LMFDB - Embedded newform 618.2.i.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [618,2,Mod(13,618)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(618, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("618.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 618 = 2 \cdot 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	618.i (of order $17$, degree $16$, 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:	$4.93475484492$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$2$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			61.1
Character	$\chi$	$=$	618.61
Dual form			618.2.i.b.385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0922684 - 0.995734i) q^{2} +(0.739009 - 0.673696i) q^{3} +(-0.982973 - 0.183750i) q^{4} +(-0.987359 - 1.98288i) q^{5} +(-0.602635 - 0.798017i) q^{6} +(-0.265584 - 0.933430i) q^{7} +(-0.273663 + 0.961826i) q^{8} +(0.0922684 - 0.995734i) q^{9} +O(q^{10})$	\(q+(0.0922684 - 0.995734i) q^{2} +(0.739009 - 0.673696i) q^{3} +(-0.982973 - 0.183750i) q^{4} +(-0.987359 - 1.98288i) q^{5} +(-0.602635 - 0.798017i) q^{6} +(-0.265584 - 0.933430i) q^{7} +(-0.273663 + 0.961826i) q^{8} +(0.0922684 - 0.995734i) q^{9} +(-2.06553 + 0.800190i) q^{10} +(-0.0650350 + 0.701840i) q^{11} +(-0.850217 + 0.526432i) q^{12} +(-0.743321 - 2.61250i) q^{13} +(-0.953953 + 0.178325i) q^{14} +(-2.06553 - 0.800190i) q^{15} +(0.932472 + 0.361242i) q^{16} +(-0.557590 + 0.738369i) q^{17} +(-0.982973 - 0.183750i) q^{18} +(-5.09590 - 4.64553i) q^{19} +(0.606194 + 2.13055i) q^{20} +(-0.825116 - 0.510890i) q^{21} +(0.692845 + 0.129515i) q^{22} +(0.433436 + 4.67751i) q^{23} +(0.445738 + 0.895163i) q^{24} +(0.0562196 - 0.0744468i) q^{25} +(-2.66994 + 0.499099i) q^{26} +(-0.602635 - 0.798017i) q^{27} +(0.0895443 + 0.966337i) q^{28} +(0.415676 + 0.834790i) q^{29} +(-0.987359 + 1.98288i) q^{30} +(-3.13283 - 1.21367i) q^{31} +(0.445738 - 0.895163i) q^{32} +(0.424765 + 0.562479i) q^{33} +(0.683771 + 0.623340i) q^{34} +(-1.58866 + 1.44825i) q^{35} +(-0.273663 + 0.961826i) q^{36} +(-1.87613 + 1.16165i) q^{37} +(-5.09590 + 4.64553i) q^{38} +(-2.30935 - 1.42989i) q^{39} +(2.17739 - 0.407025i) q^{40} +(-1.71403 + 3.44223i) q^{41} +(-0.584843 + 0.774457i) q^{42} +(-3.61276 - 2.23693i) q^{43} +(0.192890 - 0.677939i) q^{44} +(-2.06553 + 0.800190i) q^{45} +4.69755 q^{46} +8.41661 q^{47} +(0.932472 - 0.361242i) q^{48} +(5.15076 - 3.18922i) q^{49} +(-0.0689419 - 0.0628489i) q^{50} +(0.0853717 + 0.921307i) q^{51} +(0.250619 + 2.70461i) q^{52} +(-1.64371 - 1.49844i) q^{53} +(-0.850217 + 0.526432i) q^{54} +(1.45588 - 0.564011i) q^{55} +0.970477 q^{56} -6.89559 q^{57} +(0.869583 - 0.336878i) q^{58} +(2.84877 - 10.0124i) q^{59} +(1.88332 + 1.16610i) q^{60} +(2.50873 - 3.32210i) q^{61} +(-1.49755 + 3.00749i) q^{62} +(-0.953953 + 0.178325i) q^{63} +(-0.850217 - 0.526432i) q^{64} +(-4.44637 + 4.05340i) q^{65} +(0.599272 - 0.371054i) q^{66} +(0.463177 - 1.62790i) q^{67} +(0.683771 - 0.623340i) q^{68} +(3.47153 + 3.16472i) q^{69} +(1.29549 + 1.71551i) q^{70} +(-1.60239 + 3.21804i) q^{71} +(0.932472 + 0.361242i) q^{72} +(5.52680 - 11.0993i) q^{73} +(0.983586 + 1.97531i) q^{74} +(-0.00860769 - 0.0928917i) q^{75} +(4.15552 + 5.50280i) q^{76} +(0.672390 - 0.125692i) q^{77} +(-1.63687 + 2.16757i) q^{78} +(1.38292 + 2.77728i) q^{79} +(-0.204385 - 2.20566i) q^{80} +(-0.982973 - 0.183750i) q^{81} +(3.26939 + 2.02432i) q^{82} +(1.00911 + 3.54665i) q^{83} +(0.717191 + 0.653806i) q^{84} +(2.01464 + 0.376602i) q^{85} +(-2.56073 + 3.39095i) q^{86} +(0.869583 + 0.336878i) q^{87} +(-0.657250 - 0.254620i) q^{88} +(8.31484 - 1.55431i) q^{89} +(0.606194 + 2.13055i) q^{90} +(-2.24117 + 1.38768i) q^{91} +(0.433436 - 4.67751i) q^{92} +(-3.13283 + 1.21367i) q^{93} +(0.776587 - 8.38071i) q^{94} +(-4.18006 + 14.6914i) q^{95} +(-0.273663 - 0.961826i) q^{96} +(-2.65234 - 3.51227i) q^{97} +(-2.70036 - 5.42306i) q^{98} +(0.692845 + 0.129515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9	\( 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9} + q^{10} + 5 q^{11} - 2 q^{12} - 14 q^{13} + 6 q^{14} + q^{15} - 2 q^{16} + 32 q^{17} - 2 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 12 q^{22} - 15 q^{23} - 2 q^{24} - 15 q^{25} - 31 q^{26} - 2 q^{27} + 6 q^{28} + 7 q^{29} + q^{30} + 6 q^{31} - 2 q^{32} + 5 q^{33} - 2 q^{34} + 41 q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} - 14 q^{39} - 16 q^{40} - 5 q^{41} - 11 q^{42} - 3 q^{43} - 12 q^{44} + q^{45} - 66 q^{46} - 14 q^{47} - 2 q^{48} - 6 q^{49} - 15 q^{50} - 2 q^{51} + 20 q^{52} - 6 q^{53} - 2 q^{54} + 11 q^{55} + 6 q^{56} + 14 q^{57} + 24 q^{58} - 43 q^{59} + 18 q^{60} + 48 q^{61} + 6 q^{62} + 6 q^{63} - 2 q^{64} - 84 q^{65} + 5 q^{66} + 7 q^{67} - 2 q^{68} + 19 q^{69} - 10 q^{70} - 59 q^{71} - 2 q^{72} - 9 q^{73} + 21 q^{74} + 19 q^{75} - 3 q^{76} - 33 q^{77} + 20 q^{78} + 33 q^{79} + q^{80} - 2 q^{81} + 46 q^{82} + 71 q^{83} - 11 q^{84} + 42 q^{85} - 20 q^{86} + 24 q^{87} - 12 q^{88} - q^{89} + q^{90} + 50 q^{91} - 15 q^{92} + 6 q^{93} + 20 q^{94} - 5 q^{95} - 2 q^{96} - 61 q^{97} - 57 q^{98} - 12 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9 + q^10 + 5 * q^11 - 2 * q^12 - 14 * q^13 + 6 * q^14 + q^15 - 2 * q^16 + 32 * q^17 - 2 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 12 * q^22 - 15 * q^23 - 2 * q^24 - 15 * q^25 - 31 * q^26 - 2 * q^27 + 6 * q^28 + 7 * q^29 + q^30 + 6 * q^31 - 2 * q^32 + 5 * q^33 - 2 * q^34 + 41 * q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 - 14 * q^39 - 16 * q^40 - 5 * q^41 - 11 * q^42 - 3 * q^43 - 12 * q^44 + q^45 - 66 * q^46 - 14 * q^47 - 2 * q^48 - 6 * q^49 - 15 * q^50 - 2 * q^51 + 20 * q^52 - 6 * q^53 - 2 * q^54 + 11 * q^55 + 6 * q^56 + 14 * q^57 + 24 * q^58 - 43 * q^59 + 18 * q^60 + 48 * q^61 + 6 * q^62 + 6 * q^63 - 2 * q^64 - 84 * q^65 + 5 * q^66 + 7 * q^67 - 2 * q^68 + 19 * q^69 - 10 * q^70 - 59 * q^71 - 2 * q^72 - 9 * q^73 + 21 * q^74 + 19 * q^75 - 3 * q^76 - 33 * q^77 + 20 * q^78 + 33 * q^79 + q^80 - 2 * q^81 + 46 * q^82 + 71 * q^83 - 11 * q^84 + 42 * q^85 - 20 * q^86 + 24 * q^87 - 12 * q^88 - q^89 + q^90 + 50 * q^91 - 15 * q^92 + 6 * q^93 + 20 * q^94 - 5 * q^95 - 2 * q^96 - 61 * q^97 - 57 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/618\mathbb{Z}\right)^\times$.

$n$	$211$	$413$
$\chi(n)$	$e\left(\frac{6}{17}\right)$	$1$

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 $

$2$	0.0922684	−	0.995734i	0.0652436	−	0.704090i
$2$	0.0922684	−	0.995734i	0.0652436	−	0.704090i
$3$	0.739009	−	0.673696i	0.426667	−	0.388958i
$3$	0.739009	−	0.673696i	0.426667	−	0.388958i
$4$	−0.982973	−	0.183750i	−0.491487	−	0.0918748i
$5$	−0.987359	−	1.98288i	−0.441560	−	0.886773i	−0.998421	−	0.0561672i	$-0.982112\pi$
$5$	−0.987359	−	1.98288i	−0.441560	−	0.886773i	0.556861	−	0.830606i	$-0.312006\pi$
$6$	−0.602635	−	0.798017i	−0.246025	−	0.325789i
$7$	−0.265584	−	0.933430i	−0.100381	−	0.352803i	0.895320	−	0.445423i	$-0.146947\pi$
$7$	−0.265584	−	0.933430i	−0.100381	−	0.352803i	−0.995702	+	0.0926194i	$0.970476\pi$
$8$	−0.273663	+	0.961826i	−0.0967545	+	0.340057i
$9$	0.0922684	−	0.995734i	0.0307561	−	0.331911i
$10$	−2.06553	+	0.800190i	−0.653177	+	0.253042i
$11$	−0.0650350	+	0.701840i	−0.0196088	+	0.211613i	0.980292	+	0.197552i	$0.0632992\pi$
$11$	−0.0650350	+	0.701840i	−0.0196088	+	0.211613i	−0.999901	+	0.0140603i	$0.995524\pi$
$12$	−0.850217	+	0.526432i	−0.245437	+	0.151968i
$13$	−0.743321	−	2.61250i	−0.206160	−	0.724578i	−0.994066	−	0.108782i	$-0.965305\pi$
$13$	−0.743321	−	2.61250i	−0.206160	−	0.724578i	0.787905	−	0.615796i	$-0.211166\pi$
$14$	−0.953953	+	0.178325i	−0.254955	+	0.0476593i
$15$	−2.06553	−	0.800190i	−0.533317	−	0.206608i
$16$	0.932472	+	0.361242i	0.233118	+	0.0903104i
$17$	−0.557590	+	0.738369i	−0.135236	+	0.179081i	−0.860596	−	0.509289i	$-0.829909\pi$
$17$	−0.557590	+	0.738369i	−0.135236	+	0.179081i	0.725360	+	0.688370i	$0.241673\pi$
$18$	−0.982973	−	0.183750i	−0.231689	−	0.0433102i
$19$	−5.09590	−	4.64553i	−1.16908	−	1.06576i	−0.996737	−	0.0807204i	$-0.974278\pi$
$19$	−5.09590	−	4.64553i	−1.16908	−	1.06576i	−0.172343	−	0.985037i	$-0.555134\pi$
$20$	0.606194	+	2.13055i	0.135549	+	0.476405i
$21$	−0.825116	−	0.510890i	−0.180055	−	0.111485i
$22$	0.692845	+	0.129515i	0.147715	+	0.0276127i
$23$	0.433436	+	4.67751i	0.0903776	+	0.975329i	0.913330	+	0.407219i	$0.133502\pi$
$23$	0.433436	+	4.67751i	0.0903776	+	0.975329i	−0.822953	+	0.568110i	$0.807675\pi$
$24$	0.445738	+	0.895163i	0.0909860	+	0.182724i
$25$	0.0562196	−	0.0744468i	0.0112439	−	0.0148894i
$26$	−2.66994	+	0.499099i	−0.523619	+	0.0978814i
$27$	−0.602635	−	0.798017i	−0.115977	−	0.153578i
$28$	0.0895443	+	0.966337i	0.0169223	+	0.182621i
$29$	0.415676	+	0.834790i	0.0771891	+	0.155017i	0.930396	−	0.366556i	$-0.119463\pi$
$29$	0.415676	+	0.834790i	0.0771891	+	0.155017i	−0.853207	+	0.521573i	$0.825346\pi$
$30$	−0.987359	+	1.98288i	−0.180266	+	0.362024i
$31$	−3.13283	−	1.21367i	−0.562673	−	0.217981i	0.0630710	−	0.998009i	$-0.479911\pi$
$31$	−3.13283	−	1.21367i	−0.562673	−	0.217981i	−0.625744	+	0.780028i	$0.715205\pi$
$32$	0.445738	−	0.895163i	0.0787962	−	0.158244i
$33$	0.424765	+	0.562479i	0.0739421	+	0.0979151i
$34$	0.683771	+	0.623340i	0.117266	+	0.106902i
$35$	−1.58866	+	1.44825i	−0.268532	+	0.244799i
$36$	−0.273663	+	0.961826i	−0.0456105	+	0.160304i
$37$	−1.87613	+	1.16165i	−0.308433	+	0.190974i	−0.671916	−	0.740627i	$-0.734529\pi$
$37$	−1.87613	+	1.16165i	−0.308433	+	0.190974i	0.363483	+	0.931601i	$0.381587\pi$
$38$	−5.09590	+	4.64553i	−0.826665	+	0.753604i
$39$	−2.30935	−	1.42989i	−0.369793	−	0.228966i
$40$	2.17739	−	0.407025i	0.344276	−	0.0643564i
$41$	−1.71403	+	3.44223i	−0.267686	+	0.537586i	−0.987698	−	0.156376i	$-0.950019\pi$
$41$	−1.71403	+	3.44223i	−0.267686	+	0.537586i	0.720012	+	0.693962i	$0.244136\pi$
$42$	−0.584843	+	0.774457i	−0.0902433	+	0.119501i
$43$	−3.61276	−	2.23693i	−0.550940	−	0.341128i	0.222565	−	0.974918i	$-0.428557\pi$
$43$	−3.61276	−	2.23693i	−0.550940	−	0.341128i	−0.773505	+	0.633790i	$0.781498\pi$
$44$	0.192890	−	0.677939i	0.0290793	−	0.102203i
$45$	−2.06553	+	0.800190i	−0.307911	+	0.119285i
$46$	4.69755			0.692616
$47$	8.41661			1.22769			0.613845	−	0.789427i	$-0.289622\pi$
$47$	8.41661			1.22769			0.613845	+	0.789427i	$0.289622\pi$
$48$	0.932472	−	0.361242i	0.134591	−	0.0521407i
$49$	5.15076	−	3.18922i	0.735823	−	0.455603i
$50$	−0.0689419	−	0.0628489i	−0.00974986	−	0.00888817i
$51$	0.0853717	+	0.921307i	0.0119544	+	0.129009i
$52$	0.250619	+	2.70461i	0.0347546	+	0.375061i
$53$	−1.64371	−	1.49844i	−0.225780	−	0.205826i	0.552899	−	0.833249i	$-0.313522\pi$
$53$	−1.64371	−	1.49844i	−0.225780	−	0.205826i	−0.778679	+	0.627423i	$0.784110\pi$
$54$	−0.850217	+	0.526432i	−0.115700	+	0.0716383i
$55$	1.45588	−	0.564011i	0.196311	−	0.0760512i
$56$	0.970477			0.129685
$57$	−6.89559			−0.913343
$58$	0.869583	−	0.336878i	0.114182	−	0.0442343i
$59$	2.84877	−	10.0124i	0.370878	−	1.30350i	−0.521901	−	0.853006i	$-0.674777\pi$
$59$	2.84877	−	10.0124i	0.370878	−	1.30350i	0.892779	−	0.450495i	$-0.148752\pi$
$60$	1.88332	+	1.16610i	0.243136	+	0.150543i
$61$	2.50873	−	3.32210i	0.321210	−	0.425351i	−0.608551	−	0.793515i	$-0.708249\pi$
$61$	2.50873	−	3.32210i	0.321210	−	0.425351i	0.929761	+	0.368164i	$0.120013\pi$
$62$	−1.49755	+	3.00749i	−0.190189	+	0.381951i
$63$	−0.953953	+	0.178325i	−0.120187	+	0.0224668i
$64$	−0.850217	−	0.526432i	−0.106277	−	0.0658040i
$65$	−4.44637	+	4.05340i	−0.551504	+	0.502762i
$66$	0.599272	−	0.371054i	0.0737653	−	0.0456736i
$67$	0.463177	−	1.62790i	0.0565860	−	0.198879i	−0.928378	−	0.371636i	$-0.878797\pi$
$67$	0.463177	−	1.62790i	0.0565860	−	0.198879i	0.984964	+	0.172757i	$0.0552675\pi$
$68$	0.683771	−	0.623340i	0.0829194	−	0.0755911i
$69$	3.47153	+	3.16472i	0.417924	+	0.380988i
$70$	1.29549	+	1.71551i	0.154841	+	0.205042i
$71$	−1.60239	+	3.21804i	−0.190169	+	0.381911i	−0.969643	−	0.244523i	$-0.921369\pi$
$71$	−1.60239	+	3.21804i	−0.190169	+	0.381911i	0.779474	+	0.626434i	$0.215486\pi$
$72$	0.932472	+	0.361242i	0.109893	+	0.0425727i
$73$	5.52680	−	11.0993i	0.646864	−	1.29908i	−0.292537	−	0.956254i	$-0.594499\pi$
$73$	5.52680	−	11.0993i	0.646864	−	1.29908i	0.939400	−	0.342823i	$-0.111383\pi$
$74$	0.983586	+	1.97531i	0.114339	+	0.229625i
$75$	−0.00860769	−	0.0928917i	−0.000993930	−	0.0107262i
$76$	4.15552	+	5.50280i	0.476671	+	0.631214i
$77$	0.672390	−	0.125692i	0.0766260	−	0.0143239i
$78$	−1.63687	+	2.16757i	−0.185339	+	0.245429i
$79$	1.38292	+	2.77728i	0.155591	+	0.312469i	0.959219	−	0.282663i	$-0.0912177\pi$
$79$	1.38292	+	2.77728i	0.155591	+	0.312469i	−0.803629	+	0.595131i	$0.797100\pi$
$80$	−0.204385	−	2.20566i	−0.0228509	−	0.246600i
$81$	−0.982973	−	0.183750i	−0.109219	−	0.0204166i
$82$	3.26939	+	2.02432i	0.361044	+	0.223549i
$83$	1.00911	+	3.54665i	0.110764	+	0.389295i	0.997306	−	0.0733528i	$-0.0233699\pi$
$83$	1.00911	+	3.54665i	0.110764	+	0.389295i	−0.886542	+	0.462648i	$0.846899\pi$
$84$	0.717191	+	0.653806i	0.0782520	+	0.0713361i
$85$	2.01464	+	0.376602i	0.218519	+	0.0408482i
$86$	−2.56073	+	3.39095i	−0.276130	+	0.365655i
$87$	0.869583	+	0.336878i	0.0932291	+	0.0361171i
$88$	−0.657250	−	0.254620i	−0.0700630	−	0.0271426i
$89$	8.31484	−	1.55431i	0.881372	−	0.164757i	0.276437	−	0.961032i	$-0.410846\pi$
$89$	8.31484	−	1.55431i	0.881372	−	0.164757i	0.604935	+	0.796275i	$0.293199\pi$
$90$	0.606194	+	2.13055i	0.0638984	+	0.224580i
$91$	−2.24117	+	1.38768i	−0.234939	+	0.145468i
$92$	0.433436	−	4.67751i	0.0451888	−	0.487665i
$93$	−3.13283	+	1.21367i	−0.324860	+	0.125851i
$94$	0.776587	−	8.38071i	0.0800988	−	0.864404i
$95$	−4.18006	+	14.6914i	−0.428865	+	1.50731i
$96$	−0.273663	−	0.961826i	−0.0279306	−	0.0981659i
$97$	−2.65234	−	3.51227i	−0.269304	−	0.356617i	0.643189	−	0.765707i	$-0.277611\pi$
$97$	−2.65234	−	3.51227i	−0.269304	−	0.356617i	−0.912494	+	0.409090i	$0.865846\pi$
$98$	−2.70036	−	5.42306i	−0.272778	−	0.547811i
$99$	0.692845	+	0.129515i	0.0696335	+	0.0130168i
$100$	−0.0689419	+	0.0628489i	−0.00689419	+	0.00628489i
$101$	0.119891	−	1.29383i	0.0119296	−	0.128741i	−0.987687	−	0.156446i	$-0.949996\pi$
$101$	0.119891	−	1.29383i	0.0119296	−	0.128741i	0.999616	+	0.0277050i	$0.00881990\pi$
$102$	0.925254			0.0916138
$103$	10.1286	+	0.641116i	0.998003	+	0.0631710i
$103$	10.1286	+	0.641116i	0.998003	+	0.0631710i
$104$	2.71619			0.266345
$105$	−0.198351	+	2.14054i	−0.0193570	+	0.208896i
$106$	−1.64371	+	1.49844i	−0.159651	+	0.145541i
$107$	−1.51247	−	0.282730i	−0.146216	−	0.0273325i	0.110132	−	0.993917i	$-0.464872\pi$
$107$	−1.51247	−	0.282730i	−0.146216	−	0.0273325i	−0.256349	+	0.966584i	$0.582520\pi$
$108$	0.445738	+	0.895163i	0.0428912	+	0.0861371i
$109$	0.202583	+	0.268263i	0.0194039	+	0.0256949i	0.807616	−	0.589709i	$-0.200758\pi$
$109$	0.202583	+	0.268263i	0.0194039	+	0.0256949i	−0.788212	+	0.615404i	$0.788993\pi$
$110$	−0.427273	−	1.50171i	−0.0407389	−	0.143182i
$111$	−0.603877	+	2.12241i	−0.0573174	+	0.201450i
$112$	0.0895443	−	0.966337i	0.00846114	−	0.0913103i
$113$	9.09507	−	3.52345i	0.855592	−	0.331458i	0.106814	−	0.994279i	$-0.465935\pi$
$113$	9.09507	−	3.52345i	0.855592	−	0.331458i	0.748778	+	0.662821i	$0.230641\pi$
$114$	−0.636245	+	6.86617i	−0.0595898	+	0.643076i
$115$	8.84702	−	5.47784i	0.824988	−	0.510811i
$116$	−0.255206	−	0.896956i	−0.0236953	−	0.0832803i
$117$	−2.66994	+	0.499099i	−0.246836	+	0.0461417i
$118$	−9.70682	−	3.76044i	−0.893585	−	0.346177i
$119$	0.837302	+	0.324373i	0.0767554	+	0.0297352i
$120$	1.33490	−	1.76770i	0.121859	−	0.161368i
$121$	10.3244	+	1.92996i	0.938578	+	0.175451i
$122$	−3.07645	−	2.80456i	−0.278529	−	0.253913i
$123$	1.05233	+	3.69857i	0.0948857	+	0.333489i
$124$	2.85648	+	1.76866i	0.256519	+	0.158830i
$125$	−11.0901	−	2.07310i	−0.991928	−	0.185424i
$126$	0.0895443	+	0.966337i	0.00797724	+	0.0860882i
$127$	0.947323	+	1.90248i	0.0840613	+	0.168818i	0.933205	−	0.359343i	$-0.116999\pi$
$127$	0.947323	+	1.90248i	0.0840613	+	0.168818i	−0.849144	+	0.528161i	$0.822882\pi$
$128$	−0.602635	+	0.798017i	−0.0532659	+	0.0705354i
$129$	−4.17687	+	0.780792i	−0.367753	+	0.0687449i
$130$	3.62585	+	4.80140i	0.318008	+	0.421111i
$131$	0.637708	+	6.88197i	0.0557168	+	0.601280i	0.977122	+	0.212678i	$0.0682185\pi$
$131$	0.637708	+	6.88197i	0.0557168	+	0.601280i	−0.921406	+	0.388602i	$0.872958\pi$
$132$	−0.314177	−	0.630953i	−0.0273456	−	0.0549174i
$133$	−2.98289	+	5.99044i	−0.258649	+	0.519437i
$134$	−1.57822	−	0.611404i	−0.136337	−	0.0528173i
$135$	−0.987359	+	1.98288i	−0.0849784	+	0.170660i
$136$	−0.557590	−	0.738369i	−0.0478130	−	0.0633146i
$137$	−14.2307	−	12.9730i	−1.21581	−	1.10835i	−0.990988	−	0.133954i	$-0.957233\pi$
$137$	−14.2307	−	12.9730i	−1.21581	−	1.10835i	−0.224819	−	0.974401i	$-0.572179\pi$
$138$	3.47153	−	3.16472i	0.295517	−	0.269399i
$139$	3.44644	−	12.1130i	0.292323	−	1.02741i	−0.666991	−	0.745066i	$-0.732418\pi$
$139$	3.44644	−	12.1130i	0.292323	−	1.02741i	0.959314	−	0.282342i	$-0.0911114\pi$
$140$	1.82772	−	1.13168i	0.154471	−	0.0956443i
$141$	6.21995	−	5.67024i	0.523815	−	0.477520i
$142$	3.05646	+	1.89248i	0.256493	+	0.158813i
$143$	1.88190	−	0.351788i	0.157372	−	0.0294180i
$144$	0.445738	−	0.895163i	0.0371449	−	0.0745969i
$145$	1.24487	−	1.64848i	0.103381	−	0.136898i
$146$	−10.5420	−	6.52734i	−0.872464	−	0.540207i
$147$	1.65790	−	5.82691i	0.136741	−	0.480595i
$148$	2.05763	−	0.797131i	0.169136	−	0.0655238i
$149$	9.10817			0.746170			0.373085	−	0.927797i	$-0.378300\pi$
$149$	9.10817			0.746170			0.373085	+	0.927797i	$0.378300\pi$
$150$	−0.0932897			−0.00761707
$151$	−2.48290	+	0.961882i	−0.202056	+	0.0782768i	−0.460143	−	0.887845i	$-0.652202\pi$
$151$	−2.48290	+	0.961882i	−0.202056	+	0.0782768i	0.258087	+	0.966122i	$0.416908\pi$
$152$	5.86275	−	3.63006i	0.475532	−	0.294437i
$153$	0.683771	+	0.623340i	0.0552796	+	0.0503940i
$154$	−0.0631150	−	0.681119i	−0.00508595	−	0.0548861i
$155$	0.686672	+	7.41037i	0.0551548	+	0.595215i
$156$	2.00729	+	1.82989i	0.160712	+	0.146508i
$157$	15.9597	−	9.88183i	1.27372	−	0.788656i	0.288098	−	0.957601i	$-0.406977\pi$
$157$	15.9597	−	9.88183i	1.27372	−	0.788656i	0.985626	+	0.168945i	$0.0540359\pi$
$158$	2.89303	−	1.12077i	0.230157	−	0.0891635i
$159$	−2.22420			−0.176391
$160$	−2.21511			−0.175120
$161$	4.25102	−	1.64685i	0.335027	−	0.129790i
$162$	−0.273663	+	0.961826i	−0.0215010	+	0.0755682i
$163$	−2.66979	−	1.65306i	−0.209114	−	0.129478i	0.417879	−	0.908503i	$-0.362774\pi$
$163$	−2.66979	−	1.65306i	−0.209114	−	0.129478i	−0.626993	+	0.779025i	$0.715715\pi$
$164$	2.31735	−	3.06867i	0.180955	−	0.239623i
$165$	0.695937	−	1.39763i	0.0541786	−	0.108805i
$166$	3.62463	−	0.677561i	0.281326	−	0.0525889i
$167$	16.1371	+	9.99169i	1.24873	+	0.773180i	0.981686	−	0.190505i	$-0.0610125\pi$
$167$	16.1371	+	9.99169i	1.24873	+	0.773180i	0.267042	+	0.963685i	$0.413954\pi$
$168$	0.717191	−	0.653806i	0.0553325	−	0.0504422i
$169$	4.78017	−	2.95976i	0.367706	−	0.227674i
$170$	0.560883	−	1.97130i	0.0430178	−	0.151192i
$171$	−5.09590	+	4.64553i	−0.389693	+	0.355252i
$172$	3.14021	+	2.86268i	0.239439	+	0.218277i
$173$	−3.40433	−	4.50806i	−0.258826	−	0.342742i	0.649986	−	0.759946i	$-0.274775\pi$
$173$	−3.40433	−	4.50806i	−0.258826	−	0.342742i	−0.908813	+	0.417204i	$0.863010\pi$
$174$	0.415676	−	0.834790i	0.0315123	−	0.0632853i
$175$	−0.0844219	−	0.0327052i	−0.00638169	−	0.00247228i
$176$	−0.314177	+	0.630953i	−0.0236820	+	0.0475598i
$177$	−4.64003	−	9.31844i	−0.348766	−	0.700417i
$178$	−0.780486	−	8.42279i	−0.0584999	−	0.631315i
$179$	4.41351	+	5.84443i	0.329881	+	0.436833i	0.932486	−	0.361207i	$-0.117635\pi$
$179$	4.41351	+	5.84443i	0.329881	+	0.436833i	−0.602605	+	0.798040i	$0.705870\pi$
$180$	2.17739	−	0.407025i	0.162293	−	0.0303379i
$181$	−2.81485	+	3.72747i	−0.209226	+	0.277060i	−0.890514	−	0.454955i	$-0.849655\pi$
$181$	−2.81485	+	3.72747i	−0.209226	+	0.277060i	0.681288	+	0.732015i	$0.261420\pi$
$182$	1.17497	+	2.35965i	0.0870944	+	0.174909i
$183$	−0.384108	−	4.14518i	−0.0283941	−	0.306421i
$184$	−4.61757	−	0.863173i	−0.340412	−	0.0636340i
$185$	4.15582	+	2.57318i	0.305542	+	0.189184i
$186$	0.919427	+	3.23145i	0.0674157	+	0.236941i
$187$	−0.481954	−	0.439359i	−0.0352439	−	0.0321291i
$188$	−8.27331	−	1.54655i	−0.603393	−	0.112794i
$189$	−0.584843	+	0.774457i	−0.0425411	+	0.0563335i
$190$	14.2430	+	5.51778i	1.03330	+	0.400302i
$191$	−1.77002	−	0.685710i	−0.128074	−	0.0496162i	0.296352	−	0.955079i	$-0.404230\pi$
$191$	−1.77002	−	0.685710i	−0.128074	−	0.0496162i	−0.424426	+	0.905463i	$0.639524\pi$
$192$	−0.982973	+	0.183750i	−0.0709400	+	0.0132610i
$193$	−4.10355	−	14.4225i	−0.295380	−	1.03815i	−0.957423	−	0.288687i	$-0.906781\pi$
$193$	−4.10355	−	14.4225i	−0.295380	−	1.03815i	0.662044	−	0.749465i	$-0.269689\pi$
$194$	−3.74201	+	2.31696i	−0.268661	+	0.166348i
$195$	−0.555148	+	5.99100i	−0.0397550	+	0.429024i
$196$	−5.64908	+	2.18846i	−0.403506	+	0.156319i
$197$	−0.760937	+	8.21181i	−0.0542145	+	0.585068i	0.924686	+	0.380730i	$0.124327\pi$
$197$	−0.760937	+	8.21181i	−0.0542145	+	0.585068i	−0.978901	+	0.204337i	$0.934496\pi$
$198$	0.192890	−	0.677939i	0.0137081	−	0.0481790i
$199$	0.177888	+	0.625213i	0.0126102	+	0.0443202i	0.967875	−	0.251430i	$-0.0809009\pi$
$199$	0.177888	+	0.625213i	0.0126102	+	0.0443202i	−0.955265	+	0.295750i	$0.904430\pi$
$200$	0.0562196	+	0.0744468i	0.00397533	+	0.00526418i
$201$	−0.754415	−	1.51507i	−0.0532124	−	0.106865i
$202$	−1.27725	−	0.238759i	−0.0898668	−	0.0167990i
$203$	0.668821	−	0.609711i	0.0469420	−	0.0427933i
$204$	0.0853717	−	0.921307i	0.00597721	−	0.0645044i
$205$	8.51790			0.594916
$206$	1.57293	−	10.0263i	0.109591	−	0.698563i
$207$	4.69755			0.326503
$208$	0.250619	−	2.70461i	0.0173773	−	0.187531i
$209$	3.59183	−	3.27438i	0.248452	−	0.226494i
$210$	2.11311	+	0.395009i	0.145818	+	0.0272582i
$211$	11.4025	+	22.8993i	0.784979	+	1.57645i	0.816776	+	0.576955i	$0.195759\pi$
$211$	11.4025	+	22.8993i	0.784979	+	1.57645i	−0.0317972	+	0.999494i	$0.510123\pi$
$212$	1.34038	+	1.77495i	0.0920578	+	0.121904i
$213$	0.983796	+	3.45768i	0.0674086	+	0.236917i
$214$	−0.421077	+	1.47993i	−0.0287843	+	0.101166i
$215$	−0.868474	+	9.37233i	−0.0592295	+	0.639188i
$216$	0.932472	−	0.361242i	0.0634467	−	0.0245794i
$217$	−0.300843	+	3.24661i	−0.0204225	+	0.220394i
$218$	0.285810	−	0.176966i	0.0193575	−	0.0119857i
$219$	−3.39321	−	11.9259i	−0.229292	−	0.805876i
$220$	−1.53473	+	0.286890i	−0.103471	+	0.0193421i
$221$	2.34346	+	0.907861i	0.157638	+	0.0610694i
$222$	2.05763	+	0.797131i	0.138099	+	0.0535000i
$223$	−11.8988	+	15.7566i	−0.796804	+	1.05514i	0.200349	+	0.979725i	$0.435792\pi$
$223$	−11.8988	+	15.7566i	−0.796804	+	1.05514i	−0.997152	+	0.0754138i	$0.975972\pi$
$224$	−0.953953	−	0.178325i	−0.0637387	−	0.0119148i
$225$	−0.0689419	−	0.0628489i	−0.00459613	−	0.00418992i
$226$	−2.66923	−	9.38138i	−0.177555	−	0.624040i
$227$	−11.1486	−	6.90294i	−0.739961	−	0.458164i	0.103994	−	0.994578i	$-0.466838\pi$
$227$	−11.1486	−	6.90294i	−0.739961	−	0.458164i	−0.843955	+	0.536414i	$0.819779\pi$
$228$	6.77818	+	1.26706i	0.448896	+	0.0839132i
$229$	−1.16744	−	12.5986i	−0.0771463	−	0.832541i	−0.943120	−	0.332452i	$-0.892124\pi$
$229$	−1.16744	−	12.5986i	−0.0771463	−	0.832541i	0.865974	−	0.500089i	$-0.166699\pi$
$230$	−4.63817	−	9.31471i	−0.305832	−	0.614194i
$231$	0.412224	−	0.545873i	0.0271224	−	0.0359158i
$232$	−0.916678	+	0.171357i	−0.0601828	+	0.0112501i
$233$	−2.59574	−	3.43732i	−0.170053	−	0.225186i	0.705008	−	0.709199i	$-0.250943\pi$
$233$	−2.59574	−	3.43732i	−0.170053	−	0.225186i	−0.875061	+	0.484013i	$0.839179\pi$
$234$	0.250619	+	2.70461i	0.0163835	+	0.176806i
$235$	−8.31022	−	16.6892i	−0.542099	−	1.08868i
$236$	−4.64003	+	9.31844i	−0.302040	+	0.606579i
$237$	2.89303	+	1.12077i	0.187923	+	0.0728017i
$238$	0.400245	−	0.803801i	0.0259441	−	0.0521027i
$239$	15.4652	+	20.4792i	1.00036	+	1.32469i	0.945298	+	0.326207i	$0.105771\pi$
$239$	15.4652	+	20.4792i	1.00036	+	1.32469i	0.0550614	+	0.998483i	$0.482465\pi$
$240$	−1.63699	−	1.49231i	−0.105667	−	0.0963282i
$241$	−0.0143489	+	0.0130807i	−0.000924293	+	0.000842604i	−0.674158	−	0.738587i	$-0.735493\pi$
$241$	−0.0143489	+	0.0130807i	−0.000924293	+	0.000842604i	0.673233	+	0.739430i	$0.264905\pi$
$242$	2.87433	−	10.1022i	0.184769	−	0.649397i
$243$	−0.850217	+	0.526432i	−0.0545415	+	0.0337706i
$244$	−3.07645	+	2.80456i	−0.196950	+	0.179543i
$245$	−11.4095	−	7.06447i	−0.728927	−	0.451332i
$246$	3.77989	−	0.706584i	0.240997	−	0.0450501i
$247$	−8.34857	+	16.7662i	−0.531207	+	1.06681i
$248$	2.02468	−	2.68110i	0.128567	−	0.170250i
$249$	3.13510	+	1.94117i	0.198679	+	0.123017i
$250$	−3.08752	+	10.8515i	−0.195272	+	0.686309i
$251$	5.46735	−	2.11806i	0.345096	−	0.133691i	−0.182455	−	0.983214i	$-0.558404\pi$
$251$	5.46735	−	2.11806i	0.345096	−	0.133691i	0.527551	+	0.849523i	$0.323110\pi$
$252$	0.970477			0.0611343
$253$	−3.31105			−0.208164
$254$	1.98177	−	0.767743i	0.124348	−	0.0481725i
$255$	1.74255	−	1.07894i	0.109123	−	0.0675661i
$256$	0.739009	+	0.673696i	0.0461881	+	0.0421060i
$257$	0.658742	+	7.10895i	0.0410912	+	0.443444i	0.991280	+	0.131770i	$0.0420661\pi$
$257$	0.658742	+	7.10895i	0.0410912	+	0.443444i	−0.950189	+	0.311674i	$0.899110\pi$
$258$	0.392068	+	4.23109i	0.0244091	+	0.263416i
$259$	1.58259	+	1.44272i	0.0983371	+	0.0896461i
$260$	5.11547	−	3.16737i	0.317248	−	0.196432i
$261$	0.869583	−	0.336878i	0.0538258	−	0.0208522i
$262$	6.91145			0.426991
$263$	−27.4875			−1.69495			−0.847477	−	0.530832i	$-0.821879\pi$
$263$	−27.4875			−1.69495			−0.847477	+	0.530832i	$0.821879\pi$
$264$	−0.657250	+	0.254620i	−0.0404509	+	0.0156708i
$265$	−1.34830	+	4.73877i	−0.0828252	+	0.291101i
$266$	5.68966	+	3.52289i	0.348856	+	0.216002i
$267$	5.09761	−	6.75033i	0.311969	−	0.413113i
$268$	−0.754415	+	1.51507i	−0.0460833	+	0.0925476i
$269$	−8.02380	+	1.49991i	−0.489220	+	0.0914511i	−0.422579	−	0.906326i	$-0.638875\pi$
$269$	−8.02380	+	1.49991i	−0.489220	+	0.0914511i	−0.0666407	+	0.997777i	$0.521228\pi$
$270$	1.88332	+	1.16610i	0.114615	+	0.0709669i
$271$	−8.71205	+	7.94209i	−0.529220	+	0.482447i	−0.893638	−	0.448788i	$-0.851856\pi$
$271$	−8.71205	+	7.94209i	−0.529220	+	0.482447i	0.364419	+	0.931235i	$0.381268\pi$
$272$	−0.786667	+	0.487084i	−0.0476987	+	0.0295338i
$273$	−0.721376	+	2.53538i	−0.0436597	+	0.153448i
$274$	−14.2307	+	12.9730i	−0.859705	+	0.783725i
$275$	0.0485935	+	0.0442988i	0.00293030	+	0.00267132i
$276$	−2.83091	−	3.74873i	−0.170401	−	0.225647i
$277$	−9.94587	+	19.9740i	−0.597590	+	1.20012i	0.365467	+	0.930824i	$0.380909\pi$
$277$	−9.94587	+	19.9740i	−0.597590	+	1.20012i	−0.963057	+	0.269298i	$0.913208\pi$
$278$	−11.7433	−	4.54938i	−0.704316	−	0.272854i
$279$	−1.49755	+	3.00749i	−0.0896560	+	0.180053i
$280$	−0.958210	−	1.92434i	−0.0572640	−	0.115002i
$281$	−1.23823	−	13.3626i	−0.0738666	−	0.797148i	−0.949416	−	0.314020i	$-0.898324\pi$
$281$	−1.23823	−	13.3626i	−0.0738666	−	0.797148i	0.875550	−	0.483128i	$-0.160499\pi$
$282$	−5.07214	−	6.71660i	−0.302042	−	0.399968i
$283$	−21.4792	+	4.01516i	−1.27681	+	0.238676i	−0.778125	−	0.628110i	$-0.783829\pi$
$283$	−21.4792	+	4.01516i	−1.27681	+	0.238676i	−0.498680	+	0.866786i	$0.666182\pi$
$284$	2.16642	−	2.86881i	0.128554	−	0.170232i
$285$	6.80842	+	13.6732i	0.403296	+	0.809928i
$286$	−0.176648	−	1.90633i	−0.0104454	−	0.112724i
$287$	3.66830	+	0.685723i	0.216533	+	0.0404770i
$288$	−0.850217	−	0.526432i	−0.0500995	−	0.0310203i
$289$	4.41799	+	15.5276i	0.259882	+	0.913389i
$290$	−1.52658	−	1.39166i	−0.0896439	−	0.0817212i
$291$	−4.32630	−	0.808726i	−0.253612	−	0.0474084i
$292$	−7.47220	+	9.89479i	−0.437277	+	0.579049i
$293$	9.63393	+	3.73221i	0.562820	+	0.218038i	0.625809	−	0.779976i	$-0.284769\pi$
$293$	9.63393	+	3.73221i	0.562820	+	0.218038i	−0.0629885	+	0.998014i	$0.520063\pi$
$294$	−5.64908	−	2.18846i	−0.329461	−	0.127634i
$295$	−22.6661	+	4.23704i	−1.31967	+	0.246690i
$296$	−0.603877	−	2.12241i	−0.0350996	−	0.123362i
$297$	0.599272	−	0.371054i	0.0347733	−	0.0215307i
$298$	0.840396	−	9.06931i	0.0486828	−	0.525371i
$299$	11.8978	−	4.60925i	0.688070	−	0.266560i
$300$	−0.00860769	+	0.0928917i	−0.000496965	+	0.00536311i
$301$	−1.12852	+	3.96635i	−0.0650470	+	0.228616i
$302$	0.728685	+	2.56106i	0.0419311	+	0.147373i
$303$	−0.783046	−	1.03692i	−0.0449848	−	0.0595695i
$304$	−3.07363	−	6.17268i	−0.176285	−	0.354027i
$305$	−9.06436	−	1.69442i	−0.519024	−	0.0970224i
$306$	0.683771	−	0.623340i	0.0390886	−	0.0356340i
$307$	−1.84157	+	19.8737i	−0.105104	+	1.13425i	0.765895	+	0.642966i	$0.222296\pi$
$307$	−1.84157	+	19.8737i	−0.105104	+	1.13425i	−0.870998	+	0.491286i	$0.836527\pi$
$308$	−0.684037			−0.0389766
$309$	7.91706	−	6.34982i	0.450386	−	0.361229i
$310$	7.44212			0.422684
$311$	−2.18799	+	23.6122i	−0.124069	+	1.33892i	0.675059	+	0.737763i	$0.264118\pi$
$311$	−2.18799	+	23.6122i	−0.124069	+	1.33892i	−0.799129	+	0.601160i	$0.794706\pi$
$312$	2.00729	−	1.82989i	0.113640	−	0.103597i
$313$	−12.5032	−	2.33725i	−0.706721	−	0.132109i	−0.181894	−	0.983318i	$-0.558223\pi$
$313$	−12.5032	−	2.33725i	−0.706721	−	0.132109i	−0.524827	+	0.851209i	$0.675870\pi$
$314$	−8.36710	−	16.8034i	−0.472183	−	0.948271i
$315$	1.29549	+	1.71551i	0.0729927	+	0.0966579i
$316$	−0.849051	−	2.98410i	−0.0477628	−	0.167869i
$317$	5.10725	−	17.9501i	0.286852	−	1.00818i	−0.675722	−	0.737157i	$-0.736168\pi$
$317$	5.10725	−	17.9501i	0.286852	−	1.00818i	0.962573	−	0.271022i	$-0.0873615\pi$
$318$	−0.205224	+	2.21471i	−0.0115084	+	0.124195i
$319$	−0.612922	+	0.237447i	−0.0343171	+	0.0132945i
$320$	−0.204385	+	2.20566i	−0.0114254	+	0.123300i
$321$	−1.30820	+	0.810006i	−0.0730169	+	0.0452101i
$322$	−1.24759	−	4.38484i	−0.0695257	−	0.244357i
$323$	6.27154	−	1.17235i	0.348958	−	0.0652315i
$324$	0.932472	+	0.361242i	0.0518040	+	0.0200690i
$325$	−0.236282	−	0.0915360i	−0.0131066	−	0.00507751i
$326$	−1.89235	+	2.50588i	−0.104808	+	0.138788i
$327$	0.330438	+	0.0617695i	0.0182732	+	0.00341586i
$328$	−2.84176	−	2.59061i	−0.156910	−	0.143042i
$329$	−2.23532	−	7.85632i	−0.123237	−	0.433133i
$330$	−1.32745	−	0.821925i	−0.0730739	−	0.0452455i
$331$	−10.6762	−	1.99573i	−0.586818	−	0.109695i	−0.118036	−	0.993009i	$-0.537660\pi$
$331$	−10.6762	−	1.99573i	−0.586818	−	0.109695i	−0.468782	+	0.883314i	$0.655307\pi$
$332$	−0.340232	−	3.67168i	−0.0186726	−	0.201510i
$333$	0.983586	+	1.97531i	0.0539002	+	0.108246i
$334$	11.4380	−	15.1464i	0.625860	−	0.828773i
$335$	−3.68525	+	0.688893i	−0.201347	+	0.0376383i
$336$	−0.584843	−	0.774457i	−0.0319058	−	0.0422501i
$337$	−1.10427	−	11.9170i	−0.0601537	−	0.649162i	−0.971424	−	0.237352i	$-0.923720\pi$
$337$	−1.10427	−	11.9170i	−0.0601537	−	0.649162i	0.911270	−	0.411809i	$-0.135103\pi$
$338$	−2.50607	−	5.03287i	−0.136312	−	0.273752i
$339$	4.34761	−	8.73117i	0.236130	−	0.474212i
$340$	−1.91114	−	0.740379i	−0.103646	−	0.0401527i
$341$	1.05554	−	2.11981i	0.0571608	−	0.114794i
$342$	4.15552	+	5.50280i	0.224705	+	0.297557i
$343$	−9.36521	−	8.53752i	−0.505674	−	0.460982i
$344$	3.14021	−	2.86268i	0.169309	−	0.154345i
$345$	2.84763	−	10.0084i	0.153311	−	0.538832i
$346$	−4.80294	+	2.97386i	−0.258208	+	0.159875i
$347$	−12.5500	+	11.4408i	−0.673718	+	0.614175i	−0.936495	−	0.350682i	$-0.885950\pi$
$347$	−12.5500	+	11.4408i	−0.673718	+	0.614175i	0.262777	+	0.964857i	$0.415362\pi$
$348$	−0.792875	−	0.490928i	−0.0425026	−	0.0263165i
$349$	−9.08705	+	1.69866i	−0.486419	+	0.0909274i	−0.421246	−	0.906947i	$-0.638407\pi$
$349$	−9.08705	+	1.69866i	−0.486419	+	0.0909274i	−0.0651730	+	0.997874i	$0.520760\pi$
$350$	−0.0403552	+	0.0810441i	−0.00215707	+	0.00433199i
$351$	−1.63687	+	2.16757i	−0.0873698	+	0.115696i
$352$	0.599272	+	0.371054i	0.0319413	+	0.0197772i
$353$	3.47694	−	12.2202i	0.185059	−	0.650414i	−0.812650	−	0.582753i	$-0.801976\pi$
$353$	3.47694	−	12.2202i	0.185059	−	0.650414i	0.997708	−	0.0676615i	$-0.0215538\pi$
$354$	−9.70682	+	3.76044i	−0.515911	+	0.199865i
$355$	7.96314			0.422639
$356$	−8.45887			−0.448319
$357$	0.837302	−	0.324373i	0.0443147	−	0.0171676i
$358$	6.22673	−	3.85543i	0.329093	−	0.203766i
$359$	−5.39694	−	4.91996i	−0.284839	−	0.259665i	0.518647	−	0.854988i	$-0.326436\pi$
$359$	−5.39694	−	4.91996i	−0.284839	−	0.259665i	−0.803487	+	0.595323i	$0.797024\pi$
$360$	−0.204385	−	2.20566i	−0.0107720	−	0.116249i
$361$	2.63418	+	28.4274i	0.138641	+	1.49618i
$362$	3.45184	+	3.14677i	0.181425	+	0.165391i
$363$	8.92999	−	5.52922i	0.468703	−	0.290209i
$364$	2.45800	−	0.952234i	0.128834	−	0.0499106i
$365$	−27.4656			−1.43762
$366$	−4.16294			−0.217600
$367$	3.72633	−	1.44359i	0.194513	−	0.0753546i	−0.262015	−	0.965064i	$-0.584387\pi$
$367$	3.72633	−	1.44359i	0.194513	−	0.0753546i	0.456528	+	0.889709i	$0.349093\pi$
$368$	−1.28555	+	4.51823i	−0.0670137	+	0.235529i
$369$	3.26939	+	2.02432i	0.170198	+	0.105382i
$370$	2.94565	−	3.90067i	0.153137	−	0.202786i
$371$	−0.962143	+	1.93224i	−0.0499520	+	0.100317i
$372$	3.30250	−	0.617344i	0.171227	−	0.0320078i
$373$	−14.0787	−	8.71719i	−0.728969	−	0.451359i	0.111120	−	0.993807i	$-0.464556\pi$
$373$	−14.0787	−	8.71719i	−0.728969	−	0.451359i	−0.840089	+	0.542448i	$0.817497\pi$
$374$	−0.481954	+	0.439359i	−0.0249212	+	0.0227187i
$375$	−9.59232	+	5.93931i	−0.495345	+	0.306705i
$376$	−2.30332	+	8.09532i	−0.118784	+	0.417484i
$377$	1.87191	−	1.70647i	0.0964083	−	0.0878878i
$378$	0.717191	+	0.653806i	0.0368883	+	0.0336282i
$379$	0.768900	+	1.01819i	0.0394957	+	0.0523008i	0.817337	−	0.576161i	$-0.195450\pi$
$379$	0.768900	+	1.01819i	0.0394957	+	0.0523008i	−0.777841	+	0.628461i	$0.783685\pi$
$380$	6.80842	−	13.6732i	0.349265	−	0.701418i
$381$	1.98177	+	0.767743i	0.101529	+	0.0393327i
$382$	−0.846102	+	1.69920i	−0.0432903	+	0.0869387i
$383$	12.5106	+	25.1247i	0.639264	+	1.28381i	0.943549	+	0.331233i	$0.107465\pi$
$383$	12.5106	+	25.1247i	0.639264	+	1.28381i	−0.304285	+	0.952581i	$0.598418\pi$
$384$	0.0922684	+	0.995734i	0.00470855	+	0.0508133i
$385$	−0.913122	−	1.20917i	−0.0465370	−	0.0616250i
$386$	−14.7396	+	2.75530i	−0.750225	+	0.140241i
$387$	−2.56073	+	3.39095i	−0.130169	+	0.172372i
$388$	1.96180	+	3.93983i	0.0995954	+	0.200015i
$389$	−0.978243	−	10.5569i	−0.0495989	−	0.535257i	−0.983894	−	0.178755i	$-0.942793\pi$
$389$	−0.978243	−	10.5569i	−0.0495989	−	0.535257i	0.934295	−	0.356502i	$-0.116031\pi$
$390$	5.91422	+	1.10556i	0.299478	+	0.0559822i
$391$	−3.69541	−	2.28810i	−0.186885	−	0.115714i
$392$	1.65790	+	5.82691i	0.0837365	+	0.294303i
$393$	5.10762	+	4.65622i	0.257646	+	0.234875i
$394$	8.10657	+	1.51538i	0.408403	+	0.0763438i
$395$	4.14159	−	5.48435i	0.208386	−	0.275948i
$396$	−0.657250	−	0.254620i	−0.0330280	−	0.0127951i
$397$	−25.2132	−	9.76766i	−1.26542	−	0.490225i	−0.367349	−	0.930083i	$-0.619735\pi$
$397$	−25.2132	−	9.76766i	−1.26542	−	0.490225i	−0.898067	+	0.439858i	$0.855029\pi$
$398$	0.638959	−	0.119442i	0.0320281	−	0.00598709i
$399$	1.83136	+	6.43655i	0.0916825	+	0.322230i
$400$	0.0793165	−	0.0491107i	0.00396583	−	0.00245553i
$401$	−0.924480	+	9.97673i	−0.0461663	+	0.498214i	0.940987	+	0.338441i	$0.109900\pi$
$401$	−0.924480	+	9.97673i	−0.0461663	+	0.498214i	−0.987154	+	0.159773i	$0.948924\pi$
$402$	−1.57822	+	0.611404i	−0.0787143	+	0.0304941i
$403$	−0.842005	+	9.08668i	−0.0419433	+	0.452640i
$404$	−0.355590	+	1.24977i	−0.0176913	+	0.0621783i
$405$	0.606194	+	2.13055i	0.0301220	+	0.105868i
$406$	−0.545399	−	0.722225i	−0.0270677	−	0.0358434i
$407$	−0.693277	−	1.39229i	−0.0343644	−	0.0690131i
$408$	−0.909500	−	0.170015i	−0.0450270	−	0.00841700i
$409$	14.7187	−	13.4179i	0.727792	−	0.663470i	−0.222464	−	0.974941i	$-0.571410\pi$
$409$	14.7187	−	13.4179i	0.727792	−	0.663470i	0.950256	+	0.311471i	$0.100822\pi$
$410$	0.785933	−	8.48157i	0.0388145	−	0.418875i
$411$	−19.2564			−0.949848
$412$	−9.83836	−	2.49133i	−0.484701	−	0.122739i
$413$	−10.1024			−0.497108
$414$	0.433436	−	4.67751i	0.0213022	−	0.229887i
$415$	6.03624	−	5.50276i	0.296308	−	0.270120i
$416$	−2.66994	−	0.499099i	−0.130905	−	0.0244703i
$417$	−5.61351	−	11.2734i	−0.274895	−	0.552063i
$418$	−2.92900	−	3.87863i	−0.143262	−	0.189710i
$419$	0.876144	+	3.07933i	0.0428025	+	0.150435i	0.980281	−	0.197607i	$-0.0633171\pi$
$419$	0.876144	+	3.07933i	0.0428025	+	0.150435i	−0.937479	+	0.348042i	$0.886847\pi$
$420$	0.588297	−	2.06765i	0.0287060	−	0.100891i
$421$	−3.22161	+	34.7667i	−0.157012	+	1.69443i	0.444674	+	0.895692i	$0.353320\pi$
$421$	−3.22161	+	34.7667i	−0.157012	+	1.69443i	−0.601686	+	0.798733i	$0.705504\pi$
$422$	23.8537	−	9.24096i	1.16118	−	0.449843i
$423$	0.776587	−	8.38071i	0.0377590	−	0.407484i
$424$	1.89106	−	1.17089i	0.0918378	−	0.0568635i
$425$	0.0236217	+	0.0830216i	0.00114582	+	0.00402714i
$426$	3.53371	−	0.660565i	0.171209	−	0.0320045i
$427$	−3.76722	−	1.45943i	−0.182309	−	0.0706268i
$428$	1.43477	+	0.555832i	0.0693521	+	0.0268672i
$429$	1.15374	−	1.52780i	0.0557032	−	0.0737630i
$430$	9.25222	+	1.72954i	0.446182	+	0.0834058i
$431$	0.0459729	+	0.0419098i	0.00221443	+	0.00201872i	0.674802	−	0.737999i	$-0.264229\pi$
$431$	0.0459729	+	0.0419098i	0.00221443	+	0.00201872i	−0.672588	+	0.740017i	$0.734817\pi$
$432$	−0.273663	−	0.961826i	−0.0131666	−	0.0462759i
$433$	22.7896	+	14.1107i	1.09520	+	0.678117i	0.950302	−	0.311330i	$-0.100774\pi$
$433$	22.7896	+	14.1107i	1.09520	+	0.678117i	0.144895	+	0.989447i	$0.453716\pi$
$434$	3.20500	+	0.599119i	0.153845	+	0.0287586i
$435$	−0.190600	−	2.05690i	−0.00913857	−	0.0986209i
$436$	−0.149840	−	0.300919i	−0.00717604	−	0.0144114i
$437$	19.5208	−	25.8497i	0.933806	−	1.23656i
$438$	−12.1881	+	2.27835i	−0.582370	+	0.108864i
$439$	8.96575	+	11.8726i	0.427912	+	0.566647i	0.959985	−	0.280051i	$-0.0903515\pi$
$439$	8.96575	+	11.8726i	0.427912	+	0.566647i	−0.532073	+	0.846698i	$0.678587\pi$
$440$	0.144060	+	1.55465i	0.00686778	+	0.0741151i
$441$	−2.70036	−	5.42306i	−0.128589	−	0.258241i
$442$	1.12022	−	2.24970i	0.0532832	−	0.107007i
$443$	27.9647	+	10.8336i	1.32864	+	0.514719i	0.917820	−	0.396996i	$-0.129947\pi$
$443$	27.9647	+	10.8336i	1.32864	+	0.514719i	0.410823	+	0.911715i	$0.365241\pi$
$444$	0.983586	−	1.97531i	0.0466789	−	0.0937439i
$445$	−11.2918	−	14.9527i	−0.535281	−	0.708827i
$446$	14.5915	+	13.3019i	0.690927	+	0.629863i
$447$	6.73102	−	6.13613i	0.318366	−	0.290229i
$448$	−0.265584	+	0.933430i	−0.0125476	+	0.0441004i
$449$	22.2287	−	13.7634i	1.04903	−	0.649535i	0.110202	−	0.993909i	$-0.464850\pi$
$449$	22.2287	−	13.7634i	1.04903	−	0.649535i	0.938832	+	0.344374i	$0.111909\pi$
$450$	−0.0689419	+	0.0628489i	−0.00324995	+	0.00296272i
$451$	−2.30442	−	1.42684i	−0.108511	−	0.0671871i
$452$	−9.58764	+	1.79224i	−0.450965	+	0.0842999i
$453$	−1.18687	+	2.38356i	−0.0557641	+	0.111989i
$454$	−7.90216	+	10.4642i	−0.370867	+	0.491107i
$455$	4.96445	+	3.07386i	0.232737	+	0.144105i
$456$	1.88707	−	6.63235i	0.0883700	−	0.310588i
$457$	7.81493	−	3.02752i	0.365567	−	0.141621i	−0.171450	−	0.985193i	$-0.554845\pi$
$457$	7.81493	−	3.02752i	0.365567	−	0.141621i	0.537017	+	0.843571i	$0.319551\pi$
$458$	−12.6526			−0.591218
$459$	0.925254			0.0431872
$460$	−9.70293	+	3.75893i	−0.452401	+	0.175261i
$461$	16.0209	−	9.91972i	0.746168	−	0.462008i	−0.0999574	−	0.994992i	$-0.531871\pi$
$461$	16.0209	−	9.91972i	0.746168	−	0.462008i	0.846125	+	0.532984i	$0.178929\pi$
$462$	−0.505510	−	0.460833i	−0.0235184	−	0.0214399i
$463$	1.29474	+	13.9724i	0.0601715	+	0.649354i	0.971399	+	0.237451i	$0.0763121\pi$
$463$	1.29474	+	13.9724i	0.0601715	+	0.649354i	−0.911228	+	0.411903i	$0.864864\pi$
$464$	0.0860454	+	0.928578i	0.00399456	+	0.0431082i
$465$	5.49979	+	5.01372i	0.255047	+	0.232506i
$466$	−3.66216	+	2.26751i	−0.169646	+	0.105041i
$467$	20.3788	−	7.89481i	0.943021	−	0.365328i	0.159854	−	0.987141i	$-0.448898\pi$
$467$	20.3788	−	7.89481i	0.943021	−	0.365328i	0.783166	+	0.621812i	$0.213603\pi$
$468$	2.71619			0.125556
$469$	−1.64254			−0.0758454
$470$	−17.3848	+	6.73489i	−0.801899	+	0.310657i
$471$	5.13702	−	18.0548i	0.236701	−	0.831919i
$472$	8.85056	+	5.48003i	0.407380	+	0.252239i
$473$	1.80492	−	2.39010i	0.0829902	−	0.109897i
$474$	1.38292	−	2.77728i	0.0635197	−	0.127565i
$475$	−0.632334	+	0.118204i	−0.0290135	+	0.00542356i
$476$	−0.763442	−	0.472704i	−0.0349923	−	0.0216663i
$477$	−1.64371	+	1.49844i	−0.0752601	+	0.0686087i
$478$	21.8188	−	13.5096i	0.997969	−	0.617916i
$479$	4.17563	−	14.6758i	0.190790	−	0.670556i	−0.806102	−	0.591776i	$-0.798427\pi$
$479$	4.17563	−	14.6758i	0.190790	−	0.670556i	0.996892	−	0.0787799i	$-0.0251024\pi$
$480$	−1.63699	+	1.49231i	−0.0747178	+	0.0681143i
$481$	4.42937	+	4.03791i	0.201962	+	0.184113i
$482$	0.0117010	+	0.0154946i	0.000532965	+	0.000705760i
$483$	2.03206	−	4.08093i	0.0924620	−	0.185689i
$484$	−9.79393	−	3.79419i	−0.445179	−	0.172463i
$485$	−4.34561	+	8.72716i	−0.197324	+	0.396280i
$486$	0.445738	+	0.895163i	0.0202191	+	0.0406054i
$487$	−1.38396	−	14.9353i	−0.0627132	−	0.676784i	−0.967827	−	0.251615i	$-0.919038\pi$
$487$	−1.38396	−	14.9353i	−0.0627132	−	0.676784i	0.905114	−	0.425169i	$-0.139785\pi$
$488$	2.50873	+	3.32210i	0.113565	+	0.150384i
$489$	−3.08666	+	0.576997i	−0.139584	+	0.0260927i
$490$	−8.08707	+	10.7090i	−0.365336	+	0.483784i
$491$	10.6771	+	21.4425i	0.481851	+	0.967687i	0.994061	+	0.108827i	$0.0347094\pi$
$491$	10.6771	+	21.4425i	0.481851	+	0.967687i	−0.512210	+	0.858860i	$0.671173\pi$
$492$	−0.354805	−	3.82896i	−0.0159959	−	0.172623i
$493$	−0.848160	−	0.158549i	−0.0381992	−	0.00714067i
$494$	15.9244	+	9.85994i	0.716471	+	0.443620i
$495$	−0.427273	−	1.50171i	−0.0192045	−	0.0674968i
$496$	−2.48285	−	2.26342i	−0.111483	−	0.101631i
$497$	3.42938	+	0.641063i	0.153829	+	0.0287556i
$498$	2.22216	−	2.94262i	0.0995775	−	0.131862i
$499$	−23.6667	−	9.16853i	−1.05947	−	0.410440i	−0.232445	−	0.972609i	$-0.574673\pi$
$499$	−23.6667	−	9.16853i	−1.05947	−	0.410440i	−0.827022	+	0.562170i	$0.809967\pi$
$500$	10.5203	+	4.07560i	0.470484	+	0.182266i
$501$	18.6568	−	3.48757i	0.833526	−	0.155813i
$502$	−1.60456	−	5.63946i	−0.0716152	−	0.251701i
$503$	−36.7810	+	22.7738i	−1.63998	+	1.01543i	−0.680874	+	0.732401i	$0.738400\pi$
$503$	−36.7810	+	22.7738i	−1.63998	+	1.01543i	−0.959110	+	0.283034i	$0.908659\pi$
$504$	0.0895443	−	0.966337i	0.00398862	−	0.0430441i
$505$	−2.68389	+	1.03974i	−0.119431	+	0.0462680i
$506$	−0.305505	+	3.29693i	−0.0135814	+	0.146566i
$507$	1.53861	−	5.40767i	0.0683323	−	0.240163i
$508$	−0.581613	−	2.04416i	−0.0258049	−	0.0906948i
$509$	−9.70067	−	12.8458i	−0.429975	−	0.569379i	0.530522	−	0.847671i	$-0.321996\pi$
$509$	−9.70067	−	12.8458i	−0.429975	−	0.569379i	−0.960496	+	0.278293i	$0.910231\pi$
$510$	−0.913558	−	1.83467i	−0.0404530	−	0.0812407i
$511$	−11.8283	−	2.21109i	−0.523252	−	0.0978127i
$512$	0.739009	−	0.673696i	0.0326599	−	0.0297734i
$513$	−0.636245	+	6.86617i	−0.0280909	+	0.303149i
$514$	7.13941			0.314906
$515$	−8.72933	−	20.7169i	−0.384660	−	0.912896i
$516$	4.24922			0.187061
$517$	−0.547375	+	5.90711i	−0.0240735	+	0.259795i
$518$	1.58259	−	1.44272i	0.0695348	−	0.0633893i
$519$	−5.55289	−	1.03802i	−0.243745	−	0.0455638i
$520$	−2.68186	−	5.38590i	−0.117607	−	0.236187i
$521$	16.9301	+	22.4190i	0.741720	+	0.982196i	0.999871	+	0.0160910i	$0.00512216\pi$
$521$	16.9301	+	22.4190i	0.741720	+	0.982196i	−0.258151	+	0.966105i	$0.583113\pi$
$522$	−0.255206	−	0.896956i	−0.0111701	−	0.0392587i
$523$	10.3665	−	36.4346i	0.453297	−	1.59317i	−0.312385	−	0.949956i	$-0.601128\pi$
$523$	10.3665	−	36.4346i	0.453297	−	1.59317i	0.765682	−	0.643219i	$-0.222402\pi$
$524$	0.637708	−	6.88197i	0.0278584	−	0.300640i
$525$	−0.0844219	+	0.0327052i	−0.00368447	+	0.00142737i
$526$	−2.53623	+	27.3703i	−0.110585	+	1.19340i
$527$	2.64297	−	1.63646i	0.115130	−	0.0712852i
$528$	0.192890	+	0.677939i	0.00839447	+	0.0295035i
$529$	0.917108	−	0.171437i	0.0398743	−	0.00745379i
$530$	4.59415	+	1.77978i	0.199557	+	0.0773089i
$531$	−9.70682	−	3.76044i	−0.421240	−	0.163189i
$532$	4.03284	−	5.34034i	0.174846	−	0.231533i
$533$	10.2669	+	1.91922i	0.444709	+	0.0831306i
$534$	−6.25118	−	5.69871i	−0.270515	−	0.246607i
$535$	0.932732	+	3.27821i	0.0403255	+	0.141730i
$536$	1.43900	+	0.890990i	0.0621553	+	0.0384849i
$537$	7.19899	+	1.34572i	0.310659	+	0.0580723i
$538$	0.753167	+	8.12797i	0.0324714	+	0.350422i
$539$	1.90334	+	3.82242i	0.0819826	+	0.164643i
$540$	1.33490	−	1.76770i	0.0574450	−	0.0760695i
$541$	−0.496287	+	0.0927721i	−0.0213370	+	0.00398858i	−0.194407	−	0.980921i	$-0.562278\pi$
$541$	−0.496287	+	0.0927721i	−0.0213370	+	0.00398858i	0.173070	+	0.984909i	$0.444631\pi$
$542$	7.10436	+	9.40769i	0.305158	+	0.404095i
$543$	0.430977	+	4.65098i	0.0184950	+	0.199593i
$544$	0.412421	+	0.828254i	0.0176824	+	0.0355111i
$545$	0.331912	−	0.666569i	0.0142176	−	0.0285527i
$546$	2.45800	+	0.952234i	0.105193	+	0.0407519i
$547$	16.5565	−	33.2500i	0.707906	−	1.42167i	−0.190137	−	0.981758i	$-0.560893\pi$
$547$	16.5565	−	33.2500i	0.707906	−	1.42167i	0.898042	−	0.439909i	$-0.144989\pi$
$548$	11.6046	+	15.3669i	0.495723	+	0.656443i
$549$	−3.07645	−	2.80456i	−0.131300	−	0.119696i
$550$	0.0485935	−	0.0442988i	0.00207203	−	0.00188891i
$551$	1.75980	−	6.18504i	0.0749699	−	0.263492i
$552$	−3.99394	+	2.47294i	−0.169993	+	0.105255i
$553$	2.22512	−	2.02846i	0.0946215	−	0.0862589i
$554$	18.9711	+	11.7464i	0.806005	+	0.499057i
$555$	4.80473	−	0.898160i	0.203949	−	0.0381248i
$556$	−5.61351	+	11.2734i	−0.238066	+	0.478100i
$557$	11.4365	−	15.1444i	0.484581	−	0.641689i	−0.488387	−	0.872627i	$-0.662415\pi$
$557$	11.4365	−	15.1444i	0.484581	−	0.641689i	0.972969	+	0.230938i	$0.0741794\pi$
$558$	2.85648	+	1.76866i	0.120924	+	0.0748732i
$559$	−3.15854	+	11.1011i	−0.133592	+	0.469526i
$560$	−2.00455	+	0.776566i	−0.0847076	+	0.0328159i
$561$	−0.652162			−0.0275343
$562$	−13.4199			−0.566083
$563$	8.01779	−	3.10611i	0.337910	−	0.130907i	−0.186308	−	0.982491i	$-0.559652\pi$
$563$	8.01779	−	3.10611i	0.337910	−	0.130907i	0.524217	+	0.851585i	$0.324358\pi$
$564$	−7.15595	+	4.43078i	−0.301320	+	0.186569i
$565$	−15.9667	−	14.5556i	−0.671724	−	0.612357i
$566$	2.01618	+	21.7580i	0.0847463	+	0.914558i
$567$	0.0895443	+	0.966337i	0.00376051	+	0.0405823i
$568$	−2.65668	−	2.42188i	−0.111472	−	0.101620i
$569$	12.4556	−	7.71221i	0.522168	−	0.323313i	−0.239913	−	0.970794i	$-0.577119\pi$
$569$	12.4556	−	7.71221i	0.522168	−	0.323313i	0.762081	+	0.647482i	$0.224178\pi$
$570$	14.2430	−	5.51778i	0.596575	−	0.231114i
$571$	−6.01433			−0.251692			−0.125846	−	0.992050i	$-0.540165\pi$
$571$	−6.01433			−0.251692			−0.125846	+	0.992050i	$0.540165\pi$
$572$	−1.91450			−0.0800492
$573$	−1.77002	+	0.685710i	−0.0739437	+	0.0286459i
$574$	1.02127	−	3.58938i	0.0426268	−	0.149818i
$575$	0.372593	+	0.230700i	0.0155382	+	0.00962086i
$576$	−0.602635	+	0.798017i	−0.0251098	+	0.0332507i
$577$	13.6065	−	27.3255i	0.566446	−	1.13758i	−0.408006	−	0.912979i	$-0.633776\pi$
$577$	13.6065	−	27.3255i	0.566446	−	1.13758i	0.974452	−	0.224597i	$-0.0721065\pi$
$578$	15.8690	−	2.96643i	0.660064	−	0.123387i
$579$	−12.7489	−	7.89380i	−0.529827	−	0.328055i
$580$	−1.52658	+	1.39166i	−0.0633878	+	0.0577856i
$581$	3.04255	−	1.88386i	0.126226	−	0.0781559i
$582$	−1.20446	+	4.23323i	−0.0499264	+	0.175473i
$583$	1.15856	−	1.05617i	0.0479826	−	0.0437420i
$584$	9.16313	+	8.35330i	0.379173	+	0.345662i
$585$	3.62585	+	4.80140i	0.149910	+	0.198514i
$586$	4.60519	−	9.24847i	0.190239	−	0.382051i
$587$	−24.2660	−	9.40071i	−1.00157	−	0.388009i	−0.196057	−	0.980592i	$-0.562814\pi$
$587$	−24.2660	−	9.40071i	−1.00157	−	0.388009i	−0.805509	+	0.592583i	$0.798108\pi$
$588$	−2.70036	+	5.42306i	−0.111361	+	0.223643i
$589$	10.3265	+	20.7384i	0.425496	+	0.854510i
$590$	2.12759	+	22.9604i	0.0875917	+	0.945265i
$591$	4.96992	+	6.58124i	0.204435	+	0.270716i
$592$	−2.16907	+	0.405470i	−0.0891483	+	0.0166647i
$593$	−19.4559	+	25.7638i	−0.798957	+	1.05799i	0.198012	+	0.980200i	$0.436551\pi$
$593$	−19.4559	+	25.7638i	−0.798957	+	1.05799i	−0.996970	+	0.0777910i	$0.975213\pi$
$594$	−0.314177	−	0.630953i	−0.0128908	−	0.0258883i
$595$	−0.183525	−	1.98055i	−0.00752378	−	0.0811945i
$596$	−8.95308	−	1.67362i	−0.366733	−	0.0685542i
$597$	0.552664	+	0.342195i	0.0226190	+	0.0140051i
$598$	−3.49179	−	12.2724i	−0.142790	−	0.501855i
$599$	23.9145	+	21.8010i	0.977120	+	0.890763i	0.994031	−	0.109094i	$-0.0347950\pi$
$599$	23.9145	+	21.8010i	0.977120	+	0.890763i	−0.0169110	+	0.999857i	$0.505383\pi$
$600$	0.0917013	+	0.0171419i	0.00374369	+	0.000699817i
$601$	−23.7113	+	31.3988i	−0.967203	+	1.28078i	−0.00744057	+	0.999972i	$0.502368\pi$
$601$	−23.7113	+	31.3988i	−0.967203	+	1.28078i	−0.959763	+	0.280812i	$0.909396\pi$
$602$	3.84530	+	1.48968i	0.156723	+	0.0607147i
$603$	−1.57822	−	0.611404i	−0.0642699	−	0.0248983i
$604$	2.61737	−	0.489272i	0.106499	−	0.0199082i
$605$	−6.36697	−	22.3776i	−0.258854	−	0.909777i
$606$	−1.10475	+	0.684031i	−0.0448773	+	0.0277869i
$607$	2.14266	−	23.1230i	0.0869681	−	0.938535i	−0.834738	−	0.550647i	$-0.814381\pi$
$607$	2.14266	−	23.1230i	0.0869681	−	0.938535i	0.921706	−	0.387888i	$-0.126795\pi$
$608$	−6.42995	+	2.49097i	−0.260769	+	0.101022i
$609$	0.0835051	−	0.901164i	0.00338380	−	0.0365170i
$610$	−2.52355	+	8.86935i	−0.102175	+	0.359110i
$611$	−6.25625	−	21.9884i	−0.253101	−	0.889557i
$612$	−0.557590	−	0.738369i	−0.0225393	−	0.0298468i
$613$	−7.61612	−	15.2952i	−0.307612	−	0.617768i	0.686377	−	0.727246i	$-0.259200\pi$
$613$	−7.61612	−	15.2952i	−0.307612	−	0.617768i	−0.993989	+	0.109477i	$0.965082\pi$
$614$	19.6190	+	3.66743i	0.791758	+	0.148005i
$615$	6.29481	−	5.73847i	0.253831	−	0.231398i
$616$	−0.0631150	+	0.681119i	−0.00254298	+	0.0274431i
$617$	6.87139			0.276632			0.138316	−	0.990388i	$-0.455831\pi$
$617$	6.87139			0.276632			0.138316	+	0.990388i	$0.455831\pi$
$618$	−5.59224	−	8.46917i	−0.224953	−	0.340680i
$619$	38.1819			1.53466			0.767329	−	0.641253i	$-0.221585\pi$
$619$	38.1819			1.53466			0.767329	+	0.641253i	$0.221585\pi$
$620$	0.686672	−	7.41037i	0.0275774	−	0.297608i
$621$	3.47153	−	3.16472i	0.139308	−	0.126996i
$622$	23.3096	+	4.35731i	0.934628	+	0.174712i
$623$	−3.65913	−	7.34852i	−0.146600	−	0.294412i
$624$	−1.63687	−	2.16757i	−0.0655273	−	0.0867722i
$625$	6.71154	+	23.5886i	0.268462	+	0.943545i
$626$	−3.48092	+	12.2342i	−0.139126	+	0.488976i
$627$	0.448455	−	4.83960i	0.0179096	−	0.193275i
$628$	−17.5037	+	6.78099i	−0.698476	+	0.270591i
$629$	0.188385	−	2.03300i	0.00751140	−	0.0810609i
$630$	1.82772	−	1.13168i	0.0728182	−	0.0450871i
$631$	0.779908	+	2.74109i	0.0310476	+	0.109121i	0.975801	−	0.218662i	$-0.0701691\pi$
$631$	0.779908	+	2.74109i	0.0310476	+	0.109121i	−0.944753	+	0.327783i	$0.893699\pi$
$632$	−3.04971	+	0.570091i	−0.121311	+	0.0226770i
$633$	23.8537	+	9.24096i	0.948098	+	0.367295i
$634$	−17.4023	−	6.74169i	−0.691134	−	0.267747i
$635$	2.83705	−	3.75686i	0.112585	−	0.149087i
$636$	2.18633	+	0.408696i	0.0866937	+	0.0162059i
$637$	−12.1605	−	11.0858i	−0.481817	−	0.439234i
$638$	0.179881	+	0.632216i	0.00712156	+	0.0250297i
$639$	3.05646	+	1.89248i	0.120912	+	0.0748654i
$640$	2.17739	+	0.407025i	0.0860690	+	0.0160891i
$641$	2.51934	+	27.1880i	0.0995078	+	1.07386i	0.888320	+	0.459226i	$0.151873\pi$
$641$	2.51934	+	27.1880i	0.0995078	+	1.07386i	−0.788812	+	0.614635i	$0.789303\pi$
$642$	0.685845	+	1.37736i	0.0270681	+	0.0543601i
$643$	10.8883	−	14.4184i	0.429392	−	0.568607i	−0.530960	−	0.847397i	$-0.678168\pi$
$643$	10.8883	−	14.4184i	0.429392	−	0.568607i	0.960352	+	0.278790i	$0.0899332\pi$
$644$	−4.48124	+	0.837690i	−0.176586	+	0.0330096i
$645$	5.67229	+	7.51132i	0.223346	+	0.295758i
$646$	−0.588688	−	6.35296i	−0.0231616	−	0.249954i
$647$	−19.0259	−	38.2091i	−0.747985	−	1.50216i	−0.861024	−	0.508565i	$-0.830176\pi$
$647$	−19.0259	−	38.2091i	−0.747985	−	1.50216i	0.113039	−	0.993591i	$-0.463942\pi$
$648$	0.445738	−	0.895163i	0.0175103	−	0.0351653i
$649$	6.84181	+	2.65053i	0.268565	+	0.104042i
$650$	−0.112947	+	0.226828i	−0.00443014	+	0.00889692i
$651$	1.96490	+	2.60195i	0.0770105	+	0.101978i
$652$	2.32058	+	2.11549i	0.0908810	+	0.0828490i
$653$	23.9044	−	21.7917i	0.935451	−	0.852776i	−0.0538673	−	0.998548i	$-0.517155\pi$
$653$	23.9044	−	21.7917i	0.935451	−	0.852776i	0.989318	+	0.145772i	$0.0465666\pi$
$654$	0.0919949	−	0.323329i	0.00359729	−	0.0126432i
$655$	13.0165	−	8.05948i	0.508597	−	0.314910i
$656$	−2.84176	+	2.59061i	−0.110952	+	0.101146i
$657$	−10.5420	−	6.52734i	−0.411283	−	0.254656i
$658$	−8.02905	+	1.50089i	−0.313005	+	0.0585108i
$659$	0.272751	−	0.547757i	0.0106249	−	0.0213376i	−0.889787	−	0.456375i	$-0.849147\pi$
$659$	0.272751	−	0.547757i	0.0106249	−	0.0213376i	0.900412	+	0.435038i	$0.143265\pi$
$660$	−0.940901	+	1.24595i	−0.0366245	+	0.0484987i
$661$	33.0317	+	20.4524i	1.28478	+	0.795505i	0.987246	−	0.159205i	$-0.0508931\pi$
$661$	33.0317	+	20.4524i	1.28478	+	0.795505i	0.297539	+	0.954710i	$0.403834\pi$
$662$	−2.97229	+	10.4465i	−0.115521	+	0.406016i
$663$	2.34346	−	0.907861i	0.0910125	−	0.0352584i
$664$	−3.68741			−0.143099
$665$	14.8235			0.574832
$666$	2.05763	−	0.797131i	0.0797317	−	0.0308882i
$667$	−3.72457	+	2.30616i	−0.144216	+	0.0892948i
$668$	−14.0264	−	12.7868i	−0.542698	−	0.494734i
$669$	1.82181	+	19.6604i	0.0704351	+	0.760116i
$670$	0.345922	+	3.73310i	0.0133641	+	0.144222i
$671$	2.16843	+	1.97678i	0.0837111	+	0.0763128i
$672$	−0.825116	+	0.510890i	−0.0318296	+	0.0197080i
$673$	20.6235	−	7.98960i	0.794979	−	0.307976i	0.0707125	−	0.997497i	$-0.477473\pi$
$673$	20.6235	−	7.98960i	0.794979	−	0.307976i	0.724266	+	0.689520i	$0.242179\pi$
$674$	−11.9681			−0.460993
$675$	−0.0932897			−0.00359072
$676$	−5.24264	+	2.03101i	−0.201640	+	0.0781157i
$677$	0.952453	−	3.34752i	0.0366057	−	0.128656i	−0.941369	−	0.337378i	$-0.890460\pi$
$677$	0.952453	−	3.34752i	0.0366057	−	0.128656i	0.977975	+	0.208722i	$0.0669305\pi$
$678$	−8.29278	−	5.13467i	−0.318482	−	0.197196i
$679$	−2.57404	+	3.40857i	−0.0987824	+	0.130809i
$680$	−0.913558	+	1.83467i	−0.0350334	+	0.0703565i
$681$	−12.8894	+	2.40945i	−0.493924	+	0.0923303i
$682$	−2.01338	−	1.24663i	−0.0770963	−	0.0477360i
$683$	−9.37719	+	8.54844i	−0.358808	+	0.327097i	−0.832947	−	0.553353i	$-0.813348\pi$
$683$	−9.37719	+	8.54844i	−0.358808	+	0.327097i	0.474138	+	0.880450i	$0.342760\pi$
$684$	5.86275	−	3.63006i	0.224168	−	0.138799i
$685$	−11.6731	+	41.0267i	−0.446006	+	1.56755i
$686$	−9.36521	+	8.53752i	−0.357565	+	0.325964i
$687$	−9.35039	−	8.52401i	−0.356740	−	0.325211i
$688$	−2.56073	−	3.39095i	−0.0976268	−	0.129279i
$689$	−2.69287	+	5.40801i	−0.102590	+	0.206029i
$690$	−9.70293	−	3.75893i	−0.369384	−	0.143100i
$691$	9.02100	−	18.1166i	0.343175	−	0.689188i	−0.654592	−	0.755982i	$-0.727159\pi$
$691$	9.02100	−	18.1166i	0.343175	−	0.689188i	0.997767	+	0.0667943i	$0.0212771\pi$
$692$	2.51801	+	5.05685i	0.0957204	+	0.192232i
$693$	−0.0631150	−	0.681119i	−0.00239754	−	0.0258736i
$694$	10.2340	+	13.5521i	0.388479	+	0.514429i
$695$	−27.4215	+	5.12596i	−1.04016	+	0.194439i
$696$	−0.561991	+	0.744196i	−0.0213022	+	0.0282087i
$697$	−1.58591	−	3.18494i	−0.0600706	−	0.120638i
$698$	0.852971	+	9.20502i	0.0322854	+	0.348415i
$699$	−4.23398	−	0.791469i	−0.160144	−	0.0299361i
$700$	0.0769748	+	0.0476608i	0.00290938	+	0.00180141i
$701$	−3.45489	−	12.1427i	−0.130489	−	0.458622i	0.868846	−	0.495083i	$-0.164862\pi$
$701$	−3.45489	−	12.1427i	−0.130489	−	0.458622i	−0.999335	+	0.0364606i	$0.988392\pi$
$702$	2.00729	+	1.82989i	0.0757603	+	0.0690646i
$703$	14.9570	+	2.79595i	0.564115	+	0.105451i
$704$	0.424765	−	0.562479i	0.0160089	−	0.0211992i
$705$	−17.3848	−	6.73489i	−0.654748	−	0.253651i
$706$	−11.8472	−	4.58964i	−0.445876	−	0.172733i
$707$	−1.23954	+	0.231710i	−0.0466177	+	0.00871435i
$708$	2.84877	+	10.0124i	0.107063	+	0.376288i
$709$	−14.9137	+	9.23418i	−0.560097	+	0.346797i	−0.777103	−	0.629373i	$-0.783312\pi$
$709$	−14.9137	+	9.23418i	−0.560097	+	0.346797i	0.217007	+	0.976170i	$0.430371\pi$
$710$	0.734746	−	7.92917i	0.0275745	−	0.297576i
$711$	2.89303	−	1.12077i	0.108497	−	0.0420321i
$712$	−0.780486	+	8.42279i	−0.0292500	+	0.315657i
$713$	4.31906	−	15.1799i	0.161750	−	0.568492i
$714$	−0.245732	−	0.863660i	−0.00919631	−	0.0323217i
$715$	−2.55567	−	3.38425i	−0.0955765	−	0.126564i
$716$	−3.26445	−	6.55590i	−0.121998	−	0.245005i
$717$	25.2257	+	4.71549i	0.942070	+	0.176103i
$718$	−5.39694	+	4.91996i	−0.201412	+	0.183611i
$719$	1.55166	−	16.7450i	0.0578670	−	0.624485i	−0.916578	−	0.399857i	$-0.869060\pi$
$719$	1.55166	−	16.7450i	0.0578670	−	0.624485i	0.974445	−	0.224628i	$-0.0721167\pi$
$720$	−2.21511			−0.0825523
$721$	−2.09156	−	9.62463i	−0.0778938	−	0.358440i
$722$	28.5492			1.06249
$723$	−0.00179152	+	0.0193336i	−6.66273e−5	+	0.000719023i
$724$	3.45184	−	3.14677i	0.128287	−	0.116949i
$725$	0.0855166	+	0.0159858i	0.00317601	+	0.000593698i
$726$	−4.68168	−	9.40207i	−0.173753	−	0.348944i
$727$	25.4102	+	33.6485i	0.942411	+	1.24795i	0.968683	+	0.248299i	$0.0798716\pi$
$727$	25.4102	+	33.6485i	0.942411	+	1.24795i	−0.0262723	+	0.999655i	$0.508364\pi$
$728$	−0.721376	−	2.53538i	−0.0267360	−	0.0939673i
$729$	−0.273663	+	0.961826i	−0.0101357	+	0.0356232i
$730$	−2.53421	+	27.3485i	−0.0937952	+	1.01221i
$731$	3.66611	−	1.42026i	0.135596	−	0.0525302i
$732$	−0.384108	+	4.14518i	−0.0141970	+	0.153210i
$733$	43.7374	−	27.0811i	1.61548	−	1.00026i	0.643424	−	0.765510i	$-0.277513\pi$
$733$	43.7374	−	27.0811i	1.61548	−	1.00026i	0.972055	−	0.234752i	$-0.0754277\pi$
$734$	−1.09361	−	3.84363i	−0.0403657	−	0.141871i
$735$	−13.1910	+	2.46583i	−0.486558	+	0.0909535i
$736$	4.38034	+	1.69695i	0.161461	+	0.0625505i
$737$	1.11240	+	0.430946i	0.0409758	+	0.0158741i
$738$	2.31735	−	3.06867i	0.0853028	−	0.112959i
$739$	35.9618	+	6.72243i	1.32288	+	0.247289i	0.797365	−	0.603498i	$-0.206227\pi$
$739$	35.9618	+	6.72243i	1.32288	+	0.247289i	0.525512	+	0.850786i	$0.323874\pi$
$740$	−3.61224	−	3.29300i	−0.132789	−	0.121053i
$741$	5.12564	+	18.0148i	0.188295	+	0.661789i
$742$	1.83523	+	1.13632i	0.0673733	+	0.0417158i
$743$	−12.0632	−	2.25500i	−0.442556	−	0.0827280i	−0.0422446	−	0.999107i	$-0.513451\pi$
$743$	−12.0632	−	2.25500i	−0.442556	−	0.0827280i	−0.400311	+	0.916379i	$0.631098\pi$
$744$	−0.309995	−	3.34537i	−0.0113650	−	0.122647i
$745$	−8.99303	−	18.0604i	−0.329479	−	0.661684i
$746$	−9.97902	+	13.2144i	−0.365358	+	0.483812i
$747$	3.62463	−	0.677561i	0.132618	−	0.0247906i
$748$	0.393015	+	0.520437i	0.0143701	+	0.0190290i
$749$	0.137779	+	1.48688i	0.00503435	+	0.0543292i
$750$	5.02891	+	10.0994i	0.183630	+	0.368778i
$751$	−16.9436	+	34.0273i	−0.618280	+	1.24167i	0.335746	+	0.941952i	$0.391012\pi$
$751$	−16.9436	+	34.0273i	−0.618280	+	1.24167i	−0.954027	+	0.299722i	$0.903106\pi$
$752$	7.84826	+	3.04043i	0.286197	+	0.110873i
$753$	2.61349	−	5.24860i	0.0952409	−	0.191270i
$754$	−1.52648	−	2.02138i	−0.0555909	−	0.0736143i
$755$	4.35882	+	3.97359i	0.158634	+	0.144614i
$756$	0.717191	−	0.653806i	0.0260840	−	0.0237787i
$757$	−7.02180	+	24.6791i	−0.255212	+	0.896976i	0.723257	+	0.690579i	$0.242644\pi$
$757$	−7.02180	+	24.6791i	−0.255212	+	0.896976i	−0.978468	+	0.206397i	$0.933826\pi$
$758$	1.08479	−	0.671673i	0.0394013	−	0.0243963i
$759$	−2.44690	+	2.23064i	−0.0888168	+	0.0809672i
$760$	−12.9866	−	8.04098i	−0.471075	−	0.291677i
$761$	−12.3198	+	2.30297i	−0.446593	+	0.0834827i	−0.402242	−	0.915533i	$-0.631769\pi$
$761$	−12.3198	+	2.30297i	−0.446593	+	0.0834827i	−0.0443508	+	0.999016i	$0.514122\pi$
$762$	0.947323	−	1.90248i	0.0343179	−	0.0689196i
$763$	0.196602	−	0.260343i	0.00711746	−	0.00942504i
$764$	1.61388	+	0.999275i	0.0583883	+	0.0361525i
$765$	0.560883	−	1.97130i	0.0202788	−	0.0712725i
$766$	26.1719	−	10.1390i	0.945629	−	0.366339i
$767$	−28.2749			−1.02095
$768$	1.00000			0.0360844
$769$	−23.4249	+	9.07485i	−0.844723	+	0.327248i	−0.744422	−	0.667710i	$-0.767275\pi$
$769$	−23.4249	+	9.07485i	−0.844723	+	0.327248i	−0.100301	+	0.994957i	$0.531981\pi$
$770$	−1.28826	+	0.797659i	−0.0464258	+	0.0287456i
$771$	5.27609	+	4.80979i	0.190014	+	0.173220i
$772$	1.38355	+	14.9309i	0.0497952	+	0.537376i
$773$	2.42028	+	26.1190i	0.0870514	+	0.939434i	0.921508	+	0.388360i	$0.126958\pi$
$773$	2.42028	+	26.1190i	0.0870514	+	0.939434i	−0.834456	+	0.551074i	$0.814218\pi$
$774$	3.14021	+	2.86268i	0.112873	+	0.102897i
$775$	−0.266480	+	0.164997i	−0.00957225	+	0.00592688i
$776$	4.10404	−	1.58991i	0.147326	−	0.0570745i
$777$	2.14150			0.0768258
$778$	−10.6021			−0.380105
$779$	24.7255	−	9.57870i	0.885882	−	0.343193i
$780$	1.64654	−	5.78698i	0.0589555	−	0.207207i
$781$	−2.15434	−	1.33391i	−0.0770882	−	0.0477310i
$782$	−2.61931	+	3.46853i	−0.0936663	+	0.124034i
$783$	0.415676	−	0.834790i	0.0148551	−	0.0298330i
$784$	5.95502	−	1.11319i	0.212679	−	0.0397567i
$785$	−35.3525	−	21.8893i	−1.26179	−	0.781264i
$786$	5.10762	−	4.65622i	0.182183	−	0.166082i
$787$	33.3838	−	20.6704i	1.19001	−	0.736820i	0.218964	−	0.975733i	$-0.429732\pi$
$787$	33.3838	−	20.6704i	1.19001	−	0.736820i	0.971041	+	0.238913i	$0.0767911\pi$
$788$	2.25690	−	7.93217i	0.0803986	−	0.282572i
$789$	−20.3135	+	18.5182i	−0.723181	+	0.659266i
$790$	−5.07882	−	4.62995i	−0.180696	−	0.164726i
$791$	−5.70439	−	7.55384i	−0.202825	−	0.268584i
$792$	−0.314177	+	0.630953i	−0.0111638	+	0.0224199i
$793$	−10.5438	−	4.08469i	−0.374421	−	0.145051i
$794$	−12.0524	+	24.2044i	−0.427723	+	0.858984i
$795$	2.19609	+	4.41034i	0.0778872	+	0.156419i
$796$	−0.0599769	−	0.647254i	−0.00212583	−	0.0229413i
$797$	−11.3347	−	15.0096i	−0.401496	−	0.531667i	0.551691	−	0.834049i	$-0.313983\pi$
$797$	−11.3347	−	15.0096i	−0.401496	−	0.531667i	−0.953187	+	0.302382i	$0.902218\pi$
$798$	6.57807	−	1.22965i	0.232861	−	0.0435293i
$799$	−4.69302	+	6.21457i	−0.166027	+	0.219856i
$800$	−0.0415828	−	0.0835095i	−0.00147017	−	0.00295251i
$801$	−0.780486	−	8.42279i	−0.0275771	−	0.297605i
$802$	9.84887	+	1.84107i	0.347776	+	0.0650106i
$803$	7.43051	+	4.60077i	0.262217	+	0.162358i
$804$	0.463177	+	1.62790i	0.0163350	+	0.0574115i
$805$	−7.46280	−	6.80324i	−0.263029	−	0.239783i
$806$	8.97023	+	1.67683i	0.315963	+	0.0590637i
$807$	−4.91918	+	6.51405i	−0.173163	+	0.229305i
$808$	1.21163	+	0.469387i	0.0426249	+	0.0165130i
$809$	−32.0388	−	12.4119i	−1.12643	−	0.436380i	−0.275309	−	0.961356i	$-0.588780\pi$
$809$	−32.0388	−	12.4119i	−1.12643	−	0.436380i	−0.851117	+	0.524976i	$0.824074\pi$
$810$	2.17739	−	0.407025i	0.0765058	−	0.0143014i
$811$	3.50303	+	12.3119i	0.123008	+	0.432329i	0.998724	−	0.0504978i	$-0.0160808\pi$
$811$	3.50303	+	12.3119i	0.123008	+	0.432329i	−0.875716	+	0.482826i	$0.839610\pi$
$812$	−0.769467	+	0.476434i	−0.0270030	+	0.0167196i
$813$	−1.08774	+	11.7385i	−0.0381486	+	0.411689i
$814$	−1.45032	+	0.561855i	−0.0508335	+	0.0196930i
$815$	−0.641794	+	6.92606i	−0.0224810	+	0.242609i
$816$	−0.253208	+	0.889933i	−0.00886405	+	0.0311539i
$817$	8.01856	+	28.1823i	0.280534	+	0.985975i
$818$	−12.0025	−	15.8939i	−0.419659	−	0.555719i
$819$	1.17497	+	2.35965i	0.0410567	+	0.0824530i
$820$	−8.37287	−	1.56516i	−0.292393	−	0.0546578i
$821$	−29.5841	+	26.9695i	−1.03249	+	0.941241i	−0.998306	−	0.0581742i	$-0.981472\pi$
$821$	−29.5841	+	26.9695i	−1.03249	+	0.941241i	−0.0341861	+	0.999415i	$0.510884\pi$
$822$	−1.77676	+	19.1743i	−0.0619715	+	0.668779i
$823$	30.5064			1.06339			0.531693	−	0.846937i	$-0.321556\pi$
$823$	30.5064			1.06339			0.531693	+	0.846937i	$0.321556\pi$
$824$	−3.38847	+	9.56652i	−0.118043	+	0.333265i
$825$	0.0657549			0.00228929
$826$	−0.932135	+	10.0593i	−0.0324331	+	0.350009i
$827$	7.07494	−	6.44966i	0.246020	−	0.224277i	−0.541287	−	0.840838i	$-0.682063\pi$
$827$	7.07494	−	6.44966i	0.246020	−	0.224277i	0.787307	+	0.616561i	$0.211475\pi$
$828$	−4.61757	−	0.863173i	−0.160472	−	0.0299973i
$829$	5.92069	+	11.8904i	0.205634	+	0.412969i	0.973840	−	0.227234i	$-0.0729681\pi$
$829$	5.92069	+	11.8904i	0.205634	+	0.412969i	−0.768206	+	0.640203i	$0.778850\pi$
$830$	−4.92234	−	6.51823i	−0.170857	−	0.226251i
$831$	6.10631	+	21.4615i	0.211826	+	0.744490i
$832$	−0.743321	+	2.61250i	−0.0257700	+	0.0905723i
$833$	−0.517197	+	5.58144i	−0.0179198	+	0.193385i
$834$	−11.7433	+	4.54938i	−0.406637	+	0.157532i
$835$	3.87922	−	41.8635i	0.134246	−	1.44874i
$836$	−4.13234	+	2.55863i	−0.142920	+	0.0884922i
$837$	0.919427	+	3.23145i	0.0317801	+	0.111695i
$838$	3.14703	−	0.588282i	0.108712	−	0.0203219i
$839$	−1.63843	−	0.634733i	−0.0565650	−	0.0219134i	0.332793	−	0.943000i	$-0.392009\pi$
$839$	−1.63843	−	0.634733i	−0.0565650	−	0.0219134i	−0.389358	+	0.921087i	$0.627303\pi$
$840$	−2.00455	−	0.776566i	−0.0691635	−	0.0267941i
$841$	16.9523	−	22.4485i	0.584563	−	0.774086i
$842$	34.3211	+	6.41573i	1.18278	+	0.221101i
$843$	−9.91741	−	9.04091i	−0.341574	−	0.311386i
$844$	−7.00060	−	24.6045i	−0.240971	−	0.846923i
$845$	−10.5886	−	6.55619i	−0.364259	−	0.225540i
$846$	−8.27331	−	1.54655i	−0.284442	−	0.0531714i
$847$	−0.940501	−	10.1496i	−0.0323160	−	0.348745i
$848$	−0.991412	−	1.99102i	−0.0340452	−	0.0683721i
$849$	−13.1683	+	17.4377i	−0.451935	+	0.598459i
$850$	0.0848470	−	0.0158607i	0.00291023	−	0.000544016i
$851$	−6.24680	−	8.27211i	−0.214138	−	0.283564i
$852$	−0.331697	−	3.57958i	−0.0113638	−	0.122634i
$853$	−3.50491	−	7.03881i	−0.120006	−	0.241004i	0.827013	−	0.562183i	$-0.190038\pi$
$853$	−3.50491	−	7.03881i	−0.120006	−	0.241004i	−0.947018	+	0.321179i	$0.895921\pi$
$854$	−1.80080	+	3.61650i	−0.0616221	+	0.123754i
$855$	14.2430	+	5.51778i	0.487101	+	0.188704i
$856$	0.685845	−	1.37736i	0.0234417	−	0.0470773i
$857$	−24.6668	−	32.6642i	−0.842603	−	1.11579i	−0.991903	−	0.126994i	$-0.959467\pi$
$857$	−24.6668	−	32.6642i	−0.842603	−	1.11579i	0.149301	−	0.988792i	$-0.452298\pi$
$858$	−1.41483	−	1.28979i	−0.0483015	−	0.0440327i
$859$	−24.0052	+	21.8836i	−0.819046	+	0.746659i	−0.970318	−	0.241833i	$-0.922251\pi$
$859$	−24.0052	+	21.8836i	−0.819046	+	0.746659i	0.151272	+	0.988492i	$0.451663\pi$
$860$	2.57585	−	9.05317i	0.0878357	−	0.308710i
$861$	3.17287	−	1.96456i	0.108131	−	0.0669520i
$862$	0.0459729	−	0.0419098i	0.00156584	−	0.00142745i
$863$	9.23356	+	5.71718i	0.314314	+	0.194615i	0.674518	−	0.738259i	$-0.264352\pi$
$863$	9.23356	+	5.71718i	0.314314	+	0.194615i	−0.360204	+	0.932874i	$0.617293\pi$
$864$	−0.982973	+	0.183750i	−0.0334414	+	0.00625129i
$865$	−5.57767	+	11.2015i	−0.189646	+	0.380861i
$866$	16.1533	−	21.3904i	0.548910	−	0.726875i
$867$	13.7258	+	8.49867i	0.466153	+	0.288630i
$868$	0.892283	−	3.13605i	0.0302861	−	0.106444i
$869$	−2.03914	+	0.789969i	−0.0691732	+	0.0267979i
$870$	−2.06571			−0.0700343
$871$	−4.59718			−0.155769
$872$	−0.313461	+	0.121436i	−0.0106151	+	0.00411233i
$873$	−3.74201	+	2.31696i	−0.126648	+	0.0784171i
$874$	−23.9383	−	21.8226i	−0.809724	−	0.738161i
$875$	1.01026	+	10.9024i	0.0341529	+	0.368569i
$876$	1.14406	+	12.3463i	0.0386540	+	0.417143i
$877$	−1.56969	−	1.43096i	−0.0530047	−	0.0483202i	0.646760	−	0.762694i	$-0.276124\pi$
$877$	−1.56969	−	1.43096i	−0.0530047	−	0.0483202i	−0.699765	+	0.714373i	$0.746712\pi$
$878$	12.6492	−	7.83204i	0.426889	−	0.264319i
$879$	9.63393	−	3.73221i	0.324944	−	0.125884i
$880$	1.56131			0.0526318
$881$	−52.5948			−1.77196			−0.885981	−	0.463721i	$-0.846514\pi$
$881$	−52.5948			−1.77196			−0.885981	+	0.463721i	$0.846514\pi$
$882$	−5.64908	+	2.18846i	−0.190214	+	0.0736894i
$883$	10.1787	−	35.7746i	0.342542	−	1.20391i	−0.578902	−	0.815397i	$-0.696518\pi$
$883$	10.1787	−	35.7746i	0.342542	−	1.20391i	0.921443	−	0.388512i	$-0.127011\pi$
$884$	−2.13674	−	1.32301i	−0.0718663	−	0.0444977i
$885$	−13.8960	+	18.4013i	−0.467109	+	0.618553i
$886$	13.3676	−	26.8458i	0.449094	−	0.901903i
$887$	3.88060	−	0.725411i	0.130298	−	0.0243569i	−0.118197	−	0.992990i	$-0.537711\pi$
$887$	3.88060	−	0.725411i	0.130298	−	0.0243569i	0.248494	+	0.968633i	$0.420064\pi$
$888$	−1.87613	−	1.16165i	−0.0629587	−	0.0389824i
$889$	1.52424	−	1.38953i	0.0511213	−	0.0466033i
$890$	−15.9308	+	9.86393i	−0.534002	+	0.330640i
$891$	0.192890	−	0.677939i	0.00646207	−	0.0227118i
$892$	14.5915	−	13.3019i	0.488559	−	0.445380i
$893$	−42.8902	−	39.0996i	−1.43527	−	1.30842i
$894$	−5.48890	−	7.26848i	−0.183576	−	0.243094i
$895$	7.23111	−	14.5220i	0.241709	−	0.485418i
$896$	0.904943	+	0.350577i	0.0302320	+	0.0117119i
$897$	5.68738	−	11.4218i	0.189896	−	0.381363i
$898$	−11.6537	−	23.4038i	−0.388889	−	0.780993i
$899$	−0.289087	−	3.11975i	−0.00964160	−	0.104049i
$900$	0.0562196	+	0.0744468i	0.00187399	+	0.00248156i
$901$	2.02291	−	0.378148i	0.0673930	−	0.0125979i
$902$	−1.63338	+	2.16294i	−0.0543854	+	0.0720180i
$903$	1.83812	+	3.69145i	0.0611689	+	0.122844i
$904$	0.899960	+	9.71211i	0.0299322	+	0.323020i
$905$	10.1704	+	1.90118i	0.338076	+	0.0631973i
$906$	2.26388	+	1.40174i	0.0752124	+	0.0465696i
$907$	3.66091	+	12.8668i	0.121559	+	0.427234i	0.998583	−	0.0532112i	$-0.0169456\pi$
$907$	3.66091	+	12.8668i	0.121559	+	0.427234i	−0.877025	+	0.480445i	$0.840475\pi$
$908$	9.69039	+	8.83396i	0.321587	+	0.293165i
$909$	−1.27725	−	0.238759i	−0.0423636	−	0.00791913i
$910$	3.51880	−	4.65965i	0.116647	−	0.154466i
$911$	−3.35808	−	1.30093i	−0.111258	−	0.0431016i	0.304969	−	0.952362i	$-0.401354\pi$
$911$	−3.35808	−	1.30093i	−0.111258	−	0.0431016i	−0.416227	+	0.909261i	$0.636648\pi$
$912$	−6.42995	−	2.49097i	−0.212917	−	0.0824844i
$913$	−2.55481	+	0.477576i	−0.0845517	+	0.0158055i
$914$	−2.29354	−	8.06094i	−0.0758634	−	0.266632i
$915$	−7.84017	+	4.85443i	−0.259188	+	0.160482i
$916$	−1.16744	+	12.5986i	−0.0385731	+	0.416271i
$917$	6.25447	−	2.42299i	0.206541	−	0.0800143i
$918$	0.0853717	−	0.921307i	0.00281769	−	0.0304077i
$919$	13.3230	−	46.8253i	0.439484	−	1.54462i	−0.353531	−	0.935423i	$-0.615019\pi$
$919$	13.3230	−	46.8253i	0.439484	−	1.54462i	0.793015	−	0.609202i	$-0.208510\pi$
$920$	2.84763	+	10.0084i	0.0938835	+	0.329966i
$921$	12.0279	+	15.9275i	0.396332	+	0.524829i
$922$	−8.39918	−	16.8678i	−0.276612	−	0.555513i
$923$	9.59823	+	1.79422i	0.315930	+	0.0590575i
$924$	−0.505510	+	0.460833i	−0.0166300	+	0.0151603i
$925$	−0.0189941	+	0.204979i	−0.000624522	+	0.00673967i
$926$	14.0323			0.461130
$927$	1.57293	−	10.0263i	0.0516619	−	0.329306i
$928$	0.932556			0.0306127
$929$	−1.40371	+	15.1485i	−0.0460543	+	0.497005i	0.941200	+	0.337851i	$0.109700\pi$
$929$	−1.40371	+	15.1485i	−0.0460543	+	0.497005i	−0.987254	+	0.159154i	$0.949123\pi$
$930$	5.49979	−	5.01372i	0.180345	−	0.164406i
$931$	−41.0634	−	7.67608i	−1.34580	−	0.251573i
$932$	1.91994	+	3.85576i	0.0628897	+	0.126300i
$933$	14.2905	+	18.9236i	0.467849	+	0.619532i
$934$	−5.98081	−	21.0204i	−0.195698	−	0.687807i
$935$	−0.395336	+	1.38946i	−0.0129289	+	0.0454403i
$936$	0.250619	−	2.70461i	0.00819173	−	0.0884028i
$937$	22.7186	−	8.80122i	0.742183	−	0.287523i	0.0396884	−	0.999212i	$-0.487363\pi$
$937$	22.7186	−	8.80122i	0.742183	−	0.287523i	0.702495	+	0.711689i	$0.252069\pi$
$938$	−0.151554	+	1.63553i	−0.00494843	+	0.0534020i
$939$	−10.8145	+	6.69608i	−0.352919	+	0.218518i
$940$	5.10210	+	17.9320i	0.166412	+	0.584878i
$941$	5.54739	−	1.03699i	0.180840	−	0.0338048i	−0.0925506	−	0.995708i	$-0.529502\pi$
$941$	5.54739	−	1.03699i	0.180840	−	0.0338048i	0.273390	+	0.961903i	$0.411855\pi$
$942$	−17.5037	−	6.78099i	−0.570303	−	0.220937i
$943$	−16.8440	−	6.52540i	−0.548516	−	0.212496i
$944$	6.27328	−	8.30717i	0.204178	−	0.270375i
$945$	2.11311	+	0.395009i	0.0687395	+	0.0128496i
$946$	−2.21337	−	2.01775i	−0.0719627	−	0.0656027i
$947$	−6.27514	−	22.0548i	−0.203915	−	0.716685i	−0.994537	−	0.104382i	$-0.966714\pi$
$947$	−6.27514	−	22.0548i	−0.203915	−	0.716685i	0.790623	−	0.612304i	$-0.209757\pi$
$948$	−2.63783	−	1.63328i	−0.0856729	−	0.0530464i
$949$	−33.1052	−	6.18844i	−1.07464	−	0.200885i
$950$	0.0593551	+	0.640543i	0.00192573	+	0.0207820i
$951$	−8.31861	−	16.7060i	−0.269749	−	0.541730i
$952$	−0.541129	+	0.716570i	−0.0175381	+	0.0232242i
$953$	−35.3201	+	6.60247i	−1.14413	+	0.213875i	−0.721491	−	0.692423i	$-0.756543\pi$
$953$	−35.3201	+	6.60247i	−1.14413	+	0.213875i	−0.422638	+	0.906298i	$0.638896\pi$
$954$	1.34038	+	1.77495i	0.0433965	+	0.0574662i
$955$	0.387963	+	4.18679i	0.0125542	+	0.135481i
$956$	−11.4388	−	22.9722i	−0.369958	−	0.742975i
$957$	−0.292988	+	0.588399i	−0.00947095	+	0.0190202i
$958$	−14.2279	−	5.51194i	−0.459684	−	0.178083i
$959$	−8.32991	+	16.7287i	−0.268987	+	0.540198i
$960$	1.33490	+	1.76770i	0.0430838	+	0.0570521i
$961$	−14.5676	−	13.2801i	−0.469923	−	0.428392i
$962$	4.42937	−	4.03791i	0.142809	−	0.130187i
$963$	−0.421077	+	1.47993i	−0.0135690	+	0.0476902i
$964$	0.0165081	−	0.0102214i	0.000531691	−	0.000329209i
$965$	−24.5464	+	22.3770i	−0.790178	+	0.720342i
$966$	−3.87603	−	2.39993i	−0.124709	−	0.0772166i
$967$	−15.5537	+	2.90750i	−0.500175	+	0.0934989i	−0.427790	−	0.903878i	$-0.640708\pi$
$967$	−15.5537	+	2.90750i	−0.500175	+	0.0934989i	−0.0723844	+	0.997377i	$0.523061\pi$
$968$	−4.68168	+	9.40207i	−0.150475	+	0.302194i
$969$	3.84491	−	5.09149i	0.123516	−	0.163562i
$970$	8.28896	+	5.13231i	0.266143	+	0.164789i
$971$	5.00469	−	17.5896i	0.160608	−	0.564479i	−0.839179	−	0.543855i	$-0.816964\pi$
$971$	5.00469	−	17.5896i	0.160608	−	0.564479i	0.999787	−	0.0206237i	$-0.00656520\pi$
$972$	0.932472	−	0.361242i	0.0299091	−	0.0115868i
$973$	−12.2219			−0.391817
$974$	−14.9993			−0.480609
$975$	−0.236282	+	0.0915360i	−0.00756707	+	0.00293150i
$976$	3.53940	−	2.19151i	0.113294	−	0.0701484i
$977$	−36.1490	−	32.9541i	−1.15651	−	1.05430i	−0.997754	−	0.0669778i	$-0.978664\pi$
$977$	−36.1490	−	32.9541i	−1.15651	−	1.05430i	−0.158753	−	0.987318i	$-0.550747\pi$
$978$	0.289734	+	3.12673i	0.00926469	+	0.0999819i
$979$	0.550123	+	5.93677i	0.0175820	+	0.189740i
$980$	9.91714	+	9.04067i	0.316792	+	0.288794i
$981$	0.285810	−	0.176966i	0.00912522	−	0.00565010i
$982$	22.3362	−	8.65309i	0.712777	−	0.276131i
$983$	−33.9655			−1.08333			−0.541666	−	0.840594i	$-0.682206\pi$
$983$	−33.9655			−1.08333			−0.541666	+	0.840594i	$0.682206\pi$
$984$	−3.84536			−0.122586
$985$	17.0344	−	6.59916i	0.542761	−	0.210267i
$986$	−0.236131	+	0.829913i	−0.00751993	+	0.0264298i
$987$	−6.94469	−	4.29997i	−0.221052	−	0.136869i
$988$	11.2872	−	14.9467i	0.359094	−	0.475517i
$989$	8.89735	−	17.8683i	0.282919	−	0.568179i
$990$	−1.53473	+	0.286890i	−0.0487768	+	0.00911797i
$991$	−10.4920	−	6.49639i	−0.333290	−	0.206365i	0.349576	−	0.936908i	$-0.386326\pi$
$991$	−10.4920	−	6.49639i	−0.333290	−	0.206365i	−0.682866	+	0.730543i	$0.739267\pi$
$992$	−2.48285	+	2.26342i	−0.0788306	+	0.0718636i
$993$	−9.23433	+	5.71766i	−0.293043	+	0.181444i
$994$	0.954752	−	3.35560i	0.0302829	−	0.106433i
$995$	1.06409	−	0.970042i	0.0337338	−	0.0307524i
$996$	−2.72503	−	2.48419i	−0.0863459	−	0.0787147i
$997$	24.4032	+	32.3150i	0.772856	+	1.02343i	0.998785	+	0.0492826i	$0.0156935\pi$
$997$	24.4032	+	32.3150i	0.772856	+	1.02343i	−0.225929	+	0.974144i	$0.572542\pi$
$998$	−11.3131	+	22.7198i	−0.358110	+	0.719182i
$999$	2.05763	+	0.797131i	0.0651006	+	0.0252201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	618.2.i.b.61.1	✓	32
103.76	even	17	inner	618.2.i.b.385.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
618.2.i.b.61.1	✓	32	1.1	even	1	trivial
618.2.i.b.385.1	yes	32	103.76	even	17	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:	\( N \)	\(=\)	\( 618 = 2 \cdot 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	618.i (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0922684 - 0.995734i) q^{2} +(0.739009 - 0.673696i) q^{3} +(-0.982973 - 0.183750i) q^{4} +(-0.987359 - 1.98288i) q^{5} +(-0.602635 - 0.798017i) q^{6} +(-0.265584 - 0.933430i) q^{7} +(-0.273663 + 0.961826i) q^{8} +(0.0922684 - 0.995734i) q^{9} +O(q^{10})\)	\(q+(0.0922684 - 0.995734i) q^{2} +(0.739009 - 0.673696i) q^{3} +(-0.982973 - 0.183750i) q^{4} +(-0.987359 - 1.98288i) q^{5} +(-0.602635 - 0.798017i) q^{6} +(-0.265584 - 0.933430i) q^{7} +(-0.273663 + 0.961826i) q^{8} +(0.0922684 - 0.995734i) q^{9} +(-2.06553 + 0.800190i) q^{10} +(-0.0650350 + 0.701840i) q^{11} +(-0.850217 + 0.526432i) q^{12} +(-0.743321 - 2.61250i) q^{13} +(-0.953953 + 0.178325i) q^{14} +(-2.06553 - 0.800190i) q^{15} +(0.932472 + 0.361242i) q^{16} +(-0.557590 + 0.738369i) q^{17} +(-0.982973 - 0.183750i) q^{18} +(-5.09590 - 4.64553i) q^{19} +(0.606194 + 2.13055i) q^{20} +(-0.825116 - 0.510890i) q^{21} +(0.692845 + 0.129515i) q^{22} +(0.433436 + 4.67751i) q^{23} +(0.445738 + 0.895163i) q^{24} +(0.0562196 - 0.0744468i) q^{25} +(-2.66994 + 0.499099i) q^{26} +(-0.602635 - 0.798017i) q^{27} +(0.0895443 + 0.966337i) q^{28} +(0.415676 + 0.834790i) q^{29} +(-0.987359 + 1.98288i) q^{30} +(-3.13283 - 1.21367i) q^{31} +(0.445738 - 0.895163i) q^{32} +(0.424765 + 0.562479i) q^{33} +(0.683771 + 0.623340i) q^{34} +(-1.58866 + 1.44825i) q^{35} +(-0.273663 + 0.961826i) q^{36} +(-1.87613 + 1.16165i) q^{37} +(-5.09590 + 4.64553i) q^{38} +(-2.30935 - 1.42989i) q^{39} +(2.17739 - 0.407025i) q^{40} +(-1.71403 + 3.44223i) q^{41} +(-0.584843 + 0.774457i) q^{42} +(-3.61276 - 2.23693i) q^{43} +(0.192890 - 0.677939i) q^{44} +(-2.06553 + 0.800190i) q^{45} +4.69755 q^{46} +8.41661 q^{47} +(0.932472 - 0.361242i) q^{48} +(5.15076 - 3.18922i) q^{49} +(-0.0689419 - 0.0628489i) q^{50} +(0.0853717 + 0.921307i) q^{51} +(0.250619 + 2.70461i) q^{52} +(-1.64371 - 1.49844i) q^{53} +(-0.850217 + 0.526432i) q^{54} +(1.45588 - 0.564011i) q^{55} +0.970477 q^{56} -6.89559 q^{57} +(0.869583 - 0.336878i) q^{58} +(2.84877 - 10.0124i) q^{59} +(1.88332 + 1.16610i) q^{60} +(2.50873 - 3.32210i) q^{61} +(-1.49755 + 3.00749i) q^{62} +(-0.953953 + 0.178325i) q^{63} +(-0.850217 - 0.526432i) q^{64} +(-4.44637 + 4.05340i) q^{65} +(0.599272 - 0.371054i) q^{66} +(0.463177 - 1.62790i) q^{67} +(0.683771 - 0.623340i) q^{68} +(3.47153 + 3.16472i) q^{69} +(1.29549 + 1.71551i) q^{70} +(-1.60239 + 3.21804i) q^{71} +(0.932472 + 0.361242i) q^{72} +(5.52680 - 11.0993i) q^{73} +(0.983586 + 1.97531i) q^{74} +(-0.00860769 - 0.0928917i) q^{75} +(4.15552 + 5.50280i) q^{76} +(0.672390 - 0.125692i) q^{77} +(-1.63687 + 2.16757i) q^{78} +(1.38292 + 2.77728i) q^{79} +(-0.204385 - 2.20566i) q^{80} +(-0.982973 - 0.183750i) q^{81} +(3.26939 + 2.02432i) q^{82} +(1.00911 + 3.54665i) q^{83} +(0.717191 + 0.653806i) q^{84} +(2.01464 + 0.376602i) q^{85} +(-2.56073 + 3.39095i) q^{86} +(0.869583 + 0.336878i) q^{87} +(-0.657250 - 0.254620i) q^{88} +(8.31484 - 1.55431i) q^{89} +(0.606194 + 2.13055i) q^{90} +(-2.24117 + 1.38768i) q^{91} +(0.433436 - 4.67751i) q^{92} +(-3.13283 + 1.21367i) q^{93} +(0.776587 - 8.38071i) q^{94} +(-4.18006 + 14.6914i) q^{95} +(-0.273663 - 0.961826i) q^{96} +(-2.65234 - 3.51227i) q^{97} +(-2.70036 - 5.42306i) q^{98} +(0.692845 + 0.129515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9	\( 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9} + q^{10} + 5 q^{11} - 2 q^{12} - 14 q^{13} + 6 q^{14} + q^{15} - 2 q^{16} + 32 q^{17} - 2 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 12 q^{22} - 15 q^{23} - 2 q^{24} - 15 q^{25} - 31 q^{26} - 2 q^{27} + 6 q^{28} + 7 q^{29} + q^{30} + 6 q^{31} - 2 q^{32} + 5 q^{33} - 2 q^{34} + 41 q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} - 14 q^{39} - 16 q^{40} - 5 q^{41} - 11 q^{42} - 3 q^{43} - 12 q^{44} + q^{45} - 66 q^{46} - 14 q^{47} - 2 q^{48} - 6 q^{49} - 15 q^{50} - 2 q^{51} + 20 q^{52} - 6 q^{53} - 2 q^{54} + 11 q^{55} + 6 q^{56} + 14 q^{57} + 24 q^{58} - 43 q^{59} + 18 q^{60} + 48 q^{61} + 6 q^{62} + 6 q^{63} - 2 q^{64} - 84 q^{65} + 5 q^{66} + 7 q^{67} - 2 q^{68} + 19 q^{69} - 10 q^{70} - 59 q^{71} - 2 q^{72} - 9 q^{73} + 21 q^{74} + 19 q^{75} - 3 q^{76} - 33 q^{77} + 20 q^{78} + 33 q^{79} + q^{80} - 2 q^{81} + 46 q^{82} + 71 q^{83} - 11 q^{84} + 42 q^{85} - 20 q^{86} + 24 q^{87} - 12 q^{88} - q^{89} + q^{90} + 50 q^{91} - 15 q^{92} + 6 q^{93} + 20 q^{94} - 5 q^{95} - 2 q^{96} - 61 q^{97} - 57 q^{98} - 12 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9 + q^10 + 5 * q^11 - 2 * q^12 - 14 * q^13 + 6 * q^14 + q^15 - 2 * q^16 + 32 * q^17 - 2 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 12 * q^22 - 15 * q^23 - 2 * q^24 - 15 * q^25 - 31 * q^26 - 2 * q^27 + 6 * q^28 + 7 * q^29 + q^30 + 6 * q^31 - 2 * q^32 + 5 * q^33 - 2 * q^34 + 41 * q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 - 14 * q^39 - 16 * q^40 - 5 * q^41 - 11 * q^42 - 3 * q^43 - 12 * q^44 + q^45 - 66 * q^46 - 14 * q^47 - 2 * q^48 - 6 * q^49 - 15 * q^50 - 2 * q^51 + 20 * q^52 - 6 * q^53 - 2 * q^54 + 11 * q^55 + 6 * q^56 + 14 * q^57 + 24 * q^58 - 43 * q^59 + 18 * q^60 + 48 * q^61 + 6 * q^62 + 6 * q^63 - 2 * q^64 - 84 * q^65 + 5 * q^66 + 7 * q^67 - 2 * q^68 + 19 * q^69 - 10 * q^70 - 59 * q^71 - 2 * q^72 - 9 * q^73 + 21 * q^74 + 19 * q^75 - 3 * q^76 - 33 * q^77 + 20 * q^78 + 33 * q^79 + q^80 - 2 * q^81 + 46 * q^82 + 71 * q^83 - 11 * q^84 + 42 * q^85 - 20 * q^86 + 24 * q^87 - 12 * q^88 - q^89 + q^90 + 50 * q^91 - 15 * q^92 + 6 * q^93 + 20 * q^94 - 5 * q^95 - 2 * q^96 - 61 * q^97 - 57 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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