LMFDB - Embedded newform 98.2.g.b.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			51.1
Character	$\chi$	$=$	98.51
Dual form			98.2.g.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.955573 + 0.294755i) q^{2} +(-0.784496 + 1.99886i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-2.07983 + 0.313484i) q^{5} +(-1.33882 + 1.67883i) q^{6} +(2.53097 - 0.770831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-1.18087 - 1.09568i) q^{9} +O(q^{10})$	\(q+(0.955573 + 0.294755i) q^{2} +(-0.784496 + 1.99886i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-2.07983 + 0.313484i) q^{5} +(-1.33882 + 1.67883i) q^{6} +(2.53097 - 0.770831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-1.18087 - 1.09568i) q^{9} +(-2.07983 - 0.313484i) q^{10} +(1.11500 - 1.03457i) q^{11} +(-1.77418 + 1.20962i) q^{12} +(-1.28404 - 5.62575i) q^{13} +(2.64573 + 0.00943213i) q^{14} +(1.00501 - 4.40322i) q^{15} +(0.365341 + 0.930874i) q^{16} +(0.428922 + 5.72356i) q^{17} +(-0.805444 - 1.39507i) q^{18} +(2.53955 - 4.39863i) q^{19} +(-1.89503 - 0.912597i) q^{20} +(-0.444752 + 5.66378i) q^{21} +(1.37041 - 0.659954i) q^{22} +(0.232762 - 3.10600i) q^{23} +(-2.05190 + 0.632927i) q^{24} +(-0.550446 + 0.169790i) q^{25} +(0.431225 - 5.75430i) q^{26} +(-2.68744 + 1.29420i) q^{27} +(2.52541 + 0.788857i) q^{28} +(-4.81588 - 2.31920i) q^{29} +(2.25823 - 3.91137i) q^{30} +(0.901552 + 1.56153i) q^{31} +(0.0747301 + 0.997204i) q^{32} +(1.19325 + 3.04035i) q^{33} +(-1.27718 + 5.59570i) q^{34} +(-5.02235 + 2.39662i) q^{35} +(-0.358456 - 1.57050i) q^{36} +(-9.09175 + 6.19865i) q^{37} +(3.72324 - 3.45466i) q^{38} +(12.2524 + 1.84676i) q^{39} +(-1.54184 - 1.43062i) q^{40} +(1.63451 + 2.04961i) q^{41} +(-2.09442 + 5.28106i) q^{42} +(1.98627 - 2.49071i) q^{43} +(1.50405 - 0.226699i) q^{44} +(2.79948 + 1.90865i) q^{45} +(1.13793 - 2.89940i) q^{46} +(4.24327 + 1.30887i) q^{47} -2.14730 q^{48} +(5.81164 - 3.90190i) q^{49} -0.576038 q^{50} +(-11.7771 - 3.63275i) q^{51} +(2.10818 - 5.37154i) q^{52} +(-0.646629 - 0.440864i) q^{53} +(-2.94952 + 0.444569i) q^{54} +(-1.99469 + 2.50126i) q^{55} +(2.18070 + 1.49819i) q^{56} +(6.79999 + 8.52692i) q^{57} +(-3.91832 - 3.63567i) q^{58} +(-5.69709 - 0.858698i) q^{59} +(3.31080 - 3.07197i) q^{60} +(7.43578 - 5.06963i) q^{61} +(0.401228 + 1.75790i) q^{62} +(-3.83332 - 1.86290i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(4.43417 + 11.2981i) q^{65} +(0.244078 + 3.25699i) q^{66} +(5.16363 + 8.94367i) q^{67} +(-2.86980 + 4.97065i) q^{68} +(6.02586 + 2.90190i) q^{69} +(-5.50563 + 0.809778i) q^{70} +(-8.34228 + 4.01743i) q^{71} +(0.120382 - 1.60638i) q^{72} +(-9.55997 + 2.94886i) q^{73} +(-10.5149 + 3.24342i) q^{74} +(0.0924355 - 1.23347i) q^{75} +(4.57611 - 2.20374i) q^{76} +(2.02456 - 3.47794i) q^{77} +(11.1638 + 5.37618i) q^{78} +(8.33760 - 14.4412i) q^{79} +(-1.05166 - 1.82153i) q^{80} +(-0.839795 - 11.2063i) q^{81} +(0.957760 + 2.44033i) q^{82} +(-1.62663 + 7.12673i) q^{83} +(-3.55799 + 4.42910i) q^{84} +(-2.68633 - 11.7696i) q^{85} +(2.63218 - 1.79459i) q^{86} +(8.41381 - 7.80687i) q^{87} +(1.50405 + 0.226699i) q^{88} +(-10.2162 - 9.47921i) q^{89} +(2.11252 + 2.64902i) q^{90} +(-7.58638 - 13.2488i) q^{91} +(1.94199 - 2.43517i) q^{92} +(-3.82856 + 0.577062i) q^{93} +(3.66895 + 2.50145i) q^{94} +(-3.90293 + 9.94450i) q^{95} +(-2.05190 - 0.632927i) q^{96} +2.41732 q^{97} +(6.70355 - 2.01554i) q^{98} -2.45022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{21}\right)$

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 $

$2$	0.955573	+	0.294755i	0.675692	+	0.208423i
$2$	0.955573	+	0.294755i	0.675692	+	0.208423i
$3$	−0.784496	+	1.99886i	−0.452929	+	1.15404i	0.503995	+	0.863706i	$0.331863\pi$
$3$	−0.784496	+	1.99886i	−0.452929	+	1.15404i	−0.956924	+	0.290338i	$0.906232\pi$
$4$	0.826239	+	0.563320i	0.413119	+	0.281660i
$5$	−2.07983	+	0.313484i	−0.930128	+	0.140194i	−0.596593	−	0.802544i	$-0.703479\pi$
$5$	−2.07983	+	0.313484i	−0.930128	+	0.140194i	−0.333535	+	0.942738i	$0.608241\pi$
$6$	−1.33882	+	1.67883i	−0.546570	+	0.685378i
$7$	2.53097	−	0.770831i	0.956618	−	0.291347i
$7$	2.53097	−	0.770831i	0.956618	−	0.291347i
$8$	0.623490	+	0.781831i	0.220437	+	0.276419i
$9$	−1.18087	−	1.09568i	−0.393622	−	0.365228i
$10$	−2.07983	−	0.313484i	−0.657700	−	0.0991323i
$11$	1.11500	−	1.03457i	0.336185	−	0.311934i	−0.493957	−	0.869486i	$-0.664450\pi$
$11$	1.11500	−	1.03457i	0.336185	−	0.311934i	0.830142	+	0.557552i	$0.188259\pi$
$12$	−1.77418	+	1.20962i	−0.512162	+	0.349186i
$13$	−1.28404	−	5.62575i	−0.356129	−	1.56030i	−0.762742	−	0.646703i	$-0.776147\pi$
$13$	−1.28404	−	5.62575i	−0.356129	−	1.56030i	0.406613	−	0.913601i	$-0.366710\pi$
$14$	2.64573	+	0.00943213i	0.707102	+	0.00252084i
$15$	1.00501	−	4.40322i	0.259492	−	1.13691i
$16$	0.365341	+	0.930874i	0.0913353	+	0.232718i
$17$	0.428922	+	5.72356i	0.104029	+	1.38817i	0.768020	+	0.640426i	$0.221242\pi$
$17$	0.428922	+	5.72356i	0.104029	+	1.38817i	−0.663991	+	0.747741i	$0.731139\pi$
$18$	−0.805444	−	1.39507i	−0.189845	−	0.328821i
$19$	2.53955	−	4.39863i	0.582612	−	1.00911i	−0.412556	−	0.910932i	$-0.635364\pi$
$19$	2.53955	−	4.39863i	0.582612	−	1.00911i	0.995168	−	0.0981821i	$-0.0313028\pi$
$20$	−1.89503	−	0.912597i	−0.423741	−	0.204063i
$21$	−0.444752	+	5.66378i	−0.0970529	+	1.23594i
$22$	1.37041	−	0.659954i	0.292172	−	0.140703i
$23$	0.232762	−	3.10600i	0.0485343	−	0.647645i	−0.918895	−	0.394503i	$-0.870917\pi$
$23$	0.232762	−	3.10600i	0.0485343	−	0.647645i	0.967429	−	0.253142i	$-0.0814641\pi$
$24$	−2.05190	+	0.632927i	−0.418842	+	0.129196i
$25$	−0.550446	+	0.169790i	−0.110089	+	0.0339580i
$26$	0.431225	−	5.75430i	0.0845702	−	1.12851i
$27$	−2.68744	+	1.29420i	−0.517198	+	0.249070i
$28$	2.52541	+	0.788857i	0.477258	+	0.149080i
$29$	−4.81588	−	2.31920i	−0.894286	−	0.430665i	−0.0704641	−	0.997514i	$-0.522448\pi$
$29$	−4.81588	−	2.31920i	−0.894286	−	0.430665i	−0.823822	+	0.566849i	$0.808162\pi$
$30$	2.25823	−	3.91137i	0.412294	−	0.714115i
$31$	0.901552	+	1.56153i	0.161924	+	0.280460i	0.935559	−	0.353172i	$-0.114897\pi$
$31$	0.901552	+	1.56153i	0.161924	+	0.280460i	−0.773635	+	0.633632i	$0.781564\pi$
$32$	0.0747301	+	0.997204i	0.0132105	+	0.176282i
$33$	1.19325	+	3.04035i	0.207718	+	0.529257i
$34$	−1.27718	+	5.59570i	−0.219035	+	0.959655i
$35$	−5.02235	+	2.39662i	−0.848932	+	0.405102i
$36$	−0.358456	−	1.57050i	−0.0597427	−	0.261750i
$37$	−9.09175	+	6.19865i	−1.49467	+	1.01905i	−0.507102	+	0.861886i	$0.669283\pi$
$37$	−9.09175	+	6.19865i	−1.49467	+	1.01905i	−0.987572	+	0.157166i	$0.949764\pi$
$38$	3.72324	−	3.45466i	0.603990	−	0.560420i
$39$	12.2524	+	1.84676i	1.96196	+	0.295718i
$40$	−1.54184	−	1.43062i	−0.243787	−	0.226201i
$41$	1.63451	+	2.04961i	0.255268	+	0.320096i	0.892908	−	0.450238i	$-0.148661\pi$
$41$	1.63451	+	2.04961i	0.255268	+	0.320096i	−0.637641	+	0.770334i	$0.720090\pi$
$42$	−2.09442	+	5.28106i	−0.323176	+	0.814886i
$43$	1.98627	−	2.49071i	0.302904	−	0.379829i	−0.606963	−	0.794730i	$-0.707612\pi$
$43$	1.98627	−	2.49071i	0.302904	−	0.379829i	0.909867	+	0.414901i	$0.136184\pi$
$44$	1.50405	−	0.226699i	0.226744	−	0.0341762i
$45$	2.79948	+	1.90865i	0.417321	+	0.284525i
$46$	1.13793	−	2.89940i	0.167779	−	0.427493i
$47$	4.24327	+	1.30887i	0.618944	+	0.190919i	0.588341	−	0.808613i	$-0.299781\pi$
$47$	4.24327	+	1.30887i	0.618944	+	0.190919i	0.0306028	+	0.999532i	$0.490257\pi$
$48$	−2.14730			−0.309936
$49$	5.81164	−	3.90190i	0.830234	−	0.557415i
$50$	−0.576038			−0.0814641
$51$	−11.7771	−	3.63275i	−1.64912	−	0.508687i
$52$	2.10818	−	5.37154i	0.292351	−	0.744899i
$53$	−0.646629	−	0.440864i	−0.0888213	−	0.0605574i	0.518095	−	0.855323i	$-0.326641\pi$
$53$	−0.646629	−	0.440864i	−0.0888213	−	0.0605574i	−0.606916	+	0.794766i	$0.707594\pi$
$54$	−2.94952	+	0.444569i	−0.401379	+	0.0604981i
$55$	−1.99469	+	2.50126i	−0.268964	+	0.337270i
$56$	2.18070	+	1.49819i	0.291408	+	0.200204i
$57$	6.79999	+	8.52692i	0.900681	+	1.12942i
$58$	−3.91832	−	3.63567i	−0.514501	−	0.477387i
$59$	−5.69709	−	0.858698i	−0.741697	−	0.111793i	−0.232685	−	0.972552i	$-0.574751\pi$
$59$	−5.69709	−	0.858698i	−0.741697	−	0.111793i	−0.509012	+	0.860759i	$0.669989\pi$
$60$	3.31080	−	3.07197i	0.427422	−	0.396590i
$61$	7.43578	−	5.06963i	0.952054	−	0.649099i	0.0155956	−	0.999878i	$-0.495036\pi$
$61$	7.43578	−	5.06963i	0.952054	−	0.649099i	0.936458	+	0.350779i	$0.114083\pi$
$62$	0.401228	+	1.75790i	0.0509561	+	0.223253i
$63$	−3.83332	−	1.86290i	−0.482953	−	0.234703i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	4.43417	+	11.2981i	0.549991	+	1.40135i
$66$	0.244078	+	3.25699i	0.0300439	+	0.400908i
$67$	5.16363	+	8.94367i	0.630838	+	1.09264i	0.987381	+	0.158364i	$0.0506219\pi$
$67$	5.16363	+	8.94367i	0.630838	+	1.09264i	−0.356543	+	0.934279i	$0.616045\pi$
$68$	−2.86980	+	4.97065i	−0.348015	+	0.602779i
$69$	6.02586	+	2.90190i	0.725428	+	0.349348i
$70$	−5.50563	+	0.809778i	−0.658049	+	0.0967870i
$71$	−8.34228	+	4.01743i	−0.990047	+	0.476781i	−0.857549	−	0.514402i	$-0.828014\pi$
$71$	−8.34228	+	4.01743i	−0.990047	+	0.476781i	−0.132498	+	0.991183i	$0.542300\pi$
$72$	0.120382	−	1.60638i	0.0141871	−	0.189314i
$73$	−9.55997	+	2.94886i	−1.11891	+	0.345138i	−0.798412	−	0.602111i	$-0.794326\pi$
$73$	−9.55997	+	2.94886i	−1.11891	+	0.345138i	−0.320498	+	0.947249i	$0.603850\pi$
$74$	−10.5149	+	3.24342i	−1.22233	+	0.377040i
$75$	0.0924355	−	1.23347i	0.0106735	−	0.142428i
$76$	4.57611	−	2.20374i	0.524916	−	0.252786i
$77$	2.02456	−	3.47794i	0.230720	−	0.396348i
$78$	11.1638	+	5.37618i	1.26405	+	0.608733i
$79$	8.33760	−	14.4412i	0.938054	−	1.62476i	0.168957	−	0.985623i	$-0.445960\pi$
$79$	8.33760	−	14.4412i	0.938054	−	1.62476i	0.769096	−	0.639133i	$-0.220707\pi$
$80$	−1.05166	−	1.82153i	−0.117579	−	0.203653i
$81$	−0.839795	−	11.2063i	−0.0933105	−	1.24514i
$82$	0.957760	+	2.44033i	0.105767	+	0.269490i
$83$	−1.62663	+	7.12673i	−0.178546	+	0.782260i	0.803757	+	0.594958i	$0.202831\pi$
$83$	−1.62663	+	7.12673i	−0.178546	+	0.782260i	−0.982302	+	0.187302i	$0.940026\pi$
$84$	−3.55799	+	4.42910i	−0.388209	+	0.483254i
$85$	−2.68633	−	11.7696i	−0.291373	−	1.27659i
$86$	2.63218	−	1.79459i	0.283835	−	0.193515i
$87$	8.41381	−	7.80687i	0.902055	−	0.836985i
$88$	1.50405	+	0.226699i	0.160332	+	0.0241662i
$89$	−10.2162	−	9.47921i	−1.08291	−	1.00479i	−0.999966	−	0.00823971i	$-0.997377\pi$
$89$	−10.2162	−	9.47921i	−1.08291	−	1.00479i	−0.0829442	−	0.996554i	$-0.526432\pi$
$90$	2.11252	+	2.64902i	0.222679	+	0.279231i
$91$	−7.58638	−	13.2488i	−0.795269	−	1.38886i
$92$	1.94199	−	2.43517i	0.202466	−	0.253885i
$93$	−3.82856	+	0.577062i	−0.397003	+	0.0598386i
$94$	3.66895	+	2.50145i	0.378424	+	0.258005i
$95$	−3.90293	+	9.94450i	−0.400432	+	1.02028i
$96$	−2.05190	−	0.632927i	−0.209421	−	0.0645979i
$97$	2.41732			0.245441			0.122721	−	0.992441i	$-0.460838\pi$
$97$	2.41732			0.245441			0.122721	+	0.992441i	$0.460838\pi$
$98$	6.70355	−	2.01554i	0.677161	−	0.203600i
$99$	−2.45022			−0.246257
$100$	−0.550446	−	0.169790i	−0.0550446	−	0.0169790i
$101$	4.00673	−	10.2090i	0.398685	−	1.01583i	−0.580752	−	0.814081i	$-0.697241\pi$
$101$	4.00673	−	10.2090i	0.398685	−	1.01583i	0.979437	−	0.201752i	$-0.0646634\pi$
$102$	−10.1831	−	6.94272i	−1.00828	−	0.687432i
$103$	0.632127	−	0.0952778i	0.0622853	−	0.00938800i	−0.117826	−	0.993034i	$-0.537592\pi$
$103$	0.632127	−	0.0952778i	0.0622853	−	0.00938800i	0.180111	+	0.983646i	$0.442354\pi$
$104$	3.59780	−	4.51150i	0.352794	−	0.442389i
$105$	−0.850495	−	11.9191i	−0.0829998	−	1.16319i
$106$	−0.487954	−	0.611875i	−0.0473943	−	0.0594306i
$107$	8.12408	+	7.53804i	0.785384	+	0.728730i	0.967038	−	0.254632i	$-0.0819544\pi$
$107$	8.12408	+	7.53804i	0.785384	+	0.728730i	−0.181653	+	0.983363i	$0.558145\pi$
$108$	−2.94952	−	0.444569i	−0.283818	−	0.0427786i
$109$	−9.77898	+	9.07357i	−0.936657	+	0.869091i	−0.991593	−	0.129399i	$-0.958695\pi$
$109$	−9.77898	+	9.07357i	−0.936657	+	0.869091i	0.0549357	+	0.998490i	$0.482505\pi$
$110$	−2.64333	+	1.80219i	−0.252032	+	0.171832i
$111$	−5.25781	−	23.0360i	−0.499050	−	2.18648i
$112$	1.64221	+	2.07440i	0.155175	+	0.196012i
$113$	−0.433973	+	1.90136i	−0.0408248	+	0.178865i	−0.991230	−	0.132150i	$-0.957812\pi$
$113$	−0.433973	+	1.90136i	−0.0408248	+	0.178865i	0.950405	+	0.311015i	$0.100669\pi$
$114$	3.98453	+	10.1524i	0.373186	+	0.950861i
$115$	0.489574	+	6.53291i	0.0456530	+	0.609197i
$116$	−2.67261	−	4.62910i	−0.248146	−	0.429801i
$117$	−4.64776	+	8.05016i	−0.429686	+	0.744237i
$118$	−5.19088	−	2.49979i	−0.477859	−	0.230125i
$119$	5.49748	+	14.1555i	0.503954	+	1.29764i
$120$	4.06919	−	1.95962i	0.371464	−	0.178888i
$121$	−0.649139	+	8.66215i	−0.0590126	+	0.787469i
$122$	8.59973	−	2.65266i	0.778583	−	0.240161i
$123$	−5.37916	+	1.65925i	−0.485023	+	0.149610i
$124$	−0.134746	+	1.79806i	−0.0121006	+	0.161471i
$125$	10.5667	−	5.08868i	0.945118	−	0.455145i
$126$	−3.11392	−	2.91002i	−0.277410	−	0.259246i
$127$	2.49342	+	1.20077i	0.221256	+	0.106551i	0.541228	−	0.840876i	$-0.317959\pi$
$127$	2.49342	+	1.20077i	0.221256	+	0.106551i	−0.319973	+	0.947427i	$0.603674\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.42036	+	5.92424i	0.301146	+	0.521600i
$130$	0.907005	+	12.1031i	0.0795496	+	1.06152i
$131$	1.72708	+	4.40054i	0.150896	+	0.384477i	0.986256	−	0.165227i	$-0.0528357\pi$
$131$	1.72708	+	4.40054i	0.150896	+	0.384477i	−0.835359	+	0.549704i	$0.814740\pi$
$132$	−0.726781	+	3.18423i	−0.0632581	+	0.277152i
$133$	3.03693	−	13.0904i	0.263335	−	1.13508i
$134$	2.29803	+	10.0683i	0.198520	+	0.869771i
$135$	5.18371	−	3.53419i	0.446143	−	0.304175i
$136$	−4.20743	+	3.90393i	−0.360784	+	0.334759i
$137$	−15.5406	−	2.34237i	−1.32772	−	0.200122i	−0.553402	−	0.832915i	$-0.686670\pi$
$137$	−15.5406	−	2.34237i	−1.32772	−	0.200122i	−0.774321	+	0.632793i	$0.781909\pi$
$138$	4.90280	+	4.54913i	0.417354	+	0.387248i
$139$	4.49884	+	5.64136i	0.381586	+	0.478494i	0.935119	−	0.354333i	$-0.115292\pi$
$139$	4.49884	+	5.64136i	0.381586	+	0.478494i	−0.553533	+	0.832827i	$0.686721\pi$
$140$	−5.49972	−	0.849012i	−0.464811	−	0.0717546i
$141$	−5.94509	+	7.45491i	−0.500667	+	0.627816i
$142$	−9.15582	+	1.38002i	−0.768339	+	0.115808i
$143$	−7.25193	−	4.94429i	−0.606437	−	0.413462i
$144$	0.588524	−	1.49953i	0.0490436	−	0.124961i
$145$	10.7432	+	3.31385i	0.892177	+	0.275200i
$146$	−10.0044			−0.827973
$147$	3.24016	+	14.6777i	0.267244	+	1.21060i
$148$	−11.0038			−0.904505
$149$	17.9194	+	5.52740i	1.46801	+	0.452822i	0.922736	−	0.385433i	$-0.125948\pi$
$149$	17.9194	+	5.52740i	1.46801	+	0.452822i	0.545278	+	0.838255i	$0.316424\pi$
$150$	0.451899	−	1.15142i	0.0368974	−	0.0940131i
$151$	9.36069	+	6.38201i	0.761762	+	0.519361i	0.880777	−	0.473532i	$-0.157021\pi$
$151$	9.36069	+	6.38201i	0.761762	+	0.519361i	−0.119014	+	0.992893i	$0.537973\pi$
$152$	5.02237	−	0.757000i	0.407368	−	0.0614008i
$153$	5.76471	−	7.22871i	0.466049	−	0.584407i
$154$	2.95975	−	2.72668i	0.238504	−	0.219722i
$155$	−2.36459	−	2.96510i	−0.189928	−	0.238163i
$156$	9.08312	+	8.42791i	0.727232	+	0.674773i
$157$	2.06761	+	0.311642i	0.165013	+	0.0248717i	0.231029	−	0.972947i	$-0.425791\pi$
$157$	2.06761	+	0.311642i	0.165013	+	0.0248717i	−0.0660161	+	0.997819i	$0.521029\pi$
$158$	12.2238	−	11.3420i	0.972472	−	0.902323i
$159$	1.38851	−	0.946667i	0.110116	−	0.0750756i
$160$	−0.468033	−	2.05059i	−0.0370013	−	0.162113i
$161$	−1.80508	−	8.04061i	−0.142260	−	0.633689i
$162$	2.50062	−	10.9560i	0.196468	−	0.860781i
$163$	5.25961	+	13.4013i	0.411964	+	1.04967i	0.974796	+	0.223097i	$0.0716165\pi$
$163$	5.25961	+	13.4013i	0.411964	+	1.04967i	−0.562832	+	0.826571i	$0.690288\pi$
$164$	0.195909	+	2.61422i	0.0152979	+	0.204136i
$165$	−3.43485	−	5.94934i	−0.267403	−	0.463155i
$166$	−3.65500	+	6.33065i	−0.283683	+	0.491354i
$167$	7.26685	+	3.49953i	0.562326	+	0.270802i	0.693379	−	0.720574i	$-0.256121\pi$
$167$	7.26685	+	3.49953i	0.562326	+	0.270802i	−0.131053	+	0.991375i	$0.541836\pi$
$168$	−4.70542	+	3.18359i	−0.363031	+	0.245619i
$169$	−18.2878	+	8.80692i	−1.40675	+	0.677455i
$170$	0.902160	−	12.0385i	0.0691925	−	0.923310i
$171$	−7.81836	+	2.41165i	−0.597885	+	0.184423i
$172$	3.04420	−	0.939012i	0.232118	−	0.0715990i
$173$	−1.07944	+	14.4041i	−0.0820681	+	1.09512i	0.792388	+	0.610018i	$0.208838\pi$
$173$	−1.07944	+	14.4041i	−0.0820681	+	1.09512i	−0.874456	+	0.485105i	$0.838781\pi$
$174$	10.3411	−	4.98002i	0.783959	−	0.377535i
$175$	−1.26228	+	0.854035i	−0.0954197	+	0.0645590i
$176$	1.37041	+	0.659954i	0.103298	+	0.0497459i
$177$	6.18576	−	10.7141i	0.464950	−	0.805317i
$178$	−6.96823	−	12.0693i	−0.522291	−	0.904635i
$179$	−1.49759	−	19.9840i	−0.111935	−	1.49368i	−0.716762	−	0.697318i	$-0.754377\pi$
$179$	−1.49759	−	19.9840i	−0.111935	−	1.49368i	0.604827	−	0.796357i	$-0.293242\pi$
$180$	1.23785	+	3.15400i	0.0922643	+	0.235085i
$181$	−0.854888	+	3.74551i	−0.0635434	+	0.278402i	−0.996711	−	0.0810403i	$-0.974176\pi$
$181$	−0.854888	+	3.74551i	−0.0635434	+	0.278402i	0.933167	+	0.359442i	$0.117033\pi$
$182$	−3.34417	−	14.8964i	−0.247886	−	1.10419i
$183$	4.30015	+	18.8402i	0.317877	+	1.39271i
$184$	2.57349	−	1.75458i	0.189720	−	0.129349i
$185$	16.9661	−	15.7423i	1.24737	−	1.15739i
$186$	−3.82856	−	0.577062i	−0.280723	−	0.0423123i
$187$	6.39966	+	5.93802i	0.467990	+	0.434231i
$188$	2.76864	+	3.47176i	0.201924	+	0.253204i
$189$	−5.80423	+	5.34716i	−0.422196	+	0.388948i
$190$	−6.66073	+	8.35229i	−0.483220	+	0.605939i
$191$	−15.7212	+	2.36960i	−1.13755	+	0.171458i	−0.690693	−	0.723148i	$-0.742694\pi$
$191$	−15.7212	+	2.36960i	−1.13755	+	0.171458i	−0.446856	+	0.894606i	$0.647456\pi$
$192$	−1.77418	−	1.20962i	−0.128040	−	0.0872965i
$193$	1.28063	−	3.26299i	0.0921816	−	0.234875i	−0.877345	−	0.479859i	$-0.840688\pi$
$193$	1.28063	−	3.26299i	0.0921816	−	0.234875i	0.969527	+	0.244985i	$0.0787829\pi$
$194$	2.30992	+	0.712517i	0.165843	+	0.0511557i
$195$	−26.0619			−1.86633
$196$	6.99982	+	0.0499098i	0.499987	+	0.00356499i
$197$	0.678889			0.0483689			0.0241844	−	0.999708i	$-0.492301\pi$
$197$	0.678889			0.0483689			0.0241844	+	0.999708i	$0.492301\pi$
$198$	−2.34137	−	0.722216i	−0.166394	−	0.0513257i
$199$	−6.27065	+	15.9773i	−0.444514	+	1.13260i	0.516544	+	0.856260i	$0.327218\pi$
$199$	−6.27065	+	15.9773i	−0.444514	+	1.13260i	−0.961059	+	0.276344i	$0.910877\pi$
$200$	−0.475945	−	0.324494i	−0.0336544	−	0.0229452i
$201$	−21.9280	+	3.30512i	−1.54668	+	0.233125i
$202$	6.83788	−	8.57442i	0.481111	−	0.603294i
$203$	−13.9766	−	2.15761i	−0.980962	−	0.151435i
$204$	−7.68429	−	9.63580i	−0.538008	−	0.674641i
$205$	−4.04202	−	3.75045i	−0.282307	−	0.261943i
$206$	0.632127	+	0.0952778i	0.0440424	+	0.00663832i
$207$	−3.67805	+	3.41273i	−0.255642	+	0.237201i
$208$	4.76775	−	3.25060i	0.330584	−	0.225389i
$209$	−1.71909	−	7.53181i	−0.118912	−	0.520986i
$210$	2.70051	−	11.6403i	0.186353	−	0.803255i
$211$	0.926203	−	4.05796i	0.0637625	−	0.279362i	−0.932989	−	0.359906i	$-0.882809\pi$
$211$	0.926203	−	4.05796i	0.0637625	−	0.279362i	0.996751	+	0.0805444i	$0.0256659\pi$
$212$	−0.285922	−	0.728518i	−0.0196372	−	0.0500348i
$213$	−1.48581	−	19.8267i	−0.101806	−	1.35851i
$214$	5.54127	+	9.59777i	0.378794	+	0.656090i
$215$	−3.35031	+	5.80291i	−0.228489	+	0.395755i
$216$	−2.68744	−	1.29420i	−0.182857	−	0.0880594i
$217$	3.48548	+	3.25726i	0.236610	+	0.221117i
$218$	−12.0190	+	5.78805i	−0.814030	+	0.392016i
$219$	1.60539	−	21.4224i	0.108482	−	1.44759i
$220$	−3.05710	+	0.942990i	−0.206110	+	0.0635764i
$221$	31.6486	−	9.76230i	2.12891	−	0.656683i
$222$	1.76575	−	23.5623i	0.118510	−	1.58140i
$223$	10.3621	−	4.99013i	0.693899	−	0.334164i	−0.0534738	−	0.998569i	$-0.517029\pi$
$223$	10.3621	−	4.99013i	0.693899	−	0.334164i	0.747372	+	0.664405i	$0.231315\pi$
$224$	0.957815	+	2.46629i	0.0639967	+	0.164786i
$225$	0.836039	+	0.402615i	0.0557359	+	0.0268410i
$226$	−0.975129	+	1.68897i	−0.0648646	+	0.112349i
$227$	−7.84172	−	13.5823i	−0.520473	−	0.901486i	−0.999717	−	0.0238041i	$-0.992422\pi$
$227$	−7.84172	−	13.5823i	−0.520473	−	0.901486i	0.479243	−	0.877682i	$-0.340911\pi$
$228$	0.815032	+	10.8758i	0.0539768	+	0.720270i
$229$	2.82025	+	7.18587i	0.186367	+	0.474855i	0.993269	−	0.115830i	$-0.0369527\pi$
$229$	2.82025	+	7.18587i	0.186367	+	0.474855i	−0.806902	+	0.590685i	$0.798857\pi$
$230$	−1.45779	+	6.38697i	−0.0961235	+	0.421145i
$231$	5.36367	+	6.77524i	0.352904	+	0.445778i
$232$	−1.18942	−	5.21120i	−0.0780895	−	0.342132i
$233$	15.3681	−	10.4778i	1.00680	−	0.686424i	0.0567067	−	0.998391i	$-0.481940\pi$
$233$	15.3681	−	10.4778i	1.00680	−	0.686424i	0.950093	+	0.311966i	$0.100988\pi$
$234$	−6.81410	+	6.32256i	−0.445452	+	0.413319i
$235$	−9.23558	−	1.39204i	−0.602463	−	0.0908067i
$236$	−4.22343	−	3.91877i	−0.274922	−	0.255090i
$237$	22.3251	+	27.9948i	1.45017	+	1.81845i
$238$	1.08083	+	15.1471i	0.0700596	+	0.981838i
$239$	11.6918	−	14.6611i	0.756281	−	0.948347i	−0.243486	−	0.969904i	$-0.578291\pi$
$239$	11.6918	−	14.6611i	0.756281	−	0.948347i	0.999768	+	0.0215574i	$0.00686247\pi$
$240$	4.46601	−	0.673143i	0.288280	−	0.0434512i
$241$	3.33942	+	2.27678i	0.215111	+	0.146660i	0.666082	−	0.745878i	$-0.267970\pi$
$241$	3.33942	+	2.27678i	0.215111	+	0.146660i	−0.450971	+	0.892538i	$0.648922\pi$
$242$	−3.17351	+	8.08598i	−0.204001	+	0.519787i
$243$	14.5077	+	4.47503i	0.930669	+	0.287073i
$244$	8.99955			0.576137
$245$	−10.8640	+	9.93715i	−0.694078	+	0.634861i
$246$	−5.62925			−0.358908
$247$	−28.0065	−	8.63886i	−1.78201	−	0.549677i
$248$	−0.658748	+	1.67846i	−0.0418305	+	0.106582i
$249$	−12.9693	−	8.84230i	−0.821895	−	0.560358i
$250$	11.5972	−	1.74800i	0.733472	−	0.110553i
$251$	−9.26035	+	11.6121i	−0.584508	+	0.732950i	−0.982874	−	0.184277i	$-0.941006\pi$
$251$	−9.26035	+	11.6121i	−0.584508	+	0.732950i	0.398366	+	0.917226i	$0.369577\pi$
$252$	−2.11783	−	3.69858i	−0.133411	−	0.232989i
$253$	−2.95384	−	3.70399i	−0.185706	−	0.232868i
$254$	2.02871	+	1.88237i	0.127293	+	0.118111i
$255$	25.6332	+	3.86358i	1.60521	+	0.241947i
$256$	−0.733052	+	0.680173i	−0.0458157	+	0.0425108i
$257$	7.01640	−	4.78370i	0.437671	−	0.298399i	−0.324367	−	0.945931i	$-0.605151\pi$
$257$	7.01640	−	4.78370i	0.437671	−	0.298399i	0.762038	+	0.647532i	$0.224199\pi$
$258$	1.52220	+	6.66921i	0.0947683	+	0.415207i
$259$	−18.2329	+	22.6968i	−1.13293	+	1.41031i
$260$	−2.70075	+	11.8328i	−0.167494	+	0.733837i
$261$	3.14579	+	8.01534i	0.194719	+	0.496137i
$262$	0.353273	+	4.71410i	0.0218253	+	0.291238i
$263$	−5.52620	−	9.57165i	−0.340760	−	0.590214i	0.643814	−	0.765182i	$-0.277351\pi$
$263$	−5.52620	−	9.57165i	−0.340760	−	0.590214i	−0.984574	+	0.174968i	$0.944018\pi$
$264$	−1.63306	+	2.82854i	−0.100508	+	0.174085i
$265$	1.48308	+	0.714215i	0.0911050	+	0.0438738i
$266$	6.76046	−	11.6136i	0.414510	−	0.712078i
$267$	26.9622	−	12.9843i	1.65006	−	0.794626i
$268$	−0.771757	+	10.2984i	−0.0471426	+	0.629074i
$269$	1.80195	−	0.555827i	0.109867	−	0.0338894i	−0.239334	−	0.970937i	$-0.576929\pi$
$269$	1.80195	−	0.555827i	0.109867	−	0.0338894i	0.349201	+	0.937048i	$0.386453\pi$
$270$	5.99513	−	1.84925i	0.364852	−	0.112542i
$271$	0.856177	−	11.4249i	0.0520091	−	0.694013i	−0.908876	−	0.417066i	$-0.863058\pi$
$271$	0.856177	−	11.4249i	0.0520091	−	0.694013i	0.960885	−	0.276947i	$-0.0893225\pi$
$272$	−5.17121	+	2.49032i	−0.313551	+	0.150998i
$273$	32.4341	−	4.77047i	1.96300	−	0.288722i
$274$	−14.1597	−	6.81897i	−0.855422	−	0.411949i
$275$	−0.438088	+	0.758790i	−0.0264177	+	0.0457568i
$276$	3.34410	+	5.79215i	0.201291	+	0.348647i
$277$	0.0221886	+	0.296086i	0.00133318	+	0.0177901i	0.997831	−	0.0658321i	$-0.0209702\pi$
$277$	0.0221886	+	0.296086i	0.00133318	+	0.0177901i	−0.996498	+	0.0836222i	$0.973351\pi$
$278$	2.63614	+	6.71679i	0.158105	+	0.402846i
$279$	0.646334	−	2.83178i	0.0386950	−	0.169534i
$280$	−5.00513	−	2.43236i	−0.299114	−	0.145362i
$281$	−0.608997	−	2.66819i	−0.0363297	−	0.159171i	0.953509	−	0.301364i	$-0.0974418\pi$
$281$	−0.608997	−	2.66819i	−0.0363297	−	0.159171i	−0.989839	+	0.142193i	$0.954585\pi$
$282$	−7.87834	+	5.37136i	−0.469148	+	0.319860i
$283$	−21.6679	+	20.1049i	−1.28803	+	1.19511i	−0.319111	+	0.947717i	$0.603384\pi$
$283$	−21.6679	+	20.1049i	−1.28803	+	1.19511i	−0.968914	+	0.247396i	$0.920425\pi$
$284$	−9.15582	−	1.38002i	−0.543298	−	0.0818890i
$285$	−16.8159	−	15.6028i	−0.996086	−	0.924233i
$286$	−5.47240	−	6.86217i	−0.323590	−	0.405769i
$287$	5.71680	+	3.92758i	0.337452	+	0.231838i
$288$	1.00437	−	1.25944i	0.0591832	−	0.0742134i
$289$	−15.7650	+	2.37620i	−0.927355	+	0.139776i
$290$	9.28917	+	6.33325i	0.545479	+	0.371901i
$291$	−1.89638	+	4.83189i	−0.111167	+	0.283250i
$292$	−9.55997	−	2.94886i	−0.559455	−	0.172569i
$293$	−20.7861			−1.21434			−0.607170	−	0.794572i	$-0.707695\pi$
$293$	−20.7861			−1.21434			−0.607170	+	0.794572i	$0.707695\pi$
$294$	−1.23012	+	14.9807i	−0.0717419	+	0.873690i
$295$	12.1182			0.705546
$296$	−10.5149	−	3.24342i	−0.611167	−	0.188520i
$297$	−1.65755	+	4.22338i	−0.0961811	+	0.245065i
$298$	15.4941	+	10.5637i	0.897547	+	0.611937i
$299$	−17.7724	+	2.67877i	−1.02781	+	0.154917i
$300$	0.771210	−	0.967067i	0.0445258	−	0.0558336i
$301$	3.10729	−	7.83499i	0.179101	−	0.451601i
$302$	7.06369	+	8.85759i	0.406470	+	0.509697i
$303$	17.2631	+	16.0178i	0.991739	+	0.920200i
$304$	5.02237	+	0.757000i	0.288053	+	0.0434169i
$305$	−13.8759	+	12.8750i	−0.794532	+	0.737218i
$306$	7.63930	−	5.20839i	0.436710	−	0.297744i
$307$	−1.63457	−	7.16153i	−0.0932900	−	0.408730i	0.906623	−	0.421942i	$-0.138651\pi$
$307$	−1.63457	−	7.16153i	−0.0932900	−	0.408730i	−0.999913	+	0.0132121i	$0.995794\pi$
$308$	3.63196	−	1.73314i	0.206950	−	0.0987546i
$309$	−0.305454	+	1.33828i	−0.0173767	+	0.0761321i
$310$	−1.38556	−	3.53035i	−0.0786945	−	0.200510i
$311$	−1.59161	−	21.2386i	−0.0902519	−	1.20433i	−0.839993	−	0.542597i	$-0.817441\pi$
$311$	−1.59161	−	21.2386i	−0.0902519	−	1.20433i	0.749741	−	0.661731i	$-0.230178\pi$
$312$	6.19542	+	10.7308i	0.350746	+	0.607511i
$313$	−4.04865	+	7.01246i	−0.228843	+	0.396368i	−0.957465	−	0.288548i	$-0.906828\pi$
$313$	−4.04865	+	7.01246i	−0.228843	+	0.396368i	0.728622	+	0.684916i	$0.240161\pi$
$314$	1.88389	+	0.907234i	0.106314	+	0.0511982i
$315$	8.55664	+	2.67282i	0.482112	+	0.150596i
$316$	15.0238	−	7.23510i	0.845157	−	0.407006i
$317$	−1.05889	+	14.1299i	−0.0594730	+	0.793612i	0.885119	+	0.465365i	$0.154077\pi$
$317$	−1.05889	+	14.1299i	−0.0594730	+	0.793612i	−0.944592	+	0.328247i	$0.893542\pi$
$318$	1.60585	−	0.495340i	0.0900517	−	0.0277773i
$319$	−7.76908	+	2.39644i	−0.434985	+	0.134175i
$320$	0.157181	−	2.09744i	0.00878671	−	0.117250i
$321$	−21.4408	+	10.3254i	−1.19671	+	0.576305i
$322$	0.645123	−	8.21545i	0.0359513	−	0.457829i
$323$	26.2651	+	12.6486i	1.46143	+	0.703787i
$324$	5.61885	−	9.73214i	0.312158	−	0.540674i
$325$	1.66199	+	2.87866i	0.0921908	+	0.159679i
$326$	1.07585	+	14.3562i	0.0595856	+	0.795115i
$327$	−10.4653	−	26.6650i	−0.578730	−	1.47458i
$328$	−0.583350	+	2.55582i	−0.0322101	+	0.141122i
$329$	11.7485	+	0.0418838i	0.647717	+	0.00230913i
$330$	−1.52865	−	6.69747i	−0.0841496	−	0.368683i
$331$	7.51033	−	5.12046i	0.412805	−	0.281446i	−0.339057	−	0.940766i	$-0.610108\pi$
$331$	7.51033	−	5.12046i	0.412805	−	0.281446i	0.751863	+	0.659320i	$0.229156\pi$
$332$	−5.35862	+	4.97207i	−0.294092	+	0.272878i
$333$	17.5279	+	2.64190i	0.960522	+	0.144775i
$334$	5.91250	+	5.48600i	0.323518	+	0.300181i
$335$	−13.5432	−	16.9826i	−0.739942	−	0.927858i
$336$	−5.43475	+	1.65520i	−0.296490	+	0.0902988i
$337$	4.45792	−	5.59006i	0.242839	−	0.304510i	−0.645444	−	0.763808i	$-0.723328\pi$
$337$	4.45792	−	5.59006i	0.242839	−	0.304510i	0.888282	+	0.459298i	$0.151899\pi$
$338$	−20.0712	+	3.02524i	−1.09173	+	0.164551i
$339$	−3.46011	−	2.35906i	−0.187927	−	0.128127i
$340$	4.41049	−	11.2377i	0.239192	−	0.609452i
$341$	2.62074	+	0.808393i	0.141921	+	0.0437769i
$342$	−8.18186			−0.442424
$343$	11.7014	−	14.3554i	0.631816	−	0.775119i
$344$	3.18573			0.171763
$345$	−13.4425	−	4.14645i	−0.723718	−	0.223237i
$346$	−5.27716	+	13.4460i	−0.283702	+	0.722861i
$347$	10.9049	+	7.43485i	0.585407	+	0.399124i	0.819491	−	0.573093i	$-0.194257\pi$
$347$	10.9049	+	7.43485i	0.585407	+	0.399124i	−0.234084	+	0.972216i	$0.575209\pi$
$348$	11.3496	−	1.71067i	0.608402	−	0.0917018i
$349$	0.156774	−	0.196588i	0.00839192	−	0.0105231i	−0.777618	−	0.628737i	$-0.783572\pi$
$349$	0.156774	−	0.196588i	0.00839192	−	0.0105231i	0.786010	+	0.618214i	$0.212144\pi$
$350$	−1.45794	+	0.444028i	−0.0779300	+	0.0237343i
$351$	10.7317	+	13.4571i	0.572814	+	0.718286i
$352$	1.11500	+	1.03457i	0.0594297	+	0.0551427i
$353$	11.8640	+	1.78821i	0.631455	+	0.0951766i	0.456968	−	0.889483i	$-0.348935\pi$
$353$	11.8640	+	1.78821i	0.631455	+	0.0951766i	0.174487	+	0.984660i	$0.444173\pi$
$354$	9.06897	−	8.41477i	0.482010	−	0.447240i
$355$	16.0911	−	10.9707i	0.854028	−	0.582267i
$356$	−3.10116	−	13.5871i	−0.164361	−	0.720112i
$357$	−32.6078	−	0.116248i	−1.72579	−	0.00615248i
$358$	4.45933	−	19.5376i	0.235683	−	1.03259i
$359$	−8.57627	−	21.8520i	−0.452638	−	1.15330i	−0.957071	−	0.289852i	$-0.906394\pi$
$359$	−8.57627	−	21.8520i	−0.452638	−	1.15330i	0.504433	−	0.863451i	$-0.331701\pi$
$360$	0.253202	+	3.37874i	0.0133449	+	0.178075i
$361$	−3.39862	−	5.88658i	−0.178875	−	0.309820i
$362$	−1.92092	+	3.32713i	−0.100961	+	0.174870i
$363$	−16.8052	−	8.09297i	−0.882045	−	0.424771i
$364$	1.19518	−	15.2203i	0.0626445	−	0.797759i
$365$	18.9587	−	9.13002i	0.992343	−	0.477887i
$366$	−1.44414	+	19.2707i	−0.0754863	+	1.00729i
$367$	11.9125	−	3.67453i	0.621829	−	0.191809i	0.0321977	−	0.999482i	$-0.489749\pi$
$367$	11.9125	−	3.67453i	0.621829	−	0.191809i	0.589631	+	0.807673i	$0.299273\pi$
$368$	2.97633	−	0.918076i	0.155152	−	0.0478580i
$369$	0.315587	−	4.21122i	0.0164288	−	0.219227i
$370$	20.8525	−	10.0420i	1.08407	−	0.522060i
$371$	−1.97643	−	0.617373i	−0.102611	−	0.0320524i
$372$	−3.48837	−	1.67991i	−0.180864	−	0.0870994i
$373$	−0.499806	+	0.865689i	−0.0258790	+	0.0448237i	−0.878675	−	0.477421i	$-0.841572\pi$
$373$	−0.499806	+	0.865689i	−0.0258790	+	0.0448237i	0.852796	+	0.522244i	$0.174905\pi$
$374$	4.36508	+	7.56054i	0.225713	+	0.390946i
$375$	1.88200	+	25.1135i	0.0971860	+	1.29686i
$376$	1.62231	+	4.13359i	0.0836645	+	0.213174i
$377$	−6.86349	+	30.0709i	−0.353487	+	1.54873i
$378$	−7.12247	+	3.39877i	−0.366340	+	0.174814i
$379$	−4.51139	−	19.7657i	−0.231735	−	1.01530i	−0.948200	−	0.317673i	$-0.897098\pi$
$379$	−4.51139	−	19.7657i	−0.231735	−	1.01530i	0.716466	−	0.697622i	$-0.245759\pi$
$380$	−8.82669	+	6.01793i	−0.452800	+	0.308714i
$381$	−4.35625	+	4.04201i	−0.223178	+	0.207079i
$382$	−15.7212	−	2.36960i	−0.804369	−	0.121239i
$383$	−21.6833	−	20.1192i	−1.10797	−	1.02804i	−0.999423	−	0.0339513i	$-0.989191\pi$
$383$	−21.6833	−	20.1192i	−1.10797	−	1.02804i	−0.108543	−	0.994092i	$-0.534619\pi$
$384$	−1.33882	−	1.67883i	−0.0683213	−	0.0856722i
$385$	−3.12045	+	7.86819i	−0.159033	+	0.401000i
$386$	2.18551	−	2.74055i	0.111240	−	0.139490i
$387$	−5.07455	+	0.764865i	−0.257954	+	0.0388803i
$388$	1.99728	+	1.36172i	0.101397	+	0.0691310i
$389$	8.25950	−	21.0449i	0.418773	−	1.06702i	−0.553434	−	0.832893i	$-0.686683\pi$
$389$	8.25950	−	21.0449i	0.418773	−	1.06702i	0.972207	−	0.234124i	$-0.0752221\pi$
$390$	−24.9041	−	7.68188i	−1.26107	−	0.388987i
$391$	17.8772			0.904088
$392$	6.67413	+	2.11093i	0.337094	+	0.106618i
$393$	−10.1510			−0.512049
$394$	0.648728	+	0.200106i	0.0326824	+	0.0100812i
$395$	−12.8137	+	32.6488i	−0.644728	+	1.64274i
$396$	−2.02447	−	1.38026i	−0.101733	−	0.0693607i
$397$	−27.1135	+	4.08671i	−1.36079	+	0.205106i	−0.788545	−	0.614977i	$-0.789165\pi$
$397$	−27.1135	+	4.08671i	−1.36079	+	0.205106i	−0.572244	+	0.820083i	$0.693927\pi$
$398$	−10.7015	+	13.4192i	−0.536416	+	0.672644i
$399$	23.7834	+	16.3397i	1.19066	+	0.818011i
$400$	−0.359154	−	0.450365i	−0.0179577	−	0.0225182i
$401$	13.6275	+	12.6444i	0.680524	+	0.631434i	0.942722	−	0.333581i	$-0.108257\pi$
$401$	13.6275	+	12.6444i	0.680524	+	0.631434i	−0.262198	+	0.965014i	$0.584447\pi$
$402$	−21.9280	−	3.30512i	−1.09367	−	0.164844i
$403$	7.62718	−	7.07699i	0.379937	−	0.352530i
$404$	9.06144	−	6.17799i	0.450824	−	0.307366i
$405$	5.25962	+	23.0439i	0.261352	+	1.14506i
$406$	−12.7197	−	6.18142i	−0.631266	−	0.306779i
$407$	−3.72437	+	16.3175i	−0.184610	+	0.808830i
$408$	−4.50270	−	11.4727i	−0.222917	−	0.567983i
$409$	1.31613	+	17.5626i	0.0650786	+	0.868413i	0.930248	+	0.366933i	$0.119592\pi$
$409$	1.31613	+	17.5626i	0.0650786	+	0.868413i	−0.865169	+	0.501481i	$0.832789\pi$
$410$	−2.75698	−	4.77523i	−0.136158	−	0.235832i
$411$	16.8736	−	29.2260i	0.832314	−	1.44161i
$412$	0.575960	+	0.277368i	0.0283755	+	0.0136649i
$413$	−15.0811	+	2.21815i	−0.742091	+	0.109148i
$414$	−4.52056	+	2.17699i	−0.222173	+	0.106993i
$415$	1.14900	−	15.3323i	0.0564021	−	0.752633i
$416$	5.51407	−	1.70086i	0.270349	−	0.0833917i
$417$	−14.8056	+	4.56693i	−0.725035	+	0.223644i
$418$	0.577327	−	7.70390i	0.0282380	−	0.376810i
$419$	26.9649	−	12.9856i	1.31732	−	0.634389i	0.362616	−	0.931939i	$-0.381884\pi$
$419$	26.9649	−	12.9856i	1.31732	−	0.634389i	0.954706	+	0.297549i	$0.0961693\pi$
$420$	6.01157	−	10.3271i	0.293334	−	0.503913i
$421$	−26.4320	−	12.7290i	−1.28822	−	0.620373i	−0.340729	−	0.940162i	$-0.610674\pi$
$421$	−26.4320	−	12.7290i	−1.28822	−	0.620373i	−0.947489	+	0.319789i	$0.896388\pi$
$422$	2.08116	−	3.60467i	0.101309	−	0.175473i
$423$	−3.57662	−	6.19488i	−0.173901	−	0.301205i
$424$	−0.0584851	−	0.780429i	−0.00284029	−	0.0379010i
$425$	−1.20790	−	3.07768i	−0.0585919	−	0.149290i
$426$	4.42424	−	19.3838i	0.214355	−	0.939150i
$427$	14.9119	−	18.5628i	0.721639	−	0.898318i
$428$	2.46610	+	10.8047i	0.119203	+	0.522264i
$429$	15.5721	−	10.6169i	0.751826	−	0.512587i
$430$	−4.91191	+	4.55758i	−0.236873	+	0.219786i
$431$	22.4030	+	3.37671i	1.07911	+	0.162650i	0.664456	−	0.747327i	$-0.268663\pi$
$431$	22.4030	+	3.37671i	1.07911	+	0.162650i	0.414658	+	0.909978i	$0.363901\pi$
$432$	−2.18657	−	2.02884i	−0.105202	−	0.0976128i
$433$	−8.20001	−	10.2825i	−0.394067	−	0.494145i	0.544732	−	0.838610i	$-0.316631\pi$
$433$	−8.20001	−	10.2825i	−0.394067	−	0.494145i	−0.938799	+	0.344466i	$0.888060\pi$
$434$	2.37054	+	4.13991i	0.113790	+	0.198722i
$435$	−15.0520	+	18.8746i	−0.721686	+	0.904966i
$436$	−13.1911	+	1.98824i	−0.631739	+	0.0952194i
$437$	−13.0710	−	8.91166i	−0.625271	−	0.426303i
$438$	7.84844	−	19.9975i	0.375013	−	0.955518i
$439$	1.91014	+	0.589202i	0.0911662	+	0.0281211i	0.340003	−	0.940424i	$-0.389572\pi$
$439$	1.91014	+	0.589202i	0.0911662	+	0.0281211i	−0.248837	+	0.968546i	$0.580048\pi$
$440$	−3.19923			−0.152517
$441$	−11.1380	−	1.76009i	−0.530381	−	0.0838139i
$442$	33.1200			1.57536
$443$	9.76733	+	3.01282i	0.464060	+	0.143144i	0.517964	−	0.855403i	$-0.326690\pi$
$443$	9.76733	+	3.01282i	0.464060	+	0.143144i	−0.0539037	+	0.998546i	$0.517166\pi$
$444$	8.63242	−	21.9951i	0.409677	−	1.04384i
$445$	24.2194	+	16.5125i	1.14811	+	0.782769i
$446$	11.3726	−	1.71415i	0.538509	−	0.0811672i
$447$	−25.1062	+	31.4822i	−1.18748	+	1.48906i
$448$	0.188310	+	2.63904i	0.00889682	+	0.124683i
$449$	−14.1288	−	17.7169i	−0.666779	−	0.836114i	0.327284	−	0.944926i	$-0.393867\pi$
$449$	−14.1288	−	17.7169i	−0.666779	−	0.836114i	−0.994062	+	0.108812i	$0.965295\pi$
$450$	0.680223	+	0.631155i	0.0320660	+	0.0297529i
$451$	3.94294	+	0.594303i	0.185666	+	0.0279846i
$452$	−1.42964	+	1.32651i	−0.0672446	+	0.0623939i
$453$	−20.1002	+	13.7041i	−0.944390	+	0.643874i
$454$	−3.48989	−	15.2902i	−0.163789	−	0.717606i
$455$	19.9317	+	25.1771i	0.934411	+	1.18032i
$456$	−2.42689	+	10.6329i	−0.113649	+	0.497931i
$457$	−13.2183	−	33.6797i	−0.618327	−	1.57547i	−0.805146	−	0.593076i	$-0.797913\pi$
$457$	−13.2183	−	33.6797i	−0.618327	−	1.57547i	0.186820	−	0.982394i	$-0.440182\pi$
$458$	0.576878	+	7.69790i	0.0269557	+	0.359699i
$459$	−8.56015	−	14.8266i	−0.399554	−	0.692048i
$460$	−3.27561	+	5.67353i	−0.152726	+	0.264530i
$461$	30.3207	+	14.6017i	1.41218	+	0.680069i	0.975591	−	0.219594i	$-0.0704731\pi$
$461$	30.3207	+	14.6017i	1.41218	+	0.680069i	0.436586	+	0.899662i	$0.356187\pi$
$462$	3.12834	+	8.05521i	0.145544	+	0.374762i
$463$	−2.34369	+	1.12866i	−0.108921	+	0.0524534i	−0.487551	−	0.873095i	$-0.662110\pi$
$463$	−2.34369	+	1.12866i	−0.108921	+	0.0524534i	0.378630	+	0.925548i	$0.376395\pi$
$464$	0.399449	−	5.33027i	0.0185439	−	0.247452i
$465$	7.78185	−	2.40038i	0.360875	−	0.111315i
$466$	17.7738	−	5.48248i	0.823353	−	0.253971i
$467$	−0.0929301	+	1.24007i	−0.00430029	+	0.0573834i	−0.998941	−	0.0460075i	$-0.985350\pi$
$467$	−0.0929301	+	1.24007i	−0.00430029	+	0.0573834i	0.994641	+	0.103391i	$0.0329692\pi$
$468$	−8.37498	+	4.03318i	−0.387133	+	0.186434i
$469$	19.9631	+	18.6559i	0.921808	+	0.861449i
$470$	−8.41496	−	4.05243i	−0.388153	−	0.186925i
$471$	−2.24496	+	3.88838i	−0.103442	+	0.179167i
$472$	−2.88072	−	4.98955i	−0.132596	−	0.229663i
$473$	−0.362114	−	4.83207i	−0.0166500	−	0.222179i
$474$	13.0816	+	33.3315i	0.600859	+	1.53096i
$475$	−0.651041	+	2.85240i	−0.0298718	+	0.130877i
$476$	−3.43187	+	14.7927i	−0.157299	+	0.678022i
$477$	0.280534	+	1.22910i	0.0128448	+	0.0562767i
$478$	15.4938	−	10.5635i	0.708671	−	0.483164i
$479$	−23.3795	+	21.6930i	−1.06824	+	0.991180i	−0.999979	−	0.00648760i	$-0.997935\pi$
$479$	−23.3795	+	21.6930i	−1.06824	+	0.991180i	−0.0682591	+	0.997668i	$0.521744\pi$
$480$	4.46601	+	0.673143i	0.203845	+	0.0307246i
$481$	46.5463	+	43.1886i	2.12233	+	1.96923i
$482$	2.51996	+	3.15993i	0.114781	+	0.143931i
$483$	17.4882	+	2.69971i	0.795739	+	0.122841i
$484$	−5.41591	+	6.79133i	−0.246178	+	0.308697i
$485$	−5.02761	+	0.757790i	−0.228292	+	0.0344095i
$486$	12.5441	+	8.55243i	0.569013	+	0.387946i
$487$	−3.64051	+	9.27588i	−0.164967	+	0.420330i	−0.989322	−	0.145743i	$-0.953443\pi$
$487$	−3.64051	+	9.27588i	−0.164967	+	0.420330i	0.824355	+	0.566073i	$0.191538\pi$
$488$	8.59973	+	2.65266i	0.389291	+	0.120080i
$489$	−30.9134			−1.39795
$490$	−13.3104	+	6.29344i	−0.601303	+	0.284308i
$491$	3.75787			0.169590			0.0847951	−	0.996398i	$-0.472976\pi$
$491$	3.75787			0.169590			0.0847951	+	0.996398i	$0.472976\pi$
$492$	−5.37916	−	1.65925i	−0.242511	−	0.0748048i
$493$	11.2085	−	28.5587i	0.504804	−	1.28622i
$494$	−24.2159	−	16.5101i	−1.08952	−	0.742825i
$495$	5.09605	−	0.768105i	0.229050	−	0.0345238i
$496$	−1.12422	+	1.40972i	−0.0504788	+	0.0632985i
$497$	−18.0173	+	16.5985i	−0.808187	+	0.744544i
$498$	−9.78677	−	12.2722i	−0.438556	−	0.549932i
$499$	8.48357	+	7.87160i	0.379777	+	0.352381i	0.846845	−	0.531840i	$-0.178499\pi$
$499$	8.48357	+	7.87160i	0.379777	+	0.352381i	−0.467068	+	0.884221i	$0.654690\pi$
$500$	11.5972	+	1.74800i	0.518643	+	0.0781728i
$501$	−12.6959	+	11.7801i	−0.567211	+	0.526295i
$502$	−12.2717	+	8.36668i	−0.547711	+	0.373423i
$503$	−4.27151	−	18.7147i	−0.190457	−	0.834447i	−0.976369	−	0.216109i	$-0.930663\pi$
$503$	−4.27151	−	18.7147i	−0.190457	−	0.834447i	0.785912	−	0.618338i	$-0.212194\pi$
$504$	−0.933568	−	4.15851i	−0.0415844	−	0.185235i
$505$	−5.13297	+	22.4890i	−0.228414	+	1.00075i
$506$	−1.73083	−	4.41009i	−0.0769450	−	0.196053i
$507$	−3.25715	−	43.4637i	−0.144655	−	1.93029i
$508$	1.38375	+	2.39672i	0.0613938	+	0.106337i
$509$	−0.810486	+	1.40380i	−0.0359242	+	0.0622225i	−0.883428	−	0.468566i	$-0.844771\pi$
$509$	−0.810486	+	1.40380i	−0.0359242	+	0.0622225i	0.847504	+	0.530788i	$0.178104\pi$
$510$	23.3556	+	11.2474i	1.03420	+	0.498045i
$511$	−21.9229	+	14.8326i	−0.969814	+	0.656156i
$512$	−0.900969	+	0.433884i	−0.0398176	+	0.0191751i
$513$	−1.13217	+	15.1078i	−0.0499865	+	0.667023i
$514$	8.11470	−	2.50305i	0.357924	−	0.110405i
$515$	−1.28485	+	0.396323i	−0.0566172	+	0.0174641i
$516$	−0.511208	+	6.82159i	−0.0225047	+	0.300304i
$517$	6.08536	−	2.93056i	0.267634	−	0.128886i
$518$	−24.1128	+	16.3142i	−1.05946	+	0.716806i
$519$	−27.9450	−	13.4576i	−1.22665	−	0.590723i
$520$	−6.06854	+	10.5110i	−0.266123	+	0.460938i
$521$	15.3435	+	26.5758i	0.672213	+	1.16431i	0.977275	+	0.211974i	$0.0679893\pi$
$521$	15.3435	+	26.5758i	0.672213	+	1.16431i	−0.305063	+	0.952332i	$0.598677\pi$
$522$	0.643468	+	8.58648i	0.0281638	+	0.375820i
$523$	0.155612	+	0.396493i	0.00680445	+	0.0173374i	0.934236	−	0.356656i	$-0.116083\pi$
$523$	0.155612	+	0.396493i	0.00680445	+	0.0173374i	−0.927431	+	0.373994i	$0.877988\pi$
$524$	−1.05193	+	4.60880i	−0.0459537	+	0.201336i
$525$	−0.716842	−	3.19312i	−0.0312856	−	0.139359i
$526$	−2.45939	−	10.7753i	−0.107234	−	0.469825i
$527$	−8.55084	+	5.82986i	−0.372480	+	0.253953i
$528$	−2.39424	+	2.22153i	−0.104196	+	0.0966796i
$529$	13.1501	+	1.98206i	0.571742	+	0.0861763i
$530$	1.20667	+	1.11963i	0.0524146	+	0.0486336i
$531$	5.78663	+	7.25620i	0.251118	+	0.314892i
$532$	9.88329	−	9.10500i	0.428495	−	0.394752i
$533$	9.43183	−	11.8271i	0.408538	−	0.512290i
$534$	29.5915	−	4.46020i	1.28055	−	0.193012i
$535$	−19.2598	−	13.1311i	−0.832672	−	0.567706i
$536$	−3.77297	+	9.61337i	−0.162968	+	0.415234i
$537$	41.1202	+	12.6839i	1.77447	+	0.547350i
$538$	1.88572			0.0812993
$539$	2.44319	−	10.3632i	0.105236	−	0.446373i
$540$	6.27386			0.269984
$541$	12.2470	+	3.77769i	0.526538	+	0.162416i	0.546617	−	0.837383i	$-0.315915\pi$
$541$	12.2470	+	3.77769i	0.526538	+	0.162416i	−0.0200786	+	0.999798i	$0.506392\pi$
$542$	4.18569	−	10.6650i	0.179791	−	0.458099i
$543$	−6.81611	−	4.64714i	−0.292507	−	0.199428i
$544$	−5.67550	+	0.855444i	−0.243335	+	0.0366769i
$545$	17.4942	−	21.9370i	0.749369	−	0.939679i
$546$	32.3993	+	5.00160i	1.38656	+	0.214049i
$547$	1.84737	+	2.31652i	0.0789876	+	0.0990474i	0.819755	−	0.572714i	$-0.194109\pi$
$547$	1.84737	+	2.31652i	0.0789876	+	0.0990474i	−0.740768	+	0.671761i	$0.765538\pi$
$548$	−11.5207	−	10.6897i	−0.492142	−	0.456641i
$549$	−14.3354	−	2.16071i	−0.611818	−	0.0922167i
$550$	−0.642282	+	0.595951i	−0.0273870	+	0.0254114i
$551$	−22.4315	+	15.2935i	−0.955613	+	0.651526i
$552$	1.48826	+	6.52051i	0.0633447	+	0.277531i
$553$	9.97055	−	42.9770i	0.423991	−	1.82757i
$554$	−0.0660700	+	0.289472i	−0.00280705	+	0.0122985i
$555$	18.1568	+	46.2627i	0.770712	+	1.96374i
$556$	0.539220	+	7.19540i	0.0228680	+	0.305153i
$557$	−4.70066	−	8.14177i	−0.199173	−	0.344978i	0.749087	−	0.662471i	$-0.230492\pi$
$557$	−4.70066	−	8.14177i	−0.199173	−	0.344978i	−0.948261	+	0.317493i	$0.897159\pi$
$558$	1.45230	−	2.51546i	0.0614808	−	0.106488i
$559$	−16.5626	−	7.97611i	−0.700522	−	0.337354i
$560$	−4.06582	−	3.79959i	−0.171812	−	0.160562i
$561$	−16.8898	+	8.13370i	−0.713088	+	0.343405i
$562$	0.204522	−	2.72916i	0.00862724	−	0.115122i
$563$	−6.98003	+	2.15305i	−0.294173	+	0.0907404i	−0.438329	−	0.898815i	$-0.644430\pi$
$563$	−6.98003	+	2.15305i	−0.294173	+	0.0907404i	0.144156	+	0.989555i	$0.453953\pi$
$564$	−9.11156	+	2.81054i	−0.383666	+	0.118345i
$565$	0.306544	−	4.09055i	0.0128964	−	0.172091i
$566$	−26.6313	+	12.8250i	−1.11940	+	0.539074i
$567$	−10.7636	−	27.7154i	−0.452031	−	1.16394i
$568$	−8.34228	−	4.01743i	−0.350034	−	0.168568i
$569$	2.11256	−	3.65906i	0.0885631	−	0.153396i	−0.818341	−	0.574733i	$-0.805106\pi$
$569$	2.11256	−	3.65906i	0.0885631	−	0.153396i	0.906904	+	0.421337i	$0.138439\pi$
$570$	−11.4698	−	19.8662i	−0.480416	−	0.832104i
$571$	−3.34114	−	44.5844i	−0.139822	−	1.86580i	−0.422207	−	0.906499i	$-0.638744\pi$
$571$	−3.34114	−	44.5844i	−0.139822	−	1.86580i	0.282385	−	0.959301i	$-0.408875\pi$
$572$	−3.20661	−	8.17032i	−0.134075	−	0.341618i
$573$	7.59675	−	33.2836i	0.317359	−	1.39044i
$574$	4.30515	+	5.43814i	0.179693	+	0.226984i
$575$	0.399244	+	1.74920i	0.0166496	+	0.0729469i
$576$	1.33098	−	0.907446i	0.0554575	−	0.0378103i
$577$	19.9560	−	18.5165i	0.830780	−	0.770851i	−0.145040	−	0.989426i	$-0.546331\pi$
$577$	19.9560	−	18.5165i	0.830780	−	0.770851i	0.975820	+	0.218574i	$0.0701406\pi$
$578$	−15.7650	−	2.37620i	−0.655739	−	0.0988368i
$579$	5.51761	+	5.11960i	0.229304	+	0.212763i
$580$	7.00972	+	8.78991i	0.291063	+	0.364981i
$581$	1.37655	+	19.2914i	0.0571089	+	0.800343i
$582$	−3.23635	+	4.05825i	−0.134151	+	0.168220i
$583$	−1.17710	+	0.177419i	−0.0487503	+	0.00734793i
$584$	−8.26606	−	5.63570i	−0.342052	−	0.233207i
$585$	7.14296	−	18.2000i	0.295325	−	0.752476i
$586$	−19.8627	−	6.12682i	−0.820520	−	0.253097i
$587$	33.6655			1.38952			0.694762	−	0.719240i	$-0.255510\pi$
$587$	33.6655			1.38952			0.694762	+	0.719240i	$0.255510\pi$
$588$	−5.59110	+	13.9525i	−0.230573	+	0.575393i
$589$	9.15814			0.377355
$590$	11.5798	+	3.57189i	0.476732	+	0.147052i
$591$	−0.532586	+	1.35701i	−0.0219077	+	0.0558198i
$592$	−9.09175	−	6.19865i	−0.373669	−	0.254763i
$593$	10.2261	−	1.54134i	0.419936	−	0.0632951i	0.0643244	−	0.997929i	$-0.479511\pi$
$593$	10.2261	−	1.54134i	0.419936	−	0.0632951i	0.355611	+	0.934634i	$0.384273\pi$
$594$	−2.82878	+	3.54717i	−0.116066	+	0.145542i
$595$	−15.8714	−	27.7177i	−0.650662	−	1.13632i
$596$	11.6920	+	14.6613i	0.478923	+	0.600551i
$597$	−27.0172	−	25.0683i	−1.10574	−	1.02598i
$598$	−17.7724	−	2.67877i	−0.726769	−	0.109543i
$599$	−0.888333	+	0.824253i	−0.0362963	+	0.0336781i	−0.698112	−	0.715988i	$-0.745976\pi$
$599$	−0.888333	+	0.824253i	−0.0362963	+	0.0336781i	0.661816	+	0.749666i	$0.269786\pi$
$600$	1.02200	−	0.696785i	0.0417228	−	0.0284461i
$601$	2.44221	+	10.7000i	0.0996197	+	0.436462i	0.999999	+	0.00135673i	$0.000431860\pi$
$601$	2.44221	+	10.7000i	0.0996197	+	0.436462i	−0.900379	+	0.435106i	$0.856711\pi$
$602$	5.27864	−	6.57102i	0.215141	−	0.267815i
$603$	3.70187	−	16.2190i	0.150752	−	0.660487i
$604$	4.13905	+	10.5461i	0.168416	+	0.429116i
$605$	−1.36535	−	18.2193i	−0.0555093	−	0.740720i
$606$	11.7748	+	20.3946i	0.478319	+	0.828473i
$607$	4.46452	−	7.73277i	0.181209	−	0.313864i	−0.761083	−	0.648654i	$-0.775332\pi$
$607$	4.46452	−	7.73277i	0.181209	−	0.313864i	0.942293	+	0.334791i	$0.108666\pi$
$608$	4.57611	+	2.20374i	0.185586	+	0.0893734i
$609$	15.2773	−	26.2446i	0.619069	−	1.06348i
$610$	−17.0544	+	8.21296i	−0.690512	+	0.332533i
$611$	1.91488	−	25.5522i	0.0774676	−	1.03373i
$612$	8.83510	−	2.72527i	0.357138	−	0.110162i
$613$	−39.8164	+	12.2817i	−1.60817	+	0.496055i	−0.963343	−	0.268274i	$-0.913547\pi$
$613$	−39.8164	+	12.2817i	−1.60817	+	0.496055i	−0.644827	+	0.764329i	$0.723071\pi$
$614$	0.548945	−	7.32516i	0.0221536	−	0.295620i
$615$	10.6676	−	5.13724i	0.430159	−	0.207153i
$616$	3.98145	−	0.585599i	0.160417	−	0.0235945i
$617$	17.7487	+	8.54732i	0.714535	+	0.344102i	0.755581	−	0.655055i	$-0.227355\pi$
$617$	17.7487	+	8.54732i	0.714535	+	0.344102i	−0.0410457	+	0.999157i	$0.513069\pi$
$618$	−0.686348	+	1.18879i	−0.0276090	+	0.0478202i
$619$	10.4811	+	18.1537i	0.421269	+	0.729660i	0.996064	−	0.0886377i	$-0.0282513\pi$
$619$	10.4811	+	18.1537i	0.421269	+	0.729660i	−0.574794	+	0.818298i	$0.694918\pi$
$620$	−0.283415	−	3.78190i	−0.0113822	−	0.151885i
$621$	3.39426	+	8.64843i	0.136207	+	0.347049i
$622$	4.73928	−	20.7641i	0.190028	−	0.832565i
$623$	−33.1637	−	16.1167i	−1.32867	−	0.645701i
$624$	2.75722	+	12.0802i	0.110377	+	0.483594i
$625$	−18.0021	+	12.2736i	−0.720083	+	0.490944i
$626$	−5.93574	+	5.50756i	−0.237240	+	0.220126i
$627$	16.4037	+	2.47246i	0.655099	+	0.0987403i
$628$	1.53278	+	1.42221i	0.0611647	+	0.0567525i
$629$	−39.3780	−	49.3784i	−1.57010	−	1.96885i
$630$	7.38867	+	5.07619i	0.294372	+	0.202240i
$631$	−16.1209	+	20.2150i	−0.641765	+	0.804747i	−0.991222	−	0.132205i	$-0.957794\pi$
$631$	−16.1209	+	20.2150i	−0.641765	+	0.804747i	0.349458	+	0.936952i	$0.386366\pi$
$632$	16.4890	−	2.48531i	0.655895	−	0.0988603i
$633$	7.38471	+	5.03481i	0.293516	+	0.200116i
$634$	−5.17669	+	13.1900i	−0.205593	+	0.523842i
$635$	−5.56232	−	1.71575i	−0.220734	−	0.0680874i
$636$	1.68051			0.0666367
$637$	−29.4135	−	27.6847i	−1.16541	−	1.09691i
$638$	−8.13028			−0.321881
$639$	14.2529	+	4.39645i	0.563838	+	0.173921i
$640$	0.768430	−	1.95793i	0.0303749	−	0.0773939i
$641$	5.10252	+	3.47884i	0.201537	+	0.137406i	0.659883	−	0.751368i	$-0.270606\pi$
$641$	5.10252	+	3.47884i	0.201537	+	0.137406i	−0.458346	+	0.888774i	$0.651558\pi$
$642$	−23.5317	+	3.54684i	−0.928723	+	0.139983i
$643$	7.28023	−	9.12912i	0.287104	−	0.360017i	−0.617275	−	0.786748i	$-0.711763\pi$
$643$	7.28023	−	9.12912i	0.287104	−	0.360017i	0.904379	+	0.426730i	$0.140335\pi$
$644$	3.03801	−	7.66030i	0.119714	−	0.301858i
$645$	−8.97092	−	11.2492i	−0.353230	−	0.442936i
$646$	21.3700	+	19.8284i	0.840790	+	0.780139i
$647$	10.3012	+	1.55266i	0.404984	+	0.0610414i	0.348376	−	0.937355i	$-0.386733\pi$
$647$	10.3012	+	1.55266i	0.404984	+	0.0610414i	0.0566080	+	0.998396i	$0.481971\pi$
$648$	8.23782	−	7.64358i	0.323612	−	0.300268i
$649$	−7.24063	+	4.93658i	−0.284220	+	0.193778i
$650$	0.739657	+	3.24065i	0.0290117	+	0.127109i
$651$	−9.24516	+	4.41170i	−0.362346	+	0.172908i
$652$	−3.20351	+	14.0355i	−0.125459	+	0.549672i
$653$	6.80409	+	17.3365i	0.266265	+	0.678431i	0.999999	−	0.00100453i	$-0.000319752\pi$
$653$	6.80409	+	17.3365i	0.266265	+	0.678431i	−0.733735	+	0.679436i	$0.762225\pi$
$654$	−2.14066	−	28.5651i	−0.0837063	−	1.11698i
$655$	−4.97154	−	8.61096i	−0.194254	−	0.336458i
$656$	−1.31078	+	2.27033i	−0.0511772	+	0.0886415i
$657$	14.5201	+	6.99249i	0.566481	+	0.272803i
$658$	11.2142	+	3.50296i	0.437176	+	0.136560i
$659$	2.89212	−	1.39277i	0.112661	−	0.0542547i	−0.376704	−	0.926334i	$-0.622943\pi$
$659$	2.89212	−	1.39277i	0.112661	−	0.0542547i	0.489365	+	0.872079i	$0.337228\pi$
$660$	0.513374	−	6.85050i	0.0199830	−	0.266655i
$661$	−0.503766	+	0.155391i	−0.0195942	+	0.00604402i	−0.304537	−	0.952501i	$-0.598502\pi$
$661$	−0.503766	+	0.155391i	−0.0195942	+	0.00604402i	0.284943	+	0.958545i	$0.408025\pi$
$662$	8.68595	−	2.67926i	0.337589	−	0.104132i
$663$	−5.31470	+	70.9197i	−0.206406	+	2.75429i
$664$	−6.58609	+	3.17169i	−0.255590	+	0.123086i
$665$	−2.21268	+	28.1778i	−0.0858039	+	1.09269i
$666$	15.9705	+	7.69097i	0.618843	+	0.298019i
$667$	−8.32439	+	14.4183i	−0.322322	+	0.558278i
$668$	4.03280	+	6.98501i	0.156034	+	0.270258i
$669$	1.84555	+	24.6272i	0.0713532	+	0.952142i
$670$	−7.93577	−	20.2200i	−0.306586	−	0.781167i
$671$	3.04601	−	13.3455i	0.117590	−	0.515196i
$672$	−5.68118	−	0.0202536i	−0.219156	−	0.000781300i
$673$	7.26705	+	31.8390i	0.280124	+	1.22730i	0.897634	+	0.440741i	$0.145284\pi$
$673$	7.26705	+	31.8390i	0.280124	+	1.22730i	−0.617510	+	0.786563i	$0.711859\pi$
$674$	5.90757	−	4.02771i	0.227551	−	0.155142i
$675$	1.25955	−	1.16869i	0.0484801	−	0.0449829i
$676$	−20.0712	−	3.02524i	−0.771968	−	0.116355i
$677$	−33.7944	−	31.3567i	−1.29883	−	1.20513i	−0.964925	−	0.262526i	$-0.915444\pi$
$677$	−33.7944	−	31.3567i	−1.29883	−	1.20513i	−0.333901	−	0.942608i	$-0.608365\pi$
$678$	−2.61104	−	3.27414i	−0.100276	−	0.125743i
$679$	6.11816	−	1.86334i	0.234793	−	0.0715085i
$680$	7.52692	−	9.43846i	0.288644	−	0.361948i
$681$	33.3009	−	5.01930i	1.27609	−	0.192340i
$682$	2.26603	+	1.54496i	0.0867709	+	0.0591594i
$683$	−14.0669	+	35.8419i	−0.538255	+	1.37145i	0.360402	+	0.932797i	$0.382640\pi$
$683$	−14.0669	+	35.8419i	−0.538255	+	1.37145i	−0.898656	+	0.438653i	$0.855456\pi$
$684$	−7.81836	−	2.41165i	−0.298943	−	0.0922116i
$685$	33.0561			1.26301
$686$	15.4129	−	10.2686i	0.588466	−	0.392056i
$687$	−16.5760			−0.632415
$688$	3.04420	+	0.939012i	0.116059	+	0.0357995i
$689$	−1.64989	+	4.20386i	−0.0628560	+	0.160154i
$690$	−11.6231	−	7.92447i	−0.442482	−	0.301679i
$691$	30.8048	−	4.64307i	1.17187	−	0.176631i	0.465876	−	0.884850i	$-0.345739\pi$
$691$	30.8048	−	4.64307i	1.17187	−	0.176631i	0.705993	+	0.708219i	$0.250501\pi$
$692$	−9.00599	+	11.2931i	−0.342356	+	0.429301i
$693$	−6.20145	+	1.88871i	−0.235573	+	0.0717461i
$694$	8.22899	+	10.3188i	0.312368	+	0.391697i
$695$	−11.1253	−	10.3228i	−0.422006	−	0.391565i
$696$	11.3496	+	1.71067i	0.430205	+	0.0648429i
$697$	−11.0300	+	10.2343i	−0.417791	+	0.387653i
$698$	0.207754	−	0.141645i	0.00786362	−	0.00536133i
$699$	8.88748	+	38.9386i	0.336155	+	1.47279i
$700$	−1.52404	−	0.00543327i	−0.0576034	−	0.000205358i
$701$	−0.753322	+	3.30052i	−0.0284526	+	0.124659i	−0.987160	−	0.159736i	$-0.948936\pi$
$701$	−0.753322	+	3.30052i	−0.0284526	+	0.124659i	0.958707	+	0.284395i	$0.0917928\pi$
$702$	6.28834	+	16.0224i	0.237338	+	0.604728i
$703$	4.17661	+	55.7330i	0.157524	+	2.10201i
$704$	0.760519	+	1.31726i	0.0286631	+	0.0496460i
$705$	10.0278	−	17.3686i	0.377668	−	0.654140i
$706$	10.8098	+	5.20573i	0.406832	+	0.195920i
$707$	2.27153	−	28.9272i	0.0854295	−	1.08792i
$708$	11.1464	−	5.36780i	0.418906	−	0.201734i
$709$	−3.10872	+	41.4830i	−0.116750	+	1.55793i	0.564226	+	0.825621i	$0.309175\pi$
$709$	−3.10872	+	41.4830i	−0.116750	+	1.55793i	−0.680976	+	0.732306i	$0.738444\pi$
$710$	18.6099	−	5.74040i	0.698418	−	0.215433i
$711$	−25.6685	+	7.91768i	−0.962644	+	0.296936i
$712$	1.04147	−	13.8975i	0.0390309	−	0.520831i
$713$	5.05997	−	2.43675i	0.189497	−	0.0912571i
$714$	−31.1248	−	9.72239i	−1.16482	−	0.363851i
$715$	16.6327	+	8.00991i	0.622029	+	0.299553i
$716$	10.0200	−	17.3552i	0.374466	−	0.648594i
$717$	20.1333	+	34.8719i	0.751893	+	1.30232i
$718$	−1.75427	−	23.4090i	−0.0654686	−	0.873618i
$719$	4.68264	+	11.9312i	0.174633	+	0.444957i	0.991213	−	0.132275i	$-0.0422281\pi$
$719$	4.68264	+	11.9312i	0.174633	+	0.444957i	−0.816580	+	0.577232i	$0.804133\pi$
$720$	−0.753949	+	3.30327i	−0.0280980	+	0.123106i
$721$	1.52645	−	0.728408i	0.0568481	−	0.0271273i
$722$	−1.51253	−	6.62681i	−0.0562904	−	0.246624i
$723$	−7.17072	+	4.88892i	−0.266682	+	0.181821i
$724$	−2.81626	+	2.61311i	−0.104666	+	0.0971155i
$725$	3.04466	+	0.458909i	0.113076	+	0.0170434i
$726$	−13.6732	−	12.6868i	−0.507459	−	0.470853i
$727$	9.21369	+	11.5536i	0.341717	+	0.428499i	0.922761	−	0.385373i	$-0.125927\pi$
$727$	9.21369	+	11.5536i	0.341717	+	0.428499i	−0.581044	+	0.813872i	$0.697356\pi$
$728$	5.62834	−	14.1918i	0.208600	−	0.525983i
$729$	0.693582	−	0.869725i	0.0256882	−	0.0322120i
$730$	20.8075	−	3.13623i	0.770121	−	0.116077i
$731$	15.1077	+	10.3002i	0.558777	+	0.380968i
$732$	−7.06011	+	17.9889i	−0.260949	+	0.664888i
$733$	−20.1107	−	6.20333i	−0.742806	−	0.229125i	−0.0998226	−	0.995005i	$-0.531828\pi$
$733$	−20.1107	−	6.20333i	−0.742806	−	0.229125i	−0.642984	+	0.765880i	$0.722304\pi$
$734$	12.4664			0.460142
$735$	−11.3402	−	29.5114i	−0.418290	−	1.08854i
$736$	3.11471			0.114810
$737$	15.0103	+	4.63006i	0.552911	+	0.170550i
$738$	1.54285	−	3.93111i	0.0567929	−	0.144706i
$739$	10.4913	+	7.15286i	0.385929	+	0.263122i	0.740707	−	0.671829i	$-0.234491\pi$
$739$	10.4913	+	7.15286i	0.385929	+	0.263122i	−0.354777	+	0.934951i	$0.615443\pi$
$740$	22.8860	−	3.44951i	0.841306	−	0.126806i
$741$	39.2389	−	49.2040i	1.44148	−	1.80755i
$742$	−1.70665	−	1.17251i	−0.0626531	−	0.0430441i
$743$	−27.1098	−	33.9946i	−0.994561	−	1.24714i	−0.968896	−	0.247469i	$-0.920401\pi$
$743$	−27.1098	−	33.9946i	−0.994561	−	1.24714i	−0.0256648	−	0.999671i	$-0.508170\pi$
$744$	−2.83823	−	2.63349i	−0.104055	−	0.0965486i
$745$	−39.0020	−	5.87861i	−1.42892	−	0.215376i
$746$	−0.732767	+	0.679909i	−0.0268285	+	0.0248932i
$747$	9.72947	−	6.63344i	0.355983	−	0.242705i
$748$	1.94264	+	8.51128i	0.0710301	+	0.311203i
$749$	26.3724	+	12.8163i	0.963626	+	0.468297i
$750$	−5.60395	+	24.5525i	−0.204627	+	0.896532i
$751$	5.46242	+	13.9180i	0.199326	+	0.507876i	0.995231	−	0.0975467i	$-0.0310995\pi$
$751$	5.46242	+	13.9180i	0.199326	+	0.507876i	−0.795904	+	0.605422i	$0.793004\pi$
$752$	0.331843	+	4.42813i	0.0121011	+	0.161477i
$753$	−15.9463	−	27.6198i	−0.581116	−	1.00652i
$754$	−15.4221	+	26.7119i	−0.561640	+	0.972789i
$755$	−21.4693	−	10.3391i	−0.781348	−	0.376277i
$756$	−7.80784	+	1.14839i	−0.283968	+	0.0417665i
$757$	22.5103	−	10.8404i	0.818152	−	0.394001i	0.0224937	−	0.999747i	$-0.492839\pi$
$757$	22.5103	−	10.8404i	0.818152	−	0.394001i	0.795658	+	0.605746i	$0.207125\pi$
$758$	1.51508	−	20.2173i	0.0550301	−	0.734326i
$759$	9.72105	−	2.99855i	0.352852	−	0.108840i
$760$	−10.2084	+	3.14886i	−0.370296	+	0.114221i
$761$	0.545426	−	7.27821i	0.0197717	−	0.263835i	−0.978554	−	0.205991i	$-0.933958\pi$
$761$	0.545426	−	7.27821i	0.0197717	−	0.263835i	0.998326	−	0.0578440i	$-0.0184226\pi$
$762$	−5.35412	+	2.57841i	−0.193959	+	0.0934059i
$763$	−17.7561	+	30.5029i	−0.642816	+	1.10428i
$764$	−14.3243	−	6.89824i	−0.518236	−	0.249570i
$765$	−9.72352	+	16.8416i	−0.351555	+	0.608911i
$766$	−14.7898	−	25.6166i	−0.534376	−	0.925567i
$767$	2.48447	+	33.1530i	0.0897092	+	1.19709i
$768$	−0.784496	−	1.99886i	−0.0283081	−	0.0721278i
$769$	−1.16823	+	5.11834i	−0.0421274	+	0.184572i	−0.991614	−	0.129236i	$-0.958748\pi$
$769$	−1.16823	+	5.11834i	−0.0421274	+	0.184572i	0.949487	+	0.313808i	$0.101605\pi$
$770$	−5.30101	+	6.59886i	−0.191035	+	0.237806i
$771$	4.05762	+	17.7776i	0.146132	+	0.640245i
$772$	2.89621	−	1.97460i	0.104237	−	0.0710675i
$773$	24.4381	−	22.6752i	0.878977	−	0.815572i	−0.104888	−	0.994484i	$-0.533448\pi$
$773$	24.4381	−	22.6752i	0.878977	−	0.815572i	0.983865	+	0.178912i	$0.0572579\pi$
$774$	−5.07455	−	0.764865i	−0.182401	−	0.0274925i
$775$	−0.761389	−	0.706466i	−0.0273499	−	0.0253770i
$776$	1.50717	+	1.88993i	0.0541043	+	0.0678447i
$777$	−31.0642	−	54.2506i	−1.11442	−	1.94623i
$778$	14.0956	−	17.6754i	0.505353	−	0.633693i
$779$	13.1664	−	1.98451i	0.471735	−	0.0711026i
$780$	−21.5334	−	14.6812i	−0.771018	−	0.525671i
$781$	−5.14533	+	13.1101i	−0.184115	+	0.469116i
$782$	17.0830	+	5.26939i	0.610885	+	0.188433i
$783$	15.9439			0.569789
$784$	5.75541	+	3.98438i	0.205550	+	0.142299i
$785$	−4.39796			−0.156970
$786$	−9.69999	−	2.99205i	−0.345987	−	0.106723i
$787$	14.9821	−	38.1738i	0.534055	−	1.36075i	−0.368280	−	0.929715i	$-0.620053\pi$
$787$	14.9821	−	38.1738i	0.534055	−	1.36075i	0.902335	−	0.431035i	$-0.141851\pi$
$788$	0.560925	+	0.382432i	0.0199821	+	0.0136236i
$789$	23.4677	−	3.53719i	0.835473	−	0.125927i
$790$	−21.8679	+	27.4214i	−0.778023	+	0.975611i
$791$	0.367254	+	5.14681i	0.0130580	+	0.183000i
$792$	−1.52769	−	1.91566i	−0.0542841	−	0.0680701i
$793$	−38.0683	−	35.3222i	−1.35185	−	1.25433i
$794$	−27.1135	−	4.08671i	−0.962223	−	0.145032i
$795$	−2.59109	+	2.40418i	−0.0918965	+	0.0852675i
$796$	−14.1814	+	9.66872i	−0.502647	+	0.342699i
$797$	5.52971	+	24.2272i	0.195872	+	0.858173i	0.973361	+	0.229277i	$0.0736360\pi$
$797$	5.52971	+	24.2272i	0.195872	+	0.858173i	−0.777489	+	0.628897i	$0.783507\pi$
$798$	17.9105	+	22.6241i	0.634026	+	0.800884i
$799$	−5.67139	+	24.8480i	−0.200640	+	0.879059i
$800$	−0.210450	−	0.536219i	−0.00744054	−	0.0189582i
$801$	1.67770	+	22.3873i	0.0592786	+	0.791017i
$802$	9.29503	+	16.0995i	0.328219	+	0.568492i
$803$	−7.60857	+	13.1784i	−0.268500	+	0.465056i
$804$	−19.9796	−	9.62168i	−0.704627	−	0.339330i
$805$	6.27487	+	16.1572i	0.221160	+	0.569468i
$806$	9.37430	−	4.51443i	0.330196	−	0.159014i
$807$	−0.302598	+	4.03789i	−0.0106519	+	0.142140i
$808$	10.4799	−	3.23261i	0.368680	−	0.113723i
$809$	27.9005	−	8.60617i	0.980930	−	0.302577i	0.237498	−	0.971388i	$-0.423673\pi$
$809$	27.9005	−	8.60617i	0.980930	−	0.302577i	0.743432	+	0.668811i	$0.233197\pi$
$810$	−1.76636	+	23.5704i	−0.0620635	+	0.828180i
$811$	−12.4772	+	6.00872i	−0.438135	+	0.210995i	−0.639930	−	0.768433i	$-0.721037\pi$
$811$	−12.4772	+	6.00872i	−0.438135	+	0.210995i	0.201795	+	0.979428i	$0.435322\pi$
$812$	−10.3326	−	9.65598i	−0.362601	−	0.338859i
$813$	22.1651	+	10.6742i	0.777365	+	0.374359i
$814$	−8.36858	+	14.4948i	−0.293319	+	0.508043i
$815$	−15.1402	−	26.2235i	−0.530337	−	0.918570i
$816$	−0.921022	−	12.2902i	−0.0322422	−	0.430243i
$817$	−5.91146	−	15.0621i	−0.206816	−	0.526958i
$818$	−3.91900	+	17.1703i	−0.137025	+	0.600344i
$819$	−5.55804	+	23.9574i	−0.194214	+	0.837138i
$820$	−1.22697	−	5.37572i	−0.0428477	−	0.187728i
$821$	−45.9129	+	31.3029i	−1.60237	+	1.09248i	−0.663516	+	0.748162i	$0.730937\pi$
$821$	−45.9129	+	31.3029i	−1.60237	+	1.09248i	−0.938854	+	0.344316i	$0.888111\pi$
$822$	24.7385	−	22.9539i	0.862853	−	0.800611i
$823$	3.88531	+	0.585616i	0.135433	+	0.0204133i	0.216409	−	0.976303i	$-0.430566\pi$
$823$	3.88531	+	0.585616i	0.135433	+	0.0204133i	−0.0809757	+	0.996716i	$0.525804\pi$
$824$	0.468616	+	0.434812i	0.0163250	+	0.0151474i
$825$	−1.17304	−	1.47095i	−0.0408400	−	0.0512118i
$826$	−15.0649	−	2.32562i	−0.524174	−	0.0809187i
$827$	−0.587835	+	0.737121i	−0.0204410	+	0.0256322i	−0.791947	−	0.610590i	$-0.790932\pi$
$827$	−0.587835	+	0.737121i	−0.0204410	+	0.0256322i	0.771506	+	0.636222i	$0.219504\pi$
$828$	−4.96140	+	0.747811i	−0.172421	+	0.0259882i
$829$	−9.01981	−	6.14961i	−0.313271	−	0.213585i	0.396469	−	0.918048i	$-0.370235\pi$
$829$	−9.01981	−	6.14961i	−0.313271	−	0.213585i	−0.709740	+	0.704463i	$0.751188\pi$
$830$	5.61723	−	14.3125i	0.194977	−	0.496793i
$831$	−0.609242	−	0.187926i	−0.0211344	−	0.00651909i
$832$	5.77043			0.200054
$833$	24.8255	+	31.5897i	0.860153	+	1.09452i
$834$	−15.4940			−0.536513
$835$	−16.2109	−	5.00039i	−0.561000	−	0.173046i
$836$	2.82244	−	7.19147i	0.0976162	−	0.248722i
$837$	−4.44381	−	3.02974i	−0.153601	−	0.104723i
$838$	29.5945	−	4.46066i	1.02233	−	0.154091i
$839$	−5.95431	+	7.46647i	−0.205566	+	0.257771i	−0.873918	−	0.486074i	$-0.838429\pi$
$839$	−5.95431	+	7.46647i	−0.205566	+	0.257771i	0.668352	+	0.743845i	$0.267000\pi$
$840$	8.78847	−	8.09639i	0.303231	−	0.279352i
$841$	−0.267241	−	0.335110i	−0.00921522	−	0.0115555i
$842$	−21.5058	−	19.9544i	−0.741138	−	0.687676i
$843$	5.81110	+	0.875883i	0.200145	+	0.0301670i
$844$	3.05120	−	2.83110i	0.105027	−	0.0974504i
$845$	35.2746	−	24.0498i	1.21348	−	0.827338i
$846$	−1.59174	−	6.97388i	−0.0547253	−	0.239767i
$847$	5.03410	+	22.4240i	0.172974	+	0.770499i
$848$	0.174149	−	0.762996i	0.00598029	−	0.0262014i
$849$	−23.1886	−	59.0835i	−0.795829	−	2.02774i
$850$	−0.247075	−	3.29699i	−0.00847460	−	0.113086i
$851$	17.1368	+	29.6818i	0.587441	+	1.01748i
$852$	9.94117	−	17.2186i	0.340579	−	0.589900i
$853$	−26.2477	−	12.6402i	−0.898704	−	0.432793i	−0.0732832	−	0.997311i	$-0.523348\pi$
$853$	−26.2477	−	12.6402i	−0.898704	−	0.432793i	−0.825421	+	0.564518i	$0.809062\pi$
$854$	19.7209	−	13.3428i	0.674836	−	0.456580i
$855$	15.5049	−	7.46674i	0.530255	−	0.255357i
$856$	−0.828200	+	11.0516i	−0.0283073	+	0.377734i
$857$	−36.2328	+	11.1763i	−1.23769	+	0.381776i	−0.843438	−	0.537227i	$-0.819472\pi$
$857$	−36.2328	+	11.1763i	−1.23769	+	0.381776i	−0.394250	+	0.919003i	$0.628996\pi$
$858$	18.0096	−	5.55523i	0.614838	−	0.189652i
$859$	−2.67482	+	35.6930i	−0.0912637	+	1.21783i	0.744076	+	0.668095i	$0.232890\pi$
$859$	−2.67482	+	35.6930i	−0.0912637	+	1.21783i	−0.835339	+	0.549735i	$0.814729\pi$
$860$	−6.03705	+	2.90729i	−0.205862	+	0.0991378i
$861$	−12.3355	+	8.34594i	−0.420393	+	0.284429i
$862$	20.4124	+	9.83008i	0.695248	+	0.334814i
$863$	−8.52851	+	14.7718i	−0.290314	+	0.502838i	−0.973884	−	0.227047i	$-0.927093\pi$
$863$	−8.52851	+	14.7718i	−0.290314	+	0.502838i	0.683570	+	0.729885i	$0.260426\pi$
$864$	−1.49142	−	2.58321i	−0.0507391	−	0.0878826i
$865$	−2.27040	−	30.2964i	−0.0771961	−	1.03011i
$866$	−4.80489	−	12.2427i	−0.163277	−	0.416022i
$867$	7.61792	−	33.3763i	0.258718	−	1.13352i
$868$	1.04496	+	4.65471i	0.0354684	+	0.157991i
$869$	−5.64394	−	24.7277i	−0.191457	−	0.838830i
$870$	−19.9466	+	13.5994i	−0.676254	+	0.461062i
$871$	43.6846	−	40.5333i	1.48019	−	1.37342i
$872$	−13.1911	−	1.98824i	−0.446707	−	0.0673303i
$873$	−2.85452	−	2.64861i	−0.0966110	−	0.0896419i
$874$	−9.86354	−	12.3685i	−0.333639	−	0.418370i
$875$	22.8216	−	21.0245i	0.771512	−	0.710757i
$876$	13.3941	−	16.7957i	0.452546	−	0.567474i
$877$	38.3185	−	5.77559i	1.29392	−	0.195028i	0.534247	−	0.845328i	$-0.320595\pi$
$877$	38.3185	−	5.77559i	1.29392	−	0.195028i	0.759677	+	0.650301i	$0.225357\pi$
$878$	1.65161	+	1.12605i	0.0557392	+	0.0380023i
$879$	16.3067	−	41.5487i	0.550010	−	1.40140i
$880$	−3.05710	−	0.942990i	−0.103055	−	0.0317882i
$881$	−26.4760			−0.891997			−0.445999	−	0.895034i	$-0.647151\pi$
$881$	−26.4760			−0.891997			−0.445999	+	0.895034i	$0.647151\pi$
$882$	−10.1244	−	4.96488i	−0.340906	−	0.167176i
$883$	−48.2215			−1.62278			−0.811391	−	0.584504i	$-0.801289\pi$
$883$	−48.2215			−1.62278			−0.811391	+	0.584504i	$0.801289\pi$
$884$	31.6486	+	9.76230i	1.06446	+	0.328342i
$885$	−9.50664	+	24.2225i	−0.319562	+	0.814232i
$886$	8.44535	+	5.75794i	0.283727	+	0.193442i
$887$	−10.6508	+	1.60535i	−0.357618	+	0.0539023i	−0.325394	−	0.945578i	$-0.605497\pi$
$887$	−10.6508	+	1.60535i	−0.357618	+	0.0539023i	−0.0322238	+	0.999481i	$0.510259\pi$
$888$	14.7321	−	18.4734i	0.494376	−	0.619928i
$889$	7.23637	+	1.11711i	0.242700	+	0.0374665i
$890$	18.2763	+	22.9177i	0.612622	+	0.768204i
$891$	−12.5300	−	11.6262i	−0.419772	−	0.389492i
$892$	11.3726	+	1.71415i	0.380784	+	0.0573939i
$893$	16.5332	−	15.3406i	0.553264	−	0.513354i
$894$	−33.2704	+	22.6834i	−1.11273	+	0.758645i
$895$	9.37940	+	41.0939i	0.313519	+	1.37362i
$896$	−0.597927	+	2.57730i	−0.0199753	+	0.0861016i
$897$	8.58793	−	37.6262i	0.286743	−	1.25630i
$898$	−8.27893	−	21.0944i	−0.276271	−	0.703928i
$899$	−0.720248	−	9.61104i	−0.0240216	−	0.320546i
$900$	0.463967	+	0.803614i	0.0154656	+	0.0267871i
$901$	2.24596	−	3.89012i	0.0748238	−	0.129599i
$902$	3.59259	+	1.73010i	0.119620	+	0.0576061i
$903$	13.2234	+	12.3576i	0.440048	+	0.411234i
$904$	−1.75712	+	0.846185i	−0.0584410	+	0.0281437i
$905$	0.603865	−	8.05802i	0.0200731	−	0.267858i
$906$	−23.2465	+	7.17061i	−0.772315	+	0.238228i
$907$	−17.6415	+	5.44168i	−0.585776	+	0.180688i	−0.573456	−	0.819236i	$-0.694398\pi$
$907$	−17.6415	+	5.44168i	−0.585776	+	0.180688i	−0.0123195	+	0.999924i	$0.503922\pi$
$908$	1.17202	−	15.6396i	0.0388950	−	0.519018i
$909$	−15.9172	+	7.66533i	−0.527941	+	0.254243i
$910$	11.6251	+	29.9335i	0.385367	+	0.992288i
$911$	−37.7339	−	18.1717i	−1.25018	−	0.602054i	−0.312619	−	0.949879i	$-0.601206\pi$
$911$	−37.7339	−	18.1717i	−1.25018	−	0.602054i	−0.937560	+	0.347825i	$0.886920\pi$
$912$	−5.45317	+	9.44516i	−0.180572	+	0.312761i
$913$	5.55940	+	9.62916i	0.183989	+	0.318679i
$914$	−2.70379	−	36.0796i	−0.0894335	−	1.19341i
$915$	−14.8497	−	37.8364i	−0.490916	−	1.25083i
$916$	−1.71775	+	7.52594i	−0.0567560	+	0.248664i
$917$	7.76328	+	9.80635i	0.256366	+	0.323834i
$918$	−3.80963	−	16.6911i	−0.125736	−	0.550887i
$919$	−2.24993	+	1.53398i	−0.0742184	+	0.0506013i	−0.599861	−	0.800104i	$-0.704777\pi$
$919$	−2.24993	+	1.53398i	−0.0742184	+	0.0506013i	0.525642	+	0.850706i	$0.323825\pi$
$920$	−4.80239	+	4.45597i	−0.158330	+	0.146909i
$921$	15.5972	+	2.35091i	0.513946	+	0.0774650i
$922$	24.6697	+	22.8902i	0.812455	+	0.753848i
$923$	33.3129	+	41.7731i	1.09651	+	1.37498i
$924$	0.615044	+	8.61943i	0.0202335	+	0.283558i
$925$	3.95205	−	4.95571i	0.129943	−	0.162943i
$926$	−2.57225	+	0.387704i	−0.0845293	+	0.0127407i
$927$	−0.850851	−	0.580100i	−0.0279456	−	0.0190530i
$928$	1.95283	−	4.97573i	0.0641047	−	0.163336i
$929$	25.8905	+	7.98616i	0.849440	+	0.262017i	0.688760	−	0.724989i	$-0.258155\pi$
$929$	25.8905	+	7.98616i	0.849440	+	0.262017i	0.160680	+	0.987007i	$0.448631\pi$
$930$	8.14365			0.267041
$931$	−2.40407	−	35.4723i	−0.0787904	−	1.16256i
$932$	18.6001			0.609267
$933$	43.7016	+	13.4802i	1.43073	+	0.441320i
$934$	−0.454317	+	1.15758i	−0.0148657	+	0.0378772i
$935$	−15.1717	−	10.3439i	−0.496167	−	0.338281i
$936$	−9.19170	+	1.38543i	−0.300440	+	0.0452841i
$937$	−15.4321	+	19.3512i	−0.504144	+	0.632177i	−0.967159	−	0.254174i	$-0.918196\pi$
$937$	−15.4321	+	19.3512i	−0.504144	+	0.632177i	0.463014	+	0.886351i	$0.346768\pi$
$938$	13.5772	+	23.7113i	0.443312	+	0.774200i
$939$	−10.8408	−	13.5939i	−0.353776	−	0.443621i
$940$	−6.84663	−	6.35275i	−0.223313	−	0.207204i
$941$	−46.4239	−	6.99728i	−1.51338	−	0.228105i	−0.660743	−	0.750613i	$-0.729758\pi$
$941$	−46.4239	−	6.99728i	−1.51338	−	0.228105i	−0.852635	+	0.522508i	$0.824997\pi$
$942$	−3.29134	+	3.05392i	−0.107238	+	0.0995021i
$943$	6.74654	−	4.59971i	0.219697	−	0.149787i
$944$	−1.28204	−	5.61699i	−0.0417269	−	0.182817i
$945$	10.3956	−	12.9407i	0.338168	−	0.420961i
$946$	1.07825	−	4.72413i	0.0350570	−	0.153595i
$947$	−12.3948	−	31.5814i	−0.402777	−	1.02626i	−0.978064	−	0.208306i	$-0.933205\pi$
$947$	−12.3948	−	31.5814i	−0.402777	−	1.02626i	0.575287	−	0.817952i	$-0.304890\pi$
$948$	2.67583	+	35.7065i	0.0869070	+	1.15969i
$949$	28.8650	+	49.9956i	0.936996	+	1.62293i
$950$	−1.46288	+	2.53378i	−0.0474620	+	0.0822066i
$951$	−27.4130	−	13.2014i	−0.888927	−	0.428084i
$952$	−7.63962	+	13.1239i	−0.247602	+	0.425349i
$953$	−45.6677	+	21.9924i	−1.47932	+	0.712404i	−0.987401	−	0.158236i	$-0.949419\pi$
$953$	−45.6677	+	21.9924i	−1.47932	+	0.712404i	−0.491921	+	0.870640i	$0.663705\pi$
$954$	−0.0942130	+	1.25718i	−0.00305026	+	0.0407029i
$955$	31.9547	−	9.85671i	1.03403	−	0.318956i
$956$	17.9191	−	5.52732i	0.579546	−	0.178766i
$957$	1.30465	−	17.4093i	0.0421733	−	0.562764i
$958$	−28.7350	+	13.8380i	−0.928385	+	0.447087i
$959$	−41.1384	+	6.05070i	−1.32843	+	0.195387i
$960$	4.06919	+	1.95962i	0.131332	+	0.0632464i
$961$	13.8744	−	24.0312i	0.447562	−	0.775199i
$962$	31.7483	+	54.9896i	1.02361	+	1.77294i
$963$	−1.33414	−	17.8028i	−0.0429920	−	0.573688i
$964$	1.47660	+	3.76232i	0.0475581	+	0.121176i
$965$	−1.64059	+	7.18791i	−0.0528126	+	0.231387i
$966$	15.9155	+	7.73450i	0.512071	+	0.248853i
$967$	−0.704617	−	3.08713i	−0.0226590	−	0.0992754i	0.962334	−	0.271870i	$-0.0876421\pi$
$967$	−0.704617	−	3.08713i	−0.0226590	−	0.0992754i	−0.984993	+	0.172595i	$0.944785\pi$
$968$	−7.17708	+	4.89325i	−0.230680	+	0.157275i
$969$	−45.8877	+	42.5775i	−1.47412	+	1.36779i
$970$	−5.02761	−	0.757790i	−0.161427	−	0.0243312i
$971$	40.0601	+	37.1704i	1.28559	+	1.19285i	0.969766	+	0.244036i	$0.0784716\pi$
$971$	40.0601	+	37.1704i	1.28559	+	1.19285i	0.315824	+	0.948818i	$0.397719\pi$
$972$	9.46594	+	11.8699i	0.303620	+	0.380728i
$973$	15.7350	+	10.8103i	0.504440	+	0.346562i
$974$	−6.21289	+	7.79071i	−0.199074	+	0.249631i
$975$	−7.05787	+	1.06380i	−0.226033	+	0.0340690i
$976$	7.43578	+	5.06963i	0.238013	+	0.162275i
$977$	−13.2022	+	33.6386i	−0.422375	+	1.07619i	0.548403	+	0.836214i	$0.315236\pi$
$977$	−13.2022	+	33.6386i	−0.422375	+	1.07619i	−0.970778	+	0.239980i	$0.922859\pi$
$978$	−29.5400	−	9.11189i	−0.944586	−	0.291366i
$979$	−21.1979			−0.677488
$980$	−14.5741	+	2.09053i	−0.465552	+	0.0667794i
$981$	21.4894			0.686104
$982$	3.59092	+	1.10765i	0.114591	+	0.0353466i
$983$	−9.64467	+	24.5742i	−0.307617	+	0.783796i	0.690550	+	0.723284i	$0.257368\pi$
$983$	−9.64467	+	24.5742i	−0.307617	+	0.783796i	−0.998167	+	0.0605116i	$0.980727\pi$
$984$	−4.65111	−	3.17107i	−0.148272	−	0.101090i
$985$	−1.41197	+	0.212821i	−0.0449892	+	0.00678103i
$986$	19.1283	−	23.9862i	0.609170	−	0.763876i
$987$	−9.30038	+	23.4508i	−0.296034	+	0.746448i
$988$	−18.2736	−	22.9144i	−0.581361	−	0.729003i
$989$	−7.27380	−	6.74910i	−0.231293	−	0.214609i
$990$	5.09605	+	0.768105i	0.161963	+	0.0244120i
$991$	29.4043	−	27.2832i	0.934059	−	0.866680i	−0.0572329	−	0.998361i	$-0.518228\pi$
$991$	29.4043	−	27.2832i	0.934059	−	0.866680i	0.991292	+	0.131680i	$0.0420373\pi$
$992$	−1.48979	+	1.01572i	−0.0473010	+	0.0322493i
$993$	4.34327	+	19.0291i	0.137829	+	0.603870i
$994$	−22.1094	+	10.5504i	−0.701266	+	0.334637i
$995$	8.03324	−	35.1959i	0.254671	−	1.11579i
$996$	−5.73467	−	14.6117i	−0.181710	−	0.462990i
$997$	−0.689533	−	9.20118i	−0.0218377	−	0.291404i	−0.997421	−	0.0717741i	$-0.977134\pi$
$997$	−0.689533	−	9.20118i	−0.0218377	−	0.291404i	0.975583	−	0.219630i	$-0.0704851\pi$
$998$	5.78647	+	10.0225i	0.183168	+	0.317256i
$999$	16.4112	−	28.4251i	0.519229	−	0.899330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.b.51.1	yes	24
3.2	odd	2		882.2.z.b.541.2		24
4.3	odd	2		784.2.bg.b.737.2		24
7.2	even	3		686.2.e.c.589.1		24
7.3	odd	6		686.2.g.d.655.1		24
7.4	even	3		686.2.g.f.655.2		24
7.5	odd	6		686.2.e.d.589.4		24
7.6	odd	2		686.2.g.e.471.2		24
49.5	odd	42		4802.2.a.l.1.11		12
49.9	even	21		686.2.e.c.99.1		24
49.15	even	7		686.2.g.f.177.2		24
49.24	odd	42		686.2.g.e.67.2		24
49.25	even	21	inner	98.2.g.b.25.1	✓	24
49.34	odd	14		686.2.g.d.177.1		24
49.40	odd	42		686.2.e.d.99.4		24
49.44	even	21		4802.2.a.o.1.2		12
147.74	odd	42		882.2.z.b.613.2		24
196.123	odd	42		784.2.bg.b.417.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.25.1	✓	24	49.25	even	21	inner
98.2.g.b.51.1	yes	24	1.1	even	1	trivial
686.2.e.c.99.1		24	49.9	even	21
686.2.e.c.589.1		24	7.2	even	3
686.2.e.d.99.4		24	49.40	odd	42
686.2.e.d.589.4		24	7.5	odd	6
686.2.g.d.177.1		24	49.34	odd	14
686.2.g.d.655.1		24	7.3	odd	6
686.2.g.e.67.2		24	49.24	odd	42
686.2.g.e.471.2		24	7.6	odd	2
686.2.g.f.177.2		24	49.15	even	7
686.2.g.f.655.2		24	7.4	even	3
784.2.bg.b.417.2		24	196.123	odd	42
784.2.bg.b.737.2		24	4.3	odd	2
882.2.z.b.541.2		24	3.2	odd	2
882.2.z.b.613.2		24	147.74	odd	42
4802.2.a.l.1.11		12	49.5	odd	42
4802.2.a.o.1.2		12	49.44	even	21

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.955573 + 0.294755i) q^{2} +(-0.784496 + 1.99886i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-2.07983 + 0.313484i) q^{5} +(-1.33882 + 1.67883i) q^{6} +(2.53097 - 0.770831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-1.18087 - 1.09568i) q^{9} +O(q^{10})\)	\(q+(0.955573 + 0.294755i) q^{2} +(-0.784496 + 1.99886i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-2.07983 + 0.313484i) q^{5} +(-1.33882 + 1.67883i) q^{6} +(2.53097 - 0.770831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-1.18087 - 1.09568i) q^{9} +(-2.07983 - 0.313484i) q^{10} +(1.11500 - 1.03457i) q^{11} +(-1.77418 + 1.20962i) q^{12} +(-1.28404 - 5.62575i) q^{13} +(2.64573 + 0.00943213i) q^{14} +(1.00501 - 4.40322i) q^{15} +(0.365341 + 0.930874i) q^{16} +(0.428922 + 5.72356i) q^{17} +(-0.805444 - 1.39507i) q^{18} +(2.53955 - 4.39863i) q^{19} +(-1.89503 - 0.912597i) q^{20} +(-0.444752 + 5.66378i) q^{21} +(1.37041 - 0.659954i) q^{22} +(0.232762 - 3.10600i) q^{23} +(-2.05190 + 0.632927i) q^{24} +(-0.550446 + 0.169790i) q^{25} +(0.431225 - 5.75430i) q^{26} +(-2.68744 + 1.29420i) q^{27} +(2.52541 + 0.788857i) q^{28} +(-4.81588 - 2.31920i) q^{29} +(2.25823 - 3.91137i) q^{30} +(0.901552 + 1.56153i) q^{31} +(0.0747301 + 0.997204i) q^{32} +(1.19325 + 3.04035i) q^{33} +(-1.27718 + 5.59570i) q^{34} +(-5.02235 + 2.39662i) q^{35} +(-0.358456 - 1.57050i) q^{36} +(-9.09175 + 6.19865i) q^{37} +(3.72324 - 3.45466i) q^{38} +(12.2524 + 1.84676i) q^{39} +(-1.54184 - 1.43062i) q^{40} +(1.63451 + 2.04961i) q^{41} +(-2.09442 + 5.28106i) q^{42} +(1.98627 - 2.49071i) q^{43} +(1.50405 - 0.226699i) q^{44} +(2.79948 + 1.90865i) q^{45} +(1.13793 - 2.89940i) q^{46} +(4.24327 + 1.30887i) q^{47} -2.14730 q^{48} +(5.81164 - 3.90190i) q^{49} -0.576038 q^{50} +(-11.7771 - 3.63275i) q^{51} +(2.10818 - 5.37154i) q^{52} +(-0.646629 - 0.440864i) q^{53} +(-2.94952 + 0.444569i) q^{54} +(-1.99469 + 2.50126i) q^{55} +(2.18070 + 1.49819i) q^{56} +(6.79999 + 8.52692i) q^{57} +(-3.91832 - 3.63567i) q^{58} +(-5.69709 - 0.858698i) q^{59} +(3.31080 - 3.07197i) q^{60} +(7.43578 - 5.06963i) q^{61} +(0.401228 + 1.75790i) q^{62} +(-3.83332 - 1.86290i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(4.43417 + 11.2981i) q^{65} +(0.244078 + 3.25699i) q^{66} +(5.16363 + 8.94367i) q^{67} +(-2.86980 + 4.97065i) q^{68} +(6.02586 + 2.90190i) q^{69} +(-5.50563 + 0.809778i) q^{70} +(-8.34228 + 4.01743i) q^{71} +(0.120382 - 1.60638i) q^{72} +(-9.55997 + 2.94886i) q^{73} +(-10.5149 + 3.24342i) q^{74} +(0.0924355 - 1.23347i) q^{75} +(4.57611 - 2.20374i) q^{76} +(2.02456 - 3.47794i) q^{77} +(11.1638 + 5.37618i) q^{78} +(8.33760 - 14.4412i) q^{79} +(-1.05166 - 1.82153i) q^{80} +(-0.839795 - 11.2063i) q^{81} +(0.957760 + 2.44033i) q^{82} +(-1.62663 + 7.12673i) q^{83} +(-3.55799 + 4.42910i) q^{84} +(-2.68633 - 11.7696i) q^{85} +(2.63218 - 1.79459i) q^{86} +(8.41381 - 7.80687i) q^{87} +(1.50405 + 0.226699i) q^{88} +(-10.2162 - 9.47921i) q^{89} +(2.11252 + 2.64902i) q^{90} +(-7.58638 - 13.2488i) q^{91} +(1.94199 - 2.43517i) q^{92} +(-3.82856 + 0.577062i) q^{93} +(3.66895 + 2.50145i) q^{94} +(-3.90293 + 9.94450i) q^{95} +(-2.05190 - 0.632927i) q^{96} +2.41732 q^{97} +(6.70355 - 2.01554i) q^{98} -2.45022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Introduction

L-functions

Modular forms

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Database

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