LMFDB - Embedded newform 380.2.k.d.343.10

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			343.10
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.10

$q$-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} +(-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} + 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}+ \cdots - 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

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 $

$2$	−0.287770	+	1.38463i	−0.203484	+	0.979078i
$2$	−0.287770	+	1.38463i	−0.203484	+	0.979078i
$3$	−1.15541	+	1.15541i	−0.667075	+	0.667075i	−0.957038	−	0.289963i	$-0.906357\pi$
$3$	−1.15541	+	1.15541i	−0.667075	+	0.667075i	0.289963	+	0.957038i	$0.406357\pi$
$4$	−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	0.962652	+	0.270742i	$0.0872691\pi$
$7$	3.26325	+	3.26325i	1.23339	+	1.23339i	0.270742	+	0.962652i	$0.412731\pi$
$8$	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	$0.241871\pi$
$11$			4.56912i			1.37764i	−0.724932	+	0.688820i	$0.758129\pi$
$12$	3.04021	−	1.19870i	0.877632	−	0.346036i
$13$	−3.90789	−	3.90789i	−1.08385	−	1.08385i	−0.996146	−	0.0877064i	$-0.972046\pi$
$13$	−3.90789	−	3.90789i	−1.08385	−	1.08385i	−0.0877064	−	0.996146i	$-0.527954\pi$
$14$	−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	−0.100602	−	0.994927i	$-0.532077\pi$
$17$	3.68739	−	3.68739i	0.894324	−	0.894324i	0.994927	+	0.100602i	$0.0320770\pi$
$18$	−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	−0.633607	−	0.773655i	$-0.718426\pi$
$23$	0.671647	−	0.671647i	0.140048	−	0.140048i	0.773655	+	0.633607i	$0.218426\pi$
$24$	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	$-0.957493\pi$
$29$		−	1.43401i		−	0.266289i	0.991097	−	0.133145i	$-0.0425074\pi$
$30$	4.64493	−	2.26363i	0.848044	−	0.413281i
$31$			2.10503i			0.378074i	0.981970	+	0.189037i	$0.0605366\pi$
$31$			2.10503i			0.378074i	−0.981970	+	0.189037i	$0.939463\pi$
$32$	−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	−0.414670	−	0.909972i	$-0.636103\pi$
$37$	3.01280	−	3.01280i	0.495301	−	0.495301i	0.909972	+	0.414670i	$0.136103\pi$
$38$	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	−0.583698	−	0.811971i	$-0.698395\pi$
$43$	1.49689	−	1.49689i	0.228273	−	0.228273i	0.811971	+	0.583698i	$0.198395\pi$
$44$	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	0.983441	−	0.181229i	$-0.0580075\pi$
$47$	5.49969	+	5.49969i	0.802212	+	0.802212i	−0.181229	+	0.983441i	$0.558007\pi$
$48$	−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	0.985218	−	0.171305i	$-0.0547985\pi$
$53$	5.92537	+	5.92537i	0.813913	+	0.813913i	−0.171305	+	0.985218i	$0.554798\pi$
$54$	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	0.781875	−	0.623436i	$-0.214264\pi$
$67$	1.29688	+	1.29688i	0.158439	+	0.158439i	−0.623436	+	0.781875i	$0.714264\pi$
$68$	−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	$-0.964357\pi$
$71$		−	1.88311i		−	0.223484i	0.993737	−	0.111742i	$-0.0356430\pi$
$72$	0.762641	+	0.538428i	0.0898781	+	0.0634544i
$73$	−3.20108	−	3.20108i	−0.374659	−	0.374659i	0.494512	−	0.869171i	$-0.335347\pi$
$73$	−3.20108	−	3.20108i	−0.374659	−	0.374659i	−0.869171	+	0.494512i	$0.835347\pi$
$74$	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	−0.583139	−	0.812373i	$-0.698176\pi$
$83$	2.08842	−	2.08842i	0.229234	−	0.229234i	0.812373	+	0.583139i	$0.198176\pi$
$84$	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	$0.197417\pi$
$89$			10.9661i			1.16240i	−0.813759	+	0.581202i	$0.802583\pi$
$90$	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	−0.614300	−	0.789073i	$-0.710561\pi$
$97$	1.72131	−	1.72131i	0.174773	−	0.174773i	0.789073	+	0.614300i	$0.210561\pi$
$98$	−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	−0.680101	−	0.733119i	$-0.738064\pi$
$103$	0.538076	−	0.538076i	0.0530182	−	0.0530182i	0.733119	+	0.680101i	$0.238064\pi$
$104$	−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	0.803425	−	0.595406i	$-0.203009\pi$
$107$	2.15177	+	2.15177i	0.208019	+	0.208019i	−0.595406	+	0.803425i	$0.703009\pi$
$108$	3.99175	+	10.1241i	0.384107	+	0.974190i
$109$			12.9951i			1.24471i	0.782737	+	0.622353i	$0.213823\pi$
$109$			12.9951i			1.24471i	−0.782737	+	0.622353i	$0.786177\pi$
$110$	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	0.888599	−	0.458685i	$-0.151679\pi$
$113$	4.57006	+	4.57006i	0.429915	+	0.429915i	−0.458685	+	0.888599i	$0.651679\pi$
$114$	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	0.359628	−	0.933096i	$-0.382904\pi$
$127$	−6.46266	−	6.46266i	−0.573468	−	0.573468i	−0.933096	+	0.359628i	$0.882904\pi$
$128$	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	$0.163959\pi$
$131$			11.2765i			0.985230i	−0.870247	+	0.492615i	$0.836041\pi$
$132$	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	−0.465430	−	0.885085i	$-0.654100\pi$
$137$	4.91194	−	4.91194i	0.419655	−	0.419655i	0.885085	+	0.465430i	$0.154100\pi$
$138$	−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	$-0.755912\pi$
$149$		−	16.9391i		−	1.38771i	0.720116	−	0.693853i	$-0.244088\pi$
$150$	3.70513	+	10.9439i	0.302523	+	0.893566i
$151$			23.4511i			1.90842i	0.299137	+	0.954210i	$0.403301\pi$
$151$			23.4511i			1.90842i	−0.299137	+	0.954210i	$0.596699\pi$
$152$	−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	0.150010	−	0.988684i	$-0.452069\pi$
$157$	14.2678	−	14.2678i	1.13869	−	1.13869i	0.988684	−	0.150010i	$-0.0479307\pi$
$158$	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	−0.973039	−	0.230640i	$-0.925918\pi$
$163$	−9.47832	+	9.47832i	−0.742400	+	0.742400i	0.230640	+	0.973039i	$0.425918\pi$
$164$	−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	−0.996681	−	0.0814021i	$-0.974060\pi$
$167$	−13.9319	−	13.9319i	−1.07808	−	1.07808i	−0.0814021	−	0.996681i	$-0.525940\pi$
$168$	−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	0.754043	−	0.656825i	$-0.228101\pi$
$173$	1.27870	+	1.27870i	0.0972178	+	0.0972178i	−0.656825	+	0.754043i	$0.728101\pi$
$174$	−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	$-0.983703\pi$
$191$		−	1.41454i		−	0.102352i	0.998690	−	0.0511761i	$-0.0162970\pi$
$192$	11.8040	+	5.61621i	0.851880	+	0.405315i
$193$	−7.89499	−	7.89499i	−0.568294	−	0.568294i	0.363356	−	0.931650i	$-0.381631\pi$
$193$	−7.89499	−	7.89499i	−0.568294	−	0.568294i	−0.931650	+	0.363356i	$0.881631\pi$
$194$	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	−0.274617	+	0.961554i	$0.588551\pi$
$197$	−17.3505	+	17.3505i	−1.23617	+	1.23617i	−0.961554	+	0.274617i	$0.911449\pi$
$198$	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	$0.150898\pi$
$211$			13.2621i			0.913002i	−0.889723	+	0.456501i	$0.849102\pi$
$212$	−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	−0.472378	−	0.881396i	$-0.656604\pi$
$223$	6.10795	−	6.10795i	0.409019	−	0.409019i	0.881396	+	0.472378i	$0.156604\pi$
$224$	−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	0.0110855	−	0.999939i	$-0.496471\pi$
$227$	−14.8986	−	14.8986i	−0.988853	−	0.988853i	−0.999939	+	0.0110855i	$0.996471\pi$
$228$	−3.04021	+	1.19870i	−0.201343	+	0.0793860i
$229$		−	25.6102i		−	1.69237i	−0.532888	−	0.846186i	$-0.678893\pi$
$229$		−	25.6102i		−	1.69237i	0.532888	−	0.846186i	$-0.321107\pi$
$230$	−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	0.958596	−	0.284769i	$-0.0919169\pi$
$233$	10.2855	+	10.2855i	0.673827	+	0.673827i	−0.284769	+	0.958596i	$0.591917\pi$
$234$	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	$0.151895\pi$
$251$			14.5530i			0.918575i	−0.888288	+	0.459287i	$0.848105\pi$
$252$	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	−0.968889	−	0.247496i	$-0.920392\pi$
$257$	−11.5648	+	11.5648i	−0.721392	+	0.721392i	0.247496	+	0.968889i	$0.420392\pi$
$258$	−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	−0.699656	−	0.714480i	$-0.746663\pi$
$263$	0.240407	−	0.240407i	0.0148241	−	0.0148241i	0.714480	+	0.699656i	$0.246663\pi$
$264$	−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	$-0.949072\pi$
$269$		−	5.22590i		−	0.318629i	0.987228	−	0.159314i	$-0.0509283\pi$
$270$	7.53803	+	15.4679i	0.458750	+	0.941346i
$271$		−	10.0441i		−	0.610137i	−0.952330	−	0.305069i	$-0.901321\pi$
$271$		−	10.0441i		−	0.610137i	0.952330	−	0.305069i	$-0.0986794\pi$
$272$	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	−0.756304	−	0.654221i	$-0.772997\pi$
$277$	−1.69900	+	1.69900i	−0.102083	+	0.102083i	0.654221	+	0.756304i	$0.272997\pi$
$278$	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	−0.948474	−	0.316856i	$-0.897373\pi$
$283$	−10.6254	+	10.6254i	−0.631617	+	0.631617i	0.316856	+	0.948474i	$0.397373\pi$
$284$	−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	0.941692	+	0.336476i	$0.109235\pi$
$293$	21.8787	+	21.8787i	1.27817	+	1.27817i	0.336476	+	0.941692i	$0.390765\pi$
$294$	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	0.998412	−	0.0563407i	$-0.0179433\pi$
$307$	16.5064	+	16.5064i	0.942071	+	0.942071i	−0.0563407	+	0.998412i	$0.517943\pi$
$308$	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	$-0.814175\pi$
$311$		−	19.4406i		−	1.10238i	0.834381	−	0.551188i	$-0.185825\pi$
$312$	14.7313	−	20.8657i	0.833994	−	1.18129i
$313$	−8.63499	−	8.63499i	−0.488079	−	0.488079i	0.419621	−	0.907699i	$-0.362163\pi$
$313$	−8.63499	−	8.63499i	−0.488079	−	0.488079i	−0.907699	+	0.419621i	$0.862163\pi$
$314$	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	−0.213085	−	0.977034i	$-0.568351\pi$
$317$	13.6017	−	13.6017i	0.763949	−	0.763949i	0.977034	+	0.213085i	$0.0683510\pi$
$318$	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	$0.203002\pi$
$331$			21.6643i			1.19078i	−0.803437	+	0.595390i	$0.796998\pi$
$332$	−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	−0.702482	−	0.711702i	$-0.747925\pi$
$337$	0.169255	−	0.169255i	0.00921991	−	0.00921991i	0.711702	+	0.702482i	$0.247925\pi$
$338$	−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	0.974917	+	0.222569i	$0.0714443\pi$
$347$	22.3067	+	22.3067i	1.19749	+	1.19749i	0.222569	+	0.974917i	$0.428556\pi$
$348$	−1.71895	−	4.35969i	−0.0921455	−	0.233704i
$349$		−	19.1551i		−	1.02535i	−0.858583	−	0.512674i	$-0.828655\pi$
$349$		−	19.1551i		−	1.02535i	0.858583	−	0.512674i	$-0.171345\pi$
$350$	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	0.725302	−	0.688430i	$-0.241700\pi$
$353$	0.692765	+	0.692765i	0.0368721	+	0.0368721i	−0.688430	+	0.725302i	$0.741700\pi$
$354$	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	0.291395	−	0.956603i	$-0.405881\pi$
$367$	−12.7436	−	12.7436i	−0.665208	−	0.665208i	−0.956603	+	0.291395i	$0.905881\pi$
$368$	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	0.984837	−	0.173483i	$-0.0555021\pi$
$373$	15.6699	+	15.6699i	0.811354	+	0.811354i	−0.173483	+	0.984837i	$0.555502\pi$
$374$	−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	0.219671	−	0.975574i	$-0.429502\pi$
$383$	23.3914	−	23.3914i	1.19524	−	1.19524i	0.975574	−	0.219671i	$-0.0704983\pi$
$384$	−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	$0.104456\pi$
$389$			12.7135i			0.644603i	−0.946637	+	0.322301i	$0.895544\pi$
$390$	−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	0.376783	−	0.926302i	$-0.377030\pi$
$397$	25.9638	−	25.9638i	1.30308	−	1.30308i	0.926302	−	0.376783i	$-0.122970\pi$
$398$	−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	$-0.717743\pi$
$409$		−	31.3473i		−	1.55003i	0.631945	−	0.775013i	$-0.282257\pi$
$410$	−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	$-0.870000\pi$
$431$		−	16.4900i		−	0.794295i	0.917755	−	0.397148i	$-0.130000\pi$
$432$	0.745567	−	21.7524i	0.0358711	−	1.04656i
$433$	−2.04849	−	2.04849i	−0.0984443	−	0.0984443i	0.656169	−	0.754614i	$-0.272176\pi$
$433$	−2.04849	−	2.04849i	−0.0984443	−	0.0984443i	−0.754614	+	0.656169i	$0.772176\pi$
$434$	−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	−0.625683	−	0.780078i	$-0.715180\pi$
$443$	3.24964	−	3.24964i	0.154395	−	0.154395i	0.780078	+	0.625683i	$0.215180\pi$
$444$	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	$-0.654375\pi$
$449$		−	37.4922i		−	1.76937i	0.466193	−	0.884683i	$-0.345625\pi$
$450$	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	−0.590956	−	0.806704i	$-0.701249\pi$
$457$	4.61218	−	4.61218i	0.215749	−	0.215749i	0.806704	+	0.590956i	$0.201249\pi$
$458$	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	0.0799921	−	0.996795i	$-0.474510\pi$
$463$	23.1697	−	23.1697i	1.07679	−	1.07679i	0.996795	−	0.0799921i	$-0.0254895\pi$
$464$	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	0.997727	−	0.0673906i	$-0.0214674\pi$
$467$	20.1047	+	20.1047i	0.930336	+	0.930336i	−0.0673906	+	0.997727i	$0.521467\pi$
$468$	−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	0.0130478	−	0.999915i	$-0.495847\pi$
$487$	−21.7783	−	21.7783i	−0.986867	−	0.986867i	−0.999915	+	0.0130478i	$0.995847\pi$
$488$	−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	$0.0177047\pi$
$491$			2.46368i			0.111185i	−0.998454	+	0.0555923i	$0.982295\pi$
$492$	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	−0.902820	−	0.430019i	$-0.858507\pi$
$503$	−10.6038	+	10.6038i	−0.472800	+	0.472800i	0.430019	+	0.902820i	$0.358507\pi$
$504$	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	$0.123734\pi$
$509$			17.1016i			0.758015i	−0.925394	+	0.379007i	$0.876266\pi$
$510$	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	0.223581	−	0.974685i	$-0.428225\pi$
$523$	27.4034	−	27.4034i	1.19827	−	1.19827i	0.974685	−	0.223581i	$-0.0717747\pi$
$524$	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	0.285450	−	0.958394i	$-0.407857\pi$
$547$	−15.7388	−	15.7388i	−0.672943	−	0.672943i	−0.958394	+	0.285450i	$0.907857\pi$
$548$	−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	−0.976387	−	0.216029i	$-0.930690\pi$
$557$	−17.9451	+	17.9451i	−0.760359	+	0.760359i	0.216029	+	0.976387i	$0.430690\pi$
$558$	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	−0.991202	−	0.132355i	$-0.957746\pi$
$563$	−20.3784	+	20.3784i	−0.858847	+	0.858847i	0.132355	+	0.991202i	$0.457746\pi$
$564$	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	$0.105813\pi$
$569$			15.5685i			0.652665i	−0.945255	+	0.326333i	$0.894187\pi$
$570$	−4.64493	+	2.26363i	−0.194555	+	0.0948131i
$571$		−	21.2800i		−	0.890540i	−0.895396	−	0.445270i	$-0.853108\pi$
$571$		−	21.2800i		−	0.890540i	0.895396	−	0.445270i	$-0.146892\pi$
$572$	−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	−0.523375	−	0.852103i	$-0.675327\pi$
$577$	7.89632	−	7.89632i	0.328728	−	0.328728i	0.852103	+	0.523375i	$0.175327\pi$
$578$	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	0.129720	−	0.991551i	$-0.458592\pi$
$587$	−20.8805	−	20.8805i	−0.861831	−	0.861831i	−0.991551	+	0.129720i	$0.958592\pi$
$588$	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	0.791742	−	0.610855i	$-0.209174\pi$
$593$	4.40488	+	4.40488i	0.180887	+	0.180887i	−0.610855	+	0.791742i	$0.709174\pi$
$594$	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	0.517429	−	0.855726i	$-0.326889\pi$
$607$	−8.33475	−	8.33475i	−0.338297	−	0.338297i	−0.855726	+	0.517429i	$0.826889\pi$
$608$	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	0.00343930	−	0.999994i	$-0.498905\pi$
$613$	−24.6735	−	24.6735i	−0.996555	−	0.996555i	−0.999994	+	0.00343930i	$0.998905\pi$
$614$	−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	−0.759745	−	0.650221i	$-0.774676\pi$
$617$	−2.72052	+	2.72052i	−0.109524	+	0.109524i	0.650221	+	0.759745i	$0.274676\pi$
$618$	−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	$-0.785663\pi$
$631$		−	31.3301i		−	1.24723i	0.781731	−	0.623616i	$-0.214337\pi$
$632$	−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	0.233384	−	0.972385i	$-0.425020\pi$
$643$	30.5752	−	30.5752i	1.20577	−	1.20577i	0.972385	−	0.233384i	$-0.0749800\pi$
$644$	−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	0.988941	−	0.148309i	$-0.0473831\pi$
$647$	21.3825	+	21.3825i	0.840632	+	0.840632i	−0.148309	+	0.988941i	$0.547383\pi$
$648$	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	0.867605	−	0.497255i	$-0.165658\pi$
$653$	9.46388	+	9.46388i	0.370350	+	0.370350i	−0.497255	+	0.867605i	$0.665658\pi$
$654$	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	0.963080	−	0.269215i	$-0.0867641\pi$
$673$	18.0004	+	18.0004i	0.693866	+	0.693866i	−0.269215	+	0.963080i	$0.586764\pi$
$674$	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	−0.198319	−	0.980138i	$-0.563548\pi$
$677$	20.3423	−	20.3423i	0.781819	−	0.781819i	0.980138	+	0.198319i	$0.0635481\pi$
$678$	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	0.245396	−	0.969423i	$-0.421082\pi$
$683$	31.7484	−	31.7484i	1.21482	−	1.21482i	0.969423	−	0.245396i	$-0.0789181\pi$
$684$	−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	$0.0137147\pi$
$691$			2.26449i			0.0861453i	−0.999072	+	0.0430727i	$0.986285\pi$
$692$	−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	$-0.958431\pi$
$709$		−	6.93479i		−	0.260442i	0.991485	−	0.130221i	$-0.0415686\pi$
$710$	−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	0.952649	−	0.304074i	$-0.0983469\pi$
$727$	17.4875	+	17.4875i	0.648575	+	0.648575i	−0.304074	+	0.952649i	$0.598347\pi$
$728$	−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	0.691460	−	0.722414i	$-0.256968\pi$
$733$	−0.838043	−	0.838043i	−0.0309538	−	0.0309538i	−0.722414	+	0.691460i	$0.756968\pi$
$734$	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	−0.0918551	+	0.995772i	$0.529280\pi$
$743$	−29.6466	+	29.6466i	−1.08763	+	1.08763i	−0.995772	+	0.0918551i	$0.970720\pi$
$744$	−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	$-0.896753\pi$
$751$		−	17.4677i		−	0.637406i	0.947855	−	0.318703i	$-0.103247\pi$
$752$	−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	−0.525988	−	0.850492i	$-0.676305\pi$
$757$	8.92826	−	8.92826i	0.324503	−	0.324503i	0.850492	+	0.525988i	$0.176305\pi$
$758$	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	$0.174655\pi$
$769$			28.9274i			1.04315i	−0.853206	+	0.521574i	$0.825345\pi$
$770$	59.9413	−	29.2115i	2.16014	−	1.05271i
$771$		−	26.7241i		−	0.962446i
$772$	8.19082	+	20.7740i	0.294794	+	0.747672i

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23}+ \cdots - 128 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more