LMFDB - Embedded newform 966.2.y.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	966.121
Dual form			966.2.y.c.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.163478 - 3.43182i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.873534 - 2.49739i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.163478 - 3.43182i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.873534 - 2.49739i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(2.70065 - 2.12382i) q^{10} +(2.54735 - 3.57725i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.710652 + 4.94269i) q^{13} +(2.54101 - 0.737066i) q^{14} +(-3.29654 + 0.967953i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-5.41067 - 1.04282i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(-4.80880 + 0.926820i) q^{19} +(3.29654 + 0.967953i) q^{20} +(-2.63293 - 0.260130i) q^{21} +4.39154 q^{22} +(3.99070 - 2.65976i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-6.77333 + 0.646774i) q^{25} +(-3.61398 + 3.44592i) q^{26} +(0.654861 + 0.755750i) q^{27} +(2.07433 + 1.64231i) q^{28} +(-2.60987 + 3.01195i) q^{29} +(-2.70065 - 2.12382i) q^{30} +(-4.74093 - 4.52046i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-4.07697 - 1.63217i) q^{33} +(-2.28904 - 5.01230i) q^{34} +(-8.71339 - 2.58955i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-2.10899 + 1.08726i) q^{37} +(-3.54434 - 3.37952i) q^{38} +(4.63583 - 1.85590i) q^{39} +(1.12371 + 3.24675i) q^{40} +(9.83891 - 6.32308i) q^{41} +(-1.31536 - 2.29561i) q^{42} +(2.42026 + 0.710653i) q^{43} +(2.54735 + 3.57725i) q^{44} +(1.71786 + 2.97542i) q^{45} +(4.48141 + 1.70792i) q^{46} +(2.50251 - 4.33448i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(-5.47388 - 4.36311i) q^{49} +(-4.45576 - 5.14222i) q^{50} +(0.262188 + 5.50400i) q^{51} +(-4.90328 - 0.945030i) q^{52} +(-2.75186 + 1.10168i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-12.6929 - 8.15724i) q^{55} +(-0.134555 + 2.64233i) q^{56} +(2.03441 + 4.45474i) q^{57} +(-3.96733 - 0.378834i) q^{58} +(-4.27636 + 3.36296i) q^{59} +(0.163478 - 3.43182i) q^{60} +(2.69001 - 11.0884i) q^{61} +(0.932254 - 6.48397i) q^{62} +(0.367940 + 2.62004i) q^{63} +(0.841254 - 0.540641i) q^{64} +(16.8463 - 3.24685i) q^{65} +(-1.03535 - 4.26775i) q^{66} +(13.4446 - 1.28380i) q^{67} +(2.75512 - 4.77201i) q^{68} +(-3.52563 - 3.25115i) q^{69} +(-2.94488 - 8.59980i) q^{70} +(-6.18184 + 13.5363i) q^{71} +(0.723734 - 0.690079i) q^{72} +(0.281480 - 0.813284i) q^{73} +(-2.10899 - 1.08726i) q^{74} +(2.22542 + 6.42992i) q^{75} +(0.696958 - 4.84745i) q^{76} +(-6.70857 - 9.48655i) q^{77} +(4.20082 + 2.69970i) q^{78} +(5.70448 + 2.28373i) q^{79} +(-1.99291 + 2.79865i) q^{80} +(0.580057 - 0.814576i) q^{81} +(10.8578 + 4.34679i) q^{82} +(11.7429 + 7.54671i) q^{83} +(1.10697 - 2.40304i) q^{84} +(-2.69425 + 18.7389i) q^{85} +(0.825008 + 2.38371i) q^{86} +(3.54235 + 1.82621i) q^{87} +(-1.43633 + 4.15001i) q^{88} +(-0.439805 + 0.419353i) q^{89} +(-1.42725 + 3.12524i) q^{90} +(12.9646 + 2.54284i) q^{91} +(1.20824 + 4.64114i) q^{92} +(-3.27532 + 5.67303i) q^{93} +(4.98236 - 0.475758i) q^{94} +(3.96681 + 16.3514i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-5.61654 + 3.60953i) q^{97} +(0.378921 - 6.98974i) q^{98} +(-0.624982 + 4.34685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$3$	−0.235759	−	0.971812i	−0.136115	−	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	−0.163478	−	3.43182i	−0.0731095	−	1.53476i	−0.675981	−	0.736919i	$-0.736280\pi$
$5$	−0.163478	−	3.43182i	−0.0731095	−	1.53476i	0.602871	−	0.797839i	$-0.294023\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	0.873534	−	2.49739i	0.330165	−	0.943923i
$7$	0.873534	−	2.49739i	0.330165	−	0.943923i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	2.70065	−	2.12382i	0.854022	−	0.671610i
$11$	2.54735	−	3.57725i	0.768054	−	1.07858i	−0.226465	−	0.974019i	$-0.572717\pi$
$11$	2.54735	−	3.57725i	0.768054	−	1.07858i	0.994518	−	0.104561i	$-0.0333438\pi$
$12$	0.995472	+	0.0950560i	0.287368	+	0.0274403i
$13$	0.710652	+	4.94269i	0.197099	+	1.37086i	0.812647	+	0.582757i	$0.198026\pi$
$13$	0.710652	+	4.94269i	0.197099	+	1.37086i	−0.615547	+	0.788100i	$0.711065\pi$
$14$	2.54101	−	0.737066i	0.679114	−	0.196989i
$15$	−3.29654	+	0.967953i	−0.851164	+	0.249924i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	−5.41067	−	1.04282i	−1.31228	−	0.252921i	−0.515343	−	0.856984i	$-0.672335\pi$
$17$	−5.41067	−	1.04282i	−1.31228	−	0.252921i	−0.796937	+	0.604063i	$0.793548\pi$
$18$	−0.888835	−	0.458227i	−0.209501	−	0.108005i
$19$	−4.80880	+	0.926820i	−1.10321	+	0.212627i	−0.708175	−	0.706037i	$-0.750481\pi$
$19$	−4.80880	+	0.926820i	−1.10321	+	0.212627i	−0.395039	+	0.918664i	$0.629269\pi$
$20$	3.29654	+	0.967953i	0.737130	+	0.216441i
$21$	−2.63293	−	0.260130i	−0.574553	−	0.0567650i
$22$	4.39154			0.936280
$23$	3.99070	−	2.65976i	0.832119	−	0.554598i
$23$	3.99070	−	2.65976i	0.832119	−	0.554598i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−6.77333	+	0.646774i	−1.35467	+	0.129355i
$26$	−3.61398	+	3.44592i	−0.708760	+	0.675801i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	2.07433	+	1.64231i	0.392011	+	0.310367i
$29$	−2.60987	+	3.01195i	−0.484640	+	0.559305i	−0.944426	−	0.328725i	$-0.893381\pi$
$29$	−2.60987	+	3.01195i	−0.484640	+	0.559305i	0.459785	+	0.888030i	$0.347926\pi$
$30$	−2.70065	−	2.12382i	−0.493070	−	0.387754i
$31$	−4.74093	−	4.52046i	−0.851495	−	0.811899i	0.132297	−	0.991210i	$-0.457765\pi$
$31$	−4.74093	−	4.52046i	−0.851495	−	0.811899i	−0.983792	+	0.179311i	$0.942613\pi$
$32$	0.0475819	−	0.998867i	0.00841137	−	0.176576i
$33$	−4.07697	−	1.63217i	−0.709709	−	0.284125i
$34$	−2.28904	−	5.01230i	−0.392567	−	0.859602i
$35$	−8.71339	−	2.58955i	−1.47283	−	0.437714i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−2.10899	+	1.08726i	−0.346716	+	0.178745i	−0.622785	−	0.782393i	$-0.713999\pi$
$37$	−2.10899	+	1.08726i	−0.346716	+	0.178745i	0.276068	+	0.961138i	$0.410968\pi$
$38$	−3.54434	−	3.37952i	−0.574968	−	0.548231i
$39$	4.63583	−	1.85590i	0.742326	−	0.297183i
$40$	1.12371	+	3.24675i	0.177675	+	0.513357i
$41$	9.83891	−	6.32308i	1.53658	−	0.987500i	0.548055	−	0.836442i	$-0.315369\pi$
$41$	9.83891	−	6.32308i	1.53658	−	0.987500i	0.988525	−	0.151057i	$-0.0482678\pi$
$42$	−1.31536	−	2.29561i	−0.202964	−	0.354221i
$43$	2.42026	+	0.710653i	0.369086	+	0.108374i	0.461016	−	0.887392i	$-0.347485\pi$
$43$	2.42026	+	0.710653i	0.369086	+	0.108374i	−0.0919293	+	0.995766i	$0.529303\pi$
$44$	2.54735	+	3.57725i	0.384027	+	0.539290i
$45$	1.71786	+	2.97542i	0.256083	+	0.443549i
$46$	4.48141	+	1.70792i	0.660747	+	0.251819i
$47$	2.50251	−	4.33448i	0.365029	−	0.632249i	−0.623752	−	0.781623i	$-0.714392\pi$
$47$	2.50251	−	4.33448i	0.365029	−	0.632249i	0.988781	+	0.149374i	$0.0477257\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−5.47388	−	4.36311i	−0.781982	−	0.623301i
$50$	−4.45576	−	5.14222i	−0.630140	−	0.727220i
$51$	0.262188	+	5.50400i	0.0367137	+	0.770715i
$52$	−4.90328	−	0.945030i	−0.679963	−	0.131052i
$53$	−2.75186	+	1.10168i	−0.377998	+	0.151327i	−0.552878	−	0.833262i	$-0.686470\pi$
$53$	−2.75186	+	1.10168i	−0.377998	+	0.151327i	0.174880	+	0.984590i	$0.444046\pi$
$54$	−0.235759	+	0.971812i	−0.0320827	+	0.132247i
$55$	−12.6929	−	8.15724i	−1.71151	−	1.09992i
$56$	−0.134555	+	2.64233i	−0.0179807	+	0.353096i
$57$	2.03441	+	4.45474i	0.269464	+	0.590044i
$58$	−3.96733	−	0.378834i	−0.520936	−	0.0497434i
$59$	−4.27636	+	3.36296i	−0.556734	+	0.437821i	−0.856466	−	0.516203i	$-0.827345\pi$
$59$	−4.27636	+	3.36296i	−0.556734	+	0.437821i	0.299732	+	0.954023i	$0.403103\pi$
$60$	0.163478	−	3.43182i	0.0211049	−	0.443047i
$61$	2.69001	−	11.0884i	0.344420	−	1.41972i	−0.491505	−	0.870875i	$-0.663553\pi$
$61$	2.69001	−	11.0884i	0.344420	−	1.41972i	0.835925	−	0.548844i	$-0.184932\pi$
$62$	0.932254	−	6.48397i	0.118396	−	0.823465i
$63$	0.367940	+	2.62004i	0.0463561	+	0.330094i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	16.8463	−	3.24685i	2.08952	−	0.402723i
$66$	−1.03535	−	4.26775i	−0.127442	−	0.525324i
$67$	13.4446	−	1.28380i	1.64252	−	0.156841i	0.767538	−	0.641003i	$-0.221481\pi$
$67$	13.4446	−	1.28380i	1.64252	−	0.156841i	0.874979	+	0.484161i	$0.160875\pi$
$68$	2.75512	−	4.77201i	0.334108	−	0.578692i
$69$	−3.52563	−	3.25115i	−0.424435	−	0.391392i
$70$	−2.94488	−	8.59980i	−0.351980	−	1.02787i
$71$	−6.18184	+	13.5363i	−0.733649	+	1.60647i	0.0600778	+	0.998194i	$0.480865\pi$
$71$	−6.18184	+	13.5363i	−0.733649	+	1.60647i	−0.793727	+	0.608274i	$0.791862\pi$
$72$	0.723734	−	0.690079i	0.0852929	−	0.0813266i
$73$	0.281480	−	0.813284i	0.0329448	−	0.0951877i	−0.927329	−	0.374247i	$-0.877901\pi$
$73$	0.281480	−	0.813284i	0.0329448	−	0.0951877i	0.960274	+	0.279059i	$0.0900225\pi$
$74$	−2.10899	−	1.08726i	−0.245165	−	0.126392i
$75$	2.22542	+	6.42992i	0.256969	+	0.742463i
$76$	0.696958	−	4.84745i	0.0799466	−	0.556041i
$77$	−6.70857	−	9.48655i	−0.764513	−	1.08109i
$78$	4.20082	+	2.69970i	0.475649	+	0.305681i
$79$	5.70448	+	2.28373i	0.641804	+	0.256940i	0.669655	−	0.742672i	$-0.266442\pi$
$79$	5.70448	+	2.28373i	0.641804	+	0.256940i	−0.0278506	+	0.999612i	$0.508866\pi$
$80$	−1.99291	+	2.79865i	−0.222814	+	0.312899i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	10.8578	+	4.34679i	1.19904	+	0.480023i
$83$	11.7429	+	7.54671i	1.28895	+	0.828359i	0.991964	−	0.126522i	$-0.0403815\pi$
$83$	11.7429	+	7.54671i	1.28895	+	0.828359i	0.296988	+	0.954881i	$0.404018\pi$
$84$	1.10697	−	2.40304i	0.120780	−	0.262193i
$85$	−2.69425	+	18.7389i	−0.292233	+	2.03252i
$86$	0.825008	+	2.38371i	0.0889629	+	0.257042i
$87$	3.54235	+	1.82621i	0.379779	+	0.195790i
$88$	−1.43633	+	4.15001i	−0.153114	+	0.442393i
$89$	−0.439805	+	0.419353i	−0.0466193	+	0.0444514i	−0.713031	−	0.701133i	$-0.752678\pi$
$89$	−0.439805	+	0.419353i	−0.0466193	+	0.0444514i	0.666411	+	0.745584i	$0.267829\pi$
$90$	−1.42725	+	3.12524i	−0.150445	+	0.329429i
$91$	12.9646	+	2.54284i	1.35906	+	0.266562i
$92$	1.20824	+	4.64114i	0.125968	+	0.483872i
$93$	−3.27532	+	5.67303i	−0.339635	+	0.588265i
$94$	4.98236	−	0.475758i	0.513892	−	0.0490707i
$95$	3.96681	+	16.3514i	0.406986	+	1.67762i
$96$	−0.981929	+	0.189251i	−0.100218	+	0.0193154i
$97$	−5.61654	+	3.60953i	−0.570273	+	0.366492i	−0.793775	−	0.608211i	$-0.791887\pi$
$97$	−5.61654	+	3.60953i	−0.570273	+	0.366492i	0.223502	+	0.974703i	$0.428251\pi$
$98$	0.378921	−	6.98974i	0.0382768	−	0.706070i
$99$	−0.624982	+	4.34685i	−0.0628131	+	0.436874i
$100$	1.60414	−	6.61234i	0.160414	−	0.661234i
$101$	0.681636	−	14.3093i	0.0678253	−	1.42383i	−0.666740	−	0.745291i	$-0.732311\pi$
$101$	0.681636	−	14.3093i	0.0678253	−	1.42383i	0.734565	−	0.678538i	$-0.237386\pi$
$102$	−4.33135	+	3.40621i	−0.428867	+	0.337265i
$103$	−13.6784	−	1.30613i	−1.34777	−	0.128697i	−0.603923	−	0.797043i	$-0.706397\pi$
$103$	−13.6784	−	1.30613i	−1.34777	−	0.128697i	−0.743851	+	0.668346i	$0.767003\pi$
$104$	−2.07438	−	4.54227i	−0.203410	−	0.445406i
$105$	−0.462293	+	9.07828i	−0.0451152	+	0.885950i
$106$	−2.49364	−	1.60257i	−0.242204	−	0.155655i
$107$	3.62836	−	14.9563i	0.350767	−	1.44588i	−0.474058	−	0.880494i	$-0.657211\pi$
$107$	3.62836	−	14.9563i	0.350767	−	1.44588i	0.824825	−	0.565388i	$-0.191274\pi$
$108$	−0.928368	+	0.371662i	−0.0893322	+	0.0357632i
$109$	5.73767	+	1.10584i	0.549569	+	0.105921i	0.456474	−	0.889737i	$-0.349112\pi$
$109$	5.73767	+	1.10584i	0.549569	+	0.105921i	0.0930944	+	0.995657i	$0.470324\pi$
$110$	−0.717920	−	15.0710i	−0.0684510	−	1.43696i
$111$	1.55383	+	1.79321i	0.147483	+	0.170204i
$112$	−2.23043	+	1.42310i	−0.210755	+	0.134470i
$113$	3.74457	−	8.19947i	0.352260	−	0.771341i	−0.647696	−	0.761899i	$-0.724267\pi$
$113$	3.74457	−	8.19947i	0.352260	−	0.771341i	0.999955	−	0.00944204i	$-0.00300554\pi$
$114$	−2.44865	+	4.24118i	−0.229337	+	0.397223i
$115$	−9.78021	−	13.2606i	−0.912009	−	1.23655i
$116$	−1.99269	−	3.45144i	−0.185017	−	0.320458i
$117$	−2.89653	−	4.06760i	−0.267784	−	0.376050i
$118$	−5.21992	−	1.53271i	−0.480532	−	0.141097i
$119$	−7.33073	+	12.6016i	−0.672007	+	1.15519i
$120$	2.89031	−	1.85749i	0.263848	−	0.169565i
$121$	−2.70998	−	7.82996i	−0.246361	−	0.711815i
$122$	10.5927	−	4.24066i	0.959015	−	0.383932i
$123$	−8.46446	−	8.07084i	−0.763214	−	0.727724i
$124$	5.82245	−	3.00168i	0.522871	−	0.269559i
$125$	0.882139	+	6.13541i	0.0789009	+	0.548768i
$126$	−1.92080	+	1.81949i	−0.171118	+	0.162093i
$127$	−0.0684187	−	0.149816i	−0.00607117	−	0.0132940i	0.906572	−	0.422051i	$-0.138690\pi$
$127$	−0.0684187	−	0.149816i	−0.00607117	−	0.0132940i	−0.912643	+	0.408757i	$0.865962\pi$
$128$	0.928368	+	0.371662i	0.0820569	+	0.0328506i
$129$	0.120022	−	2.51958i	0.0105674	−	0.221837i
$130$	12.4166	+	11.8392i	1.08901	+	1.03837i
$131$	8.98446	+	7.06546i	0.784976	+	0.617312i	0.928074	−	0.372396i	$-0.121464\pi$
$131$	8.98446	+	7.06546i	0.784976	+	0.617312i	−0.143097	+	0.989709i	$0.545706\pi$
$132$	2.87585	−	3.31891i	0.250311	−	0.288874i
$133$	−1.88602	+	12.8190i	−0.163539	+	1.11155i
$134$	8.84438	+	10.2070i	0.764038	+	0.881747i
$135$	2.48654	−	2.37091i	0.214008	−	0.204056i
$136$	5.48529	−	0.523782i	0.470360	−	0.0449139i
$137$	5.91148	+	10.2390i	0.505052	+	0.874776i	0.999983	+	0.00584353i	$0.00186006\pi$
$137$	5.91148	+	10.2390i	0.505052	+	0.874776i	−0.494931	+	0.868932i	$0.664807\pi$
$138$	0.603244	−	4.75774i	0.0513515	−	0.405006i
$139$	−16.2660			−1.37967			−0.689834	−	0.723968i	$-0.742316\pi$
$139$	−16.2660			−1.37967			−0.689834	+	0.723968i	$0.742316\pi$
$140$	5.29700	−	7.38720i	0.447678	−	0.624333i
$141$	−4.80229	−	1.41008i	−0.404426	−	0.118750i
$142$	−14.6122	+	2.81627i	−1.22623	+	0.236336i
$143$	19.4915	+	10.0486i	1.62996	+	0.840304i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	10.7631	+	8.46422i	0.893829	+	0.702915i
$146$	0.825756	−	0.242464i	0.0683401	−	0.0200665i
$147$	−2.94960	+	6.34822i	−0.243279	+	0.523592i
$148$	−0.337679	−	2.34861i	−0.0277570	−	0.193054i
$149$	0.120617	+	0.0115175i	0.00988129	+	0.000943549i	0.0999955	−	0.994988i	$-0.468117\pi$
$149$	0.120617	+	0.0115175i	0.00988129	+	0.000943549i	−0.0901142	+	0.995931i	$0.528723\pi$
$150$	−3.94679	+	5.54249i	−0.322254	+	0.452542i
$151$	0.738549	−	0.580801i	0.0601022	−	0.0472649i	−0.587656	−	0.809111i	$-0.699949\pi$
$151$	0.738549	−	0.580801i	0.0601022	−	0.0472649i	0.647758	+	0.761846i	$0.275707\pi$
$152$	4.35289	−	2.24407i	0.353066	−	0.182018i
$153$	5.28704	−	1.55242i	0.427432	−	0.125505i
$154$	3.83617	−	10.9674i	0.309127	−	0.883777i
$155$	−14.7384	+	17.0090i	−1.18382	+	1.36620i
$156$	0.237601	+	4.98787i	0.0190233	+	0.399349i
$157$	7.53006	−	21.7567i	0.600964	−	1.73637i	−0.0727205	−	0.997352i	$-0.523168\pi$
$157$	7.53006	−	21.7567i	0.600964	−	1.73637i	0.673684	−	0.739019i	$-0.264711\pi$
$158$	1.44865	+	5.97143i	0.115249	+	0.475061i
$159$	1.71940	+	2.41456i	0.136357	+	0.191487i
$160$	−3.43571			−0.271617
$161$	−3.15642	−	12.2897i	−0.248761	−	0.968565i
$162$	1.00000			0.0785674
$163$	−6.80857	−	9.56130i	−0.533289	−	0.748899i	0.456765	−	0.889587i	$-0.349008\pi$
$163$	−6.80857	−	9.56130i	−0.533289	−	0.748899i	−0.990054	+	0.140688i	$0.955069\pi$
$164$	2.75733	+	11.3659i	0.215311	+	0.887524i
$165$	−4.93483	+	14.2583i	−0.384176	+	1.11000i
$166$	0.664187	+	13.9430i	0.0515509	+	1.08219i
$167$	8.90933	−	10.2819i	0.689424	−	0.795638i	−0.297859	−	0.954610i	$-0.596272\pi$
$167$	8.90933	−	10.2819i	0.689424	−	0.795638i	0.987283	+	0.158972i	$0.0508179\pi$
$168$	2.59957	−	0.492190i	0.200561	−	0.0379733i
$169$	−11.4518	+	3.36255i	−0.880907	+	0.258658i
$170$	−16.8271	+	8.67498i	−1.29058	+	0.665340i
$171$	3.84954	−	3.02731i	0.294381	−	0.231504i
$172$	−1.46316	+	2.05472i	−0.111565	+	0.156671i
$173$	7.87876	+	0.752330i	0.599011	+	0.0571986i	0.390157	−	0.920748i	$-0.372421\pi$
$173$	7.87876	+	0.752330i	0.599011	+	0.0571986i	0.208854	+	0.977947i	$0.433027\pi$
$174$	0.567179	+	3.94481i	0.0429977	+	0.299056i
$175$	−4.30149	+	17.4806i	−0.325162	+	1.32141i
$176$	−4.21366	+	1.23724i	−0.317616	+	0.0932606i
$177$	4.27636	+	3.36296i	0.321431	+	0.252776i
$178$	−0.596707	−	0.115006i	−0.0447251	−	0.00862006i
$179$	11.6298	+	5.99557i	0.869251	+	0.448130i	0.834334	−	0.551260i	$-0.185853\pi$
$179$	11.6298	+	5.99557i	0.869251	+	0.448130i	0.0349179	+	0.999390i	$0.488883\pi$
$180$	−3.37363	+	0.650213i	−0.251455	+	0.0484640i
$181$	4.67695	+	1.37328i	0.347635	+	0.102075i	0.450888	−	0.892580i	$-0.351107\pi$
$181$	4.67695	+	1.37328i	0.347635	+	0.102075i	−0.103254	+	0.994655i	$0.532925\pi$
$182$	5.44887	+	12.0356i	0.403897	+	0.892141i
$183$	−11.4100			−0.843451
$184$	−3.07971	+	3.67633i	−0.227039	+	0.271022i
$185$	4.07606	+	7.05994i	0.299678	+	0.519057i
$186$	−6.52098	+	0.622678i	−0.478142	+	0.0456570i
$187$	−17.5133	+	16.6989i	−1.28070	+	1.22114i
$188$	3.27760	+	3.78255i	0.239043	+	0.275871i
$189$	2.45944	−	0.975267i	0.178898	−	0.0709402i
$190$	−11.0185	+	12.7160i	−0.799366	+	0.922518i
$191$	13.8085	+	10.8591i	0.999150	+	0.785741i	0.976831	−	0.214010i	$-0.0686526\pi$
$191$	13.8085	+	10.8591i	0.999150	+	0.785741i	0.0223190	+	0.999751i	$0.492895\pi$
$192$	−0.723734	−	0.690079i	−0.0522310	−	0.0498022i
$193$	−0.556495	+	11.6823i	−0.0400574	+	0.840908i	0.886037	+	0.463615i	$0.153448\pi$
$193$	−0.556495	+	11.6823i	−0.0400574	+	0.840908i	−0.926094	+	0.377293i	$0.876855\pi$
$194$	−6.19815	−	2.48136i	−0.445001	−	0.178152i
$195$	−7.12699	−	15.6059i	−0.510374	−	1.11756i
$196$	5.91347	−	3.74578i	0.422391	−	0.267556i
$197$	−2.46765	−	17.1629i	−0.175813	−	1.22280i	−0.866324	−	0.499483i	$-0.833523\pi$
$197$	−2.46765	−	17.1629i	−0.175813	−	1.22280i	0.690511	−	0.723322i	$-0.257386\pi$
$198$	−3.90336	+	2.01232i	−0.277400	+	0.143010i
$199$	18.1249	+	17.2821i	1.28484	+	1.22509i	0.960219	+	0.279249i	$0.0900856\pi$
$199$	18.1249	+	17.2821i	1.28484	+	1.22509i	0.324622	+	0.945844i	$0.394763\pi$
$200$	6.31674	−	2.52884i	0.446661	−	0.178816i
$201$	−4.41729	−	12.7629i	−0.311572	−	0.900228i
$202$	12.0514	−	7.74497i	0.847934	−	0.544934i
$203$	5.24219	+	9.14889i	0.367930	+	0.642126i
$204$	−5.28704	−	1.55242i	−0.370167	−	0.108691i
$205$	−23.3082	−	32.7317i	−1.62791	−	2.28608i
$206$	−6.87031	−	11.8997i	−0.478677	−	0.829094i
$207$	−2.32831	+	4.19273i	−0.161828	+	0.291415i
$208$	2.49676	−	4.32452i	0.173119	−	0.299851i
$209$	−8.93420	+	19.5632i	−0.617992	+	1.35321i
$210$	−7.66311	+	4.88935i	−0.528805	+	0.337397i
$211$	7.90668	+	9.12479i	0.544318	+	0.628177i	0.959550	−	0.281539i	$-0.0908449\pi$
$211$	7.90668	+	9.12479i	0.544318	+	0.628177i	−0.415232	+	0.909716i	$0.636299\pi$
$212$	−0.141042	−	2.96084i	−0.00968681	−	0.203351i
$213$	14.6122	+	2.81627i	1.00121	+	0.192968i
$214$	14.2877	−	5.71994i	0.976688	−	0.391007i
$215$	2.04318	−	8.42208i	0.139343	−	0.574381i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−15.4307	+	7.89114i	−1.04750	+	0.535686i
$218$	2.42738	+	5.31522i	0.164403	+	0.359992i
$219$	−0.856720	−	0.0818069i	−0.0578918	−	0.00552800i
$220$	11.8600	−	9.32684i	0.799604	−	0.628816i
$221$	1.30924	−	27.4844i	0.0880691	−	1.84880i
$222$	−0.559399	+	2.30587i	−0.0375444	+	0.154760i
$223$	−0.558004	+	3.88100i	−0.0373667	+	0.259891i	−0.999938	−	0.0111376i	$-0.996455\pi$
$223$	−0.558004	+	3.88100i	−0.0373667	+	0.259891i	0.962571	+	0.271029i	$0.0873638\pi$
$224$	−2.45299	−	0.991375i	−0.163897	−	0.0662391i
$225$	5.72400	−	3.67859i	0.381600	−	0.245240i
$226$	8.85115	−	1.70592i	0.588770	−	0.113476i
$227$	−1.03643	−	4.27223i	−0.0687904	−	0.283558i	0.927019	−	0.375015i	$-0.122363\pi$
$227$	−1.03643	−	4.27223i	−0.0687904	−	0.283558i	−0.995809	+	0.0914575i	$0.970847\pi$
$228$	−4.87512	+	0.465518i	−0.322863	+	0.0308297i
$229$	−2.86413	+	4.96081i	−0.189267	+	0.327820i	−0.945006	−	0.327053i	$-0.893944\pi$
$229$	−2.86413	+	4.96081i	−0.189267	+	0.327820i	0.755739	+	0.654873i	$0.227278\pi$
$230$	5.12867	−	15.6586i	0.338174	−	1.03250i
$231$	−7.63754	+	8.75601i	−0.502513	+	0.576103i
$232$	1.65559	−	3.62523i	0.108695	−	0.238008i
$233$	−9.34495	+	8.91039i	−0.612208	+	0.583739i	−0.931421	−	0.363944i	$-0.881430\pi$
$233$	−9.34495	+	8.91039i	−0.612208	+	0.583739i	0.319213	+	0.947683i	$0.396582\pi$
$234$	1.63322	−	4.71888i	0.106767	−	0.308483i
$235$	−15.2843	−	7.87959i	−0.997036	−	0.514008i
$236$	−1.77934	−	5.14108i	−0.115825	−	0.334656i
$237$	0.874473	−	6.08209i	0.0568031	−	0.395074i
$238$	−14.5172	+	1.33820i	−0.941010	+	0.0867427i
$239$	14.2353	+	9.14848i	0.920805	+	0.591766i	0.912891	−	0.408203i	$-0.133844\pi$
$239$	14.2353	+	9.14848i	0.920805	+	0.591766i	0.00791425	+	0.999969i	$0.497481\pi$
$240$	3.18961	+	1.27693i	0.205888	+	0.0824252i
$241$	−16.6069	+	23.3211i	−1.06974	+	1.50224i	−0.219674	+	0.975573i	$0.570499\pi$
$241$	−16.6069	+	23.3211i	−1.06974	+	1.50224i	−0.850070	+	0.526670i	$0.823440\pi$
$242$	4.80616	−	6.74930i	0.308951	−	0.433862i
$243$	−0.928368	−	0.371662i	−0.0595548	−	0.0238422i
$244$	9.59869	+	6.16870i	0.614493	+	0.394911i
$245$	−14.0785	+	19.4986i	−0.899446	+	1.24572i
$246$	1.66445	−	11.5765i	0.106121	−	0.738090i
$247$	−7.99837	−	23.1098i	−0.508924	−	1.47044i
$248$	5.82245	+	3.00168i	0.369726	+	0.190607i
$249$	4.56548	−	13.1911i	0.289326	−	0.835952i
$250$	−4.48607	+	4.27746i	−0.283724	+	0.270530i
$251$	5.50573	−	12.0559i	0.347518	−	0.760959i	−0.652477	−	0.757809i	$-0.726270\pi$
$251$	5.50573	−	12.0559i	0.347518	−	0.760959i	0.999995	−	0.00315017i	$-0.00100273\pi$
$252$	−2.59628	−	0.509228i	−0.163550	−	0.0320783i
$253$	0.651091	−	21.0510i	0.0409338	−	1.32347i
$254$	0.0823498	−	0.142634i	0.00516708	−	0.00894965i
$255$	18.8459	−	1.79957i	1.18018	−	0.112693i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	−4.93281	+	0.950722i	−0.307700	+	0.0593044i	−0.340764	−	0.940149i	$-0.610686\pi$
$257$	−4.93281	+	0.950722i	−0.307700	+	0.0593044i	0.0330636	+	0.999453i	$0.489474\pi$
$258$	2.12201	−	1.36373i	0.132111	−	0.0849023i
$259$	0.873033	+	6.21673i	0.0542477	+	0.386289i
$260$	−2.44160	+	16.9817i	−0.151422	+	1.05316i
$261$	0.939589	−	3.87304i	0.0581591	−	0.239735i
$262$	−0.543854	+	11.4169i	−0.0335994	+	0.705338i
$263$	14.6923	−	11.5542i	0.905968	−	0.712461i	−0.0522096	−	0.998636i	$-0.516626\pi$
$263$	14.6923	−	11.5542i	0.905968	−	0.712461i	0.958177	+	0.286175i	$0.0923840\pi$
$264$	4.37166	+	0.417443i	0.269057	+	0.0256918i
$265$	4.23064	+	9.26381i	0.259886	+	0.569071i
$266$	−11.5361	+	5.89946i	−0.707322	+	0.361719i
$267$	0.511221	+	0.328541i	0.0312862	+	0.0201064i
$268$	−3.18410	+	13.1250i	−0.194500	+	0.801739i
$269$	24.0544	−	9.62994i	1.46662	−	0.587148i	0.505393	−	0.862889i	$-0.331348\pi$
$269$	24.0544	−	9.62994i	1.46662	−	0.587148i	0.961232	+	0.275741i	$0.0889234\pi$
$270$	3.37363	+	0.650213i	0.205312	+	0.0395707i
$271$	−0.196482	−	4.12467i	−0.0119354	−	0.250556i	−0.996948	−	0.0780717i	$-0.975124\pi$
$271$	−0.196482	−	4.12467i	−0.0119354	−	0.250556i	0.985012	−	0.172484i	$-0.0551793\pi$
$272$	3.60844	+	4.16437i	0.218794	+	0.252502i
$273$	−0.585357	−	13.1986i	−0.0354274	−	0.798818i
$274$	−4.91144	+	10.7545i	−0.296711	+	0.649706i
$275$	−14.9403	+	25.8774i	−0.900936	+	1.56047i
$276$	4.22546	−	2.26837i	0.254343	−	0.136540i
$277$	6.92725	+	11.9984i	0.416218	+	0.720911i	0.995555	−	0.0941767i	$-0.0300219\pi$
$277$	6.92725	+	11.9984i	0.416218	+	0.720911i	−0.579337	+	0.815088i	$0.696689\pi$
$278$	−9.43523	−	13.2499i	−0.565888	−	0.794678i
$279$	6.28530	+	1.84553i	0.376291	+	0.110489i
$280$	9.09000	+	0.0298072i	0.543231	+	0.00178132i
$281$	8.20774	−	5.27480i	0.489633	−	0.314668i	−0.272425	−	0.962177i	$-0.587826\pi$
$281$	8.20774	−	5.27480i	0.489633	−	0.314668i	0.762058	+	0.647509i	$0.224189\pi$
$282$	−1.63698	−	4.72976i	−0.0974810	−	0.281653i
$283$	2.33182	−	0.933520i	0.138612	−	0.0554920i	−0.301319	−	0.953523i	$-0.597427\pi$
$283$	2.33182	−	0.933520i	0.138612	−	0.0554920i	0.439932	+	0.898031i	$0.355003\pi$
$284$	−10.7700	−	10.2691i	−0.639080	−	0.609362i
$285$	14.9553	−	7.70999i	0.885875	−	0.456700i
$286$	3.12086	+	21.7061i	0.184540	+	1.28351i
$287$	−7.19656	−	30.0950i	−0.424799	−	1.77645i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	12.4056	+	4.96645i	0.729741	+	0.292144i
$290$	−0.651521	+	13.6771i	−0.0382587	+	0.803148i
$291$	4.83193	+	4.60724i	0.283253	+	0.270081i
$292$	0.676491	+	0.531998i	0.0395886	+	0.0311328i
$293$	−11.3931	+	13.1484i	−0.665595	+	0.768137i	−0.983680	−	0.179925i	$-0.942415\pi$
$293$	−11.3931	+	13.1484i	−0.665595	+	0.768137i	0.318086	+	0.948062i	$0.396960\pi$
$294$	−6.88204	+	1.27965i	−0.401369	+	0.0746309i
$295$	12.2402	+	14.1259i	0.712651	+	0.822443i
$296$	1.71725	−	1.63739i	0.0998129	−	0.0951714i
$297$	4.37166	−	0.417443i	0.253669	−	0.0242225i
$298$	0.0605826	+	0.104932i	0.00350946	+	0.00607856i
$299$	15.9824	+	17.8347i	0.924284	+	1.03140i
$300$	−6.80414			−0.392837
$301$	3.88896	−	5.42355i	0.224156	−	0.312608i
$302$	0.901507	+	0.264706i	0.0518759	+	0.0152321i
$303$	−14.0666	+	2.71112i	−0.808108	+	0.155750i
$304$	4.35289	+	2.24407i	0.249655	+	0.128706i
$305$	−38.4930	−	7.41893i	−2.20411	−	0.424806i
$306$	4.33135	+	3.40621i	0.247607	+	0.194720i
$307$	19.2988	−	5.66665i	1.10144	−	0.323413i	0.320017	−	0.947412i	$-0.396311\pi$
$307$	19.2988	−	5.66665i	1.10144	−	0.323413i	0.781425	+	0.623999i	$0.214493\pi$
$308$	11.1590	−	3.23686i	0.635841	−	0.184437i
$309$	1.95550	+	13.6008i	0.111244	+	0.773721i
$310$	−22.4042	−	2.13935i	−1.27248	−	0.121507i
$311$	−6.11068	+	8.58125i	−0.346505	+	0.486598i	−0.950645	−	0.310280i	$-0.899577\pi$
$311$	−6.11068	+	8.58125i	−0.346505	+	0.486598i	0.604140	+	0.796878i	$0.293517\pi$
$312$	−3.92517	+	3.08679i	−0.222219	+	0.174755i
$313$	−19.5017	+	10.0538i	−1.10230	+	0.568275i	−0.910646	−	0.413187i	$-0.864416\pi$
$313$	−19.5017	+	10.0538i	−1.10230	+	0.568275i	−0.191654	+	0.981462i	$0.561385\pi$
$314$	22.0903	−	6.48630i	1.24663	−	0.366043i
$315$	8.93137	−	1.69102i	0.503226	−	0.0952785i
$316$	−4.02388	+	4.64380i	−0.226361	+	0.261234i
$317$	−0.928216	−	19.4856i	−0.0521338	−	1.09442i	−0.861708	−	0.507405i	$-0.830605\pi$
$317$	−0.928216	−	19.4856i	−0.0521338	−	1.09442i	0.809574	−	0.587018i	$-0.199698\pi$
$318$	−0.969494	+	2.80117i	−0.0543665	+	0.157082i
$319$	4.12625	+	17.0086i	0.231025	+	0.952300i
$320$	−1.99291	−	2.79865i	−0.111407	−	0.156449i
$321$	−15.3901			−0.858994
$322$	8.18000	−	9.69988i	0.455853	−	0.540553i
$323$	26.9853			1.50150
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−8.01029	−	33.0189i	−0.444331	−	1.83156i
$326$	3.83905	−	11.0922i	0.212625	−	0.614340i
$327$	−0.278034	−	5.83664i	−0.0153753	−	0.322767i
$328$	−7.65895	+	8.83890i	−0.422895	+	0.488046i
$329$	−8.63884	−	10.0361i	−0.476275	−	0.553306i
$330$	−14.4769	+	4.25081i	−0.796928	+	0.233999i
$331$	11.9019	−	6.13586i	0.654188	−	0.337257i	−0.0989766	−	0.995090i	$-0.531557\pi$
$331$	11.9019	−	6.13586i	0.654188	−	0.337257i	0.753164	+	0.657833i	$0.228527\pi$
$332$	−10.9724	+	8.62877i	−0.602187	+	0.473565i
$333$	1.37633	−	1.93279i	0.0754227	−	0.105916i
$334$	13.5433	+	1.29323i	0.741057	+	0.0707624i
$335$	−6.60367	−	45.9296i	−0.360797	−	2.50940i
$336$	1.90882	+	1.83205i	0.104135	+	0.0999463i
$337$	15.8537	−	4.65508i	0.863608	−	0.253578i	0.180214	−	0.983627i	$-0.442321\pi$
$337$	15.8537	−	4.65508i	0.863608	−	0.253578i	0.683395	+	0.730049i	$0.260503\pi$
$338$	−9.38175	−	7.37789i	−0.510300	−	0.401304i
$339$	−8.85115	−	1.70592i	−0.480729	−	0.0926529i
$340$	−16.8271	−	8.67498i	−0.912578	−	0.470467i
$341$	−28.2476	+	5.44428i	−1.52969	+	0.294824i
$342$	4.69892	+	1.37973i	0.254089	+	0.0746071i
$343$	−15.6780	+	9.85906i	−0.846531	+	0.532339i
$344$	−2.52244			−0.136001
$345$	−10.5810	+	12.6308i	−0.569662	+	0.680020i
$346$	3.95730	+	6.85424i	0.212746	+	0.368486i
$347$	−21.9185	+	2.09296i	−1.17665	+	0.112356i	−0.665002	−	0.746842i	$-0.731569\pi$
$347$	−21.9185	+	2.09296i	−1.17665	+	0.112356i	−0.511644	+	0.859198i	$0.670963\pi$
$348$	−2.88435	+	2.75023i	−0.154618	+	0.147428i
$349$	6.94179	+	8.01125i	0.371586	+	0.428833i	0.910488	−	0.413536i	$-0.135706\pi$
$349$	6.94179	+	8.01125i	0.371586	+	0.428833i	−0.538902	+	0.842368i	$0.681161\pi$
$350$	−16.7344	+	6.63585i	−0.894490	+	0.354701i
$351$	−3.27006	+	3.77385i	−0.174543	+	0.201433i
$352$	−3.45199	−	2.71467i	−0.183992	−	0.144693i
$353$	−14.5103	−	13.8356i	−0.772306	−	0.736393i	0.197491	−	0.980305i	$-0.436721\pi$
$353$	−14.5103	−	13.8356i	−0.772306	−	0.736393i	−0.969797	+	0.243912i	$0.921569\pi$
$354$	−0.258859	+	5.43413i	−0.0137582	+	0.288821i
$355$	47.4649	+	19.0021i	2.51918	+	1.00853i
$356$	−0.252443	−	0.552773i	−0.0133795	−	0.0292969i
$357$	13.9747	+	4.15315i	0.739617	+	0.219808i
$358$	1.86209	+	12.9511i	0.0984145	+	0.684488i
$359$	−1.04997	+	0.541299i	−0.0554155	+	0.0285687i	−0.485712	−	0.874119i	$-0.661439\pi$
$359$	−1.04997	+	0.541299i	−0.0554155	+	0.0285687i	0.430296	+	0.902688i	$0.358409\pi$
$360$	−2.48654	−	2.37091i	−0.131052	−	0.124958i
$361$	4.62654	−	1.85219i	0.243502	−	0.0974835i
$362$	1.59426	+	4.60631i	0.0837923	+	0.242102i
$363$	−6.97034	+	4.47957i	−0.365848	+	0.235116i
$364$	−6.64329	+	11.4199i	−0.348203	+	0.598564i
$365$	−2.83706	−	0.833037i	−0.148499	−	0.0436031i
$366$	−6.61844	−	9.29430i	−0.345952	−	0.485821i
$367$	13.9057	+	24.0855i	0.725874	+	1.25725i	0.958613	+	0.284711i	$0.0918978\pi$
$367$	13.9057	+	24.0855i	0.725874	+	1.25725i	−0.232739	+	0.972539i	$0.574769\pi$
$368$	−4.78106	−	0.376178i	−0.249230	−	0.0196096i
$369$	−5.84777	+	10.1286i	−0.304423	+	0.527275i
$370$	−3.38651	+	7.41543i	−0.176056	+	0.385510i
$371$	0.347473	+	7.83482i	0.0180399	+	0.406764i
$372$	−4.28976	−	4.95065i	−0.222414	−	0.256679i
$373$	−0.724857	−	15.2166i	−0.0375317	−	0.787887i	−0.936668	−	0.350218i	$-0.886107\pi$
$373$	−0.724857	−	15.2166i	−0.0375317	−	0.787887i	0.899136	−	0.437669i	$-0.144196\pi$
$374$	−23.7612	−	4.57959i	−1.22866	−	0.236805i
$375$	5.75449	−	2.30375i	0.297161	−	0.118965i
$376$	−1.17998	+	4.86394i	−0.0608528	+	0.250839i
$377$	−16.7418	−	10.7593i	−0.862249	−	0.554134i
$378$	2.22105	+	1.43769i	0.114238	+	0.0739469i
$379$	−0.730438	−	1.59944i	−0.0375201	−	0.0821576i	0.889944	−	0.456070i	$-0.150743\pi$
$379$	−0.730438	−	1.59944i	−0.0375201	−	0.0821576i	−0.927464	+	0.373912i	$0.878016\pi$
$380$	−16.7495	−	1.59939i	−0.859233	−	0.0820468i
$381$	−0.129463	+	0.101811i	−0.00663257	+	0.00521591i
$382$	−0.835868	+	17.5470i	−0.0427667	+	0.897784i
$383$	−4.78867	+	19.7392i	−0.244689	+	1.00862i	0.708370	+	0.705841i	$0.249431\pi$
$383$	−4.78867	+	19.7392i	−0.244689	+	1.00862i	−0.953060	+	0.302783i	$0.902084\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	−31.4595	+	24.5735i	−1.60332	+	1.25238i
$386$	−9.83889	+	6.32307i	−0.500787	+	0.321836i
$387$	−2.47685	+	0.477374i	−0.125906	+	0.0242663i
$388$	−1.57402	−	6.48819i	−0.0799087	−	0.329388i
$389$	9.60453	−	0.917122i	0.486969	−	0.0464999i	0.151316	−	0.988485i	$-0.451649\pi$
$389$	9.60453	−	0.917122i	0.486969	−	0.0464999i	0.335653	+	0.941986i	$0.391043\pi$
$390$	8.57816	−	14.8578i	0.434372	−	0.752354i
$391$	−24.3660	+	10.2295i	−1.23224	+	0.517327i
$392$	6.48137	+	2.64420i	0.327359	+	0.133552i
$393$	4.74813	−	10.3970i	0.239511	−	0.524457i
$394$	12.5491	−	11.9655i	0.632214	−	0.602815i
$395$	6.90480	−	19.9501i	0.347418	−	1.00380i
$396$	−3.90336	−	2.01232i	−0.196151	−	0.101123i
$397$	−1.00738	−	2.91063i	−0.0505589	−	0.146080i	0.916894	−	0.399130i	$-0.130688\pi$
$397$	−1.00738	−	2.91063i	−0.0505589	−	0.146080i	−0.967453	+	0.253049i	$0.918567\pi$
$398$	−3.56408	+	24.7887i	−0.178651	+	1.24255i
$399$	12.9023	−	1.18934i	0.645924	−	0.0595416i
$400$	5.72400	+	3.67859i	0.286200	+	0.183930i
$401$	−22.5224	−	9.01660i	−1.12471	−	0.450268i	−0.266641	−	0.963796i	$-0.585914\pi$
$401$	−22.5224	−	9.01660i	−1.12471	−	0.450268i	−0.858073	+	0.513528i	$0.828338\pi$
$402$	7.83410	−	11.0014i	0.390729	−	0.548702i
$403$	18.9741	−	26.6454i	0.945168	−	1.32730i
$404$	13.2994	+	5.32426i	0.661668	+	0.264892i
$405$	−2.89031	−	1.85749i	−0.143621	−	0.0922993i
$406$	−4.41170	+	9.57704i	−0.218949	+	0.475300i
$407$	−1.48293	+	10.3140i	−0.0735062	+	0.511247i
$408$	−1.80222	−	5.20719i	−0.0892234	−	0.257794i
$409$	30.2916	+	15.6164i	1.49782	+	0.772181i	0.995702	−	0.0926158i	$-0.0295228\pi$
$409$	30.2916	+	15.6164i	1.49782	+	0.772181i	0.502121	+	0.864797i	$0.332553\pi$
$410$	13.1424	−	37.9725i	0.649058	−	1.87533i
$411$	8.55668	−	8.15878i	0.422070	−	0.402443i
$412$	5.70806	−	12.4989i	0.281216	−	0.615777i
$413$	4.66307	+	13.6174i	0.229455	+	0.670067i
$414$	−4.76585	+	0.535441i	−0.234229	+	0.0263155i
$415$	23.9793	−	41.5333i	1.17710	−	2.03879i
$416$	4.97091	−	0.474664i	0.243719	−	0.0232723i
$417$	3.83487	+	15.8075i	0.187794	+	0.774098i
$418$	−21.1180	+	4.07017i	−1.03292	+	0.199078i
$419$	12.9315	−	8.31059i	0.631747	−	0.405999i	−0.185209	−	0.982699i	$-0.559296\pi$
$419$	12.9315	−	8.31059i	0.631747	−	0.405999i	0.816956	+	0.576700i	$0.195660\pi$
$420$	−8.42778	−	3.40608i	−0.411234	−	0.166200i
$421$	−1.35605	+	9.43151i	−0.0660896	+	0.459664i	0.929724	+	0.368257i	$0.120045\pi$
$421$	−1.35605	+	9.43151i	−0.0660896	+	0.459664i	−0.995814	+	0.0914065i	$0.970864\pi$
$422$	−2.84651	+	11.7335i	−0.138566	+	0.571177i
$423$	−0.238149	+	4.99936i	−0.0115792	+	0.243077i
$424$	2.33002	−	1.83234i	0.113156	−	0.0889865i
$425$	37.3227	+	3.56389i	1.81042	+	0.172874i
$426$	6.18184	+	13.5363i	0.299511	+	0.655838i
$427$	−25.3421	−	16.4040i	−1.22639	−	0.793847i
$428$	12.9470	+	8.32054i	0.625818	+	0.402188i
$429$	5.17002	−	21.3111i	0.249611	−	1.02891i
$430$	8.04558	−	3.22097i	0.387993	−	0.155329i
$431$	28.4164	+	5.47681i	1.36877	+	0.263809i	0.820095	−	0.572228i	$-0.193921\pi$
$431$	28.4164	+	5.47681i	1.36877	+	0.263809i	0.548674	+	0.836036i	$0.315133\pi$
$432$	−0.0475819	−	0.998867i	−0.00228929	−	0.0480580i
$433$	−0.903569	−	1.04277i	−0.0434228	−	0.0501126i	0.733623	−	0.679557i	$-0.237828\pi$
$433$	−0.903569	−	1.04277i	−0.0434228	−	0.0501126i	−0.777045	+	0.629444i	$0.783283\pi$
$434$	−15.3786	−	7.99217i	−0.738197	−	0.383636i
$435$	5.68812	−	12.4553i	0.272725	−	0.597184i
$436$	−2.92163	+	5.06041i	−0.139921	+	0.242350i
$437$	−16.7254	+	16.4889i	−0.800082	+	0.788770i
$438$	−0.430309	−	0.745316i	−0.0205609	−	0.0356126i
$439$	−6.36153	−	8.93353i	−0.303619	−	0.426374i	0.634374	−	0.773026i	$-0.281258\pi$
$439$	−6.36153	−	8.93353i	−0.303619	−	0.426374i	−0.937994	+	0.346652i	$0.887318\pi$
$440$	14.4769	+	4.25081i	0.690160	+	0.202649i
$441$	6.86467	+	1.36981i	0.326889	+	0.0652289i
$442$	23.1475	−	14.8760i	1.10102	−	0.707580i
$443$	2.16070	+	6.24293i	0.102658	+	0.296611i	0.984620	−	0.174710i	$-0.0558988\pi$
$443$	2.16070	+	6.24293i	0.102658	+	0.296611i	−0.881962	+	0.471320i	$0.843778\pi$
$444$	−2.20279	+	0.881865i	−0.104540	+	0.0418515i
$445$	1.51105	+	1.44078i	0.0716304	+	0.0682995i
$446$	−3.48504	+	1.79666i	−0.165022	+	0.0850746i
$447$	−0.0172436	−	0.119932i	−0.000815594	−	0.00567258i
$448$	−0.615325	−	2.57320i	−0.0290714	−	0.121572i
$449$	−6.35762	−	13.9212i	−0.300035	−	0.656984i	0.698230	−	0.715874i	$-0.253971\pi$
$449$	−6.35762	−	13.9212i	−0.300035	−	0.656984i	−0.998265	+	0.0588894i	$0.981244\pi$
$450$	6.31674	+	2.52884i	0.297774	+	0.119211i
$451$	2.44388	−	51.3033i	0.115078	−	2.41578i
$452$	6.52378	+	6.22041i	0.306853	+	0.292583i
$453$	−0.738549	−	0.580801i	−0.0347000	−	0.0272884i
$454$	2.87887	−	3.32239i	0.135112	−	0.155927i
$455$	6.60716	−	44.9079i	0.309748	−	2.10532i
$456$	−3.20705	−	3.70113i	−0.150184	−	0.173321i
$457$	−10.5321	+	10.0423i	−0.492671	+	0.469761i	−0.895212	−	0.445641i	$-0.852976\pi$
$457$	−10.5321	+	10.0423i	−0.492671	+	0.469761i	0.402540	+	0.915402i	$0.368127\pi$
$458$	−5.70232	+	0.544505i	−0.266452	+	0.0254431i
$459$	−2.75512	−	4.77201i	−0.128598	−	0.222738i
$460$	15.7300	−	4.90519i	0.733417	−	0.228706i
$461$	−17.6405			−0.821600			−0.410800	−	0.911726i	$-0.634751\pi$
$461$	−17.6405			−0.821600			−0.410800	+	0.911726i	$0.634751\pi$
$462$	−11.5626	−	1.14237i	−0.537943	−	0.0531479i
$463$	−1.71341	−	0.503102i	−0.0796288	−	0.0233811i	0.241675	−	0.970357i	$-0.422303\pi$
$463$	−1.71341	−	0.503102i	−0.0796288	−	0.0233811i	−0.321304	+	0.946976i	$0.604121\pi$
$464$	3.91336	−	0.754238i	0.181673	−	0.0350146i
$465$	20.0043	+	10.3129i	0.927676	+	0.478250i
$466$	−12.6788	−	2.44364i	−0.587334	−	0.113199i
$467$	8.85891	+	6.96673i	0.409942	+	0.322382i	0.801744	−	0.597668i	$-0.203906\pi$
$467$	8.85891	+	6.96673i	0.409942	+	0.322382i	−0.391802	+	0.920049i	$0.628148\pi$
$468$	4.79125	−	1.40684i	0.221476	−	0.0650311i
$469$	8.53816	−	34.6978i	0.394255	−	1.60219i
$470$	−2.44722	−	17.0208i	−0.112882	−	0.785112i
$471$	−22.9187	−	2.18847i	−1.05604	−	0.100839i
$472$	3.15568	−	4.43153i	0.145252	−	0.203978i
$473$	8.70742	−	6.84759i	0.400368	−	0.314853i
$474$	5.46157	−	2.81563i	0.250858	−	0.129326i
$475$	31.9721	−	9.38786i	1.46698	−	0.430744i
$476$	−9.51086	−	11.0491i	−0.435930	−	0.506436i
$477$	1.94114	−	2.24019i	0.0888785	−	0.102571i
$478$	0.805159	+	16.9024i	0.0368271	+	0.773097i
$479$	6.65797	−	19.2369i	0.304210	−	0.878958i	−0.684486	−	0.729026i	$-0.739973\pi$
$479$	6.65797	−	19.2369i	0.304210	−	0.878958i	0.988696	−	0.149932i	$-0.0479055\pi$
$480$	0.810000	+	3.33887i	0.0369713	+	0.152398i
$481$	−6.87276	−	9.65144i	−0.313371	−	0.440068i
$482$	−28.6297			−1.30405
$483$	−11.1991	+	5.96486i	−0.509578	+	0.271410i
$484$	8.28566			0.376621
$485$	13.3054	+	18.6849i	0.604169	+	0.848437i
$486$	−0.235759	−	0.971812i	−0.0106942	−	0.0440823i
$487$	−6.51915	+	18.8359i	−0.295411	+	0.853534i	0.695441	+	0.718583i	$0.255209\pi$
$487$	−6.51915	+	18.8359i	−0.295411	+	0.853534i	−0.990852	+	0.134951i	$0.956912\pi$
$488$	0.542909	+	11.3971i	0.0245763	+	0.515921i
$489$	−7.68660	+	8.87081i	−0.347600	+	0.401152i
$490$	−24.0495	−	0.157724i	−1.08645	−	0.00712524i
$491$	−32.8772	+	9.65360i	−1.48373	+	0.435661i	−0.920533	−	0.390665i	$-0.872245\pi$
$491$	−32.8772	+	9.65360i	−1.48373	+	0.435661i	−0.563192	+	0.826326i	$0.690427\pi$
$492$	10.3954	−	5.35920i	0.468661	−	0.241612i
$493$	17.2621	−	13.5750i	0.777444	−	0.611389i
$494$	14.1852	−	19.9203i	0.638220	−	0.896255i
$495$	15.0198	+	1.43421i	0.675089	+	0.0644632i
$496$	0.932254	+	6.48397i	0.0418594	+	0.291139i
$497$	28.4054	+	27.2629i	1.27416	+	1.22291i
$498$	13.3934	−	3.93265i	0.600172	−	0.176226i
$499$	−5.77001	−	4.53758i	−0.258301	−	0.203130i	0.480608	−	0.876936i	$-0.340416\pi$
$499$	−5.77001	−	4.53758i	−0.258301	−	0.203130i	−0.738909	+	0.673806i	$0.764659\pi$
$500$	−6.08649	−	1.17307i	−0.272196	−	0.0524615i
$501$	−12.0925	−	6.23413i	−0.540254	−	0.278521i
$502$	13.0140	−	2.50825i	0.580845	−	0.111949i
$503$	−23.2012	−	6.81248i	−1.03449	−	0.303754i	−0.279954	−	0.960013i	$-0.590319\pi$
$503$	−23.2012	−	6.81248i	−1.03449	−	0.303754i	−0.754535	+	0.656260i	$0.772138\pi$
$504$	−1.09119	−	2.41025i	−0.0486053	−	0.107361i
$505$	−49.2184			−2.19019
$506$	17.5253	−	11.6804i	0.779096	−	0.519259i
$507$	5.96763	+	10.3362i	0.265032	+	0.459048i
$508$	0.163954	−	0.0156557i	0.00727427	−	0.000694609i
$509$	29.5615	−	28.1868i	1.31029	−	1.24936i	0.361913	−	0.932212i	$-0.382124\pi$
$509$	29.5615	−	28.1868i	1.31029	−	1.24936i	0.948376	−	0.317147i	$-0.102725\pi$
$510$	12.3976	+	14.3076i	0.548974	+	0.633550i
$511$	−1.78520	−	1.41340i	−0.0789727	−	0.0625250i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−3.84954	−	3.02731i	−0.169961	−	0.133659i
$514$	−3.63575	−	3.46668i	−0.160366	−	0.152909i
$515$	−2.24629	+	47.1554i	−0.0989833	+	2.07792i
$516$	2.34175	+	0.937495i	0.103090	+	0.0412709i
$517$	−9.13074	−	19.9935i	−0.401569	−	0.879315i
$518$	−4.55759	+	4.31721i	−0.200249	+	0.189687i
$519$	−1.12636	−	7.83404i	−0.0494419	−	0.343876i
$520$	−15.2491	+	7.86148i	−0.668719	+	0.344749i
$521$	2.18888	+	2.08709i	0.0958964	+	0.0914370i	0.736511	−	0.676425i	$-0.236472\pi$
$521$	2.18888	+	2.08709i	0.0958964	+	0.0914370i	−0.640615	+	0.767862i	$0.721320\pi$
$522$	3.69990	−	1.48122i	0.161940	−	0.0648310i
$523$	−7.86499	−	22.7244i	−0.343912	−	0.993668i	−0.975811	−	0.218617i	$-0.929845\pi$
$523$	−7.86499	−	22.7244i	−0.343912	−	0.993668i	0.631899	−	0.775051i	$-0.282276\pi$
$524$	−9.61540	+	6.17944i	−0.420051	+	0.269950i
$525$	18.0020	+	0.0590305i	0.785670	+	0.00257630i
$526$	17.9341	+	5.26594i	0.781966	+	0.229606i
$527$	20.9375	+	29.4027i	0.912054	+	1.28080i
$528$	2.19577	+	3.80319i	0.0955587	+	0.165513i
$529$	8.85139	−	21.2286i	0.384843	−	0.922982i
$530$	−5.09207	+	8.81972i	−0.221185	+	0.383104i
$531$	2.25998	−	4.94866i	0.0980747	−	0.214754i
$532$	−11.4971	−	5.97499i	−0.498464	−	0.259049i
$533$	38.2451	+	44.1372i	1.65658	+	1.91180i
$534$	0.0289150	+	0.607001i	0.00125127	+	0.0262675i
$535$	−51.9206	−	10.0069i	−2.24472	−	0.432635i
$536$	−12.5383	+	5.01958i	−0.541572	+	0.216813i
$537$	3.08474	−	12.7155i	0.133116	−	0.548713i
$538$	21.7973	+	14.0082i	0.939747	+	0.603938i
$539$	−29.5518	+	8.46706i	−1.27288	+	0.364702i
$540$	1.42725	+	3.12524i	0.0614190	+	0.134489i
$541$	−0.829318	−	0.0791903i	−0.0356552	−	0.00340466i	0.0772132	−	0.997015i	$-0.475398\pi$
$541$	−0.829318	−	0.0791903i	−0.0356552	−	0.00340466i	−0.112868	+	0.993610i	$0.536004\pi$
$542$	3.24589	−	2.55259i	0.139423	−	0.109643i
$543$	0.231933	−	4.86887i	0.00995320	−	0.208943i
$544$	−1.29909	+	5.35492i	−0.0556980	+	0.229590i
$545$	2.85708	−	19.8714i	0.122384	−	0.851199i
$546$	10.4118	−	8.13278i	0.445582	−	0.348051i
$547$	8.62283	−	5.54155i	0.368685	−	0.236940i	−0.343158	−	0.939278i	$-0.611497\pi$
$547$	8.62283	−	5.54155i	0.368685	−	0.236940i	0.711844	+	0.702338i	$0.247860\pi$
$548$	−11.6093	+	2.23751i	−0.495925	+	0.0955817i
$549$	2.69001	+	11.0884i	0.114807	+	0.473240i
$550$	−29.7454	+	2.84034i	−1.26835	+	0.121112i
$551$	9.75879	−	16.9027i	0.415738	−	0.720080i
$552$	4.29877	+	2.12617i	0.182968	+	0.0904958i
$553$	10.6864	−	12.2514i	0.454433	−	0.520982i
$554$	−5.75537	+	12.6025i	−0.244522	+	0.535429i
$555$	5.89997	−	5.62561i	0.250440	−	0.238794i
$556$	5.32010	−	15.3714i	0.225623	−	0.651894i
$557$	−4.59327	−	2.36800i	−0.194623	−	0.100335i	0.358160	−	0.933660i	$-0.383404\pi$
$557$	−4.59327	−	2.36800i	−0.194623	−	0.100335i	−0.552784	+	0.833325i	$0.686434\pi$
$558$	2.14251	+	6.19037i	0.0906995	+	0.262059i
$559$	−1.79258	+	12.4676i	−0.0758179	+	0.527325i
$560$	5.24844	+	7.42178i	0.221787	+	0.313628i
$561$	20.3571	+	13.0827i	0.859476	+	0.552352i
$562$	9.05768	+	3.62615i	0.382075	+	0.152960i
$563$	−9.60646	+	13.4904i	−0.404864	+	0.568552i	−0.965794	−	0.259311i	$-0.916504\pi$
$563$	−9.60646	+	13.4904i	−0.404864	+	0.568552i	0.560930	+	0.827863i	$0.310444\pi$
$564$	2.90320	−	4.07698i	0.122247	−	0.171672i
$565$	−28.7513	−	11.5103i	−1.20958	−	0.484241i
$566$	2.11301	+	1.35795i	0.0888165	+	0.0570789i
$567$	−1.52761	−	2.16019i	−0.0641536	−	0.0907193i
$568$	2.11780	−	14.7296i	0.0888611	−	0.618042i
$569$	−5.69896	−	16.4661i	−0.238913	−	0.690293i	−0.999172	−	0.0406737i	$-0.987050\pi$
$569$	−5.69896	−	16.4661i	−0.238913	−	0.690293i	0.760260	−	0.649619i	$-0.225072\pi$
$570$	14.9553	+	7.70999i	0.626408	+	0.322936i
$571$	5.99228	−	17.3136i	0.250769	−	0.724550i	−0.747417	−	0.664355i	$-0.768706\pi$
$571$	5.99228	−	17.3136i	0.250769	−	0.724550i	0.998187	−	0.0601955i	$-0.0191724\pi$
$572$	−15.8710	+	15.1329i	−0.663598	+	0.632740i
$573$	7.29756	−	15.9794i	0.304860	−	0.667550i
$574$	20.3402	−	23.3189i	0.848985	−	0.973314i
$575$	−25.3101	+	20.5965i	−1.05550	+	0.858933i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.64300	+	0.634330i	−0.276552	+	0.0264075i	−0.232410	−	0.972618i	$-0.574661\pi$
$577$	−6.64300	+	0.634330i	−0.276552	+	0.0264075i	−0.0441414	+	0.999025i	$0.514055\pi$
$578$	3.15040	+	12.9861i	0.131039	+	0.540152i
$579$	11.4842	−	2.21339i	0.477266	−	0.0919854i
$580$	−11.5190	+	7.40279i	−0.478299	+	0.307384i
$581$	29.1049	−	22.7343i	1.20747	−	0.943176i
$582$	−0.950149	+	6.60843i	−0.0393850	+	0.273928i
$583$	−3.06897	+	12.6505i	−0.127104	+	0.523928i
$584$	−0.0409498	+	0.859642i	−0.00169452	+	0.0355723i
$585$	−13.4858	+	10.6053i	−0.557568	+	0.438476i
$586$	−17.3190	−	1.65377i	−0.715443	−	0.0683165i
$587$	−8.90917	−	19.5084i	−0.367721	−	0.805196i	−0.999547	−	0.0300865i	$-0.990422\pi$
$587$	−8.90917	−	19.5084i	−0.367721	−	0.805196i	0.631826	−	0.775110i	$-0.282306\pi$
$588$	−5.03435	−	4.86367i	−0.207613	−	0.200575i
$589$	26.9878	+	17.3440i	1.11201	+	0.714647i
$590$	−4.40664	+	18.1644i	−0.181418	+	0.747817i
$591$	−16.0973	+	6.44439i	−0.662155	+	0.265087i
$592$	2.32988	+	0.449047i	0.0957575	+	0.0184557i
$593$	−1.37877	−	28.9440i	−0.0566193	−	1.18859i	−0.831149	−	0.556049i	$-0.812317\pi$
$593$	−1.37877	−	28.9440i	−0.0566193	−	1.18859i	0.774530	−	0.632537i	$-0.217986\pi$
$594$	2.87585	+	3.31891i	0.117998	+	0.136176i
$595$	44.4448	+	23.0977i	1.82206	+	0.946913i
$596$	−0.0503338	+	0.110216i	−0.00206175	+	0.00451461i
$597$	12.5218	−	21.6884i	0.512483	−	0.887647i
$598$	−5.25700	+	23.3640i	−0.214975	+	0.955424i
$599$	−4.12683	−	7.14787i	−0.168618	−	0.292054i	0.769316	−	0.638868i	$-0.220597\pi$
$599$	−4.12683	−	7.14787i	−0.168618	−	0.292054i	−0.937934	+	0.346814i	$0.887264\pi$
$600$	−3.94679	−	5.54249i	−0.161127	−	0.226271i
$601$	−24.3526	−	7.15057i	−0.993364	−	0.291678i	−0.255634	−	0.966774i	$-0.582284\pi$
$601$	−24.3526	−	7.15057i	−0.993364	−	0.291678i	−0.737730	+	0.675096i	$0.764102\pi$
$602$	6.67371	+	0.0218839i	0.272000	+	0.000891920i
$603$	−11.3617	+	7.30175i	−0.462686	+	0.297350i
$604$	0.307302	+	0.887891i	0.0125039	+	0.0361278i
$605$	−26.4280	+	10.5802i	−1.07445	+	0.430146i
$606$	−10.3679	−	9.88575i	−0.421166	−	0.401581i
$607$	17.1874	−	8.86070i	0.697613	−	0.359645i	−0.0726617	−	0.997357i	$-0.523149\pi$
$607$	17.1874	−	8.86070i	0.697613	−	0.359645i	0.770275	+	0.637712i	$0.220119\pi$
$608$	0.696958	+	4.84745i	0.0282654	+	0.196590i
$609$	7.65510	−	7.25135i	0.310200	−	0.293840i
$610$	−16.2849	−	35.6589i	−0.659355	−	1.44379i
$611$	23.2024	+	9.28885i	0.938670	+	0.375787i
$612$	−0.262188	+	5.50400i	−0.0105983	+	0.222486i
$613$	−26.9532	−	25.6999i	−1.08863	−	1.03801i	−0.999117	−	0.0420216i	$-0.986620\pi$
$613$	−26.9532	−	25.6999i	−1.08863	−	1.03801i	−0.0895139	−	0.995986i	$-0.528531\pi$
$614$	15.8103	+	12.4334i	0.638053	+	0.501770i
$615$	−26.3140	+	30.3679i	−1.06108	+	1.22455i
$616$	9.10950	+	7.21226i	0.367032	+	0.290590i
$617$	−15.3341	−	17.6965i	−0.617329	−	0.712436i	0.357868	−	0.933772i	$-0.383504\pi$
$617$	−15.3341	−	17.6965i	−0.617329	−	0.712436i	−0.975198	+	0.221336i	$0.928958\pi$
$618$	−9.94456	+	9.48212i	−0.400029	+	0.381427i
$619$	21.2545	−	2.02956i	0.854291	−	0.0815749i	0.341285	−	0.939960i	$-0.389138\pi$
$619$	21.2545	−	2.02956i	0.854291	−	0.0815749i	0.513006	+	0.858385i	$0.328532\pi$
$620$	−11.2531	−	19.4909i	−0.451934	−	0.782773i
$621$	4.62346	+	1.27420i	0.185533	+	0.0511319i
$622$	−10.5346			−0.422400
$623$	0.663102	+	1.46468i	0.0265666	+	0.0586813i
$624$	−4.79125	−	1.40684i	−0.191803	−	0.0563186i
$625$	−12.4945	+	2.40811i	−0.499778	+	0.0963244i
$626$	−19.5017	−	10.0538i	−0.779444	−	0.401831i
$627$	21.1180	+	4.07017i	0.843373	+	0.162547i
$628$	18.0972	+	14.2318i	0.722158	+	0.567911i
$629$	12.5449	−	3.68351i	0.500197	−	0.146871i
$630$	6.55817	+	6.29439i	0.261284	+	0.250774i
$631$	−0.850793	−	5.91740i	−0.0338695	−	0.235568i	0.965854	−	0.259088i	$-0.0834218\pi$
$631$	−0.850793	−	5.91740i	−0.0338695	−	0.235568i	−0.999723	+	0.0235198i	$0.992513\pi$
$632$	−6.11681	−	0.584085i	−0.243314	−	0.0232336i
$633$	7.00351	−	9.83505i	0.278364	−	0.390908i
$634$	15.3341	−	12.0589i	0.608996	−	0.478920i
$635$	−0.502957	+	0.259292i	−0.0199592	+	0.0102897i
$636$	−2.84413	+	0.835110i	−0.112777	+	0.0331143i
$637$	17.6755	−	30.1563i	0.700328	−	1.19484i
$638$	−11.4614	+	13.2271i	−0.453759	+	0.523666i
$639$	−0.708072	−	14.8643i	−0.0280109	−	0.588021i
$640$	1.12371	−	3.24675i	0.0444186	−	0.128339i
$641$	9.30979	+	38.3755i	0.367715	+	1.51574i	0.792175	+	0.610294i	$0.208949\pi$
$641$	9.30979	+	38.3755i	0.367715	+	1.51574i	−0.424460	+	0.905447i	$0.639536\pi$
$642$	−8.92716	−	12.5364i	−0.352327	−	0.494774i
$643$	−2.02349			−0.0797986			−0.0398993	−	0.999204i	$-0.512704\pi$
$643$	−2.02349			−0.0797986			−0.0398993	+	0.999204i	$0.512704\pi$
$644$	12.6462	+	1.03675i	0.498328	+	0.0408536i
$645$	−8.66637			−0.341238
$646$	15.6530	+	21.9816i	0.615860	+	0.864854i
$647$	3.48924	+	14.3828i	0.137176	+	0.565448i	0.998365	+	0.0571624i	$0.0182053\pi$
$647$	3.48924	+	14.3828i	0.137176	+	0.565448i	−0.861189	+	0.508285i	$0.830280\pi$
$648$	−0.327068	+	0.945001i	−0.0128484	+	0.0371231i
$649$	1.13679	+	23.8642i	0.0446230	+	0.936752i
$650$	22.2499	−	25.6778i	0.872715	−	1.00717i
$651$	11.3066	+	13.1353i	0.443142	+	0.514814i
$652$	11.2623	−	3.30691i	0.441066	−	0.129509i
$653$	17.6872	−	9.11837i	0.692153	−	0.356830i	−0.0759896	−	0.997109i	$-0.524212\pi$
$653$	17.6872	−	9.11837i	0.692153	−	0.356830i	0.768142	+	0.640279i	$0.221181\pi$
$654$	4.59311	−	3.61206i	0.179605	−	0.141243i
$655$	22.7787	−	31.9881i	0.890036	−	1.24988i
$656$	−11.6426	−	1.11173i	−0.454566	−	0.0434058i
$657$	0.122479	+	0.851857i	0.00477834	+	0.0332341i
$658$	3.16411	−	12.8585i	0.123350	−	0.501276i
$659$	−43.4990	+	12.7725i	−1.69448	+	0.497544i	−0.979474	−	0.201573i	$-0.935395\pi$
$659$	−43.4990	+	12.7725i	−1.69448	+	0.497544i	−0.715007	+	0.699117i	$0.753577\pi$
$660$	−11.8600	−	9.32684i	−0.461652	−	0.363047i
$661$	−14.8083	−	2.85406i	−0.575976	−	0.111010i	−0.107059	−	0.994253i	$-0.534143\pi$
$661$	−14.8083	−	2.85406i	−0.575976	−	0.111010i	−0.468917	+	0.883242i	$0.655356\pi$
$662$	11.9019	+	6.13586i	0.462580	+	0.238477i
$663$	−27.0183	+	5.20735i	−1.04930	+	0.202237i
$664$	−13.3934	−	3.93265i	−0.519764	−	0.152617i
$665$	44.3010	+	4.37687i	1.71792	+	0.169728i
$666$	2.37276			0.0919425
$667$	−2.40415	+	18.9614i	−0.0930892	+	0.734188i
$668$	6.80246	+	11.7822i	0.263195	+	0.455867i
$669$	3.90316	−	0.372706i	0.150905	−	0.0144097i
$670$	33.5826	−	32.0210i	1.29741	−	1.23708i
$671$	−32.8134	−	37.8687i	−1.26675	−	1.46190i
$672$	−0.385115	+	2.61757i	−0.0148561	+	0.100975i
$673$	2.96383	−	3.42044i	0.114247	−	0.131848i	−0.695745	−	0.718289i	$-0.744926\pi$
$673$	2.96383	−	3.42044i	0.114247	−	0.131848i	0.809992	+	0.586440i	$0.199471\pi$
$674$	12.9880	+	10.2139i	0.500279	+	0.393423i
$675$	−4.92439	−	4.69539i	−0.189540	−	0.180726i
$676$	0.567902	−	11.9217i	0.0218424	−	0.458528i
$677$	−31.0525	−	12.4316i	−1.19345	−	0.477783i	−0.312006	−	0.950080i	$-0.601001\pi$
$677$	−31.0525	−	12.4316i	−1.19345	−	0.477783i	−0.881440	+	0.472297i	$0.843425\pi$
$678$	−3.74457	−	8.19947i	−0.143809	−	0.314899i
$679$	4.10815	+	17.1797i	0.157656	+	0.659297i
$680$	−2.69425	−	18.7389i	−0.103320	−	0.718605i
$681$	−3.90746	+	2.01443i	−0.149734	+	0.0771933i
$682$	−20.8200	−	19.8518i	−0.797238	−	0.760165i
$683$	−32.0852	+	12.8450i	−1.22771	+	0.491499i	−0.892672	−	0.450707i	$-0.851172\pi$
$683$	−32.0852	+	12.8450i	−1.22771	+	0.491499i	−0.335034	+	0.942206i	$0.608748\pi$
$684$	1.60175	+	4.62795i	0.0612444	+	0.176954i
$685$	34.1720	−	21.9610i	1.30565	−	0.839087i
$686$	−17.1251	−	7.05209i	−0.653838	−	0.269250i
$687$	5.49622	+	1.61384i	0.209694	+	0.0615717i
$688$	−1.46316	−	2.05472i	−0.0557823	−	0.0783353i
$689$	−7.40089	−	12.8187i	−0.281951	−	0.488354i
$690$	−16.4263	−	1.29244i	−0.625340	−	0.0492024i
$691$	−23.0893	+	39.9919i	−0.878359	+	1.52136i	−0.0252182	+	0.999682i	$0.508028\pi$
$691$	−23.0893	+	39.9919i	−0.878359	+	1.52136i	−0.853141	+	0.521681i	$0.825305\pi$
$692$	−3.28784	+	7.19937i	−0.124985	+	0.273679i
$693$	10.3098	+	5.35794i	0.391637	+	0.203531i
$694$	−14.4188	−	16.6402i	−0.547332	−	0.631654i
$695$	2.65914	+	55.8222i	0.100867	+	2.11746i
$696$	−3.91336	−	0.754238i	−0.148335	−	0.0285893i
$697$	−59.8289	+	23.9519i	−2.26618	+	0.907242i
$698$	−2.49914	+	10.3016i	−0.0945939	+	0.389921i
$699$	10.8624	+	6.98083i	0.410853	+	0.264039i
$700$	−15.1123	−	9.78225i	−0.571191	−	0.369734i
$701$	3.67185	+	8.04024i	0.138684	+	0.303676i	0.966212	−	0.257749i	$-0.0829807\pi$
$701$	3.67185	+	8.04024i	0.138684	+	0.303676i	−0.827528	+	0.561425i	$0.810253\pi$
$702$	−4.97091	−	0.474664i	−0.187615	−	0.0179151i
$703$	9.13402	−	7.18307i	0.344496	−	0.270915i
$704$	0.208958	−	4.38657i	0.00787540	−	0.165325i
$705$	−4.05407	+	16.7111i	−0.152685	+	0.629377i
$706$	2.85331	−	19.8452i	0.107386	−	0.746883i
$707$	−35.1404	−	14.2020i	−1.32159	−	0.534120i
$708$	−4.57666	+	2.94124i	−0.172001	+	0.110539i
$709$	20.2522	−	3.90330i	0.760588	−	0.146591i	0.205813	−	0.978591i	$-0.434016\pi$
$709$	20.2522	−	3.90330i	0.760588	−	0.146591i	0.554775	+	0.832000i	$0.312804\pi$
$710$	12.0537	+	49.6861i	0.452368	+	1.86468i
$711$	−6.11681	+	0.584085i	−0.229398	+	0.0219049i
$712$	0.303845	−	0.526274i	0.0113871	−	0.0197230i
$713$	−30.9429	−	5.43011i	−1.15882	−	0.203359i
$714$	4.72304	+	13.7925i	0.176755	+	0.516171i
$715$	31.2985	−	68.5342i	1.17050	−	2.56303i
$716$	−9.46955	+	9.02920i	−0.353894	+	0.337437i
$717$	5.53449	−	15.9909i	0.206689	−	0.597190i
$718$	−1.04997	−	0.541299i	−0.0391847	−	0.0202011i
$719$	13.7522	+	39.7345i	0.512872	+	1.48185i	0.843002	+	0.537911i	$0.180786\pi$
$719$	13.7522	+	39.7345i	0.512872	+	1.48185i	−0.330130	+	0.943936i	$0.607093\pi$
$720$	0.488953	−	3.40074i	0.0182222	−	0.126738i
$721$	−15.2105	+	33.0193i	−0.566467	+	1.22970i
$722$	4.19240	+	2.69429i	0.156025	+	0.100271i
$723$	26.5789	+	10.6406i	0.988481	+	0.395728i
$724$	−2.82743	+	3.97056i	−0.105080	+	0.147565i
$725$	15.7294	−	22.0889i	0.584177	−	0.820361i
$726$	−7.69214	−	3.07947i	−0.285482	−	0.114290i
$727$	27.3554	+	17.5802i	1.01455	+	0.652014i	0.938568	−	0.345095i	$-0.112153\pi$
$727$	27.3554	+	17.5802i	1.01455	+	0.652014i	0.0759861	+	0.997109i	$0.475790\pi$
$728$	−13.1558	+	1.21271i	−0.487588	+	0.0449461i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−0.967086	−	2.79421i	−0.0357935	−	0.103418i
$731$	−12.3541	−	6.36900i	−0.456935	−	0.235566i
$732$	3.73184	−	10.7824i	0.137933	−	0.398531i
$733$	−10.4280	+	9.94307i	−0.385167	+	0.367256i	−0.857783	−	0.514013i	$-0.828158\pi$
$733$	−10.4280	+	9.94307i	−0.385167	+	0.367256i	0.472616	+	0.881269i	$0.343310\pi$
$734$	−11.5533	+	25.2982i	−0.426440	+	0.933774i
$735$	22.2682	+	9.08472i	0.821373	+	0.335095i
$736$	−2.46686	−	4.11274i	−0.0909296	−	0.151598i
$737$	29.6555	−	51.3649i	1.09238	−	1.89205i
$738$	−11.6426	+	1.11173i	−0.428569	+	0.0409234i
$739$	4.29299	+	17.6960i	0.157920	+	0.650956i	0.994647	+	0.103335i	$0.0329514\pi$
$739$	4.29299	+	17.6960i	0.157920	+	0.650956i	−0.836726	+	0.547621i	$0.815533\pi$
$740$	−8.00480	+	1.54280i	−0.294262	+	0.0567144i
$741$	−20.5727	+	13.2212i	−0.755755	+	0.485694i
$742$	−6.18050	+	4.82769i	−0.226893	+	0.177230i
$743$	1.78358	−	12.4051i	0.0654332	−	0.455098i	−0.930594	−	0.366052i	$-0.880709\pi$
$743$	1.78358	−	12.4051i	0.0654332	−	0.455098i	0.996028	−	0.0890456i	$-0.0283817\pi$
$744$	1.54437	−	6.36599i	0.0566195	−	0.233389i
$745$	0.0198078	−	0.415818i	0.000725703	−	0.0152344i
$746$	11.9746	−	9.41696i	0.438423	−	0.344779i
$747$	−13.8956	−	1.32687i	−0.508414	−	0.0485476i
$748$	−10.0524	−	22.0117i	−0.367553	−	0.804828i
$749$	−34.1822	−	22.1263i	−1.24899	−	0.808477i
$750$	5.21451	+	3.35116i	0.190407	+	0.122367i
$751$	−7.88509	+	32.5028i	−0.287731	+	1.18604i	0.626032	+	0.779797i	$0.284678\pi$
$751$	−7.88509	+	32.5028i	−0.287731	+	1.18604i	−0.913764	+	0.406247i	$0.866837\pi$
$752$	−4.64651	+	1.86018i	−0.169441	+	0.0678338i
$753$	−13.0140	−	2.50825i	−0.474258	−	0.0914058i
$754$	−0.946931	−	19.8785i	−0.0344852	−	0.723934i
$755$	−2.11394	−	2.43962i	−0.0769343	−	0.0887869i
$756$	0.117223	+	2.64315i	0.00426337	+	0.0961306i
$757$	−3.10947	+	6.80878i	−0.113015	+	0.247469i	−0.957685	−	0.287819i	$-0.907070\pi$
$757$	−3.10947	+	6.80878i	−0.113015	+	0.247469i	0.844669	+	0.535288i	$0.179797\pi$
$758$	0.879167	−	1.52276i	0.0319328	−	0.0553092i
$759$	−20.6111	+	4.33023i	−0.748137	+	0.157178i
$760$	−8.41286	−	14.5715i	−0.305166	−	0.528564i
$761$	18.6335	+	26.1671i	0.675465	+	0.948558i	0.999996	+	0.00268313i	$0.000854066\pi$
$761$	18.6335	+	26.1671i	0.675465	+	0.948558i	−0.324531	+	0.945875i	$0.605207\pi$
$762$	−0.158028	−	0.0464012i	−0.00572475	−	0.00168094i
$763$	7.77377	−	13.3632i	0.281429	−	0.483779i
$764$	−14.7782	+	9.49739i	−0.534658	+	0.343604i
$765$	−6.19193	−	17.8904i	−0.223870	−	0.646829i
$766$	−18.8567	+	7.54910i	−0.681322	+	0.272760i
$767$	−19.6611	−	18.7468i	−0.709921	−	0.676909i
$768$	0.888835	−	0.458227i	0.0320731	−	0.0165348i
$769$	−0.829461	−	5.76903i	−0.0299111	−	0.208036i	0.969385	−	0.245545i	$-0.0789669\pi$
$769$	−0.829461	−	5.76903i	−0.0299111	−	0.208036i	−0.999296	+	0.0375086i	$0.988058\pi$
$770$	−38.2652	−	11.3721i	−1.37898	−	0.409823i
$771$	2.08688	+	4.56962i	0.0751571	+	0.164571i
$772$	−10.8577	−	4.34678i	−0.390779	−	0.156444i
$773$	0.315349	−	6.61998i	0.0113423	−	0.238104i	−0.986076	−	0.166295i	$-0.946820\pi$
$773$	0.315349	−	6.61998i	0.0113423	−	0.238104i	0.997418	−	0.0718093i	$-0.0228773\pi$
$774$	−1.82557	−	1.74068i	−0.0656189	−	0.0625675i
$775$	35.0356	+	27.5523i	1.25851	+	0.989707i
$776$	4.37211	−	5.04568i	0.156949	−	0.181129i
$777$	5.83566	−	2.31407i	0.209353	−	0.0830169i
$778$	6.31824	+	7.29164i	0.226520	+	0.261418i
$779$	−41.4530	+	39.5253i	−1.48521	+	1.41614i
$780$	17.0786	−	1.63081i	0.611513	−	0.0583924i
$781$	32.6755	+	56.5957i	1.16922	+	2.02515i
$782$	−22.4664	−	13.9143i	−0.803395	−	0.497574i
$783$	−3.98538			−0.142426
$784$	1.60566	+	6.81336i	0.0573451	+	0.243334i
$785$	−75.8961	−	22.2851i	−2.70885	−	0.795389i
$786$	11.2233	−	2.16311i	0.400322	−	0.0771557i
$787$	−34.2289	−	17.6462i	−1.22013	−	0.629020i	−0.276815	−	0.960923i	$-0.589279\pi$
$787$	−34.2289	−	17.6462i	−1.22013	−	0.629020i	−0.943314	+	0.331903i	$0.892309\pi$
$788$	17.0260	+	3.28150i	0.606527	+	0.116899i
$789$	−14.6923	−	11.5542i	−0.523061	−	0.411339i
$790$	20.2561	−	5.94772i	0.720678	−	0.211610i
$791$	−17.2062	−	16.5142i	−0.611783	−	0.587176i
$792$	−0.624982	−	4.34685i	−0.0222078	−	0.154458i
$793$	56.7180	+	5.41591i	2.01412	+	0.192325i
$794$	1.78659	−	2.50892i	0.0634039	−	0.0890383i
$795$	8.00527	−	6.29541i	0.283918	−	0.223275i
$796$	−22.2596	+	11.4756i	−0.788972	+	0.406743i
$797$	14.7052	−	4.31784i	0.520885	−	0.152946i	−0.0107126	−	0.999943i	$-0.503410\pi$
$797$	14.7052	−	4.31784i	0.520885	−	0.152946i	0.531598	+	0.846997i	$0.321592\pi$
$798$	8.45289	+	9.82004i	0.299229	+	0.347626i
$799$	−18.0604	+	20.8428i	−0.638930	+	0.737364i
$800$	0.323754	+	6.79643i	0.0114464	+	0.240290i
$801$	0.198756	−	0.574267i	0.00702268	−	0.0202907i
$802$	−5.71956	−	23.5763i	−0.201965	−	0.832509i
$803$	−2.19229	−	3.07864i	−0.0773642	−	0.108643i
$804$	13.5057			0.476311
$805$	−41.6601	+	12.8414i	−1.46833	+	0.452599i
$806$	32.7108			1.15219
$807$	−15.0295	−	21.1060i	−0.529065	−	0.742967i
$808$	3.37737	+	13.9217i	0.118816	+	0.489764i
$809$	−14.4274	+	41.6853i	−0.507241	+	1.46558i	0.343078	+	0.939307i	$0.388531\pi$
$809$	−14.4274	+	41.6853i	−0.507241	+	1.46558i	−0.850318	+	0.526269i	$0.823591\pi$
$810$	−0.163478	−	3.43182i	−0.00574403	−	0.120582i
$811$	−13.2674	+	15.3114i	−0.465882	+	0.537656i	−0.939262	−	0.343202i	$-0.888488\pi$
$811$	−13.2674	+	15.3114i	−0.465882	+	0.537656i	0.473380	+	0.880858i	$0.343034\pi$
$812$	−10.3603	+	1.96156i	−0.363574	+	0.0688374i
$813$	−3.96208	+	1.16337i	−0.138956	+	0.0408012i
$814$	−9.26173	+	4.77475i	−0.324624	+	0.167355i
$815$	−31.6997	+	24.9289i	−1.11039	+	0.873221i
$816$	3.19626	−	4.48851i	0.111891	−	0.157129i
$817$	−12.2972	−	1.17424i	−0.430224	−	0.0410814i
$818$	4.85010	+	33.7332i	0.169580	+	1.17945i
$819$	−12.6886	+	3.68056i	−0.443375	+	0.128609i
$820$	38.5549	−	11.3207i	1.34639	−	0.395337i
$821$	15.7309	+	12.3709i	0.549011	+	0.431747i	0.853746	−	0.520690i	$-0.174325\pi$
$821$	15.7309	+	12.3709i	0.549011	+	0.431747i	−0.304735	+	0.952437i	$0.598568\pi$
$822$	11.6093	+	2.23751i	0.404921	+	0.0780422i
$823$	−10.2575	−	5.28810i	−0.357553	−	0.184331i	0.270085	−	0.962836i	$-0.412948\pi$
$823$	−10.2575	−	5.28810i	−0.357553	−	0.184331i	−0.627638	+	0.778505i	$0.715978\pi$
$824$	13.4923	−	2.60043i	0.470027	−	0.0905903i
$825$	28.6703	+	8.41836i	0.998172	+	0.293090i
$826$	−8.38754	+	11.6973i	−0.291840	+	0.407000i
$827$	25.3334			0.880929			0.440464	−	0.897770i	$-0.354814\pi$
$827$	25.3334			0.880929			0.440464	+	0.897770i	$0.354814\pi$
$828$	−3.20062	−	3.57156i	−0.111229	−	0.124120i
$829$	13.4303	+	23.2620i	0.466454	+	0.807922i	0.999266	−	0.0383118i	$-0.0121980\pi$
$829$	13.4303	+	23.2620i	0.466454	+	0.807922i	−0.532812	+	0.846234i	$0.678865\pi$
$830$	47.7414	−	4.55875i	1.65713	−	0.158236i
$831$	10.0270	−	9.56070i	0.347832	−	0.331657i
$832$	3.27006	+	3.77385i	0.113369	+	0.130835i
$833$	25.0674	+	29.3156i	0.868533	+	1.01572i
$834$	−10.6520	+	12.2931i	−0.368848	+	0.425674i
$835$	−36.7422	−	28.8944i	−1.27152	−	0.999931i
$836$	−15.5651	−	14.8413i	−0.538331	−	0.513298i
$837$	0.311692	−	6.54323i	0.0107737	−	0.226167i
$838$	14.2706	+	5.71310i	0.492971	+	0.197356i
$839$	1.42241	+	3.11465i	0.0491071	+	0.107530i	0.932595	−	0.360924i	$-0.117539\pi$
$839$	1.42241	+	3.11465i	0.0491071	+	0.107530i	−0.883488	+	0.468454i	$0.844811\pi$
$840$	−2.11408	−	8.84079i	−0.0729427	−	0.305036i
$841$	1.86671	+	12.9832i	0.0643693	+	0.447698i
$842$	−8.46926	+	4.36621i	−0.291870	+	0.150469i
$843$	−7.06116	−	6.73280i	−0.243199	−	0.231890i
$844$	−11.2090	+	4.48739i	−0.385828	+	0.154462i
$845$	13.4118	+	38.7508i	0.461380	+	1.33307i
$846$	−4.21050	+	2.70592i	−0.144760	+	0.0930315i
$847$	−21.9217	−	0.0718838i	−0.753238	−	0.00246996i
$848$	2.84413	+	0.835110i	0.0976677	+	0.0286778i
$849$	−1.45695	−	2.04601i	−0.0500025	−	0.0702187i
$850$	18.7462	+	32.4694i	0.642990	+	1.11369i
$851$	−5.52451	+	9.94834i	−0.189378	+	0.341025i
$852$	−7.44056	+	12.8874i	−0.254909	+	0.441516i
$853$	−7.85668	+	17.2037i	−0.269008	+	0.589045i	−0.995136	−	0.0985150i	$-0.968591\pi$
$853$	−7.85668	+	17.2037i	−0.269008	+	0.589045i	0.726128	+	0.687560i	$0.241318\pi$
$854$	−1.33752	−	30.1583i	−0.0457689	−	1.03200i
$855$	−11.0185	−	12.7160i	−0.376825	−	0.434879i
$856$	0.732293	+	15.3727i	0.0250292	+	0.525428i
$857$	7.71215	+	1.48639i	0.263442	+	0.0507743i	0.319262	−	0.947667i	$-0.396565\pi$
$857$	7.71215	+	1.48639i	0.263442	+	0.0507743i	−0.0558197	+	0.998441i	$0.517777\pi$
$858$	20.3584	−	8.15029i	0.695025	−	0.278246i
$859$	−12.9106	+	53.2181i	−0.440503	+	1.81578i	0.126384	+	0.991981i	$0.459663\pi$
$859$	−12.9106	+	53.2181i	−0.440503	+	1.81578i	−0.566887	+	0.823796i	$0.691852\pi$
$860$	7.29062	+	4.68540i	0.248608	+	0.159771i
$861$	−27.5500	+	14.0889i	−0.938902	+	0.480147i
$862$	12.0218	+	26.3242i	0.409466	+	0.896605i
$863$	−12.4425	−	1.18812i	−0.423549	−	0.0404441i	−0.118895	−	0.992907i	$-0.537935\pi$
$863$	−12.4425	−	1.18812i	−0.423549	−	0.0404441i	−0.304655	+	0.952463i	$0.598541\pi$
$864$	0.786053	−	0.618159i	0.0267421	−	0.0210302i
$865$	1.29386	−	27.1615i	0.0439926	−	0.923519i
$866$	0.325298	−	1.34089i	0.0110541	−	0.0455655i
$867$	1.90173	−	13.2268i	0.0645860	−	0.449205i
$868$	−2.41025	−	17.1630i	−0.0818091	−	0.582549i
$869$	22.7008	−	14.5889i	0.770070	−	0.494894i
$870$	13.4452	−	2.59135i	0.455834	−	0.0878549i
$871$	15.8999	+	65.5401i	0.538746	+	2.22074i
$872$	−5.81680	+	0.555437i	−0.196982	+	0.0188095i
$873$	3.33820	−	5.78192i	0.112981	−	0.195688i
$874$	−23.1331	−	4.05958i	−0.782489	−	0.137317i
$875$	16.0931	+	3.15645i	0.544045	+	0.106707i
$876$	0.357513	−	0.782845i	0.0120793	−	0.0264499i
$877$	−30.0440	+	28.6469i	−1.01451	+	0.967336i	−0.999470	−	0.0325504i	$-0.989637\pi$
$877$	−30.0440	+	28.6469i	−1.01451	+	0.967336i	−0.0150431	+	0.999887i	$0.504789\pi$
$878$	3.58698	−	10.3639i	0.121055	−	0.349765i
$879$	15.4638	+	7.97214i	0.521581	+	0.268894i
$880$	4.93483	+	14.2583i	0.166353	+	0.480646i
$881$	−4.44467	+	30.9134i	−0.149745	+	1.04150i	0.766892	+	0.641777i	$0.221802\pi$
$881$	−4.44467	+	30.9134i	−0.149745	+	1.04150i	−0.916636	+	0.399722i	$0.869107\pi$
$882$	2.86608	+	6.38636i	0.0965061	+	0.215040i
$883$	26.1034	+	16.7756i	0.878450	+	0.564545i	0.900326	−	0.435215i	$-0.143328\pi$
$883$	26.1034	+	16.7756i	0.878450	+	0.564545i	−0.0218768	+	0.999761i	$0.506964\pi$
$884$	25.5445	+	10.2265i	0.859156	+	0.343954i
$885$	10.8420	−	15.2255i	0.364450	−	0.511799i
$886$	−3.83201	+	5.38131i	−0.128739	+	0.180789i
$887$	15.4974	+	6.20422i	0.520351	+	0.208317i	0.616944	−	0.787007i	$-0.288370\pi$
$887$	15.4974	+	6.20422i	0.520351	+	0.208317i	−0.0965932	+	0.995324i	$0.530795\pi$
$888$	−1.99609	−	1.28281i	−0.0669844	−	0.0430483i
$889$	−0.433914	+	0.0399984i	−0.0145530	+	0.00134150i
$890$	−0.297131	+	2.06659i	−0.00995987	+	0.0692724i
$891$	−1.43633	−	4.15001i	−0.0481190	−	0.139031i
$892$	−3.48504	−	1.79666i	−0.116688	−	0.0601568i
$893$	−8.01680	+	23.1630i	−0.268272	+	0.775121i
$894$	0.0876914	−	0.0836136i	0.00293284	−	0.00279646i
$895$	18.6745	−	40.8915i	0.624221	−	1.36685i
$896$	1.73915	−	1.99383i	0.0581008	−	0.0666093i
$897$	13.5639	−	19.7365i	0.452887	−	0.658983i
$898$	7.65213	−	13.2539i	0.255355	−	0.442288i
$899$	25.9886	−	2.48161i	0.866768	−	0.0827663i
$900$	1.60414	+	6.61234i	0.0534712	+	0.220411i
$901$	16.0383	−	3.09113i	0.534313	−	0.102980i
$902$	43.2080	−	27.7681i	1.43867	−	0.924577i
$903$	−6.18752	−	2.50068i	−0.205908	−	0.0832175i
$904$	−1.28283	+	8.92230i	−0.0426664	+	0.296751i
$905$	3.94826	−	16.2750i	0.131245	−	0.540998i
$906$	0.0447064	−	0.938502i	0.00148527	−	0.0311796i
$907$	−4.05423	+	3.18828i	−0.134619	+	0.105865i	−0.683198	−	0.730233i	$-0.739411\pi$
$907$	−4.05423	+	3.18828i	−0.134619	+	0.105865i	0.548579	+	0.836099i	$0.315169\pi$
$908$	4.37625	+	0.417881i	0.145231	+	0.0138679i
$909$	5.95104	+	13.0310i	0.197384	+	0.432210i
$910$	40.4134	−	20.6671i	1.33969	−	0.685108i
$911$	−20.0671	−	12.8964i	−0.664854	−	0.427276i	0.164213	−	0.986425i	$-0.447492\pi$
$911$	−20.0671	−	12.8964i	−0.664854	−	0.427276i	−0.829067	+	0.559149i	$0.811128\pi$
$912$	1.15458	−	4.75925i	0.0382320	−	0.157595i
$913$	56.9097	−	22.7832i	1.88344	−	0.754014i
$914$	−14.2895	−	2.75407i	−0.472654	−	0.0910966i
$915$	1.86528	+	39.1571i	0.0616643	+	1.29449i
$916$	−3.75121	−	4.32912i	−0.123943	−	0.143038i
$917$	25.4934	−	16.2658i	0.841867	−	0.537143i
$918$	2.28904	−	5.01230i	0.0755495	−	0.165430i
$919$	5.36229	−	9.28777i	0.176886	−	0.306375i	−0.763927	−	0.645303i	$-0.776731\pi$
$919$	5.36229	−	9.28777i	0.176886	−	0.306375i	0.940812	+	0.338928i	$0.110064\pi$
$920$	13.1200	+	9.96802i	0.432553	+	0.328636i
$921$	−10.0568	−	17.4189i	−0.331382	−	0.573971i
$922$	−10.2325	−	14.3695i	−0.336989	−	0.473235i
$923$	−71.2991	−	20.9353i	−2.34684	−	0.689094i
$924$	−5.77644	−	10.0813i	−0.190031	−	0.331650i
$925$	13.5817	−	8.72842i	0.446563	−	0.286989i
$926$	−0.584059	−	1.68753i	−0.0191934	−	0.0554556i
$927$	12.7564	−	5.10688i	0.418974	−	0.167732i
$928$	2.88435	+	2.75023i	0.0946836	+	0.0902806i
$929$	−50.5086	+	26.0390i	−1.65714	+	0.854312i	−0.662709	+	0.748877i	$0.730593\pi$
$929$	−50.5086	+	26.0390i	−1.65714	+	0.854312i	−0.994426	+	0.105435i	$0.966376\pi$
$930$	3.20296	+	22.2771i	0.105029	+	0.730494i
$931$	30.3666	+	15.9080i	0.995224	+	0.521363i
$932$	−5.36389	−	11.7453i	−0.175700	−	0.384730i
$933$	9.78000	+	3.91532i	0.320183	+	0.128182i
$934$	−0.536254	+	11.2574i	−0.0175468	+	0.368352i
$935$	60.1706	+	57.3726i	1.96779	+	1.87628i
$936$	3.92517	+	3.08679i	0.128298	+	0.100895i
$937$	25.8845	−	29.8723i	0.845611	−	0.975887i	−0.154316	−	0.988022i	$-0.549317\pi$
$937$	25.8845	−	29.8723i	0.845611	−	0.975887i	0.999926	+	0.0121347i	$0.00386269\pi$
$938$	33.2166	−	13.1717i	1.08456	−	0.430071i
$939$	14.3681	+	16.5817i	0.468886	+	0.541123i
$940$	12.4452	−	11.8665i	0.405918	−	0.387042i
$941$	−9.93001	+	0.948201i	−0.323709	+	0.0309105i	−0.255646	−	0.966771i	$-0.582288\pi$
$941$	−9.93001	+	0.948201i	−0.323709	+	0.0309105i	−0.0680633	+	0.997681i	$0.521682\pi$
$942$	−11.5115	−	19.9384i	−0.375064	−	0.649629i
$943$	22.4463	−	51.4026i	0.730952	−	1.67390i
$944$	5.44029			0.177066
$945$	−3.74901	−	8.28094i	−0.121955	−	0.269379i
$946$	10.6287	+	3.12086i	0.345568	+	0.101468i
$947$	−3.75959	+	0.724601i	−0.122170	+	0.0235464i	−0.249970	−	0.968254i	$-0.580421\pi$
$947$	−3.75959	+	0.724601i	−0.122170	+	0.0235464i	0.127800	+	0.991800i	$0.459209\pi$
$948$	5.46157	+	2.81563i	0.177384	+	0.0914476i
$949$	4.21985	+	0.813309i	0.136982	+	0.0264011i
$950$	26.1928	+	20.5982i	0.849806	+	0.668294i
$951$	−18.7175	+	5.49597i	−0.606958	+	0.178219i
$952$	3.48351	−	14.1564i	0.112901	−	0.458813i
$953$	2.29526	+	15.9639i	0.0743507	+	0.517121i	0.992630	+	0.121187i	$0.0386700\pi$
$953$	2.29526	+	15.9639i	0.0743507	+	0.517121i	−0.918279	+	0.395934i	$0.870421\pi$
$954$	2.95077	+	0.281765i	0.0955348	+	0.00912247i
$955$	35.0093	−	49.1637i	1.13287	−	1.59090i
$956$	−13.3012	+	10.4602i	−0.430193	+	0.338307i
$957$	15.5564	−	8.01987i	0.502866	−	0.259245i
$958$	19.5319	−	5.73510i	0.631049	−	0.185293i
$959$	30.7346	−	5.81915i	0.992472	−	0.187910i
$960$	−2.24991	+	2.59654i	−0.0726157	+	0.0838030i
$961$	0.566746	+	11.8975i	0.0182821	+	0.383789i
$962$	3.87524	−	11.1968i	0.124943	−	0.360998i
$963$	3.62836	+	14.9563i	0.116922	+	0.481961i
$964$	−16.6069	−	23.3211i	−0.534872	−	0.751122i
$965$	40.1825			1.29352
$966$	−11.3550	−	5.66258i	−0.365340	−	0.182191i
$967$	27.4510			0.882764			0.441382	−	0.897319i	$-0.354488\pi$
$967$	27.4510			0.882764			0.441382	+	0.897319i	$0.354488\pi$
$968$	4.80616	+	6.74930i	0.154476	+	0.216931i
$969$	−6.36203	−	26.2246i	−0.204378	−	0.842457i
$970$	−7.50234	+	21.6766i	−0.240886	+	0.695994i
$971$	−1.42601	−	29.9357i	−0.0457630	−	0.960683i	−0.898671	−	0.438622i	$-0.855467\pi$
$971$	−1.42601	−	29.9357i	−0.0457630	−	0.960683i	0.852908	−	0.522061i	$-0.174836\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−14.2089	+	40.6226i	−0.455518	+	1.30230i
$974$	−19.1247	+	5.61552i	−0.612795	+	0.179933i
$975$	−30.1996	+	15.5690i	−0.967162	+	0.498606i
$976$	−8.96886	+	7.05319i	−0.287086	+	0.225767i
$977$	7.30995	−	10.2654i	0.233866	−	0.328419i	−0.680920	−	0.732358i	$-0.738420\pi$
$977$	7.30995	−	10.2654i	0.233866	−	0.328419i	0.914786	+	0.403939i	$0.132359\pi$
$978$	−11.6846	−	1.11575i	−0.373633	−	0.0356776i
$979$	0.379795	+	2.64153i	0.0121383	+	0.0844237i
$980$	−13.8216	−	19.6816i	−0.441515	−	0.628706i
$981$	−5.60657	+	1.64624i	−0.179004	+	0.0525603i
$982$	−26.9342	−	21.1813i	−0.859505	−	0.675922i
$983$	−52.9333	−	10.2020i	−1.68831	−	0.325395i	−0.747482	−	0.664282i	$-0.768737\pi$
$983$	−52.9333	−	10.2020i	−1.68831	−	0.325395i	−0.940827	+	0.338888i	$0.889949\pi$
$984$	10.3954	+	5.35920i	0.331393	+	0.170845i
$985$	−58.4966	+	11.2743i	−1.86386	+	0.359229i
$986$	21.0709	+	6.18696i	0.671033	+	0.197033i
$987$	−7.71648	+	10.7614i	−0.245618	+	0.342540i
$988$	24.4548			0.778009
$989$	11.5487	−	3.60130i	0.367227	−	0.114515i
$990$	7.54405	+	13.0667i	0.239766	+	0.415286i
$991$	6.42496	−	0.613509i	0.204096	−	0.0194888i	0.00749251	−	0.999972i	$-0.497615\pi$
$991$	6.42496	−	0.613509i	0.204096	−	0.0194888i	0.196603	+	0.980483i	$0.437009\pi$
$992$	−4.74093	+	4.52046i	−0.150525	+	0.143525i
$993$	−8.76887	−	10.1198i	−0.278272	−	0.321143i
$994$	−5.73094	+	38.9524i	−0.181774	+	1.23550i
$995$	56.3460	−	65.0267i	1.78629	−	2.06149i
$996$	10.9724	+	8.62877i	0.347673	+	0.273413i
$997$	7.32695	+	6.98623i	0.232047	+	0.221256i	0.797177	−	0.603745i	$-0.206326\pi$
$997$	7.32695	+	6.98623i	0.232047	+	0.221256i	−0.565130	+	0.825002i	$0.691174\pi$
$998$	0.349274	−	7.33217i	0.0110561	−	0.232096i
$999$	−2.20279	−	0.881865i	−0.0696933	−	0.0279010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.121.1	✓	160
7.4	even	3	inner	966.2.y.c.949.8	yes	160
23.4	even	11	inner	966.2.y.c.625.8	yes	160
161.4	even	33	inner	966.2.y.c.487.1	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.121.1	✓	160	1.1	even	1	trivial
966.2.y.c.487.1	yes	160	161.4	even	33	inner
966.2.y.c.625.8	yes	160	23.4	even	11	inner
966.2.y.c.949.8	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.163478 - 3.43182i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.873534 - 2.49739i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(0.580057 + 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.163478 - 3.43182i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.873534 - 2.49739i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(2.70065 - 2.12382i) q^{10} +(2.54735 - 3.57725i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(0.710652 + 4.94269i) q^{13} +(2.54101 - 0.737066i) q^{14} +(-3.29654 + 0.967953i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-5.41067 - 1.04282i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(-4.80880 + 0.926820i) q^{19} +(3.29654 + 0.967953i) q^{20} +(-2.63293 - 0.260130i) q^{21} +4.39154 q^{22} +(3.99070 - 2.65976i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-6.77333 + 0.646774i) q^{25} +(-3.61398 + 3.44592i) q^{26} +(0.654861 + 0.755750i) q^{27} +(2.07433 + 1.64231i) q^{28} +(-2.60987 + 3.01195i) q^{29} +(-2.70065 - 2.12382i) q^{30} +(-4.74093 - 4.52046i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-4.07697 - 1.63217i) q^{33} +(-2.28904 - 5.01230i) q^{34} +(-8.71339 - 2.58955i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-2.10899 + 1.08726i) q^{37} +(-3.54434 - 3.37952i) q^{38} +(4.63583 - 1.85590i) q^{39} +(1.12371 + 3.24675i) q^{40} +(9.83891 - 6.32308i) q^{41} +(-1.31536 - 2.29561i) q^{42} +(2.42026 + 0.710653i) q^{43} +(2.54735 + 3.57725i) q^{44} +(1.71786 + 2.97542i) q^{45} +(4.48141 + 1.70792i) q^{46} +(2.50251 - 4.33448i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(-5.47388 - 4.36311i) q^{49} +(-4.45576 - 5.14222i) q^{50} +(0.262188 + 5.50400i) q^{51} +(-4.90328 - 0.945030i) q^{52} +(-2.75186 + 1.10168i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-12.6929 - 8.15724i) q^{55} +(-0.134555 + 2.64233i) q^{56} +(2.03441 + 4.45474i) q^{57} +(-3.96733 - 0.378834i) q^{58} +(-4.27636 + 3.36296i) q^{59} +(0.163478 - 3.43182i) q^{60} +(2.69001 - 11.0884i) q^{61} +(0.932254 - 6.48397i) q^{62} +(0.367940 + 2.62004i) q^{63} +(0.841254 - 0.540641i) q^{64} +(16.8463 - 3.24685i) q^{65} +(-1.03535 - 4.26775i) q^{66} +(13.4446 - 1.28380i) q^{67} +(2.75512 - 4.77201i) q^{68} +(-3.52563 - 3.25115i) q^{69} +(-2.94488 - 8.59980i) q^{70} +(-6.18184 + 13.5363i) q^{71} +(0.723734 - 0.690079i) q^{72} +(0.281480 - 0.813284i) q^{73} +(-2.10899 - 1.08726i) q^{74} +(2.22542 + 6.42992i) q^{75} +(0.696958 - 4.84745i) q^{76} +(-6.70857 - 9.48655i) q^{77} +(4.20082 + 2.69970i) q^{78} +(5.70448 + 2.28373i) q^{79} +(-1.99291 + 2.79865i) q^{80} +(0.580057 - 0.814576i) q^{81} +(10.8578 + 4.34679i) q^{82} +(11.7429 + 7.54671i) q^{83} +(1.10697 - 2.40304i) q^{84} +(-2.69425 + 18.7389i) q^{85} +(0.825008 + 2.38371i) q^{86} +(3.54235 + 1.82621i) q^{87} +(-1.43633 + 4.15001i) q^{88} +(-0.439805 + 0.419353i) q^{89} +(-1.42725 + 3.12524i) q^{90} +(12.9646 + 2.54284i) q^{91} +(1.20824 + 4.64114i) q^{92} +(-3.27532 + 5.67303i) q^{93} +(4.98236 - 0.475758i) q^{94} +(3.96681 + 16.3514i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-5.61654 + 3.60953i) q^{97} +(0.378921 - 6.98974i) q^{98} +(-0.624982 + 4.34685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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