LMFDB - Embedded newform 507.2.m.b.40.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(40,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [204] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.6
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18717 - 0.292610i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-0.447170 - 0.234693i) q^{4} +(-0.808035 + 1.17064i) q^{5} +(-0.433574 + 1.14324i) q^{6} +(-0.0218939 - 0.0193963i) q^{7} +(2.29259 + 2.03106i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.30181 - 1.15330i) q^{10} +(-2.69836 + 0.665086i) q^{11} +(-0.286882 + 0.415620i) q^{12} +(3.51378 - 0.808309i) q^{13} +(0.0203161 + 0.0294330i) q^{14} +(1.06471 + 0.943248i) q^{15} +(-1.55361 - 2.25080i) q^{16} +(4.54762 + 4.02884i) q^{17} +(1.08264 + 0.568215i) q^{18} -3.61515 q^{19} +(0.636069 - 0.333835i) q^{20} +(-0.0218939 + 0.0193963i) q^{21} +3.39801 q^{22} +1.95318 q^{23} +(2.29259 - 2.03106i) q^{24} +(1.05555 + 2.78325i) q^{25} +(-4.40796 - 0.0685695i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.00523811 + 0.0138118i) q^{28} +(8.48566 + 2.09153i) q^{29} +(-0.987980 - 1.43134i) q^{30} +(2.16983 - 5.72137i) q^{31} +(-0.986427 - 2.60099i) q^{32} +(0.334986 + 2.75885i) q^{33} +(-4.21990 - 6.11358i) q^{34} +(0.0403970 - 0.00995698i) q^{35} +(0.378010 + 0.334888i) q^{36} +(4.08138 - 10.7617i) q^{37} +(4.29178 + 1.05783i) q^{38} +(-0.378877 - 3.58559i) q^{39} +(-4.23013 + 1.04263i) q^{40} +(-0.0399345 + 0.328890i) q^{41} +(0.0316672 - 0.0166202i) q^{42} +(4.41959 + 11.6535i) q^{43} +(1.36272 + 0.335879i) q^{44} +(1.06471 - 0.943248i) q^{45} +(-2.31875 - 0.571521i) q^{46} +(0.387496 - 0.203373i) q^{47} +(-2.42166 + 1.27098i) q^{48} +(-0.843654 - 6.94811i) q^{49} +(-0.438702 - 3.61304i) q^{50} +(4.54762 - 4.02884i) q^{51} +(-1.76096 - 0.463207i) q^{52} +(4.12627 + 3.65556i) q^{53} +(0.694570 - 1.00626i) q^{54} +(1.40179 - 3.69622i) q^{55} +(-0.0107987 - 0.0889355i) q^{56} +(-0.435758 + 3.58879i) q^{57} +(-9.46189 - 4.96598i) q^{58} +(-1.98925 + 2.88193i) q^{59} +(-0.254731 - 0.671671i) q^{60} +(6.33104 - 5.60881i) q^{61} +(-4.25008 + 6.15731i) q^{62} +(0.0166158 + 0.0240722i) q^{63} +(1.06929 + 8.80642i) q^{64} +(-1.89301 + 4.76651i) q^{65} +(0.409585 - 3.37324i) q^{66} +(5.63609 - 2.95805i) q^{67} +(-1.08802 - 2.86887i) q^{68} +(0.235430 - 1.93894i) q^{69} -0.0508715 q^{70} +(-1.64316 + 13.5326i) q^{71} +(-1.73991 - 2.52069i) q^{72} +(-6.42412 + 1.58340i) q^{73} +(-7.99427 + 11.5817i) q^{74} +(2.89019 - 0.712367i) q^{75} +(1.61659 + 0.848450i) q^{76} +(0.0719778 + 0.0377768i) q^{77} +(-0.599390 + 4.36755i) q^{78} +(1.20033 - 0.629983i) q^{79} +3.89025 q^{80} +(0.885456 + 0.464723i) q^{81} +(0.143646 - 0.378762i) q^{82} +(1.11709 + 9.20009i) q^{83} +(0.0143424 - 0.00353509i) q^{84} +(-8.39095 + 2.06818i) q^{85} +(-1.83686 - 15.1279i) q^{86} +(3.09911 - 8.17168i) q^{87} +(-7.53707 - 3.95576i) q^{88} +6.41430 q^{89} +(-1.53999 + 0.808248i) q^{90} +(-0.0926084 - 0.0504572i) q^{91} +(-0.873404 - 0.458398i) q^{92} +(-5.41811 - 2.84365i) q^{93} +(-0.519531 + 0.128053i) q^{94} +(2.92117 - 4.23204i) q^{95} +(-2.70093 + 0.665719i) q^{96} +(3.64170 + 5.27591i) q^{97} +(-1.03153 + 8.49542i) q^{98} +2.77912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	−1.18717	−	0.292610i	−0.839453	−	0.206907i	−0.203927	−	0.978986i	$-0.565371\pi$
$2$	−1.18717	−	0.292610i	−0.839453	−	0.206907i	−0.635526	+	0.772079i	$0.719217\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	−0.447170	−	0.234693i	−0.223585	−	0.117346i
$5$	−0.808035	+	1.17064i	−0.361364	+	0.523526i	−0.960927	−	0.276801i	$-0.910726\pi$
$5$	−0.808035	+	1.17064i	−0.361364	+	0.523526i	0.599563	+	0.800327i	$0.295341\pi$
$6$	−0.433574	+	1.14324i	−0.177006	+	0.466726i
$7$	−0.0218939	−	0.0193963i	−0.00827510	−	0.00733110i	0.658975	−	0.752165i	$-0.270990\pi$
$7$	−0.0218939	−	0.0193963i	−0.00827510	−	0.00733110i	−0.667250	+	0.744834i	$0.732529\pi$
$8$	2.29259	+	2.03106i	0.810554	+	0.718088i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	1.30181	−	1.15330i	0.411669	−	0.364707i
$11$	−2.69836	+	0.665086i	−0.813587	+	0.200531i	−0.624092	−	0.781351i	$-0.714531\pi$
$11$	−2.69836	+	0.665086i	−0.813587	+	0.200531i	−0.189494	+	0.981882i	$0.560685\pi$
$12$	−0.286882	+	0.415620i	−0.0828157	+	0.119979i
$13$	3.51378	−	0.808309i	0.974547	−	0.224185i
$13$	3.51378	−	0.808309i	0.974547	−	0.224185i
$14$	0.0203161	+	0.0294330i	0.00542971	+	0.00786629i
$15$	1.06471	+	0.943248i	0.274906	+	0.243546i
$16$	−1.55361	−	2.25080i	−0.388404	−	0.562700i
$17$	4.54762	+	4.02884i	1.10296	+	0.977137i	0.999846	−	0.0175326i	$-0.00558109\pi$
$17$	4.54762	+	4.02884i	1.10296	+	0.977137i	0.103113	+	0.994670i	$0.467120\pi$
$18$	1.08264	+	0.568215i	0.255181	+	0.133930i
$19$	−3.61515			−0.829372			−0.414686	−	0.909965i	$-0.636109\pi$
$19$	−3.61515			−0.829372			−0.414686	+	0.909965i	$0.636109\pi$
$20$	0.636069	−	0.333835i	0.142229	−	0.0746478i
$21$	−0.0218939	+	0.0193963i	−0.00477763	+	0.00423261i
$22$	3.39801			0.724459
$23$	1.95318			0.407267			0.203633	−	0.979047i	$-0.434725\pi$
$23$	1.95318			0.407267			0.203633	+	0.979047i	$0.434725\pi$
$24$	2.29259	−	2.03106i	0.467973	−	0.414588i
$25$	1.05555	+	2.78325i	0.211109	+	0.556649i
$26$	−4.40796	−	0.0685695i	−0.864472	−	0.0134476i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	0.00523811	+	0.0138118i	0.000989910	+	0.00261018i
$29$	8.48566	+	2.09153i	1.57575	+	0.388387i	0.927734	−	0.373242i	$-0.121754\pi$
$29$	8.48566	+	2.09153i	1.57575	+	0.388387i	0.648014	+	0.761629i	$0.275600\pi$
$30$	−0.987980	−	1.43134i	−0.180380	−	0.261325i
$31$	2.16983	−	5.72137i	0.389713	−	1.02759i	−0.586342	−	0.810064i	$-0.699432\pi$
$31$	2.16983	−	5.72137i	0.389713	−	1.02759i	0.976055	−	0.217525i	$-0.0697984\pi$
$32$	−0.986427	−	2.60099i	−0.174377	−	0.459795i
$33$	0.334986	+	2.75885i	0.0583135	+	0.480255i
$34$	−4.21990	−	6.11358i	−0.723707	−	1.04847i
$35$	0.0403970	−	0.00995698i	0.00682835	−	0.00168304i
$36$	0.378010	+	0.334888i	0.0630017	+	0.0558146i
$37$	4.08138	−	10.7617i	0.670975	−	1.76922i	0.0326275	−	0.999468i	$-0.489613\pi$
$37$	4.08138	−	10.7617i	0.670975	−	1.76922i	0.638348	−	0.769748i	$-0.279618\pi$
$38$	4.29178	+	1.05783i	0.696219	+	0.171603i
$39$	−0.378877	−	3.58559i	−0.0606689	−	0.574154i
$40$	−4.23013	+	1.04263i	−0.668843	+	0.164855i
$41$	−0.0399345	+	0.328890i	−0.00623673	+	0.0513641i	−0.995495	−	0.0948143i	$-0.969774\pi$
$41$	−0.0399345	+	0.328890i	−0.00623673	+	0.0513641i	0.989258	+	0.146178i	$0.0466973\pi$
$42$	0.0316672	−	0.0166202i	0.00488635	−	0.00256456i
$43$	4.41959	+	11.6535i	0.673982	+	1.77714i	0.628016	+	0.778201i	$0.283867\pi$
$43$	4.41959	+	11.6535i	0.673982	+	1.77714i	0.0459659	+	0.998943i	$0.485363\pi$
$44$	1.36272	+	0.335879i	0.205437	+	0.0506357i
$45$	1.06471	−	0.943248i	0.158717	−	0.140611i
$46$	−2.31875	−	0.571521i	−0.341881	−	0.0842662i
$47$	0.387496	−	0.203373i	0.0565221	−	0.0296651i	−0.436225	−	0.899837i	$-0.643685\pi$
$47$	0.387496	−	0.203373i	0.0565221	−	0.0296651i	0.492747	+	0.870172i	$0.335993\pi$
$48$	−2.42166	+	1.27098i	−0.349536	+	0.183451i
$49$	−0.843654	−	6.94811i	−0.120522	−	0.992588i
$50$	−0.438702	−	3.61304i	−0.0620419	−	0.510961i
$51$	4.54762	−	4.02884i	0.636794	−	0.564150i
$52$	−1.76096	−	0.463207i	−0.244201	−	0.0642352i
$53$	4.12627	+	3.65556i	0.566787	+	0.502129i	0.897151	−	0.441724i	$-0.145633\pi$
$53$	4.12627	+	3.65556i	0.566787	+	0.502129i	−0.330364	+	0.943854i	$0.607172\pi$
$54$	0.694570	−	1.00626i	0.0945190	−	0.136934i
$55$	1.40179	−	3.69622i	0.189018	−	0.498399i
$56$	−0.0107987	−	0.0889355i	−0.00144304	−	0.0118845i
$57$	−0.435758	+	3.58879i	−0.0577176	+	0.475347i
$58$	−9.46189	−	4.96598i	−1.24241	−	0.652065i
$59$	−1.98925	+	2.88193i	−0.258978	+	0.375195i	−0.930807	−	0.365512i	$-0.880894\pi$
$59$	−1.98925	+	2.88193i	−0.258978	+	0.375195i	0.671828	+	0.740707i	$0.265509\pi$
$60$	−0.254731	−	0.671671i	−0.0328857	−	0.0867124i
$61$	6.33104	−	5.60881i	0.810606	−	0.718134i	−0.152194	−	0.988351i	$-0.548634\pi$
$61$	6.33104	−	5.60881i	0.810606	−	0.718134i	0.962800	+	0.270216i	$0.0870953\pi$
$62$	−4.25008	+	6.15731i	−0.539761	+	0.781979i
$63$	0.0166158	+	0.0240722i	0.00209340	+	0.00303281i
$64$	1.06929	+	8.80642i	0.133662	+	1.10080i
$65$	−1.89301	+	4.76651i	−0.234800	+	0.591213i
$66$	0.409585	−	3.37324i	0.0504165	−	0.415217i
$67$	5.63609	−	2.95805i	0.688558	−	0.361383i	−0.0838779	−	0.996476i	$-0.526731\pi$
$67$	5.63609	−	2.95805i	0.688558	−	0.361383i	0.772436	+	0.635093i	$0.219038\pi$
$68$	−1.08802	−	2.86887i	−0.131942	−	0.347901i
$69$	0.235430	−	1.93894i	0.0283425	−	0.233421i
$70$	−0.0508715			−0.00608031
$71$	−1.64316	+	13.5326i	−0.195007	+	1.60603i	0.486139	+	0.873881i	$0.338405\pi$
$71$	−1.64316	+	13.5326i	−0.195007	+	1.60603i	−0.681147	+	0.732147i	$0.738518\pi$
$72$	−1.73991	−	2.52069i	−0.205050	−	0.297067i
$73$	−6.42412	+	1.58340i	−0.751887	+	0.185323i	−0.596592	−	0.802545i	$-0.703479\pi$
$73$	−6.42412	+	1.58340i	−0.751887	+	0.185323i	−0.155295	+	0.987868i	$0.549633\pi$
$74$	−7.99427	+	11.5817i	−0.929315	+	1.34634i
$75$	2.89019	−	0.712367i	0.333730	−	0.0822570i
$76$	1.61659	+	0.848450i	0.185435	+	0.0973239i
$77$	0.0719778	+	0.0377768i	0.00820263	+	0.00430507i
$78$	−0.599390	+	4.36755i	−0.0678676	+	0.494528i
$79$	1.20033	−	0.629983i	0.135048	−	0.0708786i	−0.395846	−	0.918317i	$-0.629549\pi$
$79$	1.20033	−	0.629983i	0.135048	−	0.0708786i	0.530894	+	0.847438i	$0.321856\pi$
$80$	3.89025			0.434943
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	0.143646	−	0.378762i	0.0158630	−	0.0418273i
$83$	1.11709	+	9.20009i	0.122617	+	1.00984i	0.916017	+	0.401140i	$0.131386\pi$
$83$	1.11709	+	9.20009i	0.122617	+	1.00984i	−0.793400	+	0.608701i	$0.791691\pi$
$84$	0.0143424	−	0.00353509i	0.00156489	−	0.000385710i
$85$	−8.39095	+	2.06818i	−0.910127	+	0.224326i
$86$	−1.83686	−	15.1279i	−0.198073	−	1.63128i
$87$	3.09911	−	8.17168i	0.332260	−	0.876097i
$88$	−7.53707	−	3.95576i	−0.803455	−	0.421686i
$89$	6.41430			0.679914			0.339957	−	0.940441i	$-0.389587\pi$
$89$	6.41430			0.679914			0.339957	+	0.940441i	$0.389587\pi$
$90$	−1.53999	+	0.808248i	−0.162329	+	0.0851968i
$91$	−0.0926084	−	0.0504572i	−0.00970799	−	0.00528935i
$92$	−0.873404	−	0.458398i	−0.0910587	−	0.0477913i
$93$	−5.41811	−	2.84365i	−0.561832	−	0.294872i
$94$	−0.519531	+	0.128053i	−0.0535855	+	0.0132076i
$95$	2.92117	−	4.23204i	0.299705	−	0.434198i
$96$	−2.70093	+	0.665719i	−0.275662	+	0.0679447i
$97$	3.64170	+	5.27591i	0.369758	+	0.535687i	0.963058	−	0.269294i	$-0.0867905\pi$
$97$	3.64170	+	5.27591i	0.369758	+	0.535687i	−0.593300	+	0.804982i	$0.702175\pi$
$98$	−1.03153	+	8.49542i	−0.104200	+	0.858167i
$99$	2.77912			0.279312
$100$	0.181200	−	1.49231i	0.0181200	−	0.149231i
$101$	2.06244	+	5.43821i	0.205221	+	0.541123i	0.997625	−	0.0688732i	$-0.0219404\pi$
$101$	2.06244	+	5.43821i	0.205221	+	0.541123i	−0.792405	+	0.609996i	$0.791171\pi$
$102$	−6.57766	+	3.45222i	−0.651285	+	0.341821i
$103$	−0.290915	+	2.39590i	−0.0286647	+	0.236075i	−0.999999	−	0.00164413i	$-0.999477\pi$
$103$	−0.290915	+	2.39590i	−0.0286647	+	0.236075i	0.971334	+	0.237719i	$0.0763997\pi$
$104$	9.69738	+	5.28357i	0.950907	+	0.518096i
$105$	−0.00501505	−	0.0413027i	−0.000489419	−	0.00403073i
$106$	−3.82891	−	5.54714i	−0.371897	−	0.538786i
$107$	−3.80062	+	5.50616i	−0.367420	+	0.532300i	−0.962470	−	0.271389i	$-0.912517\pi$
$107$	−3.80062	+	5.50616i	−0.367420	+	0.532300i	0.595050	+	0.803689i	$0.297132\pi$
$108$	0.378010	−	0.334888i	0.0363740	−	0.0322246i
$109$	6.34317	+	16.7256i	0.607566	+	1.60202i	0.786109	+	0.618087i	$0.212092\pi$
$109$	6.34317	+	16.7256i	0.607566	+	1.60202i	−0.178544	+	0.983932i	$0.557139\pi$
$110$	−2.74571	+	3.97785i	−0.261793	+	0.379273i
$111$	−10.1913	−	5.34881i	−0.967315	−	0.507686i
$112$	−0.00964249	+	0.0794130i	−0.000911130	+	0.00750383i
$113$	−2.30336	−	18.9699i	−0.216682	−	1.78453i	−0.543462	−	0.839434i	$-0.682887\pi$
$113$	−2.30336	−	18.9699i	−0.216682	−	1.78453i	0.326781	−	0.945100i	$-0.394036\pi$
$114$	1.56743	−	4.13298i	0.146804	−	0.387089i
$115$	−1.57824	+	2.28647i	−0.147171	+	0.213215i
$116$	−3.30366	−	2.92679i	−0.306738	−	0.271746i
$117$	−3.60512	−	0.0560806i	−0.333293	−	0.00518466i
$118$	3.20485	−	2.83925i	0.295031	−	0.261374i
$119$	−0.0214205	−	0.176414i	−0.00196361	−	0.0161718i
$120$	0.525146	+	4.32497i	0.0479391	+	0.394814i
$121$	−2.90120	+	1.52267i	−0.263746	+	0.138424i
$122$	−9.15718	+	4.80606i	−0.829052	+	0.435120i
$123$	0.321679	+	0.0792867i	0.0290048	+	0.00714904i
$124$	−2.31305	+	2.04918i	−0.207718	+	0.184022i
$125$	−11.0166	−	2.71535i	−0.985355	−	0.242868i
$126$	−0.0126820	−	0.0334397i	−0.00112980	−	0.00297904i
$127$	−14.3218	+	7.51666i	−1.27085	+	0.666995i	−0.959073	−	0.283159i	$-0.908618\pi$
$127$	−14.3218	+	7.51666i	−1.27085	+	0.666995i	−0.311780	+	0.950154i	$0.600925\pi$
$128$	0.636810	−	5.24461i	0.0562866	−	0.463562i
$129$	12.1013	−	2.98269i	1.06546	−	0.262612i
$130$	3.64205	−	5.10472i	0.319429	−	0.447714i
$131$	−16.2977	−	4.01703i	−1.42394	−	0.350970i	−0.549253	−	0.835656i	$-0.685088\pi$
$131$	−16.2977	−	4.01703i	−1.42394	−	0.350970i	−0.874688	+	0.484686i	$0.838934\pi$
$132$	0.497688	−	1.31230i	0.0433182	−	0.114221i
$133$	0.0791496	+	0.0701204i	0.00686314	+	0.00608021i
$134$	−7.55653	+	1.86252i	−0.652784	+	0.160897i
$135$	−0.808035	−	1.17064i	−0.0695445	−	0.100753i
$136$	2.24302	+	18.4730i	0.192338	+	1.58404i
$137$	−7.76679	−	20.4794i	−0.663562	−	1.74967i	−0.661811	−	0.749671i	$-0.730212\pi$
$137$	−7.76679	−	20.4794i	−0.663562	−	1.74967i	−0.00175123	−	0.999998i	$-0.500557\pi$
$138$	−0.846848	+	2.23296i	−0.0720885	+	0.190082i
$139$	6.82709	+	9.89074i	0.579066	+	0.838922i	0.997597	−	0.0692806i	$-0.0220704\pi$
$139$	6.82709	+	9.89074i	0.579066	+	0.838922i	−0.418531	+	0.908202i	$0.637455\pi$
$140$	−0.0204012	−	0.00502844i	−0.00172421	−	0.000424980i
$141$	−0.155183	−	0.409184i	−0.0130688	−	0.0344596i
$142$	5.91049	−	15.5847i	0.495997	−	1.30784i
$143$	−8.94385	+	4.51808i	−0.747922	+	0.377821i
$144$	0.969818	+	2.55720i	0.0808182	+	0.213100i
$145$	−9.30513	+	8.24363i	−0.772749	+	0.684596i
$146$	8.08982			0.669518
$147$	−6.99914			−0.577280
$148$	−4.35077	+	3.85444i	−0.357631	+	0.316833i
$149$	−7.29458	+	3.82849i	−0.597595	+	0.313642i	−0.736262	−	0.676697i	$-0.763411\pi$
$149$	−7.29458	+	3.82849i	−0.597595	+	0.313642i	0.138666	+	0.990339i	$0.455718\pi$
$150$	−3.63958			−0.297170
$151$	−11.8407	−	6.21446i	−0.963579	−	0.505725i	−0.0918819	−	0.995770i	$-0.529288\pi$
$151$	−11.8407	−	6.21446i	−0.963579	−	0.505725i	−0.871697	+	0.490044i	$0.836981\pi$
$152$	−8.28807	−	7.34258i	−0.672251	−	0.595562i
$153$	−3.45131	−	5.00008i	−0.279022	−	0.404233i
$154$	−0.0743957	−	0.0659088i	−0.00599497	−	0.00531108i
$155$	4.94437	+	7.16316i	0.397141	+	0.575359i
$156$	−0.672090	+	1.69229i	−0.0538102	+	0.135491i
$157$	0.333922	−	0.483769i	0.0266498	−	0.0386090i	−0.809433	−	0.587213i	$-0.800225\pi$
$157$	0.333922	−	0.483769i	0.0266498	−	0.0386090i	0.836082	+	0.548604i	$0.184841\pi$
$158$	−1.60933	+	0.396665i	−0.128032	+	0.0315570i
$159$	4.12627	−	3.65556i	0.327234	−	0.289904i
$160$	3.84189	+	0.946942i	0.303728	+	0.0748623i
$161$	−0.0427627	−	0.0378844i	−0.00337017	−	0.00298571i
$162$	−0.915201	−	0.810797i	−0.0719049	−	0.0637022i
$163$	−0.624239	+	1.64598i	−0.0488942	+	0.128923i	−0.957239	−	0.289299i	$-0.906578\pi$
$163$	−0.624239	+	1.64598i	−0.0488942	+	0.128923i	0.908344	+	0.418223i	$0.137347\pi$
$164$	0.0950457	−	0.137698i	0.00742182	−	0.0107524i
$165$	−3.50031	−	1.83710i	−0.272498	−	0.143018i
$166$	1.36586	−	11.2489i	0.106012	−	0.873084i
$167$	1.40119	+	0.345362i	0.108427	+	0.0267249i	0.293156	−	0.956065i	$-0.405294\pi$
$167$	1.40119	+	0.345362i	0.108427	+	0.0267249i	−0.184729	+	0.982790i	$0.559141\pi$
$168$	−0.0895887			−0.00691192
$169$	11.6933	−	5.68044i	0.899482	−	0.436957i
$170$	10.5666			0.810423
$171$	3.51010	+	0.865162i	0.268424	+	0.0661606i
$172$	0.758686	−	6.24834i	0.0578493	−	0.476432i
$173$	19.8064	+	10.3952i	1.50585	+	0.790332i	0.997490	−	0.0708122i	$-0.0225591\pi$
$173$	19.8064	+	10.3952i	1.50585	+	0.790332i	0.508361	+	0.861144i	$0.330251\pi$
$174$	−6.07028	+	8.79431i	−0.460187	+	0.666695i
$175$	0.0308746	−	0.0814097i	0.00233390	−	0.00615399i
$176$	5.68919	+	5.04018i	0.428839	+	0.379918i
$177$	2.62114	+	2.32212i	0.197017	+	0.174542i
$178$	−7.61483	−	1.87689i	−0.570756	−	0.140679i
$179$	13.6857	−	12.1245i	1.02292	−	0.906224i	0.0272873	−	0.999628i	$-0.491313\pi$
$179$	13.6857	−	12.1245i	1.02292	−	0.906224i	0.995628	+	0.0934035i	$0.0297746\pi$
$180$	−0.697478	+	0.171913i	−0.0519870	+	0.0128136i
$181$	−2.64062	+	3.82560i	−0.196276	+	0.284355i	−0.908748	−	0.417346i	$-0.862960\pi$
$181$	−2.64062	+	3.82560i	−0.196276	+	0.284355i	0.712472	+	0.701701i	$0.247576\pi$
$182$	0.0951772	+	0.0869992i	0.00705501	+	0.00644881i
$183$	−4.80479	−	6.96094i	−0.355180	−	0.514568i
$184$	4.47785	+	3.96703i	0.330111	+	0.292453i
$185$	9.30020	+	13.4737i	0.683765	+	0.990604i
$186$	5.60012	+	4.96127i	0.410621	+	0.363778i
$187$	−14.9506	−	7.84670i	−1.09330	−	0.573808i
$188$	−0.221007			−0.0161186
$189$	0.0258995	−	0.0135931i	0.00188391	−	0.000988753i
$190$	−4.70625	+	4.16937i	−0.341427	+	0.302478i
$191$	−11.0951			−0.802814			−0.401407	−	0.915900i	$-0.631479\pi$
$191$	−11.0951			−0.802814			−0.401407	+	0.915900i	$0.631479\pi$
$192$	8.87110			0.640216
$193$	16.5608	−	14.6716i	1.19207	−	1.05608i	0.194908	−	0.980822i	$-0.437559\pi$
$193$	16.5608	−	14.6716i	1.19207	−	1.05608i	0.997164	−	0.0752619i	$-0.0239793\pi$
$194$	−2.77951	−	7.32897i	−0.199557	−	0.526190i
$195$	4.50358	+	2.45375i	0.322508	+	0.175717i
$196$	−1.25342	+	3.30499i	−0.0895297	+	0.236070i
$197$	−1.09361	−	2.88362i	−0.0779166	−	0.205449i	0.890398	−	0.455183i	$-0.150426\pi$
$197$	−1.09361	−	2.88362i	−0.0779166	−	0.205449i	−0.968315	+	0.249734i	$0.919657\pi$
$198$	−3.29927	−	0.813198i	−0.234469	−	0.0577915i
$199$	11.0170	+	15.9608i	0.780972	+	1.13143i	0.988204	+	0.153141i	$0.0489390\pi$
$199$	11.0170	+	15.9608i	0.780972	+	1.13143i	−0.207232	+	0.978292i	$0.566446\pi$
$200$	−3.23300	+	8.52473i	−0.228608	+	0.602789i
$201$	−2.25712	−	5.95155i	−0.159205	−	0.419790i
$202$	−0.857185	−	7.05955i	−0.0603113	−	0.496709i
$203$	−0.145216	−	0.210382i	−0.0101922	−	0.0147659i
$204$	−2.97910	+	0.734282i	−0.208579	+	0.0514100i
$205$	−0.352744	−	0.312504i	−0.0246367	−	0.0218262i
$206$	1.04643	−	2.75920i	0.0729081	−	0.192243i
$207$	−1.89643	−	0.467427i	−0.131811	−	0.0324884i
$208$	−7.27840	−	6.65301i	−0.504666	−	0.461303i
$209$	9.75498	−	2.40439i	0.674766	−	0.166315i
$210$	−0.00613188	+	0.0505006i	−0.000423140	+	0.00348487i
$211$	23.6489	−	12.4119i	1.62806	−	0.854470i	0.631169	−	0.775646i	$-0.282576\pi$
$211$	23.6489	−	12.4119i	1.62806	−	0.854470i	0.996888	−	0.0788248i	$-0.0251168\pi$
$212$	−0.987210	−	2.60306i	−0.0678019	−	0.178779i
$213$	13.2359	+	3.26236i	0.906909	+	0.223533i
$214$	6.12313	−	5.42462i	0.418568	−	0.370819i
$215$	−17.2132	−	4.24268i	−1.17393	−	0.289349i
$216$	−2.71204	+	1.42339i	−0.184531	+	0.0968492i
$217$	−0.158479	+	0.0831764i	−0.0107583	+	0.00564638i
$218$	−2.63633	−	21.7121i	−0.178555	−	1.47053i
$219$	0.797517	+	6.56814i	0.0538912	+	0.443834i
$220$	−1.49432	+	1.32385i	−0.100747	+	0.0892538i
$221$	19.2359	+	10.4806i	1.29394	+	0.704999i
$222$	10.5336	+	9.33200i	0.706972	+	0.626323i
$223$	7.34677	−	10.6436i	0.491976	−	0.712751i	−0.495833	−	0.868418i	$-0.665137\pi$
$223$	7.34677	−	10.6436i	0.491976	−	0.712751i	0.987810	+	0.155667i	$0.0497527\pi$
$224$	−0.0288529	+	0.0760788i	−0.00192781	+	0.00508323i
$225$	−0.358799	−	2.95498i	−0.0239200	−	0.196999i
$226$	−2.81630	+	23.1944i	−0.187338	+	1.54287i
$227$	−12.0140	−	6.30544i	−0.797397	−	0.418506i	0.0162479	−	0.999868i	$-0.494828\pi$
$227$	−12.0140	−	6.30544i	−0.797397	−	0.418506i	−0.813645	+	0.581362i	$0.802520\pi$
$228$	1.03712	−	1.50253i	0.0686850	−	0.0995075i
$229$	3.92852	+	10.3586i	0.259604	+	0.684518i	0.999925	+	0.0122651i	$0.00390420\pi$
$229$	3.92852	+	10.3586i	0.259604	+	0.684518i	−0.740321	+	0.672253i	$0.765327\pi$
$230$	2.54268	−	2.25261i	0.167659	−	0.148533i
$231$	0.0461774	−	0.0668995i	0.00303825	−	0.00440166i
$232$	15.2061	+	22.0299i	0.998332	+	1.44633i
$233$	−0.0181691	−	0.149636i	−0.00119029	−	0.00980296i	0.992102	−	0.125437i	$-0.0400332\pi$
$233$	−0.0181691	−	0.149636i	−0.00119029	−	0.00980296i	−0.993292	+	0.115634i	$0.963110\pi$
$234$	4.26346	+	1.12147i	0.278711	+	0.0733128i
$235$	−0.0750328	+	0.617951i	−0.00489460	+	0.0403107i
$236$	1.56590	−	0.821848i	0.101931	−	0.0534977i
$237$	−0.480706	−	1.26752i	−0.0312252	−	0.0823340i
$238$	−0.0261907	+	0.215700i	−0.00169769	+	0.0139818i
$239$	7.66566			0.495850			0.247925	−	0.968779i	$-0.420251\pi$
$239$	7.66566			0.495850			0.247925	+	0.968779i	$0.420251\pi$
$240$	0.468918	−	3.86189i	0.0302685	−	0.249284i
$241$	5.45668	+	7.90537i	0.351496	+	0.509229i	0.958355	−	0.285580i	$-0.0921862\pi$
$241$	5.45668	+	7.90537i	0.351496	+	0.509229i	−0.606859	+	0.794809i	$0.707571\pi$
$242$	3.88976	−	0.958739i	0.250043	−	0.0616300i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	−4.14739	+	1.02224i	−0.265510	+	0.0654423i
$245$	8.81544	+	4.62670i	0.563198	+	0.295589i
$246$	−0.358686	−	0.188253i	−0.0228690	−	0.0120026i
$247$	−12.7028	+	2.92216i	−0.808262	+	0.185933i
$248$	16.5950	−	8.70972i	1.05378	−	0.553068i
$249$	9.26766			0.587314
$250$	12.2840	+	6.44714i	0.776908	+	0.407753i
$251$	5.03444	−	13.2747i	0.317771	−	0.837893i	−0.677021	−	0.735964i	$-0.736729\pi$
$251$	5.03444	−	13.2747i	0.317771	−	0.837893i	0.994792	−	0.101929i	$-0.0325015\pi$
$252$	−0.00178053	−	0.0146640i	−0.000112163	−	0.000923744i
$253$	−5.27039	+	1.29903i	−0.331347	+	0.0816696i
$254$	19.2018	−	4.73282i	1.20483	−	0.296963i
$255$	1.04169	+	8.57907i	0.0652330	+	0.537242i
$256$	4.00085	−	10.5494i	0.250053	−	0.659335i
$257$	−6.84297	−	3.59147i	−0.426853	−	0.224030i	0.237595	−	0.971364i	$-0.423641\pi$
$257$	−6.84297	−	3.59147i	−0.426853	−	0.224030i	−0.664448	+	0.747335i	$0.731333\pi$
$258$	−15.2390			−0.948737
$259$	−0.298094	+	0.156452i	−0.0185227	+	0.00972146i
$260$	1.96516	−	1.68716i	0.121874	−	0.104633i
$261$	−7.73855	−	4.06150i	−0.479004	−	0.251401i
$262$	18.1727	+	9.53777i	1.12271	+	0.589246i
$263$	−24.0942	+	5.93869i	−1.48571	+	0.366195i	−0.896958	−	0.442116i	$-0.854228\pi$
$263$	−24.0942	+	5.93869i	−1.48571	+	0.366195i	−0.588755	+	0.808311i	$0.700382\pi$
$264$	−4.83541	+	7.00530i	−0.297599	+	0.431147i
$265$	−7.61351	+	1.87656i	−0.467694	+	0.115276i
$266$	−0.0734458	−	0.106405i	−0.00450325	−	0.00652408i
$267$	0.773158	−	6.36753i	0.0473165	−	0.389686i
$268$	−3.21452			−0.196358
$269$	2.00528	−	16.5150i	0.122264	−	1.00693i	−0.794433	−	0.607352i	$-0.792232\pi$
$269$	2.00528	−	16.5150i	0.122264	−	1.00693i	0.916697	−	0.399583i	$-0.130845\pi$
$270$	0.616730	+	1.62618i	0.0375330	+	0.0989664i
$271$	15.1935	−	7.97418i	0.922941	−	0.484397i	0.0648501	−	0.997895i	$-0.479343\pi$
$271$	15.1935	−	7.97418i	0.922941	−	0.484397i	0.858091	+	0.513498i	$0.171651\pi$
$272$	2.00286	−	16.4950i	0.121441	−	1.00016i
$273$	−0.0612520	+	0.0858512i	−0.00370714	+	0.00519595i
$274$	3.22801	+	26.5850i	0.195011	+	1.60606i
$275$	−4.69934	−	6.80817i	−0.283381	−	0.410548i
$276$	−0.560333	+	0.811782i	−0.0337281	+	0.0488635i
$277$	−8.39631	+	7.43848i	−0.504485	+	0.446935i	−0.876577	−	0.481261i	$-0.840179\pi$
$277$	−8.39631	+	7.43848i	−0.504485	+	0.446935i	0.372092	+	0.928196i	$0.378641\pi$
$278$	−5.21075	−	13.7396i	−0.312520	−	0.824048i
$279$	−3.47599	+	5.03585i	−0.208102	+	0.301488i
$280$	0.112837	+	0.0592215i	0.00674331	+	0.00353916i
$281$	−0.759296	+	6.25337i	−0.0452958	+	0.373045i	0.952380	+	0.304912i	$0.0986271\pi$
$281$	−0.759296	+	6.25337i	−0.0452958	+	0.373045i	−0.997676	+	0.0681325i	$0.978296\pi$
$282$	0.0644967	+	0.531178i	0.00384072	+	0.0316312i
$283$	0.454869	−	1.19939i	0.0270392	−	0.0712964i	−0.920817	−	0.389995i	$-0.872477\pi$
$283$	0.454869	−	1.19939i	0.0270392	−	0.0712964i	0.947856	+	0.318699i	$0.103246\pi$
$284$	3.91078	−	5.66575i	0.232062	−	0.336200i
$285$	−3.84908	−	3.40998i	−0.228000	−	0.201990i
$286$	11.9399	−	2.74665i	0.706019	−	0.162413i
$287$	0.00725357	−	0.00642610i	0.000428165	−	0.000379321i
$288$	0.335304	+	2.76148i	0.0197580	+	0.162722i
$289$	2.40017	+	19.7672i	0.141187	+	1.16278i
$290$	13.4589	−	7.06378i	0.790334	−	0.414799i
$291$	5.67640	−	2.97920i	0.332756	−	0.174644i
$292$	3.24429	+	0.799645i	0.189858	+	0.0467957i
$293$	−24.9191	+	22.0764i	−1.45579	+	1.28972i	−0.573329	+	0.819325i	$0.694348\pi$
$293$	−24.9191	+	22.0764i	−1.45579	+	1.28972i	−0.882459	+	0.470390i	$0.844113\pi$
$294$	8.30915	+	2.04802i	0.484599	+	0.119443i
$295$	−1.76632	−	4.65739i	−0.102839	−	0.271164i
$296$	31.2146	−	16.3827i	1.81431	−	0.952225i
$297$	0.334986	−	2.75885i	0.0194378	−	0.160085i
$298$	9.78013	−	2.41059i	0.566548	−	0.139642i
$299$	6.86305	−	1.57878i	0.396900	−	0.0913029i
$300$	−1.45959	−	0.359757i	−0.0842695	−	0.0207706i
$301$	0.129273	−	0.340864i	0.00745115	−	0.0196471i
$302$	12.2384	+	10.8423i	0.704242	+	0.623904i
$303$	5.64716	−	1.39190i	0.324421	−	0.0799626i
$304$	5.61655	+	8.13698i	0.322131	+	0.466688i
$305$	1.45020	+	11.9435i	0.0830382	+	0.683881i
$306$	2.63420	+	6.94582i	0.150587	+	0.397066i
$307$	11.6832	−	30.8061i	0.666797	−	1.75820i	0.0149032	−	0.999889i	$-0.495256\pi$
$307$	11.6832	−	30.8061i	0.666797	−	1.75820i	0.651894	−	0.758310i	$-0.273975\pi$
$308$	−0.0233203	−	0.0337853i	−0.00132880	−	0.00192510i
$309$	2.34336	+	0.577587i	0.133309	+	0.0328578i
$310$	−3.77378	−	9.95063i	−0.214336	−	0.565158i
$311$	10.4684	−	27.6028i	0.593606	−	1.56521i	−0.214846	−	0.976648i	$-0.568925\pi$
$311$	10.4684	−	27.6028i	0.593606	−	1.56521i	0.808452	−	0.588562i	$-0.200306\pi$
$312$	6.41394	−	8.98982i	0.363118	−	0.508948i
$313$	−6.17387	−	16.2792i	−0.348968	−	0.920152i	−0.988477	−	0.151369i	$-0.951632\pi$
$313$	−6.17387	−	16.2792i	−0.348968	−	0.920152i	0.639510	−	0.768783i	$-0.279137\pi$
$314$	−0.537976	+	0.476605i	−0.0303597	+	0.0268964i
$315$	−0.0416060			−0.00234424
$316$	−0.684605			−0.0385120
$317$	7.24248	−	6.41627i	0.406778	−	0.360374i	−0.434784	−	0.900535i	$-0.643175\pi$
$317$	7.24248	−	6.41627i	0.406778	−	0.360374i	0.841562	+	0.540161i	$0.181637\pi$
$318$	−5.96822	+	3.13236i	−0.334681	+	0.175654i
$319$	−24.2884			−1.35989
$320$	−11.1732	−	5.86413i	−0.624599	−	0.327815i
$321$	5.00789	+	4.43661i	0.279513	+	0.247627i
$322$	0.0396811	+	0.0574879i	0.00221134	+	0.00320368i
$323$	−16.4403	−	14.5649i	−0.914764	−	0.810410i
$324$	−0.286882	−	0.415620i	−0.0159379	−	0.0230900i
$325$	5.95868	+	8.92650i	0.330528	+	0.495153i
$326$	1.22271	−	1.77140i	0.0677195	−	0.0981086i
$327$	17.3682	−	4.28088i	0.960464	−	0.236733i
$328$	−0.759550	+	0.672902i	−0.0419391	+	0.0371548i
$329$	−0.0124285	−	0.00306334i	−0.000685204	−	0.000168888i
$330$	3.61789	+	3.20517i	0.199158	+	0.176439i
$331$	0.351421	+	0.311332i	0.0193158	+	0.0171123i	0.672725	−	0.739892i	$-0.265124\pi$
$331$	0.351421	+	0.311332i	0.0193158	+	0.0171123i	−0.653410	+	0.757005i	$0.726662\pi$
$332$	1.65966	−	4.37618i	0.0910859	−	0.240174i
$333$	−6.53823	+	9.47227i	−0.358293	+	0.519077i
$334$	−1.56239	−	0.820005i	−0.0854901	−	0.0448687i
$335$	−1.09134	+	8.98803i	−0.0596265	+	0.491069i
$336$	0.0776718	+	0.0191444i	0.00423734	+	0.00104441i
$337$	−12.8024			−0.697392			−0.348696	−	0.937236i	$-0.613375\pi$
$337$	−12.8024			−0.697392			−0.348696	+	0.937236i	$0.613375\pi$
$338$	−15.5440	+	3.32206i	−0.845483	+	0.180696i
$339$	−19.1092			−1.03787
$340$	4.23757	+	1.04447i	0.229814	+	0.0566442i
$341$	−2.04978	+	16.8815i	−0.111002	+	0.914182i
$342$	−3.91392	−	2.05418i	−0.211640	−	0.111077i
$343$	−0.232607	+	0.336990i	−0.0125596	+	0.0181958i
$344$	−13.5366	+	35.6932i	−0.729847	+	1.92445i
$345$	2.07957	+	1.84234i	0.111960	+	0.0991880i
$346$	−20.4717	−	18.1364i	−1.10057	−	0.975017i
$347$	−15.9442	−	3.92989i	−0.855928	−	0.210967i	−0.213150	−	0.977020i	$-0.568372\pi$
$347$	−15.9442	−	3.92989i	−0.855928	−	0.210967i	−0.642778	+	0.766052i	$0.722218\pi$
$348$	−3.30366	+	2.92679i	−0.177095	+	0.156892i
$349$	−18.3715	+	4.52817i	−0.983405	+	0.242388i	−0.698062	−	0.716038i	$-0.745954\pi$
$349$	−18.3715	+	4.52817i	−0.983405	+	0.242388i	−0.285343	+	0.958425i	$0.592108\pi$
$350$	−0.0604746	+	0.0876126i	−0.00323250	+	0.00468309i
$351$	−0.490220	+	3.57207i	−0.0261660	+	0.190663i
$352$	4.39162	+	6.36236i	0.234074	+	0.339115i
$353$	9.45281	+	8.37446i	0.503122	+	0.445727i	0.876112	−	0.482108i	$-0.160129\pi$
$353$	9.45281	+	8.37446i	0.503122	+	0.445727i	−0.372989	+	0.927836i	$0.621667\pi$
$354$	−2.43225	−	3.52372i	−0.129272	−	0.187284i
$355$	−14.5141	−	12.8584i	−0.770329	−	0.682452i
$356$	−2.86828	−	1.50539i	−0.152019	−	0.0797855i
$357$	−0.177709			−0.00940538
$358$	−19.7949	+	10.3892i	−1.04619	+	0.549085i
$359$	−4.70748	+	4.17046i	−0.248451	+	0.220108i	−0.778152	−	0.628076i	$-0.783843\pi$
$359$	−4.70748	+	4.17046i	−0.248451	+	0.220108i	0.529701	+	0.848185i	$0.322304\pi$
$360$	4.35673			0.229620
$361$	−5.93069			−0.312142
$362$	4.25426	−	3.76895i	0.223599	−	0.198092i
$363$	1.16186	+	3.06359i	0.0609821	+	0.160797i
$364$	0.0295697	+	0.0442974i	0.00154987	+	0.00232182i
$365$	3.33732	−	8.79978i	0.174683	−	0.460602i
$366$	3.66724	+	9.66972i	0.191690	+	0.505445i
$367$	−14.9917	−	3.69512i	−0.782561	−	0.192884i	−0.172258	−	0.985052i	$-0.555106\pi$
$367$	−14.9917	−	3.69512i	−0.782561	−	0.192884i	−0.610303	+	0.792168i	$0.708952\pi$
$368$	−3.03449	−	4.39622i	−0.158184	−	0.229169i
$369$	0.117483	−	0.309777i	0.00611591	−	0.0161263i
$370$	−7.09835	−	18.7168i	−0.369026	−	0.973041i
$371$	−0.0194358	−	0.160068i	−0.00100906	−	0.00831034i
$372$	1.75543	+	2.54319i	0.0910150	+	0.131858i
$373$	20.8798	−	5.14641i	1.08112	−	0.266471i	0.341760	−	0.939787i	$-0.388977\pi$
$373$	20.8798	−	5.14641i	1.08112	−	0.266471i	0.739355	+	0.673316i	$0.235131\pi$
$374$	15.4529	+	13.6901i	0.799049	+	0.707896i
$375$	−4.02345	+	10.6090i	−0.207770	+	0.547845i
$376$	1.30143	+	0.320775i	0.0671163	+	0.0165427i
$377$	31.5073	+	0.490123i	1.62271	+	0.0252426i
$378$	−0.0347245	+	0.00855882i	−0.00178603	+	0.000440218i
$379$	−2.67859	+	22.0602i	−0.137590	+	1.13315i	0.746350	+	0.665554i	$0.231805\pi$
$379$	−2.67859	+	22.0602i	−0.137590	+	1.13315i	−0.883940	+	0.467601i	$0.845118\pi$
$380$	−2.29949	+	1.20686i	−0.117961	+	0.0619108i
$381$	5.73555	+	15.1234i	0.293841	+	0.774795i
$382$	13.1717	+	3.24654i	0.673925	+	0.166108i
$383$	9.20927	−	8.15870i	0.470572	−	0.416890i	−0.394224	−	0.919015i	$-0.628986\pi$
$383$	9.20927	−	8.15870i	0.470572	−	0.416890i	0.864795	+	0.502124i	$0.167448\pi$
$384$	−5.12961	−	1.26433i	−0.261769	−	0.0645203i
$385$	−0.102384	+	0.0537351i	−0.00521795	+	0.00273859i
$386$	−23.9535	+	12.5717i	−1.21920	+	0.639885i
$387$	−1.50230	−	12.3726i	−0.0763662	−	0.628932i
$388$	−0.390239	−	3.21391i	−0.0198114	−	0.163161i
$389$	−3.41686	+	3.02707i	−0.173242	+	0.153479i	−0.745288	−	0.666742i	$-0.767688\pi$
$389$	−3.41686	+	3.02707i	−0.173242	+	0.153479i	0.572047	+	0.820221i	$0.306150\pi$
$390$	−4.62850	−	4.23080i	−0.234373	−	0.214235i
$391$	8.88233	+	7.86906i	0.449199	+	0.397955i
$392$	12.1779	−	17.6427i	0.615076	−	0.891091i
$393$	−5.95222	+	15.6947i	−0.300250	+	0.791694i
$394$	0.454523	+	3.74333i	0.0228985	+	0.188586i
$395$	−0.232427	+	1.91421i	−0.0116947	+	0.0963141i
$396$	−1.24274	−	0.652239i	−0.0624499	−	0.0327762i
$397$	−16.3201	+	23.6438i	−0.819084	+	1.18665i	0.160781	+	0.986990i	$0.448599\pi$
$397$	−16.3201	+	23.6438i	−0.819084	+	1.18665i	−0.979866	+	0.199659i	$0.936017\pi$
$398$	−8.40867	−	22.1718i	−0.421488	−	1.11137i
$399$	0.0791496	−	0.0701204i	0.00396244	−	0.00351041i
$400$	4.62462	−	6.69992i	0.231231	−	0.334996i
$401$	−11.1156	−	16.1037i	−0.555085	−	0.804179i	0.440529	−	0.897738i	$-0.354791\pi$
$401$	−11.1156	−	16.1037i	−0.555085	−	0.804179i	−0.995614	+	0.0935594i	$0.970175\pi$
$402$	0.938098	+	7.72593i	0.0467881	+	0.385334i
$403$	2.99966	−	21.8575i	0.149424	−	1.08880i
$404$	0.354048	−	2.91585i	0.0176145	−	0.145069i
$405$	−1.25950	+	0.661038i	−0.0625852	+	0.0328472i
$406$	0.110836	+	0.292250i	0.00550068	+	0.0145041i
$407$	−3.85557	+	31.7535i	−0.191114	+	1.57396i
$408$	18.6086			0.921265
$409$	1.28644	−	10.5947i	0.0636101	−	0.523877i	−0.925723	−	0.378203i	$-0.876542\pi$
$409$	1.28644	−	10.5947i	0.0636101	−	0.523877i	0.989333	−	0.145673i	$-0.0465349\pi$
$410$	0.327324	+	0.474210i	0.0161654	+	0.0234196i
$411$	−21.2662	+	5.24165i	−1.04899	+	0.258552i
$412$	0.692388	−	1.00310i	0.0341115	−	0.0494191i
$413$	0.0994510	−	0.0245125i	0.00489367	−	0.00120618i
$414$	2.11460	+	1.10983i	0.103927	+	0.0545450i
$415$	−11.6726	−	6.12628i	−0.572987	−	0.300727i
$416$	−5.56849	−	8.34197i	−0.273018	−	0.408999i
$417$	10.6415	−	5.58511i	0.521118	−	0.273504i
$418$	−12.2843			−0.600846
$419$	−10.1086	−	5.30539i	−0.493836	−	0.259185i	0.199371	−	0.979924i	$-0.436110\pi$
$419$	−10.1086	−	5.30539i	−0.493836	−	0.259185i	−0.693206	+	0.720739i	$0.743803\pi$
$420$	−0.00745086	+	0.0196463i	−0.000363565	+	0.000958642i
$421$	−2.58716	−	21.3072i	−0.126091	−	1.03845i	−0.909140	−	0.416491i	$-0.863260\pi$
$421$	−2.58716	−	21.3072i	−0.126091	−	1.03845i	0.783049	−	0.621960i	$-0.213663\pi$
$422$	−31.7070	+	7.81508i	−1.54347	+	0.380432i
$423$	−0.424906	+	0.104730i	−0.0206597	+	0.00509215i
$424$	2.03520	+	16.7614i	0.0988382	+	0.814005i
$425$	−6.41303	+	16.9098i	−0.311078	+	0.820244i
$426$	−14.7586	−	7.74592i	−0.715057	−	0.375291i
$427$	−0.247401			−0.0119726
$428$	2.99178	−	1.57021i	0.144613	−	0.0758988i
$429$	3.40707	+	9.42323i	0.164495	+	0.454958i
$430$	19.1935	+	10.0735i	0.925594	+	0.485789i
$431$	−0.727659	−	0.381905i	−0.0350501	−	0.0183957i	0.447107	−	0.894480i	$-0.352454\pi$
$431$	−0.727659	−	0.381905i	−0.0350501	−	0.0183957i	−0.482157	+	0.876085i	$0.660147\pi$
$432$	2.65545	−	0.654511i	0.127761	−	0.0314902i
$433$	−1.97627	+	2.86312i	−0.0949733	+	0.137593i	−0.867590	−	0.497280i	$-0.834332\pi$
$433$	−1.97627	+	2.86312i	−0.0949733	+	0.137593i	0.772617	+	0.634873i	$0.218947\pi$
$434$	0.212479	−	0.0523715i	0.0101993	−	0.00251391i
$435$	7.06191	+	10.2309i	0.338593	+	0.490536i
$436$	1.08890	−	8.96787i	0.0521487	−	0.429483i
$437$	−7.06105			−0.337776
$438$	0.975120	−	8.03084i	0.0465930	−	0.383728i
$439$	−11.2661	−	29.7063i	−0.537703	−	1.41781i	−0.878534	−	0.477680i	$-0.841478\pi$
$439$	−11.2661	−	29.7063i	−0.537703	−	1.41781i	0.340831	−	0.940125i	$-0.389292\pi$
$440$	10.7210	−	5.62681i	0.511103	−	0.268248i
$441$	−0.843654	+	6.94811i	−0.0401740	+	0.330863i
$442$	−19.7695	−	18.0708i	−0.940337	−	0.859539i
$443$	0.371687	+	3.06112i	0.0176594	+	0.145438i	0.998872	−	0.0474937i	$-0.0151234\pi$
$443$	0.371687	+	3.06112i	0.0176594	+	0.145438i	−0.981212	+	0.192932i	$0.938200\pi$
$444$	3.30191	+	4.78365i	0.156702	+	0.227022i
$445$	−5.18297	+	7.50883i	−0.245696	+	0.355953i
$446$	−11.8363	+	10.4860i	−0.560464	+	0.496528i
$447$	2.92131	+	7.70287i	0.138173	+	0.364333i
$448$	0.147401	−	0.213547i	0.00696403	−	0.0100891i
$449$	32.0823	+	16.8381i	1.51406	+	0.794638i	0.998078	−	0.0619643i	$-0.0197365\pi$
$449$	32.0823	+	16.8381i	1.51406	+	0.794638i	0.515978	+	0.856602i	$0.327429\pi$
$450$	−0.438702	+	3.61304i	−0.0206806	+	0.170320i
$451$	−0.110983	−	0.914025i	−0.00522597	−	0.0430398i
$452$	−3.42210	+	9.02333i	−0.160962	+	0.424422i
$453$	−7.59638	+	11.0053i	−0.356909	+	0.517072i
$454$	12.4176	+	11.0010i	0.582786	+	0.516303i
$455$	0.133898	−	0.0676399i	0.00627723	−	0.00317101i
$456$	−8.28807	+	7.34258i	−0.388124	+	0.343848i
$457$	1.83738	+	15.1322i	0.0859492	+	0.707856i	0.970448	+	0.241312i	$0.0775778\pi$
$457$	1.83738	+	15.1322i	0.0859492	+	0.707856i	−0.884498	+	0.466543i	$0.845499\pi$
$458$	−1.63276	−	13.4470i	−0.0762937	−	0.628335i
$459$	−5.37964	+	2.82345i	−0.251100	+	0.131787i
$460$	1.24236	−	0.652040i	0.0579253	−	0.0304015i
$461$	−31.6811	−	7.80870i	−1.47554	−	0.363687i	−0.582189	−	0.813053i	$-0.697804\pi$
$461$	−31.6811	−	7.80870i	−1.47554	−	0.363687i	−0.893348	+	0.449366i	$0.851650\pi$
$462$	−0.0743957	+	0.0659088i	−0.00346120	+	0.00306635i
$463$	2.55391	+	0.629482i	0.118690	+	0.0292545i	0.298213	−	0.954499i	$-0.403609\pi$
$463$	2.55391	+	0.629482i	0.118690	+	0.0292545i	−0.179523	+	0.983754i	$0.557455\pi$
$464$	−8.47584	−	22.3490i	−0.393481	−	1.03752i
$465$	7.70691	−	4.04490i	0.357399	−	0.187578i
$466$	−0.0222152	+	0.182959i	−0.00102910	+	0.00847540i
$467$	−30.2708	+	7.46109i	−1.40077	+	0.345258i	−0.866128	−	0.499822i	$-0.833399\pi$
$467$	−30.2708	+	7.46109i	−1.40077	+	0.345258i	−0.534639	+	0.845080i	$0.679552\pi$
$468$	1.59894	+	0.871172i	0.0739109	+	0.0402699i
$469$	−0.180771	−	0.0445560i	−0.00834722	−	0.00205741i
$470$	0.269895	−	0.711655i	0.0124493	−	0.0328262i
$471$	−0.439992	−	0.389799i	−0.0202738	−	0.0179610i
$472$	−10.4139	+	2.56680i	−0.479339	+	0.118146i
$473$	−19.6763	−	28.5060i	−0.904715	−	1.31071i
$474$	0.199789	+	1.64541i	0.00917662	+	0.0755763i
$475$	−3.81596	−	10.0619i	−0.175088	−	0.461669i
$476$	−0.0318244	+	0.0839141i	−0.00145867	+	0.00384620i
$477$	−3.13154	−	4.53681i	−0.143383	−	0.207726i
$478$	−9.10041	−	2.24305i	−0.416243	−	0.102595i
$479$	2.65840	+	7.00962i	0.121465	+	0.320278i	0.981933	−	0.189227i	$-0.0605981\pi$
$479$	2.65840	+	7.00962i	0.121465	+	0.320278i	−0.860468	+	0.509504i	$0.829829\pi$
$480$	1.40313	−	3.69974i	0.0640437	−	0.168869i
$481$	5.64227	−	41.1133i	0.257265	−	1.87461i
$482$	−4.16480	−	10.9817i	−0.189701	−	0.500201i
$483$	−0.0427627	+	0.0378844i	−0.00194577	+	0.00172380i
$484$	1.65469			0.0752131
$485$	−9.11880			−0.414063
$486$	−0.915201	+	0.810797i	−0.0415143	+	0.0367785i
$487$	7.37847	−	3.87252i	0.334350	−	0.175481i	−0.289190	−	0.957272i	$-0.593386\pi$
$487$	7.37847	−	3.87252i	0.334350	−	0.175481i	0.623540	+	0.781791i	$0.285694\pi$
$488$	25.9063			1.17272
$489$	1.55874	+	0.818089i	0.0704886	+	0.0369953i
$490$	−9.11157	−	8.07215i	−0.411619	−	0.364662i
$491$	12.1111	+	17.5459i	0.546565	+	0.791836i	0.994775	−	0.102092i	$-0.0325537\pi$
$491$	12.1111	+	17.5459i	0.546565	+	0.791836i	−0.448210	+	0.893928i	$0.647938\pi$
$492$	−0.125237	−	0.110950i	−0.00564612	−	0.00500203i
$493$	30.1631	+	43.6988i	1.35848	+	1.96810i
$494$	15.9354	+	0.247889i	0.716969	+	0.0111531i
$495$	−2.24562	+	3.25335i	−0.100933	+	0.146227i
$496$	−16.2488	+	4.00496i	−0.729590	+	0.179828i
$497$	0.298458	−	0.264411i	0.0133877	−	0.0118604i
$498$	−11.0023	−	2.71181i	−0.493023	−	0.121519i
$499$	−2.14954	−	1.90433i	−0.0962268	−	0.0852495i	0.613638	−	0.789588i	$-0.289705\pi$
$499$	−2.14954	−	1.90433i	−0.0962268	−	0.0852495i	−0.709865	+	0.704338i	$0.751244\pi$
$500$	4.28902	+	3.79974i	0.191811	+	0.169929i
$501$	0.511739	−	1.34934i	0.0228628	−	0.0602843i
$502$	−9.86103	+	14.2862i	−0.440120	+	0.637623i
$503$	11.4371	+	6.00267i	0.509956	+	0.267646i	0.700016	−	0.714127i	$-0.253176\pi$
$503$	11.4371	+	6.00267i	0.509956	+	0.267646i	−0.190060	+	0.981772i	$0.560868\pi$
$504$	−0.0107987	+	0.0889355i	−0.000481013	+	0.00396150i
$505$	−8.03272	−	1.97989i	−0.357451	−	0.0881038i
$506$	6.63694			0.295048
$507$	−4.22956	−	12.2927i	−0.187841	−	0.545939i
$508$	8.16838			0.362413
$509$	5.12110	+	1.26224i	0.226989	+	0.0559477i	0.351170	−	0.936312i	$-0.385784\pi$
$509$	5.12110	+	1.26224i	0.226989	+	0.0559477i	−0.124181	+	0.992260i	$0.539630\pi$
$510$	1.27367	−	10.4896i	0.0563989	−	0.464487i
$511$	0.171361	+	0.0899372i	0.00758056	+	0.00397859i
$512$	−13.8388	+	20.0490i	−0.611596	+	0.886050i
$513$	1.28195	−	3.38022i	0.0565995	−	0.149241i
$514$	7.07284	+	6.26599i	0.311970	+	0.276381i
$515$	−2.56967	−	2.27652i	−0.113233	−	0.100316i
$516$	−6.11134	−	1.50631i	−0.269037	−	0.0663116i
$517$	−0.910343	+	0.806493i	−0.0400368	+	0.0354695i
$518$	0.399667	−	0.0985091i	0.0175604	−	0.00432824i
$519$	12.7068	−	18.4090i	0.557766	−	0.808064i
$520$	−14.0210	+	7.08284i	−0.614861	+	0.310603i
$521$	−5.36601	−	7.77400i	−0.235089	−	0.340585i	0.687628	−	0.726063i	$-0.258652\pi$
$521$	−5.36601	−	7.77400i	−0.235089	−	0.340585i	−0.922717	+	0.385478i	$0.874037\pi$
$522$	7.99850	+	7.08606i	0.350085	+	0.310148i
$523$	−2.58952	−	3.75157i	−0.113232	−	0.164045i	0.762270	−	0.647259i	$-0.224085\pi$
$523$	−2.58952	−	3.75157i	−0.113232	−	0.164045i	−0.875502	+	0.483214i	$0.839469\pi$
$524$	6.34509	+	5.62126i	0.277187	+	0.245566i
$525$	−0.0770946	−	0.0404624i	−0.00336468	−	0.00176592i
$526$	30.3416			1.32295
$527$	32.9181	−	17.2767i	1.43393	−	0.752586i
$528$	5.68919	−	5.04018i	0.247590	−	0.219346i
$529$	−19.1851			−0.834134
$530$	9.58760			0.416459
$531$	2.62114	−	2.32212i	0.113748	−	0.100772i
$532$	−0.0189365	−	0.0499316i	−0.000821004	−	0.00216481i
$533$	0.125524	+	1.18793i	0.00543706	+	0.0514548i
$534$	−2.78107	+	7.33308i	−0.120349	+	0.317333i
$535$	−3.37469	−	8.89833i	−0.145901	−	0.384708i
$536$	18.9292	+	4.66563i	0.817618	+	0.201525i
$537$	−10.3864	−	15.0473i	−0.448207	−	0.649340i
$538$	−7.21304	+	19.0192i	−0.310976	+	0.819977i
$539$	6.89758	+	18.1874i	0.297100	+	0.783388i
$540$	0.0865878	+	0.713115i	0.00372615	+	0.0306876i
$541$	7.04240	+	10.2027i	0.302776	+	0.438647i	0.944609	−	0.328197i	$-0.106441\pi$
$541$	7.04240	+	10.2027i	0.302776	+	0.438647i	−0.641833	+	0.766845i	$0.721826\pi$
$542$	−20.3706	+	5.02089i	−0.874990	+	0.215666i
$543$	3.47942	+	3.08249i	0.149316	+	0.132282i
$544$	5.99309	−	15.8025i	0.256952	−	0.677526i
$545$	−24.7051	−	6.08927i	−1.05825	−	0.260836i
$546$	0.0978372	−	0.0839967i	0.00418705	−	0.00359473i
$547$	40.4474	−	9.96939i	1.72941	−	0.426260i	0.755857	−	0.654737i	$-0.227221\pi$
$547$	40.4474	−	9.96939i	1.72941	−	0.426260i	0.973549	+	0.228477i	$0.0733746\pi$
$548$	−1.33328	+	10.9806i	−0.0569550	+	0.469066i
$549$	−7.48934	+	3.93071i	−0.319637	+	0.167759i
$550$	3.58676	+	9.45751i	0.152940	+	0.403270i
$551$	−30.6769	−	7.56119i	−1.30688	−	0.322117i
$552$	4.47785	−	3.96703i	0.190590	−	0.168848i
$553$	−0.0384992	−	0.00948921i	−0.00163715	−	0.000403522i
$554$	12.1444	−	6.37387i	0.515966	−	0.270800i
$555$	14.4964	−	7.60832i	0.615340	−	0.322955i
$556$	−0.731581	−	6.02511i	−0.0310259	−	0.255522i
$557$	−0.338126	−	2.78472i	−0.0143269	−	0.117992i	0.983791	−	0.179320i	$-0.0573897\pi$
$557$	−0.338126	−	2.78472i	−0.0143269	−	0.117992i	−0.998118	+	0.0613274i	$0.980467\pi$
$558$	5.60012	−	4.96127i	0.237072	−	0.210028i
$559$	24.9491	+	37.3754i	1.05524	+	1.58081i
$560$	−0.0851726	−	0.0754564i	−0.00359920	−	0.00318861i
$561$	−9.59159	+	13.8958i	−0.404957	+	0.586682i
$562$	2.73121	−	7.20161i	0.115209	−	0.303782i
$563$	0.0558641	+	0.460082i	0.00235439	+	0.0193901i	0.993839	−	0.110836i	$-0.0353528\pi$
$563$	0.0558641	+	0.460082i	0.00235439	+	0.0193901i	−0.991484	+	0.130226i	$0.958430\pi$
$564$	−0.0266394	+	0.219395i	−0.00112172	+	0.00923821i
$565$	24.0681	+	12.6319i	1.01255	+	0.531428i
$566$	−0.890959	+	1.29078i	−0.0374498	+	0.0542554i
$567$	−0.0103722	−	0.0273491i	−0.000435590	−	0.00114856i
$568$	−31.2527	+	27.6875i	−1.31133	+	1.16174i
$569$	−14.3399	+	20.7749i	−0.601160	+	0.870931i	−0.998915	−	0.0465606i	$-0.985174\pi$
$569$	−14.3399	+	20.7749i	−0.601160	+	0.870931i	0.397755	+	0.917492i	$0.369789\pi$
$570$	3.57170	+	5.17449i	0.149602	+	0.216736i
$571$	−0.373289	−	3.07431i	−0.0156216	−	0.128656i	0.982812	−	0.184611i	$-0.0591026\pi$
$571$	−0.373289	−	3.07431i	−0.0156216	−	0.128656i	−0.998433	+	0.0559554i	$0.982180\pi$
$572$	5.05978	+	0.0787092i	0.211560	+	0.00329100i
$573$	−1.33737	+	11.0142i	−0.0558693	+	0.460125i
$574$	−0.0104915	+	0.00550638i	−0.000437908	+	0.000229832i
$575$	2.06167	+	5.43619i	0.0859777	+	0.226705i
$576$	1.06929	−	8.80642i	0.0445539	−	0.366934i
$577$	−33.3756			−1.38945			−0.694723	−	0.719277i	$-0.744473\pi$
$577$	−33.3756			−1.38945			−0.694723	+	0.719277i	$0.744473\pi$
$578$	2.93468	−	24.1693i	0.122067	−	1.00531i
$579$	−12.5684	−	18.2085i	−0.522326	−	0.756720i
$580$	6.09569	−	1.50245i	0.253110	−	0.0623860i
$581$	0.153990	−	0.223093i	0.00638858	−	0.00925545i
$582$	−7.61057	+	1.87584i	−0.315468	+	0.0777559i
$583$	−13.5654	−	7.11969i	−0.561823	−	0.294867i
$584$	−17.9439	−	9.41768i	−0.742523	−	0.389706i
$585$	2.97871	−	4.17498i	0.123154	−	0.172614i
$586$	36.0428	−	18.9167i	1.48892	−	0.781443i
$587$	1.94507			0.0802814			0.0401407	−	0.999194i	$-0.487219\pi$
$587$	1.94507			0.0802814			0.0401407	+	0.999194i	$0.487219\pi$
$588$	3.12981	+	1.64265i	0.129071	+	0.0677417i
$589$	−7.84426	+	20.6836i	−0.323217	+	0.852254i
$590$	0.734110	+	6.04594i	0.0302228	+	0.248907i
$591$	−2.99441	+	0.738056i	−0.123174	+	0.0303596i
$592$	−30.5634	+	7.53319i	−1.25615	+	0.309612i
$593$	−2.65022	−	21.8266i	−0.108832	−	0.896309i	−0.940208	−	0.340600i	$-0.889370\pi$
$593$	−2.65022	−	21.8266i	−0.108832	−	0.896309i	0.831377	−	0.555709i	$-0.187553\pi$
$594$	−1.20495	+	3.17720i	−0.0494398	+	0.130362i
$595$	0.223825	+	0.117473i	0.00917595	+	0.00481591i
$596$	4.16044			0.170418
$597$	17.1724	−	9.01277i	0.702820	−	0.368868i
$598$	−8.60954	−	0.133929i	−0.352070	−	0.00547676i
$599$	4.69626	+	2.46479i	0.191884	+	0.100708i	0.557929	−	0.829889i	$-0.311596\pi$
$599$	4.69626	+	2.46479i	0.191884	+	0.100708i	−0.366045	+	0.930597i	$0.619288\pi$
$600$	8.07288	+	4.23697i	0.329574	+	0.172974i
$601$	20.3794	−	5.02306i	0.831291	−	0.204895i	0.199367	−	0.979925i	$-0.436111\pi$
$601$	20.3794	−	5.02306i	0.831291	−	0.204895i	0.631924	+	0.775030i	$0.282265\pi$
$602$	−0.253208	+	0.366836i	−0.0103200	+	0.0149511i
$603$	−6.18022	+	1.52329i	−0.251678	+	0.0620331i
$604$	3.83630	+	5.55784i	0.156097	+	0.226145i
$605$	0.561775	−	4.62663i	0.0228394	−	0.188099i
$606$	−7.11140			−0.288881
$607$	3.09340	−	25.4764i	0.125557	−	1.03406i	−0.784660	−	0.619926i	$-0.787163\pi$
$607$	3.09340	−	25.4764i	0.125557	−	1.03406i	0.910218	−	0.414130i	$-0.135914\pi$
$608$	3.56608	+	9.40298i	0.144624	+	0.381341i
$609$	−0.226352	+	0.118799i	−0.00917224	+	0.00481396i
$610$	1.77315	−	14.6032i	0.0717929	−	0.591267i
$611$	1.19719	−	1.02783i	0.0484329	−	0.0415814i
$612$	0.369837	+	3.04588i	0.0149498	+	0.123123i
$613$	−8.70452	−	12.6107i	−0.351572	−	0.509340i	0.606803	−	0.794852i	$-0.292452\pi$
$613$	−8.70452	−	12.6107i	−0.351572	−	0.509340i	−0.958375	+	0.285512i	$0.907836\pi$
$614$	−22.8841	+	33.1534i	−0.923528	+	1.33796i
$615$	−0.352744	+	0.312504i	−0.0142240	+	0.0126014i
$616$	0.0882886	+	0.232798i	0.00355725	+	0.00937970i
$617$	−2.05204	+	2.97289i	−0.0826119	+	0.119684i	−0.862111	−	0.506719i	$-0.830858\pi$
$617$	−2.05204	+	2.97289i	−0.0826119	+	0.119684i	0.779499	+	0.626403i	$0.215474\pi$
$618$	−2.61295	−	1.37138i	−0.105108	−	0.0551651i
$619$	−0.708651	+	5.83626i	−0.0284831	+	0.234579i	−0.999997	−	0.00240275i	$-0.999235\pi$
$619$	−0.708651	+	5.83626i	−0.0284831	+	0.234579i	0.971514	+	0.236982i	$0.0761583\pi$
$620$	−0.529832	−	4.36356i	−0.0212786	−	0.175245i
$621$	−0.692608	+	1.82626i	−0.0277934	+	0.0732852i
$622$	−20.5045	+	29.7059i	−0.822157	+	1.19110i
$623$	−0.140434	−	0.124413i	−0.00562636	−	0.00498452i
$624$	−7.48182	+	6.42340i	−0.299512	+	0.257142i
$625$	0.940095	−	0.832851i	0.0376038	−	0.0333141i
$626$	2.56596	+	21.1326i	0.102556	+	0.844628i
$627$	−1.21102	−	9.97367i	−0.0483636	−	0.398310i
$628$	−0.262857	+	0.137958i	−0.0104891	+	0.00550512i
$629$	61.9178	−	32.4970i	2.46882	−	1.29574i
$630$	0.0493933	+	0.0121744i	0.00196788	+	0.000485038i
$631$	−3.06529	+	2.71561i	−0.122027	+	0.108107i	−0.721930	−	0.691966i	$-0.756745\pi$
$631$	−3.06529	+	2.71561i	−0.122027	+	0.108107i	0.599902	+	0.800073i	$0.295206\pi$
$632$	4.03141	+	0.993652i	0.160361	+	0.0395254i
$633$	−9.47084	−	24.9726i	−0.376432	−	0.992570i
$634$	−10.4755	+	5.49796i	−0.416035	+	0.218352i
$635$	2.77320	−	22.8394i	0.110051	−	0.906353i
$636$	−2.70308	+	0.666248i	−0.107184	+	0.0264185i
$637$	−8.58064	−	23.7322i	−0.339977	−	0.940304i
$638$	28.8344	+	7.10704i	1.14156	+	0.281370i
$639$	4.83398	−	12.7462i	0.191229	−	0.504231i
$640$	5.62498	+	4.98330i	0.222347	+	0.196982i
$641$	24.2811	−	5.98476i	0.959046	−	0.236384i	0.271430	−	0.962458i	$-0.412503\pi$
$641$	24.2811	−	5.98476i	0.959046	−	0.236384i	0.687616	+	0.726074i	$0.258657\pi$
$642$	−4.64701	−	6.73235i	−0.183403	−	0.265705i
$643$	−4.40669	−	36.2923i	−0.173783	−	1.43123i	−0.774908	−	0.632075i	$-0.782204\pi$
$643$	−4.40669	−	36.2923i	−0.173783	−	1.43123i	0.601125	−	0.799155i	$-0.294719\pi$
$644$	0.0102310	+	0.0269769i	0.000403157	+	0.00106304i
$645$	−6.28658	+	16.5763i	−0.247534	+	0.652693i
$646$	15.2556	+	22.1015i	0.600222	+	0.869572i
$647$	−44.9603	−	11.0817i	−1.76757	−	0.435667i	−0.784687	−	0.619892i	$-0.787176\pi$
$647$	−44.9603	−	11.0817i	−1.76757	−	0.435667i	−0.982884	+	0.184225i	$0.941023\pi$
$648$	1.08611	+	2.86383i	0.0426664	+	0.112502i
$649$	3.45099	−	9.09951i	0.135463	−	0.357187i
$650$	−4.46196	−	12.3408i	−0.175012	−	0.484046i
$651$	0.0634673	+	0.167350i	0.00248748	+	0.00655895i
$652$	0.665441	−	0.589530i	0.0260607	−	0.0230878i
$653$	−4.31292			−0.168778			−0.0843888	−	0.996433i	$-0.526894\pi$
$653$	−4.31292			−0.168778			−0.0843888	+	0.996433i	$0.526894\pi$
$654$	−21.8716			−0.855246
$655$	17.8716	−	15.8329i	0.698303	−	0.618642i
$656$	0.802309	−	0.421084i	0.0313249	−	0.0164406i
$657$	6.61638			0.258130
$658$	0.0138583	+	0.00727339i	0.000540252	+	0.000283546i
$659$	19.0535	+	16.8799i	0.742217	+	0.657547i	0.946990	−	0.321263i	$-0.104107\pi$
$659$	19.0535	+	16.8799i	0.742217	+	0.657547i	−0.204773	+	0.978809i	$0.565646\pi$
$660$	1.13408	+	1.64299i	0.0441439	+	0.0639534i
$661$	−9.13000	−	8.08847i	−0.355116	−	0.314605i	0.466637	−	0.884449i	$-0.345465\pi$
$661$	−9.13000	−	8.08847i	−0.355116	−	0.314605i	−0.821753	+	0.569844i	$0.807004\pi$
$662$	−0.326096	−	0.472432i	−0.0126741	−	0.0183616i
$663$	12.7228	−	17.8323i	0.494112	−	0.692550i
$664$	−16.1249	+	23.3609i	−0.625767	+	0.906580i
$665$	−0.146041	+	0.0359960i	−0.00566324	+	0.00139586i
$666$	10.5336	−	9.33200i	0.408171	−	0.361608i
$667$	16.5740	+	4.08513i	0.641749	+	0.158177i
$668$	−0.545516	−	0.483285i	−0.0211066	−	0.0186988i
$669$	−9.68048	−	8.57615i	−0.374269	−	0.331573i
$670$	3.92560	−	10.3510i	0.151659	−	0.399892i
$671$	−13.3531	+	19.3453i	−0.515490	+	0.746816i
$672$	0.0720463	+	0.0378128i	0.00277924	+	0.00145866i
$673$	0.408766	−	3.36649i	0.0157568	−	0.129769i	−0.982708	−	0.185163i	$-0.940719\pi$
$673$	0.408766	−	3.36649i	0.0157568	−	0.129769i	0.998465	+	0.0553946i	$0.0176417\pi$
$674$	15.1986	+	3.74612i	0.585428	+	0.144295i
$675$	−2.97668			−0.114573
$676$	−6.56204	−	0.204206i	−0.252386	−	0.00785406i
$677$	9.63676			0.370371			0.185185	−	0.982704i	$-0.440711\pi$
$677$	9.63676			0.370371			0.185185	+	0.982704i	$0.440711\pi$
$678$	22.6858	+	5.59154i	0.871242	+	0.214742i
$679$	0.0226021	−	0.186145i	0.000867390	−	0.00714360i
$680$	−23.4376	−	12.3010i	−0.898793	−	0.471723i
$681$	−7.70759	+	11.1664i	−0.295355	+	0.427896i
$682$	7.37312	−	19.4413i	0.282331	−	0.744446i
$683$	−4.18823	−	3.71045i	−0.160258	−	0.141976i	0.579183	−	0.815198i	$-0.303372\pi$
$683$	−4.18823	−	3.71045i	−0.160258	−	0.141976i	−0.739441	+	0.673221i	$0.764910\pi$
$684$	−1.36656	−	1.21067i	−0.0522519	−	0.0462911i
$685$	30.2498	+	7.45590i	1.15579	+	0.284875i
$686$	0.374750	−	0.332000i	0.0143080	−	0.0126758i
$687$	10.7566	−	2.65128i	0.410392	−	0.101152i
$688$	19.3634	−	28.0527i	0.738222	−	1.06950i
$689$	17.4536	+	9.50951i	0.664930	+	0.362283i
$690$	−1.92970	−	2.79566i	−0.0734626	−	0.106429i
$691$	23.4177	+	20.7463i	0.890851	+	0.789225i	0.978354	−	0.206939i	$-0.0663502\pi$
$691$	23.4177	+	20.7463i	0.890851	+	0.789225i	−0.0875029	+	0.996164i	$0.527889\pi$
$692$	−6.41714	−	9.29683i	−0.243943	−	0.353412i
$693$	−0.0608456	−	0.0539045i	−0.00231133	−	0.00204766i
$694$	17.7785	+	9.33085i	0.674861	+	0.354194i
$695$	−17.0950			−0.648451
$696$	23.7022	−	12.4399i	0.898429	−	0.471532i
$697$	−1.50665	+	1.33478i	−0.0570686	+	0.0505583i
$698$	23.1350			0.875674
$699$	−0.150735			−0.00570131
$700$	−0.0329125	+	0.0291579i	−0.00124397	+	0.00110206i
$701$	1.01510	+	2.67659i	0.0383396	+	0.101093i	0.952819	−	0.303540i	$-0.0981685\pi$
$701$	1.01510	+	2.67659i	0.0383396	+	0.101093i	−0.914479	+	0.404633i	$0.867399\pi$
$702$	1.62720	−	4.09720i	0.0614146	−	0.154639i
$703$	−14.7548	+	38.9052i	−0.556488	+	1.46734i
$704$	−8.74237	−	23.0517i	−0.329490	−	0.868795i
$705$	0.604401	+	0.148972i	0.0227631	+	0.00561059i
$706$	−8.77160	−	12.7079i	−0.330124	−	0.478267i
$707$	0.0603262	−	0.159067i	0.00226880	−	0.00598234i
$708$	−0.627107	−	1.65355i	−0.0235681	−	0.0621441i
$709$	2.05516	+	16.9257i	0.0771830	+	0.635659i	0.979046	+	0.203638i	$0.0652765\pi$
$709$	2.05516	+	16.9257i	0.0771830	+	0.635659i	−0.901863	+	0.432022i	$0.857800\pi$
$710$	13.4682	+	19.5120i	0.505451	+	0.732273i
$711$	−1.31622	+	0.324419i	−0.0493620	+	0.0121666i
$712$	14.7054	+	13.0278i	0.551107	+	0.488238i
$713$	4.23808	−	11.1749i	0.158717	−	0.418503i
$714$	0.210971	+	0.0519996i	0.00789537	+	0.00194604i
$715$	1.93790	−	14.1208i	0.0724732	−	0.528088i
$716$	−8.96534	+	2.20976i	−0.335051	+	0.0825826i
$717$	0.923993	−	7.60977i	0.0345072	−	0.284192i
$718$	6.80887	−	3.57357i	0.254105	−	0.133365i
$719$	−2.61422	−	6.89312i	−0.0974938	−	0.257070i	0.877392	−	0.479773i	$-0.159281\pi$
$719$	−2.61422	−	6.89312i	−0.0974938	−	0.257070i	−0.974886	+	0.222703i	$0.928512\pi$
$720$	−3.77721	−	0.930998i	−0.140768	−	0.0346962i
$721$	0.0528407	−	0.0468128i	0.00196789	−	0.00174340i
$722$	7.04071	+	1.73538i	0.262028	+	0.0645842i
$723$	8.50546	−	4.46401i	0.316321	−	0.166018i
$724$	2.07865	−	1.09096i	0.0772523	−	0.0405451i
$725$	3.13577	+	25.8254i	0.116460	+	0.959131i
$726$	−0.482890	−	3.97696i	−0.0179217	−	0.147599i
$727$	−6.20061	+	5.49326i	−0.229968	+	0.203734i	−0.770236	−	0.637759i	$-0.779861\pi$
$727$	−6.20061	+	5.49326i	−0.229968	+	0.203734i	0.540268	+	0.841493i	$0.318323\pi$
$728$	−0.109832	−	0.303771i	−0.00407063	−	0.0112585i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−6.53685	+	9.47027i	−0.241940	+	0.350510i
$731$	−26.8515	+	70.8016i	−0.993138	+	2.61869i
$732$	0.514874	+	4.24037i	0.0190303	+	0.156729i
$733$	−2.66373	+	21.9378i	−0.0983870	+	0.810290i	0.857078	+	0.515186i	$0.172277\pi$
$733$	−2.66373	+	21.9378i	−0.0983870	+	0.810290i	−0.955465	+	0.295104i	$0.904646\pi$
$734$	16.7164	+	8.77345i	0.617014	+	0.323834i
$735$	5.65555	−	8.19348i	0.208608	−	0.302221i
$736$	−1.92667	−	5.08021i	−0.0710180	−	0.187259i
$737$	−13.2408	+	11.7304i	−0.487733	+	0.432094i
$738$	−0.230115	+	0.333379i	−0.00847066	+	0.0122719i
$739$	1.09210	+	1.58218i	0.0401736	+	0.0582015i	0.842556	−	0.538609i	$-0.181050\pi$
$739$	1.09210	+	1.58218i	0.0401736	+	0.0582015i	−0.802382	+	0.596810i	$0.796435\pi$
$740$	−0.996596	−	8.20771i	−0.0366356	−	0.301721i
$741$	1.36970	+	12.9624i	0.0503171	+	0.476187i
$742$	−0.0237641	+	0.195715i	−0.000872408	+	0.00718492i
$743$	−40.7639	+	21.3945i	−1.49548	+	0.784890i	−0.996648	−	0.0818073i	$-0.973931\pi$
$743$	−40.7639	+	21.3945i	−1.49548	+	0.784890i	−0.498835	+	0.866697i	$0.666238\pi$
$744$	−6.64591	−	17.5238i	−0.243651	−	0.642455i
$745$	1.41249	−	11.6329i	0.0517495	−	0.426196i
$746$	−26.2937			−0.962680
$747$	1.11709	−	9.20009i	0.0408723	−	0.336614i
$748$	4.84391	+	7.01762i	0.177111	+	0.256590i
$749$	0.190009	−	0.0468331i	0.00694279	−	0.00171124i
$750$	7.88080	−	11.4173i	0.287766	−	0.416901i
$751$	−23.1127	+	5.69676i	−0.843393	+	0.207878i	−0.637263	−	0.770647i	$-0.719933\pi$
$751$	−23.1127	+	5.69676i	−0.843393	+	0.207878i	−0.206131	+	0.978525i	$0.566087\pi$
$752$	−1.05977	−	0.556211i	−0.0386459	−	0.0202829i
$753$	−12.5711	−	6.59782i	−0.458116	−	0.240438i
$754$	−37.2610	−	9.80122i	−1.35697	−	0.356939i
$755$	16.8426	−	8.83966i	0.612963	−	0.321708i
$756$	−0.0147717			−0.000537241
$757$	−25.2796	−	13.2678i	−0.918802	−	0.482225i	−0.0621198	−	0.998069i	$-0.519786\pi$
$757$	−25.2796	−	13.2678i	−0.918802	−	0.482225i	−0.856683	+	0.515844i	$0.827478\pi$
$758$	9.63496	−	25.4053i	0.349957	−	0.922762i
$759$	0.654288	+	5.38855i	0.0237491	+	0.195592i
$760$	15.2926	−	3.76928i	0.554720	−	0.136726i
$761$	15.1639	−	3.73758i	0.549693	−	0.135487i	0.0453190	−	0.998973i	$-0.485570\pi$
$761$	15.1639	−	3.73758i	0.549693	−	0.135487i	0.504374	+	0.863486i	$0.331723\pi$
$762$	−2.38379	−	19.6323i	−0.0863556	−	0.711202i
$763$	0.185537	−	0.489221i	0.00671690	−	0.0177110i
$764$	4.96140	+	2.60394i	0.179497	+	0.0942073i
$765$	8.64208			0.312455
$766$	−13.3203	+	6.99101i	−0.481280	+	0.252595i
$767$	−4.66030	+	11.7344i	−0.168274	+	0.423704i
$768$	−9.99020	−	5.24326i	−0.360490	−	0.189200i
$769$	4.50348	+	2.36361i	0.162400	+	0.0852339i	0.543965	−	0.839108i	$-0.316922\pi$
$769$	4.50348	+	2.36361i	0.162400	+	0.0852339i	−0.381565	+	0.924342i	$0.624615\pi$
$770$	0.137270	−	0.0338340i	0.00494686	−	0.00121929i
$771$	−4.39011	+	6.36017i	−0.158106	+	0.229056i
$772$	−10.8488	+	2.67399i	−0.390457	+	0.0962390i
$773$	25.4266	+	36.8368i	0.914530	+	1.32493i	0.945574	+	0.325408i	$0.105502\pi$
$773$	25.4266	+	36.8368i	0.914530	+	1.32493i	−0.0310435	+	0.999518i	$0.509883\pi$
$774$	−1.83686	+	15.1279i	−0.0660244	+	0.543760i
$775$	18.2143			0.654279
$776$	−2.36676	+	19.4920i	−0.0849616	+	0.699722i
$777$	0.119380	+	0.314779i	0.00428273	+	0.0112926i
$778$	4.94213	−	2.59383i	0.177184	−	0.0929934i
$779$	0.144369	−	1.18899i	0.00517257	−	0.0425999i
$780$	−1.43799	−	2.15420i	−0.0514882	−	0.0771328i
$781$	−4.56653	−	37.6088i	−0.163403	−	1.34575i
$782$	−8.24223	−	11.9409i	−0.294742	−	0.427007i
$783$	−4.96467	+	7.19256i	−0.177423	+	0.257041i
$784$	−14.3281	+	12.6936i	−0.511718	+	0.453342i
$785$	0.296499	+	0.781804i	0.0105825	+	0.0279038i
$786$	11.6587	−	16.8906i	0.415852	−	0.602466i
$787$	16.7371	+	8.78429i	0.596612	+	0.313126i	0.735863	−	0.677131i	$-0.236777\pi$
$787$	16.7371	+	8.78429i	0.596612	+	0.313126i	−0.139250	+	0.990257i	$0.544469\pi$
$788$	−0.187734	+	1.54613i	−0.00668774	+	0.0550785i
$789$	2.99115	+	24.6344i	0.106488	+	0.877007i
$790$	0.836045	−	2.20447i	0.0297451	−	0.0784315i
$791$	−0.317515	+	0.460000i	−0.0112895	+	0.0163557i
$792$	6.37138	+	5.64455i	0.226397	+	0.200570i
$793$	17.7122	−	24.8255i	0.628979	−	0.881581i
$794$	26.2931	−	23.2937i	0.933108	−	0.826662i
$795$	0.945172	+	7.78419i	0.0335218	+	0.276077i
$796$	−1.18056	−	9.72280i	−0.0418439	−	0.344616i
$797$	30.7563	−	16.1422i	1.08945	−	0.571785i	0.178344	−	0.983968i	$-0.442926\pi$
$797$	30.7563	−	16.1422i	1.08945	−	0.571785i	0.911101	+	0.412183i	$0.135234\pi$
$798$	−0.114482	+	0.0600846i	−0.00405261	+	0.00212697i
$799$	2.58154	+	0.636293i	0.0913284	+	0.0225104i
$800$	6.19798	−	5.49094i	0.219132	−	0.194134i
$801$	−6.22791	−	1.53504i	−0.220052	−	0.0542380i
$802$	8.48392	+	22.3703i	0.299578	+	0.789921i
$803$	16.2815	−	8.54519i	0.574562	−	0.301553i
$804$	−0.387468	+	3.19108i	−0.0136649	+	0.112541i
$805$	0.0789028	−	0.0194478i	0.00278096	−	0.000685445i
$806$	−9.95683	+	25.0708i	−0.350715	+	0.883081i
$807$	−16.1528	−	3.98132i	−0.568607	−	0.140149i
$808$	−6.31700	+	16.6566i	−0.222231	+	0.585975i
$809$	22.7828	+	20.1838i	0.801002	+	0.709626i	0.960715	−	0.277538i	$-0.0895184\pi$
$809$	22.7828	+	20.1838i	0.801002	+	0.709626i	−0.159713	+	0.987163i	$0.551057\pi$
$810$	1.68866	−	0.416219i	0.0593336	−	0.0146244i
$811$	−27.7595	−	40.2166i	−0.974769	−	1.41220i	−0.910146	−	0.414287i	$-0.864031\pi$
$811$	−27.7595	−	40.2166i	−0.974769	−	1.41220i	−0.0646227	−	0.997910i	$-0.520584\pi$
$812$	0.0155611	+	0.128158i	0.000546089	+	0.00449745i
$813$	−6.08466	−	16.0439i	−0.213398	−	0.562685i
$814$	13.8686	−	36.5685i	0.486094	−	1.28172i
$815$	−1.42245	−	2.06077i	−0.0498262	−	0.0721857i
$816$	−16.1334	−	3.97652i	−0.564781	−	0.139206i
$817$	−15.9775	−	42.1292i	−0.558982	−	1.47391i
$818$	−4.62734	+	12.2013i	−0.161791	+	0.426608i
$819$	0.0778421	+	0.0711536i	0.00272002	+	0.00248631i
$820$	0.0843940	+	0.222529i	0.00294717	+	0.00777104i
$821$	−14.5213	+	12.8647i	−0.506796	+	0.448982i	−0.877366	−	0.479823i	$-0.840701\pi$
$821$	−14.5213	+	12.8647i	−0.506796	+	0.448982i	0.370569	+	0.928805i	$0.379163\pi$
$822$	26.7803			0.934070
$823$	−22.3211			−0.778064			−0.389032	−	0.921224i	$-0.627190\pi$
$823$	−22.3211			−0.778064			−0.389032	+	0.921224i	$0.627190\pi$
$824$	−5.53316	+	4.90195i	−0.192757	+	0.170768i
$825$	−7.32498	+	3.84445i	−0.255023	+	0.133846i
$826$	−0.125237			−0.00435757
$827$	−0.234734	−	0.123198i	−0.00816250	−	0.00428401i	0.460637	−	0.887589i	$-0.347621\pi$
$827$	−0.234734	−	0.123198i	−0.00816250	−	0.00428401i	−0.468799	+	0.883305i	$0.655313\pi$
$828$	0.738323	+	0.654097i	0.0256585	+	0.0227314i
$829$	−16.5056	−	23.9126i	−0.573265	−	0.830517i	0.423904	−	0.905707i	$-0.360659\pi$
$829$	−16.5056	−	23.9126i	−0.573265	−	0.830517i	−0.997169	+	0.0751895i	$0.976044\pi$
$830$	12.0648	+	10.6884i	0.418774	+	0.371001i
$831$	6.37218	+	9.23170i	0.221049	+	0.320244i
$832$	10.8756	+	30.0795i	0.377043	+	1.04282i
$833$	24.1562	−	34.9963i	0.836963	−	1.21255i
$834$	−14.2675	+	3.51663i	−0.494044	+	0.121771i
$835$	−1.53650	+	1.36122i	−0.0531729	+	0.0471071i
$836$	−4.92643	−	1.21425i	−0.170384	−	0.0419959i
$837$	4.58015	+	4.05765i	0.158313	+	0.140253i
$838$	10.4481	+	9.25624i	0.360925	+	0.319752i
$839$	−6.59291	+	17.3841i	−0.227613	+	0.600165i	−0.999360	−	0.0357636i	$-0.988614\pi$
$839$	−6.59291	+	17.3841i	−0.227613	+	0.600165i	0.771748	+	0.635929i	$0.219383\pi$
$840$	0.0723907	−	0.104876i	0.00249772	−	0.00361857i
$841$	41.9537	+	22.0190i	1.44668	+	0.759276i
$842$	−3.16331	+	26.0522i	−0.109015	+	0.897819i
$843$	6.11625	+	1.50752i	0.210655	+	0.0519218i
$844$	−13.4881			−0.464278
$845$	−2.79882	+	18.2786i	−0.0962822	+	0.628803i
$846$	0.535079			0.0183964
$847$	0.0930526	+	0.0229354i	0.00319732	+	0.000788070i
$848$	1.81729	−	14.9667i	0.0624060	−	0.513960i
$849$	−1.13582	−	0.596123i	−0.0389812	−	0.0204589i
$850$	12.5613	−	18.1982i	0.430849	−	0.624193i
$851$	7.97168	−	21.0196i	0.273266	−	0.720543i
$852$	−5.15305	−	4.56520i	−0.176540	−	0.156401i
$853$	33.5056	+	29.6834i	1.14721	+	1.01634i	0.999628	+	0.0272899i	$0.00868772\pi$
$853$	33.5056	+	29.6834i	1.14721	+	1.01634i	0.147583	+	0.989050i	$0.452851\pi$
$854$	0.293706	+	0.0723920i	0.0100504	+	0.00247720i
$855$	−3.84908	+	3.40998i	−0.131636	+	0.116619i
$856$	−19.8966	+	4.90407i	−0.680052	+	0.167618i
$857$	−12.3921	+	17.9530i	−0.423305	+	0.613263i	−0.975380	−	0.220531i	$-0.929221\pi$
$857$	−12.3921	+	17.9530i	−0.423305	+	0.613263i	0.552075	+	0.833795i	$0.313836\pi$
$858$	−1.28743	−	12.1839i	−0.0439521	−	0.415951i
$859$	8.51247	+	12.3324i	0.290442	+	0.420777i	0.940858	−	0.338800i	$-0.110021\pi$
$859$	8.51247	+	12.3324i	0.290442	+	0.420777i	−0.650417	+	0.759578i	$0.725406\pi$
$860$	6.70152	+	5.93703i	0.228520	+	0.202451i
$861$	−0.00550493	−	0.00797526i	−0.000187607	−	0.000271796i
$862$	0.752102	+	0.666305i	0.0256167	+	0.0226944i
$863$	−18.8939	−	9.91626i	−0.643154	−	0.337554i	0.111415	−	0.993774i	$-0.464462\pi$
$863$	−18.8939	−	9.91626i	−0.643154	−	0.337554i	−0.754569	+	0.656220i	$0.772154\pi$
$864$	2.78176			0.0946375
$865$	−28.1733	+	14.7865i	−0.957920	+	0.502755i
$866$	3.18393	−	2.82072i	0.108194	−	0.0958519i
$867$	19.9124			0.676260
$868$	0.0903880			0.00306797
$869$	−2.81994	+	2.49825i	−0.0956598	+	0.0847472i
$870$	−5.38998	−	14.2122i	−0.182738	−	0.481839i
$871$	17.4129	−	14.9496i	0.590015	−	0.506549i
$872$	−19.4283	+	51.2283i	−0.657926	+	1.73481i
$873$	−2.27327	−	5.99411i	−0.0769384	−	0.202870i
$874$	8.38263	+	2.06613i	0.283547	+	0.0698880i
$875$	0.188528	+	0.273130i	0.00637342	+	0.00923349i
$876$	1.18487	−	3.12425i	0.0400331	−	0.105558i
$877$	9.11792	+	24.0420i	0.307890	+	0.811840i	0.996254	+	0.0864744i	$0.0275601\pi$
$877$	9.11792	+	24.0420i	0.307890	+	0.811840i	−0.688364	+	0.725366i	$0.741671\pi$
$878$	4.68238	+	38.5629i	0.158023	+	1.30144i
$879$	18.9117	+	27.3984i	0.637877	+	0.924125i
$880$	−10.4973	+	2.58735i	−0.353864	+	0.0872197i
$881$	−15.4810	−	13.7150i	−0.521570	−	0.462070i	0.360789	−	0.932647i	$-0.382507\pi$
$881$	−15.4810	−	13.7150i	−0.521570	−	0.462070i	−0.882359	+	0.470577i	$0.844046\pi$
$882$	3.03465	−	8.00170i	0.102182	−	0.269431i
$883$	49.3990	+	12.1758i	1.66241	+	0.409747i	0.954893	−	0.296950i	$-0.0959695\pi$
$883$	49.3990	+	12.1758i	1.66241	+	0.409747i	0.707516	+	0.706697i	$0.249816\pi$
$884$	−6.14199	−	9.20111i	−0.206577	−	0.309467i
$885$	−4.83634	+	1.19205i	−0.162572	+	0.0400704i
$886$	0.454460	−	3.74282i	0.0152679	−	0.125742i
$887$	7.83440	−	4.11181i	0.263053	−	0.138061i	−0.328041	−	0.944663i	$-0.606388\pi$
$887$	7.83440	−	4.11181i	0.263053	−	0.138061i	0.591094	+	0.806602i	$0.298696\pi$
$888$	−12.5007	−	32.9618i	−0.419498	−	1.10612i
$889$	0.459354	+	0.113221i	0.0154063	+	0.00379730i
$890$	8.35021	−	7.39764i	0.279900	−	0.247969i
$891$	−2.69836	−	0.665086i	−0.0903985	−	0.0222812i
$892$	−5.78324	+	3.03528i	−0.193637	+	0.101629i
$893$	−1.40086	+	0.735226i	−0.0468778	+	0.0246034i
$894$	−1.21415	−	9.99939i	−0.0406071	−	0.334430i
$895$	3.13487	+	25.8180i	0.104787	+	0.863000i
$896$	−0.115668	+	0.102473i	−0.00386420	+	0.00342338i
$897$	−0.740015	−	7.00331i	−0.0247084	−	0.233834i
$898$	−33.1600	−	29.3772i	−1.10656	−	0.980329i
$899$	30.3789	−	44.0114i	1.01319	−	1.46786i
$900$	−0.533068	+	1.40558i	−0.0177689	+	0.0468528i
$901$	4.03706	+	33.2481i	0.134494	+	1.10766i
$902$	−0.135698	+	1.11757i	−0.00451825	+	0.0372112i
$903$	−0.322797	−	0.169417i	−0.0107420	−	0.00563784i
$904$	33.2482	−	48.1684i	1.10582	−	1.60206i
$905$	−2.34469	−	6.18243i	−0.0779401	−	0.205511i
$906$	12.2384	−	10.8423i	0.406594	−	0.360211i
$907$	−8.92666	+	12.9325i	−0.296405	+	0.429417i	−0.942685	−	0.333684i	$-0.891708\pi$
$907$	−8.92666	+	12.9325i	−0.296405	+	0.429417i	0.646280	+	0.763100i	$0.276324\pi$
$908$	3.89246	+	5.63920i	0.129176	+	0.187143i
$909$	−0.701062	−	5.77376i	−0.0232528	−	0.191504i
$910$	−0.178751	+	0.0411199i	−0.00592554	+	0.00136311i
$911$	2.50117	−	20.5990i	0.0828673	−	0.682474i	−0.890783	−	0.454429i	$-0.849843\pi$
$911$	2.50117	−	20.5990i	0.0828673	−	0.682474i	0.973651	−	0.228045i	$-0.0732334\pi$
$912$	8.75465	−	4.59480i	0.289895	−	0.152149i
$913$	−9.13317	−	24.0822i	−0.302264	−	0.797005i
$914$	2.24656	−	18.5021i	0.0743097	−	0.611995i
$915$	12.0312			0.397739
$916$	0.674386	−	5.55407i	0.0222823	−	0.183512i
$917$	0.278905	+	0.404064i	0.00921026	+	0.0133434i
$918$	7.21269	−	1.77777i	0.238054	−	0.0586751i
$919$	14.7645	−	21.3901i	0.487036	−	0.705594i	−0.500012	−	0.866019i	$-0.666671\pi$
$919$	14.7645	−	21.3901i	0.487036	−	0.705594i	0.987048	+	0.160425i	$0.0512864\pi$
$920$	−8.26222	+	2.03645i	−0.272397	+	0.0671399i
$921$	−29.1733	−	15.3113i	−0.961292	−	0.504525i
$922$	35.3259	+	18.5404i	1.16339	+	0.610597i
$923$	5.16486	+	48.8789i	0.170003	+	1.60887i
$924$	−0.0363499	+	0.0190779i	−0.00119583	+	0.000627618i
$925$	34.2606			1.12648
$926$	−2.84772	−	1.49460i	−0.0935819	−	0.0491156i
$927$	0.855837	−	2.25666i	0.0281094	−	0.0741183i
$928$	−2.93043	−	24.1343i	−0.0961962	−	0.792247i
$929$	10.3764	−	2.55754i	0.340437	−	0.0839102i	−0.0653907	−	0.997860i	$-0.520829\pi$
$929$	10.3764	−	2.55754i	0.340437	−	0.0839102i	0.405828	+	0.913949i	$0.366983\pi$
$930$	−10.3330	+	2.54685i	−0.338831	+	0.0835144i
$931$	3.04993	+	25.1185i	0.0999576	+	0.823225i
$932$	−0.0269938	+	0.0711767i	−0.000884210	+	0.00233147i
$933$	−26.1397	−	13.7192i	−0.855776	−	0.449146i
$934$	38.1197			1.24731
$935$	21.2663	−	11.1614i	0.695483	−	0.365017i
$936$	−8.15116	−	7.45077i	−0.266429	−	0.243536i
$937$	4.27286	+	2.24257i	0.139588	+	0.0732615i	0.533071	−	0.846070i	$-0.321038\pi$
$937$	4.27286	+	2.24257i	0.139588	+	0.0732615i	−0.393483	+	0.919332i	$0.628730\pi$
$938$	0.201567	+	0.105791i	0.00658141	+	0.00345419i
$939$	−16.9046	+	4.16662i	−0.551662	+	0.135973i
$940$	0.178581	−	0.258719i	0.00582467	−	0.00843849i
$941$	−3.23377	+	0.797053i	−0.105418	+	0.0259832i	−0.291672	−	0.956518i	$-0.594211\pi$
$941$	−3.23377	+	0.797053i	−0.105418	+	0.0259832i	0.186254	+	0.982502i	$0.440365\pi$
$942$	0.408284	+	0.591502i	0.0133026	+	0.0192722i
$943$	−0.0779994	+	0.642383i	−0.00254001	+	0.0209189i
$944$	9.57717			0.311710
$945$	−0.00501505	+	0.0413027i	−0.000163140	+	0.00134358i
$946$	15.0178	+	39.5988i	0.488272	+	1.28747i
$947$	−37.1920	+	19.5199i	−1.20858	+	0.634311i	−0.943966	−	0.330043i	$-0.892937\pi$
$947$	−37.1920	+	19.5199i	−1.20858	+	0.634311i	−0.264613	+	0.964355i	$0.585244\pi$
$948$	−0.0825200	+	0.679613i	−0.00268012	+	0.0220728i
$949$	−21.2931	+	10.7564i	−0.691202	+	0.349168i
$950$	1.58597	+	13.0617i	0.0514558	+	0.423777i
$951$	−5.49651	−	7.96307i	−0.178237	−	0.258220i
$952$	0.309198	−	0.447951i	0.0100212	−	0.0145182i
$953$	32.2233	−	28.5474i	1.04382	−	0.924740i	0.0465704	−	0.998915i	$-0.485171\pi$
$953$	32.2233	−	28.5474i	1.04382	−	0.924740i	0.997245	+	0.0741750i	$0.0236324\pi$
$954$	2.39014	+	6.30227i	0.0773835	+	0.204043i
$955$	8.96523	−	12.9884i	0.290108	−	0.420294i
$956$	−3.42785	−	1.79908i	−0.110865	−	0.0581863i
$957$	−2.92765	+	24.1113i	−0.0946374	+	0.779409i
$958$	−1.10487	−	9.09945i	−0.0356968	−	0.293990i
$959$	−0.227178	+	0.599019i	−0.00733596	+	0.0193433i
$960$	−7.16815	+	10.3849i	−0.231351	+	0.335170i
$961$	−4.82212	−	4.27203i	−0.155552	−	0.137807i
$962$	−18.7285	+	47.1573i	−0.603831	+	1.52041i
$963$	5.00789	−	4.43661i	0.161377	−	0.142968i
$964$	−0.584730	−	4.81568i	−0.0188329	−	0.155103i
$965$	3.79345	+	31.2419i	0.122115	+	1.00571i
$966$	0.0618518	−	0.0324623i	0.00199005	−	0.00104446i
$967$	12.9840	−	6.81455i	0.417539	−	0.219141i	−0.242852	−	0.970063i	$-0.578083\pi$
$967$	12.9840	−	6.81455i	0.417539	−	0.219141i	0.660391	+	0.750922i	$0.270391\pi$
$968$	−9.74390	−	2.40166i	−0.313181	−	0.0771921i
$969$	−16.4403	+	14.5649i	−0.528139	+	0.467891i
$970$	10.8255	+	2.66825i	0.347587	+	0.0856725i
$971$	−0.424676	−	1.11978i	−0.0136285	−	0.0359354i	0.928029	−	0.372507i	$-0.121502\pi$
$971$	−0.424676	−	1.11978i	−0.0136285	−	0.0359354i	−0.941658	+	0.336572i	$0.890733\pi$
$972$	−0.447170	+	0.234693i	−0.0143430	+	0.00752777i
$973$	0.0423722	−	0.348967i	0.00135839	−	0.0111874i
$974$	−9.89261	+	2.43831i	−0.316980	+	0.0781285i
$975$	9.57966	−	4.83926i	0.306795	−	0.154980i
$976$	−22.4603	−	5.53597i	−0.718937	−	0.177202i
$977$	8.20500	−	21.6348i	0.262501	−	0.692159i	−0.737360	−	0.675500i	$-0.763928\pi$
$977$	8.20500	−	21.6348i	0.262501	−	0.692159i	0.999861	−	0.0166587i	$-0.00530287\pi$
$978$	−1.61110	−	1.42731i	−0.0515173	−	0.0456404i
$979$	−17.3081	+	4.26606i	−0.553169	+	0.136344i
$980$	−2.85615	−	4.13784i	−0.0912362	−	0.132178i
$981$	−2.15616	−	17.7576i	−0.0688409	−	0.566956i
$982$	−9.24374	−	24.3737i	−0.294979	−	0.777797i
$983$	1.65463	−	4.36289i	0.0527744	−	0.139155i	−0.906037	−	0.423199i	$-0.860907\pi$
$983$	1.65463	−	4.36289i	0.0527744	−	0.139155i	0.958811	+	0.284044i	$0.0916763\pi$
$984$	0.576442	+	0.835121i	0.0183763	+	0.0266227i
$985$	4.25935	+	1.04984i	0.135714	+	0.0334505i
$986$	−23.0219	−	60.7038i	−0.733167	−	1.93320i
$987$	−0.00453909	+	0.0119686i	−0.000144481	+	0.000380965i
$988$	6.36613	+	1.67456i	0.202534	+	0.0532749i
$989$	8.63227	+	22.7614i	0.274490	+	0.723771i
$990$	3.61789	−	3.20517i	0.114984	−	0.101867i
$991$	−26.7231			−0.848887			−0.424443	−	0.905454i	$-0.639530\pi$
$991$	−26.7231			−0.848887			−0.424443	+	0.905454i	$0.639530\pi$
$992$	−17.0216			−0.540437
$993$	0.351421	−	0.311332i	0.0111520	−	0.00987981i
$994$	−0.431688	+	0.226567i	−0.0136923	+	0.00718628i
$995$	−27.5865			−0.874550
$996$	−4.14422	−	2.17505i	−0.131315	−	0.0689192i
$997$	4.87520	+	4.31905i	0.154399	+	0.136786i	0.736786	−	0.676126i	$-0.236343\pi$
$997$	4.87520	+	4.31905i	0.154399	+	0.136786i	−0.582387	+	0.812912i	$0.697881\pi$
$998$	1.99464	+	2.88973i	0.0631392	+	0.0914729i
$999$	8.61510	+	7.63232i	0.272570	+	0.241476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.6	✓	204
169.131	even	13	inner	507.2.m.b.469.6	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.6	✓	204	1.1	even	1	trivial
507.2.m.b.469.6	yes	204	169.131	even	13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18717 - 0.292610i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-0.447170 - 0.234693i) q^{4} +(-0.808035 + 1.17064i) q^{5} +(-0.433574 + 1.14324i) q^{6} +(-0.0218939 - 0.0193963i) q^{7} +(2.29259 + 2.03106i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(1.30181 - 1.15330i) q^{10} +(-2.69836 + 0.665086i) q^{11} +(-0.286882 + 0.415620i) q^{12} +(3.51378 - 0.808309i) q^{13} +(0.0203161 + 0.0294330i) q^{14} +(1.06471 + 0.943248i) q^{15} +(-1.55361 - 2.25080i) q^{16} +(4.54762 + 4.02884i) q^{17} +(1.08264 + 0.568215i) q^{18} -3.61515 q^{19} +(0.636069 - 0.333835i) q^{20} +(-0.0218939 + 0.0193963i) q^{21} +3.39801 q^{22} +1.95318 q^{23} +(2.29259 - 2.03106i) q^{24} +(1.05555 + 2.78325i) q^{25} +(-4.40796 - 0.0685695i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(0.00523811 + 0.0138118i) q^{28} +(8.48566 + 2.09153i) q^{29} +(-0.987980 - 1.43134i) q^{30} +(2.16983 - 5.72137i) q^{31} +(-0.986427 - 2.60099i) q^{32} +(0.334986 + 2.75885i) q^{33} +(-4.21990 - 6.11358i) q^{34} +(0.0403970 - 0.00995698i) q^{35} +(0.378010 + 0.334888i) q^{36} +(4.08138 - 10.7617i) q^{37} +(4.29178 + 1.05783i) q^{38} +(-0.378877 - 3.58559i) q^{39} +(-4.23013 + 1.04263i) q^{40} +(-0.0399345 + 0.328890i) q^{41} +(0.0316672 - 0.0166202i) q^{42} +(4.41959 + 11.6535i) q^{43} +(1.36272 + 0.335879i) q^{44} +(1.06471 - 0.943248i) q^{45} +(-2.31875 - 0.571521i) q^{46} +(0.387496 - 0.203373i) q^{47} +(-2.42166 + 1.27098i) q^{48} +(-0.843654 - 6.94811i) q^{49} +(-0.438702 - 3.61304i) q^{50} +(4.54762 - 4.02884i) q^{51} +(-1.76096 - 0.463207i) q^{52} +(4.12627 + 3.65556i) q^{53} +(0.694570 - 1.00626i) q^{54} +(1.40179 - 3.69622i) q^{55} +(-0.0107987 - 0.0889355i) q^{56} +(-0.435758 + 3.58879i) q^{57} +(-9.46189 - 4.96598i) q^{58} +(-1.98925 + 2.88193i) q^{59} +(-0.254731 - 0.671671i) q^{60} +(6.33104 - 5.60881i) q^{61} +(-4.25008 + 6.15731i) q^{62} +(0.0166158 + 0.0240722i) q^{63} +(1.06929 + 8.80642i) q^{64} +(-1.89301 + 4.76651i) q^{65} +(0.409585 - 3.37324i) q^{66} +(5.63609 - 2.95805i) q^{67} +(-1.08802 - 2.86887i) q^{68} +(0.235430 - 1.93894i) q^{69} -0.0508715 q^{70} +(-1.64316 + 13.5326i) q^{71} +(-1.73991 - 2.52069i) q^{72} +(-6.42412 + 1.58340i) q^{73} +(-7.99427 + 11.5817i) q^{74} +(2.89019 - 0.712367i) q^{75} +(1.61659 + 0.848450i) q^{76} +(0.0719778 + 0.0377768i) q^{77} +(-0.599390 + 4.36755i) q^{78} +(1.20033 - 0.629983i) q^{79} +3.89025 q^{80} +(0.885456 + 0.464723i) q^{81} +(0.143646 - 0.378762i) q^{82} +(1.11709 + 9.20009i) q^{83} +(0.0143424 - 0.00353509i) q^{84} +(-8.39095 + 2.06818i) q^{85} +(-1.83686 - 15.1279i) q^{86} +(3.09911 - 8.17168i) q^{87} +(-7.53707 - 3.95576i) q^{88} +6.41430 q^{89} +(-1.53999 + 0.808248i) q^{90} +(-0.0926084 - 0.0504572i) q^{91} +(-0.873404 - 0.458398i) q^{92} +(-5.41811 - 2.84365i) q^{93} +(-0.519531 + 0.128053i) q^{94} +(2.92117 - 4.23204i) q^{95} +(-2.70093 + 0.665719i) q^{96} +(3.64170 + 5.27591i) q^{97} +(-1.03153 + 8.49542i) q^{98} +2.77912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

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Database

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