LMFDB - Embedded newform 380.2.k.d.267.5

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			267.5
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23831 + 0.683080i) q^{2} +(0.494605 + 0.494605i) q^{3} +(1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 - 0.274617i) q^{6} +(-0.327577 + 0.327577i) q^{7} +(-0.165443 + 2.82358i) q^{8} -2.51073i q^{9} +O(q^{10})$	\(q+(-1.23831 + 0.683080i) q^{2} +(0.494605 + 0.494605i) q^{3} +(1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 - 0.274617i) q^{6} +(-0.327577 + 0.327577i) q^{7} +(-0.165443 + 2.82358i) q^{8} -2.51073i q^{9} +(-0.385706 + 3.13867i) q^{10} -2.94834i q^{11} +(1.36438 - 0.309090i) q^{12} +(0.287718 - 0.287718i) q^{13} +(0.181879 - 0.629402i) q^{14} +(1.54434 - 0.247693i) q^{15} +(-1.72387 - 3.60947i) q^{16} +(-1.74168 - 1.74168i) q^{17} +(1.71503 + 3.10905i) q^{18} -1.00000 q^{19} +(-1.66634 - 4.15010i) q^{20} -0.324042 q^{21} +(2.01395 + 3.65095i) q^{22} +(-0.570036 - 0.570036i) q^{23} +(-1.47839 + 1.31473i) q^{24} +(-1.56365 - 4.74921i) q^{25} +(-0.159749 + 0.552818i) q^{26} +(2.72563 - 2.72563i) q^{27} +(0.204710 + 0.903630i) q^{28} -1.85155i q^{29} +(-1.74317 + 1.36163i) q^{30} +1.12279i q^{31} +(4.60023 + 3.29209i) q^{32} +(1.45826 - 1.45826i) q^{33} +(3.34643 + 0.967023i) q^{34} +(0.164047 + 1.02282i) q^{35} +(-4.24747 - 2.67846i) q^{36} +(4.08314 + 4.08314i) q^{37} +(1.23831 - 0.683080i) q^{38} +0.284614 q^{39} +(4.89829 + 4.00085i) q^{40} +10.4815 q^{41} +(0.401264 - 0.221347i) q^{42} +(7.09760 + 7.09760i) q^{43} +(-4.98778 - 3.14530i) q^{44} +(-4.54839 - 3.29105i) q^{45} +(1.09526 + 0.316498i) q^{46} +(2.57471 - 2.57471i) q^{47} +(0.932630 - 2.63789i) q^{48} +6.78539i q^{49} +(5.18037 + 4.81288i) q^{50} -1.72288i q^{51} +(-0.179802 - 0.793679i) q^{52} +(5.67543 - 5.67543i) q^{53} +(-1.51334 + 5.23700i) q^{54} +(-5.34116 - 3.86466i) q^{55} +(-0.870746 - 0.979137i) q^{56} +(-0.494605 - 0.494605i) q^{57} +(1.26476 + 2.29278i) q^{58} -14.1245 q^{59} +(1.22848 - 2.87684i) q^{60} +7.69452 q^{61} +(-0.766955 - 1.39036i) q^{62} +(0.822459 + 0.822459i) q^{63} +(-7.94526 - 0.934286i) q^{64} +(-0.144086 - 0.898364i) q^{65} +(-0.809664 + 2.80189i) q^{66} +(-9.51194 + 9.51194i) q^{67} +(-4.80446 + 1.08841i) q^{68} -0.563885i q^{69} +(-0.901807 - 1.15450i) q^{70} -9.19745i q^{71} +(7.08926 + 0.415384i) q^{72} +(-4.82935 + 4.82935i) q^{73} +(-7.84529 - 2.26706i) q^{74} +(1.57559 - 3.12237i) q^{75} +(-1.06680 + 1.69172i) q^{76} +(0.965809 + 0.965809i) q^{77} +(-0.352439 + 0.194414i) q^{78} -0.164126 q^{79} +(-8.79848 - 1.60834i) q^{80} -4.83597 q^{81} +(-12.9793 + 7.15972i) q^{82} +(-1.98305 - 1.98305i) q^{83} +(-0.345689 + 0.548191i) q^{84} +(-5.43817 + 0.872213i) q^{85} +(-13.6372 - 3.94077i) q^{86} +(0.915785 - 0.915785i) q^{87} +(8.32489 + 0.487783i) q^{88} +2.27564i q^{89} +(7.88035 + 0.968404i) q^{90} +0.188500i q^{91} +(-1.57246 + 0.356228i) q^{92} +(-0.555337 + 0.555337i) q^{93} +(-1.42954 + 4.94700i) q^{94} +(-1.31079 + 1.81158i) q^{95} +(0.647013 + 3.90358i) q^{96} +(-4.13745 - 4.13745i) q^{97} +(-4.63496 - 8.40238i) q^{98} -7.40249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.23831	+	0.683080i	−0.875614	+	0.483011i
$2$	−1.23831	+	0.683080i	−0.875614	+	0.483011i
$3$	0.494605	+	0.494605i	0.285560	+	0.285560i	0.835322	−	0.549762i	$-0.185281\pi$
$3$	0.494605	+	0.494605i	0.285560	+	0.285560i	−0.549762	+	0.835322i	$0.685281\pi$
$4$	1.06680	−	1.69172i	0.533401	−	0.845862i
$5$	1.31079	−	1.81158i	0.586204	−	0.810164i
$5$	1.31079	−	1.81158i	0.586204	−	0.810164i
$6$	−0.950327	−	0.274617i	−0.387969	−	0.112112i
$7$	−0.327577	+	0.327577i	−0.123813	+	0.123813i	−0.766298	−	0.642485i	$-0.777903\pi$
$7$	−0.327577	+	0.327577i	−0.123813	+	0.123813i	0.642485	+	0.766298i	$0.277903\pi$
$8$	−0.165443	+	2.82358i	−0.0584930	+	0.998288i
$9$		−	2.51073i		−	0.836911i
$10$	−0.385706	+	3.13867i	−0.121971	+	0.992534i
$11$		−	2.94834i		−	0.888958i	−0.895789	−	0.444479i	$-0.853389\pi$
$11$		−	2.94834i		−	0.888958i	0.895789	−	0.444479i	$-0.146611\pi$
$12$	1.36438	−	0.309090i	0.393863	−	0.0892265i
$13$	0.287718	−	0.287718i	0.0797987	−	0.0797987i	−0.666081	−	0.745880i	$-0.732029\pi$
$13$	0.287718	−	0.287718i	0.0797987	−	0.0797987i	0.745880	+	0.666081i	$0.232029\pi$
$14$	0.181879	−	0.629402i	0.0486092	−	0.168215i
$15$	1.54434	−	0.247693i	0.398747	−	0.0639539i
$16$	−1.72387	−	3.60947i	−0.430966	−	0.902368i
$17$	−1.74168	−	1.74168i	−0.422419	−	0.422419i	0.463617	−	0.886036i	$-0.346551\pi$
$17$	−1.74168	−	1.74168i	−0.422419	−	0.422419i	−0.886036	+	0.463617i	$0.846551\pi$
$18$	1.71503	+	3.10905i	0.404237	+	0.732811i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−1.66634	−	4.15010i	−0.372605	−	0.927990i
$21$	−0.324042			−0.0707118
$22$	2.01395	+	3.65095i	0.429376	+	0.778384i
$23$	−0.570036	−	0.570036i	−0.118861	−	0.118861i	0.645175	−	0.764035i	$-0.276785\pi$
$23$	−0.570036	−	0.570036i	−0.118861	−	0.118861i	−0.764035	+	0.645175i	$0.776785\pi$
$24$	−1.47839	+	1.31473i	−0.301774	+	0.268368i
$25$	−1.56365	−	4.74921i	−0.312730	−	0.949842i
$26$	−0.159749	+	0.552818i	−0.0313293	+	0.108417i
$27$	2.72563	−	2.72563i	0.524549	−	0.524549i
$28$	0.204710	+	0.903630i	0.0386866	+	0.170770i
$29$		−	1.85155i		−	0.343824i	−0.985112	−	0.171912i	$-0.945006\pi$
$29$		−	1.85155i		−	0.343824i	0.985112	−	0.171912i	$-0.0549945\pi$
$30$	−1.74317	+	1.36163i	−0.318258	+	0.248598i
$31$			1.12279i			0.201659i	0.994904	+	0.100829i	$0.0321496\pi$
$31$			1.12279i			0.201659i	−0.994904	+	0.100829i	$0.967850\pi$
$32$	4.60023	+	3.29209i	0.813214	+	0.581965i
$33$	1.45826	−	1.45826i	0.253851	−	0.253851i
$34$	3.34643	+	0.967023i	0.573909	+	0.165843i
$35$	0.164047	+	1.02282i	0.0277290	+	0.172888i
$36$	−4.24747	−	2.67846i	−0.707911	−	0.446409i
$37$	4.08314	+	4.08314i	0.671264	+	0.671264i	0.958007	−	0.286743i	$-0.0925727\pi$
$37$	4.08314	+	4.08314i	0.671264	+	0.671264i	−0.286743	+	0.958007i	$0.592573\pi$
$38$	1.23831	−	0.683080i	0.200880	−	0.110810i
$39$	0.284614			0.0455747
$40$	4.89829	+	4.00085i	0.774488	+	0.632589i
$41$	10.4815			1.63694			0.818470	−	0.574550i	$-0.194823\pi$
$41$	10.4815			1.63694			0.818470	+	0.574550i	$0.194823\pi$
$42$	0.401264	−	0.221347i	0.0619163	−	0.0341546i
$43$	7.09760	+	7.09760i	1.08237	+	1.08237i	0.996288	+	0.0860866i	$0.0274362\pi$
$43$	7.09760	+	7.09760i	1.08237	+	1.08237i	0.0860866	+	0.996288i	$0.472564\pi$
$44$	−4.98778	−	3.14530i	−0.751936	−	0.474171i
$45$	−4.54839	−	3.29105i	−0.678035	−	0.490600i
$46$	1.09526	+	0.316498i	0.161487	+	0.0466651i
$47$	2.57471	−	2.57471i	0.375559	−	0.375559i	−0.493938	−	0.869497i	$-0.664443\pi$
$47$	2.57471	−	2.57471i	0.375559	−	0.375559i	0.869497	+	0.493938i	$0.164443\pi$
$48$	0.932630	−	2.63789i	0.134613	−	0.380747i
$49$			6.78539i			0.969341i
$50$	5.18037	+	4.81288i	0.732615	+	0.680643i
$51$		−	1.72288i		−	0.241252i
$52$	−0.179802	−	0.793679i	−0.0249340	−	0.110063i
$53$	5.67543	−	5.67543i	0.779580	−	0.779580i	−0.200180	−	0.979759i	$-0.564153\pi$
$53$	5.67543	−	5.67543i	0.779580	−	0.779580i	0.979759	+	0.200180i	$0.0641525\pi$
$54$	−1.51334	+	5.23700i	−0.205940	+	0.712665i
$55$	−5.34116	−	3.86466i	−0.720201	−	0.521111i
$56$	−0.870746	−	0.979137i	−0.116358	−	0.130843i
$57$	−0.494605	−	0.494605i	−0.0655120	−	0.0655120i
$58$	1.26476	+	2.29278i	0.166071	+	0.301057i
$59$	−14.1245			−1.83885			−0.919425	−	0.393265i	$-0.871345\pi$
$59$	−14.1245			−1.83885			−0.919425	+	0.393265i	$0.871345\pi$
$60$	1.22848	−	2.87684i	0.158596	−	0.371398i
$61$	7.69452			0.985182			0.492591	−	0.870261i	$-0.336050\pi$
$61$	7.69452			0.985182			0.492591	+	0.870261i	$0.336050\pi$
$62$	−0.766955	−	1.39036i	−0.0974034	−	0.176575i
$63$	0.822459	+	0.822459i	0.103620	+	0.103620i
$64$	−7.94526	−	0.934286i	−0.993157	−	0.116786i
$65$	−0.144086	−	0.898364i	−0.0178717	−	0.111428i
$66$	−0.809664	+	2.80189i	−0.0996628	+	0.344888i
$67$	−9.51194	+	9.51194i	−1.16207	+	1.16207i	−0.178047	+	0.984022i	$0.556978\pi$
$67$	−9.51194	+	9.51194i	−1.16207	+	1.16207i	−0.984022	+	0.178047i	$0.943022\pi$
$68$	−4.80446	+	1.08841i	−0.582627	+	0.131990i
$69$		−	0.563885i		−	0.0678837i
$70$	−0.901807	−	1.15450i	−0.107787	−	0.137990i
$71$		−	9.19745i		−	1.09154i	−0.837936	−	0.545768i	$-0.816238\pi$
$71$		−	9.19745i		−	1.09154i	0.837936	−	0.545768i	$-0.183762\pi$
$72$	7.08926	+	0.415384i	0.835478	+	0.0489535i
$73$	−4.82935	+	4.82935i	−0.565233	+	0.565233i	−0.930789	−	0.365556i	$-0.880879\pi$
$73$	−4.82935	+	4.82935i	−0.565233	+	0.565233i	0.365556	+	0.930789i	$0.380879\pi$
$74$	−7.84529	−	2.26706i	−0.911996	−	0.263541i
$75$	1.57559	−	3.12237i	0.181934	−	0.360540i
$76$	−1.06680	+	1.69172i	−0.122371	+	0.194054i
$77$	0.965809	+	0.965809i	0.110064	+	0.110064i
$78$	−0.352439	+	0.194414i	−0.0399058	+	0.0220131i
$79$	−0.164126			−0.0184656			−0.00923281	−	0.999957i	$-0.502939\pi$
$79$	−0.164126			−0.0184656			−0.00923281	+	0.999957i	$0.502939\pi$
$80$	−8.79848	−	1.60834i	−0.983700	−	0.179818i
$81$	−4.83597			−0.537331
$82$	−12.9793	+	7.15972i	−1.43333	+	0.790659i
$83$	−1.98305	−	1.98305i	−0.217667	−	0.217667i	0.589847	−	0.807515i	$-0.299188\pi$
$83$	−1.98305	−	1.98305i	−0.217667	−	0.217667i	−0.807515	+	0.589847i	$0.799188\pi$
$84$	−0.345689	+	0.548191i	−0.0377178	+	0.0598125i
$85$	−5.43817	+	0.872213i	−0.589852	+	0.0946048i
$86$	−13.6372	−	3.94077i	−1.47054	−	0.424944i
$87$	0.915785	−	0.915785i	0.0981825	−	0.0981825i
$88$	8.32489	+	0.487783i	0.887436	+	0.0519979i
$89$			2.27564i			0.241218i	0.992700	+	0.120609i	$0.0384847\pi$
$89$			2.27564i			0.241218i	−0.992700	+	0.120609i	$0.961515\pi$
$90$	7.88035	+	0.968404i	0.830662	+	0.102079i
$91$			0.188500i			0.0197602i
$92$	−1.57246	+	0.356228i	−0.163940	+	0.0371393i
$93$	−0.555337	+	0.555337i	−0.0575857	+	0.0575857i
$94$	−1.42954	+	4.94700i	−0.147446	+	0.510244i
$95$	−1.31079	+	1.81158i	−0.134484	+	0.185864i
$96$	0.647013	+	3.90358i	0.0660355	+	0.398407i
$97$	−4.13745	−	4.13745i	−0.420095	−	0.420095i	0.465141	−	0.885236i	$-0.346003\pi$
$97$	−4.13745	−	4.13745i	−0.420095	−	0.420095i	−0.885236	+	0.465141i	$0.846003\pi$
$98$	−4.63496	−	8.40238i	−0.468202	−	0.848769i
$99$	−7.40249			−0.743978
$100$	−9.70246	−	2.42120i	−0.970246	−	0.242120i
$101$	4.60617			0.458331			0.229165	−	0.973387i	$-0.426400\pi$
$101$	4.60617			0.458331			0.229165	+	0.973387i	$0.426400\pi$
$102$	1.17687	+	2.13346i	0.116527	+	0.211244i
$103$	10.8229	+	10.8229i	1.06641	+	1.06641i	0.997632	+	0.0687770i	$0.0219097\pi$
$103$	10.8229	+	10.8229i	1.06641	+	1.06641i	0.0687770	+	0.997632i	$0.478090\pi$
$104$	0.764796	+	0.859998i	0.0749944	+	0.0843298i
$105$	−0.424752	+	0.587029i	−0.0414516	+	0.0572882i
$106$	−3.15114	+	10.9047i	−0.306066	+	1.05916i
$107$	−5.10887	+	5.10887i	−0.493893	+	0.493893i	−0.909530	−	0.415637i	$-0.863559\pi$
$107$	−5.10887	+	5.10887i	−0.493893	+	0.493893i	0.415637	+	0.909530i	$0.363559\pi$
$108$	−1.70331	−	7.51874i	−0.163901	−	0.723491i
$109$			5.24030i			0.501930i	0.967996	+	0.250965i	$0.0807479\pi$
$109$			5.24030i			0.501930i	−0.967996	+	0.250965i	$0.919252\pi$
$110$	9.25386	+	1.13719i	0.882321	+	0.108427i
$111$			4.03908i			0.383372i
$112$	1.74708	+	0.617681i	0.165083	+	0.0583654i
$113$	−9.13170	+	9.13170i	−0.859038	+	0.859038i	−0.991225	−	0.132186i	$-0.957800\pi$
$113$	−9.13170	+	9.13170i	−0.859038	+	0.859038i	0.132186	+	0.991225i	$0.457800\pi$
$114$	0.950327	+	0.274617i	0.0890062	+	0.0257202i
$115$	−1.77986	+	0.285468i	−0.165973	+	0.0266200i
$116$	−3.13231	−	1.97524i	−0.290828	−	0.183396i
$117$	−0.722384	−	0.722384i	−0.0667844	−	0.0667844i
$118$	17.4904	−	9.64815i	1.61012	−	0.888185i
$119$	1.14107			0.104601
$120$	0.443880	+	4.40155i	0.0405205	+	0.401805i
$121$	2.30729			0.209754
$122$	−9.52816	+	5.25597i	−0.862639	+	0.475853i
$123$	5.18421	+	5.18421i	0.467445	+	0.467445i
$124$	1.89945	+	1.19779i	0.170576	+	0.107565i
$125$	−10.6532	−	3.39255i	−0.952851	−	0.303439i
$126$	−1.58026	−	0.456650i	−0.140781	−	0.0406816i
$127$	0.359207	−	0.359207i	0.0318744	−	0.0318744i	−0.690990	−	0.722864i	$-0.742825\pi$
$127$	0.359207	−	0.359207i	0.0318744	−	0.0318744i	0.722864	+	0.690990i	$0.242825\pi$
$128$	10.4769	−	4.27032i	0.926031	−	0.377446i
$129$			7.02101i			0.618166i
$130$	0.792078	+	1.01403i	0.0694698	+	0.0889360i
$131$		−	7.07602i		−	0.618235i	−0.951024	−	0.309117i	$-0.899966\pi$
$131$		−	7.07602i		−	0.618235i	0.951024	−	0.309117i	$-0.100034\pi$
$132$	−0.911301	−	4.02266i	−0.0793186	−	0.350127i
$133$	0.327577	−	0.327577i	0.0284045	−	0.0284045i
$134$	5.28127	−	18.2761i	0.456232	−	1.57882i
$135$	−1.36497	−	8.51044i	−0.117478	−	0.732462i
$136$	5.20592	−	4.62962i	0.446404	−	0.396987i
$137$	4.32753	+	4.32753i	0.369726	+	0.369726i	0.867377	−	0.497651i	$-0.165804\pi$
$137$	4.32753	+	4.32753i	0.369726	+	0.369726i	−0.497651	+	0.867377i	$0.665804\pi$
$138$	0.385178	+	0.698261i	0.0327886	+	0.0594400i
$139$	11.4346			0.969873			0.484937	−	0.874549i	$-0.338843\pi$
$139$	11.4346			0.969873			0.484937	+	0.874549i	$0.338843\pi$
$140$	1.90533	+	0.813622i	0.161030	+	0.0687636i
$141$	2.54692			0.214490
$142$	6.28260	+	11.3893i	0.527224	+	0.955765i
$143$	−0.848292	−	0.848292i	−0.0709377	−	0.0709377i
$144$	−9.06242	+	4.32817i	−0.755201	+	0.360680i
$145$	−3.35423	−	2.42700i	−0.278554	−	0.201551i
$146$	2.68138	−	9.27905i	0.221912	−	0.767939i
$147$	−3.35608	+	3.35608i	−0.276805	+	0.276805i
$148$	11.2635	−	2.55165i	0.925850	−	0.209744i
$149$			13.1136i			1.07431i	0.843484	+	0.537155i	$0.180501\pi$
$149$			13.1136i			1.07431i	−0.843484	+	0.537155i	$0.819499\pi$
$150$	0.181764	+	4.94271i	0.0148409	+	0.403570i
$151$			2.25997i			0.183914i	0.995763	+	0.0919569i	$0.0293122\pi$
$151$			2.25997i			0.183914i	−0.995763	+	0.0919569i	$0.970688\pi$
$152$	0.165443	−	2.82358i	0.0134192	−	0.229023i
$153$	−4.37289	+	4.37289i	−0.353527	+	0.353527i
$154$	−1.85569	−	0.536242i	−0.149536	−	0.0432116i
$155$	2.03402	+	1.47174i	0.163377	+	0.118213i
$156$	0.303627	−	0.481488i	0.0243096	−	0.0385499i
$157$	−11.4604	−	11.4604i	−0.914642	−	0.914642i	0.0819909	−	0.996633i	$-0.473872\pi$
$157$	−11.4604	−	11.4604i	−0.914642	−	0.914642i	−0.996633	+	0.0819909i	$0.973872\pi$
$158$	0.203238	−	0.112111i	0.0161688	−	0.00891909i
$159$	5.61418			0.445234
$160$	11.9938	−	4.01845i	0.948196	−	0.317686i
$161$	0.373461			0.0294329
$162$	5.98842	−	3.30336i	0.470494	−	0.259536i
$163$	−10.4983	−	10.4983i	−0.822289	−	0.822289i	0.164147	−	0.986436i	$-0.447513\pi$
$163$	−10.4983	−	10.4983i	−0.822289	−	0.822289i	−0.986436	+	0.164147i	$0.947513\pi$
$164$	11.1817	−	17.7319i	0.873145	−	1.38463i
$165$	−0.730282	−	4.55324i	−0.0568524	−	0.354469i
$166$	3.81020	+	1.10104i	0.295729	+	0.0854570i
$167$	15.9796	−	15.9796i	1.23654	−	1.23654i	0.275136	−	0.961405i	$-0.411277\pi$
$167$	15.9796	−	15.9796i	1.23654	−	1.23654i	0.961405	−	0.275136i	$-0.0887228\pi$
$168$	0.0536106	−	0.914961i	0.00413615	−	0.0705908i
$169$			12.8344i			0.987264i
$170$	6.13832	−	4.79477i	0.470788	−	0.367742i
$171$			2.51073i			0.192001i
$172$	19.5789	−	4.43545i	1.49288	−	0.338200i
$173$	−12.7302	+	12.7302i	−0.967858	+	0.967858i	−0.999499	−	0.0316413i	$-0.989927\pi$
$173$	−12.7302	+	12.7302i	−0.967858	+	0.967858i	0.0316413	+	0.999499i	$0.489927\pi$
$174$	−0.508467	+	1.75958i	−0.0385468	+	0.133393i
$175$	2.06795	+	1.04352i	0.156322	+	0.0788825i
$176$	−10.6419	+	5.08254i	−0.802167	+	0.383111i
$177$	−6.98603	−	6.98603i	−0.525102	−	0.525102i
$178$	−1.55445	−	2.81794i	−0.116511	−	0.211214i
$179$	3.57919			0.267522			0.133761	−	0.991014i	$-0.457295\pi$
$179$	3.57919			0.267522			0.133761	+	0.991014i	$0.457295\pi$
$180$	−10.4198	+	4.18373i	−0.776645	+	0.311837i
$181$	−7.40488			−0.550400			−0.275200	−	0.961387i	$-0.588744\pi$
$181$	−7.40488			−0.550400			−0.275200	+	0.961387i	$0.588744\pi$
$182$	−0.128761	−	0.233421i	−0.00954437	−	0.0173023i
$183$	3.80574	+	3.80574i	0.281329	+	0.281329i
$184$	1.70385	−	1.51523i	0.125610	−	0.111705i
$185$	12.7491	−	2.04479i	0.937331	−	0.150336i
$186$	0.308337	−	1.06702i	0.0226084	−	0.0782374i
$187$	−5.13506	+	5.13506i	−0.375513	+	0.375513i
$188$	−1.60899	−	7.10239i	−0.117348	−	0.517995i
$189$			1.78571i			0.129891i
$190$	0.385706	−	3.13867i	0.0279820	−	0.227703i
$191$			4.12918i			0.298777i	0.988779	+	0.149388i	$0.0477304\pi$
$191$			4.12918i			0.298777i	−0.988779	+	0.149388i	$0.952270\pi$
$192$	−3.46766	−	4.39186i	−0.250257	−	0.316955i
$193$	5.54163	−	5.54163i	0.398895	−	0.398895i	−0.478948	−	0.877843i	$-0.658982\pi$
$193$	5.54163	−	5.54163i	0.398895	−	0.398895i	0.877843	+	0.478948i	$0.158982\pi$
$194$	7.94965	+	2.29722i	0.570751	+	0.164931i
$195$	0.373069	−	0.515601i	0.0267161	−	0.0369229i
$196$	11.4790	+	7.23867i	0.819929	+	0.517048i
$197$	5.86112	+	5.86112i	0.417588	+	0.417588i	0.884371	−	0.466784i	$-0.154587\pi$
$197$	5.86112	+	5.86112i	0.417588	+	0.417588i	−0.466784	+	0.884371i	$0.654587\pi$
$198$	9.16655	−	5.05650i	0.651438	−	0.359350i
$199$	14.7472			1.04540			0.522701	−	0.852516i	$-0.324924\pi$
$199$	14.7472			1.04540			0.522701	+	0.852516i	$0.324924\pi$
$200$	13.6685	−	3.62937i	0.966508	−	0.256635i
$201$	−9.40930			−0.663681
$202$	−5.70385	+	3.14638i	−0.401321	+	0.221379i
$203$	0.606525	+	0.606525i	0.0425697	+	0.0425697i
$204$	−2.91464	−	1.83798i	−0.204066	−	0.128684i
$205$	13.7391	−	18.9881i	0.959580	−	1.32619i
$206$	−20.7949	−	6.00913i	−1.44885	−	0.418676i
$207$	−1.43121	+	1.43121i	−0.0994757	+	0.0994757i
$208$	−1.53450	−	0.542524i	−0.106398	−	0.0376172i
$209$			2.94834i			0.203941i
$210$	0.124985	−	1.01706i	0.00862478	−	0.0701839i
$211$			3.44024i			0.236836i	0.992964	+	0.118418i	$0.0377822\pi$
$211$			3.44024i			0.236836i	−0.992964	+	0.118418i	$0.962218\pi$
$212$	−3.54670	−	15.6558i	−0.243588	−	1.07525i
$213$	4.54910	−	4.54910i	0.311699	−	0.311699i
$214$	2.83657	−	9.81611i	0.193904	−	0.671015i
$215$	22.1614	−	3.55440i	1.51139	−	0.242408i
$216$	7.24512	+	8.14700i	0.492968	+	0.554333i
$217$	−0.367800	−	0.367800i	−0.0249679	−	0.0249679i
$218$	−3.57955	−	6.48910i	−0.242438	−	0.439497i
$219$	−4.77724			−0.322816
$220$	−12.2359	+	4.91294i	−0.824944	+	0.331230i
$221$	−1.00223			−0.0674170
$222$	−2.75902	−	5.00162i	−0.185173	−	0.335686i
$223$	9.96172	+	9.96172i	0.667086	+	0.667086i	0.957040	−	0.289955i	$-0.0936402\pi$
$223$	9.96172	+	9.96172i	0.667086	+	0.667086i	−0.289955	+	0.957040i	$0.593640\pi$
$224$	−2.58534	+	0.428517i	−0.172741	+	0.0286315i
$225$	−11.9240	+	3.92591i	−0.794933	+	0.261727i
$226$	5.07015	−	17.5455i	0.337262	−	1.16711i
$227$	−8.44789	+	8.44789i	−0.560706	+	0.560706i	−0.929508	−	0.368802i	$-0.879768\pi$
$227$	−8.44789	+	8.44789i	−0.560706	+	0.560706i	0.368802	+	0.929508i	$0.379768\pi$
$228$	−1.36438	+	0.309090i	−0.0903583	+	0.0204700i
$229$			8.64013i			0.570956i	0.958385	+	0.285478i	$0.0921524\pi$
$229$			8.64013i			0.570956i	−0.958385	+	0.285478i	$0.907848\pi$
$230$	2.00902	−	1.56929i	0.132471	−	0.103476i
$231$			0.955387i			0.0628599i
$232$	5.22801	+	0.306326i	0.343235	+	0.0201113i
$233$	−4.54741	+	4.54741i	−0.297911	+	0.297911i	−0.840195	−	0.542284i	$-0.817560\pi$
$233$	−4.54741	+	4.54741i	−0.297911	+	0.297911i	0.542284	+	0.840195i	$0.317560\pi$
$234$	1.38798	+	0.401086i	0.0907350	+	0.0262198i
$235$	−1.28938	−	8.03919i	−0.0841101	−	0.524419i
$236$	−15.0680	+	23.8947i	−0.980845	+	1.55541i
$237$	−0.0811775	−	0.0811775i	−0.00527304	−	0.00527304i
$238$	−1.41299	+	0.779441i	−0.0915906	+	0.0505236i
$239$	23.0971			1.49403			0.747013	−	0.664810i	$-0.231487\pi$
$239$	23.0971			1.49403			0.747013	+	0.664810i	$0.231487\pi$
$240$	−3.55627	−	5.14726i	−0.229557	−	0.332254i
$241$	19.8422			1.27815			0.639075	−	0.769145i	$-0.279317\pi$
$241$	19.8422			1.27815			0.639075	+	0.769145i	$0.279317\pi$
$242$	−2.85713	+	1.57607i	−0.183663	+	0.101313i
$243$	−10.5688	−	10.5688i	−0.677989	−	0.677989i
$244$	8.20853	−	13.0170i	0.525497	−	0.833328i
$245$	12.2923	+	8.89423i	0.785325	+	0.568231i
$246$	−9.96087	−	2.87841i	−0.635082	−	0.183520i
$247$	−0.287718	+	0.287718i	−0.0183071	+	0.0183071i
$248$	−3.17029	−	0.185758i	−0.201314	−	0.0117956i
$249$		−	1.96165i		−	0.124314i
$250$	15.5093	−	3.07598i	0.980894	−	0.194542i
$251$		−	5.82734i		−	0.367819i	−0.982943	−	0.183909i	$-0.941125\pi$
$251$		−	5.82734i		−	0.367819i	0.982943	−	0.183909i	$-0.0588753\pi$
$252$	2.26877	−	0.513973i	0.142919	−	0.0323772i
$253$	−1.68066	+	1.68066i	−0.105662	+	0.105662i
$254$	−0.199441	+	0.690175i	−0.0125140	+	0.0433054i
$255$	−3.12114	−	2.25834i	−0.195454	−	0.141423i
$256$	−10.0566	+	12.4445i	−0.628536	+	0.777781i
$257$	6.18949	+	6.18949i	0.386090	+	0.386090i	0.873290	−	0.487200i	$-0.161982\pi$
$257$	6.18949	+	6.18949i	0.386090	+	0.386090i	−0.487200	+	0.873290i	$0.661982\pi$
$258$	−4.79592	−	8.69416i	−0.298581	−	0.541275i
$259$	−2.67509			−0.166222
$260$	−1.67350	−	0.714623i	−0.103786	−	0.0443190i
$261$	−4.64874			−0.287750
$262$	4.83349	+	8.76227i	0.298614	+	0.541335i
$263$	−8.45067	−	8.45067i	−0.521091	−	0.521091i	0.396810	−	0.917901i	$-0.370117\pi$
$263$	−8.45067	−	8.45067i	−0.521091	−	0.521091i	−0.917901	+	0.396810i	$0.870117\pi$
$264$	3.87627	+	4.35879i	0.238568	+	0.268265i
$265$	−2.84219	−	17.7208i	−0.174594	−	1.08858i
$266$	−0.181879	+	0.629402i	−0.0111517	+	0.0385911i
$267$	−1.12554	+	1.12554i	−0.0688821	+	0.0688821i
$268$	5.94423	+	26.2390i	0.363101	+	1.60280i
$269$		−	1.50260i		−	0.0916154i	−0.998950	−	0.0458077i	$-0.985414\pi$
$269$		−	1.50260i		−	0.0916154i	0.998950	−	0.0458077i	$-0.0145861\pi$
$270$	7.50357	+	9.60615i	0.456652	+	0.584612i
$271$			29.6188i			1.79921i	0.436702	+	0.899606i	$0.356146\pi$
$271$			29.6188i			1.79921i	−0.436702	+	0.899606i	$0.643854\pi$
$272$	−3.28412	+	9.28895i	−0.199129	+	0.563226i
$273$	−0.0932330	+	0.0932330i	−0.00564272	+	0.00564272i
$274$	−8.31485	−	2.40275i	−0.502319	−	0.145156i
$275$	−14.0023	+	4.61017i	−0.844370	+	0.278004i
$276$	−0.953937	−	0.601553i	−0.0574203	−	0.0362093i
$277$	−18.2366	−	18.2366i	−1.09573	−	1.09573i	−0.994904	−	0.100825i	$-0.967852\pi$
$277$	−18.2366	−	18.2366i	−1.09573	−	1.09573i	−0.100825	−	0.994904i	$-0.532148\pi$
$278$	−14.1596	+	7.81078i	−0.849235	+	0.468459i
$279$	2.81902			0.168771
$280$	−2.91515	+	0.293982i	−0.174214	+	0.0175688i
$281$	16.2476			0.969249			0.484625	−	0.874722i	$-0.338956\pi$
$281$	16.2476			0.969249			0.484625	+	0.874722i	$0.338956\pi$
$282$	−3.15387	+	1.73975i	−0.187810	+	0.103601i
$283$	−6.63046	−	6.63046i	−0.394140	−	0.394140i	0.482020	−	0.876160i	$-0.339903\pi$
$283$	−6.63046	−	6.63046i	−0.394140	−	0.394140i	−0.876160	+	0.482020i	$0.839903\pi$
$284$	−15.5596	−	9.81186i	−0.923290	−	0.582227i
$285$	−1.54434	+	0.247693i	−0.0914788	+	0.0146720i
$286$	1.62990	+	0.470993i	0.0963778	+	0.0278504i
$287$	−3.43351	+	3.43351i	−0.202674	+	0.202674i
$288$	8.26556	−	11.5500i	0.487053	−	0.680587i
$289$		−	10.9331i		−	0.643125i
$290$	5.81140	+	0.714153i	0.341257	+	0.0419365i
$291$		−	4.09281i		−	0.239925i
$292$	3.01797	+	13.3219i	0.176613	+	0.779605i
$293$	−14.4511	+	14.4511i	−0.844244	+	0.844244i	−0.989408	−	0.145164i	$-0.953629\pi$
$293$	−14.4511	+	14.4511i	−0.844244	+	0.844244i	0.145164	+	0.989408i	$0.453629\pi$
$294$	1.86338	−	6.44833i	0.108675	−	0.376074i
$295$	−18.5142	+	25.5876i	−1.07794	+	1.48977i
$296$	−12.2046	+	10.8536i	−0.709379	+	0.630850i
$297$	−8.03610	−	8.03610i	−0.466302	−	0.466302i
$298$	−8.95765	−	16.2387i	−0.518903	−	0.940681i
$299$	−0.328019			−0.0189699
$300$	−3.60134	−	5.99642i	−0.207924	−	0.346204i
$301$	−4.65002			−0.268023
$302$	−1.54374	−	2.79853i	−0.0888323	−	0.161038i
$303$	2.27823	+	2.27823i	0.130881	+	0.130881i
$304$	1.72387	+	3.60947i	0.0988705	+	0.207017i
$305$	10.0859	−	13.9392i	0.577517	−	0.798158i
$306$	2.42794	−	8.40200i	0.138796	−	0.480310i
$307$	−11.3650	+	11.3650i	−0.648638	+	0.648638i	−0.952664	−	0.304026i	$-0.901669\pi$
$307$	−11.3650	+	11.3650i	−0.648638	+	0.648638i	0.304026	+	0.952664i	$0.401669\pi$
$308$	2.66421	−	0.603556i	0.151807	−	0.0343908i
$309$			10.7061i			0.609048i
$310$	−3.52406	−	0.433066i	−0.200153	−	0.0245965i
$311$		−	31.6342i		−	1.79381i	−0.442225	−	0.896904i	$-0.645811\pi$
$311$		−	31.6342i		−	1.79381i	0.442225	−	0.896904i	$-0.354189\pi$
$312$	−0.0470874	+	0.803631i	−0.00266580	+	0.0454966i
$313$	−4.11199	+	4.11199i	−0.232424	+	0.232424i	−0.813704	−	0.581280i	$-0.802552\pi$
$313$	−4.11199	+	4.11199i	−0.232424	+	0.232424i	0.581280	+	0.813704i	$0.302552\pi$
$314$	22.0199	+	6.36312i	1.24266	+	0.359092i
$315$	2.56802	−	0.411878i	0.144692	−	0.0232067i
$316$	−0.175090	+	0.277656i	−0.00984958	+	0.0156194i
$317$	21.3697	+	21.3697i	1.20024	+	1.20024i	0.974093	+	0.226149i	$0.0726137\pi$
$317$	21.3697	+	21.3697i	1.20024	+	1.20024i	0.226149	+	0.974093i	$0.427386\pi$
$318$	−6.95208	+	3.83494i	−0.389853	+	0.215053i
$319$	−5.45900			−0.305645
$320$	−12.1071	+	13.1688i	−0.676808	+	0.736159i
$321$	−5.05374			−0.282072
$322$	−0.462459	+	0.255104i	−0.0257718	+	0.0142164i
$323$	1.74168	+	1.74168i	0.0969095	+	0.0969095i
$324$	−5.15903	+	8.18114i	−0.286613	+	0.454508i
$325$	−1.81633	−	0.916545i	−0.100752	−	0.0508407i
$326$	20.1713	+	5.82891i	1.11718	+	0.322834i
$327$	−2.59188	+	2.59188i	−0.143331	+	0.143331i
$328$	−1.73410	+	29.5955i	−0.0957496	+	1.63414i
$329$			1.68683i			0.0929979i
$330$	4.01454	+	5.13946i	0.220993	+	0.282918i
$331$		−	28.8144i		−	1.58378i	−0.610661	−	0.791892i	$-0.709096\pi$
$331$		−	28.8144i		−	1.58378i	0.610661	−	0.791892i	$-0.290904\pi$
$332$	−5.47028	+	1.23925i	−0.300221	+	0.0680127i
$333$	10.2517	−	10.2517i	0.561788	−	0.561788i
$334$	−8.87230	+	30.7030i	−0.485471	+	1.68000i
$335$	4.76348	+	29.6998i	0.260256	+	1.62268i
$336$	0.558606	+	1.16962i	0.0304744	+	0.0638081i
$337$	−13.4380	−	13.4380i	−0.732016	−	0.732016i	0.239003	−	0.971019i	$-0.423179\pi$
$337$	−13.4380	−	13.4380i	−0.732016	−	0.732016i	−0.971019	+	0.239003i	$0.923179\pi$
$338$	−8.76695	−	15.8930i	−0.476859	−	0.864463i
$339$	−9.03317			−0.490614
$340$	−4.32590	+	10.1304i	−0.234605	+	0.549396i
$341$	3.31036			0.179266
$342$	−1.71503	−	3.10905i	−0.0927383	−	0.168118i
$343$	−4.51578	−	4.51578i	−0.243829	−	0.243829i
$344$	−21.2149	+	18.8664i	−1.14383	+	1.01721i
$345$	−1.02152	−	0.739135i	−0.0549969	−	0.0397937i
$346$	7.06812	−	24.4596i	0.379985	−	1.31496i
$347$	−19.6995	+	19.6995i	−1.05752	+	1.05752i	−0.0592835	+	0.998241i	$0.518882\pi$
$347$	−19.6995	+	19.6995i	−1.05752	+	1.05752i	−0.998241	+	0.0592835i	$0.981118\pi$
$348$	−0.572295	−	2.52622i	−0.0306782	−	0.135419i
$349$		−	7.57450i		−	0.405454i	−0.979235	−	0.202727i	$-0.935020\pi$
$349$		−	7.57450i		−	0.405454i	0.979235	−	0.202727i	$-0.0649804\pi$
$350$	−3.27356	+	0.120382i	−0.174979	+	0.00643470i
$351$		−	1.56843i		−	0.0837166i
$352$	9.70620	−	13.5630i	0.517342	−	0.722913i
$353$	−12.3157	+	12.3157i	−0.655498	+	0.655498i	−0.954311	−	0.298814i	$-0.903409\pi$
$353$	−12.3157	+	12.3157i	−0.655498	+	0.655498i	0.298814	+	0.954311i	$0.403409\pi$
$354$	13.4229	+	3.87882i	0.713417	+	0.206157i
$355$	−16.6619	−	12.0559i	−0.884323	−	0.639863i
$356$	3.84976	+	2.42766i	0.204037	+	0.128666i
$357$	0.564377	+	0.564377i	0.0298700	+	0.0298700i
$358$	−4.43214	+	2.44488i	−0.234246	+	0.129216i
$359$	23.4554			1.23793			0.618966	−	0.785418i	$-0.287552\pi$
$359$	23.4554			1.23793			0.618966	+	0.785418i	$0.287552\pi$
$360$	10.0451	−	12.2983i	0.529421	−	0.648177i
$361$	1.00000			0.0526316
$362$	9.16950	−	5.05813i	0.481938	−	0.265849i
$363$	1.14120	+	1.14120i	0.0598973	+	0.0598973i
$364$	0.318890	+	0.201092i	0.0167144	+	0.0105401i
$365$	2.41849	+	15.0790i	0.126589	+	0.789273i
$366$	−7.31230	−	2.11305i	−0.382220	−	0.110451i
$367$	23.3564	−	23.3564i	1.21920	−	1.21920i	0.251282	−	0.967914i	$-0.419148\pi$
$367$	23.3564	−	23.3564i	1.21920	−	1.21920i	0.967914	−	0.251282i	$-0.0808523\pi$
$368$	−1.07486	+	3.04019i	−0.0560311	+	0.158481i
$369$		−	26.3163i		−	1.36997i
$370$	−14.3905	+	11.2407i	−0.748127	+	0.584377i
$371$			3.71828i			0.193043i
$372$	0.347042	+	1.53191i	0.0179933	+	0.0794259i
$373$	6.12552	−	6.12552i	0.317168	−	0.317168i	−0.530511	−	0.847678i	$-0.678000\pi$
$373$	6.12552	−	6.12552i	0.317168	−	0.317168i	0.847678	+	0.530511i	$0.178000\pi$
$374$	2.85111	−	9.86643i	0.147428	−	0.510181i
$375$	−3.59115	−	6.94709i	−0.185446	−	0.358746i
$376$	6.84393	+	7.69586i	0.352949	+	0.396884i
$377$	−0.532725	−	0.532725i	−0.0274367	−	0.0274367i
$378$	−1.21978	−	2.21126i	−0.0627389	−	0.113735i
$379$	−22.9714			−1.17996			−0.589981	−	0.807417i	$-0.700865\pi$
$379$	−22.9714			−1.17996			−0.589981	+	0.807417i	$0.700865\pi$
$380$	1.66634	+	4.15010i	0.0854815	+	0.212896i
$381$	0.355331			0.0182041
$382$	−2.82056	−	5.11318i	−0.144312	−	0.261613i
$383$	−18.5545	−	18.5545i	−0.948090	−	0.948090i	0.0506273	−	0.998718i	$-0.483878\pi$
$383$	−18.5545	−	18.5545i	−0.948090	−	0.948090i	−0.998718	+	0.0506273i	$0.983878\pi$
$384$	7.29402	+	3.06978i	0.372221	+	0.156654i
$385$	3.01561	−	0.483666i	0.153690	−	0.0246499i
$386$	−3.07685	+	10.6476i	−0.156608	+	0.541949i
$387$	17.8202	−	17.8202i	0.905851	−	0.905851i
$388$	−11.4133	+	2.58559i	−0.579422	+	0.131263i
$389$		−	37.2211i		−	1.88718i	−0.331112	−	0.943592i	$-0.607424\pi$
$389$		−	37.2211i		−	1.88718i	0.331112	−	0.943592i	$-0.392576\pi$
$390$	−0.109777	+	0.893308i	−0.00555878	+	0.0452344i
$391$			1.98564i			0.100418i
$392$	−19.1591	−	1.12260i	−0.967681	−	0.0566997i
$393$	3.49983	−	3.49983i	0.176543	−	0.176543i
$394$	−11.2615	−	3.25424i	−0.567345	−	0.163946i
$395$	−0.215135	+	0.297327i	−0.0108246	+	0.0149602i
$396$	−7.89700	+	12.5230i	−0.396839	+	0.629303i
$397$	8.21621	+	8.21621i	0.412360	+	0.412360i	0.882560	−	0.470200i	$-0.155818\pi$
$397$	8.21621	+	8.21621i	0.412360	+	0.412360i	−0.470200	+	0.882560i	$0.655818\pi$
$398$	−18.2616	+	10.0735i	−0.915369	+	0.504941i
$399$	0.324042			0.0162224
$400$	−14.4466	+	13.8310i	−0.722331	+	0.691548i
$401$	28.5885			1.42764			0.713821	−	0.700328i	$-0.246963\pi$
$401$	28.5885			1.42764			0.713821	+	0.700328i	$0.246963\pi$
$402$	11.6516	−	6.42731i	0.581129	−	0.320565i
$403$	0.323047	+	0.323047i	0.0160921	+	0.0160921i
$404$	4.91387	−	7.79237i	0.244474	−	0.387685i
$405$	−6.33896	+	8.76076i	−0.314985	+	0.435326i
$406$	−1.16537	−	0.336758i	−0.0578363	−	0.0167130i
$407$	12.0385	−	12.0385i	0.596725	−	0.596725i
$408$	4.86471	+	0.285040i	0.240839	+	0.0141116i
$409$			8.40060i			0.415383i	0.978194	+	0.207691i	$0.0665950\pi$
$409$			8.40060i			0.415383i	−0.978194	+	0.207691i	$0.933405\pi$
$410$	−4.04278	+	32.8980i	−0.199659	+	1.62472i
$411$			4.28083i			0.211158i
$412$	29.8552	−	6.76346i	1.47086	−	0.333212i
$413$	4.62686	−	4.62686i	0.227673	−	0.227673i
$414$	0.794642	−	2.74990i	0.0390545	−	0.135150i
$415$	−6.19181	+	0.993087i	−0.303944	+	0.0487487i
$416$	2.27077	−	0.376376i	0.111334	−	0.0184534i
$417$	5.65562	+	5.65562i	0.276957	+	0.276957i
$418$	−2.01395	−	3.65095i	−0.0985057	−	0.178574i
$419$	−14.2962			−0.698416			−0.349208	−	0.937045i	$-0.613549\pi$
$419$	−14.2962			−0.698416			−0.349208	+	0.937045i	$0.613549\pi$
$420$	0.539965	+	1.34481i	0.0263476	+	0.0656199i
$421$	40.0754			1.95316			0.976579	−	0.215161i	$-0.0690275\pi$
$421$	40.0754			1.95316			0.976579	+	0.215161i	$0.0690275\pi$
$422$	−2.34996	−	4.26007i	−0.114394	−	0.207377i
$423$	−6.46440	−	6.46440i	−0.314310	−	0.314310i
$424$	15.0861	+	16.9640i	0.732645	+	0.823845i
$425$	−5.54822	+	10.9950i	−0.269128	+	0.533334i
$426$	−2.52578	+	8.74058i	−0.122374	+	0.423483i
$427$	−2.52055	+	2.52055i	−0.121978	+	0.121978i
$428$	3.19265	+	14.0930i	0.154322	+	0.681209i
$429$		−	0.839138i		−	0.0405140i
$430$	−25.0146	+	19.5394i	−1.20631	+	0.942275i
$431$			30.3005i			1.45952i	0.683702	+	0.729761i	$0.260369\pi$
$431$			30.3005i			1.45952i	−0.683702	+	0.729761i	$0.739631\pi$
$432$	−14.5367	−	5.13947i	−0.699399	−	0.247273i
$433$	4.16829	−	4.16829i	0.200315	−	0.200315i	−0.599820	−	0.800135i	$-0.704761\pi$
$433$	4.16829	−	4.16829i	0.200315	−	0.200315i	0.800135	+	0.599820i	$0.204761\pi$
$434$	0.706686	+	0.204212i	0.0339220	+	0.00980249i
$435$	−0.458615	−	2.85942i	−0.0219889	−	0.137099i
$436$	8.86515	+	5.59037i	0.424564	+	0.267730i
$437$	0.570036	+	0.570036i	0.0272685	+	0.0272685i
$438$	5.91568	−	3.26324i	0.282662	−	0.155924i
$439$	19.3441			0.923241			0.461621	−	0.887077i	$-0.347268\pi$
$439$	19.3441			0.923241			0.461621	+	0.887077i	$0.347268\pi$
$440$	11.7959	−	14.4418i	0.562345	−	0.688487i
$441$	17.0363			0.811252
$442$	1.24106	−	0.684600i	0.0590313	−	0.0325631i
$443$	−4.15922	−	4.15922i	−0.197611	−	0.197611i	0.601364	−	0.798975i	$-0.294624\pi$
$443$	−4.15922	−	4.15922i	−0.197611	−	0.197611i	−0.798975	+	0.601364i	$0.794624\pi$
$444$	6.83301	+	4.30890i	0.324280	+	0.204491i
$445$	4.12251	+	2.98289i	0.195426	+	0.141403i
$446$	−19.1403	−	5.53100i	−0.906320	−	0.261900i
$447$	−6.48606	+	6.48606i	−0.306780	+	0.306780i
$448$	2.90874	−	2.29663i	0.137425	−	0.108506i
$449$			22.1626i			1.04592i	0.852358	+	0.522959i	$0.175172\pi$
$449$			22.1626i			1.04592i	−0.852358	+	0.522959i	$0.824828\pi$
$450$	12.0838	−	13.0065i	0.569638	−	0.613133i
$451$		−	30.9031i		−	1.45517i
$452$	5.70661	+	25.1901i	0.268416	+	1.18484i
$453$	−1.11779	+	1.11779i	−0.0525184	+	0.0525184i
$454$	4.69048	−	16.2317i	0.220135	−	0.761789i
$455$	0.341483	+	0.247084i	0.0160090	+	0.0115835i
$456$	1.47839	−	1.31473i	0.0692318	−	0.0615678i
$457$	10.8450	+	10.8450i	0.507307	+	0.507307i	0.913699	−	0.406392i	$-0.133213\pi$
$457$	10.8450	+	10.8450i	0.507307	+	0.507307i	−0.406392	+	0.913699i	$0.633213\pi$
$458$	−5.90191	−	10.6991i	−0.275778	−	0.499937i
$459$	−9.49435			−0.443158
$460$	−1.41583	+	3.31558i	−0.0660134	+	0.154590i
$461$	−6.29625			−0.293245			−0.146623	−	0.989192i	$-0.546840\pi$
$461$	−6.29625			−0.293245			−0.146623	+	0.989192i	$0.546840\pi$
$462$	−0.652606	−	1.18306i	−0.0303620	−	0.0550410i
$463$	5.60774	+	5.60774i	0.260614	+	0.260614i	0.825303	−	0.564690i	$-0.191004\pi$
$463$	5.60774	+	5.60774i	0.260614	+	0.260614i	−0.564690	+	0.825303i	$0.691004\pi$
$464$	−6.68312	+	3.19182i	−0.310256	+	0.148177i
$465$	0.278107	+	1.73397i	0.0128969	+	0.0804109i
$466$	2.52484	−	8.73733i	0.116961	−	0.404749i
$467$	23.6709	−	23.6709i	1.09536	−	1.09536i	0.100413	−	0.994946i	$-0.467983\pi$
$467$	23.6709	−	23.6709i	1.09536	−	1.09536i	0.994946	−	0.100413i	$-0.0320165\pi$
$468$	−1.99272	+	0.451434i	−0.0921133	+	0.0208675i
$469$		−	6.23179i		−	0.287757i
$470$	7.08806	+	9.07422i	0.326948	+	0.418563i
$471$		−	11.3368i		−	0.522371i
$472$	2.33680	−	39.8817i	0.107560	−	1.83570i
$473$	20.9261	−	20.9261i	0.962185	−	0.962185i
$474$	0.155973	+	0.0450718i	0.00716409	+	0.00207022i
$475$	1.56365	+	4.74921i	0.0717452	+	0.217909i
$476$	1.21729	−	1.93037i	0.0557945	−	0.0884785i
$477$	−14.2495	−	14.2495i	−0.652439	−	0.652439i
$478$	−28.6012	+	15.7772i	−1.30819	+	0.721631i
$479$	12.8003			0.584863			0.292431	−	0.956286i	$-0.405536\pi$
$479$	12.8003			0.584863			0.292431	+	0.956286i	$0.405536\pi$
$480$	7.91975	+	3.94466i	0.361485	+	0.180048i
$481$	2.34959			0.107132
$482$	−24.5707	+	13.5538i	−1.11917	+	0.617360i
$483$	0.184716	+	0.184716i	0.00840485	+	0.00840485i
$484$	2.46142	−	3.90330i	0.111883	−	0.177423i
$485$	−12.9187	+	2.07199i	−0.586607	+	0.0940843i
$486$	20.3067	+	5.86806i	0.921133	+	0.266181i
$487$	10.7519	−	10.7519i	0.487215	−	0.487215i	−0.420211	−	0.907426i	$-0.638044\pi$
$487$	10.7519	−	10.7519i	0.487215	−	0.487215i	0.907426	+	0.420211i	$0.138044\pi$
$488$	−1.27301	+	21.7261i	−0.0576263	+	0.983495i
$489$		−	10.3850i		−	0.469626i
$490$	−21.2971	−	2.61716i	−0.962104	−	0.118231i
$491$			39.2711i			1.77228i	0.463417	+	0.886140i	$0.346623\pi$
$491$			39.2711i			1.77228i	−0.463417	+	0.886140i	$0.653377\pi$
$492$	14.3008	−	3.23973i	0.644729	−	0.146058i
$493$	−3.22480	+	3.22480i	−0.145238	+	0.145238i
$494$	0.159749	−	0.552818i	0.00718743	−	0.0248725i
$495$	−9.70313	+	13.4102i	−0.436123	+	0.602744i
$496$	4.05268	−	1.93554i	0.181971	−	0.0869082i
$497$	3.01287	+	3.01287i	0.135146	+	0.135146i
$498$	1.33996	+	2.42912i	0.0600452	+	0.108851i
$499$	−35.8517			−1.60494			−0.802471	−	0.596692i	$-0.796482\pi$
$499$	−35.8517			−1.60494			−0.802471	+	0.596692i	$0.796482\pi$
$500$	−17.1041	+	14.4031i	−0.764919	+	0.644126i
$501$	15.8072			0.706214
$502$	3.98054	+	7.21603i	0.177660	+	0.322067i
$503$	−8.36832	−	8.36832i	−0.373125	−	0.373125i	0.495489	−	0.868614i	$-0.334989\pi$
$503$	−8.36832	−	8.36832i	−0.373125	−	0.373125i	−0.868614	+	0.495489i	$0.834989\pi$
$504$	−2.45835	+	2.18621i	−0.109504	+	0.0973816i
$505$	6.03773	−	8.34445i	0.268675	−	0.371323i
$506$	0.933144	−	3.22919i	0.0414833	−	0.143555i
$507$	−6.34797	+	6.34797i	−0.281923	+	0.281923i
$508$	−0.224476	−	0.990881i	−0.00995953	−	0.0439632i
$509$		−	8.31464i		−	0.368540i	−0.982876	−	0.184270i	$-0.941008\pi$
$509$		−	8.31464i		−	0.368540i	0.982876	−	0.184270i	$-0.0589921\pi$
$510$	5.40756	+	0.664526i	0.239451	+	0.0294257i
$511$		−	3.16397i		−	0.139966i
$512$	3.95253	−	22.2795i	0.174679	−	0.984626i
$513$	−2.72563	+	2.72563i	−0.120340	+	0.120340i
$514$	−11.8924	−	3.43656i	−0.524551	−	0.151580i
$515$	33.7930	−	5.41997i	1.48910	−	0.238833i
$516$	11.8776	+	7.49003i	0.522883	+	0.329730i
$517$	−7.59111	−	7.59111i	−0.333856	−	0.333856i
$518$	3.31257	−	1.82730i	0.145546	−	0.0802869i
$519$	−12.5928			−0.552763
$520$	2.56044	−	0.258211i	0.112283	−	0.0113233i
$521$	−35.8196			−1.56928			−0.784642	−	0.619949i	$-0.787153\pi$
$521$	−35.8196			−1.56928			−0.784642	+	0.619949i	$0.787153\pi$
$522$	5.75657	−	3.17547i	0.251958	−	0.138986i
$523$	14.4962	+	14.4962i	0.633874	+	0.633874i	0.949038	−	0.315163i	$-0.102059\pi$
$523$	14.4962	+	14.4962i	0.633874	+	0.633874i	−0.315163	+	0.949038i	$0.602059\pi$
$524$	−11.9707	−	7.54871i	−0.522941	−	0.329767i
$525$	0.506689	+	1.53895i	0.0221137	+	0.0671651i
$526$	16.2370	+	4.69203i	0.707967	+	0.204582i
$527$	1.95554	−	1.95554i	0.0851845	−	0.0851845i
$528$	−7.77741	−	2.74971i	−0.338468	−	0.119666i
$529$		−	22.3501i		−	0.971744i
$530$	15.6242	+	20.0023i	0.678673	+	0.868845i
$531$			35.4628i			1.53895i
$532$	−0.204710	−	0.903630i	−0.00887532	−	0.0391773i
$533$	3.01573	−	3.01573i	0.130626	−	0.130626i
$534$	0.624930	−	2.16260i	0.0270434	−	0.0935850i
$535$	2.55847	+	15.9518i	0.110612	+	0.689656i
$536$	−25.2841	−	28.4315i	−1.09211	−	1.22805i
$537$	1.77029	+	1.77029i	0.0763935	+	0.0763935i
$538$	1.02640	+	1.86068i	0.0442512	+	0.0802198i
$539$	20.0056			0.861703
$540$	−15.8535	−	6.76981i	−0.682225	−	0.291326i
$541$	−43.9873			−1.89116			−0.945580	−	0.325390i	$-0.894504\pi$
$541$	−43.9873			−1.89116			−0.945580	+	0.325390i	$0.894504\pi$
$542$	−20.2320	−	36.6771i	−0.869039	−	1.57542i
$543$	−3.66249	−	3.66249i	−0.157172	−	0.157172i
$544$	−2.27836	−	13.7459i	−0.0976839	−	0.589350i
$545$	9.49323	+	6.86895i	0.406645	+	0.294233i
$546$	0.0517653	−	0.179137i	0.00221535	−	0.00766634i
$547$	25.2995	−	25.2995i	1.08173	−	1.08173i	0.0853805	−	0.996348i	$-0.472789\pi$
$547$	25.2995	−	25.2995i	1.08173	−	1.08173i	0.996348	−	0.0853805i	$-0.0272106\pi$
$548$	11.9376	−	2.70437i	0.509949	−	0.115525i
$549$		−	19.3189i		−	0.824509i
$550$	14.1900	−	15.2735i	0.605063	−	0.651264i
$551$			1.85155i			0.0788787i
$552$	1.59218	+	0.0932909i	0.0677675	+	0.00397073i
$553$	0.0537639	−	0.0537639i	0.00228627	−	0.00228627i
$554$	35.0395	+	10.1254i	1.48869	+	0.430187i
$555$	7.31712	+	5.29439i	0.310594	+	0.224734i
$556$	12.1985	−	19.3443i	0.517331	−	0.820379i
$557$	−11.2381	−	11.2381i	−0.476172	−	0.476172i	0.427733	−	0.903905i	$-0.359312\pi$
$557$	−11.2381	−	11.2381i	−0.476172	−	0.476172i	−0.903905	+	0.427733i	$0.859312\pi$
$558$	−3.49081	+	1.92562i	−0.147778	+	0.0815180i
$559$	4.08422			0.172744
$560$	3.40904	−	2.35532i	0.144058	−	0.0995306i
$561$	−5.07965			−0.214463
$562$	−20.1195	+	11.0984i	−0.848689	+	0.468158i
$563$	−0.343770	−	0.343770i	−0.0144882	−	0.0144882i	0.699826	−	0.714314i	$-0.253261\pi$
$563$	−0.343770	−	0.343770i	−0.0144882	−	0.0144882i	−0.714314	+	0.699826i	$0.753261\pi$
$564$	2.71706	−	4.30869i	0.114409	−	0.181429i
$565$	4.57306	+	28.5126i	0.192390	+	1.19953i
$566$	12.7397	+	3.68140i	0.535489	+	0.154741i
$567$	1.58415	−	1.58415i	0.0665282	−	0.0665282i
$568$	25.9698	+	1.52166i	1.08967	+	0.0638473i
$569$		−	14.2062i		−	0.595555i	−0.954635	−	0.297777i	$-0.903755\pi$
$569$		−	14.2062i		−	0.595555i	0.954635	−	0.297777i	$-0.0962453\pi$
$570$	1.74317	−	1.36163i	0.0730134	−	0.0570323i
$571$			19.1090i			0.799688i	0.916583	+	0.399844i	$0.130936\pi$
$571$			19.1090i			0.799688i	−0.916583	+	0.399844i	$0.869064\pi$
$572$	−2.34004	+	0.530117i	−0.0978418	+	0.0221653i
$573$	−2.04231	+	2.04231i	−0.0853187	+	0.0853187i
$574$	1.90637	−	6.59710i	0.0795704	−	0.275357i
$575$	−1.81588	+	3.59855i	−0.0757276	+	0.150070i
$576$	−2.34574	+	19.9484i	−0.0977393	+	0.831184i
$577$	−25.4221	−	25.4221i	−1.05834	−	1.05834i	−0.998190	−	0.0601462i	$-0.980843\pi$
$577$	−25.4221	−	25.4221i	−1.05834	−	1.05834i	−0.0601462	−	0.998190i	$-0.519157\pi$
$578$	7.46820	+	13.5385i	0.310636	+	0.563129i
$579$	5.48183			0.227817
$580$	−7.68411	+	3.08531i	−0.319065	+	0.128111i
$581$	1.29920			0.0538999
$582$	2.79572	+	5.06815i	0.115886	+	0.210082i
$583$	−16.7331	−	16.7331i	−0.693014	−	0.693014i
$584$	−12.8371	−	14.4351i	−0.531203	−	0.597327i
$585$	−2.25555	+	0.361762i	−0.0932556	+	0.0149570i
$586$	8.02363	−	27.7662i	0.331453	−	1.14701i
$587$	−29.3478	+	29.3478i	−1.21131	+	1.21131i	−0.240717	+	0.970595i	$0.577383\pi$
$587$	−29.3478	+	29.3478i	−1.21131	+	1.21131i	−0.970595	+	0.240717i	$0.922617\pi$
$588$	2.09729	+	9.25785i	0.0864909	+	0.381787i
$589$		−	1.12279i		−	0.0462637i
$590$	5.44789	−	44.3320i	0.224286	−	1.82512i
$591$			5.79788i			0.238493i
$592$	7.69919	−	21.7768i	0.316435	−	0.895019i
$593$	4.78725	−	4.78725i	0.196589	−	0.196589i	−0.601947	−	0.798536i	$-0.705608\pi$
$593$	4.78725	−	4.78725i	0.196589	−	0.196589i	0.798536	+	0.601947i	$0.205608\pi$
$594$	15.4404	+	4.46184i	0.633529	+	0.183072i
$595$	1.49570	−	2.06714i	0.0613178	−	0.0847443i
$596$	22.1846	+	13.9896i	0.908718	+	0.573038i
$597$	7.29404	+	7.29404i	0.298525	+	0.298525i
$598$	0.406188	−	0.224064i	0.0166103	−	0.00916265i
$599$	−8.94617			−0.365531			−0.182765	−	0.983157i	$-0.558505\pi$
$599$	−8.94617			−0.365531			−0.182765	+	0.983157i	$0.558505\pi$
$600$	8.55560	+	4.96540i	0.349281	+	0.202711i
$601$	−31.5967			−1.28886			−0.644429	−	0.764664i	$-0.722905\pi$
$601$	−31.5967			−1.28886			−0.644429	+	0.764664i	$0.722905\pi$
$602$	5.75815	−	3.17634i	0.234685	−	0.129458i
$603$	23.8819	+	23.8819i	0.972548	+	0.972548i
$604$	3.82325	+	2.41094i	0.155566	+	0.0980998i
$605$	3.02438	−	4.17985i	0.122959	−	0.169935i
$606$	−4.37736	−	1.26493i	−0.177818	−	0.0513844i
$607$	5.75786	−	5.75786i	0.233704	−	0.233704i	−0.580533	−	0.814237i	$-0.697156\pi$
$607$	5.75786	−	5.75786i	0.233704	−	0.233704i	0.814237	+	0.580533i	$0.197156\pi$
$608$	−4.60023	−	3.29209i	−0.186564	−	0.133512i
$609$			0.599980i			0.0243124i
$610$	−2.96782	+	24.1505i	−0.120163	+	0.977826i
$611$		−	1.48158i		−	0.0599383i
$612$	2.73271	+	12.0627i	0.110463	+	0.487607i
$613$	−24.9646	+	24.9646i	−1.00831	+	1.00831i	−0.00834470	+	0.999965i	$0.502656\pi$
$613$	−24.9646	+	24.9646i	−1.00831	+	1.00831i	−0.999965	+	0.00834470i	$0.997344\pi$
$614$	6.31016	−	21.8366i	0.254657	−	0.881255i
$615$	16.1870	−	2.59620i	0.652724	−	0.104689i
$616$	−2.88683	+	2.56726i	−0.116314	+	0.103438i
$617$	27.5683	+	27.5683i	1.10986	+	1.10986i	0.993168	+	0.116689i	$0.0372281\pi$
$617$	27.5683	+	27.5683i	1.10986	+	1.10986i	0.116689	+	0.993168i	$0.462772\pi$
$618$	−7.31312	−	13.2574i	−0.294177	−	0.533291i
$619$	36.0285			1.44811			0.724054	−	0.689743i	$-0.242277\pi$
$619$	36.0285			1.44811			0.724054	+	0.689743i	$0.242277\pi$
$620$	4.65968	−	1.87095i	0.187137	−	0.0751391i
$621$	−3.10742			−0.124696
$622$	21.6087	+	39.1728i	0.866429	+	1.57068i
$623$	−0.745448	−	0.745448i	−0.0298658	−	0.0298658i
$624$	−0.490636	−	1.02731i	−0.0196412	−	0.0411251i
$625$	−20.1100	+	14.8522i	−0.804400	+	0.594088i
$626$	2.28308	−	7.90072i	0.0912503	−	0.315776i
$627$	−1.45826	+	1.45826i	−0.0582374	+	0.0582374i
$628$	−31.6139	+	7.16188i	−1.26153	+	0.285790i
$629$		−	14.2230i		−	0.567109i
$630$	−2.89865	+	2.26420i	−0.115485	+	0.0902078i
$631$		−	20.6862i		−	0.823504i	−0.911296	−	0.411752i	$-0.864917\pi$
$631$		−	20.6862i		−	0.823504i	0.911296	−	0.411752i	$-0.135083\pi$
$632$	0.0271535	−	0.463424i	0.00108011	−	0.0184340i
$633$	−1.70156	+	1.70156i	−0.0676308	+	0.0676308i
$634$	−41.0594	−	11.8650i	−1.63068	−	0.471219i
$635$	−0.179887	−	1.12158i	−0.00713859	−	0.0445084i
$636$	5.98922	−	9.49766i	0.237488	−	0.376607i
$637$	1.95228	+	1.95228i	0.0773522	+	0.0773522i
$638$	6.75991	−	3.72893i	0.267627	−	0.147630i
$639$	−23.0923			−0.913519
$640$	5.99694	−	24.5772i	0.237050	−	0.971497i
$641$	−5.19156			−0.205054			−0.102527	−	0.994730i	$-0.532693\pi$
$641$	−5.19156			−0.205054			−0.102527	+	0.994730i	$0.532693\pi$
$642$	6.25808	−	3.45211i	0.246987	−	0.136244i
$643$	6.88159	+	6.88159i	0.271384	+	0.271384i	0.829657	−	0.558273i	$-0.188536\pi$
$643$	6.88159	+	6.88159i	0.271384	+	0.271384i	−0.558273	+	0.829657i	$0.688536\pi$
$644$	0.398409	−	0.631794i	0.0156995	−	0.0248962i
$645$	12.7191	+	9.20309i	0.500815	+	0.362371i
$646$	−3.34643	−	0.967023i	−0.131664	−	0.0380470i
$647$	20.2501	−	20.2501i	0.796113	−	0.796113i	−0.186368	−	0.982480i	$-0.559672\pi$
$647$	20.2501	−	20.2501i	0.796113	−	0.796113i	0.982480	+	0.186368i	$0.0596715\pi$
$648$	0.800080	−	13.6548i	0.0314301	−	0.536410i
$649$			41.6438i			1.63466i
$650$	2.87524	−	0.105734i	0.112776	−	0.00414725i
$651$		−	0.363831i		−	0.0142597i
$652$	−28.9598	+	6.56062i	−1.13415	+	0.256934i
$653$	10.5859	−	10.5859i	0.414257	−	0.414257i	−0.468961	−	0.883219i	$-0.655372\pi$
$653$	10.5859	−	10.5859i	0.414257	−	0.414257i	0.883219	+	0.468961i	$0.155372\pi$
$654$	1.43908	−	4.98000i	0.0562723	−	0.194733i
$655$	−12.8188	−	9.27519i	−0.500871	−	0.362411i
$656$	−18.0687	−	37.8328i	−0.705466	−	1.47712i
$657$	12.1252	+	12.1252i	0.473049	+	0.473049i
$658$	−1.15224	−	2.08881i	−0.0449190	−	0.0814303i
$659$	−29.9506			−1.16671			−0.583354	−	0.812218i	$-0.698260\pi$
$659$	−29.9506			−1.16671			−0.583354	+	0.812218i	$0.698260\pi$
$660$	−8.48189	−	3.62197i	−0.330157	−	0.140985i
$661$	−42.9876			−1.67202			−0.836012	−	0.548711i	$-0.815119\pi$
$661$	−42.9876			−1.67202			−0.836012	+	0.548711i	$0.815119\pi$
$662$	19.6826	+	35.6811i	0.764985	+	1.38678i
$663$	−0.495705	−	0.495705i	−0.0192516	−	0.0192516i
$664$	5.92738	−	5.27121i	0.230027	−	0.204563i
$665$	−0.164047	−	1.02282i	−0.00636147	−	0.0396632i
$666$	−5.69199	+	19.6974i	−0.220560	+	0.763259i
$667$	−1.05545	+	1.05545i	−0.0408671	+	0.0408671i
$668$	−9.98603	−	44.0803i	−0.386371	−	1.70552i
$669$			9.85422i			0.380986i
$670$	−26.1860	−	33.5236i	−1.01165	−	1.29513i
$671$		−	22.6860i		−	0.875785i
$672$	−1.49067	−	1.06678i	−0.0575039	−	0.0411518i
$673$	8.30925	−	8.30925i	0.320298	−	0.320298i	−0.528583	−	0.848881i	$-0.677277\pi$
$673$	8.30925	−	8.30925i	0.320298	−	0.320298i	0.848881	+	0.528583i	$0.177277\pi$
$674$	25.8196	+	7.46113i	0.994535	+	0.287392i
$675$	−17.2065	−	8.68267i	−0.662280	−	0.334196i
$676$	21.7123	+	13.6918i	0.835090	+	0.526608i
$677$	1.65901	+	1.65901i	0.0637610	+	0.0637610i	0.738268	−	0.674507i	$-0.235644\pi$
$677$	1.65901	+	1.65901i	0.0637610	+	0.0637610i	−0.674507	+	0.738268i	$0.735644\pi$
$678$	11.1858	−	6.17038i	0.429589	−	0.236972i
$679$	2.71067			0.104026
$680$	−1.56306	−	15.4994i	−0.0599405	−	0.594376i
$681$	−8.35673			−0.320230
$682$	−4.09924	+	2.26125i	−0.156968	+	0.0865875i
$683$	3.72871	+	3.72871i	0.142675	+	0.142675i	0.774837	−	0.632161i	$-0.217832\pi$
$683$	3.72871	+	3.72871i	0.142675	+	0.142675i	−0.632161	+	0.774837i	$0.717832\pi$
$684$	4.24747	+	2.67846i	0.162406	+	0.102413i
$685$	13.5122	−	2.16718i	0.516273	−	0.0828036i
$686$	8.67655	+	2.50727i	0.331272	+	0.0957282i
$687$	−4.27345	+	4.27345i	−0.163042	+	0.163042i
$688$	13.3833	−	37.8539i	0.510233	−	1.44317i
$689$		−	3.26585i		−	0.124419i
$690$	1.76985	+	0.217493i	0.0673769	+	0.00827984i
$691$			0.815388i			0.0310188i	0.999880	+	0.0155094i	$0.00493700\pi$
$691$			0.815388i			0.0310188i	−0.999880	+	0.0155094i	$0.995063\pi$
$692$	7.95538	+	35.1166i	0.302418	+	1.33493i
$693$	2.42489	−	2.42489i	0.0921139	−	0.0921139i
$694$	10.9377	−	37.8504i	0.415188	−	1.43678i
$695$	14.9884	−	20.7148i	0.568543	−	0.785756i
$696$	2.43429	+	2.73731i	0.0922714	+	0.103757i
$697$	−18.2554	−	18.2554i	−0.691474	−	0.691474i
$698$	5.17399	+	9.37955i	0.195839	+	0.355021i
$699$	−4.49834			−0.170143
$700$	3.97144	−	2.38517i	0.150106	−	0.0901511i
$701$	9.25242			0.349459			0.174730	−	0.984616i	$-0.444095\pi$
$701$	9.25242			0.349459			0.174730	+	0.984616i	$0.444095\pi$
$702$	1.07136	+	1.94220i	0.0404360	+	0.0733035i
$703$	−4.08314	−	4.08314i	−0.153999	−	0.153999i
$704$	−2.75459	+	23.4253i	−0.103818	+	0.882875i
$705$	3.33848	−	4.61396i	0.125735	−	0.173772i
$706$	6.83798	−	23.6632i	0.257351	−	0.890576i
$707$	−1.50888	+	1.50888i	−0.0567471	+	0.0567471i
$708$	−19.2712	+	4.36573i	−0.724255	+	0.164074i
$709$			25.0837i			0.942038i	0.882123	+	0.471019i	$0.156114\pi$
$709$			25.0837i			0.942038i	−0.882123	+	0.471019i	$0.843886\pi$
$710$	28.8677	+	3.54751i	1.08339	+	0.133136i
$711$			0.412076i			0.0154541i
$712$	−6.42547	−	0.376490i	−0.240805	−	0.0141096i
$713$	0.640030	−	0.640030i	0.0239693	−	0.0239693i
$714$	−1.08439	−	0.313357i	−0.0405822	−	0.0117271i
$715$	−2.64868	+	0.424815i	−0.0990551	+	0.0158872i
$716$	3.81829	−	6.05501i	0.142696	−	0.226286i
$717$	11.4239	+	11.4239i	0.426634	+	0.426634i
$718$	−29.0450	+	16.0220i	−1.08395	+	0.597934i
$719$	37.6238			1.40313			0.701565	−	0.712606i	$-0.252485\pi$
$719$	37.6238			1.40313			0.701565	+	0.712606i	$0.252485\pi$
$720$	−4.03812	+	22.0906i	−0.150492	+	0.823269i
$721$	−7.09065			−0.264070
$722$	−1.23831	+	0.683080i	−0.0460850	+	0.0254216i
$723$	9.81405	+	9.81405i	0.364988	+	0.364988i
$724$	−7.89954	+	12.5270i	−0.293584	+	0.465563i
$725$	−8.79340	+	2.89517i	−0.326579	+	0.107524i
$726$	−2.19268	−	0.633622i	−0.0813780	−	0.0235159i
$727$	−27.9775	+	27.9775i	−1.03763	+	1.03763i	−0.0383634	+	0.999264i	$0.512214\pi$
$727$	−27.9775	+	27.9775i	−1.03763	+	1.03763i	−0.999264	+	0.0383634i	$0.987786\pi$
$728$	−0.532246	−	0.0311861i	−0.0197263	−	0.00115583i
$729$			4.05317i			0.150117i
$730$	−13.2950	−	17.0204i	−0.492071	−	0.629954i
$731$		−	24.7235i		−	0.914430i
$732$	10.4982	−	2.37829i	0.388026	−	0.0879043i
$733$	13.9853	−	13.9853i	0.516559	−	0.516559i	−0.399970	−	0.916528i	$-0.630979\pi$
$733$	13.9853	−	13.9853i	0.516559	−	0.516559i	0.916528	+	0.399970i	$0.130979\pi$
$734$	−12.9681	+	44.8767i	−0.478661	+	1.65643i
$735$	1.68069	+	10.4789i	0.0619932	+	0.386522i
$736$	−0.745687	−	4.49890i	−0.0274864	−	0.165832i
$737$	28.0444	+	28.0444i	1.03303	+	1.03303i
$738$	17.9762	+	32.5876i	0.661711	+	1.19957i
$739$	40.9090			1.50486			0.752431	−	0.658671i	$-0.228881\pi$
$739$	40.9090			1.50486			0.752431	+	0.658671i	$0.228881\pi$
$740$	10.1415	−	23.7493i	0.372810	−	0.873043i
$741$	−0.284614			−0.0104555
$742$	−2.53988	−	4.60437i	−0.0932421	−	0.169032i
$743$	4.46740	+	4.46740i	0.163893	+	0.163893i	0.784289	−	0.620396i	$-0.213028\pi$
$743$	4.46740	+	4.46740i	0.163893	+	0.163893i	−0.620396	+	0.784289i	$0.713028\pi$
$744$	−1.47616	−	1.65992i	−0.0541188	−	0.0608555i
$745$	23.7564	+	17.1892i	0.870366	+	0.629764i
$746$	−3.40105	+	11.7695i	−0.124521	+	0.430912i
$747$	−4.97890	+	4.97890i	−0.182168	+	0.182168i
$748$	3.20901	+	14.1652i	0.117333	+	0.517931i
$749$		−	3.34710i		−	0.122300i
$750$	9.19237	+	6.14958i	0.335658	+	0.224551i
$751$			37.1200i			1.35453i	0.735740	+	0.677264i	$0.236834\pi$
$751$			37.1200i			1.35453i	−0.735740	+	0.677264i	$0.763166\pi$
$752$	−13.7318	−	4.85488i	−0.500746	−	0.177039i
$753$	2.88223	−	2.88223i	0.105034	−	0.105034i
$754$	1.02357	+	0.295782i	0.0372762	+	0.0107718i
$755$	4.09412	+	2.96235i	0.149000	+	0.107811i
$756$	3.02093	+	1.90500i	0.109870	+	0.0692842i
$757$	17.9260	+	17.9260i	0.651533	+	0.651533i	0.953362	−	0.301829i	$-0.0975972\pi$
$757$	17.9260	+	17.9260i	0.651533	+	0.651533i	−0.301829	+	0.953362i	$0.597597\pi$
$758$	28.4456	−	15.6913i	1.03319	−	0.569934i
$759$	−1.66252			−0.0603458
$760$	−4.89829	−	4.00085i	−0.177680	−	0.145126i
$761$	−31.7582			−1.15123			−0.575617	−	0.817719i	$-0.695238\pi$
$761$	−31.7582			−1.15123			−0.575617	+	0.817719i	$0.695238\pi$
$762$	−0.440008	+	0.242719i	−0.0159398	+	0.00879279i
$763$	−1.71660	−	1.71660i	−0.0621452	−	0.0621452i
$764$	6.98543	+	4.40501i	0.252724	+	0.159368i
$765$	2.18989	+	13.6538i	0.0791757	+	0.493653i
$766$	35.6503	+	10.3019i	1.28810	+	0.372224i
$767$	−4.06387	+	4.06387i	−0.146738	+	0.146738i
$768$	−11.1291	+	1.18107i	−0.401588	+	0.0426184i
$769$			32.9935i			1.18977i	0.803809	+	0.594887i	$0.202803\pi$
$769$			32.9935i			1.18977i	−0.803809	+	0.594887i	$0.797197\pi$
$770$	−3.40387	+	2.65883i	−0.122667	+	0.0958177i
$771$			6.12270i

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)

\(f(q)\)	\(=\)	\(q+(-1.23831 + 0.683080i) q^{2} +(0.494605 + 0.494605i) q^{3} +(1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 - 0.274617i) q^{6} +(-0.327577 + 0.327577i) q^{7} +(-0.165443 + 2.82358i) q^{8} -2.51073i q^{9} +O(q^{10})\)	\(q+(-1.23831 + 0.683080i) q^{2} +(0.494605 + 0.494605i) q^{3} +(1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 - 0.274617i) q^{6} +(-0.327577 + 0.327577i) q^{7} +(-0.165443 + 2.82358i) q^{8} -2.51073i q^{9} +(-0.385706 + 3.13867i) q^{10} -2.94834i q^{11} +(1.36438 - 0.309090i) q^{12} +(0.287718 - 0.287718i) q^{13} +(0.181879 - 0.629402i) q^{14} +(1.54434 - 0.247693i) q^{15} +(-1.72387 - 3.60947i) q^{16} +(-1.74168 - 1.74168i) q^{17} +(1.71503 + 3.10905i) q^{18} -1.00000 q^{19} +(-1.66634 - 4.15010i) q^{20} -0.324042 q^{21} +(2.01395 + 3.65095i) q^{22} +(-0.570036 - 0.570036i) q^{23} +(-1.47839 + 1.31473i) q^{24} +(-1.56365 - 4.74921i) q^{25} +(-0.159749 + 0.552818i) q^{26} +(2.72563 - 2.72563i) q^{27} +(0.204710 + 0.903630i) q^{28} -1.85155i q^{29} +(-1.74317 + 1.36163i) q^{30} +1.12279i q^{31} +(4.60023 + 3.29209i) q^{32} +(1.45826 - 1.45826i) q^{33} +(3.34643 + 0.967023i) q^{34} +(0.164047 + 1.02282i) q^{35} +(-4.24747 - 2.67846i) q^{36} +(4.08314 + 4.08314i) q^{37} +(1.23831 - 0.683080i) q^{38} +0.284614 q^{39} +(4.89829 + 4.00085i) q^{40} +10.4815 q^{41} +(0.401264 - 0.221347i) q^{42} +(7.09760 + 7.09760i) q^{43} +(-4.98778 - 3.14530i) q^{44} +(-4.54839 - 3.29105i) q^{45} +(1.09526 + 0.316498i) q^{46} +(2.57471 - 2.57471i) q^{47} +(0.932630 - 2.63789i) q^{48} +6.78539i q^{49} +(5.18037 + 4.81288i) q^{50} -1.72288i q^{51} +(-0.179802 - 0.793679i) q^{52} +(5.67543 - 5.67543i) q^{53} +(-1.51334 + 5.23700i) q^{54} +(-5.34116 - 3.86466i) q^{55} +(-0.870746 - 0.979137i) q^{56} +(-0.494605 - 0.494605i) q^{57} +(1.26476 + 2.29278i) q^{58} -14.1245 q^{59} +(1.22848 - 2.87684i) q^{60} +7.69452 q^{61} +(-0.766955 - 1.39036i) q^{62} +(0.822459 + 0.822459i) q^{63} +(-7.94526 - 0.934286i) q^{64} +(-0.144086 - 0.898364i) q^{65} +(-0.809664 + 2.80189i) q^{66} +(-9.51194 + 9.51194i) q^{67} +(-4.80446 + 1.08841i) q^{68} -0.563885i q^{69} +(-0.901807 - 1.15450i) q^{70} -9.19745i q^{71} +(7.08926 + 0.415384i) q^{72} +(-4.82935 + 4.82935i) q^{73} +(-7.84529 - 2.26706i) q^{74} +(1.57559 - 3.12237i) q^{75} +(-1.06680 + 1.69172i) q^{76} +(0.965809 + 0.965809i) q^{77} +(-0.352439 + 0.194414i) q^{78} -0.164126 q^{79} +(-8.79848 - 1.60834i) q^{80} -4.83597 q^{81} +(-12.9793 + 7.15972i) q^{82} +(-1.98305 - 1.98305i) q^{83} +(-0.345689 + 0.548191i) q^{84} +(-5.43817 + 0.872213i) q^{85} +(-13.6372 - 3.94077i) q^{86} +(0.915785 - 0.915785i) q^{87} +(8.32489 + 0.487783i) q^{88} +2.27564i q^{89} +(7.88035 + 0.968404i) q^{90} +0.188500i q^{91} +(-1.57246 + 0.356228i) q^{92} +(-0.555337 + 0.555337i) q^{93} +(-1.42954 + 4.94700i) q^{94} +(-1.31079 + 1.81158i) q^{95} +(0.647013 + 3.90358i) q^{96} +(-4.13745 - 4.13745i) q^{97} +(-4.63496 - 8.40238i) q^{98} -7.40249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

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