LMFDB - Embedded newform 671.2.f.a.538.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (of order $4$, degree $2$, 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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.3
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89459 - 1.89459i) q^{2} +0.936891i q^{3} +5.17893i q^{4} +2.40716i q^{5} +(1.77502 - 1.77502i) q^{6} +(3.07176 + 3.07176i) q^{7} +(6.02277 - 6.02277i) q^{8} +2.12224 q^{9} +O(q^{10})$	\(q+(-1.89459 - 1.89459i) q^{2} +0.936891i q^{3} +5.17893i q^{4} +2.40716i q^{5} +(1.77502 - 1.77502i) q^{6} +(3.07176 + 3.07176i) q^{7} +(6.02277 - 6.02277i) q^{8} +2.12224 q^{9} +(4.56057 - 4.56057i) q^{10} +(2.96832 + 1.47955i) q^{11} -4.85209 q^{12} +4.20910i q^{13} -11.6394i q^{14} -2.25524 q^{15} -12.4635 q^{16} +(0.0850763 - 0.0850763i) q^{17} +(-4.02076 - 4.02076i) q^{18} -5.11079 q^{19} -12.4665 q^{20} +(-2.87790 + 2.87790i) q^{21} +(-2.82061 - 8.42689i) q^{22} +(1.76200 - 1.76200i) q^{23} +(5.64268 + 5.64268i) q^{24} -0.794404 q^{25} +(7.97452 - 7.97452i) q^{26} +4.79898i q^{27} +(-15.9084 + 15.9084i) q^{28} +(5.43337 - 5.43337i) q^{29} +(4.27276 + 4.27276i) q^{30} +(-0.249849 - 0.249849i) q^{31} +(11.5676 + 11.5676i) q^{32} +(-1.38618 + 2.78099i) q^{33} -0.322369 q^{34} +(-7.39421 + 7.39421i) q^{35} +10.9909i q^{36} +(-4.12775 - 4.12775i) q^{37} +(9.68285 + 9.68285i) q^{38} -3.94347 q^{39} +(14.4977 + 14.4977i) q^{40} -7.25621 q^{41} +10.9049 q^{42} +(7.52083 - 7.52083i) q^{43} +(-7.66248 + 15.3727i) q^{44} +5.10855i q^{45} -6.67653 q^{46} +3.11058 q^{47} -11.6769i q^{48} +11.8714i q^{49} +(1.50507 + 1.50507i) q^{50} +(0.0797072 + 0.0797072i) q^{51} -21.7986 q^{52} +(7.15236 - 7.15236i) q^{53} +(9.09208 - 9.09208i) q^{54} +(-3.56151 + 7.14522i) q^{55} +37.0010 q^{56} -4.78826i q^{57} -20.5880 q^{58} +(-0.638327 - 0.638327i) q^{59} -11.6798i q^{60} +(-5.98602 - 5.01673i) q^{61} +0.946724i q^{62} +(6.51900 + 6.51900i) q^{63} -18.9048i q^{64} -10.1320 q^{65} +(7.89507 - 2.64261i) q^{66} +(-2.65165 - 2.65165i) q^{67} +(0.440604 + 0.440604i) q^{68} +(1.65080 + 1.65080i) q^{69} +28.0180 q^{70} +(-8.91667 - 8.91667i) q^{71} +(12.7817 - 12.7817i) q^{72} +7.25225i q^{73} +15.6408i q^{74} -0.744270i q^{75} -26.4684i q^{76} +(4.57315 + 13.6628i) q^{77} +(7.47125 + 7.47125i) q^{78} +(6.26892 + 6.26892i) q^{79} -30.0015i q^{80} +1.87059 q^{81} +(13.7475 + 13.7475i) q^{82} -7.47924i q^{83} +(-14.9045 - 14.9045i) q^{84} +(0.204792 + 0.204792i) q^{85} -28.4978 q^{86} +(5.09047 + 5.09047i) q^{87} +(26.7885 - 8.96653i) q^{88} +(12.4463 + 12.4463i) q^{89} +(9.67861 - 9.67861i) q^{90} +(-12.9294 + 12.9294i) q^{91} +(9.12528 + 9.12528i) q^{92} +(0.234082 - 0.234082i) q^{93} +(-5.89327 - 5.89327i) q^{94} -12.3025i q^{95} +(-10.8376 + 10.8376i) q^{96} -12.6732i q^{97} +(22.4915 - 22.4915i) q^{98} +(6.29948 + 3.13995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.89459	−	1.89459i	−1.33968	−	1.33968i	−0.896370	−	0.443306i	$-0.853805\pi$
$2$	−1.89459	−	1.89459i	−1.33968	−	1.33968i	−0.443306	−	0.896370i	$-0.646195\pi$
$3$			0.936891i			0.540914i	0.962732	+	0.270457i	$0.0871748\pi$
$3$			0.936891i			0.540914i	−0.962732	+	0.270457i	$0.912825\pi$
$4$			5.17893i			2.58947i
$5$			2.40716i			1.07651i	0.842781	+	0.538257i	$0.180917\pi$
$5$			2.40716i			1.07651i	−0.842781	+	0.538257i	$0.819083\pi$
$6$	1.77502	−	1.77502i	0.724650	−	0.724650i
$7$	3.07176	+	3.07176i	1.16102	+	1.16102i	0.984253	+	0.176763i	$0.0565626\pi$
$7$	3.07176	+	3.07176i	1.16102	+	1.16102i	0.176763	+	0.984253i	$0.443437\pi$
$8$	6.02277	−	6.02277i	2.12937	−	2.12937i
$9$	2.12224			0.707412
$10$	4.56057	−	4.56057i	1.44218	−	1.44218i
$11$	2.96832	+	1.47955i	0.894983	+	0.446101i
$11$	2.96832	+	1.47955i	0.894983	+	0.446101i
$12$	−4.85209			−1.40068
$13$			4.20910i			1.16739i	0.811971	+	0.583697i	$0.198395\pi$
$13$			4.20910i			1.16739i	−0.811971	+	0.583697i	$0.801605\pi$
$14$		−	11.6394i		−	3.11077i
$15$	−2.25524			−0.582301
$16$	−12.4635			−3.11587
$17$	0.0850763	−	0.0850763i	0.0206340	−	0.0206340i	−0.696714	−	0.717349i	$-0.745356\pi$
$17$	0.0850763	−	0.0850763i	0.0206340	−	0.0206340i	0.717349	+	0.696714i	$0.245356\pi$
$18$	−4.02076	−	4.02076i	−0.947703	−	0.947703i
$19$	−5.11079			−1.17250			−0.586248	−	0.810132i	$-0.699396\pi$
$19$	−5.11079			−1.17250			−0.586248	+	0.810132i	$0.699396\pi$
$20$	−12.4665			−2.78759
$21$	−2.87790	+	2.87790i	−0.628010	+	0.628010i
$22$	−2.82061	−	8.42689i	−0.601356	−	1.79662i
$23$	1.76200	−	1.76200i	0.367403	−	0.367403i	−0.499127	−	0.866529i	$-0.666346\pi$
$23$	1.76200	−	1.76200i	0.367403	−	0.367403i	0.866529	+	0.499127i	$0.166346\pi$
$24$	5.64268	+	5.64268i	1.15181	+	1.15181i
$25$	−0.794404			−0.158881
$26$	7.97452	−	7.97452i	1.56393	−	1.56393i
$27$			4.79898i			0.923563i
$28$	−15.9084	+	15.9084i	−3.00641	+	3.00641i
$29$	5.43337	−	5.43337i	1.00895	−	1.00895i	0.00899145	−	0.999960i	$-0.497138\pi$
$29$	5.43337	−	5.43337i	1.00895	−	1.00895i	0.999960	−	0.00899145i	$-0.00286211\pi$
$30$	4.27276	+	4.27276i	0.780095	+	0.780095i
$31$	−0.249849	−	0.249849i	−0.0448743	−	0.0448743i	0.684314	−	0.729188i	$-0.260102\pi$
$31$	−0.249849	−	0.249849i	−0.0448743	−	0.0448743i	−0.729188	+	0.684314i	$0.760102\pi$
$32$	11.5676	+	11.5676i	2.04488	+	2.04488i
$33$	−1.38618	+	2.78099i	−0.241302	+	0.484109i
$34$	−0.322369			−0.0552859
$35$	−7.39421	+	7.39421i	−1.24985	+	1.24985i
$36$			10.9909i			1.83182i
$37$	−4.12775	−	4.12775i	−0.678597	−	0.678597i	0.281086	−	0.959683i	$-0.409306\pi$
$37$	−4.12775	−	4.12775i	−0.678597	−	0.678597i	−0.959683	+	0.281086i	$0.909306\pi$
$38$	9.68285	+	9.68285i	1.57077	+	1.57077i
$39$	−3.94347			−0.631460
$40$	14.4977	+	14.4977i	2.29229	+	2.29229i
$41$	−7.25621			−1.13323			−0.566615	−	0.823983i	$-0.691747\pi$
$41$	−7.25621			−1.13323			−0.566615	+	0.823983i	$0.691747\pi$
$42$	10.9049			1.68266
$43$	7.52083	−	7.52083i	1.14692	−	1.14692i	0.159761	−	0.987156i	$-0.448928\pi$
$43$	7.52083	−	7.52083i	1.14692	−	1.14692i	0.987156	−	0.159761i	$-0.0510722\pi$
$44$	−7.66248	+	15.3727i	−1.15516	+	2.31753i
$45$			5.10855i			0.761538i
$46$	−6.67653			−0.984401
$47$	3.11058			0.453724			0.226862	−	0.973927i	$-0.427153\pi$
$47$	3.11058			0.453724			0.226862	+	0.973927i	$0.427153\pi$
$48$		−	11.6769i		−	1.68542i
$49$			11.8714i			1.69592i
$50$	1.50507	+	1.50507i	0.212849	+	0.212849i
$51$	0.0797072	+	0.0797072i	0.0111612	+	0.0111612i
$52$	−21.7986			−3.02293
$53$	7.15236	−	7.15236i	0.982452	−	0.982452i	−0.0173964	−	0.999849i	$-0.505538\pi$
$53$	7.15236	−	7.15236i	0.982452	−	0.982452i	0.999849	+	0.0173964i	$0.00553773\pi$
$54$	9.09208	−	9.09208i	1.23728	−	1.23728i
$55$	−3.56151	+	7.14522i	−0.480233	+	0.963461i
$56$	37.0010			4.94447
$57$		−	4.78826i		−	0.634220i
$58$	−20.5880			−2.70334
$59$	−0.638327	−	0.638327i	−0.0831031	−	0.0831031i	0.664333	−	0.747436i	$-0.268716\pi$
$59$	−0.638327	−	0.638327i	−0.0831031	−	0.0831031i	−0.747436	+	0.664333i	$0.768716\pi$
$60$		−	11.6798i		−	1.50785i
$61$	−5.98602	−	5.01673i	−0.766431	−	0.642327i
$61$	−5.98602	−	5.01673i	−0.766431	−	0.642327i
$62$			0.946724i			0.120234i
$63$	6.51900	+	6.51900i	0.821317	+	0.821317i
$64$		−	18.9048i		−	2.36310i
$65$	−10.1320			−1.25672
$66$	7.89507	−	2.64261i	0.971816	−	0.325282i
$67$	−2.65165	−	2.65165i	−0.323951	−	0.323951i	0.526330	−	0.850281i	$-0.323568\pi$
$67$	−2.65165	−	2.65165i	−0.323951	−	0.323951i	−0.850281	+	0.526330i	$0.823568\pi$
$68$	0.440604	+	0.440604i	0.0534311	+	0.0534311i
$69$	1.65080	+	1.65080i	0.198733	+	0.198733i
$70$	28.0180			3.34879
$71$	−8.91667	−	8.91667i	−1.05821	−	1.05821i	−0.998197	−	0.0600164i	$-0.980885\pi$
$71$	−8.91667	−	8.91667i	−1.05821	−	1.05821i	−0.0600164	−	0.998197i	$-0.519115\pi$
$72$	12.7817	−	12.7817i	1.50634	−	1.50634i
$73$			7.25225i			0.848811i	0.905472	+	0.424406i	$0.139517\pi$
$73$			7.25225i			0.848811i	−0.905472	+	0.424406i	$0.860483\pi$
$74$			15.6408i			1.81820i
$75$		−	0.744270i		−	0.0859408i
$76$		−	26.4684i		−	3.03614i
$77$	4.57315	+	13.6628i	0.521159	+	1.55702i
$78$	7.47125	+	7.47125i	0.845953	+	0.845953i
$79$	6.26892	+	6.26892i	0.705309	+	0.705309i	0.965545	−	0.260236i	$-0.0838003\pi$
$79$	6.26892	+	6.26892i	0.705309	+	0.705309i	−0.260236	+	0.965545i	$0.583800\pi$
$80$		−	30.0015i		−	3.35427i
$81$	1.87059			0.207843
$82$	13.7475	+	13.7475i	1.51816	+	1.51816i
$83$		−	7.47924i		−	0.820953i	−0.911871	−	0.410477i	$-0.865362\pi$
$83$		−	7.47924i		−	0.820953i	0.911871	−	0.410477i	$-0.134638\pi$
$84$	−14.9045	−	14.9045i	−1.62621	−	1.62621i
$85$	0.204792	+	0.204792i	0.0222128	+	0.0222128i
$86$	−28.4978			−3.07299
$87$	5.09047	+	5.09047i	0.545756	+	0.545756i
$88$	26.7885	−	8.96653i	2.85566	−	0.955835i
$89$	12.4463	+	12.4463i	1.31930	+	1.31930i	0.914329	+	0.404972i	$0.132719\pi$
$89$	12.4463	+	12.4463i	1.31930	+	1.31930i	0.404972	+	0.914329i	$0.367281\pi$
$90$	9.67861	−	9.67861i	1.02021	−	1.02021i
$91$	−12.9294	+	12.9294i	−1.35536	+	1.35536i
$92$	9.12528	+	9.12528i	0.951376	+	0.951376i
$93$	0.234082	−	0.234082i	0.0242731	−	0.0242731i
$94$	−5.89327	−	5.89327i	−0.607844	−	0.607844i
$95$		−	12.3025i		−	1.26221i
$96$	−10.8376	+	10.8376i	−1.10611	+	1.10611i
$97$		−	12.6732i		−	1.28676i	−0.765545	−	0.643382i	$-0.777531\pi$
$97$		−	12.6732i		−	1.28676i	0.765545	−	0.643382i	$-0.222469\pi$
$98$	22.4915	−	22.4915i	2.27198	−	2.27198i
$99$	6.29948	+	3.13995i	0.633121	+	0.315577i
$100$		−	4.11416i		−	0.411416i
$101$	−3.37434	−	3.37434i	−0.335760	−	0.335760i	0.519009	−	0.854769i	$-0.326301\pi$
$101$	−3.37434	−	3.37434i	−0.335760	−	0.335760i	−0.854769	+	0.519009i	$0.826301\pi$
$102$		−	0.302025i		−	0.0299049i
$103$	−4.34869			−0.428489			−0.214245	−	0.976780i	$-0.568729\pi$
$103$	−4.34869			−0.428489			−0.214245	+	0.976780i	$0.568729\pi$
$104$	25.3504	+	25.3504i	2.48581	+	2.48581i
$105$	−6.92757	−	6.92757i	−0.676061	−	0.676061i
$106$	−27.1016			−2.63234
$107$	−0.997375			−0.0964199			−0.0482099	−	0.998837i	$-0.515352\pi$
$107$	−0.997375			−0.0964199			−0.0482099	+	0.998837i	$0.515352\pi$
$108$	−24.8536			−2.39154
$109$	−5.37445			−0.514779			−0.257390	−	0.966308i	$-0.582862\pi$
$109$	−5.37445			−0.514779			−0.257390	+	0.966308i	$0.582862\pi$
$110$	20.2848	−	6.78965i	1.93408	−	0.647368i
$111$	3.86725	−	3.86725i	0.367063	−	0.367063i
$112$	−38.2848	−	38.2848i	−3.61757	−	3.61757i
$113$		−	18.0272i		−	1.69586i	−0.530108	−	0.847930i	$-0.677849\pi$
$113$		−	18.0272i		−	1.69586i	0.530108	−	0.847930i	$-0.322151\pi$
$114$	−9.07177	+	9.07177i	−0.849649	+	0.849649i
$115$	4.24141	+	4.24141i	0.395514	+	0.395514i
$116$	28.1390	+	28.1390i	2.61264	+	2.61264i
$117$			8.93270i			0.825829i
$118$			2.41873i			0.222663i
$119$	0.522668			0.0479129
$120$	−13.5828	+	13.5828i	−1.23993	+	1.23993i
$121$	6.62187	+	8.78356i	0.601988	+	0.798505i
$122$	1.83640	+	20.8457i	0.166259	+	1.88728i
$123$		−	6.79828i		−	0.612980i
$124$	1.29395	−	1.29395i	0.116200	−	0.116200i
$125$			10.1235i			0.905476i
$126$		−	24.7016i		−	2.20060i
$127$	2.28167			0.202465			0.101233	−	0.994863i	$-0.467721\pi$
$127$	2.28167			0.202465			0.101233	+	0.994863i	$0.467721\pi$
$128$	−12.6816	+	12.6816i	−1.12090	+	1.12090i
$129$	7.04620	+	7.04620i	0.620383	+	0.620383i
$130$	19.1959	+	19.1959i	1.68359	+	1.68359i
$131$			5.76991i			0.504119i	0.967712	+	0.252060i	$0.0811079\pi$
$131$			5.76991i			0.504119i	−0.967712	+	0.252060i	$0.918892\pi$
$132$	−14.4026	−	7.17891i	−1.25358	−	0.624844i
$133$	−15.6991	−	15.6991i	−1.36129	−	1.36129i
$134$			10.0476i			0.867979i
$135$	−11.5519			−0.994228
$136$		−	1.02479i		−	0.0878750i
$137$	8.38138			0.716070			0.358035	−	0.933708i	$-0.383447\pi$
$137$	8.38138			0.716070			0.358035	+	0.933708i	$0.383447\pi$
$138$		−	6.25518i		−	0.532477i
$139$	−9.19091	+	9.19091i	−0.779563	+	0.779563i	−0.979756	−	0.200193i	$-0.935843\pi$
$139$	−9.19091	+	9.19091i	−0.779563	+	0.779563i	0.200193	+	0.979756i	$0.435843\pi$
$140$	−38.2941	−	38.2941i	−3.23644	−	3.23644i
$141$			2.91427i			0.245426i
$142$			33.7868i			2.83533i
$143$	−6.22757	+	12.4940i	−0.520776	+	1.04480i
$144$	−26.4504			−2.20420
$145$	13.0790	+	13.0790i	1.08615	+	1.08615i
$146$	13.7400	−	13.7400i	1.13713	−	1.13713i
$147$	−11.1222			−0.917346
$148$	21.3773	−	21.3773i	1.75720	−	1.75720i
$149$	−19.3015			−1.58124			−0.790618	−	0.612309i	$-0.790241\pi$
$149$	−19.3015			−1.58124			−0.790618	+	0.612309i	$0.790241\pi$
$150$	−1.41008	+	1.41008i	−0.115133	+	0.115133i
$151$	−11.9215	+	11.9215i	−0.970161	+	0.970161i	−0.999568	−	0.0294069i	$-0.990638\pi$
$151$	−11.9215	+	11.9215i	−0.970161	+	0.970161i	0.0294069	+	0.999568i	$0.490638\pi$
$152$	−30.7811	+	30.7811i	−2.49668	+	2.49668i
$153$	0.180552	−	0.180552i	0.0145968	−	0.0145968i
$154$	17.2211	−	34.5496i	1.38772	−	2.78409i
$155$	0.601427	−	0.601427i	0.0483078	−	0.0483078i
$156$		−	20.4230i		−	1.63515i
$157$	1.87005	+	1.87005i	0.149246	+	0.149246i	0.777781	−	0.628535i	$-0.216345\pi$
$157$	1.87005	+	1.87005i	0.149246	+	0.149246i	−0.628535	+	0.777781i	$0.716345\pi$
$158$		−	23.7541i		−	1.88977i
$159$	6.70098	+	6.70098i	0.531422	+	0.531422i
$160$	−27.8450	+	27.8450i	−2.20134	+	2.20134i
$161$	10.8249			0.853121
$162$	−3.54400	−	3.54400i	−0.278443	−	0.278443i
$163$			1.13642i			0.0890110i	0.999009	+	0.0445055i	$0.0141712\pi$
$163$			1.13642i			0.0890110i	−0.999009	+	0.0445055i	$0.985829\pi$
$164$		−	37.5794i		−	2.93446i
$165$	−6.69429	−	3.33674i	−0.521150	−	0.259765i
$166$	−14.1701	+	14.1701i	−1.09981	+	1.09981i
$167$	13.3639			1.03413			0.517064	−	0.855947i	$-0.327025\pi$
$167$	13.3639			1.03413			0.517064	+	0.855947i	$0.327025\pi$
$168$			34.6659i			2.67453i
$169$	−4.71654			−0.362811
$170$		−	0.775993i		−	0.0595160i
$171$	−10.8463			−0.829438
$172$	38.9499	+	38.9499i	2.96990	+	2.96990i
$173$	−12.5668	−	12.5668i	−0.955439	−	0.955439i	0.0436092	−	0.999049i	$-0.486114\pi$
$173$	−12.5668	−	12.5668i	−0.955439	−	0.955439i	−0.999049	+	0.0436092i	$0.986114\pi$
$174$		−	19.2887i		−	1.46227i
$175$	−2.44022	−	2.44022i	−0.184463	−	0.184463i
$176$	−36.9956	−	18.4403i	−2.78865	−	1.38999i
$177$	0.598043	−	0.598043i	0.0449517	−	0.0449517i
$178$		−	47.1611i		−	3.53487i
$179$	−4.35468			−0.325484			−0.162742	−	0.986669i	$-0.552034\pi$
$179$	−4.35468			−0.325484			−0.162742	+	0.986669i	$0.552034\pi$
$180$	−26.4568			−1.97198
$181$	−7.72346	−	7.72346i	−0.574081	−	0.574081i	0.359186	−	0.933266i	$-0.383055\pi$
$181$	−7.72346	−	7.72346i	−0.574081	−	0.574081i	−0.933266	+	0.359186i	$0.883055\pi$
$182$	48.9916			3.63150
$183$	4.70013	−	5.60825i	0.347444	−	0.414573i
$184$		−	21.2242i		−	1.56467i
$185$	9.93613	−	9.93613i	0.730519	−	0.730519i
$186$	−0.886977			−0.0650363
$187$	0.378408	−	0.126659i	0.0276720	−	0.00926224i
$188$			16.1095i			1.17490i
$189$	−14.7413	+	14.7413i	−1.07227	+	1.07227i
$190$	−23.3081	+	23.3081i	−1.69095	+	1.69095i
$191$	−10.2168	−	10.2168i	−0.739261	−	0.739261i	0.233174	−	0.972435i	$-0.425089\pi$
$191$	−10.2168	−	10.2168i	−0.739261	−	0.739261i	−0.972435	+	0.233174i	$0.925089\pi$
$192$	17.7117			1.27823
$193$	9.55325	−	9.55325i	0.687658	−	0.687658i	−0.274056	−	0.961714i	$-0.588365\pi$
$193$	9.55325	−	9.55325i	0.687658	−	0.687658i	0.961714	+	0.274056i	$0.0883654\pi$
$194$	−24.0104	+	24.0104i	−1.72385	+	1.72385i
$195$		−	9.49255i		−	0.679776i
$196$	−61.4813			−4.39152
$197$	−5.94520			−0.423578			−0.211789	−	0.977315i	$-0.567929\pi$
$197$	−5.94520			−0.423578			−0.211789	+	0.977315i	$0.567929\pi$
$198$	−5.98600	−	17.8838i	−0.425407	−	1.27095i
$199$	15.2529			1.08125			0.540624	−	0.841264i	$-0.318188\pi$
$199$	15.2529			1.08125			0.540624	+	0.841264i	$0.318188\pi$
$200$	−4.78451	+	4.78451i	−0.338316	+	0.338316i
$201$	2.48431	−	2.48431i	0.175230	−	0.175230i
$202$			12.7860i			0.899619i
$203$	33.3800			2.34282
$204$	−0.412798	+	0.412798i	−0.0289017	+	0.0289017i
$205$		−	17.4668i		−	1.21994i
$206$	8.23898	+	8.23898i	0.574037	+	0.574037i
$207$	3.73938	−	3.73938i	0.259905	−	0.259905i
$208$		−	52.4600i		−	3.63745i
$209$	−15.1705	−	7.56167i	−1.04936	−	0.523051i
$210$			26.2498i			1.81141i
$211$	−2.28560	+	2.28560i	−0.157347	+	0.157347i	−0.781390	−	0.624043i	$-0.785489\pi$
$211$	−2.28560	+	2.28560i	−0.157347	+	0.157347i	0.624043	+	0.781390i	$0.285489\pi$
$212$	37.0416	+	37.0416i	2.54403	+	2.54403i
$213$	8.35395	−	8.35395i	0.572403	−	0.572403i
$214$	1.88962	+	1.88962i	0.129171	+	0.129171i
$215$	18.1038	+	18.1038i	1.23467	+	1.23467i
$216$	28.9031	+	28.9031i	1.96661	+	1.96661i
$217$		−	1.53496i		−	0.104200i
$218$	10.1824	+	10.1824i	0.689638	+	0.689638i
$219$	−6.79456			−0.459134
$220$	−37.0046	−	18.4448i	−2.49485	−	1.24355i
$221$	0.358095	+	0.358095i	0.0240881	+	0.0240881i
$222$	−14.6537			−0.983491
$223$	−10.8164	+	10.8164i	−0.724317	+	0.724317i	−0.969481	−	0.245165i	$-0.921158\pi$
$223$	−10.8164	+	10.8164i	−0.724317	+	0.724317i	0.245165	+	0.969481i	$0.421158\pi$
$224$			71.0658i			4.74829i
$225$	−1.68591			−0.112394
$226$	−34.1542	+	34.1542i	−2.27190	+	2.27190i
$227$	0.294884	+	0.294884i	0.0195721	+	0.0195721i	0.716825	−	0.697253i	$-0.245595\pi$
$227$	0.294884	+	0.294884i	0.0195721	+	0.0195721i	−0.697253	+	0.716825i	$0.745595\pi$
$228$	24.7980			1.64229
$229$		−	21.8955i		−	1.44690i	−0.690377	−	0.723449i	$-0.742556\pi$
$229$		−	21.8955i		−	1.44690i	0.690377	−	0.723449i	$-0.257444\pi$
$230$		−	16.0715i		−	1.05972i
$231$	−12.8005	+	4.28455i	−0.842214	+	0.281902i
$232$		−	65.4478i		−	4.29686i
$233$	3.51941	+	3.51941i	0.230564	+	0.230564i	0.812928	−	0.582364i	$-0.197872\pi$
$233$	3.51941	+	3.51941i	0.230564	+	0.230564i	−0.582364	+	0.812928i	$0.697872\pi$
$234$	16.9238	−	16.9238i	1.10634	−	1.10634i
$235$			7.48765i			0.488440i
$236$	3.30585	−	3.30585i	0.215193	−	0.215193i
$237$	−5.87330	+	5.87330i	−0.381512	+	0.381512i
$238$	−0.990241	−	0.990241i	−0.0641878	−	0.0641878i
$239$			11.7870i			0.762437i	0.924485	+	0.381218i	$0.124495\pi$
$239$			11.7870i			0.762437i	−0.924485	+	0.381218i	$0.875505\pi$
$240$	28.1082			1.81437
$241$			5.35922i			0.345217i	0.984990	+	0.172609i	$0.0552196\pi$
$241$			5.35922i			0.345217i	−0.984990	+	0.172609i	$0.944780\pi$
$242$	4.09551	−	29.1869i	0.263269	−	1.87621i
$243$			16.1495i			1.03599i
$244$	25.9813	−	31.0012i	1.66328	−	1.98465i
$245$	−28.5764			−1.82568
$246$	−12.8799	+	12.8799i	−0.821195	+	0.821195i
$247$		−	21.5118i		−	1.36877i
$248$	−3.00957			−0.191108
$249$	7.00723			0.444065
$250$	19.1799	−	19.1799i	1.21304	−	1.21304i
$251$	1.06058	−	1.06058i	0.0669433	−	0.0669433i	−0.672842	−	0.739786i	$-0.734927\pi$
$251$	1.06058	−	1.06058i	0.0669433	−	0.0669433i	0.739786	+	0.672842i	$0.234927\pi$
$252$	−33.7614	+	33.7614i	−2.12677	+	2.12677i
$253$	7.83715	−	2.62322i	0.492718	−	0.164920i
$254$	−4.32282	−	4.32282i	−0.271238	−	0.271238i
$255$	−0.191868	+	0.191868i	−0.0120152	+	0.0120152i
$256$	10.2431			0.640195
$257$	5.76009			0.359304			0.179652	−	0.983730i	$-0.442503\pi$
$257$	5.76009			0.359304			0.179652	+	0.983730i	$0.442503\pi$
$258$		−	26.6993i		−	1.66223i
$259$		−	25.3589i		−	1.57572i
$260$		−	52.4728i		−	3.25422i
$261$	11.5309	−	11.5309i	0.713744	−	0.713744i
$262$	10.9316	−	10.9316i	0.675357	−	0.675357i
$263$	26.4795			1.63279			0.816397	−	0.577491i	$-0.195968\pi$
$263$	26.4795			1.63279			0.816397	+	0.577491i	$0.195968\pi$
$264$	8.40066	+	25.0979i	0.517025	+	1.54467i
$265$	17.2169	+	17.2169i	1.05762	+	1.05762i
$266$			59.4868i			3.64737i
$267$	−11.6608	+	11.6608i	−0.713629	+	0.713629i
$268$	13.7327	−	13.7327i	0.838860	−	0.838860i
$269$	−26.4750			−1.61421			−0.807106	−	0.590407i	$-0.798967\pi$
$269$	−26.4750			−1.61421			−0.807106	+	0.590407i	$0.798967\pi$
$270$	21.8861	+	21.8861i	1.33194	+	1.33194i
$271$	22.1411			1.34498			0.672488	−	0.740108i	$-0.265225\pi$
$271$	22.1411			1.34498			0.672488	+	0.740108i	$0.265225\pi$
$272$	−1.06035	+	1.06035i	−0.0642929	+	0.0642929i
$273$	−12.1134	−	12.1134i	−0.733136	−	0.733136i
$274$	−15.8793	−	15.8793i	−0.959302	−	0.959302i
$275$	−2.35805	−	1.17536i	−0.142195	−	0.0708768i
$276$	−8.54939	+	8.54939i	−0.514613	+	0.514613i
$277$	−4.49383	−	4.49383i	−0.270008	−	0.270008i	0.559095	−	0.829103i	$-0.311149\pi$
$277$	−4.49383	−	4.49383i	−0.270008	−	0.270008i	−0.829103	+	0.559095i	$0.811149\pi$
$278$	34.8260			2.08872
$279$	−0.530239	−	0.530239i	−0.0317446	−	0.0317446i
$280$			89.0672i			5.32278i
$281$	11.7029	−	11.7029i	0.698136	−	0.698136i	−0.265873	−	0.964008i	$-0.585660\pi$
$281$	11.7029	−	11.7029i	0.698136	−	0.698136i	0.964008	+	0.265873i	$0.0856601\pi$
$282$	5.52135	−	5.52135i	0.328791	−	0.328791i
$283$	14.5366			0.864111			0.432055	−	0.901847i	$-0.357789\pi$
$283$	14.5366			0.864111			0.432055	+	0.901847i	$0.357789\pi$
$284$	46.1788	−	46.1788i	2.74021	−	2.74021i
$285$	11.5261			0.682746
$286$	35.4696	−	11.8722i	2.09736	−	0.702020i
$287$	−22.2893	−	22.2893i	−1.31570	−	1.31570i
$288$	24.5492	+	24.5492i	1.44657	+	1.44657i
$289$			16.9855i			0.999148i
$290$		−	49.5585i		−	2.91018i
$291$	11.8734			0.696029
$292$	−37.5589			−2.19797
$293$	−14.4329			−0.843176			−0.421588	−	0.906787i	$-0.638527\pi$
$293$	−14.4329			−0.843176			−0.421588	+	0.906787i	$0.638527\pi$
$294$	21.0721	+	21.0721i	1.22895	+	1.22895i
$295$	1.53655	−	1.53655i	0.0894616	−	0.0894616i
$296$	−49.7209			−2.88997
$297$	−7.10032	+	14.2449i	−0.412002	+	0.826573i
$298$	36.5683	+	36.5683i	2.11835	+	2.11835i
$299$	7.41644	+	7.41644i	0.428904	+	0.428904i
$300$	3.85452			0.222541
$301$	46.2044			2.66318
$302$	45.1728			2.59940
$303$	3.16139	−	3.16139i	0.181617	−	0.181617i
$304$	63.6982			3.65334
$305$	12.0761	−	14.4093i	0.691473	−	0.825073i
$306$	−0.684143			−0.0391099
$307$	12.9544	+	12.9544i	0.739349	+	0.739349i	0.972452	−	0.233103i	$-0.0748880\pi$
$307$	12.9544	+	12.9544i	0.739349	+	0.739349i	−0.233103	+	0.972452i	$0.574888\pi$
$308$	−70.7587	+	23.6840i	−4.03185	+	1.34952i
$309$		−	4.07425i		−	0.231776i
$310$	−2.27891			−0.129434
$311$	−19.6268	−	19.6268i	−1.11293	−	1.11293i	−0.992752	−	0.120180i	$-0.961653\pi$
$311$	−19.6268	−	19.6268i	−1.11293	−	1.11293i	−0.120180	−	0.992752i	$-0.538347\pi$
$312$	−23.7506	+	23.7506i	−1.34461	+	1.34461i
$313$	−8.67024	−	8.67024i	−0.490071	−	0.490071i	0.418257	−	0.908329i	$-0.362641\pi$
$313$	−8.67024	−	8.67024i	−0.490071	−	0.490071i	−0.908329	+	0.418257i	$0.862641\pi$
$314$		−	7.08594i		−	0.399883i
$315$	−15.6923	+	15.6923i	−0.884158	+	0.884158i
$316$	−32.4663	+	32.4663i	−1.82637	+	1.82637i
$317$	−26.5150			−1.48923			−0.744616	−	0.667493i	$-0.767367\pi$
$317$	−26.5150			−1.48923			−0.744616	+	0.667493i	$0.767367\pi$
$318$		−	25.3912i		−	1.42387i
$319$	24.1669	−	8.08905i	1.35309	−	0.452900i
$320$	45.5068			2.54391
$321$		−	0.934432i		−	0.0521549i
$322$	−20.5087	−	20.5087i	−1.14291	−	1.14291i
$323$	−0.434807	+	0.434807i	−0.0241933	+	0.0241933i
$324$			9.68765i			0.538203i
$325$		−	3.34373i		−	0.185477i
$326$	2.15304	−	2.15304i	0.119246	−	0.119246i
$327$		−	5.03528i		−	0.278451i
$328$	−43.7025	+	43.7025i	−2.41307	+	2.41307i
$329$	9.55495	+	9.55495i	0.526781	+	0.526781i
$330$	6.36117	+	19.0047i	0.350171	+	1.04617i
$331$	8.58843	−	8.58843i	0.472063	−	0.472063i	−0.430519	−	0.902582i	$-0.641669\pi$
$331$	8.58843	−	8.58843i	0.472063	−	0.472063i	0.902582	+	0.430519i	$0.141669\pi$
$332$	38.7345			2.12583
$333$	−8.76005	−	8.76005i	−0.480048	−	0.480048i
$334$	−25.3190	−	25.3190i	−1.38540	−	1.38540i
$335$	6.38294	−	6.38294i	0.348737	−	0.348737i
$336$	35.8687	−	35.8687i	1.95680	−	1.95680i
$337$	−13.0171	−	13.0171i	−0.709088	−	0.709088i	0.257256	−	0.966343i	$-0.417182\pi$
$337$	−13.0171	−	13.0171i	−0.709088	−	0.709088i	−0.966343	+	0.257256i	$0.917182\pi$
$338$	8.93590	+	8.93590i	0.486049	+	0.486049i
$339$	16.8896			0.917315
$340$	−1.06060	+	1.06060i	−0.0575193	+	0.0575193i
$341$	−0.371969	−	1.11130i	−0.0201433	−	0.0601802i
$342$	20.5493	+	20.5493i	1.11118	+	1.11118i
$343$	−14.9638	+	14.9638i	−0.807972	+	0.807972i
$344$		−	90.5925i		−	4.88442i
$345$	−3.97374	+	3.97374i	−0.213939	+	0.213939i
$346$			47.6180i			2.55996i
$347$			21.0748i			1.13136i	0.824626	+	0.565678i	$0.191386\pi$
$347$			21.0748i			1.13136i	−0.824626	+	0.565678i	$0.808614\pi$
$348$	−26.3632	+	26.3632i	−1.41322	+	1.41322i
$349$	−21.4084	−	21.4084i	−1.14597	−	1.14597i	−0.987338	−	0.158629i	$-0.949293\pi$
$349$	−21.4084	−	21.4084i	−1.14597	−	1.14597i	−0.158629	−	0.987338i	$-0.550707\pi$
$350$			9.24642i			0.494242i
$351$	−20.1994			−1.07816
$352$	17.2215	+	51.4512i	0.917911	+	2.74236i
$353$		−	32.1331i		−	1.71027i	−0.518402	−	0.855137i	$-0.673473\pi$
$353$		−	32.1331i		−	1.71027i	0.518402	−	0.855137i	$-0.326527\pi$
$354$	−2.26609			−0.120441
$355$	21.4638	−	21.4638i	1.13918	−	1.13918i
$356$	−64.4583	+	64.4583i	−3.41628	+	3.41628i
$357$			0.489683i			0.0259168i
$358$	8.25033	+	8.25033i	0.436044	+	0.436044i
$359$	−7.09835	+	7.09835i	−0.374637	+	0.374637i	−0.869163	−	0.494526i	$-0.835342\pi$
$359$	−7.09835	+	7.09835i	−0.374637	+	0.374637i	0.494526	+	0.869163i	$0.335342\pi$
$360$	30.7676	+	30.7676i	1.62160	+	1.62160i
$361$	7.12020			0.374747
$362$			29.2656i			1.53816i
$363$	−8.22923	+	6.20397i	−0.431923	+	0.325624i
$364$	−66.9602	−	66.9602i	−3.50967	−	3.50967i
$365$	−17.4573			−0.913756
$366$	−19.5301	+	1.72050i	−1.02086	+	0.0899321i
$367$	18.7065			0.976473			0.488236	−	0.872711i	$-0.337640\pi$
$367$	18.7065			0.976473			0.488236	+	0.872711i	$0.337640\pi$
$368$	−21.9606	+	21.9606i	−1.14478	+	1.14478i
$369$	−15.3994			−0.801660
$370$	−37.6498			−1.95732
$371$	43.9407			2.28129
$372$	1.21229	+	1.21229i	0.0628545	+	0.0628545i
$373$	23.0880	+	23.0880i	1.19545	+	1.19545i	0.975514	+	0.219937i	$0.0705851\pi$
$373$	23.0880	+	23.0880i	1.19545	+	1.19545i	0.219937	+	0.975514i	$0.429415\pi$
$374$	−0.956895	−	0.476961i	−0.0494799	−	0.0246631i
$375$	−9.48464			−0.489785
$376$	18.7343	−	18.7343i	0.966147	−	0.966147i
$377$	22.8696	+	22.8696i	1.17784	+	1.17784i
$378$	55.8574			2.87300
$379$	11.6151			0.596629			0.298315	−	0.954468i	$-0.403576\pi$
$379$	11.6151			0.596629			0.298315	+	0.954468i	$0.403576\pi$
$380$	63.7137			3.26844
$381$			2.13767i			0.109516i
$382$			38.7132i			1.98074i
$383$	9.35585	+	9.35585i	0.478062	+	0.478062i	0.904511	−	0.426450i	$-0.140236\pi$
$383$	9.35585	+	9.35585i	0.478062	+	0.478062i	−0.426450	+	0.904511i	$0.640236\pi$
$384$	−11.8812	−	11.8812i	−0.606312	−	0.606312i
$385$	−32.8885	+	11.0083i	−1.67615	+	0.561035i
$386$	−36.1989			−1.84248
$387$	15.9610	−	15.9610i	0.811342	−	0.811342i
$388$	65.6334			3.33203
$389$	3.87865	−	3.87865i	0.196655	−	0.196655i	−0.601909	−	0.798565i	$-0.705593\pi$
$389$	3.87865	−	3.87865i	0.196655	−	0.196655i	0.798565	+	0.601909i	$0.205593\pi$
$390$	−17.9845	+	17.9845i	−0.910679	+	0.910679i
$391$		−	0.299809i		−	0.0151620i
$392$	71.4988	+	71.4988i	3.61124	+	3.61124i
$393$	−5.40578			−0.272685
$394$	11.2637	+	11.2637i	0.567457	+	0.567457i
$395$	−15.0903	+	15.0903i	−0.759275	+	0.759275i
$396$	−16.2616	+	32.6246i	−0.817176	+	1.63945i
$397$	6.90600	+	6.90600i	0.346602	+	0.346602i	0.858842	−	0.512240i	$-0.171184\pi$
$397$	6.90600	+	6.90600i	0.346602	+	0.346602i	−0.512240	+	0.858842i	$0.671184\pi$
$398$	−28.8980	−	28.8980i	−1.44852	−	1.44852i
$399$	14.7084	−	14.7084i	0.736340	−	0.736340i
$400$	9.90102			0.495051
$401$	−26.4799	−	26.4799i	−1.32234	−	1.32234i	−0.911876	−	0.410466i	$-0.865366\pi$
$401$	−26.4799	−	26.4799i	−1.32234	−	1.32234i	−0.410466	−	0.911876i	$-0.634634\pi$
$402$	−9.41349			−0.469502
$403$	1.05164	−	1.05164i	0.0523860	−	0.0523860i
$404$	17.4755	−	17.4755i	0.869438	−	0.869438i
$405$			4.50280i			0.223746i
$406$	−63.2414	−	63.2414i	−3.13862	−	3.13862i
$407$	−6.14527	−	18.3597i	−0.304610	−	0.910055i
$408$	0.960116			0.0475328
$409$	14.4478	−	14.4478i	0.714396	−	0.714396i	−0.253056	−	0.967452i	$-0.581436\pi$
$409$	14.4478	−	14.4478i	0.714396	−	0.714396i	0.967452	+	0.253056i	$0.0814357\pi$
$410$	−33.0925	+	33.0925i	−1.63432	+	1.63432i
$411$			7.85244i			0.387332i
$412$		−	22.5216i		−	1.10956i
$413$		−	3.92158i		−	0.192968i
$414$	−14.1692			−0.696377
$415$	18.0037			0.883767
$416$	−48.6892	+	48.6892i	−2.38719	+	2.38719i
$417$	−8.61088	−	8.61088i	−0.421677	−	0.421677i
$418$	14.4156	+	43.0681i	0.705088	+	2.10653i
$419$	−8.04520	+	8.04520i	−0.393034	+	0.393034i	−0.875767	−	0.482733i	$-0.839644\pi$
$419$	−8.04520	+	8.04520i	−0.393034	+	0.393034i	0.482733	+	0.875767i	$0.339644\pi$
$420$	35.8774	−	35.8774i	1.75064	−	1.75064i
$421$	−9.64430	+	9.64430i	−0.470034	+	0.470034i	−0.901926	−	0.431891i	$-0.857846\pi$
$421$	−9.64430	+	9.64430i	−0.470034	+	0.470034i	0.431891	+	0.901926i	$0.357846\pi$
$422$	8.66055			0.421589
$423$	6.60138			0.320970
$424$		−	86.1540i		−	4.18401i
$425$	−0.0675849	+	0.0675849i	−0.00327835	+	0.00327835i
$426$	−31.6546			−1.53367
$427$	−2.97741	−	33.7978i	−0.144087	−	1.63559i
$428$		−	5.16534i		−	0.249676i
$429$	−11.7055	−	5.83456i	−0.565146	−	0.281695i
$430$		−	68.5986i		−	3.30812i
$431$	−9.08982			−0.437841			−0.218921	−	0.975743i	$-0.570254\pi$
$431$	−9.08982			−0.437841			−0.218921	+	0.975743i	$0.570254\pi$
$432$		−	59.8119i		−	2.87770i
$433$	−26.0988	−	26.0988i	−1.25423	−	1.25423i	−0.953806	−	0.300423i	$-0.902872\pi$
$433$	−26.0988	−	26.0988i	−1.25423	−	1.25423i	−0.300423	−	0.953806i	$-0.597128\pi$
$434$	−2.90811	+	2.90811i	−0.139594	+	0.139594i
$435$	−12.2536	+	12.2536i	−0.587514	+	0.587514i
$436$		−	27.8339i		−	1.33300i
$437$	−9.00522	+	9.00522i	−0.430778	+	0.430778i
$438$	12.8729	+	12.8729i	0.615091	+	0.615091i
$439$		−	3.81195i		−	0.181934i	−0.995854	−	0.0909672i	$-0.971004\pi$
$439$		−	3.81195i		−	0.181934i	0.995854	−	0.0909672i	$-0.0289959\pi$
$440$	21.5838	+	64.4841i	1.02897	+	3.07416i
$441$			25.1940i			1.19971i
$442$		−	1.35688i		−	0.0645404i
$443$	14.3144			0.680096			0.340048	−	0.940408i	$-0.389557\pi$
$443$	14.3144			0.680096			0.340048	+	0.940408i	$0.389557\pi$
$444$	20.0282	+	20.0282i	0.950497	+	0.950497i
$445$	−29.9601	+	29.9601i	−1.42024	+	1.42024i
$446$	40.9851			1.94070
$447$		−	18.0834i		−	0.855313i
$448$	58.0710	−	58.0710i	2.74359	−	2.74359i
$449$	0.293029			0.0138289			0.00691446	−	0.999976i	$-0.497799\pi$
$449$	0.293029			0.0138289			0.00691446	+	0.999976i	$0.497799\pi$
$450$	3.19411	+	3.19411i	0.150572	+	0.150572i
$451$	−21.5388	−	10.7359i	−1.01422	−	0.505535i
$452$	93.3618			4.39137
$453$	−11.1692	−	11.1692i	−0.524774	−	0.524774i
$454$		−	1.11737i		−	0.0524406i
$455$	−31.1230	−	31.1230i	−1.45907	−	1.45907i
$456$	−28.8385	−	28.8385i	−1.35049	−	1.35049i
$457$	7.40272	+	7.40272i	0.346285	+	0.346285i	0.858724	−	0.512439i	$-0.171258\pi$
$457$	7.40272	+	7.40272i	0.346285	+	0.346285i	−0.512439	+	0.858724i	$0.671258\pi$
$458$	−41.4831	+	41.4831i	−1.93838	+	1.93838i
$459$	0.408279	+	0.408279i	0.0190568	+	0.0190568i
$460$	−21.9660	+	21.9660i	−1.02417	+	1.02417i
$461$		−	5.35278i		−	0.249304i	−0.992201	−	0.124652i	$-0.960219\pi$
$461$		−	5.35278i		−	0.249304i	0.992201	−	0.124652i	$-0.0397814\pi$
$462$	32.3692	+	16.1343i	1.50595	+	0.750637i
$463$			34.6100i			1.60846i	0.594317	+	0.804231i	$0.297422\pi$
$463$			34.6100i			1.60846i	−0.594317	+	0.804231i	$0.702578\pi$
$464$	−67.7186	+	67.7186i	−3.14376	+	3.14376i
$465$	0.563471	+	0.563471i	0.0261304	+	0.0261304i
$466$		−	13.3356i		−	0.617762i
$467$	−14.9925	+	14.9925i	−0.693771	+	0.693771i	−0.963059	−	0.269289i	$-0.913211\pi$
$467$	−14.9925	+	14.9925i	−0.693771	+	0.693771i	0.269289	+	0.963059i	$0.413211\pi$
$468$	−46.2619			−2.13846
$469$		−	16.2905i		−	0.752225i
$470$	14.1860	−	14.1860i	0.654352	−	0.654352i
$471$	−1.75203	+	1.75203i	−0.0807293	+	0.0807293i
$472$	−7.68899			−0.353915
$473$	33.4517	−	11.1968i	1.53811	−	0.514830i
$474$	22.2550			1.02220
$475$	4.06003			0.186287
$476$			2.70686i			0.124069i
$477$	15.1790	−	15.1790i	0.694998	−	0.694998i
$478$	22.3315	−	22.3315i	1.02142	−	1.02142i
$479$	−4.44195			−0.202958			−0.101479	−	0.994838i	$-0.532357\pi$
$479$	−4.44195			−0.202958			−0.101479	+	0.994838i	$0.532357\pi$
$480$	−26.0878	−	26.0878i	−1.19074	−	1.19074i
$481$	17.3741	−	17.3741i	0.792191	−	0.792191i
$482$	10.1535	−	10.1535i	0.462480	−	0.462480i
$483$			10.1417i			0.461465i
$484$	−45.4894	+	34.2942i	−2.06770	+	1.55883i
$485$	30.5063			1.38522
$486$	30.5966	−	30.5966i	1.38789	−	1.38789i
$487$			18.0205i			0.816585i	0.912851	+	0.408292i	$0.133876\pi$
$487$			18.0205i			0.816585i	−0.912851	+	0.408292i	$0.866124\pi$
$488$	−66.2670	+	5.83778i	−2.99977	+	0.264264i
$489$	−1.06470			−0.0481473
$490$	54.1405	+	54.1405i	2.44582	+	2.44582i
$491$	25.6549			1.15779			0.578894	−	0.815403i	$-0.303485\pi$
$491$	25.6549			1.15779			0.578894	+	0.815403i	$0.303485\pi$
$492$	35.2078			1.58729
$493$		−	0.924502i		−	0.0416375i
$494$	−40.7561	+	40.7561i	−1.83370	+	1.83370i
$495$	−7.55835	+	15.1638i	−0.339723	+	0.681563i
$496$	3.11399	+	3.11399i	0.139822	+	0.139822i
$497$		−	54.7797i		−	2.45721i
$498$	−13.2758	−	13.2758i	−0.594904	−	0.594904i
$499$	7.58522	+	7.58522i	0.339561	+	0.339561i	0.856202	−	0.516641i	$-0.172818\pi$
$499$	7.58522	+	7.58522i	0.339561	+	0.339561i	−0.516641	+	0.856202i	$0.672818\pi$
$500$	−52.4291			−2.34470
$501$			12.5205i			0.559374i
$502$	−4.01873			−0.179365
$503$		−	5.25940i		−	0.234505i	−0.993102	−	0.117252i	$-0.962591\pi$
$503$		−	5.25940i		−	0.234505i	0.993102	−	0.117252i	$-0.0374087\pi$
$504$	78.5248			3.49777
$505$	8.12257	−	8.12257i	0.361450	−	0.361450i
$506$	−19.8181	−	9.87826i	−0.881022	−	0.439142i
$507$		−	4.41888i		−	0.196249i
$508$			11.8166i			0.524276i
$509$	4.73808	+	4.73808i	0.210012	+	0.210012i	0.804272	−	0.594261i	$-0.202555\pi$
$509$	4.73808	+	4.73808i	0.210012	+	0.210012i	−0.594261	+	0.804272i	$0.702555\pi$
$510$	0.727021			0.0321930
$511$	−22.2772	+	22.2772i	−0.985484	+	0.985484i
$512$	5.95662	+	5.95662i	0.263248	+	0.263248i
$513$		−	24.5266i		−	1.08287i
$514$	−10.9130	−	10.9130i	−0.481352	−	0.481352i
$515$		−	10.4680i		−	0.461274i
$516$	−36.4918	+	36.4918i	−1.60646	+	1.60646i
$517$	9.23320	+	4.60225i	0.406076	+	0.202407i
$518$	−48.0447	+	48.0447i	−2.11096	+	2.11096i
$519$	11.7738	−	11.7738i	0.516811	−	0.516811i
$520$	−61.0225	+	61.0225i	−2.67601	+	2.67601i
$521$	15.9491	−	15.9491i	0.698742	−	0.698742i	−0.265397	−	0.964139i	$-0.585503\pi$
$521$	15.9491	−	15.9491i	0.698742	−	0.698742i	0.964139	+	0.265397i	$0.0855031\pi$
$522$	−43.6926			−1.91237
$523$	−3.69279	+	3.69279i	−0.161474	+	0.161474i	−0.783220	−	0.621745i	$-0.786424\pi$
$523$	−3.69279	+	3.69279i	−0.161474	+	0.161474i	0.621745	+	0.783220i	$0.286424\pi$
$524$	−29.8820			−1.30540
$525$	2.28622	−	2.28622i	0.0997787	−	0.0997787i
$526$	−50.1677	−	50.1677i	−2.18741	−	2.18741i
$527$	−0.0425125			−0.00185187
$528$	17.2766	−	34.6608i	0.751866	−	1.50842i
$529$			16.7907i			0.730031i
$530$		−	65.2377i		−	2.83374i
$531$	−1.35468	−	1.35468i	−0.0587881	−	0.0587881i
$532$	81.3047	−	81.3047i	3.52501	−	3.52501i
$533$		−	30.5421i		−	1.32293i
$534$	44.1848			1.91206
$535$		−	2.40084i		−	0.103797i
$536$	−31.9406			−1.37962
$537$		−	4.07986i		−	0.176059i
$538$	50.1593	+	50.1593i	2.16252	+	2.16252i
$539$	−17.5644	+	35.2382i	−0.756550	+	1.51782i
$540$		−	59.8264i		−	2.57452i
$541$	22.0845	+	22.0845i	0.949485	+	0.949485i	0.998784	−	0.0492988i	$-0.0156987\pi$
$541$	22.0845	+	22.0845i	0.949485	+	0.949485i	−0.0492988	+	0.998784i	$0.515699\pi$
$542$	−41.9483	−	41.9483i	−1.80183	−	1.80183i
$543$	7.23604	−	7.23604i	0.310528	−	0.310528i
$544$	1.96826			0.0843884
$545$		−	12.9372i		−	0.554167i
$546$			45.8998i			1.96433i
$547$	−3.48514	+	3.48514i	−0.149014	+	0.149014i	−0.777677	−	0.628664i	$-0.783602\pi$
$547$	−3.48514	+	3.48514i	−0.149014	+	0.149014i	0.628664	+	0.777677i	$0.283602\pi$
$548$			43.4066i			1.85424i
$549$	−12.7037	−	10.6467i	−0.542182	−	0.454389i
$550$	2.24070	+	6.69435i	0.0955439	+	0.285448i
$551$	−27.7688	+	27.7688i	−1.18299	+	1.18299i
$552$	19.8848			0.846353
$553$			38.5133i			1.63775i
$554$			17.0279i			0.723446i
$555$	9.30907	+	9.30907i	0.395148	+	0.395148i
$556$	−47.5991	−	47.5991i	−2.01865	−	2.01865i
$557$	18.5181	−	18.5181i	0.784639	−	0.784639i	−0.195971	−	0.980610i	$-0.562786\pi$
$557$	18.5181	−	18.5181i	0.784639	−	0.784639i	0.980610	+	0.195971i	$0.0627858\pi$
$558$			2.00917i			0.0850550i
$559$	31.6560	+	31.6560i	1.33890	+	1.33890i
$560$	92.1575	−	92.1575i	3.89436	−	3.89436i
$561$	0.118666	+	0.354527i	0.00501008	+	0.0149682i
$562$	−44.3443			−1.87055
$563$	−31.5196			−1.32839			−0.664197	−	0.747558i	$-0.731226\pi$
$563$	−31.5196			−1.32839			−0.664197	+	0.747558i	$0.731226\pi$
$564$	−15.0928			−0.635522
$565$	43.3944			1.82562
$566$	−27.5409	−	27.5409i	−1.15763	−	1.15763i
$567$	5.74600	+	5.74600i	0.241309	+	0.241309i
$568$	−107.406			−4.50666
$569$			25.5203i			1.06987i	0.844894	+	0.534934i	$0.179664\pi$
$569$			25.5203i			1.06987i	−0.844894	+	0.534934i	$0.820336\pi$
$570$	−21.8372	−	21.8372i	−0.914659	−	0.914659i
$571$		−	0.239680i		−	0.0100303i	−0.999987	−	0.00501514i	$-0.998404\pi$
$571$		−	0.239680i		−	0.0100303i	0.999987	−	0.00501514i	$-0.00159638\pi$
$572$	−64.7054	−	32.2522i	−2.70547	−	1.34853i
$573$	9.57202	−	9.57202i	0.399877	−	0.399877i
$574$			84.4583i			3.52522i
$575$	−1.39974	+	1.39974i	−0.0583732	+	0.0583732i
$576$		−	40.1204i		−	1.67168i
$577$	5.35273	+	5.35273i	0.222837	+	0.222837i	0.809692	−	0.586855i	$-0.199634\pi$
$577$	5.35273	+	5.35273i	0.222837	+	0.222837i	−0.586855	+	0.809692i	$0.699634\pi$
$578$	32.1806	−	32.1806i	1.33854	−	1.33854i
$579$	8.95035	+	8.95035i	0.371964	+	0.371964i
$580$	−67.7351	+	67.7351i	−2.81255	+	2.81255i
$581$	22.9744	−	22.9744i	0.953140	−	0.953140i
$582$	−22.4951	−	22.4951i	−0.932453	−	0.932453i
$583$	31.8128	−	10.6482i	1.31755	−	0.441005i
$584$	43.6786	+	43.6786i	1.80743	+	1.80743i
$585$	−21.5024			−0.889016
$586$	27.3443	+	27.3443i	1.12958	+	1.12958i
$587$	11.2206	+	11.2206i	0.463124	+	0.463124i	0.899678	−	0.436554i	$-0.143801\pi$
$587$	11.2206	+	11.2206i	0.463124	+	0.463124i	−0.436554	+	0.899678i	$0.643801\pi$
$588$		−	57.6013i		−	2.37544i
$589$	1.27693	+	1.27693i	0.0526149	+	0.0526149i
$590$	−5.82227			−0.239699
$591$		−	5.57000i		−	0.229119i
$592$	51.4460	+	51.4460i	2.11442	+	2.11442i
$593$	−28.0276	−	28.0276i	−1.15096	−	1.15096i	−0.986361	−	0.164596i	$-0.947368\pi$
$593$	−28.0276	−	28.0276i	−1.15096	−	1.15096i	−0.164596	−	0.986361i	$-0.552632\pi$
$594$	40.4404	−	13.5360i	1.65929	−	0.555391i
$595$			1.25814i			0.0515789i
$596$		−	99.9609i		−	4.09456i
$597$			14.2903i			0.584863i
$598$		−	28.1022i		−	1.14918i
$599$	−22.9762	+	22.9762i	−0.938780	+	0.938780i	−0.998231	−	0.0594509i	$-0.981065\pi$
$599$	−22.9762	+	22.9762i	−0.938780	+	0.938780i	0.0594509	+	0.998231i	$0.481065\pi$
$600$	−4.48256	−	4.48256i	−0.183000	−	0.183000i
$601$	17.3113			0.706144			0.353072	−	0.935596i	$-0.385137\pi$
$601$	17.3113			0.706144			0.353072	+	0.935596i	$0.385137\pi$
$602$	−87.5383	−	87.5383i	−3.56780	−	3.56780i
$603$	−5.62743	−	5.62743i	−0.229167	−	0.229167i
$604$	−61.7408	−	61.7408i	−2.51220	−	2.51220i
$605$	−21.1434	+	15.9399i	−0.859601	+	0.648048i
$606$	−11.9791			−0.486617
$607$			10.5321i			0.427484i	0.976890	+	0.213742i	$0.0685652\pi$
$607$			10.5321i			0.427484i	−0.976890	+	0.213742i	$0.931435\pi$
$608$	−59.1196	−	59.1196i	−2.39762	−	2.39762i
$609$			31.2734i			1.26726i
$610$	−50.1788	+	4.42049i	−2.03168	+	0.178980i
$611$			13.0927i			0.529676i
$612$	0.935066	+	0.935066i	0.0377978	+	0.0377978i
$613$	−24.2405			−0.979064			−0.489532	−	0.871985i	$-0.662832\pi$
$613$	−24.2405			−0.979064			−0.489532	+	0.871985i	$0.662832\pi$
$614$		−	49.0867i		−	1.98098i
$615$	16.3645			0.659881
$616$	109.831	+	54.7448i	4.42521	+	2.20573i
$617$	−12.3115	+	12.3115i	−0.495644	+	0.495644i	−0.910079	−	0.414435i	$-0.863979\pi$
$617$	−12.3115	+	12.3115i	−0.495644	+	0.495644i	0.414435	+	0.910079i	$0.363979\pi$
$618$	−7.71903	+	7.71903i	−0.310505	+	0.310505i
$619$	−5.76806			−0.231838			−0.115919	−	0.993259i	$-0.536981\pi$
$619$	−5.76806			−0.231838			−0.115919	+	0.993259i	$0.536981\pi$
$620$	3.11475	+	3.11475i	0.125091	+	0.125091i
$621$	8.45580	+	8.45580i	0.339320	+	0.339320i
$622$			74.3693i			2.98194i
$623$			76.4639i			3.06346i
$624$	49.1493			1.96755
$625$	−28.3409			−1.13364
$626$			32.8531i			1.31307i
$627$	7.08446	−	14.2131i	0.282926	−	0.567616i
$628$	−9.68484	+	9.68484i	−0.386467	+	0.386467i
$629$	−0.702347			−0.0280044
$630$	59.4607			2.36897
$631$	4.38455	+	4.38455i	0.174546	+	0.174546i	0.788973	−	0.614427i	$-0.210613\pi$
$631$	4.38455	+	4.38455i	0.174546	+	0.174546i	−0.614427	+	0.788973i	$0.710613\pi$
$632$	75.5125			3.00373
$633$	−2.14136	−	2.14136i	−0.0851114	−	0.0851114i
$634$	50.2350	+	50.2350i	1.99509	+	1.99509i
$635$			5.49233i			0.217956i
$636$	−34.7039	+	34.7039i	−1.37610	+	1.37610i
$637$	−49.9680			−1.97981
$638$	−61.1118	−	30.4609i	−2.41944	−	1.20596i
$639$	−18.9233	−	18.9233i	−0.748593	−	0.748593i
$640$	−30.5265	−	30.5265i	−1.20667	−	1.20667i
$641$	27.1815	+	27.1815i	1.07360	+	1.07360i	0.997067	+	0.0765377i	$0.0243866\pi$
$641$	27.1815	+	27.1815i	1.07360	+	1.07360i	0.0765377	+	0.997067i	$0.475613\pi$
$642$	−1.77036	+	1.77036i	−0.0698707	+	0.0698707i
$643$	17.9404	−	17.9404i	0.707500	−	0.707500i	−0.258509	−	0.966009i	$-0.583231\pi$
$643$	17.9404	−	17.9404i	0.707500	−	0.707500i	0.966009	+	0.258509i	$0.0832310\pi$
$644$			56.0614i			2.20913i
$645$	−16.9613	+	16.9613i	−0.667851	+	0.667851i
$646$	1.64756			0.0648225
$647$	33.4764	+	33.4764i	1.31609	+	1.31609i	0.916843	+	0.399249i	$0.130729\pi$
$647$	33.4764	+	33.4764i	1.31609	+	1.31609i	0.399249	+	0.916843i	$0.369271\pi$
$648$	11.2661	−	11.2661i	0.442575	−	0.442575i
$649$	−0.950324	−	2.83920i	−0.0373035	−	0.111448i
$650$	−6.33498	+	6.33498i	−0.248479	+	0.248479i
$651$	1.43809			0.0563630
$652$	−5.88542			−0.230491
$653$	3.12189	+	3.12189i	0.122169	+	0.122169i	0.765548	−	0.643379i	$-0.222468\pi$
$653$	3.12189	+	3.12189i	0.122169	+	0.122169i	−0.643379	+	0.765548i	$0.722468\pi$
$654$	−9.53978	+	9.53978i	−0.373035	+	0.373035i
$655$	−13.8891			−0.542691
$656$	90.4376			3.53099
$657$			15.3910i			0.600459i
$658$		−	36.2054i		−	1.41143i
$659$	25.5707			0.996094			0.498047	−	0.867150i	$-0.334051\pi$
$659$	25.5707			0.996094			0.498047	+	0.867150i	$0.334051\pi$
$660$	17.2808	−	34.6693i	0.672653	−	1.34950i
$661$	−18.0328	+	18.0328i	−0.701395	+	0.701395i	−0.964710	−	0.263315i	$-0.915184\pi$
$661$	−18.0328	+	18.0328i	−0.701395	+	0.701395i	0.263315	+	0.964710i	$0.415184\pi$
$662$	−32.5431			−1.26482
$663$	−0.335496	+	0.335496i	−0.0130296	+	0.0130296i
$664$	−45.0457	−	45.0457i	−1.74811	−	1.74811i
$665$	37.7903	−	37.7903i	1.46544	−	1.46544i
$666$			33.1934i			1.28622i
$667$		−	19.1472i		−	0.741382i
$668$			69.2106i			2.67784i
$669$	−10.1337	−	10.1337i	−0.391793	−	0.391793i
$670$	−24.1861			−0.934391
$671$	−10.3459	−	23.7479i	−0.399400	−	0.916777i
$672$	−66.5809			−2.56842
$673$	22.7898	+	22.7898i	0.878483	+	0.878483i	0.993378	−	0.114895i	$-0.0366532\pi$
$673$	22.7898	+	22.7898i	0.878483	+	0.878483i	−0.114895	+	0.993378i	$0.536653\pi$
$674$			49.3242i			1.89990i
$675$		−	3.81232i		−	0.146736i
$676$		−	24.4266i		−	0.939486i
$677$	8.82713	−	8.82713i	0.339254	−	0.339254i	−0.516832	−	0.856087i	$-0.672889\pi$
$677$	8.82713	−	8.82713i	0.339254	−	0.339254i	0.856087	+	0.516832i	$0.172889\pi$
$678$	−31.9988	−	31.9988i	−1.22890	−	1.22890i
$679$	38.9289	−	38.9289i	1.49395	−	1.49395i
$680$	2.46683			0.0945986
$681$	−0.276274	+	0.276274i	−0.0105868	+	0.0105868i
$682$	−1.40072	+	2.81018i	−0.0536365	+	0.107607i
$683$	−40.5359			−1.55106			−0.775531	−	0.631310i	$-0.782518\pi$
$683$	−40.5359			−1.55106			−0.775531	+	0.631310i	$0.782518\pi$
$684$		−	56.1723i		−	2.14780i
$685$			20.1753i			0.770859i
$686$	56.7007			2.16484
$687$	20.5137			0.782648
$688$	−93.7357	+	93.7357i	−3.57364	+	3.57364i
$689$	30.1050	+	30.1050i	1.14691	+	1.14691i
$690$	15.0572			0.573218
$691$	−19.5168			−0.742454			−0.371227	−	0.928542i	$-0.621063\pi$
$691$	−19.5168			−0.742454			−0.371227	+	0.928542i	$0.621063\pi$
$692$	65.0828	−	65.0828i	2.47408	−	2.47408i
$693$	9.70531	+	28.9957i	0.368674	+	1.10145i
$694$	39.9281	−	39.9281i	1.51565	−	1.51565i
$695$	−22.1240	−	22.1240i	−0.839210	−	0.839210i
$696$	61.3175			2.32423
$697$	−0.617332	+	0.617332i	−0.0233831	+	0.0233831i
$698$			81.1204i			3.07045i
$699$	−3.29730	+	3.29730i	−0.124715	+	0.124715i
$700$	12.6377	−	12.6377i	0.477661	−	0.477661i
$701$	−9.48871	−	9.48871i	−0.358384	−	0.358384i	0.504833	−	0.863217i	$-0.331554\pi$
$701$	−9.48871	−	9.48871i	−0.358384	−	0.358384i	−0.863217	+	0.504833i	$0.831554\pi$
$702$	38.2695	+	38.2695i	1.44439	+	1.44439i
$703$	21.0960	+	21.0960i	0.795652	+	0.795652i
$704$	27.9705	−	56.1155i	1.05418	−	2.11493i
$705$	−7.01511			−0.264204
$706$	−60.8790	+	60.8790i	−2.29121	+	2.29121i
$707$		−	20.7304i		−	0.779645i
$708$	3.09722	+	3.09722i	0.116401	+	0.116401i
$709$	20.0431	+	20.0431i	0.752735	+	0.752735i	0.974989	−	0.222254i	$-0.0713414\pi$
$709$	20.0431	+	20.0431i	0.752735	+	0.752735i	−0.222254	+	0.974989i	$0.571341\pi$
$710$	−81.3302			−3.05227
$711$	13.3041	+	13.3041i	0.498944	+	0.498944i
$712$	149.922			5.61856
$713$	−0.880470			−0.0329738
$714$	0.927748	−	0.927748i	0.0347201	−	0.0347201i
$715$	−30.0749	−	14.9907i	−1.12474	−	0.560622i
$716$		−	22.5526i		−	0.842830i
$717$	−11.0431			−0.412413
$718$	26.8969			1.00378
$719$			14.4564i			0.539133i	0.962982	+	0.269567i	$0.0868804\pi$
$719$			14.4564i			0.539133i	−0.962982	+	0.269567i	$0.913120\pi$
$720$		−	63.6703i		−	2.37285i
$721$	−13.3581	−	13.3581i	−0.497483	−	0.497483i
$722$	−13.4898	−	13.4898i	−0.502040	−	0.502040i
$723$	−5.02100			−0.186733
$724$	39.9993	−	39.9993i	1.48656	−	1.48656i
$725$	−4.31629	+	4.31629i	−0.160303	+	0.160303i
$726$	27.3450	+	3.83704i	1.01487	+	0.142406i
$727$	35.8097			1.32811			0.664053	−	0.747685i	$-0.268835\pi$
$727$	35.8097			1.32811			0.664053	+	0.747685i	$0.268835\pi$
$728$			155.741i			5.77214i
$729$	−9.51852			−0.352538
$730$	33.0744	+	33.0744i	1.22414	+	1.22414i
$731$		−	1.27969i		−	0.0473310i
$732$	29.0447	+	24.3417i	1.07352	+	0.899694i
$733$			2.24531i			0.0829325i	0.999140	+	0.0414663i	$0.0132029\pi$
$733$			2.24531i			0.0829325i	−0.999140	+	0.0414663i	$0.986797\pi$
$734$	−35.4412	−	35.4412i	−1.30816	−	1.30816i
$735$		−	26.7730i		−	0.987535i
$736$	40.7643			1.50259
$737$	−3.94771	−	11.7942i	−0.145416	−	0.434445i
$738$	29.1755	+	29.1755i	1.07397	+	1.07397i
$739$	−17.5671	−	17.5671i	−0.646215	−	0.646215i	0.305861	−	0.952076i	$-0.401056\pi$
$739$	−17.5671	−	17.5671i	−0.646215	−	0.646215i	−0.952076	+	0.305861i	$0.901056\pi$
$740$	51.4585	+	51.4585i	1.89165	+	1.89165i
$741$	20.1543			0.740385
$742$	−83.2495	−	83.2495i	−3.05619	−	3.05619i
$743$	24.1457	−	24.1457i	0.885822	−	0.885822i	−0.108297	−	0.994119i	$-0.534540\pi$
$743$	24.1457	−	24.1457i	0.885822	−	0.885822i	0.994119	+	0.108297i	$0.0345398\pi$
$744$		−	2.81964i		−	0.103373i
$745$		−	46.4616i		−	1.70222i
$746$		−	87.4845i		−	3.20303i
$747$		−	15.8727i		−	0.580752i
$748$	0.655960	+	1.95975i	0.0239843	+	0.0716556i
$749$	−3.06370	−	3.06370i	−0.111945	−	0.111945i
$750$	17.9695	+	17.9695i	0.656153	+	0.656153i
$751$		−	22.2220i		−	0.810892i	−0.914119	−	0.405446i	$-0.867116\pi$
$751$		−	22.2220i		−	0.810892i	0.914119	−	0.405446i	$-0.132884\pi$
$752$	−38.7686			−1.41374
$753$	0.993649	+	0.993649i	0.0362106	+	0.0362106i
$754$		−	86.6570i		−	3.15586i
$755$	−28.6970	−	28.6970i	−1.04439	−	1.04439i
$756$	−76.3442	−	76.3442i	−2.77661	−	2.77661i
$757$	42.1790			1.53302			0.766512	−	0.642230i	$-0.221991\pi$
$757$	42.1790			1.53302			0.766512	+	0.642230i	$0.221991\pi$
$758$	−22.0059	−	22.0059i	−0.799290	−	0.799290i
$759$	2.45767	+	7.34256i	0.0892078	+	0.266518i
$760$	−74.0950	−	74.0950i	−2.68771	−	2.68771i
$761$	−25.4376	+	25.4376i	−0.922112	+	0.922112i	−0.997179	−	0.0750665i	$-0.976083\pi$
$761$	−25.4376	+	25.4376i	−0.922112	+	0.922112i	0.0750665	+	0.997179i	$0.476083\pi$
$762$	4.05001	−	4.05001i	0.146716	−	0.146716i
$763$	−16.5090	−	16.5090i	−0.597667	−	0.597667i
$764$	52.9120	−	52.9120i	1.91429	−	1.91429i
$765$	0.434617	+	0.434617i	0.0157136	+	0.0157136i
$766$		−	35.4510i		−	1.28090i
$767$	2.68678	−	2.68678i	0.0970142	−	0.0970142i
$768$			9.59669i			0.346291i
$769$	−22.8015	+	22.8015i	−0.822242	+	0.822242i	−0.986429	−	0.164187i	$-0.947500\pi$
$769$	−22.8015	+	22.8015i	−0.822242	+	0.822242i	0.164187	+	0.986429i	$0.447500\pi$
$770$	83.1663	+	41.4540i	2.99711	+	1.49390i
$771$			5.39657i			0.194353i
$772$	49.4756	+	49.4756i	1.78067	+	1.78067i
$773$			15.8969i			0.571770i	0.958264	+	0.285885i	$0.0922876\pi$
$773$			15.8969i			0.571770i	−0.958264	+	0.285885i	$0.907712\pi$
$774$	−60.4790			−2.17387
$775$	0.198481	+	0.198481i	0.00712966	+	0.00712966i
$776$	−76.3274	−	76.3274i	−2.74000	−	2.74000i
$777$	23.7585			0.852332
$778$	−14.6969			−0.526909
$779$	37.0850			1.32871
$780$	49.1613			1.76026
$781$	−13.2749	−	39.6602i	−0.475013	−	1.41915i
$782$	−0.568015	+	0.568015i	−0.0203122	+	0.0203122i
$783$	26.0746	+	26.0746i	0.931830	+	0.931830i
$784$		−	147.959i		−	5.28425i
$785$	−4.50150	+	4.50150i	−0.160665	+	0.160665i
$786$	10.2417	+	10.2417i	0.365310	+	0.365310i
$787$	6.83658	+	6.83658i	0.243698	+	0.243698i	0.818378	−	0.574680i	$-0.194874\pi$
$787$	6.83658	+	6.83658i	0.243698	+	0.243698i	−0.574680	+	0.818378i	$0.694874\pi$
$788$		−	30.7898i		−	1.09684i
$789$			24.8084i			0.883201i
$790$	57.1798			2.03436
$791$	55.3754	−	55.3754i	1.96892	−	1.96892i
$792$	56.8515	−	19.0291i	2.02013	−	0.676169i
$793$	21.1159	−	25.1958i	0.749849	−	0.894727i
$794$		−	26.1681i		−	0.928669i
$795$	−16.1303	+	16.1303i	−0.572083	+	0.572083i
$796$			78.9937i			2.79986i
$797$		−	14.6402i		−	0.518583i	−0.965799	−	0.259291i	$-0.916511\pi$
$797$		−	14.6402i		−	0.518583i	0.965799	−	0.259291i	$-0.0834890\pi$
$798$	−55.7326			−1.97291
$799$	0.264636	−	0.264636i	0.00936217	−	0.00936217i
$800$	−9.18935	−	9.18935i	−0.324893	−	0.324893i
$801$	26.4139	+	26.4139i	0.933289	+	0.933289i
$802$			100.337i			3.54302i
$803$	−10.7301	+	21.5270i	−0.378655	+	0.759671i
$804$	12.8661	+	12.8661i	0.453751	+	0.453751i
$805$			26.0572i			0.918396i
$806$	−3.98486			−0.140361
$807$		−	24.8042i		−	0.873150i
$808$	−40.6458			−1.42991
$809$		−	50.7981i		−	1.78597i	−0.450089	−	0.892984i	$-0.648608\pi$
$809$		−	50.7981i		−	1.78597i	0.450089	−	0.892984i	$-0.351392\pi$
$810$	8.53095	−	8.53095i	0.299747	−	0.299747i
$811$	21.8915	+	21.8915i	0.768713	+	0.768713i	0.977880	−	0.209167i	$-0.0670751\pi$
$811$	21.8915	+	21.8915i	0.768713	+	0.768713i	−0.209167	+	0.977880i	$0.567075\pi$
$812$			172.873i			6.06664i
$813$			20.7438i			0.727517i
$814$	−23.1413	+	46.4268i	−0.811101	+	1.62726i
$815$	−2.73553			−0.0958215
$816$	−0.993428	−	0.993428i	−0.0347769	−	0.0347769i
$817$	−38.4374	+	38.4374i	−1.34475	+	1.34475i
$818$	−54.7451			−1.91412
$819$	−27.4391	+	27.4391i	−0.958801	+	0.958801i
$820$	90.4596			3.15899
$821$	23.6107	−	23.6107i	0.824019	−	0.824019i	−0.162663	−	0.986682i	$-0.552008\pi$
$821$	23.6107	−	23.6107i	0.824019	−	0.824019i	0.986682	+	0.162663i	$0.0520083\pi$
$822$	14.8771	−	14.8771i	0.518900	−	0.518900i
$823$	−24.6667	+	24.6667i	−0.859827	+	0.859827i	−0.991317	−	0.131491i	$-0.958024\pi$
$823$	−24.6667	+	24.6667i	−0.859827	+	0.859827i	0.131491	+	0.991317i	$0.458024\pi$
$824$	−26.1912	+	26.1912i	−0.912412	+	0.912412i
$825$	1.10118	−	2.20923i	0.0383383	−	0.0769156i
$826$	−7.42977	+	7.42977i	−0.258515	+	0.258515i
$827$		−	17.8404i		−	0.620373i	−0.950676	−	0.310186i	$-0.899609\pi$
$827$		−	17.8404i		−	0.620373i	0.950676	−	0.310186i	$-0.100391\pi$
$828$	19.3660	+	19.3660i	0.673015	+	0.673015i
$829$			25.3250i			0.879575i	0.898102	+	0.439787i	$0.144946\pi$
$829$			25.3250i			0.879575i	−0.898102	+	0.439787i	$0.855054\pi$
$830$	−34.1096	−	34.1096i	−1.18396	−	1.18396i
$831$	4.21023	−	4.21023i	0.146051	−	0.146051i
$832$	79.5721			2.75867
$833$	1.00998	+	1.00998i	0.0349936	+	0.0349936i
$834$			32.6282i			1.12982i
$835$			32.1689i			1.11325i
$836$	39.1614	−	78.5669i	1.35442	−	2.71729i
$837$	1.19902	−	1.19902i	0.0414442	−	0.0414442i
$838$	30.4847			1.05308
$839$			37.4961i			1.29451i	0.762273	+	0.647255i	$0.224083\pi$
$839$			37.4961i			1.29451i	−0.762273	+	0.647255i	$0.775917\pi$
$840$	−83.4462			−2.87917
$841$		−	30.0430i		−	1.03596i
$842$	36.5440			1.25939
$843$	10.9643	+	10.9643i	0.377631	+	0.377631i
$844$	−11.8370	−	11.8370i	−0.407446	−	0.407446i
$845$		−	11.3534i		−	0.390570i
$846$	−12.5069	−	12.5069i	−0.429996	−	0.429996i
$847$	−6.64018	+	47.3218i	−0.228159	+	1.62600i
$848$	−89.1432	+	89.1432i	−3.06119	+	3.06119i
$849$			13.6192i			0.467410i
$850$	0.256091			0.00878386
$851$	−14.5462			−0.498637
$852$	43.2645	+	43.2645i	1.48222	+	1.48222i
$853$	−33.7061			−1.15407			−0.577037	−	0.816718i	$-0.695791\pi$
$853$	−33.7061			−1.15407			−0.577037	+	0.816718i	$0.695791\pi$
$854$	−58.3920	+	69.6739i	−1.99813	+	2.38419i
$855$		−	26.1088i		−	0.892900i
$856$	−6.00696	+	6.00696i	−0.205314	+	0.205314i
$857$	18.1551			0.620166			0.310083	−	0.950710i	$-0.399643\pi$
$857$	18.1551			0.620166			0.310083	+	0.950710i	$0.399643\pi$
$858$	11.1230	+	33.2312i	0.379733	+	1.13449i
$859$			11.3449i			0.387084i	0.981092	+	0.193542i	$0.0619977\pi$
$859$			11.3449i			0.387084i	−0.981092	+	0.193542i	$0.938002\pi$
$860$	−93.7585	+	93.7585i	−3.19714	+	3.19714i
$861$	20.8827	−	20.8827i	0.711680	−	0.711680i
$862$	17.2215	+	17.2215i	0.586565	+	0.586565i
$863$	−26.7684			−0.911208			−0.455604	−	0.890182i	$-0.650577\pi$
$863$	−26.7684			−0.911208			−0.455604	+	0.890182i	$0.650577\pi$
$864$	−55.5127	+	55.5127i	−1.88858	+	1.88858i
$865$	30.2504	−	30.2504i	1.02854	−	1.02854i
$866$			98.8931i			3.36052i
$867$	−15.9136			−0.540454
$868$	7.94943			0.269821
$869$	9.33300	+	27.8834i	0.316600	+	0.945878i
$870$	46.4309			1.57416
$871$	11.1611	−	11.1611i	0.378179	−	0.378179i
$872$	−32.3691	+	32.3691i	−1.09616	+	1.09616i
$873$		−	26.8954i		−	0.910272i
$874$	34.1224			1.15421
$875$	−31.0971	+	31.0971i	−1.05127	+	1.05127i
$876$		−	35.1886i		−	1.18891i
$877$	−3.72610	−	3.72610i	−0.125821	−	0.125821i	0.641392	−	0.767213i	$-0.278357\pi$
$877$	−3.72610	−	3.72610i	−0.125821	−	0.125821i	−0.767213	+	0.641392i	$0.778357\pi$
$878$	−7.22208	+	7.22208i	−0.243733	+	0.243733i
$879$		−	13.5220i		−	0.456086i
$880$	44.3887	−	89.0542i	1.49634	−	3.00202i
$881$		−	20.8297i		−	0.701771i	−0.936418	−	0.350886i	$-0.885881\pi$
$881$		−	20.8297i		−	0.701771i	0.936418	−	0.350886i	$-0.114119\pi$
$882$	47.7322	−	47.7322i	1.60723	−	1.60723i
$883$	2.91215	+	2.91215i	0.0980015	+	0.0980015i	0.754408	−	0.656406i	$-0.227924\pi$
$883$	2.91215	+	2.91215i	0.0980015	+	0.0980015i	−0.656406	+	0.754408i	$0.727924\pi$
$884$	−1.85455	+	1.85455i	−0.0623752	+	0.0623752i
$885$	1.43958	+	1.43958i	0.0483911	+	0.0483911i
$886$	−27.1198	−	27.1198i	−0.911109	−	0.911109i
$887$	−15.5014	−	15.5014i	−0.520485	−	0.520485i	0.397233	−	0.917718i	$-0.369971\pi$
$887$	−15.5014	−	15.5014i	−0.520485	−	0.520485i	−0.917718	+	0.397233i	$0.869971\pi$
$888$		−	46.5831i		−	1.56322i
$889$	7.00873	+	7.00873i	0.235065	+	0.235065i
$890$	113.524			3.80534
$891$	5.55251	+	2.76763i	0.186016	+	0.0927190i
$892$	−56.0172	−	56.0172i	−1.87559	−	1.87559i
$893$	−15.8975			−0.531990
$894$	−34.2605	+	34.2605i	−1.14584	+	1.14584i
$895$		−	10.4824i		−	0.350388i
$896$	−77.9094			−2.60277
$897$	−6.94840	+	6.94840i	−0.232000	+	0.232000i
$898$	−0.555170	−	0.555170i	−0.0185263	−	0.0185263i
$899$	−2.71505			−0.0905519
$900$		−	8.73122i		−	0.291041i
$901$		−	1.21699i		−	0.0405439i
$902$	20.4670	+	61.1473i	0.681475	+	2.03598i
$903$			43.2885i			1.44055i
$904$	−108.574	−	108.574i	−3.61111	−	3.61111i
$905$	18.5916	−	18.5916i	0.618005	−	0.618005i
$906$			42.3220i			1.40605i
$907$	27.7548	−	27.7548i	0.921582	−	0.921582i	−0.0755592	−	0.997141i	$-0.524074\pi$
$907$	27.7548	−	27.7548i	0.921582	−	0.921582i	0.997141	+	0.0755592i	$0.0240742\pi$
$908$	−1.52718	+	1.52718i	−0.0506813	+	0.0506813i
$909$	−7.16115	−	7.16115i	−0.237520	−	0.237520i
$910$			117.930i			3.90936i
$911$	17.7316			0.587475			0.293738	−	0.955886i	$-0.405101\pi$
$911$	17.7316			0.587475			0.293738	+	0.955886i	$0.405101\pi$
$912$			59.6783i			1.97614i
$913$	11.0659	−	22.2008i	0.366228	−	0.734739i
$914$		−	28.0502i		−	0.927819i
$915$	13.4999	+	11.3140i	0.446294	+	0.374028i
$916$	113.396			3.74669
$917$	−17.7238	+	17.7238i	−0.585291	+	0.585291i
$918$		−	1.54704i		−	0.0510600i
$919$	−36.4935			−1.20381			−0.601904	−	0.798569i	$-0.705591\pi$
$919$	−36.4935			−1.20381			−0.601904	+	0.798569i	$0.705591\pi$
$920$	51.0901			1.68439
$921$	−12.1369	+	12.1369i	−0.399924	+	0.399924i
$922$	−10.1413	+	10.1413i	−0.333986	+	0.333986i
$923$	37.5312	−	37.5312i	1.23535	−	1.23535i
$924$	−22.1894	−	66.2932i	−0.729977	−	2.18088i
$925$	3.27910	+	3.27910i	0.107816	+	0.107816i
$926$	65.5717	−	65.5717i	2.15482	−	2.15482i
$927$	−9.22895			−0.303118
$928$	125.702			4.12637
$929$		−	26.0195i		−	0.853671i	−0.904329	−	0.426836i	$-0.859628\pi$
$929$		−	26.0195i		−	0.853671i	0.904329	−	0.426836i	$-0.140372\pi$
$930$		−	2.13509i		−	0.0700124i
$931$		−	60.6724i		−	1.98846i
$932$	−18.2268	+	18.2268i	−0.597037	+	0.597037i
$933$	18.3881	−	18.3881i	0.602001	−	0.602001i
$934$	56.8093			1.85886
$935$	0.304889	+	0.910888i	0.00997093	+	0.0297892i
$936$	53.7996	+	53.7996i	1.75849	+	1.75849i
$937$			24.9087i			0.813731i	0.913488	+	0.406866i	$0.133378\pi$
$937$			24.9087i			0.813731i	−0.913488	+	0.406866i	$0.866622\pi$
$938$	−30.8638	+	30.8638i	−1.00774	+	1.00774i
$939$	8.12307	−	8.12307i	0.265086	−	0.265086i
$940$	−38.7780			−1.26480
$941$	2.28036	+	2.28036i	0.0743376	+	0.0743376i	0.743298	−	0.668960i	$-0.233260\pi$
$941$	2.28036	+	2.28036i	0.0743376	+	0.0743376i	−0.668960	+	0.743298i	$0.733260\pi$
$942$	6.63875			0.216302
$943$	−12.7855	+	12.7855i	−0.416352	+	0.416352i
$944$	7.95577	+	7.95577i	0.258938	+	0.258938i
$945$	−35.4846	−	35.4846i	−1.15432	−	1.15432i
$946$	−84.5906	−	42.1638i	−2.75028	−	1.37086i
$947$	−26.8256	+	26.8256i	−0.871713	+	0.871713i	−0.992659	−	0.120946i	$-0.961407\pi$
$947$	−26.8256	+	26.8256i	−0.871713	+	0.871713i	0.120946	+	0.992659i	$0.461407\pi$
$948$	−30.4174	−	30.4174i	−0.987912	−	0.987912i
$949$	−30.5254			−0.990898
$950$	−7.69209	−	7.69209i	−0.249564	−	0.249564i
$951$		−	24.8417i		−	0.805547i
$952$	3.14791	−	3.14791i	0.102024	−	0.102024i
$953$	−13.3235	+	13.3235i	−0.431589	+	0.431589i	−0.889169	−	0.457580i	$-0.848716\pi$
$953$	−13.3235	+	13.3235i	−0.431589	+	0.431589i	0.457580	+	0.889169i	$0.348716\pi$
$954$	−57.5159			−1.86215
$955$	24.5934	−	24.5934i	0.795824	−	0.795824i
$956$	−61.0440			−1.97430
$957$	7.57856	+	22.6418i	0.244980	+	0.731904i
$958$	8.41568	+	8.41568i	0.271898	+	0.271898i
$959$	25.7456	+	25.7456i	0.831369	+	0.831369i
$960$			42.6349i			1.37603i
$961$		−	30.8752i		−	0.995973i
$962$	−65.8335			−2.12256
$963$	−2.11666			−0.0682086
$964$	−27.7550			−0.893929
$965$	22.9962	+	22.9962i	0.740273	+	0.740273i
$966$	19.2144	−	19.2144i	0.618214	−	0.618214i
$967$	−7.24187			−0.232883			−0.116441	−	0.993198i	$-0.537149\pi$
$967$	−7.24187			−0.232883			−0.116441	+	0.993198i	$0.537149\pi$
$968$	92.7833	+	13.0193i	2.98217	+	0.418457i
$969$	−0.407367	−	0.407367i	−0.0130865	−	0.0130865i
$970$	−57.7968	−	57.7968i	−1.85574	−	1.85574i
$971$	−12.4269			−0.398799			−0.199400	−	0.979918i	$-0.563899\pi$
$971$	−12.4269			−0.398799			−0.199400	+	0.979918i	$0.563899\pi$
$972$	−83.6370			−2.68266
$973$	−56.4646			−1.81017
$974$	34.1413	−	34.1413i	1.09396	−	1.09396i
$975$	3.13271			0.100327
$976$	74.6065	+	62.5259i	2.38810	+	2.00140i
$977$	−17.5549			−0.561631			−0.280815	−	0.959762i	$-0.590605\pi$
$977$	−17.5549			−0.561631			−0.280815	+	0.959762i	$0.590605\pi$
$978$	2.01716	+	2.01716i	0.0645018	+	0.0645018i
$979$	18.5297	+	55.3594i	0.592210	+	1.76929i
$980$		−	147.995i		−	4.72753i
$981$	−11.4059			−0.364161
$982$	−48.6054	−	48.6054i	−1.55106	−	1.55106i
$983$	19.8538	−	19.8538i	0.633239	−	0.633239i	−0.315640	−	0.948879i	$-0.602219\pi$
$983$	19.8538	−	19.8538i	0.633239	−	0.633239i	0.948879	+	0.315640i	$0.102219\pi$
$984$	−40.9445	−	40.9445i	−1.30526	−	1.30526i
$985$		−	14.3110i		−	0.455987i
$986$	−1.75155	+	1.75155i	−0.0557807	+	0.0557807i
$987$	−8.95195	+	8.95195i	−0.284944	+	0.284944i
$988$	111.408			3.54437
$989$		−	26.5034i		−	0.842760i
$990$	43.0492	−	14.4092i	1.36819	−	0.457956i
$991$	−61.1030			−1.94100			−0.970500	−	0.241101i	$-0.922492\pi$
$991$	−61.1030			−1.94100			−0.970500	+	0.241101i	$0.922492\pi$
$992$		−	5.78032i		−	0.183525i
$993$	8.04642	+	8.04642i	0.255346	+	0.255346i
$994$	−103.785	+	103.785i	−3.29186	+	3.29186i
$995$			36.7161i			1.16398i
$996$			36.2900i			1.14989i
$997$	−3.23491	+	3.23491i	−0.102451	+	0.102451i	−0.756474	−	0.654024i	$-0.773080\pi$
$997$	−3.23491	+	3.23491i	−0.102451	+	0.102451i	0.654024	+	0.756474i	$0.273080\pi$
$998$		−	28.7418i		−	0.909805i
$999$	19.8089	−	19.8089i	0.626727	−	0.626727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.3	✓	120
11.10	odd	2	inner	671.2.f.a.538.58	yes	120
61.11	odd	4	inner	671.2.f.a.560.58	yes	120
671.560	even	4	inner	671.2.f.a.560.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.3	✓	120	1.1	even	1	trivial
671.2.f.a.538.58	yes	120	11.10	odd	2	inner
671.2.f.a.560.3	yes	120	671.560	even	4	inner
671.2.f.a.560.58	yes	120	61.11	odd	4	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89459 - 1.89459i) q^{2} +0.936891i q^{3} +5.17893i q^{4} +2.40716i q^{5} +(1.77502 - 1.77502i) q^{6} +(3.07176 + 3.07176i) q^{7} +(6.02277 - 6.02277i) q^{8} +2.12224 q^{9} +O(q^{10})\)	\(q+(-1.89459 - 1.89459i) q^{2} +0.936891i q^{3} +5.17893i q^{4} +2.40716i q^{5} +(1.77502 - 1.77502i) q^{6} +(3.07176 + 3.07176i) q^{7} +(6.02277 - 6.02277i) q^{8} +2.12224 q^{9} +(4.56057 - 4.56057i) q^{10} +(2.96832 + 1.47955i) q^{11} -4.85209 q^{12} +4.20910i q^{13} -11.6394i q^{14} -2.25524 q^{15} -12.4635 q^{16} +(0.0850763 - 0.0850763i) q^{17} +(-4.02076 - 4.02076i) q^{18} -5.11079 q^{19} -12.4665 q^{20} +(-2.87790 + 2.87790i) q^{21} +(-2.82061 - 8.42689i) q^{22} +(1.76200 - 1.76200i) q^{23} +(5.64268 + 5.64268i) q^{24} -0.794404 q^{25} +(7.97452 - 7.97452i) q^{26} +4.79898i q^{27} +(-15.9084 + 15.9084i) q^{28} +(5.43337 - 5.43337i) q^{29} +(4.27276 + 4.27276i) q^{30} +(-0.249849 - 0.249849i) q^{31} +(11.5676 + 11.5676i) q^{32} +(-1.38618 + 2.78099i) q^{33} -0.322369 q^{34} +(-7.39421 + 7.39421i) q^{35} +10.9909i q^{36} +(-4.12775 - 4.12775i) q^{37} +(9.68285 + 9.68285i) q^{38} -3.94347 q^{39} +(14.4977 + 14.4977i) q^{40} -7.25621 q^{41} +10.9049 q^{42} +(7.52083 - 7.52083i) q^{43} +(-7.66248 + 15.3727i) q^{44} +5.10855i q^{45} -6.67653 q^{46} +3.11058 q^{47} -11.6769i q^{48} +11.8714i q^{49} +(1.50507 + 1.50507i) q^{50} +(0.0797072 + 0.0797072i) q^{51} -21.7986 q^{52} +(7.15236 - 7.15236i) q^{53} +(9.09208 - 9.09208i) q^{54} +(-3.56151 + 7.14522i) q^{55} +37.0010 q^{56} -4.78826i q^{57} -20.5880 q^{58} +(-0.638327 - 0.638327i) q^{59} -11.6798i q^{60} +(-5.98602 - 5.01673i) q^{61} +0.946724i q^{62} +(6.51900 + 6.51900i) q^{63} -18.9048i q^{64} -10.1320 q^{65} +(7.89507 - 2.64261i) q^{66} +(-2.65165 - 2.65165i) q^{67} +(0.440604 + 0.440604i) q^{68} +(1.65080 + 1.65080i) q^{69} +28.0180 q^{70} +(-8.91667 - 8.91667i) q^{71} +(12.7817 - 12.7817i) q^{72} +7.25225i q^{73} +15.6408i q^{74} -0.744270i q^{75} -26.4684i q^{76} +(4.57315 + 13.6628i) q^{77} +(7.47125 + 7.47125i) q^{78} +(6.26892 + 6.26892i) q^{79} -30.0015i q^{80} +1.87059 q^{81} +(13.7475 + 13.7475i) q^{82} -7.47924i q^{83} +(-14.9045 - 14.9045i) q^{84} +(0.204792 + 0.204792i) q^{85} -28.4978 q^{86} +(5.09047 + 5.09047i) q^{87} +(26.7885 - 8.96653i) q^{88} +(12.4463 + 12.4463i) q^{89} +(9.67861 - 9.67861i) q^{90} +(-12.9294 + 12.9294i) q^{91} +(9.12528 + 9.12528i) q^{92} +(0.234082 - 0.234082i) q^{93} +(-5.89327 - 5.89327i) q^{94} -12.3025i q^{95} +(-10.8376 + 10.8376i) q^{96} -12.6732i q^{97} +(22.4915 - 22.4915i) q^{98} +(6.29948 + 3.13995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

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