LMFDB - Embedded newform 380.2.k.d.343.15

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			343.15
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.433304 + 1.34620i) q^{2} +(0.497882 - 0.497882i) q^{3} +(-1.62450 + 1.16662i) q^{4} +(-2.01079 + 0.978129i) q^{5} +(0.885982 + 0.454514i) q^{6} +(-2.91849 - 2.91849i) q^{7} +(-2.27441 - 1.68139i) q^{8} +2.50423i q^{9} +O(q^{10})$	\(q+(0.433304 + 1.34620i) 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} +(-2.27441 - 1.68139i) q^{8} +2.50423i q^{9} +(-2.18804 - 2.28309i) q^{10} +3.58797i q^{11} +(-0.227966 + 1.38965i) 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} +(-3.37118 + 1.08509i) q^{18} -1.00000 q^{19} +(2.12541 - 3.93480i) q^{20} -2.90613 q^{21} +(-4.83012 + 1.55468i) 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} +(8.14585 + 1.33629i) q^{28} +4.88207i q^{29} +(-2.22610 - 0.0473253i) q^{30} +1.57175i q^{31} +(5.65632 + 0.0780338i) 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} +(-0.433304 - 1.34620i) q^{38} -3.28481 q^{39} +(6.21796 + 1.15625i) q^{40} -3.69344 q^{41} +(-1.25924 - 3.91222i) 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} +(-1.25087 - 2.52343i) q^{48} +10.0352i q^{49} +(6.63283 + 2.45062i) q^{50} +4.58517i q^{51} +(9.20729 + 1.51042i) 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} +(-6.57224 + 2.11542i) q^{58} -5.91948 q^{59} +(-0.900866 - 3.01727i) q^{60} +0.536052 q^{61} +(-2.11589 + 0.681045i) 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} +(2.10835 - 12.8522i) q^{68} -3.50222i q^{69} +(-0.277412 + 13.0489i) q^{70} -4.08253i q^{71} +(4.21058 - 5.69563i) 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} +(-1.42332 - 4.42200i) q^{78} +3.35832 q^{79} +(1.13772 + 8.87162i) q^{80} -4.78383 q^{81} +(-1.60038 - 4.97210i) 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} +(6.03279 - 8.16051i) q^{88} -11.9105i q^{89} +(5.71737 - 5.47934i) q^{90} +19.2549i q^{91} +(-1.61039 + 9.81671i) 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} +(-13.5093 + 4.34827i) 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} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.433304	+	1.34620i	0.306392	+	0.951905i
$2$	0.433304	+	1.34620i	0.306392	+	0.951905i
$3$	0.497882	−	0.497882i	0.287453	−	0.287453i	−0.548620	−	0.836072i	$-0.684846\pi$
$3$	0.497882	−	0.497882i	0.287453	−	0.287453i	0.836072	+	0.548620i	$0.184846\pi$
$4$	−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	−0.994036	−	0.109049i	$-0.965220\pi$
$7$	−2.91849	−	2.91849i	−1.10309	−	1.10309i	−0.109049	−	0.994036i	$-0.534780\pi$
$8$	−2.27441	−	1.68139i	−0.804124	−	0.594461i
$9$			2.50423i			0.834742i
$10$	−2.18804	−	2.28309i	−0.691918	−	0.721976i
$11$			3.58797i			1.08182i	0.841082	+	0.540908i	$0.181919\pi$
$11$			3.58797i			1.08182i	−0.841082	+	0.540908i	$0.818081\pi$
$12$	−0.227966	+	1.38965i	−0.0658082	+	0.401157i
$13$	−3.29878	−	3.29878i	−0.914917	−	0.914917i	0.0817371	−	0.996654i	$-0.473953\pi$
$13$	−3.29878	−	3.29878i	−0.914917	−	0.914917i	−0.996654	+	0.0817371i	$0.973953\pi$
$14$	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	−0.124589	+	0.992208i	$0.539761\pi$
$17$	−4.60467	+	4.60467i	−1.11680	+	1.11680i	−0.992208	+	0.124589i	$0.960239\pi$
$18$	−3.37118	+	1.08509i	−0.794596	+	0.255758i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	2.12541	−	3.93480i	0.475255	−	0.879848i
$21$	−2.90613			−0.634169
$22$	−4.83012	+	1.55468i	−1.02979	+	0.331459i
$23$	3.51712	−	3.51712i	0.733370	−	0.733370i	−0.237916	−	0.971286i	$-0.576464\pi$
$23$	3.51712	−	3.51712i	0.733370	−	0.733370i	0.971286	+	0.237916i	$0.0764642\pi$
$24$	−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
$28$	8.14585	+	1.33629i	1.53942	+	0.252536i
$29$			4.88207i			0.906578i	0.891364	+	0.453289i	$0.149749\pi$
$29$			4.88207i			0.906578i	−0.891364	+	0.453289i	$0.850251\pi$
$30$	−2.22610	−	0.0473253i	−0.406427	−	0.00864038i
$31$			1.57175i			0.282295i	0.989989	+	0.141147i	$0.0450791\pi$
$31$			1.57175i			0.282295i	−0.989989	+	0.141147i	$0.954921\pi$
$32$	5.65632	+	0.0780338i	0.999905	+	0.0137946i
$33$	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	−0.995555	−	0.0941788i	$-0.969977\pi$
$37$	−5.48286	+	5.48286i	−0.901376	+	0.901376i	0.0941788	+	0.995555i	$0.469977\pi$
$38$	−0.433304	−	1.34620i	−0.0702911	−	0.218382i
$39$	−3.28481			−0.525990
$40$	6.21796	+	1.15625i	0.983146	+	0.182820i
$41$	−3.69344			−0.576819			−0.288409	−	0.957507i	$-0.593126\pi$
$41$	−3.69344			−0.576819			−0.288409	+	0.957507i	$0.593126\pi$
$42$	−1.25924	−	3.91222i	−0.194304	−	0.603669i
$43$	4.56114	−	4.56114i	0.695568	−	0.695568i	−0.267884	−	0.963451i	$-0.586324\pi$
$43$	4.56114	−	4.56114i	0.695568	−	0.695568i	0.963451	+	0.267884i	$0.0863242\pi$
$44$	−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	$-0.197187\pi$
$47$	1.60126	+	1.60126i	0.233568	+	0.233568i	−0.580612	+	0.814180i	$0.697187\pi$
$48$	−1.25087	−	2.52343i	−0.180547	−	0.364226i
$49$			10.0352i			1.43359i
$50$	6.63283	+	2.45062i	0.938024	+	0.346571i
$51$			4.58517i			0.642053i
$52$	9.20729	+	1.51042i	1.27682	+	0.209457i
$53$	2.12363	+	2.12363i	0.291703	+	0.291703i	0.837753	−	0.546050i	$-0.183869\pi$
$53$	2.12363	+	2.12363i	0.291703	+	0.291703i	−0.546050	+	0.837753i	$0.683869\pi$
$54$	−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
$58$	−6.57224	+	2.11542i	−0.862977	+	0.277768i
$59$	−5.91948			−0.770651			−0.385325	−	0.922781i	$-0.625911\pi$
$59$	−5.91948			−0.770651			−0.385325	+	0.922781i	$0.625911\pi$
$60$	−0.900866	−	3.01727i	−0.116301	−	0.389528i
$61$	0.536052			0.0686345			0.0343172	−	0.999411i	$-0.489074\pi$
$61$	0.536052			0.0686345			0.0343172	+	0.999411i	$0.489074\pi$
$62$	−2.11589	+	0.681045i	−0.268718	+	0.0864928i
$63$	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	$-0.204681\pi$
$67$	1.64255	+	1.64255i	0.200669	+	0.200669i	−0.599617	+	0.800287i	$0.704681\pi$
$68$	2.10835	−	12.8522i	0.255675	−	1.55856i
$69$		−	3.50222i		−	0.421618i
$70$	−0.277412	+	13.0489i	−0.0331570	+	1.55965i
$71$		−	4.08253i		−	0.484507i	−0.970213	−	0.242254i	$-0.922113\pi$
$71$		−	4.08253i		−	0.484507i	0.970213	−	0.242254i	$-0.0778866\pi$
$72$	4.21058	−	5.69563i	0.496222	−	0.671236i
$73$	−0.480968	−	0.480968i	−0.0562930	−	0.0562930i	0.678400	−	0.734693i	$-0.262674\pi$
$73$	−0.480968	−	0.480968i	−0.0562930	−	0.0562930i	−0.734693	+	0.678400i	$0.762674\pi$
$74$	−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
$78$	−1.42332	−	4.42200i	−0.161159	−	0.500693i
$79$	3.35832			0.377841			0.188920	−	0.981992i	$-0.439501\pi$
$79$	3.35832			0.377841			0.188920	+	0.981992i	$0.439501\pi$
$80$	1.13772	+	8.87162i	0.127201	+	0.991877i
$81$	−4.78383			−0.531536
$82$	−1.60038	−	4.97210i	−0.176733	−	0.549077i
$83$	−12.4301	+	12.4301i	−1.36439	+	1.36439i	−0.496147	+	0.868238i	$0.665252\pi$
$83$	−12.4301	+	12.4301i	−1.36439	+	1.36439i	−0.868238	+	0.496147i	$0.834748\pi$
$84$	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
$88$	6.03279	−	8.16051i	0.643097	−	0.869914i
$89$		−	11.9105i		−	1.26251i	−0.775575	−	0.631256i	$-0.782540\pi$
$89$		−	11.9105i		−	1.26251i	0.775575	−	0.631256i	$-0.217460\pi$
$90$	5.71737	−	5.47934i	0.602664	−	0.577573i
$91$			19.2549i			2.01846i
$92$	−1.61039	+	9.81671i	−0.167895	+	1.02346i
$93$	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	−0.948316	−	0.317329i	$-0.897214\pi$
$97$	−6.21450	+	6.21450i	−0.630986	+	0.630986i	0.317329	+	0.948316i	$0.397214\pi$
$98$	−13.5093	+	4.34827i	−1.36465	+	0.439241i
$99$	−8.98510			−0.903037
$100$	−0.424995	+	9.99096i	−0.0424995	+	0.999096i
$101$	2.22532			0.221427			0.110714	−	0.993852i	$-0.464686\pi$
$101$	2.22532			0.221427			0.110714	+	0.993852i	$0.464686\pi$
$102$	−6.17255	+	1.98677i	−0.611173	+	0.196720i
$103$	−7.89357	+	7.89357i	−0.777777	+	0.777777i	−0.979452	−	0.201676i	$-0.935361\pi$
$103$	−7.89357	+	7.89357i	−0.777777	+	0.777777i	0.201676	+	0.979452i	$0.435361\pi$
$104$	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	$-0.346754\pi$
$107$	−4.37844	−	4.37844i	−0.423280	−	0.423280i	−0.886331	+	0.463052i	$0.846754\pi$
$108$	−7.64895	−	1.25478i	−0.736020	−	0.120741i
$109$			10.5140i			1.00706i	0.863978	+	0.503530i	$0.167966\pi$
$109$			10.5140i			1.00706i	−0.863978	+	0.503530i	$0.832034\pi$
$110$	8.19167	−	7.85062i	0.781045	−	0.748527i
$111$			5.45964i			0.518206i
$112$	−14.7919	+	7.33235i	−1.39770	+	0.692842i
$113$	9.63168	+	9.63168i	0.906072	+	0.906072i	0.995953	−	0.0898805i	$-0.0286485\pi$
$113$	9.63168	+	9.63168i	0.906072	+	0.906072i	−0.0898805	+	0.995953i	$0.528649\pi$
$114$	−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
$118$	−2.56493	−	7.96879i	−0.236121	−	0.733587i
$119$	26.8774			2.46385
$120$	3.67149	−	2.52014i	0.335160	−	0.230056i
$121$	−1.87356			−0.170324
$122$	0.232273	+	0.721632i	0.0210290	+	0.0653335i
$123$	−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	−0.993348	−	0.115151i	$-0.963265\pi$
$127$	−12.4921	−	12.4921i	−1.10850	−	1.10850i	−0.115151	−	0.993348i	$-0.536735\pi$
$128$	−9.27970	+	6.47203i	−0.820217	+	0.572052i
$129$		−	4.54183i		−	0.399886i
$130$	−0.313560	+	14.7493i	−0.0275010	+	1.29360i
$131$		−	6.66390i		−	0.582227i	−0.956688	−	0.291114i	$-0.905974\pi$
$131$		−	6.66390i		−	0.582227i	0.956688	−	0.291114i	$-0.0940258\pi$
$132$	−4.98603	−	0.817937i	−0.433978	−	0.0711923i
$133$	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	−0.363982	−	0.931406i	$-0.618583\pi$
$137$	6.64153	−	6.64153i	0.567424	−	0.567424i	0.931406	+	0.363982i	$0.118583\pi$
$138$	4.71469	−	1.51753i	0.401341	−	0.129180i
$139$	−6.81147			−0.577741			−0.288871	−	0.957368i	$-0.593280\pi$
$139$	−6.81147			−0.577741			−0.288871	+	0.957368i	$0.593280\pi$
$140$	−17.6866	+	5.28070i	−1.49479	+	0.446300i
$141$	1.59448			0.134280
$142$	5.49589	−	1.76897i	0.461205	−	0.148449i
$143$	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
$148$	2.51045	−	15.3033i	0.206357	−	1.25793i
$149$			19.0682i			1.56212i	0.624453	+	0.781062i	$0.285322\pi$
$149$			19.0682i			1.56212i	−0.624453	+	0.781062i	$0.714678\pi$
$150$	4.52249	−	2.08225i	0.369260	−	0.170015i
$151$		−	6.08117i		−	0.494879i	−0.968903	−	0.247439i	$-0.920411\pi$
$151$		−	6.08117i		−	0.494879i	0.968903	−	0.247439i	$-0.0795891\pi$
$152$	2.27441	+	1.68139i	0.184479	+	0.136379i
$153$	−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	−0.343239	−	0.939248i	$-0.611524\pi$
$157$	7.46797	−	7.46797i	0.596009	−	0.596009i	0.939248	+	0.343239i	$0.111524\pi$
$158$	1.45517	+	4.52096i	0.115767	+	0.359668i
$159$	2.11464			0.167702
$160$	−11.4500	+	5.37570i	−0.905200	+	0.424986i
$161$	−20.5294			−1.61794
$162$	−2.07285	−	6.43998i	−0.162858	−	0.505972i
$163$	10.0388	−	10.0388i	0.786297	−	0.786297i	−0.194588	−	0.980885i	$-0.562337\pi$
$163$	10.0388	−	10.0388i	0.786297	−	0.786297i	0.980885	+	0.194588i	$0.0623370\pi$
$164$	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	−0.940968	−	0.338497i	$-0.890082\pi$
$167$	−16.5343	−	16.5343i	−1.27946	−	1.27946i	−0.338497	−	0.940968i	$-0.609918\pi$
$168$	6.60972	+	4.88634i	0.509951	+	0.376989i
$169$			8.76389i			0.674146i
$170$	20.5881	+	0.437689i	1.57903	+	0.0335692i
$171$		−	2.50423i		−	0.191503i
$172$	−2.08842	+	12.7307i	−0.159240	+	0.970707i
$173$	5.32723	+	5.32723i	0.405022	+	0.405022i	0.879998	−	0.474977i	$-0.157543\pi$
$173$	5.32723	+	5.32723i	0.405022	+	0.405022i	−0.474977	+	0.879998i	$0.657543\pi$
$174$	−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
$178$	16.0339	−	5.16086i	1.20179	−	0.386823i
$179$	13.0819			0.977785			0.488893	−	0.872344i	$-0.337401\pi$
$179$	13.0819			0.977785			0.488893	+	0.872344i	$0.337401\pi$
$180$	9.85363	+	5.32250i	0.734446	+	0.396715i
$181$	−17.1592			−1.27543			−0.637717	−	0.770271i	$-0.720121\pi$
$181$	−17.1592			−1.27543			−0.637717	+	0.770271i	$0.720121\pi$
$182$	−25.9209	+	8.34322i	−1.92139	+	0.618440i
$183$	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
$188$	−4.46932	−	0.733173i	−0.325958	−	0.0534721i
$189$		−	15.9960i		−	1.16354i
$190$	2.18804	+	2.28309i	0.158737	+	0.165633i
$191$		−	15.3156i		−	1.10820i	−0.832451	−	0.554098i	$-0.813063\pi$
$191$		−	15.3156i		−	1.10820i	0.832451	−	0.554098i	$-0.186937\pi$
$192$	4.97593	+	2.64001i	0.359107	+	0.190526i
$193$	−12.7493	−	12.7493i	−0.917717	−	0.917717i	0.0791463	−	0.996863i	$-0.474781\pi$
$193$	−12.7493	−	12.7493i	−0.917717	−	0.917717i	−0.996863	+	0.0791463i	$0.974781\pi$
$194$	−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	−0.255896	−	0.966704i	$-0.582370\pi$
$197$	9.97667	−	9.97667i	0.710808	−	0.710808i	0.966704	+	0.255896i	$0.0823705\pi$
$198$	−3.89328	−	12.0957i	−0.276683	−	0.859605i
$199$	4.22544			0.299533			0.149767	−	0.988721i	$-0.452148\pi$
$199$	4.22544			0.299533			0.149767	+	0.988721i	$0.452148\pi$
$200$	−13.6340	+	3.75699i	−0.964067	+	0.265660i
$201$	1.63559			0.115366
$202$	0.964238	+	2.99572i	0.0678436	+	0.210778i
$203$	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
$208$	−16.7193	+	8.28778i	−1.15927	+	0.574654i
$209$		−	3.58797i		−	0.248185i
$210$	6.35872	+	6.63495i	0.438793	+	0.457855i
$211$			12.8281i			0.883120i	0.897232	+	0.441560i	$0.145575\pi$
$211$			12.8281i			0.883120i	−0.897232	+	0.441560i	$0.854425\pi$
$212$	−5.92731	−	0.972350i	−0.407089	−	0.0667813i
$213$	−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
$218$	−14.1540	+	4.55576i	−0.958627	+	0.308555i
$219$	−0.478931			−0.0323631
$220$	14.1180	+	7.62590i	0.951833	+	0.514138i
$221$	30.3796			2.04355
$222$	−7.34975	+	2.36568i	−0.493283	+	0.158774i
$223$	−13.4531	+	13.4531i	−0.900887	+	0.900887i	−0.995513	−	0.0946261i	$-0.969834\pi$
$223$	−13.4531	+	13.4531i	−0.900887	+	0.900887i	0.0946261	+	0.995513i	$0.469834\pi$
$224$	−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	$-0.00141456\pi$
$227$	14.9994	+	14.9994i	0.995546	+	0.995546i	−0.00444394	+	0.999990i	$0.501415\pi$
$228$	0.227966	−	1.38965i	0.0150974	−	0.0920318i
$229$			21.4928i			1.42028i	0.704059	+	0.710141i	$0.251369\pi$
$229$			21.4928i			1.42028i	−0.704059	+	0.710141i	$0.748631\pi$
$230$	−15.7255	−	0.334314i	−1.03691	−	0.0220440i
$231$		−	10.4271i		−	0.686054i
$232$	8.20867	−	11.1038i	0.538926	−	0.729001i
$233$	−1.81711	−	1.81711i	−0.119043	−	0.119043i	0.645076	−	0.764119i	$-0.276826\pi$
$233$	−1.81711	−	1.81711i	−0.119043	−	0.119043i	−0.764119	+	0.645076i	$0.776826\pi$
$234$	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
$238$	11.6461	+	36.1823i	0.754902	+	2.34535i
$239$	−22.8925			−1.48079			−0.740396	−	0.672171i	$-0.765362\pi$
$239$	−22.8925			−1.48079			−0.740396	+	0.672171i	$0.765362\pi$
$240$	4.98347	+	3.85057i	0.321682	+	0.248553i
$241$	14.0297			0.903729			0.451865	−	0.892086i	$-0.350759\pi$
$241$	14.0297			0.903729			0.451865	+	0.892086i	$0.350759\pi$
$242$	−0.811822	−	2.52219i	−0.0521859	−	0.162132i
$243$	−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
$248$	2.64273	−	3.57480i	0.167813	−	0.227000i
$249$			12.3775i			0.784392i
$250$	−15.7342	+	1.56008i	−0.995120	+	0.0986684i
$251$			5.28898i			0.333838i	0.985971	+	0.166919i	$0.0533818\pi$
$251$			5.28898i			0.333838i	−0.985971	+	0.166919i	$0.946618\pi$
$252$	−3.34638	+	20.3991i	−0.210802	+	1.28502i
$253$	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	−0.993702	−	0.112058i	$-0.964256\pi$
$257$	−14.1338	+	14.1338i	−0.881643	+	0.881643i	0.112058	+	0.993702i	$0.464256\pi$
$258$	6.11420	−	1.96799i	0.380653	−	0.122522i
$259$	32.0033			1.98859
$260$	−19.9913	+	5.96879i	−1.23981	+	0.370169i
$261$	−12.2258			−0.756759
$262$	8.97092	−	2.88749i	0.554225	−	0.178390i
$263$	13.3767	−	13.3767i	0.824840	−	0.824840i	−0.161958	−	0.986798i	$-0.551781\pi$
$263$	13.3767	−	13.3767i	0.824840	−	0.824840i	0.986798	+	0.161958i	$0.0517809\pi$
$264$	−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
$268$	−4.58455	−	0.752077i	−0.280046	−	0.0459404i
$269$		−	19.2906i		−	1.17617i	−0.808801	−	0.588083i	$-0.799883\pi$
$269$		−	19.2906i		−	1.17617i	0.808801	−	0.588083i	$-0.200117\pi$
$270$	0.260489	−	12.2529i	0.0158529	−	0.745690i
$271$		−	15.6415i		−	0.950152i	−0.879945	−	0.475076i	$-0.842421\pi$
$271$		−	15.6415i		−	0.950152i	0.879945	−	0.475076i	$-0.157579\pi$
$272$	11.5687	+	23.3380i	0.701454	+	1.41507i
$273$	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	−0.932225	−	0.361880i	$-0.882135\pi$
$277$	−9.49242	+	9.49242i	−0.570345	+	0.570345i	0.361880	+	0.932225i	$0.382135\pi$
$278$	−2.95143	−	9.16958i	−0.177015	−	0.549955i
$279$	−3.93602			−0.235643
$280$	−14.7725	−	21.5216i	−0.882828	−	1.28616i
$281$	−6.05636			−0.361292			−0.180646	−	0.983548i	$-0.557819\pi$
$281$	−6.05636			−0.361292			−0.180646	+	0.983548i	$0.557819\pi$
$282$	0.690894	+	2.14649i	0.0411422	+	0.127821i
$283$	−9.20805	+	9.20805i	−0.547362	+	0.547362i	−0.925677	−	0.378315i	$-0.876504\pi$
$283$	−9.20805	+	9.20805i	−0.547362	+	0.547362i	0.378315	+	0.925677i	$0.376504\pi$
$284$	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
$288$	−0.195414	+	14.1647i	−0.0115149	+	0.834663i
$289$		−	25.4060i		−	1.49447i
$290$	11.1462	−	10.6822i	0.654528	−	0.627278i
$291$			6.18818i			0.362757i
$292$	1.34244	+	0.220221i	0.0785603	+	0.0128875i
$293$	8.60824	+	8.60824i	0.502899	+	0.502899i	0.912338	−	0.409439i	$-0.134276\pi$
$293$	8.60824	+	8.60824i	0.502899	+	0.502899i	−0.409439	+	0.912338i	$0.634276\pi$
$294$	−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
$298$	−25.6695	+	8.26230i	−1.48700	+	0.478622i
$299$	−23.2044			−1.34195
$300$	4.76273	+	5.18592i	0.274976	+	0.299409i
$301$	−26.6233			−1.53454
$302$	8.18646	−	2.63499i	0.471078	−	0.151627i
$303$	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	$-0.402171\pi$
$307$	−11.3998	−	11.3998i	−0.650619	−	0.650619i	−0.953142	+	0.302523i	$0.902171\pi$
$308$	−4.79459	+	29.2271i	−0.273197	+	1.66537i
$309$			7.86014i			0.447148i
$310$	3.58845	−	3.43905i	0.203810	−	0.195325i
$311$			11.0301i			0.625460i	0.949842	+	0.312730i	$0.101244\pi$
$311$			11.0301i			0.625460i	−0.949842	+	0.312730i	$0.898756\pi$
$312$	7.47099	+	5.52305i	0.422962	+	0.312681i
$313$	21.9744	+	21.9744i	1.24207	+	1.24207i	0.959143	+	0.282923i	$0.0913040\pi$
$313$	21.9744	+	21.9744i	1.24207	+	1.24207i	0.282923	+	0.959143i	$0.408696\pi$
$314$	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	−0.999708	−	0.0241817i	$-0.992302\pi$
$317$	−17.3687	+	17.3687i	−0.975526	+	0.975526i	0.0241817	+	0.999708i	$0.492302\pi$
$318$	0.916279	+	2.84672i	0.0513824	+	0.159636i
$319$	−17.5168			−0.980750
$320$	−12.1981	−	13.0846i	−0.681893	−	0.731452i
$321$	−4.35990			−0.243346
$322$	−8.89544	−	27.6366i	−0.495724	−	1.54013i
$323$	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
$328$	8.40039	+	6.21012i	0.463834	+	0.342897i
$329$		−	9.34653i		−	0.515291i
$330$	0.169802	−	7.98717i	0.00934730	−	0.439679i
$331$			24.2555i			1.33320i	0.745414	+	0.666602i	$0.232252\pi$
$331$			24.2555i			1.33320i	−0.745414	+	0.666602i	$0.767748\pi$
$332$	5.69141	−	34.6940i	0.312357	−	1.90408i
$333$	−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	−0.0717789	−	0.997421i	$-0.522868\pi$
$337$	16.9925	−	16.9925i	0.925642	−	0.925642i	0.997421	+	0.0717789i	$0.0228676\pi$
$338$	−11.7979	+	3.79743i	−0.641723	+	0.206553i
$339$	9.59089			0.520905
$340$	8.33167	+	27.9053i	0.451848	+	1.51338i
$341$	−5.63940			−0.305391
$342$	3.37118	−	1.08509i	0.182293	−	0.0586749i
$343$	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	$-0.199485\pi$
$347$	4.16317	+	4.16317i	0.223490	+	0.223490i	−0.586476	+	0.809967i	$0.699485\pi$
$348$	−6.78437	−	1.11295i	−0.363681	−	0.0596603i
$349$			25.4964i			1.36479i	0.730983	+	0.682396i	$0.239062\pi$
$349$			25.4964i			1.36479i	−0.730983	+	0.682396i	$0.760938\pi$
$350$	−12.2057	−	26.5100i	−0.652423	−	1.41702i
$351$		−	18.0803i		−	0.965057i
$352$	−0.279983	+	20.2947i	−0.0149232	+	1.08171i
$353$	8.69382	+	8.69382i	0.462725	+	0.462725i	0.899548	−	0.436822i	$-0.143896\pi$
$353$	8.69382	+	8.69382i	0.462725	+	0.462725i	−0.436822	+	0.899548i	$0.643896\pi$
$354$	−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
$358$	5.66842	+	17.6108i	0.299585	+	0.930759i
$359$	−10.8276			−0.571458			−0.285729	−	0.958310i	$-0.592236\pi$
$359$	−10.8276			−0.571458			−0.285729	+	0.958310i	$0.592236\pi$
$360$	−2.89552	+	15.5712i	−0.152607	+	0.820674i
$361$	1.00000			0.0526316
$362$	−7.43514	−	23.0997i	−0.390782	−	1.21409i
$363$	−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	0.996151	+	0.0876562i	$0.0279377\pi$
$367$	20.7628	+	20.7628i	1.08381	+	1.08381i	0.0876562	+	0.996151i	$0.472062\pi$
$368$	−8.83634	−	17.8259i	−0.460626	−	0.929240i
$369$		−	9.24922i		−	0.481495i
$370$	24.5146	+	0.521163i	1.27445	+	0.0270940i
$371$		−	12.3956i		−	0.643546i
$372$	−2.18418	−	0.358306i	−0.113245	−	0.0185773i
$373$	1.85686	+	1.85686i	0.0961447	+	0.0961447i	0.753543	−	0.657398i	$-0.228343\pi$
$373$	1.85686	+	1.85686i	0.0961447	+	0.0961447i	−0.657398	+	0.753543i	$0.728343\pi$
$374$	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
$378$	21.5338	−	6.93112i	1.10758	−	0.356498i
$379$	17.2442			0.885776			0.442888	−	0.896577i	$-0.353954\pi$
$379$	17.2442			0.885776			0.442888	+	0.896577i	$0.353954\pi$
$380$	−2.12541	+	3.93480i	−0.109031	+	0.201851i
$381$	−12.4392			−0.637282
$382$	20.6178	−	6.63629i	1.05490	−	0.339542i
$383$	−8.79528	+	8.79528i	−0.449418	+	0.449418i	−0.895161	−	0.445743i	$-0.852939\pi$
$383$	−8.79528	+	8.79528i	−0.449418	+	0.449418i	0.445743	+	0.895161i	$0.352939\pi$
$384$	−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
$388$	2.84544	−	17.3454i	0.144455	−	0.880580i
$389$			22.5652i			1.14410i	0.820219	+	0.572049i	$0.193851\pi$
$389$			22.5652i			1.14410i	−0.820219	+	0.572049i	$0.806149\pi$
$390$	7.18728	+	7.49951i	0.363942	+	0.379753i
$391$			32.3904i			1.63805i
$392$	16.8730	−	22.8240i	0.852216	−	1.15279i
$393$	−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	−0.277837	−	0.960628i	$-0.589618\pi$
$397$	13.6045	−	13.6045i	0.682791	−	0.682791i	0.960628	+	0.277837i	$0.0896175\pi$
$398$	1.83090	+	5.68827i	0.0917746	+	0.285127i
$399$	2.90613			0.145488
$400$	−10.9653	−	16.7261i	−0.548265	−	0.836305i
$401$	33.3363			1.66474			0.832368	−	0.554224i	$-0.186985\pi$
$401$	33.3363			1.66474			0.832368	+	0.554224i	$0.186985\pi$
$402$	0.708708	+	2.20183i	0.0353472	+	0.109817i
$403$	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
$408$	7.70947	−	10.4285i	0.381675	−	0.516290i
$409$		−	2.78416i		−	0.137668i	−0.997628	−	0.0688339i	$-0.978072\pi$
$409$		−	2.78416i		−	0.137668i	0.997628	−	0.0688339i	$-0.0219279\pi$
$410$	8.08139	+	8.43246i	0.399111	+	0.416450i
$411$		−	6.61340i		−	0.326215i
$412$	3.61424	−	22.0319i	0.178061	−	1.08543i
$413$	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
$418$	4.83012	−	1.55468i	0.236249	−	0.0760420i
$419$	21.3153			1.04132			0.520661	−	0.853763i	$-0.325685\pi$
$419$	21.3153			1.04132			0.520661	+	0.853763i	$0.325685\pi$
$420$	−6.17670	+	11.4350i	−0.301392	+	0.557973i
$421$	−11.5106			−0.560994			−0.280497	−	0.959855i	$-0.590499\pi$
$421$	−11.5106			−0.560994			−0.280497	+	0.959855i	$0.590499\pi$
$422$	−17.2691	+	5.55845i	−0.840647	+	0.270581i
$423$	−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
$428$	12.2208	+	2.00476i	0.590713	+	0.0969040i
$429$		−	11.7858i		−	0.569024i
$430$	−20.3934	−	0.433551i	−0.983459	−	0.0209077i
$431$		−	8.99333i		−	0.433193i	−0.976261	−	0.216597i	$-0.930504\pi$
$431$		−	8.99333i		−	0.433193i	0.976261	−	0.216597i	$-0.0694957\pi$
$432$	13.8895	−	6.88507i	0.668261	−	0.331258i
$433$	−21.6636	−	21.6636i	−1.04109	−	1.04109i	−0.999119	−	0.0419671i	$-0.986638\pi$
$433$	−21.6636	−	21.6636i	−1.04109	−	1.04109i	−0.0419671	−	0.999119i	$-0.513362\pi$
$434$	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
$438$	−0.207522	−	0.644735i	−0.00991580	−	0.0308066i
$439$	20.8810			0.996595			0.498298	−	0.867006i	$-0.333959\pi$
$439$	20.8810			0.996595			0.498298	+	0.867006i	$0.333959\pi$
$440$	−4.14861	+	22.3099i	−0.197777	+	1.06358i
$441$	−25.1303			−1.19668
$442$	13.1636	+	40.8970i	0.626128	+	1.94527i
$443$	−21.5183	+	21.5183i	−1.02237	+	1.02237i	−0.0226219	+	0.999744i	$0.507201\pi$
$443$	−21.5183	+	21.5183i	−1.02237	+	1.02237i	−0.999744	+	0.0226219i	$0.992799\pi$
$444$	−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
$448$	15.4752	−	29.1679i	0.731136	−	1.37805i
$449$			18.9308i			0.893398i	0.894684	+	0.446699i	$0.147400\pi$
$449$			18.9308i			0.893398i	−0.894684	+	0.446699i	$0.852600\pi$
$450$	−6.13692	+	16.6101i	−0.289297	+	0.783008i
$451$		−	13.2520i		−	0.624011i
$452$	−26.8832	−	4.41007i	−1.26448	−	0.207432i
$453$	−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	−0.670870	−	0.741575i	$-0.734079\pi$
$457$	1.51148	−	1.51148i	0.0707041	−	0.0707041i	0.741575	+	0.670870i	$0.234079\pi$
$458$	−28.9335	+	9.31290i	−1.35197	+	0.435163i
$459$	−25.2378			−1.17800
$460$	−6.36386	−	21.3145i	−0.296716	−	0.993792i
$461$	−17.0301			−0.793171			−0.396586	−	0.917998i	$-0.629805\pi$
$461$	−17.0301			−0.793171			−0.396586	+	0.917998i	$0.629805\pi$
$462$	14.0370	−	4.51811i	0.653059	−	0.210201i
$463$	−17.2053	+	17.2053i	−0.799599	+	0.799599i	−0.983032	−	0.183433i	$-0.941279\pi$
$463$	−17.2053	+	17.2053i	−0.799599	+	0.799599i	0.183433	+	0.983032i	$0.441279\pi$
$464$	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	$-0.154408\pi$
$467$	9.04056	+	9.04056i	0.418347	+	0.418347i	−0.466286	+	0.884634i	$0.654408\pi$
$468$	−3.78243	+	23.0571i	−0.174843	+	1.06582i
$469$		−	9.58753i		−	0.442711i
$470$	0.152205	−	7.15945i	0.00702070	−	0.330241i
$471$		−	7.43634i		−	0.342649i
$472$	13.4633	+	9.95296i	0.619699	+	0.458122i
$473$	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
$478$	−9.91940	−	30.8178i	−0.453703	−	1.40957i
$479$	21.6356			0.988556			0.494278	−	0.869304i	$-0.335432\pi$
$479$	21.6356			0.988556			0.494278	+	0.869304i	$0.335432\pi$
$480$	−3.02427	+	8.37721i	−0.138039	+	0.382365i
$481$	36.1735			1.64937
$482$	6.07910	+	18.8867i	0.276895	+	0.860265i
$483$	−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	$-0.0942258\pi$
$487$	14.6707	+	14.6707i	0.664791	+	0.664791i	−0.291715	+	0.956505i	$0.594226\pi$
$488$	−1.21920	−	0.901313i	−0.0551906	−	0.0408005i
$489$		−	9.99625i		−	0.452046i
$490$	22.9112	−	21.9573i	1.03502	−	0.991929i
$491$			30.4922i			1.37609i	0.725667	+	0.688047i	$0.241532\pi$
$491$			30.4922i			1.37609i	−0.725667	+	0.688047i	$0.758468\pi$
$492$	0.841981	−	5.13259i	0.0379594	−	0.231395i
$493$	−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
$498$	−16.6626	+	5.36322i	−0.746667	+	0.240331i
$499$	25.7578			1.15308			0.576538	−	0.817071i	$-0.304403\pi$
$499$	25.7578			1.15308			0.576538	+	0.817071i	$0.304403\pi$
$500$	−8.91788	−	20.5054i	−0.398820	−	0.917029i
$501$	−16.4643			−0.735571
$502$	−7.12001	+	2.29173i	−0.317782	+	0.102285i
$503$	−5.81236	+	5.81236i	−0.259161	+	0.259161i	−0.824713	−	0.565552i	$-0.808663\pi$
$503$	−5.81236	+	5.81236i	−0.259161	+	0.259161i	0.565552	+	0.824713i	$0.308663\pi$
$504$	−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
$508$	34.8671	+	5.71980i	1.54698	+	0.253775i
$509$		−	21.8822i		−	0.969912i	−0.874539	−	0.484956i	$-0.838836\pi$
$509$		−	21.8822i		−	0.969912i	0.874539	−	0.484956i	$-0.161164\pi$
$510$	10.4684	−	10.0325i	0.463547	−	0.444248i
$511$			2.80740i			0.124192i
$512$	7.52441	−	21.3397i	0.332535	−	0.943091i
$513$	−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
$518$	13.8672	+	43.0828i	0.609288	+	1.89295i
$519$	5.30467			0.232849
$520$	−16.6975	−	24.3259i	−0.732232	−	1.06676i
$521$	−30.5569			−1.33872			−0.669361	−	0.742937i	$-0.733432\pi$
$521$	−30.5569			−1.33872			−0.669361	+	0.742937i	$0.733432\pi$
$522$	−5.29749	−	16.4584i	−0.231865	−	0.720363i
$523$	28.6213	−	28.6213i	1.25152	−	1.25152i	0.296487	−	0.955037i	$-0.404185\pi$
$523$	28.6213	−	28.6213i	1.25152	−	1.25152i	0.955037	−	0.296487i	$-0.0958150\pi$
$524$	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
$528$	9.05401	−	4.48809i	0.394025	−	0.195319i
$529$		−	1.74027i		−	0.0756638i
$530$	0.201858	−	9.49502i	0.00876814	−	0.412437i
$531$		−	14.8237i		−	0.643295i
$532$	−8.14585	−	1.33629i	−0.353168	−	0.0579357i
$533$	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
$538$	25.9689	−	8.35866i	1.11960	−	0.360368i
$539$	−36.0059			−1.55088
$540$	16.6077	−	4.95857i	0.714683	−	0.213383i
$541$	4.01340			0.172549			0.0862747	−	0.996271i	$-0.472504\pi$
$541$	4.01340			0.172549			0.0862747	+	0.996271i	$0.472504\pi$
$542$	21.0565	−	6.77751i	0.904455	−	0.291119i
$543$	−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	$-0.265949\pi$
$547$	−1.65661	−	1.65661i	−0.0708313	−	0.0708313i	−0.741635	+	0.670804i	$0.765949\pi$
$548$	−3.04097	+	18.5373i	−0.129904	+	0.791875i
$549$			1.34240i			0.0572921i
$550$	−8.79278	+	23.7984i	−0.374925	+	1.01477i
$551$		−	4.88207i		−	0.207983i
$552$	−5.88861	+	7.96548i	−0.250636	+	0.339034i
$553$	−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	−0.480260	+	0.877126i	$0.659458\pi$
$557$	−32.0355	+	32.0355i	−1.35739	+	1.35739i	−0.877126	+	0.480260i	$0.840542\pi$
$558$	−1.70549	−	5.29866i	−0.0721992	−	0.224310i
$559$	−30.0924			−1.27277
$560$	22.5713	−	29.2121i	0.953811	−	1.23444i
$561$	−16.4515			−0.694582
$562$	−2.62424	−	8.15306i	−0.110697	−	0.343916i
$563$	23.6795	−	23.6795i	0.997973	−	0.997973i	−0.00202496	−	0.999998i	$-0.500645\pi$
$563$	23.6795	−	23.6795i	0.997973	−	0.997973i	0.999998	+	0.00202496i	$0.000644564\pi$
$564$	−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
$568$	−6.86433	+	9.28533i	−0.288021	+	0.389604i
$569$			4.84313i			0.203035i	0.994834	+	0.101517i	$0.0323697\pi$
$569$			4.84313i			0.203035i	−0.994834	+	0.101517i	$0.967630\pi$
$570$	2.22610	+	0.0473253i	0.0932409	+	0.00198224i
$571$			26.9143i			1.12633i	0.826345	+	0.563164i	$0.190416\pi$
$571$			26.9143i			1.12633i	−0.826345	+	0.563164i	$0.809584\pi$
$572$	−5.41934	+	33.0355i	−0.226594	+	1.38128i
$573$	−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	−0.412513	−	0.910952i	$-0.635349\pi$
$577$	11.9729	−	11.9729i	0.498439	−	0.498439i	0.910952	+	0.412513i	$0.135349\pi$
$578$	34.2016	−	11.0085i	1.42260	−	0.457894i
$579$	−12.6953			−0.527600
$580$	19.2100	+	10.3764i	0.797651	+	0.430856i
$581$	72.5545			3.01007
$582$	−8.33051	+	2.68136i	−0.345311	+	0.111146i
$583$	−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	$-0.254448\pi$
$587$	−0.478832	−	0.478832i	−0.0197635	−	0.0197635i	−0.716919	+	0.697156i	$0.754448\pi$
$588$	−13.9454	−	2.28768i	−0.575097	−	0.0943422i
$589$		−	1.57175i		−	0.0647628i
$590$	12.9520	+	13.5147i	0.533227	+	0.556392i
$591$		−	9.93442i		−	0.408647i
$592$	13.7750	+	27.7889i	0.566150	+	1.14212i
$593$	23.9284	+	23.9284i	0.982622	+	0.982622i	0.999852	−	0.0172293i	$-0.00548454\pi$
$593$	23.9284	+	23.9284i	0.982622	+	0.982622i	−0.0172293	+	0.999852i	$0.505485\pi$
$594$	−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
$598$	−10.0546	−	31.2377i	−0.411161	−	1.27741i
$599$	1.72828			0.0706158			0.0353079	−	0.999376i	$-0.488759\pi$
$599$	1.72828			0.0706158			0.0353079	+	0.999376i	$0.488759\pi$
$600$	−4.91757	+	8.65865i	−0.200759	+	0.353488i
$601$	−26.9304			−1.09852			−0.549258	−	0.835653i	$-0.685090\pi$
$601$	−26.9304			−1.09852			−0.549258	+	0.835653i	$0.685090\pi$
$602$	−11.5360	−	35.8402i	−0.470171	−	1.46074i
$603$	−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	$-0.392929\pi$
$607$	−15.1247	−	15.1247i	−0.613894	−	0.613894i	−0.943958	+	0.330065i	$0.892929\pi$
$608$	−5.65632	−	0.0780338i	−0.229394	−	0.00316469i
$609$		−	14.1879i		−	0.574924i
$610$	−1.17290	−	1.22386i	−0.0474894	−	0.0495524i
$611$		−	10.5644i		−	0.427391i
$612$	32.1848	+	5.27979i	1.30099	+	0.213423i
$613$	−12.3720	−	12.3720i	−0.499701	−	0.499701i	0.411644	−	0.911345i	$-0.364955\pi$
$613$	−12.3720	−	12.3720i	−0.499701	−	0.499701i	−0.911345	+	0.411644i	$0.864955\pi$
$614$	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	−0.973347	−	0.229336i	$-0.926344\pi$
$617$	−18.4809	+	18.4809i	−0.744011	+	0.744011i	0.229336	+	0.973347i	$0.426344\pi$
$618$	−10.5813	+	3.40583i	−0.425643	+	0.137002i
$619$	−16.9676			−0.681984			−0.340992	−	0.940066i	$-0.610763\pi$
$619$	−16.9676			−0.681984			−0.340992	+	0.940066i	$0.610763\pi$
$620$	6.18452	+	3.34061i	0.248376	+	0.134162i
$621$	19.2770			0.773561
$622$	−14.8487	+	4.77939i	−0.595379	+	0.191636i
$623$	−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
$628$	−3.41937	+	20.8440i	−0.136448	+	0.831766i
$629$		−	50.4936i		−	2.01331i
$630$	−32.6775	−	0.694702i	−1.30190	−	0.0276776i
$631$		−	26.7082i		−	1.06324i	−0.846984	−	0.531619i	$-0.821584\pi$
$631$		−	26.7082i		−	1.06324i	0.846984	−	0.531619i	$-0.178416\pi$
$632$	−7.63819	−	5.64665i	−0.303831	−	0.224612i
$633$	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
$638$	−7.59007	−	23.5810i	−0.300494	−	0.933581i
$639$	10.2236			0.404439
$640$	12.3290	−	22.0906i	0.487347	−	0.873208i
$641$	3.98093			0.157237			0.0786186	−	0.996905i	$-0.474949\pi$
$641$	3.98093			0.157237			0.0786186	+	0.996905i	$0.474949\pi$
$642$	−1.88916	−	5.86928i	−0.0745592	−	0.231642i
$643$	6.39670	−	6.39670i	0.252261	−	0.252261i	−0.569636	−	0.821897i	$-0.692916\pi$
$643$	6.39670	−	6.39670i	0.252261	−	0.252261i	0.821897	+	0.569636i	$0.192916\pi$
$644$	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	$-0.443610\pi$
$647$	−20.5555	−	20.5555i	−0.808120	−	0.808120i	−0.984349	+	0.176230i	$0.943610\pi$
$648$	10.8804	+	8.04348i	0.427421	+	0.315978i
$649$		−	21.2389i		−	0.833702i
$650$	−13.7962	−	29.9643i	−0.541131	−	1.17530i
$651$		−	4.56771i		−	0.179023i
$652$	−4.59647	+	28.0194i	−0.180012	+	1.09732i
$653$	−19.4414	−	19.4414i	−0.760800	−	0.760800i	0.215667	−	0.976467i	$-0.430807\pi$
$653$	−19.4414	−	19.4414i	−0.760800	−	0.760800i	−0.976467	+	0.215667i	$0.930807\pi$
$654$	−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
$658$	12.5823	−	4.04989i	0.490508	−	0.157881i
$659$	−9.30532			−0.362484			−0.181242	−	0.983439i	$-0.558012\pi$
$659$	−9.30532			−0.362484			−0.181242	+	0.983439i	$0.558012\pi$
$660$	10.8259	−	3.23228i	0.421397	−	0.125816i
$661$	20.9486			0.814805			0.407402	−	0.913249i	$-0.366435\pi$
$661$	20.9486			0.814805			0.407402	+	0.913249i	$0.366435\pi$
$662$	−32.6527	+	10.5100i	−1.26908	+	0.408483i
$663$	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
$668$	46.1493	+	7.57060i	1.78557	+	0.292915i
$669$			13.3961i			0.517924i
$670$	0.156130	−	7.34405i	0.00603181	−	0.283725i
$671$			1.92334i			0.0742498i
$672$	−16.4380	−	0.226776i	−0.634109	−	0.00874809i
$673$	−2.71457	−	2.71457i	−0.104639	−	0.104639i	0.652849	−	0.757488i	$-0.273574\pi$
$673$	−2.71457	−	2.71457i	−0.104639	−	0.104639i	−0.757488	+	0.652849i	$0.773574\pi$
$674$	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	−0.971510	−	0.236998i	$-0.923837\pi$
$677$	−19.1114	+	19.1114i	−0.734513	+	0.734513i	0.236998	+	0.971510i	$0.423837\pi$
$678$	4.15577	+	12.9112i	0.159601	+	0.495853i
$679$	36.2739			1.39206
$680$	−33.9559	+	23.3075i	−1.30215	+	0.893803i
$681$	14.9359			0.572345
$682$	−2.44357	−	7.59175i	−0.0935692	−	0.290703i
$683$	−12.0794	+	12.0794i	−0.462204	+	0.462204i	−0.899377	−	0.437173i	$-0.855980\pi$
$683$	−12.0794	+	12.0794i	−0.462204	+	0.462204i	0.437173	+	0.899377i	$0.355980\pi$
$684$	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
$688$	−11.4593	−	23.1174i	−0.436882	−	0.881342i
$689$		−	14.0108i		−	0.533768i
$690$	−7.99589	+	7.66299i	−0.304398	+	0.291725i
$691$		−	16.1397i		−	0.613985i	−0.951712	−	0.306992i	$-0.900677\pi$
$691$		−	16.1397i		−	0.613985i	0.951712	−	0.306992i	$-0.0993226\pi$
$692$	−14.8689	−	2.43919i	−0.565232	−	0.0927240i
$693$	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
$698$	−34.3232	+	11.0477i	−1.29915	+	0.418161i
$699$	−1.80941			−0.0684383
$700$	30.3989	−	27.9182i	1.14897	−	1.05521i
$701$	1.39112			0.0525418			0.0262709	−	0.999655i	$-0.491637\pi$
$701$	1.39112			0.0525418			0.0262709	+	0.999655i	$0.491637\pi$
$702$	24.3397	−	7.83427i	0.918643	−	0.295686i
$703$	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
$708$	1.34944	−	8.22601i	0.0507151	−	0.309152i
$709$		−	0.442717i		−	0.0166266i	−0.999965	−	0.00831330i	$-0.997354\pi$
$709$		−	0.442717i		−	0.0166266i	0.999965	−	0.00831330i	$-0.00264624\pi$
$710$	−9.32078	+	8.93272i	−0.349803	+	0.335239i
$711$			8.40999i			0.315399i
$712$	−20.0262	+	27.0893i	−0.750514	+	1.01522i
$713$	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
$718$	−4.69163	−	14.5761i	−0.175090	−	0.543974i
$719$	3.55928			0.132739			0.0663694	−	0.997795i	$-0.478858\pi$
$719$	3.55928			0.132739			0.0663694	+	0.997795i	$0.478858\pi$
$720$	−22.2165	+	2.84911i	−0.827961	+	0.106180i
$721$	46.0746			1.71591
$722$	0.433304	+	1.34620i	0.0161259	+	0.0501003i
$723$	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	$-0.479754\pi$
$727$	−25.1946	−	25.1946i	−0.934415	−	0.934415i	−0.997978	+	0.0635627i	$0.979754\pi$
$728$	32.3750	−	43.7935i	1.19990	−	1.62309i
$729$		−	3.79323i		−	0.140490i
$730$	−0.0457175	+	2.15047i	−0.00169208	+	0.0795923i
$731$			42.0052i			1.55362i
$732$	−0.122202	+	0.744925i	−0.00451671	+	0.0275332i
$733$	−7.66294	−	7.66294i	−0.283037	−	0.283037i	0.551282	−	0.834319i	$-0.314139\pi$
$733$	−7.66294	−	7.66294i	−0.283037	−	0.283037i	−0.834319	+	0.551282i	$0.814139\pi$
$734$	−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
$738$	12.4513	−	4.00772i	0.458338	−	0.147526i
$739$	−50.2765			−1.84945			−0.924725	−	0.380635i	$-0.875706\pi$
$739$	−50.2765			−1.84945			−0.924725	+	0.380635i	$0.875706\pi$
$740$	9.92065	+	33.2273i	0.364690	+	1.22146i
$741$	3.28481			0.120670
$742$	16.6869	−	5.37105i	0.612595	−	0.197177i
$743$	17.6854	−	17.6854i	0.648814	−	0.648814i	−0.303893	−	0.952706i	$-0.598286\pi$
$743$	17.6854	−	17.6854i	0.648814	−	0.648814i	0.952706	+	0.303893i	$0.0982864\pi$
$744$	−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
$748$	46.1134	+	7.56471i	1.68607	+	0.276593i
$749$			25.5569i			0.933827i
$750$	−7.05706	+	8.61054i	−0.257687	+	0.314412i
$751$		−	40.6953i		−	1.48499i	−0.669851	−	0.742496i	$-0.733642\pi$
$751$		−	40.6953i		−	1.48499i	0.669851	−	0.742496i	$-0.266358\pi$
$752$	8.11573	−	4.02298i	0.295950	−	0.146703i
$753$	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	−0.420978	−	0.907071i	$-0.638313\pi$
$757$	13.3742	−	13.3742i	0.486092	−	0.486092i	0.907071	+	0.420978i	$0.138313\pi$
$758$	7.47198	+	23.2141i	0.271394	+	0.843175i
$759$	12.5659			0.456113
$760$	−6.21796	−	1.15625i	−0.225549	−	0.0419417i
$761$	37.9781			1.37670			0.688352	−	0.725377i	$-0.258334\pi$
$761$	37.9781			1.37670			0.688352	+	0.725377i	$0.258334\pi$
$762$	−5.38997	−	16.7457i	−0.195258	−	0.606632i
$763$	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
$768$	−11.1633	+	1.51635i	−0.402820	+	0.0547166i
$769$		−	32.0784i		−	1.15678i	−0.815762	−	0.578388i	$-0.803682\pi$
$769$		−	32.0784i		−	1.15678i	0.815762	−	0.578388i	$-0.196318\pi$
$770$	−46.8192	−

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)

\(f(q)\)	\(=\)	\(q+(0.433304 + 1.34620i) q^{2} +(0.497882 - 0.497882i) q^{3} +(-1.62450 + 1.16662i) q^{4} +(-2.01079 + 0.978129i) q^{5} +(0.885982 + 0.454514i) q^{6} +(-2.91849 - 2.91849i) q^{7} +(-2.27441 - 1.68139i) q^{8} +2.50423i q^{9} +O(q^{10})\)	\(q+(0.433304 + 1.34620i) 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} +(-2.27441 - 1.68139i) q^{8} +2.50423i q^{9} +(-2.18804 - 2.28309i) q^{10} +3.58797i q^{11} +(-0.227966 + 1.38965i) 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} +(-3.37118 + 1.08509i) q^{18} -1.00000 q^{19} +(2.12541 - 3.93480i) q^{20} -2.90613 q^{21} +(-4.83012 + 1.55468i) 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} +(8.14585 + 1.33629i) q^{28} +4.88207i q^{29} +(-2.22610 - 0.0473253i) q^{30} +1.57175i q^{31} +(5.65632 + 0.0780338i) 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} +(-0.433304 - 1.34620i) q^{38} -3.28481 q^{39} +(6.21796 + 1.15625i) q^{40} -3.69344 q^{41} +(-1.25924 - 3.91222i) 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} +(-1.25087 - 2.52343i) q^{48} +10.0352i q^{49} +(6.63283 + 2.45062i) q^{50} +4.58517i q^{51} +(9.20729 + 1.51042i) 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} +(-6.57224 + 2.11542i) q^{58} -5.91948 q^{59} +(-0.900866 - 3.01727i) q^{60} +0.536052 q^{61} +(-2.11589 + 0.681045i) 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} +(2.10835 - 12.8522i) q^{68} -3.50222i q^{69} +(-0.277412 + 13.0489i) q^{70} -4.08253i q^{71} +(4.21058 - 5.69563i) 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} +(-1.42332 - 4.42200i) q^{78} +3.35832 q^{79} +(1.13772 + 8.87162i) q^{80} -4.78383 q^{81} +(-1.60038 - 4.97210i) 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} +(6.03279 - 8.16051i) q^{88} -11.9105i q^{89} +(5.71737 - 5.47934i) q^{90} +19.2549i q^{91} +(-1.61039 + 9.81671i) 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} +(-13.5093 + 4.34827i) 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	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more