LMFDB - Embedded newform 504.2.y.a.173.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(173,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1, 5]))

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

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

chi := DirichletCharacter("504.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.y (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.11
Character	$\chi$	$=$	504.173
Dual form			504.2.y.a.437.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33533 - 0.465720i) q^{2} +(-1.66375 - 0.481605i) q^{3} +(1.56621 + 1.24378i) q^{4} -1.79202i q^{5} +(1.99736 + 1.41794i) q^{6} +(-1.87653 + 1.86511i) q^{7} +(-1.51215 - 2.39027i) q^{8} +(2.53611 + 1.60254i) q^{9} +O(q^{10})$	\(q+(-1.33533 - 0.465720i) q^{2} +(-1.66375 - 0.481605i) q^{3} +(1.56621 + 1.24378i) q^{4} -1.79202i q^{5} +(1.99736 + 1.41794i) q^{6} +(-1.87653 + 1.86511i) q^{7} +(-1.51215 - 2.39027i) q^{8} +(2.53611 + 1.60254i) q^{9} +(-0.834578 + 2.39293i) q^{10} +5.39133 q^{11} +(-2.00677 - 2.82363i) q^{12} +(-1.44678 - 2.50590i) q^{13} +(3.37441 - 1.61660i) q^{14} +(-0.863046 + 2.98147i) q^{15} +(0.906028 + 3.89604i) q^{16} +(-1.11527 - 1.93170i) q^{17} +(-2.64021 - 3.32104i) q^{18} +(-0.315657 + 0.546733i) q^{19} +(2.22887 - 2.80668i) q^{20} +(4.02032 - 2.19932i) q^{21} +(-7.19920 - 2.51085i) q^{22} +1.33243i q^{23} +(1.36468 + 4.70507i) q^{24} +1.78867 q^{25} +(0.764883 + 4.01999i) q^{26} +(-3.44766 - 3.88763i) q^{27} +(-5.25882 + 0.587163i) q^{28} +(2.96713 - 5.13923i) q^{29} +(2.54098 - 3.57930i) q^{30} +(-3.13177 - 1.80813i) q^{31} +(0.604617 - 5.62445i) q^{32} +(-8.96981 - 2.59649i) q^{33} +(0.589620 + 3.09886i) q^{34} +(3.34231 + 3.36278i) q^{35} +(1.97888 + 5.66428i) q^{36} +(-4.92708 - 2.84465i) q^{37} +(0.676130 - 0.583062i) q^{38} +(1.20022 + 4.86596i) q^{39} +(-4.28341 + 2.70981i) q^{40} +(-4.07147 - 7.05199i) q^{41} +(-6.39272 + 1.06448i) q^{42} +(-4.99769 - 2.88542i) q^{43} +(8.44395 + 6.70562i) q^{44} +(2.87178 - 4.54476i) q^{45} +(0.620538 - 1.77923i) q^{46} +(2.44986 + 4.24328i) q^{47} +(0.368952 - 6.91837i) q^{48} +(0.0427357 - 6.99987i) q^{49} +(-2.38846 - 0.833019i) q^{50} +(0.925208 + 3.75099i) q^{51} +(0.850821 - 5.72424i) q^{52} +(-4.74975 - 8.22681i) q^{53} +(2.79322 + 6.79691i) q^{54} -9.66136i q^{55} +(7.29572 + 1.66508i) q^{56} +(0.788483 - 0.757604i) q^{57} +(-6.35554 + 5.48071i) q^{58} +(-11.6578 - 6.73061i) q^{59} +(-5.06000 + 3.59616i) q^{60} +(-0.393835 - 0.682143i) q^{61} +(3.33986 + 3.87298i) q^{62} +(-7.74800 + 1.72291i) q^{63} +(-3.42678 + 7.22891i) q^{64} +(-4.49062 + 2.59266i) q^{65} +(10.7684 + 7.64459i) q^{66} +(5.72547 + 3.30560i) q^{67} +(0.655866 - 4.41260i) q^{68} +(0.641704 - 2.21682i) q^{69} +(-2.89697 - 6.04700i) q^{70} -15.5448i q^{71} +(-0.00449015 - 8.48528i) q^{72} +(9.92471 - 5.73004i) q^{73} +(5.25447 + 6.09319i) q^{74} +(-2.97590 - 0.861433i) q^{75} +(-1.17440 + 0.463692i) q^{76} +(-10.1170 + 10.0554i) q^{77} +(0.663479 - 7.05663i) q^{78} +(0.560031 + 0.970002i) q^{79} +(6.98177 - 1.62362i) q^{80} +(3.86373 + 8.12844i) q^{81} +(2.15250 + 11.3129i) q^{82} +(10.6478 + 6.14753i) q^{83} +(9.03214 + 1.55579i) q^{84} +(-3.46165 + 1.99858i) q^{85} +(5.32977 + 6.18051i) q^{86} +(-7.41164 + 7.12139i) q^{87} +(-8.15252 - 12.8867i) q^{88} +(-5.09915 + 8.83199i) q^{89} +(-5.95136 + 4.73131i) q^{90} +(7.38870 + 2.00399i) q^{91} +(-1.65725 + 2.08686i) q^{92} +(4.33967 + 4.51655i) q^{93} +(-1.29519 - 6.80713i) q^{94} +(0.979756 + 0.565662i) q^{95} +(-3.71470 + 9.06648i) q^{96} +(13.7295 + 7.92671i) q^{97} +(-3.31704 + 9.32723i) q^{98} +(13.6730 + 8.63982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.33533	−	0.465720i	−0.944221	−	0.329314i
$2$	−1.33533	−	0.465720i	−0.944221	−	0.329314i
$3$	−1.66375	−	0.481605i	−0.960565	−	0.278055i
$3$	−1.66375	−	0.481605i	−0.960565	−	0.278055i
$4$	1.56621	+	1.24378i	0.783105	+	0.621889i
$5$		−	1.79202i		−	0.801415i	−0.916206	−	0.400707i	$-0.868764\pi$
$5$		−	1.79202i		−	0.801415i	0.916206	−	0.400707i	$-0.131236\pi$
$6$	1.99736	+	1.41794i	0.815418	+	0.578872i
$7$	−1.87653	+	1.86511i	−0.709262	+	0.704945i
$7$	−1.87653	+	1.86511i	−0.709262	+	0.704945i
$8$	−1.51215	−	2.39027i	−0.534627	−	0.845088i
$9$	2.53611	+	1.60254i	0.845371	+	0.534180i
$10$	−0.834578	+	2.39293i	−0.263917	+	0.756712i
$11$	5.39133			1.62555			0.812773	−	0.582580i	$-0.197957\pi$
$11$	5.39133			1.62555			0.812773	+	0.582580i	$0.197957\pi$
$12$	−2.00677	−	2.82363i	−0.579304	−	0.815112i
$13$	−1.44678	−	2.50590i	−0.401265	−	0.695011i	0.592614	−	0.805487i	$-0.298096\pi$
$13$	−1.44678	−	2.50590i	−0.401265	−	0.695011i	−0.993879	+	0.110475i	$0.964763\pi$
$14$	3.37441	−	1.61660i	0.901848	−	0.432054i
$15$	−0.863046	+	2.98147i	−0.222837	+	0.769811i
$16$	0.906028	+	3.89604i	0.226507	+	0.974010i
$17$	−1.11527	−	1.93170i	−0.270493	−	0.468507i	0.698495	−	0.715615i	$-0.253853\pi$
$17$	−1.11527	−	1.93170i	−0.270493	−	0.468507i	−0.968988	+	0.247108i	$0.920520\pi$
$18$	−2.64021	−	3.32104i	−0.622304	−	0.782776i
$19$	−0.315657	+	0.546733i	−0.0724166	+	0.125429i	−0.899960	−	0.435973i	$-0.856404\pi$
$19$	−0.315657	+	0.546733i	−0.0724166	+	0.125429i	0.827543	+	0.561402i	$0.189738\pi$
$20$	2.22887	−	2.80668i	0.498392	−	0.627592i
$21$	4.02032	−	2.19932i	0.877306	−	0.479932i
$22$	−7.19920	−	2.51085i	−1.53487	−	0.535315i
$23$			1.33243i			0.277830i	0.990304	+	0.138915i	$0.0443615\pi$
$23$			1.33243i			0.277830i	−0.990304	+	0.138915i	$0.955638\pi$
$24$	1.36468	+	4.70507i	0.278563	+	0.960418i
$25$	1.78867			0.357734
$26$	0.764883	+	4.01999i	0.150006	+	0.788386i
$27$	−3.44766	−	3.88763i	−0.663502	−	0.748174i
$28$	−5.25882	+	0.587163i	−0.993824	+	0.110963i
$29$	2.96713	−	5.13923i	0.550983	−	0.954330i	−0.447221	−	0.894423i	$-0.647586\pi$
$29$	2.96713	−	5.13923i	0.550983	−	0.954330i	0.998204	−	0.0599069i	$-0.0190804\pi$
$30$	2.54098	−	3.57930i	0.463917	−	0.653488i
$31$	−3.13177	−	1.80813i	−0.562483	−	0.324749i	0.191659	−	0.981462i	$-0.438613\pi$
$31$	−3.13177	−	1.80813i	−0.562483	−	0.324749i	−0.754141	+	0.656712i	$0.771947\pi$
$32$	0.604617	−	5.62445i	0.106882	−	0.994272i
$33$	−8.96981	−	2.59649i	−1.56144	−	0.451991i
$34$	0.589620	+	3.09886i	0.101119	+	0.531451i
$35$	3.34231	+	3.36278i	0.564953	+	0.568413i
$36$	1.97888	+	5.66428i	0.329813	+	0.944046i
$37$	−4.92708	−	2.84465i	−0.810007	−	0.467658i	0.0369510	−	0.999317i	$-0.488235\pi$
$37$	−4.92708	−	2.84465i	−0.810007	−	0.467658i	−0.846958	+	0.531659i	$0.821569\pi$
$38$	0.676130	−	0.583062i	0.109683	−	0.0945851i
$39$	1.20022	+	4.86596i	0.192190	+	0.779177i
$40$	−4.28341	+	2.70981i	−0.677266	+	0.428458i
$41$	−4.07147	−	7.05199i	−0.635857	−	1.10134i	−0.986333	−	0.164765i	$-0.947314\pi$
$41$	−4.07147	−	7.05199i	−0.635857	−	1.10134i	0.350476	−	0.936572i	$-0.386020\pi$
$42$	−6.39272	+	1.06448i	−0.986418	+	0.164253i
$43$	−4.99769	−	2.88542i	−0.762141	−	0.440022i	0.0679231	−	0.997691i	$-0.478363\pi$
$43$	−4.99769	−	2.88542i	−0.762141	−	0.440022i	−0.830064	+	0.557668i	$0.811696\pi$
$44$	8.44395	+	6.70562i	1.27297	+	1.01091i
$45$	2.87178	−	4.54476i	0.428100	−	0.677493i
$46$	0.620538	−	1.77923i	0.0914933	−	0.262333i
$47$	2.44986	+	4.24328i	0.357349	+	0.618946i	0.987517	−	0.157512i	$-0.0503474\pi$
$47$	2.44986	+	4.24328i	0.357349	+	0.618946i	−0.630168	+	0.776459i	$0.717014\pi$
$48$	0.368952	−	6.91837i	0.0532536	−	0.998581i
$49$	0.0427357	−	6.99987i	0.00610511	−	0.999981i
$50$	−2.38846	−	0.833019i	−0.337780	−	0.117807i
$51$	0.925208	+	3.75099i	0.129555	+	0.525243i
$52$	0.850821	−	5.72424i	0.117988	−	0.793809i
$53$	−4.74975	−	8.22681i	−0.652429	−	1.13004i	−0.982532	−	0.186095i	$-0.940417\pi$
$53$	−4.74975	−	8.22681i	−0.652429	−	1.13004i	0.330103	−	0.943945i	$-0.392917\pi$
$54$	2.79322	+	6.79691i	0.380109	+	0.924942i
$55$		−	9.66136i		−	1.30274i
$56$	7.29572	+	1.66508i	0.974931	+	0.222506i
$57$	0.788483	−	0.757604i	0.104437	−	0.100347i
$58$	−6.35554	+	5.48071i	−0.834523	+	0.719652i
$59$	−11.6578	−	6.73061i	−1.51771	−	0.876251i	−0.999783	−	0.0208259i	$-0.993370\pi$
$59$	−11.6578	−	6.73061i	−1.51771	−	0.876251i	−0.517927	−	0.855425i	$-0.673296\pi$
$60$	−5.06000	+	3.59616i	−0.653243	+	0.464263i
$61$	−0.393835	−	0.682143i	−0.0504255	−	0.0873395i	0.839711	−	0.543034i	$-0.182724\pi$
$61$	−0.393835	−	0.682143i	−0.0504255	−	0.0873395i	−0.890136	+	0.455694i	$0.849391\pi$
$62$	3.33986	+	3.87298i	0.424163	+	0.491868i
$63$	−7.74800	+	1.72291i	−0.976157	+	0.217066i
$64$	−3.42678	+	7.22891i	−0.428348	+	0.903614i
$65$	−4.49062	+	2.59266i	−0.556992	+	0.321580i
$66$	10.7684	+	7.64459i	1.32550	+	0.940984i
$67$	5.72547	+	3.30560i	0.699478	+	0.403844i	0.807153	−	0.590342i	$-0.201007\pi$
$67$	5.72547	+	3.30560i	0.699478	+	0.403844i	−0.107675	+	0.994186i	$0.534341\pi$
$68$	0.655866	−	4.41260i	0.0795354	−	0.535107i
$69$	0.641704	−	2.21682i	0.0772521	−	0.266874i
$70$	−2.89697	−	6.04700i	−0.346254	−	0.722754i
$71$		−	15.5448i		−	1.84483i	−0.386204	−	0.922414i	$-0.626214\pi$
$71$		−	15.5448i		−	1.84483i	0.386204	−	0.922414i	$-0.373786\pi$
$72$	−0.00449015	−	8.48528i	−0.000529170	−	1.00000i
$73$	9.92471	−	5.73004i	1.16160	−	0.670650i	0.209913	−	0.977720i	$-0.432682\pi$
$73$	9.92471	−	5.73004i	1.16160	−	0.670650i	0.951687	+	0.307070i	$0.0993486\pi$
$74$	5.25447	+	6.09319i	0.610820	+	0.708319i
$75$	−2.97590	−	0.861433i	−0.343627	−	0.0994698i
$76$	−1.17440	+	0.463692i	−0.134713	+	0.0531891i
$77$	−10.1170	+	10.0554i	−1.15294	+	1.14592i
$78$	0.663479	−	7.05663i	0.0751242	−	0.799006i
$79$	0.560031	+	0.970002i	0.0630084	+	0.109134i	0.895809	−	0.444440i	$-0.146597\pi$
$79$	0.560031	+	0.970002i	0.0630084	+	0.109134i	−0.832800	+	0.553573i	$0.813264\pi$
$80$	6.98177	−	1.62362i	0.780586	−	0.181526i
$81$	3.86373	+	8.12844i	0.429304	+	0.903160i
$82$	2.15250	+	11.3129i	0.237704	+	1.24930i
$83$	10.6478	+	6.14753i	1.16875	+	0.674779i	0.953386	−	0.301754i	$-0.0975722\pi$
$83$	10.6478	+	6.14753i	1.16875	+	0.674779i	0.215366	+	0.976533i	$0.430905\pi$
$84$	9.03214	+	1.55579i	0.985487	+	0.169750i
$85$	−3.46165	+	1.99858i	−0.375468	+	0.216777i
$86$	5.32977	+	6.18051i	0.574724	+	0.666461i
$87$	−7.41164	+	7.12139i	−0.794611	+	0.763493i
$88$	−8.15252	−	12.8867i	−0.869061	−	1.37373i
$89$	−5.09915	+	8.83199i	−0.540509	+	0.936189i	0.458366	+	0.888764i	$0.348435\pi$
$89$	−5.09915	+	8.83199i	−0.540509	+	0.936189i	−0.998875	+	0.0474251i	$0.984898\pi$
$90$	−5.95136	+	4.73131i	−0.627328	+	0.498724i
$91$	7.38870	+	2.00399i	0.774547	+	0.210075i
$92$	−1.65725	+	2.08686i	−0.172780	+	0.217570i
$93$	4.33967	+	4.51655i	0.450003	+	0.468344i
$94$	−1.29519	−	6.80713i	−0.133589	−	0.702101i
$95$	0.979756	+	0.565662i	0.100521	+	0.0580357i
$96$	−3.71470	+	9.06648i	−0.379130	+	0.925344i
$97$	13.7295	+	7.92671i	1.39402	+	0.804835i	0.993757	−	0.111567i	$-0.0355869\pi$
$97$	13.7295	+	7.92671i	1.39402	+	0.804835i	0.400259	+	0.916402i	$0.368920\pi$
$98$	−3.31704	+	9.32723i	−0.335072	+	0.942192i
$99$	13.6730	+	8.63982i	1.37419	+	0.868334i
$100$	2.80143	+	2.22471i	0.280143	+	0.222471i
$101$		−	4.21489i		−	0.419397i	−0.977766	−	0.209699i	$-0.932752\pi$
$101$		−	4.21489i		−	0.419397i	0.977766	−	0.209699i	$-0.0672483\pi$
$102$	0.511451	−	5.43969i	0.0506412	−	0.538610i
$103$			8.18544i			0.806535i	0.915082	+	0.403268i	$0.132126\pi$
$103$			8.18544i			0.806535i	−0.915082	+	0.403268i	$0.867874\pi$
$104$	−3.80202	+	7.24750i	−0.372819	+	0.710676i
$105$	−3.94123	−	7.20449i	−0.384624	−	0.703086i
$106$	2.51110	+	13.1976i	0.243899	+	1.28186i
$107$	2.93729	−	5.08754i	0.283959	−	0.491831i	−0.688397	−	0.725334i	$-0.741685\pi$
$107$	2.93729	−	5.08754i	0.283959	−	0.491831i	0.972356	+	0.233503i	$0.0750188\pi$
$108$	−0.564410	−	10.3770i	−0.0543104	−	0.998524i
$109$	−16.1673	+	9.33417i	−1.54854	+	0.894051i	−0.550288	+	0.834975i	$0.685482\pi$
$109$	−16.1673	+	9.33417i	−1.54854	+	0.894051i	−0.998253	+	0.0590765i	$0.981184\pi$
$110$	−4.49949	+	12.9011i	−0.429009	+	1.23007i
$111$	6.82742	+	7.10569i	0.648030	+	0.674443i
$112$	−8.96673	−	5.62120i	−0.847276	−	0.531153i
$113$	11.5918	−	6.69253i	1.09046	−	0.629580i	0.156765	−	0.987636i	$-0.449894\pi$
$113$	11.5918	−	6.69253i	1.09046	−	0.629580i	0.933700	+	0.358056i	$0.116560\pi$
$114$	−1.40572	+	0.644439i	−0.131657	+	0.0603573i
$115$	2.38773			0.222657
$116$	11.0392	−	4.35865i	1.02497	−	0.404690i
$117$	0.346602	−	8.67376i	0.0320434	−	0.801890i
$118$	12.4324	+	14.4168i	1.14449	+	1.32718i
$119$	5.69568	+	1.54480i	0.522122	+	0.141612i
$120$	8.43157	−	2.44552i	0.769693	−	0.223245i
$121$	18.0664			1.64240
$122$	0.208213	+	1.09430i	0.0188507	+	0.0990735i
$123$	3.37762	+	13.6936i	0.304550	+	1.23471i
$124$	−2.65610	−	6.72714i	−0.238525	−	0.604115i
$125$		−	12.1654i		−	1.08811i
$126$	11.1485	+	1.30774i	0.993190	+	0.116503i
$127$	8.25424			0.732446			0.366223	−	0.930527i	$-0.380651\pi$
$127$	8.25424			0.732446			0.366223	+	0.930527i	$0.380651\pi$
$128$	7.94253	−	8.05706i	0.702027	−	0.712150i
$129$	6.92526	+	7.20752i	0.609735	+	0.634587i
$130$	7.20390	−	1.37068i	0.631824	−	0.120217i
$131$		−	3.03944i		−	0.265557i	−0.991146	−	0.132779i	$-0.957610\pi$
$131$		−	3.03944i		−	0.265557i	0.991146	−	0.132779i	$-0.0423899\pi$
$132$	−10.8191	−	15.2231i	−0.941685	−	1.32500i
$133$	−0.427378	−	1.61470i	−0.0370584	−	0.140012i
$134$	−6.10591	−	7.08054i	−0.527470	−	0.611665i
$135$	−6.96670	+	6.17827i	−0.599598	+	0.531741i
$136$	−2.93083	+	5.58683i	−0.251317	+	0.479067i
$137$			6.24796i			0.533800i	0.963724	+	0.266900i	$0.0859993\pi$
$137$			6.24796i			0.533800i	−0.963724	+	0.266900i	$0.914001\pi$
$138$	−1.88931	+	2.66134i	−0.160828	+	0.226548i
$139$	−5.45318	−	9.44519i	−0.462533	−	0.801131i	0.536553	−	0.843866i	$-0.319726\pi$
$139$	−5.45318	−	9.44519i	−0.462533	−	0.801131i	−0.999086	+	0.0427357i	$0.986393\pi$
$140$	1.05221	+	9.42391i	0.0889277	+	0.796466i
$141$	−2.03236	−	8.23961i	−0.171156	−	0.693901i
$142$	−7.23952	+	20.7574i	−0.607527	+	1.74192i
$143$	−7.80007	−	13.5101i	−0.652275	−	1.12977i
$144$	−3.94577	+	11.3327i	−0.328814	+	0.944395i
$145$	−9.20959	−	5.31716i	−0.764815	−	0.441566i
$146$	−15.9214	+	3.02935i	−1.31766	+	0.250711i
$147$	−3.44228	+	11.6254i	−0.283914	+	0.958850i
$148$	−4.17873	−	10.5835i	−0.343489	−	0.869960i
$149$	6.49104			0.531767			0.265883	−	0.964005i	$-0.414336\pi$
$149$	6.49104			0.531767			0.265883	+	0.964005i	$0.414336\pi$
$150$	3.57262	+	2.53623i	0.291703	+	0.207082i
$151$	−5.57149			−0.453401			−0.226701	−	0.973964i	$-0.572794\pi$
$151$	−5.57149			−0.453401			−0.226701	+	0.973964i	$0.572794\pi$
$152$	1.78416	−	0.0722404i	0.144715	−	0.00585947i
$153$	0.267182	−	6.68628i	0.0216004	−	0.540554i
$154$	18.1925	−	8.71561i	1.46600	−	0.702324i
$155$	−3.24020	+	5.61219i	−0.260259	+	0.450782i
$156$	−4.17238	+	9.11393i	−0.334057	+	0.729698i
$157$	−0.159417	+	0.276118i	−0.0127228	+	0.0220366i	−0.872317	−	0.488941i	$-0.837383\pi$
$157$	−0.159417	+	0.276118i	−0.0127228	+	0.0220366i	0.859594	+	0.510978i	$0.170717\pi$
$158$	−0.296077	−	1.55609i	−0.0235546	−	0.123796i
$159$	3.94031	+	15.9749i	0.312487	+	1.26689i
$160$	−10.0791	−	1.08348i	−0.796824	−	0.0856570i
$161$	−2.48512	−	2.50034i	−0.195855	−	0.197054i
$162$	−1.37378	−	12.6536i	−0.107934	−	0.994158i
$163$	0.883375	+	0.510017i	0.0691913	+	0.0399476i	0.534197	−	0.845360i	$-0.320614\pi$
$163$	0.883375	+	0.510017i	0.0691913	+	0.0399476i	−0.465005	+	0.885308i	$0.653948\pi$
$164$	2.39434	−	16.1089i	0.186967	−	1.25789i
$165$	−4.65296	+	16.0741i	−0.362233	+	1.25136i
$166$	−11.3553	−	13.1679i	−0.881346	−	1.02203i
$167$	−6.69476	−	11.5957i	−0.518056	−	0.897300i	−0.999780	−	0.0209764i	$-0.993323\pi$
$167$	−6.69476	−	11.5957i	−0.518056	−	0.897300i	0.481724	−	0.876323i	$-0.340011\pi$
$168$	−11.3363	−	6.28394i	−0.874616	−	0.484816i
$169$	2.31365	−	4.00736i	0.177973	−	0.308258i
$170$	5.55322	−	1.05661i	0.425913	−	0.0810382i
$171$	−1.67670	+	0.880725i	−0.128221	+	0.0673507i
$172$	−4.23861	−	10.7352i	−0.323191	−	0.818551i
$173$	−8.64236	+	4.98967i	−0.657067	+	0.379358i	−0.791158	−	0.611611i	$-0.790522\pi$
$173$	−8.64236	+	4.98967i	−0.657067	+	0.379358i	0.134092	+	0.990969i	$0.457188\pi$
$174$	13.2136	−	6.05765i	1.00172	−	0.459229i
$175$	−3.35650	+	3.33607i	−0.253727	+	0.252183i
$176$	4.88469	+	21.0048i	0.368198	+	1.58330i
$177$	16.1541	+	16.8125i	1.21421	+	1.26370i
$178$	10.9223	−	9.41884i	0.818659	−	0.705972i
$179$	−0.106425	−	0.184334i	−0.00795460	−	0.0137778i	0.862021	−	0.506873i	$-0.169199\pi$
$179$	−0.106425	−	0.184334i	−0.00795460	−	0.0137778i	−0.869975	+	0.493095i	$0.835865\pi$
$180$	10.1505	−	3.54619i	0.756573	−	0.264317i
$181$	22.4982			1.67228			0.836139	−	0.548518i	$-0.184808\pi$
$181$	22.4982			1.67228			0.836139	+	0.548518i	$0.184808\pi$
$182$	−8.93306	−	6.11705i	−0.662162	−	0.453426i
$183$	0.326719	+	1.32459i	0.0241518	+	0.0979163i
$184$	3.18486	−	2.01484i	0.234791	−	0.148536i
$185$	−5.09767	+	8.82942i	−0.374788	+	0.649152i
$186$	−3.69145	−	8.05215i	−0.270670	−	0.590412i
$187$	−6.01278	−	10.4144i	−0.439698	−	0.761580i
$188$	−1.44071	+	9.69295i	−0.105075	+	0.706931i
$189$	13.7205	+	0.864991i	0.998019	+	0.0629188i
$190$	−1.04486	−	1.21164i	−0.0758019	−	0.0879014i
$191$	−10.3500	+	5.97555i	−0.748896	+	0.432376i	−0.825295	−	0.564702i	$-0.808991\pi$
$191$	−10.3500	+	5.97555i	−0.748896	+	0.432376i	0.0763986	+	0.997077i	$0.475658\pi$
$192$	9.18278	−	10.3767i	0.662710	−	0.748876i
$193$	−0.595933	+	1.03219i	−0.0428962	+	0.0742983i	−0.886676	−	0.462391i	$-0.846992\pi$
$193$	−0.595933	+	1.03219i	−0.0428962	+	0.0742983i	0.843780	+	0.536689i	$0.180325\pi$
$194$	−14.6417	−	16.9789i	−1.05122	−	1.21901i
$195$	8.71989	−	2.15082i	0.624444	−	0.154024i
$196$	8.77322	−	10.9101i	0.626659	−	0.779294i
$197$	−5.44225			−0.387744			−0.193872	−	0.981027i	$-0.562105\pi$
$197$	−5.44225			−0.387744			−0.193872	+	0.981027i	$0.562105\pi$
$198$	−14.2342	−	17.9048i	−1.01158	−	1.27244i
$199$	8.07803	−	4.66385i	0.572636	−	0.330612i	−0.185565	−	0.982632i	$-0.559412\pi$
$199$	8.07803	−	4.66385i	0.572636	−	0.330612i	0.758202	+	0.652020i	$0.226078\pi$
$200$	−2.70475	−	4.27541i	−0.191254	−	0.302317i
$201$	−7.93375	−	8.25711i	−0.559603	−	0.582412i
$202$	−1.96296	+	5.62827i	−0.138113	+	0.396004i
$203$	4.01730	+	15.1779i	0.281959	+	1.06528i
$204$	−3.21633	+	7.02559i	−0.225188	+	0.491890i
$205$	−12.6373	+	7.29615i	−0.882627	+	0.509585i
$206$	3.81212	−	10.9303i	0.265603	−	0.761547i
$207$	−2.13527	+	3.37919i	−0.148411	+	0.234870i
$208$	8.45225	−	7.90713i	0.586058	−	0.548261i
$209$	−1.70181	+	2.94762i	−0.117717	+	0.203891i
$210$	1.90757	+	11.4559i	0.131635	+	0.790530i
$211$	−16.6090	+	9.58924i	−1.14341	+	0.660150i	−0.947274	−	0.320426i	$-0.896174\pi$
$211$	−16.6090	+	9.58924i	−1.14341	+	0.660150i	−0.196140	+	0.980576i	$0.562841\pi$
$212$	2.79323	−	18.7926i	0.191840	−	1.29068i
$213$	−7.48645	+	25.8626i	−0.512963	+	1.77208i
$214$	−6.29162	+	5.42559i	−0.430086	+	0.370885i
$215$	−5.17072	+	8.95595i	−0.352640	+	0.610791i
$216$	−4.07909	+	14.1195i	−0.277547	+	0.960712i
$217$	9.24922	−	2.44808i	0.627878	−	0.166187i
$218$	25.9357	−	4.93478i	1.75659	−	0.334225i
$219$	−19.2718	+	4.75354i	−1.30227	+	0.321214i
$220$	12.0166	−	15.1317i	0.810159	−	1.02018i
$221$	−3.22710	+	5.58950i	−0.217078	+	0.375991i
$222$	−5.80760	−	12.6681i	−0.389780	−	0.850228i
$223$	−14.7938	−	8.54118i	−0.990664	−	0.571960i	−0.0851910	−	0.996365i	$-0.527150\pi$
$223$	−14.7938	−	8.54118i	−0.990664	−	0.571960i	−0.905473	+	0.424405i	$0.860483\pi$
$224$	9.35563	+	11.6821i	0.625099	+	0.780545i
$225$	4.53627	+	2.86642i	0.302418	+	0.191094i
$226$	−18.5957	+	3.53820i	−1.23697	+	0.235358i
$227$			9.49664i			0.630314i	0.949039	+	0.315157i	$0.102057\pi$
$227$			9.49664i			0.630314i	−0.949039	+	0.315157i	$0.897943\pi$
$228$	2.17722	−	0.205869i	0.144190	−	0.0136340i
$229$	24.5350			1.62132			0.810660	−	0.585517i	$-0.199109\pi$
$229$	24.5350			1.62132			0.810660	+	0.585517i	$0.199109\pi$
$230$	−3.18841	−	1.11202i	−0.210238	−	0.0733241i
$231$	21.6749	−	11.8573i	1.42610	−	0.780151i
$232$	−16.7709	+	0.679051i	−1.10106	+	0.0445819i
$233$	−19.2901	−	11.1371i	−1.26374	−	0.729618i	−0.289941	−	0.957045i	$-0.593636\pi$
$233$	−19.2901	−	11.1371i	−1.26374	−	0.729618i	−0.973795	+	0.227426i	$0.926969\pi$
$234$	−4.50237	+	11.4209i	−0.294329	+	0.746609i
$235$	7.60404	−	4.39019i	0.496033	−	0.286385i
$236$	−9.88710	−	25.0412i	−0.643596	−	1.63004i
$237$	−0.464592	−	1.88355i	−0.0301785	−	0.122350i
$238$	−6.88616	−	4.71541i	−0.446363	−	0.305655i
$239$	−12.4677	+	7.19824i	−0.806470	+	0.465616i	−0.845729	−	0.533613i	$-0.820834\pi$
$239$	−12.4677	+	7.19824i	−0.806470	+	0.465616i	0.0392585	+	0.999229i	$0.487500\pi$
$240$	−12.3978	−	0.661168i	−0.800278	−	0.0426782i
$241$			11.0323i			0.710653i	0.934742	+	0.355327i	$0.115630\pi$
$241$			11.0323i			0.710653i	−0.934742	+	0.355327i	$0.884370\pi$
$242$	−24.1246	−	8.41389i	−1.55079	−	0.540865i
$243$	−2.51358	−	15.3845i	−0.161246	−	0.986914i
$244$	0.231606	−	1.55822i	0.0148271	−	0.0997550i
$245$	−12.5439	−	0.0765832i	−0.801400	−	0.00489272i
$246$	1.86713	−	19.8585i	0.119044	−	1.26613i
$247$	1.82674			0.116233
$248$	0.413804	+	10.2199i	0.0262766	+	0.648967i
$249$	−14.7546	−	15.3560i	−0.935037	−	0.973147i
$250$	−5.66568	+	16.2448i	−0.358329	+	1.02741i
$251$			12.8663i			0.812115i	0.913848	+	0.406057i	$0.133097\pi$
$251$			12.8663i			0.812115i	−0.913848	+	0.406057i	$0.866903\pi$
$252$	−14.2779	−	6.93836i	−0.899425	−	0.437076i
$253$			7.18355i			0.451626i
$254$	−11.0221	−	3.84417i	−0.691590	−	0.241204i
$255$	6.72184	−	1.65799i	0.420938	−	0.103827i
$256$	−14.3582	+	7.05984i	−0.897389	+	0.441240i
$257$	12.5026			0.779892			0.389946	−	0.920838i	$-0.372494\pi$
$257$	12.5026			0.779892			0.389946	+	0.920838i	$0.372494\pi$
$258$	−5.89082	−	12.8496i	−0.366747	−	0.799984i
$259$	14.5514	−	3.85147i	0.904181	−	0.239319i
$260$	−10.2579	−	1.52469i	−0.636170	−	0.0945570i
$261$	15.7608	−	8.27871i	0.975569	−	0.512439i
$262$	−1.41553	+	4.05866i	−0.0874516	+	0.250745i
$263$		−	29.7739i		−	1.83594i	−0.396653	−	0.917969i	$-0.629828\pi$
$263$		−	29.7739i		−	1.83594i	0.396653	−	0.917969i	$-0.370172\pi$
$264$	7.35741	+	25.3666i	0.452818	+	1.56120i
$265$	−14.7426	+	8.51165i	−0.905631	+	0.522866i
$266$	−0.181306	+	2.35519i	−0.0111166	+	0.144406i
$267$	12.7372	−	12.2384i	0.779506	−	0.748979i
$268$	4.85585	+	12.2985i	0.296618	+	0.751250i
$269$	−4.58636	+	2.64794i	−0.279635	+	0.161448i	−0.633258	−	0.773940i	$-0.718283\pi$
$269$	−4.58636	+	2.64794i	−0.279635	+	0.161448i	0.353623	+	0.935388i	$0.384950\pi$
$270$	12.1802	−	5.00549i	0.741262	−	0.304625i
$271$	−13.1755	−	7.60690i	−0.800357	−	0.462086i	0.0432388	−	0.999065i	$-0.486232\pi$
$271$	−13.1755	−	7.60690i	−0.800357	−	0.462086i	−0.843596	+	0.536978i	$0.819566\pi$
$272$	6.51553	−	6.09531i	0.395062	−	0.369582i
$273$	−11.3278	−	6.89257i	−0.685590	−	0.417158i
$274$	2.90980	−	8.34309i	0.175787	−	0.504025i
$275$	9.64331			0.581513
$276$	3.76228	−	2.67387i	0.226463	−	0.160948i
$277$			25.3559i			1.52349i	0.647879	+	0.761743i	$0.275656\pi$
$277$			25.3559i			1.52349i	−0.647879	+	0.761743i	$0.724344\pi$
$278$	2.88298	+	15.1521i	0.172910	+	0.908763i
$279$	−5.04492	−	9.60440i	−0.302032	−	0.575001i
$280$	2.98386	−	13.0741i	0.178320	−	0.781324i
$281$	7.67421	+	4.43071i	0.457805	+	0.264314i	0.711121	−	0.703070i	$-0.248188\pi$
$281$	7.67421	+	4.43071i	0.457805	+	0.264314i	−0.253316	+	0.967384i	$0.581521\pi$
$282$	−1.12348	+	11.9491i	−0.0669023	+	0.711559i
$283$	14.6889	−	25.4419i	0.873164	−	1.51236i	0.0144588	−	0.999895i	$-0.495397\pi$
$283$	14.6889	−	25.4419i	0.873164	−	1.51236i	0.858705	−	0.512469i	$-0.171269\pi$
$284$	19.3343	−	24.3464i	1.14728	−	1.44469i
$285$	−1.35764	−	1.41298i	−0.0804197	−	0.0836974i
$286$	4.12373	+	21.6731i	0.243842	+	1.28156i
$287$	20.7930	+	5.63955i	1.22737	+	0.332892i
$288$	10.5468	−	13.2953i	0.621475	−	0.783434i
$289$	6.01235	−	10.4137i	0.353667	−	0.612570i
$290$	9.82153	+	11.3892i	0.576740	+	0.668800i
$291$	−19.0248	−	19.8002i	−1.11525	−	1.16071i
$292$	22.6711	+	3.36971i	1.32672	+	0.197197i
$293$	3.87316	−	2.23617i	0.226273	−	0.130639i	−0.382579	−	0.923923i	$-0.624964\pi$
$293$	3.87316	−	2.23617i	0.226273	−	0.130639i	0.608851	+	0.793284i	$0.291631\pi$
$294$	10.0108	−	13.9207i	0.583840	−	0.811869i
$295$	−12.0614	+	20.8909i	−0.702240	+	1.21632i
$296$	0.651020	+	16.0786i	0.0378398	+	0.934550i
$297$	−18.5875	−	20.9595i	−1.07855	−	1.21619i
$298$	−8.66768	−	3.02301i	−0.502105	−	0.175118i
$299$	3.33893	−	1.92773i	0.193095	−	0.111484i
$300$	−3.58945	−	5.05054i	−0.207237	−	0.291593i
$301$	14.7599	−	3.90666i	0.850749	−	0.225176i
$302$	7.43977	+	2.59475i	0.428111	+	0.149311i
$303$	−2.02991	+	7.01252i	−0.116616	+	0.402859i
$304$	−2.41609	−	0.734455i	−0.138572	−	0.0421239i
$305$	−1.22241	+	0.705760i	−0.0699951	+	0.0404117i
$306$	−3.47071	+	8.80396i	−0.198407	+	0.503289i
$307$	14.9616			0.853906			0.426953	−	0.904274i	$-0.359587\pi$
$307$	14.9616			0.853906			0.426953	+	0.904274i	$0.359587\pi$
$308$	−28.3520	+	3.16559i	−1.61551	+	0.180376i
$309$	3.94215	−	13.6185i	0.224261	−	0.774730i
$310$	6.94044	−	5.98510i	0.394191	−	0.339931i
$311$	−2.27032	+	3.93231i	−0.128738	+	0.222981i	−0.923188	−	0.384349i	$-0.874426\pi$
$311$	−2.27032	+	3.93231i	−0.128738	+	0.222981i	0.794450	+	0.607330i	$0.207759\pi$
$312$	9.81603	−	10.2269i	0.555723	−	0.578987i
$313$	3.38859	−	1.95641i	0.191535	−	0.110583i	−0.401166	−	0.916005i	$-0.631395\pi$
$313$	3.38859	−	1.95641i	0.191535	−	0.110583i	0.592701	+	0.805423i	$0.298062\pi$
$314$	0.341467	−	0.294465i	0.0192701	−	0.0166176i
$315$	3.08749	+	13.8846i	0.173960	+	0.782307i
$316$	−0.329342	+	2.21578i	−0.0185269	+	0.124648i
$317$	17.1347	+	29.6782i	0.962383	+	1.66690i	0.716489	+	0.697599i	$0.245748\pi$
$317$	17.1347	+	29.6782i	0.962383	+	1.66690i	0.245894	+	0.969297i	$0.420918\pi$
$318$	2.17819	−	23.1668i	0.122147	−	1.29913i
$319$	15.9968	−	27.7073i	0.895648	−	1.55131i
$320$	12.9543	+	6.14085i	0.724170	+	0.343284i
$321$	−7.33710	+	7.04976i	−0.409517	+	0.393479i
$322$	2.15400	+	4.49615i	0.120038	+	0.250561i
$323$	1.40817			0.0783526
$324$	−4.05857	+	17.5365i	−0.225476	+	0.974249i
$325$	−2.58782	−	4.48223i	−0.143546	−	0.248629i
$326$	−0.942072	−	1.09245i	−0.0521765	−	0.0605050i
$327$	31.3936	−	7.74346i	1.73607	−	0.428215i
$328$	−10.6995	+	20.3956i	−0.590780	+	1.12616i
$329$	−12.5114	−	3.39339i	−0.689777	−	0.187084i
$330$	13.6992	−	19.2972i	0.754119	−	1.06228i
$331$	−4.28431	+	2.47354i	−0.235487	+	0.135958i	−0.613101	−	0.790005i	$-0.710078\pi$
$331$	−4.28431	+	2.47354i	−0.235487	+	0.135958i	0.377614	+	0.925963i	$0.376745\pi$
$332$	9.03058	+	22.8719i	0.495617	+	1.25526i
$333$	−7.93697	−	15.1102i	−0.434943	−	0.828034i
$334$	3.53938	+	18.6019i	0.193666	+	1.01785i
$335$	5.92370	−	10.2602i	0.323646	−	0.560572i
$336$	12.2112	+	13.6707i	0.666174	+	0.745796i
$337$	−0.458607	−	0.794331i	−0.0249819	−	0.0432700i	0.853264	−	0.521479i	$-0.174619\pi$
$337$	−0.458607	−	0.794331i	−0.0249819	−	0.0432700i	−0.878246	+	0.478209i	$0.841286\pi$
$338$	−4.95579	+	4.27363i	−0.269559	+	0.232455i
$339$	−22.5090	+	5.55201i	−1.22252	+	0.301544i
$340$	−7.90746	−	1.17532i	−0.428842	−	0.0637409i
$341$	−16.8844	−	9.74821i	−0.914342	−	0.527895i
$342$	2.64912	−	0.395184i	0.143248	−	0.0213691i
$343$	12.9753	+	13.2152i	0.700602	+	0.713553i
$344$	0.660350	+	16.3090i	0.0356037	+	0.879324i
$345$	−3.97259	−	1.14995i	−0.213877	−	0.0619110i
$346$	13.8642	−	2.63793i	0.745343	−	0.141816i
$347$	−13.4874	+	23.3609i	−0.724041	+	1.25408i	0.235326	+	0.971916i	$0.424384\pi$
$347$	−13.4874	+	23.3609i	−0.724041	+	1.25408i	−0.959367	+	0.282160i	$0.908949\pi$
$348$	−20.4656	+	1.93515i	−1.09707	+	0.103735i
$349$	8.18283	−	14.1731i	0.438017	−	0.758667i	−0.559520	−	0.828817i	$-0.689014\pi$
$349$	8.18283	−	14.1731i	0.438017	−	0.758667i	0.997536	+	0.0701498i	$0.0223477\pi$
$350$	6.03570	−	2.89156i	0.322622	−	0.154560i
$351$	−4.75399	+	14.2640i	−0.253749	+	0.761358i
$352$	3.25969	−	30.3233i	0.173742	−	1.61623i
$353$	−21.2248			−1.12968			−0.564842	−	0.825199i	$-0.691063\pi$
$353$	−21.2248			−1.12968			−0.564842	+	0.825199i	$0.691063\pi$
$354$	−13.7411	−	29.9735i	−0.730331	−	1.59307i
$355$	−27.8565			−1.47847
$356$	−18.9714	+	7.49053i	−1.00548	+	0.396997i
$357$	−8.73218	−	5.31323i	−0.462156	−	0.281206i
$358$	0.0562649	+	0.295711i	0.00297369	+	0.0156288i
$359$	21.1858	+	12.2316i	1.11814	+	0.645560i	0.940926	−	0.338611i	$-0.109957\pi$
$359$	21.1858	+	12.2316i	1.11814	+	0.645560i	0.177217	+	0.984172i	$0.443291\pi$
$360$	−15.2058	+	0.00804644i	−0.801415	+	0.000424084i
$361$	9.30072	+	16.1093i	0.489512	+	0.847859i
$362$	−30.0425	−	10.4779i	−1.57900	−	0.550704i
$363$	−30.0580	−	8.70088i	−1.57763	−	0.456678i
$364$	9.07974	+	12.3286i	0.475908	+	0.646193i
$365$	−10.2683	−	17.7853i	−0.537469	−	0.930923i
$366$	0.180609	−	1.92092i	0.00944058	−	0.100408i
$367$		−	7.72688i		−	0.403340i	−0.979454	−	0.201670i	$-0.935363\pi$
$367$		−	7.72688i		−	0.403340i	0.979454	−	0.201670i	$-0.0646368\pi$
$368$	−5.19119	+	1.20722i	−0.270609	+	0.0629305i
$369$	0.975392	−	24.4093i	0.0507769	−	1.27070i
$370$	10.9191	−	9.41610i	0.567657	−	0.489520i
$371$	24.2570	+	6.57906i	1.25936	+	0.341568i
$372$	1.17925	+	12.4715i	0.0611413	+	0.646615i
$373$		−	11.6794i		−	0.604735i	−0.953191	−	0.302367i	$-0.902223\pi$
$373$		−	11.6794i		−	0.604735i	0.953191	−	0.302367i	$-0.0977770\pi$
$374$	3.17883	+	16.7070i	0.164374	+	0.863898i
$375$	−5.85893	+	20.2402i	−0.302554	+	1.04520i
$376$	6.43802	−	12.2723i	0.332016	−	0.632897i
$377$	−17.1712			−0.884360
$378$	−17.9185	−	7.54495i	−0.921630	−	0.388070i
$379$			9.48623i			0.487275i	0.969866	+	0.243637i	$0.0783407\pi$
$379$			9.48623i			0.487275i	−0.969866	+	0.243637i	$0.921659\pi$
$380$	0.830945	+	2.10455i	0.0426266	+	0.107961i
$381$	−13.7330	−	3.97529i	−0.703562	−	0.203660i
$382$	16.6035	−	3.15915i	0.849511	−	0.161636i
$383$	23.1477			1.18279			0.591397	−	0.806380i	$-0.298577\pi$
$383$	23.1477			1.18279			0.591397	+	0.806380i	$0.298577\pi$
$384$	−17.0947	+	9.57975i	−0.872360	+	0.488865i
$385$	18.0195	+	18.1298i	0.918358	+	0.923982i
$386$	1.27648	−	1.10077i	0.0649709	−	0.0560277i
$387$	−8.05071	−	15.3267i	−0.409241	−	0.779102i
$388$	11.6441	+	29.4913i	0.591142	+	1.49719i
$389$	6.60559			0.334917			0.167458	−	0.985879i	$-0.446444\pi$
$389$	6.60559			0.334917			0.167458	+	0.985879i	$0.446444\pi$
$390$	−12.6456	−	1.18897i	−0.640335	−	0.0602057i
$391$	2.57386	−	1.48602i	0.130165	−	0.0751511i
$392$	−16.7962	+	10.4827i	−0.848336	+	0.529458i
$393$	−1.46381	+	5.05686i	−0.0738395	+	0.255085i
$394$	7.26720	+	2.53456i	0.366116	+	0.127689i
$395$	1.73826	−	1.00359i	0.0874615	−	0.0504959i
$396$	10.6688	+	30.5380i	0.536127	+	1.53459i
$397$	−15.3979	+	26.6699i	−0.772796	+	1.33852i	0.163229	+	0.986588i	$0.447809\pi$
$397$	−15.3979	+	26.6699i	−0.772796	+	1.33852i	−0.936025	+	0.351934i	$0.885524\pi$
$398$	−12.9589	+	2.46568i	−0.649570	+	0.123593i
$399$	−0.0665973	+	2.89227i	−0.00333403	+	0.144795i
$400$	1.62059	+	6.96873i	0.0810293	+	0.348436i
$401$			18.5874i			0.928209i	0.885780	+	0.464105i	$0.153624\pi$
$401$			18.5874i			0.928209i	−0.885780	+	0.464105i	$0.846376\pi$
$402$	6.74867	+	14.7209i	0.336593	+	0.734210i
$403$			10.4639i			0.521242i
$404$	5.24239	−	6.60141i	0.260819	−	0.328432i
$405$	14.5663	−	6.92388i	0.723806	−	0.344050i
$406$	1.70425	−	22.1385i	0.0845805	−	1.09872i
$407$	−26.5635	−	15.3365i	−1.31670	−	0.760200i
$408$	7.56681	−	7.88357i	0.374613	−	0.390295i
$409$	−8.16660	−	4.71499i	−0.403812	−	0.233141i	0.284315	−	0.958731i	$-0.408234\pi$
$409$	−8.16660	−	4.71499i	−0.403812	−	0.233141i	−0.688128	+	0.725590i	$0.741567\pi$
$410$	20.2729	−	3.85732i	1.00121	−	0.190500i
$411$	3.00905	−	10.3950i	0.148426	−	0.512749i
$412$	−10.1809	+	12.8201i	−0.501576	+	0.631602i
$413$	34.4295	−	9.11279i	1.69416	−	0.448411i
$414$	4.42504	−	3.51789i	0.217479	−	0.172895i
$415$	11.0165	−	19.0811i	0.540778	−	0.936655i
$416$	−14.9690	+	6.62224i	−0.733918	+	0.324682i
$417$	4.52387	+	18.3407i	0.221535	+	0.898148i
$418$	3.64524	−	3.14348i	0.178294	−	0.153752i
$419$	−11.7367	+	6.77620i	−0.573376	+	0.331039i	−0.758497	−	0.651677i	$-0.774066\pi$
$419$	−11.7367	+	6.77620i	−0.573376	+	0.331039i	0.185120	+	0.982716i	$0.440733\pi$
$420$	2.78800	−	16.1858i	0.136040	−	0.789784i
$421$	−1.39692	−	0.806512i	−0.0680817	−	0.0393070i	0.465573	−	0.885010i	$-0.345848\pi$
$421$	−1.39692	−	0.806512i	−0.0680817	−	0.0393070i	−0.533654	+	0.845703i	$0.679182\pi$
$422$	26.6444	−	5.06963i	1.29703	−	0.246786i
$423$	−0.586907	+	14.6874i	−0.0285364	+	0.714127i
$424$	−12.4819	+	23.7934i	−0.606177	+	1.15551i
$425$	−1.99485	−	3.45518i	−0.0967644	−	0.167601i
$426$	22.0416	−	31.0485i	1.06792	−	1.50431i
$427$	2.01132	+	0.545516i	0.0973344	+	0.0263994i
$428$	10.9282	−	4.31481i	0.528234	−	0.208564i
$429$	6.47080	+	26.2340i	0.312413	+	1.26659i
$430$	11.0756	−	9.55104i	0.534112	−	0.460592i
$431$	11.0523	−	6.38102i	0.532368	−	0.307363i	−0.209612	−	0.977785i	$-0.567220\pi$
$431$	11.0523	−	6.38102i	0.532368	−	0.307363i	0.741980	+	0.670422i	$0.233887\pi$
$432$	12.0227	−	16.9545i	0.578441	−	0.815724i
$433$			38.1875i			1.83517i	0.397535	+	0.917587i	$0.369866\pi$
$433$			38.1875i			1.83517i	−0.397535	+	0.917587i	$0.630134\pi$
$434$	−13.4909	−	1.03855i	−0.647583	−	0.0498518i
$435$	12.7617	+	13.2818i	0.611875	+	0.636813i
$436$	−36.9310	−	5.48922i	−1.76867	−	0.262886i
$437$	−0.728482	−	0.420590i	−0.0348480	−	0.0201195i
$438$	27.9481	+	2.62774i	1.33541	+	0.125558i
$439$	−23.2600	+	13.4292i	−1.11014	+	0.640940i	−0.938866	−	0.344283i	$-0.888122\pi$
$439$	−23.2600	+	13.4292i	−1.11014	+	0.640940i	−0.171275	+	0.985223i	$0.554789\pi$
$440$	−23.0933	+	14.6095i	−1.10093	+	0.696479i
$441$	11.3260	−	17.6840i	0.539331	−	0.842094i
$442$	6.91239	−	5.96091i	0.328789	−	0.283531i
$443$	−5.58787	−	9.67847i	−0.265487	−	0.459838i	0.702204	−	0.711976i	$-0.252200\pi$
$443$	−5.58787	−	9.67847i	−0.265487	−	0.459838i	−0.967691	+	0.252138i	$0.918866\pi$
$444$	1.85526	+	19.6208i	0.0880470	+	0.931163i
$445$	15.8271	+	9.13777i	0.750276	+	0.433172i
$446$	15.7767	+	18.2950i	0.747051	+	0.866295i
$447$	−10.7995	−	3.12612i	−0.510797	−	0.147860i
$448$	−7.05225	−	19.9566i	−0.333188	−	0.942861i
$449$			8.36475i			0.394757i	0.980327	+	0.197378i	$0.0632428\pi$
$449$			8.36475i			0.394757i	−0.980327	+	0.197378i	$0.936757\pi$
$450$	−4.72247	−	5.94024i	−0.222619	−	0.280026i
$451$	−21.9506	−	38.0196i	−1.03361	−	1.79027i
$452$	26.4792	+	3.93573i	1.24548	+	0.185121i
$453$	9.26955	+	2.68326i	0.435521	+	0.126070i
$454$	4.42278	−	12.6812i	0.207571	−	0.595156i
$455$	3.59119	−	13.2407i	0.168357	−	0.620733i
$456$	−3.00319	−	0.739072i	−0.140637	−	0.0346102i
$457$	−16.9789	−	29.4083i	−0.794238	−	1.37566i	−0.923322	−	0.384027i	$-0.874537\pi$
$457$	−16.9789	−	29.4083i	−0.794238	−	1.37566i	0.129084	−	0.991634i	$-0.458796\pi$
$458$	−32.7623	−	11.4264i	−1.53088	−	0.533923i
$459$	−3.66467	+	10.9956i	−0.171052	+	0.513231i
$460$	3.73969	+	2.96981i	0.174364	+	0.138468i
$461$	9.28437	+	5.36033i	0.432416	+	0.249656i	0.700375	−	0.713775i	$-0.253016\pi$
$461$	9.28437	+	5.36033i	0.432416	+	0.249656i	−0.267959	+	0.963430i	$0.586349\pi$
$462$	−34.4653	+	5.73895i	−1.60347	+	0.267000i
$463$	−4.98196	−	8.62901i	−0.231531	−	0.401024i	0.726728	−	0.686926i	$-0.241040\pi$
$463$	−4.98196	−	8.62901i	−0.231531	−	0.401024i	−0.958259	+	0.285902i	$0.907707\pi$
$464$	22.7109	+	6.90379i	1.05433	+	0.320500i
$465$	8.09373	−	7.77677i	0.375338	−	0.360639i
$466$	20.5718	+	23.8555i	0.952972	+	1.10509i
$467$	9.31122	+	5.37584i	0.430872	+	0.248764i	0.699718	−	0.714419i	$-0.253309\pi$
$467$	9.31122	+	5.37584i	0.430872	+	0.248764i	−0.268846	+	0.963183i	$0.586642\pi$
$468$	11.3311	−	13.1538i	0.523780	−	0.608036i
$469$	−16.9093	+	4.47557i	−0.780801	+	0.206662i
$470$	−12.1985	+	2.32100i	−0.562675	+	0.107060i
$471$	0.398209	−	0.382615i	0.0183485	−	0.0176299i
$472$	1.54035	+	38.0429i	0.0709004	+	1.75107i
$473$	−26.9442	−	15.5562i	−1.23890	−	0.715276i
$474$	−0.256825	+	2.73153i	−0.0117963	+	0.125464i
$475$	−0.564606	+	0.977926i	−0.0259059	+	0.0448703i
$476$	6.99923	+	9.50365i	0.320809	+	0.435599i
$477$	1.13789	−	28.4758i	0.0521003	−	1.30382i
$478$	20.0009	−	3.80556i	0.914819	−	0.174062i
$479$	39.9697			1.82626			0.913130	−	0.407668i	$-0.133658\pi$
$479$	39.9697			1.82626			0.913130	+	0.407668i	$0.133658\pi$
$480$	16.2473	+	6.65680i	0.741584	+	0.303840i
$481$			16.4624i			0.750619i
$482$	5.13796	−	14.7318i	0.234028	−	0.671013i
$483$	2.93044	+	5.35679i	0.133340	+	0.243742i
$484$	28.2958	+	22.4706i	1.28617	+	1.02139i
$485$	14.2048	−	24.6034i	0.645007	−	1.11718i
$486$	−3.80840	+	21.7140i	−0.172753	+	0.984965i
$487$	17.6666	+	30.5995i	0.800552	+	1.38660i	0.919253	+	0.393667i	$0.128794\pi$
$487$	17.6666	+	30.5995i	0.800552	+	1.38660i	−0.118701	+	0.992930i	$0.537873\pi$
$488$	−1.03497	+	1.97288i	−0.0468507	+	0.0893080i
$489$	−1.22409	−	1.27398i	−0.0553551	−	0.0576113i
$490$	16.7146	+	5.94420i	0.755087	+	0.268532i
$491$	−13.0858	−	22.6653i	−0.590554	−	1.02287i	−0.994158	−	0.107936i	$-0.965576\pi$
$491$	−13.0858	−	22.6653i	−0.590554	−	1.02287i	0.403604	−	0.914934i	$-0.367757\pi$
$492$	−11.7417	+	25.6480i	−0.529358	+	1.15630i
$493$	−13.2366			−0.596147
$494$	−2.43931	−	0.850751i	−0.109750	−	0.0382771i
$495$	15.4827	−	24.5023i	0.695896	−	1.10130i
$496$	4.20707	−	13.8397i	0.188903	−	0.621421i
$497$	28.9927	+	29.1703i	1.30050	+	1.30847i
$498$	12.5507	+	27.3768i	0.562410	+	1.22679i
$499$		−	9.37352i		−	0.419616i	−0.977743	−	0.209808i	$-0.932716\pi$
$499$		−	9.37352i		−	0.419616i	0.977743	−	0.209808i	$-0.0672840\pi$
$500$	15.1311	−	19.0536i	0.676683	−	0.852103i
$501$	5.55386	+	22.5165i	0.248128	+	1.00596i
$502$	5.99210	−	17.1808i	0.267440	−	0.766815i
$503$	−6.00123			−0.267582			−0.133791	−	0.991010i	$-0.542715\pi$
$503$	−6.00123			−0.267582			−0.133791	+	0.991010i	$0.542715\pi$
$504$	15.8344	+	15.9145i	0.705320	+	0.708889i
$505$	−7.55316			−0.336111
$506$	3.34552	−	9.59241i	0.148727	−	0.426435i
$507$	−5.77929	+	5.55297i	−0.256667	+	0.246616i
$508$	12.9279	+	10.2665i	0.573582	+	0.455500i
$509$			18.0415i			0.799675i	0.916586	+	0.399838i	$0.130933\pi$
$509$			18.0415i			0.799675i	−0.916586	+	0.399838i	$0.869067\pi$
$510$	−9.74803	−	0.916530i	−0.431650	−	0.0405846i
$511$	−7.93689	+	29.2633i	−0.351107	+	1.29453i
$512$	22.4609	−	2.74030i	0.992640	−	0.121105i
$513$	3.21377	−	0.657795i	0.141891	−	0.0290424i
$514$	−16.6951	−	5.82272i	−0.736390	−	0.256829i
$515$	14.6685			0.646369
$516$	1.88185	+	19.9020i	0.0828439	+	0.876136i
$517$	13.2080	+	22.8769i	0.580887	+	1.00613i
$518$	−21.2246	−	1.63390i	−0.932557	−	0.0717895i
$519$	16.7818	−	4.13934i	0.736638	−	0.181697i
$520$	12.9877	+	6.81329i	0.569546	+	0.298782i
$521$	9.18360	+	15.9065i	0.402341	+	0.696875i	0.994008	−	0.109308i	$-0.0348634\pi$
$521$	9.18360	+	15.9065i	0.402341	+	0.696875i	−0.591667	+	0.806182i	$0.701530\pi$
$522$	−24.9014	+	3.71468i	−1.08991	+	0.162587i
$523$	15.8603	−	27.4708i	0.693521	−	1.20121i	−0.277156	−	0.960825i	$-0.589392\pi$
$523$	15.8603	−	27.4708i	0.693521	−	1.20121i	0.970677	−	0.240388i	$-0.0772747\pi$
$524$	3.78039	−	4.76040i	0.165147	−	0.207959i
$525$	7.19103	−	3.93387i	0.313842	−	0.171688i
$526$	−13.8663	+	39.7580i	−0.604599	+	1.73353i
$527$			8.06620i			0.351369i
$528$	1.98914	−	37.2992i	0.0865662	−	1.62324i
$529$	21.2246			0.922810
$530$	23.6503	−	4.49993i	1.02730	−	0.195464i
$531$	−18.7793	−	35.7516i	−0.814953	−	1.55149i
$532$	1.33896	−	3.06052i	0.0580513	−	0.132690i
$533$	−11.7811	+	20.4054i	−0.510294	+	0.883855i
$534$	−22.7081	+	10.4103i	−0.982674	+	0.450499i
$535$	−9.11696	−	5.26368i	−0.394161	−	0.227569i
$536$	−0.756512	−	18.6840i	−0.0326764	−	0.807026i
$537$	0.0882886	+	0.357940i	0.00380994	+	0.0154463i
$538$	7.35750	−	1.39991i	0.317204	−	0.0603544i
$539$	0.230402	−	37.7386i	0.00992413	−	1.62552i
$540$	−18.5957	+	1.01143i	−0.800232	+	0.0435252i
$541$	−4.09032	−	2.36155i	−0.175857	−	0.101531i	0.409488	−	0.912316i	$-0.365707\pi$
$541$	−4.09032	−	2.36155i	−0.175857	−	0.101531i	−0.585344	+	0.810785i	$0.699041\pi$
$542$	14.0510	+	16.2938i	0.603542	+	0.699880i
$543$	−37.4313	−	10.8352i	−1.60633	−	0.464985i
$544$	−11.5391	+	5.10484i	−0.494734	+	0.218868i
$545$	16.7270	+	28.9720i	0.716506	+	1.24102i
$546$	11.9163	+	14.4794i	0.509972	+	0.619663i
$547$	29.4087	+	16.9791i	1.25743	+	0.725976i	0.972574	−	0.232595i	$-0.0747217\pi$
$547$	29.4087	+	16.9791i	1.25743	+	0.725976i	0.284854	+	0.958571i	$0.408055\pi$
$548$	−7.77109	+	9.78562i	−0.331964	+	0.418021i
$549$	0.0943502	−	2.36113i	0.00402677	−	0.100770i
$550$	−12.8770	−	4.49108i	−0.549077	−	0.191500i
$551$	1.87319	+	3.24446i	0.0798006	+	0.138219i
$552$	−6.26916	+	1.81833i	−0.266833	+	0.0773933i
$553$	−2.86008	−	0.775720i	−0.121623	−	0.0329870i
$554$	11.8087	−	33.8584i	0.501705	−	1.43851i
$555$	12.7335	−	12.2349i	0.540508	−	0.519341i
$556$	3.20690	−	21.5757i	0.136003	−	0.915014i
$557$	−1.67195	−	2.89591i	−0.0708429	−	0.122704i	0.828428	−	0.560095i	$-0.189236\pi$
$557$	−1.67195	−	2.89591i	−0.0708429	−	0.122704i	−0.899271	+	0.437392i	$0.855902\pi$
$558$	2.26368	+	15.1746i	0.0958290	+	0.642391i
$559$			16.6983i			0.706262i
$560$	−10.0733	+	16.0685i	−0.425674	+	0.679020i
$561$	4.98810	+	20.2228i	0.210598	+	0.853807i
$562$	−8.18413	−	9.49048i	−0.345227	−	0.400332i
$563$	−5.56843	−	3.21493i	−0.234681	−	0.135493i	0.378049	−	0.925786i	$-0.376595\pi$
$563$	−5.56843	−	3.21493i	−0.234681	−	0.135493i	−0.612730	+	0.790293i	$0.709929\pi$
$564$	7.06515	−	15.4328i	0.297497	−	0.649837i
$565$	−11.9931	−	20.7727i	−0.504555	−	0.873915i
$566$	−31.4633	+	27.1324i	−1.32250	+	1.14046i
$567$	−22.4108	−	8.04699i	−0.941167	−	0.337942i
$568$	−37.1562	+	23.5061i	−1.55904	+	0.986295i
$569$	−6.97431	+	4.02662i	−0.292378	+	0.168805i	−0.639014	−	0.769195i	$-0.720657\pi$
$569$	−6.97431	+	4.02662i	−0.292378	+	0.168805i	0.346636	+	0.938000i	$0.387324\pi$
$570$	1.15485	+	2.51907i	0.0483712	+	0.105512i
$571$	0.270061	+	0.155920i	0.0113017	+	0.00652504i	0.505640	−	0.862744i	$-0.331256\pi$
$571$	0.270061	+	0.155920i	0.0113017	+	0.00652504i	−0.494339	+	0.869269i	$0.664590\pi$
$572$	4.58705	−	30.8612i	0.191794	−	1.29037i
$573$	20.0976	−	4.95721i	0.839588	−	0.207091i
$574$	−25.1390	−	17.2144i	−1.04928	−	0.718513i
$575$			2.38327i			0.0993894i
$576$	−20.2753	+	12.8418i	−0.844805	+	0.535074i
$577$	−23.4397	+	13.5329i	−0.975806	+	0.563382i	−0.901001	−	0.433816i	$-0.857167\pi$
$577$	−23.4397	+	13.5329i	−0.975806	+	0.563382i	−0.0748046	+	0.997198i	$0.523833\pi$
$578$	−12.8783	+	11.1056i	−0.535668	+	0.461934i
$579$	1.48859	−	1.43029i	0.0618636	−	0.0594409i
$580$	−7.81078	−	19.7825i	−0.324325	−	0.821423i
$581$	−31.4468	+	8.32335i	−1.30463	+	0.345311i
$582$	16.1830	+	35.3001i	0.670809	+	1.46323i
$583$	−25.6075	−	44.3535i	−1.06055	−	1.83693i
$584$	−28.7040	−	15.0580i	−1.18778	−	0.623106i
$585$	−15.5435	−	0.621117i	−0.642646	−	0.0256800i
$586$	−6.21338	+	1.18222i	−0.256672	+	0.0488369i
$587$	−32.1618	−	18.5686i	−1.32746	−	0.766409i	−0.342553	−	0.939499i	$-0.611292\pi$
$587$	−32.1618	−	18.5686i	−1.32746	−	0.766409i	−0.984906	+	0.173090i	$0.944625\pi$
$588$	−19.8508	+	13.9264i	−0.818633	+	0.574317i
$589$	1.97713	−	1.14150i	0.0814661	−	0.0470345i
$590$	25.8352	−	22.2790i	1.06362	−	0.917213i
$591$	9.05453	+	2.62102i	0.372454	+	0.107814i
$592$	6.61880	−	21.7734i	0.272031	−	0.894883i
$593$	−10.5332	+	18.2440i	−0.432545	+	0.749189i	−0.997092	−	0.0762115i	$-0.975718\pi$
$593$	−10.5332	+	18.2440i	−0.432545	+	0.749189i	0.564547	+	0.825401i	$0.309051\pi$
$594$	15.0591	+	36.6444i	0.617884	+	1.50354i
$595$	2.76831	−	10.2068i	0.113490	−	0.418436i
$596$	10.1663	+	8.07342i	0.416429	+	0.330700i
$597$	−15.6859	+	3.86905i	−0.641983	+	0.158350i
$598$	−5.35635	+	1.01915i	−0.219038	+	0.0416762i
$599$	39.1282	+	22.5907i	1.59873	+	0.923030i	0.991732	+	0.128330i	$0.0409615\pi$
$599$	39.1282	+	22.5907i	1.59873	+	0.923030i	0.607002	+	0.794700i	$0.292372\pi$
$600$	2.44096	+	8.41582i	0.0996516	+	0.343574i
$601$	14.9532	+	8.63326i	0.609956	+	0.352158i	0.772948	−	0.634469i	$-0.218781\pi$
$601$	14.9532	+	8.63326i	0.609956	+	0.352158i	−0.162992	+	0.986627i	$0.552115\pi$
$602$	−21.5288	−	1.65732i	−0.877448	−	0.0675471i
$603$	9.22308	+	17.5587i	0.375593	+	0.715045i
$604$	−8.72612	−	6.92970i	−0.355061	−	0.281965i
$605$		−	32.3753i		−	1.31624i
$606$	5.97647	−	8.41865i	0.242778	−	0.341984i
$607$		−	9.59841i		−	0.389587i	−0.980844	−	0.194794i	$-0.937596\pi$
$607$		−	9.59841i		−	0.389587i	0.980844	−	0.194794i	$-0.0624037\pi$
$608$	2.88422	+	2.10596i	0.116971	+	0.0854079i
$609$	0.626006	−	27.1870i	0.0253670	−	1.10167i
$610$	1.96101	−	0.373121i	0.0793990	−	0.0151072i
$611$	7.08882	−	12.2782i	0.286783	−	0.496723i
$612$	8.73472	−	10.1398i	0.353080	−	0.409877i
$613$	−10.8395	+	6.25819i	−0.437803	+	0.252766i	−0.702665	−	0.711520i	$-0.748007\pi$
$613$	−10.8395	+	6.25819i	−0.437803	+	0.252766i	0.264862	+	0.964286i	$0.414674\pi$
$614$	−19.9787	−	6.96793i	−0.806275	−	0.281203i
$615$	24.5391	−	6.05276i	0.989514	−	0.244071i
$616$	39.3336	+	8.97701i	1.58480	+	0.361694i
$617$	17.6047	−	10.1641i	0.708737	−	0.409189i	−0.101856	−	0.994799i	$-0.532478\pi$
$617$	17.6047	−	10.1641i	0.708737	−	0.409189i	0.810593	+	0.585610i	$0.199145\pi$
$618$	−11.6065	+	16.3493i	−0.466881	+	0.657663i
$619$	−11.4740			−0.461177			−0.230588	−	0.973051i	$-0.574065\pi$
$619$	−11.4740			−0.461177			−0.230588	+	0.973051i	$0.574065\pi$
$620$	−12.0552	+	4.75978i	−0.484147	+	0.191157i
$621$	5.17998	−	4.59376i	0.207865	−	0.184341i
$622$	4.86298	−	4.19360i	0.194988	−	0.168148i
$623$	−6.90391	−	26.0840i	−0.276599	−	1.04503i
$624$	−17.8705	+	9.08481i	−0.715394	+	0.363684i
$625$	−12.8573			−0.514292
$626$	−5.43603	+	1.03431i	−0.217267	+	0.0413394i
$627$	4.25097	−	4.08449i	0.169767	−	0.163119i
$628$	−0.593110	+	0.234179i	−0.0236677	+	0.00934478i
$629$			12.6902i			0.505992i
$630$	2.34350	−	19.9784i	0.0933674	−	0.795958i
$631$	−30.9292			−1.23127			−0.615635	−	0.788031i	$-0.711100\pi$
$631$	−30.9292			−1.23127			−0.615635	+	0.788031i	$0.711100\pi$
$632$	1.47171	−	2.80542i	0.0585417	−	0.111594i
$633$	32.2515	−	7.95506i	1.28188	−	0.316185i
$634$	−9.05878	−	47.6102i	−0.359770	−	1.89084i
$635$		−	14.7918i		−	0.586993i
$636$	−13.6978	+	29.9208i	−0.543154	+	1.18644i
$637$	−17.6028	+	10.0202i	−0.697448	+	0.397014i
$638$	−34.2648	+	29.5483i	−1.35656	+	1.16983i
$639$	24.9111	−	39.4233i	0.985469	−	1.55956i
$640$	−14.4384	−	14.2332i	−0.570728	−	0.562615i
$641$		−	50.1873i		−	1.98228i	−0.132824	−	0.991140i	$-0.542405\pi$
$641$		−	50.1873i		−	1.98228i	0.132824	−	0.991140i	$-0.457595\pi$
$642$	13.0807	−	5.99673i	0.516252	−	0.236672i
$643$	−4.88154	−	8.45507i	−0.192509	−	0.333436i	0.753572	−	0.657365i	$-0.228329\pi$
$643$	−4.88154	−	8.45507i	−0.192509	−	0.333436i	−0.946081	+	0.323930i	$0.894996\pi$
$644$	−0.782352	−	7.00700i	−0.0308290	−	0.276115i
$645$	12.9160	−	12.4102i	0.508567	−	0.488651i
$646$	−1.88037	−	0.655812i	−0.0739822	−	0.0258026i
$647$	7.75955	+	13.4399i	0.305059	+	0.528378i	0.977275	−	0.211978i	$-0.0679904\pi$
$647$	7.75955	+	13.4399i	0.305059	+	0.528378i	−0.672215	+	0.740356i	$0.734657\pi$
$648$	13.5866	−	21.5268i	0.533732	−	0.845653i
$649$	−62.8508	−	36.2869i	−2.46711	−	1.42439i
$650$	1.36812	+	7.19045i	0.0536622	+	0.282033i
$651$	−16.5674	−	0.381479i	−0.649327	−	0.0149513i
$652$	0.749203	+	1.89752i	0.0293410	+	0.0743125i
$653$	−18.7355			−0.733175			−0.366588	−	0.930384i	$-0.619474\pi$
$653$	−18.7355			−0.733175			−0.366588	+	0.930384i	$0.619474\pi$
$654$	−45.5271	−	4.28055i	−1.78025	−	0.167383i
$655$	−5.44673			−0.212822
$656$	23.7860	−	22.2519i	0.928686	−	0.868791i
$657$	34.3528	+	1.37273i	1.34023	+	0.0535553i
$658$	15.1265	+	10.3581i	0.589692	+	0.403801i
$659$	−3.39565	+	5.88144i	−0.132276	+	0.229109i	−0.924554	−	0.381052i	$-0.875562\pi$
$659$	−3.39565	+	5.88144i	−0.132276	+	0.229109i	0.792278	+	0.610161i	$0.208895\pi$
$660$	−27.2801	+	19.3881i	−1.06188	+	0.754681i
$661$	−19.5937	+	33.9373i	−0.762106	+	1.32001i	0.179657	+	0.983729i	$0.442501\pi$
$661$	−19.5937	+	33.9373i	−0.762106	+	1.32001i	−0.941763	+	0.336277i	$0.890832\pi$
$662$	6.87294	−	1.30771i	0.267124	−	0.0508256i
$663$	8.06102	−	7.74534i	0.313064	−	0.300804i
$664$	−1.40691	−	34.7472i	−0.0545986	−	1.34845i
$665$	−2.89356	+	0.765869i	−0.112208	+	0.0296991i
$666$	3.56135	+	23.8735i	0.137999	+	0.925080i
$667$	6.84765	+	3.95349i	0.265142	+	0.153080i
$668$	3.93704	−	26.4880i	0.152329	−	1.02485i
$669$	20.4996	+	21.3351i	0.792561	+	0.824864i
$670$	−12.6885	+	10.9419i	−0.490198	+	0.422722i
$671$	−2.12330	−	3.67766i	−0.0819689	−	0.141974i
$672$	−9.93923	−	23.9418i	−0.383414	−	0.923576i
$673$	25.5089	−	44.1826i	0.983294	−	1.70312i	0.334009	−	0.942570i	$-0.391598\pi$
$673$	25.5089	−	44.1826i	0.983294	−	1.70312i	0.649285	−	0.760545i	$-0.275068\pi$
$674$	0.242456	+	1.27428i	0.00933906	+	0.0490833i
$675$	−6.16673	−	6.95368i	−0.237357	−	0.267647i
$676$	8.60793	−	3.39870i	0.331074	−	0.130719i
$677$	19.1246	−	11.0416i	0.735020	−	0.424364i	−0.0852360	−	0.996361i	$-0.527164\pi$
$677$	19.1246	−	11.0416i	0.735020	−	0.424364i	0.820256	+	0.571997i	$0.193831\pi$
$678$	32.6426	+	3.06913i	1.25363	+	0.117869i
$679$	−40.5479	+	10.7322i	−1.55609	+	0.411865i
$680$	10.0117	+	5.25211i	0.383931	+	0.201409i
$681$	4.57364	−	15.8000i	0.175262	−	0.605458i
$682$	18.0063	+	20.8805i	0.689497	+	0.799555i
$683$	−15.2032	−	26.3326i	−0.581733	−	1.00759i	−0.995274	−	0.0971054i	$-0.969042\pi$
$683$	−15.2032	−	26.3326i	−0.581733	−	1.00759i	0.413541	−	0.910485i	$-0.364292\pi$
$684$	−3.72150	−	0.706047i	−0.142295	−	0.0269964i
$685$	11.1965			0.427795
$686$	−11.1718	−	23.6895i	−0.426540	−	0.904469i
$687$	−40.8201	−	11.8162i	−1.55738	−	0.450816i
$688$	6.71365	−	22.0855i	0.255956	−	0.842000i
$689$	−13.7437	+	23.8048i	−0.523594	+	0.906891i
$690$	4.76916	+	3.38567i	0.181559	+	0.128890i
$691$	18.5357	+	32.1047i	0.705130	+	1.22132i	0.966645	+	0.256121i	$0.0824445\pi$
$691$	18.5357	+	32.1047i	0.705130	+	1.22132i	−0.261515	+	0.965199i	$0.584222\pi$
$692$	−19.7418	−	2.93432i	−0.750471	−	0.111546i
$693$	−41.7720	+	9.28878i	−1.58679	+	0.352852i
$694$	28.8897	−	24.9131i	1.09664	−	0.945688i
$695$	−16.9260	+	9.77221i	−0.642038	+	0.370681i
$696$	28.2296	+	6.94719i	1.07004	+	0.263332i
$697$	−9.08158	+	15.7297i	−0.343989	+	0.595807i
$698$	−17.5275	+	15.1148i	−0.663424	+	0.572104i
$699$	26.7301	+	27.8196i	1.01103	+	1.05223i
$700$	−9.40631	+	1.05024i	−0.355525	+	0.0396954i
$701$	−12.8133			−0.483952			−0.241976	−	0.970282i	$-0.577796\pi$
$701$	−12.8133			−0.483952			−0.241976	+	0.970282i	$0.577796\pi$
$702$	12.9912	−	16.8332i	0.490321	−	0.635326i
$703$	3.11053	−	1.79587i	0.117316	−	0.0677324i
$704$	−18.4749	+	38.9734i	−0.696299	+	1.46887i
$705$	−14.7655	+	3.64203i	−0.556102	+	0.137167i
$706$	28.3421	+	9.88482i	1.06667	+	0.372020i
$707$	7.86123	+	7.90937i	0.295652	+	0.297463i
$708$	4.38966	+	46.4239i	0.164974	+	1.74472i
$709$	21.8962	−	12.6418i	0.822329	−	0.474772i	−0.0288897	−	0.999583i	$-0.509197\pi$
$709$	21.8962	−	12.6418i	0.822329	−	0.474772i	0.851219	+	0.524810i	$0.175864\pi$
$710$	37.1977	+	12.9733i	1.39600	+	0.486881i
$711$	−0.134165	+	3.35751i	−0.00503159	+	0.125916i
$712$	28.8215	−	1.16698i	1.08013	−	0.0437344i
$713$	2.40920	−	4.17286i	0.0902253	−	0.156275i
$714$	9.18587	+	11.1617i	0.343772	+	0.417715i
$715$	−24.2104	+	13.9779i	−0.905417	+	0.522743i
$716$	0.0625864	−	0.421076i	0.00233897	−	0.0157363i
$717$	24.2099	−	5.97154i	0.904134	−	0.223011i
$718$	−22.5935	−	26.1999i	−0.843182	−	0.977771i
$719$	−3.56334	+	6.17189i	−0.132890	+	0.230173i	−0.924790	−	0.380479i	$-0.875759\pi$
$719$	−3.56334	+	6.17189i	−0.132890	+	0.230173i	0.791899	+	0.610652i	$0.209092\pi$
$720$	20.3085	+	7.07089i	0.756852	+	0.263516i
$721$	−15.2667	−	15.3602i	−0.568563	−	0.572045i
$722$	−4.91710	−	25.8428i	−0.182995	−	0.961769i
$723$	5.31322	−	18.3550i	0.197601	−	0.682629i
$724$	35.2369	+	27.9828i	1.30957	+	1.03997i
$725$	5.30723	−	9.19238i	0.197105	−	0.341397i
$726$	36.0851	+	25.6171i	1.33924	+	0.950741i
$727$	36.1143	+	20.8506i	1.33941	+	0.773307i	0.986719	−	0.162434i	$-0.0519345\pi$
$727$	36.1143	+	20.8506i	1.33941	+	0.773307i	0.352688	+	0.935741i	$0.385268\pi$
$728$	−6.38278	−	20.6913i	−0.236561	−	0.766872i
$729$	−3.22729	+	26.8064i	−0.119529	+	0.992831i
$730$	5.42865	+	28.5314i	0.200923	+	1.05599i
$731$			12.8721i			0.476091i
$732$	−1.13578	+	2.48095i	−0.0419797	+	0.0916985i
$733$	14.3201			0.528924			0.264462	−	0.964396i	$-0.414806\pi$
$733$	14.3201			0.528924			0.264462	+	0.964396i	$0.414806\pi$
$734$	−3.59856	+	10.3179i	−0.132825	+	0.380842i
$735$	20.8330	+	6.16862i	0.768436	+	0.227533i
$736$	7.49417	+	0.805608i	0.276239	+	0.0296951i
$737$	30.8679	+	17.8216i	1.13703	+	0.656467i
$738$	−12.6704	+	32.1403i	−0.466403	+	1.18310i
$739$	−22.7633	+	13.1424i	−0.837361	+	0.483451i	−0.856366	−	0.516369i	$-0.827283\pi$
$739$	−22.7633	+	13.1424i	−0.837361	+	0.483451i	0.0190053	+	0.999819i	$0.493950\pi$
$740$	−18.9659	+	7.48836i	−0.697199	+	0.275277i
$741$	−3.03924	−	0.879770i	−0.111649	−	0.0323192i
$742$	−29.3270	−	20.0822i	−1.07663	−	0.737240i
$743$	−30.0581	+	17.3541i	−1.10273	+	0.636659i	−0.936936	−	0.349502i	$-0.886351\pi$
$743$	−30.0581	+	17.3541i	−1.10273	+	0.636659i	−0.165790	+	0.986161i	$0.553017\pi$
$744$	4.23352	−	17.2027i	0.155208	−	0.630682i
$745$		−	11.6321i		−	0.426166i
$746$	−5.43932	+	15.5958i	−0.199147	+	0.571003i
$747$	17.1524	+	32.6544i	0.627575	+	1.19476i
$748$	3.53599	−	23.7898i	0.129289	−	0.869841i
$749$	3.97690	+	15.0253i	0.145313	+	0.549012i
$750$	17.2499	−	24.2987i	0.629876	−	0.887263i
$751$	−12.1079			−0.441825			−0.220912	−	0.975294i	$-0.570903\pi$
$751$	−12.1079			−0.441825			−0.220912	+	0.975294i	$0.570903\pi$
$752$	−14.3123	+	13.3893i	−0.521917	+	0.488257i
$753$	6.19649	−	21.4063i	0.225813	−	0.780089i
$754$	22.9292	+	7.99696i	0.835031	+	0.291232i
$755$			9.98421i			0.363363i
$756$	20.4133	+	18.4200i	0.742425	+	0.669929i
$757$		−	21.4770i		−	0.780594i	−0.920689	−	0.390297i	$-0.872372\pi$
$757$		−	21.4770i		−	0.780594i	0.920689	−	0.390297i	$-0.127628\pi$
$758$	4.41792	−	12.6672i	0.160466	−	0.460095i
$759$	3.45964	−	11.9516i	0.125577	−	0.433816i
$760$	−0.129456	−	3.19725i	−0.00469587	−	0.115976i
$761$	28.2808			1.02518			0.512589	−	0.858634i	$-0.328687\pi$
$761$	28.2808			1.02518			0.512589	+	0.858634i	$0.328687\pi$
$762$	16.4867	+	11.7040i	0.597249	+	0.423993i
$763$	12.9291	−	47.6695i	0.468065	−	1.72575i
$764$	−23.6425	−	3.51409i	−0.855354	−	0.127135i
$765$	−11.9819	−	0.478796i	−0.433208	−	0.0173109i
$766$	−30.9099	−	10.7804i	−1.11682	−	0.389510i
$767$			38.9509i			1.40643i
$768$	27.2885	−	4.83079i	0.984690	−	0.174316i
$769$	−18.5576	+	10.7142i	−0.669202	+	0.386364i	−0.795774	−	0.605593i	$-0.792936\pi$
$769$	−18.5576	+	10.7142i	−0.669202	+	0.386364i	0.126572	+	0.991957i	$0.459603\pi$
$770$	−15.6185	−	32.6013i	−0.562853	−	1.17487i
$771$	−20.8012	−	6.02133i	−0.749137	−	0.216853i
$772$	−2.21717	+	0.875411i	−0.0797976	+	0.0315067i
$773$	−4.02683	+	2.32489i	−0.144835	+	0.0836205i	−0.570666	−	0.821182i	$-0.693315\pi$
$773$	−4.02683	+	2.32489i	−0.144835	+	0.0836205i	0.425831	+	0.904803i	$0.359982\pi$
$774$	3.61238	+	24.2156i	0.129844	+	0.870413i
$775$	−5.60171	−	3.23415i	−0.201219	−	0.116174i
$776$	−1.81409	−	44.8035i	−0.0651219	−	1.60835i
$777$	−26.0648	−	0.600165i	−0.935068	−	0.0215308i
$778$	−8.82064	−	3.07635i	−0.316235	−	0.110293i
$779$	5.14075			0.184186
$780$	16.3323	+	7.47697i	0.584791	+	0.267719i
$781$		−	83.8070i		−	2.99885i
$782$	−4.12901	+	0.785626i	−0.147653	+	0.0280939i
$783$	−30.2091	+	6.18319i	−1.07958	+	0.220969i
$784$	27.3105	−	6.17558i	0.975374	−	0.220556i
$785$	0.494808	+	0.285678i	0.0176605	+	0.0101963i
$786$	4.30975	−	6.07085i	0.153724	−	0.216540i
$787$	−18.9754	+	32.8663i	−0.676399	+	1.17156i	0.299659	+	0.954047i	$0.403127\pi$
$787$	−18.9754	+	32.8663i	−0.676399	+	1.17156i	−0.976058	+	0.217511i	$0.930206\pi$
$788$	−8.52371	−	6.76896i	−0.303644	−	0.241134i
$789$	−14.3393	+	49.5363i	−0.510492	+	1.76354i
$790$	−2.78854	+	0.530575i	−0.0992119	+	0.0188770i
$791$	−9.27007	+	34.1787i	−0.329606	+	1.21526i
$792$	−0.0242079	−	45.7469i	−0.000860190	−	1.62555i
$793$	−1.13959	+	1.97382i	−0.0404679	+	0.0700925i
$794$	32.9819	−	28.4420i	1.17048	−	1.00937i
$795$	28.6272	−	7.06111i	1.01530	−	0.250432i
$796$	18.4527	+	2.74271i	0.654038	+	0.0972128i
$797$	20.1513	−	11.6344i	0.713797	−	0.412111i	−0.0986686	−	0.995120i	$-0.531458\pi$
$797$	20.1513	−	11.6344i	0.713797	−	0.412111i	0.812465	+	0.583010i	$0.198125\pi$
$798$	1.43592	−	3.83112i	0.0508310	−	0.135620i
$799$	5.46451	−	9.46480i	0.193320	−	0.334841i
$800$	1.08146	−	10.0603i	0.0382354	−	0.355685i
$801$	−27.0856	+	14.2273i	−0.957023	+	0.502698i
$802$	8.65651	−	24.8203i	0.305672	−	0.876434i
$803$	53.5074	−	30.8925i	1.88823	−	1.09017i
$804$	−2.15589	−	22.8002i	−0.0760325	−	0.804101i
$805$	−4.48066	+	4.45339i	−0.157922	+	0.156961i
$806$	4.87323	−	13.9727i	0.171652	−	0.492168i
$807$	8.90581	−	2.19668i	0.313499	−	0.0773269i
$808$	−10.0747	+	6.37357i	−0.354428	+	0.224221i
$809$	41.6827	−	24.0655i	1.46549	−	0.846098i	0.466229	−	0.884664i	$-0.345612\pi$
$809$	41.6827	−	24.0655i	1.46549	−	0.846098i	0.999256	+	0.0385655i	$0.0122788\pi$
$810$	−22.6754	+	2.46184i	−0.796733	+	0.0865002i
$811$	38.8536			1.36434			0.682168	−	0.731196i	$-0.261037\pi$
$811$	38.8536			1.36434			0.682168	+	0.731196i	$0.261037\pi$
$812$	−12.5861	+	28.7685i	−0.441685	+	1.00958i
$813$	18.2573	+	19.0014i	0.640310	+	0.666408i
$814$	28.3286	+	32.8504i	0.992915	+	1.15141i
$815$	0.913959	−	1.58302i	0.0320146	−	0.0554509i
$816$	−13.7757	+	7.00315i	−0.482247	+	0.245159i
$817$	3.15511	−	1.82160i	0.110383	−	0.0637298i
$818$	8.70924	+	10.0994i	0.304511	+	0.353118i
$819$	15.5271	+	16.9230i	0.542561	+	0.591339i
$820$	−28.8675	−	4.29071i	−1.00810	−	0.149838i
$821$	−4.37422	−	7.57638i	−0.152661	−	0.264417i	0.779544	−	0.626348i	$-0.215451\pi$
$821$	−4.37422	−	7.57638i	−0.152661	−	0.264417i	−0.932205	+	0.361931i	$0.882118\pi$
$822$	−8.85925	+	12.4794i	−0.309002	+	0.435270i
$823$	15.7248	−	27.2361i	0.548131	−	0.949391i	−0.450271	−	0.892892i	$-0.648673\pi$
$823$	15.7248	−	27.2361i	0.548131	−	0.949391i	0.998403	−	0.0564993i	$-0.0179939\pi$
$824$	19.5654	−	12.3776i	0.681593	−	0.431196i
$825$	−16.0440	−	4.64427i	−0.558582	−	0.161693i
$826$	−50.2187	−	3.86590i	−1.74733	−	0.134512i
$827$	14.0862			0.489824			0.244912	−	0.969545i	$-0.421241\pi$
$827$	14.0862			0.489824			0.244912	+	0.969545i	$0.421241\pi$
$828$	−7.54724	+	2.63671i	−0.262285	+	0.0916321i
$829$	7.61791	+	13.1946i	0.264581	+	0.458268i	0.967454	−	0.253048i	$-0.0814330\pi$
$829$	7.61791	+	13.1946i	0.264581	+	0.458268i	−0.702873	+	0.711316i	$0.748100\pi$
$830$	−23.5971	+	20.3490i	−0.819067	+	0.706324i
$831$	12.2115	−	42.1858i	0.423613	−	1.46341i
$832$	23.0727	−	1.87149i	0.799903	−	0.0648822i
$833$	−13.5693	+	7.72419i	−0.470150	+	0.267627i
$834$	2.50077	−	26.5977i	0.0865947	−	0.921004i
$835$	−20.7796	+	11.9971i	−0.719109	+	0.415178i
$836$	−6.33157	+	2.49992i	−0.218982	+	0.0864614i
$837$	3.76795	+	18.4090i	0.130239	+	0.636307i
$838$	18.8282	−	3.58244i	0.650409	−	0.123753i
$839$	13.1004	−	22.6905i	0.452276	−	0.783364i	−0.546251	−	0.837621i	$-0.683946\pi$
$839$	13.1004	−	22.6905i	0.452276	−	0.783364i	0.998527	+	0.0542569i	$0.0172790\pi$
$840$	−11.2609	+	20.3149i	−0.388539	+	0.700930i
$841$	−3.10776	−	5.38281i	−0.107164	−	0.185614i
$842$	1.48974	+	1.72753i	0.0513398	+	0.0595347i
$843$	−10.6341	−	11.0675i	−0.366258	−	0.381186i
$844$	−37.9401	−	5.63922i	−1.30595	−	0.194110i
$845$	−7.18126	−	4.14610i	−0.247043	−	0.142630i
$846$	7.62394	−	19.3392i	0.262117	−	0.664896i
$847$	−33.9022	+	33.6958i	−1.16489	+	1.15780i
$848$	27.7486	−	25.9589i	0.952890	−	0.891434i
$849$	−36.6916	+	35.2547i	−1.25925	+	1.20994i
$850$	1.05464	+	5.54285i	0.0361737	+	0.190118i
$851$	3.79029	−	6.56498i	0.129930	−	0.225045i
$852$	−43.8927	+	31.1948i	−1.50374	+	1.06872i
$853$	1.77756	−	3.07882i	0.0608625	−	0.105417i	−0.833989	−	0.551782i	$-0.813948\pi$
$853$	1.77756	−	3.07882i	0.0608625	−	0.105417i	0.894851	+	0.446365i	$0.147282\pi$
$854$	−2.43171	−	1.66515i	−0.0832114	−	0.0569804i
$855$	1.57828	+	3.00468i	0.0539759	+	0.102758i
$856$	−16.6022	+	0.672221i	−0.567452	+	0.0229760i
$857$	8.91493			0.304528			0.152264	−	0.988340i	$-0.451344\pi$
$857$	8.91493			0.304528			0.152264	+	0.988340i	$0.451344\pi$
$858$	3.57703	−	38.0446i	0.122118	−	1.29882i
$859$	−25.0498			−0.854689			−0.427344	−	0.904089i	$-0.640551\pi$
$859$	−25.0498			−0.854689			−0.427344	+	0.904089i	$0.640551\pi$
$860$	−19.2377	+	7.59567i	−0.655999	+	0.259010i
$861$	−31.8782	−	19.3968i	−1.08641	−	0.661041i
$862$	−17.7302	+	3.37351i	−0.603892	+	0.114902i
$863$	−18.3314	−	10.5836i	−0.624007	−	0.360270i	0.154421	−	0.988005i	$-0.450649\pi$
$863$	−18.3314	−	10.5836i	−0.624007	−	0.360270i	−0.778427	+	0.627735i	$0.783982\pi$
$864$	−23.9503	+	17.0407i	−0.814805	+	0.579735i
$865$	8.94158	+	15.4873i	0.304023	+	0.526583i
$866$	17.7847	−	50.9929i	0.604348	−	1.73281i
$867$	−15.0183	+	14.4302i	−0.510049	+	0.490074i
$868$	17.5311	+	7.66977i	0.595044	+	0.260329i
$869$	3.01931	+	5.22960i	0.102423	+	0.177402i
$870$	−10.8554	−	23.6789i	−0.368033	−	0.802791i
$871$		−	19.1299i		−	0.648193i
$872$	46.7586	+	24.5294i	1.58344	+	0.830670i
$873$	22.1166	+	42.1050i	0.748533	+	1.42504i
$874$	0.776887	+	0.900894i	0.0262786	+	0.0304732i
$875$	22.6898	+	22.8288i	0.767057	+	0.771754i
$876$	−36.0961	−	16.5249i	−1.21957	−	0.558323i
$877$		−	29.7327i		−	1.00400i	−0.864867	−	0.502000i	$-0.832598\pi$
$877$		−	29.7327i		−	1.00400i	0.864867	−	0.502000i	$-0.167402\pi$
$878$	37.3141	−	7.09973i	1.25929	−	0.239604i
$879$	−7.52092	+	1.85509i	−0.253674	+	0.0625706i
$880$	37.6410	−	8.75346i	1.26888	−	0.295079i
$881$	22.5816			0.760794			0.380397	−	0.924823i	$-0.375787\pi$
$881$	22.5816			0.760794			0.380397	+	0.924823i	$0.375787\pi$
$882$	−23.3597	+	18.3392i	−0.786560	+	0.617513i
$883$			19.6946i			0.662776i	0.943495	+	0.331388i	$0.107517\pi$
$883$			19.6946i			0.662776i	−0.943495	+	0.331388i	$0.892483\pi$
$884$	−12.0064	+	4.74054i	−0.403820	+	0.159441i
$885$	30.1283	−	28.9484i	1.01275	−	0.973089i
$886$	2.95419	+	15.5263i	0.0992479	+	0.521617i
$887$	4.32811			0.145324			0.0726618	−	0.997357i	$-0.476851\pi$
$887$	4.32811			0.145324			0.0726618	+	0.997357i	$0.476851\pi$
$888$	6.66041	−	27.0643i	0.223509	−	0.908218i
$889$	−15.4893	+	15.3951i	−0.519496	+	0.516334i
$890$	−16.8787	−	19.5729i	−0.565776	−	0.656086i
$891$	20.8307	+	43.8231i	0.697853	+	1.46813i
$892$	−12.5468	−	31.7775i	−0.420098	−	1.06399i
$893$	−3.09326			−0.103512
$894$	12.9649	+	9.20392i	0.433612	+	0.307825i
$895$	−0.330330	+	0.190716i	−0.0110417	+	0.00637494i
$896$	0.122895	+	29.9330i	0.00410563	+	0.999992i
$897$	−6.48354	+	1.59921i	−0.216479	+	0.0533961i
$898$	3.89563	−	11.1697i	0.129999	−	0.372737i
$899$	−18.5848	+	10.7299i	−0.619837	+	0.357863i
$900$	3.53956	+	10.1315i	0.117985	+	0.337718i
$901$	−10.5945	+	18.3502i	−0.352954	+	0.611335i
$902$	11.6048	+	60.9916i	0.386399	+	2.03080i
$903$	−26.4383	−	0.608766i	−0.879811	−	0.0202585i
$904$	−33.5255	−	17.5874i	−1.11504	−	0.584948i
$905$		−	40.3172i		−	1.34019i
$906$	−11.1283	−	7.90005i	−0.369712	−	0.262462i
$907$			25.3890i			0.843027i	0.906822	+	0.421514i	$0.138501\pi$
$907$			25.3890i			0.843027i	−0.906822	+	0.421514i	$0.861499\pi$
$908$	−11.8117	+	14.8737i	−0.391986	+	0.493602i
$909$	6.75453	−	10.6894i	0.224034	−	0.354546i
$910$	−10.9619	+	16.0082i	−0.363383	+	0.530667i
$911$	33.4684	+	19.3230i	1.10886	+	0.640199i	0.938533	−	0.345189i	$-0.112185\pi$
$911$	33.4684	+	19.3230i	1.10886	+	0.640199i	0.170324	+	0.985388i	$0.445519\pi$
$912$	3.66604	+	2.38555i	0.121395	+	0.0789934i
$913$	57.4060	+	33.1434i	1.89986	+	1.09689i
$914$	8.97637	+	47.1771i	0.296912	+	1.56048i
$915$	2.37368	−	0.585486i	0.0784716	−	0.0193556i
$916$	38.4270	+	30.5161i	1.26966	+	1.00828i
$917$	5.66889	+	5.70361i	0.187203	+	0.188350i
$918$	10.0144	−	12.9761i	0.330525	−	0.428273i
$919$	21.2061	−	36.7300i	0.699525	−	1.21161i	−0.269107	−	0.963110i	$-0.586728\pi$
$919$	21.2061	−	36.7300i	0.699525	−	1.21161i	0.968631	−	0.248502i	$-0.0799382\pi$
$920$	−3.61062	−	5.70733i	−0.119039	−	0.188165i
$921$	−24.8924	−	7.20561i	−0.820232	−	0.237433i
$922$	−9.90128	−	11.4817i	−0.326081	−	0.378130i
$923$	−38.9537	+	22.4899i	−1.28218	+	0.740264i
$924$	48.6952	+	8.38776i	1.60196	+	0.275937i
$925$	−8.81293	−	5.08815i	−0.289767	−	0.167297i
$926$	2.63386	+	13.8428i	0.0865540	+	0.454902i
$927$	−13.1175	+	20.7592i	−0.430835	+	0.681821i
$928$	−27.1113	−	19.7958i	−0.889973	−	0.649828i
$929$	7.70309	+	13.3421i	0.252730	+	0.437741i	0.964277	−	0.264898i	$-0.0853382\pi$
$929$	7.70309	+	13.3421i	0.252730	+	0.437741i	−0.711546	+	0.702639i	$0.752005\pi$
$930$	−14.4296	+	6.61514i	−0.473165	+	0.216919i
$931$	3.81357	+	2.23292i	0.124985	+	0.0731810i
$932$	−16.3602	−	41.4357i	−0.535896	−	1.35727i
$933$	5.67106	−	5.44897i	0.185662	−	0.178391i
$934$	−9.92992	−	11.5149i	−0.324917	−	0.376780i
$935$	−18.6629	+	10.7750i	−0.610341	+	0.352381i
$936$	−21.2568	+	12.2876i	−0.694799	+	0.401633i
$937$		−	49.3800i		−	1.61318i	−0.591114	−	0.806588i	$-0.701312\pi$
$937$		−	49.3800i		−	1.61318i	0.591114	−	0.806588i	$-0.298688\pi$
$938$	24.6639	+	1.89866i	0.805305	+	0.0619934i
$939$	−6.57998	+	1.62300i	−0.214730	+	0.0529646i
$940$	17.3699	+	2.58178i	0.566545	+	0.0842083i
$941$	6.53069	+	3.77050i	0.212894	+	0.122915i	0.602656	−	0.798001i	$-0.294109\pi$
$941$	6.53069	+	3.77050i	0.212894	+	0.122915i	−0.389761	+	0.920916i	$0.627443\pi$
$942$	−0.709932	+	0.325463i	−0.0231308	+	0.0106041i
$943$	9.39627	−	5.42494i	0.305985	−	0.176660i
$944$	15.6605	−	51.5172i	0.509704	−	1.67674i
$945$	1.55008	−	24.5874i	0.0504241	−	0.799827i
$946$	28.7345	+	33.3211i	0.934240	+	1.08336i
$947$	11.8430	+	20.5127i	0.384846	+	0.666572i	0.991748	−	0.128204i	$-0.0409213\pi$
$947$	11.8430	+	20.5127i	0.384846	+	0.666572i	−0.606902	+	0.794777i	$0.707588\pi$
$948$	1.61508	−	3.52789i	0.0524552	−	0.114581i
$949$	−28.7178	−	16.5802i	−0.932218	−	0.538216i
$950$	1.20937	−	1.04291i	0.0392373	−	0.0338363i
$951$	−14.2147	−	57.6293i	−0.460943	−	1.86876i
$952$	−4.92025	−	15.9502i	−0.159466	−	0.516948i
$953$		−	36.2755i		−	1.17508i	−0.809196	−	0.587539i	$-0.800097\pi$
$953$		−	36.2755i		−	1.17508i	0.809196	−	0.587539i	$-0.199903\pi$
$954$	−14.7812	+	37.4946i	−0.478559	+	1.21393i
$955$	10.7083	+	18.5473i	0.346512	+	0.600177i
$956$	−28.4801	−	4.23313i	−0.921112	−	0.136909i
$957$	−39.9586	+	38.3937i	−1.29168	+	1.24109i
$958$	−53.3727	−	18.6147i	−1.72439	−	0.601413i
$959$	−11.6531	−	11.7245i	−0.376299	−	0.378604i
$960$	−18.5953	−	16.4557i	−0.600160	−	0.531106i
$961$	−8.96134	−	15.5215i	−0.289076	−	0.500694i
$962$	7.66685	−	21.9827i	0.247189	−	0.708750i
$963$	15.6023	−	8.19544i	0.502777	−	0.264094i
$964$	−13.7217	+	17.2789i	−0.441948	+	0.556516i
$965$	1.84970	+	1.06792i	0.0595438	+	0.0343776i
$966$	−1.41834	−	8.51784i	−0.0456344	−	0.274057i
$967$	15.4745	+	26.8025i	0.497625	+	0.861912i	0.999996	−	0.00274026i	$-0.000872254\pi$
$967$	15.4745	+	26.8025i	0.497625	+	0.861912i	−0.502371	+	0.864652i	$0.667539\pi$
$968$	−27.3192	−	43.1836i	−0.878072	−	1.38797i
$969$	−2.34284	−	0.678182i	−0.0752628	−	0.0217863i
$970$	−30.4264	+	26.2382i	−0.976933	+	0.842459i
$971$	−11.7614	−	6.79042i	−0.377440	−	0.217915i	0.299264	−	0.954170i	$-0.403259\pi$
$971$	−11.7614	−	6.79042i	−0.377440	−	0.217915i	−0.676704	+	0.736255i	$0.736592\pi$
$972$	15.1981	−	27.2216i	0.487479	−	0.873135i
$973$	27.8494	+	7.55341i	0.892810	+	0.242151i
$974$	−9.33998	−	49.0882i	−0.299272	−	1.57289i
$975$	2.14681	+	8.70360i	0.0687528	+	0.278738i
$976$	2.30083	−	2.15244i	0.0736478	−	0.0688979i
$977$	−8.49564	−	4.90496i	−0.271799	−	0.156923i	0.357906	−	0.933758i	$-0.383491\pi$
$977$	−8.49564	−	4.90496i	−0.271799	−	0.156923i	−0.629705	+	0.776834i	$0.716824\pi$
$978$	1.04124	+	2.27126i	0.0332952	+	0.0726269i
$979$	−27.4912	+	47.6161i	−0.878622	+	1.52182i
$980$	−19.5511	−	15.7218i	−0.624538	−	0.502214i
$981$	−55.9603	−	2.23616i	−1.78668	−	0.0713952i
$982$	6.91819	+	36.3599i	0.220768	+	1.16029i
$983$	0.425562			0.0135733			0.00678666	−	0.999977i	$-0.497840\pi$
$983$	0.425562			0.0135733			0.00678666	+	0.999977i	$0.497840\pi$
$984$	27.6239	−	28.7802i	0.880617	−	0.917480i
$985$			9.75261i			0.310744i
$986$	17.6752	+	6.16456i	0.562894	+	0.196319i
$987$	19.1816	+	11.6713i	0.610556	+	0.371502i
$988$	2.86106	+	2.27207i	0.0910226	+	0.0722840i
$989$	3.84461	−	6.65906i	0.122251	−	0.211746i
$990$	−32.0857	+	25.5080i	−1.01975	+	0.810698i
$991$	21.9251	+	37.9753i	0.696473	+	1.20633i	0.969682	+	0.244371i	$0.0785816\pi$
$991$	21.9251	+	37.9753i	0.696473	+	1.20633i	−0.273209	+	0.961955i	$0.588085\pi$
$992$	−12.0632	+	16.5213i	−0.383009	+	0.524551i
$993$	8.31928	−	2.05201i	0.264004	−	0.0651186i
$994$	−25.1297	−	52.4544i	−0.797065	−	1.66375i
$995$	−8.35771	−	14.4760i	−0.264957	−	0.458919i
$996$	−4.00938	−	42.4022i	−0.127042	−	1.34357i
$997$	18.2252			0.577198			0.288599	−	0.957450i	$-0.406811\pi$
$997$	18.2252			0.577198			0.288599	+	0.957450i	$0.406811\pi$
$998$	−4.36543	+	12.5167i	−0.138185	+	0.396210i
$999$	5.92796	+	28.9621i	0.187552	+	0.916319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.y.a.173.11	✓	184
7.3	odd	6		504.2.ca.a.101.72	yes	184
8.5	even	2	inner	504.2.y.a.173.43	yes	184
9.5	odd	6		504.2.ca.a.5.21	yes	184
56.45	odd	6		504.2.ca.a.101.21	yes	184
63.59	even	6	inner	504.2.y.a.437.43	yes	184
72.5	odd	6		504.2.ca.a.5.72	yes	184
504.437	even	6	inner	504.2.y.a.437.11	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.11	✓	184	1.1	even	1	trivial
504.2.y.a.173.43	yes	184	8.5	even	2	inner
504.2.y.a.437.11	yes	184	504.437	even	6	inner
504.2.y.a.437.43	yes	184	63.59	even	6	inner
504.2.ca.a.5.21	yes	184	9.5	odd	6
504.2.ca.a.5.72	yes	184	72.5	odd	6
504.2.ca.a.101.21	yes	184	56.45	odd	6
504.2.ca.a.101.72	yes	184	7.3	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33533 - 0.465720i) q^{2} +(-1.66375 - 0.481605i) q^{3} +(1.56621 + 1.24378i) q^{4} -1.79202i q^{5} +(1.99736 + 1.41794i) q^{6} +(-1.87653 + 1.86511i) q^{7} +(-1.51215 - 2.39027i) q^{8} +(2.53611 + 1.60254i) q^{9} +O(q^{10})\)	\(q+(-1.33533 - 0.465720i) q^{2} +(-1.66375 - 0.481605i) q^{3} +(1.56621 + 1.24378i) q^{4} -1.79202i q^{5} +(1.99736 + 1.41794i) q^{6} +(-1.87653 + 1.86511i) q^{7} +(-1.51215 - 2.39027i) q^{8} +(2.53611 + 1.60254i) q^{9} +(-0.834578 + 2.39293i) q^{10} +5.39133 q^{11} +(-2.00677 - 2.82363i) q^{12} +(-1.44678 - 2.50590i) q^{13} +(3.37441 - 1.61660i) q^{14} +(-0.863046 + 2.98147i) q^{15} +(0.906028 + 3.89604i) q^{16} +(-1.11527 - 1.93170i) q^{17} +(-2.64021 - 3.32104i) q^{18} +(-0.315657 + 0.546733i) q^{19} +(2.22887 - 2.80668i) q^{20} +(4.02032 - 2.19932i) q^{21} +(-7.19920 - 2.51085i) q^{22} +1.33243i q^{23} +(1.36468 + 4.70507i) q^{24} +1.78867 q^{25} +(0.764883 + 4.01999i) q^{26} +(-3.44766 - 3.88763i) q^{27} +(-5.25882 + 0.587163i) q^{28} +(2.96713 - 5.13923i) q^{29} +(2.54098 - 3.57930i) q^{30} +(-3.13177 - 1.80813i) q^{31} +(0.604617 - 5.62445i) q^{32} +(-8.96981 - 2.59649i) q^{33} +(0.589620 + 3.09886i) q^{34} +(3.34231 + 3.36278i) q^{35} +(1.97888 + 5.66428i) q^{36} +(-4.92708 - 2.84465i) q^{37} +(0.676130 - 0.583062i) q^{38} +(1.20022 + 4.86596i) q^{39} +(-4.28341 + 2.70981i) q^{40} +(-4.07147 - 7.05199i) q^{41} +(-6.39272 + 1.06448i) q^{42} +(-4.99769 - 2.88542i) q^{43} +(8.44395 + 6.70562i) q^{44} +(2.87178 - 4.54476i) q^{45} +(0.620538 - 1.77923i) q^{46} +(2.44986 + 4.24328i) q^{47} +(0.368952 - 6.91837i) q^{48} +(0.0427357 - 6.99987i) q^{49} +(-2.38846 - 0.833019i) q^{50} +(0.925208 + 3.75099i) q^{51} +(0.850821 - 5.72424i) q^{52} +(-4.74975 - 8.22681i) q^{53} +(2.79322 + 6.79691i) q^{54} -9.66136i q^{55} +(7.29572 + 1.66508i) q^{56} +(0.788483 - 0.757604i) q^{57} +(-6.35554 + 5.48071i) q^{58} +(-11.6578 - 6.73061i) q^{59} +(-5.06000 + 3.59616i) q^{60} +(-0.393835 - 0.682143i) q^{61} +(3.33986 + 3.87298i) q^{62} +(-7.74800 + 1.72291i) q^{63} +(-3.42678 + 7.22891i) q^{64} +(-4.49062 + 2.59266i) q^{65} +(10.7684 + 7.64459i) q^{66} +(5.72547 + 3.30560i) q^{67} +(0.655866 - 4.41260i) q^{68} +(0.641704 - 2.21682i) q^{69} +(-2.89697 - 6.04700i) q^{70} -15.5448i q^{71} +(-0.00449015 - 8.48528i) q^{72} +(9.92471 - 5.73004i) q^{73} +(5.25447 + 6.09319i) q^{74} +(-2.97590 - 0.861433i) q^{75} +(-1.17440 + 0.463692i) q^{76} +(-10.1170 + 10.0554i) q^{77} +(0.663479 - 7.05663i) q^{78} +(0.560031 + 0.970002i) q^{79} +(6.98177 - 1.62362i) q^{80} +(3.86373 + 8.12844i) q^{81} +(2.15250 + 11.3129i) q^{82} +(10.6478 + 6.14753i) q^{83} +(9.03214 + 1.55579i) q^{84} +(-3.46165 + 1.99858i) q^{85} +(5.32977 + 6.18051i) q^{86} +(-7.41164 + 7.12139i) q^{87} +(-8.15252 - 12.8867i) q^{88} +(-5.09915 + 8.83199i) q^{89} +(-5.95136 + 4.73131i) q^{90} +(7.38870 + 2.00399i) q^{91} +(-1.65725 + 2.08686i) q^{92} +(4.33967 + 4.51655i) q^{93} +(-1.29519 - 6.80713i) q^{94} +(0.979756 + 0.565662i) q^{95} +(-3.71470 + 9.06648i) q^{96} +(13.7295 + 7.92671i) q^{97} +(-3.31704 + 9.32723i) q^{98} +(13.6730 + 8.63982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

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