LMFDB - Embedded newform 731.2.f.d.259.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.5
Character	$\chi$	$=$	731.259
Dual form			731.2.f.d.302.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24230i q^{2} +(0.751257 - 0.751257i) q^{3} -3.02793 q^{4} +(-1.86200 + 1.86200i) q^{5} +(-1.68455 - 1.68455i) q^{6} +(2.49628 + 2.49628i) q^{7} +2.30493i q^{8} +1.87123i q^{9} +O(q^{10})$	\(q-2.24230i q^{2} +(0.751257 - 0.751257i) q^{3} -3.02793 q^{4} +(-1.86200 + 1.86200i) q^{5} +(-1.68455 - 1.68455i) q^{6} +(2.49628 + 2.49628i) q^{7} +2.30493i q^{8} +1.87123i q^{9} +(4.17518 + 4.17518i) q^{10} +(-0.566147 - 0.566147i) q^{11} +(-2.27475 + 2.27475i) q^{12} +6.25141 q^{13} +(5.59741 - 5.59741i) q^{14} +2.79769i q^{15} -0.887510 q^{16} +(1.77843 - 3.71984i) q^{17} +4.19586 q^{18} +2.59985i q^{19} +(5.63801 - 5.63801i) q^{20} +3.75069 q^{21} +(-1.26947 + 1.26947i) q^{22} +(-0.365188 - 0.365188i) q^{23} +(1.73159 + 1.73159i) q^{24} -1.93412i q^{25} -14.0176i q^{26} +(3.65954 + 3.65954i) q^{27} +(-7.55855 - 7.55855i) q^{28} +(6.96498 - 6.96498i) q^{29} +6.27327 q^{30} +(-1.80365 + 1.80365i) q^{31} +6.59992i q^{32} -0.850644 q^{33} +(-8.34100 - 3.98779i) q^{34} -9.29616 q^{35} -5.66594i q^{36} +(-2.94502 + 2.94502i) q^{37} +5.82965 q^{38} +(4.69642 - 4.69642i) q^{39} +(-4.29178 - 4.29178i) q^{40} +(3.54341 + 3.54341i) q^{41} -8.41019i q^{42} -1.00000i q^{43} +(1.71425 + 1.71425i) q^{44} +(-3.48423 - 3.48423i) q^{45} +(-0.818863 + 0.818863i) q^{46} +0.0106396 q^{47} +(-0.666748 + 0.666748i) q^{48} +5.46280i q^{49} -4.33689 q^{50} +(-1.45849 - 4.13061i) q^{51} -18.9288 q^{52} -1.11289i q^{53} +(8.20581 - 8.20581i) q^{54} +2.10834 q^{55} +(-5.75374 + 5.75374i) q^{56} +(1.95315 + 1.95315i) q^{57} +(-15.6176 - 15.6176i) q^{58} +2.93554i q^{59} -8.47119i q^{60} +(3.06969 + 3.06969i) q^{61} +(4.04433 + 4.04433i) q^{62} +(-4.67110 + 4.67110i) q^{63} +13.0240 q^{64} +(-11.6402 + 11.6402i) q^{65} +1.90740i q^{66} +3.86527 q^{67} +(-5.38497 + 11.2634i) q^{68} -0.548700 q^{69} +20.8448i q^{70} +(9.04089 - 9.04089i) q^{71} -4.31304 q^{72} +(-3.02621 + 3.02621i) q^{73} +(6.60362 + 6.60362i) q^{74} +(-1.45302 - 1.45302i) q^{75} -7.87215i q^{76} -2.82652i q^{77} +(-10.5308 - 10.5308i) q^{78} +(-2.32169 - 2.32169i) q^{79} +(1.65255 - 1.65255i) q^{80} -0.115166 q^{81} +(7.94540 - 7.94540i) q^{82} +14.5604i q^{83} -11.3568 q^{84} +(3.61490 + 10.2378i) q^{85} -2.24230 q^{86} -10.4650i q^{87} +(1.30493 - 1.30493i) q^{88} -1.27057 q^{89} +(-7.81271 + 7.81271i) q^{90} +(15.6053 + 15.6053i) q^{91} +(1.10576 + 1.10576i) q^{92} +2.71001i q^{93} -0.0238573i q^{94} +(-4.84093 - 4.84093i) q^{95} +(4.95823 + 4.95823i) q^{96} +(-1.51953 + 1.51953i) q^{97} +12.2493 q^{98} +(1.05939 - 1.05939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		−	2.24230i		−	1.58555i	−0.609515	−	0.792774i	$-0.708636\pi$
$2$		−	2.24230i		−	1.58555i	0.609515	−	0.792774i	$-0.291364\pi$
$3$	0.751257	−	0.751257i	0.433738	−	0.433738i	−0.456160	−	0.889898i	$-0.650775\pi$
$3$	0.751257	−	0.751257i	0.433738	−	0.433738i	0.889898	+	0.456160i	$0.150775\pi$
$4$	−3.02793			−1.51396
$5$	−1.86200	+	1.86200i	−0.832714	+	0.832714i	−0.987887	−	0.155174i	$-0.950406\pi$
$5$	−1.86200	+	1.86200i	−0.832714	+	0.832714i	0.155174	+	0.987887i	$0.450406\pi$
$6$	−1.68455	−	1.68455i	−0.687713	−	0.687713i
$7$	2.49628	+	2.49628i	0.943504	+	0.943504i	0.998487	−	0.0549831i	$-0.0175105\pi$
$7$	2.49628	+	2.49628i	0.943504	+	0.943504i	−0.0549831	+	0.998487i	$0.517510\pi$
$8$			2.30493i			0.814914i
$9$			1.87123i			0.623742i
$10$	4.17518	+	4.17518i	1.32031	+	1.32031i
$11$	−0.566147	−	0.566147i	−0.170700	−	0.170700i	0.616587	−	0.787287i	$-0.288515\pi$
$11$	−0.566147	−	0.566147i	−0.170700	−	0.170700i	−0.787287	+	0.616587i	$0.788515\pi$
$12$	−2.27475	+	2.27475i	−0.656664	+	0.656664i
$13$	6.25141			1.73383			0.866915	−	0.498456i	$-0.166099\pi$
$13$	6.25141			1.73383			0.866915	+	0.498456i	$0.166099\pi$
$14$	5.59741	−	5.59741i	1.49597	−	1.49597i
$15$			2.79769i			0.722360i
$16$	−0.887510			−0.221877
$17$	1.77843	−	3.71984i	0.431333	−	0.902193i
$17$	1.77843	−	3.71984i	0.431333	−	0.902193i
$18$	4.19586			0.988973
$19$			2.59985i			0.596446i	0.954496	+	0.298223i	$0.0963939\pi$
$19$			2.59985i			0.596446i	−0.954496	+	0.298223i	$0.903606\pi$
$20$	5.63801	−	5.63801i	1.26070	−	1.26070i
$21$	3.75069			0.818468
$22$	−1.26947	+	1.26947i	−0.270653	+	0.270653i
$23$	−0.365188	−	0.365188i	−0.0761470	−	0.0761470i	0.668008	−	0.744155i	$-0.267147\pi$
$23$	−0.365188	−	0.365188i	−0.0761470	−	0.0761470i	−0.744155	+	0.668008i	$0.767147\pi$
$24$	1.73159	+	1.73159i	0.353460	+	0.353460i
$25$		−	1.93412i		−	0.386824i
$26$		−	14.0176i		−	2.74907i
$27$	3.65954	+	3.65954i	0.704279	+	0.704279i
$28$	−7.55855	−	7.55855i	−1.42843	−	1.42843i
$29$	6.96498	−	6.96498i	1.29336	−	1.29336i	0.360670	−	0.932693i	$-0.382548\pi$
$29$	6.96498	−	6.96498i	1.29336	−	1.29336i	0.932693	−	0.360670i	$-0.117452\pi$
$30$	6.27327			1.14534
$31$	−1.80365	+	1.80365i	−0.323945	+	0.323945i	−0.850278	−	0.526333i	$-0.823566\pi$
$31$	−1.80365	+	1.80365i	−0.323945	+	0.323945i	0.526333	+	0.850278i	$0.323566\pi$
$32$			6.59992i			1.16671i
$33$	−0.850644			−0.148078
$34$	−8.34100	−	3.98779i	−1.43047	−	0.683900i
$35$	−9.29616			−1.57134
$36$		−	5.66594i		−	0.944323i
$37$	−2.94502	+	2.94502i	−0.484158	+	0.484158i	−0.906457	−	0.422299i	$-0.861223\pi$
$37$	−2.94502	+	2.94502i	−0.484158	+	0.484158i	0.422299	+	0.906457i	$0.361223\pi$
$38$	5.82965			0.945694
$39$	4.69642	−	4.69642i	0.752029	−	0.752029i
$40$	−4.29178	−	4.29178i	−0.678590	−	0.678590i
$41$	3.54341	+	3.54341i	0.553387	+	0.553387i	0.927417	−	0.374029i	$-0.122024\pi$
$41$	3.54341	+	3.54341i	0.553387	+	0.553387i	−0.374029	+	0.927417i	$0.622024\pi$
$42$		−	8.41019i		−	1.29772i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	1.71425	+	1.71425i	0.258433	+	0.258433i
$45$	−3.48423	−	3.48423i	−0.519399	−	0.519399i
$46$	−0.818863	+	0.818863i	−0.120735	+	0.120735i
$47$	0.0106396			0.00155195			0.000775976	−	1.00000i	$-0.499753\pi$
$47$	0.0106396			0.00155195			0.000775976		1.00000i	$0.499753\pi$
$48$	−0.666748	+	0.666748i	−0.0962368	+	0.0962368i
$49$			5.46280i			0.780400i
$50$	−4.33689			−0.613328
$51$	−1.45849	−	4.13061i	−0.204230	−	0.578401i
$52$	−18.9288			−2.62496
$53$		−	1.11289i		−	0.152867i	−0.997075	−	0.0764337i	$-0.975647\pi$
$53$		−	1.11289i		−	0.152867i	0.997075	−	0.0764337i	$-0.0243534\pi$
$54$	8.20581	−	8.20581i	1.11667	−	1.11667i
$55$	2.10834			0.284288
$56$	−5.75374	+	5.75374i	−0.768875	+	0.768875i
$57$	1.95315	+	1.95315i	0.258701	+	0.258701i
$58$	−15.6176	−	15.6176i	−2.05069	−	2.05069i
$59$			2.93554i			0.382175i	0.981573	+	0.191087i	$0.0612013\pi$
$59$			2.93554i			0.382175i	−0.981573	+	0.191087i	$0.938799\pi$
$60$		−	8.47119i		−	1.09363i
$61$	3.06969	+	3.06969i	0.393034	+	0.393034i	0.875767	−	0.482733i	$-0.160356\pi$
$61$	3.06969	+	3.06969i	0.393034	+	0.393034i	−0.482733	+	0.875767i	$0.660356\pi$
$62$	4.04433	+	4.04433i	0.513631	+	0.513631i
$63$	−4.67110	+	4.67110i	−0.588503	+	0.588503i
$64$	13.0240			1.62800
$65$	−11.6402	+	11.6402i	−1.44378	+	1.44378i
$66$			1.90740i			0.234785i
$67$	3.86527			0.472218			0.236109	−	0.971727i	$-0.424128\pi$
$67$	3.86527			0.472218			0.236109	+	0.971727i	$0.424128\pi$
$68$	−5.38497	+	11.2634i	−0.653023	+	1.36589i
$69$	−0.548700			−0.0660558
$70$			20.8448i			2.49143i
$71$	9.04089	−	9.04089i	1.07296	−	1.07296i	0.0758361	−	0.997120i	$-0.475837\pi$
$71$	9.04089	−	9.04089i	1.07296	−	1.07296i	0.997120	−	0.0758361i	$-0.0241626\pi$
$72$	−4.31304			−0.508296
$73$	−3.02621	+	3.02621i	−0.354191	+	0.354191i	−0.861666	−	0.507475i	$-0.830579\pi$
$73$	−3.02621	+	3.02621i	−0.354191	+	0.354191i	0.507475	+	0.861666i	$0.330579\pi$
$74$	6.60362	+	6.60362i	0.767655	+	0.767655i
$75$	−1.45302	−	1.45302i	−0.167780	−	0.167780i
$76$		−	7.87215i		−	0.902997i
$77$		−	2.82652i		−	0.322112i
$78$	−10.5308	−	10.5308i	−1.19238	−	1.19238i
$79$	−2.32169	−	2.32169i	−0.261210	−	0.261210i	0.564335	−	0.825546i	$-0.309133\pi$
$79$	−2.32169	−	2.32169i	−0.261210	−	0.261210i	−0.825546	+	0.564335i	$0.809133\pi$
$80$	1.65255	−	1.65255i	0.184760	−	0.184760i
$81$	−0.115166			−0.0127962
$82$	7.94540	−	7.94540i	0.877422	−	0.877422i
$83$			14.5604i			1.59821i	0.601191	+	0.799105i	$0.294693\pi$
$83$			14.5604i			1.59821i	−0.601191	+	0.799105i	$0.705307\pi$
$84$	−11.3568			−1.23913
$85$	3.61490	+	10.2378i	0.392091	+	1.11045i
$86$	−2.24230			−0.241794
$87$		−	10.4650i		−	1.12196i
$88$	1.30493	−	1.30493i	0.139106	−	0.139106i
$89$	−1.27057			−0.134680			−0.0673399	−	0.997730i	$-0.521451\pi$
$89$	−1.27057			−0.134680			−0.0673399	+	0.997730i	$0.521451\pi$
$90$	−7.81271	+	7.81271i	−0.823532	+	0.823532i
$91$	15.6053	+	15.6053i	1.63588	+	1.63588i
$92$	1.10576	+	1.10576i	0.115284	+	0.115284i
$93$			2.71001i			0.281015i
$94$		−	0.0238573i		−	0.00246069i
$95$	−4.84093	−	4.84093i	−0.496668	−	0.496668i
$96$	4.95823	+	4.95823i	0.506048	+	0.506048i
$97$	−1.51953	+	1.51953i	−0.154285	+	0.154285i	−0.780029	−	0.625744i	$-0.784795\pi$
$97$	−1.51953	+	1.51953i	−0.154285	+	0.154285i	0.625744	+	0.780029i	$0.284795\pi$
$98$	12.2493			1.23736
$99$	1.05939	−	1.05939i	0.106473	−	0.106473i
$100$			5.85638i			0.585638i
$101$	−14.9526			−1.48784			−0.743920	−	0.668268i	$-0.767036\pi$
$101$	−14.9526			−1.48784			−0.743920	+	0.668268i	$0.767036\pi$
$102$	−9.26209	+	3.27038i	−0.917083	+	0.323816i
$103$	−5.42123			−0.534169			−0.267085	−	0.963673i	$-0.586060\pi$
$103$	−5.42123			−0.534169			−0.267085	+	0.963673i	$0.586060\pi$
$104$			14.4090i			1.41292i
$105$	−6.98380	+	6.98380i	−0.681549	+	0.681549i
$106$	−2.49544			−0.242379
$107$	−0.100198	+	0.100198i	−0.00968654	+	0.00968654i	−0.711933	−	0.702247i	$-0.752180\pi$
$107$	−0.100198	+	0.100198i	−0.00968654	+	0.00968654i	0.702247	+	0.711933i	$0.252180\pi$
$108$	−11.0808	−	11.0808i	−1.06625	−	1.06625i
$109$	−12.9905	−	12.9905i	−1.24426	−	1.24426i	−0.958215	−	0.286050i	$-0.907658\pi$
$109$	−12.9905	−	12.9905i	−1.24426	−	1.24426i	−0.286050	−	0.958215i	$-0.592342\pi$
$110$		−	4.72753i		−	0.450753i
$111$			4.42493i			0.419996i
$112$	−2.21547	−	2.21547i	−0.209342	−	0.209342i
$113$	−12.2127	−	12.2127i	−1.14887	−	1.14887i	−0.986775	−	0.162098i	$-0.948174\pi$
$113$	−12.2127	−	12.2127i	−1.14887	−	1.14887i	−0.162098	−	0.986775i	$-0.551826\pi$
$114$	4.37956	−	4.37956i	0.410184	−	0.410184i
$115$	1.35996			0.126817
$116$	−21.0894	+	21.0894i	−1.95811	+	1.95811i
$117$			11.6978i			1.08146i
$118$	6.58237			0.605956
$119$	13.7252	−	4.84628i	1.25819	−	0.444258i
$120$	−6.44846			−0.588661
$121$		−	10.3590i		−	0.941723i
$122$	6.88319	−	6.88319i	0.623175	−	0.623175i
$123$	5.32402			0.480051
$124$	5.46132	−	5.46132i	0.490441	−	0.490441i
$125$	−5.70868	−	5.70868i	−0.510600	−	0.510600i
$126$	10.4740	+	10.4740i	0.933100	+	0.933100i
$127$			4.54614i			0.403405i	0.979447	+	0.201702i	$0.0646474\pi$
$127$			4.54614i			0.403405i	−0.979447	+	0.201702i	$0.935353\pi$
$128$		−	16.0039i		−	1.41456i
$129$	−0.751257	−	0.751257i	−0.0661445	−	0.0661445i
$130$	26.1008	+	26.1008i	2.28919	+	2.28919i
$131$	14.8012	−	14.8012i	1.29318	−	1.29318i	0.360377	−	0.932807i	$-0.382648\pi$
$131$	14.8012	−	14.8012i	1.29318	−	1.29318i	0.932807	−	0.360377i	$-0.117352\pi$
$132$	2.57569			0.224185
$133$	−6.48994	+	6.48994i	−0.562749	+	0.562749i
$134$		−	8.66711i		−	0.748724i
$135$	−13.6282			−1.17293
$136$	8.57395	+	4.09916i	0.735210	+	0.351500i
$137$	6.91503			0.590791			0.295395	−	0.955375i	$-0.404549\pi$
$137$	6.91503			0.590791			0.295395	+	0.955375i	$0.404549\pi$
$138$			1.23035i			0.104735i
$139$	10.3979	−	10.3979i	0.881937	−	0.881937i	−0.111794	−	0.993731i	$-0.535660\pi$
$139$	10.3979	−	10.3979i	0.881937	−	0.881937i	0.993731	+	0.111794i	$0.0356597\pi$
$140$	28.1481			2.37895
$141$	0.00799311	−	0.00799311i	0.000673141	−	0.000673141i
$142$	−20.2724	−	20.2724i	−1.70122	−	1.70122i
$143$	−3.53922	−	3.53922i	−0.295965	−	0.295965i
$144$		−	1.66073i		−	0.138394i
$145$			25.9376i			2.15400i
$146$	6.78568	+	6.78568i	0.561587	+	0.561587i
$147$	4.10397	+	4.10397i	0.338490	+	0.338490i
$148$	8.91730	−	8.91730i	0.732997	−	0.732997i
$149$	−8.20518			−0.672195			−0.336097	−	0.941827i	$-0.609107\pi$
$149$	−8.20518			−0.672195			−0.336097	+	0.941827i	$0.609107\pi$
$150$	−3.25812	+	3.25812i	−0.266024	+	0.266024i
$151$			18.6921i			1.52114i	0.649254	+	0.760572i	$0.275081\pi$
$151$			18.6921i			1.52114i	−0.649254	+	0.760572i	$0.724919\pi$
$152$	−5.99245			−0.486052
$153$	6.96065	+	3.32785i	0.562735	+	0.269041i
$154$	−6.33792			−0.510724
$155$		−	6.71681i		−	0.539507i
$156$	−14.2204	+	14.2204i	−1.13854	+	1.13854i
$157$	11.1092			0.886614			0.443307	−	0.896370i	$-0.353805\pi$
$157$	11.1092			0.886614			0.443307	+	0.896370i	$0.353805\pi$
$158$	−5.20593	+	5.20593i	−0.414162	+	0.414162i
$159$	−0.836068	−	0.836068i	−0.0663045	−	0.0663045i
$160$	−12.2891	−	12.2891i	−0.971537	−	0.971537i
$161$		−	1.82322i		−	0.143690i
$162$			0.258237i			0.0202890i
$163$	−5.19613	−	5.19613i	−0.406992	−	0.406992i	0.473696	−	0.880688i	$-0.342920\pi$
$163$	−5.19613	−	5.19613i	−0.406992	−	0.406992i	−0.880688	+	0.473696i	$0.842920\pi$
$164$	−10.7292	−	10.7292i	−0.837808	−	0.837808i
$165$	1.58390	−	1.58390i	0.123307	−	0.123307i
$166$	32.6488			2.53404
$167$	5.26180	−	5.26180i	0.407171	−	0.407171i	−0.473580	−	0.880751i	$-0.657039\pi$
$167$	5.26180	−	5.26180i	0.407171	−	0.407171i	0.880751	+	0.473580i	$0.157039\pi$
$168$			8.64507i			0.666981i
$169$	26.0802			2.00617
$170$	22.9563	−	8.10570i	1.76066	−	0.621679i
$171$	−4.86490			−0.372028
$172$			3.02793i			0.230877i
$173$	−10.7804	+	10.7804i	−0.819619	+	0.819619i	−0.986053	−	0.166434i	$-0.946775\pi$
$173$	−10.7804	+	10.7804i	−0.819619	+	0.819619i	0.166434	+	0.986053i	$0.446775\pi$
$174$	−23.4657			−1.77893
$175$	4.82810	−	4.82810i	0.364970	−	0.364970i
$176$	0.502461	+	0.502461i	0.0378744	+	0.0378744i
$177$	2.20534	+	2.20534i	0.165764	+	0.165764i
$178$			2.84900i			0.213541i
$179$			7.16986i			0.535901i	0.963433	+	0.267950i	$0.0863463\pi$
$179$			7.16986i			0.535901i	−0.963433	+	0.267950i	$0.913654\pi$
$180$	10.5500	+	10.5500i	0.786351	+	0.786351i
$181$	1.10473	+	1.10473i	0.0821136	+	0.0821136i	0.746971	−	0.664857i	$-0.231508\pi$
$181$	1.10473	+	1.10473i	0.0821136	+	0.0821136i	−0.664857	+	0.746971i	$0.731508\pi$
$182$	34.9917	−	34.9917i	2.59376	−	2.59376i
$183$	4.61226			0.340948
$184$	0.841732	−	0.841732i	0.0620533	−	0.0620533i
$185$		−	10.9673i		−	0.806329i
$186$	6.07666			0.445563
$187$	−3.11283	+	1.09912i	−0.227633	+	0.0803756i
$188$	−0.0322161			−0.00234960
$189$			18.2705i			1.32898i
$190$	−10.8548	+	10.8548i	−0.787492	+	0.787492i
$191$	−24.0728			−1.74185			−0.870925	−	0.491416i	$-0.836479\pi$
$191$	−24.0728			−1.74185			−0.870925	+	0.491416i	$0.836479\pi$
$192$	9.78437	−	9.78437i	0.706126	−	0.706126i
$193$	−3.28029	−	3.28029i	−0.236120	−	0.236120i	0.579121	−	0.815241i	$-0.303396\pi$
$193$	−3.28029	−	3.28029i	−0.236120	−	0.236120i	−0.815241	+	0.579121i	$0.803396\pi$
$194$	3.40724	+	3.40724i	0.244626	+	0.244626i
$195$			17.4895i			1.25245i
$196$		−	16.5410i		−	1.18150i
$197$	−0.707117	−	0.707117i	−0.0503800	−	0.0503800i	0.681468	−	0.731848i	$-0.261342\pi$
$197$	−0.707117	−	0.707117i	−0.0503800	−	0.0503800i	−0.731848	+	0.681468i	$0.761342\pi$
$198$	−2.37547	−	2.37547i	−0.168818	−	0.168818i
$199$	−2.39115	+	2.39115i	−0.169504	+	0.169504i	−0.786762	−	0.617257i	$-0.788244\pi$
$199$	−2.39115	+	2.39115i	−0.169504	+	0.169504i	0.617257	+	0.786762i	$0.288244\pi$
$200$	4.45801			0.315229
$201$	2.90381	−	2.90381i	0.204819	−	0.204819i
$202$			33.5283i			2.35904i
$203$	34.7730			2.44059
$204$	4.41621	+	12.5072i	0.309196	+	0.875679i
$205$	−13.1957			−0.921626
$206$			12.1560i			0.846952i
$207$	0.683350	−	0.683350i	0.0474961	−	0.0474961i
$208$	−5.54819			−0.384698
$209$	1.47190	−	1.47190i	0.101813	−	0.101813i
$210$	15.6598	+	15.6598i	1.08063	+	1.08063i
$211$	2.97643	+	2.97643i	0.204906	+	0.204906i	0.802098	−	0.597192i	$-0.203717\pi$
$211$	2.97643	+	2.97643i	0.204906	+	0.204906i	−0.597192	+	0.802098i	$0.703717\pi$
$212$			3.36976i			0.231436i
$213$		−	13.5841i		−	0.930765i
$214$	0.224675	+	0.224675i	0.0153585	+	0.0153585i
$215$	1.86200	+	1.86200i	0.126988	+	0.126988i
$216$	−8.43497	+	8.43497i	−0.573927	+	0.573927i
$217$	−9.00482			−0.611287
$218$	−29.1287	+	29.1287i	−1.97284	+	1.97284i
$219$			4.54692i			0.307252i
$220$	−6.38389			−0.430402
$221$	11.1177	−	23.2542i	0.747859	−	1.56425i
$222$	9.92203			0.665923
$223$			10.6052i			0.710179i	0.934832	+	0.355090i	$0.115550\pi$
$223$			10.6052i			0.710179i	−0.934832	+	0.355090i	$0.884450\pi$
$224$	−16.4752	+	16.4752i	−1.10080	+	1.10080i
$225$	3.61918			0.241279
$226$	−27.3845	+	27.3845i	−1.82159	+	1.82159i
$227$	−3.92635	−	3.92635i	−0.260601	−	0.260601i	0.564697	−	0.825298i	$-0.308993\pi$
$227$	−3.92635	−	3.92635i	−0.260601	−	0.260601i	−0.825298	+	0.564697i	$0.808993\pi$
$228$	−5.91400	−	5.91400i	−0.391665	−	0.391665i
$229$			13.1190i			0.866925i	0.901172	+	0.433462i	$0.142708\pi$
$229$			13.1190i			0.866925i	−0.901172	+	0.433462i	$0.857292\pi$
$230$		−	3.04945i		−	0.201075i
$231$	−2.12344	−	2.12344i	−0.139712	−	0.139712i
$232$	16.0538	+	16.0538i	1.05398	+	1.05398i
$233$	−2.02144	+	2.02144i	−0.132429	+	0.132429i	−0.770214	−	0.637785i	$-0.779851\pi$
$233$	−2.02144	+	2.02144i	−0.132429	+	0.132429i	0.637785	+	0.770214i	$0.279851\pi$
$234$	26.2300			1.71471
$235$	−0.0198111	+	0.0198111i	−0.00129233	+	0.00129233i
$236$		−	8.88860i		−	0.578598i
$237$	−3.48837			−0.226594
$238$	−10.8668	−	30.7761i	−0.704392	−	1.99492i
$239$	−28.9984			−1.87575			−0.937877	−	0.346969i	$-0.887211\pi$
$239$	−28.9984			−1.87575			−0.937877	+	0.346969i	$0.887211\pi$
$240$		−	2.48297i		−	0.160275i
$241$	5.77472	−	5.77472i	0.371982	−	0.371982i	−0.496217	−	0.868199i	$-0.665278\pi$
$241$	5.77472	−	5.77472i	0.371982	−	0.371982i	0.868199	+	0.496217i	$0.165278\pi$
$242$	−23.2279			−1.49315
$243$	−11.0651	+	11.0651i	−0.709829	+	0.709829i
$244$	−9.29481	−	9.29481i	−0.595039	−	0.595039i
$245$	−10.1718	−	10.1718i	−0.649850	−	0.649850i
$246$		−	11.9381i		−	0.761144i
$247$			16.2527i			1.03414i
$248$	−4.15728	−	4.15728i	−0.263988	−	0.263988i
$249$	10.9386	+	10.9386i	0.693205	+	0.693205i
$250$	−12.8006	+	12.8006i	−0.809581	+	0.809581i
$251$	7.76836			0.490334			0.245167	−	0.969481i	$-0.421157\pi$
$251$	7.76836			0.490334			0.245167	+	0.969481i	$0.421157\pi$
$252$	14.1438	−	14.1438i	0.890973	−	0.890973i
$253$			0.413501i			0.0259966i
$254$	10.1938			0.639618
$255$	10.4069	+	4.97550i	0.651708	+	0.311578i
$256$	−9.83770			−0.614856
$257$		−	6.89972i		−	0.430393i	−0.976571	−	0.215196i	$-0.930961\pi$
$257$		−	6.89972i		−	0.430393i	0.976571	−	0.215196i	$-0.0690392\pi$
$258$	−1.68455	+	1.68455i	−0.104875	+	0.104875i
$259$	−14.7032			−0.913610
$260$	35.2456	−	35.2456i	2.18584	−	2.18584i
$261$	13.0330	+	13.0330i	0.806725	+	0.806725i
$262$	−33.1887	−	33.1887i	−2.05041	−	2.05041i
$263$		−	19.9300i		−	1.22894i	−0.788942	−	0.614468i	$-0.789371\pi$
$263$		−	19.9300i		−	1.22894i	0.788942	−	0.614468i	$-0.210629\pi$
$264$		−	1.96067i		−	0.120671i
$265$	2.07221	+	2.07221i	0.127295	+	0.127295i
$266$	14.5524	+	14.5524i	0.892266	+	0.892266i
$267$	−0.954522	+	0.954522i	−0.0584158	+	0.0584158i
$268$	−11.7038			−0.714921
$269$	13.5868	−	13.5868i	0.828399	−	0.828399i	−0.158896	−	0.987295i	$-0.550794\pi$
$269$	13.5868	−	13.5868i	0.828399	−	0.828399i	0.987295	+	0.158896i	$0.0507935\pi$
$270$			30.5585i			1.85973i
$271$	31.9410			1.94028			0.970138	−	0.242554i	$-0.0779853\pi$
$271$	31.9410			1.94028			0.970138	+	0.242554i	$0.0779853\pi$
$272$	−1.57838	+	3.30139i	−0.0957031	+	0.200176i
$273$	23.4471			1.41908
$274$		−	15.5056i		−	0.936727i
$275$	−1.09500	+	1.09500i	−0.0660308	+	0.0660308i
$276$	1.66142			0.100006
$277$	−8.99971	+	8.99971i	−0.540740	+	0.540740i	−0.923746	−	0.383006i	$-0.874889\pi$
$277$	−8.99971	+	8.99971i	−0.540740	+	0.540740i	0.383006	+	0.923746i	$0.374889\pi$
$278$	−23.3152	−	23.3152i	−1.39835	−	1.39835i
$279$	−3.37504	−	3.37504i	−0.202058	−	0.202058i
$280$		−	21.4270i		−	1.28051i
$281$			28.5548i			1.70344i	0.523998	+	0.851719i	$0.324440\pi$
$281$			28.5548i			1.70344i	−0.523998	+	0.851719i	$0.675560\pi$
$282$	−0.0179230	−	0.0179230i	−0.00106730	−	0.00106730i
$283$	−10.6672	−	10.6672i	−0.634097	−	0.634097i	0.314996	−	0.949093i	$-0.397997\pi$
$283$	−10.6672	−	10.6672i	−0.634097	−	0.634097i	−0.949093	+	0.314996i	$0.897997\pi$
$284$	−27.3752	+	27.3752i	−1.62442	+	1.62442i
$285$	−7.27356			−0.430848
$286$	−7.93601	+	7.93601i	−0.469266	+	0.469266i
$287$			17.6907i			1.04425i
$288$	−12.3499			−0.727727
$289$	−10.6744	−	13.2310i	−0.627903	−	0.778292i
$290$	58.1601			3.41528
$291$			2.28311i			0.133838i
$292$	9.16314	−	9.16314i	0.536232	−	0.536232i
$293$	−10.2134			−0.596675			−0.298337	−	0.954460i	$-0.596432\pi$
$293$	−10.2134			−0.596675			−0.298337	+	0.954460i	$0.596432\pi$
$294$	9.20234	−	9.20234i	0.536692	−	0.536692i
$295$	−5.46598	−	5.46598i	−0.318242	−	0.318242i
$296$	−6.78805	−	6.78805i	−0.394547	−	0.394547i
$297$		−	4.14368i		−	0.240441i
$298$			18.3985i			1.06580i
$299$	−2.28294	−	2.28294i	−0.132026	−	0.132026i
$300$	4.39964	+	4.39964i	0.254014	+	0.254014i
$301$	2.49628	−	2.49628i	0.143883	−	0.143883i
$302$	41.9134			2.41185
$303$	−11.2333	+	11.2333i	−0.645333	+	0.645333i
$304$		−	2.30739i		−	0.132338i
$305$	−11.4316			−0.654570
$306$	7.46205	−	15.6079i	0.426577	−	0.892244i
$307$	−23.4638			−1.33915			−0.669574	−	0.742746i	$-0.733523\pi$
$307$	−23.4638			−1.33915			−0.669574	+	0.742746i	$0.733523\pi$
$308$			8.55850i			0.487666i
$309$	−4.07274	+	4.07274i	−0.231690	+	0.231690i
$310$	−15.0611			−0.855414
$311$	−3.22269	+	3.22269i	−0.182742	+	0.182742i	−0.792550	−	0.609807i	$-0.791247\pi$
$311$	−3.22269	+	3.22269i	−0.182742	+	0.182742i	0.609807	+	0.792550i	$0.291247\pi$
$312$	10.8249	+	10.8249i	0.612839	+	0.612839i
$313$	−21.4081	−	21.4081i	−1.21006	−	1.21006i	−0.971006	−	0.239054i	$-0.923163\pi$
$313$	−21.4081	−	21.4081i	−1.21006	−	1.21006i	−0.239054	−	0.971006i	$-0.576837\pi$
$314$		−	24.9103i		−	1.40577i
$315$		−	17.3952i		−	0.980109i
$316$	7.02991	+	7.02991i	0.395463	+	0.395463i
$317$	18.5174	+	18.5174i	1.04004	+	1.04004i	0.999164	+	0.0408782i	$0.0130156\pi$
$317$	18.5174	+	18.5174i	1.04004	+	1.04004i	0.0408782	+	0.999164i	$0.486984\pi$
$318$	−1.87472	+	1.87472i	−0.105129	+	0.105129i
$319$	−7.88641			−0.441554
$320$	−24.2508	+	24.2508i	−1.35566	+	1.35566i
$321$			0.150549i			0.00840285i
$322$	−4.08822			−0.227827
$323$	9.67100	+	4.62365i	0.538109	+	0.257267i
$324$	0.348713			0.0193730
$325$		−	12.0910i		−	0.670687i
$326$	−11.6513	+	11.6513i	−0.645306	+	0.645306i
$327$	−19.5184			−1.07937
$328$	−8.16729	+	8.16729i	−0.450963	+	0.450963i
$329$	0.0265595	+	0.0265595i	0.00146427	+	0.00146427i
$330$	−3.55159	−	3.55159i	−0.195509	−	0.195509i
$331$		−	8.06837i		−	0.443478i	−0.975106	−	0.221739i	$-0.928827\pi$
$331$		−	8.06837i		−	0.443478i	0.975106	−	0.221739i	$-0.0711733\pi$
$332$		−	44.0878i		−	2.41963i
$333$	−5.51079	−	5.51079i	−0.301990	−	0.301990i
$334$	−11.7986	−	11.7986i	−0.645589	−	0.645589i
$335$	−7.19715	+	7.19715i	−0.393222	+	0.393222i
$336$	−3.32877			−0.181600
$337$	20.6663	−	20.6663i	1.12576	−	1.12576i	0.134904	−	0.990859i	$-0.456927\pi$
$337$	20.6663	−	20.6663i	1.12576	−	1.12576i	0.990859	−	0.134904i	$-0.0430727\pi$
$338$		−	58.4797i		−	3.18088i
$339$	−18.3497			−0.996620
$340$	−10.9457	−	30.9993i	−0.593611	−	1.68117i
$341$	2.04226			0.110595
$342$			10.9086i			0.589869i
$343$	3.83727	−	3.83727i	0.207193	−	0.207193i
$344$	2.30493			0.124273
$345$	1.02168	−	1.02168i	0.0550055	−	0.0550055i
$346$	24.1729	+	24.1729i	1.29955	+	1.29955i
$347$	17.3930	+	17.3930i	0.933705	+	0.933705i	0.997935	−	0.0642298i	$-0.0204591\pi$
$347$	17.3930	+	17.3930i	0.933705	+	0.933705i	−0.0642298	+	0.997935i	$0.520459\pi$
$348$			31.6872i			1.69861i
$349$		−	19.6447i		−	1.05155i	−0.850622	−	0.525777i	$-0.823775\pi$
$349$		−	19.6447i		−	1.05155i	0.850622	−	0.525777i	$-0.176225\pi$
$350$	−10.8261	−	10.8261i	−0.578678	−	0.578678i
$351$	22.8773	+	22.8773i	1.22110	+	1.22110i
$352$	3.73653	−	3.73653i	0.199158	−	0.199158i
$353$	−0.963593			−0.0512869			−0.0256434	−	0.999671i	$-0.508163\pi$
$353$	−0.963593			−0.0512869			−0.0256434	+	0.999671i	$0.508163\pi$
$354$	4.94505	−	4.94505i	0.262826	−	0.262826i
$355$			33.6684i			1.78693i
$356$	3.84718			0.203900
$357$	6.67035	−	13.9520i	0.353033	−	0.738416i
$358$	16.0770			0.849697
$359$		−	5.51355i		−	0.290994i	−0.989359	−	0.145497i	$-0.953522\pi$
$359$		−	5.51355i		−	0.290994i	0.989359	−	0.145497i	$-0.0464781\pi$
$360$	8.03090	−	8.03090i	0.423265	−	0.423265i
$361$	12.2408			0.644253
$362$	2.47713	−	2.47713i	0.130195	−	0.130195i
$363$	−7.78224	−	7.78224i	−0.408461	−	0.408461i
$364$	−47.2516	−	47.2516i	−2.47666	−	2.47666i
$365$		−	11.2696i		−	0.589879i
$366$		−	10.3421i		−	0.540589i
$367$	12.7199	+	12.7199i	0.663975	+	0.663975i	0.956315	−	0.292340i	$-0.0944338\pi$
$367$	12.7199	+	12.7199i	0.663975	+	0.663975i	−0.292340	+	0.956315i	$0.594434\pi$
$368$	0.324108	+	0.324108i	0.0168953	+	0.0168953i
$369$	−6.63052	+	6.63052i	−0.345171	+	0.345171i
$370$	−24.5919			−1.27847
$371$	2.77809	−	2.77809i	0.144231	−	0.144231i
$372$		−	8.20571i		−	0.425446i
$373$	−13.8341			−0.716302			−0.358151	−	0.933664i	$-0.616593\pi$
$373$	−13.8341			−0.716302			−0.358151	+	0.933664i	$0.616593\pi$
$374$	2.46456	+	6.97991i	0.127439	+	0.360923i
$375$	−8.57737			−0.442934
$376$			0.0245236i			0.00126471i
$377$	43.5410	−	43.5410i	2.24247	−	2.24247i
$378$	40.9679			2.10716
$379$	−6.15510	+	6.15510i	−0.316166	+	0.316166i	−0.847293	−	0.531126i	$-0.821769\pi$
$379$	−6.15510	+	6.15510i	−0.316166	+	0.316166i	0.531126	+	0.847293i	$0.321769\pi$
$380$	14.6580	+	14.6580i	0.751938	+	0.751938i
$381$	3.41532	+	3.41532i	0.174972	+	0.174972i
$382$			53.9786i			2.76179i
$383$		−	34.3399i		−	1.75469i	−0.479861	−	0.877345i	$-0.659313\pi$
$383$		−	34.3399i		−	1.75469i	0.479861	−	0.877345i	$-0.340687\pi$
$384$	−12.0231	−	12.0231i	−0.613550	−	0.613550i
$385$	5.26300	+	5.26300i	0.268227	+	0.268227i
$386$	−7.35540	+	7.35540i	−0.374380	+	0.374380i
$387$	1.87123			0.0951198
$388$	4.60102	−	4.60102i	0.233581	−	0.233581i
$389$		−	4.89700i		−	0.248288i	−0.992264	−	0.124144i	$-0.960382\pi$
$389$		−	4.89700i		−	0.248288i	0.992264	−	0.124144i	$-0.0396184\pi$
$390$	39.2168			1.98582
$391$	−2.00790	+	0.708977i	−0.101544	+	0.0358545i
$392$	−12.5914			−0.635960
$393$		−	22.2390i		−	1.12181i
$394$	−1.58557	+	1.58557i	−0.0798800	+	0.0798800i
$395$	8.64599			0.435027
$396$	−3.20775	+	3.20775i	−0.161196	+	0.161196i
$397$	−10.1734	−	10.1734i	−0.510587	−	0.510587i	0.404119	−	0.914706i	$-0.367578\pi$
$397$	−10.1734	−	10.1734i	−0.510587	−	0.510587i	−0.914706	+	0.404119i	$0.867578\pi$
$398$	5.36169	+	5.36169i	0.268757	+	0.268757i
$399$			9.75122i			0.488172i
$400$			1.71655i			0.0858276i
$401$	−23.0486	−	23.0486i	−1.15099	−	1.15099i	−0.986354	−	0.164641i	$-0.947354\pi$
$401$	−23.0486	−	23.0486i	−1.15099	−	1.15099i	−0.164641	−	0.986354i	$-0.552646\pi$
$402$	−6.51123	−	6.51123i	−0.324750	−	0.324750i
$403$	−11.2754	+	11.2754i	−0.561666	+	0.561666i
$404$	45.2754			2.25254
$405$	0.214439	−	0.214439i	0.0106556	−	0.0106556i
$406$		−	77.9717i		−	3.86967i
$407$	3.33463			0.165291
$408$	9.52076	−	3.36172i	0.471348	−	0.166430i
$409$	−37.8287			−1.87051			−0.935255	−	0.353974i	$-0.884830\pi$
$409$	−37.8287			−1.87051			−0.935255	+	0.353974i	$0.884830\pi$
$410$			29.5887i			1.46128i
$411$	5.19496	−	5.19496i	0.256249	−	0.256249i
$412$	16.4151			0.808713
$413$	−7.32792	+	7.32792i	−0.360583	+	0.360583i
$414$	−1.53228	−	1.53228i	−0.0753073	−	0.0753073i
$415$	−27.1115	−	27.1115i	−1.33085	−	1.33085i
$416$			41.2588i			2.02288i
$417$		−	15.6230i		−	0.765060i
$418$	−3.30044	−	3.30044i	−0.161430	−	0.161430i
$419$	−13.9221	−	13.9221i	−0.680141	−	0.680141i	0.279891	−	0.960032i	$-0.409702\pi$
$419$	−13.9221	−	13.9221i	−0.680141	−	0.680141i	−0.960032	+	0.279891i	$0.909702\pi$
$420$	21.1465	−	21.1465i	1.03184	−	1.03184i
$421$	−22.7895			−1.11069			−0.555347	−	0.831619i	$-0.687415\pi$
$421$	−22.7895			−1.11069			−0.555347	+	0.831619i	$0.687415\pi$
$422$	6.67405	−	6.67405i	0.324888	−	0.324888i
$423$			0.0199092i			0.000968017i
$424$	2.56513			0.124574
$425$	−7.19461	−	3.43970i	−0.348990	−	0.166850i
$426$	−30.4596			−1.47577
$427$			15.3256i			0.741659i
$428$	0.303393	−	0.303393i	0.0146651	−	0.0146651i
$429$	−5.31773			−0.256742
$430$	4.17518	−	4.17518i	0.201345	−	0.201345i
$431$	−26.5229	−	26.5229i	−1.27757	−	1.27757i	−0.942026	−	0.335539i	$-0.891082\pi$
$431$	−26.5229	−	26.5229i	−1.27757	−	1.27757i	−0.335539	−	0.942026i	$-0.608918\pi$
$432$	−3.24788	−	3.24788i	−0.156264	−	0.156264i
$433$		−	37.2978i		−	1.79242i	−0.443631	−	0.896209i	$-0.646310\pi$
$433$		−	37.2978i		−	1.79242i	0.443631	−	0.896209i	$-0.353690\pi$
$434$			20.1915i			0.969225i
$435$	19.4858	+	19.4858i	0.934274	+	0.934274i
$436$	39.3343	+	39.3343i	1.88377	+	1.88377i
$437$	0.949433	−	0.949433i	0.0454175	−	0.0454175i
$438$	10.1956			0.487163
$439$	−12.2174	+	12.2174i	−0.583107	+	0.583107i	−0.935756	−	0.352649i	$-0.885281\pi$
$439$	−12.2174	+	12.2174i	−0.583107	+	0.583107i	0.352649	+	0.935756i	$0.385281\pi$
$440$			4.85956i			0.231671i
$441$	−10.2221			−0.486768
$442$	−52.1431	−	24.9293i	−2.48019	−	1.18577i
$443$	−4.27443			−0.203084			−0.101542	−	0.994831i	$-0.532378\pi$
$443$	−4.27443			−0.203084			−0.101542	+	0.994831i	$0.532378\pi$
$444$		−	13.3984i		−	0.635858i
$445$	2.36580	−	2.36580i	0.112150	−	0.112150i
$446$	23.7802			1.12602
$447$	−6.16420	+	6.16420i	−0.291557	+	0.291557i
$448$	32.5115	+	32.5115i	1.53603	+	1.53603i
$449$	−19.1896	−	19.1896i	−0.905611	−	0.905611i	0.0903031	−	0.995914i	$-0.471216\pi$
$449$	−19.1896	−	19.1896i	−0.905611	−	0.905611i	−0.995914	+	0.0903031i	$0.971216\pi$
$450$		−	8.11530i		−	0.382559i
$451$		−	4.01218i		−	0.188926i
$452$	36.9791	+	36.9791i	1.73935	+	1.73935i
$453$	14.0426	+	14.0426i	0.659778	+	0.659778i
$454$	−8.80407	+	8.80407i	−0.413195	+	0.413195i
$455$	−58.1141			−2.72443
$456$	−4.50187	+	4.50187i	−0.210820	+	0.210820i
$457$		−	24.3012i		−	1.13676i	−0.822765	−	0.568382i	$-0.807570\pi$
$457$		−	24.3012i		−	1.13676i	0.822765	−	0.568382i	$-0.192430\pi$
$458$	29.4167			1.37455
$459$	20.1211	−	7.10464i	0.939175	−	0.331616i
$460$	−4.11787			−0.191997
$461$			25.3668i			1.18145i	0.806873	+	0.590724i	$0.201158\pi$
$461$			25.3668i			1.18145i	−0.806873	+	0.590724i	$0.798842\pi$
$462$	−4.76141	+	4.76141i	−0.221521	+	0.221521i
$463$	16.7899			0.780293			0.390146	−	0.920753i	$-0.372424\pi$
$463$	16.7899			0.780293			0.390146	+	0.920753i	$0.372424\pi$
$464$	−6.18148	+	6.18148i	−0.286968	+	0.286968i
$465$	−5.04605	−	5.04605i	−0.234005	−	0.234005i
$466$	4.53268	+	4.53268i	0.209972	+	0.209972i
$467$			30.4251i			1.40791i	0.710247	+	0.703953i	$0.248583\pi$
$467$			30.4251i			1.40791i	−0.710247	+	0.703953i	$0.751417\pi$
$468$		−	35.4201i		−	1.63730i
$469$	9.64879	+	9.64879i	0.445540	+	0.445540i
$470$	0.0444224	+	0.0444224i	0.00204905	+	0.00204905i
$471$	8.34589	−	8.34589i	0.384558	−	0.384558i
$472$	−6.76620			−0.311440
$473$	−0.566147	+	0.566147i	−0.0260315	+	0.0260315i
$474$			7.82199i			0.359276i
$475$	5.02842			0.230720
$476$	−41.5589	+	14.6742i	−1.90485	+	0.672590i
$477$	2.08247			0.0953499
$478$			65.0233i			2.97410i
$479$	−11.8395	+	11.8395i	−0.540962	+	0.540962i	−0.923811	−	0.382849i	$-0.874943\pi$
$479$	−11.8395	+	11.8395i	−0.540962	+	0.540962i	0.382849	+	0.923811i	$0.374943\pi$
$480$	−18.4645			−0.842786
$481$	−18.4105	+	18.4105i	−0.839447	+	0.839447i
$482$	−12.9487	−	12.9487i	−0.589796	−	0.589796i
$483$	−1.36971	−	1.36971i	−0.0623239	−	0.0623239i
$484$			31.3662i			1.42573i
$485$		−	5.65873i		−	0.256950i
$486$	24.8114	+	24.8114i	1.12547	+	1.12547i
$487$	6.98224	+	6.98224i	0.316396	+	0.316396i	0.847381	−	0.530985i	$-0.178178\pi$
$487$	6.98224	+	6.98224i	0.316396	+	0.316396i	−0.530985	+	0.847381i	$0.678178\pi$
$488$	−7.07542	+	7.07542i	−0.320289	+	0.320289i
$489$	−7.80726			−0.353057
$490$	−22.8082	+	22.8082i	−1.03037	+	1.03037i
$491$			32.1821i			1.45236i	0.687506	+	0.726179i	$0.258705\pi$
$491$			32.1821i			1.45236i	−0.687506	+	0.726179i	$0.741295\pi$
$492$	−16.1207			−0.726779
$493$	−13.5218	−	38.2953i	−0.608992	−	1.72473i
$494$	36.4435			1.63967
$495$			3.94518i			0.177322i
$496$	1.60076	−	1.60076i	0.0718761	−	0.0718761i
$497$	45.1371			2.02468
$498$	24.5277	−	24.5277i	1.09911	−	1.09911i
$499$	26.3650	+	26.3650i	1.18026	+	1.18026i	0.979677	+	0.200581i	$0.0642831\pi$
$499$	26.3650	+	26.3650i	1.18026	+	1.18026i	0.200581	+	0.979677i	$0.435717\pi$
$500$	17.2855	+	17.2855i	0.773030	+	0.773030i
$501$		−	7.90593i		−	0.353211i
$502$		−	17.4190i		−	0.777449i
$503$	−26.6708	−	26.6708i	−1.18919	−	1.18919i	−0.977292	−	0.211899i	$-0.932035\pi$
$503$	−26.6708	−	26.6708i	−1.18919	−	1.18919i	−0.211899	−	0.977292i	$-0.567965\pi$
$504$	−10.7665	−	10.7665i	−0.479580	−	0.479580i
$505$	27.8418	−	27.8418i	1.23895	−	1.23895i
$506$	0.927194			0.0412188
$507$	19.5929	−	19.5929i	0.870152	−	0.870152i
$508$		−	13.7654i		−	0.610740i
$509$	23.6697			1.04914			0.524570	−	0.851367i	$-0.324226\pi$
$509$	23.6697			1.04914			0.524570	+	0.851367i	$0.324226\pi$
$510$	11.1566	−	23.3355i	0.494022	−	1.03331i
$511$	−15.1085			−0.668361
$512$		−	9.94878i		−	0.439678i
$513$	−9.51425	+	9.51425i	−0.420064	+	0.420064i
$514$	−15.4713			−0.682409
$515$	10.0944	−	10.0944i	0.444810	−	0.444810i
$516$	2.27475	+	2.27475i	0.100140	+	0.100140i
$517$	−0.00602361	−	0.00602361i	−0.000264918	−	0.000264918i
$518$			32.9689i			1.44857i
$519$			16.1977i			0.711000i
$520$	−26.8297	−	26.8297i	−1.17656	−	1.17656i
$521$	−19.4442	−	19.4442i	−0.851867	−	0.851867i	0.138496	−	0.990363i	$-0.455773\pi$
$521$	−19.4442	−	19.4442i	−0.851867	−	0.851867i	−0.990363	+	0.138496i	$0.955773\pi$
$522$	29.2241	−	29.2241i	1.27910	−	1.27910i
$523$	4.35606			0.190477			0.0952385	−	0.995454i	$-0.469639\pi$
$523$	4.35606			0.190477			0.0952385	+	0.995454i	$0.469639\pi$
$524$	−44.8168	+	44.8168i	−1.95783	+	1.95783i
$525$		−	7.25429i		−	0.316603i
$526$	−44.6891			−1.94854
$527$	3.50161	+	9.91695i	0.152533	+	0.431989i
$528$	0.754955			0.0328552
$529$		−	22.7333i		−	0.988403i
$530$	4.64652	−	4.64652i	0.201832	−	0.201832i
$531$	−5.49306			−0.238378
$532$	19.6511	−	19.6511i	0.851982	−	0.851982i
$533$	22.1513	+	22.1513i	0.959480	+	0.959480i
$534$	2.14033	+	2.14033i	0.0926211	+	0.0926211i
$535$		−	0.373140i		−	0.0161322i
$536$			8.90916i			0.384817i
$537$	5.38641	+	5.38641i	0.232441	+	0.232441i
$538$	−30.4656	−	30.4656i	−1.31347	−	1.31347i
$539$	3.09275	−	3.09275i	0.133214	−	0.133214i
$540$	41.2651			1.77577
$541$	−16.4850	+	16.4850i	−0.708744	+	0.708744i	−0.966271	−	0.257527i	$-0.917092\pi$
$541$	−16.4850	+	16.4850i	−0.708744	+	0.708744i	0.257527	+	0.966271i	$0.417092\pi$
$542$		−	71.6214i		−	3.07640i
$543$	1.65986			0.0712316
$544$	24.5506	+	11.7375i	1.05260	+	0.503242i
$545$	48.3768			2.07223
$546$		−	52.5756i		−	2.25003i
$547$	−5.67756	+	5.67756i	−0.242755	+	0.242755i	−0.817989	−	0.575234i	$-0.804911\pi$
$547$	−5.67756	+	5.67756i	−0.242755	+	0.242755i	0.575234	+	0.817989i	$0.304911\pi$
$548$	−20.9382			−0.894436
$549$	−5.74409	+	5.74409i	−0.245152	+	0.245152i
$550$	2.45532	+	2.45532i	0.104695	+	0.104695i
$551$	18.1079	+	18.1079i	0.771421	+	0.771421i
$552$		−	1.26471i		−	0.0538298i
$553$		−	11.5912i		−	0.492906i
$554$	20.1801	+	20.1801i	0.857370	+	0.857370i
$555$	−8.23923	−	8.23923i	−0.349736	−	0.349736i
$556$	−31.4840	+	31.4840i	−1.33522	+	1.33522i
$557$	15.8389			0.671116			0.335558	−	0.942020i	$-0.391075\pi$
$557$	15.8389			0.671116			0.335558	+	0.942020i	$0.391075\pi$
$558$	−7.56786	+	7.56786i	−0.320373	+	0.320373i
$559$		−	6.25141i		−	0.264407i
$560$	8.25043			0.348644
$561$	−1.51281	+	3.16426i	−0.0638710	+	0.133595i
$562$	64.0286			2.70088
$563$			40.4009i			1.70270i	0.524602	+	0.851348i	$0.324214\pi$
$563$			40.4009i			1.70270i	−0.524602	+	0.851348i	$0.675786\pi$
$564$	−0.0242025	+	0.0242025i	−0.00101911	+	0.00101911i
$565$	45.4801			1.91336
$566$	−23.9190	+	23.9190i	−1.00539	+	1.00539i
$567$	−0.287486	−	0.287486i	−0.0120733	−	0.0120733i
$568$	20.8386	+	20.8386i	0.874368	+	0.874368i
$569$			20.4970i			0.859278i	0.903001	+	0.429639i	$0.141359\pi$
$569$			20.4970i			0.859278i	−0.903001	+	0.429639i	$0.858641\pi$
$570$			16.3095i			0.683131i
$571$	28.9375	+	28.9375i	1.21100	+	1.21100i	0.970700	+	0.240296i	$0.0772446\pi$
$571$	28.9375	+	28.9375i	1.21100	+	1.21100i	0.240296	+	0.970700i	$0.422755\pi$
$572$	10.7165	+	10.7165i	0.448080	+	0.448080i
$573$	−18.0849	+	18.0849i	−0.755507	+	0.755507i
$574$	39.6678			1.65570
$575$	−0.706318	+	0.706318i	−0.0294555	+	0.0294555i
$576$			24.3709i			1.01545i
$577$	37.7197			1.57029			0.785147	−	0.619310i	$-0.212588\pi$
$577$	37.7197			1.57029			0.785147	+	0.619310i	$0.212588\pi$
$578$	−29.6678	+	23.9351i	−1.23402	+	0.995571i
$579$	−4.92868			−0.204829
$580$		−	78.5373i		−	3.26108i
$581$	−36.3468	+	36.3468i	−1.50792	+	1.50792i
$582$	5.11943			0.212207
$583$	−0.630061	+	0.630061i	−0.0260945	+	0.0260945i
$584$	−6.97519	−	6.97519i	−0.288635	−	0.288635i
$585$	−21.7814	−	21.7814i	−0.900549	−	0.900549i
$586$			22.9016i			0.946057i
$587$		−	35.2533i		−	1.45506i	−0.686077	−	0.727529i	$-0.740669\pi$
$587$		−	35.2533i		−	1.45506i	0.686077	−	0.727529i	$-0.259331\pi$
$588$	−12.4265	−	12.4265i	−0.512461	−	0.512461i
$589$	−4.68921	−	4.68921i	−0.193216	−	0.193216i
$590$	−12.2564	+	12.2564i	−0.504588	+	0.504588i
$591$	−1.06245			−0.0437035
$592$	2.61373	−	2.61373i	0.107424	−	0.107424i
$593$		−	2.93775i		−	0.120639i	−0.998179	−	0.0603195i	$-0.980788\pi$
$593$		−	2.93775i		−	0.120639i	0.998179	−	0.0603195i	$-0.0192119\pi$
$594$	−9.29139			−0.381230
$595$	−16.5326	+	34.5802i	−0.677770	+	1.41765i
$596$	24.8447			1.01768
$597$			3.59274i			0.147041i
$598$	−5.11905	+	5.11905i	−0.209334	+	0.209334i
$599$	28.5730			1.16746			0.583731	−	0.811947i	$-0.301592\pi$
$599$	28.5730			1.16746			0.583731	+	0.811947i	$0.301592\pi$
$600$	3.34911	−	3.34911i	0.136727	−	0.136727i
$601$	−28.2109	−	28.2109i	−1.15075	−	1.15075i	−0.986403	−	0.164342i	$-0.947450\pi$
$601$	−28.2109	−	28.2109i	−1.15075	−	1.15075i	−0.164342	−	0.986403i	$-0.552550\pi$
$602$	−5.59741	−	5.59741i	−0.228134	−	0.228134i
$603$			7.23279i			0.294542i
$604$		−	56.5984i		−	2.30296i
$605$	19.2884	+	19.2884i	0.784186	+	0.784186i
$606$	25.1884	+	25.1884i	1.02321	+	1.02321i
$607$	−16.4028	+	16.4028i	−0.665768	+	0.665768i	−0.956733	−	0.290966i	$-0.906023\pi$
$607$	−16.4028	+	16.4028i	−0.665768	+	0.665768i	0.290966	+	0.956733i	$0.406023\pi$
$608$	−17.1588			−0.695880
$609$	26.1235	−	26.1235i	1.05858	−	1.05858i
$610$			25.6331i			1.03785i
$611$	0.0665128			0.00269082
$612$	−21.0764	−	10.0765i	−0.851961	−	0.407318i
$613$	30.9689			1.25082			0.625411	−	0.780295i	$-0.284931\pi$
$613$	30.9689			1.25082			0.625411	+	0.780295i	$0.284931\pi$
$614$			52.6129i			2.12328i
$615$	−9.91335	+	9.91335i	−0.399745	+	0.399745i
$616$	6.51492			0.262494
$617$	16.0667	−	16.0667i	0.646820	−	0.646820i	−0.305403	−	0.952223i	$-0.598791\pi$
$617$	16.0667	−	16.0667i	0.646820	−	0.646820i	0.952223	+	0.305403i	$0.0987911\pi$
$618$	9.13231	+	9.13231i	0.367355	+	0.367355i
$619$	13.0433	+	13.0433i	0.524256	+	0.524256i	0.918854	−	0.394598i	$-0.129116\pi$
$619$	13.0433	+	13.0433i	0.524256	+	0.524256i	−0.394598	+	0.918854i	$0.629116\pi$
$620$			20.3380i			0.816794i
$621$		−	2.67284i		−	0.107257i
$622$	7.22626	+	7.22626i	0.289747	+	0.289747i
$623$	−3.17169	−	3.17169i	−0.127071	−	0.127071i
$624$	−4.16812	+	4.16812i	−0.166858	+	0.166858i
$625$	30.9298			1.23719
$626$	−48.0036	+	48.0036i	−1.91861	+	1.91861i
$627$		−	2.21154i		−	0.0883206i
$628$	−33.6380			−1.34230
$629$	5.71746	+	16.1925i	0.227970	+	0.645637i
$630$	−39.0054			−1.55401
$631$		−	14.5647i		−	0.579810i	−0.957055	−	0.289905i	$-0.906376\pi$
$631$		−	14.5647i		−	0.579810i	0.957055	−	0.289905i	$-0.0936238\pi$
$632$	5.35132	−	5.35132i	0.212864	−	0.212864i
$633$	4.47212			0.177751
$634$	41.5217	−	41.5217i	1.64904	−	1.64904i
$635$	−8.46494	−	8.46494i	−0.335921	−	0.335921i
$636$	2.53155	+	2.53155i	0.100383	+	0.100383i
$637$			34.1502i			1.35308i
$638$			17.6837i			0.700105i
$639$	16.9176	+	16.9176i	0.669248	+	0.669248i
$640$	29.7994	+	29.7994i	1.17793	+	1.17793i
$641$	−13.4247	+	13.4247i	−0.530242	+	0.530242i	−0.920644	−	0.390402i	$-0.872336\pi$
$641$	−13.4247	+	13.4247i	−0.530242	+	0.530242i	0.390402	+	0.920644i	$0.372336\pi$
$642$	0.337578			0.0133231
$643$	19.5985	−	19.5985i	0.772891	−	0.772891i	−0.205720	−	0.978611i	$-0.565954\pi$
$643$	19.5985	−	19.5985i	0.772891	−	0.772891i	0.978611	+	0.205720i	$0.0659536\pi$
$644$			5.52058i			0.217541i
$645$	2.79769			0.110159
$646$	10.3676	−	21.6853i	0.407909	−	0.853198i
$647$	30.2278			1.18838			0.594188	−	0.804326i	$-0.297473\pi$
$647$	30.2278			1.18838			0.594188	+	0.804326i	$0.297473\pi$
$648$		−	0.265448i		−	0.0104278i
$649$	1.66195	−	1.66195i	0.0652371	−	0.0652371i
$650$	−27.1117			−1.06341
$651$	−6.76493	+	6.76493i	−0.265139	+	0.265139i
$652$	15.7335	+	15.7335i	0.616172	+	0.616172i
$653$	−24.4134	−	24.4134i	−0.955371	−	0.955371i	0.0436751	−	0.999046i	$-0.486093\pi$
$653$	−24.4134	−	24.4134i	−0.955371	−	0.955371i	−0.999046	+	0.0436751i	$0.986093\pi$
$654$			43.7662i			1.71139i
$655$			55.1197i			2.15370i
$656$	−3.14481	−	3.14481i	−0.122784	−	0.122784i
$657$	−5.66272	−	5.66272i	−0.220924	−	0.220924i
$658$	0.0595545	−	0.0595545i	0.00232168	−	0.00232168i
$659$	0.629344			0.0245158			0.0122579	−	0.999925i	$-0.496098\pi$
$659$	0.629344			0.0245158			0.0122579	+	0.999925i	$0.496098\pi$
$660$	−4.79594	+	4.79594i	−0.186682	+	0.186682i
$661$		−	6.31903i		−	0.245782i	−0.992420	−	0.122891i	$-0.960783\pi$
$661$		−	6.31903i		−	0.245782i	0.992420	−	0.122891i	$-0.0392165\pi$
$662$	−18.0917			−0.703155
$663$	−9.11764	−	25.8222i	−0.354100	−	1.00285i
$664$	−33.5606			−1.30240
$665$		−	24.1686i		−	0.937218i
$666$	−12.3569	+	12.3569i	−0.478819	+	0.478819i
$667$	−5.08705			−0.196972
$668$	−15.9324	+	15.9324i	−0.616442	+	0.616442i
$669$	7.96726	+	7.96726i	0.308032	+	0.308032i
$670$	16.1382	+	16.1382i	0.623473	+	0.623473i
$671$		−	3.47580i		−	0.134182i
$672$			24.7543i			0.954916i
$673$	17.3138	+	17.3138i	0.667398	+	0.667398i	0.957113	−	0.289715i	$-0.0935604\pi$
$673$	17.3138	+	17.3138i	0.667398	+	0.667398i	−0.289715	+	0.957113i	$0.593560\pi$
$674$	−46.3400	−	46.3400i	−1.78495	−	1.78495i
$675$	7.07800	−	7.07800i	0.272432	−	0.272432i
$676$	−78.9689			−3.03726
$677$	32.2075	−	32.2075i	1.23783	−	1.23783i	0.276949	−	0.960885i	$-0.410677\pi$
$677$	32.2075	−	32.2075i	1.23783	−	1.23783i	0.960885	−	0.276949i	$-0.0893233\pi$
$678$			41.1457i			1.58019i
$679$	−7.58632			−0.291136
$680$	−23.5974	+	8.33208i	−0.904918	+	0.319521i
$681$	−5.89939			−0.226065
$682$		−	4.57937i		−	0.175353i
$683$	−21.5410	+	21.5410i	−0.824242	+	0.824242i	−0.986713	−	0.162471i	$-0.948053\pi$
$683$	−21.5410	+	21.5410i	−0.824242	+	0.824242i	0.162471	+	0.986713i	$0.448053\pi$
$684$	14.7306			0.563237
$685$	−12.8758	+	12.8758i	−0.491960	+	0.491960i
$686$	−8.60433	−	8.60433i	−0.328515	−	0.328515i
$687$	9.85570	+	9.85570i	0.376019	+	0.376019i
$688$			0.887510i			0.0338360i
$689$		−	6.95715i		−	0.265046i
$690$	−2.29092	−	2.29092i	−0.0872139	−	0.0872139i
$691$	2.33579	+	2.33579i	0.0888577	+	0.0888577i	0.750138	−	0.661281i	$-0.229987\pi$
$691$	2.33579	+	2.33579i	0.0888577	+	0.0888577i	−0.661281	+	0.750138i	$0.729987\pi$
$692$	32.6423	−	32.6423i	1.24087	−	1.24087i
$693$	5.28906			0.200915
$694$	39.0004	−	39.0004i	1.48044	−	1.48044i
$695$			38.7218i			1.46880i
$696$	24.1210			0.914304
$697$	19.4826	−	6.87918i	0.737956	−	0.260568i
$698$	−44.0493			−1.66729
$699$			3.03724i			0.114879i
$700$	−14.6191	+	14.6191i	−0.552552	+	0.552552i
$701$	3.55457			0.134254			0.0671272	−	0.997744i	$-0.478617\pi$
$701$	3.55457			0.134254			0.0671272	+	0.997744i	$0.478617\pi$
$702$	51.2979	−	51.2979i	1.93611	−	1.93611i
$703$	−7.65659	−	7.65659i	−0.288774	−	0.288774i
$704$	−7.37351	−	7.37351i	−0.277899	−	0.277899i
$705$			0.0297664i			0.00112107i
$706$			2.16067i			0.0813178i
$707$	−37.3259	−	37.3259i	−1.40378	−	1.40378i
$708$	−6.67762	−	6.67762i	−0.250960	−	0.250960i
$709$	−16.8953	+	16.8953i	−0.634515	+	0.634515i	−0.949197	−	0.314682i	$-0.898102\pi$
$709$	−16.8953	+	16.8953i	−0.634515	+	0.634515i	0.314682	+	0.949197i	$0.398102\pi$
$710$	75.4947			2.83327
$711$	4.34441	−	4.34441i	0.162928	−	0.162928i
$712$		−	2.92856i		−	0.109753i
$713$	1.31734			0.0493349
$714$	−31.2845	−	14.9570i	−1.17079	−	0.559750i
$715$	13.1801			0.492907
$716$		−	21.7098i		−	0.811334i
$717$	−21.7853	+	21.7853i	−0.813586	+	0.813586i
$718$	−12.3631			−0.461385
$719$	3.76308	−	3.76308i	0.140339	−	0.140339i	−0.633447	−	0.773786i	$-0.718361\pi$
$719$	3.76308	−	3.76308i	0.140339	−	0.140339i	0.773786	+	0.633447i	$0.218361\pi$
$720$	3.09229	+	3.09229i	0.115243	+	0.115243i
$721$	−13.5329	−	13.5329i	−0.503991	−	0.503991i
$722$		−	27.4476i		−	1.02149i
$723$		−	8.67659i		−	0.322686i
$724$	−3.34503	−	3.34503i	−0.124317	−	0.124317i
$725$	−13.4711	−	13.4711i	−0.500304	−	0.500304i
$726$	−17.4501	+	17.4501i	−0.647635	+	0.647635i
$727$	−1.37782			−0.0511006			−0.0255503	−	0.999674i	$-0.508134\pi$
$727$	−1.37782			−0.0511006			−0.0255503	+	0.999674i	$0.508134\pi$
$728$	−35.9690	+	35.9690i	−1.33310	+	1.33310i
$729$			16.2800i			0.602964i
$730$	−25.2699			−0.935282
$731$	−3.71984	−	1.77843i	−0.137583	−	0.0657777i
$732$	−13.9656			−0.516183
$733$			4.47200i			0.165177i	0.996584	+	0.0825885i	$0.0263187\pi$
$733$			4.47200i			0.165177i	−0.996584	+	0.0825885i	$0.973681\pi$
$734$	28.5220	−	28.5220i	1.05276	−	1.05276i
$735$	−15.2832			−0.563730
$736$	2.41021	−	2.41021i	0.0888416	−	0.0888416i
$737$	−2.18831	−	2.18831i	−0.0806075	−	0.0806075i
$738$	14.8676	+	14.8676i	0.547285	+	0.547285i
$739$			14.5190i			0.534092i	0.963684	+	0.267046i	$0.0860475\pi$
$739$			14.5190i			0.534092i	−0.963684	+	0.267046i	$0.913952\pi$
$740$			33.2081i			1.22075i
$741$	12.2100	+	12.2100i	0.448544	+	0.448544i
$742$	−6.22932	−	6.22932i	−0.228685	−	0.228685i
$743$	2.12501	−	2.12501i	0.0779591	−	0.0779591i	−0.667052	−	0.745011i	$-0.732444\pi$
$743$	2.12501	−	2.12501i	0.0779591	−	0.0779591i	0.745011	+	0.667052i	$0.232444\pi$
$744$	−6.24637			−0.229003
$745$	15.2781	−	15.2781i	0.559746	−	0.559746i
$746$			31.0202i			1.13573i
$747$	−27.2458			−0.996871
$748$	9.42542	−	3.32805i	0.344628	−	0.121686i
$749$	−0.500246			−0.0182786
$750$			19.2331i			0.702293i
$751$	21.8966	−	21.8966i	0.799019	−	0.799019i	−0.183922	−	0.982941i	$-0.558879\pi$
$751$	21.8966	−	21.8966i	0.799019	−	0.799019i	0.982941	+	0.183922i	$0.0588792\pi$
$752$	−0.00944279			−0.000344343
$753$	5.83603	−	5.83603i	0.212677	−	0.212677i
$754$	−97.6321	−	97.6321i	−3.55555	−	3.55555i
$755$	−34.8048	−	34.8048i	−1.26668	−	1.26668i
$756$		−	55.3216i		−	2.01203i
$757$			4.36575i			0.158676i	0.996848	+	0.0793379i	$0.0252806\pi$
$757$			4.36575i			0.158676i	−0.996848	+	0.0793379i	$0.974719\pi$
$758$	13.8016	+	13.8016i	0.501297	+	0.501297i
$759$	0.310645	+	0.310645i	0.0112757	+	0.0112757i
$760$	11.1580	−	11.1580i	0.404742	−	0.404742i
$761$	38.3962			1.39186			0.695931	−	0.718109i	$-0.254992\pi$
$761$	38.3962			1.39186			0.695931	+	0.718109i	$0.254992\pi$
$762$	7.65819	−	7.65819i	0.277427	−	0.277427i
$763$		−	64.8558i		−	2.34794i
$764$	72.8908			2.63710
$765$	−19.1572	+	6.76430i	−0.692631	+	0.244564i
$766$	−77.0006			−2.78215
$767$			18.3513i			0.662626i
$768$	−7.39064	+	7.39064i	−0.266687	+	0.266687i
$769$	11.0175			0.397302			0.198651	−	0.980070i	$-0.436344\pi$
$769$	11.0175			0.397302			0.198651	+	0.980070i	$0.436344\pi$
$770$	11.8012	−	11.8012i	0.425287	−	0.425287i
$771$	−5.18346	−	5.18346i	−0.186678	−	0.186678i
$772$	9.93247	+	9.93247i	0.357477	+	0.357477i
$773$		−	44.0660i		−	1.58494i	−0.609908	−	0.792472i	$-0.708794\pi$
$773$		−	44.0660i		−	1.58494i	0.609908	−	0.792472i	$-0.291206\pi$
$774$		−	4.19586i		−	0.150817i
$775$	3.48848	+	3.48848i	0.125310	+	0.125310i
$776$	−3.50240	−	3.50240i	−0.125729	−	0.125729i
$777$	−11.0458	+	11.0458i	−0.396268	+	0.396268i
$778$	−10.9806			−0.393672
$779$	−9.21232	+	9.21232i	−0.330065	+	0.330065i
$780$		−	52.9569i		−	1.89616i
$781$	−10.2370			−0.366307
$782$	1.58974	+	4.50233i	0.0568491	+	0.161003i
$783$	50.9773			1.82178
$784$		−	4.84829i		−	0.173153i
$785$	−20.6854	+	20.6854i	−0.738295	+	0.738295i
$786$	−49.8665			−1.77868
$787$	16.2276	−	16.2276i	0.578450	−	0.578450i	−0.356026	−	0.934476i	$-0.615868\pi$
$787$	16.2276	−	16.2276i	0.578450	−	0.578450i	0.934476	+	0.356026i	$0.115868\pi$
$788$	2.14110	+	2.14110i	0.0762735	+	0.0762735i
$789$	−14.9725	−	14.9725i	−0.533036	−	0.533036i
$790$		−	19.3869i		−	0.689756i
$791$		−	60.9725i		−	2.16793i
$792$	2.44181	+	2.44181i	0.0867661	+	0.0867661i
$793$	19.1899	+	19.1899i	0.681454	+	0.681454i
$794$	−22.8118	+	22.8118i	−0.809561	+	0.809561i
$795$	3.11352			0.110425
$796$	7.24024	−	7.24024i	0.256624	−	0.256624i
$797$			17.6963i			0.626836i	0.949615	+	0.313418i	$0.101474\pi$
$797$			17.6963i			0.626836i	−0.949615	+	0.313418i	$0.898526\pi$
$798$	21.8652			0.774020
$799$	0.0189219	−	0.0395777i	0.000669409	−	0.00140016i
$800$	12.7650			0.451312
$801$		−	2.37752i		−	0.0840055i
$802$	−51.6821	+	51.6821i	−1.82496	+	1.82496i
$803$	3.42656			0.120921
$804$	−8.79253	+	8.79253i	−0.310089	+	0.310089i
$805$	3.39485	+	3.39485i	0.119653	+	0.119653i
$806$	25.2828	+	25.2828i	0.890548	+	0.890548i
$807$		−	20.4143i		−	0.718617i
$808$		−	34.4647i		−	1.21246i
$809$	−6.28766	−	6.28766i	−0.221062	−	0.221062i	0.587883	−	0.808946i	$-0.299961\pi$
$809$	−6.28766	−	6.28766i	−0.221062	−	0.221062i	−0.808946	+	0.587883i	$0.799961\pi$
$810$	−0.480838	−	0.480838i	−0.0168949	−	0.0168949i
$811$	39.6849	−	39.6849i	1.39352	−	1.39352i	0.576254	−	0.817271i	$-0.304514\pi$
$811$	39.6849	−	39.6849i	1.39352	−	1.39352i	0.817271	−	0.576254i	$-0.195486\pi$
$812$	−105.290			−3.69496
$813$	23.9959	−	23.9959i	0.841572	−	0.841572i
$814$		−	7.47725i		−	0.262077i
$815$	19.3504			0.677816
$816$	1.29443	+	3.66596i	0.0453140	+	0.128334i
$817$	2.59985			0.0909571
$818$			84.8235i			2.96578i
$819$	−29.2010	+	29.2010i	−1.02036	+	1.02036i
$820$	39.9556			1.39531
$821$	2.11323	−	2.11323i	0.0737521	−	0.0737521i	−0.669269	−	0.743021i	$-0.733392\pi$
$821$	2.11323	−	2.11323i	0.0737521	−	0.0737521i	0.743021	+	0.669269i	$0.233392\pi$
$822$	−11.6487	−	11.6487i	−0.406295	−	0.406295i
$823$	30.4066	+	30.4066i	1.05991	+	1.05991i	0.998087	+	0.0618199i	$0.0196905\pi$
$823$	30.4066	+	30.4066i	1.05991	+	1.05991i	0.0618199	+	0.998087i	$0.480310\pi$
$824$		−	12.4955i		−	0.435302i
$825$			1.64525i			0.0572802i
$826$	16.4314	+	16.4314i	0.571722	+	0.571722i
$827$	−35.2453	−	35.2453i	−1.22560	−	1.22560i	−0.965612	−	0.259986i	$-0.916282\pi$
$827$	−35.2453	−	35.2453i	−1.22560	−	1.22560i	−0.259986	−	0.965612i	$-0.583718\pi$
$828$	−2.06913	+	2.06913i	−0.0719074	+	0.0719074i
$829$	−3.91836			−0.136090			−0.0680451	−	0.997682i	$-0.521676\pi$
$829$	−3.91836			−0.136090			−0.0680451	+	0.997682i	$0.521676\pi$
$830$	−60.7922	+	60.7922i	−2.11013	+	2.11013i
$831$			13.5222i			0.469080i
$832$	81.4185			2.82268
$833$	20.3207	+	9.71523i	0.704071	+	0.336613i
$834$	−35.0314			−1.21304
$835$			19.5950i			0.678113i
$836$	−4.45679	+	4.45679i	−0.154141	+	0.154141i
$837$	−13.2011			−0.456296
$838$	−31.2177	+	31.2177i	−1.07840	+	1.07840i
$839$	−1.71709	−	1.71709i	−0.0592806	−	0.0592806i	0.676845	−	0.736126i	$-0.263347\pi$
$839$	−1.71709	−	1.71709i	−0.0592806	−	0.0592806i	−0.736126	+	0.676845i	$0.763347\pi$
$840$	−16.0972	−	16.0972i	−0.555405	−	0.555405i
$841$		−	68.0218i		−	2.34558i
$842$			51.1011i			1.76106i
$843$	21.4520	+	21.4520i	0.738847	+	0.738847i
$844$	−9.01241	−	9.01241i	−0.310220	−	0.310220i
$845$	−48.5614	+	48.5614i	−1.67056	+	1.67056i
$846$	0.0446424			0.00153484
$847$	25.8588	−	25.8588i	0.888520	−	0.888520i
$848$			0.987702i			0.0339178i
$849$	−16.0276			−0.550065
$850$	−7.71286	+	16.1325i	−0.264549	+	0.553340i
$851$	2.15097			0.0737343
$852$			41.1316i			1.40914i
$853$	−22.7101	+	22.7101i	−0.777577	+	0.777577i	−0.979418	−	0.201841i	$-0.935308\pi$
$853$	−22.7101	+	22.7101i	−0.777577	+	0.777577i	0.201841	+	0.979418i	$0.435308\pi$
$854$	34.3647			1.17594
$855$	9.05847	−	9.05847i	0.309793	−	0.309793i
$856$	−0.230950	−	0.230950i	−0.00789370	−	0.00789370i
$857$	26.7190	+	26.7190i	0.912704	+	0.912704i	0.996484	−	0.0837799i	$-0.0266993\pi$
$857$	26.7190	+	26.7190i	0.912704	+	0.912704i	−0.0837799	+	0.996484i	$0.526699\pi$
$858$			11.9240i			0.407077i
$859$			32.1760i			1.09783i	0.835878	+	0.548916i	$0.184959\pi$
$859$			32.1760i			1.09783i	−0.835878	+	0.548916i	$0.815041\pi$
$860$	−5.63801	−	5.63801i	−0.192255	−	0.192255i
$861$	13.2902	+	13.2902i	0.452930	+	0.452930i
$862$	−59.4725	+	59.4725i	−2.02564	+	2.02564i
$863$	−21.9144			−0.745976			−0.372988	−	0.927836i	$-0.621667\pi$
$863$	−21.9144			−0.745976			−0.372988	+	0.927836i	$0.621667\pi$
$864$	−24.1527	+	24.1527i	−0.821691	+	0.821691i
$865$		−	40.1463i		−	1.36502i
$866$	−83.6331			−2.84197
$867$	−17.9590	−	1.92067i	−0.609921	−	0.0652293i
$868$	27.2659			0.925466
$869$			2.62884i			0.0891772i
$870$	43.6931	−	43.6931i	1.48134	−	1.48134i
$871$	24.1634			0.818746
$872$	29.9422	−	29.9422i	1.01397	−	1.01397i
$873$	−2.84338	−	2.84338i	−0.0962338	−	0.0962338i
$874$	−2.12892	−	2.12892i	−0.0720117	−	0.0720117i
$875$		−	28.5009i		−	0.963506i
$876$		−	13.7677i		−	0.465169i
$877$	−5.01919	−	5.01919i	−0.169486	−	0.169486i	0.617267	−	0.786753i	$-0.288240\pi$
$877$	−5.01919	−	5.01919i	−0.169486	−	0.169486i	−0.786753	+	0.617267i	$0.788240\pi$
$878$	27.3952	+	27.3952i	0.924544	+	0.924544i
$879$	−7.67291	+	7.67291i	−0.258801	+	0.258801i
$880$	−1.87117			−0.0630771
$881$	−15.4924	+	15.4924i	−0.521953	+	0.521953i	−0.918161	−	0.396208i	$-0.870326\pi$
$881$	−15.4924	+	15.4924i	−0.521953	+	0.521953i	0.396208	+	0.918161i	$0.370326\pi$
$882$			22.9211i			0.771795i
$883$	−11.1248			−0.374380			−0.187190	−	0.982324i	$-0.559938\pi$
$883$	−11.1248			−0.374380			−0.187190	+	0.982324i	$0.559938\pi$
$884$	−33.6637	+	70.4121i	−1.13223	+	2.36822i
$885$	−8.21272			−0.276067
$886$			9.58456i			0.322000i
$887$	−10.8416	+	10.8416i	−0.364025	+	0.364025i	−0.865292	−	0.501267i	$-0.832867\pi$
$887$	−10.8416	+	10.8416i	−0.364025	+	0.364025i	0.501267	+	0.865292i	$0.332867\pi$
$888$	−10.1991			−0.342260
$889$	−11.3484	+	11.3484i	−0.380614	+	0.380614i
$890$	−5.30484	−	5.30484i	−0.177819	−	0.177819i
$891$	0.0652008	+	0.0652008i	0.00218431	+	0.00218431i
$892$		−	32.1119i		−	1.07519i
$893$			0.0276614i			0.000925655i
$894$	13.8220	+	13.8220i	0.462277	+	0.462277i
$895$	−13.3503	−	13.3503i	−0.446252	−	0.446252i
$896$	39.9503	−	39.9503i	1.33465	−	1.33465i
$897$	−3.43015			−0.114529
$898$	−43.0288	+	43.0288i	−1.43589	+	1.43589i
$899$			25.1248i			0.837958i
$900$	−10.9586			−0.365287
$901$	−4.13978	−	1.97920i	−0.137916	−	0.0659368i
$902$	−8.99653			−0.299552
$903$		−	3.75069i		−	0.124815i
$904$	28.1493	−	28.1493i	0.936233	−	0.936233i
$905$	−4.11401			−0.136754
$906$	31.4877	−	31.4877i	1.04611	−	1.04611i
$907$	16.7294	+	16.7294i	0.555490	+	0.555490i	0.928020	−	0.372530i	$-0.121510\pi$
$907$	16.7294	+	16.7294i	0.555490	+	0.555490i	−0.372530	+	0.928020i	$0.621510\pi$
$908$	11.8887	+	11.8887i	0.394540	+	0.394540i
$909$		−	27.9797i		−	0.928029i
$910$			130.310i			4.31972i
$911$	−11.2192	−	11.2192i	−0.371708	−	0.371708i	0.496391	−	0.868099i	$-0.334658\pi$
$911$	−11.2192	−	11.2192i	−0.371708	−	0.371708i	−0.868099	+	0.496391i	$0.834658\pi$
$912$	−1.73344	−	1.73344i	−0.0574000	−	0.0574000i
$913$	8.24332	−	8.24332i	0.272814	−	0.272814i
$914$	−54.4908			−1.80239
$915$	−8.58804	+	8.58804i	−0.283912	+	0.283912i
$916$		−	39.7232i		−	1.31249i
$917$	73.8956			2.44025
$918$	−15.9308	−	45.1177i	−0.525794	−	1.48911i
$919$	32.4343			1.06991			0.534955	−	0.844881i	$-0.320329\pi$
$919$	32.4343			1.06991			0.534955	+	0.844881i	$0.320329\pi$
$920$			3.13462i			0.103345i
$921$	−17.6273	+	17.6273i	−0.580840	+	0.580840i
$922$	56.8800			1.87324
$923$	56.5184	−	56.5184i	1.86032	−	1.86032i
$924$	6.42963	+	6.42963i	0.211519	+	0.211519i
$925$	5.69602	+	5.69602i	0.187284	+	0.187284i
$926$		−	37.6481i		−	1.23719i
$927$		−	10.1443i		−	0.333184i
$928$	45.9683	+	45.9683i	1.50898	+	1.50898i
$929$	30.1462	+	30.1462i	0.989066	+	0.989066i	0.999941	−	0.0108750i	$-0.00346170\pi$
$929$	30.1462	+	30.1462i	0.989066	+	0.989066i	−0.0108750	+	0.999941i	$0.503462\pi$
$930$	−11.3148	+	11.3148i	−0.371026	+	0.371026i
$931$	−14.2024			−0.465466
$932$	6.12076	−	6.12076i	0.200492	−	0.200492i
$933$			4.84214i			0.158525i
$934$	68.2223			2.23230
$935$	3.74954	−	7.84267i	0.122623	−	0.256483i
$936$	−26.9626			−0.881300
$937$		−	23.1168i		−	0.755192i	−0.925970	−	0.377596i	$-0.876751\pi$
$937$		−	23.1168i		−	0.755192i	0.925970	−	0.377596i	$-0.123249\pi$
$938$	21.6355	−	21.6355i	0.706425	−	0.706425i
$939$	−32.1660			−1.04970
$940$	0.0599865	−	0.0599865i	0.00195654	−	0.00195654i
$941$	14.9015	+	14.9015i	0.485777	+	0.485777i	0.906971	−	0.421194i	$-0.138389\pi$
$941$	14.9015	+	14.9015i	0.485777	+	0.485777i	−0.421194	+	0.906971i	$0.638389\pi$
$942$	−18.7140	−	18.7140i	−0.609736	−	0.609736i
$943$		−	2.58802i		−	0.0842776i
$944$		−	2.60532i		−	0.0847959i
$945$	−34.0197	−	34.0197i	−1.10666	−	1.10666i
$946$	1.26947	+	1.26947i	0.0412742	+	0.0412742i
$947$	−27.2837	+	27.2837i	−0.886600	+	0.886600i	−0.994195	−	0.107594i	$-0.965685\pi$
$947$	−27.2837	+	27.2837i	−0.886600	+	0.886600i	0.107594	+	0.994195i	$0.465685\pi$
$948$	10.5625			0.343055
$949$	−18.9181	+	18.9181i	−0.614107	+	0.614107i
$950$		−	11.2752i		−	0.365817i
$951$	27.8227			0.902213
$952$	11.1703	+	31.6356i	0.362032	+	1.02532i
$953$	−50.5047			−1.63601			−0.818004	−	0.575213i	$-0.804919\pi$
$953$	−50.5047			−1.63601			−0.818004	+	0.575213i	$0.804919\pi$
$954$		−	4.66954i		−	0.151182i
$955$	44.8237	−	44.8237i	1.45046	−	1.45046i
$956$	87.8052			2.83982
$957$	−5.92472	+	5.92472i	−0.191519	+	0.191519i
$958$	26.5478	+	26.5478i	0.857722	+	0.857722i
$959$	17.2618	+	17.2618i	0.557414	+	0.557414i
$960$			36.4371i			1.17600i
$961$			24.4937i			0.790119i
$962$	41.2820	+	41.2820i	1.33098	+	1.33098i
$963$	−0.187494	−	0.187494i	−0.00604190	−	0.00604190i
$964$	−17.4854	+	17.4854i	−0.563168	+	0.563168i
$965$	12.2158			0.393241
$966$	−3.07130	+	3.07130i	−0.0988175	+	0.0988175i
$967$			50.2992i			1.61751i	0.588143	+	0.808757i	$0.299859\pi$
$967$			50.2992i			1.61751i	−0.588143	+	0.808757i	$0.700141\pi$
$968$	23.8766			0.767424
$969$	10.7390	−	3.79186i	0.344985	−	0.121812i
$970$	−12.6886			−0.407406
$971$		−	33.0075i		−	1.05926i	−0.848229	−	0.529630i	$-0.822331\pi$
$971$		−	33.0075i		−	1.05926i	0.848229	−	0.529630i	$-0.177669\pi$
$972$	33.5045	−	33.5045i	1.07466	−	1.07466i
$973$	51.9120			1.66422
$974$	15.6563	−	15.6563i	0.501660	−	0.501660i
$975$	−9.08344	−	9.08344i	−0.290903	−	0.290903i
$976$	−2.72438	−	2.72438i	−0.0872054	−	0.0872054i
$977$		−	44.1930i		−	1.41386i	−0.707284	−	0.706930i	$-0.750080\pi$
$977$		−	44.1930i		−	1.41386i	0.707284	−	0.706930i	$-0.249920\pi$
$978$			17.5063i			0.559788i
$979$	0.719328	+	0.719328i	0.0229898	+	0.0229898i
$980$	30.7994	+	30.7994i	0.983849	+	0.983849i
$981$	24.3082	−	24.3082i	0.776100	−	0.776100i
$982$	72.1620			2.30278
$983$	−2.33252	+	2.33252i	−0.0743958	+	0.0743958i	−0.743326	−	0.668930i	$-0.766753\pi$
$983$	−2.33252	+	2.33252i	−0.0743958	+	0.0743958i	0.668930	+	0.743326i	$0.266753\pi$
$984$			12.2715i			0.391200i
$985$	2.63331			0.0839043
$986$	−85.8697	+	30.3200i	−2.73465	+	0.965587i
$987$	0.0399060			0.00127022
$988$		−	49.2120i		−	1.56564i
$989$	−0.365188	+	0.365188i	−0.0116123	+	0.0116123i
$990$	8.84628			0.281153
$991$	−9.73423	+	9.73423i	−0.309218	+	0.309218i	−0.844606	−	0.535388i	$-0.820165\pi$
$991$	−9.73423	+	9.73423i	−0.309218	+	0.309218i	0.535388	+	0.844606i	$0.320165\pi$
$992$	−11.9039	−	11.9039i	−0.377951	−	0.377951i
$993$	−6.06142	−	6.06142i	−0.192353	−	0.192353i
$994$		−	101.211i		−	3.21022i
$995$		−	8.90468i		−	0.282297i
$996$	−33.1213	−	33.1213i	−1.04949	−	1.04949i
$997$	−19.3525	−	19.3525i	−0.612901	−	0.612901i	0.330800	−	0.943701i	$-0.392682\pi$
$997$	−19.3525	−	19.3525i	−0.612901	−	0.612901i	−0.943701	+	0.330800i	$0.892682\pi$
$998$	59.1183	−	59.1183i	1.87136	−	1.87136i
$999$	−21.5548			−0.681964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.d.259.5	✓	68
17.13	even	4	inner	731.2.f.d.302.30	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.d.259.5	✓	68	1.1	even	1	trivial
731.2.f.d.302.30	yes	68	17.13	even	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.24230i q^{2} +(0.751257 - 0.751257i) q^{3} -3.02793 q^{4} +(-1.86200 + 1.86200i) q^{5} +(-1.68455 - 1.68455i) q^{6} +(2.49628 + 2.49628i) q^{7} +2.30493i q^{8} +1.87123i q^{9} +O(q^{10})\)	\(q-2.24230i q^{2} +(0.751257 - 0.751257i) q^{3} -3.02793 q^{4} +(-1.86200 + 1.86200i) q^{5} +(-1.68455 - 1.68455i) q^{6} +(2.49628 + 2.49628i) q^{7} +2.30493i q^{8} +1.87123i q^{9} +(4.17518 + 4.17518i) q^{10} +(-0.566147 - 0.566147i) q^{11} +(-2.27475 + 2.27475i) q^{12} +6.25141 q^{13} +(5.59741 - 5.59741i) q^{14} +2.79769i q^{15} -0.887510 q^{16} +(1.77843 - 3.71984i) q^{17} +4.19586 q^{18} +2.59985i q^{19} +(5.63801 - 5.63801i) q^{20} +3.75069 q^{21} +(-1.26947 + 1.26947i) q^{22} +(-0.365188 - 0.365188i) q^{23} +(1.73159 + 1.73159i) q^{24} -1.93412i q^{25} -14.0176i q^{26} +(3.65954 + 3.65954i) q^{27} +(-7.55855 - 7.55855i) q^{28} +(6.96498 - 6.96498i) q^{29} +6.27327 q^{30} +(-1.80365 + 1.80365i) q^{31} +6.59992i q^{32} -0.850644 q^{33} +(-8.34100 - 3.98779i) q^{34} -9.29616 q^{35} -5.66594i q^{36} +(-2.94502 + 2.94502i) q^{37} +5.82965 q^{38} +(4.69642 - 4.69642i) q^{39} +(-4.29178 - 4.29178i) q^{40} +(3.54341 + 3.54341i) q^{41} -8.41019i q^{42} -1.00000i q^{43} +(1.71425 + 1.71425i) q^{44} +(-3.48423 - 3.48423i) q^{45} +(-0.818863 + 0.818863i) q^{46} +0.0106396 q^{47} +(-0.666748 + 0.666748i) q^{48} +5.46280i q^{49} -4.33689 q^{50} +(-1.45849 - 4.13061i) q^{51} -18.9288 q^{52} -1.11289i q^{53} +(8.20581 - 8.20581i) q^{54} +2.10834 q^{55} +(-5.75374 + 5.75374i) q^{56} +(1.95315 + 1.95315i) q^{57} +(-15.6176 - 15.6176i) q^{58} +2.93554i q^{59} -8.47119i q^{60} +(3.06969 + 3.06969i) q^{61} +(4.04433 + 4.04433i) q^{62} +(-4.67110 + 4.67110i) q^{63} +13.0240 q^{64} +(-11.6402 + 11.6402i) q^{65} +1.90740i q^{66} +3.86527 q^{67} +(-5.38497 + 11.2634i) q^{68} -0.548700 q^{69} +20.8448i q^{70} +(9.04089 - 9.04089i) q^{71} -4.31304 q^{72} +(-3.02621 + 3.02621i) q^{73} +(6.60362 + 6.60362i) q^{74} +(-1.45302 - 1.45302i) q^{75} -7.87215i q^{76} -2.82652i q^{77} +(-10.5308 - 10.5308i) q^{78} +(-2.32169 - 2.32169i) q^{79} +(1.65255 - 1.65255i) q^{80} -0.115166 q^{81} +(7.94540 - 7.94540i) q^{82} +14.5604i q^{83} -11.3568 q^{84} +(3.61490 + 10.2378i) q^{85} -2.24230 q^{86} -10.4650i q^{87} +(1.30493 - 1.30493i) q^{88} -1.27057 q^{89} +(-7.81271 + 7.81271i) q^{90} +(15.6053 + 15.6053i) q^{91} +(1.10576 + 1.10576i) q^{92} +2.71001i q^{93} -0.0238573i q^{94} +(-4.84093 - 4.84093i) q^{95} +(4.95823 + 4.95823i) q^{96} +(-1.51953 + 1.51953i) q^{97} +12.2493 q^{98} +(1.05939 - 1.05939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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