LMFDB - Embedded newform 462.2.ba.a.19.4

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			19.4
Character	$\chi$	$=$	462.19
Dual form			462.2.ba.a.73.4

$q$-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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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	0.856933	+	0.515428i	$0.172367\pi$
$5$	1.49050	+	3.34771i	0.666570	+	1.49714i	−0.190363	+	0.981714i	$0.560966\pi$
$6$	−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	−0.942193	−	0.335070i	$-0.891240\pi$
$13$	−3.29791	+	2.39607i	−0.914676	+	0.664551i	0.0275170	+	0.999621i	$0.491240\pi$
$14$	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	−0.965279	−	0.261223i	$-0.915874\pi$
$17$	0.136960	−	1.30308i	0.0332176	−	0.316044i	0.998496	−	0.0548216i	$-0.0174590\pi$
$18$	−0.207912	−	0.978148i	−0.0490053	−	0.230552i
$19$	−0.940905	−	0.199996i	−0.215858	−	0.0458821i	0.0987130	−	0.995116i	$-0.468527\pi$
$19$	−0.940905	−	0.199996i	−0.215858	−	0.0458821i	−0.314571	+	0.949234i	$0.601861\pi$
$20$	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	−0.0865929	−	0.996244i	$-0.527598\pi$
$23$	3.93007	−	6.80708i	0.819476	−	1.41937i	0.906069	−	0.423130i	$-0.139069\pi$
$24$	−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	0.173088	−	0.984906i	$-0.444626\pi$
$29$	−1.43135	−	0.465074i	−0.265795	−	0.0863621i	−0.438883	+	0.898544i	$0.644626\pi$
$30$	0.761898	−	3.58445i	0.139103	−	0.654427i
$31$	−0.606600	+	1.36245i	−0.108949	+	0.244703i	−0.959789	−	0.280721i	$-0.909426\pi$
$31$	−0.606600	+	1.36245i	−0.108949	+	0.244703i	0.850841	+	0.525424i	$0.176093\pi$
$32$	−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	0.844978	−	0.534801i	$-0.179614\pi$
$37$	1.36730	+	1.51854i	0.224782	+	0.249646i	−0.620196	+	0.784447i	$0.712947\pi$
$38$	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	0.787628	+	0.616151i	$0.211309\pi$
$41$	3.28216	+	10.1015i	0.512588	+	1.57758i	−0.275040	+	0.961433i	$0.588691\pi$
$42$	1.51175	+	2.17132i	0.233267	+	0.335042i
$43$		−	0.458990i		−	0.0699954i	−0.999387	−	0.0349977i	$-0.988858\pi$
$43$		−	0.458990i		−	0.0699954i	0.999387	−	0.0349977i	$-0.0111424\pi$
$44$	−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	−0.971393	−	0.237477i	$-0.923680\pi$
$47$	0.0864441	−	0.406687i	0.0126092	−	0.0593214i	0.984002	+	0.178155i	$0.0570130\pi$
$48$	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	0.956796	−	0.290760i	$-0.0939081\pi$
$53$	10.0534	+	4.47606i	1.38094	+	0.614834i	0.424145	+	0.905594i	$0.360575\pi$
$54$	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	0.680822	+	0.732449i	$0.261623\pi$
$59$	2.74043	+	12.8927i	0.356774	+	1.67849i	−0.324048	+	0.946041i	$0.605044\pi$
$60$	−0.383047	+	3.64445i	−0.0494512	+	0.470497i
$61$	−6.10482	+	2.71804i	−0.781642	+	0.348009i	−0.758458	−	0.651722i	$-0.774047\pi$
$61$	−6.10482	+	2.71804i	−0.781642	+	0.348009i	−0.0231838	+	0.999731i	$0.507380\pi$
$62$	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	0.570659	−	0.821187i	$-0.306688\pi$
$67$	−3.48564	−	6.03731i	−0.425839	−	0.737575i	−0.996498	+	0.0836119i	$0.973354\pi$
$68$	−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	0.0875836	−	0.996157i	$-0.472086\pi$
$71$	−7.01690	−	5.09808i	−0.832753	−	0.605031i	−0.920337	+	0.391126i	$0.872086\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	0.502494	−	0.106808i	0.0588124	−	0.0125010i	−0.178411	−	0.983956i	$-0.557096\pi$
$73$	0.502494	−	0.106808i	0.0588124	−	0.0125010i	0.237224	+	0.971455i	$0.423762\pi$
$74$	−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	0.612983	−	0.790096i	$-0.289970\pi$
$79$	12.2376	−	1.28623i	1.37684	−	0.144712i	0.763858	+	0.645385i	$0.223303\pi$
$80$	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	0.991937	+	0.126728i	$0.0404476\pi$
$83$	12.9276	+	9.39245i	1.41899	+	1.03096i	0.427051	+	0.904227i	$0.359552\pi$
$84$	−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	−0.401757	−	0.915746i	$-0.631600\pi$
$89$	−13.1670	−	7.60195i	−1.39570	−	0.805805i	−0.993938	+	0.109941i	$0.964934\pi$
$90$	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	0.406578	−	0.913616i	$-0.366722\pi$
$97$	−5.79075	−	7.97028i	−0.587962	−	0.809260i	−0.994540	+	0.104356i	$0.966722\pi$
$98$	−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	0.944593	+	0.328245i	$0.106457\pi$
$101$	18.2966	+	8.14618i	1.82058	+	0.810575i	0.875989	+	0.482330i	$0.160210\pi$
$102$	−0.876736	+	0.973714i	−0.0868098	+	0.0964121i
$103$	10.3172	−	9.28967i	1.01659	−	0.915338i	0.0201590	−	0.999797i	$-0.493583\pi$
$103$	10.3172	−	9.28967i	1.01659	−	0.915338i	0.996427	+	0.0844587i	$0.0269161\pi$
$104$	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	−0.877568	−	0.479453i	$-0.840835\pi$
$107$	1.23241	−	5.79803i	0.119141	−	0.560516i	0.996709	−	0.0810633i	$-0.0258316\pi$
$108$	−0.406737	+	0.913545i	−0.0391383	+	0.0879060i
$109$	5.16991	−	2.98485i	0.495188	−	0.285897i	−0.231536	−	0.972826i	$-0.574375\pi$
$109$	5.16991	−	2.98485i	0.495188	−	0.285897i	0.726724	+	0.686929i	$0.241042\pi$
$110$	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	0.946556	+	0.322539i	$0.104536\pi$
$113$	3.93698	+	12.1168i	0.370360	+	1.13985i	−0.576196	+	0.817312i	$0.695464\pi$
$114$	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	−0.462562	−	0.886587i	$-0.653070\pi$
$127$	5.90035	−	8.12114i	0.523571	−	0.720634i	0.986134	+	0.165953i	$0.0530698\pi$
$128$	−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	−0.436384	−	0.899760i	$-0.643741\pi$
$131$	6.42120	−	11.1219i	0.561023	−	0.971721i	0.997407	−	0.0719604i	$-0.0229255\pi$
$132$	−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	0.929763	+	0.368159i	$0.120012\pi$
$137$	−0.658120	+	6.26160i	−0.0562270	+	0.534964i	−0.985990	+	0.166805i	$0.946655\pi$
$138$	−7.18059	+	3.19701i	−0.611253	+	0.272147i
$139$	−2.30986	+	7.10902i	−0.195920	+	0.602979i	0.804045	+	0.594569i	$0.202677\pi$
$139$	−2.30986	+	7.10902i	−0.195920	+	0.602979i	−0.999965	+	0.00841039i	$0.997323\pi$
$140$	−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	0.975773	−	0.218784i	$-0.0702091\pi$
$149$	1.95629	+	4.39389i	0.160265	+	0.359961i	−0.815508	+	0.578746i	$0.803542\pi$
$150$	8.24455	−	1.75243i	0.673165	−	0.143086i
$151$	3.96951	+	3.57416i	0.323034	+	0.290861i	0.814652	−	0.579949i	$-0.196928\pi$
$151$	3.96951	+	3.57416i	0.323034	+	0.290861i	−0.491618	+	0.870811i	$0.663594\pi$
$152$	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	0.440576	−	0.897715i	$-0.354774\pi$
$157$	−5.08927	−	4.58240i	−0.406168	−	0.365715i	−0.846745	+	0.532000i	$0.821441\pi$
$158$	−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	0.998171	−	0.0604544i	$-0.0192550\pi$
$163$	0.118010	+	1.12279i	0.00924325	+	0.0879436i	−0.988928	+	0.148398i	$0.952588\pi$
$164$	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	0.122579	−	0.992459i	$-0.460884\pi$
$167$	14.2712	−	10.3687i	1.10434	−	0.802351i	0.981763	+	0.190107i	$0.0608836\pi$
$168$	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	0.552606	−	0.833443i	$-0.313634\pi$
$173$	9.44966	+	2.00859i	0.718444	+	0.152710i	0.165839	+	0.986153i	$0.446967\pi$
$174$	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	−0.0505428	+	0.998722i	$0.516095\pi$
$179$	−13.8943	+	15.4312i	−1.03851	+	1.15338i	−0.987968	+	0.154661i	$0.950572\pi$
$180$	−2.72327	+	2.45205i	−0.202981	+	0.182765i
$181$	12.3569	−	17.0078i	0.918481	−	1.26418i	−0.0457049	−	0.998955i	$-0.514553\pi$
$181$	12.3569	−	17.0078i	0.918481	−	1.26418i	0.964186	−	0.265226i	$-0.0854466\pi$
$182$	−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	−0.967518	−	0.252802i	$-0.918648\pi$
$191$	−15.4483	−	17.1571i	−1.11780	−	1.24144i	−0.150284	−	0.988643i	$-0.548019\pi$
$192$	0.994522	+	0.104528i	0.0717734	+	0.00754369i
$193$	−9.06776	−	0.953059i	−0.652711	−	0.0686027i	−0.227616	−	0.973751i	$-0.573093\pi$
$193$	−9.06776	−	0.953059i	−0.652711	−	0.0686027i	−0.425096	+	0.905148i	$0.639760\pi$
$194$	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	$-0.838757\pi$
$197$		−	13.6194i		−	0.970342i	0.874419	−	0.485171i	$-0.161243\pi$
$198$	3.31062	+	0.199569i	0.235275	+	0.0141828i
$199$	−4.34099	+	2.50627i	−0.307725	+	0.177665i	−0.645908	−	0.763415i	$-0.723521\pi$
$199$	−4.34099	+	2.50627i	−0.307725	+	0.177665i	0.338183	+	0.941080i	$0.390188\pi$
$200$	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	0.535969	−	0.844238i	$-0.319947\pi$
$211$	−6.28348	−	8.64847i	−0.432573	−	0.595386i	−0.968541	+	0.248852i	$0.919947\pi$
$212$	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	−0.585839	−	0.810428i	$-0.699235\pi$
$223$	−8.71254	+	2.83088i	−0.583435	+	0.189569i	0.00240391	+	0.999997i	$0.499235\pi$
$224$	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	−0.571417	−	0.820660i	$-0.693606\pi$
$227$	−11.4451	+	2.43274i	−0.759639	+	0.161466i	−0.188223	+	0.982126i	$0.560273\pi$
$228$	−0.714850	−	0.643654i	−0.0473421	−	0.0426270i
$229$	−5.62573	+	0.591288i	−0.371759	+	0.0390734i	−0.288566	−	0.957460i	$-0.593178\pi$
$229$	−5.62573	+	0.591288i	−0.371759	+	0.0390734i	−0.0831928	+	0.996533i	$0.526512\pi$
$230$	−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	0.412348	−	0.911026i	$-0.364709\pi$
$233$	15.3422	−	1.61253i	1.00510	−	0.105640i	0.592750	+	0.805386i	$0.298042\pi$
$234$	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	−0.779764	−	0.626073i	$-0.784661\pi$
$239$	−16.1184	+	5.23717i	−1.04261	+	0.338764i	−0.262846	+	0.964838i	$0.584661\pi$
$240$	0.383047	+	3.64445i	0.0247256	+	0.235248i
$241$	4.07564	+	7.05922i	0.262535	+	0.454724i	0.966915	−	0.255099i	$-0.0821081\pi$
$241$	4.07564	+	7.05922i	0.262535	+	0.454724i	−0.704380	+	0.709823i	$0.748775\pi$
$242$	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	0.978913	−	0.204277i	$-0.0654842\pi$
$251$	7.63843	+	10.5134i	0.482134	+	0.663600i	−0.496779	+	0.867877i	$0.665484\pi$
$252$	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	−0.490847	−	0.871246i	$-0.663313\pi$
$257$	5.19921	−	4.68139i	0.324318	−	0.292017i	0.815165	+	0.579228i	$0.196646\pi$
$258$	−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	−0.651223	−	0.758886i	$-0.725744\pi$
$263$	−5.18336	+	2.99261i	−0.319619	+	0.184532i	0.331604	+	0.943419i	$0.392410\pi$
$264$	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	−0.298332	−	0.954462i	$-0.596430\pi$
$269$	−12.9338	−	1.35940i	−0.788589	−	0.0828840i	−0.490257	+	0.871578i	$0.663097\pi$
$270$	3.64445	+	0.383047i	0.221794	+	0.0233115i
$271$	12.0433	+	13.3754i	0.731579	+	0.812500i	0.988063	−	0.154048i	$-0.0492310\pi$
$271$	12.0433	+	13.3754i	0.731579	+	0.812500i	−0.256485	+	0.966548i	$0.582564\pi$
$272$	−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	0.285270	+	0.958447i	$0.407917\pi$
$277$	−10.2835	+	23.0972i	−0.617878	+	1.38778i	−0.903148	+	0.429330i	$0.858750\pi$
$278$	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	−0.675049	−	0.737773i	$-0.735878\pi$
$281$	3.94294	−	5.42699i	0.235216	−	0.323747i	0.910265	+	0.414026i	$0.135878\pi$
$282$	−0.308980	+	0.278206i	−0.0183995	+	0.0165670i
$283$	13.8317	−	15.3616i	0.822208	−	0.913154i	−0.175242	−	0.984525i	$-0.556071\pi$
$283$	13.8317	−	15.3616i	0.822208	−	0.913154i	0.997450	+	0.0713710i	$0.0227374\pi$
$284$	−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	0.748775	+	0.662824i	$0.230642\pi$
$293$	−4.22103	+	12.9910i	−0.246595	+	0.758942i	−0.995370	+	0.0961173i	$0.969358\pi$
$294$	−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	0.475221	−	0.879866i	$-0.342368\pi$
$311$	−6.17498	−	5.55998i	−0.350151	−	0.315277i	−0.825372	+	0.564589i	$0.809035\pi$
$312$	3.98736	−	0.847540i	0.225740	−	0.0479825i
$313$	5.56536	+	12.5000i	0.314573	+	0.706542i	0.999762	−	0.0218235i	$-0.00694719\pi$
$313$	5.56536	+	12.5000i	0.314573	+	0.706542i	−0.685189	+	0.728365i	$0.740281\pi$
$314$	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	−0.995715	−	0.0924698i	$-0.970524\pi$
$317$	−0.729705	−	6.94268i	−0.0409843	−	0.389940i	0.954731	−	0.297470i	$-0.0961428\pi$
$318$	−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	0.197543	−	0.980294i	$-0.436704\pi$
$331$	17.2425	−	29.8648i	0.947731	−	1.64152i	0.750188	−	0.661224i	$-0.229963\pi$
$332$	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	−0.458895	−	0.888491i	$-0.651755\pi$
$337$	−24.8266	−	8.06665i	−1.35239	−	0.439418i	−0.893495	+	0.449072i	$0.851755\pi$
$338$	−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	−0.391195	−	0.920308i	$-0.627938\pi$
$347$	−17.9794	−	1.88971i	−0.965184	−	0.101445i	−0.573989	+	0.818863i	$0.694605\pi$
$348$	−1.00705	−	1.11844i	−0.0539835	−	0.0599547i
$349$	−1.02097	−	3.14222i	−0.0546512	−	0.168199i	0.920005	−	0.391906i	$-0.128184\pi$
$349$	−1.02097	−	3.14222i	−0.0546512	−	0.168199i	−0.974656	+	0.223707i	$0.928184\pi$
$350$	−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	−0.788013	−	0.615659i	$-0.788890\pi$
$353$	−12.1906	+	7.03827i	−0.648842	+	0.374609i	0.139170	+	0.990268i	$0.455556\pi$
$354$	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	−0.0683730	−	0.997660i	$-0.521781\pi$
$359$	17.3685	−	15.6387i	0.916675	−	0.825378i	0.985048	+	0.172282i	$0.0551141\pi$
$360$	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	−0.767755	−	0.640743i	$-0.778626\pi$
$367$	−6.26422	−	29.4709i	−0.326990	−	1.53837i	0.440765	−	0.897622i	$-0.354707\pi$
$368$	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	−0.998572	−	0.0534280i	$-0.982985\pi$
$373$	−29.8221	−	17.2178i	−1.54413	−	0.891502i	−0.545556	−	0.838074i	$-0.683681\pi$
$374$	−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	0.679025	−	0.734115i	$-0.262403\pi$
$379$	3.71197	+	2.69691i	0.190671	+	0.138531i	−0.488354	+	0.872645i	$0.662403\pi$
$380$	−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	−0.310235	−	0.950660i	$-0.600408\pi$
$383$	−8.14200	+	0.855758i	−0.416037	+	0.0437272i	−0.105802	+	0.994387i	$0.533741\pi$
$384$	−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	0.601299	−	0.799024i	$-0.294650\pi$
$389$	29.1035	−	6.18613i	1.47560	−	0.313649i	0.874306	+	0.485375i	$0.161317\pi$
$390$	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	0.733527	−	0.679660i	$-0.237873\pi$
$397$	10.1953	+	5.88627i	0.511688	+	0.295423i	−0.221839	+	0.975083i	$0.571206\pi$
$398$	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	−0.502200	−	0.864752i	$-0.667476\pi$
$401$	−3.91691	+	1.74392i	−0.195601	+	0.0870872i	0.306599	+	0.951839i	$0.400809\pi$
$402$	−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	0.318974	−	0.947763i	$-0.396662\pi$
$409$	−3.47679	−	1.54797i	−0.171916	−	0.0765420i	−0.490890	+	0.871221i	$0.663328\pi$
$410$	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	$0.266629\pi$
$419$			30.4203i			1.48613i	−0.669219	+	0.743065i	$0.733371\pi$
$420$	4.12092	−	8.77606i	0.201080	−	0.428228i
$421$	7.94598	+	24.4552i	0.387263	+	1.19187i	0.934825	+	0.355109i	$0.115556\pi$
$421$	7.94598	+	24.4552i	0.387263	+	1.19187i	−0.547562	+	0.836765i	$0.684444\pi$
$422$	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	0.566230	+	0.824247i	$0.308401\pi$
$431$	−8.82711	+	19.8260i	−0.425187	+	0.954985i	−0.991417	+	0.130738i	$0.958265\pi$
$432$	−0.207912	+	0.978148i	−0.0100032	+	0.0470611i
$433$	26.4869	+	8.60612i	1.27288	+	0.413584i	0.866067	−	0.499928i	$-0.166640\pi$
$433$	26.4869	+	8.60612i	1.27288	+	0.413584i	0.406813	+	0.913512i	$0.366640\pi$
$434$	−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	−0.794755	−	0.606930i	$-0.792401\pi$
$439$	2.68692	−	4.65388i	0.128240	−	0.222117i	0.922995	+	0.384813i	$0.125734\pi$
$440$	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	−0.362020	−	0.932170i	$-0.617913\pi$
$443$	−22.5607	−	4.79541i	−1.07189	−	0.227837i	−0.709869	+	0.704333i	$0.751246\pi$
$444$	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	−0.618963	−	0.785420i	$-0.712447\pi$
$449$	−1.34034	+	0.973816i	−0.0632547	+	0.0459572i	0.555709	+	0.831377i	$0.312447\pi$
$450$	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	0.755728	−	0.654885i	$-0.227283\pi$
$457$	−5.05851	−	11.3616i	−0.236627	−	0.531474i	−0.992356	+	0.123412i	$0.960616\pi$
$458$	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	0.938519	−	0.345227i	$-0.112198\pi$
$467$	1.16638	+	2.61973i	0.0539737	+	0.121227i	−0.884546	+	0.466454i	$0.845531\pi$
$468$	−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	0.878341	+	0.478035i	$0.158651\pi$
$479$	−1.75516	+	16.6992i	−0.0801953	+	0.763007i	−0.958536	+	0.284972i	$0.908016\pi$
$480$	−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	−0.943276	−	0.332011i	$-0.892273\pi$
$487$	−11.3537	+	12.6095i	−0.514485	+	0.571393i	0.428791	+	0.903404i	$0.358940\pi$
$488$	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	0.401130	−	0.916021i	$-0.368617\pi$
$491$	4.14870	+	1.34799i	0.187228	+	0.0608341i	−0.213902	+	0.976855i	$0.568617\pi$
$492$	−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	0.755524	−	0.655120i	$-0.227382\pi$
$499$	0.558882	+	0.620701i	0.0250190	+	0.0277864i	−0.730505	+	0.682907i	$0.760715\pi$
$500$	−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	−0.906696	−	0.421786i	$-0.861403\pi$
$503$	−9.44390	−	29.0653i	−0.421083	−	1.29596i	0.485613	−	0.874174i	$-0.338597\pi$
$504$	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	−0.783679	−	0.621166i	$-0.786659\pi$
$509$	4.17150	−	19.6254i	0.184899	−	0.869879i	0.968577	−	0.248713i	$-0.0800076\pi$
$510$	−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	0.805692	+	0.592335i	$0.201794\pi$
$521$	7.08912	+	33.3517i	0.310580	+	1.46116i	−0.495112	+	0.868829i	$0.664873\pi$
$522$	−0.157316	+	1.49677i	−0.00688556	+	0.0655117i
$523$	−28.1546	+	12.5353i	−1.23112	+	0.548128i	−0.916097	−	0.400957i	$-0.868678\pi$
$523$	−28.1546	+	12.5353i	−1.23112	+	0.548128i	−0.315020	+	0.949085i	$0.602011\pi$
$524$	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	−0.138427	−	0.990373i	$-0.544205\pi$
$541$	−1.57974	+	0.166037i	−0.0679183	+	0.00713850i	0.0705083	+	0.997511i	$0.477538\pi$
$542$	−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	−0.370689	−	0.928757i	$-0.620878\pi$
$547$	−2.91586	+	0.947420i	−0.124673	+	0.0405087i	0.246016	+	0.969266i	$0.420878\pi$
$548$	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	−0.661859	−	0.749628i	$-0.730232\pi$
$557$	−8.54638	−	40.2076i	−0.362122	−	1.70365i	0.299737	−	0.954022i	$-0.403101\pi$
$558$	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	−0.385707	−	0.922621i	$-0.626042\pi$
$563$	−31.5444	−	14.0445i	−1.32944	−	0.591903i	−0.943730	+	0.330718i	$0.892709\pi$
$564$	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	0.0683324	+	0.997663i	$0.478232\pi$
$569$	−9.53859	+	44.8755i	−0.399878	+	1.88128i	−0.468211	+	0.883617i	$0.655101\pi$
$570$	−1.43375	+	3.22025i	−0.0600530	+	0.134881i
$571$	2.52002	−	1.45494i	0.105460	−	0.0608872i	−0.446342	−	0.894862i	$-0.647274\pi$
$571$	2.52002	−	1.45494i	0.105460	−	0.0608872i	0.551802	+	0.833975i	$0.313940\pi$
$572$	−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	0.348219	−	0.937413i	$-0.386787\pi$
$577$	11.8646	+	1.24702i	0.493928	+	0.0519140i	0.145710	+	0.989327i	$0.453453\pi$
$578$	−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	0.448922	−	0.893571i	$-0.351808\pi$
$587$	6.95055	+	2.25837i	0.286880	+	0.0932130i	−0.162042	+	0.986784i	$0.551808\pi$
$588$	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	−0.279944	−	0.960016i	$-0.590316\pi$
$593$	16.8373	−	29.1631i	0.691426	−	1.19759i	0.971371	−	0.237569i	$-0.0763507\pi$
$594$	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	0.561127	+	0.827730i	$0.310368\pi$
$599$	−3.91182	+	37.2185i	−0.159833	+	1.52071i	−0.720960	+	0.692977i	$0.756299\pi$
$600$	7.70004	−	3.42828i	0.314353	−	0.139959i
$601$	−1.89560	+	5.83407i	−0.0773233	+	0.237977i	−0.982245	−	0.187601i	$-0.939929\pi$
$601$	−1.89560	+	5.83407i	−0.0773233	+	0.237977i	0.904922	+	0.425577i	$0.139929\pi$
$602$	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	0.989195	−	0.146609i	$-0.0468359\pi$
$607$	−0.218422	−	2.07815i	−0.00886547	−	0.0843494i	−0.998060	+	0.0622598i	$0.980169\pi$
$608$	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	0.0219391	−	0.999759i	$-0.493016\pi$
$613$	−24.0173	−	21.6253i	−0.970050	−	0.873437i	−0.991989	+	0.126322i	$0.959683\pi$
$614$	−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	0.980800	−	0.195018i	$-0.0624764\pi$
$619$	22.1273	+	19.9235i	0.889372	+	0.800794i	−0.0914278	+	0.995812i	$0.529143\pi$
$620$	−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	−0.349993	−	0.936752i	$-0.613816\pi$
$631$	12.1521	−	37.4003i	0.483767	−	1.48888i	0.833759	−	0.552128i	$-0.186184\pi$
$632$	−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	0.0474104	−	0.998875i	$-0.484903\pi$
$641$	26.2258	−	29.1267i	1.03586	−	1.15044i	0.988448	−	0.151562i	$-0.0484302\pi$
$642$	−4.40503	+	3.96631i	−0.173853	+	0.156538i
$643$	5.56431	−	7.65861i	0.219435	−	0.302026i	−0.685080	−	0.728467i	$-0.740233\pi$
$643$	5.56431	−	7.65861i	0.219435	−	0.302026i	0.904515	+	0.426441i	$0.140233\pi$
$644$	−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	−0.684457	−	0.729053i	$-0.739961\pi$
$647$	8.02069	−	18.0148i	0.315326	−	0.708234i	0.999783	+	0.0208193i	$0.00662747\pi$
$648$	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	0.723260	−	0.690575i	$-0.242643\pi$
$653$	−1.00000	−	1.11061i	−0.0391331	−	0.0434617i	−0.762394	+	0.647114i	$0.775976\pi$
$654$	−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	$0.0506817\pi$
$659$			8.14023i			0.317098i	−0.987351	+	0.158549i	$0.949318\pi$
$660$	−11.3121	−	4.44448i	−0.440322	−	0.173001i
$661$	7.43965	−	4.29528i	0.289369	−	0.167067i	−0.348288	−	0.937387i	$-0.613237\pi$
$661$	7.43965	−	4.29528i	0.289369	−	0.167067i	0.637657	+	0.770320i	$0.279904\pi$
$662$	−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	0.983137	−	0.182868i	$-0.0585381\pi$
$673$	13.1116	+	18.0465i	0.505413	+	0.695642i	−0.477724	+	0.878510i	$0.658538\pi$
$674$	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	−0.384790	−	0.923004i	$-0.625726\pi$
$677$	1.13600	−	0.505781i	0.0436601	−	0.0194387i	0.428451	+	0.903565i	$0.359060\pi$
$678$	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	0.999467	+	0.0326478i	$0.0103940\pi$
$683$	13.7991	+	23.9007i	0.528007	+	0.914535i	−0.471460	+	0.881888i	$0.656273\pi$
$684$	−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	−0.963127	−	0.269047i	$-0.913291\pi$
$691$	−48.6115	+	5.10928i	−1.84927	+	0.194366i	−0.886143	+	0.463413i	$0.846625\pi$
$692$	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	0.511692	−	0.859169i	$-0.329019\pi$
$701$	37.8789	−	12.3076i	1.43067	−	0.464852i	0.918974	+	0.394317i	$0.129019\pi$
$702$	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	0.156072	−	0.987746i	$-0.450117\pi$
$709$	26.4817	−	11.7904i	0.994542	−	0.442799i	0.838470	+	0.544947i	$0.183450\pi$
$710$	−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	0.398632	−	0.917111i	$-0.369485\pi$
$719$	36.2631	−	32.6515i	1.35239	−	1.21769i	0.953755	−	0.300584i	$-0.0971814\pi$
$720$	−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	$0.268252\pi$
$727$			40.2539i			1.49293i	−0.665422	+	0.746467i	$0.731748\pi$
$728$	−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	0.976238	−	0.216699i	$-0.0695290\pi$
$733$	17.8331	+	19.8057i	0.658682	+	0.731540i	−0.317557	+	0.948239i	$0.602862\pi$
$734$	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	−0.683082	−	0.730342i	$-0.739361\pi$
$739$	8.61040	−	19.3393i	0.316739	−	0.711407i	0.999821	+	0.0189348i	$0.00602748\pi$
$740$	−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	0.308061	+	0.951366i	$0.400320\pi$
$743$	−18.8609	+	25.9598i	−0.691938	+	0.952371i	−0.999999	+	0.00100460i	$0.999680\pi$
$744$	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	0.0116181	−	0.999933i	$-0.496302\pi$
$751$	−10.5364	−	2.23957i	−0.384477	−	0.0817232i	−0.396096	+	0.918209i	$0.629635\pi$
$752$	−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	0.195085	−	0.980786i	$-0.437502\pi$
$757$	32.6904	−	23.7510i	1.18815	−	0.863243i	0.993068	+	0.117543i	$0.0375018\pi$
$758$	−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	0.989497	−	0.144556i	$-0.0461755\pi$
$761$	−0.232610	−	2.21314i	−0.00843211	−	0.0802261i	−0.997929	+	0.0643303i	$0.979509\pi$
$762$	−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	0.411888	−	0.911235i	$-0.364870\pi$
$773$	−12.5475	−	11.2978i	−0.451301	−	0.406353i	−0.863189	+	0.504881i	$0.831536\pi$
$774$	−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	0.867996	+	0.496572i	$0.165408\pi$
$787$	−2.36422	+	22.4940i	−0.0842753	+	0.801826i	−0.952271	+	0.305254i	$0.901259\pi$
$788$	−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	−0.970518	−	0.241028i	$-0.922515\pi$
$797$	−12.4607	+	17.1507i	−0.441380	+	0.607508i	0.529138	+	0.848536i	$0.322515\pi$
$798$	−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	0.662316	−	0.749225i	$-0.269574\pi$
$809$	32.8341	+	3.45100i	1.15439	+	0.121331i	0.492070	+	0.870556i	$0.336240\pi$
$810$	2.45205	+	2.72327i	0.0861561	+	0.0956860i
$811$	7.12527	+	21.9293i	0.250202	+	0.770043i	0.994737	+	0.102460i	$0.0326713\pi$
$811$	7.12527	+	21.9293i	0.250202	+	0.770043i	−0.744535	+	0.667583i	$0.767329\pi$
$812$	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	0.177215	−	0.984172i	$-0.443291\pi$
$821$	33.6536	−	30.3019i	1.17452	−	1.05754i	0.997305	−	0.0733698i	$-0.0233753\pi$
$822$	4.21290	−	4.67890i	0.146942	−	0.163196i
$823$	−21.3267	−	9.49524i	−0.743400	−	0.330983i	−0.000153079	−	1.00000i	$-0.500049\pi$
$823$	−21.3267	−	9.49524i	−0.743400	−	0.330983i	−0.743247	+	0.669017i	$0.766715\pi$
$824$	−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	0.853506	−	0.521083i	$-0.174472\pi$
$827$	2.70837	+	3.72775i	0.0941791	+	0.129626i	−0.759327	+	0.650709i	$0.774472\pi$
$828$	7.68837	+	1.63421i	0.267189	+	0.0567929i
$829$	−2.50271	−	11.7743i	−0.0869225	−	0.408938i	−0.999999	−	0.00115076i	$-0.999634\pi$
$829$	−2.50271	−	11.7743i	−0.0869225	−	0.408938i	0.913077	−	0.407788i	$-0.133700\pi$
$830$	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	−0.534451	−	0.845200i	$-0.679482\pi$
$839$	−13.6148	+	4.42371i	−0.470035	+	0.152724i	0.0644160	+	0.997923i	$0.479482\pi$
$840$	−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	0.0999537	−	0.994992i	$-0.468131\pi$
$853$	−23.8162	−	17.3035i	−0.815453	−	0.592461i	−0.915406	+	0.402531i	$0.868131\pi$
$854$	−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	0.965650	−	0.259845i	$-0.0836714\pi$
$857$	7.54678	+	13.0714i	0.257793	+	0.446511i	−0.707857	+	0.706355i	$0.750338\pi$
$858$	−3.60164	+	13.0315i	−0.122958	+	0.444887i
$859$	1.56222	+	0.901945i	0.0533021	+	0.0307740i	0.526414	−	0.850228i	$-0.323536\pi$
$859$	1.56222	+	0.901945i	0.0533021	+	0.0307740i	−0.473112	+	0.881002i	$0.656869\pi$
$860$	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	−0.853408	−	0.521243i	$-0.825469\pi$
$863$	−30.4665	+	13.5646i	−1.03709	+	0.461743i	−0.183683	+	0.982986i	$0.558802\pi$
$864$	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	−0.806008	−	0.591904i	$-0.798376\pi$
$877$	5.06598	−	23.8336i	0.171066	−	0.804802i	0.977074	−	0.212898i	$-0.0682903\pi$
$878$	−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	$-0.538008\pi$
$881$		−	58.9406i		−	1.98576i	0.119123	−	0.992880i	$-0.461992\pi$
$882$	3.10217	−	6.27507i	0.104455	−	0.211293i
$883$	−16.9816	−	52.2639i	−0.571475	−	1.75882i	−0.647879	−	0.761743i	$-0.724344\pi$
$883$	−16.9816	−	52.2639i	−0.571475	−	1.75882i	0.0764041	−	0.997077i	$-0.475656\pi$
$884$	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	0.690766	−	0.723079i	$-0.257274\pi$
$887$	−2.99484	−	3.32611i	−0.100557	−	0.111680i	−0.791322	+	0.611399i	$0.790607\pi$
$888$	−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	0.859134	+	0.511750i	$0.171003\pi$
$907$	−2.63894	+	25.1079i	−0.0876247	+	0.833693i	−0.946759	+	0.321943i	$0.895664\pi$
$908$	−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	−0.427370	−	0.904077i	$-0.640560\pi$
$911$	9.06672	−	6.58736i	0.300394	−	0.218249i	0.727764	+	0.685828i	$0.240560\pi$
$912$	−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	0.989075	−	0.147413i	$-0.0470947\pi$
$919$	6.59974	+	14.8233i	0.217705	+	0.488974i	−0.771370	+	0.636387i	$0.780428\pi$
$920$	−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	0.953034	+	0.302864i	$0.0979428\pi$
$929$	16.4712	+	36.9948i	0.540401	+	1.21376i	−0.412632	+	0.910898i	$0.635391\pi$
$930$	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	−0.518577	−	0.855031i	$-0.673538\pi$
$937$	4.11270	−	2.98805i	0.134356	−	0.0976155i	0.652933	+	0.757415i	$0.273538\pi$
$938$	−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	−0.875620	−	0.483000i	$-0.839547\pi$
$941$	2.49354	−	23.7244i	0.0812870	−	0.773394i	0.956907	−	0.290394i	$-0.0937863\pi$
$942$	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	−0.920445	−	0.390873i	$-0.872173\pi$
$947$	−3.74563	+	6.48763i	−0.121717	+	0.210820i	0.798728	+	0.601692i	$0.205507\pi$
$948$	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	0.600669	−	0.799498i	$-0.294901\pi$
$953$	19.0376	+	6.18568i	0.616687	+	0.200374i	0.0160182	+	0.999872i	$0.494901\pi$
$954$	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	$-0.932540\pi$
$967$		−	13.0823i		−	0.420697i	0.977626	−	0.210349i	$-0.0674599\pi$
$968$	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	−0.984826	−	0.173542i	$-0.944479\pi$
$971$	−0.453604	+	2.13404i	−0.0145569	+	0.0684846i	0.970270	+	0.242027i	$0.0778121\pi$
$972$	−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	0.773875	−	0.633338i	$-0.218316\pi$
$977$	25.6632	+	11.4260i	0.821037	+	0.365549i	0.0471618	+	0.998887i	$0.484982\pi$
$978$	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	0.969512	−	0.245044i	$-0.0788023\pi$
$983$	−0.496929	−	2.33787i	−0.0158496	−	0.0745664i	−0.985362	+	0.170477i	$0.945469\pi$
$984$	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	0.733039	−	0.680187i	$-0.238101\pi$
$991$	−7.00558	−	12.1340i	−0.222540	−	0.385450i	−0.955578	+	0.294737i	$0.904768\pi$
$992$	−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	−0.500801	−	0.865563i	$-0.666961\pi$
$997$	−19.1425	+	4.06886i	−0.606249	+	0.128862i	−0.105448	+	0.994425i	$0.533628\pi$
$998$	−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.19.4	✓	64
7.3	odd	6		462.2.ba.b.283.8	yes	64
11.7	odd	10		462.2.ba.b.271.8	yes	64
77.73	even	30	inner	462.2.ba.a.73.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.19.4	✓	64	1.1	even	1	trivial
462.2.ba.a.73.4	yes	64	77.73	even	30	inner
462.2.ba.b.271.8	yes	64	11.7	odd	10
462.2.ba.b.283.8	yes	64	7.3	odd	6

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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