LMFDB - Embedded newform 460.2.w.a.147.23

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			147.23
Character	$\chi$	$=$	460.147
Dual form			460.2.w.a.363.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.795314 - 1.16939i) q^{2} +(0.172295 - 2.40900i) q^{3} +(-0.734951 + 1.86007i) q^{4} +(2.05495 - 0.881573i) q^{5} +(-2.95410 + 1.71443i) q^{6} +(-1.70781 - 4.57881i) q^{7} +(2.75966 - 0.619893i) q^{8} +(-2.80415 - 0.403175i) q^{9} +O(q^{10})$	\(q+(-0.795314 - 1.16939i) q^{2} +(0.172295 - 2.40900i) q^{3} +(-0.734951 + 1.86007i) q^{4} +(2.05495 - 0.881573i) q^{5} +(-2.95410 + 1.71443i) q^{6} +(-1.70781 - 4.57881i) q^{7} +(2.75966 - 0.619893i) q^{8} +(-2.80415 - 0.403175i) q^{9} +(-2.66524 - 1.70191i) q^{10} +(-0.203588 + 0.693357i) q^{11} +(4.35428 + 2.09098i) q^{12} +(4.27516 + 1.59455i) q^{13} +(-3.99617 + 5.63868i) q^{14} +(-1.76965 - 5.10228i) q^{15} +(-2.91970 - 2.73411i) q^{16} +(-0.642102 - 2.95169i) q^{17} +(1.75871 + 3.59980i) q^{18} +(-0.396341 + 0.254713i) q^{19} +(0.129497 + 4.47026i) q^{20} +(-11.3246 + 3.32521i) q^{21} +(0.972722 - 0.313363i) q^{22} +(-3.04597 + 3.70433i) q^{23} +(-1.01785 - 6.75484i) q^{24} +(3.44566 - 3.62318i) q^{25} +(-1.53544 - 6.26751i) q^{26} +(0.0857430 - 0.394154i) q^{27} +(9.77204 + 0.188563i) q^{28} +(0.693874 - 1.07969i) q^{29} +(-4.55913 + 6.12733i) q^{30} +(4.36065 + 3.77852i) q^{31} +(-0.875174 + 5.58875i) q^{32} +(1.63522 + 0.609906i) q^{33} +(-2.94101 + 3.09839i) q^{34} +(-7.54602 - 7.90367i) q^{35} +(2.81084 - 4.91959i) q^{36} +(-7.79880 + 5.83811i) q^{37} +(0.613075 + 0.260901i) q^{38} +(4.57787 - 10.0241i) q^{39} +(5.12449 - 3.70669i) q^{40} +(0.653265 + 4.54356i) q^{41} +(12.8951 + 10.5983i) q^{42} +(-0.604717 + 8.45504i) q^{43} +(-1.14006 - 0.888271i) q^{44} +(-6.11782 + 1.64356i) q^{45} +(6.75431 + 0.615831i) q^{46} +(6.70699 - 6.70699i) q^{47} +(-7.08954 + 6.56248i) q^{48} +(-12.7586 + 11.0554i) q^{49} +(-6.97730 - 1.14775i) q^{50} +(-7.22127 + 1.03826i) q^{51} +(-6.10801 + 6.78017i) q^{52} +(0.0196235 + 0.0526127i) q^{53} +(-0.529113 + 0.213209i) q^{54} +(0.192882 + 1.60429i) q^{55} +(-7.55134 - 11.5773i) q^{56} +(0.545317 + 0.998673i) q^{57} +(-1.81443 + 0.0472820i) q^{58} +(2.37681 + 5.20449i) q^{59} +(10.7912 + 0.458247i) q^{60} +(-0.0965561 + 0.111432i) q^{61} +(0.950486 - 8.10442i) q^{62} +(2.94288 + 13.5282i) q^{63} +(7.23147 - 3.42139i) q^{64} +(10.1910 - 0.492139i) q^{65} +(-0.587297 - 2.39728i) q^{66} +(-0.00376301 + 0.00689144i) q^{67} +(5.96226 + 0.974998i) q^{68} +(8.39893 + 7.97600i) q^{69} +(-3.24103 + 15.1101i) q^{70} +(0.0265406 + 0.0903890i) q^{71} +(-7.98842 + 0.625642i) q^{72} +(3.04500 - 13.9977i) q^{73} +(13.0295 + 4.47672i) q^{74} +(-8.13459 - 8.92486i) q^{75} +(-0.182492 - 0.924422i) q^{76} +(3.52244 - 0.251930i) q^{77} +(-15.3630 + 2.61902i) q^{78} +(-0.0331677 - 0.0726270i) q^{79} +(-8.41016 - 3.04455i) q^{80} +(-9.08943 - 2.66890i) q^{81} +(4.79364 - 4.37748i) q^{82} +(7.17089 - 5.36806i) q^{83} +(2.13793 - 23.5084i) q^{84} +(-3.92162 - 5.49953i) q^{85} +(10.3682 - 6.01726i) q^{86} +(-2.48142 - 1.85757i) q^{87} +(-0.132027 + 2.03963i) q^{88} +(10.3602 - 8.97720i) q^{89} +(6.78755 + 5.84698i) q^{90} -22.2983i q^{91} +(-4.65165 - 8.38821i) q^{92} +(9.85379 - 9.85379i) q^{93} +(-13.1773 - 2.50893i) q^{94} +(-0.589914 + 0.872827i) q^{95} +(13.3125 + 3.07121i) q^{96} +(-2.65918 + 3.55225i) q^{97} +(23.0752 + 6.12729i) q^{98} +(0.850435 - 1.86219i) 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.795314	−	1.16939i	−0.562372	−	0.826884i
$2$	−0.795314	−	1.16939i	−0.562372	−	0.826884i
$3$	0.172295	−	2.40900i	0.0994747	−	1.39084i	−0.665317	−	0.746561i	$-0.731704\pi$
$3$	0.172295	−	2.40900i	0.0994747	−	1.39084i	0.764792	−	0.644278i	$-0.222842\pi$
$4$	−0.734951	+	1.86007i	−0.367475	+	0.930033i
$5$	2.05495	−	0.881573i	0.919003	−	0.394252i
$5$	2.05495	−	0.881573i	0.919003	−	0.394252i
$6$	−2.95410	+	1.71443i	−1.20600	+	0.699915i
$7$	−1.70781	−	4.57881i	−0.645490	−	1.73063i	−0.682061	−	0.731295i	$-0.738916\pi$
$7$	−1.70781	−	4.57881i	−0.645490	−	1.73063i	0.0365706	−	0.999331i	$-0.488357\pi$
$8$	2.75966	−	0.619893i	0.975688	−	0.219165i
$9$	−2.80415	−	0.403175i	−0.934716	−	0.134392i
$10$	−2.66524	−	1.70191i	−0.842822	−	0.538193i
$11$	−0.203588	+	0.693357i	−0.0613841	+	0.209055i	−0.984474	−	0.175528i	$-0.943837\pi$
$11$	−0.203588	+	0.693357i	−0.0613841	+	0.209055i	0.923090	+	0.384583i	$0.125655\pi$
$12$	4.35428	+	2.09098i	1.25697	+	0.603614i
$13$	4.27516	+	1.59455i	1.18572	+	0.442249i	0.863467	−	0.504405i	$-0.168288\pi$
$13$	4.27516	+	1.59455i	1.18572	+	0.442249i	0.322249	+	0.946655i	$0.395561\pi$
$14$	−3.99617	+	5.63868i	−1.06802	+	1.50700i
$15$	−1.76965	−	5.10228i	−0.456923	−	1.31740i
$16$	−2.91970	−	2.73411i	−0.729924	−	0.683529i
$17$	−0.642102	−	2.95169i	−0.155733	−	0.715891i	−0.987092	−	0.160156i	$-0.948800\pi$
$17$	−0.642102	−	2.95169i	−0.155733	−	0.715891i	0.831359	−	0.555735i	$-0.187563\pi$
$18$	1.75871	+	3.59980i	0.414532	+	0.848480i
$19$	−0.396341	+	0.254713i	−0.0909269	+	0.0584352i	−0.585314	−	0.810807i	$-0.699029\pi$
$19$	−0.396341	+	0.254713i	−0.0909269	+	0.0584352i	0.494387	+	0.869242i	$0.335392\pi$
$20$	0.129497	+	4.47026i	0.0289564	+	0.999581i
$21$	−11.3246	+	3.32521i	−2.47123	+	0.725619i
$22$	0.972722	−	0.313363i	0.207385	−	0.0668092i
$23$	−3.04597	+	3.70433i	−0.635130	+	0.772406i
$23$	−3.04597	+	3.70433i	−0.635130	+	0.772406i
$24$	−1.01785	−	6.75484i	−0.207767	−	1.37883i
$25$	3.44566	−	3.62318i	0.689131	−	0.724636i
$26$	−1.53544	−	6.26751i	−0.301125	−	1.22916i
$27$	0.0857430	−	0.394154i	0.0165013	−	0.0758550i
$28$	9.77204	+	0.188563i	1.84674	+	0.0356351i
$29$	0.693874	−	1.07969i	0.128849	−	0.200493i	−0.770835	−	0.637035i	$-0.780161\pi$
$29$	0.693874	−	1.07969i	0.128849	−	0.200493i	0.899684	+	0.436542i	$0.143797\pi$
$30$	−4.55913	+	6.12733i	−0.832379	+	1.11869i
$31$	4.36065	+	3.77852i	0.783196	+	0.678643i	0.951690	−	0.307060i	$-0.0993451\pi$
$31$	4.36065	+	3.77852i	0.783196	+	0.678643i	−0.168495	+	0.985703i	$0.553891\pi$
$32$	−0.875174	+	5.58875i	−0.154710	+	0.987960i
$33$	1.63522	+	0.609906i	0.284656	+	0.106171i
$34$	−2.94101	+	3.09839i	−0.504379	+	0.531370i
$35$	−7.54602	−	7.90367i	−1.27551	−	1.33596i
$36$	2.81084	−	4.91959i	0.468474	−	0.819931i
$37$	−7.79880	+	5.83811i	−1.28212	+	0.959780i	−0.282115	+	0.959380i	$0.591036\pi$
$37$	−7.79880	+	5.83811i	−1.28212	+	0.959780i	−1.00000		0.000399112i	$0.999873\pi$
$38$	0.613075	+	0.260901i	0.0994539	+	0.0423237i
$39$	4.57787	−	10.0241i	0.733046	−	1.60515i
$40$	5.12449	−	3.70669i	0.810253	−	0.586080i
$41$	0.653265	+	4.54356i	0.102023	+	0.709584i	0.975062	+	0.221934i	$0.0712368\pi$
$41$	0.653265	+	4.54356i	0.102023	+	0.709584i	−0.873039	+	0.487650i	$0.837854\pi$
$42$	12.8951	+	10.5983i	1.98976	+	1.63536i
$43$	−0.604717	+	8.45504i	−0.0922184	+	1.28938i	0.714998	+	0.699126i	$0.246428\pi$
$43$	−0.604717	+	8.45504i	−0.0922184	+	1.28938i	−0.807217	+	0.590255i	$0.799027\pi$
$44$	−1.14006	−	0.888271i	−0.171871	−	0.133912i
$45$	−6.11782	+	1.64356i	−0.911990	+	0.245007i
$46$	6.75431	+	0.615831i	0.995869	+	0.0907993i
$47$	6.70699	−	6.70699i	0.978315	−	0.978315i	−0.0214548	−	0.999770i	$-0.506830\pi$
$47$	6.70699	−	6.70699i	0.978315	−	0.978315i	0.999770	+	0.0214548i	$0.00682979\pi$
$48$	−7.08954	+	6.56248i	−1.02329	+	0.947212i
$49$	−12.7586	+	11.0554i	−1.82266	+	1.57934i
$50$	−6.97730	−	1.14775i	−0.986739	−	0.162317i
$51$	−7.22127	+	1.03826i	−1.01118	+	0.145386i
$52$	−6.10801	+	6.78017i	−0.847028	+	0.940240i
$53$	0.0196235	+	0.0526127i	0.00269550	+	0.00722691i	0.938291	−	0.345848i	$-0.112409\pi$
$53$	0.0196235	+	0.0526127i	0.00269550	+	0.00722691i	−0.935595	+	0.353075i	$0.885136\pi$
$54$	−0.529113	+	0.213209i	−0.0720032	+	0.0290141i
$55$	0.192882	+	1.60429i	0.0260082	+	0.216323i
$56$	−7.55134	−	11.5773i	−1.00909	−	1.54708i
$57$	0.545317	+	0.998673i	0.0722290	+	0.132277i
$58$	−1.81443	+	0.0472820i	−0.238246	+	0.00620843i
$59$	2.37681	+	5.20449i	0.309435	+	0.677568i	0.998907	−	0.0467447i	$-0.0148847\pi$
$59$	2.37681	+	5.20449i	0.309435	+	0.677568i	−0.689472	+	0.724312i	$0.742157\pi$
$60$	10.7912	+	0.458247i	1.39314	+	0.0591594i
$61$	−0.0965561	+	0.111432i	−0.0123627	+	0.0142674i	−0.761897	−	0.647698i	$-0.775732\pi$
$61$	−0.0965561	+	0.111432i	−0.0123627	+	0.0142674i	0.749535	+	0.661965i	$0.230277\pi$
$62$	0.950486	−	8.10442i	0.120712	−	1.02926i
$63$	2.94288	+	13.5282i	0.370768	+	1.70439i
$64$	7.23147	−	3.42139i	0.903933	−	0.427674i
$65$	10.1910	−	0.492139i	1.26403	−	0.0610423i
$66$	−0.587297	−	2.39728i	−0.0722912	−	0.295085i
$67$	−0.00376301	+	0.00689144i	−0.000459725	+	0.000841924i	−0.877909	−	0.478828i	$-0.841062\pi$
$67$	−0.00376301	+	0.00689144i	−0.000459725	+	0.000841924i	0.877449	+	0.479670i	$0.159244\pi$
$68$	5.96226	+	0.974998i	0.723030	+	0.118236i
$69$	8.39893	+	7.97600i	1.01111	+	0.960198i
$70$	−3.24103	+	15.1101i	−0.387377	+	1.80601i
$71$	0.0265406	+	0.0903890i	0.00314979	+	0.0107272i	0.961053	−	0.276365i	$-0.0891297\pi$
$71$	0.0265406	+	0.0903890i	0.00314979	+	0.0107272i	−0.957903	+	0.287092i	$0.907312\pi$
$72$	−7.98842	+	0.625642i	−0.941445	+	0.0737326i
$73$	3.04500	−	13.9977i	0.356391	−	1.63830i	−0.354541	−	0.935040i	$-0.615363\pi$
$73$	3.04500	−	13.9977i	0.356391	−	1.63830i	0.710932	−	0.703261i	$-0.248273\pi$
$74$	13.0295	+	4.47672i	1.51465	+	0.520408i
$75$	−8.13459	−	8.92486i	−0.939301	−	1.03055i
$76$	−0.182492	−	0.924422i	−0.0209333	−	0.106039i
$77$	3.52244	−	0.251930i	0.401419	−	0.0287101i
$78$	−15.3630	+	2.61902i	−1.73952	+	0.296546i
$79$	−0.0331677	−	0.0726270i	−0.00373165	−	0.00817118i	0.907757	−	0.419496i	$-0.137793\pi$
$79$	−0.0331677	−	0.0726270i	−0.00373165	−	0.00817118i	−0.911489	+	0.411325i	$0.865066\pi$
$80$	−8.41016	−	3.04455i	−0.940284	−	0.340391i
$81$	−9.08943	−	2.66890i	−1.00994	−	0.296544i
$82$	4.79364	−	4.37748i	0.529369	−	0.483411i
$83$	7.17089	−	5.36806i	0.787107	−	0.589221i	−0.128307	−	0.991735i	$-0.540954\pi$
$83$	7.17089	−	5.36806i	0.787107	−	0.589221i	0.915414	+	0.402513i	$0.131863\pi$
$84$	2.13793	−	23.5084i	0.233267	−	2.56498i
$85$	−3.92162	−	5.49953i	−0.425360	−	0.596508i
$86$	10.3682	−	6.01726i	1.11803	−	0.648858i
$87$	−2.48142	−	1.85757i	−0.266037	−	0.199153i
$88$	−0.132027	+	2.03963i	−0.0140741	+	0.217426i
$89$	10.3602	−	8.97720i	1.09818	−	0.951582i	0.0991299	−	0.995075i	$-0.468394\pi$
$89$	10.3602	−	8.97720i	1.09818	−	0.951582i	0.999054	+	0.0434930i	$0.0138486\pi$
$90$	6.78755	+	5.84698i	0.715470	+	0.616326i
$91$		−	22.2983i		−	2.33750i
$92$	−4.65165	−	8.38821i	−0.484969	−	0.874532i
$93$	9.85379	−	9.85379i	1.02179	−	1.02179i
$94$	−13.1773	−	2.50893i	−1.35913	−	0.258776i
$95$	−0.589914	+	0.872827i	−0.0605239	+	0.0895501i
$96$	13.3125	+	3.07121i	1.35870	+	0.313454i
$97$	−2.65918	+	3.55225i	−0.269999	+	0.360676i	−0.914964	−	0.403536i	$-0.867781\pi$
$97$	−2.65918	+	3.55225i	−0.269999	+	0.360676i	0.644965	+	0.764212i	$0.276872\pi$
$98$	23.0752	+	6.12729i	2.33095	+	0.618950i
$99$	0.850435	−	1.86219i	0.0854720	−	0.187158i
$100$	4.20697	+	9.07201i	0.420697	+	0.907201i
$101$	2.55301	−	17.7566i	0.254034	−	1.76685i	−0.319424	−	0.947612i	$-0.603489\pi$
$101$	2.55301	−	17.7566i	0.254034	−	1.76685i	0.573458	−	0.819235i	$-0.305602\pi$
$102$	6.95731	+	7.61875i	0.688877	+	0.754368i
$103$	−4.51373	−	8.26627i	−0.444751	−	0.814500i	0.555100	−	0.831784i	$-0.312680\pi$
$103$	−4.51373	−	8.26627i	−0.444751	−	0.814500i	−0.999851	+	0.0172836i	$0.994498\pi$
$104$	12.7864	+	1.75028i	1.25381	+	0.171630i
$105$	−20.3401	+	16.8166i	−1.98499	+	1.64113i
$106$	0.0459179	−	0.0647912i	0.00445994	−	0.00629308i
$107$	0.0473755	+	0.662396i	0.00457996	+	0.0640362i	0.999228	−	0.0392843i	$-0.0125078\pi$
$107$	0.0473755	+	0.662396i	0.00457996	+	0.0640362i	−0.994648	+	0.103321i	$0.967053\pi$
$108$	0.670136	+	0.449172i	0.0644839	+	0.0432216i
$109$	−0.531762	+	0.827438i	−0.0509336	+	0.0792542i	−0.865786	−	0.500414i	$-0.833181\pi$
$109$	−0.531762	+	0.827438i	−0.0509336	+	0.0792542i	0.814853	+	0.579668i	$0.196818\pi$
$110$	1.72265	−	1.50147i	0.164248	−	0.143160i
$111$	12.7203	+	19.7932i	1.20736	+	1.87869i
$112$	−7.53271	+	18.0381i	−0.711774	+	1.70444i
$113$	−2.77375	+	5.07975i	−0.260933	+	0.477863i	−0.974997	−	0.222217i	$-0.928671\pi$
$113$	−2.77375	+	5.07975i	−0.260933	+	0.477863i	0.714064	+	0.700080i	$0.246852\pi$
$114$	0.734141	−	1.43195i	0.0687586	−	0.134114i
$115$	−2.99369	+	10.2975i	−0.279163	+	0.960244i
$116$	1.49833	+	2.08417i	0.139117	+	0.193510i
$117$	−11.3453	−	6.19500i	−1.04887	−	0.572728i
$118$	4.19578	−	6.91863i	0.386253	−	0.636912i
$119$	−12.4187	+	7.98098i	−1.13842	+	0.731616i
$120$	−8.04651	−	12.9836i	−0.734543	−	1.18523i
$121$	8.81449	+	5.66473i	0.801318	+	0.514976i
$122$	0.207100	+	0.0242886i	0.0187499	+	0.00219899i
$123$	11.0580	−	0.790883i	0.997066	−	0.0713116i
$124$	−10.2332	+	5.33407i	−0.918965	+	0.479013i
$125$	3.88656	−	10.4831i	0.347624	−	0.937634i
$126$	13.4792	−	14.2005i	1.20083	−	1.26508i
$127$	−5.93785	+	3.24231i	−0.526899	+	0.287708i	−0.720599	−	0.693352i	$-0.756133\pi$
$127$	−5.93785	+	3.24231i	−0.526899	+	0.287708i	0.193700	+	0.981061i	$0.437951\pi$
$128$	−9.75223	−	5.73533i	−0.861983	−	0.506937i
$129$	20.2640	+	2.91353i	1.78415	+	0.256522i
$130$	−8.68052	−	11.5258i	−0.761332	−	1.01088i
$131$	7.02577	+	3.20856i	0.613844	+	0.280333i	0.697976	−	0.716121i	$-0.254084\pi$
$131$	7.02577	+	3.20856i	0.613844	+	0.280333i	−0.0841315	+	0.996455i	$0.526812\pi$
$132$	−2.33627	+	2.59337i	−0.203347	+	0.225724i
$133$	1.84316	+	1.37977i	0.159822	+	0.119641i
$134$	0.0110516	−	0.00108043i	0.000954710	−	9.33349e-5i
$135$	−0.171278	−	0.885557i	−0.0147413	−	0.0762166i
$136$	−3.60172	−	7.74764i	−0.308845	−	0.664355i
$137$	1.27129	+	1.27129i	0.108614	+	0.108614i	0.759325	−	0.650711i	$-0.225529\pi$
$137$	1.27129	+	1.27129i	0.108614	+	0.108614i	−0.650711	+	0.759325i	$0.725529\pi$
$138$	2.64728	−	16.1651i	0.225351	−	1.37606i
$139$	16.6292			1.41047			0.705233	−	0.708975i	$-0.250842\pi$
$139$	16.6292			1.41047			0.705233	+	0.708975i	$0.250842\pi$
$140$	20.2473	−	8.22728i	1.71121	−	0.695332i
$141$	−15.0016	−	17.3127i	−1.26336	−	1.45800i
$142$	0.0845919	−	0.102924i	0.00709880	−	0.00863719i
$143$	−1.97597	+	2.63958i	−0.165239	+	0.220733i
$144$	7.08493	+	8.84401i	0.590411	+	0.737001i
$145$	0.474053	−	2.83041i	0.0393680	−	0.235053i
$146$	−18.7905	+	7.57173i	−1.55511	+	0.626641i
$147$	24.4343	+	32.6404i	2.01530	+	2.69213i
$148$	−5.12754	−	18.7970i	−0.421481	−	1.54511i
$149$	3.13978	−	10.6931i	0.257221	−	0.876015i	−0.725073	−	0.688672i	$-0.758194\pi$
$149$	3.13978	−	10.6931i	0.257221	−	0.876015i	0.982295	−	0.187343i	$-0.0599876\pi$
$150$	−3.96709	+	16.6106i	−0.323912	+	1.35625i
$151$	−19.6023	+	8.95208i	−1.59521	+	0.728510i	−0.997327	−	0.0730695i	$-0.976721\pi$
$151$	−19.6023	+	8.95208i	−1.59521	+	0.728510i	−0.597888	+	0.801580i	$0.703993\pi$
$152$	−0.935873	+	0.948611i	−0.0759093	+	0.0769425i
$153$	0.610497	+	8.53586i	0.0493558	+	0.690084i
$154$	−3.09605	−	3.91874i	−0.249487	−	0.315781i
$155$	12.2920	+	3.92045i	0.987315	+	0.314898i
$156$	15.2811	+	15.8824i	1.22346	+	1.27161i
$157$	−8.67615	−	1.88738i	−0.692432	−	0.150629i	−0.147441	−	0.989071i	$-0.547104\pi$
$157$	−8.67615	−	1.88738i	−0.692432	−	0.150629i	−0.544992	+	0.838441i	$0.683467\pi$
$158$	−0.0585507	+	0.0965473i	−0.00465804	+	0.00768089i
$159$	0.130125	−	0.0382082i	0.0103196	−	0.00303011i
$160$	3.12845	+	12.2561i	0.247326	+	0.968932i
$161$	22.1633	+	7.62065i	1.74672	+	0.600592i
$162$	4.10797	+	12.7517i	0.322752	+	1.00187i
$163$	1.76635	+	0.964500i	0.138351	+	0.0755455i	0.546934	−	0.837176i	$-0.315795\pi$
$163$	1.76635	+	0.964500i	0.138351	+	0.0755455i	−0.408582	+	0.912721i	$0.633977\pi$
$164$	−8.93143	−	2.12417i	−0.697428	−	0.165870i
$165$	3.89798	−	0.188240i	0.303457	−	0.0146545i
$166$	−11.9805	−	4.11628i	−0.929865	−	0.319485i
$167$	−4.44047	+	0.965965i	−0.343614	+	0.0747486i	−0.381061	−	0.924550i	$-0.624441\pi$
$167$	−4.44047	+	0.965965i	−0.343614	+	0.0747486i	0.0374469	+	0.999299i	$0.488078\pi$
$168$	−29.1908	+	16.1965i	−2.25212	+	1.24959i
$169$	5.90966	+	5.12075i	0.454589	+	0.393904i
$170$	−3.31218	+	8.95977i	−0.254032	+	0.687183i
$171$	1.21409	−	0.554458i	0.0928440	−	0.0424004i
$172$	−15.2825	−	7.33885i	−1.16528	−	0.559582i
$173$	17.1872	−	9.38495i	1.30672	−	0.713524i	0.333361	−	0.942799i	$-0.391817\pi$
$173$	17.1872	−	9.38495i	1.30672	−	0.713524i	0.973362	+	0.229275i	$0.0736355\pi$
$174$	−0.198715	+	4.37911i	−0.0150645	+	0.331979i
$175$	−22.4744	−	9.58930i	−1.69890	−	0.724883i
$176$	2.49013	−	1.46776i	0.187701	−	0.110636i
$177$	12.9472	−	4.82904i	0.973168	−	0.362973i
$178$	−18.7375	−	4.97548i	−1.40444	−	0.372928i
$179$	−2.41787	−	16.8166i	−0.180720	−	1.25693i	−0.855066	−	0.518519i	$-0.826483\pi$
$179$	−2.41787	−	16.8166i	−0.180720	−	1.25693i	0.674346	−	0.738416i	$-0.264426\pi$
$180$	1.43917	−	12.5875i	0.107269	−	0.938215i
$181$	10.0030	+	11.5440i	0.743515	+	0.858062i	0.993923	−	0.110078i	$-0.0351101\pi$
$181$	10.0030	+	11.5440i	0.743515	+	0.858062i	−0.250408	+	0.968140i	$0.580565\pi$
$182$	−26.0755	+	17.7342i	−1.93284	+	1.31454i
$183$	0.251803	+	0.251803i	0.0186138	+	0.0186138i
$184$	−6.10957	+	12.1109i	−0.450404	+	0.892825i
$185$	−10.8794	+	18.8723i	−0.799873	+	1.38752i
$186$	−19.3598	−	3.68608i	−1.41953	−	0.270276i
$187$	2.17730	+	0.155724i	0.159220	+	0.0113876i
$188$	7.54614	+	17.4048i	0.550359	+	1.26937i
$189$	−1.95119	+	0.280539i	−0.141928	+	0.0204062i
$190$	1.48984	−	0.00433159i	0.108085	−	0.000314246i
$191$	−9.61839	−	4.39257i	−0.695963	−	0.317835i	0.0358348	−	0.999358i	$-0.488591\pi$
$191$	−9.61839	−	4.39257i	−0.695963	−	0.317835i	−0.731797	+	0.681522i	$0.761318\pi$
$192$	−6.99619	−	18.0101i	−0.504906	−	1.29977i
$193$	14.8234	+	19.8017i	1.06701	+	1.42536i	0.898134	+	0.439721i	$0.144923\pi$
$193$	14.8234	+	19.8017i	1.06701	+	1.42536i	0.168876	+	0.985637i	$0.445986\pi$
$194$	6.26885	+	0.284468i	0.450078	+	0.0204236i
$195$	0.570291	−	24.6349i	0.0408394	−	1.76414i
$196$	−11.1868	−	31.8571i	−0.799060	−	2.27551i
$197$	−0.928034	+	2.48815i	−0.0661197	+	0.177274i	−0.965808	−	0.259260i	$-0.916521\pi$
$197$	−0.928034	+	2.48815i	−0.0661197	+	0.177274i	0.899688	+	0.436534i	$0.143794\pi$
$198$	−2.85400	+	0.486538i	−0.202825	+	0.0345767i
$199$	−13.6170	+	15.7148i	−0.965283	+	1.11400i	0.0281532	+	0.999604i	$0.491037\pi$
$199$	−13.6170	+	15.7148i	−0.965283	+	1.11400i	−0.993436	+	0.114392i	$0.963508\pi$
$200$	7.26286	−	12.1347i	0.513562	−	0.858053i
$201$	0.0159532	+	0.0102525i	0.00112525	+	0.000723154i
$202$	−22.7948	+	11.1366i	−1.60384	+	0.783569i
$203$	−6.12869	−	1.33322i	−0.430150	−	0.0935734i
$204$	3.37604	−	14.1951i	0.236370	−	0.993857i
$205$	5.34791	+	8.76089i	0.373514	+	0.611887i
$206$	−6.07667	+	11.8526i	−0.423382	+	0.825809i
$207$	10.0349	−	9.15942i	0.697471	−	0.636623i
$208$	−8.12248	−	16.3444i	−0.563192	−	1.13328i
$209$	−0.0959168	−	0.326662i	−0.00663470	−	0.0225957i
$210$	35.8420	+	10.4111i	2.47333	+	0.718431i
$211$	10.9387	+	17.0209i	0.753050	+	1.17177i	0.980220	+	0.197913i	$0.0634163\pi$
$211$	10.9387	+	17.0209i	0.753050	+	1.17177i	−0.227170	+	0.973855i	$0.572947\pi$
$212$	−0.112285	−	0.00216668i	−0.00771179	−	0.000148808i
$213$	0.222320	−	0.0483628i	0.0152331	−	0.00331376i
$214$	0.736921	−	0.582213i	0.0503749	−	0.0397993i
$215$	6.21108	+	17.9078i	0.423592	+	1.22130i
$216$	−0.00771162	−	1.14088i	−0.000524710	−	0.0776273i
$217$	9.85398	−	26.4196i	0.668932	−	1.79348i
$218$	1.39052	−	0.0362354i	0.0941777	−	0.00245417i
$219$	−33.1958	−	9.74715i	−2.24316	−	0.658652i
$220$	−3.12585	−	0.820304i	−0.210745	−	0.0553049i
$221$	1.96154	−	13.6428i	0.131948	−	0.917716i
$222$	13.0294	−	30.6169i	0.874473	−	2.05487i
$223$	2.08899	−	0.779154i	0.139889	−	0.0521760i	−0.278544	−	0.960423i	$-0.589852\pi$
$223$	2.08899	−	0.779154i	0.139889	−	0.0521760i	0.418434	+	0.908247i	$0.362579\pi$
$224$	27.0844	−	5.53725i	1.80965	−	0.369973i
$225$	−11.1229	+	8.77073i	−0.741527	+	0.584715i
$226$	8.14622	−	0.796395i	0.541879	−	0.0529754i
$227$	19.3366	+	1.38298i	1.28342	+	0.0917919i	0.696324	−	0.717727i	$-0.254817\pi$
$227$	19.3366	+	1.38298i	1.28342	+	0.0917919i	0.587094	+	0.809519i	$0.300272\pi$
$228$	−2.25838	+	0.280350i	−0.149565	+	0.0185666i
$229$			10.8995i			0.720260i	0.932902	+	0.360130i	$0.117268\pi$
$229$			10.8995i			0.720260i	−0.932902	+	0.360130i	$0.882732\pi$
$230$	14.4227	−	4.68892i	0.951004	−	0.309178i
$231$		−	8.52897i		−	0.561165i
$232$	1.24557	−	3.40971i	0.0817755	−	0.223858i
$233$	−0.653172	−	0.0467158i	−0.0427907	−	0.00306045i	0.0499274	−	0.998753i	$-0.484101\pi$
$233$	−0.653172	−	0.0467158i	−0.0427907	−	0.00306045i	−0.0927181	+	0.995692i	$0.529556\pi$
$234$	1.77870	+	18.1941i	0.116277	+	1.18938i
$235$	7.86984	−	19.6952i	0.513372	−	1.28478i
$236$	−11.4275	+	0.595984i	−0.743870	+	0.0387952i
$237$	−0.180673	+	0.0673877i	−0.0117360	+	0.00437730i
$238$	19.2096	+	8.17487i	1.24517	+	0.529898i
$239$	0.0762832	−	0.530561i	0.00493435	−	0.0343192i	−0.987206	−	0.159453i	$-0.949027\pi$
$239$	0.0762832	−	0.530561i	0.00493435	−	0.0343192i	0.992140	+	0.125134i	$0.0399360\pi$
$240$	−8.78336	+	19.7355i	−0.566963	+	1.27392i
$241$	−19.3461	−	5.68054i	−1.24619	−	0.365916i	−0.408856	−	0.912599i	$-0.634072\pi$
$241$	−19.3461	−	5.68054i	−1.24619	−	0.365916i	−0.837339	+	0.546683i	$0.815890\pi$
$242$	−0.386006	−	14.8128i	−0.0248134	−	0.952205i
$243$	−7.57255	+	20.3028i	−0.485780	+	1.30243i
$244$	−0.136306	−	0.261497i	−0.00872612	−	0.0167407i
$245$	−16.4722	+	33.9660i	−1.05237	+	2.17001i
$246$	−9.71943	−	12.3021i	−0.619688	−	0.784354i
$247$	−2.10058	+	0.456952i	−0.133656	+	0.0290752i
$248$	14.3762	+	7.72431i	0.912889	+	0.490494i
$249$	−11.6962	−	18.1996i	−0.741214	−	1.15335i
$250$	−15.3498	+	3.79243i	−0.970809	+	0.239854i
$251$	1.05431	+	3.59065i	0.0665475	+	0.226640i	0.986051	−	0.166441i	$-0.0532275\pi$
$251$	1.05431	+	3.59065i	0.0665475	+	0.226640i	−0.919504	+	0.393081i	$0.871409\pi$
$252$	−27.3262	−	4.46861i	−1.72139	−	0.281496i
$253$	−1.94830	−	2.86611i	−0.122488	−	0.180190i
$254$	8.51398	+	4.36501i	0.534215	+	0.273885i
$255$	−13.9241	+	8.49966i	−0.871959	+	0.532269i
$256$	1.04924	+	15.9656i	0.0655774	+	0.997847i
$257$	−4.74469	−	1.03214i	−0.295966	−	0.0643834i	0.0621307	−	0.998068i	$-0.480210\pi$
$257$	−4.74469	−	1.03214i	−0.295966	−	0.0643834i	−0.358096	+	0.933685i	$0.616574\pi$
$258$	−12.7092	−	26.0138i	−0.791242	−	1.61955i
$259$	40.0504	+	25.7389i	2.48861	+	1.59933i
$260$	−6.57445	+	19.3176i	−0.407730	+	1.19803i
$261$	−2.38103	+	2.74786i	−0.147382	+	0.170088i
$262$	−1.83563	−	10.7677i	−0.113406	−	0.665230i
$263$	−3.70039	+	9.92113i	−0.228176	+	0.611763i	−0.999701	−	0.0244350i	$-0.992221\pi$
$263$	−3.70039	+	9.92113i	−0.228176	+	0.611763i	0.771525	+	0.636198i	$0.219494\pi$
$264$	4.89074	+	0.669473i	0.301004	+	0.0412032i
$265$	0.0867073	+	0.0908170i	0.00532639	+	0.00557884i
$266$	0.147602	−	3.25272i	0.00905004	−	0.199437i
$267$	−19.8411	−	26.5046i	−1.21425	−	1.62205i
$268$	−0.0100529	−	0.0120643i	−0.000614080	−	0.000736946i
$269$	−12.7409	−	5.81856i	−0.776824	−	0.354764i	−0.0127723	−	0.999918i	$-0.504066\pi$
$269$	−12.7409	−	5.81856i	−0.776824	−	0.354764i	−0.764052	+	0.645155i	$0.776793\pi$
$270$	−0.899343	+	0.904587i	−0.0547322	+	0.0550514i
$271$	−5.73678	+	0.824824i	−0.348484	+	0.0501045i	−0.314335	−	0.949312i	$-0.601781\pi$
$271$	−5.73678	+	0.824824i	−0.348484	+	0.0501045i	−0.0341497	+	0.999417i	$0.510872\pi$
$272$	−6.19553	+	10.3736i	−0.375659	+	0.628993i
$273$	−53.7167	−	3.84190i	−3.25109	−	0.232522i
$274$	0.475561	−	2.49772i	0.0287297	−	0.150893i
$275$	1.81067	+	3.12671i	0.109187	+	0.188548i
$276$	−21.0087	+	9.76060i	−1.26457	+	0.587519i
$277$	−9.17042	−	9.17042i	−0.550997	−	0.550997i	0.375732	−	0.926729i	$-0.377391\pi$
$277$	−9.17042	−	9.17042i	−0.550997	−	0.550997i	−0.926729	+	0.375732i	$0.877391\pi$
$278$	−13.2254	−	19.4460i	−0.793207	−	1.16629i
$279$	−10.7045	−	12.3536i	−0.640861	−	0.739593i
$280$	−25.7239	−	17.1337i	−1.53730	−	1.02394i
$281$	3.99730	+	27.8018i	0.238459	+	1.65852i	0.659669	+	0.751556i	$0.270696\pi$
$281$	3.99730	+	27.8018i	0.238459	+	1.65852i	−0.421210	+	0.906963i	$0.638395\pi$
$282$	−8.31440	+	31.3118i	−0.495115	+	1.86459i
$283$	7.17908	−	2.67766i	0.426752	−	0.159170i	−0.126905	−	0.991915i	$-0.540504\pi$
$283$	7.17908	−	2.67766i	0.426752	−	0.159170i	0.553657	+	0.832745i	$0.313232\pi$
$284$	−0.187636	−	0.0170642i	−0.0111341	−	0.00101257i
$285$	2.00100	+	1.57149i	0.118529	+	0.0930869i
$286$	4.65822	+	0.211380i	0.275446	+	0.0124992i
$287$	19.6884	−	10.7507i	1.16217	−	0.634593i
$288$	4.70736	−	15.3188i	0.277384	−	0.902670i
$289$	7.16354	−	3.27148i	0.421385	−	0.192440i
$290$	−3.68688	+	1.69671i	−0.216501	+	0.0996344i
$291$	8.09922	+	7.01801i	0.474785	+	0.411403i
$292$	23.7986	+	15.9515i	1.39271	+	0.933490i
$293$	−30.0541	+	6.53788i	−1.75578	+	0.381947i	−0.971235	−	0.238123i	$-0.923468\pi$
$293$	−30.0541	+	6.53788i	−1.75578	+	0.381947i	−0.784547	+	0.620070i	$0.787104\pi$
$294$	18.7364	−	54.5326i	1.09273	−	3.18040i
$295$	9.47238	+	8.59965i	0.551503	+	0.500691i
$296$	−17.9031	+	20.9456i	−1.04059	+	1.21744i
$297$	0.255834	+	0.139696i	0.0148450	+	0.00810596i
$298$	−15.0016	+	4.83276i	−0.869017	+	0.279954i
$299$	−18.9288	+	10.9796i	−1.09468	+	0.634968i
$300$	22.5793	−	8.57155i	1.30362	−	0.494878i
$301$	39.7467	−	11.6707i	2.29096	−	0.672688i
$302$	26.0585	+	15.8031i	1.49950	+	0.909364i
$303$	−42.3358	−	9.20959i	−2.43213	−	0.529077i
$304$	1.85361	+	0.339958i	0.106312	+	0.0194979i
$305$	−0.100183	+	0.314108i	−0.00573646	+	0.0179858i
$306$	9.49623	−	7.50260i	0.542863	−	0.428895i
$307$	0.269218	+	3.76415i	0.0153651	+	0.214832i	0.999334	+	0.0364915i	$0.0116182\pi$
$307$	0.269218	+	3.76415i	0.0153651	+	0.214832i	−0.983969	+	0.178340i	$0.942927\pi$
$308$	−2.12021	+	6.73713i	−0.120810	+	0.383883i
$309$	−20.6912	+	9.44934i	−1.17708	+	0.537554i
$310$	−5.19144	−	17.4921i	−0.294854	−	0.993485i
$311$	2.52630	−	8.60378i	0.143253	−	0.487876i	−0.856340	−	0.516413i	$-0.827267\pi$
$311$	2.52630	−	8.60378i	0.143253	−	0.487876i	0.999593	+	0.0285377i	$0.00908505\pi$
$312$	6.41949	−	30.5010i	0.363432	−	1.72678i
$313$	1.37209	+	1.83290i	0.0775551	+	0.103601i	0.837641	−	0.546221i	$-0.183934\pi$
$313$	1.37209	+	1.83290i	0.0775551	+	0.103601i	−0.760086	+	0.649822i	$0.774843\pi$
$314$	4.69318	+	11.6469i	0.264851	+	0.657271i
$315$	17.9736	+	25.2054i	1.01270	+	1.42017i
$316$	0.159468	−	0.00831676i	0.00897076	−	0.000467854i
$317$	0.971648	−	1.29797i	0.0545732	−	0.0729013i	−0.772424	−	0.635107i	$-0.780956\pi$
$317$	0.971648	−	1.29797i	0.0545732	−	0.0729013i	0.826998	+	0.562205i	$0.190047\pi$
$318$	−0.148171	−	0.121780i	−0.00830900	−	0.00682907i
$319$	0.607346	+	0.700915i	0.0340049	+	0.0392437i
$320$	11.8441	−	13.4059i	0.662106	−	0.749410i
$321$	1.60388			0.0895197
$322$	−8.71529	−	31.9784i	−0.485684	−	1.78209i
$323$	1.00633	+	1.00633i	0.0559935	+	0.0559935i
$324$	11.6446	−	14.9454i	0.646923	−	0.830302i
$325$	20.5081	−	9.99541i	1.13758	−	0.554445i
$326$	−0.276926	−	2.83264i	−0.0153375	−	0.156885i
$327$	1.90168	+	1.42358i	0.105163	+	0.0787242i
$328$	4.61931	+	12.1337i	0.255059	+	0.669973i
$329$	−42.1643	−	19.2558i	−2.32459	−	1.06161i
$330$	−3.32025	−	4.40855i	−0.182774	−	0.242683i
$331$	−15.4368	−	2.21948i	−0.848484	−	0.121994i	−0.295662	−	0.955293i	$-0.595540\pi$
$331$	−15.4368	−	2.21948i	−0.848484	−	0.121994i	−0.552823	+	0.833299i	$0.686449\pi$
$332$	4.71470	+	17.2836i	0.258753	+	0.948560i
$333$	24.2228	−	13.2266i	1.32740	−	0.724815i
$334$	4.66116	+	4.42440i	0.255047	+	0.242092i
$335$	−0.00165750	+	0.0174790i	−9.05588e−5	+	0.000954978i
$336$	42.1559	+	21.2542i	2.29979	+	1.15951i
$337$	27.6995	−	1.98110i	1.50889	−	0.107918i	0.707777	−	0.706436i	$-0.249698\pi$
$337$	27.6995	−	1.98110i	1.50889	−	0.107918i	0.801109	+	0.598519i	$0.204244\pi$
$338$	1.28812	−	10.9833i	0.0700646	−	0.597413i
$339$	11.7592	+	7.55720i	0.638674	+	0.410451i
$340$	13.1117	−	3.25260i	0.711081	−	0.176397i
$341$	−3.50764	+	2.25422i	−0.189949	+	0.122073i
$342$	−1.61396	−	0.978781i	−0.0872731	−	0.0529264i
$343$	42.3858	+	23.1444i	2.28862	+	1.24968i
$344$	3.57241	+	23.7079i	0.192611	+	1.27825i
$345$	24.2908	+	8.98603i	1.30777	+	0.483791i
$346$	−24.6439	−	12.6346i	−1.32487	−	0.679242i
$347$	9.87721	−	18.0888i	0.530236	−	0.971055i	−0.466034	−	0.884767i	$-0.654318\pi$
$347$	9.87721	−	18.0888i	0.530236	−	0.971055i	0.996270	−	0.0862883i	$-0.0275006\pi$
$348$	5.27893	−	3.25039i	0.282980	−	0.174239i
$349$	9.29032	+	14.4560i	0.497299	+	0.773813i	0.995651	−	0.0931620i	$-0.0296975\pi$
$349$	9.29032	+	14.4560i	0.497299	+	0.773813i	−0.498352	+	0.866975i	$0.666061\pi$
$350$	6.66054	+	33.9078i	0.356021	+	1.81245i
$351$	0.995065	−	1.54835i	0.0531126	−	0.0826449i
$352$	−3.69682	−	1.74461i	−0.197041	−	0.0929880i
$353$	1.08737	+	15.2035i	0.0578750	+	0.809199i	0.940645	+	0.339393i	$0.110222\pi$
$353$	1.08737	+	15.2035i	0.0578750	+	0.809199i	−0.882770	+	0.469806i	$0.844324\pi$
$354$	−15.9441	−	11.2997i	−0.847419	−	0.600572i
$355$	0.134224	+	0.162348i	0.00712388	+	0.00861651i
$356$	9.08393	+	25.8685i	0.481447	+	1.37103i
$357$	17.0865	+	31.2917i	0.904316	+	1.65613i
$358$	−17.7423	+	16.2019i	−0.937708	+	0.856299i
$359$	−0.358542	+	2.49372i	−0.0189231	+	0.131613i	−0.997093	−	0.0761933i	$-0.975723\pi$
$359$	−0.358542	+	2.49372i	−0.0189231	+	0.131613i	0.978170	+	0.207807i	$0.0666325\pi$
$360$	−15.8643	+	8.32805i	−0.836121	+	0.438927i
$361$	−7.80068	+	17.0811i	−0.410562	+	0.899005i
$362$	5.54400	−	20.8785i	0.291386	−	1.09735i
$363$	15.1651	−	20.2581i	0.795959	−	1.06328i
$364$	41.4764	+	16.3882i	2.17395	+	0.858973i
$365$	−6.08262	−	31.4489i	−0.318379	−	1.64611i
$366$	0.0941937	−	0.494719i	0.00492358	−	0.0258594i
$367$	−5.13006	+	5.13006i	−0.267787	+	0.267787i	−0.828208	−	0.560421i	$-0.810639\pi$
$367$	−5.13006	+	5.13006i	−0.267787	+	0.267787i	0.560421	+	0.828208i	$0.310639\pi$
$368$	19.0214	−	2.48746i	0.991557	−	0.129668i
$369$		−	13.0042i		−	0.676970i
$370$	30.7216	−	2.28705i	1.59714	−	0.118898i
$371$	0.207390	−	0.179705i	0.0107672	−	0.00932980i
$372$	11.0867	+	25.5708i	0.574817	+	1.32578i
$373$	−29.8328	−	22.3326i	−1.54469	−	1.15634i	−0.929997	−	0.367566i	$-0.880191\pi$
$373$	−29.8328	−	22.3326i	−1.54469	−	1.15634i	−0.614688	−	0.788771i	$-0.710718\pi$
$374$	−1.54954	−	2.66997i	−0.0801247	−	0.138061i
$375$	−24.5841	−	11.1689i	−1.26952	−	0.576760i
$376$	14.3514	−	22.6666i	0.740117	−	1.16894i
$377$	4.68805	−	3.50943i	0.241447	−	0.180745i
$378$	1.87987	+	2.05859i	0.0966900	+	0.105882i
$379$	−28.9187	−	8.49131i	−1.48546	−	0.436169i	−0.564368	−	0.825524i	$-0.690880\pi$
$379$	−28.9187	−	8.49131i	−1.48546	−	0.436169i	−0.921088	+	0.389354i	$0.872698\pi$
$380$	−1.18996	−	1.73876i	−0.0610436	−	0.0891967i
$381$	6.78767	+	14.8629i	0.347743	+	0.761451i
$382$	2.51301	+	14.7411i	0.128577	+	0.754222i
$383$	19.8506	−	1.41974i	1.01432	−	0.0725454i	0.445729	−	0.895168i	$-0.352945\pi$
$383$	19.8506	−	1.41974i	1.01432	−	0.0725454i	0.568588	+	0.822623i	$0.307490\pi$
$384$	−15.4967	+	22.5050i	−0.790813	+	1.14845i
$385$	7.01635	−	3.62299i	0.357586	−	0.184645i
$386$	11.3667	−	33.0829i	0.578550	−	1.68388i
$387$	5.10458	−	23.4654i	0.259480	−	1.19281i
$388$	−4.65305	−	7.55698i	−0.236223	−	0.383648i
$389$	−1.33146	−	4.53452i	−0.0675075	−	0.229909i	0.918828	−	0.394658i	$-0.129137\pi$
$389$	−1.33146	−	4.53452i	−0.0675075	−	0.229909i	−0.986336	+	0.164749i	$0.947319\pi$
$390$	−29.2614	+	18.9256i	−1.48171	+	0.958333i
$391$	12.8899	+	6.61223i	0.651869	+	0.334395i
$392$	−28.3563	+	38.4182i	−1.43221	+	1.94041i
$393$	8.93994	−	16.3723i	0.450960	−	0.825872i
$394$	3.64770	−	0.893630i	0.183769	−	0.0450204i
$395$	−0.132184	−	0.120005i	−0.00665090	−	0.00603812i
$396$	2.83878	+	2.95049i	0.142654	+	0.148268i
$397$	2.55961	+	11.7663i	0.128463	+	0.590535i	0.995700	+	0.0926392i	$0.0295303\pi$
$397$	2.55961	+	11.7663i	0.128463	+	0.590535i	−0.867237	+	0.497896i	$0.834106\pi$
$398$	29.2066	+	3.42535i	1.46399	+	0.171697i
$399$	3.64144	−	4.20244i	0.182300	−	0.210385i
$400$	−19.9665	+	1.15777i	−0.998323	+	0.0578885i
$401$	4.44719	+	9.73799i	0.222082	+	0.486292i	0.987574	−	0.157153i	$-0.0502317\pi$
$401$	4.44719	+	9.73799i	0.222082	+	0.486292i	−0.765492	+	0.643445i	$0.777504\pi$
$402$	−0.000698625	−	0.0268094i	−3.48442e−5	−	0.00133713i
$403$	12.6174	+	23.1071i	0.628518	+	1.15105i
$404$	31.1521	+	17.7990i	1.54988	+	0.885533i
$405$	−21.0312	+	2.52854i	−1.04505	+	0.125644i
$406$	3.31519	+	8.22716i	0.164530	+	0.408307i
$407$	−2.46015	−	6.59593i	−0.121945	−	0.326948i
$408$	−19.2847	+	7.34167i	−0.954733	+	0.363467i
$409$	13.7223	−	1.97297i	0.678524	−	0.0975571i	0.205568	−	0.978643i	$-0.434096\pi$
$409$	13.7223	−	1.97297i	0.678524	−	0.0975571i	0.472957	+	0.881086i	$0.343187\pi$
$410$	5.99164	−	13.2215i	0.295906	−	0.652961i
$411$	3.28159	−	2.84351i	0.161869	−	0.140260i
$412$	18.6932	−	2.32053i	0.920947	−	0.114324i
$413$	19.7712	−	19.7712i	0.972879	−	0.972879i
$414$	−18.6918	−	4.45005i	−0.918652	−	0.218708i
$415$	10.0035	−	17.3528i	0.491052	−	0.851814i
$416$	−12.6531	+	22.4973i	−0.620367	+	1.10302i
$417$	2.86513	−	40.0597i	0.140306	−	1.96173i
$418$	−0.305712	+	0.371964i	−0.0149529	+	0.0181933i
$419$	−1.70049	−	11.8272i	−0.0830746	−	0.577796i	−0.988260	−	0.152780i	$-0.951177\pi$
$419$	−1.70049	−	11.8272i	−0.0830746	−	0.577796i	0.905186	−	0.425016i	$-0.139732\pi$
$420$	−16.3310	−	50.1933i	−0.796873	−	2.44918i
$421$	−5.34333	+	11.7003i	−0.260418	+	0.570236i	−0.994002	−	0.109363i	$-0.965119\pi$
$421$	−5.34333	+	11.7003i	−0.260418	+	0.570236i	0.733584	+	0.679599i	$0.237846\pi$
$422$	11.2044	−	26.3286i	0.545423	−	1.28165i
$423$	−21.5115	+	16.1033i	−1.04592	+	0.782969i
$424$	0.0867685	+	0.133029i	0.00421385	+	0.00646045i
$425$	−12.9070	−	7.84407i	−0.626081	−	0.380493i
$426$	−0.233369	−	0.221516i	−0.0113068	−	0.0107325i
$427$	0.675123	+	0.251808i	0.0326715	+	0.0121858i
$428$	−1.26692	−	0.398707i	−0.0612388	−	0.0192722i
$429$	6.01831	+	5.21490i	0.290567	+	0.251778i
$430$	16.0015	−	21.5055i	0.771660	−	1.03709i
$431$	−8.87060	+	13.8029i	−0.427282	+	0.664863i	−0.986426	−	0.164207i	$-0.947493\pi$
$431$	−8.87060	+	13.8029i	−0.427282	+	0.664863i	0.559144	+	0.829070i	$0.311130\pi$
$432$	−1.32801	+	0.916379i	−0.0638937	+	0.0440893i
$433$	−4.36663	+	20.0731i	−0.209847	+	0.964650i	0.744888	+	0.667190i	$0.232503\pi$
$433$	−4.36663	+	20.0731i	−0.209847	+	0.964650i	−0.954734	+	0.297460i	$0.903861\pi$
$434$	−38.7318	+	9.48869i	−1.85919	+	0.455472i
$435$	−6.73679	−	1.62966i	−0.323005	−	0.0781363i
$436$	−1.14827	−	1.59724i	−0.0549922	−	0.0764939i
$437$	0.263705	−	2.24403i	0.0126147	−	0.107346i
$438$	15.0028	+	46.5709i	0.716862	+	2.22524i
$439$	−17.9280	+	5.26414i	−0.855657	+	0.251244i	−0.680004	−	0.733208i	$-0.738022\pi$
$439$	−17.9280	+	5.26414i	−0.855657	+	0.251244i	−0.175653	+	0.984452i	$0.556204\pi$
$440$	1.52678	+	4.30774i	0.0727863	+	0.205364i
$441$	40.2343	−	25.8570i	1.91592	−	1.23129i
$442$	−17.5138	+	8.55653i	−0.833049	+	0.406993i
$443$	−3.81788	−	17.5505i	−0.181393	−	0.833849i	−0.974433	−	0.224680i	$-0.927866\pi$
$443$	−3.81788	−	17.5505i	−0.181393	−	0.833849i	0.793040	−	0.609170i	$-0.208497\pi$
$444$	−46.1655	+	9.11362i	−2.19092	+	0.432513i
$445$	13.3757	−	27.5810i	0.634071	−	1.30747i
$446$	−2.57254	−	1.82318i	−0.121813	−	0.0863299i
$447$	−25.2188	−	9.40613i	−1.19281	−	0.444894i
$448$	−28.0158	−	27.2684i	−1.32362	−	1.28831i
$449$	−1.67891	+	5.71786i	−0.0792329	+	0.269842i	−0.989576	−	0.144012i	$-0.954000\pi$
$449$	−1.67891	+	5.71786i	−0.0792329	+	0.269842i	0.910343	+	0.413854i	$0.135818\pi$
$450$	19.1026	+	6.03154i	0.900506	+	0.284329i
$451$	−3.28330	−	0.472068i	−0.154605	−	0.0222288i
$452$	−7.41010	−	8.89273i	−0.348542	−	0.418279i
$453$	18.1882	+	48.7645i	0.854557	+	2.29115i
$454$	−13.7615	−	23.7120i	−0.645857	−	1.11286i
$455$	−19.6576	−	45.8220i	−0.921563	−	2.14817i
$456$	2.12396	+	2.41796i	0.0994635	+	0.113231i
$457$	0.563700	−	7.88155i	0.0263688	−	0.368683i	−0.967085	−	0.254452i	$-0.918105\pi$
$457$	0.563700	−	7.88155i	0.0263688	−	0.368683i	0.993454	−	0.114231i	$-0.0364405\pi$
$458$	12.7458	−	8.66853i	0.595571	−	0.405054i
$459$	−1.21848			−0.0568737
$460$	−16.9538	−	13.1366i	−0.790473	−	0.612497i
$461$	23.2015			1.08060			0.540301	−	0.841472i	$-0.318310\pi$
$461$	23.2015			1.08060			0.540301	+	0.841472i	$0.318310\pi$
$462$	−9.97370	+	6.78321i	−0.464019	+	0.315584i
$463$	−1.76798	+	24.7195i	−0.0821648	+	1.14881i	0.774373	+	0.632730i	$0.218066\pi$
$463$	−1.76798	+	24.7195i	−0.0821648	+	1.14881i	−0.856538	+	0.516085i	$0.827389\pi$
$464$	−4.97790	+	1.25523i	−0.231093	+	0.0582727i
$465$	11.5622	−	28.9359i	0.536186	−	1.34187i
$466$	0.464848	+	0.800967i	0.0215337	+	0.0371041i
$467$	3.89734	+	10.4492i	0.180347	+	0.483529i	0.995394	−	0.0958651i	$-0.0305618\pi$
$467$	3.89734	+	10.4492i	0.180347	+	0.483529i	−0.815047	+	0.579395i	$0.803289\pi$
$468$	19.8613	−	16.5500i	0.918091	−	0.765023i
$469$	0.0379811	+	0.00546086i	0.00175380	+	0.000252159i
$470$	−29.2904	+	6.46099i	−1.35107	+	0.298023i
$471$	−6.04157	+	20.5757i	−0.278381	+	0.948078i
$472$	9.78543	+	12.8893i	0.450411	+	0.593277i
$473$	−5.73925	−	2.14063i	−0.263891	−	0.0984263i
$474$	0.222495	+	0.157683i	0.0102195	+	0.00724264i
$475$	−0.442784	+	2.31367i	−0.0203163	+	0.106158i
$476$	−5.71806	−	28.9651i	−0.262087	−	1.32762i
$477$	−0.0338151	−	0.155445i	−0.00154829	−	0.00711736i
$478$	−0.681103	+	0.332758i	−0.0311529	+	0.0152200i
$479$	25.2483	−	16.2261i	1.15362	−	0.741389i	0.183267	−	0.983063i	$-0.441333\pi$
$479$	25.2483	−	16.2261i	1.15362	−	0.741389i	0.970357	+	0.241674i	$0.0776965\pi$
$480$	30.0641	−	5.42477i	1.37223	−	0.247606i
$481$	−42.6503	+	12.5233i	−1.94469	+	0.571012i
$482$	8.74349	+	27.1410i	0.398255	+	1.23624i
$483$	22.1768	−	52.0785i	1.00908	−	2.36966i
$484$	−17.0150	+	12.2322i	−0.773409	+	0.556011i
$485$	−2.33292	+	9.64397i	−0.105932	+	0.437910i
$486$	29.7645	−	7.29183i	1.35014	−	0.330764i
$487$	4.87240	−	22.3981i	0.220789	−	1.01495i	−0.724640	−	0.689127i	$-0.757994\pi$
$487$	4.87240	−	22.3981i	0.220789	−	1.01495i	0.945430	−	0.325826i	$-0.105642\pi$
$488$	−0.197386	+	0.367368i	−0.00893526	+	0.0166300i
$489$	2.62782	−	4.08897i	0.118834	−	0.184909i
$490$	52.8201	−	7.75120i	2.38617	−	0.350163i
$491$	5.02821	+	4.35697i	0.226920	+	0.196627i	0.760899	−	0.648871i	$-0.224758\pi$
$491$	5.02821	+	4.35697i	0.226920	+	0.196627i	−0.533979	+	0.845498i	$0.679304\pi$
$492$	−6.65598	+	21.1499i	−0.300075	+	0.953510i
$493$	−3.63245	−	1.35483i	−0.163597	−	0.0610187i
$494$	2.20497	+	2.09297i	0.0992064	+	0.0941673i
$495$	0.105943	−	4.57644i	0.00476180	−	0.205696i
$496$	−2.40085	−	22.9546i	−0.107801	−	1.03069i
$497$	0.368547	−	0.275891i	0.0165316	−	0.0123754i
$498$	−11.9803	+	28.1518i	−0.536850	+	1.26151i
$499$	−8.92111	+	19.5345i	−0.399364	+	0.874484i	0.597971	+	0.801518i	$0.295974\pi$
$499$	−8.92111	+	19.5345i	−0.399364	+	0.874484i	−0.997334	+	0.0729664i	$0.976753\pi$
$500$	16.6428	+	14.9338i	0.744287	+	0.667859i
$501$	1.56194	+	10.8635i	0.0697824	+	0.485347i
$502$	3.36037	−	4.08860i	0.149981	−	0.182483i
$503$	−0.502498	+	7.02585i	−0.0224053	+	0.313267i	0.973874	+	0.227088i	$0.0729204\pi$
$503$	−0.502498	+	7.02585i	−0.0224053	+	0.313267i	−0.996280	+	0.0861794i	$0.972534\pi$
$504$	16.5074	+	35.5090i	0.735297	+	1.58170i
$505$	−10.4074	−	38.7396i	−0.463124	−	1.72389i
$506$	−1.80209	+	4.55778i	−0.0801126	+	0.202618i
$507$	13.3541	−	13.3541i	0.593077	−	0.593077i
$508$	−1.66689	−	13.4277i	−0.0739562	−	0.595759i
$509$	−3.37772	+	2.92681i	−0.149715	+	0.129728i	−0.726498	−	0.687169i	$-0.758853\pi$
$509$	−3.37772	+	2.92681i	−0.149715	+	0.129728i	0.576783	+	0.816897i	$0.304308\pi$
$510$	21.0134	+	9.52277i	0.930490	+	0.421676i
$511$	−69.2928	+	9.96280i	−3.06533	+	0.440729i
$512$	17.8355	−	13.9246i	0.788226	−	0.615386i
$513$	0.0664127	+	0.178059i	0.00293219	+	0.00786152i
$514$	2.56654	+	6.36928i	0.113205	+	0.280937i
$515$	−16.5628	−	13.0076i	−0.729845	−	0.573184i
$516$	−20.3124	+	35.5512i	−0.894205	+	1.56505i
$517$	3.28488	+	6.01580i	0.144469	+	0.264575i
$518$	−1.75390	−	67.3051i	−0.0770619	−	2.95722i
$519$	−19.6471	−	43.0211i	−0.862411	−	1.88842i
$520$	27.8185	−	7.67544i	1.21992	−	0.336590i
$521$	15.4467	−	17.8265i	0.676733	−	0.780992i	−0.308681	−	0.951166i	$-0.599887\pi$
$521$	15.4467	−	17.8265i	0.676733	−	0.780992i	0.985414	+	0.170174i	$0.0544329\pi$
$522$	5.10698	+	0.598947i	0.223527	+	0.0262152i
$523$	−5.61809	−	25.8260i	−0.245662	−	1.12929i	−0.920322	−	0.391161i	$-0.872073\pi$
$523$	−5.61809	−	25.8260i	−0.245662	−	1.12929i	0.674660	−	0.738129i	$-0.264290\pi$
$524$	−11.1317	+	10.7103i	−0.486292	+	0.467880i
$525$	−26.9729	+	52.4886i	−1.17719	+	2.29079i
$526$	14.5447	−	3.56321i	0.634177	−	0.155364i
$527$	8.35307	−	15.2975i	0.363865	−	0.666369i
$528$	−3.10680	−	6.25163i	−0.135206	−	0.272067i
$529$	−4.44408	−	22.5666i	−0.193221	−	0.981155i
$530$	0.0372410	−	0.173623i	0.00161764	−	0.00754169i
$531$	−4.56661	−	15.5524i	−0.198174	−	0.674918i
$532$	−3.92109	+	2.41433i	−0.170001	+	0.104674i
$533$	−4.45213	+	20.4661i	−0.192843	+	0.886485i
$534$	−15.2143	+	44.2815i	−0.658388	+	1.91625i
$535$	0.681305	+	1.31943i	0.0294554	+	0.0570438i
$536$	−0.00611269	+	0.0213507i	−0.000264028	+	0.000922211i
$537$	−40.9279	+	2.92722i	−1.76617	+	0.126319i
$538$	3.32882	+	19.5266i	0.143516	+	0.841853i
$539$	−5.06785	−	11.0970i	−0.218288	−	0.477983i
$540$	1.77308	+	0.332252i	0.0763010	+	0.0142978i
$541$	−10.6286	−	3.12083i	−0.456958	−	0.134175i	0.0451493	−	0.998980i	$-0.485624\pi$
$541$	−10.6286	−	3.12083i	−0.456958	−	0.134175i	−0.502107	+	0.864805i	$0.667442\pi$
$542$	5.52708	+	6.05254i	0.237408	+	0.259979i
$543$	29.5331	−	22.1082i	1.26739	−	0.948754i
$544$	17.0582	−	1.00530i	0.731365	−	0.0431018i
$545$	−0.363298	+	2.16913i	−0.0155620	+	0.0929155i
$546$	38.2290	+	65.8714i	1.63605	+	2.81904i
$547$	32.6294	+	24.4260i	1.39513	+	1.04438i	0.991590	+	0.129420i	$0.0413115\pi$
$547$	32.6294	+	24.4260i	1.39513	+	1.04438i	0.403541	+	0.914962i	$0.367779\pi$
$548$	−3.29903	+	1.43035i	−0.140927	+	0.0611016i
$549$	0.315684	−	0.273542i	0.0134731	−	0.0116745i
$550$	2.21630	−	4.60409i	0.0945032	−	0.196319i
$551$			0.604664i			0.0257596i
$552$	28.1225	+	16.8046i	1.19697	+	0.715252i
$553$	−0.275901	+	0.275901i	−0.0117325	+	0.0117325i
$554$	−3.43044	+	18.0172i	−0.145745	+	0.765476i
$555$	43.5889	+	29.4602i	1.85024	+	1.25052i
$556$	−12.2216	+	30.9313i	−0.518312	+	1.31178i
$557$	−7.62512	+	10.1860i	−0.323087	+	0.431594i	−0.932451	−	0.361297i	$-0.882334\pi$
$557$	−7.62512	+	10.1860i	−0.323087	+	0.431594i	0.609364	+	0.792891i	$0.291425\pi$
$558$	−5.93280	+	22.3428i	−0.251156	+	0.945845i
$559$	−16.0673	+	35.1824i	−0.679573	+	1.48806i
$560$	0.422523	+	43.7080i	0.0178548	+	1.84700i
$561$	0.750278	−	5.21830i	0.0316768	−	0.220317i
$562$	29.3321	−	26.7856i	1.23730	−	1.12988i
$563$	1.84727	+	3.38303i	0.0778533	+	0.142578i	0.913706	−	0.406377i	$-0.133208\pi$
$563$	1.84727	+	3.38303i	0.0778533	+	0.142578i	−0.835852	+	0.548954i	$0.815026\pi$
$564$	43.2283	−	15.1799i	1.82024	−	0.639190i
$565$	−1.22176	+	12.8839i	−0.0513997	+	0.542030i
$566$	−8.84085	−	6.26557i	−0.371609	−	0.263362i
$567$	3.30262	+	46.1767i	0.138697	+	1.93924i
$568$	0.129275	+	0.232991i	0.00542424	+	0.00977607i
$569$	−18.2495	+	28.3968i	−0.765059	+	1.19046i	0.211954	+	0.977280i	$0.432017\pi$
$569$	−18.2495	+	28.3968i	−0.765059	+	1.19046i	−0.977014	+	0.213176i	$0.931619\pi$
$570$	0.246258	−	3.58978i	0.0103146	−	0.150359i
$571$	14.7766	+	22.9929i	0.618382	+	0.962222i	0.999293	+	0.0376095i	$0.0119743\pi$
$571$	14.7766	+	22.9929i	0.618382	+	0.962222i	−0.380910	+	0.924612i	$0.624389\pi$
$572$	−3.45756	−	5.61539i	−0.144568	−	0.234791i
$573$	−12.2389	+	22.4139i	−0.511289	+	0.936355i
$574$	−28.2302	−	14.4733i	−1.17831	−	0.604103i
$575$	2.92607	+	23.8000i	0.122026	+	0.992527i
$576$	−21.6575	+	6.67853i	−0.902396	+	0.278272i
$577$	9.44023	+	5.15476i	0.393002	+	0.214595i	0.663584	−	0.748101i	$-0.269034\pi$
$577$	9.44023	+	5.15476i	0.393002	+	0.214595i	−0.270582	+	0.962697i	$0.587216\pi$
$578$	−9.52290	−	5.77513i	−0.396101	−	0.240214i
$579$	50.2564	−	32.2978i	2.08858	−	1.34225i
$580$	4.91635	+	2.96198i	0.204140	+	0.122990i
$581$	−36.8258	−	23.6665i	−1.52779	−	0.981852i
$582$	1.76538	−	15.0527i	0.0731773	−	0.623954i
$583$	−0.0404745	+	0.00289479i	−0.00167628	+	0.000119890i
$584$	−0.273864	−	40.5164i	−0.0113326	−	1.67658i
$585$	−28.7754	−	2.72872i	−1.18972	−	0.112819i
$586$	31.5478	+	29.9454i	1.30323	+	1.23703i
$587$	−11.3039	+	6.17241i	−0.466563	+	0.254763i	−0.695292	−	0.718728i	$-0.744725\pi$
$587$	−11.3039	+	6.17241i	−0.466563	+	0.254763i	0.228729	+	0.973490i	$0.426543\pi$
$588$	−78.6712	+	21.4603i	−3.24435	+	0.885008i
$589$	−2.69074	−	0.386870i	−0.110870	−	0.0159407i
$590$	2.52284	−	17.9163i	0.103864	−	0.737604i
$591$	5.83408	+	2.66433i	0.239982	+	0.109596i
$592$	38.7322	+	4.27732i	1.59188	+	0.175797i
$593$	6.79920	+	5.08982i	0.279210	+	0.209014i	0.729700	−	0.683768i	$-0.239660\pi$
$593$	6.79920	+	5.08982i	0.279210	+	0.209014i	−0.450490	+	0.892781i	$0.648751\pi$
$594$	−0.0401092	−	0.410271i	−0.00164570	−	0.0168336i
$595$	−18.4839	+	27.3485i	−0.757767	+	1.12118i
$596$	17.5823	+	13.6991i	0.720200	+	0.561138i
$597$	35.5110	+	35.5110i	1.45337	+	1.45337i
$598$	27.8938	+	13.4029i	1.14066	+	0.548085i
$599$	1.11541			0.0455745			0.0227873	−	0.999740i	$-0.492746\pi$
$599$	1.11541			0.0455745			0.0227873	+	0.999740i	$0.492746\pi$
$600$	−27.9812	−	19.5870i	−1.14233	−	0.799636i
$601$	15.0119	+	17.3246i	0.612347	+	0.706686i	0.974235	−	0.225536i	$-0.0724133\pi$
$601$	15.0119	+	17.3246i	0.612347	+	0.706686i	−0.361888	+	0.932221i	$0.617868\pi$
$602$	−45.2588	−	37.1976i	−1.84461	−	1.51606i
$603$	0.0133305	−	0.0178075i	0.000542860	−	0.000725176i
$604$	−2.24473	−	43.0410i	−0.0913366	−	1.75131i
$605$	23.1072	+	3.87013i	0.939443	+	0.157343i
$606$	22.9007	+	56.8317i	0.930276	+	2.30863i
$607$	9.23630	+	12.3383i	0.374890	+	0.500794i	0.947818	−	0.318811i	$-0.103284\pi$
$607$	9.23630	+	12.3383i	0.374890	+	0.500794i	−0.572928	+	0.819605i	$0.694193\pi$
$608$	−1.07666	−	2.43797i	−0.0436643	−	0.0988726i
$609$	−4.26767	+	14.5343i	−0.172935	+	0.588961i
$610$	0.446992	−	0.132662i	0.0180982	−	0.00537131i
$611$	39.3681	−	17.9788i	1.59266	−	0.727345i
$612$	−16.3260	−	5.13787i	−0.659938	−	0.207686i
$613$	−2.58326	−	36.1187i	−0.104337	−	1.45882i	−0.732515	−	0.680751i	$-0.761654\pi$
$613$	−2.58326	−	36.1187i	−0.104337	−	1.45882i	0.628178	−	0.778070i	$-0.283801\pi$
$614$	4.18766	−	3.30851i	0.169000	−	0.133520i
$615$	22.0264	−	11.3737i	0.888191	−	0.458630i
$616$	9.56457	−	2.87877i	0.385367	−	0.115989i
$617$	−28.4178	−	6.18191i	−1.14406	−	0.248874i	−0.399693	−	0.916649i	$-0.630883\pi$
$617$	−28.4178	−	6.18191i	−1.14406	−	0.248874i	−0.744363	+	0.667775i	$0.767247\pi$
$618$	27.5060	+	16.6809i	1.10645	+	0.671003i
$619$	2.18263	−	0.640879i	0.0877275	−	0.0257591i	−0.237574	−	0.971369i	$-0.576352\pi$
$619$	2.18263	−	0.640879i	0.0877275	−	0.0257591i	0.325302	+	0.945610i	$0.394534\pi$
$620$	−16.3263	+	19.9825i	−0.655680	+	0.802518i
$621$	1.19891	+	1.51820i	0.0481104	+	0.0609234i
$622$	−12.0704	+	3.88848i	−0.483978	+	0.155914i
$623$	−58.7982	−	32.1062i	−2.35570	−	1.28631i
$624$	−40.7731	+	16.7510i	−1.63223	+	0.670577i
$625$	−1.25490	−	24.9685i	−0.0501961	−	0.998739i
$626$	1.05213	−	3.06224i	0.0420516	−	0.122392i
$627$	−0.803457	+	0.174781i	−0.0320870	+	0.00698010i
$628$	9.88720	−	14.7511i	0.394542	−	0.588632i
$629$	22.2399	+	19.2710i	0.886765	+	0.768386i
$630$	15.1804	−	41.0644i	0.604800	−	1.63604i
$631$	11.1283	−	5.08211i	0.443009	−	0.202316i	−0.181406	−	0.983408i	$-0.558065\pi$
$631$	11.1283	−	5.08211i	0.443009	−	0.202316i	0.624415	+	0.781093i	$0.285337\pi$
$632$	−0.136552	−	0.179866i	−0.00543177	−	0.00715467i
$633$	42.8881	−	23.4187i	1.70465	−	0.930809i
$634$	−2.29060	−	0.103943i	−0.0909714	−	0.00412809i
$635$	−9.34366	+	11.8974i	−0.370792	+	0.472135i
$636$	−0.0245658	+	0.270123i	−0.000974097	+	0.0107111i
$637$	−72.1736	+	26.9194i	−2.85962	+	1.06658i
$638$	0.336612	−	1.26767i	0.0133266	−	0.0501876i
$639$	−0.0379811	−	0.264165i	−0.00150251	−	0.0104502i
$640$	−25.0965	−	3.18853i	−0.992025	−	0.126038i
$641$	−3.87861	−	4.47615i	−0.153196	−	0.176797i	0.673964	−	0.738764i	$-0.264590\pi$
$641$	−3.87861	−	4.47615i	−0.153196	−	0.176797i	−0.827160	+	0.561967i	$0.810045\pi$
$642$	−1.27559	−	1.87556i	−0.0503434	−	0.0740224i
$643$	−2.65592	−	2.65592i	−0.104739	−	0.104739i	0.652795	−	0.757535i	$-0.273596\pi$
$643$	−2.65592	−	2.65592i	−0.104739	−	0.104739i	−0.757535	+	0.652795i	$0.773596\pi$
$644$	−30.4639	+	35.6245i	−1.20045	+	1.40380i
$645$	44.2101	−	11.8771i	1.74077	−	0.467659i
$646$	0.376443	−	1.97713i	0.0148110	−	0.0777893i
$647$	−45.0789	−	3.22411i	−1.77224	−	0.126753i	−0.853365	−	0.521313i	$-0.825442\pi$
$647$	−45.0789	−	3.22411i	−1.77224	−	0.126753i	−0.918870	+	0.394560i	$0.870897\pi$
$648$	−26.7382	−	1.73078i	−1.05037	−	0.0679916i
$649$	−4.09246	+	0.588408i	−0.160643	+	0.0230970i
$650$	−27.9989	−	16.0325i	−1.09821	−	0.628846i
$651$	−61.9470	−	28.2902i	−2.42789	−	1.10878i
$652$	−3.09222	+	2.57667i	−0.121100	+	0.100910i
$653$	−6.93353	−	9.26211i	−0.271330	−	0.362454i	0.644093	−	0.764947i	$-0.277235\pi$
$653$	−6.93353	−	9.26211i	−0.271330	−	0.362454i	−0.915423	+	0.402492i	$0.868144\pi$
$654$	0.152288	−	3.35600i	0.00595495	−	0.131230i
$655$	17.2662	+	0.399708i	0.674646	+	0.0156179i
$656$	10.5153	−	15.0519i	0.410552	−	0.587678i
$657$	−14.1821	+	38.0238i	−0.553298	+	1.48345i
$658$	11.0163	+	64.6209i	0.429460	+	2.51918i
$659$	20.3572	−	23.4934i	0.793002	−	0.915173i	−0.204974	−	0.978767i	$-0.565711\pi$
$659$	20.3572	−	23.4934i	0.793002	−	0.915173i	0.997976	+	0.0635942i	$0.0202563\pi$
$660$	−2.51468	+	7.38885i	−0.0978840	+	0.287611i
$661$	−16.4475	−	10.5701i	−0.639732	−	0.411131i	0.180169	−	0.983636i	$-0.442335\pi$
$661$	−16.4475	−	10.5701i	−0.639732	−	0.411131i	−0.819901	+	0.572505i	$0.805972\pi$
$662$	9.68168	+	19.8169i	0.376289	+	0.770204i
$663$	−32.5277	−	7.07596i	−1.26327	−	0.274808i
$664$	16.4616	−	19.2592i	0.638834	−	0.747402i
$665$	5.00396	+	1.21048i	0.194045	+	0.0469405i
$666$	−34.7318	−	17.8066i	−1.34583	−	0.689990i
$667$	1.88600	+	5.85904i	0.0730262	+	0.226863i
$668$	1.46677	−	8.96951i	0.0567509	−	0.347041i
$669$	−1.51706	−	5.16663i	−0.0586529	−	0.199754i
$670$	0.0217580	−	0.0119630i	0.000840584	−	0.000462171i
$671$	−0.0576043	−	0.0896340i	−0.00222379	−	0.00346028i
$672$	−8.67273	−	66.2005i	−0.334558	−	2.55374i
$673$	14.5354	−	3.16197i	0.560297	−	0.121885i	0.0765065	−	0.997069i	$-0.475623\pi$
$673$	14.5354	−	3.16197i	0.560297	−	0.121885i	0.483790	+	0.875184i	$0.339260\pi$
$674$	−24.3465	−	30.8159i	−0.937791	−	1.18698i
$675$	−1.13265	−	1.66878i	−0.0435958	−	0.0642315i
$676$	−13.8682	+	7.22886i	−0.533394	+	0.278033i
$677$	0.0646147	−	0.173239i	0.00248334	−	0.00665810i	−0.935702	−	0.352791i	$-0.885233\pi$
$677$	0.0646147	−	0.173239i	0.00248334	−	0.00665810i	0.938185	+	0.346133i	$0.112505\pi$
$678$	−0.514963	−	19.7615i	−0.0197770	−	0.758935i
$679$	20.8064	+	6.10932i	0.798478	+	0.234454i
$680$	−14.2315	−	12.7459i	−0.545752	−	0.488781i
$681$	6.66323	−	46.3438i	0.255335	−	1.77590i
$682$	5.42575	+	2.30899i	0.207763	+	0.0884157i
$683$	−40.5263	+	15.1155i	−1.55070	+	0.578379i	−0.971548	−	0.236843i	$-0.923887\pi$
$683$	−40.5263	+	15.1155i	−1.55070	+	0.578379i	−0.579148	+	0.815223i	$0.696614\pi$
$684$	0.139030	+	2.66579i	0.00531594	+	0.101929i
$685$	3.73319	+	1.49171i	0.142638	+	0.0569952i
$686$	−6.64517	−	67.9726i	−0.253714	−	2.59521i
$687$	26.2570	+	1.87793i	1.00177	+	0.0716477i
$688$	24.8826	−	23.0328i	0.948642	−	0.878117i
$689$			0.256218i			0.00976114i
$690$	−8.81066	−	35.5522i	−0.335416	−	1.35345i
$691$		−	42.7118i		−	1.62483i	−0.583078	−	0.812416i	$-0.698152\pi$
$691$		−	42.7118i		−	1.62483i	0.583078	−	0.812416i	$-0.301848\pi$
$692$	4.82485	+	38.8669i	0.183413	+	1.47750i
$693$	−9.97901	−	0.713713i	−0.379071	−	0.0271117i
$694$	−29.0083	+	2.83593i	−1.10114	+	0.107650i
$695$	34.1721	−	14.6598i	1.29622	−	0.556079i
$696$	−7.99939	−	3.58805i	−0.303216	−	0.136005i
$697$	12.9917	−	4.84566i	0.492097	−	0.183543i
$698$	9.51602	−	22.3611i	0.360187	−	0.846380i
$699$	−0.225077	+	1.56544i	−0.00851319	+	0.0592105i
$700$	34.3543	−	34.7562i	1.29847	−	1.31366i
$701$	44.7198	+	13.1309i	1.68904	+	0.495948i	0.978246	−	0.207449i	$-0.0665160\pi$
$701$	44.7198	+	13.1309i	1.68904	+	0.495948i	0.710798	+	0.703397i	$0.248334\pi$
$702$	−2.60202	+	0.0678058i	−0.0982068	+	0.00255916i
$703$	1.60394	−	4.30034i	0.0604939	−	0.162190i
$704$	0.900004	+	5.71054i	0.0339202	+	0.215224i
$705$	−46.0900	−	22.3519i	−1.73585	−	0.841820i
$706$	16.9140	−	13.3631i	0.636567	−	0.502927i
$707$	−85.6641	+	18.6351i	−3.22173	+	0.700844i
$708$	−0.533186	+	27.6317i	−0.0200384	+	1.03846i
$709$	10.3241	+	16.0646i	0.387729	+	0.603318i	0.979173	−	0.203028i	$-0.0650783\pi$
$709$	10.3241	+	16.0646i	0.387729	+	0.603318i	−0.591444	+	0.806346i	$0.701442\pi$
$710$	0.0830974	−	0.286078i	0.00311859	−	0.0107363i
$711$	0.0637255	+	0.217029i	0.00238989	+	0.00813923i
$712$	23.0259	−	31.1963i	0.862931	−	1.16913i
$713$	−27.2793	+	4.64398i	−1.02162	+	0.173919i
$714$	23.0030	−	44.8675i	0.860866	−	1.67913i
$715$	−1.73353	+	7.16617i	−0.0648304	+	0.268000i
$716$	33.0571	+	7.86201i	1.23540	+	0.293817i
$717$	−1.26498	−	0.275180i	−0.0472416	−	0.0102768i
$718$	3.20128	−	1.56401i	0.119471	−	0.0583684i
$719$	34.2565	+	22.0153i	1.27755	+	0.821034i	0.990584	−	0.136906i	$-0.0437159\pi$
$719$	34.2565	+	22.0153i	1.27755	+	0.821034i	0.286969	+	0.957940i	$0.407352\pi$
$720$	22.3558	+	11.9281i	0.833153	+	0.444535i
$721$	−30.1411	+	34.7847i	−1.12251	+	1.29545i
$722$	26.1785	−	4.46280i	0.974262	−	0.166088i
$723$	−17.0177	+	45.6262i	−0.632895	+	1.69686i
$724$	−28.8244	+	10.1219i	−1.07125	+	0.376177i
$725$	−1.52106	−	6.23427i	−0.0564907	−	0.231535i
$726$	−35.7507	−	1.62229i	−1.32683	−	0.0602089i
$727$	−22.5756	−	30.1574i	−0.837281	−	1.11848i	−0.991457	−	0.130434i	$-0.958363\pi$
$727$	−22.5756	−	30.1574i	−0.837281	−	1.11848i	0.154176	−	0.988043i	$-0.450728\pi$
$728$	−13.8226	−	61.5358i	−0.512298	−	2.28067i
$729$	21.7535	+	9.93451i	0.805687	+	0.367945i
$730$	−31.9385	+	32.1247i	−1.18210	+	1.18899i
$731$	25.3450	−	3.64406i	0.937418	−	0.134780i
$732$	−0.653433	+	0.283308i	−0.0241516	+	0.0104714i
$733$	17.2652	+	1.23483i	0.637705	+	0.0456096i	0.386449	−	0.922311i	$-0.373702\pi$
$733$	17.2652	+	1.23483i	0.637705	+	0.0456096i	0.251257	+	0.967921i	$0.419156\pi$
$734$	10.0790	+	1.91903i	0.372024	+	0.0708329i
$735$	78.9861	+	45.5338i	2.91345	+	1.67954i
$736$	−18.0368	−	20.2651i	−0.664845	−	0.746982i
$737$	−0.00401213	−	0.00401213i	−0.000147789	−	0.000147789i
$738$	−15.2070	+	10.3424i	−0.559776	+	0.380709i
$739$	−14.3690	−	16.5827i	−0.528572	−	0.610004i	0.427185	−	0.904164i	$-0.359505\pi$
$739$	−14.3690	−	16.5827i	−0.528572	−	0.610004i	−0.955756	+	0.294160i	$0.904960\pi$
$740$	−27.1078	−	34.1067i	−0.996503	−	1.25379i
$741$	0.738880	+	5.13902i	0.0271434	+	0.188787i
$742$	−0.375085	−	0.0995986i	−0.0137698	−	0.00365638i
$743$	5.66931	−	2.11454i	0.207987	−	0.0775751i	−0.243312	−	0.969948i	$-0.578234\pi$
$743$	5.66931	−	2.11454i	0.207987	−	0.0775751i	0.451298	+	0.892373i	$0.350961\pi$
$744$	21.0848	−	33.3014i	0.773008	−	1.22089i
$745$	−2.97467	−	24.7418i	−0.108983	−	0.906470i
$746$	−2.38904	+	52.6476i	−0.0874690	+	1.92757i
$747$	−22.2725	+	12.1617i	−0.814908	+	0.444973i
$748$	−1.88987	+	3.93548i	−0.0691004	+	0.143895i
$749$	2.95207	−	1.34817i	0.107866	−	0.0492610i
$750$	6.49126	+	37.6312i	0.237027	+	1.37410i
$751$	13.8941	+	12.0393i	0.507002	+	0.439320i	0.870422	−	0.492306i	$-0.163846\pi$
$751$	13.8941	+	12.0393i	0.507002	+	0.439320i	−0.363421	+	0.931625i	$0.618391\pi$
$752$	−37.9200	+	1.24469i	−1.38280	+	0.0453891i
$753$	8.83154	−	1.92118i	0.321839	−	0.0700119i
$754$	−7.83236	−	2.69106i	−0.285238	−	0.0980027i
$755$	−32.3899	+	35.6770i	−1.17879	+	1.29842i
$756$	0.912207	−	3.83552i	0.0331767	−	0.139497i
$757$	−23.8752	−	13.0368i	−0.867758	−	0.473832i	−0.0172849	−	0.999851i	$-0.505502\pi$
$757$	−23.8752	−	13.0368i	−0.867758	−	0.473832i	−0.850473	+	0.526019i	$0.823684\pi$
$758$	13.0698	+	40.5706i	0.474717	+	1.47359i
$759$	−7.24014	+	4.19964i	−0.262800	+	0.152437i
$760$	−1.08690	+	2.77439i	−0.0394261	+	0.100638i
$761$	−33.9680	+	9.97391i	−1.23134	+	0.361554i	−0.831755	−	0.555143i	$-0.812664\pi$
$761$	−33.9680	+	9.97391i	−1.23134	+	0.361554i	−0.399584	+	0.916697i	$0.630845\pi$
$762$	11.9822	−	19.7581i	0.434071	−	0.715762i
$763$	4.69683	+	1.02173i	0.170037	+	0.0369892i
$764$	15.2395	−	14.6625i	0.551347	−	0.530472i
$765$	8.77953	+	17.0026i	0.317425	+	0.614730i
$766$	−17.4477	−	22.0839i	−0.630410	−	0.797925i
$767$	1.86242	+	26.0400i	0.0672480	+	0.940250i
$768$	38.6419	+	0.223171i	1.39437	+	0.00805300i
$769$	−10.1883	+	4.65285i	−0.367400	+	0.167786i	−0.590556	−	0.806997i	$-0.701091\pi$
$769$	−10.1883	+	4.65285i	−0.367400	+	0.167786i	0.223156	+	0.974783i	$0.428364\pi$
$770$	−9.81689	−	5.32344i	−0.353776	−	0.191843i
$771$	−3.30393	+	11.2521i	−0.118988	+	0.405236i
$772$	−47.7270	+	13.0192i	−1.71773	+	0.468571i
$773$	−26.9087	−	35.9458i	−0.967838	−	1.29288i	−0.956128	−	0.292949i	$-0.905363\pi$
$773$	−26.9087	−	35.9458i	−0.967838	−	1.29288i	−0.0117105	−	0.999931i	$-0.503728\pi$
$774$	−31.4999	+	12.6931i	−1.13224	+	0.456244i
$775$	28.7156	−	2.77993i	1.03149	−	0.0998581i
$776$	−5.13643	+	11.4514i	−0.184387	+	0.411082i
$777$	68.9055	−	92.0469i	2.47197	−	3.30217i
$778$	−4.24370	+	5.16336i	−0.152144	+	0.185115i
$779$	−1.41622	−	1.63440i	−0.0507413	−	0.0585586i
$780$	45.4034	+	19.1662i	1.62570	+	0.686260i
$781$	−0.0680752			−0.00243592
$782$	−2.51921	−	20.3321i	−0.0900869	−	0.727074i
$783$	−0.366069	−	0.366069i	−0.0130823	−	0.0130823i
$784$	67.4780	+	2.60511i	2.40993	+	0.0930395i
$785$	−19.4929	+	3.77019i	−0.695733	+	0.134564i
$786$	−26.2557	+	2.56682i	−0.936508	+	0.0915554i
$787$	10.0454	+	7.51993i	0.358082	+	0.268056i	0.763138	−	0.646235i	$-0.223657\pi$
$787$	10.0454	+	7.51993i	0.358082	+	0.268056i	−0.405057	+	0.914291i	$0.632748\pi$
$788$	−3.94607	−	3.55487i	−0.140573	−	0.126637i
$789$	23.2625	+	10.6236i	0.828166	+	0.378211i
$790$	−0.0352054	+	0.250017i	−0.00125255	+	0.00889520i
$791$	27.9962	+	4.02525i	0.995432	+	0.143121i
$792$	1.19255	−	5.66620i	0.0423756	−	0.201340i
$793$	−0.590476	+	0.322425i	−0.0209684	+	0.0114496i
$794$	11.7238	−	12.3511i	0.416060	−	0.438325i
$795$	0.233718	−	0.193231i	0.00828911	−	0.00685319i
$796$	−19.2228	−	36.8781i	−0.681335	−	1.30711i
$797$	−50.4530	+	3.60847i	−1.78714	+	0.127819i	−0.925268	−	0.379313i	$-0.876160\pi$
$797$	−50.4530	+	3.60847i	−1.78714	+	0.127819i	−0.861869	+	0.507132i	$0.830706\pi$
$798$	−7.81038	−	0.916001i	−0.276484	−	0.0324261i
$799$	−24.1036	−	15.4904i	−0.852722	−	0.548011i
$800$	17.2335	+	22.4278i	0.609296	+	0.792943i
$801$	−32.6710	+	20.9964i	−1.15437	+	0.741871i
$802$	7.85060	−	12.9453i	0.277214	−	0.457113i
$803$	9.08545	+	4.96103i	0.320618	+	0.175071i
$804$	−0.0307951	+	0.0221389i	−0.00108606	+	0.000780778i
$805$	52.2628	−	3.87853i	1.84202	−	0.136700i
$806$	16.9864	−	33.1321i	0.598320	−	1.16703i
$807$	−16.2121	+	29.6903i	−0.570694	+	1.04515i
$808$	−3.96173	−	50.5848i	−0.139373	−	1.77957i
$809$	18.6326	+	28.9928i	0.655086	+	1.01933i	0.996832	+	0.0795412i	$0.0253455\pi$
$809$	18.6326	+	28.9928i	0.655086	+	1.01933i	−0.341746	+	0.939793i	$0.611018\pi$
$810$	19.6832	+	22.5827i	0.691599	+	0.793474i
$811$	1.95264	−	3.03837i	0.0685666	−	0.106692i	−0.805277	−	0.592899i	$-0.797983\pi$
$811$	1.95264	−	3.03837i	0.0685666	−	0.106692i	0.873844	+	0.486207i	$0.161620\pi$
$812$	6.98416	−	10.4199i	0.245096	−	0.365668i
$813$	0.998584	+	13.9620i	0.0350219	+	0.489670i
$814$	−5.75662	+	8.12272i	−0.201770	+	0.284701i
$815$	4.48004	+	0.424834i	0.156929	+	0.0148813i
$816$	23.9226	+	16.7124i	0.837460	+	0.585050i
$817$	−1.91393	−	3.50511i	−0.0669601	−	0.122628i
$818$	−13.2207	−	14.4776i	−0.462252	−	0.506198i
$819$	−8.99014	+	62.5278i	−0.314141	+	2.18490i
$820$	−20.2263	+	3.50864i	−0.706332	+	0.122527i
$821$	4.26505	−	9.33916i	0.148851	−	0.325939i	−0.820488	−	0.571663i	$-0.806298\pi$
$821$	4.26505	−	9.33916i	0.148851	−	0.325939i	0.969340	+	0.245724i	$0.0790257\pi$
$822$	−5.93507	−	1.57597i	−0.207009	−	0.0549684i
$823$	−14.5689	+	19.4618i	−0.507841	+	0.678396i	−0.979049	−	0.203626i	$-0.934727\pi$
$823$	−14.5689	+	19.4618i	−0.507841	+	0.678396i	0.471208	+	0.882022i	$0.343818\pi$
$824$	−17.5806	−	20.0141i	−0.612448	−	0.697224i
$825$	7.84422	−	3.82318i	0.273101	−	0.133106i
$826$	−38.8447	−	7.39596i	−1.35158	−	0.257338i
$827$	−15.3652	+	15.3652i	−0.534301	+	0.534301i	−0.921849	−	0.387548i	$-0.873322\pi$
$827$	−15.3652	+	15.3652i	−0.534301	+	0.534301i	0.387548	+	0.921849i	$0.373322\pi$
$828$	9.66200	+	25.3972i	0.335778	+	0.882614i
$829$			22.8030i			0.791982i	0.918254	+	0.395991i	$0.129599\pi$
$829$			22.8030i			0.791982i	−0.918254	+	0.395991i	$0.870401\pi$
$830$	−28.2481	+	2.10291i	−0.980506	+	0.0729931i
$831$	−23.6716	+	20.5115i	−0.821158	+	0.711537i
$832$	36.3713	−	3.09603i	1.26095	−	0.107336i
$833$	40.8245	+	30.5609i	1.41449	+	1.05887i
$834$	−49.1241	+	28.5096i	−1.70103	+	0.987207i
$835$	−8.27339	+	5.89961i	−0.286312	+	0.204165i
$836$	0.678108	+	0.0616692i	0.0234529	+	0.00213288i
$837$	1.86322	−	1.39479i	0.0644022	−	0.0482109i
$838$	−12.4782	+	11.3949i	−0.431052	+	0.393630i
$839$	−8.54713	−	2.50966i	−0.295080	−	0.0866432i	0.130842	−	0.991403i	$-0.458232\pi$
$839$	−8.54713	−	2.50966i	−0.295080	−	0.0866432i	−0.425922	+	0.904760i	$0.640050\pi$
$840$	−45.7073	+	59.0168i	−1.57705	+	2.03627i
$841$	11.3628	+	24.8810i	0.391820	+	0.857965i
$842$	17.9318	−	3.05694i	0.617971	−	0.105349i
$843$	67.6635	−	4.83939i	2.33045	−	0.166677i
$844$	−39.6994	+	7.83714i	−1.36651	+	0.269765i
$845$	16.6584	+	5.31310i	0.573066	+	0.182776i
$846$	35.9394	+	12.3482i	1.23562	+	0.424538i
$847$	10.8843	−	50.0341i	0.373988	−	1.71919i
$848$	0.0865544	−	0.207266i	0.00297229	−	0.00711754i
$849$	−5.21356	−	17.7558i	−0.178929	−	0.609376i
$850$	1.09232	+	21.3318i	0.0374664	+	0.731675i
$851$	2.12868	−	46.6721i	0.0729702	−	1.59990i
$852$	−0.0734363	+	0.449075i	−0.00251589	+	0.0153850i
$853$	−14.9167	+	27.3179i	−0.510738	+	0.935346i	0.487330	+	0.873218i	$0.337971\pi$
$853$	−14.9167	+	27.3179i	−0.510738	+	0.935346i	−0.998068	+	0.0621287i	$0.980211\pi$
$854$	−0.242473	−	0.989749i	−0.00829726	−	0.0338685i
$855$	2.00611	−	2.20970i	0.0686074	−	0.0755700i
$856$	0.541355	+	1.79862i	0.0185031	+	0.0614756i
$857$	3.39933	+	15.6265i	0.116119	+	0.533791i	0.998050	+	0.0624129i	$0.0198796\pi$
$857$	3.39933	+	15.6265i	0.116119	+	0.533791i	−0.881931	+	0.471378i	$0.843757\pi$
$858$	1.31180	−	11.1852i	0.0447843	−	0.381858i
$859$	25.3890	−	29.3005i	0.866262	−	0.999720i	−0.133700	−	0.991022i	$-0.542686\pi$
$859$	25.3890	−	29.3005i	0.866262	−	0.999720i	0.999962	−	0.00869800i	$-0.00276869\pi$
$860$	−37.8746	−	1.60834i	−1.29151	−	0.0548439i
$861$	−22.5062	−	49.2817i	−0.767010	−	1.67952i
$862$	23.1959	−	0.604461i	0.790056	−	0.0205880i
$863$	2.73652	+	5.01156i	0.0931522	+	0.170596i	0.920100	−	0.391683i	$-0.128107\pi$
$863$	2.73652	+	5.01156i	0.0931522	+	0.170596i	−0.826948	+	0.562278i	$0.809925\pi$
$864$	2.12779	+	0.824149i	0.0723888	+	0.0280381i
$865$	27.0455	−	34.4374i	0.919573	−	1.17091i
$866$	26.9461	−	10.8581i	0.915666	−	0.368973i
$867$	−6.64676	−	17.8207i	−0.225736	−	0.605221i
$868$	41.8999	+	37.7461i	1.42218	+	1.28119i
$869$	0.0571090	−	0.00821104i	0.00193729	−	0.000278540i
$870$	3.45216	+	9.17404i	0.117039	+	0.311029i
$871$	−0.0270763	+	0.0234617i	−0.000917444	+	0.000794970i
$872$	−0.954561	+	2.61309i	−0.0323255	+	0.0884902i
$873$	8.88892	−	8.88892i	0.300844	−	0.300844i
$874$	−2.83387	+	1.47633i	−0.0958572	+	0.0499377i
$875$	−54.6374	+	0.107252i	−1.84708	+	0.00362579i
$876$	42.5276	−	54.5826i	1.43687	−	1.84418i
$877$	1.33300	−	18.6377i	0.0450121	−	0.629351i	−0.924009	−	0.382372i	$-0.875107\pi$
$877$	1.33300	−	18.6377i	0.0450121	−	0.629351i	0.969021	−	0.246979i	$-0.0794380\pi$
$878$	20.4142	+	16.7782i	0.688947	+	0.566237i
$879$	10.5716	+	73.5270i	0.356571	+	2.48000i
$880$	3.82317	−	5.21141i	0.128879	−	0.175677i
$881$	0.596347	−	1.30582i	0.0200915	−	0.0439941i	−0.899320	−	0.437291i	$-0.855938\pi$
$881$	0.596347	−	1.30582i	0.0200915	−	0.0439941i	0.919412	+	0.393296i	$0.128665\pi$
$882$	−62.2359	−	26.4852i	−2.09559	−	0.891803i
$883$	7.19821	−	5.38851i	0.242239	−	0.181338i	−0.471259	−	0.881995i	$-0.656200\pi$
$883$	7.19821	−	5.38851i	0.242239	−	0.181338i	0.713499	+	0.700657i	$0.247110\pi$
$884$	23.9349	+	13.6754i	0.805019	+	0.459954i
$885$	22.3486	−	21.3373i	0.751241	−	0.717246i
$886$	−17.4870	+	18.4228i	−0.587487	+	0.618925i
$887$	25.6672	+	9.57337i	0.861820	+	0.321442i	0.741223	−	0.671259i	$-0.234246\pi$
$887$	25.6672	+	9.57337i	0.861820	+	0.321442i	0.120597	+	0.992702i	$0.461519\pi$
$888$	47.3735	+	46.7374i	1.58975	+	1.56840i
$889$	24.9866	+	21.6510i	0.838024	+	0.726152i
$890$	−42.8909	+	6.29412i	−1.43771	+	0.210979i
$891$	3.70100	−	5.75886i	0.123988	−	0.192929i
$892$	−0.0860282	+	4.45830i	−0.00288044	+	0.149275i
$893$	−0.949899	+	4.36661i	−0.0317871	+	0.146123i
$894$	9.05743	+	36.9715i	0.302926	+	1.23651i
$895$	−19.7937	−	32.4259i	−0.661631	−	1.08388i
$896$	−9.60606	+	54.4484i	−0.320916	+	1.81899i
$897$	23.1886	+	47.4912i	0.774246	+	1.58569i
$898$	8.02168	−	2.58419i	0.267687	−	0.0862354i
$899$	7.10537	−	2.08633i	0.236978	−	0.0695829i
$900$	−8.13936	−	27.1354i	−0.271312	−	0.904513i
$901$	0.142696	−	0.0917053i	0.00475390	−	0.00305515i
$902$	2.05923	+	4.21491i	0.0685647	+	0.140341i
$903$	−21.2666	−	97.7608i	−0.707707	−	3.25328i
$904$	−4.50572	+	15.7378i	−0.149858	+	0.523432i
$905$	30.7326	+	14.9041i	1.02158	+	0.495429i
$906$	42.5594	−	60.0522i	1.41394	−	1.99510i
$907$	36.1890	+	13.4978i	1.20164	+	0.448187i	0.868974	−	0.494859i	$-0.164780\pi$
$907$	36.1890	+	13.4978i	1.20164	+	0.448187i	0.332663	+	0.943046i	$0.392053\pi$
$908$	−16.7839	+	34.9510i	−0.556994	+	1.15989i
$909$	−14.3180	+	48.7628i	−0.474900	+	1.61736i
$910$	−37.9498	+	59.4303i	−1.25803	+	1.97010i
$911$	52.8721	+	7.60185i	1.75173	+	0.251861i	0.942160	−	0.335164i	$-0.108792\pi$
$911$	52.8721	+	7.60185i	1.75173	+	0.251861i	0.809569	+	0.587024i	$0.199701\pi$
$912$	1.13833	−	4.40678i	0.0376938	−	0.145923i
$913$	2.26208	+	6.06486i	0.0748638	+	0.200718i
$914$	−9.66493	+	5.60912i	−0.319688	+	0.185533i
$915$	0.739426	+	0.295460i	0.0244447	+	0.00976762i
$916$	−20.2738	−	8.01060i	−0.669866	−	0.264678i
$917$	2.69273	−	37.6492i	0.0889217	−	1.24329i
$918$	0.969074	+	1.42488i	0.0319842	+	0.0470280i
$919$	4.40222			0.145216			0.0726080	−	0.997361i	$-0.476868\pi$
$919$	4.40222			0.145216			0.0726080	+	0.997361i	$0.476868\pi$
$920$	−1.87826	+	30.2733i	−0.0619245	+	0.998081i
$921$	9.11425			0.300325
$922$	−18.4525	−	27.1316i	−0.607700	−	0.893533i
$923$	−0.0306647	+	0.428748i	−0.00100934	+	0.0141124i
$924$	15.8645	+	6.26837i	0.521902	+	0.206214i
$925$	−5.71946	+	48.3726i	−0.188055	+	1.59048i
$926$	30.3129	−	17.5923i	0.996143	−	0.578120i
$927$	9.32439	+	24.9997i	0.306253	+	0.821097i
$928$	5.42685	+	4.82280i	0.178145	+	0.158316i
$929$	−45.7742	−	6.58133i	−1.50180	−	0.215926i	−0.658178	−	0.752862i	$-0.728673\pi$
$929$	−45.7742	−	6.58133i	−1.50180	−	0.215926i	−0.843623	+	0.536936i	$0.819582\pi$
$930$	−43.0330	+	9.49238i	−1.41111	+	0.311267i
$931$	2.24081	−	7.63150i	0.0734396	−	0.250112i
$932$	0.566943	−	1.18061i	0.0185708	−	0.0386721i
$933$	−20.2913	−	7.56825i	−0.664306	−	0.247773i
$934$	9.11955	−	12.8679i	0.298401	−	0.421050i
$935$	4.61153	−	1.59945i	0.150813	−	0.0523075i
$936$	−35.1494	−	10.0632i	−1.14889	−	0.328927i
$937$	−4.53182	−	20.8324i	−0.148048	−	0.680566i	−0.990006	−	0.141023i	$-0.954961\pi$
$937$	−4.53182	−	20.8324i	−0.148048	−	0.680566i	0.841958	−	0.539543i	$-0.181403\pi$
$938$	−0.0238210	−	0.0487579i	−0.000777784	−	0.00159200i
$939$	4.65186	−	2.98957i	0.151808	−	0.0975608i
$940$	30.8505	+	29.1135i	1.00623	+	0.949576i
$941$	11.4061	−	3.34912i	0.371827	−	0.109178i	−0.0904800	−	0.995898i	$-0.528840\pi$
$941$	11.4061	−	3.34912i	0.371827	−	0.109178i	0.462307	+	0.886720i	$0.347022\pi$
$942$	28.8660	−	9.29918i	0.940504	−	0.302984i
$943$	−18.8206	−	11.4196i	−0.612884	−	0.371875i
$944$	7.29011	−	21.6940i	0.237273	−	0.706080i
$945$	−3.76229	+	2.29661i	−0.122387	+	0.0747087i
$946$	2.06127	+	8.41390i	0.0670178	+	0.273560i
$947$	−1.53626	+	7.06207i	−0.0499217	+	0.229486i	−0.995347	−	0.0963515i	$-0.969283\pi$
$947$	−1.53626	+	7.06207i	−0.0499217	+	0.229486i	0.945426	+	0.325838i	$0.105646\pi$
$948$	0.00744044	−	0.385591i	0.000241654	−	0.0125234i
$949$	35.3379	−	54.9868i	1.14712	−	1.78495i
$950$	3.05774	−	1.32231i	0.0992061	−	0.0429013i
$951$	−2.95940	−	2.56434i	−0.0959653	−	0.0831544i
$952$	−29.3239	+	29.7230i	−0.950394	+	0.963329i
$953$	11.3244	+	4.22377i	0.366832	+	0.136821i	0.526119	−	0.850411i	$-0.323647\pi$
$953$	11.3244	+	4.22377i	0.366832	+	0.136821i	−0.159287	+	0.987232i	$0.550919\pi$
$954$	−0.154883	+	0.163171i	−0.00501452	+	0.00528286i
$955$	−23.6377	−	0.547207i	−0.764899	−	0.0177072i
$956$	0.930815	+	0.531828i	0.0301047	+	0.0172006i
$957$	1.79315	−	1.34233i	0.0579643	−	0.0433915i
$958$	−39.0550	−	16.6203i	−1.26181	−	0.536977i
$959$	3.64988	−	7.99213i	0.117861	−	0.258079i
$960$	−30.2541	−	30.8423i	−0.976446	−	0.995430i
$961$	0.326256	+	2.26916i	0.0105244	+	0.0731986i
$962$	48.5650	+	39.9150i	1.56580	+	1.28691i
$963$	0.134214	−	1.87656i	0.00432498	−	0.0604712i
$964$	24.7847	−	31.8102i	0.798260	−	1.02454i
$965$	47.9180	+	27.6237i	1.54254	+	0.889238i
$966$	−78.5377	+	15.4854i	−2.52691	+	0.498236i
$967$	−39.3154	+	39.3154i	−1.26430	+	1.26430i	−0.315308	+	0.948989i	$0.602108\pi$
$967$	−39.3154	+	39.3154i	−1.26430	+	1.26430i	−0.948989	+	0.315308i	$0.897892\pi$
$968$	27.8365	+	10.1687i	0.894700	+	0.326834i
$969$	2.59763	−	2.25086i	0.0834478	−	0.0723080i
$970$	13.1330	−	4.94189i	0.421674	−	0.158674i
$971$	51.2794	−	7.37286i	1.64563	−	0.236606i	0.743710	−	0.668502i	$-0.233064\pi$
$971$	51.2794	−	7.37286i	1.64563	−	0.236606i	0.901923	+	0.431896i	$0.142155\pi$
$972$	−32.1991	−	29.0070i	−1.03279	−	0.930400i
$973$	−28.3994	−	76.1417i	−0.910443	−	2.44099i
$974$	−30.0672	+	12.1158i	−0.963414	+	0.388214i
$975$	−20.5455	−	51.1262i	−0.657983	−	1.63735i
$976$	0.586581	−	0.0613511i	0.0187760	−	0.00196380i
$977$	12.6373	+	23.1435i	0.404303	+	0.740425i	0.997930	−	0.0643153i	$-0.0204863\pi$
$977$	12.6373	+	23.1435i	0.404303	+	0.740425i	−0.593627	+	0.804740i	$0.702305\pi$
$978$	−6.87154	+	0.179065i	−0.219728	+	0.00572587i
$979$	4.11519	+	9.01100i	0.131522	+	0.287993i
$980$	−51.0728	−	55.6027i	−1.63146	−	1.77616i
$981$	1.82474	−	2.10586i	0.0582595	−	0.0672351i
$982$	1.09599	−	9.34510i	0.0349745	−	0.298214i
$983$	−1.70259	−	7.82666i	−0.0543040	−	0.249632i	0.941990	−	0.335640i	$-0.108953\pi$
$983$	−1.70259	−	7.82666i	−0.0543040	−	0.249632i	−0.996294	+	0.0860082i	$0.972589\pi$
$984$	30.0261	−	9.03734i	0.957196	−	0.288100i
$985$	0.286426	+	5.93117i	0.00912630	+	0.188983i
$986$	1.30461	+	5.32528i	0.0415472	+	0.169591i
$987$	−53.6519	+	98.2562i	−1.70776	+	3.12753i
$988$	0.693858	−	4.24305i	0.0220746	−	0.134989i
$989$	−29.4783	−	27.9939i	−0.937355	−	0.890154i
$990$	−5.43591	+	3.51582i	−0.172764	+	0.111740i
$991$	7.51548	+	25.5954i	0.238737	+	0.813064i	0.988482	+	0.151337i	$0.0483579\pi$
$991$	7.51548	+	25.5954i	0.238737	+	0.813064i	−0.749745	+	0.661727i	$0.769824\pi$
$992$	−24.9335	+	21.0637i	−0.791640	+	0.668773i
$993$	−8.00643	+	36.8049i	−0.254076	+	1.16797i
$994$	−0.615736	−	0.211556i	−0.0195300	−	0.00671015i
$995$	−14.1285	+	44.2976i	−0.447903	+	1.40433i
$996$	42.4485	−	8.37984i	1.34503	−	0.265526i
$997$	39.7228	−	2.84103i	1.25803	−	0.0899764i	0.573652	−	0.819099i	$-0.305526\pi$
$997$	39.7228	−	2.84103i	1.25803	−	0.0899764i	0.684383	+	0.729123i	$0.260072\pi$
$998$	29.9385	−	5.10380i	0.947688	−	0.161558i
$999$	1.63242	+	3.57451i	0.0516476	+	0.113092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.147.23	yes	1360
4.3	odd	2	inner	460.2.w.a.147.2	yes	1360
5.3	odd	4	inner	460.2.w.a.423.14	yes	1360
20.3	even	4	inner	460.2.w.a.423.35	yes	1360
23.18	even	11	inner	460.2.w.a.87.35	yes	1360
92.87	odd	22	inner	460.2.w.a.87.14	✓	1360
115.18	odd	44	inner	460.2.w.a.363.2	yes	1360
460.363	even	44	inner	460.2.w.a.363.23	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.87.14	✓	1360	92.87	odd	22	inner
460.2.w.a.87.35	yes	1360	23.18	even	11	inner
460.2.w.a.147.2	yes	1360	4.3	odd	2	inner
460.2.w.a.147.23	yes	1360	1.1	even	1	trivial
460.2.w.a.363.2	yes	1360	115.18	odd	44	inner
460.2.w.a.363.23	yes	1360	460.363	even	44	inner
460.2.w.a.423.14	yes	1360	5.3	odd	4	inner
460.2.w.a.423.35	yes	1360	20.3	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.795314 - 1.16939i) q^{2} +(0.172295 - 2.40900i) q^{3} +(-0.734951 + 1.86007i) q^{4} +(2.05495 - 0.881573i) q^{5} +(-2.95410 + 1.71443i) q^{6} +(-1.70781 - 4.57881i) q^{7} +(2.75966 - 0.619893i) q^{8} +(-2.80415 - 0.403175i) q^{9} +O(q^{10})\)	\(q+(-0.795314 - 1.16939i) q^{2} +(0.172295 - 2.40900i) q^{3} +(-0.734951 + 1.86007i) q^{4} +(2.05495 - 0.881573i) q^{5} +(-2.95410 + 1.71443i) q^{6} +(-1.70781 - 4.57881i) q^{7} +(2.75966 - 0.619893i) q^{8} +(-2.80415 - 0.403175i) q^{9} +(-2.66524 - 1.70191i) q^{10} +(-0.203588 + 0.693357i) q^{11} +(4.35428 + 2.09098i) q^{12} +(4.27516 + 1.59455i) q^{13} +(-3.99617 + 5.63868i) q^{14} +(-1.76965 - 5.10228i) q^{15} +(-2.91970 - 2.73411i) q^{16} +(-0.642102 - 2.95169i) q^{17} +(1.75871 + 3.59980i) q^{18} +(-0.396341 + 0.254713i) q^{19} +(0.129497 + 4.47026i) q^{20} +(-11.3246 + 3.32521i) q^{21} +(0.972722 - 0.313363i) q^{22} +(-3.04597 + 3.70433i) q^{23} +(-1.01785 - 6.75484i) q^{24} +(3.44566 - 3.62318i) q^{25} +(-1.53544 - 6.26751i) q^{26} +(0.0857430 - 0.394154i) q^{27} +(9.77204 + 0.188563i) q^{28} +(0.693874 - 1.07969i) q^{29} +(-4.55913 + 6.12733i) q^{30} +(4.36065 + 3.77852i) q^{31} +(-0.875174 + 5.58875i) q^{32} +(1.63522 + 0.609906i) q^{33} +(-2.94101 + 3.09839i) q^{34} +(-7.54602 - 7.90367i) q^{35} +(2.81084 - 4.91959i) q^{36} +(-7.79880 + 5.83811i) q^{37} +(0.613075 + 0.260901i) q^{38} +(4.57787 - 10.0241i) q^{39} +(5.12449 - 3.70669i) q^{40} +(0.653265 + 4.54356i) q^{41} +(12.8951 + 10.5983i) q^{42} +(-0.604717 + 8.45504i) q^{43} +(-1.14006 - 0.888271i) q^{44} +(-6.11782 + 1.64356i) q^{45} +(6.75431 + 0.615831i) q^{46} +(6.70699 - 6.70699i) q^{47} +(-7.08954 + 6.56248i) q^{48} +(-12.7586 + 11.0554i) q^{49} +(-6.97730 - 1.14775i) q^{50} +(-7.22127 + 1.03826i) q^{51} +(-6.10801 + 6.78017i) q^{52} +(0.0196235 + 0.0526127i) q^{53} +(-0.529113 + 0.213209i) q^{54} +(0.192882 + 1.60429i) q^{55} +(-7.55134 - 11.5773i) q^{56} +(0.545317 + 0.998673i) q^{57} +(-1.81443 + 0.0472820i) q^{58} +(2.37681 + 5.20449i) q^{59} +(10.7912 + 0.458247i) q^{60} +(-0.0965561 + 0.111432i) q^{61} +(0.950486 - 8.10442i) q^{62} +(2.94288 + 13.5282i) q^{63} +(7.23147 - 3.42139i) q^{64} +(10.1910 - 0.492139i) q^{65} +(-0.587297 - 2.39728i) q^{66} +(-0.00376301 + 0.00689144i) q^{67} +(5.96226 + 0.974998i) q^{68} +(8.39893 + 7.97600i) q^{69} +(-3.24103 + 15.1101i) q^{70} +(0.0265406 + 0.0903890i) q^{71} +(-7.98842 + 0.625642i) q^{72} +(3.04500 - 13.9977i) q^{73} +(13.0295 + 4.47672i) q^{74} +(-8.13459 - 8.92486i) q^{75} +(-0.182492 - 0.924422i) q^{76} +(3.52244 - 0.251930i) q^{77} +(-15.3630 + 2.61902i) q^{78} +(-0.0331677 - 0.0726270i) q^{79} +(-8.41016 - 3.04455i) q^{80} +(-9.08943 - 2.66890i) q^{81} +(4.79364 - 4.37748i) q^{82} +(7.17089 - 5.36806i) q^{83} +(2.13793 - 23.5084i) q^{84} +(-3.92162 - 5.49953i) q^{85} +(10.3682 - 6.01726i) q^{86} +(-2.48142 - 1.85757i) q^{87} +(-0.132027 + 2.03963i) q^{88} +(10.3602 - 8.97720i) q^{89} +(6.78755 + 5.84698i) q^{90} -22.2983i q^{91} +(-4.65165 - 8.38821i) q^{92} +(9.85379 - 9.85379i) q^{93} +(-13.1773 - 2.50893i) q^{94} +(-0.589914 + 0.872827i) q^{95} +(13.3125 + 3.07121i) q^{96} +(-2.65918 + 3.55225i) q^{97} +(23.0752 + 6.12729i) q^{98} +(0.850435 - 1.86219i) 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

Modular forms

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