LMFDB - Embedded newform 380.2.k.d.343.8

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			343.8
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.8

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.974118	−	0.226042i	$-0.927422\pi$
$3$	−1.29571	+	1.29571i	−0.748076	+	0.748076i	0.226042	+	0.974118i	$0.427422\pi$
$4$	−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	0.572521	−	0.819890i	$-0.305965\pi$
$7$	−0.654476	−	0.654476i	−0.247368	−	0.247368i	−0.819890	+	0.572521i	$0.805965\pi$
$8$	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	$0.0793984\pi$
$11$			1.63748i			0.493718i	−0.969051	+	0.246859i	$0.920602\pi$
$12$	−0.822520	−	3.57132i	−0.237441	−	1.03095i
$13$	−1.87102	−	1.87102i	−0.518928	−	0.518928i	0.398319	−	0.917247i	$-0.369594\pi$
$13$	−1.87102	−	1.87102i	−0.518928	−	0.518928i	−0.917247	+	0.398319i	$0.869594\pi$
$14$	−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	−0.989914	−	0.141669i	$-0.954753\pi$
$17$	−3.49740	+	3.49740i	−0.848245	+	0.848245i	0.141669	+	0.989914i	$0.454753\pi$
$18$	−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	−0.972702	−	0.232058i	$-0.925454\pi$
$23$	−3.55200	+	3.55200i	−0.740644	+	0.740644i	0.232058	+	0.972702i	$0.425454\pi$
$24$	−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	$0.323311\pi$
$29$			9.15322i			1.69971i	−0.527017	+	0.849855i	$0.676689\pi$
$30$	2.02203	−	5.43033i	0.369170	−	0.991438i
$31$			9.35880i			1.68089i	0.541897	+	0.840445i	$0.317706\pi$
$31$			9.35880i			1.68089i	−0.541897	+	0.840445i	$0.682294\pi$
$32$	−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	−0.878917	−	0.476974i	$-0.841733\pi$
$37$	−2.44492	+	2.44492i	−0.401943	+	0.401943i	0.476974	+	0.878917i	$0.341733\pi$
$38$	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	0.0108330	−	0.999941i	$-0.496552\pi$
$43$	6.62809	−	6.62809i	1.01077	−	1.01077i	0.999941	−	0.0108330i	$-0.00344833\pi$
$44$	−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	0.222886	−	0.974844i	$-0.428452\pi$
$47$	−5.15517	−	5.15517i	−0.751958	−	0.751958i	−0.974844	+	0.222886i	$0.928452\pi$
$48$	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	0.888130	−	0.459592i	$-0.152004\pi$
$53$	3.11980	+	3.11980i	0.428538	+	0.428538i	−0.459592	+	0.888130i	$0.652004\pi$
$54$	−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	0.786398	−	0.617720i	$-0.211944\pi$
$67$	1.38069	+	1.38069i	0.168678	+	0.168678i	−0.617720	+	0.786398i	$0.711944\pi$
$68$	−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	$0.0577039\pi$
$71$			3.03831i			0.360581i	−0.983613	+	0.180291i	$0.942296\pi$
$72$	0.0537498	−	1.01032i	0.00633447	−	0.119068i
$73$	−8.96312	−	8.96312i	−1.04905	−	1.04905i	−0.998733	−	0.0503207i	$-0.983976\pi$
$73$	−8.96312	−	8.96312i	−1.04905	−	1.04905i	−0.0503207	−	0.998733i	$-0.516024\pi$
$74$	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	−0.800029	−	0.599962i	$-0.795183\pi$
$83$	−1.82270	+	1.82270i	−0.200067	+	0.200067i	0.599962	+	0.800029i	$0.295183\pi$
$84$	−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	$-0.979475\pi$
$89$		−	1.21579i		−	0.128874i	0.997922	−	0.0644369i	$-0.0205251\pi$
$90$	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	−0.821020	−	0.570899i	$-0.806595\pi$
$97$	−2.46340	+	2.46340i	−0.250121	+	0.250121i	0.570899	+	0.821020i	$0.306595\pi$
$98$	−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	−0.841187	−	0.540744i	$-0.818143\pi$
$103$	−3.04917	+	3.04917i	−0.300444	+	0.300444i	0.540744	+	0.841187i	$0.318143\pi$
$104$	−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	0.707901	−	0.706312i	$-0.249642\pi$
$107$	0.0164340	+	0.0164340i	0.00158873	+	0.00158873i	−0.706312	+	0.707901i	$0.749642\pi$
$108$	9.43646	−	2.17334i	0.908024	−	0.209130i
$109$		−	4.26197i		−	0.408223i	−0.978948	−	0.204111i	$-0.934570\pi$
$109$		−	4.26197i		−	0.408223i	0.978948	−	0.204111i	$-0.0654305\pi$
$110$	−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	0.367459	−	0.930040i	$-0.380228\pi$
$113$	−5.98031	−	5.98031i	−0.562580	−	0.562580i	−0.930040	+	0.367459i	$0.880228\pi$
$114$	−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	0.974571	+	0.224080i	$0.0719378\pi$
$127$	13.5081	+	13.5081i	1.19865	+	1.19865i	0.224080	+	0.974571i	$0.428062\pi$
$128$	−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	$-0.982022\pi$
$131$		−	1.29219i		−	0.112899i	0.998405	−	0.0564496i	$-0.0179780\pi$
$132$	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	−0.963375	−	0.268158i	$-0.913585\pi$
$137$	−8.13730	+	8.13730i	−0.695217	+	0.695217i	0.268158	+	0.963375i	$0.413585\pi$
$138$	−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	$-0.811959\pi$
$149$		−	13.5977i		−	1.11396i	0.830524	−	0.556982i	$-0.188041\pi$
$150$	−11.7592	−	5.44130i	−0.960131	−	0.444280i
$151$		−	2.61864i		−	0.213102i	−0.994307	−	0.106551i	$-0.966019\pi$
$151$		−	2.61864i		−	0.213102i	0.994307	−	0.106551i	$-0.0339808\pi$
$152$	−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	−0.312118	−	0.950043i	$-0.601039\pi$
$157$	7.99318	−	7.99318i	0.637925	−	0.637925i	0.950043	+	0.312118i	$0.101039\pi$
$158$	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	−0.584286	−	0.811548i	$-0.698625\pi$
$163$	2.90148	−	2.90148i	0.227261	−	0.227261i	0.811548	+	0.584286i	$0.198625\pi$
$164$	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	0.870592	−	0.492006i	$-0.163736\pi$
$167$	4.89240	+	4.89240i	0.378585	+	0.378585i	−0.492006	+	0.870592i	$0.663736\pi$
$168$	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	0.999116	−	0.0420334i	$-0.0133836\pi$
$173$	12.5885	+	12.5885i	0.957083	+	0.957083i	−0.0420334	+	0.999116i	$0.513384\pi$
$174$	−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	$0.0360031\pi$
$191$			3.11968i			0.225732i	−0.993610	+	0.112866i	$0.963997\pi$
$192$	−11.4069	+	9.20733i	−0.823225	+	0.664482i
$193$	8.14880	+	8.14880i	0.586563	+	0.586563i	0.936699	−	0.350136i	$-0.113865\pi$
$193$	8.14880	+	8.14880i	0.586563	+	0.586563i	−0.350136	+	0.936699i	$0.613865\pi$
$194$	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	−0.375341	+	0.926887i	$0.622474\pi$
$197$	−18.2776	+	18.2776i	−1.30223	+	1.30223i	−0.926887	+	0.375341i	$0.877526\pi$
$198$	−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	$-0.759745\pi$
$211$		−	19.9042i		−	1.37026i	0.728420	−	0.685130i	$-0.240255\pi$
$212$	−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	−0.180987	+	0.983486i	$0.557929\pi$
$223$	−17.3893	+	17.3893i	−1.16447	+	1.16447i	−0.983486	+	0.180987i	$0.942071\pi$
$224$	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	0.301836	−	0.953360i	$-0.402400\pi$
$227$	−9.81619	−	9.81619i	−0.651524	−	0.651524i	−0.953360	+	0.301836i	$0.902400\pi$
$228$	0.822520	+	3.57132i	0.0544727	+	0.236516i
$229$		−	28.3436i		−	1.87300i	−0.350673	−	0.936498i	$-0.614047\pi$
$229$		−	28.3436i		−	1.87300i	0.350673	−	0.936498i	$-0.385953\pi$
$230$	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	0.886094	−	0.463505i	$-0.153409\pi$
$233$	6.45054	+	6.45054i	0.422589	+	0.422589i	−0.463505	+	0.886094i	$0.653409\pi$
$234$	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	$0.203834\pi$
$251$			18.9320i			1.19497i	−0.801878	+	0.597487i	$0.796166\pi$
$252$	−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	−0.824455	−	0.565927i	$-0.808518\pi$
$257$	−4.14453	+	4.14453i	−0.258529	+	0.258529i	0.565927	+	0.824455i	$0.308518\pi$
$258$	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	−0.689293	−	0.724482i	$-0.742079\pi$
$263$	0.570667	−	0.570667i	0.0351889	−	0.0351889i	0.724482	+	0.689293i	$0.242079\pi$
$264$	−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	$0.153713\pi$
$269$			15.2319i			0.928705i	−0.885650	+	0.464353i	$0.846287\pi$
$270$	14.3485	+	5.34279i	0.873223	+	0.325152i
$271$		−	6.90043i		−	0.419171i	−0.977790	−	0.209586i	$-0.932788\pi$
$271$		−	6.90043i		−	0.419171i	0.977790	−	0.209586i	$-0.0672115\pi$
$272$	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	−0.395090	−	0.918643i	$-0.629286\pi$
$277$	8.71366	−	8.71366i	0.523553	−	0.523553i	0.918643	+	0.395090i	$0.129286\pi$
$278$	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	0.136871	−	0.990589i	$-0.456295\pi$
$283$	18.9668	−	18.9668i	1.12746	−	1.12746i	0.990589	−	0.136871i	$-0.0437046\pi$
$284$	−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	0.0187322	−	0.999825i	$-0.494037\pi$
$293$	−16.7936	−	16.7936i	−0.981092	−	0.981092i	−0.999825	+	0.0187322i	$0.994037\pi$
$294$	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	0.996014	−	0.0892025i	$-0.0284318\pi$
$307$	15.8886	+	15.8886i	0.906811	+	0.906811i	−0.0892025	+	0.996014i	$0.528432\pi$
$308$	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	$-0.763200\pi$
$311$		−	23.8846i		−	1.35437i	0.735813	−	0.677185i	$-0.236800\pi$
$312$	13.6945	+	0.728556i	0.775298	+	0.0412464i
$313$	2.63964	+	2.63964i	0.149201	+	0.149201i	0.777761	−	0.628560i	$-0.216355\pi$
$313$	2.63964	+	2.63964i	0.149201	+	0.149201i	−0.628560	+	0.777761i	$0.716355\pi$
$314$	−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	−0.784785	−	0.619768i	$-0.787227\pi$
$317$	−2.93804	+	2.93804i	−0.165017	+	0.165017i	0.619768	+	0.784785i	$0.287227\pi$
$318$	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	$0.0677619\pi$
$331$			7.68766i			0.422552i	−0.977426	+	0.211276i	$0.932238\pi$
$332$	−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	−0.909402	−	0.415919i	$-0.863460\pi$
$337$	−9.05913	+	9.05913i	−0.493482	+	0.493482i	0.415919	+	0.909402i	$0.363460\pi$
$338$	−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	0.998040	+	0.0625723i	$0.0199304\pi$
$347$	19.7570	+	19.7570i	1.06061	+	1.06061i	0.0625723	+	0.998040i	$0.480070\pi$
$348$	32.6890	−	7.52871i	1.75232	−	0.403581i
$349$			3.40999i			0.182533i	0.995827	+	0.0912664i	$0.0290915\pi$
$349$			3.40999i			0.182533i	−0.995827	+	0.0912664i	$0.970909\pi$
$350$	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	0.983642	−	0.180137i	$-0.0576542\pi$
$353$	15.0965	+	15.0965i	0.803504	+	0.803504i	−0.180137	+	0.983642i	$0.557654\pi$
$354$	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	0.939279	−	0.343155i	$-0.111496\pi$
$367$	11.4201	+	11.4201i	0.596124	+	0.596124i	−0.343155	+	0.939279i	$0.611496\pi$
$368$	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	0.370791	−	0.928716i	$-0.379087\pi$
$373$	−10.7753	−	10.7753i	−0.557926	−	0.557926i	−0.928716	+	0.370791i	$0.879087\pi$
$374$	−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	−0.240539	−	0.970640i	$-0.577324\pi$
$383$	14.2884	−	14.2884i	0.730101	−	0.730101i	0.970640	+	0.240539i	$0.0773241\pi$
$384$	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	$0.0256118\pi$
$389$			3.17048i			0.160750i	−0.996765	+	0.0803749i	$0.974388\pi$
$390$	−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	−0.999700	−	0.0244741i	$-0.992209\pi$
$397$	−19.4312	+	19.4312i	−0.975226	+	0.975226i	0.0244741	+	0.999700i	$0.492209\pi$
$398$	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	$-0.739159\pi$
$409$		−	29.5580i		−	1.46155i	0.682620	−	0.730774i	$-0.260841\pi$
$410$	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	$0.273312\pi$
$431$			31.4295i			1.51390i	−0.653471	+	0.756952i	$0.726688\pi$
$432$	−6.32458	+	18.3052i	−0.304291	+	0.880709i
$433$	−10.0203	−	10.0203i	−0.481545	−	0.481545i	0.424080	−	0.905625i	$-0.360598\pi$
$433$	−10.0203	−	10.0203i	−0.481545	−	0.481545i	−0.905625	+	0.424080i	$0.860598\pi$
$434$	−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	−0.956053	−	0.293195i	$-0.905282\pi$
$443$	−13.9516	+	13.9516i	−0.662858	+	0.662858i	0.293195	+	0.956053i	$0.405282\pi$
$444$	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	$0.129517\pi$
$449$			16.7718i			0.791512i	−0.918356	+	0.395756i	$0.870483\pi$
$450$	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	−0.921192	−	0.389107i	$-0.872783\pi$
$457$	−11.3747	+	11.3747i	−0.532085	+	0.532085i	0.389107	+	0.921192i	$0.372783\pi$
$458$	−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	−0.998506	−	0.0546376i	$-0.982600\pi$
$463$	−20.3096	+	20.3096i	−0.943869	+	0.943869i	0.0546376	+	0.998506i	$0.482600\pi$
$464$	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	−0.828549	−	0.559916i	$-0.810833\pi$
$467$	−30.0050	−	30.0050i	−1.38847	−	1.38847i	−0.559916	−	0.828549i	$-0.689167\pi$
$468$	−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	0.609175	−	0.793036i	$-0.291501\pi$
$487$	−4.05745	−	4.05745i	−0.183861	−	0.183861i	−0.793036	+	0.609175i	$0.791501\pi$
$488$	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	$0.0485250\pi$
$491$			6.72981i			0.303712i	−0.988403	+	0.151856i	$0.951475\pi$
$492$	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	−0.818772	−	0.574119i	$-0.805345\pi$
$503$	−5.48698	+	5.48698i	−0.244653	+	0.244653i	0.574119	+	0.818772i	$0.305345\pi$
$504$	−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	$0.0794075\pi$
$509$			11.1400i			0.493773i	−0.969044	+	0.246887i	$0.920592\pi$
$510$	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	−0.128071	−	0.991765i	$-0.540879\pi$
$523$	19.7520	−	19.7520i	0.863694	−	0.863694i	0.991765	+	0.128071i	$0.0408786\pi$
$524$	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	−0.979232	−	0.202742i	$-0.935015\pi$
$547$	−27.6440	−	27.6440i	−1.18197	−	1.18197i	−0.202742	−	0.979232i	$-0.564985\pi$
$548$	−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	−0.926043	−	0.377419i	$-0.876812\pi$
$557$	−12.9480	+	12.9480i	−0.548624	+	0.548624i	0.377419	+	0.926043i	$0.376812\pi$
$558$	−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	−0.495457	−	0.868632i	$-0.664999\pi$
$563$	8.85456	−	8.85456i	0.373175	−	0.373175i	0.868632	+	0.495457i	$0.164999\pi$
$564$	−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	$0.380536\pi$
$569$			44.3868i			1.86079i	−0.366559	+	0.930395i	$0.619464\pi$
$570$	−2.02203	+	5.43033i	−0.0846934	+	0.227451i
$571$		−	6.20459i		−	0.259654i	−0.991537	−	0.129827i	$-0.958558\pi$
$571$		−	6.20459i		−	0.259654i	0.991537	−	0.129827i	$-0.0414422\pi$
$572$	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	−0.995805	−	0.0915047i	$-0.970832\pi$
$577$	−21.7220	+	21.7220i	−0.904300	+	0.904300i	0.0915047	+	0.995805i	$0.470832\pi$
$578$	−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	0.725177	−	0.688562i	$-0.241758\pi$
$587$	0.887101	+	0.887101i	0.0366146	+	0.0366146i	−0.688562	+	0.725177i	$0.741758\pi$
$588$	−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	0.998110	−	0.0614496i	$-0.0195724\pi$
$593$	22.8092	+	22.8092i	0.936661	+	0.936661i	−0.0614496	+	0.998110i	$0.519572\pi$
$594$	−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	0.894922	+	0.446222i	$0.147231\pi$
$607$	33.0423	+	33.0423i	1.34114	+	1.34114i	0.446222	+	0.894922i	$0.352769\pi$
$608$	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	0.834574	−	0.550896i	$-0.185714\pi$
$613$	7.02354	+	7.02354i	0.283678	+	0.283678i	−0.550896	+	0.834574i	$0.685714\pi$
$614$	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	0.0511388	−	0.998692i	$-0.483715\pi$
$617$	26.0772	−	26.0772i	1.04983	−	1.04983i	0.998692	−	0.0511388i	$-0.0162851\pi$
$618$	−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	$0.0447374\pi$
$631$			7.03776i			0.280169i	−0.990140	+	0.140084i	$0.955263\pi$
$632$	−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	−0.833721	−	0.552186i	$-0.813794\pi$
$643$	−7.13901	+	7.13901i	−0.281535	+	0.281535i	0.552186	+	0.833721i	$0.313794\pi$
$644$	−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	0.436899	−	0.899511i	$-0.356077\pi$
$647$	−11.7671	−	11.7671i	−0.462612	−	0.462612i	−0.899511	+	0.436899i	$0.856077\pi$
$648$	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	0.854415	−	0.519591i	$-0.173916\pi$
$653$	8.55603	+	8.55603i	0.334823	+	0.334823i	−0.519591	+	0.854415i	$0.673916\pi$
$654$	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	0.881429	+	0.472317i	$0.156582\pi$
$673$	35.1192	+	35.1192i	1.35375	+	1.35375i	0.472317	+	0.881429i	$0.343418\pi$
$674$	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	−0.986270	−	0.165138i	$-0.947193\pi$
$677$	−21.3652	+	21.3652i	−0.821133	+	0.821133i	0.165138	+	0.986270i	$0.447193\pi$
$678$	−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	−0.869631	−	0.493703i	$-0.835643\pi$
$683$	−9.82459	+	9.82459i	−0.375927	+	0.375927i	0.493703	+	0.869631i	$0.335643\pi$
$684$	−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	$0.0186992\pi$
$691$			3.08668i			0.117423i	−0.998275	+	0.0587114i	$0.981301\pi$
$692$	−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	$0.315410\pi$
$709$			44.5478i			1.67303i	−0.547945	+	0.836514i	$0.684590\pi$
$710$	−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	0.745364	−	0.666658i	$-0.232276\pi$
$727$	2.12216	+	2.12216i	0.0787065	+	0.0787065i	−0.666658	+	0.745364i	$0.732276\pi$
$728$	−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	0.965202	+	0.261507i	$0.0842194\pi$
$733$	33.2119	+	33.2119i	1.22671	+	1.22671i	0.261507	+	0.965202i	$0.415781\pi$
$734$	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	−0.950603	−	0.310410i	$-0.899534\pi$
$743$	−17.4504	+	17.4504i	−0.640193	+	0.640193i	0.310410	+	0.950603i	$0.399534\pi$
$744$	−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	$0.0313382\pi$
$751$			5.38732i			0.196586i	−0.995158	+	0.0982930i	$0.968662\pi$
$752$	−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	−0.894151	−	0.447765i	$-0.852220\pi$
$757$	−12.2817	+	12.2817i	−0.446386	+	0.446386i	0.447765	+	0.894151i	$0.352220\pi$
$758$	−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	$-0.792985\pi$
$769$		−	33.5804i		−	1.21094i	0.795869	−	0.605469i	$-0.207015\pi$
$770$	−1.67243	+	4.49147i	−0.0602703	+	0.161861i
$771$		−	10.7402i		−	0.386798i
$772$	−22.4603	+	5.17290i	−0.808363	+	0.186177i
$773$	−8.27757	−	8.27757i	−0.297723	−	0.297723i	0.542398	−	0.840122i	$-0.317516\pi$
$773$	−8.27757	−	8.27757i	−0.297723	−	0.297723i	−0.840122	+	0.542398i	$0.817516\pi$
$774$	−1.30823	+	4.55780i	−0.0470233	+	0.163827i
$775$	7.17193	−	46.2411i	0.257623	−	1.66103i
$776$	−7.32787	+	6.58756i	−0.263055	+	0.236480i
$777$	−4.14663	+	4.14663i	−0.148759	+	0.148759i
$778$	3.92214	−	2.17273i	0.140616	−	0.0778960i
$779$	6.78865			0.243229
$780$	17.4443	+	12.8791i	0.624607	+	0.461145i
$781$	−4.97516			−0.178025
$782$	−30.7360	+	17.0266i	−1.09912	+	0.608871i
$783$	31.3373	−	31.3373i	1.11990	−	1.11990i
$784$	−22.0977	+	10.7489i	−0.789203	+	0.383890i
$785$	−16.4467	−	19.1942i	−0.587007	−	0.685069i
$786$	0.923846	−	3.21863i	0.0329525	−	0.114805i
$787$	−21.7581	−	21.7581i	−0.775591	−	0.775591i	0.203486	−	0.979078i	$-0.434773\pi$
$787$	−21.7581	−	21.7581i	−0.775591	−	0.775591i	−0.979078	+	0.203486i	$0.934773\pi$
$788$	−11.6027	−	50.3781i	−0.413330	−	1.79465i
$789$			1.47883i			0.0526479i
$790$	13.0350	−	5.96151i	0.463765	−	0.212101i
$791$			7.82793i			0.278329i
$792$	1.65438	+	0.0880139i	0.0587857	+	0.00312744i
$793$	−3.17520	−	3.17520i	−0.112755	−	0.112755i
$794$	37.3542	+	10.7218i	1.32565	+	0.380502i
$795$	−1.38948	+	18.0245i	−0.0492796	+	0.639262i
$796$	10.6909	−	17.0890i	0.378930	−	0.605704i
$797$	−0.918743	+	0.918743i	−0.0325435	+	0.0325435i	−0.723191	−	0.690648i	$-0.757326\pi$
$797$	−0.918743	+	0.918743i	−0.0325435	+	0.0325435i	0.690648	+	0.723191i	$0.257326\pi$
$798$	1.16228	+	2.09811i	0.0411441	+	0.0742722i
$799$	36.0594			1.27569
$800$	19.6094	−	20.3831i	0.693298	−	0.720651i
$801$	−0.434899			−0.0153664
$802$	9.77052	+	17.6374i	0.345009	+	0.622800i
$803$	14.6769	−	14.6769i	0.517936	−	0.517936i
$804$	3.79523	−	6.06651i	0.133847	−	0.213949i
$805$	0.799068	−	10.3656i	0.0281635	−	0.365340i
$806$	−33.6618	−	9.66197i	−1.18569	−	0.340328i
$807$	−19.7361	−	19.7361i	−0.694742	−	0.694742i
$808$	34.2274	+	1.82092i	1.20412	+	0.0640597i
$809$			9.56488i			0.336283i	0.985763	+	0.168142i	$0.0537766\pi$
$809$			9.56488i			0.336283i	−0.985763	+	0.168142i	$0.946223\pi$
$810$	−28.6002	+	13.0802i	−1.00491	+	0.459591i
$811$			21.0531i			0.739274i	0.929176	+	0.369637i	$0.120518\pi$
$811$			21.0531i			0.739274i	−0.929176	+	0.369637i	$0.879482\pi$
$812$	3.80284	+	16.5116i	0.133453	+	0.579443i
$813$	8.94093	+	8.94093i	0.313572	+	0.313572i
$814$	−2.20906	+	7.69624i	−0.0774274	+	0.269753i
$815$	−5.97005	−	6.96737i	−0.209122	−	0.244056i
$816$	−32.6006	+	15.8578i	−1.14125	+	0.555136i
$817$	−6.62809	+	6.62809i	−0.231888	+	0.231888i
$818$	−36.5656	+	20.2560i	−1.27849	+	0.708235i
$819$	0.876053			0.0306118
$820$	−24.4243	−	18.0324i	−0.852934	−	0.629718i
$821$	9.42853			0.329058			0.164529	−	0.986372i	$-0.447390\pi$
$821$	9.42853			0.329058			0.164529	+	0.986372i	$0.447390\pi$
$822$	−26.0864	+	14.4510i	−0.909869	+	0.504035i
$823$	10.8497	−	10.8497i	0.378196	−	0.378196i	−0.492255	−	0.870451i	$-0.663827\pi$
$823$	10.8497	−	10.8497i	0.378196	−	0.378196i	0.870451	+	0.492255i	$0.163827\pi$
$824$	−9.07035	+	8.15400i	−0.315981	+	0.284058i
$825$	8.85719	+	12.1090i	0.308368	+	0.421582i
$826$	−0.660465	+	2.30103i	−0.0229805	+	0.0800629i
$827$	11.1372	+	11.1372i	0.387280	+	0.387280i	0.873716	−	0.486436i	$-0.161703\pi$
$827$	11.1372	+	11.1372i	0.387280	+	0.387280i	−0.486436	+	0.873716i	$0.661703\pi$
$828$	−3.50206	+	0.806569i	−0.121705	+	0.0280302i
$829$			6.50891i			0.226064i	0.993591	+	0.113032i	$0.0360562\pi$
$829$			6.50891i			0.226064i	−0.993591	+	0.113032i	$0.963944\pi$
$830$	2.84443	−	7.63897i	0.0987317	−	0.265153i
$831$			22.5807i			0.783315i
$832$	−13.2955	−	16.4718i	−0.460940	−	0.571057i
$833$	21.4857	+	21.4857i	0.744435	+	0.744435i
$834$	−51.5765	−	14.8040i	−1.78595	−	0.512622i
$835$	11.7482	−	10.0665i	0.406563	−	0.348367i
$836$	2.77640	+	1.73692i	0.0960239	+	0.0600728i
$837$	32.0411	−	32.0411i	1.10750	−	1.10750i
$838$	8.17861	+	14.7638i	0.282526	+	0.510007i
$839$	−35.3453			−1.22026			−0.610128	−	0.792303i	$-0.708882\pi$
$839$	−35.3453			−1.22026			−0.610128	+	0.792303i	$0.708882\pi$
$840$	1.39145	−	10.6359i	0.0480096	−	0.366974i
$841$	−54.7814			−1.88901
$842$	1.52524	+	2.75332i	0.0525634	+	0.0948858i
$843$	3.18882	−	3.18882i	0.109829	−	0.109829i
$844$	33.7483	+	21.1130i	1.16166	+	0.726740i
$845$	−13.3735	−	1.03094i	−0.460063	−	0.0354655i
$846$	3.54495	+	1.01751i	0.121878	+	0.0349827i
$847$	−5.44437	−	5.44437i	−0.187071	−	0.187071i
$848$	5.76331	−	16.6807i	0.197913	−	0.572818i
$849$			49.1508i			1.68685i
$850$	−31.7406	−	14.6873i	−1.08869	−	0.503770i
$851$		−	17.3687i		−	0.595393i
$852$	10.8508	−	2.49907i	0.371741	−	0.0856169i
$853$	11.7415	+	11.7415i	0.402023	+	0.402023i	0.878945	−	0.476923i	$-0.158248\pi$
$853$	11.7415	+	11.7415i	0.402023	+	0.402023i	−0.476923	+	0.878945i	$0.658248\pi$
$854$	−0.612849	+	2.13514i	−0.0209713	+	0.0730628i
$855$	0.797493	+	0.0614774i	0.0272737	+	0.00210248i
$856$	0.0439473	+	0.0488861i	0.00150209	+	0.00167089i
$857$	3.11510	−	3.11510i	0.106410	−	0.106410i	−0.651897	−	0.758307i	$-0.726027\pi$
$857$	3.11510	−	3.11510i	0.106410	−	0.106410i	0.758307	+	0.651897i	$0.226027\pi$
$858$	9.82172	−	5.44088i	0.335308	−	0.185749i
$859$	−42.9884			−1.46674			−0.733372	−	0.679828i	$-0.762055\pi$
$859$	−42.9884			−1.46674			−0.733372	+	0.679828i	$0.762055\pi$
$860$	41.4526	−	6.24076i	1.41352	−	0.212808i
$861$	−11.5137			−0.392384
$862$	38.8807	−	21.5386i	1.32428	−	0.733606i
$863$	−1.04860	+	1.04860i	−0.0356949	+	0.0356949i	−0.724729	−	0.689034i	$-0.758035\pi$
$863$	−1.04860	+	1.04860i	−0.0356949	+	0.0356949i	0.689034	+	0.724729i	$0.258035\pi$
$864$	26.9792	−	4.72051i	0.917851	−	0.160595i
$865$	30.2289	−	25.9019i	1.02781	−	0.880690i
$866$	−5.52902	+	19.2628i	−0.187884	+	0.654578i
$867$	9.67072	+	9.67072i	0.328435	+	0.328435i
$868$	3.88825	+	16.8824i	0.131976	+	0.573027i
$869$		−	7.42215i		−	0.251779i
$870$	49.7050	+	18.5081i	1.68516	+	0.627482i
$871$		−	5.16659i		−	0.175063i
$872$	0.640411	−	12.0376i	0.0216870	−	0.407646i
$873$	0.881178	+	0.881178i	0.0298234	+	0.0298234i
$874$	−6.82829	−	1.95993i	−0.230970	−	0.0662956i
$875$	8.79715	−	5.44929i	0.297398	−	0.184220i
$876$	−24.6378	+	39.3825i	−0.832433	+	1.33061i
$877$	−19.4338	+	19.4338i	−0.656231	+	0.656231i	−0.954486	−	0.298255i	$-0.903595\pi$
$877$	−19.4338	+	19.4338i	−0.656231	+	0.656231i	0.298255	+	0.954486i	$0.403595\pi$
$878$	−19.2592	−	34.7661i	−0.649966	−	1.17330i
$879$	43.5191			1.46786
$880$	−5.37527	−	13.6240i	−0.181200	−	0.459264i
$881$	20.7366			0.698635			0.349318	−	0.937004i	$-0.386413\pi$
$881$	20.7366			0.698635			0.349318	+	0.937004i	$0.386413\pi$
$882$	1.50595	+	2.71850i	0.0507081	+	0.0915367i
$883$	22.6956	−	22.6956i	0.763768	−	0.763768i	−0.213233	−	0.977001i	$-0.568399\pi$
$883$	22.6956	−	22.6956i	0.763768	−	0.763768i	0.977001	+	0.213233i	$0.0683995\pi$
$884$	−13.8823	+	22.1902i	−0.466911	+	0.746338i
$885$	4.87590	+	5.69044i	0.163901	+	0.191282i
$886$	26.8202	+	7.69821i	0.901041	+	0.258626i
$887$	−7.85387	−	7.85387i	−0.263707	−	0.263707i	0.562851	−	0.826558i	$-0.309704\pi$
$887$	−7.85387	−	7.85387i	−0.263707	−	0.263707i	−0.826558	+	0.562851i	$0.809704\pi$
$888$	0.952028	−	17.8950i	0.0319480	−	0.600518i
$889$		−	17.6815i		−	0.593017i
$890$	1.59905	+	3.49637i	0.0536002	+	0.117199i
$891$			16.2850i			0.545567i
$892$	−11.0388	−	47.9295i	−0.369606	−	1.60480i
$893$	5.15517	+	5.15517i	0.172511	+	0.172511i
$894$	9.72160	−	33.8696i	0.325139	−	1.13277i
$895$	−2.19685	+	28.4978i	−0.0734326	+	0.952577i
$896$	−3.94064	+	9.70185i	−0.131648	+	0.324116i
$897$	−17.2222	+	17.2222i	−0.575032	+	0.575032i
$898$	20.7481	−	11.4937i	0.692373	−	0.383550i
$899$	−85.6631			−2.85703
$900$	−2.70593	−	2.33953i	−0.0901978	−	0.0779843i
$901$	−21.8224			−0.727011
$902$	−13.7517	+	7.61794i	−0.457881	+	0.253650i
$903$	11.2413	−	11.2413i	0.374089	−	0.374089i
$904$	−15.9924	−	17.7896i	−0.531898	−	0.591673i
$905$	4.31585	−	55.9857i	0.143464	−	1.86103i
$906$	1.87219	−	6.52261i	0.0621993	−	0.216699i
$907$	25.3892	+	25.3892i	0.843033	+	0.843033i	0.989252	−	0.146219i	$-0.0467105\pi$
$907$	25.3892	+	25.3892i	0.843033	+	0.843033i	−0.146219	+	0.989252i	$0.546711\pi$
$908$	27.0561	−	6.23137i	0.897887	−	0.206795i
$909$		−	4.33482i		−	0.143777i
$910$	−3.22110	−	7.04302i	−0.106778	−	0.233474i
$911$		−	14.6891i		−	0.486670i	−0.969942	−	0.243335i	$-0.921759\pi$
$911$		−	14.6891i		−	0.486670i	0.969942	−	0.243335i	$-0.0782415\pi$
$912$	−6.92777	−	2.39360i	−0.229401	−	0.0792599i
$913$	−2.98463	−	2.98463i	−0.0987767	−	0.0987767i
$914$	21.8664	+	6.27633i	0.723277	+	0.207603i
$915$	4.52437	+	5.28019i	0.149571	+	0.174558i
$916$	48.0576	+	30.0650i	1.58787	+	0.993374i
$917$	−0.845706	+	0.845706i	−0.0279277	+	0.0279277i
$918$	−16.4113	−	29.6252i	−0.541653	−	0.977776i
$919$	−48.8987			−1.61302			−0.806510	−	0.591221i	$-0.798646\pi$
$919$	−48.8987			−1.61302			−0.806510	+	0.591221i	$0.798646\pi$
$920$	19.3609	+	25.1892i	0.638309	+	0.830462i
$921$	−41.1739			−1.35673
$922$	−12.5116	−	22.5856i	−0.412049	−	0.743818i
$923$	5.68474	−	5.68474i	0.187116	−	0.187116i
$924$	−4.70882	−	2.94585i	−0.154909	−	0.0969113i
$925$	13.9538	−	10.2066i	0.458798	−	0.335590i
$926$	39.0428	+	11.2065i	1.28303	+	0.368268i
$927$	1.09071	+	1.09071i	0.0358237	+	0.0358237i
$928$	−42.3752	−	29.7548i	−1.39103	−	0.976748i
$929$		−	36.3158i		−	1.19148i	−0.803177	−	0.595741i	$-0.796859\pi$
$929$		−	36.3158i		−	1.19148i	0.803177	−	0.595741i	$-0.203141\pi$
$930$	50.8214	+	18.9237i	1.66650	+	0.620534i
$931$			6.14332i			0.201339i
$932$	−17.7794	+	4.09483i	−0.582384	+	0.134131i
$933$	30.9474	+	30.9474i	1.01317	+	1.01317i
$934$	−16.5562	+	57.6809i	−0.541735	+	1.88738i
$935$	−13.7521	+	11.7836i	−0.449743	+	0.385366i
$936$	−1.99090	+	1.78976i	−0.0650746	+	0.0585003i
$937$	−7.18027	+	7.18027i	−0.234569	+	0.234569i	−0.814597	−	0.580028i	$-0.803042\pi$
$937$	−7.18027	+	7.18027i	−0.234569	+	0.234569i	0.580028	+	0.814597i	$0.303042\pi$
$938$	−2.23572	+	1.23851i	−0.0729987	+	0.0404387i
$939$	−6.84039			−0.223228
$940$	−4.85391	−	32.2408i	−0.158317	−	1.05158i
$941$	−9.41147			−0.306805			−0.153403	−	0.988164i	$-0.549023\pi$
$941$	−9.41147			−0.306805			−0.153403	+	0.988164i	$0.549023\pi$
$942$	25.6244	−	14.1950i	0.834888	−	0.462498i
$943$	24.1133	−	24.1133i	0.785237	−	0.785237i
$944$	−3.20001	−	6.57859i	−0.104151	−	0.214115i
$945$	9.99100	+	0.770190i	0.325007	+	0.0250543i
$946$	5.98867	−	20.8642i	0.194708	−	0.678354i
$947$	−12.8991	−	12.8991i	−0.419165	−	0.419165i	0.465751	−	0.884916i	$-0.345784\pi$
$947$	−12.8991	−	12.8991i	−0.419165	−	0.419165i	−0.884916	+	0.465751i	$0.845784\pi$
$948$	3.72822	+	16.1876i	0.121087	+	0.525749i
$949$			33.5404i			1.08877i
$950$	−2.43800	−	6.63748i	−0.0790991	−	0.215348i
$951$		−	7.61368i		−	0.246891i
$952$	12.9301	+	0.687887i	0.419066	+	0.0222946i
$953$	−1.84339	−	1.84339i	−0.0597132	−	0.0597132i	0.676620	−	0.736333i	$-0.263444\pi$
$953$	−1.84339	−	1.84339i	−0.0597132	−	0.0597132i	−0.736333	+	0.676620i	$0.763444\pi$
$954$	−2.14533	−	0.615776i	−0.0694577	−	0.0199365i
$955$	6.95518	+	0.536164i	0.225064	+	0.0173499i
$956$	17.4076	−	27.8253i	0.563002	−	0.899935i
$957$	19.4203	−	19.4203i	0.627768	−	0.627768i
$958$	−25.9768	−	46.8926i	−0.839273	−	1.51503i
$959$	10.6513			0.343949
$960$	18.5669	+	27.0137i	0.599243	+	0.871862i
$961$	−56.5872			−1.82539
$962$	−6.26979	−	11.3180i	−0.202146	−	0.364908i
$963$	0.00587856	−	0.00587856i	0.000189434	−	0.000189434i
$964$	28.1106	−	44.9336i	0.905381	−	1.44721i
$965$	19.5679	−	16.7669i	0.629912	−	0.539745i
$966$	11.5809	+	3.32407i	0.372609	+	0.106950i
$967$	−13.9194	−	13.9194i	−0.447618	−	0.447618i	0.446944	−	0.894562i	$-0.352512\pi$
$967$	−13.9194	−	13.9194i	−0.447618	−	0.447618i	−0.894562	+	0.446944i	$0.852512\pi$
$968$	23.4955	+	1.24998i	0.755175	+	0.0401758i
$969$			9.06321i			0.291152i
$970$	3.84429	−	10.3242i	0.123433	−	0.331489i
$971$			52.7876i			1.69404i	0.531565	+	0.847018i	$0.321604\pi$
$971$			52.7876i			1.69404i	−0.531565	+	0.847018i	$0.678396\pi$
$972$	−1.66009	−	7.20795i	−0.0532473	−	0.231195i
$973$	13.5519	+	13.5519i	0.434454	+	0.434454i
$974$	−2.23883	+	7.79996i	−0.0717367	+	0.249927i
$975$	−23.9565	−	3.71561i	−0.767222	−	0.118995i
$976$	−2.96931	−	6.10431i	−0.0950452	−	0.195394i
$977$	4.20728	−	4.20728i	0.134603	−	0.134603i	−0.636595	−	0.771198i	$-0.719658\pi$
$977$	4.20728	−	4.20728i	0.134603	−	0.134603i	0.771198	+	0.636595i	$0.219658\pi$
$978$	9.30151	−	5.15271i	0.297430	−	0.164765i
$979$	1.99083			0.0636273
$980$	16.3182	−	22.1026i	0.521267	−	0.706041i
$981$	−1.52454			−0.0486748
$982$	8.32531	−	4.61193i	0.265671	−	0.147172i
$983$	25.3763	−	25.3763i	0.809380	−	0.809380i	−0.175160	−	0.984540i	$-0.556044\pi$
$983$	25.3763	−	25.3763i	0.809380	−	0.809380i	0.984540	+	0.175160i	$0.0560443\pi$
$984$	26.1657	−	23.5223i	0.834131	−	0.749862i
$985$	37.6079	+	43.8904i	1.19829	+	1.39847i
$986$	−17.6639	+	61.5401i	−0.562533	+	1.95984i
$987$	−8.74324	−	8.74324i	−0.278301	−	0.278301i
$988$	−5.15704	+	1.18773i	−0.164067	+	0.0377868i
$989$			47.0860i			1.49725i
$990$	−1.68446	+	0.770380i	−0.0535356	+	0.0244843i
$991$		−	53.9080i		−	1.71244i	−0.516609	−	0.856221i	$-0.672806\pi$
$991$		−	53.9080i		−	1.71244i	0.516609	−	0.856221i	$-0.327194\pi$
$992$	−43.3270	−	30.4230i	−1.37563	−	0.965933i
$993$	−9.96095	−	9.96095i	−0.316101	−	0.316101i
$994$	−3.82265	−	1.09722i	−0.121247	−	0.0348016i
$995$	−1.73219	+	22.4702i	−0.0549143	+	0.712355i
$996$	8.00864	+	5.01023i	0.253764	+	0.158755i
$997$	14.9755	−	14.9755i	0.474277	−	0.474277i	−0.429018	−	0.903296i	$-0.641140\pi$
$997$	14.9755	−	14.9755i	0.474277	−	0.474277i	0.903296	+	0.429018i	$0.141140\pi$
$998$	26.9284	+	48.6103i	0.852402	+	1.53873i
$999$	16.7410			0.529663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.d.343.8	yes	52
4.3	odd	2		380.2.k.c.343.22	yes	52
5.2	odd	4		380.2.k.c.267.22	✓	52
20.7	even	4	inner	380.2.k.d.267.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.22	✓	52	5.2	odd	4
380.2.k.c.343.22	yes	52	4.3	odd	2
380.2.k.d.267.8	yes	52	20.7	even	4	inner
380.2.k.d.343.8	yes	52	1.1	even	1	trivial

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

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