LMFDB - Embedded newform 690.2.x.a.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.2
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(-1.72143 - 0.191520i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.512913 + 2.17645i) q^{5} +(0.878295 + 1.49285i) q^{6} +(0.0972258 + 0.446940i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.92664 + 0.659376i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.72143 - 0.191520i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.512913 + 2.17645i) q^{5} +(0.878295 + 1.49285i) q^{6} +(0.0972258 + 0.446940i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.92664 + 0.659376i) q^{9} +(2.04971 - 0.893688i) q^{10} +(-1.10316 + 0.158611i) q^{11} +(0.668745 - 1.59774i) q^{12} +(-0.316107 + 1.45312i) q^{13} +(0.299529 - 0.345674i) q^{14} +(1.29978 - 3.64837i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-1.33200 + 2.43938i) q^{17} +(-1.22601 - 2.73805i) q^{18} +(2.24299 - 7.63891i) q^{19} +(-1.94378 - 1.10531i) q^{20} +(-0.0817695 - 0.787996i) q^{21} +(0.788074 + 0.788074i) q^{22} +(-1.91922 + 4.39507i) q^{23} +(-1.67982 + 0.422133i) q^{24} +(-4.47384 - 2.23266i) q^{25} +(1.35272 - 0.617765i) q^{26} +(-4.91172 - 1.69558i) q^{27} +(-0.456227 - 0.0326300i) q^{28} +(-0.653850 + 0.191988i) q^{29} +(-3.69960 + 1.14586i) q^{30} +(1.66639 - 3.64889i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(1.92939 - 0.0617597i) q^{33} +(2.75106 - 0.395543i) q^{34} +(-1.02261 - 0.0176346i) q^{35} +(-1.45720 + 2.62232i) q^{36} +(-11.0821 + 0.792606i) q^{37} +(-7.45943 + 2.78223i) q^{38} +(0.822457 - 2.44090i) q^{39} +(0.280016 + 2.21847i) q^{40} +(-7.21384 + 6.25083i) q^{41} +(-0.581821 + 0.537688i) q^{42} +(-2.55936 - 0.954594i) q^{43} +(0.158611 - 1.10316i) q^{44} +(-2.93621 + 6.03147i) q^{45} +(4.66858 - 1.09745i) q^{46} +(-5.06197 + 5.06197i) q^{47} +(1.34462 + 1.09179i) q^{48} +(6.17712 - 2.82100i) q^{49} +(0.893738 + 4.91947i) q^{50} +(2.76014 - 3.94411i) q^{51} +(-1.30520 - 0.712693i) q^{52} +(-2.23258 - 10.2630i) q^{53} +(1.58610 + 4.94816i) q^{54} +(0.220618 - 2.48232i) q^{55} +(0.247285 + 0.384783i) q^{56} +(-5.32415 + 12.7203i) q^{57} +(0.545532 + 0.408380i) q^{58} +(1.27475 - 0.819234i) q^{59} +(3.13439 + 2.27499i) q^{60} +(-5.71684 + 12.5181i) q^{61} +(-3.91972 + 0.852682i) q^{62} +(-0.0101565 + 1.37214i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-3.00050 - 1.43331i) q^{65} +(-1.20568 - 1.50755i) q^{66} +(2.21800 - 1.66037i) q^{67} +(-1.96530 - 1.96530i) q^{68} +(4.14554 - 7.19823i) q^{69} +(0.598710 + 0.829209i) q^{70} +(-12.6226 - 1.81486i) q^{71} +(2.97254 - 0.404954i) q^{72} +(-0.902364 + 0.492728i) q^{73} +(7.27576 + 8.39667i) q^{74} +(7.27380 + 4.70019i) q^{75} +(6.69756 + 4.30426i) q^{76} +(-0.178145 - 0.477625i) q^{77} +(-2.44692 + 0.804367i) q^{78} +(1.73336 + 2.69717i) q^{79} +(1.60817 - 1.55364i) q^{80} +(8.13045 + 3.85951i) q^{81} +(9.32714 + 2.02899i) q^{82} +(8.27048 - 0.591516i) q^{83} +(0.779114 + 0.143547i) q^{84} +(-4.62598 - 4.15022i) q^{85} +(0.769578 + 2.62094i) q^{86} +(1.16233 - 0.205268i) q^{87} +(-0.978177 + 0.534125i) q^{88} +(1.57892 + 3.45735i) q^{89} +(6.58805 - 1.26397i) q^{90} -0.680191 q^{91} +(-3.67633 - 3.07971i) q^{92} +(-3.56741 + 5.96216i) q^{93} +(7.08584 + 1.01879i) q^{94} +(15.4752 + 8.79984i) q^{95} +(0.0682265 - 1.73071i) q^{96} +(0.507680 - 7.09830i) q^{97} +(-5.96014 - 3.25448i) q^{98} +(-3.33314 - 0.263202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	−1.72143	−	0.191520i	−0.993868	−	0.110574i
$3$	−1.72143	−	0.191520i	−0.993868	−	0.110574i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	−0.512913	+	2.17645i	−0.229382	+	0.973337i
$5$	−0.512913	+	2.17645i	−0.229382	+	0.973337i
$6$	0.878295	+	1.49285i	0.358562	+	0.609453i
$7$	0.0972258	+	0.446940i	0.0367479	+	0.168927i	0.991863	−	0.127306i	$-0.0406330\pi$
$7$	0.0972258	+	0.446940i	0.0367479	+	0.168927i	−0.955116	+	0.296233i	$0.904269\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	2.92664	+	0.659376i	0.975547	+	0.219792i
$10$	2.04971	−	0.893688i	0.648176	−	0.282609i
$11$	−1.10316	+	0.158611i	−0.332615	+	0.0478229i	−0.306599	−	0.951839i	$-0.599191\pi$
$11$	−1.10316	+	0.158611i	−0.332615	+	0.0478229i	−0.0260160	+	0.999662i	$0.508282\pi$
$12$	0.668745	−	1.59774i	0.193050	−	0.461228i
$13$	−0.316107	+	1.45312i	−0.0876722	+	0.403023i	−0.999979	−	0.00648480i	$-0.997936\pi$
$13$	−0.316107	+	1.45312i	−0.0876722	+	0.403023i	0.912307	+	0.409507i	$0.134299\pi$
$14$	0.299529	−	0.345674i	0.0800524	−	0.0923854i
$15$	1.29978	−	3.64837i	0.335601	−	0.942004i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	−1.33200	+	2.43938i	−0.323058	+	0.591636i	−0.987853	−	0.155389i	$-0.950337\pi$
$17$	−1.33200	+	2.43938i	−0.323058	+	0.591636i	0.664796	+	0.747025i	$0.268519\pi$
$18$	−1.22601	−	2.73805i	−0.288974	−	0.645364i
$19$	2.24299	−	7.63891i	0.514576	−	1.75249i	−0.133640	−	0.991030i	$-0.542667\pi$
$19$	2.24299	−	7.63891i	0.514576	−	1.75249i	0.648216	−	0.761456i	$-0.275515\pi$
$20$	−1.94378	−	1.10531i	−0.434643	−	0.247155i
$21$	−0.0817695	−	0.787996i	−0.0178436	−	0.171955i
$22$	0.788074	+	0.788074i	0.168018	+	0.168018i
$23$	−1.91922	+	4.39507i	−0.400185	+	0.916434i
$23$	−1.91922	+	4.39507i	−0.400185	+	0.916434i
$24$	−1.67982	+	0.422133i	−0.342892	+	0.0861676i
$25$	−4.47384	−	2.23266i	−0.894768	−	0.446531i
$26$	1.35272	−	0.617765i	0.265290	−	0.121154i
$27$	−4.91172	−	1.69558i	−0.945261	−	0.326314i
$28$	−0.456227	−	0.0326300i	−0.0862189	−	0.00616650i
$29$	−0.653850	+	0.191988i	−0.121417	+	0.0356512i	−0.341877	−	0.939745i	$-0.611062\pi$
$29$	−0.653850	+	0.191988i	−0.121417	+	0.0356512i	0.220460	+	0.975396i	$0.429244\pi$
$30$	−3.69960	+	1.14586i	−0.675451	+	0.209204i
$31$	1.66639	−	3.64889i	0.299293	−	0.655359i	−0.698915	−	0.715205i	$-0.746333\pi$
$31$	1.66639	−	3.64889i	0.299293	−	0.655359i	0.998208	+	0.0598453i	$0.0190607\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	1.92939	−	0.0617597i	0.335864	−	0.0107510i
$34$	2.75106	−	0.395543i	0.471803	−	0.0678351i
$35$	−1.02261	−	0.0176346i	−0.172853	−	0.00298080i
$36$	−1.45720	+	2.62232i	−0.242866	+	0.437054i
$37$	−11.0821	+	0.792606i	−1.82188	+	0.130304i	−0.940002	−	0.341168i	$-0.889177\pi$
$37$	−11.0821	+	0.792606i	−1.82188	+	0.130304i	−0.881881	+	0.471472i	$0.843723\pi$
$38$	−7.45943	+	2.78223i	−1.21008	+	0.451337i
$39$	0.822457	−	2.44090i	0.131698	−	0.390857i
$40$	0.280016	+	2.21847i	0.0442744	+	0.350770i
$41$	−7.21384	+	6.25083i	−1.12661	+	0.976215i	−0.999876	−	0.0157214i	$-0.994996\pi$
$41$	−7.21384	+	6.25083i	−1.12661	+	0.976215i	−0.126736	+	0.991936i	$0.540450\pi$
$42$	−0.581821	+	0.537688i	−0.0897769	+	0.0829671i
$43$	−2.55936	−	0.954594i	−0.390299	−	0.145574i	0.146650	−	0.989188i	$-0.453151\pi$
$43$	−2.55936	−	0.954594i	−0.390299	−	0.145574i	−0.536950	+	0.843614i	$0.680424\pi$
$44$	0.158611	−	1.10316i	0.0239114	−	0.166308i
$45$	−2.93621	+	6.03147i	−0.437704	+	0.899119i
$46$	4.66858	−	1.09745i	0.688344	−	0.161810i
$47$	−5.06197	+	5.06197i	−0.738365	+	0.738365i	−0.972261	−	0.233897i	$-0.924852\pi$
$47$	−5.06197	+	5.06197i	−0.738365	+	0.738365i	0.233897	+	0.972261i	$0.424852\pi$
$48$	1.34462	+	1.09179i	0.194079	+	0.157587i
$49$	6.17712	−	2.82100i	0.882446	−	0.403000i
$50$	0.893738	+	4.91947i	0.126394	+	0.695719i
$51$	2.76014	−	3.94411i	0.386496	−	0.552286i
$52$	−1.30520	−	0.712693i	−0.180999	−	0.0988327i
$53$	−2.23258	−	10.2630i	−0.306669	−	1.40973i	−0.830076	−	0.557651i	$-0.811703\pi$
$53$	−2.23258	−	10.2630i	−0.306669	−	1.40973i	0.523407	−	0.852083i	$-0.324661\pi$
$54$	1.58610	+	4.94816i	0.215841	+	0.673359i
$55$	0.220618	−	2.48232i	0.0297482	−	0.334716i
$56$	0.247285	+	0.384783i	0.0330449	+	0.0514188i
$57$	−5.32415	+	12.7203i	−0.705201	+	1.68484i
$58$	0.545532	+	0.408380i	0.0716318	+	0.0536229i
$59$	1.27475	−	0.819234i	0.165959	−	0.106655i	−0.455025	−	0.890479i	$-0.650370\pi$
$59$	1.27475	−	0.819234i	0.165959	−	0.106655i	0.620984	+	0.783823i	$0.286733\pi$
$60$	3.13439	+	2.27499i	0.404648	+	0.293700i
$61$	−5.71684	+	12.5181i	−0.731966	+	1.60278i	0.0643682	+	0.997926i	$0.479497\pi$
$61$	−5.71684	+	12.5181i	−0.731966	+	1.60278i	−0.796334	+	0.604856i	$0.793230\pi$
$62$	−3.91972	+	0.852682i	−0.497804	+	0.108291i
$63$	−0.0101565	+	1.37214i	−0.00127960	+	0.172873i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	−3.00050	−	1.43331i	−0.372166	−	0.177781i
$66$	−1.20568	−	1.50755i	−0.148409	−	0.185566i
$67$	2.21800	−	1.66037i	0.270972	−	0.202847i	−0.455147	−	0.890416i	$-0.650413\pi$
$67$	2.21800	−	1.66037i	0.270972	−	0.202847i	0.726119	+	0.687569i	$0.241322\pi$
$68$	−1.96530	−	1.96530i	−0.238327	−	0.238327i
$69$	4.14554	−	7.19823i	0.499065	−	0.866565i
$70$	0.598710	+	0.829209i	0.0715595	+	0.0991094i
$71$	−12.6226	−	1.81486i	−1.49803	−	0.215384i	−0.655978	−	0.754780i	$-0.727744\pi$
$71$	−12.6226	−	1.81486i	−1.49803	−	0.215384i	−0.842053	+	0.539395i	$0.818653\pi$
$72$	2.97254	−	0.404954i	0.350318	−	0.0477242i
$73$	−0.902364	+	0.492728i	−0.105614	+	0.0576695i	−0.531188	−	0.847254i	$-0.678254\pi$
$73$	−0.902364	+	0.492728i	−0.105614	+	0.0576695i	0.425574	+	0.904924i	$0.360072\pi$
$74$	7.27576	+	8.39667i	0.845790	+	0.976093i
$75$	7.27380	+	4.70019i	0.839906	+	0.542731i
$76$	6.69756	+	4.30426i	0.768263	+	0.493732i
$77$	−0.178145	−	0.477625i	−0.0203015	−	0.0544305i
$78$	−2.44692	+	0.804367i	−0.277059	+	0.0910767i
$79$	1.73336	+	2.69717i	0.195019	+	0.303455i	0.924967	−	0.380047i	$-0.124092\pi$
$79$	1.73336	+	2.69717i	0.195019	+	0.303455i	−0.729948	+	0.683502i	$0.760456\pi$
$80$	1.60817	−	1.55364i	0.179798	−	0.173702i
$81$	8.13045	+	3.85951i	0.903383	+	0.428835i
$82$	9.32714	+	2.02899i	1.03001	+	0.224065i
$83$	8.27048	−	0.591516i	0.907803	−	0.0649273i	0.390377	−	0.920655i	$-0.372345\pi$
$83$	8.27048	−	0.591516i	0.907803	−	0.0649273i	0.517426	+	0.855728i	$0.326890\pi$
$84$	0.779114	+	0.143547i	0.0850083	+	0.0156623i
$85$	−4.62598	−	4.15022i	−0.501757	−	0.450155i
$86$	0.769578	+	2.62094i	0.0829858	+	0.282624i
$87$	1.16233	−	0.205268i	0.124614	−	0.0220070i
$88$	−0.978177	+	0.534125i	−0.104274	+	0.0569379i
$89$	1.57892	+	3.45735i	0.167365	+	0.366478i	0.974667	−	0.223660i	$-0.0718006\pi$
$89$	1.57892	+	3.45735i	0.167365	+	0.366478i	−0.807302	+	0.590138i	$0.799073\pi$
$90$	6.58805	−	1.26397i	0.694441	−	0.133234i
$91$	−0.680191			−0.0713034
$92$	−3.67633	−	3.07971i	−0.383284	−	0.321082i
$93$	−3.56741	+	5.96216i	−0.369923	+	0.618247i
$94$	7.08584	+	1.01879i	0.730849	+	0.105080i
$95$	15.4752	+	8.79984i	1.58772	+	0.902845i
$96$	0.0682265	−	1.73071i	0.00696334	−	0.176639i
$97$	0.507680	−	7.09830i	0.0515471	−	0.720723i	−0.904307	−	0.426882i	$-0.859612\pi$
$97$	0.507680	−	7.09830i	0.0515471	−	0.720723i	0.955854	−	0.293841i	$-0.0949335\pi$
$98$	−5.96014	−	3.25448i	−0.602065	−	0.328752i
$99$	−3.33314	−	0.263202i	−0.334993	−	0.0264528i
$100$	3.40265	−	3.66361i	0.340265	−	0.366361i
$101$	−12.3175	−	10.6731i	−1.22563	−	1.06202i	−0.996056	−	0.0887264i	$-0.971720\pi$
$101$	−12.3175	−	10.6731i	−1.22563	−	1.06202i	−0.229577	−	0.973291i	$-0.573734\pi$
$102$	−4.81151	+	0.154016i	−0.476411	+	0.0152499i
$103$	−11.4879	−	8.59972i	−1.13193	−	0.847356i	−0.142139	−	0.989847i	$-0.545398\pi$
$103$	−11.4879	−	8.59972i	−1.13193	−	0.847356i	−0.989796	+	0.142491i	$0.954489\pi$
$104$	0.211637	+	1.47197i	0.0207527	+	0.144338i
$105$	1.75697	+	0.226207i	0.171463	+	0.0220755i
$106$	−6.87803	+	7.93767i	−0.668054	+	0.770975i
$107$	−3.68213	−	9.87216i	−0.355965	−	0.954378i	−0.984311	−	0.176444i	$-0.943541\pi$
$107$	−3.68213	−	9.87216i	−0.355965	−	0.954378i	0.628346	−	0.777934i	$-0.283732\pi$
$108$	3.01069	−	4.23506i	0.289704	−	0.407519i
$109$	−1.18656	−	4.04107i	−0.113652	−	0.387064i	0.882946	−	0.469474i	$-0.155556\pi$
$109$	−1.18656	−	4.04107i	−0.113652	−	0.387064i	−0.996599	+	0.0824101i	$0.973738\pi$
$110$	−2.11941	+	1.31099i	−0.202078	+	0.124998i
$111$	19.2288	+	0.758024i	1.82512	+	0.0719484i
$112$	0.159842	−	0.428554i	0.0151037	−	0.0404946i
$113$	−6.01314	+	4.50138i	−0.565669	+	0.423454i	−0.843464	−	0.537186i	$-0.819487\pi$
$113$	−6.01314	+	4.50138i	−0.565669	+	0.423454i	0.277795	+	0.960640i	$0.410396\pi$
$114$	13.3737	−	3.36077i	1.25257	−	0.314765i
$115$	−8.58123	−	6.43137i	−0.800204	−	0.599728i
$116$		−	0.681454i		−	0.0632714i
$117$	−1.88328	+	4.04432i	−0.174110	+	0.373898i
$118$	−1.41976	−	0.529544i	−0.130700	−	0.0487485i
$119$	−1.21976	−	0.358154i	−0.111815	−	0.0328319i
$120$	−0.0571476	−	3.87256i	−0.00521684	−	0.353515i
$121$	−9.36262	+	2.74911i	−0.851147	+	0.249919i
$122$	13.4473	−	2.92527i	1.21746	−	0.264842i
$123$	13.6153	−	9.37876i	1.22765	−	0.845655i
$124$	3.03160	+	2.62690i	0.272246	+	0.235903i
$125$	7.15395	−	8.59191i	0.639869	−	0.768484i
$126$	1.10454	−	0.814163i	0.0984004	−	0.0725314i
$127$	−2.73392	+	3.65209i	−0.242597	+	0.324071i	−0.905269	−	0.424838i	$-0.860331\pi$
$127$	−2.73392	+	3.65209i	−0.242597	+	0.324071i	0.662673	+	0.748909i	$0.269422\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	4.22294	+	2.13344i	0.371809	+	0.187838i
$130$	0.650706	+	3.26098i	0.0570707	+	0.286007i
$131$	5.08726	−	7.91592i	0.444476	−	0.691618i	−0.544655	−	0.838661i	$-0.683339\pi$
$131$	5.08726	−	7.91592i	0.444476	−	0.691618i	0.989130	+	0.147043i	$0.0469756\pi$
$132$	−0.484314	+	1.86864i	−0.0421541	+	0.162644i
$133$	3.63221	+	0.259781i	0.314953	+	0.0225259i
$134$	−2.65840	−	0.780576i	−0.229650	−	0.0674315i
$135$	6.20963	−	9.82041i	0.534440	−	0.845207i
$136$	−0.395543	+	2.75106i	−0.0339175	+	0.235902i
$137$	7.87480	−	7.87480i	0.672790	−	0.672790i	−0.285569	−	0.958358i	$-0.592182\pi$
$137$	7.87480	−	7.87480i	0.672790	−	0.672790i	0.958358	+	0.285569i	$0.0921824\pi$
$138$	−8.24681	+	0.995058i	−0.702015	+	0.0847050i
$139$		−	5.19766i		−	0.440860i	−0.975403	−	0.220430i	$-0.929254\pi$
$139$		−	5.19766i		−	0.440860i	0.975403	−	0.220430i	$-0.0707461\pi$
$140$	0.305023	−	0.976218i	0.0257791	−	0.0825055i
$141$	9.68330	−	7.74436i	0.815481	−	0.652193i
$142$	6.11159	+	11.1925i	0.512873	+	0.939257i
$143$	0.118236	−	1.65316i	0.00988743	−	0.138244i
$144$	−2.10556	−	2.13696i	−0.175463	−	0.178080i
$145$	−0.0824825	−	1.52154i	−0.00684980	−	0.126357i
$146$	0.935216	+	0.427099i	0.0773990	+	0.0353469i
$147$	−11.1738	+	3.67311i	−0.921596	+	0.302953i
$148$	2.36168	−	10.8565i	0.194129	−	0.892397i
$149$	0.588773	+	4.09501i	0.0482342	+	0.335476i	0.999622	+	0.0274815i	$0.00874874\pi$
$149$	0.588773	+	4.09501i	0.0482342	+	0.335476i	−0.951388	+	0.307994i	$0.900342\pi$
$150$	−0.596330	−	8.63970i	−0.0486901	−	0.705428i
$151$	2.45659	−	1.57876i	0.199915	−	0.128477i	−0.436854	−	0.899533i	$-0.643907\pi$
$151$	2.45659	−	1.57876i	0.199915	−	0.128477i	0.636768	+	0.771055i	$0.280271\pi$
$152$	−0.567960	−	7.94112i	−0.0460676	−	0.644110i
$153$	−5.50676	+	6.26089i	−0.445195	+	0.506163i
$154$	−0.275601	+	0.428843i	−0.0222085	+	0.0345571i
$155$	7.08689	+	5.49837i	0.569233	+	0.441640i
$156$	2.11031	+	1.47682i	0.168960	+	0.118240i
$157$	10.3434	+	18.9426i	0.825496	+	1.51178i	0.858784	+	0.512337i	$0.171220\pi$
$157$	10.3434	+	18.9426i	0.825496	+	1.51178i	−0.0332885	+	0.999446i	$0.510598\pi$
$158$	1.12043	−	3.00398i	0.0891364	−	0.238984i
$159$	1.87766	+	18.0946i	0.148908	+	1.43500i
$160$	−2.20749	−	0.356341i	−0.174518	−	0.0281712i
$161$	−2.15093	−	0.430462i	−0.169517	−	0.0339251i
$162$	−1.78270	−	8.82168i	−0.140062	−	0.693096i
$163$	0.670511	+	0.895698i	0.0525185	+	0.0701565i	0.826032	−	0.563624i	$-0.190593\pi$
$163$	0.670511	+	0.895698i	0.0525185	+	0.0701565i	−0.773513	+	0.633780i	$0.781502\pi$
$164$	−3.96525	−	8.68269i	−0.309634	−	0.678004i
$165$	−0.855193	+	4.23089i	−0.0665767	+	0.329375i
$166$	−5.42985	−	6.26638i	−0.421438	−	0.486365i
$167$	−6.09952	+	11.1704i	−0.471995	+	0.864395i	0.527891	+	0.849312i	$0.322983\pi$
$167$	−6.09952	+	11.1704i	−0.471995	+	0.864395i	−0.999886	+	0.0150825i	$0.995199\pi$
$168$	−0.351990	−	0.709737i	−0.0271567	−	0.0547574i
$169$	9.81358	+	4.48171i	0.754891	+	0.344747i
$170$	−0.550178	+	6.19042i	−0.0421967	+	0.474783i
$171$	11.6013	−	20.8774i	0.887176	−	1.59653i
$172$	1.63698	−	2.18675i	0.124819	−	0.166738i
$173$	4.45653	−	5.95323i	0.338824	−	0.452616i	−0.598475	−	0.801141i	$-0.704227\pi$
$173$	4.45653	−	5.95323i	0.338824	−	0.452616i	0.937299	+	0.348525i	$0.113318\pi$
$174$	−0.860882	−	0.807477i	−0.0652633	−	0.0612147i
$175$	0.562891	−	2.21661i	0.0425505	−	0.167560i
$176$	1.01379	+	0.462982i	0.0764172	+	0.0348986i
$177$	−2.35130	+	1.16611i	−0.176734	+	0.0876504i
$178$	1.82154	−	3.33590i	0.136530	−	0.250036i
$179$	−0.968542	−	1.11776i	−0.0723923	−	0.0835451i	0.718398	−	0.695632i	$-0.244876\pi$
$179$	−0.968542	−	1.11776i	−0.0723923	−	0.0835451i	−0.790790	+	0.612087i	$0.790330\pi$
$180$	−4.95993	−	4.51654i	−0.369691	−	0.336643i
$181$	0.217370	+	0.475973i	0.0161570	+	0.0353788i	0.917538	−	0.397647i	$-0.130173\pi$
$181$	0.217370	+	0.475973i	0.0161570	+	0.0353788i	−0.901381	+	0.433026i	$0.857446\pi$
$182$	0.407623	+	0.544521i	0.0302150	+	0.0403626i
$183$	12.2386	−	20.4542i	0.904704	−	1.51202i
$184$	−0.262294	+	4.78865i	−0.0193366	+	0.353024i
$185$	3.95908	−	24.5261i	0.291078	−	1.80319i
$186$	6.91082	−	0.717128i	0.506726	−	0.0525824i
$187$	1.08250	−	2.90230i	0.0791603	−	0.212237i
$188$	−3.43080	−	6.28305i	−0.250217	−	0.458238i
$189$	0.280276	−	2.36010i	0.0203871	−	0.171672i
$190$	−2.22932	−	17.6621i	−0.161732	−	1.28134i
$191$	−1.22928	+	1.91279i	−0.0889474	+	0.138405i	−0.882876	−	0.469606i	$-0.844396\pi$
$191$	−1.22928	+	1.91279i	−0.0889474	+	0.138405i	0.793929	+	0.608011i	$0.208032\pi$
$192$	−1.42639	+	0.982556i	−0.102941	+	0.0709098i
$193$	1.14898	+	16.0648i	0.0827051	+	1.15637i	0.854134	+	0.520053i	$0.174088\pi$
$193$	1.14898	+	16.0648i	0.0827051	+	1.15637i	−0.771429	+	0.636316i	$0.780458\pi$
$194$	−5.98672	+	3.84743i	−0.429821	+	0.276229i
$195$	4.89064	+	3.04200i	0.350226	+	0.217842i
$196$	0.966430	+	6.72167i	0.0690307	+	0.480119i
$197$	−3.35002	+	15.3998i	−0.238679	+	1.09719i	0.689277	+	0.724498i	$0.257928\pi$
$197$	−3.35002	+	15.3998i	−0.238679	+	1.09719i	−0.927956	+	0.372691i	$0.878435\pi$
$198$	1.78677	+	2.82605i	0.126980	+	0.200838i
$199$	12.7658	+	5.82996i	0.904946	+	0.413275i	0.812848	−	0.582475i	$-0.197916\pi$
$199$	12.7658	+	5.82996i	0.904946	+	0.413275i	0.0920971	+	0.995750i	$0.470643\pi$
$200$	−4.97200	−	0.528441i	−0.351573	−	0.0373664i
$201$	−4.13613	+	2.43343i	−0.291740	+	0.171641i
$202$	−1.16271	+	16.2568i	−0.0818080	+	1.14382i
$203$	−0.149378	−	0.273565i	−0.0104843	−	0.0192005i
$204$	3.00673	+	3.75952i	0.210513	+	0.263219i
$205$	−9.90452	−	18.9067i	−0.691761	−	1.32050i
$206$			14.3501i			0.999822i
$207$	−8.51486	+	11.5973i	−0.591824	+	0.806067i
$208$	1.05154	−	1.05154i	0.0729113	−	0.0729113i
$209$	−1.26276	+	8.78271i	−0.0873471	+	0.607512i
$210$	−0.871827	−	1.54209i	−0.0601617	−	0.106414i
$211$	−2.37305	−	0.696790i	−0.163367	−	0.0479690i	0.199026	−	0.979994i	$-0.436222\pi$
$211$	−2.37305	−	0.696790i	−0.163367	−	0.0479690i	−0.362394	+	0.932025i	$0.618040\pi$
$212$	10.4763	+	0.749279i	0.719514	+	0.0514607i
$213$	21.3814	+	5.54164i	1.46503	+	0.379707i
$214$	−5.69646	+	8.86386i	−0.389402	+	0.605921i
$215$	3.39035	−	5.08070i	0.231220	−	0.346501i
$216$	−5.19458	+	0.127798i	−0.353446	+	0.00869556i
$217$	1.79285	+	0.390011i	0.121707	+	0.0264756i
$218$	−2.52396	+	3.37161i	−0.170944	+	0.228355i
$219$	1.64772	−	0.675376i	0.111343	−	0.0456377i
$220$	2.31962	+	0.911033i	0.156389	+	0.0614218i
$221$	−3.12365	−	2.70666i	−0.210120	−	0.182070i
$222$	−10.9166	−	15.8477i	−0.732673	−	1.06363i
$223$	−17.9990	+	3.91545i	−1.20531	+	0.262198i	−0.769976	−	0.638073i	$-0.779732\pi$
$223$	−17.9990	+	3.91545i	−1.20531	+	0.262198i	−0.435329	+	0.900271i	$0.643368\pi$
$224$	−0.438865	+	0.128862i	−0.0293229	+	0.00860998i
$225$	−11.6212	−	9.48413i	−0.774744	−	0.632275i
$226$	7.20708	+	2.11619i	0.479408	+	0.140767i
$227$	7.69828	+	2.87131i	0.510953	+	0.190576i	0.591699	−	0.806159i	$-0.298457\pi$
$227$	7.69828	+	2.87131i	0.510953	+	0.190576i	−0.0807458	+	0.996735i	$0.525730\pi$
$228$	−10.7050	−	8.69220i	−0.708958	−	0.575655i
$229$			5.61307i			0.370922i	0.982652	+	0.185461i	$0.0593779\pi$
$229$			5.61307i			0.370922i	−0.982652	+	0.185461i	$0.940622\pi$
$230$	−0.00603301	+	10.7238i	−0.000397805	+	0.707107i
$231$	0.215189	+	0.856317i	0.0141584	+	0.0563415i
$232$	−0.545532	+	0.408380i	−0.0358159	+	0.0268115i
$233$	−4.67114	+	12.5238i	−0.306016	+	0.820462i	0.689361	+	0.724418i	$0.257892\pi$
$233$	−4.67114	+	12.5238i	−0.306016	+	0.820462i	−0.995377	+	0.0960435i	$0.969381\pi$
$234$	4.36626	−	0.916027i	0.285431	−	0.0598826i
$235$	−8.42076	−	13.6135i	−0.549310	−	0.888045i
$236$	0.426910	+	1.45392i	0.0277895	+	0.0946422i
$237$	−2.46730	−	4.97496i	−0.160269	−	0.323158i
$238$	0.444258	+	1.19110i	0.0287970	+	0.0772077i
$239$	−2.81718	+	3.25120i	−0.182228	+	0.210302i	−0.839513	−	0.543340i	$-0.817159\pi$
$239$	−2.81718	+	3.25120i	−0.182228	+	0.210302i	0.657285	+	0.753642i	$0.271705\pi$
$240$	−3.06590	+	2.36649i	−0.197903	+	0.152756i
$241$	3.25440	+	22.6348i	0.209634	+	1.45804i	0.774353	+	0.632754i	$0.218076\pi$
$241$	3.25440	+	22.6348i	0.209634	+	1.45804i	−0.564718	+	0.825284i	$0.691015\pi$
$242$	7.81158	+	5.84768i	0.502148	+	0.375903i
$243$	−13.2568	−	8.20102i	−0.850425	−	0.526096i
$244$	−10.4004	−	9.01203i	−0.665820	−	0.576936i
$245$	2.97142	+	14.8911i	0.189837	+	0.951358i
$246$	−15.6674	−	5.27910i	−0.998918	−	0.336583i
$247$	10.3912	+	5.67404i	0.661178	+	0.361030i
$248$	0.286169	−	4.00117i	0.0181718	−	0.254074i
$249$	−14.3503	−	0.565707i	−0.909415	−	0.0358503i
$250$	−11.1654	−	0.578091i	−0.706161	−	0.0365617i
$251$	21.7902	+	3.13295i	1.37538	+	0.197750i	0.790050	−	0.613043i	$-0.210055\pi$
$251$	21.7902	+	3.13295i	1.37538	+	0.197750i	0.585333	+	0.810793i	$0.300964\pi$
$252$	−1.31370	−	0.396322i	−0.0827552	−	0.0249659i
$253$	1.42010	−	5.15287i	0.0892811	−	0.323958i
$254$	4.56203			0.286247
$255$	7.16844	+	8.03028i	0.448905	+	0.502875i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	10.6827	−	5.83317i	0.666365	−	0.363863i	−0.110191	−	0.993910i	$-0.535146\pi$
$257$	10.6827	−	5.83317i	0.666365	−	0.363863i	0.776557	+	0.630047i	$0.216965\pi$
$258$	−0.822812	−	4.65916i	−0.0512261	−	0.290067i
$259$	−1.43171	−	4.87596i	−0.0889623	−	0.302978i
$260$	2.22059	−	2.47515i	0.137715	−	0.153502i
$261$	−2.04018	+	0.130746i	−0.126284	+	0.00809296i
$262$	−9.38570	+	0.671279i	−0.579851	+	0.0414717i
$263$	12.2546	+	2.66582i	0.755650	+	0.164382i	0.573857	−	0.818955i	$-0.305446\pi$
$263$	12.2546	+	2.66582i	0.755650	+	0.164382i	0.181793	+	0.983337i	$0.441810\pi$
$264$	1.78616	−	0.732119i	0.109930	−	0.0450588i
$265$	23.4820	+	0.404942i	1.44249	+	0.0248754i
$266$	−1.96874	−	3.06342i	−0.120711	−	0.187830i
$267$	−2.05584	−	6.25397i	−0.125816	−	0.382737i
$268$	0.968235	+	2.59594i	0.0591443	+	0.158572i
$269$	−18.2745	−	11.7443i	−1.11422	−	0.716063i	−0.152007	−	0.988379i	$-0.548574\pi$
$269$	−18.2745	−	11.7443i	−1.11422	−	0.716063i	−0.962208	+	0.272317i	$0.912210\pi$
$270$	−11.5829	+	0.914094i	−0.704915	+	0.0556300i
$271$	5.26335	+	6.07423i	0.319726	+	0.368983i	0.892748	−	0.450557i	$-0.148774\pi$
$271$	5.26335	+	6.07423i	0.319726	+	0.368983i	−0.573022	+	0.819540i	$0.694229\pi$
$272$	2.43938	−	1.33200i	0.147909	−	0.0807644i
$273$	1.17090	+	0.130270i	0.0708661	+	0.00788430i
$274$	−11.0233	−	1.58491i	−0.665942	−	0.0957480i
$275$	5.28949	+	1.75338i	0.318968	+	0.105733i
$276$	5.73871	+	6.00559i	0.345430	+	0.361494i
$277$	−15.8309	−	15.8309i	−0.951186	−	0.951186i	0.0476769	−	0.998863i	$-0.484818\pi$
$277$	−15.8309	−	15.8309i	−0.951186	−	0.951186i	−0.998863	+	0.0476769i	$0.984818\pi$
$278$	−4.16094	+	3.11484i	−0.249557	+	0.186816i
$279$	7.28292	−	9.58020i	0.436017	−	0.573552i
$280$	−0.964296	+	0.340843i	−0.0576277	+	0.0203692i
$281$	−12.6499	+	10.9612i	−0.754627	+	0.653888i	−0.944720	−	0.327878i	$-0.893666\pi$
$281$	−12.6499	+	10.9612i	−0.754627	+	0.653888i	0.190093	+	0.981766i	$0.439121\pi$
$282$	−12.0027	−	3.11086i	−0.714748	−	0.185249i
$283$	8.65747	−	1.88332i	0.514633	−	0.111952i	0.0522539	−	0.998634i	$-0.483359\pi$
$283$	8.65747	−	1.88332i	0.514633	−	0.111952i	0.462379	+	0.886682i	$0.346996\pi$
$284$	5.29755	−	11.6000i	0.314352	−	0.688335i
$285$	−24.9542	−	18.1121i	−1.47816	−	1.07287i
$286$	−1.39428	+	0.896050i	−0.0824455	+	0.0529845i
$287$	−3.49512	−	2.61641i	−0.206310	−	0.154442i
$288$	−0.448912	+	2.96622i	−0.0264524	+	0.174786i
$289$	5.01455	+	7.80280i	0.294974	+	0.458988i
$290$	−1.16863	+	0.977857i	−0.0686242	+	0.0574217i
$291$	−2.23340	+	12.1220i	−0.130924	+	0.710603i
$292$	−0.218544	−	1.00463i	−0.0127893	−	0.0587915i
$293$	16.4599	+	8.98778i	0.961597	+	0.525072i	0.881740	−	0.471735i	$-0.156372\pi$
$293$	16.4599	+	8.98778i	0.961597	+	0.525072i	0.0798564	+	0.996806i	$0.474554\pi$
$294$	9.63666	+	6.74384i	0.562021	+	0.393309i
$295$	1.12918	+	3.19463i	0.0657435	+	0.185998i
$296$	−10.1064	+	4.61542i	−0.587421	+	0.268266i
$297$	5.68735	+	1.09145i	0.330014	+	0.0633321i
$298$	2.92538	−	2.92538i	0.169463	−	0.169463i
$299$	−5.77987	−	4.17816i	−0.334259	−	0.241629i
$300$	−6.55907	+	5.65497i	−0.378688	+	0.326490i
$301$	0.177810	−	1.23669i	0.0102488	−	0.0712818i
$302$	−2.73604	−	1.02049i	−0.157441	−	0.0587226i
$303$	19.1595	+	20.7321i	1.10069	+	1.19103i
$304$	−6.01683	+	5.21361i	−0.345089	+	0.299021i
$305$	−24.3128	−	18.8631i	−1.39215	−	1.08010i
$306$	8.31218	+	0.656372i	0.475176	+	0.0375223i
$307$	18.1141	−	6.75621i	1.03383	−	0.385597i	0.225445	−	0.974256i	$-0.427616\pi$
$307$	18.1141	−	6.75621i	1.03383	−	0.385597i	0.808382	+	0.588659i	$0.200344\pi$
$308$	0.508468	−	0.0363663i	0.0289726	−	0.00207216i
$309$	18.1286	+	17.0040i	1.03130	+	0.967322i
$310$	0.154658	−	8.96840i	0.00878397	−	0.509371i
$311$	−4.73023	+	0.680104i	−0.268227	+	0.0385652i	−0.275116	−	0.961411i	$-0.588716\pi$
$311$	−4.73023	+	0.680104i	−0.268227	+	0.0385652i	0.00688908	+	0.999976i	$0.497807\pi$
$312$	−0.0824071	−	2.57442i	−0.00466538	−	0.145748i
$313$	1.98187	+	27.7101i	0.112022	+	1.56627i	0.673758	+	0.738952i	$0.264679\pi$
$313$	1.98187	+	27.7101i	0.112022	+	1.56627i	−0.561737	+	0.827316i	$0.689867\pi$
$314$	8.96573	−	19.6322i	0.505966	−	1.10791i
$315$	−2.98118	−	0.725894i	−0.167971	−	0.0408995i
$316$	−3.07626	+	0.903271i	−0.173053	+	0.0508130i
$317$	−29.7953	−	2.13100i	−1.67347	−	0.119689i	−0.797903	−	0.602786i	$-0.794057\pi$
$317$	−29.7953	−	2.13100i	−1.67347	−	0.119689i	−0.875567	+	0.483097i	$0.839512\pi$
$318$	13.3603	−	12.3469i	0.749207	−	0.692378i
$319$	0.690850	−	0.315501i	0.0386802	−	0.0176646i
$320$	1.03764	+	1.98074i	0.0580056	+	0.110726i
$321$	4.44781	+	17.6994i	0.248252	+	0.987886i
$322$	0.944401	+	1.97987i	0.0526294	+	0.110334i
$323$	15.6465	+	15.6465i	0.870596	+	0.870596i
$324$	−5.99379	+	6.71376i	−0.332988	+	0.372986i
$325$	4.65853	−	5.79526i	0.258409	−	0.321463i
$326$	0.315221	−	1.07354i	0.0174585	−	0.0594581i
$327$	1.26864	+	7.18366i	0.0701561	+	0.397257i
$328$	−4.57456	+	8.37769i	−0.252588	+	0.462580i
$329$	−2.75455	−	1.77024i	−0.151863	−	0.0975967i
$330$	3.89950	−	1.85086i	0.214661	−	0.101887i
$331$	−14.5309	+	16.7695i	−0.798690	+	0.921737i	−0.998309	−	0.0581366i	$-0.981484\pi$
$331$	−14.5309	+	16.7695i	−0.798690	+	0.921737i	0.199619	+	0.979874i	$0.436030\pi$
$332$	−1.76251	+	8.10211i	−0.0967301	+	0.444661i
$333$	−32.9559	−	4.98759i	−1.80597	−	0.273318i
$334$	12.5977	−	1.81128i	0.689316	−	0.0991086i
$335$	2.47607	+	5.67899i	0.135282	+	0.310276i
$336$	−0.357234	+	0.707113i	−0.0194887	+	0.0385762i
$337$	−8.82600	+	3.29193i	−0.480783	+	0.179323i	−0.578158	−	0.815925i	$-0.696228\pi$
$337$	−8.82600	+	3.29193i	−0.480783	+	0.179323i	0.0973748	+	0.995248i	$0.468955\pi$
$338$	−2.29327	−	10.5420i	−0.124737	−	0.573408i
$339$	11.2133	−	6.59718i	0.609023	−	0.358309i
$340$	5.28539	−	3.26934i	0.286641	−	0.177305i
$341$	−1.25954	+	4.28962i	−0.0682082	+	0.232296i
$342$	−23.6656	+	3.22400i	−1.27969	+	0.174334i
$343$	3.78013	+	5.04966i	0.204108	+	0.272656i
$344$	−2.73159			−0.147278
$345$	13.5403	+	12.7146i	0.728983	+	0.684532i
$346$	−7.43651			−0.399789
$347$	−15.2241	−	20.3370i	−0.817271	−	1.09175i	−0.994203	−	0.107523i	$-0.965708\pi$
$347$	−15.2241	−	20.3370i	−0.817271	−	1.09175i	0.176931	−	0.984223i	$-0.443383\pi$
$348$	−0.130512	+	1.17307i	−0.00699617	+	0.0628834i
$349$	5.32992	−	18.1520i	0.285304	−	0.971656i	−0.684752	−	0.728776i	$-0.740090\pi$
$349$	5.32992	−	18.1520i	0.285304	−	0.971656i	0.970056	−	0.242880i	$-0.0780923\pi$
$350$	−2.11182	+	0.877747i	−0.112881	+	0.0469176i
$351$	4.01651	−	6.60133i	0.214385	−	0.352353i
$352$	−0.236905	−	1.08903i	−0.0126271	−	0.0580457i
$353$	16.5363	−	6.16772i	0.880138	−	0.328275i	0.131550	−	0.991310i	$-0.458005\pi$
$353$	16.5363	−	6.16772i	0.880138	−	0.328275i	0.748588	+	0.663035i	$0.230732\pi$
$354$	2.34260	+	1.18349i	0.124508	+	0.0629015i
$355$	10.4243	−	26.5416i	0.553262	−	1.40868i
$356$	−3.76213	+	0.540913i	−0.199393	+	0.0286683i
$357$	2.03114	+	0.850145i	0.107499	+	0.0449945i
$358$	−0.314385	+	1.44521i	−0.0166158	+	0.0763815i
$359$	−16.1324	+	18.6178i	−0.851434	+	0.982607i	−0.999980	−	0.00629819i	$-0.997995\pi$
$359$	−16.1324	+	18.6178i	−0.851434	+	0.982607i	0.148546	+	0.988905i	$0.452541\pi$
$360$	−0.643297	+	6.67729i	−0.0339047	+	0.351924i
$361$	−37.3381	−	23.9958i	−1.96517	−	1.26294i
$362$	0.250772	−	0.459254i	0.0131803	−	0.0241378i
$363$	16.6436	−	2.93928i	0.873562	−	0.154272i
$364$	0.191632	−	0.652638i	0.0100442	−	0.0342075i
$365$	−0.609562	−	2.21667i	−0.0319059	−	0.116026i
$366$	−23.7088	+	2.46023i	−1.23928	+	0.128598i
$367$	23.6388	+	23.6388i	1.23394	+	1.23394i	0.962440	+	0.271496i	$0.0875183\pi$
$367$	23.6388	+	23.6388i	1.23394	+	1.23394i	0.271496	+	0.962440i	$0.412482\pi$
$368$	3.99070	−	2.65976i	0.208030	−	0.138649i
$369$	−25.2340	+	13.5373i	−1.31363	+	0.704723i
$370$	−22.0067	+	11.5285i	−1.14408	+	0.599340i
$371$	4.36989	−	1.99566i	0.226873	−	0.103610i
$372$	−4.71559	−	5.10264i	−0.244492	−	0.264559i
$373$	−17.8308	−	1.27529i	−0.923246	−	0.0660319i	−0.398384	−	0.917219i	$-0.630429\pi$
$373$	−17.8308	−	1.27529i	−0.923246	−	0.0660319i	−0.524863	+	0.851187i	$0.675883\pi$
$374$	−2.97213	+	0.872695i	−0.153685	+	0.0451260i
$375$	−13.9605	+	13.4203i	−0.720920	+	0.693019i
$376$	−2.97384	+	6.51179i	−0.153364	+	0.335820i
$377$	−0.0722946	−	1.01081i	−0.00372336	−	0.0520594i
$378$	−2.05732	+	1.18998i	−0.105817	+	0.0612061i
$379$	−17.6538	+	2.53823i	−0.906813	+	0.130380i	−0.579912	−	0.814679i	$-0.696913\pi$
$379$	−17.6538	+	2.53823i	−0.906813	+	0.130380i	−0.326900	+	0.945059i	$0.606004\pi$
$380$	−12.8033	+	12.3692i	−0.656793	+	0.634525i
$381$	5.40571	−	5.76322i	0.276943	−	0.295259i
$382$	2.26795	−	0.162207i	0.116038	−	0.00829922i
$383$	−0.291818	+	0.108842i	−0.0149112	+	0.00556158i	−0.356909	−	0.934139i	$-0.616169\pi$
$383$	−0.291818	+	0.108842i	−0.0149112	+	0.00556158i	0.341998	+	0.939701i	$0.388897\pi$
$384$	1.64138	+	0.553059i	0.0837613	+	0.0282232i
$385$	1.13090	−	0.142743i	0.0576360	−	0.00727485i
$386$	12.1720	−	10.5471i	0.619537	−	0.536832i
$387$	−6.86090	−	4.48134i	−0.348759	−	0.227799i
$388$	6.66773	+	2.48694i	0.338503	+	0.126255i
$389$	1.63529	−	11.3737i	0.0829125	−	0.576669i	−0.905438	−	0.424478i	$-0.860458\pi$
$389$	1.63529	−	11.3737i	0.0829125	−	0.576669i	0.988351	−	0.152192i	$-0.0486331\pi$
$390$	−0.495603	−	5.73817i	−0.0250958	−	0.290563i
$391$	−8.16482	−	10.5359i	−0.412913	−	0.532825i
$392$	4.80181	−	4.80181i	0.242528	−	0.242528i
$393$	−10.2734	+	12.6524i	−0.518225	+	0.638229i
$394$	14.3357	−	6.54692i	0.722224	−	0.329829i
$395$	−6.75931	+	2.38916i	−0.340098	+	0.120212i
$396$	1.19159	−	3.12397i	0.0598798	−	0.156985i
$397$	26.7878	+	14.6272i	1.34444	+	0.734120i	0.980354	−	0.197245i	$-0.0631995\pi$
$397$	26.7878	+	14.6272i	1.34444	+	0.734120i	0.364086	+	0.931365i	$0.381381\pi$
$398$	−2.98315	−	13.7133i	−0.149532	−	0.687387i
$399$	−6.20284	−	1.14283i	−0.310530	−	0.0572133i
$400$	2.55657	+	4.29697i	0.127828	+	0.214849i
$401$	19.7870	+	30.7892i	0.988116	+	1.53754i	0.835674	+	0.549225i	$0.185077\pi$
$401$	19.7870	+	30.7892i	0.988116	+	1.53754i	0.152441	+	0.988313i	$0.451286\pi$
$402$	4.42675	+	1.85284i	0.220786	+	0.0924113i
$403$	4.77551	+	3.57490i	0.237885	+	0.178079i
$404$	13.7110	−	8.81154i	0.682149	−	0.438391i
$405$	−12.5702	+	15.7159i	−0.624620	+	0.780929i
$406$	−0.129482	+	0.283525i	−0.00642606	+	0.0140711i
$407$	12.0996	−	2.63211i	0.599755	−	0.130469i
$408$	1.20778	−	4.66000i	0.0597941	−	0.230705i
$409$	19.4087	−	16.8177i	0.959697	−	0.831583i	−0.0260764	−	0.999660i	$-0.508301\pi$
$409$	19.4087	−	16.8177i	0.959697	−	0.831583i	0.985774	+	0.168077i	$0.0537559\pi$
$410$	−9.20001	+	19.2593i	−0.454356	+	0.951150i
$411$	−15.0641	+	12.0477i	−0.743057	+	0.594271i
$412$	11.4879	−	8.59972i	0.565967	−	0.423678i
$413$	0.490087	+	0.490087i	0.0241156	+	0.0241156i
$414$	14.3869	−	0.133495i	0.707076	−	0.00656091i
$415$	−2.95463	+	18.3036i	−0.145037	+	0.898491i
$416$	−1.47197	−	0.211637i	−0.0721691	−	0.0103764i
$417$	−0.995456	+	8.94741i	−0.0487477	+	0.438157i
$418$	7.78766	−	4.25239i	0.380907	−	0.207991i
$419$	13.7300	+	15.8453i	0.670755	+	0.774092i	0.984494	−	0.175417i	$-0.0561273\pi$
$419$	13.7300	+	15.8453i	0.670755	+	0.774092i	−0.313739	+	0.949509i	$0.601582\pi$
$420$	−0.712040	+	1.62207i	−0.0347440	+	0.0791491i
$421$	−15.8544	−	10.1890i	−0.772697	−	0.496583i	0.0939053	−	0.995581i	$-0.470065\pi$
$421$	−15.8544	−	10.1890i	−0.772697	−	0.496583i	−0.866603	+	0.498999i	$0.833701\pi$
$422$	0.864306	+	2.31730i	0.0420738	+	0.112804i
$423$	−18.1523	+	11.4768i	−0.882596	+	0.558023i
$424$	−5.67838	−	8.83572i	−0.275766	−	0.429101i
$425$	11.4055	−	7.93949i	0.553246	−	0.385122i
$426$	−8.37708	−	20.4377i	−0.405871	−	0.990208i
$427$	−6.15068	−	1.33800i	−0.297652	−	0.0647503i
$428$	10.5096	−	0.751665i	0.508003	−	0.0363331i
$429$	−0.520149	+	2.82316i	−0.0251130	+	0.136303i
$430$	−6.09907	+	0.330629i	−0.294123	+	0.0159444i
$431$	−2.12348	−	7.23190i	−0.102284	−	0.348349i	0.892410	−	0.451226i	$-0.149013\pi$
$431$	−2.12348	−	7.23190i	−0.102284	−	0.348349i	−0.994694	+	0.102878i	$0.967195\pi$
$432$	3.21530	+	4.08189i	0.154696	+	0.196390i
$433$	9.37535	−	5.11933i	0.450551	−	0.246019i	−0.237918	−	0.971285i	$-0.576465\pi$
$433$	9.37535	−	5.11933i	0.450551	−	0.246019i	0.688469	+	0.725266i	$0.258283\pi$
$434$	−0.762195	−	1.66897i	−0.0365865	−	0.0801133i
$435$	−0.149418	+	2.63503i	−0.00716404	+	0.126340i
$436$	4.21167			0.201702
$437$	29.2687	+	24.5188i	1.40011	+	1.17289i
$438$	−1.52811	−	0.914333i	−0.0730159	−	0.0436885i
$439$	−24.6990	−	3.55118i	−1.17882	−	0.169488i	−0.475076	−	0.879945i	$-0.657579\pi$
$439$	−24.6990	−	3.55118i	−1.17882	−	0.169488i	−0.703741	+	0.710456i	$0.748489\pi$
$440$	−0.660775	−	2.40291i	−0.0315012	−	0.114554i
$441$	19.9383	−	4.18300i	0.949443	−	0.199190i
$442$	−0.294858	+	4.12265i	−0.0140250	+	0.196095i
$443$	−12.4508	−	6.79863i	−0.591554	−	0.323013i	0.155438	−	0.987846i	$-0.450321\pi$
$443$	−12.4508	−	6.79863i	−0.591554	−	0.323013i	−0.746992	+	0.664833i	$0.768503\pi$
$444$	−6.14470	+	18.2364i	−0.291615	+	0.865460i
$445$	−8.33458	+	1.66311i	−0.395097	+	0.0788390i
$446$	13.9209	+	12.0625i	0.659174	+	0.571177i
$447$	−0.229256	−	7.16203i	−0.0108434	−	0.338752i
$448$	0.366162	+	0.274105i	0.0172995	+	0.0129503i
$449$	−1.16490	−	8.10205i	−0.0549750	−	0.382359i	−0.998671	−	0.0515447i	$-0.983586\pi$
$449$	−1.16490	−	8.10205i	−0.0549750	−	0.382359i	0.943696	−	0.330815i	$-0.107324\pi$
$450$	−0.628134	+	14.9868i	−0.0296105	+	0.706487i
$451$	6.96657	−	8.03986i	0.328043	−	0.378582i
$452$	−2.62495	−	7.03775i	−0.123467	−	0.331028i
$453$	−4.53121	+	2.24723i	−0.212895	+	0.105584i
$454$	−2.31481	−	7.88351i	−0.108639	−	0.369991i
$455$	0.348879	−	1.48040i	0.0163557	−	0.0694022i
$456$	−0.543179	+	13.7789i	−0.0254367	+	0.645254i
$457$	6.81001	−	18.2583i	0.318559	−	0.854089i	−0.674692	−	0.738100i	$-0.735723\pi$
$457$	6.81001	−	18.2583i	0.318559	−	0.854089i	0.993250	−	0.115989i	$-0.0370038\pi$
$458$	4.49350	−	3.36379i	0.209967	−	0.157180i
$459$	10.6786	−	9.72303i	0.498433	−	0.453832i
$460$	8.58846	−	6.42171i	0.400439	−	0.299414i
$461$			11.9326i			0.555756i	0.960616	+	0.277878i	$0.0896311\pi$
$461$			11.9326i			0.555756i	−0.960616	+	0.277878i	$0.910369\pi$
$462$	0.556559	−	0.685440i	0.0258935	−	0.0318895i
$463$	−20.5413	−	7.66151i	−0.954635	−	0.356060i	−0.176601	−	0.984283i	$-0.556510\pi$
$463$	−20.5413	−	7.66151i	−0.954635	−	0.356060i	−0.778034	+	0.628222i	$0.783783\pi$
$464$	0.653850	+	0.191988i	0.0303542	+	0.00891280i
$465$	−11.1465	−	10.8223i	−0.516908	−	0.501874i
$466$	12.8251	−	3.76580i	0.594113	−	0.174447i
$467$	−36.8244	+	8.01065i	−1.70403	+	0.370689i	−0.956089	−	0.293078i	$-0.905320\pi$
$467$	−36.8244	+	8.01065i	−1.70403	+	0.370689i	−0.747940	+	0.663767i	$0.768957\pi$
$468$	−3.34992	−	2.94641i	−0.154850	−	0.136198i
$469$	0.957735	+	0.829882i	0.0442241	+	0.0383204i
$470$	−5.85177	+	14.8994i	−0.269922	+	0.687259i
$471$	−14.1776	−	34.5893i	−0.653270	−	1.59379i
$472$	0.908087	−	1.21306i	0.0417981	−	0.0558357i
$473$	2.97480	+	0.647128i	0.136781	+	0.0297550i
$474$	−2.50406	+	4.95656i	−0.115015	+	0.227662i
$475$	−27.0898	+	29.1674i	−1.24297	+	1.33829i
$476$	0.687293	−	1.06945i	0.0315020	−	0.0490181i
$477$	0.233222	−	31.5083i	0.0106785	−	1.44266i
$478$	4.29099	+	0.306898i	0.196265	+	0.0140372i
$479$	−34.7092	−	10.1915i	−1.58590	−	0.465664i	−0.634325	−	0.773066i	$-0.718722\pi$
$479$	−34.7092	−	10.1915i	−1.58590	−	0.465664i	−0.951579	+	0.307403i	$0.900540\pi$
$480$	3.73180	+	1.03619i	0.170332	+	0.0472956i
$481$	2.35137	−	16.3541i	0.107213	−	0.745684i
$482$	16.1698	−	16.1698i	0.736516	−	0.736516i
$483$	3.62023	+	1.15296i	0.164726	+	0.0524613i
$484$		−	9.75788i		−	0.443540i
$485$	15.1887	+	4.74575i	0.689682	+	0.215493i
$486$	1.37926	+	15.5273i	0.0625644	+	0.704334i
$487$	−4.22261	−	7.73313i	−0.191345	−	0.350422i	0.764340	−	0.644813i	$-0.223065\pi$
$487$	−4.22261	−	7.73313i	−0.191345	−	0.350422i	−0.955685	+	0.294392i	$0.904883\pi$
$488$	−0.981752	+	13.7267i	−0.0444418	+	0.621378i
$489$	−0.982694	−	1.67030i	−0.0444389	−	0.0755334i
$490$	10.1402	−	11.3026i	0.458089	−	0.510602i
$491$	−2.02447	−	0.924546i	−0.0913632	−	0.0417242i	0.369209	−	0.929346i	$-0.379629\pi$
$491$	−2.02447	−	0.924546i	−0.0913632	−	0.0417242i	−0.460572	+	0.887622i	$0.652356\pi$
$492$	5.16299	+	15.7061i	0.232766	+	0.708084i
$493$	0.402598	−	1.85072i	0.0181321	−	0.0833520i
$494$	−1.68493	−	11.7189i	−0.0758085	−	0.527259i
$495$	2.28246	−	7.11940i	0.102589	−	0.319993i
$496$	−3.37459	+	2.16872i	−0.151524	+	0.0973784i
$497$	−0.416112	−	5.81801i	−0.0186652	−	0.260973i
$498$	8.14696	+	11.8270i	0.365074	+	0.529983i
$499$	−9.11122	+	14.1773i	−0.407874	+	0.634664i	−0.983044	−	0.183369i	$-0.941300\pi$
$499$	−9.11122	+	14.1773i	−0.407874	+	0.634664i	0.575170	+	0.818034i	$0.304936\pi$
$500$	6.22838	+	9.28479i	0.278542	+	0.415228i
$501$	12.6393	−	18.0609i	0.564680	−	0.806904i
$502$	−10.5503	−	19.3214i	−0.470883	−	0.862357i
$503$	11.3126	−	30.3302i	0.504403	−	1.35236i	−0.396379	−	0.918087i	$-0.629733\pi$
$503$	11.3126	−	30.3302i	0.504403	−	1.35236i	0.900782	−	0.434271i	$-0.142994\pi$
$504$	0.469998	+	1.28918i	0.0209354	+	0.0574245i
$505$	29.5473	−	21.3339i	1.31484	−	0.949346i
$506$	−4.97612	+	1.95115i	−0.221216	+	0.0867392i
$507$	−16.0351	−	9.59445i	−0.712142	−	0.426105i
$508$	−2.73392	−	3.65209i	−0.121298	−	0.162036i
$509$	8.25495	+	18.0758i	0.365894	+	0.801196i	0.999618	+	0.0276370i	$0.00879824\pi$
$509$	8.25495	+	18.0758i	0.365894	+	0.801196i	−0.633724	+	0.773559i	$0.718474\pi$
$510$	2.13268	−	10.5510i	0.0944367	−	0.467206i
$511$	−0.307953	−	0.355397i	−0.0136230	−	0.0157218i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	−23.9693	+	33.7170i	−1.05827	+	1.48864i
$514$	−11.0716	−	5.05622i	−0.488346	−	0.223020i
$515$	24.6091	−	20.5918i	1.08441	−	0.907385i
$516$	−3.23676	+	3.45083i	−0.142490	+	0.151914i
$517$	4.78129	−	6.38705i	0.210281	−	0.280902i
$518$	−3.04542	+	4.06820i	−0.133808	+	0.178746i
$519$	−8.81177	+	9.39455i	−0.386794	+	0.412375i
$520$	−3.31221	−	0.294375i	−0.145250	−	0.0129092i
$521$	13.1070	+	5.98575i	0.574226	+	0.262240i	0.681292	−	0.732012i	$-0.261418\pi$
$521$	13.1070	+	5.98575i	0.574226	+	0.262240i	−0.107066	+	0.994252i	$0.534146\pi$
$522$	1.32730	+	1.55489i	0.0580943	+	0.0680558i
$523$	4.90927	−	8.99066i	0.214668	−	0.393134i	−0.748050	−	0.663642i	$-0.769010\pi$
$523$	4.90927	−	8.99066i	0.214668	−	0.393134i	0.962718	+	0.270508i	$0.0871916\pi$
$524$	6.16203	+	7.11136i	0.269189	+	0.310661i
$525$	−1.39350	+	3.70793i	−0.0608174	+	0.161827i
$526$	−5.20980	−	11.4079i	−0.227158	−	0.497407i
$527$	6.68138	+	8.92528i	0.291046	+	0.388791i
$528$	−1.65650	−	0.991152i	−0.0720897	−	0.0431343i
$529$	−15.6332	−	16.8702i	−0.679704	−	0.733486i
$530$	−13.7481	−	19.0410i	−0.597179	−	0.827089i
$531$	4.27093	−	1.55706i	0.185342	−	0.0675707i
$532$	−1.27257	+	3.41189i	−0.0551729	+	0.147924i
$533$	−6.80285	−	12.4585i	−0.294664	−	0.539637i
$534$	−3.77454	+	5.39365i	−0.163340	+	0.233406i
$535$	23.3749	−	2.95039i	1.01058	−	0.127556i
$536$	1.49791	−	2.33080i	0.0647000	−	0.100675i
$537$	1.45320	+	2.10964i	0.0627104	+	0.0910375i
$538$	1.54970	+	21.6676i	0.0668121	+	0.934155i
$539$	−6.36692	+	4.09177i	−0.274243	+	0.176245i
$540$	7.67317	+	8.72482i	0.330200	+	0.375457i
$541$	5.53521	+	38.4983i	0.237977	+	1.65517i	0.661990	+	0.749513i	$0.269712\pi$
$541$	5.53521	+	38.4983i	0.237977	+	1.65517i	−0.424012	+	0.905656i	$0.639379\pi$
$542$	1.70846	−	7.85368i	0.0733848	−	0.337345i
$543$	−0.283028	−	0.860985i	−0.0121459	−	0.0369484i
$544$	−2.52819	−	1.15458i	−0.108395	−	0.0495024i
$545$	9.40377	−	0.509777i	0.402813	−	0.0218364i
$546$	−0.597408	−	1.01542i	−0.0255667	−	0.0434560i
$547$	0.570337	−	7.97435i	0.0243858	−	0.340959i	−0.970582	−	0.240769i	$-0.922600\pi$
$547$	0.570337	−	7.97435i	0.0243858	−	0.340959i	0.994968	−	0.100190i	$-0.0319450\pi$
$548$	5.33723	+	9.77441i	0.227995	+	0.417542i
$549$	−24.9853	+	32.8665i	−1.06635	+	1.40271i
$550$	−1.76622	−	5.28521i	−0.0753118	−	0.225362i
$551$			5.42533i			0.231127i
$552$	1.36864	−	8.19310i	0.0582533	−	0.348721i
$553$	−1.03694	+	1.03694i	−0.0440954	+	0.0440954i
$554$	−3.18618	+	22.1604i	−0.135368	+	0.941504i
$555$	−11.5125	+	41.4617i	−0.488679	+	1.75995i
$556$	4.98712	+	1.46435i	0.211501	+	0.0621023i
$557$	0.144410	+	0.0103284i	0.00611883	+	0.000437628i	0.0743983	−	0.997229i	$-0.476296\pi$
$557$	0.144410	+	0.0103284i	0.00611883	+	0.000437628i	−0.0682794	+	0.997666i	$0.521751\pi$
$558$	−12.0338	−	0.0890735i	−0.509433	−	0.00377078i
$559$	2.19617	−	3.41731i	0.0928881	−	0.144537i
$560$	0.850740	+	0.567700i	0.0359503	+	0.0239897i
$561$	−2.41930	+	4.78878i	−0.102143	+	0.202182i
$562$	16.3556	+	3.55795i	0.689921	+	0.150083i
$563$	−4.76743	+	6.36855i	−0.200923	+	0.268402i	−0.889674	−	0.456596i	$-0.849069\pi$
$563$	−4.76743	+	6.36855i	−0.200923	+	0.268402i	0.688751	+	0.724998i	$0.258159\pi$
$564$	4.70256	+	11.4729i	0.198013	+	0.483096i
$565$	−6.71280	−	15.3961i	−0.282409	−	0.647719i
$566$	−6.69590	−	5.80203i	−0.281450	−	0.243878i
$567$	−0.934481	+	4.00907i	−0.0392445	+	0.168365i
$568$	−12.4610	+	2.71072i	−0.522852	+	0.113739i
$569$	7.96675	−	2.33925i	0.333984	−	0.0980665i	−0.110441	−	0.993883i	$-0.535226\pi$
$569$	7.96675	−	2.33925i	0.333984	−	0.0980665i	0.444425	+	0.895816i	$0.353408\pi$
$570$	0.454975	+	30.8310i	0.0190568	+	1.29137i
$571$	31.5177	+	9.25443i	1.31897	+	0.387286i	0.864122	−	0.503282i	$-0.167874\pi$
$571$	31.5177	+	9.25443i	1.31897	+	0.387286i	0.454852	+	0.890567i	$0.349692\pi$
$572$	1.55289	+	0.579196i	0.0649294	+	0.0242174i
$573$	2.48245	−	3.05731i	0.103706	−	0.127721i
$574$			4.36594i			0.182231i
$575$	18.3990	−	15.3779i	0.767289	−	0.641301i
$576$	2.64361	−	1.41822i	0.110150	−	0.0590924i
$577$	9.75331	−	7.30124i	0.406036	−	0.303955i	−0.376669	−	0.926348i	$-0.622931\pi$
$577$	9.75331	−	7.30124i	0.406036	−	0.303955i	0.782705	+	0.622393i	$0.213840\pi$
$578$	3.24135	−	8.69040i	0.134822	−	0.361473i
$579$	1.09884	−	27.8745i	0.0456664	−	1.15842i
$580$	1.48315	+	0.349527i	0.0615843	+	0.0145133i
$581$	1.06848	+	3.63890i	0.0443279	+	0.150967i
$582$	11.0426	−	5.47651i	0.457730	−	0.227008i
$583$	4.09072	+	10.9676i	0.169420	+	0.454233i
$584$	−0.673279	+	0.777005i	−0.0278605	+	0.0321527i
$585$	−7.83629	−	6.17325i	−0.323991	−	0.255233i
$586$	−2.66896	−	18.5630i	−0.110254	−	0.766830i
$587$	1.61565	+	1.20946i	0.0666850	+	0.0499198i	0.632100	−	0.774887i	$-0.282193\pi$
$587$	1.61565	+	1.20946i	0.0666850	+	0.0499198i	−0.565415	+	0.824806i	$0.691284\pi$
$588$	−0.376308	−	11.7560i	−0.0155187	−	0.484808i
$589$	−24.1358	−	20.9138i	−0.994500	−	0.861739i
$590$	1.88074	−	2.81843i	0.0774288	−	0.116033i
$591$	8.71618	−	25.8680i	0.358536	−	1.06407i
$592$	9.75136	+	5.32464i	0.400778	+	0.218842i
$593$	0.440196	−	6.15474i	0.0180767	−	0.252745i	−0.980376	−	0.197137i	$-0.936836\pi$
$593$	0.440196	−	6.15474i	0.0180767	−	0.252745i	0.998453	−	0.0556082i	$-0.0177098\pi$
$594$	−2.53456	−	5.20704i	−0.103994	−	0.213647i
$595$	1.40513	−	2.47104i	0.0576049	−	0.101303i
$596$	−4.09501	−	0.588773i	−0.167738	−	0.0241171i
$597$	−20.8589	−	12.4808i	−0.853699	−	0.510804i
$598$	0.118958	+	7.13091i	0.00486455	+	0.291605i
$599$	33.0192			1.34913			0.674565	−	0.738215i	$-0.264331\pi$
$599$	33.0192			1.34913			0.674565	+	0.738215i	$0.264331\pi$
$600$	8.45774	+	1.86191i	0.345286	+	0.0760122i
$601$	5.68233	+	12.4426i	0.231787	+	0.507543i	0.989410	−	0.145150i	$-0.0463665\pi$
$601$	5.68233	+	12.4426i	0.231787	+	0.507543i	−0.757623	+	0.652693i	$0.773639\pi$
$602$	−1.09658	+	0.598779i	−0.0446933	+	0.0244044i
$603$	7.58610	−	3.39682i	0.308930	−	0.138329i
$604$	0.822703	+	2.80187i	0.0334753	+	0.114006i
$605$	−1.18108	−	21.7873i	−0.0480179	−	0.885779i
$606$	5.11503	−	27.7623i	0.207784	−	1.12777i
$607$	−9.30793	+	0.665716i	−0.377797	+	0.0270206i	−0.258947	−	0.965892i	$-0.583375\pi$
$607$	−9.30793	+	0.665716i	−0.377797	+	0.0270206i	−0.118850	+	0.992912i	$0.537921\pi$
$608$	7.77946	+	1.69232i	0.315499	+	0.0686326i
$609$	0.204751	+	0.499533i	0.00829691	+	0.0202421i
$610$	−0.530580	+	30.7676i	−0.0214826	+	1.24575i
$611$	−5.75553	−	8.95577i	−0.232844	−	0.362312i
$612$	−4.45585	−	7.04759i	−0.180117	−	0.284882i
$613$	12.2307	+	32.7917i	0.493992	+	1.32444i	0.909821	+	0.415001i	$0.136219\pi$
$613$	12.2307	+	32.7917i	0.493992	+	1.32444i	−0.415829	+	0.909443i	$0.636509\pi$
$614$	−16.2640	−	10.4522i	−0.656362	−	0.421818i
$615$	13.4289	+	34.4434i	0.541507	+	1.38889i
$616$	−0.333826	−	0.385256i	−0.0134502	−	0.0155224i
$617$	32.1715	−	17.5670i	1.29517	−	0.707219i	0.324106	−	0.946021i	$-0.394936\pi$
$617$	32.1715	−	17.5670i	1.29517	−	0.707219i	0.971068	+	0.238802i	$0.0767546\pi$
$618$	2.74834	−	24.7028i	0.110554	−	0.993691i
$619$	−30.8875	−	4.44095i	−1.24147	−	0.178497i	−0.509885	−	0.860243i	$-0.670312\pi$
$619$	−30.8875	−	4.44095i	−1.24147	−	0.178497i	−0.731589	+	0.681746i	$0.761221\pi$
$620$	−7.27226	+	5.25075i	−0.292061	+	0.210875i
$621$	16.8789	−	18.3331i	0.677325	−	0.735684i
$622$	3.37917	+	3.37917i	0.135492	+	0.135492i
$623$	−1.39171	+	1.04182i	−0.0557579	+	0.0417398i
$624$	−2.01155	+	1.60876i	−0.0805263	+	0.0644021i
$625$	15.0305	+	19.9771i	0.601219	+	0.799084i
$626$	20.9954	−	18.1926i	0.839145	−	0.727123i
$627$	3.85582	−	14.8770i	0.153987	−	0.594129i
$628$	−21.0894	+	4.58771i	−0.841557	+	0.183070i
$629$	12.8279	−	28.0891i	0.511481	−	1.11999i
$630$	1.20545	+	2.82157i	0.0480262	+	0.112414i
$631$	23.9756	−	15.4082i	0.954455	−	0.613391i	0.0319967	−	0.999488i	$-0.489813\pi$
$631$	23.9756	−	15.4082i	0.954455	−	0.613391i	0.922458	+	0.386097i	$0.126177\pi$
$632$	2.56664	+	1.92136i	0.102095	+	0.0764277i
$633$	3.95159	+	1.65396i	0.157062	+	0.0657391i
$634$	16.1497	+	25.1294i	0.641386	+	0.998017i
$635$	−6.54632	−	7.82345i	−0.259783	−	0.310464i
$636$	−17.8907	−	3.29625i	−0.709412	−	0.130705i
$637$	2.14661	+	9.86783i	0.0850520	+	0.390978i
$638$	−0.666582	−	0.363982i	−0.0263902	−	0.0144102i
$639$	−35.7452	−	13.6345i	−1.41406	−	0.539373i
$640$	0.963829	−	2.01768i	0.0380987	−	0.0797558i
$641$	35.1065	−	16.0326i	1.38662	−	0.633249i	0.424391	−	0.905479i	$-0.360488\pi$
$641$	35.1065	−	16.0326i	1.38662	−	0.633249i	0.962232	+	0.272230i	$0.0877611\pi$
$642$	11.5037	−	14.1675i	0.454013	−	0.559148i
$643$	3.98881	−	3.98881i	0.157303	−	0.157303i	−0.624067	−	0.781371i	$-0.714521\pi$
$643$	3.98881	−	3.98881i	0.157303	−	0.157303i	0.781371	+	0.624067i	$0.214521\pi$
$644$	1.01901	−	1.94252i	0.0401547	−	0.0765462i
$645$	−6.80931	+	8.09674i	−0.268116	+	0.318809i
$646$	3.14908	−	21.9023i	0.123899	−	0.861735i
$647$	−18.3692	−	6.85135i	−0.722167	−	0.269354i	−0.0386128	−	0.999254i	$-0.512294\pi$
$647$	−18.3692	−	6.85135i	−0.722167	−	0.269354i	−0.683554	+	0.729900i	$0.739567\pi$
$648$	8.96658	+	0.774870i	0.352241	+	0.0304398i
$649$	−1.27632	+	1.10594i	−0.0500999	+	0.0434118i
$650$	−7.43110	−	0.256371i	−0.291472	−	0.0100557i
$651$	−3.01157	−	1.01474i	−0.118033	−	0.0397709i
$652$	−1.04832	+	0.391003i	−0.0410554	+	0.0153129i
$653$	−22.8708	+	1.63575i	−0.895005	+	0.0640120i	−0.511259	−	0.859427i	$-0.670821\pi$
$653$	−22.8708	+	1.63575i	−0.895005	+	0.0640120i	−0.383746	+	0.923439i	$0.625366\pi$
$654$	4.99055	−	5.32061i	0.195146	−	0.208052i
$655$	14.6193	+	15.1323i	0.571222	+	0.591269i
$656$	9.44812	−	1.35843i	0.368887	−	0.0530380i
$657$	−2.96579	+	0.847040i	−0.115706	+	0.0330462i
$658$	0.233589	+	3.26600i	0.00910624	+	0.127322i
$659$	−15.5989	+	34.1569i	−0.607648	+	1.33056i	0.316523	+	0.948585i	$0.397484\pi$
$659$	−15.5989	+	34.1569i	−0.607648	+	1.33056i	−0.924171	+	0.381979i	$0.875243\pi$
$660$	−3.81858	−	2.01253i	−0.148638	−	0.0783377i
$661$	3.91699	−	1.15013i	0.152353	−	0.0447350i	−0.204667	−	0.978832i	$-0.565611\pi$
$661$	3.91699	−	1.15013i	0.152353	−	0.0447350i	0.357020	+	0.934097i	$0.383793\pi$
$662$	22.1327	+	1.58296i	0.860213	+	0.0615237i
$663$	4.85877	+	5.25757i	0.188699	+	0.204187i
$664$	7.54231	−	3.44446i	0.292698	−	0.133671i
$665$	−2.42841	+	7.77207i	−0.0941696	+	0.301388i
$666$	15.7570	+	29.3715i	0.610570	+	1.13812i
$667$	0.411083	−	3.24218i	0.0159172	−	0.125538i
$668$	−8.99952	−	8.99952i	−0.348202	−	0.348202i
$669$	31.7340	−	3.29300i	1.22691	−	0.127315i
$670$	3.06241	−	5.38549i	0.118311	−	0.208060i
$671$	4.32108	−	14.7163i	0.166814	−	0.568115i
$672$	0.780155	−	0.137776i	0.0300951	−	0.00531483i
$673$	21.5950	−	39.5482i	0.832425	−	1.52447i	−0.0188925	−	0.999822i	$-0.506014\pi$
$673$	21.5950	−	39.5482i	0.832425	−	1.52447i	0.851317	−	0.524651i	$-0.175804\pi$
$674$	7.92455	+	5.09280i	0.305242	+	0.196167i
$675$	18.1886	+	18.5519i	0.700080	+	0.714065i
$676$	−7.06498	+	8.15342i	−0.271730	+	0.313593i
$677$	2.24871	−	10.3371i	0.0864248	−	0.397288i	−0.913530	−	0.406771i	$-0.866655\pi$
$677$	2.24871	−	10.3371i	0.0864248	−	0.397288i	0.999955	+	0.00948253i	$0.00301843\pi$
$678$	−12.0012	−	5.02317i	−0.460903	−	0.192914i
$679$	3.22187	−	0.463235i	0.123644	−	0.0177773i
$680$	−5.78466	−	2.27193i	−0.221832	−	0.0871247i
$681$	−12.7021	−	6.41713i	−0.486747	−	0.245905i
$682$	4.18883	−	1.56235i	0.160399	−	0.0598256i
$683$	−8.35216	−	38.3943i	−0.319586	−	1.46912i	−0.804185	−	0.594379i	$-0.797398\pi$
$683$	−8.35216	−	38.3943i	−0.319586	−	1.46912i	0.484599	−	0.874737i	$-0.338966\pi$
$684$	16.7632	+	17.0132i	0.640958	+	0.650517i
$685$	13.1000	+	21.1782i	0.500525	+	0.809177i
$686$	1.77712	−	6.05230i	0.0678506	−	0.231078i
$687$	1.07502	−	9.66251i	0.0410144	−	0.368648i
$688$	1.63698	+	2.18675i	0.0624094	+	0.0833692i
$689$	15.6191			0.595041
$690$	2.06421	−	18.4591i	0.0785830	−	0.702727i
$691$	−4.84651			−0.184370			−0.0921849	−	0.995742i	$-0.529385\pi$
$691$	−4.84651			−0.184370			−0.0921849	+	0.995742i	$0.529385\pi$
$692$	4.45653	+	5.95323i	0.169412	+	0.226308i
$693$	−0.206432	−	1.51530i	−0.00784169	−	0.0575616i
$694$	−7.15715	+	24.3750i	−0.271682	+	0.925262i
$695$	11.3124	+	2.66595i	0.429105	+	0.101125i
$696$	1.01731	−	0.598517i	0.0385609	−	0.0226867i
$697$	−5.63929	−	25.9234i	−0.213603	−	0.981918i
$698$	−17.7256	+	6.61129i	−0.670922	+	0.250241i
$699$	10.4396	−	20.6642i	0.394862	−	0.781593i
$700$	1.96824	+	1.16458i	0.0743924	+	0.0440170i
$701$	−13.7668	+	1.97937i	−0.519965	+	0.0747597i	−0.397301	−	0.917688i	$-0.630053\pi$
$701$	−13.7668	+	1.97937i	−0.519965	+	0.0747597i	−0.122665	+	0.992448i	$0.539144\pi$
$702$	−7.69164	+	0.740652i	−0.290302	+	0.0279541i
$703$	−18.8023	+	86.4328i	−0.709143	+	3.25988i
$704$	−0.729845	+	0.842286i	−0.0275071	+	0.0317449i
$705$	11.8885	+	25.0474i	0.447747	+	0.943338i
$706$	−14.8473	−	9.54181i	−0.558787	−	0.359111i
$707$	3.57268	−	6.54287i	0.134364	−	0.246070i
$708$	−0.456440	−	2.58459i	−0.0171541	−	0.0971347i
$709$	2.06020	−	7.01639i	0.0773723	−	0.263506i	−0.911718	−	0.410817i	$-0.865244\pi$
$709$	2.06020	−	7.01639i	0.0773723	−	0.263506i	0.989090	+	0.147311i	$0.0470618\pi$
$710$	−27.4947	+	7.56075i	−1.03186	+	0.283750i
$711$	3.29449	+	9.03658i	0.123553	+	0.338898i
$712$	2.68758	+	2.68758i	0.100721	+	0.100721i
$713$	12.8389	+	14.3269i	0.480822	+	0.536547i
$714$	−0.536639	−	2.13548i	−0.0200832	−	0.0799184i
$715$	3.53737	+	1.10526i	0.132290	+	0.0413345i
$716$	1.34535	−	0.614401i	0.0502781	−	0.0229612i
$717$	5.47224	−	5.05716i	0.204365	−	0.188863i
$718$	24.5720	+	1.75743i	0.917021	+	0.0655866i
$719$	28.8029	−	8.45728i	1.07417	−	0.315403i	0.303623	−	0.952792i	$-0.401804\pi$
$719$	28.8029	−	8.45728i	1.07417	−	0.315403i	0.770542	+	0.637389i	$0.219986\pi$
$720$	5.73096	−	3.48656i	0.213580	−	0.129937i
$721$	2.72664	−	5.97051i	0.101545	−	0.222353i
$722$	3.16631	+	44.2709i	0.117838	+	1.64759i
$723$	−1.26720	−	39.5876i	−0.0471275	−	1.47228i
$724$	−0.517933	+	0.0744676i	−0.0192488	+	0.00276757i
$725$	3.35386	+	0.600901i	0.124559	+	0.0223169i
$726$	−12.3271	−	11.5624i	−0.457503	−	0.429122i
$727$	30.8570	−	2.20694i	1.14442	−	0.0818508i	0.513779	−	0.857923i	$-0.328245\pi$
$727$	30.8570	−	2.20694i	1.14442	−	0.0818508i	0.630644	+	0.776072i	$0.282791\pi$
$728$	−0.637304	+	0.237702i	−0.0236201	+	0.00880983i
$729$	21.2500	+	16.6564i	0.787038	+	0.616905i
$730$	−1.40924	+	1.81638i	−0.0521584	+	0.0672273i
$731$	5.73769	−	4.97174i	0.212216	−	0.183886i
$732$	16.1776	+	17.5055i	0.597943	+	0.647021i
$733$	26.6520	+	9.94069i	0.984415	+	0.367168i	0.789566	−	0.613665i	$-0.210306\pi$
$733$	26.6520	+	9.94069i	0.984415	+	0.367168i	0.194849	+	0.980833i	$0.437578\pi$
$734$	4.75763	−	33.0900i	0.175607	−	1.22138i
$735$	−2.26315	−	26.2031i	−0.0834775	−	0.966515i
$736$	−4.52078	−	1.60079i	−0.166638	−	0.0590059i
$737$	−2.18346	+	2.18346i	−0.0804287	+	0.0804287i
$738$	25.9593	+	12.0882i	0.955575	+	0.444974i
$739$	−33.5796	+	15.3353i	−1.23524	+	0.564117i	−0.922602	−	0.385753i	$-0.873942\pi$
$739$	−33.5796	+	15.3353i	−1.23524	+	0.564117i	−0.312643	+	0.949871i	$0.601214\pi$
$740$	22.4172	+	10.7085i	0.824073	+	0.393653i
$741$	−16.8011	−	11.7576i	−0.617203	−	0.431926i
$742$	−4.21639	−	2.30232i	−0.154788	−	0.0845208i
$743$	−2.33044	−	10.7129i	−0.0854956	−	0.393017i	0.914436	−	0.404731i	$-0.132635\pi$
$743$	−2.33044	−	10.7129i	−0.0854956	−	0.393017i	−0.999931	+	0.0117140i	$0.996271\pi$
$744$	−1.25892	+	6.83292i	−0.0461544	+	0.250507i
$745$	−9.21455	−	0.818950i	−0.337595	−	0.0300040i
$746$	9.66471	+	15.0386i	0.353850	+	0.550602i
$747$	24.5947	+	3.72220i	0.899875	+	0.136188i
$748$	2.47976	+	1.85632i	0.0906689	+	0.0678739i
$749$	4.05427	−	2.60552i	0.148140	−	0.0952036i
$750$	19.1097	+	3.13354i	0.697788	+	0.114421i
$751$	−3.76965	+	8.25438i	−0.137556	+	0.301206i	−0.965856	−	0.259079i	$-0.916581\pi$
$751$	−3.76965	+	8.25438i	−0.137556	+	0.301206i	0.828300	+	0.560285i	$0.189308\pi$
$752$	6.99511	−	1.52169i	0.255085	−	0.0554904i
$753$	−36.9102	−	9.56640i	−1.34508	−	0.348619i
$754$	−0.765871	+	0.663631i	−0.0278914	+	0.0241680i
$755$	2.17606	+	6.15641i	0.0791949	+	0.224055i
$756$	2.18554	+	0.933839i	0.0794871	+	0.0339634i
$757$	0.980312	−	0.733852i	0.0356300	−	0.0266723i	−0.581314	−	0.813679i	$-0.697461\pi$
$757$	0.980312	−	0.733852i	0.0356300	−	0.0266723i	0.616944	+	0.787007i	$0.288370\pi$
$758$	12.6115	+	12.6115i	0.458069	+	0.458069i
$759$	−3.43149	+	8.59833i	−0.124555	+	0.312099i
$760$	17.5747	+	2.83697i	0.637503	+	0.102908i
$761$	−25.8904	−	3.72247i	−0.938525	−	0.134940i	−0.343957	−	0.938985i	$-0.611768\pi$
$761$	−25.8904	−	3.72247i	−0.938525	−	0.134940i	−0.594568	+	0.804046i	$0.702677\pi$
$762$	−7.85322	−	0.873720i	−0.284492	−	0.0316515i
$763$	1.69075	−	0.923219i	0.0612092	−	0.0334228i
$764$	−1.48898	−	1.71838i	−0.0538695	−	0.0621688i
$765$	−10.8020	−	15.1965i	−0.390548	−	0.549429i
$766$	0.262013	+	0.168385i	0.00946690	+	0.00608401i
$767$	0.787487	+	2.11133i	0.0284345	+	0.0762358i
$768$	−0.540895	−	1.64543i	−0.0195179	−	0.0593743i
$769$	−13.7309	−	21.3657i	−0.495149	−	0.770467i	0.500291	−	0.865857i	$-0.333226\pi$
$769$	−13.7309	−	21.3657i	−0.495149	−	0.770467i	−0.995440	+	0.0953902i	$0.969590\pi$
$770$	−0.791994	−	0.819789i	−0.0285415	−	0.0295431i
$771$	−19.5066	+	7.99545i	−0.702513	+	0.287949i
$772$	−15.7378	−	3.42354i	−0.566414	−	0.123216i
$773$	15.8666	−	1.13480i	0.570682	−	0.0408160i	0.216983	−	0.976175i	$-0.430378\pi$
$773$	15.8666	−	1.13480i	0.570682	−	0.0408160i	0.353699	+	0.935359i	$0.384924\pi$
$774$	0.524092	+	8.17800i	0.0188381	+	0.293952i
$775$	−15.6019	+	12.6041i	−0.560436	+	0.452751i
$776$	−2.00493	−	6.82816i	−0.0719728	−	0.245117i
$777$	1.53075	+	8.66783i	0.0549153	+	0.310957i
$778$	−10.0851	+	5.50688i	−0.361569	+	0.197431i
$779$	31.5690	+	69.1264i	1.13108	+	2.47671i
$780$	−4.29663	+	3.83551i	−0.153844	+	0.137333i
$781$	14.2126			0.508568
$782$	−3.54145	+	12.8502i	−0.126642	+	0.459523i
$783$	3.53706	+	0.165665i	0.126404	+	0.00592037i
$784$	−6.72167	−	0.966430i	−0.240060	−	0.0345154i
$785$	−46.5328	+	12.7960i	−1.66083	+	0.456710i
$786$	16.2854	+	0.641990i	0.580881	+	0.0228990i
$787$	1.30180	−	18.2016i	0.0464042	−	0.648816i	−0.920021	−	0.391868i	$-0.871829\pi$
$787$	1.30180	−	18.2016i	0.0464042	−	0.648816i	0.966425	−	0.256947i	$-0.0827166\pi$
$788$	−13.8322	−	7.55294i	−0.492751	−	0.269062i
$789$	−20.5849	−	6.93602i	−0.732840	−	0.246929i
$790$	5.96333	+	3.97933i	0.212166	+	0.141578i
$791$	−2.59648	−	2.24986i	−0.0923202	−	0.0799959i
$792$	−3.21496	+	0.918206i	−0.114239	+	0.0326270i
$793$	−16.3832	−	12.2643i	−0.581785	−	0.435519i
$794$	−4.34361	−	30.2105i	−0.154149	−	1.07213i
$795$	−40.3451	−	5.19436i	−1.43089	−	0.184225i
$796$	−9.19035	+	10.6062i	−0.325743	+	0.375928i
$797$	1.10254	+	2.95603i	0.0390541	+	0.104708i	0.955013	−	0.296564i	$-0.0958409\pi$
$797$	1.10254	+	2.95603i	0.0390541	+	0.104708i	−0.915959	+	0.401272i	$0.868568\pi$
$798$	2.80234	+	5.65051i	0.0992017	+	0.200026i
$799$	−5.60551	−	19.0906i	−0.198309	−	0.675378i
$800$	1.90781	−	4.62172i	0.0674512	−	0.163402i
$801$	2.34123	+	11.1595i	0.0827233	+	0.394302i
$802$	12.7901	−	34.2916i	0.451634	−	1.21088i
$803$	0.917301	−	0.686683i	0.0323708	−	0.0242325i
$804$	−1.16957	−	4.65416i	−0.0412477	−	0.164140i
$805$	2.04012	−	4.46059i	0.0719047	−	0.157215i
$806$		−	5.96535i		−	0.210121i
$807$	29.2090	+	23.7169i	1.02820	+	0.834875i
$808$	−15.2707	−	5.69568i	−0.537222	−	0.200373i
$809$	−23.9315	−	7.02691i	−0.841386	−	0.247053i	−0.167485	−	0.985875i	$-0.553564\pi$
$809$	−23.9315	−	7.02691i	−0.841386	−	0.247053i	−0.673901	+	0.738822i	$0.735383\pi$
$810$	20.1143	+	0.644815i	0.706744	+	0.0226565i
$811$	−48.7971	+	14.3281i	−1.71350	+	0.503128i	−0.983590	−	0.180418i	$-0.942255\pi$
$811$	−48.7971	+	14.3281i	−1.71350	+	0.503128i	−0.729907	+	0.683546i	$0.760437\pi$
$812$	0.304569	−	0.0662549i	0.0106883	−	0.00232509i
$813$	−7.89715	−	11.4644i	−0.276965	−	0.402074i
$814$	−9.35813	−	8.10887i	−0.328002	−	0.284216i
$815$	−2.29335	+	0.999916i	−0.0803326	+	0.0350255i
$816$	−4.45432	+	1.82576i	−0.155932	+	0.0639143i
$817$	−13.0327	+	17.4096i	−0.455956	+	0.609085i
$818$	−25.0945	−	5.45897i	−0.877407	−	0.190868i
$819$	−1.99067	−	0.448501i	−0.0695598	−	0.0156719i
$820$	20.9312	−	4.17669i	0.730951	−	0.145856i
$821$	4.07901	−	6.34707i	0.142358	−	0.221514i	−0.762751	−	0.646692i	$-0.776152\pi$
$821$	4.07901	−	6.34707i	0.142358	−	0.221514i	0.905110	+	0.425178i	$0.139788\pi$
$822$	18.6723	+	4.83949i	0.651271	+	0.168797i
$823$	30.5309	+	2.18361i	1.06424	+	0.0761160i	0.592460	−	0.805600i	$-0.298157\pi$
$823$	30.5309	+	2.18361i	1.06424	+	0.0761160i	0.471781	+	0.881716i	$0.343611\pi$
$824$	−13.7689	−	4.04290i	−0.479661	−	0.140841i
$825$	−8.76967	−	4.03136i	−0.305321	−	0.140354i
$826$	0.0986367	−	0.686034i	0.00343201	−	0.0238702i
$827$	−2.11492	+	2.11492i	−0.0735429	+	0.0735429i	−0.742921	−	0.669379i	$-0.766560\pi$
$827$	−2.11492	+	2.11492i	−0.0735429	+	0.0735429i	0.669379	+	0.742921i	$0.266560\pi$
$828$	−8.72860	−	11.4373i	−0.303340	−	0.397473i
$829$			46.0028i			1.59774i	0.601502	+	0.798871i	$0.294569\pi$
$829$			46.0028i			1.59774i	−0.601502	+	0.798871i	$0.705431\pi$
$830$	16.4235	−	8.60366i	0.570067	−	0.298637i
$831$	24.2198	+	30.2837i	0.840177	+	1.05053i
$832$	0.712693	+	1.30520i	0.0247082	+	0.0452497i
$833$	−1.34646	+	18.8259i	−0.0466519	+	0.652279i
$834$	7.75933	−	4.56508i	0.268683	−	0.158076i
$835$	−21.1833	−	19.0048i	−0.733080	−	0.657687i
$836$	−8.07118	−	3.68599i	−0.279148	−	0.127482i
$837$	−14.3718	+	15.0968i	−0.496763	+	0.521822i
$838$	4.45671	−	20.4872i	0.153954	−	0.707717i
$839$	−5.72915	−	39.8471i	−0.197792	−	1.37568i	−0.810673	−	0.585500i	$-0.800898\pi$
$839$	−5.72915	−	39.8471i	−0.197792	−	1.37568i	0.612880	−	0.790176i	$-0.290011\pi$
$840$	1.72525	−	0.402055i	0.0595267	−	0.0138722i
$841$	−24.0057	+	15.4275i	−0.827782	+	0.531984i
$842$	1.34447	+	18.7982i	0.0463336	+	0.647828i
$843$	23.8751	−	16.4462i	0.822302	−	0.566436i
$844$	1.33713	−	2.08062i	0.0460259	−	0.0716178i
$845$	−14.7877	+	19.0600i	−0.508713	+	0.655684i
$846$	20.0660	+	7.65387i	0.689882	+	0.263145i
$847$	−2.13898	−	3.91724i	−0.0734961	−	0.134598i
$848$	−3.67044	+	9.84083i	−0.126043	+	0.337935i
$849$	−15.2639	+	1.58392i	−0.523856	+	0.0543600i
$850$	−13.1909	−	4.37258i	−0.452445	−	0.149978i
$851$	17.7854	−	50.2277i	0.609675	−	1.72178i
$852$	−11.3410	+	18.9540i	−0.388536	+	0.649355i
$853$	−21.0521	−	28.1224i	−0.720812	−	0.962892i	−0.999996	−	0.00265426i	$-0.999155\pi$
$853$	−21.0521	−	28.1224i	−0.720812	−	0.962892i	0.279185	−	0.960237i	$-0.409936\pi$
$854$	2.61484	+	5.72570i	0.0894780	+	0.195930i
$855$	39.4880	+	35.9580i	1.35046	+	1.22974i
$856$	−6.89994	−	7.96295i	−0.235835	−	0.272168i
$857$	2.13358	−	3.90736i	0.0728817	−	0.133473i	−0.838697	−	0.544598i	$-0.816682\pi$
$857$	2.13358	−	3.90736i	0.0728817	−	0.133473i	0.911579	+	0.411125i	$0.134864\pi$
$858$	2.57177	−	1.27545i	0.0877987	−	0.0435433i
$859$	−24.8231	−	11.3363i	−0.846952	−	0.386790i	−0.0558239	−	0.998441i	$-0.517779\pi$
$859$	−24.8231	−	11.3363i	−0.846952	−	0.386790i	−0.791128	+	0.611651i	$0.790506\pi$
$860$	3.91972	+	4.68442i	0.133661	+	0.159737i
$861$	5.51550	+	5.17335i	0.187968	+	0.176307i
$862$	−4.51688	+	6.03385i	−0.153846	+	0.205514i
$863$	−28.3368	+	37.8535i	−0.964594	+	1.28855i	−0.00713640	+	0.999975i	$0.502272\pi$
$863$	−28.3368	+	37.8535i	−0.964594	+	1.28855i	−0.957458	+	0.288573i	$0.906819\pi$
$864$	1.34086	−	5.02017i	0.0456170	−	0.170790i
$865$	10.6711	+	12.7529i	0.362827	+	0.433611i
$866$	−9.71668	−	4.43746i	−0.330186	−	0.150791i
$867$	−7.13781	−	14.3924i	−0.242413	−	0.488790i
$868$	−0.879316	+	1.61035i	−0.0298459	+	0.0546588i
$869$	−2.33998	−	2.70048i	−0.0793783	−	0.0916075i
$870$	2.19899	−	1.45950i	0.0745527	−	0.0494816i
$871$	1.71160	+	3.74787i	0.0579952	+	0.126992i
$872$	−2.52396	−	3.37161i	−0.0854720	−	0.114177i
$873$	6.16624	−	20.4394i	0.208696	−	0.691769i
$874$	2.08823	−	38.1244i	0.0706354	−	1.28958i
$875$	4.53562	+	2.36203i	0.153332	+	0.0798512i
$876$	0.183801	+	1.77125i	0.00621007	+	0.0598451i
$877$	−4.21072	+	11.2894i	−0.142186	+	0.381215i	−0.988450	−	0.151549i	$-0.951574\pi$
$877$	−4.21072	+	11.2894i	−0.142186	+	0.381215i	0.846264	+	0.532764i	$0.178847\pi$
$878$	11.9587	+	21.9007i	0.403586	+	0.739112i
$879$	−26.6132	−	18.6242i	−0.897641	−	0.628179i
$880$	−1.52764	+	1.96899i	−0.0514968	+	0.0663746i
$881$	−23.4423	+	36.4769i	−0.789791	+	1.22894i	0.179678	+	0.983726i	$0.442495\pi$
$881$	−23.4423	+	36.4769i	−0.789791	+	1.22894i	−0.969469	+	0.245214i	$0.921142\pi$
$882$	−15.2972	−	13.4547i	−0.515085	−	0.453042i
$883$	2.19248	+	30.6549i	0.0737829	+	1.03162i	0.890619	+	0.454750i	$0.150271\pi$
$883$	2.19248	+	30.6549i	0.0737829	+	1.03162i	−0.816836	+	0.576870i	$0.804274\pi$
$884$	3.47706	−	2.23457i	0.116946	−	0.0751567i
$885$	−1.33197	−	5.71559i	−0.0447737	−	0.192127i
$886$	2.01888	+	14.0416i	0.0678256	+	0.471737i
$887$	−4.35920	+	20.0389i	−0.146368	+	0.672842i	0.844224	+	0.535991i	$0.180062\pi$
$887$	−4.35920	+	20.0389i	−0.146368	+	0.672842i	−0.990592	+	0.136851i	$0.956302\pi$
$888$	18.2813	−	6.00956i	0.613482	−	0.201667i
$889$	−1.89808	−	0.866822i	−0.0636594	−	0.0290723i
$890$	6.32611	+	5.67551i	0.212052	+	0.190243i
$891$	−9.58135	−	2.96809i	−0.320987	−	0.0994347i
$892$	1.31407	−	18.3731i	0.0439982	−	0.615176i
$893$	27.3140	+	50.0219i	0.914029	+	1.67392i
$894$	−5.59611	+	4.47557i	−0.187162	+	0.149686i
$895$	2.92952	−	1.53467i	0.0979230	−	0.0512983i
$896$		−	0.457393i		−	0.0152804i
$897$	9.14945	+	8.29938i	0.305491	+	0.277108i
$898$	−5.78793	+	5.78793i	−0.193146	+	0.193146i
$899$	−0.389028	+	2.70575i	−0.0129748	+	0.0902418i
$900$	12.3740	−	8.47843i	0.412467	−	0.282614i
$901$	28.0092	+	8.22424i	0.933121	+	0.273989i
$902$	−10.6111	−	0.758924i	−0.353313	−	0.0252694i
$903$	−0.542938	+	2.09483i	−0.0180679	+	0.0697115i
$904$	−4.06094	+	6.31895i	−0.135065	+	0.210165i
$905$	−1.14742	+	0.228961i	−0.0381416	+	0.00761091i
$906$	4.51446	+	2.28071i	0.149983	+	0.0757714i
$907$	−43.4881	−	9.46026i	−1.44400	−	0.314123i	−0.578767	−	0.815493i	$-0.696466\pi$
$907$	−43.4881	−	9.46026i	−1.44400	−	0.314123i	−0.865233	+	0.501370i	$0.832830\pi$
$908$	−4.92386	+	6.57751i	−0.163404	+	0.218282i
$909$	−29.0112	−	39.3583i	−0.962239	−	1.30543i
$910$	−1.39420	+	0.607878i	−0.0462171	+	0.0201510i
$911$	−18.5256	−	16.0525i	−0.613781	−	0.531844i	0.291548	−	0.956556i	$-0.405830\pi$
$911$	−18.5256	−	16.0525i	−0.613781	−	0.531844i	−0.905328	+	0.424712i	$0.860375\pi$
$912$	11.3561	−	7.82252i	0.376037	−	0.259030i
$913$	−9.02984	+	1.96432i	−0.298844	+	0.0650096i
$914$	−18.6976	+	5.49012i	−0.618463	+	0.181597i
$915$	38.2401	+	37.1279i	1.26418	+	1.22741i
$916$	−5.38570	−	1.58139i	−0.177949	−	0.0522504i
$917$	4.03256	+	1.50407i	0.133167	+	0.0496686i
$918$	−14.1831	−	2.72185i	−0.468113	−	0.0898343i
$919$			36.2697i			1.19643i	0.801336	+	0.598214i	$0.204123\pi$
$919$			36.2697i			1.19643i	−0.801336	+	0.598214i	$0.795877\pi$
$920$	−10.2877	−	3.02703i	−0.339176	−	0.0997983i
$921$	−32.4761	+	8.16113i	−1.07012	+	0.268918i
$922$	9.55253	−	7.15093i	0.314596	−	0.235503i
$923$	6.62731	−	17.7685i	0.218140	−	0.584857i
$924$	−0.882256	−	0.0347796i	−0.0290241	−	0.00114416i
$925$	51.3491	+	21.1965i	1.68835	+	0.696937i
$926$	6.17659	+	21.0355i	0.202975	+	0.691270i
$927$	−27.9504	−	32.7431i	−0.918013	−	1.07543i
$928$	−0.238144	−	0.638488i	−0.00781745	−	0.0209594i
$929$	−2.22575	+	2.56865i	−0.0730243	+	0.0842746i	−0.791086	−	0.611705i	$-0.790484\pi$
$929$	−2.22575	+	2.56865i	−0.0730243	+	0.0842746i	0.718062	+	0.695979i	$0.245030\pi$
$930$	−1.98386	+	15.4089i	−0.0650533	+	0.505276i
$931$	−7.69414	−	53.5139i	−0.252165	−	1.75385i
$932$	−10.7005	−	8.01029i	−0.350506	−	0.262386i
$933$	8.27301	−	0.264819i	0.270846	−	0.00866978i
$934$	28.4809	+	24.6788i	0.931923	+	0.807516i
$935$	5.76146	+	3.84463i	0.188420	+	0.125733i
$936$	−0.351195	+	4.44747i	−0.0114792	+	0.145370i
$937$	43.9004	+	23.9714i	1.43416	+	0.783112i	0.993421	−	0.114522i	$-0.0365335\pi$
$937$	43.9004	+	23.9714i	1.43416	+	0.783112i	0.440742	+	0.897634i	$0.354715\pi$
$938$	0.0904056	−	1.26404i	0.00295185	−	0.0412722i
$939$	1.89539	−	48.0806i	0.0618538	−	1.56905i
$940$	15.4344	−	4.24430i	0.503416	−	0.138434i
$941$	6.76032	+	0.971988i	0.220380	+	0.0316859i	0.251620	−	0.967826i	$-0.419037\pi$
$941$	6.76032	+	0.971988i	0.220380	+	0.0316859i	−0.0312401	+	0.999512i	$0.509946\pi$
$942$	−19.1938	+	32.0784i	−0.625369	+	1.04517i
$943$	−13.6279	−	43.7020i	−0.443784	−	1.42313i
$944$	−1.51530			−0.0493189
$945$	4.99287	+	1.82053i	0.162418	+	0.0592219i
$946$	−1.26468	−	2.76926i	−0.0411182	−	0.0900364i
$947$	−46.1915	+	25.2225i	−1.50102	+	0.819620i	−0.998977	−	0.0452223i	$-0.985600\pi$
$947$	−46.1915	+	25.2225i	−1.50102	+	0.819620i	−0.502044	+	0.864842i	$0.667419\pi$
$948$	5.46856	−	0.965753i	0.177611	−	0.0313662i
$949$	−0.430749	−	1.46700i	−0.0139827	−	0.0476207i
$950$	39.5841	+	4.20713i	1.28428	+	0.136497i
$951$	50.8824	+	9.37476i	1.64997	+	0.303997i
$952$	−1.26802	+	0.0906903i	−0.0410966	+	0.00293929i
$953$	−36.0813	−	7.84901i	−1.16879	−	0.254254i	−0.414034	−	0.910262i	$-0.635880\pi$
$953$	−36.0813	−	7.84901i	−1.16879	−	0.254254i	−0.754754	+	0.656007i	$0.772244\pi$
$954$	−25.3634	+	18.6955i	−0.821172	+	0.605289i
$955$	−3.53258	−	3.65655i	−0.114312	−	0.118323i
$956$	−2.32581	−	3.61903i	−0.0752221	−	0.117048i
$957$	−1.24967	+	0.410801i	−0.0403962	+	0.0132793i
$958$	12.6417	+	33.8937i	0.408435	+	1.09506i
$959$	4.28520	+	2.75393i	0.138376	+	0.0889290i
$960$	−1.40687	−	3.60842i	−0.0454064	−	0.116461i
$961$	9.76317	+	11.2673i	0.314941	+	0.363461i
$962$	−14.5013	+	7.91830i	−0.467540	+	0.255296i
$963$	−4.26679	−	31.3202i	−0.137495	−	1.00928i
$964$	−22.6348	−	3.25440i	−0.729019	−	0.104817i
$965$	−35.5535	−	5.73916i	−1.14451	−	0.184750i
$966$	−1.24653	−	3.58908i	−0.0401066	−	0.115477i
$967$	15.8994	+	15.8994i	0.511292	+	0.511292i	0.914922	−	0.403630i	$-0.132252\pi$
$967$	15.8994	+	15.8994i	0.511292	+	0.511292i	−0.403630	+	0.914922i	$0.632252\pi$
$968$	−7.81158	+	5.84768i	−0.251074	+	0.187952i
$969$	−23.9378	−	29.9310i	−0.768992	−	0.961523i
$970$	−5.30306	−	15.0032i	−0.170271	−	0.481723i
$971$	−24.6312	+	21.3431i	−0.790454	+	0.684932i	−0.953402	−	0.301702i	$-0.902445\pi$
$971$	−24.6312	+	21.3431i	−0.790454	+	0.684932i	0.162948	+	0.986635i	$0.447900\pi$
$972$	11.6037	−	10.4093i	0.372189	−	0.333879i
$973$	2.32304	−	0.505347i	0.0744733	−	0.0162007i
$974$	−3.66018	+	8.01467i	−0.117280	+	0.256806i
$975$	−9.12924	+	9.08394i	−0.292370	+	0.290919i
$976$	11.5771	−	7.44017i	0.370575	−	0.238154i
$977$	18.2926	+	13.6936i	0.585231	+	0.438099i	0.850425	−	0.526097i	$-0.176345\pi$
$977$	18.2926	+	13.6936i	0.585231	+	0.438099i	−0.265194	+	0.964195i	$0.585436\pi$
$978$	−0.748235	+	1.78766i	−0.0239259	+	0.0571630i
$979$	−2.29017	−	3.56357i	−0.0731942	−	0.113892i
$980$	−15.1251	−	1.34425i	−0.483152	−	0.0429405i
$981$	−0.808064	−	12.6091i	−0.0257995	−	0.402579i
$982$	0.473085	+	2.17474i	0.0150967	+	0.0693986i
$983$	−36.4192	−	19.8864i	−1.16159	−	0.634277i	−0.221488	−	0.975163i	$-0.571091\pi$
$983$	−36.4192	−	19.8864i	−1.16159	−	0.634277i	−0.940105	+	0.340886i	$0.889273\pi$
$984$	9.47928	−	13.5455i	0.302189	−	0.431814i
$985$	−31.7985	−	15.1899i	−1.01319	−	0.483990i
$986$	−1.72284	+	0.786796i	−0.0548665	+	0.0250567i
$987$	4.40273	+	3.57490i	0.140140	+	0.113790i
$988$	−8.37174	+	8.37174i	−0.266341	+	0.266341i
$989$	9.10748	−	9.41650i	0.289601	−	0.299427i
$990$	−7.06720	+	2.43930i	−0.224610	+	0.0775259i
$991$	2.41123	−	16.7705i	0.0765953	−	0.532732i	−0.915010	−	0.403431i	$-0.867818\pi$
$991$	2.41123	−	16.7705i	0.0765953	−	0.532732i	0.991605	−	0.129301i	$-0.0412734\pi$
$992$	3.75847	+	1.40184i	0.119332	+	0.0445084i
$993$	28.2256	−	26.0846i	0.895712	−	0.827770i
$994$	−4.40819	+	3.81972i	−0.139819	+	0.121154i
$995$	−19.2364	+	24.7939i	−0.609833	+	0.786019i
$996$	4.58575	−	13.6097i	0.145305	−	0.431239i
$997$	34.2672	−	12.7810i	1.08525	−	0.404779i	0.257735	−	0.966216i	$-0.417024\pi$
$997$	34.2672	−	12.7810i	1.08525	−	0.404779i	0.827520	+	0.561437i	$0.189751\pi$
$998$	16.8097	−	1.20225i	0.532101	−	0.0380566i
$999$	55.7760	+	14.8975i	1.76468	+	0.471336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.2	✓	960
3.2	odd	2	inner	690.2.x.a.77.30	yes	960
5.3	odd	4	inner	690.2.x.a.353.13	yes	960
15.8	even	4	inner	690.2.x.a.353.42	yes	960
23.3	even	11	inner	690.2.x.a.647.42	yes	960
69.26	odd	22	inner	690.2.x.a.647.13	yes	960
115.3	odd	44	inner	690.2.x.a.233.30	yes	960
345.233	even	44	inner	690.2.x.a.233.2	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.2	✓	960	1.1	even	1	trivial
690.2.x.a.77.30	yes	960	3.2	odd	2	inner
690.2.x.a.233.2	yes	960	345.233	even	44	inner
690.2.x.a.233.30	yes	960	115.3	odd	44	inner
690.2.x.a.353.13	yes	960	5.3	odd	4	inner
690.2.x.a.353.42	yes	960	15.8	even	4	inner
690.2.x.a.647.13	yes	960	69.26	odd	22	inner
690.2.x.a.647.42	yes	960	23.3	even	11	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.72143 - 0.191520i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.512913 + 2.17645i) q^{5} +(0.878295 + 1.49285i) q^{6} +(0.0972258 + 0.446940i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.92664 + 0.659376i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-1.72143 - 0.191520i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-0.512913 + 2.17645i) q^{5} +(0.878295 + 1.49285i) q^{6} +(0.0972258 + 0.446940i) q^{7} +(0.936950 - 0.349464i) q^{8} +(2.92664 + 0.659376i) q^{9} +(2.04971 - 0.893688i) q^{10} +(-1.10316 + 0.158611i) q^{11} +(0.668745 - 1.59774i) q^{12} +(-0.316107 + 1.45312i) q^{13} +(0.299529 - 0.345674i) q^{14} +(1.29978 - 3.64837i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(-1.33200 + 2.43938i) q^{17} +(-1.22601 - 2.73805i) q^{18} +(2.24299 - 7.63891i) q^{19} +(-1.94378 - 1.10531i) q^{20} +(-0.0817695 - 0.787996i) q^{21} +(0.788074 + 0.788074i) q^{22} +(-1.91922 + 4.39507i) q^{23} +(-1.67982 + 0.422133i) q^{24} +(-4.47384 - 2.23266i) q^{25} +(1.35272 - 0.617765i) q^{26} +(-4.91172 - 1.69558i) q^{27} +(-0.456227 - 0.0326300i) q^{28} +(-0.653850 + 0.191988i) q^{29} +(-3.69960 + 1.14586i) q^{30} +(1.66639 - 3.64889i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(1.92939 - 0.0617597i) q^{33} +(2.75106 - 0.395543i) q^{34} +(-1.02261 - 0.0176346i) q^{35} +(-1.45720 + 2.62232i) q^{36} +(-11.0821 + 0.792606i) q^{37} +(-7.45943 + 2.78223i) q^{38} +(0.822457 - 2.44090i) q^{39} +(0.280016 + 2.21847i) q^{40} +(-7.21384 + 6.25083i) q^{41} +(-0.581821 + 0.537688i) q^{42} +(-2.55936 - 0.954594i) q^{43} +(0.158611 - 1.10316i) q^{44} +(-2.93621 + 6.03147i) q^{45} +(4.66858 - 1.09745i) q^{46} +(-5.06197 + 5.06197i) q^{47} +(1.34462 + 1.09179i) q^{48} +(6.17712 - 2.82100i) q^{49} +(0.893738 + 4.91947i) q^{50} +(2.76014 - 3.94411i) q^{51} +(-1.30520 - 0.712693i) q^{52} +(-2.23258 - 10.2630i) q^{53} +(1.58610 + 4.94816i) q^{54} +(0.220618 - 2.48232i) q^{55} +(0.247285 + 0.384783i) q^{56} +(-5.32415 + 12.7203i) q^{57} +(0.545532 + 0.408380i) q^{58} +(1.27475 - 0.819234i) q^{59} +(3.13439 + 2.27499i) q^{60} +(-5.71684 + 12.5181i) q^{61} +(-3.91972 + 0.852682i) q^{62} +(-0.0101565 + 1.37214i) q^{63} +(0.755750 - 0.654861i) q^{64} +(-3.00050 - 1.43331i) q^{65} +(-1.20568 - 1.50755i) q^{66} +(2.21800 - 1.66037i) q^{67} +(-1.96530 - 1.96530i) q^{68} +(4.14554 - 7.19823i) q^{69} +(0.598710 + 0.829209i) q^{70} +(-12.6226 - 1.81486i) q^{71} +(2.97254 - 0.404954i) q^{72} +(-0.902364 + 0.492728i) q^{73} +(7.27576 + 8.39667i) q^{74} +(7.27380 + 4.70019i) q^{75} +(6.69756 + 4.30426i) q^{76} +(-0.178145 - 0.477625i) q^{77} +(-2.44692 + 0.804367i) q^{78} +(1.73336 + 2.69717i) q^{79} +(1.60817 - 1.55364i) q^{80} +(8.13045 + 3.85951i) q^{81} +(9.32714 + 2.02899i) q^{82} +(8.27048 - 0.591516i) q^{83} +(0.779114 + 0.143547i) q^{84} +(-4.62598 - 4.15022i) q^{85} +(0.769578 + 2.62094i) q^{86} +(1.16233 - 0.205268i) q^{87} +(-0.978177 + 0.534125i) q^{88} +(1.57892 + 3.45735i) q^{89} +(6.58805 - 1.26397i) q^{90} -0.680191 q^{91} +(-3.67633 - 3.07971i) q^{92} +(-3.56741 + 5.96216i) q^{93} +(7.08584 + 1.01879i) q^{94} +(15.4752 + 8.79984i) q^{95} +(0.0682265 - 1.73071i) q^{96} +(0.507680 - 7.09830i) q^{97} +(-5.96014 - 3.25448i) q^{98} +(-3.33314 - 0.263202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more