LMFDB - Embedded newform 380.2.k.d.267.10

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			267.10
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.287770 - 1.38463i) q^{2} +(-1.15541 - 1.15541i) q^{3} +(-1.83438 + 0.796907i) q^{4} +(-0.283261 - 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(3.26325 - 3.26325i) q^{7} +(1.63130 + 2.31060i) q^{8} -0.330062i q^{9} +O(q^{10})$	\(q+(-0.287770 - 1.38463i) q^{2} +(-1.15541 - 1.15541i) q^{3} +(-1.83438 + 0.796907i) q^{4} +(-0.283261 - 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(3.26325 - 3.26325i) q^{7} +(1.63130 + 2.31060i) q^{8} -0.330062i q^{9} +(-2.98966 + 1.03050i) q^{10} -4.56912i q^{11} +(3.04021 + 1.19870i) q^{12} +(-3.90789 + 3.90789i) q^{13} +(-5.45745 - 3.57932i) q^{14} +(-2.23548 + 2.89004i) q^{15} +(2.72988 - 2.92365i) q^{16} +(3.68739 + 3.68739i) q^{17} +(-0.457012 + 0.0949818i) q^{18} -1.00000 q^{19} +(2.28719 + 3.84301i) q^{20} -7.54078 q^{21} +(-6.32652 + 1.31485i) q^{22} +(0.671647 + 0.671647i) q^{23} +(0.784875 - 4.55450i) q^{24} +(-4.83953 + 1.25658i) q^{25} +(6.53553 + 4.28639i) q^{26} +(-3.84758 + 3.84758i) q^{27} +(-3.38553 + 8.58655i) q^{28} +1.43401i q^{29} +(4.64493 + 2.26363i) q^{30} -2.10503i q^{31} +(-4.83374 - 2.93852i) q^{32} +(-5.27920 + 5.27920i) q^{33} +(4.04454 - 6.16678i) q^{34} +(-8.16243 - 6.31372i) q^{35} +(0.263028 + 0.605458i) q^{36} +(3.01280 + 3.01280i) q^{37} +(0.287770 + 1.38463i) q^{38} +9.03041 q^{39} +(4.66295 - 4.27281i) q^{40} +3.51686 q^{41} +(2.17001 + 10.4412i) q^{42} +(1.49689 + 1.49689i) q^{43} +(3.64116 + 8.38148i) q^{44} +(-0.732095 + 0.0934937i) q^{45} +(0.736700 - 1.12326i) q^{46} +(5.49969 - 5.49969i) q^{47} +(-6.53214 + 0.223890i) q^{48} -14.2977i q^{49} +(3.13256 + 6.33933i) q^{50} -8.52089i q^{51} +(4.05432 - 10.2828i) q^{52} +(5.92537 - 5.92537i) q^{53} +(6.43468 + 4.22024i) q^{54} +(-10.1345 + 1.29425i) q^{55} +(12.8634 + 2.21674i) q^{56} +(1.15541 + 1.15541i) q^{57} +(1.98557 - 0.412665i) q^{58} -1.07843 q^{59} +(1.79761 - 7.08289i) q^{60} -11.0480 q^{61} +(-2.91467 + 0.605762i) q^{62} +(-1.07708 - 1.07708i) q^{63} +(-2.67775 + 7.53855i) q^{64} +(9.77486 + 7.56095i) q^{65} +(8.82890 + 5.79052i) q^{66} +(1.29688 - 1.29688i) q^{67} +(-9.70258 - 3.82556i) q^{68} -1.55205i q^{69} +(-6.39324 + 13.1188i) q^{70} +1.88311i q^{71} +(0.762641 - 0.538428i) q^{72} +(-3.20108 + 3.20108i) q^{73} +(3.30461 - 5.03859i) q^{74} +(7.04349 + 4.13977i) q^{75} +(1.83438 - 0.796907i) q^{76} +(-14.9102 - 14.9102i) q^{77} +(-2.59868 - 12.5037i) q^{78} -2.07546 q^{79} +(-7.25809 - 5.22686i) q^{80} +7.90087 q^{81} +(-1.01205 - 4.86954i) q^{82} +(2.08842 + 2.08842i) q^{83} +(13.8326 - 6.00930i) q^{84} +(7.13434 - 9.22333i) q^{85} +(1.64187 - 2.50339i) q^{86} +(1.65687 - 1.65687i) q^{87} +(10.5574 - 7.45358i) q^{88} -10.9661i q^{89} +(0.340129 + 0.986773i) q^{90} +25.5049i q^{91} +(-1.76729 - 0.696814i) q^{92} +(-2.43216 + 2.43216i) q^{93} +(-9.19765 - 6.03237i) q^{94} +(0.283261 + 2.21805i) q^{95} +(2.18976 + 8.98014i) q^{96} +(1.72131 + 1.72131i) q^{97} +(-19.7969 + 4.11443i) q^{98} -1.50809 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 $

$2$	−0.287770	−	1.38463i	−0.203484	−	0.979078i
$2$	−0.287770	−	1.38463i	−0.203484	−	0.979078i
$3$	−1.15541	−	1.15541i	−0.667075	−	0.667075i	0.289963	−	0.957038i	$-0.406357\pi$
$3$	−1.15541	−	1.15541i	−0.667075	−	0.667075i	−0.957038	+	0.289963i	$0.906357\pi$
$4$	−1.83438	+	0.796907i	−0.917189	+	0.398453i
$5$	−0.283261	−	2.21805i	−0.126678	−	0.991944i
$5$	−0.283261	−	2.21805i	−0.126678	−	0.991944i
$6$	−1.26732	+	1.93230i	−0.517380	+	0.788858i
$7$	3.26325	−	3.26325i	1.23339	−	1.23339i	0.270742	−	0.962652i	$-0.412731\pi$
$7$	3.26325	−	3.26325i	1.23339	−	1.23339i	0.962652	−	0.270742i	$-0.0872691\pi$
$8$	1.63130	+	2.31060i	0.576750	+	0.816921i
$9$		−	0.330062i		−	0.110021i
$10$	−2.98966	+	1.03050i	−0.945414	+	0.325873i
$11$		−	4.56912i		−	1.37764i	−0.724932	−	0.688820i	$-0.758129\pi$
$11$		−	4.56912i		−	1.37764i	0.724932	−	0.688820i	$-0.241871\pi$
$12$	3.04021	+	1.19870i	0.877632	+	0.346036i
$13$	−3.90789	+	3.90789i	−1.08385	+	1.08385i	−0.0877064	+	0.996146i	$0.527954\pi$
$13$	−3.90789	+	3.90789i	−1.08385	+	1.08385i	−0.996146	+	0.0877064i	$0.972046\pi$
$14$	−5.45745	−	3.57932i	−1.45857	−	0.956613i
$15$	−2.23548	+	2.89004i	−0.577197	+	0.746205i
$16$	2.72988	−	2.92365i	0.682470	−	0.730914i
$17$	3.68739	+	3.68739i	0.894324	+	0.894324i	0.994927	−	0.100602i	$-0.0320770\pi$
$17$	3.68739	+	3.68739i	0.894324	+	0.894324i	−0.100602	+	0.994927i	$0.532077\pi$
$18$	−0.457012	+	0.0949818i	−0.107719	+	0.0223874i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	2.28719	+	3.84301i	0.511431	+	0.859324i
$21$	−7.54078			−1.64553
$22$	−6.32652	+	1.31485i	−1.34882	+	0.280328i
$23$	0.671647	+	0.671647i	0.140048	+	0.140048i	0.773655	−	0.633607i	$-0.218426\pi$
$23$	0.671647	+	0.671647i	0.140048	+	0.140048i	−0.633607	+	0.773655i	$0.718426\pi$
$24$	0.784875	−	4.55450i	0.160212	−	0.929684i
$25$	−4.83953	+	1.25658i	−0.967905	+	0.251315i
$26$	6.53553	+	4.28639i	1.28172	+	0.840630i
$27$	−3.84758	+	3.84758i	−0.740468	+	0.740468i
$28$	−3.38553	+	8.58655i	−0.639805	+	1.62270i
$29$			1.43401i			0.266289i	0.991097	+	0.133145i	$0.0425074\pi$
$29$			1.43401i			0.266289i	−0.991097	+	0.133145i	$0.957493\pi$
$30$	4.64493	+	2.26363i	0.848044	+	0.413281i
$31$		−	2.10503i		−	0.378074i	−0.981970	−	0.189037i	$-0.939463\pi$
$31$		−	2.10503i		−	0.378074i	0.981970	−	0.189037i	$-0.0605366\pi$
$32$	−4.83374	−	2.93852i	−0.854493	−	0.519462i
$33$	−5.27920	+	5.27920i	−0.918990	+	0.918990i
$34$	4.04454	−	6.16678i	0.693633	−	1.05759i
$35$	−8.16243	−	6.31372i	−1.37970	−	1.06721i
$36$	0.263028	+	0.605458i	0.0438381	+	0.100910i
$37$	3.01280	+	3.01280i	0.495301	+	0.495301i	0.909972	−	0.414670i	$-0.136103\pi$
$37$	3.01280	+	3.01280i	0.495301	+	0.495301i	−0.414670	+	0.909972i	$0.636103\pi$
$38$	0.287770	+	1.38463i	0.0466824	+	0.224616i
$39$	9.03041			1.44602
$40$	4.66295	−	4.27281i	0.737278	−	0.675590i
$41$	3.51686			0.549241			0.274621	−	0.961553i	$-0.411448\pi$
$41$	3.51686			0.549241			0.274621	+	0.961553i	$0.411448\pi$
$42$	2.17001	+	10.4412i	0.334840	+	1.61111i
$43$	1.49689	+	1.49689i	0.228273	+	0.228273i	0.811971	−	0.583698i	$-0.198395\pi$
$43$	1.49689	+	1.49689i	0.228273	+	0.228273i	−0.583698	+	0.811971i	$0.698395\pi$
$44$	3.64116	+	8.38148i	0.548925	+	1.26356i
$45$	−0.732095	+	0.0934937i	−0.109134	+	0.0139372i
$46$	0.736700	−	1.12326i	0.108621	−	0.165616i
$47$	5.49969	−	5.49969i	0.802212	−	0.802212i	−0.181229	−	0.983441i	$-0.558007\pi$
$47$	5.49969	−	5.49969i	0.802212	−	0.802212i	0.983441	+	0.181229i	$0.0580075\pi$
$48$	−6.53214	+	0.223890i	−0.942834	+	0.0323157i
$49$		−	14.2977i		−	2.04252i
$50$	3.13256	+	6.33933i	0.443011	+	0.896516i
$51$		−	8.52089i		−	1.19316i
$52$	4.05432	−	10.2828i	0.562233	−	1.42596i
$53$	5.92537	−	5.92537i	0.813913	−	0.813913i	−0.171305	−	0.985218i	$-0.554798\pi$
$53$	5.92537	−	5.92537i	0.813913	−	0.813913i	0.985218	+	0.171305i	$0.0547985\pi$
$54$	6.43468	+	4.22024i	0.875649	+	0.574302i
$55$	−10.1345	+	1.29425i	−1.36654	+	0.174517i
$56$	12.8634	+	2.21674i	1.71895	+	0.296225i
$57$	1.15541	+	1.15541i	0.153038	+	0.153038i
$58$	1.98557	−	0.412665i	0.260718	−	0.0541855i
$59$	−1.07843			−0.140400			−0.0702000	−	0.997533i	$-0.522364\pi$
$59$	−1.07843			−0.140400			−0.0702000	+	0.997533i	$0.522364\pi$
$60$	1.79761	−	7.08289i	0.232071	−	0.914397i
$61$	−11.0480			−1.41455			−0.707277	−	0.706936i	$-0.750077\pi$
$61$	−11.0480			−1.41455			−0.707277	+	0.706936i	$0.750077\pi$
$62$	−2.91467	+	0.605762i	−0.370164	+	0.0769319i
$63$	−1.07708	−	1.07708i	−0.135699	−	0.135699i
$64$	−2.67775	+	7.53855i	−0.334719	+	0.942318i
$65$	9.77486	+	7.56095i	1.21242	+	0.937820i
$66$	8.82890	+	5.79052i	1.08676	+	0.712763i
$67$	1.29688	−	1.29688i	0.158439	−	0.158439i	−0.623436	−	0.781875i	$-0.714264\pi$
$67$	1.29688	−	1.29688i	0.158439	−	0.158439i	0.781875	+	0.623436i	$0.214264\pi$
$68$	−9.70258	−	3.82556i	−1.17661	−	0.463918i
$69$		−	1.55205i		−	0.186845i
$70$	−6.39324	+	13.1188i	−0.764138	+	1.56800i
$71$			1.88311i			0.223484i	0.993737	+	0.111742i	$0.0356430\pi$
$71$			1.88311i			0.223484i	−0.993737	+	0.111742i	$0.964357\pi$
$72$	0.762641	−	0.538428i	0.0898781	−	0.0634544i
$73$	−3.20108	+	3.20108i	−0.374659	+	0.374659i	−0.869171	−	0.494512i	$-0.835347\pi$
$73$	−3.20108	+	3.20108i	−0.374659	+	0.374659i	0.494512	+	0.869171i	$0.335347\pi$
$74$	3.30461	−	5.03859i	0.384153	−	0.585725i
$75$	7.04349	+	4.13977i	0.813312	+	0.478019i
$76$	1.83438	−	0.796907i	0.210417	−	0.0914115i
$77$	−14.9102	−	14.9102i	−1.69917	−	1.69917i
$78$	−2.59868	−	12.5037i	−0.294242	−	1.41577i
$79$	−2.07546			−0.233507			−0.116753	−	0.993161i	$-0.537249\pi$
$79$	−2.07546			−0.233507			−0.116753	+	0.993161i	$0.537249\pi$
$80$	−7.25809	−	5.22686i	−0.811479	−	0.584381i
$81$	7.90087			0.877875
$82$	−1.01205	−	4.86954i	−0.111762	−	0.537750i
$83$	2.08842	+	2.08842i	0.229234	+	0.229234i	0.812373	−	0.583139i	$-0.198176\pi$
$83$	2.08842	+	2.08842i	0.229234	+	0.229234i	−0.583139	+	0.812373i	$0.698176\pi$
$84$	13.8326	−	6.00930i	1.50926	−	0.655668i
$85$	7.13434	−	9.22333i	0.773828	−	1.00041i
$86$	1.64187	−	2.50339i	0.177048	−	0.269948i
$87$	1.65687	−	1.65687i	0.177635	−	0.177635i
$88$	10.5574	−	7.45358i	1.12542	−	0.794554i
$89$		−	10.9661i		−	1.16240i	−0.813759	−	0.581202i	$-0.802583\pi$
$89$		−	10.9661i		−	1.16240i	0.813759	−	0.581202i	$-0.197417\pi$
$90$	0.340129	+	0.986773i	0.0358527	+	0.104015i
$91$			25.5049i			2.67363i
$92$	−1.76729	−	0.696814i	−0.184253	−	0.0726479i
$93$	−2.43216	+	2.43216i	−0.252204	+	0.252204i
$94$	−9.19765	−	6.03237i	−0.948666	−	0.622191i
$95$	0.283261	+	2.21805i	0.0290620	+	0.227568i
$96$	2.18976	+	8.98014i	0.223491	+	0.916532i
$97$	1.72131	+	1.72131i	0.174773	+	0.174773i	0.789073	−	0.614300i	$-0.210561\pi$
$97$	1.72131	+	1.72131i	0.174773	+	0.174773i	−0.614300	+	0.789073i	$0.710561\pi$
$98$	−19.7969	+	4.11443i	−1.99979	+	0.415620i
$99$	−1.50809			−0.151569
$100$	7.87614	−	6.16169i	0.787614	−	0.616169i
$101$	15.3995			1.53231			0.766154	−	0.642658i	$-0.222168\pi$
$101$	15.3995			1.53231			0.766154	+	0.642658i	$0.222168\pi$
$102$	−11.7982	+	2.45205i	−1.16820	+	0.242790i
$103$	0.538076	+	0.538076i	0.0530182	+	0.0530182i	0.733119	−	0.680101i	$-0.238064\pi$
$103$	0.538076	+	0.538076i	0.0530182	+	0.0530182i	−0.680101	+	0.733119i	$0.738064\pi$
$104$	−15.4045	−	2.65465i	−1.51053	−	0.260309i
$105$	2.13601	+	16.7259i	0.208453	+	1.63228i
$106$	−9.90957	−	6.49928i	−0.962502	−	0.631266i
$107$	2.15177	−	2.15177i	0.208019	−	0.208019i	−0.595406	−	0.803425i	$-0.703009\pi$
$107$	2.15177	−	2.15177i	0.208019	−	0.208019i	0.803425	+	0.595406i	$0.203009\pi$
$108$	3.99175	−	10.1241i	0.384107	−	0.974190i
$109$		−	12.9951i		−	1.24471i	−0.782737	−	0.622353i	$-0.786177\pi$
$109$		−	12.9951i		−	1.24471i	0.782737	−	0.622353i	$-0.213823\pi$
$110$	4.70847	+	13.6601i	0.448935	+	1.30244i
$111$		−	6.96203i		−	0.660807i
$112$	−0.632338	−	18.4489i	−0.0597503	−	1.74326i
$113$	4.57006	−	4.57006i	0.429915	−	0.429915i	−0.458685	−	0.888599i	$-0.651679\pi$
$113$	4.57006	−	4.57006i	0.429915	−	0.429915i	0.888599	+	0.458685i	$0.151679\pi$
$114$	1.26732	−	1.93230i	0.118695	−	0.180976i
$115$	1.29950	−	1.68000i	0.121179	−	0.156661i
$116$	−1.14277	−	2.63052i	−0.106104	−	0.244237i
$117$	1.28984	+	1.28984i	0.119246	+	0.119246i
$118$	0.310340	+	1.49323i	0.0285692	+	0.137463i
$119$	24.0658			2.20611
$120$	−10.3245	−	0.450781i	−0.942489	−	0.0411505i
$121$	−9.87682			−0.897892
$122$	3.17929	+	15.2974i	0.287839	+	1.38496i
$123$	−4.06341	−	4.06341i	−0.366385	−	0.366385i
$124$	1.67751	+	3.86141i	0.150645	+	0.346765i
$125$	4.15801	+	10.3784i	0.371903	+	0.928271i
$126$	−1.18140	+	1.80130i	−0.105247	+	0.160472i
$127$	−6.46266	+	6.46266i	−0.573468	+	0.573468i	−0.933096	−	0.359628i	$-0.882904\pi$
$127$	−6.46266	+	6.46266i	−0.573468	+	0.573468i	0.359628	+	0.933096i	$0.382904\pi$
$128$	11.2086	+	1.53832i	0.990713	+	0.135969i
$129$		−	3.45904i		−	0.304551i
$130$	7.65618	−	15.7103i	0.671491	−	1.37789i
$131$		−	11.2765i		−	0.985230i	−0.870247	−	0.492615i	$-0.836041\pi$
$131$		−	11.2765i		−	0.985230i	0.870247	−	0.492615i	$-0.163959\pi$
$132$	5.47701	−	13.8911i	0.476713	−	1.20906i
$133$	−3.26325	+	3.26325i	−0.282960	+	0.282960i
$134$	−2.16889	−	1.42249i	−0.187364	−	0.122884i
$135$	9.62402	+	7.44427i	0.828303	+	0.640701i
$136$	−2.50486	+	14.5353i	−0.214790	+	1.24639i
$137$	4.91194	+	4.91194i	0.419655	+	0.419655i	0.885085	−	0.465430i	$-0.154100\pi$
$137$	4.91194	+	4.91194i	0.419655	+	0.419655i	−0.465430	+	0.885085i	$0.654100\pi$
$138$	−2.14901	+	0.446634i	−0.182936	+	0.0380200i
$139$	−13.9325			−1.18174			−0.590870	−	0.806767i	$-0.701215\pi$
$139$	−13.9325			−1.18174			−0.590870	+	0.806767i	$0.701215\pi$
$140$	20.0044	+	5.07705i	1.69068	+	0.429089i
$141$	−12.7088			−1.07027
$142$	2.60740	−	0.541902i	0.218808	−	0.0454754i
$143$	17.8556	+	17.8556i	1.49316	+	1.49316i
$144$	−0.964987	−	0.901029i	−0.0804156	−	0.0750858i
$145$	3.18071	−	0.406200i	0.264144	−	0.0337330i
$146$	5.35348	+	3.51113i	0.443057	+	0.290583i
$147$	−16.5196	+	16.5196i	−1.36252	+	1.36252i
$148$	−7.92753	−	3.12569i	−0.651639	−	0.256930i
$149$			16.9391i			1.38771i	0.720116	+	0.693853i	$0.244088\pi$
$149$			16.9391i			1.38771i	−0.720116	+	0.693853i	$0.755912\pi$
$150$	3.70513	−	10.9439i	0.302523	−	0.893566i
$151$		−	23.4511i		−	1.90842i	−0.299137	−	0.954210i	$-0.596699\pi$
$151$		−	23.4511i		−	1.90842i	0.299137	−	0.954210i	$-0.403301\pi$
$152$	−1.63130	−	2.31060i	−0.132316	−	0.187414i
$153$	1.21707	−	1.21707i	0.0983941	−	0.0983941i
$154$	−16.3543	+	24.9357i	−1.31787	+	2.00938i
$155$	−4.66906	+	0.596272i	−0.375028	+	0.0478937i
$156$	−16.5652	+	7.19640i	−1.32628	+	0.576173i
$157$	14.2678	+	14.2678i	1.13869	+	1.13869i	0.988684	+	0.150010i	$0.0479307\pi$
$157$	14.2678	+	14.2678i	1.13869	+	1.13869i	0.150010	+	0.988684i	$0.452069\pi$
$158$	0.597253	+	2.87373i	0.0475149	+	0.228622i
$159$	−13.6925			−1.08588
$160$	−5.14859	+	11.5539i	−0.407032	+	0.913414i
$161$	4.38351			0.345469
$162$	−2.27363	−	10.9398i	−0.178633	−	0.859508i
$163$	−9.47832	−	9.47832i	−0.742400	−	0.742400i	0.230640	−	0.973039i	$-0.425918\pi$
$163$	−9.47832	−	9.47832i	−0.742400	−	0.742400i	−0.973039	+	0.230640i	$0.925918\pi$
$164$	−6.45125	+	2.80261i	−0.503758	+	0.218847i
$165$	13.2049	+	10.2141i	1.02800	+	0.795170i
$166$	2.29069	−	3.49266i	0.177792	−	0.271083i
$167$	−13.9319	+	13.9319i	−1.07808	+	1.07808i	−0.0814021	+	0.996681i	$0.525940\pi$
$167$	−13.9319	+	13.9319i	−1.07808	+	1.07808i	−0.996681	+	0.0814021i	$0.974060\pi$
$168$	−12.3012	−	17.4237i	−0.949062	−	1.34427i
$169$		−	17.5432i		−	1.34947i
$170$	−14.8239	−	7.22420i	−1.13694	−	0.554071i
$171$			0.330062i			0.0252405i
$172$	−3.93874	−	1.55298i	−0.300326	−	0.118414i
$173$	1.27870	−	1.27870i	0.0972178	−	0.0972178i	−0.656825	−	0.754043i	$-0.728101\pi$
$173$	1.27870	−	1.27870i	0.0972178	−	0.0972178i	0.754043	+	0.656825i	$0.228101\pi$
$174$	−2.77094	−	1.81735i	−0.210064	−	0.137773i
$175$	−11.6921	+	19.8931i	−0.883838	+	1.50378i
$176$	−13.3585	−	12.4731i	−1.00694	−	0.940198i
$177$	1.24603	+	1.24603i	0.0936575	+	0.0936575i
$178$	−15.1839	+	3.15571i	−1.13808	+	0.236530i
$179$	−3.98743			−0.298034			−0.149017	−	0.988835i	$-0.547611\pi$
$179$	−3.98743			−0.298034			−0.149017	+	0.988835i	$0.547611\pi$
$180$	1.26843	−	0.754914i	0.0945434	−	0.0562680i
$181$	19.3398			1.43752			0.718758	−	0.695261i	$-0.244711\pi$
$181$	19.3398			1.43752			0.718758	+	0.695261i	$0.244711\pi$
$182$	35.3147	−	7.33952i	2.61770	−	0.544042i
$183$	12.7650	+	12.7650i	0.943615	+	0.943615i
$184$	−0.456253	+	2.64756i	−0.0336354	+	0.195181i
$185$	5.82914	−	7.53596i	0.428567	−	0.554055i
$186$	4.06754	+	2.66773i	0.298247	+	0.195608i
$187$	16.8481	−	16.8481i	1.23206	−	1.23206i
$188$	−5.70576	+	14.4712i	−0.416136	+	1.05542i
$189$			25.1113i			1.82658i
$190$	2.98966	−	1.03050i	0.216893	−	0.0747603i
$191$			1.41454i			0.102352i	0.998690	+	0.0511761i	$0.0162970\pi$
$191$			1.41454i			0.102352i	−0.998690	+	0.0511761i	$0.983703\pi$
$192$	11.8040	−	5.61621i	0.851880	−	0.405315i
$193$	−7.89499	+	7.89499i	−0.568294	+	0.568294i	−0.931650	−	0.363356i	$-0.881631\pi$
$193$	−7.89499	+	7.89499i	−0.568294	+	0.568294i	0.363356	+	0.931650i	$0.381631\pi$
$194$	1.88803	−	2.87871i	0.135553	−	0.206680i
$195$	−2.55797	−	20.0299i	−0.183180	−	1.43437i
$196$	11.3939	+	26.2273i	0.813850	+	1.87338i
$197$	−17.3505	−	17.3505i	−1.23617	−	1.23617i	−0.961554	−	0.274617i	$-0.911449\pi$
$197$	−17.3505	−	17.3505i	−1.23617	−	1.23617i	−0.274617	−	0.961554i	$-0.588551\pi$
$198$	0.433983	+	2.08814i	0.0308418	+	0.148398i
$199$	22.0059			1.55996			0.779979	−	0.625805i	$-0.215230\pi$
$199$	22.0059			1.55996			0.779979	+	0.625805i	$0.215230\pi$
$200$	−10.7981	−	9.13236i	−0.763544	−	0.645756i
$201$	−2.99685			−0.211382
$202$	−4.43151	−	21.3225i	−0.311800	−	1.50025i
$203$	4.67954	+	4.67954i	0.328439	+	0.328439i
$204$	6.79036	+	15.6305i	0.475420	+	1.09436i
$205$	−0.996190	−	7.80059i	−0.0695769	−	0.544817i
$206$	0.590192	−	0.899876i	0.0411206	−	0.0626974i
$207$	0.221685	−	0.221685i	0.0154082	−	0.0154082i
$208$	0.757252	+	22.0934i	0.0525060	+	1.53190i
$209$			4.56912i			0.316052i
$210$	22.5444	−	7.77077i	1.55571	−	0.536234i
$211$		−	13.2621i		−	0.913002i	−0.889723	−	0.456501i	$-0.849102\pi$
$211$		−	13.2621i		−	0.913002i	0.889723	−	0.456501i	$-0.150898\pi$
$212$	−6.14740	+	15.5913i	−0.422205	+	1.07082i
$213$	2.17576	−	2.17576i	0.149081	−	0.149081i
$214$	−3.59860	−	2.36018i	−0.245995	−	0.161338i
$215$	2.89617	−	3.74419i	0.197517	−	0.255352i
$216$	−15.1668	−	2.61368i	−1.03197	−	0.177838i
$217$	−6.86923	−	6.86923i	−0.466314	−	0.466314i
$218$	−17.9934	+	3.73960i	−1.21866	+	0.253278i
$219$	7.39712			0.499851
$220$	17.5592	−	10.4504i	1.18384	−	0.704568i
$221$	−28.8198			−1.93863
$222$	−9.63981	+	2.00346i	−0.646981	+	0.134464i
$223$	6.10795	+	6.10795i	0.409019	+	0.409019i	0.881396	−	0.472378i	$-0.156604\pi$
$223$	6.10795	+	6.10795i	0.409019	+	0.409019i	−0.472378	+	0.881396i	$0.656604\pi$
$224$	−25.3629	+	6.18459i	−1.69463	+	0.413225i
$225$	0.414748	+	1.59734i	0.0276499	+	0.106490i
$226$	−7.64294	−	5.01269i	−0.508401	−	0.333439i
$227$	−14.8986	+	14.8986i	−0.988853	+	0.988853i	−0.999939	−	0.0110855i	$-0.996471\pi$
$227$	−14.8986	+	14.8986i	−0.988853	+	0.988853i	0.0110855	+	0.999939i	$0.496471\pi$
$228$	−3.04021	−	1.19870i	−0.201343	−	0.0793860i
$229$			25.6102i			1.69237i	0.532888	+	0.846186i	$0.321107\pi$
$229$			25.6102i			1.69237i	−0.532888	+	0.846186i	$0.678893\pi$
$230$	−2.70013	−	1.31586i	−0.178041	−	0.0867656i
$231$			34.4547i			2.26695i
$232$	−3.31343	+	2.33930i	−0.217537	+	0.153582i
$233$	10.2855	−	10.2855i	0.673827	−	0.673827i	−0.284769	−	0.958596i	$-0.591917\pi$
$233$	10.2855	−	10.2855i	0.673827	−	0.673827i	0.958596	+	0.284769i	$0.0919169\pi$
$234$	1.41477	−	2.15713i	0.0924866	−	0.141016i
$235$	−13.7565	−	10.6408i	−0.897372	−	0.694126i
$236$	1.97825	−	0.859411i	0.128773	−	0.0559429i
$237$	2.39800	+	2.39800i	0.155767	+	0.155767i
$238$	−6.92541	−	33.3221i	−0.448908	−	2.15995i
$239$	3.19293			0.206534			0.103267	−	0.994654i	$-0.467070\pi$
$239$	3.19293			0.206534			0.103267	+	0.994654i	$0.467070\pi$
$240$	2.34690	+	14.4252i	0.151492	+	0.931144i
$241$	−11.7591			−0.757470			−0.378735	−	0.925505i	$-0.623641\pi$
$241$	−11.7591			−0.757470			−0.378735	+	0.925505i	$0.623641\pi$
$242$	2.84225	+	13.6757i	0.182707	+	0.879107i
$243$	2.41401	+	2.41401i	0.154859	+	0.154859i
$244$	20.2662	−	8.80425i	1.29741	−	0.563634i
$245$	−31.7130	+	4.04997i	−2.02607	+	0.258743i
$246$	−4.45698	+	6.79563i	−0.284167	+	0.433274i
$247$	3.90789	−	3.90789i	0.248653	−	0.248653i
$248$	4.86387	−	3.43392i	0.308856	−	0.218054i
$249$		−	4.82595i		−	0.305832i
$250$	13.1736	−	8.74387i	0.833174	−	0.553011i
$251$		−	14.5530i		−	0.918575i	−0.888288	−	0.459287i	$-0.848105\pi$
$251$		−	14.5530i		−	0.918575i	0.888288	−	0.459287i	$-0.151895\pi$
$252$	2.83409	+	1.11743i	0.178531	+	0.0703917i
$253$	3.06883	−	3.06883i	0.192936	−	0.192936i
$254$	10.8081	+	7.08861i	0.678162	+	0.444779i
$255$	−18.8998	+	2.41364i	−1.18355	+	0.151148i
$256$	−1.09552	−	15.9625i	−0.0684697	−	0.997653i
$257$	−11.5648	−	11.5648i	−0.721392	−	0.721392i	0.247496	−	0.968889i	$-0.420392\pi$
$257$	−11.5648	−	11.5648i	−0.721392	−	0.721392i	−0.968889	+	0.247496i	$0.920392\pi$
$258$	−4.78947	+	0.995406i	−0.298180	+	0.0619713i
$259$	19.6631			1.22180
$260$	−23.9561	−	6.07999i	−1.48570	−	0.377065i
$261$	0.473312			0.0292973
$262$	−15.6137	+	3.24503i	−0.964618	+	0.200478i
$263$	0.240407	+	0.240407i	0.0148241	+	0.0148241i	0.714480	−	0.699656i	$-0.246663\pi$
$263$	0.240407	+	0.240407i	0.0148241	+	0.0148241i	−0.699656	+	0.714480i	$0.746663\pi$
$264$	−20.8100	−	3.58618i	−1.28077	−	0.220714i
$265$	−14.8212	−	11.4644i	−0.910461	−	0.704251i
$266$	5.45745	+	3.57932i	0.334618	+	0.219462i
$267$	−12.6703	+	12.6703i	−0.775411	+	0.775411i
$268$	−1.34547	+	3.41246i	−0.0821879	+	0.208449i
$269$			5.22590i			0.318629i	0.987228	+	0.159314i	$0.0509283\pi$
$269$			5.22590i			0.318629i	−0.987228	+	0.159314i	$0.949072\pi$
$270$	7.53803	−	15.4679i	0.458750	−	0.941346i
$271$			10.0441i			0.610137i	0.952330	+	0.305069i	$0.0986794\pi$
$271$			10.0441i			0.610137i	−0.952330	+	0.305069i	$0.901321\pi$
$272$	20.8468	−	0.714526i	1.26402	−	0.0433245i
$273$	29.4685	−	29.4685i	1.78352	−	1.78352i
$274$	5.38769	−	8.21471i	0.325482	−	0.496269i
$275$	5.74145	+	22.1124i	0.346222	+	1.33343i
$276$	1.23684	+	2.84705i	0.0744491	+	0.171372i
$277$	−1.69900	−	1.69900i	−0.102083	−	0.102083i	0.654221	−	0.756304i	$-0.272997\pi$
$277$	−1.69900	−	1.69900i	−0.102083	−	0.102083i	−0.756304	+	0.654221i	$0.772997\pi$
$278$	4.00935	+	19.2913i	0.240465	+	1.15702i
$279$	−0.694788			−0.0415959
$280$	1.27315	−	29.1596i	0.0760854	−	1.74262i
$281$	−8.96932			−0.535065			−0.267532	−	0.963549i	$-0.586208\pi$
$281$	−8.96932			−0.535065			−0.267532	+	0.963549i	$0.586208\pi$
$282$	3.65720	+	17.5969i	0.217783	+	1.04788i
$283$	−10.6254	−	10.6254i	−0.631617	−	0.631617i	0.316856	−	0.948474i	$-0.397373\pi$
$283$	−10.6254	−	10.6254i	−0.631617	−	0.631617i	−0.948474	+	0.316856i	$0.897373\pi$
$284$	−1.50066	−	3.45434i	−0.0890480	−	0.204977i
$285$	2.23548	−	2.89004i	0.132418	−	0.171191i
$286$	19.5850	−	29.8616i	1.15809	−	1.76575i
$287$	11.4764	−	11.4764i	0.677431	−	0.677431i
$288$	−0.969894	+	1.59543i	−0.0571516	+	0.0940119i
$289$			10.1937i			0.599632i
$290$	−1.47775	−	4.28720i	−0.0867763	−	0.251753i
$291$		−	3.97764i		−	0.233173i
$292$	3.32103	−	8.42296i	0.194349	−	0.492917i
$293$	21.8787	−	21.8787i	1.27817	−	1.27817i	0.336476	−	0.941692i	$-0.390765\pi$
$293$	21.8787	−	21.8787i	1.27817	−	1.27817i	0.941692	−	0.336476i	$-0.109235\pi$
$294$	27.6274	+	18.1197i	1.61126	+	1.05676i
$295$	0.305478	+	2.39202i	0.0177856	+	0.139269i
$296$	−2.04661	+	11.8761i	−0.118957	+	0.690287i
$297$	17.5800	+	17.5800i	1.02010	+	1.02010i
$298$	23.4543	−	4.87457i	1.35867	−	0.282376i
$299$	−5.24944			−0.303583
$300$	−16.2194	−	1.98090i	−0.936429	−	0.114367i
$301$	9.76946			0.563102
$302$	−32.4709	+	6.74850i	−1.86849	+	0.388333i
$303$	−17.7927	−	17.7927i	−1.02216	−	1.02216i
$304$	−2.72988	+	2.92365i	−0.156569	+	0.167683i
$305$	3.12948	+	24.5051i	0.179193	+	1.40316i
$306$	−2.03542	−	1.33495i	−0.116357	−	0.0763139i
$307$	16.5064	−	16.5064i	0.942071	−	0.942071i	−0.0563407	−	0.998412i	$-0.517943\pi$
$307$	16.5064	−	16.5064i	0.942071	−	0.942071i	0.998412	+	0.0563407i	$0.0179433\pi$
$308$	39.2329	+	15.4689i	2.23550	+	0.881421i
$309$		−	1.24340i		−	0.0707343i
$310$	2.16923	+	6.29331i	0.123204	+	0.357436i
$311$			19.4406i			1.10238i	0.834381	+	0.551188i	$0.185825\pi$
$311$			19.4406i			1.10238i	−0.834381	+	0.551188i	$0.814175\pi$
$312$	14.7313	+	20.8657i	0.833994	+	1.18129i
$313$	−8.63499	+	8.63499i	−0.488079	+	0.488079i	−0.907699	−	0.419621i	$-0.862163\pi$
$313$	−8.63499	+	8.63499i	−0.488079	+	0.488079i	0.419621	+	0.907699i	$0.362163\pi$
$314$	15.6497	−	23.8614i	0.883165	−	1.34658i
$315$	−2.08392	+	2.69411i	−0.117415	+	0.151796i
$316$	3.80717	−	1.65394i	0.214170	−	0.0930416i
$317$	13.6017	+	13.6017i	0.763949	+	0.763949i	0.977034	−	0.213085i	$-0.0683510\pi$
$317$	13.6017	+	13.6017i	0.763949	+	0.763949i	−0.213085	+	0.977034i	$0.568351\pi$
$318$	3.94027	+	18.9589i	0.220960	+	1.06316i
$319$	6.55216			0.366850
$320$	17.4794	+	3.80401i	0.977128	+	0.212651i
$321$	−4.97234			−0.277529
$322$	−1.26144	−	6.06952i	−0.0702974	−	0.338241i
$323$	−3.68739	−	3.68739i	−0.205172	−	0.205172i
$324$	−14.4932	+	6.29626i	−0.805177	+	0.349792i
$325$	14.0018	−	23.8229i	0.776678	−	1.32146i
$326$	−10.3964	+	15.8515i	−0.575801	+	0.877934i
$327$	−15.0147	+	15.0147i	−0.830313	+	0.830313i
$328$	5.73704	+	8.12606i	0.316775	+	0.448687i
$329$		−	35.8938i		−	1.97889i
$330$	10.3428	−	21.2232i	0.569352	−	1.16830i
$331$		−	21.6643i		−	1.19078i	−0.803437	−	0.595390i	$-0.796998\pi$
$331$		−	21.6643i		−	1.19078i	0.803437	−	0.595390i	$-0.203002\pi$
$332$	−5.49522	−	2.16667i	−0.301589	−	0.118912i
$333$	0.994410	−	0.994410i	0.0544934	−	0.0544934i
$334$	23.2997	+	15.2813i	1.27490	+	0.836155i
$335$	−3.24390	−	2.50919i	−0.177233	−	0.137092i
$336$	−20.5854	+	22.0466i	−1.12303	+	1.20274i
$337$	0.169255	+	0.169255i	0.00921991	+	0.00921991i	0.711702	−	0.702482i	$-0.247925\pi$
$337$	0.169255	+	0.169255i	0.00921991	+	0.00921991i	−0.702482	+	0.711702i	$0.747925\pi$
$338$	−24.2907	+	5.04839i	−1.32124	+	0.274596i
$339$	−10.5606			−0.573571
$340$	−5.73694	+	22.6045i	−0.311129	+	1.22590i
$341$	−9.61810			−0.520849
$342$	0.457012	−	0.0949818i	0.0247124	−	0.00513603i
$343$	−23.8141	−	23.8141i	−1.28584	−	1.28584i
$344$	−1.01684	+	5.90058i	−0.0548246	+	0.318138i
$345$	−3.44254	+	0.439637i	−0.185340	+	0.0236692i
$346$	−2.13849	−	1.40255i	−0.114966	−	0.0754016i
$347$	22.3067	−	22.3067i	1.19749	−	1.19749i	0.222569	−	0.974917i	$-0.428556\pi$
$347$	22.3067	−	22.3067i	1.19749	−	1.19749i	0.974917	−	0.222569i	$-0.0714443\pi$
$348$	−1.71895	+	4.35969i	−0.0921455	+	0.233704i
$349$			19.1551i			1.02535i	0.858583	+	0.512674i	$0.171345\pi$
$349$			19.1551i			1.02535i	−0.858583	+	0.512674i	$0.828655\pi$
$350$	30.9092	+	10.4645i	1.65216	+	0.559351i
$351$		−	30.0718i		−	1.60512i
$352$	−13.4264	+	22.0859i	−0.715632	+	1.17718i
$353$	0.692765	−	0.692765i	0.0368721	−	0.0368721i	−0.688430	−	0.725302i	$-0.741700\pi$
$353$	0.692765	−	0.692765i	0.0368721	−	0.0368721i	0.725302	+	0.688430i	$0.241700\pi$
$354$	1.36672	−	2.08386i	0.0726402	−	0.110756i
$355$	4.17684	−	0.533412i	0.221684	−	0.0283106i
$356$	8.73896	+	20.1160i	0.463164	+	1.06614i
$357$	−27.8058	−	27.8058i	−1.47164	−	1.47164i
$358$	1.14746	+	5.52109i	0.0606452	+	0.291799i
$359$	13.0487			0.688684			0.344342	−	0.938844i	$-0.388102\pi$
$359$	13.0487			0.688684			0.344342	+	0.938844i	$0.388102\pi$
$360$	−1.41029	−	1.53906i	−0.0743288	−	0.0811157i
$361$	1.00000			0.0526316
$362$	−5.56541	−	26.7784i	−0.292511	−	1.40744i
$363$	11.4118	+	11.4118i	0.598962	+	0.598962i
$364$	−20.3250	−	46.7855i	−1.06532	−	2.45223i
$365$	8.00692	+	6.19343i	0.419101	+	0.324179i
$366$	14.0014	−	21.3481i	0.731862	−	1.11588i
$367$	−12.7436	+	12.7436i	−0.665208	+	0.665208i	−0.956603	−	0.291395i	$-0.905881\pi$
$367$	−12.7436	+	12.7436i	−0.665208	+	0.665208i	0.291395	+	0.956603i	$0.405881\pi$
$368$	3.79718	−	0.130149i	0.197942	−	0.00678447i
$369$		−	1.16078i		−	0.0604279i
$370$	−12.1119	−	5.90256i	−0.629670	−	0.306860i
$371$		−	38.6720i		−	2.00775i
$372$	2.52330	−	6.39971i	0.130827	−	0.331810i
$373$	15.6699	−	15.6699i	0.811354	−	0.811354i	−0.173483	−	0.984837i	$-0.555502\pi$
$373$	15.6699	−	15.6699i	0.811354	−	0.811354i	0.984837	+	0.173483i	$0.0555021\pi$
$374$	−28.1767	−	18.4800i	−1.45698	−	0.955576i
$375$	7.18709	−	16.7955i	0.371139	−	0.867315i
$376$	21.6792	+	3.73596i	1.11802	+	0.192668i
$377$	−5.60395	−	5.60395i	−0.288618	−	0.288618i
$378$	34.7697	−	7.22626i	1.78836	−	0.371679i
$379$	−4.20942			−0.216223			−0.108112	−	0.994139i	$-0.534480\pi$
$379$	−4.20942			−0.216223			−0.108112	+	0.994139i	$0.534480\pi$
$380$	−2.28719	−	3.84301i	−0.117330	−	0.197142i
$381$	14.9340			0.765093
$382$	1.95860	−	0.407061i	0.100211	−	0.0208270i
$383$	23.3914	+	23.3914i	1.19524	+	1.19524i	0.975574	+	0.219671i	$0.0704983\pi$
$383$	23.3914	+	23.3914i	1.19524	+	1.19524i	0.219671	+	0.975574i	$0.429502\pi$
$384$	−11.1732	−	14.7279i	−0.570179	−	0.751582i
$385$	−28.8481	+	37.2951i	−1.47024	+	1.90073i
$386$	13.2036	+	8.65967i	0.672043	+	0.440766i
$387$	0.494066	−	0.494066i	0.0251148	−	0.0251148i
$388$	−4.52926	−	1.78581i	−0.229938	−	0.0906608i
$389$		−	12.7135i		−	0.644603i	−0.946637	−	0.322301i	$-0.895544\pi$
$389$		−	12.7135i		−	0.644603i	0.946637	−	0.322301i	$-0.104456\pi$
$390$	−26.9979	+	9.30583i	−1.36709	+	0.471219i
$391$			4.95325i			0.250497i
$392$	33.0362	−	23.3237i	1.66858	−	1.17802i
$393$	−13.0289	+	13.0289i	−0.657223	+	0.657223i
$394$	−19.0310	+	29.0169i	−0.958767	+	1.46185i
$395$	0.587896	+	4.60347i	0.0295803	+	0.231626i
$396$	2.76641	−	1.20181i	0.139017	−	0.0603931i
$397$	25.9638	+	25.9638i	1.30308	+	1.30308i	0.926302	+	0.376783i	$0.122970\pi$
$397$	25.9638	+	25.9638i	1.30308	+	1.30308i	0.376783	+	0.926302i	$0.377030\pi$
$398$	−6.33264	−	30.4700i	−0.317426	−	1.52732i
$399$	7.54078			0.377511
$400$	−9.53753	+	17.5794i	−0.476876	+	0.878970i
$401$	11.2570			0.562146			0.281073	−	0.959686i	$-0.409310\pi$
$401$	11.2570			0.562146			0.281073	+	0.959686i	$0.409310\pi$
$402$	0.862403	+	4.14952i	0.0430127	+	0.206959i
$403$	8.22620	+	8.22620i	0.409776	+	0.409776i
$404$	−28.2485	+	12.2720i	−1.40541	+	0.610553i
$405$	−2.23801	−	17.5246i	−0.111208	−	0.870803i
$406$	5.13278	−	7.82604i	0.254736	−	0.388400i
$407$	13.7658	−	13.7658i	0.682347	−	0.682347i
$408$	19.6884	−	13.9001i	0.974720	−	0.688157i
$409$			31.3473i			1.55003i	0.631945	+	0.775013i	$0.282257\pi$
$409$			31.3473i			1.55003i	−0.631945	+	0.775013i	$0.717743\pi$
$410$	−10.5142	+	3.62412i	−0.519260	+	0.178983i
$411$		−	11.3506i		−	0.559884i
$412$	−1.41583	−	0.558238i	−0.0697530	−	0.0275024i
$413$	−3.51920	+	3.51920i	−0.173169	+	0.173169i
$414$	−0.370745	−	0.243157i	−0.0182211	−	0.0119505i
$415$	4.04066	−	5.22379i	0.198348	−	0.256426i
$416$	30.3731	−	7.40631i	1.48917	−	0.363124i
$417$	16.0977	+	16.0977i	0.788310	+	0.788310i
$418$	6.32652	−	1.31485i	0.309440	−	0.0643116i
$419$	−14.6694			−0.716648			−0.358324	−	0.933597i	$-0.616652\pi$
$419$	−14.6694			−0.716648			−0.358324	+	0.933597i	$0.616652\pi$
$420$	−17.2472	−	28.9793i	−0.841577	−	1.41405i
$421$	−2.62268			−0.127822			−0.0639108	−	0.997956i	$-0.520357\pi$
$421$	−2.62268			−0.127822			−0.0639108	+	0.997956i	$0.520357\pi$
$422$	−18.3631	+	3.81644i	−0.893901	+	0.185781i
$423$	−1.81524	−	1.81524i	−0.0882599	−	0.0882599i
$424$	23.3572	+	4.02513i	1.13433	+	0.195478i
$425$	−22.4787	−	13.2117i	−1.09038	−	0.640864i
$426$	−3.63874	−	2.38650i	−0.176297	−	0.115626i
$427$	−36.0525	+	36.0525i	−1.74470	+	1.74470i
$428$	−2.23239	+	5.66191i	−0.107907	+	0.273679i
$429$		−	41.2610i		−	1.99210i
$430$	−6.01773	−	2.93265i	−0.290201	−	0.141425i
$431$			16.4900i			0.794295i	0.917755	+	0.397148i	$0.130000\pi$
$431$			16.4900i			0.794295i	−0.917755	+	0.397148i	$0.870000\pi$
$432$	0.745567	+	21.7524i	0.0358711	+	1.04656i
$433$	−2.04849	+	2.04849i	−0.0984443	+	0.0984443i	−0.754614	−	0.656169i	$-0.772176\pi$
$433$	−2.04849	+	2.04849i	−0.0984443	+	0.0984443i	0.656169	+	0.754614i	$0.272176\pi$
$434$	−7.53456	+	11.4881i	−0.361670	+	0.551445i
$435$	−4.14435	−	3.20570i	−0.198706	−	0.153701i
$436$	10.3559	+	23.8379i	0.495957	+	1.14163i
$437$	−0.671647	−	0.671647i	−0.0321292	−	0.0321292i
$438$	−2.12867	−	10.2422i	−0.101712	−	0.489393i
$439$	−21.5207			−1.02712			−0.513562	−	0.858052i	$-0.671675\pi$
$439$	−21.5207			−1.02712			−0.513562	+	0.858052i	$0.671675\pi$
$440$	−19.5229	−	21.3056i	−0.930720	−	1.01570i
$441$	−4.71911			−0.224719
$442$	8.29347	+	39.9047i	0.394480	+	1.89807i
$443$	3.24964	+	3.24964i	0.154395	+	0.154395i	0.780078	−	0.625683i	$-0.215180\pi$
$443$	3.24964	+	3.24964i	0.154395	+	0.154395i	−0.625683	+	0.780078i	$0.715180\pi$
$444$	5.54809	+	12.7710i	0.263301	+	0.606084i
$445$	−24.3234	+	3.10627i	−1.15304	+	0.147251i
$446$	6.69954	−	10.2149i	0.317233	−	0.483690i
$447$	19.5716	−	19.5716i	0.925705	−	0.925705i
$448$	15.8620	+	33.3384i	0.749410	+	1.57509i
$449$			37.4922i			1.76937i	0.466193	+	0.884683i	$0.345625\pi$
$449$			37.4922i			1.76937i	−0.466193	+	0.884683i	$0.654375\pi$
$450$	2.09237	−	1.03394i	0.0986353	−	0.0487403i
$451$		−	16.0689i		−	0.756657i
$452$	−4.74130	+	12.0251i	−0.223012	+	0.565614i
$453$	−27.0956	+	27.0956i	−1.27306	+	1.27306i
$454$	24.9163	+	16.3416i	1.16938	+	0.766949i
$455$	56.5711	−	7.22454i	2.65210	−	0.338691i
$456$	−0.784875	+	4.55450i	−0.0367551	+	0.213284i
$457$	4.61218	+	4.61218i	0.215749	+	0.215749i	0.806704	−	0.590956i	$-0.201249\pi$
$457$	4.61218	+	4.61218i	0.215749	+	0.215749i	−0.590956	+	0.806704i	$0.701249\pi$
$458$	35.4606	−	7.36985i	1.65696	−	0.344370i
$459$	−28.3751			−1.32444
$460$	−1.04497	+	4.11733i	−0.0487218	+	0.191972i
$461$	15.1656			0.706330			0.353165	−	0.935561i	$-0.385105\pi$
$461$	15.1656			0.706330			0.353165	+	0.935561i	$0.385105\pi$
$462$	47.7069	−	9.91502i	2.21952	−	0.461289i
$463$	23.1697	+	23.1697i	1.07679	+	1.07679i	0.996795	+	0.0799921i	$0.0254895\pi$
$463$	23.1697	+	23.1697i	1.07679	+	1.07679i	0.0799921	+	0.996795i	$0.474510\pi$
$464$	4.19255	+	3.91468i	0.194634	+	0.181734i
$465$	6.08361	+	4.70573i	0.282121	+	0.218223i
$466$	−17.2015	−	11.2817i	−0.796842	−	0.522616i
$467$	20.1047	−	20.1047i	0.930336	−	0.930336i	−0.0673906	−	0.997727i	$-0.521467\pi$
$467$	20.1047	−	20.1047i	0.930336	−	0.930336i	0.997727	+	0.0673906i	$0.0214674\pi$
$468$	−3.39395	−	1.33818i	−0.156885	−	0.0618572i
$469$		−	8.46409i		−	0.390835i
$470$	−10.7748	+	22.1096i	−0.497003	+	1.01984i
$471$		−	32.9703i		−	1.51919i
$472$	−1.75924	−	2.49183i	−0.0809758	−	0.114696i
$473$	6.83946	−	6.83946i	0.314479	−	0.314479i
$474$	2.63026	−	4.01040i	0.120812	−	0.184204i
$475$	4.83953	−	1.25658i	0.222053	−	0.0576557i
$476$	−44.1458	+	19.1782i	−2.02342	+	0.879031i
$477$	−1.95574	−	1.95574i	−0.0895472	−	0.0895472i
$478$	−0.918829	−	4.42102i	−0.0420263	−	0.202213i
$479$	10.8855			0.497370			0.248685	−	0.968584i	$-0.420002\pi$
$479$	10.8855			0.497370			0.248685	+	0.968584i	$0.420002\pi$
$480$	19.2982	−	7.40072i	0.880837	−	0.337795i
$481$	−23.5474			−1.07367
$482$	3.38391	+	16.2820i	0.154133	+	0.741623i
$483$	−5.06474	−	5.06474i	−0.230454	−	0.230454i
$484$	18.1178	−	7.87090i	0.823537	−	0.357768i
$485$	3.33038	−	4.30554i	0.151225	−	0.195505i
$486$	2.64782	−	4.03718i	0.120108	−	0.183130i
$487$	−21.7783	+	21.7783i	−0.986867	+	0.986867i	−0.999915	−	0.0130478i	$-0.995847\pi$
$487$	−21.7783	+	21.7783i	−0.986867	+	0.986867i	0.0130478	+	0.999915i	$0.495847\pi$
$488$	−18.0226	−	25.5276i	−0.815845	−	1.15558i
$489$			21.9027i			0.990473i
$490$	14.7337	+	42.7451i	0.665602	+	1.93103i
$491$		−	2.46368i		−	0.111185i	−0.998454	−	0.0555923i	$-0.982295\pi$
$491$		−	2.46368i		−	0.111185i	0.998454	−	0.0555923i	$-0.0177047\pi$
$492$	10.6920	+	4.21567i	0.482032	+	0.190057i
$493$	−5.28776	+	5.28776i	−0.238149	+	0.238149i
$494$	−6.53553	−	4.28639i	−0.294047	−	0.192854i
$495$	0.427184	+	3.34503i	0.0192005	+	0.150348i
$496$	−6.15437	−	5.74647i	−0.276339	−	0.258024i
$497$	6.14507	+	6.14507i	0.275644	+	0.275644i
$498$	−6.68214	+	1.38876i	−0.299434	+	0.0622320i
$499$	23.3731			1.04632			0.523161	−	0.852234i	$-0.324753\pi$
$499$	23.3731			1.04632			0.523161	+	0.852234i	$0.324753\pi$
$500$	−15.8980	−	15.7243i	−0.710978	−	0.703214i
$501$	32.1941			1.43833
$502$	−20.1504	+	4.18790i	−0.899357	+	0.186915i
$503$	−10.6038	−	10.6038i	−0.472800	−	0.472800i	0.430019	−	0.902820i	$-0.358507\pi$
$503$	−10.6038	−	10.6038i	−0.472800	−	0.472800i	−0.902820	+	0.430019i	$0.858507\pi$
$504$	0.731663	−	4.24572i	0.0325908	−	0.189119i
$505$	−4.36208	−	34.1569i	−0.194110	−	1.51996i
$506$	−5.13230	−	3.36607i	−0.228159	−	0.149640i
$507$	−20.2695	+	20.2695i	−0.900201	+	0.900201i
$508$	6.70482	−	17.0051i	0.297478	−	0.754479i
$509$		−	17.1016i		−	0.758015i	−0.925394	−	0.379007i	$-0.876266\pi$
$509$		−	17.1016i		−	0.758015i	0.925394	−	0.379007i	$-0.123734\pi$
$510$	8.78077	+	25.4746i	0.388819	+	1.12803i
$511$			20.8919i			0.924203i
$512$	−21.7868	+	6.11039i	−0.962848	+	0.270044i
$513$	3.84758	−	3.84758i	0.169875	−	0.169875i
$514$	−12.6849	+	19.3409i	−0.559508	+	0.853091i
$515$	1.04107	−	1.34590i	0.0458748	−	0.0593074i
$516$	2.75653	+	6.34518i	0.121349	+	0.279331i
$517$	−25.1287	−	25.1287i	−1.10516	−	1.10516i
$518$	−5.65843	−	27.2260i	−0.248617	−	1.19624i
$519$	−2.95484			−0.129703
$520$	−1.52465	+	34.9199i	−0.0668605	+	1.53134i
$521$	−4.34873			−0.190521			−0.0952606	−	0.995452i	$-0.530368\pi$
$521$	−4.34873			−0.190521			−0.0952606	+	0.995452i	$0.530368\pi$
$522$	−0.136205	−	0.655360i	−0.00596153	−	0.0286843i
$523$	27.4034	+	27.4034i	1.19827	+	1.19827i	0.974685	+	0.223581i	$0.0717747\pi$
$523$	27.4034	+	27.4034i	1.19827	+	1.19827i	0.223581	+	0.974685i	$0.428225\pi$
$524$	8.98630	+	20.6853i	0.392568	+	0.903642i
$525$	36.4938	−	9.47558i	1.59272	−	0.413548i
$526$	0.263692	−	0.402056i	0.0114975	−	0.0175305i
$527$	7.76206	−	7.76206i	0.338120	−	0.338120i
$528$	1.02298	+	29.8461i	0.0445194	+	1.29889i
$529$		−	22.0978i		−	0.960773i
$530$	−11.6088	+	23.8210i	−0.504252	+	1.03472i
$531$			0.355950i			0.0154469i
$532$	3.38553	−	8.58655i	0.146781	−	0.372274i
$533$	−13.7435	+	13.7435i	−0.595297	+	0.595297i
$534$	21.1898	+	13.8975i	0.916972	+	0.601405i
$535$	−5.38224	−	4.16322i	−0.232695	−	0.179992i
$536$	5.11216	+	0.880976i	0.220812	+	0.0380524i
$537$	4.60711	+	4.60711i	0.198811	+	0.198811i
$538$	7.23591	−	1.50386i	0.311962	−	0.0648358i
$539$	−65.3276			−2.81386
$540$	−23.5865	−	5.98616i	−1.01500	−	0.257603i
$541$	15.7990			0.679254			0.339627	−	0.940560i	$-0.389699\pi$
$541$	15.7990			0.679254			0.339627	+	0.940560i	$0.389699\pi$
$542$	13.9074	−	2.89040i	0.597372	−	0.124153i
$543$	−22.3454	−	22.3454i	−0.958931	−	0.958931i
$544$	−6.98843	−	28.6594i	−0.299626	−	1.22876i
$545$	−28.8239	+	3.68101i	−1.23468	+	0.157677i
$546$	−49.2830	−	32.3227i	−2.10912	−	1.38329i
$547$	−15.7388	+	15.7388i	−0.672943	+	0.672943i	−0.958394	−	0.285450i	$-0.907857\pi$
$547$	−15.7388	+	15.7388i	−0.672943	+	0.672943i	0.285450	+	0.958394i	$0.407857\pi$
$548$	−12.9247	−	5.09599i	−0.552116	−	0.217690i
$549$			3.64653i			0.155630i
$550$	28.9651	−	14.3130i	1.23508	−	0.610309i
$551$		−	1.43401i		−	0.0610909i
$552$	3.58618	−	2.53186i	0.152638	−	0.107763i
$553$	−6.77274	+	6.77274i	−0.288006	+	0.288006i
$554$	−1.86356	+	2.84140i	−0.0791749	+	0.120719i
$555$	−15.4422	+	1.97207i	−0.655483	+	0.0837098i
$556$	25.5575	−	11.1029i	1.08388	−	0.470868i
$557$	−17.9451	−	17.9451i	−0.760359	−	0.760359i	0.216029	−	0.976387i	$-0.430690\pi$
$557$	−17.9451	−	17.9451i	−0.760359	−	0.760359i	−0.976387	+	0.216029i	$0.930690\pi$
$558$	0.199939	+	0.962022i	0.00846410	+	0.0407256i
$559$	−11.6993			−0.494830
$560$	−40.7416	+	6.62842i	−1.72165	+	0.280102i
$561$	−38.9329			−1.64375
$562$	2.58110	+	12.4192i	0.108877	+	0.523870i
$563$	−20.3784	−	20.3784i	−0.858847	−	0.858847i	0.132355	−	0.991202i	$-0.457746\pi$
$563$	−20.3784	−	20.3784i	−0.858847	−	0.858847i	−0.991202	+	0.132355i	$0.957746\pi$
$564$	23.3127	−	10.1277i	0.981641	−	0.426453i
$565$	−11.4311	−	8.84211i	−0.480912	−	0.371990i
$566$	−11.6546	+	17.7699i	−0.489879	+	0.746927i
$567$	25.7826	−	25.7826i	1.08277	−	1.08277i
$568$	−4.35112	+	3.07191i	−0.182569	+	0.128895i
$569$		−	15.5685i		−	0.652665i	−0.945255	−	0.326333i	$-0.894187\pi$
$569$		−	15.5685i		−	0.652665i	0.945255	−	0.326333i	$-0.105813\pi$
$570$	−4.64493	−	2.26363i	−0.194555	−	0.0948131i
$571$			21.2800i			0.890540i	0.895396	+	0.445270i	$0.146892\pi$
$571$			21.2800i			0.890540i	−0.895396	+	0.445270i	$0.853108\pi$
$572$	−46.9831	−	18.5246i	−1.96446	−	0.774554i
$573$	1.63437	−	1.63437i	0.0682767	−	0.0682767i
$574$	−19.1931	−	12.5880i	−0.801104	−	0.525412i
$575$	−4.09443	−	2.40648i	−0.170750	−	0.100357i
$576$	2.48819	+	0.883823i	0.103674	+	0.0368259i
$577$	7.89632	+	7.89632i	0.328728	+	0.328728i	0.852103	−	0.523375i	$-0.175327\pi$
$577$	7.89632	+	7.89632i	0.328728	+	0.328728i	−0.523375	+	0.852103i	$0.675327\pi$
$578$	14.1145	−	2.93345i	0.587086	−	0.122015i
$579$	18.2439			0.758190
$580$	−5.51092	+	3.27985i	−0.228829	+	0.136189i
$581$	13.6301			0.565471
$582$	−5.50754	+	1.14464i	−0.228295	+	0.0474470i
$583$	−27.0737	−	27.0737i	−1.12128	−	1.12128i
$584$	−12.6183	−	2.17451i	−0.522151	−	0.0899819i
$585$	2.49558	−	3.22631i	0.103180	−	0.133391i
$586$	−36.5899	−	23.9978i	−1.51151	−	0.991340i
$587$	−20.8805	+	20.8805i	−0.861831	+	0.861831i	−0.991551	−	0.129720i	$-0.958592\pi$
$587$	−20.8805	+	20.8805i	−0.861831	+	0.861831i	0.129720	+	0.991551i	$0.458592\pi$
$588$	17.1386	−	43.4678i	0.706785	−	1.79258i
$589$			2.10503i			0.0867361i
$590$	3.22415	−	1.11133i	0.132736	−	0.0457525i
$591$			40.0938i			1.64924i
$592$	17.0330	−	0.583806i	0.700051	−	0.0239943i
$593$	4.40488	−	4.40488i	0.180887	−	0.180887i	−0.610855	−	0.791742i	$-0.709174\pi$
$593$	4.40488	−	4.40488i	0.180887	−	0.180887i	0.791742	+	0.610855i	$0.209174\pi$
$594$	19.2828	−	29.4008i	0.791182	−	1.20633i
$595$	−6.81691	−	53.3792i	−0.279466	−	2.18834i
$596$	−13.4989	−	31.0727i	−0.552936	−	1.27279i
$597$	−25.4258	−	25.4258i	−1.04061	−	1.04061i
$598$	1.51063	+	7.26851i	0.0617743	+	0.297232i
$599$	22.4494			0.917256			0.458628	−	0.888628i	$-0.348341\pi$
$599$	22.4494			0.917256			0.458628	+	0.888628i	$0.348341\pi$
$600$	1.92466	+	23.0279i	0.0785740	+	0.940109i
$601$	−2.44752			−0.0998364			−0.0499182	−	0.998753i	$-0.515896\pi$
$601$	−2.44752			−0.0998364			−0.0499182	+	0.998753i	$0.515896\pi$
$602$	−2.81135	−	13.5270i	−0.114582	−	0.551321i
$603$	−0.428050	−	0.428050i	−0.0174316	−	0.0174316i
$604$	18.6883	+	43.0181i	0.760416	+	1.75038i
$605$	2.79772	+	21.9073i	0.113743	+	0.890659i
$606$	−19.5160	+	29.7564i	−0.792785	+	1.20877i
$607$	−8.33475	+	8.33475i	−0.338297	+	0.338297i	−0.855726	−	0.517429i	$-0.826889\pi$
$607$	−8.33475	+	8.33475i	−0.338297	+	0.338297i	0.517429	+	0.855726i	$0.326889\pi$
$608$	4.83374	+	2.93852i	0.196034	+	0.119173i
$609$		−	10.8136i		−	0.438188i
$610$	33.0299	−	11.3850i	1.33734	−	0.460965i
$611$			42.9843i			1.73896i
$612$	−1.26267	+	3.20245i	−0.0510405	+	0.129451i
$613$	−24.6735	+	24.6735i	−0.996555	+	0.996555i	−0.999994	−	0.00343930i	$-0.998905\pi$
$613$	−24.6735	+	24.6735i	−0.996555	+	0.996555i	0.00343930	+	0.999994i	$0.498905\pi$
$614$	−27.6053	−	18.1052i	−1.11406	−	0.730665i
$615$	−7.86186	+	10.1639i	−0.317021	+	0.409847i
$616$	10.1286	−	58.7744i	0.408091	−	2.36809i
$617$	−2.72052	−	2.72052i	−0.109524	−	0.109524i	0.650221	−	0.759745i	$-0.274676\pi$
$617$	−2.72052	−	2.72052i	−0.109524	−	0.109524i	−0.759745	+	0.650221i	$0.774676\pi$
$618$	−1.72164	+	0.357812i	−0.0692544	+	0.0143933i
$619$	−21.6528			−0.870300			−0.435150	−	0.900358i	$-0.643305\pi$
$619$	−21.6528			−0.870300			−0.435150	+	0.900358i	$0.643305\pi$
$620$	8.08964	−	4.81459i	0.324888	−	0.193359i
$621$	−5.16843			−0.207402
$622$	26.9179	−	5.59441i	1.07931	−	0.224316i
$623$	−35.7852	−	35.7852i	−1.43370	−	1.43370i
$624$	24.6519	−	26.4018i	0.986867	−	1.05692i
$625$	21.8420	−	12.1625i	0.873681	−	0.486499i
$626$	14.4411	+	9.47134i	0.577183	+	0.378551i
$627$	5.27920	−	5.27920i	0.210831	−	0.210831i
$628$	−37.5426	−	14.8024i	−1.49811	−	0.590681i
$629$			22.2188i			0.885920i
$630$	4.33002	+	2.11016i	0.172512	+	0.0840710i
$631$			31.3301i			1.24723i	0.781731	+	0.623616i	$0.214337\pi$
$631$			31.3301i			1.24723i	−0.781731	+	0.623616i	$0.785663\pi$
$632$	−3.38568	−	4.79555i	−0.134675	−	0.190757i
$633$	−15.3232	+	15.3232i	−0.609041	+	0.609041i
$634$	14.9191	−	22.7475i	0.592515	−	0.903417i
$635$	16.1652	+	12.5039i	0.641494	+	0.496202i
$636$	25.1171	−	10.9116i	0.995959	−	0.432673i
$637$	55.8736	+	55.8736i	2.21379	+	2.21379i
$638$	−1.88551	−	9.07229i	−0.0746482	−	0.359175i
$639$	0.621543			0.0245879
$640$	0.237093	−	25.2971i	0.00937193	−	0.999956i
$641$	−38.8191			−1.53326			−0.766631	−	0.642088i	$-0.778068\pi$
$641$	−38.8191			−1.53326			−0.766631	+	0.642088i	$0.778068\pi$
$642$	1.43089	+	6.88483i	0.0564727	+	0.271722i
$643$	30.5752	+	30.5752i	1.20577	+	1.20577i	0.972385	+	0.233384i	$0.0749800\pi$
$643$	30.5752	+	30.5752i	1.20577	+	1.20577i	0.233384	+	0.972385i	$0.425020\pi$
$644$	−8.04101	+	3.49325i	−0.316860	+	0.137653i
$645$	−7.67233	+	0.979811i	−0.302098	+	0.0385800i
$646$	−4.04454	+	6.16678i	−0.159130	+	0.242629i
$647$	21.3825	−	21.3825i	0.840632	−	0.840632i	−0.148309	−	0.988941i	$-0.547383\pi$
$647$	21.3825	−	21.3825i	0.840632	−	0.840632i	0.988941	+	0.148309i	$0.0473831\pi$
$648$	12.8887	+	18.2558i	0.506314	+	0.717154i
$649$			4.92749i			0.193421i
$650$	−37.0151	−	12.5317i	−1.45185	−	0.491533i
$651$			15.8735i			0.622133i
$652$	24.9402	+	9.83348i	0.976732	+	0.385109i
$653$	9.46388	−	9.46388i	0.370350	−	0.370350i	−0.497255	−	0.867605i	$-0.665658\pi$
$653$	9.46388	−	9.46388i	0.370350	−	0.370350i	0.867605	+	0.497255i	$0.165658\pi$
$654$	25.1105	+	16.4689i	0.981897	+	0.643986i
$655$	−25.0118	+	3.19419i	−0.977293	+	0.124807i
$656$	9.60061	−	10.2821i	0.374841	−	0.401448i
$657$	1.05656	+	1.05656i	0.0412202	+	0.0412202i
$658$	−49.6994	+	10.3291i	−1.93749	+	0.402672i
$659$	14.8386			0.578029			0.289014	−	0.957325i	$-0.406672\pi$
$659$	14.8386			0.578029			0.289014	+	0.957325i	$0.406672\pi$
$660$	−32.3625	−	8.21350i	−1.25971	−	0.319710i
$661$	31.5760			1.22817			0.614083	−	0.789242i	$-0.289526\pi$
$661$	31.5760			1.22817			0.614083	+	0.789242i	$0.289526\pi$
$662$	−29.9970	+	6.23434i	−1.16587	+	0.242305i
$663$	33.2987	+	33.2987i	1.29321	+	1.29321i
$664$	−1.41867	+	8.23233i	−0.0550552	+	0.319476i
$665$	8.16243	+	6.31372i	0.316525	+	0.244836i
$666$	−1.66305	−	1.09073i	−0.0644418	−	0.0422647i
$667$	−0.963149	+	0.963149i	−0.0372933	+	0.0372933i
$668$	14.4539	−	36.6588i	0.559240	−	1.41837i
$669$		−	14.1144i		−	0.545693i
$670$	−2.54080	+	5.21366i	−0.0981595	+	0.201421i
$671$			50.4797i			1.94875i
$672$	36.4502	+	22.1588i	1.40610	+	0.854793i
$673$	18.0004	−	18.0004i	0.693866	−	0.693866i	−0.269215	−	0.963080i	$-0.586764\pi$
$673$	18.0004	−	18.0004i	0.693866	−	0.693866i	0.963080	+	0.269215i	$0.0867641\pi$
$674$	0.185648	−	0.283061i	0.00715091	−	0.0109031i
$675$	13.7857	−	23.4553i	0.530611	−	0.902793i
$676$	13.9803	+	32.1808i	0.537702	+	1.23772i
$677$	20.3423	+	20.3423i	0.781819	+	0.781819i	0.980138	−	0.198319i	$-0.0635481\pi$
$677$	20.3423	+	20.3423i	0.781819	+	0.781819i	−0.198319	+	0.980138i	$0.563548\pi$
$678$	3.03901	+	14.6224i	0.116712	+	0.561571i
$679$	11.2342			0.431127
$680$	32.9497	+	1.43863i	1.26356	+	0.0551689i
$681$	34.4279			1.31928
$682$	2.76780	+	13.3175i	0.105984	+	0.509952i
$683$	31.7484	+	31.7484i	1.21482	+	1.21482i	0.969423	+	0.245396i	$0.0789181\pi$
$683$	31.7484	+	31.7484i	1.21482	+	1.21482i	0.245396	+	0.969423i	$0.421082\pi$
$684$	−0.263028	−	0.605458i	−0.0100571	−	0.0231503i
$685$	9.50359	−	12.2863i	0.363113	−	0.469436i
$686$	−26.1206	+	39.8266i	−0.997290	+	1.52059i
$687$	29.5903	−	29.5903i	1.12894	−	1.12894i
$688$	8.46272	−	0.290060i	0.322638	−	0.0110584i
$689$			46.3114i			1.76432i
$690$	1.59939	+	4.64011i	0.0608877	+	0.176646i
$691$		−	2.26449i		−	0.0861453i	−0.999072	−	0.0430727i	$-0.986285\pi$
$691$		−	2.26449i		−	0.0861453i	0.999072	−	0.0430727i	$-0.0137147\pi$
$692$	−1.32661	+	3.36463i	−0.0504303	+	0.127904i
$693$	−4.92128	+	4.92128i	−0.186944	+	0.186944i
$694$	−37.3056	−	24.4672i	−1.41610	−	0.928763i
$695$	3.94654	+	30.9031i	0.149701	+	1.17222i
$696$	6.53120	+	1.12552i	0.247565	+	0.0426627i
$697$	12.9680	+	12.9680i	0.491200	+	0.491200i
$698$	26.5226	−	5.51225i	1.00390	−	0.208642i
$699$	−23.7680			−0.898987
$700$	5.59470	−	45.8090i	0.211460	−	1.73142i
$701$	1.89491			0.0715697			0.0357849	−	0.999360i	$-0.488607\pi$
$701$	1.89491			0.0715697			0.0357849	+	0.999360i	$0.488607\pi$
$702$	−41.6382	+	8.65376i	−1.57153	+	0.326615i
$703$	−3.01280	−	3.01280i	−0.113630	−	0.113630i
$704$	34.4445	+	12.2349i	1.29818	+	0.461122i
$705$	3.59990	+	28.1887i	0.135580	+	1.06165i
$706$	−1.15858	−	0.759863i	−0.0436036	−	0.0285978i
$707$	50.2525	−	50.2525i	1.88994	−	1.88994i
$708$	−3.27866	−	1.29272i	−0.123220	−	0.0485834i
$709$			6.93479i			0.260442i	0.991485	+	0.130221i	$0.0415686\pi$
$709$			6.93479i			0.260442i	−0.991485	+	0.130221i	$0.958431\pi$
$710$	−1.94054	−	5.62986i	−0.0728274	−	0.211285i
$711$			0.685029i			0.0256906i
$712$	25.3383	−	17.8889i	0.949592	−	0.670417i
$713$	1.41383	−	1.41383i	0.0529485	−	0.0529485i
$714$	−30.4990	+	46.5024i	−1.14140	+	1.74031i
$715$	34.5469	−	44.6624i	1.29198	−	1.67028i
$716$	7.31444	−	3.17761i	0.273354	−	0.118753i
$717$	−3.68914	−	3.68914i	−0.137773	−	0.137773i
$718$	−3.75502	−	18.0676i	−0.140136	−	0.674276i
$719$	−37.3420			−1.39262			−0.696311	−	0.717740i	$-0.745177\pi$
$719$	−37.3420			−1.39262			−0.696311	+	0.717740i	$0.745177\pi$
$720$	−1.72519	+	2.39562i	−0.0642939	+	0.0892795i
$721$	3.51176			0.130785
$722$	−0.287770	−	1.38463i	−0.0107097	−	0.0515304i
$723$	13.5866	+	13.5866i	0.505290	+	0.505290i
$724$	−35.4765	+	15.4120i	−1.31847	+	0.572783i
$725$	−1.80194	−	6.93993i	−0.0669226	−	0.257743i
$726$	12.5171	−	19.0850i	0.464552	−	0.708310i
$727$	17.4875	−	17.4875i	0.648575	−	0.648575i	−0.304074	−	0.952649i	$-0.598347\pi$
$727$	17.4875	−	17.4875i	0.648575	−	0.648575i	0.952649	+	0.304074i	$0.0983469\pi$
$728$	−58.9315	+	41.6060i	−2.18415	+	1.54202i
$729$		−	29.2810i		−	1.08448i
$730$	6.27144	−	12.8689i	0.232116	−	0.476298i
$731$			11.0392i			0.408301i
$732$	−33.5883	−	13.2433i	−1.24146	−	0.489486i
$733$	−0.838043	+	0.838043i	−0.0309538	+	0.0309538i	−0.722414	−	0.691460i	$-0.756968\pi$
$733$	−0.838043	+	0.838043i	−0.0309538	+	0.0309538i	0.691460	+	0.722414i	$0.256968\pi$
$734$	21.3123	+	13.9778i	0.786650	+	0.515932i
$735$	41.3208	+	31.9621i	1.52414	+	1.17894i
$736$	−1.27292	−	5.22022i	−0.0469205	−	0.192420i
$737$	−5.92559	−	5.92559i	−0.218272	−	0.218272i
$738$	−1.60725	+	0.334038i	−0.0591636	+	0.0122961i
$739$	−2.99968			−0.110345			−0.0551725	−	0.998477i	$-0.517571\pi$
$739$	−2.99968			−0.110345			−0.0551725	+	0.998477i	$0.517571\pi$
$740$	−4.68739	+	18.4691i	−0.172312	+	0.678937i
$741$	−9.03041			−0.331740
$742$	−53.5462	+	11.1286i	−1.96574	+	0.408545i
$743$	−29.6466	−	29.6466i	−1.08763	−	1.08763i	−0.995772	−	0.0918551i	$-0.970720\pi$
$743$	−29.6466	−	29.6466i	−1.08763	−	1.08763i	−0.0918551	−	0.995772i	$-0.529280\pi$
$744$	−9.58734	−	1.65218i	−0.351489	−	0.0605719i
$745$	37.5719	−	4.79820i	1.37653	−	0.175792i
$746$	−26.2062	−	17.1876i	−0.959477	−	0.629282i
$747$	0.689307	−	0.689307i	0.0252204	−	0.0252204i
$748$	−17.4794	+	44.3322i	−0.639111	+	1.62095i
$749$		−	14.0435i		−	0.513139i
$750$	−25.3237	−	5.11819i	−0.924690	−	0.186890i
$751$			17.4677i			0.637406i	0.947855	+	0.318703i	$0.103247\pi$
$751$			17.4677i			0.637406i	−0.947855	+	0.318703i	$0.896753\pi$
$752$	−1.06570	−	31.0927i	−0.0388622	−	1.13383i
$753$	−16.8146	+	16.8146i	−0.612759	+	0.612759i
$754$	−6.14673	+	9.37202i	−0.223851	+	0.341309i
$755$	−52.0157	+	6.64278i	−1.89305	+	0.241755i
$756$	−20.0113	−	46.0635i	−0.727805	−	1.67532i
$757$	8.92826	+	8.92826i	0.324503	+	0.324503i	0.850492	−	0.525988i	$-0.176305\pi$
$757$	8.92826	+	8.92826i	0.324503	+	0.324503i	−0.525988	+	0.850492i	$0.676305\pi$
$758$	1.21134	+	5.82847i	0.0439979	+	0.211699i
$759$	−7.09151			−0.257406
$760$	−4.66295	+	4.27281i	−0.169143	+	0.154991i
$761$	21.6485			0.784756			0.392378	−	0.919804i	$-0.371653\pi$
$761$	21.6485			0.784756			0.392378	+	0.919804i	$0.371653\pi$
$762$	−4.29756	−	20.6780i	−0.155684	−	0.749086i
$763$	−42.4064	−	42.4064i	−1.53521	−	1.53521i
$764$	−1.12725	−	2.59479i	−0.0407826	−	0.0938763i
$765$	−3.04427	−	2.35477i	−0.110066	−	0.0851370i
$766$	25.6570	−	39.1197i	0.927025	−	1.41345i
$767$	4.21440	−	4.21440i	0.152173	−	0.152173i
$768$	−17.1774	+	19.7089i	−0.619835	+	0.711184i
$769$		−	28.9274i		−	1.04315i	−0.853206	−	0.521574i	$-0.825345\pi$
$769$		−	28.9274i		−	1.04315i	0.853206	−	0.521574i	$-0.174655\pi$
$770$	59.9413	+	29.2115i	2.16014

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)

\(f(q)\)	\(=\)	\(q+(-0.287770 - 1.38463i) q^{2} +(-1.15541 - 1.15541i) q^{3} +(-1.83438 + 0.796907i) q^{4} +(-0.283261 - 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(3.26325 - 3.26325i) q^{7} +(1.63130 + 2.31060i) q^{8} -0.330062i q^{9} +O(q^{10})\)	\(q+(-0.287770 - 1.38463i) q^{2} +(-1.15541 - 1.15541i) q^{3} +(-1.83438 + 0.796907i) q^{4} +(-0.283261 - 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(3.26325 - 3.26325i) q^{7} +(1.63130 + 2.31060i) q^{8} -0.330062i q^{9} +(-2.98966 + 1.03050i) q^{10} -4.56912i q^{11} +(3.04021 + 1.19870i) q^{12} +(-3.90789 + 3.90789i) q^{13} +(-5.45745 - 3.57932i) q^{14} +(-2.23548 + 2.89004i) q^{15} +(2.72988 - 2.92365i) q^{16} +(3.68739 + 3.68739i) q^{17} +(-0.457012 + 0.0949818i) q^{18} -1.00000 q^{19} +(2.28719 + 3.84301i) q^{20} -7.54078 q^{21} +(-6.32652 + 1.31485i) q^{22} +(0.671647 + 0.671647i) q^{23} +(0.784875 - 4.55450i) q^{24} +(-4.83953 + 1.25658i) q^{25} +(6.53553 + 4.28639i) q^{26} +(-3.84758 + 3.84758i) q^{27} +(-3.38553 + 8.58655i) q^{28} +1.43401i q^{29} +(4.64493 + 2.26363i) q^{30} -2.10503i q^{31} +(-4.83374 - 2.93852i) q^{32} +(-5.27920 + 5.27920i) q^{33} +(4.04454 - 6.16678i) q^{34} +(-8.16243 - 6.31372i) q^{35} +(0.263028 + 0.605458i) q^{36} +(3.01280 + 3.01280i) q^{37} +(0.287770 + 1.38463i) q^{38} +9.03041 q^{39} +(4.66295 - 4.27281i) q^{40} +3.51686 q^{41} +(2.17001 + 10.4412i) q^{42} +(1.49689 + 1.49689i) q^{43} +(3.64116 + 8.38148i) q^{44} +(-0.732095 + 0.0934937i) q^{45} +(0.736700 - 1.12326i) q^{46} +(5.49969 - 5.49969i) q^{47} +(-6.53214 + 0.223890i) q^{48} -14.2977i q^{49} +(3.13256 + 6.33933i) q^{50} -8.52089i q^{51} +(4.05432 - 10.2828i) q^{52} +(5.92537 - 5.92537i) q^{53} +(6.43468 + 4.22024i) q^{54} +(-10.1345 + 1.29425i) q^{55} +(12.8634 + 2.21674i) q^{56} +(1.15541 + 1.15541i) q^{57} +(1.98557 - 0.412665i) q^{58} -1.07843 q^{59} +(1.79761 - 7.08289i) q^{60} -11.0480 q^{61} +(-2.91467 + 0.605762i) q^{62} +(-1.07708 - 1.07708i) q^{63} +(-2.67775 + 7.53855i) q^{64} +(9.77486 + 7.56095i) q^{65} +(8.82890 + 5.79052i) q^{66} +(1.29688 - 1.29688i) q^{67} +(-9.70258 - 3.82556i) q^{68} -1.55205i q^{69} +(-6.39324 + 13.1188i) q^{70} +1.88311i q^{71} +(0.762641 - 0.538428i) q^{72} +(-3.20108 + 3.20108i) q^{73} +(3.30461 - 5.03859i) q^{74} +(7.04349 + 4.13977i) q^{75} +(1.83438 - 0.796907i) q^{76} +(-14.9102 - 14.9102i) q^{77} +(-2.59868 - 12.5037i) q^{78} -2.07546 q^{79} +(-7.25809 - 5.22686i) q^{80} +7.90087 q^{81} +(-1.01205 - 4.86954i) q^{82} +(2.08842 + 2.08842i) q^{83} +(13.8326 - 6.00930i) q^{84} +(7.13434 - 9.22333i) q^{85} +(1.64187 - 2.50339i) q^{86} +(1.65687 - 1.65687i) q^{87} +(10.5574 - 7.45358i) q^{88} -10.9661i q^{89} +(0.340129 + 0.986773i) q^{90} +25.5049i q^{91} +(-1.76729 - 0.696814i) q^{92} +(-2.43216 + 2.43216i) q^{93} +(-9.19765 - 6.03237i) q^{94} +(0.283261 + 2.21805i) q^{95} +(2.18976 + 8.98014i) q^{96} +(1.72131 + 1.72131i) q^{97} +(-19.7969 + 4.11443i) q^{98} -1.50809 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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