LMFDB - Embedded newform 462.2.ba.a.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	462.73
Dual form			462.2.ba.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994522 - 0.104528i) q^{2} +(0.743145 - 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(1.49050 - 3.34771i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49930 + 0.868052i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.994522 - 0.104528i) q^{2} +(0.743145 - 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(1.49050 - 3.34771i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49930 + 0.868052i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +(-1.83226 + 3.17357i) q^{10} +(-0.883524 - 3.19678i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-3.29791 - 2.39607i) q^{13} +(2.57634 - 0.602049i) q^{14} +(-1.13240 - 3.48517i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.136960 + 1.30308i) q^{17} +(-0.207912 + 0.978148i) q^{18} +(-0.940905 + 0.199996i) q^{19} +(2.15395 - 2.96466i) q^{20} +(-1.27650 + 2.31744i) q^{21} +(0.544530 + 3.27162i) q^{22} +(3.93007 + 6.80708i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-5.63993 - 6.26378i) q^{25} +(3.02939 + 2.72767i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-2.62516 + 0.329450i) q^{28} +(-1.43135 + 0.465074i) q^{29} +(0.761898 + 3.58445i) q^{30} +(-0.606600 - 1.36245i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.79565 - 1.78448i) q^{33} -1.31026i q^{34} +(-0.819209 + 9.66075i) q^{35} +(0.309017 - 0.951057i) q^{36} +(1.36730 - 1.51854i) q^{37} +(0.956656 - 0.100549i) q^{38} +(-4.05411 + 0.426104i) q^{39} +(-2.45205 + 2.72327i) q^{40} +(3.28216 - 10.1015i) q^{41} +(1.51175 - 2.17132i) q^{42} +0.458990i q^{43} +(-0.199569 - 3.31062i) q^{44} +(-3.17357 - 1.83226i) q^{45} +(-3.19701 - 7.18059i) q^{46} +(0.0864441 + 0.406687i) q^{47} +(0.951057 - 0.309017i) q^{48} +(5.49297 - 4.33904i) q^{49} +(4.95429 + 6.81900i) q^{50} +(0.973714 + 0.876736i) q^{51} +(-2.72767 - 3.02939i) q^{52} +(10.0534 - 4.47606i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-12.0188 - 1.80700i) q^{55} +(2.64522 - 0.0532409i) q^{56} +(-0.565406 + 0.778214i) q^{57} +(1.47212 - 0.312909i) q^{58} +(2.74043 - 12.8927i) q^{59} +(-0.383047 - 3.64445i) q^{60} +(-6.10482 - 2.71804i) q^{61} +(0.460863 + 1.41839i) q^{62} +(0.602049 + 2.57634i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-12.9369 + 7.46911i) q^{65} +(2.59380 + 2.06692i) q^{66} +(-3.48564 + 6.03731i) q^{67} +(-0.136960 + 1.30308i) q^{68} +(7.47544 + 2.42892i) q^{69} +(1.82454 - 9.52220i) q^{70} +(-7.01690 + 5.09808i) q^{71} +(-0.406737 + 0.913545i) q^{72} +(0.502494 + 0.106808i) q^{73} +(-1.51854 + 1.36730i) q^{74} +(-8.38257 - 0.881044i) q^{75} -0.961925 q^{76} +(4.98316 + 7.22275i) q^{77} +4.07644 q^{78} +(12.2376 + 1.28623i) q^{79} +(2.72327 - 2.45205i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-4.32008 + 9.70305i) q^{82} +(12.9276 - 9.39245i) q^{83} +(-1.73043 + 2.00140i) q^{84} +(4.56649 + 1.48374i) q^{85} +(0.0479776 - 0.456476i) q^{86} +(-0.752505 + 1.30338i) q^{87} +(-0.147577 + 3.31334i) q^{88} +(-13.1670 + 7.60195i) q^{89} +(2.96466 + 2.15395i) q^{90} +(10.3224 + 3.12574i) q^{91} +(2.42892 + 7.47544i) q^{92} +(-1.36245 - 0.606600i) q^{93} +(-0.0434601 - 0.413495i) q^{94} +(-0.732889 + 3.44797i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(-5.79075 + 7.97028i) q^{97} +(-5.91643 + 3.74110i) q^{98} +(-3.27162 + 0.544530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.994522	−	0.104528i	−0.703233	−	0.0739128i
$2$	−0.994522	−	0.104528i	−0.703233	−	0.0739128i
$3$	0.743145	−	0.669131i	0.429055	−	0.386323i
$3$	0.743145	−	0.669131i	0.429055	−	0.386323i
$4$	0.978148	+	0.207912i	0.489074	+	0.103956i
$5$	1.49050	−	3.34771i	0.666570	−	1.49714i	−0.190363	−	0.981714i	$-0.560966\pi$
$5$	1.49050	−	3.34771i	0.666570	−	1.49714i	0.856933	−	0.515428i	$-0.172367\pi$
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−2.49930	+	0.868052i	−0.944646	+	0.328093i
$7$	−2.49930	+	0.868052i	−0.944646	+	0.328093i
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	0.104528	−	0.994522i	0.0348428	−	0.331507i
$10$	−1.83226	+	3.17357i	−0.579412	+	1.00357i
$11$	−0.883524	−	3.19678i	−0.266392	−	0.963865i
$11$	−0.883524	−	3.19678i	−0.266392	−	0.963865i
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−3.29791	−	2.39607i	−0.914676	−	0.664551i	0.0275170	−	0.999621i	$-0.491240\pi$
$13$	−3.29791	−	2.39607i	−0.914676	−	0.664551i	−0.942193	+	0.335070i	$0.891240\pi$
$14$	2.57634	−	0.602049i	0.688556	−	0.160904i
$15$	−1.13240	−	3.48517i	−0.292385	−	0.899867i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.136960	+	1.30308i	0.0332176	+	0.316044i	0.998496	+	0.0548216i	$0.0174590\pi$
$17$	0.136960	+	1.30308i	0.0332176	+	0.316044i	−0.965279	+	0.261223i	$0.915874\pi$
$18$	−0.207912	+	0.978148i	−0.0490053	+	0.230552i
$19$	−0.940905	+	0.199996i	−0.215858	+	0.0458821i	−0.314571	−	0.949234i	$-0.601861\pi$
$19$	−0.940905	+	0.199996i	−0.215858	+	0.0458821i	0.0987130	+	0.995116i	$0.468527\pi$
$20$	2.15395	−	2.96466i	0.481639	−	0.662919i
$21$	−1.27650	+	2.31744i	−0.278555	+	0.505708i
$22$	0.544530	+	3.27162i	0.116094	+	0.697511i
$23$	3.93007	+	6.80708i	0.819476	+	1.41937i	0.906069	+	0.423130i	$0.139069\pi$
$23$	3.93007	+	6.80708i	0.819476	+	1.41937i	−0.0865929	+	0.996244i	$0.527598\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	−5.63993	−	6.26378i	−1.12799	−	1.25276i
$26$	3.02939	+	2.72767i	0.594112	+	0.534941i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−2.62516	+	0.329450i	−0.496109	+	0.0622601i
$29$	−1.43135	+	0.465074i	−0.265795	+	0.0863621i	−0.438883	−	0.898544i	$-0.644626\pi$
$29$	−1.43135	+	0.465074i	−0.265795	+	0.0863621i	0.173088	+	0.984906i	$0.444626\pi$
$30$	0.761898	+	3.58445i	0.139103	+	0.654427i
$31$	−0.606600	−	1.36245i	−0.108949	−	0.244703i	0.850841	−	0.525424i	$-0.176093\pi$
$31$	−0.606600	−	1.36245i	−0.108949	−	0.244703i	−0.959789	+	0.280721i	$0.909426\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.79565	−	1.78448i	−0.486660	−	0.310637i
$34$		−	1.31026i		−	0.224708i
$35$	−0.819209	+	9.66075i	−0.138472	+	1.63296i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	1.36730	−	1.51854i	0.224782	−	0.249646i	−0.620196	−	0.784447i	$-0.712947\pi$
$37$	1.36730	−	1.51854i	0.224782	−	0.249646i	0.844978	+	0.534801i	$0.179614\pi$
$38$	0.956656	−	0.100549i	0.155190	−	0.0163111i
$39$	−4.05411	+	0.426104i	−0.649177	+	0.0682313i
$40$	−2.45205	+	2.72327i	−0.387702	+	0.430587i
$41$	3.28216	−	10.1015i	0.512588	−	1.57758i	−0.275040	−	0.961433i	$-0.588691\pi$
$41$	3.28216	−	10.1015i	0.512588	−	1.57758i	0.787628	−	0.616151i	$-0.211309\pi$
$42$	1.51175	−	2.17132i	0.233267	−	0.335042i
$43$			0.458990i			0.0699954i	0.999387	+	0.0349977i	$0.0111424\pi$
$43$			0.458990i			0.0699954i	−0.999387	+	0.0349977i	$0.988858\pi$
$44$	−0.199569	−	3.31062i	−0.0300862	−	0.499094i
$45$	−3.17357	−	1.83226i	−0.473088	−	0.273138i
$46$	−3.19701	−	7.18059i	−0.471373	−	1.05872i
$47$	0.0864441	+	0.406687i	0.0126092	+	0.0593214i	0.984002	−	0.178155i	$-0.0570130\pi$
$47$	0.0864441	+	0.406687i	0.0126092	+	0.0593214i	−0.971393	+	0.237477i	$0.923680\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	5.49297	−	4.33904i	0.784710	−	0.619863i
$50$	4.95429	+	6.81900i	0.700643	+	0.964352i
$51$	0.973714	+	0.876736i	0.136347	+	0.122768i
$52$	−2.72767	−	3.02939i	−0.378260	−	0.420100i
$53$	10.0534	−	4.47606i	1.38094	−	0.614834i	0.424145	−	0.905594i	$-0.360575\pi$
$53$	10.0534	−	4.47606i	1.38094	−	0.614834i	0.956796	+	0.290760i	$0.0939081\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−12.0188	−	1.80700i	−1.62061	−	0.243656i
$56$	2.64522	−	0.0532409i	0.353482	−	0.00711461i
$57$	−0.565406	+	0.778214i	−0.0748898	+	0.103077i
$58$	1.47212	−	0.312909i	0.193299	−	0.0410870i
$59$	2.74043	−	12.8927i	0.356774	−	1.67849i	−0.324048	−	0.946041i	$-0.605044\pi$
$59$	2.74043	−	12.8927i	0.356774	−	1.67849i	0.680822	−	0.732449i	$-0.261623\pi$
$60$	−0.383047	−	3.64445i	−0.0494512	−	0.470497i
$61$	−6.10482	−	2.71804i	−0.781642	−	0.348009i	−0.0231838	−	0.999731i	$-0.507380\pi$
$61$	−6.10482	−	2.71804i	−0.781642	−	0.348009i	−0.758458	+	0.651722i	$0.774047\pi$
$62$	0.460863	+	1.41839i	0.0585296	+	0.180136i
$63$	0.602049	+	2.57634i	0.0758510	+	0.324589i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−12.9369	+	7.46911i	−1.60462	+	0.926430i
$66$	2.59380	+	2.06692i	0.319275	+	0.254421i
$67$	−3.48564	+	6.03731i	−0.425839	+	0.737575i	−0.996498	−	0.0836119i	$-0.973354\pi$
$67$	−3.48564	+	6.03731i	−0.425839	+	0.737575i	0.570659	+	0.821187i	$0.306688\pi$
$68$	−0.136960	+	1.30308i	−0.0166088	+	0.158022i
$69$	7.47544	+	2.42892i	0.899937	+	0.292407i
$70$	1.82454	−	9.52220i	0.218075	−	1.13812i
$71$	−7.01690	+	5.09808i	−0.832753	+	0.605031i	−0.920337	−	0.391126i	$-0.872086\pi$
$71$	−7.01690	+	5.09808i	−0.832753	+	0.605031i	0.0875836	+	0.996157i	$0.472086\pi$
$72$	−0.406737	+	0.913545i	−0.0479344	+	0.107662i
$73$	0.502494	+	0.106808i	0.0588124	+	0.0125010i	0.237224	−	0.971455i	$-0.423762\pi$
$73$	0.502494	+	0.106808i	0.0588124	+	0.0125010i	−0.178411	+	0.983956i	$0.557096\pi$
$74$	−1.51854	+	1.36730i	−0.176526	+	0.158945i
$75$	−8.38257	−	0.881044i	−0.967936	−	0.101734i
$76$	−0.961925			−0.110340
$77$	4.98316	+	7.22275i	0.567883	+	0.823109i
$78$	4.07644			0.461566
$79$	12.2376	+	1.28623i	1.37684	+	0.144712i	0.763858	−	0.645385i	$-0.223303\pi$
$79$	12.2376	+	1.28623i	1.37684	+	0.144712i	0.612983	+	0.790096i	$0.289970\pi$
$80$	2.72327	−	2.45205i	0.304471	−	0.274147i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−4.32008	+	9.70305i	−0.477072	+	1.07152i
$83$	12.9276	−	9.39245i	1.41899	−	1.03096i	0.427051	−	0.904227i	$-0.359552\pi$
$83$	12.9276	−	9.39245i	1.41899	−	1.03096i	0.991937	−	0.126728i	$-0.0404476\pi$
$84$	−1.73043	+	2.00140i	−0.188805	+	0.218371i
$85$	4.56649	+	1.48374i	0.495305	+	0.160934i
$86$	0.0479776	−	0.456476i	0.00517355	−	0.0492231i
$87$	−0.752505	+	1.30338i	−0.0806771	+	0.139737i
$88$	−0.147577	+	3.31334i	−0.0157318	+	0.353203i
$89$	−13.1670	+	7.60195i	−1.39570	+	0.805805i	−0.993938	−	0.109941i	$-0.964934\pi$
$89$	−13.1670	+	7.60195i	−1.39570	+	0.805805i	−0.401757	+	0.915746i	$0.631600\pi$
$90$	2.96466	+	2.15395i	0.312503	+	0.227047i
$91$	10.3224	+	3.12574i	1.08208	+	0.327667i
$92$	2.42892	+	7.47544i	0.253232	+	0.779368i
$93$	−1.36245	−	0.606600i	−0.141279	−	0.0629015i
$94$	−0.0434601	−	0.413495i	−0.00448257	−	0.0426488i
$95$	−0.732889	+	3.44797i	−0.0751928	+	0.353754i
$96$	−0.978148	+	0.207912i	−0.0998318	+	0.0212199i
$97$	−5.79075	+	7.97028i	−0.587962	+	0.809260i	−0.994540	−	0.104356i	$-0.966722\pi$
$97$	−5.79075	+	7.97028i	−0.587962	+	0.809260i	0.406578	+	0.913616i	$0.366722\pi$
$98$	−5.91643	+	3.74110i	−0.597650	+	0.377908i
$99$	−3.27162	+	0.544530i	−0.328810	+	0.0547273i
$100$	−4.21437	−	7.29951i	−0.421437	−	0.729951i
$101$	18.2966	−	8.14618i	1.82058	−	0.810575i	0.875989	−	0.482330i	$-0.160210\pi$
$101$	18.2966	−	8.14618i	1.82058	−	0.810575i	0.944593	−	0.328245i	$-0.106457\pi$
$102$	−0.876736	−	0.973714i	−0.0868098	−	0.0964121i
$103$	10.3172	+	9.28967i	1.01659	+	0.915338i	0.996427	−	0.0844587i	$-0.0269161\pi$
$103$	10.3172	+	9.28967i	1.01659	+	0.915338i	0.0201590	+	0.999797i	$0.493583\pi$
$104$	2.39607	+	3.29791i	0.234954	+	0.323387i
$105$	5.85551	+	7.72749i	0.571440	+	0.754126i
$106$	−10.4662	+	3.40068i	−1.01657	+	0.330303i
$107$	1.23241	+	5.79803i	0.119141	+	0.560516i	0.996709	+	0.0810633i	$0.0258316\pi$
$107$	1.23241	+	5.79803i	0.119141	+	0.560516i	−0.877568	+	0.479453i	$0.840835\pi$
$108$	−0.406737	−	0.913545i	−0.0391383	−	0.0879060i
$109$	5.16991	+	2.98485i	0.495188	+	0.285897i	0.726724	−	0.686929i	$-0.241042\pi$
$109$	5.16991	+	2.98485i	0.495188	+	0.285897i	−0.231536	+	0.972826i	$0.574375\pi$
$110$	11.7640	+	3.05341i	1.12166	+	0.291131i
$111$		−	2.04339i		−	0.193950i
$112$	−2.63629	−	0.223551i	−0.249106	−	0.0211236i
$113$	3.93698	−	12.1168i	0.370360	−	1.13985i	−0.576196	−	0.817312i	$-0.695464\pi$
$113$	3.93698	−	12.1168i	0.370360	−	1.13985i	0.946556	−	0.322539i	$-0.104536\pi$
$114$	0.643654	−	0.714850i	0.0602837	−	0.0669518i
$115$	28.6459	−	3.01080i	2.67124	−	0.280759i
$116$	−1.49677	+	0.157316i	−0.138971	+	0.0146065i
$117$	−2.72767	+	3.02939i	−0.252173	+	0.280067i
$118$	−4.07308	+	12.5356i	−0.374957	+	1.15400i
$119$	−1.47345	−	3.13791i	−0.135071	−	0.287651i
$120$			3.66452i			0.334524i
$121$	−9.43877	+	5.64886i	−0.858070	+	0.513533i
$122$	5.78726	+	3.34128i	0.523954	+	0.302505i
$123$	−4.32008	−	9.70305i	−0.389528	−	0.874894i
$124$	−0.310076	−	1.45879i	−0.0278457	−	0.131003i
$125$	−11.9498	+	3.88271i	−1.06882	+	0.347280i
$126$	−0.329450	−	2.62516i	−0.0293497	−	0.233868i
$127$	5.90035	+	8.12114i	0.523571	+	0.720634i	0.986134	−	0.165953i	$-0.0530698\pi$
$127$	5.90035	+	8.12114i	0.523571	+	0.720634i	−0.462562	+	0.886587i	$0.653070\pi$
$128$	−0.743145	−	0.669131i	−0.0656853	−	0.0591433i
$129$	0.307124	+	0.341096i	0.0270408	+	0.0300319i
$130$	13.6468	−	6.07592i	1.19690	−	0.532894i
$131$	6.42120	+	11.1219i	0.561023	+	0.971721i	0.997407	+	0.0719604i	$0.0229255\pi$
$131$	6.42120	+	11.1219i	0.561023	+	0.971721i	−0.436384	+	0.899760i	$0.643741\pi$
$132$	−2.36354	−	2.32673i	−0.205720	−	0.202516i
$133$	2.17799	−	1.31660i	0.188856	−	0.114164i
$134$	4.09762	−	5.63989i	0.353980	−	0.487212i
$135$	−3.58445	+	0.761898i	−0.308500	+	0.0655737i
$136$	0.272419	−	1.28163i	0.0233597	−	0.109899i
$137$	−0.658120	−	6.26160i	−0.0562270	−	0.534964i	−0.985990	−	0.166805i	$-0.946655\pi$
$137$	−0.658120	−	6.26160i	−0.0562270	−	0.534964i	0.929763	−	0.368159i	$-0.120012\pi$
$138$	−7.18059	−	3.19701i	−0.611253	−	0.272147i
$139$	−2.30986	−	7.10902i	−0.195920	−	0.602979i	−0.999965	−	0.00841039i	$-0.997323\pi$
$139$	−2.30986	−	7.10902i	−0.195920	−	0.602979i	0.804045	−	0.594569i	$-0.202677\pi$
$140$	−2.80989	+	9.27932i	−0.237479	+	0.784245i
$141$	0.336367	+	0.244385i	0.0283272	+	0.0205809i
$142$	7.51136	−	4.33669i	0.630339	−	0.363927i
$143$	−4.74593	+	12.6597i	−0.396874	+	1.05866i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−0.576490	+	5.48494i	−0.0478749	+	0.455499i
$146$	−0.488577	−	0.158748i	−0.0404349	−	0.0131381i
$147$	1.17869	−	6.90005i	0.0972168	−	0.569107i
$148$	1.65314	−	1.20108i	0.135887	−	0.0987278i
$149$	1.95629	−	4.39389i	0.160265	−	0.359961i	−0.815508	−	0.578746i	$-0.803542\pi$
$149$	1.95629	−	4.39389i	0.160265	−	0.359961i	0.975773	+	0.218784i	$0.0702091\pi$
$150$	8.24455	+	1.75243i	0.673165	+	0.143086i
$151$	3.96951	−	3.57416i	0.323034	−	0.290861i	−0.491618	−	0.870811i	$-0.663594\pi$
$151$	3.96951	−	3.57416i	0.323034	−	0.290861i	0.814652	+	0.579949i	$0.196928\pi$
$152$	0.956656	+	0.100549i	0.0775950	+	0.00815557i
$153$	1.31026			0.105928
$154$	−4.20088	−	7.70407i	−0.338516	−	0.620811i
$155$	−5.46521			−0.438976
$156$	−4.05411	−	0.426104i	−0.324589	−	0.0341157i
$157$	−5.08927	+	4.58240i	−0.406168	+	0.365715i	−0.846745	−	0.532000i	$-0.821441\pi$
$157$	−5.08927	+	4.58240i	−0.406168	+	0.365715i	0.440576	+	0.897715i	$0.354774\pi$
$158$	−12.0361	−	2.55836i	−0.957544	−	0.203532i
$159$	4.47606	−	10.0534i	0.354975	−	0.797287i
$160$	−2.96466	+	2.15395i	−0.234377	+	0.170285i
$161$	−15.7313	−	13.6014i	−1.23980	−	1.07194i
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	0.118010	−	1.12279i	0.00924325	−	0.0879436i	−0.988928	−	0.148398i	$-0.952588\pi$
$163$	0.118010	−	1.12279i	0.00924325	−	0.0879436i	0.998171	+	0.0604544i	$0.0192550\pi$
$164$	5.31065	−	9.19832i	0.414692	−	0.718268i
$165$	−10.1408	+	6.69926i	−0.789461	+	0.521537i
$166$	−13.8386	+	7.98970i	−1.07408	+	0.620121i
$167$	14.2712	+	10.3687i	1.10434	+	0.802351i	0.981763	−	0.190107i	$-0.0608836\pi$
$167$	14.2712	+	10.3687i	1.10434	+	0.802351i	0.122579	+	0.992459i	$0.460884\pi$
$168$	1.93015	−	1.80956i	0.148915	−	0.139611i
$169$	1.11783	+	3.44034i	0.0859873	+	0.264642i
$170$	−4.38638	−	1.95294i	−0.336420	−	0.149784i
$171$	0.100549	+	0.956656i	0.00768914	+	0.0731573i
$172$	−0.0954295	+	0.448960i	−0.00727643	+	0.0342329i
$173$	9.44966	−	2.00859i	0.718444	−	0.152710i	0.165839	−	0.986153i	$-0.446967\pi$
$173$	9.44966	−	2.00859i	0.718444	−	0.152710i	0.552606	+	0.833443i	$0.313634\pi$
$174$	0.884623	−	1.21758i	0.0670631	−	0.0923045i
$175$	19.5331	+	10.7593i	1.47657	+	0.813326i
$176$	0.493107	−	3.27976i	0.0371694	−	0.247221i
$177$	−6.59038	−	11.4149i	−0.495363	−	0.857994i
$178$	13.8895	−	6.18398i	1.04106	−	0.463509i
$179$	−13.8943	−	15.4312i	−1.03851	−	1.15338i	−0.987968	−	0.154661i	$-0.950572\pi$
$179$	−13.8943	−	15.4312i	−1.03851	−	1.15338i	−0.0505428	−	0.998722i	$-0.516095\pi$
$180$	−2.72327	−	2.45205i	−0.202981	−	0.182765i
$181$	12.3569	+	17.0078i	0.918481	+	1.26418i	0.964186	+	0.265226i	$0.0854466\pi$
$181$	12.3569	+	17.0078i	0.918481	+	1.26418i	−0.0457049	+	0.998955i	$0.514553\pi$
$182$	−9.93910	−	4.18760i	−0.736735	−	0.310406i
$183$	−6.35549	+	2.06502i	−0.469811	+	0.152651i
$184$	−1.63421	−	7.68837i	−0.120476	−	0.566795i
$185$	−3.04567	−	6.84068i	−0.223922	−	0.502937i
$186$	1.29158	+	0.745692i	0.0947029	+	0.0546768i
$187$	4.04466	−	1.58914i	0.295775	−	0.116209i
$188$			0.415773i			0.0303234i
$189$	2.17132	+	1.51175i	0.157940	+	0.109963i
$190$	1.08928	−	3.35247i	0.0790250	−	0.243214i
$191$	−15.4483	+	17.1571i	−1.11780	+	1.24144i	−0.150284	+	0.988643i	$0.548019\pi$
$191$	−15.4483	+	17.1571i	−1.11780	+	1.24144i	−0.967518	+	0.252802i	$0.918648\pi$
$192$	0.994522	−	0.104528i	0.0717734	−	0.00754369i
$193$	−9.06776	+	0.953059i	−0.652711	+	0.0686027i	−0.425096	−	0.905148i	$-0.639760\pi$
$193$	−9.06776	+	0.953059i	−0.652711	+	0.0686027i	−0.227616	+	0.973751i	$0.573093\pi$
$194$	6.59215	−	7.32132i	0.473289	−	0.525640i
$195$	−4.61617	+	14.2071i	−0.330571	+	1.01739i
$196$	6.27507	−	3.10217i	0.448220	−	0.221583i
$197$			13.6194i			0.970342i	0.874419	+	0.485171i	$0.161243\pi$
$197$			13.6194i			0.970342i	−0.874419	+	0.485171i	$0.838757\pi$
$198$	3.31062	−	0.199569i	0.235275	−	0.0141828i
$199$	−4.34099	−	2.50627i	−0.307725	−	0.177665i	0.338183	−	0.941080i	$-0.390188\pi$
$199$	−4.34099	−	2.50627i	−0.307725	−	0.177665i	−0.645908	+	0.763415i	$0.723521\pi$
$200$	3.42828	+	7.70004i	0.242416	+	0.544475i
$201$	1.44941	+	6.81895i	0.102234	+	0.480972i
$202$	−19.0479	+	6.18904i	−1.34021	+	0.435459i
$203$	3.17366	−	2.40484i	0.222747	−	0.168787i
$204$	0.770152	+	1.06002i	0.0539215	+	0.0742165i
$205$	−28.9247	−	26.0439i	−2.02019	−	1.81899i
$206$	−9.28967	−	10.3172i	−0.647242	−	0.718835i
$207$	7.18059	−	3.19701i	0.499086	−	0.222207i
$208$	−2.03822	−	3.53030i	−0.141325	−	0.244782i
$209$	1.47065	+	2.83116i	0.101727	+	0.195836i
$210$	−5.01569	−	8.29723i	−0.346116	−	0.572563i
$211$	−6.28348	+	8.64847i	−0.432573	+	0.595386i	−0.968541	−	0.248852i	$-0.919947\pi$
$211$	−6.28348	+	8.64847i	−0.432573	+	0.595386i	0.535969	+	0.844238i	$0.319947\pi$
$212$	10.7643	−	2.28803i	0.739298	−	0.157143i
$213$	−1.80330	+	8.48384i	−0.123560	+	0.581303i
$214$	−0.619599	−	5.89509i	−0.0423549	−	0.402980i
$215$	1.53657	+	0.684123i	0.104793	+	0.0466568i
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	2.69875	+	2.87860i	0.183203	+	0.195412i
$218$	−4.82959	−	3.50890i	−0.327101	−	0.237653i
$219$	0.444894	−	0.256860i	0.0300632	−	0.0173570i
$220$	−11.3804	−	4.26636i	−0.767269	−	0.287638i
$221$	2.67060	−	4.62562i	0.179644	−	0.311153i
$222$	−0.213593	+	2.03220i	−0.0143354	+	0.136392i
$223$	−8.71254	−	2.83088i	−0.583435	−	0.189569i	0.00240391	−	0.999997i	$-0.499235\pi$
$223$	−8.71254	−	2.83088i	−0.583435	−	0.189569i	−0.585839	+	0.810428i	$0.699235\pi$
$224$	2.59848	+	0.497894i	0.173618	+	0.0332669i
$225$	−6.81900	+	4.95429i	−0.454600	+	0.330286i
$226$	−5.18196	+	11.6389i	−0.344699	+	0.774207i
$227$	−11.4451	−	2.43274i	−0.759639	−	0.161466i	−0.188223	−	0.982126i	$-0.560273\pi$
$227$	−11.4451	−	2.43274i	−0.759639	−	0.161466i	−0.571417	+	0.820660i	$0.693606\pi$
$228$	−0.714850	+	0.643654i	−0.0473421	+	0.0426270i
$229$	−5.62573	−	0.591288i	−0.371759	−	0.0390734i	−0.0831928	−	0.996533i	$-0.526512\pi$
$229$	−5.62573	−	0.591288i	−0.371759	−	0.0390734i	−0.288566	+	0.957460i	$0.593178\pi$
$230$	−28.8037			−1.89926
$231$	8.53617	+	2.03317i	0.561639	+	0.133773i
$232$	1.50501			0.0988088
$233$	15.3422	+	1.61253i	1.00510	+	0.105640i	0.592750	−	0.805386i	$-0.298042\pi$
$233$	15.3422	+	1.61253i	1.00510	+	0.105640i	0.412348	+	0.911026i	$0.364709\pi$
$234$	3.02939	−	2.72767i	0.198037	−	0.178314i
$235$	1.49032	+	0.316776i	0.0972175	+	0.0206642i
$236$	5.36110	−	12.0412i	0.348978	−	0.783817i
$237$	9.95498	−	7.23272i	0.646646	−	0.469816i
$238$	1.13737	+	3.27473i	0.0737251	+	0.212269i
$239$	−16.1184	−	5.23717i	−1.04261	−	0.338764i	−0.262846	−	0.964838i	$-0.584661\pi$
$239$	−16.1184	−	5.23717i	−1.04261	−	0.338764i	−0.779764	+	0.626073i	$0.784661\pi$
$240$	0.383047	−	3.64445i	0.0247256	−	0.235248i
$241$	4.07564	−	7.05922i	0.262535	−	0.454724i	−0.704380	−	0.709823i	$-0.748775\pi$
$241$	4.07564	−	7.05922i	0.262535	−	0.454724i	0.966915	+	0.255099i	$0.0821081\pi$
$242$	9.97753	−	4.63129i	0.641380	−	0.297711i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−5.40630	−	3.92791i	−0.346103	−	0.251459i
$245$	−6.33858	−	24.8562i	−0.404957	−	1.58800i
$246$	3.28216	+	10.1015i	0.209263	+	0.644046i
$247$	3.58223	+	1.59491i	0.227932	+	0.101482i
$248$	0.155892	+	1.48321i	0.00989915	+	0.0941841i
$249$	3.32230	−	15.6302i	0.210542	−	0.990524i
$250$	12.2901	−	2.61235i	0.777297	−	0.165220i
$251$	7.63843	−	10.5134i	0.482134	−	0.663600i	−0.496779	−	0.867877i	$-0.665484\pi$
$251$	7.63843	−	10.5134i	0.482134	−	0.663600i	0.978913	+	0.204277i	$0.0654842\pi$
$252$	0.0532409	+	2.64522i	0.00335386	+	0.166633i
$253$	18.2884	−	18.5778i	1.14978	−	1.16797i
$254$	−5.01914	−	8.69340i	−0.314929	−	0.545473i
$255$	4.38638	−	1.95294i	0.274686	−	0.122298i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	5.19921	+	4.68139i	0.324318	+	0.292017i	0.815165	−	0.579228i	$-0.196646\pi$
$257$	5.19921	+	4.68139i	0.324318	+	0.292017i	−0.490847	+	0.871246i	$0.663313\pi$
$258$	−0.269788	−	0.371331i	−0.0167963	−	0.0231181i
$259$	−2.09911	+	4.98215i	−0.130432	+	0.309576i
$260$	−14.2071	+	4.61617i	−0.881087	+	0.286282i
$261$	0.312909	+	1.47212i	0.0193686	+	0.0911221i
$262$	−5.22348	−	11.7321i	−0.322708	−	0.724813i
$263$	−5.18336	−	2.99261i	−0.319619	−	0.184532i	0.331604	−	0.943419i	$-0.392410\pi$
$263$	−5.18336	−	2.99261i	−0.319619	−	0.184532i	−0.651223	+	0.758886i	$0.725744\pi$
$264$	2.10739	+	2.56104i	0.129701	+	0.157621i
$265$		−	40.3274i		−	2.47729i
$266$	−2.30369	+	1.08173i	−0.141248	+	0.0663250i
$267$	−4.69826	+	14.4598i	−0.287529	+	0.884923i
$268$	−4.66470	+	5.18068i	−0.284942	+	0.316460i
$269$	−12.9338	+	1.35940i	−0.788589	+	0.0828840i	−0.490257	−	0.871578i	$-0.663097\pi$
$269$	−12.9338	+	1.35940i	−0.788589	+	0.0828840i	−0.298332	+	0.954462i	$0.596430\pi$
$270$	3.64445	−	0.383047i	0.221794	−	0.0233115i
$271$	12.0433	−	13.3754i	0.731579	−	0.812500i	−0.256485	−	0.966548i	$-0.582564\pi$
$271$	12.0433	−	13.3754i	0.731579	−	0.812500i	0.988063	+	0.154048i	$0.0492310\pi$
$272$	−0.404893	+	1.24613i	−0.0245503	+	0.0755579i
$273$	9.76255	−	4.58414i	0.590856	−	0.277445i
$274$			6.29609i			0.380361i
$275$	−15.0409	+	23.5638i	−0.907000	+	1.42095i
$276$	6.80708	+	3.93007i	0.409738	+	0.236562i
$277$	−10.2835	−	23.0972i	−0.617878	−	1.38778i	−0.903148	−	0.429330i	$-0.858750\pi$
$277$	−10.2835	−	23.0972i	−0.617878	−	1.38778i	0.285270	−	0.958447i	$-0.407917\pi$
$278$	1.55411	+	7.31152i	0.0932094	+	0.438516i
$279$	−1.41839	+	0.460863i	−0.0849168	+	0.0275911i
$280$	3.76445	−	8.93477i	0.224969	−	0.533955i
$281$	3.94294	+	5.42699i	0.235216	+	0.323747i	0.910265	−	0.414026i	$-0.135878\pi$
$281$	3.94294	+	5.42699i	0.235216	+	0.323747i	−0.675049	+	0.737773i	$0.735878\pi$
$282$	−0.308980	−	0.278206i	−0.0183995	−	0.0165670i
$283$	13.8317	+	15.3616i	0.822208	+	0.913154i	0.997450	−	0.0713710i	$-0.0227374\pi$
$283$	13.8317	+	15.3616i	0.822208	+	0.913154i	−0.175242	+	0.984525i	$0.556071\pi$
$284$	−7.92352	+	3.52778i	−0.470174	+	0.209335i
$285$	1.76250	+	3.05274i	0.104401	+	0.180829i
$286$	6.04323	−	12.0942i	0.357343	−	0.715148i
$287$	0.565488	+	28.0956i	0.0333797	+	1.65843i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	14.9492	−	3.17756i	0.879367	−	0.186915i
$290$	1.14666	−	5.39463i	0.0673344	−	0.316784i
$291$	1.02979	+	9.79784i	0.0603676	+	0.574360i
$292$	0.469306	+	0.208949i	0.0274641	+	0.0122278i
$293$	−4.22103	−	12.9910i	−0.246595	−	0.758942i	−0.995370	−	0.0961173i	$-0.969358\pi$
$293$	−4.22103	−	12.9910i	−0.246595	−	0.758942i	0.748775	−	0.662824i	$-0.230642\pi$
$294$	−1.89349	+	6.73904i	−0.110430	+	0.393029i
$295$	−39.0765	−	28.3907i	−2.27512	−	1.65297i
$296$	−1.76963	+	1.02170i	−0.102858	+	0.0593848i
$297$	−2.06692	+	2.59380i	−0.119935	+	0.150508i
$298$	−2.40486	+	4.16533i	−0.139310	+	0.241291i
$299$	3.34924	−	31.8659i	0.193691	−	1.84285i
$300$	−8.01621	−	2.60462i	−0.462816	−	0.150378i
$301$	−0.398427	−	1.14715i	−0.0229650	−	0.0661208i
$302$	−4.32137	+	3.13966i	−0.248667	+	0.180667i
$303$	8.14618	−	18.2966i	0.467986	−	1.05111i
$304$	−0.940905	−	0.199996i	−0.0539646	−	0.0114705i
$305$	−18.1984	+	16.3859i	−1.04204	+	0.938256i
$306$	−1.30308	−	0.136960i	−0.0744923	−	0.00782946i
$307$	18.9146			1.07951			0.539755	−	0.841822i	$-0.318517\pi$
$307$	18.9146			1.07951			0.539755	+	0.841822i	$0.318517\pi$
$308$	3.37257	+	8.10097i	0.192170	+	0.461596i
$309$	13.8832			0.789787
$310$	5.43527	+	0.571270i	0.308703	+	0.0324460i
$311$	−6.17498	+	5.55998i	−0.350151	+	0.315277i	−0.825372	−	0.564589i	$-0.809035\pi$
$311$	−6.17498	+	5.55998i	−0.350151	+	0.315277i	0.475221	+	0.879866i	$0.342368\pi$
$312$	3.98736	+	0.847540i	0.225740	+	0.0479825i
$313$	5.56536	−	12.5000i	0.314573	−	0.706542i	−0.685189	−	0.728365i	$-0.740281\pi$
$313$	5.56536	−	12.5000i	0.314573	−	0.706542i	0.999762	+	0.0218235i	$0.00694719\pi$
$314$	5.54038	−	4.02532i	0.312662	−	0.227162i
$315$	9.52220	+	1.82454i	0.536515	+	0.102801i
$316$	11.7028	+	3.80246i	0.658333	+	0.213905i
$317$	−0.729705	+	6.94268i	−0.0409843	+	0.389940i	0.954731	+	0.297470i	$0.0961428\pi$
$317$	−0.729705	+	6.94268i	−0.0409843	+	0.389940i	−0.995715	+	0.0924698i	$0.970524\pi$
$318$	−5.50241	+	9.53045i	−0.308560	+	0.534441i
$319$	2.75137	+	4.16480i	0.154047	+	0.233184i
$320$	3.17357	−	1.83226i	0.177408	−	0.102427i
$321$	4.79550	+	3.48413i	0.267658	+	0.194465i
$322$	14.2234	+	15.1713i	0.792639	+	0.845462i
$323$	−0.389477	−	1.19869i	−0.0216711	−	0.0666967i
$324$	−0.913545	−	0.406737i	−0.0507525	−	0.0225965i
$325$	3.59152	+	34.1711i	0.199222	+	1.89547i
$326$	−0.234727	+	1.10430i	−0.0130003	+	0.0611617i
$327$	5.83925	−	1.24117i	0.322911	−	0.0686369i
$328$	−6.24305	+	8.59282i	−0.344715	+	0.474459i
$329$	−0.569075	−	0.941395i	−0.0313741	−	0.0519008i
$330$	10.7855	−	5.60256i	0.593723	−	0.308411i
$331$	17.2425	+	29.8648i	0.947731	+	1.64152i	0.750188	+	0.661224i	$0.229963\pi$
$331$	17.2425	+	29.8648i	0.947731	+	1.64152i	0.197543	+	0.980294i	$0.436704\pi$
$332$	14.5979	−	6.49941i	0.801164	−	0.356701i
$333$	−1.36730	−	1.51854i	−0.0749273	−	0.0832152i
$334$	−13.1092	−	11.8036i	−0.717306	−	0.645865i
$335$	15.0158	+	20.6675i	0.820402	+	1.12919i
$336$	−2.10873	+	1.59789i	−0.115041	+	0.0871721i
$337$	−24.8266	+	8.06665i	−1.35239	+	0.439418i	−0.893495	−	0.449072i	$-0.851755\pi$
$337$	−24.8266	+	8.06665i	−1.35239	+	0.439418i	−0.458895	+	0.888491i	$0.651755\pi$
$338$	−0.752098	−	3.53834i	−0.0409087	−	0.192460i
$339$	−5.18196	−	11.6389i	−0.281446	−	0.632137i
$340$	4.15821	+	2.40074i	0.225511	+	0.130199i
$341$	−3.81949	+	3.14292i	−0.206837	+	0.170199i
$342$		−	0.961925i		−	0.0520150i
$343$	−9.96206	+	15.6127i	−0.537901	+	0.843008i
$344$	0.141836	−	0.436526i	0.00764727	−	0.0235359i
$345$	19.2734	−	21.4053i	1.03765	−	1.15242i
$346$	−9.60785	+	1.00983i	−0.516521	+	0.0542886i
$347$	−17.9794	+	1.88971i	−0.965184	+	0.101445i	−0.573989	−	0.818863i	$-0.694605\pi$
$347$	−17.9794	+	1.88971i	−0.965184	+	0.101445i	−0.391195	+	0.920308i	$0.627938\pi$
$348$	−1.00705	+	1.11844i	−0.0539835	+	0.0599547i
$349$	−1.02097	+	3.14222i	−0.0546512	+	0.168199i	−0.974656	−	0.223707i	$-0.928184\pi$
$349$	−1.02097	+	3.14222i	−0.0546512	+	0.168199i	0.920005	+	0.391906i	$0.128184\pi$
$350$	−18.3015	−	12.7421i	−0.978256	−	0.681095i
$351$			4.07644i			0.217584i
$352$	−0.833235	+	3.21025i	−0.0444115	+	0.171107i
$353$	−12.1906	−	7.03827i	−0.648842	−	0.374609i	0.139170	−	0.990268i	$-0.455556\pi$
$353$	−12.1906	−	7.03827i	−0.648842	−	0.374609i	−0.788013	+	0.615659i	$0.788890\pi$
$354$	5.36110	+	12.0412i	0.284939	+	0.639984i
$355$	6.60822	+	31.0892i	0.350728	+	1.65005i
$356$	−14.4598	+	4.69826i	−0.766366	+	0.249007i
$357$	−3.19465	−	1.34599i	−0.169079	−	0.0712373i
$358$	12.2052	+	16.7990i	0.645065	+	0.887856i
$359$	17.3685	+	15.6387i	0.916675	+	0.825378i	0.985048	−	0.172282i	$-0.0551141\pi$
$359$	17.3685	+	15.6387i	0.916675	+	0.825378i	−0.0683730	+	0.997660i	$0.521781\pi$
$360$	2.45205	+	2.72327i	0.129234	+	0.143529i
$361$	−16.5121	+	7.35164i	−0.869056	+	0.386929i
$362$	−10.5114	−	18.2063i	−0.552467	−	0.956902i
$363$	−3.23455	+	10.5137i	−0.169770	+	0.551826i
$364$	9.44693	+	5.20358i	0.495154	+	0.272742i
$365$	1.10653	−	1.52301i	0.0579184	−	0.0797178i
$366$	6.53653	−	1.38938i	0.341670	−	0.0726241i
$367$	−6.26422	+	29.4709i	−0.326990	+	1.53837i	0.440765	+	0.897622i	$0.354707\pi$
$367$	−6.26422	+	29.4709i	−0.326990	+	1.53837i	−0.767755	+	0.640743i	$0.778626\pi$
$368$	0.821608	+	7.81708i	0.0428293	+	0.407493i
$369$	−9.70305	−	4.32008i	−0.505120	−	0.224894i
$370$	2.31394	+	7.12157i	0.120296	+	0.370233i
$371$	−21.2410	+	19.9139i	−1.10278	+	1.03388i
$372$	−1.20655	−	0.876613i	−0.0625569	−	0.0454503i
$373$	−29.8221	+	17.2178i	−1.54413	+	0.891502i	−0.545556	+	0.838074i	$0.683681\pi$
$373$	−29.8221	+	17.2178i	−1.54413	+	0.891502i	−0.998572	+	0.0534280i	$0.982985\pi$
$374$	−4.18861	+	1.15765i	−0.216588	+	0.0598605i
$375$	−6.28236	+	10.8814i	−0.324420	+	0.561911i
$376$	0.0434601	−	0.413495i	0.00224128	−	0.0213244i
$377$	5.83482	+	1.89585i	0.300508	+	0.0976411i
$378$	−2.00140	−	1.73043i	−0.102941	−	0.0890037i
$379$	3.71197	−	2.69691i	0.190671	−	0.138531i	−0.488354	−	0.872645i	$-0.662403\pi$
$379$	3.71197	−	2.69691i	0.190671	−	0.138531i	0.679025	+	0.734115i	$0.262403\pi$
$380$	−1.43375	+	3.22025i	−0.0735496	+	0.165195i
$381$	9.81892	+	2.08707i	0.503038	+	0.106924i
$382$	17.1571	−	15.4483i	0.877834	−	0.790405i
$383$	−8.14200	−	0.855758i	−0.416037	−	0.0437272i	−0.105802	−	0.994387i	$-0.533741\pi$
$383$	−8.14200	−	0.855758i	−0.416037	−	0.0437272i	−0.310235	+	0.950660i	$0.600408\pi$
$384$	−1.00000			−0.0510310
$385$	31.6071	−	5.91668i	1.61084	−	0.301542i
$386$	9.11770			0.464079
$387$	0.456476	+	0.0479776i	0.0232040	+	0.00243884i
$388$	−7.32132	+	6.59215i	−0.371684	+	0.334666i
$389$	29.1035	+	6.18613i	1.47560	+	0.313649i	0.874306	−	0.485375i	$-0.161317\pi$
$389$	29.1035	+	6.18613i	1.47560	+	0.313649i	0.601299	+	0.799024i	$0.294650\pi$
$390$	6.07592	−	13.6468i	0.307666	−	0.691030i
$391$	−8.33193	+	6.05350i	−0.421364	+	0.306139i
$392$	−6.56496	+	2.42925i	−0.331581	+	0.122696i
$393$	12.2139	+	3.96852i	0.616108	+	0.200185i
$394$	1.42361	−	13.5448i	0.0717207	−	0.682377i
$395$	22.5461	−	39.0509i	1.13442	−	1.96486i
$396$	−3.31334	−	0.147577i	−0.166502	−	0.00741604i
$397$	10.1953	−	5.88627i	0.511688	−	0.295423i	−0.221839	−	0.975083i	$-0.571206\pi$
$397$	10.1953	−	5.88627i	0.511688	−	0.295423i	0.733527	+	0.679660i	$0.237873\pi$
$398$	4.05524	+	2.94630i	0.203271	+	0.147685i
$399$	0.737587	−	2.43579i	0.0369255	−	0.121942i
$400$	−2.60462	−	8.01621i	−0.130231	−	0.400811i
$401$	−3.91691	−	1.74392i	−0.195601	−	0.0870872i	0.306599	−	0.951839i	$-0.400809\pi$
$401$	−3.91691	−	1.74392i	−0.195601	−	0.0870872i	−0.502200	+	0.864752i	$0.667476\pi$
$402$	−0.728698	−	6.93310i	−0.0363442	−	0.345792i
$403$	−1.26401	+	5.94669i	−0.0629647	+	0.296226i
$404$	19.5905	−	4.16409i	0.974663	−	0.207171i
$405$	−2.15395	+	2.96466i	−0.107031	+	0.147315i
$406$	−3.40765	+	2.05993i	−0.169119	+	0.102233i
$407$	−6.06246	−	3.02928i	−0.300505	−	0.150156i
$408$	−0.655131	−	1.13472i	−0.0324338	−	0.0561770i
$409$	−3.47679	+	1.54797i	−0.171916	+	0.0765420i	−0.490890	−	0.871221i	$-0.663328\pi$
$409$	−3.47679	+	1.54797i	−0.171916	+	0.0765420i	0.318974	+	0.947763i	$0.396662\pi$
$410$	26.0439	+	28.9247i	1.28622	+	1.42849i
$411$	−4.67890	−	4.21290i	−0.230793	−	0.207807i
$412$	8.16033	+	11.2317i	0.402031	+	0.553348i
$413$	4.34239	+	34.6016i	0.213675	+	1.70263i
$414$	−7.47544	+	2.42892i	−0.367398	+	0.119375i
$415$	−12.1747	−	57.2773i	−0.597631	−	2.81163i
$416$	1.65804	+	3.72402i	0.0812920	+	0.182585i
$417$	−6.47342	−	3.73743i	−0.317005	−	0.183023i
$418$	−1.16666	−	2.96938i	−0.0570632	−	0.145237i
$419$		−	30.4203i		−	1.48613i	−0.669219	−	0.743065i	$-0.733371\pi$
$419$		−	30.4203i		−	1.48613i	0.669219	−	0.743065i	$-0.266629\pi$
$420$	4.12092	+	8.77606i	0.201080	+	0.428228i
$421$	7.94598	−	24.4552i	0.387263	−	1.19187i	−0.547562	−	0.836765i	$-0.684444\pi$
$421$	7.94598	−	24.4552i	0.387263	−	1.19187i	0.934825	−	0.355109i	$-0.115556\pi$
$422$	7.15307	−	7.94429i	0.348206	−	0.386722i
$423$	0.413495	−	0.0434601i	0.0201048	−	0.00211310i
$424$	−10.9445	+	1.15032i	−0.531513	+	0.0558643i
$425$	7.38978	−	8.20719i	0.358457	−	0.398107i
$426$	2.68022	−	8.24887i	0.129857	−	0.399659i
$427$	17.6172	+	1.49389i	0.852554	+	0.0722945i
$428$			5.92756i			0.286519i
$429$	4.94407	+	12.5836i	0.238702	+	0.607543i
$430$	−1.45664	−	0.840991i	−0.0702454	−	0.0405562i
$431$	−8.82711	−	19.8260i	−0.425187	−	0.954985i	−0.991417	−	0.130738i	$-0.958265\pi$
$431$	−8.82711	−	19.8260i	−0.425187	−	0.954985i	0.566230	−	0.824247i	$-0.308401\pi$
$432$	−0.207912	−	0.978148i	−0.0100032	−	0.0470611i
$433$	26.4869	−	8.60612i	1.27288	−	0.413584i	0.406813	−	0.913512i	$-0.366640\pi$
$433$	26.4869	−	8.60612i	1.27288	−	0.413584i	0.866067	+	0.499928i	$0.166640\pi$
$434$	−2.38307	−	3.14493i	−0.114391	−	0.150961i
$435$	3.24172	+	4.46185i	0.155429	+	0.213929i
$436$	4.43635	+	3.99451i	0.212463	+	0.191302i
$437$	−5.05921	−	5.61882i	−0.242015	−	0.268785i
$438$	−0.469306	+	0.208949i	−0.0224243	+	0.00998395i
$439$	2.68692	+	4.65388i	0.128240	+	0.222117i	0.922995	−	0.384813i	$-0.125734\pi$
$439$	2.68692	+	4.65388i	0.128240	+	0.222117i	−0.794755	+	0.606930i	$0.792401\pi$
$440$	10.8721	+	5.43257i	0.518309	+	0.258988i
$441$	−3.74110	−	5.91643i	−0.178147	−	0.281735i
$442$	−3.13948	+	4.32113i	−0.149330	+	0.205535i
$443$	−22.5607	+	4.79541i	−1.07189	+	0.227837i	−0.709869	−	0.704333i	$-0.751246\pi$
$443$	−22.5607	+	4.79541i	−1.07189	+	0.227837i	−0.362020	+	0.932170i	$0.617913\pi$
$444$	0.424845	−	1.99874i	0.0201622	−	0.0948559i
$445$	5.82381	+	55.4098i	0.276075	+	2.62668i
$446$	8.36890	+	3.72608i	0.396279	+	0.176435i
$447$	−1.48628	−	4.57431i	−0.0702987	−	0.216357i
$448$	−2.53220	−	0.766781i	−0.119635	−	0.0362270i
$449$	−1.34034	−	0.973816i	−0.0632547	−	0.0459572i	0.555709	−	0.831377i	$-0.312447\pi$
$449$	−1.34034	−	0.973816i	−0.0632547	−	0.0459572i	−0.618963	+	0.785420i	$0.712447\pi$
$450$	7.29951	−	4.21437i	0.344102	−	0.198667i
$451$	−35.1920	−	1.56746i	−1.65713	−	0.0738090i
$452$	6.37017	−	11.0335i	0.299628	−	0.518970i
$453$	0.558339	−	5.31224i	0.0262331	−	0.249591i
$454$	11.1281	+	3.61575i	0.522269	+	0.169696i
$455$	25.8495	−	29.8974i	1.21185	−	1.40161i
$456$	0.778214	−	0.565406i	0.0364432	−	0.0264775i
$457$	−5.05851	+	11.3616i	−0.236627	+	0.531474i	−0.992356	−	0.123412i	$-0.960616\pi$
$457$	−5.05851	+	11.3616i	−0.236627	+	0.531474i	0.755728	+	0.654885i	$0.227283\pi$
$458$	5.53310	+	1.17610i	0.258545	+	0.0549554i
$459$	0.973714	−	0.876736i	0.0454491	−	0.0409225i
$460$	28.6459	+	3.01080i	1.33562	+	0.140379i
$461$	−3.65626			−0.170289			−0.0851445	−	0.996369i	$-0.527135\pi$
$461$	−3.65626			−0.170289			−0.0851445	+	0.996369i	$0.527135\pi$
$462$	−8.27689	−	2.91430i	−0.385076	−	0.135586i
$463$	7.07416			0.328764			0.164382	−	0.986397i	$-0.447437\pi$
$463$	7.07416			0.328764			0.164382	+	0.986397i	$0.447437\pi$
$464$	−1.49677	−	0.157316i	−0.0694856	−	0.00730323i
$465$	−4.06144	+	3.65694i	−0.188345	+	0.169587i
$466$	−15.0896	−	3.20739i	−0.699011	−	0.148579i
$467$	1.16638	−	2.61973i	0.0539737	−	0.121227i	−0.884546	−	0.466454i	$-0.845531\pi$
$467$	1.16638	−	2.61973i	0.0539737	−	0.121227i	0.938519	+	0.345227i	$0.112198\pi$
$468$	−3.29791	+	2.39607i	−0.152446	+	0.110759i
$469$	3.47096	−	18.1148i	0.160274	−	0.836462i
$470$	−1.44904	−	0.470821i	−0.0668392	−	0.0217174i
$471$	−0.715841	+	6.81077i	−0.0329842	+	0.313824i
$472$	−6.59038	+	11.4149i	−0.303347	+	0.525412i
$473$	1.46729	−	0.405529i	0.0674661	−	0.0186462i
$474$	−10.6565	+	6.15252i	−0.489468	+	0.282594i
$475$	6.55937	+	4.76566i	0.300964	+	0.218663i
$476$	−0.788841	−	3.37568i	−0.0361565	−	0.154724i
$477$	−3.40068	−	10.4662i	−0.155706	−	0.479215i
$478$	15.4826	+	6.89331i	0.708159	+	0.315293i
$479$	−1.75516	−	16.6992i	−0.0801953	−	0.763007i	−0.958536	−	0.284972i	$-0.908016\pi$
$479$	−1.75516	−	16.6992i	−0.0801953	−	0.763007i	0.878341	−	0.478035i	$-0.158651\pi$
$480$	−0.761898	+	3.58445i	−0.0347757	+	0.163607i
$481$	−8.14774	+	1.73186i	−0.371505	+	0.0789658i
$482$	−4.79121	+	6.59453i	−0.218233	+	0.300373i
$483$	−20.7918	+	0.418481i	−0.946058	+	0.0190415i
$484$	−10.4070	+	3.56299i	−0.473044	+	0.161954i
$485$	18.0511	+	31.2654i	0.819658	+	1.41969i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−11.3537	−	12.6095i	−0.514485	−	0.571393i	0.428791	−	0.903404i	$-0.358940\pi$
$487$	−11.3537	−	12.6095i	−0.514485	−	0.571393i	−0.943276	+	0.332011i	$0.892273\pi$
$488$	4.96611	+	4.47150i	0.224805	+	0.202415i
$489$	−0.663594	−	0.913359i	−0.0300088	−	0.0413035i
$490$	3.70568	+	25.3826i	0.167406	+	1.14667i
$491$	4.14870	−	1.34799i	0.187228	−	0.0608341i	−0.213902	−	0.976855i	$-0.568617\pi$
$491$	4.14870	−	1.34799i	0.187228	−	0.0608341i	0.401130	+	0.916021i	$0.368617\pi$
$492$	−2.20829	−	10.3892i	−0.0995576	−	0.468382i
$493$	−0.802068	−	1.80147i	−0.0361233	−	0.0811343i
$494$	−3.39589	−	1.96062i	−0.152788	−	0.0882123i
$495$	−3.05341	+	11.7640i	−0.137241	+	0.528755i
$496$		−	1.49138i		−	0.0669651i
$497$	13.1119	−	18.8327i	0.588151	−	0.844760i
$498$	−4.93790	+	15.1973i	−0.221273	+	0.681008i
$499$	0.558882	−	0.620701i	0.0250190	−	0.0277864i	−0.730505	−	0.682907i	$-0.760715\pi$
$499$	0.558882	−	0.620701i	0.0250190	−	0.0277864i	0.755524	+	0.655120i	$0.227382\pi$
$500$	−12.4959	+	1.31337i	−0.558833	+	0.0587357i
$501$	17.5436	−	1.84391i	0.783790	−	0.0823796i
$502$	−8.69554	+	9.65738i	−0.388101	+	0.431030i
$503$	−9.44390	+	29.0653i	−0.421083	+	1.29596i	0.485613	+	0.874174i	$0.338597\pi$
$503$	−9.44390	+	29.0653i	−0.421083	+	1.29596i	−0.906696	+	0.421786i	$0.861403\pi$
$504$	0.223551	−	2.63629i	0.00995776	−	0.117430i
$505$		−	73.3936i		−	3.26597i
$506$	−20.1301	+	16.5643i	−0.894893	+	0.736375i
$507$	3.13275	+	1.80869i	0.139130	+	0.0803270i
$508$	4.08293	+	9.17042i	0.181151	+	0.406872i
$509$	4.17150	+	19.6254i	0.184899	+	0.869879i	0.968577	+	0.248713i	$0.0800076\pi$
$509$	4.17150	+	19.6254i	0.184899	+	0.869879i	−0.783679	+	0.621166i	$0.786659\pi$
$510$	−4.56649	+	1.48374i	−0.202207	+	0.0657012i
$511$	−1.34860	+	0.169245i	−0.0596584	+	0.00748695i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	0.714850	+	0.643654i	0.0315614	+	0.0284180i
$514$	−4.68139	−	5.19921i	−0.206487	−	0.229327i
$515$	46.4769	−	20.6928i	2.04802	−	0.911836i
$516$	0.229495	+	0.397497i	0.0101030	+	0.0174988i
$517$	1.22371	−	0.635660i	0.0538189	−	0.0279563i
$518$	2.60839	−	4.73544i	0.114606	−	0.208063i
$519$	5.67846	−	7.81573i	0.249257	−	0.343072i
$520$	14.6118	−	3.10583i	0.640769	−	0.136200i
$521$	7.08912	−	33.3517i	0.310580	−	1.46116i	−0.495112	−	0.868829i	$-0.664873\pi$
$521$	7.08912	−	33.3517i	0.310580	−	1.46116i	0.805692	−	0.592335i	$-0.201794\pi$
$522$	−0.157316	−	1.49677i	−0.00688556	−	0.0655117i
$523$	−28.1546	−	12.5353i	−1.23112	−	0.548128i	−0.315020	−	0.949085i	$-0.602011\pi$
$523$	−28.1546	−	12.5353i	−1.23112	−	0.548128i	−0.916097	+	0.400957i	$0.868678\pi$
$524$	3.96852	+	12.2139i	0.173366	+	0.533565i
$525$	21.7153	−	5.07451i	0.947734	−	0.221470i
$526$	4.84215	+	3.51803i	0.211128	+	0.153393i
$527$	1.69230	−	0.977051i	0.0737179	−	0.0425610i
$528$	−1.82814	−	2.76729i	−0.0795596	−	0.120431i
$529$	−19.3909	+	33.5860i	−0.843082	+	1.46026i
$530$	−4.21536	+	40.1065i	−0.183104	+	1.74212i
$531$	−12.5356	−	4.07308i	−0.544001	−	0.176757i
$532$	2.40414	−	0.835001i	0.104233	−	0.0362019i
$533$	−35.0281	+	25.4494i	−1.51724	+	1.10234i
$534$	6.18398	−	13.8895i	0.267607	−	0.601055i
$535$	21.2470	+	4.51619i	0.918588	+	0.195252i
$536$	5.18068	−	4.66470i	0.223771	−	0.201484i
$537$	−20.6510	−	2.17051i	−0.891156	−	0.0936643i
$538$	13.0051			0.560688
$539$	−18.7241	−	13.7262i	−0.806505	−	0.591228i
$540$	−3.66452			−0.157696
$541$	−1.57974	−	0.166037i	−0.0679183	−	0.00713850i	0.0705083	−	0.997511i	$-0.477538\pi$
$541$	−1.57974	−	0.166037i	−0.0679183	−	0.00713850i	−0.138427	+	0.990373i	$0.544205\pi$
$542$	−13.3754	+	12.0433i	−0.574525	+	0.517304i
$543$	20.5634	+	4.37089i	0.882461	+	0.187573i
$544$	0.532931	−	1.19698i	0.0228492	−	0.0513202i
$545$	17.6982	−	12.8585i	0.758106	−	0.550796i
$546$	−10.1882	+	3.53856i	−0.436017	+	0.151437i
$547$	−2.91586	−	0.947420i	−0.124673	−	0.0405087i	0.246016	−	0.969266i	$-0.420878\pi$
$547$	−2.91586	−	0.947420i	−0.124673	−	0.0405087i	−0.370689	+	0.928757i	$0.620878\pi$
$548$	0.658120	−	6.26160i	0.0281135	−	0.267482i
$549$	−3.34128	+	5.78726i	−0.142602	+	0.246994i
$550$	17.4216	−	21.8625i	0.742859	−	0.932221i
$551$	1.25375	−	0.723854i	0.0534116	−	0.0308372i
$552$	−6.35898	−	4.62007i	−0.270656	−	0.196643i
$553$	−31.7020	+	7.40823i	−1.34811	+	0.315030i
$554$	7.81289	+	24.0456i	0.331938	+	1.02160i
$555$	−6.84068	−	3.04567i	−0.290371	−	0.129281i
$556$	−0.781336	−	7.43392i	−0.0331360	−	0.315268i
$557$	−8.54638	+	40.2076i	−0.362122	+	1.70365i	0.299737	+	0.954022i	$0.403101\pi$
$557$	−8.54638	+	40.2076i	−0.362122	+	1.70365i	−0.661859	+	0.749628i	$0.730232\pi$
$558$	1.45879	−	0.310076i	0.0617556	−	0.0131266i
$559$	1.09977	−	1.51371i	0.0465155	−	0.0640231i
$560$	−4.67777	+	8.49233i	−0.197672	+	0.358867i
$561$	1.94243	−	3.88736i	0.0820095	−	0.164125i
$562$	−3.35407	−	5.80941i	−0.141483	−	0.245055i
$563$	−31.5444	+	14.0445i	−1.32944	+	0.591903i	−0.943730	−	0.330718i	$-0.892709\pi$
$563$	−31.5444	+	14.0445i	−1.32944	+	0.591903i	−0.385707	+	0.922621i	$0.626042\pi$
$564$	0.278206	+	0.308980i	0.0117146	+	0.0130104i
$565$	−34.6954	−	31.2399i	−1.45965	−	1.31427i
$566$	−12.1502	−	16.7233i	−0.510710	−	0.702932i
$567$	2.62516	−	0.329450i	0.110246	−	0.0138356i
$568$	8.24887	−	2.68022i	0.346115	−	0.112459i
$569$	−9.53859	−	44.8755i	−0.399878	−	1.88128i	−0.468211	−	0.883617i	$-0.655101\pi$
$569$	−9.53859	−	44.8755i	−0.399878	−	1.88128i	0.0683324	−	0.997663i	$-0.478232\pi$
$570$	−1.43375	−	3.22025i	−0.0600530	−	0.134881i
$571$	2.52002	+	1.45494i	0.105460	+	0.0608872i	0.551802	−	0.833975i	$-0.313940\pi$
$571$	2.52002	+	1.45494i	0.105460	+	0.0608872i	−0.446342	+	0.894862i	$0.647274\pi$
$572$	−7.27431	+	11.3963i	−0.304154	+	0.476503i
$573$			23.0872i			0.964480i
$574$	2.37441	−	28.0008i	0.0991058	−	1.16873i
$575$	20.4727	−	63.0085i	0.853771	−	2.62764i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	11.8646	−	1.24702i	0.493928	−	0.0519140i	0.145710	−	0.989327i	$-0.453453\pi$
$577$	11.8646	−	1.24702i	0.493928	−	0.0519140i	0.348219	+	0.937413i	$0.386787\pi$
$578$	−15.1995	+	1.59753i	−0.632215	+	0.0664485i
$579$	−6.10093	+	6.77577i	−0.253546	+	0.281592i
$580$	−1.70428	+	5.24522i	−0.0707662	+	0.217796i
$581$	−24.1568	+	34.6964i	−1.00219	+	1.43945i
$582$		−	9.85181i		−	0.408371i
$583$	−23.1914	−	28.1838i	−0.960489	−	1.16725i
$584$	−0.444894	−	0.256860i	−0.0184099	−	0.0106289i
$585$	6.07592	+	13.6468i	0.251209	+	0.564224i
$586$	2.83998	+	13.3610i	0.117318	+	0.551939i
$587$	6.95055	−	2.25837i	0.286880	−	0.0932130i	−0.162042	−	0.986784i	$-0.551808\pi$
$587$	6.95055	−	2.25837i	0.286880	−	0.0932130i	0.448922	+	0.893571i	$0.351808\pi$
$588$	2.58753	−	6.50420i	0.106708	−	0.268229i
$589$	0.843236	+	1.16062i	0.0347450	+	0.0478223i
$590$	35.8948	+	32.3198i	1.47777	+	1.33059i
$591$	9.11316	+	10.1212i	0.374865	+	0.416330i
$592$	1.86673	−	0.831122i	0.0767222	−	0.0341589i
$593$	16.8373	+	29.1631i	0.691426	+	1.19759i	0.971371	+	0.237569i	$0.0763507\pi$
$593$	16.8373	+	29.1631i	0.691426	+	1.19759i	−0.279944	+	0.960016i	$0.590316\pi$
$594$	2.32673	−	2.36354i	0.0954668	−	0.0969773i
$595$	−12.7010	+	0.255635i	−0.520689	+	0.0104800i
$596$	2.82708	−	3.89114i	0.115802	−	0.159387i
$597$	−4.90301	+	1.04217i	−0.200667	+	0.0426531i
$598$	−6.66178	+	31.3412i	−0.272421	+	1.28164i
$599$	−3.91182	−	37.2185i	−0.159833	−	1.52071i	−0.720960	−	0.692977i	$-0.756299\pi$
$599$	−3.91182	−	37.2185i	−0.159833	−	1.52071i	0.561127	−	0.827730i	$-0.310368\pi$
$600$	7.70004	+	3.42828i	0.314353	+	0.139959i
$601$	−1.89560	−	5.83407i	−0.0773233	−	0.237977i	0.904922	−	0.425577i	$-0.139929\pi$
$601$	−1.89560	−	5.83407i	−0.0773233	−	0.237977i	−0.982245	+	0.187601i	$0.939929\pi$
$602$	0.276335	+	1.18252i	0.0112626	+	0.0481958i
$603$	5.63989	+	4.09762i	0.229674	+	0.166868i
$604$	4.62588	−	2.67075i	0.188224	−	0.108671i
$605$	4.84228	+	40.0179i	0.196867	+	1.62696i
$606$	−10.0141	+	17.3449i	−0.406794	+	0.704588i
$607$	−0.218422	+	2.07815i	−0.00886547	+	0.0843494i	−0.998060	−	0.0622598i	$-0.980169\pi$
$607$	−0.218422	+	2.07815i	−0.00886547	+	0.0843494i	0.989195	+	0.146609i	$0.0468359\pi$
$608$	0.914845	+	0.297251i	0.0371019	+	0.0120551i
$609$	0.749336	−	3.91074i	0.0303646	−	0.158471i
$610$	19.8115	−	14.3939i	0.802145	−	0.582793i
$611$	0.689368	−	1.54835i	0.0278888	−	0.0626393i
$612$	1.28163	+	0.272419i	0.0518068	+	0.0110119i
$613$	−24.0173	+	21.6253i	−0.970050	+	0.873437i	−0.991989	−	0.126322i	$-0.959683\pi$
$613$	−24.0173	+	21.6253i	−0.970050	+	0.873437i	0.0219391	+	0.999759i	$0.493016\pi$
$614$	−18.8109	−	1.97711i	−0.759148	−	0.0797896i
$615$	−38.9220			−1.56949
$616$	−2.50731	−	8.40913i	−0.101022	−	0.338813i
$617$	16.7436			0.674072			0.337036	−	0.941492i	$-0.390576\pi$
$617$	16.7436			0.674072			0.337036	+	0.941492i	$0.390576\pi$
$618$	−13.8071	−	1.45119i	−0.555404	−	0.0583754i
$619$	22.1273	−	19.9235i	0.889372	−	0.800794i	−0.0914278	−	0.995812i	$-0.529143\pi$
$619$	22.1273	−	19.9235i	0.889372	−	0.800794i	0.980800	+	0.195018i	$0.0624764\pi$
$620$	−5.34578	−	1.13628i	−0.214692	−	0.0456342i
$621$	3.19701	−	7.18059i	0.128291	−	0.288147i
$622$	6.72233	−	4.88406i	0.269541	−	0.195833i
$623$	26.3093	−	30.4291i	1.05406	−	1.21912i
$624$	−3.87693	−	1.25969i	−0.155201	−	0.0504280i
$625$	−0.407660	+	3.87863i	−0.0163064	+	0.155145i
$626$	−6.84147	+	11.8498i	−0.273440	+	0.473613i
$627$	2.98733	+	1.11990i	0.119302	+	0.0447247i
$628$	−5.93079	+	3.42415i	−0.236664	+	0.136638i
$629$	2.16604	+	1.57372i	0.0863658	+	0.0627484i
$630$	−9.27932	−	2.80989i	−0.369697	−	0.111949i
$631$	12.1521	+	37.4003i	0.483767	+	1.48888i	0.833759	+	0.552128i	$0.186184\pi$
$631$	12.1521	+	37.4003i	0.483767	+	1.48888i	−0.349993	+	0.936752i	$0.613816\pi$
$632$	−11.2412	−	5.00491i	−0.447151	−	0.199085i
$633$	1.11742	+	10.6315i	0.0444135	+	0.422566i
$634$	1.45142	−	6.82837i	0.0576431	−	0.271189i
$635$	35.9817	−	7.64814i	1.42789	−	0.303507i
$636$	6.46847	−	8.90308i	0.256491	−	0.353030i
$637$	−28.5120	+	1.14820i	−1.12969	+	0.0454933i
$638$	−2.30096	−	4.42959i	−0.0910958	−	0.175369i
$639$	4.33669	+	7.51136i	0.171557	+	0.297145i
$640$	−3.34771	+	1.49050i	−0.132330	+	0.0589170i
$641$	26.2258	+	29.1267i	1.03586	+	1.15044i	0.988448	+	0.151562i	$0.0484302\pi$
$641$	26.2258	+	29.1267i	1.03586	+	1.15044i	0.0474104	+	0.998875i	$0.484903\pi$
$642$	−4.40503	−	3.96631i	−0.173853	−	0.156538i
$643$	5.56431	+	7.65861i	0.219435	+	0.302026i	0.904515	−	0.426441i	$-0.140233\pi$
$643$	5.56431	+	7.65861i	0.219435	+	0.302026i	−0.685080	+	0.728467i	$0.740233\pi$
$644$	−12.5596	−	16.5749i	−0.494919	−	0.653143i
$645$	1.59966	−	0.519761i	0.0629865	−	0.0204656i
$646$	0.262046	+	1.23283i	0.0103101	+	0.0485051i
$647$	8.02069	+	18.0148i	0.315326	+	0.708234i	0.999783	−	0.0208193i	$-0.00662747\pi$
$647$	8.02069	+	18.0148i	0.315326	+	0.708234i	−0.684457	+	0.729053i	$0.739961\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−43.6364	+	2.63048i	−1.71288	+	0.103255i
$650$		−	34.3593i		−	1.34768i
$651$	3.93172	+	0.333400i	0.154096	+	0.0130670i
$652$	0.348872	−	1.07372i	0.0136629	−	0.0420500i
$653$	−1.00000	+	1.11061i	−0.0391331	+	0.0434617i	−0.762394	−	0.647114i	$-0.775976\pi$
$653$	−1.00000	+	1.11061i	−0.0391331	+	0.0434617i	0.723260	+	0.690575i	$0.242643\pi$
$654$	−5.93700	+	0.624004i	−0.232155	+	0.0244005i
$655$	46.8035	−	4.91925i	1.82876	−	0.192211i
$656$	7.10704	−	7.89317i	0.277483	−	0.308177i
$657$	0.158748	−	0.488577i	0.00619336	−	0.0190612i
$658$	0.467555	+	0.995722i	0.0182272	+	0.0388173i
$659$		−	8.14023i		−	0.317098i	−0.987351	−	0.158549i	$-0.949318\pi$
$659$		−	8.14023i		−	0.317098i	0.987351	−	0.158549i	$-0.0506817\pi$
$660$	−11.3121	+	4.44448i	−0.440322	+	0.173001i
$661$	7.43965	+	4.29528i	0.289369	+	0.167067i	0.637657	−	0.770320i	$-0.279904\pi$
$661$	7.43965	+	4.29528i	0.289369	+	0.167067i	−0.348288	+	0.937387i	$0.613237\pi$
$662$	−14.0263	−	31.5035i	−0.545147	−	1.22442i
$663$	−1.11050	−	5.22449i	−0.0431282	−	0.202902i
$664$	−15.1973	+	4.93790i	−0.589770	+	0.191628i
$665$	−1.16131	−	9.25369i	−0.0450336	−	0.358843i
$666$	1.20108	+	1.65314i	0.0465407	+	0.0640578i
$667$	−8.79110	−	7.91554i	−0.340393	−	0.306491i
$668$	11.8036	+	13.1092i	0.456696	+	0.507212i
$669$	−8.36890	+	3.72608i	−0.323561	+	0.144058i
$670$	−12.7732	−	22.1239i	−0.493473	−	0.854720i
$671$	−3.29522	+	21.9172i	−0.127210	+	0.846104i
$672$	2.26420	−	1.36872i	0.0873435	−	0.0527994i
$673$	13.1116	−	18.0465i	0.505413	−	0.695642i	−0.477724	−	0.878510i	$-0.658538\pi$
$673$	13.1116	−	18.0465i	0.505413	−	0.695642i	0.983137	+	0.182868i	$0.0585381\pi$
$674$	25.5338	−	5.42737i	0.983524	−	0.209055i
$675$	−1.75243	+	8.24455i	−0.0674512	+	0.317333i
$676$	0.378120	+	3.59757i	0.0145431	+	0.138368i
$677$	1.13600	+	0.505781i	0.0436601	+	0.0194387i	0.428451	−	0.903565i	$-0.359060\pi$
$677$	1.13600	+	0.505781i	0.0436601	+	0.0194387i	−0.384790	+	0.923004i	$0.625726\pi$
$678$	3.93698	+	12.1168i	0.151199	+	0.465342i
$679$	7.55419	−	24.9468i	0.289903	−	0.957369i
$680$	−3.88448	−	2.82224i	−0.148963	−	0.108228i
$681$	−10.1332	+	5.85040i	−0.388305	+	0.224188i
$682$	4.12709	−	2.72646i	0.158035	−	0.104401i
$683$	13.7991	−	23.9007i	0.528007	−	0.914535i	−0.471460	−	0.881888i	$-0.656273\pi$
$683$	13.7991	−	23.9007i	0.528007	−	0.914535i	0.999467	−	0.0326478i	$-0.0103940\pi$
$684$	−0.100549	+	0.956656i	−0.00384457	+	0.0365786i
$685$	−21.9429	−	7.12969i	−0.838397	−	0.272412i
$686$	11.5395	−	14.4859i	0.440579	−	0.553074i
$687$	−4.57638	+	3.32493i	−0.174600	+	0.126854i
$688$	−0.186688	+	0.419309i	−0.00711742	+	0.0159860i
$689$	−43.8802	−	9.32702i	−1.67170	−	0.355331i
$690$	−21.4053	+	19.2734i	−0.814886	+	0.733726i
$691$	−48.6115	−	5.10928i	−1.84927	−	0.194366i	−0.886143	−	0.463413i	$-0.846625\pi$
$691$	−48.6115	−	5.10928i	−1.84927	−	0.194366i	−0.963127	+	0.269047i	$0.913291\pi$
$692$	9.66077			0.367247
$693$	7.70407	−	4.20088i	0.292653	−	0.159578i
$694$	18.0784			0.686247
$695$	−27.2418	−	2.86323i	−1.03334	−	0.108608i
$696$	1.11844	−	1.00705i	0.0423944	−	0.0381721i
$697$	13.6126	+	2.89344i	0.515613	+	0.109597i
$698$	1.34383	−	3.01828i	0.0508646	−	0.114244i
$699$	12.4804	−	9.06757i	0.472054	−	0.342967i
$700$	16.8693	+	14.5853i	0.637600	+	0.551274i
$701$	37.8789	+	12.3076i	1.43067	+	0.464852i	0.918974	−	0.394317i	$-0.129019\pi$
$701$	37.8789	+	12.3076i	1.43067	+	0.464852i	0.511692	+	0.859169i	$0.329019\pi$
$702$	0.426104	−	4.05411i	0.0160823	−	0.153013i
$703$	−0.982795	+	1.70225i	−0.0370668	+	0.0642016i
$704$	1.16423	−	3.10557i	0.0438787	−	0.117046i
$705$	1.31949	−	0.761805i	0.0496947	−	0.0286912i
$706$	11.3882	+	8.27398i	0.428599	+	0.311395i
$707$	−38.6574	+	36.2421i	−1.45386	+	1.36303i
$708$	−4.07308	−	12.5356i	−0.153076	−	0.471118i
$709$	26.4817	+	11.7904i	0.994542	+	0.442799i	0.838470	−	0.544947i	$-0.183450\pi$
$709$	26.4817	+	11.7904i	0.994542	+	0.442799i	0.156072	+	0.987746i	$0.450117\pi$
$710$	−3.32231	−	31.6097i	−0.124684	−	1.18629i
$711$	2.55836	−	12.0361i	0.0959460	−	0.451391i
$712$	14.8717	−	3.16107i	0.557339	−	0.118466i
$713$	6.89030	−	9.48368i	0.258044	−	0.355167i
$714$	3.03646	+	1.67255i	0.113637	+	0.0625936i
$715$	35.3071	+	34.7572i	1.32041	+	1.29985i
$716$	−10.3824	−	17.9828i	−0.388007	−	0.672048i
$717$	−15.4826	+	6.89331i	−0.578209	+	0.257435i
$718$	−15.6387	−	17.3685i	−0.583630	−	0.648187i
$719$	36.2631	+	32.6515i	1.35239	+	1.21769i	0.953755	+	0.300584i	$0.0971814\pi$
$719$	36.2631	+	32.6515i	1.35239	+	1.21769i	0.398632	+	0.917111i	$0.369485\pi$
$720$	−2.15395	−	2.96466i	−0.0802731	−	0.110486i
$721$	−33.8497	−	14.2618i	−1.26063	−	0.531136i
$722$	17.1901	−	5.58539i	0.639748	−	0.207867i
$723$	−1.69475	−	7.97316i	−0.0630284	−	0.296525i
$724$	8.55075	+	19.2053i	0.317786	+	0.713759i
$725$	10.9858	+	6.34268i	0.408004	+	0.235561i
$726$	4.31581	−	10.1180i	0.160175	−	0.375514i
$727$		−	40.2539i		−	1.49293i	−0.665422	−	0.746467i	$-0.731748\pi$
$727$		−	40.2539i		−	1.49293i	0.665422	−	0.746467i	$-0.268252\pi$
$728$	−8.85126	−	6.16255i	−0.328049	−	0.228399i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−1.25966	+	1.39900i	−0.0466223	+	0.0517793i
$731$	−0.598103	+	0.0628631i	−0.0221216	+	0.00232508i
$732$	−6.64595	+	0.698517i	−0.245641	+	0.0258179i
$733$	17.8331	−	19.8057i	0.658682	−	0.731540i	−0.317557	−	0.948239i	$-0.602862\pi$
$733$	17.8331	−	19.8057i	0.658682	−	0.731540i	0.976238	+	0.216699i	$0.0695290\pi$
$734$	9.31045	−	28.6546i	0.343655	−	1.05766i
$735$	−21.3425	−	14.2304i	−0.787231	−	0.524897i
$736$		−	7.86014i		−	0.289729i
$737$	22.3796	+	5.80872i	0.824363	+	0.213967i
$738$	9.19832	+	5.31065i	0.338595	+	0.195488i
$739$	8.61040	+	19.3393i	0.316739	+	0.711407i	0.999821	−	0.0189348i	$-0.00602748\pi$
$739$	8.61040	+	19.3393i	0.316739	+	0.711407i	−0.683082	+	0.730342i	$0.739361\pi$
$740$	−1.55685	−	7.32443i	−0.0572311	−	0.269251i
$741$	3.72932	−	1.21173i	0.137000	−	0.0445139i
$742$	23.2062	−	17.5845i	0.851926	−	0.645547i
$743$	−18.8609	−	25.9598i	−0.691938	−	0.952371i	−0.999999	−	0.00100460i	$-0.999680\pi$
$743$	−18.8609	−	25.9598i	−0.691938	−	0.952371i	0.308061	−	0.951366i	$-0.400320\pi$
$744$	1.10831	+	0.997930i	0.0406328	+	0.0365859i
$745$	−11.7936	−	13.0982i	−0.432085	−	0.479879i
$746$	31.4584	−	14.0062i	1.15178	−	0.512803i
$747$	−7.98970	−	13.8386i	−0.292328	−	0.506326i
$748$	4.28668	−	0.713476i	0.156736	−	0.0260873i
$749$	−8.11314	−	13.4212i	−0.296448	−	0.490400i
$750$	7.38535	−	10.1651i	0.269675	−	0.371176i
$751$	−10.5364	+	2.23957i	−0.384477	+	0.0817232i	−0.396096	−	0.918209i	$-0.629635\pi$
$751$	−10.5364	+	2.23957i	−0.384477	+	0.0817232i	0.0116181	+	0.999933i	$0.496302\pi$
$752$	−0.0864441	+	0.406687i	−0.00315229	+	0.0148304i
$753$	−1.35838	−	12.9241i	−0.0495020	−	0.470980i
$754$	−5.60469	−	2.49537i	−0.204111	−	0.0908759i
$755$	−6.04872	−	18.6161i	−0.220136	−	0.677508i
$756$	1.80956	+	1.93015i	0.0658131	+	0.0701990i
$757$	32.6904	+	23.7510i	1.18815	+	0.863243i	0.993068	−	0.117543i	$-0.0375018\pi$
$757$	32.6904	+	23.7510i	1.18815	+	0.863243i	0.195085	+	0.980786i	$0.437502\pi$
$758$	−3.97354	+	2.29413i	−0.144326	+	0.0833264i
$759$	1.15998	−	26.0433i	0.0421045	−	0.945312i
$760$	1.76250	−	3.05274i	0.0639326	−	0.110734i
$761$	−0.232610	+	2.21314i	−0.00843211	+	0.0802261i	−0.997929	−	0.0643303i	$-0.979509\pi$
$761$	−0.232610	+	2.21314i	−0.00843211	+	0.0802261i	0.989497	+	0.144556i	$0.0461755\pi$
$762$	−9.54697	−	3.10200i	−0.345850	−	0.112374i
$763$	−15.5122	−	2.97228i	−0.561578	−	0.107604i
$764$	−18.6779	+	13.5703i	−0.675743	+	0.490956i
$765$	1.95294	−	4.38638i	0.0706087	−	0.158590i
$766$	8.00794	+	1.70214i	0.289339	+	0.0615008i
$767$	−39.9296	+	35.9528i	−1.44177	+	1.29818i
$768$	0.994522	+	0.104528i	0.0358867	+	0.00377185i
$769$	19.6739			0.709457			0.354729	−	0.934969i	$-0.384573\pi$
$769$	19.6739			0.709457			0.354729	+	0.934969i	$0.384573\pi$
$770$	−32.0524	+	2.58043i	−1.15509	+	0.0929921i
$771$	6.99623			0.251963
$772$	−9.06776	−	0.953059i	−0.326356	−	0.0343014i
$773$	−12.5475	+	11.2978i	−0.451301	+	0.406353i	−0.863189	−	0.504881i	$-0.831536\pi$
$773$	−12.5475	+	11.2978i	−0.451301	+	0.406353i	0.411888	+	0.911235i	$0.364870\pi$
$774$	−0.448960	−	0.0954295i	−0.0161375	−	0.00343014i
$775$	−5.11288	+	11.4837i	−0.183660	+	0.412507i
$776$	7.97028	−	5.79075i	0.286117	−	0.207876i
$777$	1.77377	+	5.10704i	0.0636336	+	0.183214i
$778$	−28.2974	−	9.19439i	−1.01451	−	0.329635i
$779$	−1.06796	+	10.1609i	−0.0382635	+	0.364053i
$780$	−7.46911	+	12.9369i	−0.267437	+	0.463215i
$781$	22.4970	+	17.9272i	0.805007	+	0.641486i
$782$	8.91905	−	5.14942i	0.318945	−	0.184143i
$783$	1.21758	+	0.884623i	0.0435127	+	0.0316139i
$784$	6.78293	−	1.72972i	0.242247	−	0.0617755i
$785$	7.75501	+	23.8675i	0.276788	+	0.851866i
$786$	−11.7321	−	5.22348i	−0.418471	−	0.186315i
$787$	−2.36422	−	22.4940i	−0.0842753	−	0.801826i	−0.952271	−	0.305254i	$-0.901259\pi$
$787$	−2.36422	−	22.4940i	−0.0842753	−	0.801826i	0.867996	−	0.496572i	$-0.165408\pi$
$788$	−2.83163	+	13.3218i	−0.100873	+	0.474569i
$789$	−5.85443	+	1.24440i	−0.208423	+	0.0443017i
$790$	−26.5045	+	36.4803i	−0.942987	+	1.29791i
$791$	0.678307	+	33.7009i	0.0241178	+	1.19827i
$792$	3.27976	+	0.493107i	0.116541	+	0.0175218i
$793$	13.6205	+	23.5914i	0.483679	+	0.837757i
$794$	−10.7547	+	4.78832i	−0.381672	+	0.169931i
$795$	−26.9843	−	29.9691i	−0.957035	−	1.06290i
$796$	−3.72505	−	3.35405i	−0.132031	−	0.118881i
$797$	−12.4607	−	17.1507i	−0.441380	−	0.607508i	0.529138	−	0.848536i	$-0.322515\pi$
$797$	−12.4607	−	17.1507i	−0.441380	−	0.607508i	−0.970518	+	0.241028i	$0.922515\pi$
$798$	−0.988155	+	2.34535i	−0.0349803	+	0.0830244i
$799$	−0.518108	+	0.168344i	−0.0183294	+	0.00595557i
$800$	1.75243	+	8.24455i	0.0619579	+	0.291489i
$801$	6.18398	+	13.8895i	0.218500	+	0.490760i
$802$	3.71316	+	2.14379i	0.131116	+	0.0757000i
$803$	−0.102523	−	1.70073i	−0.00361795	−	0.0600174i
$804$			6.97129i			0.245858i
$805$	−68.9810	+	32.3910i	−2.43126	+	1.14163i
$806$	1.87868	−	5.78199i	0.0661737	−	0.203662i
$807$	−8.70208	+	9.66464i	−0.306328	+	0.340212i
$808$	−19.9184	+	2.09351i	−0.700728	+	0.0736495i
$809$	32.8341	−	3.45100i	1.15439	−	0.121331i	0.492070	−	0.870556i	$-0.336240\pi$
$809$	32.8341	−	3.45100i	1.15439	−	0.121331i	0.662316	+	0.749225i	$0.269574\pi$
$810$	2.45205	−	2.72327i	0.0861561	−	0.0956860i
$811$	7.12527	−	21.9293i	0.250202	−	0.770043i	−0.744535	−	0.667583i	$-0.767329\pi$
$811$	7.12527	−	21.9293i	0.250202	−	0.770043i	0.994737	−	0.102460i	$-0.0326713\pi$
$812$	3.60431	−	1.69245i	0.126486	−	0.0593934i
$813$		−	17.9984i		−	0.631233i
$814$	5.71260	+	3.64638i	0.200227	+	0.127806i
$815$	−3.58288	−	2.06858i	−0.125503	−	0.0724591i
$816$	0.532931	+	1.19698i	0.0186563	+	0.0419028i
$817$	−0.0917960	−	0.431866i	−0.00321154	−	0.0151091i
$818$	3.61955	−	1.17606i	0.126555	−	0.0411201i
$819$	4.18760	−	9.93910i	0.146327	−	0.347300i
$820$	−22.8778	−	31.4886i	−0.798928	−	1.09963i
$821$	33.6536	+	30.3019i	1.17452	+	1.05754i	0.997305	+	0.0733698i	$0.0233753\pi$
$821$	33.6536	+	30.3019i	1.17452	+	1.05754i	0.177215	+	0.984172i	$0.443291\pi$
$822$	4.21290	+	4.67890i	0.146942	+	0.163196i
$823$	−21.3267	+	9.49524i	−0.743400	+	0.330983i	−0.743247	−	0.669017i	$-0.766715\pi$
$823$	−21.3267	+	9.49524i	−0.743400	+	0.330983i	−0.000153079		1.00000i	$0.500049\pi$
$824$	−6.94159	−	12.0232i	−0.241822	−	0.418848i
$825$	4.58970	+	27.5756i	0.159793	+	0.960060i
$826$	−0.701755	−	34.8659i	−0.0244172	−	1.21314i
$827$	2.70837	−	3.72775i	0.0941791	−	0.129626i	−0.759327	−	0.650709i	$-0.774472\pi$
$827$	2.70837	−	3.72775i	0.0941791	−	0.129626i	0.853506	+	0.521083i	$0.174472\pi$
$828$	7.68837	−	1.63421i	0.267189	−	0.0567929i
$829$	−2.50271	+	11.7743i	−0.0869225	+	0.408938i	0.913077	+	0.407788i	$0.133700\pi$
$829$	−2.50271	+	11.7743i	−0.0869225	+	0.408938i	−0.999999	+	0.00115076i	$0.999634\pi$
$830$	6.12086	+	58.2361i	0.212458	+	2.02140i
$831$	−23.0972	−	10.2835i	−0.801233	−	0.356732i
$832$	−1.25969	−	3.87693i	−0.0436719	−	0.134408i
$833$	6.40645	+	6.56353i	0.221970	+	0.227413i
$834$	6.04729	+	4.39361i	0.209401	+	0.152138i
$835$	55.9825	−	32.3215i	1.93736	−	1.11853i
$836$	0.849884	+	3.07506i	0.0293939	+	0.106353i
$837$	−0.745692	+	1.29158i	−0.0257749	+	0.0446434i
$838$	−3.17979	+	30.2537i	−0.109844	+	1.04510i
$839$	−13.6148	−	4.42371i	−0.470035	−	0.152724i	0.0644160	−	0.997923i	$-0.479482\pi$
$839$	−13.6148	−	4.42371i	−0.470035	−	0.152724i	−0.534451	+	0.845200i	$0.679482\pi$
$840$	−3.18100	−	9.15874i	−0.109755	−	0.316006i
$841$	−21.6290	+	15.7144i	−0.745828	+	0.541876i
$842$	−10.4587	+	23.4907i	−0.360431	+	0.809542i
$843$	6.56154	+	1.39470i	0.225992	+	0.0480360i
$844$	−7.94429	+	7.15307i	−0.273454	+	0.246219i
$845$	13.1834	+	1.38563i	0.453523	+	0.0476671i
$846$	−0.415773			−0.0142946
$847$	18.6868	−	22.3115i	0.642086	−	0.766633i
$848$	11.0048			0.377907
$849$	20.5579	+	2.16072i	0.705545	+	0.0741557i
$850$	−8.20719	+	7.38978i	−0.281504	+	0.253467i
$851$	15.7104	+	3.33934i	0.538544	+	0.114471i
$852$	−3.52778	+	7.92352i	−0.120860	+	0.271455i
$853$	−23.8162	+	17.3035i	−0.815453	+	0.592461i	−0.915406	−	0.402531i	$-0.868131\pi$
$853$	−23.8162	+	17.3035i	−0.815453	+	0.592461i	0.0999537	+	0.994992i	$0.468131\pi$
$854$	−17.3645	−	3.32720i	−0.594201	−	0.113855i
$855$	3.35247	+	1.08928i	0.114652	+	0.0372527i
$856$	0.619599	−	5.89509i	0.0211774	−	0.201490i
$857$	7.54678	−	13.0714i	0.257793	−	0.446511i	−0.707857	−	0.706355i	$-0.750338\pi$
$857$	7.54678	−	13.0714i	0.257793	−	0.446511i	0.965650	+	0.259845i	$0.0836714\pi$
$858$	−3.60164	−	13.0315i	−0.122958	−	0.444887i
$859$	1.56222	−	0.901945i	0.0533021	−	0.0307740i	−0.473112	−	0.881002i	$-0.656869\pi$
$859$	1.56222	−	0.901945i	0.0533021	−	0.0307740i	0.526414	+	0.850228i	$0.323536\pi$
$860$	1.36075	+	0.988644i	0.0464012	+	0.0337125i
$861$	19.2199	+	20.5008i	0.655012	+	0.698664i
$862$	6.70637	+	20.6401i	0.228420	+	0.703004i
$863$	−30.4665	−	13.5646i	−1.03709	−	0.461743i	−0.183683	−	0.982986i	$-0.558802\pi$
$863$	−30.4665	−	13.5646i	−1.03709	−	0.461743i	−0.853408	+	0.521243i	$0.825469\pi$
$864$	0.104528	+	0.994522i	0.00355613	+	0.0338343i
$865$	7.36052	−	34.6285i	0.250265	−	1.17740i
$866$	−27.2414	+	5.79034i	−0.925700	+	0.196764i
$867$	8.98325	−	12.3644i	0.305087	−	0.419916i
$868$	2.04128	+	3.37680i	0.0692856	+	0.114616i
$869$	−6.70046	−	40.2574i	−0.227297	−	1.36564i
$870$	−2.75758	−	4.77626i	−0.0934905	−	0.161930i
$871$	25.9612	−	11.5587i	0.879661	−	0.391650i
$872$	−3.99451	−	4.43635i	−0.135271	−	0.150234i
$873$	7.32132	+	6.59215i	0.247789	+	0.223110i
$874$	4.44417	+	6.11687i	0.150326	+	0.206906i
$875$	26.4956	−	20.0770i	0.895714	−	0.678728i
$876$	0.488577	−	0.158748i	0.0165075	−	0.00536360i
$877$	5.06598	+	23.8336i	0.171066	+	0.804802i	0.977074	+	0.212898i	$0.0682903\pi$
$877$	5.06598	+	23.8336i	0.171066	+	0.804802i	−0.806008	+	0.591904i	$0.798376\pi$
$878$	−2.18573	−	4.90924i	−0.0737650	−	0.165679i
$879$	−11.8295	−	6.82977i	−0.398999	−	0.230362i
$880$	−10.2447	−	6.53926i	−0.345349	−	0.220438i
$881$			58.9406i			1.98576i	0.119123	+	0.992880i	$0.461992\pi$
$881$			58.9406i			1.98576i	−0.119123	+	0.992880i	$0.538008\pi$
$882$	3.10217	+	6.27507i	0.104455	+	0.211293i
$883$	−16.9816	+	52.2639i	−0.571475	+	1.75882i	0.0764041	+	0.997077i	$0.475656\pi$
$883$	−16.9816	+	52.2639i	−0.571475	+	1.75882i	−0.647879	+	0.761743i	$0.724344\pi$
$884$	3.57397	−	3.96929i	0.120205	−	0.133502i
$885$	−48.0366	+	5.04885i	−1.61473	+	0.169715i
$886$	22.9383	−	2.41091i	0.770628	−	0.0809963i
$887$	−2.99484	+	3.32611i	−0.100557	+	0.111680i	−0.791322	−	0.611399i	$-0.790607\pi$
$887$	−2.99484	+	3.32611i	−0.100557	+	0.111680i	0.690766	+	0.723079i	$0.257274\pi$
$888$	−0.631443	+	1.94338i	−0.0211898	+	0.0652156i
$889$	−21.7963	−	15.1753i	−0.731024	−	0.508964i
$890$		−	55.7151i		−	1.86757i
$891$	0.199569	+	3.31062i	0.00668583	+	0.110910i
$892$	−7.93358	−	4.58045i	−0.265636	−	0.153365i
$893$	−0.162671	−	0.365366i	−0.00544359	−	0.0122265i
$894$	0.999995	+	4.70461i	0.0334448	+	0.157346i
$895$	−72.3686	+	23.5140i	−2.41902	+	0.785986i
$896$	2.43818	+	1.02727i	0.0814539	+	0.0343186i
$897$	−18.8335	−	25.9220i	−0.628831	−	0.865512i
$898$	1.23121	+	1.10858i	0.0410859	+	0.0369940i
$899$	1.50190	+	1.66802i	0.0500910	+	0.0556317i
$900$	−7.70004	+	3.42828i	−0.256668	+	0.114276i
$901$	7.20959	+	12.4874i	0.240186	+	0.416015i
$902$	34.8354	+	5.23744i	1.15989	+	0.174388i
$903$	−1.06368	−	0.585901i	−0.0353972	−	0.0194976i
$904$	−7.48858	+	10.3071i	−0.249067	+	0.342811i
$905$	75.3552	−	16.0172i	2.50489	−	0.532431i
$906$	−1.11056	+	5.22478i	−0.0368959	+	0.173582i
$907$	−2.63894	−	25.1079i	−0.0876247	−	0.833693i	−0.946759	−	0.321943i	$-0.895664\pi$
$907$	−2.63894	−	25.1079i	−0.0876247	−	0.833693i	0.859134	−	0.511750i	$-0.171003\pi$
$908$	−10.6892	−	4.75915i	−0.354734	−	0.157938i
$909$	−6.18904	−	19.0479i	−0.205277	−	0.631779i
$910$	−28.8331	+	27.0316i	−0.955807	+	0.896090i
$911$	9.06672	+	6.58736i	0.300394	+	0.218249i	0.727764	−	0.685828i	$-0.240560\pi$
$911$	9.06672	+	6.58736i	0.300394	+	0.218249i	−0.427370	+	0.904077i	$0.640560\pi$
$912$	−0.833052	+	0.480963i	−0.0275851	+	0.0159263i
$913$	−41.4474	−	33.0282i	−1.37171	−	1.09307i
$914$	6.21841	−	10.7706i	0.205687	−	0.356260i
$915$	−2.55973	+	24.3542i	−0.0846222	+	0.805126i
$916$	−5.37986	−	1.74802i	−0.177755	−	0.0577562i
$917$	−25.7028	−	22.2229i	−0.848783	−	0.733864i
$918$	−1.06002	+	0.770152i	−0.0349860	+	0.0254188i
$919$	6.59974	−	14.8233i	0.217705	−	0.488974i	−0.771370	−	0.636387i	$-0.780428\pi$
$919$	6.59974	−	14.8233i	0.217705	−	0.488974i	0.989075	+	0.147413i	$0.0470947\pi$
$920$	−28.1742	−	5.98862i	−0.928877	−	0.197439i
$921$	14.0563	−	12.6563i	0.463169	−	0.417039i
$922$	3.63623	+	0.382183i	0.119753	+	0.0125865i
$923$	35.3565			1.16377
$924$	7.92692	+	3.76351i	0.260776	+	0.123810i
$925$	−17.2232			−0.566296
$926$	−7.03541	−	0.739451i	−0.231198	−	0.0242999i
$927$	10.3172	−	9.28967i	0.338862	−	0.305113i
$928$	1.47212	+	0.312909i	0.0483248	+	0.0102718i
$929$	16.4712	−	36.9948i	0.540401	−	1.21376i	−0.412632	−	0.910898i	$-0.635391\pi$
$929$	16.4712	−	36.9948i	0.540401	−	1.21376i	0.953034	−	0.302864i	$-0.0979428\pi$
$930$	4.42145	−	3.21237i	0.144985	−	0.105338i
$931$	−4.30058	+	5.18119i	−0.140946	+	0.169807i
$932$	14.6716	+	4.76710i	0.480586	+	0.156152i
$933$	−0.868554	+	8.26374i	−0.0284352	+	0.270543i
$934$	−1.43383	+	2.48346i	−0.0469163	+	0.0812614i
$935$	0.708591	−	15.9090i	0.0231734	−	0.520279i
$936$	3.53030	−	2.03822i	0.115392	−	0.0666214i
$937$	4.11270	+	2.98805i	0.134356	+	0.0976155i	0.652933	−	0.757415i	$-0.273538\pi$
$937$	4.11270	+	2.98805i	0.134356	+	0.0976155i	−0.518577	+	0.855031i	$0.673538\pi$
$938$	−5.34545	+	17.6527i	−0.174535	+	0.576381i
$939$	−4.22826	−	13.0133i	−0.137984	−	0.424672i
$940$	1.39189	+	0.619708i	0.0453984	+	0.0202127i
$941$	2.49354	+	23.7244i	0.0812870	+	0.773394i	0.956907	+	0.290394i	$0.0937863\pi$
$941$	2.49354	+	23.7244i	0.0812870	+	0.773394i	−0.875620	+	0.483000i	$0.839547\pi$
$942$	1.42384	−	6.69864i	0.0463912	−	0.218253i
$943$	81.6606	−	17.3575i	2.65923	−	0.565238i
$944$	7.74745	−	10.6635i	0.252158	−	0.347066i
$945$	8.29723	−	5.01569i	0.269909	−	0.163161i
$946$	−1.50164	+	0.249934i	−0.0488226	+	0.00812605i
$947$	−3.74563	−	6.48763i	−0.121717	−	0.210820i	0.798728	−	0.601692i	$-0.205507\pi$
$947$	−3.74563	−	6.48763i	−0.121717	−	0.210820i	−0.920445	+	0.390873i	$0.872173\pi$
$948$	11.2412	−	5.00491i	0.365097	−	0.162552i
$949$	−1.40126	−	1.55626i	−0.0454868	−	0.0505182i
$950$	−6.02529	−	5.42519i	−0.195486	−	0.176016i
$951$	4.10328	+	5.64769i	0.133058	+	0.183139i
$952$	0.431665	+	3.43965i	0.0139903	+	0.111480i
$953$	19.0376	−	6.18568i	0.616687	−	0.200374i	0.0160182	−	0.999872i	$-0.494901\pi$
$953$	19.0376	−	6.18568i	0.616687	−	0.200374i	0.600669	+	0.799498i	$0.294901\pi$
$954$	2.28803	+	10.7643i	0.0740777	+	0.348508i
$955$	34.4113	+	77.2891i	1.11352	+	2.50102i
$956$	−14.6773	−	8.47392i	−0.474697	−	0.274066i
$957$	4.83146	+	1.25403i	0.156179	+	0.0405369i
$958$			16.7912i			0.542499i
$959$	7.08023	+	15.0783i	0.228632	+	0.486904i
$960$	1.13240	−	3.48517i	0.0365481	−	0.112483i
$961$	19.2548	−	21.3846i	0.621121	−	0.689825i
$962$	8.28414	−	0.870698i	0.267091	−	0.0280724i
$963$	5.89509	−	0.619599i	0.189966	−	0.0199663i
$964$	5.45428	−	6.05759i	0.175670	−	0.195102i
$965$	−10.3249	+	31.7767i	−0.332370	+	1.02293i
$966$	20.7216	+	1.75714i	0.666707	+	0.0565351i
$967$			13.0823i			0.420697i	0.977626	+	0.210349i	$0.0674599\pi$
$967$			13.0823i			0.420697i	−0.977626	+	0.210349i	$0.932540\pi$
$968$	10.7224	−	2.45564i	0.344631	−	0.0789274i
$969$	−1.09152	−	0.630187i	−0.0350645	−	0.0202445i
$970$	−14.6841	−	32.9810i	−0.471478	−	1.05896i
$971$	−0.453604	−	2.13404i	−0.0145569	−	0.0684846i	0.970270	−	0.242027i	$-0.0778121\pi$
$971$	−0.453604	−	2.13404i	−0.0145569	−	0.0684846i	−0.984826	+	0.173542i	$0.944479\pi$
$972$	−0.951057	+	0.309017i	−0.0305052	+	0.00991172i
$973$	11.9440	+	15.7625i	0.382908	+	0.505322i
$974$	9.97343	+	13.7273i	0.319569	+	0.439850i
$975$	25.5339	+	22.9909i	0.817740	+	0.736297i
$976$	−4.47150	−	4.96611i	−0.143129	−	0.158961i
$977$	25.6632	−	11.4260i	0.821037	−	0.365549i	0.0471618	−	0.998887i	$-0.484982\pi$
$977$	25.6632	−	11.4260i	0.821037	−	0.365549i	0.773875	+	0.633338i	$0.218316\pi$
$978$	0.564487	+	0.977720i	0.0180503	+	0.0312640i
$979$	35.9351	+	35.3753i	1.14849	+	1.13060i
$980$	−1.03218	−	25.6309i	−0.0329717	−	0.818749i
$981$	3.50890	−	4.82959i	0.112031	−	0.154197i
$982$	−4.26688	+	0.906953i	−0.136161	+	0.0289420i
$983$	−0.496929	+	2.33787i	−0.0158496	+	0.0745664i	−0.985362	−	0.170477i	$-0.945469\pi$
$983$	−0.496929	+	2.33787i	−0.0158496	+	0.0745664i	0.969512	+	0.245044i	$0.0788023\pi$
$984$	1.11023	+	10.5631i	0.0353928	+	0.336740i
$985$	45.5938	+	20.2997i	1.45274	+	0.646801i
$986$	0.609369	+	1.87544i	0.0194062	+	0.0597263i
$987$	−1.05282	−	0.318807i	−0.0335117	−	0.0101477i
$988$	3.17234	+	2.30484i	0.100926	+	0.0733268i
$989$	−3.12438	+	1.80386i	−0.0993496	+	0.0573595i
$990$	4.26636	−	11.3804i	0.135594	−	0.361694i
$991$	−7.00558	+	12.1340i	−0.222540	+	0.385450i	−0.955578	−	0.294737i	$-0.904768\pi$
$991$	−7.00558	+	12.1340i	−0.222540	+	0.385450i	0.733039	+	0.680187i	$0.238101\pi$
$992$	−0.155892	+	1.48321i	−0.00494958	+	0.0470921i
$993$	32.7971	+	10.6564i	1.04078	+	0.338171i
$994$	−15.0087	+	17.3589i	−0.476046	+	0.550591i
$995$	−14.8605	+	10.7968i	−0.471110	+	0.342281i
$996$	6.49941	−	14.5979i	0.205942	−	0.462552i
$997$	−19.1425	−	4.06886i	−0.606249	−	0.128862i	−0.105448	−	0.994425i	$-0.533628\pi$
$997$	−19.1425	−	4.06886i	−0.606249	−	0.128862i	−0.500801	+	0.865563i	$0.666961\pi$
$998$	−0.620701	+	0.558882i	−0.0196480	+	0.0176911i
$999$	−2.03220	−	0.213593i	−0.0642959	−	0.00675777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.a.73.4	yes	64
7.5	odd	6		462.2.ba.b.271.8	yes	64
11.8	odd	10		462.2.ba.b.283.8	yes	64
77.19	even	30	inner	462.2.ba.a.19.4	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.19.4	✓	64	77.19	even	30	inner
462.2.ba.a.73.4	yes	64	1.1	even	1	trivial
462.2.ba.b.271.8	yes	64	7.5	odd	6
462.2.ba.b.283.8	yes	64	11.8	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994522 - 0.104528i) q^{2} +(0.743145 - 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(1.49050 - 3.34771i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49930 + 0.868052i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.994522 - 0.104528i) q^{2} +(0.743145 - 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(1.49050 - 3.34771i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-2.49930 + 0.868052i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +(-1.83226 + 3.17357i) q^{10} +(-0.883524 - 3.19678i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-3.29791 - 2.39607i) q^{13} +(2.57634 - 0.602049i) q^{14} +(-1.13240 - 3.48517i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.136960 + 1.30308i) q^{17} +(-0.207912 + 0.978148i) q^{18} +(-0.940905 + 0.199996i) q^{19} +(2.15395 - 2.96466i) q^{20} +(-1.27650 + 2.31744i) q^{21} +(0.544530 + 3.27162i) q^{22} +(3.93007 + 6.80708i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-5.63993 - 6.26378i) q^{25} +(3.02939 + 2.72767i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-2.62516 + 0.329450i) q^{28} +(-1.43135 + 0.465074i) q^{29} +(0.761898 + 3.58445i) q^{30} +(-0.606600 - 1.36245i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.79565 - 1.78448i) q^{33} -1.31026i q^{34} +(-0.819209 + 9.66075i) q^{35} +(0.309017 - 0.951057i) q^{36} +(1.36730 - 1.51854i) q^{37} +(0.956656 - 0.100549i) q^{38} +(-4.05411 + 0.426104i) q^{39} +(-2.45205 + 2.72327i) q^{40} +(3.28216 - 10.1015i) q^{41} +(1.51175 - 2.17132i) q^{42} +0.458990i q^{43} +(-0.199569 - 3.31062i) q^{44} +(-3.17357 - 1.83226i) q^{45} +(-3.19701 - 7.18059i) q^{46} +(0.0864441 + 0.406687i) q^{47} +(0.951057 - 0.309017i) q^{48} +(5.49297 - 4.33904i) q^{49} +(4.95429 + 6.81900i) q^{50} +(0.973714 + 0.876736i) q^{51} +(-2.72767 - 3.02939i) q^{52} +(10.0534 - 4.47606i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-12.0188 - 1.80700i) q^{55} +(2.64522 - 0.0532409i) q^{56} +(-0.565406 + 0.778214i) q^{57} +(1.47212 - 0.312909i) q^{58} +(2.74043 - 12.8927i) q^{59} +(-0.383047 - 3.64445i) q^{60} +(-6.10482 - 2.71804i) q^{61} +(0.460863 + 1.41839i) q^{62} +(0.602049 + 2.57634i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-12.9369 + 7.46911i) q^{65} +(2.59380 + 2.06692i) q^{66} +(-3.48564 + 6.03731i) q^{67} +(-0.136960 + 1.30308i) q^{68} +(7.47544 + 2.42892i) q^{69} +(1.82454 - 9.52220i) q^{70} +(-7.01690 + 5.09808i) q^{71} +(-0.406737 + 0.913545i) q^{72} +(0.502494 + 0.106808i) q^{73} +(-1.51854 + 1.36730i) q^{74} +(-8.38257 - 0.881044i) q^{75} -0.961925 q^{76} +(4.98316 + 7.22275i) q^{77} +4.07644 q^{78} +(12.2376 + 1.28623i) q^{79} +(2.72327 - 2.45205i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-4.32008 + 9.70305i) q^{82} +(12.9276 - 9.39245i) q^{83} +(-1.73043 + 2.00140i) q^{84} +(4.56649 + 1.48374i) q^{85} +(0.0479776 - 0.456476i) q^{86} +(-0.752505 + 1.30338i) q^{87} +(-0.147577 + 3.31334i) q^{88} +(-13.1670 + 7.60195i) q^{89} +(2.96466 + 2.15395i) q^{90} +(10.3224 + 3.12574i) q^{91} +(2.42892 + 7.47544i) q^{92} +(-1.36245 - 0.606600i) q^{93} +(-0.0434601 - 0.413495i) q^{94} +(-0.732889 + 3.44797i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(-5.79075 + 7.97028i) q^{97} +(-5.91643 + 3.74110i) q^{98} +(-3.27162 + 0.544530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Introduction

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