LMFDB - Embedded newform 920.2.bb.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

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

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05929 + 0.936962i) q^{2} +(0.272959 - 1.89847i) q^{3} +(0.244204 - 1.98504i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.48965 + 2.26679i) q^{6} +(-0.510137 - 0.588729i) q^{7} +(1.60122 + 2.33154i) q^{8} +(-0.651210 - 0.191212i) q^{9} +(0.752412 - 1.19745i) q^{10} +(-0.344646 + 0.536279i) q^{11} +(-3.70188 - 1.00545i) q^{12} +(3.54957 + 3.07572i) q^{13} +(1.09200 + 0.145658i) q^{14} +(0.272959 + 1.89847i) q^{15} +(-3.88073 - 0.969508i) q^{16} +(4.90669 - 2.24081i) q^{17} +(0.868981 - 0.407609i) q^{18} +(2.35087 + 1.07360i) q^{19} +(0.324937 + 1.97343i) q^{20} +(-1.25693 + 0.807782i) q^{21} +(-0.137392 - 0.890997i) q^{22} +(-2.81852 + 3.88020i) q^{23} +(4.86344 - 2.40345i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-6.64187 + 0.0677230i) q^{26} +(1.84953 - 4.04990i) q^{27} +(-1.29323 + 0.868869i) q^{28} +(5.16378 - 2.35822i) q^{29} +(-2.06794 - 1.75529i) q^{30} +(1.14997 - 0.165341i) q^{31} +(5.01922 - 2.60910i) q^{32} +(0.924037 + 0.800682i) q^{33} +(-3.09807 + 6.97105i) q^{34} +(0.655337 + 0.421160i) q^{35} +(-0.538591 + 1.24598i) q^{36} +(-4.79915 - 1.40916i) q^{37} +(-3.49618 + 1.06541i) q^{38} +(6.80805 - 5.89921i) q^{39} +(-2.19323 - 1.78599i) q^{40} +(9.81972 - 2.88333i) q^{41} +(0.574600 - 2.03338i) q^{42} +(-11.7594 - 1.69075i) q^{43} +(0.980369 + 0.815095i) q^{44} +0.678702 q^{45} +(-0.649963 - 6.75111i) q^{46} +5.76144i q^{47} +(-2.89986 + 7.10282i) q^{48} +(0.909841 - 6.32808i) q^{49} +(-0.384574 + 1.36092i) q^{50} +(-2.91479 - 9.92686i) q^{51} +(6.97223 - 6.29491i) q^{52} +(2.42105 + 2.79404i) q^{53} +(1.83541 + 6.02296i) q^{54} +(0.179598 - 0.611654i) q^{55} +(0.555808 - 2.13209i) q^{56} +(2.67990 - 4.17000i) q^{57} +(-3.26039 + 7.33631i) q^{58} +(0.808707 - 0.933298i) q^{59} +(3.83519 - 0.0782182i) q^{60} +(-2.05660 - 14.3040i) q^{61} +(-1.06324 + 1.25262i) q^{62} +(0.219634 + 0.480931i) q^{63} +(-2.87220 + 7.46662i) q^{64} +(-4.27232 - 1.95110i) q^{65} +(-1.72903 + 0.0176299i) q^{66} +(-3.92380 - 6.10555i) q^{67} +(-3.24985 - 10.2872i) q^{68} +(6.59711 + 6.41001i) q^{69} +(-1.08880 + 0.167894i) q^{70} +(2.23939 + 3.48456i) q^{71} +(-0.596909 - 1.82450i) q^{72} +(4.64901 - 10.1799i) q^{73} +(6.40403 - 3.00391i) q^{74} +(-0.796764 - 1.74467i) q^{75} +(2.70524 - 4.40437i) q^{76} +(0.491540 - 0.0706727i) q^{77} +(-1.68439 + 12.6279i) q^{78} +(10.7816 - 12.4426i) q^{79} +(3.99667 - 0.163091i) q^{80} +(-8.89665 - 5.71753i) q^{81} +(-7.70039 + 12.2550i) q^{82} +(-0.377510 + 1.28568i) q^{83} +(1.29653 + 2.69232i) q^{84} +(-4.07662 + 3.53241i) q^{85} +(14.0409 - 9.22715i) q^{86} +(-3.06751 - 10.4470i) q^{87} +(-1.80221 + 0.0551434i) q^{88} +(10.5368 + 1.51496i) q^{89} +(-0.718944 + 0.635918i) q^{90} -3.65877i q^{91} +(7.01404 + 6.54242i) q^{92} -2.22832i q^{93} +(-5.39825 - 6.10306i) q^{94} +(-2.55811 - 0.367801i) q^{95} +(-3.58326 - 10.2410i) q^{96} +(2.86214 + 9.74756i) q^{97} +(4.96539 + 7.55578i) q^{98} +(0.326980 - 0.283330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

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 $

$2$	−1.05929	+	0.936962i	−0.749033	+	0.662532i
$2$	−1.05929	+	0.936962i	−0.749033	+	0.662532i
$3$	0.272959	−	1.89847i	0.157593	−	1.09608i	−0.745459	−	0.666552i	$-0.767770\pi$
$3$	0.272959	−	1.89847i	0.157593	−	1.09608i	0.903052	−	0.429532i	$-0.141321\pi$
$4$	0.244204	−	1.98504i	0.122102	−	0.992518i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	1.48965	+	2.26679i	0.608148	+	0.925413i
$7$	−0.510137	−	0.588729i	−0.192814	−	0.222519i	0.651108	−	0.758985i	$-0.274304\pi$
$7$	−0.510137	−	0.588729i	−0.192814	−	0.222519i	−0.843922	+	0.536466i	$0.819759\pi$
$8$	1.60122	+	2.33154i	0.566116	+	0.824325i
$9$	−0.651210	−	0.191212i	−0.217070	−	0.0637375i
$10$	0.752412	−	1.19745i	0.237933	−	0.378666i
$11$	−0.344646	+	0.536279i	−0.103915	+	0.161694i	−0.889317	−	0.457291i	$-0.848820\pi$
$11$	−0.344646	+	0.536279i	−0.103915	+	0.161694i	0.785402	+	0.618986i	$0.212456\pi$
$12$	−3.70188	−	1.00545i	−1.06864	−	0.290248i
$13$	3.54957	+	3.07572i	0.984473	+	0.853051i	0.989146	−	0.146938i	$-0.0469418\pi$
$13$	3.54957	+	3.07572i	0.984473	+	0.853051i	−0.00467239	+	0.999989i	$0.501487\pi$
$14$	1.09200	+	0.145658i	0.291850	+	0.0389288i
$15$	0.272959	+	1.89847i	0.0704777	+	0.490183i
$16$	−3.88073	−	0.969508i	−0.970182	−	0.242377i
$17$	4.90669	−	2.24081i	1.19005	−	0.543476i	0.280813	−	0.959763i	$-0.409396\pi$
$17$	4.90669	−	2.24081i	1.19005	−	0.543476i	0.909233	+	0.416286i	$0.136669\pi$
$18$	0.868981	−	0.407609i	0.204821	−	0.0960743i
$19$	2.35087	+	1.07360i	0.539326	+	0.246302i	0.666404	−	0.745591i	$-0.267833\pi$
$19$	2.35087	+	1.07360i	0.539326	+	0.246302i	−0.127078	+	0.991893i	$0.540560\pi$
$20$	0.324937	+	1.97343i	0.0726580	+	0.441272i
$21$	−1.25693	+	0.807782i	−0.274285	+	0.176272i
$22$	−0.137392	−	0.890997i	−0.0292921	−	0.189961i
$23$	−2.81852	+	3.88020i	−0.587702	+	0.809078i
$23$	−2.81852	+	3.88020i	−0.587702	+	0.809078i
$24$	4.86344	−	2.40345i	0.992745	−	0.490603i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−6.64187	+	0.0677230i	−1.30258	+	0.0132816i
$27$	1.84953	−	4.04990i	0.355941	−	0.779403i
$28$	−1.29323	+	0.868869i	−0.244397	+	0.164201i
$29$	5.16378	−	2.35822i	0.958889	−	0.437910i	0.126417	−	0.991977i	$-0.459652\pi$
$29$	5.16378	−	2.35822i	0.958889	−	0.437910i	0.832472	+	0.554067i	$0.186925\pi$
$30$	−2.06794	−	1.75529i	−0.377552	−	0.320470i
$31$	1.14997	−	0.165341i	0.206541	−	0.0296961i	−0.0382676	−	0.999268i	$-0.512184\pi$
$31$	1.14997	−	0.165341i	0.206541	−	0.0296961i	0.244809	+	0.969571i	$0.421275\pi$
$32$	5.01922	−	2.60910i	0.887281	−	0.461228i
$33$	0.924037	+	0.800682i	0.160854	+	0.139381i
$34$	−3.09807	+	6.97105i	−0.531314	+	1.19553i
$35$	0.655337	+	0.421160i	0.110772	+	0.0711890i
$36$	−0.538591	+	1.24598i	−0.0897652	+	0.207663i
$37$	−4.79915	−	1.40916i	−0.788975	−	0.231664i	−0.137668	−	0.990478i	$-0.543961\pi$
$37$	−4.79915	−	1.40916i	−0.788975	−	0.231664i	−0.651307	+	0.758814i	$0.725779\pi$
$38$	−3.49618	+	1.06541i	−0.567156	+	0.172832i
$39$	6.80805	−	5.89921i	1.09016	−	0.944630i
$40$	−2.19323	−	1.78599i	−0.346780	−	0.282389i
$41$	9.81972	−	2.88333i	1.53358	−	0.450300i	0.597438	−	0.801915i	$-0.296186\pi$
$41$	9.81972	−	2.88333i	1.53358	−	0.450300i	0.936145	+	0.351615i	$0.114367\pi$
$42$	0.574600	−	2.03338i	0.0886626	−	0.313757i
$43$	−11.7594	−	1.69075i	−1.79330	−	0.257837i	−0.836371	−	0.548164i	$-0.815327\pi$
$43$	−11.7594	−	1.69075i	−1.79330	−	0.257837i	−0.956928	+	0.290326i	$0.906236\pi$
$44$	0.980369	+	0.815095i	0.147796	+	0.122880i
$45$	0.678702			0.101175
$46$	−0.649963	−	6.75111i	−0.0958319	−	0.995398i
$47$			5.76144i			0.840393i	0.907433	+	0.420196i	$0.138039\pi$
$47$			5.76144i			0.840393i	−0.907433	+	0.420196i	$0.861961\pi$
$48$	−2.89986	+	7.10282i	−0.418559	+	1.02520i
$49$	0.909841	−	6.32808i	0.129977	−	0.904012i
$50$	−0.384574	+	1.36092i	−0.0543870	+	0.192463i
$51$	−2.91479	−	9.92686i	−0.408152	−	1.39004i
$52$	6.97223	−	6.29491i	0.966874	−	0.872948i
$53$	2.42105	+	2.79404i	0.332557	+	0.383791i	0.897260	−	0.441503i	$-0.145555\pi$
$53$	2.42105	+	2.79404i	0.332557	+	0.383791i	−0.564703	+	0.825294i	$0.691009\pi$
$54$	1.83541	+	6.02296i	0.249768	+	0.819622i
$55$	0.179598	−	0.611654i	0.0242170	−	0.0824754i
$56$	0.555808	−	2.13209i	0.0742730	−	0.284913i
$57$	2.67990	−	4.17000i	0.354961	−	0.552331i
$58$	−3.26039	+	7.33631i	−0.428111	+	0.963304i
$59$	0.808707	−	0.933298i	0.105285	−	0.121505i	−0.700661	−	0.713494i	$-0.747112\pi$
$59$	0.808707	−	0.933298i	0.105285	−	0.121505i	0.805946	+	0.591989i	$0.201657\pi$
$60$	3.83519	−	0.0782182i	0.495121	−	0.0100979i
$61$	−2.05660	−	14.3040i	−0.263321	−	1.83144i	−0.507435	−	0.861690i	$-0.669406\pi$
$61$	−2.05660	−	14.3040i	−0.263321	−	1.83144i	0.244114	−	0.969746i	$-0.421503\pi$
$62$	−1.06324	+	1.25262i	−0.135032	+	0.159083i
$63$	0.219634	+	0.480931i	0.0276712	+	0.0605916i
$64$	−2.87220	+	7.46662i	−0.359025	+	0.933328i
$65$	−4.27232	−	1.95110i	−0.529916	−	0.242004i
$66$	−1.72903	+	0.0176299i	−0.212829	+	0.00217009i
$67$	−3.92380	−	6.10555i	−0.479369	−	0.745912i	0.514379	−	0.857563i	$-0.328023\pi$
$67$	−3.92380	−	6.10555i	−0.479369	−	0.745912i	−0.993747	+	0.111651i	$0.964386\pi$
$68$	−3.24985	−	10.2872i	−0.394102	−	1.24750i
$69$	6.59711	+	6.41001i	0.794199	+	0.771675i
$70$	−1.08880	+	0.167894i	−0.130137	+	0.0200672i
$71$	2.23939	+	3.48456i	0.265767	+	0.413541i	0.948330	−	0.317285i	$-0.102771\pi$
$71$	2.23939	+	3.48456i	0.265767	+	0.413541i	−0.682564	+	0.730826i	$0.739135\pi$
$72$	−0.596909	−	1.82450i	−0.0703464	−	0.215019i
$73$	4.64901	−	10.1799i	0.544126	−	1.19147i	−0.415346	−	0.909664i	$-0.636339\pi$
$73$	4.64901	−	10.1799i	0.544126	−	1.19147i	0.959471	−	0.281806i	$-0.0909333\pi$
$74$	6.40403	−	3.00391i	0.744454	−	0.349197i
$75$	−0.796764	−	1.74467i	−0.0920023	−	0.201457i
$76$	2.70524	−	4.40437i	0.310312	−	0.505216i
$77$	0.491540	−	0.0706727i	0.0560161	−	0.00805391i
$78$	−1.68439	+	12.6279i	−0.190719	+	1.42983i
$79$	10.7816	−	12.4426i	1.21302	−	1.39990i	0.321505	−	0.946908i	$-0.395811\pi$
$79$	10.7816	−	12.4426i	1.21302	−	1.39990i	0.891515	−	0.452991i	$-0.149643\pi$
$80$	3.99667	−	0.163091i	0.446842	−	0.0182341i
$81$	−8.89665	−	5.71753i	−0.988517	−	0.635281i
$82$	−7.70039	+	12.2550i	−0.850366	+	1.35334i
$83$	−0.377510	+	1.28568i	−0.0414371	+	0.141122i	−0.977613	−	0.210409i	$-0.932520\pi$
$83$	−0.377510	+	1.28568i	−0.0414371	+	0.141122i	0.936176	+	0.351531i	$0.114339\pi$
$84$	1.29653	+	2.69232i	0.141463	+	0.293756i
$85$	−4.07662	+	3.53241i	−0.442172	+	0.383144i
$86$	14.0409	−	9.22715i	1.51407	−	0.994989i
$87$	−3.06751	−	10.4470i	−0.328872	−	1.12003i
$88$	−1.80221	+	0.0551434i	−0.192116	+	0.00587830i
$89$	10.5368	+	1.51496i	1.11690	+	0.160586i	0.675950	−	0.736947i	$-0.263733\pi$
$89$	10.5368	+	1.51496i	1.11690	+	0.160586i	0.440947	+	0.897533i	$0.354643\pi$
$90$	−0.718944	+	0.635918i	−0.0757834	+	0.0670316i
$91$		−	3.65877i		−	0.383544i
$92$	7.01404	+	6.54242i	0.731264	+	0.682094i
$93$		−	2.22832i		−	0.231066i
$94$	−5.39825	−	6.10306i	−0.556787	−	0.629482i
$95$	−2.55811	−	0.367801i	−0.262456	−	0.0377355i
$96$	−3.58326	−	10.2410i	−0.365715	−	1.04522i
$97$	2.86214	+	9.74756i	0.290606	+	0.989714i	0.967339	+	0.253486i	$0.0815771\pi$
$97$	2.86214	+	9.74756i	0.290606	+	0.989714i	−0.676733	+	0.736229i	$0.736605\pi$
$98$	4.96539	+	7.55578i	0.501580	+	0.763249i
$99$	0.326980	−	0.283330i	0.0328627	−	0.0284757i
$100$	−0.867753	−	1.80194i	−0.0867753	−	0.180194i
$101$	−4.80326	+	16.3584i	−0.477942	+	1.62772i	0.269218	+	0.963079i	$0.413235\pi$
$101$	−4.80326	+	16.3584i	−0.477942	+	1.62772i	−0.747161	+	0.664643i	$0.768583\pi$
$102$	12.3887	+	7.78441i	1.22666	+	0.770771i
$103$	7.13811	+	4.58738i	0.703339	+	0.452008i	0.842805	−	0.538218i	$-0.180902\pi$
$103$	7.13811	+	4.58738i	0.703339	+	0.452008i	−0.139467	+	0.990227i	$0.544539\pi$
$104$	−1.48754	+	13.2009i	−0.145865	+	1.29445i
$105$	0.978440	−	1.12918i	0.0954859	−	0.110197i
$106$	−5.18251	−	0.691276i	−0.503370	−	0.0671427i
$107$	−6.17709	+	0.888131i	−0.597162	+	0.0858589i	−0.434266	−	0.900784i	$-0.642992\pi$
$107$	−6.17709	+	0.888131i	−0.597162	+	0.0858589i	−0.162895	+	0.986643i	$0.552083\pi$
$108$	−7.58753	−	4.66038i	−0.730110	−	0.448445i
$109$	−1.43543	−	3.14316i	−0.137490	−	0.301060i	0.828346	−	0.560217i	$-0.189282\pi$
$109$	−1.43543	−	3.14316i	−0.137490	−	0.301060i	−0.965835	+	0.259157i	$0.916555\pi$
$110$	0.382850	+	0.816197i	0.0365033	+	0.0778213i
$111$	−3.98522	+	8.72640i	−0.378260	+	0.828274i
$112$	1.40892	+	2.77928i	0.133131	+	0.262617i
$113$	5.65249	+	8.79545i	0.531742	+	0.827406i	0.998372	−	0.0570467i	$-0.0181684\pi$
$113$	5.65249	+	8.79545i	0.531742	+	0.827406i	−0.466630	+	0.884453i	$0.654532\pi$
$114$	1.06834	+	6.92822i	0.100059	+	0.648887i
$115$	1.61117	−	4.51709i	0.150242	−	0.421221i
$116$	−3.42013	−	10.8262i	−0.317551	−	1.00518i
$117$	−1.72340	−	2.68166i	−0.159328	−	0.247919i
$118$	0.0178066	+	1.74636i	0.00163923	+	0.160766i
$119$	−3.82231	−	1.74559i	−0.350391	−	0.160018i
$120$	−3.98930	+	3.67628i	−0.364172	+	0.335597i
$121$	4.40075	+	9.63630i	0.400068	+	0.876027i
$122$	15.5808	+	13.2251i	1.41062	+	1.19735i
$123$	−2.79354	−	19.4295i	−0.251885	−	1.75190i
$124$	−0.0473796	−	2.32311i	−0.00425481	−	0.208622i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−0.683270	−	0.303658i	−0.0608706	−	0.0270520i
$127$	−4.19456	+	6.52686i	−0.372207	+	0.579165i	−0.975945	−	0.218018i	$-0.930041\pi$
$127$	−4.19456	+	6.52686i	−0.372207	+	0.579165i	0.603738	+	0.797183i	$0.293677\pi$
$128$	−3.95344	−	10.6005i	−0.349438	−	0.936959i
$129$	−6.41969	+	21.8635i	−0.565223	+	1.92497i
$130$	6.35374	−	1.93621i	0.557260	−	0.169817i
$131$	0.595917	+	0.687724i	0.0520655	+	0.0600868i	0.781185	−	0.624300i	$-0.214616\pi$
$131$	0.595917	+	0.687724i	0.0520655	+	0.0600868i	−0.729119	+	0.684386i	$0.760070\pi$
$132$	1.81504	−	1.63871i	0.157979	−	0.142632i
$133$	−0.567201	−	1.93171i	−0.0491826	−	0.167500i
$134$	9.87713	+	2.79112i	0.853254	+	0.241116i
$135$	−0.633619	+	4.40692i	−0.0545333	+	0.379287i
$136$	13.0812	+	7.85213i	1.12171	+	0.673315i
$137$		−	8.67905i		−	0.741501i	−0.928732	−	0.370751i	$-0.879100\pi$
$137$		−	8.67905i		−	0.741501i	0.928732	−	0.370751i	$-0.120900\pi$
$138$	−12.9942	−	0.608840i	−1.10614	−	0.0518279i
$139$	−0.328402			−0.0278547			−0.0139274	−	0.999903i	$-0.504433\pi$
$139$	−0.328402			−0.0278547			−0.0139274	+	0.999903i	$0.504433\pi$
$140$	0.996053	−	1.19802i	0.0841818	−	0.101251i
$141$	10.9379	+	1.57264i	0.921141	+	0.132440i
$142$	−5.63707	−	1.59295i	−0.473052	−	0.133677i
$143$	−2.87279	+	0.843526i	−0.240235	+	0.0705392i
$144$	2.34179	+	1.37340i	0.195149	+	0.114450i
$145$	−4.29022	+	3.71750i	−0.356283	+	0.308721i
$146$	4.61353	+	15.1395i	0.381818	+	1.25295i
$147$	−11.7653	−	3.45462i	−0.970389	−	0.284932i
$148$	−3.96920	+	9.18235i	−0.326266	+	0.754785i
$149$	7.87005	+	5.05777i	0.644739	+	0.414349i	0.821740	−	0.569862i	$-0.193003\pi$
$149$	7.87005	+	5.05777i	0.644739	+	0.414349i	−0.177001	+	0.984211i	$0.556640\pi$
$150$	2.47869	+	1.10158i	0.202385	+	0.0899435i
$151$	8.05269	+	6.97769i	0.655319	+	0.567837i	0.917772	−	0.397108i	$-0.129986\pi$
$151$	8.05269	+	6.97769i	0.655319	+	0.567837i	−0.262453	+	0.964945i	$0.584532\pi$
$152$	1.26109	+	7.20023i	0.102288	+	0.584015i
$153$	−3.62375	+	0.521017i	−0.292963	+	0.0421217i
$154$	−0.454467	+	0.535417i	−0.0366220	+	0.0431451i
$155$	−1.05681	+	0.482628i	−0.0848849	+	0.0387656i
$156$	−10.0476	−	14.9548i	−0.804451	−	1.19735i
$157$	−0.924695	+	2.02480i	−0.0737987	+	0.161597i	−0.942936	−	0.332975i	$-0.891948\pi$
$157$	−0.924695	+	2.02480i	−0.0737987	+	0.161597i	0.869137	+	0.494571i	$0.164675\pi$
$158$	0.237395	+	23.2822i	0.0188861	+	1.85224i
$159$	5.96525	−	3.83364i	0.473075	−	0.304027i
$160$	−4.08084	+	3.91749i	−0.322619	+	0.309705i
$161$	3.72222	−	0.320089i	0.293352	−	0.0252266i
$162$	14.7813	−	2.27928i	1.16133	−	0.179077i
$163$	−1.91399	+	1.23005i	−0.149915	+	0.0963446i	−0.613448	−	0.789735i	$-0.710218\pi$
$163$	−1.91399	+	1.23005i	−0.149915	+	0.0963446i	0.463533	+	0.886080i	$0.346582\pi$
$164$	−3.32549	−	20.1966i	−0.259677	−	1.57709i
$165$	−1.11218	−	0.507918i	−0.0865835	−	0.0395413i
$166$	−0.804740	−	1.71562i	−0.0624599	−	0.133158i
$167$	13.9991	−	6.39316i	1.08328	−	0.494717i	0.207898	−	0.978150i	$-0.433338\pi$
$167$	13.9991	−	6.39316i	1.08328	−	0.494717i	0.875381	+	0.483433i	$0.160610\pi$
$168$	−3.89600	−	1.63716i	−0.300583	−	0.126310i
$169$	1.28930	+	8.96727i	0.0991769	+	0.689790i
$170$	1.00860	−	7.56150i	0.0773562	−	0.579941i
$171$	−1.32562	−	1.14866i	−0.101373	−	0.0878400i
$172$	−6.22791	+	22.9300i	−0.474874	+	1.74840i
$173$	−4.10074	+	6.38088i	−0.311774	+	0.485129i	−0.961411	−	0.275115i	$-0.911284\pi$
$173$	−4.10074	+	6.38088i	−0.311774	+	0.485129i	0.649638	+	0.760244i	$0.274921\pi$
$174$	13.0378	+	8.19228i	0.988395	+	0.621055i
$175$	−0.747446	−	0.219470i	−0.0565016	−	0.0165904i
$176$	1.85740	−	1.74702i	0.140007	−	0.131686i
$177$	−1.55110	−	1.79006i	−0.116588	−	0.134549i
$178$	−12.5810	+	8.26778i	−0.942987	+	0.619697i
$179$	17.4045	−	5.11043i	1.30088	−	0.381972i	0.443321	−	0.896363i	$-0.353800\pi$
$179$	17.4045	−	5.11043i	1.30088	−	0.381972i	0.857556	+	0.514391i	$0.171982\pi$
$180$	0.165742	−	1.34725i	0.0123537	−	0.100418i
$181$	0.963805	−	6.70341i	0.0716391	−	0.498261i	−0.922137	−	0.386864i	$-0.873558\pi$
$181$	0.963805	−	6.70341i	0.0716391	−	0.498261i	0.993776	−	0.111397i	$-0.0355325\pi$
$182$	3.42813	+	3.87571i	0.254110	+	0.287287i
$183$	−27.7171			−2.04890
$184$	−13.5599	−	0.358451i	−0.999651	−	0.0264254i
$185$	5.00175			0.367736
$186$	2.08785	+	2.36044i	0.153089	+	0.173076i
$187$	−0.489369	+	3.40364i	−0.0357862	+	0.248899i
$188$	11.4367	+	1.40697i	0.834105	+	0.102614i
$189$	−3.32780	+	0.977132i	−0.242062	+	0.0710759i
$190$	3.05440	−	2.00724i	0.221590	−	0.145621i
$191$	−13.6132	−	15.7104i	−0.985014	−	1.13677i	−0.990601	−	0.136782i	$-0.956324\pi$
$191$	−13.6132	−	15.7104i	−0.985014	−	1.13677i	0.00558741	−	0.999984i	$-0.498221\pi$
$192$	13.3912	+	7.49087i	0.966425	+	0.540607i
$193$	−10.0059	−	2.93801i	−0.720243	−	0.211482i	−0.0989852	−	0.995089i	$-0.531560\pi$
$193$	−10.0059	−	2.93801i	−0.720243	−	0.211482i	−0.621257	+	0.783607i	$0.713378\pi$
$194$	−12.1649	−	7.64380i	−0.873392	−	0.548793i
$195$	−4.87028	+	7.57830i	−0.348768	+	0.542693i
$196$	−12.3393	−	3.35141i	−0.881377	−	0.239387i
$197$	−13.9141	−	12.0567i	−0.991341	−	0.859002i	−0.00133140	−	0.999999i	$-0.500424\pi$
$197$	−13.9141	−	12.0567i	−0.991341	−	0.859002i	−0.990010	+	0.140997i	$0.954969\pi$
$198$	−0.0808984	+	0.606497i	−0.00574920	+	0.0431018i
$199$	−3.71032	−	25.8058i	−0.263017	−	1.82933i	−0.509845	−	0.860267i	$-0.670297\pi$
$199$	−3.71032	−	25.8058i	−0.263017	−	1.82933i	0.246827	−	0.969060i	$-0.420612\pi$
$200$	2.60756	+	1.09574i	0.184382	+	0.0774802i
$201$	−12.6623	+	5.78266i	−0.893127	+	0.407877i
$202$	−10.2391	−	21.8288i	−0.720424	−	1.53587i
$203$	−4.02259	−	1.83705i	−0.282330	−	0.128936i
$204$	−20.4170	+	3.36178i	−1.42947	+	0.235371i
$205$	−8.60962	+	5.53307i	−0.601322	+	0.386446i
$206$	−11.8596	+	1.82875i	−0.826294	+	0.127415i
$207$	2.57739	−	1.98789i	0.179141	−	0.138168i
$208$	−10.7930	−	15.3774i	−0.748358	−	1.06623i
$209$	−1.38597	+	0.890707i	−0.0958694	+	0.0616115i
$210$	0.0215439	+	2.11289i	0.00148667	+	0.145803i
$211$	−8.38104	+	18.3519i	−0.576974	+	1.26340i	0.366026	+	0.930605i	$0.380718\pi$
$211$	−8.38104	+	18.3519i	−0.576974	+	1.26340i	−0.943000	+	0.332793i	$0.892009\pi$
$212$	6.13750	−	4.12355i	0.421525	−	0.283207i
$213$	7.22659	−	3.30028i	0.495158	−	0.226131i
$214$	5.71120	−	6.72849i	0.390410	−	0.459950i
$215$	11.7594	−	1.69075i	0.801988	−	0.115308i
$216$	12.4040	−	2.17252i	0.843986	−	0.147821i
$217$	−0.683984	−	0.592676i	−0.0464319	−	0.0402334i
$218$	4.46557	+	1.98458i	0.302446	+	0.134413i
$219$	−18.0573	−	11.6047i	−1.22020	−	0.784174i
$220$	−1.17030	−	0.505876i	−0.0789013	−	0.0341062i
$221$	24.3087	+	7.13769i	1.63518	+	0.480133i
$222$	−3.95480	−	12.9778i	−0.265429	−	0.871014i
$223$	−10.2106	+	8.84749i	−0.683749	+	0.592472i	−0.925901	−	0.377766i	$-0.876692\pi$
$223$	−10.2106	+	8.84749i	−0.683749	+	0.592472i	0.242152	+	0.970238i	$0.422147\pi$
$224$	−4.09655	−	1.62396i	−0.273712	−	0.108506i
$225$	−0.651210	+	0.191212i	−0.0434140	+	0.0127475i
$226$	−14.2286	−	4.02079i	−0.946475	−	0.267459i
$227$	16.4265	+	2.36178i	1.09027	+	0.156757i	0.663921	−	0.747803i	$-0.268891\pi$
$227$	16.4265	+	2.36178i	1.09027	+	0.156757i	0.426347	+	0.904560i	$0.359800\pi$
$228$	−7.62316	−	6.33803i	−0.504856	−	0.419746i
$229$	−6.39355			−0.422498			−0.211249	−	0.977432i	$-0.567753\pi$
$229$	−6.39355			−0.422498			−0.211249	+	0.977432i	$0.567753\pi$
$230$	2.52564	+	6.29453i	0.166536	+	0.415049i
$231$		−	0.952465i		−	0.0626676i
$232$	13.7666	+	8.26355i	0.903823	+	0.542529i
$233$	−3.09842	+	21.5500i	−0.202984	+	1.41179i	0.592383	+	0.805657i	$0.298187\pi$
$233$	−3.09842	+	21.5500i	−0.202984	+	1.41179i	−0.795367	+	0.606129i	$0.792722\pi$
$234$	4.33820	+	1.22591i	0.283597	+	0.0801399i
$235$	−1.62319	−	5.52807i	−0.105885	−	0.360611i
$236$	−1.65514	−	1.83323i	−0.107740	−	0.119333i
$237$	−20.6790	−	23.8648i	−1.34324	−	1.55018i
$238$	5.68450	−	1.73227i	0.368472	−	0.112286i
$239$	3.28854	−	11.1997i	0.212718	−	0.724451i	−0.782134	−	0.623111i	$-0.785869\pi$
$239$	3.28854	−	11.1997i	0.212718	−	0.724451i	0.994852	−	0.101341i	$-0.0323132\pi$
$240$	0.781304	−	7.63209i	0.0504330	−	0.492649i
$241$	−7.39848	+	11.5123i	−0.476578	+	0.741570i	−0.993422	−	0.114509i	$-0.963470\pi$
$241$	−7.39848	+	11.5123i	−0.476578	+	0.741570i	0.516844	+	0.856080i	$0.327107\pi$
$242$	−13.6905	−	6.08433i	−0.880061	−	0.391116i
$243$	−4.53621	+	5.23506i	−0.290998	+	0.335829i
$244$	−28.8961	+	0.589333i	−1.84988	+	0.0377282i
$245$	0.909841	+	6.32808i	0.0581276	+	0.404287i
$246$	21.1639	+	17.9641i	1.34936	+	1.14535i
$247$	5.04246	+	11.0414i	0.320844	+	0.702550i
$248$	2.22686	+	2.41646i	0.141406	+	0.153446i
$249$	2.33778	+	1.06763i	0.148151	+	0.0676583i
$250$	−0.0144191	−	1.41414i	−0.000911944	−	0.0894381i
$251$	−9.04315	−	14.0714i	−0.570798	−	0.888180i	0.429088	−	0.903263i	$-0.358835\pi$
$251$	−9.04315	−	14.0714i	−0.570798	−	0.888180i	−0.999886	+	0.0150832i	$0.995199\pi$
$252$	1.00830	−	0.318535i	0.0635169	−	0.0200658i
$253$	−1.10948	−	2.84881i	−0.0697524	−	0.179103i
$254$	−1.67215	−	10.8440i	−0.104920	−	0.680413i
$255$	5.59344	+	8.70356i	0.350275	+	0.545038i
$256$	14.1201	+	7.52480i	0.882507	+	0.470300i
$257$	−10.7204	+	23.4745i	−0.668722	+	1.46430i	0.205443	+	0.978669i	$0.434136\pi$
$257$	−10.7204	+	23.4745i	−0.668722	+	1.46430i	−0.874165	+	0.485628i	$0.838591\pi$
$258$	−13.6849	−	29.1748i	−0.851985	−	1.81635i
$259$	1.61861	+	3.54426i	0.100576	+	0.220230i
$260$	−4.91632	+	8.00423i	−0.304897	+	0.496401i
$261$	−3.81362	+	0.548316i	−0.236057	+	0.0339399i
$262$	−1.27562	−	0.170151i	−0.0788082	−	0.0105119i
$263$	−8.38215	+	9.67352i	−0.516866	+	0.596495i	−0.952843	−	0.303463i	$-0.901857\pi$
$263$	−8.38215	+	9.67352i	−0.516866	+	0.596495i	0.435978	+	0.899957i	$0.356403\pi$
$264$	−0.387242	+	3.43650i	−0.0238331	+	0.211502i
$265$	−3.11015	−	1.99877i	−0.191055	−	0.122784i
$266$	2.41077	+	1.51480i	0.147814	+	0.0928784i
$267$	5.75222	−	19.5903i	0.352030	−	1.19891i
$268$	−13.0779	+	6.29788i	−0.798863	+	0.384704i
$269$	−20.0819	+	17.4011i	−1.22442	+	1.06096i	−0.228238	+	0.973605i	$0.573297\pi$
$269$	−20.0819	+	17.4011i	−1.22442	+	1.06096i	−0.996177	+	0.0873567i	$0.972158\pi$
$270$	−3.45793	−	5.26190i	−0.210443	−	0.320229i
$271$	2.37096	+	8.07475i	0.144026	+	0.490506i	0.999632	−	0.0271205i	$-0.00863378\pi$
$271$	2.37096	+	8.07475i	0.144026	+	0.490506i	−0.855607	+	0.517627i	$0.826816\pi$
$272$	−21.2140	+	3.93890i	−1.28629	+	0.238831i
$273$	−6.94608	−	0.998695i	−0.420396	−	0.0604438i
$274$	8.13194	+	9.19366i	0.491268	+	0.555409i
$275$			0.637476i			0.0384413i
$276$	14.3351	−	11.5301i	0.862874	−	0.694033i
$277$		−	17.2624i		−	1.03719i	−0.855019	−	0.518597i	$-0.826454\pi$
$277$		−	17.2624i		−	1.03719i	0.855019	−	0.518597i	$-0.173546\pi$
$278$	0.347874	−	0.307700i	0.0208641	−	0.0184546i
$279$	−0.780488	−	0.112217i	−0.0467266	−	0.00671827i
$280$	0.0673856	+	2.20232i	0.00402706	+	0.131614i
$281$	2.86828	+	9.76846i	0.171107	+	0.582737i	0.999737	+	0.0229403i	$0.00730276\pi$
$281$	2.86828	+	9.76846i	0.171107	+	0.582737i	−0.828630	+	0.559797i	$0.810879\pi$
$282$	−13.0600	+	8.58255i	−0.777711	+	0.511083i
$283$	1.90867	−	1.65387i	0.113458	−	0.0983123i	−0.596284	−	0.802774i	$-0.703357\pi$
$283$	1.90867	−	1.65387i	0.113458	−	0.0983123i	0.709742	+	0.704461i	$0.248811\pi$
$284$	7.46384	−	3.59432i	0.442897	−	0.213284i
$285$	−1.39652	+	4.75610i	−0.0827226	+	0.281727i
$286$	2.25277	−	3.58523i	0.133209	−	0.211999i
$287$	−6.70690	−	4.31026i	−0.395896	−	0.254427i
$288$	−3.76746	+	0.739335i	−0.222000	+	0.0435657i
$289$	7.92172	−	9.14216i	0.465984	−	0.537774i
$290$	1.06145	−	7.95770i	0.0623304	−	0.467292i
$291$	19.2867	−	2.77301i	1.13061	−	0.162557i
$292$	−19.0722	−	11.7144i	−1.11612	−	0.685535i
$293$	−0.272194	−	0.596021i	−0.0159017	−	0.0348199i	0.901515	−	0.432749i	$-0.142456\pi$
$293$	−0.272194	−	0.596021i	−0.0159017	−	0.0348199i	−0.917416	+	0.397929i	$0.869729\pi$
$294$	15.6998	−	7.36423i	0.915630	−	0.429490i
$295$	−0.513009	+	1.12333i	−0.0298685	+	0.0654029i
$296$	−4.39897	−	13.4458i	−0.255685	−	0.781521i
$297$	1.53444	+	2.38764i	0.0890375	+	0.138545i
$298$	−13.0756	+	2.01627i	−0.757451	+	0.116799i
$299$	−21.9389	+	5.10407i	−1.26876	+	0.295176i
$300$	−3.65780	+	1.15555i	−0.211183	+	0.0667156i
$301$	5.00353	+	7.78565i	0.288399	+	0.448757i
$302$	−15.0680	+	0.153639i	−0.867066	+	0.00884093i
$303$	29.7449	+	13.5840i	1.70880	+	0.780382i
$304$	−8.08221	−	6.44555i	−0.463546	−	0.369678i
$305$	6.00319	+	13.1452i	0.343742	+	0.752689i
$306$	3.35044	−	3.94723i	0.191532	−	0.225648i
$307$	2.60740	+	18.1349i	0.148812	+	1.03501i	0.918168	+	0.396191i	$0.129668\pi$
$307$	2.60740	+	18.1349i	0.148812	+	1.03501i	−0.769356	+	0.638820i	$0.779423\pi$
$308$	−0.0202517	−	0.992982i	−0.00115395	−	0.0565804i
$309$	10.6574	−	12.2993i	0.606280	−	0.699685i
$310$	0.667265	−	1.50143i	0.0378981	−	0.0852757i
$311$	4.72658	−	7.35470i	0.268020	−	0.417047i	−0.680990	−	0.732292i	$-0.738450\pi$
$311$	4.72658	−	7.35470i	0.268020	−	0.417047i	0.949010	+	0.315245i	$0.102087\pi$
$312$	24.6555	+	6.42735i	1.39584	+	0.363877i
$313$	−1.33943	+	4.56166i	−0.0757088	+	0.257840i	−0.988647	−	0.150258i	$-0.951990\pi$
$313$	−1.33943	+	4.56166i	−0.0757088	+	0.257840i	0.912938	+	0.408098i	$0.133808\pi$
$314$	−0.917637	−	3.01126i	−0.0517852	−	0.169935i
$315$	−0.346231	−	0.399572i	−0.0195079	−	0.0225133i
$316$	−22.0661	−	24.4403i	−1.24131	−	1.37487i
$317$	−8.93742	−	30.4380i	−0.501975	−	1.70957i	−0.686841	−	0.726807i	$-0.741003\pi$
$317$	−8.93742	−	30.4380i	−0.501975	−	1.70957i	0.184866	−	0.982764i	$-0.440815\pi$
$318$	−2.72698	+	9.65016i	−0.152922	+	0.541154i
$319$	−0.515010	+	3.58198i	−0.0288350	+	0.200552i
$320$	0.652263	−	7.97337i	0.0364626	−	0.445725i
$321$			11.9695i			0.668070i
$322$	−3.64301	+	3.82665i	−0.203017	+	0.213251i
$323$	13.9407			0.775682
$324$	−13.5221	+	16.2639i	−0.751228	+	0.903551i
$325$	4.64895	+	0.668418i	0.257877	+	0.0370771i
$326$	0.874969	−	3.09631i	0.0484600	−	0.171489i
$327$	−6.35901	+	1.86717i	−0.351654	+	0.103255i
$328$	22.4461	+	18.2783i	1.23938	+	1.00925i
$329$	3.39193	−	2.93913i	0.187003	−	0.162039i
$330$	1.65403	−	0.504041i	0.0910513	−	0.0277465i
$331$	13.1961	+	3.87473i	0.725324	+	0.212974i	0.623495	−	0.781828i	$-0.285712\pi$
$331$	13.1961	+	3.87473i	0.725324	+	0.212974i	0.101829	+	0.994802i	$0.467530\pi$
$332$	2.45993	+	1.06334i	0.135006	+	0.0583583i
$333$	2.85580	+	1.83531i	0.156497	+	0.100575i
$334$	−8.83896	+	19.8888i	−0.483647	+	1.08827i
$335$	5.48499	+	4.75277i	0.299677	+	0.259672i
$336$	5.66097	−	1.91617i	0.308831	−	0.104536i
$337$	24.8993	−	3.57998i	1.35635	−	0.195014i	0.574514	−	0.818494i	$-0.305191\pi$
$337$	24.8993	−	3.57998i	1.35635	−	0.195014i	0.781839	+	0.623480i	$0.214282\pi$
$338$	−9.76774	−	8.29095i	−0.531295	−	0.450968i
$339$	18.2408	−	8.33030i	0.990704	−	0.452440i
$340$	6.01644	+	8.95487i	0.326287	+	0.485646i
$341$	−0.307664	+	0.673690i	−0.0166609	+	0.0364824i
$342$	2.48047	−	0.0252918i	0.134128	−	0.00136762i
$343$	−8.77703	+	5.64066i	−0.473915	+	0.304567i
$344$	−14.8874	−	30.1249i	−0.802674	−	1.62423i
$345$	−8.13579	−	4.29174i	−0.438016	−	0.231060i
$346$	−1.63475	−	10.6015i	−0.0878849	−	0.569938i
$347$	7.63364	−	4.90584i	0.409795	−	0.263359i	−0.319462	−	0.947599i	$-0.603502\pi$
$347$	7.63364	−	4.90584i	0.409795	−	0.263359i	0.729257	+	0.684240i	$0.239866\pi$
$348$	−21.4867	+	3.53792i	−1.15181	+	0.189652i
$349$	17.0030	+	7.76503i	0.910152	+	0.415652i	0.814767	−	0.579788i	$-0.196865\pi$
$349$	17.0030	+	7.76503i	0.910152	+	0.415652i	0.0953846	+	0.995440i	$0.469592\pi$
$350$	0.997399	−	0.467845i	0.0533132	−	0.0250074i
$351$	19.0214	−	8.68677i	1.01529	−	0.463665i
$352$	−0.330646	+	3.59092i	−0.0176235	+	0.191397i
$353$	0.586620	+	4.08003i	0.0312226	+	0.217158i	0.999459	−	0.0328769i	$-0.0104669\pi$
$353$	0.586620	+	4.08003i	0.0312226	+	0.217158i	−0.968237	+	0.250035i	$0.919558\pi$
$354$	3.32028	+	0.442881i	0.176471	+	0.0235388i
$355$	−3.13039	−	2.71250i	−0.166144	−	0.143965i
$356$	5.58038	−	20.5459i	0.295760	−	1.08893i
$357$	−4.35729	+	6.78008i	−0.230612	+	0.358840i
$358$	−13.6482	+	21.7208i	−0.721331	+	1.14798i
$359$	−22.2072	−	6.52063i	−1.17205	−	0.344146i	−0.362947	−	0.931810i	$-0.618230\pi$
$359$	−22.2072	−	6.52063i	−1.17205	−	0.344146i	−0.809105	+	0.587664i	$0.800048\pi$
$360$	1.08675	+	1.58242i	0.0572767	+	0.0834010i
$361$	−8.06841	−	9.31144i	−0.424653	−	0.490076i
$362$	5.25989	+	8.00393i	0.276454	+	0.420677i
$363$	19.4955	−	5.72439i	1.02325	−	0.300452i
$364$	−7.26279	−	0.893488i	−0.380674	−	0.0468315i
$365$	−1.59268	+	11.0773i	−0.0833647	+	0.579814i
$366$	29.3605	−	25.9698i	1.53470	−	1.35747i
$367$	−12.9604			−0.676526			−0.338263	−	0.941052i	$-0.609839\pi$
$367$	−12.9604			−0.676526			−0.338263	+	0.941052i	$0.609839\pi$
$368$	14.6998	−	12.3254i	0.766280	−	0.642507i
$369$	−6.94602			−0.361596
$370$	−5.29832	+	4.68645i	−0.275447	+	0.243637i
$371$	0.409867	−	2.85069i	0.0212792	−	0.148000i
$372$	−4.42329	−	0.544166i	−0.229337	−	0.0282137i
$373$	−5.87463	+	1.72495i	−0.304177	+	0.0893143i	−0.430259	−	0.902705i	$-0.641578\pi$
$373$	−5.87463	+	1.72495i	−0.304177	+	0.0893143i	0.126082	+	0.992020i	$0.459760\pi$
$374$	−2.67069	−	4.06397i	−0.138098	−	0.210143i
$375$	1.25602	+	1.44952i	0.0648605	+	0.0748531i
$376$	−13.4331	+	9.22533i	−0.692757	+	0.475760i
$377$	25.5824	+	7.51167i	1.31756	+	0.386871i
$378$	2.60959	−	4.15310i	0.134223	−	0.213612i
$379$	−5.33936	+	8.30821i	−0.274265	+	0.426764i	−0.950874	−	0.309578i	$-0.899812\pi$
$379$	−5.33936	+	8.30821i	−0.274265	+	0.426764i	0.676609	+	0.736342i	$0.263449\pi$
$380$	−1.35480	+	4.98812i	−0.0694997	+	0.255885i
$381$	11.2461	+	9.74481i	0.576156	+	0.499242i
$382$	29.1404	+	3.88693i	1.49095	+	0.198873i
$383$	−1.53174	−	10.6535i	−0.0782681	−	0.544366i	−0.990797	−	0.135355i	$-0.956783\pi$
$383$	−1.53174	−	10.6535i	−0.0782681	−	0.544366i	0.912529	−	0.409012i	$-0.134126\pi$
$384$	−21.2039	+	4.61200i	−1.08205	+	0.235355i
$385$	−0.451718	+	0.206293i	−0.0230217	+	0.0105137i
$386$	13.3520	−	6.26297i	0.679600	−	0.318777i
$387$	7.33457	+	3.34959i	0.372837	+	0.170269i
$388$	20.0482	−	3.30105i	1.01779	−	0.167586i
$389$	−30.9110	+	19.8653i	−1.56725	+	1.00721i	−0.586968	+	0.809610i	$0.699679\pi$
$389$	−30.9110	+	19.8653i	−1.56725	+	1.00721i	−0.980283	+	0.197601i	$0.936685\pi$
$390$	−1.94153	−	12.5909i	−0.0983131	−	0.637566i
$391$	−5.13480	+	25.3547i	−0.259678	+	1.28224i
$392$	16.2111	−	8.01131i	0.818782	−	0.404632i
$393$	1.46829	−	0.943610i	0.0740652	−	0.0475988i
$394$	26.0358	−	0.265471i	1.31166	−	0.0133742i
$395$	−6.83935	+	14.9761i	−0.344125	+	0.753528i
$396$	−0.482569	−	0.718257i	−0.0242500	−	0.0360937i
$397$	7.74945	−	3.53906i	0.388934	−	0.177620i	−0.211344	−	0.977412i	$-0.567784\pi$
$397$	7.74945	−	3.53906i	0.388934	−	0.177620i	0.600278	+	0.799792i	$0.295057\pi$
$398$	28.1094	+	23.8595i	1.40900	+	1.19597i
$399$	−3.82212	+	0.549538i	−0.191345	+	0.0275113i
$400$	−3.78883	+	1.28248i	−0.189442	+	0.0641239i
$401$	25.1701	+	21.8100i	1.25693	+	1.08914i	0.992179	+	0.124824i	$0.0398365\pi$
$401$	25.1701	+	21.8100i	1.25693	+	1.08914i	0.264755	+	0.964316i	$0.414709\pi$
$402$	7.99491	−	17.9896i	0.398750	−	0.897239i
$403$	4.59045	+	2.95010i	0.228666	+	0.146955i
$404$	31.2990	+	13.5294i	1.55719	+	0.673115i
$405$	10.1471	+	2.97945i	0.504213	+	0.148050i
$406$	5.98235	−	1.82303i	0.296899	−	0.0904756i
$407$	2.40971	−	2.08802i	0.119445	−	0.103499i
$408$	18.4777	−	22.6910i	0.914782	−	1.12337i
$409$	14.6955	−	4.31498i	0.726645	−	0.213362i	0.102569	−	0.994726i	$-0.467294\pi$
$409$	14.6955	−	4.31498i	0.726645	−	0.213362i	0.624076	+	0.781364i	$0.285476\pi$
$410$	3.93584	−	13.9280i	0.194377	−	0.687857i
$411$	−16.4769	−	2.36902i	−0.812747	−	0.116855i
$412$	10.8493	−	13.0491i	0.534506	−	0.642885i
$413$	−0.962012			−0.0473375
$414$	−0.867634	+	4.52067i	−0.0426419	+	0.222179i
$415$		−	1.33996i		−	0.0657759i
$416$	25.8409	+	6.17653i	1.26696	+	0.302829i
$417$	−0.0896404	+	0.623462i	−0.00438971	+	0.0305311i
$418$	0.633587	−	2.24212i	0.0309898	−	0.109666i
$419$	−2.78261	−	9.47669i	−0.135939	−	0.462966i	0.863181	−	0.504894i	$-0.168468\pi$
$419$	−2.78261	−	9.47669i	−0.135939	−	0.462966i	−0.999121	+	0.0419274i	$0.986650\pi$
$420$	−2.00252	−	2.21799i	−0.0977131	−	0.108227i
$421$	10.2180	+	11.7922i	0.497994	+	0.574716i	0.947984	−	0.318318i	$-0.103118\pi$
$421$	10.2180	+	11.7922i	0.497994	+	0.574716i	−0.449990	+	0.893034i	$0.648573\pi$
$422$	−8.31707	−	27.2928i	−0.404869	−	1.32859i
$423$	1.10166	−	3.75191i	0.0535645	−	0.182424i
$424$	−2.63780	+	10.1187i	−0.128103	+	0.491405i
$425$	2.91630	−	4.53784i	0.141461	−	0.220118i
$426$	−4.56285	+	10.2670i	−0.221071	+	0.497438i
$427$	−7.37202	+	8.50777i	−0.356757	+	0.411720i
$428$	0.254500	+	12.4786i	0.0123017	+	0.603177i
$429$	0.817258	+	5.68415i	0.0394576	+	0.274434i
$430$	−10.8725	+	12.8092i	−0.524320	+	0.617712i
$431$	11.6855	+	25.5876i	0.562869	+	1.23251i	0.950508	+	0.310700i	$0.100564\pi$
$431$	11.6855	+	25.5876i	0.562869	+	1.23251i	−0.387639	+	0.921811i	$0.626709\pi$
$432$	−11.1039	+	13.9234i	−0.534237	+	0.669891i
$433$	−0.135444	−	0.0618552i	−0.00650902	−	0.00297257i	0.412158	−	0.911112i	$-0.364775\pi$
$433$	−0.135444	−	0.0618552i	−0.00650902	−	0.00297257i	−0.418667	+	0.908140i	$0.637502\pi$
$434$	1.27985	−	0.0130499i	0.0614350	−	0.000626414i
$435$	5.88651	+	9.15959i	0.282237	+	0.439169i
$436$	−6.58982	+	2.08181i	−0.315595	+	0.0997007i
$437$	−10.7918	+	6.09586i	−0.516240	+	0.291605i
$438$	30.0012	−	4.62620i	1.43351	−	0.221048i
$439$	−21.3193	−	33.1734i	−1.01751	−	1.58328i	−0.793383	−	0.608723i	$-0.791682\pi$
$439$	−21.3193	−	33.1734i	−1.01751	−	1.58328i	−0.224131	−	0.974559i	$-0.571954\pi$
$440$	1.71367	−	0.560651i	0.0816962	−	0.0267280i
$441$	−1.80251	+	3.94694i	−0.0858336	+	0.187949i
$442$	−32.4378	+	15.2154i	−1.54291	+	0.723725i
$443$	7.29317	+	15.9698i	0.346509	+	0.758748i	0.999998	+	0.00181286i	$0.000577051\pi$
$443$	7.29317	+	15.9698i	0.346509	+	0.758748i	−0.653490	+	0.756936i	$0.726696\pi$
$444$	16.3490	+	10.0418i	0.775890	+	0.476564i
$445$	−10.5368	+	1.51496i	−0.499492	+	0.0718161i
$446$	2.52620	−	18.9390i	0.119619	−	0.896787i
$447$	11.7502	−	13.5605i	0.555767	−	0.641389i
$448$	5.86104	−	2.11805i	0.276908	−	0.100069i
$449$	−17.3802	−	11.1696i	−0.820221	−	0.527124i	0.0619358	−	0.998080i	$-0.480273\pi$
$449$	−17.3802	−	11.1696i	−0.820221	−	0.527124i	−0.882157	+	0.470956i	$0.843909\pi$
$450$	0.510663	−	0.812709i	0.0240729	−	0.0383115i
$451$	−1.83805	+	6.25984i	−0.0865506	+	0.294764i
$452$	18.8396	−	9.07250i	0.886142	−	0.426735i
$453$	15.4450	−	13.3832i	0.725670	−	0.628797i
$454$	−19.6134	+	12.8892i	−0.920503	+	0.604921i
$455$	1.03080	+	3.51057i	0.0483244	+	0.164578i
$456$	14.0137	−	0.428784i	0.656249	−	0.0200797i
$457$	0.274805	+	0.0395110i	0.0128548	+	0.00184825i	0.148739	−	0.988876i	$-0.452478\pi$
$457$	0.274805	+	0.0395110i	0.0128548	+	0.00184825i	−0.135884	+	0.990725i	$0.543388\pi$
$458$	6.77264	−	5.99051i	0.316465	−	0.279918i
$459$		−	24.0160i		−	1.12097i
$460$	−8.57313	−	4.30132i	−0.399724	−	0.200550i
$461$		−	19.7062i		−	0.917811i	−0.888485	−	0.458905i	$-0.848242\pi$
$461$		−	19.7062i		−	0.917811i	0.888485	−	0.458905i	$-0.151758\pi$
$462$	0.892424	+	1.00894i	0.0415193	+	0.0469401i
$463$	−6.63848	−	0.954470i	−0.308516	−	0.0443580i	−0.0136822	−	0.999906i	$-0.504355\pi$
$463$	−6.63848	−	0.954470i	−0.308516	−	0.0443580i	−0.294834	+	0.955548i	$0.595264\pi$
$464$	−22.3255	+	4.14528i	−1.03644	+	0.192440i
$465$	0.627790	+	2.13806i	0.0291131	+	0.0991501i
$466$	−16.9094	−	25.7308i	−0.783311	−	1.19196i
$467$	4.23467	−	3.66937i	0.195957	−	0.169798i	−0.551355	−	0.834270i	$-0.685889\pi$
$467$	4.23467	−	3.66937i	0.195957	−	0.169798i	0.747313	+	0.664472i	$0.231344\pi$
$468$	−5.74405	+	2.76613i	−0.265519	+	0.127865i
$469$	−1.59284	+	5.42473i	−0.0735507	+	0.250491i
$470$	6.89902	+	4.33498i	0.318228	+	0.199958i
$471$	3.59162	+	2.30819i	0.165493	+	0.106356i
$472$	3.47094	+	0.391123i	0.159763	+	0.0180029i
$473$	4.95956	−	5.72363i	0.228041	−	0.263173i
$474$	44.2655	+	5.90441i	2.03318	+	0.271199i
$475$	2.55811	−	0.367801i	0.117374	−	0.0168758i
$476$	−4.39849	+	7.16114i	−0.201604	+	0.328230i
$477$	−1.04236	−	2.28244i	−0.0477262	−	0.104506i
$478$	7.01020	+	14.9450i	0.320639	+	0.683571i
$479$	−10.0271	+	21.9563i	−0.458150	+	1.00321i	0.529755	+	0.848151i	$0.322284\pi$
$479$	−10.0271	+	21.9563i	−0.458150	+	1.00321i	−0.987905	+	0.155059i	$0.950443\pi$
$480$	6.32335	+	8.81667i	0.288620	+	0.402424i
$481$	−12.7007	−	19.7627i	−0.579104	−	0.901103i
$482$	−2.94939	−	19.1270i	−0.134341	−	0.871209i
$483$	0.408333	−	7.15390i	0.0185798	−	0.325514i
$484$	20.2031	−	6.38242i	0.918322	−	0.290110i
$485$	−5.49241	−	8.54635i	−0.249397	−	0.388070i
$486$	−0.0998808	−	9.79572i	−0.00453069	−	0.444343i
$487$	34.1825	+	15.6106i	1.54896	+	0.707385i	0.992357	−	0.123396i	$-0.0393786\pi$
$487$	34.1825	+	15.6106i	1.54896	+	0.707385i	0.556599	+	0.830781i	$0.312106\pi$
$488$	30.0573	−	27.6988i	1.36063	−	1.25387i
$489$	1.81277	+	3.96940i	0.0819761	+	0.179503i
$490$	−6.89296	−	5.85081i	−0.311392	−	0.264313i
$491$	2.07575	+	14.4371i	0.0936772	+	0.651539i	0.981515	+	0.191383i	$0.0612973\pi$
$491$	2.07575	+	14.4371i	0.0936772	+	0.651539i	−0.887838	+	0.460156i	$0.847794\pi$
$492$	−39.2504	+	0.800507i	−1.76955	+	0.0360897i
$493$	20.0527	−	23.1421i	0.903129	−	1.04227i
$494$	−15.6869	−	6.97153i	−0.705785	−	0.313664i
$495$	−0.233912	+	0.363974i	−0.0105135	+	0.0163594i
$496$	−4.62303	−	0.473264i	−0.207580	−	0.0212502i
$497$	0.909066	−	3.09600i	0.0407772	−	0.138874i
$498$	−3.47673	+	1.05948i	−0.155796	+	0.0474765i
$499$	23.3870	+	26.9901i	1.04695	+	1.20824i	0.977561	+	0.210653i	$0.0675589\pi$
$499$	23.3870	+	26.9901i	1.04695	+	1.20824i	0.0693872	+	0.997590i	$0.477896\pi$
$500$	1.34027	+	1.48448i	0.0599387	+	0.0663879i
$501$	−8.31606	−	28.3219i	−0.371534	−	1.26533i
$502$	22.7637	+	6.43266i	1.01599	+	0.287104i
$503$	−1.45703	+	10.1339i	−0.0649657	+	0.451847i	0.931211	+	0.364481i	$0.118754\pi$
$503$	−1.45703	+	10.1339i	−0.0649657	+	0.451847i	−0.996176	+	0.0873650i	$0.972155\pi$
$504$	−0.769630	+	1.28216i	−0.0342820	+	0.0571120i
$505$		−	17.0490i		−	0.758671i
$506$	3.84449	+	1.97818i	0.170908	+	0.0879408i
$507$	17.3760			0.771697
$508$	11.9317	+	9.92023i	0.529384	+	0.440139i
$509$	23.7783	+	3.41880i	1.05395	+	0.151536i	0.647445	−	0.762112i	$-0.275837\pi$
$509$	23.7783	+	3.41880i	1.05395	+	0.151536i	0.406508	+	0.913647i	$0.366746\pi$
$510$	−14.0800	−	3.97878i	−0.623473	−	0.176183i
$511$	−8.36485	+	2.45614i	−0.370039	+	0.108653i
$512$	−22.0078	+	5.25904i	−0.972616	+	0.232419i
$513$	8.69598	−	7.53511i	0.383937	−	0.332683i
$514$	−10.6386	−	34.9110i	−0.469249	−	1.53986i
$515$	−8.14138	−	2.39053i	−0.358752	−	0.105339i
$516$	41.8320	+	18.0825i	1.84155	+	0.796036i
$517$	−3.08974	−	1.98566i	−0.135887	−	0.0873291i
$518$	−5.03542	−	2.23784i	−0.221244	−	0.0983249i
$519$	10.9946	+	9.52686i	0.482609	+	0.418183i
$520$	−2.29183	−	13.0852i	−0.100503	−	0.573826i
$521$	4.15671	−	0.597645i	0.182109	−	0.0261833i	−0.0506569	−	0.998716i	$-0.516132\pi$
$521$	4.15671	−	0.597645i	0.182109	−	0.0261833i	0.232766	+	0.972533i	$0.425222\pi$
$522$	3.52599	−	4.15405i	0.154328	−	0.181818i
$523$	−26.0102	+	11.8785i	−1.13735	+	0.519409i	−0.892901	−	0.450253i	$-0.851334\pi$
$523$	−26.0102	+	11.8785i	−1.13735	+	0.519409i	−0.244447	+	0.969663i	$0.578606\pi$
$524$	1.51068	−	1.01497i	0.0659945	−	0.0443392i
$525$	−0.620679	+	1.35910i	−0.0270887	+	0.0593159i
$526$	−0.184563	−	18.1008i	−0.00804733	−	0.789234i
$527$	5.27205	−	3.38814i	0.229654	−	0.147590i
$528$	−2.80967	−	4.00309i	−0.122275	−	0.174212i
$529$	−7.11191	−	21.8728i	−0.309214	−	0.950993i
$530$	5.16734	−	0.796807i	0.224455	−	0.0346111i
$531$	−0.705096	+	0.453138i	−0.0305986	+	0.0196645i
$532$	−3.97302	+	0.654182i	−0.172252	+	0.0283624i
$533$	43.7241	+	19.9681i	1.89390	+	0.864915i
$534$	12.2621	+	26.1415i	0.530631	+	1.13125i
$535$	5.67666	−	2.59244i	0.245423	−	0.112081i
$536$	7.95251	−	18.9248i	0.343496	−	0.817429i
$537$	−4.95129	−	34.4370i	−0.213664	−	1.48606i
$538$	4.96848	−	37.2488i	0.214207	−	1.60591i
$539$	3.08005	+	2.66888i	0.132667	+	0.114957i
$540$	8.59316	+	2.33395i	0.369791	+	0.100437i
$541$	−21.0924	+	32.8204i	−0.906832	+	1.41106i	0.00477181	+	0.999989i	$0.498481\pi$
$541$	−21.0924	+	32.8204i	−0.906832	+	1.41106i	−0.911604	+	0.411070i	$0.865155\pi$
$542$	−10.0773	−	6.33203i	−0.432856	−	0.271984i
$543$	−12.4632	−	3.65951i	−0.534846	−	0.157045i
$544$	18.7813	−	24.0492i	0.805240	−	1.03110i
$545$	2.26282	+	2.61143i	0.0969285	+	0.111861i
$546$	8.29367	−	5.45030i	0.354936	−	0.233251i
$547$	−23.2679	+	6.83208i	−0.994865	+	0.292119i	−0.738347	−	0.674421i	$-0.764393\pi$
$547$	−23.2679	+	6.83208i	−0.994865	+	0.292119i	−0.256518	+	0.966540i	$0.582575\pi$
$548$	−17.2282	−	2.11946i	−0.735953	−	0.0905389i
$549$	−1.39582	+	9.70813i	−0.0595721	+	0.414333i
$550$	−0.597291	−	0.675274i	−0.0254686	−	0.0287938i
$551$	14.6711			0.625012
$552$	−4.38181	+	25.6453i	−0.186502	+	1.09154i
$553$	−12.8254			−0.545391
$554$	16.1742	+	18.2859i	0.687175	+	0.776893i
$555$	1.36527	−	9.49569i	0.0579527	−	0.403070i
$556$	−0.0801973	+	0.651890i	−0.00340112	+	0.0276463i
$557$	6.97772	−	2.04884i	0.295655	−	0.0868122i	−0.130541	−	0.991443i	$-0.541671\pi$
$557$	6.97772	−	2.04884i	0.295655	−	0.0868122i	0.426196	+	0.904631i	$0.359853\pi$
$558$	0.931909	−	0.612417i	0.0394508	−	0.0259257i
$559$	−36.5407	−	42.1702i	−1.54551	−	1.78361i
$560$	−2.13487	−	2.26976i	−0.0902146	−	0.0959149i
$561$	6.32813	+	1.85811i	0.267174	+	0.0784494i
$562$	−12.1910	−	7.66019i	−0.514247	−	0.323126i
$563$	−12.0356	+	18.7277i	−0.507239	+	0.789279i	−0.996564	−	0.0828222i	$-0.973607\pi$
$563$	−12.0356	+	18.7277i	−0.507239	+	0.789279i	0.489326	+	0.872101i	$0.337243\pi$
$564$	5.79283	−	21.3281i	0.243922	−	0.898077i
$565$	−7.90149	−	6.84668i	−0.332418	−	0.288042i
$566$	−0.472225	+	3.54028i	−0.0198491	+	0.148809i
$567$	1.17243	+	8.15444i	0.0492375	+	0.342454i
$568$	−4.53865	+	10.8008i	−0.190437	+	0.453190i
$569$	−10.4171	+	4.75734i	−0.436708	+	0.199438i	−0.621623	−	0.783317i	$-0.713526\pi$
$569$	−10.4171	+	4.75734i	−0.436708	+	0.199438i	0.184915	+	0.982755i	$0.440799\pi$
$570$	−2.97697	−	6.34659i	−0.124691	−	0.265830i
$571$	9.58694	+	4.37821i	0.401201	+	0.183222i	0.605788	−	0.795626i	$-0.292858\pi$
$571$	9.58694	+	4.37821i	0.401201	+	0.183222i	−0.204587	+	0.978848i	$0.565585\pi$
$572$	0.972882	+	5.90858i	0.0406783	+	0.247050i
$573$	−33.5416	+	21.5559i	−1.40122	+	0.900511i
$574$	11.1431	−	1.71828i	0.465105	−	0.0717196i
$575$	−0.273293	+	4.78804i	−0.0113971	+	0.199675i
$576$	3.29811	−	4.31314i	0.137421	−	0.179714i
$577$	−26.7727	+	17.2058i	−1.11456	+	0.716286i	−0.962283	−	0.272052i	$-0.912298\pi$
$577$	−26.7727	+	17.2058i	−1.11456	+	0.716286i	−0.152280	+	0.988337i	$0.548662\pi$
$578$	0.174425	+	17.1066i	0.00725513	+	0.711540i
$579$	−8.30893	+	18.1940i	−0.345307	+	0.756118i
$580$	6.33167	+	9.42407i	0.262908	+	0.391313i
$581$	0.949499	−	0.433622i	0.0393919	−	0.0179897i
$582$	−17.8321	+	21.0083i	−0.739163	+	0.870824i
$583$	−2.33279	+	0.335405i	−0.0966143	+	0.0138910i
$584$	31.1790	−	5.46089i	1.29020	−	0.225973i
$585$	2.40910	+	2.08750i	0.0996040	+	0.0863073i
$586$	0.846782	+	0.376326i	0.0349802	+	0.0155459i
$587$	−5.93136	−	3.81185i	−0.244813	−	0.157332i	0.412480	−	0.910966i	$-0.364663\pi$
$587$	−5.93136	−	3.81185i	−0.244813	−	0.157332i	−0.657294	+	0.753635i	$0.728299\pi$
$588$	−9.73068	+	22.5110i	−0.401287	+	0.928337i
$589$	2.88094	+	0.845921i	0.118707	+	0.0348556i
$590$	−0.509093	−	1.67061i	−0.0209590	−	0.0687778i
$591$	−26.6872	+	23.1246i	−1.09777	+	0.951220i
$592$	17.2580	+	10.1214i	0.709299	+	0.415986i
$593$	2.22790	−	0.654169i	0.0914887	−	0.0268635i	−0.235668	−	0.971834i	$-0.575728\pi$
$593$	2.22790	−	0.654169i	0.0914887	−	0.0268635i	0.327157	+	0.944970i	$0.393910\pi$
$594$	−3.86256	−	1.09150i	−0.158483	−	0.0447846i
$595$	4.15927	+	0.598013i	0.170514	+	0.0245161i
$596$	11.9618	−	14.3872i	0.489972	−	0.589322i
$597$	−50.0044			−2.04654
$598$	18.4574	−	25.9627i	0.754781	−	1.06169i
$599$			2.89657i			0.118351i	0.998248	+	0.0591753i	$0.0188471\pi$
$599$			2.89657i			0.118351i	−0.998248	+	0.0591753i	$0.981153\pi$
$600$	2.79198	−	4.65129i	0.113982	−	0.189888i
$601$	3.75460	−	26.1138i	0.153153	−	1.06520i	−0.757739	−	0.652558i	$-0.773696\pi$
$601$	3.75460	−	26.1138i	0.153153	−	1.06520i	0.910892	−	0.412646i	$-0.135395\pi$
$602$	−12.5951	−	3.55916i	−0.513336	−	0.145061i
$603$	1.38776	+	4.72627i	0.0565139	+	0.192469i
$604$	15.8175	−	14.2809i	0.643604	−	0.581081i
$605$	−6.93735	−	8.00613i	−0.282043	−	0.325495i
$606$	−44.2363	+	13.4804i	−1.79698	+	0.547602i
$607$	11.4245	−	38.9083i	0.463707	−	1.57924i	−0.313240	−	0.949674i	$-0.601415\pi$
$607$	11.4245	−	38.9083i	0.463707	−	1.57924i	0.776947	−	0.629566i	$-0.216767\pi$
$608$	14.6007	−	0.744989i	0.592135	−	0.0302133i
$609$	−4.58560	+	7.13533i	−0.185818	+	0.289138i
$610$	−18.6756	−	8.29981i	−0.756155	−	0.336050i
$611$	−17.7206	+	20.4506i	−0.716898	+	0.827344i
$612$	0.149301	+	7.32051i	0.00603513	+	0.295914i
$613$	−2.77686	−	19.3135i	−0.112156	−	0.780063i	−0.965815	−	0.259231i	$-0.916531\pi$
$613$	−2.77686	−	19.3135i	−0.112156	−	0.780063i	0.853659	−	0.520832i	$-0.174378\pi$
$614$	−19.7537	−	16.7671i	−0.797194	−	0.676665i
$615$	8.15430	+	17.8554i	0.328813	+	0.720000i
$616$	0.951839	+	1.03288i	0.0383507	+	0.0416161i
$617$	−36.3632	−	16.6065i	−1.46393	−	0.668553i	−0.485329	−	0.874332i	$-0.661300\pi$
$617$	−36.3632	−	16.6065i	−1.46393	−	0.668553i	−0.978599	+	0.205778i	$0.934027\pi$
$618$	0.234662	+	23.0142i	0.00943947	+	0.925767i
$619$	5.11181	+	7.95412i	0.205461	+	0.319703i	0.928657	−	0.370939i	$-0.120964\pi$
$619$	5.11181	+	7.95412i	0.205461	+	0.319703i	−0.723196	+	0.690643i	$0.757328\pi$
$620$	0.699957	+	2.21566i	0.0281109	+	0.0889831i
$621$	10.5015	+	18.5912i	0.421410	+	0.746041i
$622$	1.88424	+	12.2194i	0.0755512	+	0.489954i
$623$	−4.48330	−	6.97616i	−0.179620	−	0.279494i
$624$	−32.1395	+	16.2928i	−1.28661	+	0.652233i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−2.85526	−	6.08713i	−0.114119	−	0.243291i
$627$	1.31267	+	2.87435i	0.0524230	+	0.114790i
$628$	3.79348	+	2.33002i	0.151376	+	0.0929777i
$629$	−26.7056	+	3.83968i	−1.06482	+	0.153098i
$630$	0.741143	+	0.0988584i	0.0295279	+	0.00393861i
$631$	−12.5083	+	14.4354i	−0.497949	+	0.574664i	−0.947972	−	0.318353i	$-0.896870\pi$
$631$	−12.5083	+	14.4354i	−0.497949	+	0.574664i	0.450023	+	0.893017i	$0.351416\pi$
$632$	46.2740	+	5.21439i	1.84068	+	0.207417i
$633$	32.5529	+	20.9205i	1.29386	+	0.831514i
$634$	37.9866	+	23.8688i	1.50864	+	0.947951i
$635$	2.18582	−	7.44422i	0.0867416	−	0.295415i
$636$	−6.15316	−	12.7774i	−0.243989	−	0.506658i
$637$	22.6930	−	19.6636i	0.899128	−	0.779099i
$638$	−2.81063	−	4.27691i	−0.111274	−	0.169324i
$639$	−0.792021	−	2.69738i	−0.0313319	−	0.106707i
$640$	6.77980	+	9.05728i	0.267995	+	0.358020i
$641$	−29.9862	−	4.31136i	−1.18438	−	0.170289i	−0.478157	−	0.878275i	$-0.658695\pi$
$641$	−29.9862	−	4.31136i	−1.18438	−	0.170289i	−0.706226	+	0.707986i	$0.749604\pi$
$642$	−11.2149	−	12.6792i	−0.442618	−	0.500407i
$643$		−	1.14280i		−	0.0450675i	−0.999746	−	0.0225338i	$-0.992827\pi$
$643$		−	1.14280i		−	0.0450675i	0.999746	−	0.0225338i	$-0.00717333\pi$
$644$	0.273594	−	7.46690i	0.0107811	−	0.294237i
$645$		−	22.7865i		−	0.897217i
$646$	−14.7673	+	13.0619i	−0.581012	+	0.513914i
$647$	23.3894	+	3.36289i	0.919532	+	0.132209i	0.585796	−	0.810458i	$-0.300782\pi$
$647$	23.3894	+	3.36289i	0.919532	+	0.132209i	0.333735	+	0.942667i	$0.391691\pi$
$648$	−0.914806	−	29.8980i	−0.0359370	−	1.17450i
$649$	0.221791	+	0.755350i	0.00870605	+	0.0296501i
$650$	−5.55088	+	3.64784i	−0.217723	+	0.143080i
$651$	−1.31188	+	1.13675i	−0.0514165	+	0.0445527i
$652$	1.97428	+	4.09972i	0.0773187	+	0.160557i
$653$	2.07662	−	7.07232i	0.0812644	−	0.276761i	−0.908830	−	0.417168i	$-0.863023\pi$
$653$	2.07662	−	7.07232i	0.0812644	−	0.276761i	0.990094	+	0.140407i	$0.0448410\pi$
$654$	4.98659	−	7.93604i	0.194991	−	0.310324i
$655$	−0.765532	−	0.491978i	−0.0299118	−	0.0192232i
$656$	−40.9031	+	1.66912i	−1.59700	+	0.0651682i
$657$	−4.97401	+	5.74031i	−0.194055	+	0.223951i
$658$	−0.839201	+	6.29151i	−0.0327155	+	0.245268i
$659$	−31.8131	+	4.57404i	−1.23926	+	0.178179i	−0.730611	−	0.682793i	$-0.760765\pi$
$659$	−31.8131	+	4.57404i	−1.23926	+	0.178179i	−0.508651	+	0.860973i	$0.669856\pi$
$660$	−1.27983	+	2.08369i	−0.0498175	+	0.0811075i
$661$	13.5693	+	29.7126i	0.527785	+	1.15569i	0.966407	+	0.257016i	$0.0827392\pi$
$661$	13.5693	+	29.7126i	0.527785	+	1.15569i	−0.438623	+	0.898671i	$0.644533\pi$
$662$	−17.6090	+	8.25978i	−0.684394	+	0.321026i
$663$	20.1860	−	44.2011i	0.783958	−	1.71663i
$664$	−3.60210	+	1.17847i	−0.139788	+	0.0457337i
$665$	1.08845	+	1.69366i	0.0422083	+	0.0656774i
$666$	−4.74475	+	0.731644i	−0.183855	+	0.0283506i
$667$	−5.40384	+	26.6832i	−0.209238	+	1.03318i
$668$	−9.27201	−	29.3499i	−0.358745	−	1.13558i
$669$	14.0097	+	21.7995i	0.541645	+	0.842815i
$670$	−10.2634	+	0.104649i	−0.396509	+	0.00404296i
$671$	8.37972	+	3.82689i	0.323496	+	0.147735i
$672$	−4.20124	+	7.33390i	−0.162066	+	0.282911i
$673$	−1.80487	−	3.95211i	−0.0695725	−	0.152343i	0.871651	−	0.490127i	$-0.163050\pi$
$673$	−1.80487	−	3.95211i	−0.0695725	−	0.152343i	−0.941223	+	0.337785i	$0.890322\pi$
$674$	−23.0214	+	27.1220i	−0.886751	+	1.04470i
$675$	−0.633619	−	4.40692i	−0.0243880	−	0.169622i
$676$	18.1152	−	0.369457i	0.696739	−	0.0142099i
$677$	33.3137	−	38.4460i	1.28035	−	1.47760i	0.481016	−	0.876712i	$-0.340268\pi$
$677$	33.3137	−	38.4460i	1.28035	−	1.47760i	0.799332	−	0.600889i	$-0.205187\pi$
$678$	−11.5172	+	25.9152i	−0.442315	+	0.995266i
$679$	4.27859	−	6.65761i	0.164197	−	0.255496i
$680$	−14.7635	−	3.84866i	−0.566156	−	0.147589i
$681$	8.96754	−	30.5406i	0.343637	−	1.17032i
$682$	−0.305316	−	1.00190i	−0.0116911	−	0.0383649i
$683$	−26.4453	−	30.5195i	−1.01190	−	1.16780i	−0.985764	−	0.168137i	$-0.946225\pi$
$683$	−26.4453	−	30.5195i	−1.01190	−	1.16780i	−0.0261369	−	0.999658i	$-0.508321\pi$
$684$	−2.60385	+	2.35090i	−0.0995605	+	0.0898888i
$685$	2.44517	+	8.32749i	0.0934252	+	0.318177i
$686$	4.01237	−	14.1989i	0.153193	−	0.542115i
$687$	−1.74518	+	12.1380i	−0.0665827	+	0.463093i
$688$	43.9960	+	17.9622i	1.67733	+	0.684804i
$689$			17.3641i			0.661520i
$690$	12.6394	−	3.07671i	0.481173	−	0.117129i
$691$	−14.7469			−0.560997			−0.280499	−	0.959854i	$-0.590500\pi$
$691$	−14.7469			−0.560997			−0.280499	+	0.959854i	$0.590500\pi$
$692$	11.6649	+	9.69836i	0.443431	+	0.368676i
$693$	−0.333609	−	0.0479657i	−0.0126728	−	0.00182207i
$694$	−3.48967	+	12.3492i	−0.132466	+	0.468767i
$695$	0.315100	−	0.0925216i	0.0119524	−	0.00350954i
$696$	19.4458	−	23.8799i	0.737093	−	0.905167i
$697$	41.7213	−	36.1517i	1.58031	−	1.36934i
$698$	−25.2867	+	7.70576i	−0.957117	+	0.291667i
$699$	40.0663	+	11.7645i	1.51545	+	0.444975i
$700$	−0.618185	+	1.43011i	−0.0233652	+	0.0540531i
$701$	−16.5352	−	10.6265i	−0.624525	−	0.401358i	0.189754	−	0.981832i	$-0.439231\pi$
$701$	−16.5352	−	10.6265i	−0.624525	−	0.401358i	−0.814279	+	0.580474i	$0.802867\pi$
$702$	−12.0100	+	27.0241i	−0.453289	+	1.01996i
$703$	−9.76928	−	8.46513i	−0.368455	−	0.319268i
$704$	−3.01430	−	4.11364i	−0.113606	−	0.155039i
$705$	−10.9379	+	1.57264i	−0.411947	+	0.0592290i
$706$	−4.44424	−	3.77231i	−0.167261	−	0.141973i
$707$	12.0810	−	5.51721i	0.454353	−	0.207496i
$708$	−3.93212	+	2.64184i	−0.147778	+	0.0992864i
$709$	5.78101	−	12.6586i	0.217110	−	0.475405i	−0.769470	−	0.638683i	$-0.779479\pi$
$709$	5.78101	−	12.6586i	0.217110	−	0.475405i	0.986580	+	0.163278i	$0.0522068\pi$
$710$	5.85751	−	0.0597254i	0.219828	−	0.00224145i
$711$	−9.40023	+	6.04116i	−0.352536	+	0.226561i
$712$	13.3395	+	26.9928i	0.499919	+	1.01160i
$713$	−2.59966	+	4.92814i	−0.0973580	+	0.184560i
$714$	−1.73703	−	11.2647i	−0.0650066	−	0.421571i
$715$	2.51877	−	1.61872i	0.0941967	−	0.0605365i
$716$	−5.89413	−	35.7966i	−0.220274	−	1.33778i
$717$	−20.3648	−	9.30027i	−0.760536	−	0.347325i
$718$	29.6335	−	13.9001i	1.10591	−	0.518746i
$719$	−14.8268	+	6.77118i	−0.552947	+	0.252522i	−0.672236	−	0.740337i	$-0.734666\pi$
$719$	−14.8268	+	6.77118i	−0.552947	+	0.252522i	0.119289	+	0.992860i	$0.461939\pi$
$720$	−2.63386	−	0.658007i	−0.0981581	−	0.0245225i
$721$	−0.940685	−	6.54261i	−0.0350329	−	0.243660i
$722$	17.2713	+	2.30375i	0.642770	+	0.0857368i
$723$	19.8362	+	17.1882i	0.737717	+	0.639236i
$724$	−13.0711	−	3.55019i	−0.485785	−	0.131942i
$725$	3.06910	−	4.77561i	0.113983	−	0.177362i
$726$	−15.2879	+	24.3303i	−0.567387	+	0.902983i
$727$	−1.52687	−	0.448328i	−0.0566283	−	0.0166276i	0.253296	−	0.967389i	$-0.418485\pi$
$727$	−1.52687	−	0.448328i	−0.0566283	−	0.0166276i	−0.309924	+	0.950761i	$0.600304\pi$
$728$	8.53059	−	5.85850i	0.316165	−	0.217130i
$729$	−12.0760	−	13.9364i	−0.447258	−	0.516163i
$730$	−8.69193	−	13.2264i	−0.321703	−	0.489532i
$731$	−61.4886	+	18.0547i	−2.27424	+	0.667776i
$732$	−6.76863	+	55.0193i	−0.250176	+	2.03357i
$733$	−2.89221	+	20.1158i	−0.106826	+	0.742993i	0.864049	+	0.503408i	$0.167921\pi$
$733$	−2.89221	+	20.1158i	−0.106826	+	0.742993i	−0.970875	+	0.239585i	$0.922989\pi$
$734$	13.7288	−	12.1434i	0.506741	−	0.448220i
$735$	12.2620			0.452292
$736$	−4.02293	+	26.8294i	−0.148287	+	0.988944i
$737$	4.62660			0.170423
$738$	7.35788	−	6.50816i	0.270847	−	0.239569i
$739$	1.77321	−	12.3330i	0.0652287	−	0.453675i	−0.930864	−	0.365365i	$-0.880944\pi$
$739$	1.77321	−	12.3330i	0.0652287	−	0.453675i	0.996093	−	0.0883103i	$-0.0281467\pi$
$740$	1.22145	−	9.92866i	0.0449014	−	0.364985i
$741$	22.3382	−	6.55910i	0.820616	−	0.240955i
$742$	2.23682	+	3.40374i	0.0821161	+	0.124955i
$743$	−34.4017	−	39.7017i	−1.26208	−	1.45651i	−0.833026	−	0.553233i	$-0.813394\pi$
$743$	−34.4017	−	39.7017i	−1.26208	−	1.45651i	−0.429050	−	0.903281i	$-0.641152\pi$
$744$	5.19543	−	3.56803i	0.190474	−	0.130810i
$745$	−8.97619	−	2.63565i	−0.328862	−	0.0965627i
$746$	4.60674	−	7.33153i	0.168665	−	0.268426i
$747$	0.491676	−	0.765062i	0.0179895	−	0.0279922i
$748$	6.63684	+	1.80260i	0.242667	+	0.0659095i
$749$	3.67403	+	3.18357i	0.134246	+	0.116325i
$750$	−2.68864	−	0.358628i	−0.0981753	−	0.0130952i
$751$	−1.84744	−	12.8493i	−0.0674142	−	0.468876i	−0.995365	−	0.0961725i	$-0.969340\pi$
$751$	−1.84744	−	12.8493i	−0.0674142	−	0.468876i	0.927951	−	0.372703i	$-0.121569\pi$
$752$	5.58577	−	22.3586i	0.203692	−	0.815334i
$753$	−29.1826	+	13.3272i	−1.06347	+	0.485672i
$754$	−34.1374	+	16.0127i	−1.24321	+	0.583147i
$755$	−9.69234	−	4.42634i	−0.352740	−	0.161091i
$756$	1.12698	+	6.84443i	0.0409877	+	0.248929i
$757$	−0.514225	+	0.330472i	−0.0186898	+	0.0120112i	−0.549952	−	0.835196i	$-0.685354\pi$
$757$	−0.514225	+	0.330472i	−0.0186898	+	0.0120112i	0.531263	+	0.847207i	$0.321718\pi$
$758$	−2.12853	−	13.8036i	−0.0773116	−	0.501370i
$759$	−5.71122	+	1.32871i	−0.207304	+	0.0482291i
$760$	−3.23855	−	6.55328i	−0.117475	−	0.237712i
$761$	17.3420	−	11.1450i	0.628648	−	0.404007i	−0.187161	−	0.982329i	$-0.559929\pi$
$761$	17.3420	−	11.1450i	0.628648	−	0.404007i	0.815809	+	0.578322i	$0.196292\pi$
$762$	−21.0435	+	0.214567i	−0.762324	+	0.00777294i
$763$	−1.11820	+	2.44852i	−0.0404817	+	0.0886425i
$764$	−34.5101	+	23.1860i	−1.24853	+	0.838842i
$765$	3.33018	−	1.52084i	0.120403	−	0.0549861i
$766$	11.6044	+	9.84996i	0.419286	+	0.355894i
$767$	5.74113	−	0.825449i	0.207300	−	0.0298052i
$768$	18.1398	−	24.7527i	0.654565	−	0.893185i
$769$	−26.4944	−	22.9575i	−0.955412	−	0.827869i	0.0297392	−	0.999558i	$-0.490532\pi$
$769$	−26.4944	−	22.9575i	−0.955412	−	0.827869i	−0.985151	+	0.171688i	$0.945078\pi$
$770$	0.285213	−	0.641767i	0.0102784	−	0.0231277i
$771$	41.6394	+	26.7600i	1.49961	+	0.963738i
$772$	−8.27554	+	19.1446i	−0.297843	+	0.689031i
$773$	2.87517	+	0.844225i	0.103413	+	0.0303647i	0.333029	−	0.942916i	$-0.391929\pi$
$773$	2.87517	+	0.844225i	0.103413	+	0.0303647i	−0.229617	+	0.973281i	$0.573747\pi$
$774$	−10.9079	+	3.32402i	−0.392076	+	0.119479i
$775$	0.878028	−	0.760815i	0.0315397	−	0.0273293i
$776$	−18.1439	+	22.2812i	−0.651330	+	0.799848i
$777$	7.17050	−	2.10545i	0.257240	−	0.0755325i
$778$	14.1308	−	50.0056i	0.506614	−	1.79279i
$779$	26.1804	+	3.76417i	0.938010	+	0.134866i
$780$	13.8539	+	11.5183i	0.496047	+	0.412422i
$781$	−2.64049			−0.0944842
$782$	−18.3171	−	31.6692i	−0.655019	−	1.13249i
$783$		−	25.2744i		−	0.903232i
$784$	−9.66598	+	23.6755i	−0.345213	+	0.845553i
$785$	0.316786	−	2.20330i	0.0113066	−	0.0786390i
$786$	−0.671219	+	2.37529i	−0.0239416	+	0.0847237i
$787$	9.33064	+	31.7772i	0.332601	+	1.13274i	0.940803	+	0.338954i	$0.110073\pi$
$787$	9.33064	+	31.7772i	0.332601	+	1.13274i	−0.608202	+	0.793782i	$0.708109\pi$
$788$	−27.3308	+	24.6758i	−0.973620	+	0.879038i
$789$	16.0769	+	18.5537i	0.572353	+	0.660531i
$790$	−6.78715	−	22.2723i	−0.241476	−	0.792412i
$791$	2.29459	−	7.81467i	0.0815864	−	0.277858i
$792$	1.18416	+	0.308695i	0.0420773	+	0.0109690i
$793$	36.6950	−	57.0985i	1.30308	−	2.02763i
$794$	−4.89298	+	11.0098i	−0.173645	+	0.390725i
$795$	−4.64356	+	5.35895i	−0.164690	+	0.190062i
$796$	−52.1315	+	1.06322i	−1.84775	+	0.0376847i
$797$	−1.54787	−	10.7657i	−0.0548285	−	0.381340i	−0.998698	−	0.0510207i	$-0.983753\pi$
$797$	−1.54787	−	10.7657i	−0.0548285	−	0.381340i	0.943869	−	0.330320i	$-0.107157\pi$
$798$	3.53385	−	4.16330i	0.125097	−	0.147379i
$799$	12.9103	+	28.2696i	0.456733	+	1.00011i
$800$	2.81185	−	4.90851i	0.0994140	−	0.173542i
$801$	−6.57198	−	3.00132i	−0.232209	−	0.106047i
$802$	−47.0976	+	0.480225i	−1.66308	+	0.0169573i
$803$	3.85702	+	6.00163i	0.136111	+	0.211793i
$804$	8.38660	+	26.5472i	0.295773	+	0.936247i
$805$	−3.48126	+	1.35579i	−0.122698	+	0.0477854i
$806$	−7.62676	+	1.17605i	−0.268641	+	0.0414247i
$807$	27.5539	+	42.8747i	0.969943	+	1.50926i
$808$	−45.8314	+	14.9944i	−1.61234	+	0.527500i
$809$	−7.53529	+	16.5000i	−0.264927	+	0.580109i	−0.994611	−	0.103675i	$-0.966940\pi$
$809$	−7.53529	+	16.5000i	−0.264927	+	0.580109i	0.729684	+	0.683784i	$0.239667\pi$
$810$	−13.5404	+	6.35132i	−0.475760	+	0.223163i
$811$	−13.2591	−	29.0334i	−0.465591	−	1.01950i	−0.986177	−	0.165693i	$-0.947014\pi$
$811$	−13.2591	−	29.0334i	−0.465591	−	1.01950i	0.520586	−	0.853809i	$-0.325713\pi$
$812$	−4.62895	+	7.53636i	−0.162444	+	0.264474i
$813$	15.9769	−	2.29713i	0.560333	−	0.0805637i
$814$	−0.596188	+	4.46963i	−0.0208964	+	0.156661i
$815$	1.48991	−	1.71945i	0.0521894	−	0.0602298i
$816$	1.68733	+	41.3493i	0.0590684	+	1.44752i
$817$	−25.8297	−	16.5997i	−0.903666	−	0.580751i
$818$	−11.5239	+	18.3399i	−0.402922	+	0.641241i
$819$	−0.699603	+	2.38263i	−0.0244461	+	0.0832558i
$820$	8.88083	+	18.4416i	0.310132	+	0.644009i
$821$	−8.73441	+	7.56841i	−0.304833	+	0.264139i	−0.793821	−	0.608151i	$-0.791912\pi$
$821$	−8.73441	+	7.56841i	−0.304833	+	0.264139i	0.488988	+	0.872290i	$0.337366\pi$
$822$	19.6736	−	12.9288i	0.686195	−	0.450942i
$823$	6.78089	+	23.0936i	0.236367	+	0.804992i	0.989174	+	0.146750i	$0.0468814\pi$
$823$	6.78089	+	23.0936i	0.236367	+	0.804992i	−0.752806	+	0.658242i	$0.771300\pi$
$824$	0.733982	+	23.9882i	0.0255695	+	0.835669i
$825$	1.21023	+	0.174005i	0.0421348	+	0.00605807i
$826$	1.01905	−	0.901368i	0.0354574	−	0.0313626i
$827$			46.5553i			1.61889i	0.587198	+	0.809444i	$0.300231\pi$
$827$			46.5553i			1.61889i	−0.587198	+	0.809444i	$0.699769\pi$
$828$	−3.31662	−	5.60166i	−0.115260	−	0.194671i
$829$			14.0827i			0.489112i	0.969635	+	0.244556i	$0.0786423\pi$
$829$			14.0827i			0.489112i	−0.969635	+	0.244556i	$0.921358\pi$
$830$	1.25549	+	1.41941i	0.0435787	+	0.0492684i
$831$	−32.7721	−	4.71191i	−1.13685	−	0.163455i
$832$	−33.1603	+	17.6692i	−1.14963	+	0.612570i
$833$	−9.71572	−	33.0887i	−0.336630	−	1.14646i
$834$	−0.489205	−	0.744419i	−0.0169398	−	0.0257771i
$835$	−11.6308	+	10.0782i	−0.402502	+	0.348770i
$836$	1.42963	+	2.96871i	0.0494447	+	0.102675i
$837$	1.45729	−	4.96307i	0.0503713	−	0.171549i
$838$	11.8269	+	7.43139i	0.408553	+	0.256713i
$839$	−38.9420	−	25.0265i	−1.34443	−	0.864010i	−0.347153	−	0.937809i	$-0.612852\pi$
$839$	−38.9420	−	25.0265i	−1.34443	−	0.864010i	−0.997273	+	0.0737983i	$0.976488\pi$
$840$	4.19943	+	0.473212i	0.144894	+	0.0163274i
$841$	2.11244	−	2.43789i	0.0728429	−	0.0840652i
$842$	−21.8727	−	2.91751i	−0.753782	−	0.100544i
$843$	19.3281	−	2.77896i	0.665694	−	0.0957123i
$844$	34.3825	+	21.1183i	1.18349	+	0.726921i
$845$	−3.76345	−	8.24080i	−0.129467	−	0.283492i
$846$	2.34841	+	5.00658i	0.0807402	+	0.172130i
$847$	3.42819	−	7.50668i	0.117794	−	0.257933i
$848$	−6.68659	−	13.1901i	−0.229618	−	0.452951i
$849$	−2.61883	−	4.07499i	−0.0898782	−	0.139853i
$850$	1.16258	+	7.53937i	0.0398760	+	0.258598i
$851$	18.9943	−	14.6499i	0.651116	−	0.502193i
$852$	−4.78640	−	15.1510i	−0.163979	−	0.519064i
$853$	−6.75444	−	10.5101i	−0.231268	−	0.359860i	0.706152	−	0.708060i	$-0.250429\pi$
$853$	−6.75444	−	10.5101i	−0.231268	−	0.359860i	−0.937420	+	0.348200i	$0.886793\pi$
$854$	−0.162321	−	15.9195i	−0.00555453	−	0.544755i
$855$	1.59554	+	0.728657i	0.0545662	+	0.0249196i
$856$	−11.9616	−	12.9801i	−0.408839	−	0.443649i
$857$	−0.569942	−	1.24800i	−0.0194689	−	0.0426309i	0.899648	−	0.436616i	$-0.143823\pi$
$857$	−0.569942	−	1.24800i	−0.0194689	−	0.0426309i	−0.919117	+	0.393986i	$0.871096\pi$
$858$	−6.19155	−	5.25545i	−0.211376	−	0.179418i
$859$	−5.71079	−	39.7194i	−0.194850	−	1.35521i	−0.818950	−	0.573865i	$-0.805443\pi$
$859$	−5.71079	−	39.7194i	−0.194850	−	1.35521i	0.624100	−	0.781345i	$-0.285466\pi$
$860$	−0.484497	−	23.7558i	−0.0165212	−	0.810066i
$861$	−10.0136	+	11.5563i	−0.341263	+	0.393839i
$862$	−36.3530	−	16.1559i	−1.23819	−	0.550274i
$863$	11.3012	−	17.5850i	0.384697	−	0.598600i	−0.593862	−	0.804567i	$-0.702398\pi$
$863$	11.3012	−	17.5850i	0.384697	−	0.598600i	0.978559	+	0.205967i	$0.0660340\pi$
$864$	−1.28341	−	25.1529i	−0.0436625	−	0.855720i
$865$	2.13693	−	7.27772i	0.0726579	−	0.247450i
$866$	0.201431	−	0.0613831i	0.00684490	−	0.00208588i
$867$	−15.1938	−	17.5346i	−0.516009	−	0.595506i
$868$	−1.34351	+	1.21300i	−0.0456018	+	0.0411719i
$869$	2.95688	+	10.0702i	0.100305	+	0.341608i
$870$	−14.8177	−	4.18725i	−0.502368	−	0.141961i
$871$	4.85117	−	33.7406i	0.164375	−	1.14326i
$872$	5.02997	−	8.37966i	0.170336	−	0.283771i
$873$		−	6.89498i		−	0.233360i
$874$	5.72005	−	16.5688i	0.193484	−	0.560447i
$875$	0.779001			0.0263350
$876$	−27.4454	+	33.0104i	−0.927296	+	1.11532i
$877$	44.7353	+	6.43196i	1.51060	+	0.217192i	0.847282	−	0.531143i	$-0.178237\pi$
$877$	44.7353	+	6.43196i	1.51060	+	0.217192i	0.663321	+	0.748335i	$0.269146\pi$
$878$	53.6656	+	15.1651i	1.81113	+	0.511796i
$879$	−1.20583	+	0.354063i	−0.0406715	+	0.0119422i
$880$	−1.28997	+	2.19954i	−0.0434850	+	0.0741465i
$881$	−35.0876	+	30.4036i	−1.18213	+	1.02432i	−0.182980	+	0.983117i	$0.558574\pi$
$881$	−35.0876	+	30.4036i	−1.18213	+	1.02432i	−0.999151	+	0.0412056i	$0.986880\pi$
$882$	−1.78875	−	5.86984i	−0.0602303	−	0.197648i
$883$	42.1873	+	12.3873i	1.41972	+	0.416866i	0.899407	−	0.437112i	$-0.143999\pi$
$883$	42.1873	+	12.3873i	1.41972	+	0.416866i	0.520309	+	0.853978i	$0.325817\pi$
$884$	20.1049	−	46.5106i	0.676199	−	1.56432i
$885$	1.99258	+	1.28056i	0.0669800	+	0.0430454i
$886$	−22.6887	−	10.0833i	−0.762242	−	0.338755i
$887$	9.51375	+	8.24371i	0.319440	+	0.276797i	0.799789	−	0.600281i	$-0.204945\pi$
$887$	9.51375	+	8.24371i	0.319440	+	0.276797i	−0.480349	+	0.877077i	$0.659490\pi$
$888$	−26.7272	+	4.68117i	−0.896906	+	0.157090i
$889$	5.98235	−	0.860132i	0.200642	−	0.0288479i
$890$	9.74209	−	11.4774i	0.326556	−	0.384722i
$891$	6.13238	−	2.80057i	0.205443	−	0.0938225i
$892$	15.0691	+	22.4289i	0.504552	+	0.750975i
$893$	−6.18551	+	13.5444i	−0.206990	+	0.453246i
$894$	0.258724	+	25.3741i	0.00865301	+	0.848636i
$895$	−15.2598	+	9.80685i	−0.510077	+	0.327807i
$896$	−4.22402	+	7.73521i	−0.141115	+	0.258415i
$897$	3.70150	+	43.0436i	0.123590	+	1.43719i
$898$	28.8761	−	4.45272i	0.963609	−	0.148589i
$899$	5.54829	−	3.56567i	0.185046	−	0.118922i
$900$	0.220535	+	1.33937i	0.00735117	+	0.0446456i
$901$	18.1402	+	8.28437i	0.604339	+	0.275992i
$902$	−3.91819	−	8.35319i	−0.130461	−	0.278131i
$903$	16.1466	−	7.37390i	0.537325	−	0.245388i
$904$	−11.4561	+	27.2625i	−0.381024	+	0.906736i
$905$	0.963805	+	6.70341i	0.0320380	+	0.222829i
$906$	−3.82127	+	28.6481i	−0.126953	+	0.951769i
$907$	−20.3950	−	17.6724i	−0.677206	−	0.586802i	0.246853	−	0.969053i	$-0.420604\pi$
$907$	−20.3950	−	17.6724i	−0.677206	−	0.586802i	−0.924059	+	0.382251i	$0.875149\pi$
$908$	8.69964	−	32.0305i	0.288708	−	1.06297i
$909$	6.25586	−	9.73431i	0.207494	−	0.322867i
$910$	−4.38118	−	2.75290i	−0.145235	−	0.0912579i
$911$	47.6709	+	13.9974i	1.57941	+	0.463756i	0.949722	−	0.313095i	$-0.101366\pi$
$911$	47.6709	+	13.9974i	1.57941	+	0.463756i	0.629685	+	0.776851i	$0.283184\pi$
$912$	−14.4428	+	13.5845i	−0.478249	+	0.449827i
$913$	−0.559376	−	0.645554i	−0.0185126	−	0.0213647i
$914$	−0.328120	+	0.215628i	−0.0108532	+	0.00713235i
$915$	26.5943	−	7.80880i	0.879181	−	0.258151i
$916$	−1.56133	+	12.6914i	−0.0515879	+	0.419336i
$917$	0.100885	−	0.701667i	0.00333150	−	0.0231711i
$918$	22.5021	+	25.4400i	0.742680	+	0.839645i
$919$	−36.3075			−1.19767			−0.598837	−	0.800871i	$-0.704370\pi$
$919$	−36.3075			−1.19767			−0.598837	+	0.800871i	$0.704370\pi$
$920$	13.1116	−	3.47634i	0.432278	−	0.114612i
$921$	35.1402			1.15791
$922$	18.4640	+	20.8747i	0.608079	+	0.687471i
$923$	−2.76865	+	19.2564i	−0.0911313	+	0.633832i
$924$	−1.89068	−	0.232596i	−0.0621987	−	0.00765185i
$925$	−4.79915	+	1.40916i	−0.157795	+	0.0463328i
$926$	7.92640	−	5.20894i	0.260478	−	0.171176i
$927$	−3.77124	−	4.35224i	−0.123864	−	0.142946i
$928$	19.7653	−	25.3092i	0.648828	−	0.830817i
$929$	−2.03497	−	0.597521i	−0.0667652	−	0.0196040i	0.248179	−	0.968714i	$-0.420168\pi$
$929$	−2.03497	−	0.597521i	−0.0667652	−	0.0196040i	−0.314945	+	0.949110i	$0.601986\pi$
$930$	−2.66829	−	1.67661i	−0.0874968	−	0.0549784i
$931$	8.93278	−	13.8997i	0.292760	−	0.455543i
$932$	42.0208	+	11.4131i	1.37644	+	0.373847i
$933$	−12.6725	−	10.9808i	−0.414880	−	0.359496i
$934$	−1.04771	+	7.85466i	−0.0342820	+	0.257012i
$935$	−0.489369	−	3.40364i	−0.0160041	−	0.111311i
$936$	3.49287	−	8.31210i	0.114168	−	0.271690i
$937$	24.6983	−	11.2793i	0.806857	−	0.368479i	0.0311040	−	0.999516i	$-0.490098\pi$
$937$	24.6983	−	11.2793i	0.806857	−	0.368479i	0.775753	+	0.631037i	$0.217370\pi$
$938$	−3.39547	−	7.23881i	−0.110866	−	0.236355i
$939$	8.29458	+	3.78801i	0.270683	+	0.123617i
$940$	−11.3698	+	1.87210i	−0.370842	+	0.0610613i
$941$	−41.1033	+	26.4155i	−1.33993	+	0.861121i	−0.996936	−	0.0782172i	$-0.975077\pi$
$941$	−41.1033	+	26.4155i	−1.33993	+	0.861121i	−0.342993	+	0.939338i	$0.611441\pi$
$942$	−5.96727	+	0.920157i	−0.194424	+	0.0299803i
$943$	−16.4892	+	46.2292i	−0.536961	+	1.50543i
$944$	−4.04321	+	2.83783i	−0.131595	+	0.0923634i
$945$	2.91772	−	1.87510i	0.0949133	−	0.0609971i
$946$	0.109202	+	10.7099i	0.00355048	+	0.348210i
$947$	−3.67581	+	8.04889i	−0.119448	+	0.261554i	−0.959906	−	0.280322i	$-0.909559\pi$
$947$	−3.67581	+	8.04889i	−0.119448	+	0.261554i	0.840458	+	0.541876i	$0.182286\pi$
$948$	−52.4223	+	35.2206i	−1.70260	+	1.14391i
$949$	47.8126	−	21.8353i	1.55206	−	0.708803i
$950$	−2.36517	+	2.78646i	−0.0767363	+	0.0904047i
$951$	−60.2253	+	8.65909i	−1.95294	+	0.280790i
$952$	−2.05043	−	11.7070i	−0.0664549	−	0.379425i
$953$	10.8734	+	9.42183i	0.352223	+	0.305203i	0.812944	−	0.582342i	$-0.197864\pi$
$953$	10.8734	+	9.42183i	0.352223	+	0.305203i	−0.460721	+	0.887545i	$0.652409\pi$
$954$	3.24272	+	1.44113i	0.104987	+	0.0466582i
$955$	17.4879	+	11.2388i	0.565894	+	0.363678i
$956$	−21.4288	−	9.26289i	−0.693057	−	0.299583i
$957$	6.65970	+	1.95547i	0.215278	+	0.0632112i
$958$	−9.95058	−	32.6532i	−0.321489	−	1.05498i
$959$	−5.10961	+	4.42750i	−0.164998	+	0.142972i
$960$	−14.9592	−	3.41471i	−0.482805	−	0.110209i
$961$	−28.4492	+	8.35343i	−0.917716	+	0.269466i
$962$	31.9707	+	9.03442i	1.03078	+	0.291281i
$963$	4.19240	+	0.602776i	0.135098	+	0.0194242i
$964$	21.0455	+	17.4976i	0.677830	+	0.563560i
$965$	10.4284			0.335700
$966$	6.27039	+	7.96067i	0.201746	+	0.256130i
$967$			58.4325i			1.87906i	0.342462	+	0.939532i	$0.388739\pi$
$967$			58.4325i			1.87906i	−0.342462	+	0.939532i	$0.611261\pi$
$968$	−15.4209	+	25.6904i	−0.495646	+	0.825720i
$969$	3.80524	−	26.4660i	0.122242	−	0.850212i
$970$	13.8257	+	3.90692i	0.443916	+	0.125444i
$971$	3.17720	+	10.8205i	0.101961	+	0.347248i	0.994634	−	0.103458i	$-0.0329906\pi$
$971$	3.17720	+	10.8205i	0.101961	+	0.347248i	−0.892673	+	0.450706i	$0.851172\pi$
$972$	9.28402	+	10.2830i	0.297785	+	0.329826i
$973$	0.167530	+	0.193340i	0.00537077	+	0.00619820i
$974$	−50.8358	+	15.4915i	−1.62889	+	0.496379i
$975$	2.53794	−	8.64344i	0.0812793	−	0.276812i
$976$	−5.88671	+	57.5037i	−0.188429	+	1.84065i
$977$	−0.409650	+	0.637428i	−0.0131059	+	0.0203931i	−0.847745	−	0.530405i	$-0.822040\pi$
$977$	−0.409650	+	0.637428i	−0.0131059	+	0.0203931i	0.834639	+	0.550798i	$0.185676\pi$
$978$	−5.63943	−	2.50627i	−0.180329	−	0.0801417i
$979$	−4.44390	+	5.12853i	−0.142028	+	0.163909i
$980$	12.7837	−	0.260721i	0.408359	−	0.00832843i
$981$	0.333757	+	2.32133i	0.0106560	+	0.0741143i
$982$	−15.7259	−	13.3483i	−0.501833	−	0.425960i
$983$	−4.03385	−	8.83289i	−0.128660	−	0.281725i	0.834329	−	0.551267i	$-0.185855\pi$
$983$	−4.03385	−	8.83289i	−0.128660	−	0.281725i	−0.962989	+	0.269541i	$0.913128\pi$
$984$	40.8277	−	37.6241i	1.30154	−	1.19941i
$985$	16.7473	+	7.64822i	0.533613	+	0.243693i
$986$	0.441533	+	43.3029i	0.0140613	+	1.37904i
$987$	−4.65399	−	7.24175i	−0.148138	−	0.230507i
$988$	23.1490	−	7.31309i	0.736469	−	0.232660i
$989$	39.7047	−	40.8636i	1.26254	−	1.29939i
$990$	−0.0932484	−	0.604721i	−0.00296363	−	0.0192193i
$991$	10.5431	+	16.4054i	0.334914	+	0.521136i	0.967339	−	0.253485i	$-0.0815769\pi$
$991$	10.5431	+	16.4054i	0.334914	+	0.521136i	−0.632426	+	0.774621i	$0.717941\pi$
$992$	5.34057	−	3.83028i	0.169563	−	0.121611i
$993$	10.9581	−	23.9948i	0.347744	−	0.761452i
$994$	1.93786	+	4.13133i	0.0614653	+	0.131038i
$995$	10.8304	+	23.7152i	0.343346	+	0.751822i
$996$	2.69018	−	4.37986i	0.0852416	−	0.138781i
$997$	−46.0224	+	6.61702i	−1.45754	+	0.209563i	−0.825075	−	0.565023i	$-0.808867\pi$
$997$	−46.0224	+	6.61702i	−1.45754	+	0.209563i	−0.632468	+	0.774586i	$0.717958\pi$
$998$	−50.0624	−	6.67765i	−1.58470	−	0.211377i
$999$	−14.5831	+	16.8298i	−0.461389	+	0.532471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.12	✓	480
8.3	odd	2		920.2.bb.b.11.7	yes	480
23.21	odd	22		920.2.bb.b.251.7	yes	480
184.67	even	22	inner	920.2.bb.a.251.12	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.12	✓	480	1.1	even	1	trivial
920.2.bb.a.251.12	yes	480	184.67	even	22	inner
920.2.bb.b.11.7	yes	480	8.3	odd	2
920.2.bb.b.251.7	yes	480	23.21	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05929 + 0.936962i) q^{2} +(0.272959 - 1.89847i) q^{3} +(0.244204 - 1.98504i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.48965 + 2.26679i) q^{6} +(-0.510137 - 0.588729i) q^{7} +(1.60122 + 2.33154i) q^{8} +(-0.651210 - 0.191212i) q^{9} +(0.752412 - 1.19745i) q^{10} +(-0.344646 + 0.536279i) q^{11} +(-3.70188 - 1.00545i) q^{12} +(3.54957 + 3.07572i) q^{13} +(1.09200 + 0.145658i) q^{14} +(0.272959 + 1.89847i) q^{15} +(-3.88073 - 0.969508i) q^{16} +(4.90669 - 2.24081i) q^{17} +(0.868981 - 0.407609i) q^{18} +(2.35087 + 1.07360i) q^{19} +(0.324937 + 1.97343i) q^{20} +(-1.25693 + 0.807782i) q^{21} +(-0.137392 - 0.890997i) q^{22} +(-2.81852 + 3.88020i) q^{23} +(4.86344 - 2.40345i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-6.64187 + 0.0677230i) q^{26} +(1.84953 - 4.04990i) q^{27} +(-1.29323 + 0.868869i) q^{28} +(5.16378 - 2.35822i) q^{29} +(-2.06794 - 1.75529i) q^{30} +(1.14997 - 0.165341i) q^{31} +(5.01922 - 2.60910i) q^{32} +(0.924037 + 0.800682i) q^{33} +(-3.09807 + 6.97105i) q^{34} +(0.655337 + 0.421160i) q^{35} +(-0.538591 + 1.24598i) q^{36} +(-4.79915 - 1.40916i) q^{37} +(-3.49618 + 1.06541i) q^{38} +(6.80805 - 5.89921i) q^{39} +(-2.19323 - 1.78599i) q^{40} +(9.81972 - 2.88333i) q^{41} +(0.574600 - 2.03338i) q^{42} +(-11.7594 - 1.69075i) q^{43} +(0.980369 + 0.815095i) q^{44} +0.678702 q^{45} +(-0.649963 - 6.75111i) q^{46} +5.76144i q^{47} +(-2.89986 + 7.10282i) q^{48} +(0.909841 - 6.32808i) q^{49} +(-0.384574 + 1.36092i) q^{50} +(-2.91479 - 9.92686i) q^{51} +(6.97223 - 6.29491i) q^{52} +(2.42105 + 2.79404i) q^{53} +(1.83541 + 6.02296i) q^{54} +(0.179598 - 0.611654i) q^{55} +(0.555808 - 2.13209i) q^{56} +(2.67990 - 4.17000i) q^{57} +(-3.26039 + 7.33631i) q^{58} +(0.808707 - 0.933298i) q^{59} +(3.83519 - 0.0782182i) q^{60} +(-2.05660 - 14.3040i) q^{61} +(-1.06324 + 1.25262i) q^{62} +(0.219634 + 0.480931i) q^{63} +(-2.87220 + 7.46662i) q^{64} +(-4.27232 - 1.95110i) q^{65} +(-1.72903 + 0.0176299i) q^{66} +(-3.92380 - 6.10555i) q^{67} +(-3.24985 - 10.2872i) q^{68} +(6.59711 + 6.41001i) q^{69} +(-1.08880 + 0.167894i) q^{70} +(2.23939 + 3.48456i) q^{71} +(-0.596909 - 1.82450i) q^{72} +(4.64901 - 10.1799i) q^{73} +(6.40403 - 3.00391i) q^{74} +(-0.796764 - 1.74467i) q^{75} +(2.70524 - 4.40437i) q^{76} +(0.491540 - 0.0706727i) q^{77} +(-1.68439 + 12.6279i) q^{78} +(10.7816 - 12.4426i) q^{79} +(3.99667 - 0.163091i) q^{80} +(-8.89665 - 5.71753i) q^{81} +(-7.70039 + 12.2550i) q^{82} +(-0.377510 + 1.28568i) q^{83} +(1.29653 + 2.69232i) q^{84} +(-4.07662 + 3.53241i) q^{85} +(14.0409 - 9.22715i) q^{86} +(-3.06751 - 10.4470i) q^{87} +(-1.80221 + 0.0551434i) q^{88} +(10.5368 + 1.51496i) q^{89} +(-0.718944 + 0.635918i) q^{90} -3.65877i q^{91} +(7.01404 + 6.54242i) q^{92} -2.22832i q^{93} +(-5.39825 - 6.10306i) q^{94} +(-2.55811 - 0.367801i) q^{95} +(-3.58326 - 10.2410i) q^{96} +(2.86214 + 9.74756i) q^{97} +(4.96539 + 7.55578i) q^{98} +(0.326980 - 0.283330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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