LMFDB - Embedded newform 370.2.v.b.169.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(99,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.v (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.10
Character	$\chi$	$=$	370.169
Dual form			370.2.v.b.289.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(1.01326 + 2.78391i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.23483 + 0.0743186i) q^{5} +2.96257i q^{6} +(-1.02406 - 0.180569i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-4.42531 + 3.71328i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(1.01326 + 2.78391i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.23483 + 0.0743186i) q^{5} +2.96257i q^{6} +(-1.02406 - 0.180569i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-4.42531 + 3.71328i) q^{9} +(-2.12547 - 0.694521i) q^{10} +(-1.08964 - 1.88731i) q^{11} +(-1.01326 + 2.78391i) q^{12} +(3.72808 + 3.12823i) q^{13} +(-0.900543 - 0.519929i) q^{14} +(-2.47136 - 6.14626i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.949228 - 0.796496i) q^{17} +(-5.42845 + 1.97579i) q^{18} +(1.59512 + 4.38255i) q^{19} +(-1.75975 - 1.37959i) q^{20} +(-0.534950 - 3.03385i) q^{21} +(-0.378428 - 2.14617i) q^{22} +(2.09433 - 3.62748i) q^{23} +(-1.90431 + 2.26946i) q^{24} +(4.98895 - 0.332179i) q^{25} +(2.43333 + 4.21465i) q^{26} +(-7.12443 - 4.11329i) q^{27} +(-0.668408 - 0.796577i) q^{28} +(6.14779 - 3.54943i) q^{29} +(-0.220174 - 6.62085i) q^{30} +3.83594i q^{31} +(-0.173648 + 0.984808i) q^{32} +(4.15002 - 4.94580i) q^{33} +(1.16440 - 0.423807i) q^{34} +(2.30202 + 0.327436i) q^{35} -5.77684 q^{36} +(-5.16263 - 3.21671i) q^{37} +4.66382i q^{38} +(-4.93119 + 13.5483i) q^{39} +(-1.18178 - 1.89826i) q^{40} +(-5.14883 - 4.32038i) q^{41} +(0.534950 - 3.03385i) q^{42} -2.74566 q^{43} +(0.378428 - 2.14617i) q^{44} +(9.61387 - 8.62744i) q^{45} +(3.20869 - 2.69241i) q^{46} +(10.9104 + 6.29914i) q^{47} +(-2.56566 + 1.48129i) q^{48} +(-5.56176 - 2.02431i) q^{49} +(4.80169 + 1.39418i) q^{50} +(3.17919 + 1.83550i) q^{51} +(0.845087 + 4.79272i) q^{52} +(9.66804 - 1.70474i) q^{53} +(-5.28795 - 6.30193i) q^{54} +(2.57543 + 4.13685i) q^{55} +(-0.355652 - 0.977146i) q^{56} +(-10.5844 + 8.88133i) q^{57} +(6.99101 - 1.23270i) q^{58} +(-5.46090 + 0.962903i) q^{59} +(2.05757 - 6.29687i) q^{60} +(1.79209 - 2.13573i) q^{61} +(-1.31197 + 3.60460i) q^{62} +(5.20229 - 3.00354i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-8.56412 - 6.71400i) q^{65} +(5.59130 - 3.22814i) q^{66} +(8.75050 + 1.54295i) q^{67} +1.23913 q^{68} +(12.2207 + 2.15483i) q^{69} +(2.05120 + 1.09503i) q^{70} +(6.94924 - 2.52932i) q^{71} +(-5.42845 - 1.97579i) q^{72} +7.86051i q^{73} +(-3.75111 - 4.78845i) q^{74} +(5.97986 + 13.5522i) q^{75} +(-1.59512 + 4.38255i) q^{76} +(0.775066 + 2.12948i) q^{77} +(-9.26761 + 11.0447i) q^{78} +(-15.6757 - 2.76405i) q^{79} +(-0.461264 - 2.18798i) q^{80} +(1.22272 - 6.93437i) q^{81} +(-3.36066 - 5.82084i) q^{82} +(-2.02137 - 2.40898i) q^{83} +(1.54033 - 2.66792i) q^{84} +(-2.06217 + 1.85058i) q^{85} +(-2.58008 - 0.939073i) q^{86} +(16.1106 + 13.5184i) q^{87} +(1.08964 - 1.88731i) q^{88} +(-12.0974 + 2.13309i) q^{89} +(11.9848 - 4.81901i) q^{90} +(-3.25291 - 3.87667i) q^{91} +(3.93605 - 1.43260i) q^{92} +(-10.6789 + 3.88680i) q^{93} +(8.09802 + 9.65085i) q^{94} +(-3.89053 - 9.67573i) q^{95} +(-2.91756 + 0.514445i) q^{96} +(5.15005 - 8.92014i) q^{97} +(-4.53398 - 3.80446i) q^{98} +(11.8301 + 4.30581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	1.01326	+	2.78391i	0.585006	+	1.60729i	0.779511	+	0.626388i	$0.215468\pi$
$3$	1.01326	+	2.78391i	0.585006	+	1.60729i	−0.194505	+	0.980901i	$0.562310\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−2.23483	+	0.0743186i	−0.999448	+	0.0332363i
$5$	−2.23483	+	0.0743186i	−0.999448	+	0.0332363i
$6$			2.96257i			1.20947i
$7$	−1.02406	−	0.180569i	−0.387058	−	0.0682488i	−0.0232669	−	0.999729i	$-0.507407\pi$
$7$	−1.02406	−	0.180569i	−0.387058	−	0.0682488i	−0.363791	+	0.931480i	$0.618518\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−4.42531	+	3.71328i	−1.47510	+	1.23776i
$10$	−2.12547	−	0.694521i	−0.672134	−	0.219627i
$11$	−1.08964	−	1.88731i	−0.328539	−	0.569046i	0.653683	−	0.756768i	$-0.273223\pi$
$11$	−1.08964	−	1.88731i	−0.328539	−	0.569046i	−0.982222	+	0.187722i	$0.939890\pi$
$12$	−1.01326	+	2.78391i	−0.292503	+	0.803645i
$13$	3.72808	+	3.12823i	1.03398	+	0.867615i	0.991319	−	0.131475i	$-0.0419713\pi$
$13$	3.72808	+	3.12823i	1.03398	+	0.867615i	0.0426633	+	0.999090i	$0.486416\pi$
$14$	−0.900543	−	0.519929i	−0.240680	−	0.138957i
$15$	−2.47136	−	6.14626i	−0.638103	−	1.58696i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.949228	−	0.796496i	0.230221	−	0.193179i	−0.520378	−	0.853936i	$-0.674209\pi$
$17$	0.949228	−	0.796496i	0.230221	−	0.193179i	0.750600	+	0.660757i	$0.229765\pi$
$18$	−5.42845	+	1.97579i	−1.27950	+	0.465699i
$19$	1.59512	+	4.38255i	0.365945	+	1.00543i	0.976888	+	0.213752i	$0.0685684\pi$
$19$	1.59512	+	4.38255i	0.365945	+	1.00543i	−0.610942	+	0.791675i	$0.709209\pi$
$20$	−1.75975	−	1.37959i	−0.393493	−	0.308486i
$21$	−0.534950	−	3.03385i	−0.116736	−	0.662041i
$22$	−0.378428	−	2.14617i	−0.0806812	−	0.457566i
$23$	2.09433	−	3.62748i	0.436697	−	0.756382i	−0.560735	−	0.827995i	$-0.689481\pi$
$23$	2.09433	−	3.62748i	0.436697	−	0.756382i	0.997432	+	0.0716133i	$0.0228148\pi$
$24$	−1.90431	+	2.26946i	−0.388715	+	0.463252i
$25$	4.98895	−	0.332179i	0.997791	−	0.0664358i
$26$	2.43333	+	4.21465i	0.477215	+	0.826561i
$27$	−7.12443	−	4.11329i	−1.37110	−	0.791603i
$28$	−0.668408	−	0.796577i	−0.126317	−	0.150539i
$29$	6.14779	−	3.54943i	1.14162	−	0.659112i	0.194785	−	0.980846i	$-0.437599\pi$
$29$	6.14779	−	3.54943i	1.14162	−	0.659112i	0.946830	+	0.321734i	$0.104266\pi$
$30$	−0.220174	−	6.62085i	−0.0401981	−	1.20880i
$31$			3.83594i			0.688955i	0.938795	+	0.344477i	$0.111944\pi$
$31$			3.83594i			0.688955i	−0.938795	+	0.344477i	$0.888056\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	4.15002	−	4.94580i	0.722425	−	0.860953i
$34$	1.16440	−	0.423807i	0.199693	−	0.0726823i
$35$	2.30202	+	0.327436i	0.389113	+	0.0553467i
$36$	−5.77684			−0.962806
$37$	−5.16263	−	3.21671i	−0.848731	−	0.528824i
$37$	−5.16263	−	3.21671i	−0.848731	−	0.528824i
$38$			4.66382i			0.756571i
$39$	−4.93119	+	13.5483i	−0.789622	+	2.16947i
$40$	−1.18178	−	1.89826i	−0.186856	−	0.300142i
$41$	−5.14883	−	4.32038i	−0.804113	−	0.674731i	0.145082	−	0.989420i	$-0.453655\pi$
$41$	−5.14883	−	4.32038i	−0.804113	−	0.674731i	−0.949195	+	0.314689i	$0.898100\pi$
$42$	0.534950	−	3.03385i	0.0825446	−	0.468133i
$43$	−2.74566			−0.418710			−0.209355	−	0.977840i	$-0.567136\pi$
$43$	−2.74566			−0.418710			−0.209355	+	0.977840i	$0.567136\pi$
$44$	0.378428	−	2.14617i	0.0570502	−	0.323548i
$45$	9.61387	−	8.62744i	1.43315	−	1.28610i
$46$	3.20869	−	2.69241i	0.473096	−	0.396975i
$47$	10.9104	+	6.29914i	1.59145	+	0.918824i	0.993059	+	0.117621i	$0.0375267\pi$
$47$	10.9104	+	6.29914i	1.59145	+	0.918824i	0.598392	+	0.801204i	$0.295807\pi$
$48$	−2.56566	+	1.48129i	−0.370322	+	0.213805i
$49$	−5.56176	−	2.02431i	−0.794536	−	0.289188i
$50$	4.80169	+	1.39418i	0.679062	+	0.197166i
$51$	3.17919	+	1.83550i	0.445175	+	0.257022i
$52$	0.845087	+	4.79272i	0.117192	+	0.664631i
$53$	9.66804	−	1.70474i	1.32801	−	0.234163i	0.535763	−	0.844368i	$-0.320024\pi$
$53$	9.66804	−	1.70474i	1.32801	−	0.234163i	0.792244	+	0.610205i	$0.208913\pi$
$54$	−5.28795	−	6.30193i	−0.719598	−	0.857584i
$55$	2.57543	+	4.13685i	0.347271	+	0.557813i
$56$	−0.355652	−	0.977146i	−0.0475260	−	0.130577i
$57$	−10.5844	+	8.88133i	−1.40193	+	1.17636i
$58$	6.99101	−	1.23270i	0.917964	−	0.161862i
$59$	−5.46090	+	0.962903i	−0.710948	+	0.125359i	−0.517415	−	0.855734i	$-0.673106\pi$
$59$	−5.46090	+	0.962903i	−0.710948	+	0.125359i	−0.193533	+	0.981094i	$0.561995\pi$
$60$	2.05757	−	6.29687i	0.265631	−	0.812923i
$61$	1.79209	−	2.13573i	0.229453	−	0.273452i	−0.639017	−	0.769192i	$-0.720659\pi$
$61$	1.79209	−	2.13573i	0.229453	−	0.273452i	0.868471	+	0.495740i	$0.165103\pi$
$62$	−1.31197	+	3.60460i	−0.166620	+	0.457785i
$63$	5.20229	−	3.00354i	0.655427	−	0.378411i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−8.56412	−	6.71400i	−1.06225	−	0.832770i
$66$	5.59130	−	3.22814i	0.688242	−	0.397357i
$67$	8.75050	+	1.54295i	1.06904	+	0.188501i	0.680366	−	0.732873i	$-0.261821\pi$
$67$	8.75050	+	1.54295i	1.06904	+	0.188501i	0.388677	+	0.921374i	$0.372932\pi$
$68$	1.23913			0.150266
$69$	12.2207	+	2.15483i	1.47120	+	0.259411i
$70$	2.05120	+	1.09503i	0.245166	+	0.130881i
$71$	6.94924	−	2.52932i	0.824723	−	0.300175i	0.105032	−	0.994469i	$-0.466506\pi$
$71$	6.94924	−	2.52932i	0.824723	−	0.300175i	0.719691	+	0.694294i	$0.244283\pi$
$72$	−5.42845	−	1.97579i	−0.639749	−	0.232850i
$73$			7.86051i			0.920003i	0.887918	+	0.460002i	$0.152151\pi$
$73$			7.86051i			0.920003i	−0.887918	+	0.460002i	$0.847849\pi$
$74$	−3.75111	−	4.78845i	−0.436057	−	0.556645i
$75$	5.97986	+	13.5522i	0.690495	+	1.56487i
$76$	−1.59512	+	4.38255i	−0.182973	+	0.502713i
$77$	0.775066	+	2.12948i	0.0883270	+	0.242676i
$78$	−9.26761	+	11.0447i	−1.04935	+	1.25057i
$79$	−15.6757	−	2.76405i	−1.76365	−	0.310980i	−0.804518	−	0.593928i	$-0.797576\pi$
$79$	−15.6757	−	2.76405i	−1.76365	−	0.310980i	−0.959135	+	0.282948i	$0.908688\pi$
$80$	−0.461264	−	2.18798i	−0.0515709	−	0.244623i
$81$	1.22272	−	6.93437i	0.135857	−	0.770485i
$82$	−3.36066	−	5.82084i	−0.371123	−	0.642804i
$83$	−2.02137	−	2.40898i	−0.221874	−	0.264420i	0.643612	−	0.765352i	$-0.277435\pi$
$83$	−2.02137	−	2.40898i	−0.221874	−	0.264420i	−0.865487	+	0.500932i	$0.832991\pi$
$84$	1.54033	−	2.66792i	0.168063	−	0.291094i
$85$	−2.06217	+	1.85058i	−0.223674	+	0.200724i
$86$	−2.58008	−	0.939073i	−0.278217	−	0.101263i
$87$	16.1106	+	13.5184i	1.72724	+	1.44932i
$88$	1.08964	−	1.88731i	0.116156	−	0.201188i
$89$	−12.0974	+	2.13309i	−1.28232	+	0.226107i	−0.772964	−	0.634450i	$-0.781227\pi$
$89$	−12.0974	+	2.13309i	−1.28232	+	0.226107i	−0.509354	+	0.860557i	$0.670116\pi$
$90$	11.9848	−	4.81901i	1.26331	−	0.507968i
$91$	−3.25291	−	3.87667i	−0.340998	−	0.406385i
$92$	3.93605	−	1.43260i	0.410361	−	0.149359i
$93$	−10.6789	+	3.88680i	−1.10735	+	0.403042i
$94$	8.09802	+	9.65085i	0.835247	+	0.995409i
$95$	−3.89053	−	9.67573i	−0.399160	−	0.992709i
$96$	−2.91756	+	0.514445i	−0.297773	+	0.0525054i
$97$	5.15005	−	8.92014i	0.522908	−	0.905703i	−0.476737	−	0.879046i	$-0.658180\pi$
$97$	5.15005	−	8.92014i	0.522908	−	0.905703i	0.999645	−	0.0266572i	$-0.00848626\pi$
$98$	−4.53398	−	3.80446i	−0.458002	−	0.384309i
$99$	11.8301	+	4.30581i	1.18897	+	0.432751i
$100$	4.03528	+	2.95237i	0.403528	+	0.295237i
$101$	9.17761	−	15.8961i	0.913206	−	1.58172i	0.103699	−	0.994609i	$-0.466932\pi$
$101$	9.17761	−	15.8961i	0.913206	−	1.58172i	0.809507	−	0.587110i	$-0.199735\pi$
$102$	2.35968	+	2.81216i	0.233643	+	0.278445i
$103$	−3.84868	−	6.66610i	−0.379221	−	0.656830i	0.611728	−	0.791068i	$-0.290475\pi$
$103$	−3.84868	−	6.66610i	−0.379221	−	0.656830i	−0.990949	+	0.134238i	$0.957141\pi$
$104$	−0.845087	+	4.79272i	−0.0828676	+	0.469965i
$105$	1.42099	+	6.74039i	0.138675	+	0.657795i
$106$	9.66804	+	1.70474i	0.939043	+	0.165579i
$107$	3.98847	−	4.75327i	0.385580	−	0.459516i	−0.537987	−	0.842953i	$-0.680815\pi$
$107$	3.98847	−	4.75327i	0.385580	−	0.459516i	0.923567	+	0.383437i	$0.125260\pi$
$108$	−2.81366	−	7.73046i	−0.270744	−	0.743864i
$109$	3.63900	−	9.99807i	0.348553	−	0.957641i	−0.634274	−	0.773109i	$-0.718701\pi$
$109$	3.63900	−	9.99807i	0.348553	−	0.957641i	0.982826	−	0.184532i	$-0.0590771\pi$
$110$	1.00522	+	4.76821i	0.0958444	+	0.454631i
$111$	3.72395	−	17.6317i	0.353461	−	1.67352i
$112$		−	1.03986i		−	0.0982573i
$113$	−8.02406	−	2.92052i	−0.754840	−	0.274739i	−0.0641993	−	0.997937i	$-0.520449\pi$
$113$	−8.02406	−	2.92052i	−0.754840	−	0.274739i	−0.690641	+	0.723198i	$0.742672\pi$
$114$	−12.9836	+	4.72566i	−1.21603	+	0.442598i
$115$	−4.41088	+	8.26246i	−0.411317	+	0.770478i
$116$	6.99101	+	1.23270i	0.649099	+	0.114454i
$117$	−28.1139			−2.59913
$118$	−5.46090	−	0.962903i	−0.502716	−	0.0886424i
$119$	−1.11589	+	0.644259i	−0.102293	+	0.0590591i
$120$	4.08714	−	5.21339i	0.373103	−	0.475916i
$121$	3.12537	−	5.41329i	0.284124	−	0.492117i
$122$	2.41447	−	1.39400i	0.218596	−	0.126207i
$123$	6.81045	−	18.7115i	0.614077	−	1.68716i
$124$	−2.46569	+	2.93850i	−0.221426	+	0.263885i
$125$	−11.1248	+	1.11314i	−0.995031	+	0.0995620i
$126$	5.91583	−	1.04312i	0.527024	−	0.0929285i
$127$	−7.84470	+	1.38323i	−0.696105	+	0.122742i	−0.510494	−	0.859881i	$-0.670537\pi$
$127$	−7.84470	+	1.38323i	−0.696105	+	0.122742i	−0.185611	+	0.982623i	$0.559426\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−2.78207	−	7.64368i	−0.244948	−	0.672988i
$130$	−5.75131	−	9.23820i	−0.504423	−	0.810244i
$131$	−0.957846	−	1.14152i	−0.0836874	−	0.0997347i	0.722576	−	0.691292i	$-0.242958\pi$
$131$	−0.957846	−	1.14152i	−0.0836874	−	0.0997347i	−0.806263	+	0.591557i	$0.798514\pi$
$132$	6.35820	−	1.12112i	0.553410	−	0.0975811i
$133$	−0.842143	−	4.77603i	−0.0730230	−	0.414134i
$134$	7.69506	+	4.44274i	0.664752	+	0.383795i
$135$	16.2276	+	8.66304i	1.39665	+	0.745596i
$136$	1.16440	+	0.423807i	0.0998465	+	0.0363411i
$137$	−7.50310	+	4.33192i	−0.641033	+	0.370101i	−0.785012	−	0.619480i	$-0.787343\pi$
$137$	−7.50310	+	4.33192i	−0.641033	+	0.370101i	0.143979	+	0.989581i	$0.454010\pi$
$138$	10.7467	+	6.20460i	0.914818	+	0.528170i
$139$	−8.67914	+	7.28266i	−0.736155	+	0.617707i	−0.931802	−	0.362967i	$-0.881764\pi$
$139$	−8.67914	+	7.28266i	−0.736155	+	0.617707i	0.195647	+	0.980674i	$0.437319\pi$
$140$	1.55298	+	1.73054i	0.131251	+	0.146257i
$141$	−6.48113	+	36.7563i	−0.545810	+	3.09544i
$142$	7.39523			0.620594
$143$	1.84168	−	10.4447i	0.154009	−	0.873429i
$144$	−4.42531	−	3.71328i	−0.368776	−	0.309440i
$145$	−13.4755	+	8.38927i	−1.11908	+	0.696691i
$146$	−2.68845	+	7.38647i	−0.222498	+	0.611308i
$147$		−	17.5346i		−	1.44623i
$148$	−1.88714	−	5.78262i	−0.155122	−	0.475328i
$149$	−6.54925			−0.536536			−0.268268	−	0.963344i	$-0.586451\pi$
$149$	−6.54925			−0.536536			−0.268268	+	0.963344i	$0.586451\pi$
$150$	0.984105	+	14.7801i	0.0803518	+	1.20679i
$151$	8.10149	−	2.94870i	0.659290	−	0.239962i	0.00936007	−	0.999956i	$-0.497021\pi$
$151$	8.10149	−	2.94870i	0.659290	−	0.239962i	0.649930	+	0.759994i	$0.274798\pi$
$152$	−2.99784	+	3.57269i	−0.243157	+	0.289784i
$153$	−1.24302	+	7.04950i	−0.100492	+	0.569918i
$154$			2.26614i			0.182611i
$155$	−0.285081	−	8.57268i	−0.0228983	−	0.688574i
$156$	−12.4862	+	7.20892i	−0.999697	+	0.577175i
$157$	13.4128	+	15.9848i	1.07046	+	1.27572i	0.959442	+	0.281906i	$0.0909667\pi$
$157$	13.4128	+	15.9848i	1.07046	+	1.27572i	0.111018	+	0.993818i	$0.464589\pi$
$158$	−13.7850	−	7.95876i	−1.09667	−	0.633165i
$159$	14.5421	+	25.1876i	1.15326	+	1.99751i
$160$	0.314885	−	2.21379i	0.0248939	−	0.175015i
$161$	−2.79973	+	3.33659i	−0.220649	+	0.262960i
$162$	3.52067	−	6.09798i	0.276610	−	0.479103i
$163$	1.12186	+	6.36237i	0.0878706	+	0.498339i	0.996700	+	0.0811713i	$0.0258661\pi$
$163$	1.12186	+	6.36237i	0.0878706	+	0.498339i	−0.908830	+	0.417168i	$0.863023\pi$
$164$	−1.16715	−	6.61921i	−0.0911388	−	0.516874i
$165$	−8.90703	+	11.3615i	−0.693411	+	0.884488i
$166$	−1.07555	−	2.95505i	−0.0834789	−	0.229356i
$167$	13.5908	−	4.94663i	1.05168	−	0.382782i	0.242386	−	0.970180i	$-0.422070\pi$
$167$	13.5908	−	4.94663i	1.05168	−	0.382782i	0.809298	+	0.587398i	$0.199848\pi$
$168$	2.35992	−	1.98021i	0.182072	−	0.152776i
$169$	1.85532	+	10.5221i	0.142717	+	0.809389i
$170$	−2.57074	+	1.03367i	−0.197167	+	0.0792792i
$171$	−23.3326	−	13.4711i	−1.78429	−	1.03016i
$172$	−2.10330	−	1.76488i	−0.160375	−	0.134571i
$173$	4.76783	−	13.0995i	0.362491	−	0.995936i	−0.615655	−	0.788016i	$-0.711108\pi$
$173$	4.76783	−	13.0995i	0.362491	−	0.995936i	0.978146	−	0.207920i	$-0.0666694\pi$
$174$	10.5154	+	18.2133i	0.797173	+	1.38074i
$175$	−5.16897	−	0.560681i	−0.390737	−	0.0423835i
$176$	1.66943	−	1.40082i	0.125838	−	0.105590i
$177$	−8.21394	−	14.2270i	−0.617397	−	1.06936i
$178$	−12.0974	−	2.13309i	−0.906736	−	0.159882i
$179$			4.19437i			0.313502i	0.987638	+	0.156751i	$0.0501020\pi$
$179$			4.19437i			0.313502i	−0.987638	+	0.156751i	$0.949898\pi$
$180$	12.9103	−	0.429326i	0.962274	−	0.0320001i
$181$	−18.2159	−	15.2850i	−1.35398	−	1.13612i	−0.977791	−	0.209580i	$-0.932790\pi$
$181$	−18.2159	−	15.2850i	−1.35398	−	1.13612i	−0.376188	−	0.926543i	$-0.622765\pi$
$182$	−1.73084	−	4.75544i	−0.128298	−	0.352497i
$183$	7.76152	+	2.82496i	0.573748	+	0.208827i
$184$	4.18865			0.308792
$185$	11.7767	+	6.80514i	0.865839	+	0.500324i
$186$	−11.3642			−0.833267
$187$	−2.53756	−	0.923595i	−0.185564	−	0.0675399i
$188$	4.30887	+	11.8385i	0.314256	+	0.863412i
$189$	6.55311	+	5.49871i	0.476669	+	0.399972i
$190$	−0.346608	−	10.4229i	−0.0251456	−	0.756153i
$191$			23.4781i			1.69882i	0.527736	+	0.849409i	$0.323041\pi$
$191$			23.4781i			1.69882i	−0.527736	+	0.849409i	$0.676959\pi$
$192$	−2.91756	−	0.514445i	−0.210557	−	0.0371269i
$193$	−5.64549	−	9.77828i	−0.406371	−	0.703856i	0.588109	−	0.808782i	$-0.299873\pi$
$193$	−5.64549	−	9.77828i	−0.406371	−	0.703856i	−0.994480	+	0.104926i	$0.966539\pi$
$194$	7.89033	−	6.62077i	0.566493	−	0.475344i
$195$	10.0135	−	30.6447i	0.717081	−	2.19452i
$196$	−2.95935	−	5.12574i	−0.211382	−	0.366124i
$197$	−7.67079	+	21.0753i	−0.546521	+	1.50155i	0.291855	+	0.956463i	$0.405727\pi$
$197$	−7.67079	+	21.0753i	−0.546521	+	1.50155i	−0.838376	+	0.545092i	$0.816495\pi$
$198$	9.64401	+	8.09228i	0.685370	+	0.575093i
$199$	3.27114	+	1.88859i	0.231885	+	0.133879i	0.611441	−	0.791290i	$-0.290590\pi$
$199$	3.27114	+	1.88859i	0.231885	+	0.133879i	−0.379556	+	0.925169i	$0.623923\pi$
$200$	2.78215	+	4.15447i	0.196728	+	0.293765i
$201$	4.57110	+	25.9240i	0.322420	+	1.82854i
$202$	14.0609	−	11.7985i	0.989322	−	0.830140i
$203$	−6.93662	+	2.52472i	−0.486855	+	0.177201i
$204$	1.25556	+	3.44962i	0.0879067	+	0.241522i
$205$	11.8279	+	9.27268i	0.826094	+	0.647632i
$206$	−1.33663	−	7.58041i	−0.0931275	−	0.528152i
$207$	4.20179	+	23.8296i	0.292045	+	1.65627i
$208$	−2.43333	+	4.21465i	−0.168721	+	0.292233i
$209$	6.53315	−	7.78590i	0.451907	−	0.538562i
$210$	−0.970052	+	6.81991i	−0.0669399	+	0.470618i
$211$	4.20745	+	7.28751i	0.289653	+	0.501693i	0.973727	−	0.227719i	$-0.0731269\pi$
$211$	4.20745	+	7.28751i	0.289653	+	0.501693i	−0.684074	+	0.729412i	$0.739794\pi$
$212$	8.50193	+	4.90859i	0.583915	+	0.337123i
$213$	14.0828	+	16.7832i	0.964936	+	1.14997i
$214$	5.37365	−	3.10248i	0.367335	−	0.212081i
$215$	6.13610	−	0.204054i	0.418479	−	0.0139164i
$216$		−	8.22658i		−	0.559748i
$217$	0.692653	−	3.92823i	0.0470203	−	0.266666i
$218$	6.83908	−	8.15050i	0.463201	−	0.552021i
$219$	−21.8829	+	7.96474i	−1.47871	+	0.538207i
$220$	−0.686223	+	4.82446i	−0.0462652	+	0.325265i
$221$	6.03042			0.405650
$222$	9.52975	−	15.2947i	0.639595	−	1.02651i
$223$			23.1615i			1.55101i	0.631342	+	0.775504i	$0.282504\pi$
$223$			23.1615i			1.55101i	−0.631342	+	0.775504i	$0.717496\pi$
$224$	0.355652	−	0.977146i	0.0237630	−	0.0652883i
$225$	−20.8442	+	19.9954i	−1.38961	+	1.33303i
$226$	−6.54128	−	5.48878i	−0.435119	−	0.365108i
$227$	0.942780	−	5.34677i	0.0625745	−	0.354878i	−0.937404	−	0.348245i	$-0.886778\pi$
$227$	0.942780	−	5.34677i	0.0625745	−	0.354878i	0.999978	−	0.00663250i	$-0.00211121\pi$
$228$	−13.8169			−0.915046
$229$	3.76717	−	21.3647i	0.248942	−	1.41182i	−0.562216	−	0.826990i	$-0.690051\pi$
$229$	3.76717	−	21.3647i	0.248942	−	1.41182i	0.811158	−	0.584827i	$-0.198838\pi$
$230$	−6.97080	+	6.25556i	−0.459641	+	0.412479i
$231$	−5.14293	+	4.31543i	−0.338380	+	0.283934i
$232$	6.14779	+	3.54943i	0.403622	+	0.233031i
$233$	−9.50761	+	5.48922i	−0.622864	+	0.359611i	−0.777983	−	0.628285i	$-0.783757\pi$
$233$	−9.50761	+	5.48922i	−0.622864	+	0.359611i	0.155119	+	0.987896i	$0.450424\pi$
$234$	−26.4184	−	9.61552i	−1.72703	−	0.628586i
$235$	−24.8511	−	13.2667i	−1.62111	−	0.865423i
$236$	−4.80223	−	2.77257i	−0.312599	−	0.180479i
$237$	−8.18869	−	46.4404i	−0.531913	−	3.01663i
$238$	−1.26894	+	0.223749i	−0.0822533	+	0.0145035i
$239$	−14.9013	−	17.7587i	−0.963885	−	1.14871i	−0.988834	−	0.149024i	$-0.952387\pi$
$239$	−14.9013	−	17.7587i	−0.963885	−	1.14871i	0.0249490	−	0.999689i	$-0.492058\pi$
$240$	5.62374	−	3.50110i	0.363011	−	0.225995i
$241$	4.51890	+	12.4156i	0.291088	+	0.799757i	0.995908	+	0.0903713i	$0.0288054\pi$
$241$	4.51890	+	12.4156i	0.291088	+	0.799757i	−0.704820	+	0.709386i	$0.748972\pi$
$242$	4.78834	−	4.01789i	0.307806	−	0.258280i
$243$	−3.76124	+	0.663208i	−0.241284	+	0.0425448i
$244$	2.74564	−	0.484130i	0.175771	−	0.0309933i
$245$	12.5800	+	4.11066i	0.803709	+	0.262620i
$246$	12.7995	−	15.2538i	0.816063	−	0.972546i
$247$	−7.76290	+	21.3284i	−0.493942	+	1.35709i
$248$	−3.32202	+	1.91797i	−0.210948	+	0.121791i
$249$	4.65820	−	8.06824i	0.295201	−	0.511304i
$250$	−10.8346	−	2.75890i	−0.685240	−	0.174488i
$251$	9.92843	−	5.73218i	0.626677	−	0.361812i	−0.152787	−	0.988259i	$-0.548825\pi$
$251$	9.92843	−	5.73218i	0.626677	−	0.361812i	0.779464	+	0.626447i	$0.215491\pi$
$252$	5.91583	+	1.04312i	0.372662	+	0.0657104i
$253$	−9.12826			−0.573888
$254$	−7.84470	−	1.38323i	−0.492220	−	0.0867917i
$255$	−7.24136	−	3.86577i	−0.453472	−	0.242084i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−10.9493	−	3.98521i	−0.682998	−	0.248591i	−0.0228635	−	0.999739i	$-0.507278\pi$
$257$	−10.9493	−	3.98521i	−0.682998	−	0.248591i	−0.660134	+	0.751148i	$0.729501\pi$
$258$		−	8.13423i		−	0.506415i
$259$	4.70600	+	4.22632i	0.292417	+	0.262611i
$260$	−2.24482	−	10.6481i	−0.139218	−	0.660369i
$261$	−14.0259	+	38.5358i	−0.868180	+	2.38531i
$262$	−0.509659	−	1.40028i	−0.0314868	−	0.0865094i
$263$	−0.165448	+	0.197173i	−0.0102019	+	0.0121582i	−0.771121	−	0.636688i	$-0.780304\pi$
$263$	−0.165448	+	0.197173i	−0.0102019	+	0.0121582i	0.760919	+	0.648846i	$0.224748\pi$
$264$	6.35820	+	1.12112i	0.391320	+	0.0690003i
$265$	−21.4798	+	4.52831i	−1.31949	+	0.278172i
$266$	0.842143	−	4.77603i	0.0516351	−	0.292837i
$267$	−18.1961	−	31.5166i	−1.11358	−	1.92878i
$268$	5.71148	+	6.80668i	0.348884	+	0.415784i
$269$	9.34933	−	16.1935i	0.570039	−	0.987336i	−0.426523	−	0.904477i	$-0.640262\pi$
$269$	9.34933	−	16.1935i	0.570039	−	0.987336i	0.996561	−	0.0828590i	$-0.0264051\pi$
$270$	12.2860	+	13.6908i	0.747704	+	0.833193i
$271$	20.6928	+	7.53158i	1.25700	+	0.457511i	0.882761	−	0.469822i	$-0.155682\pi$
$271$	20.6928	+	7.53158i	1.25700	+	0.457511i	0.374239	+	0.927332i	$0.377904\pi$
$272$	0.949228	+	0.796496i	0.0575554	+	0.0482947i
$273$	7.49625	−	12.9839i	0.453694	−	0.785820i
$274$	−8.53221	+	1.50446i	−0.515450	+	0.0908877i
$275$	−6.06309	−	9.05376i	−0.365618	−	0.545962i
$276$	7.97647	+	9.50599i	0.480127	+	0.572193i
$277$	−0.636745	+	0.231756i	−0.0382583	+	0.0139249i	−0.361078	−	0.932535i	$-0.617591\pi$
$277$	−0.636745	+	0.231756i	−0.0382583	+	0.0139249i	0.322820	+	0.946460i	$0.395369\pi$
$278$	−10.6465	+	3.87502i	−0.638537	+	0.232408i
$279$	−14.2439	−	16.9752i	−0.852760	−	1.01628i
$280$	0.867443	+	2.15733i	0.0518397	+	0.128925i
$281$	−23.9729	+	4.22707i	−1.43010	+	0.252166i	−0.834454	−	0.551078i	$-0.814217\pi$
$281$	−23.9729	+	4.22707i	−1.43010	+	0.252166i	−0.595650	+	0.803244i	$0.703106\pi$
$282$	−18.6617	+	32.3230i	−1.11129	+	1.92480i
$283$	9.98739	+	8.38041i	0.593688	+	0.498164i	0.889410	−	0.457110i	$-0.151116\pi$
$283$	9.98739	+	8.38041i	0.593688	+	0.498164i	−0.295721	+	0.955274i	$0.595560\pi$
$284$	6.94924	+	2.52932i	0.412362	+	0.150087i
$285$	22.9942	−	20.6349i	1.36206	−	1.22231i
$286$	5.30291	−	9.18491i	0.313568	−	0.543115i
$287$	4.49258	+	5.35405i	0.265189	+	0.316040i
$288$	−2.88842	−	5.00289i	−0.170202	−	0.294798i
$289$	−2.68539	+	15.2296i	−0.157964	+	0.895860i
$290$	−15.5321	+	3.27445i	−0.912077	+	0.192282i
$291$	30.0512	+	5.29884i	1.76163	+	0.310623i
$292$	−5.05264	+	6.02150i	−0.295683	+	0.352382i
$293$	−5.56418	−	15.2874i	−0.325063	−	0.893102i	−0.989341	−	0.145617i	$-0.953483\pi$
$293$	−5.56418	−	15.2874i	−0.325063	−	0.893102i	0.664278	−	0.747485i	$-0.268739\pi$
$294$	5.99718	−	16.4771i	0.349762	−	0.960964i
$295$	12.1326	−	2.55777i	0.706389	−	0.148919i
$296$	0.204440	−	6.07933i	0.0118828	−	0.353354i
$297$			17.9280i			1.04029i
$298$	−6.15429	−	2.23998i	−0.356508	−	0.129758i
$299$	19.1554	−	6.97200i	1.10779	−	0.403201i
$300$	−4.13035	+	14.2254i	−0.238466	+	0.821302i
$301$	2.81172	+	0.495783i	0.162065	+	0.0285765i
$302$	8.62142			0.496107
$303$	53.5525	+	9.44275i	3.07651	+	0.542472i
$304$	−4.03898	+	2.33191i	−0.231652	+	0.133744i
$305$	−3.84629	+	4.90618i	−0.220238	+	0.280927i
$306$	−3.57912	+	6.19922i	−0.204605	+	0.354386i
$307$	−5.90124	+	3.40708i	−0.336801	+	0.194452i	−0.658857	−	0.752268i	$-0.728960\pi$
$307$	−5.90124	+	3.40708i	−0.336801	+	0.194452i	0.322055	+	0.946721i	$0.395626\pi$
$308$	−0.775066	+	2.12948i	−0.0441635	+	0.121338i
$309$	14.6581	−	17.4688i	0.833870	−	0.993768i
$310$	2.66414	−	8.15318i	0.151313	−	0.463070i
$311$	10.5243	−	1.85571i	0.596776	−	0.105228i	0.132903	−	0.991129i	$-0.457570\pi$
$311$	10.5243	−	1.85571i	0.596776	−	0.105228i	0.463874	+	0.885901i	$0.346459\pi$
$312$	−14.1988	+	2.50363i	−0.803849	+	0.141740i
$313$	−8.27157	+	6.94067i	−0.467537	+	0.392310i	−0.845895	−	0.533349i	$-0.820933\pi$
$313$	−8.27157	+	6.94067i	−0.467537	+	0.392310i	0.378358	+	0.925659i	$0.376489\pi$
$314$	7.13682	+	19.6082i	0.402754	+	1.10656i
$315$	−11.4030	+	7.09905i	−0.642488	+	0.399986i
$316$	−10.2316	−	12.1935i	−0.575572	−	0.685939i
$317$	−19.3568	+	3.41313i	−1.08719	+	0.191700i	−0.688391	−	0.725339i	$-0.741683\pi$
$317$	−19.3568	+	3.41313i	−1.08719	+	0.191700i	−0.398796	+	0.917040i	$0.630572\pi$
$318$	5.05040	+	28.6423i	0.283213	+	1.60618i
$319$	−13.3978	−	7.73520i	−0.750131	−	0.433088i
$320$	1.05305	−	1.97258i	0.0588675	−	0.110271i
$321$	17.2740	+	6.28723i	0.964142	+	0.350919i
$322$	−3.77206	+	2.17780i	−0.210209	+	0.121364i
$323$	5.00482	+	2.88953i	0.278476	+	0.160778i
$324$	5.39398	−	4.52609i	0.299666	−	0.251449i
$325$	19.6383	+	14.3682i	1.08934	+	0.797004i
$326$	−1.12186	+	6.36237i	−0.0621339	+	0.352379i
$327$	31.5210			1.74311
$328$	1.16715	−	6.61921i	0.0644448	−	0.365485i
$329$	−10.0355	−	8.42079i	−0.553275	−	0.464253i
$330$	−12.2557	+	7.62989i	−0.674655	+	0.420012i
$331$	1.90329	−	5.22924i	0.104614	−	0.287425i	−0.876331	−	0.481709i	$-0.840016\pi$
$331$	1.90329	−	5.22924i	0.104614	−	0.287425i	0.980945	+	0.194284i	$0.0622384\pi$
$332$		−	3.14470i		−	0.172588i
$333$	34.7908	−	4.93533i	1.90653	−	0.270454i
$334$	14.4630			0.791379
$335$	−19.6706	−	2.79791i	−1.07472	−	0.152866i
$336$	2.89487	−	1.05365i	0.157928	−	0.0574811i
$337$	16.1526	−	19.2500i	0.879891	−	1.04861i	−0.118559	−	0.992947i	$-0.537827\pi$
$337$	16.1526	−	19.2500i	0.879891	−	1.04861i	0.998449	−	0.0556659i	$-0.0177282\pi$
$338$	−1.85532	+	10.5221i	−0.100916	+	0.572325i
$339$		−	25.2975i		−	1.37397i
$340$	−2.76924	+	0.0920903i	−0.150183	+	0.00499430i
$341$	7.23961	−	4.17979i	0.392047	−	0.226348i
$342$	−17.3181	−	20.6389i	−0.936453	−	1.11602i
$343$	11.6338	+	6.71680i	0.628168	+	0.362673i
$344$	−1.37283	−	2.37782i	−0.0740182	−	0.128203i
$345$	−27.4713	−	3.90747i	−1.47900	−	0.210371i
$346$	8.96058	−	10.6788i	0.481724	−	0.574096i
$347$	9.20588	−	15.9450i	0.494197	−	0.855975i	−0.505780	−	0.862662i	$-0.668795\pi$
$347$	9.20588	−	15.9450i	0.494197	−	0.855975i	0.999978	+	0.00668732i	$0.00212866\pi$
$348$	3.65197	+	20.7114i	0.195766	+	1.11025i
$349$	0.779178	+	4.41894i	0.0417085	+	0.236540i	0.998534	−	0.0541212i	$-0.0172357\pi$
$349$	0.779178	+	4.41894i	0.0417085	+	0.236540i	−0.956826	+	0.290662i	$0.906125\pi$
$350$	−4.66548	−	2.29476i	−0.249380	−	0.122660i
$351$	−13.6931	−	37.6215i	−0.730884	−	2.00809i
$352$	2.04785	−	0.745358i	0.109151	−	0.0397277i
$353$	−13.8187	+	11.5953i	−0.735495	+	0.617153i	−0.931624	−	0.363425i	$-0.881607\pi$
$353$	−13.8187	+	11.5953i	−0.735495	+	0.617153i	0.196129	+	0.980578i	$0.437163\pi$
$354$	−2.85267	−	16.1783i	−0.151618	−	0.859867i
$355$	−15.3424	+	6.16906i	−0.814291	+	0.327420i
$356$	−10.6382	−	6.14199i	−0.563826	−	0.325525i
$357$	−2.92424	−	2.45373i	−0.154767	−	0.129865i
$358$	−1.43456	+	3.94142i	−0.0758187	+	0.208310i
$359$	5.17902	+	8.97032i	0.273338	+	0.473435i	0.969714	−	0.244241i	$-0.0785389\pi$
$359$	5.17902	+	8.97032i	0.273338	+	0.473435i	−0.696376	+	0.717677i	$0.745206\pi$
$360$	12.2785	+	4.01214i	0.647135	+	0.211458i
$361$	−2.10753	+	1.76843i	−0.110923	+	0.0930753i
$362$	−11.8896	−	20.5934i	−0.624904	−	1.08237i
$363$	18.2369	+	3.21566i	0.957190	+	0.168778i
$364$		−	5.06063i		−	0.265249i
$365$	−0.584182	−	17.5669i	−0.0305775	−	0.919495i
$366$	6.32725	+	5.30919i	0.330731	+	0.277516i
$367$	8.07354	+	22.1819i	0.421435	+	1.15788i	0.950885	+	0.309543i	$0.100176\pi$
$367$	8.07354	+	22.1819i	0.421435	+	1.15788i	−0.529450	+	0.848341i	$0.677602\pi$
$368$	3.93605	+	1.43260i	0.205181	+	0.0746796i
$369$	38.8280			2.02131
$370$	8.73896	+	10.4226i	0.454317	+	0.541845i
$371$	−10.2085			−0.529997
$372$	−10.6789	−	3.88680i	−0.553675	−	0.201521i
$373$	1.85733	+	5.10298i	0.0961690	+	0.264222i	0.978444	−	0.206512i	$-0.0662113\pi$
$373$	1.85733	+	5.10298i	0.0961690	+	0.264222i	−0.882275	+	0.470734i	$0.843989\pi$
$374$	−2.06863	−	1.73579i	−0.106967	−	0.0897556i
$375$	−14.3712	−	29.8425i	−0.742124	−	1.54106i
$376$			12.5983i			0.649707i
$377$	34.0229	+	5.99915i	1.75227	+	0.308972i
$378$	4.27724	+	7.40839i	0.219997	+	0.381047i
$379$	−10.1044	+	8.47863i	−0.519030	+	0.435518i	−0.864294	−	0.502988i	$-0.832234\pi$
$379$	−10.1044	+	8.47863i	−0.519030	+	0.435518i	0.345263	+	0.938506i	$0.387790\pi$
$380$	3.23912	−	9.91282i	0.166163	−	0.508517i
$381$	−11.7995	−	20.4374i	−0.604507	−	1.04704i
$382$	−8.02999	+	22.0622i	−0.410850	+	1.12880i
$383$	−19.4060	−	16.2835i	−0.991599	−	0.832050i	−0.00580066	−	0.999983i	$-0.501846\pi$
$383$	−19.4060	−	16.2835i	−0.991599	−	0.832050i	−0.985798	+	0.167933i	$0.946291\pi$
$384$	−2.56566	−	1.48129i	−0.130928	−	0.0755916i
$385$	−1.89040	−	4.70142i	−0.0963439	−	0.239607i
$386$	−1.96066	−	11.1194i	−0.0997949	−	0.565965i
$387$	12.1504	−	10.1954i	0.617641	−	0.518262i
$388$	9.67892	−	3.52284i	0.491373	−	0.178845i
$389$	−10.9359	−	30.0462i	−0.554473	−	1.52340i	−0.827540	−	0.561407i	$-0.810260\pi$
$389$	−10.9359	−	30.0462i	−0.554473	−	1.52340i	0.273067	−	0.961995i	$-0.411962\pi$
$390$	19.8907	−	25.3718i	1.00721	−	1.28475i
$391$	−0.901283	−	5.11143i	−0.0455798	−	0.258496i
$392$	−1.02777	−	5.82878i	−0.0519103	−	0.294398i
$393$	2.20733	−	3.82321i	0.111345	−	0.192855i
$394$	−14.4164	+	17.1808i	−0.726286	+	0.865554i
$395$	35.2380	+	5.01219i	1.77301	+	0.252191i
$396$	6.29468	+	10.9027i	0.316319	+	0.547881i
$397$	19.3984	+	11.1997i	0.973580	+	0.562097i	0.900326	−	0.435217i	$-0.143328\pi$
$397$	19.3984	+	11.1997i	0.973580	+	0.562097i	0.0732541	+	0.997313i	$0.476662\pi$
$398$	2.42793	+	2.89349i	0.121701	+	0.145038i
$399$	12.4427	−	7.18380i	0.622915	−	0.359640i
$400$	1.19346	+	4.85548i	0.0596728	+	0.242774i
$401$		−	13.1395i		−	0.656155i	−0.944651	−	0.328077i	$-0.893599\pi$
$401$		−	13.1395i		−	0.656155i	0.944651	−	0.328077i	$-0.106401\pi$
$402$	−4.57110	+	25.9240i	−0.227986	+	1.29297i
$403$	−11.9997	+	14.3007i	−0.597747	+	0.712367i
$404$	17.2483	−	6.27785i	0.858133	−	0.312335i
$405$	−2.21721	+	15.5880i	−0.110174	+	0.774575i
$406$	−7.38180			−0.366352
$407$	−0.445532	+	13.2486i	−0.0220842	+	0.656707i
$408$			3.67101i			0.181742i
$409$	4.63814	−	12.7432i	0.229341	−	0.630110i	−0.770633	−	0.637279i	$-0.780060\pi$
$409$	4.63814	−	12.7432i	0.229341	−	0.630110i	0.999974	+	0.00716921i	$0.00228205\pi$
$410$	7.94311	+	12.7588i	0.392282	+	0.630114i
$411$	−19.6622	−	16.4986i	−0.969867	−	0.813815i
$412$	1.33663	−	7.58041i	0.0658511	−	0.373460i
$413$	5.76615			0.283734
$414$	−4.20179	+	23.8296i	−0.206507	+	1.17116i
$415$	4.69646	+	5.23344i	0.230540	+	0.256899i
$416$	−3.72808	+	3.12823i	−0.182784	+	0.153374i
$417$	−29.0685	−	16.7827i	−1.42349	−	0.821852i
$418$	8.80208	−	5.08189i	0.430524	−	0.248563i
$419$	16.8943	+	6.14901i	0.825339	+	0.300399i	0.719944	−	0.694032i	$-0.244167\pi$
$419$	16.8943	+	6.14901i	0.825339	+	0.300399i	0.105394	+	0.994430i	$0.466389\pi$
$420$	−3.24410	+	6.07684i	−0.158296	+	0.296519i
$421$	−7.37400	−	4.25738i	−0.359387	−	0.207492i	0.309425	−	0.950924i	$-0.399863\pi$
$421$	−7.37400	−	4.25738i	−0.359387	−	0.207492i	−0.668812	+	0.743432i	$0.733197\pi$
$422$	1.46123	+	8.28705i	0.0711316	+	0.403407i
$423$	−71.6726	+	12.6378i	−3.48484	+	0.614471i
$424$	6.31036	+	7.52040i	0.306458	+	0.365223i
$425$	4.47107	−	4.28900i	0.216879	−	0.208047i
$426$	7.49329	+	20.5876i	0.363051	+	0.997474i
$427$	−2.22085	+	1.86352i	−0.107475	+	0.0901819i
$428$	6.11069	−	1.07748i	0.295371	−	0.0520819i
$429$	30.9432	−	5.45612i	1.49395	−	0.263424i
$430$	5.83584	+	1.90692i	0.281429	+	0.0919599i
$431$	−17.5896	+	20.9624i	−0.847259	+	1.00972i	0.152511	+	0.988302i	$0.451264\pi$
$431$	−17.5896	+	20.9624i	−0.847259	+	1.00972i	−0.999771	+	0.0214225i	$0.993180\pi$
$432$	2.81366	−	7.73046i	0.135372	−	0.371932i
$433$	32.2086	−	18.5956i	1.54785	−	0.893649i	0.549540	−	0.835467i	$-0.314803\pi$
$433$	32.2086	−	18.5956i	1.54785	−	0.893649i	0.998306	−	0.0581819i	$-0.0185303\pi$
$434$	1.99441	−	3.45443i	0.0957349	−	0.165818i
$435$	−37.0091	−	29.0140i	−1.77445	−	1.39112i
$436$	9.21427	−	5.31986i	0.441283	−	0.254775i
$437$	19.2383	+	3.39224i	0.920294	+	0.162273i
$438$	−23.2873			−1.11271
$439$	26.5940	+	4.68923i	1.26926	+	0.223805i	0.767414	−	0.641152i	$-0.221543\pi$
$439$	26.5940	+	4.68923i	1.26926	+	0.223805i	0.501847	+	0.864957i	$0.332654\pi$
$440$	−2.29490	+	4.29881i	−0.109405	+	0.204938i
$441$	32.1294	−	11.6941i	1.52997	−	0.556863i
$442$	5.66674	+	2.06252i	0.269539	+	0.0981043i
$443$		−	38.8839i		−	1.84743i	−0.383078	−	0.923716i	$-0.625136\pi$
$443$		−	38.8839i		−	1.84743i	0.383078	−	0.923716i	$-0.374864\pi$
$444$	14.1861	−	11.1129i	0.673243	−	0.527396i
$445$	26.8771	−	5.66616i	1.27409	−	0.268602i
$446$	−7.92170	+	21.7647i	−0.375103	+	1.03059i
$447$	−6.63609	−	18.2325i	−0.313877	−	0.862369i
$448$	0.668408	−	0.796577i	0.0315793	−	0.0376347i
$449$	5.21545	+	0.919625i	0.246132	+	0.0433998i	0.295353	−	0.955388i	$-0.404563\pi$
$449$	5.21545	+	0.919625i	0.246132	+	0.0433998i	−0.0492208	+	0.998788i	$0.515674\pi$
$450$	−26.4260	+	11.6604i	−1.24573	+	0.549675i
$451$	−2.54354	+	14.4251i	−0.119771	+	0.679253i
$452$	−4.26952	−	7.39502i	−0.200821	−	0.347832i
$453$	16.4178	+	19.5660i	0.771377	+	0.919291i
$454$	2.71463	−	4.70187i	0.127404	−	0.220670i
$455$	7.55782	+	8.42196i	0.354316	+	0.394827i
$456$	−12.9836	−	4.72566i	−0.608015	−	0.221299i
$457$	−1.73260	−	1.45383i	−0.0810477	−	0.0680071i	0.601364	−	0.798975i	$-0.294624\pi$
$457$	−1.73260	−	1.45383i	−0.0810477	−	0.0680071i	−0.682411	+	0.730968i	$0.739069\pi$
$458$	10.8471	−	18.7878i	0.506853	−	0.877895i
$459$	−10.0389	+	1.77013i	−0.468577	+	0.0826228i
$460$	−8.68994	+	3.49415i	−0.405170	+	0.162916i
$461$	−9.26256	−	11.0387i	−0.431400	−	0.514123i	0.505925	−	0.862577i	$-0.331151\pi$
$461$	−9.26256	−	11.0387i	−0.431400	−	0.514123i	−0.937326	+	0.348454i	$0.886707\pi$
$462$	−6.30873	+	2.29619i	−0.293509	+	0.106828i
$463$	−24.3007	+	8.84473i	−1.12935	+	0.411049i	−0.838056	−	0.545584i	$-0.816308\pi$
$463$	−24.3007	+	8.84473i	−1.12935	+	0.411049i	−0.291293	+	0.956634i	$0.594086\pi$
$464$	4.56306	+	5.43804i	0.211835	+	0.252455i
$465$	23.5767	−	9.47999i	1.09334	−	0.439624i
$466$	−10.8117	+	1.90639i	−0.500840	+	0.0883117i
$467$	5.22034	−	9.04190i	0.241569	−	0.418409i	−0.719593	−	0.694396i	$-0.755671\pi$
$467$	5.22034	−	9.04190i	0.241569	−	0.418409i	0.961161	+	0.275987i	$0.0890048\pi$
$468$	−21.5365	−	18.0713i	−0.995525	−	0.835345i
$469$	−8.68242	−	3.16014i	−0.400917	−	0.145922i
$470$	−18.8150	−	20.9662i	−0.867869	−	0.967098i
$471$	−30.9095	+	53.5368i	−1.42423	+	2.46685i
$472$	−3.56435	−	4.24782i	−0.164062	−	0.195522i
$473$	2.99179	+	5.18193i	0.137563	+	0.238265i
$474$	8.18869	−	46.4404i	0.376119	−	2.13308i
$475$	9.41377	+	21.3345i	0.431933	+	0.978894i
$476$	−1.26894	−	0.223749i	−0.0581618	−	0.0102555i
$477$	−36.4539	+	43.4441i	−1.66911	+	1.98917i
$478$	−7.92881	−	21.7842i	−0.362655	−	0.996388i
$479$	−13.4231	+	36.8797i	−0.613318	+	1.68508i	0.109454	+	0.993992i	$0.465090\pi$
$479$	−13.4231	+	36.8797i	−0.613318	+	1.68508i	−0.722772	+	0.691087i	$0.757132\pi$
$480$	6.48204	−	1.36653i	0.295863	−	0.0623732i
$481$	−9.18408	−	28.1420i	−0.418758	−	1.28317i
$482$			13.2124i			0.601807i
$483$	−12.1256	−	4.41336i	−0.551734	−	0.200815i
$484$	5.87377	−	2.13788i	0.266989	−	0.0971762i
$485$	−10.8466	+	20.3178i	−0.492517	+	0.922583i
$486$	−3.76124	−	0.663208i	−0.170613	−	0.0300837i
$487$	8.96191			0.406103			0.203051	−	0.979168i	$-0.434914\pi$
$487$	8.96191			0.406103			0.203051	+	0.979168i	$0.434914\pi$
$488$	2.74564	+	0.484130i	0.124289	+	0.0219155i
$489$	−16.5755	+	9.56987i	−0.749570	+	0.432765i
$490$	10.4154	+	8.16538i	0.470522	+	0.368874i
$491$	−19.8119	+	34.3153i	−0.894100	+	1.54863i	−0.0591861	+	0.998247i	$0.518851\pi$
$491$	−19.8119	+	34.3153i	−0.894100	+	1.54863i	−0.834914	+	0.550380i	$0.814483\pi$
$492$	17.2447	−	9.95621i	0.777449	−	0.448861i
$493$	3.00854	−	8.26591i	0.135498	−	0.372278i
$494$	−14.5895	+	17.3871i	−0.656412	+	0.782281i
$495$	−26.7584	−	8.74357i	−1.20270	−	0.392994i
$496$	−3.77766	+	0.666103i	−0.169622	+	0.0299089i
$497$	−7.57316	+	1.33535i	−0.339702	+	0.0598987i
$498$	7.13677	−	5.98846i	0.319806	−	0.268349i
$499$	−1.84436	−	5.06733i	−0.0825648	−	0.226845i	0.891540	−	0.452942i	$-0.149626\pi$
$499$	−1.84436	−	5.06733i	−0.0825648	−	0.226845i	−0.974105	+	0.226097i	$0.927403\pi$
$500$	−9.23759	−	6.29816i	−0.413118	−	0.281662i
$501$	27.5419	+	32.8232i	1.23048	+	1.46643i
$502$	11.2902	−	1.99077i	0.503906	−	0.0888523i
$503$	0.834435	+	4.73232i	0.0372056	+	0.211004i	0.997743	−	0.0671471i	$-0.0213897\pi$
$503$	0.834435	+	4.73232i	0.0372056	+	0.211004i	−0.960537	+	0.278151i	$0.910279\pi$
$504$	5.20229	+	3.00354i	0.231728	+	0.133788i
$505$	−19.3290	+	36.2071i	−0.860131	+	1.61120i
$506$	−8.57775	−	3.12205i	−0.381328	−	0.138792i
$507$	−27.4125	+	15.8266i	−1.21743	+	0.702885i
$508$	−6.89851	−	3.98286i	−0.306072	−	0.176711i
$509$	−11.0720	+	9.29049i	−0.490757	+	0.411794i	−0.854297	−	0.519785i	$-0.826012\pi$
$509$	−11.0720	+	9.29049i	−0.490757	+	0.411794i	0.363541	+	0.931578i	$0.381568\pi$
$510$	−5.48248	−	6.10933i	−0.242768	−	0.270526i
$511$	1.41937	−	8.04963i	0.0627891	−	0.356095i
$512$	−1.00000			−0.0441942
$513$	6.66241	−	37.7844i	0.294153	−	1.66822i
$514$	−8.92594	−	7.48975i	−0.393706	−	0.330359i
$515$	9.09656	+	14.6116i	0.400842	+	0.643864i
$516$	2.78207	−	7.64368i	0.122474	−	0.336494i
$517$		−	27.4552i		−	1.20748i
$518$	2.97671	+	5.58099i	0.130789	+	0.245215i
$519$	41.2988			1.81282
$520$	1.53244	−	10.7737i	0.0672019	−	0.472460i
$521$	0.111350	−	0.0405279i	0.00487831	−	0.00177556i	−0.339580	−	0.940577i	$-0.610285\pi$
$521$	0.111350	−	0.0405279i	0.00487831	−	0.00177556i	0.344458	+	0.938802i	$0.388063\pi$
$522$	−26.3600	+	31.4147i	−1.15375	+	1.37498i
$523$	−6.46190	+	36.6473i	−0.282559	+	1.60247i	0.431317	+	0.902201i	$0.358049\pi$
$523$	−6.46190	+	36.6473i	−0.282559	+	1.60247i	−0.713876	+	0.700272i	$0.753062\pi$
$524$		−	1.49014i		−	0.0650972i
$525$	−3.67662	−	14.9580i	−0.160461	−	0.652823i
$526$	−0.222907	+	0.128695i	−0.00971920	+	0.00561138i
$527$	3.05531	+	3.64118i	0.133091	+	0.158612i
$528$	5.59130	+	3.22814i	0.243330	+	0.140487i
$529$	2.72759	+	4.72433i	0.118591	+	0.205406i
$530$	−21.7331	−	3.09128i	−0.944027	−	0.134277i
$531$	20.5907	−	24.5390i	0.893558	−	1.06490i
$532$	2.42485	−	4.19997i	0.105131	−	0.182092i
$533$	−5.68010	−	32.2135i	−0.246033	−	1.39532i
$534$	−6.31944	−	35.8393i	−0.273469	−	1.55092i
$535$	−8.56030	+	10.9192i	−0.370094	+	0.472077i
$536$	3.03902	+	8.34963i	0.131265	+	0.360649i
$537$	−11.6767	+	4.24998i	−0.503888	+	0.183400i
$538$	14.3240	−	12.0193i	0.617552	−	0.518187i
$539$	2.23980	+	12.7025i	0.0964751	+	0.547138i
$540$	6.86257	+	17.0672i	0.295318	+	0.734454i
$541$	−15.3004	−	8.83367i	−0.657814	−	0.379789i	0.133630	−	0.991031i	$-0.457337\pi$
$541$	−15.3004	−	8.83367i	−0.657814	−	0.379789i	−0.791444	+	0.611242i	$0.790670\pi$
$542$	16.8690	+	14.1547i	0.724584	+	0.607998i
$543$	24.0945	−	66.1991i	1.03399	−	2.84088i
$544$	0.619564	+	1.07312i	0.0265636	+	0.0460095i
$545$	−7.38951	+	22.6145i	−0.316532	+	0.968697i
$546$	11.4849	−	9.63699i	0.491509	−	0.412425i
$547$	−1.84100	−	3.18871i	−0.0787157	−	0.136340i	0.823980	−	0.566618i	$-0.191749\pi$
$547$	−1.84100	−	3.18871i	−0.0787157	−	0.136340i	−0.902696	+	0.430279i	$0.858415\pi$
$548$	−8.53221	−	1.50446i	−0.364478	−	0.0642673i
$549$			16.1058i			0.687378i
$550$	−2.60088	−	10.5815i	−0.110902	−	0.451195i
$551$	25.3620	+	21.2813i	1.08046	+	0.906612i
$552$	4.24419	+	11.6608i	0.180645	+	0.496318i
$553$	15.5537	+	5.66110i	0.661413	+	0.240734i
$554$	−0.677610			−0.0287889
$555$	−7.01204	+	39.6806i	−0.297644	+	1.68435i
$556$	−11.3298			−0.480491
$557$	30.4917	+	11.0981i	1.29198	+	0.470241i	0.894375	−	0.447318i	$-0.147621\pi$
$557$	30.4917	+	11.0981i	1.29198	+	0.470241i	0.397601	+	0.917558i	$0.369843\pi$
$558$	−7.57902	−	20.8232i	−0.320846	−	0.881516i
$559$	−10.2361	−	8.58907i	−0.432939	−	0.363279i
$560$	0.0772807	+	2.32391i	0.00326571	+	0.0982030i
$561$		−	8.00016i		−	0.337767i
$562$	−23.9729	−	4.22707i	−1.01124	−	0.178308i
$563$	−3.17479	−	5.49889i	−0.133801	−	0.231751i	0.791338	−	0.611379i	$-0.209385\pi$
$563$	−3.17479	−	5.49889i	−0.133801	−	0.231751i	−0.925139	+	0.379629i	$0.876052\pi$
$564$	−28.5913	+	23.9910i	−1.20391	+	1.01020i
$565$	18.1495	+	5.93054i	0.763555	+	0.249500i
$566$	6.51880	+	11.2909i	0.274006	+	0.474592i
$567$	−2.50427	+	6.88042i	−0.105169	+	0.288951i
$568$	5.66507	+	4.75356i	0.237701	+	0.199455i
$569$	−1.24518	−	0.718906i	−0.0522007	−	0.0301381i	0.473672	−	0.880701i	$-0.342928\pi$
$569$	−1.24518	−	0.718906i	−0.0522007	−	0.0301381i	−0.525873	+	0.850563i	$0.676261\pi$
$570$	28.6651	−	11.5260i	1.20065	−	0.482770i
$571$	−6.75144	−	38.2893i	−0.282539	−	1.60236i	−0.713946	−	0.700201i	$-0.753094\pi$
$571$	−6.75144	−	38.2893i	−0.282539	−	1.60236i	0.431407	−	0.902157i	$-0.358017\pi$
$572$	8.12453	−	6.81729i	0.339704	−	0.285045i
$573$	−65.3609	+	23.7894i	−2.73049	+	0.993818i
$574$	2.39045	+	6.56772i	0.0997756	+	0.274131i
$575$	9.24353	−	18.7930i	0.385482	−	0.783723i
$576$	−1.00314	−	5.68907i	−0.0417974	−	0.237045i
$577$	6.83944	+	38.7884i	0.284730	+	1.61478i	0.706249	+	0.707963i	$0.250386\pi$
$577$	6.83944	+	38.7884i	0.284730	+	1.61478i	−0.421520	+	0.906819i	$0.638503\pi$
$578$	−7.73228	+	13.3927i	−0.321620	+	0.557063i
$579$	21.5015	−	25.6245i	0.893571	−	1.06492i
$580$	−15.7153	−	2.23532i	−0.652544	−	0.0928168i
$581$	1.63502	+	2.83194i	0.0678320	+	0.117488i
$582$	26.4266	+	15.2574i	1.09542	+	0.632439i
$583$	−13.7521	−	16.3891i	−0.569552	−	0.678766i
$584$	−6.80740	+	3.93026i	−0.281692	+	0.162635i
$585$	62.8299	−	2.08939i	2.59770	−	0.0863855i
$586$		−	16.2686i		−	0.672048i
$587$	−3.12951	+	17.7483i	−0.129169	+	0.732551i	0.849576	+	0.527467i	$0.176858\pi$
$587$	−3.12951	+	17.7483i	−0.129169	+	0.732551i	−0.978744	+	0.205085i	$0.934253\pi$
$588$	11.2710	−	13.4323i	0.464808	−	0.553937i
$589$	−16.8112	+	6.11878i	−0.692693	+	0.252120i
$590$	12.2757	+	1.74608i	0.505385	+	0.0718850i
$591$	−66.4443			−2.73315
$592$	2.27136	−	5.64278i	0.0933524	−	0.231917i
$593$			3.27681i			0.134562i	0.997734	+	0.0672811i	$0.0214324\pi$
$593$			3.27681i			0.134562i	−0.997734	+	0.0672811i	$0.978568\pi$
$594$	−6.13175	+	16.8469i	−0.251589	+	0.691235i
$595$	2.44594	−	1.52274i	0.100274	−	0.0624263i
$596$	−5.01702	−	4.20978i	−0.205505	−	0.172439i
$597$	−1.94316	+	11.0202i	−0.0795281	+	0.451026i
$598$	20.3848			0.833595
$599$	3.41713	−	19.3795i	0.139620	−	0.791824i	−0.831910	−	0.554910i	$-0.812753\pi$
$599$	3.41713	−	19.3795i	0.139620	−	0.791824i	0.971530	−	0.236915i	$-0.0761361\pi$
$600$	−8.74662	+	11.9548i	−0.357079	+	0.488053i
$601$	36.6049	−	30.7152i	1.49315	−	1.25290i	0.602567	−	0.798068i	$-0.294145\pi$
$601$	36.6049	−	30.7152i	1.49315	−	1.25290i	0.890579	−	0.454830i	$-0.150300\pi$
$602$	2.47259	+	1.42755i	0.100775	+	0.0581826i
$603$	−44.4531	+	25.6650i	−1.81027	+	1.04516i
$604$	8.10149	+	2.94870i	0.329645	+	0.119981i
$605$	−6.58236	+	12.3301i	−0.267611	+	0.501289i
$606$	47.0933	+	27.1893i	1.91303	+	1.10449i
$607$	−0.557052	−	3.15920i	−0.0226100	−	0.128228i	0.971414	−	0.237394i	$-0.0762932\pi$
$607$	−0.557052	−	3.15920i	−0.0226100	−	0.128228i	−0.994024	+	0.109166i	$0.965182\pi$
$608$	−4.59296	+	0.809863i	−0.186269	+	0.0328443i
$609$	−14.0572	−	16.7527i	−0.569626	−	0.678854i
$610$	−5.29234	+	3.29479i	−0.214281	+	0.133402i
$611$	20.9698	+	57.6140i	0.848347	+	2.33081i
$612$	−5.48353	+	4.60123i	−0.221659	+	0.185994i
$613$	2.09394	−	0.369219i	0.0845736	−	0.0149126i	−0.131201	−	0.991356i	$-0.541883\pi$
$613$	2.09394	−	0.369219i	0.0845736	−	0.0149126i	0.215775	+	0.976443i	$0.430772\pi$
$614$	−6.71064	+	1.18327i	−0.270819	+	0.0477528i
$615$	−13.8296	+	42.3233i	−0.557663	+	1.70664i
$616$	−1.45665	+	1.73597i	−0.0586900	+	0.0699441i
$617$	−11.0588	+	30.3837i	−0.445209	+	1.22320i	0.490814	+	0.871264i	$0.336699\pi$
$617$	−11.0588	+	30.3837i	−0.445209	+	1.22320i	−0.936023	+	0.351938i	$0.885523\pi$
$618$	19.7488	−	11.4020i	0.794414	−	0.458655i
$619$	−1.27227	+	2.20364i	−0.0511370	+	0.0885718i	−0.890461	−	0.455060i	$-0.849618\pi$
$619$	−1.27227	+	2.20364i	−0.0511370	+	0.0885718i	0.839324	+	0.543632i	$0.182951\pi$
$620$	5.29202	−	6.75030i	0.212533	−	0.271098i
$621$	−29.8418	+	17.2292i	−1.19751	+	0.691382i
$622$	10.5243	+	1.85571i	0.421984	+	0.0744072i
$623$	12.7736			0.511763
$624$	−14.1988	−	2.50363i	−0.568407	−	0.100225i
$625$	24.7793	−	3.31445i	0.991173	−	0.132578i
$626$	−10.1466	+	3.69305i	−0.405539	+	0.147604i
$627$	28.2950	+	10.2985i	1.12999	+	0.411284i
$628$			20.8667i			0.832670i
$629$	−7.46261	+	1.05862i	−0.297554	+	0.0422101i
$630$	−13.1434	+	2.77085i	−0.523644	+	0.110393i
$631$	7.18407	−	19.7381i	0.285993	−	0.785760i	−0.710624	−	0.703572i	$-0.751587\pi$
$631$	7.18407	−	19.7381i	0.285993	−	0.785760i	0.996617	−	0.0821875i	$-0.0261906\pi$
$632$	−5.44411	−	14.9576i	−0.216555	−	0.594980i
$633$	−16.0245	+	19.0973i	−0.636918	+	0.759049i
$634$	−19.3568	−	3.41313i	−0.768757	−	0.135553i
$635$	17.4288	−	3.67430i	0.691641	−	0.145810i
$636$	−5.05040	+	28.6423i	−0.200262	+	1.13574i
$637$	−14.4021	−	24.9452i	−0.570634	−	0.988366i
$638$	−9.94418	−	11.8510i	−0.393694	−	0.469186i
$639$	−21.3605	+	36.9975i	−0.845009	+	1.46360i
$640$	1.66421	−	1.49345i	0.0657837	−	0.0590340i
$641$	44.8926	+	16.3396i	1.77315	+	0.645374i	0.999937	+	0.0112264i	$0.00357354\pi$
$641$	44.8926	+	16.3396i	1.77315	+	0.645374i	0.773212	+	0.634147i	$0.218649\pi$
$642$	14.0819	+	11.8161i	0.555769	+	0.466345i
$643$	−3.81531	+	6.60831i	−0.150461	+	0.260606i	−0.931397	−	0.364005i	$-0.881409\pi$
$643$	−3.81531	+	6.60831i	−0.150461	+	0.260606i	0.780936	+	0.624611i	$0.214742\pi$
$644$	−4.28943	+	0.756342i	−0.169027	+	0.0298041i
$645$	6.78553	+	16.8756i	0.267180	+	0.664475i
$646$	3.71471	+	4.42702i	0.146153	+	0.174179i
$647$	−34.6407	+	12.6082i	−1.36187	+	0.495679i	−0.916631	−	0.399735i	$-0.869102\pi$
$647$	−34.6407	+	12.6082i	−1.36187	+	0.495679i	−0.445235	+	0.895414i	$0.646880\pi$
$648$	6.61670	−	2.40828i	0.259928	−	0.0946062i
$649$	7.76771	+	9.25720i	0.304909	+	0.363377i
$650$	13.5398	+	20.2184i	0.531074	+	0.793031i
$651$	11.6377	−	2.05203i	0.456116	−	0.0804255i
$652$	−3.23026	+	5.59497i	−0.126507	+	0.219116i
$653$	1.49310	+	1.25286i	0.0584295	+	0.0490282i	0.671535	−	0.740973i	$-0.265635\pi$
$653$	1.49310	+	1.25286i	0.0584295	+	0.0490282i	−0.613105	+	0.790001i	$0.710080\pi$
$654$	29.6200	+	10.7808i	1.15823	+	0.421563i
$655$	2.22546	+	2.47991i	0.0869559	+	0.0968981i
$656$	3.36066	−	5.82084i	0.131212	−	0.227266i
$657$	−29.1883	−	34.7852i	−1.13874	−	1.35710i
$658$	−6.55021	−	11.3453i	−0.255354	−	0.442286i
$659$	−1.01443	+	5.75312i	−0.0395166	+	0.224110i	−0.998170	−	0.0604655i	$-0.980741\pi$
$659$	−1.01443	+	5.75312i	−0.0395166	+	0.224110i	0.958654	+	0.284575i	$0.0918526\pi$
$660$	−14.1262	+	2.97805i	−0.549861	+	0.115920i
$661$	−31.5199	−	5.55781i	−1.22598	−	0.216174i	−0.477084	−	0.878858i	$-0.658306\pi$
$661$	−31.5199	−	5.55781i	−1.22598	−	0.216174i	−0.748899	+	0.662684i	$0.769417\pi$
$662$	3.57701	−	4.26292i	0.139024	−	0.165683i
$663$	6.11038	+	16.7881i	0.237307	+	0.651997i
$664$	1.07555	−	2.95505i	0.0417394	−	0.114678i
$665$	2.23700	+	10.6110i	0.0867469	+	0.411478i
$666$	34.3807	+	7.26147i	1.33222	+	0.281376i
$667$		−	29.7346i		−	1.15133i
$668$	13.5908	+	4.94663i	0.525842	+	0.191391i
$669$	−64.4795	+	23.4686i	−2.49292	+	0.907349i
$670$	−17.5273	−	9.35690i	−0.677140	−	0.361489i
$671$	−5.98352	−	1.05506i	−0.230991	−	0.0407300i
$672$	3.08065			0.118839
$673$	15.2333	+	2.68605i	0.587202	+	0.103540i	0.459352	−	0.888254i	$-0.348081\pi$
$673$	15.2333	+	2.68605i	0.587202	+	0.103540i	0.127849	+	0.991794i	$0.459193\pi$
$674$	21.7624	−	12.5645i	0.838256	−	0.483968i
$675$	−36.9098	−	18.1544i	−1.42066	−	0.698765i
$676$	−5.34219	+	9.25295i	−0.205469	+	0.355883i
$677$	−16.7515	+	9.67147i	−0.643812	+	0.371705i	−0.786081	−	0.618123i	$-0.787893\pi$
$677$	−16.7515	+	9.67147i	−0.643812	+	0.371705i	0.142270	+	0.989828i	$0.454560\pi$
$678$	8.65225	−	23.7719i	0.332288	−	0.912953i
$679$	−6.88466	+	8.20482i	−0.264209	+	0.314872i
$680$	−2.63374	−	0.860601i	−0.100999	−	0.0330025i
$681$	15.8402	−	2.79305i	0.606998	−	0.107030i
$682$	8.23259	−	1.45163i	0.315242	−	0.0555857i
$683$	−11.4191	+	9.58180i	−0.436942	+	0.366638i	−0.834563	−	0.550912i	$-0.814280\pi$
$683$	−11.4191	+	9.58180i	−0.436942	+	0.366638i	0.397622	+	0.917549i	$0.369836\pi$
$684$	−9.21475	−	25.3173i	−0.352335	−	0.968031i
$685$	16.4462	−	10.2387i	0.628378	−	0.391202i
$686$	8.63495	+	10.2907i	0.329684	+	0.392902i
$687$	63.2944	−	11.1605i	2.41483	−	0.425800i
$688$	−0.476780	−	2.70395i	−0.0181771	−	0.103087i
$689$	41.3760	+	23.8884i	1.57630	+	0.910077i
$690$	−24.4781	−	13.0676i	−0.931867	−	0.497473i
$691$	−33.6488	−	12.2472i	−1.28006	−	0.465904i	−0.389608	−	0.920981i	$-0.627390\pi$
$691$	−33.6488	−	12.2472i	−1.28006	−	0.465904i	−0.890452	+	0.455077i	$0.849612\pi$
$692$	12.0726	−	6.97009i	0.458930	−	0.264963i
$693$	−11.3373	−	6.54557i	−0.430667	−	0.248646i
$694$	14.1042	−	11.8348i	0.535389	−	0.449245i
$695$	18.8552	−	16.9205i	0.715218	−	0.641833i
$696$	−3.65197	+	20.7114i	−0.138428	+	0.785062i
$697$	−8.32859			−0.315468
$698$	−0.779178	+	4.41894i	−0.0294923	+	0.167259i
$699$	−24.9152	−	20.9063i	−0.942378	−	0.790749i
$700$	−3.59926	−	3.75206i	−0.136039	−	0.141814i
$701$	2.29765	−	6.31275i	0.0867812	−	0.238429i	−0.888709	−	0.458471i	$-0.848397\pi$
$701$	2.29765	−	6.31275i	0.0867812	−	0.238429i	0.975490	+	0.220042i	$0.0706194\pi$
$702$		−	40.0360i		−	1.51106i
$703$	5.86241	−	27.7566i	0.221105	−	1.04686i
$704$	2.17928			0.0821348
$705$	11.7526	−	82.6259i	0.442627	−	3.11187i
$706$	−16.9511	+	6.16971i	−0.637964	+	0.232200i
$707$	−12.2688	+	14.6213i	−0.461414	+	0.549892i
$708$	2.85267	−	16.1783i	0.107210	−	0.608018i
$709$		−	11.1645i		−	0.419293i	−0.977777	−	0.209646i	$-0.932769\pi$
$709$		−	11.1645i		−	0.419293i	0.977777	−	0.209646i	$-0.0672313\pi$
$710$	−16.5271	+	0.549603i	−0.620251	+	0.0206262i
$711$	79.6336	−	45.9765i	2.98649	−	1.72425i
$712$	−7.89599	−	9.41008i	−0.295915	−	0.352658i
$713$	13.9148	+	8.03370i	0.521113	+	0.300865i
$714$	−1.90866	−	3.30590i	−0.0714299	−	0.123720i
$715$	−3.33962	+	23.4790i	−0.124895	+	0.878066i
$716$	−2.69609	+	3.21307i	−0.100758	+	0.120078i
$717$	34.3396	−	59.4780i	1.28244	−	2.22125i
$718$	1.79865	+	10.2007i	0.0671252	+	0.380686i
$719$	−2.85513	−	16.1922i	−0.106478	−	0.603868i	−0.990620	−	0.136649i	$-0.956367\pi$
$719$	−2.85513	−	16.1922i	−0.106478	−	0.603868i	0.884141	−	0.467220i	$-0.154744\pi$
$720$	10.1658	+	7.96968i	0.378857	+	0.297012i
$721$	2.73758	+	7.52144i	0.101953	+	0.280113i
$722$	−2.58527	+	0.940963i	−0.0962139	+	0.0350190i
$723$	−29.9850	+	25.1604i	−1.11515	+	0.935725i
$724$	−4.12922	−	23.4180i	−0.153461	−	0.870321i
$725$	29.4920	−	19.7501i	1.09530	−	0.733500i
$726$	16.0373	+	9.25912i	0.595199	+	0.343638i
$727$	−5.81383	−	4.87838i	−0.215623	−	0.180929i	0.528578	−	0.848885i	$-0.322725\pi$
$727$	−5.81383	−	4.87838i	−0.215623	−	0.180929i	−0.744201	+	0.667955i	$0.767170\pi$
$728$	1.73084	−	4.75544i	0.0641491	−	0.176248i
$729$	−16.2194	−	28.0929i	−0.600720	−	1.04048i
$730$	5.45929	−	16.7073i	0.202057	−	0.618366i
$731$	−2.60626	+	2.18691i	−0.0963960	+	0.0808859i
$732$	4.12982	+	7.15305i	0.152642	+	0.264384i
$733$	−21.4817	−	3.78780i	−0.793443	−	0.139905i	−0.237787	−	0.971317i	$-0.576422\pi$
$733$	−21.4817	−	3.78780i	−0.793443	−	0.139905i	−0.555657	+	0.831412i	$0.687533\pi$
$734$			23.6054i			0.871293i
$735$	1.30314	+	39.1868i	0.0480672	+	1.44543i
$736$	3.20869	+	2.69241i	0.118274	+	0.0992437i
$737$	−6.62287	−	18.1962i	−0.243957	−	0.670265i
$738$	36.4864	+	13.2800i	1.34308	+	0.488842i
$739$	38.1034			1.40166			0.700828	−	0.713331i	$-0.252814\pi$
$739$	38.1034			1.40166			0.700828	+	0.713331i	$0.252814\pi$
$740$	4.64720	+	12.7829i	0.170835	+	0.469910i
$741$	−67.2421			−2.47020
$742$	−9.59283	−	3.49150i	−0.352164	−	0.128177i
$743$	−1.92370	−	5.28533i	−0.0705738	−	0.193900i	0.899391	−	0.437145i	$-0.144010\pi$
$743$	−1.92370	−	5.28533i	−0.0705738	−	0.193900i	−0.969965	+	0.243245i	$0.921788\pi$
$744$	−8.70551	−	7.30479i	−0.319160	−	0.267807i
$745$	14.6365	−	0.486731i	0.536239	−	0.0178325i
$746$			5.43048i			0.198824i
$747$	17.8904	+	3.15456i	0.654576	+	0.115419i
$748$	−1.35021	−	2.33862i	−0.0493684	−	0.0855086i
$749$	−4.94272	+	4.14744i	−0.180603	+	0.151544i
$750$	−3.29775	−	32.9580i	−0.120417	−	1.20346i
$751$	−21.9873	−	38.0831i	−0.802328	−	1.38967i	−0.918080	−	0.396395i	$-0.870261\pi$
$751$	−21.9873	−	38.0831i	−0.802328	−	1.38967i	0.115751	−	0.993278i	$-0.463072\pi$
$752$	−4.30887	+	11.8385i	−0.157128	+	0.431706i
$753$	26.0180	+	21.8317i	0.948147	+	0.795590i
$754$	29.9192	+	17.2739i	1.08959	+	0.629077i
$755$	−17.8863	+	7.19194i	−0.650950	+	0.261742i
$756$	1.48547	+	8.42451i	0.0540260	+	0.306397i
$757$	−12.6664	+	10.6284i	−0.460368	+	0.386294i	−0.843266	−	0.537496i	$-0.819370\pi$
$757$	−12.6664	+	10.6284i	−0.460368	+	0.386294i	0.382899	+	0.923790i	$0.374926\pi$
$758$	−12.3949	+	4.51139i	−0.450204	+	0.163861i
$759$	−9.24929	−	25.4122i	−0.335728	−	0.922405i
$760$	6.43416	−	8.20716i	0.233392	−	0.297705i
$761$	0.374025	+	2.12120i	0.0135584	+	0.0768935i	0.990836	−	0.135069i	$-0.0431256\pi$
$761$	0.374025	+	2.12120i	0.0135584	+	0.0768935i	−0.977278	+	0.211963i	$0.932015\pi$
$762$	−4.09793	−	23.2405i	−0.148452	−	0.841914i
$763$	−5.53190	+	9.58153i	−0.200268	+	0.346875i
$764$	−15.0914	+	17.9853i	−0.545989	+	0.650685i
$765$	2.25402	−	15.8468i	0.0814944	−	0.572943i
$766$	−12.6664	−	21.9388i	−0.457654	−	0.792680i
$767$	−23.3708	−	13.4932i	−0.843872	−	0.487209i
$768$	−1.90431	−	2.26946i	−0.0687157	−	0.0818922i
$769$	−12.4128	+	7.16654i	−0.447617	+	0.258432i	−0.706823	−	0.707390i	$-0.749872\pi$
$769$	−12.4128	+	7.16654i	−0.447617	+	0.258432i	0.259206	+	0.965822i	$0.416539\pi$
$770$	−0.168416	−	5.06445i	−0.00606931	−	0.182510i
$771$		−	34.5199i		−	1.24320i
$772$	1.96066	−	11.1194i	0.0705657	−	0.400198i
$773$	28.8965	−	34.4375i	1.03934	−	1.23863i	0.0688112	−	0.997630i	$-0.478079\pi$
$773$	28.8965	−	34.4375i	1.03934	−	1.23863i	0.970525	−	0.241002i	$-0.0774762\pi$
$774$	14.9047	−	5.42487i	0.535739	−	0.194993i
$775$	1.27422	+	19.1373i	0.0457713	+	0.687432i
$776$	10.3001			0.369752
$777$	−6.99728	+	17.3834i	−0.251026	+	0.623627i
$778$		−	31.9745i		−	1.14634i
$779$	10.7213	−	29.4566i	0.384131	−	1.05539i
$780$	27.3688	−	17.0387i	0.979962	−	0.610083i
$781$	−12.3458	−	10.3593i	−0.441767	−	0.370687i
$782$	0.901283	−	5.11143i	0.0322298	−	0.182784i
$783$	−58.3993			−2.08702
$784$	1.02777	−	5.82878i	0.0367061	−	0.208171i
$785$	−31.1634	−	34.7265i	−1.11227	−	1.23944i
$786$	3.38182	−	2.83769i	0.120626	−	0.101217i
$787$	8.24982	+	4.76304i	0.294074	+	0.169784i	0.639778	−	0.768560i	$-0.279026\pi$
$787$	8.24982	+	4.76304i	0.294074	+	0.169784i	−0.345703	+	0.938344i	$0.612360\pi$
$788$	−19.4231	+	11.2139i	−0.691920	+	0.399480i
$789$	−0.716552	−	0.260804i	−0.0255099	−	0.00928485i
$790$	31.3986	+	16.7620i	1.11711	+	0.596366i
$791$	7.68976	+	4.43969i	0.273417	+	0.157857i
$792$	2.18612	+	12.3981i	0.0776804	+	0.440547i
$793$	13.3621	−	2.35610i	0.474502	−	0.0836674i
$794$	14.3981	+	17.1589i	0.510968	+	0.608948i
$795$	−34.3710	−	55.2093i	−1.21901	−	1.95807i
$796$	1.29187	+	3.54940i	0.0457893	+	0.125805i
$797$	0.852660	−	0.715467i	0.0302028	−	0.0253431i	−0.627561	−	0.778567i	$-0.715947\pi$
$797$	0.852660	−	0.715467i	0.0302028	−	0.0253431i	0.657764	+	0.753224i	$0.271502\pi$
$798$	14.1493	−	2.49491i	0.500881	−	0.0883188i
$799$	15.3737	−	2.71080i	0.543883	−	0.0959013i
$800$	−0.539190	+	4.97084i	−0.0190632	+	0.175746i
$801$	45.6139	−	54.3605i	1.61169	−	1.92073i
$802$	4.49397	−	12.3471i	0.158688	−	0.435991i
$803$	14.8352	−	8.56514i	0.523525	−	0.302257i
$804$	−13.1620	+	22.7972i	−0.464186	+	0.803994i
$805$	6.00895	−	7.66478i	0.211788	−	0.270148i
$806$	−16.1671	+	9.33410i	−0.569463	+	0.328780i
$807$	54.5545	+	9.61944i	1.92041	+	0.338620i
$808$	18.3552			0.645734
$809$	−19.1609	−	3.37858i	−0.673660	−	0.118784i	−0.173654	−	0.984807i	$-0.555558\pi$
$809$	−19.1609	−	3.37858i	−0.673660	−	0.118784i	−0.500006	+	0.866022i	$0.666669\pi$
$810$	−7.41492	+	13.8896i	−0.260534	+	0.488031i
$811$	13.0779	−	4.75997i	0.459228	−	0.167145i	−0.102039	−	0.994780i	$-0.532537\pi$
$811$	13.0779	−	4.75997i	0.459228	−	0.167145i	0.561266	+	0.827635i	$0.310314\pi$
$812$	−6.93662	−	2.52472i	−0.243428	−	0.0886004i
$813$			65.2384i			2.28801i
$814$	−4.94994	+	12.2972i	−0.173495	+	0.431017i
$815$	−2.98000	−	14.1354i	−0.104385	−	0.495143i
$816$	−1.25556	+	3.44962i	−0.0439534	+	0.120761i
$817$	−4.37966	−	12.0330i	−0.153225	−	0.420982i
$818$	8.71685	−	10.3883i	0.304778	−	0.363220i
$819$	28.7903	+	5.07651i	1.00602	+	0.177388i
$820$	3.10031	+	14.7061i	0.108267	+	0.513559i
$821$	−2.96002	+	16.7871i	−0.103305	+	0.585874i	0.888578	+	0.458725i	$0.151694\pi$
$821$	−2.96002	+	16.7871i	−0.103305	+	0.585874i	−0.991884	+	0.127149i	$0.959417\pi$
$822$	−12.8336	−	22.2285i	−0.447624	−	0.775307i
$823$	−6.62471	−	7.89502i	−0.230923	−	0.275203i	0.638123	−	0.769934i	$-0.279711\pi$
$823$	−6.62471	−	7.89502i	−0.230923	−	0.275203i	−0.869046	+	0.494731i	$0.835267\pi$
$824$	3.84868	−	6.66610i	0.134075	−	0.232225i
$825$	19.0614	−	26.0529i	0.663631	−	0.907046i
$826$	5.41841	+	1.97214i	0.188531	+	0.0686196i
$827$	28.7668	+	24.1382i	1.00032	+	0.839369i	0.987029	−	0.160543i	$-0.0513245\pi$
$827$	28.7668	+	24.1382i	1.00032	+	0.839369i	0.0132919	+	0.999912i	$0.495769\pi$
$828$	−12.0986	+	20.9554i	−0.420455	+	0.728249i
$829$	35.3243	−	6.22863i	1.22686	−	0.216329i	0.477586	−	0.878585i	$-0.341512\pi$
$829$	35.3243	−	6.22863i	1.22686	−	0.216329i	0.749278	+	0.662256i	$0.230401\pi$
$830$	2.62329	+	6.52411i	0.0910557	+	0.226455i
$831$	−1.29038	−	1.53781i	−0.0447627	−	0.0533461i
$832$	−4.57316	+	1.66450i	−0.158546	+	0.0577060i
$833$	−6.89173	+	2.50838i	−0.238784	+	0.0869104i
$834$	−21.5754	−	25.7126i	−0.747095	−	0.890354i
$835$	−30.0055	+	12.0649i	−1.03838	+	0.417525i
$836$	10.0094	−	1.76492i	0.346181	−	0.0610410i
$837$	15.7783	−	27.3289i	0.545379	−	0.944624i
$838$	13.7723	+	11.5564i	0.475757	+	0.399208i
$839$	−38.0230	−	13.8393i	−1.31270	−	0.477784i	−0.411589	−	0.911370i	$-0.635026\pi$
$839$	−38.0230	−	13.8393i	−1.31270	−	0.477784i	−0.901112	+	0.433585i	$0.857248\pi$
$840$	−5.12685	+	4.60081i	−0.176893	+	0.158743i
$841$	10.6969	−	18.5275i	0.368857	−	0.638880i
$842$	−5.47319	−	6.52269i	−0.188618	−	0.224787i
$843$	−36.0586	−	62.4553i	−1.24192	−	2.15107i
$844$	−1.46123	+	8.28705i	−0.0502977	+	0.285252i
$845$	−4.92832	−	23.3772i	−0.169539	−	0.804199i
$846$	−71.6726	−	12.6378i	−2.46415	−	0.434497i
$847$	−4.17804	+	4.97919i	−0.143559	+	0.171087i
$848$	3.35767	+	9.22513i	0.115303	+	0.316792i
$849$	−13.2105	+	36.2955i	−0.453382	+	1.24566i
$850$	5.66836	−	2.50114i	0.194423	−	0.0857885i
$851$	−22.4808	+	11.9905i	−0.770632	+	0.411029i
$852$			21.9089i			0.750587i
$853$	23.4858	+	8.54812i	0.804138	+	0.292682i	0.711200	−	0.702990i	$-0.248152\pi$
$853$	23.4858	+	8.54812i	0.804138	+	0.292682i	0.0929377	+	0.995672i	$0.470374\pi$
$854$	−2.72428	+	0.991556i	−0.0932229	+	0.0339304i
$855$	53.1455	+	28.3715i	1.81754	+	0.970285i
$856$	6.11069	+	1.07748i	0.208859	+	0.0368275i
$857$	−39.7960			−1.35941			−0.679703	−	0.733487i	$-0.737891\pi$
$857$	−39.7960			−1.35941			−0.679703	+	0.733487i	$0.737891\pi$
$858$	30.9432	+	5.45612i	1.05638	+	0.186269i
$859$	−47.3299	+	27.3260i	−1.61488	+	0.932350i	−0.626659	+	0.779293i	$0.715578\pi$
$859$	−47.3299	+	27.3260i	−1.61488	+	0.932350i	−0.988217	+	0.153056i	$0.951088\pi$
$860$	4.83169	+	3.78789i	0.164759	+	0.129166i
$861$	−10.3530	+	17.9320i	−0.352831	+	0.611120i
$862$	−23.6983	+	13.6822i	−0.807169	+	0.466019i
$863$	−13.4552	+	36.9677i	−0.458019	+	1.25840i	0.468939	+	0.883231i	$0.344637\pi$
$863$	−13.4552	+	36.9677i	−0.458019	+	1.25840i	−0.926958	+	0.375166i	$0.877586\pi$
$864$	5.28795	−	6.30193i	0.179900	−	0.214396i
$865$	−9.68176	+	29.6295i	−0.329190	+	1.00743i
$866$	36.6263	−	6.45820i	1.24461	−	0.219458i
$867$	−45.1189	+	7.95567i	−1.53232	+	0.270189i
$868$	3.05562	−	2.56397i	0.103714	−	0.0870268i
$869$	11.8643	+	32.5968i	0.402467	+	1.10577i
$870$	−24.8538	−	39.9221i	−0.842624	−	1.35349i
$871$	27.7958	+	33.1258i	0.941826	+	1.12242i
$872$	10.4781	−	1.84757i	0.354833	−	0.0625666i
$873$	10.3324	+	58.5980i	0.349699	+	1.98324i
$874$	16.9179	+	9.76756i	0.572257	+	0.330393i
$875$	11.5934	+	0.868878i	0.391930	+	0.0293734i
$876$	−21.8829	−	7.96474i	−0.739356	−	0.269104i
$877$	19.3974	−	11.1991i	0.655002	−	0.378166i	−0.135368	−	0.990795i	$-0.543222\pi$
$877$	19.3974	−	11.1991i	0.655002	−	0.378166i	0.790370	+	0.612630i	$0.209888\pi$
$878$	23.3863	+	13.5021i	0.789251	+	0.455674i
$879$	36.9209	−	30.9803i	1.24531	−	1.04494i
$880$	−3.62678	+	3.25466i	−0.122259	+	0.109714i
$881$	−4.51092	+	25.5827i	−0.151977	+	0.861903i	0.809521	+	0.587091i	$0.199727\pi$
$881$	−4.51092	+	25.5827i	−0.151977	+	0.861903i	−0.961498	+	0.274812i	$0.911384\pi$
$882$	34.1913			1.15128
$883$	2.07977	−	11.7950i	0.0699898	−	0.396932i	−0.929607	−	0.368551i	$-0.879854\pi$
$883$	2.07977	−	11.7950i	0.0699898	−	0.396932i	0.999597	−	0.0283805i	$-0.00903501\pi$
$884$	4.61957	+	3.87628i	0.155373	+	0.130373i
$885$	19.4141	+	31.1844i	0.652598	+	1.04825i
$886$	13.2991	−	36.5390i	0.446792	−	1.22755i
$887$		−	41.4594i		−	1.39207i	−0.718008	−	0.696035i	$-0.754946\pi$
$887$		−	41.4594i		−	1.39207i	0.718008	−	0.696035i	$-0.245054\pi$
$888$	17.1314	−	5.59079i	0.574893	−	0.187615i
$889$	8.28321			0.277810
$890$	27.1941	+	3.86804i	0.911549	+	0.129657i
$891$	−14.4196	+	5.24832i	−0.483076	+	0.175825i
$892$	−14.8879	+	17.7427i	−0.498485	+	0.594071i
$893$	−10.2029	+	57.8635i	−0.341427	+	1.93633i
$894$		−	19.4026i		−	0.648921i
$895$	−0.311719	−	9.37371i	−0.0104196	−	0.313329i
$896$	0.900543	−	0.519929i	0.0300850	−	0.0173696i
$897$	38.8188	+	46.2624i	1.29612	+	1.54466i
$898$	4.58639	+	2.64795i	0.153050	+	0.0883634i
$899$	13.6154	+	23.5825i	0.454098	+	0.786521i
$900$	−28.8204	+	1.91894i	−0.960679	+	0.0639648i
$901$	7.81935	−	9.31874i	0.260500	−	0.310452i
$902$	−7.32383	+	12.6852i	−0.243857	+	0.422372i
$903$	1.46879	+	8.32994i	0.0488784	+	0.277203i
$904$	−1.48279	−	8.40930i	−0.0493168	−	0.279689i
$905$	41.8455	+	32.8056i	1.39099	+	1.09049i
$906$	8.73574	+	24.0012i	0.290226	+	0.797388i
$907$	16.6264	−	6.05151i	0.552070	−	0.200937i	−0.0508959	−	0.998704i	$-0.516208\pi$
$907$	16.6264	−	6.05151i	0.552070	−	0.200937i	0.602966	+	0.797767i	$0.293985\pi$
$908$	4.15905	−	3.48986i	0.138023	−	0.115815i
$909$	18.4128	+	104.424i	0.610714	+	3.46353i
$910$	4.22155	+	10.4990i	0.139943	+	0.348038i
$911$	9.24569	+	5.33800i	0.306323	+	0.176856i	0.645280	−	0.763946i	$-0.276741\pi$
$911$	9.24569	+	5.33800i	0.306323	+	0.176856i	−0.338957	+	0.940802i	$0.610074\pi$
$912$	−10.5844	−	8.88133i	−0.350483	−	0.294090i
$913$	−2.34393	+	6.43988i	−0.0775726	+	0.213129i
$914$	−1.13088	−	1.95873i	−0.0374060	−	0.0647891i
$915$	−17.5556	−	5.73649i	−0.580372	−	0.189643i
$916$	16.6188	−	13.9448i	0.549100	−	0.460749i
$917$	0.774768	+	1.34194i	0.0255851	+	0.0443147i
$918$	−10.0389	−	1.77013i	−0.331334	−	0.0584231i
$919$		−	17.3974i		−	0.573886i	−0.957948	−	0.286943i	$-0.907361\pi$
$919$		−	17.3974i		−	0.573886i	0.957948	−	0.286943i	$-0.0926391\pi$
$920$	−9.36094	+	0.311295i	−0.308621	+	0.0102631i
$921$	−15.4645	−	12.9762i	−0.509572	−	0.427582i
$922$	−4.92851	−	13.5410i	−0.162312	−	0.445948i
$923$	33.8196	+	12.3093i	1.11319	+	0.405166i
$924$	−6.71361			−0.220862
$925$	−26.8247	−	14.3331i	−0.881989	−	0.471270i
$926$	−25.8603			−0.849821
$927$	41.7847	+	15.2084i	1.37239	+	0.499509i
$928$	2.42795	+	6.67074i	0.0797014	+	0.218978i
$929$	−22.4746	−	18.8584i	−0.737368	−	0.618726i	0.194761	−	0.980851i	$-0.437607\pi$
$929$	−22.4746	−	18.8584i	−0.737368	−	0.618726i	−0.932129	+	0.362125i	$0.882051\pi$
$930$	25.3972	−	0.844574i	0.832806	−	0.0276947i
$931$		−	27.6037i		−	0.904675i
$932$	−10.8117	−	1.90639i	−0.354148	−	0.0624458i
$933$	15.8299	+	27.4183i	0.518249	+	0.897633i
$934$	7.99803	−	6.71114i	0.261703	−	0.219595i
$935$	5.73965	+	1.87549i	0.187707	+	0.0613351i
$936$	−14.0570	−	24.3474i	−0.459466	−	0.795818i
$937$	8.27156	−	22.7259i	0.270220	−	0.742424i	−0.728153	−	0.685414i	$-0.759621\pi$
$937$	8.27156	−	22.7259i	0.270220	−	0.742424i	0.998374	−	0.0570097i	$-0.0181566\pi$
$938$	−7.07798	−	5.93913i	−0.231104	−	0.193919i
$939$	−27.7034	−	15.9946i	−0.904068	−	0.521964i
$940$	−10.5094	−	26.1369i	−0.342779	−	0.852491i
$941$	−0.439588	−	2.49303i	−0.0143301	−	0.0812703i	0.976804	−	0.214135i	$-0.0686934\pi$
$941$	−0.439588	−	2.49303i	−0.0143301	−	0.0812703i	−0.991134	+	0.132865i	$0.957582\pi$
$942$	−47.3561	+	39.7365i	−1.54294	+	1.29468i
$943$	−26.4554	+	9.62900i	−0.861508	+	0.313563i
$944$	−1.89655	−	5.21073i	−0.0617274	−	0.169595i
$945$	−15.0538	−	11.8017i	−0.489699	−	0.383909i
$946$	1.03904	+	5.89267i	0.0337820	+	0.191587i
$947$	−7.06389	−	40.0613i	−0.229546	−	1.30182i	−0.853802	−	0.520598i	$-0.825709\pi$
$947$	−7.06389	−	40.0613i	−0.229546	−	1.30182i	0.624256	−	0.781219i	$-0.285402\pi$
$948$	23.5784	−	40.8390i	0.765791	−	1.32639i
$949$	−24.5895	+	29.3046i	−0.798208	+	0.951268i
$950$	1.54922	+	23.2676i	0.0502634	+	0.754900i
$951$	−29.1153	−	50.4292i	−0.944129	−	1.63528i
$952$	−1.11589	−	0.644259i	−0.0361662	−	0.0208805i
$953$	17.0251	+	20.2897i	0.551497	+	0.657248i	0.967724	−	0.252012i	$-0.0810924\pi$
$953$	17.0251	+	20.2897i	0.551497	+	0.657248i	−0.416227	+	0.909261i	$0.636648\pi$
$954$	−49.1143	+	28.3561i	−1.59013	+	0.918064i
$955$	−1.74486	−	52.4697i	−0.0564624	−	1.69788i
$956$		−	23.1823i		−	0.749769i
$957$	7.95868	−	45.1359i	0.257268	−	1.45904i
$958$	−25.2272	+	30.0646i	−0.815055	+	0.971345i
$959$	8.46583	−	3.08131i	0.273376	−	0.0995007i
$960$	6.55850	+	0.932870i	0.211675	+	0.0301083i
$961$	16.2856			0.525342
$962$	0.994939	−	29.5860i	0.0320781	−	0.953891i
$963$			35.8450i			1.15509i
$964$	−4.51890	+	12.4156i	−0.145544	+	0.399879i
$965$	13.3434	+	21.4333i	0.429540	+	0.689961i
$966$	−9.88488	−	8.29440i	−0.318041	−	0.266868i
$967$	−0.649935	+	3.68597i	−0.0209005	+	0.118533i	−0.993473	−	0.114067i	$-0.963612\pi$
$967$	−0.649935	+	3.68597i	−0.0209005	+	0.118533i	0.972573	+	0.232600i	$0.0747232\pi$
$968$	6.25073			0.200906
$969$	−2.97302	+	16.8608i	−0.0955070	+	0.541647i
$970$	−17.1415	+	15.3827i	−0.550381	+	0.493909i
$971$	17.8111	−	14.9453i	0.571585	−	0.479616i	−0.310587	−	0.950545i	$-0.600526\pi$
$971$	17.8111	−	14.9453i	0.571585	−	0.479616i	0.882171	+	0.470929i	$0.156081\pi$
$972$	−3.30758	−	1.90963i	−0.106091	−	0.0612515i
$973$	10.2030	−	5.89069i	0.327093	−	0.188847i
$974$	8.42144	+	3.06515i	0.269840	+	0.0982139i
$975$	−20.1010	+	69.2300i	−0.643747	+	2.21714i
$976$	2.41447	+	1.39400i	0.0772854	+	0.0446208i
$977$	3.00197	+	17.0250i	0.0960414	+	0.544678i	0.994423	+	0.105463i	$0.0336324\pi$
$977$	3.00197	+	17.0250i	0.0960414	+	0.544678i	−0.898382	+	0.439215i	$0.855257\pi$
$978$	−18.8490	+	3.32358i	−0.602724	+	0.106276i
$979$	17.2076	+	20.5072i	0.549957	+	0.655413i
$980$	6.99459	+	11.2352i	0.223434	+	0.358897i
$981$	21.0219	+	57.7572i	0.671178	+	1.84405i
$982$	−30.3537	+	25.4697i	−0.968624	+	0.812772i
$983$	−13.9086	+	2.45246i	−0.443615	+	0.0782213i	−0.390994	−	0.920393i	$-0.627869\pi$
$983$	−13.9086	+	2.45246i	−0.443615	+	0.0782213i	−0.0526211	+	0.998615i	$0.516758\pi$
$984$	19.6099	−	3.45775i	0.625141	−	0.110229i
$985$	15.5766	−	47.6699i	0.496313	−	1.51889i
$986$	5.65421	−	6.73843i	0.180067	−	0.214595i
$987$	13.2741	−	36.4704i	0.422520	−	1.16086i
$988$	−19.6564	+	11.3486i	−0.625352	+	0.361047i
$989$	−5.75032	+	9.95984i	−0.182849	+	0.316705i
$990$	−22.1541	−	17.3682i	−0.704105	−	0.551997i
$991$	−19.1508	+	11.0567i	−0.608346	+	0.351229i	−0.772318	−	0.635236i	$-0.780903\pi$
$991$	−19.1508	+	11.0567i	−0.608346	+	0.351229i	0.163972	+	0.986465i	$0.447569\pi$
$992$	−3.77766	−	0.666103i	−0.119941	−	0.0211488i
$993$	16.4862			0.523175
$994$	−7.57316	−	1.33535i	−0.240206	−	0.0423548i
$995$	−7.45081	−	3.97758i	−0.236207	−	0.126098i
$996$	8.75455	−	3.18639i	0.277398	−	0.100965i
$997$	−32.5651	−	11.8527i	−1.03135	−	0.375379i	−0.229753	−	0.973249i	$-0.573792\pi$
$997$	−32.5651	−	11.8527i	−1.03135	−	0.375379i	−0.801593	+	0.597870i	$0.796014\pi$
$998$		−	5.39254i		−	0.170698i
$999$	23.5495	+	44.1527i	0.745074	+	1.39693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.v.b.169.10	yes	60
5.4	even	2		370.2.v.a.169.1	✓	60
37.30	even	18		370.2.v.a.289.1	yes	60
185.104	even	18	inner	370.2.v.b.289.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.v.a.169.1	✓	60	5.4	even	2
370.2.v.a.289.1	yes	60	37.30	even	18
370.2.v.b.169.10	yes	60	1.1	even	1	trivial
370.2.v.b.289.10	yes	60	185.104	even	18	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.01326 + 2.78391i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.23483 + 0.0743186i) q^{5} +2.96257i q^{6} +(-1.02406 - 0.180569i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-4.42531 + 3.71328i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.01326 + 2.78391i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.23483 + 0.0743186i) q^{5} +2.96257i q^{6} +(-1.02406 - 0.180569i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-4.42531 + 3.71328i) q^{9} +(-2.12547 - 0.694521i) q^{10} +(-1.08964 - 1.88731i) q^{11} +(-1.01326 + 2.78391i) q^{12} +(3.72808 + 3.12823i) q^{13} +(-0.900543 - 0.519929i) q^{14} +(-2.47136 - 6.14626i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.949228 - 0.796496i) q^{17} +(-5.42845 + 1.97579i) q^{18} +(1.59512 + 4.38255i) q^{19} +(-1.75975 - 1.37959i) q^{20} +(-0.534950 - 3.03385i) q^{21} +(-0.378428 - 2.14617i) q^{22} +(2.09433 - 3.62748i) q^{23} +(-1.90431 + 2.26946i) q^{24} +(4.98895 - 0.332179i) q^{25} +(2.43333 + 4.21465i) q^{26} +(-7.12443 - 4.11329i) q^{27} +(-0.668408 - 0.796577i) q^{28} +(6.14779 - 3.54943i) q^{29} +(-0.220174 - 6.62085i) q^{30} +3.83594i q^{31} +(-0.173648 + 0.984808i) q^{32} +(4.15002 - 4.94580i) q^{33} +(1.16440 - 0.423807i) q^{34} +(2.30202 + 0.327436i) q^{35} -5.77684 q^{36} +(-5.16263 - 3.21671i) q^{37} +4.66382i q^{38} +(-4.93119 + 13.5483i) q^{39} +(-1.18178 - 1.89826i) q^{40} +(-5.14883 - 4.32038i) q^{41} +(0.534950 - 3.03385i) q^{42} -2.74566 q^{43} +(0.378428 - 2.14617i) q^{44} +(9.61387 - 8.62744i) q^{45} +(3.20869 - 2.69241i) q^{46} +(10.9104 + 6.29914i) q^{47} +(-2.56566 + 1.48129i) q^{48} +(-5.56176 - 2.02431i) q^{49} +(4.80169 + 1.39418i) q^{50} +(3.17919 + 1.83550i) q^{51} +(0.845087 + 4.79272i) q^{52} +(9.66804 - 1.70474i) q^{53} +(-5.28795 - 6.30193i) q^{54} +(2.57543 + 4.13685i) q^{55} +(-0.355652 - 0.977146i) q^{56} +(-10.5844 + 8.88133i) q^{57} +(6.99101 - 1.23270i) q^{58} +(-5.46090 + 0.962903i) q^{59} +(2.05757 - 6.29687i) q^{60} +(1.79209 - 2.13573i) q^{61} +(-1.31197 + 3.60460i) q^{62} +(5.20229 - 3.00354i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-8.56412 - 6.71400i) q^{65} +(5.59130 - 3.22814i) q^{66} +(8.75050 + 1.54295i) q^{67} +1.23913 q^{68} +(12.2207 + 2.15483i) q^{69} +(2.05120 + 1.09503i) q^{70} +(6.94924 - 2.52932i) q^{71} +(-5.42845 - 1.97579i) q^{72} +7.86051i q^{73} +(-3.75111 - 4.78845i) q^{74} +(5.97986 + 13.5522i) q^{75} +(-1.59512 + 4.38255i) q^{76} +(0.775066 + 2.12948i) q^{77} +(-9.26761 + 11.0447i) q^{78} +(-15.6757 - 2.76405i) q^{79} +(-0.461264 - 2.18798i) q^{80} +(1.22272 - 6.93437i) q^{81} +(-3.36066 - 5.82084i) q^{82} +(-2.02137 - 2.40898i) q^{83} +(1.54033 - 2.66792i) q^{84} +(-2.06217 + 1.85058i) q^{85} +(-2.58008 - 0.939073i) q^{86} +(16.1106 + 13.5184i) q^{87} +(1.08964 - 1.88731i) q^{88} +(-12.0974 + 2.13309i) q^{89} +(11.9848 - 4.81901i) q^{90} +(-3.25291 - 3.87667i) q^{91} +(3.93605 - 1.43260i) q^{92} +(-10.6789 + 3.88680i) q^{93} +(8.09802 + 9.65085i) q^{94} +(-3.89053 - 9.67573i) q^{95} +(-2.91756 + 0.514445i) q^{96} +(5.15005 - 8.92014i) q^{97} +(-4.53398 - 3.80446i) q^{98} +(11.8301 + 4.30581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more