LMFDB - Embedded newform 380.2.k.c.267.4

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			267.4
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34620 + 0.433304i) q^{2} +(-0.497882 - 0.497882i) q^{3} +(1.62450 - 1.16662i) q^{4} +(-2.01079 - 0.978129i) q^{5} +(0.885982 + 0.454514i) q^{6} +(2.91849 - 2.91849i) q^{7} +(-1.68139 + 2.27441i) q^{8} -2.50423i q^{9} +O(q^{10})$	\(q+(-1.34620 + 0.433304i) q^{2} +(-0.497882 - 0.497882i) q^{3} +(1.62450 - 1.16662i) q^{4} +(-2.01079 - 0.978129i) q^{5} +(0.885982 + 0.454514i) q^{6} +(2.91849 - 2.91849i) q^{7} +(-1.68139 + 2.27441i) q^{8} -2.50423i q^{9} +(3.13074 + 0.445474i) q^{10} +3.58797i q^{11} +(-1.38965 - 0.227966i) q^{12} +(-3.29878 + 3.29878i) q^{13} +(-2.66427 + 5.19345i) q^{14} +(0.514142 + 1.48813i) q^{15} +(1.27798 - 3.79035i) q^{16} +(-4.60467 - 4.60467i) q^{17} +(1.08509 + 3.37118i) q^{18} +1.00000 q^{19} +(-4.40762 + 0.756866i) q^{20} -2.90613 q^{21} +(-1.55468 - 4.83012i) q^{22} +(-3.51712 - 3.51712i) q^{23} +(1.96952 - 0.295252i) q^{24} +(3.08653 + 3.93362i) q^{25} +(3.01144 - 5.87018i) q^{26} +(-2.74046 + 2.74046i) q^{27} +(1.33629 - 8.14585i) q^{28} -4.88207i q^{29} +(-1.33695 - 1.78054i) q^{30} +1.57175i q^{31} +(-0.0780338 + 5.65632i) q^{32} +(1.78639 - 1.78639i) q^{33} +(8.19402 + 4.20358i) q^{34} +(-8.72312 + 3.01380i) q^{35} +(-2.92149 - 4.06811i) q^{36} +(-5.48286 - 5.48286i) q^{37} +(-1.34620 + 0.433304i) q^{38} +3.28481 q^{39} +(5.60558 - 2.92873i) q^{40} -3.69344 q^{41} +(3.91222 - 1.25924i) q^{42} +(-4.56114 - 4.56114i) q^{43} +(4.18582 + 5.82865i) q^{44} +(-2.44946 + 5.03546i) q^{45} +(6.25872 + 3.21076i) q^{46} +(-1.60126 + 1.60126i) q^{47} +(-2.52343 + 1.25087i) q^{48} -10.0352i q^{49} +(-5.85953 - 3.95803i) q^{50} +4.58517i q^{51} +(-1.51042 + 9.20729i) q^{52} +(2.12363 - 2.12363i) q^{53} +(2.50175 - 4.87665i) q^{54} +(3.50950 - 7.21465i) q^{55} +(1.73071 + 11.5450i) q^{56} +(-0.497882 - 0.497882i) q^{57} +(2.11542 + 6.57224i) q^{58} +5.91948 q^{59} +(2.57131 + 1.81765i) q^{60} +0.536052 q^{61} +(-0.681045 - 2.11589i) q^{62} +(-7.30856 - 7.30856i) q^{63} +(-2.34585 - 7.64833i) q^{64} +(9.85977 - 3.40651i) q^{65} +(-1.63078 + 3.17888i) q^{66} +(-1.64255 + 1.64255i) q^{67} +(-12.8522 - 2.10835i) q^{68} +3.50222i q^{69} +(10.4372 - 7.83693i) q^{70} -4.08253i q^{71} +(5.69563 + 4.21058i) q^{72} +(-0.480968 + 0.480968i) q^{73} +(9.75675 + 5.00527i) q^{74} +(0.421752 - 3.49521i) q^{75} +(1.62450 - 1.16662i) q^{76} +(10.4715 + 10.4715i) q^{77} +(-4.42200 + 1.42332i) q^{78} -3.35832 q^{79} +(-6.27719 + 6.37157i) q^{80} -4.78383 q^{81} +(4.97210 - 1.60038i) q^{82} +(12.4301 + 12.4301i) q^{83} +(-4.72100 + 3.39036i) q^{84} +(4.75505 + 13.7630i) q^{85} +(8.11656 + 4.16384i) q^{86} +(-2.43070 + 2.43070i) q^{87} +(-8.16051 - 6.03279i) q^{88} +11.9105i q^{89} +(1.11557 - 7.84009i) q^{90} +19.2549i q^{91} +(-9.81671 - 1.61039i) q^{92} +(0.782547 - 0.782547i) q^{93} +(1.46178 - 2.84945i) q^{94} +(-2.01079 - 0.978129i) q^{95} +(2.85503 - 2.77733i) q^{96} +(-6.21450 - 6.21450i) q^{97} +(4.34827 + 13.5093i) q^{98} +8.98510 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 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 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * 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 $

$2$	−1.34620	+	0.433304i	−0.951905	+	0.306392i
$2$	−1.34620	+	0.433304i	−0.951905	+	0.306392i
$3$	−0.497882	−	0.497882i	−0.287453	−	0.287453i	0.548620	−	0.836072i	$-0.315154\pi$
$3$	−0.497882	−	0.497882i	−0.287453	−	0.287453i	−0.836072	+	0.548620i	$0.815154\pi$
$4$	1.62450	−	1.16662i	0.812248	−	0.583312i
$5$	−2.01079	−	0.978129i	−0.899251	−	0.437433i
$5$	−2.01079	−	0.978129i	−0.899251	−	0.437433i
$6$	0.885982	+	0.454514i	0.361701	+	0.185555i
$7$	2.91849	−	2.91849i	1.10309	−	1.10309i	0.109049	−	0.994036i	$-0.465220\pi$
$7$	2.91849	−	2.91849i	1.10309	−	1.10309i	0.994036	−	0.109049i	$-0.0347805\pi$
$8$	−1.68139	+	2.27441i	−0.594461	+	0.804124i
$9$		−	2.50423i		−	0.834742i
$10$	3.13074	+	0.445474i	0.990028	+	0.140871i
$11$			3.58797i			1.08182i	0.841082	+	0.540908i	$0.181919\pi$
$11$			3.58797i			1.08182i	−0.841082	+	0.540908i	$0.818081\pi$
$12$	−1.38965	−	0.227966i	−0.401157	−	0.0658082i
$13$	−3.29878	+	3.29878i	−0.914917	+	0.914917i	−0.996654	−	0.0817371i	$-0.973953\pi$
$13$	−3.29878	+	3.29878i	−0.914917	+	0.914917i	0.0817371	+	0.996654i	$0.473953\pi$
$14$	−2.66427	+	5.19345i	−0.712056	+	1.38801i
$15$	0.514142	+	1.48813i	0.132751	+	0.384233i
$16$	1.27798	−	3.79035i	0.319494	−	0.947588i
$17$	−4.60467	−	4.60467i	−1.11680	−	1.11680i	−0.992208	−	0.124589i	$-0.960239\pi$
$17$	−4.60467	−	4.60467i	−1.11680	−	1.11680i	−0.124589	−	0.992208i	$-0.539761\pi$
$18$	1.08509	+	3.37118i	0.255758	+	0.794596i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−4.40762	+	0.756866i	−0.985575	+	0.169240i
$21$	−2.90613			−0.634169
$22$	−1.55468	−	4.83012i	−0.331459	−	1.02979i
$23$	−3.51712	−	3.51712i	−0.733370	−	0.733370i	0.237916	−	0.971286i	$-0.423536\pi$
$23$	−3.51712	−	3.51712i	−0.733370	−	0.733370i	−0.971286	+	0.237916i	$0.923536\pi$
$24$	1.96952	−	0.295252i	0.402027	−	0.0602682i
$25$	3.08653	+	3.93362i	0.617305	+	0.786724i
$26$	3.01144	−	5.87018i	0.590591	−	1.15124i
$27$	−2.74046	+	2.74046i	−0.527401	+	0.527401i
$28$	1.33629	−	8.14585i	0.252536	−	1.53942i
$29$		−	4.88207i		−	0.906578i	−0.891364	−	0.453289i	$-0.850251\pi$
$29$		−	4.88207i		−	0.906578i	0.891364	−	0.453289i	$-0.149749\pi$
$30$	−1.33695	−	1.78054i	−0.244092	−	0.325080i
$31$			1.57175i			0.282295i	0.989989	+	0.141147i	$0.0450791\pi$
$31$			1.57175i			0.282295i	−0.989989	+	0.141147i	$0.954921\pi$
$32$	−0.0780338	+	5.65632i	−0.0137946	+	0.999905i
$33$	1.78639	−	1.78639i	0.310971	−	0.310971i
$34$	8.19402	+	4.20358i	1.40526	+	0.720908i
$35$	−8.72312	+	3.01380i	−1.47448	+	0.509425i
$36$	−2.92149	−	4.06811i	−0.486915	−	0.678018i
$37$	−5.48286	−	5.48286i	−0.901376	−	0.901376i	0.0941788	−	0.995555i	$-0.469977\pi$
$37$	−5.48286	−	5.48286i	−0.901376	−	0.901376i	−0.995555	+	0.0941788i	$0.969977\pi$
$38$	−1.34620	+	0.433304i	−0.218382	+	0.0702911i
$39$	3.28481			0.525990
$40$	5.60558	−	2.92873i	0.886320	−	0.463073i
$41$	−3.69344			−0.576819			−0.288409	−	0.957507i	$-0.593126\pi$
$41$	−3.69344			−0.576819			−0.288409	+	0.957507i	$0.593126\pi$
$42$	3.91222	−	1.25924i	0.603669	−	0.194304i
$43$	−4.56114	−	4.56114i	−0.695568	−	0.695568i	0.267884	−	0.963451i	$-0.413676\pi$
$43$	−4.56114	−	4.56114i	−0.695568	−	0.695568i	−0.963451	+	0.267884i	$0.913676\pi$
$44$	4.18582	+	5.82865i	0.631036	+	0.878702i
$45$	−2.44946	+	5.03546i	−0.365143	+	0.750643i
$46$	6.25872	+	3.21076i	0.922798	+	0.473400i
$47$	−1.60126	+	1.60126i	−0.233568	+	0.233568i	−0.814180	−	0.580612i	$-0.802813\pi$
$47$	−1.60126	+	1.60126i	−0.233568	+	0.233568i	0.580612	+	0.814180i	$0.302813\pi$
$48$	−2.52343	+	1.25087i	−0.364226	+	0.180547i
$49$		−	10.0352i		−	1.43359i
$50$	−5.85953	−	3.95803i	−0.828662	−	0.559749i
$51$			4.58517i			0.642053i
$52$	−1.51042	+	9.20729i	−0.209457	+	1.27682i
$53$	2.12363	−	2.12363i	0.291703	−	0.291703i	−0.546050	−	0.837753i	$-0.683869\pi$
$53$	2.12363	−	2.12363i	0.291703	−	0.291703i	0.837753	+	0.546050i	$0.183869\pi$
$54$	2.50175	−	4.87665i	0.340445	−	0.663628i
$55$	3.50950	−	7.21465i	0.473221	−	0.972824i
$56$	1.73071	+	11.5450i	0.231276	+	1.54276i
$57$	−0.497882	−	0.497882i	−0.0659461	−	0.0659461i
$58$	2.11542	+	6.57224i	0.277768	+	0.862977i
$59$	5.91948			0.770651			0.385325	−	0.922781i	$-0.374089\pi$
$59$	5.91948			0.770651			0.385325	+	0.922781i	$0.374089\pi$
$60$	2.57131	+	1.81765i	0.331955	+	0.234657i
$61$	0.536052			0.0686345			0.0343172	−	0.999411i	$-0.489074\pi$
$61$	0.536052			0.0686345			0.0343172	+	0.999411i	$0.489074\pi$
$62$	−0.681045	−	2.11589i	−0.0864928	−	0.268718i
$63$	−7.30856	−	7.30856i	−0.920792	−	0.920792i
$64$	−2.34585	−	7.64833i	−0.293232	−	0.956041i
$65$	9.85977	−	3.40651i	1.22295	−	0.422525i
$66$	−1.63078	+	3.17888i	−0.200736	+	0.391293i
$67$	−1.64255	+	1.64255i	−0.200669	+	0.200669i	−0.800287	−	0.599617i	$-0.795319\pi$
$67$	−1.64255	+	1.64255i	−0.200669	+	0.200669i	0.599617	+	0.800287i	$0.295319\pi$
$68$	−12.8522	−	2.10835i	−1.55856	−	0.255675i
$69$			3.50222i			0.421618i
$70$	10.4372	−	7.83693i	1.24748	−	0.936692i
$71$		−	4.08253i		−	0.484507i	−0.970213	−	0.242254i	$-0.922113\pi$
$71$		−	4.08253i		−	0.484507i	0.970213	−	0.242254i	$-0.0778866\pi$
$72$	5.69563	+	4.21058i	0.671236	+	0.496222i
$73$	−0.480968	+	0.480968i	−0.0562930	+	0.0562930i	−0.734693	−	0.678400i	$-0.762674\pi$
$73$	−0.480968	+	0.480968i	−0.0562930	+	0.0562930i	0.678400	+	0.734693i	$0.262674\pi$
$74$	9.75675	+	5.00527i	1.13420	+	0.581851i
$75$	0.421752	−	3.49521i	0.0486998	−	0.403592i
$76$	1.62450	−	1.16662i	0.186342	−	0.133821i
$77$	10.4715	+	10.4715i	1.19333	+	1.19333i
$78$	−4.42200	+	1.42332i	−0.500693	+	0.161159i
$79$	−3.35832			−0.377841			−0.188920	−	0.981992i	$-0.560499\pi$
$79$	−3.35832			−0.377841			−0.188920	+	0.981992i	$0.560499\pi$
$80$	−6.27719	+	6.37157i	−0.701811	+	0.712363i
$81$	−4.78383			−0.531536
$82$	4.97210	−	1.60038i	0.549077	−	0.176733i
$83$	12.4301	+	12.4301i	1.36439	+	1.36439i	0.868238	+	0.496147i	$0.165252\pi$
$83$	12.4301	+	12.4301i	1.36439	+	1.36439i	0.496147	+	0.868238i	$0.334748\pi$
$84$	−4.72100	+	3.39036i	−0.515103	+	0.369919i
$85$	4.75505	+	13.7630i	0.515758	+	1.49281i
$86$	8.11656	+	4.16384i	0.875231	+	0.448998i
$87$	−2.43070	+	2.43070i	−0.260598	+	0.260598i
$88$	−8.16051	−	6.03279i	−0.869914	−	0.643097i
$89$			11.9105i			1.26251i	0.775575	+	0.631256i	$0.217460\pi$
$89$			11.9105i			1.26251i	−0.775575	+	0.631256i	$0.782540\pi$
$90$	1.11557	−	7.84009i	0.117591	−	0.826418i
$91$			19.2549i			2.01846i
$92$	−9.81671	−	1.61039i	−1.02346	−	0.167895i
$93$	0.782547	−	0.782547i	0.0811463	−	0.0811463i
$94$	1.46178	−	2.84945i	0.150771	−	0.293898i
$95$	−2.01079	−	0.978129i	−0.206302	−	0.100354i
$96$	2.85503	−	2.77733i	0.291391	−	0.283460i
$97$	−6.21450	−	6.21450i	−0.630986	−	0.630986i	0.317329	−	0.948316i	$-0.397214\pi$
$97$	−6.21450	−	6.21450i	−0.630986	−	0.630986i	−0.948316	+	0.317329i	$0.897214\pi$
$98$	4.34827	+	13.5093i	0.439241	+	1.36465i
$99$	8.98510			0.903037
$100$	9.60311	+	2.78933i	0.960311	+	0.278933i
$101$	2.22532			0.221427			0.110714	−	0.993852i	$-0.464686\pi$
$101$	2.22532			0.221427			0.110714	+	0.993852i	$0.464686\pi$
$102$	−1.98677	−	6.17255i	−0.196720	−	0.611173i
$103$	7.89357	+	7.89357i	0.777777	+	0.777777i	0.979452	−	0.201676i	$-0.0646387\pi$
$103$	7.89357	+	7.89357i	0.777777	+	0.777777i	−0.201676	+	0.979452i	$0.564639\pi$
$104$	−1.95623	−	13.0493i	−0.191824	−	1.27959i
$105$	5.84361	+	2.84257i	0.570278	+	0.277406i
$106$	−1.93865	+	3.77900i	−0.188298	+	0.367049i
$107$	4.37844	−	4.37844i	0.423280	−	0.423280i	−0.463052	−	0.886331i	$-0.653246\pi$
$107$	4.37844	−	4.37844i	0.423280	−	0.423280i	0.886331	+	0.463052i	$0.153246\pi$
$108$	−1.25478	+	7.64895i	−0.120741	+	0.736020i
$109$		−	10.5140i		−	1.00706i	−0.863978	−	0.503530i	$-0.832034\pi$
$109$		−	10.5140i		−	1.00706i	0.863978	−	0.503530i	$-0.167966\pi$
$110$	−1.59835	+	11.2330i	−0.152397	+	1.07103i
$111$			5.45964i			0.518206i
$112$	−7.33235	−	14.7919i	−0.692842	−	1.39770i
$113$	9.63168	−	9.63168i	0.906072	−	0.906072i	−0.0898805	−	0.995953i	$-0.528649\pi$
$113$	9.63168	−	9.63168i	0.906072	−	0.906072i	0.995953	+	0.0898805i	$0.0286485\pi$
$114$	0.885982	+	0.454514i	0.0829799	+	0.0425691i
$115$	3.63198	+	10.5124i	0.338684	+	0.980284i
$116$	−5.69555	−	7.93091i	−0.528818	−	0.736366i
$117$	8.26089	+	8.26089i	0.763720	+	0.763720i
$118$	−7.96879	+	2.56493i	−0.733587	+	0.236121i
$119$	−26.8774			−2.46385
$120$	−4.24908	−	1.33276i	−0.387887	−	0.121664i
$121$	−1.87356			−0.170324
$122$	−0.721632	+	0.232273i	−0.0653335	+	0.0210290i
$123$	1.83890	+	1.83890i	0.165808	+	0.165808i
$124$	1.83364	+	2.55330i	0.164666	+	0.229293i
$125$	−2.35876	−	10.9287i	−0.210974	−	0.977492i
$126$	13.0056	+	6.67194i	1.15863	+	0.594383i
$127$	12.4921	−	12.4921i	1.10850	−	1.10850i	0.115151	−	0.993348i	$-0.463265\pi$
$127$	12.4921	−	12.4921i	1.10850	−	1.10850i	0.993348	−	0.115151i	$-0.0367351\pi$
$128$	6.47203	+	9.27970i	0.572052	+	0.820217i
$129$			4.54183i			0.399886i
$130$	−11.7972	+	8.85811i	−1.03468	+	0.776908i
$131$		−	6.66390i		−	0.582227i	−0.956688	−	0.291114i	$-0.905974\pi$
$131$		−	6.66390i		−	0.582227i	0.956688	−	0.291114i	$-0.0940258\pi$
$132$	0.817937	−	4.98603i	0.0711923	−	0.433978i
$133$	2.91849	−	2.91849i	0.253065	−	0.253065i
$134$	1.49947	−	2.92292i	0.129535	−	0.252502i
$135$	8.19100	−	2.82995i	0.704969	−	0.243564i
$136$	18.2152	−	2.73065i	1.56194	−	0.234151i
$137$	6.64153	+	6.64153i	0.567424	+	0.567424i	0.931406	−	0.363982i	$-0.118583\pi$
$137$	6.64153	+	6.64153i	0.567424	+	0.567424i	−0.363982	+	0.931406i	$0.618583\pi$
$138$	−1.51753	−	4.71469i	−0.129180	−	0.401341i
$139$	6.81147			0.577741			0.288871	−	0.957368i	$-0.406720\pi$
$139$	6.81147			0.577741			0.288871	+	0.957368i	$0.406720\pi$
$140$	−10.6547	+	15.0725i	−0.900487	+	1.27386i
$141$	1.59448			0.134280
$142$	1.76897	+	5.49589i	0.148449	+	0.461205i
$143$	−11.8359	−	11.8359i	−0.989771	−	0.989771i
$144$	−9.49190	−	3.20034i	−0.790992	−	0.266695i
$145$	−4.77530	+	9.81681i	−0.396567	+	0.815241i
$146$	0.439072	−	0.855882i	0.0363379	−	0.0708333i
$147$	−4.99633	+	4.99633i	−0.412090	+	0.412090i
$148$	−15.3033	−	2.51045i	−1.25793	−	0.206357i
$149$		−	19.0682i		−	1.56212i	−0.624453	−	0.781062i	$-0.714678\pi$
$149$		−	19.0682i		−	1.56212i	0.624453	−	0.781062i	$-0.285322\pi$
$150$	0.946723	+	4.88799i	0.0772996	+	0.399102i
$151$		−	6.08117i		−	0.494879i	−0.968903	−	0.247439i	$-0.920411\pi$
$151$		−	6.08117i		−	0.494879i	0.968903	−	0.247439i	$-0.0795891\pi$
$152$	−1.68139	+	2.27441i	−0.136379	+	0.184479i
$153$	−11.5311	+	11.5311i	−0.932238	+	0.932238i
$154$	−18.6340	−	9.55934i	−1.50157	−	0.770313i
$155$	1.53737	−	3.16045i	0.123485	−	0.253854i
$156$	5.33616	−	3.83214i	0.427235	−	0.306817i
$157$	7.46797	+	7.46797i	0.596009	+	0.596009i	0.939248	−	0.343239i	$-0.111524\pi$
$157$	7.46797	+	7.46797i	0.596009	+	0.596009i	−0.343239	+	0.939248i	$0.611524\pi$
$158$	4.52096	−	1.45517i	0.359668	−	0.115767i
$159$	−2.11464			−0.167702
$160$	5.68952	−	11.2973i	0.449796	−	0.893131i
$161$	−20.5294			−1.61794
$162$	6.43998	−	2.07285i	0.505972	−	0.162858i
$163$	−10.0388	−	10.0388i	−0.786297	−	0.786297i	0.194588	−	0.980885i	$-0.437663\pi$
$163$	−10.0388	−	10.0388i	−0.786297	−	0.786297i	−0.980885	+	0.194588i	$0.937663\pi$
$164$	−5.99998	+	4.30886i	−0.468520	+	0.336466i
$165$	−5.33937	+	1.84473i	−0.415669	+	0.143612i
$166$	−22.1195	−	11.3474i	−1.71680	−	0.880730i
$167$	16.5343	−	16.5343i	1.27946	−	1.27946i	0.338497	−	0.940968i	$-0.390082\pi$
$167$	16.5343	−	16.5343i	1.27946	−	1.27946i	0.940968	−	0.338497i	$-0.109918\pi$
$168$	4.88634	−	6.60972i	0.376989	−	0.509951i
$169$		−	8.76389i		−	0.674146i
$170$	−12.3648	−	16.4673i	−0.948336	−	1.26299i
$171$		−	2.50423i		−	0.191503i
$172$	−12.7307	−	2.08842i	−0.970707	−	0.159240i
$173$	5.32723	−	5.32723i	0.405022	−	0.405022i	−0.474977	−	0.879998i	$-0.657543\pi$
$173$	5.32723	−	5.32723i	0.405022	−	0.405022i	0.879998	+	0.474977i	$0.157543\pi$
$174$	2.21897	−	4.32543i	0.168220	−	0.327910i
$175$	20.4882	+	2.47223i	1.54876	+	0.186883i
$176$	13.5997	+	4.58534i	1.02512	+	0.345633i
$177$	−2.94721	−	2.94721i	−0.221526	−	0.221526i
$178$	−5.16086	−	16.0339i	−0.386823	−	1.20179i
$179$	−13.0819			−0.977785			−0.488893	−	0.872344i	$-0.662599\pi$
$179$	−13.0819			−0.977785			−0.488893	+	0.872344i	$0.662599\pi$
$180$	1.89536	+	11.0377i	0.141272	+	0.822701i
$181$	−17.1592			−1.27543			−0.637717	−	0.770271i	$-0.720121\pi$
$181$	−17.1592			−1.27543			−0.637717	+	0.770271i	$0.720121\pi$
$182$	−8.34322	−	25.9209i	−0.618440	−	1.92139i
$183$	−0.266891	−	0.266891i	−0.0197292	−	0.0197292i
$184$	13.9130	−	2.08571i	1.02568	−	0.153761i
$185$	5.66192	+	16.3878i	0.416272	+	1.20486i
$186$	−0.714382	+	1.39254i	−0.0523811	+	0.102106i
$187$	16.5215	−	16.5215i	1.20817	−	1.20817i
$188$	−0.733173	+	4.46932i	−0.0534721	+	0.325958i
$189$			15.9960i			1.16354i
$190$	3.13074	+	0.445474i	0.227128	+	0.0323181i
$191$		−	15.3156i		−	1.10820i	−0.832451	−	0.554098i	$-0.813063\pi$
$191$		−	15.3156i		−	1.10820i	0.832451	−	0.554098i	$-0.186937\pi$
$192$	−2.64001	+	4.97593i	−0.190526	+	0.359107i
$193$	−12.7493	+	12.7493i	−0.917717	+	0.917717i	−0.996863	−	0.0791463i	$-0.974781\pi$
$193$	−12.7493	+	12.7493i	−0.917717	+	0.917717i	0.0791463	+	0.996863i	$0.474781\pi$
$194$	11.0587	+	5.67318i	0.793969	+	0.407310i
$195$	−6.60505	−	3.21297i	−0.472997	−	0.230085i
$196$	−11.7073	−	16.3021i	−0.836233	−	1.16443i
$197$	9.97667	+	9.97667i	0.710808	+	0.710808i	0.966704	−	0.255896i	$-0.0823705\pi$
$197$	9.97667	+	9.97667i	0.710808	+	0.710808i	−0.255896	+	0.966704i	$0.582370\pi$
$198$	−12.0957	+	3.89328i	−0.859605	+	0.276683i
$199$	−4.22544			−0.299533			−0.149767	−	0.988721i	$-0.547852\pi$
$199$	−4.22544			−0.299533			−0.149767	+	0.988721i	$0.547852\pi$
$200$	−14.1363	+	0.406068i	−0.999588	+	0.0287133i
$201$	1.63559			0.115366
$202$	−2.99572	+	0.964238i	−0.210778	+	0.0678436i
$203$	−14.2483	−	14.2483i	−1.00003	−	1.00003i
$204$	5.34917	+	7.44860i	0.374517	+	0.521506i
$205$	7.42673	+	3.61267i	0.518705	+	0.252319i
$206$	−14.0466	−	7.20600i	−0.978675	−	0.502066i
$207$	−8.80766	+	8.80766i	−0.612175	+	0.612175i
$208$	8.28778	+	16.7193i	0.574654	+	1.15927i
$209$			3.58797i			0.248185i
$210$	−9.09834	−	1.29461i	−0.627845	−	0.0893363i
$211$			12.8281i			0.883120i	0.897232	+	0.441560i	$0.145575\pi$
$211$			12.8281i			0.883120i	−0.897232	+	0.441560i	$0.854425\pi$
$212$	0.972350	−	5.92731i	0.0667813	−	0.407089i
$213$	−2.03262	+	2.03262i	−0.139273	+	0.139273i
$214$	−3.99705	+	7.79144i	−0.273233	+	0.532612i
$215$	4.71010	+	13.6329i	0.321226	+	0.929754i
$216$	−1.62514	−	10.8407i	−0.110577	−	0.737616i
$217$	4.58714	+	4.58714i	0.311395	+	0.311395i
$218$	4.55576	+	14.1540i	0.308555	+	0.958627i
$219$	0.478931			0.0323631
$220$	−2.71561	−	15.8144i	−0.183087	−	1.06621i
$221$	30.3796			2.04355
$222$	−2.36568	−	7.34975i	−0.158774	−	0.493283i
$223$	13.4531	+	13.4531i	0.900887	+	0.900887i	0.995513	−	0.0946261i	$-0.0301655\pi$
$223$	13.4531	+	13.4531i	0.900887	+	0.900887i	−0.0946261	+	0.995513i	$0.530166\pi$
$224$	16.2802	+	16.7356i	1.08776	+	1.11820i
$225$	9.85067	−	7.72936i	0.656711	−	0.515291i
$226$	−8.79270	+	17.1396i	−0.584882	+	1.14011i
$227$	−14.9994	+	14.9994i	−0.995546	+	0.995546i	−0.999990	−	0.00444394i	$-0.998585\pi$
$227$	−14.9994	+	14.9994i	−0.995546	+	0.995546i	0.00444394	+	0.999990i	$0.498585\pi$
$228$	−1.38965	−	0.227966i	−0.0920318	−	0.0150974i
$229$		−	21.4928i		−	1.42028i	−0.704059	−	0.710141i	$-0.748631\pi$
$229$		−	21.4928i		−	1.42028i	0.704059	−	0.710141i	$-0.251369\pi$
$230$	−9.44441	−	12.5780i	−0.622746	−	0.829368i
$231$		−	10.4271i		−	0.686054i
$232$	11.1038	+	8.20867i	0.729001	+	0.538926i
$233$	−1.81711	+	1.81711i	−0.119043	+	0.119043i	−0.764119	−	0.645076i	$-0.776826\pi$
$233$	−1.81711	+	1.81711i	−0.119043	+	0.119043i	0.645076	+	0.764119i	$0.276826\pi$
$234$	−14.7003	−	7.54132i	−0.960986	−	0.492991i
$235$	4.78604	−	1.65356i	0.312207	−	0.107866i
$236$	9.61617	−	6.90581i	0.625960	−	0.449530i
$237$	1.67205	+	1.67205i	0.108611	+	0.108611i
$238$	36.1823	−	11.6461i	2.34535	−	0.754902i
$239$	22.8925			1.48079			0.740396	−	0.672171i	$-0.234638\pi$
$239$	22.8925			1.48079			0.740396	+	0.672171i	$0.234638\pi$
$240$	6.29760	−	0.0469882i	0.406508	−	0.00303307i
$241$	14.0297			0.903729			0.451865	−	0.892086i	$-0.350759\pi$
$241$	14.0297			0.903729			0.451865	+	0.892086i	$0.350759\pi$
$242$	2.52219	−	0.811822i	0.162132	−	0.0521859i
$243$	10.6032	+	10.6032i	0.680193	+	0.680193i
$244$	0.870815	−	0.625372i	0.0557482	−	0.0400353i
$245$	−9.81568	+	20.1786i	−0.627101	+	1.28916i
$246$	−3.27233	−	1.67872i	−0.208636	−	0.107031i
$247$	−3.29878	+	3.29878i	−0.209896	+	0.209896i
$248$	−3.57480	−	2.64273i	−0.227000	−	0.167813i
$249$		−	12.3775i		−	0.784392i
$250$	7.91079	+	13.6901i	0.500323	+	0.865839i
$251$			5.28898i			0.333838i	0.985971	+	0.166919i	$0.0533818\pi$
$251$			5.28898i			0.333838i	−0.985971	+	0.166919i	$0.946618\pi$
$252$	−20.3991	−	3.34638i	−1.28502	−	0.210802i
$253$	12.6193	−	12.6193i	0.793371	−	0.793371i
$254$	−11.4040	+	22.2298i	−0.715551	+	1.39482i
$255$	4.48489	−	9.21980i	0.280855	−	0.577367i
$256$	−12.7336	−	9.68796i	−0.795847	−	0.605497i
$257$	−14.1338	−	14.1338i	−0.881643	−	0.881643i	0.112058	−	0.993702i	$-0.464256\pi$
$257$	−14.1338	−	14.1338i	−0.881643	−	0.881643i	−0.993702	+	0.112058i	$0.964256\pi$
$258$	−1.96799	−	6.11420i	−0.122522	−	0.380653i
$259$	−32.0033			−1.98859
$260$	12.0430	−	17.0365i	0.746878	−	1.05656i
$261$	−12.2258			−0.756759
$262$	2.88749	+	8.97092i	0.178390	+	0.554225i
$263$	−13.3767	−	13.3767i	−0.824840	−	0.824840i	0.161958	−	0.986798i	$-0.448219\pi$
$263$	−13.3767	−	13.3767i	−0.824840	−	0.824840i	−0.986798	+	0.161958i	$0.948219\pi$
$264$	1.05936	+	7.06660i	0.0651990	+	0.434919i
$265$	−6.34735	+	2.19298i	−0.389915	+	0.134714i
$266$	−2.66427	+	5.19345i	−0.163357	+	0.318431i
$267$	5.93003	−	5.93003i	0.362912	−	0.362912i
$268$	−0.752077	+	4.58455i	−0.0459404	+	0.280046i
$269$			19.2906i			1.17617i	0.808801	+	0.588083i	$0.200117\pi$
$269$			19.2906i			1.17617i	−0.808801	+	0.588083i	$0.799883\pi$
$270$	−9.80047	+	7.35887i	−0.596438	+	0.447846i
$271$		−	15.6415i		−	0.950152i	−0.879945	−	0.475076i	$-0.842421\pi$
$271$		−	15.6415i		−	0.950152i	0.879945	−	0.475076i	$-0.157579\pi$
$272$	−23.3380	+	11.5687i	−1.41507	+	0.701454i
$273$	9.58668	−	9.58668i	0.580212	−	0.580212i
$274$	−11.8186	−	6.06301i	−0.713988	−	0.366280i
$275$	−14.1137	+	11.0744i	−0.851090	+	0.667810i
$276$	4.08578	+	5.68935i	0.245935	+	0.342459i
$277$	−9.49242	−	9.49242i	−0.570345	−	0.570345i	0.361880	−	0.932225i	$-0.382135\pi$
$277$	−9.49242	−	9.49242i	−0.570345	−	0.570345i	−0.932225	+	0.361880i	$0.882135\pi$
$278$	−9.16958	+	2.95143i	−0.549955	+	0.177015i
$279$	3.93602			0.235643
$280$	7.81236	−	24.9073i	0.466878	−	1.48850i
$281$	−6.05636			−0.361292			−0.180646	−	0.983548i	$-0.557819\pi$
$281$	−6.05636			−0.361292			−0.180646	+	0.983548i	$0.557819\pi$
$282$	−2.14649	+	0.690894i	−0.127821	+	0.0411422i
$283$	9.20805	+	9.20805i	0.547362	+	0.547362i	0.925677	−	0.378315i	$-0.123496\pi$
$283$	9.20805	+	9.20805i	0.547362	+	0.547362i	−0.378315	+	0.925677i	$0.623496\pi$
$284$	−4.76278	−	6.63205i	−0.282619	−	0.393540i
$285$	0.514142	+	1.48813i	0.0304551	+	0.0881491i
$286$	21.0621	+	10.8050i	1.24543	+	0.638911i
$287$	−10.7793	+	10.7793i	−0.636280	+	0.636280i
$288$	14.1647	+	0.195414i	0.834663	+	0.0115149i
$289$			25.4060i			1.49447i
$290$	2.17484	−	15.2845i	0.127711	−	0.897538i
$291$			6.18818i			0.362757i
$292$	−0.220221	+	1.34244i	−0.0128875	+	0.0785603i
$293$	8.60824	−	8.60824i	0.502899	−	0.502899i	−0.409439	−	0.912338i	$-0.634276\pi$
$293$	8.60824	−	8.60824i	0.502899	−	0.502899i	0.912338	+	0.409439i	$0.134276\pi$
$294$	4.56112	−	8.89097i	0.266010	−	0.518532i
$295$	−11.9028	−	5.79002i	−0.693009	−	0.337108i
$296$	21.6891	−	3.25143i	1.26065	−	0.188985i
$297$	−9.83269	−	9.83269i	−0.570551	−	0.570551i
$298$	8.26230	+	25.6695i	0.478622	+	1.48700i
$299$	23.2044			1.34195
$300$	−3.39246	−	6.16998i	−0.195864	−	0.356224i
$301$	−26.6233			−1.53454
$302$	2.63499	+	8.18646i	0.151627	+	0.471078i
$303$	−1.10795	−	1.10795i	−0.0636499	−	0.0636499i
$304$	1.27798	−	3.79035i	0.0732969	−	0.217392i
$305$	−1.07789	−	0.524328i	−0.0617196	−	0.0300230i
$306$	10.5267	−	20.5197i	0.601772	−	1.17303i
$307$	11.3998	−	11.3998i	0.650619	−	0.650619i	−0.302523	−	0.953142i	$-0.597829\pi$
$307$	11.3998	−	11.3998i	0.650619	−	0.650619i	0.953142	+	0.302523i	$0.0978290\pi$
$308$	29.2271	+	4.79459i	1.66537	+	0.273197i
$309$		−	7.86014i		−	0.447148i
$310$	−0.700174	+	4.92075i	−0.0397672	+	0.279480i
$311$			11.0301i			0.625460i	0.949842	+	0.312730i	$0.101244\pi$
$311$			11.0301i			0.625460i	−0.949842	+	0.312730i	$0.898756\pi$
$312$	−5.52305	+	7.47099i	−0.312681	+	0.422962i
$313$	21.9744	−	21.9744i	1.24207	−	1.24207i	0.282923	−	0.959143i	$-0.408696\pi$
$313$	21.9744	−	21.9744i	1.24207	−	1.24207i	0.959143	−	0.282923i	$-0.0913040\pi$
$314$	−13.2893	−	6.81747i	−0.749956	−	0.384732i
$315$	7.54724	+	21.8447i	0.425239	+	1.23081i
$316$	−5.45558	+	3.91790i	−0.306900	+	0.220399i
$317$	−17.3687	−	17.3687i	−0.975526	−	0.975526i	0.0241817	−	0.999708i	$-0.492302\pi$
$317$	−17.3687	−	17.3687i	−0.975526	−	0.975526i	−0.999708	+	0.0241817i	$0.992302\pi$
$318$	2.84672	−	0.916279i	0.159636	−	0.0513824i
$319$	17.5168			0.980750
$320$	−2.76405	+	17.6737i	−0.154515	+	0.987990i
$321$	−4.35990			−0.243346
$322$	27.6366	−	8.89544i	1.54013	−	0.495724i
$323$	−4.60467	−	4.60467i	−0.256211	−	0.256211i
$324$	−7.77131	+	5.58093i	−0.431739	+	0.310052i
$325$	−23.1579	−	2.79437i	−1.28457	−	0.155004i
$326$	17.8640	+	9.16433i	0.989396	+	0.507565i
$327$	−5.23475	+	5.23475i	−0.289482	+	0.289482i
$328$	6.21012	−	8.40039i	0.342897	−	0.463834i
$329$			9.34653i			0.515291i
$330$	6.38852	−	4.79694i	0.351676	−	0.264063i
$331$			24.2555i			1.33320i	0.745414	+	0.666602i	$0.232252\pi$
$331$			24.2555i			1.33320i	−0.745414	+	0.666602i	$0.767748\pi$
$332$	34.6940	+	5.69141i	1.90408	+	0.312357i
$333$	−13.7303	+	13.7303i	−0.752417	+	0.752417i
$334$	−15.0941	+	29.4228i	−0.825912	+	1.60995i
$335$	4.90944	−	1.69619i	0.268232	−	0.0926728i
$336$	−3.71396	+	11.0153i	−0.202613	+	0.600931i
$337$	16.9925	+	16.9925i	0.925642	+	0.925642i	0.997421	−	0.0717789i	$-0.0228676\pi$
$337$	16.9925	+	16.9925i	0.925642	+	0.925642i	−0.0717789	+	0.997421i	$0.522868\pi$
$338$	3.79743	+	11.7979i	0.206553	+	0.641723i
$339$	−9.59089			−0.520905
$340$	23.7808	+	16.8106i	1.28969	+	0.911680i
$341$	−5.63940			−0.305391
$342$	1.08509	+	3.37118i	0.0586749	+	0.182293i
$343$	−8.85807	−	8.85807i	−0.478291	−	0.478291i
$344$	18.0430	−	2.70483i	0.972811	−	0.145835i
$345$	3.42563	−	7.04223i	0.184430	−	0.379141i
$346$	−4.86320	+	9.47981i	−0.261447	+	0.509638i
$347$	−4.16317	+	4.16317i	−0.223490	+	0.223490i	−0.809967	−	0.586476i	$-0.800515\pi$
$347$	−4.16317	+	4.16317i	−0.223490	+	0.223490i	0.586476	+	0.809967i	$0.300515\pi$
$348$	−1.11295	+	6.78437i	−0.0596603	+	0.363681i
$349$		−	25.4964i		−	1.36479i	−0.730983	−	0.682396i	$-0.760938\pi$
$349$		−	25.4964i		−	1.36479i	0.730983	−	0.682396i	$-0.239062\pi$
$350$	−28.6524	+	5.54951i	−1.53154	+	0.296634i
$351$		−	18.0803i		−	0.965057i
$352$	−20.2947	−	0.279983i	−1.08171	−	0.0149232i
$353$	8.69382	−	8.69382i	0.462725	−	0.462725i	−0.436822	−	0.899548i	$-0.643896\pi$
$353$	8.69382	−	8.69382i	0.462725	−	0.462725i	0.899548	+	0.436822i	$0.143896\pi$
$354$	5.24456	+	2.69049i	0.278745	+	0.142998i
$355$	−3.99324	+	8.20910i	−0.211939	+	0.435694i
$356$	13.8951	+	19.3486i	0.736438	+	1.02547i
$357$	13.3818	+	13.3818i	0.708239	+	0.708239i
$358$	17.6108	−	5.66842i	0.930759	−	0.299585i
$359$	10.8276			0.571458			0.285729	−	0.958310i	$-0.407764\pi$
$359$	10.8276			0.571458			0.285729	+	0.958310i	$0.407764\pi$
$360$	−7.33420	−	14.0376i	−0.386546	−	0.739849i
$361$	1.00000			0.0526316
$362$	23.0997	−	7.43514i	1.21409	−	0.390782i
$363$	0.932815	+	0.932815i	0.0489601	+	0.0489601i
$364$	22.4632	+	31.2795i	1.17739	+	1.63949i
$365$	1.43757	−	0.496675i	0.0752459	−	0.0259971i
$366$	0.474933	+	0.243643i	0.0248251	+	0.0127354i
$367$	−20.7628	+	20.7628i	−1.08381	+	1.08381i	−0.0876562	+	0.996151i	$0.527938\pi$
$367$	−20.7628	+	20.7628i	−1.08381	+	1.08381i	−0.996151	+	0.0876562i	$0.972062\pi$
$368$	−17.8259	+	8.83634i	−0.929240	+	0.460626i
$369$			9.24922i			0.481495i
$370$	−14.7230	−	19.6079i	−0.765410	−	1.01937i
$371$		−	12.3956i		−	0.643546i
$372$	0.358306	−	2.18418i	0.0185773	−	0.113245i
$373$	1.85686	−	1.85686i	0.0961447	−	0.0961447i	−0.657398	−	0.753543i	$-0.728343\pi$
$373$	1.85686	−	1.85686i	0.0961447	−	0.0961447i	0.753543	+	0.657398i	$0.228343\pi$
$374$	−15.0823	+	29.3999i	−0.779889	+	1.52024i
$375$	−4.26682	+	6.61559i	−0.220338	+	0.341627i
$376$	−0.949575	−	6.33427i	−0.0489706	−	0.326665i
$377$	16.1049	+	16.1049i	0.829444	+	0.829444i
$378$	−6.93112	−	21.5338i	−0.356498	−	1.10758i
$379$	−17.2442			−0.885776			−0.442888	−	0.896577i	$-0.646046\pi$
$379$	−17.2442			−0.885776			−0.442888	+	0.896577i	$0.646046\pi$
$380$	−4.40762	+	0.756866i	−0.226106	+	0.0388264i
$381$	−12.4392			−0.637282
$382$	6.63629	+	20.6178i	0.339542	+	1.05490i
$383$	8.79528	+	8.79528i	0.449418	+	0.449418i	0.895161	−	0.445743i	$-0.147061\pi$
$383$	8.79528	+	8.79528i	0.449418	+	0.449418i	−0.445743	+	0.895161i	$0.647061\pi$
$384$	1.39789	−	7.84251i	0.0713357	−	0.400211i
$385$	−10.8134	−	31.2983i	−0.551104	−	1.59511i
$386$	11.6388	−	22.6874i	0.592399	−	1.15476i
$387$	−11.4221	+	11.4221i	−0.580620	+	0.580620i
$388$	−17.3454	−	2.84544i	−0.880580	−	0.144455i
$389$		−	22.5652i		−	1.14410i	−0.820219	−	0.572049i	$-0.806149\pi$
$389$		−	22.5652i		−	1.14410i	0.820219	−	0.572049i	$-0.193851\pi$
$390$	10.2839	+	1.46330i	0.520745	+	0.0740970i
$391$			32.3904i			1.63805i
$392$	22.8240	+	16.8730i	1.15279	+	0.852216i
$393$	−3.31784	+	3.31784i	−0.167363	+	0.167363i
$394$	−17.7535	−	9.10764i	−0.894408	−	0.458836i
$395$	6.75287	+	3.28487i	0.339774	+	0.165280i
$396$	14.5963	−	10.4822i	0.733490	−	0.526752i
$397$	13.6045	+	13.6045i	0.682791	+	0.682791i	0.960628	−	0.277837i	$-0.0896175\pi$
$397$	13.6045	+	13.6045i	0.682791	+	0.682791i	−0.277837	+	0.960628i	$0.589618\pi$
$398$	5.68827	−	1.83090i	0.285127	−	0.0917746i
$399$	−2.90613			−0.145488
$400$	18.8543	−	6.67196i	0.942715	−	0.333598i
$401$	33.3363			1.66474			0.832368	−	0.554224i	$-0.186985\pi$
$401$	33.3363			1.66474			0.832368	+	0.554224i	$0.186985\pi$
$402$	−2.20183	+	0.708708i	−0.109817	+	0.0353472i
$403$	−5.18486	−	5.18486i	−0.258276	−	0.258276i
$404$	3.61502	−	2.59611i	0.179854	−	0.129161i
$405$	9.61926	+	4.67920i	0.477985	+	0.232511i
$406$	25.3548	+	13.0072i	1.25834	+	0.645535i
$407$	19.6724	−	19.6724i	0.975123	−	0.975123i
$408$	−10.4285	−	7.70947i	−0.516290	−	0.381675i
$409$			2.78416i			0.137668i	0.997628	+	0.0688339i	$0.0219279\pi$
$409$			2.78416i			0.137668i	−0.997628	+	0.0688339i	$0.978072\pi$
$410$	−11.5632	−	1.64533i	−0.571067	−	0.0812573i
$411$		−	6.61340i		−	0.326215i
$412$	22.0319	+	3.61424i	1.08543	+	0.178061i
$413$	17.2759	−	17.2759i	0.850093	−	0.850093i
$414$	8.04046	−	15.6732i	0.395167	−	0.770298i
$415$	−12.8361	−	37.1527i	−0.630098	−	1.82375i
$416$	−18.4015	−	18.9164i	−0.902209	−	0.927451i
$417$	−3.39131	−	3.39131i	−0.166073	−	0.166073i
$418$	−1.55468	−	4.83012i	−0.0760420	−	0.236249i
$419$	−21.3153			−1.04132			−0.520661	−	0.853763i	$-0.674315\pi$
$419$	−21.3153			−1.04132			−0.520661	+	0.853763i	$0.674315\pi$
$420$	12.8091	−	2.19955i	0.625021	−	0.107327i
$421$	−11.5106			−0.560994			−0.280497	−	0.959855i	$-0.590499\pi$
$421$	−11.5106			−0.560994			−0.280497	+	0.959855i	$0.590499\pi$
$422$	−5.55845	−	17.2691i	−0.270581	−	0.840647i
$423$	4.00992	+	4.00992i	0.194969	+	0.194969i
$424$	1.25935	+	8.40065i	0.0611593	+	0.407972i
$425$	3.90058	−	32.3255i	0.189206	−	1.56802i
$426$	1.85557	−	3.61705i	0.0899025	−	0.175247i
$427$	1.56446	−	1.56446i	0.0757096	−	0.0757096i
$428$	2.00476	−	12.2208i	0.0969040	−	0.590713i
$429$			11.7858i			0.569024i
$430$	−12.2479	−	16.3116i	−0.590646	−	0.786617i
$431$		−	8.99333i		−	0.433193i	−0.976261	−	0.216597i	$-0.930504\pi$
$431$		−	8.99333i		−	0.433193i	0.976261	−	0.216597i	$-0.0694957\pi$
$432$	6.88507	+	13.8895i	0.331258	+	0.668261i
$433$	−21.6636	+	21.6636i	−1.04109	+	1.04109i	−0.0419671	+	0.999119i	$0.513362\pi$
$433$	−21.6636	+	21.6636i	−1.04109	+	1.04109i	−0.999119	+	0.0419671i	$0.986638\pi$
$434$	−8.16281	−	4.18757i	−0.391828	−	0.201010i
$435$	7.26515	−	2.51008i	0.348337	−	0.120349i
$436$	−12.2659	−	17.0800i	−0.587431	−	0.817983i
$437$	−3.51712	−	3.51712i	−0.168247	−	0.168247i
$438$	−0.644735	+	0.207522i	−0.0308066	+	0.00991580i
$439$	−20.8810			−0.996595			−0.498298	−	0.867006i	$-0.666041\pi$
$439$	−20.8810			−0.996595			−0.498298	+	0.867006i	$0.666041\pi$
$440$	10.5082	+	20.1127i	0.500959	+	0.958835i
$441$	−25.1303			−1.19668
$442$	−40.8970	+	13.1636i	−1.94527	+	0.626128i
$443$	21.5183	+	21.5183i	1.02237	+	1.02237i	0.999744	+	0.0226219i	$0.00720139\pi$
$443$	21.5183	+	21.5183i	1.02237	+	1.02237i	0.0226219	+	0.999744i	$0.492799\pi$
$444$	6.36935	+	8.86916i	0.302276	+	0.420912i
$445$	11.6500	−	23.9495i	0.552264	−	1.13531i
$446$	−23.9398	−	12.2813i	−1.13358	−	0.581535i
$447$	−9.49370	+	9.49370i	−0.449037	+	0.449037i
$448$	−29.1679	−	15.4752i	−1.37805	−	0.731136i
$449$		−	18.9308i		−	0.893398i	−0.894684	−	0.446699i	$-0.852600\pi$
$449$		−	18.9308i		−	0.893398i	0.894684	−	0.446699i	$-0.147400\pi$
$450$	−9.91179	+	14.6736i	−0.467246	+	0.691719i
$451$		−	13.2520i		−	0.624011i
$452$	4.41007	−	26.8832i	0.207432	−	1.26448i
$453$	−3.02771	+	3.02771i	−0.142254	+	0.142254i
$454$	13.6929	−	26.6915i	0.642639	−	1.25269i
$455$	18.8338	−	38.7175i	0.882941	−	1.81510i
$456$	1.96952	−	0.295252i	0.0922313	−	0.0138265i
$457$	1.51148	+	1.51148i	0.0707041	+	0.0707041i	0.741575	−	0.670870i	$-0.234079\pi$
$457$	1.51148	+	1.51148i	0.0707041	+	0.0707041i	−0.670870	+	0.741575i	$0.734079\pi$
$458$	9.31290	+	28.9335i	0.435163	+	1.35197i
$459$	25.2378			1.17800
$460$	18.1641	+	12.8402i	0.846907	+	0.598675i
$461$	−17.0301			−0.793171			−0.396586	−	0.917998i	$-0.629805\pi$
$461$	−17.0301			−0.793171			−0.396586	+	0.917998i	$0.629805\pi$
$462$	4.51811	+	14.0370i	0.210201	+	0.653059i
$463$	17.2053	+	17.2053i	0.799599	+	0.799599i	0.983032	−	0.183433i	$-0.0587210\pi$
$463$	17.2053	+	17.2053i	0.799599	+	0.799599i	−0.183433	+	0.983032i	$0.558721\pi$
$464$	−18.5048	−	6.23917i	−0.859063	−	0.289646i
$465$	−2.33897	+	0.808103i	−0.108467	+	0.0374749i
$466$	1.65883	−	3.23355i	0.0768437	−	0.149791i
$467$	−9.04056	+	9.04056i	−0.418347	+	0.418347i	−0.884634	−	0.466286i	$-0.845592\pi$
$467$	−9.04056	+	9.04056i	−0.418347	+	0.418347i	0.466286	+	0.884634i	$0.345592\pi$
$468$	23.0571	+	3.78243i	1.06582	+	0.174843i
$469$			9.58753i			0.442711i
$470$	−5.72646	+	4.29982i	−0.264142	+	0.198336i
$471$		−	7.43634i		−	0.342649i
$472$	−9.95296	+	13.4633i	−0.458122	+	0.619699i
$473$	16.3653	−	16.3653i	0.752476	−	0.752476i
$474$	−2.97541	−	1.52640i	−0.136665	−	0.0701100i
$475$	3.08653	+	3.93362i	0.141620	+	0.180487i
$476$	−43.6622	+	31.3558i	−2.00125	+	1.43719i
$477$	−5.31805	−	5.31805i	−0.243497	−	0.243497i
$478$	−30.8178	+	9.91940i	−1.40957	+	0.453703i
$479$	−21.6356			−0.988556			−0.494278	−	0.869304i	$-0.664568\pi$
$479$	−21.6356			−0.988556			−0.494278	+	0.869304i	$0.664568\pi$
$480$	−8.45745	+	2.79203i	−0.386028	+	0.127438i
$481$	36.1735			1.64937
$482$	−18.8867	+	6.07910i	−0.860265	+	0.276895i
$483$	10.2212	+	10.2212i	0.465081	+	0.465081i
$484$	−3.04360	+	2.18575i	−0.138345	+	0.0993521i
$485$	6.41745	+	18.5746i	0.291401	+	0.843429i
$486$	−18.8683	−	9.67956i	−0.855885	−	0.439074i
$487$	−14.6707	+	14.6707i	−0.664791	+	0.664791i	−0.956505	−	0.291715i	$-0.905774\pi$
$487$	−14.6707	+	14.6707i	−0.664791	+	0.664791i	0.291715	+	0.956505i	$0.405774\pi$
$488$	−0.901313	+	1.21920i	−0.0408005	+	0.0551906i
$489$			9.99625i			0.452046i
$490$	4.47040	−	31.4175i	0.201952	−	1.41930i
$491$			30.4922i			1.37609i	0.725667	+	0.688047i	$0.241532\pi$
$491$			30.4922i			1.37609i	−0.725667	+	0.688047i	$0.758468\pi$
$492$	5.13259	+	0.841981i	0.231395	+	0.0379594i
$493$	−22.4804	+	22.4804i	−1.01246	+	1.01246i
$494$	3.01144	−	5.87018i	0.135491	−	0.264112i
$495$	−18.0671	−	8.78859i	−0.812057	−	0.395018i
$496$	5.95749	+	2.00866i	0.267499	+	0.0901914i
$497$	−11.9148	−	11.9148i	−0.534453	−	0.534453i
$498$	5.36322	+	16.6626i	0.240331	+	0.746667i
$499$	−25.7578			−1.15308			−0.576538	−	0.817071i	$-0.695597\pi$
$499$	−25.7578			−1.15308			−0.576538	+	0.817071i	$0.695597\pi$
$500$	−16.5815	−	15.0018i	−0.741546	−	0.670902i
$501$	−16.4643			−0.735571
$502$	−2.29173	−	7.12001i	−0.102285	−	0.317782i
$503$	5.81236	+	5.81236i	0.259161	+	0.259161i	0.824713	−	0.565552i	$-0.191337\pi$
$503$	5.81236	+	5.81236i	0.259161	+	0.259161i	−0.565552	+	0.824713i	$0.691337\pi$
$504$	28.9112	−	4.33409i	1.28781	−	0.193056i
$505$	−4.47464	−	2.17665i	−0.199119	−	0.0968596i
$506$	−11.5201	+	22.4561i	−0.512132	+	0.998297i
$507$	−4.36339	+	4.36339i	−0.193785	+	0.193785i
$508$	5.71980	−	34.8671i	0.253775	−	1.54698i
$509$			21.8822i			0.969912i	0.874539	+	0.484956i	$0.161164\pi$
$509$			21.8822i			0.969912i	−0.874539	+	0.484956i	$0.838836\pi$
$510$	−2.04258	+	14.3550i	−0.0904468	+	0.635650i
$511$			2.80740i			0.124192i
$512$	21.3397	+	7.52441i	0.943091	+	0.332535i
$513$	−2.74046	+	2.74046i	−0.120994	+	0.120994i
$514$	25.1511	+	12.9027i	1.10937	+	0.569113i
$515$	−8.15136	−	23.5932i	−0.359192	−	1.03964i
$516$	5.29861	+	7.37818i	0.233258	+	0.324806i
$517$	−5.74529	−	5.74529i	−0.252678	−	0.252678i
$518$	43.0828	−	13.8672i	1.89295	−	0.609288i
$519$	−5.30467			−0.232849
$520$	−8.83034	+	28.1528i	−0.387236	+	1.23458i
$521$	−30.5569			−1.33872			−0.669361	−	0.742937i	$-0.733432\pi$
$521$	−30.5569			−1.33872			−0.669361	+	0.742937i	$0.733432\pi$
$522$	16.4584	−	5.29749i	0.720363	−	0.231865i
$523$	−28.6213	−	28.6213i	−1.25152	−	1.25152i	−0.955037	−	0.296487i	$-0.904185\pi$
$523$	−28.6213	−	28.6213i	−1.25152	−	1.25152i	−0.296487	−	0.955037i	$-0.595815\pi$
$524$	−7.77427	−	10.8255i	−0.339620	−	0.472913i
$525$	−8.96984	−	11.4316i	−0.391476	−	0.498916i
$526$	23.8038	+	12.2115i	1.03789	+	0.532445i
$527$	7.23740	−	7.23740i	0.315266	−	0.315266i
$528$	−4.48809	−	9.05401i	−0.195319	−	0.394025i
$529$			1.74027i			0.0756638i
$530$	7.59456	−	5.70252i	0.329887	−	0.247702i
$531$		−	14.8237i		−	0.643295i
$532$	1.33629	−	8.14585i	0.0579357	−	0.353168i
$533$	12.1839	−	12.1839i	0.527741	−	0.527741i
$534$	−5.41349	+	10.5525i	−0.234265	+	0.456651i
$535$	−13.0868	+	4.52143i	−0.565791	+	0.195478i
$536$	−0.974059	−	6.49759i	−0.0420729	−	0.280653i
$537$	6.51324	+	6.51324i	0.281067	+	0.281067i
$538$	−8.35866	−	25.9689i	−0.360368	−	1.11960i
$539$	36.0059			1.55088
$540$	10.0048	−	14.1531i	0.430536	−	0.609051i
$541$	4.01340			0.172549			0.0862747	−	0.996271i	$-0.472504\pi$
$541$	4.01340			0.172549			0.0862747	+	0.996271i	$0.472504\pi$
$542$	6.77751	+	21.0565i	0.291119	+	0.904455i
$543$	8.54327	+	8.54327i	0.366627	+	0.366627i
$544$	26.4048	−	25.6862i	1.13210	−	1.10129i
$545$	−10.2841	+	21.1415i	−0.440521	+	0.905600i
$546$	−8.75162	+	17.0595i	−0.374535	+	0.730079i
$547$	1.65661	−	1.65661i	0.0708313	−	0.0708313i	−0.670804	−	0.741635i	$-0.734051\pi$
$547$	1.65661	−	1.65661i	0.0708313	−	0.0708313i	0.741635	+	0.670804i	$0.234051\pi$
$548$	18.5373	+	3.04097i	0.791875	+	0.129904i
$549$		−	1.34240i		−	0.0572921i
$550$	14.2013	−	21.0238i	0.605545	−	0.896459i
$551$		−	4.88207i		−	0.207983i
$552$	−7.96548	−	5.88861i	−0.339034	−	0.250636i
$553$	−9.80122	+	9.80122i	−0.416790	+	0.416790i
$554$	16.8918	+	8.66558i	0.717663	+	0.368165i
$555$	5.34023	−	10.9782i	0.226680	−	0.465997i
$556$	11.0652	−	7.94642i	0.469269	−	0.337003i
$557$	−32.0355	−	32.0355i	−1.35739	−	1.35739i	−0.877126	−	0.480260i	$-0.840542\pi$
$557$	−32.0355	−	32.0355i	−1.35739	−	1.35739i	−0.480260	−	0.877126i	$-0.659458\pi$
$558$	−5.29866	+	1.70549i	−0.224310	+	0.0721992i
$559$	30.0924			1.27277
$560$	0.275435	+	36.9153i	0.0116393	+	1.55995i
$561$	−16.4515			−0.694582
$562$	8.15306	−	2.62424i	0.343916	−	0.110697i
$563$	−23.6795	−	23.6795i	−0.997973	−	0.997973i	0.00202496	−	0.999998i	$-0.499355\pi$
$563$	−23.6795	−	23.6795i	−0.997973	−	0.997973i	−0.999998	+	0.00202496i	$0.999355\pi$
$564$	2.59023	−	1.86016i	0.109068	−	0.0783269i
$565$	−28.7883	+	9.94622i	−1.21113	+	0.418441i
$566$	−16.3857	−	8.40598i	−0.688744	−	0.353330i
$567$	−13.9615	+	13.9615i	−0.586330	+	0.586330i
$568$	9.28533	+	6.86433i	0.389604	+	0.288021i
$569$		−	4.84313i		−	0.203035i	−0.994834	−	0.101517i	$-0.967630\pi$
$569$		−	4.84313i		−	0.203035i	0.994834	−	0.101517i	$-0.0323697\pi$
$570$	−1.33695	−	1.78054i	−0.0559986	−	0.0745784i
$571$			26.9143i			1.12633i	0.826345	+	0.563164i	$0.190416\pi$
$571$			26.9143i			1.12633i	−0.826345	+	0.563164i	$0.809584\pi$
$572$	−33.0355	−	5.41934i	−1.38128	−	0.226594i
$573$	−7.62536	+	7.62536i	−0.318554	+	0.318554i
$574$	9.84034	−	19.1817i	0.410728	−	0.800630i
$575$	2.97933	−	24.6907i	0.124246	−	1.02967i
$576$	−19.1532	+	5.87455i	−0.798048	+	0.244773i
$577$	11.9729	+	11.9729i	0.498439	+	0.498439i	0.910952	−	0.412513i	$-0.135349\pi$
$577$	11.9729	+	11.9729i	0.498439	+	0.498439i	−0.412513	+	0.910952i	$0.635349\pi$
$578$	−11.0085	−	34.2016i	−0.457894	−	1.42260i
$579$	12.6953			0.527600
$580$	3.69507	+	21.5183i	0.153430	+	0.893501i
$581$	72.5545			3.01007
$582$	−2.68136	−	8.33051i	−0.111146	−	0.345311i
$583$	7.61953	+	7.61953i	0.315569	+	0.315569i
$584$	−0.285222	−	1.90261i	−0.0118026	−	0.0787306i
$585$	−8.53067	−	24.6911i	−0.352700	−	1.02085i
$586$	−7.85841	+	15.3184i	−0.324628	+	0.632796i
$587$	0.478832	−	0.478832i	0.0197635	−	0.0197635i	−0.697156	−	0.716919i	$-0.745552\pi$
$587$	0.478832	−	0.478832i	0.0197635	−	0.0197635i	0.716919	+	0.697156i	$0.245552\pi$
$588$	−2.28768	+	13.9454i	−0.0943422	+	0.575097i
$589$			1.57175i			0.0647628i
$590$	18.5324	+	2.63698i	0.762966	+	0.108563i
$591$		−	9.93442i		−	0.408647i
$592$	−27.7889	+	13.7750i	−1.14212	+	0.566150i
$593$	23.9284	−	23.9284i	0.982622	−	0.982622i	−0.0172293	−	0.999852i	$-0.505485\pi$
$593$	23.9284	−	23.9284i	0.982622	−	0.982622i	0.999852	+	0.0172293i	$0.00548454\pi$
$594$	17.4973	+	8.97621i	0.717922	+	0.368298i
$595$	54.0447	+	26.2896i	2.21562	+	1.07777i
$596$	−22.2454	−	30.9762i	−0.911206	−	1.26883i
$597$	2.10377	+	2.10377i	0.0861016	+	0.0861016i
$598$	−31.2377	+	10.0546i	−1.27741	+	0.411161i
$599$	−1.72828			−0.0706158			−0.0353079	−	0.999376i	$-0.511241\pi$
$599$	−1.72828			−0.0706158			−0.0353079	+	0.999376i	$0.511241\pi$
$600$	7.24039	+	6.83604i	0.295588	+	0.279080i
$601$	−26.9304			−1.09852			−0.549258	−	0.835653i	$-0.685090\pi$
$601$	−26.9304			−1.09852			−0.549258	+	0.835653i	$0.685090\pi$
$602$	35.8402	−	11.5360i	1.46074	−	0.470171i
$603$	4.11332	+	4.11332i	0.167507	+	0.167507i
$604$	−7.09444	−	9.87884i	−0.288669	−	0.401964i
$605$	3.76734	+	1.83259i	0.153164	+	0.0745053i
$606$	1.97159	+	1.01144i	0.0800905	+	0.0410869i
$607$	15.1247	−	15.1247i	0.613894	−	0.613894i	−0.330065	−	0.943958i	$-0.607071\pi$
$607$	15.1247	−	15.1247i	0.613894	−	0.613894i	0.943958	+	0.330065i	$0.107071\pi$
$608$	−0.0780338	+	5.65632i	−0.00316469	+	0.229394i
$609$			14.1879i			0.574924i
$610$	1.67824	+	0.238798i	0.0679500	+	0.00966863i
$611$		−	10.5644i		−	0.427391i
$612$	−5.27979	+	32.1848i	−0.213423	+	1.30099i
$613$	−12.3720	+	12.3720i	−0.499701	+	0.499701i	−0.911345	−	0.411644i	$-0.864955\pi$
$613$	−12.3720	+	12.3720i	−0.499701	+	0.499701i	0.411644	+	0.911345i	$0.364955\pi$
$614$	−10.4068	+	20.2859i	−0.419983	+	0.818672i
$615$	−1.89895	−	5.49632i	−0.0765732	−	0.221633i
$616$	−41.4230	+	6.20975i	−1.66898	+	0.250198i
$617$	−18.4809	−	18.4809i	−0.744011	−	0.744011i	0.229336	−	0.973347i	$-0.426344\pi$
$617$	−18.4809	−	18.4809i	−0.744011	−	0.744011i	−0.973347	+	0.229336i	$0.926344\pi$
$618$	3.40583	+	10.5813i	0.137002	+	0.425643i
$619$	16.9676			0.681984			0.340992	−	0.940066i	$-0.389237\pi$
$619$	16.9676			0.681984			0.340992	+	0.940066i	$0.389237\pi$
$620$	−1.18960	−	6.92768i	−0.0477756	−	0.278223i
$621$	19.2770			0.773561
$622$	−4.77939	−	14.8487i	−0.191636	−	0.595379i
$623$	34.7607	+	34.7607i	1.39266	+	1.39266i
$624$	4.19790	−	12.4506i	0.168051	−	0.498422i
$625$	−5.94671	+	24.2824i	−0.237868	+	0.971297i
$626$	−20.0603	+	39.1034i	−0.801770	+	1.56289i
$627$	1.78639	−	1.78639i	0.0713415	−	0.0713415i
$628$	20.8440	+	3.41937i	0.831766	+	0.136448i
$629$			50.4936i			2.01331i
$630$	−19.6254	−	26.1370i	−0.781896	−	1.04132i
$631$		−	26.7082i		−	1.06324i	−0.846984	−	0.531619i	$-0.821584\pi$
$631$		−	26.7082i		−	1.06324i	0.846984	−	0.531619i	$-0.178416\pi$
$632$	5.64665	−	7.63819i	0.224612	−	0.303831i
$633$	6.38687	−	6.38687i	0.253855	−	0.253855i
$634$	30.9077	+	15.8558i	1.22750	+	0.629715i
$635$	−37.3380	+	12.9001i	−1.48171	+	0.511925i
$636$	−3.43522	+	2.46699i	−0.136215	+	0.0978224i
$637$	33.1038	+	33.1038i	1.31162	+	1.31162i
$638$	−23.5810	+	7.59007i	−0.933581	+	0.300494i
$639$	−10.2236			−0.404439
$640$	−3.93713	−	24.9900i	−0.155629	−	0.987816i
$641$	3.98093			0.157237			0.0786186	−	0.996905i	$-0.474949\pi$
$641$	3.98093			0.157237			0.0786186	+	0.996905i	$0.474949\pi$
$642$	5.86928	−	1.88916i	0.231642	−	0.0745592i
$643$	−6.39670	−	6.39670i	−0.252261	−	0.252261i	0.569636	−	0.821897i	$-0.307084\pi$
$643$	−6.39670	−	6.39670i	−0.252261	−	0.252261i	−0.821897	+	0.569636i	$0.807084\pi$
$644$	−33.3499	+	23.9500i	−1.31417	+	0.943764i
$645$	4.44249	−	9.13264i	0.174923	−	0.359598i
$646$	8.19402	+	4.20358i	0.322390	+	0.165388i
$647$	20.5555	−	20.5555i	0.808120	−	0.808120i	−0.176230	−	0.984349i	$-0.556390\pi$
$647$	20.5555	−	20.5555i	0.808120	−	0.808120i	0.984349	+	0.176230i	$0.0563901\pi$
$648$	8.04348	−	10.8804i	0.315978	−	0.427421i
$649$			21.2389i			0.833702i
$650$	32.3859	−	6.27263i	1.27028	−	0.246033i
$651$		−	4.56771i		−	0.179023i
$652$	−28.0194	−	4.59647i	−1.09732	−	0.180012i
$653$	−19.4414	+	19.4414i	−0.760800	+	0.760800i	−0.976467	−	0.215667i	$-0.930807\pi$
$653$	−19.4414	+	19.4414i	−0.760800	+	0.760800i	0.215667	+	0.976467i	$0.430807\pi$
$654$	4.77877	−	9.31524i	0.186865	−	0.364255i
$655$	−6.51815	+	13.3997i	−0.254685	+	0.523569i
$656$	−4.72013	+	13.9995i	−0.184290	+	0.546587i
$657$	1.20445	+	1.20445i	0.0469901	+	0.0469901i
$658$	−4.04989	−	12.5823i	−0.157881	−	0.490508i
$659$	9.30532			0.362484			0.181242	−	0.983439i	$-0.441988\pi$
$659$	9.30532			0.362484			0.181242	+	0.983439i	$0.441988\pi$
$660$	−6.52168	+	9.22579i	−0.253856	+	0.359113i
$661$	20.9486			0.814805			0.407402	−	0.913249i	$-0.366435\pi$
$661$	20.9486			0.814805			0.407402	+	0.913249i	$0.366435\pi$
$662$	−10.5100	−	32.6527i	−0.408483	−	1.26908i
$663$	−15.1255	−	15.1255i	−0.587425	−	0.587425i
$664$	−49.1711	+	7.37128i	−1.90821	+	0.286061i
$665$	−8.72312	+	3.01380i	−0.338268	+	0.116870i
$666$	12.5343	−	24.4331i	0.485695	−	0.946764i
$667$	−17.1708	+	17.1708i	−0.664857	+	0.664857i
$668$	7.57060	−	46.1493i	0.292915	−	1.78557i
$669$		−	13.3961i		−	0.517924i
$670$	−5.87411	+	4.41069i	−0.226937	+	0.170400i
$671$			1.92334i			0.0742498i
$672$	0.226776	−	16.4380i	0.00874809	−	0.634109i
$673$	−2.71457	+	2.71457i	−0.104639	+	0.104639i	−0.757488	−	0.652849i	$-0.773574\pi$
$673$	−2.71457	+	2.71457i	−0.104639	+	0.104639i	0.652849	+	0.757488i	$0.273574\pi$
$674$	−30.2382	−	15.5124i	−1.16473	−	0.597514i
$675$	−19.2384	−	2.32142i	−0.740487	−	0.0893515i
$676$	−10.2242	−	14.2369i	−0.393237	−	0.547573i
$677$	−19.1114	−	19.1114i	−0.734513	−	0.734513i	0.236998	−	0.971510i	$-0.423837\pi$
$677$	−19.1114	−	19.1114i	−0.734513	−	0.734513i	−0.971510	+	0.236998i	$0.923837\pi$
$678$	12.9112	−	4.15577i	0.495853	−	0.159601i
$679$	−36.2739			−1.39206
$680$	−39.2977	−	12.3260i	−1.50700	−	0.472682i
$681$	14.9359			0.572345
$682$	7.59175	−	2.44357i	0.290703	−	0.0935692i
$683$	12.0794	+	12.0794i	0.462204	+	0.462204i	0.899377	−	0.437173i	$-0.144020\pi$
$683$	12.0794	+	12.0794i	0.462204	+	0.462204i	−0.437173	+	0.899377i	$0.644020\pi$
$684$	−2.92149	−	4.06811i	−0.111706	−	0.155548i
$685$	−6.85842	−	19.8510i	−0.262047	−	0.758467i
$686$	15.7629	+	8.08648i	0.601832	+	0.308743i
$687$	−10.7009	+	10.7009i	−0.408264	+	0.408264i
$688$	−23.1174	+	11.4593i	−0.881342	+	0.436882i
$689$			14.0108i			0.533768i
$690$	−1.56015	+	10.9646i	−0.0593939	+	0.417414i
$691$		−	16.1397i		−	0.613985i	−0.951712	−	0.306992i	$-0.900677\pi$
$691$		−	16.1397i		−	0.613985i	0.951712	−	0.306992i	$-0.0993226\pi$
$692$	2.43919	−	14.8689i	0.0927240	−	0.565232i
$693$	26.2229	−	26.2229i	0.996126	−	0.996126i
$694$	3.80053	−	7.40836i	0.144266	−	0.281217i
$695$	−13.6964	−	6.66249i	−0.519534	−	0.252723i
$696$	−1.44144	−	9.61535i	−0.0546378	−	0.364469i
$697$	17.0071	+	17.0071i	0.644190	+	0.644190i
$698$	11.0477	+	34.3232i	0.418161	+	1.29915i
$699$	1.80941			0.0684383
$700$	36.1672	−	19.8859i	1.36699	−	0.751617i
$701$	1.39112			0.0525418			0.0262709	−	0.999655i	$-0.491637\pi$
$701$	1.39112			0.0525418			0.0262709	+	0.999655i	$0.491637\pi$
$702$	7.83427	+	24.3397i	0.295686	+	0.918643i
$703$	−5.48286	−	5.48286i	−0.206790	−	0.206790i
$704$	27.4420	−	8.41686i	1.03426	−	0.317222i
$705$	−3.20616	−	1.55961i	−0.120751	−	0.0587383i
$706$	−7.93654	+	15.4707i	−0.298696	+	0.582246i
$707$	6.49457	−	6.49457i	0.244253	−	0.244253i
$708$	−8.22601	−	1.34944i	−0.309152	−	0.0507151i
$709$			0.442717i			0.0166266i	0.999965	+	0.00831330i	$0.00264624\pi$
$709$			0.442717i			0.0166266i	−0.999965	+	0.00831330i	$0.997354\pi$
$710$	1.81866	−	12.7814i	0.0682532	−	0.479676i
$711$			8.40999i			0.315399i
$712$	−27.0893	−	20.0262i	−1.01522	−	0.750514i
$713$	5.52803	−	5.52803i	0.207026	−	0.207026i
$714$	−23.8129	−	12.2161i	−0.891175	−	0.457178i
$715$	12.2225	+	35.3766i	0.457094	+	1.32301i
$716$	−21.2515	+	15.2616i	−0.794204	+	0.570354i
$717$	−11.3978	−	11.3978i	−0.425658	−	0.425658i
$718$	−14.5761	+	4.69163i	−0.543974	+	0.175090i
$719$	−3.55928			−0.132739			−0.0663694	−	0.997795i	$-0.521142\pi$
$719$	−3.55928			−0.132739			−0.0663694	+	0.997795i	$0.521142\pi$
$720$	15.9558	+	15.7195i	0.594639	+	0.585831i
$721$	46.0746			1.71591
$722$	−1.34620	+	0.433304i	−0.0501003	+	0.0161259i
$723$	−6.98512	−	6.98512i	−0.259779	−	0.259779i
$724$	−27.8751	+	20.0183i	−1.03597	+	0.743976i
$725$	19.2042	−	15.0686i	0.713227	−	0.559635i
$726$	−1.65994	−	0.851561i	−0.0616063	−	0.0316044i
$727$	25.1946	−	25.1946i	0.934415	−	0.934415i	−0.0635627	−	0.997978i	$-0.520246\pi$
$727$	25.1946	−	25.1946i	0.934415	−	0.934415i	0.997978	+	0.0635627i	$0.0202463\pi$
$728$	−43.7935	−	32.3750i	−1.62309	−	1.19990i
$729$			3.79323i			0.140490i
$730$	−1.72004	+	1.29153i	−0.0636617	+	0.0478016i
$731$			42.0052i			1.55362i
$732$	−0.744925	−	0.122202i	−0.0275332	−	0.00451671i
$733$	−7.66294	+	7.66294i	−0.283037	+	0.283037i	−0.834319	−	0.551282i	$-0.814139\pi$
$733$	−7.66294	+	7.66294i	−0.283037	+	0.283037i	0.551282	+	0.834319i	$0.314139\pi$
$734$	18.9542	−	36.9473i	0.699612	−	1.36375i
$735$	14.9336	−	5.15950i	0.550834	−	0.190311i
$736$	20.1684	−	19.6195i	0.743417	−	0.723184i
$737$	−5.89343	−	5.89343i	−0.217087	−	0.217087i
$738$	−4.00772	−	12.4513i	−0.147526	−	0.458338i
$739$	50.2765			1.84945			0.924725	−	0.380635i	$-0.124294\pi$
$739$	50.2765			1.84945			0.924725	+	0.380635i	$0.124294\pi$
$740$	28.3162	+	20.0166i	1.04092	+	0.735825i
$741$	3.28481			0.120670
$742$	5.37105	+	16.6869i	0.197177	+	0.612595i
$743$	−17.6854	−	17.6854i	−0.648814	−	0.648814i	0.303893	−	0.952706i	$-0.401714\pi$
$743$	−17.6854	−	17.6854i	−0.648814	−	0.648814i	−0.952706	+	0.303893i	$0.901714\pi$
$744$	0.464063	+	3.09560i	0.0170134	+	0.113490i
$745$	−18.6511	+	38.3420i	−0.683324	+	1.40474i
$746$	−1.69512	+	3.30429i	−0.0620627	+	0.120979i
$747$	31.1279	−	31.1279i	1.13891	−	1.13891i
$748$	7.56471	−	46.1134i	0.276593	−	1.68607i
$749$		−	25.5569i		−	0.933827i
$750$	2.87742	−	10.7547i	0.105069	−	0.392707i
$751$		−	40.6953i		−	1.48499i	−0.669851	−	0.742496i	$-0.733642\pi$
$751$		−	40.6953i		−	1.48499i	0.669851	−	0.742496i	$-0.266358\pi$
$752$	4.02298	+	8.11573i	0.146703	+	0.295950i
$753$	2.63329	−	2.63329i	0.0959625	−	0.0959625i
$754$	−28.6587	−	14.7021i	−1.04369	−	0.535417i
$755$	−5.94817	+	12.2279i	−0.216476	+	0.445020i
$756$	18.6613	+	25.9854i	0.678705	+	0.945081i
$757$	13.3742	+	13.3742i	0.486092	+	0.486092i	0.907071	−	0.420978i	$-0.138313\pi$
$757$	13.3742	+	13.3742i	0.486092	+	0.486092i	−0.420978	+	0.907071i	$0.638313\pi$
$758$	23.2141	−	7.47198i	0.843175	−	0.271394i
$759$	−12.5659			−0.456113
$760$	5.60558	−	2.92873i	0.203336	−	0.106236i
$761$	37.9781			1.37670			0.688352	−	0.725377i	$-0.258334\pi$
$761$	37.9781			1.37670			0.688352	+	0.725377i	$0.258334\pi$
$762$	16.7457	−	5.38997i	0.606632	−	0.195258i
$763$	−30.6851	−	30.6851i	−1.11087	−	1.11087i
$764$	−17.8675	−	24.8801i	−0.646424	−	0.900130i
$765$	34.4656	−	11.9077i	1.24611	−	0.430525i
$766$	−15.6512	−	8.02916i	−0.565501	−	0.290105i
$767$	−19.5271	+	19.5271i	−0.705081	+	0.705081i
$768$	1.51635	+	11.1633i	0.0547166	+	0.402820i
$769$			32.0784i			1.15678i	0.815762	+	0.578388i	$0.196318\pi$
$769$			32.0784i			1.15678i	−0.815762	+	0.578388i	$0.803682\pi$
$770$	28.1187	+	37.4482i	1.01333	+	1.34954i
$771$			14.0740i

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)

\(f(q)\)	\(=\)	\(q+(-1.34620 + 0.433304i) q^{2} +(-0.497882 - 0.497882i) q^{3} +(1.62450 - 1.16662i) q^{4} +(-2.01079 - 0.978129i) q^{5} +(0.885982 + 0.454514i) q^{6} +(2.91849 - 2.91849i) q^{7} +(-1.68139 + 2.27441i) q^{8} -2.50423i q^{9} +O(q^{10})\)	\(q+(-1.34620 + 0.433304i) q^{2} +(-0.497882 - 0.497882i) q^{3} +(1.62450 - 1.16662i) q^{4} +(-2.01079 - 0.978129i) q^{5} +(0.885982 + 0.454514i) q^{6} +(2.91849 - 2.91849i) q^{7} +(-1.68139 + 2.27441i) q^{8} -2.50423i q^{9} +(3.13074 + 0.445474i) q^{10} +3.58797i q^{11} +(-1.38965 - 0.227966i) q^{12} +(-3.29878 + 3.29878i) q^{13} +(-2.66427 + 5.19345i) q^{14} +(0.514142 + 1.48813i) q^{15} +(1.27798 - 3.79035i) q^{16} +(-4.60467 - 4.60467i) q^{17} +(1.08509 + 3.37118i) q^{18} +1.00000 q^{19} +(-4.40762 + 0.756866i) q^{20} -2.90613 q^{21} +(-1.55468 - 4.83012i) q^{22} +(-3.51712 - 3.51712i) q^{23} +(1.96952 - 0.295252i) q^{24} +(3.08653 + 3.93362i) q^{25} +(3.01144 - 5.87018i) q^{26} +(-2.74046 + 2.74046i) q^{27} +(1.33629 - 8.14585i) q^{28} -4.88207i q^{29} +(-1.33695 - 1.78054i) q^{30} +1.57175i q^{31} +(-0.0780338 + 5.65632i) q^{32} +(1.78639 - 1.78639i) q^{33} +(8.19402 + 4.20358i) q^{34} +(-8.72312 + 3.01380i) q^{35} +(-2.92149 - 4.06811i) q^{36} +(-5.48286 - 5.48286i) q^{37} +(-1.34620 + 0.433304i) q^{38} +3.28481 q^{39} +(5.60558 - 2.92873i) q^{40} -3.69344 q^{41} +(3.91222 - 1.25924i) q^{42} +(-4.56114 - 4.56114i) q^{43} +(4.18582 + 5.82865i) q^{44} +(-2.44946 + 5.03546i) q^{45} +(6.25872 + 3.21076i) q^{46} +(-1.60126 + 1.60126i) q^{47} +(-2.52343 + 1.25087i) q^{48} -10.0352i q^{49} +(-5.85953 - 3.95803i) q^{50} +4.58517i q^{51} +(-1.51042 + 9.20729i) q^{52} +(2.12363 - 2.12363i) q^{53} +(2.50175 - 4.87665i) q^{54} +(3.50950 - 7.21465i) q^{55} +(1.73071 + 11.5450i) q^{56} +(-0.497882 - 0.497882i) q^{57} +(2.11542 + 6.57224i) q^{58} +5.91948 q^{59} +(2.57131 + 1.81765i) q^{60} +0.536052 q^{61} +(-0.681045 - 2.11589i) q^{62} +(-7.30856 - 7.30856i) q^{63} +(-2.34585 - 7.64833i) q^{64} +(9.85977 - 3.40651i) q^{65} +(-1.63078 + 3.17888i) q^{66} +(-1.64255 + 1.64255i) q^{67} +(-12.8522 - 2.10835i) q^{68} +3.50222i q^{69} +(10.4372 - 7.83693i) q^{70} -4.08253i q^{71} +(5.69563 + 4.21058i) q^{72} +(-0.480968 + 0.480968i) q^{73} +(9.75675 + 5.00527i) q^{74} +(0.421752 - 3.49521i) q^{75} +(1.62450 - 1.16662i) q^{76} +(10.4715 + 10.4715i) q^{77} +(-4.42200 + 1.42332i) q^{78} -3.35832 q^{79} +(-6.27719 + 6.37157i) q^{80} -4.78383 q^{81} +(4.97210 - 1.60038i) q^{82} +(12.4301 + 12.4301i) q^{83} +(-4.72100 + 3.39036i) q^{84} +(4.75505 + 13.7630i) q^{85} +(8.11656 + 4.16384i) q^{86} +(-2.43070 + 2.43070i) q^{87} +(-8.16051 - 6.03279i) q^{88} +11.9105i q^{89} +(1.11557 - 7.84009i) q^{90} +19.2549i q^{91} +(-9.81671 - 1.61039i) q^{92} +(0.782547 - 0.782547i) q^{93} +(1.46178 - 2.84945i) q^{94} +(-2.01079 - 0.978129i) q^{95} +(2.85503 - 2.77733i) q^{96} +(-6.21450 - 6.21450i) q^{97} +(4.34827 + 13.5093i) q^{98} +8.98510 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Introduction

L-functions

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Varieties

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