0.204799	−	0.354723i
$779$	2.42295e12	−	4.19666e12i	0.235736	−	0.408306i
$780$	2.47478e11	+	2.91497e11i	0.0239393	+	0.0281974i
$781$	−4.94829e12	−	8.57069e12i	−0.475911	−	0.824301i
$782$	9.03108e11			0.0863593
$783$	−1.05973e13	−	5.87594e12i	−1.00755	−	0.558662i
$784$	6.14905e12			0.581281
$785$	−2.96770e11	−	5.14021e11i	−0.0278937	−	0.0483134i
$786$	4.46476e11	+	5.25892e11i	0.0417251	+	0.0491467i
$787$	1.90682e12	−	3.30271e12i	0.177184	−	0.306891i	−0.763731	−	0.645535i	$-0.776635\pi$
$787$	1.90682e12	−	3.30271e12i	0.177184	−	0.306891i	0.940915	+	0.338643i	$0.109968\pi$
$788$	2.36081e11	−	4.08905e11i	0.0218119	−	0.0377793i
$789$	1.98939e12	−	5.56561e12i	0.182757	−	0.511289i
$790$	−3.57561e12	−	6.19314e12i	−0.326609	−	0.565703i
$791$	−8.82902e12			−0.801897
$792$	−1.23482e13	+	4.65661e12i	−1.11517	+	0.420539i
$793$	−5.33916e11			−0.0479451
$794$	−3.58026e12	−	6.20119e12i	−0.319685	−	0.553710i
$795$	−3.90970e12	+	7.12692e11i	−0.347129	+	0.0632775i
$796$	2.11998e12	−	3.67192e12i	0.187164	−	0.324178i
$797$	8.93658e12	−	1.54786e13i	0.784529	−	1.35884i	−0.144751	−	0.989468i	$-0.546238\pi$
$797$	8.93658e12	−	1.54786e13i	0.784529	−	1.35884i	0.929280	−	0.369376i	$-0.120428\pi$
$798$	1.46233e13	−	2.66566e12i	1.27653	−	0.232697i
$799$	−7.03941e12	−	1.21926e13i	−0.611048	−	1.05837i
$800$	4.78518e12			0.413041
$801$	−8.32005e11	+	5.05961e12i	−0.0714133	+	0.434281i
$802$	1.94953e13			1.66397
$803$	7.78517e12	+	1.34843e13i	0.660767	+	1.14448i
$804$	−1.25931e12	+	3.52310e12i	−0.106287	+	0.297354i
$805$	−1.80478e11	+	3.12597e11i	−0.0151476	+	0.0262363i
$806$	−3.34861e12	+	5.79996e12i	−0.279484	+	0.484080i
$807$	−5.74073e12	−	6.76184e12i	−0.476471	−	0.561221i
$808$	6.60650e11	+	1.14428e12i	0.0545281	+	0.0944454i
$809$	1.16949e13			0.959908			0.479954	−	0.877294i	$-0.340653\pi$
$809$	1.16949e13			0.959908			0.479954	+	0.877294i	$0.340653\pi$
$810$	−6.65161e12	−	2.24839e12i	−0.542931	−	0.183522i
$811$	−3.78089e12			−0.306902			−0.153451	−	0.988156i	$-0.549039\pi$
$811$	−3.78089e12			−0.306902			−0.153451	+	0.988156i	$0.549039\pi$
$812$	1.46466e12	+	2.53687e12i	0.118232	+	0.204784i
$813$	1.48740e13	+	1.75196e13i	1.19404	+	1.40643i
$814$	5.79198e12	−	1.00320e13i	0.462400	−	0.800900i
$815$	2.47408e12	−	4.28524e12i	0.196429	−	0.340224i
$816$	−4.69105e12	+	1.31239e13i	−0.370394	+	1.03623i
$817$	1.01499e13	+	1.75801e13i	0.797006	+	1.38045i
$818$	−9.74701e11			−0.0761170
$819$	−3.85221e11	+	2.34261e12i	−0.0299180	+	0.181938i
$820$	5.53363e11			0.0427413
$821$	−3.66299e12	−	6.34448e12i	−0.281379	−	0.487362i	0.690346	−	0.723480i	$-0.257458\pi$
$821$	−3.66299e12	−	6.34448e12i	−0.281379	−	0.487362i	−0.971725	+	0.236117i	$0.924125\pi$
$822$	3.54353e12	−	6.45945e11i	0.270716	−	0.0493483i
$823$	−3.23057e12	+	5.59552e12i	−0.245460	+	0.425149i	−0.962261	−	0.272129i	$-0.912272\pi$
$823$	−3.23057e12	+	5.59552e12i	−0.245460	+	0.425149i	0.716801	+	0.697278i	$0.245606\pi$
$824$	−1.60332e11	+	2.77703e11i	−0.0121157	+	0.0209850i
$825$	−1.43360e13	+	2.61329e12i	−1.07742	+	0.196401i
$826$	−5.61517e12	−	9.72576e12i	−0.419713	−	0.726965i
$827$	−1.17187e13			−0.871176			−0.435588	−	0.900146i	$-0.643460\pi$
$827$	−1.17187e13			−0.871176			−0.435588	+	0.900146i	$0.643460\pi$
$828$	−3.00993e11	+	1.13507e11i	−0.0222546	+	0.00839237i
$829$	−2.81041e12			−0.206669			−0.103334	−	0.994647i	$-0.532951\pi$
$829$	−2.81041e12			−0.206669			−0.103334	+	0.994647i	$0.532951\pi$
$830$	4.28867e12	+	7.42819e12i	0.313668	+	0.543290i
$831$	8.15071e12	−	2.28028e13i	0.592913	−	1.65876i
$832$	1.01867e12	−	1.76439e12i	0.0737018	−	0.127655i
$833$	−3.06626e12	+	5.31091e12i	−0.220651	+	0.382179i
$834$	3.14521e12	+	3.70465e12i	0.225114	+	0.265155i
$835$	3.27446e12	+	5.67153e12i	0.233105	+	0.403749i
$836$	−9.43650e12			−0.668163
$837$	−4.73072e11	−	2.73007e13i	−0.0333168	−	1.92269i
$838$	−1.88209e13			−1.31839
$839$	8.01390e12	+	1.38805e13i	0.558361	+	0.967109i	0.997634	+	0.0687556i	$0.0219029\pi$
$839$	8.01390e12	+	1.38805e13i	0.558361	+	0.967109i	−0.439273	+	0.898354i	$0.644764\pi$
$840$	−2.75054e12	−	3.23978e12i	−0.190617	−	0.224522i
$841$	−2.37384e12	+	4.11162e12i	−0.163633	+	0.283420i
$842$	4.12300e12	−	7.14125e12i	0.282689	−	0.489632i
$843$	1.20618e12	−	3.37447e12i	0.0822600	−	0.230135i
$844$	3.10913e11	+	5.38517e11i	0.0210910	+	0.0365307i
$845$	−6.99912e12			−0.472268
$846$	1.74682e13	+	1.43170e13i	1.17241	+	0.960916i
$847$	−1.25393e13			−0.837141
$848$	−6.32749e12	−	1.09595e13i	−0.420194	−	0.727798i
$849$	−1.01989e13	+	1.85914e12i	−0.673703	+	0.122808i
$850$	−5.87061e12	+	1.01682e13i	−0.385743	+	0.668127i
$851$	−3.53490e11	+	6.12263e11i	−0.0231044	+	0.0400179i
$852$	2.79423e12	−	5.09356e11i	0.181671	−	0.0331164i
$853$	8.96613e12	+	1.55298e13i	0.579875	+	1.00437i	0.995493	+	0.0948337i	$0.0302319\pi$
$853$	8.96613e12	+	1.55298e13i	0.579875	+	1.00437i	−0.415618	+	0.909539i	$0.636435\pi$
$854$	−2.37004e12			−0.152474
$855$	9.72222e12	+	7.96837e12i	0.622183	+	0.509943i
$856$	−1.51902e13			−0.967011
$857$	2.18082e12	+	3.77729e12i	0.138104	+	0.239203i	0.926779	−	0.375607i	$-0.122566\pi$
$857$	2.18082e12	+	3.77729e12i	0.138104	+	0.239203i	−0.788675	+	0.614810i	$0.789233\pi$
$858$	2.28474e12	−	6.39191e12i	0.143928	−	0.402659i
$859$	−3.67580e12	+	6.36667e12i	−0.230347	+	0.398973i	−0.957910	−	0.287068i	$-0.907319\pi$
$859$	−3.67580e12	+	6.36667e12i	−0.230347	+	0.398973i	0.727563	+	0.686041i	$0.240653\pi$
$860$	−1.15904e12	+	2.00751e12i	−0.0722527	+	0.125145i
$861$	2.22355e12	+	2.61905e12i	0.137890	+	0.162416i
$862$	−4.95248e12	−	8.57795e12i	−0.305520	−	0.529177i
$863$	1.41639e13			0.869231			0.434615	−	0.900616i	$-0.356884\pi$
$863$	1.41639e13			0.869231			0.434615	+	0.900616i	$0.356884\pi$
$864$	−1.57450e11	−	9.08636e12i	−0.00961241	−	0.554725i
$865$	5.84471e12			0.354969
$866$	−7.03956e12	−	1.21929e13i	−0.425319	−	0.736674i
$867$	1.77191e12	+	2.08708e12i	0.106501	+	0.125445i
$868$	−3.30042e12	+	5.71649e12i	−0.197347	+	0.341815i
$869$	−1.40933e13	+	2.44104e13i	−0.838350	+	1.45206i
$870$	−3.75535e12	+	1.05061e13i	−0.222236	+	0.621737i
$871$	2.40916e12	+	4.17278e12i	0.141835	+	0.245666i
$872$	8.03695e12			0.470725
$873$	1.05868e13	−	3.99238e12i	0.616883	−	0.232631i
$874$	2.59381e12			0.150362
$875$	−5.49810e12	−	9.52299e12i	−0.317085	−	0.549208i
$876$	−4.39618e12	+	8.01372e11i	−0.252236	+	0.0459797i
$877$	2.34330e12	−	4.05872e12i	0.133761	−	0.231681i	−0.791362	−	0.611347i	$-0.790628\pi$
$877$	2.34330e12	−	4.05872e12i	0.133761	−	0.231681i	0.925124	+	0.379666i	$0.123961\pi$
$878$	3.84939e12	−	6.66733e12i	0.218608	−	0.378640i
$879$	2.80923e13	−	5.12089e12i	1.58722	−	0.289331i
$880$	7.96346e12	+	1.37931e13i	0.447641	+	0.775337i
$881$	1.22598e13			0.685635			0.342817	−	0.939402i	$-0.388619\pi$
$881$	1.22598e13			0.685635			0.342817	+	0.939402i	$0.388619\pi$
$882$	1.59633e12	−	9.70761e12i	0.0888204	−	0.540137i
$883$	−6.77194e12			−0.374878			−0.187439	−	0.982276i	$-0.560019\pi$
$883$	−6.77194e12			−0.374878			−0.187439	+	0.982276i	$0.560019\pi$
$884$	−6.07181e11	−	1.05167e12i	−0.0334413	−	0.0579220i
$885$	3.19667e12	−	8.94316e12i	0.175167	−	0.490057i
$886$	−5.42145e12	+	9.39023e12i	−0.295573	+	0.511947i
$887$	1.08701e13	−	1.88276e13i	0.589627	−	1.02126i	−0.404654	−	0.914470i	$-0.632608\pi$
$887$	1.08701e13	−	1.88276e13i	0.589627	−	1.02126i	0.994281	−	0.106795i	$-0.0340587\pi$
$888$	−5.38729e12	−	6.34554e12i	−0.290745	−	0.342460i
$889$	1.13915e13	+	1.97306e13i	0.611676	+	1.05945i
$890$	4.72125e12			0.252233
$891$	5.43396e12	+	2.71360e13i	0.288846	+	1.44244i
$892$	6.18875e12			0.327311
$893$	−2.02179e13	−	3.50183e13i	−1.06391	−	1.84274i
$894$	−8.22252e12	−	9.68506e12i	−0.430513	−	0.507088i
$895$	8.34709e12	−	1.44576e13i	0.434842	−	0.753169i
$896$	8.37063e12	−	1.44984e13i	0.433883	−	0.751507i
$897$	−1.39440e11	+	3.90104e11i	−0.00719153	+	0.0201194i
$898$	−2.09601e13	−	3.63040e13i	−1.07560	−	1.86299i
$899$	−4.33882e13			−2.21540
$900$	6.78606e11	−	4.12676e12i	0.0344768	−	0.209661i
$901$	1.26210e13			0.638015
$902$	−4.91159e12	−	8.50713e12i	−0.247055	−	0.427911i
$903$	−1.41588e13	+	2.58098e12i	−0.708649	+	0.129178i
$904$	9.06989e12	−	1.57095e13i	0.451694	−	0.782356i
$905$	−4.96700e12	+	8.60309e12i	−0.246136	+	0.426320i
$906$	2.02763e12	−	3.69613e11i	0.0999797	−	0.0182251i
$907$	1.13948e13	+	1.97364e13i	0.559079	+	0.968354i	0.997574	+	0.0696198i	$0.0221786\pi$
$907$	1.13948e13	+	1.97364e13i	0.559079	+	0.968354i	−0.438494	+	0.898734i	$0.644488\pi$
$908$	8.65954e12			0.422774
$909$	2.59260e12	−	9.77687e11i	0.125950	−	0.0474966i
$910$	2.18595e12			0.105671
$911$	5.63882e12	+	9.76672e12i	0.271241	+	0.469803i	0.969180	−	0.246354i	$-0.0792326\pi$
$911$	5.63882e12	+	9.76672e12i	0.271241	+	0.469803i	−0.697939	+	0.716157i	$0.745899\pi$
$912$	−1.34731e13	+	3.76931e13i	−0.644900	+	1.80420i
$913$	1.69039e13	−	2.92784e13i	0.805134	−	1.39453i
$914$	−1.59872e13	+	2.76906e13i	−0.757728	+	1.31242i
$915$	−1.29719e12	−	1.52792e12i	−0.0611797	−	0.0720618i
$916$	4.49375e12	+	7.78340e12i	0.210901	+	0.365292i
$917$	8.75637e11			0.0408942
$918$	1.95011e13	+	1.08129e13i	0.906290	+	0.502515i
$919$	−2.27954e12			−0.105421			−0.0527105	−	0.998610i	$-0.516786\pi$
$919$	−2.27954e12			−0.105421			−0.0527105	+	0.998610i	$0.516786\pi$
$920$	−3.70803e11	−	6.42250e11i	−0.0170647	−	0.0295569i
$921$	−7.46849e12	−	8.79692e12i	−0.342030	−	0.402867i
$922$	−3.69483e12	+	6.39963e12i	−0.168386	+	0.291653i
$923$	1.82891e12	−	3.16776e12i	0.0829438	−	0.143663i
$924$	2.25186e12	−	6.29992e12i	0.101629	−	0.284322i
$925$	−4.59569e12	−	7.95997e12i	−0.206402	−	0.357498i
$926$	4.03450e13			1.80318
$927$	5.20081e11	+	4.26260e11i	0.0231320	+	0.0189590i
$928$	−1.44407e13			−0.639179
$929$	9.43673e12	+	1.63449e13i	0.415672	+	0.719965i	0.995499	−	0.0947745i	$-0.0302130\pi$
$929$	9.43673e12	+	1.63449e13i	0.415672	+	0.719965i	−0.579827	+	0.814740i	$0.696880\pi$
$930$	−2.47335e13	+	4.50863e12i	−1.08421	+	0.197639i
$931$	−8.80659e12	+	1.52535e13i	−0.384179	+	0.665418i
$932$	3.42953e12	−	5.94012e12i	0.148889	−	0.257884i
$933$	−3.20340e13	+	5.83941e12i	−1.38402	+	0.252291i
$934$	−2.73064e12	−	4.72961e12i	−0.117410	−	0.203359i
$935$	−1.58841e13			−0.679689
$936$	−3.77249e12	−	3.09195e12i	−0.160652	−	0.131671i
$937$	−1.08798e13			−0.461096			−0.230548	−	0.973061i	$-0.574052\pi$
$937$	−1.08798e13			−0.461096			−0.230548	+	0.973061i	$0.574052\pi$
$938$	1.06942e13	+	1.85229e13i	0.451061	+	0.781261i
$939$	−2.97536e12	+	8.32399e12i	−0.124895	+	0.349411i
$940$	2.30872e12	−	3.99882e12i	0.0964486	−	0.167054i
$941$	−1.41900e13	+	2.45778e13i	−0.589970	+	1.02186i	0.404266	+	0.914641i	$0.367527\pi$
$941$	−1.41900e13	+	2.45778e13i	−0.589970	+	1.02186i	−0.994236	+	0.107216i	$0.965806\pi$
$942$	−1.95708e12	−	2.30518e12i	−0.0809802	−	0.0953842i
$943$	2.99759e11	+	5.19198e11i	0.0123444	+	0.0213811i
$944$	3.02427e13			1.23950
$945$	−7.63983e12	+	4.58915e12i	−0.311631	+	0.187193i
$946$	4.11500e13			1.67055
$947$	−1.79187e12	−	3.10361e12i	−0.0723988	−	0.125398i	0.827553	−	0.561387i	$-0.189732\pi$
$947$	−1.79187e12	−	3.10361e12i	−0.0723988	−	0.125398i	−0.899952	+	0.435989i	$0.856399\pi$
$948$	−5.23552e12	−	6.16676e12i	−0.210534	−	0.247982i
$949$	−2.87743e12	+	4.98385e12i	−0.115161	+	0.199465i
$950$	−1.68610e13	+	2.92040e13i	−0.671624	+	1.16329i
$951$	1.09305e13	−	3.05796e13i	0.433337	−	1.21232i
$952$	6.74837e12	+	1.16885e13i	0.266276	+	0.461204i
$953$	2.91182e12			0.114353			0.0571763	−	0.998364i	$-0.481790\pi$
$953$	2.91182e12			0.114353			0.0571763	+	0.998364i	$0.481790\pi$
$954$	−1.89447e13	+	7.14417e12i	−0.740490	+	0.279244i
$955$	−6.88926e12			−0.268014
$956$	−7.63428e11	−	1.32230e12i	−0.0295602	−	0.0511998i
$957$	4.32632e13	−	7.88637e12i	1.66730	−	0.303930i
$958$	−1.95591e13	+	3.38773e13i	−0.750245	+	1.29946i
$959$	2.28597e12	−	3.95941e12i	0.0872743	−	0.151163i
$960$	7.52411e12	−	1.37156e12i	0.285913	−	0.0521186i
$961$	−3.56649e13	−	6.17735e13i	−1.34892	−	2.33640i
$962$	4.28148e12			0.161178
$963$	−5.16874e12	+	3.14323e13i	−0.193672	+	1.17776i
$964$	4.37505e12			0.163168
$965$	−3.51522e12	−	6.08853e12i	−0.130491	−	0.226016i
$966$	−6.18971e11	+	1.73166e12i	−0.0228704	+	0.0639832i
$967$	1.34163e13	−	2.32377e13i	0.493417	−	0.854623i	−0.506555	−	0.862208i	$-0.669081\pi$
$967$	1.34163e13	−	2.32377e13i	0.493417	−	0.854623i	0.999971	+	0.00758529i	$0.00241450\pi$
$968$	1.28814e13	−	2.23112e13i	0.471546	−	0.816742i
$969$	−2.58369e13	−	3.04326e13i	−0.941422	−	1.10887i
$970$	−5.20902e12	−	9.02228e12i	−0.188922	−	0.327223i
$971$	5.18797e13			1.87288			0.936442	−	0.350824i	$-0.114098\pi$
$971$	5.18797e13			1.87288			0.936442	+	0.350824i	$0.114098\pi$
$972$	−7.85845e12	−	1.15279e12i	−0.282383	−	0.0414240i
$973$	6.16844e12			0.220632
$974$	2.32179e13	+	4.02146e13i	0.826624	+	1.43175i
$975$	−3.48580e12	−	4.10582e12i	−0.123533	−	0.145505i
$976$	3.19120e12	−	5.52731e12i	0.112572	−	0.194980i
$977$	−2.77975e13	+	4.81466e13i	−0.976067	+	1.69060i	−0.299700	+	0.954034i	$0.596887\pi$
$977$	−2.77975e13	+	4.81466e13i	−0.976067	+	1.69060i	−0.676367	+	0.736565i	$0.736447\pi$
$978$	8.48516e12	−	2.37385e13i	0.296576	−	0.829714i
$979$	−9.30445e12	−	1.61158e13i	−0.323719	−	0.560698i
$980$	−2.01129e12			−0.0696557
$981$	2.73472e12	−	1.66305e13i	0.0942763	−	0.573315i
$982$	−2.96003e13			−1.01577
$983$	−2.01121e13	−	3.48351e13i	−0.687015	−	1.18994i	−0.972799	−	0.231650i	$-0.925587\pi$
$983$	−2.01121e13	−	3.48351e13i	−0.687015	−	1.18994i	0.285785	−	0.958294i	$-0.407746\pi$
$984$	−6.94429e12	+	1.26586e12i	−0.236129	+	0.0430436i
$985$	1.14133e12	−	1.97685e12i	0.0386322	−	0.0669129i
$986$	1.77163e13	−	3.06856e13i	0.596935	−	1.03392i
$987$	2.82033e13	−	5.14113e12i	0.945961	−	0.172437i
$988$	−1.74388e12	−	3.02049e12i	−0.0582252	−	0.100849i
$989$	−2.51142e12			−0.0834710
$990$	2.38428e13	−	8.99129e12i	0.788858	−	0.297484i
$991$	1.34682e13			0.443588			0.221794	−	0.975094i	$-0.428809\pi$
$991$	1.34682e13			0.443588			0.221794	+	0.975094i	$0.428809\pi$
$992$	−1.62701e13	−	2.81806e13i	−0.533442	−	0.923949i
$993$	−7.29365e12	+	2.04051e13i	−0.238053	+	0.665988i
$994$	8.11847e12	−	1.40616e13i	0.263776	−	0.456874i
$995$	1.02490e13	−	1.77518e13i	0.331496	−	0.574169i
$996$	6.27960e12	+	7.39655e12i	0.202192	+	0.238156i
$997$	1.87292e13	+	3.24399e13i	0.600331	+	1.03980i	0.992771	+	0.120026i	$0.0382977\pi$
$997$	1.87292e13	+	3.24399e13i	0.600331	+	1.03980i	−0.392440	+	0.919778i	$0.628369\pi$
$998$	−5.18065e13			−1.65309
$999$	−1.49636e13	+	8.98846e12i	−0.475326	+	0.285523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.10.c.a.4.2	✓	16
3.2	odd	2		27.10.c.a.10.7		16
9.2	odd	6		27.10.c.a.19.7		16
9.4	even	3		81.10.a.c.1.7		8
9.5	odd	6		81.10.a.d.1.2		8
9.7	even	3	inner	9.10.c.a.7.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.2	✓	16	1.1	even	1	trivial
9.10.c.a.7.2	yes	16	9.7	even	3	inner
27.10.c.a.10.7		16	3.2	odd	2
27.10.c.a.19.7		16	9.2	odd	6
81.10.a.c.1.7		8	9.4	even	3
81.10.a.d.1.2		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+(-12.8270 - 22.2170i) q^{2} +(-90.7998 - 106.950i) q^{3} +(-73.0637 + 126.550i) q^{4} +(-353.226 + 611.805i) q^{5} +(-1211.43 + 3389.15i) q^{6} +(2284.21 + 3956.36i) q^{7} -9386.09 q^{8} +(-3193.79 + 19422.2i) q^{9} +18123.3 q^{10} +(-35716.7 - 61863.1i) q^{11} +(20168.8 - 3676.53i) q^{12} +(13201.0 - 22864.9i) q^{13} +(58599.1 - 101497. i) q^{14} +(97505.6 - 17774.1i) q^{15} +(157804. + 273325. i) q^{16} -314759. q^{17} +(472469. - 178171. i) q^{18} -904019. q^{19} +(-51616.0 - 89401.5i) q^{20} +(215729. - 603534. i) q^{21} +(-916276. + 1.58704e6i) q^{22} +(55921.2 - 96858.3i) q^{23} +(852255. + 1.00385e6i) q^{24} +(727026. + 1.25925e6i) q^{25} -677318. q^{26} +(2.36720e6 - 1.42195e6i) q^{27} -667571. q^{28} +(-2.19402e6 - 3.80015e6i) q^{29} +(-1.64559e6 - 1.93829e6i) q^{30} +(4.94392e6 - 8.56313e6i) q^{31} +(1.64546e6 - 2.85003e6i) q^{32} +(-3.37322e6 + 9.43708e6i) q^{33} +(4.03742e6 + 6.99301e6i) q^{34} -3.22736e6 q^{35} +(-2.22452e6 - 1.82323e6i) q^{36} -6.32122e6 q^{37} +(1.15959e7 + 2.00846e7i) q^{38} +(-3.64406e6 + 664268. i) q^{39} +(3.31541e6 - 5.74246e6i) q^{40} +(-2.68019e6 + 4.64223e6i) q^{41} +(-1.61759e7 + 2.94867e6i) q^{42} +(-1.12275e7 - 1.94466e7i) q^{43} +1.04384e7 q^{44} +(-1.07544e7 - 8.81438e6i) q^{45} -2.86920e6 q^{46} +(2.23644e7 + 3.87363e7i) q^{47} +(1.49036e7 - 4.16950e7i) q^{48} +(9.74159e6 - 1.68729e7i) q^{49} +(1.86511e7 - 3.23047e7i) q^{50} +(2.85801e7 + 3.36636e7i) q^{51} +(1.92903e6 + 3.34118e6i) q^{52} -4.00972e7 q^{53} +(-6.19556e7 - 3.43528e7i) q^{54} +5.04642e7 q^{55} +(-2.14398e7 - 3.71348e7i) q^{56} +(8.20848e7 + 9.66852e7i) q^{57} +(-5.62853e7 + 9.74890e7i) q^{58} +(4.79118e7 - 8.29857e7i) q^{59} +(-4.87481e6 + 1.36380e7i) q^{60} +(-1.01113e7 - 1.75132e7i) q^{61} -2.53663e8 q^{62} +(-8.41364e7 + 3.17284e7i) q^{63} +7.71659e7 q^{64} +(9.32588e6 + 1.61529e7i) q^{65} +(2.52932e8 - 4.61065e7i) q^{66} +(-9.12489e7 + 1.58048e8i) q^{67} +(2.29975e7 - 3.98328e7i) q^{68} +(-1.54367e7 + 2.81392e6i) q^{69} +(4.13974e7 + 7.17024e7i) q^{70} +1.38543e8 q^{71} +(2.99772e7 - 1.82298e8i) q^{72} -2.17970e8 q^{73} +(8.10823e7 + 1.40439e8i) q^{74} +(6.86631e7 - 1.92095e8i) q^{75} +(6.60510e7 - 1.14404e8i) q^{76} +(1.63169e8 - 2.82617e8i) q^{77} +(6.15004e7 + 7.24395e7i) q^{78} +(-1.97294e8 - 3.41722e8i) q^{79} -2.22962e8 q^{80} +(-3.67020e8 - 1.24061e8i) q^{81} +1.37515e8 q^{82} +(2.36638e8 + 4.09870e8i) q^{83} +(6.06153e7 + 7.13970e7i) q^{84} +(1.11181e8 - 1.92571e8i) q^{85} +(-2.88030e8 + 4.98883e8i) q^{86} +(-2.07211e8 + 5.79704e8i) q^{87} +(3.35240e8 + 5.80653e8i) q^{88} +2.60507e8 q^{89} +(-5.78820e7 + 3.51994e8i) q^{90} +1.20616e8 q^{91} +(8.17161e6 + 1.41537e7i) q^{92} +(-1.36474e9 + 2.48775e8i) q^{93} +(5.73736e8 - 9.93741e8i) q^{94} +(3.19323e8 - 5.53083e8i) q^{95} +(-4.54219e8 + 8.27988e7i) q^{96} +(-2.87421e8 - 4.97828e8i) q^{97} -4.99822e8 q^{98} +(1.31559e9 - 4.96118e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16}+ \cdots + 1672014609 q^{99}+O(q^{100}) \) 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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