LMFDB - Embedded newform 9.10.c.a.7.6

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			7.6
Root			$0.500000 + 9.36376i$ of defining polynomial
Character	$\chi$	$=$	9.7
Dual form			9.10.c.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.85925 - 15.3447i) q^{2} +(64.7679 + 124.451i) q^{3} +(99.0272 + 171.520i) q^{4} +(369.939 + 640.753i) q^{5} +(2483.46 + 108.703i) q^{6} +(3013.67 - 5219.83i) q^{7} +12581.1 q^{8} +(-11293.2 + 16120.9i) q^{9} +13109.5 q^{10} +(-9215.52 + 15961.8i) q^{11} +(-14932.1 + 23433.1i) q^{12} +(-58793.0 - 101832. i) q^{13} +(-53397.7 - 92487.6i) q^{14} +(-55782.3 + 87539.5i) q^{15} +(60757.3 - 105235. i) q^{16} -468308. q^{17} +(147320. + 316110. i) q^{18} +834842. q^{19} +(-73268.0 + 126904. i) q^{20} +(844803. + 36977.8i) q^{21} +(163285. + 282819. i) q^{22} +(-660262. - 1.14361e6i) q^{23} +(814852. + 1.56573e6i) q^{24} +(702853. - 1.21738e6i) q^{25} -2.08345e6 q^{26} +(-2.73771e6 - 361342. i) q^{27} +1.19374e6 q^{28} +(-32123.4 + 55639.3i) q^{29} +(849076. + 1.63150e6i) q^{30} +(-3.70875e6 - 6.42375e6i) q^{31} +(2.14423e6 + 3.71392e6i) q^{32} +(-2.58333e6 - 113075. i) q^{33} +(-4.14886e6 + 7.18604e6i) q^{34} +4.45949e6 q^{35} +(-3.88340e6 - 340612. i) q^{36} +3.68044e6 q^{37} +(7.39608e6 - 1.28104e7i) q^{38} +(8.86528e6 - 1.39123e7i) q^{39} +(4.65424e6 + 8.06138e6i) q^{40} +(1.26806e7 + 2.19634e7i) q^{41} +(8.05174e6 - 1.26356e7i) q^{42} +(-1.21419e7 + 2.10304e7i) q^{43} -3.65035e6 q^{44} +(-1.45073e7 - 1.27243e6i) q^{45} -2.33977e7 q^{46} +(-3.51686e6 + 6.09137e6i) q^{47} +(1.70317e7 + 745492. i) q^{48} +(2.01239e6 + 3.48557e6i) q^{49} +(-1.24535e7 - 2.15701e7i) q^{50} +(-3.03313e7 - 5.82816e7i) q^{51} +(1.16442e7 - 2.01684e7i) q^{52} -3.10597e7 q^{53} +(-2.97987e7 + 3.88080e7i) q^{54} -1.36367e7 q^{55} +(3.79153e7 - 6.56712e7i) q^{56} +(5.40710e7 + 1.03897e8i) q^{57} +(569179. + 985846. i) q^{58} +(7.68270e7 + 1.33068e8i) q^{59} +(-2.05388e7 - 898999. i) q^{60} +(7.75804e7 - 1.34373e8i) q^{61} -1.31427e8 q^{62} +(5.01142e7 + 1.07532e8i) q^{63} +1.38201e8 q^{64} +(4.34996e7 - 7.53435e7i) q^{65} +(-2.46215e7 + 3.86386e7i) q^{66} +(6.98640e6 + 1.21008e7i) q^{67} +(-4.63753e7 - 8.03244e7i) q^{68} +(9.95597e7 - 1.56240e8i) q^{69} +(3.95078e7 - 6.84295e7i) q^{70} -3.45182e8 q^{71} +(-1.42081e8 + 2.02819e8i) q^{72} -3.01511e8 q^{73} +(3.26059e7 - 5.64751e7i) q^{74} +(1.97027e8 + 8.62402e6i) q^{75} +(8.26721e7 + 1.43192e8i) q^{76} +(5.55451e7 + 9.62069e7i) q^{77} +(-1.34941e8 - 2.59288e8i) q^{78} +(-1.79834e8 + 3.11482e8i) q^{79} +8.99059e7 q^{80} +(-1.32346e8 - 3.64114e8i) q^{81} +4.49361e8 q^{82} +(5.25069e7 - 9.09446e7i) q^{83} +(7.73161e7 + 1.48563e8i) q^{84} +(-1.73245e8 - 3.00070e8i) q^{85} +(2.15137e8 + 3.72628e8i) q^{86} +(-9.00495e6 - 394154. i) q^{87} +(-1.15941e8 + 2.00817e8i) q^{88} +8.60555e8 q^{89} +(-1.48049e8 + 2.11337e8i) q^{90} -7.08730e8 q^{91} +(1.30768e8 - 2.26497e8i) q^{92} +(5.59236e8 - 8.77612e8i) q^{93} +(6.23135e7 + 1.07930e8i) q^{94} +(3.08840e8 + 5.34927e8i) q^{95} +(-3.23325e8 + 5.07396e8i) q^{96} +(-4.74261e7 + 8.21444e7i) q^{97} +7.13133e7 q^{98} +(-1.53245e8 - 3.28822e8i) 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 $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

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

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 $

$2$	8.85925	−	15.3447i	0.391527	−	0.678145i	−0.601124	−	0.799156i	$-0.705280\pi$
$2$	8.85925	−	15.3447i	0.391527	−	0.678145i	0.992651	+	0.121011i	$0.0386135\pi$
$3$	64.7679	+	124.451i	0.461651	+	0.887061i
$3$	64.7679	+	124.451i	0.461651	+	0.887061i
$4$	99.0272	+	171.520i	0.193413	+	0.335000i
$5$	369.939	+	640.753i	0.264707	+	0.458485i	0.967487	−	0.252922i	$-0.0813916\pi$
$5$	369.939	+	640.753i	0.264707	+	0.458485i	−0.702780	+	0.711407i	$0.748058\pi$
$6$	2483.46	+	108.703i	0.782306	+	0.0342422i
$7$	3013.67	−	5219.83i	0.474411	−	0.821703i	−0.525160	−	0.851004i	$-0.675995\pi$
$7$	3013.67	−	5219.83i	0.474411	−	0.821703i	0.999571	+	0.0293001i	$0.00932785\pi$
$8$	12581.1			1.08596
$9$	−11293.2	+	16120.9i	−0.573756	+	0.819026i
$10$	13109.5			0.414560
$11$	−9215.52	+	15961.8i	−0.189781	+	0.328711i	−0.945177	−	0.326558i	$-0.894111\pi$
$11$	−9215.52	+	15961.8i	−0.189781	+	0.328711i	0.755396	+	0.655268i	$0.227445\pi$
$12$	−14932.1	+	23433.1i	−0.207877	+	0.326222i
$13$	−58793.0	−	101832.i	−0.570927	−	0.988874i	−0.996471	−	0.0839366i	$-0.973251\pi$
$13$	−58793.0	−	101832.i	−0.570927	−	0.988874i	0.425544	−	0.904938i	$-0.360083\pi$
$14$	−53397.7	−	92487.6i	−0.371490	−	0.643439i
$15$	−55782.3	+	87539.5i	−0.284502	+	0.446471i
$16$	60757.3	−	105235.i	0.231771	−	0.401438i
$17$	−468308.			−1.35992			−0.679958	−	0.733251i	$-0.738002\pi$
$17$	−468308.			−1.35992			−0.679958	+	0.733251i	$0.738002\pi$
$18$	147320.	+	316110.i	0.330778	+	0.709761i
$19$	834842.			1.46965			0.734824	−	0.678258i	$-0.237265\pi$
$19$	834842.			1.46965			0.734824	+	0.678258i	$0.237265\pi$
$20$	−73268.0	+	126904.i	−0.102395	+	0.177354i
$21$	844803.	+	36977.8i	0.947914	+	0.0414910i
$22$	163285.	+	282819.i	0.148609	+	0.257398i
$23$	−660262.	−	1.14361e6i	−0.491973	−	0.852122i	0.507984	−	0.861366i	$-0.330391\pi$
$23$	−660262.	−	1.14361e6i	−0.491973	−	0.852122i	−0.999957	+	0.00924405i	$0.997057\pi$
$24$	814852.	+	1.56573e6i	0.501335	+	0.963313i
$25$	702853.	−	1.21738e6i	0.359861	−	0.623297i
$26$	−2.08345e6			−0.894134
$27$	−2.73771e6	−	361342.i	−0.991402	−	0.130852i
$28$	1.19374e6			0.367028
$29$	−32123.4	+	55639.3i	−0.00843394	+	0.0146080i	−0.870212	−	0.492678i	$-0.836018\pi$
$29$	−32123.4	+	55639.3i	−0.00843394	+	0.0146080i	0.861778	+	0.507286i	$0.169351\pi$
$30$	849076.	+	1.63150e6i	0.191382	+	0.367740i
$31$	−3.70875e6	−	6.42375e6i	−0.721274	−	1.24928i	−0.960489	−	0.278317i	$-0.910224\pi$
$31$	−3.70875e6	−	6.42375e6i	−0.721274	−	1.24928i	0.239215	−	0.970967i	$-0.423110\pi$
$32$	2.14423e6	+	3.71392e6i	0.361491	+	0.626121i
$33$	−2.58333e6	−	113075.i	−0.379199	−	0.0165979i
$34$	−4.14886e6	+	7.18604e6i	−0.532444	+	0.922220i
$35$	4.45949e6			0.502318
$36$	−3.88340e6	−	340612.i	−0.385346	−	0.0337986i
$37$	3.68044e6			0.322843			0.161422	−	0.986886i	$-0.448392\pi$
$37$	3.68044e6			0.322843			0.161422	+	0.986886i	$0.448392\pi$
$38$	7.39608e6	−	1.28104e7i	0.575407	−	0.996635i
$39$	8.86528e6	−	1.39123e7i	0.613623	−	0.962962i
$40$	4.65424e6	+	8.06138e6i	0.287461	+	0.497897i
$41$	1.26806e7	+	2.19634e7i	0.700827	+	1.21387i	0.968176	+	0.250269i	$0.0805190\pi$
$41$	1.26806e7	+	2.19634e7i	0.700827	+	1.21387i	−0.267349	+	0.963600i	$0.586148\pi$
$42$	8.05174e6	−	1.26356e7i	0.399271	−	0.626578i
$43$	−1.21419e7	+	2.10304e7i	−0.541601	+	0.938081i	0.457211	+	0.889358i	$0.348848\pi$
$43$	−1.21419e7	+	2.10304e7i	−0.541601	+	0.938081i	−0.998812	+	0.0487226i	$0.984485\pi$
$44$	−3.65035e6			−0.146824
$45$	−1.45073e7	−	1.27243e6i	−0.527388	−	0.0462571i
$46$	−2.33977e7			−0.770484
$47$	−3.51686e6	+	6.09137e6i	−0.105127	+	0.182085i	−0.913790	−	0.406187i	$-0.866858\pi$
$47$	−3.51686e6	+	6.09137e6i	−0.105127	+	0.182085i	0.808663	+	0.588272i	$0.200192\pi$
$48$	1.70317e7	+	745492.i	0.463098	+	0.0202702i
$49$	2.01239e6	+	3.48557e6i	0.0498690	+	0.0863757i
$50$	−1.24535e7	−	2.15701e7i	−0.281791	−	0.488076i
$51$	−3.03313e7	−	5.82816e7i	−0.627807	−	1.20633i
$52$	1.16442e7	−	2.01684e7i	0.220849	−	0.382521i
$53$	−3.10597e7			−0.540700			−0.270350	−	0.962762i	$-0.587139\pi$
$53$	−3.10597e7			−0.540700			−0.270350	+	0.962762i	$0.587139\pi$
$54$	−2.97987e7	+	3.88080e7i	−0.476898	+	0.621082i
$55$	−1.36367e7			−0.200945
$56$	3.79153e7	−	6.56712e7i	0.515191	−	0.892337i
$57$	5.40710e7	+	1.03897e8i	0.678465	+	1.30367i
$58$	569179.	+	985846.i	0.00660424	+	0.0114389i
$59$	7.68270e7	+	1.33068e8i	0.825429	+	1.42969i	0.901591	+	0.432590i	$0.142400\pi$
$59$	7.68270e7	+	1.33068e8i	0.825429	+	1.42969i	−0.0761619	+	0.997095i	$0.524267\pi$
$60$	−2.05388e7	−	898999.i	−0.204594	−	0.00895527i
$61$	7.75804e7	−	1.34373e8i	0.717410	−	1.24259i	−0.244612	−	0.969621i	$-0.578661\pi$
$61$	7.75804e7	−	1.34373e8i	0.717410	−	1.24259i	0.962023	−	0.272970i	$-0.0880060\pi$
$62$	−1.31427e8			−1.12959
$63$	5.01142e7	+	1.07532e8i	0.400801	+	0.860012i
$64$	1.38201e8			1.02968
$65$	4.34996e7	−	7.53435e7i	0.302256	−	0.523523i
$66$	−2.46215e7	+	3.86386e7i	−0.159723	+	0.250654i
$67$	6.98640e6	+	1.21008e7i	0.0423562	+	0.0733631i	0.886426	−	0.462870i	$-0.153180\pi$
$67$	6.98640e6	+	1.21008e7i	0.0423562	+	0.0733631i	−0.844070	+	0.536233i	$0.819847\pi$
$68$	−4.63753e7	−	8.03244e7i	−0.263025	−	0.455572i
$69$	9.95597e7	−	1.56240e8i	0.528765	−	0.829794i
$70$	3.95078e7	−	6.84295e7i	0.196671	−	0.340645i
$71$	−3.45182e8			−1.61207			−0.806037	−	0.591865i	$-0.798392\pi$
$71$	−3.45182e8			−1.61207			−0.806037	+	0.591865i	$0.798392\pi$
$72$	−1.42081e8	+	2.02819e8i	−0.623076	+	0.889430i
$73$	−3.01511e8			−1.24265			−0.621327	−	0.783551i	$-0.713406\pi$
$73$	−3.01511e8			−1.24265			−0.621327	+	0.783551i	$0.713406\pi$
$74$	3.26059e7	−	5.64751e7i	0.126402	−	0.218935i
$75$	1.97027e8	+	8.62402e6i	0.719033	+	0.0314727i
$76$	8.26721e7	+	1.43192e8i	0.284248	+	0.492333i
$77$	5.55451e7	+	9.62069e7i	0.180068	+	0.311888i
$78$	−1.34941e8	−	2.59288e8i	−0.412778	−	0.793152i
$79$	−1.79834e8	+	3.11482e8i	−0.519458	+	0.899728i	0.480286	+	0.877112i	$0.340533\pi$
$79$	−1.79834e8	+	3.11482e8i	−0.519458	+	0.899728i	−0.999744	+	0.0226159i	$0.992801\pi$
$80$	8.99059e7			0.245405
$81$	−1.32346e8	−	3.64114e8i	−0.341608	−	0.939843i
$82$	4.49361e8			1.09757
$83$	5.25069e7	−	9.09446e7i	0.121441	−	0.210342i	−0.798895	−	0.601470i	$-0.794582\pi$
$83$	5.25069e7	−	9.09446e7i	0.121441	−	0.210342i	0.920336	+	0.391128i	$0.127915\pi$
$84$	7.73161e7	+	1.48563e8i	0.169439	+	0.325576i
$85$	−1.73245e8	−	3.00070e8i	−0.359978	−	0.623501i
$86$	2.15137e8	+	3.72628e8i	0.424103	+	0.734569i
$87$	−9.00495e6	−	394154.i	−0.0168517	−	0.000737615i
$88$	−1.15941e8	+	2.00817e8i	−0.206095	+	0.356967i
$89$	8.60555e8			1.45386			0.726932	−	0.686710i	$-0.240946\pi$
$89$	8.60555e8			1.45386			0.726932	+	0.686710i	$0.240946\pi$
$90$	−1.48049e8	+	2.11337e8i	−0.237856	+	0.339535i
$91$	−7.08730e8			−1.08342
$92$	1.30768e8	−	2.26497e8i	0.190308	−	0.329622i
$93$	5.59236e8	−	8.77612e8i	0.775214	−	1.21655i
$94$	6.23135e7	+	1.07930e8i	0.0823202	+	0.142583i
$95$	3.08840e8	+	5.34927e8i	0.389025	+	0.673812i
$96$	−3.23325e8	+	5.07396e8i	−0.388525	+	0.609714i
$97$	−4.74261e7	+	8.21444e7i	−0.0543932	+	0.0942118i	−0.891940	−	0.452154i	$-0.850656\pi$
$97$	−4.74261e7	+	8.21444e7i	−0.0543932	+	0.0942118i	0.837547	+	0.546366i	$0.183989\pi$
$98$	7.13133e7			0.0781004
$99$	−1.53245e8	−	3.28822e8i	−0.160334	−	0.344035i
$100$	2.78406e8			0.278406
$101$	−2.38579e8	+	4.13231e8i	−0.228132	+	0.395137i	−0.957255	−	0.289247i	$-0.906595\pi$
$101$	−2.38579e8	+	4.13231e8i	−0.228132	+	0.395137i	0.729122	+	0.684383i	$0.239929\pi$
$102$	−1.16303e9	−	5.09066e7i	−1.06387	−	0.0465665i
$103$	−1.68556e8	−	2.91947e8i	−0.147563	−	0.255586i	0.782763	−	0.622319i	$-0.213809\pi$
$103$	−1.68556e8	−	2.91947e8i	−0.147563	−	0.255586i	−0.930326	+	0.366733i	$0.880476\pi$
$104$	−7.39681e8	−	1.28116e9i	−0.620004	−	1.07388i
$105$	2.88832e8	+	5.54989e8i	0.231896	+	0.445587i
$106$	−2.75166e8	+	4.76602e8i	−0.211699	+	0.366673i
$107$	−1.05652e9			−0.779203			−0.389602	−	0.920983i	$-0.627387\pi$
$107$	−1.05652e9			−0.779203			−0.389602	+	0.920983i	$0.627387\pi$
$108$	−2.09130e8	−	5.05354e8i	−0.147914	−	0.357428i
$109$	5.44814e8			0.369683			0.184841	−	0.982768i	$-0.440823\pi$
$109$	5.44814e8			0.369683			0.184841	+	0.982768i	$0.440823\pi$
$110$	−1.20811e8	+	2.09251e8i	−0.0786756	+	0.136270i
$111$	2.38374e8	+	4.58035e8i	0.149041	+	0.286382i
$112$	−3.66205e8	−	6.34285e8i	−0.219909	−	0.380893i
$113$	−5.45264e8	−	9.44426e8i	−0.314597	−	0.544897i	0.664755	−	0.747061i	$-0.268536\pi$
$113$	−5.45264e8	−	9.44426e8i	−0.314597	−	0.544897i	−0.979352	+	0.202164i	$0.935203\pi$
$114$	2.07330e9	+	9.07500e7i	1.14971	+	0.0503240i
$115$	4.88513e8	−	8.46130e8i	0.260457	−	0.451125i
$116$	−1.27244e7			−0.00652492
$117$	2.30559e9	+	2.02223e8i	1.13749	+	0.0997686i
$118$	2.72252e9			1.29271
$119$	−1.41133e9	+	2.44449e9i	−0.645158	+	1.11745i
$120$	−7.01803e8	+	1.10134e9i	−0.308958	+	0.484850i
$121$	1.00912e9	+	1.74785e9i	0.427966	+	0.741259i
$122$	−1.37461e9	−	2.38089e9i	−0.561772	−	0.973017i
$123$	−1.91208e9	+	3.00063e9i	−0.753238	+	1.18206i
$124$	7.34535e8	−	1.27225e9i	0.279007	−	0.483254i
$125$	2.48512e9			0.910443
$126$	2.09402e9	+	1.83666e8i	0.740138	+	0.0649173i
$127$	−1.90290e9			−0.649082			−0.324541	−	0.945872i	$-0.605210\pi$
$127$	−1.90290e9			−0.649082			−0.324541	+	0.945872i	$0.605210\pi$
$128$	1.26507e8	−	2.19117e8i	0.0416553	−	0.0721491i
$129$	−3.40367e9	−	1.48982e8i	−1.08217	−	0.0473673i
$130$	−7.70748e8	−	1.33497e9i	−0.236683	−	0.409947i
$131$	3.85457e8	+	6.67631e8i	0.114355	+	0.198069i	0.917522	−	0.397686i	$-0.130187\pi$
$131$	3.85457e8	+	6.67631e8i	0.114355	+	0.198069i	−0.803167	+	0.595754i	$0.796853\pi$
$132$	−2.36426e8	−	4.54291e8i	−0.0677816	−	0.130242i
$133$	2.51594e9	−	4.35773e9i	0.697217	−	1.20761i
$134$	2.47577e8			0.0663345
$135$	−7.81252e8	−	1.88787e9i	−0.202437	−	0.489181i
$136$	−5.89184e9			−1.47681
$137$	2.11984e8	−	3.67166e8i	0.0514114	−	0.0890472i	−0.839174	−	0.543862i	$-0.816961\pi$
$137$	2.11984e8	−	3.67166e8i	0.0514114	−	0.0890472i	0.890586	+	0.454815i	$0.150295\pi$
$138$	−1.51542e9	−	2.91188e9i	−0.355695	−	0.683466i
$139$	1.24855e9	+	2.16255e9i	0.283687	+	0.491359i	0.972290	−	0.233779i	$-0.0751092\pi$
$139$	1.24855e9	+	2.16255e9i	0.283687	+	0.491359i	−0.688603	+	0.725138i	$0.741776\pi$
$140$	4.41611e8	+	7.64893e8i	0.0971547	+	0.168277i
$141$	−9.85859e8	−	4.31519e7i	−0.210053	−	0.00919419i
$142$	−3.05805e9	+	5.29670e9i	−0.631171	+	1.09322i
$143$	2.16723e9			0.433404
$144$	1.01033e9	+	2.16790e9i	0.195809	+	0.420154i
$145$	−4.75347e7			−0.00893007
$146$	−2.67116e9	+	4.62659e9i	−0.486533	+	0.842700i
$147$	−3.03445e8	+	4.76198e8i	−0.0535984	+	0.0841123i
$148$	3.64463e8	+	6.31269e8i	0.0624419	+	0.108153i
$149$	−1.77396e9	−	3.07258e9i	−0.294853	−	0.510700i	0.680098	−	0.733121i	$-0.261937\pi$
$149$	−1.77396e9	−	3.07258e9i	−0.294853	−	0.510700i	−0.974951	+	0.222422i	$0.928604\pi$
$150$	1.87784e9	−	2.94691e9i	0.302864	−	0.475287i
$151$	−2.12395e9	+	3.67879e9i	−0.332466	+	0.575849i	−0.982995	−	0.183633i	$-0.941214\pi$
$151$	−2.12395e9	+	3.67879e9i	−0.332466	+	0.575849i	0.650529	+	0.759482i	$0.274547\pi$
$152$	1.05032e10			1.59598
$153$	5.28872e9	−	7.54955e9i	0.780260	−	1.11381i
$154$	1.96835e9			0.282007
$155$	2.74402e9	−	4.75279e9i	0.381852	−	0.661387i
$156$	3.26415e9	+	1.42875e8i	0.441275	+	0.0193150i
$157$	9.15878e8	+	1.58635e9i	0.120307	+	0.208377i	0.919889	−	0.392180i	$-0.128279\pi$
$157$	9.15878e8	+	1.58635e9i	0.120307	+	0.208377i	−0.799582	+	0.600557i	$0.794946\pi$
$158$	3.18639e9	+	5.51900e9i	0.406764	+	0.704536i
$159$	−2.01167e9	−	3.86542e9i	−0.249615	−	0.479634i
$160$	−1.58647e9	+	2.74785e9i	−0.191378	+	0.331477i
$161$	−7.95925e9			−0.933589
$162$	−6.75970e9	−	1.19498e9i	−0.771099	−	0.136314i
$163$	4.81775e9			0.534564			0.267282	−	0.963618i	$-0.413874\pi$
$163$	4.81775e9			0.534564			0.267282	+	0.963618i	$0.413874\pi$
$164$	−2.51144e9	+	4.34994e9i	−0.271098	+	0.469555i
$165$	−8.83221e8	−	1.69711e9i	−0.0927666	−	0.178251i
$166$	−9.30344e8	−	1.61140e9i	−0.0950949	−	0.164709i
$167$	7.53553e8	+	1.30519e9i	0.0749704	+	0.129853i	0.901073	−	0.433667i	$-0.142780\pi$
$167$	7.53553e8	+	1.30519e9i	0.0749704	+	0.129853i	−0.826103	+	0.563519i	$0.809447\pi$
$168$	1.06286e10	+	4.65221e8i	1.02940	+	0.0450576i
$169$	−1.61098e9	+	2.79030e9i	−0.151915	+	0.263124i
$170$	−6.13930e9			−0.563766
$171$	−9.42808e9	+	1.34584e10i	−0.843219	+	1.20368i
$172$	−4.80953e9			−0.419010
$173$	1.08021e10	−	1.87099e10i	0.916859	−	1.58805i	0.112703	−	0.993629i	$-0.464049\pi$
$173$	1.08021e10	−	1.87099e10i	0.916859	−	1.58805i	0.804156	−	0.594418i	$-0.202618\pi$
$174$	−8.58253e7	+	1.34686e8i	−0.00709813	+	0.0111391i
$175$	−4.23634e9	−	7.33755e9i	−0.341444	−	0.591398i
$176$	1.11982e9	+	1.93959e9i	0.0879714	+	0.152371i
$177$	−1.15846e10	+	1.81798e10i	−0.887158	+	1.39222i
$178$	7.62388e9	−	1.32049e10i	0.569227	−	0.985931i
$179$	−1.94882e10			−1.41884			−0.709418	−	0.704788i	$-0.751042\pi$
$179$	−1.94882e10			−1.41884			−0.709418	+	0.704788i	$0.751042\pi$
$180$	−1.21837e9	−	2.61430e9i	−0.0865074	−	0.185622i
$181$	7.45903e9			0.516569			0.258285	−	0.966069i	$-0.416843\pi$
$181$	7.45903e9			0.516569			0.258285	+	0.966069i	$0.416843\pi$
$182$	−6.27882e9	+	1.08752e10i	−0.424187	+	0.734713i
$183$	2.17476e10	+	9.51912e8i	1.43345	+	0.0627432i
$184$	−8.30683e9	−	1.43879e10i	−0.534263	−	0.925371i
$185$	1.36154e9	+	2.35825e9i	0.0854587	+	0.148019i
$186$	−8.51226e9	−	1.63563e10i	−0.521479	−	1.00202i
$187$	4.31571e9	−	7.47503e9i	0.258086	−	0.447018i
$188$	−1.39306e9			−0.0813315
$189$	−1.01367e10	+	1.32014e10i	−0.577854	+	0.752560i
$190$	1.09444e10			0.609256
$191$	3.28300e9	−	5.68633e9i	0.178493	−	0.309159i	−0.762872	−	0.646550i	$-0.776211\pi$
$191$	3.28300e9	−	5.68633e9i	0.178493	−	0.309159i	0.941365	+	0.337391i	$0.109544\pi$
$192$	8.95097e9	+	1.71993e10i	0.475351	+	0.913386i
$193$	9.40057e9	+	1.62823e10i	0.487693	+	0.844709i	0.999900	−	0.0141532i	$-0.00450525\pi$
$193$	9.40057e9	+	1.62823e10i	0.487693	+	0.844709i	−0.512207	+	0.858862i	$0.671172\pi$
$194$	8.40320e8	+	1.45548e9i	0.0425929	+	0.0737730i
$195$	1.21940e10	+	5.33741e8i	0.603934	+	0.0264347i
$196$	−3.98564e8	+	6.90333e8i	−0.0192906	+	0.0334123i
$197$	−1.66201e9			−0.0786206			−0.0393103	−	0.999227i	$-0.512516\pi$
$197$	−1.66201e9			−0.0786206			−0.0393103	+	0.999227i	$0.512516\pi$
$198$	−6.40331e9	−	5.61632e8i	−0.296081	−	0.0259692i
$199$	1.45345e10			0.656996			0.328498	−	0.944505i	$-0.393458\pi$
$199$	1.45345e10			0.656996			0.328498	+	0.944505i	$0.393458\pi$
$200$	8.84267e9	−	1.53160e10i	0.390795	−	0.676876i
$201$	−1.05347e9	+	1.65321e9i	−0.0455238	+	0.0714407i
$202$	4.22727e9	+	7.32185e9i	0.178640	+	0.309414i
$203$	1.93619e8	+	3.35357e8i	0.00800230	+	0.0138604i
$204$	6.99284e9	−	1.09739e10i	0.282695	−	0.443635i
$205$	−9.38206e9	+	1.62502e10i	−0.371027	+	0.642638i
$206$	−5.97312e9			−0.231099
$207$	2.58925e10	+	2.27102e9i	0.980183	+	0.0859716i
$208$	−1.42884e10			−0.529296
$209$	−7.69351e9	+	1.33255e10i	−0.278911	+	0.483089i
$210$	1.10750e10	+	4.84761e8i	0.392967	+	0.0172005i
$211$	−6.96607e8	−	1.20656e9i	−0.0241945	−	0.0419061i	0.853675	−	0.520807i	$-0.174369\pi$
$211$	−6.96607e8	−	1.20656e9i	−0.0241945	−	0.0419061i	−0.877869	+	0.478901i	$0.841035\pi$
$212$	−3.07576e9	−	5.32737e9i	−0.104578	−	0.181135i
$213$	−2.23567e10	−	4.29583e10i	−0.744216	−	1.43001i
$214$	−9.35998e9	+	1.62120e10i	−0.305079	+	0.528413i
$215$	−1.79671e10			−0.573462
$216$	−3.44434e10	−	4.54609e9i	−1.07662	−	0.142101i
$217$	−4.47078e10			−1.36872
$218$	4.82665e9	−	8.36000e9i	0.144741	−	0.250699i
$219$	−1.95282e10	−	3.75234e10i	−0.573673	−	1.10231i
$220$	−1.35041e9	−	2.33897e9i	−0.0388653	−	0.0673167i
$221$	2.75333e10	+	4.76890e10i	0.776412	+	1.34479i
$222$	9.14022e9	+	4.00075e8i	0.252562	+	0.0110549i
$223$	1.43684e10	−	2.48867e10i	0.389077	−	0.673900i	−0.603249	−	0.797553i	$-0.706127\pi$
$223$	1.43684e10	−	2.48867e10i	0.389077	−	0.673900i	0.992326	+	0.123653i	$0.0394608\pi$
$224$	2.58481e10			0.685981
$225$	1.16877e10	+	2.50788e10i	0.304024	+	0.652356i
$226$	−1.93225e10			−0.492693
$227$	1.92088e10	−	3.32705e10i	0.480157	−	0.831656i	−0.519584	−	0.854419i	$-0.673913\pi$
$227$	1.92088e10	−	3.32705e10i	0.480157	−	0.831656i	0.999741	+	0.0227637i	$0.00724652\pi$
$228$	−1.24660e10	+	1.95629e10i	−0.305506	+	0.479432i
$229$	6.69528e9	+	1.15966e10i	0.160883	+	0.278657i	0.935185	−	0.354158i	$-0.115233\pi$
$229$	6.69528e9	+	1.15966e10i	0.160883	+	0.278657i	−0.774303	+	0.632815i	$0.781899\pi$
$230$	−8.65573e9	−	1.49922e10i	−0.203952	−	0.353255i
$231$	−8.37554e9	+	1.31438e10i	−0.193535	+	0.303715i
$232$	−4.04148e8	+	7.00004e8i	−0.00915892	+	0.0158637i
$233$	4.50134e10			1.00055			0.500276	−	0.865866i	$-0.333232\pi$
$233$	4.50134e10			1.00055			0.500276	+	0.865866i	$0.333232\pi$
$234$	2.35289e10	−	3.35870e10i	0.513015	−	0.732319i
$235$	−5.20409e9			−0.111311
$236$	−1.52159e10	+	2.63548e10i	−0.319297	+	0.553038i
$237$	−5.04118e10	−	2.20657e9i	−1.03792	−	0.0454307i
$238$	2.50066e10	+	4.33127e10i	0.505194	+	0.875022i
$239$	3.27972e10	+	5.68064e10i	0.650199	+	1.12618i	0.983074	+	0.183207i	$0.0586478\pi$
$239$	3.27972e10	+	5.68064e10i	0.650199	+	1.12618i	−0.332876	+	0.942971i	$0.608019\pi$
$240$	5.82301e9	+	1.11889e10i	0.113291	+	0.217689i
$241$	−1.34067e10	+	2.32210e10i	−0.256002	+	0.443409i	−0.965167	−	0.261634i	$-0.915739\pi$
$241$	−1.34067e10	+	2.32210e10i	−0.256002	+	0.443409i	0.709165	+	0.705043i	$0.249072\pi$
$242$	3.57603e10			0.670242
$243$	3.67427e10	−	4.00535e10i	0.675994	−	0.736907i
$244$	3.07303e10			0.555025
$245$	−1.48893e9	+	2.57889e9i	−0.0264013	+	0.0457284i
$246$	2.91042e10	+	5.59236e10i	0.506696	+	0.973614i
$247$	−4.90829e10	−	8.50140e10i	−0.839061	−	1.45330i
$248$	−4.66602e10	−	8.08179e10i	−0.783275	−	1.35667i
$249$	1.47189e10	+	6.44260e8i	0.242649	+	0.0106210i
$250$	2.20163e10	−	3.81334e10i	0.356464	−	0.617413i
$251$	−4.29625e10			−0.683216			−0.341608	−	0.939842i	$-0.610972\pi$
$251$	−4.29625e10			−0.683216			−0.341608	+	0.939842i	$0.610972\pi$
$252$	−1.34812e10	+	1.92442e10i	−0.210585	+	0.300605i
$253$	2.43387e10			0.373469
$254$	−1.68583e10	+	2.91994e10i	−0.254133	+	0.440172i
$255$	2.61233e10	−	4.09955e10i	0.386899	−	0.607163i
$256$	3.31379e10	+	5.73965e10i	0.482219	+	0.835229i
$257$	−4.72752e10	−	8.18831e10i	−0.675981	−	1.17083i	−0.976181	−	0.216958i	$-0.930387\pi$
$257$	−4.72752e10	−	8.18831e10i	−0.675981	−	1.17083i	0.300200	−	0.953876i	$-0.402947\pi$
$258$	−3.24401e10	+	5.09084e10i	−0.455820	+	0.715320i
$259$	1.10916e10	−	1.92113e10i	0.153160	−	0.265281i
$260$	1.72306e10			0.233841
$261$	−5.34179e8	−	1.14621e9i	−0.00712532	−	0.0152890i
$262$	1.36594e10			0.179092
$263$	−5.62344e10	+	9.74008e10i	−0.724771	+	1.25534i	0.234297	+	0.972165i	$0.424721\pi$
$263$	−5.62344e10	+	9.74008e10i	−0.724771	+	1.25534i	−0.959068	+	0.283176i	$0.908612\pi$
$264$	−3.25012e10	−	1.42260e9i	−0.411795	−	0.0180246i
$265$	−1.14902e10	−	1.99016e10i	−0.143127	−	0.247903i
$266$	−4.45787e10	−	7.72125e10i	−0.545959	−	0.945628i
$267$	5.57363e10	+	1.07097e11i	0.671178	+	1.28967i
$268$	−1.38369e9	+	2.39662e9i	−0.0163844	+	0.0283787i
$269$	−1.11208e11			−1.29494			−0.647472	−	0.762089i	$-0.724174\pi$
$269$	−1.11208e11			−1.29494			−0.647472	+	0.762089i	$0.724174\pi$
$270$	−3.58900e10	−	4.73703e9i	−0.410995	−	0.0542461i
$271$	1.30075e10			0.146498			0.0732491	−	0.997314i	$-0.476663\pi$
$271$	1.30075e10			0.146498			0.0732491	+	0.997314i	$0.476663\pi$
$272$	−2.84531e10	+	4.92823e10i	−0.315188	+	0.545922i
$273$	−4.59030e10	−	8.82024e10i	−0.500160	−	0.961056i
$274$	−3.75603e9	−	6.50564e9i	−0.0402580	−	0.0697288i
$275$	1.29543e10	+	2.24375e10i	0.136590	+	0.236580i
$276$	3.66574e10	+	1.60452e9i	0.380251	+	0.0166439i
$277$	−2.12715e10	+	3.68434e10i	−0.217090	+	0.376011i	−0.953917	−	0.300070i	$-0.902990\pi$
$277$	−2.12715e10	+	3.68434e10i	−0.217090	+	0.376011i	0.736827	+	0.676081i	$0.236323\pi$
$278$	4.42448e10			0.444284
$279$	1.45440e11	+	1.27565e10i	1.43703	+	0.126042i
$280$	5.61053e10			0.545498
$281$	6.91828e10	−	1.19828e11i	0.661941	−	1.14652i	−0.318164	−	0.948036i	$-0.603066\pi$
$281$	6.91828e10	−	1.19828e11i	0.661941	−	1.14652i	0.980105	−	0.198480i	$-0.0636005\pi$
$282$	−9.39612e9	+	1.47454e10i	−0.0884765	+	0.138847i
$283$	−4.40394e10	−	7.62785e10i	−0.408134	−	0.706909i	0.586547	−	0.809915i	$-0.300487\pi$
$283$	−4.40394e10	−	7.62785e10i	−0.408134	−	0.706909i	−0.994681	+	0.103007i	$0.967154\pi$
$284$	−3.41824e10	−	5.92056e10i	−0.311795	−	0.540046i
$285$	−4.65694e10	+	7.30817e10i	−0.418118	+	0.656156i
$286$	1.92001e10	−	3.32555e10i	0.169690	−	0.293911i
$287$	1.52860e11			1.32992
$288$	−8.40871e10	−	7.37526e9i	−0.720217	−	0.0631700i
$289$	1.00725e11			0.849370
$290$	−4.21122e8	+	7.29405e8i	−0.00349637	+	0.00605589i
$291$	−1.32947e10	−	5.81919e8i	−0.108682	−	0.00475712i
$292$	−2.98578e10	−	5.17152e10i	−0.240345	−	0.416289i
$293$	7.58720e10	+	1.31414e11i	0.601419	+	1.04169i	0.992606	+	0.121377i	$0.0387310\pi$
$293$	7.58720e10	+	1.31414e11i	0.601419	+	1.04169i	−0.391188	+	0.920311i	$0.627936\pi$
$294$	4.61881e9	+	8.87503e9i	0.0360551	+	0.0692798i
$295$	−5.68425e10	+	9.84542e10i	−0.436993	+	0.756894i
$296$	4.63040e10			0.350595
$297$	3.09970e10	−	4.03686e10i	0.231162	−	0.301051i
$298$	−6.28638e10			−0.461772
$299$	−7.76376e10	+	1.34472e11i	−0.561761	+	0.972999i
$300$	1.80318e10	+	3.46480e10i	0.128527	+	0.246964i
$301$	7.31835e10	+	1.26758e11i	0.513883	+	0.890071i
$302$	3.76332e10	+	6.51826e10i	0.260339	+	0.450921i
$303$	−6.68795e10	−	2.92737e9i	−0.455828	−	0.0199520i
$304$	5.07227e10	−	8.78544e10i	0.340621	−	0.589973i
$305$	1.14800e11			0.759613
$306$	−6.89913e10	−	1.48037e11i	−0.449829	−	0.965215i
$307$	−1.76213e11			−1.13218			−0.566089	−	0.824344i	$-0.691544\pi$
$307$	−1.76213e11			−1.13218			−0.566089	+	0.824344i	$0.691544\pi$
$308$	−1.10010e10	+	1.90542e10i	−0.0696550	+	0.120646i
$309$	2.54162e10	−	3.98858e10i	0.158598	−	0.248889i
$310$	−4.86200e10	−	8.42123e10i	−0.299011	−	0.517902i
$311$	−4.99482e10	−	8.65128e10i	−0.302760	−	0.524395i	0.674000	−	0.738731i	$-0.264575\pi$
$311$	−4.99482e10	−	8.65128e10i	−0.302760	−	0.524395i	−0.976760	+	0.214336i	$0.931241\pi$
$312$	1.11535e11	−	1.75033e11i	0.666370	−	1.04574i
$313$	−9.17125e10	+	1.58851e11i	−0.540106	+	0.935491i	0.458791	+	0.888544i	$0.348283\pi$
$313$	−9.17125e10	+	1.58851e11i	−0.540106	+	0.935491i	−0.998897	+	0.0469470i	$0.985051\pi$
$314$	3.24560e10			0.188413
$315$	−5.03621e10	+	7.18910e10i	−0.288208	+	0.411412i
$316$	−7.12340e10			−0.401879
$317$	1.29176e11	−	2.23739e11i	0.718479	−	1.24444i	−0.243123	−	0.969995i	$-0.578172\pi$
$317$	1.29176e11	−	2.23739e11i	0.718479	−	1.24444i	0.961602	−	0.274447i	$-0.0884947\pi$
$318$	−7.71356e10	−	3.37629e9i	−0.422993	−	0.0185147i
$319$	−5.92068e8	−	1.02549e9i	−0.00320120	−	0.00554465i
$320$	5.11258e10	+	8.85525e10i	0.272562	+	0.472091i
$321$	−6.84286e10	−	1.31485e11i	−0.359720	−	0.691201i
$322$	−7.05130e10	+	1.22132e11i	−0.365526	+	0.633109i
$323$	−3.90964e11			−1.99860
$324$	4.93471e10	−	5.87572e10i	0.248776	−	0.296216i
$325$	−1.65291e11			−0.821817
$326$	4.26816e10	−	7.39268e10i	0.209296	−	0.362512i
$327$	3.52865e10	+	6.78028e10i	0.170665	+	0.327931i
$328$	1.59535e11	+	2.76324e11i	0.761071	+	1.31821i
$329$	2.11973e10	+	3.67148e10i	0.0997468	+	0.172766i
$330$	−3.38662e10	−	1.48235e9i	−0.157201	−	0.00688080i
$331$	1.41624e11	−	2.45301e11i	0.648503	−	1.12324i	−0.334978	−	0.942226i	$-0.608729\pi$
$331$	1.41624e11	−	2.45301e11i	0.648503	−	1.12324i	0.983481	−	0.181014i	$-0.0579379\pi$
$332$	2.07984e10			0.0939528
$333$	−4.15641e10	+	5.93319e10i	−0.185233	+	0.264417i
$334$	2.67037e10			0.117412
$335$	−5.16908e9	+	8.95311e9i	−0.0224239	+	0.0388394i
$336$	5.52193e10	−	8.66560e10i	0.236355	−	0.370913i
$337$	1.49793e11	+	2.59450e11i	0.632642	+	1.09577i	0.987010	+	0.160662i	$0.0513628\pi$
$337$	1.49793e11	+	2.59450e11i	0.632642	+	1.09577i	−0.354368	+	0.935106i	$0.615304\pi$
$338$	2.85442e10	+	4.94399e10i	0.118958	+	0.206041i
$339$	8.22194e10	−	1.29027e11i	0.338124	−	0.530619i
$340$	3.43120e10	−	5.94302e10i	0.139249	−	0.241186i
$341$	1.36712e11			0.547537
$342$	1.22989e11	+	2.63902e11i	0.486126	+	1.04310i
$343$	2.67484e11			1.04345
$344$	−1.52759e11	+	2.64586e11i	−0.588157	+	1.01872i
$345$	1.36942e11	+	5.99406e9i	0.520416	+	0.0227790i
$346$	−1.91398e11	−	3.31511e11i	−0.717951	−	1.24353i
$347$	2.73670e10	+	4.74010e10i	0.101332	+	0.175511i	0.912233	−	0.409671i	$-0.134356\pi$
$347$	2.73670e10	+	4.74010e10i	0.101332	+	0.175511i	−0.810902	+	0.585182i	$0.801023\pi$
$348$	−8.24130e8	−	1.58356e9i	−0.00301224	−	0.00578800i
$349$	1.52107e11	−	2.63458e11i	0.548828	−	0.950598i	−0.449527	−	0.893267i	$-0.648408\pi$
$349$	1.52107e11	−	2.63458e11i	0.548828	−	0.950598i	0.998355	−	0.0573311i	$-0.0182591\pi$
$350$	−1.50123e11			−0.534738
$351$	1.24161e11	+	3.00032e11i	0.436621	+	1.05508i
$352$	−7.90410e10			−0.274417
$353$	2.65017e11	−	4.59022e11i	0.908421	−	1.57343i	0.0921629	−	0.995744i	$-0.470622\pi$
$353$	2.65017e11	−	4.59022e11i	0.908421	−	1.57343i	0.816258	−	0.577687i	$-0.196045\pi$
$354$	1.76332e11	+	3.38821e11i	0.596782	+	1.14672i
$355$	−1.27696e11	−	2.21176e11i	−0.426727	−	0.739112i
$356$	8.52184e10	+	1.47603e11i	0.281195	+	0.487045i
$357$	−3.95629e11	−	1.73170e10i	−1.28908	−	0.0564242i
$358$	−1.72651e11	+	2.99039e11i	−0.555513	+	0.962177i
$359$	−4.60506e11			−1.46322			−0.731611	−	0.681722i	$-0.761231\pi$
$359$	−4.60506e11			−1.46322			−0.731611	+	0.681722i	$0.761231\pi$
$360$	−1.82518e11	−	1.60086e10i	−0.572723	−	0.0502334i
$361$	3.74274e11			1.15986
$362$	6.60814e10	−	1.14456e11i	0.202251	−	0.350309i
$363$	−1.52164e11	+	2.38791e11i	−0.459971	+	0.721836i
$364$	−7.01836e10	−	1.21562e11i	−0.209546	−	0.362944i
$365$	−1.11541e11	−	1.93194e11i	−0.328939	−	0.569738i
$366$	2.07275e11	−	3.25277e11i	0.603783	−	0.947520i
$367$	2.26386e11	−	3.92112e11i	0.651407	−	1.12827i	−0.331374	−	0.943499i	$-0.607512\pi$
$367$	2.26386e11	−	3.92112e11i	0.651407	−	1.12827i	0.982782	−	0.184771i	$-0.0591544\pi$
$368$	−1.60463e11			−0.456100
$369$	−4.97274e11	−	4.36158e10i	−1.39629	−	0.122469i
$370$	4.82488e10			0.133838
$371$	−9.36038e10	+	1.62127e11i	−0.256514	+	0.444295i
$372$	2.05908e11	+	9.01275e9i	0.557480	+	0.0244014i
$373$	5.05651e10	+	8.75814e10i	0.135257	+	0.234273i	0.925696	−	0.378269i	$-0.123481\pi$
$373$	5.05651e10	+	8.75814e10i	0.135257	+	0.234273i	−0.790438	+	0.612542i	$0.790147\pi$
$374$	−7.64679e10	−	1.32446e11i	−0.202096	−	0.350040i
$375$	1.60956e11	+	3.09277e11i	0.420307	+	0.807619i
$376$	−4.42459e10	+	7.66362e10i	−0.114164	+	0.197737i
$377$	7.55452e9			0.0192606
$378$	1.12768e11	+	2.72499e11i	0.284100	+	0.686517i
$379$	−5.06871e11			−1.26189			−0.630944	−	0.775829i	$-0.717332\pi$
$379$	−5.06871e11			−1.26189			−0.630944	+	0.775829i	$0.717332\pi$
$380$	−6.11672e10	+	1.05945e11i	−0.150485	+	0.260647i
$381$	−1.23247e11	−	2.36819e11i	−0.299650	−	0.575776i
$382$	−5.81699e10	−	1.00753e11i	−0.139770	−	0.242088i
$383$	1.48470e11	+	2.57157e11i	0.352569	+	0.610667i	0.986699	−	0.162560i	$-0.0519750\pi$
$383$	1.48470e11	+	2.57157e11i	0.352569	+	0.610667i	−0.634130	+	0.773226i	$0.718642\pi$
$384$	3.54630e10	+	1.55225e9i	0.0832310	+	0.00364309i
$385$	−4.10966e10	+	7.11813e10i	−0.0953306	+	0.165117i
$386$	3.33128e11			0.763781
$387$	−2.01908e11	−	4.33241e11i	−0.457566	−	0.981815i
$388$	−1.87859e10			−0.0420813
$389$	2.64170e10	−	4.57556e10i	0.0584939	−	0.101314i	−0.835296	−	0.549801i	$-0.814704\pi$
$389$	2.64170e10	−	4.57556e10i	0.0584939	−	0.101314i	0.893790	+	0.448487i	$0.148037\pi$
$390$	1.16220e11	−	1.82384e11i	0.254383	−	0.399205i
$391$	3.09206e11	+	5.35561e11i	0.669042	+	1.15881i
$392$	2.53182e10	+	4.38523e10i	0.0541558	+	0.0938005i
$393$	−5.81223e10	+	9.12116e10i	−0.122907	+	0.192878i
$394$	−1.47242e10	+	2.55030e10i	−0.0307821	+	0.0533162i
$395$	−2.66111e11			−0.550016
$396$	4.12243e10	−	5.88469e10i	0.0842413	−	0.120253i
$397$	4.35046e11			0.878978			0.439489	−	0.898248i	$-0.355160\pi$
$397$	4.35046e11			0.878978			0.439489	+	0.898248i	$0.355160\pi$
$398$	1.28765e11	−	2.23028e11i	0.257232	−	0.445539i
$399$	7.05278e11	+	3.08706e10i	1.39310	+	0.0609771i
$400$	−8.54069e10	−	1.47929e11i	−0.166810	−	0.288924i
$401$	−2.02055e10	−	3.49970e10i	−0.0390230	−	0.0675897i	0.845854	−	0.533414i	$-0.179091\pi$
$401$	−2.02055e10	−	3.49970e10i	−0.0390230	−	0.0675897i	−0.884877	+	0.465824i	$0.845758\pi$
$402$	1.60351e10	+	3.08113e10i	0.0306234	+	0.0588427i
$403$	−4.36097e11	+	7.55343e11i	−0.823589	+	1.42650i
$404$	−9.45034e10			−0.176495
$405$	1.84347e11	−	2.19501e11i	0.340478	−	0.405405i
$406$	6.86126e9			0.0125325
$407$	−3.39172e10	+	5.87462e10i	−0.0612695	+	0.106122i
$408$	−3.81602e11	−	7.33247e11i	−0.681773	−	1.31002i
$409$	−1.20679e11	−	2.09022e11i	−0.213244	−	0.369349i	0.739484	−	0.673174i	$-0.235069\pi$
$409$	−1.20679e11	−	2.09022e11i	−0.213244	−	0.369349i	−0.952728	+	0.303825i	$0.901736\pi$
$410$	1.66236e11	+	2.87929e11i	0.290535	+	0.503221i
$411$	5.94240e10	+	2.60104e9i	0.102724	+	0.00449634i
$412$	3.33833e10	−	5.78215e10i	0.0570809	−	0.0988671i
$413$	9.26125e11			1.56637
$414$	2.64236e11	−	3.77192e11i	0.442070	−	0.631046i
$415$	7.76973e10			0.128585
$416$	2.52132e11	−	4.36705e11i	0.412770	−	0.714938i
$417$	−1.88266e11	+	2.95447e11i	−0.304902	+	0.478484i
$418$	1.36318e11	+	2.36109e11i	0.218403	+	0.378285i
$419$	1.87685e11	+	3.25080e11i	0.297486	+	0.515262i	0.975560	−	0.219732i	$-0.0705184\pi$
$419$	1.87685e11	+	3.25080e11i	0.297486	+	0.515262i	−0.678074	+	0.734994i	$0.737185\pi$
$420$	−6.65897e10	+	1.04500e11i	−0.104420	+	0.163867i
$421$	−3.63197e11	+	6.29075e11i	−0.563472	+	0.975962i	0.433718	+	0.901049i	$0.357201\pi$
$421$	−3.63197e11	+	6.29075e11i	−0.563472	+	0.975962i	−0.997190	+	0.0749136i	$0.976132\pi$
$422$	−2.46857e10			−0.0378912
$423$	−5.84817e10	−	1.25486e11i	−0.0888154	−	0.190574i
$424$	−3.90766e11			−0.587179
$425$	−3.29152e11	+	5.70108e11i	−0.489380	+	0.847632i
$426$	−8.57245e11	−	3.75223e10i	−1.26114	−	0.0552010i
$427$	−4.67603e11	−	8.09913e11i	−0.680694	−	1.17900i
$428$	−1.04624e11	−	1.81215e11i	−0.150708	−	0.261033i
$429$	1.40367e11	+	2.69715e11i	0.200082	+	0.384456i
$430$	−1.59175e11	+	2.75699e11i	−0.224526	+	0.388890i
$431$	8.99614e11			1.25576			0.627882	−	0.778308i	$-0.283922\pi$
$431$	8.99614e11			1.25576			0.627882	+	0.778308i	$0.283922\pi$
$432$	−2.04361e11	+	2.66147e11i	−0.282307	+	0.367659i
$433$	−7.77024e11			−1.06228			−0.531140	−	0.847284i	$-0.678236\pi$
$433$	−7.77024e11			−1.06228			−0.531140	+	0.847284i	$0.678236\pi$
$434$	−3.96078e11	+	6.86027e11i	−0.535892	+	0.928191i
$435$	−3.07872e9	−	5.91576e9i	−0.00412258	−	0.00792152i
$436$	5.39515e10	+	9.34467e10i	0.0715013	+	0.123844i
$437$	−5.51215e11	−	9.54732e11i	−0.723027	−	1.25232i
$438$	−7.48790e11	−	3.27752e10i	−0.972135	−	0.0425512i
$439$	7.63494e11	−	1.32241e12i	0.981104	−	1.69932i	0.322994	−	0.946401i	$-0.395311\pi$
$439$	7.63494e11	−	1.32241e12i	0.981104	−	1.69932i	0.658110	−	0.752921i	$-0.271356\pi$
$440$	−1.71565e11			−0.218218
$441$	−7.89170e10	−	6.92179e9i	−0.0993566	−	0.00871454i
$442$	9.75696e11			1.21595
$443$	−1.39049e11	+	2.40841e11i	−0.171535	+	0.297107i	−0.938957	−	0.344036i	$-0.888206\pi$
$443$	−1.39049e11	+	2.40841e11i	−0.171535	+	0.297107i	0.767422	+	0.641143i	$0.221539\pi$
$444$	−5.49567e10	+	8.62439e10i	−0.0671116	+	0.105319i
$445$	3.18353e11	+	5.51403e11i	0.384847	+	0.666575i
$446$	−2.54586e11	−	4.40956e11i	−0.304668	−	0.527701i
$447$	2.67492e11	−	4.19776e11i	0.316903	−	0.497318i
$448$	4.16491e11	−	7.21384e11i	0.488489	−	0.846088i
$449$	3.39438e11			0.394141			0.197071	−	0.980389i	$-0.436857\pi$
$449$	3.39438e11			0.394141			0.197071	+	0.980389i	$0.436857\pi$
$450$	4.88370e11	+	4.28348e10i	0.561426	+	0.0492425i
$451$	−4.67432e11			−0.532015
$452$	1.07992e11	−	1.87048e11i	0.121694	−	0.210780i
$453$	−5.95393e11	−	2.60609e10i	−0.664297	−	0.0290768i
$454$	−3.40350e11	−	5.89504e11i	−0.375989	−	0.651232i
$455$	−2.62187e11	−	4.54121e11i	−0.286787	−	0.496730i
$456$	6.80273e11	+	1.30714e12i	0.736786	+	1.41573i
$457$	−4.10189e11	+	7.10468e11i	−0.439907	+	0.761942i	−0.997682	−	0.0680509i	$-0.978322\pi$
$457$	−4.10189e11	+	7.10468e11i	−0.439907	+	0.761942i	0.557775	+	0.829992i	$0.311655\pi$
$458$	2.37261e11			0.251960
$459$	1.28209e12	+	1.69220e11i	1.34822	+	0.177948i
$460$	1.93504e11			0.201503
$461$	−4.95721e11	+	8.58613e11i	−0.511190	+	0.885408i	0.488725	+	0.872438i	$0.337462\pi$
$461$	−4.95721e11	+	8.58613e11i	−0.511190	+	0.885408i	−0.999916	+	0.0129702i	$0.995871\pi$
$462$	1.27486e11	+	2.44964e11i	0.130189	+	0.250157i
$463$	2.46462e11	+	4.26884e11i	0.249250	+	0.431713i	0.963318	−	0.268363i	$-0.0864827\pi$
$463$	2.46462e11	+	4.26884e11i	0.249250	+	0.431713i	−0.714068	+	0.700076i	$0.753149\pi$
$464$	3.90346e9	+	6.76099e9i	0.00390948	+	0.00677141i
$465$	7.69215e11	+	3.36692e10i	0.762973	+	0.0333960i
$466$	3.98785e11	−	6.90716e11i	0.391744	−	0.678520i
$467$	−9.59285e11			−0.933301			−0.466650	−	0.884442i	$-0.654539\pi$
$467$	−9.59285e11			−0.933301			−0.466650	+	0.884442i	$0.654539\pi$
$468$	1.93631e11	+	4.15481e11i	0.186582	+	0.400355i
$469$	8.42188e10			0.0803769
$470$	−4.61043e10	+	7.98550e10i	−0.0435814	+	0.0754852i
$471$	−1.38104e11	+	2.16727e11i	−0.129304	+	0.202917i
$472$	9.66568e11	+	1.67415e12i	0.896383	+	1.55258i
$473$	−2.23788e11	−	3.87613e11i	−0.205571	−	0.356060i
$474$	−4.80470e11	+	7.54005e11i	−0.437184	+	0.686075i
$475$	5.86772e11	−	1.01632e12i	0.528869	−	0.916027i
$476$	−5.59039e11			−0.499127
$477$	3.50765e11	−	5.00711e11i	0.310230	−	0.442847i
$478$	1.16223e12			1.01828
$479$	5.29978e10	−	9.17948e10i	0.0459989	−	0.0796725i	−0.842109	−	0.539307i	$-0.818686\pi$
$479$	5.29978e10	−	9.17948e10i	0.0459989	−	0.0796725i	0.888108	+	0.459634i	$0.152020\pi$
$480$	−4.44726e11	−	1.94660e10i	−0.382390	−	0.0167375i
$481$	−2.16384e11	−	3.74788e11i	−0.184320	−	0.319251i
$482$	2.37546e11	+	4.11442e11i	0.200464	+	0.347214i
$483$	−5.15504e11	−	9.90539e11i	−0.430993	−	0.828151i
$484$	−1.99861e11	+	3.46170e11i	−0.165548	+	0.286738i
$485$	−7.01790e10			−0.0575929
$486$	−2.89095e11	−	9.18650e11i	−0.235059	−	0.746942i
$487$	−4.79462e11			−0.386255			−0.193127	−	0.981174i	$-0.561863\pi$
$487$	−4.79462e11			−0.386255			−0.193127	+	0.981174i	$0.561863\pi$
$488$	9.76047e11	−	1.69056e12i	0.779079	−	1.34940i
$489$	3.12035e11	+	5.99575e11i	0.246782	+	0.474191i
$490$	2.63815e10	+	4.56942e10i	0.0206737	+	0.0358079i
$491$	−6.09225e11	−	1.05521e12i	−0.473054	−	0.819354i	0.526470	−	0.850194i	$-0.323515\pi$
$491$	−6.09225e11	−	1.05521e12i	−0.473054	−	0.819354i	−0.999524	+	0.0308399i	$0.990182\pi$
$492$	−7.04017e11	−	3.08154e10i	−0.541677	−	0.0237096i
$493$	1.50437e10	−	2.60564e10i	0.0114694	−	0.0198657i
$494$	−1.73935e12			−1.31406
$495$	1.54003e11	−	2.19836e11i	0.115294	−	0.164579i
$496$	−9.01335e11			−0.668680
$497$	−1.04026e12	+	1.80179e12i	−0.764785	+	1.32465i
$498$	1.40285e11	−	2.20150e11i	0.102206	−	0.160393i
$499$	−9.38654e11	−	1.62580e12i	−0.677724	−	1.17385i	−0.975665	−	0.219269i	$-0.929633\pi$
$499$	−9.38654e11	−	1.62580e12i	−0.677724	−	1.17385i	0.297940	−	0.954585i	$-0.403700\pi$
$500$	2.46095e11	+	4.26249e11i	0.176091	+	0.304999i
$501$	−1.13627e11	+	1.78315e11i	−0.0805770	+	0.126450i
$502$	−3.80616e11	+	6.59246e11i	−0.267498	+	0.463320i
$503$	1.91484e12			1.33375			0.666877	−	0.745168i	$-0.267630\pi$
$503$	1.91484e12			1.33375			0.666877	+	0.745168i	$0.267630\pi$
$504$	6.30492e11	+	1.35287e12i	0.435253	+	0.933939i
$505$	−3.53039e11			−0.241552
$506$	2.15622e11	−	3.73469e11i	0.146223	−	0.253266i
$507$	−4.51596e11	−	1.97667e10i	−0.303539	−	0.0132862i
$508$	−1.88439e11	−	3.26386e11i	−0.125541	−	0.217443i
$509$	6.73207e11	+	1.16603e12i	0.444548	+	0.769979i	0.998021	−	0.0628880i	$-0.0200311\pi$
$509$	6.73207e11	+	1.16603e12i	0.444548	+	0.769979i	−0.553473	+	0.832867i	$0.686698\pi$
$510$	−3.97630e11	−	7.64044e11i	−0.260263	−	0.500095i
$511$	−9.08654e11	+	1.57384e12i	−0.589528	+	1.02109i
$512$	1.30385e12			0.838519
$513$	−2.28555e12	−	3.01664e11i	−1.45701	−	0.192307i
$514$	−1.67529e12			−1.05866
$515$	1.24711e11	−	2.16005e11i	0.0781216	−	0.135311i
$516$	−3.11503e11	−	5.98552e11i	−0.193436	−	0.371688i
$517$	−6.48194e10	−	1.12270e11i	−0.0399022	−	0.0691127i
$518$	−1.96527e11	−	3.40395e11i	−0.119933	−	0.207730i
$519$	3.02810e12	+	1.32542e11i	1.83196	+	0.0801866i
$520$	5.47273e11	−	9.47905e11i	0.328238	−	0.568525i
$521$	1.22696e12			0.729557			0.364778	−	0.931094i	$-0.381145\pi$
$521$	1.22696e12			0.729557			0.364778	+	0.931094i	$0.381145\pi$
$522$	−2.23206e10	−	1.95773e9i	−0.0131580	−	0.00115408i
$523$	2.16646e12			1.26617			0.633087	−	0.774080i	$-0.281787\pi$
$523$	2.16646e12			1.26617			0.633087	+	0.774080i	$0.281787\pi$
$524$	−7.63414e10	+	1.32227e11i	−0.0442354	+	0.0766179i
$525$	6.38789e11	−	1.00245e12i	0.366978	−	0.575901i
$526$	9.96389e11	+	1.72580e12i	0.567536	+	0.983001i
$527$	1.73684e12	+	3.00830e12i	0.980872	+	1.69892i
$528$	−1.68856e11	+	2.64986e11i	−0.0945502	+	0.148378i
$529$	2.86834e10	−	4.96811e10i	0.0159250	−	0.0275829i
$530$	−4.07178e11			−0.224152
$531$	−3.01280e12	−	2.64252e11i	−1.64454	−	0.144243i
$532$	9.96586e11			0.539402
$533$	1.49106e12	−	2.58258e12i	0.800242	−	1.38606i
$534$	2.13715e12	+	9.35450e10i	1.13737	+	0.0497835i
$535$	−3.90848e11	−	6.76968e11i	−0.206260	−	0.357253i
$536$	8.78967e10	+	1.52242e11i	0.0459971	+	0.0796694i
$537$	−1.26221e12	−	2.42533e12i	−0.655007	−	1.25859i
$538$	−9.85221e11	+	1.70645e12i	−0.507006	+	0.878161i
$539$	−7.41811e10			−0.0378568
$540$	2.46442e11	−	3.20951e11i	0.124722	−	0.162430i
$541$	−1.66976e12			−0.838041			−0.419021	−	0.907977i	$-0.637626\pi$
$541$	−1.66976e12			−0.838041			−0.419021	+	0.907977i	$0.637626\pi$
$542$	1.15237e11	−	1.99596e11i	0.0573580	−	0.0993470i
$543$	4.83105e11	+	9.28285e11i	0.238475	+	0.458229i
$544$	−1.00416e12	−	1.73926e12i	−0.491597	−	0.851471i
$545$	2.01548e11	+	3.49091e11i	0.0978575	+	0.169494i
$546$	−1.76010e12	−	7.70412e10i	−0.847562	−	0.0370985i
$547$	−8.71587e11	+	1.50963e12i	−0.416263	+	0.720988i	−0.995560	−	0.0941279i	$-0.969994\pi$
$547$	−8.71587e11	+	1.50963e12i	−0.416263	+	0.720988i	0.579297	+	0.815116i	$0.303327\pi$
$548$	8.39686e10			0.0397745
$549$	1.29008e12	+	2.76817e12i	0.606096	+	1.30052i
$550$	4.59063e11			0.213914
$551$	−2.68180e10	+	4.64501e10i	−0.0123949	+	0.0214686i
$552$	1.25257e12	−	1.96567e12i	0.574218	−	0.901123i
$553$	1.08392e12	+	1.87741e12i	0.492873	+	0.853681i
$554$	3.76900e11	+	6.52809e11i	0.169993	+	0.294437i
$555$	−2.05303e11	+	3.22184e11i	−0.0918497	+	0.144140i
$556$	−2.47281e11	+	4.28302e11i	−0.109737	+	0.190070i
$557$	−3.88681e12			−1.71098			−0.855490	−	0.517820i	$-0.826744\pi$
$557$	−3.88681e12			−1.71098			−0.855490	+	0.517820i	$0.826744\pi$
$558$	1.48424e12	−	2.11872e12i	0.648112	−	0.925167i
$559$	2.85544e12			1.23686
$560$	2.70947e11	−	4.69293e11i	0.116423	−	0.201650i
$561$	1.20980e12	+	5.29538e10i	0.515679	+	0.0225717i
$562$	−1.22582e12	−	2.12317e12i	−0.518336	−	0.897785i
$563$	−1.40604e12	−	2.43533e12i	−0.589806	−	1.02157i	−0.994257	−	0.107015i	$-0.965871\pi$
$563$	−1.40604e12	−	2.43533e12i	−0.589806	−	1.02157i	0.404451	−	0.914560i	$-0.367463\pi$
$564$	−9.02254e10	−	1.73368e11i	−0.0375468	−	0.0721461i
$565$	4.03429e11	−	6.98759e11i	0.166552	−	0.288476i
$566$	−1.56063e12			−0.639183
$567$	−2.29946e12	−	4.06497e11i	−0.934334	−	0.165171i
$568$	−4.34277e12			−1.75065
$569$	−9.10981e11	+	1.57787e12i	−0.364338	+	0.631051i	−0.988670	−	0.150108i	$-0.952038\pi$
$569$	−9.10981e11	+	1.57787e12i	−0.364338	+	0.631051i	0.624332	+	0.781159i	$0.285371\pi$
$570$	7.08845e11	+	1.36204e12i	0.281264	+	0.540448i
$571$	1.68248e12	+	2.91413e12i	0.662348	+	1.14722i	0.979997	+	0.199012i	$0.0637733\pi$
$571$	1.68248e12	+	2.91413e12i	0.662348	+	1.14722i	−0.317649	+	0.948208i	$0.602893\pi$
$572$	2.14615e11	+	3.71724e11i	0.0838259	+	0.145191i
$573$	9.20304e11	+	4.02825e10i	0.356645	+	0.0156106i
$574$	1.35423e12	−	2.34559e12i	0.520700	−	0.901879i
$575$	−1.85627e12			−0.708167
$576$	−1.56073e12	+	2.22792e12i	−0.590783	+	0.843331i
$577$	2.47809e12			0.930737			0.465368	−	0.885117i	$-0.345922\pi$
$577$	2.47809e12			0.930737			0.465368	+	0.885117i	$0.345922\pi$
$578$	8.92348e11	−	1.54559e12i	0.332551	−	0.575996i
$579$	−1.41749e12	+	2.22448e12i	−0.524165	+	0.822575i
$580$	−4.70723e9	−	8.15317e9i	−0.00172719	−	0.00299158i
$581$	−3.16477e11	−	5.48154e11i	−0.115226	−	0.199577i
$582$	−1.26710e11	+	1.98847e11i	−0.0457781	+	0.0718399i
$583$	2.86232e11	−	4.95768e11i	0.102615	−	0.177734i
$584$	−3.79334e12			−1.34947
$585$	7.23353e11	+	1.55212e12i	0.255358	+	0.547930i
$586$	2.68868e12			0.941888
$587$	5.73505e11	−	9.93340e11i	0.199373	−	0.345324i	−0.748952	−	0.662624i	$-0.769443\pi$
$587$	5.73505e11	−	9.93340e11i	0.199373	−	0.345324i	0.948325	+	0.317300i	$0.102776\pi$
$588$	−1.11727e11	−	4.89038e9i	−0.0385443	−	0.00168712i
$589$	−3.09622e12	−	5.36282e12i	−1.06002	−	1.83601i
$590$	1.00717e12	+	1.74446e12i	0.342189	+	0.592690i
$591$	−1.07645e11	−	2.06840e11i	−0.0362953	−	0.0697413i
$592$	2.23613e11	−	3.87310e11i	0.0748256	−	0.129602i
$593$	3.07354e12			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$593$	3.07354e12			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$594$	−3.44833e11	−	8.33276e11i	−0.113650	−	0.274631i
$595$	−2.08842e12			−0.683111
$596$	3.51340e11	−	6.08539e11i	0.114056	−	0.197551i
$597$	9.41372e11	+	1.80884e12i	0.303303	+	0.582796i
$598$	1.37562e12	+	2.38265e12i	0.439890	+	0.761912i
$599$	−6.51632e11	−	1.12866e12i	−0.206815	−	0.358214i	0.743895	−	0.668297i	$-0.232976\pi$
$599$	−6.51632e11	−	1.12866e12i	−0.206815	−	0.358214i	−0.950709	+	0.310083i	$0.899643\pi$
$600$	2.47881e12	+	1.08500e11i	0.780841	+	0.0341781i
$601$	3.02726e12	−	5.24336e12i	0.946486	−	1.63936i	0.193737	−	0.981053i	$-0.437939\pi$
$601$	3.02726e12	−	5.24336e12i	0.946486	−	1.63936i	0.752749	−	0.658308i	$-0.228728\pi$
$602$	2.59341e12			0.804797
$603$	−2.73975e11	−	2.40303e10i	−0.0843884	−	0.00740169i
$604$	−8.41315e11			−0.257213
$605$	−7.46627e11	+	1.29320e12i	−0.226571	+	0.392432i
$606$	−6.37422e11	+	1.00031e12i	−0.191999	+	0.301306i
$607$	2.03918e12	+	3.53196e12i	0.609685	+	1.05601i	0.991292	+	0.131681i	$0.0420376\pi$
$607$	2.03918e12	+	3.53196e12i	0.609685	+	1.05601i	−0.381607	+	0.924325i	$0.624629\pi$
$608$	1.79010e12	+	3.10054e12i	0.531264	+	0.920177i
$609$	−2.91954e10	+	4.58165e10i	−0.00860075	+	0.0134972i
$610$	1.01704e12	−	1.76157e12i	0.297409	−	0.515128i
$611$	8.27066e11			0.240079
$612$	1.81863e12	+	1.59511e11i	0.524038	+	0.0459632i
$613$	2.84192e12			0.812904			0.406452	−	0.913672i	$-0.366766\pi$
$613$	2.84192e12			0.812904			0.406452	+	0.913672i	$0.366766\pi$
$614$	−1.56111e12	+	2.70393e12i	−0.443279	+	0.767781i
$615$	−2.63001e12	−	1.15118e11i	−0.741345	−	0.0324493i
$616$	6.98819e11	+	1.21039e12i	0.195547	+	0.338697i
$617$	−2.91123e12	−	5.04240e12i	−0.808711	−	1.40073i	−0.913757	−	0.406262i	$-0.866832\pi$
$617$	−2.91123e12	−	5.04240e12i	−0.808711	−	1.40073i	0.105045	−	0.994467i	$-0.466501\pi$
$618$	−3.86866e11	−	7.43362e11i	−0.106687	−	0.204999i
$619$	−2.75415e12	+	4.77032e12i	−0.754014	+	1.30599i	0.191849	+	0.981424i	$0.438551\pi$
$619$	−2.75415e12	+	4.77032e12i	−0.754014	+	1.30599i	−0.945863	+	0.324566i	$0.894782\pi$
$620$	1.08693e12			0.295420
$621$	1.39437e12	+	3.36944e12i	0.376241	+	0.909172i
$622$	−1.77001e12			−0.474155
$623$	2.59343e12	−	4.49195e12i	0.689728	−	1.19464i
$624$	−9.25430e11	−	1.77821e12i	−0.244350	−	0.469518i
$625$	−4.53417e11	−	7.85341e11i	−0.118861	−	0.205873i
$626$	1.62501e12	+	2.81460e12i	0.422933	+	0.732541i
$627$	−2.15667e12	−	9.43994e10i	−0.557289	−	0.0243930i
$628$	−1.81394e11	+	3.14183e11i	−0.0465376	+	0.0806055i
$629$	−1.72358e12			−0.439039
$630$	6.56973e11	+	1.40969e12i	0.166156	+	0.356526i
$631$	−3.74010e12			−0.939184			−0.469592	−	0.882884i	$-0.655599\pi$
$631$	−3.74010e12			−0.939184			−0.469592	+	0.882884i	$0.655599\pi$
$632$	−2.26251e12	+	3.91879e12i	−0.564111	+	0.977069i
$633$	1.05040e11	−	1.64840e11i	0.0260039	−	0.0408080i
$634$	−2.28880e12	−	3.96432e12i	−0.562609	−	0.974467i
$635$	−7.03957e11	−	1.21929e12i	−0.171816	−	0.297595i
$636$	4.63788e11	−	7.27825e11i	0.112399	−	0.176388i
$637$	2.36629e11	−	4.09854e11i	0.0569431	−	0.0986284i
$638$	−2.09811e10			−0.00501344
$639$	3.89822e12	−	5.56464e12i	0.924938	−	1.32033i
$640$	1.87200e11			0.0441058
$641$	7.09241e11	−	1.22844e12i	0.165933	−	0.287405i	−0.771053	−	0.636771i	$-0.780270\pi$
$641$	7.09241e11	−	1.22844e12i	0.165933	−	0.287405i	0.936986	+	0.349366i	$0.113603\pi$
$642$	−2.62383e12	−	1.14847e11i	−0.609575	−	0.0266816i
$643$	3.55066e11	+	6.14992e11i	0.0819142	+	0.141880i	0.904072	−	0.427380i	$-0.140563\pi$
$643$	3.55066e11	+	6.14992e11i	0.0819142	+	0.141880i	−0.822158	+	0.569259i	$0.807230\pi$
$644$	−7.88183e11	−	1.36517e12i	−0.180568	−	0.312753i
$645$	−1.16369e12	−	2.23603e12i	−0.264739	−	0.508696i
$646$	−3.46365e12	+	5.99921e12i	−0.782505	+	1.35534i
$647$	1.71001e12			0.383645			0.191823	−	0.981430i	$-0.438560\pi$
$647$	1.71001e12			0.383645			0.191823	+	0.981430i	$0.438560\pi$
$648$	−1.66506e12	−	4.58096e12i	−0.370972	−	1.02063i
$649$	−2.83200e12			−0.626603
$650$	−1.46436e12	+	2.53634e12i	−0.321764	+	0.557311i
$651$	−2.89563e12	−	5.56395e12i	−0.631872	−	1.21414i
$652$	4.77088e11	+	8.26341e11i	0.103391	+	0.179079i
$653$	9.38362e11	+	1.62529e12i	0.201958	+	0.349801i	0.949159	−	0.314796i	$-0.101936\pi$
$653$	9.38362e11	+	1.62529e12i	0.201958	+	0.349801i	−0.747201	+	0.664598i	$0.768603\pi$
$654$	1.35302e12	+	5.92230e10i	0.289205	+	0.0126587i
$655$	−2.85191e11	+	4.93965e11i	−0.0605410	+	0.104860i
$656$	3.08175e12			0.649725
$657$	3.40504e12	−	4.86062e12i	0.712980	−	1.01777i
$658$	7.51169e11			0.156214
$659$	−1.05120e12	+	1.82073e12i	−0.217121	+	0.376064i	−0.953927	−	0.300040i	$-0.903000\pi$
$659$	−1.05120e12	+	1.82073e12i	−0.217121	+	0.376064i	0.736806	+	0.676105i	$0.236333\pi$
$660$	2.03625e11	−	3.19550e11i	0.0417718	−	0.0655528i
$661$	3.07493e12	+	5.32593e12i	0.626511	+	1.08515i	0.988247	+	0.152868i	$0.0488509\pi$
$661$	3.07493e12	+	5.32593e12i	0.626511	+	1.08515i	−0.361736	+	0.932281i	$0.617816\pi$
$662$	−2.50937e12	−	4.34636e12i	−0.507813	−	0.879558i
$663$	−4.15169e12	+	6.51526e12i	−0.834475	+	1.30955i
$664$	6.60595e11	−	1.14418e12i	0.131880	−	0.228423i
$665$	3.72297e12			0.738231
$666$	5.42203e11	+	1.16342e12i	0.106789	+	0.229142i
$667$	8.48395e10			0.0165971
$668$	−1.49245e11	+	2.58499e11i	−0.0290004	+	0.0502302i
$669$	4.02779e12	+	1.76300e11i	0.777409	+	0.0340278i
$670$	9.15884e10	+	1.58636e11i	0.0175592	+	0.0304134i
$671$	1.42989e12	+	2.47664e12i	0.272302	+	0.471641i
$672$	1.67412e12	+	3.21682e12i	0.316684	+	0.608507i
$673$	−1.87092e12	+	3.24053e12i	−0.351551	+	0.608904i	−0.986521	−	0.163632i	$-0.947679\pi$
$673$	−1.87092e12	+	3.24053e12i	−0.351551	+	0.608904i	0.634971	+	0.772536i	$0.281012\pi$
$674$	5.30823e12			0.990787
$675$	−2.36409e12	+	3.07885e12i	−0.438327	+	0.570849i
$676$	−6.38124e11			−0.117529
$677$	−1.97991e12	+	3.42930e12i	−0.362240	+	0.627418i	−0.988329	−	0.152333i	$-0.951321\pi$
$677$	−1.97991e12	+	3.42930e12i	−0.362240	+	0.627418i	0.626089	+	0.779751i	$0.284655\pi$
$678$	−1.25148e12	−	2.40472e12i	−0.227452	−	0.437049i
$679$	2.85853e11	+	4.95112e11i	0.0516094	+	0.0893902i
$680$	−2.17962e12	−	3.77521e12i	−0.390922	−	0.677097i
$681$	5.38467e12	+	2.35692e11i	0.959394	+	0.0419935i
$682$	1.21117e12	−	2.09781e12i	0.214376	−	0.371309i
$683$	3.62977e12			0.638243			0.319121	−	0.947714i	$-0.396612\pi$
$683$	3.62977e12			0.638243			0.319121	+	0.947714i	$0.396612\pi$
$684$	−3.24202e12	−	2.84357e11i	−0.566322	−	0.0496720i
$685$	3.13684e11			0.0544358
$686$	2.36971e12	−	4.10445e12i	0.408541	−	0.707614i
$687$	−1.00957e12	+	1.58432e12i	−0.172914	+	0.271355i
$688$	1.47542e12	+	2.55550e12i	0.251054	+	0.434839i
$689$	1.82609e12	+	3.16289e12i	0.308700	+	0.534684i
$690$	1.30518e12	−	2.04823e12i	0.219205	−	0.343999i
$691$	1.63408e12	−	2.83030e12i	0.272660	−	0.472260i	−0.696882	−	0.717185i	$-0.745430\pi$
$691$	1.63408e12	−	2.83030e12i	0.272660	−	0.472260i	0.969542	+	0.244925i	$0.0787634\pi$
$692$	4.27883e12			0.709328
$693$	−2.17823e12	−	1.91052e11i	−0.358759	−	0.0314667i
$694$	9.69805e11			0.158696
$695$	−9.23773e11	+	1.60002e12i	−0.150187	+	0.260132i
$696$	−1.13292e11	−	4.95890e9i	−0.0183003	−	0.000801020i
$697$	−5.93841e12	−	1.02856e13i	−0.953066	−	1.65076i
$698$	−2.69512e12	−	4.66808e12i	−0.429762	−	0.744370i
$699$	2.91542e12	+	5.60197e12i	0.461906	+	0.887552i
$700$	8.39025e11	−	1.45323e12i	0.132079	−	0.228768i
$701$	−5.82077e12			−0.910435			−0.455218	−	0.890380i	$-0.650439\pi$
$701$	−5.82077e12			−0.910435			−0.455218	+	0.890380i	$0.650439\pi$
$702$	5.70387e12	+	7.52838e11i	0.886446	+	0.117000i
$703$	3.07258e12			0.474466
$704$	−1.27359e12	+	2.20593e12i	−0.195413	+	0.338465i
$705$	−3.37058e11	−	6.47655e11i	−0.0513870	−	0.0987399i
$706$	−4.69570e12	−	8.13319e12i	−0.711343	−	1.23208i
$707$	1.43800e12	+	2.49069e12i	0.216457	+	0.374914i
$708$	−4.26539e12	−	1.86700e11i	−0.637983	−	0.0279250i
$709$	3.41640e12	−	5.91738e12i	0.507763	−	0.879471i	−0.492197	−	0.870484i	$-0.663806\pi$
$709$	3.41640e12	−	5.91738e12i	0.507763	−	0.879471i	0.999960	−	0.00898692i	$-0.00286067\pi$
$710$	−4.52517e12			−0.668301
$711$	−2.99046e12	−	6.41673e12i	−0.438858	−	0.941674i
$712$	1.08267e13			1.57884
$713$	−4.89750e12	+	8.48272e12i	−0.709695	+	1.22923i
$714$	−3.77070e12	+	5.91738e12i	−0.542975	+	0.852094i
$715$	8.01743e11	+	1.38866e12i	0.114725	+	0.198710i
$716$	−1.92986e12	−	3.34261e12i	−0.274421	−	0.475310i
$717$	−4.94543e12	+	7.76088e12i	−0.698823	+	1.09667i
$718$	−4.07974e12	+	7.06632e12i	−0.572892	+	0.992277i
$719$	−5.93643e12			−0.828411			−0.414205	−	0.910183i	$-0.635940\pi$
$719$	−5.93643e12			−0.828411			−0.414205	+	0.910183i	$0.635940\pi$
$720$	−1.01533e12	+	1.44936e12i	−0.140803	+	0.200993i
$721$	−2.03189e12			−0.280021
$722$	3.31579e12	−	5.74311e12i	0.454119	−	0.786557i
$723$	−3.75821e12	−	1.64500e11i	−0.511515	−	0.0223894i
$724$	7.38647e11	+	1.27937e12i	0.0999110	+	0.173051i
$725$	4.51561e10	+	7.82126e10i	0.00607009	+	0.0105137i
$726$	2.31612e12	+	4.45041e12i	0.309418	+	0.594546i
$727$	−2.98924e12	+	5.17751e12i	−0.396877	+	0.687411i	−0.993339	−	0.115231i	$-0.963239\pi$
$727$	−2.98924e12	+	5.17751e12i	−0.396877	+	0.687411i	0.596462	+	0.802641i	$0.296573\pi$
$728$	−8.91661e12			−1.17655
$729$	7.36446e12	+	1.97850e12i	0.965755	+	0.259455i
$730$	−3.95266e12			−0.515154
$731$	5.68617e12	−	9.84873e12i	0.736532	−	1.27571i
$732$	1.99033e12	+	3.82442e12i	0.256228	+	0.492341i
$733$	−4.73505e11	−	8.20135e11i	−0.0605838	−	0.104934i	0.834143	−	0.551549i	$-0.185963\pi$
$733$	−4.73505e11	−	8.20135e11i	−0.0605838	−	0.104934i	−0.894727	+	0.446614i	$0.852630\pi$
$734$	−4.01123e12	−	6.94765e12i	−0.510088	−	0.883498i
$735$	−4.17381e11	−	1.82691e10i	−0.0527521	−	0.00230900i
$736$	2.83152e12	−	4.90433e12i	0.355688	−	0.616069i
$737$	−2.57533e11			−0.0321536
$738$	−5.07474e12	+	7.24410e12i	−0.629739	+	0.898941i
$739$	8.03141e12			0.990585			0.495293	−	0.868726i	$-0.335061\pi$
$739$	8.03141e12			0.990585			0.495293	+	0.868726i	$0.335061\pi$
$740$	−2.69658e11	+	4.67062e11i	−0.0330576	+	0.0572574i
$741$	7.40111e12	−	1.16146e13i	0.901810	−	1.41522i
$742$	1.65852e12	+	2.87264e12i	0.200864	+	0.347907i
$743$	2.22290e12	+	3.85017e12i	0.267590	+	0.463479i	0.968239	−	0.250027i	$-0.0804395\pi$
$743$	2.22290e12	+	3.85017e12i	0.267590	+	0.463479i	−0.700649	+	0.713506i	$0.747106\pi$
$744$	7.03580e12	−	1.10413e13i	0.841851	−	1.32112i
$745$	1.31251e12	−	2.27334e12i	0.156099	−	0.270371i
$746$	1.79188e12			0.211828
$747$	8.73135e11	+	1.87352e12i	0.102598	+	0.220148i
$748$	1.70949e12			0.199668
$749$	−3.18400e12	+	5.51485e12i	−0.369662	+	0.640274i
$750$	6.17170e12	+	2.70141e11i	0.712245	+	0.0311756i
$751$	1.10885e12	+	1.92058e12i	0.127202	+	0.220320i	0.922591	−	0.385779i	$-0.126067\pi$
$751$	1.10885e12	+	1.92058e12i	0.127202	+	0.220320i	−0.795390	+	0.606098i	$0.792734\pi$
$752$	4.27349e11	+	7.40191e11i	0.0487307	+	0.0844041i
$753$	−2.78259e12	−	5.34674e12i	−0.315408	−	0.606055i
$754$	6.69274e10	−	1.15922e11i	0.00754107	−	0.0130615i
$755$	−3.14292e12			−0.352024
$756$	−3.26811e12	−	4.31349e11i	−0.363872	−	0.0480265i
$757$	−9.93039e12			−1.09909			−0.549547	−	0.835463i	$-0.685200\pi$
$757$	−9.93039e12			−1.09909			−0.549547	+	0.835463i	$0.685200\pi$
$758$	−4.49050e12	+	7.77777e12i	−0.494064	+	0.855743i
$759$	1.57636e12	+	3.02898e12i	0.172412	+	0.331290i
$760$	3.88555e12	+	6.72998e12i	0.422466	+	0.731733i
$761$	4.26425e11	+	7.38590e11i	0.0460906	+	0.0798312i	0.888150	−	0.459553i	$-0.151990\pi$
$761$	4.26425e11	+	7.38590e11i	0.0460906	+	0.0798312i	−0.842060	+	0.539384i	$0.818657\pi$
$762$	−4.72578e12	−	2.06851e11i	−0.507781	−	0.0222260i
$763$	1.64189e12	−	2.84384e12i	0.175381	−	0.303770i
$764$	1.30043e12			0.138091
$765$	6.79390e12	+	5.95891e11i	0.717204	+	0.0629057i
$766$	5.26133e12			0.552161
$767$	9.03378e12	−	1.56470e13i	0.942519	−	1.63249i
$768$	−4.99679e12	+	7.84150e12i	−0.518282	+	0.813343i
$769$	3.38623e12	+	5.86513e12i	0.349179	+	0.604796i	0.986104	−	0.166130i	$-0.0531271\pi$
$769$	3.38623e12	+	5.86513e12i	0.349179	+	0.604796i	−0.636925	+	0.770926i	$0.719794\pi$
$770$	7.28170e11	+	1.26123e12i	0.0746491	+	0.129296i
$771$	7.12854e12	−	1.11869e13i	0.726534	−	1.14015i
$772$	−1.86183e12	+	3.22478e12i	−0.188652	+	0.326755i
$773$	3.60630e12			0.363291			0.181645	−	0.983364i	$-0.441858\pi$
$773$	3.60630e12			0.363291			0.181645	+	0.983364i	$0.441858\pi$
$774$	−8.43669e12	−	7.39980e11i	−0.844963	−	0.0741115i
$775$	−1.04268e13			−1.03823
$776$	−5.96673e11	+	1.03347e12i	−0.0590688	+	0.102310i
$777$	3.10925e12	+	1.36094e11i	0.306028	+	0.0133951i
$778$	−4.68070e11	−	8.10721e11i	−0.0458039	−	0.0793348i
$779$	1.05863e13	+	1.83360e13i	1.02997	+	1.78396i
$780$	1.11599e12	+	2.14437e12i	0.107953	+	0.207431i
$781$	3.18103e12	−	5.50970e12i	0.305941	−	0.529906i
$782$	1.09574e13			1.04779
$783$	1.08049e11	−	1.40717e11i	0.0102729	−	0.0133788i
$784$	4.89071e11			0.0462327
$785$	−6.77638e11	+	1.17370e12i	−0.0636919	+	0.110318i
$786$	8.84693e11	+	1.69993e12i	0.0826782	+	0.158866i
$787$	−1.79432e12	−	3.10785e12i	−0.166730	−	0.288785i	0.770538	−	0.637394i	$-0.219987\pi$
$787$	−1.79432e12	−	3.10785e12i	−0.166730	−	0.288785i	−0.937268	+	0.348609i	$0.886654\pi$
$788$	−1.64584e11	−	2.85069e11i	−0.0152062	−	0.0263379i
$789$	−1.57638e13	−	6.89996e11i	−1.44816	−	0.0633870i
$790$	−2.35754e12	+	4.08338e12i	−0.215346	+	0.372991i
$791$	−6.57299e12			−0.596992
$792$	−1.92799e12	−	4.13695e12i	−0.174117	−	0.373609i
$793$	−1.82447e13			−1.63835
$794$	3.85418e12	−	6.67564e12i	0.344144	−	0.596075i
$795$	1.73258e12	−	2.71895e12i	0.153830	−	0.241407i
$796$	1.43932e12	+	2.49297e12i	0.127071	+	0.220094i
$797$	−2.62673e12	−	4.54963e12i	−0.230597	−	0.399405i	0.727387	−	0.686227i	$-0.240734\pi$
$797$	−2.62673e12	−	4.54963e12i	−0.230597	−	0.399405i	−0.957984	+	0.286822i	$0.907401\pi$
$798$	6.72193e12	−	1.05488e13i	0.586788	−	0.920850i
$799$	1.64697e12	−	2.85264e12i	0.142964	−	0.247621i
$800$	6.02833e12			0.520346
$801$	−9.71846e12	+	1.38729e13i	−0.834163	+	1.19075i
$802$	−7.16023e11			−0.0611142
$803$	2.77858e12	−	4.81264e12i	0.235832	−	0.408473i
$804$	−3.87881e11	−	1.69779e10i	−0.0327375	−	0.00143295i
$805$	−2.94443e12	−	5.09991e12i	−0.247127	−	0.428037i
$806$	7.72699e12	+	1.33835e13i	0.644916	+	1.11703i
$807$	−7.20271e12	−	1.38400e13i	−0.597813	−	1.14870i
$808$	−3.00159e12	+	5.19891e12i	−0.247742	+	0.429103i
$809$	−7.22017e12			−0.592623			−0.296312	−	0.955091i	$-0.595757\pi$
$809$	−7.22017e12			−0.592623			−0.296312	+	0.955091i	$0.595757\pi$
$810$	−1.73499e12	−	4.77336e12i	−0.141617	−	0.389621i
$811$	−8.41322e12			−0.682918			−0.341459	−	0.939897i	$-0.610921\pi$
$811$	−8.41322e12			−0.682918			−0.341459	+	0.939897i	$0.610921\pi$
$812$	−3.83470e10	+	6.64190e10i	−0.00309549	+	0.00536155i
$813$	8.42468e11	+	1.61880e12i	0.0676310	+	0.129953i
$814$	6.00961e11	+	1.04090e12i	0.0479774	+	0.0830993i
$815$	1.78227e12	+	3.08698e12i	0.141503	+	0.245090i
$816$	−7.97609e12	−	3.49120e11i	−0.629774	−	0.0275657i
$817$	−1.01366e13	+	1.75571e13i	−0.795963	+	1.37865i
$818$	−4.27650e12			−0.333963
$819$	8.00387e12	−	1.14254e13i	0.621616	−	0.887345i
$820$	−3.71632e12			−0.287045
$821$	1.73801e12	−	3.01032e12i	0.133508	−	0.231243i	−0.791518	−	0.611145i	$-0.790709\pi$
$821$	1.73801e12	−	3.01032e12i	0.133508	−	0.231243i	0.925027	+	0.379902i	$0.124042\pi$
$822$	5.66365e11	−	8.88800e11i	0.0432686	−	0.0679017i
$823$	−6.61717e11	−	1.14613e12i	−0.0502774	−	0.0870831i	0.839791	−	0.542909i	$-0.182677\pi$
$823$	−6.61717e11	−	1.14613e12i	−0.0502774	−	0.0870831i	−0.890069	+	0.455826i	$0.849344\pi$
$824$	−2.12062e12	−	3.67302e12i	−0.160247	−	0.277556i
$825$	−1.95336e12	+	3.06541e12i	−0.146804	+	0.230381i
$826$	8.20477e12	−	1.42111e13i	0.613277	−	1.06223i
$827$	3.65944e11			0.0272044			0.0136022	−	0.999907i	$-0.495670\pi$
$827$	3.65944e11			0.0272044			0.0136022	+	0.999907i	$0.495670\pi$
$828$	2.17453e12	+	4.66598e12i	0.160779	+	0.344990i
$829$	2.59469e13			1.90805			0.954025	−	0.299728i	$-0.0968960\pi$
$829$	2.59469e13			1.90805			0.954025	+	0.299728i	$0.0968960\pi$
$830$	6.88340e11	−	1.19224e12i	0.0503445	−	0.0871992i
$831$	−5.96291e12	−	2.61002e11i	−0.433764	−	0.0189862i
$832$	−8.12523e12	−	1.40733e13i	−0.587869	−	1.01822i
$833$	−9.42421e11	−	1.63232e12i	−0.0678176	−	0.117464i
$834$	2.86564e12	+	5.50633e12i	0.205104	+	0.394107i
$835$	−5.57537e11	+	9.65682e11i	−0.0396903	+	0.0687456i
$836$	−3.04747e12			−0.215780
$837$	7.83230e12	+	1.89265e13i	0.551601	+	1.33292i
$838$	6.65101e12			0.465896
$839$	7.12846e12	−	1.23469e13i	0.496669	−	0.860255i	−0.503324	−	0.864098i	$-0.667890\pi$
$839$	7.12846e12	−	1.23469e13i	0.496669	−	0.860255i	0.999993	+	0.00384244i	$0.00122309\pi$
$840$	3.63382e12	+	6.98238e12i	0.251830	+	0.483890i
$841$	7.25151e12	+	1.25600e13i	0.499858	+	0.865779i
$842$	6.43530e12	+	1.11463e13i	0.441230	+	0.764232i
$843$	1.93936e13	+	8.48873e11i	1.32262	+	0.0578920i
$844$	1.37966e11	−	2.38964e11i	0.00935904	−	0.0162103i
$845$	−2.38386e12			−0.160851
$846$	−2.44365e12	−	2.14332e11i	−0.164011	−	0.0143853i
$847$	1.21646e13			0.812127
$848$	−1.88710e12	+	3.26856e12i	−0.125318	+	0.217058i
$849$	6.64062e12	−	1.04212e13i	0.438656	−	0.688385i
$850$	5.83208e12	+	1.01015e13i	0.383212	+	0.663742i
$851$	−2.43005e12	−	4.20898e12i	−0.158830	−	0.275102i
$852$	5.15429e12	−	8.08866e12i	0.335113	−	0.525894i
$853$	1.79052e10	−	3.10127e10i	0.00115800	−	0.00200571i	−0.865446	−	0.501003i	$-0.832965\pi$
$853$	1.79052e10	−	3.10127e10i	0.00115800	−	0.00200571i	0.866604	+	0.498997i	$0.166298\pi$
$854$	−1.65705e13			−1.06604
$855$	−1.21113e13	−	1.06228e12i	−0.775075	−	0.0679816i
$856$	−1.32922e13			−0.846184
$857$	−6.97342e12	+	1.20783e13i	−0.441603	+	0.764880i	−0.997809	−	0.0661654i	$-0.978923\pi$
$857$	−6.97342e12	+	1.20783e13i	−0.441603	+	0.764880i	0.556205	+	0.831045i	$0.312257\pi$
$858$	5.38224e12	+	2.35585e11i	0.339055	+	0.0148407i
$859$	7.06018e12	+	1.22286e13i	0.442432	+	0.766314i	0.997869	−	0.0652438i	$-0.0207825\pi$
$859$	7.06018e12	+	1.22286e13i	0.442432	+	0.766314i	−0.555437	+	0.831558i	$0.687449\pi$
$860$	−1.77923e12	−	3.08172e12i	−0.110915	−	0.192110i
$861$	9.90042e12	+	1.90236e13i	0.613959	+	1.17972i
$862$	7.96991e12	−	1.38043e13i	0.491666	−	0.851591i
$863$	−2.25669e13			−1.38492			−0.692458	−	0.721458i	$-0.743472\pi$
$863$	−2.25669e13			−1.38492			−0.692458	+	0.721458i	$0.743472\pi$
$864$	−4.52828e12	−	1.09424e13i	−0.276453	−	0.668039i
$865$	1.59845e13			0.970795
$866$	−6.88385e12	+	1.19232e13i	−0.415911	+	0.720380i
$867$	6.52374e12	+	1.25353e13i	0.392113	+	0.753443i
$868$	−4.42729e12	−	7.66829e12i	−0.264728	−	0.458522i
$869$	−3.31453e12	−	5.74094e12i	−0.197167	−	0.341503i
$870$	−1.18051e11	−	5.16718e9i	−0.00698605	−	0.000305785i
$871$	8.21503e11	−	1.42288e12i	0.0483646	−	0.0837699i
$872$	6.85437e12			0.401461
$873$	−7.88647e11	−	1.69223e12i	−0.0459535	−	0.0986040i
$874$	−1.95334e13			−1.13234
$875$	7.48934e12	−	1.29719e13i	0.431924	−	0.748114i
$876$	4.50220e12	−	7.06532e12i	0.258319	−	0.405381i
$877$	−1.52634e13	−	2.64371e13i	−0.871273	−	1.50909i	−0.860681	−	0.509145i	$-0.829962\pi$
$877$	−1.52634e13	−	2.64371e13i	−0.871273	−	1.50909i	−0.0105925	−	0.999944i	$-0.503372\pi$
$878$	−1.35280e13	−	2.34311e13i	−0.768258	−	1.33066i
$879$	−1.14406e13	+	1.79538e13i	−0.646396	+	1.01439i
$880$	−8.28530e11	+	1.43506e12i	−0.0465732	+	0.0806671i
$881$	2.00261e13			1.11997			0.559983	−	0.828504i	$-0.310808\pi$
$881$	2.00261e13			1.11997			0.559983	+	0.828504i	$0.310808\pi$
$882$	−8.05358e11	+	1.14963e12i	−0.0448106	+	0.0639662i
$883$	1.87899e13			1.04016			0.520080	−	0.854117i	$-0.325902\pi$
$883$	1.87899e13			1.04016			0.520080	+	0.854117i	$0.325902\pi$
$884$	−5.45308e12	+	9.44502e12i	−0.300336	+	0.520197i
$885$	−1.59343e13	−	6.97459e11i	−0.873150	−	0.0382185i
$886$	2.46375e12	+	4.26734e12i	0.134321	+	0.232651i
$887$	−1.44494e13	−	2.50272e13i	−0.783781	−	1.35755i	−0.929724	−	0.368256i	$-0.879955\pi$
$887$	−1.44494e13	−	2.50272e13i	−0.783781	−	1.35755i	0.145943	−	0.989293i	$-0.453378\pi$
$888$	2.99901e12	+	5.76259e12i	0.161853	+	0.310999i
$889$	−5.73472e12	+	9.93282e12i	−0.307931	+	0.533353i
$890$	1.12815e13			0.602713
$891$	7.03154e12	+	1.24303e12i	0.373767	+	0.0660743i
$892$	5.69143e12			0.301009
$893$	−2.93602e12	+	5.08534e12i	−0.154500	+	0.267601i
$894$	−4.07155e12	−	7.82347e12i	−0.213177	−	0.409620i
$895$	−7.20942e12	−	1.24871e13i	−0.375575	−	0.650515i
$896$	−7.62502e11	−	1.32069e12i	−0.0395235	−	0.0684567i
$897$	−2.17637e13	−	9.52614e11i	−1.12245	−	0.0491305i
$898$	3.00717e12	−	5.20856e12i	0.154317	−	0.267285i
$899$	4.76551e11			0.0243327
$900$	−3.14411e12	+	4.48816e12i	−0.159737	+	0.228022i
$901$	1.45455e13			0.735306
$902$	−4.14110e12	+	7.17259e12i	−0.208299	+	0.360784i
$903$	−1.10352e13	+	1.73176e13i	−0.552313	+	0.866748i
$904$	−6.86003e12	−	1.18819e13i	−0.341639	−	0.591737i
$905$	2.75938e12	+	4.77939e12i	0.136739	+	0.236839i
$906$	−5.67464e12	+	8.90524e12i	−0.279809	+	0.439105i
$907$	−1.38734e12	+	2.40294e12i	−0.0680691	+	0.117899i	−0.898051	−	0.439891i	$-0.855017\pi$
$907$	−1.38734e12	+	2.40294e12i	−0.0680691	+	0.117899i	0.829982	+	0.557790i	$0.188351\pi$
$908$	7.60876e12			0.371473
$909$	−3.96733e12	−	8.51283e12i	−0.192735	−	0.413558i
$910$	−9.29112e12			−0.449140
$911$	−1.79009e13	+	3.10053e13i	−0.861079	+	1.49143i	0.00980917	+	0.999952i	$0.496878\pi$
$911$	−1.79009e13	+	3.10053e13i	−0.861079	+	1.49143i	−0.870888	+	0.491481i	$0.836456\pi$
$912$	1.42188e13	+	6.22369e11i	0.680591	+	0.0297900i
$913$	9.67757e11	+	1.67620e12i	0.0460944	+	0.0798378i
$914$	7.26794e12	+	1.25884e13i	0.344471	+	0.596642i
$915$	7.43535e12	+	1.42870e13i	0.350676	+	0.673823i
$916$	−1.32603e12	+	2.29675e12i	−0.0622334	+	0.107791i
$917$	4.64656e12			0.217005
$918$	1.39550e13	−	1.81741e13i	0.648541	−	0.844619i
$919$	−1.46068e13			−0.675516			−0.337758	−	0.941233i	$-0.609669\pi$
$919$	−1.46068e13			−0.675516			−0.337758	+	0.941233i	$0.609669\pi$
$920$	6.14604e12	−	1.06452e13i	0.282846	−	0.489903i
$921$	−1.14129e13	−	2.19299e13i	−0.522671	−	1.00431i
$922$	8.78343e12	+	1.52133e13i	0.400290	+	0.693323i
$923$	2.02943e13	+	3.51507e13i	0.920376	+	1.59414i
$924$	−3.08383e12	−	1.34982e11i	−0.139177	−	0.00609188i
$925$	2.58681e12	−	4.48048e12i	0.116179	−	0.201227i
$926$	8.73386e12			0.390352
$927$	6.61000e12	+	5.79761e11i	0.293997	+	0.0257864i
$928$	−2.75520e11			−0.0121952
$929$	1.98224e13	−	3.43333e13i	0.873142	−	1.51233i	0.0144124	−	0.999896i	$-0.495412\pi$
$929$	1.98224e13	−	3.43333e13i	0.873142	−	1.51233i	0.858729	−	0.512430i	$-0.171254\pi$
$930$	7.33131e12	−	1.15051e13i	0.321372	−	0.504331i
$931$	1.68003e12	+	2.90990e12i	0.0732899	+	0.126942i
$932$	4.45755e12	+	7.72070e12i	0.193519	+	0.335185i
$933$	7.53159e12	−	1.18194e13i	0.325401	−	0.510654i
$934$	−8.49855e12	+	1.47199e13i	−0.365413	+	0.632914i
$935$	6.38619e12			0.273268
$936$	2.90069e13	+	2.54419e12i	1.23527	+	0.108345i
$937$	−1.72240e13			−0.729973			−0.364987	−	0.931013i	$-0.618926\pi$
$937$	−1.72240e13			−0.729973			−0.364987	+	0.931013i	$0.618926\pi$
$938$	7.46116e11	−	1.29231e12i	0.0314698	−	0.0545073i
$939$	−2.57092e13	−	1.12531e12i	−1.07918	−	0.0472366i
$940$	−5.15346e11	−	8.92606e11i	−0.0215290	−	0.0372893i
$941$	−2.06449e13	−	3.57581e13i	−0.858341	−	1.48669i	−0.873510	−	0.486806i	$-0.838162\pi$
$941$	−2.06449e13	−	3.57581e13i	−0.858341	−	1.48669i	0.0151687	−	0.999885i	$-0.495171\pi$
$942$	2.10211e12	+	4.03919e12i	0.0869812	+	0.167134i
$943$	1.67450e13	−	2.90032e13i	0.689576	−	1.19438i
$944$	1.86712e13			0.765241
$945$	−1.22088e13	−	1.61140e12i	−0.497999	−	0.0657296i
$946$	−7.93040e12			−0.321947
$947$	−8.80925e12	+	1.52581e13i	−0.355929	+	0.616488i	−0.987277	−	0.159013i	$-0.949169\pi$
$947$	−8.80925e12	+	1.52581e13i	−0.355929	+	0.616488i	0.631347	+	0.775500i	$0.282502\pi$
$948$	−4.61367e12	−	8.86516e12i	−0.185528	−	0.356491i
$949$	1.77267e13	+	3.07036e13i	0.709464	+	1.22883i
$950$	−1.03967e13	−	1.80076e13i	−0.414133	−	0.717300i
$951$	3.62110e13	+	1.58499e12i	1.43558	+	0.0628367i
$952$	−1.77561e13	+	3.07544e13i	−0.700616	+	1.21350i
$953$	4.44553e13			1.74584			0.872922	−	0.487859i	$-0.162222\pi$
$953$	4.44553e13			1.74584			0.872922	+	0.487859i	$0.162222\pi$
$954$	−4.57573e12	−	9.81830e12i	−0.178851	−	0.383768i
$955$	4.85804e12			0.188993
$956$	−6.49563e12	+	1.12508e13i	−0.251513	+	0.435634i
$957$	8.92767e10	−	1.40103e11i	0.00344060	−	0.00539936i
$958$	−9.39042e11	−	1.62647e12i	−0.0360197	−	0.0623879i
$959$	−1.27770e12	−	2.21304e12i	−0.0487803	−	0.0844899i
$960$	−7.70916e12	+	1.20980e13i	−0.292945	+	0.459721i
$961$	−1.42899e13	+	2.47508e13i	−0.540472	+	0.936126i
$962$	−7.66800e12			−0.288665
$963$	1.19315e13	−	1.70320e13i	0.447073	−	0.638188i
$964$	−5.31050e12			−0.198056
$965$	−6.95527e12	+	1.20469e13i	−0.258191	+	0.447200i
$966$	−1.97665e13	−	8.65196e11i	−0.730352	−	0.0319681i
$967$	7.41879e12	+	1.28497e13i	0.272844	+	0.472579i	0.969589	−	0.244739i	$-0.0787024\pi$
$967$	7.41879e12	+	1.28497e13i	0.272844	+	0.472579i	−0.696745	+	0.717319i	$0.745369\pi$
$968$	1.26959e13	+	2.19899e13i	0.464754	+	0.804978i
$969$	−2.53219e13	−	4.86559e13i	−0.922655	−	1.77288i
$970$	−6.21734e11	+	1.07687e12i	−0.0225492	+	0.0390564i
$971$	−3.34482e13			−1.20750			−0.603749	−	0.797174i	$-0.706327\pi$
$971$	−3.34482e13			−1.20750			−0.603749	+	0.797174i	$0.706327\pi$
$972$	1.05085e13	+	2.33573e12i	0.377610	+	0.0839314i
$973$	1.50508e13			0.538336
$974$	−4.24768e12	+	7.35719e12i	−0.151229	+	0.261937i
$975$	−1.07056e13	−	2.05707e13i	−0.379393	−	0.729002i
$976$	−9.42714e12	−	1.63283e13i	−0.332549	−	0.575992i
$977$	−1.02021e13	−	1.76705e13i	−0.358231	−	0.620475i	0.629434	−	0.777054i	$-0.283287\pi$
$977$	−1.02021e13	−	1.76705e13i	−0.358231	−	0.620475i	−0.987665	+	0.156579i	$0.949953\pi$
$978$	1.19647e13	+	5.23704e11i	0.418192	+	0.0183046i
$979$	−7.93047e12	+	1.37360e13i	−0.275916	+	0.477900i
$980$	−5.89777e11			−0.0204254
$981$	−6.15272e12	+	8.78289e12i	−0.212108	+	0.302780i
$982$	−2.15891e13			−0.740855
$983$	−1.15500e13	+	2.00051e13i	−0.394539	+	0.683361i	−0.993042	−	0.117759i	$-0.962429\pi$
$983$	−1.15500e13	+	2.00051e13i	−0.394539	+	0.683361i	0.598504	+	0.801120i	$0.295762\pi$
$984$	−2.40560e13	+	3.77513e13i	−0.817987	+	1.28367i
$985$	−6.14842e11	−	1.06494e12i	−0.0208114	−	0.0360464i
$986$	−2.66551e11	−	4.61680e11i	−0.00898120	−	0.0155559i
$987$	−3.19630e12	+	5.01597e12i	−0.107206	+	0.168239i
$988$	9.72108e12	−	1.68374e13i	0.324570	−	0.562172i
$989$	3.20674e13			1.06581
$990$	−2.00896e12	−	4.31071e12i	−0.0664682	−	0.142623i
$991$	−4.59514e13			−1.51345			−0.756724	−	0.653734i	$-0.773201\pi$
$991$	−4.59514e13			−1.51345			−0.756724	+	0.653734i	$0.773201\pi$
$992$	1.59049e13	−	2.75480e13i	0.521468	−	0.903209i
$993$	3.97007e13	+	1.73773e12i	1.29577	+	0.0567167i
$994$	1.84319e13	+	3.19250e13i	0.598869	+	1.03727i
$995$	5.37689e12	+	9.31305e12i	0.173911	+	0.301223i
$996$	1.34707e12	+	2.58839e12i	0.0433734	+	0.0833419i
$997$	2.19764e13	−	3.80642e13i	0.704414	−	1.22008i	−0.262489	−	0.964935i	$-0.584543\pi$
$997$	2.19764e13	−	3.80642e13i	0.704414	−	1.22008i	0.966903	−	0.255146i	$-0.0821234\pi$
$998$	−3.32631e13			−1.06139
$999$	−1.00760e13	−	1.32990e12i	−0.320067	−	0.0422448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.10.c.a.7.6	yes	16
3.2	odd	2		27.10.c.a.19.3		16
9.2	odd	6		81.10.a.d.1.6		8
9.4	even	3	inner	9.10.c.a.4.6	✓	16
9.5	odd	6		27.10.c.a.10.3		16
9.7	even	3		81.10.a.c.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.6	✓	16	9.4	even	3	inner
9.10.c.a.7.6	yes	16	1.1	even	1	trivial
27.10.c.a.10.3		16	9.5	odd	6
27.10.c.a.19.3		16	3.2	odd	2
81.10.a.c.1.3		8	9.7	even	3
81.10.a.d.1.6		8	9.2	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+(8.85925 - 15.3447i) q^{2} +(64.7679 + 124.451i) q^{3} +(99.0272 + 171.520i) q^{4} +(369.939 + 640.753i) q^{5} +(2483.46 + 108.703i) q^{6} +(3013.67 - 5219.83i) q^{7} +12581.1 q^{8} +(-11293.2 + 16120.9i) q^{9} +13109.5 q^{10} +(-9215.52 + 15961.8i) q^{11} +(-14932.1 + 23433.1i) q^{12} +(-58793.0 - 101832. i) q^{13} +(-53397.7 - 92487.6i) q^{14} +(-55782.3 + 87539.5i) q^{15} +(60757.3 - 105235. i) q^{16} -468308. q^{17} +(147320. + 316110. i) q^{18} +834842. q^{19} +(-73268.0 + 126904. i) q^{20} +(844803. + 36977.8i) q^{21} +(163285. + 282819. i) q^{22} +(-660262. - 1.14361e6i) q^{23} +(814852. + 1.56573e6i) q^{24} +(702853. - 1.21738e6i) q^{25} -2.08345e6 q^{26} +(-2.73771e6 - 361342. i) q^{27} +1.19374e6 q^{28} +(-32123.4 + 55639.3i) q^{29} +(849076. + 1.63150e6i) q^{30} +(-3.70875e6 - 6.42375e6i) q^{31} +(2.14423e6 + 3.71392e6i) q^{32} +(-2.58333e6 - 113075. i) q^{33} +(-4.14886e6 + 7.18604e6i) q^{34} +4.45949e6 q^{35} +(-3.88340e6 - 340612. i) q^{36} +3.68044e6 q^{37} +(7.39608e6 - 1.28104e7i) q^{38} +(8.86528e6 - 1.39123e7i) q^{39} +(4.65424e6 + 8.06138e6i) q^{40} +(1.26806e7 + 2.19634e7i) q^{41} +(8.05174e6 - 1.26356e7i) q^{42} +(-1.21419e7 + 2.10304e7i) q^{43} -3.65035e6 q^{44} +(-1.45073e7 - 1.27243e6i) q^{45} -2.33977e7 q^{46} +(-3.51686e6 + 6.09137e6i) q^{47} +(1.70317e7 + 745492. i) q^{48} +(2.01239e6 + 3.48557e6i) q^{49} +(-1.24535e7 - 2.15701e7i) q^{50} +(-3.03313e7 - 5.82816e7i) q^{51} +(1.16442e7 - 2.01684e7i) q^{52} -3.10597e7 q^{53} +(-2.97987e7 + 3.88080e7i) q^{54} -1.36367e7 q^{55} +(3.79153e7 - 6.56712e7i) q^{56} +(5.40710e7 + 1.03897e8i) q^{57} +(569179. + 985846. i) q^{58} +(7.68270e7 + 1.33068e8i) q^{59} +(-2.05388e7 - 898999. i) q^{60} +(7.75804e7 - 1.34373e8i) q^{61} -1.31427e8 q^{62} +(5.01142e7 + 1.07532e8i) q^{63} +1.38201e8 q^{64} +(4.34996e7 - 7.53435e7i) q^{65} +(-2.46215e7 + 3.86386e7i) q^{66} +(6.98640e6 + 1.21008e7i) q^{67} +(-4.63753e7 - 8.03244e7i) q^{68} +(9.95597e7 - 1.56240e8i) q^{69} +(3.95078e7 - 6.84295e7i) q^{70} -3.45182e8 q^{71} +(-1.42081e8 + 2.02819e8i) q^{72} -3.01511e8 q^{73} +(3.26059e7 - 5.64751e7i) q^{74} +(1.97027e8 + 8.62402e6i) q^{75} +(8.26721e7 + 1.43192e8i) q^{76} +(5.55451e7 + 9.62069e7i) q^{77} +(-1.34941e8 - 2.59288e8i) q^{78} +(-1.79834e8 + 3.11482e8i) q^{79} +8.99059e7 q^{80} +(-1.32346e8 - 3.64114e8i) q^{81} +4.49361e8 q^{82} +(5.25069e7 - 9.09446e7i) q^{83} +(7.73161e7 + 1.48563e8i) q^{84} +(-1.73245e8 - 3.00070e8i) q^{85} +(2.15137e8 + 3.72628e8i) q^{86} +(-9.00495e6 - 394154. i) q^{87} +(-1.15941e8 + 2.00817e8i) q^{88} +8.60555e8 q^{89} +(-1.48049e8 + 2.11337e8i) q^{90} -7.08730e8 q^{91} +(1.30768e8 - 2.26497e8i) q^{92} +(5.59236e8 - 8.77612e8i) q^{93} +(6.23135e7 + 1.07930e8i) q^{94} +(3.08840e8 + 5.34927e8i) q^{95} +(-3.23325e8 + 5.07396e8i) q^{96} +(-4.74261e7 + 8.21444e7i) q^{97} +7.13133e7 q^{98} +(-1.53245e8 - 3.28822e8i) 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

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