LMFDB - Embedded newform 627.2.bo.b.4.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(4,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([0, 18, 10]))

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

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

chi := DirichletCharacter("627.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.bo (of order $45$, degree $24$, 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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$20$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	627.4
Dual form			627.2.bo.b.157.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0487923 - 0.0723376i) q^{2} +(0.990268 + 0.139173i) q^{3} +(0.746361 - 1.84731i) q^{4} +(0.661518 - 2.65320i) q^{5} +(-0.0382500 - 0.0784241i) q^{6} +(2.64052 + 0.561260i) q^{7} +(-0.340743 + 0.0724271i) q^{8} +(0.961262 + 0.275637i) q^{9} +(-0.224203 + 0.0816033i) q^{10} +(2.85803 + 1.68276i) q^{11} +(0.996193 - 1.72546i) q^{12} +(-2.97917 + 2.87695i) q^{13} +(-0.0882369 - 0.218394i) q^{14} +(1.02433 - 2.53532i) q^{15} +(-2.84454 - 2.74694i) q^{16} +(4.52873 - 1.29859i) q^{17} +(-0.0269632 - 0.0829843i) q^{18} +(-0.557398 + 4.32311i) q^{19} +(-4.40756 - 3.20228i) q^{20} +(2.53671 + 0.923288i) q^{21} +(-0.0177232 - 0.288848i) q^{22} +(-1.15680 - 0.970672i) q^{23} +(-0.347507 + 0.0243000i) q^{24} +(-2.18715 - 1.16293i) q^{25} +(0.353473 + 0.0751329i) q^{26} +(0.913545 + 0.406737i) q^{27} +(3.00760 - 4.45896i) q^{28} +(-4.09301 - 5.23882i) q^{29} +(-0.233378 + 0.0496061i) q^{30} +(-9.02148 + 4.01662i) q^{31} +(-0.180898 + 1.02592i) q^{32} +(2.59602 + 2.06414i) q^{33} +(-0.314904 - 0.264236i) q^{34} +(3.23589 - 6.63456i) q^{35} +(1.22664 - 1.57002i) q^{36} +(-1.87827 - 5.78074i) q^{37} +(0.339920 - 0.170614i) q^{38} +(-3.35058 + 2.43434i) q^{39} +(-0.0332436 + 0.951972i) q^{40} +(1.57890 + 0.221900i) q^{41} +(-0.0569836 - 0.228549i) q^{42} +(-6.21220 + 5.21265i) q^{43} +(5.24169 - 4.02372i) q^{44} +(1.36721 - 2.36808i) q^{45} +(-0.0137730 + 0.131042i) q^{46} +(-0.0439304 - 1.25800i) q^{47} +(-2.43456 - 3.11609i) q^{48} +(0.262524 + 0.116883i) q^{49} +(0.0225927 + 0.214955i) q^{50} +(4.66539 - 0.655678i) q^{51} +(3.09108 + 7.65070i) q^{52} +(-0.256863 - 1.03022i) q^{53} +(-0.0151516 - 0.0859293i) q^{54} +(6.35534 - 6.46976i) q^{55} -0.940389 q^{56} +(-1.15363 + 4.20347i) q^{57} +(-0.179256 + 0.551693i) q^{58} +(-0.342150 + 9.79790i) q^{59} +(-3.91899 - 3.78453i) q^{60} +(11.1246 + 0.777905i) q^{61} +(0.730732 + 0.456612i) q^{62} +(2.38353 + 1.26734i) q^{63} +(-7.14197 + 3.17981i) q^{64} +(5.66237 + 9.80751i) q^{65} +(0.0226493 - 0.288504i) q^{66} +(6.81972 - 2.48218i) q^{67} +(0.981168 - 9.33519i) q^{68} +(-1.01045 - 1.12222i) q^{69} +(-0.637814 + 0.0896390i) q^{70} +(-1.00699 + 4.03883i) q^{71} +(-0.347507 - 0.0243000i) q^{72} +(-4.15826 + 2.21099i) q^{73} +(-0.326519 + 0.417925i) q^{74} +(-2.00401 - 1.45600i) q^{75} +(7.57010 + 4.25629i) q^{76} +(6.60222 + 6.04746i) q^{77} +(0.339576 + 0.123596i) q^{78} +(0.294092 - 0.602978i) q^{79} +(-9.16991 + 5.73000i) q^{80} +(0.848048 + 0.529919i) q^{81} +(-0.0609866 - 0.125041i) q^{82} +(0.609377 + 5.79783i) q^{83} +(3.59890 - 3.99698i) q^{84} +(-0.449594 - 12.8747i) q^{85} +(0.680178 + 0.195038i) q^{86} +(-3.32408 - 5.75747i) q^{87} +(-1.09573 - 0.366389i) q^{88} +(2.34465 - 13.2972i) q^{89} +(-0.238011 + 0.0166433i) q^{90} +(-9.48129 + 5.92457i) q^{91} +(-2.65652 + 1.41250i) q^{92} +(-9.49269 + 2.72199i) q^{93} +(-0.0888574 + 0.0645587i) q^{94} +(11.1014 + 4.33871i) q^{95} +(-0.321918 + 0.990762i) q^{96} +(5.32664 + 7.89706i) q^{97} +(-0.00435409 - 0.0246933i) q^{98} +(2.28348 + 2.40535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 18 q^{5} + 3 q^{7} + 12 q^{10} + 3 q^{11} - 240 q^{12} + 42 q^{14} - 12 q^{15} + 72 q^{16} - 18 q^{17} - 102 q^{20} + 24 q^{22} + 54 q^{23} - 18 q^{25} - 12 q^{26} + 60 q^{27} + 36 q^{29} + 12 q^{30}+ \cdots - 6 q^{99}+O(q^{100}) $ 480 * q + 18 * q^5 + 3 * q^7 + 12 * q^10 + 3 * q^11 - 240 * q^12 + 42 * q^14 - 12 * q^15 + 72 * q^16 - 18 * q^17 - 102 * q^20 + 24 * q^22 + 54 * q^23 - 18 * q^25 - 12 * q^26 + 60 * q^27 + 36 * q^29 + 12 * q^30 + 60 * q^31 - 30 * q^32 - 21 * q^33 - 84 * q^34 + 12 * q^35 + 36 * q^37 - 90 * q^38 - 12 * q^39 + 300 * q^40 - 63 * q^41 - 18 * q^42 - 24 * q^43 - 15 * q^44 + 6 * q^45 - 6 * q^46 + 24 * q^48 + 39 * q^49 + 12 * q^51 - 21 * q^52 + 9 * q^53 + 45 * q^55 + 156 * q^56 + 30 * q^57 + 12 * q^58 - 69 * q^59 - 36 * q^60 + 12 * q^61 - 90 * q^62 + 60 * q^64 - 66 * q^65 + 30 * q^66 + 72 * q^67 + 24 * q^68 + 18 * q^69 - 96 * q^70 + 72 * q^71 + 18 * q^73 + 57 * q^74 - 102 * q^75 + 48 * q^76 - 114 * q^77 - 216 * q^78 - 24 * q^79 - 30 * q^80 - 24 * q^82 + 78 * q^83 - 36 * q^84 - 36 * q^85 - 189 * q^86 - 24 * q^87 + 120 * q^88 - 318 * q^89 - 18 * q^90 - 48 * q^91 + 354 * q^92 + 12 * q^93 - 282 * q^94 + 6 * q^95 + 60 * q^96 + 120 * q^97 - 96 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−0.0487923	−	0.0723376i	−0.0345014	−	0.0511504i	0.811392	−	0.584502i	$-0.198710\pi$
$2$	−0.0487923	−	0.0723376i	−0.0345014	−	0.0511504i	−0.845894	+	0.533352i	$0.820932\pi$
$3$	0.990268	+	0.139173i	0.571732	+	0.0803516i
$3$	0.990268	+	0.139173i	0.571732	+	0.0803516i
$4$	0.746361	−	1.84731i	0.373181	−	0.923654i
$5$	0.661518	−	2.65320i	0.295840	−	1.18655i	−0.619869	−	0.784706i	$-0.712814\pi$
$5$	0.661518	−	2.65320i	0.295840	−	1.18655i	0.915708	−	0.401843i	$-0.131630\pi$
$6$	−0.0382500	−	0.0784241i	−0.0156155	−	0.0320165i
$7$	2.64052	+	0.561260i	0.998023	+	0.212136i	0.677832	−	0.735217i	$-0.262920\pi$
$7$	2.64052	+	0.561260i	0.998023	+	0.212136i	0.320191	+	0.947353i	$0.396253\pi$
$8$	−0.340743	+	0.0724271i	−0.120471	+	0.0256068i
$9$	0.961262	+	0.275637i	0.320421	+	0.0918791i
$10$	−0.224203	+	0.0816033i	−0.0708993	+	0.0258052i
$11$	2.85803	+	1.68276i	0.861728	+	0.507371i
$11$	2.85803	+	1.68276i	0.861728	+	0.507371i
$12$	0.996193	−	1.72546i	0.287576	−	0.498097i
$13$	−2.97917	+	2.87695i	−0.826274	+	0.797924i	−0.981802	−	0.189908i	$-0.939181\pi$
$13$	−2.97917	+	2.87695i	−0.826274	+	0.797924i	0.155528	+	0.987832i	$0.450292\pi$
$14$	−0.0882369	−	0.218394i	−0.0235823	−	0.0583683i
$15$	1.02433	−	2.53532i	0.264482	−	0.654616i
$16$	−2.84454	−	2.74694i	−0.711135	−	0.686735i
$17$	4.52873	−	1.29859i	1.09838	−	0.314955i	0.322967	−	0.946410i	$-0.395320\pi$
$17$	4.52873	−	1.29859i	1.09838	−	0.314955i	0.775413	+	0.631455i	$0.217542\pi$
$18$	−0.0269632	−	0.0829843i	−0.00635529	−	0.0195596i
$19$	−0.557398	+	4.32311i	−0.127876	+	0.991790i
$19$	−0.557398	+	4.32311i	−0.127876	+	0.991790i
$20$	−4.40756	−	3.20228i	−0.985559	−	0.716051i
$21$	2.53671	+	0.923288i	0.553556	+	0.201478i
$22$	−0.0177232	−	0.288848i	−0.00377859	−	0.0615827i
$23$	−1.15680	−	0.970672i	−0.241210	−	0.202399i	0.514166	−	0.857690i	$-0.328101\pi$
$23$	−1.15680	−	0.970672i	−0.241210	−	0.202399i	−0.755376	+	0.655291i	$0.772546\pi$
$24$	−0.347507	+	0.0243000i	−0.0709345	+	0.00496022i
$25$	−2.18715	−	1.16293i	−0.437429	−	0.232585i
$26$	0.353473	+	0.0751329i	0.0693217	+	0.0147348i
$27$	0.913545	+	0.406737i	0.175812	+	0.0782765i
$28$	3.00760	−	4.45896i	0.568384	−	0.842663i
$29$	−4.09301	−	5.23882i	−0.760054	−	0.972824i	−0.999998	−	0.00203773i	$-0.999351\pi$
$29$	−4.09301	−	5.23882i	−0.760054	−	0.972824i	0.239944	−	0.970787i	$-0.422871\pi$
$30$	−0.233378	+	0.0496061i	−0.0426089	+	0.00905679i
$31$	−9.02148	+	4.01662i	−1.62031	+	0.721407i	−0.998110	−	0.0614543i	$-0.980426\pi$
$31$	−9.02148	+	4.01662i	−1.62031	+	0.721407i	−0.622196	+	0.782861i	$0.713759\pi$
$32$	−0.180898	+	1.02592i	−0.0319785	+	0.181359i
$33$	2.59602	+	2.06414i	0.451909	+	0.359321i
$34$	−0.314904	−	0.264236i	−0.0540057	−	0.0453161i
$35$	3.23589	−	6.63456i	0.546965	−	1.12145i
$36$	1.22664	−	1.57002i	0.204439	−	0.261670i
$37$	−1.87827	−	5.78074i	−0.308786	−	0.950347i	−0.978237	−	0.207490i	$-0.933470\pi$
$37$	−1.87827	−	5.78074i	−0.308786	−	0.950347i	0.669451	−	0.742857i	$-0.266530\pi$
$38$	0.339920	−	0.170614i	0.0551423	−	0.0276772i
$39$	−3.35058	+	2.43434i	−0.536521	+	0.389806i
$40$	−0.0332436	+	0.951972i	−0.00525627	+	0.150520i
$41$	1.57890	+	0.221900i	0.246583	+	0.0346550i	0.261382	−	0.965235i	$-0.415822\pi$
$41$	1.57890	+	0.221900i	0.246583	+	0.0346550i	−0.0147986	+	0.999890i	$0.504711\pi$
$42$	−0.0569836	−	0.228549i	−0.00879277	−	0.0352659i
$43$	−6.21220	+	5.21265i	−0.947351	+	0.794922i	−0.978849	−	0.204582i	$-0.934417\pi$
$43$	−6.21220	+	5.21265i	−0.947351	+	0.794922i	0.0314982	+	0.999504i	$0.489972\pi$
$44$	5.24169	−	4.02372i	0.790215	−	0.606598i
$45$	1.36721	−	2.36808i	0.203812	−	0.353013i
$46$	−0.0137730	+	0.131042i	−0.00203072	+	0.0193210i
$47$	−0.0439304	−	1.25800i	−0.00640791	−	0.183499i	−0.998374	−	0.0569972i	$-0.981847\pi$
$47$	−0.0439304	−	1.25800i	−0.00640791	−	0.183499i	0.991966	−	0.126501i	$-0.0403748\pi$
$48$	−2.43456	−	3.11609i	−0.351398	−	0.449769i
$49$	0.262524	+	0.116883i	0.0375034	+	0.0166976i
$50$	0.0225927	+	0.214955i	0.00319508	+	0.0303992i
$51$	4.66539	−	0.655678i	0.653285	−	0.0918133i
$52$	3.09108	+	7.65070i	0.428656	+	1.06096i
$53$	−0.256863	−	1.03022i	−0.0352828	−	0.141512i	0.950071	−	0.312034i	$-0.101010\pi$
$53$	−0.256863	−	1.03022i	−0.0352828	−	0.141512i	−0.985354	+	0.170522i	$0.945455\pi$
$54$	−0.0151516	−	0.0859293i	−0.00206188	−	0.0116935i
$55$	6.35534	−	6.46976i	0.856954	−	0.872382i
$56$	−0.940389			−0.125665
$57$	−1.15363	+	4.20347i	−0.152803	+	0.556763i
$58$	−0.179256	+	0.551693i	−0.0235374	+	0.0724408i
$59$	−0.342150	+	9.79790i	−0.0445442	+	1.27558i	0.747148	+	0.664658i	$0.231423\pi$
$59$	−0.342150	+	9.79790i	−0.0445442	+	1.27558i	−0.791692	+	0.610920i	$0.790800\pi$
$60$	−3.91899	−	3.78453i	−0.505940	−	0.488580i
$61$	11.1246	+	0.777905i	1.42435	+	0.0996005i	0.761023	−	0.648725i	$-0.224698\pi$
$61$	11.1246	+	0.777905i	1.42435	+	0.0996005i	0.663331	+	0.748326i	$0.269142\pi$
$62$	0.730732	+	0.456612i	0.0928030	+	0.0579898i
$63$	2.38353	+	1.26734i	0.300296	+	0.159670i
$64$	−7.14197	+	3.17981i	−0.892746	+	0.397476i
$65$	5.66237	+	9.80751i	0.702331	+	1.21647i
$66$	0.0226493	−	0.288504i	0.00278793	−	0.0355124i
$67$	6.81972	−	2.48218i	0.833161	−	0.303246i	0.110006	−	0.993931i	$-0.464913\pi$
$67$	6.81972	−	2.48218i	0.833161	−	0.303246i	0.723156	+	0.690685i	$0.242691\pi$
$68$	0.981168	−	9.33519i	0.118984	−	1.13206i
$69$	−1.01045	−	1.12222i	−0.121644	−	0.135100i
$70$	−0.637814	+	0.0896390i	−0.0762334	+	0.0107139i
$71$	−1.00699	+	4.03883i	−0.119508	+	0.479321i	0.880478	+	0.474087i	$0.157222\pi$
$71$	−1.00699	+	4.03883i	−0.119508	+	0.479321i	−0.999986	+	0.00523435i	$0.998334\pi$
$72$	−0.347507	−	0.0243000i	−0.0409540	−	0.00286379i
$73$	−4.15826	+	2.21099i	−0.486687	+	0.258776i	−0.694633	−	0.719364i	$-0.744433\pi$
$73$	−4.15826	+	2.21099i	−0.486687	+	0.258776i	0.207946	+	0.978140i	$0.433322\pi$
$74$	−0.326519	+	0.417925i	−0.0379571	+	0.0485828i
$75$	−2.00401	−	1.45600i	−0.231404	−	0.168125i
$76$	7.57010	+	4.25629i	0.868351	+	0.488230i
$77$	6.60222	+	6.04746i	0.752393	+	0.689172i
$78$	0.339576	+	0.123596i	0.0384494	+	0.0139944i
$79$	0.294092	−	0.602978i	0.0330880	−	0.0678404i	−0.881610	−	0.471979i	$-0.843540\pi$
$79$	0.294092	−	0.602978i	0.0330880	−	0.0678404i	0.914698	+	0.404139i	$0.132429\pi$
$80$	−9.16991	+	5.73000i	−1.02523	+	0.640633i
$81$	0.848048	+	0.529919i	0.0942276	+	0.0588799i
$82$	−0.0609866	−	0.125041i	−0.00673484	−	0.0138085i
$83$	0.609377	+	5.79783i	0.0668878	+	0.636395i	0.975688	+	0.219164i	$0.0703328\pi$
$83$	0.609377	+	5.79783i	0.0668878	+	0.636395i	−0.908800	+	0.417231i	$0.863000\pi$
$84$	3.59890	−	3.99698i	0.392672	−	0.436107i
$85$	−0.449594	−	12.8747i	−0.0487654	−	1.39646i
$86$	0.680178	+	0.195038i	0.0733455	+	0.0210315i
$87$	−3.32408	−	5.75747i	−0.356379	−	0.617266i
$88$	−1.09573	−	0.366389i	−0.116805	−	0.0390572i
$89$	2.34465	−	13.2972i	0.248532	−	1.40950i	−0.563613	−	0.826039i	$-0.690589\pi$
$89$	2.34465	−	13.2972i	0.248532	−	1.40950i	0.812145	−	0.583456i	$-0.198300\pi$
$90$	−0.238011	+	0.0166433i	−0.0250886	+	0.00175436i
$91$	−9.48129	+	5.92457i	−0.993910	+	0.621064i
$92$	−2.65652	+	1.41250i	−0.276962	+	0.147263i
$93$	−9.49269	+	2.72199i	−0.984346	+	0.282257i
$94$	−0.0888574	+	0.0645587i	−0.00916494	+	0.00665872i
$95$	11.1014	+	4.33871i	1.13898	+	0.445142i
$96$	−0.321918	+	0.990762i	−0.0328556	+	0.101119i
$97$	5.32664	+	7.89706i	0.540838	+	0.801825i	0.996072	−	0.0885466i	$-0.0282222\pi$
$97$	5.32664	+	7.89706i	0.540838	+	0.801825i	−0.455234	+	0.890372i	$0.650444\pi$
$98$	−0.00435409	−	0.0246933i	−0.000439830	−	0.00249440i
$99$	2.28348	+	2.40535i	0.229499	+	0.241747i
$100$	−3.78069	+	3.17237i	−0.378069	+	0.317237i
$101$	4.31855	−	4.17038i	0.429712	−	0.414968i	−0.448093	−	0.893987i	$-0.647897\pi$
$101$	4.31855	−	4.17038i	0.429712	−	0.414968i	0.877804	+	0.479019i	$0.159008\pi$
$102$	−0.275065	−	0.305491i	−0.0272355	−	0.0302481i
$103$	−9.05572	+	10.0574i	−0.892286	+	0.990984i	−0.999995	−	0.00319832i	$-0.998982\pi$
$103$	−9.05572	+	10.0574i	−0.892286	+	0.990984i	0.107709	+	0.994182i	$0.465649\pi$
$104$	0.806762	−	1.19607i	0.0791096	−	0.117285i
$105$	4.12775	−	6.11964i	0.402827	−	0.597216i
$106$	−0.0619907	+	0.0688477i	−0.00602107	+	0.00668708i
$107$	−4.95185	−	5.49958i	−0.478713	−	0.531665i	0.454616	−	0.890688i	$-0.349777\pi$
$107$	−4.95185	−	5.49958i	−0.478713	−	0.531665i	−0.933329	+	0.359023i	$0.883110\pi$
$108$	1.43320	−	1.38403i	0.137910	−	0.133178i
$109$	−6.59322	+	5.53237i	−0.631516	+	0.529905i	−0.901400	−	0.432988i	$-0.857459\pi$
$109$	−6.59322	+	5.53237i	−0.631516	+	0.529905i	0.269884	+	0.962893i	$0.413015\pi$
$110$	−0.778098	−	0.144055i	−0.0741887	−	0.0137351i
$111$	−1.05547	−	5.98588i	−0.100181	−	0.568155i
$112$	−5.96932	−	8.84989i	−0.564048	−	0.836236i
$113$	0.825482	−	2.54057i	0.0776548	−	0.238997i	−0.904692	−	0.426066i	$-0.859899\pi$
$113$	0.825482	−	2.54057i	0.0776548	−	0.238997i	0.982347	+	0.187070i	$0.0598990\pi$
$114$	0.360357	−	0.121646i	0.0337505	−	0.0113932i
$115$	−3.34064	+	2.42711i	−0.311516	+	0.226330i
$116$	−12.7326	+	3.65101i	−1.18219	+	0.338988i
$117$	−3.65676	+	1.94433i	−0.338068	+	0.179754i
$118$	0.725451	−	0.453312i	0.0667831	−	0.0417307i
$119$	12.6871	−	0.887166i	1.16302	−	0.0813264i
$120$	−0.165409	+	0.938081i	−0.0150997	+	0.0856347i
$121$	5.33665	+	9.61874i	0.485150	+	0.874431i
$122$	−0.486521	−	0.842679i	−0.0440475	−	0.0762926i
$123$	1.53265	+	0.439482i	0.138195	+	0.0396267i
$124$	0.686658	+	19.6633i	0.0616637	+	1.76582i
$125$	4.61613	−	5.12673i	0.412879	−	0.458549i
$126$	−0.0246212	−	0.234255i	−0.00219343	−	0.0208691i
$127$	−5.22656	−	10.7160i	−0.463782	−	0.950894i	−0.994637	−	0.103431i	$-0.967018\pi$
$127$	−5.22656	−	10.7160i	−0.463782	−	0.950894i	0.530855	−	0.847463i	$-0.321871\pi$
$128$	2.34540	+	1.46557i	0.207306	+	0.129539i
$129$	−6.87720	+	4.29735i	−0.605504	+	0.378361i
$130$	0.433171	−	0.888133i	0.0379917	−	0.0778944i
$131$	4.81366	+	1.75203i	0.420571	+	0.153075i	0.543632	−	0.839324i	$-0.317049\pi$
$131$	4.81366	+	1.75203i	0.420571	+	0.153075i	−0.123061	+	0.992399i	$0.539271\pi$
$132$	5.75068	−	3.25505i	0.500532	−	0.283316i
$133$	−3.89821	+	11.1024i	−0.338018	+	0.962703i
$134$	−0.512304	−	0.372211i	−0.0442563	−	0.0321541i
$135$	1.68348	−	2.15476i	0.144891	−	0.185452i
$136$	−1.44908	+	0.770490i	−0.124258	+	0.0660689i
$137$	−17.8226	−	1.24628i	−1.52269	−	0.106477i	−0.716271	−	0.697822i	$-0.754152\pi$
$137$	−17.8226	−	1.24628i	−1.52269	−	0.106477i	−0.806418	+	0.591346i	$0.798597\pi$
$138$	−0.0318764	+	0.127849i	−0.00271350	+	0.0108833i
$139$	12.3320	−	1.73315i	1.04599	−	0.147004i	0.404814	−	0.914399i	$-0.367336\pi$
$139$	12.3320	−	1.73315i	1.04599	−	0.147004i	0.641174	+	0.767395i	$0.278448\pi$
$140$	−9.84094	−	10.9295i	−0.831711	−	0.923708i
$141$	0.131577	−	1.25187i	0.0110808	−	0.105427i
$142$	0.341293	−	0.124220i	0.0286406	−	0.0104243i
$143$	−13.3558	+	3.20919i	−1.11687	+	0.268366i
$144$	−1.97719	−	3.42459i	−0.164766	−	0.285383i
$145$	−16.6073	+	7.39403i	−1.37916	+	0.614041i
$146$	0.362828	+	0.192919i	0.0300279	+	0.0159661i
$147$	0.243702	+	0.152282i	0.0201002	+	0.0125600i
$148$	−12.0807	−	0.844763i	−0.993025	−	0.0694391i
$149$	−10.4476	−	10.0891i	−0.855900	−	0.826533i	0.130405	−	0.991461i	$-0.458372\pi$
$149$	−10.4476	−	10.0891i	−0.855900	−	0.826533i	−0.986306	+	0.164927i	$0.947261\pi$
$150$	−0.00754313	+	0.216007i	−0.000615894	+	0.0176369i
$151$	−4.24516	+	13.0653i	−0.345466	+	1.06324i	0.615868	+	0.787850i	$0.288806\pi$
$151$	−4.24516	+	13.0653i	−0.345466	+	1.06324i	−0.961334	+	0.275386i	$0.911194\pi$
$152$	−0.123181	−	1.51344i	−0.00999133	−	0.122756i
$153$	4.71124			0.380881
$154$	0.115321	−	0.772658i	0.00929281	−	0.0622625i
$155$	4.68905	+	26.5929i	0.376633	+	2.13599i
$156$	1.99623	+	8.00644i	0.159826	+	0.641028i
$157$	−3.01375	−	7.45928i	−0.240523	−	0.595316i	0.757844	−	0.652436i	$-0.226253\pi$
$157$	−3.01375	−	7.45928i	−0.240523	−	0.595316i	−0.998367	+	0.0571199i	$0.981808\pi$
$158$	−0.0579674	+	0.00814679i	−0.00461164	+	0.000648124i
$159$	−0.110984	−	1.05594i	−0.00880162	−	0.0837418i
$160$	2.60231	+	1.15862i	0.205731	+	0.0915973i
$161$	−2.50976	−	3.21235i	−0.197797	−	0.253168i
$162$	−0.00304515	−	0.0872017i	−0.000239250	−	0.00685121i
$163$	−0.113637	+	1.08119i	−0.00890076	+	0.0846851i	−0.998070	−	0.0620911i	$-0.980223\pi$
$163$	−0.113637	+	1.08119i	−0.00890076	+	0.0846851i	0.989170	+	0.146776i	$0.0468897\pi$
$164$	1.58835	−	2.75110i	0.124029	−	0.214825i
$165$	7.19390	−	5.52230i	0.560045	−	0.429911i
$166$	0.389668	−	0.326970i	0.0302441	−	0.0253778i
$167$	1.56643	+	6.28262i	0.121214	+	0.486164i	0.999961	+	0.00887484i	$0.00282499\pi$
$167$	1.56643	+	6.28262i	0.121214	+	0.486164i	−0.878746	+	0.477289i	$0.841619\pi$
$168$	−0.931237	−	0.130877i	−0.0718465	−	0.0100974i
$169$	0.144915	−	4.14982i	0.0111473	−	0.319217i
$170$	−0.909388	+	0.660709i	−0.0697468	+	0.0506740i
$171$	−1.72742	+	4.00200i	−0.132099	+	0.306041i
$172$	4.99284	+	15.3664i	0.380700	+	1.17167i
$173$	4.99632	−	6.39500i	0.379863	−	0.486203i	−0.559643	−	0.828734i	$-0.689062\pi$
$173$	4.99632	−	6.39500i	0.379863	−	0.486203i	0.939507	+	0.342531i	$0.111284\pi$
$174$	−0.254292	+	0.521376i	−0.0192778	+	0.0395254i
$175$	−5.12251	−	4.29829i	−0.387225	−	0.324920i
$176$	−3.50734	−	12.6375i	−0.264376	−	0.952588i
$177$	−1.70243	+	9.65493i	−0.127962	+	0.725709i
$178$	−1.07628	+	0.479193i	−0.0806709	+	0.0359170i
$179$	23.3277	−	4.95846i	1.74360	−	0.370613i	0.777517	−	0.628862i	$-0.216479\pi$
$179$	23.3277	−	4.95846i	1.74360	−	0.370613i	0.966078	+	0.258249i	$0.0831456\pi$
$180$	−3.35415	−	4.29311i	−0.250003	−	0.319990i
$181$	5.47227	−	8.11297i	0.406751	−	0.603032i	−0.568888	−	0.822415i	$-0.692626\pi$
$181$	5.47227	−	8.11297i	0.406751	−	0.603032i	0.975639	+	0.219382i	$0.0704042\pi$
$182$	0.891183	+	0.396780i	0.0660589	+	0.0294113i
$183$	10.9080	+	2.31857i	0.806345	+	0.171394i
$184$	0.464475	+	0.246966i	0.0342415	+	0.0182065i
$185$	−16.5800	+	1.15939i	−1.21898	+	0.0852397i
$186$	0.660072	+	0.553866i	0.0483988	+	0.0406114i
$187$	15.1285	+	3.90935i	1.10630	+	0.285880i
$188$	−2.35671	−	0.857771i	−0.171881	−	0.0625594i
$189$	2.18395	+	1.58673i	0.158859	+	0.115418i
$190$	−0.227810	−	1.01474i	−0.0165271	−	0.0736171i
$191$	6.58464	+	20.2655i	0.476448	+	1.46636i	0.843995	+	0.536351i	$0.180198\pi$
$191$	6.58464	+	20.2655i	0.476448	+	1.46636i	−0.367547	+	0.930005i	$0.619802\pi$
$192$	−7.51501	+	2.15489i	−0.542349	+	0.155516i
$193$	12.4144	+	11.9885i	0.893609	+	0.862949i	0.991213	−	0.132277i	$-0.0422288\pi$
$193$	12.4144	+	11.9885i	0.893609	+	0.862949i	−0.0976035	+	0.995225i	$0.531118\pi$
$194$	0.311355	−	0.770632i	0.0223540	−	0.0553281i
$195$	4.24232	+	10.5001i	0.303799	+	0.751929i
$196$	0.411856	−	0.397725i	0.0294183	−	0.0284089i
$197$	−9.18282	+	15.9051i	−0.654249	+	1.13319i	0.327833	+	0.944736i	$0.393682\pi$
$197$	−9.18282	+	15.9051i	−0.654249	+	1.13319i	−0.982082	+	0.188457i	$0.939652\pi$
$198$	0.0625808	−	0.282544i	0.00444743	−	0.0200795i
$199$	3.62716	−	1.32018i	0.257123	−	0.0935851i	−0.210243	−	0.977649i	$-0.567425\pi$
$199$	3.62716	−	1.32018i	0.257123	−	0.0935851i	0.467366	+	0.884064i	$0.345203\pi$
$200$	0.829482	+	0.237850i	0.0586532	+	0.0168185i
$201$	7.09880	−	1.50890i	0.500711	−	0.106429i
$202$	−0.512387	−	0.108911i	−0.0360514	−	0.00766296i
$203$	−7.86735	−	16.1305i	−0.552180	−	1.13214i
$204$	2.27083	−	9.10779i	0.158990	−	0.637673i
$205$	1.63322	−	4.04236i	0.114069	−	0.282331i
$206$	1.16938	+	0.164345i	0.0814743	+	0.0114505i
$207$	−0.844436	−	1.25193i	−0.0586923	−	0.0870150i
$208$	16.3772			1.13556
$209$	−8.86781	+	11.4176i	−0.613399	+	0.789773i
$210$	−0.644082			−0.0444459
$211$	0.916646	+	1.35898i	0.0631045	+	0.0935563i	0.859269	−	0.511524i	$-0.170919\pi$
$211$	0.916646	+	1.35898i	0.0631045	+	0.0935563i	−0.796165	+	0.605080i	$0.793141\pi$
$212$	−2.09485	−	0.294412i	−0.143875	−	0.0202203i
$213$	−1.55929	+	3.85938i	−0.106841	+	0.264440i
$214$	−0.156214	+	0.626542i	−0.0106786	+	0.0428295i
$215$	9.72075	+	19.9305i	0.662950	+	1.35925i
$216$	−0.340743	−	0.0724271i	−0.0231846	−	0.00492804i
$217$	−26.0758	+	5.54258i	−1.77014	+	0.376255i
$218$	0.721896	+	0.207000i	0.0488930	+	0.0140198i
$219$	−4.42550	+	1.61075i	−0.299048	+	0.108844i
$220$	−7.20826	−	16.5690i	−0.485981	−	1.11708i
$221$	−9.75589	+	16.8977i	−0.656252	+	1.13666i
$222$	−0.381505	+	0.368415i	−0.0256050	+	0.0247264i
$223$	−6.95375	−	17.2111i	−0.465657	−	1.15254i	−0.959177	−	0.282808i	$-0.908734\pi$
$223$	−6.95375	−	17.2111i	−0.465657	−	1.15254i	0.493519	−	0.869735i	$-0.335710\pi$
$224$	−1.05347	+	2.60744i	−0.0703882	+	0.174217i
$225$	−1.78187	−	1.72074i	−0.118792	−	0.114716i
$226$	−0.224056	+	0.0642470i	−0.0149040	+	0.00427365i
$227$	−4.54492	−	13.9878i	−0.301657	−	0.928404i	−0.980904	−	0.194494i	$-0.937693\pi$
$227$	−4.54492	−	13.9878i	−0.301657	−	0.928404i	0.679247	−	0.733910i	$-0.262307\pi$
$228$	6.90407	+	5.26842i	0.457233	+	0.348910i
$229$	14.9086	+	10.8317i	0.985185	+	0.715779i	0.958861	−	0.283875i	$-0.0916200\pi$
$229$	14.9086	+	10.8317i	0.985185	+	0.715779i	0.0263235	+	0.999653i	$0.491620\pi$
$230$	0.338569	+	0.123229i	0.0223246	+	0.00812548i
$231$	5.69632	+	6.90745i	0.374791	+	0.454477i
$232$	1.77410	+	1.48864i	0.116475	+	0.0977343i
$233$	26.5637	−	1.85752i	1.74025	−	0.121690i	0.836009	−	0.548715i	$-0.184883\pi$
$233$	26.5637	−	1.85752i	1.74025	−	0.121690i	0.904240	+	0.427025i	$0.140438\pi$
$234$	0.319070	+	0.169653i	0.0208583	+	0.0110905i
$235$	−3.36680	−	0.715635i	−0.219626	−	0.0466829i
$236$	17.8444	+	7.94483i	1.16157	+	0.517164i
$237$	0.375149	−	0.556181i	0.0243685	−	0.0361278i
$238$	−0.683207	−	0.874465i	−0.0442857	−	0.0566831i
$239$	−6.21716	+	1.32150i	−0.402154	+	0.0854806i	−0.404548	−	0.914517i	$-0.632571\pi$
$239$	−6.21716	+	1.32150i	−0.402154	+	0.0854806i	0.00239398	+	0.999997i	$0.499238\pi$
$240$	−9.87813	+	4.39803i	−0.637631	+	0.283891i
$241$	−0.845402	+	4.79452i	−0.0544572	+	0.308842i	−0.999854	−	0.0170792i	$-0.994563\pi$
$241$	−0.845402	+	4.79452i	−0.0544572	+	0.308842i	0.945397	+	0.325921i	$0.105674\pi$
$242$	0.435409	−	0.855361i	0.0279891	−	0.0549847i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	9.73997	−	19.9699i	0.623538	−	1.27844i
$245$	0.483779	−	0.619208i	0.0309075	−	0.0395598i
$246$	−0.0429907	−	0.132312i	−0.00274099	−	0.00843589i
$247$	−10.7768	−	14.4829i	−0.685712	−	0.921526i
$248$	2.78309	−	2.02204i	0.176727	−	0.128399i
$249$	−0.203456	+	5.82622i	−0.0128935	+	0.369222i
$250$	−0.596087	−	0.0837745i	−0.0376998	−	0.00529837i
$251$	−6.40060	−	25.6714i	−0.404003	−	1.62037i	−0.735928	−	0.677060i	$-0.763254\pi$
$251$	−6.40060	−	25.6714i	−0.404003	−	1.62037i	0.331925	−	0.943306i	$-0.392302\pi$
$252$	4.12015	−	3.45722i	0.259545	−	0.217784i
$253$	−1.67277	−	4.72083i	−0.105166	−	0.296796i
$254$	−0.520156	+	0.900936i	−0.0326375	+	0.0565298i
$255$	1.34659	−	12.8120i	0.0843269	−	0.802317i
$256$	0.537257	+	15.3850i	0.0335785	+	0.961564i
$257$	−2.94433	−	3.76857i	−0.183662	−	0.235077i	0.687364	−	0.726313i	$-0.258768\pi$
$257$	−2.94433	−	3.76857i	−0.183662	−	0.235077i	−0.871027	+	0.491236i	$0.836545\pi$
$258$	0.646414	+	0.287802i	0.0402440	+	0.0179178i
$259$	−1.71513	−	16.3184i	−0.106573	−	1.01397i
$260$	22.3437	−	3.14020i	1.38570	−	0.194747i
$261$	−2.49044	−	6.16406i	−0.154155	−	0.381546i
$262$	−0.108132	−	0.433693i	−0.00668041	−	0.0267937i
$263$	2.40737	+	13.6529i	0.148445	+	0.841872i	0.964536	+	0.263950i	$0.0850253\pi$
$263$	2.40737	+	13.6529i	0.148445	+	0.841872i	−0.816092	+	0.577922i	$0.803864\pi$
$264$	−1.03407	−	0.515319i	−0.0636429	−	0.0317157i
$265$	−2.90331			−0.178349
$266$	0.993325	−	0.259726i	0.0609047	−	0.0159248i
$267$	4.17243	−	12.8414i	0.255349	−	0.785883i
$268$	0.504631	−	14.4507i	0.0308252	−	0.882719i
$269$	−22.1260	−	21.3668i	−1.34904	−	1.30276i	−0.915886	−	0.401437i	$-0.868511\pi$
$269$	−22.1260	−	21.3668i	−1.34904	−	1.30276i	−0.433157	−	0.901319i	$-0.642600\pi$
$270$	−0.238011	−	0.0166433i	−0.0144849	−	0.00101288i
$271$	4.44966	+	2.78046i	0.270298	+	0.168901i	0.658296	−	0.752759i	$-0.271278\pi$
$271$	4.44966	+	2.78046i	0.270298	+	0.168901i	−0.387998	+	0.921660i	$0.626833\pi$
$272$	−16.4493	−	8.74627i	−0.997387	−	0.530320i
$273$	−10.2136	+	4.54737i	−0.618153	+	0.275219i
$274$	0.779454	+	1.35005i	0.0470885	+	0.0815597i
$275$	−4.29400	−	7.00412i	−0.258938	−	0.422364i
$276$	−2.82725	+	1.02904i	−0.170181	+	0.0619406i
$277$	2.56060	−	24.3625i	0.153852	−	1.46380i	−0.596420	−	0.802672i	$-0.703411\pi$
$277$	2.56060	−	24.3625i	0.153852	−	1.46380i	0.750272	−	0.661129i	$-0.229923\pi$
$278$	−0.727079	−	0.807504i	−0.0436073	−	0.0484308i
$279$	−9.77914	+	1.37437i	−0.585462	+	0.0822813i
$280$	−0.622084	+	2.49504i	−0.0371766	+	0.149107i
$281$	−6.56914	−	0.459359i	−0.391882	−	0.0274031i	−0.127543	−	0.991833i	$-0.540709\pi$
$281$	−6.56914	−	0.459359i	−0.391882	−	0.0274031i	−0.264339	+	0.964430i	$0.585154\pi$
$282$	−0.0969774	+	0.0515638i	−0.00577492	+	0.00307058i
$283$	16.5960	−	21.2419i	0.986530	−	1.26270i	0.0217165	−	0.999764i	$-0.493087\pi$
$283$	16.5960	−	21.2419i	0.986530	−	1.26270i	0.964813	−	0.262936i	$-0.0846909\pi$
$284$	6.70939	+	4.87466i	0.398129	+	0.289258i
$285$	10.3895	+	5.84150i	0.615421	+	0.346020i
$286$	0.883804	+	0.809541i	0.0522604	+	0.0478692i
$287$	4.04458	+	1.47211i	0.238744	+	0.0868958i
$288$	−0.456673	+	0.936318i	−0.0269097	+	0.0551730i
$289$	4.40628	−	2.75335i	0.259193	−	0.161962i
$290$	1.34517	+	0.840557i	0.0789912	+	0.0493592i
$291$	4.17574	+	8.56153i	0.244786	+	0.501886i
$292$	0.980810	+	9.33178i	0.0573976	+	0.546101i
$293$	−5.96134	+	6.62074i	−0.348265	+	0.386788i	−0.891672	−	0.452682i	$-0.850467\pi$
$293$	−5.96134	+	6.62074i	−0.348265	+	0.386788i	0.543407	+	0.839469i	$0.317134\pi$
$294$	−0.000875078	−	0.0250590i	−5.10356e−5	−	0.00146147i
$295$	25.7695	+	7.38928i	1.50036	+	0.430221i
$296$	1.05869	+	1.83371i	0.0615351	+	0.106582i
$297$	1.92650	+	2.69974i	0.111787	+	0.156655i
$298$	−0.220060	+	1.24803i	−0.0127478	+	0.0722961i
$299$	6.23889	−	0.436266i	0.360804	−	0.0252299i
$300$	−4.18540	+	2.61533i	−0.241644	+	0.150996i
$301$	−19.3291	+	10.2775i	−1.11411	+	0.592383i
$302$	1.15224	−	0.330399i	0.0663039	−	0.0190124i
$303$	4.85693	−	3.52876i	0.279023	−	0.202722i
$304$	13.4609	−	10.7661i	0.772034	−	0.617480i
$305$	9.42304	−	29.0011i	0.539562	−	1.66060i
$306$	−0.229872	−	0.340800i	−0.0131409	−	0.0194822i
$307$	−3.20927	−	18.2007i	−0.183163	−	1.03877i	−0.928293	−	0.371849i	$-0.878724\pi$
$307$	−3.20927	−	18.2007i	−0.183163	−	1.03877i	0.745131	−	0.666918i	$-0.232387\pi$
$308$	16.0992	−	7.68275i	0.917335	−	0.437765i
$309$	−10.3673	+	8.69920i	−0.589775	+	0.494880i
$310$	1.69488	−	1.63672i	0.0962625	−	0.0929596i
$311$	5.69209	+	6.32171i	0.322769	+	0.358471i	0.882591	−	0.470142i	$-0.155797\pi$
$311$	5.69209	+	6.32171i	0.322769	+	0.358471i	−0.559822	+	0.828613i	$0.689131\pi$
$312$	0.965372	−	1.07215i	0.0546534	−	0.0606988i
$313$	3.19865	−	4.74219i	0.180798	−	0.268044i	−0.727734	−	0.685860i	$-0.759426\pi$
$313$	3.19865	−	4.74219i	0.180798	−	0.268044i	0.908532	+	0.417815i	$0.137204\pi$
$314$	−0.392539	+	0.581963i	−0.0221522	+	0.0328421i
$315$	4.93927	−	5.48562i	0.278296	−	0.309079i
$316$	−0.894388	−	0.993319i	−0.0503133	−	0.0558786i
$317$	0.644410	−	0.622300i	0.0361937	−	0.0349518i	−0.676342	−	0.736588i	$-0.736436\pi$
$317$	0.644410	−	0.622300i	0.0361937	−	0.0349518i	0.712535	+	0.701636i	$0.247547\pi$
$318$	−0.0709692	+	0.0595502i	−0.00397976	+	0.00333941i
$319$	−2.88228	−	21.8602i	−0.161377	−	1.22394i
$320$	3.71214	+	21.0526i	0.207515	+	1.17688i
$321$	−4.13826	−	6.13522i	−0.230975	−	0.342435i
$322$	−0.109916	+	0.338288i	−0.00612540	+	0.0188520i
$323$	3.08966	+	20.3021i	0.171913	+	1.12964i
$324$	1.61187	−	1.17110i	0.0895486	−	0.0650609i
$325$	9.86158	−	2.82776i	0.547022	−	0.156856i
$326$	0.0837551	−	0.0445334i	0.00463876	−	0.00246647i
$327$	−7.29901	+	4.56093i	−0.403636	+	0.252220i
$328$	−0.554071	+	0.0387444i	−0.0305935	+	0.00213930i
$329$	0.590068	−	3.34644i	0.0325315	−	0.184495i
$330$	−0.750477	−	0.250944i	−0.0413124	−	0.0138140i
$331$	4.04625	+	7.00831i	0.222402	+	0.385212i	0.955537	−	0.294872i	$-0.0952769\pi$
$331$	4.04625	+	7.00831i	0.222402	+	0.385212i	−0.733135	+	0.680083i	$0.761944\pi$
$332$	11.1652	+	3.20157i	0.612770	+	0.175709i
$333$	−0.212127	−	6.07452i	−0.0116245	−	0.332882i
$334$	0.378040	−	0.419856i	0.0206854	−	0.0229735i
$335$	−2.07435	−	19.7361i	−0.113334	−	1.07830i
$336$	−4.67956	−	9.59453i	−0.255291	−	0.523424i
$337$	−12.4340	−	7.76964i	−0.677325	−	0.423239i	0.147168	−	0.989111i	$-0.452984\pi$
$337$	−12.4340	−	7.76964i	−0.677325	−	0.423239i	−0.824493	+	0.565872i	$0.808540\pi$
$338$	−0.307258	+	0.191996i	−0.0167126	+	0.0104432i
$339$	1.17103	−	2.40096i	0.0636015	−	0.130402i
$340$	−24.1191	−	8.77864i	−1.30804	−	0.476088i
$341$	−32.5427	−	3.70135i	−1.76228	−	0.200439i
$342$	0.373780	−	0.0703099i	0.0202117	−	0.00380192i
$343$	−14.6601	−	10.6512i	−0.791569	−	0.575109i
$344$	1.73922	−	2.22610i	0.0937727	−	0.120024i
$345$	−3.64591	+	1.93857i	−0.196289	+	0.104369i
$346$	−0.706381	−	0.0493949i	−0.0379753	−	0.00265549i
$347$	−6.10995	+	24.5057i	−0.327999	+	1.31553i	0.549314	+	0.835616i	$0.314889\pi$
$347$	−6.10995	+	24.5057i	−0.327999	+	1.31553i	−0.877313	+	0.479918i	$0.840666\pi$
$348$	−13.1168	+	1.84345i	−0.703134	+	0.0988190i
$349$	2.77389	+	3.08072i	0.148483	+	0.164907i	0.812798	−	0.582546i	$-0.197943\pi$
$349$	2.77389	+	3.08072i	0.148483	+	0.164907i	−0.664315	+	0.747453i	$0.731277\pi$
$350$	−0.0609892	+	0.580273i	−0.00326001	+	0.0310169i
$351$	−3.89177	+	1.41649i	−0.207728	+	0.0756066i
$352$	−2.24339	+	2.62771i	−0.119573	+	0.140057i
$353$	14.2145	+	24.6202i	0.756562	+	1.31040i	0.944594	+	0.328241i	$0.106456\pi$
$353$	14.2145	+	24.6202i	0.756562	+	1.31040i	−0.188032	+	0.982163i	$0.560211\pi$
$354$	0.781479	−	0.347937i	0.0415352	−	0.0184926i
$355$	10.0497	+	5.34352i	0.533383	+	0.283605i
$356$	−22.8140	−	14.2558i	−1.20914	−	0.755554i
$357$	12.6871	+	0.887166i	0.671471	+	0.0469538i
$358$	−1.49690	−	1.44554i	−0.0791134	−	0.0763989i
$359$	0.919912	−	26.3428i	0.0485511	−	1.39032i	−0.693731	−	0.720234i	$-0.744034\pi$
$359$	0.919912	−	26.3428i	0.0485511	−	1.39032i	0.742282	−	0.670088i	$-0.233743\pi$
$360$	−0.294355	+	0.905931i	−0.0155139	+	0.0477467i
$361$	−18.3786	−	4.81939i	−0.967296	−	0.253652i
$362$	−0.853877			−0.0448788
$363$	3.94604	+	10.2678i	0.207114	+	0.538922i
$364$	3.86804	+	21.9367i	0.202740	+	1.14980i
$365$	3.11543	+	12.4953i	0.163069	+	0.654035i
$366$	−0.364508	−	0.902189i	−0.0190531	−	0.0471582i
$367$	−10.1409	+	1.42521i	−0.529350	+	0.0743953i	−0.398785	−	0.917044i	$-0.630568\pi$
$367$	−10.1409	+	1.42521i	−0.529350	+	0.0743953i	−0.130565	+	0.991440i	$0.541679\pi$
$368$	0.624191	+	5.93878i	0.0325382	+	0.309580i
$369$	1.45658	+	0.648509i	0.0758263	+	0.0337600i
$370$	0.892843	+	1.14279i	0.0464167	+	0.0594106i
$371$	−0.100030	−	2.86449i	−0.00519331	−	0.148717i
$372$	−2.05663	+	19.5675i	−0.106631	+	1.01453i
$373$	−6.10103	+	10.5673i	−0.315899	+	0.547153i	−0.979628	−	0.200820i	$-0.935639\pi$
$373$	−6.10103	+	10.5673i	−0.315899	+	0.547153i	0.663729	+	0.747973i	$0.268973\pi$
$374$	−0.455360	−	1.28510i	−0.0235461	−	0.0664511i
$375$	5.28471	−	4.43440i	0.272901	−	0.228991i
$376$	0.106082	+	0.425474i	0.00547079	+	0.0219421i
$377$	27.2656	+	3.83194i	1.40425	+	0.197355i
$378$	0.00822042	−	0.235402i	0.000422813	−	0.0121078i
$379$	30.0871	−	21.8596i	1.54547	−	1.12285i	0.598689	−	0.800982i	$-0.295689\pi$
$379$	30.0871	−	21.8596i	1.54547	−	1.12285i	0.946784	−	0.321870i	$-0.104311\pi$
$380$	16.3006	−	17.2694i	0.836201	−	0.885903i
$381$	−3.68431	−	11.3391i	−0.188753	−	0.580922i
$382$	1.14467	−	1.46511i	0.0585666	−	0.0749618i
$383$	0.171229	−	0.351072i	0.00874941	−	0.0179389i	−0.894375	−	0.447319i	$-0.852379\pi$
$383$	0.171229	−	0.351072i	0.00874941	−	0.0179389i	0.903124	+	0.429380i	$0.141268\pi$
$384$	2.11861	+	1.77772i	0.108115	+	0.0907190i
$385$	20.4126	−	13.5165i	1.04032	−	0.688866i
$386$	0.261488	−	1.48297i	0.0133094	−	0.0754814i
$387$	−7.40835	+	3.29841i	−0.376588	+	0.167668i
$388$	18.5639	−	3.94588i	0.942439	−	0.200322i
$389$	22.6035	+	28.9312i	1.14604	+	1.46687i	0.861180	+	0.508299i	$0.169726\pi$
$389$	22.6035	+	28.9312i	1.14604	+	1.46687i	0.284862	+	0.958568i	$0.408052\pi$
$390$	0.552560	−	0.819204i	0.0279800	−	0.0414820i
$391$	−6.49936	−	2.89370i	−0.328687	−	0.146341i
$392$	−0.0979185	−	0.0208132i	−0.00494563	−	0.00105123i
$393$	4.52297	+	2.40491i	0.228154	+	0.121312i
$394$	1.59859	−	0.111784i	0.0805357	−	0.00563160i
$395$	−1.40528	−	1.17917i	−0.0707072	−	0.0593304i
$396$	6.14773	−	2.42304i	0.308935	−	0.121762i
$397$	−21.4112	−	7.79304i	−1.07460	−	0.391121i	−0.256703	−	0.966490i	$-0.582636\pi$
$397$	−21.4112	−	7.79304i	−1.07460	−	0.391121i	−0.817894	+	0.575369i	$0.804858\pi$
$398$	−0.272476	−	0.197966i	−0.0136580	−	0.00992312i
$399$	−5.40543	+	10.4519i	−0.270610	+	0.523247i
$400$	3.02694	+	9.31596i	0.151347	+	0.465798i
$401$	10.5399	−	3.02226i	0.526336	−	0.150925i	−0.00193814	−	0.999998i	$-0.500617\pi$
$401$	10.5399	−	3.02226i	0.526336	−	0.150925i	0.528275	+	0.849074i	$0.322839\pi$
$402$	−0.455517	−	0.439887i	−0.0227191	−	0.0219396i
$403$	15.3209	−	37.9206i	0.763190	−	1.88896i
$404$	−4.48077	−	11.0903i	−0.222927	−	0.551763i
$405$	1.96698	−	1.89949i	0.0977402	−	0.0943866i
$406$	−0.782972	+	1.35615i	−0.0388583	+	0.0673045i
$407$	4.35942	−	19.6822i	0.216088	−	0.975610i
$408$	−1.54221	+	0.561318i	−0.0763507	+	0.0277894i
$409$	37.5866	+	10.7778i	1.85854	+	0.532927i	0.999789	+	0.0205276i	$0.00653459\pi$
$409$	37.5866	+	10.7778i	1.85854	+	0.532927i	0.858747	+	0.512399i	$0.171243\pi$
$410$	−0.372103	+	0.0790929i	−0.0183769	+	0.00390612i
$411$	−17.4757	−	3.71458i	−0.862014	−	0.183227i
$412$	11.8203	+	24.2351i	0.582343	+	1.19398i
$413$	−6.40263	+	25.6795i	−0.315053	+	1.26361i
$414$	−0.0493594	+	0.122169i	−0.00242588	+	0.00600427i
$415$	15.7859	+	2.21857i	0.774902	+	0.108905i
$416$	−2.41261	−	3.57684i	−0.118288	−	0.175369i
$417$	12.4532			0.609836
$418$	1.25860	+	0.0843842i	0.0615603	+	0.00412737i
$419$	−10.2146			−0.499016			−0.249508	−	0.968373i	$-0.580269\pi$
$419$	−10.2146			−0.499016			−0.249508	+	0.968373i	$0.580269\pi$
$420$	−8.22408	−	12.1927i	−0.401294	−	0.594943i
$421$	−21.5792	−	3.03276i	−1.05170	−	0.147807i	−0.407923	−	0.913016i	$-0.633747\pi$
$421$	−21.5792	−	3.03276i	−1.05170	−	0.147807i	−0.643782	+	0.765209i	$0.722636\pi$
$422$	0.0535803	−	0.132616i	0.00260825	−	0.00645564i
$423$	0.304524	−	1.22138i	0.0148065	−	0.0593855i
$424$	0.162140	+	0.332437i	0.00787422	+	0.0161445i
$425$	−11.4152	−	2.42637i	−0.553718	−	0.117696i
$426$	0.355259	−	0.0755127i	0.0172124	−	0.00365860i
$427$	28.9380	+	8.29785i	1.40041	+	0.401561i
$428$	−13.8553	+	5.04291i	−0.669721	+	0.243758i
$429$	−13.6724	+	1.31919i	−0.660111	+	0.0636912i
$430$	0.967425	−	1.67563i	0.0466534	−	0.0808060i
$431$	24.4665	−	23.6270i	1.17851	−	1.13807i	0.190823	−	0.981624i	$-0.438884\pi$
$431$	24.4665	−	23.6270i	1.17851	−	1.13807i	0.987686	−	0.156449i	$-0.0500046\pi$
$432$	−1.48134	−	3.66643i	−0.0712708	−	0.176401i
$433$	2.28243	−	5.64922i	0.109687	−	0.271484i	−0.862350	−	0.506312i	$-0.831008\pi$
$433$	2.28243	−	5.64922i	0.109687	−	0.271484i	0.972037	+	0.234828i	$0.0754527\pi$
$434$	1.67323	+	1.61582i	0.0803178	+	0.0775620i
$435$	−17.4747	+	5.01079i	−0.837847	+	0.240249i
$436$	5.29907	+	16.3089i	0.253779	+	0.781053i
$437$	4.84112	−	4.45993i	0.231582	−	0.213348i
$438$	0.332448	+	0.241538i	0.0158850	+	0.0115411i
$439$	39.2407	+	14.2825i	1.87286	+	0.681664i	0.964910	+	0.262581i	$0.0845738\pi$
$439$	39.2407	+	14.2825i	1.87286	+	0.681664i	0.907948	+	0.419083i	$0.137648\pi$
$440$	−1.69695	+	2.66482i	−0.0808989	+	0.127040i
$441$	0.220136	+	0.184716i	0.0104827	+	0.00879602i
$442$	1.69835	−	0.118760i	0.0807823	−	0.00564885i
$443$	−27.1633	−	14.4430i	−1.29057	−	0.686208i	−0.324842	−	0.945768i	$-0.605311\pi$
$443$	−27.1633	−	14.4430i	−1.29057	−	0.686208i	−0.965727	+	0.259560i	$0.916422\pi$
$444$	−11.8455	−	2.51785i	−0.562164	−	0.119492i
$445$	−33.7290	−	15.0171i	−1.59891	−	0.711880i
$446$	−0.905722	+	1.34279i	−0.0428872	+	0.0635828i
$447$	−8.94179	−	11.4450i	−0.422932	−	0.541328i
$448$	−20.6432	+	4.38785i	−0.975301	+	0.207307i
$449$	4.52238	−	2.01349i	0.213424	−	0.0950227i	−0.297240	−	0.954803i	$-0.596066\pi$
$449$	4.52238	−	2.01349i	0.213424	−	0.0950227i	0.510664	+	0.859780i	$0.329399\pi$
$450$	−0.0375321	+	0.212855i	−0.00176928	+	0.0100341i
$451$	4.13915	+	3.29111i	0.194905	+	0.154972i
$452$	−4.07711	−	3.42110i	−0.191771	−	0.160915i
$453$	−6.02218	+	12.3473i	−0.282947	+	0.580126i
$454$	−0.790088	+	1.01127i	−0.0370806	+	0.0474611i
$455$	9.44704	+	29.0750i	0.442884	+	1.36306i
$456$	0.0886476	−	1.51585i	0.00415130	−	0.0709864i
$457$	−22.6522	+	16.4578i	−1.05963	+	0.769864i	−0.974019	−	0.226464i	$-0.927283\pi$
$457$	−22.6522	+	16.4578i	−1.05963	+	0.769864i	−0.0856081	+	0.996329i	$0.527283\pi$
$458$	0.0561160	−	1.60695i	0.00262213	−	0.0750879i
$459$	4.66539	+	0.655678i	0.217762	+	0.0306044i
$460$	1.99031	+	7.98269i	0.0927986	+	0.372195i
$461$	−0.923828	+	0.775184i	−0.0430270	+	0.0361039i	−0.664048	−	0.747690i	$-0.731163\pi$
$461$	−0.923828	+	0.775184i	−0.0430270	+	0.0361039i	0.621021	+	0.783794i	$0.286718\pi$
$462$	0.221732	−	0.749089i	0.0103159	−	0.0348508i
$463$	1.77264	−	3.07031i	0.0823816	−	0.142689i	−0.821891	−	0.569645i	$-0.807081\pi$
$463$	1.77264	−	3.07031i	0.0823816	−	0.142689i	0.904272	+	0.426956i	$0.140414\pi$
$464$	−2.74798	+	26.1453i	−0.127572	+	1.21377i
$465$	0.942396	+	26.9867i	0.0437026	+	1.25148i
$466$	−1.43047	−	1.83092i	−0.0662655	−	0.0848159i
$467$	−30.2105	−	13.4506i	−1.39798	−	0.622420i	−0.437105	−	0.899411i	$-0.643996\pi$
$467$	−30.2105	−	13.4506i	−1.39798	−	0.622420i	−0.960872	+	0.276991i	$0.910663\pi$
$468$	0.862521	+	8.20634i	0.0398701	+	0.379338i
$469$	19.4008	−	2.72660i	0.895844	−	0.125903i
$470$	0.112507	+	0.278463i	0.00518954	+	0.0128446i
$471$	−1.94629	−	7.80612i	−0.0896801	−	0.359687i
$472$	−0.593048	−	3.36335i	−0.0272973	−	0.154811i
$473$	−26.5263	+	4.44428i	−1.21968	+	0.204348i
$474$	−0.0585371			−0.00268870
$475$	6.24658	−	8.80707i	0.286613	−	0.404096i
$476$	7.83027	−	24.0991i	0.358900	−	1.10458i
$477$	0.0370549	−	1.06111i	0.00169663	−	0.0485850i
$478$	0.398943	+	0.385255i	0.0182472	+	0.0176212i
$479$	−27.9401	−	1.95377i	−1.27662	−	0.0892698i	−0.584702	−	0.811248i	$-0.698789\pi$
$479$	−27.9401	−	1.95377i	−1.27662	−	0.0892698i	−0.691916	+	0.721978i	$0.743233\pi$
$480$	2.41574	+	1.50952i	0.110263	+	0.0688999i
$481$	22.2266	+	11.8181i	1.01345	+	0.538859i
$482$	0.388073	−	0.172781i	0.0176762	−	0.00786996i
$483$	−2.03826	−	3.53038i	−0.0927442	−	0.160638i
$484$	21.7519	−	2.67939i	0.988720	−	0.121790i
$485$	24.4762	−	8.90860i	1.11141	−	0.404519i
$486$	0.00912062	−	0.0867769i	0.000413720	−	0.00393628i
$487$	20.7809	+	23.0796i	0.941674	+	1.04583i	0.998873	+	0.0474717i	$0.0151164\pi$
$487$	20.7809	+	23.0796i	0.941674	+	1.04583i	−0.0571990	+	0.998363i	$0.518217\pi$
$488$	−3.84695	+	0.540654i	−0.174143	+	0.0244743i
$489$	−0.263004	+	1.05485i	−0.0118934	+	0.0477020i
$490$	−0.0683967	−	0.00478276i	−0.00308985	−	0.000216063i
$491$	−27.5962	+	14.6732i	−1.24540	+	0.662191i	−0.955535	−	0.294876i	$-0.904722\pi$
$491$	−27.5962	+	14.6732i	−1.24540	+	0.662191i	−0.289865	+	0.957068i	$0.593610\pi$
$492$	1.95577	−	2.50327i	0.0881730	−	0.112856i
$493$	−25.3393	−	18.4101i	−1.14122	−	0.829148i
$494$	−0.521833	+	1.48622i	−0.0234784	+	0.0668683i
$495$	7.89245	−	4.46736i	0.354739	−	0.200793i
$496$	36.6954	+	13.3560i	1.64767	+	0.599704i
$497$	−4.92582	+	10.0994i	−0.220953	+	0.453022i
$498$	0.431381	−	0.269557i	0.0193307	−	0.0120791i
$499$	−19.4238	−	12.1374i	−0.869530	−	0.543343i	0.0202175	−	0.999796i	$-0.493564\pi$
$499$	−19.4238	−	12.1374i	−0.869530	−	0.543343i	−0.889748	+	0.456453i	$0.849120\pi$
$500$	−6.02535	−	12.3538i	−0.269462	−	0.552479i
$501$	0.676817	+	6.43949i	0.0302380	+	0.287695i
$502$	−1.54471	+	1.71557i	−0.0689437	+	0.0765697i
$503$	−0.267672	−	7.66513i	−0.0119349	−	0.341771i	−0.990640	−	0.136500i	$-0.956415\pi$
$503$	−0.267672	−	7.66513i	−0.0119349	−	0.341771i	0.978705	−	0.205271i	$-0.0658076\pi$
$504$	−0.903960	−	0.259206i	−0.0402656	−	0.0115460i
$505$	−8.20806	−	14.2168i	−0.365254	−	0.632638i
$506$	−0.259875	+	0.351344i	−0.0115528	+	0.0156191i
$507$	0.721047	−	4.08926i	0.0320228	−	0.181610i
$508$	−23.6967	+	1.65704i	−1.05137	+	0.0735191i
$509$	4.14614	−	2.59079i	0.183774	−	0.114835i	−0.434912	−	0.900473i	$-0.643221\pi$
$509$	4.14614	−	2.59079i	0.183774	−	0.114835i	0.618687	+	0.785638i	$0.287665\pi$
$510$	−0.992490	+	0.527717i	−0.0439482	+	0.0233677i
$511$	−12.2209	+	3.50429i	−0.540621	+	0.155021i
$512$	5.56161	−	4.04074i	0.245791	−	0.178577i
$513$	−2.26758	+	3.72265i	−0.100116	+	0.164359i
$514$	−0.128949	+	0.396863i	−0.00568768	+	0.0175049i
$515$	20.6938	+	30.6798i	0.911877	+	1.35191i
$516$	2.80566	+	15.9117i	0.123512	+	0.700473i
$517$	1.99136	−	3.66933i	0.0875799	−	0.161377i
$518$	−1.09675	+	0.920278i	−0.0481882	+	0.0404347i
$519$	5.83771	−	5.63741i	0.256247	−	0.247455i
$520$	−2.63974	−	2.93173i	−0.115760	−	0.128565i
$521$	−3.83529	+	4.25952i	−0.168027	+	0.186613i	−0.821278	−	0.570529i	$-0.806738\pi$
$521$	−3.83529	+	4.25952i	−0.168027	+	0.186613i	0.653250	+	0.757142i	$0.273405\pi$
$522$	−0.324379	+	0.480911i	−0.0141977	+	0.0210489i
$523$	−14.5050	+	21.5045i	−0.634258	+	0.940326i	0.365696	+	0.930734i	$0.380831\pi$
$523$	−14.5050	+	21.5045i	−0.634258	+	0.940326i	−0.999954	+	0.00959194i	$0.996947\pi$
$524$	6.82926	−	7.58466i	0.298338	−	0.331337i
$525$	−4.47445	−	4.96938i	−0.195281	−	0.216881i
$526$	0.870154	−	0.840298i	0.0379405	−	0.0366387i
$527$	−35.6399	+	29.9055i	−1.55250	+	1.30270i
$528$	−1.71441	−	13.0027i	−0.0746099	−	0.565868i
$529$	−3.59792	−	20.4048i	−0.156431	−	0.887166i
$530$	0.141659	+	0.210018i	0.00615327	+	0.00912260i
$531$	−3.02956	+	9.32404i	−0.131472	+	0.404629i
$532$	17.6001	+	15.4876i	0.763063	+	0.671474i
$533$	−5.34222	+	3.88135i	−0.231397	+	0.168120i
$534$	−1.13250	+	0.324739i	−0.0490081	+	0.0140528i
$535$	−17.8672	+	9.50018i	−0.772469	+	0.410729i
$536$	−2.14399	+	1.33972i	−0.0926064	+	0.0578669i
$537$	23.7908	−	1.66361i	1.02665	−	0.0717902i
$538$	−0.466045	+	2.64307i	−0.0200926	+	0.113951i
$539$	0.553614	+	0.775819i	0.0238458	+	0.0334169i
$540$	−2.72402	−	4.71814i	−0.117223	−	0.203036i
$541$	−8.94106	−	2.56381i	−0.384406	−	0.110227i	0.0778681	−	0.996964i	$-0.475189\pi$
$541$	−8.94106	−	2.56381i	−0.384406	−	0.110227i	−0.462274	+	0.886737i	$0.652966\pi$
$542$	−0.0159777	−	0.457543i	−0.000686303	−	0.0196531i
$543$	6.54812	−	7.27242i	0.281007	−	0.312090i
$544$	0.513018	+	4.88104i	0.0219955	+	0.209273i
$545$	10.3170	+	21.1529i	0.441930	+	0.906092i
$546$	0.827289	+	0.516947i	0.0354047	+	0.0221233i
$547$	−3.74936	+	2.34286i	−0.160311	+	0.100173i	−0.607702	−	0.794165i	$-0.707909\pi$
$547$	−3.74936	+	2.34286i	−0.160311	+	0.100173i	0.447391	+	0.894338i	$0.352353\pi$
$548$	−15.6044	+	31.9937i	−0.666586	+	1.36670i
$549$	10.4792	+	3.81411i	0.447241	+	0.162782i
$550$	−0.297146	+	0.652365i	−0.0126704	+	0.0278169i
$551$	24.9294	−	14.7745i	1.06203	−	0.629413i
$552$	0.425584	+	0.309205i	0.0181140	+	0.0131606i
$553$	1.11498	−	1.42712i	0.0474140	−	0.0606871i
$554$	−1.88726	+	1.00348i	−0.0801821	+	0.0426336i
$555$	−16.5800	−	1.15939i	−0.703781	−	0.0492132i
$556$	6.00247	−	24.0746i	0.254562	−	1.02099i
$557$	−5.38801	+	0.757235i	−0.228297	+	0.0320851i	−0.252394	−	0.967625i	$-0.581218\pi$
$557$	−5.38801	+	0.757235i	−0.228297	+	0.0320851i	0.0240967	+	0.999710i	$0.492329\pi$
$558$	0.576565	+	0.640340i	0.0244079	+	0.0271078i
$559$	3.51065	−	33.4016i	0.148485	−	1.41274i
$560$	−27.4294	+	9.98347i	−1.15910	+	0.421879i
$561$	14.4372	+	5.97678i	0.609538	+	0.252340i
$562$	0.287295	+	0.497609i	0.0121188	+	0.0209904i
$563$	−19.1535	+	8.52770i	−0.807225	+	0.359400i	−0.768500	−	0.639850i	$-0.778996\pi$
$563$	−19.1535	+	8.52770i	−0.807225	+	0.359400i	−0.0387255	+	0.999250i	$0.512330\pi$
$564$	−2.21439	−	1.17741i	−0.0932428	−	0.0495781i
$565$	−6.19458	−	3.87080i	−0.260608	−	0.162846i
$566$	−2.34634	−	0.164072i	−0.0986242	−	0.00689648i
$567$	1.94187	+	1.87524i	0.0815507	+	0.0787526i
$568$	0.0506049	−	1.44914i	0.00212334	−	0.0608044i
$569$	−9.76230	+	30.0453i	−0.409257	+	1.25956i	0.508031	+	0.861339i	$0.330373\pi$
$569$	−9.76230	+	30.0453i	−0.409257	+	1.25956i	−0.917288	+	0.398224i	$0.869627\pi$
$570$	−0.0843682	−	1.03657i	−0.00353380	−	0.0434172i
$571$	21.1879			0.886686			0.443343	−	0.896352i	$-0.353792\pi$
$571$	21.1879			0.886686			0.443343	+	0.896352i	$0.353792\pi$
$572$	−4.03987	+	27.0675i	−0.168916	+	1.13175i
$573$	3.70016	+	20.9846i	0.154576	+	0.876646i
$574$	−0.0908558	−	0.364403i	−0.00379225	−	0.0152099i
$575$	1.40128	+	3.46828i	0.0584372	+	0.144637i
$576$	−7.74177	+	1.08804i	−0.322574	+	0.0453348i
$577$	2.02741	+	19.2895i	0.0844021	+	0.803032i	0.952068	+	0.305885i	$0.0989523\pi$
$577$	2.02741	+	19.2895i	0.0844021	+	0.803032i	−0.867666	+	0.497147i	$0.834381\pi$
$578$	−0.414163	−	0.184397i	−0.0172269	−	0.00766991i
$579$	10.6251	+	13.5995i	0.441565	+	0.565178i
$580$	1.26404	+	36.1974i	0.0524864	+	1.50301i
$581$	−1.64502	+	15.6513i	−0.0682470	+	0.649326i
$582$	0.415576	−	0.719800i	0.0172262	−	0.0298366i
$583$	0.999491	−	3.37664i	0.0413947	−	0.139846i
$584$	1.25676	−	1.05455i	0.0520052	−	0.0436375i
$585$	2.73970	+	10.9883i	0.113273	+	0.454312i
$586$	0.769796	+	0.108188i	0.0318000	+	0.00446919i
$587$	0.640921	−	18.3536i	0.0264536	−	0.757533i	−0.911607	−	0.411062i	$-0.865158\pi$
$587$	0.640921	−	18.3536i	0.0264536	−	0.757533i	0.938061	−	0.346471i	$-0.112620\pi$
$588$	0.463201	−	0.336535i	0.0191021	−	0.0138785i
$589$	−12.3358	−	41.2398i	−0.508286	−	1.69925i
$590$	−0.722830	−	2.22464i	−0.0297584	−	0.0915871i
$591$	−11.3070	+	14.4723i	−0.465109	+	0.595312i
$592$	−10.5365	+	21.6031i	−0.433048	+	0.887880i
$593$	−25.0131	−	20.9885i	−1.02717	−	0.861894i	−0.0366547	−	0.999328i	$-0.511670\pi$
$593$	−25.0131	−	20.9885i	−1.02717	−	0.861894i	−0.990511	+	0.137434i	$0.956115\pi$
$594$	0.101294	−	0.271085i	0.00415616	−	0.0111227i
$595$	6.03889	−	34.2483i	0.247570	−	1.40404i
$596$	−26.4354	+	11.7698i	−1.08284	+	0.482110i
$597$	3.77560	−	0.802528i	0.154525	−	0.0328453i
$598$	−0.335968	−	0.430020i	−0.0137388	−	0.0175848i
$599$	8.73739	−	12.9537i	0.357000	−	0.529274i	−0.607166	−	0.794575i	$-0.707694\pi$
$599$	8.73739	−	12.9537i	0.357000	−	0.529274i	0.964166	+	0.265301i	$0.0854713\pi$
$600$	0.788307	+	0.350977i	0.0321825	+	0.0143286i
$601$	13.9750	+	2.97048i	0.570052	+	0.121168i	0.483915	−	0.875115i	$-0.339214\pi$
$601$	13.9750	+	2.97048i	0.570052	+	0.121168i	0.0861369	+	0.996283i	$0.472548\pi$
$602$	1.68656	+	0.896759i	0.0687390	+	0.0365492i
$603$	7.23972	−	0.506250i	0.294824	−	0.0206161i
$604$	20.9671	+	17.5935i	0.853141	+	0.715870i
$605$	29.0508	−	7.79625i	1.18108	−	0.316963i
$606$	−0.492243	−	0.179162i	−0.0199960	−	0.00727795i
$607$	2.52229	+	1.83255i	0.102377	+	0.0743810i	0.637796	−	0.770205i	$-0.279846\pi$
$607$	2.52229	+	1.83255i	0.102377	+	0.0743810i	−0.535419	+	0.844586i	$0.679846\pi$
$608$	−4.33435	−	1.35389i	−0.175781	−	0.0549074i
$609$	−5.54586	−	17.0684i	−0.224730	−	0.691647i
$610$	−2.55764	+	0.733392i	−0.103556	+	0.0296942i
$611$	3.75009	+	3.62142i	0.151713	+	0.146507i
$612$	3.51629	−	8.70312i	0.142137	−	0.351803i
$613$	−7.23679	−	17.9117i	−0.292291	−	0.723446i	−0.999859	−	0.0168006i	$-0.994652\pi$
$613$	−7.23679	−	17.9117i	−0.292291	−	0.723446i	0.707568	−	0.706646i	$-0.249792\pi$
$614$	−1.16000	+	1.12020i	−0.0468140	+	0.0452077i
$615$	2.17991	−	3.77572i	0.0879026	−	0.152252i
$616$	−2.68766	−	1.58245i	−0.108289	−	0.0637586i
$617$	5.88120	−	2.14058i	0.236768	−	0.0861766i	−0.220911	−	0.975294i	$-0.570903\pi$
$617$	5.88120	−	2.14058i	0.236768	−	0.0861766i	0.457679	+	0.889117i	$0.348681\pi$
$618$	1.13512	+	0.325491i	0.0456614	+	0.0130932i
$619$	7.80136	−	1.65823i	0.313563	−	0.0666499i	−0.0484419	−	0.998826i	$-0.515426\pi$
$619$	7.80136	−	1.65823i	0.313563	−	0.0666499i	0.362005	+	0.932176i	$0.382092\pi$
$620$	52.6250	+	11.1858i	2.11347	+	0.449232i
$621$	−0.661983	−	1.35727i	−0.0265645	−	0.0544652i
$622$	0.179567	−	0.720202i	0.00719997	−	0.0288775i
$623$	13.6543	−	33.7955i	0.547046	−	1.35399i
$624$	16.2178	+	2.27927i	0.649233	+	0.0912437i
$625$	−17.4745	−	25.9070i	−0.698979	−	1.03628i
$626$	−0.499107			−0.0199483
$627$	−10.3705	+	10.0723i	−0.414159	+	0.402250i
$628$	−16.0289			−0.639624
$629$	−16.0130	−	23.7403i	−0.638482	−	0.946588i
$630$	−0.637814	−	0.0896390i	−0.0254111	−	0.00357130i
$631$	−4.81924	+	11.9280i	−0.191851	+	0.474848i	−0.992195	−	0.124693i	$-0.960205\pi$
$631$	−4.81924	+	11.9280i	−0.191851	+	0.474848i	0.800345	+	0.599540i	$0.204650\pi$
$632$	−0.0565378	+	0.226761i	−0.00224895	+	0.00902006i
$633$	0.718591	+	1.47333i	0.0285614	+	0.0585596i
$634$	−0.0764579	−	0.0162516i	−0.00303653	−	0.000645435i
$635$	−31.8893	+	6.77828i	−1.26549	+	0.268988i
$636$	−2.03349	−	0.583093i	−0.0806330	−	0.0231212i
$637$	−1.11837	+	0.407054i	−0.0443114	+	0.0161280i
$638$	−1.44068	+	1.27511i	−0.0570372	+	0.0504821i
$639$	−2.08124	+	3.60481i	−0.0823325	+	0.142604i
$640$	5.43997	−	5.25332i	0.215034	−	0.207656i
$641$	−17.8180	−	44.1011i	−0.703768	−	1.74189i	−0.669889	−	0.742461i	$-0.733658\pi$
$641$	−17.8180	−	44.1011i	−0.703768	−	1.74189i	−0.0338792	−	0.999426i	$-0.510786\pi$
$642$	−0.241892	+	0.598703i	−0.00954671	+	0.0236289i
$643$	−26.1642	−	25.2664i	−1.03181	−	0.996411i	−0.0318186	−	0.999494i	$-0.510130\pi$
$643$	−26.1642	−	25.2664i	−1.03181	−	0.996411i	−0.999995	+	0.00308258i	$0.999019\pi$
$644$	−7.80738	+	2.23873i	−0.307654	+	0.0882184i
$645$	6.85236	+	21.0894i	0.269811	+	0.830394i
$646$	1.31785	−	1.21408i	0.0518501	−	0.0477675i
$647$	30.3455	+	22.0473i	1.19300	+	0.866767i	0.993578	−	0.113146i	$-0.0360927\pi$
$647$	30.3455	+	22.0473i	1.19300	+	0.866767i	0.199425	+	0.979913i	$0.436093\pi$
$648$	−0.327347	−	0.119144i	−0.0128594	−	0.00468044i
$649$	−17.4654	+	27.4269i	−0.685576	+	1.07660i
$650$	−0.685723	−	0.575390i	−0.0268963	−	0.0225686i
$651$	−26.5934	+	1.85959i	−1.04228	+	0.0728832i
$652$	1.91247	+	1.01688i	0.0748982	+	0.0398241i
$653$	−45.6342	−	9.69984i	−1.78580	−	0.379584i	−0.808011	−	0.589167i	$-0.799456\pi$
$653$	−45.6342	−	9.69984i	−1.78580	−	0.379584i	−0.977791	+	0.209583i	$0.932789\pi$
$654$	0.686062	+	0.305455i	0.0268271	+	0.0119442i
$655$	7.83281	−	11.6126i	0.306053	−	0.453742i
$656$	−3.88171	−	4.96836i	−0.151555	−	0.193982i
$657$	−4.60661	+	0.979164i	−0.179721	+	0.0382008i
$658$	−0.270864	+	0.120596i	−0.0105594	+	0.00470134i
$659$	2.07003	−	11.7397i	0.0806368	−	0.457314i	−0.917576	−	0.397560i	$-0.869857\pi$
$659$	2.07003	−	11.7397i	0.0806368	−	0.457314i	0.998213	−	0.0597545i	$-0.0190318\pi$
$660$	−4.83215	−	17.4110i	−0.188091	−	0.677722i
$661$	−9.13680	−	7.66668i	−0.355380	−	0.298199i	0.447566	−	0.894251i	$-0.352291\pi$
$661$	−9.13680	−	7.66668i	−0.355380	−	0.298199i	−0.802946	+	0.596051i	$0.796735\pi$
$662$	0.309538	−	0.634648i	0.0120305	−	0.0246663i
$663$	−12.0127	+	15.3755i	−0.466533	+	0.597135i
$664$	−0.627561	−	1.93143i	−0.0243541	−	0.0749542i
$665$	26.8783	+	17.6872i	1.04229	+	0.685881i
$666$	−0.429066	+	0.311735i	−0.0166260	+	0.0120795i
$667$	−0.350369	+	10.0333i	−0.0135663	+	0.388489i
$668$	12.7751	+	1.79542i	0.494282	+	0.0694668i
$669$	−4.49075	−	18.0114i	−0.173622	−	0.696361i
$670$	−1.32645	+	1.11302i	−0.0512452	+	0.0429999i
$671$	30.4853	+	20.9432i	1.17687	+	0.808504i
$672$	−1.40611	+	2.43545i	−0.0542418	+	0.0939495i
$673$	−4.90692	+	46.6862i	−0.189148	+	1.79962i	0.329000	+	0.944330i	$0.393288\pi$
$673$	−4.90692	+	46.6862i	−0.189148	+	1.79962i	−0.518148	+	0.855291i	$0.673378\pi$
$674$	0.0446478	+	1.27855i	0.00171977	+	0.0492477i
$675$	−1.52505	−	1.95198i	−0.0586993	−	0.0751317i
$676$	−7.55783	−	3.36496i	−0.290686	−	0.129422i
$677$	−1.89600	−	18.0393i	−0.0728693	−	0.693305i	−0.968586	−	0.248680i	$-0.920003\pi$
$677$	−1.89600	−	18.0393i	−0.0728693	−	0.693305i	0.895716	−	0.444626i	$-0.146663\pi$
$678$	−0.230817	+	0.0324392i	−0.00886447	+	0.00124582i
$679$	9.63279	+	23.8420i	0.369673	+	0.914972i
$680$	1.08567	+	4.35440i	0.0416337	+	0.166984i
$681$	−2.55396	−	14.4842i	−0.0978679	−	0.555037i
$682$	1.32008	+	2.53465i	0.0505486	+	0.0970569i
$683$	28.5433			1.09218			0.546090	−	0.837726i	$-0.316116\pi$
$683$	28.5433			1.09218			0.546090	+	0.837726i	$0.316116\pi$
$684$	6.10366	+	6.17801i	0.233379	+	0.236222i
$685$	−15.0966	+	46.4626i	−0.576812	+	1.77524i
$686$	−0.0551807	+	1.58017i	−0.00210681	+	0.0603311i
$687$	13.2560	+	12.8012i	0.505747	+	0.488394i
$688$	31.9897	+	2.23694i	1.21960	+	0.0852825i
$689$	3.72914	+	2.33022i	0.142069	+	0.0887745i
$690$	0.318124	+	0.169149i	0.0121108	+	0.00643941i
$691$	−30.4895	+	13.5748i	−1.15988	+	0.516410i	−0.894207	−	0.447654i	$-0.852260\pi$
$691$	−30.4895	+	13.5748i	−1.15988	+	0.516410i	−0.265669	+	0.964064i	$0.585593\pi$
$692$	−8.08448	−	14.0027i	−0.307326	−	0.532304i
$693$	4.67956	+	7.63301i	0.177762	+	0.289954i
$694$	2.07080	−	0.753709i	0.0786065	−	0.0286104i
$695$	3.55945	−	33.8659i	0.135017	−	1.28461i
$696$	1.54965	+	1.72106i	0.0587394	+	0.0652368i
$697$	7.43859	−	1.04543i	0.281757	−	0.0395983i
$698$	0.0875071	−	0.350972i	0.00331219	−	0.0132845i
$699$	26.5637	+	1.85752i	1.00473	+	0.0702578i
$700$	−11.7635	+	6.25477i	−0.444619	+	0.236408i
$701$	−9.12006	+	11.6731i	−0.344460	+	0.440889i	−0.928778	−	0.370636i	$-0.879140\pi$
$701$	−9.12006	+	11.6731i	−0.344460	+	0.440889i	0.584318	+	0.811525i	$0.301362\pi$
$702$	0.292354	+	0.212408i	0.0110342	+	0.00801681i
$703$	26.0377	−	4.89783i	0.982031	−	0.184725i
$704$	−25.7628	−	2.93022i	−0.970972	−	0.110437i
$705$	−3.23444	−	1.17724i	−0.121816	−	0.0443374i
$706$	1.08741	−	2.22952i	0.0409252	−	0.0839091i
$707$	13.7439	−	8.58814i	0.516892	−	0.322990i
$708$	16.5650	+	10.3510i	0.622551	+	0.389013i
$709$	−15.2987	−	31.3669i	−0.574554	−	1.17801i	−0.966176	−	0.257883i	$-0.916975\pi$
$709$	−15.2987	−	31.3669i	−0.574554	−	1.17801i	0.391623	−	0.920126i	$-0.371914\pi$
$710$	−0.103811	−	0.987693i	−0.00389595	−	0.0370675i
$711$	0.448903	−	0.498557i	0.0168352	−	0.0186974i
$712$	0.164153	+	4.70072i	0.00615189	+	0.176167i
$713$	14.3349	+	4.11046i	0.536846	+	0.153938i
$714$	−0.554856	−	0.961039i	−0.0207650	−	0.0359660i
$715$	−0.320458	+	37.5585i	−0.0119845	+	1.40461i
$716$	8.25110	−	46.7943i	0.308358	−	1.74878i
$717$	−6.34057	+	0.443376i	−0.236793	+	0.0165582i
$718$	−1.95046	+	1.21878i	−0.0727906	+	0.0454846i
$719$	46.8861	−	24.9298i	1.74856	−	0.929724i	0.808650	−	0.588290i	$-0.200199\pi$
$719$	46.8861	−	24.9298i	1.74856	−	0.929724i	0.939906	−	0.341433i	$-0.110912\pi$
$720$	−10.3941	+	2.98046i	−0.387365	+	0.111075i
$721$	−29.5566	+	21.4741i	−1.10075	+	0.799739i
$722$	0.548112	+	1.56461i	0.0203986	+	0.0582289i
$723$	−1.50444	+	4.63020i	−0.0559508	+	0.172199i
$724$	−10.9029	−	16.1642i	−0.405202	−	0.600737i
$725$	2.85966	+	16.2179i	0.106205	+	0.602319i
$726$	0.550215	−	0.786439i	0.0204204	−	0.0291875i
$727$	−22.5304	+	18.9053i	−0.835607	+	0.701158i	−0.956571	−	0.291499i	$-0.905846\pi$
$727$	−22.5304	+	18.9053i	−0.835607	+	0.701158i	0.120964	+	0.992657i	$0.461401\pi$
$728$	2.80158	−	2.70546i	0.103834	−	0.100271i
$729$	0.669131	+	0.743145i	0.0247826	+	0.0275239i
$730$	0.751872	−	0.835038i	0.0278280	−	0.0309061i
$731$	−21.3643	+	31.6738i	−0.790186	+	1.17150i
$732$	12.4245	−	18.4200i	0.459221	−	0.680823i
$733$	2.70748	−	3.00696i	0.100003	−	0.111065i	−0.691066	−	0.722792i	$-0.742858\pi$
$733$	2.70748	−	3.00696i	0.100003	−	0.111065i	0.791069	+	0.611728i	$0.209525\pi$
$734$	0.597893	+	0.664028i	0.0220686	+	0.0245097i
$735$	0.565248	−	0.545853i	0.0208495	−	0.0201341i
$736$	1.20510	−	1.01120i	0.0444205	−	0.0372732i
$737$	23.6679	+	4.38181i	0.871817	+	0.161406i
$738$	−0.0241581	−	0.137007i	−0.000889272	−	0.00504331i
$739$	−10.2834	−	15.2458i	−0.378281	−	0.560825i	0.591034	−	0.806647i	$-0.298720\pi$
$739$	−10.2834	−	15.2458i	−0.378281	−	0.560825i	−0.969315	+	0.245822i	$0.920942\pi$
$740$	−10.2329	+	31.4937i	−0.376169	+	1.15773i
$741$	−8.65631	−	15.8418i	−0.317997	−	0.581963i
$742$	−0.202329	+	0.147001i	−0.00742775	+	0.00539657i
$743$	−18.4490	+	5.29017i	−0.676828	+	0.194077i	−0.596405	−	0.802683i	$-0.703405\pi$
$743$	−18.4490	+	5.29017i	−0.676828	+	0.194077i	−0.0804229	+	0.996761i	$0.525627\pi$
$744$	3.03742	−	1.61503i	0.111357	−	0.0592097i
$745$	−33.6798	+	21.0455i	−1.23393	+	0.771046i
$746$	1.06209	−	0.0742689i	0.0388860	−	0.00271918i
$747$	−1.01233	+	5.74120i	−0.0370392	+	0.210060i
$748$	18.5131	−	25.0292i	0.676905	−	0.915157i
$749$	−9.98876	−	17.3010i	−0.364981	−	0.632166i
$750$	−0.578626	−	0.165918i	−0.0211284	−	0.00605848i
$751$	−1.20429	−	34.4865i	−0.0439453	−	1.25843i	−0.798420	−	0.602101i	$-0.794331\pi$
$751$	−1.20429	−	34.4865i	−0.0439453	−	1.25843i	0.754475	−	0.656329i	$-0.227892\pi$
$752$	−3.33070	+	3.69911i	−0.121458	+	0.134893i
$753$	−2.76554	−	26.3124i	−0.100782	−	0.958876i
$754$	−1.05316	−	2.15930i	−0.0383538	−	0.0786370i
$755$	31.8565	+	19.9062i	1.15938	+	0.724460i
$756$	4.56120	−	2.85016i	0.165889	−	0.103659i
$757$	−10.0020	+	20.5072i	−0.363529	+	0.745345i	−0.999656	−	0.0262395i	$-0.991647\pi$
$757$	−10.0020	+	20.5072i	−0.363529	+	0.745345i	0.636126	+	0.771585i	$0.280536\pi$
$758$	−3.04929	−	1.10985i	−0.110755	−	0.0403116i
$759$	−0.999475	−	4.90769i	−0.0362786	−	0.178138i
$760$	−4.09695	−	0.674343i	−0.148612	−	0.0244610i
$761$	7.43119	+	5.39908i	0.269381	+	0.195716i	0.714272	−	0.699868i	$-0.246758\pi$
$761$	7.43119	+	5.39908i	0.269381	+	0.195716i	−0.444892	+	0.895584i	$0.646758\pi$
$762$	−0.640480	+	0.819777i	−0.0232021	+	0.0296974i
$763$	−20.5146	+	10.9078i	−0.742680	+	0.394890i
$764$	42.3511	+	2.96148i	1.53221	+	0.107142i
$765$	3.11657	−	12.4999i	0.112680	−	0.451934i
$766$	−0.0337504	+	0.00474330i	−0.00121945	+	0.000171383i
$767$	−27.1688	−	30.1740i	−0.981008	−	1.08952i
$768$	−1.60915	+	15.3101i	−0.0580653	+	0.552454i
$769$	25.7727	−	9.38050i	0.929388	−	0.338269i	0.167421	−	0.985886i	$-0.446456\pi$
$769$	25.7727	−	9.38050i	0.929388	−	0.338269i	0.761967	+	0.647616i	$0.224234\pi$
$770$	−1.97373	−	0.817096i	−0.0711284	−	0.0294461i
$771$	−2.39119	−	4.14167i	−0.0861167	−	0.149158i
$772$	31.4120	−	13.9855i	1.13054	−	0.503351i
$773$	−28.0725	−	14.9264i	−1.00970	−	0.536866i	−0.119690	−	0.992811i	$-0.538190\pi$
$773$	−28.0725	−	14.9264i	−1.00970	−	0.536866i	−0.890008	+	0.455945i	$0.849301\pi$
$774$	0.600069	+	0.374965i	0.0215690	+	0.0134778i
$775$	24.4024	+	1.70638i	0.876558	+	0.0612949i
$776$	−2.38697	−	2.30507i	−0.0856874	−	0.0827473i
$777$	0.572639	−	16.3982i	0.0205433	−	0.588284i
$778$	0.989933	−	3.04670i	0.0354908	−	0.109229i
$779$	−1.83938	+	6.70209i	−0.0659025	+	0.240127i
$780$	22.5633			0.807894
$781$	−9.67439	+	9.84857i	−0.346177	+	0.352409i
$782$	0.107795	+	0.611338i	0.00385475	+	0.0218614i
$783$	−1.60833	−	6.45068i	−0.0574772	−	0.230528i
$784$	−0.425688	−	1.05362i	−0.0152032	−	0.0376291i
$785$	−21.7847	+	3.06163i	−0.777528	+	0.109274i
$786$	−0.0467211	−	0.444522i	−0.00166649	−	0.0158556i
$787$	18.3447	+	8.16759i	0.653918	+	0.291143i	0.706753	−	0.707460i	$-0.250159\pi$
$787$	18.3447	+	8.16759i	0.653918	+	0.291143i	−0.0528349	+	0.998603i	$0.516826\pi$
$788$	22.5280	+	28.8345i	0.802525	+	1.02719i
$789$	0.483829	+	13.8550i	0.0172248	+	0.493253i
$790$	−0.0167314	+	0.159189i	−0.000595277	+	0.00566368i
$791$	3.60562	−	6.24512i	0.128201	−	0.222051i
$792$	−0.952292	−	0.654220i	−0.0338382	−	0.0232467i
$793$	−35.3800	+	29.6873i	−1.25638	+	1.05423i
$794$	0.480972	+	1.92907i	0.0170691	+	0.0684603i
$795$	−2.87505	−	0.404062i	−0.101968	−	0.0143306i
$796$	0.268395	−	7.68582i	0.00951300	−	0.272417i
$797$	32.3092	−	23.4740i	1.14445	−	0.831492i	0.156718	−	0.987643i	$-0.449909\pi$
$797$	32.3092	−	23.4740i	1.14445	−	0.831492i	0.987733	+	0.156151i	$0.0499087\pi$
$798$	1.01981	−	0.118954i	0.0361007	−	0.00421093i
$799$	−1.83258	−	5.64011i	−0.0648322	−	0.199533i
$800$	1.58872	−	2.03347i	0.0561698	−	0.0718941i
$801$	5.91901	−	12.1358i	0.209138	−	0.428796i
$802$	−0.732888	−	0.614966i	−0.0258792	−	0.0217152i
$803$	−15.6050	−	0.678285i	−0.550688	−	0.0239362i
$804$	2.51087	−	14.2399i	0.0885516	−	0.502201i
$805$	−10.1833	+	4.53388i	−0.358913	+	0.159798i
$806$	−3.49063	+	0.741956i	−0.122952	+	0.0261343i
$807$	−18.9369	−	24.2382i	−0.666612	−	0.853224i
$808$	−1.16947	+	1.73381i	−0.0411417	+	0.0609950i
$809$	21.8289	+	9.71885i	0.767463	+	0.341696i	0.752846	−	0.658197i	$-0.228680\pi$
$809$	21.8289	+	9.71885i	0.767463	+	0.341696i	0.0146168	+	0.999893i	$0.495347\pi$
$810$	−0.233378	−	0.0496061i	−0.00820008	−	0.00174298i
$811$	34.0778	+	18.1195i	1.19663	+	0.636261i	0.943565	−	0.331187i	$-0.107449\pi$
$811$	34.0778	+	18.1195i	1.19663	+	0.636261i	0.253068	+	0.967448i	$0.418560\pi$
$812$	−35.6698	+	2.49428i	−1.25177	+	0.0875320i
$813$	4.01939	+	3.37267i	0.140966	+	0.118285i
$814$	−1.63647	+	0.644990i	−0.0573581	+	0.0226069i
$815$	2.79344	+	1.01673i	0.0978498	+	0.0356144i
$816$	−15.0720	−	10.9505i	−0.527626	−	0.383343i
$817$	−19.0722	−	29.7616i	−0.667253	−	1.04122i
$818$	−1.05430	−	3.24479i	−0.0368626	−	0.113452i
$819$	−10.7470	+	3.08166i	−0.375532	+	0.107682i
$820$	−6.24852	−	6.03412i	−0.218208	−	0.210721i
$821$	−19.0855	+	47.2384i	−0.666090	+	1.64863i	0.0914241	+	0.995812i	$0.470858\pi$
$821$	−19.0855	+	47.2384i	−0.666090	+	1.64863i	−0.757514	+	0.652819i	$0.773586\pi$
$822$	0.583977	+	1.44539i	0.0203685	+	0.0504139i
$823$	0.789585	−	0.762493i	0.0275232	−	0.0265788i	−0.680770	−	0.732498i	$-0.738355\pi$
$823$	0.789585	−	0.762493i	0.0275232	−	0.0265788i	0.708293	+	0.705919i	$0.249466\pi$
$824$	2.35724	−	4.08286i	0.0821184	−	0.142233i
$825$	−3.27743	−	7.53356i	−0.114105	−	0.262285i
$826$	2.16999	−	0.789813i	0.0755038	−	0.0274811i
$827$	16.8670	+	4.83653i	0.586522	+	0.168182i	0.555758	−	0.831344i	$-0.312428\pi$
$827$	16.8670	+	4.83653i	0.586522	+	0.168182i	0.0307641	+	0.999527i	$0.490206\pi$
$828$	−2.94295	+	0.625543i	−0.102275	+	0.0217391i
$829$	−28.0667	−	5.96577i	−0.974798	−	0.207200i	−0.307137	−	0.951665i	$-0.599371\pi$
$829$	−28.0667	−	5.96577i	−0.974798	−	0.207200i	−0.667661	+	0.744466i	$0.732704\pi$
$830$	−0.609747	−	1.25017i	−0.0211646	−	0.0433939i
$831$	5.92629	−	23.7691i	0.205581	−	0.824539i
$832$	12.1290	−	30.0203i	0.420497	−	1.04077i
$833$	1.34068	+	0.188421i	0.0464519	+	0.00652839i
$834$	−0.607621	−	0.900835i	−0.0210402	−	0.0311934i
$835$	17.7053			0.612717
$836$	14.4733	+	24.9032i	0.500568	+	0.861297i
$837$	−9.87524			−0.341338
$838$	0.498394	+	0.738900i	0.0172167	+	0.0255249i
$839$	15.8849	+	2.23248i	0.548409	+	0.0770739i	0.407936	−	0.913011i	$-0.366249\pi$
$839$	15.8849	+	2.23248i	0.548409	+	0.0770739i	0.140473	+	0.990084i	$0.455138\pi$
$840$	−0.963273	+	2.38418i	−0.0332361	+	0.0822622i
$841$	−3.67673	+	14.7466i	−0.126784	+	0.508502i
$842$	0.833515	+	1.70896i	0.0287248	+	0.0588946i
$843$	−6.44128	−	1.36914i	−0.221850	−	0.0471556i
$844$	3.19461	−	0.679036i	0.109963	−	0.0233734i
$845$	−10.9144	−	3.12967i	−0.375468	−	0.107664i
$846$	−0.103210	+	0.0375654i	−0.00354843	+	0.00129152i
$847$	8.69292	+	28.3937i	0.298692	+	0.975621i
$848$	−2.09930	+	3.63609i	−0.0720903	+	0.124864i
$849$	19.3908	−	18.7255i	0.665490	−	0.642656i
$850$	0.381455	+	0.944134i	0.0130838	+	0.0323835i
$851$	−3.43841	+	8.51035i	−0.117867	+	0.291731i
$852$	5.96567	+	5.76098i	0.204381	+	0.197368i
$853$	1.52697	−	0.437850i	0.0522823	−	0.0149917i	−0.249394	−	0.968402i	$-0.580231\pi$
$853$	1.52697	−	0.437850i	0.0522823	−	0.0149917i	0.301677	+	0.953410i	$0.402454\pi$
$854$	−0.811707	−	2.49818i	−0.0277760	−	0.0854859i
$855$	9.47541	+	7.23059i	0.324052	+	0.247281i
$856$	2.08562	+	1.51529i	0.0712852	+	0.0517917i
$857$	−13.2868	−	4.83599i	−0.453867	−	0.165194i	0.104963	−	0.994476i	$-0.466528\pi$
$857$	−13.2868	−	4.83599i	−0.453867	−	0.165194i	−0.558830	+	0.829282i	$0.688750\pi$
$858$	0.762537	+	0.924664i	0.0260326	+	0.0315675i
$859$	−14.0886	−	11.8218i	−0.480698	−	0.403353i	0.369981	−	0.929039i	$-0.379364\pi$
$859$	−14.0886	−	11.8218i	−0.480698	−	0.403353i	−0.850679	+	0.525686i	$0.823809\pi$
$860$	44.0730	−	3.08188i	1.50288	−	0.105091i
$861$	3.80034	+	2.02068i	0.129515	+	0.0688646i
$862$	−2.90290	−	0.617030i	−0.0988730	−	0.0210161i
$863$	37.3532	+	16.6307i	1.27152	+	0.566117i	0.927843	−	0.372971i	$-0.121661\pi$
$863$	37.3532	+	16.6307i	1.27152	+	0.566117i	0.343676	+	0.939088i	$0.388328\pi$
$864$	−0.582539	+	0.863649i	−0.0198184	+	0.0293819i
$865$	−13.6621	−	17.4867i	−0.464525	−	0.594564i
$866$	−0.520016	+	0.110533i	−0.0176709	+	0.00375606i
$867$	4.74659	−	2.11332i	0.161203	−	0.0717720i
$868$	−9.22310	+	52.3068i	−0.313052	+	1.77541i
$869$	1.85519	−	1.22844i	0.0629330	−	0.0416721i
$870$	1.21510	+	1.01959i	0.0411957	+	0.0345673i
$871$	−13.1760	+	27.0149i	−0.446453	+	0.915364i
$872$	1.84590	−	2.36264i	0.0625100	−	0.0800092i
$873$	2.94357	+	9.05936i	0.0996246	+	0.306613i
$874$	−0.558830	−	0.132585i	−0.0189027	−	0.00448474i
$875$	15.0664	−	10.9464i	0.509338	−	0.370056i
$876$	−0.327468	+	9.37747i	−0.0110641	+	0.316835i
$877$	−10.4391	−	1.46713i	−0.352505	−	0.0495413i	−0.0393014	−	0.999227i	$-0.512513\pi$
$877$	−10.4391	−	1.46713i	−0.352505	−	0.0495413i	−0.313203	+	0.949686i	$0.601402\pi$
$878$	−0.881487	−	3.53545i	−0.0297488	−	0.119316i
$879$	−6.82476	+	5.72665i	−0.230193	+	0.193155i
$880$	−35.8501	+	0.945749i	−1.20851	+	0.0318812i
$881$	20.4501	−	35.4206i	0.688981	−	1.19335i	−0.283187	−	0.959065i	$-0.591392\pi$
$881$	20.4501	−	35.4206i	0.688981	−	1.19335i	0.972168	−	0.234285i	$-0.0752751\pi$
$882$	0.00262097	−	0.0249369i	8.82527e−5	−	0.000839668i
$883$	−0.601063	−	17.2122i	−0.0202274	−	0.579236i	−0.966620	−	0.256216i	$-0.917524\pi$
$883$	−0.601063	−	17.2122i	−0.0202274	−	0.579236i	0.946392	−	0.323020i	$-0.104698\pi$
$884$	23.9339	+	30.6339i	0.804983	+	1.03033i
$885$	24.4903	+	10.9038i	0.823233	+	0.366527i
$886$	0.280590	+	2.66964i	0.00942661	+	0.0896882i
$887$	−22.4682	+	3.15771i	−0.754410	+	0.106025i	−0.505886	−	0.862600i	$-0.668834\pi$
$887$	−22.4682	+	3.15771i	−0.754410	+	0.106025i	−0.248524	+	0.968626i	$0.579945\pi$
$888$	0.793185	+	1.96320i	0.0266175	+	0.0658807i
$889$	−7.78636	−	31.2294i	−0.261146	−	1.04740i
$890$	0.559414	+	3.17260i	0.0187516	+	0.106346i
$891$	1.53202	+	2.94158i	0.0513246	+	0.0985468i
$892$	−36.9843			−1.23833
$893$	5.46298	+	0.511292i	0.182811	+	0.0171097i
$894$	−0.391610	+	1.20525i	−0.0130974	+	0.0403097i
$895$	2.27590	−	65.1733i	0.0760750	−	2.17850i
$896$	5.37051	+	5.18624i	0.179416	+	0.173260i
$897$	6.23889	+	0.436266i	0.208311	+	0.0145665i
$898$	−0.366309	−	0.228895i	−0.0122239	−	0.00763833i
$899$	57.9674	+	30.8218i	1.93332	+	1.02797i
$900$	−4.50865	+	2.00738i	−0.150288	+	0.0669127i
$901$	−2.50110	−	4.33204i	−0.0833238	−	0.144321i
$902$	0.0361124	−	0.459996i	0.00120241	−	0.0153162i
$903$	−20.5713	+	7.48735i	−0.684571	+	0.249164i
$904$	−0.0972706	+	0.925468i	−0.00323517	+	0.0307806i
$905$	−17.9054	−	19.8859i	−0.595195	−	0.661030i
$906$	1.18701	−	0.166823i	0.0394357	−	0.00554233i
$907$	−8.73273	+	35.0251i	−0.289966	+	1.16299i	0.631766	+	0.775159i	$0.282331\pi$
$907$	−8.73273	+	35.0251i	−0.289966	+	1.16299i	−0.921731	+	0.387829i	$0.873225\pi$
$908$	−29.2320	−	2.04410i	−0.970097	−	0.0678358i
$909$	5.30077	−	2.81847i	0.175815	−	0.0934827i
$910$	1.64227	−	2.10201i	0.0544408	−	0.0696810i
$911$	−31.4332	−	22.8376i	−1.04143	−	0.756642i	−0.0708643	−	0.997486i	$-0.522576\pi$
$911$	−31.4332	−	22.8376i	−1.04143	−	0.756642i	−0.970564	+	0.240844i	$0.922576\pi$
$912$	14.8282	−	8.78797i	0.491012	−	0.290999i
$913$	−8.01474	+	17.5958i	−0.265249	+	0.582336i
$914$	2.29577	+	0.835593i	0.0759374	+	0.0276390i
$915$	13.3675	−	27.4075i	0.441916	−	0.906063i
$916$	31.1367	−	19.4563i	1.02878	−	0.642856i
$917$	11.7272	+	7.32798i	0.387267	+	0.241991i
$918$	−0.180205	−	0.369475i	−0.00594765	−	0.0121945i
$919$	1.51696	+	14.4329i	0.0500400	+	0.476098i	0.990632	+	0.136559i	$0.0436044\pi$
$919$	1.51696	+	14.4329i	0.0500400	+	0.476098i	−0.940592	+	0.339539i	$0.889729\pi$
$920$	0.962509	−	1.06897i	0.0317330	−	0.0352430i
$921$	−0.644993	−	18.4702i	−0.0212532	−	0.608613i
$922$	0.101151	+	0.0290045i	0.00333122	+	0.000955211i
$923$	−8.61953	−	14.9295i	−0.283715	−	0.491409i
$924$	17.0117	−	5.36741i	0.559644	−	0.176575i
$925$	−2.61451	+	14.8276i	−0.0859645	+	0.487529i
$926$	−0.308590	+	0.0215787i	−0.0101409	+	0.000709120i
$927$	−11.4771	+	7.17169i	−0.376958	+	0.235549i
$928$	6.11504	−	3.25142i	0.200736	−	0.106733i
$929$	−31.3850	+	8.99951i	−1.02971	+	0.295264i	−0.747622	−	0.664125i	$-0.768804\pi$
$929$	−31.3850	+	8.99951i	−1.02971	+	0.295264i	−0.282087	+	0.959389i	$0.591027\pi$
$930$	1.90617	−	1.38491i	0.0625058	−	0.0454131i
$931$	−0.651628	+	1.06977i	−0.0213563	+	0.0350603i
$932$	16.3947	−	50.4578i	0.537028	−	1.65280i
$933$	4.75688	+	7.05237i	0.155733	+	0.230884i
$934$	0.501058	+	2.84164i	0.0163951	+	0.0929814i
$935$	20.3801	−	37.5528i	0.666499	−	1.22811i
$936$	1.10519	−	0.927367i	0.0361243	−	0.0303119i
$937$	−39.1897	+	37.8451i	−1.28027	+	1.23634i	−0.323255	+	0.946312i	$0.604777\pi$
$937$	−39.1897	+	37.8451i	−1.28027	+	1.23634i	−0.957017	+	0.290033i	$0.906334\pi$
$938$	−1.14384	−	1.27037i	−0.0373478	−	0.0414789i
$939$	3.82750	−	4.25087i	0.124906	−	0.138722i
$940$	−3.83485	+	5.68539i	−0.125079	+	0.185437i
$941$	8.74113	−	12.9593i	0.284953	−	0.422460i	−0.659200	−	0.751967i	$-0.729105\pi$
$941$	8.74113	−	12.9593i	0.284953	−	0.422460i	0.944153	+	0.329508i	$0.106883\pi$
$942$	−0.469712	+	0.521668i	−0.0153040	+	0.0169969i
$943$	−1.61109	−	1.78929i	−0.0524642	−	0.0582674i
$944$	27.8875	−	26.9307i	0.907662	−	0.876519i
$945$	5.65465	−	4.74482i	0.183946	−	0.154349i
$946$	1.61577	+	1.70200i	0.0525331	+	0.0553368i
$947$	−5.79217	−	32.8490i	−0.188220	−	1.06745i	−0.921748	−	0.387790i	$-0.873238\pi$
$947$	−5.79217	−	32.8490i	−0.188220	−	1.06745i	0.733527	−	0.679660i	$-0.237873\pi$
$948$	−0.747441	−	1.10813i	−0.0242758	−	0.0359903i
$949$	6.02727	−	18.5500i	0.195654	−	0.602160i
$950$	−0.941867	−	0.0221447i	−0.0305582	−	0.000718468i
$951$	0.724746	−	0.526559i	0.0235015	−	0.0170748i
$952$	−4.25877	+	1.22118i	−0.138028	+	0.0395788i
$953$	18.5995	−	9.88954i	0.602498	−	0.320354i	−0.140053	−	0.990144i	$-0.544727\pi$
$953$	18.5995	−	9.88954i	0.602498	−	0.320354i	0.742550	+	0.669790i	$0.233616\pi$
$954$	−0.0785663	+	0.0490937i	−0.00254368	+	0.00158947i
$955$	58.1242	−	4.06444i	1.88086	−	0.131522i
$956$	−2.19903	+	12.4713i	−0.0711217	+	0.403351i
$957$	0.188124	−	22.0486i	0.00608119	−	0.712731i
$958$	1.22193	+	2.11645i	0.0394789	+	0.0683794i
$959$	−46.3615	−	13.2940i	−1.49709	−	0.429284i
$960$	0.746059	+	21.3643i	0.0240790	+	0.689531i
$961$	44.5109	−	49.4343i	1.43583	−	1.59466i
$962$	−0.229595	−	2.18445i	−0.00740244	−	0.0704296i
$963$	−3.24413	−	6.65145i	−0.104541	−	0.214340i
$964$	8.22598	+	5.14016i	0.264941	+	0.165553i
$965$	40.0202	−	25.0074i	1.28830	−	0.805017i
$966$	−0.155927	+	0.319698i	−0.00501688	+	0.0102861i
$967$	47.3971	+	17.2511i	1.52419	+	0.554759i	0.962190	−	0.272381i	$-0.0878110\pi$
$967$	47.3971	+	17.2511i	1.52419	+	0.554759i	0.561997	+	0.827139i	$0.310033\pi$
$968$	−2.51508	−	2.89100i	−0.0808378	−	0.0929202i
$969$	0.234092	+	20.5345i	0.00752011	+	0.659663i
$970$	−1.83868	−	1.33588i	−0.0590363	−	0.0428924i
$971$	4.20814	−	5.38617i	0.135046	−	0.172851i	−0.715734	−	0.698373i	$-0.753908\pi$
$971$	4.20814	−	5.38617i	0.135046	−	0.172851i	0.850780	+	0.525522i	$0.176130\pi$
$972$	1.75917	−	0.935369i	0.0564255	−	0.0300020i
$973$	33.5357	+	2.34505i	1.07511	+	0.0751787i
$974$	0.655569	−	2.62935i	0.0210058	−	0.0842497i
$975$	10.1592	−	1.42778i	0.325353	−	0.0457254i
$976$	−29.5074	−	32.7713i	−0.944509	−	1.04898i
$977$	2.55712	−	24.3294i	0.0818096	−	0.778366i	−0.874306	−	0.485375i	$-0.838683\pi$
$977$	2.55712	−	24.3294i	0.0818096	−	0.778366i	0.956115	−	0.292990i	$-0.0946504\pi$
$978$	0.0891378	−	0.0324435i	0.00285031	−	0.00103743i
$979$	29.0770	−	34.0582i	0.929303	−	1.08850i
$980$	−0.782795	−	1.35584i	−0.0250055	−	0.0433108i
$981$	−7.86274	+	3.50072i	−0.251038	+	0.111769i
$982$	2.40791	+	1.28031i	0.0768393	+	0.0408562i
$983$	39.6559	+	24.7798i	1.26483	+	0.790352i	0.985472	−	0.169835i	$-0.0543236\pi$
$983$	39.6559	+	24.7798i	1.26483	+	0.790352i	0.279356	+	0.960188i	$0.409879\pi$
$984$	−0.554071	−	0.0387444i	−0.0176632	−	0.00123513i
$985$	36.1249	+	34.8854i	1.15104	+	1.11154i
$986$	−0.0953774	+	2.73125i	−0.00303743	+	0.0869807i
$987$	1.05006	−	3.23175i	0.0334238	−	0.102868i
$988$	−34.7978	+	9.09862i	−1.10707	+	0.289466i
$989$	12.2461			0.389402
$990$	−0.708249	−	0.352948i	−0.0225096	−	0.0112174i
$991$	−1.06187	−	6.02216i	−0.0337314	−	0.191300i	0.963286	−	0.268477i	$-0.0865205\pi$
$991$	−1.06187	−	6.02216i	−0.0337314	−	0.191300i	−0.997017	+	0.0771770i	$0.975409\pi$
$992$	−2.48878	−	9.98194i	−0.0790188	−	0.316927i
$993$	3.03150	+	7.50324i	0.0962019	+	0.238108i
$994$	0.970911	−	0.136453i	0.0307954	−	0.00432801i
$995$	−1.10327	−	10.4969i	−0.0349761	−	0.332775i
$996$	10.6110	+	4.72431i	0.336222	+	0.149695i
$997$	−20.9317	−	26.7914i	−0.662914	−	0.848492i	0.332603	−	0.943067i	$-0.392073\pi$
$997$	−20.9317	−	26.7914i	−0.662914	−	0.848492i	−0.995518	+	0.0945750i	$0.969851\pi$
$998$	0.0697466	+	1.99728i	0.00220779	+	0.0632228i
$999$	0.635348	−	6.04493i	0.0201015	−	0.191253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.bo.b.4.10	✓	480
11.3	even	5	inner	627.2.bo.b.289.10	yes	480
19.5	even	9	inner	627.2.bo.b.499.10	yes	480
209.157	even	45	inner	627.2.bo.b.157.10	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.bo.b.4.10	✓	480	1.1	even	1	trivial
627.2.bo.b.157.10	yes	480	209.157	even	45	inner
627.2.bo.b.289.10	yes	480	11.3	even	5	inner
627.2.bo.b.499.10	yes	480	19.5	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.bo (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0487923 - 0.0723376i) q^{2} +(0.990268 + 0.139173i) q^{3} +(0.746361 - 1.84731i) q^{4} +(0.661518 - 2.65320i) q^{5} +(-0.0382500 - 0.0784241i) q^{6} +(2.64052 + 0.561260i) q^{7} +(-0.340743 + 0.0724271i) q^{8} +(0.961262 + 0.275637i) q^{9} +(-0.224203 + 0.0816033i) q^{10} +(2.85803 + 1.68276i) q^{11} +(0.996193 - 1.72546i) q^{12} +(-2.97917 + 2.87695i) q^{13} +(-0.0882369 - 0.218394i) q^{14} +(1.02433 - 2.53532i) q^{15} +(-2.84454 - 2.74694i) q^{16} +(4.52873 - 1.29859i) q^{17} +(-0.0269632 - 0.0829843i) q^{18} +(-0.557398 + 4.32311i) q^{19} +(-4.40756 - 3.20228i) q^{20} +(2.53671 + 0.923288i) q^{21} +(-0.0177232 - 0.288848i) q^{22} +(-1.15680 - 0.970672i) q^{23} +(-0.347507 + 0.0243000i) q^{24} +(-2.18715 - 1.16293i) q^{25} +(0.353473 + 0.0751329i) q^{26} +(0.913545 + 0.406737i) q^{27} +(3.00760 - 4.45896i) q^{28} +(-4.09301 - 5.23882i) q^{29} +(-0.233378 + 0.0496061i) q^{30} +(-9.02148 + 4.01662i) q^{31} +(-0.180898 + 1.02592i) q^{32} +(2.59602 + 2.06414i) q^{33} +(-0.314904 - 0.264236i) q^{34} +(3.23589 - 6.63456i) q^{35} +(1.22664 - 1.57002i) q^{36} +(-1.87827 - 5.78074i) q^{37} +(0.339920 - 0.170614i) q^{38} +(-3.35058 + 2.43434i) q^{39} +(-0.0332436 + 0.951972i) q^{40} +(1.57890 + 0.221900i) q^{41} +(-0.0569836 - 0.228549i) q^{42} +(-6.21220 + 5.21265i) q^{43} +(5.24169 - 4.02372i) q^{44} +(1.36721 - 2.36808i) q^{45} +(-0.0137730 + 0.131042i) q^{46} +(-0.0439304 - 1.25800i) q^{47} +(-2.43456 - 3.11609i) q^{48} +(0.262524 + 0.116883i) q^{49} +(0.0225927 + 0.214955i) q^{50} +(4.66539 - 0.655678i) q^{51} +(3.09108 + 7.65070i) q^{52} +(-0.256863 - 1.03022i) q^{53} +(-0.0151516 - 0.0859293i) q^{54} +(6.35534 - 6.46976i) q^{55} -0.940389 q^{56} +(-1.15363 + 4.20347i) q^{57} +(-0.179256 + 0.551693i) q^{58} +(-0.342150 + 9.79790i) q^{59} +(-3.91899 - 3.78453i) q^{60} +(11.1246 + 0.777905i) q^{61} +(0.730732 + 0.456612i) q^{62} +(2.38353 + 1.26734i) q^{63} +(-7.14197 + 3.17981i) q^{64} +(5.66237 + 9.80751i) q^{65} +(0.0226493 - 0.288504i) q^{66} +(6.81972 - 2.48218i) q^{67} +(0.981168 - 9.33519i) q^{68} +(-1.01045 - 1.12222i) q^{69} +(-0.637814 + 0.0896390i) q^{70} +(-1.00699 + 4.03883i) q^{71} +(-0.347507 - 0.0243000i) q^{72} +(-4.15826 + 2.21099i) q^{73} +(-0.326519 + 0.417925i) q^{74} +(-2.00401 - 1.45600i) q^{75} +(7.57010 + 4.25629i) q^{76} +(6.60222 + 6.04746i) q^{77} +(0.339576 + 0.123596i) q^{78} +(0.294092 - 0.602978i) q^{79} +(-9.16991 + 5.73000i) q^{80} +(0.848048 + 0.529919i) q^{81} +(-0.0609866 - 0.125041i) q^{82} +(0.609377 + 5.79783i) q^{83} +(3.59890 - 3.99698i) q^{84} +(-0.449594 - 12.8747i) q^{85} +(0.680178 + 0.195038i) q^{86} +(-3.32408 - 5.75747i) q^{87} +(-1.09573 - 0.366389i) q^{88} +(2.34465 - 13.2972i) q^{89} +(-0.238011 + 0.0166433i) q^{90} +(-9.48129 + 5.92457i) q^{91} +(-2.65652 + 1.41250i) q^{92} +(-9.49269 + 2.72199i) q^{93} +(-0.0888574 + 0.0645587i) q^{94} +(11.1014 + 4.33871i) q^{95} +(-0.321918 + 0.990762i) q^{96} +(5.32664 + 7.89706i) q^{97} +(-0.00435409 - 0.0246933i) q^{98} +(2.28348 + 2.40535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 18 q^{5} + 3 q^{7} + 12 q^{10} + 3 q^{11} - 240 q^{12} + 42 q^{14} - 12 q^{15} + 72 q^{16} - 18 q^{17} - 102 q^{20} + 24 q^{22} + 54 q^{23} - 18 q^{25} - 12 q^{26} + 60 q^{27} + 36 q^{29} + 12 q^{30}+ \cdots - 6 q^{99}+O(q^{100}) \) 480 * q + 18 * q^5 + 3 * q^7 + 12 * q^10 + 3 * q^11 - 240 * q^12 + 42 * q^14 - 12 * q^15 + 72 * q^16 - 18 * q^17 - 102 * q^20 + 24 * q^22 + 54 * q^23 - 18 * q^25 - 12 * q^26 + 60 * q^27 + 36 * q^29 + 12 * q^30 + 60 * q^31 - 30 * q^32 - 21 * q^33 - 84 * q^34 + 12 * q^35 + 36 * q^37 - 90 * q^38 - 12 * q^39 + 300 * q^40 - 63 * q^41 - 18 * q^42 - 24 * q^43 - 15 * q^44 + 6 * q^45 - 6 * q^46 + 24 * q^48 + 39 * q^49 + 12 * q^51 - 21 * q^52 + 9 * q^53 + 45 * q^55 + 156 * q^56 + 30 * q^57 + 12 * q^58 - 69 * q^59 - 36 * q^60 + 12 * q^61 - 90 * q^62 + 60 * q^64 - 66 * q^65 + 30 * q^66 + 72 * q^67 + 24 * q^68 + 18 * q^69 - 96 * q^70 + 72 * q^71 + 18 * q^73 + 57 * q^74 - 102 * q^75 + 48 * q^76 - 114 * q^77 - 216 * q^78 - 24 * q^79 - 30 * q^80 - 24 * q^82 + 78 * q^83 - 36 * q^84 - 36 * q^85 - 189 * q^86 - 24 * q^87 + 120 * q^88 - 318 * q^89 - 18 * q^90 - 48 * q^91 + 354 * q^92 + 12 * q^93 - 282 * q^94 + 6 * q^95 + 60 * q^96 + 120 * q^97 - 96 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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