LMFDB - Embedded newform 462.2.bc.b.95.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.10
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.b.107.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(0.713675 - 1.57818i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.25353 + 2.81547i) q^{5} +(1.49494 + 0.874731i) q^{6} +(1.28350 + 2.31358i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.98134 - 2.25262i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(0.713675 - 1.57818i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.25353 + 2.81547i) q^{5} +(1.49494 + 0.874731i) q^{6} +(1.28350 + 2.31358i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.98134 - 2.25262i) q^{9} +(-2.66902 - 1.54096i) q^{10} +(-3.25565 + 0.633032i) q^{11} +(-1.02620 + 1.39532i) q^{12} +(-1.85644 + 2.55517i) q^{13} +(-2.43506 + 1.03463i) q^{14} +(3.54872 + 3.98763i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.684127 + 6.50903i) q^{17} +(2.44739 - 1.73502i) q^{18} +(-0.878223 - 4.13171i) q^{19} +(1.81151 - 2.49332i) q^{20} +(4.56725 - 0.374454i) q^{21} +(-0.289256 - 3.30399i) q^{22} +(-0.815547 + 0.470856i) q^{23} +(-1.28041 - 1.16643i) q^{24} +(-3.00989 - 3.34282i) q^{25} +(-2.34712 - 2.11336i) q^{26} +(-4.96909 + 1.51927i) q^{27} +(-0.774430 - 2.52987i) q^{28} +(2.13594 + 6.57373i) q^{29} +(-4.33673 + 3.11246i) q^{30} +(6.76396 - 3.01151i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.32444 + 5.58980i) q^{33} -6.54489 q^{34} +(-8.12271 + 0.713516i) q^{35} +(1.46969 + 2.61534i) q^{36} +(-0.820875 + 0.911674i) q^{37} +(4.20088 - 0.441530i) q^{38} +(2.70763 + 4.75337i) q^{39} +(2.29031 + 2.06220i) q^{40} +(-0.788646 + 2.42720i) q^{41} +(-0.105005 + 4.58137i) q^{42} +1.24741i q^{43} +(3.31612 + 0.0576896i) q^{44} +(8.82586 - 2.75466i) q^{45} +(-0.383029 - 0.860297i) q^{46} +(2.14061 + 10.0708i) q^{47} +(1.29388 - 1.15147i) q^{48} +(-3.70527 + 5.93894i) q^{49} +(3.63913 - 2.64398i) q^{50} +(10.7607 + 3.56566i) q^{51} +(2.34712 - 2.11336i) q^{52} +(-2.44967 - 5.50204i) q^{53} +(-0.991538 - 5.10067i) q^{54} +(2.29877 - 9.95972i) q^{55} +(2.59696 - 0.505744i) q^{56} +(-7.14738 - 1.56270i) q^{57} +(-6.76099 + 1.43709i) q^{58} +(2.34885 - 11.0505i) q^{59} +(-2.64210 - 4.63831i) q^{60} +(3.62706 - 8.14652i) q^{61} +(2.28798 + 7.04169i) q^{62} +(2.66858 - 7.47521i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.86691 - 8.42973i) q^{65} +(-5.42074 - 1.90147i) q^{66} +(-3.14450 + 5.44644i) q^{67} +(0.684127 - 6.50903i) q^{68} +(0.161062 + 1.62312i) q^{69} +(0.139447 - 8.15279i) q^{70} +(-6.06001 - 8.34089i) q^{71} +(-2.75464 + 1.18826i) q^{72} +(-0.0996603 + 0.468865i) q^{73} +(-0.820875 - 0.911674i) q^{74} +(-7.42368 + 2.36447i) q^{75} +4.22402i q^{76} +(-5.64319 - 6.71970i) q^{77} +(-5.01035 + 2.19594i) q^{78} +(16.5959 + 1.74430i) q^{79} +(-2.29031 + 2.06220i) q^{80} +(-1.14862 + 8.92640i) q^{81} +(-2.33147 - 1.03804i) q^{82} +(9.93212 - 7.21611i) q^{83} +(-4.54530 - 0.583314i) q^{84} +(-19.1836 - 6.23312i) q^{85} +(-1.24057 - 0.130390i) q^{86} +(11.8989 + 1.32061i) q^{87} +(-0.404003 + 3.29193i) q^{88} +(5.63638 - 3.25417i) q^{89} +(1.81702 + 9.06545i) q^{90} +(-8.29431 - 1.01546i) q^{91} +(0.895621 - 0.291005i) q^{92} +(0.0745528 - 12.8240i) q^{93} +(-10.2394 + 1.07620i) q^{94} +(12.7336 + 2.70661i) q^{95} +(1.00991 + 1.40715i) q^{96} +(7.13209 + 5.18176i) q^{97} +(-5.51910 - 4.30576i) q^{98} +(7.87652 + 6.07951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	0.713675	−	1.57818i	0.412041	−	0.911165i
$3$	0.713675	−	1.57818i	0.412041	−	0.911165i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−1.25353	+	2.81547i	−0.560595	+	1.25912i	0.381685	+	0.924292i	$0.375344\pi$
$5$	−1.25353	+	2.81547i	−0.560595	+	1.25912i	−0.942280	+	0.334825i	$0.891323\pi$
$6$	1.49494	+	0.874731i	0.610307	+	0.357107i
$7$	1.28350	+	2.31358i	0.485116	+	0.874450i
$7$	1.28350	+	2.31358i	0.485116	+	0.874450i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.98134	−	2.25262i	−0.660445	−	0.750874i
$10$	−2.66902	−	1.54096i	−0.844018	−	0.487294i
$11$	−3.25565	+	0.633032i	−0.981616	+	0.190866i
$11$	−3.25565	+	0.633032i	−0.981616	+	0.190866i
$12$	−1.02620	+	1.39532i	−0.296239	+	0.402793i
$13$	−1.85644	+	2.55517i	−0.514884	+	0.708676i	−0.984733	−	0.174070i	$-0.944308\pi$
$13$	−1.85644	+	2.55517i	−0.514884	+	0.708676i	0.469850	+	0.882746i	$0.344308\pi$
$14$	−2.43506	+	1.03463i	−0.650798	+	0.276517i
$15$	3.54872	+	3.98763i	0.916276	+	1.02960i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.684127	+	6.50903i	0.165925	+	1.57867i	0.687960	+	0.725748i	$0.258506\pi$
$17$	0.684127	+	6.50903i	0.165925	+	1.57867i	−0.522035	+	0.852924i	$0.674827\pi$
$18$	2.44739	−	1.73502i	0.576855	−	0.408948i
$19$	−0.878223	−	4.13171i	−0.201478	−	0.947880i	−0.956399	−	0.292064i	$-0.905658\pi$
$19$	−0.878223	−	4.13171i	−0.201478	−	0.947880i	0.754921	−	0.655816i	$-0.227675\pi$
$20$	1.81151	−	2.49332i	0.405065	−	0.557524i
$21$	4.56725	−	0.374454i	0.996656	−	0.0817126i
$22$	−0.289256	−	3.30399i	−0.0616695	−	0.704412i
$23$	−0.815547	+	0.470856i	−0.170053	+	0.0981803i	−0.582611	−	0.812751i	$-0.697969\pi$
$23$	−0.815547	+	0.470856i	−0.170053	+	0.0981803i	0.412558	+	0.910931i	$0.364636\pi$
$24$	−1.28041	−	1.16643i	−0.261362	−	0.238097i
$25$	−3.00989	−	3.34282i	−0.601978	−	0.668564i
$26$	−2.34712	−	2.11336i	−0.460308	−	0.414463i
$27$	−4.96909	+	1.51927i	−0.956301	+	0.292384i
$28$	−0.774430	−	2.52987i	−0.146354	−	0.478101i
$29$	2.13594	+	6.57373i	0.396633	+	1.22071i	0.927682	+	0.373370i	$0.121798\pi$
$29$	2.13594	+	6.57373i	0.396633	+	1.22071i	−0.531049	+	0.847341i	$0.678202\pi$
$30$	−4.33673	+	3.11246i	−0.791775	+	0.568255i
$31$	6.76396	−	3.01151i	1.21484	−	0.540883i	0.303618	−	0.952794i	$-0.401805\pi$
$31$	6.76396	−	3.01151i	1.21484	−	0.540883i	0.911224	+	0.411911i	$0.135139\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.32444	+	5.58980i	−0.230555	+	0.973059i
$34$	−6.54489			−1.12244
$35$	−8.12271	+	0.713516i	−1.37299	+	0.120606i
$36$	1.46969	+	2.61534i	0.244949	+	0.435890i
$37$	−0.820875	+	0.911674i	−0.134951	+	0.149878i	−0.806832	−	0.590781i	$-0.798820\pi$
$37$	−0.820875	+	0.911674i	−0.134951	+	0.149878i	0.671881	+	0.740659i	$0.265487\pi$
$38$	4.20088	−	0.441530i	0.681473	−	0.0716257i
$39$	2.70763	+	4.75337i	0.433569	+	0.761148i
$40$	2.29031	+	2.06220i	0.362130	+	0.326063i
$41$	−0.788646	+	2.42720i	−0.123166	+	0.379065i	−0.993562	−	0.113286i	$-0.963862\pi$
$41$	−0.788646	+	2.42720i	−0.123166	+	0.379065i	0.870397	+	0.492351i	$0.163862\pi$
$42$	−0.105005	+	4.58137i	−0.0162026	+	0.706921i
$43$			1.24741i			0.190228i	0.995466	+	0.0951139i	$0.0303215\pi$
$43$			1.24741i			0.190228i	−0.995466	+	0.0951139i	$0.969678\pi$
$44$	3.31612	+	0.0576896i	0.499924	+	0.00869703i
$45$	8.82586	−	2.75466i	1.31568	−	0.410641i
$46$	−0.383029	−	0.860297i	−0.0564745	−	0.126844i
$47$	2.14061	+	10.0708i	0.312240	+	1.46898i	0.802108	+	0.597179i	$0.203712\pi$
$47$	2.14061	+	10.0708i	0.312240	+	1.46898i	−0.489868	+	0.871797i	$0.662955\pi$
$48$	1.29388	−	1.15147i	0.186756	−	0.166200i
$49$	−3.70527	+	5.93894i	−0.529324	+	0.848420i
$50$	3.63913	−	2.64398i	0.514651	−	0.373916i
$51$	10.7607	+	3.56566i	1.50680	+	0.499292i
$52$	2.34712	−	2.11336i	0.325487	−	0.293070i
$53$	−2.44967	−	5.50204i	−0.336487	−	0.755763i	−0.999971	−	0.00757264i	$-0.997590\pi$
$53$	−2.44967	−	5.50204i	−0.336487	−	0.755763i	0.663484	−	0.748191i	$-0.269077\pi$
$54$	−0.991538	−	5.10067i	−0.134931	−	0.694113i
$55$	2.29877	−	9.95972i	0.309966	−	1.34297i
$56$	2.59696	−	0.505744i	0.347034	−	0.0675829i
$57$	−7.14738	−	1.56270i	−0.946693	−	0.206985i
$58$	−6.76099	+	1.43709i	−0.887761	+	0.188699i
$59$	2.34885	−	11.0505i	0.305795	−	1.43865i	−0.509932	−	0.860215i	$-0.670330\pi$
$59$	2.34885	−	11.0505i	0.305795	−	1.43865i	0.815727	−	0.578437i	$-0.196337\pi$
$60$	−2.64210	−	4.63831i	−0.341093	−	0.598804i
$61$	3.62706	−	8.14652i	0.464398	−	1.04306i	−0.517851	−	0.855471i	$-0.673268\pi$
$61$	3.62706	−	8.14652i	0.464398	−	1.04306i	0.982249	−	0.187584i	$-0.0600657\pi$
$62$	2.28798	+	7.04169i	0.290574	+	0.894295i
$63$	2.66858	−	7.47521i	0.336209	−	0.941787i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.86691	−	8.42973i	−0.603665	−	1.04558i
$66$	−5.42074	−	1.90147i	−0.667247	−	0.234055i
$67$	−3.14450	+	5.44644i	−0.384162	+	0.665388i	−0.991653	−	0.128939i	$-0.958843\pi$
$67$	−3.14450	+	5.44644i	−0.384162	+	0.665388i	0.607491	+	0.794327i	$0.292176\pi$
$68$	0.684127	−	6.50903i	0.0829626	−	0.789336i
$69$	0.161062	+	1.62312i	0.0193896	+	0.195401i
$70$	0.139447	−	8.15279i	0.0166671	−	0.974445i
$71$	−6.06001	−	8.34089i	−0.719191	−	0.989881i	−0.999550	−	0.0299863i	$-0.990454\pi$
$71$	−6.06001	−	8.34089i	−0.719191	−	0.989881i	0.280359	−	0.959895i	$-0.409546\pi$
$72$	−2.75464	+	1.18826i	−0.324637	+	0.140038i
$73$	−0.0996603	+	0.468865i	−0.0116644	+	0.0548765i	−0.983595	−	0.180392i	$-0.942263\pi$
$73$	−0.0996603	+	0.468865i	−0.0116644	+	0.0548765i	0.971931	+	0.235268i	$0.0755968\pi$
$74$	−0.820875	−	0.911674i	−0.0954248	−	0.105980i
$75$	−7.42368	+	2.36447i	−0.857212	+	0.273026i
$76$			4.22402i			0.484528i
$77$	−5.64319	−	6.71970i	−0.643101	−	0.765781i
$78$	−5.01035	+	2.19594i	−0.567311	+	0.248641i
$79$	16.5959	+	1.74430i	1.86719	+	0.196249i	0.969618	−	0.244624i	$-0.0786647\pi$
$79$	16.5959	+	1.74430i	1.86719	+	0.196249i	0.897569	+	0.440874i	$0.145331\pi$
$80$	−2.29031	+	2.06220i	−0.256065	+	0.230562i
$81$	−1.14862	+	8.92640i	−0.127625	+	0.991823i
$82$	−2.33147	−	1.03804i	−0.257468	−	0.114632i
$83$	9.93212	−	7.21611i	1.09019	−	0.792071i	0.110760	−	0.993847i	$-0.464671\pi$
$83$	9.93212	−	7.21611i	1.09019	−	0.792071i	0.979432	+	0.201777i	$0.0646715\pi$
$84$	−4.54530	−	0.583314i	−0.495933	−	0.0636447i
$85$	−19.1836	−	6.23312i	−2.08075	−	0.676077i
$86$	−1.24057	−	0.130390i	−0.133775	−	0.0140603i
$87$	11.8989	+	1.32061i	1.27570	+	0.141584i
$88$	−0.404003	+	3.29193i	−0.0430668	+	0.350921i
$89$	5.63638	−	3.25417i	0.597455	−	0.344941i	−0.170585	−	0.985343i	$-0.554566\pi$
$89$	5.63638	−	3.25417i	0.597455	−	0.344941i	0.768040	+	0.640402i	$0.221232\pi$
$90$	1.81702	+	9.06545i	0.191531	+	0.955582i
$91$	−8.29431	−	1.01546i	−0.869480	−	0.106449i
$92$	0.895621	−	0.291005i	0.0933750	−	0.0303394i
$93$	0.0745528	−	12.8240i	0.00773077	−	1.32979i
$94$	−10.2394	+	1.07620i	−1.05611	+	0.111002i
$95$	12.7336	+	2.70661i	1.30644	+	0.277692i
$96$	1.00991	+	1.40715i	0.103074	+	0.143617i
$97$	7.13209	+	5.18176i	0.724154	+	0.526128i	0.887709	−	0.460406i	$-0.152296\pi$
$97$	7.13209	+	5.18176i	0.724154	+	0.526128i	−0.163555	+	0.986534i	$0.552296\pi$
$98$	−5.51910	−	4.30576i	−0.557513	−	0.434947i
$99$	7.87652	+	6.07951i	0.791620	+	0.611014i
$100$	2.24911	+	3.89557i	0.224911	+	0.389557i
$101$	9.79140	−	4.35941i	0.974281	−	0.433778i	0.143056	−	0.989715i	$-0.454307\pi$
$101$	9.79140	−	4.35941i	0.974281	−	0.433778i	0.831225	+	0.555937i	$0.187640\pi$
$102$	−4.67092	+	10.3290i	−0.462490	+	1.02273i
$103$	0.440469	−	0.489190i	0.0434007	−	0.0482014i	−0.721054	−	0.692879i	$-0.756342\pi$
$103$	0.440469	−	0.489190i	0.0434007	−	0.0482014i	0.764454	+	0.644678i	$0.223009\pi$
$104$	1.85644	+	2.55517i	0.182039	+	0.250555i
$105$	−4.67092	+	13.3284i	−0.455835	+	1.30071i
$106$	5.72796	−	1.86113i	0.556349	−	0.180769i
$107$	−6.46092	+	1.37331i	−0.624600	+	0.132763i	−0.509330	−	0.860571i	$-0.670107\pi$
$107$	−6.46092	+	1.37331i	−0.624600	+	0.132763i	−0.115270	+	0.993334i	$0.536773\pi$
$108$	5.17637	−	0.452941i	0.498097	−	0.0435843i
$109$	−7.42308	−	4.28572i	−0.711003	−	0.410498i	0.100430	−	0.994944i	$-0.467978\pi$
$109$	−7.42308	−	4.28572i	−0.711003	−	0.410498i	−0.811432	+	0.584447i	$0.801312\pi$
$110$	9.66487	+	3.32725i	0.921509	+	0.317241i
$111$	0.852952	+	1.94613i	0.0809586	+	0.184719i
$112$	0.231517	+	2.63560i	0.0218763	+	0.249041i
$113$	−6.35140	−	2.06370i	−0.597490	−	0.194136i	−0.00536916	−	0.999986i	$-0.501709\pi$
$113$	−6.35140	−	2.06370i	−0.597490	−	0.194136i	−0.592121	+	0.805849i	$0.701709\pi$
$114$	2.30125	−	6.94487i	0.215532	−	0.650447i
$115$	−0.303371	−	2.88638i	−0.0282895	−	0.269156i
$116$	−0.722504	−	6.87417i	−0.0670828	−	0.638250i
$117$	9.43406	−	0.880789i	0.872179	−	0.0814290i
$118$	10.7444	+	3.49108i	0.989105	+	0.321380i
$119$	−14.1811	+	9.93711i	−1.29998	+	0.910933i
$120$	4.88908	−	2.14279i	0.446310	−	0.195609i
$121$	10.1985	−	4.12186i	0.927140	−	0.374715i
$122$	7.72276	+	4.45874i	0.699186	+	0.403675i
$123$	3.26774	+	2.97686i	0.294642	+	0.268415i
$124$	−7.24227	+	1.53939i	−0.650375	+	0.138242i
$125$	−1.47078	+	0.477886i	−0.131551	+	0.0427434i
$126$	7.15531	+	3.43533i	0.637446	+	0.306043i
$127$	−1.28837	−	1.77329i	−0.114324	−	0.157354i	0.748020	−	0.663676i	$-0.231005\pi$
$127$	−1.28837	−	1.77329i	−0.114324	−	0.157354i	−0.862344	+	0.506322i	$0.831005\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	1.96864	+	0.890244i	0.173329	+	0.0783816i
$130$	8.89228	−	3.95910i	0.779905	−	0.347236i
$131$	5.63954	+	9.76796i	0.492729	+	0.853431i	0.999965	−	0.00837614i	$-0.00266624\pi$
$131$	5.63954	+	9.76796i	0.492729	+	0.853431i	−0.507236	+	0.861807i	$0.669333\pi$
$132$	2.45768	−	5.19228i	0.213914	−	0.451930i
$133$	8.43184	−	7.33488i	0.731133	−	0.636015i
$134$	−5.08791	−	3.69658i	−0.439529	−	0.319336i
$135$	1.95142	−	15.8948i	0.167952	−	1.36800i
$136$	6.40187	+	1.36076i	0.548955	+	0.116684i
$137$	−13.8537	+	1.45608i	−1.18360	+	0.124402i	−0.675808	−	0.737077i	$-0.736205\pi$
$137$	−13.8537	+	1.45608i	−1.18360	+	0.124402i	−0.507793	+	0.861479i	$0.669539\pi$
$138$	−1.63107	−	0.00948225i	−0.138846	−	0.000807183i
$139$	15.1592	−	4.92553i	1.28579	−	0.417778i	0.415172	−	0.909743i	$-0.363721\pi$
$139$	15.1592	−	4.92553i	1.28579	−	0.417778i	0.870615	+	0.491965i	$0.163721\pi$
$140$	8.09355	+	0.990882i	0.684030	+	0.0837448i
$141$	17.4213	+	3.80899i	1.46714	+	0.320775i
$142$	8.92864	−	5.15495i	0.749275	−	0.432594i
$143$	4.42642	−	9.49393i	0.370156	−	0.793922i
$144$	−0.893815	−	2.86376i	−0.0744846	−	0.238646i
$145$	−21.1856	−	2.22670i	−1.75937	−	0.184917i
$146$	−0.455879	−	0.148124i	−0.0377288	−	0.0122588i
$147$	6.72838	+	10.0861i	0.554948	+	0.831885i
$148$	0.992484	−	0.721082i	0.0815817	−	0.0592726i
$149$	−8.47818	−	3.77473i	−0.694560	−	0.309238i	0.0289218	−	0.999582i	$-0.490793\pi$
$149$	−8.47818	−	3.77473i	−0.694560	−	0.309238i	−0.723481	+	0.690344i	$0.757459\pi$
$150$	−1.57554	−	7.63016i	−0.128642	−	0.623000i
$151$	−9.98655	+	8.99193i	−0.812694	+	0.731753i	−0.966588	−	0.256334i	$-0.917485\pi$
$151$	−9.98655	+	8.99193i	−0.812694	+	0.731753i	0.153894	+	0.988087i	$0.450818\pi$
$152$	−4.20088	−	0.441530i	−0.340736	−	0.0358128i
$153$	13.3069	−	14.4377i	1.07580	−	1.16722i
$154$	7.27277	−	4.90987i	0.586056	−	0.395649i
$155$			22.8187i			1.83284i
$156$	−1.66019	−	5.21244i	−0.132921	−	0.417329i
$157$	5.24970	+	5.83038i	0.418971	+	0.465315i	0.915272	−	0.402836i	$-0.131975\pi$
$157$	5.24970	+	5.83038i	0.418971	+	0.465315i	−0.496301	+	0.868151i	$0.665309\pi$
$158$	−3.46949	+	16.3227i	−0.276018	+	1.29856i
$159$	−10.4315	−	0.0606439i	−0.827272	−	0.00480937i
$160$	−1.81151	−	2.49332i	−0.143212	−	0.197114i
$161$	−2.13611	−	1.28249i	−0.168349	−	0.101074i
$162$	−8.75744	−	2.07539i	−0.688049	−	0.163058i
$163$	−1.58467	+	15.0772i	−0.124121	+	1.18094i	0.738203	+	0.674579i	$0.235675\pi$
$163$	−1.58467	+	15.0772i	−0.124121	+	1.18094i	−0.862324	+	0.506356i	$0.830992\pi$
$164$	1.27606	−	2.21019i	0.0996432	−	0.172587i
$165$	−14.0777	−	10.7359i	−1.09595	−	0.835788i
$166$	6.13839	+	10.6320i	0.476431	+	0.825203i
$167$	6.50759	+	4.72804i	0.503572	+	0.365867i	0.810380	−	0.585905i	$-0.199261\pi$
$167$	6.50759	+	4.72804i	0.503572	+	0.365867i	−0.306807	+	0.951772i	$0.599261\pi$
$168$	1.05523	−	4.45943i	0.0814129	−	0.344052i
$169$	0.934697	+	2.87670i	0.0718998	+	0.221285i
$170$	8.20420	−	18.4269i	0.629234	−	1.41328i
$171$	−7.56714	+	10.1646i	−0.578674	+	0.777308i
$172$	0.259351	−	1.22015i	0.0197753	−	0.0930355i
$173$	13.5630	−	2.88292i	1.03118	−	0.219184i	0.338907	−	0.940820i	$-0.389943\pi$
$173$	13.5630	−	2.88292i	1.03118	−	0.219184i	0.692273	+	0.721636i	$0.256610\pi$
$174$	−2.55715	+	11.6957i	−0.193857	+	0.886649i
$175$	3.87069	−	11.2541i	0.292596	−	0.850731i
$176$	−3.23166	−	0.745890i	−0.243596	−	0.0562235i
$177$	−15.7634	−	11.5934i	−1.18485	−	0.871412i
$178$	2.64718	+	5.94566i	0.198414	+	0.445646i
$179$	−0.0930807	+	0.0838102i	−0.00695718	+	0.00626427i	−0.672602	−	0.740005i	$-0.734823\pi$
$179$	−0.0930807	+	0.0838102i	−0.00695718	+	0.00626427i	0.665645	+	0.746269i	$0.268157\pi$
$180$	−9.20572	+	0.859470i	−0.686154	+	0.0640611i
$181$	−9.06514	+	6.58621i	−0.673806	+	0.489549i	−0.871297	−	0.490756i	$-0.836721\pi$
$181$	−9.06514	+	6.58621i	−0.673806	+	0.489549i	0.197491	+	0.980305i	$0.436721\pi$
$182$	1.87689	−	8.14273i	0.139124	−	0.603579i
$183$	−10.2682	−	11.5381i	−0.759045	−	0.852925i
$184$	0.195793	+	0.921133i	0.0144340	+	0.0679069i
$185$	−1.53780	−	3.45396i	−0.113061	−	0.253940i
$186$	12.7460	+	1.41462i	0.934580	+	0.103725i
$187$	−6.34771	−	20.7581i	−0.464190	−	1.51798i
$188$		−	10.2958i		−	0.750897i
$189$	−9.89276	−	9.54638i	−0.719592	−	0.694397i
$190$	−4.02281	+	12.3809i	−0.291845	+	0.898207i
$191$	11.9706	+	10.7784i	0.866160	+	0.779894i	0.976842	−	0.213962i	$-0.0686368\pi$
$191$	11.9706	+	10.7784i	0.866160	+	0.779894i	−0.110682	+	0.993856i	$0.535303\pi$
$192$	−1.50501	+	0.857291i	−0.108615	+	0.0618696i
$193$	5.35261	−	0.562582i	0.385289	−	0.0404955i	0.0900958	−	0.995933i	$-0.471283\pi$
$193$	5.35261	−	0.562582i	0.385289	−	0.0404955i	0.295193	+	0.955438i	$0.404616\pi$
$194$	−5.89888	+	6.55137i	−0.423515	+	0.470361i
$195$	−16.7771	+	1.66479i	−1.20143	+	0.119218i
$196$	4.85907	−	5.03879i	0.347077	−	0.359913i
$197$	21.1572			1.50739			0.753694	−	0.657226i	$-0.228270\pi$
$197$	21.1572			1.50739			0.753694	+	0.657226i	$0.228270\pi$
$198$	−6.86953	+	7.19789i	−0.488196	+	0.511532i
$199$	−9.58513	+	16.6019i	−0.679472	+	1.17688i	0.295668	+	0.955291i	$0.404458\pi$
$199$	−9.58513	+	16.6019i	−0.679472	+	1.17688i	−0.975140	+	0.221589i	$0.928876\pi$
$200$	−4.10932	+	1.82959i	−0.290573	+	0.129371i
$201$	6.35133	+	8.84959i	0.447988	+	0.624202i
$202$	3.31205	+	10.1934i	0.233035	+	0.717209i
$203$	−12.4674	+	13.3790i	−0.875037	+	0.939023i
$204$	−9.78421	−	5.72502i	−0.685032	−	0.400831i
$205$	−5.84513	−	5.26298i	−0.408241	−	0.367582i
$206$	0.440469	+	0.489190i	0.0306889	+	0.0340835i
$207$	2.67653	+	0.904195i	0.186032	+	0.0628459i
$208$	−2.73522	+	1.57918i	−0.189654	+	0.109497i
$209$	5.47470	+	12.8955i	0.378693	+	0.891999i
$210$	−12.7671	−	6.03852i	−0.881013	−	0.416697i
$211$	−7.30474	+	10.0541i	−0.502879	+	0.692154i	−0.982698	−	0.185213i	$-0.940702\pi$
$211$	−7.30474	+	10.0541i	−0.502879	+	0.692154i	0.479819	+	0.877368i	$0.340702\pi$
$212$	1.25220	+	5.89112i	0.0860012	+	0.404604i
$213$	−17.4883	+	3.61113i	−1.19828	+	0.247431i
$214$	−0.690437	−	6.56907i	−0.0471973	−	0.449053i
$215$	−3.51204	−	1.56366i	−0.239519	−	0.106641i
$216$	−0.0906184	+	5.19536i	−0.00616580	+	0.353500i
$217$	15.6489	+	11.7837i	1.06231	+	0.799927i
$218$	5.03817	−	6.93444i	0.341228	−	0.469660i
$219$	0.668830	+	0.491900i	0.0451954	+	0.0332395i
$220$	−4.31928	+	9.26413i	−0.291206	+	0.624588i
$221$	−17.9017	−	10.3356i	−1.20420	−	0.695245i
$222$	−2.02463	+	0.644853i	−0.135884	+	0.0432797i
$223$	−4.44688	+	13.6861i	−0.297785	+	0.916489i	0.684486	+	0.729026i	$0.260027\pi$
$223$	−4.44688	+	13.6861i	−0.297785	+	0.916489i	−0.982272	+	0.187463i	$0.939973\pi$
$224$	−2.64536	−	0.0452468i	−0.176751	−	0.00302318i
$225$	−1.56652	+	13.4034i	−0.104434	+	0.893560i
$226$	2.71629	−	6.10089i	0.180685	−	0.405825i
$227$	−15.8516	−	3.36935i	−1.05210	−	0.223632i	−0.350768	−	0.936462i	$-0.614079\pi$
$227$	−15.8516	−	3.36935i	−1.05210	−	0.223632i	−0.701336	+	0.712831i	$0.747413\pi$
$228$	6.66628	+	3.01458i	0.441485	+	0.199645i
$229$	0.825233	−	7.85157i	0.0545329	−	0.518846i	−0.932824	−	0.360333i	$-0.882663\pi$
$229$	0.825233	−	7.85157i	0.0545329	−	0.518846i	0.987357	−	0.158514i	$-0.0506702\pi$
$230$	2.90228			0.191371
$231$	−14.6323	+	4.11031i	−0.962737	+	0.270438i
$232$	6.91203			0.453797
$233$	1.54271	−	14.6779i	0.101067	−	0.961584i	−0.820049	−	0.572294i	$-0.806054\pi$
$233$	1.54271	−	14.6779i	0.101067	−	0.961584i	0.921115	−	0.389290i	$-0.127280\pi$
$234$	−0.110164	+	9.47445i	−0.00720163	+	0.619364i
$235$	−31.0373	−	6.59719i	−2.02465	−	0.430353i
$236$	−4.59505	+	10.3207i	−0.299112	+	0.671818i
$237$	14.5969	−	24.9466i	0.948172	−	1.62045i
$238$	−8.40035	−	15.1421i	−0.544514	−	0.981516i
$239$	0.406865	−	1.25220i	0.0263179	−	0.0809981i	−0.937035	−	0.349236i	$-0.886441\pi$
$239$	0.406865	−	1.25220i	0.0263179	−	0.0809981i	0.963353	+	0.268238i	$0.0864412\pi$
$240$	1.62000	+	5.08628i	0.104571	+	0.328318i
$241$	−14.9809	−	8.64925i	−0.965007	−	0.557147i	−0.0672967	−	0.997733i	$-0.521437\pi$
$241$	−14.9809	−	8.64925i	−0.965007	−	0.557147i	−0.897710	+	0.440586i	$0.854771\pi$
$242$	3.03324	+	10.5735i	0.194984	+	0.679692i
$243$	13.2678	+	8.18329i	0.851128	+	0.524958i
$244$	−5.24156	+	7.21439i	−0.335557	+	0.461854i
$245$	−12.0762	−	17.8767i	−0.771523	−	1.14210i
$246$	−3.30213	+	2.93867i	−0.210536	+	0.187363i
$247$	12.1876	+	5.42627i	0.775478	+	0.345265i
$248$	−0.773936	−	7.36351i	−0.0491450	−	0.467583i
$249$	−4.30004	−	20.8247i	−0.272504	−	1.31971i
$250$	−0.321529	−	1.51268i	−0.0203353	−	0.0956701i
$251$	3.11981	−	4.29405i	0.196921	−	0.271038i	−0.699126	−	0.714999i	$-0.746427\pi$
$251$	3.11981	−	4.29405i	0.196921	−	0.271038i	0.896046	+	0.443961i	$0.146427\pi$
$252$	−4.16444	+	6.75703i	−0.262335	+	0.425653i
$253$	2.35707	−	2.04921i	0.148188	−	0.128833i
$254$	1.89824	−	1.09595i	0.119106	−	0.0687661i
$255$	−23.5279	+	25.8268i	−1.47337	+	1.61734i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−5.27859	−	4.75286i	−0.329269	−	0.296475i	0.487869	−	0.872917i	$-0.337774\pi$
$257$	−5.27859	−	4.75286i	−0.329269	−	0.296475i	−0.817139	+	0.576441i	$0.804441\pi$
$258$	−1.09115	+	1.86480i	−0.0679318	+	0.116097i
$259$	−3.16282	−	0.729026i	−0.196528	−	0.0452994i
$260$	3.00791	+	9.25741i	0.186543	+	0.574120i
$261$	10.5761	−	17.8362i	0.654647	−	1.10403i
$262$	−10.3039	+	4.58761i	−0.636580	+	0.283424i
$263$	3.24743	−	5.62471i	0.200245	−	0.346835i	−0.748362	−	0.663290i	$-0.769159\pi$
$263$	3.24743	−	5.62471i	0.200245	−	0.346835i	0.948607	+	0.316456i	$0.102493\pi$
$264$	4.90694	+	2.98696i	0.302001	+	0.183835i
$265$	18.5616			1.14023
$266$	6.41333	+	9.15235i	0.393227	+	0.561167i
$267$	−1.11313	−	11.2177i	−0.0681225	−	0.686510i
$268$	4.20816	−	4.67364i	0.257055	−	0.285488i
$269$	−21.2008	+	2.22830i	−1.29264	+	0.135862i	−0.725764	−	0.687944i	$-0.758514\pi$
$269$	−21.2008	+	2.22830i	−1.29264	+	0.135862i	−0.566873	+	0.823805i	$0.691847\pi$
$270$	15.6037	+	3.60219i	0.949612	+	0.219222i
$271$	11.6244	+	10.4666i	0.706132	+	0.635804i	0.941856	−	0.336016i	$-0.109080\pi$
$271$	11.6244	+	10.4666i	0.706132	+	0.635804i	−0.235725	+	0.971820i	$0.575746\pi$
$272$	−2.02248	+	6.22456i	−0.122631	+	0.377419i
$273$	−7.52203	+	12.3653i	−0.455254	+	0.748379i
$274$		−	13.9300i		−	0.841543i
$275$	11.9153	+	8.97771i	0.718518	+	0.541376i
$276$	0.179923	−	1.62114i	0.0108301	−	0.0975811i
$277$	2.05477	+	4.61509i	0.123459	+	0.277294i	0.964693	−	0.263378i	$-0.0848366\pi$
$277$	2.05477	+	4.61509i	0.123459	+	0.277294i	−0.841233	+	0.540672i	$0.818170\pi$
$278$	3.31397	+	15.5910i	0.198759	+	0.935087i
$279$	−20.1855	−	9.26984i	−1.20847	−	0.554971i
$280$	−1.83146	+	7.94564i	−0.109451	+	0.474843i
$281$	−6.05472	+	4.39901i	−0.361195	+	0.262423i	−0.753550	−	0.657390i	$-0.771660\pi$
$281$	−6.05472	+	4.39901i	−0.361195	+	0.262423i	0.392356	+	0.919814i	$0.371660\pi$
$282$	−5.60914	+	16.9277i	−0.334020	+	1.00803i
$283$	7.05404	−	6.35148i	0.419319	−	0.377557i	−0.432290	−	0.901735i	$-0.642294\pi$
$283$	7.05404	−	6.35148i	0.419319	−	0.377557i	0.851609	+	0.524178i	$0.175627\pi$
$284$	4.19342	+	9.41857i	0.248833	+	0.558889i
$285$	13.3592	−	18.1643i	0.791330	−	1.07596i
$286$	8.97923	+	5.39455i	0.530953	+	0.318987i
$287$	−6.62774	+	1.29072i	−0.391223	+	0.0761885i
$288$	2.94150	−	0.589575i	0.173329	−	0.0347410i
$289$	−25.2710	+	5.37151i	−1.48653	+	0.315971i
$290$	4.42900	−	20.8368i	0.260080	−	1.22358i
$291$	13.2678	−	7.55765i	0.777771	−	0.443037i
$292$	0.194965	−	0.437899i	0.0114095	−	0.0256261i
$293$	7.22868	+	22.2476i	0.422304	+	1.29972i	0.905552	+	0.424234i	$0.139457\pi$
$293$	7.22868	+	22.2476i	0.422304	+	1.29972i	−0.483249	+	0.875483i	$0.660543\pi$
$294$	−10.7341	+	5.63724i	−0.626027	+	0.328771i
$295$	28.1680	+	20.4652i	1.64000	+	1.19153i
$296$	0.613389	+	1.06242i	0.0356525	+	0.0617520i
$297$	15.2159	−	8.09181i	0.882914	−	0.469534i
$298$	4.64026	−	8.03717i	0.268803	−	0.465581i
$299$	0.310896	−	2.95798i	0.0179796	−	0.171064i
$300$	7.75305	−	0.769336i	0.447623	−	0.0444176i
$301$	−2.88597	+	1.60104i	−0.166345	+	0.0922826i
$302$	−7.89879	−	10.8718i	−0.454524	−	0.625599i
$303$	0.107922	−	18.5639i	0.00619993	−	1.06647i
$304$	0.878223	−	4.13171i	0.0503695	−	0.236970i
$305$	18.3897	+	20.4238i	1.05299	+	1.16946i
$306$	12.9676	+	14.7432i	0.741309	+	0.842811i
$307$			32.9371i			1.87982i	0.341425	+	0.939909i	$0.389090\pi$
$307$			32.9371i			1.87982i	−0.341425	+	0.939909i	$0.610910\pi$
$308$	4.12277	+	7.74615i	0.234916	+	0.441378i
$309$	−0.457681	−	1.04426i	−0.0260366	−	0.0594061i
$310$	−22.6937	−	2.38521i	−1.28892	−	0.135471i
$311$	22.4324	−	20.1982i	1.27202	−	1.14534i	0.289909	−	0.957054i	$-0.406375\pi$
$311$	22.4324	−	20.1982i	1.27202	−	1.14534i	0.982115	−	0.188281i	$-0.0602915\pi$
$312$	5.35742	−	1.10624i	0.303304	−	0.0626287i
$313$	6.72088	+	2.99233i	0.379886	+	0.169136i	0.587791	−	0.809013i	$-0.299998\pi$
$313$	6.72088	+	2.99233i	0.379886	+	0.169136i	−0.207905	+	0.978149i	$0.566664\pi$
$314$	−6.34718	+	4.61150i	−0.358192	+	0.260242i
$315$	17.7011	+	16.8837i	0.997343	+	0.951288i
$316$	−15.8706	−	5.15667i	−0.892791	−	0.290085i
$317$	5.07186	+	0.533074i	0.284864	+	0.0299404i	0.245883	−	0.969300i	$-0.420922\pi$
$317$	5.07186	+	0.533074i	0.284864	+	0.0299404i	0.0389811	+	0.999240i	$0.487589\pi$
$318$	1.15070	−	10.3680i	0.0645281	−	0.581410i
$319$	−11.1152	−	20.0497i	−0.622334	−	1.12257i
$320$	2.66902	−	1.54096i	0.149203	−	0.0861422i
$321$	−2.44366	+	11.1766i	−0.136392	+	0.623818i
$322$	1.49875	−	1.99035i	0.0835218	−	0.110918i
$323$	26.2927	−	8.54300i	1.46296	−	0.475345i
$324$	2.97942	−	8.49253i	0.165524	−	0.471807i
$325$	14.1292	−	1.48503i	0.783745	−	0.0823749i
$326$	−14.8289	−	3.15199i	−0.821299	−	0.174572i
$327$	−12.0613	+	8.65639i	−0.666993	+	0.478699i
$328$	2.06470	+	1.50009i	0.114004	+	0.0828288i
$329$	−20.5521	+	17.8783i	−1.13307	+	0.985663i
$330$	12.1486	−	12.8784i	0.668758	−	0.708931i
$331$	−11.3458	−	19.6515i	−0.623621	−	1.08014i	−0.988806	−	0.149208i	$-0.952328\pi$
$331$	−11.3458	−	19.6515i	−0.623621	−	1.08014i	0.365185	−	0.930935i	$-0.381006\pi$
$332$	−11.2154	+	4.99341i	−0.615525	+	0.274049i
$333$	3.68009	+	0.0427901i	0.201667	+	0.00234488i
$334$	−5.38237	+	5.97773i	−0.294510	+	0.327087i
$335$	−11.3926	−	15.6805i	−0.622442	−	0.856718i
$336$	4.32470	+	1.51559i	0.235931	+	0.0826821i
$337$	19.9563	−	6.48418i	1.08709	−	0.353216i	0.289967	−	0.957037i	$-0.406356\pi$
$337$	19.9563	−	6.48418i	1.08709	−	0.353216i	0.797120	+	0.603821i	$0.206356\pi$
$338$	−2.95865	+	0.628880i	−0.160929	+	0.0342065i
$339$	−7.78973	+	8.55088i	−0.423080	+	0.464420i
$340$	17.4684	+	10.0854i	0.947358	+	0.546958i
$341$	−20.1147	+	14.0862i	−1.08927	+	0.762811i
$342$	−9.31795	−	8.58818i	−0.503857	−	0.464396i
$343$	−18.4959	−	0.949813i	−0.998684	−	0.0512851i
$344$	1.18636	+	0.385470i	0.0639640	+	0.0207832i
$345$	−4.77175	−	1.58116i	−0.256902	−	0.0851269i
$346$	1.44940	+	13.7901i	0.0779201	+	0.741360i
$347$	0.0103379	+	0.0983583i	0.000554966	+	0.00528015i	0.994796	−	0.101888i	$-0.0324883\pi$
$347$	0.0103379	+	0.0983583i	0.000554966	+	0.00528015i	−0.994241	+	0.107168i	$0.965822\pi$
$348$	−11.3643	−	3.76568i	−0.609193	−	0.201862i
$349$	3.52948	+	1.14680i	0.188928	+	0.0613866i	0.401953	−	0.915660i	$-0.368331\pi$
$349$	3.52948	+	1.14680i	0.188928	+	0.0613866i	−0.213025	+	0.977047i	$0.568331\pi$
$350$	10.7879	+	5.02586i	0.576636	+	0.268643i
$351$	5.34281	−	15.5173i	0.285178	−	0.828252i
$352$	1.07960	−	3.13599i	0.0575431	−	0.167149i
$353$	6.79914	+	3.92549i	0.361882	+	0.208933i	0.669906	−	0.742446i	$-0.266334\pi$
$353$	6.79914	+	3.92549i	0.361882	+	0.208933i	−0.308024	+	0.951379i	$0.599668\pi$
$354$	13.1776	−	14.4652i	0.700382	−	0.768817i
$355$	31.0799	−	6.60624i	1.64955	−	0.350623i
$356$	−6.18979	+	2.01119i	−0.328058	+	0.106593i
$357$	5.56191	+	29.4722i	0.294368	+	1.55984i
$358$	−0.0736215	−	0.101331i	−0.00389102	−	0.00535553i
$359$	23.8912	−	26.5339i	1.26093	−	1.40040i	0.381503	−	0.924368i	$-0.375407\pi$
$359$	23.8912	−	26.5339i	1.26093	−	1.40040i	0.879426	−	0.476036i	$-0.157927\pi$
$360$	0.107497	−	9.24513i	0.00566561	−	0.487261i
$361$	1.05757	−	0.470861i	0.0556617	−	0.0247822i
$362$	−5.60256	−	9.70392i	−0.294464	−	0.510027i
$363$	0.773385	−	19.0369i	0.0405922	−	0.999176i
$364$	7.90194	+	2.71775i	0.414174	+	0.142449i
$365$	−1.19515	−	0.868326i	−0.0625569	−	0.0454503i
$366$	12.5483	−	9.00585i	0.655908	−	0.470744i
$367$	28.2753	+	6.01010i	1.47596	+	0.313725i	0.874440	−	0.485133i	$-0.161229\pi$
$367$	28.2753	+	6.01010i	1.47596	+	0.313725i	0.601519	+	0.798858i	$0.294562\pi$
$368$	−0.936553	+	0.0984357i	−0.0488212	+	0.00513132i
$369$	7.03014	−	3.03258i	0.365975	−	0.157870i
$370$	3.59578	−	1.16834i	0.186936	−	0.0607391i
$371$	9.58525	−	12.7293i	0.497641	−	0.660874i
$372$	−2.73919	+	12.5283i	−0.142020	+	0.649561i
$373$	−22.2105	+	12.8232i	−1.15001	+	0.663961i	−0.948891	−	0.315605i	$-0.897793\pi$
$373$	−22.2105	+	12.8232i	−1.15001	+	0.663961i	−0.201124	+	0.979566i	$0.564459\pi$
$374$	21.3079	−	4.14312i	1.10180	−	0.214236i
$375$	−0.295468	+	2.66222i	−0.0152579	+	0.137476i
$376$	10.2394	+	1.07620i	0.528055	+	0.0555009i
$377$	−20.7622	−	6.74606i	−1.06931	−	0.347440i
$378$	10.5282	−	8.84070i	0.541510	−	0.454716i
$379$	−0.104403	+	0.0758535i	−0.00536284	+	0.00389633i	−0.590463	−	0.807064i	$-0.701055\pi$
$379$	−0.104403	+	0.0758535i	−0.00536284	+	0.00389633i	0.585101	+	0.810961i	$0.301055\pi$
$380$	−11.8926	−	5.29493i	−0.610078	−	0.271624i
$381$	−3.71805	+	0.767733i	−0.190482	+	0.0393321i
$382$	−11.9706	+	10.7784i	−0.612468	+	0.551468i
$383$	−20.7093	−	2.17664i	−1.05820	−	0.111221i	−0.440591	−	0.897708i	$-0.645231\pi$
$383$	−20.7093	−	2.17664i	−1.05820	−	0.111221i	−0.617607	+	0.786487i	$0.711898\pi$
$384$	−0.695278	−	1.58638i	−0.0354808	−	0.0809544i
$385$	25.9930	−	7.46489i	1.32473	−	0.380446i
$386$			5.38209i			0.273941i
$387$	2.80994	−	2.47153i	0.142837	−	0.125635i
$388$	−5.89888	−	6.55137i	−0.299470	−	0.332596i
$389$	−3.69086	+	17.3642i	−0.187134	+	0.880397i	0.779930	+	0.625866i	$0.215254\pi$
$389$	−3.69086	+	17.3642i	−0.187134	+	0.880397i	−0.967065	+	0.254531i	$0.918079\pi$
$390$	0.0980114	−	16.8592i	0.00496300	−	0.853697i
$391$	−3.62276	−	4.98629i	−0.183211	−	0.252168i
$392$	4.50327	+	5.35915i	0.227450	+	0.270678i
$393$	19.4404	−	1.92908i	0.980641	−	0.0973091i
$394$	−2.21153	+	21.0413i	−0.111415	+	1.06005i
$395$	−25.7145	+	44.5388i	−1.29384	+	2.24099i
$396$	−6.44040	−	7.58428i	−0.323642	−	0.381124i
$397$	−6.68970	−	11.5869i	−0.335746	−	0.581530i	0.647882	−	0.761741i	$-0.275655\pi$
$397$	−6.68970	−	11.5869i	−0.335746	−	0.581530i	−0.983628	+	0.180211i	$0.942322\pi$
$398$	−15.5091	−	11.2680i	−0.777399	−	0.564814i
$399$	−5.55820	−	18.5417i	−0.278258	−	0.928247i
$400$	−1.39002	−	4.27805i	−0.0695012	−	0.213903i
$401$	−9.46995	+	21.2698i	−0.472907	+	1.06217i	0.506861	+	0.862028i	$0.330806\pi$
$401$	−9.46995	+	21.2698i	−0.472907	+	1.06217i	−0.979768	+	0.200138i	$0.935861\pi$
$402$	−9.46501	+	5.39150i	−0.472072	+	0.268904i
$403$	−4.86196	+	22.8737i	−0.242192	+	1.13942i
$404$	−10.4838	+	2.22840i	−0.521589	+	0.110867i
$405$	−23.6922	−	14.4234i	−1.17727	−	0.716705i
$406$	−12.0025	−	13.7976i	−0.595676	−	0.684761i
$407$	2.09536	−	3.48773i	0.103863	−	0.172881i
$408$	6.71638	−	9.13219i	0.332510	−	0.452111i
$409$	3.11517	+	6.99678i	0.154035	+	0.345969i	0.974036	−	0.226394i	$-0.0726937\pi$
$409$	3.11517	+	6.99678i	0.154035	+	0.345969i	−0.820001	+	0.572363i	$0.806027\pi$
$410$	5.84513	−	5.26298i	0.288670	−	0.259920i
$411$	−7.58908	+	22.9029i	−0.374342	+	1.12972i
$412$	−0.532552	+	0.386922i	−0.0262370	+	0.0190623i
$413$	28.5809	−	8.74902i	1.40637	−	0.430511i
$414$	−1.17902	+	2.56736i	−0.0579455	+	0.126179i
$415$	7.86655	+	37.0092i	0.386154	+	1.81671i
$416$	−1.28462	−	2.88531i	−0.0629838	−	0.141464i
$417$	3.04536	−	27.4393i	0.149132	−	1.34371i
$418$	−13.3971	+	4.09676i	−0.655274	+	0.200379i
$419$		−	1.41006i		−	0.0688859i	−0.999407	−	0.0344430i	$-0.989034\pi$
$419$		−	1.41006i		−	0.0688859i	0.999407	−	0.0344430i	$-0.0109657\pi$
$420$	7.33996	−	12.0660i	0.358154	−	0.588758i
$421$	8.76429	−	26.9737i	0.427145	−	1.31462i	−0.473780	−	0.880643i	$-0.657111\pi$
$421$	8.76429	−	26.9737i	0.427145	−	1.31462i	0.900925	−	0.433975i	$-0.142889\pi$
$422$	−9.23549	−	8.31567i	−0.449577	−	0.404801i
$423$	18.4444	−	24.7756i	0.896798	−	1.20463i
$424$	−5.98974	+	0.629547i	−0.290887	+	0.0305735i
$425$	19.6994	−	21.8784i	0.955561	−	1.06126i
$426$	−1.76332	−	17.7700i	−0.0854331	−	0.860960i
$427$	23.5029	−	2.06455i	1.13739	−	0.0999104i
$428$	6.60526			0.319277
$429$	−11.8241	−	13.7613i	−0.570875	−	0.664401i
$430$	1.92220	−	3.32935i	0.0926969	−	0.160556i
$431$	2.29839	−	1.02331i	0.110710	−	0.0492911i	−0.350634	−	0.936512i	$-0.614034\pi$
$431$	2.29839	−	1.02331i	0.110710	−	0.0492911i	0.461344	+	0.887221i	$0.347367\pi$
$432$	−5.15743	−	0.633185i	−0.248137	−	0.0304641i
$433$	4.56670	+	14.0549i	0.219462	+	0.675433i	0.998807	+	0.0488383i	$0.0155519\pi$
$433$	4.56670	+	14.0549i	0.219462	+	0.675433i	−0.779345	+	0.626595i	$0.784448\pi$
$434$	−13.3549	+	14.3314i	−0.641054	+	0.687930i
$435$	−18.6338	+	31.8457i	−0.893422	+	1.52688i
$436$	6.36982	+	5.73541i	0.305059	+	0.274676i
$437$	2.66167	+	2.95609i	0.127325	+	0.141409i
$438$	−0.559117	+	0.613749i	−0.0267156	+	0.0293261i
$439$	29.7430	−	17.1721i	1.41956	−	0.819581i	0.423296	−	0.905991i	$-0.360873\pi$
$439$	29.7430	−	17.1721i	1.41956	−	0.819581i	0.996260	+	0.0864107i	$0.0275397\pi$
$440$	−8.76190	−	5.26398i	−0.417707	−	0.250951i
$441$	20.7196	−	3.42045i	0.986646	−	0.162879i
$442$	12.1502	−	16.7233i	0.577925	−	0.795446i
$443$	−0.0902981	−	0.424819i	−0.00429019	−	0.0201838i	0.975950	−	0.217993i	$-0.0699508\pi$
$443$	−0.0902981	−	0.424819i	−0.00429019	−	0.0201838i	−0.980241	+	0.197809i	$0.936618\pi$
$444$	−0.429689	−	2.08094i	−0.0203922	−	0.0987572i
$445$	2.09665	+	19.9483i	0.0993906	+	0.945638i
$446$	−13.1463	−	5.85311i	−0.622495	−	0.277153i
$447$	−12.0079	+	10.6862i	−0.567954	+	0.505440i
$448$	0.321515	−	2.62614i	0.0151901	−	0.124074i
$449$	−14.0701	+	19.3658i	−0.664008	+	0.913928i	−0.999606	−	0.0280772i	$-0.991062\pi$
$449$	−14.0701	+	19.3658i	−0.664008	+	0.913928i	0.335598	+	0.942005i	$0.391062\pi$
$450$	−13.1662	−	2.95897i	−0.620662	−	0.139487i
$451$	1.03106	−	8.40136i	0.0485507	−	0.395605i
$452$	5.78354	+	3.33913i	0.272035	+	0.157059i
$453$	7.06377	+	22.1779i	0.331885	+	1.04201i
$454$	5.00783	−	15.4125i	0.235029	−	0.723345i
$455$	13.2562	−	22.0795i	0.621458	−	1.03510i
$456$	−3.69488	+	6.31466i	−0.173029	+	0.295711i
$457$	−0.625599	+	1.40512i	−0.0292643	+	0.0657287i	−0.927586	−	0.373609i	$-0.878120\pi$
$457$	−0.625599	+	1.40512i	−0.0292643	+	0.0657287i	0.898322	+	0.439338i	$0.144787\pi$
$458$	7.72230	+	1.64142i	0.360839	+	0.0766987i
$459$	−13.2885	−	31.3046i	−0.620253	−	1.46117i
$460$	−0.303371	+	2.88638i	−0.0141447	+	0.134578i
$461$	−26.6732			−1.24229			−0.621147	−	0.783694i	$-0.713333\pi$
$461$	−26.6732			−1.24229			−0.621147	+	0.783694i	$0.713333\pi$
$462$	−2.55829	−	14.9818i	−0.119023	−	0.697018i
$463$	−21.7003			−1.00850			−0.504250	−	0.863557i	$-0.668231\pi$
$463$	−21.7003			−1.00850			−0.504250	+	0.863557i	$0.668231\pi$
$464$	−0.722504	+	6.87417i	−0.0335414	+	0.319125i
$465$	36.0122	+	16.2852i	1.67002	+	0.755206i
$466$	14.4363	+	3.06853i	0.668748	+	0.142147i
$467$	14.7550	−	33.1404i	0.682782	−	1.53355i	−0.155217	−	0.987880i	$-0.549608\pi$
$467$	14.7550	−	33.1404i	0.682782	−	1.53355i	0.837998	−	0.545673i	$-0.183726\pi$
$468$	−9.41103	−	1.09991i	−0.435025	−	0.0508433i
$469$	−16.6367	−	0.284557i	−0.768212	−	0.0131396i
$470$	9.80533	−	30.1777i	0.452286	−	1.39199i
$471$	12.9480	−	4.12399i	0.596612	−	0.190024i
$472$	−9.78381	−	5.64868i	−0.450336	−	0.260002i
$473$	−0.789649	−	4.06112i	−0.0363081	−	0.186731i
$474$	23.2841	+	17.1246i	1.06947	+	0.786559i
$475$	−11.1682	+	15.3718i	−0.512434	+	0.705304i
$476$	15.9372	−	6.77155i	0.730481	−	0.310373i
$477$	−7.54041	+	16.4196i	−0.345252	+	0.751800i
$478$	1.20281	+	0.535526i	0.0550153	+	0.0244944i
$479$	0.618868	+	5.88814i	0.0282768	+	0.269036i	0.999521	+	0.0309500i	$0.00985327\pi$
$479$	0.618868	+	5.88814i	0.0282768	+	0.269036i	−0.971244	+	0.238086i	$0.923480\pi$
$480$	−5.22775	+	1.07947i	−0.238613	+	0.0492707i
$481$	−0.805577	−	3.78994i	−0.0367311	−	0.172806i
$482$	10.1678	−	13.9948i	0.463131	−	0.637445i
$483$	−3.54849	+	2.45590i	−0.161462	+	0.111747i
$484$	−10.8327	+	1.91139i	−0.492394	+	0.0868816i
$485$	−23.5294	+	13.5847i	−1.06841	+	0.616849i
$486$	−9.52532	+	12.3397i	−0.432077	+	0.559740i
$487$	1.22064	+	1.35566i	0.0553125	+	0.0614308i	0.770166	−	0.637843i	$-0.220173\pi$
$487$	1.22064	+	1.35566i	0.0553125	+	0.0614308i	−0.714854	+	0.699274i	$0.753507\pi$
$488$	−6.62698	−	5.96696i	−0.299989	−	0.270111i
$489$	22.6636	+	13.2611i	1.02488	+	0.599688i
$490$	19.0411	−	10.1415i	0.860189	−	0.458145i
$491$	4.72757	+	14.5500i	0.213352	+	0.656631i	0.999266	+	0.0382954i	$0.0121928\pi$
$491$	4.72757	+	14.5500i	0.213352	+	0.656631i	−0.785914	+	0.618336i	$0.787807\pi$
$492$	−2.57740	−	3.59121i	−0.116198	−	0.161904i
$493$	−41.3274	+	18.4001i	−1.86129	+	0.828701i
$494$	−6.67049	+	11.5536i	−0.300120	+	0.519823i
$495$	−26.9901	+	14.5553i	−1.21312	+	0.654211i
$496$	7.40407			0.332453
$497$	11.5193	−	24.7258i	0.516710	−	1.10910i
$498$	21.1601	−	2.09972i	0.948206	−	0.0940905i
$499$	27.6948	−	30.7582i	1.23979	−	1.37693i	0.340104	−	0.940388i	$-0.389538\pi$
$499$	27.6948	−	30.7582i	1.23979	−	1.37693i	0.899686	−	0.436538i	$-0.143796\pi$
$500$	1.53800	−	0.161650i	0.0687814	−	0.00722922i
$501$	12.1060	−	6.89589i	0.540858	−	0.308086i
$502$	3.94442	+	3.55157i	0.176048	+	0.158514i
$503$	−0.145451	+	0.447653i	−0.00648535	+	0.0199599i	−0.954247	−	0.299020i	$-0.903340\pi$
$503$	−0.145451	+	0.447653i	−0.00648535	+	0.0199599i	0.947761	+	0.318980i	$0.103340\pi$
$504$	−6.28471	−	4.84793i	−0.279943	−	0.215944i
$505$			33.0321i			1.46991i
$506$	1.79160	+	2.55836i	0.0796465	+	0.113733i
$507$	5.20704	+	0.577906i	0.231253	+	0.0256657i
$508$	0.891528	+	2.00240i	0.0395551	+	0.0888423i
$509$	−7.92969	−	37.3063i	−0.351478	−	1.65357i	−0.698422	−	0.715686i	$-0.746114\pi$
$509$	−7.92969	−	37.3063i	−0.351478	−	1.65357i	0.346945	−	0.937886i	$-0.387219\pi$
$510$	−23.2260	−	26.0986i	−1.02846	−	1.15567i
$511$	−1.21267	+	0.371215i	−0.0536453	+	0.0164216i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	10.6412	+	19.1966i	0.469819	+	0.847550i
$514$	5.27859	−	4.75286i	0.232829	−	0.209640i
$515$	0.825161	+	1.85334i	0.0363609	+	0.0816680i
$516$	−1.74053	−	1.28009i	−0.0766225	−	0.0563530i
$517$	−13.3442	−	31.4319i	−0.586878	−	1.38237i
$518$	1.05564	−	3.06929i	0.0463820	−	0.134857i
$519$	5.12984	−	23.4625i	0.225175	−	1.02989i
$520$	−9.52110	+	2.02377i	−0.417528	+	0.0887483i
$521$	6.77646	−	31.8807i	0.296882	−	1.39672i	−0.536442	−	0.843937i	$-0.680232\pi$
$521$	6.77646	−	31.8807i	0.296882	−	1.39672i	0.833325	−	0.552784i	$-0.186435\pi$
$522$	16.6330	+	12.3826i	0.728007	+	0.541971i
$523$	−8.05494	+	18.0917i	−0.352218	+	0.791094i	0.647364	+	0.762181i	$0.275871\pi$
$523$	−8.05494	+	18.0917i	−0.352218	+	0.791094i	−0.999582	+	0.0289133i	$0.990795\pi$
$524$	−3.48542	−	10.7270i	−0.152261	−	0.468613i
$525$	−14.9987	−	14.1404i	−0.654595	−	0.617140i
$526$	5.25445	+	3.81758i	0.229105	+	0.166455i
$527$	24.2294	+	41.9666i	1.05545	+	1.82809i
$528$	−3.48351	+	4.56784i	−0.151600	+	0.198790i
$529$	−11.0566	+	19.1506i	−0.480721	+	0.832634i
$530$	−1.94021	+	18.4599i	−0.0842774	+	0.801846i
$531$	−29.5465	+	16.6036i	−1.28221	+	0.720537i
$532$	−9.77259	+	5.42152i	−0.423696	+	0.235053i
$533$	−4.73784	−	6.52108i	−0.205219	−	0.282459i
$534$	11.2726	+	0.0655335i	0.487812	+	0.00283591i
$535$	4.23243	−	19.9120i	0.182984	−	0.860871i
$536$	4.20816	+	4.67364i	0.181765	+	0.201871i
$537$	0.0658386	+	0.206712i	0.00284115	+	0.00892027i
$538$		−	21.3176i		−	0.919067i
$539$	8.30353	−	21.6807i	0.357658	−	0.933852i
$540$	−5.21349	+	15.1417i	−0.224353	+	0.651595i
$541$	−27.3195	−	2.87140i	−1.17456	−	0.123451i	−0.502922	−	0.864332i	$-0.667742\pi$
$541$	−27.3195	−	2.87140i	−1.17456	−	0.123451i	−0.671637	+	0.740881i	$0.734408\pi$
$542$	−11.6244	+	10.4666i	−0.499310	+	0.449581i
$543$	3.92469	+	19.0069i	0.168425	+	0.815663i
$544$	−5.97905	−	2.66205i	−0.256350	−	0.114134i
$545$	21.3714	−	15.5272i	0.915449	−	0.665113i
$546$	−11.5112	−	8.77334i	−0.492636	−	0.375465i
$547$	−12.5373	−	4.07360i	−0.536055	−	0.174175i	0.0284643	−	0.999595i	$-0.490938\pi$
$547$	−12.5373	−	4.07360i	−0.536055	−	0.174175i	−0.564519	+	0.825420i	$0.690938\pi$
$548$	13.8537	+	1.45608i	0.591801	+	0.0622008i
$549$	−25.5375	+	7.97058i	−1.08991	+	0.340176i
$550$	−10.1740	+	10.9116i	−0.433821	+	0.465271i
$551$	25.2850	−	14.5983i	1.07718	−	0.621908i
$552$	1.59345	+	0.348393i	0.0678218	+	0.0148286i
$553$	17.2652	+	40.6347i	0.734193	+	1.72796i
$554$	−4.80459	+	1.56111i	−0.204128	+	0.0663251i
$555$	−6.54848	−	0.0380698i	−0.277967	−	0.00161597i
$556$	−15.8520	+	1.66611i	−0.672275	+	0.0706590i
$557$	10.0877	+	2.14421i	0.427431	+	0.0908532i	0.416604	−	0.909088i	$-0.363220\pi$
$557$	10.0877	+	2.14421i	0.427431	+	0.0908532i	0.0108270	+	0.999941i	$0.496554\pi$
$558$	11.3290	−	19.1059i	0.479595	−	0.808818i
$559$	−3.18734	−	2.31574i	−0.134810	−	0.0979452i
$560$	−7.71068	−	2.65197i	−0.325836	−	0.112066i
$561$	−37.2903	−	4.79667i	−1.57440	−	0.202516i
$562$	−3.74202	−	6.48138i	−0.157848	−	0.273400i
$563$	5.76820	−	2.56817i	0.243101	−	0.108235i	−0.281570	−	0.959541i	$-0.590855\pi$
$563$	5.76820	−	2.56817i	0.243101	−	0.108235i	0.524671	+	0.851305i	$0.324188\pi$
$564$	−16.2486	−	7.34784i	−0.684191	−	0.309400i
$565$	13.7719	−	15.2953i	0.579390	−	0.643478i
$566$	5.57934	+	7.67931i	0.234517	+	0.322785i
$567$	−22.1262	+	8.79959i	−0.929212	+	0.369548i
$568$	−9.80530	+	3.18594i	−0.411421	+	0.133679i
$569$	−29.7627	+	6.32627i	−1.24772	+	0.265211i	−0.783994	−	0.620768i	$-0.786821\pi$
$569$	−29.7627	+	6.32627i	−1.24772	+	0.265211i	−0.463725	+	0.885979i	$0.653487\pi$
$570$	16.6684	+	15.1847i	0.698163	+	0.636017i
$571$	−11.8491	−	6.84107i	−0.495868	−	0.286290i	0.231137	−	0.972921i	$-0.425755\pi$
$571$	−11.8491	−	6.84107i	−0.495868	−	0.286290i	−0.727006	+	0.686631i	$0.759089\pi$
$572$	−6.30359	+	8.36616i	−0.263566	+	0.349807i
$573$	25.5533	−	11.1995i	1.06751	−	0.467867i
$574$	−0.590857	−	6.72635i	−0.0246619	−	0.280752i
$575$	4.02869	+	1.30900i	0.168008	+	0.0545892i
$576$	0.278875	+	2.98701i	0.0116198	+	0.124459i
$577$	−4.06452	−	38.6714i	−0.169208	−	1.60991i	−0.668660	−	0.743568i	$-0.733132\pi$
$577$	−4.06452	−	38.6714i	−0.169208	−	1.60991i	0.499452	−	0.866342i	$-0.333535\pi$
$578$	−2.70055	−	25.6940i	−0.112328	−	1.06873i
$579$	2.93216	−	8.84890i	0.121857	−	0.367748i
$580$	20.2597	+	6.58277i	0.841238	+	0.273335i
$581$	29.4429	+	13.7169i	1.22150	+	0.569071i
$582$	6.12939	+	13.9851i	0.254071	+	0.579700i
$583$	11.4582	+	16.3620i	0.474551	+	0.677645i
$584$	0.415120	+	0.239670i	0.0171778	+	0.00991761i
$585$	−9.34603	+	27.6654i	−0.386411	+	1.14382i
$586$	−22.8813	+	4.86357i	−0.945218	+	0.200912i
$587$	3.93016	−	1.27698i	0.162215	−	0.0527068i	−0.226784	−	0.973945i	$-0.572821\pi$
$587$	3.93016	−	1.27698i	0.162215	−	0.0527068i	0.388999	+	0.921238i	$0.372821\pi$
$588$	−4.48434	−	11.2646i	−0.184931	−	0.464543i
$589$	−18.3829	−	25.3020i	−0.757456	−	1.04255i
$590$	−23.2975	+	25.8745i	−0.959142	+	1.06524i
$591$	15.0994	−	33.3900i	0.621105	−	1.37348i
$592$	−1.12072	+	0.498976i	−0.0460612	+	0.0205078i
$593$	11.9654	+	20.7247i	0.491359	+	0.851060i	0.999951	−	0.00994862i	$-0.00316680\pi$
$593$	11.9654	+	20.7247i	0.491359	+	0.851060i	−0.508591	+	0.861008i	$0.669833\pi$
$594$	6.45699	+	15.9783i	0.264934	+	0.655599i
$595$	−10.2013	−	52.3828i	−0.418211	−	2.14749i
$596$	7.50810	+	5.45496i	0.307544	+	0.223444i
$597$	19.3602	+	26.9755i	0.792362	+	1.10403i
$598$	2.90927	+	0.618385i	0.118969	+	0.0252877i
$599$	20.9951	−	2.20667i	0.857835	−	0.0901621i	0.334610	−	0.942357i	$-0.391395\pi$
$599$	20.9951	−	2.20667i	0.857835	−	0.0901621i	0.523225	+	0.852195i	$0.324729\pi$
$600$	−0.0452932	+	7.79100i	−0.00184909	+	0.318066i
$601$	25.8399	−	8.39589i	1.05403	−	0.342475i	0.269782	−	0.962921i	$-0.413048\pi$
$601$	25.8399	−	8.39589i	1.05403	−	0.342475i	0.784249	+	0.620446i	$0.213048\pi$
$602$	−1.29061	−	3.03752i	−0.0526012	−	0.123800i
$603$	18.4991	−	3.70784i	0.753341	−	0.150995i
$604$	11.6378	−	6.71911i	0.473537	−	0.273397i
$605$	−1.17918	+	33.8806i	−0.0479404	+	1.37744i
$606$	18.4509	+	2.04778i	0.749516	+	0.0831854i
$607$	−8.36565	−	0.879265i	−0.339551	−	0.0356883i	−0.0667815	−	0.997768i	$-0.521273\pi$
$607$	−8.36565	−	0.879265i	−0.339551	−	0.0356883i	−0.272770	+	0.962079i	$0.587940\pi$
$608$	4.01728	+	1.30529i	0.162922	+	0.0529367i
$609$	12.2169	+	29.2241i	0.495054	+	1.18422i
$610$	−22.2342	+	16.1541i	−0.900234	+	0.654059i
$611$	−29.7065	−	13.2262i	−1.20180	−	0.535074i
$612$	−16.0179	+	11.3555i	−0.647485	+	0.459019i
$613$	2.54581	−	2.29226i	0.102824	−	0.0925835i	−0.616115	−	0.787656i	$-0.711294\pi$
$613$	2.54581	−	2.29226i	0.102824	−	0.0925835i	0.718940	+	0.695073i	$0.244628\pi$
$614$	−32.7566	−	3.44286i	−1.32195	−	0.138943i
$615$	−12.4775	+	5.46864i	−0.503140	+	0.220517i
$616$	−8.13466	+	3.29049i	−0.327755	+	0.132578i
$617$		−	3.55740i		−	0.143215i	−0.997433	−	0.0716077i	$-0.977187\pi$
$617$		−	3.55740i		−	0.143215i	0.997433	−	0.0716077i	$-0.0228130\pi$
$618$	1.08638	−	0.346018i	0.0437008	−	0.0139189i
$619$	16.3170	+	18.1219i	0.655837	+	0.728380i	0.975707	−	0.219081i	$-0.0703059\pi$
$619$	16.3170	+	18.1219i	0.655837	+	0.728380i	−0.319870	+	0.947461i	$0.603639\pi$
$620$	4.74428	−	22.3201i	0.190535	−	0.896396i
$621$	3.33716	−	3.57876i	0.133916	−	0.143611i
$622$	17.7427	+	24.4208i	0.711419	+	0.979184i
$623$	14.7630	+	8.86348i	0.591469	+	0.355108i
$624$	0.540180	+	5.44371i	0.0216245	+	0.217923i
$625$	2.84915	−	27.1078i	0.113966	−	1.08431i
$626$	−3.67846	+	6.37128i	−0.147021	+	0.254647i
$627$	24.2586	+	0.563105i	0.968796	+	0.0224882i
$628$	−3.92277	−	6.79444i	−0.156536	−	0.271128i
$629$	−6.49570	−	4.71940i	−0.259000	−	0.188175i
$630$	−18.6415	+	15.8393i	−0.742694	+	0.631053i
$631$	4.73303	+	14.5668i	0.188419	+	0.579894i	0.999990	−	0.00435903i	$-0.00138753\pi$
$631$	4.73303	+	14.5668i	0.188419	+	0.579894i	−0.811571	+	0.584253i	$0.801388\pi$
$632$	6.78735	−	15.2446i	0.269986	−	0.606399i
$633$	10.6540	+	18.7036i	0.423460	+	0.743402i
$634$	−1.06031	+	4.98836i	−0.0421102	+	0.198113i
$635$	6.60765	−	1.40450i	0.262216	−	0.0557358i
$636$	10.1909	+	2.22815i	0.404097	+	0.0883519i
$637$	−8.29638	−	20.4929i	−0.328715	−	0.811957i
$638$	21.1017	−	8.95859i	0.835424	−	0.354674i
$639$	−6.78197	+	30.1770i	−0.268290	+	1.19378i
$640$	1.25353	+	2.81547i	0.0495501	+	0.111291i
$641$	−11.6753	+	10.5125i	−0.461148	+	0.415220i	−0.866683	−	0.498860i	$-0.833752\pi$
$641$	−11.6753	+	10.5125i	−0.461148	+	0.415220i	0.405534	+	0.914080i	$0.367085\pi$
$642$	−10.8600	−	3.59855i	−0.428608	−	0.142023i
$643$	23.3131	−	16.9380i	0.919379	−	0.667968i	−0.0239904	−	0.999712i	$-0.507637\pi$
$643$	23.3131	−	16.9380i	0.919379	−	0.667968i	0.943369	+	0.331744i	$0.107637\pi$
$644$	1.82279	+	1.69858i	0.0718280	+	0.0669336i
$645$	−4.97420	+	4.42670i	−0.195859	+	0.174301i
$646$	5.74787	+	27.0416i	0.226147	+	1.06394i
$647$	−13.9072	−	31.2360i	−0.546747	−	1.22801i	−0.949806	−	0.312841i	$-0.898719\pi$
$647$	−13.9072	−	31.2360i	−0.546747	−	1.22801i	0.403058	−	0.915174i	$-0.367947\pi$
$648$	8.13457	+	3.85081i	0.319556	+	0.151274i
$649$	−0.651740	+	37.4635i	−0.0255830	+	1.47057i
$650$			14.2070i			0.557244i
$651$	29.7650	−	16.2871i	1.16658	−	0.638342i
$652$	4.68477	−	14.4182i	0.183470	−	0.564661i
$653$	16.5847	+	14.9329i	0.649008	+	0.584369i	0.926471	−	0.376367i	$-0.122827\pi$
$653$	16.5847	+	14.9329i	0.649008	+	0.584369i	−0.277463	+	0.960736i	$0.589494\pi$
$654$	−7.34821	−	12.9001i	−0.287338	−	0.504434i
$655$	−34.5707	+	3.63353i	−1.35079	+	0.141974i
$656$	−1.70770	+	1.89659i	−0.0666743	+	0.0740493i
$657$	1.25364	−	0.704481i	0.0489090	−	0.0274844i
$658$	−15.6321	−	22.3083i	−0.609402	−	0.869667i
$659$	−25.6988			−1.00108			−0.500541	−	0.865713i	$-0.666865\pi$
$659$	−25.6988			−1.00108			−0.500541	+	0.865713i	$0.666865\pi$
$660$	11.5380	+	13.4282i	0.449114	+	0.522692i
$661$	−3.56073	+	6.16737i	−0.138496	+	0.239883i	−0.926928	−	0.375240i	$-0.877560\pi$
$661$	−3.56073	+	6.16737i	−0.138496	+	0.239883i	0.788431	+	0.615123i	$0.210894\pi$
$662$	20.7298	−	9.22949i	0.805686	−	0.358714i
$663$	−29.0874	+	20.8760i	−1.12966	+	0.810756i
$664$	−3.79373	−	11.6759i	−0.147225	−	0.453113i
$665$	10.0816	+	32.9341i	0.390947	+	1.27713i
$666$	−0.427229	+	3.65545i	−0.0165548	+	0.141646i
$667$	−4.83724	−	4.35547i	−0.187299	−	0.168644i
$668$	−5.38237	−	5.97773i	−0.208250	−	0.231285i
$669$	18.4256	+	16.7854i	0.712374	+	0.648962i
$670$	16.7855	−	9.69109i	0.648479	−	0.374400i
$671$	−6.65145	+	28.8183i	−0.256777	+	1.11252i
$672$	−1.95934	+	4.14258i	−0.0755831	+	0.159804i
$673$	22.0224	−	30.3112i	0.848901	−	1.16841i	−0.135203	−	0.990818i	$-0.543169\pi$
$673$	22.0224	−	30.3112i	0.848901	−	1.16841i	0.984104	−	0.177594i	$-0.0568313\pi$
$674$	4.36266	+	20.5247i	0.168044	+	0.790583i
$675$	20.0351	+	12.0379i	0.771150	+	0.463340i
$676$	−0.316172	−	3.00817i	−0.0121605	−	0.115699i
$677$	20.1849	+	8.98688i	0.775767	+	0.345394i	0.756137	−	0.654413i	$-0.227084\pi$
$677$	20.1849	+	8.98688i	0.775767	+	0.345394i	0.0196304	+	0.999807i	$0.493751\pi$
$678$	−7.68979	−	8.64087i	−0.295325	−	0.331851i
$679$	−2.83439	+	23.1514i	−0.108774	+	0.888469i
$680$	−11.8561	+	16.3185i	−0.454661	+	0.625787i
$681$	−16.6303	+	22.6121i	−0.637275	+	0.866496i
$682$	−11.9065	−	21.4769i	−0.455923	−	0.822394i
$683$	−26.0305	−	15.0287i	−0.996031	−	0.575059i	−0.0889592	−	0.996035i	$-0.528354\pi$
$683$	−26.0305	−	15.0287i	−0.996031	−	0.575059i	−0.907071	+	0.420977i	$0.861687\pi$
$684$	9.51512	−	8.36920i	0.363820	−	0.320004i
$685$	13.2665	−	40.8299i	0.506885	−	1.56003i
$686$	2.87796	−	18.2953i	0.109881	−	0.698517i
$687$	−11.8023	−	6.90584i	−0.450285	−	0.263474i
$688$	−0.507366	+	1.13956i	−0.0193432	+	0.0434454i
$689$	18.6063	+	3.95489i	0.708843	+	0.150669i
$690$	2.07128	−	4.58033i	0.0788524	−	0.174370i
$691$	3.91547	−	37.2532i	0.148951	−	1.41718i	−0.623360	−	0.781935i	$-0.714233\pi$
$691$	3.91547	−	37.2532i	0.148951	−	1.41718i	0.772312	−	0.635244i	$-0.219100\pi$
$692$	−13.8661			−0.527108
$693$	−3.95591	+	26.0260i	−0.150273	+	0.988645i
$694$	−0.0989001			−0.00375420
$695$	−5.13483	+	48.8546i	−0.194775	+	1.85316i
$696$	4.93295	−	10.9085i	0.186983	−	0.413484i
$697$	−16.3383	−	3.47281i	−0.618856	−	0.131542i
$698$	−1.50944	+	3.39027i	−0.0571333	+	0.128324i
$699$	−22.0635	−	12.9100i	−0.834519	−	0.488300i
$700$	−6.12597	+	10.2034i	−0.231540	+	0.385653i
$701$	−2.35501	+	7.24797i	−0.0889474	+	0.273752i	−0.985629	−	0.168924i	$-0.945971\pi$
$701$	−2.35501	+	7.24797i	−0.0889474	+	0.273752i	0.896682	+	0.442676i	$0.145971\pi$
$702$	14.8738	+	6.93554i	0.561376	+	0.261765i
$703$	4.48769	+	2.59097i	0.169256	+	0.0977202i
$704$	3.00596	+	1.40149i	0.113292	+	0.0528207i
$705$	−32.5622	+	44.2744i	−1.22636	+	1.66747i
$706$	−4.61468	+	6.35157i	−0.173676	+	0.239044i
$707$	22.6531	+	17.0579i	0.851957	+	0.641527i
$708$	13.0085	+	14.6174i	0.488891	+	0.549357i
$709$	24.0158	+	10.6925i	0.901933	+	0.401566i	0.804691	−	0.593694i	$-0.202331\pi$
$709$	24.0158	+	10.6925i	0.901933	+	0.401566i	0.0972421	+	0.995261i	$0.468998\pi$
$710$	3.32132	+	31.6002i	0.124647	+	1.18593i
$711$	−28.9528	−	40.8404i	−1.08582	−	1.53163i
$712$	−1.35316	−	6.36611i	−0.0507118	−	0.238580i
$713$	−4.09833	+	5.64087i	−0.153484	+	0.211252i
$714$	−29.8921	+	2.45076i	−1.11869	+	0.0917173i
$715$	21.1812	+	24.3634i	0.792133	+	0.911138i
$716$	0.108472	−	0.0626262i	0.00405378	−	0.00234045i
$717$	−1.68583	−	1.53577i	−0.0629586	−	0.0573545i
$718$	23.8912	+	26.5339i	0.891611	+	0.990235i
$719$	10.0853	+	9.08084i	0.376118	+	0.338658i	0.835410	−	0.549627i	$-0.185230\pi$
$719$	10.0853	+	9.08084i	0.376118	+	0.338658i	−0.459292	+	0.888285i	$0.651897\pi$
$720$	9.18324	+	1.07329i	0.342239	+	0.0399991i
$721$	1.69712	+	0.391184i	0.0632040	+	0.0145685i
$722$	0.357736	+	1.10100i	0.0133135	+	0.0409749i
$723$	−24.3416	+	17.4699i	−0.905275	+	0.649714i
$724$	10.2364	−	4.55753i	0.380432	−	0.169379i
$725$	15.5459	−	26.9263i	0.577360	−	1.00002i
$726$	18.8517	+	2.75904i	0.699653	+	0.102398i
$727$	−9.71879			−0.360450			−0.180225	−	0.983625i	$-0.557683\pi$
$727$	−9.71879			−0.360450			−0.180225	+	0.983625i	$0.557683\pi$
$728$	−3.52884	+	7.57457i	−0.130788	+	0.280732i
$729$	22.3836	−	15.0988i	0.829023	−	0.559214i
$730$	0.988496	−	1.09784i	0.0365859	−	0.0406328i
$731$	−8.11942	+	0.853385i	−0.300308	+	0.0315636i
$732$	7.64487	+	13.4209i	0.282563	+	0.496050i
$733$	4.26339	+	3.83878i	0.157472	+	0.141789i	0.744100	−	0.668068i	$-0.232878\pi$
$733$	4.26339	+	3.83878i	0.157472	+	0.141789i	−0.586628	+	0.809856i	$0.699545\pi$
$734$	−8.93276	+	27.4922i	−0.329714	+	1.01476i
$735$	−36.8313	+	6.30039i	−1.35854	+	0.232393i
$736$		−	0.941712i		−	0.0347120i
$737$	6.78964	−	19.7223i	0.250099	−	0.726479i
$738$	2.28112	+	7.30862i	0.0839691	+	0.269034i
$739$	−4.39103	−	9.86241i	−0.161527	−	0.362794i	0.814592	−	0.580035i	$-0.196961\pi$
$739$	−4.39103	−	9.86241i	−0.161527	−	0.362794i	−0.976118	+	0.217240i	$0.930294\pi$
$740$	0.786078	+	3.69821i	0.0288968	+	0.135949i
$741$	17.2616	−	15.3617i	0.634122	−	0.564326i
$742$	11.6577	+	10.8633i	0.427967	+	0.398805i
$743$	17.7155	−	12.8711i	0.649918	−	0.472193i	−0.213325	−	0.976981i	$-0.568429\pi$
$743$	17.7155	−	12.8711i	0.649918	−	0.472193i	0.863243	+	0.504788i	$0.168429\pi$
$744$	−12.1733	−	4.03374i	−0.446296	−	0.147884i
$745$	21.2553	−	19.1383i	0.778733	−	0.701175i
$746$	−10.4313	−	23.4292i	−0.381919	−	0.857804i
$747$	−35.9340	−	8.07579i	−1.31476	−	0.295478i
$748$	1.89315	+	21.6242i	0.0692203	+	0.790660i
$749$	−11.4698	−	13.1852i	−0.419098	−	0.481776i
$750$	−2.61675	−	0.572127i	−0.0955503	−	0.0208911i
$751$	−50.8622	+	10.8111i	−1.85599	+	0.394503i	−0.993715	−	0.111939i	$-0.964294\pi$
$751$	−50.8622	+	10.8111i	−1.85599	+	0.394503i	−0.862274	+	0.506442i	$0.830961\pi$
$752$	−2.14061	+	10.0708i	−0.0780601	+	0.367244i
$753$	−4.55027	−	7.98819i	−0.165821	−	0.291106i
$754$	8.87935	−	19.9433i	0.323367	−	0.726294i
$755$	−12.7981	−	39.3885i	−0.465770	−	1.43349i
$756$	7.69178	+	11.3946i	0.279747	+	0.414417i
$757$	−16.4528	−	11.9537i	−0.597988	−	0.434464i	0.247176	−	0.968971i	$-0.420497\pi$
$757$	−16.4528	−	11.9537i	−0.597988	−	0.434464i	−0.845164	+	0.534507i	$0.820497\pi$
$758$	−0.0645249	−	0.111760i	−0.00234365	−	0.00405932i
$759$	−1.55185	−	5.18236i	−0.0563286	−	0.188108i
$760$	6.50904	−	11.2740i	0.236108	−	0.408950i
$761$	−0.528610	+	5.02939i	−0.0191621	+	0.182315i	−0.999916	−	0.0129308i	$-0.995884\pi$
$761$	−0.528610	+	5.02939i	−0.0191621	+	0.182315i	0.980754	+	0.195246i	$0.0625506\pi$
$762$	−0.374885	−	3.77793i	−0.0135806	−	0.136860i
$763$	0.387830	−	22.6746i	0.0140404	−	0.820875i
$764$	−9.46804	−	13.0316i	−0.342542	−	0.471468i
$765$	23.9682	+	55.5633i	0.866573	+	2.00889i
$766$	4.32943	−	20.3684i	0.156429	−	0.735939i
$767$	23.8754	+	26.5163i	0.862090	+	0.957448i
$768$	1.65036	−	0.525648i	0.0595523	−	0.0189677i
$769$			30.0408i			1.08330i	0.840605	+	0.541649i	$0.182200\pi$
$769$			30.0408i			1.08330i	−0.840605	+	0.541649i	$0.817800\pi$
$770$	4.70699	+	26.6309i	0.169628	+	0.959712i
$771$	−11.2681	+	4.93859i	−0.405811	+	0.177859i
$772$	−5.35261	−	0.562582i	−0.192645	−	0.0202478i
$773$	−21.0556	+	18.9586i	−0.757319	+	0.681893i	−0.954412	−	0.298492i	$-0.903516\pi$
$773$	−21.0556	+	18.9586i	−0.757319	+	0.681893i	0.197094	+	0.980385i	$0.436850\pi$
$774$	2.16427	+	3.05289i	0.0777932	+	0.109734i
$775$	−30.4257	−	13.5464i	−1.09292	−	0.486601i
$776$	7.13209	−	5.18176i	0.256027	−	0.186014i
$777$	−3.40776	+	4.47122i	−0.122253	+	0.160404i
$778$	−16.8832	−	5.48569i	−0.605293	−	0.196672i
$779$	10.7211	+	1.12683i	0.384124	+	0.0403730i
$780$	16.7566	+	1.85974i	0.599981	+	0.0665893i
$781$	25.0093	+	23.3189i	0.894904	+	0.834414i
$782$	5.33766	−	3.08170i	0.190874	−	0.110201i
$783$	−20.6009	−	29.4204i	−0.736217	−	1.05140i
$784$	−5.80052	+	3.91842i	−0.207161	+	0.139944i
$785$	−22.9959	+	7.47182i	−0.820759	+	0.266681i
$786$	−0.113571	+	19.5356i	−0.00405094	+	0.696812i
$787$	−21.4385	+	2.25328i	−0.764201	+	0.0803208i	−0.478606	−	0.878030i	$-0.658858\pi$
$787$	−21.4385	+	2.25328i	−0.764201	+	0.0803208i	−0.285595	+	0.958350i	$0.592191\pi$
$788$	−20.6949	−	4.39883i	−0.737224	−	0.156702i
$789$	−6.55923	−	9.13926i	−0.233515	−	0.325366i
$790$	−41.6069	−	30.2292i	−1.48031	−	1.07551i
$791$	−3.37749	−	17.3432i	−0.120090	−	0.616653i
$792$	8.21594	−	5.61234i	0.291941	−	0.199426i
$793$	14.0823	+	24.3913i	0.500078	+	0.866160i
$794$	12.2227	−	5.44189i	0.433767	−	0.193126i
$795$	13.2469	−	29.2936i	0.469820	−	1.03894i
$796$	12.8274	−	14.2463i	0.454655	−	0.504946i
$797$	−6.90639	−	9.50583i	−0.244637	−	0.336714i	0.668987	−	0.743274i	$-0.266728\pi$
$797$	−6.90639	−	9.50583i	−0.244637	−	0.336714i	−0.913624	+	0.406560i	$0.866728\pi$
$798$	19.0211	−	3.58962i	0.673341	−	0.127071i
$799$	−64.0867	+	20.8230i	−2.26722	+	0.736665i
$800$	4.39991	−	0.935231i	0.155560	−	0.0330654i
$801$	−18.4980	−	6.24905i	−0.653594	−	0.220799i
$802$	−20.1635	−	11.6414i	−0.711996	−	0.411071i
$803$	0.0276529	−	1.58955i	0.000975850	−	0.0560940i
$804$	−4.37261	−	9.97672i	−0.154210	−	0.351852i
$805$	6.28848	−	4.40653i	0.221640	−	0.155310i
$806$	−22.2402	−	7.22628i	−0.783378	−	0.254535i
$807$	−11.6138	+	35.0491i	−0.408827	+	1.23379i
$808$	−1.12034	−	10.6593i	−0.0394134	−	0.374993i
$809$	−4.24113	−	40.3516i	−0.149110	−	1.41869i	−0.771624	−	0.636079i	$-0.780555\pi$
$809$	−4.24113	−	40.3516i	−0.149110	−	1.41869i	0.622514	−	0.782609i	$-0.286111\pi$
$810$	16.8209	−	22.0548i	0.591026	−	0.774925i
$811$	−35.8012	−	11.6325i	−1.25715	−	0.408473i	−0.396672	−	0.917961i	$-0.629835\pi$
$811$	−35.8012	−	11.6325i	−1.25715	−	0.408473i	−0.860478	+	0.509488i	$0.829835\pi$
$812$	14.9766	−	10.4945i	0.525575	−	0.368286i
$813$	24.8144	−	10.8757i	0.870277	−	0.381426i
$814$	3.24960	+	2.44845i	0.113898	+	0.0858182i
$815$	−40.4629	−	23.3613i	−1.41735	−	0.818310i
$816$	8.38011	+	7.63416i	0.293362	+	0.267249i
$817$	5.15393	−	1.09550i	0.180313	−	0.0383268i
$818$	−7.28408	+	2.36674i	−0.254682	+	0.0827511i
$819$	14.1464	+	20.6959i	0.494314	+	0.723174i
$820$	4.62316	+	6.36324i	0.161448	+	0.222214i
$821$	23.0487	−	25.5982i	0.804406	−	0.893383i	−0.191709	−	0.981452i	$-0.561403\pi$
$821$	23.0487	−	25.5982i	0.804406	−	0.893383i	0.996114	+	0.0880689i	$0.0280696\pi$
$822$	−21.9841	−	9.94150i	−0.766785	−	0.346750i
$823$	21.7047	−	9.66356i	0.756579	−	0.336851i	0.00806310	−	0.999967i	$-0.497433\pi$
$823$	21.7047	−	9.66356i	0.756579	−	0.336851i	0.748516	+	0.663117i	$0.230767\pi$
$824$	−0.329135	−	0.570079i	−0.0114660	−	0.0198596i
$825$	22.6721	−	12.3973i	0.789342	−	0.431620i
$826$	5.71358	+	29.3389i	0.198801	+	1.02083i
$827$	16.7875	+	12.1969i	0.583760	+	0.424126i	0.840078	−	0.542466i	$-0.182509\pi$
$827$	16.7875	+	12.1969i	0.583760	+	0.424126i	−0.256318	+	0.966593i	$0.582509\pi$
$828$	−2.43005	−	1.44092i	−0.0844501	−	0.0500754i
$829$	−44.6026	−	9.48057i	−1.54911	−	0.329274i	−0.647584	−	0.761994i	$-0.724220\pi$
$829$	−44.6026	−	9.48057i	−1.54911	−	0.329274i	−0.901528	+	0.432721i	$0.857554\pi$
$830$	−37.6287	+	3.95494i	−1.30611	+	0.137278i
$831$	8.74991	+	0.0508679i	0.303531	+	0.00176459i
$832$	3.00378	−	0.975988i	0.104137	−	0.0338363i
$833$	−41.1916	−	20.0547i	−1.42721	−	0.694855i
$834$	26.9706	+	5.89686i	0.933916	+	0.204192i
$835$	−21.4691	+	12.3952i	−0.742969	+	0.428954i
$836$	−2.67394	−	13.7519i	−0.0924801	−	0.475621i
$837$	−29.0354	+	25.2407i	−1.00361	+	0.872447i
$838$	1.40234	+	0.147391i	0.0484429	+	0.00509155i
$839$	11.1698	+	3.62928i	0.385624	+	0.125297i	0.495412	−	0.868658i	$-0.335017\pi$
$839$	11.1698	+	3.62928i	0.385624	+	0.125297i	−0.109788	+	0.993955i	$0.535017\pi$
$840$	11.2326	+	8.56099i	0.387562	+	0.295382i
$841$	−15.1902	+	11.0364i	−0.523802	+	0.380564i
$842$	25.9098	+	11.5358i	0.892912	+	0.397550i
$843$	2.62135	+	12.6949i	0.0902841	+	0.437237i
$844$	9.23549	−	8.31567i	0.317899	−	0.286237i
$845$	−9.27094	−	0.974415i	−0.318930	−	0.0335209i
$846$	22.7119	+	20.9331i	0.780852	+	0.719696i
$847$	22.6260	+	18.3047i	0.777440	+	0.628957i
$848$		−	6.02273i		−	0.206821i
$849$	−4.98952	−	15.6655i	−0.171240	−	0.537638i
$850$	19.6994	+	21.8784i	0.675684	+	0.750423i
$851$	0.240195	−	1.13003i	0.00823376	−	0.0387368i
$852$	17.8570	+	0.103812i	0.611770	+	0.00355655i
$853$	20.6310	+	28.3961i	0.706391	+	0.972264i	0.999867	+	0.0162977i	$0.00518794\pi$
$853$	20.6310	+	28.3961i	0.706391	+	0.972264i	−0.293476	+	0.955966i	$0.594812\pi$
$854$	−0.403488	+	23.5900i	−0.0138071	+	0.807232i
$855$	−19.1326	−	34.0467i	−0.654320	−	1.16437i
$856$	−0.690437	+	6.56907i	−0.0235987	+	0.224526i
$857$	−12.2401	+	21.2004i	−0.418112	+	0.724192i	−0.995750	−	0.0921019i	$-0.970641\pi$
$857$	−12.2401	+	21.2004i	−0.418112	+	0.724192i	0.577637	+	0.816293i	$0.303975\pi$
$858$	14.9219	−	10.3209i	0.509424	−	0.352351i
$859$	−14.9776	−	25.9419i	−0.511028	−	0.885126i	−0.999918	−	0.0127809i	$-0.995932\pi$
$859$	−14.9776	−	25.9419i	−0.511028	−	0.885126i	0.488891	−	0.872345i	$-0.337402\pi$
$860$	3.11019	+	2.25969i	0.106057	+	0.0770546i
$861$	−2.69307	+	11.3810i	−0.0917795	+	0.387862i
$862$	0.777457	+	2.39277i	0.0264803	+	0.0814980i
$863$	−10.5892	+	23.7838i	−0.360462	+	0.809611i	0.638730	+	0.769431i	$0.279460\pi$
$863$	−10.5892	+	23.7838i	−0.360462	+	0.809611i	−0.999192	+	0.0401804i	$0.987207\pi$
$864$	1.16881	−	5.06299i	0.0397639	−	0.172246i
$865$	−8.88490	+	41.8002i	−0.302096	+	1.42125i
$866$	−14.4552	+	3.07255i	−0.491208	+	0.104409i
$867$	−9.55803	+	43.7158i	−0.324608	+	1.48467i
$868$	−12.8569	−	14.7797i	−0.436393	−	0.501657i
$869$	−55.1347	+	4.82691i	−1.87032	+	0.163742i
$870$	−29.7235	−	21.8605i	−1.00772	−	0.741140i
$871$	−8.07899	−	18.1457i	−0.273746	−	0.614844i
$872$	−6.36982	+	5.73541i	−0.215709	+	0.194226i
$873$	−2.45849	−	26.3327i	−0.0832074	−	0.891227i
$874$	−3.21812	+	2.33810i	−0.108854	+	0.0790874i
$875$	−2.99337	−	2.78940i	−0.101194	−	0.0942989i
$876$	−0.551943	−	0.620208i	−0.0186484	−	0.0209549i
$877$	−4.67127	−	21.9766i	−0.157737	−	0.742096i	−0.983908	−	0.178676i	$-0.942819\pi$
$877$	−4.67127	−	21.9766i	−0.157737	−	0.742096i	0.826171	−	0.563420i	$-0.190515\pi$
$878$	13.9691	+	31.3750i	0.471433	+	1.05886i
$879$	40.2697	+	4.46936i	1.35826	+	0.150748i
$880$	6.15101	−	8.16366i	0.207351	−	0.275197i
$881$		−	7.69766i		−	0.259341i	−0.991557	−	0.129670i	$-0.958608\pi$
$881$		−	7.69766i		−	0.259341i	0.991557	−	0.129670i	$-0.0413919\pi$
$882$	1.23593	+	20.9636i	0.0416159	+	0.705881i
$883$	15.7346	−	48.4262i	0.529512	−	1.62967i	−0.225705	−	0.974196i	$-0.572468\pi$
$883$	15.7346	−	48.4262i	0.529512	−	1.62967i	0.755217	−	0.655475i	$-0.227532\pi$
$884$	15.3616	+	13.8317i	0.516668	+	0.465210i
$885$	52.4007	−	29.8488i	1.76143	−	1.00335i
$886$	0.431931	−	0.0453978i	0.0145110	−	0.00152517i
$887$	31.6616	−	35.1638i	1.06309	−	1.18069i	0.0801494	−	0.996783i	$-0.474460\pi$
$887$	31.6616	−	35.1638i	1.06309	−	1.18069i	0.982944	−	0.183903i	$-0.0588731\pi$
$888$	2.11446	−	0.209818i	0.0709566	−	0.00704102i
$889$	2.44902	−	5.25675i	0.0821374	−	0.176306i
$890$	−20.0581			−0.672350
$891$	−1.91119	−	29.7884i	−0.0640271	−	0.997948i
$892$	7.19521	−	12.4625i	0.240913	−	0.417274i
$893$	39.7297	−	17.6888i	1.32950	−	0.591933i
$894$	−9.37250	−	13.0591i	−0.313463	−	0.436762i
$895$	−0.119286	−	0.367124i	−0.00398729	−	0.0122716i
$896$	2.57815	+	0.594260i	0.0861299	+	0.0198528i
$897$	−4.44635	−	2.60168i	−0.148459	−	0.0868677i
$898$	−17.7890	−	16.0173i	−0.593626	−	0.534503i
$899$	34.2442	+	38.0320i	1.14211	+	1.26844i
$900$	4.31901	−	12.7848i	0.143967	−	0.426160i
$901$	34.1371	−	19.7091i	1.13727	−	0.656604i
$902$	8.24756	+	1.90359i	0.274614	+	0.0633827i
$903$	0.467097	+	5.69722i	0.0155440	+	0.189592i
$904$	−3.92538	+	5.40283i	−0.130556	+	0.179695i
$905$	−7.17987	−	33.7786i	−0.238667	−	1.12284i
$906$	−22.7948	+	4.70685i	−0.757307	+	0.156375i
$907$	−6.08487	−	57.8937i	−0.202045	−	1.92233i	−0.356440	−	0.934318i	$-0.616010\pi$
$907$	−6.08487	−	57.8937i	−0.202045	−	1.92233i	0.154396	−	0.988009i	$-0.450657\pi$
$908$	14.8046	+	6.59145i	0.491309	+	0.218745i
$909$	−29.2202	−	13.4189i	−0.969172	−	0.445076i
$910$	20.5729	+	15.4915i	0.681985	+	0.513537i
$911$	12.1683	−	16.7483i	0.403154	−	0.554894i	−0.558378	−	0.829587i	$-0.688576\pi$
$911$	12.1683	−	16.7483i	0.403154	−	0.554894i	0.961532	+	0.274692i	$0.0885760\pi$
$912$	−5.89384	−	4.33470i	−0.195165	−	0.143536i
$913$	−27.7675	+	29.7805i	−0.918970	+	0.985590i
$914$	−1.33203	−	0.769047i	−0.0440596	−	0.0254378i
$915$	45.3568	−	14.4463i	1.49945	−	0.477581i
$916$	−2.43963	+	7.50842i	−0.0806077	+	0.248085i
$917$	−15.3606	+	25.5846i	−0.507252	+	0.844880i
$918$	32.5221	−	9.94346i	1.07339	−	0.328183i
$919$	4.11659	−	9.24602i	0.135794	−	0.304998i	−0.832830	−	0.553529i	$-0.813281\pi$
$919$	4.11659	−	9.24602i	0.135794	−	0.304998i	0.968624	+	0.248531i	$0.0799476\pi$
$920$	−2.83886	−	0.603418i	−0.0935943	−	0.0198941i
$921$	51.9808	+	23.5064i	1.71283	+	0.774561i
$922$	2.78811	−	26.5270i	0.0918214	−	0.873622i
$923$	32.5624			1.07181
$924$	15.1672	−	0.978253i	0.498963	−	0.0321821i
$925$	5.51831			0.181441
$926$	2.26830	−	21.5815i	0.0745411	−	0.709211i
$927$	−1.97468	−	0.0229605i	−0.0648569	−	0.000754121i
$928$	−6.76099	−	1.43709i	−0.221940	−	0.0471749i
$929$	−21.6246	+	48.5696i	−0.709480	+	1.59352i	0.0921829	+	0.995742i	$0.470616\pi$
$929$	−21.6246	+	48.5696i	−0.709480	+	1.59352i	−0.801663	+	0.597776i	$0.796051\pi$
$930$	−19.9602	+	34.1126i	−0.654522	+	1.11860i
$931$	27.7920	+	10.0934i	0.910848	+	0.330798i
$932$	−4.56072	+	14.0364i	−0.149391	+	0.459779i
$933$	−15.8671	−	49.8174i	−0.519465	−	1.63095i
$934$	31.4165	+	18.1383i	1.02798	+	0.593504i
$935$	66.4008	+	8.14906i	2.17154	+	0.266503i
$936$	2.07760	−	9.24450i	0.0679086	−	0.302166i
$937$	18.8079	−	25.8869i	0.614428	−	0.845688i	−0.382504	−	0.923954i	$-0.624938\pi$
$937$	18.8079	−	25.8869i	0.614428	−	0.845688i	0.996933	+	0.0782658i	$0.0249383\pi$
$938$	2.02201	−	16.5158i	0.0660209	−	0.539261i
$939$	9.51897	−	8.47124i	0.310640	−	0.276448i
$940$	28.9875	+	12.9060i	0.945467	+	0.420949i
$941$	−2.16084	−	20.5590i	−0.0704414	−	0.670205i	−0.971586	−	0.236686i	$-0.923939\pi$
$941$	−2.16084	−	20.5590i	−0.0704414	−	0.670205i	0.901145	−	0.433518i	$-0.142728\pi$
$942$	2.74797	+	13.3081i	0.0895337	+	0.433603i
$943$	−0.499685	−	2.35083i	−0.0162720	−	0.0765537i
$944$	6.64043	−	9.13976i	0.216127	−	0.297474i
$945$	39.2784	−	15.8861i	1.27773	−	0.516776i
$946$	4.12142	−	0.360820i	0.133999	−	0.0117313i
$947$	12.8536	−	7.42105i	0.417687	−	0.241152i	−0.276400	−	0.961043i	$-0.589142\pi$
$947$	12.8536	−	7.42105i	0.417687	−	0.241152i	0.694087	+	0.719891i	$0.255808\pi$
$948$	−19.4646	+	21.3666i	−0.632182	+	0.693953i
$949$	−1.01302	−	1.12507i	−0.0328839	−	0.0365213i
$950$	−14.1201	−	12.7138i	−0.458118	−	0.412491i
$951$	4.46095	−	7.62389i	0.144656	−	0.247222i
$952$	5.06856	+	16.5577i	0.164273	+	0.536639i
$953$	2.80251	+	8.62523i	0.0907822	+	0.279399i	0.986132	−	0.165966i	$-0.0530741\pi$
$953$	2.80251	+	8.62523i	0.0907822	+	0.279399i	−0.895349	+	0.445364i	$0.853074\pi$
$954$	−15.5414	−	9.21542i	−0.503172	−	0.298360i
$955$	−45.3516	+	20.1918i	−1.46754	+	0.653392i
$956$	−0.658321	+	1.14024i	−0.0212916	+	0.0368782i
$957$	−39.5748	+	3.23296i	−1.27927	+	0.104507i
$958$	−5.92057			−0.191285
$959$	−21.1499	−	30.1827i	−0.682967	−	0.974651i
$960$	−0.527105	−	5.31195i	−0.0170122	−	0.171442i
$961$	15.9389	−	17.7019i	0.514157	−	0.571029i
$962$	3.85339	−	0.405007i	0.124238	−	0.0130580i
$963$	15.8948	+	11.8330i	0.512203	+	0.381314i
$964$	12.8553	+	11.5750i	0.414041	+	0.372804i
$965$	−5.12571	+	15.7753i	−0.165003	+	0.507826i
$966$	−2.07153	−	3.78576i	−0.0666504	−	0.121805i
$967$		−	20.1273i		−	0.647250i	−0.946185	−	0.323625i	$-0.895098\pi$
$967$		−	20.1273i		−	0.647250i	0.946185	−	0.323625i	$-0.104902\pi$
$968$	−0.768602	−	10.9731i	−0.0247038	−	0.352689i
$969$	5.28198	−	47.5916i	0.169682	−	1.52886i
$970$	−11.0508	−	24.8205i	−0.354819	−	0.796937i
$971$	3.99296	+	18.7854i	0.128140	+	0.602851i	0.994616	+	0.103632i	$0.0330465\pi$
$971$	3.99296	+	18.7854i	0.128140	+	0.602851i	−0.866476	+	0.499219i	$0.833620\pi$
$972$	−11.2764	−	10.7630i	−0.361692	−	0.345223i
$973$	30.8524	+	28.7501i	0.989082	+	0.921685i
$974$	−1.47582	+	1.07225i	−0.0472885	+	0.0343571i
$975$	7.73997	−	23.3583i	0.247877	−	0.748063i
$976$	6.62698	−	5.96696i	0.212124	−	0.190998i
$977$	−11.3042	−	25.3896i	−0.361653	−	0.812286i	−0.999125	−	0.0418131i	$-0.986687\pi$
$977$	−11.3042	−	25.3896i	−0.361653	−	0.812286i	0.637472	−	0.770473i	$-0.279980\pi$
$978$	−15.5575	+	21.1533i	−0.497473	+	0.676408i
$979$	−16.2901	+	14.1624i	−0.520634	+	0.452634i
$980$	8.09557	+	19.9969i	0.258604	+	0.638776i
$981$	5.05351	+	25.2129i	0.161346	+	0.804985i
$982$	−14.9644	+	3.18079i	−0.477534	+	0.101503i
$983$	−4.58218	+	21.5574i	−0.146149	+	0.687576i	0.842667	+	0.538435i	$0.180984\pi$
$983$	−4.58218	+	21.5574i	−0.146149	+	0.687576i	−0.988816	+	0.149141i	$0.952349\pi$
$984$	3.84095	−	2.18790i	0.122445	−	0.0697477i
$985$	−26.5211	+	59.5675i	−0.845034	+	1.89798i
$986$	−13.9795	−	43.0243i	−0.445197	−	1.37017i
$987$	13.5478	+	45.1943i	0.431230	+	1.43855i
$988$	−10.7931	−	7.84164i	−0.343374	−	0.249476i
$989$	−0.587349	−	1.01732i	−0.0186766	−	0.0323489i
$990$	−11.6543	−	28.3637i	−0.370398	−	0.901458i
$991$	23.8211	−	41.2593i	0.756701	−	1.31065i	−0.187823	−	0.982203i	$-0.560143\pi$
$991$	23.8211	−	41.2593i	0.756701	−	1.31065i	0.944524	−	0.328442i	$-0.106524\pi$
$992$	−0.773936	+	7.36351i	−0.0245725	+	0.233792i
$993$	−39.1109	+	3.88097i	−1.24115	+	0.123159i
$994$	23.3863	+	14.0407i	0.741767	+	0.445345i
$995$	−34.7270	−	47.7976i	−1.10092	−	1.51529i
$996$	−0.123617	+	21.2636i	−0.00391695	+	0.673764i
$997$	−0.0746478	+	0.351190i	−0.00236412	+	0.0111223i	−0.979314	−	0.202347i	$-0.935143\pi$
$997$	−0.0746478	+	0.351190i	−0.00236412	+	0.0111223i	0.976950	+	0.213469i	$0.0684764\pi$
$998$	27.6948	+	30.7582i	0.876664	+	0.973634i
$999$	2.69392	−	5.77732i	0.0852318	−	0.182786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.95.10	yes	128
3.2	odd	2		462.2.bc.a.95.1	✓	128
7.2	even	3	inner	462.2.bc.b.359.13	yes	128
11.8	odd	10		462.2.bc.a.305.9	yes	128
21.2	odd	6		462.2.bc.a.359.9	yes	128
33.8	even	10	inner	462.2.bc.b.305.13	yes	128
77.30	odd	30		462.2.bc.a.107.1	yes	128
231.107	even	30	inner	462.2.bc.b.107.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.1	✓	128	3.2	odd	2
462.2.bc.a.107.1	yes	128	77.30	odd	30
462.2.bc.a.305.9	yes	128	11.8	odd	10
462.2.bc.a.359.9	yes	128	21.2	odd	6
462.2.bc.b.95.10	yes	128	1.1	even	1	trivial
462.2.bc.b.107.10	yes	128	231.107	even	30	inner
462.2.bc.b.305.13	yes	128	33.8	even	10	inner
462.2.bc.b.359.13	yes	128	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.713675 - 1.57818i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.25353 + 2.81547i) q^{5} +(1.49494 + 0.874731i) q^{6} +(1.28350 + 2.31358i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.98134 - 2.25262i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.713675 - 1.57818i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.25353 + 2.81547i) q^{5} +(1.49494 + 0.874731i) q^{6} +(1.28350 + 2.31358i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.98134 - 2.25262i) q^{9} +(-2.66902 - 1.54096i) q^{10} +(-3.25565 + 0.633032i) q^{11} +(-1.02620 + 1.39532i) q^{12} +(-1.85644 + 2.55517i) q^{13} +(-2.43506 + 1.03463i) q^{14} +(3.54872 + 3.98763i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.684127 + 6.50903i) q^{17} +(2.44739 - 1.73502i) q^{18} +(-0.878223 - 4.13171i) q^{19} +(1.81151 - 2.49332i) q^{20} +(4.56725 - 0.374454i) q^{21} +(-0.289256 - 3.30399i) q^{22} +(-0.815547 + 0.470856i) q^{23} +(-1.28041 - 1.16643i) q^{24} +(-3.00989 - 3.34282i) q^{25} +(-2.34712 - 2.11336i) q^{26} +(-4.96909 + 1.51927i) q^{27} +(-0.774430 - 2.52987i) q^{28} +(2.13594 + 6.57373i) q^{29} +(-4.33673 + 3.11246i) q^{30} +(6.76396 - 3.01151i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.32444 + 5.58980i) q^{33} -6.54489 q^{34} +(-8.12271 + 0.713516i) q^{35} +(1.46969 + 2.61534i) q^{36} +(-0.820875 + 0.911674i) q^{37} +(4.20088 - 0.441530i) q^{38} +(2.70763 + 4.75337i) q^{39} +(2.29031 + 2.06220i) q^{40} +(-0.788646 + 2.42720i) q^{41} +(-0.105005 + 4.58137i) q^{42} +1.24741i q^{43} +(3.31612 + 0.0576896i) q^{44} +(8.82586 - 2.75466i) q^{45} +(-0.383029 - 0.860297i) q^{46} +(2.14061 + 10.0708i) q^{47} +(1.29388 - 1.15147i) q^{48} +(-3.70527 + 5.93894i) q^{49} +(3.63913 - 2.64398i) q^{50} +(10.7607 + 3.56566i) q^{51} +(2.34712 - 2.11336i) q^{52} +(-2.44967 - 5.50204i) q^{53} +(-0.991538 - 5.10067i) q^{54} +(2.29877 - 9.95972i) q^{55} +(2.59696 - 0.505744i) q^{56} +(-7.14738 - 1.56270i) q^{57} +(-6.76099 + 1.43709i) q^{58} +(2.34885 - 11.0505i) q^{59} +(-2.64210 - 4.63831i) q^{60} +(3.62706 - 8.14652i) q^{61} +(2.28798 + 7.04169i) q^{62} +(2.66858 - 7.47521i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.86691 - 8.42973i) q^{65} +(-5.42074 - 1.90147i) q^{66} +(-3.14450 + 5.44644i) q^{67} +(0.684127 - 6.50903i) q^{68} +(0.161062 + 1.62312i) q^{69} +(0.139447 - 8.15279i) q^{70} +(-6.06001 - 8.34089i) q^{71} +(-2.75464 + 1.18826i) q^{72} +(-0.0996603 + 0.468865i) q^{73} +(-0.820875 - 0.911674i) q^{74} +(-7.42368 + 2.36447i) q^{75} +4.22402i q^{76} +(-5.64319 - 6.71970i) q^{77} +(-5.01035 + 2.19594i) q^{78} +(16.5959 + 1.74430i) q^{79} +(-2.29031 + 2.06220i) q^{80} +(-1.14862 + 8.92640i) q^{81} +(-2.33147 - 1.03804i) q^{82} +(9.93212 - 7.21611i) q^{83} +(-4.54530 - 0.583314i) q^{84} +(-19.1836 - 6.23312i) q^{85} +(-1.24057 - 0.130390i) q^{86} +(11.8989 + 1.32061i) q^{87} +(-0.404003 + 3.29193i) q^{88} +(5.63638 - 3.25417i) q^{89} +(1.81702 + 9.06545i) q^{90} +(-8.29431 - 1.01546i) q^{91} +(0.895621 - 0.291005i) q^{92} +(0.0745528 - 12.8240i) q^{93} +(-10.2394 + 1.07620i) q^{94} +(12.7336 + 2.70661i) q^{95} +(1.00991 + 1.40715i) q^{96} +(7.13209 + 5.18176i) q^{97} +(-5.51910 - 4.30576i) q^{98} +(7.87652 + 6.07951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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