LMFDB - Embedded newform 804.2.w.a.59.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(59,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("804.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.w (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$1320$
Relative dimension:	$132$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			59.12
Character	$\chi$	$=$	804.59
Dual form			804.2.w.a.695.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33982 + 0.452629i) q^{2} +(-0.379728 + 1.68991i) q^{3} +(1.59025 - 1.21289i) q^{4} +(2.40444 - 3.74138i) q^{5} +(-0.256136 - 2.43606i) q^{6} +(-1.84812 - 0.265720i) q^{7} +(-1.58167 + 2.34485i) q^{8} +(-2.71161 - 1.28341i) q^{9} +O(q^{10})$	\(q+(-1.33982 + 0.452629i) q^{2} +(-0.379728 + 1.68991i) q^{3} +(1.59025 - 1.21289i) q^{4} +(2.40444 - 3.74138i) q^{5} +(-0.256136 - 2.43606i) q^{6} +(-1.84812 - 0.265720i) q^{7} +(-1.58167 + 2.34485i) q^{8} +(-2.71161 - 1.28341i) q^{9} +(-1.52806 + 6.10110i) q^{10} +(1.18522 + 0.761693i) q^{11} +(1.44581 + 3.14796i) q^{12} +(-1.48640 - 3.25476i) q^{13} +(2.59643 - 0.480496i) q^{14} +(5.40957 + 5.48399i) q^{15} +(1.05781 - 3.85759i) q^{16} +(1.61770 + 5.50939i) q^{17} +(4.21399 + 0.492193i) q^{18} +(2.48280 - 0.356973i) q^{19} +(-0.714200 - 8.86605i) q^{20} +(1.15083 - 3.02227i) q^{21} +(-1.93275 - 0.484070i) q^{22} +(0.504696 + 0.582450i) q^{23} +(-3.36199 - 3.56329i) q^{24} +(-6.13951 - 13.4436i) q^{25} +(3.46472 + 3.68802i) q^{26} +(3.19853 - 4.09504i) q^{27} +(-3.26127 + 1.81900i) q^{28} -3.88926i q^{29} +(-9.73008 - 4.89905i) q^{30} +(-9.51540 - 4.34554i) q^{31} +(0.328775 + 5.64729i) q^{32} +(-1.73726 + 1.71368i) q^{33} +(-4.66115 - 6.64939i) q^{34} +(-5.43785 + 6.27562i) q^{35} +(-5.86879 + 1.24793i) q^{36} +5.04960 q^{37} +(-3.16494 + 1.60207i) q^{38} +(6.06470 - 1.27596i) q^{39} +(4.96993 + 11.5557i) q^{40} +(-1.06981 - 3.64343i) q^{41} +(-0.173939 + 4.57020i) q^{42} +(-1.02654 - 3.49608i) q^{43} +(2.80864 - 0.226249i) q^{44} +(-11.3216 + 7.05928i) q^{45} +(-0.939838 - 0.551940i) q^{46} +(-2.96778 - 3.42500i) q^{47} +(6.11732 + 3.25245i) q^{48} +(-3.37150 - 0.989962i) q^{49} +(14.3108 + 15.2332i) q^{50} +(-9.92467 + 0.641709i) q^{51} +(-6.31141 - 3.37307i) q^{52} +(0.936205 - 3.18842i) q^{53} +(-2.43193 + 6.93439i) q^{54} +(5.69956 - 2.60290i) q^{55} +(3.54620 - 3.91329i) q^{56} +(-0.339535 + 4.33127i) q^{57} +(1.76039 + 5.21093i) q^{58} +(4.92372 - 10.7815i) q^{59} +(15.2540 + 2.15975i) q^{60} +(8.17315 - 5.25256i) q^{61} +(14.7159 + 1.51531i) q^{62} +(4.67037 + 3.09244i) q^{63} +(-2.99663 - 7.41756i) q^{64} +(-15.7513 - 2.26469i) q^{65} +(1.55195 - 3.08236i) q^{66} +(-4.50769 - 6.83233i) q^{67} +(9.25482 + 6.79924i) q^{68} +(-1.17594 + 0.631720i) q^{69} +(4.44523 - 10.8695i) q^{70} +(5.05955 + 1.48562i) q^{71} +(7.29829 - 4.32838i) q^{72} +(-4.10190 + 2.63613i) q^{73} +(-6.76557 + 2.28560i) q^{74} +(25.0499 - 5.27031i) q^{75} +(3.51532 - 3.57903i) q^{76} +(-1.98803 - 1.72264i) q^{77} +(-7.54809 + 4.45463i) q^{78} +(-4.25031 + 1.94105i) q^{79} +(-11.8893 - 13.2330i) q^{80} +(5.70570 + 6.96025i) q^{81} +(3.08247 + 4.39732i) q^{82} +(6.87622 + 4.41908i) q^{83} +(-1.83556 - 6.20199i) q^{84} +(24.5024 + 7.19454i) q^{85} +(2.95781 + 4.21948i) q^{86} +(6.57252 + 1.47686i) q^{87} +(-3.66068 + 1.57441i) q^{88} +(1.44515 + 1.25223i) q^{89} +(11.9738 - 14.5827i) q^{90} +(1.88220 + 6.41017i) q^{91} +(1.50904 + 0.314105i) q^{92} +(10.9568 - 14.4301i) q^{93} +(5.52656 + 3.24559i) q^{94} +(4.63417 - 10.1474i) q^{95} +(-9.66828 - 1.58883i) q^{96} -7.14998 q^{97} +(4.96530 - 0.199665i) q^{98} +(-2.23629 - 3.58654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9	$ 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9} - 26 q^{10} - 15 q^{12} - 44 q^{13} - 34 q^{16} - 13 q^{18} - 66 q^{21} + 74 q^{22} + 13 q^{24} + 80 q^{25} - 110 q^{28} - 36 q^{30} - 22 q^{33} - 54 q^{34} - 37 q^{36} - 72 q^{37} - 22 q^{40} + q^{42} - 154 q^{45} - 82 q^{46} + 11 q^{48} + 96 q^{49} - 14 q^{52} - 138 q^{54} - 6 q^{57} + 74 q^{58} + 3 q^{60} - 28 q^{61} - 6 q^{64} - 4 q^{66} - 38 q^{69} - 18 q^{70} - 145 q^{72} + 96 q^{73} + 14 q^{76} - 51 q^{78} - 38 q^{81} - 74 q^{82} - 41 q^{84} - 76 q^{85} + 6 q^{88} - 5 q^{90} + 78 q^{93} - 22 q^{94} + 184 q^{96} - 128 q^{97}+O(q^{100}) $ 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9 - 26 * q^10 - 15 * q^12 - 44 * q^13 - 34 * q^16 - 13 * q^18 - 66 * q^21 + 74 * q^22 + 13 * q^24 + 80 * q^25 - 110 * q^28 - 36 * q^30 - 22 * q^33 - 54 * q^34 - 37 * q^36 - 72 * q^37 - 22 * q^40 + q^42 - 154 * q^45 - 82 * q^46 + 11 * q^48 + 96 * q^49 - 14 * q^52 - 138 * q^54 - 6 * q^57 + 74 * q^58 + 3 * q^60 - 28 * q^61 - 6 * q^64 - 4 * q^66 - 38 * q^69 - 18 * q^70 - 145 * q^72 + 96 * q^73 + 14 * q^76 - 51 * q^78 - 38 * q^81 - 74 * q^82 - 41 * q^84 - 76 * q^85 + 6 * q^88 - 5 * q^90 + 78 * q^93 - 22 * q^94 + 184 * q^96 - 128 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$	$-1$

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 $

$2$	−1.33982	+	0.452629i	−0.947398	+	0.320057i
$2$	−1.33982	+	0.452629i	−0.947398	+	0.320057i
$3$	−0.379728	+	1.68991i	−0.219236	+	0.975672i
$3$	−0.379728	+	1.68991i	−0.219236	+	0.975672i
$4$	1.59025	−	1.21289i	0.795127	−	0.606443i
$5$	2.40444	−	3.74138i	1.07530	−	1.67319i	0.449259	−	0.893402i	$-0.351688\pi$
$5$	2.40444	−	3.74138i	1.07530	−	1.67319i	0.626038	−	0.779793i	$-0.284676\pi$
$6$	−0.256136	−	2.43606i	−0.104567	−	0.994518i
$7$	−1.84812	−	0.265720i	−0.698525	−	0.100433i	−0.216101	−	0.976371i	$-0.569334\pi$
$7$	−1.84812	−	0.265720i	−0.698525	−	0.100433i	−0.482423	+	0.875938i	$0.660243\pi$
$8$	−1.58167	+	2.34485i	−0.559205	+	0.829029i
$9$	−2.71161	−	1.28341i	−0.903871	−	0.427805i
$10$	−1.52806	+	6.10110i	−0.483216	+	1.92934i
$11$	1.18522	+	0.761693i	0.357357	+	0.229659i	0.706984	−	0.707230i	$-0.250055\pi$
$11$	1.18522	+	0.761693i	0.357357	+	0.229659i	−0.349627	+	0.936889i	$0.613692\pi$
$12$	1.44581	+	3.14796i	0.417369	+	0.908737i
$13$	−1.48640	−	3.25476i	−0.412254	−	0.902709i	−0.995879	−	0.0906867i	$-0.971094\pi$
$13$	−1.48640	−	3.25476i	−0.412254	−	0.902709i	0.583626	−	0.812023i	$-0.301633\pi$
$14$	2.59643	−	0.480496i	0.693925	−	0.128418i
$15$	5.40957	+	5.48399i	1.39674	+	1.41596i
$16$	1.05781	−	3.85759i	0.264453	−	0.964398i
$17$	1.61770	+	5.50939i	0.392350	+	1.33622i	0.884836	+	0.465902i	$0.154270\pi$
$17$	1.61770	+	5.50939i	0.392350	+	1.33622i	−0.492486	+	0.870321i	$0.663912\pi$
$18$	4.21399	+	0.492193i	0.993248	+	0.116011i
$19$	2.48280	−	0.356973i	0.569593	−	0.0818952i	0.148500	−	0.988912i	$-0.452556\pi$
$19$	2.48280	−	0.356973i	0.569593	−	0.0818952i	0.421093	+	0.907017i	$0.361646\pi$
$20$	−0.714200	−	8.86605i	−0.159700	−	1.98251i
$21$	1.15083	−	3.02227i	0.251131	−	0.659512i
$22$	−1.93275	−	0.484070i	−0.412063	−	0.103204i
$23$	0.504696	+	0.582450i	0.105236	+	0.121449i	0.805924	−	0.592019i	$-0.201669\pi$
$23$	0.504696	+	0.582450i	0.105236	+	0.121449i	−0.700688	+	0.713468i	$0.747123\pi$
$24$	−3.36199	−	3.56329i	−0.686263	−	0.727354i
$25$	−6.13951	−	13.4436i	−1.22790	−	2.68873i
$26$	3.46472	+	3.68802i	0.679487	+	0.723281i
$27$	3.19853	−	4.09504i	0.615558	−	0.788092i
$28$	−3.26127	+	1.81900i	−0.616322	+	0.343759i
$29$		−	3.88926i		−	0.722218i	−0.932524	−	0.361109i	$-0.882398\pi$
$29$		−	3.88926i		−	0.722218i	0.932524	−	0.361109i	$-0.117602\pi$
$30$	−9.73008	−	4.89905i	−1.77646	−	0.894441i
$31$	−9.51540	−	4.34554i	−1.70902	−	0.780482i	−0.996922	−	0.0783981i	$-0.975019\pi$
$31$	−9.51540	−	4.34554i	−1.70902	−	0.780482i	−0.712094	−	0.702084i	$-0.752253\pi$
$32$	0.328775	+	5.64729i	0.0581198	+	0.998310i
$33$	−1.73726	+	1.71368i	−0.302417	+	0.298313i
$34$	−4.66115	−	6.64939i	−0.799380	−	1.14036i
$35$	−5.43785	+	6.27562i	−0.919165	+	1.06077i
$36$	−5.86879	+	1.24793i	−0.978131	+	0.207988i
$37$	5.04960			0.830149			0.415075	−	0.909787i	$-0.363756\pi$
$37$	5.04960			0.830149			0.415075	+	0.909787i	$0.363756\pi$
$38$	−3.16494	+	1.60207i	−0.513421	+	0.259890i
$39$	6.06470	−	1.27596i	0.971129	−	0.204318i
$40$	4.96993	+	11.5557i	0.785815	+	1.82711i
$41$	−1.06981	−	3.64343i	−0.167076	−	0.569008i	−0.999881	−	0.0154412i	$-0.995085\pi$
$41$	−1.06981	−	3.64343i	−0.167076	−	0.569008i	0.832805	−	0.553566i	$-0.186733\pi$
$42$	−0.173939	+	4.57020i	−0.0268394	+	0.705197i
$43$	−1.02654	−	3.49608i	−0.156546	−	0.533146i	0.843446	−	0.537214i	$-0.180523\pi$
$43$	−1.02654	−	3.49608i	−0.156546	−	0.533146i	−0.999992	+	0.00406782i	$0.998705\pi$
$44$	2.80864	−	0.226249i	0.423419	−	0.0341083i
$45$	−11.3216	+	7.05928i	−1.68773	+	1.05234i
$46$	−0.939838	−	0.551940i	−0.138571	−	0.0813792i
$47$	−2.96778	−	3.42500i	−0.432895	−	0.499588i	0.496827	−	0.867850i	$-0.334498\pi$
$47$	−2.96778	−	3.42500i	−0.432895	−	0.499588i	−0.929722	+	0.368262i	$0.879953\pi$
$48$	6.11732	+	3.25245i	0.882959	+	0.469451i
$49$	−3.37150	−	0.989962i	−0.481643	−	0.141423i
$50$	14.3108	+	15.2332i	2.02386	+	2.15430i
$51$	−9.92467	+	0.641709i	−1.38973	+	0.0898573i
$52$	−6.31141	−	3.37307i	−0.875236	−	0.467760i
$53$	0.936205	−	3.18842i	0.128598	−	0.437963i	−0.869871	−	0.493279i	$-0.835798\pi$
$53$	0.936205	−	3.18842i	0.128598	−	0.437963i	0.998469	+	0.0553155i	$0.0176165\pi$
$54$	−2.43193	+	6.93439i	−0.330944	+	0.943650i
$55$	5.69956	−	2.60290i	0.768529	−	0.350975i
$56$	3.54620	−	3.91329i	0.473880	−	0.522935i
$57$	−0.339535	+	4.33127i	−0.0449725	+	0.573691i
$58$	1.76039	+	5.21093i	0.231151	+	0.684228i
$59$	4.92372	−	10.7815i	0.641014	−	1.40363i	−0.258189	−	0.966094i	$-0.583126\pi$
$59$	4.92372	−	10.7815i	0.641014	−	1.40363i	0.899203	−	0.437531i	$-0.144147\pi$
$60$	15.2540	+	2.15975i	1.96929	+	0.278822i
$61$	8.17315	−	5.25256i	1.04646	−	0.672522i	0.0998868	−	0.994999i	$-0.468152\pi$
$61$	8.17315	−	5.25256i	1.04646	−	0.672522i	0.946577	+	0.322477i	$0.104516\pi$
$62$	14.7159	+	1.51531i	1.86892	+	0.192444i
$63$	4.67037	+	3.09244i	0.588411	+	0.389610i
$64$	−2.99663	−	7.41756i	−0.374579	−	0.927195i
$65$	−15.7513	−	2.26469i	−1.95370	−	0.280900i
$66$	1.55195	−	3.08236i	0.191032	−	0.379412i
$67$	−4.50769	−	6.83233i	−0.550702	−	0.834702i
$67$	−4.50769	−	6.83233i	−0.550702	−	0.834702i
$68$	9.25482	+	6.79924i	1.12231	+	0.824529i
$69$	−1.17594	+	0.631720i	−0.141566	+	0.0760502i
$70$	4.44523	−	10.8695i	0.531307	−	1.29916i
$71$	5.05955	+	1.48562i	0.600458	+	0.176310i	0.567814	−	0.823157i	$-0.307789\pi$
$71$	5.05955	+	1.48562i	0.600458	+	0.176310i	0.0326438	+	0.999467i	$0.489607\pi$
$72$	7.29829	−	4.32838i	0.860112	−	0.510105i
$73$	−4.10190	+	2.63613i	−0.480091	+	0.308536i	−0.758210	−	0.652011i	$-0.773926\pi$
$73$	−4.10190	+	2.63613i	−0.480091	+	0.308536i	0.278118	+	0.960547i	$0.410289\pi$
$74$	−6.76557	+	2.28560i	−0.786482	+	0.265695i
$75$	25.0499	−	5.27031i	2.89252	−	0.608563i
$76$	3.51532	−	3.57903i	0.403234	−	0.410543i
$77$	−1.98803	−	1.72264i	−0.226557	−	0.196313i
$78$	−7.54809	+	4.45463i	−0.854652	+	0.504387i
$79$	−4.25031	+	1.94105i	−0.478197	+	0.218385i	−0.639906	−	0.768453i	$-0.721027\pi$
$79$	−4.25031	+	1.94105i	−0.478197	+	0.218385i	0.161709	+	0.986839i	$0.448299\pi$
$80$	−11.8893	−	13.2330i	−1.32926	−	1.47950i
$81$	5.70570	+	6.96025i	0.633966	+	0.773361i
$82$	3.08247	+	4.39732i	0.340402	+	0.485603i
$83$	6.87622	+	4.41908i	0.754763	+	0.485057i	0.860572	−	0.509330i	$-0.170107\pi$
$83$	6.87622	+	4.41908i	0.754763	+	0.485057i	−0.105808	+	0.994387i	$0.533743\pi$
$84$	−1.83556	−	6.20199i	−0.200276	−	0.676693i
$85$	24.5024	+	7.19454i	2.65765	+	0.780358i
$86$	2.95781	+	4.21948i	0.318949	+	0.454998i
$87$	6.57252	+	1.47686i	0.704648	+	0.158336i
$88$	−3.66068	+	1.57441i	−0.390230	+	0.167832i
$89$	1.44515	+	1.25223i	0.153186	+	0.132736i	0.728082	−	0.685490i	$-0.240412\pi$
$89$	1.44515	+	1.25223i	0.153186	+	0.132736i	−0.574896	+	0.818226i	$0.694958\pi$
$90$	11.9738	−	14.5827i	1.26214	−	1.53715i
$91$	1.88220	+	6.41017i	0.197308	+	0.671968i
$92$	1.50904	+	0.314105i	0.157328	+	0.0327477i
$93$	10.9568	−	14.4301i	1.13617	−	1.49633i
$94$	5.52656	+	3.24559i	0.570021	+	0.334757i
$95$	4.63417	−	10.1474i	0.475455	−	1.04110i
$96$	−9.66828	−	1.58883i	−0.986765	−	0.162159i
$97$	−7.14998			−0.725970			−0.362985	−	0.931795i	$-0.618242\pi$
$97$	−7.14998			−0.725970			−0.362985	+	0.931795i	$0.618242\pi$
$98$	4.96530	−	0.199665i	0.501571	−	0.0201692i
$99$	−2.23629	−	3.58654i	−0.224755	−	0.360461i
$100$	−26.0690	−	13.9323i	−2.60690	−	1.39323i
$101$	2.73886	−	0.393789i	0.272527	−	0.0391835i	−0.00469627	−	0.999989i	$-0.501495\pi$
$101$	2.73886	−	0.393789i	0.272527	−	0.0391835i	0.277223	+	0.960805i	$0.410586\pi$
$102$	13.0069	−	5.35197i	1.28787	−	0.529924i
$103$	9.43754	+	4.30998i	0.929909	+	0.424675i	0.822001	−	0.569486i	$-0.192858\pi$
$103$	9.43754	+	4.30998i	0.929909	+	0.424675i	0.107908	+	0.994161i	$0.465585\pi$
$104$	9.98293	+	1.66258i	0.978907	+	0.163030i
$105$	−8.54034	−	11.5725i	−0.833452	−	1.12936i
$106$	0.188823	+	4.69567i	0.0183401	+	0.456084i
$107$	−5.95498	+	3.82703i	−0.575689	+	0.369973i	−0.795853	−	0.605490i	$-0.792977\pi$
$107$	−5.95498	+	3.82703i	−0.575689	+	0.369973i	0.220164	+	0.975463i	$0.429341\pi$
$108$	0.119656	−	10.3916i	0.0115139	−	0.999934i
$109$	1.65304	+	3.61965i	0.158333	+	0.346700i	0.972128	−	0.234452i	$-0.0753295\pi$
$109$	1.65304	+	3.61965i	0.158333	+	0.346700i	−0.813795	+	0.581152i	$0.802602\pi$
$110$	−6.45826	+	6.06722i	−0.615771	+	0.578487i
$111$	−1.91747	+	8.53339i	−0.181998	+	0.809953i
$112$	−2.98001	+	6.84822i	−0.281584	+	0.647096i
$113$	9.73248	+	15.1440i	0.915555	+	1.42463i	0.905342	+	0.424683i	$0.139614\pi$
$113$	9.73248	+	15.1440i	0.915555	+	1.42463i	0.0102127	+	0.999948i	$0.496749\pi$
$114$	−1.50554	−	5.95682i	−0.141007	−	0.557907i
$115$	3.39268	−	0.487793i	0.316369	−	0.0454869i
$116$	−4.71723	−	6.18492i	−0.437984	−	0.574255i
$117$	−0.146664	+	10.7333i	−0.0135591	+	0.992297i
$118$	−1.71692	+	16.6739i	−0.158055	+	1.53495i
$119$	−1.52576	−	10.6119i	−0.139866	−	0.972789i
$120$	−21.4153	+	4.01075i	−1.95494	+	0.366129i
$121$	−3.74500	−	8.20041i	−0.340455	−	0.745492i
$122$	−8.57311	+	10.7369i	−0.776173	+	0.972074i
$123$	6.56331	−	0.424370i	0.591794	−	0.0382642i
$124$	−20.4025	+	4.63059i	−1.83220	+	0.415839i
$125$	−43.0492	−	6.18954i	−3.85044	−	0.553609i
$126$	−7.65719	−	2.02937i	−0.682157	−	0.180791i
$127$	9.88329	+	1.42100i	0.877000	+	0.126094i	0.566088	−	0.824345i	$-0.308456\pi$
$127$	9.88329	+	1.42100i	0.877000	+	0.126094i	0.310913	+	0.950439i	$0.399365\pi$
$128$	7.37236	+	8.58186i	0.651631	+	0.758536i
$129$	6.29787	−	0.407207i	0.554496	−	0.0358526i
$130$	22.1290	−	4.09519i	1.94084	−	0.359172i
$131$	−10.3802	−	11.9794i	−0.906926	−	1.04665i	−0.998705	−	0.0508688i	$-0.983801\pi$
$131$	−10.3802	−	11.9794i	−0.906926	−	1.04665i	0.0917795	−	0.995779i	$-0.470745\pi$
$132$	−0.684179	+	4.83228i	−0.0595502	+	0.420596i
$133$	−4.68337			−0.406100
$134$	9.13202	+	7.11380i	0.788886	+	0.614539i
$135$	−7.63043	−	21.8132i	−0.656723	−	1.87738i
$136$	−15.4774	−	4.92078i	−1.32717	−	0.421953i
$137$	−1.81980	+	1.57686i	−0.155476	+	0.134721i	−0.729125	−	0.684380i	$-0.760073\pi$
$137$	−1.81980	+	1.57686i	−0.155476	+	0.134721i	0.573649	+	0.819101i	$0.305527\pi$
$138$	1.28961	−	1.37866i	0.109779	−	0.117359i
$139$	−11.5619	+	17.9907i	−0.980670	+	1.52595i	−0.135970	+	0.990713i	$0.543415\pi$
$139$	−11.5619	+	17.9907i	−0.980670	+	1.52595i	−0.844700	+	0.535240i	$0.820221\pi$
$140$	−1.03596	+	16.5753i	−0.0875543	+	1.40087i
$141$	6.91490	−	3.71472i	0.582340	−	0.312836i
$142$	−7.45134	+	0.299634i	−0.625302	+	0.0251447i
$143$	0.717423	−	4.98979i	0.0599939	−	0.417267i
$144$	−7.81927	+	9.10269i	−0.651606	+	0.758558i
$145$	−14.5512	−	9.35149i	−1.20841	−	0.776599i
$146$	4.30263	−	5.38859i	0.356088	−	0.445963i
$147$	2.95320	−	5.32163i	0.243576	−	0.438920i
$148$	8.03014	−	6.12459i	0.660074	−	0.503438i
$149$	9.09974	−	1.30834i	0.745480	−	0.107184i	0.240901	−	0.970550i	$-0.422557\pi$
$149$	9.09974	−	1.30834i	0.745480	−	0.107184i	0.504578	+	0.863366i	$0.331648\pi$
$150$	−31.1770	+	18.3996i	−2.54559	+	1.50232i
$151$	1.15709	+	3.94070i	0.0941629	+	0.320689i	0.993082	−	0.117426i	$-0.0374643\pi$
$151$	1.15709	+	3.94070i	0.0941629	+	0.320689i	−0.898919	+	0.438115i	$0.855646\pi$
$152$	−3.08993	+	6.38640i	−0.250626	+	0.518006i
$153$	2.68424	−	17.0155i	0.217008	−	1.37562i
$154$	3.44333	+	1.40819i	0.277471	+	0.113475i
$155$	−39.1375	+	25.1521i	−3.14360	+	2.02027i
$156$	8.09681	−	9.38490i	0.648263	−	0.751393i
$157$	−2.74875	−	3.17223i	−0.219374	−	0.253171i	0.635386	−	0.772195i	$-0.280841\pi$
$157$	−2.74875	−	3.17223i	−0.219374	−	0.253171i	−0.854760	+	0.519024i	$0.826296\pi$
$158$	4.81609	−	4.52448i	0.383147	−	0.359948i
$159$	5.03265	+	2.79284i	0.399115	+	0.221486i
$160$	21.9192	+	12.3485i	1.73286	+	0.976233i
$161$	−0.777971	−	1.21055i	−0.0613127	−	0.0954045i
$162$	−10.7950	−	6.74293i	−0.848138	−	0.529775i
$163$		−	13.9200i		−	1.09030i	−0.838340	−	0.545148i	$-0.816474\pi$
$163$		−	13.9200i		−	1.09030i	0.838340	−	0.545148i	$-0.183526\pi$
$164$	−6.12032	−	4.49642i	−0.477917	−	0.351111i
$165$	2.23440	+	10.6202i	0.173948	+	0.826778i
$166$	−11.2131	−	2.80841i	−0.870307	−	0.217975i
$167$	2.19736	+	15.2830i	0.170037	+	1.18263i	0.878801	+	0.477188i	$0.158344\pi$
$167$	2.19736	+	15.2830i	0.170037	+	1.18263i	−0.708764	+	0.705445i	$0.750747\pi$
$168$	5.26653	+	7.47875i	0.406321	+	0.576998i
$169$	0.129086	−	0.148973i	0.00992966	−	0.0114594i
$170$	−36.0853	+	1.45107i	−2.76762	+	0.111292i
$171$	−7.19054	−	2.21849i	−0.549874	−	0.169652i
$172$	−5.87280	−	4.31457i	−0.447797	−	0.328983i
$173$	16.2241	+	7.40932i	1.23350	+	0.563320i	0.922097	−	0.386958i	$-0.126474\pi$
$173$	16.2241	+	7.40932i	1.23350	+	0.563320i	0.311402	+	0.950278i	$0.399202\pi$
$174$	−9.47448	+	0.996180i	−0.718259	+	0.0755202i
$175$	7.77432	+	26.4769i	0.587683	+	2.00146i
$176$	4.19204	−	3.76636i	0.315987	−	0.283900i
$177$	16.3500	+	12.4147i	1.22894	+	0.933145i
$178$	−2.50304	−	1.02365i	−0.187611	−	0.0767258i
$179$	−12.0146	+	13.8656i	−0.898012	+	1.03636i	0.101127	+	0.994873i	$0.467755\pi$
$179$	−12.0146	+	13.8656i	−0.898012	+	1.03636i	−0.999139	+	0.0414873i	$0.986790\pi$
$180$	−9.44217	+	24.9579i	−0.703778	+	1.86025i
$181$	12.0059	+	13.8555i	0.892391	+	1.02987i	0.999366	+	0.0356128i	$0.0113383\pi$
$181$	12.0059	+	13.8555i	0.892391	+	1.02987i	−0.106974	+	0.994262i	$0.534116\pi$
$182$	−5.42324	−	7.73656i	−0.401997	−	0.573472i
$183$	5.77280	+	15.8065i	0.426738	+	1.16845i
$184$	−2.16402	+	0.262191i	−0.159534	+	0.0193290i
$185$	12.1414	−	18.8925i	0.892657	−	1.38900i
$186$	−8.14876	+	24.2931i	−0.597496	+	1.78126i
$187$	−2.27913	+	7.76202i	−0.166667	+	0.567615i
$188$	−8.87366	−	1.84704i	−0.647178	−	0.134709i
$189$	−6.99942	+	6.71823i	−0.509133	+	0.488679i
$190$	−1.61595	+	15.6933i	−0.117233	+	1.13851i
$191$	11.3135	−	13.0564i	0.818614	−	0.944730i	−0.180633	−	0.983551i	$-0.557814\pi$
$191$	11.3135	−	13.0564i	0.818614	−	0.944730i	0.999246	+	0.0388202i	$0.0123599\pi$
$192$	13.6729	−	2.24739i	0.986759	−	0.162191i
$193$	−0.336008	+	0.735755i	−0.0241864	+	0.0529608i	−0.921340	−	0.388759i	$-0.872904\pi$
$193$	−0.336008	+	0.735755i	−0.0241864	+	0.0529608i	0.897153	+	0.441719i	$0.145631\pi$
$194$	9.57971	−	3.23629i	0.687783	−	0.232352i
$195$	9.80832	−	25.7583i	0.702388	−	1.84459i
$196$	−6.56225	+	2.51496i	−0.468732	+	0.179640i
$197$	5.53029	−	18.8344i	0.394017	−	1.34190i	−0.488888	−	0.872347i	$-0.662597\pi$
$197$	5.53029	−	18.8344i	0.394017	−	1.34190i	0.882905	−	0.469552i	$-0.155584\pi$
$198$	4.61960	+	3.79313i	0.328301	+	0.269566i
$199$	−9.71041	−	1.39615i	−0.688353	−	0.0989702i	−0.210742	−	0.977542i	$-0.567588\pi$
$199$	−9.71041	−	1.39615i	−0.688353	−	0.0989702i	−0.477611	+	0.878572i	$0.658497\pi$
$200$	41.2340	+	6.86722i	2.91568	+	0.485585i
$201$	13.2577	−	5.02318i	0.935129	−	0.354308i
$202$	−3.49135	+	1.76730i	−0.245651	+	0.124347i
$203$	−1.03345	+	7.18784i	−0.0725343	+	0.504487i
$204$	−15.0044	+	13.0580i	−1.05052	+	0.914242i
$205$	−16.2037	−	4.75784i	−1.13172	−	0.332302i
$206$	−14.5955	−	1.50291i	−1.01691	−	0.104713i
$207$	−0.621016	−	2.22711i	−0.0431636	−	0.154795i
$208$	−14.1279	+	2.29100i	−0.979593	+	0.158852i
$209$	3.21456	+	1.46804i	0.222356	+	0.101547i
$210$	16.6806	+	11.6395i	1.15107	+	0.803204i
$211$	−1.10759	−	0.959732i	−0.0762496	−	0.0660706i	0.615902	−	0.787823i	$-0.288792\pi$
$211$	−1.10759	−	0.959732i	−0.0762496	−	0.0660706i	−0.692152	+	0.721752i	$0.743337\pi$
$212$	−2.37839	−	6.20591i	−0.163348	−	0.426223i
$213$	−4.43182	+	7.98607i	−0.303663	+	0.547197i
$214$	6.24639	−	7.82294i	0.426994	−	0.534765i
$215$	−15.5484	−	4.56542i	−1.06039	−	0.311359i
$216$	4.54323	+	13.9771i	0.309128	+	0.951021i
$217$	16.4309	+	10.5595i	1.11540	+	0.716827i
$218$	−3.85314	−	4.10148i	−0.260968	−	0.277787i
$219$	−2.89723	−	7.93287i	−0.195777	−	0.536053i
$220$	5.90673	−	11.0522i	0.398231	−	0.745139i
$221$	15.5272	−	13.4544i	1.04447	−	0.905041i
$222$	−1.29338	−	12.3011i	−0.0868062	−	0.825598i
$223$	16.2085	+	14.0448i	1.08540	+	0.940507i	0.998447	−	0.0557051i	$-0.0177407\pi$
$223$	16.2085	+	14.0448i	1.08540	+	0.940507i	0.0869557	+	0.996212i	$0.472286\pi$
$224$	0.892981	−	10.5243i	0.0596648	−	0.703181i
$225$	−0.605789	+	44.3335i	−0.0403859	+	2.95557i
$226$	−19.8944	−	15.8851i	−1.32336	−	1.05666i
$227$	−6.03152	+	1.77101i	−0.400326	+	0.117546i	−0.475697	−	0.879609i	$-0.657804\pi$
$227$	−6.03152	+	1.77101i	−0.400326	+	0.117546i	0.0753710	+	0.997156i	$0.475986\pi$
$228$	4.71339	+	7.29964i	0.312152	+	0.483430i
$229$	2.13113	−	4.66653i	0.140829	−	0.308373i	−0.826055	−	0.563590i	$-0.809420\pi$
$229$	2.13113	−	4.66653i	0.140829	−	0.308373i	0.966884	+	0.255217i	$0.0821470\pi$
$230$	−4.32480	+	2.18918i	−0.285169	+	0.144350i
$231$	3.66602	−	2.70547i	0.241206	−	0.178007i
$232$	9.11973	+	6.15154i	0.598740	+	0.403868i
$233$	−6.43316	−	5.57437i	−0.421451	−	0.365189i	0.418164	−	0.908371i	$-0.362674\pi$
$233$	−6.43316	−	5.57437i	−0.421451	−	0.365189i	−0.839615	+	0.543183i	$0.817219\pi$
$234$	−4.66171	−	14.4472i	−0.304746	−	0.944440i
$235$	−19.9501	+	2.86839i	−1.30140	+	0.187113i
$236$	−5.24670	−	23.1172i	−0.341531	−	1.50480i
$237$	−1.66625	−	7.91972i	−0.108234	−	0.514441i
$238$	6.84749	+	13.5274i	0.443857	+	0.876854i
$239$	−14.4445			−0.934335			−0.467168	−	0.884169i	$-0.654726\pi$
$239$	−14.4445			−0.934335			−0.467168	+	0.884169i	$0.654726\pi$
$240$	26.8773	−	15.0669i	1.73492	−	0.972563i
$241$	17.2375	−	11.0779i	1.11037	−	0.713590i	0.148994	−	0.988838i	$-0.452397\pi$
$241$	17.2375	−	11.0779i	1.11037	−	0.713590i	0.961373	+	0.275249i	$0.0887601\pi$
$242$	8.72938	+	9.29200i	0.561146	+	0.597312i
$243$	−13.9288	+	6.99914i	−0.893534	+	0.448995i
$244$	6.62662	−	18.2660i	0.424226	−	1.16936i
$245$	−11.8104	+	10.2338i	−0.754537	+	0.653810i
$246$	−8.60159	+	3.53933i	−0.548418	+	0.225659i
$247$	−4.85230	−	7.55033i	−0.308744	−	0.480416i
$248$	25.2399	−	15.4390i	1.60273	−	0.980375i
$249$	−10.0790	+	9.94217i	−0.638728	+	0.630059i
$250$	60.4799	−	11.1924i	3.82508	−	0.707872i
$251$	23.6230	−	6.93634i	1.49107	−	0.437818i	0.568188	−	0.822899i	$-0.307645\pi$
$251$	23.6230	−	6.93634i	1.49107	−	0.437818i	0.922883	+	0.385081i	$0.125826\pi$
$252$	11.1778	−	0.746865i	0.704138	−	0.0470481i
$253$	0.154526	+	1.07475i	0.00971499	+	0.0675692i
$254$	−13.8851	+	2.56957i	−0.871226	+	0.161229i
$255$	−21.4624	+	38.6749i	−1.34403	+	2.42192i
$256$	−13.7621	−	8.16123i	−0.860129	−	0.510077i
$257$	−15.7015	+	24.4320i	−0.979434	+	1.52403i	−0.133287	+	0.991077i	$0.542553\pi$
$257$	−15.7015	+	24.4320i	−0.979434	+	1.52403i	−0.846146	+	0.532951i	$0.821083\pi$
$258$	−8.25372	+	3.39619i	−0.513854	+	0.211437i
$259$	−9.33228	−	1.34178i	−0.579880	−	0.0833741i
$260$	−27.7953	+	15.5031i	−1.72379	+	0.961458i
$261$	−4.99153	+	10.5462i	−0.308968	+	0.652792i
$262$	19.3299	+	11.3519i	1.19421	+	0.701325i
$263$	−7.09561	−	4.56007i	−0.437534	−	0.281186i	0.303273	−	0.952904i	$-0.401920\pi$
$263$	−7.09561	−	4.56007i	−0.437534	−	0.281186i	−0.740807	+	0.671718i	$0.765557\pi$
$264$	−1.27055	−	6.78408i	−0.0781970	−	0.417531i
$265$	−9.67803	−	11.1690i	−0.594517	−	0.686109i
$266$	6.27489	−	2.11983i	0.384738	−	0.129975i
$267$	−2.66492	+	1.96667i	−0.163091	+	0.120358i
$268$	−15.4552	−	5.39782i	−0.944077	−	0.329724i
$269$			14.6552i			0.893541i	0.894649	+	0.446770i	$0.147426\pi$
$269$			14.6552i			0.893541i	−0.894649	+	0.446770i	$0.852574\pi$
$270$	20.0967	+	25.7721i	1.22305	+	1.56844i
$271$	14.3014	−	12.3922i	0.868748	−	0.752774i	−0.101513	−	0.994834i	$-0.532368\pi$
$271$	14.3014	−	12.3922i	0.868748	−	0.752774i	0.970261	+	0.242060i	$0.0778230\pi$
$272$	22.9642	−	0.412531i	1.39241	−	0.0250134i
$273$	−11.5474	+	0.746628i	−0.698878	+	0.0451880i
$274$	1.72447	−	2.93641i	0.104179	−	0.177395i
$275$	2.96328	−	20.6101i	0.178693	−	1.24283i
$276$	−1.10383	+	2.43087i	−0.0664430	+	0.146321i
$277$	−2.56881	+	17.8665i	−0.154345	+	1.07349i	0.754482	+	0.656321i	$0.227888\pi$
$277$	−2.56881	+	17.8665i	−0.154345	+	1.07349i	−0.908827	+	0.417173i	$0.863021\pi$
$278$	7.34782	−	29.3376i	0.440693	−	1.75956i
$279$	20.2250	+	23.9956i	1.21084	+	1.43658i
$280$	−6.11447	−	22.6769i	−0.365410	−	1.35520i
$281$	10.3910	−	4.74542i	0.619876	−	0.283088i	−0.0806192	−	0.996745i	$-0.525690\pi$
$281$	10.3910	−	4.74542i	0.619876	−	0.283088i	0.700495	+	0.713657i	$0.252962\pi$
$282$	−7.58336	+	8.10696i	−0.451582	+	0.482763i
$283$	−12.0434	+	1.73158i	−0.715908	+	0.102932i	−0.490637	−	0.871364i	$-0.663236\pi$
$283$	−12.0434	+	1.73158i	−0.715908	+	0.102932i	−0.225271	+	0.974296i	$0.572327\pi$
$284$	9.84786	−	3.77415i	0.584363	−	0.223955i
$285$	15.3885	+	11.6846i	0.911537	+	0.692135i
$286$	1.29730	+	7.01016i	0.0767111	+	0.414520i
$287$	1.00900	+	7.01777i	0.0595595	+	0.414246i
$288$	6.35630	−	15.7352i	0.374549	−	0.927207i
$289$	−13.4351	+	8.63421i	−0.790299	+	0.507894i
$290$	23.7288	+	5.94305i	1.39340	+	0.348988i
$291$	2.71504	−	12.0828i	0.159159	−	0.708309i
$292$	−3.32573	+	9.16726i	−0.194624	+	0.536473i
$293$	18.4764	−	8.43790i	1.07940	−	0.492947i	0.205307	−	0.978698i	$-0.434181\pi$
$293$	18.4764	−	8.43790i	1.07940	−	0.492947i	0.874098	+	0.485750i	$0.161454\pi$
$294$	−1.54805	+	8.46675i	−0.0902839	+	0.493791i
$295$	−28.4987	−	44.3448i	−1.65926	−	2.58186i
$296$	−7.98681	+	11.8405i	−0.464224	+	0.688218i
$297$	6.91013	−	2.41722i	0.400966	−	0.140261i
$298$	−11.5998	+	5.87176i	−0.671961	+	0.340142i
$299$	1.14556	−	2.50842i	0.0662493	−	0.145066i
$300$	33.4435	−	38.7638i	1.93086	−	2.23803i
$301$	0.968195	+	6.73395i	0.0558059	+	0.388138i
$302$	−3.33398	−	4.75610i	−0.191849	−	0.273683i
$303$	−0.374553	+	4.77798i	−0.0215175	+	0.274487i
$304$	1.24928	−	9.95525i	0.0716514	−	0.570973i
$305$		−	43.2083i		−	2.47410i
$306$	4.10531	+	24.0128i	0.234685	+	1.37272i
$307$	9.86008	+	4.50295i	0.562744	+	0.256997i	0.676414	−	0.736522i	$-0.263533\pi$
$307$	9.86008	+	4.50295i	0.562744	+	0.256997i	−0.113669	+	0.993519i	$0.536260\pi$
$308$	−5.25084	−	0.328177i	−0.299194	−	0.0186996i
$309$	−10.8672	+	14.3120i	−0.618213	+	0.814182i
$310$	41.0527	−	51.4142i	2.33164	−	2.92013i
$311$	8.00725	−	2.35114i	0.454050	−	0.133321i	−0.0467080	−	0.998909i	$-0.514873\pi$
$311$	8.00725	−	2.35114i	0.454050	−	0.133321i	0.500758	+	0.865588i	$0.333055\pi$
$312$	−6.60042	+	16.2390i	−0.373675	+	0.919350i
$313$	2.70871	−	3.12602i	0.153106	−	0.176693i	−0.674015	−	0.738717i	$-0.735432\pi$
$313$	2.70871	−	3.12602i	0.153106	−	0.176693i	0.827121	+	0.562024i	$0.189977\pi$
$314$	5.11868	+	3.00606i	0.288864	+	0.169642i
$315$	22.7996	−	10.0380i	1.28461	−	0.565579i
$316$	−4.40480	+	8.24191i	−0.247789	+	0.463643i
$317$	−4.48305	+	15.2679i	−0.251793	+	0.857529i	0.732467	+	0.680803i	$0.238369\pi$
$317$	−4.48305	+	15.2679i	−0.251793	+	0.857529i	−0.984260	+	0.176726i	$0.943449\pi$
$318$	−8.00698	−	1.46398i	−0.449009	−	0.0820961i
$319$	2.96243	−	4.60963i	0.165864	−	0.258089i
$320$	−34.9571	−	6.62353i	−1.95416	−	0.370267i
$321$	−4.20608	−	11.5166i	−0.234760	−	0.642795i
$322$	1.59027	+	1.26979i	0.0886225	+	0.0707625i
$323$	5.98313	+	13.1012i	0.332910	+	0.728972i
$324$	17.5155	+	4.14819i	0.973083	+	0.230455i
$325$	−34.6301	+	39.9653i	−1.92093	+	2.21688i
$326$	6.30058	+	18.6503i	0.348957	+	1.03294i
$327$	−6.74461	+	1.41901i	−0.372978	+	0.0784716i
$328$	10.2354	+	3.25417i	0.565153	+	0.179681i
$329$	4.57473	+	7.11842i	0.252213	+	0.392451i
$330$	−7.80069	−	13.2178i	−0.429414	−	0.727615i
$331$	−9.31087	+	31.7099i	−0.511771	+	1.74293i	0.145577	+	0.989347i	$0.453496\pi$
$331$	−9.31087	+	31.7099i	−0.511771	+	1.74293i	−0.657349	+	0.753587i	$0.728322\pi$
$332$	16.2948	−	1.31262i	0.894292	−	0.0720392i
$333$	−13.6926	−	6.48073i	−0.750348	−	0.355142i
$334$	−9.86160	−	19.4819i	−0.539603	−	1.06600i
$335$	−36.4008	+	0.437064i	−1.98879	+	0.0238794i
$336$	−10.4413	−	7.63642i	−0.569620	−	0.416601i
$337$	0.782887	−	5.44510i	0.0426466	−	0.296613i	−0.957325	−	0.289015i	$-0.906672\pi$
$337$	0.782887	−	5.44510i	0.0426466	−	0.296613i	0.999971	−	0.00759843i	$-0.00241868\pi$
$338$	−0.105522	+	0.258025i	−0.00573967	+	0.0140347i
$339$	−29.2878	+	10.6964i	−1.59069	+	0.580951i
$340$	47.6911	−	18.2774i	2.58641	−	0.991233i
$341$	−7.96786	−	12.3982i	−0.431484	−	0.671402i
$342$	10.6382	−	0.282265i	0.575248	−	0.0152632i
$343$	17.8567	+	8.15487i	0.964170	+	0.440322i
$344$	9.82142	+	3.12256i	0.529535	+	0.168357i
$345$	−0.463965	+	5.91856i	−0.0249790	+	0.318644i
$346$	−25.0912	−	2.58366i	−1.34891	−	0.138898i
$347$	6.96399	+	15.2490i	0.373847	+	0.818610i	0.999265	+	0.0383208i	$0.0122009\pi$
$347$	6.96399	+	15.2490i	0.373847	+	0.818610i	−0.625419	+	0.780289i	$0.715072\pi$
$348$	12.2432	−	5.62313i	0.656306	−	0.301432i
$349$	2.29604	+	0.674177i	0.122904	+	0.0360879i	0.342606	−	0.939479i	$-0.388690\pi$
$349$	2.29604	+	0.674177i	0.122904	+	0.0360879i	−0.219702	+	0.975567i	$0.570509\pi$
$350$	−22.4004	−	31.9555i	−1.19735	−	1.70809i
$351$	−18.0827	−	4.32359i	−0.965184	−	0.230776i
$352$	−3.91183	+	6.94370i	−0.208501	+	0.370100i
$353$	2.12119	−	7.22411i	0.112900	−	0.384501i	−0.883586	−	0.468270i	$-0.844878\pi$
$353$	2.12119	−	7.22411i	0.112900	−	0.384501i	0.996485	+	0.0837689i	$0.0266957\pi$
$354$	−27.5254	−	9.23298i	−1.46296	−	0.490727i
$355$	17.7236	−	15.3576i	0.940672	−	0.815097i
$356$	3.81697	+	0.238560i	0.202299	+	0.0126437i
$357$	18.5125	+	1.45123i	0.979787	+	0.0768070i
$358$	9.82146	−	24.0156i	0.519080	−	1.26926i
$359$	−6.08297	+	1.78612i	−0.321047	+	0.0942678i	−0.438285	−	0.898836i	$-0.644414\pi$
$359$	−6.08297	+	1.78612i	−0.321047	+	0.0942678i	0.117238	+	0.993104i	$0.462596\pi$
$360$	1.35417	−	37.7130i	0.0713710	−	1.98765i
$361$	−12.1935	+	3.58033i	−0.641763	+	0.188439i
$362$	−22.3572	−	13.1298i	−1.17507	−	0.690085i
$363$	15.2801	−	3.21480i	0.801995	−	0.168733i
$364$	10.7680	+	7.91091i	0.564395	+	0.414644i
$365$			21.6852i			1.13505i
$366$	−14.8890	−	18.5649i	−0.778260	−	0.970404i
$367$	−19.6849	−	17.0570i	−1.02754	−	0.890369i	−0.0335067	−	0.999438i	$-0.510668\pi$
$367$	−19.6849	−	17.0570i	−1.02754	−	0.890369i	−0.994034	+	0.109069i	$0.965213\pi$
$368$	2.78073	−	1.33079i	0.144956	−	0.0693721i
$369$	−1.77512	+	11.2526i	−0.0924091	+	0.585785i
$370$	−7.71611	+	30.8081i	−0.401142	+	1.60164i
$371$	−2.57745	+	5.64382i	−0.133814	+	0.293013i
$372$	−0.0778850	−	36.2369i	−0.00403815	−	1.87880i
$373$	−9.21496			−0.477133			−0.238566	−	0.971126i	$-0.576677\pi$
$373$	−9.21496			−0.477133			−0.238566	+	0.971126i	$0.576677\pi$
$374$	−0.459678	−	11.4313i	−0.0237694	−	0.591100i
$375$	26.8068	−	70.3991i	1.38430	−	3.63539i
$376$	12.7252	−	1.54177i	0.656250	−	0.0795107i
$377$	−12.6586	+	5.78101i	−0.651953	+	0.297737i
$378$	6.33711	−	12.1694i	0.325946	−	0.625925i
$379$	21.9906	−	19.0550i	1.12958	−	0.978788i	0.129663	−	0.991558i	$-0.458610\pi$
$379$	21.9906	−	19.0550i	1.12958	−	0.978788i	0.999918	+	0.0127700i	$0.00406493\pi$
$380$	−4.93815	−	21.7577i	−0.253322	−	1.11614i
$381$	−6.15433	+	16.1623i	−0.315296	+	0.828020i
$382$	−9.24832	+	22.6141i	−0.473185	+	1.15704i
$383$	−0.527627	−	3.66973i	−0.0269605	−	0.187514i	0.971891	−	0.235432i	$-0.0756505\pi$
$383$	−0.527627	−	3.66973i	−0.0269605	−	0.187514i	−0.998851	+	0.0479178i	$0.984741\pi$
$384$	−17.3021	+	9.19988i	−0.882943	+	0.469479i
$385$	−11.2251	+	3.29600i	−0.572086	+	0.167980i
$386$	0.117167	−	1.13787i	0.00596366	−	0.0579160i
$387$	−1.70333	+	10.7975i	−0.0865852	+	0.548867i
$388$	−11.3703	+	8.67211i	−0.577238	+	0.440260i
$389$	0.169990	−	0.0776317i	0.00861882	−	0.00393608i	−0.411101	−	0.911590i	$-0.634856\pi$
$389$	0.169990	−	0.0776317i	0.00861882	−	0.00393608i	0.419720	+	0.907654i	$0.362128\pi$
$390$	−1.48246	+	38.9511i	−0.0750672	+	1.97237i
$391$	−2.39250	+	3.72280i	−0.120994	+	0.188270i
$392$	7.65392	−	6.33986i	0.386581	−	0.320211i
$393$	24.1859	−	12.9928i	1.22002	−	0.655399i
$394$	1.11540	+	27.7380i	0.0561932	+	1.39742i
$395$	−2.95740	+	20.5691i	−0.148803	+	1.03495i
$396$	−7.90633	−	2.99115i	−0.397308	−	0.150311i
$397$	−4.50837	−	2.89735i	−0.226269	−	0.145414i	0.422595	−	0.906319i	$-0.361119\pi$
$397$	−4.50837	−	2.89735i	−0.226269	−	0.145414i	−0.648864	+	0.760904i	$0.724756\pi$
$398$	13.6422	−	2.52463i	0.683820	−	0.126548i
$399$	1.77841	−	7.91450i	0.0890317	−	0.396220i
$400$	−58.3546	+	9.46285i	−2.91773	+	0.473142i
$401$		−	5.33008i		−	0.266172i	−0.991105	−	0.133086i	$-0.957511\pi$
$401$		−	5.33008i		−	0.266172i	0.991105	−	0.133086i	$-0.0424886\pi$
$402$	−15.4894	+	12.7310i	−0.772541	+	0.634965i
$403$			37.4296i			1.86450i
$404$	3.87787	−	3.94816i	0.192931	−	0.196428i
$405$	39.7599	−	4.61170i	1.97568	−	0.229157i
$406$	−1.86878	−	10.0982i	−0.0927458	−	0.501165i
$407$	5.98488	+	3.84625i	0.296659	+	0.190651i
$408$	14.1929	−	24.2868i	0.702652	−	1.20238i
$409$	0.374980	−	2.60804i	0.0185416	−	0.128959i	−0.978448	−	0.206492i	$-0.933795\pi$
$409$	0.374980	−	2.60804i	0.0185416	−	0.128959i	0.996990	+	0.0775328i	$0.0247043\pi$
$410$	23.8636	−	0.959607i	1.17854	−	0.0473916i
$411$	−1.97374	−	3.67408i	−0.0973572	−	0.181229i
$412$	20.2356	−	4.59270i	0.996937	−	0.226266i
$413$	−11.9645	+	18.6171i	−0.588734	+	0.916088i
$414$	1.84011	+	2.70285i	0.0904364	+	0.132838i
$415$	33.0669	−	15.1011i	1.62319	−	0.741286i
$416$	17.8919	−	9.46423i	0.877223	−	0.464022i
$417$	−26.0124	−	26.3702i	−1.27383	−	1.29136i
$418$	−4.97143	−	0.511912i	−0.243160	−	0.0250384i
$419$	−9.37121	+	2.75164i	−0.457814	+	0.134426i	−0.502504	−	0.864575i	$-0.667588\pi$
$419$	−9.37121	+	2.75164i	−0.457814	+	0.134426i	0.0446907	+	0.999001i	$0.485770\pi$
$420$	−27.6175	−	8.04478i	−1.34759	−	0.392545i
$421$	−1.48326	−	10.3163i	−0.0722897	−	0.502786i	−0.993510	−	0.113745i	$-0.963715\pi$
$421$	−1.48326	−	10.3163i	−0.0722897	−	0.502786i	0.921220	−	0.389041i	$-0.127194\pi$
$422$	1.91838	+	0.784544i	0.0933851	+	0.0381910i
$423$	3.65178	+	13.0962i	0.177556	+	0.636758i
$424$	5.99559	+	7.23829i	0.291172	+	0.351522i
$425$	64.1344	−	55.5727i	3.11097	−	2.69567i
$426$	2.32312	−	12.7059i	0.112556	−	0.615603i
$427$	−16.5007	+	7.53561i	−0.798524	+	0.364674i
$428$	−4.82817	+	13.3087i	−0.233378	+	0.643298i
$429$	8.15988	+	3.10714i	0.393963	+	0.150014i
$430$	22.8985	−	0.920798i	1.10427	−	0.0444048i
$431$	13.7427			0.661963			0.330982	−	0.943637i	$-0.392620\pi$
$431$	13.7427			0.661963			0.330982	+	0.943637i	$0.392620\pi$
$432$	−12.4136	−	16.6704i	−0.597248	−	0.802057i
$433$	5.42766	−	11.8849i	0.260837	−	0.571153i	−0.733223	−	0.679988i	$-0.761985\pi$
$433$	5.42766	−	11.8849i	0.260837	−	0.571153i	0.994060	+	0.108835i	$0.0347122\pi$
$434$	−26.7941	−	6.71077i	−1.28616	−	0.322127i
$435$	21.3287	−	21.0392i	1.02263	−	1.00875i
$436$	7.01898	+	3.75122i	0.336148	+	0.179651i
$437$	1.46098	+	1.26594i	0.0698881	+	0.0605584i
$438$	7.47242	+	9.31727i	0.357046	+	0.445196i
$439$		−	25.3776i		−	1.21120i	−0.795767	−	0.605602i	$-0.792932\pi$
$439$		−	25.3776i		−	1.21120i	0.795767	−	0.605602i	$-0.207068\pi$
$440$	−2.91142	+	17.4815i	−0.138797	+	0.833400i
$441$	7.87168	+	7.01143i	0.374842	+	0.333877i
$442$	−14.7139	+	25.0546i	−0.699867	+	1.19173i
$443$	−12.6790	+	3.72288i	−0.602396	+	0.176879i	−0.568689	−	0.822552i	$-0.692549\pi$
$443$	−12.6790	+	3.72288i	−0.602396	+	0.176879i	−0.0337065	+	0.999432i	$0.510731\pi$
$444$	7.30076	+	15.8959i	0.346479	+	0.754387i
$445$	8.15984	−	2.39594i	0.386813	−	0.113579i
$446$	−28.0736	−	11.4811i	−1.32932	−	0.543644i
$447$	−1.24443	+	15.8746i	−0.0588597	+	0.750842i
$448$	3.56715	+	14.5048i	0.168532	+	0.685289i
$449$	−20.6454	+	17.8894i	−0.974319	+	0.844252i	−0.987811	−	0.155657i	$-0.950251\pi$
$449$	−20.6454	+	17.8894i	−0.974319	+	0.844252i	0.0134925	+	0.999909i	$0.495705\pi$
$450$	−19.2550	−	59.6733i	−0.907688	−	2.81302i
$451$	1.50722	−	5.13312i	0.0709722	−	0.241709i
$452$	33.8451	+	12.2785i	1.59194	+	0.577530i
$453$	−7.09882	+	0.458995i	−0.333532	+	0.0215655i
$454$	7.27956	−	5.10289i	0.341647	−	0.239490i
$455$	28.5085	+	8.37084i	1.33650	+	0.392431i
$456$	−9.61914	−	7.64680i	−0.450457	−	0.358094i
$457$	11.6264	+	25.4583i	0.543861	+	1.19089i	0.959590	+	0.281401i	$0.0907990\pi$
$457$	11.6264	+	25.4583i	0.543861	+	1.19089i	−0.415730	+	0.909488i	$0.636474\pi$
$458$	−0.743134	+	7.21694i	−0.0347244	+	0.337225i
$459$	27.7355	+	10.9974i	1.29458	+	0.513315i
$460$	4.80358	−	4.89064i	0.223968	−	0.228027i
$461$	18.6253	+	8.50589i	0.867467	+	0.396159i	0.798883	−	0.601487i	$-0.205425\pi$
$461$	18.6253	+	8.50589i	0.867467	+	0.396159i	0.0685837	+	0.997645i	$0.478152\pi$
$462$	−3.68725	+	5.28420i	−0.171546	+	0.245843i
$463$	11.4950	+	17.8866i	0.534219	+	0.831261i	0.998518	−	0.0544173i	$-0.0173301\pi$
$463$	11.4950	+	17.8866i	0.534219	+	0.831261i	−0.464299	+	0.885678i	$0.653694\pi$
$464$	−15.0032	−	4.11412i	−0.696506	−	0.190993i
$465$	−27.6433	−	75.6899i	−1.28193	−	3.51003i
$466$	11.1424	+	4.55683i	0.516163	+	0.211091i
$467$	−3.07036	+	21.3548i	−0.142079	+	0.988183i	0.786643	+	0.617408i	$0.211817\pi$
$467$	−3.07036	+	21.3548i	−0.142079	+	0.988183i	−0.928723	+	0.370776i	$0.879092\pi$
$468$	12.7851	+	17.2466i	0.590990	+	0.797225i
$469$	6.51528	+	13.8248i	0.300848	+	0.638368i
$470$	25.4312	−	12.8731i	1.17306	−	0.593792i
$471$	6.40456	−	3.44057i	0.295107	−	0.158533i
$472$	17.4932	+	28.5981i	0.805188	+	1.31633i
$473$	1.44626	−	4.92552i	0.0664993	−	0.226476i
$474$	5.81718	+	9.85684i	0.267192	+	0.452740i
$475$	−20.0422	−	31.1862i	−0.919598	−	1.43092i
$476$	−15.2973	−	15.0250i	−0.701153	−	0.688670i
$477$	−6.63069	+	7.44423i	−0.303598	+	0.340848i
$478$	19.3530	−	6.53799i	0.885187	−	0.299041i
$479$	−9.00255	+	10.3895i	−0.411337	+	0.474708i	−0.923178	−	0.384372i	$-0.874418\pi$
$479$	−9.00255	+	10.3895i	−0.411337	+	0.474708i	0.511841	+	0.859080i	$0.328964\pi$
$480$	−29.1912	+	32.3524i	−1.33239	+	1.47668i
$481$	−7.50573	−	16.4353i	−0.342232	−	0.749383i
$482$	−18.0811	+	22.6446i	−0.823570	+	1.03143i
$483$	2.34114	−	0.855026i	0.106525	−	0.0389050i
$484$	−15.9017	−	8.49847i	−0.722803	−	0.386294i
$485$	−17.1917	+	26.7508i	−0.780633	+	1.21469i
$486$	15.4941	−	15.6822i	0.702829	−	0.711359i
$487$	5.80490	−	19.7697i	0.263045	−	0.895850i	−0.717000	−	0.697074i	$-0.754485\pi$
$487$	5.80490	−	19.7697i	0.263045	−	0.895850i	0.980045	−	0.198776i	$-0.0636968\pi$
$488$	−0.610770	+	27.4726i	−0.0276483	+	1.24363i
$489$	23.5235	+	5.28579i	1.06377	+	0.239032i
$490$	11.1917	−	19.0571i	0.505591	−	0.860914i
$491$	−5.01308	+	5.78540i	−0.226237	+	0.261091i	−0.857508	−	0.514471i	$-0.827988\pi$
$491$	−5.01308	+	5.78540i	−0.226237	+	0.261091i	0.631271	+	0.775563i	$0.282534\pi$
$492$	9.92261	−	8.63540i	0.447346	−	0.389314i
$493$	21.4275	−	6.29167i	0.965044	−	0.283363i
$494$	9.91872	+	7.91981i	0.446264	+	0.356329i
$495$	−18.7956	−	0.256830i	−0.844800	−	0.0115436i
$496$	−26.8288	+	32.1098i	−1.20465	+	1.44177i
$497$	−8.95591	−	4.09003i	−0.401728	−	0.183463i
$498$	9.00390	−	17.8828i	0.403474	−	0.801347i
$499$			0.763124i			0.0341621i	0.999854	+	0.0170811i	$0.00543733\pi$
$499$			0.763124i			0.0341621i	−0.999854	+	0.0170811i	$0.994563\pi$
$500$	−75.9664	+	42.3708i	−3.39732	+	1.89488i
$501$	−26.6613	−	2.09002i	−1.19114	−	0.0933754i
$502$	−28.5111	+	19.9859i	−1.27251	+	0.892016i
$503$	3.57004	+	24.8302i	0.159180	+	1.10712i	0.900148	+	0.435583i	$0.143458\pi$
$503$	3.57004	+	24.8302i	0.159180	+	1.10712i	−0.740968	+	0.671540i	$0.765633\pi$
$504$	−14.6383	+	6.06008i	−0.652041	+	0.269938i
$505$	5.11211	−	11.1940i	0.227486	−	0.498125i
$506$	−0.693503	−	1.37004i	−0.0308300	−	0.0609056i
$507$	0.202734	+	0.274712i	0.00900371	+	0.0122004i
$508$	17.4405	−	9.72756i	0.773795	−	0.431590i
$509$	14.4242	+	22.4446i	0.639344	+	0.994838i	0.998113	+	0.0614117i	$0.0195602\pi$
$509$	14.4242	+	22.4446i	0.639344	+	0.994838i	−0.358769	+	0.933426i	$0.616803\pi$
$510$	11.2504	−	61.5320i	0.498177	−	2.72468i
$511$	8.28129	−	3.78194i	0.366343	−	0.167303i
$512$	22.1327	+	4.70550i	0.978138	+	0.207956i
$513$	6.47950	−	11.3090i	0.286077	−	0.499303i
$514$	9.97861	−	39.8416i	0.440137	−	1.75734i
$515$	38.8172	−	24.9463i	1.71049	−	1.09927i
$516$	9.52131	−	8.28616i	0.419152	−	0.364778i
$517$	−0.908666	−	6.31991i	−0.0399631	−	0.277949i
$518$	13.1109	−	2.42631i	0.576061	−	0.106606i
$519$	−18.6819	+	24.6039i	−0.820043	+	1.07999i
$520$	30.2237	−	33.3523i	1.32540	−	1.46260i
$521$	20.9466	−	3.01167i	0.917687	−	0.131943i	0.332743	−	0.943017i	$-0.392026\pi$
$521$	20.9466	−	3.01167i	0.917687	−	0.131943i	0.584944	+	0.811074i	$0.301117\pi$
$522$	1.91427	−	16.3893i	0.0837852	−	0.717342i
$523$	39.1696	−	17.8881i	1.71277	−	0.782194i	0.716337	−	0.697755i	$-0.245817\pi$
$523$	39.1696	−	17.8881i	1.71277	−	0.782194i	0.996429	−	0.0844391i	$-0.0269098\pi$
$524$	−31.0369	−	6.46029i	−1.35585	−	0.282219i
$525$	−47.6958	+	3.08391i	−2.08161	+	0.134593i
$526$	11.5709	+	2.89801i	0.504514	+	0.126359i
$527$	8.54817	−	59.4538i	0.372364	−	2.58985i
$528$	4.77299	+	8.51438i	0.207718	+	0.370541i
$529$	3.18871	−	22.1780i	0.138640	−	0.964260i
$530$	18.0223	+	10.5840i	0.782838	+	0.459739i
$531$	−27.1883	+	22.9160i	−1.17987	+	0.994468i
$532$	−7.44775	+	5.68040i	−0.322901	+	0.246277i
$533$	−10.2683	+	8.89756i	−0.444771	+	0.385396i
$534$	2.68035	−	3.84122i	0.115990	−	0.166226i
$535$			31.4817i			1.36107i
$536$	23.1505	+	0.236649i	0.999948	+	0.0102217i
$537$	−18.8693	−	25.5687i	−0.814272	−	1.10337i
$538$	−6.63335	−	19.6353i	−0.285984	−	0.846539i
$539$	−3.24192	−	3.74137i	−0.139639	−	0.161152i
$540$	−38.5912	−	25.4337i	−1.66070	−	1.09449i
$541$	17.4623	+	11.2224i	0.750764	+	0.482487i	0.859215	−	0.511615i	$-0.170953\pi$
$541$	17.4623	+	11.2224i	0.750764	+	0.482487i	−0.108451	+	0.994102i	$0.534589\pi$
$542$	−13.5523	+	23.0766i	−0.582119	+	0.991226i
$543$	−27.9736	+	15.0276i	−1.20046	+	0.644896i
$544$	−30.5813	+	10.9470i	−1.31116	+	0.469348i
$545$	17.5171	+	2.51858i	0.750351	+	0.107884i
$546$	15.1335	−	6.22702i	0.647653	−	0.266492i
$547$	11.5191	−	17.9241i	0.492522	−	0.766379i	−0.502654	−	0.864488i	$-0.667643\pi$
$547$	11.5191	−	17.9241i	0.492522	−	0.766379i	0.995176	+	0.0981085i	$0.0312792\pi$
$548$	−0.981384	+	4.71482i	−0.0419227	+	0.201407i
$549$	−28.9036	+	3.75339i	−1.23358	+	0.160191i
$550$	5.35844	+	28.9551i	0.228485	+	1.23465i
$551$	−1.38836	−	9.65626i	−0.0591462	−	0.411371i
$552$	0.378659	−	3.75657i	0.0161168	−	0.159890i
$553$	8.37087	−	2.45791i	0.355966	−	0.104521i
$554$	−4.64514	−	25.1007i	−0.197353	−	1.06643i
$555$	27.3162	+	27.6920i	1.15951	+	1.17546i
$556$	3.43429	+	42.6331i	0.145646	+	1.80805i
$557$	3.93903	+	6.12925i	0.166902	+	0.259705i	0.914622	−	0.404309i	$-0.132488\pi$
$557$	3.93903	+	6.12925i	0.166902	+	0.259705i	−0.747720	+	0.664014i	$0.768852\pi$
$558$	−37.9590	−	22.9955i	−1.60693	−	0.973476i
$559$	−9.85305	+	8.53772i	−0.416740	+	0.361107i
$560$	18.4565	+	27.6155i	0.779931	+	1.16697i
$561$	−12.2517	−	6.79899i	−0.517267	−	0.287054i
$562$	−11.7742	+	11.0613i	−0.496665	+	0.466593i
$563$	−1.29835	+	0.834401i	−0.0547191	+	0.0351658i	−0.567714	−	0.823226i	$-0.692172\pi$
$563$	−1.29835	+	0.834401i	−0.0547191	+	0.0351658i	0.512995	+	0.858391i	$0.328536\pi$
$564$	6.49091	−	14.2943i	0.273317	−	0.601901i
$565$	80.0607			3.36818
$566$	15.3523	−	7.77123i	0.645306	−	0.326649i
$567$	−8.69535	−	14.3795i	−0.365171	−	0.603882i
$568$	−11.4861	+	9.51412i	−0.481946	+	0.399204i
$569$	24.5571	−	3.53077i	1.02949	−	0.148018i	0.393186	−	0.919459i	$-0.371373\pi$
$569$	24.5571	−	3.53077i	1.02949	−	0.148018i	0.636300	+	0.771441i	$0.280464\pi$
$570$	−25.9067	−	8.69000i	−1.08511	−	0.363984i
$571$	−4.32207	−	3.74510i	−0.180873	−	0.156727i	0.559719	−	0.828683i	$-0.310909\pi$
$571$	−4.32207	−	3.74510i	−0.180873	−	0.156727i	−0.740592	+	0.671955i	$0.765455\pi$
$572$	−4.91116	−	8.80518i	−0.205346	−	0.368163i
$573$	17.7682	+	24.0767i	0.742277	+	1.00582i
$574$	−4.52833	−	8.94586i	−0.189009	−	0.373393i
$575$	4.73167	−	10.3609i	0.197324	−	0.432080i
$576$	−1.39410	+	23.9595i	−0.0580874	+	0.998312i
$577$	6.57180	−	1.92965i	0.273588	−	0.0803326i	−0.142061	−	0.989858i	$-0.545373\pi$
$577$	6.57180	−	1.92965i	0.273588	−	0.0803326i	0.415648	+	0.909525i	$0.363555\pi$
$578$	14.0926	−	17.6494i	0.586173	−	0.734119i
$579$	−1.11577	−	0.847211i	−0.0463699	−	0.0352089i
$580$	−34.4824	+	2.77771i	−1.43180	+	0.115338i
$581$	−11.5339	−	9.99415i	−0.478505	−	0.414627i
$582$	1.83137	+	17.4178i	0.0759126	+	0.721990i
$583$	3.53820	−	3.06587i	0.146537	−	0.126975i
$584$	0.306530	−	13.7878i	0.0126843	−	0.570544i
$585$	39.8048	+	26.3563i	1.64573	+	1.08970i
$586$	−20.9359	+	19.6683i	−0.864854	+	0.812489i
$587$	0.0479125	+	0.0307915i	0.00197756	+	0.00127090i	0.541629	−	0.840618i	$-0.317808\pi$
$587$	0.0479125	+	0.0307915i	0.00197756	+	0.00127090i	−0.539652	+	0.841888i	$0.681444\pi$
$588$	−1.75819	−	12.0446i	−0.0725065	−	0.496712i
$589$	−25.1761	−	7.39236i	−1.03736	−	0.304597i
$590$	58.2550	+	46.5149i	2.39832	+	1.91499i
$591$	29.7286	+	16.4977i	1.22287	+	0.678624i
$592$	5.34154	−	19.4793i	0.219536	−	0.800594i
$593$	27.3956	+	23.7384i	1.12500	+	0.974821i	0.999850	−	0.0173162i	$-0.00551218\pi$
$593$	27.3956	+	23.7384i	1.12500	+	0.974821i	0.125154	+	0.992137i	$0.460058\pi$
$594$	−8.16425	+	6.36637i	−0.334983	+	0.261215i
$595$	−43.3716	−	19.8072i	−1.77806	−	0.812014i
$596$	12.8840	−	13.1175i	0.527750	−	0.537316i
$597$	6.04668	−	15.8796i	0.247474	−	0.649909i
$598$	−0.399460	+	3.87935i	−0.0163352	+	0.158639i
$599$	−43.1291	−	12.6639i	−1.76221	−	0.517431i	−0.769571	−	0.638561i	$-0.779530\pi$
$599$	−43.1291	−	12.6639i	−1.76221	−	0.517431i	−0.992637	+	0.121130i	$0.961348\pi$
$600$	−27.2627	+	67.0742i	−1.11299	+	2.73829i
$601$	−1.83881	+	12.7892i	−0.0750067	+	0.521683i	0.917331	+	0.398126i	$0.130339\pi$
$601$	−1.83881	+	12.7892i	−0.0750067	+	0.521683i	−0.992337	+	0.123557i	$0.960570\pi$
$602$	−4.34519	−	8.58407i	−0.177097	−	0.349860i
$603$	3.45441	+	24.3119i	0.140674	+	0.990056i
$604$	6.61969	+	4.86329i	0.269351	+	0.197884i
$605$	−39.6854	−	5.70590i	−1.61344	−	0.231978i
$606$	−1.66082	−	6.57118i	−0.0674660	−	0.266936i
$607$	2.07444	−	7.06490i	0.0841989	−	0.286755i	−0.906621	−	0.421947i	$-0.861347\pi$
$607$	2.07444	−	7.06490i	0.0841989	−	0.286755i	0.990819	+	0.135192i	$0.0431650\pi$
$608$	2.83221	+	13.9037i	0.114861	+	0.563871i
$609$	−11.7544	−	4.47587i	−0.476312	−	0.181371i
$610$	19.5573	+	57.8914i	0.791853	+	2.34396i
$611$	−6.73626	+	14.7504i	−0.272520	+	0.596735i
$612$	−16.3693	−	30.3147i	−0.661688	−	1.22540i
$613$	4.64745	−	5.36344i	0.187709	−	0.216627i	−0.654093	−	0.756414i	$-0.726950\pi$
$613$	4.64745	−	5.36344i	0.187709	−	0.216627i	0.841802	+	0.539787i	$0.181495\pi$
$614$	−15.2489	−	1.57019i	−0.615397	−	0.0633679i
$615$	14.1933	−	25.5762i	0.572330	−	1.03133i
$616$	7.18374	−	1.93698i	0.289441	−	0.0780433i
$617$	−0.532229	+	1.81261i	−0.0214267	+	0.0729727i	−0.969512	−	0.245042i	$-0.921198\pi$
$617$	−0.532229	+	1.81261i	−0.0214267	+	0.0729727i	0.948086	+	0.318015i	$0.103016\pi$
$618$	8.08209	−	24.0944i	0.325109	−	0.969218i
$619$	11.0833	−	17.2460i	0.445476	−	0.693174i	−0.543803	−	0.839213i	$-0.683016\pi$
$619$	11.0833	−	17.2460i	0.445476	−	0.693174i	0.989279	+	0.146039i	$0.0466524\pi$
$620$	−31.7318	+	87.4676i	−1.27438	+	3.51278i
$621$	3.99945	−	0.203766i	0.160492	−	0.00817685i
$622$	−9.66411	+	6.77443i	−0.387495	+	0.271630i
$623$	−2.33807	−	2.69828i	−0.0936729	−	0.108104i
$624$	1.49317	−	24.7449i	0.0597745	−	0.990588i
$625$	−78.2749	+	90.3340i	−3.13099	+	3.61336i
$626$	−2.21427	+	5.41436i	−0.0885000	+	0.216401i
$627$	−3.70152	+	4.87488i	−0.147825	+	0.194684i
$628$	−8.21876	−	1.71072i	−0.327964	−	0.0682653i
$629$	8.16875	+	27.8202i	0.325709	+	1.10926i
$630$	−26.0039	+	23.7689i	−1.03602	+	0.946977i
$631$	8.80762	+	4.02231i	0.350626	+	0.160126i	0.582940	−	0.812515i	$-0.301902\pi$
$631$	8.80762	+	4.02231i	0.350626	+	0.160126i	−0.232314	+	0.972641i	$0.574630\pi$
$632$	2.17112	−	13.0364i	0.0863626	−	0.518562i
$633$	2.04245	−	1.50729i	0.0811799	−	0.0599095i
$634$	−0.904185	−	22.4854i	−0.0359098	−	0.893009i
$635$	29.0803	−	33.5604i	1.15401	−	1.33180i
$636$	11.3906	−	1.66271i	0.451666	−	0.0659309i
$637$	1.78931	+	12.4449i	0.0708950	+	0.493086i
$638$	−1.88268	+	7.51696i	−0.0745359	+	0.297599i
$639$	−11.8129	−	10.5219i	−0.467310	−	0.416241i
$640$	49.8343	−	6.94823i	1.96988	−	0.274653i
$641$			21.5900i			0.852753i	0.904546	+	0.426376i	$0.140210\pi$
$641$			21.5900i			0.852753i	−0.904546	+	0.426376i	$0.859790\pi$
$642$	10.8482	+	13.5264i	0.428143	+	0.533846i
$643$	−8.08860	−	12.5861i	−0.318983	−	0.496347i	0.644323	−	0.764754i	$-0.277139\pi$
$643$	−8.08860	−	12.5861i	−0.318983	−	0.496347i	−0.963306	+	0.268406i	$0.913503\pi$
$644$	−2.70543	−	0.981486i	−0.106609	−	0.0386760i
$645$	13.6193	−	24.5418i	0.536260	−	0.966333i
$646$	−13.9463	−	14.8452i	−0.548712	−	0.584077i
$647$	−9.96506	−	11.5003i	−0.391767	−	0.452123i	0.525264	−	0.850939i	$-0.323967\pi$
$647$	−9.96506	−	11.5003i	−0.391767	−	0.452123i	−0.917031	+	0.398816i	$0.869421\pi$
$648$	−25.3453	+	2.37018i	−0.995656	+	0.0931093i
$649$	14.0478	−	9.02800i	0.551426	−	0.354380i
$650$	28.3088	−	69.2210i	1.11036	−	2.71507i
$651$	−24.0840	+	23.7571i	−0.943925	+	0.931115i
$652$	−16.8833	−	22.1363i	−0.661202	−	0.866923i
$653$	−8.27837	−	28.1936i	−0.323958	−	1.10330i	−0.947033	−	0.321137i	$-0.895935\pi$
$653$	−8.27837	−	28.1936i	−0.323958	−	1.10330i	0.623075	−	0.782162i	$-0.285883\pi$
$654$	8.39430	−	4.95403i	0.328243	−	0.193718i
$655$	−69.7782	+	10.0326i	−2.72646	+	0.392006i
$656$	−15.1865	+	0.272812i	−0.592934	+	0.0106515i
$657$	14.5060	−	1.88373i	0.565934	−	0.0734915i
$658$	−9.35134	−	7.46677i	−0.364553	−	0.291085i
$659$	24.1499	+	15.5202i	0.940748	+	0.604582i	0.918607	−	0.395173i	$-0.129315\pi$
$659$	24.1499	+	15.5202i	0.940748	+	0.604582i	0.0221413	+	0.999755i	$0.492952\pi$
$660$	16.4343	+	14.1787i	0.639705	+	0.551904i
$661$	−3.49895	+	24.3357i	−0.136093	+	0.946551i	0.801296	+	0.598268i	$0.204144\pi$
$661$	−3.49895	+	24.3357i	−0.136093	+	0.946551i	−0.937390	+	0.348283i	$0.886765\pi$
$662$	−1.87791	−	46.7000i	−0.0729869	−	1.81505i
$663$	16.8407	+	31.3486i	0.654037	+	1.21748i
$664$	−21.2380	+	9.13417i	−0.824194	+	0.354474i
$665$	−11.2609	+	17.5223i	−0.436678	+	0.679484i
$666$	21.2790	+	2.48538i	0.824544	+	0.0963063i
$667$	2.26530	−	1.96290i	0.0877129	−	0.0760036i
$668$	22.0309	+	21.6387i	0.852401	+	0.837226i
$669$	−29.8893	+	22.0578i	−1.15559	+	0.852804i
$670$	48.5728	−	17.0616i	1.87653	−	0.659149i
$671$	13.6878			0.528412
$672$	17.4460	+	5.50541i	0.672993	+	0.212376i
$673$	27.7847	+	32.0653i	1.07102	+	1.23603i	0.970503	+	0.241091i	$0.0775051\pi$
$673$	27.7847	+	32.0653i	1.07102	+	1.23603i	0.100520	+	0.994935i	$0.467949\pi$
$674$	1.41568	+	7.64983i	0.0545300	+	0.294660i
$675$	−74.6897	−	17.8584i	−2.87481	−	0.687370i
$676$	0.0245919	−	0.393471i	0.000945842	−	0.0151335i
$677$	−13.0889	−	1.88190i	−0.503047	−	0.0723272i	−0.113880	−	0.993495i	$-0.536328\pi$
$677$	−13.0889	−	1.88190i	−0.503047	−	0.0723272i	−0.389167	+	0.921167i	$0.627237\pi$
$678$	34.3990	−	27.5878i	1.32108	−	1.05950i
$679$	13.2140	+	1.89989i	0.507108	+	0.0729111i
$680$	−55.6248	+	46.0749i	−2.13311	+	1.76689i
$681$	−0.702525	−	10.8652i	−0.0269208	−	0.416357i
$682$	16.2873	+	13.0050i	0.623674	+	0.497985i
$683$	−13.1324	−	28.7560i	−0.502499	−	1.10032i	−0.975649	−	0.219337i	$-0.929610\pi$
$683$	−13.1324	−	28.7560i	−0.502499	−	1.10032i	0.473150	−	0.880982i	$-0.343117\pi$
$684$	−14.1256	+	5.19335i	−0.540104	+	0.198573i
$685$	1.52405	+	10.6000i	0.0582311	+	0.405006i
$686$	−27.6159	−	2.84364i	−1.05438	−	0.108571i
$687$	7.07678	+	5.37344i	0.269996	+	0.205009i
$688$	−14.5723	+	0.261779i	−0.555565	+	0.00998021i
$689$	−11.7691	+	1.69215i	−0.448368	+	0.0644656i
$690$	−2.05728	−	8.13982i	−0.0783193	−	0.309878i
$691$	26.0067	+	40.4672i	0.989341	+	1.53945i	0.834133	+	0.551563i	$0.185968\pi$
$691$	26.0067	+	40.4672i	0.989341	+	1.53945i	0.155208	+	0.987882i	$0.450395\pi$
$692$	34.7872	−	7.89534i	1.32241	−	0.300136i
$693$	3.17991	+	7.22260i	0.120795	+	0.274364i
$694$	−16.2327	−	17.2789i	−0.616184	−	0.655897i
$695$	39.5101	+	86.5151i	1.49870	+	3.28170i
$696$	−13.8586	+	13.0757i	−0.525308	+	0.495631i
$697$	18.3424	−	11.7880i	0.694769	−	0.446501i
$698$	−3.38144	+	0.135975i	−0.127989	+	0.00514672i
$699$	11.8630	−	8.75475i	0.448702	−	0.331135i
$700$	44.4766	+	32.6756i	1.68106	+	1.23502i
$701$	−42.2151	−	19.2790i	−1.59444	−	0.728157i	−0.597180	−	0.802107i	$-0.703712\pi$
$701$	−42.2151	−	19.2790i	−1.59444	−	0.728157i	−0.997262	+	0.0739499i	$0.976440\pi$
$702$	26.1846	−	2.39191i	0.988275	−	0.0902768i
$703$	12.5371	−	1.80257i	0.472847	−	0.0679852i
$704$	2.09825	−	11.0739i	0.0790807	−	0.417365i
$705$	2.72827	−	34.8031i	0.102753	−	1.31076i
$706$	0.427823	+	10.6392i	0.0161013	+	0.400410i
$707$	−5.16639			−0.194302
$708$	41.0583	−	0.0882478i	1.54307	−	0.00331656i
$709$	−10.1234	+	22.1672i	−0.380193	+	0.832506i	0.618707	+	0.785621i	$0.287657\pi$
$709$	−10.1234	+	22.1672i	−0.380193	+	0.832506i	−0.998900	+	0.0468848i	$0.985071\pi$
$710$	−16.7952	+	28.5987i	−0.630314	+	1.07329i
$711$	14.0164	+	0.191525i	0.525655	+	0.00718273i
$712$	−5.22204	+	1.40804i	−0.195704	+	0.0527686i
$713$	−2.27133	−	7.73542i	−0.0850618	−	0.289694i
$714$	−25.4604	+	6.43492i	−0.952831	+	0.240821i
$715$	−16.9437	−	14.6818i	−0.633657	−	0.549067i
$716$	−2.28888	+	36.6221i	−0.0855394	+	1.36863i
$717$	5.48497	−	24.4099i	0.204840	−	0.911604i
$718$	7.34165	−	5.14641i	0.273988	−	0.192062i
$719$	−15.1803	−	4.45733i	−0.566129	−	0.166230i	−0.0138708	−	0.999904i	$-0.504415\pi$
$719$	−15.1803	−	4.45733i	−0.566129	−	0.166230i	−0.552258	+	0.833673i	$0.686234\pi$
$720$	15.2556	+	51.1417i	0.568544	+	1.90594i
$721$	−16.2965	−	10.4731i	−0.606913	−	0.390039i
$722$	14.7166	−	10.3161i	0.547694	−	0.383927i
$723$	12.1751	+	33.3365i	0.452797	+	1.23980i
$724$	35.8976	+	7.47204i	1.33412	+	0.277696i
$725$	−52.2859	+	23.8782i	−1.94185	+	0.886812i
$726$	−19.0175	+	11.2235i	−0.705804	+	0.416542i
$727$	−18.8044	−	16.2941i	−0.697418	−	0.604316i	0.232276	−	0.972650i	$-0.425383\pi$
$727$	−18.8044	−	16.2941i	−0.697418	−	0.604316i	−0.929693	+	0.368334i	$0.879928\pi$
$728$	−18.0079	−	5.72532i	−0.667417	−	0.212194i
$729$	−6.53877	−	26.1963i	−0.242177	−	0.970232i
$730$	−9.81534	−	29.0543i	−0.363282	−	1.07535i
$731$	17.6006	−	11.3112i	0.650982	−	0.418360i
$732$	28.3516	+	18.1345i	1.04791	+	0.670271i
$733$	−28.8697	−	8.47692i	−1.06633	−	0.313102i	−0.298931	−	0.954275i	$-0.596630\pi$
$733$	−28.8697	−	8.47692i	−1.06633	−	0.313102i	−0.767397	+	0.641173i	$0.778448\pi$
$734$	34.0947	+	13.9435i	1.25846	+	0.514662i
$735$	−12.8094	−	23.8446i	−0.472483	−	0.879520i
$736$	−3.12333	+	3.04166i	−0.115128	+	0.112117i
$737$	−0.138456	−	11.5313i	−0.00510009	−	0.424760i
$738$	−2.71489	−	15.8799i	−0.0999365	−	0.584548i
$739$	−8.25248	−	1.18653i	−0.303573	−	0.0436471i	−0.0111547	−	0.999938i	$-0.503551\pi$
$739$	−8.25248	−	1.18653i	−0.303573	−	0.0436471i	−0.292418	+	0.956291i	$0.594460\pi$
$740$	−3.60642	−	44.7700i	−0.132575	−	1.64578i
$741$	14.6019	−	5.33290i	0.536416	−	0.195909i
$742$	0.898766	−	8.72835i	0.0329947	−	0.320428i
$743$	14.0889	−	9.05441i	0.516873	−	0.332174i	−0.256061	−	0.966661i	$-0.582425\pi$
$743$	14.0889	−	9.05441i	0.516873	−	0.332174i	0.772934	+	0.634487i	$0.218788\pi$
$744$	16.5062	+	48.5158i	0.605148	+	1.77868i
$745$	16.9847	−	37.1914i	0.622272	−	1.36259i
$746$	12.3464	−	4.17096i	0.452035	−	0.152710i
$747$	−12.9741	−	20.8079i	−0.474699	−	0.761320i
$748$	5.79004	+	15.1079i	0.211705	+	0.552400i
$749$	12.0224	−	5.49047i	0.439291	−	0.200617i
$750$	−4.05166	+	106.456i	−0.147946	+	3.88722i
$751$	−8.83915	+	30.1034i	−0.322545	+	1.09849i	0.625466	+	0.780251i	$0.284909\pi$
$751$	−8.83915	+	30.1034i	−0.322545	+	1.09849i	−0.948011	+	0.318237i	$0.896909\pi$
$752$	−16.3516	+	7.82548i	−0.596282	+	0.285366i
$753$	2.75150	+	42.5548i	0.100270	+	1.55078i
$754$	14.3437	−	13.4752i	0.522366	−	0.490738i
$755$	17.5258	+	5.14604i	0.637829	+	0.187283i
$756$	−2.98240	+	19.1732i	−0.108469	+	0.697322i
$757$	−15.2934	−	17.6495i	−0.555847	−	0.641481i	0.406389	−	0.913700i	$-0.366788\pi$
$757$	−15.2934	−	17.6495i	−0.555847	−	0.641481i	−0.962235	+	0.272219i	$0.912242\pi$
$758$	−20.8387	+	35.4839i	−0.756896	+	1.28883i
$759$	−1.87492	−	0.146978i	−0.0680553	−	0.00533496i
$760$	16.4644	+	26.9163i	0.597227	+	0.976356i
$761$	−8.38471	−	28.5557i	−0.303946	−	1.03514i	−0.959900	−	0.280343i	$-0.909552\pi$
$761$	−8.38471	−	28.5557i	−0.303946	−	1.03514i	0.655954	−	0.754801i	$-0.272266\pi$
$762$	0.930185	−	24.4403i	0.0336970	−	0.885378i
$763$	−2.09321	−	7.12881i	−0.0757792	−	0.258080i
$764$	2.15531	−	34.4850i	0.0779764	−	1.24762i
$765$	−57.2074	−	50.9555i	−2.06834	−	1.84230i
$766$	2.36795	+	4.67797i	0.0855576	+	0.169022i
$767$	−42.4097			−1.53133
$768$	19.0176	−	20.1576i	0.686239	−	0.727376i
$769$	27.1646	−	31.3496i	0.979581	−	1.13050i	−0.0118587	−	0.999930i	$-0.503775\pi$
$769$	27.1646	−	31.3496i	0.979581	−	1.13050i	0.991440	−	0.130567i	$-0.0416797\pi$
$770$	13.5478	−	9.49688i	0.488230	−	0.342244i
$771$	−35.3257	−	35.8117i	−1.27222	−	1.28973i
$772$	0.358049	+	1.57758i	0.0128865	+	0.0567783i
$773$	−25.3022	−	11.5551i	−0.910058	−	0.415609i	−0.0953249	−	0.995446i	$-0.530389\pi$
$773$	−25.3022	−	11.5551i	−0.910058	−	0.415609i	−0.814733	+	0.579837i	$0.803116\pi$
$774$	−2.60509	−	15.2377i	−0.0936381	−	0.547708i
$775$			154.601i			5.55344i
$776$	11.3089	−	16.7656i	0.405966	−	0.601850i
$777$	5.81122	−	15.2612i	0.208476	−	0.547494i
$778$	−0.192618	+	0.180955i	−0.00690568	+	0.00648755i
$779$	−3.95672	−	8.66401i	−0.141764	−	0.310420i
$780$	−15.6442	−	52.8586i	−0.560151	−	1.89264i
$781$	4.86509	+	5.61461i	0.174086	+	0.200906i
$782$	1.52048	−	6.07080i	0.0543721	−	0.217092i
$783$	−15.9267	−	12.4399i	−0.569174	−	0.444567i
$784$	−7.38529	+	11.9587i	−0.263760	+	0.427096i
$785$	−18.4777	+	2.65669i	−0.659497	+	0.0948213i
$786$	−26.5239	+	28.3553i	−0.946076	+	1.01140i
$787$	−1.43248	−	4.87857i	−0.0510623	−	0.173902i	0.930014	−	0.367524i	$-0.119795\pi$
$787$	−1.43248	−	4.87857i	−0.0510623	−	0.173902i	−0.981076	+	0.193622i	$0.937976\pi$
$788$	−14.0495	−	36.6592i	−0.500492	−	1.30593i
$789$	10.4005	−	10.2594i	0.370268	−	0.365244i
$790$	−5.34780	−	28.8976i	−0.190266	−	1.02813i
$791$	−13.9627	−	30.5741i	−0.496458	−	1.08709i
$792$	11.9470	+	0.428983i	0.424517	+	0.0152432i
$793$	−29.2444	−	18.7943i	−1.03850	−	0.667403i
$794$	7.35185	+	1.84132i	0.260907	+	0.0653461i
$795$	22.5497	−	12.1138i	0.799757	−	0.429634i
$796$	−17.1354	+	9.55740i	−0.607348	+	0.338753i
$797$	12.0318	+	1.72991i	0.426188	+	0.0612766i	0.352072	−	0.935973i	$-0.385477\pi$
$797$	12.0318	+	1.72991i	0.426188	+	0.0612766i	0.0741165	+	0.997250i	$0.476386\pi$
$798$	1.19958	+	11.4090i	0.0424647	+	0.403874i
$799$	14.0687	−	21.8913i	0.497714	−	0.774458i
$800$	73.9017	−	39.0915i	2.61282	−	1.38209i
$801$	−2.31156	−	5.25029i	−0.0816750	−	0.185510i
$802$	2.41255	+	7.14137i	0.0851901	+	0.252170i
$803$	−6.86957			−0.242422
$804$	14.9906	−	24.0683i	0.528678	−	0.848822i
$805$	−6.39970			−0.225560
$806$	−16.9417	−	50.1491i	−0.596747	−	1.76643i
$807$	−24.7660	−	5.56497i	−0.871803	−	0.195896i
$808$	−3.40861	+	7.04507i	−0.119914	+	0.247845i
$809$	25.2755	−	39.3295i	0.888640	−	1.38275i	−0.0349576	−	0.999389i	$-0.511130\pi$
$809$	25.2755	−	39.3295i	0.888640	−	1.38275i	0.923598	−	0.383363i	$-0.125234\pi$
$810$	−51.1838	+	24.1753i	−1.79842	+	0.849435i
$811$	−18.8618	−	2.71192i	−0.662328	−	0.0952284i	−0.197051	−	0.980393i	$-0.563136\pi$
$811$	−18.8618	−	2.71192i	−0.662328	−	0.0952284i	−0.465277	+	0.885165i	$0.654045\pi$
$812$	7.07457	+	12.6839i	0.248269	+	0.445119i
$813$	15.5112	+	28.8738i	0.544000	+	1.01265i
$814$	−9.75960	−	2.44436i	−0.342074	−	0.0856748i
$815$	−52.0798	−	33.4697i	−1.82428	−	1.17239i
$816$	−8.02301	+	38.9642i	−0.280861	+	1.36402i
$817$	−3.79670	−	8.31361i	−0.132830	−	0.290856i
$818$	0.678069	+	3.66404i	0.0237081	+	0.128110i
$819$	3.12311	−	19.7975i	0.109130	−	0.691782i
$820$	−31.5387	+	12.0871i	−1.10138	+	0.422099i
$821$	−4.75761	−	16.2029i	−0.166042	−	0.565486i	−0.999909	−	0.0135207i	$-0.995696\pi$
$821$	−4.75761	−	16.2029i	−0.166042	−	0.565486i	0.833867	−	0.551966i	$-0.186122\pi$
$822$	4.30745	+	4.02925i	0.150240	+	0.140536i
$823$	33.6510	−	4.83828i	1.17300	−	0.168652i	0.471858	−	0.881674i	$-0.343583\pi$
$823$	33.6510	−	4.83828i	1.17300	−	0.168652i	0.701141	+	0.713023i	$0.252674\pi$
$824$	−25.0333	+	15.3126i	−0.872078	+	0.533441i
$825$	33.7040	+	12.8339i	1.17342	+	0.446819i
$826$	7.60366	−	30.3591i	0.264565	−	1.05633i
$827$	−19.0408	−	21.9743i	−0.662114	−	0.764120i	0.321007	−	0.947077i	$-0.395979\pi$
$827$	−19.0408	−	21.9743i	−0.662114	−	0.764120i	−0.983121	+	0.182956i	$0.941433\pi$
$828$	−3.68881	−	2.78845i	−0.128195	−	0.0969055i
$829$	4.28030	+	9.37256i	0.148661	+	0.325522i	0.969283	−	0.245950i	$-0.0790998\pi$
$829$	4.28030	+	9.37256i	0.148661	+	0.325522i	−0.820622	+	0.571472i	$0.806373\pi$
$830$	−37.4686	+	35.1999i	−1.30055	+	1.22181i
$831$	−29.2174	−	11.1255i	−1.01354	−	0.385939i
$832$	−19.6882	+	20.7788i	−0.682566	+	0.720375i
$833$		−	20.1764i		−	0.699070i
$834$	46.7879	+	23.5575i	1.62013	+	0.815730i
$835$	62.4628	+	28.5258i	2.16162	+	0.987177i
$836$	6.89254	−	1.56434i	0.238383	−	0.0541039i
$837$	−48.2305	+	25.0666i	−1.66709	+	0.866430i
$838$	11.3103	−	7.92839i	0.390708	−	0.273882i
$839$	5.71346	−	6.59368i	0.197250	−	0.227639i	−0.648504	−	0.761211i	$-0.724605\pi$
$839$	5.71346	−	6.59368i	0.197250	−	0.227639i	0.845755	+	0.533572i	$0.179151\pi$
$840$	40.6438	−	1.72188i	1.40235	−	0.0594105i
$841$	13.8736			0.478401
$842$	6.65677	+	13.1507i	0.229407	+	0.453202i
$843$	4.07359	+	19.3619i	0.140302	+	0.666859i
$844$	−2.92539	−	0.182837i	−0.100696	−	0.00629351i
$845$	−0.246985	−	0.841153i	−0.00849654	−	0.0289365i
$846$	−10.8204	−	15.8937i	−0.372015	−	0.546435i
$847$	4.74221	+	16.1505i	0.162944	+	0.554937i
$848$	−11.3093	−	6.98425i	−0.388363	−	0.239840i
$849$	1.64700	−	21.0099i	0.0565248	−	0.721058i
$850$	−60.7749	+	103.487i	−2.08456	+	3.54957i
$851$	2.54851	+	2.94114i	0.0873619	+	0.100821i
$852$	2.63848	+	18.0752i	0.0903929	+	0.619245i
$853$	−19.5706	−	5.74644i	−0.670084	−	0.196754i	−0.0710437	−	0.997473i	$-0.522633\pi$
$853$	−19.5706	−	5.74644i	−0.670084	−	0.196754i	−0.599040	+	0.800719i	$0.704451\pi$
$854$	18.6972	−	17.5651i	0.639804	−	0.601065i
$855$	−25.5894	+	21.5683i	−0.875139	+	0.737620i
$856$	0.445009	−	20.0166i	0.0152101	−	0.684154i
$857$	−15.7172	+	53.5279i	−0.536889	+	1.82848i	0.0227515	+	0.999741i	$0.492757\pi$
$857$	−15.7172	+	53.5279i	−0.536889	+	1.82848i	−0.559641	+	0.828735i	$0.689061\pi$
$858$	−12.3392	−	0.469623i	−0.421253	−	0.0160327i
$859$	−1.11819	+	0.510660i	−0.0381521	+	0.0174235i	−0.434400	−	0.900720i	$-0.643039\pi$
$859$	−1.11819	+	0.510660i	−0.0381521	+	0.0174235i	0.396248	+	0.918144i	$0.370312\pi$
$860$	−30.2632	+	11.5982i	−1.03197	+	0.395497i
$861$	−12.2426	−	0.959714i	−0.417225	−	0.0327070i
$862$	−18.4128	+	6.22035i	−0.627143	+	0.211866i
$863$	12.2439	−	26.8104i	0.416788	−	0.912638i	−0.578501	−	0.815682i	$-0.696362\pi$
$863$	12.2439	−	26.8104i	0.416788	−	0.912638i	0.995289	−	0.0969560i	$-0.0309106\pi$
$864$	24.1775	+	16.7167i	0.822536	+	0.568714i
$865$	66.7310	−	42.8854i	2.26892	−	1.45815i
$866$	−1.89265	+	18.3804i	−0.0643147	+	0.624592i
$867$	−9.48938	−	25.9828i	−0.322276	−	0.882421i
$868$	38.9368	−	3.13654i	1.32160	−	0.106461i
$869$	−6.51603	−	0.936863i	−0.221041	−	0.0317809i
$870$	−19.0537	+	37.8429i	−0.645981	+	1.28299i
$871$	−15.5374	+	24.8271i	−0.526464	+	0.841233i
$872$	−11.1021	−	1.84897i	−0.375965	−	0.0626142i
$873$	19.3880	+	9.17638i	0.656184	+	0.310573i
$874$	−2.53046	−	1.03486i	−0.0855940	−	0.0350047i
$875$	77.9155	+	22.8781i	2.63403	+	0.773420i
$876$	−14.2290	−	9.10126i	−0.480753	−	0.307503i
$877$	−11.0966	+	7.13133i	−0.374704	+	0.240808i	−0.714415	−	0.699722i	$-0.753307\pi$
$877$	−11.0966	+	7.13133i	−0.374704	+	0.240808i	0.339711	+	0.940530i	$0.389671\pi$
$878$	11.4866	+	34.0014i	0.387655	+	1.14749i
$879$	7.24331	+	34.4277i	0.244311	+	1.16122i
$880$	−4.01187	−	24.7400i	−0.135240	−	0.833985i
$881$	17.7892	+	15.4144i	0.599332	+	0.519324i	0.900847	−	0.434137i	$-0.142947\pi$
$881$	17.7892	+	15.4144i	0.599332	+	0.519324i	−0.301514	+	0.953462i	$0.597492\pi$
$882$	−13.7202	−	5.83112i	−0.461984	−	0.196344i
$883$	−8.68773	+	3.96755i	−0.292365	+	0.133519i	−0.556198	−	0.831050i	$-0.687740\pi$
$883$	−8.68773	+	3.96755i	−0.292365	+	0.133519i	0.263833	+	0.964568i	$0.415013\pi$
$884$	8.37354	−	40.2286i	0.281633	−	1.35304i
$885$	85.7606	−	31.3213i	2.88281	−	1.05286i
$886$	15.3025	−	10.7269i	0.514097	−	0.360376i
$887$	33.0438	+	21.2359i	1.10950	+	0.713033i	0.961184	−	0.275907i	$-0.0889782\pi$
$887$	33.0438	+	21.2359i	1.10950	+	0.713033i	0.148316	+	0.988940i	$0.452615\pi$
$888$	−16.9767	−	17.9932i	−0.569700	−	0.603812i
$889$	−17.8879	−	5.25238i	−0.599943	−	0.176159i
$890$	−9.84827	+	6.90352i	−0.330115	+	0.231407i
$891$	1.46092	+	12.5954i	0.0489428	+	0.421962i
$892$	42.8104	+	2.67565i	1.43340	+	0.0895872i
$893$	−8.59104	−	7.44418i	−0.287488	−	0.249110i
$894$	−5.51798	−	21.8324i	−0.184549	−	0.730185i
$895$	22.9880	+	78.2899i	0.768404	+	2.61694i
$896$	−11.3447	−	17.8193i	−0.378998	−	0.595301i
$897$	3.80401	+	2.88841i	0.127012	+	0.0964412i
$898$	19.5640	−	33.3133i	0.652859	−	1.11168i
$899$	−16.9009	+	37.0079i	−0.563678	+	1.23428i
$900$	52.8081	+	71.2363i	1.76027	+	2.37454i
$901$	19.0807			0.635672
$902$	0.303991	+	7.55968i	0.0101218	+	0.251710i
$903$	−11.7474	−	0.920900i	−0.390930	−	0.0306456i
$904$	−50.9041	−	1.13170i	−1.69304	−	0.0376397i
$905$	80.7062	−	11.6038i	2.68277	−	0.385723i
$906$	9.30341	−	3.82810i	0.309085	−	0.127180i
$907$	−37.9893	−	17.3491i	−1.26141	−	0.576069i	−0.331365	−	0.943503i	$-0.607509\pi$
$907$	−37.9893	−	17.3491i	−1.26141	−	0.576069i	−0.930050	+	0.367434i	$0.880236\pi$
$908$	−7.44361	+	10.1319i	−0.247025	+	0.336239i
$909$	−7.93214	−	2.44729i	−0.263092	−	0.0811715i
$910$	−41.9852	+	1.68831i	−1.39180	+	0.0559671i
$911$	30.0718	−	19.3260i	0.996323	−	0.640298i	0.0625044	−	0.998045i	$-0.480091\pi$
$911$	30.0718	−	19.3260i	0.996323	−	0.640298i	0.933819	+	0.357747i	$0.116455\pi$
$912$	16.3491	+	5.89147i	0.541373	+	0.195086i
$913$	4.78384	+	10.4751i	0.158322	+	0.346677i
$914$	−27.1005	−	28.8472i	−0.896405	−	0.954180i
$915$	73.0182	+	16.4074i	2.41391	+	0.542411i
$916$	−2.27093	−	10.0058i	−0.0750335	−	0.330600i
$917$	16.0008	+	24.8977i	0.528392	+	0.822195i
$918$	−42.1384	−	2.18069i	−1.39077	−	0.0719736i
$919$	46.2081	−	6.64372i	1.52426	−	0.219156i	0.671324	−	0.741164i	$-0.265726\pi$
$919$	46.2081	−	6.64372i	1.52426	−	0.219156i	0.852940	+	0.522008i	$0.174817\pi$
$920$	−4.22230	+	8.72684i	−0.139205	+	0.287715i
$921$	−11.3537	+	14.9528i	−0.374118	+	0.492711i
$922$	−28.8046	−	2.96604i	−0.948630	−	0.0976812i
$923$	−2.68518	−	18.6759i	−0.0883839	−	0.614724i
$924$	2.54848	−	8.74884i	0.0838388	−	0.287816i
$925$	−31.0020	−	67.8850i	−1.01934	−	2.23205i
$926$	−23.4973	−	18.7619i	−0.772169	−	0.616555i
$927$	−20.0595	−	23.7993i	−0.658840	−	0.781671i
$928$	21.9638	−	1.27869i	0.720997	−	0.0419752i
$929$	3.28520	+	0.472341i	0.107784	+	0.0154970i	0.195996	−	0.980605i	$-0.437206\pi$
$929$	3.28520	+	0.472341i	0.107784	+	0.0154970i	−0.0882117	+	0.996102i	$0.528115\pi$
$930$	71.2966	+	88.8989i	2.33791	+	2.91511i
$931$	−8.72415	−	1.25434i	−0.285923	−	0.0411095i
$932$	−16.9914	−	1.06196i	−0.556573	−	0.0347858i
$933$	0.932649	+	14.4244i	0.0305336	+	0.472232i
$934$	−5.55207	−	30.0014i	−0.181669	−	0.981677i
$935$	23.5606	+	27.1904i	0.770514	+	0.889221i
$936$	−24.9361	−	17.3205i	−0.815061	−	0.566139i
$937$	−37.6322			−1.22939			−0.614696	−	0.788764i	$-0.710721\pi$
$937$	−37.6322			−1.22939			−0.614696	+	0.788764i	$0.710721\pi$
$938$	−14.9868	−	15.5737i	−0.489337	−	0.508501i
$939$	4.25413	+	5.76453i	0.138828	+	0.188118i
$940$	−28.2466	+	28.7586i	−0.921303	+	0.938003i
$941$	−15.8146	+	13.7034i	−0.515542	+	0.446719i	−0.873362	−	0.487071i	$-0.838065\pi$
$941$	−15.8146	+	13.7034i	−0.515542	+	0.446719i	0.357821	+	0.933790i	$0.383520\pi$
$942$	−7.02368	+	7.50864i	−0.228844	+	0.244645i
$943$	1.58219	−	2.46193i	0.0515231	−	0.0801715i
$944$	−36.3821	−	30.3985i	−1.18414	−	0.989387i
$945$	8.30577	+	42.3410i	0.270187	+	1.37735i
$946$	0.291697	+	7.25395i	0.00948387	+	0.235846i
$947$	6.13670	−	42.6817i	0.199416	−	1.38697i	−0.606569	−	0.795031i	$-0.707455\pi$
$947$	6.13670	−	42.6817i	0.199416	−	1.38697i	0.805985	−	0.591936i	$-0.201636\pi$
$948$	−12.2555	−	10.5734i	−0.398040	−	0.343408i
$949$	14.6771	+	9.43237i	0.476437	+	0.306188i
$950$	40.9688	+	32.7124i	1.32920	+	1.06133i
$951$	−24.0990	−	13.3736i	−0.781465	−	0.433669i
$952$	27.2965	+	13.2068i	0.884685	+	0.428036i
$953$	5.11450	−	0.735354i	0.165675	−	0.0238204i	−0.0589782	−	0.998259i	$-0.518784\pi$
$953$	5.11450	−	0.735354i	0.165675	−	0.0238204i	0.224653	+	0.974439i	$0.427875\pi$
$954$	5.51448	−	12.9752i	0.178538	−	0.420087i
$955$	−21.6465	−	73.7213i	−0.700465	−	2.38557i
$956$	−22.9704	+	17.5195i	−0.742915	+	0.566621i
$957$	6.66495	+	6.75665i	0.215447	+	0.218411i
$958$	7.35924	−	17.9949i	0.237766	−	0.581389i
$959$	3.78221	−	2.43068i	0.122134	−	0.0784908i
$960$	24.4674	−	56.5593i	0.789681	−	1.82544i
$961$	51.3585	+	59.2709i	1.65673	+	1.91196i
$962$	17.4954	+	18.6230i	0.564075	+	0.600431i
$963$	21.0593	−	2.73473i	0.678625	−	0.0881254i
$964$	13.9758	−	38.5238i	0.450131	−	1.24077i
$965$	1.94483	+	3.02621i	0.0626062	+	0.0974172i
$966$	−2.74970	+	2.20525i	−0.0884702	+	0.0709528i
$967$		−	43.3712i		−	1.39472i	−0.716719	−	0.697362i	$-0.754357\pi$
$967$		−	43.3712i		−	1.39472i	0.716719	−	0.697362i	$-0.245643\pi$
$968$	25.1521	+	4.18889i	0.808418	+	0.134636i
$969$	−24.4119	+	5.13607i	−0.784224	+	0.164994i
$970$	10.9256	−	43.6227i	0.350801	−	1.40064i
$971$	5.57896	+	38.8025i	0.179037	+	1.24523i	0.858996	+	0.511982i	$0.171089\pi$
$971$	5.57896	+	38.8025i	0.179037	+	1.24523i	−0.679959	+	0.733251i	$0.738002\pi$
$972$	−13.6612	+	28.0245i	−0.438183	+	0.898886i
$973$	26.1484	−	30.1768i	0.838278	−	0.967424i
$974$	1.17079	+	29.1154i	0.0375145	+	0.932916i
$975$	−54.3879	−	73.6978i	−1.74181	−	2.36022i
$976$	−11.6166	−	37.0849i	−0.371838	−	1.18706i
$977$	−41.2800	−	18.8519i	−1.32066	−	0.603126i	−0.374623	−	0.927177i	$-0.622228\pi$
$977$	−41.2800	−	18.8519i	−1.32066	−	0.603126i	−0.946040	+	0.324051i	$0.894955\pi$
$978$	−33.9099	+	3.56540i	−1.08432	+	0.114009i
$979$	0.759003	+	2.58493i	0.0242578	+	0.0826146i
$980$	−6.36912	+	30.5989i	−0.203454	+	0.977446i
$981$	0.163106	−	11.9366i	0.00520759	−	0.381108i
$982$	4.09800	−	10.0205i	0.130772	−	0.319766i
$983$	6.49826	−	7.49939i	0.207262	−	0.239194i	−0.642595	−	0.766206i	$-0.722142\pi$
$983$	6.49826	−	7.49939i	0.207262	−	0.239194i	0.849858	+	0.527012i	$0.176688\pi$
$984$	−9.38592	+	16.0612i	−0.299212	+	0.512012i
$985$	−57.1695	−	65.9771i	−1.82157	−	2.10221i
$986$	−25.8612	+	18.1284i	−0.823589	+	0.577327i
$987$	−13.7667	+	5.02784i	−0.438198	+	0.160038i
$988$	−16.8741	−	6.12165i	−0.536836	−	0.194756i
$989$	1.51820	−	2.36236i	0.0482759	−	0.0751188i
$990$	25.2991	−	8.16334i	0.804057	−	0.259448i
$991$	17.0087	−	57.9262i	0.540298	−	1.84009i	−0.00215255	−	0.999998i	$-0.500685\pi$
$991$	17.0087	−	57.9262i	0.540298	−	1.84009i	0.542450	−	0.840088i	$-0.317497\pi$
$992$	21.4121	−	55.1650i	0.679835	−	1.75149i
$993$	−50.0514	−	27.7757i	−1.58833	−	0.881435i
$994$	13.8506	+	1.42621i	0.439315	+	0.0452366i
$995$	−28.5716	+	32.9734i	−0.905780	+	1.04533i
$996$	−3.96937	+	28.0352i	−0.125774	+	0.888329i
$997$	15.9684	−	34.9659i	0.505724	−	1.10738i	−0.468842	−	0.883282i	$-0.655329\pi$
$997$	15.9684	−	34.9659i	0.505724	−	1.10738i	0.974566	−	0.224100i	$-0.0719441\pi$
$998$	−0.345412	−	1.02245i	−0.0109338	−	0.0323651i
$999$	16.1513	−	20.6783i	0.511005	−	0.654234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.w.a.59.12	✓	1320
3.2	odd	2	inner	804.2.w.a.59.121	yes	1320
4.3	odd	2	inner	804.2.w.a.59.25	yes	1320
12.11	even	2	inner	804.2.w.a.59.108	yes	1320
67.25	even	11	inner	804.2.w.a.695.108	yes	1320
201.92	odd	22	inner	804.2.w.a.695.25	yes	1320
268.159	odd	22	inner	804.2.w.a.695.121	yes	1320
804.695	even	22	inner	804.2.w.a.695.12	yes	1320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.w.a.59.12	✓	1320	1.1	even	1	trivial
804.2.w.a.59.25	yes	1320	4.3	odd	2	inner
804.2.w.a.59.108	yes	1320	12.11	even	2	inner
804.2.w.a.59.121	yes	1320	3.2	odd	2	inner
804.2.w.a.695.12	yes	1320	804.695	even	22	inner
804.2.w.a.695.25	yes	1320	201.92	odd	22	inner
804.2.w.a.695.108	yes	1320	67.25	even	11	inner
804.2.w.a.695.121	yes	1320	268.159	odd	22	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.w (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33982 + 0.452629i) q^{2} +(-0.379728 + 1.68991i) q^{3} +(1.59025 - 1.21289i) q^{4} +(2.40444 - 3.74138i) q^{5} +(-0.256136 - 2.43606i) q^{6} +(-1.84812 - 0.265720i) q^{7} +(-1.58167 + 2.34485i) q^{8} +(-2.71161 - 1.28341i) q^{9} +O(q^{10})\)	\(q+(-1.33982 + 0.452629i) q^{2} +(-0.379728 + 1.68991i) q^{3} +(1.59025 - 1.21289i) q^{4} +(2.40444 - 3.74138i) q^{5} +(-0.256136 - 2.43606i) q^{6} +(-1.84812 - 0.265720i) q^{7} +(-1.58167 + 2.34485i) q^{8} +(-2.71161 - 1.28341i) q^{9} +(-1.52806 + 6.10110i) q^{10} +(1.18522 + 0.761693i) q^{11} +(1.44581 + 3.14796i) q^{12} +(-1.48640 - 3.25476i) q^{13} +(2.59643 - 0.480496i) q^{14} +(5.40957 + 5.48399i) q^{15} +(1.05781 - 3.85759i) q^{16} +(1.61770 + 5.50939i) q^{17} +(4.21399 + 0.492193i) q^{18} +(2.48280 - 0.356973i) q^{19} +(-0.714200 - 8.86605i) q^{20} +(1.15083 - 3.02227i) q^{21} +(-1.93275 - 0.484070i) q^{22} +(0.504696 + 0.582450i) q^{23} +(-3.36199 - 3.56329i) q^{24} +(-6.13951 - 13.4436i) q^{25} +(3.46472 + 3.68802i) q^{26} +(3.19853 - 4.09504i) q^{27} +(-3.26127 + 1.81900i) q^{28} -3.88926i q^{29} +(-9.73008 - 4.89905i) q^{30} +(-9.51540 - 4.34554i) q^{31} +(0.328775 + 5.64729i) q^{32} +(-1.73726 + 1.71368i) q^{33} +(-4.66115 - 6.64939i) q^{34} +(-5.43785 + 6.27562i) q^{35} +(-5.86879 + 1.24793i) q^{36} +5.04960 q^{37} +(-3.16494 + 1.60207i) q^{38} +(6.06470 - 1.27596i) q^{39} +(4.96993 + 11.5557i) q^{40} +(-1.06981 - 3.64343i) q^{41} +(-0.173939 + 4.57020i) q^{42} +(-1.02654 - 3.49608i) q^{43} +(2.80864 - 0.226249i) q^{44} +(-11.3216 + 7.05928i) q^{45} +(-0.939838 - 0.551940i) q^{46} +(-2.96778 - 3.42500i) q^{47} +(6.11732 + 3.25245i) q^{48} +(-3.37150 - 0.989962i) q^{49} +(14.3108 + 15.2332i) q^{50} +(-9.92467 + 0.641709i) q^{51} +(-6.31141 - 3.37307i) q^{52} +(0.936205 - 3.18842i) q^{53} +(-2.43193 + 6.93439i) q^{54} +(5.69956 - 2.60290i) q^{55} +(3.54620 - 3.91329i) q^{56} +(-0.339535 + 4.33127i) q^{57} +(1.76039 + 5.21093i) q^{58} +(4.92372 - 10.7815i) q^{59} +(15.2540 + 2.15975i) q^{60} +(8.17315 - 5.25256i) q^{61} +(14.7159 + 1.51531i) q^{62} +(4.67037 + 3.09244i) q^{63} +(-2.99663 - 7.41756i) q^{64} +(-15.7513 - 2.26469i) q^{65} +(1.55195 - 3.08236i) q^{66} +(-4.50769 - 6.83233i) q^{67} +(9.25482 + 6.79924i) q^{68} +(-1.17594 + 0.631720i) q^{69} +(4.44523 - 10.8695i) q^{70} +(5.05955 + 1.48562i) q^{71} +(7.29829 - 4.32838i) q^{72} +(-4.10190 + 2.63613i) q^{73} +(-6.76557 + 2.28560i) q^{74} +(25.0499 - 5.27031i) q^{75} +(3.51532 - 3.57903i) q^{76} +(-1.98803 - 1.72264i) q^{77} +(-7.54809 + 4.45463i) q^{78} +(-4.25031 + 1.94105i) q^{79} +(-11.8893 - 13.2330i) q^{80} +(5.70570 + 6.96025i) q^{81} +(3.08247 + 4.39732i) q^{82} +(6.87622 + 4.41908i) q^{83} +(-1.83556 - 6.20199i) q^{84} +(24.5024 + 7.19454i) q^{85} +(2.95781 + 4.21948i) q^{86} +(6.57252 + 1.47686i) q^{87} +(-3.66068 + 1.57441i) q^{88} +(1.44515 + 1.25223i) q^{89} +(11.9738 - 14.5827i) q^{90} +(1.88220 + 6.41017i) q^{91} +(1.50904 + 0.314105i) q^{92} +(10.9568 - 14.4301i) q^{93} +(5.52656 + 3.24559i) q^{94} +(4.63417 - 10.1474i) q^{95} +(-9.66828 - 1.58883i) q^{96} -7.14998 q^{97} +(4.96530 - 0.199665i) q^{98} +(-2.23629 - 3.58654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9	\( 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9} - 26 q^{10} - 15 q^{12} - 44 q^{13} - 34 q^{16} - 13 q^{18} - 66 q^{21} + 74 q^{22} + 13 q^{24} + 80 q^{25} - 110 q^{28} - 36 q^{30} - 22 q^{33} - 54 q^{34} - 37 q^{36} - 72 q^{37} - 22 q^{40} + q^{42} - 154 q^{45} - 82 q^{46} + 11 q^{48} + 96 q^{49} - 14 q^{52} - 138 q^{54} - 6 q^{57} + 74 q^{58} + 3 q^{60} - 28 q^{61} - 6 q^{64} - 4 q^{66} - 38 q^{69} - 18 q^{70} - 145 q^{72} + 96 q^{73} + 14 q^{76} - 51 q^{78} - 38 q^{81} - 74 q^{82} - 41 q^{84} - 76 q^{85} + 6 q^{88} - 5 q^{90} + 78 q^{93} - 22 q^{94} + 184 q^{96} - 128 q^{97}+O(q^{100}) \) 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9 - 26 * q^10 - 15 * q^12 - 44 * q^13 - 34 * q^16 - 13 * q^18 - 66 * q^21 + 74 * q^22 + 13 * q^24 + 80 * q^25 - 110 * q^28 - 36 * q^30 - 22 * q^33 - 54 * q^34 - 37 * q^36 - 72 * q^37 - 22 * q^40 + q^42 - 154 * q^45 - 82 * q^46 + 11 * q^48 + 96 * q^49 - 14 * q^52 - 138 * q^54 - 6 * q^57 + 74 * q^58 + 3 * q^60 - 28 * q^61 - 6 * q^64 - 4 * q^66 - 38 * q^69 - 18 * q^70 - 145 * q^72 + 96 * q^73 + 14 * q^76 - 51 * q^78 - 38 * q^81 - 74 * q^82 - 41 * q^84 - 76 * q^85 + 6 * q^88 - 5 * q^90 + 78 * q^93 - 22 * q^94 + 184 * q^96 - 128 * q^97

Introduction

L-functions

Modular forms

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