LMFDB - Embedded newform 483.2.y.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(4,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 12]))

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

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

chi := DirichletCharacter("483.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	483.4
Dual form			483.2.y.a.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.957403 + 1.34448i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(-0.236882 - 0.684426i) q^{4} +(0.115570 - 2.42610i) q^{5} +(-1.08087 - 1.24739i) q^{6} +(2.21964 - 1.43986i) q^{7} +(-2.02036 - 0.593231i) q^{8} +(-0.888835 - 0.458227i) q^{9} +(3.15121 + 2.47814i) q^{10} +(-0.243478 - 0.341917i) q^{11} +(0.720980 - 0.0688452i) q^{12} +(-0.871137 + 6.05889i) q^{13} +(-0.189222 + 4.36280i) q^{14} +(2.33047 + 0.684288i) q^{15} +(3.87050 - 3.04379i) q^{16} +(5.69918 - 1.09843i) q^{17} +(1.46705 - 0.756318i) q^{18} +(4.77961 + 0.921194i) q^{19} +(-1.68786 + 0.495602i) q^{20} +(0.875972 + 2.49653i) q^{21} +0.692809 q^{22} +(3.96736 + 2.69445i) q^{23} +(1.05283 - 1.82355i) q^{24} +(-0.895267 - 0.0854877i) q^{25} +(-7.31205 - 6.97203i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-1.51127 - 1.17810i) q^{28} +(-0.408146 - 0.471026i) q^{29} +(-3.15121 + 2.47814i) q^{30} +(-5.22627 + 4.98324i) q^{31} +(0.186324 + 3.91143i) q^{32} +(0.389681 - 0.156005i) q^{33} +(-3.97960 + 8.71410i) q^{34} +(-3.23673 - 5.55148i) q^{35} +(-0.103073 + 0.716887i) q^{36} +(6.81960 + 3.51575i) q^{37} +(-5.81454 + 5.54416i) q^{38} +(-5.68272 - 2.27502i) q^{39} +(-1.67273 + 4.83304i) q^{40} +(3.15401 + 2.02696i) q^{41} +(-4.19521 - 1.21246i) q^{42} +(-0.780351 + 0.229132i) q^{43} +(-0.176341 + 0.247637i) q^{44} +(-1.21443 + 2.10345i) q^{45} +(-7.42101 + 2.75438i) q^{46} +(-4.23304 - 7.33184i) q^{47} +(2.04549 + 4.47900i) q^{48} +(2.85361 - 6.39194i) q^{49} +(0.972069 - 1.12183i) q^{50} +(-0.276169 + 5.79750i) q^{51} +(4.35322 - 0.839014i) q^{52} +(-3.64474 - 1.45913i) q^{53} +(0.389128 + 1.60401i) q^{54} +(-0.857666 + 0.551188i) q^{55} +(-5.33864 + 1.59227i) q^{56} +(-2.02206 + 4.42770i) q^{57} +(1.02405 - 0.0977847i) q^{58} +(-2.86469 - 2.25282i) q^{59} +(-0.0837024 - 1.75713i) q^{60} +(-2.90741 - 11.9845i) q^{61} +(-1.69624 - 11.7976i) q^{62} +(-2.63268 + 0.262700i) q^{63} +(2.84736 + 1.82989i) q^{64} +(14.5988 + 2.81369i) q^{65} +(-0.163336 + 0.673280i) q^{66} +(11.4516 + 1.09349i) q^{67} +(-2.10183 - 3.64047i) q^{68} +(-3.55384 + 3.22029i) q^{69} +(10.5627 + 0.963278i) q^{70} +(5.27225 + 11.5446i) q^{71} +(1.52393 + 1.45307i) q^{72} +(-1.53039 - 4.42177i) q^{73} +(-11.2560 + 5.80286i) q^{74} +(0.294145 - 0.849877i) q^{75} +(-0.501715 - 3.48950i) q^{76} +(-1.03275 - 0.408359i) q^{77} +(8.49938 - 5.46222i) q^{78} +(0.449012 - 0.179757i) q^{79} +(-6.93725 - 9.74201i) q^{80} +(0.580057 + 0.814576i) q^{81} +(-5.74488 + 2.29990i) q^{82} +(-7.46719 + 4.79887i) q^{83} +(1.50119 - 1.19092i) q^{84} +(-2.00625 - 13.9538i) q^{85} +(0.439046 - 1.26854i) q^{86} +(0.553973 - 0.285593i) q^{87} +(0.289077 + 0.835234i) q^{88} +(-2.05570 - 1.96010i) q^{89} +(-1.66536 - 3.64663i) q^{90} +(6.79034 + 14.7029i) q^{91} +(0.904352 - 3.35363i) q^{92} +(-3.61063 - 6.25380i) q^{93} +(13.9103 + 1.32827i) q^{94} +(2.78729 - 11.4894i) q^{95} +(-3.84510 - 0.741083i) q^{96} +(-5.73513 - 3.68574i) q^{97} +(5.86181 + 9.95630i) q^{98} +(0.0597365 + 0.415476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21}+ \cdots - 10 q^{99}+O(q^{100}) $ 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.957403	+	1.34448i	−0.676986	+	0.950694i	0.323005	+	0.946397i	$0.395307\pi$
$2$	−0.957403	+	1.34448i	−0.676986	+	0.950694i	−0.999991	+	0.00429672i	$0.998632\pi$
$3$	−0.235759	+	0.971812i	−0.136115	+	0.561076i
$3$	−0.235759	+	0.971812i	−0.136115	+	0.561076i
$4$	−0.236882	−	0.684426i	−0.118441	−	0.342213i
$5$	0.115570	−	2.42610i	0.0516843	−	1.08499i	−0.812869	−	0.582446i	$-0.802096\pi$
$5$	0.115570	−	2.42610i	0.0516843	−	1.08499i	0.864554	−	0.502541i	$-0.167601\pi$
$6$	−1.08087	−	1.24739i	−0.441263	−	0.509245i
$7$	2.21964	−	1.43986i	0.838945	−	0.544216i
$7$	2.21964	−	1.43986i	0.838945	−	0.544216i
$8$	−2.02036	−	0.593231i	−0.714305	−	0.209739i
$9$	−0.888835	−	0.458227i	−0.296278	−	0.152742i
$10$	3.15121	+	2.47814i	0.996501	+	0.783657i
$11$	−0.243478	−	0.341917i	−0.0734114	−	0.103092i	0.776238	−	0.630440i	$-0.217126\pi$
$11$	−0.243478	−	0.341917i	−0.0734114	−	0.103092i	−0.849649	+	0.527348i	$0.823186\pi$
$12$	0.720980	−	0.0688452i	0.208129	−	0.0198739i
$13$	−0.871137	+	6.05889i	−0.241610	+	1.68043i	0.402437	+	0.915448i	$0.368163\pi$
$13$	−0.871137	+	6.05889i	−0.241610	+	1.68043i	−0.644047	+	0.764986i	$0.722746\pi$
$14$	−0.189222	+	4.36280i	−0.0505716	+	1.16601i
$15$	2.33047	+	0.684288i	0.601725	+	0.176682i
$16$	3.87050	−	3.04379i	0.967625	−	0.760949i
$17$	5.69918	−	1.09843i	1.38225	−	0.266408i	0.556692	−	0.830719i	$-0.312070\pi$
$17$	5.69918	−	1.09843i	1.38225	−	0.266408i	0.825562	+	0.564311i	$0.190858\pi$
$18$	1.46705	−	0.756318i	0.345788	−	0.178266i
$19$	4.77961	+	0.921194i	1.09652	+	0.211336i	0.705263	−	0.708946i	$-0.250829\pi$
$19$	4.77961	+	0.921194i	1.09652	+	0.211336i	0.391255	+	0.920282i	$0.372041\pi$
$20$	−1.68786	+	0.495602i	−0.377418	+	0.110820i
$21$	0.875972	+	2.49653i	0.191153	+	0.544788i
$22$	0.692809			0.147707
$23$	3.96736	+	2.69445i	0.827252	+	0.561831i
$23$	3.96736	+	2.69445i	0.827252	+	0.561831i
$24$	1.05283	−	1.82355i	0.214907	−	0.372230i
$25$	−0.895267	−	0.0854877i	−0.179053	−	0.0170975i
$26$	−7.31205	−	6.97203i	−1.43401	−	1.36733i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−1.51127	−	1.17810i	−0.285603	−	0.222640i
$29$	−0.408146	−	0.471026i	−0.0757909	−	0.0874673i	0.716588	−	0.697497i	$-0.245703\pi$
$29$	−0.408146	−	0.471026i	−0.0757909	−	0.0874673i	−0.792379	+	0.610030i	$0.791158\pi$
$30$	−3.15121	+	2.47814i	−0.575330	+	0.452445i
$31$	−5.22627	+	4.98324i	−0.938667	+	0.895017i	−0.994638	−	0.103416i	$-0.967023\pi$
$31$	−5.22627	+	4.98324i	−0.938667	+	0.895017i	0.0559716	+	0.998432i	$0.482174\pi$
$32$	0.186324	+	3.91143i	0.0329378	+	0.691450i
$33$	0.389681	−	0.156005i	0.0678348	−	0.0271570i
$34$	−3.97960	+	8.71410i	−0.682495	+	1.49446i
$35$	−3.23673	−	5.55148i	−0.547107	−	0.938372i
$36$	−0.103073	+	0.716887i	−0.0171788	+	0.119481i
$37$	6.81960	+	3.51575i	1.12114	+	0.577986i	0.916173	−	0.400784i	$-0.131262\pi$
$37$	6.81960	+	3.51575i	1.12114	+	0.577986i	0.204963	+	0.978770i	$0.434292\pi$
$38$	−5.81454	+	5.54416i	−0.943244	+	0.899381i
$39$	−5.68272	−	2.27502i	−0.909964	−	0.364294i
$40$	−1.67273	+	4.83304i	−0.264482	+	0.764171i
$41$	3.15401	+	2.02696i	0.492574	+	0.316558i	0.763240	−	0.646115i	$-0.223607\pi$
$41$	3.15401	+	2.02696i	0.492574	+	0.316558i	−0.270666	+	0.962673i	$0.587244\pi$
$42$	−4.19521	−	1.21246i	−0.647335	−	0.187086i
$43$	−0.780351	+	0.229132i	−0.119002	+	0.0349422i	−0.340691	−	0.940175i	$-0.610661\pi$
$43$	−0.780351	+	0.229132i	−0.119002	+	0.0349422i	0.221689	+	0.975117i	$0.428843\pi$
$44$	−0.176341	+	0.247637i	−0.0265845	+	0.0373327i
$45$	−1.21443	+	2.10345i	−0.181036	+	0.313564i
$46$	−7.42101	+	2.75438i	−1.09417	+	0.406112i
$47$	−4.23304	−	7.33184i	−0.617452	−	1.06946i	−0.989949	−	0.141425i	$-0.954831\pi$
$47$	−4.23304	−	7.33184i	−0.617452	−	1.06946i	0.372496	−	0.928034i	$-0.378502\pi$
$48$	2.04549	+	4.47900i	0.295241	+	0.646488i
$49$	2.85361	−	6.39194i	0.407658	−	0.913135i
$50$	0.972069	−	1.12183i	0.137471	−	0.158650i
$51$	−0.276169	+	5.79750i	−0.0386714	+	0.811812i
$52$	4.35322	−	0.839014i	0.603682	−	0.116350i
$53$	−3.64474	−	1.45913i	−0.500643	−	0.200427i	0.107575	−	0.994197i	$-0.465691\pi$
$53$	−3.64474	−	1.45913i	−0.500643	−	0.200427i	−0.608218	+	0.793770i	$0.708116\pi$
$54$	0.389128	+	1.60401i	0.0529536	+	0.218278i
$55$	−0.857666	+	0.551188i	−0.115648	+	0.0743222i
$56$	−5.33864	+	1.59227i	−0.713406	+	0.212777i
$57$	−2.02206	+	4.42770i	−0.267829	+	0.586463i
$58$	1.02405	−	0.0977847i	0.134464	−	0.0128398i
$59$	−2.86469	−	2.25282i	−0.372951	−	0.293292i	0.414037	−	0.910260i	$-0.364118\pi$
$59$	−2.86469	−	2.25282i	−0.372951	−	0.293292i	−0.786988	+	0.616968i	$0.788361\pi$
$60$	−0.0837024	−	1.75713i	−0.0108059	−	0.226844i
$61$	−2.90741	−	11.9845i	−0.372255	−	1.53446i	−0.782599	−	0.622526i	$-0.786107\pi$
$61$	−2.90741	−	11.9845i	−0.372255	−	1.53446i	0.410344	−	0.911931i	$-0.365409\pi$
$62$	−1.69624	−	11.7976i	−0.215423	−	1.49830i
$63$	−2.63268	+	0.262700i	−0.331686	+	0.0330971i
$64$	2.84736	+	1.82989i	0.355920	+	0.228736i
$65$	14.5988	+	2.81369i	1.81076	+	0.348996i
$66$	−0.163336	+	0.673280i	−0.0201053	+	0.0828750i
$67$	11.4516	+	1.09349i	1.39903	+	0.133591i	0.767148	−	0.641471i	$-0.221675\pi$
$67$	11.4516	+	1.09349i	1.39903	+	0.133591i	0.631885	+	0.775062i	$0.282281\pi$
$68$	−2.10183	−	3.64047i	−0.254884	−	0.441472i
$69$	−3.55384	+	3.22029i	−0.427831	+	0.387677i
$70$	10.5627	+	0.963278i	1.26249	+	0.115134i
$71$	5.27225	+	11.5446i	0.625701	+	1.37009i	0.911299	+	0.411745i	$0.135081\pi$
$71$	5.27225	+	11.5446i	0.625701	+	1.37009i	−0.285598	+	0.958350i	$0.592192\pi$
$72$	1.52393	+	1.45307i	0.179597	+	0.171246i
$73$	−1.53039	−	4.42177i	−0.179119	−	0.517529i	0.819323	−	0.573332i	$-0.194349\pi$
$73$	−1.53039	−	4.42177i	−0.179119	−	0.517529i	−0.998442	+	0.0558028i	$0.982228\pi$
$74$	−11.2560	+	5.80286i	−1.30848	+	0.674569i
$75$	0.294145	−	0.849877i	0.0339650	−	0.0981353i
$76$	−0.501715	−	3.48950i	−0.0575506	−	0.400273i
$77$	−1.03275	−	0.408359i	−0.117692	−	0.0465368i
$78$	8.49938	−	5.46222i	0.962365	−	0.618475i
$79$	0.449012	−	0.179757i	0.0505178	−	0.0202243i	−0.346266	−	0.938136i	$-0.612551\pi$
$79$	0.449012	−	0.179757i	0.0505178	−	0.0202243i	0.396784	+	0.917912i	$0.370126\pi$
$80$	−6.93725	−	9.74201i	−0.775608	−	1.08919i
$81$	0.580057	+	0.814576i	0.0644508	+	0.0905084i
$82$	−5.74488	+	2.29990i	−0.634416	+	0.253982i
$83$	−7.46719	+	4.79887i	−0.819631	+	0.526745i	−0.881967	−	0.471311i	$-0.843781\pi$
$83$	−7.46719	+	4.79887i	−0.819631	+	0.526745i	0.0623367	+	0.998055i	$0.480145\pi$
$84$	1.50119	−	1.19092i	0.163793	−	0.129940i
$85$	−2.00625	−	13.9538i	−0.217608	−	1.51350i
$86$	0.439046	−	1.26854i	0.0473436	−	0.136790i
$87$	0.553973	−	0.285593i	0.0593921	−	0.0306188i
$88$	0.289077	+	0.835234i	0.0308158	+	0.0890363i
$89$	−2.05570	−	1.96010i	−0.217903	−	0.207770i	0.573263	−	0.819371i	$-0.305677\pi$
$89$	−2.05570	−	1.96010i	−0.217903	−	0.207770i	−0.791166	+	0.611601i	$0.790526\pi$
$90$	−1.66536	−	3.64663i	−0.175544	−	0.384389i
$91$	6.79034	+	14.7029i	0.711821	+	1.54128i
$92$	0.904352	−	3.35363i	0.0942852	−	0.349640i
$93$	−3.61063	−	6.25380i	−0.374405	−	0.648489i
$94$	13.9103	+	1.32827i	1.43474	+	0.137001i
$95$	2.78729	−	11.4894i	0.285970	−	1.17878i
$96$	−3.84510	−	0.741083i	−0.392439	−	0.0756364i
$97$	−5.73513	−	3.68574i	−0.582314	−	0.374230i	0.216071	−	0.976378i	$-0.430676\pi$
$97$	−5.73513	−	3.68574i	−0.582314	−	0.374230i	−0.798385	+	0.602147i	$0.794312\pi$
$98$	5.86181	+	9.95630i	0.592133	+	1.00574i
$99$	0.0597365	+	0.415476i	0.00600374	+	0.0417569i
$100$	0.153563	+	0.632995i	0.0153563	+	0.0632995i
$101$	0.169940	+	3.56749i	0.0169097	+	0.354978i	0.991427	+	0.130664i	$0.0417110\pi$
$101$	0.169940	+	3.56749i	0.0169097	+	0.354978i	−0.974517	+	0.224314i	$0.927986\pi$
$102$	−7.53024	−	5.92184i	−0.745605	−	0.586350i
$103$	19.7970	−	1.89039i	1.95066	−	0.186265i	0.956304	−	0.292375i	$-0.0944456\pi$
$103$	19.7970	−	1.89039i	1.95066	−	0.186265i	0.994354	+	0.106110i	$0.0338395\pi$
$104$	5.35433	−	11.7243i	0.525035	−	1.14967i
$105$	6.15808	−	1.83668i	0.600967	−	0.179241i
$106$	5.45126	−	3.50331i	0.529473	−	0.340272i
$107$	−0.794196	−	3.27372i	−0.0767778	−	0.316483i	0.920453	−	0.390854i	$-0.127820\pi$
$107$	−0.794196	−	3.27372i	−0.0767778	−	0.316483i	−0.997231	+	0.0743712i	$0.976305\pi$
$108$	−0.672379	−	0.269180i	−0.0646997	−	0.0259019i
$109$	−10.5500	+	2.03335i	−1.01051	+	0.194759i	−0.667529	−	0.744584i	$-0.732648\pi$
$109$	−10.5500	+	2.03335i	−1.01051	+	0.194759i	−0.342979	+	0.939343i	$0.611436\pi$
$110$	0.0800677	−	1.68083i	0.00763416	−	0.160261i
$111$	−5.02443	+	5.79850i	−0.476898	+	0.550369i
$112$	4.20848	−	12.3291i	0.397664	−	1.16499i
$113$	1.16459	+	2.55010i	0.109556	+	0.239893i	0.956467	−	0.291841i	$-0.0942678\pi$
$113$	1.16459	+	2.55010i	0.109556	+	0.239893i	−0.846911	+	0.531734i	$0.821540\pi$
$114$	−4.01704	−	6.95773i	−0.376231	−	0.651651i
$115$	6.99552	−	9.31384i	0.652335	−	0.868520i
$116$	−0.225700	+	0.390923i	−0.0209557	+	0.0362963i
$117$	3.55064	−	4.98618i	0.328257	−	0.460972i
$118$	5.77154	−	1.69468i	0.531313	−	0.156008i
$119$	11.0686	−	10.6441i	1.01465	−	0.975746i
$120$	−4.30244	−	2.76501i	−0.392758	−	0.252410i
$121$	3.54012	−	10.2285i	0.321829	−	0.929865i
$122$	18.8965	+	7.56502i	1.71081	+	0.684905i
$123$	−2.71341	+	2.58723i	−0.244660	+	0.233283i
$124$	4.64867	+	2.39656i	0.417463	+	0.215217i
$125$	1.41744	−	9.85853i	0.126780	−	0.881774i
$126$	2.16734	−	3.79110i	0.193082	−	0.337738i
$127$	−3.21746	+	7.04526i	−0.285504	+	0.625166i	−0.996990	−	0.0775344i	$-0.975295\pi$
$127$	−3.21746	+	7.04526i	−0.285504	+	0.625166i	0.711486	+	0.702700i	$0.248023\pi$
$128$	−12.4571	+	4.98706i	−1.10106	+	0.440798i
$129$	−0.0386981	−	0.812373i	−0.00340718	−	0.0715255i
$130$	−17.7599	+	16.9341i	−1.55765	+	1.48521i
$131$	−14.8350	+	11.6664i	−1.29614	+	1.01930i	−0.298243	+	0.954490i	$0.596401\pi$
$131$	−14.8350	+	11.6664i	−1.29614	+	1.01930i	−0.997898	+	0.0648067i	$0.979357\pi$
$132$	−0.199082	−	0.229753i	−0.0173279	−	0.0199974i
$133$	11.9354	−	4.83725i	1.03493	−	0.419442i
$134$	−12.4340	+	14.3496i	−1.07413	+	1.23961i
$135$	−1.75785	−	1.67610i	−0.151291	−	0.144256i
$136$	−12.1660	−	1.16171i	−1.04323	−	0.0996161i
$137$	4.81734	−	8.34388i	0.411573	−	0.712865i	−0.583489	−	0.812121i	$-0.698313\pi$
$137$	4.81734	−	8.34388i	0.411573	−	0.712865i	0.995062	+	0.0992557i	$0.0316462\pi$
$138$	−0.927174	−	7.86119i	−0.0789263	−	0.669189i
$139$	−17.0999			−1.45040			−0.725199	−	0.688539i	$-0.758252\pi$
$139$	−17.0999			−1.45040			−0.725199	+	0.688539i	$0.758252\pi$
$140$	−3.03286	+	3.53035i	−0.256323	+	0.298369i
$141$	8.12315	−	2.38517i	0.684092	−	0.200868i
$142$	−20.5692	−	3.96440i	−1.72613	−	0.332685i
$143$	2.28374	−	1.17735i	0.190976	−	0.0984550i
$144$	−4.83498	+	0.931867i	−0.402915	+	0.0776556i
$145$	−1.18993	+	0.935769i	−0.0988181	+	0.0777114i
$146$	7.41020	+	2.17583i	0.613272	+	0.180073i
$147$	5.53900	+	4.28013i	0.456849	+	0.353019i
$148$	0.790828	−	5.50033i	0.0650057	−	0.452124i
$149$	4.67883	−	0.446774i	0.383304	−	0.0366011i	0.0983745	−	0.995149i	$-0.468636\pi$
$149$	4.67883	−	0.446774i	0.383304	−	0.0366011i	0.284930	+	0.958548i	$0.408030\pi$
$150$	0.861031	+	1.20915i	0.0703029	+	0.0987266i
$151$	1.11189	+	0.874401i	0.0904844	+	0.0711577i	0.662376	−	0.749171i	$-0.269548\pi$
$151$	1.11189	+	0.874401i	0.0904844	+	0.0711577i	−0.571892	+	0.820329i	$0.693790\pi$
$152$	−9.11004	−	4.69655i	−0.738922	−	0.380941i
$153$	−5.56896	−	1.63520i	−0.450224	−	0.132198i
$154$	1.53779	−	0.997548i	0.123918	−	0.0803847i
$155$	11.4859	+	13.2554i	0.922567	+	1.06470i
$156$	−0.210946	+	4.42831i	−0.0168892	+	0.354549i
$157$	1.61628	+	4.66995i	0.128994	+	0.372702i	0.990941	−	0.134294i	$-0.0428768\pi$
$157$	1.61628	+	4.66995i	0.128994	+	0.372702i	−0.861948	+	0.506997i	$0.830756\pi$
$158$	−0.188204	+	0.775789i	−0.0149727	+	0.0617185i
$159$	2.27728	−	3.19799i	0.180600	−	0.253617i
$160$	9.51107			0.751916
$161$	12.6857	+	0.268259i	0.999776	+	0.0211418i
$162$	−1.65053			−0.129678
$163$	5.08569	−	7.14186i	0.398342	−	0.559393i	−0.565880	−	0.824487i	$-0.691464\pi$
$163$	5.08569	−	7.14186i	0.398342	−	0.559393i	0.964223	+	0.265094i	$0.0854030\pi$
$164$	0.640175	−	2.63884i	0.0499893	−	0.206059i
$165$	−0.333449	−	0.963437i	−0.0259590	−	0.0750035i
$166$	0.697102	−	14.6340i	0.0541056	−	1.13582i
$167$	8.59292	+	9.91676i	0.664940	+	0.767382i	0.983576	−	0.180495i	$-0.0577700\pi$
$167$	8.59292	+	9.91676i	0.664940	+	0.767382i	−0.318636	+	0.947877i	$0.603225\pi$
$168$	−0.288758	−	5.56354i	−0.0222782	−	0.429237i
$169$	−23.4779	−	6.89372i	−1.80599	−	0.530286i
$170$	20.6814	+	10.6620i	1.58619	+	0.817738i
$171$	−3.82617	−	3.00893i	−0.292595	−	0.230099i
$172$	0.341675	+	0.479815i	0.0260524	+	0.0365855i
$173$	6.31277	−	0.602797i	0.479951	−	0.0458298i	0.147723	−	0.989029i	$-0.452806\pi$
$173$	6.31277	−	0.602797i	0.479951	−	0.0458298i	0.332228	+	0.943199i	$0.392200\pi$
$174$	−0.146400	+	1.01823i	−0.0110986	+	0.0771922i
$175$	−2.11026	+	1.09931i	−0.159521	+	0.0830998i
$176$	−1.98311	−	0.582293i	−0.149482	−	0.0438920i
$177$	2.86469	−	2.25282i	0.215323	−	0.169332i
$178$	4.60345	−	0.887243i	0.345044	−	0.0665017i
$179$	−13.4941	+	6.95669i	−1.00860	+	0.519967i	−0.881631	−	0.471940i	$-0.843554\pi$
$179$	−13.4941	+	6.95669i	−1.00860	+	0.519967i	−0.126965	+	0.991907i	$0.540524\pi$
$180$	1.72733	+	0.332916i	0.128748	+	0.0248141i
$181$	−11.9736	+	3.51577i	−0.889992	+	0.261325i	−0.694597	−	0.719399i	$-0.744417\pi$
$181$	−11.9736	+	3.51577i	−0.889992	+	0.261325i	−0.195395	+	0.980725i	$0.562599\pi$
$182$	−26.2689	−	4.94707i	−1.94718	−	0.366701i
$183$	12.3321			0.911616
$184$	−6.41706	−	7.79731i	−0.473072	−	0.574825i
$185$	9.31772	−	16.1388i	0.685052	−	1.18655i
$186$	11.8650	+	1.13297i	0.869981	+	0.0830732i
$187$	−1.76320	−	1.68121i	−0.128938	−	0.122942i
$188$	−4.01537	+	4.63398i	−0.292851	+	0.337968i
$189$	0.365382	−	2.62040i	0.0265776	−	0.190606i
$190$	12.7787	+	14.7474i	0.927066	+	1.06989i
$191$	−0.396203	+	0.311578i	−0.0286682	+	0.0225450i	−0.632390	−	0.774650i	$-0.717926\pi$
$191$	−0.396203	+	0.311578i	−0.0286682	+	0.0225450i	0.603722	+	0.797195i	$0.293684\pi$
$192$	−2.44960	+	2.33569i	−0.176785	+	0.168564i
$193$	−1.14655	−	24.0691i	−0.0825307	−	1.73253i	−0.538576	−	0.842577i	$-0.681037\pi$
$193$	−1.14655	−	24.0691i	−0.0825307	−	1.73253i	0.456045	−	0.889957i	$-0.349266\pi$
$194$	10.4462	−	4.18205i	0.749997	−	0.300254i
$195$	−6.17618	+	13.5240i	−0.442286	+	0.968470i
$196$	−5.05078	−	0.438947i	−0.360770	−	0.0313533i
$197$	−2.69941	+	18.7748i	−0.192325	+	1.33765i	0.633507	+	0.773737i	$0.281615\pi$
$197$	−2.69941	+	18.7748i	−0.192325	+	1.33765i	−0.825833	+	0.563915i	$0.809294\pi$
$198$	−0.615793	−	0.317464i	−0.0437625	−	0.0225612i
$199$	−8.61200	+	8.21152i	−0.610488	+	0.582100i	−0.930943	−	0.365164i	$-0.881013\pi$
$199$	−8.61200	+	8.21152i	−0.610488	+	0.582100i	0.320455	+	0.947264i	$0.396164\pi$
$200$	1.75805	+	0.703816i	0.124313	+	0.0497673i
$201$	−3.76248	+	10.8710i	−0.265385	+	0.766779i
$202$	−4.95913	−	3.18704i	−0.348923	−	0.224239i
$203$	−1.58415	−	0.457835i	−0.111185	−	0.0321337i
$204$	4.03337	−	1.18431i	0.282393	−	0.0829180i
$205$	5.28213	−	7.41771i	0.368920	−	0.518075i
$206$	−16.4121	+	28.4266i	−1.14349	+	1.98058i
$207$	−2.29166	−	4.21287i	−0.159282	−	0.292815i
$208$	15.0703	+	26.1025i	1.04494	+	1.80988i
$209$	−0.848758	−	1.85852i	−0.0587098	−	0.128557i
$210$	−3.42638	+	10.0379i	−0.236443	+	0.692680i
$211$	−8.72529	+	10.0695i	−0.600674	+	0.693215i	−0.971918	−	0.235321i	$-0.924386\pi$
$211$	−8.72529	+	10.0695i	−0.600674	+	0.693215i	0.371244	+	0.928535i	$0.378931\pi$
$212$	−0.135295	+	2.84019i	−0.00929210	+	0.195065i
$213$	−12.4622	+	2.40189i	−0.853895	+	0.164575i
$214$	5.16183	+	2.06649i	0.352856	+	0.141262i
$215$	0.465712	+	1.91969i	0.0317613	+	0.130922i
$216$	−1.77139	+	1.13840i	−0.120528	+	0.0774584i
$217$	−4.42528	+	18.5861i	−0.300408	+	1.26171i
$218$	7.36681	−	16.1311i	0.498943	−	1.09253i
$219$	4.65793	−	0.444778i	0.314754	−	0.0300553i
$220$	0.580413	+	0.456442i	0.0391314	+	0.0307733i
$221$	1.69048	+	35.4876i	0.113714	+	2.38715i
$222$	−2.98559	−	12.3068i	−0.200380	−	0.825976i
$223$	−2.97284	−	20.6765i	−0.199076	−	1.38460i	−0.806974	−	0.590587i	$-0.798896\pi$
$223$	−2.97284	−	20.6765i	−0.199076	−	1.38460i	0.607898	−	0.794015i	$-0.292013\pi$
$224$	6.04549	+	8.41369i	0.403931	+	0.562163i
$225$	0.756573	+	0.486220i	0.0504382	+	0.0324147i
$226$	−4.54356	−	0.875699i	−0.302233	−	0.0582506i
$227$	3.05516	−	12.5935i	0.202778	−	0.835862i	−0.775966	−	0.630775i	$-0.782737\pi$
$227$	3.05516	−	12.5935i	0.202778	−	0.835862i	0.978744	−	0.205087i	$-0.0657477\pi$
$228$	3.50942	+	0.335109i	0.232417	+	0.0221931i
$229$	0.441905	+	0.765402i	0.0292019	+	0.0505792i	0.880257	−	0.474497i	$-0.157370\pi$
$229$	0.441905	+	0.765402i	0.0292019	+	0.0505792i	−0.851055	+	0.525076i	$0.824037\pi$
$230$	5.82478	+	18.3225i	0.384075	+	1.20815i
$231$	0.640327	−	0.907361i	0.0421304	−	0.0597000i
$232$	0.545175	+	1.19377i	0.0357925	+	0.0783746i
$233$	5.04466	+	4.81007i	0.330487	+	0.315118i	0.837095	−	0.547058i	$-0.184252\pi$
$233$	5.04466	+	4.81007i	0.330487	+	0.315118i	−0.506608	+	0.862177i	$0.669101\pi$
$234$	3.30444	+	9.54756i	0.216018	+	0.624144i
$235$	−18.2770	+	9.42246i	−1.19226	+	0.614654i
$236$	−0.863292	+	2.49432i	−0.0561955	+	0.162366i
$237$	0.0688316	+	0.478734i	0.00447109	+	0.0310971i
$238$	3.71381	+	25.0722i	0.240730	+	1.62519i
$239$	11.6683	−	7.49879i	0.754762	−	0.485056i	−0.105809	−	0.994386i	$-0.533743\pi$
$239$	11.6683	−	7.49879i	0.754762	−	0.485056i	0.860571	+	0.509330i	$0.170107\pi$
$240$	11.1029	−	4.44494i	0.716690	−	0.286919i
$241$	−8.91891	−	12.5249i	−0.574518	−	0.806797i	0.420416	−	0.907331i	$-0.361884\pi$
$241$	−8.91891	−	12.5249i	−0.574518	−	0.806797i	−0.994934	+	0.100534i	$0.967945\pi$
$242$	10.3628	+	14.5524i	0.666143	+	0.935467i
$243$	−0.928368	+	0.371662i	−0.0595548	+	0.0238422i
$244$	−7.51378	+	4.82881i	−0.481020	+	0.309133i
$245$	−15.1777	−	7.66187i	−0.969670	−	0.489499i
$246$	−0.880665	−	6.12516i	−0.0561492	−	0.390526i
$247$	−9.74511	+	28.1566i	−0.620066	+	1.79156i
$248$	13.5152	−	6.96755i	0.858214	−	0.442440i
$249$	−2.90314	−	8.38808i	−0.183979	−	0.531573i
$250$	11.8976	+	11.3443i	0.752469	+	0.717478i
$251$	−6.82450	−	14.9436i	−0.430759	−	0.943230i	−0.993203	−	0.116395i	$-0.962866\pi$
$251$	−6.82450	−	14.9436i	−0.430759	−	0.943230i	0.562444	−	0.826835i	$-0.309861\pi$
$252$	0.803433	+	1.73964i	0.0506115	+	0.109587i
$253$	−0.0446882	−	2.01255i	−0.00280952	−	0.126528i
$254$	−6.39184	−	11.0710i	−0.401060	−	0.694655i
$255$	14.0334	+	1.34003i	0.878806	+	0.0839158i
$256$	3.62548	−	14.9444i	0.226592	−	0.934027i
$257$	−23.7273	−	4.57306i	−1.48007	−	0.285260i	−0.615645	−	0.788024i	$-0.711104\pi$
$257$	−23.7273	−	4.57306i	−1.48007	−	0.285260i	−0.864424	+	0.502764i	$0.832317\pi$
$258$	1.12927	+	0.725740i	0.0703055	+	0.0451826i
$259$	20.1993	−	2.01557i	1.25512	−	0.125241i
$260$	−1.53244	−	10.6583i	−0.0950376	−	0.661001i
$261$	0.146938	+	0.605688i	0.00909525	+	0.0374911i
$262$	−1.48218	−	31.1149i	−0.0915696	−	1.92228i
$263$	21.0145	+	16.5260i	1.29581	+	1.01904i	0.997922	+	0.0644361i	$0.0205249\pi$
$263$	21.0145	+	16.5260i	1.29581	+	1.01904i	0.297889	+	0.954601i	$0.403718\pi$
$264$	−0.879843	+	0.0840148i	−0.0541506	+	0.00517075i
$265$	−3.96123	+	8.67388i	−0.243336	+	0.532832i
$266$	−4.92339	+	20.6782i	−0.301872	+	1.26786i
$267$	2.38950	−	1.53564i	0.146235	−	0.0939795i
$268$	−1.96426	−	8.09678i	−0.119986	−	0.494590i
$269$	−14.5579	−	5.82809i	−0.887608	−	0.355345i	−0.117360	−	0.993089i	$-0.537443\pi$
$269$	−14.5579	−	5.82809i	−0.887608	−	0.355345i	−0.770248	+	0.637745i	$0.779868\pi$
$270$	3.93646	−	0.758691i	0.239565	−	0.0461724i
$271$	−1.02814	+	21.5834i	−0.0624553	+	1.31110i	0.722424	+	0.691450i	$0.243028\pi$
$271$	−1.02814	+	21.5834i	−0.0624553	+	1.31110i	−0.784879	+	0.619649i	$0.787275\pi$
$272$	18.7153	−	21.5986i	1.13478	−	1.30961i
$273$	−15.8893	+	3.13260i	−0.961664	+	0.189593i
$274$	6.60608	+	14.4653i	0.399088	+	0.873880i
$275$	0.188748	+	0.326922i	0.0113820	+	0.0197141i
$276$	3.04589	+	1.66951i	0.183341	+	0.100493i
$277$	−6.46923	+	11.2050i	−0.388698	+	0.673245i	−0.992275	−	0.124060i	$-0.960408\pi$
$277$	−6.46923	+	11.2050i	−0.388698	+	0.673245i	0.603576	+	0.797305i	$0.293742\pi$
$278$	16.3715	−	22.9906i	0.981899	−	1.37888i
$279$	6.92875	−	2.03447i	0.414814	−	0.121800i
$280$	3.24604	+	13.1361i	0.193988	+	0.785033i
$281$	−15.5930	−	10.0210i	−0.930199	−	0.597803i	−0.0145992	−	0.999893i	$-0.504647\pi$
$281$	−15.5930	−	10.0210i	−0.930199	−	0.597803i	−0.915600	+	0.402091i	$0.868284\pi$
$282$	−4.57030	+	13.2050i	−0.272157	+	0.786347i
$283$	−3.25723	−	1.30400i	−0.193622	−	0.0775147i	0.272825	−	0.962064i	$-0.412042\pi$
$283$	−3.25723	−	1.30400i	−0.193622	−	0.0775147i	−0.466447	+	0.884549i	$0.654466\pi$
$284$	6.65254	−	6.34318i	0.394755	−	0.376398i
$285$	10.5084	+	5.41744i	0.622462	+	0.320902i
$286$	−0.603532	+	4.19765i	−0.0356876	+	0.248213i
$287$	9.91931	−	0.0422112i	0.585519	−	0.00249165i
$288$	1.62671	−	3.56200i	0.0958548	−	0.209893i
$289$	15.4919	−	6.20201i	0.911287	−	0.364824i
$290$	−0.118887	−	2.49575i	−0.00698129	−	0.146555i
$291$	4.93395	−	4.70451i	0.289233	−	0.275784i
$292$	−2.66385	+	2.09488i	−0.155890	+	0.122593i
$293$	−9.08147	−	10.4806i	−0.530545	−	0.612282i	0.425694	−	0.904867i	$-0.360030\pi$
$293$	−9.08147	−	10.4806i	−0.530545	−	0.612282i	−0.956239	+	0.292585i	$0.905485\pi$
$294$	−11.0576	+	3.34929i	−0.644893	+	0.195335i
$295$	−5.79664	+	6.68968i	−0.337493	+	0.389488i
$296$	−11.6924	−	11.1487i	−0.679606	−	0.648003i
$297$	−0.417848	−	0.0398997i	−0.0242460	−	0.00231521i
$298$	−3.87884	+	6.71835i	−0.224695	+	0.389184i
$299$	−19.7815	+	21.6906i	−1.14399	+	1.25440i
$300$	−0.651355			−0.0376060
$301$	−1.40218	+	1.63218i	−0.0808203	+	0.0940776i
$302$	−2.24015	+	0.657766i	−0.128906	+	0.0378502i
$303$	−3.50699	−	0.675917i	−0.201471	−	0.0388304i
$304$	21.3034	−	10.9827i	1.22183	−	0.629899i
$305$	−29.4116	+	5.66863i	−1.68411	+	0.324585i
$306$	7.53024	−	5.92184i	0.430475	−	0.338529i
$307$	−4.98939	−	1.46502i	−0.284760	−	0.0836130i	0.136234	−	0.990677i	$-0.456500\pi$
$307$	−4.98939	−	1.46502i	−0.284760	−	0.0836130i	−0.420993	+	0.907064i	$0.638318\pi$
$308$	−0.0348522	+	0.803571i	−0.00198589	+	0.0457877i
$309$	−2.83022	+	19.6846i	−0.161006	+	1.11982i
$310$	−28.8183	+	2.75181i	−1.63677	+	0.156292i
$311$	15.3205	+	21.5146i	0.868743	+	1.21998i	0.974230	+	0.225558i	$0.0724206\pi$
$311$	15.3205	+	21.5146i	0.868743	+	1.21998i	−0.105487	+	0.994421i	$0.533640\pi$
$312$	10.1315	+	7.96752i	0.573584	+	0.451072i
$313$	−23.8271	−	12.2837i	−1.34679	−	0.694317i	−0.374308	−	0.927305i	$-0.622120\pi$
$313$	−23.8271	−	12.2837i	−1.34679	−	0.694317i	−0.972480	+	0.232987i	$0.925150\pi$
$314$	−7.82611	−	2.29795i	−0.441653	−	0.129681i
$315$	0.333081	+	6.41751i	0.0187670	+	0.361586i
$316$	−0.229393	−	0.264734i	−0.0129044	−	0.0148924i
$317$	0.409460	−	8.59563i	0.0229976	−	0.482779i	−0.957762	−	0.287561i	$-0.907156\pi$
$317$	0.409460	−	8.59563i	0.0229976	−	0.482779i	0.980760	−	0.195218i	$-0.0625414\pi$
$318$	2.11938	+	6.12354i	0.118849	+	0.343391i
$319$	−0.0616772	+	0.254237i	−0.00345326	+	0.0142345i
$320$	4.76857	−	6.69652i	0.266571	−	0.374347i
$321$	3.36868			0.188021
$322$	−12.5060	+	16.7990i	−0.696934	+	0.936169i
$323$	28.2517			1.57197
$324$	0.420112	−	0.589964i	0.0233395	−	0.0327758i
$325$	1.29786	−	5.34986i	0.0719924	−	0.296757i
$326$	4.73306	+	13.6753i	0.262140	+	0.757403i
$327$	0.511228	−	10.7320i	0.0282710	−	0.593481i
$328$	−5.16978	−	5.96625i	−0.285453	−	0.329431i
$329$	−19.9527	−	10.1791i	−1.10003	−	0.561190i
$330$	1.61457	+	0.474081i	0.0888792	+	0.0260973i
$331$	−14.5591	−	7.50576i	−0.800242	−	0.412554i	0.00905041	−	0.999959i	$-0.497119\pi$
$331$	−14.5591	−	7.50576i	−0.800242	−	0.412554i	−0.809293	+	0.587405i	$0.800149\pi$
$332$	5.05331	+	3.97397i	0.277337	+	0.218100i
$333$	−4.45050	−	6.24985i	−0.243886	−	0.342489i
$334$	−21.5598	+	2.05871i	−1.17970	+	0.112648i
$335$	3.97638	−	27.6563i	0.217253	−	1.51103i
$336$	10.9894	+	6.99655i	0.599520	+	0.381693i
$337$	19.4752	+	5.71843i	1.06088	+	0.311503i	0.765206	−	0.643786i	$-0.222637\pi$
$337$	19.4752	+	5.71843i	1.06088	+	0.311503i	0.295675	+	0.955289i	$0.404455\pi$
$338$	31.7463	−	24.9655i	1.72677	−	1.35795i
$339$	−2.75278	+	0.530555i	−0.149511	+	0.0288158i
$340$	−9.07507	+	4.67852i	−0.492165	+	0.253728i
$341$	2.97634	+	0.573643i	0.161178	+	0.0310645i
$342$	7.70865	−	2.26346i	0.416836	−	0.122394i
$343$	−2.86952	−	18.2966i	−0.154939	−	0.987924i
$344$	1.71252			0.0923327
$345$	7.40204	+	8.99414i	0.398512	+	0.484228i
$346$	−5.23342	+	9.06454i	−0.281350	+	0.487313i
$347$	18.8789	+	1.80271i	1.01347	+	0.0967748i	0.588555	−	0.808457i	$-0.299697\pi$
$347$	18.8789	+	1.80271i	1.01347	+	0.0967748i	0.424917	+	0.905232i	$0.360303\pi$
$348$	−0.326693	−	0.311501i	−0.0175126	−	0.0166982i
$349$	1.30868	−	1.51030i	0.0700522	−	0.0808445i	−0.719642	−	0.694346i	$-0.755694\pi$
$349$	1.30868	−	1.51030i	0.0700522	−	0.0808445i	0.789694	+	0.613501i	$0.210239\pi$
$350$	0.542370	−	3.88970i	0.0289909	−	0.207913i
$351$	4.00853	+	4.62609i	0.213959	+	0.246922i
$352$	1.29202	−	1.01606i	0.0688649	−	0.0541559i
$353$	−22.4209	+	21.3783i	−1.19335	+	1.13785i	−0.206119	+	0.978527i	$0.566083\pi$
$353$	−22.4209	+	21.3783i	−1.19335	+	1.13785i	−0.987226	+	0.159326i	$0.949068\pi$
$354$	0.286215	+	6.00838i	0.0152121	+	0.319342i
$355$	28.6178	−	11.4568i	1.51887	−	0.608065i
$356$	−0.854587	+	1.87128i	−0.0452930	+	0.0991778i
$357$	7.73458	+	13.2660i	0.409358	+	0.702111i
$358$	3.56613	−	24.8030i	0.188476	−	1.31088i
$359$	−11.6998	−	6.03167i	−0.617492	−	0.318339i	0.120947	−	0.992659i	$-0.461407\pi$
$359$	−11.6998	−	6.03167i	−0.617492	−	0.318339i	−0.738440	+	0.674319i	$0.764437\pi$
$360$	3.70141	−	3.52929i	0.195081	−	0.186010i
$361$	4.35708	+	1.74431i	0.229320	+	0.0918058i
$362$	6.73668	−	19.4644i	0.354072	−	1.02302i
$363$	9.10557	+	5.85179i	0.477918	+	0.307140i
$364$	8.45451	−	8.13033i	0.443137	−	0.426145i
$365$	−10.9045	+	3.20186i	−0.570770	+	0.167593i
$366$	−11.8068	+	16.5803i	−0.617151	+	0.866668i
$367$	9.17583	−	15.8930i	0.478974	−	0.829608i	−0.520735	−	0.853718i	$-0.674342\pi$
$367$	9.17583	−	15.8930i	0.478974	−	0.829608i	0.999709	+	0.0241105i	$0.00767535\pi$
$368$	23.5570	−	1.64698i	1.22799	−	0.0858547i
$369$	−1.87459	−	3.24689i	−0.0975873	−	0.169026i
$370$	12.7775	+	27.9788i	0.664271	+	1.45455i
$371$	−10.1909	+	2.00916i	−0.529088	+	0.104310i
$372$	−3.42497	+	3.95262i	−0.177576	+	0.204934i
$373$	−0.347852	+	7.30231i	−0.0180111	+	0.378099i	0.971808	+	0.235772i	$0.0757617\pi$
$373$	−0.347852	+	7.30231i	−0.0180111	+	0.378099i	−0.989820	+	0.142328i	$0.954541\pi$
$374$	3.94845	−	0.761001i	0.204169	−	0.0393504i
$375$	9.24646	+	3.70173i	0.477485	+	0.191156i
$376$	4.20279	+	17.3241i	0.216742	+	0.893423i
$377$	3.20944	−	2.06259i	0.165295	−	0.106229i
$378$	3.17327	+	3.00003i	0.163215	+	0.154305i
$379$	2.08203	−	4.55902i	0.106947	−	0.234181i	−0.848591	−	0.529050i	$-0.822549\pi$
$379$	2.08203	−	4.55902i	0.106947	−	0.234181i	0.955538	+	0.294868i	$0.0952758\pi$
$380$	−8.52388	+	0.813932i	−0.437266	+	0.0417538i
$381$	−6.08812	−	4.78775i	−0.311904	−	0.245284i
$382$	−0.0395851	−	0.830994i	−0.00202535	−	0.0425174i
$383$	−7.01417	−	28.9128i	−0.358407	−	1.47737i	−0.810677	−	0.585493i	$-0.800901\pi$
$383$	−7.01417	−	28.9128i	−0.358407	−	1.47737i	0.452270	−	0.891881i	$-0.350614\pi$
$384$	−1.90961	−	13.2817i	−0.0974496	−	0.677777i
$385$	−1.11008	+	2.45836i	−0.0565747	+	0.125290i
$386$	33.4583	+	21.5023i	1.70298	+	1.09444i
$387$	0.798597	+	0.153917i	0.0405950	+	0.00782404i
$388$	−1.16407	+	4.79835i	−0.0590966	+	0.243599i
$389$	24.5506	+	2.34430i	1.24477	+	0.118861i	0.696570	−	0.717489i	$-0.254709\pi$
$389$	24.5506	+	2.34430i	1.24477	+	0.118861i	0.548197	+	0.836350i	$0.315315\pi$
$390$	−12.2696	−	21.2517i	−0.621298	−	1.07612i
$391$	25.5704	+	10.9983i	1.29315	+	0.556207i
$392$	−9.55721	+	11.2212i	−0.482712	+	0.566754i
$393$	−7.84004	−	17.1673i	−0.395478	−	0.865975i
$394$	−22.6581	−	21.6044i	−1.14150	−	1.08841i
$395$	−0.384217	−	1.11012i	−0.0193321	−	0.0558564i
$396$	0.270212	−	0.139304i	0.0135787	−	0.00700029i
$397$	11.3013	−	32.6530i	0.567196	−	1.63881i	−0.187152	−	0.982331i	$-0.559926\pi$
$397$	11.3013	−	32.6530i	0.567196	−	1.63881i	0.754348	−	0.656475i	$-0.227953\pi$
$398$	−2.79511	−	19.4404i	−0.140106	−	0.974461i
$399$	1.88701	+	12.7394i	0.0944689	+	0.637767i
$400$	−3.72534	+	2.39413i	−0.186267	+	0.119707i
$401$	−16.4038	+	6.56708i	−0.819165	+	0.327944i	−0.743118	−	0.669160i	$-0.766654\pi$
$401$	−16.4038	+	6.56708i	−0.819165	+	0.327944i	−0.0760469	+	0.997104i	$0.524230\pi$
$402$	−11.0136	−	15.4665i	−0.549311	−	0.771399i
$403$	−25.6401	−	36.0065i	−1.27723	−	1.79361i
$404$	2.40142	−	0.961385i	0.119475	−	0.0478307i
$405$	2.04328	−	1.31314i	0.101532	−	0.0652504i
$406$	2.13222	−	1.69153i	0.105820	−	0.0839493i
$407$	−0.458329	−	3.18775i	−0.0227185	−	0.158011i
$408$	3.99721	−	11.5492i	0.197891	−	0.571770i
$409$	14.4558	−	7.45248i	0.714793	−	0.368501i	−0.0621547	−	0.998067i	$-0.519797\pi$
$409$	14.4558	−	7.45248i	0.714793	−	0.368501i	0.776948	+	0.629565i	$0.216767\pi$
$410$	4.91587	+	14.2035i	0.242778	+	0.701460i
$411$	6.97294	+	6.64869i	0.343950	+	0.327956i
$412$	−5.98339	−	13.1018i	−0.294780	−	0.645479i
$413$	−9.60232	−	0.875692i	−0.472499	−	0.0430900i
$414$	7.85819	+	0.952307i	0.386209	+	0.0468033i
$415$	10.7796	+	18.6708i	0.529149	+	0.916513i
$416$	−23.8612	−	2.27847i	−1.16989	−	0.111711i
$417$	4.03146	−	16.6179i	0.197422	−	0.813783i
$418$	3.31136	+	0.638212i	0.161964	+	0.0312160i
$419$	−13.6232	−	8.75508i	−0.665535	−	0.427714i	0.163778	−	0.986497i	$-0.447632\pi$
$419$	−13.6232	−	8.75508i	−0.665535	−	0.427714i	−0.829314	+	0.558784i	$0.811268\pi$
$420$	−2.71581	−	3.77968i	−0.132518	−	0.184429i
$421$	0.118782	+	0.826150i	0.00578910	+	0.0402641i	0.992511	−	0.122153i	$-0.0389800\pi$
$421$	0.118782	+	0.826150i	0.00578910	+	0.0402641i	−0.986722	+	0.162417i	$0.948071\pi$
$422$	−5.18470	−	21.3716i	−0.252387	−	1.04035i
$423$	0.402832	+	8.45649i	0.0195864	+	0.411169i
$424$	6.49807	+	5.11014i	0.315574	+	0.248170i
$425$	−5.19619	+	0.496176i	−0.252052	+	0.0240681i
$426$	8.70203	−	19.0548i	0.421615	−	0.923207i
$427$	−23.7094	−	22.4150i	−1.14738	−	1.08474i
$428$	−2.05249	+	1.31905i	−0.0992108	+	0.0637589i
$429$	0.605750	+	2.49694i	0.0292459	+	0.120553i
$430$	−3.02687	−	1.21178i	−0.145969	−	0.0584371i
$431$	−16.0456	+	3.09253i	−0.772889	+	0.148962i	−0.560423	−	0.828206i	$-0.689362\pi$
$431$	−16.0456	+	3.09253i	−0.772889	+	0.148962i	−0.212466	+	0.977169i	$0.568149\pi$
$432$	0.234292	−	4.91839i	0.0112724	−	0.236636i
$433$	20.9897	−	24.2234i	1.00870	−	1.16410i	0.0222986	−	0.999751i	$-0.492902\pi$
$433$	20.9897	−	24.2234i	1.00870	−	1.16410i	0.986402	−	0.164351i	$-0.0525530\pi$
$434$	−20.7520	−	23.7441i	−0.996126	−	1.13975i
$435$	−0.628855	−	1.37700i	−0.0301513	−	0.0660222i
$436$	3.89078	+	6.73904i	0.186335	+	0.322741i
$437$	16.4803	+	16.5331i	0.788361	+	0.790886i
$438$	−3.86152	+	6.68835i	−0.184510	+	0.319582i
$439$	−17.4810	+	24.5487i	−0.834324	+	1.17164i	0.148830	+	0.988863i	$0.452449\pi$
$439$	−17.4810	+	24.5487i	−0.834324	+	1.17164i	−0.983154	+	0.182781i	$0.941490\pi$
$440$	2.05977	−	0.604804i	0.0981959	−	0.0288329i
$441$	−5.46535	+	4.37379i	−0.260255	+	0.208276i
$442$	−49.3310	−	31.7031i	−2.34644	−	1.50796i
$443$	−12.4742	+	36.0418i	−0.592666	+	1.71240i	0.103606	+	0.994618i	$0.466962\pi$
$443$	−12.4742	+	36.0418i	−0.592666	+	1.71240i	−0.696272	+	0.717778i	$0.745159\pi$
$444$	5.15884	+	2.06529i	0.244828	+	0.0980142i
$445$	−4.99299	+	4.76080i	−0.236690	+	0.225684i
$446$	30.6455	+	15.7988i	1.45111	+	0.748097i
$447$	−0.668895	+	4.65227i	−0.0316377	+	0.220045i
$448$	8.95491	−	0.0381072i	0.423080	−	0.00180040i
$449$	10.1949	−	22.3237i	0.481127	−	1.05352i	−0.501025	−	0.865433i	$-0.667044\pi$
$449$	10.1949	−	22.3237i	0.481127	−	1.05352i	0.982152	−	0.188088i	$-0.0602290\pi$
$450$	−1.37806	+	0.551692i	−0.0649624	+	0.0260070i
$451$	−0.0748804	−	1.57193i	−0.00352598	−	0.0740194i
$452$	1.46948	−	1.40115i	0.0691187	−	0.0659046i
$453$	−1.11189	+	0.874401i	−0.0522412	+	0.0410829i
$454$	14.0068	+	16.1647i	0.657371	+	0.758647i
$455$	36.4555	−	14.7749i	1.70906	−	0.692657i
$456$	6.71194	−	7.74599i	0.314315	−	0.362739i
$457$	−10.5779	−	10.0860i	−0.494815	−	0.471805i	0.401098	−	0.916035i	$-0.368629\pi$
$457$	−10.5779	−	10.0860i	−0.494815	−	0.471805i	−0.895913	+	0.444230i	$0.853477\pi$
$458$	−1.45215	−	0.138664i	−0.0678546	−	0.00647933i
$459$	2.90203	−	5.02647i	0.135455	−	0.234616i
$460$	−8.03174	−	2.58163i	−0.374482	−	0.120369i
$461$	−7.74020			−0.360497			−0.180249	−	0.983621i	$-0.557690\pi$
$461$	−7.74020			−0.360497			−0.180249	+	0.983621i	$0.557690\pi$
$462$	0.606882	+	1.72962i	0.0282347	+	0.0804692i
$463$	−7.13859	+	2.09608i	−0.331759	+	0.0974131i	−0.443370	−	0.896339i	$-0.646217\pi$
$463$	−7.13859	+	2.09608i	−0.331759	+	0.0974131i	0.111611	+	0.993752i	$0.464399\pi$
$464$	−3.01344	−	0.580792i	−0.139895	−	0.0269626i
$465$	−15.5896	+	8.03702i	−0.722953	+	0.372708i
$466$	−11.2968	+	2.17729i	−0.523316	+	0.100861i
$467$	−1.91720	+	1.50770i	−0.0887176	+	0.0697683i	−0.661533	−	0.749916i	$-0.730094\pi$
$467$	−1.91720	+	1.50770i	−0.0887176	+	0.0697683i	0.572815	+	0.819685i	$0.305851\pi$
$468$	−4.25375	−	1.24901i	−0.196630	−	0.0577357i
$469$	26.9929	−	14.0615i	1.24641	−	0.649300i
$470$	4.83013	−	33.5943i	0.222797	−	1.54959i
$471$	−4.91936	+	0.469742i	−0.226672	+	0.0216446i
$472$	4.45126	+	6.25092i	0.204886	+	0.287722i
$473$	0.268342	+	0.211027i	0.0123384	+	0.00970302i
$474$	−0.709550	−	0.365798i	−0.0325907	−	0.0168017i
$475$	−4.20028	−	1.23331i	−0.192722	−	0.0565883i
$476$	−9.90706	−	5.05420i	−0.454089	−	0.231659i
$477$	2.57096	+	2.96704i	0.117716	+	0.135852i
$478$	−1.08930	+	22.8673i	−0.0498235	+	1.04592i
$479$	−5.12407	−	14.8050i	−0.234125	−	0.676459i	−0.999461	−	0.0328286i	$-0.989548\pi$
$479$	−5.12407	−	14.8050i	−0.234125	−	0.676459i	0.765336	−	0.643631i	$-0.222573\pi$
$480$	−2.24232	+	9.24297i	−0.102347	+	0.421882i
$481$	−27.2423	+	38.2565i	−1.24214	+	1.74435i
$482$	25.3785			1.15596
$483$	−3.25147	+	12.2649i	−0.147947	+	0.558073i
$484$	−7.83925			−0.356329
$485$	−9.60480	+	13.4881i	−0.436132	+	0.612461i
$486$	0.389128	−	1.60401i	0.0176512	−	0.0727592i
$487$	−5.68985	−	16.4398i	−0.257832	−	0.744956i	−0.997413	−	0.0718885i	$-0.977097\pi$
$487$	−5.68985	−	16.4398i	−0.257832	−	0.744956i	0.739581	−	0.673068i	$-0.235024\pi$
$488$	−1.23557	+	25.9377i	−0.0559314	+	1.17415i
$489$	5.74154	+	6.62609i	0.259641	+	0.299642i
$490$	24.8325	−	13.0707i	1.12182	−	0.590475i
$491$	20.1655	+	5.92112i	0.910055	+	0.267216i	0.703064	−	0.711127i	$-0.251815\pi$
$491$	20.1655	+	5.92112i	0.910055	+	0.267216i	0.206991	+	0.978343i	$0.433633\pi$
$492$	2.41353	+	1.24426i	0.108810	+	0.0560955i
$493$	−2.84349	−	2.23614i	−0.128064	−	0.100711i
$494$	−28.5262	−	40.0594i	−1.28345	−	1.80236i
$495$	1.01489	−	0.0969105i	0.0456160	−	0.00435580i
$496$	−5.06033	+	35.1953i	−0.227215	+	1.58032i
$497$	28.3251	+	18.0336i	1.27056	+	0.808918i
$498$	14.0571	+	4.12754i	0.629915	+	0.184960i
$499$	9.68328	−	7.61501i	0.433483	−	0.340895i	−0.377454	−	0.926028i	$-0.623200\pi$
$499$	9.68328	−	7.61501i	0.433483	−	0.340895i	0.810937	+	0.585134i	$0.198958\pi$
$500$	−7.08320	+	1.36518i	−0.316770	+	0.0610525i
$501$	−11.6631	+	6.01274i	−0.521068	+	0.268629i
$502$	26.6252	+	5.13159i	1.18834	+	0.229034i
$503$	23.4080	−	6.87321i	1.04371	−	0.306461i	0.285437	−	0.958397i	$-0.407861\pi$
$503$	23.4080	−	6.87321i	1.04371	−	0.306461i	0.758274	+	0.651936i	$0.226043\pi$
$504$	5.47479	+	1.03104i	0.243867	+	0.0459260i
$505$	8.67473			0.386020
$506$	2.74862	+	1.86674i	0.122191	+	0.0829866i
$507$	12.2345	−	21.1908i	0.543354	−	0.941116i
$508$	5.58412	+	0.533219i	0.247755	+	0.0236578i
$509$	6.92361	+	6.60165i	0.306883	+	0.292613i	0.827833	−	0.560975i	$-0.189574\pi$
$509$	6.92361	+	6.60165i	0.306883	+	0.292613i	−0.520949	+	0.853588i	$0.674422\pi$
$510$	−15.2373	+	17.5848i	−0.674718	+	0.778666i
$511$	−9.76364	−	7.61119i	−0.431918	−	0.336699i
$512$	−0.952643	−	1.09941i	−0.0421013	−	0.0485875i
$513$	3.82617	−	3.00893i	0.168930	−	0.132848i
$514$	28.8650	−	27.5227i	1.27318	−	1.21398i
$515$	−2.29834	−	48.2481i	−0.101277	−	2.12607i
$516$	−0.546842	+	0.218923i	−0.0240734	+	0.00963753i
$517$	−1.47623	+	3.23249i	−0.0649245	+	0.142165i
$518$	−16.6289	+	29.0873i	−0.730633	+	1.27802i
$519$	−0.902488	+	6.27694i	−0.0396148	+	0.275527i
$520$	−27.8257	−	14.3451i	−1.22024	−	0.629076i
$521$	−19.8547	+	18.9314i	−0.869849	+	0.829399i	−0.986498	−	0.163774i	$-0.947633\pi$
$521$	−19.8547	+	18.9314i	−0.869849	+	0.829399i	0.116649	+	0.993173i	$0.462785\pi$
$522$	−0.955017	−	0.382331i	−0.0418000	−	0.0167342i
$523$	−13.5888	+	39.2622i	−0.594196	+	1.71682i	0.0980748	+	0.995179i	$0.468732\pi$
$523$	−13.5888	+	39.2622i	−0.594196	+	1.71682i	−0.692271	+	0.721638i	$0.743390\pi$
$524$	11.4989	+	7.38991i	0.502333	+	0.322830i
$525$	−0.570807	−	2.30995i	−0.0249120	−	0.100814i
$526$	−42.3383	+	12.4316i	−1.84604	+	0.542046i
$527$	−24.3118	+	34.1411i	−1.05904	+	1.48721i
$528$	1.03341	−	1.78993i	0.0449736	−	0.0778966i
$529$	8.47991	+	21.3797i	0.368692	+	0.929552i
$530$	−7.86940	−	13.6302i	−0.341825	−	0.592058i
$531$	1.51394	+	3.31506i	0.0656993	+	0.143861i
$532$	−6.13802	−	7.02304i	−0.266117	−	0.304487i
$533$	−15.0287	+	17.3441i	−0.650966	+	0.751254i
$534$	−0.223072	+	4.68287i	−0.00965329	+	0.202647i
$535$	−8.03417	+	1.54846i	−0.347348	+	0.0669458i
$536$	−22.4876	−	9.00267i	−0.971316	−	0.388856i
$537$	−3.57924	−	14.7538i	−0.154455	−	0.636674i
$538$	21.7735	−	13.9930i	0.938723	−	0.603281i
$539$	−2.88031	+	0.580601i	−0.124064	+	0.0250082i
$540$	−0.730765	+	1.60015i	−0.0314471	+	0.0688596i
$541$	31.3950	−	2.99786i	1.34978	−	0.128888i	0.605013	−	0.796215i	$-0.293168\pi$
$541$	31.3950	−	2.99786i	1.34978	−	0.128888i	0.744765	+	0.667327i	$0.232562\pi$
$542$	−28.0342	−	22.0463i	−1.20417	−	0.946972i
$543$	−0.593780	−	12.4650i	−0.0254815	−	0.534923i
$544$	5.35832	+	22.0873i	0.229736	+	0.946985i
$545$	3.71386	+	25.8304i	0.159084	+	1.10645i
$546$	11.0007	−	24.3621i	0.470788	−	1.04260i
$547$	−16.9316	−	10.8813i	−0.723942	−	0.465250i	0.126064	−	0.992022i	$-0.459766\pi$
$547$	−16.9316	−	10.8813i	−0.723942	−	0.465250i	−0.850006	+	0.526773i	$0.823402\pi$
$548$	−6.85190	−	1.32060i	−0.292699	−	0.0564131i
$549$	−2.90741	+	11.9845i	−0.124085	+	0.511486i
$550$	−0.620250	−	0.0592267i	−0.0264475	−	0.00252543i
$551$	−1.51687	−	2.62730i	−0.0646210	−	0.111927i
$552$	9.09039	−	4.39789i	0.386913	−	0.187187i
$553$	0.737819	−	1.04551i	0.0313753	−	0.0444596i
$554$	−8.87133	−	19.4255i	−0.376907	−	0.825311i
$555$	13.4871	+	12.8599i	0.572495	+	0.545873i
$556$	4.05067	+	11.7036i	0.171787	+	0.496345i
$557$	8.52210	−	4.39345i	0.361093	−	0.186156i	−0.268127	−	0.963384i	$-0.586405\pi$
$557$	8.52210	−	4.39345i	0.361093	−	0.186156i	0.629220	+	0.777227i	$0.283374\pi$
$558$	−3.89830	+	11.2634i	−0.165028	+	0.476818i
$559$	−0.708491	−	4.92766i	−0.0299660	−	0.208418i
$560$	−29.4253	−	11.6351i	−1.24345	−	0.491672i
$561$	2.04950	−	1.31714i	0.0865302	−	0.0556096i
$562$	28.4018	−	11.3704i	1.19806	−	0.479631i
$563$	22.0782	+	31.0044i	0.930484	+	1.30668i	0.951739	+	0.306908i	$0.0992943\pi$
$563$	22.0782	+	31.0044i	0.930484	+	1.30668i	−0.0212554	+	0.999774i	$0.506766\pi$
$564$	−3.55670	−	4.99469i	−0.149764	−	0.210314i
$565$	6.32141	−	2.53071i	0.265944	−	0.106468i
$566$	4.87169	−	3.13085i	0.204772	−	0.131599i
$567$	2.46039	+	0.972865i	0.103327	+	0.0408565i
$568$	−3.80322	−	26.4519i	−0.159579	−	1.10990i
$569$	10.9849	−	31.7389i	0.460513	−	1.33056i	−0.440882	−	0.897565i	$-0.645334\pi$
$569$	10.9849	−	31.7389i	0.460513	−	1.33056i	0.901395	−	0.432999i	$-0.142545\pi$
$570$	−17.3444	+	8.94167i	−0.726478	+	0.374525i
$571$	12.5645	+	36.3028i	0.525808	+	1.51922i	0.825058	+	0.565049i	$0.191143\pi$
$571$	12.5645	+	36.3028i	0.525808	+	1.51922i	−0.299249	+	0.954175i	$0.596736\pi$
$572$	−1.34679	−	1.28416i	−0.0563120	−	0.0536934i
$573$	−0.209386	−	0.458492i	−0.00874724	−	0.0191538i
$574$	−9.44003	+	13.3768i	−0.394019	+	0.558336i
$575$	−3.32151	−	2.75141i	−0.138516	−	0.114742i
$576$	−1.69233	−	2.93121i	−0.0705139	−	0.122134i
$577$	−27.3802	−	2.61449i	−1.13985	−	0.108843i	−0.491990	−	0.870601i	$-0.663730\pi$
$577$	−27.3802	−	2.61449i	−1.13985	−	0.108843i	−0.647862	+	0.761758i	$0.724337\pi$
$578$	−6.49346	+	26.7664i	−0.270092	+	1.11334i
$579$	23.6610	+	4.56028i	0.983316	+	0.189519i
$580$	0.922337	+	0.592750i	0.0382980	+	0.0246126i
$581$	−9.66478	+	21.4035i	−0.400962	+	0.887966i
$582$	1.60137	+	11.1377i	0.0663787	+	0.461674i
$583$	0.388511	+	1.60146i	0.0160905	+	0.0663259i
$584$	0.468805	+	9.84143i	0.0193993	+	0.407241i
$585$	−11.6866	−	9.19048i	−0.483183	−	0.379979i
$586$	22.7856	−	2.17576i	0.941265	−	0.0898799i
$587$	−18.7751	+	41.1118i	−0.774932	+	1.69686i	−0.0594508	+	0.998231i	$0.518935\pi$
$587$	−18.7751	+	41.1118i	−0.774932	+	1.69686i	−0.715481	+	0.698632i	$0.753792\pi$
$588$	1.61734	−	4.80492i	0.0666979	−	0.198152i
$589$	−29.5701	+	19.0035i	−1.21841	+	0.783027i
$590$	−3.44445	−	14.1982i	−0.141806	−	0.584531i
$591$	−17.6092	−	7.04966i	−0.724346	−	0.289984i
$592$	37.0965	−	7.14976i	1.52466	−	0.293853i
$593$	0.00432666	−	0.0908278i	0.000177675	−	0.00372985i	−0.998777	−	0.0494468i	$-0.984254\pi$
$593$	0.00432666	−	0.0908278i	0.000177675	−	0.00372985i	0.998954	+	0.0457169i	$0.0145572\pi$
$594$	0.453694	−	0.523590i	0.0186153	−	0.0214832i
$595$	−24.5446	−	28.0836i	−1.00623	−	1.15132i
$596$	−1.41411	−	3.09648i	−0.0579244	−	0.126837i
$597$	−5.94970	−	10.3052i	−0.243505	−	0.421763i
$598$	−10.2238	−	47.3625i	−0.418082	−	1.93680i
$599$	−6.93932	+	12.0193i	−0.283533	+	0.491093i	−0.972252	−	0.233935i	$-0.924840\pi$
$599$	−6.93932	+	12.0193i	−0.283533	+	0.491093i	0.688719	+	0.725028i	$0.258173\pi$
$600$	−1.09845	+	1.54256i	−0.0448441	+	0.0629747i
$601$	−20.4507	+	6.00486i	−0.834200	+	0.244943i	−0.670820	−	0.741620i	$-0.734058\pi$
$601$	−20.4507	+	6.00486i	−0.834200	+	0.244943i	−0.163380	+	0.986563i	$0.552240\pi$
$602$	−0.851996	−	3.44787i	−0.0347248	−	0.140525i
$603$	−9.67750	−	6.21935i	−0.394098	−	0.253272i
$604$	0.335075	−	0.968137i	0.0136340	−	0.0393929i
$605$	−24.4063	−	9.77081i	−0.992257	−	0.397240i
$606$	4.26636	−	4.06797i	0.173309	−	0.165250i
$607$	5.67239	+	2.92432i	0.230235	+	0.118695i	0.569485	−	0.822002i	$-0.307143\pi$
$607$	5.67239	+	2.92432i	0.230235	+	0.118695i	−0.339249	+	0.940696i	$0.610173\pi$
$608$	−2.71263	+	18.8668i	−0.110012	+	0.765148i
$609$	0.818407	−	1.43156i	0.0331635	−	0.0580096i
$610$	20.5374	−	44.9706i	0.831535	−	1.82081i
$611$	48.1104	−	19.2605i	1.94634	−	0.779196i
$612$	0.200018	+	4.19889i	0.00808524	+	0.169730i
$613$	14.9884	−	14.2914i	0.605376	−	0.577225i	−0.324139	−	0.946010i	$-0.605074\pi$
$613$	14.9884	−	14.2914i	0.605376	−	0.577225i	0.929515	+	0.368784i	$0.120226\pi$
$614$	6.74655	−	5.30555i	0.272269	−	0.214115i
$615$	5.96331	+	6.88202i	0.240464	+	0.277510i
$616$	1.84427	+	1.43769i	0.0743077	+	0.0579261i
$617$	−6.70943	+	7.74310i	−0.270112	+	0.311725i	−0.874558	−	0.484920i	$-0.838849\pi$
$617$	−6.70943	+	7.74310i	−0.270112	+	0.311725i	0.604447	+	0.796645i	$0.293394\pi$
$618$	−23.7560	−	22.6513i	−0.955608	−	0.911170i
$619$	22.9858	+	2.19487i	0.923876	+	0.0882195i	0.546140	−	0.837694i	$-0.316097\pi$
$619$	22.9858	+	2.19487i	0.923876	+	0.0882195i	0.377736	+	0.925913i	$0.376703\pi$
$620$	6.35154	−	11.0012i	0.255084	−	0.441818i
$621$	4.63440	−	1.23384i	0.185972	−	0.0495125i
$622$	−43.5938			−1.74795
$623$	−7.38518	−	1.39081i	−0.295881	−	0.0557215i
$624$	−28.9197	+	8.49158i	−1.15771	+	0.339935i
$625$	−28.1695	−	5.42922i	−1.12678	−	0.217169i
$626$	39.3274	−	20.2747i	1.57184	−	0.810340i
$627$	2.00624	−	0.386670i	0.0801213	−	0.0154421i
$628$	2.81336	−	2.21245i	0.112265	−	0.0882865i
$629$	42.7280	+	12.5461i	1.70368	+	0.500244i
$630$	−8.94714	−	5.69632i	−0.356462	−	0.226947i
$631$	−1.06854	+	7.43188i	−0.0425381	+	0.295859i	0.957436	+	0.288646i	$0.0932050\pi$
$631$	−1.06854	+	7.43188i	−0.0425381	+	0.295859i	−0.999974	+	0.00721280i	$0.997704\pi$
$632$	−1.01380	+	0.0968063i	−0.0403269	+	0.00385075i
$633$	−7.72861	−	10.8533i	−0.307185	−	0.431381i
$634$	11.1647	+	8.78000i	0.443406	+	0.348698i
$635$	16.7207	+	8.62012i	0.663541	+	0.342079i
$636$	−2.72824	−	0.801082i	−0.108182	−	0.0317650i
$637$	36.2422	+	22.8580i	1.43597	+	0.905665i
$638$	−0.282768	−	0.326331i	−0.0111949	−	0.0129196i
$639$	0.603887	−	12.6772i	0.0238894	−	0.501501i
$640$	10.6595	+	30.7985i	0.421352	+	1.21742i
$641$	9.86705	−	40.6725i	0.389725	−	1.60647i	−0.352160	−	0.935940i	$-0.614553\pi$
$641$	9.86705	−	40.6725i	0.389725	−	1.60647i	0.741884	−	0.670528i	$-0.233932\pi$
$642$	−3.22518	+	4.52914i	−0.127288	+	0.178751i
$643$	12.0368			0.474684			0.237342	−	0.971426i	$-0.423724\pi$
$643$	12.0368			0.474684			0.237342	+	0.971426i	$0.423724\pi$
$644$	−2.82142	−	8.74599i	−0.111180	−	0.344640i
$645$	−1.97538			−0.0777803
$646$	−27.0483	+	37.9840i	−1.06420	+	1.49446i
$647$	−3.54640	+	14.6185i	−0.139423	+	0.574711i	0.858644	+	0.512572i	$0.171307\pi$
$647$	−3.54640	+	14.6185i	−0.139423	+	0.574711i	−0.998068	+	0.0621386i	$0.980208\pi$
$648$	−0.688691	−	1.98984i	−0.0270544	−	0.0781684i
$649$	−0.0727875	+	1.52800i	−0.00285716	+	0.0599792i
$650$	5.95022	+	6.86692i	0.233387	+	0.269343i
$651$	−17.0189	−	8.68238i	−0.667023	−	0.340289i
$652$	−6.09278	−	1.78900i	−0.238612	−	0.0700627i
$653$	16.0481	+	8.27334i	0.628009	+	0.323761i	0.742684	−	0.669642i	$-0.233552\pi$
$653$	16.0481	+	8.27334i	0.628009	+	0.323761i	−0.114675	+	0.993403i	$0.536583\pi$
$654$	13.9396	+	10.9622i	0.545080	+	0.428656i
$655$	26.5894	+	37.3396i	1.03893	+	1.45898i
$656$	18.3773	−	1.75482i	0.717511	−	0.0685140i
$657$	−0.665908	+	4.63149i	−0.0259795	+	0.180692i
$658$	32.7883	−	17.0806i	1.27822	−	0.665870i
$659$	−31.5862	−	9.27455i	−1.23042	−	0.361285i	−0.399014	−	0.916945i	$-0.630648\pi$
$659$	−31.5862	−	9.27455i	−1.23042	−	0.361285i	−0.831410	+	0.555659i	$0.812466\pi$
$660$	−0.580413	+	0.456442i	−0.0225925	+	0.0177670i
$661$	−44.6021	+	8.59636i	−1.73482	+	0.334359i	−0.956107	−	0.293019i	$-0.905340\pi$
$661$	−44.6021	+	8.59636i	−1.73482	+	0.334359i	−0.778715	+	0.627378i	$0.784128\pi$
$662$	24.0303	−	12.3885i	0.933965	−	0.481493i
$663$	−34.8858	−	6.72369i	−1.35485	−	0.261126i
$664$	17.9332	−	5.26567i	0.695945	−	0.204348i
$665$	−10.3563	−	29.5156i	−0.401600	−	1.14457i
$666$	12.6637			0.490710
$667$	−0.350110	−	2.96846i	−0.0135563	−	0.114939i
$668$	4.75178	−	8.23032i	0.183852	−	0.318441i
$669$	20.7946	+	1.98564i	0.803964	+	0.0767693i
$670$	33.3765	+	31.8245i	1.28945	+	1.22949i
$671$	−3.38981	+	3.91205i	−0.130862	+	0.151023i
$672$	−9.60180	+	3.89147i	−0.370397	+	0.150117i
$673$	29.3431	+	33.8637i	1.13109	+	1.30535i	0.946562	+	0.322523i	$0.104531\pi$
$673$	29.3431	+	33.8637i	1.13109	+	1.30535i	0.184530	+	0.982827i	$0.440924\pi$
$674$	−26.3339	+	20.7092i	−1.01435	+	0.797690i
$675$	−0.650883	+	0.620615i	−0.0250525	+	0.0238875i
$676$	0.843243	+	17.7018i	0.0324324	+	0.680840i
$677$	−4.90202	+	1.96247i	−0.188400	+	0.0754240i	−0.463944	−	0.885864i	$-0.653566\pi$
$677$	−4.90202	+	1.96247i	−0.188400	+	0.0754240i	0.275544	+	0.961288i	$0.411142\pi$
$678$	1.92220	−	4.20903i	0.0738216	−	0.161647i
$679$	−18.0369	+	0.0767551i	−0.692191	+	0.00294559i
$680$	−4.22446	+	29.3818i	−0.162001	+	1.12674i
$681$	11.5183	+	5.93807i	0.441381	+	0.227548i
$682$	−3.62081	+	3.45244i	−0.138648	+	0.132201i
$683$	14.7102	+	5.88909i	0.562871	+	0.225340i	0.635609	−	0.772012i	$-0.280749\pi$
$683$	14.7102	+	5.88909i	0.562871	+	0.225340i	−0.0727374	+	0.997351i	$0.523174\pi$
$684$	−1.15304	+	3.33149i	−0.0440876	+	0.127383i
$685$	−19.6864	−	12.6517i	−0.752178	−	0.483395i
$686$	27.3468	+	13.6592i	1.04411	+	0.521511i
$687$	−0.848009	+	0.248998i	−0.0323536	+	0.00949987i
$688$	−2.32292	+	3.26208i	−0.0885604	+	0.124366i
$689$	12.0158	−	20.8119i	0.457765	−	0.792872i
$690$	−19.1792	+	1.34091i	−0.730141	+	0.0510475i
$691$	1.30635	+	2.26266i	0.0496957	+	0.0860755i	0.889803	−	0.456344i	$-0.150842\pi$
$691$	1.30635	+	2.26266i	0.0496957	+	0.0860755i	−0.840107	+	0.542420i	$0.817508\pi$
$692$	−1.90795	−	4.17783i	−0.0725294	−	0.158817i
$693$	0.730821	+	0.836196i	0.0277616	+	0.0317645i
$694$	−20.4984	+	23.6564i	−0.778110	+	0.897986i
$695$	−1.97623	+	41.4862i	−0.0749628	+	1.57366i
$696$	−1.28865	+	0.248366i	−0.0488460	+	0.00941429i
$697$	20.2018	+	8.08757i	0.765196	+	0.306338i
$698$	0.777639	+	3.20547i	0.0294341	+	0.121329i
$699$	−5.86381	+	3.76844i	−0.221790	+	0.142536i
$700$	1.25228	+	1.18391i	0.0473316	+	0.0447476i
$701$	−10.2584	+	22.4628i	−0.387455	+	0.848408i	0.610935	+	0.791681i	$0.290794\pi$
$701$	−10.2584	+	22.4628i	−0.387455	+	0.848408i	−0.998390	+	0.0567272i	$0.981933\pi$
$702$	−10.0575	+	0.960373i	−0.379595	+	0.0362470i
$703$	29.3564	+	23.0861i	1.10720	+	0.870708i
$704$	−0.0676001	−	1.41910i	−0.00254777	−	0.0534844i
$705$	−4.84788	−	19.9833i	−0.182582	−	0.752613i
$706$	−7.27694	−	50.6122i	−0.273871	−	1.90482i
$707$	5.51388	+	7.67384i	0.207371	+	0.288605i
$708$	−2.22048	−	1.42702i	−0.0834507	−	0.0536305i
$709$	35.8104	+	6.90189i	1.34489	+	0.259206i	0.810354	−	0.585941i	$-0.199275\pi$
$709$	35.8104	+	6.90189i	1.34489	+	0.259206i	0.534534	+	0.845147i	$0.320487\pi$
$710$	−11.9952	+	49.4450i	−0.450173	+	1.85564i
$711$	−0.481467	−	0.0459745i	−0.0180564	−	0.00172418i
$712$	2.99045	+	5.17961i	0.112072	+	0.194114i
$713$	−34.1616	+	5.68841i	−1.27936	+	0.213033i
$714$	−25.2410	−	2.30188i	−0.944622	−	0.0861457i
$715$	−2.59244	−	5.67666i	−0.0969519	−	0.212295i
$716$	7.95784	+	7.58779i	0.297399	+	0.283569i
$717$	4.53649	+	13.1073i	0.169418	+	0.489502i
$718$	19.3109	−	9.95547i	0.720677	−	0.371535i
$719$	2.18837	−	6.32287i	0.0816123	−	0.235803i	−0.896811	−	0.442414i	$-0.854122\pi$
$719$	2.18837	−	6.32287i	0.0816123	−	0.235803i	0.978423	+	0.206611i	$0.0662434\pi$
$720$	1.70203	+	11.8379i	0.0634309	+	0.441172i
$721$	41.2204	−	32.7009i	1.53513	−	1.21785i
$722$	−6.51668	+	4.18801i	−0.242526	+	0.155862i
$723$	14.2745	−	5.71465i	0.530875	−	0.212530i
$724$	5.24262	+	7.36223i	0.194840	+	0.273615i
$725$	0.325133	+	0.456586i	0.0120751	+	0.0169572i
$726$	−16.5853	+	6.63977i	−0.615540	+	0.246425i
$727$	16.0819	−	10.3352i	0.596443	−	0.383311i	−0.207309	−	0.978276i	$-0.566470\pi$
$727$	16.0819	−	10.3352i	0.596443	−	0.383311i	0.803752	+	0.594965i	$0.202834\pi$
$728$	−4.99673	−	33.7333i	−0.185191	−	1.25024i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	6.13519	−	17.7265i	0.227073	−	0.656086i
$731$	−4.19568	+	2.16302i	−0.155183	+	0.0800022i
$732$	−2.92126	−	8.44041i	−0.107973	−	0.311967i
$733$	−17.3366	−	16.5304i	−0.640343	−	0.610566i	0.298707	−	0.954345i	$-0.403445\pi$
$733$	−17.3366	−	16.5304i	−0.640343	−	0.610566i	−0.939051	+	0.343779i	$0.888293\pi$
$734$	12.5829	+	27.5528i	0.464444	+	1.01699i
$735$	11.0242	−	12.9435i	0.406633	−	0.477430i
$736$	−9.79993	+	16.0201i	−0.361230	+	0.590509i
$737$	−2.41432	−	4.18173i	−0.0889328	−	0.154036i
$738$	6.16013	+	0.588221i	0.226757	+	0.0216527i
$739$	−1.75981	+	7.25403i	−0.0647356	+	0.266844i	−0.994977	−	0.100104i	$-0.968082\pi$
$739$	−1.75981	+	7.25403i	−0.0647356	+	0.266844i	0.930241	+	0.366948i	$0.119597\pi$
$740$	−13.2530	−	2.55430i	−0.487189	−	0.0938980i
$741$	−25.0654	−	16.1086i	−0.920802	−	0.591764i
$742$	7.05556	−	15.6251i	0.259018	−	0.573617i
$743$	−0.222916	−	1.55042i	−0.00817801	−	0.0568793i	0.985324	−	0.170696i	$-0.0546015\pi$
$743$	−0.222916	−	1.55042i	−0.00817801	−	0.0568793i	−0.993502	+	0.113816i	$0.963692\pi$
$744$	3.58483	+	14.7769i	0.131426	+	0.541746i
$745$	−0.543190	−	11.4030i	−0.0199009	−	0.417772i
$746$	−9.48481	−	7.45894i	−0.347264	−	0.273091i
$747$	8.83607	−	0.843743i	0.323295	−	0.0308709i
$748$	−0.732991	+	1.60503i	−0.0268008	+	0.0586855i
$749$	−6.47653	−	6.12295i	−0.236647	−	0.223728i
$750$	−13.8295	+	8.88768i	−0.504982	+	0.324532i
$751$	−4.98511	−	20.5489i	−0.181909	−	0.749840i	−0.987533	−	0.157413i	$-0.949685\pi$
$751$	−4.98511	−	20.5489i	−0.181909	−	0.749840i	0.805624	−	0.592428i	$-0.201830\pi$
$752$	−38.7006	−	15.4934i	−1.41127	−	0.564986i
$753$	16.1313	−	3.10905i	0.587856	−	0.113300i
$754$	−0.299619	+	6.28977i	−0.0109115	+	0.229060i
$755$	2.24989	−	2.59651i	0.0818819	−	0.0944967i
$756$	−1.88002	+	0.370649i	−0.0683757	+	0.0134804i
$757$	5.80833	+	12.7185i	0.211107	+	0.462260i	0.985332	−	0.170651i	$-0.0545870\pi$
$757$	5.80833	+	12.7185i	0.211107	+	0.462260i	−0.774224	+	0.632911i	$0.781860\pi$
$758$	4.13618	+	7.16408i	0.150233	+	0.260211i
$759$	1.96635	+	0.431048i	0.0713741	+	0.0156460i
$760$	−12.4472	+	21.5591i	−0.451506	+	0.782032i
$761$	1.04304	−	1.46475i	0.0378103	−	0.0530971i	−0.795238	−	0.606297i	$-0.792654\pi$
$761$	1.04304	−	1.46475i	0.0378103	−	0.0530971i	0.833048	+	0.553200i	$0.186594\pi$
$762$	12.2658	−	3.60158i	0.444345	−	0.130471i
$763$	−20.4895	+	19.7038i	−0.741770	+	0.713327i
$764$	0.307105	+	0.197364i	0.0111107	+	0.00714039i
$765$	−4.61076	+	13.3219i	−0.166702	+	0.481655i
$766$	45.5882	+	18.2508i	1.64717	+	0.659426i
$767$	16.1451	−	15.3943i	0.582966	−	0.555857i
$768$	13.6684	+	7.04657i	0.493217	+	0.254271i
$769$	4.97179	−	34.5796i	0.179287	−	1.24697i	−0.679129	−	0.734019i	$-0.737642\pi$
$769$	4.97179	−	34.5796i	0.179287	−	1.24697i	0.858417	−	0.512953i	$-0.171448\pi$
$770$	−2.24243	−	3.84612i	−0.0808117	−	0.138605i
$771$	10.0381	−	21.9803i	0.361513	−	0.791602i
$772$	−16.2019	+	6.48627i	−0.583120	+	0.233446i
$773$	1.27081	+	26.6776i	0.0457079	+	0.959527i	0.898961	+	0.438030i	$0.144323\pi$
$773$	1.27081	+	26.6776i	0.0457079	+	0.959527i	−0.853253	+	0.521498i	$0.825373\pi$
$774$	−0.971519	+	0.926341i	−0.0349205	+	0.0332966i
$775$	5.10492	−	4.01455i	0.183374	−	0.144207i
$776$	9.40051	+	10.8488i	0.337459	+	0.389448i
$777$	−2.80340	+	20.1051i	−0.100571	+	0.721265i
$778$	−26.6567	+	30.7635i	−0.955690	+	1.10293i
$779$	13.2077	+	12.5935i	0.473216	+	0.451210i
$780$	10.7192	+	1.02356i	0.383808	+	0.0366492i
$781$	2.66363	−	4.61354i	0.0953121	−	0.165085i
$782$	−39.2682	+	23.8492i	−1.40423	+	0.852845i
$783$	−0.623257			−0.0222734
$784$	−8.41087	−	33.4258i	−0.300388	−	1.19378i
$785$	11.5166	−	3.38157i	0.411044	−	0.120693i
$786$	30.5872	+	5.89521i	1.09101	+	0.210275i
$787$	11.8479	−	6.10800i	0.422331	−	0.217727i	−0.233942	−	0.972251i	$-0.575162\pi$
$787$	11.8479	−	6.10800i	0.422331	−	0.217727i	0.656273	+	0.754524i	$0.272132\pi$
$788$	13.4894	−	2.59987i	0.480541	−	0.0926167i
$789$	−21.0145	+	16.5260i	−0.748137	+	0.588341i
$790$	1.86039	+	0.546261i	0.0661899	+	0.0194351i
$791$	6.25677	+	3.98346i	0.222465	+	0.141636i
$792$	0.125784	−	0.874849i	0.00446955	−	0.0310864i
$793$	75.1454	−	7.17552i	2.66849	−	0.254810i
$794$	33.0815	+	46.4565i	1.17402	+	1.64868i
$795$	−7.49548	−	5.89451i	−0.265837	−	0.209057i
$796$	7.66021	+	3.94911i	0.271509	+	0.139973i
$797$	−3.67526	−	1.07915i	−0.130184	−	0.0382256i	0.215991	−	0.976395i	$-0.430702\pi$
$797$	−3.67526	−	1.07915i	−0.130184	−	0.0382256i	−0.346176	+	0.938170i	$0.612520\pi$
$798$	−18.9345	−	9.65967i	−0.670276	−	0.341949i
$799$	−32.1784	−	37.1358i	−1.13839	−	1.31377i
$800$	0.167569	−	3.51771i	0.00592446	−	0.124370i
$801$	0.929004	+	2.68418i	0.0328248	+	0.0948409i
$802$	6.87569	−	28.3420i	0.242789	−	1.00079i
$803$	−1.13926	+	1.59987i	−0.0402037	+	0.0564582i
$804$	8.33164			0.293834
$805$	2.11691	−	30.7459i	0.0746113	−	1.08365i
$806$	72.9581			2.56984
$807$	9.09595	−	12.7735i	0.320193	−	0.449648i
$808$	1.77300	−	7.30841i	0.0623740	−	0.257109i
$809$	−10.0343	−	28.9923i	−0.352789	−	1.01932i	−0.972180	−	0.234234i	$-0.924742\pi$
$809$	−10.0343	−	28.9923i	−0.352789	−	1.01932i	0.619392	−	0.785082i	$-0.287379\pi$
$810$	−0.190751	+	4.00437i	−0.00670232	+	0.140699i
$811$	−0.412673	−	0.476250i	−0.0144909	−	0.0167234i	0.748458	−	0.663182i	$-0.230795\pi$
$811$	−0.412673	−	0.476250i	−0.0144909	−	0.0167234i	−0.762949	+	0.646459i	$0.776249\pi$
$812$	0.0619026	+	1.19269i	0.00217235	+	0.0418550i
$813$	−20.7326	−	6.08764i	−0.727124	−	0.213503i
$814$	4.72468	+	2.43574i	0.165600	+	0.0853728i
$815$	−16.7391	−	13.1638i	−0.586346	−	0.461108i
$816$	16.5775	+	23.2798i	0.580328	+	0.814956i
$817$	−3.94085	+	0.376305i	−0.137873	+	0.0131652i
$818$	−3.82028	+	26.5706i	−0.133573	+	0.929020i
$819$	0.701750	−	16.1799i	0.0245211	−	0.565373i
$820$	−6.32811	−	1.85810i	−0.220987	−	0.0648877i
$821$	16.5765	−	13.0359i	0.578524	−	0.454956i	−0.285520	−	0.958373i	$-0.592166\pi$
$821$	16.5765	−	13.0359i	0.578524	−	0.454956i	0.864044	+	0.503417i	$0.167924\pi$
$822$	−15.6150	+	3.00954i	−0.544635	+	0.104970i
$823$	−30.6644	+	15.8086i	−1.06889	+	0.551053i	−0.900584	−	0.434681i	$-0.856861\pi$
$823$	−30.6644	+	15.8086i	−1.06889	+	0.551053i	−0.168310	+	0.985734i	$0.553831\pi$
$824$	−41.1185	−	7.92494i	−1.43243	−	0.276078i
$825$	−0.362206	+	0.106353i	−0.0126104	+	0.00370274i
$826$	10.3706	−	12.0718i	0.360841	−	0.420031i
$827$	−20.0136			−0.695939			−0.347970	−	0.937506i	$-0.613129\pi$
$827$	−20.0136			−0.695939			−0.347970	+	0.937506i	$0.613129\pi$
$828$	−2.34054	+	2.56643i	−0.0813395	+	0.0891895i
$829$	3.62610	−	6.28059i	0.125940	−	0.218134i	−0.796160	−	0.605086i	$-0.793139\pi$
$829$	3.62610	−	6.28059i	0.125940	−	0.218134i	0.922100	+	0.386952i	$0.126472\pi$
$830$	−35.4230	−	3.38249i	−1.22955	−	0.117408i
$831$	−9.36400	−	8.92856i	−0.324834	−	0.309728i
$832$	−13.5675	+	15.6578i	−0.470370	+	0.542836i
$833$	9.24215	−	39.5633i	0.320221	−	1.37079i
$834$	18.4828	+	21.3303i	0.640007	+	0.738607i
$835$	25.0522	−	19.7013i	0.866966	−	0.681790i
$836$	−1.07096	+	1.02116i	−0.0370401	+	0.0353176i
$837$	0.343602	+	7.21308i	0.0118766	+	0.249321i
$838$	24.8139	−	9.93400i	0.857183	−	0.343164i
$839$	3.06372	−	6.70860i	0.105771	−	0.231607i	−0.849345	−	0.527838i	$-0.823003\pi$
$839$	3.06372	−	6.70860i	0.105771	−	0.231607i	0.955116	+	0.296232i	$0.0957300\pi$
$840$	−13.5311	+	0.0575811i	−0.466868	+	0.00198674i
$841$	4.07185	−	28.3203i	0.140409	−	0.976563i
$842$	−1.22447	−	0.631257i	−0.0421980	−	0.0217546i
$843$	13.4147	−	12.7909i	0.462027	−	0.440542i
$844$	8.95871	+	3.58652i	0.308371	+	0.123453i
$845$	−19.4382	+	56.1630i	−0.668695	+	1.93207i
$846$	−11.7553	−	7.55467i	−0.404155	−	0.259735i
$847$	−6.86982	−	27.8009i	−0.236050	−	0.955250i
$848$	−18.5482	+	5.44626i	−0.636949	+	0.187025i
$849$	2.03516	−	2.85799i	0.0698466	−	0.0980858i
$850$	4.30775	−	7.46124i	0.147755	−	0.255919i
$851$	17.5828	+	32.3233i	0.602732	+	1.10803i
$852$	4.59598	+	7.96047i	0.157456	+	0.272721i
$853$	7.22512	+	15.8208i	0.247384	+	0.541694i	0.992065	−	0.125726i	$-0.0401259\pi$
$853$	7.22512	+	15.8208i	0.247384	+	0.541694i	−0.744682	+	0.667420i	$0.767399\pi$
$854$	52.8361	−	10.4167i	1.80801	−	0.356452i
$855$	−7.74218	+	8.93495i	−0.264777	+	0.305569i
$856$	−0.337511	+	7.08523i	−0.0115359	+	0.242168i
$857$	24.2702	−	4.67770i	0.829055	−	0.159787i	0.242967	−	0.970035i	$-0.421879\pi$
$857$	24.2702	−	4.67770i	0.829055	−	0.159787i	0.586088	+	0.810247i	$0.300667\pi$
$858$	−3.93704	−	1.57615i	−0.134408	−	0.0538090i
$859$	−3.26353	−	13.4525i	−0.111350	−	0.458992i	−1.00000		0.000405202i	$-0.999871\pi$
$859$	−3.26353	−	13.4525i	−0.111350	−	0.458992i	0.888650	−	0.458587i	$-0.151644\pi$
$860$	1.20357	−	0.773486i	0.0410413	−	0.0263757i
$861$	−2.29755	+	9.64966i	−0.0783001	+	0.328859i
$862$	11.2042	−	24.5339i	0.381618	−	0.835626i
$863$	−12.9177	+	1.23349i	−0.439722	+	0.0419884i	−0.312570	−	0.949895i	$-0.601190\pi$
$863$	−12.9177	+	1.23349i	−0.439722	+	0.0419884i	−0.127152	+	0.991883i	$0.540584\pi$
$864$	3.07808	+	2.42063i	0.104718	+	0.0823514i
$865$	−0.732883	−	15.3851i	−0.0249188	−	0.523109i
$866$	12.4724	+	51.4119i	0.423829	+	1.74705i
$867$	2.37484	+	16.5174i	0.0806538	+	0.560959i
$868$	13.7691	−	1.37394i	0.467353	−	0.0466346i
$869$	−0.170787	−	0.109758i	−0.00579354	−	0.00372328i
$870$	2.45342	+	0.472859i	0.0831789	+	0.0160314i
$871$	−16.6012	+	68.4312i	−0.562512	+	2.31870i
$872$	22.5211	+	2.15050i	0.762659	+	0.0728251i
$873$	3.40868	+	5.90400i	0.115366	+	0.199820i
$874$	−38.0068	+	6.32869i	−1.28560	+	0.214071i
$875$	−11.0487	−	23.9233i	−0.373514	−	0.808756i
$876$	−1.40780	−	3.08265i	−0.0475651	−	0.104153i
$877$	0.562643	+	0.536479i	0.0189991	+	0.0181156i	0.699519	−	0.714614i	$-0.253398\pi$
$877$	0.562643	+	0.536479i	0.0189991	+	0.0181156i	−0.680520	+	0.732729i	$0.738246\pi$
$878$	−16.2689	−	47.0060i	−0.549049	−	1.58637i
$879$	12.3262	−	6.35459i	0.415752	−	0.214335i
$880$	−1.64189	+	4.74393i	−0.0553481	+	0.159918i
$881$	1.63620	+	11.3800i	0.0551249	+	0.383402i	0.998643	+	0.0520807i	$0.0165853\pi$
$881$	1.63620	+	11.3800i	0.0551249	+	0.383402i	−0.943518	+	0.331321i	$0.892506\pi$
$882$	−0.647948	−	11.5355i	−0.0218176	−	0.388422i
$883$	−40.5463	+	26.0575i	−1.36449	+	0.876906i	−0.998555	−	0.0537334i	$-0.982888\pi$
$883$	−40.5463	+	26.0575i	−1.36449	+	0.876906i	−0.365937	+	0.930640i	$0.619252\pi$
$884$	23.8882	−	9.56338i	0.803446	−	0.321651i
$885$	−5.13450	−	7.21039i	−0.172594	−	0.242375i
$886$	−36.5148	−	51.2779i	−1.22674	−	1.72271i
$887$	30.3482	−	12.1496i	1.01899	−	0.407943i	0.198806	−	0.980039i	$-0.436294\pi$
$887$	30.3482	−	12.1496i	1.01899	−	0.407943i	0.820187	+	0.572096i	$0.193869\pi$
$888$	13.5910	−	8.73440i	0.456084	−	0.293107i
$889$	3.00258	+	20.2706i	0.100703	+	0.679856i
$890$	−1.62053	−	11.2710i	−0.0543201	−	0.377805i
$891$	0.137286	−	0.396663i	0.00459927	−	0.0132887i
$892$	−13.4473	+	6.93258i	−0.450250	+	0.232120i
$893$	−13.4782	−	38.9428i	−0.451032	−	1.30317i
$894$	−5.61450	−	5.35342i	−0.187777	−	0.179045i
$895$	15.3181	+	33.5421i	0.512029	+	1.12119i
$896$	−20.4695	+	29.0059i	−0.683839	+	0.969019i
$897$	−16.4155	−	24.3376i	−0.548097	−	0.812609i
$898$	20.2532	+	35.0797i	0.675860	+	1.17062i
$899$	4.48032	+	0.427819i	0.149427	+	0.0142686i
$900$	0.153563	−	0.632995i	0.00511876	−	0.0210998i
$901$	−22.3748	−	4.31238i	−0.745411	−	0.143666i
$902$	2.18513	+	1.40430i	0.0727569	+	0.0467580i
$903$	−1.25560	−	1.74746i	−0.0417837	−	0.0581517i
$904$	−0.840095	−	5.84299i	−0.0279412	−	0.194335i
$905$	7.14584	+	29.4556i	0.237536	+	0.979136i
$906$	−0.111090	−	2.33208i	−0.00369073	−	0.0774780i
$907$	−24.7398	−	19.4556i	−0.821472	−	0.646013i	0.116320	−	0.993212i	$-0.462890\pi$
$907$	−24.7398	−	19.4556i	−0.821472	−	0.646013i	−0.937791	+	0.347199i	$0.887133\pi$
$908$	−9.34305	+	0.892153i	−0.310060	+	0.0296071i
$909$	1.48367	−	3.24878i	0.0492101	−	0.107755i
$910$	−15.0380	+	63.1593i	−0.498504	+	2.09371i
$911$	12.6120	−	8.10523i	0.417854	−	0.268538i	−0.314776	−	0.949166i	$-0.601929\pi$
$911$	12.6120	−	8.10523i	0.417854	−	0.268538i	0.732629	+	0.680628i	$0.238293\pi$
$912$	5.65062	+	23.2922i	0.187111	+	0.771280i
$913$	3.45891	+	1.38474i	0.114473	+	0.0458282i
$914$	23.6879	−	4.56546i	0.783525	−	0.151012i
$915$	1.42522	−	29.9190i	0.0471162	−	0.989091i
$916$	0.419181	−	0.483761i	0.0138501	−	0.0159839i
$917$	−16.1304	+	47.2555i	−0.532674	+	1.56051i
$918$	3.97960	+	8.71410i	0.131346	+	0.287608i
$919$	10.1177	+	17.5244i	0.333753	+	0.578077i	0.983244	−	0.182292i	$-0.0583516\pi$
$919$	10.1177	+	17.5244i	0.333753	+	0.578077i	−0.649492	+	0.760369i	$0.725018\pi$
$920$	−19.6587	+	14.6673i	−0.648128	+	0.483568i
$921$	2.60002	−	4.50336i	0.0856734	−	0.148391i
$922$	7.41050	−	10.4066i	0.244052	−	0.342723i
$923$	−74.5405	+	21.8871i	−2.45353	+	0.720421i
$924$	−0.772703	−	0.223319i	−0.0254201	−	0.00734665i
$925$	−5.80482	−	3.73053i	−0.190861	−	0.122659i
$926$	4.01636	−	11.6045i	0.131986	−	0.381348i
$927$	−18.4625	−	7.39128i	−0.606389	−	0.242761i
$928$	1.76634	−	1.68420i	0.0579829	−	0.0552866i
$929$	−21.9701	−	11.3264i	−0.720817	−	0.371607i	0.0584574	−	0.998290i	$-0.481382\pi$
$929$	−21.9701	−	11.3264i	−0.720817	−	0.371607i	−0.779274	+	0.626683i	$0.784412\pi$
$930$	4.11993	−	28.6547i	0.135098	−	0.939625i
$931$	19.5274	−	27.9223i	0.639983	−	0.915115i
$932$	2.09715	−	4.59211i	0.0686944	−	0.150420i
$933$	−24.5200	+	9.81634i	−0.802750	+	0.321373i
$934$	−0.191550	−	4.02113i	−0.00626771	−	0.131575i
$935$	−4.28255	+	4.08341i	−0.140054	+	0.133542i
$936$	−10.1315	+	7.96752i	−0.331159	+	0.260426i
$937$	13.8663	+	16.0026i	0.452992	+	0.522781i	0.935603	−	0.353054i	$-0.114857\pi$
$937$	13.8663	+	16.0026i	0.452992	+	0.522781i	−0.482611	+	0.875835i	$0.660311\pi$
$938$	−6.93758	+	49.7540i	−0.226520	+	1.62453i
$939$	17.5549	−	20.2595i	0.572883	−	0.661142i
$940$	10.7785	+	10.2773i	0.351555	+	0.335207i
$941$	2.31598	+	0.221149i	0.0754988	+	0.00720926i	0.132737	−	0.991151i	$-0.457623\pi$
$941$	2.31598	+	0.221149i	0.0754988	+	0.00720926i	−0.0572383	+	0.998361i	$0.518229\pi$
$942$	4.07825	−	7.06374i	0.132877	−	0.230149i
$943$	7.05157	+	16.5400i	0.229631	+	0.538617i
$944$	−17.9449			−0.584056
$945$	−6.31514	−	1.18929i	−0.205431	−	0.0386877i
$946$	−0.540634	+	0.158744i	−0.0175775	+	0.00516123i
$947$	−21.0707	−	4.06105i	−0.684706	−	0.131966i	−0.164977	−	0.986297i	$-0.552755\pi$
$947$	−21.0707	−	4.06105i	−0.684706	−	0.131966i	−0.519729	+	0.854331i	$0.673967\pi$
$948$	0.311353	−	0.160514i	0.0101123	−	0.00521324i
$949$	28.1242	−	5.42049i	0.912950	−	0.175957i
$950$	5.67953	−	4.46643i	0.184268	−	0.144910i
$951$	8.25680	+	2.42442i	0.267745	+	0.0786171i
$952$	−28.6769	+	14.9388i	−0.929423	+	0.484168i
$953$	−1.78221	+	12.3956i	−0.0577315	+	0.401531i	0.940381	+	0.340122i	$0.110468\pi$
$953$	−1.78221	+	12.3956i	−0.0577315	+	0.401531i	−0.998113	+	0.0614090i	$0.980441\pi$
$954$	−6.45058	+	0.615956i	−0.208845	+	0.0199423i
$955$	0.710131	+	0.997239i	0.0229793	+	0.0322699i
$956$	−7.89638	−	6.20978i	−0.255387	−	0.200839i
$957$	−0.232529	−	0.119877i	−0.00751661	−	0.00387508i
$958$	24.8109	+	7.28515i	0.801605	+	0.235373i
$959$	−1.32125	−	25.4567i	−0.0426654	−	0.822040i
$960$	5.38352	+	6.21292i	0.173752	+	0.200521i
$961$	1.00620	−	21.1227i	0.0324580	−	0.681377i
$962$	−25.3534	−	73.2538i	−0.817426	−	2.36180i
$963$	−0.794196	+	3.27372i	−0.0255926	+	0.105494i
$964$	−6.45961	+	9.07125i	−0.208050	+	0.292165i
$965$	−58.5267			−1.88404
$966$	−13.3770	−	16.1140i	−0.430398	−	0.518460i
$967$	23.0935			0.742638			0.371319	−	0.928505i	$-0.378906\pi$
$967$	23.0935			0.742638			0.371319	+	0.928505i	$0.378906\pi$
$968$	−13.2202	+	18.5651i	−0.424913	+	0.596706i
$969$	−6.66060	+	27.4554i	−0.213969	+	0.881993i
$970$	−8.93882	−	25.8270i	−0.287008	−	0.829255i
$971$	1.75839	−	36.9132i	0.0564295	−	1.18460i	−0.776096	−	0.630614i	$-0.782803\pi$
$971$	1.75839	−	36.9132i	0.0564295	−	1.18460i	0.832526	−	0.553986i	$-0.186894\pi$
$972$	0.474289	+	0.547359i	0.0152128	+	0.0175565i
$973$	−37.9557	+	24.6215i	−1.21680	+	0.789329i
$974$	27.5505	+	8.08955i	0.882774	+	0.259206i
$975$	4.89307	+	2.52255i	0.156704	+	0.0807863i
$976$	−47.7314	−	37.5364i	−1.52785	−	1.20151i
$977$	−22.1259	−	31.0714i	−0.707869	−	0.994063i	−0.999298	−	0.0374707i	$-0.988070\pi$
$977$	−22.1259	−	31.0714i	−0.707869	−	0.994063i	0.291428	−	0.956593i	$-0.405869\pi$
$978$	−14.4056	+	1.37557i	−0.460642	+	0.0439860i
$979$	−0.169676	+	1.18012i	−0.00542286	+	0.0377168i
$980$	−1.64865	+	12.2030i	−0.0526641	+	0.389810i
$981$	10.3090	+	3.02698i	0.329140	+	0.0966442i
$982$	−27.2673	+	21.4433i	−0.870136	+	0.684282i
$983$	0.101990	−	0.0196570i	0.00325299	−	0.000626962i	−0.187624	−	0.982241i	$-0.560079\pi$
$983$	0.101990	−	0.0196570i	0.00325299	−	0.000626962i	0.190877	+	0.981614i	$0.438867\pi$
$984$	7.01689	−	3.61746i	0.223690	−	0.115320i
$985$	45.2378	+	8.71886i	1.44139	+	0.277806i
$986$	5.72882	−	1.68213i	0.182443	−	0.0535701i
$987$	14.5962	−	16.9904i	0.464601	−	0.540811i
$988$	21.5796			0.686537
$989$	−3.71332	−	1.19356i	−0.118077	−	0.0379532i
$990$	−0.841367	+	1.45729i	−0.0267404	+	0.0463157i
$991$	19.3310	+	1.84588i	0.614069	+	0.0586365i	0.397456	−	0.917621i	$-0.369893\pi$
$991$	19.3310	+	1.84588i	0.614069	+	0.0586365i	0.216613	+	0.976258i	$0.430499\pi$
$992$	−20.4654	−	19.5137i	−0.649777	−	0.619561i
$993$	10.7266	−	12.3792i	0.340399	−	0.392842i
$994$	−51.3645	+	20.8173i	−1.62918	+	0.660284i
$995$	18.9267	+	21.8426i	0.600018	+	0.692457i
$996$	−5.05331	+	3.97397i	−0.160120	+	0.125920i
$997$	−19.8777	+	18.9533i	−0.629533	+	0.600258i	−0.936161	−	0.351571i	$-0.885648\pi$
$997$	−19.8777	+	18.9533i	−0.629533	+	0.600258i	0.306628	+	0.951829i	$0.400799\pi$
$998$	0.967468	+	20.3097i	0.0306247	+	0.642891i
$999$	7.12292	−	2.85159i	0.225359	−	0.0902202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.a.4.5	✓	320
7.2	even	3	inner	483.2.y.a.142.12	yes	320
23.6	even	11	inner	483.2.y.a.466.12	yes	320
161.121	even	33	inner	483.2.y.a.121.5	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.a.4.5	✓	320	1.1	even	1	trivial
483.2.y.a.121.5	yes	320	161.121	even	33	inner
483.2.y.a.142.12	yes	320	7.2	even	3	inner
483.2.y.a.466.12	yes	320	23.6	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.957403 + 1.34448i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(-0.236882 - 0.684426i) q^{4} +(0.115570 - 2.42610i) q^{5} +(-1.08087 - 1.24739i) q^{6} +(2.21964 - 1.43986i) q^{7} +(-2.02036 - 0.593231i) q^{8} +(-0.888835 - 0.458227i) q^{9} +(3.15121 + 2.47814i) q^{10} +(-0.243478 - 0.341917i) q^{11} +(0.720980 - 0.0688452i) q^{12} +(-0.871137 + 6.05889i) q^{13} +(-0.189222 + 4.36280i) q^{14} +(2.33047 + 0.684288i) q^{15} +(3.87050 - 3.04379i) q^{16} +(5.69918 - 1.09843i) q^{17} +(1.46705 - 0.756318i) q^{18} +(4.77961 + 0.921194i) q^{19} +(-1.68786 + 0.495602i) q^{20} +(0.875972 + 2.49653i) q^{21} +0.692809 q^{22} +(3.96736 + 2.69445i) q^{23} +(1.05283 - 1.82355i) q^{24} +(-0.895267 - 0.0854877i) q^{25} +(-7.31205 - 6.97203i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-1.51127 - 1.17810i) q^{28} +(-0.408146 - 0.471026i) q^{29} +(-3.15121 + 2.47814i) q^{30} +(-5.22627 + 4.98324i) q^{31} +(0.186324 + 3.91143i) q^{32} +(0.389681 - 0.156005i) q^{33} +(-3.97960 + 8.71410i) q^{34} +(-3.23673 - 5.55148i) q^{35} +(-0.103073 + 0.716887i) q^{36} +(6.81960 + 3.51575i) q^{37} +(-5.81454 + 5.54416i) q^{38} +(-5.68272 - 2.27502i) q^{39} +(-1.67273 + 4.83304i) q^{40} +(3.15401 + 2.02696i) q^{41} +(-4.19521 - 1.21246i) q^{42} +(-0.780351 + 0.229132i) q^{43} +(-0.176341 + 0.247637i) q^{44} +(-1.21443 + 2.10345i) q^{45} +(-7.42101 + 2.75438i) q^{46} +(-4.23304 - 7.33184i) q^{47} +(2.04549 + 4.47900i) q^{48} +(2.85361 - 6.39194i) q^{49} +(0.972069 - 1.12183i) q^{50} +(-0.276169 + 5.79750i) q^{51} +(4.35322 - 0.839014i) q^{52} +(-3.64474 - 1.45913i) q^{53} +(0.389128 + 1.60401i) q^{54} +(-0.857666 + 0.551188i) q^{55} +(-5.33864 + 1.59227i) q^{56} +(-2.02206 + 4.42770i) q^{57} +(1.02405 - 0.0977847i) q^{58} +(-2.86469 - 2.25282i) q^{59} +(-0.0837024 - 1.75713i) q^{60} +(-2.90741 - 11.9845i) q^{61} +(-1.69624 - 11.7976i) q^{62} +(-2.63268 + 0.262700i) q^{63} +(2.84736 + 1.82989i) q^{64} +(14.5988 + 2.81369i) q^{65} +(-0.163336 + 0.673280i) q^{66} +(11.4516 + 1.09349i) q^{67} +(-2.10183 - 3.64047i) q^{68} +(-3.55384 + 3.22029i) q^{69} +(10.5627 + 0.963278i) q^{70} +(5.27225 + 11.5446i) q^{71} +(1.52393 + 1.45307i) q^{72} +(-1.53039 - 4.42177i) q^{73} +(-11.2560 + 5.80286i) q^{74} +(0.294145 - 0.849877i) q^{75} +(-0.501715 - 3.48950i) q^{76} +(-1.03275 - 0.408359i) q^{77} +(8.49938 - 5.46222i) q^{78} +(0.449012 - 0.179757i) q^{79} +(-6.93725 - 9.74201i) q^{80} +(0.580057 + 0.814576i) q^{81} +(-5.74488 + 2.29990i) q^{82} +(-7.46719 + 4.79887i) q^{83} +(1.50119 - 1.19092i) q^{84} +(-2.00625 - 13.9538i) q^{85} +(0.439046 - 1.26854i) q^{86} +(0.553973 - 0.285593i) q^{87} +(0.289077 + 0.835234i) q^{88} +(-2.05570 - 1.96010i) q^{89} +(-1.66536 - 3.64663i) q^{90} +(6.79034 + 14.7029i) q^{91} +(0.904352 - 3.35363i) q^{92} +(-3.61063 - 6.25380i) q^{93} +(13.9103 + 1.32827i) q^{94} +(2.78729 - 11.4894i) q^{95} +(-3.84510 - 0.741083i) q^{96} +(-5.73513 - 3.68574i) q^{97} +(5.86181 + 9.95630i) q^{98} +(0.0597365 + 0.415476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21}+ \cdots - 10 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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