LMFDB - Embedded newform 230.2.l.a.83.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			83.9
Character	$\chi$	$=$	230.83
Dual form			230.2.l.a.97.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.479249 - 0.877679i) q^{2} +(-0.0548882 + 0.767437i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(2.20989 - 0.341164i) q^{5} +(0.647258 + 0.415968i) q^{6} +(-0.484532 + 0.180721i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(2.38352 + 0.342698i) q^{9} +O(q^{10})$	\(q+(0.479249 - 0.877679i) q^{2} +(-0.0548882 + 0.767437i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(2.20989 - 0.341164i) q^{5} +(0.647258 + 0.415968i) q^{6} +(-0.484532 + 0.180721i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(2.38352 + 0.342698i) q^{9} +(0.759654 - 2.10308i) q^{10} +(0.0487894 - 0.166162i) q^{11} +(0.675284 - 0.368733i) q^{12} +(0.678467 - 1.81904i) q^{13} +(-0.0735963 + 0.511873i) q^{14} +(0.140525 + 1.71468i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-0.00793746 - 0.0364879i) q^{17} +(1.44308 - 1.92773i) q^{18} +(0.624467 - 0.401321i) q^{19} +(-1.48176 - 1.67463i) q^{20} +(-0.112097 - 0.381767i) q^{21} +(-0.122454 - 0.122454i) q^{22} +(-4.61791 - 1.29419i) q^{23} -0.769398i q^{24} +(4.76721 - 1.50787i) q^{25} +(-1.27138 - 1.46725i) q^{26} +(-0.884468 + 4.06583i) q^{27} +(0.413990 + 0.309909i) q^{28} +(-1.50901 + 2.34806i) q^{29} +(1.57228 + 0.698421i) q^{30} +(-1.86943 + 2.15743i) q^{31} +(0.599278 + 0.800541i) q^{32} +(0.124841 + 0.0465631i) q^{33} +(-0.0358287 - 0.0105203i) q^{34} +(-1.00911 + 0.564678i) q^{35} +(-1.00033 - 2.19042i) q^{36} +(-6.38904 + 4.78278i) q^{37} +(-0.0529555 - 0.740414i) q^{38} +(1.35876 + 0.620525i) q^{39} +(-2.17992 + 0.497947i) q^{40} +(-0.673689 - 4.68561i) q^{41} +(-0.388791 - 0.0845763i) q^{42} +(-6.52582 - 0.466736i) q^{43} +(-0.166162 + 0.0487894i) q^{44} +(5.38422 - 0.0558469i) q^{45} +(-3.34901 + 3.43280i) q^{46} +(-5.54415 + 5.54415i) q^{47} +(-0.675284 - 0.368733i) q^{48} +(-5.08814 + 4.40890i) q^{49} +(0.961256 - 4.90673i) q^{50} +(0.0284379 - 0.00408875i) q^{51} +(-1.89708 + 0.412685i) q^{52} +(-0.476831 - 1.27843i) q^{53} +(3.14462 + 2.72483i) q^{54} +(0.0511308 - 0.383844i) q^{55} +(0.470405 - 0.214827i) q^{56} +(0.273713 + 0.501267i) q^{57} +(1.33766 + 2.44973i) q^{58} +(2.12411 - 0.970050i) q^{59} +(1.36650 - 1.04524i) q^{60} +(6.29529 + 5.45490i) q^{61} +(0.997614 + 2.67471i) q^{62} +(-1.21682 + 0.264703i) q^{63} +(0.989821 - 0.142315i) q^{64} +(0.878745 - 4.25135i) q^{65} +(0.100697 - 0.0872547i) q^{66} +(0.468349 + 0.255738i) q^{67} +(-0.0264043 + 0.0264043i) q^{68} +(1.24668 - 3.47292i) q^{69} +(0.0119934 + 1.15629i) q^{70} +(13.0620 - 3.83536i) q^{71} +(-2.40189 - 0.171787i) q^{72} +(-3.75133 - 0.816052i) q^{73} +(1.13580 + 7.89967i) q^{74} +(0.895532 + 3.74130i) q^{75} +(-0.675225 - 0.308365i) q^{76} +(0.00638885 + 0.0893278i) q^{77} +(1.19581 - 0.895169i) q^{78} +(0.561663 + 1.22987i) q^{79} +(-0.607687 + 2.15191i) q^{80} +(3.85973 + 1.13332i) q^{81} +(-4.43532 - 1.65429i) q^{82} +(-6.52994 - 8.72298i) q^{83} +(-0.260559 + 0.300701i) q^{84} +(-0.0299893 - 0.0779263i) q^{85} +(-3.53714 + 5.50389i) q^{86} +(-1.71917 - 1.28695i) q^{87} +(-0.0368113 + 0.169219i) q^{88} +(0.385607 + 0.445015i) q^{89} +(2.53137 - 4.75238i) q^{90} +1.00400i q^{91} +(1.40789 + 4.58452i) q^{92} +(-1.55309 - 1.55309i) q^{93} +(2.20896 + 7.52302i) q^{94} +(1.24309 - 1.09992i) q^{95} +(-0.647258 + 0.415968i) q^{96} +(3.69871 - 4.94090i) q^{97} +(1.43111 + 6.57871i) q^{98} +(0.173234 - 0.379329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{21}{22}\right)$

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 $

$2$	0.479249	−	0.877679i	0.338880	−	0.620613i
$2$	0.479249	−	0.877679i	0.338880	−	0.620613i
$3$	−0.0548882	+	0.767437i	−0.0316897	+	0.443080i	0.956693	+	0.291097i	$0.0940204\pi$
$3$	−0.0548882	+	0.767437i	−0.0316897	+	0.443080i	−0.988383	+	0.151983i	$0.951434\pi$
$4$	−0.540641	−	0.841254i	−0.270320	−	0.420627i
$5$	2.20989	−	0.341164i	0.988292	−	0.152573i
$5$	2.20989	−	0.341164i	0.988292	−	0.152573i
$6$	0.647258	+	0.415968i	0.264242	+	0.169818i
$7$	−0.484532	+	0.180721i	−0.183136	+	0.0683061i	−0.439359	−	0.898311i	$-0.644794\pi$
$7$	−0.484532	+	0.180721i	−0.183136	+	0.0683061i	0.256223	+	0.966618i	$0.417522\pi$
$8$	−0.997452	+	0.0713392i	−0.352653	+	0.0252222i
$9$	2.38352	+	0.342698i	0.794506	+	0.114233i
$10$	0.759654	−	2.10308i	0.240224	−	0.665051i
$11$	0.0487894	−	0.166162i	0.0147106	−	0.0500996i	−0.951811	−	0.306686i	$-0.900780\pi$
$11$	0.0487894	−	0.166162i	0.0147106	−	0.0500996i	0.966521	+	0.256587i	$0.0825979\pi$
$12$	0.675284	−	0.368733i	0.194938	−	0.106444i
$13$	0.678467	−	1.81904i	0.188173	−	0.504511i	−0.808267	−	0.588816i	$-0.799594\pi$
$13$	0.678467	−	1.81904i	0.188173	−	0.504511i	0.996440	+	0.0843049i	$0.0268670\pi$
$14$	−0.0735963	+	0.511873i	−0.0196694	+	0.136804i
$15$	0.140525	+	1.71468i	0.0362835	+	0.442728i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	−0.00793746	−	0.0364879i	−0.00192512	−	0.00884962i	0.976174	−	0.216988i	$-0.0696232\pi$
$17$	−0.00793746	−	0.0364879i	−0.00192512	−	0.00884962i	−0.978099	+	0.208138i	$0.933260\pi$
$18$	1.44308	−	1.92773i	0.340137	−	0.454369i
$19$	0.624467	−	0.401321i	0.143263	−	0.0920693i	−0.467046	−	0.884233i	$-0.654682\pi$
$19$	0.624467	−	0.401321i	0.143263	−	0.0920693i	0.610309	+	0.792164i	$0.291045\pi$
$20$	−1.48176	−	1.67463i	−0.331332	−	0.374458i
$21$	−0.112097	−	0.381767i	−0.0244615	−	0.0833084i
$22$	−0.122454	−	0.122454i	−0.0261073	−	0.0261073i
$23$	−4.61791	−	1.29419i	−0.962900	−	0.269858i
$23$	−4.61791	−	1.29419i	−0.962900	−	0.269858i
$24$		−	0.769398i		−	0.157053i
$25$	4.76721	−	1.50787i	0.953443	−	0.301574i
$26$	−1.27138	−	1.46725i	−0.249338	−	0.287751i
$27$	−0.884468	+	4.06583i	−0.170216	+	0.782470i
$28$	0.413990	+	0.309909i	0.0782367	+	0.0585672i
$29$	−1.50901	+	2.34806i	−0.280216	+	0.436025i	−0.952621	−	0.304158i	$-0.901625\pi$
$29$	−1.50901	+	2.34806i	−0.280216	+	0.436025i	0.672405	+	0.740183i	$0.265261\pi$
$30$	1.57228	+	0.698421i	0.287058	+	0.127514i
$31$	−1.86943	+	2.15743i	−0.335759	+	0.387487i	−0.898373	−	0.439233i	$-0.855250\pi$
$31$	−1.86943	+	2.15743i	−0.335759	+	0.387487i	0.562614	+	0.826720i	$0.309796\pi$
$32$	0.599278	+	0.800541i	0.105938	+	0.141517i
$33$	0.124841	+	0.0465631i	0.0217320	+	0.00810560i
$34$	−0.0358287	−	0.0105203i	−0.00614457	−	0.00180421i
$35$	−1.00911	+	0.564678i	−0.170570	+	0.0954480i
$36$	−1.00033	−	2.19042i	−0.166722	−	0.365070i
$37$	−6.38904	+	4.78278i	−1.05035	+	0.786284i	−0.977474	−	0.211057i	$-0.932309\pi$
$37$	−6.38904	+	4.78278i	−1.05035	+	0.786284i	−0.0728781	+	0.997341i	$0.523218\pi$
$38$	−0.0529555	−	0.740414i	−0.00859051	−	0.120111i
$39$	1.35876	+	0.620525i	0.217576	+	0.0993635i
$40$	−2.17992	+	0.497947i	−0.344676	+	0.0787323i
$41$	−0.673689	−	4.68561i	−0.105212	−	0.731769i	−0.972321	−	0.233649i	$-0.924933\pi$
$41$	−0.673689	−	4.68561i	−0.105212	−	0.731769i	0.867108	−	0.498119i	$-0.165976\pi$
$42$	−0.388791	−	0.0845763i	−0.0599918	−	0.0130504i
$43$	−6.52582	−	0.466736i	−0.995178	−	0.0711765i	−0.435760	−	0.900063i	$-0.643521\pi$
$43$	−6.52582	−	0.466736i	−0.995178	−	0.0711765i	−0.559417	+	0.828886i	$0.688975\pi$
$44$	−0.166162	+	0.0487894i	−0.0250498	+	0.00735529i
$45$	5.38422	−	0.0558469i	0.802633	−	0.00832516i
$46$	−3.34901	+	3.43280i	−0.493785	+	0.506139i
$47$	−5.54415	+	5.54415i	−0.808698	+	0.808698i	−0.984437	−	0.175739i	$-0.943769\pi$
$47$	−5.54415	+	5.54415i	−0.808698	+	0.808698i	0.175739	+	0.984437i	$0.443769\pi$
$48$	−0.675284	−	0.368733i	−0.0974689	−	0.0532220i
$49$	−5.08814	+	4.40890i	−0.726877	+	0.629842i
$50$	0.961256	−	4.90673i	0.135942	−	0.693916i
$51$	0.0284379	−	0.00408875i	0.00398210	−	0.000572539i
$52$	−1.89708	+	0.412685i	−0.263078	+	0.0572291i
$53$	−0.476831	−	1.27843i	−0.0654978	−	0.175606i	0.900078	−	0.435730i	$-0.143510\pi$
$53$	−0.476831	−	1.27843i	−0.0654978	−	0.175606i	−0.965575	+	0.260123i	$0.916237\pi$
$54$	3.14462	+	2.72483i	0.427928	+	0.370802i
$55$	0.0511308	−	0.383844i	0.00689448	−	0.0517575i
$56$	0.470405	−	0.214827i	0.0628604	−	0.0287074i
$57$	0.273713	+	0.501267i	0.0362541	+	0.0663945i
$58$	1.33766	+	2.44973i	0.175643	+	0.321666i
$59$	2.12411	−	0.970050i	0.276536	−	0.126290i	−0.272320	−	0.962207i	$-0.587791\pi$
$59$	2.12411	−	0.970050i	0.276536	−	0.126290i	0.548856	+	0.835917i	$0.315064\pi$
$60$	1.36650	−	1.04524i	0.176415	−	0.134940i
$61$	6.29529	+	5.45490i	0.806029	+	0.698428i	0.956993	−	0.290111i	$-0.0936924\pi$
$61$	6.29529	+	5.45490i	0.806029	+	0.698428i	−0.150964	+	0.988539i	$0.548238\pi$
$62$	0.997614	+	2.67471i	0.126697	+	0.339688i
$63$	−1.21682	+	0.264703i	−0.153305	+	0.0333495i
$64$	0.989821	−	0.142315i	0.123728	−	0.0177894i
$65$	0.878745	−	4.25135i	0.108995	−	0.527315i
$66$	0.100697	−	0.0872547i	0.0123950	−	0.0107403i
$67$	0.468349	+	0.255738i	0.0572179	+	0.0312433i	0.507603	−	0.861591i	$-0.330532\pi$
$67$	0.468349	+	0.255738i	0.0572179	+	0.0312433i	−0.450385	+	0.892834i	$0.648713\pi$
$68$	−0.0264043	+	0.0264043i	−0.00320199	+	0.00320199i
$69$	1.24668	−	3.47292i	0.150083	−	0.418090i
$70$	0.0119934	+	1.15629i	0.00143349	+	0.138203i
$71$	13.0620	−	3.83536i	1.55018	−	0.455173i	0.609024	−	0.793152i	$-0.291561\pi$
$71$	13.0620	−	3.83536i	1.55018	−	0.455173i	0.941154	+	0.337978i	$0.109743\pi$
$72$	−2.40189	−	0.171787i	−0.283066	−	0.0202453i
$73$	−3.75133	−	0.816052i	−0.439060	−	0.0955117i	−0.0123987	−	0.999923i	$-0.503947\pi$
$73$	−3.75133	−	0.816052i	−0.439060	−	0.0955117i	−0.426661	+	0.904411i	$0.640310\pi$
$74$	1.13580	+	7.89967i	0.132034	+	0.918318i
$75$	0.895532	+	3.74130i	0.103407	+	0.432008i
$76$	−0.675225	−	0.308365i	−0.0774536	−	0.0353719i
$77$	0.00638885	+	0.0893278i	0.000728077	+	0.0101798i
$78$	1.19581	−	0.895169i	0.135398	−	0.101358i
$79$	0.561663	+	1.22987i	0.0631920	+	0.138371i	0.938593	−	0.345026i	$-0.112130\pi$
$79$	0.561663	+	1.22987i	0.0631920	+	0.138371i	−0.875401	+	0.483397i	$0.839403\pi$
$80$	−0.607687	+	2.15191i	−0.0679414	+	0.240591i
$81$	3.85973	+	1.13332i	0.428859	+	0.125924i
$82$	−4.43532	−	1.65429i	−0.489800	−	0.182686i
$83$	−6.52994	−	8.72298i	−0.716754	−	0.957472i	0.283245	−	0.959048i	$-0.408589\pi$
$83$	−6.52994	−	8.72298i	−0.716754	−	0.957472i	−0.999999	+	0.00157614i	$0.999498\pi$
$84$	−0.260559	+	0.300701i	−0.0284293	+	0.0328091i
$85$	−0.0299893	−	0.0779263i	−0.00325279	−	0.00845229i
$86$	−3.53714	+	5.50389i	−0.381419	+	0.593500i
$87$	−1.71917	−	1.28695i	−0.184314	−	0.137976i
$88$	−0.0368113	+	0.169219i	−0.00392410	+	0.0180388i
$89$	0.385607	+	0.445015i	0.0408743	+	0.0471715i	0.775819	−	0.630956i	$-0.217337\pi$
$89$	0.385607	+	0.445015i	0.0408743	+	0.0471715i	−0.734944	+	0.678127i	$0.762792\pi$
$90$	2.53137	−	4.75238i	0.266830	−	0.500945i
$91$			1.00400i			0.105247i
$92$	1.40789	+	4.58452i	0.146782	+	0.477970i
$93$	−1.55309	−	1.55309i	−0.161048	−	0.161048i
$94$	2.20896	+	7.52302i	0.227837	+	0.775940i
$95$	1.24309	−	1.09992i	0.127538	−	0.112849i
$96$	−0.647258	+	0.415968i	−0.0660605	+	0.0424545i
$97$	3.69871	−	4.94090i	0.375547	−	0.501672i	−0.572455	−	0.819936i	$-0.694009\pi$
$97$	3.69871	−	4.94090i	0.375547	−	0.501672i	0.948002	+	0.318264i	$0.103100\pi$
$98$	1.43111	+	6.57871i	0.144564	+	0.664550i
$99$	0.173234	−	0.379329i	0.0174106	−	0.0381240i
$100$	−3.84585	−	3.19522i	−0.384585	−	0.319522i
$101$	2.43762	−	16.9540i	0.242552	−	1.68699i	−0.396666	−	0.917963i	$-0.629833\pi$
$101$	2.43762	−	16.9540i	0.242552	−	1.68699i	0.639218	−	0.769025i	$-0.279258\pi$
$102$	0.0100402	−	0.0269188i	0.000994129	−	0.00266536i
$103$	−16.8086	+	9.17821i	−1.65620	+	0.904356i	−0.669310	+	0.742983i	$0.733410\pi$
$103$	−16.8086	+	9.17821i	−1.65620	+	0.904356i	−0.986894	+	0.161372i	$0.948408\pi$
$104$	−0.546970	+	1.86281i	−0.0536348	+	0.182663i
$105$	−0.377967	−	0.805419i	−0.0368858	−	0.0786008i
$106$	−1.35058	−	0.194184i	−0.131180	−	0.0188608i
$107$	10.3881	−	0.742969i	1.00425	−	0.0718255i	0.440485	−	0.897760i	$-0.354806\pi$
$107$	10.3881	−	0.742969i	1.00425	−	0.0718255i	0.563766	+	0.825934i	$0.309352\pi$
$108$	3.89858	−	1.45409i	0.375141	−	0.139920i
$109$	−12.3070	−	7.90920i	−1.17879	−	0.757564i	−0.203629	−	0.979048i	$-0.565274\pi$
$109$	−12.3070	−	7.90920i	−1.17879	−	0.757564i	−0.975164	+	0.221484i	$0.928910\pi$
$110$	−0.312387	−	0.228833i	−0.0297850	−	0.0218184i
$111$	−3.31980	−	5.16571i	−0.315101	−	0.490307i
$112$	0.0368921	−	0.515820i	0.00348598	−	0.0487404i
$113$	6.70879	−	12.2862i	0.631109	−	1.15579i	−0.345019	−	0.938596i	$-0.612127\pi$
$113$	6.70879	−	12.2862i	0.631109	−	1.15579i	0.976128	−	0.217195i	$-0.0696907\pi$
$114$	0.571128			0.0534911
$115$	−10.6466	−	1.28455i	−0.992800	−	0.119785i
$116$	2.79115			0.259152
$117$	2.24052	−	4.10321i	0.207136	−	0.379341i
$118$	0.166587	−	2.32919i	0.0153355	−	0.214419i
$119$	0.0104401	+	0.0162451i	0.000957041	+	0.00148918i
$120$	−0.262491	−	1.70028i	−0.0239620	−	0.155214i
$121$	9.22856	+	5.93084i	0.838960	+	0.539167i
$122$	7.80466	−	2.91099i	0.706600	−	0.263548i
$123$	3.63289	−	0.259829i	0.327566	−	0.0234280i
$124$	2.82564	+	0.406266i	0.253750	+	0.0364837i
$125$	10.0206	−	4.95863i	0.896268	−	0.443513i
$126$	−0.350836	+	1.19484i	−0.0312550	+	0.106445i
$127$	8.71683	−	4.75975i	0.773494	−	0.422359i	−0.0434657	−	0.999055i	$-0.513840\pi$
$127$	8.71683	−	4.75975i	0.773494	−	0.422359i	0.816959	+	0.576696i	$0.195658\pi$
$128$	0.349464	−	0.936950i	0.0308886	−	0.0828154i
$129$	0.716381	−	4.98254i	0.0630738	−	0.438688i
$130$	−3.31018	−	2.80871i	−0.290322	−	0.246340i
$131$	3.81773	−	8.35966i	0.333556	−	0.730387i	−0.666327	−	0.745660i	$-0.732134\pi$
$131$	3.81773	−	8.35966i	0.333556	−	0.730387i	0.999883	+	0.0152731i	$0.00486175\pi$
$132$	−0.0283225	−	0.130197i	−0.00246516	−	0.0113322i
$133$	−0.230047	+	0.307307i	−0.0199476	+	0.0266469i
$134$	0.448911	−	0.288498i	0.0387800	−	0.0249224i
$135$	−0.567458	+	9.28679i	−0.0488390	+	0.799279i
$136$	0.0105203	+	0.0358287i	0.000902105	+	0.00307229i
$137$	6.09741	+	6.09741i	0.520937	+	0.520937i	0.917854	−	0.396918i	$-0.129920\pi$
$137$	6.09741	+	6.09741i	0.520937	+	0.520937i	−0.396918	+	0.917854i	$0.629920\pi$
$138$	−2.45064	−	2.75858i	−0.208612	−	0.234826i
$139$			2.62456i			0.222612i	0.993786	+	0.111306i	$0.0355034\pi$
$139$			2.62456i			0.222612i	−0.993786	+	0.111306i	$0.964497\pi$
$140$	1.02060	+	0.543625i	0.0862565	+	0.0459447i
$141$	−3.95048	−	4.55910i	−0.332691	−	0.383945i
$142$	2.89375	−	13.3024i	0.242838	−	1.11631i
$143$	−0.269153	−	0.201485i	−0.0225077	−	0.0168490i
$144$	−1.30188	+	2.02576i	−0.108490	+	0.168813i
$145$	−2.53367	+	5.70378i	−0.210410	+	0.473673i
$146$	−2.51405	+	2.90137i	−0.208065	+	0.240119i
$147$	−3.10427	−	4.14682i	−0.256036	−	0.342024i
$148$	7.47770	+	2.78904i	0.614663	+	0.229258i
$149$	−6.69926	−	1.96708i	−0.548825	−	0.161150i	−0.00444786	−	0.999990i	$-0.501416\pi$
$149$	−6.69926	−	1.96708i	−0.548825	−	0.161150i	−0.544377	+	0.838841i	$0.683234\pi$
$150$	3.71284	+	1.00703i	0.303152	+	0.0822233i
$151$	8.79777	+	19.2644i	0.715952	+	1.56772i	0.819491	+	0.573091i	$0.194256\pi$
$151$	8.79777	+	19.2644i	0.715952	+	1.56772i	−0.103539	+	0.994625i	$0.533017\pi$
$152$	−0.594246	+	0.444847i	−0.0481997	+	0.0360819i
$153$	−0.00641474	−	0.0896897i	−0.000518601	−	0.00725099i
$154$	0.0814630	+	0.0372029i	0.00656447	+	0.00299790i
$155$	−3.39519	+	5.40547i	−0.272708	+	0.434178i
$156$	−0.212582	−	1.47854i	−0.0170202	−	0.118378i
$157$	−9.29348	−	2.02167i	−0.741700	−	0.161347i	−0.174189	−	0.984712i	$-0.555730\pi$
$157$	−9.29348	−	2.02167i	−0.741700	−	0.161347i	−0.567512	+	0.823365i	$0.692094\pi$
$158$	1.34861	+	0.0964543i	0.107289	+	0.00767349i
$159$	1.00729	−	0.295767i	0.0798833	−	0.0234559i
$160$	1.59745	+	1.56465i	0.126290	+	0.123697i
$161$	2.47141	−	0.207476i	0.194774	−	0.0163514i
$162$	2.84446	−	2.84446i	0.223482	−	0.223482i
$163$	4.95347	+	2.70480i	0.387986	+	0.211856i	0.661389	−	0.750043i	$-0.269967\pi$
$163$	4.95347	+	2.70480i	0.387986	+	0.211856i	−0.273403	+	0.961900i	$0.588149\pi$
$164$	−3.57756	+	3.09997i	−0.279361	+	0.242067i
$165$	0.291770	+	0.0603082i	0.0227142	+	0.00469499i
$166$	−10.7854	+	1.55071i	−0.837113	+	0.120359i
$167$	1.01960	−	0.221800i	0.0788990	−	0.0171634i	−0.172942	−	0.984932i	$-0.555327\pi$
$167$	1.01960	−	0.221800i	0.0788990	−	0.0171634i	0.251841	+	0.967768i	$0.418964\pi$
$168$	0.139046	+	0.372797i	0.0107276	+	0.0287619i
$169$	6.97615	+	6.04487i	0.536627	+	0.464990i
$170$	−0.0827666	−	0.0110251i	−0.00634791	−	0.000845588i
$171$	1.62596	−	0.742551i	0.124340	−	0.0567843i
$172$	3.13548	+	5.74220i	0.239078	+	0.437839i
$173$	8.66522	+	15.8692i	0.658804	+	1.20651i	0.966900	+	0.255155i	$0.0821264\pi$
$173$	8.66522	+	15.8692i	0.658804	+	1.20651i	−0.308096	+	0.951355i	$0.599692\pi$
$174$	−1.95344	+	0.892105i	−0.148090	+	0.0676303i
$175$	−2.03736	+	1.59215i	−0.154010	+	0.120355i
$176$	0.130878	+	0.113406i	0.00986530	+	0.00854833i
$177$	0.627864	+	1.68337i	0.0471931	+	0.126530i
$178$	0.575382	−	0.125167i	0.0431267	−	0.00938164i
$179$	5.89824	−	0.848038i	0.440855	−	0.0633854i	0.0816863	−	0.996658i	$-0.473969\pi$
$179$	5.89824	−	0.848038i	0.440855	−	0.0633854i	0.359168	+	0.933273i	$0.383060\pi$
$180$	−2.95791	−	4.49930i	−0.220470	−	0.335358i
$181$	−6.88239	+	5.96362i	−0.511564	+	0.443273i	−0.871996	−	0.489513i	$-0.837175\pi$
$181$	−6.88239	+	5.96362i	−0.511564	+	0.443273i	0.360432	+	0.932785i	$0.382629\pi$
$182$	0.881186	+	0.481164i	0.0653179	+	0.0356662i
$183$	−4.53183	+	4.53183i	−0.335002	+	0.335002i
$184$	4.69847	+	0.961456i	0.346376	+	0.0708795i
$185$	−12.4874	+	12.7491i	−0.918089	+	0.937334i
$186$	−2.10743	+	0.618796i	−0.154524	+	0.0453723i
$187$	−0.00645016		0.000461324i	−0.000471682		3.37354e-5i
$188$	7.66144	+	1.66664i	0.558768	+	0.121552i
$189$	−0.306229	−	2.12987i	−0.0222748	−	0.154925i
$190$	−0.369629	−	1.61817i	−0.0268157	−	0.117394i
$191$	−20.4922	−	9.35849i	−1.48277	−	0.677157i	−0.500687	−	0.865628i	$-0.666919\pi$
$191$	−20.4922	−	9.35849i	−1.48277	−	0.677157i	−0.982079	+	0.188472i	$0.939647\pi$
$192$	0.0548882	+	0.767437i	0.00396121	+	0.0553850i
$193$	12.5711	−	9.41058i	0.904885	−	0.677388i	−0.0419461	−	0.999120i	$-0.513356\pi$
$193$	12.5711	−	9.41058i	0.904885	−	0.677388i	0.946831	+	0.321732i	$0.104265\pi$
$194$	−2.56392	−	5.61420i	−0.184079	−	0.403076i
$195$	3.21441	+	0.907730i	0.230189	+	0.0650039i
$196$	6.45985	+	1.89678i	0.461418	+	0.135485i
$197$	5.24165	+	1.95503i	0.373452	+	0.139290i	0.529180	−	0.848510i	$-0.322500\pi$
$197$	5.24165	+	1.95503i	0.373452	+	0.139290i	−0.155728	+	0.987800i	$0.549772\pi$
$198$	−0.249907	−	0.333837i	−0.0177601	−	0.0237247i
$199$	−1.40259	+	1.61867i	−0.0994267	+	0.114744i	−0.803282	−	0.595599i	$-0.796915\pi$
$199$	−1.40259	+	1.61867i	−0.0994267	+	0.114744i	0.703855	+	0.710343i	$0.251460\pi$
$200$	−4.64750	+	1.84412i	−0.328628	+	0.130399i
$201$	−0.221969	+	0.345391i	−0.0156565	+	0.0243620i
$202$	−13.7120	−	10.2646i	−0.964770	−	0.722218i
$203$	0.306818	−	1.41042i	0.0215344	−	0.0989921i
$204$	−0.0188143	−	0.0217129i	−0.00131727	−	0.00152021i
$205$	−3.08734	−	10.1248i	−0.215629	−	0.707149i
$206$			19.1512i			1.33433i
$207$	−10.5633	−	4.66728i	−0.734203	−	0.324398i
$208$	1.37281	+	1.37281i	0.0951874	+	0.0951874i
$209$	−0.0362167	−	0.123343i	−0.00250516	−	0.00853179i
$210$	−0.888040	−	0.0542626i	−0.0612806	−	0.00374447i
$211$	−8.42811	+	5.41642i	−0.580215	+	0.372882i	−0.797584	−	0.603208i	$-0.793889\pi$
$211$	−8.42811	+	5.41642i	−0.580215	+	0.372882i	0.217369	+	0.976090i	$0.430253\pi$
$212$	−0.817693	+	1.09231i	−0.0561594	+	0.0750202i
$213$	2.22645	+	10.2348i	0.152554	+	0.701277i
$214$	4.32638	−	9.47345i	0.295745	−	0.647592i
$215$	−14.5806	+	1.19494i	−0.994386	+	0.0814944i
$216$	0.592161	−	4.11857i	0.0402915	−	0.280233i
$217$	0.515903	−	1.38319i	0.0350218	−	0.0938971i
$218$	−12.8398	+	7.01108i	−0.869624	+	0.474851i
$219$	0.832173	−	2.83412i	0.0562330	−	0.191512i
$220$	−0.350553	+	0.164508i	−0.0236343	+	0.0110911i
$221$	−0.0717583	−	0.0103173i	−0.00482699	−	0.000694016i
$222$	−6.12484	+	0.438057i	−0.411072	+	0.0294005i
$223$	13.3484	−	4.97871i	0.893878	−	0.333399i	0.139796	−	0.990180i	$-0.455355\pi$
$223$	13.3484	−	4.97871i	0.893878	−	0.333399i	0.754081	+	0.656781i	$0.228082\pi$
$224$	−0.435043	−	0.279585i	−0.0290676	−	0.0186806i
$225$	11.8795	−	1.96032i	0.791965	−	0.130688i
$226$	−7.56818	−	11.7763i	−0.503428	−	0.783349i
$227$	−0.489586	+	6.84531i	−0.0324950	+	0.454339i	0.954991	+	0.296634i	$0.0958641\pi$
$227$	−0.489586	+	6.84531i	−0.0324950	+	0.454339i	−0.987486	+	0.157705i	$0.949590\pi$
$228$	0.273713	−	0.501267i	0.0181271	−	0.0331972i
$229$	−19.4811			−1.28735			−0.643673	−	0.765300i	$-0.722590\pi$
$229$	−19.4811			−1.28735			−0.643673	+	0.765300i	$0.722590\pi$
$230$	−6.22979	+	8.72867i	−0.410780	+	0.575551i
$231$	−0.0689042			−0.00453356
$232$	1.33766	−	2.44973i	0.0878214	−	0.160833i
$233$	1.33177	−	18.6206i	0.0872474	−	1.21988i	−0.745607	−	0.666386i	$-0.767840\pi$
$233$	1.33177	−	18.6206i	0.0872474	−	1.21988i	0.832855	−	0.553492i	$-0.186705\pi$
$234$	−2.52753	−	3.93291i	−0.165230	−	0.257103i
$235$	−10.3605	+	14.1434i	−0.675844	+	0.922616i
$236$	−1.96444	−	1.26247i	−0.127874	−	0.0821798i
$237$	−0.974676	+	0.363535i	−0.0633120	+	0.0236142i
$238$	0.0192614	−	0.00137760i	0.00124853	−	8.92966e-5i
$239$	18.3752	+	2.64195i	1.18859	+	0.170893i	0.708104	−	0.706109i	$-0.249551\pi$
$239$	18.3752	+	2.64195i	1.18859	+	0.170893i	0.480487	+	0.877002i	$0.340460\pi$
$240$	−1.61810	−	0.584476i	−0.104448	−	0.0377278i
$241$	−6.70519	+	22.8358i	−0.431919	+	1.47098i	0.400222	+	0.916418i	$0.368933\pi$
$241$	−6.70519	+	22.8358i	−0.431919	+	1.47098i	−0.832141	+	0.554564i	$0.812885\pi$
$242$	9.62815	−	5.25737i	0.618921	−	0.337956i
$243$	−5.44389	+	14.5956i	−0.349225	+	0.936310i
$244$	1.18546	−	8.24507i	0.0758914	−	0.527837i
$245$	−9.74006	+	11.4791i	−0.622269	+	0.733370i
$246$	1.51301	−	3.31303i	0.0964660	−	0.211231i
$247$	−0.306338	−	1.40821i	−0.0194918	−	0.0896025i
$248$	1.71076	−	2.28530i	0.108633	−	0.145117i
$249$	7.05276	−	4.53253i	0.446950	−	0.287238i
$250$	0.450267	−	11.1713i	0.0284774	−	0.706533i
$251$	−4.86667	−	16.5744i	−0.307182	−	1.04616i	−0.957961	−	0.286898i	$-0.907376\pi$
$251$	−4.86667	−	16.5744i	−0.307182	−	1.04616i	0.650780	−	0.759267i	$-0.274442\pi$
$252$	0.880546	+	0.880546i	0.0554692	+	0.0554692i
$253$	−0.440350	+	0.704176i	−0.0276846	+	0.0442712i
$254$		−	9.93168i		−	0.623169i
$255$	0.0614496	−	0.0187377i	0.00384812	−	0.00117340i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−5.52430	+	25.3948i	−0.344596	+	1.58408i	0.399966	+	0.916530i	$0.369022\pi$
$257$	−5.52430	+	25.3948i	−0.344596	+	1.58408i	−0.744562	+	0.667553i	$0.767342\pi$
$258$	−4.02974	−	3.01663i	−0.250881	−	0.187807i
$259$	2.23134	−	3.47204i	0.138649	−	0.215742i
$260$	−4.05154	+	1.55920i	−0.251266	+	0.0966977i
$261$	−4.40143	+	5.07952i	−0.272442	+	0.314414i
$262$	−5.50745	−	7.35710i	−0.340252	−	0.454523i
$263$	22.3229	+	8.32601i	1.37649	+	0.513404i	0.925372	−	0.379061i	$-0.123753\pi$
$263$	22.3229	+	8.32601i	1.37649	+	0.513404i	0.451117	+	0.892465i	$0.351026\pi$
$264$	−0.127844	−	0.0375385i	−0.00786827	−	0.00231033i
$265$	−1.48990	−	2.66252i	−0.0915239	−	0.163557i
$266$	0.159467	+	0.349184i	0.00977755	+	0.0214098i
$267$	−0.362686	+	0.271503i	−0.0221960	+	0.0166157i
$268$	−0.0380681	−	0.532262i	−0.00232538	−	0.0325131i
$269$	−15.5683	−	7.10978i	−0.949213	−	0.433491i	−0.120218	−	0.992747i	$-0.538359\pi$
$269$	−15.5683	−	7.10978i	−0.949213	−	0.433491i	−0.828995	+	0.559256i	$0.811087\pi$
$270$	7.87886	+	4.94873i	0.479492	+	0.301170i
$271$	−2.27405	−	15.8163i	−0.138139	−	0.960774i	−0.934502	−	0.355957i	$-0.884155\pi$
$271$	−2.27405	−	15.8163i	−0.138139	−	0.960774i	0.796364	−	0.604818i	$-0.206754\pi$
$272$	0.0364879	+	0.00793746i	0.00221241	+	0.000481279i
$273$	−0.770504	−	0.0551075i	−0.0466330	−	0.00333526i
$274$	8.27374	−	2.42939i	0.499835	−	0.146765i
$275$	−0.0179605	−	0.865696i	−0.00108306	−	0.0522034i
$276$	−3.59561	+	0.828828i	−0.216430	+	0.0498896i
$277$	−6.17463	+	6.17463i	−0.370998	+	0.370998i	−0.867841	−	0.496843i	$-0.834493\pi$
$277$	−6.17463	+	6.17463i	−0.370998	+	0.370998i	0.496843	+	0.867841i	$0.334493\pi$
$278$	2.30352	+	1.25782i	0.138156	+	0.0754388i
$279$	−5.19516	+	4.50163i	−0.311026	+	0.269506i
$280$	0.966250	−	0.635228i	0.0577445	−	0.0379621i
$281$	−17.5108	+	2.51767i	−1.04460	+	0.150191i	−0.643191	−	0.765706i	$-0.722390\pi$
$281$	−17.5108	+	2.51767i	−1.04460	+	0.150191i	−0.401413	+	0.915897i	$0.631481\pi$
$282$	−5.89469	+	1.28231i	−0.351024	+	0.0763605i
$283$	2.23277	+	5.98628i	0.132724	+	0.355848i	0.986263	−	0.165182i	$-0.0528210\pi$
$283$	2.23277	+	5.98628i	0.132724	+	0.355848i	−0.853539	+	0.521029i	$0.825548\pi$
$284$	−10.2884	−	8.91493i	−0.610503	−	0.529004i
$285$	0.775889	+	1.01436i	0.0459597	+	0.0600857i
$286$	−0.305830	+	0.139668i	−0.0180841	+	0.00825875i
$287$	1.17321	+	2.14857i	0.0692524	+	0.126826i
$288$	1.15404	+	2.11348i	0.0680027	+	0.124538i
$289$	15.4625	−	7.06148i	0.909557	−	0.415381i
$290$	3.79183	+	4.95728i	0.222664	+	0.291101i
$291$	3.58881	+	3.10972i	0.210380	+	0.182295i
$292$	1.34162	+	3.59701i	0.0785121	+	0.210499i
$293$	−0.633795	+	0.137874i	−0.0370267	+	0.00805467i	−0.231040	−	0.972944i	$-0.574213\pi$
$293$	−0.633795	+	0.137874i	−0.0370267	+	0.00805467i	0.194014	+	0.980999i	$0.437849\pi$
$294$	−5.12730	+	0.737194i	−0.299030	+	0.0429940i
$295$	4.36311	−	2.86838i	0.254030	−	0.167003i
$296$	6.03156	−	5.22638i	0.350577	−	0.303777i
$297$	0.632433	+	0.345334i	0.0366975	+	0.0200383i
$298$	−4.93708	+	4.93708i	−0.285997	+	0.285997i
$299$	−5.48729	+	7.52210i	−0.317338	+	0.435014i
$300$	2.66322	−	2.77607i	0.153761	−	0.160276i
$301$	3.24631	−	0.953203i	0.187114	−	0.0549417i
$302$	21.1243	+	1.51084i	1.21557	+	0.0869391i
$303$	12.8774	+	2.80130i	0.739785	+	0.160930i
$304$	0.105641	+	0.734750i	0.00605893	+	0.0421408i
$305$	15.7729	+	9.90698i	0.903153	+	0.567272i
$306$	−0.0817931	−	0.0373536i	−0.00467580	−	0.00213537i
$307$	−1.30911	−	18.3038i	−0.0747150	−	1.04465i	−0.887114	−	0.461550i	$-0.847293\pi$
$307$	−1.30911	−	18.3038i	−0.0747150	−	1.04465i	0.812399	−	0.583102i	$-0.198161\pi$
$308$	0.0716933	−	0.0536689i	0.00408510	−	0.00305807i
$309$	−6.12110	−	13.4033i	−0.348217	−	0.762490i
$310$	3.11713	+	5.57045i	0.177041	+	0.316380i
$311$	13.5307	+	3.97298i	0.767258	+	0.225287i	0.641863	−	0.766820i	$-0.278162\pi$
$311$	13.5307	+	3.97298i	0.767258	+	0.225287i	0.125395	+	0.992107i	$0.459980\pi$
$312$	−1.39957	−	0.522011i	−0.0792348	−	0.0295530i
$313$	16.8674	+	22.5322i	0.953400	+	1.27359i	0.961835	+	0.273629i	$0.0882240\pi$
$313$	16.8674	+	22.5322i	0.953400	+	1.27359i	−0.00843540	+	0.999964i	$0.502685\pi$
$314$	−6.22827	+	7.18781i	−0.351482	+	0.405631i
$315$	−2.59873	+	1.00010i	−0.146422	+	0.0563493i
$316$	0.730974	−	1.13742i	0.0411205	−	0.0639848i
$317$	−4.18985	−	3.13648i	−0.235325	−	0.176162i	0.475107	−	0.879928i	$-0.342409\pi$
$317$	−4.18985	−	3.13648i	−0.235325	−	0.176162i	−0.710432	+	0.703766i	$0.751500\pi$
$318$	0.223154	−	1.02582i	0.0125139	−	0.0575254i
$319$	0.316534	+	0.365300i	0.0177225	+	0.0204529i
$320$	2.13884	−	0.652192i	0.119565	−	0.0364586i
$321$			8.01297i			0.447240i
$322$	1.00232	−	2.26854i	0.0558573	−	0.126421i
$323$	−0.0196000	−	0.0196000i	−0.00109058	−	0.00109058i
$324$	−1.13332	−	3.85973i	−0.0629622	−	0.214430i
$325$	0.491520	−	9.69480i	0.0272646	−	0.537771i
$326$	4.74789	−	3.05129i	0.262961	−	0.168995i
$327$	6.74532	−	9.01070i	0.373017	−	0.498293i
$328$	1.00624	+	4.62561i	0.0555603	+	0.255407i
$329$	1.68437	−	3.68826i	0.0928625	−	0.203340i
$330$	0.192761	−	0.227177i	0.0106112	−	0.0125057i
$331$	2.84927	−	19.8171i	0.156610	−	1.08925i	−0.748213	−	0.663458i	$-0.769088\pi$
$331$	2.84927	−	19.8171i	0.156610	−	1.08925i	0.904823	−	0.425788i	$-0.140003\pi$
$332$	−3.80789	+	10.2093i	−0.208985	+	0.560310i
$333$	−16.8674	+	9.21032i	−0.924330	+	0.504722i
$334$	0.293973	−	1.00118i	0.0160855	−	0.0547821i
$335$	1.12225	+	0.405368i	0.0613149	+	0.0221476i
$336$	0.393834	+	0.0566248i	0.0214854	+	0.00308914i
$337$	31.4726	−	2.25096i	1.71442	−	0.122618i	0.820735	−	0.571309i	$-0.193564\pi$
$337$	31.4726	−	2.25096i	1.71442	−	0.122618i	0.893687	+	0.448691i	$0.148110\pi$
$338$	8.64877	−	3.22582i	0.470431	−	0.175462i
$339$	9.06067	+	5.82294i	0.492108	+	0.316259i
$340$	−0.0493423	+	0.0673587i	−0.00267596	+	0.00365304i
$341$	0.267274	+	0.415887i	0.0144737	+	0.0225216i
$342$	0.127518	−	1.78294i	0.00689540	−	0.0964103i
$343$	3.40345	−	6.23294i	0.183769	−	0.336547i
$344$	6.54249			0.352747
$345$	1.57019	−	8.10008i	0.0845360	−	0.436094i
$346$	18.0808			0.972031
$347$	14.9988	−	27.4683i	0.805178	−	1.47457i	−0.0735719	−	0.997290i	$-0.523440\pi$
$347$	14.9988	−	27.4683i	0.805178	−	1.47457i	0.878750	−	0.477283i	$-0.158378\pi$
$348$	−0.153201	+	2.14203i	−0.00821245	+	0.114825i
$349$	−10.0687	−	15.6672i	−0.538966	−	0.838647i	0.459815	−	0.888015i	$-0.347916\pi$
$349$	−10.0687	−	15.6672i	−0.538966	−	0.838647i	−0.998781	+	0.0493677i	$0.984279\pi$
$350$	0.420990	+	2.55118i	0.0225028	+	0.136367i
$351$	6.79583	+	4.36742i	0.362735	+	0.233115i
$352$	0.162258	−	0.0605190i	0.00864836	−	0.00322567i
$353$	4.72854	−	0.338192i	0.251675	−	0.0180001i	0.0550681	−	0.998483i	$-0.482462\pi$
$353$	4.72854	−	0.338192i	0.251675	−	0.0180001i	0.196607	+	0.980482i	$0.437008\pi$
$354$	1.77836	+	0.255690i	0.0945188	+	0.0135897i
$355$	27.5571	−	12.9320i	1.46258	−	0.686360i
$356$	0.165895	−	0.564987i	0.00879242	−	0.0299442i
$357$	−0.0130401	+	0.00712044i	−0.000690156	+	0.000376854i
$358$	2.08242	−	5.58318i	0.110059	−	0.295080i
$359$	5.14292	−	35.7698i	0.271433	−	1.88786i	−0.162187	−	0.986760i	$-0.551855\pi$
$359$	5.14292	−	35.7698i	0.271433	−	1.88786i	0.433620	−	0.901096i	$-0.357236\pi$
$360$	−5.36652	+	0.439811i	−0.282840	+	0.0231801i
$361$	−7.66398	+	16.7818i	−0.403368	+	0.883252i
$362$	1.93577	+	8.89859i	0.101742	+	0.467699i
$363$	−5.05808	+	6.75681i	−0.265480	+	0.354640i
$364$	0.844615	−	0.542801i	0.0442699	−	0.0284505i
$365$	−8.56843	−	0.523563i	−0.448492	−	0.0274046i
$366$	1.80562	+	6.14936i	0.0943811	+	0.321432i
$367$	−22.4658	−	22.4658i	−1.17271	−	1.17271i	−0.981562	−	0.191143i	$-0.938781\pi$
$367$	−22.4658	−	22.4658i	−1.17271	−	1.17271i	−0.191143	−	0.981562i	$-0.561219\pi$
$368$	3.09559	−	3.66297i	0.161369	−	0.190945i
$369$		−	11.3991i		−	0.593413i
$370$	5.20508	+	17.0699i	0.270599	+	0.887421i
$371$	0.462080	+	0.533268i	0.0239900	+	0.0276859i
$372$	−0.466877	+	2.14620i	−0.0242065	+	0.111275i
$373$	−10.7748	−	8.06590i	−0.557897	−	0.417637i	0.282771	−	0.959187i	$-0.408746\pi$
$373$	−10.7748	−	8.06590i	−0.557897	−	0.417637i	−0.840668	+	0.541551i	$0.817837\pi$
$374$	−0.00349613	+	0.00544008i	−0.000180780	+	0.000281300i
$375$	3.25543	+	7.96234i	0.168109	+	0.411173i
$376$	5.13451	−	5.92554i	0.264792	−	0.305587i
$377$	3.24741	+	4.33803i	0.167250	+	0.223420i
$378$	−2.01610	−	0.751966i	−0.103697	−	0.0386769i
$379$	19.7329	+	5.79411i	1.01361	+	0.297624i	0.746031	−	0.665912i	$-0.231957\pi$
$379$	19.7329	+	5.79411i	1.01361	+	0.297624i	0.267582	+	0.963535i	$0.413775\pi$
$380$	−1.59738	−	0.451089i	−0.0819436	−	0.0231404i
$381$	3.17436	+	6.95087i	0.162627	+	0.356104i
$382$	−18.0346	+	13.5006i	−0.922732	+	0.690749i
$383$	0.168744	+	2.35935i	0.00862243	+	0.120557i	0.999940	−	0.0109302i	$-0.00347925\pi$
$383$	0.168744	+	2.35935i	0.00862243	+	0.120557i	−0.991318	+	0.131487i	$0.958025\pi$
$384$	0.699869	+	0.319619i	0.0357150	+	0.0163105i
$385$	0.0445941	+	0.195225i	0.00227273	+	0.00994958i
$386$	−2.23480	−	15.5434i	−0.113748	−	0.791137i
$387$	−15.3944	−	3.34886i	−0.782544	−	0.170232i
$388$	−6.15622	−	0.440301i	−0.312535	−	0.0223529i
$389$	−35.8875	+	10.5375i	−1.81957	+	0.534274i	−0.999290	−	0.0376863i	$-0.988001\pi$
$389$	−35.8875	+	10.5375i	−1.81957	+	0.534274i	−0.820281	+	0.571960i	$0.806183\pi$
$390$	2.33720	−	2.38619i	0.118349	−	0.120829i
$391$	−0.0105679	+	0.178770i	−0.000534441	+	0.00904081i
$392$	4.76065	−	4.76065i	0.240449	−	0.240449i
$393$	6.20596	+	3.38871i	0.313049	+	0.170938i
$394$	4.22795	−	3.66354i	0.213001	−	0.184566i
$395$	1.66080	+	2.52625i	0.0835639	+	0.127110i
$396$	−0.412769	+	0.0593472i	−0.0207424	+	0.00298231i
$397$	3.99895	−	0.869918i	0.200701	−	0.0436599i	−0.111091	−	0.993810i	$-0.535434\pi$
$397$	3.99895	−	0.869918i	0.200701	−	0.0436599i	0.311792	+	0.950150i	$0.399071\pi$
$398$	0.748485	+	2.00677i	0.0375182	+	0.100590i
$399$	−0.223212	−	0.193414i	−0.0111746	−	0.00968282i
$400$	−0.608765	+	4.96280i	−0.0304382	+	0.248140i
$401$	1.06811	−	0.487791i	0.0533391	−	0.0243591i	−0.388567	−	0.921421i	$-0.627030\pi$
$401$	1.06811	−	0.487791i	0.0533391	−	0.0243591i	0.441906	+	0.897061i	$0.354302\pi$
$402$	0.196764	+	0.360346i	0.00981370	+	0.0179724i
$403$	2.65612	+	4.86431i	0.132311	+	0.242309i
$404$	−15.5805	+	7.11538i	−0.775159	+	0.354003i
$405$	8.91622	+	1.18771i	0.443051	+	0.0590176i
$406$	−1.09085	−	0.945231i	−0.0541382	−	0.0469110i
$407$	0.482996	+	1.29496i	0.0239412	+	0.0641889i
$408$	−0.0280737	+	0.00610706i	−0.00138986	+	0.000302345i
$409$	16.1523	−	2.32235i	0.798679	−	0.114833i	0.269121	−	0.963106i	$-0.413267\pi$
$409$	16.1523	−	2.32235i	0.798679	−	0.114833i	0.529558	+	0.848274i	$0.322358\pi$
$410$	−10.3660	−	2.14262i	−0.511938	−	0.105817i
$411$	−5.01405	+	4.34470i	−0.247325	+	0.214308i
$412$	16.8086	+	9.17821i	0.828102	+	0.452178i
$413$	−0.853892	+	0.853892i	−0.0420173	+	0.0420173i
$414$	−9.15884	+	7.03444i	−0.450133	+	0.345724i
$415$	−17.4064	−	17.0490i	−0.854447	−	0.836904i
$416$	1.86281	−	0.546970i	0.0913316	−	0.0268174i
$417$	−2.01418	−	0.144057i	−0.0986349	−	0.00705451i
$418$	−0.125612	−	0.0273252i	−0.00614389	−	0.00133652i
$419$	1.08360	+	7.53661i	0.0529373	+	0.368187i	0.999020	+	0.0442619i	$0.0140936\pi$
$419$	1.08360	+	7.53661i	0.0529373	+	0.368187i	−0.946083	+	0.323925i	$0.894997\pi$
$420$	−0.473217	+	0.753408i	−0.0230906	+	0.0367626i
$421$	−13.7612	−	6.28453i	−0.670680	−	0.306289i	0.0508158	−	0.998708i	$-0.483818\pi$
$421$	−13.7612	−	6.28453i	−0.670680	−	0.306289i	−0.721496	+	0.692419i	$0.756545\pi$
$422$	0.714713	+	9.99299i	0.0347917	+	0.486451i
$423$	−15.1146	+	11.3146i	−0.734895	+	0.550136i
$424$	0.566819	+	1.24116i	0.0275272	+	0.0602761i
$425$	−0.0928586	−	0.161977i	−0.00450431	−	0.00785704i
$426$	10.0499	+	2.95092i	0.486919	+	0.142972i
$427$	−4.03608	−	1.50538i	−0.195320	−	0.0728504i
$428$	−6.24124	−	8.33731i	−0.301681	−	0.402999i
$429$	0.169401	−	0.195499i	0.00817873	−	0.00943876i
$430$	−5.93894	+	13.3697i	−0.286401	+	0.644745i
$431$	11.7759	−	18.3237i	0.567227	−	0.882623i	−0.432593	−	0.901589i	$-0.642401\pi$
$431$	11.7759	−	18.3237i	0.567227	−	0.882623i	0.999820	+	0.0189665i	$0.00603759\pi$
$432$	−3.33099	−	2.49355i	−0.160262	−	0.119971i
$433$	5.05381	−	23.2320i	0.242871	−	1.11646i	−0.680560	−	0.732692i	$-0.738263\pi$
$433$	5.05381	−	23.2320i	0.242871	−	1.11646i	0.923431	−	0.383765i	$-0.125373\pi$
$434$	−0.966751	−	1.11569i	−0.0464055	−	0.0535548i
$435$	−4.23823	−	2.25750i	−0.203207	−	0.108239i
$436$			14.6293i			0.700617i
$437$	−3.40312	+	1.04508i	−0.162793	+	0.0499930i
$438$	−2.08863	−	2.08863i	−0.0997986	−	0.0997986i
$439$	11.2578	+	38.3406i	0.537306	+	1.82990i	0.557609	+	0.830104i	$0.311719\pi$
$439$	11.2578	+	38.3406i	0.537306	+	1.82990i	−0.0203028	+	0.999794i	$0.506463\pi$
$440$	−0.0236174	+	0.386513i	−0.00112592	+	0.0184263i
$441$	−13.6386	+	8.76498i	−0.649456	+	0.417380i
$442$	−0.0434454	+	0.0580362i	−0.00206649	+	0.00276050i
$443$	−5.79657	−	26.6464i	−0.275403	−	1.26601i	−0.882095	−	0.471071i	$-0.843868\pi$
$443$	−5.79657	−	26.6464i	−0.275403	−	1.26601i	0.606692	−	0.794937i	$-0.292496\pi$
$444$	−2.55085	+	5.58558i	−0.121058	+	0.265080i
$445$	1.00397	+	0.851877i	0.0475929	+	0.0403828i
$446$	2.02752	−	14.1017i	0.0960057	−	0.667734i
$447$	1.87732	−	5.03330i	0.0887943	−	0.238067i
$448$	−0.453880	+	0.247837i	−0.0214438	+	0.0117092i
$449$	−5.02183	+	17.1028i	−0.236995	+	0.807130i	0.751998	+	0.659166i	$0.229090\pi$
$449$	−5.02183	+	17.1028i	−0.236995	+	0.807130i	−0.988993	+	0.147965i	$0.952728\pi$
$450$	3.97270	−	11.3659i	0.187275	−	0.535791i
$451$	−0.811437	−	0.116667i	−0.0382091	−	0.00549364i
$452$	−13.9629	+	0.998644i	−0.656758	+	0.0469723i
$453$	−15.2671	+	5.69435i	−0.717312	+	0.267544i
$454$	5.77335	+	3.71031i	0.270957	+	0.174133i
$455$	0.342528	+	2.21872i	0.0160579	+	0.104015i
$456$	−0.308775	−	0.480464i	−0.0144597	−	0.0224998i
$457$	−1.46234	+	20.4462i	−0.0684055	+	0.956434i	0.841137	+	0.540822i	$0.181887\pi$
$457$	−1.46234	+	20.4462i	−0.0684055	+	0.956434i	−0.909542	+	0.415611i	$0.863568\pi$
$458$	−9.33629	+	17.0981i	−0.436256	+	0.798944i
$459$	0.155374			0.00725225
$460$	4.67535	+	9.65097i	0.217989	+	0.449979i
$461$	−31.3469			−1.45997			−0.729985	−	0.683463i	$-0.760473\pi$
$461$	−31.3469			−1.45997			−0.729985	+	0.683463i	$0.760473\pi$
$462$	−0.0330222	+	0.0604757i	−0.00153633	+	0.00281359i
$463$	2.13022	−	29.7844i	0.0989999	−	1.38420i	−0.668768	−	0.743471i	$-0.733178\pi$
$463$	2.13022	−	29.7844i	0.0989999	−	1.38420i	0.767768	−	0.640728i	$-0.221367\pi$
$464$	−1.50901	−	2.34806i	−0.0700540	−	0.109006i
$465$	−3.96201	−	2.90229i	−0.183734	−	0.134590i
$466$	−15.7047	−	10.0928i	−0.727505	−	0.467539i
$467$	20.1445	−	7.51351i	0.932177	−	0.347684i	0.162931	−	0.986637i	$-0.447905\pi$
$467$	20.1445	−	7.51351i	0.932177	−	0.347684i	0.769245	+	0.638953i	$0.220632\pi$
$468$	−4.66315	+	0.333515i	−0.215554	+	0.0154167i
$469$	−0.273147	−	0.0392726i	−0.0126127	−	0.00181344i
$470$	7.44814	+	15.8714i	0.343557	+	0.732094i
$471$	2.06161	−	7.02120i	0.0949939	−	0.323520i
$472$	−2.04950	+	1.11911i	−0.0943359	+	0.0515113i
$473$	−0.395945	+	1.06157i	−0.0182055	+	0.0488110i
$474$	−0.148045	+	1.02968i	−0.00679994	+	0.0472946i
$475$	2.37183	−	2.85480i	0.108827	−	0.130987i
$476$	0.00802190	−	0.0175655i	0.000367683	−	0.000805114i
$477$	−0.698419	−	3.21058i	−0.0319784	−	0.147002i
$478$	11.1251	−	14.8613i	0.508848	−	0.679742i
$479$	6.11879	−	3.93231i	0.279575	−	0.179672i	−0.393337	−	0.919394i	$-0.628680\pi$
$479$	6.11879	−	3.93231i	0.279575	−	0.179672i	0.672912	+	0.739722i	$0.265043\pi$
$480$	−1.28846	+	1.14006i	−0.0588097	+	0.0520366i
$481$	4.36531	+	14.8669i	0.199041	+	0.677871i
$482$	16.8290	+	16.8290i	0.766541	+	0.766541i
$483$	0.0235735	+	1.90804i	0.00107263	+	0.0868188i
$484$		−	10.9700i		−	0.498637i
$485$	6.48807	−	12.1807i	0.294608	−	0.553097i
$486$	10.2013	+	11.7729i	0.462740	+	0.534031i
$487$	−4.34511	+	19.9741i	−0.196896	+	0.905115i	0.767582	+	0.640951i	$0.221460\pi$
$487$	−4.34511	+	19.9741i	−0.196896	+	0.905115i	−0.964478	+	0.264164i	$0.914904\pi$
$488$	−6.66839	−	4.99190i	−0.301864	−	0.225973i
$489$	−2.34765	+	3.65302i	−0.106164	+	0.165195i
$490$	5.40702	+	14.0500i	0.244264	+	0.634713i
$491$	1.30525	−	1.50634i	0.0589052	−	0.0679802i	−0.725532	−	0.688188i	$-0.758406\pi$
$491$	1.30525	−	1.50634i	0.0589052	−	0.0679802i	0.784437	+	0.620208i	$0.212952\pi$
$492$	−2.18267	−	2.91570i	−0.0984023	−	0.131450i
$493$	0.0976537	+	0.0364229i	0.00439810	+	0.00164041i
$494$	−1.38277	−	0.406019i	−0.0622139	−	0.0182676i
$495$	0.253414	−	0.897376i	0.0113901	−	0.0403340i
$496$	−1.18588	−	2.59672i	−0.0532477	−	0.116596i
$497$	−5.63584	+	4.21893i	−0.252802	+	0.189245i
$498$	−0.598081	−	8.36227i	−0.0268007	−	0.374722i
$499$	18.6776	+	8.52977i	0.836123	+	0.381845i	0.787004	−	0.616948i	$-0.211631\pi$
$499$	18.6776	+	8.52977i	0.836123	+	0.381845i	0.0491196	+	0.998793i	$0.484358\pi$
$500$	−9.58900	−	5.74901i	−0.428833	−	0.257104i
$501$	0.114254	+	0.794653i	0.00510449	+	0.0355025i
$502$	−16.8793	−	3.67187i	−0.753361	−	0.163884i
$503$	−9.09393	−	0.650411i	−0.405478	−	0.0290004i	−0.132889	−	0.991131i	$-0.542425\pi$
$503$	−9.09393	−	0.650411i	−0.405478	−	0.0290004i	−0.272589	+	0.962131i	$0.587880\pi$
$504$	1.19484	−	0.350836i	0.0532223	−	0.0156275i
$505$	−0.397240	−	38.2981i	−0.0176770	−	1.70424i
$506$	0.407003	+	0.723962i	0.0180935	+	0.0321840i
$507$	−5.02197	+	5.02197i	−0.223033	+	0.223033i
$508$	−8.71683	−	4.75975i	−0.386747	−	0.211180i
$509$	−26.0404	+	22.5641i	−1.15422	+	1.00014i	−0.154293	+	0.988025i	$0.549310\pi$
$509$	−26.0404	+	22.5641i	−1.15422	+	1.00014i	−0.999927	+	0.0121121i	$0.996145\pi$
$510$	0.0130040	−	0.0629130i	0.000575826	−	0.00278583i
$511$	1.96512	−	0.282541i	0.0869316	−	0.0124989i
$512$	−0.977147	+	0.212565i	−0.0431842	+	0.00939415i
$513$	1.07938	+	2.89394i	0.0476559	+	0.127770i
$514$	19.6410	+	17.0190i	0.866325	+	0.750675i
$515$	−34.0139	+	26.0173i	−1.49883	+	1.14646i
$516$	−4.57888	+	2.09110i	−0.201574	+	0.0920558i
$517$	0.650729	+	1.19172i	0.0286190	+	0.0524119i
$518$	−1.97797	−	3.62237i	−0.0869069	−	0.159158i
$519$	−12.6542	+	5.77898i	−0.555458	+	0.253669i
$520$	−0.573218	+	4.30320i	−0.0251373	+	0.188708i
$521$	4.91330	+	4.25740i	0.215256	+	0.186520i	0.755814	−	0.654786i	$-0.227241\pi$
$521$	4.91330	+	4.25740i	0.215256	+	0.186520i	−0.540558	+	0.841307i	$0.681787\pi$
$522$	2.34881	+	6.29739i	0.102804	+	0.275629i
$523$	−3.44104	+	0.748553i	−0.150466	+	0.0327319i	−0.287167	−	0.957880i	$-0.592714\pi$
$523$	−3.44104	+	0.748553i	−0.150466	+	0.0327319i	0.136701	+	0.990612i	$0.456350\pi$
$524$	−9.09661	+	1.30790i	−0.397387	+	0.0571357i
$525$	−1.11005	−	1.65094i	−0.0484463	−	0.0720528i
$526$	18.0058	−	15.6021i	0.785090	−	0.680284i
$527$	0.0935588	+	0.0510870i	0.00407549	+	0.00222538i
$528$	−0.0942160	+	0.0942160i	−0.00410023	+	0.00410023i
$529$	19.6501	+	11.9529i	0.854354	+	0.519692i
$530$	−3.05087	+	0.0316446i	−0.132521	+	0.00137455i
$531$	5.39530	−	1.58420i	0.234136	−	0.0687485i
$532$	0.382896	+	0.0273852i	0.0166006	+	0.00118730i
$533$	−8.98039	−	1.95356i	−0.388984	−	0.0846182i
$534$	0.0644759	+	0.448440i	0.00279014	+	0.0194059i
$535$	22.7030	−	5.18592i	0.981536	−	0.224207i
$536$	−0.485399	−	0.221675i	−0.0209661	−	0.00957488i
$537$	0.327073	+	4.57307i	0.0141142	+	0.197343i
$538$	−13.7012	+	10.2566i	−0.590700	+	0.442192i
$539$	0.484342	+	1.06056i	0.0208621	+	0.0456816i
$540$	8.11933	−	4.54344i	0.349400	−	0.195519i
$541$	−11.8212	−	3.47101i	−0.508232	−	0.149231i	0.0175560	−	0.999846i	$-0.494411\pi$
$541$	−11.8212	−	3.47101i	−0.508232	−	0.149231i	−0.525788	+	0.850615i	$0.676230\pi$
$542$	−14.9715	−	5.58408i	−0.643081	−	0.239857i
$543$	−4.19894	−	5.60913i	−0.180194	−	0.240711i
$544$	0.0244533	−	0.0282207i	0.00104843	−	0.00120995i
$545$	−29.8954	−	13.2798i	−1.28058	−	0.568842i
$546$	−0.417630	+	0.649845i	−0.0178729	+	0.0278108i
$547$	5.44291	+	4.07451i	0.232722	+	0.174214i	0.709274	−	0.704933i	$-0.249023\pi$
$547$	5.44291	+	4.07451i	0.232722	+	0.174214i	−0.476552	+	0.879146i	$0.658114\pi$
$548$	1.83296	−	8.42597i	0.0783001	−	0.359940i
$549$	13.1355	+	15.1592i	0.560611	+	0.646980i
$550$	−0.768411	−	0.399120i	−0.0327651	−	0.0170186i
$551$			2.07189i			0.0882653i
$552$	−0.995748	+	3.55301i	−0.0423818	+	0.151226i
$553$	−0.494406	−	0.494406i	−0.0210243	−	0.0210243i
$554$	2.46016	+	8.37853i	0.104522	+	0.355970i
$555$	−9.09874	−	10.2830i	−0.386220	−	0.436491i
$556$	2.20792	−	1.41894i	0.0936365	−	0.0601766i
$557$	17.9930	−	24.0359i	0.762389	−	1.01843i	−0.236515	−	0.971628i	$-0.576005\pi$
$557$	17.9930	−	24.0359i	0.762389	−	1.01843i	0.998904	−	0.0468044i	$-0.0149037\pi$
$558$	1.46121	+	6.71709i	0.0618581	+	0.284357i
$559$	−5.27656	+	11.5541i	−0.223175	+	0.488685i
$560$	−0.0944518	−	1.15249i	−0.00399132	−	0.0487016i
$561$	0.000708075	−	0.00492477i	2.98949e−5	−	0.000207924i
$562$	−6.18231	+	16.5754i	−0.260785	+	0.699191i
$563$	10.6520	−	5.81643i	0.448928	−	0.245133i	−0.238847	−	0.971057i	$-0.576769\pi$
$563$	10.6520	−	5.81643i	0.448928	−	0.245133i	0.687775	+	0.725924i	$0.258588\pi$
$564$	−1.69957	+	5.78819i	−0.0715647	+	0.243727i
$565$	10.6340	−	29.4400i	0.447378	−	1.23855i
$566$	6.32409	+	0.909267i	0.265821	+	0.0382193i
$567$	−2.07498	+	0.148405i	−0.0871408	+	0.00623243i
$568$	−12.7551	+	4.75742i	−0.535194	+	0.199617i
$569$	5.81031	+	3.73406i	0.243581	+	0.156540i	0.656736	−	0.754121i	$-0.271937\pi$
$569$	5.81031	+	3.73406i	0.243581	+	0.156540i	−0.413155	+	0.910661i	$0.635573\pi$
$570$	1.26213	−	0.194849i	0.0528648	−	0.00816131i
$571$	10.1711	+	15.8265i	0.425646	+	0.662319i	0.986154	−	0.165830i	$-0.0530305\pi$
$571$	10.1711	+	15.8265i	0.425646	+	0.662319i	−0.560508	+	0.828149i	$0.689394\pi$
$572$	−0.0239852	+	0.335357i	−0.00100287	+	0.0140220i
$573$	8.30684	−	15.2128i	0.347023	−	0.635525i
$574$	2.44802			0.102178
$575$	−23.9660	+	0.793520i	−0.999452	+	0.0330921i
$576$	2.40803			0.100334
$577$	1.16180	−	2.12767i	0.0483662	−	0.0885760i	−0.852378	−	0.522926i	$-0.824840\pi$
$577$	1.16180	−	2.12767i	0.0483662	−	0.0885760i	0.900744	+	0.434350i	$0.143022\pi$
$578$	1.21267	−	16.9553i	0.0504403	−	0.705247i
$579$	6.53203	+	10.1640i	0.271462	+	0.422403i
$580$	6.16813	−	0.952241i	0.256118	−	0.0395397i
$581$	4.74039	+	3.04646i	0.196664	+	0.126389i
$582$	4.44927	−	1.65949i	0.184428	−	0.0687882i
$583$	−0.235691	+	0.0168570i	−0.00976133	+	0.000698144i
$584$	3.79999	+	0.546356i	0.157245	+	0.0226084i
$585$	3.55143	−	9.83201i	0.146834	−	0.406504i
$586$	−0.182737	+	0.622345i	−0.00754879	+	0.0257088i
$587$	−26.6977	+	14.5781i	−1.10193	+	0.601701i	−0.924020	−	0.382345i	$-0.875117\pi$
$587$	−26.6977	+	14.5781i	−1.10193	+	0.601701i	−0.177914	+	0.984046i	$0.556935\pi$
$588$	−1.81023	+	4.85342i	−0.0746527	+	0.200152i
$589$	−0.301573	+	2.09749i	−0.0124261	+	0.0864255i
$590$	−0.426497	−	5.20407i	−0.0175586	−	0.214248i
$591$	−1.78807	+	3.91533i	−0.0735514	+	0.161055i
$592$	−1.69646	−	7.79851i	−0.0697242	−	0.320517i
$593$	−12.4393	+	16.6169i	−0.510819	+	0.682374i	−0.979604	−	0.200938i	$-0.935601\pi$
$593$	−12.4393	+	16.6169i	−0.510819	+	0.682374i	0.468785	+	0.883312i	$0.344692\pi$
$594$	0.606185	−	0.389572i	0.0248721	−	0.0159843i
$595$	0.0286137	+	0.0323380i	0.00117305	+	0.00132573i
$596$	1.96708	+	6.69926i	0.0805748	+	0.274413i
$597$	−1.16524	−	1.16524i	−0.0476902	−	0.0476902i
$598$	3.97221	+	8.42103i	0.162436	+	0.344362i
$599$			19.1370i			0.781918i	0.920408	+	0.390959i	$0.127857\pi$
$599$			19.1370i			0.781918i	−0.920408	+	0.390959i	$0.872143\pi$
$600$	−1.16015	−	3.66788i	−0.0473630	−	0.149741i
$601$	18.9846	+	21.9093i	0.774396	+	0.893701i	0.996691	−	0.0812787i	$-0.0259004\pi$
$601$	18.9846	+	21.9093i	0.774396	+	0.893701i	−0.222295	+	0.974979i	$0.571355\pi$
$602$	0.719186	−	3.30604i	0.0293118	−	0.134744i
$603$	1.02868	+	0.770057i	0.0418909	+	0.0313592i
$604$	11.4498	−	17.8163i	0.465887	−	0.724935i
$605$	22.4175	+	9.95803i	0.911400	+	0.404851i
$606$	8.63010	−	9.95966i	0.350574	−	0.404584i
$607$	−5.56479	−	7.43369i	−0.225868	−	0.301724i	0.673264	−	0.739402i	$-0.264892\pi$
$607$	−5.56479	−	7.43369i	−0.225868	−	0.301724i	−0.899132	+	0.437678i	$0.855801\pi$
$608$	0.695503	+	0.259409i	0.0282064	+	0.0105204i
$609$	1.06557	+	0.312879i	0.0431790	+	0.0126785i
$610$	16.2543	−	9.09563i	0.658117	−	0.368271i
$611$	6.32352	+	13.8466i	0.255822	+	0.560172i
$612$	−0.0719837	+	0.0538864i	−0.00290977	+	0.00217823i
$613$	0.520083	+	7.27171i	0.0210060	+	0.293702i	0.997086	+	0.0762890i	$0.0243072\pi$
$613$	0.520083	+	7.27171i	0.0210060	+	0.293702i	−0.976080	+	0.217413i	$0.930238\pi$
$614$	−16.6922	−	7.62309i	−0.673644	−	0.307643i
$615$	7.93963	−	1.81361i	0.320157	−	0.0731316i
$616$	−0.0127451	−	0.0886444i	−0.000513517	−	0.00357159i
$617$	−6.42199	−	1.39702i	−0.258539	−	0.0562418i	0.0814273	−	0.996679i	$-0.474052\pi$
$617$	−6.42199	−	1.39702i	−0.258539	−	0.0562418i	−0.339967	+	0.940437i	$0.610416\pi$
$618$	−14.6974	−	1.05118i	−0.591215	−	0.0422845i
$619$	−36.1629	+	10.6184i	−1.45351	+	0.426790i	−0.910701	−	0.413066i	$-0.864458\pi$
$619$	−36.1629	+	10.6184i	−1.45351	+	0.426790i	−0.542810	+	0.839855i	$0.682640\pi$
$620$	6.38295	−	0.0662060i	0.256345	−	0.00265890i
$621$	9.34636	−	17.6310i	0.375056	−	0.707506i
$622$	9.97160	−	9.97160i	0.399825	−	0.399825i
$623$	−0.267262	−	0.145936i	−0.0107076	−	0.00584681i
$624$	−1.12890	+	0.978196i	−0.0451921	+	0.0391592i
$625$	20.4527	−	14.3767i	0.818106	−	0.575067i
$626$	27.8597	−	4.00562i	1.11350	−	0.160097i
$627$	0.0966457	−	0.0210240i	0.00385966	−	0.000839617i
$628$	3.32370	+	8.91117i	0.132630	+	0.355594i
$629$	0.225226	+	0.195160i	0.00898036	+	0.00778153i
$630$	−0.367672	+	2.76015i	−0.0146484	+	0.109967i
$631$	1.54908	−	0.707443i	0.0616681	−	0.0281629i	−0.384342	−	0.923191i	$-0.625572\pi$
$631$	1.54908	−	0.707443i	0.0616681	−	0.0281629i	0.446010	+	0.895028i	$0.352844\pi$
$632$	−0.647969	−	1.18667i	−0.0257748	−	0.0472031i
$633$	−3.69416	−	6.76534i	−0.146830	−	0.268898i
$634$	−4.76080	+	2.17419i	−0.189076	+	0.0863479i
$635$	17.6394	−	13.4924i	0.699997	−	0.535429i
$636$	−0.793398	−	0.687483i	−0.0314603	−	0.0272605i
$637$	4.56783	+	12.2468i	0.180984	+	0.485237i
$638$	0.472315	−	0.102746i	0.0186991	−	0.00406775i
$639$	32.4479	−	4.66531i	1.28362	−	0.184557i
$640$	0.452623	−	2.18978i	0.0178915	−	0.0865586i
$641$	−1.88752	+	1.63555i	−0.0745526	+	0.0646002i	−0.691340	−	0.722530i	$-0.742979\pi$
$641$	−1.88752	+	1.63555i	−0.0745526	+	0.0646002i	0.616787	+	0.787130i	$0.288434\pi$
$642$	7.03281	+	3.84021i	0.277563	+	0.151561i
$643$	0.315723	−	0.315723i	0.0124509	−	0.0124509i	−0.700854	−	0.713305i	$-0.747198\pi$
$643$	0.315723	−	0.315723i	0.0124509	−	0.0124509i	0.713305	+	0.700854i	$0.247198\pi$
$644$	−1.51068	−	1.96691i	−0.0595293	−	0.0775072i
$645$	−0.116743	−	11.2553i	−0.00459675	−	0.443175i
$646$	−0.0265959	+	0.00780925i	−0.00104640	+	0.000307251i
$647$	16.5377	+	1.18280i	0.650164	+	0.0465006i	0.392526	−	0.919741i	$-0.371601\pi$
$647$	16.5377	+	1.18280i	0.650164	+	0.0465006i	0.257638	+	0.966242i	$0.417056\pi$
$648$	−3.93075	−	0.855082i	−0.154414	−	0.0335908i
$649$	−0.0575508	−	0.400274i	−0.00225907	−	0.0157121i
$650$	−8.27336	−	5.07762i	−0.324508	−	0.199161i
$651$	1.03319	+	0.471844i	0.0404941	+	0.0184930i
$652$	−0.402626	−	5.62945i	−0.0157681	−	0.220466i
$653$	−16.4318	+	12.3007i	−0.643026	+	0.481364i	−0.870336	−	0.492459i	$-0.836098\pi$
$653$	−16.4318	+	12.3007i	−0.643026	+	0.481364i	0.227309	+	0.973823i	$0.427007\pi$
$654$	−4.67581	−	10.2386i	−0.182839	−	0.400361i
$655$	5.58473	−	19.7764i	0.218214	−	0.772727i
$656$	4.54204	+	1.33366i	0.177337	+	0.0520708i
$657$	−8.66170	−	3.23065i	−0.337925	−	0.126040i
$658$	−2.42988	−	3.24593i	−0.0947264	−	0.126540i
$659$	2.34169	−	2.70245i	0.0912192	−	0.105273i	−0.708305	−	0.705907i	$-0.750540\pi$
$659$	2.34169	−	2.70245i	0.0912192	−	0.105273i	0.799524	+	0.600634i	$0.205085\pi$
$660$	−0.107008	−	0.278057i	−0.00416528	−	0.0108234i
$661$	9.84225	−	15.3148i	0.382819	−	0.595678i	−0.595356	−	0.803462i	$-0.702989\pi$
$661$	9.84225	−	15.3148i	0.382819	−	0.595678i	0.978175	+	0.207784i	$0.0666252\pi$
$662$	−16.0275	−	11.9981i	−0.622928	−	0.466318i
$663$	0.0118566	−	0.0545037i	0.000460470	−	0.00211675i
$664$	7.13559	+	8.23492i	0.276915	+	0.319577i
$665$	−0.403536	+	0.757598i	−0.0156485	+	0.0293784i
$666$			19.2182i			0.744691i
$667$	10.0073	−	8.89020i	0.387485	−	0.344230i
$668$	−0.737828	−	0.737828i	−0.0285474	−	0.0285474i
$669$	3.08818	+	10.5174i	0.119396	+	0.406625i
$670$	0.893619	−	0.790700i	0.0345235	−	0.0305474i
$671$	1.21354	−	0.779893i	0.0468481	−	0.0301074i
$672$	0.238443	−	0.318523i	0.00919814	−	0.0122873i
$673$	−2.04272	−	9.39022i	−0.0787410	−	0.361966i	0.920870	−	0.389871i	$-0.127480\pi$
$673$	−2.04272	−	9.39022i	−0.0787410	−	0.361966i	−0.999611	+	0.0279043i	$0.991117\pi$
$674$	13.1076	−	28.7016i	0.504885	−	1.10554i
$675$	1.91430	+	20.7164i	0.0736816	+	0.797373i
$676$	1.31368	−	9.13682i	0.0505260	−	0.351416i
$677$	−12.9631	+	34.7554i	−0.498212	+	1.33576i	0.408018	+	0.912974i	$0.366220\pi$
$677$	−12.9631	+	34.7554i	−0.498212	+	1.33576i	−0.906230	+	0.422785i	$0.861053\pi$
$678$	9.45299	−	5.16172i	0.363040	−	0.198235i
$679$	−0.899217	+	3.06245i	−0.0345088	+	0.117526i
$680$	0.0354721	+	0.0755883i	0.00136029	+	0.00289868i
$681$	−5.22647	−	0.751453i	−0.200279	−	0.0287957i
$682$	0.493106	−	0.0352677i	0.0188820	−	0.00135047i
$683$	15.3842	−	5.73801i	0.588660	−	0.219559i	−0.0374433	−	0.999299i	$-0.511921\pi$
$683$	15.3842	−	5.73801i	0.588660	−	0.219559i	0.626104	+	0.779740i	$0.284649\pi$
$684$	−1.50373	−	0.966391i	−0.0574967	−	0.0369509i
$685$	15.5548	+	11.3944i	0.594319	+	0.435356i
$686$	−3.83943	−	5.97426i	−0.146590	−	0.228098i
$687$	1.06928	−	14.9505i	0.0407956	−	0.570398i
$688$	3.13548	−	5.74220i	0.119539	−	0.218919i
$689$	−2.64904			−0.100920
$690$	−6.35676	−	5.26008i	−0.241998	−	0.200248i
$691$	−0.841551			−0.0320141			−0.0160071	−	0.999872i	$-0.505095\pi$
$691$	−0.841551			−0.0320141			−0.0160071	+	0.999872i	$0.505095\pi$
$692$	8.66522	−	15.8692i	0.329402	−	0.603255i
$693$	−0.0153845	+	0.215104i	−0.000584410	+	0.00817112i
$694$	−16.9201	−	26.3283i	−0.642280	−	0.999407i
$695$	0.895405	+	5.79998i	0.0339647	+	0.220006i
$696$	1.80660	+	1.16103i	0.0684788	+	0.0440087i
$697$	−0.165621	+	0.0617733i	−0.00627333	+	0.00233983i
$698$	−18.5762	+	1.32860i	−0.703120	+	0.0502881i
$699$	14.2171	+	2.04410i	0.537739	+	0.0773151i
$700$	2.44088	+	0.853158i	0.0922566	+	0.0322464i
$701$	4.79228	−	16.3210i	0.181002	−	0.616436i	−0.818140	−	0.575019i	$-0.804995\pi$
$701$	4.79228	−	16.3210i	0.181002	−	0.616436i	0.999142	−	0.0414167i	$-0.0131871\pi$
$702$	7.09009	−	3.87148i	0.267598	−	0.146120i
$703$	−2.07032	+	5.55074i	−0.0780836	+	0.209350i
$704$	0.0246456	−	0.171414i	0.000928865	−	0.00646040i
$705$	−10.2855	−	8.72734i	−0.387375	−	0.328691i
$706$	1.96932	−	4.31222i	0.0741164	−	0.162292i
$707$	1.88284	+	8.65529i	0.0708116	+	0.325516i
$708$	1.07669	−	1.43829i	0.0404645	−	0.0540543i
$709$	21.9678	−	14.1178i	0.825018	−	0.530207i	−0.0586735	−	0.998277i	$-0.518687\pi$
$709$	21.9678	−	14.1178i	0.825018	−	0.530207i	0.883691	+	0.468071i	$0.155051\pi$
$710$	1.85658	−	30.3840i	0.0696761	−	1.14029i
$711$	0.917258	+	3.12390i	0.0343999	+	0.117155i
$712$	−0.416372	−	0.416372i	−0.0156042	−	0.0156042i
$713$	11.4250	−	7.54344i	0.427869	−	0.282504i
$714$			0.0148575i			0.000556028i
$715$	−0.663537	−	0.353434i	−0.0248149	−	0.0132177i
$716$	−3.90224	−	4.50343i	−0.145834	−	0.168301i
$717$	−3.03611	+	13.9568i	−0.113386	+	0.521225i
$718$	−28.9296	−	21.6565i	−1.07964	−	0.808212i
$719$	15.7487	−	24.5055i	0.587328	−	0.913901i	−0.412667	−	0.910882i	$-0.635403\pi$
$719$	15.7487	−	24.5055i	0.587328	−	0.913901i	0.999995	−	0.00301898i	$-0.000960974\pi$
$720$	−2.18589	+	4.92086i	−0.0814632	+	0.183390i
$721$	6.48562	−	7.48480i	0.241537	−	0.278749i
$722$	11.0561	+	14.7692i	0.411464	+	0.549652i
$723$	−17.1570	−	6.39923i	−0.638076	−	0.237990i
$724$	8.73782	+	2.56566i	0.324739	+	0.0953518i
$725$	−3.65319	+	13.4691i	−0.135676	+	0.500230i
$726$	3.50623	+	7.67757i	0.130128	+	0.284941i
$727$	−36.8464	+	27.5829i	−1.36656	+	1.02299i	−0.371020	+	0.928625i	$0.620992\pi$
$727$	−36.8464	+	27.5829i	−1.36656	+	1.02299i	−0.995538	+	0.0943667i	$0.969917\pi$
$728$	−0.0716242	−	1.00144i	−0.00265457	−	0.0371158i
$729$	0.0750512	+	0.0342747i	0.00277967	+	0.00126943i
$730$	−4.56593	+	7.26942i	−0.168993	+	0.269053i
$731$	0.0347682	+	0.241818i	0.00128595	+	0.00894397i
$732$	6.26251	+	1.36232i	0.231469	+	0.0503530i
$733$	13.1447	+	0.940124i	0.485509	+	0.0347243i	0.311949	−	0.950099i	$-0.399018\pi$
$733$	13.1447	+	0.940124i	0.485509	+	0.0347243i	0.173560	+	0.984823i	$0.444473\pi$
$734$	−30.4845	+	8.95105i	−1.12520	+	0.330389i
$735$	−8.27484	−	8.10495i	−0.305222	−	0.298955i
$736$	−1.73136	−	4.47241i	−0.0638186	−	0.164855i
$737$	0.0653443	−	0.0653443i	0.00240699	−	0.00240699i
$738$	−10.0047	−	5.46301i	−0.368280	−	0.201096i
$739$	−21.9426	+	19.0133i	−0.807170	+	0.699417i	−0.957252	−	0.289257i	$-0.906592\pi$
$739$	−21.9426	+	19.0133i	−0.807170	+	0.699417i	0.150081	+	0.988674i	$0.452046\pi$
$740$	17.4764	+	3.61234i	0.642446	+	0.132792i
$741$	1.09753	−	0.157801i	0.0403188	−	0.00579697i
$742$	0.689490	−	0.149989i	0.0253120	−	0.00550628i
$743$	−7.09036	−	19.0100i	−0.260120	−	0.697409i	−0.999704	−	0.0243440i	$-0.992250\pi$
$743$	−7.09036	−	19.0100i	−0.260120	−	0.697409i	0.739584	−	0.673065i	$-0.235022\pi$
$744$	1.65993	+	1.43833i	0.0608558	+	0.0527319i
$745$	−15.4757	−	2.06148i	−0.566987	−	0.0755268i
$746$	−12.2431	+	5.59122i	−0.448251	+	0.204709i
$747$	−12.5749	−	23.0292i	−0.460091	−	0.842593i
$748$	0.00309913	+	0.00567563i	0.000113315	+	0.000207521i
$749$	−4.89907	+	2.23733i	−0.179008	+	0.0817503i
$750$	8.54853	+	0.958722i	0.312148	+	0.0350076i
$751$	16.3234	+	14.1443i	0.595651	+	0.516135i	0.899693	−	0.436524i	$-0.143791\pi$
$751$	16.3234	+	14.1443i	0.595651	+	0.516135i	−0.304041	+	0.952659i	$0.598336\pi$
$752$	−2.74002	−	7.34627i	−0.0999181	−	0.267891i
$753$	12.9869	−	2.82513i	0.473269	−	0.102953i
$754$	5.36372	−	0.771187i	0.195335	−	0.0280850i
$755$	26.0144	+	39.5707i	0.946762	+	1.44013i
$756$	−1.62620	+	1.40911i	−0.0591442	+	0.0512488i
$757$	14.6666	+	8.00854i	0.533065	+	0.291075i	0.723149	−	0.690692i	$-0.242694\pi$
$757$	14.6666	+	8.00854i	0.533065	+	0.291075i	−0.190084	+	0.981768i	$0.560876\pi$
$758$	14.5424	−	14.5424i	0.528202	−	0.528202i
$759$	−0.516241	−	0.376592i	−0.0187384	−	0.0136694i
$760$	−1.16145	+	1.18580i	−0.0421303	+	0.0430134i
$761$	−29.3655	+	8.62248i	−1.06450	+	0.312565i	−0.766661	−	0.642052i	$-0.778083\pi$
$761$	−29.3655	+	8.62248i	−1.06450	+	0.312565i	−0.297837	+	0.954617i	$0.596265\pi$
$762$	7.62194	+	0.545132i	0.276114	+	0.0197481i
$763$	7.39247	+	1.60813i	0.267625	+	0.0582183i
$764$	3.20608	+	22.2987i	0.115992	+	0.806740i
$765$	−0.0447748	−	0.196016i	−0.00161884	−	0.00708697i
$766$	2.15162	+	0.982614i	0.0777413	+	0.0355033i
$767$	−0.323420	−	4.52200i	−0.0116780	−	0.163280i
$768$	0.615934	−	0.461083i	0.0222256	−	0.0166379i
$769$	−16.3318	−	35.7616i	−0.588939	−	1.28960i	−0.936081	−	0.351784i	$-0.885575\pi$
$769$	−16.3318	−	35.7616i	−0.588939	−	1.28960i	0.347142	−	0.937812i	$-0.387152\pi$
$770$	0.192716	+	0.0544220i	0.00694502	+	0.00196123i
$771$	−19.1857	−	5.63343i	−0.690956	−	0.202883i
$772$	−14.7131	−	5.48771i	−0.529537	−	0.197507i
$773$	31.3660	+	41.9001i	1.12816	+	1.50704i	0.834398	+	0.551162i	$0.185815\pi$
$773$	31.3660	+	41.9001i	1.12816	+	1.50704i	0.293759	+	0.955879i	$0.405094\pi$
$774$	−10.3170	+	11.9064i	−0.370837	+	0.427968i
$775$	−5.65883	+	13.1038i	−0.203271	+	0.470703i
$776$	−3.33680	+	5.19217i	−0.119784	+	0.186388i
$777$	2.54210	+	1.90299i	0.0911972	+	0.0682694i
$778$	−7.95050	+	36.5478i	−0.285039	+	1.31030i
$779$	−2.30113	−	2.65564i	−0.0824465	−	0.0951483i
$780$	−0.974209	−	3.19489i	−0.0348823	−	0.114395i
$781$		−	2.35753i		−	0.0843592i
$782$	0.151838	+	0.0949508i	0.00542973	+	0.00339543i
$783$	−8.21217	−	8.21217i	−0.293479	−	0.293479i
$784$	−1.89678	−	6.45985i	−0.0677423	−	0.230709i
$785$	−21.2273	−	1.29707i	−0.757634	−	0.0462943i
$786$	5.94840	−	3.82281i	0.212173	−	0.136355i
$787$	7.53106	−	10.0603i	0.268453	−	0.358611i	−0.645976	−	0.763358i	$-0.723549\pi$
$787$	7.53106	−	10.0603i	0.268453	−	0.358611i	0.914429	+	0.404746i	$0.132640\pi$
$788$	−1.18917	−	5.46653i	−0.0423624	−	0.194737i
$789$	−7.61495	+	16.6744i	−0.271100	+	0.593625i
$790$	3.01318	−	0.246943i	0.107204	−	0.00878586i
$791$	−1.03024	+	7.16548i	−0.0366311	+	0.254775i
$792$	−0.145731	+	0.390721i	−0.00517834	+	0.0138837i
$793$	14.1938	−	7.75041i	0.504037	−	0.275225i
$794$	1.15298	−	3.92670i	0.0409178	−	0.139353i
$795$	2.12509	−	0.997264i	0.0753693	−	0.0353693i
$796$	2.12001	+	0.304811i	0.0751416	+	0.0108037i
$797$	35.2451	−	2.52078i	1.24845	−	0.0892907i	0.568581	−	0.822627i	$-0.307492\pi$
$797$	35.2451	−	2.52078i	1.24845	−	0.0892907i	0.679866	+	0.733336i	$0.262038\pi$
$798$	−0.276730	+	0.103215i	−0.00979612	+	0.00365376i
$799$	0.246301	+	0.158288i	0.00871351	+	0.00559983i
$800$	4.06400	+	2.91272i	0.143684	+	0.102980i
$801$	0.766596	+	1.19285i	0.0270863	+	0.0421472i
$802$	0.0837684	−	1.17123i	0.00295796	−	0.0413577i
$803$	−0.318622	+	0.583512i	−0.0112439	+	0.0205917i
$804$	0.410567			0.0144796
$805$	5.39076	−	1.30166i	0.189999	−	0.0458773i
$806$	5.54225			0.195217
$807$	6.31082	−	11.5574i	0.222152	−	0.406840i
$808$	−1.22192	+	17.0847i	−0.0429871	+	0.601039i
$809$	−15.6813	−	24.4006i	−0.551326	−	0.857881i	0.448020	−	0.894023i	$-0.352129\pi$
$809$	−15.6813	−	24.4006i	−0.551326	−	0.857881i	−0.999347	+	0.0361428i	$0.988493\pi$
$810$	5.31552	−	7.25638i	0.186768	−	0.254963i
$811$	−40.0512	−	25.7393i	−1.40639	−	0.903830i	−0.406436	−	0.913679i	$-0.633228\pi$
$811$	−40.0512	−	25.7393i	−1.40639	−	0.903830i	−0.999951	+	0.00984935i	$0.996865\pi$
$812$	−1.35240	+	0.504419i	−0.0474599	+	0.0177016i
$813$	12.2629	−	0.877058i	0.430078	−	0.0307598i
$814$	1.36804	+	0.196694i	0.0479497	+	0.00689412i
$815$	11.8694	+	4.28736i	0.415767	+	0.150180i
$816$	−0.00809426	+	0.0275665i	−0.000283356	+	0.000965021i
$817$	−4.26247	+	2.32748i	−0.149125	+	0.0814284i
$818$	5.70269	−	15.2895i	0.199390	−	0.534585i
$819$	−0.344067	+	2.39304i	−0.0120227	+	0.0836196i
$820$	−6.84841	+	8.07113i	−0.239157	+	0.281856i
$821$	14.5894	−	31.9463i	0.509174	−	1.11494i	−0.464204	−	0.885728i	$-0.653660\pi$
$821$	14.5894	−	31.9463i	0.509174	−	1.11494i	0.973378	−	0.229207i	$-0.0736132\pi$
$822$	1.41027	+	6.48292i	0.0491889	+	0.226118i
$823$	−22.5238	+	30.0883i	−0.785132	+	1.04881i	0.212301	+	0.977204i	$0.431904\pi$
$823$	−22.5238	+	30.0883i	−0.785132	+	1.04881i	−0.997433	+	0.0716087i	$0.977187\pi$
$824$	16.1110	−	10.3539i	0.561255	−	0.360696i
$825$	0.665353	+	0.0337330i	0.0231646	+	0.00117443i
$826$	0.340216	+	1.15867i	0.0118376	+	0.0403153i
$827$	14.6325	+	14.6325i	0.508823	+	0.508823i	0.914165	−	0.405342i	$-0.132848\pi$
$827$	14.6325	+	14.6325i	0.508823	+	0.508823i	−0.405342	+	0.914165i	$0.632848\pi$
$828$	1.78461	+	11.4098i	0.0620196	+	0.396517i
$829$			2.12753i			0.0738923i	0.999317	+	0.0369461i	$0.0117630\pi$
$829$			2.12753i			0.0738923i	−0.999317	+	0.0369461i	$0.988237\pi$
$830$	−23.3056	+	7.10651i	−0.808949	+	0.246671i
$831$	−4.39973	−	5.07756i	−0.152625	−	0.176138i
$832$	0.412685	−	1.89708i	0.0143073	−	0.0657695i
$833$	0.201258	+	0.150660i	0.00697319	+	0.00522006i
$834$	−1.09173	+	1.69877i	−0.0378035	+	0.0588235i
$835$	2.17753	−	0.838005i	0.0753566	−	0.0290004i
$836$	−0.0841823	+	0.0971515i	−0.00291150	+	0.00336006i
$837$	−7.11832	−	9.50896i	−0.246045	−	0.328678i
$838$	7.13404	+	2.66086i	0.246441	+	0.0919178i
$839$	39.5914	+	11.6251i	1.36685	+	0.401343i	0.881172	−	0.472796i	$-0.156755\pi$
$839$	39.5914	+	11.6251i	1.36685	+	0.401343i	0.485676	+	0.874139i	$0.338573\pi$
$840$	0.434462	+	0.776403i	0.0149904	+	0.0267884i
$841$	8.81074	+	19.2928i	0.303819	+	0.665270i
$842$	−12.1108	+	9.06607i	−0.417367	+	0.312437i
$843$	−0.971017	−	13.5766i	−0.0334436	−	0.467603i
$844$	9.11316	+	4.16184i	0.313688	+	0.143257i
$845$	17.4788	+	10.9785i	0.601290	+	0.377671i
$846$	2.68696	+	18.6882i	0.0923797	+	0.642515i
$847$	−5.54335	−	1.20588i	−0.190472	−	0.0414346i
$848$	1.36099	+	0.0973398i	0.0467365	+	0.00334266i
$849$	−4.71665	+	1.38493i	−0.161875	+	0.0475308i
$850$	−0.186666	+	0.00387274i	−0.00640260	+	0.000132834i
$851$	35.6938	−	13.8178i	1.22357	−	0.473667i
$852$	7.40636	−	7.40636i	0.253738	−	0.253738i
$853$	−47.6898	−	26.0406i	−1.63287	−	0.891613i	−0.992320	−	0.123694i	$-0.960526\pi$
$853$	−47.6898	−	26.0406i	−1.63287	−	0.891613i	−0.640547	−	0.767919i	$-0.721292\pi$
$854$	−3.25553	+	2.82093i	−0.111402	+	0.0965302i
$855$	3.33986	−	2.19568i	0.114221	−	0.0750905i
$856$	−10.3086	+	1.48215i	−0.352340	+	0.0506589i
$857$	−44.6105	+	9.70442i	−1.52386	+	0.331497i	−0.895017	−	0.446032i	$-0.852837\pi$
$857$	−44.6105	+	9.70442i	−1.52386	+	0.331497i	−0.628848	+	0.777528i	$0.716473\pi$
$858$	−0.0904000	−	0.242372i	−0.00308621	−	0.00827444i
$859$	−23.7470	−	20.5769i	−0.810236	−	0.702073i	0.147707	−	0.989031i	$-0.452811\pi$
$859$	−23.7470	−	20.5769i	−0.810236	−	0.702073i	−0.957943	+	0.286958i	$0.907356\pi$
$860$	8.88810	+	11.6199i	0.303082	+	0.396236i
$861$	−1.71329	+	0.782434i	−0.0583888	+	0.0266653i
$862$	−10.4387	−	19.1171i	−0.355545	−	0.651132i
$863$	7.77807	+	14.2445i	0.264769	+	0.484888i	0.975913	−	0.218158i	$-0.0700048\pi$
$863$	7.77807	+	14.2445i	0.264769	+	0.484888i	−0.711145	+	0.703046i	$0.751823\pi$
$864$	−3.78491	+	1.72851i	−0.128765	+	0.0588051i
$865$	24.5632	+	32.1128i	0.835172	+	1.09187i
$866$	−17.9682	−	15.5695i	−0.610584	−	0.529074i
$867$	4.57053	+	12.2541i	0.155223	+	0.416170i
$868$	−1.44253	+	0.313804i	−0.0489627	+	0.0106512i
$869$	0.231760	−	0.0333221i	0.00786193	−	0.00113037i
$870$	−4.01253	+	2.63790i	−0.136037	+	0.0894331i
$871$	0.782956	−	0.678436i	0.0265295	−	0.0229879i
$872$	12.8398	+	7.01108i	0.434812	+	0.237425i
$873$	10.5092	−	10.5092i	0.355681	−	0.355681i
$874$	−0.713695	+	3.48770i	−0.0241411	+	0.117973i
$875$	−3.95916	+	4.21354i	−0.133844	+	0.142444i
$876$	−2.83412	+	0.832173i	−0.0957560	+	0.0281165i
$877$	18.8679	+	1.34946i	0.637122	+	0.0455679i	0.386164	−	0.922430i	$-0.373800\pi$
$877$	18.8679	+	1.34946i	0.637122	+	0.0455679i	0.250958	+	0.967998i	$0.419254\pi$
$878$	39.0460	+	8.49395i	1.31774	+	0.286657i
$879$	−0.0710216	−	0.493966i	−0.00239550	−	0.0166611i
$880$	0.327916	+	0.205965i	0.0110540	+	0.00694307i
$881$	−21.2059	−	9.68439i	−0.714443	−	0.326275i	0.0248199	−	0.999692i	$-0.492099\pi$
$881$	−21.2059	−	9.68439i	−0.714443	−	0.326275i	−0.739263	+	0.673417i	$0.764826\pi$
$882$	1.15657	+	16.1709i	0.0389436	+	0.544503i
$883$	−22.7313	+	17.0164i	−0.764969	+	0.572649i	−0.908937	−	0.416933i	$-0.863105\pi$
$883$	−22.7313	+	17.0164i	−0.764969	+	0.572649i	0.143968	+	0.989582i	$0.454014\pi$
$884$	0.0301160	+	0.0659449i	0.00101291	+	0.00221797i
$885$	1.96181	+	3.50585i	0.0659457	+	0.117848i
$886$	−26.1650	−	7.68273i	−0.879029	−	0.258106i
$887$	31.4915	+	11.7457i	1.05738	+	0.394383i	0.817205	−	0.576346i	$-0.195522\pi$
$887$	31.4915	+	11.7457i	1.05738	+	0.394383i	0.240176	+	0.970729i	$0.422795\pi$
$888$	3.67986	+	4.91571i	0.123488	+	0.164961i
$889$	−3.36339	+	3.88156i	−0.112805	+	0.130183i
$890$	1.22883	−	0.472904i	0.0411904	−	0.0158518i
$891$	0.376628	−	0.586045i	0.0126175	−	0.0196333i
$892$	−11.4051	−	8.53773i	−0.381870	−	0.285864i
$893$	−1.23716	+	5.68713i	−0.0413999	+	0.190312i
$894$	−3.51791	−	4.05989i	−0.117657	−	0.135783i
$895$	12.7451	−	3.88634i	0.426022	−	0.129906i
$896$			0.517137i			0.0172763i
$897$	−5.47155	−	4.62402i	−0.182690	−	0.154392i
$898$	12.6040	+	12.6040i	0.420602	+	0.420602i
$899$	−2.24481	−	7.64513i	−0.0748687	−	0.254979i
$900$	−8.07166	−	8.93382i	−0.269055	−	0.297794i
$901$	−0.0428626	+	0.0275461i	−0.00142796	+	0.000917694i
$902$	−0.491277	+	0.656269i	−0.0163577	+	0.0218514i
$903$	0.553340	+	2.54366i	0.0184140	+	0.0846477i
$904$	−5.81520	+	12.7335i	−0.193411	+	0.423511i
$905$	−13.1747	+	15.5270i	−0.437943	+	0.516134i
$906$	−2.31895	+	16.1286i	−0.0770419	+	0.535839i
$907$	−6.54757	+	17.5547i	−0.217408	+	0.582894i	−0.999172	−	0.0406802i	$-0.987048\pi$
$907$	−6.54757	+	17.5547i	−0.217408	+	0.582894i	0.781764	+	0.623575i	$0.214320\pi$
$908$	6.02333	−	3.28899i	0.199891	−	0.109149i
$909$	11.6202	−	39.5748i	0.385418	−	1.31261i
$910$	2.11148	+	0.762689i	0.0699948	+	0.0252829i
$911$	−58.7134	−	8.44171i	−1.94526	−	0.279686i	−0.946222	−	0.323518i	$-0.895134\pi$
$911$	−58.7134	−	8.44171i	−1.94526	−	0.279686i	−0.999039	+	0.0438320i	$0.986043\pi$
$912$	−0.569673	+	0.0407438i	−0.0188638	+	0.00134916i
$913$	−1.76802	+	0.659436i	−0.0585128	+	0.0218242i
$914$	17.2444	+	11.0823i	0.570394	+	0.366570i
$915$	−8.46873	+	11.5609i	−0.279968	+	0.382193i
$916$	10.5323	+	16.3885i	0.347996	+	0.541492i
$917$	−0.339044	+	4.74046i	−0.0111962	+	0.156544i
$918$	0.0744629	−	0.136369i	0.00245764	−	0.00450084i
$919$	−47.5393			−1.56818			−0.784088	−	0.620649i	$-0.786869\pi$
$919$	−47.5393			−1.56818			−0.784088	+	0.620649i	$0.786869\pi$
$920$	10.7111	+	0.521761i	0.353135	+	0.0172019i
$921$	14.1189			0.465232
$922$	−15.0230	+	27.5125i	−0.494755	+	0.906076i
$923$	1.88549	−	26.3625i	0.0620615	−	0.867733i
$924$	0.0372524	+	0.0579659i	0.00122551	+	0.00190694i
$925$	−23.2461	+	32.4344i	−0.764328	+	1.06644i
$926$	−25.1203	−	16.1438i	−0.825503	−	0.530518i
$927$	−43.2090	+	16.1161i	−1.41917	+	0.529323i
$928$	−2.78404	+	0.199118i	−0.0913905	+	0.00653638i
$929$	28.9337	+	4.16004i	0.949285	+	0.136487i	0.599528	−	0.800354i	$-0.295355\pi$
$929$	28.9337	+	4.16004i	0.949285	+	0.136487i	0.349757	+	0.936840i	$0.386264\pi$
$930$	−4.44607	+	2.08645i	−0.145792	+	0.0684174i
$931$	−1.40799	+	4.79519i	−0.0461451	+	0.157156i
$932$	−16.3847	+	8.94671i	−0.536698	+	0.293059i
$933$	−3.79169	+	10.1659i	−0.124134	+	0.332817i
$934$	3.05978	−	21.2813i	0.100119	−	0.696344i
$935$	−0.0144115	+	0.00118109i	−0.000471307	+	3.86257e-5i
$936$	−1.94209	+	4.25259i	−0.0634793	+	0.139000i
$937$	−2.75016	−	12.6423i	−0.0898440	−	0.413006i	0.910155	−	0.414267i	$-0.135962\pi$
$937$	−2.75016	−	12.6423i	−0.0898440	−	0.413006i	−0.999999	+	0.00126130i	$0.999599\pi$
$938$	−0.165374	+	0.220914i	−0.00539965	+	0.00721309i
$939$	−18.2178	+	11.7079i	−0.594517	+	0.382073i
$940$	17.4995	+	1.06929i	0.570771	+	0.0348763i
$941$	3.89502	+	13.2652i	0.126974	+	0.432434i	0.998301	−	0.0582691i	$-0.0185582\pi$
$941$	3.89502	+	13.2652i	0.126974	+	0.432434i	−0.871327	+	0.490703i	$0.836740\pi$
$942$	−5.17433	−	5.17433i	−0.168589	−	0.168589i
$943$	−2.95304	+	22.5096i	−0.0961643	+	0.733013i
$944$			2.33514i			0.0760022i
$945$	−1.40337	−	4.60229i	−0.0456515	−	0.149713i
$946$	0.741960	+	0.856268i	0.0241232	+	0.0278397i
$947$	−5.44697	+	25.0393i	−0.177003	+	0.813668i	0.799926	+	0.600099i	$0.204872\pi$
$947$	−5.44697	+	25.0393i	−0.177003	+	0.813668i	−0.976928	+	0.213568i	$0.931491\pi$
$948$	0.832775	+	0.623408i	0.0270473	+	0.0202473i
$949$	−4.02959	+	6.27016i	−0.130806	+	0.203538i
$950$	−1.36890	−	3.44986i	−0.0444130	−	0.111928i
$951$	2.63702	−	3.04329i	0.0855114	−	0.0986854i
$952$	−0.0115724	−	0.0154589i	−0.000375063	−	0.000501026i
$953$	1.56352	+	0.583162i	0.0506473	+	0.0188905i	0.374660	−	0.927162i	$-0.377759\pi$
$953$	1.56352	+	0.583162i	0.0506473	+	0.0188905i	−0.324013	+	0.946053i	$0.605032\pi$
$954$	−3.15257	−	0.925680i	−0.102068	−	0.0299700i
$955$	−48.4783	−	13.6900i	−1.56872	−	0.442998i
$956$	−7.71181	−	16.8865i	−0.249418	−	0.546149i
$957$	−0.297719	+	0.222870i	−0.00962389	+	0.00720435i
$958$	−0.518880	−	7.25489i	−0.0167642	−	0.234395i
$959$	−4.05631	−	1.85246i	−0.130985	−	0.0598189i
$960$	0.383119	+	1.67722i	0.0123651	+	0.0541322i
$961$	3.25200	+	22.6181i	0.104903	+	0.729617i
$962$	15.1404	+	3.29360i	0.488147	+	0.106190i
$963$	25.0147	+	1.78909i	0.806089	+	0.0576526i
$964$	22.8358	−	6.70519i	0.735491	−	0.215960i
$965$	24.5701	−	25.0851i	0.790939	−	0.807519i
$966$	1.68594	+	0.893736i	0.0542443	+	0.0287555i
$967$	19.8249	−	19.8249i	0.637526	−	0.637526i	−0.312419	−	0.949945i	$-0.601139\pi$
$967$	19.8249	−	19.8249i	0.637526	−	0.637526i	0.949945	+	0.312419i	$0.101139\pi$
$968$	−9.62815	−	5.25737i	−0.309460	−	0.168978i
$969$	0.0161176	−	0.0139660i	0.000517772	−	0.000448652i
$970$	−7.58134	−	11.5320i	−0.243422	−	0.370271i
$971$	7.48161	−	1.07569i	0.240096	−	0.0345206i	−0.0212161	−	0.999775i	$-0.506754\pi$
$971$	7.48161	−	1.07569i	0.240096	−	0.0345206i	0.261312	+	0.965254i	$0.415845\pi$
$972$	15.2218	−	3.31130i	0.488240	−	0.106210i
$973$	−0.474312	−	1.27168i	−0.0152058	−	0.0407682i
$974$	15.4485	+	13.3862i	0.495002	+	0.428921i
$975$	7.41317	+	0.909340i	0.237411	+	0.0291222i
$976$	−7.57710	+	3.46035i	−0.242537	+	0.110763i
$977$	−9.19645	−	16.8420i	−0.294220	−	0.538824i	0.688197	−	0.725524i	$-0.258403\pi$
$977$	−9.19645	−	16.8420i	−0.294220	−	0.538824i	−0.982417	+	0.186700i	$0.940221\pi$
$978$	2.08107	+	3.81119i	0.0665452	+	0.121868i
$979$	0.0927579	−	0.0423611i	0.00296456	−	0.00135387i
$980$	14.9227	+	1.98781i	0.476687	+	0.0634982i
$981$	−26.6234	−	23.0693i	−0.850019	−	0.736546i
$982$	−0.696543	−	1.86751i	−0.0222276	−	0.0595945i
$983$	−32.6835	+	7.10987i	−1.04244	+	0.226769i	−0.701021	−	0.713141i	$-0.747272\pi$
$983$	−32.6835	+	7.10987i	−1.04244	+	0.226769i	−0.341422	+	0.939910i	$0.610908\pi$
$984$	−3.60509	+	0.518334i	−0.114926	+	0.0165239i
$985$	12.2504	+	2.53214i	0.390332	+	0.0806808i
$986$	0.0787681	−	0.0682529i	0.00250849	−	0.00217362i
$987$	2.73806	+	1.49509i	0.0871533	+	0.0475893i
$988$	−1.01905	+	1.01905i	−0.0324202	+	0.0324202i
$989$	29.5316	+	10.6010i	0.939049	+	0.337092i
$990$	−0.666160	−	0.652482i	−0.0211719	−	0.0207373i
$991$	−36.1435	+	10.6127i	−1.14814	+	0.337124i	−0.799812	−	0.600250i	$-0.795068\pi$
$991$	−36.1435	+	10.6127i	−1.14814	+	0.337124i	−0.348325	+	0.937374i	$0.613249\pi$
$992$	−2.84742	−	0.203652i	−0.0904057	−	0.00646595i
$993$	15.0520	+	3.27436i	0.477660	+	0.103909i
$994$	1.00190	+	6.96838i	0.0317784	+	0.221023i
$995$	−2.54732	+	4.05559i	−0.0807556	+	0.128571i
$996$	−7.62602	−	3.48269i	−0.241640	−	0.110353i
$997$	−2.69198	−	37.6388i	−0.0852559	−	1.19203i	−0.842425	−	0.538814i	$-0.818872\pi$
$997$	−2.69198	−	37.6388i	−0.0852559	−	1.19203i	0.757169	−	0.653220i	$-0.226582\pi$
$998$	16.4376	−	12.3050i	0.520323	−	0.389509i
$999$	−13.7951	−	30.2070i	−0.436457	−	0.955707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.83.9	yes	240
5.2	odd	4	inner	230.2.l.a.37.10	✓	240
23.5	odd	22	inner	230.2.l.a.143.10	yes	240
115.97	even	44	inner	230.2.l.a.97.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.37.10	✓	240	5.2	odd	4	inner
230.2.l.a.83.9	yes	240	1.1	even	1	trivial
230.2.l.a.97.9	yes	240	115.97	even	44	inner
230.2.l.a.143.10	yes	240	23.5	odd	22	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.479249 - 0.877679i) q^{2} +(-0.0548882 + 0.767437i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(2.20989 - 0.341164i) q^{5} +(0.647258 + 0.415968i) q^{6} +(-0.484532 + 0.180721i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(2.38352 + 0.342698i) q^{9} +O(q^{10})\)	\(q+(0.479249 - 0.877679i) q^{2} +(-0.0548882 + 0.767437i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(2.20989 - 0.341164i) q^{5} +(0.647258 + 0.415968i) q^{6} +(-0.484532 + 0.180721i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(2.38352 + 0.342698i) q^{9} +(0.759654 - 2.10308i) q^{10} +(0.0487894 - 0.166162i) q^{11} +(0.675284 - 0.368733i) q^{12} +(0.678467 - 1.81904i) q^{13} +(-0.0735963 + 0.511873i) q^{14} +(0.140525 + 1.71468i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-0.00793746 - 0.0364879i) q^{17} +(1.44308 - 1.92773i) q^{18} +(0.624467 - 0.401321i) q^{19} +(-1.48176 - 1.67463i) q^{20} +(-0.112097 - 0.381767i) q^{21} +(-0.122454 - 0.122454i) q^{22} +(-4.61791 - 1.29419i) q^{23} -0.769398i q^{24} +(4.76721 - 1.50787i) q^{25} +(-1.27138 - 1.46725i) q^{26} +(-0.884468 + 4.06583i) q^{27} +(0.413990 + 0.309909i) q^{28} +(-1.50901 + 2.34806i) q^{29} +(1.57228 + 0.698421i) q^{30} +(-1.86943 + 2.15743i) q^{31} +(0.599278 + 0.800541i) q^{32} +(0.124841 + 0.0465631i) q^{33} +(-0.0358287 - 0.0105203i) q^{34} +(-1.00911 + 0.564678i) q^{35} +(-1.00033 - 2.19042i) q^{36} +(-6.38904 + 4.78278i) q^{37} +(-0.0529555 - 0.740414i) q^{38} +(1.35876 + 0.620525i) q^{39} +(-2.17992 + 0.497947i) q^{40} +(-0.673689 - 4.68561i) q^{41} +(-0.388791 - 0.0845763i) q^{42} +(-6.52582 - 0.466736i) q^{43} +(-0.166162 + 0.0487894i) q^{44} +(5.38422 - 0.0558469i) q^{45} +(-3.34901 + 3.43280i) q^{46} +(-5.54415 + 5.54415i) q^{47} +(-0.675284 - 0.368733i) q^{48} +(-5.08814 + 4.40890i) q^{49} +(0.961256 - 4.90673i) q^{50} +(0.0284379 - 0.00408875i) q^{51} +(-1.89708 + 0.412685i) q^{52} +(-0.476831 - 1.27843i) q^{53} +(3.14462 + 2.72483i) q^{54} +(0.0511308 - 0.383844i) q^{55} +(0.470405 - 0.214827i) q^{56} +(0.273713 + 0.501267i) q^{57} +(1.33766 + 2.44973i) q^{58} +(2.12411 - 0.970050i) q^{59} +(1.36650 - 1.04524i) q^{60} +(6.29529 + 5.45490i) q^{61} +(0.997614 + 2.67471i) q^{62} +(-1.21682 + 0.264703i) q^{63} +(0.989821 - 0.142315i) q^{64} +(0.878745 - 4.25135i) q^{65} +(0.100697 - 0.0872547i) q^{66} +(0.468349 + 0.255738i) q^{67} +(-0.0264043 + 0.0264043i) q^{68} +(1.24668 - 3.47292i) q^{69} +(0.0119934 + 1.15629i) q^{70} +(13.0620 - 3.83536i) q^{71} +(-2.40189 - 0.171787i) q^{72} +(-3.75133 - 0.816052i) q^{73} +(1.13580 + 7.89967i) q^{74} +(0.895532 + 3.74130i) q^{75} +(-0.675225 - 0.308365i) q^{76} +(0.00638885 + 0.0893278i) q^{77} +(1.19581 - 0.895169i) q^{78} +(0.561663 + 1.22987i) q^{79} +(-0.607687 + 2.15191i) q^{80} +(3.85973 + 1.13332i) q^{81} +(-4.43532 - 1.65429i) q^{82} +(-6.52994 - 8.72298i) q^{83} +(-0.260559 + 0.300701i) q^{84} +(-0.0299893 - 0.0779263i) q^{85} +(-3.53714 + 5.50389i) q^{86} +(-1.71917 - 1.28695i) q^{87} +(-0.0368113 + 0.169219i) q^{88} +(0.385607 + 0.445015i) q^{89} +(2.53137 - 4.75238i) q^{90} +1.00400i q^{91} +(1.40789 + 4.58452i) q^{92} +(-1.55309 - 1.55309i) q^{93} +(2.20896 + 7.52302i) q^{94} +(1.24309 - 1.09992i) q^{95} +(-0.647258 + 0.415968i) q^{96} +(3.69871 - 4.94090i) q^{97} +(1.43111 + 6.57871i) q^{98} +(0.173234 - 0.379329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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