LMFDB - Embedded newform 134.2.e.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [134,2,Mod(9,134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(134, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("134.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 134 = 2 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	134.e (of order $11$, degree $10$, 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:	$1.06999538709$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	134.9
Dual form			134.2.e.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(-2.37231 - 0.696574i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.22065 + 1.40870i) q^{5} +(1.61912 + 1.86856i) q^{6} +(3.70806 + 2.38303i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.61889 + 1.68306i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(-2.37231 - 0.696574i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.22065 + 1.40870i) q^{5} +(1.61912 + 1.86856i) q^{6} +(3.70806 + 2.38303i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.61889 + 1.68306i) q^{9} +(1.78848 - 0.525144i) q^{10} +(2.18491 - 2.52152i) q^{11} +(-0.351868 - 2.44730i) q^{12} +(0.744433 + 5.17765i) q^{13} +(-1.83106 - 4.00946i) q^{14} +(3.87702 - 2.49161i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.77403 + 3.88459i) q^{17} +(-1.29322 - 2.83175i) q^{18} +(-4.05108 + 2.60347i) q^{19} +(-1.78848 - 0.525144i) q^{20} +(-7.13673 - 8.23622i) q^{21} +(-3.20129 + 0.939985i) q^{22} +(5.05204 + 1.48341i) q^{23} +(-1.02710 + 2.24903i) q^{24} +(0.217112 + 1.51005i) q^{25} +(2.17299 - 4.75818i) q^{26} +(-0.183085 - 0.211292i) q^{27} +(-0.627293 + 4.36292i) q^{28} -4.30658 q^{29} -4.60862 q^{30} +(1.54596 - 10.7524i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-6.93970 + 4.45987i) q^{33} +(3.59258 - 2.30881i) q^{34} +(-7.88321 + 2.31472i) q^{35} +(-0.443037 + 3.08139i) q^{36} +3.81691 q^{37} +4.81552 q^{38} +(1.84058 - 12.8015i) q^{39} +(1.22065 + 1.40870i) q^{40} +(0.694600 - 1.52096i) q^{41} +(1.55096 + 10.7872i) q^{42} +(-0.0539481 + 0.118130i) q^{43} +(3.20129 + 0.939985i) q^{44} +(-5.56766 + 1.63481i) q^{45} +(-3.44805 - 3.97927i) q^{46} +(-3.07008 - 0.901458i) q^{47} +(2.07997 - 1.33671i) q^{48} +(5.16300 + 11.3054i) q^{49} +(0.633748 - 1.38771i) q^{50} +(6.91447 - 7.97972i) q^{51} +(-4.40050 + 2.82803i) q^{52} +(-1.93990 - 4.24779i) q^{53} +(0.0397882 + 0.276733i) q^{54} +(0.885065 + 6.15577i) q^{55} +(2.88648 - 3.33118i) q^{56} +(11.4239 - 3.35437i) q^{57} +(3.62293 + 2.32831i) q^{58} +(-0.222565 + 1.54797i) q^{59} +(3.87702 + 2.49161i) q^{60} +(2.32071 + 2.67825i) q^{61} +(-7.11374 + 8.20969i) q^{62} +(5.70023 + 12.4818i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-8.20245 - 5.27140i) q^{65} +8.24924 q^{66} +(-0.871382 - 8.13884i) q^{67} -4.27051 q^{68} +(-10.9517 - 7.03824i) q^{69} +(7.88321 + 2.31472i) q^{70} +(5.37105 + 11.7610i) q^{71} +(2.03863 - 2.35271i) q^{72} +(-1.68054 - 1.93945i) q^{73} +(-3.21099 - 2.06358i) q^{74} +(0.536802 - 3.73354i) q^{75} +(-4.05108 - 2.60347i) q^{76} +(14.1106 - 4.14325i) q^{77} +(-8.46943 + 9.77425i) q^{78} +(0.503206 + 3.49987i) q^{79} +(-0.265272 - 1.84501i) q^{80} +(-3.59250 - 7.86648i) q^{81} +(-1.40663 + 0.903985i) q^{82} +(-4.55517 + 5.25694i) q^{83} +(4.52723 - 9.91324i) q^{84} +(-3.30677 - 7.24081i) q^{85} +(0.109250 - 0.0702106i) q^{86} +(10.2166 + 2.99985i) q^{87} +(-2.18491 - 2.52152i) q^{88} +(1.58880 - 0.466514i) q^{89} +(5.56766 + 1.63481i) q^{90} +(-9.57807 + 20.9730i) q^{91} +(0.749334 + 5.21173i) q^{92} +(-11.1573 + 24.4312i) q^{93} +(2.09535 + 2.41817i) q^{94} +(1.27742 - 8.88468i) q^{95} -2.47246 q^{96} +9.63273 q^{97} +(1.76877 - 12.3020i) q^{98} +(9.96588 - 2.92625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9} + 3 q^{10} + q^{11} - q^{12} - 11 q^{13} - 22 q^{14} + 18 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 16 q^{19} - 3 q^{20} - 27 q^{21} - q^{22} + 12 q^{24} + 2 q^{25} - 11 q^{26} + 14 q^{27} - 11 q^{28} + 26 q^{30} + 18 q^{31} + 3 q^{32} + 9 q^{33} - 14 q^{34} - 90 q^{35} - 8 q^{36} - 48 q^{37} + 28 q^{38} - q^{39} + 3 q^{40} - 51 q^{41} - 17 q^{42} + 10 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} + 10 q^{47} + 10 q^{48} - 19 q^{49} - 24 q^{50} + 4 q^{51} + 11 q^{52} - 8 q^{53} - 25 q^{54} + 25 q^{55} + 31 q^{57} + 22 q^{58} + 66 q^{59} + 18 q^{60} + 34 q^{61} - 29 q^{62} + 80 q^{63} - 3 q^{64} + 26 q^{65} + 90 q^{66} - 3 q^{67} - 8 q^{68} - 46 q^{69} + 90 q^{70} + 39 q^{71} - 3 q^{72} + 78 q^{73} - 18 q^{74} - 11 q^{75} + 16 q^{76} + 73 q^{77} - 10 q^{78} + 34 q^{79} + 8 q^{80} - 134 q^{81} + 7 q^{82} - 11 q^{83} + 6 q^{84} - 31 q^{85} + q^{86} - 110 q^{87} - q^{88} - 30 q^{89} + 4 q^{90} + 14 q^{91} + 11 q^{92} - 13 q^{93} + 23 q^{94} - 39 q^{95} - 10 q^{96} + 24 q^{97} + 19 q^{98} - 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9 + 3 * q^10 + q^11 - q^12 - 11 * q^13 - 22 * q^14 + 18 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 16 * q^19 - 3 * q^20 - 27 * q^21 - q^22 + 12 * q^24 + 2 * q^25 - 11 * q^26 + 14 * q^27 - 11 * q^28 + 26 * q^30 + 18 * q^31 + 3 * q^32 + 9 * q^33 - 14 * q^34 - 90 * q^35 - 8 * q^36 - 48 * q^37 + 28 * q^38 - q^39 + 3 * q^40 - 51 * q^41 - 17 * q^42 + 10 * q^43 + q^44 - 4 * q^45 - 11 * q^46 + 10 * q^47 + 10 * q^48 - 19 * q^49 - 24 * q^50 + 4 * q^51 + 11 * q^52 - 8 * q^53 - 25 * q^54 + 25 * q^55 + 31 * q^57 + 22 * q^58 + 66 * q^59 + 18 * q^60 + 34 * q^61 - 29 * q^62 + 80 * q^63 - 3 * q^64 + 26 * q^65 + 90 * q^66 - 3 * q^67 - 8 * q^68 - 46 * q^69 + 90 * q^70 + 39 * q^71 - 3 * q^72 + 78 * q^73 - 18 * q^74 - 11 * q^75 + 16 * q^76 + 73 * q^77 - 10 * q^78 + 34 * q^79 + 8 * q^80 - 134 * q^81 + 7 * q^82 - 11 * q^83 + 6 * q^84 - 31 * q^85 + q^86 - 110 * q^87 - q^88 - 30 * q^89 + 4 * q^90 + 14 * q^91 + 11 * q^92 - 13 * q^93 + 23 * q^94 - 39 * q^95 - 10 * q^96 + 24 * q^97 + 19 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/134\mathbb{Z}\right)^\times$.

$n$	$69$
$\chi(n)$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$	−2.37231	−	0.696574i	−1.36965	−	0.402167i	−0.487499	−	0.873124i	$-0.662091\pi$
$3$	−2.37231	−	0.696574i	−1.36965	−	0.402167i	−0.882156	+	0.470957i	$0.843909\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−1.22065	+	1.40870i	−0.545890	+	0.629991i	−0.959921	−	0.280272i	$-0.909575\pi$
$5$	−1.22065	+	1.40870i	−0.545890	+	0.629991i	0.414030	+	0.910263i	$0.364121\pi$
$6$	1.61912	+	1.86856i	0.661003	+	0.762838i
$7$	3.70806	+	2.38303i	1.40152	+	0.900700i	0.999886	−	0.0151026i	$-0.00480748\pi$
$7$	3.70806	+	2.38303i	1.40152	+	0.900700i	0.401630	+	0.915802i	$0.368444\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	2.61889	+	1.68306i	0.872962	+	0.561019i
$10$	1.78848	−	0.525144i	0.565566	−	0.166065i
$11$	2.18491	−	2.52152i	0.658774	−	0.760266i	−0.323802	−	0.946125i	$-0.604961\pi$
$11$	2.18491	−	2.52152i	0.658774	−	0.760266i	0.982576	+	0.185859i	$0.0595068\pi$
$12$	−0.351868	−	2.44730i	−0.101576	−	0.706474i
$13$	0.744433	+	5.17765i	0.206469	+	1.43602i	0.784562	+	0.620050i	$0.212888\pi$
$13$	0.744433	+	5.17765i	0.206469	+	1.43602i	−0.578094	+	0.815971i	$0.696203\pi$
$14$	−1.83106	−	4.00946i	−0.489371	−	1.07157i
$15$	3.87702	−	2.49161i	1.00104	−	0.643331i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−1.77403	+	3.88459i	−0.430267	+	0.942152i	0.563017	+	0.826445i	$0.309641\pi$
$17$	−1.77403	+	3.88459i	−0.430267	+	0.942152i	−0.993283	+	0.115707i	$0.963087\pi$
$18$	−1.29322	−	2.83175i	−0.304815	−	0.667451i
$19$	−4.05108	+	2.60347i	−0.929381	+	0.597277i	−0.915365	−	0.402625i	$-0.868098\pi$
$19$	−4.05108	+	2.60347i	−0.929381	+	0.597277i	−0.0140157	+	0.999902i	$0.504461\pi$
$20$	−1.78848	−	0.525144i	−0.399915	−	0.117426i
$21$	−7.13673	−	8.23622i	−1.55736	−	1.79729i
$22$	−3.20129	+	0.939985i	−0.682518	+	0.200405i
$23$	5.05204	+	1.48341i	1.05342	+	0.309313i	0.762200	−	0.647342i	$-0.224119\pi$
$23$	5.05204	+	1.48341i	1.05342	+	0.309313i	0.291224	+	0.956655i	$0.405938\pi$
$24$	−1.02710	+	2.24903i	−0.209656	+	0.459082i
$25$	0.217112	+	1.51005i	0.0434225	+	0.302010i
$26$	2.17299	−	4.75818i	0.426158	−	0.933157i
$27$	−0.183085	−	0.211292i	−0.0352348	−	0.0406631i
$28$	−0.627293	+	4.36292i	−0.118547	+	0.824514i
$29$	−4.30658			−0.799712			−0.399856	−	0.916578i	$-0.630940\pi$
$29$	−4.30658			−0.799712			−0.399856	+	0.916578i	$0.630940\pi$
$30$	−4.60862			−0.841416
$31$	1.54596	−	10.7524i	0.277663	−	1.93119i	−0.0788236	−	0.996889i	$-0.525116\pi$
$31$	1.54596	−	10.7524i	0.277663	−	1.93119i	0.356487	−	0.934300i	$-0.383975\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$	−6.93970	+	4.45987i	−1.20805	+	0.776364i
$34$	3.59258	−	2.30881i	0.616123	−	0.395958i
$35$	−7.88321	+	2.31472i	−1.33251	+	0.391259i
$36$	−0.443037	+	3.08139i	−0.0738395	+	0.513565i
$37$	3.81691			0.627495			0.313748	−	0.949506i	$-0.398415\pi$
$37$	3.81691			0.627495			0.313748	+	0.949506i	$0.398415\pi$
$38$	4.81552			0.781181
$39$	1.84058	−	12.8015i	0.294729	−	2.04989i
$40$	1.22065	+	1.40870i	0.193001	+	0.222735i
$41$	0.694600	−	1.52096i	0.108478	−	0.237534i	−0.847606	−	0.530626i	$-0.821957\pi$
$41$	0.694600	−	1.52096i	0.108478	−	0.237534i	0.956084	+	0.293092i	$0.0946842\pi$
$42$	1.55096	+	10.7872i	0.239318	+	1.66449i
$43$	−0.0539481	+	0.118130i	−0.00822701	+	0.0180146i	−0.913701	−	0.406387i	$-0.866788\pi$
$43$	−0.0539481	+	0.118130i	−0.00822701	+	0.0180146i	0.905474	+	0.424402i	$0.139516\pi$
$44$	3.20129	+	0.939985i	0.482613	+	0.141708i
$45$	−5.56766	+	1.63481i	−0.829978	+	0.243704i
$46$	−3.44805	−	3.97927i	−0.508388	−	0.586711i
$47$	−3.07008	−	0.901458i	−0.447818	−	0.131491i	0.0500450	−	0.998747i	$-0.484064\pi$
$47$	−3.07008	−	0.901458i	−0.447818	−	0.131491i	−0.497863	+	0.867256i	$0.665882\pi$
$48$	2.07997	−	1.33671i	0.300218	−	0.192938i
$49$	5.16300	+	11.3054i	0.737572	+	1.61506i
$50$	0.633748	−	1.38771i	0.0896255	−	0.196252i
$51$	6.91447	−	7.97972i	0.968219	−	1.11738i
$52$	−4.40050	+	2.82803i	−0.610240	+	0.392178i
$53$	−1.93990	−	4.24779i	−0.266466	−	0.583479i	0.728346	−	0.685210i	$-0.240289\pi$
$53$	−1.93990	−	4.24779i	−0.266466	−	0.583479i	−0.994812	+	0.101730i	$0.967562\pi$
$54$	0.0397882	+	0.276733i	0.00541449	+	0.0376586i
$55$	0.885065	+	6.15577i	0.119342	+	0.830043i
$56$	2.88648	−	3.33118i	0.385723	−	0.445148i
$57$	11.4239	−	3.35437i	1.51314	−	0.444297i
$58$	3.62293	+	2.32831i	0.475714	+	0.305723i
$59$	−0.222565	+	1.54797i	−0.0289755	+	0.201529i	−0.999167	−	0.0408111i	$-0.987006\pi$
$59$	−0.222565	+	1.54797i	−0.0289755	+	0.201529i	0.970191	+	0.242340i	$0.0779149\pi$
$60$	3.87702	+	2.49161i	0.500521	+	0.321665i
$61$	2.32071	+	2.67825i	0.297137	+	0.342914i	0.884612	−	0.466328i	$-0.154423\pi$
$61$	2.32071	+	2.67825i	0.297137	+	0.342914i	−0.587475	+	0.809242i	$0.699878\pi$
$62$	−7.11374	+	8.20969i	−0.903445	+	1.04263i
$63$	5.70023	+	12.4818i	0.718161	+	1.57255i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−8.20245	−	5.27140i	−1.01739	−	0.653836i
$66$	8.24924			1.01541
$67$	−0.871382	−	8.13884i	−0.106456	−	0.994317i
$67$	−0.871382	−	8.13884i	−0.106456	−	0.994317i
$68$	−4.27051			−0.517875
$69$	−10.9517	−	7.03824i	−1.31843	−	0.847304i
$70$	7.88321	+	2.31472i	0.942224	+	0.276662i
$71$	5.37105	+	11.7610i	0.637426	+	1.39577i	0.902141	+	0.431442i	$0.141995\pi$
$71$	5.37105	+	11.7610i	0.637426	+	1.39577i	−0.264715	+	0.964327i	$0.585278\pi$
$72$	2.03863	−	2.35271i	0.240255	−	0.277269i
$73$	−1.68054	−	1.93945i	−0.196693	−	0.226995i	0.648832	−	0.760931i	$-0.275258\pi$
$73$	−1.68054	−	1.93945i	−0.196693	−	0.226995i	−0.845525	+	0.533936i	$0.820712\pi$
$74$	−3.21099	−	2.06358i	−0.373269	−	0.239886i
$75$	0.536802	−	3.73354i	0.0619846	−	0.431112i
$76$	−4.05108	−	2.60347i	−0.464690	−	0.298638i
$77$	14.1106	−	4.14325i	1.60805	−	0.472167i
$78$	−8.46943	+	9.77425i	−0.958975	+	1.10672i
$79$	0.503206	+	3.49987i	0.0566151	+	0.393766i	0.998351	+	0.0574120i	$0.0182849\pi$
$79$	0.503206	+	3.49987i	0.0566151	+	0.393766i	−0.941736	+	0.336354i	$0.890806\pi$
$80$	−0.265272	−	1.84501i	−0.0296583	−	0.206278i
$81$	−3.59250	−	7.86648i	−0.399167	−	0.874054i
$82$	−1.40663	+	0.903985i	−0.155336	+	0.0998284i
$83$	−4.55517	+	5.25694i	−0.499994	+	0.577024i	−0.948509	−	0.316751i	$-0.897408\pi$
$83$	−4.55517	+	5.25694i	−0.499994	+	0.577024i	0.448514	+	0.893776i	$0.351953\pi$
$84$	4.52723	−	9.91324i	0.493961	−	1.08162i
$85$	−3.30677	−	7.24081i	−0.358669	−	0.785376i
$86$	0.109250	−	0.0702106i	0.0117807	−	0.00757101i
$87$	10.2166	+	2.99985i	1.09533	+	0.321618i
$88$	−2.18491	−	2.52152i	−0.232912	−	0.268795i
$89$	1.58880	−	0.466514i	0.168412	−	0.0494503i	−0.196439	−	0.980516i	$-0.562938\pi$
$89$	1.58880	−	0.466514i	0.168412	−	0.0494503i	0.364852	+	0.931066i	$0.381120\pi$
$90$	5.56766	+	1.63481i	0.586883	+	0.172324i
$91$	−9.57807	+	20.9730i	−1.00405	+	2.19857i
$92$	0.749334	+	5.21173i	0.0781234	+	0.543360i
$93$	−11.1573	+	24.4312i	−1.15696	+	2.53340i
$94$	2.09535	+	2.41817i	0.216119	+	0.249415i
$95$	1.27742	−	8.88468i	0.131061	−	0.911549i
$96$	−2.47246			−0.252345
$97$	9.63273			0.978055			0.489028	−	0.872268i	$-0.337352\pi$
$97$	9.63273			0.978055			0.489028	+	0.872268i	$0.337352\pi$
$98$	1.76877	−	12.3020i	0.178672	−	1.24269i
$99$	9.96588	−	2.92625i	1.00161	−	0.294099i
$100$	−1.28340	+	0.824789i	−0.128340	+	0.0824789i
$101$	9.32080	−	5.99011i	0.927454	−	0.596039i	0.0126428	−	0.999920i	$-0.495976\pi$
$101$	9.32080	−	5.99011i	0.927454	−	0.596039i	0.914811	+	0.403881i	$0.132339\pi$
$102$	−10.1310	+	2.97472i	−1.00312	+	0.294542i
$103$	0.773734	−	5.38144i	0.0762382	−	0.530249i	−0.915535	−	0.402239i	$-0.868232\pi$
$103$	0.773734	−	5.38144i	0.0762382	−	0.530249i	0.991773	−	0.128010i	$-0.0408588\pi$
$104$	5.23089			0.512931
$105$	20.3138			1.98242
$106$	−0.664581	+	4.62226i	−0.0645498	+	0.448954i
$107$	−10.1719	−	11.7390i	−0.983352	−	1.13485i	−0.990862	−	0.134877i	$-0.956936\pi$
$107$	−10.1719	−	11.7390i	−0.983352	−	1.13485i	0.00751059	−	0.999972i	$-0.497609\pi$
$108$	0.116141	−	0.254314i	0.0111757	−	0.0244714i
$109$	−1.75574	−	12.2115i	−0.168170	−	1.16965i	−0.882664	−	0.470005i	$-0.844252\pi$
$109$	−1.75574	−	12.2115i	−0.168170	−	1.16965i	0.714494	−	0.699641i	$-0.246657\pi$
$110$	2.58349	−	5.65706i	0.246326	−	0.539380i
$111$	−9.05489	−	2.65876i	−0.859452	−	0.252358i
$112$	−4.22924	+	1.24182i	−0.399625	+	0.117341i
$113$	4.92605	+	5.68497i	0.463404	+	0.534797i	0.938565	−	0.345102i	$-0.112156\pi$
$113$	4.92605	+	5.68497i	0.463404	+	0.534797i	−0.475161	+	0.879899i	$0.657610\pi$
$114$	−11.4239	−	3.35437i	−1.06995	−	0.314165i
$115$	−8.25645	+	5.30610i	−0.769918	+	0.494796i
$116$	−1.78902	−	3.91740i	−0.166106	−	0.363722i
$117$	−6.76468	+	14.8126i	−0.625395	+	1.36942i
$118$	1.02413	−	1.18191i	0.0942788	−	0.108804i
$119$	−15.8353	+	10.1767i	−1.45162	+	0.932900i
$120$	−1.91449	−	4.19215i	−0.174768	−	0.382689i
$121$	−0.0187655	−	0.130517i	−0.00170596	−	0.0118652i
$122$	−0.504339	−	3.50776i	−0.0456607	−	0.317577i
$123$	−2.70727	+	3.12435i	−0.244106	+	0.281714i
$124$	10.4229	−	3.06045i	0.936008	−	0.274837i
$125$	−10.2326	−	6.57611i	−0.915234	−	0.588185i
$126$	1.95281	−	13.5821i	0.173970	−	1.20999i
$127$	−16.5301	−	10.6233i	−1.46681	−	0.942662i	−0.998244	−	0.0592345i	$-0.981134\pi$
$127$	−16.5301	−	10.6233i	−1.46681	−	0.942662i	−0.468567	−	0.883428i	$-0.655230\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$	0.210268	−	0.242662i	0.0185131	−	0.0213652i
$130$	4.05041	+	8.86916i	0.355244	+	0.777877i
$131$	2.58906	+	0.760218i	0.226208	+	0.0664205i	0.392872	−	0.919593i	$-0.371482\pi$
$131$	2.58906	+	0.760218i	0.226208	+	0.0664205i	−0.166665	+	0.986014i	$0.553300\pi$
$132$	−6.93970	−	4.45987i	−0.604023	−	0.388182i
$133$	−21.2258			−1.84051
$134$	−3.66713	+	7.31793i	−0.316792	+	0.632173i
$135$	0.521129			0.0448517
$136$	3.59258	+	2.30881i	0.308061	+	0.197979i
$137$	−12.5307	−	3.67935i	−1.07057	−	0.314348i	−0.301471	−	0.953475i	$-0.597478\pi$
$137$	−12.5307	−	3.67935i	−1.07057	−	0.314348i	−0.769101	+	0.639127i	$0.779296\pi$
$138$	5.40801	+	11.8419i	0.460360	+	1.00805i
$139$	9.50719	−	10.9719i	0.806390	−	0.930623i	−0.192324	−	0.981332i	$-0.561602\pi$
$139$	9.50719	−	10.9719i	0.806390	−	0.930623i	0.998714	+	0.0507082i	$0.0161478\pi$
$140$	−5.38035	−	6.20925i	−0.454722	−	0.524778i
$141$	6.65526	+	4.27708i	0.560474	+	0.360195i
$142$	1.84004	−	12.7978i	0.154413	−	1.07396i
$143$	14.6820	+	9.43557i	1.22777	+	0.789042i
$144$	−2.98698	+	0.877055i	−0.248915	+	0.0730879i
$145$	5.25682	−	6.06669i	0.436555	−	0.503811i
$146$	0.365217	+	2.54014i	0.0302255	+	0.210223i
$147$	−4.37321	−	30.4163i	−0.360696	−	2.50870i
$148$	1.58560	+	3.47198i	0.130336	+	0.285395i
$149$	8.91165	−	5.72717i	0.730071	−	0.469188i	−0.122056	−	0.992523i	$-0.538949\pi$
$149$	8.91165	−	5.72717i	0.730071	−	0.469188i	0.852127	+	0.523335i	$0.175312\pi$
$150$	−2.47009	+	2.85064i	−0.201682	+	0.232754i
$151$	4.01232	−	8.78576i	0.326518	−	0.714975i	−0.673182	−	0.739477i	$-0.735073\pi$
$151$	4.01232	−	8.78576i	0.326518	−	0.714975i	0.999700	+	0.0245022i	$0.00780007\pi$
$152$	2.00044	+	4.38035i	0.162257	+	0.355294i
$153$	−11.1840	+	7.18751i	−0.904172	+	0.581076i
$154$	−14.1106	−	4.14325i	−1.13707	−	0.333873i
$155$	13.2599	+	15.3027i	1.06506	+	1.22914i
$156$	12.4093	−	3.64370i	0.993539	−	0.291729i
$157$	19.0998	+	5.60822i	1.52433	+	0.447585i	0.933310	−	0.359070i	$-0.116906\pi$
$157$	19.0998	+	5.60822i	1.52433	+	0.447585i	0.591023	+	0.806655i	$0.298724\pi$
$158$	1.46885	−	3.21633i	0.116855	−	0.255878i
$159$	1.64315	+	11.4284i	0.130310	+	0.906329i
$160$	−0.774325	+	1.69554i	−0.0612158	+	0.134044i
$161$	15.1983	+	17.5397i	1.19779	+	1.38233i
$162$	−1.23074	+	8.55996i	−0.0966958	+	0.672534i
$163$	14.5955			1.14320			0.571602	−	0.820531i	$-0.306322\pi$
$163$	14.5955			1.14320			0.571602	+	0.820531i	$0.306322\pi$
$164$	1.67206			0.130566
$165$	2.18829	−	15.2199i	0.170358	−	1.18487i
$166$	6.67417	−	1.95971i	0.518016	−	0.152103i
$167$	−9.60080	+	6.17006i	−0.742932	+	0.477453i	−0.856545	−	0.516072i	$-0.827394\pi$
$167$	−9.60080	+	6.17006i	−0.742932	+	0.477453i	0.113614	+	0.993525i	$0.463757\pi$
$168$	−9.16805	+	5.89195i	−0.707330	+	0.454574i
$169$	−13.7804	+	4.04630i	−1.06003	+	0.311254i
$170$	−1.13285	+	7.87913i	−0.0868854	+	0.604301i
$171$	−14.9911			−1.14640
$172$	−0.129866			−0.00990216
$173$	−2.72240	+	18.9347i	−0.206980	+	1.43958i	0.575957	+	0.817480i	$0.304629\pi$
$173$	−2.72240	+	18.9347i	−0.206980	+	1.43958i	−0.782938	+	0.622100i	$0.786280\pi$
$174$	−6.97287	−	8.04712i	−0.528612	−	0.610051i
$175$	−2.79342	+	6.11674i	−0.211163	+	0.462382i
$176$	0.474826	+	3.30248i	0.0357913	+	0.248934i
$177$	1.60627	−	3.51724i	0.120735	−	0.264372i
$178$	−1.58880	−	0.466514i	−0.119086	−	0.0349667i
$179$	23.3477	−	6.85552i	1.74509	−	0.512405i	0.755357	−	0.655314i	$-0.227464\pi$
$179$	23.3477	−	6.85552i	1.74509	−	0.512405i	0.989736	+	0.142908i	$0.0456454\pi$
$180$	−3.79997	−	4.38540i	−0.283233	−	0.326868i
$181$	2.44709	+	0.718532i	0.181891	+	0.0534080i	0.371410	−	0.928469i	$-0.378875\pi$
$181$	2.44709	+	0.718532i	0.181891	+	0.0534080i	−0.189519	+	0.981877i	$0.560693\pi$
$182$	19.3965	−	12.4653i	1.43776	−	0.923993i
$183$	−3.63986	−	7.97018i	−0.269066	−	0.589173i
$184$	2.18729	−	4.78951i	0.161250	−	0.353087i
$185$	−4.65910	+	5.37688i	−0.342544	+	0.395316i
$186$	22.5946	−	14.5207i	1.65672	−	1.06471i
$187$	5.91897	+	12.9607i	0.432838	+	0.947782i
$188$	−0.455364	−	3.16713i	−0.0332108	−	0.230986i
$189$	−0.175378	−	1.21978i	−0.0127569	−	0.0887259i
$190$	−5.87806	+	6.78364i	−0.426439	+	0.492137i
$191$	15.8568	−	4.65598i	1.14736	−	0.336895i	0.347850	−	0.937550i	$-0.386912\pi$
$191$	15.8568	−	4.65598i	1.14736	−	0.336895i	0.799508	+	0.600655i	$0.205094\pi$
$192$	2.07997	+	1.33671i	0.150109	+	0.0964691i
$193$	0.977080	−	6.79574i	0.0703317	−	0.489168i	−0.923961	−	0.382486i	$-0.875068\pi$
$193$	0.977080	−	6.79574i	0.0703317	−	0.489168i	0.994293	−	0.106682i	$-0.0340228\pi$
$194$	−8.10357	−	5.20785i	−0.581802	−	0.373902i
$195$	15.7869	+	18.2190i	1.13052	+	1.30469i
$196$	−8.13897	+	9.39287i	−0.581355	+	0.670919i
$197$	6.82968	+	14.9549i	0.486595	+	1.06549i	0.980597	+	0.196033i	$0.0628060\pi$
$197$	6.82968	+	14.9549i	0.486595	+	1.06549i	−0.494003	+	0.869460i	$0.664467\pi$
$198$	−9.96588	−	2.92625i	−0.708244	−	0.207959i
$199$	−18.3977	−	11.8235i	−1.30418	−	0.838143i	−0.310516	−	0.950568i	$-0.600502\pi$
$199$	−18.3977	−	11.8235i	−1.30418	−	0.838143i	−0.993660	+	0.112425i	$0.964138\pi$
$200$	1.52558			0.107875
$201$	−3.60211	+	19.9148i	−0.254073	+	1.40468i
$202$	−11.0797			−0.779562
$203$	−15.9691	−	10.2627i	−1.12081	−	0.720300i
$204$	10.1310	+	2.97472i	0.709311	+	0.208272i
$205$	1.29472	+	2.83504i	0.0904272	+	0.198008i
$206$	−3.56033	+	4.10884i	−0.248060	+	0.286276i
$207$	10.7341	+	12.3878i	0.746069	+	0.861009i
$208$	−4.40050	−	2.82803i	−0.305120	−	0.196089i
$209$	−2.28653	+	15.9032i	−0.158163	+	1.10005i
$210$	−17.0891	−	10.9825i	−1.17926	−	0.757863i
$211$	−10.8012	+	3.17153i	−0.743588	+	0.218337i	−0.631516	−	0.775363i	$-0.717567\pi$
$211$	−10.8012	+	3.17153i	−0.743588	+	0.218337i	−0.112072	+	0.993700i	$0.535749\pi$
$212$	3.05806	−	3.52919i	0.210029	−	0.242386i
$213$	−4.54943	−	31.6420i	−0.311722	−	2.16807i
$214$	2.21056	+	15.3748i	0.151111	+	1.05100i
$215$	−0.100558	−	0.220192i	−0.00685801	−	0.0150170i
$216$	−0.235197	+	0.151152i	−0.0160031	+	0.0102846i
$217$	31.3558	−	36.1865i	2.12857	−	2.45650i
$218$	−5.12499	+	11.2222i	−0.347108	+	0.760061i
$219$	2.63580	+	5.77160i	0.178111	+	0.390008i
$220$	−5.23181	+	3.36228i	−0.352729	+	0.226685i
$221$	−21.4337	−	6.29350i	−1.44179	−	0.423347i
$222$	6.18003	+	7.13213i	0.414776	+	0.478677i
$223$	3.36728	−	0.988721i	0.225489	−	0.0662097i	−0.167036	−	0.985951i	$-0.553420\pi$
$223$	3.36728	−	0.988721i	0.225489	−	0.0662097i	0.392526	+	0.919741i	$0.371601\pi$
$224$	4.22924	+	1.24182i	0.282578	+	0.0829723i
$225$	−1.97291	+	4.32006i	−0.131527	+	0.288004i
$226$	−1.07053	−	7.44572i	−0.0712108	−	0.495282i
$227$	−2.08589	+	4.56747i	−0.138446	+	0.303154i	−0.966137	−	0.258030i	$-0.916927\pi$
$227$	−2.08589	+	4.56747i	−0.138446	+	0.303154i	0.827691	+	0.561184i	$0.189654\pi$
$228$	7.79691	+	8.99811i	0.516363	+	0.595914i
$229$	0.384415	−	2.67367i	0.0254029	−	0.176681i	−0.973170	−	0.230087i	$-0.926099\pi$
$229$	0.384415	−	2.67367i	0.0254029	−	0.176681i	0.998573	+	0.0534065i	$0.0170079\pi$
$230$	9.81446			0.647146
$231$	−36.3608			−2.39237
$232$	−0.612891	+	4.26275i	−0.0402382	+	0.279863i
$233$	−3.66050	+	1.07482i	−0.239807	+	0.0704138i	−0.399428	−	0.916765i	$-0.630791\pi$
$233$	−3.66050	+	1.07482i	−0.239807	+	0.0704138i	0.159620	+	0.987178i	$0.448973\pi$
$234$	13.6991	−	8.80388i	0.895539	−	0.575528i
$235$	5.01738	−	3.22447i	0.327298	−	0.210341i
$236$	−1.50054	+	0.440599i	−0.0976769	+	0.0286805i
$237$	1.24416	−	8.65331i	0.0808167	−	0.562093i
$238$	18.8235			1.22015
$239$	−0.0731197			−0.00472972			−0.00236486	−	0.999997i	$-0.500753\pi$
$239$	−0.0731197			−0.00472972			−0.00236486	+	0.999997i	$0.500753\pi$
$240$	−0.655876	+	4.56171i	−0.0423366	+	0.294457i
$241$	2.66243	+	3.07261i	0.171502	+	0.197924i	0.834993	−	0.550260i	$-0.185471\pi$
$241$	2.66243	+	3.07261i	0.171502	+	0.197924i	−0.663491	+	0.748184i	$0.730926\pi$
$242$	−0.0547763	+	0.119943i	−0.00352116	+	0.00771026i
$243$	3.16232	+	21.9944i	0.202863	+	1.41094i
$244$	−1.47216	+	3.22358i	−0.0942453	+	0.206368i
$245$	−22.2282	−	6.52677i	−1.42010	−	0.416980i
$246$	3.96665	−	1.16471i	0.252905	−	0.0742595i
$247$	−16.4956	−	19.0369i	−1.04959	−	1.21129i
$248$	−10.4229	−	3.06045i	−0.661858	−	0.194339i
$249$	14.4681	−	9.29810i	0.916880	−	0.589243i
$250$	5.05292	+	11.0644i	0.319575	+	0.699771i
$251$	0.969047	−	2.12192i	0.0611657	−	0.133934i	−0.876581	−	0.481255i	$-0.840181\pi$
$251$	0.969047	−	2.12192i	0.0611657	−	0.133934i	0.937746	+	0.347321i	$0.112908\pi$
$252$	−8.98585	+	10.3702i	−0.566055	+	0.653262i
$253$	14.7787	−	9.49769i	0.929128	−	0.597114i
$254$	8.16265	+	17.8737i	0.512170	+	1.12150i
$255$	2.80092	+	19.4809i	0.175401	+	1.21994i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	12.3837	−	14.2915i	0.772473	−	0.891482i	−0.224069	−	0.974573i	$-0.571934\pi$
$257$	12.3837	−	14.2915i	0.772473	−	0.891482i	0.996542	+	0.0830918i	$0.0264795\pi$
$258$	−0.308082	+	0.0904609i	−0.0191803	+	0.00563185i
$259$	14.1533	+	9.09579i	0.879445	+	0.565185i
$260$	1.38761	−	9.65103i	0.0860558	−	0.598532i
$261$	−11.2785	−	7.24822i	−0.698119	−	0.448654i
$262$	−1.76705	−	2.03929i	−0.109169	−	0.125988i
$263$	3.53303	−	4.07734i	0.217856	−	0.251419i	−0.636293	−	0.771447i	$-0.719533\pi$
$263$	3.53303	−	4.07734i	0.217856	−	0.251419i	0.854149	+	0.520028i	$0.174079\pi$
$264$	3.42686	+	7.50377i	0.210908	+	0.461825i
$265$	8.35181	+	2.45231i	0.513048	+	0.150644i
$266$	17.8563	+	11.4755i	1.09484	+	0.703609i
$267$	−4.09409			−0.250554
$268$	7.04136	−	4.17363i	0.430120	−	0.254945i
$269$	−14.8631			−0.906218			−0.453109	−	0.891455i	$-0.649685\pi$
$269$	−14.8631			−0.906218			−0.453109	+	0.891455i	$0.649685\pi$
$270$	−0.438402	−	0.281744i	−0.0266803	−	0.0171464i
$271$	−21.2494	−	6.23940i	−1.29081	−	0.379017i	−0.436936	−	0.899493i	$-0.643936\pi$
$271$	−21.2494	−	6.23940i	−1.29081	−	0.379017i	−0.853876	+	0.520476i	$0.825754\pi$
$272$	−1.77403	−	3.88459i	−0.107567	−	0.235538i
$273$	37.3314	−	43.0828i	2.25940	−	2.60749i
$274$	8.55231	+	9.86989i	0.516664	+	0.596262i
$275$	4.28198	+	2.75186i	0.258213	+	0.165944i
$276$	1.85270	−	12.8858i	0.111519	−	0.775635i
$277$	−0.203499	−	0.130781i	−0.0122271	−	0.00785785i	0.534513	−	0.845160i	$-0.320495\pi$
$277$	−0.203499	−	0.130781i	−0.0122271	−	0.00785785i	−0.546740	+	0.837302i	$0.684131\pi$
$278$	−13.9298	+	4.09016i	−0.835455	+	0.245312i
$279$	22.1456	−	25.5574i	1.32582	−	1.53008i
$280$	1.16926	+	8.13239i	0.0698767	+	0.486003i
$281$	−0.480518	−	3.34208i	−0.0286653	−	0.199372i	0.970456	−	0.241277i	$-0.0775663\pi$
$281$	−0.480518	−	3.34208i	−0.0286653	−	0.199372i	−0.999122	+	0.0419055i	$0.986657\pi$
$282$	−3.28640	−	7.19622i	−0.195702	−	0.428528i
$283$	−11.4122	+	7.33417i	−0.678384	+	0.435971i	−0.833939	−	0.551856i	$-0.813920\pi$
$283$	−11.4122	+	7.33417i	−0.678384	+	0.435971i	0.155555	+	0.987827i	$0.450283\pi$
$284$	−8.46693	+	9.77135i	−0.502420	+	0.579823i
$285$	−9.21928	+	20.1874i	−0.546103	+	1.19580i
$286$	−7.25006	−	15.8754i	−0.428705	−	0.938733i
$287$	6.20011	−	3.98457i	0.365981	−	0.235202i
$288$	2.98698	+	0.877055i	0.176009	+	0.0516810i
$289$	−0.810234	−	0.935060i	−0.0476608	−	0.0550035i
$290$	−7.70222	+	2.26158i	−0.452290	+	0.132804i
$291$	−22.8518	−	6.70990i	−1.33960	−	0.393342i
$292$	1.06606	−	2.33435i	0.0623866	−	0.136608i
$293$	−0.645063	−	4.48651i	−0.0376850	−	0.262105i	0.962265	−	0.272114i	$-0.0877229\pi$
$293$	−0.645063	−	4.48651i	−0.0376850	−	0.262105i	−0.999950	+	0.0100095i	$0.996814\pi$
$294$	−12.7653	+	27.9522i	−0.744490	+	1.63021i
$295$	−1.90896	−	2.20306i	−0.111144	−	0.128267i
$296$	0.543202	−	3.77806i	0.0315730	−	0.219595i
$297$	−0.932799			−0.0541265
$298$	−10.5933			−0.613653
$299$	−3.91968	+	27.2620i	−0.226681	+	1.57660i
$300$	3.61914	−	1.06268i	0.208951	−	0.0613537i
$301$	−0.481550	+	0.309473i	−0.0277561	+	0.0178377i
$302$	−8.12532	+	5.22183i	−0.467560	+	0.300482i
$303$	−26.2844	+	7.71779i	−1.51000	+	0.443376i
$304$	0.685320	−	4.76651i	0.0393058	−	0.273378i
$305$	−6.60562			−0.378237
$306$	13.2944			0.759992
$307$	3.43638	−	23.9006i	0.196125	−	1.36408i	−0.619273	−	0.785176i	$-0.712573\pi$
$307$	3.43638	−	23.9006i	0.196125	−	1.36408i	0.815398	−	0.578901i	$-0.196518\pi$
$308$	9.63059	+	11.1143i	0.548754	+	0.633296i
$309$	−5.58410	+	12.2275i	−0.317669	+	0.695597i
$310$	−2.88164	−	20.0423i	−0.163666	−	1.13832i
$311$	12.7292	−	27.8730i	0.721806	−	1.58054i	−0.0895493	−	0.995982i	$-0.528543\pi$
$311$	12.7292	−	27.8730i	0.721806	−	1.58054i	0.811356	−	0.584553i	$-0.198730\pi$
$312$	−12.4093	−	3.64370i	−0.702538	−	0.206284i
$313$	−8.60335	+	2.52617i	−0.486290	+	0.142788i	−0.515681	−	0.856780i	$-0.672461\pi$
$313$	−8.60335	+	2.52617i	−0.486290	+	0.142788i	0.0293916	+	0.999568i	$0.490643\pi$
$314$	−13.0358	−	15.0441i	−0.735651	−	0.848987i
$315$	−24.5410	−	7.20590i	−1.38273	−	0.406007i
$316$	−2.97456	+	1.91163i	−0.167332	+	0.107538i
$317$	2.19777	+	4.81245i	0.123439	+	0.270294i	0.961256	−	0.275657i	$-0.0888955\pi$
$317$	2.19777	+	4.81245i	0.123439	+	0.270294i	−0.837817	+	0.545952i	$0.816168\pi$
$318$	4.79634	−	10.5025i	0.268965	−	0.588952i
$319$	−9.40948	+	10.8591i	−0.526830	+	0.607994i
$320$	1.56808	−	1.00774i	0.0876583	−	0.0563346i
$321$	15.9538	+	34.9339i	0.890454	+	1.94982i
$322$	−3.30290	−	22.9722i	−0.184063	−	1.28019i
$323$	−2.92667	−	20.3554i	−0.162844	−	1.13261i
$324$	5.66322	−	6.53571i	0.314624	−	0.363095i
$325$	−7.65687	+	2.24826i	−0.424727	+	0.124711i
$326$	−12.2785	−	7.89090i	−0.680042	−	0.437036i
$327$	−4.34101	+	30.1924i	−0.240058	+	1.66964i
$328$	−1.40663	−	0.903985i	−0.0776680	−	0.0499142i
$329$	−9.23586	−	10.6588i	−0.509190	−	0.587636i
$330$	−10.0694	+	11.6207i	−0.554303	+	0.639700i
$331$	9.74723	+	21.3435i	0.535756	+	1.17314i	0.963122	+	0.269064i	$0.0867144\pi$
$331$	9.74723	+	21.3435i	0.535756	+	1.17314i	−0.427366	+	0.904079i	$0.640558\pi$
$332$	−6.67417	−	1.95971i	−0.366293	−	0.107553i
$333$	9.99605	+	6.42407i	0.547780	+	0.352037i
$334$	11.4125			0.624464
$335$	12.5289	+	8.70713i	0.684524	+	0.475722i
$336$	10.8981			0.594539
$337$	−12.6570	−	8.13418i	−0.689472	−	0.443097i	0.148426	−	0.988924i	$-0.452579\pi$
$337$	−12.6570	−	8.13418i	−0.689472	−	0.443097i	−0.837898	+	0.545827i	$0.816216\pi$
$338$	13.7804	+	4.04630i	0.749557	+	0.220090i
$339$	−7.72613	−	16.9179i	−0.419626	−	0.918853i
$340$	5.21279	−	6.01588i	0.282703	−	0.326257i
$341$	−23.7346	−	27.3912i	−1.28530	−	1.48331i
$342$	12.6113	+	8.10480i	0.681942	+	0.438257i
$343$	−3.40529	+	23.6843i	−0.183868	+	1.27883i
$344$	0.109250	+	0.0702106i	0.00589036	+	0.00378550i
$345$	23.2830	−	6.83649i	1.25351	−	0.368064i
$346$	12.5271	−	14.4571i	0.673462	−	0.777216i
$347$	0.965432	+	6.71473i	0.0518271	+	0.360465i	0.999188	+	0.0402970i	$0.0128304\pi$
$347$	0.965432	+	6.71473i	0.0518271	+	0.360465i	−0.947361	+	0.320168i	$0.896260\pi$
$348$	1.51535	+	10.5395i	0.0812313	+	0.564976i
$349$	−3.06325	−	6.70758i	−0.163972	−	0.359049i	0.809755	−	0.586769i	$-0.199600\pi$
$349$	−3.06325	−	6.70758i	−0.163972	−	0.359049i	−0.973727	+	0.227720i	$0.926873\pi$
$350$	5.65694	−	3.63549i	0.302376	−	0.194325i
$351$	0.957698	−	1.10524i	0.0511182	−	0.0589935i
$352$	1.38601	−	3.03494i	0.0738745	−	0.161763i
$353$	11.4891	+	25.1576i	0.611502	+	1.33900i	0.921542	+	0.388279i	$0.126930\pi$
$353$	11.4891	+	25.1576i	0.611502	+	1.33900i	−0.310040	+	0.950723i	$0.600343\pi$
$354$	−3.25284	+	2.09048i	−0.172887	+	0.111107i
$355$	−23.1238	−	6.78977i	−1.22729	−	0.360364i
$356$	1.08437	+	1.25143i	0.0574713	+	0.0663254i
$357$	44.6552	−	13.1119i	2.36340	−	0.693957i
$358$	−23.3477	−	6.85552i	−1.23397	−	0.362325i
$359$	−5.03685	+	11.0292i	−0.265835	+	0.582097i	−0.994730	−	0.102528i	$-0.967307\pi$
$359$	−5.03685	+	11.0292i	−0.265835	+	0.582097i	0.728895	+	0.684625i	$0.240034\pi$
$360$	0.825812	+	5.74365i	0.0435241	+	0.302717i
$361$	1.74028	−	3.81069i	0.0915939	−	0.200563i
$362$	−1.67016	−	1.92747i	−0.0877816	−	0.101305i
$363$	−0.0463971	+	0.322699i	−0.00243522	+	0.0169373i
$364$	−23.0566			−1.20850
$365$	4.78346			0.250377
$366$	−1.24696	+	8.67280i	−0.0651797	+	0.453334i
$367$	−23.1562	+	6.79928i	−1.20874	+	0.354919i	−0.823190	−	0.567766i	$-0.807808\pi$
$367$	−23.1562	+	6.79928i	−1.20874	+	0.354919i	−0.385554	+	0.922685i	$0.625990\pi$
$368$	−4.42947	+	2.84665i	−0.230902	+	0.148392i
$369$	4.37894	−	2.81417i	0.227959	−	0.146500i
$370$	6.82644	−	2.00443i	0.354890	−	0.104205i
$371$	2.92933	−	20.3739i	0.152083	−	1.05776i
$372$	−26.8583			−1.39254
$373$	−19.2041			−0.994352			−0.497176	−	0.867650i	$-0.665630\pi$
$373$	−19.2041			−0.994352			−0.497176	+	0.867650i	$0.665630\pi$
$374$	2.02775	−	14.1033i	0.104852	−	0.729264i
$375$	19.6942	+	22.7284i	1.01701	+	1.17369i
$376$	−1.32920	+	2.91054i	−0.0685483	+	0.150100i
$377$	−3.20596	−	22.2980i	−0.165115	−	1.14840i
$378$	−0.511925	+	1.12096i	−0.0263306	+	0.0576560i
$379$	21.9708	+	6.45122i	1.12857	+	0.331377i	0.792144	−	0.610334i	$-0.208965\pi$
$379$	21.9708	+	6.45122i	1.12857	+	0.331377i	0.336422	+	0.941711i	$0.390783\pi$
$380$	8.61245	−	2.52884i	0.441809	−	0.129727i
$381$	31.8147	+	36.7161i	1.62992	+	1.88102i
$382$	−15.8568	−	4.65598i	−0.811305	−	0.238221i
$383$	23.0037	−	14.7836i	1.17543	−	0.755405i	0.200892	−	0.979613i	$-0.435616\pi$
$383$	23.0037	−	14.7836i	1.17543	−	0.755405i	0.974541	+	0.224208i	$0.0719797\pi$
$384$	−1.02710	−	2.24903i	−0.0524139	−	0.114770i
$385$	−11.3875	+	24.9351i	−0.580360	+	1.27081i
$386$	−4.49603	+	5.18869i	−0.228842	+	0.264097i
$387$	−0.340103	+	0.218571i	−0.0172884	+	0.0111106i
$388$	4.00158	+	8.76224i	0.203149	+	0.444835i
$389$	5.03691	+	35.0325i	0.255382	+	1.77622i	0.564737	+	0.825271i	$0.308978\pi$
$389$	5.03691	+	35.0325i	0.255382	+	1.77622i	−0.309355	+	0.950947i	$0.600113\pi$
$390$	−3.43081	−	23.8618i	−0.173726	−	1.20829i
$391$	−14.7250	+	16.9935i	−0.744673	+	0.859398i
$392$	11.9251	−	3.50153i	0.602309	−	0.176854i
$393$	−5.61252	−	3.60695i	−0.283114	−	0.181946i
$394$	2.33974	−	16.2733i	0.117875	−	0.819836i
$395$	−5.54451	−	3.56324i	−0.278975	−	0.179286i
$396$	6.80178	+	7.84967i	0.341802	+	0.394461i
$397$	8.30941	−	9.58956i	0.417037	−	0.481286i	−0.507895	−	0.861419i	$-0.669576\pi$
$397$	8.30941	−	9.58956i	0.417037	−	0.481286i	0.924932	+	0.380133i	$0.124122\pi$
$398$	9.08485	+	19.8931i	0.455383	+	0.997149i
$399$	50.3542	+	14.7853i	2.52086	+	0.740192i
$400$	−1.28340	−	0.824789i	−0.0641699	−	0.0412395i
$401$	14.7477			0.736466			0.368233	−	0.929734i	$-0.379963\pi$
$401$	14.7477			0.736466			0.368233	+	0.929734i	$0.379963\pi$
$402$	13.7971	−	14.8060i	0.688135	−	0.738455i
$403$	56.8230			2.83056
$404$	9.32080	+	5.99011i	0.463727	+	0.298019i
$405$	15.4667	+	4.54144i	0.768547	+	0.225666i
$406$	7.88560	+	17.2671i	0.391356	+	0.856950i
$407$	8.33958	−	9.62439i	0.413378	−	0.477063i
$408$	−6.91447	−	7.97972i	−0.342317	−	0.395055i
$409$	−3.04778	−	1.95869i	−0.150703	−	0.0968509i	0.463116	−	0.886298i	$-0.346731\pi$
$409$	−3.04778	−	1.95869i	−0.150703	−	0.0968509i	−0.613819	+	0.789447i	$0.710368\pi$
$410$	0.443551	−	3.08497i	0.0219054	−	0.152356i
$411$	27.1639	+	17.4571i	1.33989	+	0.861098i
$412$	5.21655	−	1.53172i	0.257001	−	0.0754623i
$413$	−4.51414	+	5.20960i	−0.222126	+	0.256348i
$414$	−2.33273	−	16.2245i	−0.114648	−	0.797392i
$415$	−1.84521	−	12.8337i	−0.0905780	−	0.629984i
$416$	2.17299	+	4.75818i	0.106540	+	0.233289i
$417$	−30.1968	+	19.4063i	−1.47874	+	0.950329i
$418$	10.5215	−	12.1424i	0.514622	−	0.593905i
$419$	−0.886183	+	1.94047i	−0.0432929	+	0.0947982i	−0.930043	−	0.367452i	$-0.880230\pi$
$419$	−0.886183	+	1.94047i	−0.0432929	+	0.0947982i	0.886750	+	0.462250i	$0.152958\pi$
$420$	8.43866	+	18.4781i	0.411765	+	0.901639i
$421$	18.2178	−	11.7079i	0.887881	−	0.570606i	−0.0152920	−	0.999883i	$-0.504868\pi$
$421$	18.2178	−	11.7079i	0.887881	−	0.570606i	0.903173	+	0.429277i	$0.141231\pi$
$422$	10.8012	+	3.17153i	0.525796	+	0.154388i
$423$	−6.52300	−	7.52794i	−0.317159	−	0.366021i
$424$	−4.48063	+	1.31563i	−0.217599	+	0.0638928i
$425$	−6.25109	−	1.83549i	−0.303222	−	0.0890341i
$426$	−13.2797	+	29.0785i	−0.643405	+	1.40886i
$427$	2.22302	+	15.4614i	0.107579	+	0.748231i
$428$	6.45259	−	14.1292i	0.311898	−	0.682961i
$429$	−28.2578	−	32.6112i	−1.36430	−	1.57449i
$430$	−0.0344497	+	0.239603i	−0.00166131	+	0.0115547i
$431$	−5.63644			−0.271498			−0.135749	−	0.990743i	$-0.543344\pi$
$431$	−5.63644			−0.271498			−0.135749	+	0.990743i	$0.543344\pi$
$432$	0.279579			0.0134512
$433$	0.126849	−	0.882254i	0.00609598	−	0.0423984i	−0.986546	−	0.163481i	$-0.947728\pi$
$433$	0.126849	−	0.882254i	0.00609598	−	0.0423984i	0.992642	+	0.121083i	$0.0386367\pi$
$434$	−45.9421	+	13.4898i	−2.20529	+	0.647532i
$435$	−16.6967	+	10.7303i	−0.800546	+	0.514480i
$436$	10.3786	−	6.66991i	0.497044	−	0.319431i
$437$	−24.3282	+	7.14341i	−1.16378	+	0.341716i
$438$	0.902985	−	6.28040i	0.0431463	−	0.300089i
$439$	25.3673			1.21071			0.605357	−	0.795954i	$-0.293031\pi$
$439$	25.3673			1.21071			0.605357	+	0.795954i	$0.293031\pi$
$440$	6.21907			0.296482
$441$	−5.50631	+	38.2972i	−0.262205	+	1.82368i
$442$	14.6287	+	16.8824i	0.695814	+	0.803012i
$443$	2.55692	−	5.59888i	0.121483	−	0.266011i	−0.839114	−	0.543956i	$-0.816926\pi$
$443$	2.55692	−	5.59888i	0.121483	−	0.266011i	0.960597	+	0.277945i	$0.0896533\pi$
$444$	−1.34305	−	9.34110i	−0.0637382	−	0.443309i
$445$	−1.28219	+	2.80759i	−0.0607814	+	0.133093i
$446$	−3.36728	−	0.988721i	−0.159445	−	0.0468173i
$447$	−25.1306	+	7.37901i	−1.18864	+	0.349015i
$448$	−2.88648	−	3.33118i	−0.136374	−	0.157383i
$449$	6.97186	+	2.04712i	0.329022	+	0.0966096i	0.442072	−	0.896980i	$-0.354244\pi$
$449$	6.97186	+	2.04712i	0.329022	+	0.0966096i	−0.113049	+	0.993589i	$0.536062\pi$
$450$	3.99531	−	2.56763i	0.188341	−	0.121039i
$451$	−2.31749	−	5.07460i	−0.109126	−	0.238954i
$452$	−3.12487	+	6.84252i	−0.146982	+	0.321845i
$453$	−15.6384	+	18.0477i	−0.734756	+	0.847954i
$454$	4.22413	−	2.71468i	0.198248	−	0.127406i
$455$	−17.8533	−	39.0933i	−0.836977	−	1.83272i
$456$	−1.69443	−	11.7850i	−0.0793490	−	0.551884i
$457$	1.71723	+	11.9436i	0.0803288	+	0.558699i	0.989749	+	0.142820i	$0.0456170\pi$
$457$	1.71723	+	11.9436i	0.0803288	+	0.558699i	−0.909420	+	0.415879i	$0.863474\pi$
$458$	−1.76888	+	2.04140i	−0.0826545	+	0.0953884i
$459$	1.14558	−	0.336373i	0.0534712	−	0.0157005i
$460$	−8.25645	−	5.30610i	−0.384959	−	0.247398i
$461$	3.48385	−	24.2307i	0.162259	−	1.12854i	−0.732103	−	0.681194i	$-0.761461\pi$
$461$	3.48385	−	24.2307i	0.162259	−	1.12854i	0.894362	−	0.447344i	$-0.147630\pi$
$462$	30.5887	+	19.6582i	1.42311	+	0.914580i
$463$	0.0101683	+	0.0117348i	0.000472559	+	0.000545363i	0.755986	−	0.654588i	$-0.227158\pi$
$463$	0.0101683	+	0.0117348i	0.000472559	+	0.000545363i	−0.755513	+	0.655133i	$0.772612\pi$
$464$	2.82021	−	3.25470i	0.130925	−	0.151096i
$465$	−20.7971	−	45.5392i	−0.964441	−	2.11183i
$466$	3.66050	+	1.07482i	0.169569	+	0.0497900i
$467$	12.8224	+	8.24045i	0.593349	+	0.381322i	0.802581	−	0.596544i	$-0.203460\pi$
$467$	12.8224	+	8.24045i	0.593349	+	0.381322i	−0.209231	+	0.977866i	$0.567096\pi$
$468$	−16.2842			−0.752736
$469$	16.1639	−	32.2558i	0.746381	−	1.48944i
$470$	−5.96417			−0.275107
$471$	−41.4042	−	26.6089i	−1.90781	−	1.22607i
$472$	1.50054	+	0.440599i	0.0690680	+	0.0202802i
$473$	0.179995	+	0.394134i	0.00827617	+	0.0181223i
$474$	−5.72498	+	6.60698i	−0.262957	+	0.303469i
$475$	−4.81090	−	5.55208i	−0.220739	−	0.254747i
$476$	−15.8353	−	10.1767i	−0.725811	−	0.466450i
$477$	2.06889	−	14.3895i	0.0947280	−	0.658848i
$478$	0.0615122	+	0.0395315i	0.00281350	+	0.00180813i
$479$	−27.4875	+	8.07105i	−1.25593	+	0.368776i	−0.840980	−	0.541066i	$-0.818021\pi$
$479$	−27.4875	+	8.07105i	−1.25593	+	0.368776i	−0.414955	+	0.909842i	$0.636203\pi$
$480$	3.01801	−	3.48297i	0.137753	−	0.158975i
$481$	2.84143	+	19.7626i	0.129558	+	0.901096i
$482$	−0.578602	−	4.02426i	−0.0263546	−	0.183300i
$483$	−23.8373	−	52.1964i	−1.08464	−	2.37502i
$484$	0.110927	−	0.0712885i	0.00504214	−	0.00324039i
$485$	−11.7582	+	13.5696i	−0.533911	+	0.616166i
$486$	9.23075	−	20.2125i	0.418716	−	0.916859i
$487$	10.6515	+	23.3235i	0.482664	+	1.05689i	0.981722	+	0.190318i	$0.0609520\pi$
$487$	10.6515	+	23.3235i	0.482664	+	1.05689i	−0.499058	+	0.866568i	$0.666321\pi$
$488$	2.98126	−	1.91594i	0.134955	−	0.0867304i
$489$	−34.6250	−	10.1668i	−1.56579	−	0.459759i
$490$	15.1709	+	17.5081i	0.685350	+	0.790936i
$491$	13.8678	−	4.07194i	0.625844	−	0.183764i	0.0465933	−	0.998914i	$-0.485164\pi$
$491$	13.8678	−	4.07194i	0.625844	−	0.183764i	0.579250	+	0.815150i	$0.303345\pi$
$492$	−3.96665	−	1.16471i	−0.178830	−	0.0525094i
$493$	7.64002	−	16.7293i	0.344089	−	0.753451i
$494$	3.58484	+	24.9331i	0.161289	+	1.12179i
$495$	−8.04261	+	17.6109i	−0.361489	+	0.791550i
$496$	7.11374	+	8.20969i	0.319416	+	0.368626i
$497$	−8.11049	+	56.4097i	−0.363805	+	2.53032i
$498$	−17.1983			−0.770674
$499$	−36.9188			−1.65271			−0.826357	−	0.563147i	$-0.809591\pi$
$499$	−36.9188			−1.65271			−0.826357	+	0.563147i	$0.809591\pi$
$500$	1.73105	−	12.0397i	0.0774151	−	0.538434i
$501$	27.0740	−	7.94964i	1.20958	−	0.355164i
$502$	−1.96241	+	1.26116i	−0.0875866	+	0.0562885i
$503$	−0.889310	+	0.571525i	−0.0396524	+	0.0254830i	−0.560317	−	0.828278i	$-0.689321\pi$
$503$	−0.889310	+	0.571525i	−0.0396524	+	0.0254830i	0.520664	+	0.853761i	$0.325684\pi$
$504$	13.1659	−	3.86587i	0.586457	−	0.172199i
$505$	−2.93912	+	20.4420i	−0.130789	+	0.909659i
$506$	−17.5675			−0.780969
$507$	35.5100			1.57706
$508$	2.79640	−	19.4494i	0.124070	−	0.862927i
$509$	−25.5087	−	29.4387i	−1.13065	−	1.30485i	−0.946775	−	0.321897i	$-0.895680\pi$
$509$	−25.5087	−	29.4387i	−1.13065	−	1.30485i	−0.183880	−	0.982949i	$-0.558866\pi$
$510$	8.17586	−	17.9026i	0.362033	−	0.792742i
$511$	−1.60980	−	11.1964i	−0.0712132	−	0.495298i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	1.29178	+	0.379302i	0.0570336	+	0.0167466i
$514$	−18.1444	+	5.32768i	−0.800316	+	0.234994i
$515$	6.63639	+	7.65880i	0.292434	+	0.337487i
$516$	0.308082	+	0.0904609i	0.0135625	+	0.00398232i
$517$	−8.98089	+	5.77167i	−0.394979	+	0.253838i
$518$	−6.98898	−	15.3037i	−0.307078	−	0.672407i
$519$	19.6478	−	43.0227i	0.862443	−	1.88849i
$520$	−6.38507	+	7.36877i	−0.280004	+	0.323142i
$521$	1.42068	−	0.913014i	0.0622410	−	0.0399999i	−0.509150	−	0.860678i	$-0.670040\pi$
$521$	1.42068	−	0.913014i	0.0622410	−	0.0399999i	0.571391	+	0.820678i	$0.306404\pi$
$522$	5.56935	+	12.1952i	0.243764	+	0.533769i
$523$	2.48926	+	17.3132i	0.108848	+	0.757052i	0.969008	+	0.247029i	$0.0794542\pi$
$523$	2.48926	+	17.3132i	0.108848	+	0.757052i	−0.860161	+	0.510023i	$0.829637\pi$
$524$	0.384018	+	2.67090i	0.0167759	+	0.116679i
$525$	10.8876	−	12.5650i	0.475175	−	0.548381i
$526$	−5.17655	+	1.51997i	−0.225708	+	0.0662739i
$527$	39.0261	+	25.0806i	1.70000	+	1.09253i
$528$	1.17399	−	8.16527i	0.0510913	−	0.355348i
$529$	3.97378	+	2.55379i	0.172773	+	0.111034i
$530$	−5.70017	−	6.57835i	−0.247600	−	0.285745i
$531$	−3.18820	+	3.67937i	−0.138356	+	0.159671i
$532$	−8.81751	−	19.3076i	−0.382287	−	0.837093i
$533$	8.39208	+	2.46414i	0.363501	+	0.106734i
$534$	3.44417	+	2.21343i	0.149044	+	0.0957845i
$535$	28.9530			1.25175
$536$	−8.18001	−	0.295765i	−0.353323	−	0.0127751i
$537$	−60.1635			−2.59625
$538$	12.5036	+	8.03559i	0.539069	+	0.346439i
$539$	39.7874	+	11.6826i	1.71377	+	0.503207i
$540$	0.216485	+	0.474036i	0.00931603	+	0.0203993i
$541$	−11.6037	+	13.3914i	−0.498883	+	0.575742i	−0.948218	−	0.317622i	$-0.897116\pi$
$541$	−11.6037	+	13.3914i	−0.498883	+	0.575742i	0.449334	+	0.893364i	$0.351661\pi$
$542$	14.5029	+	16.7372i	0.622953	+	0.718926i
$543$	−5.30476	−	3.40916i	−0.227649	−	0.146301i
$544$	−0.607757	+	4.22704i	−0.0260574	+	0.181233i
$545$	19.3455	+	12.4326i	0.828668	+	0.532553i
$546$	−54.6975	+	16.0606i	−2.34084	+	0.687332i
$547$	−7.57760	+	8.74501i	−0.323995	+	0.373910i	−0.894258	−	0.447552i	$-0.852296\pi$
$547$	−7.57760	+	8.74501i	−0.323995	+	0.373910i	0.570263	+	0.821462i	$0.306841\pi$
$548$	−1.85859	−	12.9268i	−0.0793952	−	0.552206i
$549$	1.57005	+	10.9199i	0.0670080	+	0.466051i
$550$	−2.11446	−	4.63003i	−0.0901610	−	0.197425i
$551$	17.4463	−	11.2121i	0.743237	−	0.477649i
$552$	−8.52519	+	9.83859i	−0.362856	+	0.418758i
$553$	−6.47437	+	14.1769i	−0.275318	+	0.602863i
$554$	0.100489	+	0.220039i	0.00426935	+	0.00934858i
$555$	14.7982	−	9.51024i	0.628150	−	0.403687i
$556$	13.9298	+	4.09016i	0.590756	+	0.173461i
$557$	14.8651	+	17.1552i	0.629853	+	0.726889i	0.977547	−	0.210719i	$-0.0675806\pi$
$557$	14.8651	+	17.1552i	0.629853	+	0.726889i	−0.347694	+	0.937608i	$0.613035\pi$
$558$	−32.4474	+	9.52743i	−1.37361	+	0.403328i
$559$	−0.651796	−	0.191384i	−0.0275680	−	0.00809470i
$560$	3.41306	−	7.47355i	0.144228	−	0.315815i
$561$	−5.01353	−	34.8699i	−0.211671	−	1.47221i
$562$	−1.40263	+	3.07132i	−0.0591662	+	0.129556i
$563$	−28.7818	−	33.2160i	−1.21301	−	1.39989i	−0.891525	−	0.452972i	$-0.850364\pi$
$563$	−28.7818	−	33.2160i	−1.21301	−	1.39989i	−0.321485	−	0.946915i	$-0.604182\pi$
$564$	−1.12587	+	7.83060i	−0.0474077	+	0.329728i
$565$	−14.0214			−0.589885
$566$	13.5657			0.570209
$567$	5.42482	−	37.7304i	0.227821	−	1.58453i
$568$	12.4056	−	3.64262i	0.520528	−	0.152841i
$569$	13.1791	−	8.46968i	0.552496	−	0.355068i	−0.234413	−	0.972137i	$-0.575317\pi$
$569$	13.1791	−	8.46968i	0.552496	−	0.355068i	0.786909	+	0.617070i	$0.211680\pi$
$570$	18.6699	−	11.9984i	0.781995	−	0.502558i
$571$	7.07740	−	2.07811i	0.296180	−	0.0869663i	−0.130267	−	0.991479i	$-0.541583\pi$
$571$	7.07740	−	2.07811i	0.296180	−	0.0869663i	0.426447	+	0.904513i	$0.359765\pi$
$572$	−2.48376	+	17.2749i	−0.103851	+	0.722301i
$573$	−40.8605			−1.70697
$574$	−7.37009			−0.307621
$575$	−1.14317	+	7.95090i	−0.0476733	+	0.331575i
$576$	−2.03863	−	2.35271i	−0.0849430	−	0.0980294i
$577$	−18.0200	+	39.4582i	−0.750181	+	1.64267i	0.0158585	+	0.999874i	$0.494952\pi$
$577$	−18.0200	+	39.4582i	−0.750181	+	1.64267i	−0.766040	+	0.642793i	$0.777775\pi$
$578$	0.176081	+	1.22467i	0.00732399	+	0.0509395i
$579$	−7.05167	+	15.4410i	−0.293057	+	0.641706i
$580$	7.70222	+	2.26158i	0.319817	+	0.0939068i
$581$	−29.4183	+	8.63799i	−1.22048	+	0.358364i
$582$	15.5965	+	17.9994i	0.646497	+	0.746098i
$583$	−14.9494	−	4.38953i	−0.619140	−	0.181796i
$584$	−2.15887	+	1.38742i	−0.0893348	+	0.0574120i
$585$	−12.6092	−	27.6104i	−0.521328	−	1.14155i
$586$	−1.88293	+	4.12304i	−0.0777832	+	0.170321i
$587$	12.8218	−	14.7972i	0.529214	−	0.610746i	−0.426699	−	0.904393i	$-0.640324\pi$
$587$	12.8218	−	14.7972i	0.529214	−	0.610746i	0.955914	+	0.293648i	$0.0948692\pi$
$588$	25.8510	−	16.6134i	1.06608	−	0.685126i
$589$	21.7307	+	47.5837i	0.895399	+	1.96065i
$590$	0.414856	+	2.88539i	0.0170794	+	0.118790i
$591$	−5.78493	−	40.2351i	−0.237960	−	1.65505i
$592$	−2.49954	+	2.88462i	−0.102731	+	0.118557i
$593$	15.6487	−	4.59488i	0.642616	−	0.188689i	0.0558416	−	0.998440i	$-0.482216\pi$
$593$	15.6487	−	4.59488i	0.642616	−	0.188689i	0.586774	+	0.809751i	$0.300398\pi$
$594$	0.784721	+	0.504309i	0.0321975	+	0.0206921i
$595$	4.99334	−	34.7295i	0.204707	−	1.42377i
$596$	8.91165	+	5.72717i	0.365035	+	0.234594i
$597$	35.4091	+	40.8643i	1.44920	+	1.67246i
$598$	18.0364	−	20.8151i	0.737563	−	0.851193i
$599$	−18.1943	−	39.8399i	−0.743397	−	1.62781i	−0.777885	−	0.628407i	$-0.783707\pi$
$599$	−18.1943	−	39.8399i	−0.743397	−	1.62781i	0.0344877	−	0.999405i	$-0.489020\pi$
$600$	−3.61914	−	1.06268i	−0.147751	−	0.0433836i
$601$	−15.8996	−	10.2181i	−0.648559	−	0.416804i	0.174580	−	0.984643i	$-0.444143\pi$
$601$	−15.8996	−	10.2181i	−0.648559	−	0.416804i	−0.823139	+	0.567839i	$0.807780\pi$
$602$	0.572419			0.0233301
$603$	11.4161	−	22.7813i	0.464898	−	0.927726i
$604$	9.65859			0.393002
$605$	0.206766	+	0.132880i	0.00840623	+	0.00540236i
$606$	26.2844	+	7.71779i	1.06773	+	0.313514i
$607$	−1.79886	−	3.93896i	−0.0730137	−	0.159878i	0.869606	−	0.493747i	$-0.164373\pi$
$607$	−1.79886	−	3.93896i	−0.0730137	−	0.159878i	−0.942619	+	0.333869i	$0.891646\pi$
$608$	−3.15350	+	3.63933i	−0.127891	+	0.147594i
$609$	30.7349	+	35.4700i	1.24544	+	1.43732i
$610$	5.55700	+	3.57127i	0.224997	+	0.144596i
$611$	2.38196	−	16.5669i	0.0963637	−	0.670224i
$612$	−11.1840	−	7.18751i	−0.452086	−	0.290538i
$613$	15.6440	−	4.59348i	0.631853	−	0.185529i	0.0499042	−	0.998754i	$-0.484108\pi$
$613$	15.6440	−	4.59348i	0.631853	−	0.185529i	0.581949	+	0.813225i	$0.302290\pi$
$614$	−15.8125	+	18.2486i	−0.638140	+	0.736453i
$615$	−1.09666	−	7.62747i	−0.0442218	−	0.307569i
$616$	−2.09293	−	14.5566i	−0.0843264	−	0.586503i
$617$	−5.71080	−	12.5049i	−0.229908	−	0.503428i	0.759157	−	0.650907i	$-0.225611\pi$
$617$	−5.71080	−	12.5049i	−0.229908	−	0.503428i	−0.989065	+	0.147479i	$0.952884\pi$
$618$	11.3083	−	7.26742i	0.454887	−	0.292338i
$619$	9.18970	−	10.6055i	0.369365	−	0.426270i	−0.540390	−	0.841414i	$-0.681723\pi$
$619$	9.18970	−	10.6055i	0.369365	−	0.426270i	0.909756	+	0.415144i	$0.136269\pi$
$620$	−8.41148	+	18.4186i	−0.337813	+	0.739707i
$621$	−0.611521	−	1.33904i	−0.0245395	−	0.0537340i
$622$	−25.7778	+	16.5664i	−1.03359	+	0.664251i
$623$	7.00308	+	2.05629i	0.280573	+	0.0823835i
$624$	8.46943	+	9.77425i	0.339049	+	0.391283i
$625$	14.4353	−	4.23859i	0.577412	−	0.169544i
$626$	8.60335	+	2.52617i	0.343859	+	0.100966i
$627$	16.5021	−	36.1346i	0.659031	−	1.44308i
$628$	2.83294	+	19.7036i	0.113047	+	0.786258i
$629$	−6.77132	+	14.8271i	−0.269990	+	0.591196i
$630$	16.7494	+	19.3299i	0.667314	+	0.770121i
$631$	4.20052	−	29.2153i	0.167220	−	1.16304i	−0.717377	−	0.696685i	$-0.754658\pi$
$631$	4.20052	−	29.2153i	0.167220	−	1.16304i	0.884597	−	0.466356i	$-0.154433\pi$
$632$	3.53586			0.140649
$633$	27.8331			1.10627
$634$	0.752924	−	5.23670i	0.0299024	−	0.207976i
$635$	35.1425	−	10.3188i	1.39459	−	0.409488i
$636$	−9.71302	+	6.24218i	−0.385146	+	0.247519i
$637$	−54.6919	+	35.1483i	−2.16697	+	1.39263i
$638$	13.7866	−	4.04812i	0.545818	−	0.160267i
$639$	−5.72818	+	39.8404i	−0.226603	+	1.57606i
$640$	−1.86398			−0.0736803
$641$	−37.1317			−1.46662			−0.733308	−	0.679897i	$-0.762025\pi$
$641$	−37.1317			−1.46662			−0.733308	+	0.679897i	$0.762025\pi$
$642$	5.46553	−	38.0136i	0.215707	−	1.50028i
$643$	13.5807	+	15.6730i	0.535571	+	0.618081i	0.957460	−	0.288566i	$-0.0931784\pi$
$643$	13.5807	+	15.6730i	0.535571	+	0.618081i	−0.421889	+	0.906647i	$0.638633\pi$
$644$	−9.64112	+	21.1111i	−0.379913	+	0.831894i
$645$	0.0851757	+	0.592410i	0.00335379	+	0.0233261i
$646$	−8.54290	+	18.7063i	−0.336116	+	0.735991i
$647$	−26.8093	−	7.87193i	−1.05398	−	0.309477i	−0.291557	−	0.956553i	$-0.594173\pi$
$647$	−26.8093	−	7.87193i	−1.05398	−	0.309477i	−0.762426	+	0.647076i	$0.775992\pi$
$648$	−8.29768	+	2.43642i	−0.325964	+	0.0957115i
$649$	3.41695	+	3.94337i	0.134127	+	0.154791i
$650$	7.65687	+	2.24826i	0.300327	+	0.0881841i
$651$	−99.5923	+	64.0041i	−3.90333	+	2.50852i
$652$	6.06317	+	13.2765i	0.237452	+	0.519947i
$653$	5.51047	−	12.0662i	0.215641	−	0.472189i	−0.770638	−	0.637273i	$-0.780062\pi$
$653$	5.51047	−	12.0662i	0.215641	−	0.472189i	0.986279	+	0.165084i	$0.0527896\pi$
$654$	19.9751	−	23.0525i	0.781090	−	0.901425i
$655$	−4.23126	+	2.71926i	−0.165329	+	0.106250i
$656$	0.694600	+	1.52096i	0.0271196	+	0.0593836i
$657$	−1.13695	−	7.90764i	−0.0443565	−	0.308507i
$658$	2.00715	+	13.9600i	0.0782467	+	0.544218i
$659$	−30.1198	+	34.7601i	−1.17330	+	1.35406i	−0.250810	+	0.968036i	$0.580697\pi$
$659$	−30.1198	+	34.7601i	−1.17330	+	1.35406i	−0.922489	+	0.386023i	$0.873848\pi$
$660$	14.7536	−	4.33204i	0.574282	−	0.168624i
$661$	17.6078	+	11.3159i	0.684866	+	0.440137i	0.836257	−	0.548337i	$-0.184739\pi$
$661$	17.6078	+	11.3159i	0.684866	+	0.440137i	−0.151391	+	0.988474i	$0.548375\pi$
$662$	3.33925	−	23.2250i	0.129784	−	0.902666i
$663$	46.4635	+	29.8603i	1.80449	+	1.15968i
$664$	4.55517	+	5.25694i	0.176775	+	0.204009i
$665$	25.9092	−	29.9008i	1.00472	−	1.15950i
$666$	−4.93609	−	10.8085i	−0.191270	−	0.418822i
$667$	−21.7570	−	6.38844i	−0.842436	−	0.247361i
$668$	−9.60080	−	6.17006i	−0.371466	−	0.238727i
$669$	−8.67694			−0.335470
$670$	−5.83251	−	14.0985i	−0.225329	−	0.544673i
$671$	11.8238			0.456452
$672$	−9.16805	−	5.89195i	−0.353665	−	0.227287i
$673$	−28.4728	−	8.36038i	−1.09755	−	0.322269i	−0.317670	−	0.948201i	$-0.602900\pi$
$673$	−28.4728	−	8.36038i	−1.09755	−	0.322269i	−0.779877	+	0.625932i	$0.784719\pi$
$674$	6.25010	+	13.6858i	0.240745	+	0.527158i
$675$	0.279311	−	0.322342i	0.0107507	−	0.0124069i
$676$	−9.40524	−	10.8542i	−0.361740	−	0.417470i
$677$	−12.6179	−	8.10903i	−0.484945	−	0.311655i	0.275225	−	0.961380i	$-0.411248\pi$
$677$	−12.6179	−	8.10903i	−0.484945	−	0.311655i	−0.760170	+	0.649725i	$0.774884\pi$
$678$	−2.64686	+	18.4093i	−0.101652	+	0.707004i
$679$	35.7188	+	22.9551i	1.37076	+	0.880934i
$680$	−7.63771	+	2.24263i	−0.292893	+	0.0860010i
$681$	8.12997	−	9.38249i	0.311541	−	0.359538i
$682$	5.15802	+	35.8748i	0.197511	+	1.37372i
$683$	2.77059	+	19.2699i	0.106014	+	0.737342i	0.971608	+	0.236596i	$0.0760317\pi$
$683$	2.77059	+	19.2699i	0.106014	+	0.737342i	−0.865594	+	0.500746i	$0.833059\pi$
$684$	−6.22753	−	13.6364i	−0.238115	−	0.521400i
$685$	20.4787	−	13.1609i	0.782452	−	0.502851i
$686$	15.6694	−	18.0835i	0.598261	−	0.690429i
$687$	−2.77436	+	6.07500i	−0.105848	+	0.231776i
$688$	−0.0539481	−	0.118130i	−0.00205675	−	0.00450366i
$689$	20.5494	−	13.2063i	0.782871	−	0.503121i
$690$	−23.2830	−	6.83649i	−0.886367	−	0.260261i
$691$	4.46605	+	5.15409i	0.169896	+	0.196071i	0.834312	−	0.551292i	$-0.185865\pi$
$691$	4.46605	+	5.15409i	0.169896	+	0.196071i	−0.664416	+	0.747363i	$0.731320\pi$
$692$	−18.3545	+	5.38938i	−0.697735	+	0.204874i
$693$	43.9274	+	12.8983i	1.66866	+	0.489964i
$694$	2.81808	−	6.17074i	0.106973	−	0.234238i
$695$	3.85119	+	26.7856i	0.146084	+	1.01604i
$696$	4.42328	−	9.68564i	0.167664	−	0.367133i
$697$	4.67607	+	5.39647i	0.177119	+	0.204406i
$698$	−1.04942	+	7.29890i	−0.0397212	+	0.276267i
$699$	9.43253			0.356771
$700$	−6.72441			−0.254159
$701$	−5.36604	+	37.3216i	−0.202673	+	1.40962i	0.593639	+	0.804732i	$0.297691\pi$
$701$	−5.36604	+	37.3216i	−0.202673	+	1.40962i	−0.796311	+	0.604887i	$0.793218\pi$
$702$	−1.40321	+	0.412019i	−0.0529606	+	0.0155506i
$703$	−15.4626	+	9.93719i	−0.583182	+	0.374788i
$704$	−2.80680	+	1.80382i	−0.105785	+	0.0679839i
$705$	−14.1489	+	4.15448i	−0.532877	+	0.156467i
$706$	3.93598	−	27.3754i	0.148133	−	1.03029i
$707$	48.8367			1.83669
$708$	3.86666			0.145318
$709$	3.90375	−	27.1511i	0.146608	−	1.01968i	−0.775111	−	0.631825i	$-0.782306\pi$
$709$	3.90375	−	27.1511i	0.146608	−	1.01968i	0.921719	−	0.387858i	$-0.126785\pi$
$710$	15.7822	+	18.2136i	0.592295	+	0.683545i
$711$	−4.57264	+	10.0127i	−0.171488	+	0.375505i
$712$	−0.235655	−	1.63902i	−0.00883156	−	0.0614248i
$713$	23.7605	−	52.0283i	0.889839	−	1.94847i
$714$	−44.6552	−	13.1119i	−1.67118	−	0.490702i
$715$	−31.2135	+	9.16511i	−1.16732	+	0.342756i
$716$	15.9350	+	18.3900i	0.595519	+	0.687266i
$717$	0.173463	+	0.0509332i	0.00647808	+	0.00190214i
$718$	10.2001	−	6.55520i	0.380664	−	0.244638i
$719$	−6.45584	−	14.1363i	−0.240762	−	0.527196i	0.750220	−	0.661188i	$-0.229948\pi$
$719$	−6.45584	−	14.1363i	−0.240762	−	0.527196i	−0.990982	+	0.133992i	$0.957220\pi$
$720$	2.41053	−	5.27833i	0.0898353	−	0.196712i
$721$	15.6932	−	18.1109i	0.584444	−	0.674484i
$722$	−3.52424	+	2.26489i	−0.131158	+	0.0842904i
$723$	−4.17582	−	9.14377i	−0.155300	−	0.340060i
$724$	0.362960	+	2.52444i	0.0134893	+	0.0938202i
$725$	−0.935012	−	6.50315i	−0.0347255	−	0.241521i
$726$	0.213496	−	0.246388i	0.00792358	−	0.00914430i
$727$	−26.8388	+	7.88058i	−0.995396	+	0.292275i	−0.738566	−	0.674182i	$-0.764496\pi$
$727$	−26.8388	+	7.88058i	−0.995396	+	0.292275i	−0.256831	+	0.966456i	$0.582678\pi$
$728$	19.3965	+	12.4653i	0.718881	+	0.461997i
$729$	4.12650	−	28.7004i	0.152833	−	1.06298i
$730$	−4.02410	−	2.58613i	−0.148939	−	0.0957170i
$731$	−0.363181	−	0.419133i	−0.0134327	−	0.0155022i
$732$	5.73788	−	6.62186i	0.212078	−	0.244751i
$733$	−4.59475	−	10.0611i	−0.169711	−	0.371615i	0.805597	−	0.592464i	$-0.201845\pi$
$733$	−4.59475	−	10.0611i	−0.169711	−	0.371615i	−0.975308	+	0.220849i	$0.929117\pi$
$734$	23.1562	+	6.79928i	0.854711	+	0.250966i
$735$	48.1857	+	30.9671i	1.77736	+	1.14224i
$736$	5.26532			0.194082
$737$	−22.4261	−	15.5854i	−0.826076	−	0.574095i
$738$	−5.20526			−0.191608
$739$	−4.70089	−	3.02108i	−0.172925	−	0.111132i	0.451315	−	0.892365i	$-0.350955\pi$
$739$	−4.70089	−	3.02108i	−0.172925	−	0.111132i	−0.624240	+	0.781232i	$0.714591\pi$
$740$	−6.82644	−	2.00443i	−0.250945	−	0.0736841i
$741$	25.8721	+	56.6519i	0.950434	+	2.08116i
$742$	−13.4793	+	15.5559i	−0.494840	+	0.571076i
$743$	−20.4714	−	23.6253i	−0.751025	−	0.866729i	0.243643	−	0.969865i	$-0.421658\pi$
$743$	−20.4714	−	23.6253i	−0.751025	−	0.866729i	−0.994667	+	0.103137i	$0.967112\pi$
$744$	22.5946	+	14.5207i	0.828360	+	0.532355i
$745$	−2.81011	+	19.5447i	−0.102954	+	0.716063i
$746$	16.1555	+	10.3825i	0.591496	+	0.380132i
$747$	−20.7772	+	6.10074i	−0.760198	+	0.223214i
$748$	−9.33067	+	10.7682i	−0.341163	+	0.393723i
$749$	−9.74366	−	67.7686i	−0.356026	−	2.47621i
$750$	−4.27997	−	29.7678i	−0.156282	−	1.08697i
$751$	18.9885	+	41.5789i	0.692899	+	1.51724i	0.848374	+	0.529397i	$0.177582\pi$
$751$	18.9885	+	41.5789i	0.692899	+	1.51724i	−0.155475	+	0.987840i	$0.549691\pi$
$752$	2.69175	−	1.72989i	0.0981582	−	0.0630824i
$753$	−3.77695	+	4.35884i	−0.137640	+	0.158845i
$754$	−9.35816	+	20.4915i	−0.340804	+	0.746257i
$755$	7.47889	+	16.3765i	0.272185	+	0.596001i
$756$	1.03670	−	0.666244i	0.0377043	−	0.0242311i
$757$	33.9562	+	9.97045i	1.23416	+	0.362382i	0.832819	−	0.553546i	$-0.186726\pi$
$757$	33.9562	+	9.97045i	1.23416	+	0.362382i	0.401342	+	0.915928i	$0.368544\pi$
$758$	−14.9953	−	17.3054i	−0.544652	−	0.628562i
$759$	−41.6755	+	12.2370i	−1.51272	+	0.444176i
$760$	−8.61245	−	2.52884i	−0.312406	−	0.0917308i
$761$	6.09458	−	13.3453i	0.220928	−	0.483766i	−0.766418	−	0.642342i	$-0.777963\pi$
$761$	6.09458	−	13.3453i	0.220928	−	0.483766i	0.987347	+	0.158576i	$0.0506903\pi$
$762$	−6.91400	−	48.0879i	−0.250468	−	1.74204i
$763$	22.5898	−	49.4648i	0.817807	−	1.79075i
$764$	10.8224	+	12.4897i	0.391540	+	0.451861i
$765$	3.52664	−	24.5283i	0.127506	−	0.886823i
$766$	−27.3445			−0.987998
$767$	−8.18054			−0.295382
$768$	−0.351868	+	2.44730i	−0.0126970	+	0.0883092i
$769$	11.5797	−	3.40009i	0.417573	−	0.122611i	−0.0661951	−	0.997807i	$-0.521086\pi$
$769$	11.5797	−	3.40009i	0.417573	−	0.122611i	0.483768	+	0.875196i	$0.339268\pi$
$770$	23.0607	−	14.8202i	0.831049	−	0.534083i
$771$	−39.3331	+	25.2778i	−1.41655	+	0.910359i
$772$	6.58751	−	1.93427i	0.237090	−	0.0696159i
$773$	2.22656	−	15.4860i	0.0800837	−	0.556994i	−0.909793	−	0.415063i	$-0.863760\pi$
$773$	2.22656	−	15.4860i	0.0800837	−	0.556994i	0.989876	−	0.141931i	$-0.0453313\pi$
$774$	0.404282			0.0145316
$775$	16.5723			0.595295
$776$	1.37088	−	9.53468i	0.0492117	−	0.342275i
$777$	−27.2402	−	31.4369i	−0.977237	−	1.12779i
$778$	14.7027	−	32.1944i	0.527116	−	1.15422i
$779$	1.14590	+	7.96990i	0.0410561	+	0.285551i
$780$	−10.0145	+	21.9287i	−0.358576	+	0.785173i
$781$	41.3907	+	12.1534i	1.48107	+	0.434883i
$782$	21.5748	−	6.33493i	0.771513	−	0.226537i
$783$	0.788471	+	0.909944i	0.0281777	+	0.0325188i
$784$	−11.9251	−	3.50153i	−0.425896	−	0.125054i
$785$	−31.2145	+	20.0603i	−1.11409	+	0.715984i
$786$	2.77149	+	6.06871i	0.0988557	+	0.216464i
$787$	−9.30539	+	20.3760i	−0.331701	+	0.726324i	−0.999843	−	0.0177094i	$-0.994363\pi$
$787$	−9.30539	+	20.3760i	−0.331701	+	0.726324i	0.668142	+	0.744034i	$0.267090\pi$
$788$	−10.7663	+	12.4250i	−0.383534	+	0.442622i
$789$	−11.2216	+	7.21170i	−0.399500	+	0.256743i
$790$	2.73791	+	5.99518i	0.0974104	+	0.213299i
$791$	4.71868	+	32.8191i	0.167777	+	1.16691i
$792$	−1.47817	−	10.2809i	−0.0525244	−	0.365315i
$793$	−12.1394	+	14.0096i	−0.431082	+	0.497496i
$794$	−12.1748	+	3.57485i	−0.432068	+	0.126867i
$795$	−18.1049	−	11.6353i	−0.642114	−	0.412662i
$796$	3.11233	−	21.6467i	0.110314	−	0.767249i
$797$	−25.1021	−	16.1322i	−0.889163	−	0.571430i	0.0143950	−	0.999896i	$-0.495418\pi$
$797$	−25.1021	−	16.1322i	−0.889163	−	0.571430i	−0.903558	+	0.428466i	$0.859054\pi$
$798$	−34.3671	−	39.6617i	−1.21658	−	1.40401i
$799$	8.94823	−	10.3268i	0.316566	−	0.365336i
$800$	0.633748	+	1.38771i	0.0224064	+	0.0490631i
$801$	4.94605	+	1.45229i	0.174760	+	0.0513142i
$802$	−12.4066	−	7.97322i	−0.438091	−	0.281544i
$803$	−8.56218			−0.302153
$804$	−19.6115	+	4.99633i	−0.691646	+	0.176207i
$805$	−43.2600			−1.52471
$806$	−47.8026	−	30.7208i	−1.68377	−	1.08210i
$807$	35.2599	+	10.3532i	1.24121	+	0.364451i
$808$	−4.60265	−	10.0784i	−0.161921	−	0.354557i
$809$	−19.7152	+	22.7525i	−0.693149	+	0.799936i	−0.987810	−	0.155666i	$-0.950248\pi$
$809$	−19.7152	+	22.7525i	−0.693149	+	0.799936i	0.294661	+	0.955602i	$0.404793\pi$
$810$	−10.5561	−	12.1824i	−0.370905	−	0.428047i
$811$	15.7781	+	10.1399i	0.554042	+	0.356061i	0.787509	−	0.616303i	$-0.211371\pi$
$811$	15.7781	+	10.1399i	0.554042	+	0.356061i	−0.233466	+	0.972365i	$0.575007\pi$
$812$	2.70149	−	18.7893i	0.0948036	−	0.659374i
$813$	46.0641	+	29.6036i	1.61554	+	1.03824i
$814$	−12.2190	+	3.58783i	−0.428277	+	0.125754i
$815$	−17.8159	+	20.5606i	−0.624064	+	0.720208i
$816$	1.50266	+	10.4512i	0.0526035	+	0.365866i
$817$	−0.0889995	−	0.619005i	−0.00311370	−	0.0216563i
$818$	1.50501	+	3.29551i	0.0526214	+	0.115225i
$819$	−60.3827	+	38.8056i	−2.10994	+	1.35598i
$820$	−2.04100	+	2.35544i	−0.0712748	+	0.0822555i
$821$	14.0343	−	30.7309i	0.489802	−	1.07252i	−0.489849	−	0.871807i	$-0.662948\pi$
$821$	14.0343	−	30.7309i	0.489802	−	1.07252i	0.979651	−	0.200709i	$-0.0643247\pi$
$822$	−13.4136	−	29.3718i	−0.467854	−	1.02446i
$823$	32.9230	−	21.1583i	1.14762	−	0.737533i	0.178459	−	0.983947i	$-0.442889\pi$
$823$	32.9230	−	21.1583i	1.14762	−	0.737533i	0.969165	+	0.246414i	$0.0792523\pi$
$824$	−5.21655	−	1.53172i	−0.181727	−	0.0533599i
$825$	−8.24132	−	9.51099i	−0.286926	−	0.331130i
$826$	6.61406	−	1.94206i	0.230133	−	0.0675730i
$827$	−25.8323	−	7.58506i	−0.898279	−	0.263758i	−0.200179	−	0.979759i	$-0.564152\pi$
$827$	−25.8323	−	7.58506i	−0.898279	−	0.263758i	−0.698099	+	0.716001i	$0.745971\pi$
$828$	−6.80922	+	14.9101i	−0.236637	+	0.518162i
$829$	4.93288	+	34.3089i	0.171326	+	1.19160i	0.876087	+	0.482154i	$0.160145\pi$
$829$	4.93288	+	34.3089i	0.171326	+	1.19160i	−0.704761	+	0.709445i	$0.748946\pi$
$830$	−5.38615	+	11.7940i	−0.186956	+	0.409377i
$831$	0.391664	+	0.452004i	0.0135867	+	0.0156799i
$832$	0.744433	−	5.17765i	0.0258086	−	0.179503i
$833$	−53.0762			−1.83898
$834$	35.8950			1.24294
$835$	3.02741	−	21.0561i	0.104768	−	0.728677i
$836$	−15.4159	+	4.52652i	−0.533170	+	0.156553i
$837$	−2.55494	+	1.64196i	−0.0883115	+	0.0567543i
$838$	1.79460	−	1.15332i	0.0619935	−	0.0398408i
$839$	19.8969	−	5.84226i	0.686917	−	0.201697i	0.0803943	−	0.996763i	$-0.474382\pi$
$839$	19.8969	−	5.84226i	0.686917	−	0.201697i	0.606523	+	0.795066i	$0.292564\pi$
$840$	2.89096	−	20.1070i	0.0997475	−	0.693759i
$841$	−10.4534			−0.360460
$842$	−21.6555			−0.746299
$843$	−1.18806	+	8.26316i	−0.0409191	+	0.284598i
$844$	−7.37192	−	8.50765i	−0.253752	−	0.292845i
$845$	11.1210	−	24.3516i	0.382575	−	0.837722i
$846$	1.41758	+	9.85951i	0.0487375	+	0.338977i
$847$	0.241442	−	0.528685i	0.00829605	−	0.0181658i
$848$	4.48063	+	1.31563i	0.153866	+	0.0451790i
$849$	32.1821	−	9.44950i	1.10449	−	0.324306i
$850$	4.26641	+	4.92370i	0.146337	+	0.168882i
$851$	19.2832	+	5.66205i	0.661018	+	0.194093i
$852$	26.8927	−	17.2829i	0.921327	−	0.592101i
$853$	14.2317	+	31.1631i	0.487285	+	1.06701i	0.980396	+	0.197039i	$0.0631326\pi$
$853$	14.2317	+	31.1631i	0.487285	+	1.06701i	−0.493110	+	0.869967i	$0.664140\pi$
$854$	6.48896	−	14.2088i	0.222047	−	0.486216i
$855$	18.2988	−	21.1180i	0.625807	−	0.722220i
$856$	−13.0671	+	8.39771i	−0.446624	+	0.287028i
$857$	20.5224	+	44.9379i	0.701033	+	1.53505i	0.838714	+	0.544572i	$0.183308\pi$
$857$	20.5224	+	44.9379i	0.701033	+	1.53505i	−0.137681	+	0.990477i	$0.543965\pi$
$858$	6.14101	+	42.7116i	0.209650	+	1.45815i
$859$	−1.74946	−	12.1678i	−0.0596908	−	0.415158i	−0.997656	−	0.0684290i	$-0.978201\pi$
$859$	−1.74946	−	12.1678i	−0.0596908	−	0.415158i	0.937965	−	0.346729i	$-0.112708\pi$
$860$	0.158520	−	0.182942i	0.00540549	−	0.00623827i
$861$	−17.4841	+	5.13381i	−0.595858	+	0.174960i
$862$	4.74167	+	3.04729i	0.161502	+	0.103791i
$863$	0.110694	−	0.769896i	0.00376808	−	0.0262076i	−0.987851	−	0.155406i	$-0.950331\pi$
$863$	0.110694	−	0.769896i	0.00376808	−	0.0262076i	0.991619	+	0.129199i	$0.0412405\pi$
$864$	−0.235197	−	0.151152i	−0.00800155	−	0.00514229i
$865$	−23.3503	−	26.9477i	−0.793934	−	0.916248i
$866$	−0.583695	+	0.673620i	−0.0198348	+	0.0228905i
$867$	1.27079	+	2.78264i	0.0431583	+	0.0945035i
$868$	45.9421	+	13.4898i	1.55938	+	0.457874i
$869$	9.92444	+	6.37805i	0.336664	+	0.216361i
$870$	19.8474			0.672890
$871$	41.4913	−	10.5705i	1.40588	−	0.358169i
$872$	−12.3370			−0.417785
$873$	25.2270	+	16.2124i	0.853806	+	0.548708i
$874$	24.3282	+	7.14341i	0.822914	+	0.241629i
$875$	−22.2722	−	48.7693i	−0.752937	−	1.64870i
$876$	−4.15508	+	4.79522i	−0.140387	+	0.162015i
$877$	−2.57487	−	2.97156i	−0.0869473	−	0.100343i	0.710609	−	0.703587i	$-0.248420\pi$
$877$	−2.57487	−	2.97156i	−0.0869473	−	0.100343i	−0.797556	+	0.603245i	$0.793874\pi$
$878$	−21.3403	−	13.7146i	−0.720200	−	0.462845i
$879$	−1.59490	+	11.0927i	−0.0537945	+	0.374149i
$880$	−5.23181	−	3.36228i	−0.176364	−	0.113342i
$881$	8.97561	−	2.63548i	0.302396	−	0.0887915i	−0.127015	−	0.991901i	$-0.540539\pi$
$881$	8.97561	−	2.63548i	0.302396	−	0.0887915i	0.429411	+	0.903109i	$0.358721\pi$
$882$	25.3372	−	29.2407i	0.853149	−	0.984586i
$883$	−1.24577	−	8.66449i	−0.0419233	−	0.291583i	−0.999987	−	0.00502899i	$-0.998399\pi$
$883$	−1.24577	−	8.66449i	−0.0419233	−	0.291583i	0.958064	−	0.286554i	$-0.0925099\pi$
$884$	−3.17911	−	22.1112i	−0.106925	−	0.743680i
$885$	2.99405	+	6.55606i	0.100644	+	0.220380i
$886$	−5.17800	+	3.32770i	−0.173958	+	0.111796i
$887$	17.9012	−	20.6591i	0.601065	−	0.693666i	−0.370932	−	0.928660i	$-0.620962\pi$
$887$	17.9012	−	20.6591i	0.601065	−	0.693666i	0.971997	+	0.234994i	$0.0755072\pi$
$888$	−3.92034	+	8.58434i	−0.131558	+	0.288072i
$889$	−35.9792	−	78.7835i	−1.20670	−	2.64231i
$890$	2.59654	−	1.66870i	0.0870363	−	0.0559348i
$891$	−27.6847	−	8.12897i	−0.927474	−	0.272331i
$892$	2.29819	+	2.65225i	0.0769491	+	0.0888040i
$893$	14.7841	−	4.34099i	0.494730	−	0.145266i
$894$	25.1306	+	7.37901i	0.840493	+	0.246791i
$895$	−18.8420	+	41.2582i	−0.629818	+	1.37911i
$896$	0.627293	+	4.36292i	0.0209564	+	0.145755i
$897$	28.2887	−	61.9436i	0.944532	−	2.06824i
$898$	−4.75834	−	5.49142i	−0.158788	−	0.183251i
$899$	−6.65781	+	46.3061i	−0.222051	+	1.54440i
$900$	−4.74924			−0.158308
$901$	19.9424			0.664378
$902$	−0.793938	+	5.52196i	−0.0264352	+	0.183861i
$903$	1.35796	−	0.398732i	0.0451900	−	0.0132690i
$904$	6.32815	−	4.06686i	0.210471	−	0.135262i
$905$	−3.99924	+	2.57015i	−0.132939	+	0.0854348i
$906$	22.9132	−	6.72792i	0.761239	−	0.223520i
$907$	0.270346	−	1.88030i	0.00897670	−	0.0624343i	−0.984841	−	0.173461i	$-0.944505\pi$
$907$	0.270346	−	1.88030i	0.00897670	−	0.0624343i	0.993817	+	0.111027i	$0.0354140\pi$
$908$	−5.02123			−0.166635
$909$	34.4918			1.14402
$910$	−6.11628	+	42.5396i	−0.202753	+	1.41018i
$911$	11.3759	+	13.1285i	0.376900	+	0.434966i	0.912231	−	0.409676i	$-0.134358\pi$
$911$	11.3759	+	13.1285i	0.376900	+	0.434966i	−0.535331	+	0.844643i	$0.679813\pi$
$912$	−4.94602	+	10.8303i	−0.163779	+	0.358626i
$913$	3.30285	+	22.9719i	0.109309	+	0.760257i
$914$	5.01258	−	10.9760i	0.165801	−	0.363055i
$915$	15.6706	+	4.60130i	0.518054	+	0.152114i
$916$	2.59174	−	0.761005i	0.0856336	−	0.0251443i
$917$	7.78879	+	8.98874i	0.257209	+	0.296834i
$918$	−1.14558	−	0.336373i	−0.0378098	−	0.0111020i
$919$	23.6715	−	15.2128i	0.780851	−	0.501822i	−0.0884650	−	0.996079i	$-0.528196\pi$
$919$	23.6715	−	15.2128i	0.780851	−	0.501822i	0.869316	+	0.494257i	$0.164560\pi$
$920$	4.07707	+	8.92755i	0.134417	+	0.294333i
$921$	−24.8007	+	54.3059i	−0.817210	+	1.78944i
$922$	−16.0309	+	18.5007i	−0.527950	+	0.609287i
$923$	−56.8957	+	36.5646i	−1.87274	+	1.20354i
$924$	−15.1048	−	33.0750i	−0.496913	−	1.08809i
$925$	0.828697	+	5.76371i	0.0272474	+	0.189510i
$926$	−0.00220977	−	0.0153693i	−7.26177e−5	−	0.000505067i
$927$	11.0836	−	12.7911i	0.364033	−	0.420116i
$928$	−4.13214	+	1.21330i	−0.135644	+	0.0398287i
$929$	−43.8298	−	28.1677i	−1.43801	−	0.924153i	−0.999679	−	0.0253389i	$-0.991934\pi$
$929$	−43.8298	−	28.1677i	−1.43801	−	0.924153i	−0.438331	−	0.898814i	$-0.644430\pi$
$930$	−7.12476	+	49.5538i	−0.233630	+	1.62493i
$931$	−50.3490	−	32.3573i	−1.65012	−	1.06047i
$932$	−2.49832	−	2.88321i	−0.0818351	−	0.0944427i
$933$	−49.6132	+	57.2567i	−1.62426	+	1.87450i
$934$	−6.33176	−	13.8646i	−0.207181	−	0.453664i
$935$	−25.4828	−	7.48242i	−0.833376	−	0.244701i
$936$	13.6991	+	8.80388i	0.447769	+	0.287764i
$937$	34.6032			1.13044			0.565218	−	0.824941i	$-0.308792\pi$
$937$	34.6032			1.13044			0.565218	+	0.824941i	$0.308792\pi$
$938$	−31.0368	+	18.3965i	−1.01339	+	0.600666i
$939$	22.1695			0.723474
$940$	5.01738	+	3.22447i	0.163649	+	0.105171i
$941$	10.7029	+	3.14264i	0.348903	+	0.102447i	0.451488	−	0.892277i	$-0.350893\pi$
$941$	10.7029	+	3.14264i	0.348903	+	0.102447i	−0.102585	+	0.994724i	$0.532711\pi$
$942$	20.4456	+	44.7696i	0.666154	+	1.45867i
$943$	5.76536	−	6.65358i	0.187746	−	0.216670i
$944$	−1.02413	−	1.18191i	−0.0333326	−	0.0384679i
$945$	1.93238	+	1.24187i	0.0628603	+	0.0403979i
$946$	0.0616635	−	0.428879i	0.00200485	−	0.0139441i
$947$	−19.6513	−	12.6291i	−0.638580	−	0.410391i	0.180897	−	0.983502i	$-0.442100\pi$
$947$	−19.6513	−	12.6291i	−0.638580	−	0.410391i	−0.819477	+	0.573111i	$0.805736\pi$
$948$	8.38817	−	2.46299i	0.272435	−	0.0799941i
$949$	8.79073	−	10.1450i	0.285359	−	0.329322i
$950$	1.04551	+	7.27168i	0.0339208	+	0.235924i
$951$	−1.86158	−	12.9476i	−0.0603658	−	0.419853i
$952$	7.81956	+	17.1224i	0.253433	+	0.554941i
$953$	1.24244	−	0.798468i	0.0402466	−	0.0258649i	−0.520363	−	0.853945i	$-0.674203\pi$
$953$	1.24244	−	0.798468i	0.0402466	−	0.0258649i	0.560609	+	0.828080i	$0.310567\pi$
$954$	−9.51999	+	10.9867i	−0.308221	+	0.355706i
$955$	−12.7967	+	28.0208i	−0.414091	+	0.906733i
$956$	−0.0303750	−	0.0665120i	−0.000982398	−	0.00215115i
$957$	29.8864	−	19.2068i	0.966090	−	0.620868i
$958$	27.4875	+	8.07105i	0.888080	+	0.260764i
$959$	−37.6967	−	43.5043i	−1.21729	−	1.40483i
$960$	−4.42194	+	1.29840i	−0.142718	+	0.0419057i
$961$	−83.4799	−	24.5119i	−2.69290	−	0.790707i
$962$	8.29410	−	18.1615i	0.267412	−	0.585552i
$963$	−6.88164	−	47.8629i	−0.221758	−	1.54236i
$964$	−1.68893	+	3.69824i	−0.0543968	+	0.119112i
$965$	8.38050	+	9.67162i	0.269778	+	0.311340i
$966$	−8.16630	+	56.7979i	−0.262746	+	1.82744i
$967$	−19.5847			−0.629800			−0.314900	−	0.949125i	$-0.601971\pi$
$967$	−19.5847			−0.629800			−0.314900	+	0.949125i	$0.601971\pi$
$968$	−0.131859			−0.00423812
$969$	−7.23608	+	50.3281i	−0.232456	+	1.61677i
$970$	17.2279	−	5.05857i	0.553155	−	0.162421i
$971$	18.9560	−	12.1823i	0.608327	−	0.390948i	−0.199902	−	0.979816i	$-0.564062\pi$
$971$	18.9560	−	12.1823i	0.608327	−	0.390948i	0.808229	+	0.588868i	$0.200426\pi$
$972$	−18.6931	+	12.0133i	−0.599582	+	0.385328i
$973$	61.3996	−	18.0285i	1.96838	−	0.577969i
$974$	3.64903	−	25.3796i	0.116922	−	0.813214i
$975$	19.7306			0.631884
$976$	−3.54383			−0.113435
$977$	−4.17864	+	29.0631i	−0.133687	+	0.929811i	0.807004	+	0.590546i	$0.201087\pi$
$977$	−4.17864	+	29.0631i	−0.133687	+	0.929811i	−0.940691	+	0.339265i	$0.889822\pi$
$978$	23.6318	+	27.2725i	0.755661	+	0.872079i
$979$	2.29506	−	5.02547i	0.0733503	−	0.160615i
$980$	−3.29695	−	22.9308i	−0.105317	−	0.732496i
$981$	15.9545	−	34.9355i	0.509388	−	1.11540i
$982$	−13.8678	−	4.07194i	−0.442538	−	0.129941i
$983$	14.5163	−	4.26237i	0.462998	−	0.135948i	−0.0419105	−	0.999121i	$-0.513344\pi$
$983$	14.5163	−	4.26237i	0.462998	−	0.135948i	0.504908	+	0.863173i	$0.331526\pi$
$984$	2.70727	+	3.12435i	0.0863046	+	0.0996008i
$985$	−29.4037	−	8.63369i	−0.936878	−	0.275092i
$986$	−15.4717	+	9.94309i	−0.492721	+	0.316652i
$987$	14.4857	+	31.7193i	0.461086	+	1.00964i
$988$	10.4641	−	22.9131i	0.332907	−	0.728964i
$989$	−0.447784	+	0.516770i	−0.0142387	+	0.0164323i
$990$	16.2870	−	10.4670i	0.517636	−	0.332664i
$991$	−12.7471	−	27.9123i	−0.404925	−	0.886663i	−0.996747	−	0.0805938i	$-0.974318\pi$
$991$	−12.7471	−	27.9123i	−0.404925	−	0.886663i	0.591822	−	0.806069i	$-0.298409\pi$
$992$	−1.54596	−	10.7524i	−0.0490844	−	0.341389i
$993$	−8.25618	−	57.4230i	−0.262002	−	1.82226i
$994$	37.3204	−	43.0700i	1.18373	−	1.36610i
$995$	39.1128	−	11.4846i	1.23996	−	0.364085i
$996$	14.4681	+	9.29810i	0.458440	+	0.294621i
$997$	−0.743843	+	5.17354i	−0.0235577	+	0.163848i	−0.998204	−	0.0599027i	$-0.980921\pi$
$997$	−0.743843	+	5.17354i	−0.0235577	+	0.163848i	0.974646	+	0.223750i	$0.0718300\pi$
$998$	31.0581	+	19.9598i	0.983127	+	0.631817i
$999$	−0.698819	−	0.806480i	−0.0221097	−	0.0255159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	134.2.e.a.9.1	✓	30
67.15	even	11	inner	134.2.e.a.15.1	yes	30
67.22	even	11		8978.2.a.k.1.12		15
67.45	odd	22		8978.2.a.l.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
134.2.e.a.9.1	✓	30	1.1	even	1	trivial
134.2.e.a.15.1	yes	30	67.15	even	11	inner
8978.2.a.k.1.12		15	67.22	even	11
8978.2.a.l.1.4		15	67.45	odd	22

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:	\( N \)	\(=\)	\( 134 = 2 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	134.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-2.37231 - 0.696574i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.22065 + 1.40870i) q^{5} +(1.61912 + 1.86856i) q^{6} +(3.70806 + 2.38303i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.61889 + 1.68306i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-2.37231 - 0.696574i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.22065 + 1.40870i) q^{5} +(1.61912 + 1.86856i) q^{6} +(3.70806 + 2.38303i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.61889 + 1.68306i) q^{9} +(1.78848 - 0.525144i) q^{10} +(2.18491 - 2.52152i) q^{11} +(-0.351868 - 2.44730i) q^{12} +(0.744433 + 5.17765i) q^{13} +(-1.83106 - 4.00946i) q^{14} +(3.87702 - 2.49161i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.77403 + 3.88459i) q^{17} +(-1.29322 - 2.83175i) q^{18} +(-4.05108 + 2.60347i) q^{19} +(-1.78848 - 0.525144i) q^{20} +(-7.13673 - 8.23622i) q^{21} +(-3.20129 + 0.939985i) q^{22} +(5.05204 + 1.48341i) q^{23} +(-1.02710 + 2.24903i) q^{24} +(0.217112 + 1.51005i) q^{25} +(2.17299 - 4.75818i) q^{26} +(-0.183085 - 0.211292i) q^{27} +(-0.627293 + 4.36292i) q^{28} -4.30658 q^{29} -4.60862 q^{30} +(1.54596 - 10.7524i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-6.93970 + 4.45987i) q^{33} +(3.59258 - 2.30881i) q^{34} +(-7.88321 + 2.31472i) q^{35} +(-0.443037 + 3.08139i) q^{36} +3.81691 q^{37} +4.81552 q^{38} +(1.84058 - 12.8015i) q^{39} +(1.22065 + 1.40870i) q^{40} +(0.694600 - 1.52096i) q^{41} +(1.55096 + 10.7872i) q^{42} +(-0.0539481 + 0.118130i) q^{43} +(3.20129 + 0.939985i) q^{44} +(-5.56766 + 1.63481i) q^{45} +(-3.44805 - 3.97927i) q^{46} +(-3.07008 - 0.901458i) q^{47} +(2.07997 - 1.33671i) q^{48} +(5.16300 + 11.3054i) q^{49} +(0.633748 - 1.38771i) q^{50} +(6.91447 - 7.97972i) q^{51} +(-4.40050 + 2.82803i) q^{52} +(-1.93990 - 4.24779i) q^{53} +(0.0397882 + 0.276733i) q^{54} +(0.885065 + 6.15577i) q^{55} +(2.88648 - 3.33118i) q^{56} +(11.4239 - 3.35437i) q^{57} +(3.62293 + 2.32831i) q^{58} +(-0.222565 + 1.54797i) q^{59} +(3.87702 + 2.49161i) q^{60} +(2.32071 + 2.67825i) q^{61} +(-7.11374 + 8.20969i) q^{62} +(5.70023 + 12.4818i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-8.20245 - 5.27140i) q^{65} +8.24924 q^{66} +(-0.871382 - 8.13884i) q^{67} -4.27051 q^{68} +(-10.9517 - 7.03824i) q^{69} +(7.88321 + 2.31472i) q^{70} +(5.37105 + 11.7610i) q^{71} +(2.03863 - 2.35271i) q^{72} +(-1.68054 - 1.93945i) q^{73} +(-3.21099 - 2.06358i) q^{74} +(0.536802 - 3.73354i) q^{75} +(-4.05108 - 2.60347i) q^{76} +(14.1106 - 4.14325i) q^{77} +(-8.46943 + 9.77425i) q^{78} +(0.503206 + 3.49987i) q^{79} +(-0.265272 - 1.84501i) q^{80} +(-3.59250 - 7.86648i) q^{81} +(-1.40663 + 0.903985i) q^{82} +(-4.55517 + 5.25694i) q^{83} +(4.52723 - 9.91324i) q^{84} +(-3.30677 - 7.24081i) q^{85} +(0.109250 - 0.0702106i) q^{86} +(10.2166 + 2.99985i) q^{87} +(-2.18491 - 2.52152i) q^{88} +(1.58880 - 0.466514i) q^{89} +(5.56766 + 1.63481i) q^{90} +(-9.57807 + 20.9730i) q^{91} +(0.749334 + 5.21173i) q^{92} +(-11.1573 + 24.4312i) q^{93} +(2.09535 + 2.41817i) q^{94} +(1.27742 - 8.88468i) q^{95} -2.47246 q^{96} +9.63273 q^{97} +(1.76877 - 12.3020i) q^{98} +(9.96588 - 2.92625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9	\( 30 q + 3 q^{2} - q^{3} - 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{8} - 8 q^{9} + 3 q^{10} + q^{11} - q^{12} - 11 q^{13} - 22 q^{14} + 18 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 16 q^{19} - 3 q^{20} - 27 q^{21} - q^{22} + 12 q^{24} + 2 q^{25} - 11 q^{26} + 14 q^{27} - 11 q^{28} + 26 q^{30} + 18 q^{31} + 3 q^{32} + 9 q^{33} - 14 q^{34} - 90 q^{35} - 8 q^{36} - 48 q^{37} + 28 q^{38} - q^{39} + 3 q^{40} - 51 q^{41} - 17 q^{42} + 10 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} + 10 q^{47} + 10 q^{48} - 19 q^{49} - 24 q^{50} + 4 q^{51} + 11 q^{52} - 8 q^{53} - 25 q^{54} + 25 q^{55} + 31 q^{57} + 22 q^{58} + 66 q^{59} + 18 q^{60} + 34 q^{61} - 29 q^{62} + 80 q^{63} - 3 q^{64} + 26 q^{65} + 90 q^{66} - 3 q^{67} - 8 q^{68} - 46 q^{69} + 90 q^{70} + 39 q^{71} - 3 q^{72} + 78 q^{73} - 18 q^{74} - 11 q^{75} + 16 q^{76} + 73 q^{77} - 10 q^{78} + 34 q^{79} + 8 q^{80} - 134 q^{81} + 7 q^{82} - 11 q^{83} + 6 q^{84} - 31 q^{85} + q^{86} - 110 q^{87} - q^{88} - 30 q^{89} + 4 q^{90} + 14 q^{91} + 11 q^{92} - 13 q^{93} + 23 q^{94} - 39 q^{95} - 10 q^{96} + 24 q^{97} + 19 q^{98} - 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 - 3 * q^4 - 3 * q^5 + q^6 + 3 * q^8 - 8 * q^9 + 3 * q^10 + q^11 - q^12 - 11 * q^13 - 22 * q^14 + 18 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 16 * q^19 - 3 * q^20 - 27 * q^21 - q^22 + 12 * q^24 + 2 * q^25 - 11 * q^26 + 14 * q^27 - 11 * q^28 + 26 * q^30 + 18 * q^31 + 3 * q^32 + 9 * q^33 - 14 * q^34 - 90 * q^35 - 8 * q^36 - 48 * q^37 + 28 * q^38 - q^39 + 3 * q^40 - 51 * q^41 - 17 * q^42 + 10 * q^43 + q^44 - 4 * q^45 - 11 * q^46 + 10 * q^47 + 10 * q^48 - 19 * q^49 - 24 * q^50 + 4 * q^51 + 11 * q^52 - 8 * q^53 - 25 * q^54 + 25 * q^55 + 31 * q^57 + 22 * q^58 + 66 * q^59 + 18 * q^60 + 34 * q^61 - 29 * q^62 + 80 * q^63 - 3 * q^64 + 26 * q^65 + 90 * q^66 - 3 * q^67 - 8 * q^68 - 46 * q^69 + 90 * q^70 + 39 * q^71 - 3 * q^72 + 78 * q^73 - 18 * q^74 - 11 * q^75 + 16 * q^76 + 73 * q^77 - 10 * q^78 + 34 * q^79 + 8 * q^80 - 134 * q^81 + 7 * q^82 - 11 * q^83 + 6 * q^84 - 31 * q^85 + q^86 - 110 * q^87 - q^88 - 30 * q^89 + 4 * q^90 + 14 * q^91 + 11 * q^92 - 13 * q^93 + 23 * q^94 - 39 * q^95 - 10 * q^96 + 24 * q^97 + 19 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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