LMFDB - Embedded newform 460.2.w.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			3.4
Character	$\chi$	$=$	460.3
Dual form			460.2.w.a.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39894 - 0.207265i) q^{2} +(-0.826183 - 2.21508i) q^{3} +(1.91408 + 0.579903i) q^{4} +(-2.13268 + 0.672078i) q^{5} +(0.696675 + 3.27001i) q^{6} +(-2.06386 - 0.448965i) q^{7} +(-2.55750 - 1.20797i) q^{8} +(-1.95677 + 1.69555i) q^{9} +O(q^{10})$	\(q+(-1.39894 - 0.207265i) q^{2} +(-0.826183 - 2.21508i) q^{3} +(1.91408 + 0.579903i) q^{4} +(-2.13268 + 0.672078i) q^{5} +(0.696675 + 3.27001i) q^{6} +(-2.06386 - 0.448965i) q^{7} +(-2.55750 - 1.20797i) q^{8} +(-1.95677 + 1.69555i) q^{9} +(3.12279 - 0.498170i) q^{10} +(1.40142 + 0.201494i) q^{11} +(-0.296850 - 4.71896i) q^{12} +(0.538729 + 2.47650i) q^{13} +(2.79417 + 1.05584i) q^{14} +(3.25069 + 4.16880i) q^{15} +(3.32743 + 2.21996i) q^{16} +(-5.62112 + 3.06936i) q^{17} +(3.08883 - 1.96641i) q^{18} +(0.0212593 - 0.00624230i) q^{19} +(-4.47186 + 0.0496673i) q^{20} +(0.710631 + 4.94255i) q^{21} +(-1.91875 - 0.572345i) q^{22} +(4.79582 + 0.00977332i) q^{23} +(-0.562797 + 6.66308i) q^{24} +(4.09662 - 2.86665i) q^{25} +(-0.240361 - 3.57614i) q^{26} +(-0.852446 - 0.465471i) q^{27} +(-3.69004 - 2.05620i) q^{28} +(-1.90165 + 6.47644i) q^{29} +(-3.68349 - 6.50566i) q^{30} +(5.83201 - 2.66339i) q^{31} +(-4.19476 - 3.79526i) q^{32} +(-0.711506 - 3.27074i) q^{33} +(8.49980 - 3.12881i) q^{34} +(4.70329 - 0.429577i) q^{35} +(-4.72867 + 2.11069i) q^{36} +(5.99221 + 0.428571i) q^{37} +(-0.0310344 + 0.00432631i) q^{38} +(5.04056 - 3.23937i) q^{39} +(6.26617 + 0.857377i) q^{40} +(-2.77115 + 3.19808i) q^{41} +(0.0302831 - 7.06163i) q^{42} +(2.92446 + 7.84079i) q^{43} +(2.56559 + 1.19837i) q^{44} +(3.03361 - 4.93116i) q^{45} +(-6.70706 - 1.00768i) q^{46} +(-0.485564 - 0.485564i) q^{47} +(2.16834 - 9.20462i) q^{48} +(-2.30948 - 1.05470i) q^{49} +(-6.32510 + 3.16120i) q^{50} +(11.4430 + 9.91539i) q^{51} +(-0.404956 + 5.05263i) q^{52} +(9.67913 + 2.10557i) q^{53} +(1.09605 + 0.827849i) q^{54} +(-3.12420 + 0.512144i) q^{55} +(4.73598 + 3.64132i) q^{56} +(-0.0313913 - 0.0419339i) q^{57} +(4.00264 - 8.66603i) q^{58} +(-1.16631 - 0.749541i) q^{59} +(3.80459 + 9.86451i) q^{60} +(2.81542 + 6.16491i) q^{61} +(-8.71067 + 2.51716i) q^{62} +(4.79974 - 2.62085i) q^{63} +(5.08160 + 6.17878i) q^{64} +(-2.81333 - 4.91950i) q^{65} +(0.317448 + 4.72305i) q^{66} +(-5.90829 + 7.89254i) q^{67} +(-12.5392 + 2.61531i) q^{68} +(-3.94058 - 10.6312i) q^{69} +(-6.66867 - 0.373872i) q^{70} +(-11.7241 + 1.68567i) q^{71} +(7.05261 - 1.97264i) q^{72} +(8.87718 + 4.84731i) q^{73} +(-8.29393 - 1.84152i) q^{74} +(-9.73443 - 6.70598i) q^{75} +(0.0443120 + 0.000380063i) q^{76} +(-2.80188 - 1.04505i) q^{77} +(-7.72286 + 3.48696i) q^{78} +(-4.54914 - 2.92356i) q^{79} +(-8.58831 - 2.49818i) q^{80} +(-1.43221 + 9.96127i) q^{81} +(4.53953 - 3.89957i) q^{82} +(-5.37776 - 0.384625i) q^{83} +(-1.50599 + 9.87255i) q^{84} +(9.92518 - 10.3238i) q^{85} +(-2.46604 - 11.5750i) q^{86} +(15.9170 - 1.13840i) q^{87} +(-3.34074 - 2.20820i) q^{88} +(-9.58899 - 4.37915i) q^{89} +(-5.26591 + 6.26965i) q^{90} -5.35301i q^{91} +(9.17393 + 2.79982i) q^{92} +(-10.7179 - 10.7179i) q^{93} +(0.578636 + 0.779917i) q^{94} +(-0.0411439 + 0.0276007i) q^{95} +(-4.94118 + 12.4273i) q^{96} +(-0.185165 - 2.58895i) q^{97} +(3.01222 + 1.95414i) q^{98} +(-3.08390 + 1.98190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	−1.39894	−	0.207265i	−0.989202	−	0.146558i
$2$	−1.39894	−	0.207265i	−0.989202	−	0.146558i
$3$	−0.826183	−	2.21508i	−0.476997	−	1.27888i	−0.923328	−	0.384011i	$-0.874542\pi$
$3$	−0.826183	−	2.21508i	−0.476997	−	1.27888i	0.446331	−	0.894868i	$-0.352730\pi$
$4$	1.91408	+	0.579903i	0.957041	+	0.289951i
$5$	−2.13268	+	0.672078i	−0.953762	+	0.300562i
$5$	−2.13268	+	0.672078i	−0.953762	+	0.300562i
$6$	0.696675	+	3.27001i	0.284416	+	1.33498i
$7$	−2.06386	−	0.448965i	−0.780066	−	0.169693i	−0.195135	−	0.980776i	$-0.562515\pi$
$7$	−2.06386	−	0.448965i	−0.780066	−	0.169693i	−0.584931	+	0.811083i	$0.698878\pi$
$8$	−2.55750	−	1.20797i	−0.904212	−	0.427083i
$9$	−1.95677	+	1.69555i	−0.652256	+	0.565183i
$10$	3.12279	−	0.498170i	0.987513	−	0.157535i
$11$	1.40142	+	0.201494i	0.422545	+	0.0607528i	0.350308	−	0.936635i	$-0.386077\pi$
$11$	1.40142	+	0.201494i	0.422545	+	0.0607528i	0.0722374	+	0.997387i	$0.476986\pi$
$12$	−0.296850	−	4.71896i	−0.0856933	−	1.36225i
$13$	0.538729	+	2.47650i	0.149416	+	0.686856i	0.989516	+	0.144424i	$0.0461329\pi$
$13$	0.538729	+	2.47650i	0.149416	+	0.686856i	−0.840099	+	0.542432i	$0.817503\pi$
$14$	2.79417	+	1.05584i	0.746773	+	0.282186i
$15$	3.25069	+	4.16880i	0.839325	+	1.07638i
$16$	3.32743	+	2.21996i	0.831856	+	0.554991i
$17$	−5.62112	+	3.06936i	−1.36332	+	0.744430i	−0.983548	−	0.180649i	$-0.942180\pi$
$17$	−5.62112	+	3.06936i	−1.36332	+	0.744430i	−0.379774	+	0.925079i	$0.623998\pi$
$18$	3.08883	−	1.96641i	0.728045	−	0.463487i
$19$	0.0212593	−	0.00624230i	0.00487722	−	0.00143208i	−0.279293	−	0.960206i	$-0.590100\pi$
$19$	0.0212593	−	0.00624230i	0.00487722	−	0.00143208i	0.284170	+	0.958774i	$0.408282\pi$
$20$	−4.47186	+	0.0496673i	−0.999938	+	0.0111059i
$21$	0.710631	+	4.94255i	0.155072	+	1.07855i
$22$	−1.91875	−	0.572345i	−0.409079	−	0.122024i
$23$	4.79582	+	0.00977332i	0.999998	+	0.00203788i
$23$	4.79582	+	0.00977332i	0.999998	+	0.00203788i
$24$	−0.562797	+	6.66308i	−0.114880	+	1.36010i
$25$	4.09662	−	2.86665i	0.819324	−	0.573330i
$26$	−0.240361	−	3.57614i	−0.0471386	−	0.701338i
$27$	−0.852446	−	0.465471i	−0.164053	−	0.0895799i
$28$	−3.69004	−	2.05620i	−0.697353	−	0.388584i
$29$	−1.90165	+	6.47644i	−0.353128	+	1.20264i	0.571124	+	0.820864i	$0.306507\pi$
$29$	−1.90165	+	6.47644i	−0.353128	+	1.20264i	−0.924253	+	0.381781i	$0.875311\pi$
$30$	−3.68349	−	6.50566i	−0.672510	−	1.18777i
$31$	5.83201	−	2.66339i	1.04746	−	0.478359i	0.184079	−	0.982912i	$-0.441070\pi$
$31$	5.83201	−	2.66339i	1.04746	−	0.478359i	0.863381	+	0.504553i	$0.168343\pi$
$32$	−4.19476	−	3.79526i	−0.741535	−	0.670914i
$33$	−0.711506	−	3.27074i	−0.123857	−	0.569363i
$34$	8.49980	−	3.12881i	1.45770	−	0.536586i
$35$	4.70329	−	0.429577i	0.795001	−	0.0726118i
$36$	−4.72867	+	2.11069i	−0.788111	+	0.351781i
$37$	5.99221	+	0.428571i	0.985113	+	0.0704567i	0.554591	−	0.832123i	$-0.312875\pi$
$37$	5.99221	+	0.428571i	0.985113	+	0.0704567i	0.430522	+	0.902580i	$0.358329\pi$
$38$	−0.0310344	+	0.00432631i	−0.00503444	+	0.000701821i
$39$	5.04056	−	3.23937i	0.807135	−	0.518714i
$40$	6.26617	+	0.857377i	0.990769	+	0.135563i
$41$	−2.77115	+	3.19808i	−0.432781	+	0.499456i	−0.929688	−	0.368348i	$-0.879924\pi$
$41$	−2.77115	+	3.19808i	−0.432781	+	0.499456i	0.496907	+	0.867804i	$0.334469\pi$
$42$	0.0302831	−	7.06163i	0.00467279	−	1.08963i
$43$	2.92446	+	7.84079i	0.445976	+	1.19571i	0.944407	+	0.328779i	$0.106637\pi$
$43$	2.92446	+	7.84079i	0.445976	+	1.19571i	−0.498430	+	0.866930i	$0.666090\pi$
$44$	2.56559	+	1.19837i	0.386778	+	0.180661i
$45$	3.03361	−	4.93116i	0.452224	−	0.735094i
$46$	−6.70706	−	1.00768i	−0.988901	−	0.148574i
$47$	−0.485564	−	0.485564i	−0.0708268	−	0.0708268i	0.670806	−	0.741633i	$-0.265948\pi$
$47$	−0.485564	−	0.485564i	−0.0708268	−	0.0708268i	−0.741633	+	0.670806i	$0.765948\pi$
$48$	2.16834	−	9.20462i	0.312973	−	1.32857i
$49$	−2.30948	−	1.05470i	−0.329925	−	0.150672i
$50$	−6.32510	+	3.16120i	−0.894504	+	0.447061i
$51$	11.4430	+	9.91539i	1.60234	+	1.38843i
$52$	−0.404956	+	5.05263i	−0.0561573	+	0.700673i
$53$	9.67913	+	2.10557i	1.32953	+	0.289222i	0.820559	−	0.571561i	$-0.193662\pi$
$53$	9.67913	+	2.10557i	1.32953	+	0.289222i	0.508972	+	0.860783i	$0.330026\pi$
$54$	1.09605	+	0.827849i	0.149153	+	0.112656i
$55$	−3.12420	+	0.512144i	−0.421268	+	0.0690574i
$56$	4.73598	+	3.64132i	0.632872	+	0.486591i
$57$	−0.0313913	−	0.0419339i	−0.00415788	−	0.00555428i
$58$	4.00264	−	8.66603i	0.525573	−	1.13790i
$59$	−1.16631	−	0.749541i	−0.151840	−	0.0975820i	0.462514	−	0.886612i	$-0.346947\pi$
$59$	−1.16631	−	0.749541i	−0.151840	−	0.0975820i	−0.614355	+	0.789030i	$0.710584\pi$
$60$	3.80459	+	9.86451i	0.491171	+	1.27350i
$61$	2.81542	+	6.16491i	0.360477	+	0.789335i	0.999792	+	0.0203902i	$0.00649086\pi$
$61$	2.81542	+	6.16491i	0.360477	+	0.789335i	−0.639315	+	0.768945i	$0.720782\pi$
$62$	−8.71067	+	2.51716i	−1.10626	+	0.319680i
$63$	4.79974	−	2.62085i	0.604710	−	0.330197i
$64$	5.08160	+	6.17878i	0.635200	+	0.772347i
$65$	−2.81333	−	4.91950i	−0.348951	−	0.610189i
$66$	0.317448	+	4.72305i	0.0390751	+	0.581367i
$67$	−5.90829	+	7.89254i	−0.721812	+	0.964228i	0.278181	+	0.960529i	$0.410268\pi$
$67$	−5.90829	+	7.89254i	−0.721812	+	0.964228i	−0.999993	+	0.00369921i	$0.998823\pi$
$68$	−12.5392	+	2.61531i	−1.52060	+	0.317153i
$69$	−3.94058	−	10.6312i	−0.474390	−	1.27985i
$70$	−6.66867	−	0.373872i	−0.797058	−	0.0446862i
$71$	−11.7241	+	1.68567i	−1.39139	+	0.200052i	−0.796931	−	0.604071i	$-0.793544\pi$
$71$	−11.7241	+	1.68567i	−1.39139	+	0.200052i	−0.594463	+	0.804123i	$0.702635\pi$
$72$	7.05261	−	1.97264i	0.831158	−	0.232478i
$73$	8.87718	+	4.84731i	1.03899	+	0.567334i	0.905778	−	0.423753i	$-0.139287\pi$
$73$	8.87718	+	4.84731i	1.03899	+	0.567334i	0.133217	+	0.991087i	$0.457469\pi$
$74$	−8.29393	−	1.84152i	−0.964150	−	0.214072i
$75$	−9.73443	−	6.70598i	−1.12404	−	0.774340i
$76$	0.0443120		0.000380063i	0.00508294		4.35962e-5i
$77$	−2.80188	−	1.04505i	−0.319304	−	0.119094i
$78$	−7.72286	+	3.48696i	−0.874441	+	0.394821i
$79$	−4.54914	−	2.92356i	−0.511819	−	0.328926i	0.259110	−	0.965848i	$-0.416571\pi$
$79$	−4.54914	−	2.92356i	−0.511819	−	0.328926i	−0.770928	+	0.636922i	$0.780207\pi$
$80$	−8.58831	−	2.49818i	−0.960203	−	0.279305i
$81$	−1.43221	+	9.96127i	−0.159135	+	1.10681i
$82$	4.53953	−	3.89957i	0.501308	−	0.430636i
$83$	−5.37776	−	0.384625i	−0.590286	−	0.0422181i	−0.226998	−	0.973895i	$-0.572891\pi$
$83$	−5.37776	−	0.384625i	−0.590286	−	0.0422181i	−0.363288	+	0.931677i	$0.618346\pi$
$84$	−1.50599	+	9.87255i	−0.164317	+	1.07718i
$85$	9.92518	−	10.3238i	1.07654	−	1.11977i
$86$	−2.46604	−	11.5750i	−0.265920	−	1.24816i
$87$	15.9170	−	1.13840i	1.70648	−	0.122050i
$88$	−3.34074	−	2.20820i	−0.356124	−	0.235395i
$89$	−9.58899	−	4.37915i	−1.01643	−	0.464189i	−0.163684	−	0.986513i	$-0.552338\pi$
$89$	−9.58899	−	4.37915i	−1.01643	−	0.464189i	−0.852747	+	0.522324i	$0.825065\pi$
$90$	−5.26591	+	6.26965i	−0.555075	+	0.660879i
$91$		−	5.35301i		−	0.561148i
$92$	9.17393	+	2.79982i	0.956448	+	0.291901i
$93$	−10.7179	−	10.7179i	−1.11140	−	1.11140i
$94$	0.578636	+	0.779917i	0.0596818	+	0.0804423i
$95$	−0.0411439	+	0.0276007i	−0.00422128	+	0.00283177i
$96$	−4.94118	+	12.4273i	−0.504307	+	1.26836i
$97$	−0.185165	−	2.58895i	−0.0188007	−	0.262868i	−0.998155	−	0.0607169i	$-0.980661\pi$
$97$	−0.185165	−	2.58895i	−0.0188007	−	0.262868i	0.979354	−	0.202151i	$-0.0647932\pi$
$98$	3.01222	+	1.95414i	0.304280	+	0.197398i
$99$	−3.08390	+	1.98190i	−0.309944	+	0.199189i
$100$	9.50365	−	3.11136i	0.950365	−	0.311136i
$101$	2.52570	+	2.91481i	0.251316	+	0.290034i	0.867364	−	0.497675i	$-0.165813\pi$
$101$	2.52570	+	2.91481i	0.251316	+	0.290034i	−0.616048	+	0.787709i	$0.711267\pi$
$102$	−13.9530	−	16.2428i	−1.38155	−	1.60828i
$103$	0.469057	+	0.626586i	0.0462175	+	0.0617394i	0.823055	−	0.567962i	$-0.192268\pi$
$103$	0.469057	+	0.626586i	0.0462175	+	0.0617394i	−0.776837	+	0.629702i	$0.783177\pi$
$104$	1.61374	−	6.98441i	0.158240	−	0.684877i
$105$	−4.83733	−	10.0633i	−0.472075	−	0.982074i
$106$	−13.1041	−	4.95171i	−1.27279	−	0.480953i
$107$	−5.03998	+	13.5127i	−0.487233	+	1.30632i	0.428139	+	0.903713i	$0.359169\pi$
$107$	−5.03998	+	13.5127i	−0.487233	+	1.30632i	−0.915372	+	0.402609i	$0.868103\pi$
$108$	−1.36172	−	1.38529i	−0.131032	−	0.133299i
$109$	−4.29017	+	14.6110i	−0.410924	+	1.39948i	0.451038	+	0.892505i	$0.351054\pi$
$109$	−4.29017	+	14.6110i	−0.410924	+	1.39948i	−0.861962	+	0.506973i	$0.830764\pi$
$110$	4.47673	−	0.0689227i	0.426840	−	0.00657152i
$111$	−4.00134	−	13.6273i	−0.379791	−	1.29345i
$112$	−5.87065	−	6.07559i	−0.554725	−	0.574090i
$113$	4.61498	−	6.16489i	0.434141	−	0.579944i	−0.529108	−	0.848554i	$-0.677473\pi$
$113$	4.61498	−	6.16489i	0.434141	−	0.579944i	0.963249	+	0.268610i	$0.0865643\pi$
$114$	0.0352232	+	0.0651694i	0.00329896	+	0.00610367i
$115$	−10.2345	+	3.20232i	−0.954373	+	0.298618i
$116$	−7.39563	+	11.2937i	−0.686667	+	1.04859i
$117$	−5.25319	−	3.93249i	−0.485657	−	0.363558i
$118$	1.47625	+	1.29030i	0.135899	+	0.118782i
$119$	12.9792	−	3.81105i	1.18981	−	0.349358i
$120$	−3.27785	−	14.5884i	−0.299225	−	1.33174i
$121$	−8.63103	−	2.53430i	−0.784639	−	0.230391i
$122$	−2.66084	−	9.20789i	−0.240901	−	0.833643i
$123$	9.37350	+	3.49613i	0.845180	+	0.315236i
$124$	12.7075	−	1.71595i	1.14116	−	0.154097i
$125$	−6.81016	+	8.86689i	−0.609119	+	0.793079i
$126$	−7.25777	+	2.67161i	−0.646573	+	0.238006i
$127$	−3.78082	+	2.83028i	−0.335493	+	0.251147i	−0.753720	−	0.657195i	$-0.771743\pi$
$127$	−3.78082	+	2.83028i	−0.335493	+	0.251147i	0.418227	+	0.908343i	$0.362652\pi$
$128$	−5.82823	−	9.69700i	−0.515148	−	0.857101i
$129$	14.9519	−	12.9559i	1.31644	−	1.14070i
$130$	2.91605	+	7.46520i	0.255755	+	0.654741i
$131$	−3.02619	−	4.70884i	−0.264399	−	0.411413i	0.683516	−	0.729935i	$-0.260450\pi$
$131$	−3.02619	−	4.70884i	−0.264399	−	0.411413i	−0.947915	+	0.318522i	$0.896813\pi$
$132$	0.534831	−	6.67307i	0.0465510	−	0.580817i
$133$	−0.0466788	+	0.00333854i	−0.00404757	+	0.000289488i
$134$	9.90120	−	9.81664i	0.855333	−	0.848029i
$135$	2.13082	+	0.419789i	0.183392	+	0.0361297i
$136$	18.0837	−	1.05974i	1.55067	−	0.0908716i
$137$	−8.54455	+	8.54455i	−0.730010	+	0.730010i	−0.970621	−	0.240612i	$-0.922652\pi$
$137$	−8.54455	+	8.54455i	−0.730010	+	0.730010i	0.240612	+	0.970621i	$0.422652\pi$
$138$	3.30917	+	15.6892i	0.281695	+	1.33555i
$139$	−19.3111			−1.63794			−0.818972	−	0.573834i	$-0.805455\pi$
$139$	−19.3111			−1.63794			−0.818972	+	0.573834i	$0.805455\pi$
$140$	9.25159	+	1.90520i	0.781902	+	0.161019i
$141$	−0.674400	+	1.47673i	−0.0567947	+	0.124363i
$142$	16.7507	+	0.0718338i	1.40569	+	0.00602816i
$143$	0.255987	+	3.57917i	0.0214067	+	0.299305i
$144$	−10.2751	+	1.29786i	−0.856255	+	0.108155i
$145$	−0.297058	−	15.0902i	−0.0246693	−	1.25317i
$146$	−11.4140	−	8.62103i	−0.944628	−	0.713481i
$147$	−0.428203	+	5.98706i	−0.0353176	+	0.493804i
$148$	11.2211	+	4.29522i	0.922365	+	0.353065i
$149$	13.4727	+	1.93708i	1.10373	+	0.158692i	0.670006	−	0.742356i	$-0.266291\pi$
$149$	13.4727	+	1.93708i	1.10373	+	0.158692i	0.433720	+	0.901048i	$0.357201\pi$
$150$	12.2280	+	11.3989i	0.998412	+	0.930715i
$151$	8.18153	−	12.7307i	0.665803	−	1.03601i	−0.329955	−	0.943997i	$-0.607033\pi$
$151$	8.18153	−	12.7307i	0.665803	−	1.03601i	0.995758	−	0.0920133i	$-0.0293302\pi$
$152$	−0.0619112	−	0.00971600i	−0.00502166	−	0.000788072i
$153$	5.79497	−	15.5369i	0.468495	−	1.25608i
$154$	3.70307	+	2.04269i	0.298402	+	0.164605i
$155$	−10.6478	+	9.59971i	−0.855251	+	0.771067i
$156$	11.5266	−	3.27739i	0.922863	−	0.262401i
$157$	0.755572	−	1.38373i	0.0603012	−	0.110433i	−0.845790	−	0.533516i	$-0.820870\pi$
$157$	0.755572	−	1.38373i	0.0603012	−	0.110433i	0.906091	+	0.423083i	$0.139052\pi$
$158$	5.75804	+	5.03277i	0.458085	+	0.400385i
$159$	−3.33273	−	23.1797i	−0.264303	−	1.83827i
$160$	11.4968	+	5.27486i	0.908900	+	0.417014i
$161$	−9.89352	−	2.17333i	−0.779718	−	0.171282i
$162$	4.06820	−	13.6384i	0.319628	−	1.07153i
$163$	−15.1649	−	11.3523i	−1.18781	−	0.889184i	−0.192069	−	0.981381i	$-0.561520\pi$
$163$	−15.1649	−	11.3523i	−1.18781	−	0.889184i	−0.995741	+	0.0921977i	$0.970611\pi$
$164$	−7.15879	+	4.51439i	−0.559008	+	0.352515i
$165$	3.71561	+	6.49725i	0.289260	+	0.505810i
$166$	7.44346	+	1.65269i	0.577725	+	0.128274i
$167$	4.32699	+	7.92428i	0.334832	+	0.613199i	0.989801	−	0.142456i	$-0.0455001\pi$
$167$	4.32699	+	7.92428i	0.334832	+	0.613199i	−0.654969	+	0.755656i	$0.727318\pi$
$168$	4.15303	−	13.4990i	0.320413	−	1.04147i
$169$	5.98241	−	2.73208i	0.460186	−	0.210160i
$170$	−16.0245	+	12.3853i	−1.22902	+	0.949906i
$171$	−0.0310154	+	0.0482609i	−0.00237181	+	0.00369061i
$172$	1.05077	+	16.7038i	0.0801203	+	1.27365i
$173$	−13.9536	+	10.4455i	−1.06087	+	0.794158i	−0.979281	−	0.202508i	$-0.935091\pi$
$173$	−13.9536	+	10.4455i	−1.06087	+	0.794158i	−0.0815902	+	0.996666i	$0.526000\pi$
$174$	−22.5029	−	1.70646i	−1.70594	−	0.129367i
$175$	−9.74188	+	4.07712i	−0.736417	+	0.308202i
$176$	4.21582	+	3.78157i	0.317780	+	0.285046i
$177$	−0.696711	+	3.20273i	−0.0523680	+	0.240732i
$178$	12.5068	+	8.11364i	0.937425	+	0.608143i
$179$	1.47652	−	1.70399i	0.110360	−	0.127362i	−0.697882	−	0.716213i	$-0.745874\pi$
$179$	1.47652	−	1.70399i	0.110360	−	0.127362i	0.808242	+	0.588851i	$0.200419\pi$
$180$	8.66618	−	7.67944i	0.645939	−	0.572392i
$181$	−7.60027	+	16.6423i	−0.564923	+	1.23701i	0.384533	+	0.923111i	$0.374362\pi$
$181$	−7.60027	+	16.6423i	−0.564923	+	1.23701i	−0.949457	+	0.313898i	$0.898365\pi$
$182$	−1.10949	+	7.48856i	−0.0822409	+	0.555089i
$183$	11.3297	−	11.3297i	0.837518	−	0.837518i
$184$	−12.2535	−	5.81822i	−0.903340	−	0.428925i
$185$	−13.0675	+	3.11323i	−0.960740	+	0.228889i
$186$	12.7723	+	17.2152i	0.936513	+	1.26228i
$187$	−8.49603	+	3.16886i	−0.621291	+	0.231730i
$188$	−0.647830	−	1.21099i	−0.0472479	−	0.0883205i
$189$	1.55035	+	1.34339i	0.112771	+	0.0977169i
$190$	0.0632787	−	0.0300841i	0.00459072	−	0.00218253i
$191$	6.80357	+	10.5866i	0.492289	+	0.766016i	0.995152	−	0.0983497i	$-0.0313564\pi$
$191$	6.80357	+	10.5866i	0.492289	+	0.766016i	−0.502863	+	0.864366i	$0.667720\pi$
$192$	9.48817	−	16.3610i	0.684750	−	1.18075i
$193$	−1.08150	+	15.1213i	−0.0778478	+	1.08845i	0.796975	+	0.604012i	$0.206432\pi$
$193$	−1.08150	+	15.1213i	−0.0778478	+	1.08845i	−0.874823	+	0.484443i	$0.839022\pi$
$194$	−0.277562	+	3.66017i	−0.0199278	+	0.262785i
$195$	−8.57277	+	10.2962i	−0.613909	+	0.737324i
$196$	−3.80890	−	3.35806i	−0.272064	−	0.239861i
$197$	10.2314	−	2.22571i	0.728958	−	0.158575i	0.167254	−	0.985914i	$-0.446510\pi$
$197$	10.2314	−	2.22571i	0.728958	−	0.158575i	0.561703	+	0.827339i	$0.310146\pi$
$198$	4.72498	−	2.13339i	0.335790	−	0.151613i
$199$	9.16384	+	20.0660i	0.649607	+	1.42244i	0.891898	+	0.452238i	$0.149374\pi$
$199$	9.16384	+	20.0660i	0.649607	+	1.42244i	−0.242290	+	0.970204i	$0.577899\pi$
$200$	−13.9399	+	2.38285i	−0.985703	+	0.168493i
$201$	22.3640	+	6.56666i	1.57743	+	0.463176i
$202$	−2.92917	−	4.60114i	−0.206096	−	0.323735i
$203$	6.83245	−	12.5127i	0.479544	−	0.878219i
$204$	16.1528	+	25.6147i	1.13092	+	1.79339i
$205$	3.76061	−	8.68290i	0.262653	−	0.606440i
$206$	−0.526314	−	0.973777i	−0.0366700	−	0.0678463i
$207$	−9.40088	+	8.11242i	−0.653406	+	0.563853i
$208$	−3.70515	+	9.43631i	−0.256906	+	0.654291i
$209$	0.0310511	−	0.00446447i	0.00214785	−	0.000308814i
$210$	4.68138	+	15.0805i	0.323046	+	1.04066i
$211$	1.79828	+	6.12437i	0.123798	+	0.421619i	0.997947	−	0.0640391i	$-0.0203982\pi$
$211$	1.79828	+	6.12437i	0.123798	+	0.421619i	−0.874149	+	0.485658i	$0.838580\pi$
$212$	17.3056	+	9.64318i	1.18856	+	0.662297i
$213$	13.4202	+	24.5772i	0.919534	+	1.68400i
$214$	9.85135	−	17.8589i	0.673424	−	1.22081i
$215$	−11.5066	−	14.7564i	−0.784741	−	1.00638i
$216$	1.61785	+	2.22017i	0.110081	+	0.151064i
$217$	−13.2322	+	2.87849i	−0.898261	+	0.195405i
$218$	9.03004	−	19.5507i	0.611592	−	1.32414i
$219$	3.40301	−	23.6685i	0.229954	−	1.59937i
$220$	−6.27698	−	0.831449i	−0.423194	−	0.0560563i
$221$	−10.6295	−	12.2671i	−0.715019	−	0.825176i
$222$	2.77319	+	19.8932i	0.186124	+	1.33514i
$223$	4.85262	−	22.3071i	0.324955	−	1.49380i	−0.467570	−	0.883956i	$-0.654870\pi$
$223$	4.85262	−	22.3071i	0.324955	−	1.49380i	0.792525	−	0.609839i	$-0.208766\pi$
$224$	6.95345	+	9.71619i	0.464597	+	0.649190i
$225$	−3.15559	+	12.5554i	−0.210373	+	0.837026i
$226$	−7.73386	+	7.66781i	−0.514449	+	0.510055i
$227$	8.85193	−	3.30160i	0.587523	−	0.219135i	−0.0380821	−	0.999275i	$-0.512125\pi$
$227$	8.85193	−	3.30160i	0.587523	−	0.219135i	0.625605	+	0.780140i	$0.284852\pi$
$228$	−0.0357680	−	0.0984688i	−0.00236879	−	0.00652126i
$229$			1.03594i			0.0684566i	0.999414	+	0.0342283i	$0.0108973\pi$
$229$			1.03594i			0.0684566i	−0.999414	+	0.0342283i	$0.989103\pi$
$230$	14.9812	−	2.35861i	0.987832	−	0.155522i
$231$			7.06980i			0.465158i
$232$	12.6868	−	14.2663i	0.832932	−	0.936632i
$233$	20.8123	−	7.76259i	1.36346	−	0.508544i	0.441999	−	0.897016i	$-0.354270\pi$
$233$	20.8123	−	7.76259i	1.36346	−	0.508544i	0.921461	+	0.388472i	$0.126997\pi$
$234$	6.53384	+	6.59012i	0.427131	+	0.430810i
$235$	1.36189	+	0.709215i	0.0888398	+	0.0462641i
$236$	−1.79775	−	2.11103i	−0.117024	−	0.137416i
$237$	−2.71750	+	12.4921i	−0.176520	+	0.811451i
$238$	−18.9471	+	2.64130i	−1.22816	+	0.171210i
$239$	2.18786	+	2.52493i	0.141521	+	0.163324i	0.822085	−	0.569364i	$-0.192811\pi$
$239$	2.18786	+	2.52493i	0.141521	+	0.163324i	−0.680564	+	0.732689i	$0.738265\pi$
$240$	1.56185	+	21.0878i	0.100817	+	1.36121i
$241$	1.99659	−	13.8866i	0.128612	−	0.894514i	−0.818705	−	0.574215i	$-0.805307\pi$
$241$	1.99659	−	13.8866i	0.128612	−	0.894514i	0.947316	−	0.320299i	$-0.103783\pi$
$242$	11.5491	+	5.33425i	0.742401	+	0.342899i
$243$	20.4011	−	4.43800i	1.30873	−	0.284698i
$244$	1.81390	+	13.4328i	0.116123	+	0.859948i
$245$	5.63421	+	0.697191i	0.359956	+	0.0445419i
$246$	−12.3884	−	6.83369i	−0.789853	−	0.435700i
$247$	0.0269120	+	0.0492857i	0.00171237	+	0.00313597i
$248$	−18.1327	−	0.233292i	−1.15142	−	0.0148140i
$249$	3.59104	+	12.2300i	0.227573	+	0.775042i
$250$	11.3648	−	10.9928i	0.718774	−	0.695244i
$251$	8.37253	−	1.20379i	0.528469	−	0.0759824i	0.127084	−	0.991892i	$-0.459438\pi$
$251$	8.37253	−	1.20379i	0.528469	−	0.0759824i	0.401385	+	0.915909i	$0.368529\pi$
$252$	10.7069	−	2.23315i	0.674473	−	0.140675i
$253$	6.71901	+	0.980027i	0.422420	+	0.0616138i
$254$	5.87576	−	3.17578i	0.368678	−	0.199266i
$255$	−31.0681	−	13.4558i	−1.94556	−	0.842632i
$256$	6.14352	+	14.7735i	0.383970	+	0.923346i
$257$	8.60531	−	15.7594i	0.536785	−	0.983047i	−0.458742	−	0.888569i	$-0.651700\pi$
$257$	8.60531	−	15.7594i	0.536785	−	0.983047i	0.995527	−	0.0944781i	$-0.0301182\pi$
$258$	−23.6021	+	15.0255i	−1.46940	+	0.935448i
$259$	−12.1747	−	3.57480i	−0.756497	−	0.222128i
$260$	−2.53212	−	11.0478i	−0.157035	−	0.685155i
$261$	−7.26003	−	15.8972i	−0.449384	−	0.984014i
$262$	3.25749	+	7.21462i	0.201248	+	0.445721i
$263$	−24.7830	+	5.39121i	−1.52819	+	0.332436i	−0.896590	−	0.442862i	$-0.853963\pi$
$263$	−24.7830	+	5.39121i	−1.52819	+	0.332436i	−0.631595	+	0.775298i	$0.717600\pi$
$264$	−2.13129	+	9.22440i	−0.131172	+	0.567723i
$265$	−22.0576	+	2.01464i	−1.35499	+	0.123758i
$266$	0.0659930	+	0.00500445i	0.00404629	+	0.000306843i
$267$	−1.77791	+	24.8584i	−0.108806	+	1.52131i
$268$	−15.8859	+	11.6808i	−0.970383	+	0.713516i
$269$	12.5788	+	19.5730i	0.766943	+	1.19339i	0.976485	+	0.215586i	$0.0691663\pi$
$269$	12.5788	+	19.5730i	0.766943	+	1.19339i	−0.209542	+	0.977800i	$0.567197\pi$
$270$	−2.89390	−	1.02891i	−0.176117	−	0.0626172i
$271$	−18.1079	−	15.6906i	−1.09998	−	0.953136i	−0.100850	−	0.994902i	$-0.532156\pi$
$271$	−18.1079	−	15.6906i	−1.09998	−	0.953136i	−0.999127	+	0.0417653i	$0.986702\pi$
$272$	−25.5177	−	2.26561i	−1.54724	−	0.137373i
$273$	−11.8574	+	4.42257i	−0.717641	+	0.267666i
$274$	13.7243	−	10.1823i	0.829116	−	0.615138i
$275$	6.31872	−	3.19195i	0.381033	−	0.192482i
$276$	−1.37752	−	22.6342i	−0.0829170	−	1.36242i
$277$	18.6553	−	18.6553i	1.12089	−	1.12089i	0.129281	−	0.991608i	$-0.458733\pi$
$277$	18.6553	−	18.6553i	1.12089	−	1.12089i	0.991608	−	0.129281i	$-0.0412670\pi$
$278$	27.0151	+	4.00250i	1.62026	+	0.240054i
$279$	−6.89598	+	15.1001i	−0.412851	+	0.904018i
$280$	−12.5476	−	4.58280i	−0.749861	−	0.273875i
$281$	20.5734	−	23.7430i	1.22731	−	1.41639i	0.349801	−	0.936824i	$-0.386249\pi$
$281$	20.5734	−	23.7430i	1.22731	−	1.41639i	0.877506	−	0.479565i	$-0.159205\pi$
$282$	1.24952	−	1.92608i	0.0744079	−	0.114697i
$283$	−3.61504	+	16.6181i	−0.214892	+	0.987841i	0.735679	+	0.677331i	$0.236863\pi$
$283$	−3.61504	+	16.6181i	−0.214892	+	0.987841i	−0.950570	+	0.310510i	$0.899500\pi$
$284$	−23.4184	−	3.57232i	−1.38963	−	0.211978i
$285$	0.0951303	+	0.0683340i	0.00563504	+	0.00404776i
$286$	0.383724	−	5.06011i	0.0226901	−	0.299211i
$287$	7.15510	−	5.35624i	0.422352	−	0.316169i
$288$	14.6432	+	0.314026i	0.862860	+	0.0185042i
$289$	12.9851	−	20.2052i	0.763829	−	1.18854i
$290$	−2.71210	+	21.1719i	−0.159260	+	1.24326i
$291$	−5.58176	+	2.54910i	−0.327209	+	0.149431i
$292$	14.1807	+	14.4260i	0.829862	+	0.844220i
$293$	−5.40990	−	9.90750i	−0.316050	−	0.578802i	0.670569	−	0.741847i	$-0.266050\pi$
$293$	−5.40990	−	9.90750i	−0.316050	−	0.578802i	−0.986619	+	0.163045i	$0.947868\pi$
$294$	1.83994	−	8.28680i	0.107307	−	0.483296i
$295$	2.99111	+	0.814679i	0.174149	+	0.0474324i
$296$	−14.8074	−	8.33449i	−0.860661	−	0.484433i
$297$	−1.10085	−	0.824085i	−0.0638777	−	0.0478183i
$298$	−18.4460	−	5.50228i	−1.06855	−	0.318739i
$299$	2.55944	+	11.8821i	0.148016	+	0.687159i
$300$	−14.7437	−	18.4808i	−0.851227	−	1.06699i
$301$	−2.51544	−	17.4953i	−0.144988	−	1.00841i
$302$	−14.0841	+	16.1138i	−0.810450	+	0.927244i
$303$	4.36986	−	8.00279i	0.251042	−	0.459748i
$304$	0.0845965	+	0.0264241i	0.00485194	+	0.00151553i
$305$	−10.1477	−	11.2556i	−0.581054	−	0.644492i
$306$	−11.3271	+	20.5342i	−0.647526	+	1.17386i
$307$	1.65516	−	4.43766i	0.0944650	−	0.253270i	−0.881120	−	0.472893i	$-0.843210\pi$
$307$	1.65516	−	4.43766i	0.0944650	−	0.253270i	0.975585	+	0.219622i	$0.0704825\pi$
$308$	−4.75700	−	3.62512i	−0.271055	−	0.206561i
$309$	1.00041	−	1.55667i	0.0569116	−	0.0885561i
$310$	16.8853	−	11.2225i	0.959022	−	0.637397i
$311$	23.1775	+	3.33242i	1.31428	+	0.188964i	0.763565	−	0.645731i	$-0.223447\pi$
$311$	23.1775	+	3.33242i	1.31428	+	0.188964i	0.550712	+	0.834695i	$0.314356\pi$
$312$	−16.8043	+	2.19583i	−0.951355	+	0.124314i
$313$	−2.10534	+	29.4365i	−0.119001	+	1.66385i	0.490784	+	0.871281i	$0.336710\pi$
$313$	−2.10534	+	29.4365i	−0.119001	+	1.66385i	−0.609785	+	0.792567i	$0.708744\pi$
$314$	−1.34380	+	1.77915i	−0.0758351	+	0.100403i
$315$	−8.47487	+	8.81523i	−0.477505	+	0.496682i
$316$	−7.01206	−	8.23399i	−0.394459	−	0.463198i
$317$	−0.369436	−	5.16540i	−0.0207496	−	0.290117i	−0.997223	−	0.0744780i	$-0.976271\pi$
$317$	−0.369436	−	5.16540i	−0.0207496	−	0.290117i	0.976473	−	0.215640i	$-0.0691836\pi$
$318$	−0.142022	+	33.1178i	−0.00796423	+	1.85715i
$319$	−3.96999	+	8.69307i	−0.222277	+	0.486718i
$320$	−14.9900	−	9.76210i	−0.837969	−	0.545718i
$321$	34.0957			1.90304
$322$	13.3900	+	5.09094i	0.746196	+	0.283707i
$323$	−0.100341	+	0.100341i	−0.00558314	+	0.00558314i
$324$	−8.51794	+	18.2361i	−0.473219	+	1.01312i
$325$	9.30622	+	8.60092i	0.516216	+	0.477093i
$326$	18.8620	+	19.0244i	1.04467	+	1.05367i
$327$	35.9090	−	2.56826i	1.98577	−	0.142025i
$328$	10.9504	−	4.83161i	0.604636	−	0.266781i
$329$	0.784135	+	1.22014i	0.0432308	+	0.0672684i
$330$	−3.85127	−	9.85939i	−0.212006	−	0.542742i
$331$	16.9078	−	14.6507i	0.929339	−	0.805277i	−0.0517847	−	0.998658i	$-0.516491\pi$
$331$	16.9078	−	14.6507i	0.929339	−	0.805277i	0.981124	+	0.193381i	$0.0619455\pi$
$332$	−10.0704	−	3.85478i	−0.552687	−	0.211559i
$333$	−12.4520	+	9.32147i	−0.682367	+	0.510813i
$334$	−4.41078	−	11.9825i	−0.241347	−	0.655651i
$335$	7.29606	−	20.8031i	0.398626	−	1.13659i
$336$	−8.60771	+	18.0235i	−0.469589	+	0.983265i
$337$	−17.6196	−	6.57179i	−0.959803	−	0.357988i	−0.179758	−	0.983711i	$-0.557531\pi$
$337$	−17.6196	−	6.57179i	−0.959803	−	0.357988i	−0.780046	+	0.625723i	$0.784804\pi$
$338$	−8.93532	+	2.58208i	−0.486017	+	0.140446i
$339$	−17.4686	−	5.12924i	−0.948763	−	0.278582i
$340$	24.9844	−	14.0050i	1.35497	−	0.759525i
$341$	8.70977	−	2.55742i	0.471661	−	0.138492i
$342$	0.0533916	−	0.0610859i	0.00288709	−	0.00330315i
$343$	16.1288	+	12.0739i	0.870875	+	0.651929i
$344$	1.99215	−	23.5855i	0.107409	−	1.27164i
$345$	15.5490	+	20.0246i	0.837130	+	1.07809i
$346$	21.6852	−	11.7206i	1.16581	−	0.630103i
$347$	2.03891	−	2.72366i	0.109454	−	0.146214i	−0.742469	−	0.669880i	$-0.766345\pi$
$347$	2.03891	−	2.72366i	0.109454	−	0.146214i	0.851923	+	0.523667i	$0.175436\pi$
$348$	31.1266	+	7.05130i	1.66856	+	0.377989i
$349$	−1.55095	−	5.28206i	−0.0830206	−	0.282742i	0.907511	−	0.420029i	$-0.137980\pi$
$349$	−1.55095	−	5.28206i	−0.0830206	−	0.282742i	−0.990531	+	0.137287i	$0.956162\pi$
$350$	14.4734	−	3.68452i	0.773635	−	0.196946i
$351$	0.693499	−	2.36184i	0.0370163	−	0.126066i
$352$	−5.11391	−	6.16399i	−0.272572	−	0.328542i
$353$	0.333136	−	0.893172i	0.0177310	−	0.0475387i	−0.927783	−	0.373121i	$-0.878288\pi$
$353$	0.333136	−	0.893172i	0.0177310	−	0.0475387i	0.945514	+	0.325582i	$0.105560\pi$
$354$	1.63847	−	4.33603i	0.0870838	−	0.230458i
$355$	23.8708	−	11.4745i	1.26693	−	0.609003i
$356$	−15.8146	−	13.9427i	−0.838175	−	0.738963i
$357$	−19.1650	−	25.6015i	−1.01432	−	1.35497i
$358$	−2.41874	+	2.07776i	−0.127834	+	0.109813i
$359$	9.64440	+	11.1302i	0.509012	+	0.587431i	0.950845	−	0.309666i	$-0.100217\pi$
$359$	9.64440	+	11.1302i	0.509012	+	0.587431i	−0.441833	+	0.897097i	$0.645672\pi$
$360$	−13.7152	+	8.94691i	−0.722853	+	0.471544i
$361$	−15.9834	+	10.2719i	−0.841232	+	0.540627i
$362$	14.0817	−	21.7063i	0.740117	−	1.14086i
$363$	1.51713	+	21.2123i	0.0796287	+	1.11335i
$364$	3.10423	−	10.2461i	0.162706	−	0.537042i
$365$	−22.1899	−	4.37158i	−1.16147	−	0.228819i
$366$	−18.1979	+	13.5014i	−0.951220	+	0.705729i
$367$	10.3925	+	10.3925i	0.542483	+	0.542483i	0.924256	−	0.381773i	$-0.124687\pi$
$367$	10.3925	+	10.3925i	0.542483	+	0.542483i	−0.381773	+	0.924256i	$0.624687\pi$
$368$	15.9360	+	10.6791i	0.830724	+	0.556685i
$369$		−	10.9565i		−	0.570374i
$370$	18.9259	−	1.64680i	0.983912	−	0.0856131i
$371$	−19.0310	−	8.69119i	−0.988043	−	0.451224i
$372$	−14.2997	−	26.7304i	−0.741403	−	1.38591i
$373$	−26.2158	+	1.87499i	−1.35740	+	0.0970832i	−0.730978	−	0.682401i	$-0.760936\pi$
$373$	−26.2158	+	1.87499i	−1.35740	+	0.0970832i	−0.626422	+	0.779484i	$0.715481\pi$
$374$	12.5423	−	2.67212i	0.648544	−	0.138172i
$375$	25.2673	+	7.75940i	1.30480	+	0.400694i
$376$	0.655282	+	1.82838i	0.0337936	+	0.0942914i
$377$	−17.0634	−	1.22040i	−0.878808	−	0.0628536i
$378$	−1.89041	−	2.20065i	−0.0972324	−	0.113189i
$379$	−0.824399	+	5.73382i	−0.0423466	+	0.294527i	0.957632	+	0.287994i	$0.0929884\pi$
$379$	−0.824399	+	5.73382i	−0.0423466	+	0.294527i	−0.999979	+	0.00653241i	$0.997921\pi$
$380$	−0.0947586	+	0.0289706i	−0.00486102	+	0.00148616i
$381$	9.39296	+	6.03649i	0.481216	+	0.309259i
$382$	−7.32358	−	16.2201i	−0.374707	−	0.829894i
$383$	−22.3434	−	8.33367i	−1.14170	−	0.425831i	−0.293734	−	0.955887i	$-0.594898\pi$
$383$	−22.3434	−	8.33367i	−1.14170	−	0.425831i	−0.847962	+	0.530056i	$0.822171\pi$
$384$	−16.6645	+	20.9215i	−0.850405	+	1.06765i
$385$	6.67785	+	0.345666i	0.340335	+	0.0176168i
$386$	4.64706	−	20.9297i	0.236529	−	1.06529i
$387$	−19.0169	−	10.3840i	−0.966685	−	0.527850i
$388$	1.14692	−	5.06284i	0.0582259	−	0.257027i
$389$	23.8304	−	3.42630i	1.20825	−	0.173720i	0.491392	−	0.870939i	$-0.336488\pi$
$389$	23.8304	−	3.42630i	1.20825	−	0.173720i	0.716859	+	0.697218i	$0.245579\pi$
$390$	14.1268	−	12.6269i	0.715341	−	0.639389i
$391$	−26.9879	+	14.6652i	−1.36484	+	0.741650i
$392$	4.63243	+	5.48718i	0.233973	+	0.277145i
$393$	−7.93028	+	10.5936i	−0.400030	+	0.534377i
$394$	−14.7745	+	0.993028i	−0.744327	+	0.0500280i
$395$	11.6667	+	3.17762i	0.587016	+	0.159884i
$396$	−7.05216	+	2.00516i	−0.354384	+	0.100763i
$397$	−16.3367	+	8.92052i	−0.819916	+	0.447708i	−0.833714	−	0.552197i	$-0.813790\pi$
$397$	−16.3367	+	8.92052i	−0.819916	+	0.447708i	0.0137976	+	0.999905i	$0.495608\pi$
$398$	−8.66071	−	29.9705i	−0.434122	−	1.50229i
$399$	0.0459604	+	0.100639i	0.00230090	+	0.00503826i
$400$	19.9951	−	0.444210i	0.999753	−	0.0222105i
$401$	−5.86759	−	3.77087i	−0.293013	−	0.188308i	0.385872	−	0.922552i	$-0.373900\pi$
$401$	−5.86759	−	3.77087i	−0.293013	−	0.188308i	−0.678886	+	0.734244i	$0.737537\pi$
$402$	−29.9249	−	13.8216i	−1.49252	−	0.689361i
$403$	9.73774	+	13.0081i	0.485071	+	0.647979i
$404$	3.14409	+	7.04384i	0.156424	+	0.350444i
$405$	−3.64030	−	22.2067i	−0.180888	−	1.10346i
$406$	−12.1516	+	16.0884i	−0.603076	+	0.798455i
$407$	8.31127	+	1.80801i	0.411974	+	0.0896195i
$408$	−17.2879	−	39.1814i	−0.855877	−	1.93977i
$409$	−28.3425	−	24.5589i	−1.40144	−	1.21436i	−0.946030	−	0.324079i	$-0.894946\pi$
$409$	−28.3425	−	24.5589i	−1.40144	−	1.21436i	−0.455414	−	0.890280i	$-0.650509\pi$
$410$	−7.06054	+	11.3674i	−0.348695	+	0.561398i
$411$	25.9862	+	11.8675i	1.28181	+	0.585382i
$412$	0.534454	+	1.47135i	0.0263307	+	0.0724880i
$413$	2.07058	+	2.07058i	0.101887	+	0.101887i
$414$	14.8327	−	9.40035i	0.728988	−	0.462002i
$415$	11.7275	−	2.79399i	0.575682	−	0.137152i
$416$	7.13911	−	12.4329i	0.350024	−	0.609574i
$417$	15.9545	+	42.7756i	0.781294	+	2.09473i
$418$	−0.0443640		0.000190251i	−0.00216992		9.30548e-6i
$419$	−15.3931	+	17.7645i	−0.752000	+	0.867854i	−0.994761	−	0.102232i	$-0.967402\pi$
$419$	−15.3931	+	17.7645i	−0.752000	+	0.867854i	0.242760	+	0.970086i	$0.421947\pi$
$420$	−3.42333	−	22.0671i	−0.167041	−	1.07676i
$421$	−17.4317	+	11.2026i	−0.849567	+	0.545984i	−0.891440	−	0.453139i	$-0.850304\pi$
$421$	−17.4317	+	11.2026i	−0.849567	+	0.545984i	0.0418725	+	0.999123i	$0.486668\pi$
$422$	−1.24632	−	8.94036i	−0.0606700	−	0.435210i
$423$	1.77343	+	0.126839i	0.0862273	+	0.00616710i
$424$	−22.2109	−	17.0771i	−1.07866	−	0.829338i
$425$	−14.2288	+	28.6878i	−0.690199	+	1.39156i
$426$	−13.6800	−	37.1636i	−0.662800	−	1.80058i
$427$	−3.04280	−	13.9875i	−0.147251	−	0.676904i
$428$	−17.4830	+	22.9417i	−0.845072	+	1.10893i
$429$	7.71667	−	3.52408i	0.372564	−	0.170144i
$430$	13.0385	+	23.0283i	0.628774	+	1.11052i
$431$	3.05139	−	10.3921i	0.146980	−	0.500569i	−0.852784	−	0.522263i	$-0.825088\pi$
$431$	3.05139	−	10.3921i	0.146980	−	0.500569i	0.999765	+	0.0216940i	$0.00690595\pi$
$432$	−1.80312	−	3.44122i	−0.0867528	−	0.165566i
$433$	−2.26264	−	1.23549i	−0.108735	−	0.0593740i	0.423961	−	0.905680i	$-0.360639\pi$
$433$	−2.26264	−	1.23549i	−0.108735	−	0.0593740i	−0.532696	+	0.846306i	$0.678821\pi$
$434$	19.1077	−	1.28428i	0.917200	−	0.0616472i
$435$	−33.1807	+	13.1253i	−1.59089	+	0.629310i
$436$	−16.6847	+	25.4787i	−0.799052	+	1.22021i
$437$	0.102017	−	0.0297292i	0.00488013	−	0.00142214i
$438$	−9.66625	+	32.4055i	−0.461871	+	1.54839i
$439$	−3.29216	−	22.8975i	−0.157126	−	1.09284i	−0.903895	−	0.427754i	$-0.859305\pi$
$439$	−3.29216	−	22.8975i	−0.157126	−	1.09284i	0.746769	−	0.665084i	$-0.231604\pi$
$440$	8.60880	+	2.46415i	0.410409	+	0.117474i
$441$	6.30740	−	1.85202i	0.300353	−	0.0881915i
$442$	12.3276	+	19.3641i	0.586362	+	0.921058i
$443$	−11.8141	+	6.45097i	−0.561303	+	0.306495i	−0.734738	−	0.678350i	$-0.762695\pi$
$443$	−11.8141	+	6.45097i	−0.561303	+	0.306495i	0.173435	+	0.984845i	$0.444513\pi$
$444$	0.243622	−	28.4042i	0.0115618	−	1.34800i
$445$	23.3934	+	2.89475i	1.10895	+	0.137225i
$446$	−11.4120	+	30.2006i	−0.540374	+	1.43004i
$447$	−6.84012	−	31.4435i	−0.323527	−	1.48723i
$448$	−7.71366	−	15.0336i	−0.364436	−	0.710271i
$449$	−18.2051	−	2.61750i	−0.859152	−	0.123527i	−0.301362	−	0.953510i	$-0.597441\pi$
$449$	−18.2051	−	2.61750i	−0.859152	−	0.123527i	−0.557790	+	0.829982i	$0.688350\pi$
$450$	7.01678	−	16.9102i	0.330774	−	0.797156i
$451$	−4.52795	+	3.92349i	−0.213213	+	0.184750i
$452$	12.4085	−	9.12387i	0.583646	−	0.429151i
$453$	−34.9590	−	7.60487i	−1.64252	−	0.357308i
$454$	−13.0676	+	2.78406i	−0.613295	+	0.130662i
$455$	3.59764	+	11.4162i	0.168660	+	0.535202i
$456$	0.0296283	+	0.145166i	0.00138747	+	0.00679801i
$457$	6.12170	+	16.4129i	0.286361	+	0.767764i	0.997879	+	0.0650960i	$0.0207354\pi$
$457$	6.12170	+	16.4129i	0.286361	+	0.767764i	−0.711518	+	0.702668i	$0.751992\pi$
$458$	0.214713	−	1.44922i	0.0100329	−	0.0677174i
$459$	6.22040			0.290343
$460$	−21.4467	+	0.194490i	−0.999959	+	0.00906816i
$461$	−9.31534			−0.433859			−0.216929	−	0.976187i	$-0.569604\pi$
$461$	−9.31534			−0.433859			−0.216929	+	0.976187i	$0.569604\pi$
$462$	1.46532	−	9.89024i	0.0681728	−	0.460136i
$463$	8.69733	+	23.3185i	0.404199	+	1.08370i	0.966477	+	0.256752i	$0.0826524\pi$
$463$	8.69733	+	23.3185i	0.404199	+	1.08370i	−0.562278	+	0.826948i	$0.690075\pi$
$464$	−20.7051	+	17.3283i	−0.961209	+	0.804445i
$465$	30.0612	+	15.6546i	1.39405	+	0.725965i
$466$	−30.7241	+	6.54576i	−1.42327	+	0.303227i
$467$	−3.59872	−	0.782854i	−0.166529	−	0.0362261i	0.128528	−	0.991706i	$-0.458975\pi$
$467$	−3.59872	−	0.782854i	−0.166529	−	0.0362261i	−0.295057	+	0.955480i	$0.595339\pi$
$468$	−7.77457	−	10.5734i	−0.359380	−	0.488757i
$469$	15.7374	−	13.6365i	0.726683	−	0.629675i
$470$	−1.75821	−	1.27442i	−0.0811002	−	0.0587847i
$471$	−3.68931	−	0.530443i	−0.169995	−	0.0244415i
$472$	2.07741	+	3.32582i	0.0956205	+	0.153083i
$473$	2.51854	+	11.5775i	0.115802	+	0.532335i
$474$	6.39080	−	16.9125i	0.293539	−	0.776818i
$475$	0.0691969	−	0.0865154i	0.00317497	−	0.00396960i
$476$	27.0534	+	0.232036i	1.23999	+	0.0106354i
$477$	−22.5099	+	12.2913i	−1.03066	+	0.562782i
$478$	−2.53737	−	3.98570i	−0.116057	−	0.182302i
$479$	−7.38672	+	2.16894i	−0.337508	+	0.0991013i	−0.446095	−	0.894986i	$-0.647186\pi$
$479$	−7.38672	+	2.16894i	−0.337508	+	0.0991013i	0.108587	+	0.994087i	$0.465367\pi$
$480$	2.18581	−	29.8243i	0.0997682	−	1.36129i
$481$	2.16682	+	15.0706i	0.0987985	+	0.687158i
$482$	−5.67132	+	19.0127i	−0.258321	+	0.866006i
$483$	3.35976	+	23.7105i	0.152874	+	1.07887i
$484$	−15.0509	−	9.85602i	−0.684130	−	0.448001i
$485$	2.13487	+	5.39695i	0.0969396	+	0.245063i
$486$	−29.4599	+	1.98007i	−1.33633	+	0.0898177i
$487$	−20.6152	−	11.2568i	−0.934166	−	0.510093i	−0.0613355	−	0.998117i	$-0.519536\pi$
$487$	−20.6152	−	11.2568i	−0.934166	−	0.510093i	−0.872830	+	0.488024i	$0.837718\pi$
$488$	0.246609	−	19.1677i	0.0111634	−	0.867681i
$489$	−12.6173	+	42.9707i	−0.570576	+	1.94320i
$490$	−7.73743	−	2.14310i	−0.349541	−	0.0968155i
$491$	35.6269	−	16.2703i	1.60782	−	0.734268i	0.609534	−	0.792760i	$-0.291357\pi$
$491$	35.6269	−	16.2703i	1.60782	−	0.734268i	0.998288	+	0.0584926i	$0.0186294\pi$
$492$	15.9142	+	12.1276i	0.717469	+	0.546755i
$493$	−9.18912	−	42.2417i	−0.413857	−	1.90247i
$494$	−0.0274332	−	0.0745258i	−0.00123428	−	0.00335307i
$495$	5.24498	−	6.29939i	0.235744	−	0.283136i
$496$	25.3182	+	4.08462i	1.13682	+	0.183405i
$497$	24.9537	+	1.78472i	1.11933	+	0.0800558i
$498$	−2.48882	−	17.8533i	−0.111527	−	0.800026i
$499$	−10.8198	+	6.95345i	−0.484360	+	0.311279i	−0.759934	−	0.650001i	$-0.774769\pi$
$499$	−10.8198	+	6.95345i	−0.484360	+	0.311279i	0.275574	+	0.961280i	$0.411132\pi$
$500$	−18.1771	+	13.0227i	−0.812907	+	0.582394i
$501$	13.9781	−	16.1315i	0.624494	−	0.720704i
$502$	−11.9622	−	0.0512987i	−0.533899	−	0.00228957i
$503$	−11.7695	−	31.5553i	−0.524776	−	1.40698i	−0.881239	−	0.472670i	$-0.843290\pi$
$503$	−11.7695	−	31.5553i	−0.524776	−	1.40698i	0.356463	−	0.934309i	$-0.383983\pi$
$504$	−15.4412	+	0.904882i	−0.687808	+	0.0403067i
$505$	−7.34547	−	4.51888i	−0.326869	−	0.201088i
$506$	−9.19638	−	2.76362i	−0.408829	−	0.122858i
$507$	−10.9943	−	10.9943i	−0.488276	−	0.488276i
$508$	−8.87809	+	3.22489i	−0.393901	+	0.143081i
$509$	−6.94133	−	3.17000i	−0.307669	−	0.140508i	0.255597	−	0.966783i	$-0.417728\pi$
$509$	−6.94133	−	3.17000i	−0.307669	−	0.140508i	−0.563266	+	0.826276i	$0.690455\pi$
$510$	40.6736	+	25.2632i	1.80106	+	1.11867i
$511$	−16.1450	−	13.9897i	−0.714212	−	0.618868i
$512$	−5.53240	−	21.9407i	−0.244500	−	0.969649i
$513$	−0.0210280	−	0.00457437i	−0.000928410	−	0.000201963i
$514$	−15.3047	+	20.2630i	−0.675062	+	0.893762i
$515$	−1.42146	−	1.02106i	−0.0626371	−	0.0449934i
$516$	36.1322	−	16.1280i	1.59063	−	0.709994i
$517$	−0.582643	−	0.778320i	−0.0256246	−	0.0342305i
$518$	16.2907	+	7.52433i	0.715774	+	0.330600i
$519$	34.6659	+	22.2784i	1.52166	+	0.977914i
$520$	1.25248	+	15.9800i	0.0549247	+	0.700771i
$521$	6.57875	+	14.4055i	0.288220	+	0.631115i	0.997254	−	0.0740602i	$-0.0235957\pi$
$521$	6.57875	+	14.4055i	0.288220	+	0.631115i	−0.709033	+	0.705175i	$0.750868\pi$
$522$	6.86143	+	23.7441i	0.300316	+	1.03925i
$523$	−33.2054	+	18.1315i	−1.45197	+	0.792837i	−0.995304	−	0.0967996i	$-0.969139\pi$
$523$	−33.2054	+	18.1315i	−1.45197	+	0.792837i	−0.456669	+	0.889637i	$0.650958\pi$
$524$	−3.06170	−	10.7680i	−0.133751	−	0.470402i
$525$	17.0798	+	18.2106i	0.745422	+	0.794777i
$526$	35.7874	−	2.40536i	1.56041	−	0.104879i
$527$	−24.6075	+	32.8718i	−1.07192	+	1.43192i
$528$	4.89345	−	12.4627i	0.212960	−	0.542368i
$529$	22.9998	+	0.0937422i	0.999992	+	0.00407575i
$530$	31.2748	+	1.75339i	1.35849	+	0.0761624i
$531$	3.55308	−	0.510856i	0.154191	−	0.0221692i
$532$	−0.0912832	−	0.0206790i	−0.00395763	−	0.000896546i
$533$	−9.41293	−	5.13985i	−0.407719	−	0.222632i
$534$	7.63946	−	34.4070i	0.330592	−	1.48894i
$535$	1.66706	−	32.2055i	0.0720731	−	1.39236i
$536$	24.6444	−	13.0481i	1.06448	−	0.563593i
$537$	−4.99436	−	1.86280i	−0.215522	−	0.0803857i
$538$	−13.5402	−	29.9886i	−0.583761	−	1.29290i
$539$	−3.02404	−	1.94343i	−0.130254	−	0.0837095i
$540$	3.83514	+	2.03918i	0.165038	+	0.0877524i
$541$	−1.01999	+	7.09418i	−0.0438528	+	0.305003i	0.956077	+	0.293117i	$0.0946925\pi$
$541$	−1.01999	+	7.09418i	−0.0438528	+	0.305003i	−0.999929	+	0.0118857i	$0.996217\pi$
$542$	22.0798	+	25.7034i	0.948410	+	1.10406i
$543$	43.1432	+	3.08566i	1.85145	+	0.132419i
$544$	35.2283	+	8.45838i	1.51040	+	0.362650i
$545$	−0.670169	−	34.0438i	−0.0287069	−	1.45828i
$546$	17.5044	−	3.72931i	0.749120	−	0.159600i
$547$	39.8333	−	2.84893i	1.70315	−	0.121812i	0.814429	−	0.580264i	$-0.197051\pi$
$547$	39.8333	−	2.84893i	1.70315	−	0.121812i	0.888719	+	0.458452i	$0.151596\pi$
$548$	−21.3100	+	11.4000i	−0.910317	+	0.486982i
$549$	−15.9620	−	7.28961i	−0.681242	−	0.311113i
$550$	−9.50110	+	3.15570i	−0.405128	+	0.134560i
$551$			0.149555i			0.00637127i
$552$	−2.76419	+	31.9494i	−0.117652	+	1.35986i
$553$	8.07622	+	8.07622i	0.343436	+	0.343436i
$554$	−29.9643	+	22.2311i	−1.27306	+	0.944510i
$555$	17.6922	+	26.3735i	0.750992	+	1.11949i
$556$	−36.9630	−	11.1985i	−1.56758	−	0.474924i
$557$	1.57774	+	22.0597i	0.0668510	+	0.934699i	0.914615	+	0.404326i	$0.132494\pi$
$557$	1.57774	+	22.0597i	0.0668510	+	0.934699i	−0.847764	+	0.530374i	$0.822052\pi$
$558$	12.7768	−	19.6949i	0.540885	−	0.833750i
$559$	−17.8422	+	11.4665i	−0.754644	+	0.484980i
$560$	16.6035	+	9.01174i	0.701625	+	0.380816i
$561$	14.0386	+	16.2014i	0.592708	+	0.684022i
$562$	−33.7021	+	28.9510i	−1.42164	+	1.22122i
$563$	−7.89015	−	10.5400i	−0.332530	−	0.444209i	0.602849	−	0.797856i	$-0.294032\pi$
$563$	−7.89015	−	10.5400i	−0.332530	−	0.444209i	−0.935379	+	0.353647i	$0.884941\pi$
$564$	−2.14722	+	2.43550i	−0.0904142	+	0.102553i
$565$	−5.69898	+	16.2494i	−0.239758	+	0.683615i
$566$	8.50157	−	22.4984i	0.357347	−	0.945680i
$567$	7.42815	−	19.9156i	0.311953	−	0.836378i
$568$	32.0206	+	9.85128i	1.34355	+	0.413351i
$569$	−1.82358	+	6.21054i	−0.0764484	+	0.260359i	−0.988845	−	0.148948i	$-0.952411\pi$
$569$	−1.82358	+	6.21054i	−0.0764484	+	0.260359i	0.912397	+	0.409307i	$0.134230\pi$
$570$	−0.118919	−	0.115313i	−0.00498096	−	0.00482991i
$571$	2.13135	+	7.25872i	0.0891944	+	0.303768i	0.991993	−	0.126296i	$-0.0403090\pi$
$571$	2.13135	+	7.25872i	0.0891944	+	0.303768i	−0.902798	+	0.430064i	$0.858491\pi$
$572$	−1.58559	+	6.99928i	−0.0662969	+	0.292654i
$573$	17.8291	−	23.8169i	0.744822	−	0.994966i
$574$	−11.1197	+	6.01007i	−0.464129	+	0.250856i
$575$	19.6747	−	13.7079i	0.820491	−	0.571659i
$576$	−20.4199	−	3.47433i	−0.850831	−	0.144764i
$577$	−1.28511	−	0.962020i	−0.0534998	−	0.0400494i	0.572193	−	0.820119i	$-0.306093\pi$
$577$	−1.28511	−	0.962020i	−0.0534998	−	0.0400494i	−0.625693	+	0.780069i	$0.715184\pi$
$578$	−22.3532	+	25.5746i	−0.929772	+	1.06376i
$579$	34.3885	−	10.0974i	1.42914	−	0.419632i
$580$	8.18227	−	29.0562i	0.339750	−	1.20649i
$581$	10.9263	+	3.20824i	0.453298	+	0.133100i
$582$	8.33690	−	2.40915i	0.345576	−	0.0998625i
$583$	13.1403	+	4.90108i	0.544216	+	0.202982i
$584$	−16.8480	−	23.1204i	−0.697174	−	0.956728i
$585$	13.8463	+	4.85617i	0.572473	+	0.200778i
$586$	5.51467	+	14.9813i	0.227809	+	0.618872i
$587$	21.6720	−	16.2234i	0.894498	−	0.669613i	−0.0497808	−	0.998760i	$-0.515852\pi$
$587$	21.6720	−	16.2234i	0.894498	−	0.669613i	0.944278	+	0.329148i	$0.106761\pi$
$588$	−4.29153	+	11.2114i	−0.176980	+	0.462351i
$589$	0.107359	−	0.0930269i	0.00442364	−	0.00383311i
$590$	−4.01554	−	1.75964i	−0.165317	−	0.0724433i
$591$	−13.3832	−	20.8246i	−0.550509	−	0.856609i
$592$	18.9872	+	14.7285i	0.780370	+	0.605339i
$593$	0.659168	−	0.0471446i	0.0270688	−	0.00193600i	−0.0577982	−	0.998328i	$-0.518408\pi$
$593$	0.659168	−	0.0471446i	0.0270688	−	0.00193600i	0.0848670	+	0.996392i	$0.472953\pi$
$594$	1.36922	+	1.38101i	0.0561798	+	0.0566637i
$595$	−25.1192	+	16.8508i	−1.02979	+	0.690815i
$596$	24.6645	+	11.5206i	1.01030	+	0.471902i
$597$	36.8769	−	36.8769i	1.50927	−	1.50927i
$598$	−1.11778	−	17.1529i	−0.0457093	−	0.701433i
$599$	27.8332			1.13723			0.568616	−	0.822603i	$-0.307479\pi$
$599$	27.8332			1.13723			0.568616	+	0.822603i	$0.307479\pi$
$600$	16.7952	+	28.9095i	0.685659	+	1.18022i
$601$	10.7645	−	23.5710i	0.439093	−	0.961480i	−0.552671	−	0.833400i	$-0.686391\pi$
$601$	10.7645	−	23.5710i	0.439093	−	0.961480i	0.991764	−	0.128080i	$-0.0408815\pi$
$602$	−0.107194	+	24.9963i	−0.00436890	+	1.01877i
$603$	−1.82105	−	25.4617i	−0.0741590	−	1.03688i
$604$	23.0427	−	19.6231i	0.937594	−	0.798454i
$605$	20.1105	−	0.395884i	0.817606	−	0.0160950i
$606$	−7.77188	+	10.2897i	−0.315711	+	0.417992i
$607$	−2.77576	+	38.8102i	−0.112665	+	1.57526i	0.555673	+	0.831401i	$0.312461\pi$
$607$	−2.77576	+	38.8102i	−0.112665	+	1.57526i	−0.668338	+	0.743858i	$0.732994\pi$
$608$	−0.112869	−	0.0544997i	−0.00457744	−	0.00221026i
$609$	−33.3615	−	4.79666i	−1.35188	−	0.194371i
$610$	11.8631	+	17.8492i	0.480324	+	0.722691i
$611$	0.940910	−	1.46409i	0.0380652	−	0.0592305i
$612$	20.1020	−	26.3784i	0.812573	−	1.06628i
$613$	3.57363	−	9.58128i	0.144338	−	0.386984i	−0.844584	−	0.535423i	$-0.820152\pi$
$613$	3.57363	−	9.58128i	0.144338	−	0.386984i	0.988922	+	0.148439i	$0.0474248\pi$
$614$	−3.23524	+	5.86497i	−0.130564	+	0.236691i
$615$	−22.3403	−	1.15640i	−0.900848	−	0.0466307i
$616$	5.90341	+	6.05730i	0.237855	+	0.244056i
$617$	−14.6688	+	26.8639i	−0.590544	+	1.08150i	0.396038	+	0.918234i	$0.370385\pi$
$617$	−14.6688	+	26.8639i	−0.590544	+	1.08150i	−0.986582	+	0.163267i	$0.947797\pi$
$618$	−1.72217	+	1.97035i	−0.0692757	+	0.0792590i
$619$	0.580321	+	4.03622i	0.0233251	+	0.162229i	0.998155	−	0.0607214i	$-0.0193401\pi$
$619$	0.580321	+	4.03622i	0.0233251	+	0.162229i	−0.974830	+	0.222951i	$0.928431\pi$
$620$	−25.9476	+	12.2000i	−1.04208	+	0.489962i
$621$	−4.08363	−	2.24065i	−0.163870	−	0.0899140i
$622$	−31.7333	−	9.46575i	−1.27239	−	0.379542i
$623$	17.8243	+	13.3431i	0.714114	+	0.534579i
$624$	23.9634	+	0.411096i	0.959302	+	0.0164570i
$625$	8.56463	−	23.4872i	0.342585	−	0.939487i
$626$	9.04639	−	40.7436i	0.361566	−	1.62844i
$627$	−0.0355431	−	0.0650923i	−0.00141945	−	0.00259954i
$628$	2.24866	−	2.21041i	0.0897311	−	0.0882050i
$629$	−34.9984	+	15.9832i	−1.39548	+	0.637293i
$630$	13.6829	−	10.5755i	0.545142	−	0.421337i
$631$	−14.2750	+	22.2123i	−0.568277	+	0.884256i	−0.999841	−	0.0178261i	$-0.994325\pi$
$631$	−14.2750	+	22.2123i	−0.568277	+	0.884256i	0.431564	+	0.902082i	$0.357962\pi$
$632$	8.10285	+	12.9722i	0.322314	+	0.516008i
$633$	12.0803	−	9.04319i	0.480148	−	0.359434i
$634$	−0.553783	+	7.30266i	−0.0219936	+	0.290026i
$635$	6.16109	−	8.57708i	0.244495	−	0.340371i
$636$	7.06283	−	46.3005i	0.280059	−	1.83593i
$637$	1.36778	−	6.28760i	0.0541936	−	0.249124i
$638$	7.35555	−	11.3383i	0.291209	−	0.448886i
$639$	20.0832	−	23.1772i	0.794479	−	0.916877i
$640$	18.9469	+	16.7635i	0.748941	+	0.662637i
$641$	2.66824	−	5.84263i	0.105389	−	0.230770i	−0.849590	−	0.527444i	$-0.823150\pi$
$641$	2.66824	−	5.84263i	0.105389	−	0.230770i	0.954979	+	0.296674i	$0.0958776\pi$
$642$	−47.6980	−	7.06684i	−1.88249	−	0.278906i
$643$	27.3754	−	27.3754i	1.07958	−	1.07958i	0.0830320	−	0.996547i	$-0.473540\pi$
$643$	27.3754	−	27.3754i	1.07958	−	1.07958i	0.996547	−	0.0830320i	$-0.0264604\pi$
$644$	−17.6767	−	9.89721i	−0.696559	−	0.390005i
$645$	−23.1801	+	37.6795i	−0.912717	+	1.48363i
$646$	0.161169	−	0.119575i	0.00634111	−	0.00470460i
$647$	−5.02998	+	1.87609i	−0.197749	+	0.0737566i	−0.446387	−	0.894840i	$-0.647290\pi$
$647$	−5.02998	+	1.87609i	−0.197749	+	0.0737566i	0.248638	+	0.968596i	$0.420017\pi$
$648$	15.6958	−	23.7459i	0.616590	−	0.932825i
$649$	−1.48346	−	1.28543i	−0.0582311	−	0.0504575i
$650$	−11.2362	−	13.9610i	−0.440720	−	0.547597i
$651$	17.3083	+	26.9323i	0.678367	+	1.05556i
$652$	−22.4437	−	30.5235i	−0.878963	−	1.19539i
$653$	1.63448	−	22.8531i	0.0639623	−	0.894310i	−0.859626	−	0.510924i	$-0.829303\pi$
$653$	1.63448	−	22.8531i	0.0639623	−	0.894310i	0.923588	−	0.383386i	$-0.125242\pi$
$654$	−50.7670	−	3.84981i	−1.98515	−	0.150540i
$655$	9.61858	+	8.00860i	0.375829	+	0.312922i
$656$	−16.3204	+	4.48952i	−0.637206	+	0.175286i
$657$	−25.5894	+	5.56664i	−0.998338	+	0.217175i
$658$	−0.844069	−	1.86943i	−0.0329052	−	0.0728779i
$659$	11.8268	+	25.8970i	0.460705	+	1.00880i	0.987326	+	0.158703i	$0.0507314\pi$
$659$	11.8268	+	25.8970i	0.460705	+	1.00880i	−0.526621	+	0.850100i	$0.676541\pi$
$660$	3.34421	+	14.5910i	0.130173	+	0.567952i
$661$	−5.93064	−	1.74139i	−0.230675	−	0.0677324i	0.164352	−	0.986402i	$-0.447447\pi$
$661$	−5.93064	−	1.74139i	−0.230675	−	0.0677324i	−0.395027	+	0.918669i	$0.629265\pi$
$662$	−26.6897	+	16.9911i	−1.03732	+	0.660379i
$663$	−18.3908	+	33.6802i	−0.714238	+	1.30803i
$664$	13.2890	+	7.47987i	0.515713	+	0.290275i
$665$	0.0973071	−	0.0384918i	0.00377341	−	0.00149265i
$666$	19.3517	−	10.4593i	0.749862	−	0.405291i
$667$	−9.18329	+	31.0413i	−0.355579	+	1.20192i
$668$	3.68689	+	17.6770i	0.142650	+	0.683942i
$669$	−53.4213	+	7.68082i	−2.06539	+	0.296958i
$670$	−14.5185	+	27.5901i	−0.560899	+	1.06590i
$671$	2.70340	+	9.20694i	0.104364	+	0.355430i
$672$	15.7773	−	23.4298i	0.608624	−	0.903826i
$673$	18.1206	+	33.1855i	0.698499	+	1.27921i	0.950273	+	0.311419i	$0.100804\pi$
$673$	18.1206	+	33.1855i	0.698499	+	1.27921i	−0.251774	+	0.967786i	$0.581014\pi$
$674$	23.2868	+	12.8455i	0.896973	+	0.494790i
$675$	−4.82649	+	0.536807i	−0.185772	+	0.0206617i
$676$	13.0352	−	1.76020i	0.501353	−	0.0677001i
$677$	30.1105	−	6.55013i	1.15724	−	0.251742i	0.407329	−	0.913282i	$-0.366460\pi$
$677$	30.1105	−	6.55013i	1.15724	−	0.251742i	0.749910	+	0.661540i	$0.230097\pi$
$678$	23.3744	+	10.7961i	0.897690	+	0.414623i
$679$	−0.780193	+	5.42636i	−0.0299411	+	0.208245i
$680$	−37.8545	+	14.4137i	−1.45165	+	0.552742i
$681$	−14.6266	−	16.8800i	−0.560494	−	0.646844i
$682$	−12.7145	+	1.77246i	−0.486865	+	0.0678709i
$683$	−4.31931	+	19.8555i	−0.165274	+	0.759751i	0.817647	+	0.575720i	$0.195278\pi$
$683$	−4.31931	+	19.8555i	−0.165274	+	0.759751i	−0.982920	+	0.184031i	$0.941085\pi$
$684$	−0.0873527	+	0.0743895i	−0.00334001	+	0.00284435i
$685$	12.4802	−	23.9654i	0.476842	−	0.915669i
$686$	−20.0608	−	20.2336i	−0.765926	−	0.772523i
$687$	2.29468	−	0.855873i	0.0875477	−	0.0326536i
$688$	−7.67534	+	32.5818i	−0.292619	+	1.24217i
$689$			25.1047i			0.956411i
$690$	−17.6018	−	31.2360i	−0.670088	−	1.18913i
$691$			12.9881i			0.494089i	0.969004	+	0.247044i	$0.0794594\pi$
$691$			12.9881i			0.494089i	−0.969004	+	0.247044i	$0.920541\pi$
$692$	−32.7657	+	11.9019i	−1.24556	+	0.452441i
$693$	7.25455	−	2.70581i	0.275578	−	0.102785i
$694$	−3.41684	+	3.38766i	−0.129701	+	0.128594i
$695$	41.1843	−	12.9785i	1.56221	−	0.492304i
$696$	−42.0828	−	16.3158i	−1.59514	−	0.618449i
$697$	5.76091	−	26.4825i	0.218210	−	1.00310i
$698$	1.07491	+	7.71076i	0.0406859	+	0.291856i
$699$	−34.3896	−	39.6877i	−1.30073	−	1.50113i
$700$	−21.0111	+	2.15461i	−0.794145	+	0.0814365i
$701$	−0.750409	+	5.21921i	−0.0283426	+	0.197127i	−0.999073	−	0.0430441i	$-0.986294\pi$
$701$	−0.750409	+	5.21921i	−0.0283426	+	0.197127i	0.970731	+	0.240171i	$0.0772035\pi$
$702$	−1.45969	+	3.16034i	−0.0550925	+	0.119279i
$703$	0.130065	−	0.0282940i	0.00490551	−	0.00106713i
$704$	5.87649	+	9.68300i	0.221479	+	0.364942i
$705$	0.445800	−	3.60264i	0.0167898	−	0.135683i
$706$	−0.651161	+	1.18045i	−0.0245068	+	0.0444268i
$707$	−3.90404	−	7.14971i	−0.146826	−	0.268892i
$708$	−3.19084	+	5.72627i	−0.119919	+	0.215206i
$709$	−7.33609	−	24.9844i	−0.275513	−	0.938310i	−0.974727	−	0.223398i	$-0.928285\pi$
$709$	−7.33609	−	24.9844i	−0.275513	−	0.938310i	0.699215	−	0.714912i	$-0.253533\pi$
$710$	−35.7721	+	11.1046i	−1.34250	+	0.416748i
$711$	13.8586	−	1.99257i	0.519740	−	0.0747273i
$712$	19.2340	+	22.7829i	0.720823	+	0.853825i
$713$	27.9953	−	12.7161i	1.04843	−	0.476223i
$714$	21.5045	+	39.7872i	0.804786	+	1.48900i
$715$	−2.95142	−	7.46117i	−0.110377	−	0.279032i
$716$	3.81432	−	2.40534i	0.142548	−	0.0898919i
$717$	3.78535	−	6.93236i	0.141367	−	0.258894i
$718$	−11.1851	−	17.5695i	−0.417423	−	0.655688i
$719$	−46.8061	−	13.7435i	−1.74557	−	0.512547i	−0.755752	−	0.654858i	$-0.772728\pi$
$719$	−46.8061	−	13.7435i	−1.74557	−	0.512547i	−0.989822	+	0.142311i	$0.954547\pi$
$720$	21.0411	−	9.67355i	0.784156	−	0.360512i
$721$	−0.686752	−	1.50378i	−0.0255760	−	0.0560036i
$722$	24.4889	−	11.0570i	0.911382	−	0.411500i
$723$	−32.4095	+	7.05026i	−1.20532	+	0.262202i
$724$	−24.1984	+	27.4472i	−0.899328	+	1.02007i
$725$	10.7753	+	31.9829i	0.400186	+	1.18782i
$726$	2.27417	−	29.9892i	0.0844025	−	1.11300i
$727$	−0.266684	+	3.72873i	−0.00989076	+	0.138291i	−0.999998	−	0.00202210i	$-0.999356\pi$
$727$	−0.266684	+	3.72873i	−0.00989076	+	0.138291i	0.990107	+	0.140313i	$0.0448109\pi$
$728$	−6.46629	+	13.6903i	−0.239657	+	0.507397i
$729$	−10.3631	−	16.1253i	−0.383818	−	0.597232i
$730$	30.1364	+	10.7148i	1.11540	+	0.396572i
$731$	−40.5050	−	35.0978i	−1.49813	−	1.29814i
$732$	28.2562	−	15.1159i	1.04438	−	0.558700i
$733$	2.88760	−	1.07702i	0.106656	−	0.0397806i	−0.295570	−	0.955321i	$-0.595509\pi$
$733$	2.88760	−	1.07702i	0.106656	−	0.0397806i	0.402226	+	0.915541i	$0.368237\pi$
$734$	−12.3845	−	16.6925i	−0.457120	−	0.616130i
$735$	−3.11055	−	13.0562i	−0.114734	−	0.481587i
$736$	−20.0802	−	18.2424i	−0.740167	−	0.672423i
$737$	−9.87031	+	9.87031i	−0.363578	+	0.363578i
$738$	−2.27090	+	15.3276i	−0.0835930	+	0.564215i
$739$	5.67783	−	12.4327i	0.208862	−	0.457345i	−0.775989	−	0.630747i	$-0.782749\pi$
$739$	5.67783	−	12.4327i	0.208862	−	0.457345i	0.984851	+	0.173402i	$0.0554760\pi$
$740$	−26.8176	−	1.61889i	−0.985835	−	0.0595117i
$741$	0.0869377	−	0.100331i	0.00319373	−	0.00368577i
$742$	24.8220	+	16.1029i	0.911243	+	0.591158i
$743$	8.65498	−	39.7863i	0.317521	−	1.45962i	−0.491005	−	0.871157i	$-0.663370\pi$
$743$	8.65498	−	39.7863i	0.317521	−	1.45962i	0.808525	−	0.588461i	$-0.200266\pi$
$744$	14.4641	+	40.3581i	0.530281	+	1.47960i
$745$	−30.0348	+	4.92353i	−1.10039	+	0.180384i
$746$	37.0630	+	2.81060i	1.35697	+	0.102903i
$747$	11.1752	−	8.36564i	0.408878	−	0.306083i
$748$	−18.0997	+	1.13858i	−0.661792	+	0.0416306i
$749$	16.4685	−	25.6256i	0.601748	−	0.936337i
$750$	−33.7393	−	16.0920i	−1.23199	−	0.587596i
$751$	1.27171	−	0.580770i	0.0464053	−	0.0211926i	−0.392077	−	0.919932i	$-0.628243\pi$
$751$	1.27171	−	0.580770i	0.0464053	−	0.0211926i	0.438483	+	0.898740i	$0.355516\pi$
$752$	−0.537744	−	2.69361i	−0.0196095	−	0.0982260i
$753$	−9.58374	−	17.5513i	−0.349251	−	0.639605i
$754$	23.6177	+	5.24389i	0.860106	+	0.190971i
$755$	−8.89253	+	32.6491i	−0.323632	+	1.18822i
$756$	2.18846	+	3.47040i	0.0795937	+	0.126217i
$757$	−21.9046	−	16.3976i	−0.796136	−	0.595980i	0.121870	−	0.992546i	$-0.461111\pi$
$757$	−21.9046	−	16.3976i	−0.796136	−	0.595980i	−0.918006	+	0.396566i	$0.870202\pi$
$758$	2.34171	−	7.85042i	0.0850546	−	0.285140i
$759$	−3.38029	−	15.6928i	−0.122697	−	0.569614i
$760$	0.138567	−	0.0208881i	0.00502634	−	0.000757690i
$761$	4.59554	+	31.9627i	0.166588	+	1.15865i	0.885872	+	0.463930i	$0.153561\pi$
$761$	4.59554	+	31.9627i	0.166588	+	1.15865i	−0.719283	+	0.694717i	$0.755530\pi$
$762$	−11.8891	−	10.3915i	−0.430696	−	0.376446i
$763$	15.4141	−	28.2289i	0.558029	−	1.02195i
$764$	6.88342	+	24.2090i	0.249033	+	0.875849i
$765$	−1.91678	+	37.0299i	−0.0693013	+	1.33882i
$766$	29.5299	+	16.2893i	1.06696	+	0.588558i
$767$	1.22791	−	3.29216i	0.0443373	−	0.118873i
$768$	27.6489	−	25.8141i	0.997695	−	0.931484i
$769$	5.15290	−	8.01808i	0.185818	−	0.289139i	−0.735829	−	0.677167i	$-0.763207\pi$
$769$	5.15290	−	8.01808i	0.185818	−	0.289139i	0.921648	+	0.388028i	$0.126844\pi$
$770$	−9.27029	−	1.86765i	−0.334078	−	0.0673055i
$771$	−42.0181	−	6.04129i	−1.51324	−	0.217572i
$772$	−10.8390	+	28.3163i	−0.390103	+	1.01912i
$773$	2.75413	−	38.5077i	0.0990590	−	1.38503i	−0.668340	−	0.743856i	$-0.732995\pi$
$773$	2.75413	−	38.5077i	0.0990590	−	1.38503i	0.767399	−	0.641170i	$-0.221551\pi$
$774$	24.4514	+	18.4682i	0.878886	+	0.663826i
$775$	16.2565	−	27.6292i	0.583952	−	0.992471i
$776$	−2.65382	+	6.84491i	−0.0952666	+	0.245718i
$777$	2.14002	+	29.9213i	0.0767727	+	1.07342i
$778$	−34.0476	−	0.146010i	−1.22066	−	0.00523470i
$779$	−0.0389494	+	0.0852874i	−0.00139551	+	0.00305574i
$780$	−22.3798	+	14.7364i	−0.801324	+	0.527646i
$781$	−16.7701			−0.600080
$782$	40.7941	−	14.9221i	1.45879	−	0.533614i
$783$	4.63565	−	4.63565i	0.165665	−	0.165665i
$784$	−5.34321	−	8.63639i	−0.190829	−	0.308443i
$785$	−0.681419	+	3.45885i	−0.0243209	+	0.123452i
$786$	13.2897	−	13.1762i	0.474028	−	0.469980i
$787$	−36.9551	+	2.64308i	−1.31731	+	0.0942156i	−0.712227	−	0.701949i	$-0.752313\pi$
$787$	−36.9551	+	2.64308i	−1.31731	+	0.0942156i	−0.605080	+	0.796165i	$0.706859\pi$
$788$	20.8745	+	1.67304i	0.743622	+	0.0595995i
$789$	32.4173	+	50.4423i	1.15409	+	1.79579i
$790$	−15.6625	−	6.86341i	−0.557245	−	0.244189i
$791$	−12.2925	+	10.6515i	−0.437071	+	0.378724i
$792$	10.2812	−	1.34345i	0.365325	−	0.0477373i
$793$	−13.7506	+	10.2936i	−0.488299	+	0.365536i
$794$	24.7030	−	9.09328i	0.876678	−	0.322708i
$795$	22.6862	+	47.1949i	0.804596	+	1.67383i
$796$	5.90401	+	43.7221i	0.209262	+	1.54969i
$797$	46.8159	+	17.4614i	1.65830	+	0.618515i	0.991894	−	0.127072i	$-0.0405578\pi$
$797$	46.8159	+	17.4614i	1.65830	+	0.618515i	0.666409	+	0.745586i	$0.267831\pi$
$798$	−0.0434370	−	0.150315i	−0.00153765	−	0.00532108i
$799$	4.21979	+	1.23904i	0.149285	+	0.0438341i
$800$	−28.0640	−	3.52285i	−0.992213	−	0.124551i
$801$	26.1885	−	7.68963i	0.925325	−	0.271700i
$802$	7.42685	+	6.49138i	0.262251	+	0.229218i
$803$	11.4640	+	8.58183i	0.404555	+	0.302846i
$804$	38.9985	+	25.5381i	1.37537	+	0.900658i
$805$	22.5603	−	2.01421i	0.795147	−	0.0709915i
$806$	−10.9264	−	20.2159i	−0.384867	−	0.712074i
$807$	32.9634	−	44.0340i	1.16037	−	1.55007i
$808$	−2.93846	−	10.5056i	−0.103375	−	0.369585i
$809$	1.67858	+	5.71671i	0.0590156	+	0.200989i	0.983724	−	0.179689i	$-0.0575090\pi$
$809$	1.67858	+	5.71671i	0.0590156	+	0.200989i	−0.924708	+	0.380677i	$0.875691\pi$
$810$	0.489900	+	31.8204i	0.0172133	+	1.11806i
$811$	−8.55071	+	29.1210i	−0.300256	+	1.02258i	0.661790	+	0.749690i	$0.269797\pi$
$811$	−8.55071	+	29.1210i	−0.300256	+	1.02258i	−0.962046	+	0.272888i	$0.912021\pi$
$812$	20.3340	−	19.9882i	0.713584	−	0.701447i
$813$	−19.7955	+	53.0739i	−0.694260	+	1.86138i
$814$	−11.2523	−	4.25193i	−0.394391	−	0.149030i
$815$	39.9716	+	14.0188i	1.40014	+	0.491059i
$816$	16.0638	+	58.3957i	0.562346	+	2.04426i
$817$	0.111117	+	0.148434i	0.00388748	+	0.00519306i
$818$	34.5593	+	40.2309i	1.20834	+	1.40664i
$819$	9.07629	+	10.4746i	0.317151	+	0.366012i
$820$	12.2334	−	14.4390i	0.427208	−	0.504232i
$821$	−3.01574	+	1.93810i	−0.105250	+	0.0676402i	−0.592207	−	0.805786i	$-0.701743\pi$
$821$	−3.01574	+	1.93810i	−0.105250	+	0.0676402i	0.486957	+	0.873426i	$0.338107\pi$
$822$	−33.8936	−	21.9880i	−1.18217	−	0.766920i
$823$	2.24324	+	31.3645i	0.0781943	+	1.09330i	0.873414	+	0.486978i	$0.161901\pi$
$823$	2.24324	+	31.3645i	0.0781943	+	1.09330i	−0.795220	+	0.606321i	$0.792645\pi$
$824$	−0.442713	−	2.16910i	−0.0154226	−	0.0755642i
$825$	−12.2908	−	11.3594i	−0.427912	−	0.395482i
$826$	−2.46747	−	3.32578i	−0.0858541	−	0.115719i
$827$	19.4020	+	19.4020i	0.674673	+	0.674673i	0.958790	−	0.284117i	$-0.0917003\pi$
$827$	19.4020	+	19.4020i	0.674673	+	0.674673i	−0.284117	+	0.958790i	$0.591700\pi$
$828$	−22.6985	+	10.0763i	−0.788827	+	0.350174i
$829$			3.29890i			0.114575i	0.998358	+	0.0572877i	$0.0182452\pi$
$829$			3.29890i			0.114575i	−0.998358	+	0.0572877i	$0.981755\pi$
$830$	−16.9852	+	1.47794i	−0.589566	+	0.0512999i
$831$	−56.7358	−	25.9104i	−1.96814	−	0.898821i
$832$	−12.5641	+	15.9133i	−0.435582	+	0.551693i
$833$	16.2191	−	1.16001i	0.561959	−	0.0401921i
$834$	−13.4535	−	63.1475i	−0.465858	−	2.18662i
$835$	−14.5538	−	13.9919i	−0.503655	−	0.484208i
$836$	0.0620233	+	0.00946125i	0.00214512	+	0.000327224i
$837$	−6.21120	−	0.444234i	−0.214691	−	0.0153550i
$838$	25.2160	−	21.6611i	0.871071	−	0.748272i
$839$	−1.08990	+	7.58043i	−0.0376276	+	0.261706i	−0.999948	−	0.0102129i	$-0.996749\pi$
$839$	−1.08990	+	7.58043i	−0.0376276	+	0.261706i	0.962320	+	0.271919i	$0.0876582\pi$
$840$	0.215310	+	31.5801i	0.00742891	+	1.08962i
$841$	−13.9316	−	8.95333i	−0.480402	−	0.308735i
$842$	26.7078	−	12.0589i	0.920412	−	0.415577i
$843$	−69.5902	−	25.9558i	−2.39681	−	0.893965i
$844$	−0.109488	+	12.7654i	−0.00376874	+	0.439402i
$845$	−10.9224	+	9.84728i	−0.375742	+	0.338757i
$846$	−2.45464	−	0.545010i	−0.0843924	−	0.0187378i
$847$	16.6754	+	9.10548i	0.572975	+	0.312868i
$848$	27.5323	+	28.4934i	0.945463	+	0.978469i
$849$	39.7971	−	5.72195i	1.36583	−	0.196377i
$850$	25.8513	−	37.1835i	0.886691	−	1.27538i
$851$	28.7334	+	2.11391i	0.984967	+	0.0724641i
$852$	11.4349	+	54.8251i	0.391753	+	1.87828i
$853$	3.61851	−	4.83377i	0.123896	−	0.165505i	−0.734305	−	0.678820i	$-0.762492\pi$
$853$	3.61851	−	4.83377i	0.123896	−	0.165505i	0.858200	+	0.513315i	$0.171583\pi$
$854$	1.35758	+	20.1984i	0.0464556	+	0.691176i
$855$	0.0337108	−	0.123770i	0.00115288	−	0.00423284i
$856$	29.2127	−	28.4706i	0.998470	−	0.973104i
$857$	42.4740	−	23.1926i	1.45089	−	0.792243i	0.455689	−	0.890139i	$-0.349393\pi$
$857$	42.4740	−	23.1926i	1.45089	−	0.792243i	0.995197	+	0.0978957i	$0.0312112\pi$
$858$	−11.5256	+	3.33060i	−0.393477	+	0.113705i
$859$	−8.75477	−	19.1703i	−0.298709	−	0.654081i	0.699453	−	0.714678i	$-0.253427\pi$
$859$	−8.75477	−	19.1703i	−0.298709	−	0.654081i	−0.998162	+	0.0605969i	$0.980700\pi$
$860$	−13.4672	−	34.9177i	−0.459228	−	1.19068i
$861$	−17.7759	−	11.4239i	−0.605803	−	0.389326i
$862$	−6.42264	+	13.9055i	−0.218756	+	0.473623i
$863$	5.83770	+	7.79826i	0.198718	+	0.265456i	0.888820	−	0.458256i	$-0.151526\pi$
$863$	5.83770	+	7.79826i	0.198718	+	0.265456i	−0.690103	+	0.723711i	$0.742435\pi$
$864$	1.80922	+	5.18779i	0.0615510	+	0.176492i
$865$	22.7383	−	31.6548i	0.773124	−	1.07630i
$866$	2.90923	+	2.19735i	0.0988595	+	0.0746689i
$867$	−55.4843	−	12.0699i	−1.88435	−	0.409914i
$868$	−26.9968	−	2.16373i	−0.916331	−	0.0734417i
$869$	−5.78620	−	5.01377i	−0.196283	−	0.170080i
$870$	49.1383	−	11.4844i	1.66594	−	0.389356i
$871$	−22.7288	−	10.3799i	−0.770137	−	0.351710i
$872$	28.6218	−	32.1852i	0.969255	−	1.08993i
$873$	4.75202	+	4.75202i	0.160831	+	0.160831i
$874$	−0.148878	+	0.0204449i	−0.00503586	+	0.000691560i
$875$	18.0361	−	15.2425i	0.609733	−	0.515290i
$876$	20.2390	−	43.3300i	0.683814	−	1.46398i
$877$	0.256104	+	0.686641i	0.00864801	+	0.0231862i	0.941202	−	0.337844i	$-0.109698\pi$
$877$	0.256104	+	0.686641i	0.00864801	+	0.0231862i	−0.932554	+	0.361031i	$0.882425\pi$
$878$	−0.140294	+	32.7147i	−0.00473468	+	1.10407i
$879$	−17.4764	+	20.1688i	−0.589463	+	0.680277i
$880$	−11.5325	−	5.23150i	−0.388760	−	0.176354i
$881$	−6.59011	+	4.23521i	−0.222027	+	0.142688i	−0.646926	−	0.762553i	$-0.723946\pi$
$881$	−6.59011	+	4.23521i	−0.222027	+	0.142688i	0.424900	+	0.905241i	$0.360309\pi$
$882$	−9.20756	+	1.28357i	−0.310035	+	0.0432200i
$883$	−21.0367	−	1.50458i	−0.707942	−	0.0506330i	−0.287275	−	0.957848i	$-0.592749\pi$
$883$	−21.0367	−	1.50458i	−0.707942	−	0.0506330i	−0.420667	+	0.907215i	$0.638204\pi$
$884$	−13.2320	−	29.6444i	−0.445042	−	0.997049i
$885$	−0.666624	−	7.29863i	−0.0224083	−	0.245341i
$886$	17.8643	−	6.57590i	0.600162	−	0.220922i
$887$	3.14114	+	14.4396i	0.105469	+	0.484835i	0.999334	+	0.0364973i	$0.0116200\pi$
$887$	3.14114	+	14.4396i	0.105469	+	0.484835i	−0.893864	+	0.448337i	$0.852016\pi$
$888$	−6.22800	+	39.6854i	−0.208998	+	1.33175i
$889$	9.07378	−	4.14385i	0.304325	−	0.138980i
$890$	−32.1260	−	8.89821i	−1.07687	−	0.298269i
$891$	−4.01428	+	13.6714i	−0.134483	+	0.458008i
$892$	22.2243	−	39.8836i	0.744124	−	1.33540i
$893$	−0.0133538	−	0.00729173i	−0.000446868	−	0.000244008i
$894$	3.05181	+	45.4054i	0.102068	+	1.51858i
$895$	−2.00372	+	4.62640i	−0.0669769	+	0.154643i
$896$	7.67504	+	22.6299i	0.256405	+	0.756012i
$897$	24.2053	−	15.4862i	0.808190	−	0.517068i
$898$	24.9254	+	7.43501i	0.831771	+	0.248109i
$899$	6.15881	+	42.8355i	0.205408	+	1.42864i
$900$	−13.3210	+	22.2021i	−0.444032	+	0.740071i
$901$	−60.8703	+	17.8731i	−2.02788	+	0.595440i
$902$	7.14755	−	4.55026i	0.237987	−	0.151507i
$903$	−36.6753	+	20.0262i	−1.22048	+	0.666431i
$904$	−19.2498	+	10.1919i	−0.640240	+	0.338979i
$905$	5.02402	−	40.6005i	0.167004	−	1.34961i
$906$	47.3295	+	17.8845i	1.57242	+	0.594174i
$907$	−6.67411	−	30.6804i	−0.221610	−	1.01872i	−0.944691	−	0.327962i	$-0.893638\pi$
$907$	−6.67411	−	30.6804i	−0.221610	−	1.01872i	0.723081	−	0.690763i	$-0.242725\pi$
$908$	18.8579	−	1.18627i	0.625822	−	0.0393679i
$909$	−9.88440	−	1.42116i	−0.327845	−	0.0471370i
$910$	−2.66671	−	16.7163i	−0.0884006	−	0.554141i
$911$	15.3698	−	13.3180i	0.509225	−	0.441246i	−0.361965	−	0.932192i	$-0.617894\pi$
$911$	15.3698	−	13.3180i	0.509225	−	0.441246i	0.871190	+	0.490946i	$0.163349\pi$
$912$	−0.0113605	−	0.209219i	−0.000376185	−	0.00692795i
$913$	−7.45902	−	1.62261i	−0.246858	−	0.0537006i
$914$	−5.16209	−	24.2296i	−0.170747	−	0.801442i
$915$	−16.5482	+	31.7771i	−0.547066	+	1.05052i
$916$	−0.600742	+	1.98287i	−0.0198491	+	0.0655158i
$917$	4.13152	+	11.0770i	0.136435	+	0.365796i
$918$	−8.70199	−	1.28927i	−0.287208	−	0.0425522i
$919$	−47.5665			−1.56907			−0.784537	−	0.620082i	$-0.787099\pi$
$919$	−47.5665			−1.56907			−0.784537	+	0.620082i	$0.787099\pi$
$920$	30.0431	+	4.17307i	0.990490	+	0.137582i
$921$	−11.1972			−0.368962
$922$	13.0316	+	1.93074i	0.429174	+	0.0635856i
$923$	−10.4907	−	28.1265i	−0.345304	−	0.925796i
$924$	−4.09979	+	13.5322i	−0.134873	+	0.445176i
$925$	25.7764	−	15.4219i	0.847522	−	0.507068i
$926$	−7.33398	−	34.4238i	−0.241010	−	1.13124i
$927$	−1.98024	−	0.430775i	−0.0650397	−	0.0141485i
$928$	32.5568	−	19.9498i	1.06873	−	0.654885i
$929$	−29.3931	+	25.4692i	−0.964355	+	0.835619i	−0.986437	−	0.164137i	$-0.947516\pi$
$929$	−29.3931	+	25.4692i	−0.964355	+	0.835619i	0.0220820	+	0.999756i	$0.492970\pi$
$930$	−38.8092	−	28.1305i	−1.27260	−	0.922436i
$931$	−0.0556816	−	0.00800581i	−0.00182489	−	0.000262380i
$932$	44.3380	−	2.78912i	1.45234	−	0.0913607i
$933$	−11.7673	−	54.0933i	−0.385244	−	1.77094i
$934$	4.87215	+	1.84106i	0.159422	+	0.0602412i
$935$	15.9896	−	12.4681i	0.522915	−	0.407752i
$936$	8.68468	+	16.4030i	0.283868	+	0.536150i
$937$	−21.8559	+	11.9342i	−0.714002	+	0.389874i	−0.794813	−	0.606855i	$-0.792431\pi$
$937$	−21.8559	+	11.9342i	−0.714002	+	0.389874i	0.0808109	+	0.996729i	$0.474249\pi$
$938$	−24.8420	+	15.8149i	−0.811121	+	0.516374i
$939$	66.9436	−	19.6564i	2.18462	−	0.641463i
$940$	2.19549	+	2.14726i	0.0716091	+	0.0700359i
$941$	3.05745	+	21.2650i	0.0996699	+	0.693220i	0.976986	+	0.213306i	$0.0684230\pi$
$941$	3.05745	+	21.2650i	0.0996699	+	0.693220i	−0.877316	+	0.479914i	$0.840668\pi$
$942$	5.05120	+	1.50672i	0.164577	+	0.0490917i
$943$	−13.3212	+	15.3103i	−0.433798	+	0.498573i
$944$	−2.21685	−	5.08321i	−0.0721524	−	0.165444i
$945$	−4.20925	−	1.82305i	−0.136927	−	0.0593039i
$946$	−1.12368	−	16.7183i	−0.0365339	−	0.543559i
$947$	−51.2081	−	27.9617i	−1.66404	−	0.908634i	−0.984583	−	0.174919i	$-0.944034\pi$
$947$	−51.2081	−	27.9617i	−1.66404	−	0.908634i	−0.679457	−	0.733715i	$-0.737785\pi$
$948$	−12.4457	+	22.3351i	−0.404219	+	0.725410i
$949$	−7.22194	+	24.5957i	−0.234434	+	0.798409i
$950$	−0.114734	+	0.106688i	−0.00372247	+	0.00346141i
$951$	−11.1366	+	5.08590i	−0.361128	+	0.164921i
$952$	−37.7980	−	5.93182i	−1.22504	−	0.192251i
$953$	−10.5092	−	48.3100i	−0.340426	−	1.56491i	−0.755514	−	0.655133i	$-0.772613\pi$
$953$	−10.5092	−	48.3100i	−0.340426	−	1.56491i	0.415087	−	0.909782i	$-0.363751\pi$
$954$	34.0376	−	12.5294i	1.10201	−	0.405653i
$955$	−21.6248	−	18.0052i	−0.699762	−	0.582634i
$956$	2.72354	+	6.10167i	0.0880855	+	0.197342i
$957$	22.5358	+	1.61179i	0.728479	+	0.0521019i
$958$	10.7831	−	1.50321i	0.348388	−	0.0485666i
$959$	21.4710	−	13.7985i	0.693333	−	0.445578i
$960$	−9.23935	+	41.2695i	−0.298199	+	1.33197i
$961$	6.61799	−	7.63756i	0.213483	−	0.246373i
$962$	0.0923378	−	21.5320i	0.00297709	−	0.694218i
$963$	−13.0494	−	34.9868i	−0.420510	−	1.12743i
$964$	11.8745	−	25.4223i	0.382452	−	0.818796i
$965$	−7.85621	−	32.9757i	−0.252900	−	1.06153i
$966$	0.214248	−	33.8660i	0.00689332	−	1.08962i
$967$	−9.00402	−	9.00402i	−0.289550	−	0.289550i	0.547352	−	0.836902i	$-0.315636\pi$
$967$	−9.00402	−	9.00402i	−0.289550	−	0.289550i	−0.836902	+	0.547352i	$0.815636\pi$
$968$	19.0125	+	16.9075i	0.611085	+	0.543428i
$969$	0.305165	+	0.139364i	0.00980330	+	0.00447702i
$970$	−1.86797	−	7.99251i	−0.0599769	−	0.256624i
$971$	4.90667	+	4.25165i	0.157462	+	0.136442i	0.730029	−	0.683416i	$-0.239507\pi$
$971$	4.90667	+	4.25165i	0.157462	+	0.136442i	−0.572566	+	0.819858i	$0.694052\pi$
$972$	41.6231	+	3.33599i	1.33506	+	0.107002i
$973$	39.8553	+	8.67000i	1.27770	+	0.277947i
$974$	26.5064	+	20.0204i	0.849320	+	0.641495i
$975$	11.3631	−	27.7200i	0.363911	−	0.887750i
$976$	−4.31778	+	26.7634i	−0.138209	+	0.856675i
$977$	4.49628	+	6.00633i	0.143849	+	0.192160i	0.866679	−	0.498866i	$-0.166250\pi$
$977$	4.49628	+	6.00633i	0.143849	+	0.192160i	−0.722830	+	0.691026i	$0.757159\pi$
$978$	26.5573	−	57.4985i	0.849208	−	1.83860i
$979$	−12.5559	−	8.06917i	−0.401287	−	0.257892i
$980$	10.3800	+	4.60177i	0.331578	+	0.146998i
$981$	−16.3788	−	35.8645i	−0.522934	−	1.14506i
$982$	−53.2123	+	15.3770i	−1.69807	+	0.490699i
$983$	27.2137	−	14.8598i	0.867981	−	0.473953i	0.0174311	−	0.999848i	$-0.494451\pi$
$983$	27.2137	−	14.8598i	0.867981	−	0.473953i	0.850550	+	0.525895i	$0.176269\pi$
$984$	−19.7495	−	20.2643i	−0.629590	−	0.646002i
$985$	−20.3244	+	11.6230i	−0.647591	+	0.370340i
$986$	4.09984	+	60.9983i	0.130566	+	1.94258i
$987$	2.05487	−	2.74498i	0.0654072	−	0.0873738i
$988$	0.0229309	+	0.109943i	0.000729530	+	0.00349776i
$989$	13.9486	+	37.6316i	0.443539	+	1.19662i
$990$	−8.64306	+	7.72538i	−0.274695	+	0.245529i
$991$	−14.5442	+	2.09114i	−0.462011	+	0.0664272i	−0.369390	−	0.929274i	$-0.620434\pi$
$991$	−14.5442	+	2.09114i	−0.462011	+	0.0664272i	−0.0926208	+	0.995701i	$0.529524\pi$
$992$	−34.5721	−	10.9617i	−1.09767	−	0.348035i
$993$	−46.4216	−	25.3481i	−1.47314	−	0.804397i
$994$	−34.5389	−	7.66874i	−1.09551	−	0.243238i
$995$	−33.0294	−	36.6355i	−1.04710	−	1.16142i
$996$	−0.218641	+	25.4916i	−0.00692790	+	0.807733i
$997$	26.5874	+	9.91660i	0.842033	+	0.314062i	0.733213	−	0.679999i	$-0.238020\pi$
$997$	26.5874	+	9.91660i	0.842033	+	0.314062i	0.108820	+	0.994061i	$0.465293\pi$
$998$	16.5775	−	7.48492i	0.524750	−	0.236931i
$999$	−4.90855	−	3.15453i	−0.155300	−	0.0998050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.3.4	✓	1360
4.3	odd	2	inner	460.2.w.a.3.26	yes	1360
5.2	odd	4	inner	460.2.w.a.187.37	yes	1360
20.7	even	4	inner	460.2.w.a.187.60	yes	1360
23.8	even	11	inner	460.2.w.a.123.60	yes	1360
92.31	odd	22	inner	460.2.w.a.123.37	yes	1360
115.77	odd	44	inner	460.2.w.a.307.26	yes	1360
460.307	even	44	inner	460.2.w.a.307.4	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.4	✓	1360	1.1	even	1	trivial
460.2.w.a.3.26	yes	1360	4.3	odd	2	inner
460.2.w.a.123.37	yes	1360	92.31	odd	22	inner
460.2.w.a.123.60	yes	1360	23.8	even	11	inner
460.2.w.a.187.37	yes	1360	5.2	odd	4	inner
460.2.w.a.187.60	yes	1360	20.7	even	4	inner
460.2.w.a.307.4	yes	1360	460.307	even	44	inner
460.2.w.a.307.26	yes	1360	115.77	odd	44	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39894 - 0.207265i) q^{2} +(-0.826183 - 2.21508i) q^{3} +(1.91408 + 0.579903i) q^{4} +(-2.13268 + 0.672078i) q^{5} +(0.696675 + 3.27001i) q^{6} +(-2.06386 - 0.448965i) q^{7} +(-2.55750 - 1.20797i) q^{8} +(-1.95677 + 1.69555i) q^{9} +O(q^{10})\)	\(q+(-1.39894 - 0.207265i) q^{2} +(-0.826183 - 2.21508i) q^{3} +(1.91408 + 0.579903i) q^{4} +(-2.13268 + 0.672078i) q^{5} +(0.696675 + 3.27001i) q^{6} +(-2.06386 - 0.448965i) q^{7} +(-2.55750 - 1.20797i) q^{8} +(-1.95677 + 1.69555i) q^{9} +(3.12279 - 0.498170i) q^{10} +(1.40142 + 0.201494i) q^{11} +(-0.296850 - 4.71896i) q^{12} +(0.538729 + 2.47650i) q^{13} +(2.79417 + 1.05584i) q^{14} +(3.25069 + 4.16880i) q^{15} +(3.32743 + 2.21996i) q^{16} +(-5.62112 + 3.06936i) q^{17} +(3.08883 - 1.96641i) q^{18} +(0.0212593 - 0.00624230i) q^{19} +(-4.47186 + 0.0496673i) q^{20} +(0.710631 + 4.94255i) q^{21} +(-1.91875 - 0.572345i) q^{22} +(4.79582 + 0.00977332i) q^{23} +(-0.562797 + 6.66308i) q^{24} +(4.09662 - 2.86665i) q^{25} +(-0.240361 - 3.57614i) q^{26} +(-0.852446 - 0.465471i) q^{27} +(-3.69004 - 2.05620i) q^{28} +(-1.90165 + 6.47644i) q^{29} +(-3.68349 - 6.50566i) q^{30} +(5.83201 - 2.66339i) q^{31} +(-4.19476 - 3.79526i) q^{32} +(-0.711506 - 3.27074i) q^{33} +(8.49980 - 3.12881i) q^{34} +(4.70329 - 0.429577i) q^{35} +(-4.72867 + 2.11069i) q^{36} +(5.99221 + 0.428571i) q^{37} +(-0.0310344 + 0.00432631i) q^{38} +(5.04056 - 3.23937i) q^{39} +(6.26617 + 0.857377i) q^{40} +(-2.77115 + 3.19808i) q^{41} +(0.0302831 - 7.06163i) q^{42} +(2.92446 + 7.84079i) q^{43} +(2.56559 + 1.19837i) q^{44} +(3.03361 - 4.93116i) q^{45} +(-6.70706 - 1.00768i) q^{46} +(-0.485564 - 0.485564i) q^{47} +(2.16834 - 9.20462i) q^{48} +(-2.30948 - 1.05470i) q^{49} +(-6.32510 + 3.16120i) q^{50} +(11.4430 + 9.91539i) q^{51} +(-0.404956 + 5.05263i) q^{52} +(9.67913 + 2.10557i) q^{53} +(1.09605 + 0.827849i) q^{54} +(-3.12420 + 0.512144i) q^{55} +(4.73598 + 3.64132i) q^{56} +(-0.0313913 - 0.0419339i) q^{57} +(4.00264 - 8.66603i) q^{58} +(-1.16631 - 0.749541i) q^{59} +(3.80459 + 9.86451i) q^{60} +(2.81542 + 6.16491i) q^{61} +(-8.71067 + 2.51716i) q^{62} +(4.79974 - 2.62085i) q^{63} +(5.08160 + 6.17878i) q^{64} +(-2.81333 - 4.91950i) q^{65} +(0.317448 + 4.72305i) q^{66} +(-5.90829 + 7.89254i) q^{67} +(-12.5392 + 2.61531i) q^{68} +(-3.94058 - 10.6312i) q^{69} +(-6.66867 - 0.373872i) q^{70} +(-11.7241 + 1.68567i) q^{71} +(7.05261 - 1.97264i) q^{72} +(8.87718 + 4.84731i) q^{73} +(-8.29393 - 1.84152i) q^{74} +(-9.73443 - 6.70598i) q^{75} +(0.0443120 + 0.000380063i) q^{76} +(-2.80188 - 1.04505i) q^{77} +(-7.72286 + 3.48696i) q^{78} +(-4.54914 - 2.92356i) q^{79} +(-8.58831 - 2.49818i) q^{80} +(-1.43221 + 9.96127i) q^{81} +(4.53953 - 3.89957i) q^{82} +(-5.37776 - 0.384625i) q^{83} +(-1.50599 + 9.87255i) q^{84} +(9.92518 - 10.3238i) q^{85} +(-2.46604 - 11.5750i) q^{86} +(15.9170 - 1.13840i) q^{87} +(-3.34074 - 2.20820i) q^{88} +(-9.58899 - 4.37915i) q^{89} +(-5.26591 + 6.26965i) q^{90} -5.35301i q^{91} +(9.17393 + 2.79982i) q^{92} +(-10.7179 - 10.7179i) q^{93} +(0.578636 + 0.779917i) q^{94} +(-0.0411439 + 0.0276007i) q^{95} +(-4.94118 + 12.4273i) q^{96} +(-0.185165 - 2.58895i) q^{97} +(3.01222 + 1.95414i) q^{98} +(-3.08390 + 1.98190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

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