LMFDB - Embedded newform 462.2.bc.b.107.10

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			107.10
Character	$\chi$	$=$	462.107
Dual form			462.2.bc.b.95.10

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

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

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 $

$2$	−0.104528	−	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	−0.942280	−	0.334825i	$-0.891323\pi$
$5$	−1.25353	−	2.81547i	−0.560595	−	1.25912i	0.381685	−	0.924292i	$-0.375344\pi$
$6$	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	0.469850	−	0.882746i	$-0.344308\pi$
$13$	−1.85644	−	2.55517i	−0.514884	−	0.708676i	−0.984733	+	0.174070i	$0.944308\pi$
$14$	−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	−0.522035	−	0.852924i	$-0.674827\pi$
$17$	0.684127	−	6.50903i	0.165925	−	1.57867i	0.687960	−	0.725748i	$-0.258506\pi$
$18$	2.44739	+	1.73502i	0.576855	+	0.408948i
$19$	−0.878223	+	4.13171i	−0.201478	+	0.947880i	0.754921	+	0.655816i	$0.227675\pi$
$19$	−0.878223	+	4.13171i	−0.201478	+	0.947880i	−0.956399	+	0.292064i	$0.905658\pi$
$20$	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	0.412558	−	0.910931i	$-0.364636\pi$
$23$	−0.815547	−	0.470856i	−0.170053	−	0.0981803i	−0.582611	+	0.812751i	$0.697969\pi$
$24$	−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	−0.531049	−	0.847341i	$-0.678202\pi$
$29$	2.13594	−	6.57373i	0.396633	−	1.22071i	0.927682	−	0.373370i	$-0.121798\pi$
$30$	−4.33673	−	3.11246i	−0.791775	−	0.568255i
$31$	6.76396	+	3.01151i	1.21484	+	0.540883i	0.911224	−	0.411911i	$-0.135139\pi$
$31$	6.76396	+	3.01151i	1.21484	+	0.540883i	0.303618	+	0.952794i	$0.401805\pi$
$32$	−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	0.671881	−	0.740659i	$-0.265487\pi$
$37$	−0.820875	−	0.911674i	−0.134951	−	0.149878i	−0.806832	+	0.590781i	$0.798820\pi$
$38$	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	0.870397	−	0.492351i	$-0.163862\pi$
$41$	−0.788646	−	2.42720i	−0.123166	−	0.379065i	−0.993562	+	0.113286i	$0.963862\pi$
$42$	−0.105005	−	4.58137i	−0.0162026	−	0.706921i
$43$		−	1.24741i		−	0.190228i	−0.995466	−	0.0951139i	$-0.969678\pi$
$43$		−	1.24741i		−	0.190228i	0.995466	−	0.0951139i	$-0.0303215\pi$
$44$	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	−0.489868	−	0.871797i	$-0.662955\pi$
$47$	2.14061	−	10.0708i	0.312240	−	1.46898i	0.802108	−	0.597179i	$-0.203712\pi$
$48$	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	0.663484	+	0.748191i	$0.269077\pi$
$53$	−2.44967	+	5.50204i	−0.336487	+	0.755763i	−0.999971	+	0.00757264i	$0.997590\pi$
$54$	−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	0.815727	+	0.578437i	$0.196337\pi$
$59$	2.34885	+	11.0505i	0.305795	+	1.43865i	−0.509932	+	0.860215i	$0.670330\pi$
$60$	−2.64210	+	4.63831i	−0.341093	+	0.598804i
$61$	3.62706	+	8.14652i	0.464398	+	1.04306i	0.982249	+	0.187584i	$0.0600657\pi$
$61$	3.62706	+	8.14652i	0.464398	+	1.04306i	−0.517851	+	0.855471i	$0.673268\pi$
$62$	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	0.607491	−	0.794327i	$-0.292176\pi$
$67$	−3.14450	−	5.44644i	−0.384162	−	0.665388i	−0.991653	+	0.128939i	$0.958843\pi$
$68$	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	0.280359	+	0.959895i	$0.409546\pi$
$71$	−6.06001	+	8.34089i	−0.719191	+	0.989881i	−0.999550	+	0.0299863i	$0.990454\pi$
$72$	−2.75464	−	1.18826i	−0.324637	−	0.140038i
$73$	−0.0996603	−	0.468865i	−0.0116644	−	0.0548765i	0.971931	−	0.235268i	$-0.0755968\pi$
$73$	−0.0996603	−	0.468865i	−0.0116644	−	0.0548765i	−0.983595	+	0.180392i	$0.942263\pi$
$74$	−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	0.897569	−	0.440874i	$-0.145331\pi$
$79$	16.5959	−	1.74430i	1.86719	−	0.196249i	0.969618	+	0.244624i	$0.0786647\pi$
$80$	−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	0.979432	−	0.201777i	$-0.0646715\pi$
$83$	9.93212	+	7.21611i	1.09019	+	0.792071i	0.110760	+	0.993847i	$0.464671\pi$
$84$	−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	0.768040	−	0.640402i	$-0.221232\pi$
$89$	5.63638	+	3.25417i	0.597455	+	0.344941i	−0.170585	+	0.985343i	$0.554566\pi$
$90$	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	−0.163555	−	0.986534i	$-0.552296\pi$
$97$	7.13209	−	5.18176i	0.724154	−	0.526128i	0.887709	+	0.460406i	$0.152296\pi$
$98$	−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	0.831225	−	0.555937i	$-0.187640\pi$
$101$	9.79140	+	4.35941i	0.974281	+	0.433778i	0.143056	+	0.989715i	$0.454307\pi$
$102$	−4.67092	−	10.3290i	−0.462490	−	1.02273i
$103$	0.440469	+	0.489190i	0.0434007	+	0.0482014i	0.764454	−	0.644678i	$-0.223009\pi$
$103$	0.440469	+	0.489190i	0.0434007	+	0.0482014i	−0.721054	+	0.692879i	$0.756342\pi$
$104$	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	−0.115270	−	0.993334i	$-0.536773\pi$
$107$	−6.46092	−	1.37331i	−0.624600	−	0.132763i	−0.509330	+	0.860571i	$0.670107\pi$
$108$	5.17637	+	0.452941i	0.498097	+	0.0435843i
$109$	−7.42308	+	4.28572i	−0.711003	+	0.410498i	−0.811432	−	0.584447i	$-0.801312\pi$
$109$	−7.42308	+	4.28572i	−0.711003	+	0.410498i	0.100430	+	0.994944i	$0.467978\pi$
$110$	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	−0.592121	−	0.805849i	$-0.701709\pi$
$113$	−6.35140	+	2.06370i	−0.597490	+	0.194136i	−0.00536916	+	0.999986i	$0.501709\pi$
$114$	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	−0.862344	−	0.506322i	$-0.831005\pi$
$127$	−1.28837	+	1.77329i	−0.114324	+	0.157354i	0.748020	+	0.663676i	$0.231005\pi$
$128$	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	−0.507236	−	0.861807i	$-0.669333\pi$
$131$	5.63954	−	9.76796i	0.492729	−	0.853431i	0.999965	+	0.00837614i	$0.00266624\pi$
$132$	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	−0.507793	−	0.861479i	$-0.669539\pi$
$137$	−13.8537	−	1.45608i	−1.18360	−	0.124402i	−0.675808	+	0.737077i	$0.736205\pi$
$138$	−1.63107	+	0.00948225i	−0.138846	+	0.000807183i
$139$	15.1592	+	4.92553i	1.28579	+	0.417778i	0.870615	−	0.491965i	$-0.163721\pi$
$139$	15.1592	+	4.92553i	1.28579	+	0.417778i	0.415172	+	0.909743i	$0.363721\pi$
$140$	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	−0.723481	−	0.690344i	$-0.757459\pi$
$149$	−8.47818	+	3.77473i	−0.694560	+	0.309238i	0.0289218	+	0.999582i	$0.490793\pi$
$150$	−1.57554	+	7.63016i	−0.128642	+	0.623000i
$151$	−9.98655	−	8.99193i	−0.812694	−	0.731753i	0.153894	−	0.988087i	$-0.450818\pi$
$151$	−9.98655	−	8.99193i	−0.812694	−	0.731753i	−0.966588	+	0.256334i	$0.917485\pi$
$152$	−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	−0.496301	−	0.868151i	$-0.665309\pi$
$157$	5.24970	−	5.83038i	0.418971	−	0.465315i	0.915272	+	0.402836i	$0.131975\pi$
$158$	−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	−0.862324	−	0.506356i	$-0.830992\pi$
$163$	−1.58467	−	15.0772i	−0.124121	−	1.18094i	0.738203	−	0.674579i	$-0.235675\pi$
$164$	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	−0.306807	−	0.951772i	$-0.599261\pi$
$167$	6.50759	−	4.72804i	0.503572	−	0.365867i	0.810380	+	0.585905i	$0.199261\pi$
$168$	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	0.692273	−	0.721636i	$-0.256610\pi$
$173$	13.5630	+	2.88292i	1.03118	+	0.219184i	0.338907	+	0.940820i	$0.389943\pi$
$174$	−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	0.665645	−	0.746269i	$-0.268157\pi$
$179$	−0.0930807	−	0.0838102i	−0.00695718	−	0.00626427i	−0.672602	+	0.740005i	$0.734823\pi$
$180$	−9.20572	−	0.859470i	−0.686154	−	0.0640611i
$181$	−9.06514	−	6.58621i	−0.673806	−	0.489549i	0.197491	−	0.980305i	$-0.436721\pi$
$181$	−9.06514	−	6.58621i	−0.673806	−	0.489549i	−0.871297	+	0.490756i	$0.836721\pi$
$182$	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	−0.110682	−	0.993856i	$-0.535303\pi$
$191$	11.9706	−	10.7784i	0.866160	−	0.779894i	0.976842	+	0.213962i	$0.0686368\pi$
$192$	−1.50501	−	0.857291i	−0.108615	−	0.0618696i
$193$	5.35261	+	0.562582i	0.385289	+	0.0404955i	0.295193	−	0.955438i	$-0.404616\pi$
$193$	5.35261	+	0.562582i	0.385289	+	0.0404955i	0.0900958	+	0.995933i	$0.471283\pi$
$194$	−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	−0.975140	−	0.221589i	$-0.928876\pi$
$199$	−9.58513	−	16.6019i	−0.679472	−	1.17688i	0.295668	−	0.955291i	$-0.404458\pi$
$200$	−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	0.479819	−	0.877368i	$-0.340702\pi$
$211$	−7.30474	−	10.0541i	−0.502879	−	0.692154i	−0.982698	+	0.185213i	$0.940702\pi$
$212$	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	−0.982272	−	0.187463i	$-0.939973\pi$
$223$	−4.44688	−	13.6861i	−0.297785	−	0.916489i	0.684486	−	0.729026i	$-0.260027\pi$
$224$	−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	−0.701336	−	0.712831i	$-0.747413\pi$
$227$	−15.8516	+	3.36935i	−1.05210	+	0.223632i	−0.350768	+	0.936462i	$0.614079\pi$
$228$	6.66628	−	3.01458i	0.441485	−	0.199645i
$229$	0.825233	+	7.85157i	0.0545329	+	0.518846i	0.987357	+	0.158514i	$0.0506702\pi$
$229$	0.825233	+	7.85157i	0.0545329	+	0.518846i	−0.932824	+	0.360333i	$0.882663\pi$
$230$	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	0.921115	+	0.389290i	$0.127280\pi$
$233$	1.54271	+	14.6779i	0.101067	+	0.961584i	−0.820049	+	0.572294i	$0.806054\pi$
$234$	−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	0.963353	−	0.268238i	$-0.0864412\pi$
$239$	0.406865	+	1.25220i	0.0263179	+	0.0809981i	−0.937035	+	0.349236i	$0.886441\pi$
$240$	1.62000	−	5.08628i	0.104571	−	0.328318i
$241$	−14.9809	+	8.64925i	−0.965007	+	0.557147i	−0.897710	−	0.440586i	$-0.854771\pi$
$241$	−14.9809	+	8.64925i	−0.965007	+	0.557147i	−0.0672967	+	0.997733i	$0.521437\pi$
$242$	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	0.896046	−	0.443961i	$-0.146427\pi$
$251$	3.11981	+	4.29405i	0.196921	+	0.271038i	−0.699126	+	0.714999i	$0.746427\pi$
$252$	−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	−0.817139	−	0.576441i	$-0.804441\pi$
$257$	−5.27859	+	4.75286i	−0.329269	+	0.296475i	0.487869	+	0.872917i	$0.337774\pi$
$258$	−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	0.948607	−	0.316456i	$-0.102493\pi$
$263$	3.24743	+	5.62471i	0.200245	+	0.346835i	−0.748362	+	0.663290i	$0.769159\pi$
$264$	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	−0.566873	−	0.823805i	$-0.691847\pi$
$269$	−21.2008	−	2.22830i	−1.29264	−	0.135862i	−0.725764	+	0.687944i	$0.758514\pi$
$270$	15.6037	−	3.60219i	0.949612	−	0.219222i
$271$	11.6244	−	10.4666i	0.706132	−	0.635804i	−0.235725	−	0.971820i	$-0.575746\pi$
$271$	11.6244	−	10.4666i	0.706132	−	0.635804i	0.941856	+	0.336016i	$0.109080\pi$
$272$	−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	−0.841233	−	0.540672i	$-0.818170\pi$
$277$	2.05477	−	4.61509i	0.123459	−	0.277294i	0.964693	+	0.263378i	$0.0848366\pi$
$278$	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	0.392356	−	0.919814i	$-0.371660\pi$
$281$	−6.05472	−	4.39901i	−0.361195	−	0.262423i	−0.753550	+	0.657390i	$0.771660\pi$
$282$	−5.60914	−	16.9277i	−0.334020	−	1.00803i
$283$	7.05404	+	6.35148i	0.419319	+	0.377557i	0.851609	−	0.524178i	$-0.175627\pi$
$283$	7.05404	+	6.35148i	0.419319	+	0.377557i	−0.432290	+	0.901735i	$0.642294\pi$
$284$	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	−0.483249	−	0.875483i	$-0.660543\pi$
$293$	7.22868	−	22.2476i	0.422304	−	1.29972i	0.905552	−	0.424234i	$-0.139457\pi$
$294$	−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	$-0.610910\pi$
$307$		−	32.9371i		−	1.87982i	0.341425	−	0.939909i	$-0.389090\pi$
$308$	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	0.982115	+	0.188281i	$0.0602915\pi$
$311$	22.4324	+	20.1982i	1.27202	+	1.14534i	0.289909	+	0.957054i	$0.406375\pi$
$312$	5.35742	+	1.10624i	0.303304	+	0.0626287i
$313$	6.72088	−	2.99233i	0.379886	−	0.169136i	−0.207905	−	0.978149i	$-0.566664\pi$
$313$	6.72088	−	2.99233i	0.379886	−	0.169136i	0.587791	+	0.809013i	$0.299998\pi$
$314$	−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	0.0389811	−	0.999240i	$-0.487589\pi$
$317$	5.07186	−	0.533074i	0.284864	−	0.0299404i	0.245883	+	0.969300i	$0.420922\pi$
$318$	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	0.365185	+	0.930935i	$0.381006\pi$
$331$	−11.3458	+	19.6515i	−0.623621	+	1.08014i	−0.988806	+	0.149208i	$0.952328\pi$
$332$	−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	0.797120	−	0.603821i	$-0.206356\pi$
$337$	19.9563	+	6.48418i	1.08709	+	0.353216i	0.289967	+	0.957037i	$0.406356\pi$
$338$	−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	−0.994241	−	0.107168i	$-0.965822\pi$
$347$	0.0103379	−	0.0983583i	0.000554966	−	0.00528015i	0.994796	+	0.101888i	$0.0324883\pi$
$348$	−11.3643	+	3.76568i	−0.609193	+	0.201862i
$349$	3.52948	−	1.14680i	0.188928	−	0.0613866i	−0.213025	−	0.977047i	$-0.568331\pi$
$349$	3.52948	−	1.14680i	0.188928	−	0.0613866i	0.401953	+	0.915660i	$0.368331\pi$
$350$	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	−0.308024	−	0.951379i	$-0.599668\pi$
$353$	6.79914	−	3.92549i	0.361882	−	0.208933i	0.669906	+	0.742446i	$0.266334\pi$
$354$	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	0.879426	+	0.476036i	$0.157927\pi$
$359$	23.8912	+	26.5339i	1.26093	+	1.40040i	0.381503	+	0.924368i	$0.375407\pi$
$360$	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	0.601519	−	0.798858i	$-0.294562\pi$
$367$	28.2753	−	6.01010i	1.47596	−	0.313725i	0.874440	+	0.485133i	$0.161229\pi$
$368$	−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	−0.201124	−	0.979566i	$-0.564459\pi$
$373$	−22.2105	−	12.8232i	−1.15001	−	0.663961i	−0.948891	+	0.315605i	$0.897793\pi$
$374$	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	0.585101	−	0.810961i	$-0.301055\pi$
$379$	−0.104403	−	0.0758535i	−0.00536284	−	0.00389633i	−0.590463	+	0.807064i	$0.701055\pi$
$380$	−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	−0.617607	−	0.786487i	$-0.711898\pi$
$383$	−20.7093	+	2.17664i	−1.05820	+	0.111221i	−0.440591	+	0.897708i	$0.645231\pi$
$384$	−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	−0.967065	−	0.254531i	$-0.918079\pi$
$389$	−3.69086	−	17.3642i	−0.187134	−	0.880397i	0.779930	−	0.625866i	$-0.215254\pi$
$390$	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	−0.983628	−	0.180211i	$-0.942322\pi$
$397$	−6.68970	+	11.5869i	−0.335746	+	0.581530i	0.647882	+	0.761741i	$0.275655\pi$
$398$	−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	−0.979768	−	0.200138i	$-0.935861\pi$
$401$	−9.46995	−	21.2698i	−0.472907	−	1.06217i	0.506861	−	0.862028i	$-0.330806\pi$
$402$	−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	−0.820001	−	0.572363i	$-0.806027\pi$
$409$	3.11517	−	6.99678i	0.154035	−	0.345969i	0.974036	+	0.226394i	$0.0726937\pi$
$410$	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	$0.0109657\pi$
$419$			1.41006i			0.0688859i	−0.999407	+	0.0344430i	$0.989034\pi$
$420$	7.33996	+	12.0660i	0.358154	+	0.588758i
$421$	8.76429	+	26.9737i	0.427145	+	1.31462i	0.900925	+	0.433975i	$0.142889\pi$
$421$	8.76429	+	26.9737i	0.427145	+	1.31462i	−0.473780	+	0.880643i	$0.657111\pi$
$422$	−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	0.461344	−	0.887221i	$-0.347367\pi$
$431$	2.29839	+	1.02331i	0.110710	+	0.0492911i	−0.350634	+	0.936512i	$0.614034\pi$
$432$	−5.15743	+	0.633185i	−0.248137	+	0.0304641i
$433$	4.56670	−	14.0549i	0.219462	−	0.675433i	−0.779345	−	0.626595i	$-0.784448\pi$
$433$	4.56670	−	14.0549i	0.219462	−	0.675433i	0.998807	−	0.0488383i	$-0.0155519\pi$
$434$	−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	0.996260	−	0.0864107i	$-0.0275397\pi$
$439$	29.7430	+	17.1721i	1.41956	+	0.819581i	0.423296	+	0.905991i	$0.360873\pi$
$440$	−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	−0.980241	−	0.197809i	$-0.936618\pi$
$443$	−0.0902981	+	0.424819i	−0.00429019	+	0.0201838i	0.975950	+	0.217993i	$0.0699508\pi$
$444$	−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	0.335598	−	0.942005i	$-0.391062\pi$
$449$	−14.0701	−	19.3658i	−0.664008	−	0.913928i	−0.999606	+	0.0280772i	$0.991062\pi$
$450$	−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	0.898322	−	0.439338i	$-0.144787\pi$
$457$	−0.625599	−	1.40512i	−0.0292643	−	0.0657287i	−0.927586	+	0.373609i	$0.878120\pi$
$458$	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	0.837998	+	0.545673i	$0.183726\pi$
$467$	14.7550	+	33.1404i	0.682782	+	1.53355i	−0.155217	+	0.987880i	$0.549608\pi$
$468$	−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	−0.971244	−	0.238086i	$-0.923480\pi$
$479$	0.618868	−	5.88814i	0.0282768	−	0.269036i	0.999521	−	0.0309500i	$-0.00985327\pi$
$480$	−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	−0.714854	−	0.699274i	$-0.753507\pi$
$487$	1.22064	−	1.35566i	0.0553125	−	0.0614308i	0.770166	+	0.637843i	$0.220173\pi$
$488$	−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	−0.785914	−	0.618336i	$-0.787807\pi$
$491$	4.72757	−	14.5500i	0.213352	−	0.656631i	0.999266	−	0.0382954i	$-0.0121928\pi$
$492$	−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	0.899686	+	0.436538i	$0.143796\pi$
$499$	27.6948	+	30.7582i	1.23979	+	1.37693i	0.340104	+	0.940388i	$0.389538\pi$
$500$	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	0.947761	−	0.318980i	$-0.103340\pi$
$503$	−0.145451	−	0.447653i	−0.00648535	−	0.0199599i	−0.954247	+	0.299020i	$0.903340\pi$
$504$	−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	0.346945	+	0.937886i	$0.387219\pi$
$509$	−7.92969	+	37.3063i	−0.351478	+	1.65357i	−0.698422	+	0.715686i	$0.746114\pi$
$510$	−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	0.833325	+	0.552784i	$0.186435\pi$
$521$	6.77646	+	31.8807i	0.296882	+	1.39672i	−0.536442	+	0.843937i	$0.680232\pi$
$522$	16.6330	−	12.3826i	0.728007	−	0.541971i
$523$	−8.05494	−	18.0917i	−0.352218	−	0.791094i	−0.999582	−	0.0289133i	$-0.990795\pi$
$523$	−8.05494	−	18.0917i	−0.352218	−	0.791094i	0.647364	−	0.762181i	$-0.275871\pi$
$524$	−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	−0.671637	−	0.740881i	$-0.734408\pi$
$541$	−27.3195	+	2.87140i	−1.17456	+	0.123451i	−0.502922	+	0.864332i	$0.667742\pi$
$542$	−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	−0.564519	−	0.825420i	$-0.690938\pi$
$547$	−12.5373	+	4.07360i	−0.536055	+	0.174175i	0.0284643	+	0.999595i	$0.490938\pi$
$548$	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	0.0108270	−	0.999941i	$-0.496554\pi$
$557$	10.0877	−	2.14421i	0.427431	−	0.0908532i	0.416604	+	0.909088i	$0.363220\pi$
$558$	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	0.524671	−	0.851305i	$-0.324188\pi$
$563$	5.76820	+	2.56817i	0.243101	+	0.108235i	−0.281570	+	0.959541i	$0.590855\pi$
$564$	−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	−0.463725	−	0.885979i	$-0.653487\pi$
$569$	−29.7627	−	6.32627i	−1.24772	−	0.265211i	−0.783994	+	0.620768i	$0.786821\pi$
$570$	16.6684	−	15.1847i	0.698163	−	0.636017i
$571$	−11.8491	+	6.84107i	−0.495868	+	0.286290i	−0.727006	−	0.686631i	$-0.759089\pi$
$571$	−11.8491	+	6.84107i	−0.495868	+	0.286290i	0.231137	+	0.972921i	$0.425755\pi$
$572$	−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	0.499452	+	0.866342i	$0.333535\pi$
$577$	−4.06452	+	38.6714i	−0.169208	+	1.60991i	−0.668660	+	0.743568i	$0.733132\pi$
$578$	−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	0.388999	−	0.921238i	$-0.372821\pi$
$587$	3.93016	+	1.27698i	0.162215	+	0.0527068i	−0.226784	+	0.973945i	$0.572821\pi$
$588$	−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	−0.508591	−	0.861008i	$-0.669833\pi$
$593$	11.9654	−	20.7247i	0.491359	−	0.851060i	0.999951	+	0.00994862i	$0.00316680\pi$
$594$	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	0.523225	−	0.852195i	$-0.324729\pi$
$599$	20.9951	+	2.20667i	0.857835	+	0.0901621i	0.334610	+	0.942357i	$0.391395\pi$
$600$	−0.0452932	−	7.79100i	−0.00184909	−	0.318066i
$601$	25.8399	+	8.39589i	1.05403	+	0.342475i	0.784249	−	0.620446i	$-0.213048\pi$
$601$	25.8399	+	8.39589i	1.05403	+	0.342475i	0.269782	+	0.962921i	$0.413048\pi$
$602$	−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	−0.272770	−	0.962079i	$-0.587940\pi$
$607$	−8.36565	+	0.879265i	−0.339551	+	0.0356883i	−0.0667815	+	0.997768i	$0.521273\pi$
$608$	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	0.718940	−	0.695073i	$-0.244628\pi$
$613$	2.54581	+	2.29226i	0.102824	+	0.0925835i	−0.616115	+	0.787656i	$0.711294\pi$
$614$	−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	$0.0228130\pi$
$617$			3.55740i			0.143215i	−0.997433	+	0.0716077i	$0.977187\pi$
$618$	1.08638	+	0.346018i	0.0437008	+	0.0139189i
$619$	16.3170	−	18.1219i	0.655837	−	0.728380i	−0.319870	−	0.947461i	$-0.603639\pi$
$619$	16.3170	−	18.1219i	0.655837	−	0.728380i	0.975707	+	0.219081i	$0.0703059\pi$
$620$	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	−0.811571	−	0.584253i	$-0.801388\pi$
$631$	4.73303	−	14.5668i	0.188419	−	0.579894i	0.999990	+	0.00435903i	$0.00138753\pi$
$632$	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	0.405534	−	0.914080i	$-0.367085\pi$
$641$	−11.6753	−	10.5125i	−0.461148	−	0.415220i	−0.866683	+	0.498860i	$0.833752\pi$
$642$	−10.8600	+	3.59855i	−0.428608	+	0.142023i
$643$	23.3131	+	16.9380i	0.919379	+	0.667968i	0.943369	−	0.331744i	$-0.107637\pi$
$643$	23.3131	+	16.9380i	0.919379	+	0.667968i	−0.0239904	+	0.999712i	$0.507637\pi$
$644$	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	0.403058	+	0.915174i	$0.367947\pi$
$647$	−13.9072	+	31.2360i	−0.546747	+	1.22801i	−0.949806	+	0.312841i	$0.898719\pi$
$648$	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	−0.277463	−	0.960736i	$-0.589494\pi$
$653$	16.5847	−	14.9329i	0.649008	−	0.584369i	0.926471	+	0.376367i	$0.122827\pi$
$654$	−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	0.788431	−	0.615123i	$-0.210894\pi$
$661$	−3.56073	−	6.16737i	−0.138496	−	0.239883i	−0.926928	+	0.375240i	$0.877560\pi$
$662$	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	0.984104	+	0.177594i	$0.0568313\pi$
$673$	22.0224	+	30.3112i	0.848901	+	1.16841i	−0.135203	+	0.990818i	$0.543169\pi$
$674$	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	0.0196304	−	0.999807i	$-0.493751\pi$
$677$	20.1849	−	8.98688i	0.775767	−	0.345394i	0.756137	+	0.654413i	$0.227084\pi$
$678$	−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	−0.907071	−	0.420977i	$-0.861687\pi$
$683$	−26.0305	+	15.0287i	−0.996031	+	0.575059i	−0.0889592	+	0.996035i	$0.528354\pi$
$684$	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	0.772312	+	0.635244i	$0.219100\pi$
$691$	3.91547	+	37.2532i	0.148951	+	1.41718i	−0.623360	+	0.781935i	$0.714233\pi$
$692$	−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	0.896682	−	0.442676i	$-0.145971\pi$
$701$	−2.35501	−	7.24797i	−0.0889474	−	0.273752i	−0.985629	+	0.168924i	$0.945971\pi$
$702$	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	0.0972421	−	0.995261i	$-0.468998\pi$
$709$	24.0158	−	10.6925i	0.901933	−	0.401566i	0.804691	+	0.593694i	$0.202331\pi$
$710$	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	−0.459292	−	0.888285i	$-0.651897\pi$
$719$	10.0853	−	9.08084i	0.376118	−	0.338658i	0.835410	+	0.549627i	$0.185230\pi$
$720$	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	−0.586628	−	0.809856i	$-0.699545\pi$
$733$	4.26339	−	3.83878i	0.157472	−	0.141789i	0.744100	+	0.668068i	$0.232878\pi$
$734$	−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	−0.976118	−	0.217240i	$-0.930294\pi$
$739$	−4.39103	+	9.86241i	−0.161527	+	0.362794i	0.814592	+	0.580035i	$0.196961\pi$
$740$	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	0.863243	−	0.504788i	$-0.168429\pi$
$743$	17.7155	+	12.8711i	0.649918	+	0.472193i	−0.213325	+	0.976981i	$0.568429\pi$
$744$	−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	−0.862274	−	0.506442i	$-0.830961\pi$
$751$	−50.8622	−	10.8111i	−1.85599	−	0.394503i	−0.993715	+	0.111939i	$0.964294\pi$
$752$	−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	−0.845164	−	0.534507i	$-0.820497\pi$
$757$	−16.4528	+	11.9537i	−0.597988	+	0.434464i	0.247176	+	0.968971i	$0.420497\pi$
$758$	−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	0.980754	−	0.195246i	$-0.0625506\pi$
$761$	−0.528610	−	5.02939i	−0.0191621	−	0.182315i	−0.999916	+	0.0129308i	$0.995884\pi$
$762$	−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	$-0.817800\pi$
$769$		−	30.0408i		−	1.08330i	0.840605	−	0.541649i	$-0.182200\pi$
$770$	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	0.197094	−	0.980385i	$-0.436850\pi$
$773$	−21.0556	−	18.9586i	−0.757319	−	0.681893i	−0.954412	+	0.298492i	$0.903516\pi$
$774$	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	−0.285595	−	0.958350i	$-0.592191\pi$
$787$	−21.4385	−	2.25328i	−0.764201	−	0.0803208i	−0.478606	+	0.878030i	$0.658858\pi$
$788$	−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	−0.913624	−	0.406560i	$-0.866728\pi$
$797$	−6.90639	+	9.50583i	−0.244637	+	0.336714i	0.668987	+	0.743274i	$0.266728\pi$
$798$	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	0.622514	+	0.782609i	$0.286111\pi$
$809$	−4.24113	+	40.3516i	−0.149110	+	1.41869i	−0.771624	+	0.636079i	$0.780555\pi$
$810$	16.8209	+	22.0548i	0.591026	+	0.774925i
$811$	−35.8012	+	11.6325i	−1.25715	+	0.408473i	−0.860478	−	0.509488i	$-0.829835\pi$
$811$	−35.8012	+	11.6325i	−1.25715	+	0.408473i	−0.396672	+	0.917961i	$0.629835\pi$
$812$	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	0.996114	−	0.0880689i	$-0.0280696\pi$
$821$	23.0487	+	25.5982i	0.804406	+	0.893383i	−0.191709	+	0.981452i	$0.561403\pi$
$822$	−21.9841	+	9.94150i	−0.766785	+	0.346750i
$823$	21.7047	+	9.66356i	0.756579	+	0.336851i	0.748516	−	0.663117i	$-0.230767\pi$
$823$	21.7047	+	9.66356i	0.756579	+	0.336851i	0.00806310	+	0.999967i	$0.497433\pi$
$824$	−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	−0.256318	−	0.966593i	$-0.582509\pi$
$827$	16.7875	−	12.1969i	0.583760	−	0.424126i	0.840078	+	0.542466i	$0.182509\pi$
$828$	−2.43005	+	1.44092i	−0.0844501	+	0.0500754i
$829$	−44.6026	+	9.48057i	−1.54911	+	0.329274i	−0.901528	−	0.432721i	$-0.857554\pi$
$829$	−44.6026	+	9.48057i	−1.54911	+	0.329274i	−0.647584	+	0.761994i	$0.724220\pi$
$830$	−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	−0.109788	−	0.993955i	$-0.535017\pi$
$839$	11.1698	−	3.62928i	0.385624	−	0.125297i	0.495412	+	0.868658i	$0.335017\pi$
$840$	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	−0.293476	−	0.955966i	$-0.594812\pi$
$853$	20.6310	−	28.3961i	0.706391	−	0.972264i	0.999867	−	0.0162977i	$-0.00518794\pi$
$854$	−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	0.577637	−	0.816293i	$-0.303975\pi$
$857$	−12.2401	−	21.2004i	−0.418112	−	0.724192i	−0.995750	+	0.0921019i	$0.970641\pi$
$858$	14.9219	+	10.3209i	0.509424	+	0.352351i
$859$	−14.9776	+	25.9419i	−0.511028	+	0.885126i	0.488891	+	0.872345i	$0.337402\pi$
$859$	−14.9776	+	25.9419i	−0.511028	+	0.885126i	−0.999918	+	0.0127809i	$0.995932\pi$
$860$	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	−0.999192	−	0.0401804i	$-0.987207\pi$
$863$	−10.5892	−	23.7838i	−0.360462	−	0.809611i	0.638730	−	0.769431i	$-0.279460\pi$
$864$	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	0.826171	+	0.563420i	$0.190515\pi$
$877$	−4.67127	+	21.9766i	−0.157737	+	0.742096i	−0.983908	+	0.178676i	$0.942819\pi$
$878$	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	$0.0413919\pi$
$881$			7.69766i			0.259341i	−0.991557	+	0.129670i	$0.958608\pi$
$882$	1.23593	−	20.9636i	0.0416159	−	0.705881i
$883$	15.7346	+	48.4262i	0.529512	+	1.62967i	0.755217	+	0.655475i	$0.227532\pi$
$883$	15.7346	+	48.4262i	0.529512	+	1.62967i	−0.225705	+	0.974196i	$0.572468\pi$
$884$	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	0.982944	+	0.183903i	$0.0588731\pi$
$887$	31.6616	+	35.1638i	1.06309	+	1.18069i	0.0801494	+	0.996783i	$0.474460\pi$
$888$	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	0.154396	+	0.988009i	$0.450657\pi$
$907$	−6.08487	+	57.8937i	−0.202045	+	1.92233i	−0.356440	+	0.934318i	$0.616010\pi$
$908$	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	0.961532	−	0.274692i	$-0.0885760\pi$
$911$	12.1683	+	16.7483i	0.403154	+	0.554894i	−0.558378	+	0.829587i	$0.688576\pi$
$912$	−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	0.968624	−	0.248531i	$-0.0799476\pi$
$919$	4.11659	+	9.24602i	0.135794	+	0.304998i	−0.832830	+	0.553529i	$0.813281\pi$
$920$	−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	−0.801663	−	0.597776i	$-0.796051\pi$
$929$	−21.6246	−	48.5696i	−0.709480	−	1.59352i	0.0921829	−	0.995742i	$-0.470616\pi$
$930$	−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	0.996933	−	0.0782658i	$-0.0249383\pi$
$937$	18.8079	+	25.8869i	0.614428	+	0.845688i	−0.382504	+	0.923954i	$0.624938\pi$
$938$	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	0.901145	+	0.433518i	$0.142728\pi$
$941$	−2.16084	+	20.5590i	−0.0704414	+	0.670205i	−0.971586	+	0.236686i	$0.923939\pi$
$942$	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	0.694087	−	0.719891i	$-0.255808\pi$
$947$	12.8536	+	7.42105i	0.417687	+	0.241152i	−0.276400	+	0.961043i	$0.589142\pi$
$948$	−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	−0.895349	−	0.445364i	$-0.853074\pi$
$953$	2.80251	−	8.62523i	0.0907822	−	0.279399i	0.986132	+	0.165966i	$0.0530741\pi$
$954$	−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	$0.104902\pi$
$967$			20.1273i			0.647250i	−0.946185	+	0.323625i	$0.895098\pi$
$968$	−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	−0.866476	−	0.499219i	$-0.833620\pi$
$971$	3.99296	−	18.7854i	0.128140	−	0.602851i	0.994616	−	0.103632i	$-0.0330465\pi$
$972$	−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	0.637472	+	0.770473i	$0.279980\pi$
$977$	−11.3042	+	25.3896i	−0.361653	+	0.812286i	−0.999125	+	0.0418131i	$0.986687\pi$
$978$	−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	−0.988816	−	0.149141i	$-0.952349\pi$
$983$	−4.58218	−	21.5574i	−0.146149	−	0.687576i	0.842667	−	0.538435i	$-0.180984\pi$
$984$	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	0.944524	+	0.328442i	$0.106524\pi$
$991$	23.8211	+	41.2593i	0.756701	+	1.31065i	−0.187823	+	0.982203i	$0.560143\pi$
$992$	−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	0.976950	−	0.213469i	$-0.0684764\pi$
$997$	−0.0746478	−	0.351190i	−0.00236412	−	0.0111223i	−0.979314	+	0.202347i	$0.935143\pi$
$998$	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.107.10	yes	128
3.2	odd	2		462.2.bc.a.107.1	yes	128
7.4	even	3	inner	462.2.bc.b.305.13	yes	128
11.7	odd	10		462.2.bc.a.359.9	yes	128
21.11	odd	6		462.2.bc.a.305.9	yes	128
33.29	even	10	inner	462.2.bc.b.359.13	yes	128
77.18	odd	30		462.2.bc.a.95.1	✓	128
231.95	even	30	inner	462.2.bc.b.95.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.1	✓	128	77.18	odd	30
462.2.bc.a.107.1	yes	128	3.2	odd	2
462.2.bc.a.305.9	yes	128	21.11	odd	6
462.2.bc.a.359.9	yes	128	11.7	odd	10
462.2.bc.b.95.10	yes	128	231.95	even	30	inner
462.2.bc.b.107.10	yes	128	1.1	even	1	trivial
462.2.bc.b.305.13	yes	128	7.4	even	3	inner
462.2.bc.b.359.13	yes	128	33.29	even	10	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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