LMFDB - Embedded newform 380.2.k.c.267.19

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			267.19
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.683080 - 1.23831i) q^{2} +(-0.494605 - 0.494605i) q^{3} +(-1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 + 0.274617i) q^{6} +(0.327577 - 0.327577i) q^{7} +(-2.82358 + 0.165443i) q^{8} -2.51073i q^{9} +O(q^{10})$	\(q+(0.683080 - 1.23831i) 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} +(-2.82358 + 0.165443i) q^{8} -2.51073i q^{9} +(-1.34791 - 2.86062i) q^{10} +2.94834i q^{11} +(-0.309090 + 1.36438i) 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} +(-3.10905 - 1.71503i) q^{18} +1.00000 q^{19} +(-4.46305 - 0.284901i) q^{20} -0.324042 q^{21} +(3.65095 + 2.01395i) 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} +(-0.903630 - 0.204710i) q^{28} -1.85155i q^{29} +(-0.748189 + 2.08156i) q^{30} -1.12279i q^{31} +(3.29209 + 4.60023i) 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} +(0.683080 - 1.23831i) q^{38} -0.284614 q^{39} +(-3.40142 + 5.33201i) q^{40} +10.4815 q^{41} +(-0.221347 + 0.401264i) 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} +(2.63789 - 0.932630i) q^{48} +6.78539i q^{49} +(-6.94907 - 1.30782i) q^{50} +1.72288i q^{51} +(-0.793679 - 0.179802i) 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} +(-2.29278 - 1.26476i) q^{58} +14.1245 q^{59} +(2.06653 + 2.34836i) q^{60} +7.69452 q^{61} +(-1.39036 - 0.766955i) 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} +(-1.08841 + 4.80446i) q^{68} -0.563885i q^{69} +(-1.37862 - 0.495527i) q^{70} +9.19745i q^{71} +(0.415384 + 7.08926i) 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} +(-0.194414 + 0.352439i) q^{78} +0.164126 q^{79} +(4.27922 + 7.85419i) q^{80} -4.83597 q^{81} +(7.15972 - 12.9793i) 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} +(-0.487783 - 8.32489i) q^{88} +2.27564i q^{89} +(-7.18224 + 3.38425i) q^{90} -0.188500i q^{91} +(0.356228 - 1.57246i) 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} +(8.40238 + 4.63496i) 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.683080	−	1.23831i	0.483011	−	0.875614i
$2$	0.683080	−	1.23831i	0.483011	−	0.875614i
$3$	−0.494605	−	0.494605i	−0.285560	−	0.285560i	0.549762	−	0.835322i	$-0.314719\pi$
$3$	−0.494605	−	0.494605i	−0.285560	−	0.285560i	−0.835322	+	0.549762i	$0.814719\pi$
$4$	−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	−0.642485	−	0.766298i	$-0.722097\pi$
$7$	0.327577	−	0.327577i	0.123813	−	0.123813i	0.766298	+	0.642485i	$0.222097\pi$
$8$	−2.82358	+	0.165443i	−0.998288	+	0.0584930i
$9$		−	2.51073i		−	0.836911i
$10$	−1.34791	−	2.86062i	−0.426248	−	0.904606i
$11$			2.94834i			0.888958i	0.895789	+	0.444479i	$0.146611\pi$
$11$			2.94834i			0.888958i	−0.895789	+	0.444479i	$0.853389\pi$
$12$	−0.309090	+	1.36438i	−0.0892265	+	0.393863i
$13$	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	$0.846551\pi$
$18$	−3.10905	−	1.71503i	−0.732811	−	0.404237i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−4.46305	−	0.284901i	−0.997969	−	0.0637057i
$21$	−0.324042			−0.0707118
$22$	3.65095	+	2.01395i	0.778384	+	0.429376i
$23$	0.570036	+	0.570036i	0.118861	+	0.118861i	0.764035	−	0.645175i	$-0.223215\pi$
$23$	0.570036	+	0.570036i	0.118861	+	0.118861i	−0.645175	+	0.764035i	$0.723215\pi$
$24$	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
$28$	−0.903630	−	0.204710i	−0.170770	−	0.0386866i
$29$		−	1.85155i		−	0.343824i	−0.985112	−	0.171912i	$-0.945006\pi$
$29$		−	1.85155i		−	0.343824i	0.985112	−	0.171912i	$-0.0549945\pi$
$30$	−0.748189	+	2.08156i	−0.136600	+	0.380039i
$31$		−	1.12279i		−	0.201659i	−0.994904	−	0.100829i	$-0.967850\pi$
$31$		−	1.12279i		−	0.201659i	0.994904	−	0.100829i	$-0.0321496\pi$
$32$	3.29209	+	4.60023i	0.581965	+	0.813214i
$33$	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	$0.592573\pi$
$38$	0.683080	−	1.23831i	0.110810	−	0.200880i
$39$	−0.284614			−0.0455747
$40$	−3.40142	+	5.33201i	−0.537811	+	0.843065i
$41$	10.4815			1.63694			0.818470	−	0.574550i	$-0.194823\pi$
$41$	10.4815			1.63694			0.818470	+	0.574550i	$0.194823\pi$
$42$	−0.221347	+	0.401264i	−0.0341546	+	0.0619163i
$43$	−7.09760	−	7.09760i	−1.08237	−	1.08237i	−0.996288	−	0.0860866i	$-0.972564\pi$
$43$	−7.09760	−	7.09760i	−1.08237	−	1.08237i	−0.0860866	−	0.996288i	$-0.527436\pi$
$44$	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	−0.869497	−	0.493938i	$-0.835557\pi$
$47$	−2.57471	+	2.57471i	−0.375559	+	0.375559i	0.493938	+	0.869497i	$0.335557\pi$
$48$	2.63789	−	0.932630i	0.380747	−	0.134613i
$49$			6.78539i			0.969341i
$50$	−6.94907	−	1.30782i	−0.982747	−	0.184953i
$51$			1.72288i			0.241252i
$52$	−0.793679	−	0.179802i	−0.110063	−	0.0249340i
$53$	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
$58$	−2.29278	−	1.26476i	−0.301057	−	0.166071i
$59$	14.1245			1.83885			0.919425	−	0.393265i	$-0.128655\pi$
$59$	14.1245			1.83885			0.919425	+	0.393265i	$0.128655\pi$
$60$	2.06653	+	2.34836i	0.266788	+	0.303172i
$61$	7.69452			0.985182			0.492591	−	0.870261i	$-0.336050\pi$
$61$	7.69452			0.985182			0.492591	+	0.870261i	$0.336050\pi$
$62$	−1.39036	−	0.766955i	−0.176575	−	0.0974034i
$63$	−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	$-0.443022\pi$
$67$	9.51194	−	9.51194i	1.16207	−	1.16207i	0.984022	−	0.178047i	$-0.0569778\pi$
$68$	−1.08841	+	4.80446i	−0.131990	+	0.582627i
$69$		−	0.563885i		−	0.0678837i
$70$	−1.37862	−	0.495527i	−0.164776	−	0.0592267i
$71$			9.19745i			1.09154i	0.837936	+	0.545768i	$0.183762\pi$
$71$			9.19745i			1.09154i	−0.837936	+	0.545768i	$0.816238\pi$
$72$	0.415384	+	7.08926i	0.0489535	+	0.835478i
$73$	−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
$78$	−0.194414	+	0.352439i	−0.0220131	+	0.0399058i
$79$	0.164126			0.0184656			0.00923281	−	0.999957i	$-0.497061\pi$
$79$	0.164126			0.0184656			0.00923281	+	0.999957i	$0.497061\pi$
$80$	4.27922	+	7.85419i	0.478431	+	0.878125i
$81$	−4.83597			−0.537331
$82$	7.15972	−	12.9793i	0.790659	−	1.43333i
$83$	1.98305	+	1.98305i	0.217667	+	0.217667i	0.807515	−	0.589847i	$-0.200812\pi$
$83$	1.98305	+	1.98305i	0.217667	+	0.217667i	−0.589847	+	0.807515i	$0.700812\pi$
$84$	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
$88$	−0.487783	−	8.32489i	−0.0519979	−	0.887436i
$89$			2.27564i			0.241218i	0.992700	+	0.120609i	$0.0384847\pi$
$89$			2.27564i			0.241218i	−0.992700	+	0.120609i	$0.961515\pi$
$90$	−7.18224	+	3.38425i	−0.757075	+	0.356732i
$91$		−	0.188500i		−	0.0197602i
$92$	0.356228	−	1.57246i	0.0371393	−	0.163940i
$93$	−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	$0.846003\pi$
$98$	8.40238	+	4.63496i	0.848769	+	0.468202i
$99$	7.40249			0.743978
$100$	−6.36625	+	7.71173i	−0.636625	+	0.771173i
$101$	4.60617			0.458331			0.229165	−	0.973387i	$-0.426400\pi$
$101$	4.60617			0.458331			0.229165	+	0.973387i	$0.426400\pi$
$102$	2.13346	+	1.17687i	0.211244	+	0.116527i
$103$	−10.8229	−	10.8229i	−1.06641	−	1.06641i	−0.997632	−	0.0687770i	$-0.978090\pi$
$103$	−10.8229	−	10.8229i	−1.06641	−	1.06641i	−0.0687770	−	0.997632i	$-0.521910\pi$
$104$	−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	−0.415637	−	0.909530i	$-0.636441\pi$
$107$	5.10887	−	5.10887i	0.493893	−	0.493893i	0.909530	+	0.415637i	$0.136441\pi$
$108$	7.51874	+	1.70331i	0.723491	+	0.163901i
$109$			5.24030i			0.501930i	0.967996	+	0.250965i	$0.0807479\pi$
$109$			5.24030i			0.501930i	−0.967996	+	0.250965i	$0.919252\pi$
$110$	8.43407	−	3.97411i	0.804157	−	0.378917i
$111$		−	4.03908i		−	0.383372i
$112$	0.617681	+	1.74708i	0.0583654	+	0.165083i
$113$	−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
$118$	9.64815	−	17.4904i	0.888185	−	1.61012i
$119$	−1.14107			−0.104601
$120$	4.31960	−	0.954882i	0.394323	−	0.0871684i
$121$	2.30729			0.209754
$122$	5.25597	−	9.52816i	0.475853	−	0.862639i
$123$	−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	−0.722864	−	0.690990i	$-0.757175\pi$
$127$	−0.359207	+	0.359207i	−0.0318744	+	0.0318744i	0.690990	+	0.722864i	$0.257175\pi$
$128$	4.27032	−	10.4769i	0.377446	−	0.926031i
$129$			7.02101i			0.618166i
$130$	−1.21087	−	0.435232i	−0.106200	−	0.0381724i
$131$			7.07602i			0.618235i	0.951024	+	0.309117i	$0.100034\pi$
$131$			7.07602i			0.618235i	−0.951024	+	0.309117i	$0.899966\pi$
$132$	−4.02266	−	0.911301i	−0.350127	−	0.0793186i
$133$	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	$0.665804\pi$
$138$	−0.698261	−	0.385178i	−0.0594400	−	0.0327886i
$139$	−11.4346			−0.969873			−0.484937	−	0.874549i	$-0.661157\pi$
$139$	−11.4346			−0.969873			−0.484937	+	0.874549i	$0.661157\pi$
$140$	−1.55532	+	1.36867i	−0.131449	+	0.115673i
$141$	2.54692			0.214490
$142$	11.3893	+	6.28260i	0.955765	+	0.527224i
$143$	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
$148$	2.55165	−	11.2635i	0.209744	−	0.925850i
$149$			13.1136i			1.07431i	0.843484	+	0.537155i	$0.180501\pi$
$149$			13.1136i			1.07431i	−0.843484	+	0.537155i	$0.819499\pi$
$150$	2.79019	+	4.08390i	0.227818	+	0.333449i
$151$		−	2.25997i		−	0.183914i	−0.995763	−	0.0919569i	$-0.970688\pi$
$151$		−	2.25997i		−	0.183914i	0.995763	−	0.0919569i	$-0.0293122\pi$
$152$	−2.82358	+	0.165443i	−0.229023	+	0.0134192i
$153$	−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	$0.973872\pi$
$158$	0.112111	−	0.203238i	0.00891909	−	0.0161688i
$159$	−5.61418			−0.445234
$160$	12.6489	+	0.0660585i	0.999986	+	0.00522239i
$161$	0.373461			0.0294329
$162$	−3.30336	+	5.98842i	−0.259536	+	0.470494i
$163$	10.4983	+	10.4983i	0.822289	+	0.822289i	0.986436	−	0.164147i	$-0.0524870\pi$
$163$	10.4983	+	10.4983i	0.822289	+	0.822289i	−0.164147	+	0.986436i	$0.552487\pi$
$164$	−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	$0.588723\pi$
$167$	−15.9796	+	15.9796i	−1.23654	+	1.23654i	−0.961405	+	0.275136i	$0.911277\pi$
$168$	0.914961	−	0.0536106i	0.0705908	−	0.00413615i
$169$			12.8344i			0.987264i
$170$	−2.63464	+	7.32990i	−0.202068	+	0.562178i
$171$		−	2.51073i		−	0.192001i
$172$	−4.43545	+	19.5789i	−0.338200	+	1.49288i
$173$	−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
$178$	2.81794	+	1.55445i	0.211214	+	0.116511i
$179$	−3.57919			−0.267522			−0.133761	−	0.991014i	$-0.542705\pi$
$179$	−3.57919			−0.267522			−0.133761	+	0.991014i	$0.542705\pi$
$180$	−0.715309	+	11.2055i	−0.0533160	+	0.835211i
$181$	−7.40488			−0.550400			−0.275200	−	0.961387i	$-0.588744\pi$
$181$	−7.40488			−0.550400			−0.275200	+	0.961387i	$0.588744\pi$
$182$	−0.233421	−	0.128761i	−0.0173023	−	0.00954437i
$183$	−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
$188$	7.10239	+	1.60899i	0.517995	+	0.117348i
$189$			1.78571i			0.129891i
$190$	−1.34791	−	2.86062i	−0.0977880	−	0.207531i
$191$		−	4.12918i		−	0.298777i	−0.988779	−	0.149388i	$-0.952270\pi$
$191$		−	4.12918i		−	0.298777i	0.988779	−	0.149388i	$-0.0477304\pi$
$192$	−4.39186	−	3.46766i	−0.316955	−	0.250257i
$193$	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	$0.654587\pi$
$198$	5.05650	−	9.16655i	0.359350	−	0.651438i
$199$	−14.7472			−1.04540			−0.522701	−	0.852516i	$-0.675076\pi$
$199$	−14.7472			−1.04540			−0.522701	+	0.852516i	$0.675076\pi$
$200$	5.20082	+	13.1511i	0.367754	+	0.929923i
$201$	−9.40930			−0.663681
$202$	3.14638	−	5.70385i	0.221379	−	0.401321i
$203$	−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
$208$	0.542524	+	1.53450i	0.0376172	+	0.106398i
$209$			2.94834i			0.203941i
$210$	0.436781	+	0.926961i	0.0301408	+	0.0639664i
$211$		−	3.44024i		−	0.236836i	−0.992964	−	0.118418i	$-0.962218\pi$
$211$		−	3.44024i		−	0.236836i	0.992964	−	0.118418i	$-0.0377822\pi$
$212$	−15.6558	−	3.54670i	−1.07525	−	0.243588i
$213$	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
$218$	6.48910	+	3.57955i	0.439497	+	0.242438i
$219$	4.77724			0.322816
$220$	0.839984	−	13.1586i	0.0566317	−	0.887152i
$221$	−1.00223			−0.0674170
$222$	−5.00162	−	2.75902i	−0.335686	−	0.185173i
$223$	−9.96172	−	9.96172i	−0.667086	−	0.667086i	0.289955	−	0.957040i	$-0.406360\pi$
$223$	−9.96172	−	9.96172i	−0.667086	−	0.667086i	−0.957040	+	0.289955i	$0.906360\pi$
$224$	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	−0.368802	−	0.929508i	$-0.620232\pi$
$227$	8.44789	−	8.44789i	0.560706	−	0.560706i	0.929508	+	0.368802i	$0.120232\pi$
$228$	−0.309090	+	1.36438i	−0.0204700	+	0.0903583i
$229$			8.64013i			0.570956i	0.958385	+	0.285478i	$0.0921524\pi$
$229$			8.64013i			0.570956i	−0.958385	+	0.285478i	$0.907848\pi$
$230$	0.862294	−	2.39901i	0.0568580	−	0.158186i
$231$		−	0.955387i		−	0.0628599i
$232$	0.306326	+	5.22801i	0.0201113	+	0.343235i
$233$	−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
$238$	−0.779441	+	1.41299i	−0.0505236	+	0.0915906i
$239$	−23.0971			−1.49403			−0.747013	−	0.664810i	$-0.768513\pi$
$239$	−23.0971			−1.49403			−0.747013	+	0.664810i	$0.768513\pi$
$240$	1.76820	−	6.00124i	0.114137	−	0.387378i
$241$	19.8422			1.27815			0.639075	−	0.769145i	$-0.279317\pi$
$241$	19.8422			1.27815			0.639075	+	0.769145i	$0.279317\pi$
$242$	1.57607	−	2.85713i	0.101313	−	0.183663i
$243$	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
$248$	0.185758	+	3.17029i	0.0117956	+	0.201314i
$249$		−	1.96165i		−	0.124314i
$250$	−11.4780	+	10.8745i	−0.725933	+	0.687766i
$251$			5.82734i			0.367819i	0.982943	+	0.183909i	$0.0588753\pi$
$251$			5.82734i			0.367819i	−0.982943	+	0.183909i	$0.941125\pi$
$252$	−0.513973	+	2.26877i	−0.0323772	+	0.142919i
$253$	−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	$0.661982\pi$
$258$	8.69416	+	4.79592i	0.541275	+	0.298581i
$259$	2.67509			0.166222
$260$	−1.36607	+	1.20213i	−0.0847203	+	0.0745530i
$261$	−4.64874			−0.287750
$262$	8.76227	+	4.83349i	0.541335	+	0.298614i
$263$	8.45067	+	8.45067i	0.521091	+	0.521091i	0.917901	−	0.396810i	$-0.129883\pi$
$263$	8.45067	+	8.45067i	0.521091	+	0.521091i	−0.396810	+	0.917901i	$0.629883\pi$
$264$	−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
$268$	−26.2390	−	5.94423i	−1.60280	−	0.363101i
$269$		−	1.50260i		−	0.0916154i	−0.998950	−	0.0458077i	$-0.985414\pi$
$269$		−	1.50260i		−	0.0916154i	0.998950	−	0.0458077i	$-0.0145861\pi$
$270$	11.4709	+	4.12307i	0.698098	+	0.250922i
$271$		−	29.6188i		−	1.79921i	−0.436702	−	0.899606i	$-0.643854\pi$
$271$		−	29.6188i		−	1.79921i	0.436702	−	0.899606i	$-0.356146\pi$
$272$	9.28895	−	3.28412i	0.563226	−	0.199129i
$273$	−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	$-0.532148\pi$
$278$	−7.81078	+	14.1596i	−0.468459	+	0.849235i
$279$	−2.81902			−0.168771
$280$	0.632419	+	2.86087i	0.0377943	+	0.170970i
$281$	16.2476			0.969249			0.484625	−	0.874722i	$-0.338956\pi$
$281$	16.2476			0.969249			0.484625	+	0.874722i	$0.338956\pi$
$282$	1.73975	−	3.15387i	0.103601	−	0.187810i
$283$	6.63046	+	6.63046i	0.394140	+	0.394140i	0.876160	−	0.482020i	$-0.160097\pi$
$283$	6.63046	+	6.63046i	0.394140	+	0.394140i	−0.482020	+	0.876160i	$0.660097\pi$
$284$	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
$288$	11.5500	−	8.26556i	0.680587	−	0.487053i
$289$		−	10.9331i		−	0.643125i
$290$	−5.29657	+	2.49573i	−0.311025	+	0.146554i
$291$			4.09281i			0.239925i
$292$	13.3219	+	3.01797i	0.779605	+	0.176613i
$293$	−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
$298$	16.2387	+	8.95765i	0.940681	+	0.518903i
$299$	0.328019			0.0189699
$300$	6.96304	−	0.665481i	0.402011	−	0.0384216i
$301$	−4.65002			−0.268023
$302$	−2.79853	−	1.54374i	−0.161038	−	0.0888323i
$303$	−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	−0.304026	−	0.952664i	$-0.598331\pi$
$307$	11.3650	−	11.3650i	0.648638	−	0.648638i	0.952664	+	0.304026i	$0.0983310\pi$
$308$	0.603556	−	2.66421i	0.0343908	−	0.151807i
$309$			10.7061i			0.609048i
$310$	−3.21187	+	1.51342i	−0.182422	+	0.0859567i
$311$			31.6342i			1.79381i	0.442225	+	0.896904i	$0.354189\pi$
$311$			31.6342i			1.79381i	−0.442225	+	0.896904i	$0.645811\pi$
$312$	0.803631	−	0.0470874i	0.0454966	−	0.00266580i
$313$	−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	$0.427386\pi$
$318$	−3.83494	+	6.95208i	−0.215053	+	0.389853i
$319$	5.45900			0.305645
$320$	8.72204	−	15.6181i	0.487577	−	0.873080i
$321$	−5.05374			−0.282072
$322$	0.255104	−	0.462459i	0.0142164	−	0.0257718i
$323$	−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
$328$	−29.5955	+	1.73410i	−1.63414	+	0.0957496i
$329$			1.68683i			0.0929979i
$330$	−6.13714	−	2.20592i	−0.337839	−	0.121432i
$331$			28.8144i			1.58378i	0.610661	+	0.791892i	$0.290904\pi$
$331$			28.8144i			1.58378i	−0.610661	+	0.791892i	$0.709096\pi$
$332$	1.23925	−	5.47028i	0.0680127	−	0.300221i
$333$	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	$0.923179\pi$
$338$	15.8930	+	8.76695i	0.864463	+	0.476859i
$339$	9.03317			0.490614
$340$	7.27699	+	8.26940i	0.394650	+	0.448471i
$341$	3.31036			0.179266
$342$	−3.10905	−	1.71503i	−0.168118	−	0.0927383i
$343$	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	$-0.481118\pi$
$347$	19.6995	−	19.6995i	1.05752	−	1.05752i	0.998241	−	0.0592835i	$-0.0188816\pi$
$348$	2.52622	+	0.572295i	0.135419	+	0.0306782i
$349$		−	7.57450i		−	0.405454i	−0.979235	−	0.202727i	$-0.935020\pi$
$349$		−	7.57450i		−	0.405454i	0.979235	−	0.202727i	$-0.0649804\pi$
$350$	−2.70477	+	1.84795i	−0.144576	+	0.0987769i
$351$			1.56843i			0.0837166i
$352$	−13.5630	+	9.70620i	−0.722913	+	0.517342i
$353$	−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
$358$	−2.44488	+	4.43214i	−0.129216	+	0.234246i
$359$	−23.4554			−1.23793			−0.618966	−	0.785418i	$-0.712448\pi$
$359$	−23.4554			−1.23793			−0.618966	+	0.785418i	$0.712448\pi$
$360$	13.3873	+	8.54005i	0.705570	+	0.450100i
$361$	1.00000			0.0526316
$362$	−5.05813	+	9.16950i	−0.265849	+	0.481938i
$363$	−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	$0.580852\pi$
$367$	−23.3564	+	23.3564i	−1.21920	+	1.21920i	−0.967914	+	0.251282i	$0.919148\pi$
$368$	−3.04019	+	1.07486i	−0.158481	+	0.0560311i
$369$		−	26.3163i		−	1.36997i
$370$	6.17657	−	17.1840i	0.321105	−	0.893355i
$371$		−	3.71828i		−	0.193043i
$372$	1.53191	+	0.347042i	0.0794259	+	0.0179933i
$373$	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
$378$	2.21126	+	1.21978i	0.113735	+	0.0627389i
$379$	22.9714			1.17996			0.589981	−	0.807417i	$-0.299135\pi$
$379$	22.9714			1.17996			0.589981	+	0.807417i	$0.299135\pi$
$380$	−4.46305	−	0.284901i	−0.228950	−	0.0146151i
$381$	0.355331			0.0182041
$382$	−5.11318	−	2.82056i	−0.261613	−	0.144312i
$383$	18.5545	+	18.5545i	0.948090	+	0.948090i	0.998718	−	0.0506273i	$-0.0161221\pi$
$383$	18.5545	+	18.5545i	0.948090	+	0.948090i	−0.0506273	+	0.998718i	$0.516122\pi$
$384$	−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
$388$	−2.58559	+	11.4133i	−0.131263	+	0.579422i
$389$		−	37.2211i		−	1.88718i	−0.331112	−	0.943592i	$-0.607424\pi$
$389$		−	37.2211i		−	1.88718i	0.331112	−	0.943592i	$-0.392576\pi$
$390$	0.383635	+	0.814171i	0.0194261	+	0.0412271i
$391$		−	1.98564i		−	0.100418i
$392$	−1.12260	−	19.1591i	−0.0566997	−	0.967681i
$393$	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	$0.655818\pi$
$398$	−10.0735	+	18.2616i	−0.504941	+	0.915369i
$399$	−0.324042			−0.0162224
$400$	19.8377	+	2.54305i	0.991883	+	0.127153i
$401$	28.5885			1.42764			0.713821	−	0.700328i	$-0.246963\pi$
$401$	28.5885			1.42764			0.713821	+	0.700328i	$0.246963\pi$
$402$	−6.42731	+	11.6516i	−0.320565	+	0.581129i
$403$	−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
$408$	−0.285040	−	4.86471i	−0.0141116	−	0.240839i
$409$			8.40060i			0.415383i	0.978194	+	0.207691i	$0.0665950\pi$
$409$			8.40060i			0.415383i	−0.978194	+	0.207691i	$0.933405\pi$
$410$	−14.1282	−	29.9836i	−0.697742	−	1.48079i
$411$		−	4.28083i		−	0.211158i
$412$	−6.76346	+	29.8552i	−0.333212	+	1.47086i
$413$	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
$418$	3.65095	+	2.01395i	0.178574	+	0.0985057i
$419$	14.2962			0.698416			0.349208	−	0.937045i	$-0.386451\pi$
$419$	14.2962			0.698416			0.349208	+	0.937045i	$0.386451\pi$
$420$	1.44622	+	0.0923198i	0.0705682	+	0.00450475i
$421$	40.0754			1.95316			0.976579	−	0.215161i	$-0.0690275\pi$
$421$	40.0754			1.95316			0.976579	+	0.215161i	$0.0690275\pi$
$422$	−4.26007	−	2.34996i	−0.207377	−	0.114394i
$423$	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
$428$	−14.0930	−	3.19265i	−0.681209	−	0.154322i
$429$		−	0.839138i		−	0.0405140i
$430$	−10.7366	+	29.8705i	−0.517763	+	1.44048i
$431$		−	30.3005i		−	1.45952i	−0.683702	−	0.729761i	$-0.739631\pi$
$431$		−	30.3005i		−	1.45952i	0.683702	−	0.729761i	$-0.260369\pi$
$432$	−5.13947	−	14.5367i	−0.247273	−	0.699399i
$433$	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
$438$	3.26324	−	5.91568i	0.155924	−	0.282662i
$439$	−19.3441			−0.923241			−0.461621	−	0.887077i	$-0.652732\pi$
$439$	−19.3441			−0.923241			−0.461621	+	0.887077i	$0.652732\pi$
$440$	−15.7206	−	10.0285i	−0.749450	−	0.478092i
$441$	17.0363			0.811252
$442$	−0.684600	+	1.24106i	−0.0325631	+	0.0590313i
$443$	4.15922	+	4.15922i	0.197611	+	0.197611i	0.798975	−	0.601364i	$-0.205376\pi$
$443$	4.15922	+	4.15922i	0.197611	+	0.197611i	−0.601364	+	0.798975i	$0.705376\pi$
$444$	−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
$448$	2.29663	−	2.90874i	0.108506	−	0.137425i
$449$			22.1626i			1.04592i	0.852358	+	0.522959i	$0.175172\pi$
$449$			22.1626i			1.04592i	−0.852358	+	0.522959i	$0.824828\pi$
$450$	−3.28358	+	17.4473i	−0.154789	+	0.822472i
$451$			30.9031i			1.45517i
$452$	25.1901	+	5.70661i	1.18484	+	0.268416i
$453$	−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	$0.633213\pi$
$458$	10.6991	+	5.90191i	0.499937	+	0.275778i
$459$	9.49435			0.443158
$460$	−2.38169	−	2.70650i	−0.111047	−	0.126191i
$461$	−6.29625			−0.293245			−0.146623	−	0.989192i	$-0.546840\pi$
$461$	−6.29625			−0.293245			−0.146623	+	0.989192i	$0.546840\pi$
$462$	−1.18306	−	0.652606i	−0.0550410	−	0.0303620i
$463$	−5.60774	−	5.60774i	−0.260614	−	0.260614i	0.564690	−	0.825303i	$-0.308996\pi$
$463$	−5.60774	−	5.60774i	−0.260614	−	0.260614i	−0.825303	+	0.564690i	$0.808996\pi$
$464$	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	$0.532017\pi$
$467$	−23.6709	+	23.6709i	−1.09536	+	1.09536i	−0.994946	+	0.100413i	$0.967983\pi$
$468$	−0.451434	+	1.99272i	−0.0208675	+	0.0921133i
$469$		−	6.23179i		−	0.287757i
$470$	10.8357	+	3.89476i	0.499815	+	0.179652i
$471$			11.3368i			0.522371i
$472$	−39.8817	+	2.33680i	−1.83570	+	0.107560i
$473$	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
$478$	−15.7772	+	28.6012i	−0.721631	+	1.30819i
$479$	−12.8003			−0.584863			−0.292431	−	0.956286i	$-0.594464\pi$
$479$	−12.8003			−0.584863			−0.292431	+	0.956286i	$0.594464\pi$
$480$	−6.22355	−	6.28890i	−0.284065	−	0.287048i
$481$	2.34959			0.107132
$482$	13.5538	−	24.5707i	0.617360	−	1.11917i
$483$	−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	−0.907426	−	0.420211i	$-0.861956\pi$
$487$	−10.7519	+	10.7519i	−0.487215	+	0.487215i	0.420211	+	0.907426i	$0.361956\pi$
$488$	−21.7261	+	1.27301i	−0.983495	+	0.0576263i
$489$		−	10.3850i		−	0.469626i
$490$	19.4104	−	9.14612i	0.876872	−	0.413180i
$491$		−	39.2711i		−	1.77228i	−0.463417	−	0.886140i	$-0.653377\pi$
$491$		−	39.2711i		−	1.77228i	0.463417	−	0.886140i	$-0.346623\pi$
$492$	−3.23973	+	14.3008i	−0.146058	+	0.644729i
$493$	−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
$498$	−2.42912	−	1.33996i	−0.108851	−	0.0600452i
$499$	35.8517			1.60494			0.802471	−	0.596692i	$-0.203518\pi$
$499$	35.8517			1.60494			0.802471	+	0.596692i	$0.203518\pi$
$500$	5.62560	+	21.6415i	0.251584	+	0.967835i
$501$	15.8072			0.706214
$502$	7.21603	+	3.98054i	0.322067	+	0.177660i
$503$	8.36832	+	8.36832i	0.373125	+	0.373125i	0.868614	−	0.495489i	$-0.165011\pi$
$503$	8.36832	+	8.36832i	0.373125	+	0.373125i	−0.495489	+	0.868614i	$0.665011\pi$
$504$	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
$508$	0.990881	+	0.224476i	0.0439632	+	0.00995953i
$509$		−	8.31464i		−	0.368540i	−0.982876	−	0.184270i	$-0.941008\pi$
$509$		−	8.31464i		−	0.368540i	0.982876	−	0.184270i	$-0.0589921\pi$
$510$	4.92851	−	2.32230i	0.218238	−	0.102833i
$511$			3.16397i			0.139966i
$512$	−22.2795	+	3.95253i	−0.984626	+	0.174679i
$513$	−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
$518$	1.82730	−	3.31257i	0.0802869	−	0.145546i
$519$	12.5928			0.552763
$520$	0.555468	+	2.51277i	0.0243589	+	0.110192i
$521$	−35.8196			−1.56928			−0.784642	−	0.619949i	$-0.787153\pi$
$521$	−35.8196			−1.56928			−0.784642	+	0.619949i	$0.787153\pi$
$522$	−3.17547	+	5.75657i	−0.138986	+	0.251958i
$523$	−14.4962	−	14.4962i	−0.633874	−	0.633874i	0.315163	−	0.949038i	$-0.397941\pi$
$523$	−14.4962	−	14.4962i	−0.633874	−	0.633874i	−0.949038	+	0.315163i	$0.897941\pi$
$524$	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
$528$	2.74971	+	7.77741i	0.119666	+	0.338468i
$529$		−	22.3501i		−	0.971744i
$530$	−23.8852	−	8.58523i	−1.03751	−	0.372918i
$531$		−	35.4628i		−	1.53895i
$532$	−0.903630	−	0.204710i	−0.0391773	−	0.00887532i
$533$	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
$538$	−1.86068	−	1.02640i	−0.0802198	−	0.0442512i
$539$	−20.0056			−0.861703
$540$	12.9412	−	11.3881i	0.556900	−	0.490066i
$541$	−43.9873			−1.89116			−0.945580	−	0.325390i	$-0.894504\pi$
$541$	−43.9873			−1.89116			−0.945580	+	0.325390i	$0.894504\pi$
$542$	−36.6771	−	20.2320i	−1.57542	−	0.869039i
$543$	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	$0.527211\pi$
$547$	−25.2995	+	25.2995i	−1.08173	+	1.08173i	−0.996348	+	0.0853805i	$0.972789\pi$
$548$	2.70437	−	11.9376i	0.115525	−	0.509949i
$549$		−	19.3189i		−	0.824509i
$550$	3.85589	−	20.4882i	0.164416	−	0.873621i
$551$		−	1.85155i		−	0.0788787i
$552$	0.0932909	+	1.59218i	0.00397073	+	0.0677675i
$553$	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	$0.859312\pi$
$558$	−1.92562	+	3.49081i	−0.0815180	+	0.147778i
$559$	−4.08422			−0.172744
$560$	3.97463	+	1.17108i	0.167959	+	0.0494871i
$561$	−5.07965			−0.214463
$562$	11.0984	−	20.1195i	0.468158	−	0.848689i
$563$	0.343770	+	0.343770i	0.0144882	+	0.0144882i	0.714314	−	0.699826i	$-0.246739\pi$
$563$	0.343770	+	0.343770i	0.0144882	+	0.0144882i	−0.699826	+	0.714314i	$0.746739\pi$
$564$	−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
$568$	−1.52166	−	25.9698i	−0.0638473	−	1.08967i
$569$		−	14.2062i		−	0.595555i	−0.954635	−	0.297777i	$-0.903755\pi$
$569$		−	14.2062i		−	0.595555i	0.954635	−	0.297777i	$-0.0962453\pi$
$570$	−0.748189	+	2.08156i	−0.0313382	+	0.0871869i
$571$		−	19.1090i		−	0.799688i	−0.916583	−	0.399844i	$-0.869064\pi$
$571$		−	19.1090i		−	0.799688i	0.916583	−	0.399844i	$-0.130936\pi$
$572$	0.530117	−	2.34004i	0.0221653	−	0.0978418i
$573$	−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	$-0.519157\pi$
$578$	−13.5385	−	7.46820i	−0.563129	−	0.310636i
$579$	−5.48183			−0.227817
$580$	−0.527507	+	8.26356i	−0.0219036	+	0.343126i
$581$	1.29920			0.0538999
$582$	5.06815	+	2.79572i	0.210082	+	0.115886i
$583$	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	$-0.422617\pi$
$587$	29.3478	−	29.3478i	1.21131	−	1.21131i	0.970595	−	0.240717i	$-0.0773825\pi$
$588$	−9.25785	−	2.09729i	−0.381787	−	0.0864909i
$589$		−	1.12279i		−	0.0462637i
$590$	−19.0386	−	40.4047i	−0.783806	−	1.66344i
$591$		−	5.79788i		−	0.238493i
$592$	−21.7768	+	7.69919i	−0.895019	+	0.316435i
$593$	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
$598$	0.224064	−	0.406188i	0.00916265	−	0.0166103i
$599$	8.94617			0.365531			0.182765	−	0.983157i	$-0.441495\pi$
$599$	8.94617			0.365531			0.182765	+	0.983157i	$0.441495\pi$
$600$	3.93225	−	9.07695i	0.160533	−	0.370565i
$601$	−31.5967			−1.28886			−0.644429	−	0.764664i	$-0.722905\pi$
$601$	−31.5967			−1.28886			−0.644429	+	0.764664i	$0.722905\pi$
$602$	−3.17634	+	5.75815i	−0.129458	+	0.234685i
$603$	−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	−0.814237	−	0.580533i	$-0.802844\pi$
$607$	−5.75786	+	5.75786i	−0.233704	+	0.233704i	0.580533	+	0.814237i	$0.302844\pi$
$608$	3.29209	+	4.60023i	0.133512	+	0.186564i
$609$			0.599980i			0.0243124i
$610$	−10.3716	−	22.0111i	−0.419932	−	0.891202i
$611$			1.48158i			0.0599383i
$612$	12.0627	+	2.73271i	0.487607	+	0.110463i
$613$	−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	$0.462772\pi$
$618$	13.2574	+	7.31312i	0.533291	+	0.294177i
$619$	−36.0285			−1.44811			−0.724054	−	0.689743i	$-0.757723\pi$
$619$	−36.0285			−1.44811			−0.724054	+	0.689743i	$0.757723\pi$
$620$	−0.319883	+	5.01107i	−0.0128468	+	0.201249i
$621$	−3.10742			−0.124696
$622$	39.1728	+	21.6087i	1.57068	+	0.866429i
$623$	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
$628$	−7.16188	+	31.6139i	−0.285790	+	1.26153i
$629$		−	14.2230i		−	0.567109i
$630$	−1.24413	+	3.46134i	−0.0495675	+	0.137903i
$631$			20.6862i			0.823504i	0.911296	+	0.411752i	$0.135083\pi$
$631$			20.6862i			0.823504i	−0.911296	+	0.411752i	$0.864917\pi$
$632$	−0.463424	+	0.0271535i	−0.0184340	+	0.00108011i
$633$	−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
$638$	3.72893	−	6.75991i	0.147630	−	0.267627i
$639$	23.0923			0.913519
$640$	−13.3822	−	21.4690i	−0.528976	−	0.848637i
$641$	−5.19156			−0.205054			−0.102527	−	0.994730i	$-0.532693\pi$
$641$	−5.19156			−0.205054			−0.102527	+	0.994730i	$0.532693\pi$
$642$	−3.45211	+	6.25808i	−0.136244	+	0.246987i
$643$	−6.88159	−	6.88159i	−0.271384	−	0.271384i	0.558273	−	0.829657i	$-0.311464\pi$
$643$	−6.88159	−	6.88159i	−0.271384	−	0.271384i	−0.829657	+	0.558273i	$0.811464\pi$
$644$	−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	−0.982480	−	0.186368i	$-0.940328\pi$
$647$	−20.2501	+	20.2501i	−0.796113	+	0.796113i	0.186368	+	0.982480i	$0.440328\pi$
$648$	13.6548	−	0.800080i	0.536410	−	0.0314301i
$649$			41.6438i			1.63466i
$650$	−2.37566	+	1.62309i	−0.0931810	+	0.0636630i
$651$			0.363831i			0.0142597i
$652$	6.56062	−	28.9598i	0.256934	−	1.13415i
$653$	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
$658$	2.08881	+	1.15224i	0.0814303	+	0.0449190i
$659$	29.9506			1.16671			0.583354	−	0.812218i	$-0.301740\pi$
$659$	29.9506			1.16671			0.583354	+	0.812218i	$0.301740\pi$
$660$	−6.92376	+	6.09284i	−0.269507	+	0.237164i
$661$	−42.9876			−1.67202			−0.836012	−	0.548711i	$-0.815119\pi$
$661$	−42.9876			−1.67202			−0.836012	+	0.548711i	$0.815119\pi$
$662$	35.6811	+	19.6826i	1.38678	+	0.764985i
$663$	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
$668$	44.0803	+	9.98603i	1.70552	+	0.386371i
$669$			9.85422i			0.380986i
$670$	−40.0313	−	14.3887i	−1.54654	−	0.555885i
$671$			22.6860i			0.875785i
$672$	−1.06678	−	1.49067i	−0.0411518	−	0.0575039i
$673$	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	$0.735644\pi$
$678$	6.17038	−	11.1858i	0.236972	−	0.429589i
$679$	−2.71067			−0.104026
$680$	15.2108	−	3.36247i	0.583308	−	0.128945i
$681$	−8.35673			−0.320230
$682$	2.26125	−	4.09924i	0.0865875	−	0.156968i
$683$	−3.72871	−	3.72871i	−0.142675	−	0.142675i	0.632161	−	0.774837i	$-0.282168\pi$
$683$	−3.72871	−	3.72871i	−0.142675	−	0.142675i	−0.774837	+	0.632161i	$0.782168\pi$
$684$	−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
$688$	37.8539	−	13.3833i	1.44317	−	0.510233i
$689$		−	3.26585i		−	0.124419i
$690$	−1.61306	+	0.760068i	−0.0614080	+	0.0289353i
$691$		−	0.815388i		−	0.0310188i	−0.999880	−	0.0155094i	$-0.995063\pi$
$691$		−	0.815388i		−	0.0310188i	0.999880	−	0.0155094i	$-0.00493700\pi$
$692$	35.1166	+	7.95538i	1.33493	+	0.302418i
$693$	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
$698$	−9.37955	−	5.17399i	−0.355021	−	0.195839i
$699$	4.49834			0.170143
$700$	0.440749	+	4.61163i	0.0166587	+	0.174303i
$701$	9.25242			0.349459			0.174730	−	0.984616i	$-0.444095\pi$
$701$	9.25242			0.349459			0.174730	+	0.984616i	$0.444095\pi$
$702$	1.94220	+	1.07136i	0.0733035	+	0.0404360i
$703$	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
$708$	−4.36573	+	19.2712i	−0.164074	+	0.724255i
$709$			25.0837i			0.942038i	0.882123	+	0.471019i	$0.156114\pi$
$709$			25.0837i			0.942038i	−0.882123	+	0.471019i	$0.843886\pi$
$710$	26.3104	−	12.3974i	0.987411	−	0.465265i
$711$		−	0.412076i		−	0.0154541i
$712$	−0.376490	−	6.42547i	−0.0141096	−	0.240805i
$713$	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
$718$	−16.0220	+	29.0450i	−0.597934	+	1.08395i
$719$	−37.6238			−1.40313			−0.701565	−	0.712606i	$-0.747515\pi$
$719$	−37.6238			−1.40313			−0.701565	+	0.712606i	$0.747515\pi$
$720$	19.7198	−	10.7440i	0.734912	−	0.400404i
$721$	−7.09065			−0.264070
$722$	0.683080	−	1.23831i	0.0254216	−	0.0460850i
$723$	−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	$-0.487786\pi$
$727$	27.9775	−	27.9775i	1.03763	−	1.03763i	0.999264	−	0.0383634i	$-0.0122145\pi$
$728$	0.0311861	+	0.532246i	0.00115583	+	0.0197263i
$729$			4.05317i			0.150117i
$730$	20.3245	+	7.30537i	0.752243	+	0.270384i
$731$			24.7235i			0.914430i
$732$	−2.37829	+	10.4982i	−0.0879043	+	0.388026i
$733$	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
$738$	−32.5876	−	17.9762i	−1.19957	−	0.661711i
$739$	−40.9090			−1.50486			−0.752431	−	0.658671i	$-0.771119\pi$
$739$	−40.9090			−1.50486			−0.752431	+	0.658671i	$0.771119\pi$
$740$	−17.0600	−	19.3866i	−0.627137	−	0.712664i
$741$	−0.284614			−0.0104555
$742$	−4.60437	−	2.53988i	−0.169032	−	0.0932421i
$743$	−4.46740	−	4.46740i	−0.163893	−	0.163893i	0.620396	−	0.784289i	$-0.286972\pi$
$743$	−4.46740	−	4.46740i	−0.163893	−	0.163893i	−0.784289	+	0.620396i	$0.786972\pi$
$744$	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
$748$	−14.1652	−	3.20901i	−0.517931	−	0.117333i
$749$		−	3.34710i		−	0.122300i
$750$	11.0557	+	0.298479i	0.403696	+	0.0108989i
$751$		−	37.1200i		−	1.35453i	−0.735740	−	0.677264i	$-0.763166\pi$
$751$		−	37.1200i		−	1.35453i	0.735740	−	0.677264i	$-0.236834\pi$
$752$	−4.85488	−	13.7318i	−0.177039	−	0.500746i
$753$	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	$0.597597\pi$
$758$	15.6913	−	28.4456i	0.569934	−	1.03319i
$759$	1.66252			0.0603458
$760$	−3.40142	+	5.33201i	−0.123382	+	0.193412i
$761$	−31.7582			−1.15123			−0.575617	−	0.817719i	$-0.695238\pi$
$761$	−31.7582			−1.15123			−0.575617	+	0.817719i	$0.695238\pi$
$762$	0.242719	−	0.440008i	0.00879279	−	0.0159398i
$763$	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
$768$	−1.18107	+	11.1291i	−0.0426184	+	0.401588i
$769$			32.9935i			1.18977i	0.803809	+	0.594887i	$0.202803\pi$
$769$			32.9935i			1.18977i	−0.803809	+	0.594887i	$0.797197\pi$
$770$	1.46098	−	4.06464i	0.0526501	−	0.146479i
$771$

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)

\(f(q)\)	\(=\)	\(q+(0.683080 - 1.23831i) q^{2} +(-0.494605 - 0.494605i) q^{3} +(-1.06680 - 1.69172i) q^{4} +(1.31079 - 1.81158i) q^{5} +(-0.950327 + 0.274617i) q^{6} +(0.327577 - 0.327577i) q^{7} +(-2.82358 + 0.165443i) q^{8} -2.51073i q^{9} +O(q^{10})\)	\(q+(0.683080 - 1.23831i) 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} +(-2.82358 + 0.165443i) q^{8} -2.51073i q^{9} +(-1.34791 - 2.86062i) q^{10} +2.94834i q^{11} +(-0.309090 + 1.36438i) 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} +(-3.10905 - 1.71503i) q^{18} +1.00000 q^{19} +(-4.46305 - 0.284901i) q^{20} -0.324042 q^{21} +(3.65095 + 2.01395i) 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} +(-0.903630 - 0.204710i) q^{28} -1.85155i q^{29} +(-0.748189 + 2.08156i) q^{30} -1.12279i q^{31} +(3.29209 + 4.60023i) 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} +(0.683080 - 1.23831i) q^{38} -0.284614 q^{39} +(-3.40142 + 5.33201i) q^{40} +10.4815 q^{41} +(-0.221347 + 0.401264i) 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} +(2.63789 - 0.932630i) q^{48} +6.78539i q^{49} +(-6.94907 - 1.30782i) q^{50} +1.72288i q^{51} +(-0.793679 - 0.179802i) 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} +(-2.29278 - 1.26476i) q^{58} +14.1245 q^{59} +(2.06653 + 2.34836i) q^{60} +7.69452 q^{61} +(-1.39036 - 0.766955i) 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} +(-1.08841 + 4.80446i) q^{68} -0.563885i q^{69} +(-1.37862 - 0.495527i) q^{70} +9.19745i q^{71} +(0.415384 + 7.08926i) 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} +(-0.194414 + 0.352439i) q^{78} +0.164126 q^{79} +(4.27922 + 7.85419i) q^{80} -4.83597 q^{81} +(7.15972 - 12.9793i) 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} +(-0.487783 - 8.32489i) q^{88} +2.27564i q^{89} +(-7.18224 + 3.38425i) q^{90} -0.188500i q^{91} +(0.356228 - 1.57246i) 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} +(8.40238 + 4.63496i) 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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