LMFDB - Embedded newform 475.2.j.d.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, not 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.4
Character	$\chi$	$=$	475.349
Dual form			475.2.j.d.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28275 + 0.740597i) q^{2} +(0.157277 - 0.0908038i) q^{3} +(0.0969683 - 0.167954i) q^{4} +(-0.134498 + 0.232958i) q^{6} -1.30422i q^{7} -2.67513i q^{8} +(-1.48351 + 2.56951i) q^{9} +4.98247 q^{11} -0.0352204i q^{12} +(-0.351723 - 0.203067i) q^{13} +(0.965899 + 1.67299i) q^{14} +(2.17513 + 3.76744i) q^{16} +(-2.38173 + 1.37510i) q^{17} -4.39473i q^{18} +(4.35785 - 0.0955054i) q^{19} +(-0.118428 - 0.205123i) q^{21} +(-6.39128 + 3.69001i) q^{22} +(6.02510 + 3.47860i) q^{23} +(-0.242912 - 0.420736i) q^{24} +0.601564 q^{26} +1.08366i q^{27} +(-0.219048 - 0.126468i) q^{28} +(-2.00728 + 3.47672i) q^{29} -2.57321 q^{31} +(-0.946844 - 0.546661i) q^{32} +(0.783628 - 0.452428i) q^{33} +(2.03678 - 3.52781i) q^{34} +(0.287707 + 0.498323i) q^{36} +3.71348i q^{37} +(-5.51931 + 3.34992i) q^{38} -0.0737572 q^{39} +(0.607965 + 1.05303i) q^{41} +(0.303827 + 0.175415i) q^{42} +(-2.70426 + 1.56130i) q^{43} +(0.483142 - 0.836826i) q^{44} -10.3050 q^{46} +(5.63617 + 3.25405i) q^{47} +(0.684196 + 0.395020i) q^{48} +5.29902 q^{49} +(-0.249728 + 0.432541i) q^{51} +(-0.0682119 + 0.0393822i) q^{52} +(5.47490 + 3.16094i) q^{53} +(-0.802553 - 1.39006i) q^{54} -3.48895 q^{56} +(0.676717 - 0.410731i) q^{57} -5.94636i q^{58} +(5.61636 + 9.72783i) q^{59} +(-0.467072 + 0.808992i) q^{61} +(3.30079 - 1.90571i) q^{62} +(3.35120 + 1.93482i) q^{63} -7.08110 q^{64} +(-0.670133 + 1.16071i) q^{66} +(-4.58585 - 2.64764i) q^{67} +0.533363i q^{68} +1.26348 q^{69} +(0.817659 + 1.41623i) q^{71} +(6.87378 + 3.96858i) q^{72} +(-6.65794 + 3.84396i) q^{73} +(-2.75019 - 4.76347i) q^{74} +(0.406533 - 0.741180i) q^{76} -6.49822i q^{77} +(0.0946121 - 0.0546243i) q^{78} +(-7.27699 - 12.6041i) q^{79} +(-4.35213 - 7.53811i) q^{81} +(-1.55974 - 0.900514i) q^{82} +15.2643i q^{83} -0.0459350 q^{84} +(2.31260 - 4.00553i) q^{86} +0.729076i q^{87} -13.3288i q^{88} +(7.10727 - 12.3101i) q^{89} +(-0.264844 + 0.458723i) q^{91} +(1.16849 - 0.674627i) q^{92} +(-0.404707 + 0.233658i) q^{93} -9.63975 q^{94} -0.198556 q^{96} +(15.8329 - 9.14111i) q^{97} +(-6.79733 + 3.92444i) q^{98} +(-7.39155 + 12.8025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46}+ \cdots - 40 q^{99}+O(q^{100}) $ 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.28275	+	0.740597i	−0.907043	+	0.523681i	−0.879478	−	0.475939i	$-0.842108\pi$
$2$	−1.28275	+	0.740597i	−0.907043	+	0.523681i	−0.0275641	+	0.999620i	$0.508775\pi$
$3$	0.157277	−	0.0908038i	0.0908038	−	0.0524256i	−0.453910	−	0.891047i	$-0.649971\pi$
$3$	0.157277	−	0.0908038i	0.0908038	−	0.0524256i	0.544714	+	0.838622i	$0.316638\pi$
$4$	0.0969683	−	0.167954i	0.0484841	−	0.0839770i
$5$		0			0
$5$		0			0
$6$	−0.134498	+	0.232958i	−0.0549086	+	0.0951045i
$7$		−	1.30422i		−	0.492948i	−0.969149	−	0.246474i	$-0.920728\pi$
$7$		−	1.30422i		−	0.492948i	0.969149	−	0.246474i	$-0.0792719\pi$
$8$		−	2.67513i		−	0.945802i
$9$	−1.48351	+	2.56951i	−0.494503	+	0.856505i
$10$		0			0
$11$	4.98247			1.50227			0.751136	−	0.660147i	$-0.229506\pi$
$11$	4.98247			1.50227			0.751136	+	0.660147i	$0.229506\pi$
$12$		−	0.0352204i		−	0.0101672i
$13$	−0.351723	−	0.203067i	−0.0975504	−	0.0563207i	0.450431	−	0.892811i	$-0.351270\pi$
$13$	−0.351723	−	0.203067i	−0.0975504	−	0.0563207i	−0.547982	+	0.836490i	$0.684604\pi$
$14$	0.965899	+	1.67299i	0.258147	+	0.447124i
$15$		0			0
$16$	2.17513	+	3.76744i	0.543783	+	0.941859i
$17$	−2.38173	+	1.37510i	−0.577656	+	0.333510i	−0.760201	−	0.649688i	$-0.774900\pi$
$17$	−2.38173	+	1.37510i	−0.577656	+	0.333510i	0.182546	+	0.983197i	$0.441566\pi$
$18$		−	4.39473i		−	1.03585i
$19$	4.35785	−	0.0955054i	0.999760	−	0.0219104i
$19$	4.35785	−	0.0955054i	0.999760	−	0.0219104i
$20$		0			0
$21$	−0.118428	−	0.205123i	−0.0258431	−	0.0447615i
$22$	−6.39128	+	3.69001i	−1.36262	+	0.786712i
$23$	6.02510	+	3.47860i	1.25632	+	0.725337i	0.972357	−	0.233498i	$-0.0750171\pi$
$23$	6.02510	+	3.47860i	1.25632	+	0.725337i	0.283964	+	0.958835i	$0.408350\pi$
$24$	−0.242912	−	0.420736i	−0.0495842	−	0.0858824i
$25$		0			0
$26$	0.601564			0.117976
$27$			1.08366i			0.208550i
$28$	−0.219048	−	0.126468i	−0.0413963	−	0.0239001i
$29$	−2.00728	+	3.47672i	−0.372743	+	0.645610i	−0.989986	−	0.141162i	$-0.954916\pi$
$29$	−2.00728	+	3.47672i	−0.372743	+	0.645610i	0.617243	+	0.786772i	$0.288249\pi$
$30$		0			0
$31$	−2.57321			−0.462163			−0.231081	−	0.972934i	$-0.574226\pi$
$31$	−2.57321			−0.462163			−0.231081	+	0.972934i	$0.574226\pi$
$32$	−0.946844	−	0.546661i	−0.167380	−	0.0966369i
$33$	0.783628	−	0.452428i	0.136412	−	0.0787576i
$34$	2.03678	−	3.52781i	0.349305	−	0.605015i
$35$		0			0
$36$	0.287707	+	0.498323i	0.0479511	+	0.0830538i
$37$			3.71348i			0.610492i	0.952274	+	0.305246i	$0.0987387\pi$
$37$			3.71348i			0.610492i	−0.952274	+	0.305246i	$0.901261\pi$
$38$	−5.51931	+	3.34992i	−0.895351	+	0.543429i
$39$	−0.0737572			−0.0118106
$40$		0			0
$41$	0.607965	+	1.05303i	0.0949482	+	0.164455i	0.909587	−	0.415514i	$-0.136398\pi$
$41$	0.607965	+	1.05303i	0.0949482	+	0.164455i	−0.814639	+	0.579969i	$0.803065\pi$
$42$	0.303827	+	0.175415i	0.0468816	+	0.0270671i
$43$	−2.70426	+	1.56130i	−0.412396	+	0.238097i	−0.691819	−	0.722071i	$-0.743190\pi$
$43$	−2.70426	+	1.56130i	−0.412396	+	0.238097i	0.279423	+	0.960168i	$0.409857\pi$
$44$	0.483142	−	0.836826i	0.0728364	−	0.126156i
$45$		0			0
$46$	−10.3050			−1.51938
$47$	5.63617	+	3.25405i	0.822120	+	0.474651i	0.851147	−	0.524927i	$-0.175907\pi$
$47$	5.63617	+	3.25405i	0.822120	+	0.474651i	−0.0290269	+	0.999579i	$0.509241\pi$
$48$	0.684196	+	0.395020i	0.0987551	+	0.0570163i
$49$	5.29902			0.757003
$50$		0			0
$51$	−0.249728	+	0.432541i	−0.0349689	+	0.0605679i
$52$	−0.0682119	+	0.0393822i	−0.00945929	+	0.00546132i
$53$	5.47490	+	3.16094i	0.752036	+	0.434188i	0.826429	−	0.563041i	$-0.190369\pi$
$53$	5.47490	+	3.16094i	0.752036	+	0.434188i	−0.0743934	+	0.997229i	$0.523702\pi$
$54$	−0.802553	−	1.39006i	−0.109214	−	0.189164i
$55$		0			0
$56$	−3.48895			−0.466231
$57$	0.676717	−	0.410731i	0.0896334	−	0.0544026i
$58$		−	5.94636i		−	0.780795i
$59$	5.61636	+	9.72783i	0.731188	+	1.26646i	0.956376	+	0.292140i	$0.0943672\pi$
$59$	5.61636	+	9.72783i	0.731188	+	1.26646i	−0.225187	+	0.974315i	$0.572299\pi$
$60$		0			0
$61$	−0.467072	+	0.808992i	−0.0598024	+	0.103581i	−0.894377	−	0.447315i	$-0.852380\pi$
$61$	−0.467072	+	0.808992i	−0.0598024	+	0.103581i	0.834574	+	0.550896i	$0.185714\pi$
$62$	3.30079	−	1.90571i	0.419201	−	0.242026i
$63$	3.35120	+	1.93482i	0.422212	+	0.243764i
$64$	−7.08110			−0.885138
$65$		0			0
$66$	−0.670133	+	1.16071i	−0.0824877	+	0.142873i
$67$	−4.58585	−	2.64764i	−0.560251	−	0.323461i	0.192995	−	0.981200i	$-0.438180\pi$
$67$	−4.58585	−	2.64764i	−0.560251	−	0.323461i	−0.753246	+	0.657739i	$0.771513\pi$
$68$			0.533363i			0.0646797i
$69$	1.26348			0.152105
$70$		0			0
$71$	0.817659	+	1.41623i	0.0970383	+	0.168075i	0.910457	−	0.413603i	$-0.135730\pi$
$71$	0.817659	+	1.41623i	0.0970383	+	0.168075i	−0.813419	+	0.581678i	$0.802396\pi$
$72$	6.87378	+	3.96858i	0.810083	+	0.467702i
$73$	−6.65794	+	3.84396i	−0.779252	+	0.449902i	−0.836165	−	0.548478i	$-0.815208\pi$
$73$	−6.65794	+	3.84396i	−0.779252	+	0.449902i	0.0569129	+	0.998379i	$0.481874\pi$
$74$	−2.75019	−	4.76347i	−0.319703	−	0.553742i
$75$		0			0
$76$	0.406533	−	0.741180i	0.0466325	−	0.0850191i
$77$		−	6.49822i		−	0.740541i
$78$	0.0946121	−	0.0546243i	0.0107127	−	0.00618499i
$79$	−7.27699	−	12.6041i	−0.818725	−	1.41807i	−0.906622	−	0.421944i	$-0.861348\pi$
$79$	−7.27699	−	12.6041i	−0.818725	−	1.41807i	0.0878971	−	0.996130i	$-0.471985\pi$
$80$		0			0
$81$	−4.35213	−	7.53811i	−0.483570	−	0.837567i
$82$	−1.55974	−	0.900514i	−0.172244	−	0.0994452i
$83$			15.2643i			1.67547i	0.546077	+	0.837735i	$0.316121\pi$
$83$			15.2643i			1.67547i	−0.546077	+	0.837735i	$0.683879\pi$
$84$	−0.0459350			−0.00501192
$85$		0			0
$86$	2.31260	−	4.00553i	0.249374	−	0.431928i
$87$			0.729076i			0.0781652i
$88$		−	13.3288i		−	1.42085i
$89$	7.10727	−	12.3101i	0.753369	−	1.30487i	−0.192812	−	0.981236i	$-0.561761\pi$
$89$	7.10727	−	12.3101i	0.753369	−	1.30487i	0.946181	−	0.323638i	$-0.104906\pi$
$90$		0			0
$91$	−0.264844	+	0.458723i	−0.0277632	+	0.0480872i
$92$	1.16849	−	0.674627i	0.121823	−	0.0703347i
$93$	−0.404707	+	0.233658i	−0.0419661	+	0.0242292i
$94$	−9.63975			−0.994264
$95$		0			0
$96$	−0.198556			−0.0202650
$97$	15.8329	−	9.14111i	1.60758	−	0.928139i	0.617676	−	0.786433i	$-0.288074\pi$
$97$	15.8329	−	9.14111i	1.60758	−	0.928139i	0.989909	−	0.141707i	$-0.0452590\pi$
$98$	−6.79733	+	3.92444i	−0.686634	+	0.396428i
$99$	−7.39155	+	12.8025i	−0.742878	+	1.28670i
$100$		0			0
$101$	7.99763	−	13.8523i	0.795794	−	1.37836i	−0.126540	−	0.991962i	$-0.540387\pi$
$101$	7.99763	−	13.8523i	0.795794	−	1.37836i	0.922334	−	0.386394i	$-0.126280\pi$
$102$		−	0.739791i		−	0.0732502i
$103$		−	5.30941i		−	0.523152i	−0.965183	−	0.261576i	$-0.915758\pi$
$103$		−	5.30941i		−	0.523152i	0.965183	−	0.261576i	$-0.0842422\pi$
$104$	−0.543232	+	0.940905i	−0.0532682	+	0.0922633i
$105$		0			0
$106$	−9.36392			−0.909504
$107$		−	13.0024i		−	1.25699i	−0.777814	−	0.628494i	$-0.783671\pi$
$107$		−	13.0024i		−	1.25699i	0.777814	−	0.628494i	$-0.216329\pi$
$108$	0.182004	+	0.105080i	0.0175134	+	0.0101114i
$109$	−4.09697	−	7.09616i	−0.392418	−	0.679689i	0.600350	−	0.799738i	$-0.295028\pi$
$109$	−4.09697	−	7.09616i	−0.392418	−	0.679689i	−0.992768	+	0.120049i	$0.961695\pi$
$110$		0			0
$111$	0.337198	+	0.584044i	0.0320054	+	0.0554350i
$112$	4.91355	−	2.83684i	0.464287	−	0.268056i
$113$			6.54779i			0.615964i	0.951392	+	0.307982i	$0.0996536\pi$
$113$			6.54779i			0.615964i	−0.951392	+	0.307982i	$0.900346\pi$
$114$	−0.563874	+	1.02804i	−0.0528117	+	0.0962848i
$115$		0			0
$116$	0.389286	+	0.674263i	0.0361443	+	0.0626037i
$117$	1.04357	−	0.602504i	0.0964779	−	0.0557016i
$118$	−14.4088	−	8.31892i	−1.32644	−	0.765819i
$119$	1.79342	+	3.10630i	0.164403	+	0.284754i
$120$		0			0
$121$	13.8250			1.25682
$122$		−	1.38365i		−	0.125270i
$123$	0.191238	+	0.110411i	0.0172433	+	0.00995544i
$124$	−0.249520	+	0.432181i	−0.0224076	+	0.0388110i
$125$		0			0
$126$	−5.73168			−0.510619
$127$	−13.0844	−	7.55431i	−1.16106	−	0.670336i	−0.209500	−	0.977809i	$-0.567183\pi$
$127$	−13.0844	−	7.55431i	−1.16106	−	0.670336i	−0.951557	+	0.307472i	$0.900517\pi$
$128$	10.9770	−	6.33757i	0.970238	−	0.560167i
$129$	−0.283545	+	0.491114i	−0.0249647	+	0.0432402i
$130$		0			0
$131$	1.24679	+	2.15950i	0.108933	+	0.188677i	0.915338	−	0.402686i	$-0.131923\pi$
$131$	1.24679	+	2.15950i	0.108933	+	0.188677i	−0.806406	+	0.591363i	$0.798590\pi$
$132$		−	0.175485i		−	0.0152740i
$133$	−0.124560	−	5.68358i	−0.0108007	−	0.492829i
$134$	7.84335			0.677562
$135$		0			0
$136$	3.67856	+	6.37145i	0.315434	+	0.546348i
$137$	15.2491	+	8.80405i	1.30282	+	0.752181i	0.980886	−	0.194583i	$-0.0623352\pi$
$137$	15.2491	+	8.80405i	1.30282	+	0.752181i	0.321930	+	0.946764i	$0.395669\pi$
$138$	−1.62073	+	0.935729i	−0.137966	+	0.0796546i
$139$	1.57736	−	2.73207i	0.133790	−	0.231731i	−0.791345	−	0.611370i	$-0.790619\pi$
$139$	1.57736	−	2.73207i	0.133790	−	0.231731i	0.925135	+	0.379639i	$0.123952\pi$
$140$		0			0
$141$	1.18192			0.0995356
$142$	−2.09771	−	1.21111i	−0.176036	−	0.101634i
$143$	−1.75245	−	1.01178i	−0.146547	−	0.0846091i
$144$	−12.9073			−1.07561
$145$		0			0
$146$	5.69365	−	9.86170i	0.471210	−	0.816160i
$147$	0.833413	−	0.481171i	0.0687388	−	0.0396863i
$148$	0.623693	+	0.360090i	0.0512673	+	0.0295992i
$149$	−3.18694	−	5.51994i	−0.261084	−	0.452211i	0.705446	−	0.708764i	$-0.250747\pi$
$149$	−3.18694	−	5.51994i	−0.261084	−	0.452211i	−0.966530	+	0.256552i	$0.917413\pi$
$150$		0			0
$151$	4.96340			0.403915			0.201958	−	0.979394i	$-0.435270\pi$
$151$	4.96340			0.403915			0.201958	+	0.979394i	$0.435270\pi$
$152$	−0.255489	−	11.6578i	−0.0207229	−	0.945575i
$153$		−	8.15987i		−	0.659686i
$154$	4.81257	+	8.33561i	0.387808	+	0.671703i
$155$		0			0
$156$	−0.00715211	+	0.0123878i	−0.000572627	+	0.000991819i
$157$	−1.81432	+	1.04750i	−0.144798	+	0.0835993i	−0.570649	−	0.821194i	$-0.693308\pi$
$157$	−1.81432	+	1.04750i	−0.144798	+	0.0835993i	0.425851	+	0.904793i	$0.359975\pi$
$158$	18.6691	+	10.7786i	1.48524	+	0.857502i
$159$	1.14810			0.0910503
$160$		0			0
$161$	4.53684	−	7.85804i	0.357553	−	0.619300i
$162$	11.1654	+	6.44635i	0.877237	+	0.506473i
$163$		−	9.55821i		−	0.748656i	−0.927296	−	0.374328i	$-0.877873\pi$
$163$		−	9.55821i		−	0.748656i	0.927296	−	0.374328i	$-0.122127\pi$
$164$	0.235813			0.0184139
$165$		0			0
$166$	−11.3047	−	19.5803i	−0.877412	−	1.51972i
$167$	−14.4968	−	8.36974i	−1.12180	−	0.647670i	−0.179938	−	0.983678i	$-0.557590\pi$
$167$	−14.4968	−	8.36974i	−1.12180	−	0.647670i	−0.941859	+	0.336008i	$0.890923\pi$
$168$	−0.548731	+	0.316810i	−0.0423355	+	0.0244424i
$169$	−6.41753	−	11.1155i	−0.493656	−	0.855037i
$170$		0			0
$171$	−6.21951	+	11.3392i	−0.475618	+	0.867134i
$172$			0.605588i			0.0461757i
$173$	−12.1030	+	6.98769i	−0.920177	+	0.531264i	−0.883691	−	0.468070i	$-0.844950\pi$
$173$	−12.1030	+	6.98769i	−0.920177	+	0.531264i	−0.0364853	+	0.999334i	$0.511616\pi$
$174$	−0.539952	−	0.935224i	−0.0409336	−	0.0708992i
$175$		0			0
$176$	10.8375	+	18.7712i	0.816910	+	1.41493i
$177$	1.76665	+	1.01997i	0.132789	+	0.0766660i
$178$			21.0545i			1.57810i
$179$	9.86133			0.737071			0.368535	−	0.929614i	$-0.379859\pi$
$179$	9.86133			0.737071			0.368535	+	0.929614i	$0.379859\pi$
$180$		0			0
$181$	−7.38629	+	12.7934i	−0.549019	+	0.950929i	0.449323	+	0.893369i	$0.351665\pi$
$181$	−7.38629	+	12.7934i	−0.549019	+	0.950929i	−0.998342	+	0.0575593i	$0.981668\pi$
$182$		−	0.784570i		−	0.0581562i
$183$			0.169648i			0.0125407i
$184$	9.30570	−	16.1179i	0.686025	−	1.18823i
$185$		0			0
$186$	0.346092	−	0.599450i	0.0253767	−	0.0439538i
$187$	−11.8669	+	6.85138i	−0.867796	+	0.501022i
$188$	1.09306	−	0.631078i	0.0797196	−	0.0460261i
$189$	1.41332			0.102804
$190$		0			0
$191$	−20.6797			−1.49633			−0.748166	−	0.663512i	$-0.769065\pi$
$191$	−20.6797			−1.49633			−0.748166	+	0.663512i	$0.769065\pi$
$192$	−1.11369	+	0.642991i	−0.0803739	+	0.0464039i
$193$	−17.5615	+	10.1391i	−1.26410	+	0.729831i	−0.973866	−	0.227123i	$-0.927068\pi$
$193$	−17.5615	+	10.1391i	−1.26410	+	0.729831i	−0.290238	+	0.956954i	$0.593735\pi$
$194$	−13.5398	+	23.4516i	−0.972099	+	1.68372i
$195$		0			0
$196$	0.513837	−	0.889991i	0.0367026	−	0.0635708i
$197$			15.9172i			1.13406i	0.823698	+	0.567028i	$0.191907\pi$
$197$			15.9172i			1.13406i	−0.823698	+	0.567028i	$0.808093\pi$
$198$		−	21.8966i		−	1.55613i
$199$	−6.61785	+	11.4625i	−0.469127	+	0.812552i	−0.999377	−	0.0352892i	$-0.988765\pi$
$199$	−6.61785	+	11.4625i	−0.469127	+	0.812552i	0.530250	+	0.847841i	$0.322098\pi$
$200$		0			0
$201$	−0.961665			−0.0678306
$202$			23.6921i			1.66697i
$203$	4.53439	+	2.61793i	0.318252	+	0.183743i
$204$	0.0484314	+	0.0838856i	0.00339087	+	0.00587317i
$205$		0			0
$206$	3.93214	+	6.81066i	0.273965	+	0.474521i
$207$	−17.8766	+	10.3211i	−1.24251	+	0.717363i
$208$		−	1.76679i		−	0.122505i
$209$	21.7129	−	0.475853i	1.50191	−	0.0329154i
$210$		0			0
$211$	4.88917	+	8.46829i	0.336584	+	0.582981i	0.983788	−	0.179336i	$-0.0573950\pi$
$211$	4.88917	+	8.46829i	0.336584	+	0.582981i	−0.647204	+	0.762317i	$0.724062\pi$
$212$	1.06178	−	0.613021i	0.0729236	−	0.0421025i
$213$	0.257198	+	0.148493i	0.0176229	+	0.0101746i
$214$	9.62954	+	16.6788i	0.658262	+	1.14014i
$215$		0			0
$216$	2.89892			0.197247
$217$			3.35603i			0.227822i
$218$	10.5108	+	6.06841i	0.711880	+	0.411004i
$219$	−0.698093	+	1.20913i	−0.0471727	+	0.0817056i
$220$		0			0
$221$	1.11695			0.0751340
$222$	−0.865083	−	0.499456i	−0.0580606	−	0.0335213i
$223$	22.3971	−	12.9310i	1.49982	−	0.865923i	0.499822	−	0.866128i	$-0.333399\pi$
$223$	22.3971	−	12.9310i	1.49982	−	0.865923i	1.00000		0.000205308i	$6.53517e-5\pi$
$224$	−0.712964	+	1.23489i	−0.0476369	+	0.0825095i
$225$		0			0
$226$	−4.84927	−	8.39918i	−0.322569	−	0.558705i
$227$			2.28573i			0.151709i	0.997119	+	0.0758545i	$0.0241684\pi$
$227$			2.28573i			0.151709i	−0.997119	+	0.0758545i	$0.975832\pi$
$228$	−0.00336373	−	0.153485i	−0.000222769	−	0.0101648i
$229$	21.8805			1.44590			0.722952	−	0.690898i	$-0.242785\pi$
$229$	21.8805			1.44590			0.722952	+	0.690898i	$0.242785\pi$
$230$		0			0
$231$	−0.590064	−	1.02202i	−0.0388233	−	0.0672440i
$232$	9.30068	+	5.36975i	0.610619	+	0.352541i
$233$	1.77868	−	1.02692i	0.116525	−	0.0672758i	−0.440605	−	0.897701i	$-0.645236\pi$
$233$	1.77868	−	1.02692i	0.116525	−	0.0672758i	0.557130	+	0.830425i	$0.311903\pi$
$234$	−0.892426	+	1.54573i	−0.0583397	+	0.101047i
$235$		0			0
$236$	2.17844			0.141804
$237$	−2.28900	−	1.32156i	−0.148687	−	0.0858443i
$238$	−4.60103	−	2.65641i	−0.298241	−	0.172189i
$239$	−7.68110			−0.496849			−0.248425	−	0.968651i	$-0.579913\pi$
$239$	−7.68110			−0.496849			−0.248425	+	0.968651i	$0.579913\pi$
$240$		0			0
$241$	−7.26832	+	12.5891i	−0.468194	+	0.810935i	−0.999339	−	0.0363455i	$-0.988428\pi$
$241$	−7.26832	+	12.5891i	−0.468194	+	0.810935i	0.531146	+	0.847280i	$0.321762\pi$
$242$	−17.7341	+	10.2388i	−1.13999	+	0.658174i
$243$	−4.18440	−	2.41586i	−0.268429	−	0.154978i
$244$	0.0905823	+	0.156893i	0.00579894	+	0.0100441i
$245$		0			0
$246$	−0.327081			−0.0208539
$247$	−1.55215	−	0.851346i	−0.0987610	−	0.0541698i
$248$			6.88368i			0.437114i
$249$	1.38605	+	2.40072i	0.0878376	+	0.152139i
$250$		0			0
$251$	−3.59365	+	6.22439i	−0.226829	+	0.392880i	−0.956867	−	0.290527i	$-0.906169\pi$
$251$	−3.59365	+	6.22439i	−0.226829	+	0.392880i	0.730037	+	0.683407i	$0.239503\pi$
$252$	0.649921	−	0.375232i	0.0409412	−	0.0236374i
$253$	30.0199	+	17.3320i	1.88734	+	1.08965i
$254$	22.3788			1.40417
$255$		0			0
$256$	−2.30606	+	3.99422i	−0.144129	+	0.249639i
$257$	7.53951	+	4.35294i	0.470302	+	0.271529i	0.716366	−	0.697725i	$-0.245804\pi$
$257$	7.53951	+	4.35294i	0.470302	+	0.271529i	−0.246064	+	0.969254i	$0.579137\pi$
$258$		−	0.839970i		−	0.0522943i
$259$	4.84318			0.300940
$260$		0			0
$261$	−5.95565	−	10.3155i	−0.368645	−	0.638513i
$262$	−3.19864	−	1.84674i	−0.197613	−	0.114092i
$263$	−26.4339	+	15.2616i	−1.62998	+	0.941072i	−0.645888	+	0.763432i	$0.723513\pi$
$263$	−26.4339	+	15.2616i	−1.62998	+	0.941072i	−0.984096	+	0.177639i	$0.943154\pi$
$264$	−1.21030	−	2.09631i	−0.0744890	−	0.129019i
$265$		0			0
$266$	4.36903	+	7.19838i	0.267882	+	0.441361i
$267$		−	2.58147i		−	0.157983i
$268$	−0.889365	+	0.513475i	−0.0543266	+	0.0313655i
$269$	−9.20379	−	15.9414i	−0.561165	−	0.971966i	−0.997395	−	0.0721309i	$-0.977020\pi$
$269$	−9.20379	−	15.9414i	−0.561165	−	0.971966i	0.436230	−	0.899835i	$-0.356313\pi$
$270$		0			0
$271$	5.73694	+	9.93668i	0.348494	+	0.603610i	0.985982	−	0.166850i	$-0.0533597\pi$
$271$	5.73694	+	9.93668i	0.348494	+	0.603610i	−0.637488	+	0.770460i	$0.720026\pi$
$272$	−10.3612	−	5.98202i	−0.628238	−	0.362714i
$273$			0.0961953i			0.00582201i
$274$	−26.0810			−1.57561
$275$		0			0
$276$	0.122517	−	0.212206i	0.00737468	−	0.0127733i
$277$			1.79689i			0.107965i	0.998542	+	0.0539823i	$0.0171914\pi$
$277$			1.79689i			0.107965i	−0.998542	+	0.0539823i	$0.982809\pi$
$278$			4.67276i			0.280253i
$279$	3.81739	−	6.61191i	0.228541	−	0.395844i
$280$		0			0
$281$	7.09550	−	12.2898i	0.423282	−	0.733146i	−0.572976	−	0.819572i	$-0.694211\pi$
$281$	7.09550	−	12.2898i	0.423282	−	0.733146i	0.996258	+	0.0864258i	$0.0275446\pi$
$282$	−1.51611	+	0.875326i	−0.0902830	+	0.0521249i
$283$	15.5094	−	8.95435i	0.921938	−	0.532281i	0.0376851	−	0.999290i	$-0.488002\pi$
$283$	15.5094	−	8.95435i	0.921938	−	0.532281i	0.884253	+	0.467009i	$0.154668\pi$
$284$	0.317148			0.0188193
$285$		0			0
$286$	2.99728			0.177233
$287$	1.37337	−	0.792918i	0.0810677	−	0.0468045i
$288$	2.80930	−	1.62195i	0.165540	−	0.0955744i
$289$	−4.71823	+	8.17221i	−0.277543	+	0.480718i
$290$		0			0
$291$	1.66010	−	2.87537i	0.0973166	−	0.168557i
$292$			1.49097i			0.0872524i
$293$		−	33.3088i		−	1.94592i	−0.230970	−	0.972961i	$-0.574190\pi$
$293$		−	33.3088i		−	1.94592i	0.230970	−	0.972961i	$-0.425810\pi$
$294$	−0.712708	+	1.23445i	−0.0415660	+	0.0719944i
$295$		0			0
$296$	9.93404			0.577404
$297$			5.39929i			0.313299i
$298$	8.17610	+	4.72048i	0.473629	+	0.273450i
$299$	−1.41278	−	2.44700i	−0.0817031	−	0.141514i
$300$		0			0
$301$	2.03628	+	3.52694i	0.117369	+	0.203289i
$302$	−6.36681	+	3.67588i	−0.366369	+	0.211523i
$303$		−	2.90486i		−	0.166880i
$304$	9.83871	+	16.2102i	0.564289	+	0.929719i
$305$		0			0
$306$	6.04317	+	10.4671i	0.345465	+	0.598363i
$307$	−13.4728	+	7.77854i	−0.768935	+	0.443945i	−0.832495	−	0.554033i	$-0.813088\pi$
$307$	−13.4728	+	7.77854i	−0.768935	+	0.443945i	0.0635594	+	0.997978i	$0.479755\pi$
$308$	−1.09140	−	0.630122i	−0.0621884	−	0.0359045i
$309$	−0.482115	−	0.835048i	−0.0274266	−	0.0475042i
$310$		0			0
$311$	29.1959			1.65555			0.827773	−	0.561063i	$-0.189608\pi$
$311$	29.1959			1.65555			0.827773	+	0.561063i	$0.189608\pi$
$312$			0.197310i			0.0111705i
$313$	−27.6158	−	15.9440i	−1.56094	−	0.901207i	−0.997163	−	0.0752782i	$-0.976016\pi$
$313$	−27.6158	−	15.9440i	−1.56094	−	0.901207i	−0.563774	−	0.825929i	$-0.690651\pi$
$314$	1.55155	−	2.68736i	0.0875588	−	0.151656i
$315$		0			0
$316$	−2.82255			−0.158781
$317$	−11.7520	−	6.78505i	−0.660061	−	0.381086i	0.132239	−	0.991218i	$-0.457783\pi$
$317$	−11.7520	−	6.78505i	−0.660061	−	0.381086i	−0.792300	+	0.610131i	$0.791117\pi$
$318$	−1.47273	+	0.850280i	−0.0825865	+	0.0476813i
$319$	−10.0012	+	17.3227i	−0.559962	+	0.969882i
$320$		0			0
$321$	−1.18067	−	2.04498i	−0.0658984	−	0.114139i
$322$			13.4399i			0.748976i
$323$	−10.2479	+	6.21993i	−0.570210	+	0.346086i
$324$	−1.68807			−0.0937819
$325$		0			0
$326$	7.07878	+	12.2608i	0.392057	+	0.679063i
$327$	−1.28872	−	0.744041i	−0.0712662	−	0.0411456i
$328$	2.81698	−	1.62639i	0.155542	−	0.0898022i
$329$	4.24398	−	7.35079i	0.233978	−	0.405262i
$330$		0			0
$331$	−29.4274			−1.61747			−0.808737	−	0.588171i	$-0.799848\pi$
$331$	−29.4274			−1.61747			−0.808737	+	0.588171i	$0.799848\pi$
$332$	2.56369	+	1.48015i	0.140701	+	0.0812337i
$333$	−9.54183	−	5.50898i	−0.522889	−	0.301890i
$334$	24.7944			1.35669
$335$		0			0
$336$	0.515192	−	0.892339i	0.0281060	−	0.0486811i
$337$	13.4336	−	7.75588i	0.731773	−	0.422489i	−0.0872973	−	0.996182i	$-0.527823\pi$
$337$	13.4336	−	7.75588i	0.731773	−	0.422489i	0.819071	+	0.573693i	$0.194490\pi$
$338$	16.4642	+	9.50560i	0.895534	+	0.517037i
$339$	0.594564	+	1.02982i	0.0322923	+	0.0559319i
$340$		0			0
$341$	−12.8210			−0.694294
$342$	−0.419720	−	19.1516i	−0.0226959	−	1.03560i
$343$		−	16.0406i		−	0.866110i
$344$	4.17669	+	7.23425i	0.225192	+	0.390044i
$345$		0			0
$346$	10.3501	−	17.9269i	0.556426	−	0.963759i
$347$	19.5615	−	11.2938i	1.05012	−	0.606285i	0.127434	−	0.991847i	$-0.459326\pi$
$347$	19.5615	−	11.2938i	1.05012	−	0.606285i	0.922682	+	0.385562i	$0.125992\pi$
$348$	0.122451	+	0.0706973i	0.00656408	+	0.00378977i
$349$	−25.4885			−1.36437			−0.682184	−	0.731181i	$-0.738970\pi$
$349$	−25.4885			−1.36437			−0.682184	+	0.731181i	$0.738970\pi$
$350$		0			0
$351$	0.220055	−	0.381147i	0.0117457	−	0.0203441i
$352$	−4.71762	−	2.72372i	−0.251450	−	0.145175i
$353$			10.2959i			0.547994i	0.961730	+	0.273997i	$0.0883459\pi$
$353$			10.2959i			0.547994i	−0.961730	+	0.273997i	$0.911654\pi$
$354$	−3.02156			−0.160594
$355$		0			0
$356$	−1.37836	−	2.38739i	−0.0730529	−	0.126531i
$357$	0.564128	+	0.325699i	0.0298568	+	0.0172378i
$358$	−12.6496	+	7.30328i	−0.668555	+	0.385990i
$359$	0.991256	+	1.71691i	0.0523165	+	0.0906148i	0.890998	−	0.454008i	$-0.150006\pi$
$359$	0.991256	+	1.71691i	0.0523165	+	0.0906148i	−0.838681	+	0.544623i	$0.816673\pi$
$360$		0			0
$361$	18.9818	−	0.832397i	0.999040	−	0.0438103i
$362$		−	21.8811i		−	1.15004i
$363$	2.17436	−	1.25537i	0.114124	−	0.0658897i
$364$	0.0513629	+	0.0889631i	0.00269215	+	0.00466294i
$365$		0			0
$366$	−0.125641	−	0.217616i	−0.00656734	−	0.0113750i
$367$	−4.56763	−	2.63712i	−0.238428	−	0.137657i	0.376026	−	0.926609i	$-0.377290\pi$
$367$	−4.56763	−	2.63712i	−0.238428	−	0.137657i	−0.614454	+	0.788953i	$0.710624\pi$
$368$			30.2656i			1.57770i
$369$	−3.60769			−0.187809
$370$		0			0
$371$	4.12255	−	7.14046i	0.214032	−	0.370714i
$372$			0.0906295i			0.00469892i
$373$		−	31.7192i		−	1.64236i	−0.570670	−	0.821179i	$-0.693317\pi$
$373$		−	31.7192i		−	1.64236i	0.570670	−	0.821179i	$-0.306683\pi$
$374$	10.1482	−	17.5772i	0.524752	−	0.908897i
$375$		0			0
$376$	8.70500	−	15.0775i	0.448926	−	0.777563i
$377$	1.41202	−	0.815227i	0.0727225	−	0.0419863i
$378$	−1.81294	+	1.04670i	−0.0932477	+	0.0538366i
$379$	−35.5119			−1.82412			−0.912062	−	0.410052i	$-0.865510\pi$
$379$	−35.5119			−1.82412			−0.912062	+	0.410052i	$0.865510\pi$
$380$		0			0
$381$	−2.74384			−0.140571
$382$	26.5269	−	15.3153i	1.35724	−	0.783601i
$383$	12.0639	−	6.96509i	0.616436	−	0.355899i	−0.159044	−	0.987271i	$-0.550841\pi$
$383$	12.0639	−	6.96509i	0.616436	−	0.355899i	0.775480	+	0.631372i	$0.217508\pi$
$384$	1.15095	−	1.99350i	0.0587342	−	0.101731i
$385$		0			0
$386$	15.0180	−	26.0120i	0.764398	−	1.32398i
$387$		−	9.26484i		−	0.470958i
$388$		−	3.54559i		−	0.180000i
$389$	−0.471434	+	0.816548i	−0.0239027	+	0.0414006i	−0.877729	−	0.479157i	$-0.840943\pi$
$389$	−0.471434	+	0.816548i	−0.0239027	+	0.0414006i	0.853827	+	0.520557i	$0.174276\pi$
$390$		0			0
$391$	−19.1336			−0.967628
$392$		−	14.1756i		−	0.715974i
$393$	0.392183	+	0.226427i	0.0197830	+	0.0114217i
$394$	−11.7883	−	20.4179i	−0.593884	−	1.02864i
$395$		0			0
$396$	1.43349	+	2.48288i	0.0720356	+	0.124769i
$397$	24.7386	−	14.2828i	1.24159	−	0.716834i	0.272174	−	0.962248i	$-0.412257\pi$
$397$	24.7386	−	14.2828i	1.24159	−	0.716834i	0.969418	+	0.245414i	$0.0789239\pi$
$398$		−	19.6047i		−	0.982693i
$399$	−0.535682	−	0.882586i	−0.0268176	−	0.0441846i
$400$		0			0
$401$	3.58365	+	6.20707i	0.178959	+	0.309966i	0.941524	−	0.336945i	$-0.109394\pi$
$401$	3.58365	+	6.20707i	0.178959	+	0.309966i	−0.762565	+	0.646911i	$0.776060\pi$
$402$	1.23358	−	0.712206i	0.0615252	−	0.0355216i
$403$	0.905058	+	0.522535i	0.0450841	+	0.0260293i
$404$	−1.55103	−	2.68647i	−0.0771668	−	0.133657i
$405$		0			0
$406$	−7.75534			−0.384891
$407$			18.5023i			0.917125i
$408$	1.15710	+	0.668055i	0.0572852	+	0.0330736i
$409$	−5.26624	+	9.12140i	−0.260399	+	0.451024i	−0.966348	−	0.257238i	$-0.917187\pi$
$409$	−5.26624	+	9.12140i	−0.260399	+	0.451024i	0.705949	+	0.708263i	$0.250521\pi$
$410$		0			0
$411$	3.19777			0.157734
$412$	−0.891737	−	0.514845i	−0.0439327	−	0.0253646i
$413$	12.6872	−	7.32495i	0.624296	−	0.360437i
$414$	15.2875	−	26.4787i	0.751339	−	1.30136i
$415$		0			0
$416$	0.222018	+	0.384546i	0.0108853	+	0.0188539i
$417$		−	0.572922i		−	0.0280561i
$418$	−27.4998	+	16.6909i	−1.34506	+	0.816379i
$419$	−2.52693			−0.123448			−0.0617242	−	0.998093i	$-0.519660\pi$
$419$	−2.52693			−0.123448			−0.0617242	+	0.998093i	$0.519660\pi$
$420$		0			0
$421$	−7.43346	−	12.8751i	−0.362285	−	0.627495i	0.626052	−	0.779781i	$-0.284670\pi$
$421$	−7.43346	−	12.8751i	−0.362285	−	0.627495i	−0.988336	+	0.152286i	$0.951336\pi$
$422$	−12.5432	−	7.24181i	−0.610592	−	0.352526i
$423$	−16.7226	+	9.65481i	−0.813082	+	0.469433i
$424$	8.45592	−	14.6461i	0.410656	−	0.711276i
$425$		0			0
$426$	−0.439895			−0.0213130
$427$	1.05510	+	0.609163i	0.0510599	+	0.0294794i
$428$	−2.18380	−	1.26082i	−0.105558	−	0.0609440i
$429$	−0.367493			−0.0177427
$430$		0			0
$431$	2.09034	−	3.62057i	0.100688	−	0.174397i	−0.811280	−	0.584657i	$-0.801229\pi$
$431$	2.09034	−	3.62057i	0.100688	−	0.174397i	0.911968	+	0.410261i	$0.134562\pi$
$432$	−4.08261	+	2.35709i	−0.196425	+	0.113406i
$433$	21.9150	+	12.6527i	1.05317	+	0.608048i	0.923535	−	0.383514i	$-0.125286\pi$
$433$	21.9150	+	12.6527i	1.05317	+	0.608048i	0.129635	+	0.991562i	$0.458620\pi$
$434$	−2.48546	−	4.30495i	−0.119306	−	0.206644i
$435$		0			0
$436$	−1.58910			−0.0761043
$437$	26.5887	+	14.5838i	1.27191	+	0.697637i
$438$		−	2.06802i		−	0.0988139i
$439$	14.4561	+	25.0386i	0.689950	+	1.19503i	0.971854	+	0.235585i	$0.0757008\pi$
$439$	14.4561	+	25.0386i	0.689950	+	1.19503i	−0.281904	+	0.959443i	$0.590966\pi$
$440$		0			0
$441$	−7.86114	+	13.6159i	−0.374340	+	0.648376i
$442$	−1.43277	+	0.827208i	−0.0681498	+	0.0393463i
$443$	3.97388	+	2.29432i	0.188805	+	0.109007i	0.591423	−	0.806362i	$-0.298566\pi$
$443$	3.97388	+	2.29432i	0.188805	+	0.109007i	−0.402618	+	0.915368i	$0.631900\pi$
$444$	0.130790			0.00620702
$445$		0			0
$446$	−19.1533	+	33.1745i	−0.906935	+	1.57086i
$447$	−1.00246	−	0.578773i	−0.0474149	−	0.0273750i
$448$			9.23529i			0.436327i
$449$	−29.2171			−1.37884			−0.689420	−	0.724362i	$-0.742135\pi$
$449$	−29.2171			−1.37884			−0.689420	+	0.724362i	$0.742135\pi$
$450$		0			0
$451$	3.02917	+	5.24668i	0.142638	+	0.247056i
$452$	1.09973	+	0.634928i	0.0517268	+	0.0298645i
$453$	0.780628	−	0.450696i	0.0366771	−	0.0211755i
$454$	−1.69280	−	2.93202i	−0.0794471	−	0.137606i
$455$		0			0
$456$	−1.09876	−	1.81031i	−0.0514541	−	0.0847754i
$457$			23.7113i			1.10917i	0.832128	+	0.554584i	$0.187122\pi$
$457$			23.7113i			1.10917i	−0.832128	+	0.554584i	$0.812878\pi$
$458$	−28.0673	+	16.2046i	−1.31150	+	0.757193i
$459$	−1.49013	−	2.58098i	−0.0695534	−	0.120470i
$460$		0			0
$461$	−17.5109	−	30.3298i	−0.815565	−	1.41260i	−0.908922	−	0.416967i	$-0.863093\pi$
$461$	−17.5109	−	30.3298i	−0.815565	−	1.41260i	0.0933568	−	0.995633i	$-0.470240\pi$
$462$	1.51381	+	0.873999i	0.0704289	+	0.0406621i
$463$			20.4936i			0.952417i	0.879332	+	0.476209i	$0.157989\pi$
$463$			20.4936i			0.952417i	−0.879332	+	0.476209i	$0.842011\pi$
$464$	−17.4644			−0.810765
$465$		0			0
$466$	−1.52107	+	2.63457i	−0.0704621	+	0.122044i
$467$		−	9.24346i		−	0.427736i	−0.976863	−	0.213868i	$-0.931394\pi$
$467$		−	9.24346i		−	0.427736i	0.976863	−	0.213868i	$-0.0686063\pi$
$468$		−	0.233695i		−	0.0108026i
$469$	−3.45310	+	5.98095i	−0.159449	+	0.276174i
$470$		0			0
$471$	−0.190233	+	0.329494i	−0.00876549	+	0.0151823i
$472$	26.0232	−	15.0245i	1.19782	−	0.691559i
$473$	−13.4739	+	7.77916i	−0.619530	+	0.357686i
$474$	3.91496			0.179820
$475$		0			0
$476$	0.695620			0.0318837
$477$	−16.2441	+	9.37856i	−0.743768	+	0.429415i
$478$	9.85295	−	5.68860i	0.450663	−	0.260191i
$479$	1.88377	−	3.26278i	0.0860715	−	0.149080i	−0.819776	−	0.572685i	$-0.805902\pi$
$479$	1.88377	−	3.26278i	0.0860715	−	0.149080i	0.905847	+	0.423604i	$0.139235\pi$
$480$		0			0
$481$	0.754086	−	1.30611i	0.0343834	−	0.0595537i
$482$		−	21.5316i		−	0.980737i
$483$		−	1.64785i		−	0.0749798i
$484$	1.34059	−	2.32197i	0.0609359	−	0.105544i
$485$		0			0
$486$	7.15673			0.324636
$487$		−	11.7981i		−	0.534621i	−0.963610	−	0.267311i	$-0.913865\pi$
$487$		−	11.7981i		−	0.534621i	0.963610	−	0.267311i	$-0.0861349\pi$
$488$	2.16416	+	1.24948i	0.0979669	+	0.0565612i
$489$	−0.867922	−	1.50328i	−0.0392488	−	0.0679809i
$490$		0			0
$491$	−3.91782	−	6.78586i	−0.176809	−	0.306241i	0.763977	−	0.645243i	$-0.223244\pi$
$491$	−3.91782	−	6.78586i	−0.176809	−	0.306241i	−0.940786	+	0.339002i	$0.889911\pi$
$492$	0.0370880	−	0.0214128i	0.00167206	−	0.000965362i
$493$		−	11.0408i		−	0.497254i
$494$	2.62153	−	0.0574526i	0.117948	−	0.00258491i
$495$		0			0
$496$	−5.59707	−	9.69442i	−0.251316	−	0.435292i
$497$	1.84707	−	1.06641i	0.0828523	−	0.0478348i
$498$	−3.55593	−	2.05301i	−0.159345	−	0.0919978i
$499$	0.529796	+	0.917633i	0.0237169	+	0.0410789i	0.877640	−	0.479320i	$-0.159117\pi$
$499$	0.529796	+	0.917633i	0.0237169	+	0.0410789i	−0.853923	+	0.520399i	$0.825783\pi$
$500$		0			0
$501$	−3.04002			−0.135818
$502$		−	10.6458i		−	0.475145i
$503$	−4.65671	−	2.68855i	−0.207633	−	0.119877i	0.392578	−	0.919719i	$-0.371583\pi$
$503$	−4.65671	−	2.68855i	−0.207633	−	0.119877i	−0.600211	+	0.799842i	$0.704917\pi$
$504$	5.17589	−	8.96490i	0.230552	−	0.399329i
$505$		0			0
$506$	−51.3441			−2.28253
$507$	−2.01866	−	1.16547i	−0.0896517	−	0.0517604i
$508$	−2.53755	+	1.46506i	−0.112586	+	0.0650014i
$509$	16.9240	−	29.3132i	0.750142	−	1.29928i	−0.197611	−	0.980280i	$-0.563318\pi$
$509$	16.9240	−	29.3132i	0.750142	−	1.29928i	0.947753	−	0.319004i	$-0.103348\pi$
$510$		0			0
$511$	5.01336	+	8.68339i	0.221778	+	0.384131i
$512$			18.5188i			0.818423i
$513$	0.103495	+	4.72242i	0.00456942	+	0.208500i
$514$	−12.8951			−0.568778
$515$		0			0
$516$	0.0549897	+	0.0952450i	0.00242079	+	0.00419293i
$517$	28.0821	+	16.2132i	1.23505	+	0.713056i
$518$	−6.21260	+	3.58684i	−0.272966	+	0.157597i
$519$	−1.26902	+	2.19800i	−0.0557037	+	0.0964817i
$520$		0			0
$521$	−29.5742			−1.29567			−0.647834	−	0.761782i	$-0.724325\pi$
$521$	−29.5742			−1.29567			−0.647834	+	0.761782i	$0.724325\pi$
$522$	15.2792	+	8.82147i	0.668754	+	0.386105i
$523$	20.8232	+	12.0223i	0.910536	+	0.525698i	0.880604	−	0.473854i	$-0.157137\pi$
$523$	20.8232	+	12.0223i	0.910536	+	0.525698i	0.0299323	+	0.999552i	$0.490471\pi$
$524$	0.483596			0.0211260
$525$		0			0
$526$	22.6054	−	39.1537i	0.985643	−	1.70718i
$527$	6.12871	−	3.53841i	0.266971	−	0.154136i
$528$	3.40899	+	1.96818i	0.148357	+	0.0856540i
$529$	12.7013	+	21.9992i	0.552228	+	0.956488i
$530$		0			0
$531$	−33.3277			−1.44630
$532$	−0.966659	−	0.530207i	−0.0419100	−	0.0229874i
$533$		−	0.493831i		−	0.0213902i
$534$	1.91183	+	3.31138i	0.0827329	+	0.143298i
$535$		0			0
$536$	−7.08279	+	12.2678i	−0.305930	+	0.529886i
$537$	1.55096	−	0.895447i	0.0669289	−	0.0386414i
$538$	23.6124	+	13.6326i	1.01800	+	0.587743i
$539$	26.4022			1.13722
$540$		0			0
$541$	13.0959	−	22.6827i	0.563035	−	0.975205i	−0.434195	−	0.900819i	$-0.642967\pi$
$541$	13.0959	−	22.6827i	0.563035	−	0.975205i	0.997230	−	0.0743856i	$-0.0236996\pi$
$542$	−14.7181	−	8.49753i	−0.632199	−	0.365000i
$543$			2.68282i			0.115131i
$544$	3.00684			0.128917
$545$		0			0
$546$	−0.0712420	−	0.123395i	−0.00304888	−	0.00528081i
$547$	12.9284	+	7.46421i	0.552778	+	0.319146i	0.750242	−	0.661164i	$-0.229937\pi$
$547$	12.9284	+	7.46421i	0.552778	+	0.319146i	−0.197464	+	0.980310i	$0.563270\pi$
$548$	2.95735	−	1.70743i	0.126332	−	0.0729377i
$549$	−1.38581	−	2.40029i	−0.0591449	−	0.102442i
$550$		0			0
$551$	−8.41540	+	15.3427i	−0.358508	+	0.653622i
$552$		−	3.37997i		−	0.143861i
$553$	−16.4385	+	9.49077i	−0.699036	+	0.403588i
$554$	−1.33077	−	2.30496i	−0.0565390	−	0.0979284i
$555$		0			0
$556$	−0.305908	−	0.529848i	−0.0129734	−	0.0224706i
$557$	4.56841	+	2.63757i	0.193570	+	0.111758i	0.593653	−	0.804721i	$-0.297685\pi$
$557$	4.56841	+	2.63757i	0.193570	+	0.111758i	−0.400083	+	0.916479i	$0.631019\pi$
$558$			11.3086i			0.478730i
$559$	1.26820			0.0536391
$560$		0			0
$561$	−1.24426	+	2.15513i	−0.0525328	+	0.0909895i
$562$			21.0196i			0.886660i
$563$		−	17.8950i		−	0.754186i	−0.926175	−	0.377093i	$-0.876924\pi$
$563$		−	17.8950i		−	0.754186i	0.926175	−	0.377093i	$-0.123076\pi$
$564$	0.114609	−	0.198508i	0.00482590	−	0.00835870i
$565$		0			0
$566$	−13.2631	+	22.9724i	−0.557491	+	0.965603i
$567$	−9.83132	+	5.67612i	−0.412877	+	0.238375i
$568$	3.78859	−	2.18735i	0.158966	−	0.0917790i
$569$	−6.81848			−0.285846			−0.142923	−	0.989734i	$-0.545650\pi$
$569$	−6.81848			−0.285846			−0.142923	+	0.989734i	$0.545650\pi$
$570$		0			0
$571$	5.16915			0.216322			0.108161	−	0.994133i	$-0.465504\pi$
$571$	5.16915			0.216322			0.108161	+	0.994133i	$0.465504\pi$
$572$	−0.339864	+	0.196221i	−0.0142104	+	0.00820440i
$573$	−3.25244	+	1.87780i	−0.135873	+	0.0784461i
$574$	−1.17447	+	2.03423i	−0.0490213	+	0.0849073i
$575$		0			0
$576$	10.5049	−	18.1950i	0.437703	−	0.758125i
$577$		−	28.5621i		−	1.18905i	−0.804076	−	0.594527i	$-0.797339\pi$
$577$		−	28.5621i		−	1.18905i	0.804076	−	0.594527i	$-0.202661\pi$
$578$		−	13.9772i		−	0.581376i
$579$	−1.84135	+	3.18930i	−0.0765237	+	0.132543i
$580$		0			0
$581$	19.9079			0.825919
$582$			4.91785i			0.203851i
$583$	27.2786	+	15.7493i	1.12976	+	0.652269i
$584$	10.2831	+	17.8108i	0.425518	+	0.737018i
$585$		0			0
$586$	24.6684	+	42.7269i	1.01904	+	1.76503i
$587$	−34.9228	+	20.1627i	−1.44142	+	0.832204i	−0.997945	−	0.0640822i	$-0.979588\pi$
$587$	−34.9228	+	20.1627i	−1.44142	+	0.832204i	−0.443476	+	0.896286i	$0.646255\pi$
$588$		−	0.186633i		−	0.00769663i
$589$	−11.2137	+	0.245756i	−0.462052	+	0.0101262i
$590$		0			0
$591$	1.44535	+	2.50341i	0.0594536	+	0.102977i
$592$	−13.9903	+	8.07730i	−0.574997	+	0.331975i
$593$	−23.9806	−	13.8452i	−0.984767	−	0.568555i	−0.0810610	−	0.996709i	$-0.525831\pi$
$593$	−23.9806	−	13.8452i	−0.984767	−	0.568555i	−0.903706	+	0.428154i	$0.859164\pi$
$594$	−3.99870	−	6.92595i	−0.164069	−	0.284175i
$595$		0			0
$596$	−1.23613			−0.0506338
$597$			2.40371i			0.0983771i
$598$	3.62449	+	2.09260i	0.148216	+	0.0855727i
$599$	−1.31466	+	2.27706i	−0.0537156	+	0.0930382i	−0.891633	−	0.452759i	$-0.850440\pi$
$599$	−1.31466	+	2.27706i	−0.0537156	+	0.0930382i	0.837917	+	0.545797i	$0.183773\pi$
$600$		0			0
$601$	27.7009			1.12994			0.564972	−	0.825110i	$-0.308887\pi$
$601$	27.7009			1.12994			0.564972	+	0.825110i	$0.308887\pi$
$602$	−5.22408	−	3.01613i	−0.212918	−	0.122928i
$603$	13.6063	−	7.85561i	0.554092	−	0.319905i
$604$	0.481292	−	0.833622i	0.0195835	−	0.0339196i
$605$		0			0
$606$	2.15133	+	3.72622i	0.0873919	+	0.151367i
$607$		−	32.0668i		−	1.30155i	−0.759271	−	0.650775i	$-0.774444\pi$
$607$		−	32.0668i		−	1.30155i	0.759271	−	0.650775i	$-0.225556\pi$
$608$	−4.17842	−	2.29184i	−0.169457	−	0.0929463i
$609$	0.950874			0.0385313
$610$		0			0
$611$	−1.32158	−	2.28904i	−0.0534654	−	0.0926048i
$612$	−1.37048	−	0.791248i	−0.0553985	−	0.0319843i
$613$	−10.7909	+	6.23014i	−0.435841	+	0.251633i	−0.701832	−	0.712343i	$-0.747634\pi$
$613$	−10.7909	+	6.23014i	−0.435841	+	0.251633i	0.265991	+	0.963976i	$0.414301\pi$
$614$	11.5215	−	19.9559i	0.464971	−	0.805354i
$615$		0			0
$616$	−17.3836			−0.700405
$617$	22.9271	+	13.2370i	0.923009	+	0.532900i	0.884594	−	0.466362i	$-0.154436\pi$
$617$	22.9271	+	13.2370i	0.923009	+	0.532900i	0.0384155	+	0.999262i	$0.487769\pi$
$618$	1.23687	+	0.714106i	0.0497541	+	0.0287256i
$619$	−33.3766			−1.34152			−0.670760	−	0.741674i	$-0.734032\pi$
$619$	−33.3766			−1.34152			−0.670760	+	0.741674i	$0.734032\pi$
$620$		0			0
$621$	−3.76960	+	6.52914i	−0.151269	+	0.262005i
$622$	−37.4511	+	21.6224i	−1.50165	+	0.866978i
$623$	−16.0551	−	9.26942i	−0.643234	−	0.371371i
$624$	−0.160431	−	0.277875i	−0.00642240	−	0.0111239i
$625$		0			0
$626$	47.2323			1.88778
$627$	3.37173	−	2.04645i	0.134654	−	0.0817275i
$628$			0.406296i			0.0162130i
$629$	−5.10638	−	8.84452i	−0.203605	−	0.352654i
$630$		0			0
$631$	−20.0601	+	34.7450i	−0.798578	+	1.38318i	0.121964	+	0.992535i	$0.461081\pi$
$631$	−20.0601	+	34.7450i	−0.798578	+	1.38318i	−0.920542	+	0.390643i	$0.872253\pi$
$632$	−33.7176	+	19.4669i	−1.34122	+	0.774351i
$633$	1.53791	+	0.887911i	0.0611263	+	0.0352913i
$634$	20.1000			0.798271
$635$		0			0
$636$	0.111329	−	0.192828i	0.00441450	−	0.00764613i
$637$	−1.86379	−	1.07606i	−0.0738459	−	0.0426349i
$638$		−	29.6276i		−	1.17297i
$639$	−4.85202			−0.191943
$640$		0			0
$641$	−0.203273	−	0.352079i	−0.00802880	−	0.0139063i	0.861983	−	0.506937i	$-0.169222\pi$
$641$	−0.203273	−	0.352079i	−0.00802880	−	0.0139063i	−0.870012	+	0.493031i	$0.835889\pi$
$642$	3.02901	+	1.74880i	0.119545	+	0.0690195i
$643$	21.7975	−	12.5848i	0.859610	−	0.496296i	−0.00427137	−	0.999991i	$-0.501360\pi$
$643$	21.7975	−	12.5848i	0.859610	−	0.496296i	0.863882	+	0.503695i	$0.168026\pi$
$644$	−0.879860	−	1.52396i	−0.0346713	−	0.0600525i
$645$		0			0
$646$	8.53908	−	15.5682i	0.335965	−	0.612523i
$647$			18.3604i			0.721821i	0.932600	+	0.360911i	$0.117534\pi$
$647$			18.3604i			0.721821i	−0.932600	+	0.360911i	$0.882466\pi$
$648$	−20.1654	+	11.6425i	−0.792173	+	0.457361i
$649$	27.9834	+	48.4686i	1.09844	+	1.90256i
$650$		0			0
$651$	0.304740	+	0.527825i	0.0119437	+	0.0206871i
$652$	−1.60534	−	0.926843i	−0.0628699	−	0.0362980i
$653$		−	33.0301i		−	1.29257i	−0.763097	−	0.646284i	$-0.776322\pi$
$653$		−	33.0301i		−	1.29257i	0.763097	−	0.646284i	$-0.223678\pi$
$654$	2.20414			0.0861886
$655$		0			0
$656$	−2.64481	+	4.58094i	−0.103262	+	0.178856i
$657$		−	22.8102i		−	0.889911i
$658$			12.5723i			0.490120i
$659$	−13.2310	+	22.9167i	−0.515406	+	0.892709i	0.484434	+	0.874828i	$0.339025\pi$
$659$	−13.2310	+	22.9167i	−0.515406	+	0.892709i	−0.999840	+	0.0178814i	$0.994308\pi$
$660$		0			0
$661$	7.79673	−	13.5043i	0.303258	−	0.525258i	−0.673614	−	0.739083i	$-0.735259\pi$
$661$	7.79673	−	13.5043i	0.303258	−	0.525258i	0.976872	+	0.213825i	$0.0685924\pi$
$662$	37.7480	−	21.7938i	1.46712	−	0.847041i
$663$	0.175670	−	0.101423i	0.00682246	−	0.00393895i
$664$	40.8339			1.58466
$665$		0			0
$666$	16.3197			0.632377
$667$	−24.1882	+	13.9651i	−0.936570	+	0.540729i
$668$	−2.81146	+	1.62320i	−0.108779	+	0.0628034i
$669$	2.34837	−	4.06749i	0.0907931	−	0.157258i
$670$		0			0
$671$	−2.32717	+	4.03078i	−0.0898395	+	0.155607i
$672$			0.258959i			0.00998958i
$673$			6.13645i			0.236543i	0.992981	+	0.118271i	$0.0377353\pi$
$673$			6.13645i			0.236543i	−0.992981	+	0.118271i	$0.962265\pi$
$674$	−11.4880	+	19.8977i	−0.442500	+	0.766432i
$675$		0			0
$676$	−2.48919			−0.0957379
$677$			22.2754i			0.856112i	0.903752	+	0.428056i	$0.140801\pi$
$677$			22.2754i			0.856112i	−0.903752	+	0.428056i	$0.859199\pi$
$678$	−1.52536	−	0.880665i	−0.0585810	−	0.0338217i
$679$	−11.9220	−	20.6495i	−0.457524	−	0.792455i
$680$		0			0
$681$	0.207553	+	0.359492i	0.00795344	+	0.0137758i
$682$	16.4461	−	9.49517i	0.629754	−	0.363589i
$683$		−	16.7397i		−	0.640527i	−0.947328	−	0.320264i	$-0.896228\pi$
$683$		−	16.7397i		−	0.640527i	0.947328	−	0.320264i	$-0.103772\pi$
$684$	1.30138	+	2.14414i	0.0497594	+	0.0819832i
$685$		0			0
$686$	11.8796	+	20.5761i	0.453566	+	0.785599i
$687$	3.44130	−	1.98683i	0.131294	−	0.0758024i
$688$	−11.7642	−	6.79208i	−0.448507	−	0.258946i
$689$	−1.28377	−	2.22355i	−0.0489076	−	0.0847104i
$690$		0			0
$691$	36.7557			1.39825			0.699126	−	0.714999i	$-0.253573\pi$
$691$	36.7557			1.39825			0.699126	+	0.714999i	$0.253573\pi$
$692$			2.71034i			0.103032i
$693$	16.6973	+	9.64018i	0.634277	+	0.366200i
$694$	−16.7284	+	28.9744i	−0.635000	+	1.09985i
$695$		0			0
$696$	1.95037			0.0739288
$697$	−2.89602	−	1.67202i	−0.109695	−	0.0633323i
$698$	32.6954	−	18.8767i	1.23754	−	0.714494i
$699$	0.186497	−	0.323021i	0.00705395	−	0.0122178i
$700$		0			0
$701$	−17.7053	−	30.6665i	−0.668721	−	1.15826i	−0.978262	−	0.207372i	$-0.933509\pi$
$701$	−17.7053	−	30.6665i	−0.668721	−	1.15826i	0.309541	−	0.950886i	$-0.399824\pi$
$702$			0.651889i			0.0246040i
$703$	0.354657	+	16.1828i	0.0133761	+	0.610345i
$704$	−35.2814			−1.32972
$705$		0			0
$706$	−7.62510	−	13.2071i	−0.286974	−	0.497054i
$707$	−18.0664	−	10.4306i	−0.679457	−	0.392285i
$708$	0.342618	−	0.197810i	0.0128764	−	0.00743417i
$709$	16.9184	−	29.3036i	0.635386	−	1.10052i	−0.351048	−	0.936358i	$-0.614174\pi$
$709$	16.9184	−	29.3036i	0.635386	−	1.10052i	0.986433	−	0.164163i	$-0.0524922\pi$
$710$		0			0
$711$	43.1819			1.61945
$712$	−32.9313	−	19.0129i	−1.23415	−	0.712538i
$713$	−15.5039	−	8.95117i	−0.580625	−	0.335224i
$714$	−0.964848			−0.0361085
$715$		0			0
$716$	0.956237	−	1.65625i	0.0357362	−	0.0618970i
$717$	−1.20806	+	0.697474i	−0.0451158	+	0.0260476i
$718$	−2.54307	−	1.46824i	−0.0949066	−	0.0547943i
$719$	13.4970	+	23.3775i	0.503353	+	0.871833i	0.999992	+	0.00387581i	$0.00123371\pi$
$719$	13.4970	+	23.3775i	0.503353	+	0.871833i	−0.496640	+	0.867957i	$0.665433\pi$
$720$		0			0
$721$	−6.92463			−0.257887
$722$	−23.7324	+	15.1256i	−0.883229	+	0.562916i
$723$			2.63997i			0.0981814i
$724$	1.43247	+	2.48111i	0.0532374	+	0.0922099i
$725$		0			0
$726$	−1.85944	+	3.22065i	−0.0690104	+	0.119529i
$727$	18.7090	−	10.8016i	0.693878	−	0.400610i	−0.111185	−	0.993800i	$-0.535465\pi$
$727$	18.7090	−	10.8016i	0.693878	−	0.400610i	0.805063	+	0.593189i	$0.202131\pi$
$728$	1.22714	+	0.708492i	0.0454810	+	0.0262584i
$729$	25.2353			0.934640
$730$		0			0
$731$	4.29388	−	7.43723i	0.158815	−	0.275076i
$732$	0.0284930	+	0.0164504i	0.00105313	+	0.000608026i
$733$		−	17.2551i		−	0.637332i	−0.947867	−	0.318666i	$-0.896765\pi$
$733$		−	17.2551i		−	0.637332i	0.947867	−	0.318666i	$-0.103235\pi$
$734$	7.81217			0.288353
$735$		0			0
$736$	−3.80322	−	6.58737i	−0.140189	−	0.242814i
$737$	−22.8489	−	13.1918i	−0.841650	−	0.485927i
$738$	4.62777	−	2.67184i	0.170350	−	0.0983519i
$739$	2.39553	+	4.14918i	0.0881210	+	0.152630i	0.906717	−	0.421740i	$-0.138580\pi$
$739$	2.39553	+	4.14918i	0.0881210	+	0.152630i	−0.818596	+	0.574370i	$0.805247\pi$
$740$		0			0
$741$	−0.321423	+	0.00704420i	−0.0118078	+	0.000258775i
$742$			12.2126i			0.448338i
$743$	12.5465	−	7.24373i	0.460287	−	0.265747i	−0.251878	−	0.967759i	$-0.581048\pi$
$743$	12.5465	−	7.24373i	0.460287	−	0.265747i	0.712165	+	0.702012i	$0.247715\pi$
$744$	0.625065	+	1.08264i	0.0229160	+	0.0396917i
$745$		0			0
$746$	23.4912	+	40.6879i	0.860072	+	1.48969i
$747$	−39.2217	−	22.6447i	−1.43505	−	0.828525i
$748$			2.65746i			0.0971665i
$749$	−16.9579			−0.619630
$750$		0			0
$751$	−3.22637	+	5.58824i	−0.117732	+	0.203918i	−0.918869	−	0.394564i	$-0.870896\pi$
$751$	−3.22637	+	5.58824i	−0.117732	+	0.203918i	0.801137	+	0.598482i	$0.204229\pi$
$752$			28.3119i			1.03243i
$753$			1.30527i			0.0475667i
$754$	−1.20751	+	2.09147i	−0.0439749	+	0.0761668i
$755$		0			0
$756$	0.137047	−	0.237373i	0.00498437	−	0.00863318i
$757$	−32.0074	+	18.4795i	−1.16333	+	0.671649i	−0.952100	−	0.305788i	$-0.901080\pi$
$757$	−32.0074	+	18.4795i	−1.16333	+	0.671649i	−0.211230	+	0.977436i	$0.567747\pi$
$758$	45.5530	−	26.3000i	1.65456	−	0.955260i
$759$	6.29525			0.228503
$760$		0			0
$761$	48.3893			1.75411			0.877055	−	0.480389i	$-0.159505\pi$
$761$	48.3893			1.75411			0.877055	+	0.480389i	$0.159505\pi$
$762$	3.51967	−	2.03208i	0.127504	−	0.0736145i
$763$	−9.25493	+	5.34333i	−0.335051	+	0.193442i
$764$	−2.00528	+	3.47324i	−0.0725484	+	0.125657i
$765$		0			0
$766$	−10.3167	+	17.8690i	−0.372756	+	0.645632i
$767$		−	4.56200i		−	0.164724i
$768$			0.837598i			0.0302242i
$769$	20.7177	−	35.8841i	0.747098	−	1.29401i	−0.202110	−	0.979363i	$-0.564780\pi$
$769$	20.7177	−	35.8841i	0.747098	−	1.29401i	0.949208	−	0.314649i	$-0.101887\pi$
$770$		0			0
$771$	1.58105			0.0569403
$772$			3.93270i			0.141541i
$773$	33.6285	+	19.4154i	1.20953	+	0.698325i	0.962658	−	0.270722i	$-0.0872623\pi$
$773$	33.6285	+	19.4154i	1.20953	+	0.698325i	0.246877	+	0.969047i	$0.420596\pi$
$774$	6.86151	+	11.8845i	0.246632	+	0.427179i
$775$		0			0
$776$	−24.4537	−	42.3550i	−0.877836	−	1.52046i
$777$	0.761720	−	0.439779i	0.0273266	−	0.0157770i
$778$		−	1.39657i		−	0.0500695i
$779$	2.74999	+	4.53087i	0.0985287	+	0.162335i
$780$		0			0
$781$	4.07397	+	7.05632i	0.145778	+	0.252495i
$782$	24.5437	−	14.1703i	0.877680	−	0.506729i
$783$	−3.76757	−	2.17521i	−0.134642	−	0.0777355i
$784$	11.5261	+	19.9637i	0.411645	+	0.712990i
$785$		0			0
$786$	−0.670764			−0.0239254
$787$			51.4952i			1.83561i	0.397037	+	0.917803i	$0.370038\pi$
$787$			51.4952i			1.83561i	−0.397037	+	0.917803i	$0.629962\pi$
$788$	2.67336	+	1.54347i	0.0952347	+	0.0549838i
$789$	−2.77163	+	4.80060i	−0.0986725	+	0.170906i
$790$		0			0
$791$	8.53973			0.303638
$792$	34.2485	+	19.7734i	1.21697	+	0.702615i
$793$	0.328560	−	0.189694i	0.0116675	−	0.00673623i
$794$	−21.1556	+	36.6426i	−0.750785	+	1.30040i
$795$		0			0
$796$	1.28344	+	2.22299i	0.0454905	+	0.0787918i
$797$		−	7.50433i		−	0.265817i	−0.991128	−	0.132908i	$-0.957568\pi$
$797$		−	7.50433i		−	0.265817i	0.991128	−	0.132908i	$-0.0424316\pi$
$798$	1.34079	+	0.735414i	0.0474634	+	0.0260334i
$799$	−17.8985			−0.633203
$800$		0			0
$801$	21.0874	+	36.5244i	0.745087	+	1.29053i
$802$	−9.19387	−	5.30809i	−0.324647	−	0.187435i
$803$	−33.1730	+	19.1524i	−1.17065	+	0.675875i
$804$	−0.0932510	+	0.161515i	−0.00328871	+	0.00569621i
$805$		0			0
$806$	−1.54795			−0.0545243
$807$	−2.89509	−	1.67148i	−0.101912	−	0.0588388i
$808$	−37.0567	−	21.3947i	−1.30365	−	0.752663i
$809$	17.9109			0.629714			0.314857	−	0.949139i	$-0.398043\pi$
$809$	17.9109			0.629714			0.314857	+	0.949139i	$0.398043\pi$
$810$		0			0
$811$	−2.57516	+	4.46030i	−0.0904260	+	0.156622i	−0.907690	−	0.419640i	$-0.862156\pi$
$811$	−2.57516	+	4.46030i	−0.0904260	+	0.156622i	0.817264	+	0.576263i	$0.195490\pi$
$812$	0.879385	−	0.507713i	0.0308604	−	0.0178172i
$813$	1.80458	+	1.04187i	0.0632893	+	0.0365401i
$814$	−13.7028	−	23.7339i	−0.480281	−	0.831871i
$815$		0			0
$816$	−2.17276			−0.0760619
$817$	−11.6356	+	7.06221i	−0.407080	+	0.247075i
$818$		−	15.6007i		−	0.545464i
$819$	−0.785796	−	1.36104i	−0.0274579	−	0.0475586i
$820$		0			0
$821$	0.690525	−	1.19602i	0.0240995	−	0.0417415i	−0.853724	−	0.520726i	$-0.825661\pi$
$821$	0.690525	−	1.19602i	0.0240995	−	0.0417415i	0.877824	+	0.478984i	$0.158995\pi$
$822$	−4.10194	+	2.36826i	−0.143072	+	0.0826025i
$823$	−12.4846	−	7.20798i	−0.435185	−	0.251254i	0.266368	−	0.963871i	$-0.414176\pi$
$823$	−12.4846	−	7.20798i	−0.435185	−	0.251254i	−0.701553	+	0.712617i	$0.747510\pi$
$824$	−14.2034			−0.494798
$825$		0			0
$826$	−10.8497	+	18.7922i	−0.377509	+	0.653864i
$827$	8.20404	+	4.73660i	0.285282	+	0.164708i	0.635812	−	0.771844i	$-0.280665\pi$
$827$	8.20404	+	4.73660i	0.285282	+	0.164708i	−0.350530	+	0.936552i	$0.613999\pi$
$828$			4.00326i			0.139123i
$829$	12.3950			0.430497			0.215248	−	0.976559i	$-0.430944\pi$
$829$	12.3950			0.430497			0.215248	+	0.976559i	$0.430944\pi$
$830$		0			0
$831$	0.163164	+	0.282609i	0.00566011	+	0.00980359i
$832$	2.49059	+	1.43794i	0.0863455	+	0.0498516i
$833$	−12.6209	+	7.28666i	−0.437287	+	0.252468i
$834$	0.424304	+	0.734916i	0.0146925	+	0.0254481i
$835$		0			0
$836$	2.02554	−	3.69291i	0.0700548	−	0.127722i
$837$		−	2.78848i		−	0.0963839i
$838$	3.24142	−	1.87144i	0.111973	−	0.0646477i
$839$	6.26491	+	10.8511i	0.216289	+	0.374623i	0.953670	−	0.300853i	$-0.0972714\pi$
$839$	6.26491	+	10.8511i	0.216289	+	0.374623i	−0.737382	+	0.675476i	$0.763938\pi$
$840$		0			0
$841$	6.44162	+	11.1572i	0.222125	+	0.384732i
$842$	19.0706	+	11.0104i	0.657215	+	0.379443i
$843$		−	2.57720i		−	0.0887633i
$844$	1.89638			0.0652760
$845$		0			0
$846$	14.3007	−	24.7695i	0.491667	−	0.851592i
$847$		−	18.0308i		−	0.619547i
$848$			27.5018i			0.944416i
$849$	1.62618	−	2.81663i	0.0558103	−	0.0966663i
$850$		0			0
$851$	−12.9177	+	22.3741i	−0.442813	+	0.766974i
$852$	0.0498801	−	0.0287983i	0.00170886	−	0.000986613i
$853$	3.00771	−	1.73650i	0.102982	−	0.0594567i	−0.447624	−	0.894222i	$-0.647730\pi$
$853$	3.00771	−	1.73650i	0.102982	−	0.0594567i	0.550606	+	0.834765i	$0.314397\pi$
$854$	−1.80458			−0.0617513
$855$		0			0
$856$	−34.7831			−1.18886
$857$	14.4295	−	8.33085i	0.492901	−	0.284577i	−0.232876	−	0.972506i	$-0.574814\pi$
$857$	14.4295	−	8.33085i	0.492901	−	0.284577i	0.725777	+	0.687930i	$0.241480\pi$
$858$	0.471402	−	0.272164i	0.0160934	−	0.00929154i
$859$	20.4042	−	35.3412i	0.696183	−	1.20583i	−0.273597	−	0.961844i	$-0.588213\pi$
$859$	20.4042	−	35.3412i	0.696183	−	1.20583i	0.969780	−	0.243981i	$-0.0784533\pi$
$860$		0			0
$861$	0.144000	−	0.249415i	0.00490751	−	0.00850005i
$862$			6.19239i			0.210914i
$863$			4.07050i			0.138561i	0.997597	+	0.0692806i	$0.0220704\pi$
$863$			4.07050i			0.138561i	−0.997597	+	0.0692806i	$0.977930\pi$
$864$	0.592392	−	1.02605i	0.0201536	−	0.0349071i
$865$		0			0
$866$	−37.4821			−1.27369
$867$			1.71373i			0.0582014i
$868$	0.563658	+	0.325428i	0.0191318	+	0.0110458i
$869$	−36.2574	−	62.7996i	−1.22995	−	2.13033i
$870$		0			0
$871$	1.07530	+	1.86247i	0.0364351	+	0.0631075i
$872$	−18.9831	+	10.9599i	−0.642851	+	0.371150i
$873$			54.2437i			1.83587i
$874$	−44.9075	+	0.984178i	−1.51902	+	0.0332903i
$875$		0			0
$876$	0.135386	+	0.234495i	0.00457426	+	0.00792285i
$877$	22.9621	−	13.2572i	0.775376	−	0.447663i	−0.0594132	−	0.998233i	$-0.518923\pi$
$877$	22.9621	−	13.2572i	0.775376	−	0.447663i	0.834789	+	0.550570i	$0.185590\pi$
$878$	−37.0871	−	21.4122i	−1.25163	−	0.722628i
$879$	−3.02457	−	5.23871i	−0.102016	−	0.176697i
$880$		0			0
$881$	−22.3730			−0.753766			−0.376883	−	0.926261i	$-0.623004\pi$
$881$	−22.3730			−0.753766			−0.376883	+	0.926261i	$0.623004\pi$
$882$		−	23.2878i		−	0.784140i
$883$	−17.0726	−	9.85689i	−0.574540	−	0.331711i	0.184421	−	0.982847i	$-0.440959\pi$
$883$	−17.0726	−	9.85689i	−0.574540	−	0.331711i	−0.758961	+	0.651137i	$0.774292\pi$
$884$	0.108308	−	0.187596i	0.00364281	−	0.00630953i
$885$		0			0
$886$	−6.79667			−0.228339
$887$	9.89139	+	5.71080i	0.332120	+	0.191750i	0.656782	−	0.754080i	$-0.271917\pi$
$887$	9.89139	+	5.71080i	0.332120	+	0.191750i	−0.324662	+	0.945830i	$0.605250\pi$
$888$	1.56239	−	0.902049i	0.0524305	−	0.0302708i
$889$	−9.85245	+	17.0649i	−0.330441	+	0.572340i
$890$		0			0
$891$	−21.6844	−	37.5584i	−0.726453	−	1.25825i
$892$		−	5.01558i		−	0.167934i
$893$	24.8724	+	13.6424i	0.832323	+	0.456524i
$894$	1.71455			0.0573431
$895$		0			0
$896$	−8.26556	−	14.3164i	−0.276133	−	0.478276i
$897$	−0.444395	−	0.256571i	−0.0148379	−	0.00856667i
$898$	37.4783	−	21.6381i	1.25067	−	0.722073i
$899$	5.16517	−	8.94634i	0.172268	−	0.298377i
$900$		0			0
$901$	−17.3864			−0.579223
$902$	−7.77135	−	4.48679i	−0.258758	−	0.149394i
$903$	0.640519	+	0.369804i	0.0213151	+	0.0123063i
$904$	17.5162			0.582580
$905$		0			0
$906$	−0.667568	+	1.15626i	−0.0221784	+	0.0384142i
$907$	9.29964	−	5.36915i	0.308789	−	0.178280i	−0.337595	−	0.941291i	$-0.609613\pi$
$907$	9.29964	−	5.36915i	0.308789	−	0.178280i	0.646385	+	0.763012i	$0.276280\pi$
$908$	0.383897	+	0.221643i	0.0127401	+	0.00735548i
$909$	23.7291	+	41.1000i	0.787045	+	1.36320i
$910$		0			0
$911$	−27.5952			−0.914269			−0.457134	−	0.889398i	$-0.651124\pi$
$911$	−27.5952			−0.914269			−0.457134	+	0.889398i	$0.651124\pi$
$912$	3.01935	+	1.65610i	0.0999807	+	0.0548388i
$913$			76.0538i			2.51701i
$914$	−17.5605	−	30.4157i	−0.580850	−	1.00606i
$915$		0			0
$916$	2.12171	−	3.67492i	0.0701034	−	0.121423i
$917$	2.81646	−	1.62608i	0.0930077	−	0.0536980i
$918$	3.82294	+	2.20717i	0.126176	+	0.0728476i
$919$	49.2639			1.62507			0.812533	−	0.582915i	$-0.198088\pi$
$919$	49.2639			1.62507			0.812533	+	0.582915i	$0.198088\pi$
$920$		0			0
$921$	−1.41264	+	2.44677i	−0.0465482	+	0.0806238i
$922$	44.9243	+	25.9371i	1.47950	+	0.854192i
$923$		−	0.664160i		−	0.0218611i
$924$	−0.228870			−0.00752927
$925$		0			0
$926$	−15.1775	−	26.2882i	−0.498763	−	0.863883i
$927$	13.6426	+	7.87657i	0.448082	+	0.258700i
$928$	3.80117	−	2.19461i	0.124779	−	0.0720415i
$929$	21.5374	+	37.3039i	0.706619	+	1.22390i	0.966104	+	0.258153i	$0.0831138\pi$
$929$	21.5374	+	37.3039i	0.706619	+	1.22390i	−0.259485	+	0.965747i	$0.583553\pi$
$930$		0			0
$931$	23.0923	−	0.506085i	0.756821	−	0.0165863i
$932$		−	0.398315i		−	0.0130472i
$933$	4.59183	−	2.65110i	0.150330	−	0.0867930i
$934$	6.84568	+	11.8571i	0.223998	+	0.387975i
$935$		0			0
$936$	−1.61178	−	2.79168i	−0.0526826	−	0.0912490i
$937$	−37.6239	−	21.7222i	−1.22912	−	0.709633i	−0.262275	−	0.964993i	$-0.584473\pi$
$937$	−37.6239	−	21.7222i	−1.22912	−	0.709633i	−0.966846	+	0.255360i	$0.917806\pi$
$938$		−	10.2294i		−	0.334003i
$939$	−5.79110			−0.188985
$940$		0			0
$941$	−14.6471	+	25.3694i	−0.477480	+	0.827020i	−0.999667	−	0.0258111i	$-0.991783\pi$
$941$	−14.6471	+	25.3694i	−0.477480	+	0.827020i	0.522186	+	0.852831i	$0.325117\pi$
$942$		−	0.563545i		−	0.0183613i
$943$			8.45946i			0.275478i
$944$	−24.4326	+	42.3186i	−0.795215	+	1.37735i
$945$		0			0
$946$	11.5224	−	19.9575i	0.374627	−	0.648873i
$947$	−1.73715	+	1.00294i	−0.0564498	+	0.0325913i	−0.527959	−	0.849270i	$-0.677043\pi$
$947$	−1.73715	+	1.00294i	−0.0564498	+	0.0325913i	0.471509	+	0.881861i	$0.343709\pi$
$948$	−0.443921	+	0.256298i	−0.0144179	+	0.00832418i
$949$	3.12233			0.101355
$950$		0			0
$951$	−2.46443			−0.0799148
$952$	8.30975	−	4.79764i	0.269321	−	0.155492i
$953$	16.6614	−	9.61946i	0.539716	−	0.311605i	−0.205248	−	0.978710i	$-0.565800\pi$
$953$	16.6614	−	9.61946i	0.539716	−	0.311605i	0.744964	+	0.667105i	$0.232467\pi$
$954$	13.8915	−	24.0607i	0.449753	−	0.778995i
$955$		0			0
$956$	−0.744823	+	1.29007i	−0.0240893	+	0.0417239i
$957$			3.63260i			0.117425i
$958$			5.58045i			0.180296i
$959$	11.4824	−	19.8881i	0.370786	−	0.642220i
$960$		0			0
$961$	−24.3786			−0.786406
$962$			2.23390i			0.0720237i
$963$	33.4098	+	19.2892i	1.07662	+	0.621585i
$964$	1.40959	+	2.44149i	0.0453999	+	0.0786350i
$965$		0			0
$966$	1.22039	+	2.11378i	0.0392655	+	0.0680099i
$967$	24.6075	−	14.2071i	0.791324	−	0.456871i	−0.0491047	−	0.998794i	$-0.515637\pi$
$967$	24.6075	−	14.2071i	0.791324	−	0.456871i	0.840428	+	0.541923i	$0.182303\pi$
$968$		−	36.9838i		−	1.18870i
$969$	−1.04697	+	1.90880i	−0.0336334	+	0.0613196i
$970$		0			0
$971$	−8.98811	−	15.5679i	−0.288442	−	0.499597i	0.684996	−	0.728547i	$-0.259804\pi$
$971$	−8.98811	−	15.5679i	−0.288442	−	0.499597i	−0.973438	+	0.228950i	$0.926471\pi$
$972$	−0.811508	+	0.468524i	−0.0260291	+	0.0150279i
$973$	−3.56321	−	2.05722i	−0.114231	−	0.0659515i
$974$	8.73761	+	15.1340i	0.279971	+	0.484924i
$975$		0			0
$976$	−4.06377			−0.130078
$977$			13.2288i			0.423226i	0.977354	+	0.211613i	$0.0678716\pi$
$977$			13.2288i			0.423226i	−0.977354	+	0.211613i	$0.932128\pi$
$978$	2.22666	+	1.28556i	0.0712006	+	0.0411077i
$979$	35.4118	−	61.3350i	1.13177	−	1.96027i
$980$		0			0
$981$	24.3116			0.776208
$982$	10.0512	+	5.80305i	0.320746	+	0.185183i
$983$	−42.0225	+	24.2617i	−1.34031	+	0.773828i	−0.986853	−	0.161623i	$-0.948327\pi$
$983$	−42.0225	+	24.2617i	−1.34031	+	0.773828i	−0.353457	+	0.935451i	$0.614994\pi$
$984$	0.295364	−	0.511586i	0.00941587	−	0.0163088i
$985$		0			0
$986$	8.17680	+	14.1626i	0.260403	+	0.451030i
$987$		−	1.54148i		−	0.0490658i
$988$	−0.293496	+	0.178136i	−0.00933736	+	0.00566727i
$989$	−21.7246			−0.690802
$990$		0			0
$991$	−20.1402	−	34.8838i	−0.639773	−	1.10812i	−0.985482	−	0.169778i	$-0.945695\pi$
$991$	−20.1402	−	34.8838i	−0.639773	−	1.10812i	0.345709	−	0.938342i	$-0.387638\pi$
$992$	2.43643	+	1.40667i	0.0773568	+	0.0446619i
$993$	−4.62824	+	2.67212i	−0.146873	+	0.0847971i
$994$	−1.57955	+	2.73587i	−0.0501004	+	0.0867764i
$995$		0			0
$996$	0.537613			0.0170349
$997$	−23.8668	−	13.7795i	−0.755869	−	0.436401i	0.0719414	−	0.997409i	$-0.477081\pi$
$997$	−23.8668	−	13.7795i	−0.755869	−	0.436401i	−0.827811	+	0.561008i	$0.810414\pi$
$998$	−1.35919	−	0.784730i	−0.0430245	−	0.0248402i
$999$	−4.02413			−0.127318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.d.349.4		24
5.2	odd	4		475.2.e.h.26.1	yes	12
5.3	odd	4		475.2.e.f.26.6	✓	12
5.4	even	2	inner	475.2.j.d.349.9		24
19.11	even	3	inner	475.2.j.d.49.9		24
95.7	odd	12		9025.2.a.br.1.6		6
95.12	even	12		9025.2.a.by.1.1		6
95.49	even	6	inner	475.2.j.d.49.4		24
95.68	odd	12		475.2.e.f.201.6	yes	12
95.83	odd	12		9025.2.a.bz.1.1		6
95.87	odd	12		475.2.e.h.201.1	yes	12
95.88	even	12		9025.2.a.bs.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.6	✓	12	5.3	odd	4
475.2.e.f.201.6	yes	12	95.68	odd	12
475.2.e.h.26.1	yes	12	5.2	odd	4
475.2.e.h.201.1	yes	12	95.87	odd	12
475.2.j.d.49.4		24	95.49	even	6	inner
475.2.j.d.49.9		24	19.11	even	3	inner
475.2.j.d.349.4		24	1.1	even	1	trivial
475.2.j.d.349.9		24	5.4	even	2	inner
9025.2.a.br.1.6		6	95.7	odd	12
9025.2.a.bs.1.6		6	95.88	even	12
9025.2.a.by.1.1		6	95.12	even	12
9025.2.a.bz.1.1		6	95.83	odd	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28275 + 0.740597i) q^{2} +(0.157277 - 0.0908038i) q^{3} +(0.0969683 - 0.167954i) q^{4} +(-0.134498 + 0.232958i) q^{6} -1.30422i q^{7} -2.67513i q^{8} +(-1.48351 + 2.56951i) q^{9} +4.98247 q^{11} -0.0352204i q^{12} +(-0.351723 - 0.203067i) q^{13} +(0.965899 + 1.67299i) q^{14} +(2.17513 + 3.76744i) q^{16} +(-2.38173 + 1.37510i) q^{17} -4.39473i q^{18} +(4.35785 - 0.0955054i) q^{19} +(-0.118428 - 0.205123i) q^{21} +(-6.39128 + 3.69001i) q^{22} +(6.02510 + 3.47860i) q^{23} +(-0.242912 - 0.420736i) q^{24} +0.601564 q^{26} +1.08366i q^{27} +(-0.219048 - 0.126468i) q^{28} +(-2.00728 + 3.47672i) q^{29} -2.57321 q^{31} +(-0.946844 - 0.546661i) q^{32} +(0.783628 - 0.452428i) q^{33} +(2.03678 - 3.52781i) q^{34} +(0.287707 + 0.498323i) q^{36} +3.71348i q^{37} +(-5.51931 + 3.34992i) q^{38} -0.0737572 q^{39} +(0.607965 + 1.05303i) q^{41} +(0.303827 + 0.175415i) q^{42} +(-2.70426 + 1.56130i) q^{43} +(0.483142 - 0.836826i) q^{44} -10.3050 q^{46} +(5.63617 + 3.25405i) q^{47} +(0.684196 + 0.395020i) q^{48} +5.29902 q^{49} +(-0.249728 + 0.432541i) q^{51} +(-0.0682119 + 0.0393822i) q^{52} +(5.47490 + 3.16094i) q^{53} +(-0.802553 - 1.39006i) q^{54} -3.48895 q^{56} +(0.676717 - 0.410731i) q^{57} -5.94636i q^{58} +(5.61636 + 9.72783i) q^{59} +(-0.467072 + 0.808992i) q^{61} +(3.30079 - 1.90571i) q^{62} +(3.35120 + 1.93482i) q^{63} -7.08110 q^{64} +(-0.670133 + 1.16071i) q^{66} +(-4.58585 - 2.64764i) q^{67} +0.533363i q^{68} +1.26348 q^{69} +(0.817659 + 1.41623i) q^{71} +(6.87378 + 3.96858i) q^{72} +(-6.65794 + 3.84396i) q^{73} +(-2.75019 - 4.76347i) q^{74} +(0.406533 - 0.741180i) q^{76} -6.49822i q^{77} +(0.0946121 - 0.0546243i) q^{78} +(-7.27699 - 12.6041i) q^{79} +(-4.35213 - 7.53811i) q^{81} +(-1.55974 - 0.900514i) q^{82} +15.2643i q^{83} -0.0459350 q^{84} +(2.31260 - 4.00553i) q^{86} +0.729076i q^{87} -13.3288i q^{88} +(7.10727 - 12.3101i) q^{89} +(-0.264844 + 0.458723i) q^{91} +(1.16849 - 0.674627i) q^{92} +(-0.404707 + 0.233658i) q^{93} -9.63975 q^{94} -0.198556 q^{96} +(15.8329 - 9.14111i) q^{97} +(-6.79733 + 3.92444i) q^{98} +(-7.39155 + 12.8025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 2 q^{6} + 14 q^{9} - 4 q^{11} - 12 q^{14} + 12 q^{16} + 12 q^{19} - 6 q^{21} + 22 q^{24} + 76 q^{26} + 6 q^{29} - 12 q^{31} - 2 q^{34} - 26 q^{36} - 32 q^{39} - 22 q^{41} + 42 q^{44} - 48 q^{46}+ \cdots - 40 q^{99}+O(q^{100}) \) 24 * q + 4 * q^4 + 2 * q^6 + 14 * q^9 - 4 * q^11 - 12 * q^14 + 12 * q^16 + 12 * q^19 - 6 * q^21 + 22 * q^24 + 76 * q^26 + 6 * q^29 - 12 * q^31 - 2 * q^34 - 26 * q^36 - 32 * q^39 - 22 * q^41 + 42 * q^44 - 48 * q^46 - 16 * q^49 + 34 * q^51 + 36 * q^54 + 16 * q^56 + 8 * q^59 - 50 * q^61 + 88 * q^64 - 68 * q^66 - 52 * q^69 - 36 * q^71 - 12 * q^74 + 48 * q^76 + 6 * q^79 - 4 * q^81 - 148 * q^84 - 18 * q^86 + 24 * q^89 + 22 * q^91 - 32 * q^94 - 52 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more