LMFDB - Embedded newform 380.2.k.d.267.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.8
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.685298 + 1.23708i) q^{2} +(-1.29571 - 1.29571i) q^{3} +(-1.06073 - 1.69554i) q^{4} +(0.171865 + 2.22945i) q^{5} +(2.49084 - 0.714946i) q^{6} +(-0.654476 + 0.654476i) q^{7} +(2.82443 - 0.150262i) q^{8} +0.357708i q^{9} +O(q^{10})$	\(q+(-0.685298 + 1.23708i) q^{2} +(-1.29571 - 1.29571i) q^{3} +(-1.06073 - 1.69554i) q^{4} +(0.171865 + 2.22945i) q^{5} +(2.49084 - 0.714946i) q^{6} +(-0.654476 + 0.654476i) q^{7} +(2.82443 - 0.150262i) q^{8} +0.357708i q^{9} +(-2.87579 - 1.31523i) q^{10} -1.63748i q^{11} +(-0.822520 + 3.57132i) q^{12} +(-1.87102 + 1.87102i) q^{13} +(-0.361127 - 1.25815i) q^{14} +(2.66603 - 3.11140i) q^{15} +(-1.74969 + 3.59702i) q^{16} +(-3.49740 - 3.49740i) q^{17} +(-0.442513 - 0.245137i) q^{18} -1.00000 q^{19} +(3.59782 - 2.65626i) q^{20} +1.69602 q^{21} +(2.02569 + 1.12216i) q^{22} +(-3.55200 - 3.55200i) q^{23} +(-3.85433 - 3.46494i) q^{24} +(-4.94092 + 0.766330i) q^{25} +(-1.03239 - 3.59681i) q^{26} +(-3.42363 + 3.42363i) q^{27} +(1.80391 + 0.415464i) q^{28} -9.15322i q^{29} +(2.02203 + 5.43033i) q^{30} -9.35880i q^{31} +(-3.25074 - 4.62954i) q^{32} +(-2.12169 + 2.12169i) q^{33} +(6.72333 - 1.92980i) q^{34} +(-1.57160 - 1.34664i) q^{35} +(0.606507 - 0.379432i) q^{36} +(-2.44492 - 2.44492i) q^{37} +(0.685298 - 1.23708i) q^{38} +4.84858 q^{39} +(0.820422 + 6.27112i) q^{40} -6.78865 q^{41} +(-1.16228 + 2.09811i) q^{42} +(6.62809 + 6.62809i) q^{43} +(-2.77640 + 1.73692i) q^{44} +(-0.797493 + 0.0614774i) q^{45} +(6.82829 - 1.95993i) q^{46} +(-5.15517 + 5.15517i) q^{47} +(6.92777 - 2.39360i) q^{48} +6.14332i q^{49} +(2.43800 - 6.63748i) q^{50} +9.06321i q^{51} +(5.15704 + 1.18773i) q^{52} +(3.11980 - 3.11980i) q^{53} +(-1.88910 - 6.58152i) q^{54} +(3.65068 - 0.281425i) q^{55} +(-1.75018 + 1.94686i) q^{56} +(1.29571 + 1.29571i) q^{57} +(11.3233 + 6.27269i) q^{58} +1.82890 q^{59} +(-8.10344 - 1.21999i) q^{60} +1.69704 q^{61} +(11.5776 + 6.41357i) q^{62} +(-0.234111 - 0.234111i) q^{63} +(7.95484 - 0.848808i) q^{64} +(-4.49291 - 3.84979i) q^{65} +(-1.17071 - 4.07868i) q^{66} +(1.38069 - 1.38069i) q^{67} +(-2.22017 + 9.63979i) q^{68} +9.20470i q^{69} +(2.74292 - 1.02135i) q^{70} -3.03831i q^{71} +(0.0537498 + 1.01032i) q^{72} +(-8.96312 + 8.96312i) q^{73} +(4.70006 - 1.34906i) q^{74} +(7.39492 + 5.40905i) q^{75} +(1.06073 + 1.69554i) q^{76} +(1.07169 + 1.07169i) q^{77} +(-3.32273 + 5.99808i) q^{78} -4.53268 q^{79} +(-8.32011 - 3.28266i) q^{80} +9.94517 q^{81} +(4.65225 - 8.39810i) q^{82} +(-1.82270 - 1.82270i) q^{83} +(-1.79902 - 2.87566i) q^{84} +(7.19622 - 8.39838i) q^{85} +(-12.7417 + 3.65726i) q^{86} +(-11.8599 + 11.8599i) q^{87} +(-0.246050 - 4.62494i) q^{88} +1.21579i q^{89} +(0.470468 - 1.02869i) q^{90} -2.44907i q^{91} +(-2.25483 + 9.79027i) q^{92} +(-12.1263 + 12.1263i) q^{93} +(-2.84453 - 9.91018i) q^{94} +(-0.171865 - 2.22945i) q^{95} +(-1.78652 + 10.2105i) q^{96} +(-2.46340 - 2.46340i) q^{97} +(-7.59978 - 4.21001i) q^{98} +0.585738 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.685298	+	1.23708i	−0.484579	+	0.874747i
$2$	−0.685298	+	1.23708i	−0.484579	+	0.874747i
$3$	−1.29571	−	1.29571i	−0.748076	−	0.748076i	0.226042	−	0.974118i	$-0.427422\pi$
$3$	−1.29571	−	1.29571i	−0.748076	−	0.748076i	−0.974118	+	0.226042i	$0.927422\pi$
$4$	−1.06073	−	1.69554i	−0.530366	−	0.847769i
$5$	0.171865	+	2.22945i	0.0768603	+	0.997042i
$5$	0.171865	+	2.22945i	0.0768603	+	0.997042i
$6$	2.49084	−	0.714946i	1.01688	−	0.291876i
$7$	−0.654476	+	0.654476i	−0.247368	+	0.247368i	−0.819890	−	0.572521i	$-0.805965\pi$
$7$	−0.654476	+	0.654476i	−0.247368	+	0.247368i	0.572521	+	0.819890i	$0.305965\pi$
$8$	2.82443	−	0.150262i	0.998588	−	0.0531255i
$9$			0.357708i			0.119236i
$10$	−2.87579	−	1.31523i	−0.909405	−	0.415912i
$11$		−	1.63748i		−	0.493718i	−0.969051	−	0.246859i	$-0.920602\pi$
$11$		−	1.63748i		−	0.493718i	0.969051	−	0.246859i	$-0.0793984\pi$
$12$	−0.822520	+	3.57132i	−0.237441	+	1.03095i
$13$	−1.87102	+	1.87102i	−0.518928	+	0.518928i	−0.917247	−	0.398319i	$-0.869594\pi$
$13$	−1.87102	+	1.87102i	−0.518928	+	0.518928i	0.398319	+	0.917247i	$0.369594\pi$
$14$	−0.361127	−	1.25815i	−0.0965154	−	0.336255i
$15$	2.66603	−	3.11140i	0.688366	−	0.803361i
$16$	−1.74969	+	3.59702i	−0.437423	+	0.899256i
$17$	−3.49740	−	3.49740i	−0.848245	−	0.848245i	0.141669	−	0.989914i	$-0.454753\pi$
$17$	−3.49740	−	3.49740i	−0.848245	−	0.848245i	−0.989914	+	0.141669i	$0.954753\pi$
$18$	−0.442513	−	0.245137i	−0.104301	−	0.0577792i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	3.59782	−	2.65626i	0.804497	−	0.593957i
$21$	1.69602			0.370101
$22$	2.02569	+	1.12216i	0.431878	+	0.239245i
$23$	−3.55200	−	3.55200i	−0.740644	−	0.740644i	0.232058	−	0.972702i	$-0.425454\pi$
$23$	−3.55200	−	3.55200i	−0.740644	−	0.740644i	−0.972702	+	0.232058i	$0.925454\pi$
$24$	−3.85433	−	3.46494i	−0.786762	−	0.707278i
$25$	−4.94092	+	0.766330i	−0.988185	+	0.153266i
$26$	−1.03239	−	3.59681i	−0.202469	−	0.705392i
$27$	−3.42363	+	3.42363i	−0.658879	+	0.658879i
$28$	1.80391	+	0.415464i	0.340907	+	0.0785154i
$29$		−	9.15322i		−	1.69971i	−0.527017	−	0.849855i	$-0.676689\pi$
$29$		−	9.15322i		−	1.69971i	0.527017	−	0.849855i	$-0.323311\pi$
$30$	2.02203	+	5.43033i	0.369170	+	0.991438i
$31$		−	9.35880i		−	1.68089i	−0.541897	−	0.840445i	$-0.682294\pi$
$31$		−	9.35880i		−	1.68089i	0.541897	−	0.840445i	$-0.317706\pi$
$32$	−3.25074	−	4.62954i	−0.574655	−	0.818395i
$33$	−2.12169	+	2.12169i	−0.369338	+	0.369338i
$34$	6.72333	−	1.92980i	1.15304	−	0.330958i
$35$	−1.57160	−	1.34664i	−0.265650	−	0.227624i
$36$	0.606507	−	0.379432i	0.101084	−	0.0632387i
$37$	−2.44492	−	2.44492i	−0.401943	−	0.401943i	0.476974	−	0.878917i	$-0.341733\pi$
$37$	−2.44492	−	2.44492i	−0.401943	−	0.401943i	−0.878917	+	0.476974i	$0.841733\pi$
$38$	0.685298	−	1.23708i	0.111170	−	0.200681i
$39$	4.84858			0.776395
$40$	0.820422	+	6.27112i	0.129720	+	0.991551i
$41$	−6.78865			−1.06021			−0.530104	−	0.847932i	$-0.677847\pi$
$41$	−6.78865			−1.06021			−0.530104	+	0.847932i	$0.677847\pi$
$42$	−1.16228	+	2.09811i	−0.179343	+	0.323745i
$43$	6.62809	+	6.62809i	1.01077	+	1.01077i	0.999941	+	0.0108330i	$0.00344833\pi$
$43$	6.62809	+	6.62809i	1.01077	+	1.01077i	0.0108330	+	0.999941i	$0.496552\pi$
$44$	−2.77640	+	1.73692i	−0.418558	+	0.261851i
$45$	−0.797493	+	0.0614774i	−0.118883	+	0.00916451i
$46$	6.82829	−	1.95993i	1.00678	−	0.288976i
$47$	−5.15517	+	5.15517i	−0.751958	+	0.751958i	−0.974844	−	0.222886i	$-0.928452\pi$
$47$	−5.15517	+	5.15517i	−0.751958	+	0.751958i	0.222886	+	0.974844i	$0.428452\pi$
$48$	6.92777	−	2.39360i	0.999938	−	0.345486i
$49$			6.14332i			0.877618i
$50$	2.43800	−	6.63748i	0.344785	−	0.938682i
$51$			9.06321i			1.26910i
$52$	5.15704	+	1.18773i	0.715152	+	0.164709i
$53$	3.11980	−	3.11980i	0.428538	−	0.428538i	−0.459592	−	0.888130i	$-0.652004\pi$
$53$	3.11980	−	3.11980i	0.428538	−	0.428538i	0.888130	+	0.459592i	$0.152004\pi$
$54$	−1.88910	−	6.58152i	−0.257074	−	0.895631i
$55$	3.65068	−	0.281425i	0.492257	−	0.0379473i
$56$	−1.75018	+	1.94686i	−0.233878	+	0.260161i
$57$	1.29571	+	1.29571i	0.171620	+	0.171620i
$58$	11.3233	+	6.27269i	1.48682	+	0.823644i
$59$	1.82890			0.238102			0.119051	−	0.992888i	$-0.462015\pi$
$59$	1.82890			0.238102			0.119051	+	0.992888i	$0.462015\pi$
$60$	−8.10344	−	1.21999i	−1.04615	−	0.157500i
$61$	1.69704			0.217284			0.108642	−	0.994081i	$-0.465350\pi$
$61$	1.69704			0.217284			0.108642	+	0.994081i	$0.465350\pi$
$62$	11.5776	+	6.41357i	1.47035	+	0.814524i
$63$	−0.234111	−	0.234111i	−0.0294952	−	0.0294952i
$64$	7.95484	−	0.848808i	0.994355	−	0.106101i
$65$	−4.49291	−	3.84979i	−0.557277	−	0.477508i
$66$	−1.17071	−	4.07868i	−0.144104	−	0.502051i
$67$	1.38069	−	1.38069i	0.168678	−	0.168678i	−0.617720	−	0.786398i	$-0.711944\pi$
$67$	1.38069	−	1.38069i	0.168678	−	0.168678i	0.786398	+	0.617720i	$0.211944\pi$
$68$	−2.22017	+	9.63979i	−0.269235	+	1.16900i
$69$			9.20470i			1.10812i
$70$	2.74292	−	1.02135i	0.327842	−	0.122074i
$71$		−	3.03831i		−	0.360581i	−0.983613	−	0.180291i	$-0.942296\pi$
$71$		−	3.03831i		−	0.360581i	0.983613	−	0.180291i	$-0.0577039\pi$
$72$	0.0537498	+	1.01032i	0.00633447	+	0.119068i
$73$	−8.96312	+	8.96312i	−1.04905	+	1.04905i	−0.0503207	+	0.998733i	$0.516024\pi$
$73$	−8.96312	+	8.96312i	−1.04905	+	1.04905i	−0.998733	+	0.0503207i	$0.983976\pi$
$74$	4.70006	−	1.34906i	0.546371	−	0.156825i
$75$	7.39492	+	5.40905i	0.853892	+	0.624583i
$76$	1.06073	+	1.69554i	0.121674	+	0.194491i
$77$	1.07169	+	1.07169i	0.122130	+	0.122130i
$78$	−3.32273	+	5.99808i	−0.376225	+	0.679149i
$79$	−4.53268			−0.509966			−0.254983	−	0.966946i	$-0.582070\pi$
$79$	−4.53268			−0.509966			−0.254983	+	0.966946i	$0.582070\pi$
$80$	−8.32011	−	3.28266i	−0.930216	−	0.367012i
$81$	9.94517			1.10502
$82$	4.65225	−	8.39810i	0.513755	−	0.927415i
$83$	−1.82270	−	1.82270i	−0.200067	−	0.200067i	0.599962	−	0.800029i	$-0.295183\pi$
$83$	−1.82270	−	1.82270i	−0.200067	−	0.200067i	−0.800029	+	0.599962i	$0.795183\pi$
$84$	−1.79902	−	2.87566i	−0.196289	−	0.313760i
$85$	7.19622	−	8.39838i	0.780539	−	0.910932i
$86$	−12.7417	+	3.65726i	−1.37397	+	0.394372i
$87$	−11.8599	+	11.8599i	−1.27151	+	1.27151i
$88$	−0.246050	−	4.62494i	−0.0262290	−	0.493020i
$89$			1.21579i			0.128874i	0.997922	+	0.0644369i	$0.0205251\pi$
$89$			1.21579i			0.128874i	−0.997922	+	0.0644369i	$0.979475\pi$
$90$	0.470468	−	1.02869i	0.0495917	−	0.108434i
$91$		−	2.44907i		−	0.256733i
$92$	−2.25483	+	9.79027i	−0.235082	+	1.02071i
$93$	−12.1263	+	12.1263i	−1.25743	+	1.25743i
$94$	−2.84453	−	9.91018i	−0.293390	−	1.02216i
$95$	−0.171865	−	2.22945i	−0.0176330	−	0.228737i
$96$	−1.78652	+	10.2105i	−0.182336	+	1.04211i
$97$	−2.46340	−	2.46340i	−0.250121	−	0.250121i	0.570899	−	0.821020i	$-0.306595\pi$
$97$	−2.46340	−	2.46340i	−0.250121	−	0.250121i	−0.821020	+	0.570899i	$0.806595\pi$
$98$	−7.59978	−	4.21001i	−0.767694	−	0.425275i
$99$	0.585738			0.0588689
$100$	6.54034	+	7.56465i	0.654034	+	0.756465i
$101$	12.1183			1.20582			0.602909	−	0.797810i	$-0.294008\pi$
$101$	12.1183			1.20582			0.602909	+	0.797810i	$0.294008\pi$
$102$	−11.2119	−	6.21101i	−1.11015	−	0.614981i
$103$	−3.04917	−	3.04917i	−0.300444	−	0.300444i	0.540744	−	0.841187i	$-0.318143\pi$
$103$	−3.04917	−	3.04917i	−0.300444	−	0.300444i	−0.841187	+	0.540744i	$0.818143\pi$
$104$	−5.00343	+	5.56571i	−0.490626	+	0.545763i
$105$	0.291486	+	3.78119i	0.0284461	+	0.369006i
$106$	1.72145	+	5.99744i	0.167202	+	0.582523i
$107$	0.0164340	−	0.0164340i	0.00158873	−	0.00158873i	−0.706312	−	0.707901i	$-0.749642\pi$
$107$	0.0164340	−	0.0164340i	0.00158873	−	0.00158873i	0.707901	+	0.706312i	$0.249642\pi$
$108$	9.43646	+	2.17334i	0.908024	+	0.209130i
$109$			4.26197i			0.408223i	0.978948	+	0.204111i	$0.0654305\pi$
$109$			4.26197i			0.408223i	−0.978948	+	0.204111i	$0.934570\pi$
$110$	−2.15366	+	4.70904i	−0.205343	+	0.448989i
$111$			6.33580i			0.601368i
$112$	−1.20903	−	3.49929i	−0.114243	−	0.330652i
$113$	−5.98031	+	5.98031i	−0.562580	+	0.562580i	−0.930040	−	0.367459i	$-0.880228\pi$
$113$	−5.98031	+	5.98031i	−0.562580	+	0.562580i	0.367459	+	0.930040i	$0.380228\pi$
$114$	−2.49084	+	0.714946i	−0.233288	+	0.0669609i
$115$	7.30856	−	8.52949i	0.681527	−	0.795379i
$116$	−15.5196	+	9.70912i	−1.44096	+	0.901469i
$117$	−0.669278	−	0.669278i	−0.0618748	−	0.0618748i
$118$	−1.25334	+	2.26249i	−0.115379	+	0.208279i
$119$	4.57793			0.419658
$120$	7.06250	−	9.18855i	0.644715	−	0.838796i
$121$	8.31867			0.756243
$122$	−1.16298	+	2.09938i	−0.105291	+	0.190069i
$123$	8.79609	+	8.79609i	0.793117	+	0.793117i
$124$	−15.8682	+	9.92718i	−1.42501	+	0.891487i
$125$	−2.55767	−	10.8839i	−0.228765	−	0.973482i
$126$	0.450050	−	0.129178i	0.0400936	−	0.0115081i
$127$	13.5081	−	13.5081i	1.19865	−	1.19865i	0.224080	−	0.974571i	$-0.428062\pi$
$127$	13.5081	−	13.5081i	1.19865	−	1.19865i	0.974571	−	0.224080i	$-0.0719378\pi$
$128$	−4.40140	+	10.4225i	−0.389032	+	0.921224i
$129$		−	17.1761i		−	1.51227i
$130$	7.84148	−	2.91984i	0.687744	−	0.256087i
$131$			1.29219i			0.112899i	0.998405	+	0.0564496i	$0.0179780\pi$
$131$			1.29219i			0.112899i	−0.998405	+	0.0564496i	$0.982022\pi$
$132$	5.84794	+	1.34686i	0.508998	+	0.117229i
$133$	0.654476	−	0.654476i	0.0567502	−	0.0567502i
$134$	0.761838	+	2.65420i	0.0658128	+	0.229288i
$135$	−8.22123	−	7.04443i	−0.707571	−	0.606288i
$136$	−10.4037	−	9.35266i	−0.892111	−	0.801984i
$137$	−8.13730	−	8.13730i	−0.695217	−	0.695217i	0.268158	−	0.963375i	$-0.413585\pi$
$137$	−8.13730	−	8.13730i	−0.695217	−	0.695217i	−0.963375	+	0.268158i	$0.913585\pi$
$138$	−11.3869	−	6.30797i	−0.969321	−	0.536970i
$139$	−20.7065			−1.75630			−0.878152	−	0.478382i	$-0.841223\pi$
$139$	−20.7065			−1.75630			−0.878152	+	0.478382i	$0.841223\pi$
$140$	−0.616229	+	4.09314i	−0.0520809	+	0.345933i
$141$	13.3592			1.12504
$142$	3.75864	+	2.08215i	0.315418	+	0.174730i
$143$	3.06375	+	3.06375i	0.256204	+	0.256204i
$144$	−1.28668	−	0.625879i	−0.107224	−	0.0521566i
$145$	20.4067	−	1.57312i	1.69468	−	0.130640i
$146$	−4.94568	−	17.2305i	−0.409308	−	1.42601i
$147$	7.95994	−	7.95994i	0.656525	−	0.656525i
$148$	−1.55205	+	6.73886i	−0.127578	+	0.553931i
$149$			13.5977i			1.11396i	0.830524	+	0.556982i	$0.188041\pi$
$149$			13.5977i			1.11396i	−0.830524	+	0.556982i	$0.811959\pi$
$150$	−11.7592	+	5.44130i	−0.960131	+	0.444280i
$151$			2.61864i			0.213102i	0.994307	+	0.106551i	$0.0339808\pi$
$151$			2.61864i			0.213102i	−0.994307	+	0.106551i	$0.966019\pi$
$152$	−2.82443	+	0.150262i	−0.229092	+	0.0121878i
$153$	1.25105	−	1.25105i	0.101141	−	0.101141i
$154$	−2.06019	+	0.591337i	−0.166015	+	0.0476513i
$155$	20.8650	−	1.60845i	1.67592	−	0.129194i
$156$	−5.14305	−	8.22095i	−0.411774	−	0.658203i
$157$	7.99318	+	7.99318i	0.637925	+	0.637925i	0.950043	−	0.312118i	$-0.101039\pi$
$157$	7.99318	+	7.99318i	0.637925	+	0.637925i	−0.312118	+	0.950043i	$0.601039\pi$
$158$	3.10624	−	5.60728i	0.247119	−	0.446091i
$159$	−8.08470			−0.641158
$160$	9.76266	−	8.04303i	0.771806	−	0.635858i
$161$	4.64940			0.366424
$162$	−6.81541	+	12.3030i	−0.535469	+	0.966612i
$163$	2.90148	+	2.90148i	0.227261	+	0.227261i	0.811548	−	0.584286i	$-0.198625\pi$
$163$	2.90148	+	2.90148i	0.227261	+	0.227261i	−0.584286	+	0.811548i	$0.698625\pi$
$164$	7.20094	+	11.5104i	0.562299	+	0.898812i
$165$	−5.09485	−	4.36556i	−0.396633	−	0.339858i
$166$	3.50392	−	1.00573i	0.271957	−	0.0780599i
$167$	4.89240	−	4.89240i	0.378585	−	0.378585i	−0.492006	−	0.870592i	$-0.663736\pi$
$167$	4.89240	−	4.89240i	0.378585	−	0.378585i	0.870592	+	0.492006i	$0.163736\pi$
$168$	4.79028	−	0.254846i	0.369578	−	0.0196618i
$169$			5.99857i			0.461428i
$170$	5.45791	+	14.6577i	0.418603	+	1.12419i
$171$		−	0.357708i		−	0.0273546i
$172$	4.20754	−	18.2688i	0.320822	−	1.39298i
$173$	12.5885	−	12.5885i	0.957083	−	0.957083i	−0.0420334	−	0.999116i	$-0.513384\pi$
$173$	12.5885	−	12.5885i	0.957083	−	0.957083i	0.999116	+	0.0420334i	$0.0133836\pi$
$174$	−6.54406	−	22.7992i	−0.496104	−	1.72840i
$175$	2.73217	−	3.73526i	0.206533	−	0.282359i
$176$	5.89004	+	2.86508i	0.443978	+	0.215964i
$177$	−2.36971	−	2.36971i	−0.178119	−	0.178119i
$178$	−1.50403	−	0.833181i	−0.112732	−	0.0624496i
$179$	−12.7824			−0.955403			−0.477701	−	0.878522i	$-0.658530\pi$
$179$	−12.7824			−0.955403			−0.477701	+	0.878522i	$0.658530\pi$
$180$	0.950164	+	1.28697i	0.0708210	+	0.0959249i
$181$	25.1119			1.86655			0.933275	−	0.359163i	$-0.116938\pi$
$181$	25.1119			1.86655			0.933275	+	0.359163i	$0.116938\pi$
$182$	3.02970	+	1.67835i	0.224576	+	0.124407i
$183$	−2.19887	−	2.19887i	−0.162545	−	0.162545i
$184$	−10.5661	−	9.49866i	−0.778945	−	0.700251i
$185$	5.03064	−	5.87104i	0.369860	−	0.431647i
$186$	−6.69104	−	23.3112i	−0.490611	−	1.70926i
$187$	−5.72691	+	5.72691i	−0.418793	+	0.418793i
$188$	14.2090	+	3.27253i	1.03630	+	0.238673i
$189$		−	4.48137i		−	0.325972i
$190$	2.87579	+	1.31523i	0.208632	+	0.0954168i
$191$		−	3.11968i		−	0.225732i	−0.993610	−	0.112866i	$-0.963997\pi$
$191$		−	3.11968i		−	0.225732i	0.993610	−	0.112866i	$-0.0360031\pi$
$192$	−11.4069	−	9.20733i	−0.823225	−	0.664482i
$193$	8.14880	−	8.14880i	0.586563	−	0.586563i	−0.350136	−	0.936699i	$-0.613865\pi$
$193$	8.14880	−	8.14880i	0.586563	−	0.586563i	0.936699	+	0.350136i	$0.113865\pi$
$194$	4.73559	−	1.35926i	0.339996	−	0.0975891i
$195$	0.833301	+	10.8097i	0.0596740	+	0.774098i
$196$	10.4162	−	6.51642i	0.744017	−	0.465459i
$197$	−18.2776	−	18.2776i	−1.30223	−	1.30223i	−0.926887	−	0.375341i	$-0.877526\pi$
$197$	−18.2776	−	18.2776i	−1.30223	−	1.30223i	−0.375341	−	0.926887i	$-0.622474\pi$
$198$	−0.401405	+	0.724604i	−0.0285266	+	0.0514954i
$199$	−10.0788			−0.714468			−0.357234	−	0.934015i	$-0.616280\pi$
$199$	−10.0788			−0.714468			−0.357234	+	0.934015i	$0.616280\pi$
$200$	−13.8402	+	2.90688i	−0.978647	+	0.205547i
$201$	−3.57793			−0.252368
$202$	−8.30466	+	14.9913i	−0.584314	+	1.05479i
$203$	5.99056	+	5.99056i	0.420455	+	0.420455i
$204$	15.3670	−	9.61364i	1.07591	−	0.673090i
$205$	−1.16673	−	15.1350i	−0.0814880	−	1.05707i
$206$	5.86166	−	1.68248i	0.408401	−	0.117224i
$207$	1.27058	−	1.27058i	0.0883113	−	0.0883113i
$208$	−3.45639	−	10.0038i	−0.239658	−	0.693640i
$209$			1.63748i			0.113267i
$210$	−4.87739	−	2.23065i	−0.336572	−	0.153930i
$211$			19.9042i			1.37026i	0.728420	+	0.685130i	$0.240255\pi$
$211$			19.9042i			1.37026i	−0.728420	+	0.685130i	$0.759745\pi$
$212$	−8.59902	−	1.98047i	−0.590583	−	0.136019i
$213$	−3.93676	+	3.93676i	−0.269742	+	0.269742i
$214$	0.00906797	+	0.0315923i	0.000619873	+	0.00215961i
$215$	−13.6379	+	15.9162i	−0.930096	+	1.08547i
$216$	−9.15538	+	10.1843i	−0.622945	+	0.692951i
$217$	6.12511	+	6.12511i	0.415799	+	0.415799i
$218$	−5.27240	−	2.92072i	−0.357092	−	0.197816i
$219$	23.2271			1.56954
$220$	−4.34956	−	5.89134i	−0.293247	−	0.397194i
$221$	13.0874			0.880355
$222$	−7.83789	−	4.34191i	−0.526045	−	0.291410i
$223$	−17.3893	−	17.3893i	−1.16447	−	1.16447i	−0.983486	−	0.180987i	$-0.942071\pi$
$223$	−17.3893	−	17.3893i	−1.16447	−	1.16447i	−0.180987	−	0.983486i	$-0.557929\pi$
$224$	5.15745	+	0.902392i	0.344597	+	0.0602936i
$225$	−0.274122	−	1.76741i	−0.0182748	−	0.117827i
$226$	−3.29982	−	11.4964i	−0.219501	−	0.764730i
$227$	−9.81619	+	9.81619i	−0.651524	+	0.651524i	−0.953360	−	0.301836i	$-0.902400\pi$
$227$	−9.81619	+	9.81619i	−0.651524	+	0.651524i	0.301836	+	0.953360i	$0.402400\pi$
$228$	0.822520	−	3.57132i	0.0544727	−	0.236516i
$229$			28.3436i			1.87300i	0.350673	+	0.936498i	$0.385953\pi$
$229$			28.3436i			1.87300i	−0.350673	+	0.936498i	$0.614047\pi$
$230$	5.54311	+	14.8865i	0.365502	+	0.981588i
$231$		−	2.77718i		−	0.182725i
$232$	−1.37538	−	25.8527i	−0.0902980	−	1.69731i
$233$	6.45054	−	6.45054i	0.422589	−	0.422589i	−0.463505	−	0.886094i	$-0.653409\pi$
$233$	6.45054	−	6.45054i	0.422589	−	0.422589i	0.886094	+	0.463505i	$0.153409\pi$
$234$	1.28661	−	0.369295i	0.0841081	−	0.0241416i
$235$	−12.3792	−	10.6072i	−0.807530	−	0.691938i
$236$	−1.93997	−	3.10096i	−0.126281	−	0.201856i
$237$	5.87302	+	5.87302i	0.381493	+	0.381493i
$238$	−3.13725	+	5.66326i	−0.203358	+	0.367095i
$239$	−16.4109			−1.06153			−0.530767	−	0.847518i	$-0.678096\pi$
$239$	−16.4109			−1.06153			−0.530767	+	0.847518i	$0.678096\pi$
$240$	6.52705	+	15.0338i	0.421319	+	0.970426i
$241$	−26.5011			−1.70709			−0.853543	−	0.521022i	$-0.825551\pi$
$241$	−26.5011			−1.70709			−0.853543	+	0.521022i	$0.825551\pi$
$242$	−5.70077	+	10.2909i	−0.366460	+	0.661522i
$243$	−2.61511	−	2.61511i	−0.167760	−	0.167760i
$244$	−1.80011	−	2.87740i	−0.115240	−	0.184207i
$245$	−13.6963	+	1.05582i	−0.875022	+	0.0674540i
$246$	−16.9094	+	4.85352i	−1.07810	+	0.309449i
$247$	1.87102	−	1.87102i	0.119050	−	0.119050i
$248$	−1.40627	−	26.4333i	−0.0892982	−	1.67852i
$249$			4.72337i			0.299331i
$250$	15.2170	+	4.29465i	0.962405	+	0.271617i
$251$		−	18.9320i		−	1.19497i	−0.801878	−	0.597487i	$-0.796166\pi$
$251$		−	18.9320i		−	1.19497i	0.801878	−	0.597487i	$-0.203834\pi$
$252$	−0.148615	+	0.645273i	−0.00936185	+	0.0406484i
$253$	−5.81632	+	5.81632i	−0.365669	+	0.365669i
$254$	7.45352	+	25.9677i	0.467676	+	1.62936i
$255$	−20.2060	+	1.55765i	−1.26535	+	0.0975437i
$256$	−9.87715	−	12.5874i	−0.617322	−	0.786711i
$257$	−4.14453	−	4.14453i	−0.258529	−	0.258529i	0.565927	−	0.824455i	$-0.308518\pi$
$257$	−4.14453	−	4.14453i	−0.258529	−	0.258529i	−0.824455	+	0.565927i	$0.808518\pi$
$258$	21.2482	+	11.7708i	1.32286	+	0.732816i
$259$	3.20028			0.198856
$260$	−1.76168	+	11.7015i	−0.109255	+	0.725696i
$261$	3.27418			0.202666
$262$	−1.59854	−	0.885535i	−0.0987582	−	0.0547085i
$263$	0.570667	+	0.570667i	0.0351889	+	0.0351889i	0.724482	−	0.689293i	$-0.242079\pi$
$263$	0.570667	+	0.570667i	0.0351889	+	0.0351889i	−0.689293	+	0.724482i	$0.742079\pi$
$264$	−5.67375	+	6.31137i	−0.349195	+	0.388438i
$265$	7.49164	+	6.41927i	0.460208	+	0.394333i
$266$	0.361127	+	1.25815i	0.0221421	+	0.0771421i
$267$	1.57531	−	1.57531i	0.0964075	−	0.0964075i
$268$	−3.80555	−	0.876467i	−0.232461	−	0.0535388i
$269$		−	15.2319i		−	0.928705i	−0.885650	−	0.464353i	$-0.846287\pi$
$269$		−	15.2319i		−	0.928705i	0.885650	−	0.464353i	$-0.153713\pi$
$270$	14.3485	−	5.34279i	0.873223	−	0.325152i
$271$			6.90043i			0.419171i	0.977790	+	0.209586i	$0.0672115\pi$
$271$			6.90043i			0.419171i	−0.977790	+	0.209586i	$0.932788\pi$
$272$	18.6996	−	6.46086i	1.13383	−	0.391747i
$273$	−3.17328	+	3.17328i	−0.192056	+	0.192056i
$274$	15.6430	−	4.49001i	0.945027	−	0.271252i
$275$	1.25485	+	8.09065i	0.0756701	+	0.487884i
$276$	15.6069	−	9.76372i	0.939426	−	0.587707i
$277$	8.71366	+	8.71366i	0.523553	+	0.523553i	0.918643	−	0.395090i	$-0.129286\pi$
$277$	8.71366	+	8.71366i	0.523553	+	0.523553i	−0.395090	+	0.918643i	$0.629286\pi$
$278$	14.1901	−	25.6156i	0.851068	−	1.53632i
$279$	3.34772			0.200422
$280$	−4.64124	−	3.56735i	−0.277367	−	0.213190i
$281$	−2.46107			−0.146815			−0.0734076	−	0.997302i	$-0.523387\pi$
$281$	−2.46107			−0.146815			−0.0734076	+	0.997302i	$0.523387\pi$
$282$	−9.15501	+	16.5263i	−0.545173	+	0.984130i
$283$	18.9668	+	18.9668i	1.12746	+	1.12746i	0.990589	+	0.136871i	$0.0437046\pi$
$283$	18.9668	+	18.9668i	1.12746	+	1.12746i	0.136871	+	0.990589i	$0.456295\pi$
$284$	−5.15157	+	3.22284i	−0.305690	+	0.191240i
$285$	−2.66603	+	3.11140i	−0.157922	+	0.184304i
$286$	−5.88969	+	1.69052i	−0.348264	+	0.0999626i
$287$	4.44300	−	4.44300i	0.262262	−	0.262262i
$288$	1.65602	−	1.16282i	0.0975821	−	0.0685196i
$289$			7.46367i			0.439039i
$290$	−12.0386	+	26.3227i	−0.706930	+	1.54572i
$291$			6.38369i			0.374219i
$292$	24.7048	+	5.68983i	1.44574	+	0.332972i
$293$	−16.7936	+	16.7936i	−0.981092	+	0.981092i	−0.999825	−	0.0187322i	$-0.994037\pi$
$293$	−16.7936	+	16.7936i	−0.981092	+	0.981092i	0.0187322	+	0.999825i	$0.494037\pi$
$294$	4.39215	+	15.3020i	0.256155	+	0.892432i
$295$	0.314323	+	4.07744i	0.0183006	+	0.237398i
$296$	−7.27290	−	6.53814i	−0.422729	−	0.380022i
$297$	5.60612	+	5.60612i	0.325300	+	0.325300i
$298$	−16.8214	−	9.31846i	−0.974438	−	0.539804i
$299$	13.2917			0.768681
$300$	1.32721	−	18.2759i	0.0766263	−	1.05516i
$301$	−8.67585			−0.500067
$302$	−3.23947	−	1.79455i	−0.186411	−	0.103265i
$303$	−15.7018	−	15.7018i	−0.902044	−	0.902044i
$304$	1.74969	−	3.59702i	0.100352	−	0.206303i
$305$	0.291662	+	3.78348i	0.0167005	+	0.216642i
$306$	0.690305	+	2.40499i	0.0394621	+	0.137484i
$307$	15.8886	−	15.8886i	0.906811	−	0.906811i	−0.0892025	−	0.996014i	$-0.528432\pi$
$307$	15.8886	−	15.8886i	0.906811	−	0.906811i	0.996014	+	0.0892025i	$0.0284318\pi$
$308$	0.680313	−	2.95386i	0.0387644	−	0.168312i
$309$			7.90166i			0.449510i
$310$	−12.3090	+	26.9139i	−0.699103	+	1.52861i
$311$			23.8846i			1.35437i	0.735813	+	0.677185i	$0.236800\pi$
$311$			23.8846i			1.35437i	−0.735813	+	0.677185i	$0.763200\pi$
$312$	13.6945	−	0.728556i	0.775298	−	0.0412464i
$313$	2.63964	−	2.63964i	0.149201	−	0.149201i	−0.628560	−	0.777761i	$-0.716355\pi$
$313$	2.63964	−	2.63964i	0.149201	−	0.149201i	0.777761	+	0.628560i	$0.216355\pi$
$314$	−15.3659	+	4.41049i	−0.867148	+	0.248898i
$315$	0.481704	−	0.562175i	0.0271409	−	0.0316750i
$316$	4.80796	+	7.68532i	0.270469	+	0.432333i
$317$	−2.93804	−	2.93804i	−0.165017	−	0.165017i	0.619768	−	0.784785i	$-0.287227\pi$
$317$	−2.93804	−	2.93804i	−0.165017	−	0.165017i	−0.784785	+	0.619768i	$0.787227\pi$
$318$	5.54043	−	10.0014i	0.310692	−	0.560852i
$319$	−14.9882			−0.839177
$320$	3.25954	+	17.5891i	0.182214	+	0.983259i
$321$	−0.0425872			−0.00237699
$322$	−3.18622	+	5.75167i	−0.177561	+	0.320528i
$323$	3.49740	+	3.49740i	0.194601	+	0.194601i
$324$	−10.5492	−	16.8624i	−0.586065	−	0.936800i
$325$	7.81075	−	10.6784i	0.433263	−	0.592330i
$326$	−5.57774	+	1.60098i	−0.308922	+	0.0886702i
$327$	5.52226	−	5.52226i	0.305382	−	0.305382i
$328$	−19.1741	+	1.02007i	−1.05871	+	0.0563241i
$329$		−	6.74786i		−	0.372022i
$330$	8.89203	−	3.31102i	0.489490	−	0.182266i
$331$		−	7.68766i		−	0.422552i	−0.977426	−	0.211276i	$-0.932238\pi$
$331$		−	7.68766i		−	0.422552i	0.977426	−	0.211276i	$-0.0677619\pi$
$332$	−1.15706	+	5.02385i	−0.0635018	+	0.275720i
$333$	0.874568	−	0.874568i	0.0479260	−	0.0479260i
$334$	2.69953	+	9.40504i	0.147712	+	0.514621i
$335$	3.31547	+	2.84089i	0.181143	+	0.155214i
$336$	−2.96751	+	6.10061i	−0.161891	+	0.332815i
$337$	−9.05913	−	9.05913i	−0.493482	−	0.493482i	0.415919	−	0.909402i	$-0.363460\pi$
$337$	−9.05913	−	9.05913i	−0.493482	−	0.493482i	−0.909402	+	0.415919i	$0.863460\pi$
$338$	−7.42071	−	4.11081i	−0.403633	−	0.223599i
$339$	15.4974			0.841706
$340$	−21.8730	−	3.29302i	−1.18623	−	0.178589i
$341$	−15.3248			−0.829885
$342$	0.442513	+	0.245137i	0.0239284	+	0.0132555i
$343$	−8.60198	−	8.60198i	−0.464463	−	0.464463i
$344$	19.7165	+	17.7246i	1.06304	+	0.955649i
$345$	−20.5214	+	1.58197i	−1.10484	+	0.0851701i
$346$	6.94608	+	24.1998i	0.373423	+	1.30099i
$347$	19.7570	−	19.7570i	1.06061	−	1.06061i	0.0625723	−	0.998040i	$-0.480070\pi$
$347$	19.7570	−	19.7570i	1.06061	−	1.06061i	0.998040	−	0.0625723i	$-0.0199304\pi$
$348$	32.6890	+	7.52871i	1.75232	+	0.403581i
$349$		−	3.40999i		−	0.182533i	−0.995827	−	0.0912664i	$-0.970909\pi$
$349$		−	3.40999i		−	0.182533i	0.995827	−	0.0912664i	$-0.0290915\pi$
$350$	2.74846	+	5.93968i	0.146911	+	0.317489i
$351$		−	12.8114i		−	0.683821i
$352$	−7.58077	+	5.32301i	−0.404056	+	0.283717i
$353$	15.0965	−	15.0965i	0.803504	−	0.803504i	−0.180137	−	0.983642i	$-0.557654\pi$
$353$	15.0965	−	15.0965i	0.803504	−	0.803504i	0.983642	+	0.180137i	$0.0576542\pi$
$354$	4.55549	−	1.30756i	0.242121	−	0.0694962i
$355$	6.77378	−	0.522180i	0.359515	−	0.0277144i
$356$	2.06142	−	1.28963i	0.109255	−	0.0683503i
$357$	−5.93165	−	5.93165i	−0.313936	−	0.313936i
$358$	8.75977	−	15.8129i	0.462968	−	0.835736i
$359$	0.0640071			0.00337816			0.00168908	−	0.999999i	$-0.499462\pi$
$359$	0.0640071			0.00337816			0.00168908	+	0.999999i	$0.499462\pi$
$360$	−2.24323	+	0.293471i	−0.118228	+	0.0154673i
$361$	1.00000			0.0526316
$362$	−17.2091	+	31.0654i	−0.904491	+	1.63276i
$363$	−10.7786	−	10.7786i	−0.565727	−	0.565727i
$364$	−4.15250	+	2.59781i	−0.217650	+	0.136162i
$365$	−21.5233	−	18.4424i	−1.12658	−	0.965320i
$366$	4.22706	−	1.21330i	0.220952	−	0.0634200i
$367$	11.4201	−	11.4201i	0.596124	−	0.596124i	−0.343155	−	0.939279i	$-0.611496\pi$
$367$	11.4201	−	11.4201i	0.596124	−	0.596124i	0.939279	+	0.343155i	$0.111496\pi$
$368$	18.9915	−	6.56172i	0.990003	−	0.342053i
$369$		−	2.42835i		−	0.126415i
$370$	3.81545	+	10.2467i	0.198356	+	0.532702i
$371$			4.08367i			0.212014i
$372$	33.4232	+	7.69781i	1.73291	+	0.399113i
$373$	−10.7753	+	10.7753i	−0.557926	+	0.557926i	−0.928716	−	0.370791i	$-0.879087\pi$
$373$	−10.7753	+	10.7753i	−0.557926	+	0.557926i	0.370791	+	0.928716i	$0.379087\pi$
$374$	−3.16000	−	11.0093i	−0.163400	−	0.569277i
$375$	−10.7883	+	17.4163i	−0.557105	+	0.899372i
$376$	−13.7858	+	15.3350i	−0.710948	+	0.790845i
$377$	17.1259	+	17.1259i	0.882026	+	0.882026i
$378$	5.54381	+	3.07107i	0.285143	+	0.157959i
$379$	30.2324			1.55294			0.776468	−	0.630157i	$-0.217009\pi$
$379$	30.2324			1.55294			0.776468	+	0.630157i	$0.217009\pi$
$380$	−3.59782	+	2.65626i	−0.184564	+	0.136263i
$381$	−35.0051			−1.79336
$382$	3.85929	+	2.13791i	0.197459	+	0.109385i
$383$	14.2884	+	14.2884i	0.730101	+	0.730101i	0.970640	−	0.240539i	$-0.0773241\pi$
$383$	14.2884	+	14.2884i	0.730101	+	0.730101i	−0.240539	+	0.970640i	$0.577324\pi$
$384$	19.2074	−	7.80153i	0.980172	−	0.398120i
$385$	−2.20509	+	2.57346i	−0.112382	+	0.131156i
$386$	4.49636	+	15.6651i	0.228858	+	0.797331i
$387$	−2.37092	+	2.37092i	−0.120521	+	0.120521i
$388$	−1.56378	+	6.78980i	−0.0793889	+	0.344700i
$389$		−	3.17048i		−	0.160750i	−0.996765	−	0.0803749i	$-0.974388\pi$
$389$		−	3.17048i		−	0.160750i	0.996765	−	0.0803749i	$-0.0256118\pi$
$390$	−13.9435	−	6.37700i	−0.706057	−	0.322912i
$391$			24.8456i			1.25649i
$392$	0.923106	+	17.3514i	0.0466239	+	0.876378i
$393$	1.67430	−	1.67430i	0.0844571	−	0.0844571i
$394$	35.1365	−	10.0853i	1.77015	−	0.508088i
$395$	−0.779008	−	10.1054i	−0.0391962	−	0.508457i
$396$	−0.621311	−	0.993140i	−0.0312221	−	0.0499072i
$397$	−19.4312	−	19.4312i	−0.975226	−	0.975226i	0.0244741	−	0.999700i	$-0.492209\pi$
$397$	−19.4312	−	19.4312i	−0.975226	−	0.975226i	−0.999700	+	0.0244741i	$0.992209\pi$
$398$	6.90699	−	12.4683i	0.346216	−	0.624979i
$399$	−1.69602			−0.0849070
$400$	5.88860	−	19.1135i	0.294430	−	0.955673i
$401$	−14.2573			−0.711977			−0.355988	−	0.934490i	$-0.615856\pi$
$401$	−14.2573			−0.711977			−0.355988	+	0.934490i	$0.615856\pi$
$402$	2.45195	−	4.42618i	0.122292	−	0.220758i
$403$	17.5105	+	17.5105i	0.872260	+	0.872260i
$404$	−12.8543	−	20.5471i	−0.639525	−	1.02225i
$405$	1.70923	+	22.1723i	0.0849321	+	1.10175i
$406$	−11.5161	+	3.30548i	−0.571535	+	0.164048i
$407$	−4.00350	+	4.00350i	−0.198446	+	0.198446i
$408$	1.36185	+	25.5984i	0.0674218	+	1.26731i
$409$			29.5580i			1.46155i	0.682620	+	0.730774i	$0.260841\pi$
$409$			29.5580i			1.46155i	−0.682620	+	0.730774i	$0.739159\pi$
$410$	19.5227	+	8.92863i	0.964159	+	0.440954i
$411$			21.0871i			1.04015i
$412$	−1.93563	+	8.40434i	−0.0953616	+	0.414052i
$413$	−1.19697	+	1.19697i	−0.0588990	+	0.0588990i
$414$	0.701082	+	2.44253i	0.0344563	+	0.120044i
$415$	3.75037	−	4.37688i	0.184098	−	0.214853i
$416$	14.7442	+	2.57977i	0.722893	+	0.126483i
$417$	26.8296	+	26.8296i	1.31385	+	1.31385i
$418$	−2.02569	−	1.12216i	−0.0990796	−	0.0548866i
$419$	−11.9344			−0.583033			−0.291516	−	0.956566i	$-0.594160\pi$
$419$	−11.9344			−0.583033			−0.291516	+	0.956566i	$0.594160\pi$
$420$	6.10196	−	4.50505i	0.297745	−	0.219824i
$421$	−2.22566			−0.108472			−0.0542361	−	0.998528i	$-0.517272\pi$
$421$	−2.22566			−0.108472			−0.0542361	+	0.998528i	$0.517272\pi$
$422$	−24.6231	−	13.6403i	−1.19863	−	0.664000i
$423$	−1.84404	−	1.84404i	−0.0896604	−	0.0896604i
$424$	8.34289	−	9.28046i	0.405167	−	0.450699i
$425$	19.9606	+	14.6002i	0.968230	+	0.708216i
$426$	−2.17223	−	7.56794i	−0.105245	−	0.366668i
$427$	−1.11067	+	1.11067i	−0.0537493	+	0.0537493i
$428$	−0.0452965	−	0.0104324i	−0.00218949	−	0.000504268i
$429$		−	7.93944i		−	0.383320i
$430$	−10.3435	−	27.7785i	−0.498810	−	1.33960i
$431$		−	31.4295i		−	1.51390i	−0.653471	−	0.756952i	$-0.726688\pi$
$431$		−	31.4295i		−	1.51390i	0.653471	−	0.756952i	$-0.273312\pi$
$432$	−6.32458	−	18.3052i	−0.304291	−	0.880709i
$433$	−10.0203	+	10.0203i	−0.481545	+	0.481545i	−0.905625	−	0.424080i	$-0.860598\pi$
$433$	−10.0203	+	10.0203i	−0.481545	+	0.481545i	0.424080	+	0.905625i	$0.360598\pi$
$434$	−11.7748	+	3.37972i	−0.565207	+	0.162232i
$435$	−28.4793	−	24.4028i	−1.36548	−	1.17002i
$436$	7.22633	−	4.52081i	0.346078	−	0.216507i
$437$	3.55200	+	3.55200i	0.169915	+	0.169915i
$438$	−15.9175	+	28.7338i	−0.760568	+	1.37295i
$439$	28.1034			1.34130			0.670650	−	0.741773i	$-0.266015\pi$
$439$	28.1034			1.34130			0.670650	+	0.741773i	$0.266015\pi$
$440$	10.2688	−	1.34342i	0.489546	−	0.0640451i
$441$	−2.19751			−0.104644
$442$	−8.96879	+	16.1902i	−0.426602	+	0.770089i
$443$	−13.9516	−	13.9516i	−0.662858	−	0.662858i	0.293195	−	0.956053i	$-0.405282\pi$
$443$	−13.9516	−	13.9516i	−0.662858	−	0.662858i	−0.956053	+	0.293195i	$0.905282\pi$
$444$	10.7426	−	6.72059i	0.509821	−	0.318945i
$445$	−2.71056	+	0.208952i	−0.128493	+	0.00990529i
$446$	33.4288	−	9.59508i	1.58290	−	0.454340i
$447$	17.6186	−	17.6186i	0.833330	−	0.833330i
$448$	−4.65073	+	5.76177i	−0.219726	+	0.272218i
$449$		−	16.7718i		−	0.791512i	−0.918356	−	0.395756i	$-0.870483\pi$
$449$		−	16.7718i		−	0.791512i	0.918356	−	0.395756i	$-0.129517\pi$
$450$	2.37428	+	0.872090i	0.111925	+	0.0411107i
$451$			11.1162i			0.523444i
$452$	16.4833	+	3.79633i	0.775311	+	0.178564i
$453$	3.39299	−	3.39299i	0.159417	−	0.159417i
$454$	−5.41639	−	18.8704i	−0.254204	−	0.885633i
$455$	5.46010	−	0.420910i	0.255973	−	0.0197326i
$456$	3.85433	+	3.46494i	0.180496	+	0.162261i
$457$	−11.3747	−	11.3747i	−0.532085	−	0.532085i	0.389107	−	0.921192i	$-0.372783\pi$
$457$	−11.3747	−	11.3747i	−0.532085	−	0.532085i	−0.921192	+	0.389107i	$0.872783\pi$
$458$	−35.0633	−	19.4238i	−1.63840	−	0.907615i
$459$	23.9477			1.11778
$460$	−22.2145	−	3.34443i	−1.03576	−	0.155935i
$461$	18.2572			0.850323			0.425162	−	0.905117i	$-0.360217\pi$
$461$	18.2572			0.850323			0.425162	+	0.905117i	$0.360217\pi$
$462$	3.43560	+	1.90320i	0.159839	+	0.0885449i
$463$	−20.3096	−	20.3096i	−0.943869	−	0.943869i	0.0546376	−	0.998506i	$-0.482600\pi$
$463$	−20.3096	−	20.3096i	−0.943869	−	0.943869i	−0.998506	+	0.0546376i	$0.982600\pi$
$464$	32.9243	+	16.0153i	1.52847	+	0.743493i
$465$	−29.1190	−	24.9508i	−1.35036	−	1.15707i
$466$	3.55929	+	12.4004i	0.164881	+	0.574436i
$467$	−30.0050	+	30.0050i	−1.38847	+	1.38847i	−0.559916	+	0.828549i	$0.689167\pi$
$467$	−30.0050	+	30.0050i	−1.38847	+	1.38847i	−0.828549	+	0.559916i	$0.810833\pi$
$468$	−0.424861	+	1.84471i	−0.0196392	+	0.0852718i
$469$			1.80725i			0.0834512i
$470$	21.6054	−	8.04495i	0.996583	−	0.371086i
$471$		−	20.7136i		−	0.954433i
$472$	5.16560	−	0.274813i	0.237766	−	0.0126493i
$473$	10.8533	−	10.8533i	0.499037	−	0.499037i
$474$	−11.2902	+	3.24062i	−0.518574	+	0.148847i
$475$	4.94092	−	0.766330i	0.226705	−	0.0351616i
$476$	−4.85596	−	7.76205i	−0.222573	−	0.355773i
$477$	1.11598	+	1.11598i	0.0510971	+	0.0510971i
$478$	11.2464	−	20.3016i	0.514397	−	0.928574i
$479$	37.9059			1.73196			0.865982	−	0.500075i	$-0.166694\pi$
$479$	37.9059			1.73196			0.865982	+	0.500075i	$0.166694\pi$
$480$	−23.0709	−	2.22814i	−1.05304	−	0.101700i
$481$	9.14900			0.417158
$482$	18.1612	−	32.7840i	0.827218	−	1.49327i
$483$	−6.02425	−	6.02425i	−0.274113	−	0.274113i
$484$	−8.82389	−	14.1046i	−0.401086	−	0.641119i
$485$	5.06867	−	5.91541i	0.230156	−	0.268605i
$486$	5.02723	−	1.44297i	0.228040	−	0.0654545i
$487$	−4.05745	+	4.05745i	−0.183861	+	0.183861i	−0.793036	−	0.609175i	$-0.791501\pi$
$487$	−4.05745	+	4.05745i	−0.183861	+	0.183861i	0.609175	+	0.793036i	$0.291501\pi$
$488$	4.79319	−	0.255001i	0.216977	−	0.0115433i
$489$		−	7.51893i		−	0.340018i
$490$	8.07988	−	17.6669i	0.365012	−	0.798110i
$491$		−	6.72981i		−	0.303712i	−0.988403	−	0.151856i	$-0.951475\pi$
$491$		−	6.72981i		−	0.303712i	0.988403	−	0.151856i	$-0.0485250\pi$
$492$	5.58380	−	24.2444i	0.251737	−	1.09302i
$493$	−32.0125	+	32.0125i	−1.44177	+	1.44177i
$494$	1.03239	+	3.59681i	0.0464496	+	0.161828i
$495$	0.100668	+	1.30588i	0.00452468	+	0.0586947i
$496$	33.6638	+	16.3750i	1.51155	+	0.735261i
$497$	1.98850	+	1.98850i	0.0891965	+	0.0891965i
$498$	−5.84318	−	3.23691i	−0.261839	−	0.145050i
$499$	−39.2944			−1.75906			−0.879529	−	0.475846i	$-0.842142\pi$
$499$	−39.2944			−1.75906			−0.879529	+	0.475846i	$0.842142\pi$
$500$	−15.7410	+	15.8815i	−0.703958	+	0.710241i
$501$	−12.6782			−0.566421
$502$	23.4203	+	12.9740i	1.04530	+	0.579060i
$503$	−5.48698	−	5.48698i	−0.244653	−	0.244653i	0.574119	−	0.818772i	$-0.305345\pi$
$503$	−5.48698	−	5.48698i	−0.244653	−	0.244653i	−0.818772	+	0.574119i	$0.805345\pi$
$504$	−0.696409	−	0.626053i	−0.0310205	−	0.0278866i
$505$	2.08271	+	27.0172i	0.0926796	+	1.20225i
$506$	−3.20934	−	11.1812i	−0.142672	−	0.497063i
$507$	7.77238	−	7.77238i	0.345184	−	0.345184i
$508$	−37.2320	−	8.57502i	−1.65190	−	0.380455i
$509$		−	11.1400i		−	0.493773i	−0.969044	−	0.246887i	$-0.920592\pi$
$509$		−	11.1400i		−	0.493773i	0.969044	−	0.246887i	$-0.0794075\pi$
$510$	11.9202	−	26.0639i	0.527836	−	1.15413i
$511$		−	11.7323i		−	0.519006i
$512$	22.3404	−	3.59271i	0.987314	−	0.158777i
$513$	3.42363	−	3.42363i	0.151157	−	0.151157i
$514$	7.96735	−	2.28687i	0.351425	−	0.100870i
$515$	6.27394	−	7.32203i	0.276463	−	0.322647i
$516$	−29.1227	+	18.2193i	−1.28206	+	0.802058i
$517$	8.44146	+	8.44146i	0.371255	+	0.371255i
$518$	−2.19315	+	3.95901i	−0.0963614	+	0.173949i
$519$	−32.6219			−1.43194
$520$	−13.2684	−	10.1984i	−0.581858	−	0.447228i
$521$	−22.2876			−0.976436			−0.488218	−	0.872722i	$-0.662353\pi$
$521$	−22.2876			−0.976436			−0.488218	+	0.872722i	$0.662353\pi$
$522$	−2.24379	+	4.05042i	−0.0982079	+	0.177282i
$523$	19.7520	+	19.7520i	0.863694	+	0.863694i	0.991765	−	0.128071i	$-0.0408786\pi$
$523$	19.7520	+	19.7520i	0.863694	+	0.863694i	−0.128071	+	0.991765i	$0.540879\pi$
$524$	2.19096	−	1.37067i	0.0957123	−	0.0598779i
$525$	−8.37989	+	1.29971i	−0.365728	+	0.0567239i
$526$	−1.09704	+	0.314884i	−0.0478331	+	0.0137296i
$527$	−32.7315	+	32.7315i	−1.42581	+	1.42581i
$528$	−3.91945	−	11.3441i	−0.170572	−	0.493687i
$529$			2.23343i			0.0971058i
$530$	−13.0752	+	4.86864i	−0.567949	+	0.211480i
$531$			0.654211i			0.0283903i
$532$	−1.80391	−	0.415464i	−0.0782095	−	0.0180127i
$533$	12.7017	−	12.7017i	0.550171	−	0.550171i
$534$	0.869227	+	3.02834i	0.0376151	+	0.131049i
$535$	0.0394632	+	0.0338144i	0.00170614	+	0.00146192i
$536$	3.69219	−	4.10712i	0.159479	−	0.177401i
$537$	16.5623	+	16.5623i	0.714714	+	0.714714i
$538$	18.8431	+	10.4384i	0.812382	+	0.450031i
$539$	10.0595			0.433295
$540$	−3.22356	+	21.4117i	−0.138720	+	0.921411i
$541$	20.4533			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$541$	20.4533			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$542$	−8.53639	−	4.72886i	−0.366669	−	0.203122i
$543$	−32.5376	−	32.5376i	−1.39632	−	1.39632i
$544$	−4.82223	+	27.5605i	−0.206751	+	1.18165i
$545$	−9.50186	+	0.732483i	−0.407015	+	0.0313761i
$546$	−1.75096	−	6.10024i	−0.0749340	−	0.261066i
$547$	−27.6440	+	27.6440i	−1.18197	+	1.18197i	−0.202742	+	0.979232i	$0.564985\pi$
$547$	−27.6440	+	27.6440i	−1.18197	+	1.18197i	−0.979232	+	0.202742i	$0.935015\pi$
$548$	−5.16560	+	22.4286i	−0.220663	+	0.958102i
$549$			0.607046i			0.0259081i
$550$	−10.8687	−	3.99216i	−0.463444	−	0.170226i
$551$			9.15322i			0.389940i
$552$	1.38311	+	25.9981i	0.0588692	+	1.10655i
$553$	2.96653	−	2.96653i	0.126150	−	0.126150i
$554$	−16.7509	+	4.80803i	−0.711679	+	0.204274i
$555$	−14.1254	+	1.08890i	−0.599589	+	0.0462213i
$556$	21.9641	+	35.1087i	0.931484	+	1.48894i
$557$	−12.9480	−	12.9480i	−0.548624	−	0.548624i	0.377419	−	0.926043i	$-0.376812\pi$
$557$	−12.9480	−	12.9480i	−0.548624	−	0.548624i	−0.926043	+	0.377419i	$0.876812\pi$
$558$	−2.29418	+	4.14139i	−0.0971205	+	0.175319i
$559$	−24.8026			−1.04904
$560$	7.59372	−	3.29689i	0.320893	−	0.139319i
$561$	14.8408			0.626579
$562$	1.68657	−	3.04454i	0.0711435	−	0.128426i
$563$	8.85456	+	8.85456i	0.373175	+	0.373175i	0.868632	−	0.495457i	$-0.164999\pi$
$563$	8.85456	+	8.85456i	0.373175	+	0.373175i	−0.495457	+	0.868632i	$0.664999\pi$
$564$	−14.1705	−	22.6510i	−0.596685	−	0.953777i
$565$	−14.3606	−	12.3050i	−0.604156	−	0.517676i
$566$	−36.4614	+	10.4655i	−1.53259	+	0.439899i
$567$	−6.50887	+	6.50887i	−0.273347	+	0.273347i
$568$	−0.456542	−	8.58151i	−0.0191561	−	0.360072i
$569$		−	44.3868i		−	1.86079i	−0.366559	−	0.930395i	$-0.619464\pi$
$569$		−	44.3868i		−	1.86079i	0.366559	−	0.930395i	$-0.380536\pi$
$570$	−2.02203	−	5.43033i	−0.0846934	−	0.227451i
$571$			6.20459i			0.259654i	0.991537	+	0.129827i	$0.0414422\pi$
$571$			6.20459i			0.259654i	−0.991537	+	0.129827i	$0.958558\pi$
$572$	1.94488	−	8.44452i	0.0813197	−	0.353083i
$573$	−4.04219	+	4.04219i	−0.168865	+	0.168865i
$574$	2.45157	+	8.54113i	0.102326	+	0.356500i
$575$	20.2722	+	14.8282i	0.845408	+	0.618377i
$576$	0.303625	+	2.84551i	0.0126510	+	0.118563i
$577$	−21.7220	−	21.7220i	−0.904300	−	0.904300i	0.0915047	−	0.995805i	$-0.470832\pi$
$577$	−21.7220	−	21.7220i	−0.904300	−	0.904300i	−0.995805	+	0.0915047i	$0.970832\pi$
$578$	−9.23315	−	5.11484i	−0.384049	−	0.212749i
$579$	−21.1169			−0.877588
$580$	−24.3133	−	32.9316i	−1.00955	−	1.36741i
$581$	2.38582			0.0989807
$582$	−7.89713	−	4.37473i	−0.327347	−	0.181338i
$583$	−5.10860	−	5.10860i	−0.211577	−	0.211577i
$584$	−23.9689	+	26.6625i	−0.991841	+	1.10330i
$585$	1.37710	−	1.60715i	0.0569360	−	0.0664475i
$586$	−9.26639	−	32.2836i	−0.382791	−	1.33362i
$587$	0.887101	−	0.887101i	0.0366146	−	0.0366146i	−0.688562	−	0.725177i	$-0.741758\pi$
$587$	0.887101	−	0.887101i	0.0366146	−	0.0366146i	0.725177	+	0.688562i	$0.241758\pi$
$588$	−21.9397	−	5.05301i	−0.904780	−	0.208383i
$589$			9.35880i			0.385623i
$590$	−5.25953	−	2.40542i	−0.216531	−	0.0990296i
$591$			47.3649i			1.94833i
$592$	13.0723	−	4.51658i	0.537268	−	0.185630i
$593$	22.8092	−	22.8092i	0.936661	−	0.936661i	−0.0614496	−	0.998110i	$-0.519572\pi$
$593$	22.8092	−	22.8092i	0.936661	−	0.936661i	0.998110	+	0.0614496i	$0.0195724\pi$
$594$	−10.7771	+	3.09335i	−0.442189	+	0.126922i
$595$	0.786786	+	10.2063i	0.0322551	+	0.418417i
$596$	23.0554	−	14.4235i	0.944384	−	0.590809i
$597$	13.0592	+	13.0592i	0.534477	+	0.534477i
$598$	−9.10880	+	16.4429i	−0.372487	+	0.672402i
$599$	40.9165			1.67180			0.835902	−	0.548879i	$-0.184945\pi$
$599$	40.9165			1.67180			0.835902	+	0.548879i	$0.184945\pi$
$600$	21.6992	+	14.1663i	0.885868	+	0.578338i
$601$	−0.0826848			−0.00337278			−0.00168639	−	0.999999i	$-0.500537\pi$
$601$	−0.0826848			−0.00337278			−0.00168639	+	0.999999i	$0.500537\pi$
$602$	5.94554	−	10.7327i	0.242322	−	0.437433i
$603$	0.493883	+	0.493883i	0.0201125	+	0.0201125i
$604$	4.44001	−	2.77768i	0.180661	−	0.113022i
$605$	1.42969	+	18.5461i	0.0581251	+	0.754006i
$606$	30.1848	−	8.66395i	1.22617	−	0.351949i
$607$	33.0423	−	33.0423i	1.34114	−	1.34114i	0.446222	−	0.894922i	$-0.352769\pi$
$607$	33.0423	−	33.0423i	1.34114	−	1.34114i	0.894922	−	0.446222i	$-0.147231\pi$
$608$	3.25074	+	4.62954i	0.131835	+	0.187753i
$609$		−	15.5240i		−	0.629064i
$610$	−4.88034	−	2.23200i	−0.197599	−	0.0903712i
$611$		−	19.2908i		−	0.780424i
$612$	−3.44823	−	0.794172i	−0.139386	−	0.0321025i
$613$	7.02354	−	7.02354i	0.283678	−	0.283678i	−0.550896	−	0.834574i	$-0.685714\pi$
$613$	7.02354	−	7.02354i	0.283678	−	0.283678i	0.834574	+	0.550896i	$0.185714\pi$
$614$	8.76704	+	30.5439i	0.353809	+	1.23265i
$615$	−18.0987	+	21.1222i	−0.729811	+	0.851730i
$616$	3.18794	+	2.86588i	0.128446	+	0.115469i
$617$	26.0772	+	26.0772i	1.04983	+	1.04983i	0.998692	+	0.0511388i	$0.0162851\pi$
$617$	26.0772	+	26.0772i	1.04983	+	1.04983i	0.0511388	+	0.998692i	$0.483715\pi$
$618$	−9.77498	−	5.41499i	−0.393207	−	0.217823i
$619$	−43.1018			−1.73241			−0.866204	−	0.499690i	$-0.833447\pi$
$619$	−43.1018			−1.73241			−0.866204	+	0.499690i	$0.833447\pi$
$620$	−24.8594	−	33.6713i	−0.998377	−	1.35227i
$621$	24.3215			0.975988
$622$	−29.5471	−	16.3681i	−1.18473	−	0.656300i
$623$	−0.795707	−	0.795707i	−0.0318793	−	0.0318793i
$624$	−8.48353	+	17.4405i	−0.339613	+	0.698177i
$625$	23.8255	−	7.57276i	0.953019	−	0.302910i
$626$	1.45650	+	5.07438i	0.0582136	+	0.202813i
$627$	2.12169	−	2.12169i	0.0847320	−	0.0847320i
$628$	5.07411	−	22.0313i	0.202479	−	0.879146i
$629$			17.1018i			0.681892i
$630$	0.365344	+	0.981164i	0.0145557	+	0.0390905i
$631$		−	7.03776i		−	0.280169i	−0.990140	−	0.140084i	$-0.955263\pi$
$631$		−	7.03776i		−	0.280169i	0.990140	−	0.140084i	$-0.0447374\pi$
$632$	−12.8022	+	0.681088i	−0.509246	+	0.0270922i
$633$	25.7900	−	25.7900i	1.02506	−	1.02506i
$634$	5.64803	−	1.62116i	0.224312	−	0.0643844i
$635$	32.4373	+	27.7941i	1.28723	+	1.10298i
$636$	8.57570	+	13.7079i	0.340049	+	0.543554i
$637$	−11.4943	−	11.4943i	−0.455420	−	0.455420i
$638$	10.2714	−	18.5416i	0.406647	−	0.734068i
$639$	1.08683			0.0429943
$640$	−23.9928	−	8.02145i	−0.948400	−	0.317076i
$641$	−16.1047			−0.636096			−0.318048	−	0.948075i	$-0.603027\pi$
$641$	−16.1047			−0.636096			−0.318048	+	0.948075i	$0.603027\pi$
$642$	0.0291850	−	0.0526838i	0.00115184	−	0.00207926i
$643$	−7.13901	−	7.13901i	−0.281535	−	0.281535i	0.552186	−	0.833721i	$-0.313794\pi$
$643$	−7.13901	−	7.13901i	−0.281535	−	0.281535i	−0.833721	+	0.552186i	$0.813794\pi$
$644$	−4.93177	−	7.88323i	−0.194339	−	0.310643i
$645$	38.2933	−	2.95197i	1.50780	−	0.116234i
$646$	−6.72333	+	1.92980i	−0.264526	+	0.0759271i
$647$	−11.7671	+	11.7671i	−0.462612	+	0.462612i	−0.899511	−	0.436899i	$-0.856077\pi$
$647$	−11.7671	+	11.7671i	−0.462612	+	0.462612i	0.436899	+	0.899511i	$0.356077\pi$
$648$	28.0895	−	1.49438i	1.10346	−	0.0587047i
$649$		−	2.99478i		−	0.117555i
$650$	7.85732	+	16.9804i	0.308190	+	0.666026i
$651$		−	15.8727i		−	0.622099i
$652$	1.84187	−	7.99726i	0.0721333	−	0.313197i
$653$	8.55603	−	8.55603i	0.334823	−	0.334823i	−0.519591	−	0.854415i	$-0.673916\pi$
$653$	8.55603	−	8.55603i	0.334823	−	0.334823i	0.854415	+	0.519591i	$0.173916\pi$
$654$	3.04708	+	10.6159i	0.119150	+	0.415113i
$655$	−2.88088	+	0.222082i	−0.112565	+	0.00867746i
$656$	11.8781	−	24.4189i	0.463760	−	0.953399i
$657$	−3.20618	−	3.20618i	−0.125085	−	0.125085i
$658$	8.34764	+	4.62430i	0.325425	+	0.180274i
$659$	31.2472			1.21722			0.608608	−	0.793471i	$-0.291728\pi$
$659$	31.2472			1.21722			0.608608	+	0.793471i	$0.291728\pi$
$660$	−1.99770	+	13.2692i	−0.0777604	+	0.516503i
$661$	−38.6574			−1.50360			−0.751799	−	0.659392i	$-0.770814\pi$
$661$	−38.6574			−1.50360			−0.751799	+	0.659392i	$0.770814\pi$
$662$	9.51025	+	5.26834i	0.369626	+	0.204760i
$663$	−16.9575	−	16.9575i	−0.658573	−	0.658573i
$664$	−5.42198	−	4.87421i	−0.210413	−	0.189156i
$665$	1.57160	+	1.34664i	0.0609442	+	0.0522205i
$666$	0.482570	+	1.68125i	0.0186992	+	0.0651471i
$667$	−32.5122	+	32.5122i	−1.25888	+	1.25888i
$668$	−13.4848	−	3.10572i	−0.521741	−	0.120164i
$669$			45.0628i			1.74223i
$670$	−5.78649	+	2.15465i	−0.223552	+	0.0832412i
$671$		−	2.77887i		−	0.107277i
$672$	−5.51331	−	7.85178i	−0.212681	−	0.302889i
$673$	35.1192	−	35.1192i	1.35375	−	1.35375i	0.472317	−	0.881429i	$-0.343418\pi$
$673$	35.1192	−	35.1192i	1.35375	−	1.35375i	0.881429	−	0.472317i	$-0.156582\pi$
$674$	17.4151	−	4.99866i	0.670804	−	0.192541i
$675$	14.2923	−	19.5395i	0.550110	−	0.752078i
$676$	10.1708	−	6.36288i	0.391184	−	0.244726i
$677$	−21.3652	−	21.3652i	−0.821133	−	0.821133i	0.165138	−	0.986270i	$-0.447193\pi$
$677$	−21.3652	−	21.3652i	−0.821133	−	0.821133i	−0.986270	+	0.165138i	$0.947193\pi$
$678$	−10.6204	+	19.1716i	−0.407873	+	0.736280i
$679$	3.22447			0.123744
$680$	19.0633	−	24.8020i	0.731043	−	0.951112i
$681$	25.4378			0.974779
$682$	10.5021	−	18.9580i	0.402145	−	0.725940i
$683$	−9.82459	−	9.82459i	−0.375927	−	0.375927i	0.493703	−	0.869631i	$-0.335643\pi$
$683$	−9.82459	−	9.82459i	−0.375927	−	0.375927i	−0.869631	+	0.493703i	$0.835643\pi$
$684$	−0.606507	+	0.379432i	−0.0231904	+	0.0145080i
$685$	16.7432	−	19.5403i	0.639726	−	0.746595i
$686$	16.5363	−	4.74641i	0.631358	−	0.181219i
$687$	36.7249	−	36.7249i	1.40114	−	1.40114i
$688$	−35.4385	+	12.2443i	−1.35108	+	0.466808i
$689$			11.6744i			0.444760i
$690$	12.1063	−	26.4708i	0.460879	−	1.00773i
$691$		−	3.08668i		−	0.117423i	−0.998275	−	0.0587114i	$-0.981301\pi$
$691$		−	3.08668i		−	0.117423i	0.998275	−	0.0587114i	$-0.0186992\pi$
$692$	−34.6972	−	7.99122i	−1.31899	−	0.303780i
$693$	−0.383351	+	0.383351i	−0.0145623	+	0.0145623i
$694$	10.9016	+	37.9805i	0.413818	+	1.44172i
$695$	−3.55872	−	46.1642i	−0.134990	−	1.75111i
$696$	−31.7153	+	35.2795i	−1.20217	+	1.33727i
$697$	23.7426	+	23.7426i	0.899317	+	0.899317i
$698$	4.21843	+	2.33686i	0.159670	+	0.0884516i
$699$	−16.7160			−0.632257
$700$	−9.23137	−	0.670387i	−0.348913	−	0.0253382i
$701$	30.1439			1.13852			0.569261	−	0.822157i	$-0.307230\pi$
$701$	30.1439			1.13852			0.569261	+	0.822157i	$0.307230\pi$
$702$	15.8487	+	8.77961i	0.598170	+	0.331365i
$703$	2.44492	+	2.44492i	0.0922120	+	0.0922120i
$704$	−1.38990	−	13.0259i	−0.0523839	−	0.490931i
$705$	2.29597	+	29.7836i	0.0864713	+	1.12172i
$706$	8.32995	+	29.0211i	0.313502	+	1.09222i
$707$	−7.93114	+	7.93114i	−0.298281	+	0.298281i
$708$	−1.50431	+	6.53157i	−0.0565353	+	0.245471i
$709$		−	44.5478i		−	1.67303i	−0.547945	−	0.836514i	$-0.684590\pi$
$709$		−	44.5478i		−	1.67303i	0.547945	−	0.836514i	$-0.315410\pi$
$710$	−3.99608	+	8.73755i	−0.149970	+	0.327914i
$711$		−	1.62137i		−	0.0608063i
$712$	0.182687	+	3.43393i	0.00684649	+	0.128692i
$713$	−33.2425	+	33.2425i	−1.24494	+	1.24494i
$714$	11.4029	−	3.27297i	0.426742	−	0.122488i
$715$	−6.30394	+	7.35704i	−0.235754	+	0.275138i
$716$	13.5587	+	21.6731i	0.506713	+	0.809961i
$717$	21.2637	+	21.2637i	0.794108	+	0.794108i
$718$	−0.0438639	+	0.0791818i	−0.00163699	+	0.00295504i
$719$	38.5729			1.43853			0.719263	−	0.694737i	$-0.244479\pi$
$719$	38.5729			1.43853			0.719263	+	0.694737i	$0.244479\pi$
$720$	1.17423	−	2.97617i	0.0437610	−	0.110915i
$721$	3.99122			0.148641
$722$	−0.685298	+	1.23708i	−0.0255042	+	0.0460393i
$723$	34.3376	+	34.3376i	1.27703	+	1.27703i
$724$	−26.6370	−	42.5781i	−0.989955	−	1.58240i
$725$	7.01438	+	45.2254i	0.260508	+	1.67963i
$726$	20.7205	−	5.94741i	0.769008	−	0.220729i
$727$	2.12216	−	2.12216i	0.0787065	−	0.0787065i	−0.666658	−	0.745364i	$-0.732276\pi$
$727$	2.12216	−	2.12216i	0.0787065	−	0.0787065i	0.745364	+	0.666658i	$0.232276\pi$
$728$	−0.368002	−	6.91724i	−0.0136391	−	0.256370i
$729$		−	23.0587i		−	0.854025i
$730$	37.5646	−	13.9875i	1.39033	−	0.517700i
$731$		−	46.3622i		−	1.71477i
$732$	−1.39585	+	6.06068i	−0.0515923	+	0.224009i
$733$	33.2119	−	33.2119i	1.22671	−	1.22671i	0.261507	−	0.965202i	$-0.415781\pi$
$733$	33.2119	−	33.2119i	1.22671	−	1.22671i	0.965202	−	0.261507i	$-0.0842194\pi$
$734$	6.30139	+	21.9537i	0.232589	+	0.810327i
$735$	19.1144	+	16.3783i	0.705043	+	0.604122i
$736$	−4.89751	+	27.9908i	−0.180525	+	1.03175i
$737$	−2.26084	−	2.26084i	−0.0832792	−	0.0832792i
$738$	3.00406	+	1.66415i	0.110581	+	0.0612580i
$739$	43.5911			1.60352			0.801762	−	0.597644i	$-0.203896\pi$
$739$	43.5911			1.60352			0.801762	+	0.597644i	$0.203896\pi$
$740$	−15.2907	−	2.30205i	−0.562098	−	0.0846249i
$741$	−4.84858			−0.178117
$742$	−5.05183	−	2.79853i	−0.185458	−	0.102737i
$743$	−17.4504	−	17.4504i	−0.640193	−	0.640193i	0.310410	−	0.950603i	$-0.399534\pi$
$743$	−17.4504	−	17.4504i	−0.640193	−	0.640193i	−0.950603	+	0.310410i	$0.899534\pi$
$744$	−32.4277	+	36.0719i	−1.18886	+	1.32246i
$745$	−30.3154	+	2.33696i	−1.11067	+	0.0856197i
$746$	−5.94563	−	20.7143i	−0.217685	−	0.758403i
$747$	0.651994	−	0.651994i	0.0238552	−	0.0238552i
$748$	15.7849	+	3.63547i	0.577154	+	0.132926i
$749$			0.0215113i			0.000786005i
$750$	−14.1521	−	25.2813i	−0.516762	−	0.923143i
$751$		−	5.38732i		−	0.196586i	−0.995158	−	0.0982930i	$-0.968662\pi$
$751$		−	5.38732i		−	0.196586i	0.995158	−	0.0982930i	$-0.0313382\pi$
$752$	−9.52329	−	27.5632i	−0.347279	−	1.00513i
$753$	−24.5303	+	24.5303i	−0.893932	+	0.893932i
$754$	−32.9224	+	9.44973i	−1.19896	+	0.344139i
$755$	−5.83814	+	0.450053i	−0.212472	+	0.0163791i
$756$	−7.59833	+	4.75353i	−0.276349	+	0.172884i
$757$	−12.2817	−	12.2817i	−0.446386	−	0.446386i	0.447765	−	0.894151i	$-0.352220\pi$
$757$	−12.2817	−	12.2817i	−0.446386	−	0.446386i	−0.894151	+	0.447765i	$0.852220\pi$
$758$	−20.7182	+	37.3999i	−0.752520	+	1.35843i
$759$	15.0725			0.547096
$760$	−0.820422	−	6.27112i	−0.0297598	−	0.227477i
$761$	6.67732			0.242053			0.121026	−	0.992649i	$-0.461381\pi$
$761$	6.67732			0.242053			0.121026	+	0.992649i	$0.461381\pi$
$762$	23.9889	−	43.3041i	0.869027	−	1.56874i
$763$	−2.78935	−	2.78935i	−0.100981	−	0.100981i
$764$	−5.28953	+	3.30915i	−0.191369	+	0.119721i
$765$	3.00417	+	2.57414i	0.108616	+	0.0930683i
$766$	−27.4676	+	7.88405i	−0.992446	+	0.284862i
$767$	−3.42190	+	3.42190i	−0.123558	+	0.123558i
$768$	−3.51166	+	29.1074i	−0.126716	+	1.05032i
$769$			33.5804i			1.21094i	0.795869	+	0.605469i	$0.207015\pi$
$769$			33.5804i			1.21094i	−0.795869	+	0.605469i	$0.792985\pi$
$770$	−1.67243	−	4.49147i	−0.0602703	−	0.161861i
$771$			10.7402i

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.685298 + 1.23708i) q^{2} +(-1.29571 - 1.29571i) q^{3} +(-1.06073 - 1.69554i) q^{4} +(0.171865 + 2.22945i) q^{5} +(2.49084 - 0.714946i) q^{6} +(-0.654476 + 0.654476i) q^{7} +(2.82443 - 0.150262i) q^{8} +0.357708i q^{9} +O(q^{10})\)	\(q+(-0.685298 + 1.23708i) q^{2} +(-1.29571 - 1.29571i) q^{3} +(-1.06073 - 1.69554i) q^{4} +(0.171865 + 2.22945i) q^{5} +(2.49084 - 0.714946i) q^{6} +(-0.654476 + 0.654476i) q^{7} +(2.82443 - 0.150262i) q^{8} +0.357708i q^{9} +(-2.87579 - 1.31523i) q^{10} -1.63748i q^{11} +(-0.822520 + 3.57132i) q^{12} +(-1.87102 + 1.87102i) q^{13} +(-0.361127 - 1.25815i) q^{14} +(2.66603 - 3.11140i) q^{15} +(-1.74969 + 3.59702i) q^{16} +(-3.49740 - 3.49740i) q^{17} +(-0.442513 - 0.245137i) q^{18} -1.00000 q^{19} +(3.59782 - 2.65626i) q^{20} +1.69602 q^{21} +(2.02569 + 1.12216i) q^{22} +(-3.55200 - 3.55200i) q^{23} +(-3.85433 - 3.46494i) q^{24} +(-4.94092 + 0.766330i) q^{25} +(-1.03239 - 3.59681i) q^{26} +(-3.42363 + 3.42363i) q^{27} +(1.80391 + 0.415464i) q^{28} -9.15322i q^{29} +(2.02203 + 5.43033i) q^{30} -9.35880i q^{31} +(-3.25074 - 4.62954i) q^{32} +(-2.12169 + 2.12169i) q^{33} +(6.72333 - 1.92980i) q^{34} +(-1.57160 - 1.34664i) q^{35} +(0.606507 - 0.379432i) q^{36} +(-2.44492 - 2.44492i) q^{37} +(0.685298 - 1.23708i) q^{38} +4.84858 q^{39} +(0.820422 + 6.27112i) q^{40} -6.78865 q^{41} +(-1.16228 + 2.09811i) q^{42} +(6.62809 + 6.62809i) q^{43} +(-2.77640 + 1.73692i) q^{44} +(-0.797493 + 0.0614774i) q^{45} +(6.82829 - 1.95993i) q^{46} +(-5.15517 + 5.15517i) q^{47} +(6.92777 - 2.39360i) q^{48} +6.14332i q^{49} +(2.43800 - 6.63748i) q^{50} +9.06321i q^{51} +(5.15704 + 1.18773i) q^{52} +(3.11980 - 3.11980i) q^{53} +(-1.88910 - 6.58152i) q^{54} +(3.65068 - 0.281425i) q^{55} +(-1.75018 + 1.94686i) q^{56} +(1.29571 + 1.29571i) q^{57} +(11.3233 + 6.27269i) q^{58} +1.82890 q^{59} +(-8.10344 - 1.21999i) q^{60} +1.69704 q^{61} +(11.5776 + 6.41357i) q^{62} +(-0.234111 - 0.234111i) q^{63} +(7.95484 - 0.848808i) q^{64} +(-4.49291 - 3.84979i) q^{65} +(-1.17071 - 4.07868i) q^{66} +(1.38069 - 1.38069i) q^{67} +(-2.22017 + 9.63979i) q^{68} +9.20470i q^{69} +(2.74292 - 1.02135i) q^{70} -3.03831i q^{71} +(0.0537498 + 1.01032i) q^{72} +(-8.96312 + 8.96312i) q^{73} +(4.70006 - 1.34906i) q^{74} +(7.39492 + 5.40905i) q^{75} +(1.06073 + 1.69554i) q^{76} +(1.07169 + 1.07169i) q^{77} +(-3.32273 + 5.99808i) q^{78} -4.53268 q^{79} +(-8.32011 - 3.28266i) q^{80} +9.94517 q^{81} +(4.65225 - 8.39810i) q^{82} +(-1.82270 - 1.82270i) q^{83} +(-1.79902 - 2.87566i) q^{84} +(7.19622 - 8.39838i) q^{85} +(-12.7417 + 3.65726i) q^{86} +(-11.8599 + 11.8599i) q^{87} +(-0.246050 - 4.62494i) q^{88} +1.21579i q^{89} +(0.470468 - 1.02869i) q^{90} -2.44907i q^{91} +(-2.25483 + 9.79027i) q^{92} +(-12.1263 + 12.1263i) q^{93} +(-2.84453 - 9.91018i) q^{94} +(-0.171865 - 2.22945i) q^{95} +(-1.78652 + 10.2105i) q^{96} +(-2.46340 - 2.46340i) q^{97} +(-7.59978 - 4.21001i) q^{98} +0.585738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

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