LMFDB - Embedded newform 375.2.i.d.349.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(49,375)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("375.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.5
Character	$\chi$	$=$	375.349
Dual form			375.2.i.d.274.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.32085 - 0.754089i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.19965 - 2.32468i) q^{4} +(1.97423 + 1.43436i) q^{6} +3.44028i q^{7} +(2.80415 - 3.85959i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.00942 - 3.10669i) q^{11} +(3.76141 + 1.22216i) q^{12} +(-3.07385 - 0.998755i) q^{13} +(2.59428 + 7.98437i) q^{14} +(1.15323 - 3.54927i) q^{16} +(2.97030 - 4.08826i) q^{17} +2.44028i q^{18} +(-2.49274 - 1.81108i) q^{19} +(-2.78325 + 2.02215i) q^{21} +(-4.68544 - 6.44895i) q^{22} +(-1.47190 + 0.478250i) q^{23} +4.77071 q^{24} -7.88709 q^{26} +(-0.951057 + 0.309017i) q^{27} +(7.99756 + 11.0077i) q^{28} +(-2.52590 + 1.83517i) q^{29} +(-6.02080 - 4.37437i) q^{31} +0.434479i q^{32} +(1.92004 - 2.64270i) q^{33} +(3.81069 - 11.7281i) q^{34} +(1.22216 + 3.76141i) q^{36} +(5.47655 + 1.77944i) q^{37} +(-7.15098 - 2.32349i) q^{38} +(-0.998755 - 3.07385i) q^{39} +(1.67476 - 5.15437i) q^{41} +(-4.93461 + 6.79191i) q^{42} +2.53106i q^{43} +(-10.4519 - 7.59371i) q^{44} +(-3.05541 + 2.21989i) q^{46} +(4.15659 + 5.72106i) q^{47} +(3.54927 - 1.15323i) q^{48} -4.83555 q^{49} +5.05337 q^{51} +(-12.1570 + 3.95006i) q^{52} +(5.96693 + 8.21277i) q^{53} +(-1.97423 + 1.43436i) q^{54} +(13.2781 + 9.64708i) q^{56} -3.08119i q^{57} +(-4.47834 + 6.16391i) q^{58} +(-0.534773 + 1.64586i) q^{59} +(2.42149 + 7.45259i) q^{61} +(-17.2720 - 5.61202i) q^{62} +(-3.27190 - 1.06311i) q^{63} +(2.63409 + 8.10689i) q^{64} +(2.46328 - 7.58119i) q^{66} +(1.08687 - 1.49595i) q^{67} -19.9860i q^{68} +(-1.25207 - 0.909685i) q^{69} +(0.577613 - 0.419660i) q^{71} +(2.80415 + 3.85959i) q^{72} +(1.78825 - 0.581036i) q^{73} +14.0521 q^{74} -12.1861 q^{76} +(10.6879 - 3.47270i) q^{77} +(-4.63591 - 6.38079i) q^{78} +(-10.7868 + 7.83708i) q^{79} +(-0.809017 - 0.587785i) q^{81} -13.2254i q^{82} +(2.32614 - 3.20166i) q^{83} +(-4.20457 + 12.9403i) q^{84} +(1.90864 + 5.87419i) q^{86} +(-2.96937 - 0.964807i) q^{87} +(-14.8211 - 4.81567i) q^{88} +(-2.63713 - 8.11624i) q^{89} +(3.43600 - 10.5749i) q^{91} +(-3.59779 + 4.95193i) q^{92} -7.44212i q^{93} +(13.9610 + 10.1433i) q^{94} +(-0.351501 + 0.255380i) q^{96} +(-6.26157 - 8.61831i) q^{97} +(-11.2226 + 3.64643i) q^{98} +3.26656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49}+ \cdots - 12 q^{99}+O(q^{100}) $ 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.32085	−	0.754089i	1.64109	−	0.533221i	0.664306	−	0.747461i	$-0.268727\pi$
$2$	2.32085	−	0.754089i	1.64109	−	0.533221i	0.976781	+	0.214240i	$0.0687273\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	3.19965	−	2.32468i	1.59982	−	1.16234i
$5$		0			0
$5$		0			0
$6$	1.97423	+	1.43436i	0.805976	+	0.585576i
$7$			3.44028i			1.30030i	0.759804	+	0.650152i	$0.225295\pi$
$7$			3.44028i			1.30030i	−0.759804	+	0.650152i	$0.774705\pi$
$8$	2.80415	−	3.85959i	0.991418	−	1.36457i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−1.00942	−	3.10669i	−0.304353	−	0.936701i	−0.979918	−	0.199401i	$-0.936100\pi$
$11$	−1.00942	−	3.10669i	−0.304353	−	0.936701i	0.675565	−	0.737300i	$-0.263900\pi$
$12$	3.76141	+	1.22216i	1.08583	+	0.352806i
$13$	−3.07385	−	0.998755i	−0.852533	−	0.277005i	−0.150026	−	0.988682i	$-0.547936\pi$
$13$	−3.07385	−	0.998755i	−0.852533	−	0.277005i	−0.702506	+	0.711677i	$0.747936\pi$
$14$	2.59428	+	7.98437i	0.693350	+	2.13391i
$15$		0			0
$16$	1.15323	−	3.54927i	0.288307	−	0.887317i
$17$	2.97030	−	4.08826i	0.720403	−	0.991550i	−0.279107	−	0.960260i	$-0.590039\pi$
$17$	2.97030	−	4.08826i	0.720403	−	0.991550i	0.999510	−	0.0312897i	$-0.00996144\pi$
$18$			2.44028i			0.575180i
$19$	−2.49274	−	1.81108i	−0.571873	−	0.415490i	0.263912	−	0.964547i	$-0.414987\pi$
$19$	−2.49274	−	1.81108i	−0.571873	−	0.415490i	−0.835785	+	0.549056i	$0.814987\pi$
$20$		0			0
$21$	−2.78325	+	2.02215i	−0.607354	+	0.441269i
$22$	−4.68544	−	6.44895i	−0.998938	−	1.37492i
$23$	−1.47190	+	0.478250i	−0.306913	+	0.0997219i	−0.458424	−	0.888734i	$-0.651586\pi$
$23$	−1.47190	+	0.478250i	−0.306913	+	0.0997219i	0.151512	+	0.988455i	$0.451586\pi$
$24$	4.77071			0.973817
$25$		0			0
$26$	−7.88709			−1.54679
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	7.99756	+	11.0077i	1.51140	+	2.08026i
$29$	−2.52590	+	1.83517i	−0.469047	+	0.340783i	−0.797070	−	0.603887i	$-0.793618\pi$
$29$	−2.52590	+	1.83517i	−0.469047	+	0.340783i	0.328022	+	0.944670i	$0.393618\pi$
$30$		0			0
$31$	−6.02080	−	4.37437i	−1.08137	−	0.785659i	−0.103446	−	0.994635i	$-0.532987\pi$
$31$	−6.02080	−	4.37437i	−1.08137	−	0.785659i	−0.977921	+	0.208976i	$0.932987\pi$
$32$			0.434479i			0.0768057i
$33$	1.92004	−	2.64270i	0.334236	−	0.460036i
$34$	3.81069	−	11.7281i	0.653528	−	2.01135i
$35$		0			0
$36$	1.22216	+	3.76141i	0.203693	+	0.626902i
$37$	5.47655	+	1.77944i	0.900339	+	0.292538i	0.722377	−	0.691499i	$-0.243050\pi$
$37$	5.47655	+	1.77944i	0.900339	+	0.292538i	0.177962	+	0.984037i	$0.443050\pi$
$38$	−7.15098	−	2.32349i	−1.16004	−	0.376921i
$39$	−0.998755	−	3.07385i	−0.159929	−	0.492210i
$40$		0			0
$41$	1.67476	−	5.15437i	0.261553	−	0.804977i	−0.730915	−	0.682469i	$-0.760906\pi$
$41$	1.67476	−	5.15437i	0.261553	−	0.804977i	0.992468	−	0.122508i	$-0.0390938\pi$
$42$	−4.93461	+	6.79191i	−0.761427	+	1.04801i
$43$			2.53106i			0.385982i	0.981201	+	0.192991i	$0.0618189\pi$
$43$			2.53106i			0.385982i	−0.981201	+	0.192991i	$0.938181\pi$
$44$	−10.4519	−	7.59371i	−1.57568	−	1.14480i
$45$		0			0
$46$	−3.05541	+	2.21989i	−0.450496	+	0.327305i
$47$	4.15659	+	5.72106i	0.606301	+	0.834502i	0.996267	−	0.0863273i	$-0.0275131\pi$
$47$	4.15659	+	5.72106i	0.606301	+	0.834502i	−0.389966	+	0.920829i	$0.627513\pi$
$48$	3.54927	−	1.15323i	0.512293	−	0.166454i
$49$	−4.83555			−0.690793
$50$		0			0
$51$	5.05337			0.707614
$52$	−12.1570	+	3.95006i	−1.68588	+	0.547774i
$53$	5.96693	+	8.21277i	0.819621	+	1.12811i	0.989767	+	0.142692i	$0.0455759\pi$
$53$	5.96693	+	8.21277i	0.819621	+	1.12811i	−0.170147	+	0.985419i	$0.554424\pi$
$54$	−1.97423	+	1.43436i	−0.268659	+	0.195192i
$55$		0			0
$56$	13.2781	+	9.64708i	1.77436	+	1.28915i
$57$		−	3.08119i		−	0.408114i
$58$	−4.47834	+	6.16391i	−0.588035	+	0.809361i
$59$	−0.534773	+	1.64586i	−0.0696215	+	0.214273i	−0.979814	−	0.199913i	$-0.935934\pi$
$59$	−0.534773	+	1.64586i	−0.0696215	+	0.214273i	0.910192	+	0.414187i	$0.135934\pi$
$60$		0			0
$61$	2.42149	+	7.45259i	0.310040	+	0.954206i	0.977748	+	0.209783i	$0.0672756\pi$
$61$	2.42149	+	7.45259i	0.310040	+	0.954206i	−0.667708	+	0.744424i	$0.732724\pi$
$62$	−17.2720	−	5.61202i	−2.19355	−	0.712727i
$63$	−3.27190	−	1.06311i	−0.412221	−	0.133939i
$64$	2.63409	+	8.10689i	0.329261	+	1.01336i
$65$		0			0
$66$	2.46328	−	7.58119i	0.303209	−	0.933180i
$67$	1.08687	−	1.49595i	0.132783	−	0.182760i	−0.737448	−	0.675404i	$-0.763969\pi$
$67$	1.08687	−	1.49595i	0.132783	−	0.182760i	0.870231	+	0.492644i	$0.163969\pi$
$68$		−	19.9860i		−	2.42366i
$69$	−1.25207	−	0.909685i	−0.150732	−	0.109513i
$70$		0			0
$71$	0.577613	−	0.419660i	0.0685500	−	0.0498045i	−0.552982	−	0.833193i	$-0.686510\pi$
$71$	0.577613	−	0.419660i	0.0685500	−	0.0498045i	0.621533	+	0.783388i	$0.286510\pi$
$72$	2.80415	+	3.85959i	0.330473	+	0.454857i
$73$	1.78825	−	0.581036i	0.209298	−	0.0680052i	−0.202491	−	0.979284i	$-0.564904\pi$
$73$	1.78825	−	0.581036i	0.209298	−	0.0680052i	0.411790	+	0.911279i	$0.364904\pi$
$74$	14.0521			1.63352
$75$		0			0
$76$	−12.1861			−1.39784
$77$	10.6879	−	3.47270i	1.21800	−	0.395751i
$78$	−4.63591	−	6.38079i	−0.524914	−	0.722482i
$79$	−10.7868	+	7.83708i	−1.21361	+	0.881740i	−0.995554	−	0.0941957i	$-0.969972\pi$
$79$	−10.7868	+	7.83708i	−1.21361	+	0.881740i	−0.218058	+	0.975936i	$0.569972\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		−	13.2254i		−	1.46050i
$83$	2.32614	−	3.20166i	0.255328	−	0.351428i	−0.662041	−	0.749468i	$-0.730309\pi$
$83$	2.32614	−	3.20166i	0.255328	−	0.351428i	0.917368	+	0.398040i	$0.130309\pi$
$84$	−4.20457	+	12.9403i	−0.458756	+	1.41190i
$85$		0			0
$86$	1.90864	+	5.87419i	0.205814	+	0.633430i
$87$	−2.96937	−	0.964807i	−0.318350	−	0.103438i
$88$	−14.8211	−	4.81567i	−1.57993	−	0.513352i
$89$	−2.63713	−	8.11624i	−0.279535	−	0.860320i	−0.987984	−	0.154558i	$-0.950605\pi$
$89$	−2.63713	−	8.11624i	−0.279535	−	0.860320i	0.708449	−	0.705762i	$-0.249395\pi$
$90$		0			0
$91$	3.43600	−	10.5749i	0.360191	−	1.10855i
$92$	−3.59779	+	4.95193i	−0.375095	+	0.516274i
$93$		−	7.44212i		−	0.771712i
$94$	13.9610	+	10.1433i	1.43997	+	1.04620i
$95$		0			0
$96$	−0.351501	+	0.255380i	−0.0358749	+	0.0260646i
$97$	−6.26157	−	8.61831i	−0.635766	−	0.875057i	0.362615	−	0.931939i	$-0.381884\pi$
$97$	−6.26157	−	8.61831i	−0.635766	−	0.875057i	−0.998381	+	0.0568823i	$0.981884\pi$
$98$	−11.2226	+	3.64643i	−1.13365	+	0.368345i
$99$	3.26656			0.328302
$100$		0			0
$101$	1.76173			0.175299			0.0876496	−	0.996151i	$-0.472064\pi$
$101$	1.76173			0.175299			0.0876496	+	0.996151i	$0.472064\pi$
$102$	11.7281	−	3.81069i	1.16126	−	0.377315i
$103$	−9.35416	−	12.8749i	−0.921693	−	1.26860i	−0.963013	−	0.269456i	$-0.913156\pi$
$103$	−9.35416	−	12.8749i	−0.921693	−	1.26860i	0.0413198	−	0.999146i	$-0.486844\pi$
$104$	−12.4743	+	9.06313i	−1.22321	+	0.888713i
$105$		0			0
$106$	20.0415	+	14.5610i	1.94660	+	1.41429i
$107$			15.7807i			1.52558i	0.646649	+	0.762788i	$0.276170\pi$
$107$			15.7807i			1.52558i	−0.646649	+	0.762788i	$0.723830\pi$
$108$	−2.32468	+	3.19965i	−0.223692	+	0.307886i
$109$	3.06539	−	9.43429i	0.293611	−	0.903641i	−0.690074	−	0.723739i	$-0.742422\pi$
$109$	3.06539	−	9.43429i	0.293611	−	0.903641i	0.983685	−	0.179902i	$-0.0575781\pi$
$110$		0			0
$111$	1.77944	+	5.47655i	0.168897	+	0.519811i
$112$	12.2105	+	3.96743i	1.15378	+	0.374887i
$113$	5.24399	+	1.70388i	0.493313	+	0.160287i	0.545100	−	0.838371i	$-0.316492\pi$
$113$	5.24399	+	1.70388i	0.493313	+	0.160287i	−0.0517868	+	0.998658i	$0.516492\pi$
$114$	−2.32349	−	7.15098i	−0.217615	−	0.669751i
$115$		0			0
$116$	−3.81580	+	11.7438i	−0.354288	+	1.09039i
$117$	1.89974	−	2.61477i	0.175631	−	0.241736i
$118$			4.22306i			0.388764i
$119$	14.0648	+	10.2187i	1.28932	+	0.936743i
$120$		0			0
$121$	0.266626	−	0.193715i	0.0242387	−	0.0176105i
$122$	11.2398	+	15.4703i	1.01761	+	1.40061i
$123$	5.15437	−	1.67476i	0.464754	−	0.151008i
$124$	−29.4334			−2.64320
$125$		0			0
$126$	−8.39527			−0.747910
$127$	−0.943532	+	0.306572i	−0.0837250	+	0.0272039i	−0.350580	−	0.936533i	$-0.614016\pi$
$127$	−0.943532	+	0.306572i	−0.0837250	+	0.0272039i	0.266855	+	0.963737i	$0.414016\pi$
$128$	11.7159	+	16.1255i	1.03555	+	1.42531i
$129$	−2.04767	+	1.48772i	−0.180287	+	0.130986i
$130$		0			0
$131$	10.2029	+	7.41286i	0.891434	+	0.647665i	0.936252	−	0.351330i	$-0.114271\pi$
$131$	10.2029	+	7.41286i	0.891434	+	0.647665i	−0.0448175	+	0.998995i	$0.514271\pi$
$132$		−	12.9192i		−	1.12447i
$133$	6.23063	−	8.57573i	0.540264	−	0.743610i
$134$	1.39438	−	4.29147i	0.120456	−	0.370727i
$135$		0			0
$136$	−7.44984	−	22.9282i	−0.638818	−	1.96608i
$137$	−7.83732	−	2.54650i	−0.669588	−	0.217562i	−0.0455566	−	0.998962i	$-0.514506\pi$
$137$	−7.83732	−	2.54650i	−0.669588	−	0.217562i	−0.624031	+	0.781400i	$0.714506\pi$
$138$	−3.59186	−	1.16706i	−0.305759	−	0.0993471i
$139$	−2.49182	−	7.66904i	−0.211354	−	0.650479i	−0.999392	−	0.0348539i	$-0.988903\pi$
$139$	−2.49182	−	7.66904i	−0.211354	−	0.650479i	0.788039	−	0.615626i	$-0.211097\pi$
$140$		0			0
$141$	−2.18525	+	6.72551i	−0.184031	+	0.566390i
$142$	1.02409	−	1.40954i	0.0859397	−	0.118286i
$143$			10.5577i			0.882875i
$144$	3.01919	+	2.19357i	0.251599	+	0.182797i
$145$		0			0
$146$	3.71209	−	2.69699i	0.307215	−	0.223205i
$147$	−2.84226	−	3.91204i	−0.234426	−	0.322660i
$148$	21.6597	−	7.03765i	1.78041	−	0.578491i
$149$	19.1101			1.56556			0.782781	−	0.622298i	$-0.213801\pi$
$149$	19.1101			1.56556			0.782781	+	0.622298i	$0.213801\pi$
$150$		0			0
$151$	1.58550			0.129026			0.0645132	−	0.997917i	$-0.479451\pi$
$151$	1.58550			0.129026			0.0645132	+	0.997917i	$0.479451\pi$
$152$	−13.9800	+	4.54239i	−1.13393	+	0.368437i
$153$	2.97030	+	4.08826i	0.240134	+	0.330517i
$154$	22.1862	−	16.1192i	1.78782	−	1.29892i
$155$		0			0
$156$	−10.3414	−	7.51345i	−0.827973	−	0.601558i
$157$			21.8510i			1.74390i	0.489599	+	0.871948i	$0.337143\pi$
$157$			21.8510i			1.74390i	−0.489599	+	0.871948i	$0.662857\pi$
$158$	−19.1247	+	26.3229i	−1.52148	+	2.09414i
$159$	−3.13700	+	9.65469i	−0.248780	+	0.765667i
$160$		0			0
$161$	−1.64531	−	5.06376i	−0.129669	−	0.399080i
$162$	−2.32085	−	0.754089i	−0.182343	−	0.0592468i
$163$	9.63786	+	3.13153i	0.754896	+	0.245280i	0.661087	−	0.750310i	$-0.270096\pi$
$163$	9.63786	+	3.13153i	0.754896	+	0.245280i	0.0938092	+	0.995590i	$0.470096\pi$
$164$	−6.62363	−	20.3854i	−0.517219	−	1.59184i
$165$		0			0
$166$	2.98429	−	9.18469i	0.231626	−	0.712870i
$167$	0.888195	−	1.22250i	0.0687306	−	0.0945996i	−0.773268	−	0.634080i	$-0.781379\pi$
$167$	0.888195	−	1.22250i	0.0687306	−	0.0945996i	0.841998	+	0.539480i	$0.181379\pi$
$168$			16.4126i			1.26626i
$169$	−2.06617	−	1.50116i	−0.158936	−	0.115474i
$170$		0			0
$171$	2.49274	−	1.81108i	0.190624	−	0.138497i
$172$	5.88389	+	8.09848i	0.448643	+	0.617504i
$173$	13.1772	−	4.28153i	1.00184	−	0.325518i	0.238241	−	0.971206i	$-0.423429\pi$
$173$	13.1772	−	4.28153i	1.00184	−	0.325518i	0.763602	+	0.645688i	$0.223429\pi$
$174$	−7.61901			−0.577595
$175$		0			0
$176$	−12.1906			−0.918897
$177$	−1.64586	+	0.534773i	−0.123711	+	0.0401960i
$178$	−12.2407	−	16.8479i	−0.917482	−	1.26281i
$179$	11.6949	−	8.49685i	0.874119	−	0.635085i	−0.0575701	−	0.998341i	$-0.518335\pi$
$179$	11.6949	−	8.49685i	0.874119	−	0.635085i	0.931689	+	0.363257i	$0.118335\pi$
$180$		0			0
$181$	−13.9068	−	10.1039i	−1.03369	−	0.751017i	−0.0646435	−	0.997908i	$-0.520591\pi$
$181$	−13.9068	−	10.1039i	−1.03369	−	0.751017i	−0.969043	+	0.246891i	$0.920591\pi$
$182$		−	27.1338i		−	2.01129i
$183$	−4.60595	+	6.33955i	−0.340482	+	0.468633i
$184$	−2.28159	+	7.02201i	−0.168201	+	0.517670i
$185$		0			0
$186$	−5.61202	−	17.2720i	−0.411493	−	1.26645i
$187$	−15.6992	−	5.10099i	−1.14804	−	0.373021i
$188$	26.5993	+	8.64262i	1.93995	+	0.630328i
$189$	−1.06311	−	3.27190i	−0.0773296	−	0.237996i
$190$		0			0
$191$	3.25778	−	10.0264i	0.235725	−	0.725486i	−0.761300	−	0.648400i	$-0.775438\pi$
$191$	3.25778	−	10.0264i	0.235725	−	0.725486i	0.997024	−	0.0770858i	$-0.0245615\pi$
$192$	−5.01034	+	6.89613i	−0.361590	+	0.497686i
$193$		−	0.682908i		−	0.0491568i	−0.999698	−	0.0245784i	$-0.992176\pi$
$193$		−	0.682908i		−	0.0491568i	0.999698	−	0.0245784i	$-0.00782434\pi$
$194$	−21.0311	−	15.2800i	−1.50995	−	1.09704i
$195$		0			0
$196$	−15.4721	+	11.2411i	−1.10515	+	0.802936i
$197$	−13.6937	−	18.8478i	−0.975639	−	1.34285i	−0.939146	−	0.343518i	$-0.888381\pi$
$197$	−13.6937	−	18.8478i	−0.975639	−	1.34285i	−0.0364929	−	0.999334i	$-0.511619\pi$
$198$	7.58119	−	2.46328i	0.538772	−	0.175058i
$199$	−10.1946			−0.722679			−0.361339	−	0.932434i	$-0.617680\pi$
$199$	−10.1946			−0.722679			−0.361339	+	0.932434i	$0.617680\pi$
$200$		0			0
$201$	1.84910			0.130425
$202$	4.08872	−	1.32850i	0.287681	−	0.0934733i
$203$	−6.31351	−	8.68980i	−0.443122	−	0.609905i
$204$	16.1690	−	11.7475i	1.13206	−	0.822488i
$205$		0			0
$206$	−31.4184	−	22.8268i	−2.18902	−	1.59042i
$207$		−	1.54765i		−	0.107569i
$208$	−7.08969	+	9.75813i	−0.491582	+	0.676604i
$209$	−3.11023	+	9.57230i	−0.215139	+	0.662130i
$210$		0			0
$211$	5.64172	+	17.3634i	0.388392	+	1.19535i	0.933990	+	0.357300i	$0.116303\pi$
$211$	5.64172	+	17.3634i	0.388392	+	1.19535i	−0.545598	+	0.838047i	$0.683697\pi$
$212$	38.1841	+	12.4068i	2.62250	+	0.852101i
$213$	0.679025	+	0.220629i	0.0465260	+	0.0151172i
$214$	11.9000	+	36.6245i	0.813470	+	2.50360i
$215$		0			0
$216$	−1.47423	+	4.53722i	−0.100309	+	0.308718i
$217$	15.0491	−	20.7133i	1.02160	−	1.40611i
$218$		−	24.2071i		−	1.63951i
$219$	1.52117	+	1.10520i	0.102791	+	0.0746823i
$220$		0			0
$221$	−13.2134	+	9.60011i	−0.888831	+	0.645774i
$222$	8.25961	+	11.3684i	0.554349	+	0.762996i
$223$	−16.3813	+	5.32262i	−1.09698	+	0.356429i	−0.800938	−	0.598748i	$-0.795665\pi$
$223$	−16.3813	+	5.32262i	−1.09698	+	0.356429i	−0.296037	+	0.955176i	$0.595665\pi$
$224$	−1.49473			−0.0998708
$225$		0			0
$226$	13.4554			0.895039
$227$	−4.11692	+	1.33767i	−0.273250	+	0.0887842i	−0.442437	−	0.896800i	$-0.645886\pi$
$227$	−4.11692	+	1.33767i	−0.273250	+	0.0887842i	0.169187	+	0.985584i	$0.445886\pi$
$228$	−7.16279	−	9.85874i	−0.474367	−	0.652911i
$229$	16.4349	−	11.9407i	1.08605	−	0.789062i	0.107322	−	0.994224i	$-0.465772\pi$
$229$	16.4349	−	11.9407i	1.08605	−	0.789062i	0.978728	+	0.205163i	$0.0657723\pi$
$230$		0			0
$231$	9.09165	+	6.60547i	0.598187	+	0.434608i
$232$			14.8950i			0.977906i
$233$	−0.200409	+	0.275839i	−0.0131292	+	0.0180708i	−0.815531	−	0.578713i	$-0.803555\pi$
$233$	−0.200409	+	0.275839i	−0.0131292	+	0.0180708i	0.802402	+	0.596784i	$0.203555\pi$
$234$	2.43724	−	7.50107i	0.159328	−	0.490360i
$235$		0			0
$236$	2.11502	+	6.50936i	0.137676	+	0.423723i
$237$	−12.6807	−	4.12020i	−0.823697	−	0.267635i
$238$	40.3480	+	13.1099i	2.61537	+	0.849786i
$239$	2.21407	+	6.81421i	0.143216	+	0.440774i	0.996777	−	0.0802185i	$-0.0255618\pi$
$239$	2.21407	+	6.81421i	0.143216	+	0.440774i	−0.853561	+	0.520993i	$0.825562\pi$
$240$		0			0
$241$	−3.88194	+	11.9474i	−0.250058	+	0.769599i	0.744705	+	0.667393i	$0.232590\pi$
$241$	−3.88194	+	11.9474i	−0.250058	+	0.769599i	−0.994763	+	0.102206i	$0.967410\pi$
$242$	0.472720	−	0.650643i	0.0303876	−	0.0418249i
$243$		−	1.00000i		−	0.0641500i
$244$	25.0728	+	18.2165i	1.60512	+	1.16619i
$245$		0			0
$246$	10.6996	−	7.77370i	0.682181	−	0.495633i
$247$	5.85348	+	8.05662i	0.372448	+	0.512631i
$248$	−33.7665	+	10.9714i	−2.14417	+	0.696684i
$249$	3.95747			0.250795
$250$		0			0
$251$	17.0160			1.07404			0.537022	−	0.843568i	$-0.319549\pi$
$251$	17.0160			1.07404			0.537022	+	0.843568i	$0.319549\pi$
$252$	−12.9403	+	4.20457i	−0.815164	+	0.264863i
$253$	2.97154	+	4.08998i	0.186819	+	0.257135i
$254$	−1.95861	+	1.42301i	−0.122894	+	0.0892879i
$255$		0			0
$256$	25.5586	+	18.5694i	1.59741	+	1.16059i
$257$		−	4.13200i		−	0.257747i	−0.991661	−	0.128874i	$-0.958864\pi$
$257$		−	4.13200i		−	0.257747i	0.991661	−	0.128874i	$-0.0411361\pi$
$258$	−3.63045	+	4.99689i	−0.226022	+	0.311093i
$259$	−6.12177	+	18.8409i	−0.380388	+	1.17072i
$260$		0			0
$261$	−0.964807	−	2.96937i	−0.0597201	−	0.183799i
$262$	29.2694	+	9.51020i	1.80827	+	0.587542i
$263$	−0.986940	−	0.320676i	−0.0608573	−	0.0197737i	0.278430	−	0.960456i	$-0.410186\pi$
$263$	−0.986940	−	0.320676i	−0.0608573	−	0.0197737i	−0.339287	+	0.940683i	$0.610186\pi$
$264$	−4.81567	−	14.8211i	−0.296384	−	0.912176i
$265$		0			0
$266$	7.99348	−	24.6014i	0.490112	−	1.50841i
$267$	5.01611	−	6.90408i	0.306981	−	0.422523i
$268$		−	7.31315i		−	0.446722i
$269$	−12.7741	−	9.28093i	−0.778851	−	0.565869i	0.125783	−	0.992058i	$-0.459856\pi$
$269$	−12.7741	−	9.28093i	−0.778851	−	0.565869i	−0.904634	+	0.426189i	$0.859856\pi$
$270$		0			0
$271$	11.0838	−	8.05286i	0.673294	−	0.489176i	−0.197832	−	0.980236i	$-0.563390\pi$
$271$	11.0838	−	8.05286i	0.673294	−	0.489176i	0.871126	+	0.491059i	$0.163390\pi$
$272$	−11.0849	−	15.2571i	−0.672122	−	0.925096i
$273$	10.5749	−	3.43600i	0.640023	−	0.207956i
$274$	−20.1095			−1.21486
$275$		0			0
$276$	−6.12092			−0.368436
$277$	6.63827	−	2.15691i	0.398855	−	0.129596i	−0.102719	−	0.994710i	$-0.532754\pi$
$277$	6.63827	−	2.15691i	0.398855	−	0.129596i	0.501574	+	0.865114i	$0.332754\pi$
$278$	−11.5663	−	15.9196i	−0.693699	−	0.954795i
$279$	6.02080	−	4.37437i	0.360456	−	0.261886i
$280$		0			0
$281$	−6.43834	−	4.67773i	−0.384079	−	0.279050i	0.378946	−	0.925419i	$-0.376287\pi$
$281$	−6.43834	−	4.67773i	−0.384079	−	0.279050i	−0.763025	+	0.646369i	$0.776287\pi$
$282$			17.2567i			1.02762i
$283$	−16.3376	+	22.4868i	−0.971169	+	1.33670i	−0.0297149	+	0.999558i	$0.509460\pi$
$283$	−16.3376	+	22.4868i	−0.971169	+	1.33670i	−0.941454	+	0.337141i	$0.890540\pi$
$284$	0.872582	−	2.68553i	0.0517782	−	0.159357i
$285$		0			0
$286$	7.96141	+	24.5027i	0.470768	+	1.44888i
$287$	17.7325	+	5.76163i	1.04672	+	0.340099i
$288$	−0.413214	−	0.134261i	−0.0243488	−	0.00791142i
$289$	−2.63794	−	8.11876i	−0.155173	−	0.477574i
$290$		0			0
$291$	3.29190	−	10.1314i	0.192975	−	0.593915i
$292$	4.37103	−	6.01621i	0.255795	−	0.352072i
$293$		−	14.2098i		−	0.830146i	−0.909788	−	0.415073i	$-0.863756\pi$
$293$		−	14.2098i		−	0.830146i	0.909788	−	0.415073i	$-0.136244\pi$
$294$	−9.54649	−	6.93593i	−0.556763	−	0.404512i
$295$		0			0
$296$	22.2250	−	16.1474i	1.29180	−	0.938548i
$297$	1.92004	+	2.64270i	0.111412	+	0.153345i
$298$	44.3517	−	14.4107i	2.56922	−	0.834791i
$299$	5.00206			0.289276
$300$		0			0
$301$	−8.70755			−0.501895
$302$	3.67971	−	1.19561i	0.211744	−	0.0687997i
$303$	1.03552	+	1.42527i	0.0594892	+	0.0818798i
$304$	−9.30270	+	6.75881i	−0.533547	+	0.387644i
$305$		0			0
$306$	9.97652	+	7.24837i	0.570320	+	0.414362i
$307$			23.2911i			1.32930i	0.747157	+	0.664648i	$0.231418\pi$
$307$			23.2911i			1.32930i	−0.747157	+	0.664648i	$0.768582\pi$
$308$	26.1245	−	35.9573i	1.48858	−	2.04886i
$309$	4.91777	−	15.1354i	0.279762	−	0.861020i
$310$		0			0
$311$	−2.33284	−	7.17976i	−0.132283	−	0.407127i	0.862874	−	0.505419i	$-0.168662\pi$
$311$	−2.33284	−	7.17976i	−0.132283	−	0.407127i	−0.995158	+	0.0982923i	$0.968662\pi$
$312$	−14.6645	−	4.76477i	−0.830211	−	0.269752i
$313$	−30.1072	−	9.78241i	−1.70176	−	0.552934i	−0.712830	−	0.701337i	$-0.752587\pi$
$313$	−30.1072	−	9.78241i	−1.70176	−	0.552934i	−0.988927	+	0.148402i	$0.952587\pi$
$314$	16.4776	+	50.7127i	0.929883	+	2.86188i
$315$		0			0
$316$	−16.2953	+	50.1518i	−0.916682	+	2.82126i
$317$	−15.1861	+	20.9019i	−0.852938	+	1.17397i	0.130270	+	0.991479i	$0.458416\pi$
$317$	−15.1861	+	20.9019i	−0.852938	+	1.17397i	−0.983208	+	0.182490i	$0.941584\pi$
$318$			24.7726i			1.38918i
$319$	8.25100	+	5.99471i	0.461968	+	0.335639i
$320$		0			0
$321$	−12.7668	+	9.27565i	−0.712575	+	0.517716i
$322$	−7.63705	−	10.5115i	−0.425596	−	0.585783i
$323$	−14.8083	+	4.81152i	−0.823959	+	0.267720i
$324$	−3.95498			−0.219721
$325$		0			0
$326$	24.7295			1.36964
$327$	9.43429	−	3.06539i	0.521717	−	0.169516i
$328$	−15.1975	−	20.9175i	−0.839139	−	1.15498i
$329$	−19.6821	+	14.2999i	−1.08511	+	0.788376i
$330$		0			0
$331$	−16.2679	−	11.8193i	−0.894166	−	0.649650i	0.0427948	−	0.999084i	$-0.486374\pi$
$331$	−16.2679	−	11.8193i	−0.894166	−	0.649650i	−0.936961	+	0.349434i	$0.886374\pi$
$332$		−	15.6517i		−	0.859001i
$333$	−3.38469	+	4.65863i	−0.185480	+	0.255291i
$334$	1.13949	−	3.50700i	0.0623504	−	0.191895i
$335$		0			0
$336$	3.96743	+	12.2105i	0.216441	+	0.666137i
$337$	−3.21816	−	1.04564i	−0.175304	−	0.0569599i	0.220050	−	0.975489i	$-0.429378\pi$
$337$	−3.21816	−	1.04564i	−0.175304	−	0.0569599i	−0.395354	+	0.918529i	$0.629378\pi$
$338$	−5.92729	−	1.92589i	−0.322402	−	0.104755i
$339$	1.70388	+	5.24399i	0.0925419	+	0.284815i
$340$		0			0
$341$	−7.51225	+	23.1203i	−0.406811	+	1.25204i
$342$	4.41955	−	6.08299i	0.238982	−	0.328930i
$343$			7.44633i			0.402064i
$344$	9.76882	+	7.09747i	0.526700	+	0.382670i
$345$		0			0
$346$	27.3536	−	19.8735i	1.47054	−	1.06841i
$347$	−17.1612	−	23.6204i	−0.921262	−	1.26801i	−0.963172	−	0.268887i	$-0.913344\pi$
$347$	−17.1612	−	23.6204i	−0.921262	−	1.26801i	0.0419100	−	0.999121i	$-0.486656\pi$
$348$	−11.7438	+	3.81580i	−0.629534	+	0.204548i
$349$	20.3979			1.09187			0.545937	−	0.837826i	$-0.316174\pi$
$349$	20.3979			1.09187			0.545937	+	0.837826i	$0.316174\pi$
$350$		0			0
$351$	3.23204			0.172513
$352$	1.34979	−	0.438573i	0.0719440	−	0.0233760i
$353$	1.09532	+	1.50757i	0.0582978	+	0.0802400i	0.837170	−	0.546942i	$-0.184208\pi$
$353$	1.09532	+	1.50757i	0.0582978	+	0.0802400i	−0.778873	+	0.627182i	$0.784208\pi$
$354$	−3.41653	+	2.48225i	−0.181586	+	0.131930i
$355$		0			0
$356$	−27.3055	−	19.8386i	−1.44719	−	1.05145i
$357$			17.3850i			0.920113i
$358$	20.7347	−	28.5389i	1.09586	−	1.50833i
$359$	−1.18599	+	3.65011i	−0.0625943	+	0.192645i	−0.977463	−	0.211105i	$-0.932294\pi$
$359$	−1.18599	+	3.65011i	−0.0625943	+	0.192645i	0.914869	+	0.403751i	$0.132294\pi$
$360$		0			0
$361$	−2.93759	−	9.04097i	−0.154610	−	0.475841i
$362$	−39.8949	−	12.9626i	−2.09683	−	0.681301i
$363$	0.313438	+	0.101842i	0.0164512	+	0.00534532i
$364$	−13.5893	−	41.8236i	−0.712274	−	2.19215i
$365$		0			0
$366$	−5.90913	+	18.1864i	−0.308875	+	0.950620i
$367$	−15.0638	+	20.7335i	−0.786324	+	1.08228i	0.208232	+	0.978079i	$0.433229\pi$
$367$	−15.0638	+	20.7335i	−0.786324	+	1.08228i	−0.994556	+	0.104203i	$0.966771\pi$
$368$			5.77570i			0.301079i
$369$	4.38457	+	3.18557i	0.228251	+	0.165834i
$370$		0			0
$371$	−28.2543	+	20.5279i	−1.46689	+	1.06576i
$372$	−17.3005	−	23.8122i	−0.896991	−	1.23460i
$373$	−20.3877	+	6.62437i	−1.05564	+	0.342997i	−0.784878	−	0.619651i	$-0.787274\pi$
$373$	−20.3877	+	6.62437i	−1.05564	+	0.342997i	−0.270758	+	0.962648i	$0.587274\pi$
$374$	−40.2821			−2.08294
$375$		0			0
$376$	33.7366			1.73983
$377$	9.59712	−	3.11829i	0.494277	−	0.160600i
$378$	−4.93461	−	6.79191i	−0.253809	−	0.349338i
$379$	−20.9304	+	15.2068i	−1.07512	+	0.781120i	−0.976826	−	0.214037i	$-0.931339\pi$
$379$	−20.9304	+	15.2068i	−1.07512	+	0.781120i	−0.0982945	+	0.995157i	$0.531339\pi$
$380$		0			0
$381$	−0.802617	−	0.583135i	−0.0411193	−	0.0298749i
$382$		−	25.7264i		−	1.31628i
$383$	−8.54263	+	11.7579i	−0.436508	+	0.600802i	−0.969432	−	0.245362i	$-0.921093\pi$
$383$	−8.54263	+	11.7579i	−0.436508	+	0.600802i	0.532924	+	0.846163i	$0.321093\pi$
$384$	−6.15940	+	18.9567i	−0.314321	+	0.967379i
$385$		0			0
$386$	−0.514974	−	1.58493i	−0.0262115	−	0.0806706i
$387$	−2.40718	−	0.782139i	−0.122364	−	0.0397584i
$388$	−40.0696	−	13.0194i	−2.03423	−	0.660960i
$389$	−7.13973	−	21.9738i	−0.361999	−	1.11412i	−0.951839	−	0.306598i	$-0.900809\pi$
$389$	−7.13973	−	21.9738i	−0.361999	−	1.11412i	0.589840	−	0.807520i	$-0.299191\pi$
$390$		0			0
$391$	−2.41677	+	7.43806i	−0.122221	+	0.376159i
$392$	−13.5596	+	18.6632i	−0.684864	+	0.942635i
$393$			12.6115i			0.636167i
$394$	−45.9940	−	33.4166i	−2.31715	−	1.68350i
$395$		0			0
$396$	10.4519	−	7.59371i	0.525225	−	0.381598i
$397$	8.19052	+	11.2733i	0.411070	+	0.565790i	0.963479	−	0.267784i	$-0.0862912\pi$
$397$	8.19052	+	11.2733i	0.411070	+	0.565790i	−0.552409	+	0.833573i	$0.686291\pi$
$398$	−23.6602	+	7.68766i	−1.18598	+	0.385348i
$399$	10.6002			0.530673
$400$		0			0
$401$	−27.5822			−1.37739			−0.688694	−	0.725052i	$-0.741816\pi$
$401$	−27.5822			−1.37739			−0.688694	+	0.725052i	$0.741816\pi$
$402$	4.29147	−	1.39438i	0.214039	−	0.0695456i
$403$	14.1381	+	19.4594i	0.704270	+	0.969344i
$404$	5.63693	−	4.09547i	0.280448	−	0.203757i
$405$		0			0
$406$	−21.2056	−	15.4068i	−1.05242	−	0.764625i
$407$		−	18.8101i		−	0.932383i
$408$	14.1704	−	19.5039i	0.701541	−	0.965588i
$409$	−4.08288	+	12.5658i	−0.201886	+	0.621340i	0.797941	+	0.602735i	$0.205922\pi$
$409$	−4.08288	+	12.5658i	−0.201886	+	0.621340i	−0.999827	+	0.0186048i	$0.994078\pi$
$410$		0			0
$411$	−2.54650	−	7.83732i	−0.125610	−	0.386587i
$412$	−59.8601	−	19.4497i	−2.94909	−	0.958218i
$413$	−5.66223	−	1.83977i	−0.278620	−	0.0905292i
$414$	−1.16706	−	3.59186i	−0.0573581	−	0.176530i
$415$		0			0
$416$	0.433937	−	1.33552i	0.0212755	−	0.0654794i
$417$	4.73973	−	6.52367i	0.232105	−	0.319466i
$418$			24.5612i			1.20133i
$419$	−7.15797	−	5.20057i	−0.349690	−	0.254064i	0.399049	−	0.916930i	$-0.369340\pi$
$419$	−7.15797	−	5.20057i	−0.349690	−	0.254064i	−0.748739	+	0.662865i	$0.769340\pi$
$420$		0			0
$421$	30.3192	−	22.0282i	1.47767	−	1.07359i	0.499367	−	0.866390i	$-0.333566\pi$
$421$	30.3192	−	22.0282i	1.47767	−	1.07359i	0.978299	−	0.207197i	$-0.0664341\pi$
$422$	26.1871	+	36.0435i	1.27477	+	1.75457i
$423$	−6.72551	+	2.18525i	−0.327005	+	0.106250i
$424$	48.4301			2.35197
$425$		0			0
$426$	1.74229			0.0844140
$427$	−25.6390	+	8.33062i	−1.24076	+	0.403147i
$428$	36.6850	+	50.4926i	1.77324	+	2.44065i
$429$	−8.54132	+	6.20563i	−0.412379	+	0.299611i
$430$		0			0
$431$	21.5397	+	15.6495i	1.03753	+	0.753809i	0.969802	−	0.243895i	$-0.0784252\pi$
$431$	21.5397	+	15.6495i	1.03753	+	0.753809i	0.0677274	+	0.997704i	$0.478425\pi$
$432$			3.73192i			0.179552i
$433$	20.5708	−	28.3133i	0.988571	−	1.36065i	0.0564887	−	0.998403i	$-0.482010\pi$
$433$	20.5708	−	28.3133i	0.988571	−	1.36065i	0.932082	−	0.362248i	$-0.117990\pi$
$434$	19.3069	−	59.4206i	0.926762	−	2.85228i
$435$		0			0
$436$	−12.1235	−	37.3124i	−0.580613	−	1.78694i
$437$	4.53521	+	1.47358i	0.216949	+	0.0704909i
$438$	4.36383	+	1.41789i	0.208512	+	0.0677496i
$439$	−6.19701	−	19.0724i	−0.295767	−	0.910277i	−0.982963	−	0.183805i	$-0.941159\pi$
$439$	−6.19701	−	19.0724i	−0.295767	−	0.910277i	0.687196	−	0.726472i	$-0.258841\pi$
$440$		0			0
$441$	1.49427	−	4.59888i	0.0711556	−	0.218994i
$442$	−23.4270	+	32.2445i	−1.11431	+	1.53371i
$443$			4.14871i			0.197111i	0.995132	+	0.0985556i	$0.0314222\pi$
$443$			4.14871i			0.197111i	−0.995132	+	0.0985556i	$0.968578\pi$
$444$	18.4248	+	13.3864i	0.874402	+	0.635291i
$445$		0			0
$446$	−34.0048	+	24.7060i	−1.61018	+	1.16986i
$447$	11.2326	+	15.4604i	0.531286	+	0.731252i
$448$	−27.8900	+	9.06201i	−1.31768	+	0.428140i
$449$	8.34804			0.393969			0.196984	−	0.980407i	$-0.436885\pi$
$449$	8.34804			0.393969			0.196984	+	0.980407i	$0.436885\pi$
$450$		0			0
$451$	−17.7035			−0.833627
$452$	20.7399	−	6.73880i	0.975523	−	0.316967i
$453$	0.931936	+	1.28270i	0.0437862	+	0.0602665i
$454$	−8.54602	+	6.20905i	−0.401085	+	0.291405i
$455$		0			0
$456$	−11.8921	−	8.64014i	−0.556900	−	0.404612i
$457$		−	20.5774i		−	0.962571i	−0.876564	−	0.481285i	$-0.840170\pi$
$457$		−	20.5774i		−	0.962571i	0.876564	−	0.481285i	$-0.159830\pi$
$458$	29.1386	−	40.1059i	1.36156	−	1.87402i
$459$	−1.56158	+	4.80604i	−0.0728882	+	0.224327i
$460$		0			0
$461$	8.86541	+	27.2849i	0.412903	+	1.27079i	0.914113	+	0.405460i	$0.132889\pi$
$461$	8.86541	+	27.2849i	0.412903	+	1.27079i	−0.501210	+	0.865326i	$0.667111\pi$
$462$	26.0815	+	8.47438i	1.21342	+	0.394264i
$463$	38.1181	+	12.3853i	1.77150	+	0.575594i	0.998284	−	0.0585520i	$-0.0186483\pi$
$463$	38.1181	+	12.3853i	1.77150	+	0.575594i	0.773213	+	0.634146i	$0.218648\pi$
$464$	3.60058	+	11.0815i	0.167153	+	0.514444i
$465$		0			0
$466$	−0.257111	+	0.791307i	−0.0119105	+	0.0366566i
$467$	4.78569	−	6.58694i	0.221456	−	0.304807i	−0.683805	−	0.729665i	$-0.739676\pi$
$467$	4.78569	−	6.58694i	0.221456	−	0.304807i	0.905260	+	0.424858i	$0.139676\pi$
$468$		−	12.7827i		−	0.590878i
$469$	5.14650	+	3.73915i	0.237643	+	0.172658i
$470$		0			0
$471$	−17.6778	+	12.8437i	−0.814550	+	0.591805i
$472$	4.85276	+	6.67925i	0.223366	+	0.307438i
$473$	7.86319	−	2.55491i	0.361550	−	0.117475i
$474$	−32.5369			−1.49447
$475$		0			0
$476$	68.7575			3.15149
$477$	−9.65469	+	3.13700i	−0.442058	+	0.143633i
$478$	10.2770	+	14.1451i	0.470061	+	0.646983i
$479$	−22.7027	+	16.4945i	−1.03731	+	0.753652i	−0.969759	−	0.244064i	$-0.921519\pi$
$479$	−22.7027	+	16.4945i	−1.03731	+	0.753652i	−0.0675535	+	0.997716i	$0.521519\pi$
$480$		0			0
$481$	−15.0569	−	10.9395i	−0.686534	−	0.498796i
$482$			30.6554i			1.39631i
$483$	3.12957	−	4.30749i	0.142401	−	0.195998i
$484$	0.402784	−	1.23964i	0.0183084	−	0.0563473i
$485$		0			0
$486$	−0.754089	−	2.32085i	−0.0342062	−	0.105276i
$487$	14.4725	+	4.70239i	0.655810	+	0.213086i	0.617974	−	0.786198i	$-0.287954\pi$
$487$	14.4725	+	4.70239i	0.655810	+	0.213086i	0.0378360	+	0.999284i	$0.487954\pi$
$488$	35.5541	+	11.5522i	1.60946	+	0.522945i
$489$	3.13153	+	9.63786i	0.141613	+	0.435839i
$490$		0			0
$491$	2.56246	−	7.88645i	0.115642	−	0.355910i	−0.876438	−	0.481514i	$-0.840087\pi$
$491$	2.56246	−	7.88645i	0.115642	−	0.355910i	0.992080	+	0.125604i	$0.0400869\pi$
$492$	12.5989	−	17.3409i	0.568002	−	0.781788i
$493$			15.7775i			0.710585i
$494$	19.6604	+	14.2842i	0.884565	+	0.642674i
$495$		0			0
$496$	−22.4691	+	16.3248i	−1.00889	+	0.733005i
$497$	1.44375	+	1.98715i	0.0647611	+	0.0891360i
$498$	9.18469	−	2.98429i	0.411576	−	0.133729i
$499$	24.4006			1.09232			0.546160	−	0.837681i	$-0.316089\pi$
$499$	24.4006			1.09232			0.546160	+	0.837681i	$0.316089\pi$
$500$		0			0
$501$	1.51109			0.0675104
$502$	39.4916	−	12.8316i	1.76260	−	0.572703i
$503$	−6.15596	−	8.47295i	−0.274481	−	0.377790i	0.649415	−	0.760434i	$-0.275014\pi$
$503$	−6.15596	−	8.47295i	−0.274481	−	0.377790i	−0.923896	+	0.382644i	$0.875014\pi$
$504$	−13.2781	+	9.64708i	−0.591452	+	0.429715i
$505$		0			0
$506$	9.98070	+	7.25141i	0.443696	+	0.322364i
$507$		−	2.55393i		−	0.113424i
$508$	−2.30629	+	3.17433i	−0.102325	+	0.140838i
$509$	3.41769	−	10.5186i	0.151486	−	0.466227i	−0.846302	−	0.532704i	$-0.821176\pi$
$509$	3.41769	−	10.5186i	0.151486	−	0.466227i	0.997788	+	0.0664770i	$0.0211759\pi$
$510$		0			0
$511$	1.99893	+	6.15207i	0.0884274	+	0.272152i
$512$	35.4071	+	11.5045i	1.56479	+	0.508431i
$513$	2.93039	+	0.952141i	0.129380	+	0.0420381i
$514$	−3.11590	−	9.58974i	−0.137436	−	0.422985i
$515$		0			0
$516$	−3.09335	+	9.52034i	−0.136177	+	0.419110i
$517$	13.5778	−	18.6882i	0.597150	−	0.821906i
$518$			48.3432i			2.12408i
$519$	11.2092	+	8.14395i	0.492029	+	0.357480i
$520$		0			0
$521$	33.5105	−	24.3468i	1.46812	−	1.06665i	0.486967	−	0.873420i	$-0.338103\pi$
$521$	33.5105	−	24.3468i	1.46812	−	1.06665i	0.981153	−	0.193231i	$-0.0618968\pi$
$522$	−4.47834	−	6.16391i	−0.196012	−	0.269787i
$523$	−12.9748	+	4.21576i	−0.567347	+	0.184342i	−0.578624	−	0.815594i	$-0.696410\pi$
$523$	−12.9748	+	4.21576i	−0.567347	+	0.184342i	0.0112775	+	0.999936i	$0.496410\pi$
$524$	49.8783			2.17894
$525$		0			0
$526$	−2.53235			−0.110416
$527$	−35.7671	+	11.6214i	−1.55804	+	0.506238i
$528$	−7.16543	−	9.86236i	−0.311835	−	0.429204i
$529$	−16.6696	+	12.1112i	−0.724766	+	0.526573i
$530$		0			0
$531$	−1.40005	−	1.01720i	−0.0607572	−	0.0441427i
$532$		−	41.9235i		−	1.81762i
$533$	−10.2959	+	14.1711i	−0.445965	+	0.613818i
$534$	6.43533	−	19.8059i	0.278484	−	0.857086i
$535$		0			0
$536$	−2.72600	−	8.38976i	−0.117745	−	0.362382i
$537$	13.7482	+	4.46706i	0.593278	+	0.192768i
$538$	−36.6454	−	11.9068i	−1.57990	−	0.513339i
$539$	4.88112	+	15.0225i	0.210245	+	0.647066i
$540$		0			0
$541$	4.53011	−	13.9423i	0.194765	−	0.599424i	−0.805214	−	0.592984i	$-0.797950\pi$
$541$	4.53011	−	13.9423i	0.194765	−	0.599424i	0.999979	−	0.00644072i	$-0.00205016\pi$
$542$	19.6513	−	27.0476i	0.844094	−	1.16180i
$543$		−	17.1898i		−	0.737685i
$544$	1.77626	+	1.29053i	0.0761566	+	0.0553310i
$545$		0			0
$546$	21.9517	−	15.9489i	0.939447	−	0.682548i
$547$	15.6423	+	21.5298i	0.668818	+	0.920549i	0.999733	−	0.0231115i	$-0.00735726\pi$
$547$	15.6423	+	21.5298i	0.668818	+	0.920549i	−0.330915	+	0.943661i	$0.607357\pi$
$548$	−30.9965	+	10.0714i	−1.32410	+	0.430227i
$549$	−7.83611			−0.334437
$550$		0			0
$551$	9.62005			0.409828
$552$	−7.02201	+	2.28159i	−0.298877	+	0.0971109i
$553$	−26.9618	−	37.1097i	−1.14653	−	1.57806i
$554$	13.7799	−	10.0117i	0.585453	−	0.425356i
$555$		0			0
$556$	−25.8010	−	18.7455i	−1.09421	−	0.794988i
$557$			10.3141i			0.437020i	0.975835	+	0.218510i	$0.0701197\pi$
$557$			10.3141i			0.437020i	−0.975835	+	0.218510i	$0.929880\pi$
$558$	10.6747	−	14.6925i	0.451896	−	0.621981i
$559$	2.52790	−	7.78008i	0.106919	−	0.329063i
$560$		0			0
$561$	−5.10099	−	15.6992i	−0.215364	−	0.662822i
$562$	−18.4698	−	6.00121i	−0.779103	−	0.253146i
$563$	−32.7193	−	10.6311i	−1.37895	−	0.448049i	−0.476628	−	0.879105i	$-0.658141\pi$
$563$	−32.7193	−	10.6311i	−1.37895	−	0.448049i	−0.902325	+	0.431056i	$0.858141\pi$
$564$	8.64262	+	26.5993i	0.363920	+	1.12003i
$565$		0			0
$566$	−20.9600	+	64.5083i	−0.881016	+	2.71149i
$567$	2.02215	−	2.78325i	0.0849222	−	0.116885i
$568$		−	3.40614i		−	0.142918i
$569$	−9.87387	−	7.17378i	−0.413934	−	0.300741i	0.361259	−	0.932466i	$-0.382347\pi$
$569$	−9.87387	−	7.17378i	−0.413934	−	0.300741i	−0.775193	+	0.631725i	$0.782347\pi$
$570$		0			0
$571$	−34.0308	+	24.7248i	−1.42415	+	1.03470i	−0.433076	+	0.901357i	$0.642572\pi$
$571$	−34.0308	+	24.7248i	−1.42415	+	1.03470i	−0.991070	+	0.133345i	$0.957428\pi$
$572$	24.5432	+	33.7808i	1.02620	+	1.41245i
$573$	10.0264	−	3.25778i	0.418859	−	0.136096i
$574$	45.4992			1.89910
$575$		0			0
$576$	−8.52409			−0.355170
$577$	16.6768	−	5.41863i	0.694266	−	0.225581i	0.0594353	−	0.998232i	$-0.481070\pi$
$577$	16.6768	−	5.41863i	0.694266	−	0.225581i	0.634830	+	0.772652i	$0.281070\pi$
$578$	−12.2445	−	16.8532i	−0.509305	−	0.700999i
$579$	0.552485	−	0.401404i	0.0229605	−	0.0166818i
$580$		0			0
$581$	11.0146	+	8.00260i	0.456964	+	0.332004i
$582$		−	25.9959i		−	1.07756i
$583$	19.4913	−	26.8275i	0.807249	−	1.11108i
$584$	2.77196	−	8.53120i	0.114704	−	0.353024i
$585$		0			0
$586$	−10.7155	−	32.9788i	−0.442651	−	1.36234i
$587$	20.8395	+	6.77115i	0.860137	+	0.279475i	0.705686	−	0.708525i	$-0.250639\pi$
$587$	20.8395	+	6.77115i	0.860137	+	0.279475i	0.154451	+	0.988000i	$0.450639\pi$
$588$	−18.1885	−	5.90980i	−0.750081	−	0.243716i
$589$	7.08595	+	21.8083i	0.291971	+	0.898595i
$590$		0			0
$591$	7.19923	−	22.1569i	0.296137	−	0.911415i
$592$	12.6314	−	17.3856i	0.519148	−	0.714545i
$593$		−	38.0061i		−	1.56072i	−0.625330	−	0.780361i	$-0.715035\pi$
$593$		−	38.0061i		−	1.56072i	0.625330	−	0.780361i	$-0.284965\pi$
$594$	6.44895	+	4.68544i	0.264604	+	0.192246i
$595$		0			0
$596$	61.1456	−	44.4249i	2.50462	−	1.81971i
$597$	−5.99226	−	8.24764i	−0.245247	−	0.337553i
$598$	11.6090	−	3.77200i	0.474728	−	0.154248i
$599$	−16.3154			−0.666629			−0.333314	−	0.942816i	$-0.608167\pi$
$599$	−16.3154			−0.666629			−0.333314	+	0.942816i	$0.608167\pi$
$600$		0			0
$601$	2.31871			0.0945822			0.0472911	−	0.998881i	$-0.484941\pi$
$601$	2.31871			0.0945822			0.0472911	+	0.998881i	$0.484941\pi$
$602$	−20.2089	+	6.56626i	−0.823653	+	0.267621i
$603$	1.08687	+	1.49595i	0.0442609	+	0.0609199i
$604$	5.07305	−	3.68579i	0.206420	−	0.149973i
$605$		0			0
$606$	3.47807	+	2.52697i	0.141287	+	0.102651i
$607$		−	32.2134i		−	1.30750i	−0.756709	−	0.653752i	$-0.773194\pi$
$607$		−	32.2134i		−	1.30750i	0.756709	−	0.653752i	$-0.226806\pi$
$608$	0.786876	−	1.08304i	0.0319120	−	0.0439231i
$609$	3.31921	−	10.2155i	0.134501	−	0.413952i
$610$		0			0
$611$	−7.06281	−	21.7371i	−0.285731	−	0.879389i
$612$	19.0078	+	6.17601i	0.768345	+	0.249651i
$613$	24.6782	+	8.01843i	0.996742	+	0.323861i	0.761563	−	0.648091i	$-0.224432\pi$
$613$	24.6782	+	8.01843i	0.996742	+	0.323861i	0.235179	+	0.971952i	$0.424432\pi$
$614$	17.5636	+	54.0552i	0.708809	+	2.18149i
$615$		0			0
$616$	16.5673	−	50.9888i	0.667514	−	2.05440i
$617$	−1.11899	+	1.54016i	−0.0450488	+	0.0620043i	−0.830947	−	0.556351i	$-0.812201\pi$
$617$	−1.11899	+	1.54016i	−0.0450488	+	0.0620043i	0.785898	+	0.618356i	$0.212201\pi$
$618$		−	38.8353i		−	1.56218i
$619$	−16.0829	−	11.6849i	−0.646425	−	0.469655i	0.215627	−	0.976476i	$-0.430821\pi$
$619$	−16.0829	−	11.6849i	−0.646425	−	0.469655i	−0.862052	+	0.506821i	$0.830821\pi$
$620$		0			0
$621$	1.25207	−	0.909685i	0.0502440	−	0.0365044i
$622$	−10.8283	−	14.9039i	−0.434177	−	0.597594i
$623$	27.9222	−	9.07246i	1.11868	−	0.363480i
$624$	−12.0617			−0.482855
$625$		0			0
$626$	−77.2509			−3.08757
$627$	−9.57230	+	3.11023i	−0.382281	+	0.124211i
$628$	50.7965	+	69.9154i	2.02700	+	2.78993i
$629$	23.5418	−	17.1041i	0.938673	−	0.681986i
$630$		0			0
$631$	26.6152	+	19.3371i	1.05953	+	0.769796i	0.974002	−	0.226539i	$-0.0727412\pi$
$631$	26.6152	+	19.3371i	1.05953	+	0.769796i	0.0855315	+	0.996335i	$0.472741\pi$
$632$			63.6090i			2.53023i
$633$	−10.7312	+	14.7702i	−0.426526	+	0.587063i
$634$	−19.4828	+	59.9618i	−0.773760	+	2.38139i
$635$		0			0
$636$	12.4068	+	38.1841i	0.491961	+	1.51410i
$637$	14.8638	+	4.82953i	0.588923	+	0.191353i
$638$	23.6699	+	7.69080i	0.937099	+	0.304482i
$639$	0.220629	+	0.679025i	0.00872793	+	0.0268618i
$640$		0			0
$641$	−12.5963	+	38.7673i	−0.497523	+	1.53122i	0.315465	+	0.948937i	$0.397839\pi$
$641$	−12.5963	+	38.7673i	−0.497523	+	1.53122i	−0.812988	+	0.582280i	$0.802161\pi$
$642$	−22.6352	+	31.1547i	−0.893341	+	1.22958i
$643$			24.9947i			0.985695i	0.870116	+	0.492847i	$0.164044\pi$
$643$			24.9947i			0.985695i	−0.870116	+	0.492847i	$0.835956\pi$
$644$	−17.0360	−	12.3774i	−0.671314	−	0.487738i
$645$		0			0
$646$	−30.7396	+	22.3336i	−1.20943	+	0.878705i
$647$	−18.8228	−	25.9073i	−0.739999	−	1.01852i	−0.998619	−	0.0525420i	$-0.983268\pi$
$647$	−18.8228	−	25.9073i	−0.739999	−	1.01852i	0.258620	−	0.965979i	$-0.416732\pi$
$648$	−4.53722	+	1.47423i	−0.178239	+	0.0579132i
$649$	5.65299			0.221899
$650$		0			0
$651$	25.6030			1.00346
$652$	38.1176	−	12.3852i	1.49280	−	0.485040i
$653$	26.2606	+	36.1446i	1.02766	+	1.41445i	0.906693	+	0.421791i	$0.138599\pi$
$653$	26.2606	+	36.1446i	1.02766	+	1.41445i	0.120964	+	0.992657i	$0.461401\pi$
$654$	19.5840	−	14.2286i	0.765794	−	0.556382i
$655$		0			0
$656$	−16.3629	−	11.8883i	−0.638862	−	0.464161i
$657$			1.88027i			0.0733564i
$658$	−34.8957	+	48.0298i	−1.36038	+	1.87240i
$659$	7.42307	−	22.8458i	0.289162	−	0.889948i	−0.695959	−	0.718082i	$-0.745020\pi$
$659$	7.42307	−	22.8458i	0.289162	−	0.889948i	0.985120	−	0.171866i	$-0.0549796\pi$
$660$		0			0
$661$	11.7095	+	36.0382i	0.455447	+	1.40172i	0.870610	+	0.491974i	$0.163725\pi$
$661$	11.7095	+	36.0382i	0.455447	+	1.40172i	−0.415163	+	0.909747i	$0.636275\pi$
$662$	−46.6682	−	15.1634i	−1.81381	−	0.589343i
$663$	−15.5333	−	5.04708i	−0.603264	−	0.196012i
$664$	−5.83423	−	17.9559i	−0.226412	−	0.696824i
$665$		0			0
$666$	−4.34233	+	13.3643i	−0.168262	+	0.517857i
$667$	2.84020	−	3.90920i	0.109973	−	0.151365i
$668$		−	5.97633i		−	0.231231i
$669$	−13.9348	−	10.1242i	−0.538750	−	0.391425i
$670$		0			0
$671$	20.7085	−	15.0456i	0.799444	−	0.580830i
$672$	−0.878580	−	1.20926i	−0.0338920	−	0.0466483i
$673$	17.5249	−	5.69418i	0.675534	−	0.219494i	0.0488951	−	0.998804i	$-0.484430\pi$
$673$	17.5249	−	5.69418i	0.675534	−	0.219494i	0.626639	+	0.779310i	$0.284430\pi$
$674$	−8.25737			−0.318062
$675$		0			0
$676$	−10.1008			−0.388491
$677$	−21.6996	+	7.05064i	−0.833985	+	0.270978i	−0.694723	−	0.719277i	$-0.744473\pi$
$677$	−21.6996	+	7.05064i	−0.833985	+	0.270978i	−0.139262	+	0.990256i	$0.544473\pi$
$678$	7.90887	+	10.8856i	0.303738	+	0.418060i
$679$	29.6494	−	21.5416i	1.13784	−	0.826690i
$680$		0			0
$681$	−3.50206	−	2.54440i	−0.134199	−	0.0975015i
$682$			59.3236i			2.27162i
$683$	18.9304	−	26.0555i	0.724353	−	0.996987i	−0.275015	−	0.961440i	$-0.588683\pi$
$683$	18.9304	−	26.0555i	0.724353	−	0.996987i	0.999368	−	0.0355465i	$-0.0113172\pi$
$684$	3.76570	−	11.5896i	0.143985	−	0.443141i
$685$		0			0
$686$	5.61519	+	17.2818i	0.214389	+	0.659822i
$687$	19.3204	+	6.27758i	0.737120	+	0.239505i
$688$	8.98339	+	2.91888i	0.342489	+	0.111281i
$689$	−10.1389	−	31.2043i	−0.386261	−	1.18879i
$690$		0			0
$691$	7.59466	−	23.3740i	0.288915	−	0.889188i	−0.696283	−	0.717767i	$-0.745164\pi$
$691$	7.59466	−	23.3740i	0.288915	−	0.889188i	0.985198	−	0.171421i	$-0.0548358\pi$
$692$	32.2092	−	44.3321i	1.22441	−	1.68525i
$693$			11.2379i			0.426893i
$694$	−57.6404	−	41.8782i	−2.18800	−	1.58967i
$695$		0			0
$696$	−12.0503	+	8.75508i	−0.456767	+	0.331860i
$697$	−16.0979	−	22.1568i	−0.609751	−	0.839251i
$698$	47.3404	−	15.3818i	1.79186	−	0.582211i
$699$	−0.340956			−0.0128961
$700$		0			0
$701$	−3.66355			−0.138370			−0.0691852	−	0.997604i	$-0.522040\pi$
$701$	−3.66355			−0.138370			−0.0691852	+	0.997604i	$0.522040\pi$
$702$	7.50107	−	2.43724i	0.283109	−	0.0919879i
$703$	−10.4289	−	14.3541i	−0.393333	−	0.541377i
$704$	22.5267	−	16.3666i	0.849005	−	0.616838i
$705$		0			0
$706$	3.67890	+	2.67288i	0.138457	+	0.100595i
$707$			6.06087i			0.227942i
$708$	−4.02300	+	5.53719i	−0.151194	+	0.208100i
$709$	8.24980	−	25.3903i	0.309828	−	0.953552i	−0.668003	−	0.744158i	$-0.732851\pi$
$709$	8.24980	−	25.3903i	0.309828	−	0.953552i	0.977831	−	0.209394i	$-0.0671491\pi$
$710$		0			0
$711$	−4.12020	−	12.6807i	−0.154519	−	0.475562i
$712$	−38.7202	−	12.5810i	−1.45110	−	0.471492i
$713$	10.9541	+	3.55919i	0.410233	+	0.133293i
$714$	13.1099	+	40.3480i	0.490624	+	1.50999i
$715$		0			0
$716$	17.6671	−	54.3739i	0.660252	−	2.03205i
$717$	−4.21141	+	5.79651i	−0.157278	+	0.216475i
$718$			9.36569i			0.349524i
$719$	14.4570	+	10.5036i	0.539156	+	0.391720i	0.823771	−	0.566922i	$-0.191866\pi$
$719$	14.4570	+	10.5036i	0.539156	+	0.391720i	−0.284616	+	0.958642i	$0.591866\pi$
$720$		0			0
$721$	44.2933	−	32.1810i	1.64957	−	1.19848i
$722$	−13.6354	−	18.7675i	−0.507457	−	0.698455i
$723$	−11.9474	+	3.88194i	−0.444328	+	0.144371i
$724$	−67.9853			−2.52665
$725$		0			0
$726$	0.804239			0.0298481
$727$	−32.4050	+	10.5290i	−1.20184	+	0.390500i	−0.840436	−	0.541910i	$-0.817701\pi$
$727$	−32.4050	+	10.5290i	−1.20184	+	0.390500i	−0.361400	+	0.932411i	$0.617701\pi$
$728$	−31.1797	−	42.9152i	−1.15560	−	1.59054i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	10.3476	+	7.51799i	0.382721	+	0.278063i
$732$			30.9917i			1.14549i
$733$	−23.6176	+	32.5068i	−0.872335	+	1.20067i	0.106150	+	0.994350i	$0.466147\pi$
$733$	−23.6176	+	32.5068i	−0.872335	+	1.20067i	−0.978485	+	0.206316i	$0.933853\pi$
$734$	−19.3258	+	59.4788i	−0.713330	+	2.19540i
$735$		0			0
$736$	−0.207789	−	0.639509i	−0.00765921	−	0.0235726i
$737$	−5.74457	−	1.86652i	−0.211604	−	0.0687542i
$738$	12.5781	+	4.08688i	0.463007	+	0.150440i
$739$	−4.78203	−	14.7176i	−0.175910	−	0.541395i	0.823764	−	0.566933i	$-0.191870\pi$
$739$	−4.78203	−	14.7176i	−0.175910	−	0.541395i	−0.999674	+	0.0255381i	$0.991870\pi$
$740$		0			0
$741$	−3.07736	+	9.47113i	−0.113050	+	0.347931i
$742$	−50.0939	+	68.9484i	−1.83901	+	2.53118i
$743$		−	17.1140i		−	0.627853i	−0.949447	−	0.313926i	$-0.898355\pi$
$743$		−	17.1140i		−	0.627853i	0.949447	−	0.313926i	$-0.101645\pi$
$744$	−28.7235	−	20.8688i	−1.05305	−	0.765089i
$745$		0			0
$746$	−42.3214	+	30.7483i	−1.54950	+	1.12577i
$747$	2.32614	+	3.20166i	0.0851092	+	0.117143i
$748$	−62.0902	+	20.1743i	−2.27024	+	0.737647i
$749$	−54.2900			−1.98371
$750$		0			0
$751$	−11.1559			−0.407086			−0.203543	−	0.979066i	$-0.565246\pi$
$751$	−11.1559			−0.407086			−0.203543	+	0.979066i	$0.565246\pi$
$752$	25.0991	−	8.15518i	0.915268	−	0.297389i
$753$	10.0018	+	13.7663i	0.364485	+	0.501671i
$754$	19.9220	−	14.4742i	0.725516	−	0.527118i
$755$		0			0
$756$	−11.0077	−	7.99756i	−0.400346	−	0.290868i
$757$		−	24.6773i		−	0.896911i	−0.893805	−	0.448456i	$-0.851974\pi$
$757$		−	24.6773i		−	0.896911i	0.893805	−	0.448456i	$-0.148026\pi$
$758$	−37.1089	+	51.0760i	−1.34786	+	1.85516i
$759$	−1.56223	+	4.80806i	−0.0567054	+	0.174521i
$760$		0			0
$761$	−12.4372	−	38.2779i	−0.450850	−	1.38757i	−0.875939	−	0.482422i	$-0.839757\pi$
$761$	−12.4372	−	38.2779i	−0.450850	−	1.38757i	0.425089	−	0.905151i	$-0.360243\pi$
$762$	−2.30249	−	0.748123i	−0.0834103	−	0.0271016i
$763$	32.4566	+	10.5458i	1.17501	+	0.381784i
$764$	−12.8845	−	39.6543i	−0.466143	−	1.43464i
$765$		0			0
$766$	−10.9596	+	33.7302i	−0.395987	+	1.21872i
$767$	3.28763	−	4.52503i	0.118709	−	0.163389i
$768$			31.5921i			1.13998i
$769$	17.8801	+	12.9907i	0.644773	+	0.468455i	0.861487	−	0.507780i	$-0.169534\pi$
$769$	17.8801	+	12.9907i	0.644773	+	0.468455i	−0.216714	+	0.976235i	$0.569534\pi$
$770$		0			0
$771$	3.34286	−	2.42873i	0.120390	−	0.0874685i
$772$	−1.58754	−	2.18507i	−0.0571370	−	0.0786423i
$773$	−4.66049	+	1.51429i	−0.167626	+	0.0544651i	−0.391628	−	0.920124i	$-0.628088\pi$
$773$	−4.66049	+	1.51429i	−0.167626	+	0.0544651i	0.224002	+	0.974589i	$0.428088\pi$
$774$	−6.17649			−0.222009
$775$		0			0
$776$	−50.8215			−1.82439
$777$	−18.8409	+	6.12177i	−0.675913	+	0.219617i
$778$	−33.1405	−	45.6139i	−1.18814	−	1.63534i
$779$	−13.5097	+	9.81537i	−0.484035	+	0.351672i
$780$		0			0
$781$	−1.88681	−	1.37085i	−0.0675153	−	0.0490528i
$782$			19.0851i			0.682481i
$783$	1.83517	−	2.52590i	0.0655837	−	0.0902682i
$784$	−5.57648	+	17.1627i	−0.199160	+	0.612952i
$785$		0			0
$786$	9.51020	+	29.2694i	0.339218	+	1.04400i
$787$	3.55198	+	1.15411i	0.126614	+	0.0411395i	0.371639	−	0.928377i	$-0.378796\pi$
$787$	3.55198	+	1.15411i	0.126614	+	0.0411395i	−0.245024	+	0.969517i	$0.578796\pi$
$788$	−87.6303	−	28.4728i	−3.12170	−	1.01430i
$789$	−0.320676	−	0.986940i	−0.0114164	−	0.0351360i
$790$		0			0
$791$	−5.86182	+	18.0408i	−0.208422	+	0.641458i
$792$	9.15994	−	12.6076i	0.325484	−	0.447991i
$793$		−	25.3266i		−	0.899375i
$794$	27.5100	+	19.9872i	0.976294	+	0.709319i
$795$		0			0
$796$	−32.6193	+	23.6993i	−1.15616	+	0.839998i
$797$	1.96557	+	2.70538i	0.0696242	+	0.0958295i	0.842409	−	0.538839i	$-0.181137\pi$
$797$	1.96557	+	2.70538i	0.0696242	+	0.0958295i	−0.772785	+	0.634668i	$0.781137\pi$
$798$	24.6014	−	7.99348i	0.870880	−	0.282966i
$799$	35.7355			1.26423
$800$		0			0
$801$	8.53392			0.301531
$802$	−64.0140	+	20.7994i	−2.26041	+	0.734453i
$803$	−3.61019	−	4.96901i	−0.127401	−	0.175352i
$804$	5.91646	−	4.29856i	0.208658	−	0.151599i
$805$		0			0
$806$	47.4866	+	34.5010i	1.67264	+	1.21525i
$807$		−	15.7897i		−	0.555823i
$808$	4.94017	−	6.79957i	0.173795	−	0.239208i
$809$	−10.5954	+	32.6094i	−0.372516	+	1.14649i	0.572624	+	0.819818i	$0.305926\pi$
$809$	−10.5954	+	32.6094i	−0.372516	+	1.14649i	−0.945140	+	0.326667i	$0.894074\pi$
$810$		0			0
$811$	−1.07152	−	3.29778i	−0.0376260	−	0.115801i	0.930479	−	0.366344i	$-0.119391\pi$
$811$	−1.07152	−	3.29778i	−0.0376260	−	0.115801i	−0.968105	+	0.250543i	$0.919391\pi$
$812$	−40.4020	−	13.1274i	−1.41783	−	0.460682i
$813$	13.0298	+	4.23364i	0.456975	+	0.148480i
$814$	−14.1845	−	43.6554i	−0.497167	−	1.53012i
$815$		0			0
$816$	5.82768	−	17.9358i	0.204010	−	0.627877i
$817$	4.58394	−	6.30926i	0.160372	−	0.220733i
$818$			32.2422i			1.12732i
$819$	8.99556	+	6.53566i	0.314330	+	0.228374i
$820$		0			0
$821$	11.8771	−	8.62922i	0.414514	−	0.301162i	−0.360913	−	0.932600i	$-0.617535\pi$
$821$	11.8771	−	8.62922i	0.414514	−	0.301162i	0.775427	+	0.631438i	$0.217535\pi$
$822$	−11.8201	−	16.2689i	−0.412273	−	0.567445i
$823$	19.8483	−	6.44912i	0.691870	−	0.224802i	0.0580851	−	0.998312i	$-0.481501\pi$
$823$	19.8483	−	6.44912i	0.691870	−	0.224802i	0.633785	+	0.773510i	$0.281501\pi$
$824$	−75.9223			−2.64488
$825$		0			0
$826$	−14.5285			−0.505512
$827$	43.0710	−	13.9946i	1.49773	−	0.486641i	0.558372	−	0.829590i	$-0.311426\pi$
$827$	43.0710	−	13.9946i	1.49773	−	0.486641i	0.939354	+	0.342950i	$0.111426\pi$
$828$	−3.59779	−	4.95193i	−0.125032	−	0.172091i
$829$	−7.81291	+	5.67641i	−0.271354	+	0.197150i	−0.715137	−	0.698984i	$-0.753636\pi$
$829$	−7.81291	+	5.67641i	−0.271354	+	0.197150i	0.443784	+	0.896134i	$0.353636\pi$
$830$		0			0
$831$	5.64685	+	4.10268i	0.195887	+	0.142320i
$832$		−	27.5502i		−	0.955131i
$833$	−14.3630	+	19.7690i	−0.497649	+	0.684955i
$834$	6.08075	−	18.7146i	0.210559	−	0.648035i
$835$		0			0
$836$	12.3009	+	37.8583i	0.425436	+	1.30936i
$837$	7.07787	+	2.29974i	0.244647	+	0.0794907i
$838$	−20.5342	−	6.67198i	−0.709344	−	0.230480i
$839$	7.77848	+	23.9397i	0.268543	+	0.826490i	0.990856	+	0.134924i	$0.0430789\pi$
$839$	7.77848	+	23.9397i	0.268543	+	0.826490i	−0.722313	+	0.691566i	$0.756921\pi$
$840$		0			0
$841$	−5.94919	+	18.3097i	−0.205144	+	0.631370i
$842$	53.7550	−	73.9874i	1.85252	−	2.54977i
$843$		−	7.95823i		−	0.274096i
$844$	58.4159	+	42.4416i	2.01076	+	1.46090i
$845$		0			0
$846$	−13.9610	+	10.1433i	−0.479989	+	0.348733i
$847$	0.666435	+	0.917269i	0.0228990	+	0.0315177i
$848$	36.0305	−	11.7070i	1.23729	−	0.402021i
$849$	−27.7952			−0.953928
$850$		0			0
$851$	−8.91196			−0.305498
$852$	2.68553	−	0.872582i	0.0920048	−	0.0298942i
$853$	1.88589	+	2.59571i	0.0645717	+	0.0888753i	0.840081	−	0.542460i	$-0.182507\pi$
$853$	1.88589	+	2.59571i	0.0645717	+	0.0888753i	−0.775510	+	0.631336i	$0.782507\pi$
$854$	−53.2222	+	38.6682i	−1.82123	+	1.32320i
$855$		0			0
$856$	60.9069	+	44.2514i	2.08175	+	1.51248i
$857$		−	19.4569i		−	0.664634i	−0.943168	−	0.332317i	$-0.892170\pi$
$857$		−	19.4569i		−	0.664634i	0.943168	−	0.332317i	$-0.107830\pi$
$858$	−15.1435	+	20.8432i	−0.516991	+	0.711577i
$859$	−5.20173	+	16.0093i	−0.177481	+	0.546230i	−0.999738	−	0.0228862i	$-0.992714\pi$
$859$	−5.20173	+	16.0093i	−0.177481	+	0.546230i	0.822257	+	0.569116i	$0.192714\pi$
$860$		0			0
$861$	5.76163	+	17.7325i	0.196356	+	0.604322i
$862$	61.7914	+	20.0772i	2.10462	+	0.683833i
$863$	3.62560	+	1.17803i	0.123417	+	0.0401006i	0.370074	−	0.929002i	$-0.379332\pi$
$863$	3.62560	+	1.17803i	0.123417	+	0.0401006i	−0.246657	+	0.969103i	$0.579332\pi$
$864$	−0.134261	−	0.413214i	−0.00456766	−	0.0140578i
$865$		0			0
$866$	26.3910	−	81.2231i	0.896802	−	2.76007i
$867$	5.01767	−	6.90623i	0.170409	−	0.234548i
$868$		−	101.259i		−	3.43697i
$869$	35.2358	+	25.6003i	1.19529	+	0.868431i
$870$		0			0
$871$	−4.83497	+	3.51281i	−0.163827	+	0.119027i
$872$	−27.8166	−	38.2863i	−0.941990	−	1.29654i
$873$	10.1314	−	3.29190i	0.342897	−	0.111414i
$874$	11.6367			0.393619
$875$		0			0
$876$	7.43645			0.251254
$877$	−24.4851	+	7.95569i	−0.826803	+	0.268644i	−0.691698	−	0.722187i	$-0.743137\pi$
$877$	−24.4851	+	7.95569i	−0.826803	+	0.268644i	−0.135105	+	0.990831i	$0.543137\pi$
$878$	−28.7646	−	39.5911i	−0.970759	−	1.33613i
$879$	11.4960	−	8.35231i	0.387749	−	0.281717i
$880$		0			0
$881$	−36.6110	−	26.5995i	−1.23346	−	0.896159i	−0.236313	−	0.971677i	$-0.575939\pi$
$881$	−36.6110	−	26.5995i	−1.23346	−	0.896159i	−0.997144	+	0.0755181i	$0.975939\pi$
$882$		−	11.8001i		−	0.397330i
$883$	26.0964	−	35.9186i	0.878212	−	1.20876i	−0.0987003	−	0.995117i	$-0.531469\pi$
$883$	26.0964	−	35.9186i	0.878212	−	1.20876i	0.976913	−	0.213639i	$-0.0685315\pi$
$884$	−19.9611	+	61.4340i	−0.671365	+	2.06625i
$885$		0			0
$886$	3.12850	+	9.62853i	0.105104	+	0.323477i
$887$	37.0844	+	12.0495i	1.24517	+	0.404581i	0.856189	−	0.516664i	$-0.172826\pi$
$887$	37.0844	+	12.0495i	1.24517	+	0.404581i	0.388984	+	0.921245i	$0.372826\pi$
$888$	26.1270	+	8.48919i	0.876766	+	0.284878i
$889$	−1.05470	−	3.24602i	−0.0353734	−	0.108868i
$890$		0			0
$891$	−1.00942	+	3.10669i	−0.0338170	+	0.104078i
$892$	−40.0411	+	55.1119i	−1.34068	+	1.84528i
$893$		−	21.7890i		−	0.729142i
$894$	37.7278	+	27.4108i	1.26181	+	0.916755i
$895$		0			0
$896$	−55.4764	+	40.3059i	−1.85334	+	1.34653i
$897$	2.94014	+	4.04675i	0.0981683	+	0.135117i
$898$	19.3745	−	6.29517i	0.646537	−	0.210072i
$899$	23.2356			0.774952
$900$		0			0
$901$	51.2995			1.70903
$902$	−41.0872	+	13.3500i	−1.36805	+	0.444508i
$903$	−5.11817	−	7.04455i	−0.170322	−	0.234428i
$904$	21.2812	−	15.4617i	0.707803	−	0.514249i
$905$		0			0
$906$	3.13015	+	2.27419i	0.103992	+	0.0755548i
$907$		−	11.0201i		−	0.365915i	−0.983121	−	0.182958i	$-0.941433\pi$
$907$		−	11.0201i		−	0.365915i	0.983121	−	0.182958i	$-0.0585671\pi$
$908$	−10.0630	+	13.8506i	−0.333954	+	0.459648i
$909$	−0.544406	+	1.67551i	−0.0180568	+	0.0555731i
$910$		0			0
$911$	−16.3540	−	50.3325i	−0.541833	−	1.66759i	−0.728404	−	0.685148i	$-0.759737\pi$
$911$	−16.3540	−	50.3325i	−0.541833	−	1.66759i	0.186571	−	0.982441i	$-0.440263\pi$
$912$	−10.9360	−	3.55332i	−0.362127	−	0.117662i
$913$	−12.2946	−	3.99477i	−0.406893	−	0.132207i
$914$	−15.5172	−	47.7570i	−0.513263	−	1.57966i
$915$		0			0
$916$	24.8277	−	76.4119i	0.820331	−	2.52472i
$917$	−25.5023	+	35.1010i	−0.842162	+	1.15914i
$918$			12.3317i			0.407005i
$919$	−38.5129	−	27.9812i	−1.27042	−	0.923016i	−0.271203	−	0.962522i	$-0.587421\pi$
$919$	−38.5129	−	27.9812i	−1.27042	−	0.923016i	−0.999219	+	0.0395064i	$0.987421\pi$
$920$		0			0
$921$	−18.8429	+	13.6902i	−0.620896	+	0.451107i
$922$	41.1505	+	56.6388i	1.35522	+	1.86530i
$923$	−2.19463	+	0.713080i	−0.0722372	+	0.0234713i
$924$	44.4457			1.46216
$925$		0			0
$926$	97.8059			3.21410
$927$	15.1354	−	4.91777i	0.497110	−	0.161521i
$928$	−0.797343	−	1.09745i	−0.0261741	−	0.0360255i
$929$	17.5465	−	12.7483i	0.575682	−	0.418258i	−0.261483	−	0.965208i	$-0.584211\pi$
$929$	17.5465	−	12.7483i	0.575682	−	0.418258i	0.837165	+	0.546951i	$0.184211\pi$
$930$		0			0
$931$	12.0538	+	8.75757i	0.395046	+	0.287018i
$932$			1.34848i			0.0441708i
$933$	4.43733	−	6.10746i	0.145272	−	0.199949i
$934$	6.13972	−	18.8961i	0.200898	−	0.618300i
$935$		0			0
$936$	−4.76477	−	14.6645i	−0.155741	−	0.479323i
$937$	−2.09317	−	0.680112i	−0.0683809	−	0.0222183i	0.274627	−	0.961551i	$-0.411446\pi$
$937$	−2.09317	−	0.680112i	−0.0683809	−	0.0222183i	−0.343008	+	0.939333i	$0.611446\pi$
$938$	14.7639	+	4.79708i	0.482058	+	0.156630i
$939$	−9.78241	−	30.1072i	−0.319237	−	0.982510i
$940$		0			0
$941$	−5.18833	+	15.9680i	−0.169135	+	0.520543i	−0.999317	−	0.0369489i	$-0.988236\pi$
$941$	−5.18833	+	15.9680i	−0.169135	+	0.520543i	0.830183	+	0.557492i	$0.188236\pi$
$942$	−31.3422	+	43.1388i	−1.02118	+	1.40554i
$943$			8.38767i			0.273140i
$944$	5.22489	+	3.79611i	0.170056	+	0.123553i
$945$		0			0
$946$	16.3226	−	11.8591i	0.530695	−	0.385572i
$947$	21.5207	+	29.6207i	0.699329	+	0.962544i	0.999961	+	0.00880418i	$0.00280249\pi$
$947$	21.5207	+	29.6207i	0.699329	+	0.962544i	−0.300632	+	0.953740i	$0.597198\pi$
$948$	−50.1518	+	16.2953i	−1.62885	+	0.529247i
$949$	−6.07711			−0.197271
$950$		0			0
$951$	−25.8362			−0.837796
$952$	78.8796	−	25.6295i	2.55650	−	0.830658i
$953$	−25.8201	−	35.5383i	−0.836394	−	1.15120i	−0.986699	−	0.162558i	$-0.948026\pi$
$953$	−25.8201	−	35.5383i	−0.836394	−	1.15120i	0.150305	−	0.988640i	$-0.451974\pi$
$954$	−20.0415	+	14.5610i	−0.648867	+	0.471430i
$955$		0			0
$956$	22.9251	+	16.6561i	0.741450	+	0.538695i
$957$			10.1988i			0.329680i
$958$	−40.2512	+	55.4010i	−1.30046	+	1.78993i
$959$	8.76068	−	26.9626i	0.282897	−	0.870668i
$960$		0			0
$961$	7.53541	+	23.1916i	0.243078	+	0.748116i
$962$	−43.1940	−	14.0346i	−1.39263	−	0.452493i
$963$	−15.0083	−	4.87650i	−0.483636	−	0.157143i
$964$	15.3530	+	47.2517i	0.494487	+	1.52188i
$965$		0			0
$966$	4.01503	−	12.3570i	0.129182	−	0.397580i
$967$	−14.3899	+	19.8059i	−0.462747	+	0.636916i	−0.975076	−	0.221873i	$-0.928783\pi$
$967$	−14.3899	+	19.8059i	−0.462747	+	0.636916i	0.512329	+	0.858789i	$0.328783\pi$
$968$		−	1.57227i		−	0.0505348i
$969$	−12.5967	−	9.15206i	−0.404665	−	0.294007i
$970$		0			0
$971$	15.8773	−	11.5355i	0.509526	−	0.370192i	−0.303118	−	0.952953i	$-0.598028\pi$
$971$	15.8773	−	11.5355i	0.509526	−	0.370192i	0.812644	+	0.582761i	$0.198028\pi$
$972$	−2.32468	−	3.19965i	−0.0745642	−	0.102629i
$973$	26.3837	−	8.57257i	0.845822	−	0.274824i
$974$	37.1344			1.18986
$975$		0			0
$976$	29.2438			0.936070
$977$	29.0298	−	9.43236i	0.928746	−	0.301768i	0.194696	−	0.980864i	$-0.437628\pi$
$977$	29.0298	−	9.43236i	0.928746	−	0.301768i	0.734050	+	0.679096i	$0.237628\pi$
$978$	14.5356	+	20.0066i	0.464798	+	0.639739i
$979$	−22.5526	+	16.3854i	−0.720785	+	0.523681i
$980$		0			0
$981$	8.02529	+	5.83071i	0.256228	+	0.186160i
$982$		−	20.2356i		−	0.645743i
$983$	6.09271	−	8.38590i	0.194327	−	0.267469i	−0.700723	−	0.713433i	$-0.747139\pi$
$983$	6.09271	−	8.38590i	0.194327	−	0.267469i	0.895051	+	0.445964i	$0.147139\pi$
$984$	7.98977	−	24.5900i	0.254705	−	0.783901i
$985$		0			0
$986$	11.8977	+	36.6173i	0.378899	+	1.16613i
$987$	−23.1376	−	7.51788i	−0.736479	−	0.239297i
$988$	37.4582	+	12.1709i	1.19170	+	0.387208i
$989$	−1.21048	−	3.72546i	−0.0384909	−	0.118463i
$990$		0			0
$991$	−3.12376	+	9.61395i	−0.0992295	+	0.305397i	−0.988333	−	0.152309i	$-0.951329\pi$
$991$	−3.12376	+	9.61395i	−0.0992295	+	0.305397i	0.889103	+	0.457707i	$0.151329\pi$
$992$	1.90057	−	2.61591i	0.0603431	−	0.0830552i
$993$		−	20.1083i		−	0.638116i
$994$	4.84921	+	3.52316i	0.153808	+	0.111748i
$995$		0			0
$996$	12.6625	−	9.19986i	0.401227	−	0.291509i
$997$	12.5574	+	17.2838i	0.397697	+	0.547382i	0.960164	−	0.279437i	$-0.0901478\pi$
$997$	12.5574	+	17.2838i	0.397697	+	0.547382i	−0.562467	+	0.826819i	$0.690148\pi$
$998$	56.6300	−	18.4002i	1.79259	−	0.582448i
$999$	−5.75838			−0.182187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.d.349.5		24
5.2	odd	4		75.2.g.c.31.3	✓	12
5.3	odd	4		375.2.g.c.151.1		12
5.4	even	2	inner	375.2.i.d.349.2		24
15.2	even	4		225.2.h.d.181.1		12
25.2	odd	20		1875.2.a.j.1.6		6
25.3	odd	20		375.2.g.c.226.1		12
25.4	even	10	inner	375.2.i.d.274.5		24
25.11	even	5		1875.2.b.f.1249.2		12
25.14	even	10		1875.2.b.f.1249.11		12
25.21	even	5	inner	375.2.i.d.274.2		24
25.22	odd	20		75.2.g.c.46.3	yes	12
25.23	odd	20		1875.2.a.k.1.1		6
75.2	even	20		5625.2.a.p.1.1		6
75.23	even	20		5625.2.a.q.1.6		6
75.47	even	20		225.2.h.d.46.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.3	✓	12	5.2	odd	4
75.2.g.c.46.3	yes	12	25.22	odd	20
225.2.h.d.46.1		12	75.47	even	20
225.2.h.d.181.1		12	15.2	even	4
375.2.g.c.151.1		12	5.3	odd	4
375.2.g.c.226.1		12	25.3	odd	20
375.2.i.d.274.2		24	25.21	even	5	inner
375.2.i.d.274.5		24	25.4	even	10	inner
375.2.i.d.349.2		24	5.4	even	2	inner
375.2.i.d.349.5		24	1.1	even	1	trivial
1875.2.a.j.1.6		6	25.2	odd	20
1875.2.a.k.1.1		6	25.23	odd	20
1875.2.b.f.1249.2		12	25.11	even	5
1875.2.b.f.1249.11		12	25.14	even	10
5625.2.a.p.1.1		6	75.2	even	20
5625.2.a.q.1.6		6	75.23	even	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.32085 - 0.754089i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.19965 - 2.32468i) q^{4} +(1.97423 + 1.43436i) q^{6} +3.44028i q^{7} +(2.80415 - 3.85959i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.00942 - 3.10669i) q^{11} +(3.76141 + 1.22216i) q^{12} +(-3.07385 - 0.998755i) q^{13} +(2.59428 + 7.98437i) q^{14} +(1.15323 - 3.54927i) q^{16} +(2.97030 - 4.08826i) q^{17} +2.44028i q^{18} +(-2.49274 - 1.81108i) q^{19} +(-2.78325 + 2.02215i) q^{21} +(-4.68544 - 6.44895i) q^{22} +(-1.47190 + 0.478250i) q^{23} +4.77071 q^{24} -7.88709 q^{26} +(-0.951057 + 0.309017i) q^{27} +(7.99756 + 11.0077i) q^{28} +(-2.52590 + 1.83517i) q^{29} +(-6.02080 - 4.37437i) q^{31} +0.434479i q^{32} +(1.92004 - 2.64270i) q^{33} +(3.81069 - 11.7281i) q^{34} +(1.22216 + 3.76141i) q^{36} +(5.47655 + 1.77944i) q^{37} +(-7.15098 - 2.32349i) q^{38} +(-0.998755 - 3.07385i) q^{39} +(1.67476 - 5.15437i) q^{41} +(-4.93461 + 6.79191i) q^{42} +2.53106i q^{43} +(-10.4519 - 7.59371i) q^{44} +(-3.05541 + 2.21989i) q^{46} +(4.15659 + 5.72106i) q^{47} +(3.54927 - 1.15323i) q^{48} -4.83555 q^{49} +5.05337 q^{51} +(-12.1570 + 3.95006i) q^{52} +(5.96693 + 8.21277i) q^{53} +(-1.97423 + 1.43436i) q^{54} +(13.2781 + 9.64708i) q^{56} -3.08119i q^{57} +(-4.47834 + 6.16391i) q^{58} +(-0.534773 + 1.64586i) q^{59} +(2.42149 + 7.45259i) q^{61} +(-17.2720 - 5.61202i) q^{62} +(-3.27190 - 1.06311i) q^{63} +(2.63409 + 8.10689i) q^{64} +(2.46328 - 7.58119i) q^{66} +(1.08687 - 1.49595i) q^{67} -19.9860i q^{68} +(-1.25207 - 0.909685i) q^{69} +(0.577613 - 0.419660i) q^{71} +(2.80415 + 3.85959i) q^{72} +(1.78825 - 0.581036i) q^{73} +14.0521 q^{74} -12.1861 q^{76} +(10.6879 - 3.47270i) q^{77} +(-4.63591 - 6.38079i) q^{78} +(-10.7868 + 7.83708i) q^{79} +(-0.809017 - 0.587785i) q^{81} -13.2254i q^{82} +(2.32614 - 3.20166i) q^{83} +(-4.20457 + 12.9403i) q^{84} +(1.90864 + 5.87419i) q^{86} +(-2.96937 - 0.964807i) q^{87} +(-14.8211 - 4.81567i) q^{88} +(-2.63713 - 8.11624i) q^{89} +(3.43600 - 10.5749i) q^{91} +(-3.59779 + 4.95193i) q^{92} -7.44212i q^{93} +(13.9610 + 10.1433i) q^{94} +(-0.351501 + 0.255380i) q^{96} +(-6.26157 - 8.61831i) q^{97} +(-11.2226 + 3.64643i) q^{98} +3.26656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49}+ \cdots - 12 q^{99}+O(q^{100}) \) 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

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Database

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