LMFDB - Embedded newform 230.2.l.a.217.12

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			217.12
Character	$\chi$	$=$	230.217
Dual form			230.2.l.a.53.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713392 - 0.997452i) q^{2} +(2.04831 - 0.445581i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.87827 - 1.21330i) q^{5} +(-0.298322 - 2.07487i) q^{6} +(-0.714388 + 0.390085i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(1.26811 - 0.579129i) q^{9} +O(q^{10})$	\(q+(0.0713392 - 0.997452i) q^{2} +(2.04831 - 0.445581i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.87827 - 1.21330i) q^{5} +(-0.298322 - 2.07487i) q^{6} +(-0.714388 + 0.390085i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(1.26811 - 0.579129i) q^{9} +(-1.07621 - 1.96004i) q^{10} +(0.227504 + 0.197133i) q^{11} +(-2.09087 + 0.149542i) q^{12} +(-1.18286 + 2.16625i) q^{13} +(0.338128 + 0.740396i) q^{14} +(3.30666 - 3.32212i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-3.11810 - 2.33418i) q^{17} +(-0.487187 - 1.30620i) q^{18} +(-0.734740 + 5.11023i) q^{19} +(-2.03183 + 0.933640i) q^{20} +(-1.28947 + 1.11733i) q^{21} +(0.212861 - 0.212861i) q^{22} +(4.11702 - 2.45971i) q^{23} +2.09621i q^{24} +(2.05583 - 4.55780i) q^{25} +(2.07635 + 1.33439i) q^{26} +(-2.69487 + 2.01736i) q^{27} +(0.762632 - 0.284447i) q^{28} +(-2.53852 + 0.364985i) q^{29} +(-3.07777 - 3.53523i) q^{30} +(-1.50555 + 0.967558i) q^{31} +(0.349464 - 0.936950i) q^{32} +(0.553837 + 0.302418i) q^{33} +(-2.55068 + 2.94364i) q^{34} +(-0.868528 + 1.59945i) q^{35} +(-1.33763 + 0.392762i) q^{36} +(-0.689729 - 0.257255i) q^{37} +(5.04480 + 1.09743i) q^{38} +(-1.45762 + 4.96421i) q^{39} +(0.786312 + 2.09325i) q^{40} +(-0.0867320 + 0.189917i) q^{41} +(1.02250 + 1.36589i) q^{42} +(-2.18548 - 10.0465i) q^{43} +(-0.197133 - 0.227504i) q^{44} +(1.67921 - 2.62636i) q^{45} +(-2.15974 - 4.28200i) q^{46} +(8.33589 + 8.33589i) q^{47} +(2.09087 + 0.149542i) q^{48} +(-3.42630 + 5.33143i) q^{49} +(-4.39953 - 2.37574i) q^{50} +(-7.42690 - 3.39175i) q^{51} +(1.47912 - 1.97587i) q^{52} +(4.39871 + 8.05563i) q^{53} +(1.81997 + 2.83192i) q^{54} +(0.666496 + 0.0942409i) q^{55} +(-0.229317 - 0.780981i) q^{56} +(0.772052 + 10.7947i) q^{57} +(0.182959 + 2.55809i) q^{58} +(0.263189 + 0.896340i) q^{59} +(-3.74579 + 2.81772i) q^{60} +(-2.69749 - 4.19738i) q^{61} +(0.857688 + 1.57074i) q^{62} +(-0.680016 + 0.908396i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(0.406563 + 5.50399i) q^{65} +(0.341158 - 0.530852i) q^{66} +(9.87075 + 0.705970i) q^{67} +(2.75418 + 2.75418i) q^{68} +(7.33690 - 6.87271i) q^{69} +(1.53342 + 0.980418i) q^{70} +(5.22431 + 6.02918i) q^{71} +(0.296336 + 1.36224i) q^{72} +(-2.91218 - 3.89022i) q^{73} +(-0.305805 + 0.669619i) q^{74} +(2.18009 - 10.2518i) q^{75} +(1.45452 - 4.95365i) q^{76} +(-0.239425 - 0.0520837i) q^{77} +(4.84758 + 1.80805i) q^{78} +(-11.3120 + 3.32150i) q^{79} +(2.14402 - 0.634978i) q^{80} +(-7.35984 + 8.49371i) q^{81} +(0.183245 + 0.100060i) q^{82} +(0.392931 - 1.05349i) q^{83} +(1.43536 - 0.922448i) q^{84} +(-8.68871 - 0.601055i) q^{85} +(-10.1768 + 1.46321i) q^{86} +(-5.03704 + 1.87872i) q^{87} +(-0.240988 + 0.180401i) q^{88} +(-11.4942 - 7.38685i) q^{89} +(-2.49987 - 1.86230i) q^{90} -2.00896i q^{91} +(-4.42516 + 1.84876i) q^{92} +(-2.65270 + 2.65270i) q^{93} +(8.90933 - 7.71997i) q^{94} +(4.82018 + 10.4899i) q^{95} +(0.298322 - 2.07487i) q^{96} +(-4.27471 - 11.4609i) q^{97} +(5.07342 + 3.79791i) q^{98} +(0.402667 + 0.118234i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$3$	2.04831	−	0.445581i	1.18259	−	0.257257i	0.422065	−	0.906566i	$-0.361305\pi$
$3$	2.04831	−	0.445581i	1.18259	−	0.257257i	0.760525	+	0.649309i	$0.224942\pi$
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	1.87827	−	1.21330i	0.839990	−	0.542602i
$5$	1.87827	−	1.21330i	0.839990	−	0.542602i
$6$	−0.298322	−	2.07487i	−0.121789	−	0.847064i
$7$	−0.714388	+	0.390085i	−0.270013	+	0.147438i	−0.608552	−	0.793514i	$-0.708249\pi$
$7$	−0.714388	+	0.390085i	−0.270013	+	0.147438i	0.338539	+	0.940953i	$0.390067\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	1.26811	−	0.579129i	0.422705	−	0.193043i
$10$	−1.07621	−	1.96004i	−0.340327	−	0.619820i
$11$	0.227504	+	0.197133i	0.0685951	+	0.0594380i	0.688484	−	0.725252i	$-0.258277\pi$
$11$	0.227504	+	0.197133i	0.0685951	+	0.0594380i	−0.619888	+	0.784690i	$0.712822\pi$
$12$	−2.09087	+	0.149542i	−0.603582	+	0.0431690i
$13$	−1.18286	+	2.16625i	−0.328068	+	0.600811i	−0.988702	−	0.149897i	$-0.952106\pi$
$13$	−1.18286	+	2.16625i	−0.328068	+	0.600811i	0.660634	+	0.750708i	$0.270288\pi$
$14$	0.338128	+	0.740396i	0.0903684	+	0.197879i
$15$	3.30666	−	3.32212i	0.853775	−	0.857769i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−3.11810	−	2.33418i	−0.756251	−	0.566123i	0.150088	−	0.988673i	$-0.452044\pi$
$17$	−3.11810	−	2.33418i	−0.756251	−	0.566123i	−0.906340	+	0.422550i	$0.861135\pi$
$18$	−0.487187	−	1.30620i	−0.114831	−	0.307874i
$19$	−0.734740	+	5.11023i	−0.168561	+	1.17237i	0.713300	+	0.700859i	$0.247200\pi$
$19$	−0.734740	+	5.11023i	−0.168561	+	1.17237i	−0.881861	+	0.471509i	$0.843709\pi$
$20$	−2.03183	+	0.933640i	−0.454330	+	0.208768i
$21$	−1.28947	+	1.11733i	−0.281385	+	0.243822i
$22$	0.212861	−	0.212861i	0.0453821	−	0.0453821i
$23$	4.11702	−	2.45971i	0.858457	−	0.512885i
$23$	4.11702	−	2.45971i	0.858457	−	0.512885i
$24$			2.09621i			0.427887i
$25$	2.05583	−	4.55780i	0.411166	−	0.911561i
$26$	2.07635	+	1.33439i	0.407206	+	0.261695i
$27$	−2.69487	+	2.01736i	−0.518628	+	0.388240i
$28$	0.762632	−	0.284447i	0.144124	−	0.0537554i
$29$	−2.53852	+	0.364985i	−0.471392	+	0.0677760i	−0.373917	−	0.927462i	$-0.621986\pi$
$29$	−2.53852	+	0.364985i	−0.471392	+	0.0677760i	−0.0974748	+	0.995238i	$0.531077\pi$
$30$	−3.07777	−	3.53523i	−0.561920	−	0.645442i
$31$	−1.50555	+	0.967558i	−0.270405	+	0.173778i	−0.668815	−	0.743429i	$-0.733198\pi$
$31$	−1.50555	+	0.967558i	−0.270405	+	0.173778i	0.398411	+	0.917207i	$0.369562\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	0.553837	+	0.302418i	0.0964106	+	0.0526442i
$34$	−2.55068	+	2.94364i	−0.437438	+	0.504830i
$35$	−0.868528	+	1.59945i	−0.146808	+	0.270357i
$36$	−1.33763	+	0.392762i	−0.222938	+	0.0654604i
$37$	−0.689729	−	0.257255i	−0.113391	−	0.0422925i	0.292128	−	0.956379i	$-0.405637\pi$
$37$	−0.689729	−	0.257255i	−0.113391	−	0.0422925i	−0.405519	+	0.914087i	$0.632909\pi$
$38$	5.04480	+	1.09743i	0.818374	+	0.178026i
$39$	−1.45762	+	4.96421i	−0.233407	+	0.794910i
$40$	0.786312	+	2.09325i	0.124327	+	0.330973i
$41$	−0.0867320	+	0.189917i	−0.0135453	+	0.0296600i	−0.916284	−	0.400530i	$-0.868826\pi$
$41$	−0.0867320	+	0.189917i	−0.0135453	+	0.0296600i	0.902738	+	0.430190i	$0.141553\pi$
$42$	1.02250	+	1.36589i	0.157774	+	0.210762i
$43$	−2.18548	−	10.0465i	−0.333283	−	1.53208i	−0.773272	−	0.634075i	$-0.781381\pi$
$43$	−2.18548	−	10.0465i	−0.333283	−	1.53208i	0.439988	−	0.898003i	$-0.354983\pi$
$44$	−0.197133	−	0.227504i	−0.0297190	−	0.0342975i
$45$	1.67921	−	2.62636i	0.250322	−	0.391515i
$46$	−2.15974	−	4.28200i	−0.318436	−	0.631346i
$47$	8.33589	+	8.33589i	1.21591	+	1.21591i	0.969050	+	0.246864i	$0.0794002\pi$
$47$	8.33589	+	8.33589i	1.21591	+	1.21591i	0.246864	+	0.969050i	$0.420600\pi$
$48$	2.09087	+	0.149542i	0.301791	+	0.0215845i
$49$	−3.42630	+	5.33143i	−0.489472	+	0.761633i
$50$	−4.39953	−	2.37574i	−0.622187	−	0.335980i
$51$	−7.42690	−	3.39175i	−1.03997	−	0.474940i
$52$	1.47912	−	1.97587i	0.205116	−	0.274003i
$53$	4.39871	+	8.05563i	0.604209	+	1.10653i	0.983442	+	0.181225i	$0.0580061\pi$
$53$	4.39871	+	8.05563i	0.604209	+	1.10653i	−0.379233	+	0.925301i	$0.623812\pi$
$54$	1.81997	+	2.83192i	0.247666	+	0.385376i
$55$	0.666496	+	0.0942409i	0.0898703	+	0.0127074i
$56$	−0.229317	−	0.780981i	−0.0306437	−	0.104363i
$57$	0.772052	+	10.7947i	0.102261	+	1.42979i
$58$	0.182959	+	2.55809i	0.0240236	+	0.335894i
$59$	0.263189	+	0.896340i	0.0342643	+	0.116693i	0.974849	−	0.222864i	$-0.0715407\pi$
$59$	0.263189	+	0.896340i	0.0342643	+	0.116693i	−0.940585	+	0.339558i	$0.889723\pi$
$60$	−3.74579	+	2.81772i	−0.483579	+	0.363766i
$61$	−2.69749	−	4.19738i	−0.345379	−	0.537420i	0.624495	−	0.781029i	$-0.285305\pi$
$61$	−2.69749	−	4.19738i	−0.345379	−	0.537420i	−0.969873	+	0.243609i	$0.921669\pi$
$62$	0.857688	+	1.57074i	0.108926	+	0.199484i
$63$	−0.680016	+	0.908396i	−0.0856740	+	0.114447i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	0.406563	+	5.50399i	0.0504280	+	0.682685i
$66$	0.341158	−	0.530852i	0.0419936	−	0.0653433i
$67$	9.87075	+	0.705970i	1.20590	+	0.0862479i	0.659781	−	0.751458i	$-0.270649\pi$
$67$	9.87075	+	0.705970i	1.20590	+	0.0862479i	0.546122	+	0.837706i	$0.316103\pi$
$68$	2.75418	+	2.75418i	0.333993	+	0.333993i
$69$	7.33690	−	6.87271i	0.883259	−	0.827377i
$70$	1.53342	+	0.980418i	0.183278	+	0.117182i
$71$	5.22431	+	6.02918i	0.620012	+	0.715532i	0.975709	−	0.219069i	$-0.0703020\pi$
$71$	5.22431	+	6.02918i	0.620012	+	0.715532i	−0.355697	+	0.934601i	$0.615757\pi$
$72$	0.296336	+	1.36224i	0.0349236	+	0.160541i
$73$	−2.91218	−	3.89022i	−0.340845	−	0.455316i	0.597066	−	0.802192i	$-0.296333\pi$
$73$	−2.91218	−	3.89022i	−0.340845	−	0.455316i	−0.937911	+	0.346876i	$0.887242\pi$
$74$	−0.305805	+	0.669619i	−0.0355491	+	0.0778416i
$75$	2.18009	−	10.2518i	0.251735	−	1.18378i
$76$	1.45452	−	4.95365i	0.166845	−	0.568223i
$77$	−0.239425	−	0.0520837i	−0.0272850	−	0.00593549i
$78$	4.84758	+	1.80805i	0.548880	+	0.204722i
$79$	−11.3120	+	3.32150i	−1.27270	+	0.373697i	−0.847206	−	0.531265i	$-0.821717\pi$
$79$	−11.3120	+	3.32150i	−1.27270	+	0.373697i	−0.425491	+	0.904963i	$0.639899\pi$
$80$	2.14402	−	0.634978i	0.239708	−	0.0709927i
$81$	−7.35984	+	8.49371i	−0.817760	+	0.943745i
$82$	0.183245	+	0.100060i	0.0202361	+	0.0110497i
$83$	0.392931	−	1.05349i	0.0431298	−	0.115635i	−0.913599	−	0.406616i	$-0.866709\pi$
$83$	0.392931	−	1.05349i	0.0431298	−	0.115635i	0.956729	+	0.290981i	$0.0939815\pi$
$84$	1.43536	−	0.922448i	0.156610	−	0.100647i
$85$	−8.68871	−	0.601055i	−0.942423	−	0.0651935i
$86$	−10.1768	+	1.46321i	−1.09740	+	0.157782i
$87$	−5.03704	+	1.87872i	−0.540028	+	0.201420i
$88$	−0.240988	+	0.180401i	−0.0256894	+	0.0192308i
$89$	−11.4942	−	7.38685i	−1.21838	−	0.783004i	−0.236337	−	0.971671i	$-0.575947\pi$
$89$	−11.4942	−	7.38685i	−1.21838	−	0.783004i	−0.982041	+	0.188667i	$0.939583\pi$
$90$	−2.49987	−	1.86230i	−0.263510	−	0.196303i
$91$		−	2.00896i		−	0.210597i
$92$	−4.42516	+	1.84876i	−0.461355	+	0.192747i
$93$	−2.65270	+	2.65270i	−0.275072	+	0.275072i
$94$	8.90933	−	7.71997i	0.918927	−	0.796255i
$95$	4.82018	+	10.4899i	0.494540	+	1.07624i
$96$	0.298322	−	2.07487i	0.0304473	−	0.211766i
$97$	−4.27471	−	11.4609i	−0.434031	−	1.16368i	−0.951410	−	0.307926i	$-0.900365\pi$
$97$	−4.27471	−	11.4609i	−0.434031	−	1.16368i	0.517380	−	0.855756i	$-0.326907\pi$
$98$	5.07342	+	3.79791i	0.512492	+	0.383647i
$99$	0.402667	+	0.118234i	0.0404696	+	0.0118829i
$100$	−2.68355	+	4.21884i	−0.268355	+	0.421884i
$101$	−0.0176928	−	0.0387419i	−0.00176050	−	0.00385496i	0.908750	−	0.417342i	$-0.137038\pi$
$101$	−0.0176928	−	0.0387419i	−0.00176050	−	0.00385496i	−0.910510	+	0.413487i	$0.864311\pi$
$102$	−3.91294	+	7.16601i	−0.387439	+	0.709541i
$103$	12.8681	−	0.920342i	1.26793	−	0.0906840i	0.578888	−	0.815407i	$-0.303487\pi$
$103$	12.8681	−	0.920342i	1.26793	−	0.0906840i	0.689040	+	0.724723i	$0.258032\pi$
$104$	−1.86531	−	1.61630i	−0.182909	−	0.158492i
$105$	−1.06632	+	3.66316i	−0.104063	+	0.357488i
$106$	8.34891	−	3.81282i	0.810917	−	0.370334i
$107$	2.44394	−	11.2346i	0.236264	−	1.08609i	−0.694222	−	0.719761i	$-0.744251\pi$
$107$	2.44394	−	11.2346i	0.236264	−	1.08609i	0.930486	−	0.366328i	$-0.119385\pi$
$108$	2.95454	−	1.61330i	0.284301	−	0.155240i
$109$	−2.48985	−	17.3173i	−0.238485	−	1.65870i	−0.659545	−	0.751665i	$-0.729251\pi$
$109$	−2.48985	−	17.3173i	−0.238485	−	1.65870i	0.421061	−	0.907032i	$-0.361658\pi$
$110$	0.141548	−	0.658075i	0.0134961	−	0.0627450i
$111$	−1.52740	−	0.219607i	−0.144975	−	0.0208442i
$112$	−0.795350	+	0.173018i	−0.0751535	+	0.0163486i
$113$	0.618060	−	8.64161i	0.0581422	−	0.812934i	−0.881805	−	0.471614i	$-0.843671\pi$
$113$	0.618060	−	8.64161i	0.0581422	−	0.812934i	0.939947	−	0.341320i	$-0.110874\pi$
$114$	10.8223			1.01360
$115$	4.74853	−	9.61517i	0.442802	−	0.896619i
$116$	2.56463			0.238120
$117$	−0.245468	+	3.43209i	−0.0226935	+	0.317297i
$118$	0.912832	−	0.198574i	0.0840330	−	0.0182803i
$119$	3.13807	+	0.451186i	0.287666	+	0.0413601i
$120$	2.54332	+	3.93726i	0.232173	+	0.359421i
$121$	−1.55257	−	10.7983i	−0.141142	−	0.981667i
$122$	−4.37912	+	2.39118i	−0.396467	+	0.216487i
$123$	−0.0930303	+	0.427653i	−0.00838826	+	0.0385602i
$124$	1.62792	−	0.743447i	0.146192	−	0.0667635i
$125$	−1.66855	−	11.0551i	−0.149240	−	0.988801i
$126$	0.857569	+	0.743088i	0.0763983	+	0.0661995i
$127$	5.83366	−	0.417232i	0.517654	−	0.0370233i	0.189931	−	0.981797i	$-0.439173\pi$
$127$	5.83366	−	0.417232i	0.517654	−	0.0370233i	0.327722	+	0.944774i	$0.393719\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	−8.95308	−	19.6045i	−0.788275	−	1.72608i
$130$	5.51897	−	0.0128777i	0.484045	−	0.00112945i
$131$	−5.15494	−	1.51363i	−0.450389	−	0.132246i	0.0486686	−	0.998815i	$-0.484502\pi$
$131$	−5.15494	−	1.51363i	−0.450389	−	0.132246i	−0.499057	+	0.866569i	$0.666320\pi$
$132$	−0.505161	−	0.378159i	−0.0439686	−	0.0329145i
$133$	−1.46854	−	3.93730i	−0.127338	−	0.341407i
$134$	1.40834	−	9.79523i	0.121662	−	0.846179i
$135$	−2.61406	+	7.05882i	−0.224982	+	0.607527i
$136$	2.94364	−	2.55068i	0.252415	−	0.218719i
$137$	0.574330	−	0.574330i	0.0490683	−	0.0490683i	−0.682147	−	0.731215i	$-0.738954\pi$
$137$	0.574330	−	0.574330i	0.0490683	−	0.0490683i	0.731215	+	0.682147i	$0.238954\pi$
$138$	−6.33179	−	7.80850i	−0.538997	−	0.664704i
$139$			9.74328i			0.826414i	0.910637	+	0.413207i	$0.135591\pi$
$139$			9.74328i			0.826414i	−0.910637	+	0.413207i	$0.864409\pi$
$140$	1.08731	−	1.45957i	0.0918947	−	0.123356i
$141$	20.7888	+	13.3601i	1.75073	+	1.12513i
$142$	6.38652	−	4.78089i	0.535945	−	0.401203i
$143$	−0.696148	+	0.259650i	−0.0582148	+	0.0217130i
$144$	1.37991	−	0.198401i	0.114992	−	0.0165334i
$145$	−4.32521	+	3.76552i	−0.359189	+	0.312710i
$146$	−4.08806	+	2.62724i	−0.338331	+	0.217432i
$147$	−4.64253	+	12.4471i	−0.382909	+	1.02662i
$148$	0.646097	+	0.352796i	0.0531088	+	0.0289996i
$149$	−3.61941	+	4.17702i	−0.296513	+	0.342195i	−0.884384	−	0.466760i	$-0.845421\pi$
$149$	−3.61941	+	4.17702i	−0.296513	+	0.342195i	0.587870	+	0.808955i	$0.299966\pi$
$150$	−10.0702	−	2.90589i	−0.822225	−	0.237265i
$151$	8.89604	−	2.61211i	0.723950	−	0.212571i	0.101060	−	0.994880i	$-0.467777\pi$
$151$	8.89604	−	2.61211i	0.723950	−	0.212571i	0.622890	+	0.782310i	$0.285958\pi$
$152$	−4.83727	−	1.80421i	−0.392354	−	0.146341i
$153$	−5.30591	−	1.15423i	−0.428957	−	0.0933139i
$154$	−0.0690314	+	0.235099i	−0.00556271	+	0.0189449i
$155$	−1.65390	+	3.64401i	−0.132844	+	0.292694i
$156$	2.14927	−	4.70624i	0.172079	−	0.376801i
$157$	−13.1600	−	17.5797i	−1.05028	−	1.40301i	−0.910829	−	0.412785i	$-0.864556\pi$
$157$	−13.1600	−	17.5797i	−1.05028	−	1.40301i	−0.139454	−	0.990229i	$-0.544535\pi$
$158$	2.50605	+	11.5201i	0.199370	+	0.916490i
$159$	12.5993	+	14.5404i	0.999192	+	1.15313i
$160$	−0.480407	−	2.18385i	−0.0379795	−	0.172649i
$161$	−1.98165	+	3.36318i	−0.156176	+	0.265055i
$162$	7.94702	+	7.94702i	0.624377	+	0.624377i
$163$	−20.4057	−	1.45945i	−1.59830	−	0.114313i	−0.756459	−	0.654041i	$-0.773073\pi$
$163$	−20.4057	−	1.45945i	−1.59830	−	0.114313i	−0.841839	+	0.539728i	$0.818527\pi$
$164$	0.112877	−	0.175640i	0.00881423	−	0.0137152i
$165$	1.40718	−	0.103944i	0.109549	−	0.00809205i
$166$	−1.02277	−	0.467085i	−0.0793826	−	0.0362528i
$167$	12.4570	−	16.6406i	0.963949	−	1.28768i	0.00622950	−	0.999981i	$-0.498017\pi$
$167$	12.4570	−	16.6406i	0.963949	−	1.28768i	0.957719	−	0.287704i	$-0.0928920\pi$
$168$	−0.817701	−	1.49751i	−0.0630870	−	0.115535i
$169$	3.73484	+	5.81152i	0.287295	+	0.447040i
$170$	−1.21937	+	8.62369i	−0.0935213	+	0.661407i
$171$	2.02775	+	6.90587i	0.155066	+	0.528105i
$172$	0.733472	+	10.2553i	0.0559267	+	0.781958i
$173$	1.23353	+	17.2471i	0.0937839	+	1.31127i	0.798592	+	0.601872i	$0.205578\pi$
$173$	1.23353	+	17.2471i	0.0937839	+	1.31127i	−0.704809	+	0.709398i	$0.748967\pi$
$174$	1.51459	+	5.15823i	0.114821	+	0.391045i
$175$	0.309274	+	4.05799i	0.0233789	+	0.306755i
$176$	0.162750	+	0.253243i	0.0122677	+	0.0190889i
$177$	0.938484	+	1.71871i	0.0705408	+	0.129186i
$178$	−8.18801	+	10.9379i	−0.613717	+	0.819830i
$179$	14.9118	+	6.80998i	1.11456	+	0.509002i	0.885607	−	0.464436i	$-0.153743\pi$
$179$	14.9118	+	6.80998i	1.11456	+	0.509002i	0.228952	+	0.973438i	$0.426470\pi$
$180$	−2.03589	+	2.36065i	−0.151746	+	0.175953i
$181$	−7.04082	+	10.9557i	−0.523340	+	0.814333i	−0.997824	−	0.0659311i	$-0.978998\pi$
$181$	−7.04082	+	10.9557i	−0.523340	+	0.814333i	0.474484	+	0.880264i	$0.342635\pi$
$182$	−2.00385	−	0.143318i	−0.148535	−	0.0106234i
$183$	−7.39556	−	7.39556i	−0.546696	−	0.546696i
$184$	1.52836	+	4.54578i	0.112673	+	0.335119i
$185$	−1.60763	+	0.353648i	−0.118195	+	0.0260007i
$186$	2.45670	+	2.83518i	0.180134	+	0.207886i
$187$	−0.249236	−	1.14572i	−0.0182259	−	0.0837833i
$188$	−7.06472	−	9.43736i	−0.515248	−	0.688290i
$189$	1.13824	−	2.49240i	0.0827950	−	0.181296i
$190$	10.8070	−	4.05956i	0.784023	−	0.294511i
$191$	−2.53147	+	8.62141i	−0.183171	+	0.623823i	0.815794	+	0.578342i	$0.196300\pi$
$191$	−2.53147	+	8.62141i	−0.183171	+	0.623823i	−0.998965	+	0.0454809i	$0.985518\pi$
$192$	−2.04831	−	0.445581i	−0.147824	−	0.0321571i
$193$	−16.9887	−	6.33647i	−1.22287	−	0.456109i	−0.346642	−	0.937997i	$-0.612678\pi$
$193$	−16.9887	−	6.33647i	−1.22287	−	0.456109i	−0.876232	+	0.481889i	$0.839951\pi$
$194$	−11.7367	+	3.44620i	−0.842645	+	0.247423i
$195$	3.28524	+	11.0927i	0.235261	+	0.794364i
$196$	4.15017	−	4.78955i	0.296441	−	0.342111i
$197$	13.4100	+	7.32240i	0.955421	+	0.521699i	0.879752	−	0.475433i	$-0.157709\pi$
$197$	13.4100	+	7.32240i	0.955421	+	0.521699i	0.0756696	+	0.997133i	$0.475891\pi$
$198$	0.146658	−	0.393206i	0.0104226	−	0.0279440i
$199$	−8.28311	+	5.32323i	−0.587174	+	0.377354i	−0.800236	−	0.599685i	$-0.795293\pi$
$199$	−8.28311	+	5.32323i	−0.587174	+	0.377354i	0.213062	+	0.977039i	$0.431656\pi$
$200$	4.01665	+	2.97768i	0.284020	+	0.210554i
$201$	20.5329	−	2.95218i	1.44828	−	0.208231i
$202$	−0.0399053	+	0.0148839i	−0.00280773	+	0.00104723i
$203$	1.67112	−	1.25098i	0.117289	−	0.0878017i
$204$	6.86861	+	4.41418i	0.480899	+	0.309055i
$205$	0.0675185	+	0.461947i	0.00471570	+	0.0322638i
$206$		−	12.9009i		−	0.898850i
$207$	3.79636	−	5.50348i	0.263865	−	0.382518i
$208$	−1.74525	+	1.74525i	−0.121012	+	0.121012i
$209$	−1.17455	+	1.01776i	−0.0812456	+	0.0703997i
$210$	3.57776	+	1.32493i	0.246889	+	0.0914291i
$211$	−1.26338	+	8.78703i	−0.0869749	+	0.604924i	0.898990	+	0.437970i	$0.144302\pi$
$211$	−1.26338	+	8.78703i	−0.0869749	+	0.604924i	−0.985965	+	0.166954i	$0.946607\pi$
$212$	−3.20750	−	8.59964i	−0.220292	−	0.590625i
$213$	13.3875	+	10.0217i	0.917295	+	0.686678i
$214$	−11.0316	−	3.23917i	−0.754106	−	0.221425i
$215$	−16.2943	−	16.2185i	−1.11126	−	1.10609i
$216$	−1.39842	−	3.06210i	−0.0951502	−	0.208350i
$217$	0.698116	−	1.27850i	0.0473912	−	0.0867905i
$218$	−17.4508	+	1.24811i	−1.18192	+	0.0845324i
$219$	−7.69845	−	6.67075i	−0.520213	−	0.450767i
$220$	−0.646300	−	0.188134i	−0.0435736	−	0.0126840i
$221$	8.74473	−	3.99358i	0.588234	−	0.268638i
$222$	−0.328012	+	1.50784i	−0.0220147	+	0.101200i
$223$	15.4248	−	8.42256i	1.03292	−	0.564016i	0.128966	−	0.991649i	$-0.458834\pi$
$223$	15.4248	−	8.42256i	1.03292	−	0.564016i	0.903953	+	0.427633i	$0.140652\pi$
$224$	0.115837	+	0.805667i	0.00773971	+	0.0538309i
$225$	−0.0325290	−	6.97041i	−0.00216860	−	0.464694i
$226$	−8.57550	−	1.23297i	−0.570434	−	0.0820160i
$227$	12.3747	−	2.69194i	0.821335	−	0.178670i	0.217786	−	0.975997i	$-0.430117\pi$
$227$	12.3747	−	2.69194i	0.821335	−	0.178670i	0.603549	+	0.797326i	$0.293753\pi$
$228$	0.772052	−	10.7947i	0.0511304	−	0.714897i
$229$	9.06938			0.599322			0.299661	−	0.954046i	$-0.403127\pi$
$229$	9.06938			0.599322			0.299661	+	0.954046i	$0.403127\pi$
$230$	−9.25192	−	5.42237i	−0.610053	−	0.357540i
$231$	−0.513623			−0.0337939
$232$	0.182959	−	2.55809i	0.0120118	−	0.167947i
$233$	−24.5313	+	5.33646i	−1.60710	+	0.349603i	−0.924497	−	0.381188i	$-0.875515\pi$
$233$	−24.5313	+	5.33646i	−1.60710	+	0.349603i	−0.682601	+	0.730791i	$0.739151\pi$
$234$	3.40583	+	0.489685i	0.222646	+	0.0320117i
$235$	25.7710	+	5.54319i	1.68111	+	0.361598i
$236$	−0.132948	−	0.924672i	−0.00865416	−	0.0601910i
$237$	−21.6904	+	11.8438i	−1.40894	+	0.769340i
$238$	0.673903	−	3.09788i	0.0436827	−	0.200806i
$239$	1.22371	−	0.558848i	0.0791549	−	0.0361489i	−0.375444	−	0.926845i	$-0.622510\pi$
$239$	1.22371	−	0.558848i	0.0791549	−	0.0361489i	0.454599	+	0.890696i	$0.349783\pi$
$240$	4.10866	−	2.25596i	0.265213	−	0.145622i
$241$	16.6323	+	14.4120i	1.07138	+	0.928357i	0.997622	−	0.0689191i	$-0.0219550\pi$
$241$	16.6323	+	14.4120i	1.07138	+	0.928357i	0.0737588	+	0.997276i	$0.476500\pi$
$242$	−10.8816	+	0.778266i	−0.699495	+	0.0500289i
$243$	−6.45065	+	11.8135i	−0.413810	+	0.757836i
$244$	2.07269	+	4.53855i	0.132690	+	0.290551i
$245$	0.0330659	+	14.1710i	0.00211250	+	0.905352i
$246$	0.419927	+	0.123302i	0.0267736	+	0.00786143i
$247$	−10.2010	−	7.63635i	−0.649072	−	0.485889i
$248$	−0.625418	−	1.67681i	−0.0397141	−	0.106478i
$249$	0.335427	−	2.33295i	0.0212568	−	0.147845i
$250$	−11.1460	+	0.875639i	−0.704935	+	0.0553803i
$251$	6.92815	−	6.00328i	0.437301	−	0.378923i	−0.408204	−	0.912891i	$-0.633845\pi$
$251$	6.92815	−	6.00328i	0.437301	−	0.378923i	0.845505	+	0.533967i	$0.179299\pi$
$252$	0.802373	−	0.802373i	0.0505447	−	0.0505447i
$253$	1.42153	+	0.252007i	0.0893708	+	0.0158435i
$254$		−	5.84856i		−	0.366972i
$255$	−18.0649	+	2.64038i	−1.13127	+	0.165347i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	18.4353	−	13.8005i	1.14996	−	0.860850i	0.158005	−	0.987438i	$-0.449494\pi$
$257$	18.4353	−	13.8005i	1.14996	−	0.860850i	0.991955	+	0.126589i	$0.0404029\pi$
$258$	−20.1933	+	7.53170i	−1.25718	+	0.468903i
$259$	0.593086	−	0.0852728i	0.0368525	−	0.00529860i
$260$	0.380874	−	5.50582i	0.0236208	−	0.341457i
$261$	−3.00777	+	1.93297i	−0.186176	+	0.119648i
$262$	−1.87752	+	5.03382i	−0.115993	+	0.310991i
$263$	12.7488	+	6.96136i	0.786123	+	0.429256i	0.821564	−	0.570116i	$-0.193102\pi$
$263$	12.7488	+	6.96136i	0.786123	+	0.429256i	−0.0354408	+	0.999372i	$0.511284\pi$
$264$	−0.413233	+	0.476896i	−0.0254327	+	0.0293509i
$265$	18.0358	+	9.79375i	1.10793	+	0.601625i
$266$	−4.03203	+	1.18391i	−0.247220	+	0.0725903i
$267$	−26.8350	−	10.0089i	−1.64227	−	0.612537i
$268$	−9.66981	−	2.10354i	−0.590677	−	0.128494i
$269$	4.07193	−	13.8677i	0.248270	−	0.845529i	−0.737200	−	0.675675i	$-0.763852\pi$
$269$	4.07193	−	13.8677i	0.248270	−	0.845529i	0.985469	−	0.169854i	$-0.0543296\pi$
$270$	6.85435	+	3.11097i	0.417143	+	0.189328i
$271$	−9.10100	+	19.9284i	−0.552846	+	1.21056i	0.402594	+	0.915379i	$0.368109\pi$
$271$	−9.10100	+	19.9284i	−0.552846	+	1.21056i	−0.955440	+	0.295186i	$0.904619\pi$
$272$	−2.33418	−	3.11810i	−0.141531	−	0.189063i
$273$	−0.895158	−	4.11497i	−0.0541774	−	0.249049i
$274$	−0.531895	−	0.613839i	−0.0321329	−	0.0370834i
$275$	1.36620	−	0.631647i	0.0823853	−	0.0380897i
$276$	−8.24031	+	5.75860i	−0.496008	+	0.346627i
$277$	12.6669	+	12.6669i	0.761080	+	0.761080i	0.976518	−	0.215438i	$-0.0691178\pi$
$277$	12.6669	+	12.6669i	0.761080	+	0.761080i	−0.215438	+	0.976518i	$0.569118\pi$
$278$	9.71845	+	0.695077i	0.582874	+	0.0416880i
$279$	−1.34887	+	2.09888i	−0.0807546	+	0.125657i
$280$	−1.37828	−	1.18867i	−0.0823680	−	0.0710364i
$281$	−11.4051	−	5.20854i	−0.680372	−	0.310715i	0.0450850	−	0.998983i	$-0.485644\pi$
$281$	−11.4051	−	5.20854i	−0.680372	−	0.310715i	−0.725457	+	0.688268i	$0.758371\pi$
$282$	14.8091	−	19.7827i	0.881871	−	1.17804i
$283$	1.04150	+	1.90736i	0.0619105	+	0.113381i	0.906801	−	0.421558i	$-0.138517\pi$
$283$	1.04150	+	1.90736i	0.0619105	+	0.113381i	−0.844891	+	0.534939i	$0.820335\pi$
$284$	−4.31310	−	6.71131i	−0.255935	−	0.398243i
$285$	14.5473	+	19.3387i	0.861707	+	1.14552i
$286$	0.209326	+	0.712897i	0.0123777	+	0.0421545i
$287$	−0.0121234	−	0.169507i	−0.000715621	−	0.0100057i
$288$	−0.0994537	−	1.39054i	−0.00586037	−	0.0819386i
$289$	−0.515293	−	1.75493i	−0.0303114	−	0.103231i
$290$	3.44737	+	4.58282i	0.202437	+	0.269112i
$291$	−13.8627	−	21.5708i	−0.812645	−	1.26450i
$292$	2.32891	+	4.26507i	0.136289	+	0.249594i
$293$	−14.2893	+	19.0883i	−0.834793	+	1.11515i	0.157038	+	0.987593i	$0.449805\pi$
$293$	−14.2893	+	19.0883i	−0.834793	+	1.11515i	−0.991831	+	0.127560i	$0.959285\pi$
$294$	12.0842	+	5.51866i	0.704764	+	0.321855i
$295$	1.58187	+	1.36425i	0.0920998	+	0.0794295i
$296$	0.397989	−	0.619283i	0.0231326	−	0.0359951i
$297$	−1.01078	−	0.0722926i	−0.0586515	−	0.00419484i
$298$	3.90817	+	3.90817i	0.226394	+	0.226394i
$299$	0.458490	+	11.8280i	0.0265152	+	0.684032i
$300$	−3.61688	+	9.83720i	−0.208821	+	0.567951i
$301$	5.48028	+	6.32458i	0.315878	+	0.364543i
$302$	−1.97082	−	9.05972i	−0.113408	−	0.521329i
$303$	−0.0535029	−	0.0714716i	−0.00307366	−	0.00410593i
$304$	−2.14470	+	4.69623i	−0.123007	+	0.269347i
$305$	−10.1593	−	4.61098i	−0.581719	−	0.264024i
$306$	−1.52981	+	5.21004i	−0.0874533	+	0.297838i
$307$	−26.6437	−	5.79598i	−1.52064	−	0.330794i	−0.626797	−	0.779183i	$-0.715634\pi$
$307$	−26.6437	−	5.79598i	−1.52064	−	0.330794i	−0.893839	+	0.448389i	$0.851998\pi$
$308$	0.229576	+	0.0856274i	0.0130813	+	0.00487907i
$309$	25.9476	−	7.61891i	1.47611	−	0.433425i
$310$	3.51674	+	1.90965i	0.199738	+	0.108461i
$311$	−13.2381	+	15.2776i	−0.750663	+	0.866311i	−0.994632	−	0.103472i	$-0.967005\pi$
$311$	−13.2381	+	15.2776i	−0.750663	+	0.866311i	0.243970	+	0.969783i	$0.421550\pi$
$312$	−4.54093	−	2.47953i	−0.257079	−	0.140376i
$313$	−3.02103	+	8.09970i	−0.170759	+	0.457822i	−0.993936	−	0.109963i	$-0.964927\pi$
$313$	−3.02103	+	8.09970i	−0.170759	+	0.457822i	0.823177	+	0.567785i	$0.192199\pi$
$314$	−18.4737	+	11.8723i	−1.04253	+	0.669995i
$315$	−0.175105	+	2.53128i	−0.00986604	+	0.142621i
$316$	11.6695	−	1.67783i	0.656462	−	0.0943851i
$317$	26.1851	−	9.76654i	1.47070	−	0.548543i	0.518786	−	0.854904i	$-0.326384\pi$
$317$	26.1851	−	9.76654i	1.47070	−	0.548543i	0.951916	+	0.306361i	$0.0991113\pi$
$318$	15.4022	−	11.5299i	0.863712	−	0.646566i
$319$	−0.649475	−	0.417393i	−0.0363636	−	0.0233695i
$320$	−2.21256	+	0.323389i	−0.123686	+	0.0180780i
$321$		−	24.1008i		−	1.34518i
$322$	3.21324	+	2.21653i	0.179067	+	0.123522i
$323$	14.2192	−	14.2192i	0.791178	−	0.791178i
$324$	8.49371	−	7.35984i	0.471873	−	0.408880i
$325$	7.44160	+	9.84471i	0.412786	+	0.546086i
$326$	−2.91145	+	20.2496i	−0.161251	+	1.12152i
$327$	−12.8162	−	34.3617i	−0.708740	−	1.90021i
$328$	−0.167140	−	0.125120i	−0.00922878	−	0.00690857i
$329$	−9.20677	−	2.70335i	−0.507586	−	0.149041i
$330$	−0.00329238	−	1.41101i	−0.000181239	−	0.0776735i
$331$	−7.66937	−	16.7936i	−0.421547	−	0.923059i	−0.994624	−	0.103557i	$-0.966978\pi$
$331$	−7.66937	−	16.7936i	−0.421547	−	0.923059i	0.573077	−	0.819502i	$-0.305750\pi$
$332$	−0.538858	+	0.986845i	−0.0295737	+	0.0541602i
$333$	−1.02364	+	0.0732121i	−0.0560951	+	0.00401200i
$334$	−15.7095	−	13.6123i	−0.859585	−	0.744835i
$335$	19.3965	−	10.6501i	1.05974	−	0.581879i
$336$	−1.55203	+	0.708787i	−0.0846700	+	0.0386675i
$337$	−4.17172	+	19.1771i	−0.227248	+	1.04464i	0.712207	+	0.701969i	$0.247696\pi$
$337$	−4.17172	+	19.1771i	−0.227248	+	1.04464i	−0.939455	+	0.342672i	$0.888668\pi$
$338$	6.06316	−	3.31073i	0.329792	−	0.180080i
$339$	−2.58457	−	17.9760i	−0.140374	−	0.976325i
$340$	8.51473	+	1.83147i	0.461776	+	0.0993253i
$341$	−0.533257	−	0.0766707i	−0.0288775	−	0.00415195i
$342$	7.03293	−	1.52992i	0.380297	−	0.0827286i
$343$	0.774463	−	10.8284i	0.0418171	−	0.584679i
$344$	10.2815			0.554340
$345$	5.44209	−	21.8107i	0.292992	−	1.17425i
$346$	17.2911			0.929576
$347$	−1.88329	+	26.3318i	−0.101100	+	1.41357i	0.653273	+	0.757122i	$0.273395\pi$
$347$	−1.88329	+	26.3318i	−0.101100	+	1.41357i	−0.754374	+	0.656445i	$0.772059\pi$
$348$	5.25314	−	1.14275i	0.281598	−	0.0612579i
$349$	19.2927	+	2.77387i	1.03271	+	0.148482i	0.637772	−	0.770225i	$-0.279856\pi$
$349$	19.2927	+	2.77387i	1.03271	+	0.148482i	0.394940	+	0.918707i	$0.370765\pi$
$350$	4.06971	−	0.0189922i	0.217535	−	0.00101518i
$351$	−1.18244	−	8.22404i	−0.0631139	−	0.438967i
$352$	0.264209	−	0.144269i	0.0140824	−	0.00768956i
$353$	2.75591	−	12.6687i	0.146683	−	0.674289i	−0.843801	−	0.536656i	$-0.819687\pi$
$353$	2.75591	−	12.6687i	0.146683	−	0.674289i	0.990483	−	0.137632i	$-0.0439492\pi$
$354$	1.78128	−	0.813482i	0.0946738	−	0.0432361i
$355$	17.1279	+	4.98582i	0.909053	+	0.264620i
$356$	10.3259	+	8.94745i	0.547272	+	0.474214i
$357$	6.62876	−	0.474098i	0.350831	−	0.0250919i
$358$	7.85642	−	14.3880i	0.415225	−	0.760427i
$359$	−10.4494	−	22.8811i	−0.551500	−	1.20762i	−0.956078	−	0.293113i	$-0.905309\pi$
$359$	−10.4494	−	22.8811i	−0.551500	−	1.20762i	0.404578	−	0.914504i	$-0.367419\pi$
$360$	2.20940	+	2.19911i	0.116445	+	0.115903i
$361$	−7.34426	−	2.15647i	−0.386540	−	0.113498i
$362$	10.4255	+	7.80445i	0.547954	+	0.410193i
$363$	−7.99167	−	21.4265i	−0.419454	−	1.12460i
$364$	−0.285906	+	1.98852i	−0.0149855	+	0.104227i
$365$	−10.1899	−	3.77356i	−0.533362	−	0.197517i
$366$	−7.90431	+	6.84913i	−0.413165	+	0.358010i
$367$	2.73519	−	2.73519i	0.142776	−	0.142776i	−0.632106	−	0.774882i	$-0.717809\pi$
$367$	2.73519	−	2.73519i	0.142776	−	0.142776i	0.774882	+	0.632106i	$0.217809\pi$
$368$	4.64323	−	1.20018i	0.242045	−	0.0625636i
$369$			0.291065i			0.0151522i
$370$	0.238061	+	1.62876i	0.0123762	+	0.0846752i
$371$	−6.28477	−	4.03897i	−0.326289	−	0.209693i
$372$	3.00322	−	2.24818i	0.155709	−	0.116563i
$373$	11.9937	−	4.47342i	0.621011	−	0.231625i	−0.0192106	−	0.999815i	$-0.506115\pi$
$373$	11.9937	−	4.47342i	0.621011	−	0.231625i	0.640221	+	0.768190i	$0.278843\pi$
$374$	−1.16058	+	0.166866i	−0.0600122	+	0.00862845i
$375$	−8.34367	−	21.9008i	−0.430865	−	1.13095i
$376$	−9.91731	+	6.37347i	−0.511446	+	0.328686i
$377$	2.21208	−	5.93082i	0.113928	−	0.305453i
$378$	−2.40485	−	1.31315i	−0.123692	−	0.0675411i
$379$	7.86590	−	9.07773i	0.404044	−	0.466292i	−0.516866	−	0.856066i	$-0.672902\pi$
$379$	7.86590	−	9.07773i	0.404044	−	0.466292i	0.920910	+	0.389775i	$0.127447\pi$
$380$	−3.27825	−	11.0691i	−0.168171	−	0.567832i
$381$	11.7632	−	3.45399i	0.602648	−	0.176953i
$382$	8.41885	+	3.14007i	0.430746	+	0.160660i
$383$	−5.58401	−	1.21473i	−0.285329	−	0.0620696i	0.0676228	−	0.997711i	$-0.478459\pi$
$383$	−5.58401	−	1.21473i	−0.285329	−	0.0620696i	−0.352952	+	0.935641i	$0.614822\pi$
$384$	−0.590571	+	2.01130i	−0.0301374	+	0.102639i
$385$	−0.512899	+	0.192666i	−0.0261398	+	0.00981916i
$386$	−7.53228	+	16.4934i	−0.383383	+	0.839492i
$387$	−8.58967	−	11.4745i	−0.436637	−	0.583279i
$388$	2.60014	+	11.9526i	0.132002	+	0.606803i
$389$	23.5502	+	27.1783i	1.19404	+	1.37800i	0.907566	+	0.419909i	$0.137938\pi$
$389$	23.5502	+	27.1783i	1.19404	+	1.37800i	0.286474	+	0.958088i	$0.407517\pi$
$390$	11.2988	−	2.48553i	0.572136	−	0.125860i
$391$	−18.5787	−	1.94023i	−0.939565	−	0.0981218i
$392$	−4.48128	−	4.48128i	−0.226339	−	0.226339i
$393$	−11.2333	−	0.803423i	−0.566646	−	0.0405273i
$394$	8.26040	−	12.8534i	0.416153	−	0.647547i
$395$	−17.2170	+	19.9634i	−0.866283	+	1.00447i
$396$	−0.381742	−	0.174336i	−0.0191833	−	0.00876070i
$397$	−18.6907	+	24.9679i	−0.938059	+	1.25310i	0.0292683	+	0.999572i	$0.490682\pi$
$397$	−18.6907	+	24.9679i	−0.938059	+	1.25310i	−0.967328	+	0.253529i	$0.918409\pi$
$398$	4.71876	+	8.64176i	0.236530	+	0.433172i
$399$	−4.76240	−	7.41044i	−0.238418	−	0.370986i
$400$	3.25663	−	3.79399i	0.162832	−	0.189699i
$401$	−8.94339	−	30.4584i	−0.446612	−	1.52102i	−0.808329	−	0.588732i	$-0.799627\pi$
$401$	−8.94339	−	30.4584i	−0.446612	−	1.52102i	0.361717	−	0.932288i	$-0.382191\pi$
$402$	−1.47986	−	20.6912i	−0.0738087	−	1.03198i
$403$	−0.315116	−	4.40589i	−0.0156970	−	0.219473i
$404$	0.0119992	+	0.0408655i	0.000596982	+	0.00203313i
$405$	−3.51842	+	24.8832i	−0.174832	+	1.23645i
$406$	−1.12858	−	1.75610i	−0.0560104	−	0.0871539i
$407$	−0.106202	−	0.194495i	−0.00526426	−	0.00964077i
$408$	4.89294	−	6.53620i	0.242237	−	0.323590i
$409$	31.6575	+	14.4575i	1.56536	+	0.714877i	0.994359	−	0.106070i	$-0.0338267\pi$
$409$	31.6575	+	14.4575i	1.56536	+	0.714877i	0.571004	+	0.820947i	$0.306554\pi$
$410$	0.465587	−	0.0343915i	0.0229937	−	0.00169848i
$411$	0.920493	−	1.43231i	0.0454046	−	0.0706509i
$412$	−12.8681	−	0.920342i	−0.633964	−	0.0453420i
$413$	−0.537668	−	0.537668i	−0.0264569	−	0.0264569i
$414$	−5.21863	−	4.17930i	−0.256481	−	0.205401i
$415$	−0.540161	−	2.45548i	−0.0265155	−	0.120535i
$416$	1.61630	+	1.86531i	0.0792458	+	0.0914545i
$417$	4.34142	+	19.9572i	0.212600	+	0.977308i
$418$	0.931372	+	1.24417i	0.0455549	+	0.0608542i
$419$	1.63468	−	3.57946i	0.0798595	−	0.174868i	−0.865490	−	0.500925i	$-0.832993\pi$
$419$	1.63468	−	3.57946i	0.0798595	−	0.174868i	0.945350	+	0.326058i	$0.105720\pi$
$420$	1.57679	−	3.47412i	0.0769396	−	0.169520i
$421$	−2.56072	+	8.72101i	−0.124802	+	0.425036i	−0.998063	−	0.0622169i	$-0.980183\pi$
$421$	−2.56072	+	8.72101i	−0.124802	+	0.425036i	0.873261	+	0.487253i	$0.162001\pi$
$422$	8.67451	+	1.88702i	0.422269	+	0.0918589i
$423$	15.3984	+	5.74331i	0.748697	+	0.279249i
$424$	−8.80655	+	2.58584i	−0.427684	+	0.125579i
$425$	−17.0490	+	9.41303i	−0.827000	+	0.456599i
$426$	10.9513	−	12.6384i	0.530590	−	0.612334i
$427$	3.56439	+	1.94631i	0.172493	+	0.0941883i
$428$	−4.01791	+	10.7724i	−0.194213	+	0.520705i
$429$	−1.31023	+	0.842033i	−0.0632584	+	0.0406537i
$430$	−17.3396	+	15.0958i	−0.836188	+	0.727984i
$431$	9.50992	−	1.36732i	0.458077	−	0.0658615i	0.0905860	−	0.995889i	$-0.471126\pi$
$431$	9.50992	−	1.36732i	0.458077	−	0.0658615i	0.367491	+	0.930027i	$0.380217\pi$
$432$	−3.15406	+	1.17641i	−0.151750	+	0.0565998i
$433$	4.47317	−	3.34858i	0.214967	−	0.160922i	−0.486368	−	0.873754i	$-0.661679\pi$
$433$	4.47317	−	3.34858i	0.214967	−	0.160922i	0.701335	+	0.712832i	$0.252588\pi$
$434$	−1.22544	−	0.787545i	−0.0588232	−	0.0378034i
$435$	−7.18150	+	9.64017i	−0.344327	+	0.462211i
$436$			17.4954i			0.837877i
$437$	9.54476	+	22.8462i	0.456588	+	1.09288i
$438$	−7.20295	+	7.20295i	−0.344170	+	0.344170i
$439$	−22.8695	+	19.8165i	−1.09150	+	0.945790i	−0.998754	−	0.0498996i	$-0.984110\pi$
$439$	−22.8695	+	19.8165i	−1.09150	+	0.945790i	−0.0927459	+	0.995690i	$0.529564\pi$
$440$	−0.233761	+	0.631232i	−0.0111441	+	0.0300928i
$441$	−1.25736	+	8.74513i	−0.0598743	+	0.416435i
$442$	−3.35957	−	9.00735i	−0.159798	−	0.428436i
$443$	10.8986	+	8.15863i	0.517810	+	0.387628i	0.825977	−	0.563705i	$-0.190624\pi$
$443$	10.8986	+	8.15863i	0.517810	+	0.387628i	−0.308166	+	0.951333i	$0.599715\pi$
$444$	1.48060	+	0.434744i	0.0702663	+	0.0206320i
$445$	−30.5516	+	0.0712875i	−1.44828	+	0.00337935i
$446$	−7.30071	−	15.9863i	−0.345699	−	0.756975i
$447$	−5.55245	+	10.1685i	−0.262622	+	0.480956i
$448$	0.811878	−	0.0580666i	0.0383576	−	0.00274339i
$449$	−30.2476	−	26.2097i	−1.42747	−	1.23691i	−0.929039	−	0.369981i	$-0.879364\pi$
$449$	−30.2476	−	26.2097i	−1.42747	−	1.23691i	−0.498431	−	0.866929i	$-0.666090\pi$
$450$	−6.95497	−	0.464817i	−0.327860	−	0.0219117i
$451$	−0.0571708	+	0.0261090i	−0.00269207	+	0.00122943i
$452$	−1.84160	+	8.46569i	−0.0866215	+	0.398193i
$453$	17.0579	−	9.31432i	0.801450	−	0.437625i
$454$	−1.80228	−	12.5352i	−0.0845854	−	0.588304i
$455$	−2.43747	−	3.77339i	−0.114270	−	0.176899i
$456$	−10.7121	−	1.54017i	−0.501641	−	0.0721251i
$457$	4.75942	−	1.03535i	0.222636	−	0.0484316i	−0.0998632	−	0.995001i	$-0.531841\pi$
$457$	4.75942	−	1.03535i	0.222636	−	0.0484316i	0.322500	+	0.946570i	$0.395477\pi$
$458$	0.647002	−	9.04627i	0.0302324	−	0.422705i
$459$	13.1118			0.612005
$460$	−6.06858	+	8.84152i	−0.282949	+	0.412238i
$461$	6.99829			0.325943			0.162971	−	0.986631i	$-0.447892\pi$
$461$	6.99829			0.325943			0.162971	+	0.986631i	$0.447892\pi$
$462$	−0.0366415	+	0.512315i	−0.00170472	+	0.0238350i
$463$	−26.8587	+	5.84275i	−1.24823	+	0.271536i	−0.787672	−	0.616095i	$-0.788714\pi$
$463$	−26.8587	+	5.84275i	−1.24823	+	0.271536i	−0.460557	+	0.887630i	$0.652350\pi$
$464$	−2.53852	−	0.364985i	−0.117848	−	0.0169440i
$465$	−1.76399	+	8.20100i	−0.0818030	+	0.380312i
$466$	3.57282	+	24.8495i	0.165508	+	1.15113i
$467$	−12.8253	+	7.00315i	−0.593485	+	0.324067i	−0.747769	−	0.663959i	$-0.768875\pi$
$467$	−12.8253	+	7.00315i	−0.593485	+	0.324067i	0.154284	+	0.988027i	$0.450693\pi$
$468$	0.731407	−	3.36222i	0.0338093	−	0.155419i
$469$	−7.32693	+	3.34610i	−0.338326	+	0.154508i
$470$	7.36754	−	25.3099i	0.339840	−	1.16746i
$471$	−34.7889	−	30.1447i	−1.60299	−	1.38900i
$472$	−0.931800	+	0.0666437i	−0.0428896	+	0.00306752i
$473$	1.48330	−	2.71645i	0.0682020	−	0.124903i
$474$	10.2663	+	22.4800i	0.471546	+	1.03254i
$475$	21.7809	+	13.8546i	0.999378	+	0.635691i
$476$	−3.04192	−	0.893187i	−0.139426	−	0.0409392i
$477$	10.2433	+	7.66805i	0.469009	+	0.351096i
$478$	−0.470126	−	1.26046i	−0.0215030	−	0.0576519i
$479$	−2.09468	+	14.5688i	−0.0957082	+	0.665665i	0.884331	+	0.466861i	$0.154615\pi$
$479$	−2.09468	+	14.5688i	−0.0957082	+	0.665665i	−0.980039	+	0.198805i	$0.936294\pi$
$480$	−1.95710	−	4.25913i	−0.0893292	−	0.194402i
$481$	1.37314	−	1.18983i	0.0626096	−	0.0542516i
$482$	15.5618	−	15.5618i	0.708820	−	0.708820i
$483$	−2.56045	+	7.77180i	−0.116505	+	0.353629i
$484$			10.9094i			0.495881i
$485$	−21.9346	−	16.3403i	−0.995998	−	0.741974i
$486$	11.3232	+	7.27698i	0.513631	+	0.330091i
$487$	−6.91522	+	5.17667i	−0.313359	+	0.234577i	−0.744367	−	0.667770i	$-0.767249\pi$
$487$	−6.91522	+	5.17667i	−0.313359	+	0.234577i	0.431009	+	0.902348i	$0.358158\pi$
$488$	4.67485	−	1.74363i	0.211621	−	0.0789304i
$489$	−42.4474	+	6.10302i	−1.91954	+	0.275988i
$490$	14.1373	+	0.977966i	0.638656	+	0.0441800i
$491$	17.5085	−	11.2520i	0.790149	−	0.507798i	−0.0822389	−	0.996613i	$-0.526207\pi$
$491$	17.5085	−	11.2520i	0.790149	−	0.507798i	0.872387	+	0.488815i	$0.162571\pi$
$492$	0.152945	−	0.410061i	0.00689528	−	0.0184870i
$493$	8.76732	+	4.78732i	0.394860	+	0.215610i
$494$	−8.34462	+	9.63020i	−0.375442	+	0.433283i
$495$	0.899771	−	0.266479i	0.0404417	−	0.0119773i
$496$	−1.71716	+	0.504203i	−0.0771026	+	0.0226394i
$497$	−6.08408	−	2.26925i	−0.272908	−	0.101790i
$498$	−2.30307	−	0.501003i	−0.103203	−	0.0224505i
$499$	−7.13127	+	24.2869i	−0.319239	+	1.08723i	0.631019	+	0.775767i	$0.282637\pi$
$499$	−7.13127	+	24.2869i	−0.319239	+	1.08723i	−0.950259	+	0.311462i	$0.899181\pi$
$500$	0.0782621	+	11.1801i	0.00349999	+	0.499988i
$501$	18.1009	−	39.6355i	0.808690	−	1.77078i
$502$	−5.49373	−	7.33877i	−0.245197	−	0.327545i
$503$	7.11973	+	32.7289i	0.317453	+	1.45931i	0.808665	+	0.588269i	$0.200190\pi$
$503$	7.11973	+	32.7289i	0.317453	+	1.45931i	−0.491212	+	0.871040i	$0.663446\pi$
$504$	−0.743088	−	0.857569i	−0.0330998	−	0.0381992i
$505$	−0.0802373	−	0.0513012i	−0.00357051	−	0.00228287i
$506$	0.352776	−	1.39993i	0.0156828	−	0.0622345i
$507$	10.2396	+	10.2396i	0.454756	+	0.454756i
$508$	−5.83366	−	0.417232i	−0.258827	−	0.0185117i
$509$	−0.0394504	+	0.0613860i	−0.00174861	+	0.00272089i	−0.842127	−	0.539280i	$-0.818697\pi$
$509$	−0.0394504	+	0.0613860i	−0.00174861	+	0.00272089i	0.840378	+	0.542001i	$0.182333\pi$
$510$	1.34492	+	18.2073i	0.0595540	+	0.806232i
$511$	3.59795	+	1.64313i	0.159164	+	0.0726877i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	−8.32912	−	15.2536i	−0.367740	−	0.673465i
$514$	−12.4501	−	19.3728i	−0.549153	−	0.854498i
$515$	23.0531	−	17.3414i	1.01584	−	0.764154i
$516$	6.07194	+	20.6791i	0.267302	+	0.910347i
$517$	0.253167	+	3.53973i	0.0111343	+	0.155677i
$518$	−0.0427453	−	0.597658i	−0.00187812	−	0.0262596i
$519$	10.2116	+	34.7776i	0.448241	+	1.52657i
$520$	−5.46462	−	0.772684i	−0.239640	−	0.0338844i
$521$	21.5883	+	33.5921i	0.945801	+	1.47170i	0.880621	+	0.473822i	$0.157126\pi$
$521$	21.5883	+	33.5921i	0.945801	+	1.47170i	0.0651807	+	0.997873i	$0.479238\pi$
$522$	1.71348	+	3.13800i	0.0749969	+	0.137347i
$523$	−16.1411	+	21.5620i	−0.705802	+	0.942841i	−0.999916	−	0.0129296i	$-0.995884\pi$
$523$	−16.1411	+	21.5620i	−0.705802	+	0.942841i	0.294115	+	0.955770i	$0.404975\pi$
$524$	4.88705	+	2.23184i	0.213492	+	0.0974985i
$525$	2.44165	+	8.17419i	0.106562	+	0.356751i
$526$	7.85311	−	12.2197i	0.342412	−	0.532803i
$527$	6.95292	+	0.497282i	0.302874	+	0.0216620i
$528$	0.446202	+	0.446202i	0.0194184	+	0.0194184i
$529$	10.8996	−	20.2533i	0.473897	−	0.880580i
$530$	11.0555	−	17.2912i	0.480218	−	0.751082i
$531$	0.852850	+	0.984241i	0.0370105	+	0.0427124i
$532$	0.893253	+	4.10622i	0.0387274	+	0.178027i
$533$	−0.308816	−	0.412529i	−0.0133763	−	0.0178686i
$534$	−11.8978	+	26.0526i	−0.514869	+	1.12741i
$535$	−9.04050	−	24.0669i	−0.390855	−	1.04050i
$536$	−2.78801	+	9.49510i	−0.120424	+	0.410126i
$537$	33.5783	+	7.30450i	1.44901	+	0.315213i
$538$	−13.5419	−	5.05086i	−0.583832	−	0.217758i
$539$	−1.83050	+	0.537484i	−0.0788453	+	0.0231511i
$540$	3.59203	−	6.61495i	0.154576	−	0.284662i
$541$	12.2196	−	14.1021i	0.525360	−	0.606298i	−0.429605	−	0.903017i	$-0.641347\pi$
$541$	12.2196	−	14.1021i	0.525360	−	0.606298i	0.954965	+	0.296719i	$0.0958926\pi$
$542$	19.2284	+	10.4995i	0.825929	+	0.450992i
$543$	−9.54008	+	25.5779i	−0.409404	+	1.09765i
$544$	−3.27668	+	2.10579i	−0.140486	+	0.0902851i
$545$	−25.6876	−	29.5057i	−1.10034	−	1.26389i
$546$	−4.16835	+	0.599318i	−0.178389	+	0.0256484i
$547$	−35.9612	+	13.4128i	−1.53759	+	0.573491i	−0.968550	−	0.248820i	$-0.919957\pi$
$547$	−35.9612	+	13.4128i	−1.53759	+	0.573491i	−0.569039	+	0.822311i	$0.692685\pi$
$548$	−0.650220	+	0.486749i	−0.0277760	+	0.0207929i
$549$	−5.85155	−	3.76056i	−0.249738	−	0.160497i
$550$	−0.532573	−	1.40779i	−0.0227090	−	0.0600282i
$551$		−	13.2406i		−	0.564069i
$552$	5.15607	+	8.63013i	0.219457	+	0.367323i
$553$	6.78547	−	6.78547i	0.288548	−	0.288548i
$554$	13.5383	−	11.7310i	0.575186	−	0.498401i
$555$	−3.13533	+	1.44071i	−0.133087	+	0.0611547i
$556$	1.38661	−	9.64410i	0.0588055	−	0.409001i
$557$	−5.09024	−	13.6475i	−0.215680	−	0.578261i	0.783383	−	0.621540i	$-0.213493\pi$
$557$	−5.09024	−	13.6475i	−0.215680	−	0.578261i	−0.999063	+	0.0432783i	$0.986220\pi$
$558$	1.99731	+	1.49516i	0.0845527	+	0.0632953i
$559$	24.3484	+	7.14935i	1.02983	+	0.302385i
$560$	−1.28396	+	1.28997i	−0.0542574	+	0.0545112i
$561$	−1.02102	−	2.23573i	−0.0431076	−	0.0943925i
$562$	−6.00890	+	11.0045i	−0.253470	+	0.464196i
$563$	15.9899	−	1.14362i	0.673892	−	0.0481977i	0.269801	−	0.962916i	$-0.413042\pi$
$563$	15.9899	−	1.14362i	0.673892	−	0.0481977i	0.404092	+	0.914718i	$0.367588\pi$
$564$	−18.6758	−	16.1827i	−0.786394	−	0.681414i
$565$	−9.32394	−	16.9812i	−0.392261	−	0.714405i
$566$	1.97680	−	0.902773i	0.0830910	−	0.0379464i
$567$	1.94451	−	8.93877i	0.0816617	−	0.375393i
$568$	−7.00190	+	3.82333i	−0.293793	+	0.160423i
$569$	2.29829	+	15.9849i	0.0963492	+	0.670124i	0.979561	+	0.201149i	$0.0644674\pi$
$569$	2.29829	+	15.9849i	0.0963492	+	0.670124i	−0.883211	+	0.468975i	$0.844623\pi$
$570$	20.3272	−	13.1306i	0.851413	−	0.549981i
$571$	19.1922	+	2.75942i	0.803169	+	0.115478i	0.531660	−	0.846958i	$-0.321568\pi$
$571$	19.1922	+	2.75942i	0.803169	+	0.115478i	0.271509	+	0.962436i	$0.412477\pi$
$572$	0.726014	−	0.157935i	0.0303562	−	0.00660358i
$573$	−1.34369	+	18.7873i	−0.0561335	+	0.784849i
$574$	−0.169940			−0.00709316
$575$	−2.74701	−	23.8213i	−0.114558	−	0.993417i
$576$	−1.39410			−0.0580873
$577$	−1.21051	+	16.9251i	−0.0503940	+	0.704600i	0.907967	+	0.419041i	$0.137634\pi$
$577$	−1.21051	+	16.9251i	−0.0503940	+	0.704600i	−0.958361	+	0.285559i	$0.907821\pi$
$578$	−1.78722	+	0.388785i	−0.0743384	+	0.0161713i
$579$	−37.6215	−	5.40915i	−1.56350	−	0.224797i
$580$	4.81708	−	3.11165i	0.200018	−	0.129204i
$581$	0.130245	+	0.905876i	0.00540349	+	0.0375821i
$582$	−22.5048	+	12.2885i	−0.932852	+	0.509376i
$583$	−0.587310	+	2.69982i	−0.0243239	+	0.111815i
$584$	4.42035	−	2.01871i	0.182915	−	0.0835346i
$585$	3.70308	+	6.74423i	0.153104	+	0.278840i
$586$	18.0203	+	15.6147i	0.744412	+	0.645037i
$587$	28.3976	−	2.03104i	1.17210	−	0.0838300i	0.528321	−	0.849045i	$-0.322822\pi$
$587$	28.3976	−	2.03104i	1.17210	−	0.0838300i	0.643775	+	0.765215i	$0.277367\pi$
$588$	6.36668	−	11.6597i	0.262557	−	0.480838i
$589$	−3.83826	−	8.40461i	−0.158153	−	0.346306i
$590$	1.47362	−	1.48051i	0.0606679	−	0.0609517i
$591$	30.7304	+	9.02327i	1.26408	+	0.371168i
$592$	−0.589313	−	0.441154i	−0.0242206	−	0.0181313i
$593$	−4.97613	−	13.3415i	−0.204345	−	0.547870i	0.793838	−	0.608130i	$-0.208080\pi$
$593$	−4.97613	−	13.3415i	−0.204345	−	0.547870i	−0.998183	+	0.0602595i	$0.980807\pi$
$594$	−0.144217	+	1.00305i	−0.00591729	+	0.0411556i
$595$	6.44157	−	2.95995i	0.264079	−	0.121346i
$596$	4.17702	−	3.61941i	0.171097	−	0.148257i
$597$	−14.5944	+	14.5944i	−0.597309	+	0.597309i
$598$	11.8306	+	0.386479i	0.483789	+	0.0158043i
$599$		−	43.8086i		−	1.78997i	−0.446095	−	0.894986i	$-0.647186\pi$
$599$		−	43.8086i		−	1.78997i	0.446095	−	0.894986i	$-0.352814\pi$
$600$	9.55411	+	4.30945i	0.390045	+	0.175932i
$601$	−8.35808	−	5.37141i	−0.340933	−	0.219105i	0.358958	−	0.933354i	$-0.383132\pi$
$601$	−8.35808	−	5.37141i	−0.340933	−	0.219105i	−0.699892	+	0.714249i	$0.746768\pi$
$602$	6.69943	−	5.01513i	0.273048	−	0.204401i
$603$	12.9261	−	4.82118i	0.526391	−	0.196334i
$604$	−9.17724	+	1.31949i	−0.373417	+	0.0536892i
$605$	−16.0177	−	18.3985i	−0.651213	−	0.748006i
$606$	−0.0751063	+	0.0482679i	−0.00305099	+	0.00196075i
$607$	8.43382	−	22.6120i	0.342318	−	0.917791i	−0.645719	−	0.763575i	$-0.723442\pi$
$607$	8.43382	−	22.6120i	0.342318	−	0.917791i	0.988037	−	0.154216i	$-0.0492850\pi$
$608$	4.53126	+	2.47426i	0.183767	+	0.100344i
$609$	2.86554	−	3.30701i	0.116118	−	0.134007i
$610$	−5.32398	+	9.80447i	−0.215562	+	0.396971i
$611$	−27.9179	+	8.19743i	−1.12944	+	0.331633i
$612$	5.08764	+	1.89759i	0.205655	+	0.0767055i
$613$	25.6187	+	5.57300i	1.03473	+	0.225091i	0.697690	−	0.716400i	$-0.254211\pi$
$613$	25.6187	+	5.57300i	1.03473	+	0.225091i	0.337038	+	0.941491i	$0.390575\pi$
$614$	−7.68195	+	26.1623i	−0.310018	+	1.05583i
$615$	0.344134	+	0.916124i	0.0138768	+	0.0369417i
$616$	0.101787	−	0.222882i	0.00410111	−	0.00898018i
$617$	1.22708	+	1.63919i	0.0494004	+	0.0659912i	0.824561	−	0.565773i	$-0.191422\pi$
$617$	1.22708	+	1.63919i	0.0494004	+	0.0659912i	−0.775161	+	0.631764i	$0.782331\pi$
$618$	−5.74842	−	26.4250i	−0.231235	−	1.06297i
$619$	14.7869	+	17.0650i	0.594336	+	0.685900i	0.970624	−	0.240602i	$-0.0773450\pi$
$619$	14.7869	+	17.0650i	0.594336	+	0.685900i	−0.376288	+	0.926503i	$0.622800\pi$
$620$	2.15566	−	3.37155i	0.0865735	−	0.135405i
$621$	−6.13271	+	14.9341i	−0.246097	+	0.599284i
$622$	14.2942	+	14.2942i	0.573147	+	0.573147i
$623$	11.0928	+	0.793372i	0.444423	+	0.0317858i
$624$	−2.79716	+	4.35247i	−0.111976	+	0.174238i
$625$	−16.5471	−	18.7401i	−0.661886	−	0.749605i
$626$	7.86354	+	3.59116i	0.314290	+	0.143532i
$627$	−1.95235	+	2.60804i	−0.0779694	+	0.104155i
$628$	10.5242	+	19.2736i	0.419961	+	0.769102i
$629$	1.55016	+	2.41210i	0.0618091	+	0.0961768i
$630$	2.51234	+	0.355238i	0.100094	+	0.0141530i
$631$	1.17828	+	4.01284i	0.0469064	+	0.159749i	0.979616	−	0.200880i	$-0.0643803\pi$
$631$	1.17828	+	4.01284i	0.0469064	+	0.159749i	−0.932709	+	0.360629i	$0.882562\pi$
$632$	−0.841056	−	11.7595i	−0.0334554	−	0.467768i
$633$	1.32754	+	18.5615i	0.0527650	+	0.737751i
$634$	−7.87363	−	26.8151i	−0.312702	−	1.06496i
$635$	10.4510	−	7.86163i	0.414735	−	0.311979i
$636$	−10.4018	−	16.1855i	−0.412457	−	0.641796i
$637$	−7.49638	−	13.7286i	−0.297018	−	0.543947i
$638$	−0.462662	+	0.618044i	−0.0183170	+	0.0244686i
$639$	10.1167	+	4.62014i	0.400210	+	0.182770i
$640$	0.164723	+	2.22999i	0.00651125	+	0.0881482i
$641$	−17.2725	+	26.8765i	−0.682223	+	1.06156i	0.311561	+	0.950226i	$0.399148\pi$
$641$	−17.2725	+	26.8765i	−0.682223	+	1.06156i	−0.993783	+	0.111333i	$0.964488\pi$
$642$	−24.0394	−	1.71933i	−0.948761	−	0.0678567i
$643$	0.653134	+	0.653134i	0.0257571	+	0.0257571i	0.719868	−	0.694111i	$-0.244202\pi$
$643$	0.653134	+	0.653134i	0.0257571	+	0.0257571i	−0.694111	+	0.719868i	$0.744202\pi$
$644$	2.44011	−	3.04693i	0.0961538	−	0.120066i
$645$	−40.6024	−	25.9599i	−1.59872	−	1.02217i
$646$	−13.1686	−	15.1974i	−0.518112	−	0.597933i
$647$	−3.31706	−	15.2483i	−0.130407	−	0.599473i	−0.995244	−	0.0974185i	$-0.968941\pi$
$647$	−3.31706	−	15.2483i	−0.130407	−	0.599473i	0.864836	−	0.502054i	$-0.167422\pi$
$648$	−6.73515	−	8.99711i	−0.264582	−	0.353440i
$649$	−0.116822	+	0.255804i	−0.00458566	+	0.0100412i
$650$	10.3505	−	6.72032i	0.405980	−	0.263593i
$651$	0.860277	−	2.92983i	0.0337169	−	0.114829i
$652$	19.9903	+	4.34863i	0.782881	+	0.170305i
$653$	22.9823	+	8.57196i	0.899367	+	0.335447i	0.756268	−	0.654262i	$-0.227020\pi$
$653$	22.9823	+	8.57196i	0.899367	+	0.335447i	0.143099	+	0.989708i	$0.454293\pi$
$654$	−35.1884	+	10.3323i	−1.37598	+	0.404023i
$655$	−11.5189	+	3.41146i	−0.450079	+	0.133297i
$656$	−0.136724	+	0.157788i	−0.00533819	+	0.00616060i
$657$	−5.94592	−	3.24672i	−0.231973	−	0.126667i
$658$	−3.35327	+	8.99046i	−0.130724	+	0.350484i
$659$	25.7327	−	16.5374i	1.00241	−	0.644207i	0.0669885	−	0.997754i	$-0.478661\pi$
$659$	25.7327	−	16.5374i	1.00241	−	0.644207i	0.935417	+	0.353547i	$0.115025\pi$
$660$	−1.40765	−	0.0973763i	−0.0547927	−	0.00379037i
$661$	21.5702	−	3.10132i	0.838983	−	0.120627i	0.290589	−	0.956848i	$-0.406149\pi$
$661$	21.5702	−	3.10132i	0.838983	−	0.120627i	0.548393	+	0.836220i	$0.315240\pi$
$662$	−17.2979	+	6.45179i	−0.672303	+	0.250756i
$663$	16.1324	−	12.0766i	0.626531	−	0.469015i
$664$	0.945889	+	0.607886i	0.0367076	+	0.0235906i
$665$	−7.53542	−	5.61356i	−0.292211	−	0.217685i
$666$			1.02625i			0.0397665i
$667$	−9.55339	+	7.74669i	−0.369909	+	0.299953i
$668$	−14.6984	+	14.6984i	−0.568697	+	0.568697i
$669$	27.8417	−	24.1250i	1.07642	−	0.932725i
$670$	−9.23926	−	20.1069i	−0.356944	−	0.776796i
$671$	0.213753	−	1.48669i	0.00825186	−	0.0573929i
$672$	0.596260	+	1.59864i	0.0230012	+	0.0616687i
$673$	22.0899	+	16.5363i	0.851502	+	0.637426i	0.933250	−	0.359227i	$-0.116959\pi$
$673$	22.0899	+	16.5363i	0.851502	+	0.637426i	−0.0817484	+	0.996653i	$0.526050\pi$
$674$	18.8306	+	5.52916i	0.725328	+	0.212975i
$675$	3.65452	+	16.4300i	0.140662	+	0.632392i
$676$	−2.86976	−	6.28389i	−0.110375	−	0.241688i
$677$	5.38555	−	9.86289i	0.206983	−	0.379062i	−0.753479	−	0.657472i	$-0.771626\pi$
$677$	5.38555	−	9.86289i	0.206983	−	0.379062i	0.960462	+	0.278410i	$0.0898075\pi$
$678$	−18.1146	+	1.29558i	−0.695688	+	0.0497566i
$679$	7.52454	+	6.52005i	0.288765	+	0.250217i
$680$	2.43424	−	8.36238i	0.0933487	−	0.320683i
$681$	24.1476	−	11.0278i	0.925338	−	0.422587i
$682$	−0.114517	+	0.526428i	−0.00438510	+	0.0201580i
$683$	13.1711	−	7.19199i	0.503980	−	0.275194i	−0.207082	−	0.978324i	$-0.566397\pi$
$683$	13.1711	−	7.19199i	0.503980	−	0.275194i	0.711062	+	0.703130i	$0.248215\pi$
$684$	−1.02430	−	7.12416i	−0.0391650	−	0.272399i
$685$	0.381917	−	1.77558i	0.0145923	−	0.0678415i
$686$	−10.7456	−	1.54498i	−0.410268	−	0.0589876i
$687$	18.5769	−	4.04115i	0.708751	−	0.154179i
$688$	0.733472	−	10.2553i	0.0279634	−	0.390979i
$689$	−22.6536			−0.863034
$690$	−21.3669	−	6.98418i	−0.813422	−	0.265883i
$691$	−4.76506			−0.181272			−0.0906358	−	0.995884i	$-0.528890\pi$
$691$	−4.76506			−0.181272			−0.0906358	+	0.995884i	$0.528890\pi$
$692$	1.23353	−	17.2471i	0.0468919	−	0.655635i
$693$	−0.333782	+	0.0726098i	−0.0126793	+	0.00275822i
$694$	26.1304	+	3.75698i	0.991896	+	0.142613i
$695$	11.8215	+	18.3005i	0.448414	+	0.694179i
$696$	−0.765085	−	5.32128i	−0.0290005	−	0.201703i
$697$	0.713740	−	0.389731i	0.0270348	−	0.0147621i
$698$	4.14312	−	19.0456i	0.156819	−	0.720887i
$699$	−47.8697	+	21.8614i	−1.81060	+	0.826873i
$700$	0.271386	−	4.06070i	0.0102574	−	0.153480i
$701$	−29.3222	−	25.4078i	−1.10748	−	0.959641i	−0.108080	−	0.994142i	$-0.534470\pi$
$701$	−29.3222	−	25.4078i	−1.10748	−	0.959641i	−0.999405	+	0.0345012i	$0.989016\pi$
$702$	−8.28744	+	0.592729i	−0.312789	+	0.0223711i
$703$	1.82141	−	3.33566i	0.0686957	−	0.125807i
$704$	−0.125053	−	0.273828i	−0.00471311	−	0.0103203i
$705$	55.2568	−	0.128933i	2.08109	−	0.00485591i
$706$	−12.4399	−	3.65267i	−0.468180	−	0.137470i
$707$	0.0277522	+	0.0207750i	0.00104373	+	0.000781325i
$708$	−0.684334	−	1.83477i	−0.0257189	−	0.0689549i
$709$	−5.15863	+	35.8790i	−0.193736	+	1.34747i	0.628274	+	0.777992i	$0.283762\pi$
$709$	−5.15863	+	35.8790i	−0.193736	+	1.34747i	−0.822010	+	0.569473i	$0.807147\pi$
$710$	6.19500	−	16.7285i	0.232494	−	0.627811i
$711$	−12.4213	+	10.7631i	−0.465835	+	0.403649i
$712$	9.66129	−	9.66129i	0.362072	−	0.362072i
$713$	−3.81846	+	7.68667i	−0.143002	+	0.287868i
$714$		−	6.64569i		−	0.248709i
$715$	−0.992525	+	1.33233i	−0.0371183	+	0.0498262i
$716$	−13.7908	−	8.86283i	−0.515388	−	0.331219i
$717$	2.25751	−	1.68995i	0.0843083	−	0.0631124i
$718$	−23.5682	+	8.79050i	−0.879559	+	0.328058i
$719$	−14.2638	+	2.05083i	−0.531951	+	0.0764830i	−0.403056	−	0.915175i	$-0.632052\pi$
$719$	−14.2638	+	2.05083i	−0.531951	+	0.0764830i	−0.128895	+	0.991658i	$0.541143\pi$
$720$	2.35112	−	2.04689i	0.0876212	−	0.0762829i
$721$	−8.83378	+	5.67712i	−0.328987	+	0.211427i
$722$	−2.67491	+	7.17171i	−0.0995498	+	0.266903i
$723$	40.4897	+	22.1091i	1.50583	+	0.822245i
$724$	8.52832	−	9.84220i	0.316952	−	0.365783i
$725$	−3.55524	+	12.3204i	−0.132038	+	0.457570i
$726$	−21.9420	+	6.44276i	−0.814345	+	0.239113i
$727$	−26.1604	−	9.75731i	−0.970234	−	0.361879i	−0.186142	−	0.982523i	$-0.559598\pi$
$727$	−26.1604	−	9.75731i	−0.970234	−	0.361879i	−0.784092	+	0.620644i	$0.786871\pi$
$728$	1.96305	+	0.427036i	0.0727556	+	0.0158270i
$729$	1.54996	−	5.27869i	0.0574060	−	0.195507i
$730$	−4.49089	+	9.89470i	−0.166215	+	0.366219i
$731$	−16.6358	+	36.4274i	−0.615298	+	1.34732i
$732$	6.26779	+	8.37279i	0.231664	+	0.309467i
$733$	−10.1349	−	46.5893i	−0.374340	−	1.72081i	−0.650329	−	0.759653i	$-0.725369\pi$
$733$	−10.1349	−	46.5893i	−0.374340	−	1.72081i	0.275989	−	0.961161i	$-0.410995\pi$
$734$	−2.53309	−	2.92335i	−0.0934982	−	0.107903i
$735$	6.38207	+	29.0118i	0.235406	+	1.07012i
$736$	−0.865877	−	4.71702i	−0.0319166	−	0.173872i
$737$	2.10647	+	2.10647i	0.0775927	+	0.0775927i
$738$	0.290323	+	0.0207643i	0.0106870	+	0.000764346i
$739$	20.0775	−	31.2412i	0.738564	−	1.14923i	−0.245150	−	0.969485i	$-0.578837\pi$
$739$	20.0775	−	31.2412i	0.738564	−	1.14923i	0.983714	−	0.179742i	$-0.0575264\pi$
$740$	1.64159	−	0.121260i	0.0603461	−	0.00445759i
$741$	−24.2973	−	11.0962i	−0.892584	−	0.407629i
$742$	−4.47703	+	5.98062i	−0.164357	+	0.219555i
$743$	0.539228	+	0.987522i	0.0197824	+	0.0362287i	0.887383	−	0.461033i	$-0.152521\pi$
$743$	0.539228	+	0.987522i	0.0197824	+	0.0362287i	−0.867601	+	0.497261i	$0.834339\pi$
$744$	−2.02820	−	3.15595i	−0.0743576	−	0.115703i
$745$	−1.73028	+	12.2370i	−0.0633926	+	0.448329i
$746$	−3.60640	−	12.2823i	−0.132040	−	0.449686i
$747$	−0.111824	−	1.56350i	−0.00409142	−	0.0572055i
$748$	0.0836462	+	1.16953i	0.00305841	+	0.0427621i
$749$	2.63653	+	8.97920i	0.0963367	+	0.328093i
$750$	−22.4402	+	6.76003i	−0.819401	+	0.246841i
$751$	−13.0237	−	20.2653i	−0.475243	−	0.739492i	0.518021	−	0.855368i	$-0.326669\pi$
$751$	−13.0237	−	20.2653i	−0.475243	−	0.739492i	−0.993264	+	0.115876i	$0.963033\pi$
$752$	5.64974	+	10.3467i	0.206025	+	0.377306i
$753$	11.5160	−	15.3836i	0.419667	−	0.560609i
$754$	−5.75790	−	2.62954i	−0.209690	−	0.0957624i
$755$	13.5399	−	15.6998i	0.492769	−	0.571374i
$756$	−1.48136	+	2.30505i	−0.0538767	+	0.0838337i
$757$	−28.1278	−	2.01174i	−1.02232	−	0.0731179i	−0.449901	−	0.893078i	$-0.648541\pi$
$757$	−28.1278	−	2.01174i	−1.02232	−	0.0731179i	−0.572420	+	0.819960i	$0.693995\pi$
$758$	−8.49345	−	8.49345i	−0.308496	−	0.308496i
$759$	3.02402	−	0.117220i	0.109765	−	0.00425482i
$760$	−11.2748	+	2.48024i	−0.408978	+	0.0899677i
$761$	28.1673	+	32.5067i	1.02106	+	1.17837i	0.983838	+	0.179062i	$0.0573062\pi$
$761$	28.1673	+	32.5067i	1.02106	+	1.17837i	0.0372245	+	0.999307i	$0.488148\pi$
$762$	−2.60601	−	11.9796i	−0.0944059	−	0.433977i
$763$	8.53395	+	11.4000i	0.308950	+	0.412709i
$764$	3.73266	−	8.17339i	0.135043	−	0.295703i
$765$	−11.3664	+	4.26967i	−0.410952	+	0.154370i
$766$	−1.60999	+	5.48312i	−0.0581713	+	0.198113i
$767$	−2.25302	−	0.490114i	−0.0813517	−	0.0176970i
$768$	1.96404	+	0.732550i	0.0708713	+	0.0264336i
$769$	−8.04491	+	2.36220i	−0.290107	+	0.0851830i	−0.423548	−	0.905874i	$-0.639215\pi$
$769$	−8.04491	+	2.36220i	−0.290107	+	0.0851830i	0.133441	+	0.991057i	$0.457397\pi$
$770$	0.155585	+	0.525337i	0.00560690	+	0.0189318i
$771$	31.6118	−	36.4820i	1.13847	−	1.31387i
$772$	15.9140	+	8.68972i	0.572758	+	0.312750i
$773$	16.5185	−	44.2879i	0.594131	−	1.59293i	−0.196413	−	0.980521i	$-0.562929\pi$
$773$	16.5185	−	44.2879i	0.594131	−	1.59293i	0.790544	−	0.612405i	$-0.209798\pi$
$774$	−12.0580	+	7.74920i	−0.433416	+	0.278539i
$775$	1.31479	+	8.85113i	0.0472286	+	0.317942i
$776$	12.1077	−	1.74082i	0.434640	−	0.0624918i
$777$	1.17682	−	0.438933i	0.0422183	−	0.0157466i
$778$	28.7891	−	21.5513i	1.03214	−	0.772651i
$779$	−0.906793	−	0.582760i	−0.0324892	−	0.0208796i
$780$	−1.67315	−	11.4473i	−0.0599083	−	0.409880i
$781$			2.40155i			0.0859342i
$782$	−3.26068	+	18.3929i	−0.116602	+	0.657731i
$783$	6.10469	−	6.10469i	0.218164	−	0.218164i
$784$	−4.78955	+	4.15017i	−0.171055	+	0.148220i
$785$	−46.0475	−	17.0525i	−1.64350	−	0.608631i
$786$	−1.60275	+	11.1474i	−0.0571683	+	0.397614i
$787$	11.4394	+	30.6702i	0.407771	+	1.09328i	0.964847	+	0.262814i	$0.0846506\pi$
$787$	11.4394	+	30.6702i	0.407771	+	1.09328i	−0.557076	+	0.830462i	$0.688077\pi$
$788$	−12.2314	−	9.15631i	−0.435725	−	0.326180i
$789$	29.2152	+	8.57837i	1.04009	+	0.305398i
$790$	18.6843	+	18.5973i	0.664759	+	0.661664i
$791$	2.92943	+	6.41456i	0.104159	+	0.228075i
$792$	−0.201125	+	0.368332i	−0.00714665	+	0.0130881i
$793$	12.2834	−	0.878524i	0.436195	−	0.0311973i
$794$	23.5709	+	20.4243i	0.836499	+	0.724830i
$795$	41.3068	+	12.0242i	1.46500	+	0.426453i
$796$	8.95637	−	4.09024i	0.317450	−	0.144975i
$797$	0.716161	−	3.29214i	0.0253677	−	0.116613i	−0.962722	−	0.270493i	$-0.912813\pi$
$797$	0.716161	−	3.29214i	0.0253677	−	0.116613i	0.988090	+	0.153880i	$0.0491769\pi$
$798$	−7.73130	+	4.22161i	−0.273685	+	0.149443i
$799$	−6.53467	−	45.4497i	−0.231180	−	1.60789i
$800$	−3.55199	−	3.51900i	−0.125582	−	0.124415i
$801$	−18.8538	−	2.71077i	−0.666168	−	0.0957805i
$802$	−31.0188	+	6.74773i	−1.09531	+	0.238271i
$803$	0.104359	−	1.45913i	0.00368275	−	0.0514916i
$804$	−20.7440			−0.731585
$805$	0.358446	+	8.72129i	0.0126336	+	0.307385i
$806$	−4.41715			−0.155587
$807$	2.16135	−	30.2197i	0.0760832	−	1.06378i
$808$	0.0416174	−	0.00905330i	0.00146409	−	0.000318494i
$809$	10.9616	+	1.57605i	0.385391	+	0.0554108i	0.332287	−	0.943178i	$-0.392180\pi$
$809$	10.9616	+	1.57605i	0.385391	+	0.0554108i	0.0531033	+	0.998589i	$0.483089\pi$
$810$	24.5688	+	5.28460i	0.863259	+	0.185682i
$811$	−2.55531	−	17.7726i	−0.0897291	−	0.624080i	−0.984214	−	0.176982i	$-0.943367\pi$
$811$	−2.55531	−	17.7726i	−0.0897291	−	0.624080i	0.894485	−	0.447098i	$-0.147542\pi$
$812$	−1.83214	+	1.00042i	−0.0642955	+	0.0351080i
$813$	−9.76189	+	44.8747i	−0.342364	+	1.57382i
$814$	−0.201576	+	0.0920567i	−0.00706524	+	0.00322659i
$815$	−40.0983	+	22.0169i	−1.40458	+	0.771219i
$816$	−6.17049	−	5.34676i	−0.216010	−	0.187174i
$817$	52.9458	−	3.78676i	1.85234	−	0.132482i
$818$	16.6791	−	30.5455i	0.583170	−	1.06800i
$819$	−1.16345	−	2.54760i	−0.0406542	−	0.0890203i
$820$	−0.00108933	−	0.466854i	−3.80412e−5	−	0.0163032i
$821$	6.16076	+	1.80896i	0.215012	+	0.0631332i	0.387464	−	0.921885i	$-0.373351\pi$
$821$	6.16076	+	1.80896i	0.215012	+	0.0631332i	−0.172453	+	0.985018i	$0.555169\pi$
$822$	−1.36300	−	1.02033i	−0.0475400	−	0.0355880i
$823$	−13.1639	−	35.2937i	−0.458864	−	1.23026i	−0.936177	−	0.351529i	$-0.885662\pi$
$823$	−13.1639	−	35.2937i	−0.458864	−	1.23026i	0.477313	−	0.878733i	$-0.341611\pi$
$824$	−1.83599	+	12.7696i	−0.0639599	+	0.444851i
$825$	2.51695	−	1.90256i	0.0876291	−	0.0662387i
$826$	−0.574655	+	0.497941i	−0.0199948	+	0.0173256i
$827$	−16.4514	+	16.4514i	−0.572070	+	0.572070i	−0.932706	−	0.360636i	$-0.882560\pi$
$827$	−16.4514	+	16.4514i	−0.572070	+	0.572070i	0.360636	+	0.932706i	$0.382560\pi$
$828$	−4.54094	+	4.90718i	−0.157809	+	0.170536i
$829$			13.5903i			0.472010i	0.971752	+	0.236005i	$0.0758381\pi$
$829$			13.5903i			0.472010i	−0.971752	+	0.236005i	$0.924162\pi$
$830$	−2.48776	+	0.363613i	−0.0863514	+	0.0126212i
$831$	31.5898	+	20.3015i	1.09584	+	0.704252i
$832$	1.97587	−	1.47912i	0.0685008	−	0.0512791i
$833$	23.1281	−	8.62634i	0.801341	−	0.298885i
$834$	20.2161	−	2.90663i	0.700025	−	0.100648i
$835$	3.20768	−	46.3695i	0.111006	−	1.60468i
$836$	1.30744	−	0.840241i	0.0452188	−	0.0290604i
$837$	2.10535	−	5.64467i	0.0727716	−	0.195108i
$838$	−3.45372	−	1.88587i	−0.119307	−	0.0651464i
$839$	−11.9659	+	13.8094i	−0.413108	+	0.476752i	−0.923725	−	0.383056i	$-0.874872\pi$
$839$	−11.9659	+	13.8094i	−0.413108	+	0.476752i	0.510617	+	0.859808i	$0.329417\pi$
$840$	−3.35279	−	1.82062i	−0.115682	−	0.0628172i
$841$	−21.5144	+	6.31720i	−0.741876	+	0.217834i
$842$	8.51611	+	3.17635i	0.293485	+	0.109464i
$843$	−25.6820	−	5.58677i	−0.884534	−	0.192419i
$844$	2.50105	−	8.51779i	0.0860896	−	0.293194i
$845$	14.0661	+	6.38417i	0.483890	+	0.219622i
$846$	6.82719	−	14.9495i	0.234724	−	0.513973i
$847$	5.32141	+	7.10857i	0.182846	+	0.244253i
$848$	1.95100	+	8.96858i	0.0669974	+	0.307982i
$849$	2.98319	+	3.44278i	0.102383	+	0.118156i
$850$	8.17278	+	17.6771i	0.280324	+	0.606320i
$851$	−3.47240	+	0.637409i	−0.119032	+	0.0218501i
$852$	−11.8250	−	11.8250i	−0.405117	−	0.405117i
$853$	25.8828	+	1.85118i	0.886211	+	0.0633830i	0.507019	−	0.861935i	$-0.330747\pi$
$853$	25.8828	+	1.85118i	0.886211	+	0.0633830i	0.379192	+	0.925318i	$0.376202\pi$
$854$	2.19563	−	3.41646i	0.0751328	−	0.116909i
$855$	12.1875	+	10.5109i	0.416805	+	0.359464i
$856$	10.4583	+	4.77617i	0.357459	+	0.163246i
$857$	−1.84664	+	2.46683i	−0.0630801	+	0.0842652i	−0.830972	−	0.556315i	$-0.812215\pi$
$857$	−1.84664	+	2.46683i	−0.0630801	+	0.0842652i	0.767892	+	0.640580i	$0.221306\pi$
$858$	0.746417	+	1.36696i	0.0254822	+	0.0466672i
$859$	17.7335	+	27.5938i	0.605058	+	0.941488i	0.999743	+	0.0226719i	$0.00721731\pi$
$859$	17.7335	+	27.5938i	0.605058	+	0.941488i	−0.394685	+	0.918816i	$0.629146\pi$
$860$	13.8203	+	18.3723i	0.471270	+	0.626490i
$861$	−0.100362	−	0.341800i	−0.00342031	−	0.0116485i
$862$	−0.685407	−	9.58324i	−0.0233450	−	0.326406i
$863$	0.0537695	+	0.751796i	0.00183034	+	0.0255914i	0.998285	−	0.0585376i	$-0.0186438\pi$
$863$	0.0537695	+	0.751796i	0.00183034	+	0.0255914i	−0.996455	+	0.0841290i	$0.973189\pi$
$864$	0.948399	+	3.22995i	0.0322652	+	0.109885i
$865$	23.2427	+	30.8981i	0.790275	+	1.05057i
$866$	−3.02093	−	4.70066i	−0.102655	−	0.159735i
$867$	−1.83744	−	3.36502i	−0.0624028	−	0.114282i
$868$	−0.872960	+	1.16614i	−0.0296302	+	0.0395813i
$869$	−3.22830	−	1.47431i	−0.109513	−	0.0500127i
$870$	9.10329	+	7.85093i	0.308630	+	0.266171i
$871$	−13.2051	+	20.5475i	−0.447437	+	0.696225i
$872$	17.4508	+	1.24811i	0.590959	+	0.0422662i
$873$	−12.0582	−	12.0582i	−0.408107	−	0.408107i
$874$	23.4689	−	7.89061i	0.793846	−	0.266904i
$875$	5.50444	+	7.24677i	0.186084	+	0.244986i
$876$	6.67075	+	7.69845i	0.225384	+	0.260107i
$877$	−1.34970	−	6.20445i	−0.0455760	−	0.209509i	0.948728	−	0.316095i	$-0.102372\pi$
$877$	−1.34970	−	6.20445i	−0.0455760	−	0.209509i	−0.994304	+	0.106586i	$0.966008\pi$
$878$	18.1345	+	24.2249i	0.612011	+	0.817550i
$879$	−20.7635	+	45.4658i	−0.700337	+	1.53352i
$880$	0.612948	+	0.278197i	0.0206625	+	0.00937803i
$881$	−11.3154	+	38.5366i	−0.381224	+	1.29833i	0.515937	+	0.856627i	$0.327444\pi$
$881$	−11.3154	+	38.5366i	−0.381224	+	1.29833i	−0.897161	+	0.441704i	$0.854374\pi$
$882$	8.63315	+	1.87803i	0.290693	+	0.0632365i
$883$	−51.3273	−	19.1441i	−1.72730	−	0.644250i	−0.728148	−	0.685420i	$-0.759619\pi$
$883$	−51.3273	−	19.1441i	−1.72730	−	0.644250i	−0.999152	+	0.0411700i	$0.986891\pi$
$884$	−9.22407	+	2.70843i	−0.310239	+	0.0910944i
$885$	3.84803	+	2.08954i	0.129350	+	0.0702391i
$886$	8.91534	−	10.2889i	0.299517	−	0.345661i
$887$	−21.9292	−	11.9742i	−0.736310	−	0.402056i	0.0668936	−	0.997760i	$-0.478691\pi$
$887$	−21.9292	−	11.9742i	−0.736310	−	0.402056i	−0.803204	+	0.595704i	$0.796873\pi$
$888$	0.539262	−	1.44582i	0.0180964	−	0.0485184i
$889$	−4.00474	+	2.57369i	−0.134315	+	0.0863189i
$890$	−2.10842	+	30.4788i	−0.0706744	+	1.02165i
$891$	−3.34879	+	0.481483i	−0.112189	+	0.0161303i
$892$	−16.4664	+	6.14166i	−0.551337	+	0.205638i
$893$	−48.7230	+	36.4736i	−1.63045	+	1.22054i
$894$	9.74653	+	6.26372i	0.325973	+	0.209490i
$895$	36.2709	−	5.30138i	1.21240	−	0.177206i
$896$		−	0.813951i		−	0.0271922i
$897$	6.20947	+	24.0231i	0.207328	+	0.802107i
$898$	−28.3007	+	28.3007i	−0.944407	+	0.944407i
$899$	3.46873	−	3.00567i	0.115689	−	0.100245i
$900$	−0.959794	+	6.90409i	−0.0319931	+	0.230136i
$901$	5.08769	−	35.3857i	0.169496	−	1.17887i
$902$	0.0219640	+	0.0588878i	0.000731321	+	0.00196075i
$903$	14.0434	+	10.5128i	0.467335	+	0.349843i
$904$	8.31274	+	2.44084i	0.276478	+	0.0811812i
$905$	0.0679482	+	29.1205i	0.00225867	+	0.967997i
$906$	−8.07369	−	17.6789i	−0.268230	−	0.587343i
$907$	3.20017	−	5.86067i	0.106260	−	0.194600i	−0.819139	−	0.573595i	$-0.805548\pi$
$907$	3.20017	−	5.86067i	0.106260	−	0.194600i	0.925399	+	0.378995i	$0.123730\pi$
$908$	−12.6318	+	0.903444i	−0.419201	+	0.0299818i
$909$	−0.0448730	−	0.0388827i	−0.00148834	−	0.00128966i
$910$	−3.93766	+	2.16207i	−0.130532	+	0.0716718i
$911$	8.83434	−	4.03451i	0.292695	−	0.133669i	−0.263656	−	0.964617i	$-0.584928\pi$
$911$	8.83434	−	4.03451i	0.292695	−	0.133669i	0.556351	+	0.830948i	$0.312201\pi$
$912$	−2.30044	+	10.5750i	−0.0761752	+	0.350172i
$913$	0.297071	−	0.162213i	0.00983162	−	0.00536847i
$914$	−0.693178	−	4.82116i	−0.0229283	−	0.159470i
$915$	−22.8639	−	4.91789i	−0.755857	−	0.162580i
$916$	−8.97707	−	1.29071i	−0.296611	−	0.0426462i
$917$	4.27307	−	0.929549i	0.141109	−	0.0306964i
$918$	0.935383	−	13.0784i	0.0308722	−	0.431650i
$919$	−33.7587			−1.11360			−0.556799	−	0.830647i	$-0.687971\pi$
$919$	−33.7587			−1.11360			−0.556799	+	0.830647i	$0.687971\pi$
$920$	8.38606	+	6.68386i	0.276480	+	0.220360i
$921$	−57.1570			−1.88339
$922$	0.499252	−	6.98046i	0.0164420	−	0.229889i
$923$	−19.2404	+	4.18549i	−0.633305	+	0.137767i
$924$	0.508395	+	0.0730962i	0.0167250	+	0.00240469i
$925$	−2.59048	+	2.61477i	−0.0851746	+	0.0859733i
$926$	3.91179	+	27.2071i	0.128549	+	0.894080i
$927$	15.7852	−	8.61936i	0.518453	−	0.283097i
$928$	−0.545151	+	2.50602i	−0.0178955	+	0.0822641i
$929$	−21.4577	+	9.79942i	−0.704006	+	0.321509i	−0.735053	−	0.678009i	$-0.762843\pi$
$929$	−21.4577	+	9.79942i	−0.704006	+	0.321509i	0.0310477	+	0.999518i	$0.490116\pi$
$930$	8.05426	+	2.34455i	0.264110	+	0.0768807i
$931$	−24.7274	−	21.4264i	−0.810408	−	0.702222i
$932$	25.0411	−	1.79097i	0.820247	−	0.0586652i
$933$	−20.3082	+	37.1918i	−0.664862	+	1.21760i
$934$	6.07036	+	13.2922i	0.198628	+	0.434935i
$935$	−1.85823	−	1.84958i	−0.0607706	−	0.0604877i
$936$	−3.30148	−	0.969401i	−0.107912	−	0.0316859i
$937$	−25.0577	−	18.7580i	−0.818599	−	0.612796i	0.105729	−	0.994395i	$-0.466283\pi$
$937$	−25.0577	−	18.7580i	−0.818599	−	0.612796i	−0.924328	+	0.381599i	$0.875373\pi$
$938$	2.81487	+	7.54697i	0.0919089	+	0.246417i
$939$	−2.57892	+	17.9368i	−0.0841598	+	0.585344i
$940$	−24.7198	−	9.15436i	−0.806271	−	0.298582i
$941$	−16.3451	+	14.1631i	−0.532836	+	0.461705i	−0.879239	−	0.476381i	$-0.841948\pi$
$941$	−16.3451	+	14.1631i	−0.532836	+	0.461705i	0.346403	+	0.938086i	$0.387403\pi$
$942$	−32.5497	+	32.5497i	−1.06053	+	1.06053i
$943$	0.110063	+	0.995226i	0.00358415	+	0.0324090i
$944$			0.934181i			0.0304050i
$945$	−0.886091	−	6.06244i	−0.0288245	−	0.197211i
$946$	−2.60372	−	1.67331i	−0.0846541	−	0.0544039i
$947$	6.04113	−	4.52233i	0.196310	−	0.146956i	−0.496601	−	0.867979i	$-0.665419\pi$
$947$	6.04113	−	4.52233i	0.196310	−	0.146956i	0.692911	+	0.721023i	$0.256328\pi$
$948$	23.1552	−	8.63643i	0.752044	−	0.280498i
$949$	11.8719	−	1.70693i	0.385379	−	0.0554092i
$950$	15.3731	−	20.7371i	0.498769	−	0.672799i
$951$	49.2833	−	31.6724i	1.59812	−	1.02705i
$952$	−1.10792	+	2.97045i	−0.0359079	+	0.0962727i
$953$	−49.9461	−	27.2726i	−1.61791	−	0.883448i	−0.994859	−	0.101270i	$-0.967710\pi$
$953$	−49.9461	−	27.2726i	−1.61791	−	0.883448i	−0.623055	−	0.782178i	$-0.714109\pi$
$954$	8.37926	−	9.67018i	0.271288	−	0.313084i
$955$	5.70552	+	19.2648i	0.184626	+	0.623394i
$956$	−1.29078	+	0.379008i	−0.0417469	+	0.0122580i
$957$	−1.51631	−	0.565553i	−0.0490152	−	0.0182817i
$958$	14.3822	+	3.12867i	0.464669	+	0.101083i
$959$	−0.186257	+	0.634333i	−0.00601455	+	0.0204837i
$960$	−4.38790	+	1.64828i	−0.141619	+	0.0531979i
$961$	−11.5474	+	25.2852i	−0.372495	+	0.815651i
$962$	−1.08884	−	1.45452i	−0.0351056	−	0.0468956i
$963$	−3.40708	−	15.6621i	−0.109792	−	0.504704i
$964$	−14.4120	−	16.6323i	−0.464178	−	0.535691i
$965$	−39.5975	+	8.71072i	−1.27469	+	0.280408i
$966$	7.56933	+	3.10836i	0.243539	+	0.100010i
$967$	16.1247	+	16.1247i	0.518535	+	0.518535i	0.917128	−	0.398593i	$-0.130501\pi$
$967$	16.1247	+	16.1247i	0.518535	+	0.518535i	−0.398593	+	0.917128i	$0.630501\pi$
$968$	10.8816	+	0.778266i	0.349747	+	0.0250144i
$969$	22.7895	−	35.4611i	0.732103	−	1.13917i
$970$	−17.8635	+	20.7130i	−0.573561	+	0.665054i
$971$	6.79056	+	3.10114i	0.217919	+	0.0995204i	0.521384	−	0.853322i	$-0.325416\pi$
$971$	6.79056	+	3.10114i	0.217919	+	0.0995204i	−0.303464	+	0.952843i	$0.598143\pi$
$972$	8.06623	−	10.7752i	0.258724	−	0.345615i
$973$	−3.80071	−	6.96048i	−0.121845	−	0.223143i
$974$	4.67016	+	7.26690i	0.149641	+	0.232847i
$975$	19.6293	+	16.8491i	0.628640	+	0.539604i
$976$	−1.40569	−	4.78733i	−0.0449949	−	0.153239i
$977$	−0.0514210	−	0.718959i	−0.00164510	−	0.0230015i	0.996563	−	0.0828352i	$-0.0263975\pi$
$977$	−0.0514210	−	0.718959i	−0.00164510	−	0.0230015i	−0.998208	+	0.0598337i	$0.980943\pi$
$978$	3.05930	+	42.7747i	0.0978258	+	1.36778i
$979$	−1.15877	−	3.94642i	−0.0370346	−	0.126128i
$980$	1.98401	−	14.0315i	0.0633770	−	0.448219i
$981$	−13.1864	−	20.5184i	−0.421008	−	0.655102i
$982$	−9.97433	−	18.2666i	−0.318294	−	0.582911i
$983$	−25.3890	+	33.9157i	−0.809782	+	1.08174i	0.185299	+	0.982682i	$0.440674\pi$
$983$	−25.3890	+	33.9157i	−0.809782	+	1.08174i	−0.995081	+	0.0990600i	$0.968416\pi$
$984$	−0.398105	−	0.181809i	−0.0126911	−	0.00579584i
$985$	34.0718	−	2.51679i	1.08562	−	0.0801915i
$986$	5.40058	−	8.40346i	0.171989	−	0.267621i
$987$	−20.0628	−	1.43492i	−0.638607	−	0.0456741i
$988$	9.01037	+	9.01037i	0.286658	+	0.286658i
$989$	−33.7092	−	35.9860i	−1.07189	−	1.14429i
$990$	−0.201611	−	0.916489i	−0.00640761	−	0.0291279i
$991$	−12.6315	−	14.5775i	−0.401252	−	0.463070i	0.518783	−	0.854906i	$-0.326385\pi$
$991$	−12.6315	−	14.5775i	−0.401252	−	0.463070i	−0.920035	+	0.391836i	$0.871840\pi$
$992$	0.380417	+	1.74875i	0.0120783	+	0.0555229i
$993$	−23.1921	−	30.9810i	−0.735980	−	0.983154i
$994$	−2.69750	+	5.90670i	−0.0855594	+	0.187349i
$995$	−9.09929	+	20.0483i	−0.288467	+	0.635575i
$996$	−0.664026	+	2.26147i	−0.0210405	+	0.0716573i
$997$	22.3298	+	4.85755i	0.707192	+	0.153840i	0.551756	−	0.834006i	$-0.313958\pi$
$997$	22.3298	+	4.85755i	0.707192	+	0.153840i	0.155436	+	0.987846i	$0.450322\pi$
$998$	23.7162	+	8.84570i	0.750725	+	0.280006i
$999$	2.37771	−	0.698157i	0.0752273	−	0.0220887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.217.12	yes	240
5.3	odd	4	inner	230.2.l.a.33.6	yes	240
23.7	odd	22	inner	230.2.l.a.7.6	✓	240
115.53	even	44	inner	230.2.l.a.53.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.6	✓	240	23.7	odd	22	inner
230.2.l.a.33.6	yes	240	5.3	odd	4	inner
230.2.l.a.53.12	yes	240	115.53	even	44	inner
230.2.l.a.217.12	yes	240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(2.04831 - 0.445581i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.87827 - 1.21330i) q^{5} +(-0.298322 - 2.07487i) q^{6} +(-0.714388 + 0.390085i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(1.26811 - 0.579129i) q^{9} +O(q^{10})\)	\(q+(0.0713392 - 0.997452i) q^{2} +(2.04831 - 0.445581i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(1.87827 - 1.21330i) q^{5} +(-0.298322 - 2.07487i) q^{6} +(-0.714388 + 0.390085i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(1.26811 - 0.579129i) q^{9} +(-1.07621 - 1.96004i) q^{10} +(0.227504 + 0.197133i) q^{11} +(-2.09087 + 0.149542i) q^{12} +(-1.18286 + 2.16625i) q^{13} +(0.338128 + 0.740396i) q^{14} +(3.30666 - 3.32212i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-3.11810 - 2.33418i) q^{17} +(-0.487187 - 1.30620i) q^{18} +(-0.734740 + 5.11023i) q^{19} +(-2.03183 + 0.933640i) q^{20} +(-1.28947 + 1.11733i) q^{21} +(0.212861 - 0.212861i) q^{22} +(4.11702 - 2.45971i) q^{23} +2.09621i q^{24} +(2.05583 - 4.55780i) q^{25} +(2.07635 + 1.33439i) q^{26} +(-2.69487 + 2.01736i) q^{27} +(0.762632 - 0.284447i) q^{28} +(-2.53852 + 0.364985i) q^{29} +(-3.07777 - 3.53523i) q^{30} +(-1.50555 + 0.967558i) q^{31} +(0.349464 - 0.936950i) q^{32} +(0.553837 + 0.302418i) q^{33} +(-2.55068 + 2.94364i) q^{34} +(-0.868528 + 1.59945i) q^{35} +(-1.33763 + 0.392762i) q^{36} +(-0.689729 - 0.257255i) q^{37} +(5.04480 + 1.09743i) q^{38} +(-1.45762 + 4.96421i) q^{39} +(0.786312 + 2.09325i) q^{40} +(-0.0867320 + 0.189917i) q^{41} +(1.02250 + 1.36589i) q^{42} +(-2.18548 - 10.0465i) q^{43} +(-0.197133 - 0.227504i) q^{44} +(1.67921 - 2.62636i) q^{45} +(-2.15974 - 4.28200i) q^{46} +(8.33589 + 8.33589i) q^{47} +(2.09087 + 0.149542i) q^{48} +(-3.42630 + 5.33143i) q^{49} +(-4.39953 - 2.37574i) q^{50} +(-7.42690 - 3.39175i) q^{51} +(1.47912 - 1.97587i) q^{52} +(4.39871 + 8.05563i) q^{53} +(1.81997 + 2.83192i) q^{54} +(0.666496 + 0.0942409i) q^{55} +(-0.229317 - 0.780981i) q^{56} +(0.772052 + 10.7947i) q^{57} +(0.182959 + 2.55809i) q^{58} +(0.263189 + 0.896340i) q^{59} +(-3.74579 + 2.81772i) q^{60} +(-2.69749 - 4.19738i) q^{61} +(0.857688 + 1.57074i) q^{62} +(-0.680016 + 0.908396i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(0.406563 + 5.50399i) q^{65} +(0.341158 - 0.530852i) q^{66} +(9.87075 + 0.705970i) q^{67} +(2.75418 + 2.75418i) q^{68} +(7.33690 - 6.87271i) q^{69} +(1.53342 + 0.980418i) q^{70} +(5.22431 + 6.02918i) q^{71} +(0.296336 + 1.36224i) q^{72} +(-2.91218 - 3.89022i) q^{73} +(-0.305805 + 0.669619i) q^{74} +(2.18009 - 10.2518i) q^{75} +(1.45452 - 4.95365i) q^{76} +(-0.239425 - 0.0520837i) q^{77} +(4.84758 + 1.80805i) q^{78} +(-11.3120 + 3.32150i) q^{79} +(2.14402 - 0.634978i) q^{80} +(-7.35984 + 8.49371i) q^{81} +(0.183245 + 0.100060i) q^{82} +(0.392931 - 1.05349i) q^{83} +(1.43536 - 0.922448i) q^{84} +(-8.68871 - 0.601055i) q^{85} +(-10.1768 + 1.46321i) q^{86} +(-5.03704 + 1.87872i) q^{87} +(-0.240988 + 0.180401i) q^{88} +(-11.4942 - 7.38685i) q^{89} +(-2.49987 - 1.86230i) q^{90} -2.00896i q^{91} +(-4.42516 + 1.84876i) q^{92} +(-2.65270 + 2.65270i) q^{93} +(8.90933 - 7.71997i) q^{94} +(4.82018 + 10.4899i) q^{95} +(0.298322 - 2.07487i) q^{96} +(-4.27471 - 11.4609i) q^{97} +(5.07342 + 3.79791i) q^{98} +(0.402667 + 0.118234i) 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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