LMFDB - Embedded newform 600.2.bq.a.67.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(67,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 10, 0, 13]))

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

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

chi := DirichletCharacter("600.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bq (of order $20$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$60$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.11
Character	$\chi$	$=$	600.67
Dual form			600.2.bq.a.403.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21959 + 0.715968i) q^{2} +(-0.156434 + 0.987688i) q^{3} +(0.974780 - 1.74637i) q^{4} +(1.86666 + 1.23110i) q^{5} +(-0.516368 - 1.31657i) q^{6} +(-2.13082 + 2.13082i) q^{7} +(0.0615147 + 2.82776i) q^{8} +(-0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-1.21959 + 0.715968i) q^{2} +(-0.156434 + 0.987688i) q^{3} +(0.974780 - 1.74637i) q^{4} +(1.86666 + 1.23110i) q^{5} +(-0.516368 - 1.31657i) q^{6} +(-2.13082 + 2.13082i) q^{7} +(0.0615147 + 2.82776i) q^{8} +(-0.951057 - 0.309017i) q^{9} +(-3.15797 - 0.164961i) q^{10} +(-0.0873587 - 0.268863i) q^{11} +(1.57238 + 1.23597i) q^{12} +(-2.99402 + 1.52553i) q^{13} +(1.07312 - 4.12432i) q^{14} +(-1.50795 + 1.65109i) q^{15} +(-2.09961 - 3.40465i) q^{16} +(-0.216929 - 1.36963i) q^{17} +(1.38114 - 0.304053i) q^{18} +(-0.0549118 + 0.0755796i) q^{19} +(3.96953 - 2.05982i) q^{20} +(-1.77125 - 2.43792i) q^{21} +(0.299038 + 0.265355i) q^{22} +(-1.84517 + 3.62135i) q^{23} +(-2.80257 - 0.381601i) q^{24} +(1.96881 + 4.59606i) q^{25} +(2.55923 - 4.00413i) q^{26} +(0.453990 - 0.891007i) q^{27} +(1.64412 + 5.79828i) q^{28} +(2.28992 - 1.66373i) q^{29} +(0.656946 - 3.09329i) q^{30} +(-5.56242 + 7.65602i) q^{31} +(4.99827 + 2.64902i) q^{32} +(0.279218 - 0.0442238i) q^{33} +(1.24518 + 1.51507i) q^{34} +(-6.60076 + 1.35427i) q^{35} +(-1.46673 + 1.35967i) q^{36} +(-0.630361 - 1.23715i) q^{37} +(0.0128571 - 0.131491i) q^{38} +(-1.03838 - 3.19580i) q^{39} +(-3.36641 + 5.35418i) q^{40} +(2.92379 - 8.99849i) q^{41} +(3.90567 + 1.70509i) q^{42} +(-5.49497 + 5.49497i) q^{43} +(-0.554689 - 0.109521i) q^{44} +(-1.39487 - 1.74767i) q^{45} +(-0.342426 - 5.73762i) q^{46} +(0.289550 - 1.82814i) q^{47} +(3.69119 - 1.54115i) q^{48} -2.08080i q^{49} +(-5.69176 - 4.19569i) q^{50} +1.38671 q^{51} +(-0.254376 + 6.71571i) q^{52} +(-0.674962 - 0.106904i) q^{53} +(0.0842514 + 1.41170i) q^{54} +(0.167927 - 0.609421i) q^{55} +(-6.15653 - 5.89437i) q^{56} +(-0.0660590 - 0.0660590i) q^{57} +(-1.60158 + 3.66857i) q^{58} +(-2.89245 - 0.939813i) q^{59} +(1.41349 + 4.24288i) q^{60} +(-11.1166 + 3.61199i) q^{61} +(1.30239 - 13.3197i) q^{62} +(2.68499 - 1.36807i) q^{63} +(-7.99243 + 0.347897i) q^{64} +(-7.46687 - 0.838285i) q^{65} +(-0.308868 + 0.253846i) q^{66} +(-2.31795 - 14.6350i) q^{67} +(-2.60334 - 0.956254i) q^{68} +(-3.28811 - 2.38895i) q^{69} +(7.08058 - 6.37757i) q^{70} +(5.56713 + 7.66249i) q^{71} +(0.815321 - 2.70837i) q^{72} +(7.54080 + 3.84223i) q^{73} +(1.65454 + 1.05750i) q^{74} +(-4.84747 + 1.22559i) q^{75} +(0.0784629 + 0.169570i) q^{76} +(0.759044 + 0.386752i) q^{77} +(3.55448 + 3.15411i) q^{78} +(-2.61351 + 1.89883i) q^{79} +(0.272209 - 8.94013i) q^{80} +(0.809017 + 0.587785i) q^{81} +(2.87682 + 13.0678i) q^{82} +(-16.3194 + 2.58475i) q^{83} +(-5.98409 + 0.716823i) q^{84} +(1.28122 - 2.82369i) q^{85} +(2.76737 - 10.6358i) q^{86} +(1.28502 + 2.52199i) q^{87} +(0.754904 - 0.263568i) q^{88} +(5.80221 - 1.88525i) q^{89} +(2.95243 + 1.13275i) q^{90} +(3.12909 - 9.63034i) q^{91} +(4.52557 + 6.75236i) q^{92} +(-6.69161 - 6.69161i) q^{93} +(0.955762 + 2.43689i) q^{94} +(-0.195547 + 0.0734795i) q^{95} +(-3.39830 + 4.52234i) q^{96} +(4.23446 + 0.670672i) q^{97} +(1.48979 + 2.53772i) q^{98} +0.282699i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 12 q^{8}+O(q^{10}) $ 480 * q + 12 * q^8	$ 480 q + 12 q^{8} - 8 q^{10} + 8 q^{12} - 8 q^{17} + 20 q^{20} + 28 q^{22} + 8 q^{25} - 4 q^{28} - 8 q^{30} - 20 q^{32} + 48 q^{35} + 20 q^{38} - 108 q^{40} - 20 q^{42} + 32 q^{43} - 140 q^{44} - 16 q^{48} + 124 q^{50} - 132 q^{52} + 152 q^{58} - 20 q^{60} + 116 q^{62} - 60 q^{64} + 8 q^{65} - 48 q^{67} - 72 q^{68} - 4 q^{70} - 12 q^{72} + 40 q^{73} + 24 q^{78} - 76 q^{80} + 120 q^{81} - 64 q^{82} - 80 q^{83} - 80 q^{84} - 132 q^{88} + 200 q^{89} - 48 q^{90} - 216 q^{92} - 40 q^{94} + 20 q^{96} - 56 q^{97} - 192 q^{98}+O(q^{100}) $ 480 * q + 12 * q^8 - 8 * q^10 + 8 * q^12 - 8 * q^17 + 20 * q^20 + 28 * q^22 + 8 * q^25 - 4 * q^28 - 8 * q^30 - 20 * q^32 + 48 * q^35 + 20 * q^38 - 108 * q^40 - 20 * q^42 + 32 * q^43 - 140 * q^44 - 16 * q^48 + 124 * q^50 - 132 * q^52 + 152 * q^58 - 20 * q^60 + 116 * q^62 - 60 * q^64 + 8 * q^65 - 48 * q^67 - 72 * q^68 - 4 * q^70 - 12 * q^72 + 40 * q^73 + 24 * q^78 - 76 * q^80 + 120 * q^81 - 64 * q^82 - 80 * q^83 - 80 * q^84 - 132 * q^88 + 200 * q^89 - 48 * q^90 - 216 * q^92 - 40 * q^94 + 20 * q^96 - 56 * q^97 - 192 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−1.21959	+	0.715968i	−0.862378	+	0.506266i
$2$	−1.21959	+	0.715968i	−0.862378	+	0.506266i
$3$	−0.156434	+	0.987688i	−0.0903175	+	0.570242i
$3$	−0.156434	+	0.987688i	−0.0903175	+	0.570242i
$4$	0.974780	−	1.74637i	0.487390	−	0.873184i
$5$	1.86666	+	1.23110i	0.834794	+	0.550563i
$5$	1.86666	+	1.23110i	0.834794	+	0.550563i
$6$	−0.516368	−	1.31657i	−0.210806	−	0.537489i
$7$	−2.13082	+	2.13082i	−0.805375	+	0.805375i	−0.983930	−	0.178555i	$-0.942858\pi$
$7$	−2.13082	+	2.13082i	−0.805375	+	0.805375i	0.178555	+	0.983930i	$0.442858\pi$
$8$	0.0615147	+	2.82776i	0.0217487	+	0.999763i
$9$	−0.951057	−	0.309017i	−0.317019	−	0.103006i
$10$	−3.15797	−	0.164961i	−0.998638	−	0.0521654i
$11$	−0.0873587	−	0.268863i	−0.0263397	−	0.0810651i	0.937023	−	0.349269i	$-0.113570\pi$
$11$	−0.0873587	−	0.268863i	−0.0263397	−	0.0810651i	−0.963362	+	0.268204i	$0.913570\pi$
$12$	1.57238	+	1.23597i	0.453907	+	0.356794i
$13$	−2.99402	+	1.52553i	−0.830391	+	0.423105i	−0.816883	−	0.576803i	$-0.804300\pi$
$13$	−2.99402	+	1.52553i	−0.830391	+	0.423105i	−0.0135080	+	0.999909i	$0.504300\pi$
$14$	1.07312	−	4.12432i	0.286804	−	1.10227i
$15$	−1.50795	+	1.65109i	−0.389350	+	0.426309i
$16$	−2.09961	−	3.40465i	−0.524901	−	0.851163i
$17$	−0.216929	−	1.36963i	−0.0526129	−	0.332185i	−0.999929	−	0.0118856i	$-0.996217\pi$
$17$	−0.216929	−	1.36963i	−0.0526129	−	0.332185i	0.947316	−	0.320299i	$-0.103783\pi$
$18$	1.38114	−	0.304053i	0.325538	−	0.0716660i
$19$	−0.0549118	+	0.0755796i	−0.0125976	+	0.0173392i	−0.815269	−	0.579082i	$-0.803411\pi$
$19$	−0.0549118	+	0.0755796i	−0.0125976	+	0.0173392i	0.802672	+	0.596421i	$0.203411\pi$
$20$	3.96953	−	2.05982i	0.887613	−	0.460590i
$21$	−1.77125	−	2.43792i	−0.386519	−	0.531998i
$22$	0.299038	+	0.265355i	0.0637552	+	0.0565739i
$23$	−1.84517	+	3.62135i	−0.384744	+	0.755103i	−0.999433	−	0.0336667i	$-0.989282\pi$
$23$	−1.84517	+	3.62135i	−0.384744	+	0.755103i	0.614689	+	0.788770i	$0.289282\pi$
$24$	−2.80257	−	0.381601i	−0.572072	−	0.0778941i
$25$	1.96881	+	4.59606i	0.393762	+	0.919213i
$26$	2.55923	−	4.00413i	0.501907	−	0.785275i
$27$	0.453990	−	0.891007i	0.0873705	−	0.171474i
$28$	1.64412	+	5.79828i	0.310709	+	1.09577i
$29$	2.28992	−	1.66373i	0.425228	−	0.308946i	−0.354510	−	0.935052i	$-0.615352\pi$
$29$	2.28992	−	1.66373i	0.425228	−	0.308946i	0.779738	+	0.626106i	$0.215352\pi$
$30$	0.656946	−	3.09329i	0.119941	−	0.564754i
$31$	−5.56242	+	7.65602i	−0.999041	+	1.37506i	−0.0731285	+	0.997323i	$0.523298\pi$
$31$	−5.56242	+	7.65602i	−0.999041	+	1.37506i	−0.925912	+	0.377739i	$0.876702\pi$
$32$	4.99827	+	2.64902i	0.883578	+	0.468284i
$33$	0.279218	−	0.0442238i	0.0486057	−	0.00769838i
$34$	1.24518	+	1.51507i	0.213546	+	0.259833i
$35$	−6.60076	+	1.35427i	−1.11573	+	0.228913i
$36$	−1.46673	+	1.35967i	−0.244455	+	0.226612i
$37$	−0.630361	−	1.23715i	−0.103631	−	0.203387i	0.833369	−	0.552717i	$-0.186409\pi$
$37$	−0.630361	−	1.23715i	−0.103631	−	0.203387i	−0.937000	+	0.349331i	$0.886409\pi$
$38$	0.0128571	−	0.131491i	0.00208570	−	0.0213307i
$39$	−1.03838	−	3.19580i	−0.166274	−	0.511738i
$40$	−3.36641	+	5.35418i	−0.532277	+	0.846570i
$41$	2.92379	−	8.99849i	0.456619	−	1.40533i	−0.412605	−	0.910910i	$-0.635381\pi$
$41$	2.92379	−	8.99849i	0.456619	−	1.40533i	0.869224	−	0.494418i	$-0.164619\pi$
$42$	3.90567	+	1.70509i	0.602658	+	0.263102i
$43$	−5.49497	+	5.49497i	−0.837975	+	0.837975i	−0.988592	−	0.150617i	$-0.951874\pi$
$43$	−5.49497	+	5.49497i	−0.837975	+	0.837975i	0.150617	+	0.988592i	$0.451874\pi$
$44$	−0.554689	−	0.109521i	−0.0836225	−	0.0165110i
$45$	−1.39487	−	1.74767i	−0.207934	−	0.260527i
$46$	−0.342426	−	5.73762i	−0.0504879	−	0.845967i
$47$	0.289550	−	1.82814i	0.0422352	−	0.266662i	−0.957530	−	0.288334i	$-0.906899\pi$
$47$	0.289550	−	1.82814i	0.0422352	−	0.266662i	0.999765	+	0.0216714i	$0.00689877\pi$
$48$	3.69119	−	1.54115i	0.532777	−	0.222446i
$49$		−	2.08080i		−	0.297257i
$50$	−5.69176	−	4.19569i	−0.804937	−	0.593360i
$51$	1.38671			0.194178
$52$	−0.254376	+	6.71571i	−0.0352755	+	0.931302i
$53$	−0.674962	−	0.106904i	−0.0927132	−	0.0146843i	0.109905	−	0.993942i	$-0.464945\pi$
$53$	−0.674962	−	0.106904i	−0.0927132	−	0.0146843i	−0.202619	+	0.979258i	$0.564945\pi$
$54$	0.0842514	+	1.41170i	0.0114652	+	0.192108i
$55$	0.167927	−	0.609421i	0.0226432	−	0.0821743i
$56$	−6.15653	−	5.89437i	−0.822700	−	0.787669i
$57$	−0.0660590	−	0.0660590i	−0.00874973	−	0.00874973i
$58$	−1.60158	+	3.66857i	−0.210298	+	0.481706i
$59$	−2.89245	−	0.939813i	−0.376565	−	0.122353i	0.114619	−	0.993410i	$-0.463435\pi$
$59$	−2.89245	−	0.939813i	−0.376565	−	0.122353i	−0.491183	+	0.871056i	$0.663435\pi$
$60$	1.41349	+	4.24288i	0.182481	+	0.547754i
$61$	−11.1166	+	3.61199i	−1.42333	+	0.462468i	−0.916658	−	0.399672i	$-0.869124\pi$
$61$	−11.1166	+	3.61199i	−1.42333	+	0.462468i	−0.506671	+	0.862139i	$0.669124\pi$
$62$	1.30239	−	13.3197i	0.165404	−	1.69160i
$63$	2.68499	−	1.36807i	0.338277	−	0.172361i
$64$	−7.99243	+	0.347897i	−0.999054	+	0.0434872i
$65$	−7.46687	−	0.838285i	−0.926151	−	0.103976i
$66$	−0.308868	+	0.253846i	−0.0380190	+	0.0312463i
$67$	−2.31795	−	14.6350i	−0.283183	−	1.78795i	−0.561519	−	0.827464i	$-0.689783\pi$
$67$	−2.31795	−	14.6350i	−0.283183	−	1.78795i	0.278336	−	0.960484i	$-0.410217\pi$
$68$	−2.60334	−	0.956254i	−0.315701	−	0.115963i
$69$	−3.28811	−	2.38895i	−0.395842	−	0.287596i
$70$	7.08058	−	6.37757i	0.846291	−	0.762266i
$71$	5.56713	+	7.66249i	0.660697	+	0.909371i	0.999504	−	0.0314849i	$-0.0100236\pi$
$71$	5.56713	+	7.66249i	0.660697	+	0.909371i	−0.338808	+	0.940856i	$0.610024\pi$
$72$	0.815321	−	2.70837i	0.0960865	−	0.319184i
$73$	7.54080	+	3.84223i	0.882584	+	0.449699i	0.835690	−	0.549201i	$-0.185068\pi$
$73$	7.54080	+	3.84223i	0.882584	+	0.449699i	0.0468933	+	0.998900i	$0.485068\pi$
$74$	1.65454	+	1.05750i	0.192336	+	0.122931i
$75$	−4.84747	+	1.22559i	−0.559737	+	0.141519i
$76$	0.0784629	+	0.169570i	0.00900032	+	0.0194510i
$77$	0.759044	+	0.386752i	0.0865011	+	0.0440745i
$78$	3.55448	+	3.15411i	0.402466	+	0.357132i
$79$	−2.61351	+	1.89883i	−0.294043	+	0.213635i	−0.725019	−	0.688728i	$-0.758169\pi$
$79$	−2.61351	+	1.89883i	−0.294043	+	0.213635i	0.430976	+	0.902363i	$0.358169\pi$
$80$	0.272209	−	8.94013i	0.0304339	−	0.999537i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	2.87682	+	13.0678i	0.317691	+	1.44309i
$83$	−16.3194	+	2.58475i	−1.79129	+	0.283713i	−0.961589	−	0.274492i	$-0.911490\pi$
$83$	−16.3194	+	2.58475i	−1.79129	+	0.283713i	−0.829703	+	0.558205i	$0.811490\pi$
$84$	−5.98409	+	0.716823i	−0.652918	+	0.0782118i
$85$	1.28122	−	2.82369i	0.138968	−	0.306272i
$86$	2.76737	−	10.6358i	0.298413	−	1.14689i
$87$	1.28502	+	2.52199i	0.137769	+	0.270386i
$88$	0.754904	−	0.263568i	0.0804731	−	0.0280965i
$89$	5.80221	−	1.88525i	0.615033	−	0.199836i	0.0150992	−	0.999886i	$-0.495194\pi$
$89$	5.80221	−	1.88525i	0.615033	−	0.199836i	0.599934	+	0.800050i	$0.295194\pi$
$90$	2.95243	+	1.13275i	0.311214	+	0.119403i
$91$	3.12909	−	9.63034i	0.328018	−	1.00953i
$92$	4.52557	+	6.75236i	0.471823	+	0.703982i
$93$	−6.69161	−	6.69161i	−0.693887	−	0.693887i
$94$	0.955762	+	2.43689i	0.0985793	+	0.251346i
$95$	−0.195547	+	0.0734795i	−0.0200627	+	0.00753884i
$96$	−3.39830	+	4.52234i	−0.346838	+	0.461559i
$97$	4.23446	+	0.670672i	0.429944	+	0.0680965i	0.367656	−	0.929962i	$-0.380160\pi$
$97$	4.23446	+	0.670672i	0.429944	+	0.0680965i	0.0622879	+	0.998058i	$0.480160\pi$
$98$	1.48979	+	2.53772i	0.150491	+	0.256348i
$99$			0.282699i			0.0284123i
$100$	9.94558	+	1.04189i	0.994558	+	0.104189i
$101$		−	1.64913i		−	0.164095i	−0.996628	−	0.0820474i	$-0.973854\pi$
$101$		−	1.64913i		−	0.164095i	0.996628	−	0.0820474i	$-0.0261459\pi$
$102$	−1.69121	+	0.992836i	−0.167454	+	0.0983054i
$103$	12.5396	+	1.98607i	1.23556	+	0.195693i	0.739836	−	0.672787i	$-0.234903\pi$
$103$	12.5396	+	1.98607i	1.23556	+	0.195693i	0.495723	+	0.868481i	$0.334903\pi$
$104$	−4.49800	−	8.37251i	−0.441065	−	0.820993i
$105$	−0.305007	−	6.73134i	−0.0297657	−	0.656912i
$106$	0.899714	−	0.352873i	0.0873880	−	0.0342741i
$107$	9.25644	+	9.25644i	0.894854	+	0.894854i	0.994975	−	0.100121i	$-0.0319230\pi$
$107$	9.25644	+	9.25644i	0.894854	+	0.894854i	−0.100121	+	0.994975i	$0.531923\pi$
$108$	−1.11348	−	1.66137i	−0.107145	−	0.159865i
$109$	−4.61422	+	14.2011i	−0.441962	+	1.36022i	0.443819	+	0.896117i	$0.353623\pi$
$109$	−4.61422	+	14.2011i	−0.441962	+	1.36022i	−0.885781	+	0.464103i	$0.846377\pi$
$110$	0.231525	+	0.863471i	0.0220750	+	0.0823288i
$111$	1.32053	−	0.429067i	0.125339	−	0.0407252i
$112$	11.7286	+	2.78082i	1.10825	+	0.262763i
$113$	6.57508	+	12.9043i	0.618532	+	1.21394i	0.961556	+	0.274610i	$0.0885488\pi$
$113$	6.57508	+	12.9043i	0.618532	+	1.21394i	−0.343024	+	0.939327i	$0.611451\pi$
$114$	0.127861	+	0.0332685i	0.0119753	+	0.00311588i
$115$	−7.90252	+	4.48823i	−0.736913	+	0.418530i
$116$	−0.673307	−	5.62081i	−0.0625150	−	0.521880i
$117$	3.31889	−	0.525661i	0.306832	−	0.0485974i
$118$	4.20046	−	0.924716i	0.386684	−	0.0851270i
$119$	3.38068	+	2.45621i	0.309906	+	0.225160i
$120$	−4.76164	−	4.16255i	−0.434676	−	0.379987i
$121$	8.83453	−	6.41866i	0.803139	−	0.583515i
$122$	10.9715	−	12.3642i	0.993316	−	1.11940i
$123$	8.43032	+	4.29546i	0.760137	+	0.387309i
$124$	7.94809	+	17.1770i	0.713759	+	1.54254i
$125$	−1.98310	+	11.0031i	−0.177374	+	0.984143i
$126$	−2.29508	+	3.59085i	−0.204462	+	0.319898i
$127$	−4.17261	−	2.12605i	−0.370259	−	0.188656i	0.258953	−	0.965890i	$-0.416622\pi$
$127$	−4.17261	−	2.12605i	−0.370259	−	0.188656i	−0.629212	+	0.777233i	$0.716622\pi$
$128$	9.49838	−	6.14661i	0.839546	−	0.543289i
$129$	−4.56772	−	6.28692i	−0.402165	−	0.553532i
$130$	9.70668	−	4.32368i	0.851332	−	0.379212i
$131$	13.9354	+	10.1246i	1.21754	+	0.884594i	0.995893	−	0.0905335i	$-0.0288572\pi$
$131$	13.9354	+	10.1246i	1.21754	+	0.884594i	0.221646	+	0.975127i	$0.428857\pi$
$132$	0.194945	−	0.530727i	0.0169678	−	0.0461938i
$133$	−0.0440394	−	0.278054i	−0.00381870	−	0.0241103i
$134$	13.3051	+	16.1890i	1.14939	+	1.39852i
$135$	1.94436	−	1.10430i	0.167344	−	0.0950428i
$136$	3.85965	−	0.697674i	0.330962	−	0.0598250i
$137$	1.13994	−	0.580827i	0.0973914	−	0.0496234i	−0.404616	−	0.914487i	$-0.632595\pi$
$137$	1.13994	−	0.580827i	0.0973914	−	0.0496234i	0.502008	+	0.864863i	$0.332595\pi$
$138$	5.72055	+	0.559352i	0.486966	+	0.0476152i
$139$	−6.67343	+	2.16833i	−0.566033	+	0.183915i	−0.578034	−	0.816013i	$-0.696180\pi$
$139$	−6.67343	+	2.16833i	−0.566033	+	0.183915i	0.0120011	+	0.999928i	$0.496180\pi$
$140$	−4.06924	+	12.8475i	−0.343914	+	1.08581i
$141$	1.76034	+	0.571970i	0.148247	+	0.0481685i
$142$	−12.2757	−	5.35919i	−1.03015	−	0.449733i
$143$	0.671711	+	0.671711i	0.0561713	+	0.0561713i
$144$	0.944749	+	3.88683i	0.0787291	+	0.323903i
$145$	6.32270	−	0.286491i	0.525072	−	0.0237918i
$146$	−11.9476	+	0.713039i	−0.988787	+	0.0590115i
$147$	2.05518	+	0.325509i	0.169509	+	0.0268475i
$148$	−2.77499	−	0.105110i	−0.228103	−	0.00863999i
$149$	9.66403			0.791708			0.395854	−	0.918313i	$-0.370449\pi$
$149$	9.66403			0.791708			0.395854	+	0.918313i	$0.370449\pi$
$150$	5.03442	−	4.96534i	0.411059	−	0.405418i
$151$			7.38361i			0.600869i	0.953802	+	0.300435i	$0.0971318\pi$
$151$			7.38361i			0.600869i	−0.953802	+	0.300435i	$0.902868\pi$
$152$	−0.217099	−	0.150628i	−0.0176090	−	0.0122176i
$153$	−0.216929	+	1.36963i	−0.0175376	+	0.110728i
$154$	−1.20262	+	0.0717733i	−0.0969100	+	0.00578366i
$155$	−19.8084	+	7.44328i	−1.59105	+	0.597859i
$156$	−6.59324	−	1.30181i	−0.527881	−	0.104228i
$157$	10.7431	−	10.7431i	0.857392	−	0.857392i	−0.133638	−	0.991030i	$-0.542666\pi$
$157$	10.7431	−	10.7431i	0.857392	−	0.857392i	0.991030	+	0.133638i	$0.0426660\pi$
$158$	1.82790	−	4.18698i	0.145420	−	0.333098i
$159$	0.211175	−	0.649929i	0.0167472	−	0.0515427i
$160$	6.06886	+	11.0981i	0.479786	+	0.877386i
$161$	−3.78472	−	11.6482i	−0.298278	−	0.918004i
$162$	−1.40750	−	0.137625i	−0.110584	−	0.0108128i
$163$	−2.37169	−	4.65471i	−0.185765	−	0.364585i	0.779277	−	0.626680i	$-0.215587\pi$
$163$	−2.37169	−	4.65471i	−0.185765	−	0.364585i	−0.965042	+	0.262095i	$0.915587\pi$
$164$	−12.8646	−	13.8776i	−1.00456	−	1.08366i
$165$	0.575648	+	0.261194i	0.0448142	+	0.0203339i
$166$	18.0524	−	14.8365i	1.40114	−	1.15154i
$167$	23.4952	−	3.72127i	1.81811	−	0.287961i	0.847889	−	0.530174i	$-0.177873\pi$
$167$	23.4952	−	3.72127i	1.81811	−	0.287961i	0.970223	+	0.242213i	$0.0778732\pi$
$168$	6.78489	−	5.15865i	0.523466	−	0.397998i
$169$	−1.00431	+	1.38231i	−0.0772542	+	0.106331i
$170$	0.459118	+	4.36105i	0.0352127	+	0.334477i
$171$	0.0755796	−	0.0549118i	0.00577972	−	0.00419921i
$172$	4.23985	+	14.9526i	0.323286	+	1.14013i
$173$	−7.29157	+	14.3105i	−0.554368	+	1.08801i	0.428473	+	0.903554i	$0.359052\pi$
$173$	−7.29157	+	14.3105i	−0.554368	+	1.08801i	−0.982841	+	0.184454i	$0.940948\pi$
$174$	−3.37286	−	2.15576i	−0.255696	−	0.163427i
$175$	−13.9886	−	5.59821i	−1.05744	−	0.423185i
$176$	−0.731965	+	0.861932i	−0.0551739	+	0.0649705i
$177$	1.38072	−	2.70982i	0.103781	−	0.203682i
$178$	−5.72651	+	6.45342i	−0.429220	+	0.483704i
$179$	2.17494	+	2.99355i	0.162563	+	0.223748i	0.882526	−	0.470264i	$-0.155841\pi$
$179$	2.17494	+	2.99355i	0.162563	+	0.223748i	−0.719963	+	0.694012i	$0.755841\pi$
$180$	−4.41176	+	0.732356i	−0.328833	+	0.0545866i
$181$	14.1867	−	19.5263i	1.05449	−	1.45138i	0.169633	−	0.985507i	$-0.445742\pi$
$181$	14.1867	−	19.5263i	1.05449	−	1.45138i	0.884853	−	0.465869i	$-0.154258\pi$
$182$	3.07882	+	13.9854i	0.228218	+	1.03666i
$183$	−1.82851	−	11.5447i	−0.135167	−	0.853411i
$184$	−10.3538	−	4.99492i	−0.763292	−	0.368231i
$185$	0.346386	−	3.08537i	0.0254668	−	0.226841i
$186$	12.9520	+	3.37002i	0.949684	+	0.247102i
$187$	−0.349292	+	0.177973i	−0.0255428	+	0.0130147i
$188$	−2.91037	−	2.28770i	−0.212260	−	0.166848i
$189$	0.931203	+	2.86595i	0.0677351	+	0.208467i
$190$	0.185878	−	0.229620i	0.0134850	−	0.0166584i
$191$	11.7919	+	3.83142i	0.853232	+	0.277232i	0.702799	−	0.711388i	$-0.251933\pi$
$191$	11.7919	+	3.83142i	0.853232	+	0.277232i	0.150433	+	0.988620i	$0.451933\pi$
$192$	0.906678	−	7.94845i	0.0654338	−	0.573630i
$193$	−12.4507	+	12.4507i	−0.896217	+	0.896217i	−0.995099	−	0.0988817i	$-0.968473\pi$
$193$	−12.4507	+	12.4507i	−0.896217	+	0.896217i	0.0988817	+	0.995099i	$0.468473\pi$
$194$	−5.64447	+	2.21379i	−0.405249	+	0.158941i
$195$	1.99604	−	7.24380i	0.142939	−	0.518740i
$196$	−3.63385	−	2.02833i	−0.259560	−	0.144880i
$197$	2.04993	−	12.9427i	0.146051	−	0.922133i	−0.800442	−	0.599410i	$-0.795402\pi$
$197$	2.04993	−	12.9427i	0.146051	−	0.922133i	0.946494	−	0.322723i	$-0.104598\pi$
$198$	−0.202403	−	0.344776i	−0.0143842	−	0.0245021i
$199$	0.793485			0.0562487			0.0281243	−	0.999604i	$-0.491047\pi$
$199$	0.793485			0.0562487			0.0281243	+	0.999604i	$0.491047\pi$
$200$	−12.8754	+	5.85004i	−0.910431	+	0.413660i
$201$	14.8174			1.04514
$202$	1.18073	+	2.01126i	0.0830755	+	0.141512i
$203$	−1.33431	+	8.42452i	−0.0936504	+	0.591285i
$204$	1.35173	−	2.42170i	0.0946403	−	0.169553i
$205$	16.5357	−	13.1976i	1.15490	−	0.921762i
$206$	−16.7150	+	6.55573i	−1.16459	+	0.456759i
$207$	2.87392	−	2.87392i	0.199751	−	0.199751i
$208$	11.4801	+	6.99058i	0.796005	+	0.484709i
$209$	0.0251176	+	0.00816119i	0.00173742	+	0.000564521i
$210$	5.19141	+	7.99108i	0.358241	+	0.551437i
$211$	0.737794	+	2.27070i	0.0507919	+	0.156321i	0.973235	−	0.229811i	$-0.0738108\pi$
$211$	0.737794	+	2.27070i	0.0507919	+	0.156321i	−0.922443	+	0.386132i	$0.873811\pi$
$212$	−0.844633	+	1.07453i	−0.0580096	+	0.0737987i
$213$	−8.43905	+	4.29991i	−0.578234	+	0.294625i
$214$	−17.9163	−	4.66172i	−1.22474	−	0.318668i
$215$	−17.0220	+	3.49239i	−1.16089	+	0.238179i
$216$	2.54748	+	1.22897i	0.173334	+	0.0836205i
$217$	−4.46108	−	28.1661i	−0.302838	−	1.91204i
$218$	−4.54010	−	20.6231i	−0.307494	−	1.39677i
$219$	−4.97456	+	6.84690i	−0.336150	+	0.462671i
$220$	−0.900582	−	0.887314i	−0.0607172	−	0.0598227i
$221$	2.73890	+	3.76977i	0.184238	+	0.253582i
$222$	−1.30330	+	1.46874i	−0.0874720	+	0.0985755i
$223$	−3.18349	+	6.24794i	−0.213182	+	0.418393i	−0.972691	−	0.232103i	$-0.925439\pi$
$223$	−3.18349	+	6.24794i	−0.213182	+	0.418393i	0.759509	+	0.650497i	$0.225439\pi$
$224$	−16.2950	+	5.00584i	−1.08876	+	0.334467i
$225$	−0.452187	−	4.97951i	−0.0301458	−	0.331967i
$226$	−17.2580	−	11.0304i	−1.14798	−	0.733731i
$227$	−1.04374	+	2.04845i	−0.0692754	+	0.135961i	−0.923047	−	0.384687i	$-0.874309\pi$
$227$	−1.04374	+	2.04845i	−0.0692754	+	0.135961i	0.853772	+	0.520648i	$0.174309\pi$
$228$	−0.179756	+	0.0509704i	−0.0119047	+	0.00337559i
$229$	6.71009	−	4.87517i	0.443415	−	0.322160i	−0.343575	−	0.939125i	$-0.611638\pi$
$229$	6.71009	−	4.87517i	0.443415	−	0.322160i	0.786991	+	0.616965i	$0.211638\pi$
$230$	6.42437	−	11.1317i	0.423611	−	0.734004i
$231$	−0.500731	+	0.689198i	−0.0329457	+	0.0453459i
$232$	4.84548	+	6.37300i	0.318121	+	0.418408i
$233$	−2.30467	+	0.365023i	−0.150984	+	0.0239135i	−0.231469	−	0.972842i	$-0.574353\pi$
$233$	−2.30467	+	0.365023i	−0.150984	+	0.0239135i	0.0804850	+	0.996756i	$0.474353\pi$
$234$	−3.67132	+	3.01731i	−0.240002	+	0.197248i
$235$	2.79111	−	3.05605i	0.182072	−	0.199355i
$236$	−4.46076	+	4.13517i	−0.290371	+	0.269177i
$237$	−1.46661	−	2.87838i	−0.0952664	−	0.186971i
$238$	−5.88159	−	0.575099i	−0.381247	−	0.0372781i
$239$	−0.820128	−	2.52409i	−0.0530497	−	0.163270i	0.921022	−	0.389512i	$-0.127356\pi$
$239$	−0.820128	−	2.52409i	−0.0530497	−	0.163270i	−0.974071	+	0.226241i	$0.927356\pi$
$240$	8.78748	+	1.66740i	0.567229	+	0.107630i
$241$	−7.98863	+	24.5865i	−0.514593	+	1.58375i	0.269428	+	0.963021i	$0.413165\pi$
$241$	−7.98863	+	24.5865i	−0.514593	+	1.58375i	−0.784021	+	0.620734i	$0.786835\pi$
$242$	−6.17892	+	14.1534i	−0.397196	+	0.909812i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−4.52834	+	22.9345i	−0.289897	+	1.46823i
$245$	2.56167	−	3.88414i	0.163659	−	0.248149i
$246$	−13.3569	+	0.797151i	−0.851606	+	0.0508245i
$247$	0.0491081	−	0.310056i	0.00312467	−	0.0197284i
$248$	−21.9915	−	15.2582i	−1.39646	−	0.968898i
$249$		−	16.5229i		−	1.04709i
$250$	−5.45927	−	14.8390i	−0.345274	−	0.938502i
$251$	28.6590			1.80894			0.904471	−	0.426535i	$-0.140266\pi$
$251$	28.6590			1.80894			0.904471	+	0.426535i	$0.140266\pi$
$252$	0.228120	−	6.02255i	0.0143702	−	0.379385i
$253$	1.13484	+	0.179740i	0.0713465	+	0.0113002i
$254$	6.61104	−	0.394551i	0.414813	−	0.0247564i
$255$	2.58850	+	1.70717i	0.162098	+	0.106907i
$256$	−7.18331	+	14.2969i	−0.448957	+	0.893553i
$257$	12.1532	+	12.1532i	0.758095	+	0.758095i	0.975975	−	0.217881i	$-0.0699144\pi$
$257$	12.1532	+	12.1532i	0.758095	+	0.758095i	−0.217881	+	0.975975i	$0.569914\pi$
$258$	10.0720	+	4.39710i	0.627052	+	0.273752i
$259$	3.97934	+	1.29297i	0.247264	+	0.0803409i
$260$	−8.74251	+	12.2228i	−0.542188	+	0.758024i
$261$	−2.69196	+	0.874672i	−0.166628	+	0.0541409i
$262$	−24.2443	−	2.37059i	−1.49782	−	0.146456i
$263$	16.9128	−	8.61750i	1.04289	−	0.531378i	0.153318	−	0.988177i	$-0.451004\pi$
$263$	16.9128	−	8.61750i	1.04289	−	0.531378i	0.889570	+	0.456799i	$0.151004\pi$
$264$	0.142230	+	0.786841i	0.00875367	+	0.0484267i
$265$	−1.12831	−	1.03050i	−0.0693118	−	0.0633028i
$266$	0.252788	+	0.307580i	0.0154994	+	0.0188589i
$267$	0.954376	+	6.02569i	0.0584069	+	0.368766i
$268$	−27.8176	−	10.2179i	−1.69923	−	0.624157i
$269$	2.54733	+	1.85075i	0.155314	+	0.112842i	0.662728	−	0.748860i	$-0.269399\pi$
$269$	2.54733	+	1.85075i	0.155314	+	0.112842i	−0.507414	+	0.861702i	$0.669399\pi$
$270$	−1.58067	+	2.73888i	−0.0961966	+	0.166683i
$271$	−9.04482	−	12.4491i	−0.549434	−	0.756231i	0.440502	−	0.897752i	$-0.354801\pi$
$271$	−9.04482	−	12.4491i	−0.549434	−	0.756231i	−0.989935	+	0.141521i	$0.954801\pi$
$272$	−4.20766	+	3.61426i	−0.255127	+	0.219146i
$273$	9.02228	+	4.59708i	0.546053	+	0.278228i
$274$	−0.974398	+	1.52453i	−0.0588655	+	0.0921000i
$275$	1.06372	−	0.930845i	0.0641445	−	0.0561321i
$276$	−7.37718	+	3.41355i	−0.444054	+	0.205472i
$277$	−9.22022	−	4.69794i	−0.553989	−	0.282272i	0.154500	−	0.987993i	$-0.450623\pi$
$277$	−9.22022	−	4.69794i	−0.553989	−	0.282272i	−0.708490	+	0.705721i	$0.750623\pi$
$278$	6.58637	−	7.42242i	0.395024	−	0.445167i
$279$	7.65602	−	5.56242i	0.458354	−	0.333014i
$280$	−4.23558	−	18.5820i	−0.253124	−	1.11049i
$281$	−2.89362	−	2.10234i	−0.172619	−	0.125415i	0.498121	−	0.867107i	$-0.334023\pi$
$281$	−2.89362	−	2.10234i	−0.172619	−	0.125415i	−0.670740	+	0.741692i	$0.734023\pi$
$282$	−2.55640	+	0.562781i	−0.152231	+	0.0335131i
$283$	20.7906	−	3.29291i	1.23588	−	0.195743i	0.495901	−	0.868379i	$-0.334838\pi$
$283$	20.7906	−	3.29291i	1.23588	−	0.195743i	0.739974	+	0.672636i	$0.234838\pi$
$284$	18.8083	−	2.25301i	1.11607	−	0.133691i
$285$	−0.0419845	−	0.204634i	−0.00248695	−	0.0121215i
$286$	−1.30013	−	0.338286i	−0.0768785	−	0.0200033i
$287$	12.9441	+	25.4042i	0.764067	+	1.49957i
$288$	−3.93505	−	4.06391i	−0.231875	−	0.239468i
$289$	14.3391	−	4.65906i	0.843478	−	0.274063i
$290$	−7.50596	+	4.87625i	−0.440765	+	0.286343i
$291$	−1.32483	+	4.07741i	−0.0776629	+	0.239022i
$292$	14.0606	−	9.42368i	0.822832	−	0.551479i
$293$	−16.4570	−	16.4570i	−0.961431	−	0.961431i	0.0378525	−	0.999283i	$-0.487948\pi$
$293$	−16.4570	−	16.4570i	−0.961431	−	0.961431i	−0.999283	+	0.0378525i	$0.987948\pi$
$294$	−2.73953	+	1.07446i	−0.159772	+	0.0626637i
$295$	−4.24220	−	5.31519i	−0.246991	−	0.309462i
$296$	3.45959	−	1.85861i	0.201085	−	0.108030i
$297$	−0.279218	−	0.0442238i	−0.0162019	−	0.00256613i
$298$	−11.7861	+	6.91913i	−0.682752	+	0.400815i
$299$		−	13.6572i		−	0.789818i
$300$	−2.58489	+	9.66014i	−0.149239	+	0.557729i
$301$		−	23.4176i		−	1.34977i
$302$	−5.28642	−	9.00494i	−0.304200	−	0.518176i
$303$	1.62883	+	0.257981i	0.0935738	+	0.0148206i
$304$	0.372616	+	0.0282682i	0.0213710	+	0.00162129i
$305$	−25.1975	−	6.94320i	−1.44280	−	0.397567i
$306$	−0.716050	−	1.82570i	−0.0409338	−	0.104368i
$307$	−20.6531	−	20.6531i	−1.17873	−	1.17873i	−0.980068	−	0.198664i	$-0.936340\pi$
$307$	−20.6531	−	20.6531i	−1.17873	−	1.17873i	−0.198664	−	0.980068i	$-0.563660\pi$
$308$	1.41531	−	0.948572i	0.0806450	−	0.0540499i
$309$	−3.92324	+	12.0745i	−0.223185	+	0.686893i
$310$	18.8289	−	23.2599i	1.06941	−	1.32107i
$311$	−18.3590	+	5.96519i	−1.04104	+	0.338255i	−0.779147	−	0.626841i	$-0.784347\pi$
$311$	−18.3590	+	5.96519i	−1.04104	+	0.338255i	−0.261895	+	0.965096i	$0.584347\pi$
$312$	8.97308	−	3.13287i	0.508000	−	0.177364i
$313$	13.9124	+	27.3046i	0.786375	+	1.54335i	0.838622	+	0.544714i	$0.183362\pi$
$313$	13.9124	+	27.3046i	0.786375	+	1.54335i	−0.0522469	+	0.998634i	$0.516638\pi$
$314$	−5.41042	+	20.7938i	−0.305328	+	1.17346i
$315$	6.69618	+	0.751762i	0.377287	+	0.0423570i
$316$	0.768453	+	6.41510i	0.0432288	+	0.360877i
$317$	−24.5629	+	3.89038i	−1.37959	+	0.218506i	−0.801758	−	0.597649i	$-0.796102\pi$
$317$	−24.5629	+	3.89038i	−1.37959	+	0.218506i	−0.577833	+	0.816155i	$0.696102\pi$
$318$	0.207782	+	0.943839i	0.0116519	+	0.0529278i
$319$	−0.647358	−	0.470333i	−0.0362451	−	0.0263336i
$320$	−15.3474	−	9.19004i	−0.857947	−	0.513739i
$321$	−10.5905	+	7.69446i	−0.591105	+	0.429463i
$322$	12.9555	+	11.4962i	0.721982	+	0.640659i
$323$	0.115428	+	0.0588137i	0.00642260	+	0.00327248i
$324$	1.81510	−	0.839880i	0.100839	−	0.0466600i
$325$	−12.9061	−	10.7572i	−0.715900	−	0.596703i
$326$	6.22511	+	3.97877i	0.344777	+	0.220363i
$327$	−13.3045	−	6.77896i	−0.735738	−	0.374877i
$328$	25.6254	+	7.71422i	1.41493	+	0.425947i
$329$	3.27847	+	4.51243i	0.180748	+	0.248778i
$330$	−0.889059	+	0.0935974i	−0.0489411	+	0.00515237i
$331$	5.36622	+	3.89879i	0.294954	+	0.214297i	0.725414	−	0.688313i	$-0.241648\pi$
$331$	5.36622	+	3.89879i	0.294954	+	0.214297i	−0.430459	+	0.902610i	$0.641648\pi$
$332$	−11.3940	+	31.0193i	−0.625325	+	1.70241i
$333$	0.217207	+	1.37139i	0.0119029	+	0.0751519i
$334$	−25.9901	+	21.3602i	−1.42211	+	1.16878i
$335$	13.6902	−	30.1721i	0.747978	−	1.64848i
$336$	−4.58134	+	11.1492i	−0.249933	+	0.608237i
$337$	−27.0765	+	13.7961i	−1.47495	+	0.751524i	−0.992249	−	0.124262i	$-0.960344\pi$
$337$	−27.0765	+	13.7961i	−1.47495	+	0.751524i	−0.482699	+	0.875786i	$0.660344\pi$
$338$	0.235149	−	2.40489i	0.0127904	−	0.130809i
$339$	−13.7740	+	4.47545i	−0.748102	+	0.243073i
$340$	−3.68230	−	4.98996i	−0.199701	−	0.270619i
$341$	2.54434	+	0.826707i	0.137784	+	0.0447687i
$342$	−0.0528608	+	0.121082i	−0.00285838	+	0.00654738i
$343$	−10.4819	−	10.4819i	−0.565971	−	0.565971i
$344$	−15.8765	−	15.2004i	−0.856002	−	0.819552i
$345$	−3.19675	−	8.50734i	−0.172107	−	0.458020i
$346$	−1.35317	−	22.6734i	−0.0727467	−	1.21893i
$347$	−12.3965	−	1.96342i	−0.665480	−	0.105402i	−0.185450	−	0.982654i	$-0.559374\pi$
$347$	−12.3965	−	1.96342i	−0.665480	−	0.105402i	−0.480030	+	0.877252i	$0.659374\pi$
$348$	5.65694	+	0.214272i	0.303244	+	0.0114862i
$349$	16.1106			0.862380			0.431190	−	0.902261i	$-0.358094\pi$
$349$	16.1106			0.862380			0.431190	+	0.902261i	$0.358094\pi$
$350$	21.0684	−	3.18786i	1.12615	−	0.170399i
$351$			3.36026i			0.179358i
$352$	0.275579	−	1.57526i	0.0146884	−	0.0839618i
$353$	0.0487602	−	0.307859i	0.00259524	−	0.0163857i	−0.986357	−	0.164622i	$-0.947360\pi$
$353$	0.0487602	−	0.307859i	0.00259524	−	0.0163857i	0.988952	+	0.148236i	$0.0473596\pi$
$354$	0.256234	+	4.29341i	0.0136187	+	0.228192i
$355$	0.958651	+	21.1569i	0.0508799	+	1.12289i
$356$	2.36354	−	11.9705i	0.125267	−	0.634435i
$357$	−2.95482	+	2.95482i	−0.156386	+	0.156386i
$358$	−4.79581	−	2.09370i	−0.253467	−	0.110656i
$359$	−3.85088	+	11.8518i	−0.203242	+	0.625514i	0.796539	+	0.604587i	$0.206662\pi$
$359$	−3.85088	+	11.8518i	−0.203242	+	0.625514i	−0.999781	+	0.0209270i	$0.993338\pi$
$360$	4.85618	−	4.05185i	0.255943	−	0.213551i
$361$	5.86863	+	18.0618i	0.308875	+	0.950620i
$362$	−3.32168	+	33.9712i	−0.174584	+	1.78549i
$363$	4.95761	+	9.72986i	0.260207	+	0.510685i
$364$	−13.7680	−	14.8520i	−0.721637	−	0.778457i
$365$	9.34592	+	16.4556i	0.489188	+	0.861323i
$366$	10.4957	+	12.7706i	0.548618	+	0.667532i
$367$	−0.0371810	+	0.00588889i	−0.00194083	+	0.000307397i	−0.157405	−	0.987534i	$-0.550313\pi$
$367$	−0.0371810	+	0.00588889i	−0.00194083	+	0.000307397i	0.155464	+	0.987842i	$0.450313\pi$
$368$	16.2035	−	1.32125i	0.844668	−	0.0688747i
$369$	−5.56137	+	7.65457i	−0.289513	+	0.398481i
$370$	1.78658	+	4.01088i	0.0928798	+	0.208516i
$371$	1.66602	−	1.21043i	0.0864953	−	0.0628425i
$372$	−18.2089	+	5.16316i	−0.944085	+	0.267698i
$373$	−10.7737	+	21.1446i	−0.557843	+	1.09483i	0.424094	+	0.905618i	$0.360593\pi$
$373$	−10.7737	+	21.1446i	−0.557843	+	1.09483i	−0.981937	+	0.189210i	$0.939407\pi$
$374$	0.298569	−	0.467136i	0.0154386	−	0.0241550i
$375$	−10.5574	−	3.67995i	−0.545180	−	0.190032i
$376$	5.18736	+	0.706319i	0.267518	+	0.0364256i
$377$	−4.31801	+	8.47456i	−0.222389	+	0.436462i
$378$	−3.18761	−	2.82856i	−0.163953	−	0.145485i
$379$	3.25104	+	4.47467i	0.166995	+	0.229848i	0.884310	−	0.466900i	$-0.154629\pi$
$379$	3.25104	+	4.47467i	0.166995	+	0.229848i	−0.717315	+	0.696749i	$0.754629\pi$
$380$	−0.0622933	+	0.413124i	−0.00319558	+	0.0211928i
$381$	2.75261	−	3.78865i	0.141021	−	0.194098i
$382$	−17.1244	+	3.76987i	−0.876161	+	0.192884i
$383$	−3.34339	−	21.1093i	−0.170839	−	1.07864i	−0.912864	−	0.408263i	$-0.866135\pi$
$383$	−3.34339	−	21.1093i	−0.170839	−	1.07864i	0.742025	−	0.670372i	$-0.233865\pi$
$384$	4.58507	+	10.3430i	0.233981	+	0.527813i
$385$	0.940745	+	1.65639i	0.0479448	+	0.0844174i
$386$	6.27038	−	24.0989i	0.319154	−	1.22660i
$387$	6.92407	−	3.52799i	0.351970	−	0.179338i
$388$	5.29891	−	6.74117i	0.269011	−	0.342231i
$389$	−4.14873	−	12.7685i	−0.210349	−	0.647387i	−0.999451	−	0.0331256i	$-0.989454\pi$
$389$	−4.14873	−	12.7685i	−0.210349	−	0.647387i	0.789102	−	0.614262i	$-0.210546\pi$
$390$	2.75199	+	10.2635i	0.139352	+	0.519715i
$391$	5.36018	+	1.74163i	0.271076	+	0.0880780i
$392$	5.88400	−	0.128000i	0.297187	−	0.00646497i
$393$	−12.1800	+	12.1800i	−0.614398	+	0.614398i
$394$	6.76652	+	17.2525i	0.340893	+	0.869167i
$395$	−7.21617	+	0.326975i	−0.363085	+	0.0164519i
$396$	0.493696	+	0.275569i	0.0248092	+	0.0138479i
$397$	0.543516	−	3.43163i	0.0272783	−	0.172228i	−0.970288	−	0.241953i	$-0.922212\pi$
$397$	0.543516	−	3.43163i	0.0272783	−	0.172228i	0.997566	+	0.0697245i	$0.0222120\pi$
$398$	−0.967724	+	0.568110i	−0.0485076	+	0.0284768i
$399$	0.281520			0.0140936
$400$	11.5143	−	16.3530i	0.575714	−	0.817651i
$401$	−15.6586			−0.781955			−0.390978	−	0.920400i	$-0.627863\pi$
$401$	−15.6586			−0.781955			−0.390978	+	0.920400i	$0.627863\pi$
$402$	−18.0711	+	10.6088i	−0.901305	+	0.529118i
$403$	4.97452	−	31.4079i	0.247798	−	1.56454i
$404$	−2.87999	−	1.60754i	−0.143285	−	0.0799782i
$405$	0.786537	+	2.09317i	0.0390833	+	0.104010i
$406$	−4.40437	−	11.2297i	−0.218585	−	0.557323i
$407$	−0.277556	+	0.277556i	−0.0137580	+	0.0137580i
$408$	0.0853028	+	3.92127i	0.00422312	+	0.194132i
$409$	34.6398	+	11.2552i	1.71283	+	0.556532i	0.990800	−	0.135333i	$-0.0432103\pi$
$409$	34.6398	+	11.2552i	1.71283	+	0.556532i	0.722028	+	0.691864i	$0.243210\pi$
$410$	−10.7176	+	27.9347i	−0.529307	+	1.37959i
$411$	0.395351	+	1.21676i	0.0195012	+	0.0600185i
$412$	15.6917	−	19.9627i	0.773076	−	0.983491i
$413$	8.16586	−	4.16072i	0.401816	−	0.204735i
$414$	−1.44736	+	5.56262i	−0.0711337	+	0.273388i
$415$	−33.6449	−	15.2660i	−1.65156	−	0.749377i
$416$	−19.0061	−	0.306197i	−0.931849	−	0.0150126i
$417$	−1.09768	−	6.93047i	−0.0537535	−	0.339386i
$418$	−0.0364762	+	0.00803009i	−0.00178411	+	0.000392764i
$419$	15.5333	−	21.3797i	0.758850	−	1.04447i	−0.238459	−	0.971153i	$-0.576642\pi$
$419$	15.5333	−	21.3797i	0.758850	−	1.04447i	0.997309	−	0.0733144i	$-0.0233577\pi$
$420$	−12.0527	−	6.02893i	−0.588113	−	0.294182i
$421$	10.6122	+	14.6064i	0.517207	+	0.711874i	0.985114	−	0.171903i	$-0.0549917\pi$
$421$	10.6122	+	14.6064i	0.517207	+	0.711874i	−0.467907	+	0.883778i	$0.654992\pi$
$422$	−2.52555	−	2.24107i	−0.122942	−	0.109094i
$423$	−0.840306	+	1.64919i	−0.0408571	+	0.0801865i
$424$	0.260777	−	1.91521i	0.0126645	−	0.0930106i
$425$	5.86783	−	3.69356i	0.284631	−	0.179164i
$426$	7.21355	−	11.2862i	0.349498	−	0.546818i
$427$	15.9909	−	31.3839i	0.773854	−	1.51877i
$428$	25.1882	−	7.14216i	1.21752	−	0.345229i
$429$	−0.768520	+	0.558362i	−0.0371045	+	0.0269580i
$430$	18.2594	−	16.4465i	0.880547	−	0.793121i
$431$	−23.2147	+	31.9523i	−1.11821	+	1.53909i	−0.309485	+	0.950904i	$0.600157\pi$
$431$	−23.2147	+	31.9523i	−1.11821	+	1.53909i	−0.808727	+	0.588184i	$0.799843\pi$
$432$	−3.98677	+	0.325083i	−0.191813	+	0.0156406i
$433$	14.4130	−	2.28280i	0.692646	−	0.109704i	0.199820	−	0.979833i	$-0.435964\pi$
$433$	14.4130	−	2.28280i	0.692646	−	0.109704i	0.492825	+	0.870128i	$0.335964\pi$
$434$	25.6067	+	31.1570i	1.22916	+	1.49559i
$435$	−0.706124	+	6.28968i	−0.0338561	+	0.301567i
$436$	20.3025	+	21.9011i	0.972315	+	1.04887i
$437$	−0.172378	−	0.338312i	−0.00824598	−	0.0161837i
$438$	1.16475	−	11.9120i	0.0556539	−	0.569178i
$439$	−3.39101	−	10.4365i	−0.161844	−	0.498105i	0.836946	−	0.547286i	$-0.184339\pi$
$439$	−3.39101	−	10.4365i	−0.161844	−	0.498105i	−0.998790	+	0.0491807i	$0.984339\pi$
$440$	1.73362	+	0.437368i	0.0826473	+	0.0208507i
$441$	−0.643003	+	1.97896i	−0.0306192	+	0.0942362i
$442$	−6.03936	−	2.63660i	−0.287263	−	0.125410i
$443$	−4.16873	+	4.16873i	−0.198063	+	0.198063i	−0.799169	−	0.601106i	$-0.794727\pi$
$443$	−4.16873	+	4.16873i	−0.198063	+	0.198063i	0.601106	+	0.799169i	$0.294727\pi$
$444$	0.537920	−	2.72438i	0.0255285	−	0.129293i
$445$	13.1517	+	3.62396i	0.623448	+	0.171792i
$446$	−0.590790	−	9.89918i	−0.0279747	−	0.468740i
$447$	−1.51179	+	9.54505i	−0.0715051	+	0.451465i
$448$	16.2891	−	17.7718i	0.769590	−	0.839636i
$449$		−	4.78534i		−	0.225834i	−0.993604	−	0.112917i	$-0.963981\pi$
$449$		−	4.78534i		−	0.225834i	0.993604	−	0.112917i	$-0.0360195\pi$
$450$	4.11665	+	5.74919i	0.194061	+	0.271019i
$451$	−2.67478			−0.125950
$452$	28.9450	+	1.09637i	1.36146	+	0.0515688i
$453$	−7.29270	−	1.15505i	−0.342641	−	0.0542690i
$454$	−0.193697	−	3.24555i	−0.00909064	−	0.152321i
$455$	17.6968	−	14.1243i	0.829639	−	0.662159i
$456$	0.182735	−	0.190863i	0.00855737	−	0.00893796i
$457$	−16.6177	−	16.6177i	−0.777342	−	0.777342i	0.202036	−	0.979378i	$-0.435244\pi$
$457$	−16.6177	−	16.6177i	−0.777342	−	0.777342i	−0.979378	+	0.202036i	$0.935244\pi$
$458$	−4.69307	+	10.7499i	−0.219293	+	0.502310i
$459$	−1.31884	−	0.428516i	−0.0615580	−	0.0200014i
$460$	0.134884	+	18.1757i	0.00628899	+	0.847448i
$461$	−2.70116	+	0.877660i	−0.125806	+	0.0408767i	−0.371243	−	0.928536i	$-0.621068\pi$
$461$	−2.70116	+	0.877660i	−0.125806	+	0.0408767i	0.245438	+	0.969412i	$0.421068\pi$
$462$	0.117242	−	1.19904i	0.00545458	−	0.0557845i
$463$	31.8297	−	16.2180i	1.47925	−	0.753716i	0.486475	−	0.873694i	$-0.338282\pi$
$463$	31.8297	−	16.2180i	1.47925	−	0.753716i	0.992777	+	0.119978i	$0.0382824\pi$
$464$	−10.4723	−	4.30322i	−0.486166	−	0.199772i
$465$	−4.25292	−	20.7289i	−0.197224	−	0.961281i
$466$	2.54939	−	2.09524i	0.118098	−	0.0970602i
$467$	2.26802	+	14.3197i	0.104951	+	0.662636i	0.982936	+	0.183948i	$0.0588877\pi$
$467$	2.26802	+	14.3197i	0.104951	+	0.662636i	−0.877985	+	0.478689i	$0.841112\pi$
$468$	2.31719	−	6.30842i	0.107112	−	0.291607i
$469$	36.1237	+	26.2454i	1.66804	+	1.21190i
$470$	−1.21596	+	5.72546i	−0.0560882	+	0.264096i
$471$	8.93024	+	12.2914i	0.411484	+	0.566359i
$472$	2.47964	−	8.23695i	0.114135	−	0.379137i
$473$	1.95743	+	0.997358i	0.0900025	+	0.0458586i
$474$	3.84948	+	2.46039i	0.176812	+	0.113009i
$475$	−0.455480	−	0.103576i	−0.0208988	−	0.00475241i
$476$	7.58486	−	3.50965i	0.347652	−	0.160864i
$477$	0.608892	+	0.310246i	0.0278793	+	0.0142052i
$478$	2.80739	+	2.49117i	0.128407	+	0.113943i
$479$	22.7636	−	16.5387i	1.04009	−	0.755673i	0.0697901	−	0.997562i	$-0.477767\pi$
$479$	22.7636	−	16.5387i	1.04009	−	0.755673i	0.970304	+	0.241889i	$0.0777670\pi$
$480$	−11.9109	+	4.25801i	−0.543655	+	0.194351i
$481$	3.77462	+	2.74242i	0.172108	+	0.125044i
$482$	−7.86030	−	35.7049i	−0.358027	−	1.62632i
$483$	12.0968	−	1.91595i	0.550424	−	0.0871786i
$484$	−2.59762	−	21.6851i	−0.118074	−	0.985688i
$485$	7.07862	+	6.46494i	0.321423	+	0.293558i
$486$	0.356112	−	1.36864i	0.0161536	−	0.0620829i
$487$	1.64612	+	3.23070i	0.0745930	+	0.146397i	0.925291	−	0.379257i	$-0.123821\pi$
$487$	1.64612	+	3.23070i	0.0745930	+	0.146397i	−0.850698	+	0.525654i	$0.823821\pi$
$488$	−10.8977	−	31.2128i	−0.493314	−	1.41293i
$489$	4.96842	−	1.61434i	0.224680	−	0.0730029i
$490$	−0.343252	+	6.57111i	−0.0155065	+	0.296853i
$491$	6.24832	−	19.2304i	0.281983	−	0.867854i	−0.705304	−	0.708905i	$-0.749189\pi$
$491$	6.24832	−	19.2304i	0.281983	−	0.867854i	0.987287	−	0.158949i	$-0.0508105\pi$
$492$	15.7192	−	10.5353i	0.708675	−	0.474969i
$493$	−2.77544	−	2.77544i	−0.125000	−	0.125000i
$494$	0.162099	+	0.413300i	0.00729317	+	0.0185953i
$495$	−0.348029	+	0.527701i	−0.0156427	+	0.0237184i
$496$	37.7450	+	2.86349i	1.69480	+	0.128575i
$497$	−28.1900	−	4.46485i	−1.26449	−	0.200276i
$498$	11.8298	+	20.1511i	0.530108	+	0.902991i
$499$		−	38.3720i		−	1.71777i	−0.512171	−	0.858883i	$-0.671159\pi$
$499$		−	38.3720i		−	1.71777i	0.512171	−	0.858883i	$-0.328841\pi$
$500$	17.2823	+	14.1888i	0.772888	+	0.634542i
$501$			23.7881i			1.06277i
$502$	−34.9522	+	20.5189i	−1.55999	+	0.915805i
$503$	−19.0365	−	3.01509i	−0.848797	−	0.134436i	−0.283142	−	0.959078i	$-0.591377\pi$
$503$	−19.0365	−	3.01509i	−0.848797	−	0.134436i	−0.565655	+	0.824642i	$0.691377\pi$
$504$	4.03374	+	7.50835i	0.179677	+	0.334449i
$505$	2.03024	−	3.07836i	0.0903444	−	0.136985i
$506$	−1.51272	+	0.593297i	−0.0672485	+	0.0263753i
$507$	−1.20818	−	1.20818i	−0.0536572	−	0.0536572i
$508$	−7.78024	+	5.21448i	−0.345192	+	0.231355i
$509$	−8.91678	+	27.4430i	−0.395229	+	1.21639i	0.533553	+	0.845766i	$0.320856\pi$
$509$	−8.91678	+	27.4430i	−0.395229	+	1.21639i	−0.928783	+	0.370624i	$0.879144\pi$
$510$	−4.37918	−	0.228753i	−0.193913	−	0.0101293i
$511$	−24.2552	+	7.88099i	−1.07299	+	0.348635i
$512$	−1.47542	−	22.5793i	−0.0652051	−	0.997872i
$513$	0.0424125	+	0.0832392i	0.00187256	+	0.00367510i
$514$	−23.5231	−	6.12057i	−1.03756	−	0.269967i
$515$	20.9620	+	19.1447i	0.923696	+	0.843616i
$516$	−15.4318	+	1.84855i	−0.679347	+	0.0813777i
$517$	−0.516814	+	0.0818553i	−0.0227295	+	0.00359999i
$518$	−5.77887	+	1.27219i	−0.253909	+	0.0558970i
$519$	−12.9937	−	9.44046i	−0.570359	−	0.414390i
$520$	1.91114	−	21.1661i	0.0838092	−	0.928194i
$521$	20.3759	−	14.8040i	0.892686	−	0.648575i	−0.0438908	−	0.999036i	$-0.513975\pi$
$521$	20.3759	−	14.8040i	0.892686	−	0.648575i	0.936577	+	0.350462i	$0.113975\pi$
$522$	2.65685	−	2.99410i	0.116287	−	0.131048i
$523$	−1.71718	−	0.874949i	−0.0750872	−	0.0382589i	0.416044	−	0.909345i	$-0.363416\pi$
$523$	−1.71718	−	0.874949i	−0.0750872	−	0.0382589i	−0.491131	+	0.871086i	$0.663416\pi$
$524$	31.2653	−	14.4670i	1.36583	−	0.631993i
$525$	7.71758	−	12.9406i	0.336823	−	0.564774i
$526$	−14.4568	+	22.6188i	−0.630345	+	0.986227i
$527$	11.6926	+	5.95767i	0.509337	+	0.259520i
$528$	−0.736815	−	0.857789i	−0.0320658	−	0.0373305i
$529$	3.80956	+	5.24341i	0.165633	+	0.227974i
$530$	2.11388	+	0.448941i	0.0918210	+	0.0195008i
$531$	2.46046	+	1.78763i	0.106775	+	0.0775766i
$532$	−0.528514	−	0.194133i	−0.0229140	−	0.00841671i
$533$	4.97358	+	31.4020i	0.215430	+	1.36017i
$534$	−5.47815	−	6.66555i	−0.237063	−	0.288447i
$535$	5.88303	+	28.6742i	0.254346	+	1.23969i
$536$	41.2416	−	7.45488i	1.78137	−	0.322002i
$537$	−3.29693	+	1.67987i	−0.142273	+	0.0724917i
$538$	−4.43177	−	0.433336i	−0.191067	−	0.0186824i
$539$	−0.559450	+	0.181776i	−0.0240972	+	0.00782966i
$540$	−0.0331872	−	4.47201i	−0.00142815	−	0.192445i
$541$	3.83258	+	1.24528i	0.164775	+	0.0535388i	0.390243	−	0.920712i	$-0.372391\pi$
$541$	3.83258	+	1.24528i	0.164775	+	0.0535388i	−0.225468	+	0.974251i	$0.572391\pi$
$542$	19.9441	+	8.70698i	0.856673	+	0.373997i
$543$	17.0666	+	17.0666i	0.732398	+	0.732398i
$544$	2.54391	−	7.42044i	0.109069	−	0.318149i
$545$	−26.0961	+	20.8280i	−1.11783	+	0.892176i
$546$	−14.2948	+	0.853125i	−0.611761	+	0.0365104i
$547$	−26.4425	−	4.18808i	−1.13060	−	0.179069i	−0.437021	−	0.899451i	$-0.643967\pi$
$547$	−26.4425	−	4.18808i	−1.13060	−	0.179069i	−0.693578	+	0.720382i	$0.743967\pi$
$548$	0.0968505	−	2.55693i	0.00413725	−	0.109227i
$549$	11.6886			0.498859
$550$	−0.630839	+	1.89683i	−0.0268991	+	0.0808812i
$551$			0.264430i			0.0112651i
$552$	6.55312	−	9.44495i	0.278919	−	0.402004i
$553$	1.52287	−	9.61500i	0.0647588	−	0.408871i
$554$	14.6084	−	0.871842i	0.620653	−	0.0370410i
$555$	2.99320	+	0.824780i	0.127054	+	0.0350100i
$556$	−2.71843	+	13.7679i	−0.115287	+	0.583889i
$557$	−17.7123	+	17.7123i	−0.750494	+	0.750494i	−0.974571	−	0.224078i	$-0.928063\pi$
$557$	−17.7123	+	17.7123i	−0.750494	+	0.750494i	0.224078	+	0.974571i	$0.428063\pi$
$558$	−5.35466	+	12.2653i	−0.226681	+	0.519232i
$559$	8.06930	−	24.8348i	0.341295	−	1.05040i
$560$	18.4698	+	19.6298i	0.780491	+	0.829513i
$561$	−0.121141	−	0.372833i	−0.00511457	−	0.0157410i
$562$	5.03422	+	0.492243i	0.212356	+	0.0207640i
$563$	−2.30556	−	4.52492i	−0.0971678	−	0.190703i	0.837306	−	0.546735i	$-0.184129\pi$
$563$	−2.30556	−	4.52492i	−0.0971678	−	0.190703i	−0.934474	+	0.356032i	$0.884129\pi$
$564$	2.71482	−	2.51666i	0.114314	−	0.105970i
$565$	−3.61304	+	32.1825i	−0.152002	+	1.35393i
$566$	−22.9984	+	18.9014i	−0.966693	+	0.794486i
$567$	−2.97634	+	0.471405i	−0.124994	+	0.0197972i
$568$	−21.3252	+	16.2138i	−0.894786	+	0.680318i
$569$	19.5402	−	26.8947i	0.819167	−	1.12749i	−0.170677	−	0.985327i	$-0.554595\pi$
$569$	19.5402	−	26.8947i	0.819167	−	1.12749i	0.989844	−	0.142159i	$-0.0454045\pi$
$570$	0.197715	+	0.219510i	0.00828139	+	0.00919425i
$571$	−25.9184	+	18.8308i	−1.08465	+	0.788046i	−0.978488	−	0.206303i	$-0.933857\pi$
$571$	−25.9184	+	18.8308i	−1.08465	+	0.788046i	−0.106164	+	0.994349i	$0.533857\pi$
$572$	1.82783	−	0.518284i	0.0764252	−	0.0216705i
$573$	−5.62891	+	11.0474i	−0.235151	+	0.461510i
$574$	−33.9751	−	21.7151i	−1.41809	−	0.906371i
$575$	−20.2767	−	1.35077i	−0.845598	−	0.0563311i
$576$	7.70876	+	2.13893i	0.321198	+	0.0891220i
$577$	−16.7127	+	32.8004i	−0.695757	+	1.36550i	0.224612	+	0.974448i	$0.427888\pi$
$577$	−16.7127	+	32.8004i	−0.695757	+	1.36550i	−0.920369	+	0.391051i	$0.872112\pi$
$578$	−14.1521	+	15.9485i	−0.588648	+	0.663369i
$579$	−10.3497	−	14.2451i	−0.430117	−	0.592005i
$580$	5.66293	−	11.3210i	0.235140	−	0.470080i
$581$	29.2662	−	40.2815i	1.21417	−	1.67116i
$582$	−1.30355	−	5.92129i	−0.0540338	−	0.245445i
$583$	0.0302215	+	0.190811i	0.00125165	+	0.00790259i
$584$	−10.4010	+	21.5599i	−0.430397	+	0.892155i
$585$	6.84237	+	3.10465i	0.282897	+	0.128361i
$586$	31.8535	+	8.28807i	1.31586	+	0.342377i
$587$	23.4414	−	11.9440i	0.967528	−	0.492980i	0.102516	−	0.994731i	$-0.467311\pi$
$587$	23.4414	−	11.9440i	0.967528	−	0.492980i	0.865012	+	0.501751i	$0.167311\pi$
$588$	2.57181	−	3.27181i	0.106060	−	0.134927i
$589$	−0.273196	−	0.840812i	−0.0112569	−	0.0346450i
$590$	8.97924	+	3.44505i	0.369669	+	0.141830i
$591$	12.4627	+	4.04938i	0.512648	+	0.166569i
$592$	−2.88856	+	4.74369i	−0.118719	+	0.194965i
$593$	−4.43203	+	4.43203i	−0.182002	+	0.182002i	−0.792228	−	0.610226i	$-0.791079\pi$
$593$	−4.43203	+	4.43203i	−0.182002	+	0.182002i	0.610226	+	0.792228i	$0.291079\pi$
$594$	0.372194	−	0.145977i	0.0152713	−	0.00598949i
$595$	3.28674	+	8.74683i	0.134743	+	0.358585i
$596$	9.42031	−	16.8770i	0.385871	−	0.691307i
$597$	−0.124128	+	0.783716i	−0.00508024	+	0.0320754i
$598$	9.77813	+	16.6562i	0.399858	+	0.681121i
$599$	−29.7462			−1.21540			−0.607699	−	0.794168i	$-0.707907\pi$
$599$	−29.7462			−1.21540			−0.607699	+	0.794168i	$0.707907\pi$
$600$	−3.76385	−	13.6321i	−0.153659	−	0.556527i
$601$	−40.3102			−1.64429			−0.822143	−	0.569281i	$-0.807222\pi$
$601$	−40.3102			−1.64429			−0.822143	+	0.569281i	$0.807222\pi$
$602$	16.7662	+	28.5598i	0.683341	+	1.16401i
$603$	−2.31795	+	14.6350i	−0.0943944	+	0.595983i
$604$	12.8945	+	7.19740i	0.524670	+	0.292858i
$605$	24.3930	−	1.10528i	0.991717	−	0.0449362i
$606$	−2.17120	+	0.851559i	−0.0881991	+	0.0345922i
$607$	7.71252	−	7.71252i	0.313042	−	0.313042i	−0.533045	−	0.846087i	$-0.678952\pi$
$607$	7.71252	−	7.71252i	0.313042	−	0.313042i	0.846087	+	0.533045i	$0.178952\pi$
$608$	−0.474676	+	0.232305i	−0.0192506	+	0.00942122i
$609$	−8.11207	−	2.63577i	−0.328717	−	0.106807i
$610$	35.7016	−	9.57276i	1.44552	−	0.387590i
$611$	1.92197	+	5.91521i	0.0777545	+	0.239304i
$612$	2.18043	+	1.71393i	0.0881385	+	0.0692815i
$613$	−12.0458	+	6.13766i	−0.486527	+	0.247898i	−0.680006	−	0.733207i	$-0.738023\pi$
$613$	−12.0458	+	6.13766i	−0.486527	+	0.247898i	0.193479	+	0.981104i	$0.438023\pi$
$614$	39.9751	+	10.4013i	1.61326	+	0.419761i
$615$	10.4484	+	18.3967i	0.421320	+	0.741826i
$616$	−1.04695	+	2.17018i	−0.0421828	+	0.0874392i
$617$	2.61995	+	16.5417i	0.105475	+	0.665945i	0.982607	+	0.185696i	$0.0594539\pi$
$617$	2.61995	+	16.5417i	0.105475	+	0.665945i	−0.877132	+	0.480250i	$0.840546\pi$
$618$	−3.86021	−	17.5348i	−0.155281	−	0.705352i
$619$	−8.12418	+	11.1820i	−0.326538	+	0.449441i	−0.940449	−	0.339934i	$-0.889595\pi$
$619$	−8.12418	+	11.1820i	−0.326538	+	0.449441i	0.613911	+	0.789375i	$0.289595\pi$
$620$	−6.31015	+	41.8484i	−0.253422	+	1.68067i
$621$	2.38895	+	3.28811i	0.0958654	+	0.131947i
$622$	18.1195	−	20.4195i	0.726524	−	0.818747i
$623$	−8.34634	+	16.3806i	−0.334389	+	0.656275i
$624$	−8.70040	+	10.2452i	−0.348295	+	0.410138i
$625$	−17.2476	+	18.0975i	−0.689903	+	0.723901i
$626$	−36.5166	−	23.3395i	−1.45950	−	0.932834i
$627$	−0.0119900	+	0.0235316i	−0.000478833	+	0.000939763i
$628$	−8.28924	−	29.2336i	−0.330777	−	1.16655i
$629$	−1.55770	+	1.13174i	−0.0621096	+	0.0451253i
$630$	−8.70481	+	3.87741i	−0.346808	+	0.154480i
$631$	14.5721	−	20.0567i	0.580104	−	0.798445i	−0.413602	−	0.910458i	$-0.635730\pi$
$631$	14.5721	−	20.0567i	0.580104	−	0.798445i	0.993707	+	0.112012i	$0.0357296\pi$
$632$	−5.53020	−	7.27358i	−0.219979	−	0.289327i
$633$	−2.35816	+	0.373495i	−0.0937284	+	0.0148451i
$634$	27.1712	−	22.3309i	1.07911	−	0.886874i
$635$	−5.17145	−	9.10548i	−0.205223	−	0.361340i
$636$	−0.929166	−	1.00233i	−0.0368438	−	0.0397448i
$637$	3.17432	+	6.22996i	0.125771	+	0.246840i
$638$	1.12625	+	0.110124i	0.0445888	+	0.00435986i
$639$	−2.92681	−	9.00780i	−0.115783	−	0.356343i
$640$	25.2973	+	0.219793i	0.999962	+	0.00868807i
$641$	−2.94028	+	9.04926i	−0.116134	+	0.357424i	−0.992182	−	0.124800i	$-0.960171\pi$
$641$	−2.94028	+	9.04926i	−0.116134	+	0.357424i	0.876048	+	0.482224i	$0.160171\pi$
$642$	7.40706	−	16.9665i	0.292333	−	0.669615i
$643$	17.0309	−	17.0309i	0.671631	−	0.671631i	−0.286461	−	0.958092i	$-0.592479\pi$
$643$	17.0309	−	17.0309i	0.671631	−	0.671631i	0.958092	+	0.286461i	$0.0924788\pi$
$644$	−24.0313	−	4.74489i	−0.946964	−	0.186975i
$645$	−0.786554	−	17.3588i	−0.0309705	−	0.683502i
$646$	−0.182883	+	0.0109146i	−0.00719545	+	0.000429430i
$647$	1.65699	−	10.4619i	0.0651432	−	0.411298i	−0.933470	−	0.358655i	$-0.883235\pi$
$647$	1.65699	−	10.4619i	0.0651432	−	0.411298i	0.998613	−	0.0526429i	$-0.0167645\pi$
$648$	−1.61235	+	2.32386i	−0.0633390	+	0.0912899i
$649$			0.859772i			0.0337490i
$650$	23.4419	+	3.87903i	0.919466	+	0.152148i
$651$	28.5172			1.11768
$652$	−10.4407	−	0.395470i	−0.408890	−	0.0154878i
$653$	0.575286	+	0.0911163i	0.0225127	+	0.00356566i	0.167681	−	0.985841i	$-0.446372\pi$
$653$	0.575286	+	0.0911163i	0.0225127	+	0.00356566i	−0.145168	+	0.989407i	$0.546372\pi$
$654$	21.0794	−	1.25804i	0.824271	−	0.0491931i
$655$	13.5481	+	36.0550i	0.529370	+	1.40878i
$656$	−36.7755	+	8.93881i	−1.43584	+	0.349002i
$657$	−5.98441	−	5.98441i	−0.233474	−	0.233474i
$658$	−7.22913	−	3.15602i	−0.281821	−	0.123034i
$659$	26.2895	+	8.54198i	1.02409	+	0.332748i	0.772453	−	0.635072i	$-0.219030\pi$
$659$	26.2895	+	8.54198i	1.02409	+	0.332748i	0.251641	+	0.967821i	$0.419030\pi$
$660$	1.01727	−	0.750688i	0.0395972	−	0.0292205i
$661$	−25.4345	+	8.26418i	−0.989289	+	0.321439i	−0.758577	−	0.651583i	$-0.774105\pi$
$661$	−25.4345	+	8.26418i	−0.989289	+	0.321439i	−0.230711	+	0.973022i	$0.574105\pi$
$662$	−9.33598	−	0.912867i	−0.362853	−	0.0354796i
$663$	−4.15182	+	2.11546i	−0.161243	+	0.0821576i
$664$	−8.31293	−	45.9885i	−0.322604	−	1.78470i
$665$	0.260105	−	0.573248i	0.0100864	−	0.0222296i
$666$	−1.24678	−	1.51702i	−0.0483116	−	0.0587833i
$667$	1.79964	+	11.3625i	0.0696822	+	0.439956i
$668$	16.4039	−	44.6587i	0.634687	−	1.72790i
$669$	−5.67301	−	4.12169i	−0.219331	−	0.159354i
$670$	4.90583	+	46.5992i	0.189529	+	1.80029i
$671$	1.94226	+	2.67329i	0.0749800	+	0.103201i
$672$	−2.39511	−	16.8775i	−0.0923935	−	0.651063i
$673$	−32.5965	−	16.6088i	−1.25650	−	0.640221i	−0.306326	−	0.951927i	$-0.599100\pi$
$673$	−32.5965	−	16.6088i	−1.25650	−	0.640221i	−0.950179	+	0.311706i	$0.899100\pi$
$674$	23.1445	−	36.2115i	0.891492	−	1.39481i
$675$	4.98894	+	0.332348i	0.192024	+	0.0127921i
$676$	1.43504	+	3.10133i	0.0551939	+	0.119282i
$677$	−32.8308	−	16.7281i	−1.26179	−	0.642913i	−0.310312	−	0.950635i	$-0.600434\pi$
$677$	−32.8308	−	16.7281i	−1.26179	−	0.642913i	−0.951476	+	0.307721i	$0.900434\pi$
$678$	13.5943	−	15.3200i	0.522087	−	0.588359i
$679$	−10.4520	+	7.59379i	−0.401109	+	0.291423i
$680$	8.06353	+	3.44927i	0.309222	+	0.132274i
$681$	−1.85996	−	1.35134i	−0.0712737	−	0.0517834i
$682$	−3.69494	+	0.813427i	−0.141487	+	0.0311477i
$683$	−20.2038	+	3.19997i	−0.773078	+	0.122444i	−0.530496	−	0.847687i	$-0.677994\pi$
$683$	−20.2038	+	3.19997i	−0.773078	+	0.122444i	−0.242582	+	0.970131i	$0.577994\pi$
$684$	−0.0222227	−	0.185517i	−0.000849707	−	0.00709342i
$685$	2.84292	+	0.319167i	0.108623	+	0.0121947i
$686$	20.2883	+	5.27889i	0.774613	+	0.201549i
$687$	3.76546	+	7.39012i	0.143661	+	0.281951i
$688$	30.2457	+	7.17119i	1.15311	+	0.273399i
$689$	2.18393	−	0.709603i	0.0832012	−	0.0270337i
$690$	9.98969	+	8.08666i	0.380301	+	0.307854i
$691$	−1.61527	+	4.97128i	−0.0614476	+	0.189116i	−0.977068	−	0.212928i	$-0.931700\pi$
$691$	−1.61527	+	4.97128i	−0.0614476	+	0.189116i	0.915620	+	0.402044i	$0.131700\pi$
$692$	17.8837	+	26.6834i	0.679838	+	1.01435i
$693$	−0.602381	−	0.602381i	−0.0228826	−	0.0228826i
$694$	16.5244	−	6.48096i	0.627257	−	0.246014i
$695$	−15.1264	−	4.16810i	−0.573778	−	0.158105i
$696$	−7.05254	+	3.78886i	−0.267326	+	0.143617i
$697$	−12.9589	−	2.05248i	−0.490853	−	0.0777434i
$698$	−19.6483	+	11.5347i	−0.743697	+	0.436593i
$699$		−	2.33339i		−	0.0882570i
$700$	−23.4123	+	18.9722i	−0.884903	+	0.717081i
$701$		−	29.0077i		−	1.09561i	−0.836607	−	0.547803i	$-0.815464\pi$
$701$		−	29.0077i		−	1.09561i	0.836607	−	0.547803i	$-0.184536\pi$
$702$	−2.40584	−	4.09813i	−0.0908026	−	0.154674i
$703$	0.128118	+	0.0202919i	0.00483205	+	0.000765322i
$704$	0.791745	+	2.11847i	0.0298400	+	0.0798430i
$705$	2.58180	+	3.23482i	0.0972363	+	0.121830i
$706$	0.160950	+	0.410372i	0.00605744	+	0.0154445i
$707$	3.51401	+	3.51401i	0.132158	+	0.132158i
$708$	−3.38644	−	5.05273i	−0.127270	−	0.189893i
$709$	−9.19960	+	28.3135i	−0.345498	+	1.06333i	0.615818	+	0.787888i	$0.288826\pi$
$709$	−9.19960	+	28.3135i	−0.345498	+	1.06333i	−0.961316	+	0.275446i	$0.911174\pi$
$710$	−16.3168	−	25.1163i	−0.612359	−	0.942598i
$711$	3.07237	−	0.998273i	0.115223	−	0.0374382i
$712$	5.68796	+	16.2913i	0.213165	+	0.610541i
$713$	−17.4615	−	34.2701i	−0.653938	−	1.28343i
$714$	1.48810	−	5.71922i	0.0556908	−	0.214036i
$715$	0.426913	+	2.08079i	0.0159656	+	0.0778173i
$716$	7.34793	−	0.880195i	0.274605	−	0.0328944i
$717$	2.62131	−	0.415175i	0.0978948	−	0.0155050i
$718$	−3.78902	−	17.2114i	−0.141405	−	0.642323i
$719$	3.22089	+	2.34011i	0.120119	+	0.0872714i	0.646223	−	0.763149i	$-0.276348\pi$
$719$	3.22089	+	2.34011i	0.120119	+	0.0872714i	−0.526104	+	0.850420i	$0.676348\pi$
$720$	−3.02154	+	8.41845i	−0.112606	+	0.313737i
$721$	−30.9515	+	22.4876i	−1.15269	+	0.837482i
$722$	−20.0889	−	17.8261i	−0.747633	−	0.663420i
$723$	−23.0341	−	11.7365i	−0.856647	−	0.436483i
$724$	−20.2712	−	43.8090i	−0.753373	−	1.62815i
$725$	12.1550	+	7.24907i	0.451426	+	0.269224i
$726$	−13.0125	−	8.31692i	−0.482939	−	0.308670i
$727$	26.6627	+	13.5853i	0.988866	+	0.503852i	0.872111	−	0.489309i	$-0.162751\pi$
$727$	26.6627	+	13.5853i	0.988866	+	0.503852i	0.116755	+	0.993161i	$0.462751\pi$
$728$	27.4248	+	8.25590i	1.01643	+	0.305984i
$729$	−0.587785	−	0.809017i	−0.0217698	−	0.0299636i
$730$	−23.1798	−	13.3776i	−0.857923	−	0.495127i
$731$	8.71811	+	6.33408i	0.322451	+	0.234274i
$732$	−21.9438	−	8.06034i	−0.811065	−	0.297919i
$733$	−3.39386	−	21.4280i	−0.125355	−	0.791461i	−0.967623	−	0.252401i	$-0.918780\pi$
$733$	−3.39386	−	21.4280i	−0.125355	−	0.791461i	0.842268	−	0.539060i	$-0.181220\pi$
$734$	0.0411291	−	0.0338024i	0.00151810	−	0.00124767i
$735$	3.43559	+	3.13774i	0.126724	+	0.115737i
$736$	−18.8157	+	13.2126i	−0.693554	+	0.487023i
$737$	−3.73231	+	1.90170i	−0.137481	+	0.0700502i
$738$	1.30215	−	13.3172i	0.0479327	−	0.490212i
$739$	6.09760	−	1.98123i	0.224304	−	0.0728807i	−0.194709	−	0.980861i	$-0.562376\pi$
$739$	6.09760	−	1.98123i	0.224304	−	0.0728807i	0.419013	+	0.907980i	$0.362376\pi$
$740$	−5.05055	−	3.61248i	−0.185662	−	0.132797i
$741$	0.298557	+	0.0970070i	0.0109678	+	0.00356364i
$742$	−1.16522	+	2.66904i	−0.0427766	+	0.0979835i
$743$	−21.4253	−	21.4253i	−0.786019	−	0.786019i	0.194820	−	0.980839i	$-0.437588\pi$
$743$	−21.4253	−	21.4253i	−0.786019	−	0.786019i	−0.980839	+	0.194820i	$0.937588\pi$
$744$	18.5106	−	19.3339i	0.678632	−	0.708814i
$745$	18.0394	+	11.8973i	0.660913	+	0.435885i
$746$	−1.99938	−	33.5013i	−0.0732027	−	1.22657i
$747$	16.3194	+	2.58475i	0.597097	+	0.0945709i
$748$	−0.0296763	+	0.783478i	−0.00108507	+	0.0286468i
$749$	−39.4477			−1.44139
$750$	15.5103	−	3.07072i	0.566358	−	0.112127i
$751$		−	4.73646i		−	0.172836i	−0.996259	−	0.0864180i	$-0.972458\pi$
$751$		−	4.73646i		−	0.172836i	0.996259	−	0.0864180i	$-0.0275421\pi$
$752$	−6.83214	+	2.85257i	−0.249142	+	0.104022i
$753$	−4.48326	+	28.3062i	−0.163379	+	1.03154i
$754$	−0.801334	−	13.4270i	−0.0291829	−	0.488983i
$755$	−9.08992	+	13.7827i	−0.330816	+	0.501602i
$756$	5.91272	+	1.16745i	0.215044	+	0.0424596i
$757$	32.5386	−	32.5386i	1.18264	−	1.18264i	0.203579	−	0.979059i	$-0.434743\pi$
$757$	32.5386	−	32.5386i	1.18264	−	1.18264i	0.979059	−	0.203579i	$-0.0652573\pi$
$758$	−7.16864	−	3.12961i	−0.260377	−	0.113672i
$759$	−0.355055	+	1.09275i	−0.0128877	+	0.0396642i
$760$	−0.219811	−	0.548440i	−0.00797339	−	0.0198940i
$761$	−15.6782	−	48.2527i	−0.568336	−	1.74916i	−0.657826	−	0.753170i	$-0.728524\pi$
$761$	−15.6782	−	48.2527i	−0.568336	−	1.74916i	0.0894905	−	0.995988i	$-0.471476\pi$
$762$	−0.644500	+	6.59136i	−0.0233478	+	0.238780i
$763$	−20.4280	−	40.0921i	−0.739542	−	1.45143i
$764$	18.1856	−	16.8582i	0.657932	−	0.609909i
$765$	−2.09108	+	2.28957i	−0.0756031	+	0.0827797i
$766$	19.1911	+	23.3509i	0.693404	+	0.843701i
$767$	10.0937	−	1.59869i	0.364464	−	0.0577255i
$768$	−12.9971	−	9.33139i	−0.468993	−	0.336718i
$769$	16.5014	−	22.7122i	0.595054	−	0.819022i	−0.400190	−	0.916432i	$-0.631056\pi$
$769$	16.5014	−	22.7122i	0.595054	−	0.819022i	0.995244	+	0.0974102i	$0.0310559\pi$
$770$	−2.33324	−	1.34657i	−0.0840842	−	0.0485269i
$771$	−13.9047	+	10.1024i	−0.500767	+	0.363828i
$772$	9.60677	+	33.8801i	0.345755	+	1.21937i
$773$	−20.2623	+	39.7669i	−0.728783	+	1.43032i	0.167060	+	0.985947i	$0.446573\pi$
$773$	−20.2623	+	39.7669i	−0.728783	+	1.43032i	−0.895843	+	0.444370i	$0.853427\pi$
$774$	−5.91857	+	9.26009i	−0.212739	+	0.332847i
$775$	−46.1389	−	10.4920i	−1.65736	−	0.376884i
$776$	−1.63602	+	12.0153i	−0.0587296	+	0.431323i
$777$	−1.89955	+	3.72808i	−0.0681460	+	0.133744i
$778$	14.2015	+	12.6019i	0.509150	+	0.451800i
$779$	0.519552	+	0.715102i	0.0186149	+	0.0256212i
$780$	−10.7047	−	10.5469i	−0.383288	−	0.377641i
$781$	1.57382	−	2.16618i	0.0563157	−	0.0775120i
$782$	−7.78416	+	1.71365i	−0.278361	+	0.0612801i
$783$	−0.442788	−	2.79565i	−0.0158239	−	0.0999084i
$784$	−7.08441	+	4.36886i	−0.253015	+	0.156031i
$785$	33.2794	−	6.82789i	1.18779	−	0.243698i
$786$	6.13405	−	23.5750i	0.218794	−	0.840891i
$787$	−8.99340	+	4.58236i	−0.320580	+	0.163344i	−0.606874	−	0.794798i	$-0.707577\pi$
$787$	−8.99340	+	4.58236i	−0.320580	+	0.163344i	0.286294	+	0.958142i	$0.407577\pi$
$788$	−20.6046	−	16.1963i	−0.734008	−	0.576968i
$789$	5.86566	+	18.0526i	0.208823	+	0.642691i
$790$	8.56664	−	5.56532i	0.304787	−	0.198005i
$791$	−41.5071	−	13.4865i	−1.47582	−	0.479524i
$792$	−0.799404	+	0.0173901i	−0.0284056	+	0.000617932i
$793$	27.7730	−	27.7730i	0.986247	−	0.986247i
$794$	1.79407	+	4.57431i	0.0636691	+	0.162336i
$795$	1.19432	−	0.953218i	0.0423580	−	0.0338071i
$796$	0.773474	−	1.38572i	0.0274151	−	0.0491155i
$797$	6.71993	−	42.4280i	0.238032	−	1.50288i	−0.521975	−	0.852961i	$-0.674805\pi$
$797$	6.71993	−	42.4280i	0.238032	−	1.50288i	0.760007	−	0.649915i	$-0.225195\pi$
$798$	−0.343338	+	0.201559i	−0.0121540	+	0.00713512i
$799$	−2.56670			−0.0908032
$800$	−2.33441	+	28.1878i	−0.0825337	+	0.996588i
$801$	−6.10080			−0.215561
$802$	19.0971	−	11.2111i	0.674341	−	0.395877i
$803$	0.374277	−	2.36309i	0.0132079	−	0.0833916i
$804$	14.4437	−	25.8767i	0.509391	−	0.912599i
$805$	7.27524	−	26.4025i	0.256418	−	0.930565i
$806$	16.4202	+	41.8662i	0.578376	+	1.47467i
$807$	−2.22645	+	2.22645i	−0.0783748	+	0.0783748i
$808$	4.66335	−	0.101446i	0.164056	−	0.00356885i
$809$	−27.7947	−	9.03103i	−0.977208	−	0.317514i	−0.223486	−	0.974707i	$-0.571744\pi$
$809$	−27.7947	−	9.03103i	−0.977208	−	0.317514i	−0.753722	+	0.657193i	$0.771744\pi$
$810$	−2.45789	−	1.98967i	−0.0863615	−	0.0699097i
$811$	7.64133	+	23.5176i	0.268323	+	0.825814i	0.990909	+	0.134533i	$0.0429534\pi$
$811$	7.64133	+	23.5176i	0.268323	+	0.825814i	−0.722586	+	0.691281i	$0.757047\pi$
$812$	13.4117	+	10.5423i	0.470657	+	0.369961i
$813$	13.7108	−	6.98599i	0.480858	−	0.245009i
$814$	0.139783	−	0.537225i	0.00489938	−	0.0188297i
$815$	1.30326	−	11.6085i	0.0456511	−	0.406629i
$816$	−2.91153	−	4.72125i	−0.101924	−	0.165277i
$817$	−0.113569	−	0.717047i	−0.00397328	−	0.0250863i
$818$	−50.3045	+	11.0744i	−1.75886	+	0.387206i
$819$	−5.95188	+	8.19206i	−0.207976	+	0.286254i
$820$	−6.92923	−	41.7422i	−0.241979	−	1.45770i
$821$	17.8856	+	24.6175i	0.624213	+	0.859155i	0.997651	−	0.0684998i	$-0.0218213\pi$
$821$	17.8856	+	24.6175i	0.624213	+	0.859155i	−0.373438	+	0.927655i	$0.621821\pi$
$822$	−1.35333	−	1.20089i	−0.0472027	−	0.0418858i
$823$	−20.0687	+	39.3871i	−0.699552	+	1.37295i	0.218243	+	0.975894i	$0.429967\pi$
$823$	−20.0687	+	39.3871i	−0.699552	+	1.37295i	−0.917795	+	0.397054i	$0.870033\pi$
$824$	−4.84476	+	35.5810i	−0.168775	+	1.23952i
$825$	0.752983	+	1.19624i	0.0262155	+	0.0416476i
$826$	−6.98004	+	10.9208i	−0.242867	+	0.379985i
$827$	21.9177	−	43.0160i	0.762155	−	1.49581i	−0.103204	−	0.994660i	$-0.532910\pi$
$827$	21.9177	−	43.0160i	0.762155	−	1.49581i	0.865359	−	0.501152i	$-0.167090\pi$
$828$	−2.21748	−	7.82036i	−0.0770627	−	0.271776i
$829$	−45.8230	+	33.2923i	−1.59150	+	1.15629i	−0.689734	+	0.724063i	$0.742272\pi$
$829$	−45.8230	+	33.2923i	−1.59150	+	1.15629i	−0.901764	+	0.432228i	$0.857728\pi$
$830$	51.9627	−	5.47048i	1.80365	−	0.189883i
$831$	6.08246	−	8.37179i	0.210998	−	0.290414i
$832$	23.3988	−	13.2343i	0.811206	−	0.458816i
$833$	−2.84993	+	0.451385i	−0.0987444	+	0.0156396i
$834$	6.30070	+	7.66640i	0.218176	+	0.265466i
$835$	48.4387	+	21.9785i	1.67629	+	0.760597i
$836$	0.0387366	−	0.0359092i	0.00133973	−	0.00124194i
$837$	4.29628	+	8.43191i	0.148501	+	0.291450i
$838$	−3.63698	+	37.1957i	−0.125637	+	1.28490i
$839$	−11.0621	−	34.0456i	−0.381905	−	1.17538i	−0.938701	−	0.344734i	$-0.887969\pi$
$839$	−11.0621	−	34.0456i	−0.381905	−	1.17538i	0.556795	−	0.830650i	$-0.312031\pi$
$840$	19.0158	−	1.27656i	0.656109	−	0.0440456i
$841$	−6.48573	+	19.9610i	−0.223646	+	0.688312i
$842$	−23.4002	−	10.2158i	−0.806425	−	0.352060i
$843$	2.52912	−	2.52912i	0.0871074	−	0.0871074i
$844$	4.68466	+	0.924971i	0.161253	+	0.0318388i
$845$	−3.57644	+	1.34390i	−0.123033	+	0.0462315i
$846$	−0.155944	−	2.61296i	−0.00536145	−	0.0898356i
$847$	−5.14779	+	32.5018i	−0.176880	+	1.11678i
$848$	1.05319	+	2.52247i	0.0361665	+	0.0866219i
$849$			21.0498i			0.722427i
$850$	−4.51185	+	8.70579i	−0.154755	+	0.298606i
$851$	5.64328			0.193449
$852$	−0.716992	+	18.9292i	−0.0245638	+	0.648502i
$853$	−11.8495	−	1.87678i	−0.405721	−	0.0642598i	−0.0497610	−	0.998761i	$-0.515846\pi$
$853$	−11.8495	−	1.87678i	−0.405721	−	0.0642598i	−0.355960	+	0.934501i	$0.615846\pi$
$854$	2.96759	+	49.7243i	0.101549	+	1.70153i
$855$	0.208683	−	0.00945573i	0.00713680	−	0.000323379i
$856$	−25.6056	+	26.7444i	−0.875181	+	0.914105i
$857$	36.2767	+	36.2767i	1.23919	+	1.23919i	0.960333	+	0.278856i	$0.0899551\pi$
$857$	36.2767	+	36.2767i	1.23919	+	1.23919i	0.278856	+	0.960333i	$0.410045\pi$
$858$	0.537507	−	1.23121i	0.0183502	−	0.0420327i
$859$	19.8652	+	6.45461i	0.677793	+	0.220228i	0.627629	−	0.778513i	$-0.284025\pi$
$859$	19.8652	+	6.45461i	0.677793	+	0.220228i	0.0501644	+	0.998741i	$0.484025\pi$
$860$	−10.4938	+	33.1311i	−0.357835	+	1.12976i
$861$	−27.1164	+	8.81065i	−0.924124	+	0.300266i
$862$	5.43552	−	55.5896i	0.185134	−	1.89339i
$863$	22.8038	−	11.6191i	0.776249	−	0.395519i	−0.0205299	−	0.999789i	$-0.506535\pi$
$863$	22.8038	−	11.6191i	0.776249	−	0.395519i	0.796779	+	0.604270i	$0.206535\pi$
$864$	4.62946	−	3.25086i	0.157497	−	0.110597i
$865$	−31.2285	+	17.7362i	−1.06180	+	0.603048i
$866$	−15.9435	+	13.1033i	−0.541783	+	0.445269i
$867$	2.35857	+	14.8914i	0.0801012	+	0.505739i
$868$	−53.5370	−	19.6651i	−1.81717	−	0.667478i
$869$	0.738837	+	0.536797i	0.0250633	+	0.0182096i
$870$	−3.64202	−	8.17636i	−0.123476	−	0.277205i
$871$	29.2661	+	40.2813i	0.991643	+	1.36488i
$872$	−40.4412	−	12.1743i	−1.36951	−	0.412275i
$873$	−3.81996	−	1.94637i	−0.129286	−	0.0658745i
$874$	0.452451	+	0.289183i	0.0153044	+	0.00978176i
$875$	−19.2199	−	27.6712i	−0.649752	−	0.935457i
$876$	7.10810	+	15.3616i	0.240161	+	0.519022i
$877$	19.1884	+	9.77699i	0.647947	+	0.330145i	0.746890	−	0.664948i	$-0.231546\pi$
$877$	19.1884	+	9.77699i	0.647947	+	0.330145i	−0.0989430	+	0.995093i	$0.531546\pi$
$878$	11.6078	+	10.3003i	0.391744	+	0.347619i
$879$	18.8289	−	13.6800i	0.635082	−	0.461414i
$880$	−2.42745	+	0.707812i	−0.0818292	+	0.0238603i
$881$	12.0677	+	8.76768i	0.406570	+	0.295391i	0.772212	−	0.635365i	$-0.219150\pi$
$881$	12.0677	+	8.76768i	0.406570	+	0.295391i	−0.365642	+	0.930756i	$0.619150\pi$
$882$	−0.632674	−	2.87388i	−0.0213032	−	0.0967686i
$883$	3.93229	−	0.622813i	0.132332	−	0.0209593i	−0.0899170	−	0.995949i	$-0.528660\pi$
$883$	3.93229	−	0.622813i	0.132332	−	0.0209593i	0.222249	+	0.974990i	$0.428660\pi$
$884$	9.25324	−	1.10843i	0.311220	−	0.0372805i
$885$	5.91338	−	3.35850i	0.198776	−	0.112895i
$886$	2.09945	−	8.06881i	0.0705324	−	0.271077i
$887$	−3.92853	−	7.71018i	−0.131907	−	0.258883i	0.815600	−	0.578616i	$-0.196407\pi$
$887$	−3.92853	−	7.71018i	−0.131907	−	0.258883i	−0.947508	+	0.319733i	$0.896407\pi$
$888$	1.29453	+	3.70775i	0.0434415	+	0.124424i
$889$	13.4213	−	4.36085i	0.450136	−	0.146258i
$890$	−18.6342	+	4.99643i	−0.624620	+	0.167481i
$891$	0.0873587	−	0.268863i	0.00292663	−	0.00900723i
$892$	7.80801	+	11.6499i	0.261432	+	0.390068i
$893$	0.122271	+	0.122271i	0.00409164	+	0.00409164i
$894$	−4.99019	−	12.7234i	−0.166897	−	0.425534i
$895$	0.374522	+	8.26549i	0.0125189	+	0.276285i
$896$	−7.14201	+	33.3367i	−0.238598	+	1.11370i
$897$	13.4891	+	2.13646i	0.450387	+	0.0713344i
$898$	3.42615	+	5.83614i	0.114332	+	0.194755i
$899$			26.7860i			0.893364i
$900$	−9.13684	−	4.06425i	−0.304561	−	0.135475i
$901$			0.947641i			0.0315705i
$902$	3.26212	−	1.91505i	0.108617	−	0.0637643i
$903$	23.1293	+	3.66332i	0.769695	+	0.121908i
$904$	−36.0859	+	19.3866i	−1.20020	+	0.644787i
$905$	50.5203	−	18.9837i	1.67935	−	0.631039i
$906$	9.72106	−	3.81266i	0.322961	−	0.126667i
$907$	13.7535	+	13.7535i	0.456678	+	0.456678i	0.897563	−	0.440885i	$-0.145336\pi$
$907$	13.7535	+	13.7535i	0.456678	+	0.456678i	−0.440885	+	0.897563i	$0.645336\pi$
$908$	2.55994	+	3.81955i	0.0849546	+	0.126756i
$909$	−0.509610	+	1.56842i	−0.0169027	+	0.0520211i
$910$	−11.4702	+	29.8962i	−0.380234	+	0.991049i
$911$	−17.2226	+	5.59595i	−0.570609	+	0.185402i	−0.580089	−	0.814553i	$-0.696982\pi$
$911$	−17.2226	+	5.59595i	−0.570609	+	0.185402i	0.00948031	+	0.999955i	$0.496982\pi$
$912$	−0.0862101	+	0.363606i	−0.00285470	+	0.0120402i
$913$	2.12059	+	4.16189i	0.0701812	+	0.137738i
$914$	32.1644	+	8.36897i	1.06390	+	0.276821i
$915$	10.7995	−	23.8011i	0.357020	−	0.786841i
$916$	−1.97297	−	16.4705i	−0.0651888	−	0.544201i
$917$	−51.2676	+	8.11999i	−1.69300	+	0.268146i
$918$	1.91524	−	0.421632i	0.0632122	−	0.0139159i
$919$	−9.62088	−	6.98998i	−0.317364	−	0.230578i	0.417686	−	0.908591i	$-0.362841\pi$
$919$	−9.62088	−	6.98998i	−0.317364	−	0.230578i	−0.735050	+	0.678013i	$0.762841\pi$
$920$	−13.1777	−	22.0703i	−0.434457	−	0.727637i
$921$	23.6296	−	17.1679i	0.778623	−	0.565703i
$922$	2.66592	−	3.00432i	0.0877974	−	0.0989422i
$923$	−28.3574	−	14.4488i	−0.933396	−	0.475589i
$924$	0.715490	+	1.54628i	0.0235379	+	0.0508688i
$925$	4.44497	−	5.33289i	0.146150	−	0.175344i
$926$	−27.2075	+	42.5683i	−0.894093	+	1.39888i
$927$	−11.3121	−	5.76380i	−0.371538	−	0.189308i
$928$	15.8529	−	2.24971i	0.520396	−	0.0738504i
$929$	−7.42668	−	10.2220i	−0.243662	−	0.335371i	0.669617	−	0.742706i	$-0.266458\pi$
$929$	−7.42668	−	10.2220i	−0.243662	−	0.335371i	−0.913279	+	0.407335i	$0.866458\pi$
$930$	20.0280	+	22.2358i	0.656745	+	0.729139i
$931$	0.157266	+	0.114261i	0.00515419	+	0.00374474i
$932$	−1.60908	+	4.38061i	−0.0527071	+	0.143492i
$933$	−3.01977	−	19.0661i	−0.0988630	−	0.624196i
$934$	−13.0185	−	15.8403i	−0.425978	−	0.518310i
$935$	−0.871111	−	0.0977972i	−0.0284884	−	0.00319831i
$936$	1.69060	+	9.35269i	0.0552591	+	0.305702i
$937$	28.6133	−	14.5792i	0.934755	−	0.476282i	0.0808594	−	0.996726i	$-0.474234\pi$
$937$	28.6133	−	14.5792i	0.934755	−	0.476282i	0.853896	+	0.520444i	$0.174234\pi$
$938$	−62.8468	−	6.14513i	−2.05202	−	0.200645i
$939$	−29.1448	+	9.46973i	−0.951105	+	0.309033i
$940$	−2.61628	−	7.85329i	−0.0853335	−	0.256146i
$941$	−9.55987	−	3.10619i	−0.311643	−	0.101259i	0.149020	−	0.988834i	$-0.452388\pi$
$941$	−9.55987	−	3.10619i	−0.311643	−	0.101259i	−0.460663	+	0.887575i	$0.652388\pi$
$942$	−19.6915	−	8.59668i	−0.641582	−	0.280095i
$943$	27.1918	+	27.1918i	0.885486	+	0.885486i
$944$	2.87326	+	11.8210i	0.0935168	+	0.384741i
$945$	−1.79002	+	6.49614i	−0.0582294	+	0.211319i
$946$	−3.10132	+	0.185089i	−0.100833	+	0.00601777i
$947$	−18.7753	−	2.97371i	−0.610114	−	0.0966326i	−0.156271	−	0.987714i	$-0.549947\pi$
$947$	−18.7753	−	2.97371i	−0.610114	−	0.0966326i	−0.453843	+	0.891082i	$0.649947\pi$
$948$	−6.45633	−	0.244551i	−0.209692	−	0.00794264i
$949$	−28.4387			−0.923159
$950$	0.629654	−	0.199788i	0.0204287	−	0.00648199i
$951$		−	24.8691i		−	0.806436i
$952$	−6.73760	+	9.71084i	−0.218367	+	0.314730i
$953$	2.20490	−	13.9212i	0.0714238	−	0.450952i	−0.925896	−	0.377780i	$-0.876688\pi$
$953$	2.20490	−	13.9212i	0.0714238	−	0.450952i	0.997319	−	0.0731724i	$-0.0233123\pi$
$954$	−0.964723	+	0.0575754i	−0.0312341	+	0.00186407i
$955$	17.2946	+	21.6689i	0.559640	+	0.701189i
$956$	−5.20744	−	1.02819i	−0.168421	−	0.0332541i
$957$	0.565812	−	0.565812i	0.0182901	−	0.0182901i
$958$	−15.9210	+	36.4684i	−0.514383	+	1.17824i
$959$	−1.19136	+	3.66664i	−0.0384711	+	0.118402i
$960$	11.4778	−	13.7208i	0.370443	−	0.442838i
$961$	−18.0945	−	55.6893i	−0.583695	−	1.79643i
$962$	−6.56696	−	0.642114i	−0.211727	−	0.0207026i
$963$	−5.94300	−	11.6638i	−0.191511	−	0.375861i
$964$	35.1499	+	37.9175i	1.13210	+	1.22124i
$965$	−38.5690	+	7.91314i	−1.24158	+	0.254733i
$966$	−13.3814	+	10.9976i	−0.430538	+	0.353842i
$967$	23.2805	−	3.68727i	0.748651	−	0.118575i	0.229561	−	0.973294i	$-0.426271\pi$
$967$	23.2805	−	3.68727i	0.748651	−	0.118575i	0.519090	+	0.854720i	$0.326271\pi$
$968$	18.6939	+	24.5871i	0.600844	+	0.790259i
$969$	−0.0761465	+	0.104807i	−0.00244618	+	0.00336688i
$970$	−13.2617	−	2.81649i	−0.425806	−	0.0904319i
$971$	3.05972	−	2.22302i	0.0981911	−	0.0713400i	−0.537606	−	0.843196i	$-0.680671\pi$
$971$	3.05972	−	2.22302i	0.0981911	−	0.0713400i	0.635797	+	0.771856i	$0.280671\pi$
$972$	0.545595	+	1.92414i	0.0175000	+	0.0617169i
$973$	9.59956	−	18.8402i	0.307748	−	0.603989i
$974$	−4.32066	−	2.76154i	−0.138443	−	0.0884856i
$975$	12.6437	−	11.0644i	0.404924	−	0.354344i
$976$	35.6380	+	30.2643i	1.14074	+	0.968735i
$977$	−26.1594	+	51.3408i	−0.836914	+	1.64254i	−0.0728979	+	0.997339i	$0.523225\pi$
$977$	−26.1594	+	51.3408i	−0.836914	+	1.64254i	−0.764016	+	0.645197i	$0.776775\pi$
$978$	−4.90360	+	5.52605i	−0.156800	+	0.176704i
$979$	−1.01375	−	1.39530i	−0.0323995	−	0.0445941i
$980$	−4.28608	−	8.25980i	−0.136914	−	0.263850i
$981$	8.77677	−	12.0802i	0.280221	−	0.385691i
$982$	6.14795	+	27.9267i	0.196189	+	0.891176i
$983$	−3.05428	−	19.2840i	−0.0974165	−	0.615063i	−0.987299	−	0.158873i	$-0.949214\pi$
$983$	−3.05428	−	19.2840i	−0.0974165	−	0.615063i	0.889883	−	0.456190i	$-0.150786\pi$
$984$	−11.6279	+	24.1031i	−0.370685	+	0.768380i
$985$	19.7603	−	21.6360i	0.629615	−	0.689380i
$986$	5.37202	+	1.39776i	0.171080	+	0.0445139i
$987$	−4.96974	+	2.53221i	−0.158189	+	0.0806011i
$988$	−0.493603	−	0.387998i	−0.0157036	−	0.0123438i
$989$	−9.76005	−	30.0383i	−0.310351	−	0.955163i
$990$	0.0466344	−	0.892755i	0.00148214	−	0.0283736i
$991$	−15.0537	−	4.89123i	−0.478196	−	0.155375i	0.0599944	−	0.998199i	$-0.480892\pi$
$991$	−15.0537	−	4.89123i	−0.478196	−	0.155375i	−0.538190	+	0.842824i	$0.680892\pi$
$992$	−48.0834	+	23.5319i	−1.52665	+	0.747139i
$993$	−4.69025	+	4.69025i	−0.148841	+	0.148841i
$994$	37.5768	−	14.7378i	1.19186	−	0.467456i
$995$	1.48116	+	0.976856i	0.0469561	+	0.0309684i
$996$	−28.8550	−	16.1062i	−0.914306	−	0.510344i
$997$	−0.876456	+	5.53373i	−0.0277577	+	0.175255i	−0.997672	−	0.0681901i	$-0.978278\pi$
$997$	−0.876456	+	5.53373i	−0.0277577	+	0.175255i	0.969915	+	0.243445i	$0.0782776\pi$
$998$	27.4731	+	46.7980i	0.869646	+	1.48136i
$999$	−1.38849			−0.0439298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bq.a.67.11	✓	480
8.3	odd	2	inner	600.2.bq.a.67.32	yes	480
25.3	odd	20	inner	600.2.bq.a.403.32	yes	480
200.3	even	20	inner	600.2.bq.a.403.11	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bq.a.67.11	✓	480	1.1	even	1	trivial
600.2.bq.a.67.32	yes	480	8.3	odd	2	inner
600.2.bq.a.403.11	yes	480	200.3	even	20	inner
600.2.bq.a.403.32	yes	480	25.3	odd	20	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21959 + 0.715968i) q^{2} +(-0.156434 + 0.987688i) q^{3} +(0.974780 - 1.74637i) q^{4} +(1.86666 + 1.23110i) q^{5} +(-0.516368 - 1.31657i) q^{6} +(-2.13082 + 2.13082i) q^{7} +(0.0615147 + 2.82776i) q^{8} +(-0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-1.21959 + 0.715968i) q^{2} +(-0.156434 + 0.987688i) q^{3} +(0.974780 - 1.74637i) q^{4} +(1.86666 + 1.23110i) q^{5} +(-0.516368 - 1.31657i) q^{6} +(-2.13082 + 2.13082i) q^{7} +(0.0615147 + 2.82776i) q^{8} +(-0.951057 - 0.309017i) q^{9} +(-3.15797 - 0.164961i) q^{10} +(-0.0873587 - 0.268863i) q^{11} +(1.57238 + 1.23597i) q^{12} +(-2.99402 + 1.52553i) q^{13} +(1.07312 - 4.12432i) q^{14} +(-1.50795 + 1.65109i) q^{15} +(-2.09961 - 3.40465i) q^{16} +(-0.216929 - 1.36963i) q^{17} +(1.38114 - 0.304053i) q^{18} +(-0.0549118 + 0.0755796i) q^{19} +(3.96953 - 2.05982i) q^{20} +(-1.77125 - 2.43792i) q^{21} +(0.299038 + 0.265355i) q^{22} +(-1.84517 + 3.62135i) q^{23} +(-2.80257 - 0.381601i) q^{24} +(1.96881 + 4.59606i) q^{25} +(2.55923 - 4.00413i) q^{26} +(0.453990 - 0.891007i) q^{27} +(1.64412 + 5.79828i) q^{28} +(2.28992 - 1.66373i) q^{29} +(0.656946 - 3.09329i) q^{30} +(-5.56242 + 7.65602i) q^{31} +(4.99827 + 2.64902i) q^{32} +(0.279218 - 0.0442238i) q^{33} +(1.24518 + 1.51507i) q^{34} +(-6.60076 + 1.35427i) q^{35} +(-1.46673 + 1.35967i) q^{36} +(-0.630361 - 1.23715i) q^{37} +(0.0128571 - 0.131491i) q^{38} +(-1.03838 - 3.19580i) q^{39} +(-3.36641 + 5.35418i) q^{40} +(2.92379 - 8.99849i) q^{41} +(3.90567 + 1.70509i) q^{42} +(-5.49497 + 5.49497i) q^{43} +(-0.554689 - 0.109521i) q^{44} +(-1.39487 - 1.74767i) q^{45} +(-0.342426 - 5.73762i) q^{46} +(0.289550 - 1.82814i) q^{47} +(3.69119 - 1.54115i) q^{48} -2.08080i q^{49} +(-5.69176 - 4.19569i) q^{50} +1.38671 q^{51} +(-0.254376 + 6.71571i) q^{52} +(-0.674962 - 0.106904i) q^{53} +(0.0842514 + 1.41170i) q^{54} +(0.167927 - 0.609421i) q^{55} +(-6.15653 - 5.89437i) q^{56} +(-0.0660590 - 0.0660590i) q^{57} +(-1.60158 + 3.66857i) q^{58} +(-2.89245 - 0.939813i) q^{59} +(1.41349 + 4.24288i) q^{60} +(-11.1166 + 3.61199i) q^{61} +(1.30239 - 13.3197i) q^{62} +(2.68499 - 1.36807i) q^{63} +(-7.99243 + 0.347897i) q^{64} +(-7.46687 - 0.838285i) q^{65} +(-0.308868 + 0.253846i) q^{66} +(-2.31795 - 14.6350i) q^{67} +(-2.60334 - 0.956254i) q^{68} +(-3.28811 - 2.38895i) q^{69} +(7.08058 - 6.37757i) q^{70} +(5.56713 + 7.66249i) q^{71} +(0.815321 - 2.70837i) q^{72} +(7.54080 + 3.84223i) q^{73} +(1.65454 + 1.05750i) q^{74} +(-4.84747 + 1.22559i) q^{75} +(0.0784629 + 0.169570i) q^{76} +(0.759044 + 0.386752i) q^{77} +(3.55448 + 3.15411i) q^{78} +(-2.61351 + 1.89883i) q^{79} +(0.272209 - 8.94013i) q^{80} +(0.809017 + 0.587785i) q^{81} +(2.87682 + 13.0678i) q^{82} +(-16.3194 + 2.58475i) q^{83} +(-5.98409 + 0.716823i) q^{84} +(1.28122 - 2.82369i) q^{85} +(2.76737 - 10.6358i) q^{86} +(1.28502 + 2.52199i) q^{87} +(0.754904 - 0.263568i) q^{88} +(5.80221 - 1.88525i) q^{89} +(2.95243 + 1.13275i) q^{90} +(3.12909 - 9.63034i) q^{91} +(4.52557 + 6.75236i) q^{92} +(-6.69161 - 6.69161i) q^{93} +(0.955762 + 2.43689i) q^{94} +(-0.195547 + 0.0734795i) q^{95} +(-3.39830 + 4.52234i) q^{96} +(4.23446 + 0.670672i) q^{97} +(1.48979 + 2.53772i) q^{98} +0.282699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 12 q^{8}+O(q^{10}) \) 480 * q + 12 * q^8	\( 480 q + 12 q^{8} - 8 q^{10} + 8 q^{12} - 8 q^{17} + 20 q^{20} + 28 q^{22} + 8 q^{25} - 4 q^{28} - 8 q^{30} - 20 q^{32} + 48 q^{35} + 20 q^{38} - 108 q^{40} - 20 q^{42} + 32 q^{43} - 140 q^{44} - 16 q^{48} + 124 q^{50} - 132 q^{52} + 152 q^{58} - 20 q^{60} + 116 q^{62} - 60 q^{64} + 8 q^{65} - 48 q^{67} - 72 q^{68} - 4 q^{70} - 12 q^{72} + 40 q^{73} + 24 q^{78} - 76 q^{80} + 120 q^{81} - 64 q^{82} - 80 q^{83} - 80 q^{84} - 132 q^{88} + 200 q^{89} - 48 q^{90} - 216 q^{92} - 40 q^{94} + 20 q^{96} - 56 q^{97} - 192 q^{98}+O(q^{100}) \) 480 * q + 12 * q^8 - 8 * q^10 + 8 * q^12 - 8 * q^17 + 20 * q^20 + 28 * q^22 + 8 * q^25 - 4 * q^28 - 8 * q^30 - 20 * q^32 + 48 * q^35 + 20 * q^38 - 108 * q^40 - 20 * q^42 + 32 * q^43 - 140 * q^44 - 16 * q^48 + 124 * q^50 - 132 * q^52 + 152 * q^58 - 20 * q^60 + 116 * q^62 - 60 * q^64 + 8 * q^65 - 48 * q^67 - 72 * q^68 - 4 * q^70 - 12 * q^72 + 40 * q^73 + 24 * q^78 - 76 * q^80 + 120 * q^81 - 64 * q^82 - 80 * q^83 - 80 * q^84 - 132 * q^88 + 200 * q^89 - 48 * q^90 - 216 * q^92 - 40 * q^94 + 20 * q^96 - 56 * q^97 - 192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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