LMFDB - Embedded newform 375.2.i.d.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			349.2
Character	$\chi$	$=$	375.349
Dual form			375.2.i.d.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32085 + 0.754089i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.19965 - 2.32468i) q^{4} +(1.97423 + 1.43436i) q^{6} -3.44028i q^{7} +(-2.80415 + 3.85959i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 24 * q + 20 * q^4 + 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	−0.976781	−	0.214240i	$-0.931273\pi$
$2$	−2.32085	+	0.754089i	−1.64109	+	0.533221i	−0.664306	+	0.747461i	$0.731273\pi$
$3$	−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	$-0.774705\pi$
$7$		−	3.44028i		−	1.30030i	0.759804	−	0.650152i	$-0.225295\pi$
$8$	−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	0.702506	−	0.711677i	$-0.252064\pi$
$13$	3.07385	+	0.998755i	0.852533	+	0.277005i	0.150026	+	0.988682i	$0.452064\pi$
$14$	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	$0.409961\pi$
$17$	−2.97030	+	4.08826i	−0.720403	+	0.991550i	−0.999510	+	0.0312897i	$0.990039\pi$
$18$		−	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	−0.151512	−	0.988455i	$-0.548414\pi$
$23$	1.47190	−	0.478250i	0.306913	−	0.0997219i	0.458424	+	0.888734i	$0.348414\pi$
$24$	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	−0.177962	−	0.984037i	$-0.556950\pi$
$37$	−5.47655	−	1.77944i	−0.900339	−	0.292538i	−0.722377	+	0.691499i	$0.756950\pi$
$38$	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	$-0.938181\pi$
$43$		−	2.53106i		−	0.385982i	0.981201	−	0.192991i	$-0.0618189\pi$
$44$	−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	0.389966	−	0.920829i	$-0.372487\pi$
$47$	−4.15659	−	5.72106i	−0.606301	−	0.834502i	−0.996267	+	0.0863273i	$0.972487\pi$
$48$	−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	$-0.954424\pi$
$53$	−5.96693	−	8.21277i	−0.819621	−	1.12811i	0.170147	−	0.985419i	$-0.445576\pi$
$54$	−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	−0.870231	−	0.492644i	$-0.836031\pi$
$67$	−1.08687	+	1.49595i	−0.132783	+	0.182760i	0.737448	+	0.675404i	$0.236031\pi$
$68$			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	−0.411790	−	0.911279i	$-0.635096\pi$
$73$	−1.78825	+	0.581036i	−0.209298	+	0.0680052i	0.202491	+	0.979284i	$0.435096\pi$
$74$	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	−0.917368	−	0.398040i	$-0.869691\pi$
$83$	−2.32614	+	3.20166i	−0.255328	+	0.351428i	0.662041	+	0.749468i	$0.269691\pi$
$84$	−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	0.998381	−	0.0568823i	$-0.0181160\pi$
$97$	6.26157	+	8.61831i	0.635766	+	0.875057i	−0.362615	+	0.931939i	$0.618116\pi$
$98$	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	$0.0868438\pi$
$103$	9.35416	+	12.8749i	0.921693	+	1.26860i	−0.0413198	+	0.999146i	$0.513156\pi$
$104$	−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	$-0.723830\pi$
$107$		−	15.7807i		−	1.52558i	0.646649	−	0.762788i	$-0.276170\pi$
$108$	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	0.0517868	−	0.998658i	$-0.483508\pi$
$113$	−5.24399	−	1.70388i	−0.493313	−	0.160287i	−0.545100	+	0.838371i	$0.683508\pi$
$114$	−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	−0.266855	−	0.963737i	$-0.585984\pi$
$127$	0.943532	−	0.306572i	0.0837250	−	0.0272039i	0.350580	+	0.936533i	$0.385984\pi$
$128$	−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	0.624031	−	0.781400i	$-0.285494\pi$
$137$	7.83732	+	2.54650i	0.669588	+	0.217562i	0.0455566	+	0.998962i	$0.485494\pi$
$138$	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	$-0.662857\pi$
$157$		−	21.8510i		−	1.74390i	0.489599	−	0.871948i	$-0.337143\pi$
$158$	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	−0.0938092	−	0.995590i	$-0.529904\pi$
$163$	−9.63786	−	3.13153i	−0.754896	−	0.245280i	−0.661087	+	0.750310i	$0.729904\pi$
$164$	−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	−0.841998	−	0.539480i	$-0.818621\pi$
$167$	−0.888195	+	1.22250i	−0.0687306	+	0.0945996i	0.773268	+	0.634080i	$0.218621\pi$
$168$		−	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	−0.763602	−	0.645688i	$-0.776571\pi$
$173$	−13.1772	+	4.28153i	−1.00184	+	0.325518i	−0.238241	+	0.971206i	$0.576571\pi$
$174$	−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	$0.00782434\pi$
$193$			0.682908i			0.0491568i	−0.999698	+	0.0245784i	$0.992176\pi$
$194$	−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	$0.111619\pi$
$197$	13.6937	+	18.8478i	0.975639	+	1.34285i	0.0364929	+	0.999334i	$0.488381\pi$
$198$	−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	0.296037	−	0.955176i	$-0.404335\pi$
$223$	16.3813	−	5.32262i	1.09698	−	0.356429i	0.800938	+	0.598748i	$0.204335\pi$
$224$	−1.49473			−0.0998708
$225$		0			0
$226$	13.4554			0.895039
$227$	4.11692	−	1.33767i	0.273250	−	0.0887842i	−0.169187	−	0.985584i	$-0.554114\pi$
$227$	4.11692	−	1.33767i	0.273250	−	0.0887842i	0.442437	+	0.896800i	$0.354114\pi$
$228$	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	−0.802402	−	0.596784i	$-0.796445\pi$
$233$	0.200409	−	0.275839i	0.0131292	−	0.0180708i	0.815531	+	0.578713i	$0.196445\pi$
$234$	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	$0.0411361\pi$
$257$			4.13200i			0.257747i	−0.991661	+	0.128874i	$0.958864\pi$
$258$	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	0.339287	−	0.940683i	$-0.389814\pi$
$263$	0.986940	+	0.320676i	0.0608573	+	0.0197737i	−0.278430	+	0.960456i	$0.589814\pi$
$264$	−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	−0.501574	−	0.865114i	$-0.667246\pi$
$277$	−6.63827	+	2.15691i	−0.398855	+	0.129596i	0.102719	+	0.994710i	$0.467246\pi$
$278$	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	$-0.490540\pi$
$283$	16.3376	−	22.4868i	0.971169	−	1.33670i	0.941454	−	0.337141i	$-0.109460\pi$
$284$	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	$0.136244\pi$
$293$			14.2098i			0.830146i	−0.909788	+	0.415073i	$0.863756\pi$
$294$	−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	$-0.768582\pi$
$307$		−	23.2911i		−	1.32930i	0.747157	−	0.664648i	$-0.231418\pi$
$308$	−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	0.988927	−	0.148402i	$-0.0474130\pi$
$313$	30.1072	+	9.78241i	1.70176	+	0.552934i	0.712830	+	0.701337i	$0.247413\pi$
$314$	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	$-0.541584\pi$
$317$	15.1861	−	20.9019i	0.852938	−	1.17397i	0.983208	−	0.182490i	$-0.0584156\pi$
$318$		−	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	0.395354	−	0.918529i	$-0.370622\pi$
$337$	3.21816	+	1.04564i	0.175304	+	0.0569599i	−0.220050	+	0.975489i	$0.570622\pi$
$338$	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	$0.0866557\pi$
$347$	17.1612	+	23.6204i	0.921262	+	1.26801i	−0.0419100	+	0.999121i	$0.513344\pi$
$348$	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	0.778873	−	0.627182i	$-0.215792\pi$
$353$	−1.09532	−	1.50757i	−0.0582978	−	0.0802400i	−0.837170	+	0.546942i	$0.815792\pi$
$354$	−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	$-0.566771\pi$
$367$	15.0638	−	20.7335i	0.786324	−	1.08228i	0.994556	−	0.104203i	$-0.0332291\pi$
$368$		−	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	0.270758	−	0.962648i	$-0.412726\pi$
$373$	20.3877	−	6.62437i	1.05564	−	0.342997i	0.784878	+	0.619651i	$0.212726\pi$
$374$	−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	−0.532924	−	0.846163i	$-0.678907\pi$
$383$	8.54263	−	11.7579i	0.436508	−	0.600802i	0.969432	+	0.245362i	$0.0789067\pi$
$384$	−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	0.552409	−	0.833573i	$-0.313709\pi$
$397$	−8.19052	−	11.2733i	−0.411070	−	0.565790i	−0.963479	+	0.267784i	$0.913709\pi$
$398$	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	$0.517990\pi$
$433$	−20.5708	+	28.3133i	−0.988571	+	1.36065i	−0.932082	+	0.362248i	$0.882010\pi$
$434$	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	$-0.968578\pi$
$443$		−	4.14871i		−	0.197111i	0.995132	−	0.0985556i	$-0.0314222\pi$
$444$	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	$0.159830\pi$
$457$			20.5774i			0.962571i	−0.876564	+	0.481285i	$0.840170\pi$
$458$	−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	−0.773213	−	0.634146i	$-0.781352\pi$
$463$	−38.1181	−	12.3853i	−1.77150	−	0.575594i	−0.998284	+	0.0585520i	$0.981352\pi$
$464$	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	−0.905260	−	0.424858i	$-0.860324\pi$
$467$	−4.78569	+	6.58694i	−0.221456	+	0.304807i	0.683805	+	0.729665i	$0.260324\pi$
$468$			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	−0.0378360	−	0.999284i	$-0.512046\pi$
$487$	−14.4725	−	4.70239i	−0.655810	−	0.213086i	−0.617974	+	0.786198i	$0.712046\pi$
$488$	−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	0.923896	−	0.382644i	$-0.124986\pi$
$503$	6.15596	+	8.47295i	0.274481	+	0.377790i	−0.649415	+	0.760434i	$0.724986\pi$
$504$	−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	−0.0112775	−	0.999936i	$-0.503590\pi$
$523$	12.9748	−	4.21576i	0.567347	−	0.184342i	0.578624	+	0.815594i	$0.303590\pi$
$524$	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	0.330915	−	0.943661i	$-0.392643\pi$
$547$	−15.6423	−	21.5298i	−0.668818	−	0.920549i	−0.999733	+	0.0231115i	$0.992643\pi$
$548$	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	$-0.929880\pi$
$557$		−	10.3141i		−	0.437020i	0.975835	−	0.218510i	$-0.0701197\pi$
$558$	−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	0.902325	−	0.431056i	$-0.141859\pi$
$563$	32.7193	+	10.6311i	1.37895	+	0.448049i	0.476628	+	0.879105i	$0.341859\pi$
$564$	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	−0.634830	−	0.772652i	$-0.718930\pi$
$577$	−16.6768	+	5.41863i	−0.694266	+	0.225581i	−0.0594353	+	0.998232i	$0.518930\pi$
$578$	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	−0.154451	−	0.988000i	$-0.549361\pi$
$587$	−20.8395	−	6.77115i	−0.860137	−	0.279475i	−0.705686	+	0.708525i	$0.749361\pi$
$588$	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	$0.284965\pi$
$593$			38.0061i			1.56072i	−0.625330	+	0.780361i	$0.715035\pi$
$594$	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	$0.226806\pi$
$607$			32.2134i			1.30750i	−0.756709	+	0.653752i	$0.773194\pi$
$608$	−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	−0.235179	−	0.971952i	$-0.575568\pi$
$613$	−24.6782	−	8.01843i	−0.996742	−	0.323861i	−0.761563	+	0.648091i	$0.775568\pi$
$614$	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	−0.785898	−	0.618356i	$-0.787799\pi$
$617$	1.11899	−	1.54016i	0.0450488	−	0.0620043i	0.830947	+	0.556351i	$0.187799\pi$
$618$			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	$-0.835956\pi$
$643$		−	24.9947i		−	0.985695i	0.870116	−	0.492847i	$-0.164044\pi$
$644$	−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	$0.0167323\pi$
$647$	18.8228	+	25.9073i	0.739999	+	1.01852i	−0.258620	+	0.965979i	$0.583268\pi$
$648$	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	$-0.861401\pi$
$653$	−26.2606	−	36.1446i	−1.02766	−	1.41445i	−0.120964	−	0.992657i	$-0.538599\pi$
$654$	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	−0.626639	−	0.779310i	$-0.715570\pi$
$673$	−17.5249	+	5.69418i	−0.675534	+	0.219494i	−0.0488951	+	0.998804i	$0.515570\pi$
$674$	−8.25737			−0.318062
$675$		0			0
$676$	−10.1008			−0.388491
$677$	21.6996	−	7.05064i	0.833985	−	0.270978i	0.139262	−	0.990256i	$-0.455527\pi$
$677$	21.6996	−	7.05064i	0.833985	−	0.270978i	0.694723	+	0.719277i	$0.255527\pi$
$678$	−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	$0.411317\pi$
$683$	−18.9304	+	26.0555i	−0.724353	+	0.996987i	−0.999368	+	0.0355465i	$0.988683\pi$
$684$	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	0.361400	−	0.932411i	$-0.382299\pi$
$727$	32.4050	−	10.5290i	1.20184	−	0.390500i	0.840436	+	0.541910i	$0.182299\pi$
$728$	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	$-0.533853\pi$
$733$	23.6176	−	32.5068i	0.872335	−	1.20067i	0.978485	−	0.206316i	$-0.0661475\pi$
$734$	−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	$0.101645\pi$
$743$			17.1140i			0.627853i	−0.949447	+	0.313926i	$0.898355\pi$
$744$	−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	$0.148026\pi$
$757$			24.6773i			0.896911i	−0.893805	+	0.448456i	$0.851974\pi$
$758$	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	−0.224002	−	0.974589i	$-0.571912\pi$
$773$	4.66049	−	1.51429i	0.167626	−	0.0544651i	0.391628	+	0.920124i	$0.371912\pi$
$774$	−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	0.245024	−	0.969517i	$-0.421204\pi$
$787$	−3.55198	−	1.15411i	−0.126614	−	0.0411395i	−0.371639	+	0.928377i	$0.621204\pi$
$788$	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	0.772785	−	0.634668i	$-0.218863\pi$
$797$	−1.96557	−	2.70538i	−0.0696242	−	0.0958295i	−0.842409	+	0.538839i	$0.818863\pi$
$798$	−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	−0.633785	−	0.773510i	$-0.718499\pi$
$823$	−19.8483	+	6.44912i	−0.691870	+	0.224802i	−0.0580851	+	0.998312i	$0.518499\pi$
$824$	−75.9223			−2.64488
$825$		0			0
$826$	−14.5285			−0.505512
$827$	−43.0710	+	13.9946i	−1.49773	+	0.486641i	−0.939354	−	0.342950i	$-0.888574\pi$
$827$	−43.0710	+	13.9946i	−1.49773	+	0.486641i	−0.558372	+	0.829590i	$0.688574\pi$
$828$	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	0.775510	−	0.631336i	$-0.217493\pi$
$853$	−1.88589	−	2.59571i	−0.0645717	−	0.0888753i	−0.840081	+	0.542460i	$0.817493\pi$
$854$	−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	$0.107830\pi$
$857$			19.4569i			0.664634i	−0.943168	+	0.332317i	$0.892170\pi$
$858$	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	0.246657	−	0.969103i	$-0.420668\pi$
$863$	−3.62560	−	1.17803i	−0.123417	−	0.0401006i	−0.370074	+	0.929002i	$0.620668\pi$
$864$	−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	0.135105	−	0.990831i	$-0.456863\pi$
$877$	24.4851	−	7.95569i	0.826803	−	0.268644i	0.691698	+	0.722187i	$0.256863\pi$
$878$	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	$0.468531\pi$
$883$	−26.0964	+	35.9186i	−0.878212	+	1.20876i	−0.976913	+	0.213639i	$0.931469\pi$
$884$	−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	−0.388984	−	0.921245i	$-0.627174\pi$
$887$	−37.0844	−	12.0495i	−1.24517	−	0.404581i	−0.856189	+	0.516664i	$0.827174\pi$
$888$	−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	$0.0585671\pi$
$907$			11.0201i			0.365915i	−0.983121	+	0.182958i	$0.941433\pi$
$908$	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	0.343008	−	0.939333i	$-0.388554\pi$
$937$	2.09317	+	0.680112i	0.0683809	+	0.0222183i	−0.274627	+	0.961551i	$0.588554\pi$
$938$	−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	$-0.997198\pi$
$947$	−21.5207	−	29.6207i	−0.699329	−	0.962544i	0.300632	−	0.953740i	$-0.402802\pi$
$948$	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	$0.0519744\pi$
$953$	25.8201	+	35.5383i	0.836394	+	1.15120i	−0.150305	+	0.988640i	$0.548026\pi$
$954$	−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	−0.512329	−	0.858789i	$-0.671217\pi$
$967$	14.3899	−	19.8059i	0.462747	−	0.636916i	0.975076	+	0.221873i	$0.0712171\pi$
$968$			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	−0.734050	−	0.679096i	$-0.762372\pi$
$977$	−29.0298	+	9.43236i	−0.928746	+	0.301768i	−0.194696	+	0.980864i	$0.562372\pi$
$978$	−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	−0.895051	−	0.445964i	$-0.852861\pi$
$983$	−6.09271	+	8.38590i	−0.194327	+	0.267469i	0.700723	+	0.713433i	$0.252861\pi$
$984$	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	0.562467	−	0.826819i	$-0.309852\pi$
$997$	−12.5574	−	17.2838i	−0.397697	−	0.547382i	−0.960164	+	0.279437i	$0.909852\pi$
$998$	−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.349.2		24
5.2	odd	4		375.2.g.c.151.1		12
5.3	odd	4		75.2.g.c.31.3	✓	12
5.4	even	2	inner	375.2.i.d.349.5		24
15.8	even	4		225.2.h.d.181.1		12
25.2	odd	20		1875.2.a.k.1.1		6
25.3	odd	20		75.2.g.c.46.3	yes	12
25.4	even	10	inner	375.2.i.d.274.2		24
25.11	even	5		1875.2.b.f.1249.11		12
25.14	even	10		1875.2.b.f.1249.2		12
25.21	even	5	inner	375.2.i.d.274.5		24
25.22	odd	20		375.2.g.c.226.1		12
25.23	odd	20		1875.2.a.j.1.6		6
75.2	even	20		5625.2.a.q.1.6		6
75.23	even	20		5625.2.a.p.1.1		6
75.53	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	5.3	odd	4
75.2.g.c.46.3	yes	12	25.3	odd	20
225.2.h.d.46.1		12	75.53	even	20
225.2.h.d.181.1		12	15.8	even	4
375.2.g.c.151.1		12	5.2	odd	4
375.2.g.c.226.1		12	25.22	odd	20
375.2.i.d.274.2		24	25.4	even	10	inner
375.2.i.d.274.5		24	25.21	even	5	inner
375.2.i.d.349.2		24	1.1	even	1	trivial
375.2.i.d.349.5		24	5.4	even	2	inner
1875.2.a.j.1.6		6	25.23	odd	20
1875.2.a.k.1.1		6	25.2	odd	20
1875.2.b.f.1249.2		12	25.14	even	10
1875.2.b.f.1249.11		12	25.11	even	5
5625.2.a.p.1.1		6	75.23	even	20
5625.2.a.q.1.6		6	75.2	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.32085 + 0.754089i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(3.19965 - 2.32468i) q^{4} +(1.97423 + 1.43436i) q^{6} -3.44028i q^{7} +(-2.80415 + 3.85959i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) \) 24 * q + 20 * q^4 + 6 * q^9	\( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) \) 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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