LMFDB - Embedded newform 380.2.k.d.343.5

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			343.5
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.5

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−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	−0.549762	−	0.835322i	$-0.685281\pi$
$3$	0.494605	−	0.494605i	0.285560	−	0.285560i	0.835322	+	0.549762i	$0.185281\pi$
$4$	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	$-0.277903\pi$
$7$	−0.327577	−	0.327577i	−0.123813	−	0.123813i	−0.766298	+	0.642485i	$0.777903\pi$
$8$	−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	$0.146611\pi$
$11$			2.94834i			0.888958i	−0.895789	+	0.444479i	$0.853389\pi$
$12$	1.36438	+	0.309090i	0.393863	+	0.0892265i
$13$	0.287718	+	0.287718i	0.0797987	+	0.0797987i	0.745880	−	0.666081i	$-0.232029\pi$
$13$	0.287718	+	0.287718i	0.0797987	+	0.0797987i	−0.666081	+	0.745880i	$0.732029\pi$
$14$	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	−0.886036	−	0.463617i	$-0.846551\pi$
$17$	−1.74168	+	1.74168i	−0.422419	+	0.422419i	0.463617	+	0.886036i	$0.346551\pi$
$18$	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	−0.764035	−	0.645175i	$-0.776785\pi$
$23$	−0.570036	+	0.570036i	−0.118861	+	0.118861i	0.645175	+	0.764035i	$0.276785\pi$
$24$	−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	$0.0549945\pi$
$29$			1.85155i			0.343824i	−0.985112	+	0.171912i	$0.945006\pi$
$30$	−1.74317	−	1.36163i	−0.318258	−	0.248598i
$31$		−	1.12279i		−	0.201659i	−0.994904	−	0.100829i	$-0.967850\pi$
$31$		−	1.12279i		−	0.201659i	0.994904	−	0.100829i	$-0.0321496\pi$
$32$	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	−0.286743	−	0.958007i	$-0.592573\pi$
$37$	4.08314	−	4.08314i	0.671264	−	0.671264i	0.958007	+	0.286743i	$0.0925727\pi$
$38$	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	0.0860866	−	0.996288i	$-0.472564\pi$
$43$	7.09760	−	7.09760i	1.08237	−	1.08237i	0.996288	−	0.0860866i	$-0.0274362\pi$
$44$	−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	$-0.164443\pi$
$47$	2.57471	+	2.57471i	0.375559	+	0.375559i	−0.493938	+	0.869497i	$0.664443\pi$
$48$	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	0.979759	−	0.200180i	$-0.0641525\pi$
$53$	5.67543	+	5.67543i	0.779580	+	0.779580i	−0.200180	+	0.979759i	$0.564153\pi$
$54$	−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	−0.984022	−	0.178047i	$-0.943022\pi$
$67$	−9.51194	−	9.51194i	−1.16207	−	1.16207i	−0.178047	−	0.984022i	$-0.556978\pi$
$68$	−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	$0.183762\pi$
$71$			9.19745i			1.09154i	−0.837936	+	0.545768i	$0.816238\pi$
$72$	7.08926	−	0.415384i	0.835478	−	0.0489535i
$73$	−4.82935	−	4.82935i	−0.565233	−	0.565233i	0.365556	−	0.930789i	$-0.380879\pi$
$73$	−4.82935	−	4.82935i	−0.565233	−	0.565233i	−0.930789	+	0.365556i	$0.880879\pi$
$74$	−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	−0.807515	−	0.589847i	$-0.799188\pi$
$83$	−1.98305	+	1.98305i	−0.217667	+	0.217667i	0.589847	+	0.807515i	$0.299188\pi$
$84$	−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	$-0.961515\pi$
$89$		−	2.27564i		−	0.241218i	0.992700	−	0.120609i	$-0.0384847\pi$
$90$	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	−0.885236	−	0.465141i	$-0.846003\pi$
$97$	−4.13745	+	4.13745i	−0.420095	+	0.420095i	0.465141	+	0.885236i	$0.346003\pi$
$98$	−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	0.0687770	−	0.997632i	$-0.478090\pi$
$103$	10.8229	−	10.8229i	1.06641	−	1.06641i	0.997632	−	0.0687770i	$-0.0219097\pi$
$104$	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	$-0.363559\pi$
$107$	−5.10887	−	5.10887i	−0.493893	−	0.493893i	−0.909530	+	0.415637i	$0.863559\pi$
$108$	−1.70331	+	7.51874i	−0.163901	+	0.723491i
$109$		−	5.24030i		−	0.501930i	−0.967996	−	0.250965i	$-0.919252\pi$
$109$		−	5.24030i		−	0.501930i	0.967996	−	0.250965i	$-0.0807479\pi$
$110$	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	0.132186	−	0.991225i	$-0.457800\pi$
$113$	−9.13170	−	9.13170i	−0.859038	−	0.859038i	−0.991225	+	0.132186i	$0.957800\pi$
$114$	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	0.722864	−	0.690990i	$-0.242825\pi$
$127$	0.359207	+	0.359207i	0.0318744	+	0.0318744i	−0.690990	+	0.722864i	$0.742825\pi$
$128$	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	$0.100034\pi$
$131$			7.07602i			0.618235i	−0.951024	+	0.309117i	$0.899966\pi$
$132$	−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	−0.497651	−	0.867377i	$-0.665804\pi$
$137$	4.32753	−	4.32753i	0.369726	−	0.369726i	0.867377	+	0.497651i	$0.165804\pi$
$138$	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	$-0.819499\pi$
$149$		−	13.1136i		−	1.07431i	0.843484	−	0.537155i	$-0.180501\pi$
$150$	0.181764	−	4.94271i	0.0148409	−	0.403570i
$151$		−	2.25997i		−	0.183914i	−0.995763	−	0.0919569i	$-0.970688\pi$
$151$		−	2.25997i		−	0.183914i	0.995763	−	0.0919569i	$-0.0293122\pi$
$152$	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	−0.996633	−	0.0819909i	$-0.973872\pi$
$157$	−11.4604	+	11.4604i	−0.914642	+	0.914642i	0.0819909	+	0.996633i	$0.473872\pi$
$158$	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	−0.986436	−	0.164147i	$-0.947513\pi$
$163$	−10.4983	+	10.4983i	−0.822289	+	0.822289i	0.164147	+	0.986436i	$0.447513\pi$
$164$	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	0.961405	+	0.275136i	$0.0887228\pi$
$167$	15.9796	+	15.9796i	1.23654	+	1.23654i	0.275136	+	0.961405i	$0.411277\pi$
$168$	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	0.0316413	−	0.999499i	$-0.489927\pi$
$173$	−12.7302	−	12.7302i	−0.967858	−	0.967858i	−0.999499	+	0.0316413i	$0.989927\pi$
$174$	−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	$-0.952270\pi$
$191$		−	4.12918i		−	0.298777i	0.988779	−	0.149388i	$-0.0477304\pi$
$192$	−3.46766	+	4.39186i	−0.250257	+	0.316955i
$193$	5.54163	+	5.54163i	0.398895	+	0.398895i	0.877843	−	0.478948i	$-0.158982\pi$
$193$	5.54163	+	5.54163i	0.398895	+	0.398895i	−0.478948	+	0.877843i	$0.658982\pi$
$194$	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	−0.466784	−	0.884371i	$-0.654587\pi$
$197$	5.86112	−	5.86112i	0.417588	−	0.417588i	0.884371	+	0.466784i	$0.154587\pi$
$198$	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	$-0.962218\pi$
$211$		−	3.44024i		−	0.236836i	0.992964	−	0.118418i	$-0.0377822\pi$
$212$	−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	−0.289955	−	0.957040i	$-0.593640\pi$
$223$	9.96172	−	9.96172i	0.667086	−	0.667086i	0.957040	+	0.289955i	$0.0936402\pi$
$224$	−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	$-0.379768\pi$
$227$	−8.44789	−	8.44789i	−0.560706	−	0.560706i	−0.929508	+	0.368802i	$0.879768\pi$
$228$	−1.36438	−	0.309090i	−0.0903583	−	0.0204700i
$229$		−	8.64013i		−	0.570956i	−0.958385	−	0.285478i	$-0.907848\pi$
$229$		−	8.64013i		−	0.570956i	0.958385	−	0.285478i	$-0.0921524\pi$
$230$	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	0.542284	−	0.840195i	$-0.317560\pi$
$233$	−4.54741	−	4.54741i	−0.297911	−	0.297911i	−0.840195	+	0.542284i	$0.817560\pi$
$234$	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	$0.0588753\pi$
$251$			5.82734i			0.367819i	−0.982943	+	0.183909i	$0.941125\pi$
$252$	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	−0.487200	−	0.873290i	$-0.661982\pi$
$257$	6.18949	−	6.18949i	0.386090	−	0.386090i	0.873290	+	0.487200i	$0.161982\pi$
$258$	−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	−0.917901	−	0.396810i	$-0.870117\pi$
$263$	−8.45067	+	8.45067i	−0.521091	+	0.521091i	0.396810	+	0.917901i	$0.370117\pi$
$264$	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	$0.0145861\pi$
$269$			1.50260i			0.0916154i	−0.998950	+	0.0458077i	$0.985414\pi$
$270$	7.50357	−	9.60615i	0.456652	−	0.584612i
$271$		−	29.6188i		−	1.79921i	−0.436702	−	0.899606i	$-0.643854\pi$
$271$		−	29.6188i		−	1.79921i	0.436702	−	0.899606i	$-0.356146\pi$
$272$	−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	−0.100825	+	0.994904i	$0.532148\pi$
$277$	−18.2366	+	18.2366i	−1.09573	+	1.09573i	−0.994904	+	0.100825i	$0.967852\pi$
$278$	−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	−0.876160	−	0.482020i	$-0.839903\pi$
$283$	−6.63046	+	6.63046i	−0.394140	+	0.394140i	0.482020	+	0.876160i	$0.339903\pi$
$284$	−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	0.145164	−	0.989408i	$-0.453629\pi$
$293$	−14.4511	−	14.4511i	−0.844244	−	0.844244i	−0.989408	+	0.145164i	$0.953629\pi$
$294$	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	0.304026	−	0.952664i	$-0.401669\pi$
$307$	−11.3650	−	11.3650i	−0.648638	−	0.648638i	−0.952664	+	0.304026i	$0.901669\pi$
$308$	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	$0.354189\pi$
$311$			31.6342i			1.79381i	−0.442225	+	0.896904i	$0.645811\pi$
$312$	−0.0470874	−	0.803631i	−0.00266580	−	0.0454966i
$313$	−4.11199	−	4.11199i	−0.232424	−	0.232424i	0.581280	−	0.813704i	$-0.302552\pi$
$313$	−4.11199	−	4.11199i	−0.232424	−	0.232424i	−0.813704	+	0.581280i	$0.802552\pi$
$314$	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	0.226149	−	0.974093i	$-0.427386\pi$
$317$	21.3697	−	21.3697i	1.20024	−	1.20024i	0.974093	−	0.226149i	$-0.0726137\pi$
$318$	−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	$0.290904\pi$
$331$			28.8144i			1.58378i	−0.610661	+	0.791892i	$0.709096\pi$
$332$	−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	−0.971019	−	0.239003i	$-0.923179\pi$
$337$	−13.4380	+	13.4380i	−0.732016	+	0.732016i	0.239003	+	0.971019i	$0.423179\pi$
$338$	−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	−0.998241	−	0.0592835i	$-0.981118\pi$
$347$	−19.6995	−	19.6995i	−1.05752	−	1.05752i	−0.0592835	−	0.998241i	$-0.518882\pi$
$348$	−0.572295	+	2.52622i	−0.0306782	+	0.135419i
$349$			7.57450i			0.405454i	0.979235	+	0.202727i	$0.0649804\pi$
$349$			7.57450i			0.405454i	−0.979235	+	0.202727i	$0.935020\pi$
$350$	−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	0.298814	−	0.954311i	$-0.403409\pi$
$353$	−12.3157	−	12.3157i	−0.655498	−	0.655498i	−0.954311	+	0.298814i	$0.903409\pi$
$354$	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	0.967914	+	0.251282i	$0.0808523\pi$
$367$	23.3564	+	23.3564i	1.21920	+	1.21920i	0.251282	+	0.967914i	$0.419148\pi$
$368$	−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	0.847678	−	0.530511i	$-0.178000\pi$
$373$	6.12552	+	6.12552i	0.317168	+	0.317168i	−0.530511	+	0.847678i	$0.678000\pi$
$374$	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	−0.998718	−	0.0506273i	$-0.983878\pi$
$383$	−18.5545	+	18.5545i	−0.948090	+	0.948090i	0.0506273	+	0.998718i	$0.483878\pi$
$384$	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	$0.392576\pi$
$389$			37.2211i			1.88718i	−0.331112	+	0.943592i	$0.607424\pi$
$390$	−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	−0.470200	−	0.882560i	$-0.655818\pi$
$397$	8.21621	−	8.21621i	0.412360	−	0.412360i	0.882560	+	0.470200i	$0.155818\pi$
$398$	−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	$-0.933405\pi$
$409$		−	8.40060i		−	0.415383i	0.978194	−	0.207691i	$-0.0665950\pi$
$410$	−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	$-0.739631\pi$
$431$		−	30.3005i		−	1.45952i	0.683702	−	0.729761i	$-0.260369\pi$
$432$	−14.5367	+	5.13947i	−0.699399	+	0.247273i
$433$	4.16829	+	4.16829i	0.200315	+	0.200315i	0.800135	−	0.599820i	$-0.204761\pi$
$433$	4.16829	+	4.16829i	0.200315	+	0.200315i	−0.599820	+	0.800135i	$0.704761\pi$
$434$	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	−0.798975	−	0.601364i	$-0.794624\pi$
$443$	−4.15922	+	4.15922i	−0.197611	+	0.197611i	0.601364	+	0.798975i	$0.294624\pi$
$444$	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	$-0.824828\pi$
$449$		−	22.1626i		−	1.04592i	0.852358	−	0.522959i	$-0.175172\pi$
$450$	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	−0.406392	−	0.913699i	$-0.633213\pi$
$457$	10.8450	−	10.8450i	0.507307	−	0.507307i	0.913699	+	0.406392i	$0.133213\pi$
$458$	−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	−0.564690	−	0.825303i	$-0.691004\pi$
$463$	5.60774	−	5.60774i	0.260614	−	0.260614i	0.825303	+	0.564690i	$0.191004\pi$
$464$	−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	0.994946	+	0.100413i	$0.0320165\pi$
$467$	23.6709	+	23.6709i	1.09536	+	1.09536i	0.100413	+	0.994946i	$0.467983\pi$
$468$	−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	0.907426	−	0.420211i	$-0.138044\pi$
$487$	10.7519	+	10.7519i	0.487215	+	0.487215i	−0.420211	+	0.907426i	$0.638044\pi$
$488$	−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	$-0.653377\pi$
$491$		−	39.2711i		−	1.77228i	0.463417	−	0.886140i	$-0.346623\pi$
$492$	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	−0.868614	−	0.495489i	$-0.834989\pi$
$503$	−8.36832	+	8.36832i	−0.373125	+	0.373125i	0.495489	+	0.868614i	$0.334989\pi$
$504$	−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	$0.0589921\pi$
$509$			8.31464i			0.368540i	−0.982876	+	0.184270i	$0.941008\pi$
$510$	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	−0.315163	−	0.949038i	$-0.602059\pi$
$523$	14.4962	−	14.4962i	0.633874	−	0.633874i	0.949038	+	0.315163i	$0.102059\pi$
$524$	−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	0.996348	+	0.0853805i	$0.0272106\pi$
$547$	25.2995	+	25.2995i	1.08173	+	1.08173i	0.0853805	+	0.996348i	$0.472789\pi$
$548$	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	−0.903905	−	0.427733i	$-0.859312\pi$
$557$	−11.2381	+	11.2381i	−0.476172	+	0.476172i	0.427733	+	0.903905i	$0.359312\pi$
$558$	−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	−0.714314	−	0.699826i	$-0.753261\pi$
$563$	−0.343770	+	0.343770i	−0.0144882	+	0.0144882i	0.699826	+	0.714314i	$0.253261\pi$
$564$	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	$0.0962453\pi$
$569$			14.2062i			0.595555i	−0.954635	+	0.297777i	$0.903755\pi$
$570$	1.74317	+	1.36163i	0.0730134	+	0.0570323i
$571$		−	19.1090i		−	0.799688i	−0.916583	−	0.399844i	$-0.869064\pi$
$571$		−	19.1090i		−	0.799688i	0.916583	−	0.399844i	$-0.130936\pi$
$572$	−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	−0.0601462	+	0.998190i	$0.519157\pi$
$577$	−25.4221	+	25.4221i	−1.05834	+	1.05834i	−0.998190	+	0.0601462i	$0.980843\pi$
$578$	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	−0.970595	−	0.240717i	$-0.922617\pi$
$587$	−29.3478	−	29.3478i	−1.21131	−	1.21131i	−0.240717	−	0.970595i	$-0.577383\pi$
$588$	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	0.798536	−	0.601947i	$-0.205608\pi$
$593$	4.78725	+	4.78725i	0.196589	+	0.196589i	−0.601947	+	0.798536i	$0.705608\pi$
$594$	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	0.814237	−	0.580533i	$-0.197156\pi$
$607$	5.75786	+	5.75786i	0.233704	+	0.233704i	−0.580533	+	0.814237i	$0.697156\pi$
$608$	−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	−0.999965	−	0.00834470i	$-0.997344\pi$
$613$	−24.9646	−	24.9646i	−1.00831	−	1.00831i	−0.00834470	−	0.999965i	$-0.502656\pi$
$614$	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	0.116689	−	0.993168i	$-0.462772\pi$
$617$	27.5683	−	27.5683i	1.10986	−	1.10986i	0.993168	−	0.116689i	$-0.0372281\pi$
$618$	−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	$0.135083\pi$
$631$			20.6862i			0.823504i	−0.911296	+	0.411752i	$0.864917\pi$
$632$	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	−0.558273	−	0.829657i	$-0.688536\pi$
$643$	6.88159	−	6.88159i	0.271384	−	0.271384i	0.829657	+	0.558273i	$0.188536\pi$
$644$	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	$-0.0596715\pi$
$647$	20.2501	+	20.2501i	0.796113	+	0.796113i	−0.186368	+	0.982480i	$0.559672\pi$
$648$	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	0.883219	−	0.468961i	$-0.155372\pi$
$653$	10.5859	+	10.5859i	0.414257	+	0.414257i	−0.468961	+	0.883219i	$0.655372\pi$
$654$	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	0.848881	−	0.528583i	$-0.177277\pi$
$673$	8.30925	+	8.30925i	0.320298	+	0.320298i	−0.528583	+	0.848881i	$0.677277\pi$
$674$	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	−0.674507	−	0.738268i	$-0.735644\pi$
$677$	1.65901	−	1.65901i	0.0637610	−	0.0637610i	0.738268	+	0.674507i	$0.235644\pi$
$678$	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	−0.632161	−	0.774837i	$-0.717832\pi$
$683$	3.72871	−	3.72871i	0.142675	−	0.142675i	0.774837	+	0.632161i	$0.217832\pi$
$684$	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	$-0.995063\pi$
$691$		−	0.815388i		−	0.0310188i	0.999880	−	0.0155094i	$-0.00493700\pi$
$692$	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	$-0.843886\pi$
$709$		−	25.0837i		−	0.942038i	0.882123	−	0.471019i	$-0.156114\pi$
$710$	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	−0.999264	−	0.0383634i	$-0.987786\pi$
$727$	−27.9775	−	27.9775i	−1.03763	−	1.03763i	−0.0383634	−	0.999264i	$-0.512214\pi$
$728$	−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	0.916528	−	0.399970i	$-0.130979\pi$
$733$	13.9853	+	13.9853i	0.516559	+	0.516559i	−0.399970	+	0.916528i	$0.630979\pi$
$734$	−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	−0.620396	−	0.784289i	$-0.713028\pi$
$743$	4.46740	−	4.46740i	0.163893	−	0.163893i	0.784289	+	0.620396i	$0.213028\pi$
$744$	−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	$-0.763166\pi$
$751$		−	37.1200i		−	1.35453i	0.735740	−	0.677264i	$-0.236834\pi$
$752$	−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	−0.301829	−	0.953362i	$-0.597597\pi$
$757$	17.9260	−	17.9260i	0.651533	−	0.651533i	0.953362	+	0.301829i	$0.0975972\pi$
$758$	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	$-0.797197\pi$
$769$		−	32.9935i		−	1.18977i	0.803809	−	0.594887i	$-0.202803\pi$
$770$	−3.40387	−	2.65883i	−0.122667	−	0.0958177i
$771$		−	6.12270i		−	0.220504i
$772$	−3.46309	+	15.2867i	−0.124639	+	0.550182i
$773$	−13.8810	−	13.8810i	−0.499265	−	0.499265i	0.411944	−	0.911209i	$-0.364850\pi$
$773$	−13.8810	−	13.8810i	−0.499265	−	0.499265i	−0.911209	+	0.411944i	$0.864850\pi$
$774$	−9.89422	−	34.2394i	−0.355640	−	1.23071i
$775$	5.33236	+	1.75565i	0.191544	+	0.0630648i
$776$	12.3670	+	10.9979i	0.443948	+	0.394803i
$777$	−1.32311	+	1.32311i	−0.0474663	+	0.0474663i
$778$	25.4250	−	46.0911i	0.911530	−	1.65244i
$779$	−10.4815			−0.375540
$780$	−0.474263	+	1.18117i	−0.0169814	+	0.0422928i
$781$	−27.1172			−0.970330
$782$	−1.35635	+	2.45882i	−0.0485029	+	0.0879274i
$783$	−5.04665	+	5.04665i	−0.180352	+	0.180352i
$784$	24.4917	+	11.6971i	0.874702	+	0.417753i
$785$	−35.7837	−	5.73926i	−1.27718	−	0.204843i
$786$	−1.94320	−	6.72453i	−0.0693115	−	0.239856i
$787$	28.4639	+	28.4639i	1.01463	+	1.01463i	0.999891	+	0.0147356i	$0.00469066\pi$
$787$	28.4639	+	28.4639i	1.01463	+	1.01463i	0.0147356	+	0.999891i	$0.495309\pi$
$788$	16.1681	+	3.66275i	0.575963	+	0.130480i
$789$			8.35948i			0.297605i
$790$	0.0633043	+	0.515137i	0.00225227	+	0.0183277i
$791$			5.98267i			0.212719i
$792$	1.22469	+	20.9016i	0.0435176	+	0.742705i
$793$	2.21385	+	2.21385i	0.0786163	+	0.0786163i
$794$	−15.7865	+	4.56185i	−0.560243	+	0.161894i
$795$	7.35903	+	10.1705i	0.260998	+	0.360712i
$796$	15.7324	+	24.9482i	0.557619	+	0.884266i
$797$	20.8840	−	20.8840i	0.739750	−	0.739750i	−0.232779	−	0.972530i	$-0.574782\pi$
$797$	20.8840	−	20.8840i	0.739750	−	0.739750i	0.972530	+	0.232779i	$0.0747820\pi$
$798$	−0.401264	−	0.221347i	−0.0142046	−	0.00783560i
$799$	−8.96861			−0.317287
$800$	8.44168	+	26.9951i	0.298458	+	0.954423i
$801$	5.71353			0.201878
$802$	−35.4013	−	19.5283i	−1.25006	−	0.689567i
$803$	14.2386	−	14.2386i	0.502468	−	0.502468i
$804$	−10.0379	−	15.9180i	−0.354008	−	0.561383i
$805$	0.489530	+	0.676555i	0.0172537	+	0.0238454i
$806$	−0.620698	+	0.179364i	−0.0218632	+	0.00631783i
$807$	0.743195	+	0.743195i	0.0261617	+	0.0261617i
$808$	−0.762060	−	13.0059i	−0.0268092	−	0.457546i
$809$			23.6436i			0.831266i	0.909532	+	0.415633i	$0.136440\pi$
$809$			23.6436i			0.831266i	−0.909532	+	0.415633i	$0.863560\pi$
$810$	1.86526	+	15.1785i	0.0655387	+	0.533319i
$811$			2.24873i			0.0789635i	0.999220	+	0.0394817i	$0.0125707\pi$
$811$			2.24873i			0.0789635i	−0.999220	+	0.0394817i	$0.987429\pi$
$812$	1.67312	+	0.379031i	0.0587149	+	0.0133014i
$813$	−14.6496	−	14.6496i	−0.513783	−	0.513783i
$814$	−6.68407	−	23.1306i	−0.234277	−	0.810726i
$815$	−32.7796	−	5.25743i	−1.14822	−	0.184160i
$816$	−6.21870	−	2.97002i	−0.217698	−	0.103971i
$817$	−7.09760	+	7.09760i	−0.248314	+	0.248314i
$818$	−5.73828	+	10.4025i	−0.200634	+	0.363715i
$819$	0.473273			0.0165375
$820$	−17.4658	+	43.4994i	−0.609932	+	1.51906i
$821$	−26.4934			−0.924625			−0.462312	−	0.886717i	$-0.652980\pi$
$821$	−26.4934			−0.924625			−0.462312	+	0.886717i	$0.652980\pi$
$822$	−2.92415	+	5.30098i	−0.101991	+	0.184893i
$823$	−34.3245	+	34.3245i	−1.19648	+	1.19648i	−0.221262	+	0.975214i	$0.571018\pi$
$823$	−34.3245	+	34.3245i	−1.19648	+	1.19648i	−0.975214	+	0.221262i	$0.928982\pi$
$824$	−32.3499	−	28.7687i	−1.12696	−	1.00221i
$825$	−9.20581	+	4.64538i	−0.320505	+	0.161732i
$826$	−2.56895	−	8.88998i	−0.0893851	−	0.309322i
$827$	−27.3304	−	27.3304i	−0.950371	−	0.950371i	0.0484541	−	0.998825i	$-0.484571\pi$
$827$	−27.3304	−	27.3304i	−0.950371	−	0.950371i	−0.998825	+	0.0484541i	$0.984571\pi$
$828$	0.894393	−	3.94802i	0.0310823	−	0.137203i
$829$		−	27.1022i		−	0.941297i	−0.882321	−	0.470648i	$-0.844020\pi$
$829$		−	27.1022i		−	0.941297i	0.882321	−	0.470648i	$-0.155980\pi$
$830$	6.98899	+	5.45925i	0.242591	+	0.189493i
$831$			18.0398i			0.625793i
$832$	−2.55481	−	2.01719i	−0.0885720	−	0.0699333i
$833$	11.8180	+	11.8180i	0.409468	+	0.409468i
$834$	−10.8666	+	3.14015i	−0.376281	+	0.108734i
$835$	−8.00242	+	49.8944i	−0.276935	+	1.72667i
$836$	4.98778	−	3.14530i	0.172506	−	0.108782i
$837$	3.06031	−	3.06031i	0.105780	−	0.105780i
$838$	17.7031	+	9.76546i	0.611543	+	0.337342i
$839$	−32.8801			−1.13515			−0.567573	−	0.823323i	$-0.692118\pi$
$839$	−32.8801			−1.13515			−0.567573	+	0.823323i	$0.692118\pi$
$840$	−1.58725	+	1.29644i	−0.0547654	+	0.0447315i
$841$	25.5718			0.881785
$842$	−49.6256	−	27.3747i	−1.71021	−	0.943396i
$843$	8.03613	−	8.03613i	0.276779	−	0.276779i
$844$	5.81994	−	3.67005i	0.200330	−	0.126328i
$845$	23.2506	−	16.8233i	0.799846	−	0.578738i
$846$	12.4206	−	3.58920i	0.427029	−	0.123399i
$847$	−0.755816	−	0.755816i	−0.0259701	−	0.0259701i
$848$	−30.2690	+	10.7016i	−1.03944	+	0.367495i
$849$			6.55891i			0.225101i
$850$	−0.640054	+	17.4050i	−0.0219537	+	0.596987i
$851$			4.65507i			0.159574i
$852$	−2.84284	+	12.5488i	−0.0973940	+	0.429916i
$853$	20.4055	+	20.4055i	0.698672	+	0.698672i	0.964124	−	0.265452i	$-0.0855212\pi$
$853$	20.4055	+	20.4055i	0.698672	+	0.698672i	−0.265452	+	0.964124i	$0.585521\pi$
$854$	1.39947	+	4.84295i	0.0478889	+	0.165722i
$855$	4.54839	−	3.29105i	0.155552	−	0.112551i
$856$	−13.5801	+	15.2706i	−0.464158	+	0.521937i
$857$	2.57518	−	2.57518i	0.0879665	−	0.0879665i	−0.661754	−	0.749721i	$-0.730188\pi$
$857$	2.57518	−	2.57518i	0.0879665	−	0.0879665i	0.749721	+	0.661754i	$0.230188\pi$
$858$	0.573199	−	1.03911i	0.0195687	−	0.0354746i
$859$	−48.7635			−1.66379			−0.831895	−	0.554933i	$-0.812744\pi$
$859$	−48.7635			−1.66379			−0.831895	+	0.554933i	$0.812744\pi$
$860$	17.6287	+	41.2828i	0.601134	+	1.40773i
$861$	−3.39646			−0.115751
$862$	−20.6977	+	37.5213i	−0.704965	+	1.27798i
$863$	−0.809522	+	0.809522i	−0.0275565	+	0.0275565i	−0.720751	−	0.693194i	$-0.756203\pi$
$863$	−0.809522	+	0.809522i	−0.0275565	+	0.0275565i	0.693194	+	0.720751i	$0.256203\pi$
$864$	21.5116	+	3.56552i	0.731839	+	0.121301i
$865$	6.37514	−	39.7484i	0.216761	−	1.35149i
$866$	−2.31434	−	8.00890i	−0.0786445	−	0.272154i
$867$	5.40757	+	5.40757i	0.183651	+	0.183651i
$868$	−1.01459	−	0.229847i	−0.0344373	−	0.00780150i
$869$		−	0.483899i		−	0.0164152i
$870$	2.52112	−	3.22757i	0.0854740	−	0.109425i
$871$		−	5.47352i		−	0.185463i
$872$	−14.7964	+	0.866973i	−0.501071	+	0.0293594i
$873$	−10.3880	−	10.3880i	−0.351582	−	0.351582i
$874$	−1.09526	+	0.316498i	−0.0370477	+	0.0107057i
$875$	4.60107	+	2.37842i	0.155544	+	0.0804054i
$876$	−5.09637	−	8.08177i	−0.172190	−	0.273058i
$877$	−18.6769	+	18.6769i	−0.630676	+	0.630676i	−0.948238	−	0.317562i	$-0.897136\pi$
$877$	−18.6769	+	18.6769i	−0.630676	+	0.630676i	0.317562	+	0.948238i	$0.397136\pi$
$878$	−23.9538	−	13.2135i	−0.808403	−	0.445935i
$879$	−14.2952			−0.482165
$880$	−4.74195	−	25.9409i	−0.159851	−	0.874468i
$881$	−33.9283			−1.14307			−0.571536	−	0.820577i	$-0.693652\pi$
$881$	−33.9283			−1.14307			−0.571536	+	0.820577i	$0.693652\pi$
$882$	−21.0961	−	11.6372i	−0.710344	−	0.391843i
$883$	16.3593	−	16.3593i	0.550535	−	0.550535i	−0.376060	−	0.926595i	$-0.622721\pi$
$883$	16.3593	−	16.3593i	0.550535	−	0.550535i	0.926595	+	0.376060i	$0.122721\pi$
$884$	−1.06918	−	1.69549i	−0.0359603	−	0.0570255i
$885$	−21.8130	−	3.49853i	−0.733236	−	0.117602i
$886$	7.99147	−	2.30931i	0.268479	−	0.0775827i
$887$	−33.6480	−	33.6480i	−1.12979	−	1.12979i	−0.990211	−	0.139579i	$-0.955425\pi$
$887$	−33.6480	−	33.6480i	−1.12979	−	1.12979i	−0.139579	−	0.990211i	$-0.544575\pi$
$888$	−11.4047	+	0.668239i	−0.382716	+	0.0224246i
$889$		−	0.235336i		−	0.00789291i
$890$	−7.14248	+	0.877728i	−0.239417	+	0.0294215i
$891$		−	14.2581i		−	0.477664i
$892$	27.4797	+	6.22530i	0.920087	+	0.208438i
$893$	−2.57471	−	2.57471i	−0.0861592	−	0.0861592i
$894$	3.60122	+	12.4622i	0.120443	+	0.416799i
$895$	4.69158	+	6.48400i	0.156822	+	0.216736i
$896$	−2.03312	−	4.83084i	−0.0679217	−	0.161387i
$897$	−0.162240	+	0.162240i	−0.00541703	+	0.00541703i
$898$	−15.1388	+	27.4441i	−0.505189	+	0.915820i
$899$	2.07890			0.0693352
$900$	−6.07899	−	24.3603i	−0.202633	−	0.812010i
$901$	−19.7695			−0.658618
$902$	21.1093	−	38.2675i	0.702863	−	1.27417i
$903$	−2.29992	+	2.29992i	−0.0765367	+	0.0765367i
$904$	−24.2734	+	27.2949i	−0.807320	+	0.907815i
$905$	−9.70625	−	13.4145i	−0.322647	−	0.445914i
$906$	0.620626	+	2.14771i	0.0206189	+	0.0713529i
$907$	9.92358	+	9.92358i	0.329507	+	0.329507i	0.852399	−	0.522892i	$-0.175147\pi$
$907$	9.92358	+	9.92358i	0.329507	+	0.329507i	−0.522892	+	0.852399i	$0.675147\pi$
$908$	5.27927	−	23.3037i	0.175199	−	0.773361i
$909$			11.5649i			0.383582i
$910$	−0.591639	+	0.0727055i	−0.0196126	+	0.00241016i
$911$		−	32.8155i		−	1.08722i	−0.839337	−	0.543612i	$-0.817056\pi$
$911$		−	32.8155i		−	1.08722i	0.839337	−	0.543612i	$-0.182944\pi$
$912$	−0.932630	−	2.63789i	−0.0308825	−	0.0873494i
$913$	−5.84669	−	5.84669i	−0.193497	−	0.193497i
$914$	−20.8374	+	6.02141i	−0.689240	+	0.199171i
$915$	11.8829	+	1.90587i	0.392838	+	0.0630063i
$916$	14.6167	−	9.21731i	0.482950	−	0.304549i
$917$	2.31794	−	2.31794i	0.0765452	−	0.0765452i
$918$	11.7569	+	6.48540i	0.388036	+	0.214050i
$919$	13.4713			0.444377			0.222188	−	0.975004i	$-0.428680\pi$
$919$	13.4713			0.444377			0.222188	+	0.975004i	$0.428680\pi$
$920$	−0.511575	+	5.07282i	−0.0168661	+	0.167246i
$921$	−11.2424			−0.370450
$922$	7.79668	+	4.30084i	0.256770	+	0.141641i
$923$	−2.64628	+	2.64628i	−0.0871032	+	0.0871032i
$924$	1.61625	−	1.01921i	0.0531708	−	0.0335295i
$925$	13.0071	+	25.7763i	0.427670	+	0.847519i
$926$	−10.7746	+	3.11356i	−0.354077	+	0.102318i
$927$	27.1733	+	27.1733i	0.892489	+	0.892489i
$928$	6.09547	+	8.51756i	0.200094	+	0.279603i
$929$			30.3568i			0.995973i	0.867185	+	0.497987i	$0.165927\pi$
$929$			30.3568i			0.995973i	−0.867185	+	0.497987i	$0.834073\pi$
$930$	−1.52882	+	1.95721i	−0.0501320	+	0.0641796i
$931$			6.78539i			0.222382i
$932$	2.84178	−	12.5442i	0.0930855	−	0.410897i
$933$	15.6464	+	15.6464i	0.512240	+	0.512240i
$934$	−13.1427	−	45.4810i	−0.430042	−	1.48818i
$935$	2.57158	−	16.0336i	0.0840996	−	0.524353i
$936$	2.15923	+	1.92020i	0.0705765	+	0.0627637i
$937$	−27.4311	+	27.4311i	−0.896135	+	0.896135i	−0.995092	−	0.0989565i	$-0.968450\pi$
$937$	−27.4311	+	27.4311i	−0.896135	+	0.896135i	0.0989565	+	0.995092i	$0.468450\pi$
$938$	4.25681	−	7.71686i	0.138990	−	0.251964i
$939$	−4.06762			−0.132742
$940$	−14.9756	+	6.39494i	−0.488451	+	0.208580i
$941$	12.9566			0.422372			0.211186	−	0.977446i	$-0.432267\pi$
$941$	12.9566			0.422372			0.211186	+	0.977446i	$0.432267\pi$
$942$	7.74392	−	14.0384i	0.252311	−	0.457395i
$943$	−5.97484	+	5.97484i	−0.194568	+	0.194568i
$944$	24.3487	−	50.9819i	0.792483	−	1.65932i
$945$	3.23496	−	2.34070i	0.105233	−	0.0761428i
$946$	−11.6187	−	40.2072i	−0.377757	−	1.30725i
$947$	−22.3305	−	22.3305i	−0.725642	−	0.725642i	0.244106	−	0.969748i	$-0.421505\pi$
$947$	−22.3305	−	22.3305i	−0.725642	−	0.725642i	−0.969748	+	0.244106i	$0.921505\pi$
$948$	−0.223930	−	0.0507296i	−0.00727292	−	0.00164762i
$949$		−	2.77899i		−	0.0902097i
$950$	−5.18037	+	4.81288i	−0.168073	+	0.156150i
$951$		−	21.1391i		−	0.685483i
$952$	−0.188782	−	3.22190i	−0.00611846	−	0.104422i
$953$	1.79070	+	1.79070i	0.0580064	+	0.0580064i	0.735515	−	0.677509i	$-0.236940\pi$
$953$	1.79070	+	1.79070i	0.0580064	+	0.0580064i	−0.677509	+	0.735515i	$0.736940\pi$
$954$	27.3787	−	7.91167i	0.886420	−	0.256150i
$955$	7.48033	−	5.41249i	0.242058	−	0.175144i
$956$	24.6400	+	39.0739i	0.796915	+	1.26374i
$957$	−2.70005	+	2.70005i	−0.0872801	+	0.0872801i
$958$	−15.8507	−	8.74367i	−0.512114	−	0.282495i
$959$	−2.83520			−0.0915533
$960$	−12.5016	−	0.525125i	−0.403487	−	0.0169483i
$961$	29.7393			0.959334
$962$	−2.90951	−	1.60496i	−0.0938063	−	0.0517459i
$963$	12.8270	−	12.8270i	0.413344	−	0.413344i
$964$	21.1677	+	33.5676i	0.681766	+	1.08114i
$965$	−2.77519	+	17.3030i	−0.0893364	+	0.557004i
$966$	−0.354910	+	0.102559i	−0.0114190	+	0.00329978i
$967$	−11.6241	−	11.6241i	−0.373807	−	0.373807i	0.495055	−	0.868862i	$-0.335148\pi$
$967$	−11.6241	−	11.6241i	−0.373807	−	0.373807i	−0.868862	+	0.495055i	$0.835148\pi$
$968$	−0.381726	−	6.51483i	−0.0122691	−	0.209395i
$969$		−	1.72288i		−	0.0553470i
$970$	14.5819	+	11.3903i	0.468198	+	0.365719i
$971$		−	16.0160i		−	0.513977i	−0.966415	−	0.256988i	$-0.917270\pi$
$971$		−	16.0160i		−	0.513977i	0.966415	−	0.256988i	$-0.0827302\pi$
$972$	−29.1543	−	6.60468i	−0.935125	−	0.211845i
$973$	−3.74573	−	3.74573i	−0.120082	−	0.120082i
$974$	−5.96973	−	20.6586i	−0.191282	−	0.661943i
$975$	−0.445036	+	1.35169i	−0.0142526	+	0.0432887i
$976$	−13.2643	+	27.7731i	−0.424580	+	0.888996i
$977$	10.3212	−	10.3212i	0.330205	−	0.330205i	−0.522459	−	0.852664i	$-0.674985\pi$
$977$	10.3212	−	10.3212i	0.330205	−	0.330205i	0.852664	+	0.522459i	$0.174985\pi$
$978$	7.09379	−	12.8598i	0.226834	−	0.411211i
$979$	6.70937			0.214432
$980$	28.1600	+	11.3068i	0.899539	+	0.361181i
$981$	13.1570			0.420071
$982$	−26.8253	+	48.6296i	−0.856031	+	1.55183i
$983$	−20.0695	+	20.0695i	−0.640119	+	0.640119i	−0.950585	−	0.310466i	$-0.899515\pi$
$983$	−20.0695	+	20.0695i	−0.640119	+	0.640119i	0.310466	+	0.950585i	$0.399515\pi$
$984$	−15.4958	−	13.7804i	−0.493987	−	0.439302i
$985$	18.3006	+	2.93519i	0.583106	+	0.0935228i
$986$	1.79049	+	6.19609i	0.0570209	+	0.197324i
$987$	−0.834314	−	0.834314i	−0.0265565	−	0.0265565i
$988$	0.179802	−	0.793679i	0.00572025	−	0.0252503i
$989$			8.09177i			0.257303i
$990$	2.85518	+	23.2340i	0.0907437	+	0.738424i
$991$		−	59.6794i		−	1.89578i	−0.318599	−	0.947890i	$-0.603212\pi$
$991$		−	59.6794i		−	1.89578i	0.318599	−	0.947890i	$-0.396788\pi$
$992$	−3.69632	−	5.16509i	−0.117358	−	0.163992i
$993$	14.2518	+	14.2518i	0.452266	+	0.452266i
$994$	−5.78890	+	1.67282i	−0.183613	+	0.0530588i
$995$	19.3305	+	26.7158i	0.612819	+	0.846947i
$996$	−3.31857	+	2.09269i	−0.105153	+	0.0663094i
$997$	−8.77680	+	8.77680i	−0.277964	+	0.277964i	−0.832296	−	0.554332i	$-0.812974\pi$
$997$	−8.77680	+	8.77680i	−0.277964	+	0.277964i	0.554332	+	0.832296i	$0.312974\pi$
$998$	44.3953	+	24.4896i	1.40531	+	0.775204i
$999$	22.2583			0.704221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.d.343.5	yes	52
4.3	odd	2		380.2.k.c.343.19	yes	52
5.2	odd	4		380.2.k.c.267.19	✓	52
20.7	even	4	inner	380.2.k.d.267.5	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.19	✓	52	5.2	odd	4
380.2.k.c.343.19	yes	52	4.3	odd	2
380.2.k.d.267.5	yes	52	20.7	even	4	inner
380.2.k.d.343.5	yes	52	1.1	even	1	trivial

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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