LMFDB - Embedded newform 380.2.k.d.267.3

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			267.3
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34889 - 0.424847i) q^{2} +(-2.38733 - 2.38733i) q^{3} +(1.63901 + 1.14614i) q^{4} +(-2.23504 - 0.0679064i) q^{5} +(2.20600 + 4.23450i) q^{6} +(-0.160827 + 0.160827i) q^{7} +(-1.72391 - 2.24235i) q^{8} +8.39872i q^{9} +O(q^{10})$	\(q+(-1.34889 - 0.424847i) q^{2} +(-2.38733 - 2.38733i) q^{3} +(1.63901 + 1.14614i) q^{4} +(-2.23504 - 0.0679064i) q^{5} +(2.20600 + 4.23450i) q^{6} +(-0.160827 + 0.160827i) q^{7} +(-1.72391 - 2.24235i) q^{8} +8.39872i q^{9} +(2.98597 + 1.04115i) q^{10} -1.27667i q^{11} +(-1.17663 - 6.64909i) q^{12} +(-2.46886 + 2.46886i) q^{13} +(0.285264 - 0.148611i) q^{14} +(5.17366 + 5.49789i) q^{15} +(1.37271 + 3.75708i) q^{16} +(0.959316 + 0.959316i) q^{17} +(3.56817 - 11.3290i) q^{18} -1.00000 q^{19} +(-3.58542 - 2.67297i) q^{20} +0.767894 q^{21} +(-0.542389 + 1.72209i) q^{22} +(-0.0542050 - 0.0542050i) q^{23} +(-1.23770 + 9.46878i) q^{24} +(4.99078 + 0.303546i) q^{25} +(4.37910 - 2.28133i) q^{26} +(12.8885 - 12.8885i) q^{27} +(-0.447927 + 0.0792659i) q^{28} -7.88865i q^{29} +(-4.64294 - 9.61407i) q^{30} -3.42919i q^{31} +(-0.255442 - 5.65108i) q^{32} +(-3.04783 + 3.04783i) q^{33} +(-0.886449 - 1.70157i) q^{34} +(0.370375 - 0.348533i) q^{35} +(-9.62615 + 13.7656i) q^{36} +(7.17676 + 7.17676i) q^{37} +(1.34889 + 0.424847i) q^{38} +11.7880 q^{39} +(3.70073 + 5.12880i) q^{40} +3.86199 q^{41} +(-1.03580 - 0.326238i) q^{42} +(3.02774 + 3.02774i) q^{43} +(1.46325 - 2.09247i) q^{44} +(0.570327 - 18.7714i) q^{45} +(0.0500878 + 0.0961455i) q^{46} +(-6.79762 + 6.79762i) q^{47} +(5.69231 - 12.2465i) q^{48} +6.94827i q^{49} +(-6.60305 - 2.52977i) q^{50} -4.58041i q^{51} +(-6.87615 + 1.21681i) q^{52} +(3.97772 - 3.97772i) q^{53} +(-22.8609 + 11.9096i) q^{54} +(-0.0866940 + 2.85340i) q^{55} +(0.637881 + 0.0833797i) q^{56} +(2.38733 + 2.38733i) q^{57} +(-3.35147 + 10.6409i) q^{58} -2.19183 q^{59} +(2.17830 + 14.9409i) q^{60} -3.31415 q^{61} +(-1.45688 + 4.62560i) q^{62} +(-1.35074 - 1.35074i) q^{63} +(-2.05628 + 7.73122i) q^{64} +(5.68564 - 5.35034i) q^{65} +(5.40606 - 2.81633i) q^{66} +(-7.49464 + 7.49464i) q^{67} +(0.472813 + 2.67184i) q^{68} +0.258811i q^{69} +(-0.647668 + 0.312779i) q^{70} +13.6649i q^{71} +(18.8329 - 14.4786i) q^{72} +(8.19387 - 8.19387i) q^{73} +(-6.63163 - 12.7297i) q^{74} +(-11.1900 - 12.6393i) q^{75} +(-1.63901 - 1.14614i) q^{76} +(0.205323 + 0.205323i) q^{77} +(-15.9007 - 5.00809i) q^{78} +10.9072 q^{79} +(-2.81292 - 8.49044i) q^{80} -36.3423 q^{81} +(-5.20940 - 1.64075i) q^{82} +(10.4107 + 10.4107i) q^{83} +(1.25859 + 0.880118i) q^{84} +(-2.07896 - 2.20925i) q^{85} +(-2.79776 - 5.37041i) q^{86} +(-18.8328 + 18.8328i) q^{87} +(-2.86274 + 2.20086i) q^{88} +7.73938i q^{89} +(-8.74430 + 25.0783i) q^{90} -0.794117i q^{91} +(-0.0267158 - 0.150969i) q^{92} +(-8.18662 + 8.18662i) q^{93} +(12.0572 - 6.28129i) q^{94} +(2.23504 + 0.0679064i) q^{95} +(-12.8812 + 14.1008i) q^{96} +(5.62142 + 5.62142i) q^{97} +(2.95195 - 9.37245i) q^{98} +10.7224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.34889	−	0.424847i	−0.953809	−	0.300412i
$2$	−1.34889	−	0.424847i	−0.953809	−	0.300412i
$3$	−2.38733	−	2.38733i	−1.37833	−	1.37833i	−0.847446	−	0.530881i	$-0.821861\pi$
$3$	−2.38733	−	2.38733i	−1.37833	−	1.37833i	−0.530881	−	0.847446i	$-0.678139\pi$
$4$	1.63901	+	1.14614i	0.819505	+	0.573072i
$5$	−2.23504	−	0.0679064i	−0.999539	−	0.0303686i
$5$	−2.23504	−	0.0679064i	−0.999539	−	0.0303686i
$6$	2.20600	+	4.23450i	0.900595	+	1.72873i
$7$	−0.160827	+	0.160827i	−0.0607868	+	0.0607868i	−0.736847	−	0.676060i	$-0.763686\pi$
$7$	−0.160827	+	0.160827i	−0.0607868	+	0.0607868i	0.676060	+	0.736847i	$0.263686\pi$
$8$	−1.72391	−	2.24235i	−0.609493	−	0.792791i
$9$			8.39872i			2.79957i
$10$	2.98597	+	1.04115i	0.944246	+	0.329240i
$11$		−	1.27667i		−	0.384930i	−0.981304	−	0.192465i	$-0.938352\pi$
$11$		−	1.27667i		−	0.384930i	0.981304	−	0.192465i	$-0.0616482\pi$
$12$	−1.17663	−	6.64909i	−0.339665	−	1.91943i
$13$	−2.46886	+	2.46886i	−0.684738	+	0.684738i	−0.961064	−	0.276326i	$-0.910883\pi$
$13$	−2.46886	+	2.46886i	−0.684738	+	0.684738i	0.276326	+	0.961064i	$0.410883\pi$
$14$	0.285264	−	0.148611i	0.0762401	−	0.0397179i
$15$	5.17366	+	5.49789i	1.33583	+	1.41955i
$16$	1.37271	+	3.75708i	0.343176	+	0.939271i
$17$	0.959316	+	0.959316i	0.232668	+	0.232668i	0.813806	−	0.581137i	$-0.197392\pi$
$17$	0.959316	+	0.959316i	0.232668	+	0.232668i	−0.581137	+	0.813806i	$0.697392\pi$
$18$	3.56817	−	11.3290i	0.841026	−	2.67026i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−3.58542	−	2.67297i	−0.801723	−	0.597695i
$21$	0.767894			0.167568
$22$	−0.542389	+	1.72209i	−0.115638	+	0.367150i
$23$	−0.0542050	−	0.0542050i	−0.0113025	−	0.0113025i	0.701433	−	0.712735i	$-0.252544\pi$
$23$	−0.0542050	−	0.0542050i	−0.0113025	−	0.0113025i	−0.712735	+	0.701433i	$0.752544\pi$
$24$	−1.23770	+	9.46878i	−0.252644	+	1.93281i
$25$	4.99078	+	0.303546i	0.998155	+	0.0607093i
$26$	4.37910	−	2.28133i	0.858813	−	0.447406i
$27$	12.8885	−	12.8885i	2.48040	−	2.48040i
$28$	−0.447927	+	0.0792659i	−0.0846503	+	0.0149798i
$29$		−	7.88865i		−	1.46489i	−0.680829	−	0.732443i	$-0.738380\pi$
$29$		−	7.88865i		−	1.46489i	0.680829	−	0.732443i	$-0.261620\pi$
$30$	−4.64294	−	9.61407i	−0.847681	−	1.75528i
$31$		−	3.42919i		−	0.615901i	−0.951402	−	0.307950i	$-0.900357\pi$
$31$		−	3.42919i		−	0.615901i	0.951402	−	0.307950i	$-0.0996431\pi$
$32$	−0.255442	−	5.65108i	−0.0451562	−	0.998980i
$33$	−3.04783	+	3.04783i	−0.530560	+	0.530560i
$34$	−0.886449	−	1.70157i	−0.152025	−	0.291818i
$35$	0.370375	−	0.348533i	0.0626048	−	0.0589128i
$36$	−9.62615	+	13.7656i	−1.60436	+	2.29426i
$37$	7.17676	+	7.17676i	1.17985	+	1.17985i	0.979782	+	0.200070i	$0.0641169\pi$
$37$	7.17676	+	7.17676i	1.17985	+	1.17985i	0.200070	+	0.979782i	$0.435883\pi$
$38$	1.34889	+	0.424847i	0.218819	+	0.0689193i
$39$	11.7880			1.88759
$40$	3.70073	+	5.12880i	0.585136	+	0.810935i
$41$	3.86199			0.603141			0.301570	−	0.953444i	$-0.402489\pi$
$41$	3.86199			0.603141			0.301570	+	0.953444i	$0.402489\pi$
$42$	−1.03580	−	0.326238i	−0.159828	−	0.0503396i
$43$	3.02774	+	3.02774i	0.461726	+	0.461726i	0.899221	−	0.437495i	$-0.144134\pi$
$43$	3.02774	+	3.02774i	0.461726	+	0.461726i	−0.437495	+	0.899221i	$0.644134\pi$
$44$	1.46325	−	2.09247i	0.220593	−	0.315452i
$45$	0.570327	−	18.7714i	0.0850193	−	2.79828i
$46$	0.0500878	+	0.0961455i	0.00738504	+	0.0141759i
$47$	−6.79762	+	6.79762i	−0.991534	+	0.991534i	−0.999964	−	0.00843031i	$-0.997317\pi$
$47$	−6.79762	+	6.79762i	−0.991534	+	0.991534i	0.00843031	+	0.999964i	$0.497317\pi$
$48$	5.69231	−	12.2465i	0.821614	−	1.76763i
$49$			6.94827i			0.992610i
$50$	−6.60305	−	2.52977i	−0.933812	−	0.357763i
$51$		−	4.58041i		−	0.641386i
$52$	−6.87615	+	1.21681i	−0.953550	+	0.168742i
$53$	3.97772	−	3.97772i	0.546382	−	0.546382i	−0.379010	−	0.925392i	$-0.623736\pi$
$53$	3.97772	−	3.97772i	0.546382	−	0.546382i	0.925392	+	0.379010i	$0.123736\pi$
$54$	−22.8609	+	11.9096i	−3.11097	+	1.62069i
$55$	−0.0866940	+	2.85340i	−0.0116898	+	0.384753i
$56$	0.637881	+	0.0833797i	0.0852404	+	0.0111421i
$57$	2.38733	+	2.38733i	0.316210	+	0.316210i
$58$	−3.35147	+	10.6409i	−0.440070	+	1.39722i
$59$	−2.19183			−0.285352			−0.142676	−	0.989769i	$-0.545571\pi$
$59$	−2.19183			−0.285352			−0.142676	+	0.989769i	$0.545571\pi$
$60$	2.17830	+	14.9409i	0.281218	+	1.92886i
$61$	−3.31415			−0.424333			−0.212167	−	0.977234i	$-0.568052\pi$
$61$	−3.31415			−0.424333			−0.212167	+	0.977234i	$0.568052\pi$
$62$	−1.45688	+	4.62560i	−0.185024	+	0.587452i
$63$	−1.35074	−	1.35074i	−0.170177	−	0.170177i
$64$	−2.05628	+	7.73122i	−0.257036	+	0.966402i
$65$	5.68564	−	5.35034i	0.705217	−	0.663627i
$66$	5.40606	−	2.81633i	0.665440	−	0.346666i
$67$	−7.49464	+	7.49464i	−0.915616	+	0.915616i	−0.996707	−	0.0810907i	$-0.974160\pi$
$67$	−7.49464	+	7.49464i	−0.915616	+	0.915616i	0.0810907	+	0.996707i	$0.474160\pi$
$68$	0.472813	+	2.67184i	0.0573370	+	0.324009i
$69$			0.258811i			0.0311572i
$70$	−0.647668	+	0.312779i	−0.0774112	+	0.0373843i
$71$			13.6649i			1.62172i	0.585240	+	0.810860i	$0.301000\pi$
$71$			13.6649i			1.62172i	−0.585240	+	0.810860i	$0.699000\pi$
$72$	18.8329	−	14.4786i	2.21948	−	1.70632i
$73$	8.19387	−	8.19387i	0.959020	−	0.959020i	−0.0401727	−	0.999193i	$-0.512791\pi$
$73$	8.19387	−	8.19387i	0.959020	−	0.959020i	0.999193	+	0.0401727i	$0.0127908\pi$
$74$	−6.63163	−	12.7297i	−0.770911	−	1.47980i
$75$	−11.1900	−	12.6393i	−1.29211	−	1.45946i
$76$	−1.63901	−	1.14614i	−0.188007	−	0.131472i
$77$	0.205323	+	0.205323i	0.0233987	+	0.0233987i
$78$	−15.9007	−	5.00809i	−1.80040	−	0.567054i
$79$	10.9072			1.22716			0.613581	−	0.789632i	$-0.289729\pi$
$79$	10.9072			1.22716			0.613581	+	0.789632i	$0.289729\pi$
$80$	−2.81292	−	8.49044i	−0.314494	−	0.949260i
$81$	−36.3423			−4.03804
$82$	−5.20940	−	1.64075i	−0.575281	−	0.181191i
$83$	10.4107	+	10.4107i	1.14272	+	1.14272i	0.987951	+	0.154767i	$0.0494625\pi$
$83$	10.4107	+	10.4107i	1.14272	+	1.14272i	0.154767	+	0.987951i	$0.450537\pi$
$84$	1.25859	+	0.880118i	0.137323	+	0.0960287i
$85$	−2.07896	−	2.20925i	−0.225495	−	0.239627i
$86$	−2.79776	−	5.37041i	−0.301690	−	0.579107i
$87$	−18.8328	+	18.8328i	−2.01909	+	2.01909i
$88$	−2.86274	+	2.20086i	−0.305169	+	0.234612i
$89$			7.73938i			0.820372i	0.912002	+	0.410186i	$0.134536\pi$
$89$			7.73938i			0.820372i	−0.912002	+	0.410186i	$0.865464\pi$
$90$	−8.74430	+	25.0783i	−0.921731	+	2.64349i
$91$		−	0.794117i		−	0.0832461i
$92$	−0.0267158	−	0.150969i	−0.00278531	−	0.0157396i
$93$	−8.18662	+	8.18662i	−0.848913	+	0.848913i
$94$	12.0572	−	6.28129i	1.24360	−	0.647865i
$95$	2.23504	+	0.0679064i	0.229310	+	0.00696705i
$96$	−12.8812	+	14.1008i	−1.31468	+	1.43916i
$97$	5.62142	+	5.62142i	0.570769	+	0.570769i	0.932343	−	0.361574i	$-0.117761\pi$
$97$	5.62142	+	5.62142i	0.570769	+	0.570769i	−0.361574	+	0.932343i	$0.617761\pi$
$98$	2.95195	−	9.37245i	0.298192	−	0.946761i
$99$	10.7224			1.07764
$100$	7.83202	+	6.21767i	0.783202	+	0.621767i
$101$	−7.59386			−0.755617			−0.377809	−	0.925884i	$-0.623322\pi$
$101$	−7.59386			−0.755617			−0.377809	+	0.925884i	$0.623322\pi$
$102$	−1.94598	+	6.17848i	−0.192680	+	0.611760i
$103$	−10.1411	−	10.1411i	−0.999235	−	0.999235i	0.000764420	−	1.00000i	$-0.499757\pi$
$103$	−10.1411	−	10.1411i	−0.999235	−	0.999235i	−1.00000		0.000764420i	$0.999757\pi$
$104$	9.79213	+	1.27996i	0.960197	+	0.125511i
$105$	−1.71627	−	0.0521449i	−0.167491	−	0.00508882i
$106$	−7.05543	+	3.67559i	−0.685284	+	0.357004i
$107$	−3.24223	+	3.24223i	−0.313438	+	0.313438i	−0.846240	−	0.532802i	$-0.821139\pi$
$107$	−3.24223	+	3.24223i	−0.313438	+	0.313438i	0.532802	+	0.846240i	$0.321139\pi$
$108$	35.8966	−	6.35231i	3.45415	−	0.611251i
$109$			8.15239i			0.780857i	0.920633	+	0.390429i	$0.127673\pi$
$109$			8.15239i			0.780857i	−0.920633	+	0.390429i	$0.872327\pi$
$110$	1.32920	−	3.81209i	0.126734	−	0.363469i
$111$		−	34.2666i		−	3.25244i
$112$	−0.825007	−	0.383472i	−0.0779559	−	0.0362347i
$113$	0.730745	−	0.730745i	0.0687427	−	0.0687427i	−0.671900	−	0.740642i	$-0.734521\pi$
$113$	0.730745	−	0.730745i	0.0687427	−	0.0687427i	0.740642	+	0.671900i	$0.234521\pi$
$114$	−2.20600	−	4.23450i	−0.206611	−	0.396597i
$115$	0.117469	+	0.124831i	0.0109541	+	0.0116406i
$116$	9.04153	−	12.9296i	0.839485	−	1.20048i
$117$	−20.7352	−	20.7352i	−1.91697	−	1.91697i
$118$	2.95653	+	0.931192i	0.272171	+	0.0857231i
$119$	−0.308567			−0.0282863
$120$	3.40929	−	21.0790i	0.311225	−	1.92424i
$121$	9.37012			0.851829
$122$	4.47042	+	1.40801i	0.404733	+	0.127475i
$123$	−9.21985	−	9.21985i	−0.831326	−	0.831326i
$124$	3.93035	−	5.62048i	0.352956	−	0.504734i
$125$	−11.1340	−	1.01734i	−0.995851	−	0.0909939i
$126$	1.24814	+	2.39586i	0.111193	+	0.213440i
$127$	−0.256560	+	0.256560i	−0.0227660	+	0.0227660i	−0.718398	−	0.695632i	$-0.755124\pi$
$127$	−0.256560	+	0.256560i	−0.0227660	+	0.0227660i	0.695632	+	0.718398i	$0.255124\pi$
$128$	6.05829	−	9.55495i	0.535482	−	0.844547i
$129$		−	14.4564i		−	1.27282i
$130$	−9.94238	+	4.80149i	−0.872004	+	0.421118i
$131$			3.58694i			0.313392i	0.987647	+	0.156696i	$0.0500843\pi$
$131$			3.58694i			0.313392i	−0.987647	+	0.156696i	$0.949916\pi$
$132$	−8.48869	+	1.50217i	−0.738846	+	0.130747i
$133$	0.160827	−	0.160827i	0.0139455	−	0.0139455i
$134$	13.2935	−	6.92537i	1.14839	−	0.598261i
$135$	−29.6816	+	27.9311i	−2.55458	+	2.40393i
$136$	0.497352	−	3.80490i	0.0426476	−	0.326267i
$137$	11.5928	+	11.5928i	0.990443	+	0.990443i	0.999955	−	0.00951143i	$-0.00302763\pi$
$137$	11.5928	+	11.5928i	0.990443	+	0.990443i	−0.00951143	+	0.999955i	$0.503028\pi$
$138$	0.109955	−	0.349107i	0.00936000	−	0.0297180i
$139$	16.6503			1.41226			0.706128	−	0.708084i	$-0.250440\pi$
$139$	16.6503			1.41226			0.706128	+	0.708084i	$0.250440\pi$
$140$	1.00652	−	0.146745i	0.0850662	−	0.0124022i
$141$	32.4563			2.73332
$142$	5.80548	−	18.4324i	0.487185	−	1.54681i
$143$	3.15191	+	3.15191i	0.263576	+	0.263576i
$144$	−31.5547	+	11.5290i	−2.62956	+	0.960747i
$145$	−0.535690	+	17.6314i	−0.0444866	+	1.46421i
$146$	−14.5338	+	7.57149i	−1.20282	+	0.626621i
$147$	16.5878	−	16.5878i	1.36814	−	1.36814i
$148$	3.53717	+	19.9884i	0.290754	+	1.64303i
$149$		−	2.14843i		−	0.176006i	−0.996120	−	0.0880030i	$-0.971951\pi$
$149$		−	2.14843i		−	0.176006i	0.996120	−	0.0880030i	$-0.0280485\pi$
$150$	9.72428	+	21.8031i	0.793984	+	1.78021i
$151$		−	7.90290i		−	0.643129i	−0.946888	−	0.321564i	$-0.895791\pi$
$151$		−	7.90290i		−	0.643129i	0.946888	−	0.321564i	$-0.104209\pi$
$152$	1.72391	+	2.24235i	0.139827	+	0.181879i
$153$	−8.05703	+	8.05703i	−0.651372	+	0.651372i
$154$	−0.189727	−	0.364188i	−0.0152886	−	0.0293471i
$155$	−0.232864	+	7.66437i	−0.0187041	+	0.615617i
$156$	19.3206	+	13.5107i	1.54689	+	1.08172i
$157$	−0.592648	−	0.592648i	−0.0472984	−	0.0472984i	0.683062	−	0.730360i	$-0.260648\pi$
$157$	−0.592648	−	0.592648i	−0.0472984	−	0.0472984i	−0.730360	+	0.683062i	$0.760648\pi$
$158$	−14.7127	−	4.63392i	−1.17048	−	0.368654i
$159$	−18.9923			−1.50619
$160$	0.187177	+	12.6477i	0.0147977	+	0.999891i
$161$	0.0174352			0.00137409
$162$	49.0218	+	15.4399i	3.85152	+	1.21308i
$163$	−1.63202	−	1.63202i	−0.127830	−	0.127830i	0.640297	−	0.768127i	$-0.278811\pi$
$163$	−1.63202	−	1.63202i	−0.127830	−	0.127830i	−0.768127	+	0.640297i	$0.778811\pi$
$164$	6.32983	+	4.42639i	0.494277	+	0.345643i
$165$	7.01899	−	6.60505i	0.546428	−	0.514203i
$166$	−9.61989	−	18.4658i	−0.746648	−	1.43322i
$167$	−9.18170	+	9.18170i	−0.710501	+	0.710501i	−0.966640	−	0.256139i	$-0.917550\pi$
$167$	−9.18170	+	9.18170i	−0.710501	+	0.710501i	0.256139	+	0.966640i	$0.417550\pi$
$168$	−1.32378	−	1.72189i	−0.102132	−	0.132847i
$169$			0.809487i			0.0622682i
$170$	1.86570	+	3.86328i	0.143093	+	0.296300i
$171$		−	8.39872i		−	0.642266i
$172$	1.49227	+	8.43272i	0.113784	+	0.642989i
$173$	−3.89271	+	3.89271i	−0.295957	+	0.295957i	−0.839428	−	0.543471i	$-0.817110\pi$
$173$	−3.89271	+	3.89271i	−0.295957	+	0.295957i	0.543471	+	0.839428i	$0.317110\pi$
$174$	33.4045	−	17.4024i	2.53239	−	1.31927i
$175$	−0.851469	+	0.753832i	−0.0643650	+	0.0569844i
$176$	4.79655	−	1.75249i	0.361554	−	0.132099i
$177$	5.23262	+	5.23262i	0.393308	+	0.393308i
$178$	3.28805	−	10.4396i	0.246450	−	0.782479i
$179$	6.93200			0.518122			0.259061	−	0.965861i	$-0.416587\pi$
$179$	6.93200			0.518122			0.259061	+	0.965861i	$0.416587\pi$
$180$	22.4496	−	30.1129i	1.67329	−	2.24448i
$181$	−10.8214			−0.804346			−0.402173	−	0.915564i	$-0.631745\pi$
$181$	−10.8214			−0.804346			−0.402173	+	0.915564i	$0.631745\pi$
$182$	−0.337378	+	1.07118i	−0.0250081	+	0.0794009i
$183$	7.91197	+	7.91197i	0.584870	+	0.584870i
$184$	−0.0281023	+	0.214991i	−0.00207173	+	0.0158494i
$185$	−15.5530	−	16.5277i	−1.14348	−	1.21514i
$186$	14.5209	−	7.56479i	1.06473	−	0.554677i
$187$	1.22473	−	1.22473i	0.0895611	−	0.0895611i
$188$	−18.9324	+	3.35031i	−1.38079	+	0.244346i
$189$			4.14565i			0.301551i
$190$	−2.98597	−	1.04115i	−0.216625	−	0.0755328i
$191$		−	7.21749i		−	0.522239i	−0.965306	−	0.261120i	$-0.915908\pi$
$191$		−	7.21749i		−	0.522239i	0.965306	−	0.261120i	$-0.0840917\pi$
$192$	23.3660	−	13.5480i	1.68630	−	0.977739i
$193$	1.46141	−	1.46141i	0.105195	−	0.105195i	−0.652550	−	0.757745i	$-0.726301\pi$
$193$	1.46141	−	1.46141i	0.105195	−	0.105195i	0.757745	+	0.652550i	$0.226301\pi$
$194$	−5.19443	−	9.97092i	−0.372939	−	0.715871i
$195$	−26.3465	−	0.800478i	−1.88672	−	0.0573234i
$196$	−7.96372	+	11.3883i	−0.568837	+	0.813449i
$197$	14.9281	+	14.9281i	1.06358	+	1.06358i	0.997837	+	0.0657442i	$0.0209421\pi$
$197$	14.9281	+	14.9281i	1.06358	+	1.06358i	0.0657442	+	0.997837i	$0.479058\pi$
$198$	−14.4633	−	4.55538i	−1.02786	−	0.323736i
$199$	−0.900066			−0.0638040			−0.0319020	−	0.999491i	$-0.510156\pi$
$199$	−0.900066			−0.0638040			−0.0319020	+	0.999491i	$0.510156\pi$
$200$	−7.92298	−	11.7144i	−0.560239	−	0.828331i
$201$	35.7844			2.52404
$202$	10.2433	+	3.22623i	0.720715	+	0.226997i
$203$	1.26871	+	1.26871i	0.0890457	+	0.0890457i
$204$	5.24982	−	7.50734i	0.367561	−	0.525619i
$205$	−8.63168	−	0.262253i	−0.602863	−	0.0183166i
$206$	9.37084	+	17.9877i	0.652897	+	1.25326i
$207$	0.455253	−	0.455253i	0.0316423	−	0.0316423i
$208$	−12.6647	−	5.88669i	−0.878140	−	0.408169i
$209$			1.27667i			0.0883090i
$210$	2.29291	+	0.799491i	0.158226	+	0.0551701i
$211$			21.3747i			1.47149i	0.677256	+	0.735747i	$0.263169\pi$
$211$			21.3747i			1.47149i	−0.677256	+	0.735747i	$0.736831\pi$
$212$	11.0786	−	1.96048i	0.760879	−	0.134646i
$213$	32.6226	−	32.6226i	2.23526	−	2.23526i
$214$	5.75086	−	2.99596i	0.393121	−	0.204799i
$215$	−6.56151	−	6.97271i	−0.447491	−	0.475535i
$216$	−51.1193	−	6.68199i	−3.47823	−	0.454652i
$217$	0.551506	+	0.551506i	0.0374386	+	0.0374386i
$218$	3.46352	−	10.9967i	0.234579	−	0.744789i
$219$	−39.1230			−2.64369
$220$	−3.41250	+	4.57739i	−0.230071	+	0.308608i
$221$	−4.73683			−0.318634
$222$	−14.5581	+	46.2219i	−0.977074	+	3.10221i
$223$	−2.10250	−	2.10250i	−0.140794	−	0.140794i	0.633197	−	0.773991i	$-0.281742\pi$
$223$	−2.10250	−	2.10250i	−0.140794	−	0.140794i	−0.773991	+	0.633197i	$0.781742\pi$
$224$	0.949927	+	0.867764i	0.0634697	+	0.0579799i
$225$	−2.54940	+	41.9161i	−0.169960	+	2.79441i
$226$	−1.29615	+	0.675240i	−0.0862186	+	0.0449163i
$227$	6.53500	−	6.53500i	0.433743	−	0.433743i	−0.456156	−	0.889900i	$-0.650774\pi$
$227$	6.53500	−	6.53500i	0.433743	−	0.433743i	0.889900	+	0.456156i	$0.150774\pi$
$228$	1.17663	+	6.64909i	0.0779244	+	0.440347i
$229$		−	8.38136i		−	0.553856i	−0.960891	−	0.276928i	$-0.910684\pi$
$229$		−	8.38136i		−	0.553856i	0.960891	−	0.276928i	$-0.0893164\pi$
$230$	−0.105419	−	0.218290i	−0.00695113	−	0.0143936i
$231$		−	0.980347i		−	0.0645021i
$232$	−17.6891	+	13.5993i	−1.16135	+	0.892838i
$233$	−0.208004	+	0.208004i	−0.0136268	+	0.0136268i	−0.713887	−	0.700261i	$-0.753067\pi$
$233$	−0.208004	+	0.208004i	−0.0136268	+	0.0136268i	0.700261	+	0.713887i	$0.253067\pi$
$234$	19.1603	+	36.7789i	1.25254	+	2.40431i
$235$	15.6545	−	14.7313i	1.02119	−	0.960965i
$236$	−3.59243	−	2.51215i	−0.233847	−	0.163527i
$237$	−26.0392	−	26.0392i	−1.69143	−	1.69143i
$238$	0.416224	+	0.131094i	0.0269798	+	0.00849756i
$239$	−10.5978			−0.685512			−0.342756	−	0.939425i	$-0.611360\pi$
$239$	−10.5978			−0.685512			−0.342756	+	0.939425i	$0.611360\pi$
$240$	−13.5541	+	26.9849i	−0.874915	+	1.74187i
$241$	−14.4100			−0.928231			−0.464115	−	0.885775i	$-0.653628\pi$
$241$	−14.4100			−0.928231			−0.464115	+	0.885775i	$0.653628\pi$
$242$	−12.6393	−	3.98087i	−0.812482	−	0.255900i
$243$	48.0956	+	48.0956i	3.08534	+	3.08534i
$244$	−5.43192	−	3.79849i	−0.347743	−	0.243174i
$245$	0.471832	−	15.5296i	0.0301442	−	0.992152i
$246$	8.51954	+	16.3536i	0.543186	+	1.04267i
$247$	2.46886	−	2.46886i	0.157090	−	0.157090i
$248$	−7.68945	+	5.91161i	−0.488281	+	0.375387i
$249$		−	49.7074i		−	3.15008i
$250$	14.5863	+	6.10252i	0.922517	+	0.385957i
$251$		−	13.7214i		−	0.866086i	−0.901373	−	0.433043i	$-0.857440\pi$
$251$		−	13.7214i		−	0.866086i	0.901373	−	0.433043i	$-0.142560\pi$
$252$	−0.665732	−	3.76202i	−0.0419372	−	0.236985i
$253$	−0.0692019	+	0.0692019i	−0.00435068	+	0.00435068i
$254$	0.455070	−	0.237072i	0.0285536	−	0.0148752i
$255$	−0.311039	+	10.2374i	−0.0194780	+	0.641090i
$256$	−12.2314	+	10.3147i	−0.764460	+	0.644671i
$257$	−8.06572	−	8.06572i	−0.503126	−	0.503126i	0.409282	−	0.912408i	$-0.365779\pi$
$257$	−8.06572	−	8.06572i	−0.503126	−	0.503126i	−0.912408	+	0.409282i	$0.865779\pi$
$258$	−6.14178	+	19.5002i	−0.382371	+	1.21403i
$259$	−2.30843			−0.143439
$260$	15.4511	−	2.25269i	0.958235	−	0.139706i
$261$	66.2546			4.10105
$262$	1.52390	−	4.83839i	0.0941469	−	0.298916i
$263$	−2.37761	−	2.37761i	−0.146610	−	0.146610i	0.629992	−	0.776602i	$-0.283058\pi$
$263$	−2.37761	−	2.37761i	−0.146610	−	0.146610i	−0.776602	+	0.629992i	$0.783058\pi$
$264$	12.0885	+	1.58013i	0.743996	+	0.0972504i
$265$	−9.16047	+	8.62024i	−0.562723	+	0.529537i
$266$	−0.285264	+	0.148611i	−0.0174907	+	0.00911192i
$267$	18.4765	−	18.4765i	1.13074	−	1.13074i
$268$	−20.8737	+	3.69385i	−1.27507	+	0.225638i
$269$			23.8777i			1.45585i	0.685656	+	0.727926i	$0.259515\pi$
$269$			23.8777i			1.45585i	−0.685656	+	0.727926i	$0.740485\pi$
$270$	51.9037	−	25.0659i	3.15876	−	1.52546i
$271$			2.92804i			0.177866i	0.996038	+	0.0889329i	$0.0283457\pi$
$271$			2.92804i			0.177866i	−0.996038	+	0.0889329i	$0.971654\pi$
$272$	−2.28737	+	4.92109i	−0.138692	+	0.298385i
$273$	−1.89582	+	1.89582i	−0.114740	+	0.114740i
$274$	−10.7123	−	20.5627i	−0.647153	−	1.24224i
$275$	0.387528	−	6.37157i	0.0233688	−	0.384220i
$276$	−0.296635	+	0.424194i	−0.0178553	+	0.0255335i
$277$	−10.0172	−	10.0172i	−0.601873	−	0.601873i	0.338936	−	0.940809i	$-0.389933\pi$
$277$	−10.0172	−	10.0172i	−0.601873	−	0.601873i	−0.940809	+	0.338936i	$0.889933\pi$
$278$	−22.4594	−	7.07382i	−1.34702	−	0.424259i
$279$	28.8008			1.72426
$280$	−1.42002	−	0.229673i	−0.0848627	−	0.0137256i
$281$	4.26038			0.254153			0.127077	−	0.991893i	$-0.459441\pi$
$281$	4.26038			0.254153			0.127077	+	0.991893i	$0.459441\pi$
$282$	−43.7800	−	13.7890i	−2.60706	−	0.821122i
$283$	−11.8818	−	11.8818i	−0.706298	−	0.706298i	0.259457	−	0.965755i	$-0.416457\pi$
$283$	−11.8818	−	11.8818i	−0.706298	−	0.706298i	−0.965755	+	0.259457i	$0.916457\pi$
$284$	−15.6619	+	22.3968i	−0.929363	+	1.32901i
$285$	−5.17366	−	5.49789i	−0.306461	−	0.325667i
$286$	−2.91250	−	5.59067i	−0.172220	−	0.330583i
$287$	−0.621111	+	0.621111i	−0.0366630	+	0.0366630i
$288$	47.4619	−	2.14538i	2.79672	−	0.126418i
$289$		−	15.1594i		−	0.891731i
$290$	8.21325	−	23.5553i	0.482299	−	1.38321i
$291$		−	26.8404i		−	1.57341i
$292$	22.8212	−	4.03847i	1.33551	−	0.236334i
$293$	−7.64975	+	7.64975i	−0.446903	+	0.446903i	−0.894324	−	0.447421i	$-0.852343\pi$
$293$	−7.64975	+	7.64975i	−0.446903	+	0.446903i	0.447421	+	0.894324i	$0.352343\pi$
$294$	−29.4225	+	15.3279i	−1.71595	+	0.893940i
$295$	4.89881	+	0.148839i	0.285220	+	0.00866574i
$296$	3.72075	−	28.4649i	0.216264	−	1.65449i
$297$	−16.4544	−	16.4544i	−0.954781	−	0.954781i
$298$	−0.912753	+	2.89799i	−0.0528744	+	0.167876i
$299$	0.267649			0.0154785
$300$	−3.85401	−	33.5413i	−0.222511	−	1.93651i
$301$	−0.973883			−0.0561337
$302$	−3.35752	+	10.6601i	−0.193204	+	0.613422i
$303$	18.1291	+	18.1291i	1.04149	+	1.04149i
$304$	−1.37271	−	3.75708i	−0.0787300	−	0.215484i
$305$	7.40724	+	0.225052i	0.424137	+	0.0128864i
$306$	14.2910	−	7.44504i	0.816965	−	0.425605i
$307$	−6.24802	+	6.24802i	−0.356593	+	0.356593i	−0.862556	−	0.505962i	$-0.831137\pi$
$307$	−6.24802	+	6.24802i	−0.356593	+	0.356593i	0.505962	+	0.862556i	$0.331137\pi$
$308$	0.101196	+	0.571855i	0.00576620	+	0.0325845i
$309$			48.4205i			2.75455i
$310$	3.57029	−	10.2395i	0.202779	−	0.581562i
$311$			14.6784i			0.832335i	0.909288	+	0.416168i	$0.136627\pi$
$311$			14.6784i			0.832335i	−0.909288	+	0.416168i	$0.863373\pi$
$312$	−20.3214	−	26.4328i	−1.15047	−	1.49646i
$313$	7.75450	−	7.75450i	0.438310	−	0.438310i	−0.453133	−	0.891443i	$-0.649694\pi$
$313$	7.75450	−	7.75450i	0.438310	−	0.438310i	0.891443	+	0.453133i	$0.149694\pi$
$314$	0.547632	+	1.05120i	0.0309047	+	0.0593227i
$315$	2.92723	+	3.11067i	0.164931	+	0.175267i
$316$	17.8771	+	12.5013i	1.00566	+	0.703252i
$317$	−14.1160	−	14.1160i	−0.792835	−	0.792835i	0.189119	−	0.981954i	$-0.439437\pi$
$317$	−14.1160	−	14.1160i	−0.792835	−	0.792835i	−0.981954	+	0.189119i	$0.939437\pi$
$318$	25.6185	+	8.06882i	1.43662	+	0.452477i
$319$	−10.0712			−0.563879
$320$	5.12087	−	17.1399i	0.286265	−	0.958150i
$321$	15.4806			0.864040
$322$	−0.0235182	−	0.00740731i	−0.00131062	−	0.000412793i
$323$	−0.959316	−	0.959316i	−0.0533778	−	0.0533778i
$324$	−59.5654	−	41.6536i	−3.30919	−	2.31409i
$325$	−13.0709	+	11.5721i	−0.725045	+	0.641905i
$326$	1.50806	+	2.89477i	0.0835235	+	0.160327i
$327$	19.4625	−	19.4625i	1.07628	−	1.07628i
$328$	−6.65771	−	8.65993i	−0.367610	−	0.478165i
$329$		−	2.18648i		−	0.120544i
$330$	−12.2740	+	5.92749i	−0.675661	+	0.326298i
$331$			6.99692i			0.384585i	0.981338	+	0.192293i	$0.0615923\pi$
$331$			6.99692i			0.384585i	−0.981338	+	0.192293i	$0.938408\pi$
$332$	5.13105	+	28.9953i	0.281603	+	1.59132i
$333$	−60.2756	+	60.2756i	−3.30308	+	3.30308i
$334$	16.2859	−	8.48429i	0.891126	−	0.464240i
$335$	17.2597	−	16.2419i	0.943000	−	0.887388i
$336$	1.05409	+	2.88504i	0.0575055	+	0.157392i
$337$	−17.3481	−	17.3481i	−0.945013	−	0.945013i	0.0535524	−	0.998565i	$-0.482946\pi$
$337$	−17.3481	−	17.3481i	−0.945013	−	0.945013i	−0.998565	+	0.0535524i	$0.982946\pi$
$338$	0.343908	−	1.09191i	0.0187061	−	0.0593920i
$339$	−3.48907			−0.189500
$340$	−0.875320	−	6.00377i	−0.0474709	−	0.325600i
$341$	−4.37794			−0.237079
$342$	−3.56817	+	11.3290i	−0.192945	+	0.612599i
$343$	−2.24326	−	2.24326i	−0.121124	−	0.121124i
$344$	1.56971	−	12.0088i	0.0846333	−	0.647471i
$345$	0.0175749	−	0.578452i	0.000946201	−	0.0311428i
$346$	6.90465	−	3.59703i	0.371196	−	0.193378i
$347$	−13.9082	+	13.9082i	−0.746632	+	0.746632i	−0.973845	−	0.227213i	$-0.927039\pi$
$347$	−13.9082	+	13.9082i	−0.746632	+	0.746632i	0.227213	+	0.973845i	$0.427039\pi$
$348$	−52.4524	+	9.28205i	−2.81174	+	0.497570i
$349$			21.1583i			1.13258i	0.824207	+	0.566289i	$0.191621\pi$
$349$			21.1583i			1.13258i	−0.824207	+	0.566289i	$0.808379\pi$
$350$	1.46880	−	0.655093i	0.0785108	−	0.0350162i
$351$			63.6399i			3.39685i
$352$	−7.21456	+	0.326115i	−0.384538	+	0.0173820i
$353$	8.12686	−	8.12686i	0.432549	−	0.432549i	−0.456946	−	0.889495i	$-0.651057\pi$
$353$	8.12686	−	8.12686i	0.432549	−	0.432549i	0.889495	+	0.456946i	$0.151057\pi$
$354$	−4.83517	−	9.28130i	−0.256986	−	0.493295i
$355$	0.927931	−	30.5415i	0.0492495	−	1.62097i
$356$	−8.87044	+	12.6849i	−0.470133	+	0.672299i
$357$	0.736653	+	0.736653i	0.0389878	+	0.0389878i
$358$	−9.35051	−	2.94504i	−0.494190	−	0.155650i
$359$	14.2215			0.750583			0.375292	−	0.926907i	$-0.377543\pi$
$359$	14.2215			0.750583			0.375292	+	0.926907i	$0.377543\pi$
$360$	−43.0754	+	31.0814i	−2.27027	+	1.63813i
$361$	1.00000			0.0526316
$362$	14.5968	+	4.59743i	0.767193	+	0.241636i
$363$	−22.3696	−	22.3696i	−1.17410	−	1.17410i
$364$	0.910173	−	1.30156i	0.0477060	−	0.0682205i
$365$	−18.8700	+	17.7572i	−0.987702	+	0.929454i
$366$	−7.31100	−	14.0338i	−0.382152	−	0.733557i
$367$	−10.0322	+	10.0322i	−0.523679	+	0.523679i	−0.918680	−	0.395002i	$-0.870744\pi$
$367$	−10.0322	+	10.0322i	−0.523679	+	0.523679i	0.395002	+	0.918680i	$0.370744\pi$
$368$	0.129245	−	0.278060i	0.00673738	−	0.0144949i
$369$			32.4357i			1.68854i
$370$	13.9575	+	28.9016i	0.725616	+	1.50252i
$371$			1.27945i			0.0664256i
$372$	−22.8010	+	4.03490i	−1.18218	+	0.209200i
$373$	−6.35722	+	6.35722i	−0.329164	+	0.329164i	−0.852269	−	0.523104i	$-0.824774\pi$
$373$	−6.35722	+	6.35722i	−0.329164	+	0.329164i	0.523104	+	0.852269i	$0.324774\pi$
$374$	−2.17235	+	1.13170i	−0.112329	+	0.0585189i
$375$	24.1517	+	29.0092i	1.24719	+	1.49803i
$376$	26.9611	+	3.52418i	1.39041	+	0.181746i
$377$	19.4760	+	19.4760i	1.00306	+	1.00306i
$378$	1.76127	−	5.59202i	0.0905897	−	0.287622i
$379$	−7.89329			−0.405451			−0.202725	−	0.979236i	$-0.564980\pi$
$379$	−7.89329			−0.405451			−0.202725	+	0.979236i	$0.564980\pi$
$380$	3.58542	+	2.67297i	0.183928	+	0.137121i
$381$	1.22499			0.0627580
$382$	−3.06633	+	9.73560i	−0.156887	+	0.498117i
$383$	7.46245	+	7.46245i	0.381313	+	0.381313i	0.871575	−	0.490262i	$-0.163099\pi$
$383$	7.46245	+	7.46245i	0.381313	+	0.381313i	−0.490262	+	0.871575i	$0.663099\pi$
$384$	−37.2740	+	8.34771i	−1.90213	+	0.425992i
$385$	−0.444961	−	0.472846i	−0.0226773	−	0.0240985i
$386$	−2.59216	+	1.35041i	−0.131938	+	0.0687339i
$387$	−25.4291	+	25.4291i	−1.29264	+	1.29264i
$388$	2.77060	+	15.6565i	0.140656	+	0.794840i
$389$			22.7018i			1.15102i	0.817793	+	0.575512i	$0.195197\pi$
$389$			22.7018i			1.15102i	−0.817793	+	0.575512i	$0.804803\pi$
$390$	35.1985	+	12.2730i	1.78235	+	0.621468i
$391$		−	0.103999i		−	0.00525948i
$392$	15.5805	−	11.9782i	0.786932	−	0.604989i
$393$	8.56322	−	8.56322i	0.431957	−	0.431957i
$394$	−13.7942	−	26.4785i	−0.694941	−	1.33397i
$395$	−24.3781	−	0.740672i	−1.22660	−	0.0372672i
$396$	17.5741	+	12.2894i	0.883131	+	0.617566i
$397$	12.3412	+	12.3412i	0.619389	+	0.619389i	0.945375	−	0.325986i	$-0.105696\pi$
$397$	12.3412	+	12.3412i	0.619389	+	0.619389i	−0.325986	+	0.945375i	$0.605696\pi$
$398$	1.21409	+	0.382390i	0.0608568	+	0.0191675i
$399$	−0.767894			−0.0384428
$400$	5.71042	+	19.1675i	0.285521	+	0.958373i
$401$	−24.8121			−1.23906			−0.619529	−	0.784974i	$-0.712676\pi$
$401$	−24.8121			−1.23906			−0.619529	+	0.784974i	$0.712676\pi$
$402$	−48.2692	−	15.2029i	−2.40745	−	0.758252i
$403$	8.46618	+	8.46618i	0.421731	+	0.421731i
$404$	−12.4464	−	8.70366i	−0.619232	−	0.433023i
$405$	81.2264	+	2.46788i	4.03617	+	0.122630i
$406$	−1.17234	−	2.25035i	−0.0581822	−	0.111683i
$407$	9.16234	−	9.16234i	0.454160	−	0.454160i
$408$	−10.2709	+	7.89621i	−0.508485	+	0.390921i
$409$		−	6.90477i		−	0.341419i	−0.985321	−	0.170709i	$-0.945394\pi$
$409$		−	6.90477i		−	0.341419i	0.985321	−	0.170709i	$-0.0546059\pi$
$410$	11.5318	+	4.02090i	0.569514	+	0.198578i
$411$		−	55.3520i		−	2.73031i
$412$	−4.99821	−	28.2446i	−0.246244	−	1.39151i
$413$	0.352504	−	0.352504i	0.0173456	−	0.0173456i
$414$	−0.807499	+	0.420673i	−0.0396864	+	0.0206750i
$415$	−22.5612	−	23.9751i	−1.10749	−	1.17689i
$416$	14.5824	+	13.3211i	0.714959	+	0.653119i
$417$	−39.7497	−	39.7497i	−1.94655	−	1.94655i
$418$	0.542389	−	1.72209i	0.0265291	−	0.0842300i
$419$	−29.8227			−1.45693			−0.728467	−	0.685081i	$-0.759767\pi$
$419$	−29.8227			−1.45693			−0.728467	+	0.685081i	$0.759767\pi$
$420$	−2.75322	−	2.05256i	−0.134343	−	0.100155i
$421$	8.57883			0.418107			0.209053	−	0.977904i	$-0.432962\pi$
$421$	8.57883			0.418107			0.209053	+	0.977904i	$0.432962\pi$
$422$	9.08098	−	28.8321i	0.442055	−	1.40353i
$423$	−57.0913	−	57.0913i	−2.77587	−	2.77587i
$424$	−15.7767	−	2.06223i	−0.766183	−	0.100151i
$425$	4.49654	+	5.07893i	0.218114	+	0.246364i
$426$	−57.8639	+	30.1447i	−2.80351	+	1.46051i
$427$	0.533004	−	0.533004i	0.0257939	−	0.0257939i
$428$	−9.03010	+	1.59798i	−0.436487	+	0.0772413i
$429$		−	15.0493i		−	0.726589i
$430$	5.88841	+	12.1931i	0.283965	+	0.588002i
$431$			21.0872i			1.01574i	0.861435	+	0.507868i	$0.169566\pi$
$431$			21.0872i			1.01574i	−0.861435	+	0.507868i	$0.830434\pi$
$432$	66.1155	+	30.7312i	3.18098	+	1.47855i
$433$	28.3368	−	28.3368i	1.36178	−	1.36178i	0.490126	−	0.871652i	$-0.336951\pi$
$433$	28.3368	−	28.3368i	1.36178	−	1.36178i	0.871652	−	0.490126i	$-0.163049\pi$
$434$	−0.509615	−	0.978226i	−0.0244623	−	0.0469564i
$435$	43.3710	−	40.8132i	2.07948	−	1.95684i
$436$	−9.34382	+	13.3618i	−0.447488	+	0.639916i
$437$	0.0542050	+	0.0542050i	0.00259298	+	0.00259298i
$438$	52.7726	+	16.6213i	2.52157	+	0.794196i
$439$	32.3844			1.54562			0.772810	−	0.634637i	$-0.218850\pi$
$439$	32.3844			1.54562			0.772810	+	0.634637i	$0.218850\pi$
$440$	6.54778	−	4.72460i	0.312153	−	0.225237i
$441$	−58.3566			−2.77888
$442$	6.38946	+	2.01243i	0.303916	+	0.0957215i
$443$	28.7488	+	28.7488i	1.36590	+	1.36590i	0.866203	+	0.499693i	$0.166554\pi$
$443$	28.7488	+	28.7488i	1.36590	+	1.36590i	0.499693	+	0.866203i	$0.333446\pi$
$444$	39.2745	−	56.1633i	1.86388	−	2.66539i
$445$	0.525553	−	17.2978i	0.0249136	−	0.819994i
$446$	1.94280	+	3.72928i	0.0919942	+	0.176586i
$447$	−5.12901	+	5.12901i	−0.242594	+	0.242594i
$448$	−0.912681	−	1.57409i	−0.0431201	−	0.0743689i
$449$		−	12.7630i		−	0.602324i	−0.953573	−	0.301162i	$-0.902625\pi$
$449$		−	12.7630i		−	0.602324i	0.953573	−	0.301162i	$-0.0973745\pi$
$450$	21.2468	−	55.4572i	1.00158	−	2.61428i
$451$		−	4.93048i		−	0.232167i
$452$	2.03524	−	0.360159i	0.0957296	−	0.0169404i
$453$	−18.8668	+	18.8668i	−0.886442	+	0.886442i
$454$	−11.5914	+	6.03862i	−0.544010	+	0.283406i
$455$	−0.0539256	+	1.77488i	−0.00252807	+	0.0832077i
$456$	1.23770	−	9.46878i	0.0579606	−	0.443416i
$457$	27.8527	+	27.8527i	1.30290	+	1.30290i	0.926430	+	0.376466i	$0.122861\pi$
$457$	27.8527	+	27.8527i	1.30290	+	1.30290i	0.376466	+	0.926430i	$0.377139\pi$
$458$	−3.56080	+	11.3055i	−0.166385	+	0.528273i
$459$	24.7284			1.15422
$460$	0.0494589	+	0.339236i	0.00230603	+	0.0158170i
$461$	6.97642			0.324924			0.162462	−	0.986715i	$-0.448056\pi$
$461$	6.97642			0.324924			0.162462	+	0.986715i	$0.448056\pi$
$462$	−0.416498	+	1.32238i	−0.0193772	+	0.0615227i
$463$	10.7779	+	10.7779i	0.500891	+	0.500891i	0.911715	−	0.410824i	$-0.134759\pi$
$463$	10.7779	+	10.7779i	0.500891	+	0.500891i	−0.410824	+	0.911715i	$0.634759\pi$
$464$	29.6383	−	10.8288i	1.37592	−	0.502714i
$465$	18.8533	−	17.7415i	0.874302	−	0.822741i
$466$	0.368944	−	0.192204i	0.0170910	−	0.00890369i
$467$	19.9311	−	19.9311i	0.922300	−	0.922300i	−0.0748915	−	0.997192i	$-0.523861\pi$
$467$	19.9311	−	19.9311i	0.922300	−	0.922300i	0.997192	+	0.0748915i	$0.0238610\pi$
$468$	−10.2197	−	57.7508i	−0.472405	−	2.66953i
$469$		−	2.41068i		−	0.111315i
$470$	−27.3748	+	13.2202i	−1.26270	+	0.609800i
$471$			2.82970i			0.130385i
$472$	3.77851	+	4.91485i	0.173920	+	0.226224i
$473$	3.86542	−	3.86542i	0.177732	−	0.177732i
$474$	24.0614	+	46.1868i	1.10518	+	2.12143i
$475$	−4.99078	−	0.303546i	−0.228993	−	0.0139277i
$476$	−0.505745	−	0.353663i	−0.0231808	−	0.0162101i
$477$	33.4078	+	33.4078i	1.52964	+	1.52964i
$478$	14.2952	+	4.50243i	0.653847	+	0.205936i
$479$	15.5357			0.709844			0.354922	−	0.934896i	$-0.384507\pi$
$479$	15.5357			0.709844			0.354922	+	0.934896i	$0.384507\pi$
$480$	29.7475	−	30.6412i	1.35778	−	1.39857i
$481$	−35.4368			−1.61578
$482$	19.4375	+	6.12205i	0.885355	+	0.278852i
$483$	−0.0416237	−	0.0416237i	−0.00189394	−	0.00189394i
$484$	15.3577	+	10.7395i	0.698078	+	0.488159i
$485$	−12.1824	−	12.9458i	−0.553172	−	0.587839i
$486$	−44.4424	−	85.3090i	−2.01595	−	3.86970i
$487$	−3.19324	+	3.19324i	−0.144699	+	0.144699i	−0.775745	−	0.631046i	$-0.782626\pi$
$487$	−3.19324	+	3.19324i	−0.144699	+	0.144699i	0.631046	+	0.775745i	$0.282626\pi$
$488$	5.71328	+	7.43148i	0.258628	+	0.336408i
$489$			7.79235i			0.352382i
$490$	−7.23417	+	20.7473i	−0.326807	+	0.937268i
$491$			35.1004i			1.58406i	0.610483	+	0.792029i	$0.290975\pi$
$491$			35.1004i			1.58406i	−0.610483	+	0.792029i	$0.709025\pi$
$492$	−4.54414	−	25.6787i	−0.204866	−	1.15769i
$493$	7.56771	−	7.56771i	0.340832	−	0.340832i
$494$	−4.37910	+	2.28133i	−0.197025	+	0.102642i
$495$	−23.9649	−	0.728118i	−1.07714	−	0.0327265i
$496$	12.8838	−	4.70727i	0.578498	−	0.211363i
$497$	−2.19768	−	2.19768i	−0.0985792	−	0.0985792i
$498$	−21.1180	+	67.0498i	−0.946322	+	3.00457i
$499$	34.4557			1.54245			0.771225	−	0.636563i	$-0.219644\pi$
$499$	34.4557			1.54245			0.771225	+	0.636563i	$0.219644\pi$
$500$	−17.0826	−	14.4286i	−0.763959	−	0.645265i
$501$	43.8396			1.95861
$502$	−5.82949	+	18.5086i	−0.260183	+	0.826081i
$503$	−4.90702	−	4.90702i	−0.218793	−	0.218793i	0.589197	−	0.807990i	$-0.299444\pi$
$503$	−4.90702	−	4.90702i	−0.218793	−	0.218793i	−0.807990	+	0.589197i	$0.799444\pi$
$504$	−0.700283	+	5.35738i	−0.0311931	+	0.238637i
$505$	16.9726	+	0.515672i	0.755269	+	0.0229471i
$506$	0.122746	−	0.0639455i	0.00545672	−	0.00284272i
$507$	1.93252	−	1.93252i	0.0858260	−	0.0858260i
$508$	−0.714558	+	0.126449i	−0.0317034	+	0.00561028i
$509$		−	35.7090i		−	1.58277i	−0.611316	−	0.791386i	$-0.709360\pi$
$509$		−	35.7090i		−	1.58277i	0.611316	−	0.791386i	$-0.290640\pi$
$510$	4.76889	−	13.6770i	0.211170	−	0.605627i
$511$			2.63559i			0.116592i
$512$	20.8810	−	8.71699i	0.922816	−	0.385240i
$513$	−12.8885	+	12.8885i	−0.569043	+	0.569043i
$514$	7.45307	+	14.3065i	0.328741	+	0.631031i
$515$	21.9772	+	23.3544i	0.968429	+	1.02912i
$516$	16.5692	−	23.6943i	0.729417	−	1.04308i
$517$	8.67831	+	8.67831i	0.381671	+	0.381671i
$518$	3.11382	+	0.980730i	0.136813	+	0.0430908i
$519$	18.5864			0.815852
$520$	−21.7988	−	3.52572i	−0.955943	−	0.154613i
$521$	−14.1094			−0.618143			−0.309071	−	0.951039i	$-0.600018\pi$
$521$	−14.1094			−0.618143			−0.309071	+	0.951039i	$0.600018\pi$
$522$	−89.3701	−	28.1481i	−3.91162	−	1.23201i
$523$	2.81308	+	2.81308i	0.123007	+	0.123007i	0.765931	−	0.642923i	$-0.222279\pi$
$523$	2.81308	+	2.81308i	0.123007	+	0.123007i	−0.642923	+	0.765931i	$0.722279\pi$
$524$	−4.11115	+	5.87903i	−0.179596	+	0.256826i
$525$	3.83239	+	0.233092i	0.167259	+	0.0101729i
$526$	2.19702	+	4.21726i	0.0957945	+	0.183881i
$527$	3.28968	−	3.28968i	0.143301	−	0.143301i
$528$	−15.6347	−	7.26719i	−0.680415	−	0.316264i
$529$		−	22.9941i		−	0.999745i
$530$	16.0187	−	7.73596i	0.695810	−	0.336029i
$531$		−	18.4085i		−	0.798862i
$532$	0.447927	−	0.0792659i	0.0194201	−	0.00343661i
$533$	−9.53469	+	9.53469i	−0.412993	+	0.412993i
$534$	−32.7724	+	17.0731i	−1.41820	+	0.738823i
$535$	7.46667	−	7.02633i	0.322812	−	0.303775i
$536$	29.7257	+	3.88555i	1.28395	+	0.167830i
$537$	−16.5490	−	16.5490i	−0.714142	−	0.714142i
$538$	10.1444	−	32.2084i	0.437356	−	1.38860i
$539$	8.87064			0.382086
$540$	−80.6615	+	11.7600i	−3.47112	+	0.506072i
$541$	−4.41063			−0.189628			−0.0948138	−	0.995495i	$-0.530226\pi$
$541$	−4.41063			−0.189628			−0.0948138	+	0.995495i	$0.530226\pi$
$542$	1.24397	−	3.94961i	0.0534331	−	0.169650i
$543$	25.8342	+	25.8342i	1.10865	+	1.10865i
$544$	5.17613	−	5.66622i	0.221925	−	0.242937i
$545$	0.553599	−	18.2209i	0.0237136	−	0.780497i
$546$	3.36269	−	1.75182i	0.143910	−	0.0749710i
$547$	−3.81017	+	3.81017i	−0.162911	+	0.162911i	−0.783855	−	0.620944i	$-0.786750\pi$
$547$	−3.81017	+	3.81017i	−0.162911	+	0.162911i	0.620944	+	0.783855i	$0.286750\pi$
$548$	5.71371	+	32.2879i	0.244077	+	1.37927i
$549$		−	27.8346i		−	1.18795i
$550$	−3.22968	+	8.42991i	−0.137714	+	0.359453i
$551$			7.88865i			0.336068i
$552$	0.580345	−	0.446166i	0.0247011	−	0.0189901i
$553$	−1.75418	+	1.75418i	−0.0745952	+	0.0745952i
$554$	9.25629	+	17.7678i	0.393262	+	0.754882i
$555$	−2.32692	+	76.5871i	−0.0987723	+	3.25094i
$556$	27.2899	+	19.0836i	1.15735	+	0.809325i
$557$	6.33681	+	6.33681i	0.268499	+	0.268499i	0.828495	−	0.559996i	$-0.189197\pi$
$557$	6.33681	+	6.33681i	0.268499	+	0.268499i	−0.559996	+	0.828495i	$0.689197\pi$
$558$	−38.8491	−	12.2359i	−1.64461	−	0.517989i
$559$	−14.9501			−0.632322
$560$	1.81788	+	0.913097i	0.0768195	+	0.0385854i
$561$	−5.84767			−0.246889
$562$	−5.74679	−	1.81001i	−0.242414	−	0.0763507i
$563$	23.8896	+	23.8896i	1.00682	+	1.00682i	0.999977	+	0.00684829i	$0.00217990\pi$
$563$	23.8896	+	23.8896i	1.00682	+	1.00682i	0.00684829	+	0.999977i	$0.497820\pi$
$564$	53.1963	+	37.1997i	2.23997	+	1.56639i
$565$	−1.68286	+	1.58362i	−0.0707987	+	0.0666234i
$566$	10.9793	+	21.0751i	0.461493	+	0.885854i
$567$	5.84482	−	5.84482i	0.245459	−	0.245459i
$568$	30.6414	−	23.5570i	1.28569	−	0.988428i
$569$		−	9.19694i		−	0.385556i	−0.981242	−	0.192778i	$-0.938250\pi$
$569$		−	9.19694i		−	0.385556i	0.981242	−	0.192778i	$-0.0617497\pi$
$570$	4.64294	+	9.61407i	0.194471	+	0.402689i
$571$		−	23.9873i		−	1.00384i	−0.864915	−	0.501918i	$-0.832628\pi$
$571$		−	23.9873i		−	1.00384i	0.864915	−	0.501918i	$-0.167372\pi$
$572$	1.55347	+	8.77857i	0.0649538	+	0.367050i
$573$	−17.2306	+	17.2306i	−0.719817	+	0.719817i
$574$	1.10169	−	0.573933i	0.0459835	−	0.0239555i
$575$	−0.254071	−	0.286979i	−0.0105955	−	0.0119678i
$576$	−64.9323	−	17.2702i	−2.70551	−	0.719590i
$577$	−18.9804	−	18.9804i	−0.790165	−	0.790165i	0.191356	−	0.981521i	$-0.438712\pi$
$577$	−18.9804	−	18.9804i	−0.790165	−	0.790165i	−0.981521	+	0.191356i	$0.938712\pi$
$578$	−6.44044	+	20.4484i	−0.267887	+	0.850541i
$579$	−6.97776			−0.289986
$580$	−21.0862	+	28.2841i	−0.875555	+	1.17443i
$581$	−3.34862			−0.138924
$582$	−11.4031	+	36.2048i	−0.472673	+	1.50074i
$583$	−5.07823	−	5.07823i	−0.210319	−	0.210319i
$584$	−32.4990	−	4.24807i	−1.34482	−	0.175786i
$585$	44.9360	+	47.7521i	1.85787	+	1.97431i
$586$	13.5686	−	7.06870i	0.560516	−	0.292005i
$587$	−3.01360	+	3.01360i	−0.124385	+	0.124385i	−0.766559	−	0.642174i	$-0.778033\pi$
$587$	−3.01360	+	3.01360i	−0.124385	+	0.124385i	0.642174	+	0.766559i	$0.278033\pi$
$588$	46.1997	−	8.17556i	1.90524	−	0.337155i
$589$			3.42919i			0.141297i
$590$	−6.54473	−	2.28201i	−0.269442	−	0.0939491i
$591$		−	71.2765i		−	2.93193i
$592$	−17.1121	+	36.8152i	−0.703303	+	1.51310i
$593$	−17.0890	+	17.0890i	−0.701760	+	0.701760i	−0.964788	−	0.263028i	$-0.915279\pi$
$593$	−17.0890	+	17.0890i	−0.701760	+	0.701760i	0.263028	+	0.964788i	$0.415279\pi$
$594$	15.2046	+	29.1858i	0.623851	+	1.19751i
$595$	0.689659	+	0.0209537i	0.0282733	+	0.000859018i
$596$	2.46241	−	3.52129i	0.100864	−	0.144238i
$597$	2.14876	+	2.14876i	0.0879428	+	0.0879428i
$598$	−0.361029	−	0.113710i	−0.0147636	−	0.00464994i
$599$	−37.9717			−1.55148			−0.775740	−	0.631052i	$-0.782623\pi$
$599$	−37.9717			−1.55148			−0.775740	+	0.631052i	$0.782623\pi$
$600$	−9.05130	+	46.8809i	−0.369518	+	1.91390i
$601$	29.2792			1.19433			0.597163	−	0.802120i	$-0.296295\pi$
$601$	29.2792			1.19433			0.597163	+	0.802120i	$0.296295\pi$
$602$	1.31366	+	0.413752i	0.0535408	+	0.0168633i
$603$	−62.9454	−	62.9454i	−2.56333	−	2.56333i
$604$	9.05786	−	12.9529i	0.368559	−	0.527047i
$605$	−20.9426	−	0.636291i	−0.851436	−	0.0258689i
$606$	−16.7520	−	32.1562i	−0.680505	−	1.30626i
$607$	−20.0211	+	20.0211i	−0.812630	+	0.812630i	−0.985028	−	0.172397i	$-0.944849\pi$
$607$	−20.0211	+	20.0211i	−0.812630	+	0.812630i	0.172397	+	0.985028i	$0.444849\pi$
$608$	0.255442	+	5.65108i	0.0103595	+	0.229182i
$609$		−	6.05765i		−	0.245468i
$610$	−9.89594	−	3.45052i	−0.400675	−	0.139707i
$611$		−	33.5647i		−	1.35788i
$612$	−22.4401	+	3.97103i	−0.907086	+	0.160519i
$613$	19.8845	−	19.8845i	0.803128	−	0.803128i	−0.180456	−	0.983583i	$-0.557757\pi$
$613$	19.8845	−	19.8845i	0.803128	−	0.803128i	0.983583	+	0.180456i	$0.0577572\pi$
$614$	11.0823	−	5.77344i	0.447247	−	0.232997i
$615$	19.9806	+	21.2328i	0.805696	+	0.856188i
$616$	0.106448	−	0.814363i	0.00428892	−	0.0328116i
$617$	14.0460	+	14.0460i	0.565471	+	0.565471i	0.930856	−	0.365386i	$-0.119063\pi$
$617$	14.0460	+	14.0460i	0.565471	+	0.565471i	−0.365386	+	0.930856i	$0.619063\pi$
$618$	20.5713	−	65.3140i	0.827500	−	2.62731i
$619$	−16.5482			−0.665127			−0.332563	−	0.943081i	$-0.607914\pi$
$619$	−16.5482			−0.665127			−0.332563	+	0.943081i	$0.607914\pi$
$620$	−9.16614	+	12.2951i	−0.368121	+	0.493782i
$621$	−1.39725			−0.0560696
$622$	6.23607	−	19.7995i	0.250044	−	0.793889i
$623$	−1.24470	−	1.24470i	−0.0498678	−	0.0498678i
$624$	16.1814	+	44.2884i	0.647775	+	1.77295i
$625$	24.8157	+	3.02987i	0.992629	+	0.121195i
$626$	−13.7545	+	7.16549i	−0.549739	+	0.286391i
$627$	3.04783	−	3.04783i	0.121719	−	0.121719i
$628$	−0.292095	−	1.65062i	−0.0116559	−	0.0658667i
$629$			13.7696i			0.549028i
$630$	−2.62695	−	5.43958i	−0.104660	−	0.216718i
$631$			16.9860i			0.676202i	0.941110	+	0.338101i	$0.109785\pi$
$631$			16.9860i			0.676202i	−0.941110	+	0.338101i	$0.890215\pi$
$632$	−18.8031	−	24.4579i	−0.747947	−	0.972883i
$633$	51.0285	−	51.0285i	2.02820	−	2.02820i
$634$	13.0438	+	25.0381i	0.518036	+	0.994391i
$635$	0.590842	−	0.555998i	0.0234469	−	0.0220641i
$636$	−31.1285	−	21.7679i	−1.23433	−	0.863154i
$637$	−17.1543	−	17.1543i	−0.679678	−	0.679678i
$638$	13.5849	+	4.27872i	0.537833	+	0.169396i
$639$	−114.767			−4.54012
$640$	−14.1893	+	20.9443i	−0.560883	+	0.827895i
$641$	−26.6524			−1.05270			−0.526352	−	0.850267i	$-0.676441\pi$
$641$	−26.6524			−1.05270			−0.526352	+	0.850267i	$0.676441\pi$
$642$	−20.8816	−	6.57687i	−0.824130	−	0.259568i
$643$	5.61548	+	5.61548i	0.221453	+	0.221453i	0.809110	−	0.587657i	$-0.199950\pi$
$643$	5.61548	+	5.61548i	0.221453	+	0.221453i	−0.587657	+	0.809110i	$0.699950\pi$
$644$	0.0285765	+	0.0199833i	0.00112607	+	0.000787452i
$645$	−0.981685	+	32.3107i	−0.0386538	+	1.27223i
$646$	0.886449	+	1.70157i	0.0348769	+	0.0669476i
$647$	19.8609	−	19.8609i	0.780814	−	0.780814i	−0.199154	−	0.979968i	$-0.563819\pi$
$647$	19.8609	−	19.8609i	0.780814	−	0.780814i	0.979968	+	0.199154i	$0.0638194\pi$
$648$	62.6508	+	81.4923i	2.46116	+	3.20132i
$649$			2.79824i			0.109840i
$650$	22.5476	−	10.0564i	0.884391	−	0.394443i
$651$		−	2.63326i		−	0.103205i
$652$	−0.804365	−	4.54543i	−0.0315014	−	0.178013i
$653$	−7.55738	+	7.55738i	−0.295743	+	0.295743i	−0.839344	−	0.543601i	$-0.817061\pi$
$653$	−7.55738	+	7.55738i	−0.295743	+	0.295743i	0.543601	+	0.839344i	$0.317061\pi$
$654$	−34.5213	+	17.9842i	−1.34989	+	0.703236i
$655$	0.243576	−	8.01694i	0.00951730	−	0.313248i
$656$	5.30137	+	14.5098i	0.206984	+	0.566513i
$657$	68.8180	+	68.8180i	2.68485	+	2.68485i
$658$	−0.928919	+	2.94932i	−0.0362130	+	0.114976i
$659$	22.1818			0.864079			0.432039	−	0.901855i	$-0.357794\pi$
$659$	22.1818			0.864079			0.432039	+	0.901855i	$0.357794\pi$
$660$	19.0745	−	2.78097i	0.742475	−	0.108249i
$661$	−24.5297			−0.954094			−0.477047	−	0.878878i	$-0.658293\pi$
$661$	−24.5297			−0.954094			−0.477047	+	0.878878i	$0.658293\pi$
$662$	2.97262	−	9.43808i	0.115534	−	0.366821i
$663$	11.3084	+	11.3084i	0.439181	+	0.439181i
$664$	5.39734	−	41.2914i	0.209458	−	1.60242i
$665$	−0.370375	+	0.348533i	−0.0143625	+	0.0135155i
$666$	106.913	−	55.6972i	4.14280	−	2.15822i
$667$	−0.427604	+	0.427604i	−0.0165569	+	0.0165569i
$668$	−25.5725	+	4.52534i	−0.989428	+	0.175091i
$669$			10.0387i			0.388120i
$670$	−30.1818	+	14.5757i	−1.16602	+	0.563110i
$671$			4.23107i			0.163339i
$672$	−0.196152	−	4.33943i	−0.00756674	−	0.167397i
$673$	25.1623	−	25.1623i	0.969935	−	0.969935i	−0.0296262	−	0.999561i	$-0.509432\pi$
$673$	25.1623	−	25.1623i	0.969935	−	0.969935i	0.999561	+	0.0296262i	$0.00943168\pi$
$674$	16.0304	+	30.7710i	0.617468	+	1.18526i
$675$	68.2361	−	60.4116i	2.62641	−	2.32524i
$676$	−0.927789	+	1.32676i	−0.0356842	+	0.0510291i
$677$	9.34369	+	9.34369i	0.359107	+	0.359107i	0.863484	−	0.504377i	$-0.168278\pi$
$677$	9.34369	+	9.34369i	0.359107	+	0.359107i	−0.504377	+	0.863484i	$0.668278\pi$
$678$	4.70637	+	1.48232i	0.180747	+	0.0569282i
$679$	−1.80815			−0.0693904
$680$	−1.36998	+	8.47031i	−0.0525362	+	0.324822i
$681$	−31.2024			−1.19568
$682$	5.90536	+	1.85996i	0.226128	+	0.0712214i
$683$	7.50006	+	7.50006i	0.286982	+	0.286982i	0.835886	−	0.548904i	$-0.184955\pi$
$683$	7.50006	+	7.50006i	0.286982	+	0.286982i	−0.548904	+	0.835886i	$0.684955\pi$
$684$	9.62615	−	13.7656i	0.368065	−	0.526340i
$685$	−25.1232	−	26.6977i	−0.959908	−	1.02006i
$686$	2.07286	+	3.97895i	0.0791423	+	0.151917i
$687$	−20.0091	+	20.0091i	−0.763395	+	0.763395i
$688$	−7.21928	+	15.5317i	−0.275232	+	0.592139i
$689$			19.6409i			0.748257i
$690$	−0.269460	+	0.772801i	−0.0102582	+	0.0294200i
$691$		−	27.3416i		−	1.04012i	−0.854129	−	0.520061i	$-0.825909\pi$
$691$		−	27.3416i		−	1.04012i	0.854129	−	0.520061i	$-0.174091\pi$
$692$	−10.8418	+	1.91858i	−0.412143	+	0.0729335i
$693$	−1.72445	+	1.72445i	−0.0655063	+	0.0655063i
$694$	24.6695	−	12.8518i	0.936442	−	0.487847i
$695$	−37.2139	−	1.13066i	−1.41161	−	0.0428883i
$696$	74.6959	+	9.76378i	2.83134	+	0.370095i
$697$	3.70487	+	3.70487i	0.140332	+	0.140332i
$698$	8.98905	−	28.5402i	0.340240	−	1.08026i
$699$	0.993148			0.0375643
$700$	−2.25957	+	0.259632i	−0.0854036	+	0.00981316i
$701$	−12.4767			−0.471240			−0.235620	−	0.971845i	$-0.575712\pi$
$701$	−12.4767			−0.471240			−0.235620	+	0.971845i	$0.575712\pi$
$702$	27.0373	−	85.8433i	1.02046	−	3.23995i
$703$	−7.17676	−	7.17676i	−0.270676	−	0.270676i
$704$	9.87020	+	2.62519i	0.371997	+	0.0989408i
$705$	−72.5411	−	2.20399i	−2.73206	−	0.0830072i
$706$	−14.4149	+	7.50957i	−0.542512	+	0.282626i
$707$	1.22130	−	1.22130i	0.0459316	−	0.0459316i
$708$	2.57898	+	14.5737i	0.0969238	+	0.547712i
$709$		−	15.3526i		−	0.576581i	−0.957543	−	0.288290i	$-0.906913\pi$
$709$		−	15.3526i		−	0.576581i	0.957543	−	0.288290i	$-0.0930868\pi$
$710$	−14.2271	+	40.8028i	−0.533935	+	1.53130i
$711$			91.6069i			3.43553i
$712$	17.3544	−	13.3420i	0.650384	−	0.500011i
$713$	−0.185879	+	0.185879i	−0.00696124	+	0.00696124i
$714$	−0.680699	−	1.30663i	−0.0254745	−	0.0488994i
$715$	−6.83061	−	7.25868i	−0.255450	−	0.271459i
$716$	11.3616	+	7.94508i	0.424604	+	0.296921i
$717$	25.3004	+	25.3004i	0.944859	+	0.944859i
$718$	−19.1833	−	6.04197i	−0.715913	−	0.225484i
$719$	−1.36187			−0.0507891			−0.0253945	−	0.999678i	$-0.508084\pi$
$719$	−1.36187			−0.0507891			−0.0253945	+	0.999678i	$0.508084\pi$
$720$	71.3088	−	23.6249i	2.65752	−	0.880448i
$721$	3.26193			0.121481
$722$	−1.34889	−	0.424847i	−0.0502005	−	0.0158112i
$723$	34.4015	+	34.4015i	1.27941	+	1.27941i
$724$	−17.7363	−	12.4029i	−0.659166	−	0.460948i
$725$	2.39457	−	39.3705i	0.0889322	−	1.46218i
$726$	20.6705	+	39.6778i	0.767153	+	1.47258i
$727$	21.9576	−	21.9576i	0.814363	−	0.814363i	−0.170921	−	0.985285i	$-0.554674\pi$
$727$	21.9576	−	21.9576i	0.814363	−	0.814363i	0.985285	+	0.170921i	$0.0546744\pi$
$728$	−1.78069	+	1.36898i	−0.0659967	+	0.0507379i
$729$		−	120.614i		−	4.46717i
$730$	32.9977	−	15.9356i	1.22130	−	0.589804i
$731$			5.80912i			0.214858i
$732$	3.89954	+	22.0361i	0.144131	+	0.814477i
$733$	4.67075	−	4.67075i	0.172518	−	0.172518i	−0.615567	−	0.788085i	$-0.711073\pi$
$733$	4.67075	−	4.67075i	0.172518	−	0.172518i	0.788085	+	0.615567i	$0.211073\pi$
$734$	17.7946	−	9.27022i	0.656809	−	0.342170i
$735$	−38.2008	+	35.9480i	−1.40906	+	1.32596i
$736$	−0.292471	+	0.320163i	−0.0107806	+	0.0118014i
$737$	9.56818	+	9.56818i	0.352448	+	0.352448i
$738$	13.7802	−	43.7522i	0.507257	−	1.61054i
$739$	−32.9476			−1.21200			−0.605999	−	0.795465i	$-0.707227\pi$
$739$	−32.9476			−1.21200			−0.605999	+	0.795465i	$0.707227\pi$
$740$	−6.54837	−	44.9149i	−0.240723	−	1.65111i
$741$	−11.7880			−0.433042
$742$	0.543570	−	1.72584i	0.0199551	−	0.0633574i
$743$	6.53186	+	6.53186i	0.239631	+	0.239631i	0.816697	−	0.577066i	$-0.195803\pi$
$743$	6.53186	+	6.53186i	0.239631	+	0.239631i	−0.577066	+	0.816697i	$0.695803\pi$
$744$	32.4703	+	4.24431i	1.19042	+	0.155604i
$745$	−0.145892	+	4.80181i	−0.00534506	+	0.175925i
$746$	11.2760	−	5.87434i	0.412845	−	0.215075i
$747$	−87.4362	+	87.4362i	−3.19912	+	3.19912i
$748$	3.41106	−	0.603626i	0.124721	−	0.0220708i
$749$		−	1.04287i		−	0.0381058i
$750$	−20.2536	−	49.3910i	−0.739555	−	1.80351i
$751$		−	2.59443i		−	0.0946722i	−0.998879	−	0.0473361i	$-0.984927\pi$
$751$		−	2.59443i		−	0.0946722i	0.998879	−	0.0473361i	$-0.0150732\pi$
$752$	−34.8703	−	16.2081i	−1.27159	−	0.591048i
$753$	−32.7575	+	32.7575i	−1.19375	+	1.19375i
$754$	−17.9966	−	34.5452i	−0.655398	−	1.25806i
$755$	−0.536657	+	17.6633i	−0.0195309	+	0.642832i
$756$	−4.75151	+	6.79475i	−0.172811	+	0.247123i
$757$	−36.3370	−	36.3370i	−1.32069	−	1.32069i	−0.913216	−	0.407475i	$-0.866409\pi$
$757$	−36.3370	−	36.3370i	−1.32069	−	1.32069i	−0.407475	−	0.913216i	$-0.633591\pi$
$758$	10.6472	+	3.35344i	0.386723	+	0.121802i
$759$	0.330416			0.0119933
$760$	−3.70073	−	5.12880i	−0.134239	−	0.186041i
$761$	−2.04769			−0.0742288			−0.0371144	−	0.999311i	$-0.511817\pi$
$761$	−2.04769			−0.0742288			−0.0371144	+	0.999311i	$0.511817\pi$
$762$	−1.65237	−	0.520432i	−0.0598592	−	0.0188533i
$763$	−1.31112	−	1.31112i	−0.0474658	−	0.0474658i
$764$	8.27229	−	11.8295i	0.299281	−	0.427978i
$765$	18.5549	−	17.4606i	0.670853	−	0.631290i
$766$	−6.89562	−	13.2364i	−0.249149	−	0.478251i
$767$	5.41131	−	5.41131i	0.195391	−	0.195391i
$768$	53.8250	+	4.57562i	1.94224	+	0.165108i
$769$			51.4727i			1.85615i	0.372390	+	0.928076i	$0.378538\pi$
$769$			51.4727i			1.85615i	−0.372390	+	0.928076i	$0.621462\pi$
$770$	0.399316	+	0.826858i	0.0143903	+	0.0297979i
$771$			38.5111i			1.3

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)

\(f(q)\)	\(=\)	\(q+(-1.34889 - 0.424847i) q^{2} +(-2.38733 - 2.38733i) q^{3} +(1.63901 + 1.14614i) q^{4} +(-2.23504 - 0.0679064i) q^{5} +(2.20600 + 4.23450i) q^{6} +(-0.160827 + 0.160827i) q^{7} +(-1.72391 - 2.24235i) q^{8} +8.39872i q^{9} +O(q^{10})\)	\(q+(-1.34889 - 0.424847i) q^{2} +(-2.38733 - 2.38733i) q^{3} +(1.63901 + 1.14614i) q^{4} +(-2.23504 - 0.0679064i) q^{5} +(2.20600 + 4.23450i) q^{6} +(-0.160827 + 0.160827i) q^{7} +(-1.72391 - 2.24235i) q^{8} +8.39872i q^{9} +(2.98597 + 1.04115i) q^{10} -1.27667i q^{11} +(-1.17663 - 6.64909i) q^{12} +(-2.46886 + 2.46886i) q^{13} +(0.285264 - 0.148611i) q^{14} +(5.17366 + 5.49789i) q^{15} +(1.37271 + 3.75708i) q^{16} +(0.959316 + 0.959316i) q^{17} +(3.56817 - 11.3290i) q^{18} -1.00000 q^{19} +(-3.58542 - 2.67297i) q^{20} +0.767894 q^{21} +(-0.542389 + 1.72209i) q^{22} +(-0.0542050 - 0.0542050i) q^{23} +(-1.23770 + 9.46878i) q^{24} +(4.99078 + 0.303546i) q^{25} +(4.37910 - 2.28133i) q^{26} +(12.8885 - 12.8885i) q^{27} +(-0.447927 + 0.0792659i) q^{28} -7.88865i q^{29} +(-4.64294 - 9.61407i) q^{30} -3.42919i q^{31} +(-0.255442 - 5.65108i) q^{32} +(-3.04783 + 3.04783i) q^{33} +(-0.886449 - 1.70157i) q^{34} +(0.370375 - 0.348533i) q^{35} +(-9.62615 + 13.7656i) q^{36} +(7.17676 + 7.17676i) q^{37} +(1.34889 + 0.424847i) q^{38} +11.7880 q^{39} +(3.70073 + 5.12880i) q^{40} +3.86199 q^{41} +(-1.03580 - 0.326238i) q^{42} +(3.02774 + 3.02774i) q^{43} +(1.46325 - 2.09247i) q^{44} +(0.570327 - 18.7714i) q^{45} +(0.0500878 + 0.0961455i) q^{46} +(-6.79762 + 6.79762i) q^{47} +(5.69231 - 12.2465i) q^{48} +6.94827i q^{49} +(-6.60305 - 2.52977i) q^{50} -4.58041i q^{51} +(-6.87615 + 1.21681i) q^{52} +(3.97772 - 3.97772i) q^{53} +(-22.8609 + 11.9096i) q^{54} +(-0.0866940 + 2.85340i) q^{55} +(0.637881 + 0.0833797i) q^{56} +(2.38733 + 2.38733i) q^{57} +(-3.35147 + 10.6409i) q^{58} -2.19183 q^{59} +(2.17830 + 14.9409i) q^{60} -3.31415 q^{61} +(-1.45688 + 4.62560i) q^{62} +(-1.35074 - 1.35074i) q^{63} +(-2.05628 + 7.73122i) q^{64} +(5.68564 - 5.35034i) q^{65} +(5.40606 - 2.81633i) q^{66} +(-7.49464 + 7.49464i) q^{67} +(0.472813 + 2.67184i) q^{68} +0.258811i q^{69} +(-0.647668 + 0.312779i) q^{70} +13.6649i q^{71} +(18.8329 - 14.4786i) q^{72} +(8.19387 - 8.19387i) q^{73} +(-6.63163 - 12.7297i) q^{74} +(-11.1900 - 12.6393i) q^{75} +(-1.63901 - 1.14614i) q^{76} +(0.205323 + 0.205323i) q^{77} +(-15.9007 - 5.00809i) q^{78} +10.9072 q^{79} +(-2.81292 - 8.49044i) q^{80} -36.3423 q^{81} +(-5.20940 - 1.64075i) q^{82} +(10.4107 + 10.4107i) q^{83} +(1.25859 + 0.880118i) q^{84} +(-2.07896 - 2.20925i) q^{85} +(-2.79776 - 5.37041i) q^{86} +(-18.8328 + 18.8328i) q^{87} +(-2.86274 + 2.20086i) q^{88} +7.73938i q^{89} +(-8.74430 + 25.0783i) q^{90} -0.794117i q^{91} +(-0.0267158 - 0.150969i) q^{92} +(-8.18662 + 8.18662i) q^{93} +(12.0572 - 6.28129i) q^{94} +(2.23504 + 0.0679064i) q^{95} +(-12.8812 + 14.1008i) q^{96} +(5.62142 + 5.62142i) q^{97} +(2.95195 - 9.37245i) q^{98} +10.7224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

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Varieties

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