LMFDB - Embedded newform 380.2.bb.a.299.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			299.45
Character	$\chi$	$=$	380.299
Dual form			380.2.bb.a.319.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09519 - 0.894745i) q^{2} +(3.18304 + 0.561256i) q^{3} +(0.398864 - 1.95982i) q^{4} +(-2.22982 + 0.167093i) q^{5} +(3.98820 - 2.23333i) q^{6} +(-1.17014 - 2.02675i) q^{7} +(-1.31671 - 2.50325i) q^{8} +(6.99766 + 2.54694i) q^{9} +O(q^{10})$	\(q+(1.09519 - 0.894745i) q^{2} +(3.18304 + 0.561256i) q^{3} +(0.398864 - 1.95982i) q^{4} +(-2.22982 + 0.167093i) q^{5} +(3.98820 - 2.23333i) q^{6} +(-1.17014 - 2.02675i) q^{7} +(-1.31671 - 2.50325i) q^{8} +(6.99766 + 2.54694i) q^{9} +(-2.29256 + 2.17811i) q^{10} +(0.778220 + 0.449305i) q^{11} +(2.36956 - 6.01433i) q^{12} +(1.01543 + 5.75878i) q^{13} +(-3.09494 - 1.17269i) q^{14} +(-7.19138 - 0.719634i) q^{15} +(-3.68181 - 1.56341i) q^{16} +(-0.219912 - 0.604202i) q^{17} +(9.94260 - 3.47175i) q^{18} +(-3.32121 - 2.82304i) q^{19} +(-0.561921 + 4.43669i) q^{20} +(-2.58709 - 7.10797i) q^{21} +(1.25431 - 0.204235i) q^{22} +(-1.50724 + 1.26472i) q^{23} +(-2.78618 - 8.70697i) q^{24} +(4.94416 - 0.745173i) q^{25} +(6.26471 + 5.39838i) q^{26} +(12.4470 + 7.18628i) q^{27} +(-4.43879 + 1.48488i) q^{28} +(-3.19032 + 8.76534i) q^{29} +(-8.51978 + 5.64631i) q^{30} +(-2.12932 - 3.68810i) q^{31} +(-5.43112 + 1.58206i) q^{32} +(2.22493 + 1.86694i) q^{33} +(-0.781451 - 0.464949i) q^{34} +(2.94786 + 4.32375i) q^{35} +(7.78267 - 12.6983i) q^{36} -3.38747 q^{37} +(-6.16324 - 0.120111i) q^{38} +18.9003i q^{39} +(3.35430 + 5.36178i) q^{40} +(-6.32042 - 1.11446i) q^{41} +(-9.19316 - 5.46976i) q^{42} +(5.23859 + 4.39570i) q^{43} +(1.19096 - 1.34596i) q^{44} +(-16.0291 - 4.50995i) q^{45} +(-0.519102 + 2.73370i) q^{46} +(5.59404 + 2.03606i) q^{47} +(-10.8419 - 7.04283i) q^{48} +(0.761533 - 1.31901i) q^{49} +(4.74803 - 5.23986i) q^{50} +(-0.360875 - 2.04663i) q^{51} +(11.6912 + 0.306911i) q^{52} +(5.84953 - 4.90834i) q^{53} +(20.0617 - 3.26658i) q^{54} +(-1.81036 - 0.871833i) q^{55} +(-3.53272 + 5.59780i) q^{56} +(-8.98711 - 10.8499i) q^{57} +(4.34874 + 12.4542i) q^{58} +(-7.26432 + 2.64400i) q^{59} +(-4.27874 + 13.8068i) q^{60} +(1.01831 - 0.854462i) q^{61} +(-5.63191 - 2.13395i) q^{62} +(-3.02626 - 17.1628i) q^{63} +(-4.53255 + 6.59212i) q^{64} +(-3.22647 - 12.6713i) q^{65} +(4.10714 + 0.0539000i) q^{66} +(0.893785 - 2.45565i) q^{67} +(-1.27184 + 0.189993i) q^{68} +(-5.50744 + 3.17972i) q^{69} +(7.09710 + 2.09773i) q^{70} +(-3.69048 - 3.09668i) q^{71} +(-2.83826 - 20.8705i) q^{72} +(0.372573 + 0.0656946i) q^{73} +(-3.70991 + 3.03092i) q^{74} +(16.1557 + 0.403024i) q^{75} +(-6.85737 + 5.38298i) q^{76} -2.10301i q^{77} +(16.9110 + 20.6994i) q^{78} +(2.25143 - 12.7685i) q^{79} +(8.47100 + 2.87090i) q^{80} +(18.4723 + 15.5001i) q^{81} +(-7.91920 + 4.43462i) q^{82} +(-2.23058 - 3.86348i) q^{83} +(-14.9623 + 2.23512i) q^{84} +(0.591320 + 1.31051i) q^{85} +(9.67026 + 0.126907i) q^{86} +(-15.0745 + 26.1098i) q^{87} +(0.100034 - 2.53969i) q^{88} +(-0.805285 + 0.141993i) q^{89} +(-21.5901 + 9.40270i) q^{90} +(10.4834 - 8.79660i) q^{91} +(1.87745 + 3.45838i) q^{92} +(-4.70776 - 12.9345i) q^{93} +(7.94827 - 2.77537i) q^{94} +(7.87741 + 5.73990i) q^{95} +(-18.1754 + 1.98752i) q^{96} +(5.80238 - 2.11189i) q^{97} +(-0.346160 - 2.12594i) q^{98} +(4.30137 + 5.12617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$	$-1$

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 $

$2$	1.09519	−	0.894745i	0.774413	−	0.632680i
$2$	1.09519	−	0.894745i	0.774413	−	0.632680i
$3$	3.18304	+	0.561256i	1.83773	+	0.324041i	0.981339	−	0.192287i	$-0.0615904\pi$
$3$	3.18304	+	0.561256i	1.83773	+	0.324041i	0.856391	+	0.516328i	$0.172702\pi$
$4$	0.398864	−	1.95982i	0.199432	−	0.979912i
$5$	−2.22982	+	0.167093i	−0.997204	+	0.0747262i
$5$	−2.22982	+	0.167093i	−0.997204	+	0.0747262i
$6$	3.98820	−	2.23333i	1.62818	−	0.911753i
$7$	−1.17014	−	2.02675i	−0.442272	−	0.766038i	0.555585	−	0.831459i	$-0.312494\pi$
$7$	−1.17014	−	2.02675i	−0.442272	−	0.766038i	−0.997858	+	0.0654214i	$0.979161\pi$
$8$	−1.31671	−	2.50325i	−0.465528	−	0.885033i
$9$	6.99766	+	2.54694i	2.33255	+	0.848980i
$10$	−2.29256	+	2.17811i	−0.724970	+	0.688780i
$11$	0.778220	+	0.449305i	0.234642	+	0.135471i	0.612712	−	0.790307i	$-0.290079\pi$
$11$	0.778220	+	0.449305i	0.234642	+	0.135471i	−0.378070	+	0.925777i	$0.623412\pi$
$12$	2.36956	−	6.01433i	0.684034	−	1.73619i
$13$	1.01543	+	5.75878i	0.281629	+	1.59720i	0.717084	+	0.696987i	$0.245476\pi$
$13$	1.01543	+	5.75878i	0.281629	+	1.59720i	−0.435455	+	0.900210i	$0.643413\pi$
$14$	−3.09494	−	1.17269i	−0.827159	−	0.313413i
$15$	−7.19138	−	0.719634i	−1.85681	−	0.185809i
$16$	−3.68181	−	1.56341i	−0.920454	−	0.390852i
$17$	−0.219912	−	0.604202i	−0.0533364	−	0.146541i	0.910164	−	0.414249i	$-0.135956\pi$
$17$	−0.219912	−	0.604202i	−0.0533364	−	0.146541i	−0.963500	+	0.267709i	$0.913734\pi$
$18$	9.94260	−	3.47175i	2.34349	−	0.818299i
$19$	−3.32121	−	2.82304i	−0.761939	−	0.647649i
$19$	−3.32121	−	2.82304i	−0.761939	−	0.647649i
$20$	−0.561921	+	4.43669i	−0.125649	+	0.992075i
$21$	−2.58709	−	7.10797i	−0.564549	−	1.55109i
$22$	1.25431	−	0.204235i	0.267420	−	0.0435430i
$23$	−1.50724	+	1.26472i	−0.314281	+	0.263713i	−0.786259	−	0.617897i	$-0.787985\pi$
$23$	−1.50724	+	1.26472i	−0.314281	+	0.263713i	0.471978	+	0.881611i	$0.343540\pi$
$24$	−2.78618	−	8.70697i	−0.568726	−	1.77730i
$25$	4.94416	−	0.745173i	0.988832	−	0.149035i
$26$	6.26471	+	5.39838i	1.22861	+	1.05871i
$27$	12.4470	+	7.18628i	2.39543	+	1.38300i
$28$	−4.43879	+	1.48488i	−0.838853	+	0.280615i
$29$	−3.19032	+	8.76534i	−0.592428	+	1.62768i	0.173558	+	0.984824i	$0.444474\pi$
$29$	−3.19032	+	8.76534i	−0.592428	+	1.62768i	−0.765985	+	0.642858i	$0.777748\pi$
$30$	−8.51978	+	5.64631i	−1.55549	+	1.03087i
$31$	−2.12932	−	3.68810i	−0.382438	−	0.662401i	0.608972	−	0.793191i	$-0.291582\pi$
$31$	−2.12932	−	3.68810i	−0.382438	−	0.662401i	−0.991410	+	0.130790i	$0.958249\pi$
$32$	−5.43112	+	1.58206i	−0.960096	+	0.279672i
$33$	2.22493	+	1.86694i	0.387311	+	0.324992i
$34$	−0.781451	−	0.464949i	−0.134018	−	0.0797381i
$35$	2.94786	+	4.32375i	0.498279	+	0.730847i
$36$	7.78267	−	12.6983i	1.29711	−	2.11638i
$37$	−3.38747			−0.556896			−0.278448	−	0.960451i	$-0.589820\pi$
$37$	−3.38747			−0.556896			−0.278448	+	0.960451i	$0.589820\pi$
$38$	−6.16324	−	0.120111i	−0.999810	−	0.0194846i
$39$			18.9003i			3.02648i
$40$	3.35430	+	5.36178i	0.530361	+	0.847772i
$41$	−6.32042	−	1.11446i	−0.987084	−	0.174050i	−0.343274	−	0.939235i	$-0.611536\pi$
$41$	−6.32042	−	1.11446i	−0.987084	−	0.174050i	−0.643810	+	0.765186i	$0.722647\pi$
$42$	−9.19316	−	5.46976i	−1.41853	−	0.844002i
$43$	5.23859	+	4.39570i	0.798877	+	0.670338i	0.947925	−	0.318492i	$-0.103176\pi$
$43$	5.23859	+	4.39570i	0.798877	+	0.670338i	−0.149048	+	0.988830i	$0.547621\pi$
$44$	1.19096	−	1.34596i	0.179544	−	0.202911i
$45$	−16.0291	−	4.50995i	−2.38947	−	0.672304i
$46$	−0.519102	+	2.73370i	−0.0765375	+	0.403062i
$47$	5.59404	+	2.03606i	0.815974	+	0.296990i	0.716089	−	0.698009i	$-0.245930\pi$
$47$	5.59404	+	2.03606i	0.815974	+	0.296990i	0.0998850	+	0.994999i	$0.468153\pi$
$48$	−10.8419	−	7.04283i	−1.56489	−	1.01654i
$49$	0.761533	−	1.31901i	0.108790	−	0.188431i
$50$	4.74803	−	5.23986i	0.671474	−	0.741029i
$51$	−0.360875	−	2.04663i	−0.0505327	−	0.286585i
$52$	11.6912	+	0.306911i	1.62128	+	0.0425609i
$53$	5.84953	−	4.90834i	0.803495	−	0.674213i	−0.145551	−	0.989351i	$-0.546495\pi$
$53$	5.84953	−	4.90834i	0.803495	−	0.674213i	0.949046	+	0.315138i	$0.102051\pi$
$54$	20.0617	−	3.26658i	2.73005	−	0.444525i
$55$	−1.81036	−	0.871833i	−0.244109	−	0.117558i
$56$	−3.53272	+	5.59780i	−0.472079	+	0.748038i
$57$	−8.98711	−	10.8499i	−1.19037	−	1.43710i
$58$	4.34874	+	12.4542i	0.571018	+	1.63532i
$59$	−7.26432	+	2.64400i	−0.945734	+	0.344219i	−0.768428	−	0.639937i	$-0.778961\pi$
$59$	−7.26432	+	2.64400i	−0.945734	+	0.344219i	−0.177306	+	0.984156i	$0.556738\pi$
$60$	−4.27874	+	13.8068i	−0.552383	+	1.78245i
$61$	1.01831	−	0.854462i	0.130381	−	0.109403i	−0.575265	−	0.817967i	$-0.695101\pi$
$61$	1.01831	−	0.854462i	0.130381	−	0.109403i	0.705646	+	0.708564i	$0.250657\pi$
$62$	−5.63191	−	2.13395i	−0.715253	−	0.271012i
$63$	−3.02626	−	17.1628i	−0.381273	−	2.16231i
$64$	−4.53255	+	6.59212i	−0.566568	+	0.824015i
$65$	−3.22647	−	12.6713i	−0.400194	−	1.57169i
$66$	4.10714	+	0.0539000i	0.505554	+	0.00663463i
$67$	0.893785	−	2.45565i	0.109193	−	0.300006i	−0.873046	−	0.487637i	$-0.837859\pi$
$67$	0.893785	−	2.45565i	0.109193	−	0.300006i	0.982239	+	0.187631i	$0.0600811\pi$
$68$	−1.27184	+	0.189993i	−0.154234	+	0.0230401i
$69$	−5.50744	+	3.17972i	−0.663018	+	0.382793i
$70$	7.09710	+	2.09773i	0.848266	+	0.250727i
$71$	−3.69048	−	3.09668i	−0.437979	−	0.367508i	0.396973	−	0.917830i	$-0.370061\pi$
$71$	−3.69048	−	3.09668i	−0.437979	−	0.367508i	−0.834953	+	0.550322i	$0.814505\pi$
$72$	−2.83826	−	20.8705i	−0.334492	−	2.45961i
$73$	0.372573	+	0.0656946i	0.0436063	+	0.00768897i	0.195409	−	0.980722i	$-0.437397\pi$
$73$	0.372573	+	0.0656946i	0.0436063	+	0.00768897i	−0.151802	+	0.988411i	$0.548508\pi$
$74$	−3.70991	+	3.03092i	−0.431268	+	0.352337i
$75$	16.1557	+	0.403024i	1.86550	+	0.0465372i
$76$	−6.85737	+	5.38298i	−0.786594	+	0.617471i
$77$		−	2.10301i		−	0.239660i
$78$	16.9110	+	20.6994i	1.91479	+	2.34374i
$79$	2.25143	−	12.7685i	0.253306	−	1.43657i	−0.547078	−	0.837082i	$-0.684260\pi$
$79$	2.25143	−	12.7685i	0.253306	−	1.43657i	0.800384	−	0.599488i	$-0.204629\pi$
$80$	8.47100	+	2.87090i	0.947087	+	0.320977i
$81$	18.4723	+	15.5001i	2.05248	+	1.72224i
$82$	−7.91920	+	4.43462i	−0.874529	+	0.489722i
$83$	−2.23058	−	3.86348i	−0.244838	−	0.424072i	0.717248	−	0.696818i	$-0.245401\pi$
$83$	−2.23058	−	3.86348i	−0.244838	−	0.424072i	−0.962086	+	0.272746i	$0.912068\pi$
$84$	−14.9623	+	2.23512i	−1.63252	+	0.243872i
$85$	0.591320	+	1.31051i	0.0641377	+	0.142145i
$86$	9.67026	+	0.126907i	1.04277	+	0.0136848i
$87$	−15.0745	+	26.1098i	−1.61616	+	2.79927i
$88$	0.100034	−	2.53969i	0.0106637	−	0.270731i
$89$	−0.805285	+	0.141993i	−0.0853600	+	0.0150513i	−0.216165	−	0.976357i	$-0.569355\pi$
$89$	−0.805285	+	0.141993i	−0.0853600	+	0.0150513i	0.130805	+	0.991408i	$0.458244\pi$
$90$	−21.5901	+	9.40270i	−2.27579	+	0.991131i
$91$	10.4834	−	8.79660i	1.09896	−	0.922134i
$92$	1.87745	+	3.45838i	0.195738	+	0.360561i
$93$	−4.70776	−	12.9345i	−0.488172	−	1.34124i
$94$	7.94827	−	2.77537i	0.819801	−	0.286257i
$95$	7.87741	+	5.73990i	0.808205	+	0.588901i
$96$	−18.1754	+	1.98752i	−1.85502	+	0.202850i
$97$	5.80238	−	2.11189i	0.589142	−	0.214430i	−0.0302100	−	0.999544i	$-0.509618\pi$
$97$	5.80238	−	2.11189i	0.589142	−	0.214430i	0.619352	+	0.785113i	$0.287395\pi$
$98$	−0.346160	−	2.12594i	−0.0349675	−	0.214753i
$99$	4.30137	+	5.12617i	0.432303	+	0.515199i
$100$	0.511642	−	9.98690i	0.0511642	−	0.998690i
$101$	−1.20694	−	6.84492i	−0.120095	−	0.681095i	−0.984101	−	0.177612i	$-0.943163\pi$
$101$	−1.20694	−	6.84492i	−0.120095	−	0.681095i	0.864005	−	0.503483i	$-0.167948\pi$
$102$	−2.22643	−	1.91855i	−0.220450	−	0.189964i
$103$	−4.29098	−	2.47740i	−0.422802	−	0.244105i	0.273473	−	0.961880i	$-0.411828\pi$
$103$	−4.29098	−	2.47740i	−0.422802	−	0.244105i	−0.696276	+	0.717775i	$0.745161\pi$
$104$	13.0786	−	10.1245i	1.28247	−	0.992790i
$105$	6.95642	+	15.4172i	0.678877	+	1.50456i
$106$	2.01461	−	10.6094i	0.195677	−	1.03047i
$107$	−8.16547	+	4.71434i	−0.789386	+	0.455752i	−0.839746	−	0.542979i	$-0.817296\pi$
$107$	−8.16547	+	4.71434i	−0.789386	+	0.455752i	0.0503603	+	0.998731i	$0.483963\pi$
$108$	19.0485	−	21.5276i	1.83294	−	2.07149i
$109$	3.00677	−	3.58333i	0.287996	−	0.343220i	−0.602577	−	0.798061i	$-0.705859\pi$
$109$	3.00677	−	3.58333i	0.287996	−	0.343220i	0.890573	+	0.454840i	$0.150304\pi$
$110$	−2.76275	+	0.664992i	−0.263418	+	0.0634045i
$111$	−10.7824	−	1.90124i	−1.02342	−	0.180457i
$112$	1.13962	+	9.29151i	0.107684	+	0.877965i
$113$	5.24843			0.493731			0.246865	−	0.969050i	$-0.420599\pi$
$113$	5.24843			0.493731			0.246865	+	0.969050i	$0.420599\pi$
$114$	−19.5504	−	3.84148i	−1.83107	−	0.359787i
$115$	3.14954	−	3.07195i	0.293696	−	0.286461i
$116$	15.9060	+	9.74864i	1.47684	+	0.905139i
$117$	−7.56164	+	42.8842i	−0.699074	+	3.96465i
$118$	−5.59008	+	9.39538i	−0.514608	+	0.864915i
$119$	−0.967236	+	1.15271i	−0.0886664	+	0.105669i
$120$	7.66754	+	18.9494i	0.699947	+	1.72983i
$121$	−5.09625	−	8.82696i	−0.463295	−	0.802451i
$122$	0.350711	−	1.84692i	0.0317519	−	0.167212i
$123$	−19.4927	−	7.09475i	−1.75759	−	0.639712i
$124$	−8.07733	+	2.70205i	−0.725365	+	0.242651i
$125$	−10.9001	+	2.48773i	−0.974931	+	0.222510i
$126$	−18.6706	−	16.0887i	−1.66331	−	1.43330i
$127$	9.49433	−	1.67411i	0.842486	−	0.148553i	0.264282	−	0.964445i	$-0.414865\pi$
$127$	9.49433	−	1.67411i	0.842486	−	0.148553i	0.578204	+	0.815892i	$0.303754\pi$
$128$	0.934283	+	11.2751i	0.0825797	+	0.996584i
$129$	14.2075	+	16.9319i	1.25090	+	1.49077i
$130$	−14.8712	−	10.9906i	−1.30429	−	0.963940i
$131$	5.00866	+	13.7612i	0.437608	+	1.20232i	0.941043	+	0.338286i	$0.109847\pi$
$131$	5.00866	+	13.7612i	0.437608	+	1.20232i	−0.503435	+	0.864033i	$0.667931\pi$
$132$	4.54631	−	3.61581i	0.395706	−	0.314716i
$133$	−1.83528	+	10.0346i	−0.159139	+	0.870111i
$134$	−1.21832	−	3.48911i	−0.105247	−	0.301413i
$135$	−28.9553	−	13.9443i	−2.49208	−	1.20013i
$136$	−1.22291	+	1.34605i	−0.104864	+	0.115423i
$137$	8.59083	+	10.2382i	0.733964	+	0.874705i	0.995907	−	0.0903788i	$-0.0288078\pi$
$137$	8.59083	+	10.2382i	0.733964	+	0.874705i	−0.261943	+	0.965083i	$0.584363\pi$
$138$	−3.18663	+	8.41014i	−0.271264	+	0.715918i
$139$	−10.2890	+	1.81423i	−0.872702	+	0.153881i	−0.592023	−	0.805921i	$-0.701671\pi$
$139$	−10.2890	+	1.81423i	−0.872702	+	0.153881i	−0.280679	+	0.959802i	$0.590560\pi$
$140$	9.64958	−	4.05269i	0.815538	−	0.342515i
$141$	16.6633	+	9.62056i	1.40330	+	0.810197i
$142$	−6.81250	−	0.0894037i	−0.571692	−	0.00750259i
$143$	−1.79722	+	4.93783i	−0.150291	+	0.412922i
$144$	−21.7822	−	20.3176i	−1.81518	−	1.69313i
$145$	5.64920	−	20.0782i	0.469141	−	1.66740i
$146$	0.466816	−	0.261409i	0.0386340	−	0.0216344i
$147$	3.16430	−	3.77106i	0.260987	−	0.311032i
$148$	−1.35114	+	6.63884i	−0.111063	+	0.545709i
$149$	0.803330	−	4.55591i	0.0658114	−	0.373235i	−0.934059	−	0.357119i	$-0.883759\pi$
$149$	0.803330	−	4.55591i	0.0658114	−	0.373235i	0.999870	−	0.0161155i	$-0.00512996\pi$
$150$	18.0541	−	14.0138i	1.47411	−	1.14422i
$151$	22.9712			1.86937			0.934684	−	0.355480i	$-0.115682\pi$
$151$	22.9712			1.86937			0.934684	+	0.355480i	$0.115682\pi$
$152$	−2.69369	+	12.0310i	−0.218487	+	0.975840i
$153$		−	4.78810i		−	0.387095i
$154$	−1.88165	−	2.30318i	−0.151628	−	0.185596i
$155$	5.36425	+	7.86798i	0.430867	+	0.631971i
$156$	37.0413	+	7.53867i	2.96568	+	0.603576i
$157$	11.2630	−	13.4227i	0.898884	−	1.07125i	−0.0982172	−	0.995165i	$-0.531314\pi$
$157$	11.2630	−	13.4227i	0.898884	−	1.07125i	0.997101	−	0.0760836i	$-0.0242416\pi$
$158$	−8.95882	−	15.9984i	−0.712725	−	1.27276i
$159$	21.3741	−	12.3404i	1.69508	−	0.978655i
$160$	11.8461	−	4.43521i	0.936513	−	0.350634i
$161$	4.32696	+	1.57488i	0.341012	+	0.124118i
$162$	34.0993	+	0.447502i	2.67910	+	0.0351590i
$163$	−3.53461	+	6.12212i	−0.276852	+	0.479521i	−0.970601	−	0.240696i	$-0.922624\pi$
$163$	−3.53461	+	6.12212i	−0.276852	+	0.479521i	0.693749	+	0.720217i	$0.255958\pi$
$164$	−4.70514	+	11.9424i	−0.367410	+	0.932544i
$165$	−5.27314	−	3.79116i	−0.410513	−	0.295141i
$166$	−5.89973	−	2.23543i	−0.457907	−	0.173503i
$167$	0.444373	+	0.529583i	0.0343866	+	0.0409803i	0.782964	−	0.622067i	$-0.213707\pi$
$167$	0.444373	+	0.529583i	0.0343866	+	0.0409803i	−0.748577	+	0.663048i	$0.769263\pi$
$168$	−14.3866	+	15.8353i	−1.10995	+	1.22172i
$169$	−19.9164	+	7.24897i	−1.53203	+	0.557613i
$170$	1.82018	+	0.906176i	0.139601	+	0.0695005i
$171$	−16.0506	−	28.2136i	−1.22742	−	2.15755i
$172$	10.7043	−	8.51342i	0.816194	−	0.649142i
$173$	−6.09286	+	2.21762i	−0.463231	+	0.168602i	−0.563084	−	0.826400i	$-0.690385\pi$
$173$	−6.09286	+	2.21762i	−0.463231	+	0.168602i	0.0998524	+	0.995002i	$0.468163\pi$
$174$	6.85223	+	42.0830i	0.519466	+	3.19030i
$175$	−7.29565	−	9.14860i	−0.551499	−	0.691569i
$176$	−2.16281	−	2.87093i	−0.163028	−	0.216405i
$177$	−24.6066	+	4.33880i	−1.84954	+	0.326125i
$178$	−0.754889	+	0.876034i	−0.0565813	+	0.0656615i
$179$	3.68009	−	6.37411i	0.275063	−	0.476423i	−0.695088	−	0.718925i	$-0.744635\pi$
$179$	3.68009	−	6.37411i	0.275063	−	0.476423i	0.970151	+	0.242501i	$0.0779679\pi$
$180$	−15.2321	+	29.6153i	−1.13534	+	2.20739i
$181$	4.50680	−	12.3823i	0.334988	−	0.920372i	−0.651805	−	0.758387i	$-0.725988\pi$
$181$	4.50680	−	12.3823i	0.334988	−	0.920372i	0.986793	−	0.161986i	$-0.0517898\pi$
$182$	3.61054	−	19.0139i	0.267631	−	1.40940i
$183$	3.72089	−	2.14826i	0.275056	−	0.158804i
$184$	5.15052	+	2.10773i	0.379702	+	0.155384i
$185$	7.55343	−	0.566022i	0.555339	−	0.0416147i
$186$	−16.7289	−	9.95339i	−1.22662	−	0.729818i
$187$	0.100332	−	0.569009i	0.00733698	−	0.0416101i
$188$	6.22159	−	10.1512i	0.453756	−	0.740353i
$189$		−	33.6359i		−	2.44665i
$190$	13.7630	−	0.762008i	0.998471	−	0.0552819i
$191$			1.08457i			0.0784764i	0.999230	+	0.0392382i	$0.0124931\pi$
$191$			1.08457i			0.0784764i	−0.999230	+	0.0392382i	$0.987507\pi$
$192$	−18.1271	+	18.4391i	−1.30821	+	1.33072i
$193$	1.15017	−	6.52294i	0.0827911	−	0.469532i	−0.915020	−	0.403408i	$-0.867826\pi$
$193$	1.15017	−	6.52294i	0.0827911	−	0.469532i	0.997811	−	0.0661240i	$-0.0210633\pi$
$194$	4.46508	−	7.50456i	0.320574	−	0.538796i
$195$	−3.15811	−	42.1443i	−0.226157	−	3.01801i
$196$	−2.28129	−	2.01858i	−0.162949	−	0.144184i
$197$	11.1160	−	6.41784i	0.791984	−	0.457252i	−0.0486762	−	0.998815i	$-0.515500\pi$
$197$	11.1160	−	6.41784i	0.791984	−	0.457252i	0.840661	+	0.541562i	$0.182167\pi$
$198$	9.29740	+	1.76548i	0.660738	+	0.125467i
$199$	−0.191357	+	0.525748i	−0.0135649	+	0.0372693i	−0.946290	−	0.323318i	$-0.895202\pi$
$199$	−0.191357	+	0.525748i	−0.0135649	+	0.0372693i	0.932725	+	0.360588i	$0.117424\pi$
$200$	−8.37538	−	11.3953i	−0.592229	−	0.805770i
$201$	4.22320	−	7.31480i	0.297882	−	0.515947i
$202$	−7.44629	−	6.41655i	−0.523919	−	0.451467i
$203$	21.4982	−	3.79072i	1.50888	−	0.266056i
$204$	−4.15497	−	0.109074i	−0.290906	−	0.00763671i
$205$	14.2796	+	1.42895i	0.997330	+	0.0998019i
$206$	−6.91605	+	1.12612i	−0.481864	+	0.0784604i
$207$	−13.7683	+	5.01126i	−0.956965	+	0.348307i
$208$	5.26469	−	22.7903i	0.365041	−	1.58022i
$209$	−1.31623	−	3.68918i	−0.0910455	−	0.255186i
$210$	21.4130	+	10.6605i	1.47764	+	0.735641i
$211$	−7.68276	+	2.79630i	−0.528903	+	0.192505i	−0.592649	−	0.805461i	$-0.701918\pi$
$211$	−7.68276	+	2.79630i	−0.528903	+	0.192505i	0.0637453	+	0.997966i	$0.479695\pi$
$212$	−7.28631	−	13.4218i	−0.500426	−	0.921814i
$213$	−10.0089	−	11.9282i	−0.685800	−	0.817305i
$214$	−4.72458	+	12.4691i	−0.322966	+	0.852369i
$215$	−12.4156	−	8.92627i	−0.846736	−	0.608766i
$216$	1.59997	−	40.6203i	0.108864	−	2.76386i
$217$	−4.98322	+	8.63119i	−0.338283	+	0.585924i
$218$	0.0868079	−	6.61470i	0.00587937	−	0.448004i
$219$	1.14904	+	0.418217i	0.0776451	+	0.0282605i
$220$	−2.43073	+	3.20025i	−0.163880	+	0.215761i
$221$	3.25616	−	1.87994i	0.219033	−	0.126459i
$222$	−13.5099	+	7.56533i	−0.906725	+	0.507752i
$223$	6.14743	−	7.32622i	0.411662	−	0.490600i	−0.519877	−	0.854241i	$-0.674022\pi$
$223$	6.14743	−	7.32622i	0.411662	−	0.490600i	0.931539	+	0.363641i	$0.118467\pi$
$224$	9.56163	+	9.15627i	0.638863	+	0.611779i
$225$	36.4955	+	7.37802i	2.43303	+	0.491868i
$226$	5.74800	−	4.69600i	0.382352	−	0.312373i
$227$			19.7614i			1.31161i	0.754932	+	0.655804i	$0.227670\pi$
$227$			19.7614i			1.31161i	−0.754932	+	0.655804i	$0.772330\pi$
$228$	−24.8485	+	13.2855i	−1.64563	+	0.879855i
$229$	−18.4695			−1.22050			−0.610249	−	0.792209i	$-0.708931\pi$
$229$	−18.4695			−1.22050			−0.610249	+	0.792209i	$0.708931\pi$
$230$	0.700721	−	6.18239i	0.0462042	−	0.407655i
$231$	1.18032	−	6.69395i	0.0776596	−	0.440430i
$232$	26.1426	−	3.55523i	1.71634	−	0.233412i
$233$	−16.5409	+	19.7127i	−1.08363	+	1.29142i	−0.129648	+	0.991560i	$0.541385\pi$
$233$	−16.5409	+	19.7127i	−1.08363	+	1.29142i	−0.953983	+	0.299861i	$0.903060\pi$
$234$	30.0890	+	53.7319i	1.96698	+	3.51257i
$235$	−12.8139	−	3.60532i	−0.835886	−	0.235185i
$236$	2.28429	+	15.2914i	0.148694	+	0.995384i
$237$	14.3328	−	39.3791i	0.931016	−	2.55794i
$238$	−0.0279249	+	2.12786i	−0.00181010	+	0.137929i
$239$	−2.24315	−	1.29508i	−0.145097	−	0.0837720i	0.425694	−	0.904867i	$-0.360030\pi$
$239$	−2.24315	−	1.29508i	−0.145097	−	0.0837720i	−0.570791	+	0.821095i	$0.693363\pi$
$240$	25.3522	+	13.8926i	1.63648	+	0.896764i
$241$	0.475181	−	0.0837873i	0.0306091	−	0.00539721i	−0.158323	−	0.987387i	$-0.550609\pi$
$241$	0.475181	−	0.0837873i	0.0306091	−	0.00539721i	0.188932	+	0.981990i	$0.439498\pi$
$242$	−13.4792	−	5.10732i	−0.866477	−	0.328311i
$243$	22.3832	+	26.6752i	1.43588	+	1.71122i
$244$	−1.26843	−	2.33652i	−0.0812027	−	0.149580i
$245$	−1.47768	+	3.06840i	−0.0944056	+	0.196033i
$246$	−27.6961	+	9.67089i	−1.76584	+	0.616593i
$247$	12.8848	−	21.9927i	0.819839	−	1.39936i
$248$	−6.42853	+	10.1864i	−0.408212	+	0.646836i
$249$	−4.93163	−	13.5495i	−0.312529	−	0.858667i
$250$	−9.71170	+	12.4773i	−0.614222	+	0.789133i
$251$	2.88497	+	3.43818i	0.182098	+	0.217016i	0.849370	−	0.527799i	$-0.176982\pi$
$251$	2.88497	+	3.43818i	0.182098	+	0.217016i	−0.667272	+	0.744814i	$0.732538\pi$
$252$	−34.8431	−	0.914682i	−2.19491	−	0.0576196i
$253$	−1.74121	+	0.307022i	−0.109469	+	0.0193023i
$254$	8.90016	−	10.3285i	0.558446	−	0.648065i
$255$	1.14666	+	4.50330i	0.0718068	+	0.282008i
$256$	11.1115	+	11.5123i	0.694470	+	0.719522i
$257$	−25.3165	−	9.21445i	−1.57920	−	0.574782i	−0.604170	−	0.796855i	$-0.706495\pi$
$257$	−25.3165	−	9.21445i	−1.57920	−	0.574782i	−0.975030	+	0.222073i	$0.928718\pi$
$258$	30.7096	+	5.83144i	1.91190	+	0.363050i
$259$	3.96382	+	6.86554i	0.246300	+	0.426604i
$260$	−26.1205	+	1.26916i	−1.61993	+	0.0787100i
$261$	−44.6496	+	53.2113i	−2.76374	+	3.29370i
$262$	17.7981	+	10.5896i	1.09957	+	0.654226i
$263$	−1.47283	+	8.35282i	−0.0908184	+	0.515057i	0.905130	+	0.425134i	$0.139773\pi$
$263$	−1.47283	+	8.35282i	−0.0908184	+	0.515057i	−0.995949	+	0.0899226i	$0.971338\pi$
$264$	1.74383	−	8.02778i	0.107325	−	0.494076i
$265$	−12.2232	+	11.9221i	−0.750867	+	0.732370i
$266$	6.96844	+	12.6319i	0.427262	+	0.774510i
$267$	−2.64295			−0.161746
$268$	−4.45615	−	2.73113i	−0.272203	−	0.166830i
$269$	19.9130	+	3.51120i	1.21412	+	0.214082i	0.743792	−	0.668411i	$-0.233025\pi$
$269$	19.9130	+	3.51120i	1.21412	+	0.214082i	0.470326	+	0.882493i	$0.344136\pi$
$270$	−44.1880	+	10.6360i	−2.68920	+	0.647288i
$271$	−13.4995	+	16.0880i	−0.820034	+	0.977279i	−0.999980	−	0.00639786i	$-0.997963\pi$
$271$	−13.4995	+	16.0880i	−0.820034	+	0.977279i	0.179945	+	0.983677i	$0.442408\pi$
$272$	−0.134940	+	2.56837i	−0.00818194	+	0.155730i
$273$	38.3062	−	22.1161i	2.31840	−	1.33853i
$274$	18.5691	+	3.52608i	1.12180	+	0.213018i
$275$	4.18245	+	1.64153i	0.252211	+	0.0989879i
$276$	4.03497	+	12.0619i	0.242877	+	0.726040i
$277$	26.0119	+	15.0180i	1.56291	+	0.902344i	0.996961	+	0.0779005i	$0.0248216\pi$
$277$	26.0119	+	15.0180i	1.56291	+	0.902344i	0.565944	+	0.824443i	$0.308512\pi$
$278$	−9.64510	+	11.1930i	−0.578475	+	0.671309i
$279$	−5.50692	−	31.2313i	−0.329691	−	1.86977i
$280$	6.94196	−	13.0724i	0.414861	−	0.781223i
$281$	−7.12164	−	8.48724i	−0.424841	−	0.506306i	0.510585	−	0.859827i	$-0.329429\pi$
$281$	−7.12164	−	8.48724i	−0.424841	−	0.506306i	−0.935427	+	0.353521i	$0.884984\pi$
$282$	26.8574	−	4.37310i	1.59933	−	0.260414i
$283$	−28.5634	+	10.3962i	−1.69792	+	0.617992i	−0.995586	−	0.0938549i	$-0.970081\pi$
$283$	−28.5634	+	10.3962i	−1.69792	+	0.617992i	−0.702334	+	0.711847i	$0.747859\pi$
$284$	−7.54095	+	5.99753i	−0.447473	+	0.355888i
$285$	21.8526	+	22.6916i	1.29443	+	1.34413i
$286$	2.44980	+	7.01590i	0.144860	+	0.414859i
$287$	5.13707	+	14.1140i	0.303231	+	0.833121i
$288$	−42.0346	−	2.76201i	−2.47691	−	0.162753i
$289$	12.7061	−	10.6616i	0.747415	−	0.627156i
$290$	−11.7779	−	27.0439i	−0.691622	−	1.58807i
$291$	19.6545	−	3.46562i	1.15217	−	0.203158i
$292$	0.277356	−	0.703973i	0.0162310	−	0.0411969i
$293$	−8.19598	+	14.1959i	−0.478814	+	0.829331i	−0.999705	−	0.0242928i	$-0.992267\pi$
$293$	−8.19598	+	14.1959i	−0.478814	+	0.829331i	0.520891	+	0.853623i	$0.325600\pi$
$294$	0.0913558	−	6.96125i	0.00532798	−	0.405988i
$295$	15.7563	−	7.10944i	0.917367	−	0.413928i
$296$	4.46031	+	8.47968i	0.259250	+	0.492872i
$297$	6.45767	+	11.1850i	0.374712	+	0.649020i
$298$	−3.19658	−	5.70835i	−0.185173	−	0.330676i
$299$	−8.81375	−	7.39562i	−0.509713	−	0.427700i
$300$	7.23379	−	31.5016i	0.417643	−	1.81874i
$301$	2.77907	−	15.7609i	0.160183	−	0.908442i
$302$	25.1577	−	20.5533i	1.44766	−	1.18271i
$303$		−	22.4651i		−	1.29058i
$304$	7.81454	+	15.5863i	0.448195	+	0.893936i
$305$	−2.12786	+	2.07544i	−0.121841	+	0.118840i
$306$	−4.28413	−	5.24386i	−0.244907	−	0.299772i
$307$	11.7927	+	2.07936i	0.673042	+	0.118675i	0.499716	−	0.866189i	$-0.333438\pi$
$307$	11.7927	+	2.07936i	0.673042	+	0.118675i	0.173326	+	0.984865i	$0.444549\pi$
$308$	−4.12152	−	0.838814i	−0.234845	−	0.0477958i
$309$	−12.2679	−	10.2940i	−0.697896	−	0.585605i
$310$	12.9147	+	3.81726i	0.733505	+	0.216806i
$311$	−11.4964	+	6.63743i	−0.651899	+	0.376374i	−0.789183	−	0.614158i	$-0.789496\pi$
$311$	−11.4964	+	6.63743i	−0.651899	+	0.376374i	0.137284	+	0.990532i	$0.456163\pi$
$312$	47.3123	−	24.8863i	2.67853	−	1.40891i
$313$	−1.79615	+	4.93488i	−0.101524	+	0.278936i	−0.980047	−	0.198764i	$-0.936307\pi$
$313$	−1.79615	+	4.93488i	−0.101524	+	0.278936i	0.878523	+	0.477700i	$0.158529\pi$
$314$	0.325172	−	24.7779i	0.0183505	−	1.39830i
$315$	9.61578	+	37.7642i	0.541788	+	2.12777i
$316$	−24.1260	−	9.50531i	−1.35719	−	0.534716i
$317$	−3.04766	−	17.2841i	−0.171174	−	0.970773i	−0.942468	−	0.334295i	$-0.891502\pi$
$317$	−3.04766	−	17.2841i	−0.171174	−	0.970773i	0.771295	−	0.636478i	$-0.219609\pi$
$318$	12.3672	−	32.6394i	0.693517	−	1.83033i
$319$	−6.42108	+	5.38793i	−0.359512	+	0.301666i
$320$	9.00525	−	15.4566i	0.503409	−	0.864048i
$321$	−28.6370	+	10.4230i	−1.59836	+	0.581756i
$322$	6.14795	−	2.14673i	0.342612	−	0.119633i
$323$	−0.975311	+	2.62750i	−0.0542678	+	0.146198i
$324$	37.7455	−	30.0201i	2.09697	−	1.66778i
$325$	9.31172	+	27.7156i	0.516521	+	1.53739i
$326$	1.60668	+	9.86743i	0.0889858	+	0.546506i
$327$	11.5818	−	9.71831i	0.640477	−	0.537424i
$328$	5.53239	+	17.2890i	0.305475	+	0.954627i
$329$	−2.41924	−	13.7202i	−0.133377	−	0.756418i
$330$	−9.16718	+	0.566087i	−0.504637	+	0.0311621i
$331$	11.4967	−	19.9130i	0.631918	−	1.09451i	−0.355241	−	0.934775i	$-0.615601\pi$
$331$	11.4967	−	19.9130i	0.631918	−	1.09451i	0.987159	−	0.159740i	$-0.0510656\pi$
$332$	−8.46143	+	2.83054i	−0.464381	+	0.155346i
$333$	−23.7044	−	8.62768i	−1.29899	−	0.472794i
$334$	0.960512	+	0.182391i	0.0525569	+	0.00998002i
$335$	−1.58265	+	5.62500i	−0.0864696	+	0.307327i
$336$	−1.58746	+	30.2149i	−0.0866033	+	1.64836i
$337$	−4.14920	−	3.48159i	−0.226021	−	0.189654i	0.522744	−	0.852490i	$-0.324908\pi$
$337$	−4.14920	−	3.48159i	−0.226021	−	0.189654i	−0.748765	+	0.662836i	$0.769353\pi$
$338$	−15.3262	+	25.7591i	−0.833634	+	1.40111i
$339$	16.7060	+	2.94571i	0.907343	+	0.159989i
$340$	2.80423	−	0.636166i	0.152081	−	0.0345009i
$341$		−	3.82686i		−	0.207236i
$342$	−42.8224	−	16.5379i	−2.31557	−	0.894268i
$343$	−19.9464			−1.07700
$344$	4.10584	−	18.9014i	0.221372	−	1.01909i
$345$	11.7493	−	8.01045i	0.632559	−	0.431268i
$346$	−4.68861	+	7.88026i	−0.252061	+	0.423645i
$347$	20.3891	+	17.1085i	1.09455	+	0.918433i	0.997046	−	0.0768024i	$-0.0244710\pi$
$347$	20.3891	+	17.1085i	1.09455	+	0.918433i	0.0974997	+	0.995236i	$0.468915\pi$
$348$	45.1580	+	39.9577i	2.42072	+	2.14196i
$349$	13.8114	+	23.9220i	0.739305	+	1.28051i	0.952808	+	0.303572i	$0.0981793\pi$
$349$	13.8114	+	23.9220i	0.739305	+	1.28051i	−0.213503	+	0.976942i	$0.568487\pi$
$350$	−16.1758	−	3.49168i	−0.864630	−	0.186638i
$351$	−28.7452	+	78.9767i	−1.53430	+	4.21546i
$352$	−4.93743	−	1.20904i	−0.263166	−	0.0644420i
$353$	4.07736	+	2.35406i	0.217016	+	0.125294i	0.604568	−	0.796554i	$-0.293346\pi$
$353$	4.07736	+	2.35406i	0.217016	+	0.125294i	−0.387552	+	0.921848i	$0.626679\pi$
$354$	−23.0667	+	26.7684i	−1.22598	+	1.42272i
$355$	8.74653	+	6.28838i	0.464217	+	0.333752i
$356$	−0.0429173	+	1.63485i	−0.00227461	+	0.0866470i
$357$	−3.72572	+	3.12625i	−0.197186	+	0.165459i
$358$	−1.67281	−	10.2736i	−0.0884109	−	0.542975i
$359$	8.15475	+	22.4050i	0.430391	+	1.18249i	0.945573	+	0.325410i	$0.105502\pi$
$359$	8.15475	+	22.4050i	0.430391	+	1.18249i	−0.515182	+	0.857081i	$0.672276\pi$
$360$	9.81612	+	46.0631i	0.517355	+	2.42774i
$361$	3.06093	+	18.7518i	0.161102	+	0.986938i
$362$	−6.14324	−	17.5934i	−0.322882	−	0.924689i
$363$	−11.2674	−	30.9569i	−0.591384	−	1.62482i
$364$	−13.0583	−	24.0542i	−0.684443	−	1.26078i
$365$	−0.841745	−	0.0842326i	−0.0440590	−	0.00440894i
$366$	2.15292	−	5.68198i	0.112535	−	0.297002i
$367$	−1.75517	−	9.95409i	−0.0916194	−	0.519599i	−0.995731	−	0.0923029i	$-0.970577\pi$
$367$	−1.75517	−	9.95409i	−0.0916194	−	0.519599i	0.904112	−	0.427296i	$-0.140534\pi$
$368$	7.52666	−	2.30005i	0.392354	−	0.119898i
$369$	−41.3897	−	23.8964i	−2.15466	−	1.24400i
$370$	7.76596	−	7.37829i	0.403733	−	0.383579i
$371$	−16.7928	−	6.11206i	−0.871836	−	0.317322i
$372$	−27.2270	+	4.06728i	−1.41165	+	0.210879i
$373$	−12.2014	−	21.1335i	−0.631766	−	1.09425i	−0.987191	−	0.159546i	$-0.948997\pi$
$373$	−12.2014	−	21.1335i	−0.631766	−	1.09425i	0.355425	−	0.934705i	$-0.384336\pi$
$374$	−0.399236	−	0.712942i	−0.0206440	−	0.0368654i
$375$	−36.0916	+	1.80083i	−1.86376	+	0.0929946i
$376$	−2.26895	−	16.6842i	−0.117012	−	0.860422i
$377$	−53.7171	−	9.47178i	−2.76657	−	0.487821i
$378$	−30.0955	−	36.8376i	−1.54795	−	1.89472i
$379$	22.9057			1.17659			0.588293	−	0.808648i	$-0.299800\pi$
$379$	22.9057			1.17659			0.588293	+	0.808648i	$0.299800\pi$
$380$	14.3912	−	13.1489i	0.738253	−	0.674523i
$381$	31.1605			1.59640
$382$	0.970409	+	1.18780i	0.0496504	+	0.0607732i
$383$	−35.4425	−	6.24947i	−1.81103	−	0.319333i	−0.837247	−	0.546825i	$-0.815836\pi$
$383$	−35.4425	−	6.24947i	−1.81103	−	0.319333i	−0.973780	+	0.227492i	$0.926947\pi$
$384$	−3.35434	+	36.4134i	−0.171175	+	1.85821i
$385$	0.351397	+	4.68931i	0.0179089	+	0.238990i
$386$	−4.57672	−	8.17295i	−0.232949	−	0.415992i
$387$	25.4623	+	44.1020i	1.29432	+	2.24183i
$388$	−1.82457	−	12.2140i	−0.0926288	−	0.620071i
$389$	20.5377	+	7.47511i	1.04130	+	0.379003i	0.805374	−	0.592767i	$-0.201965\pi$
$389$	20.5377	+	7.47511i	1.04130	+	0.379003i	0.235929	+	0.971770i	$0.424187\pi$
$390$	−41.1671	−	43.3301i	−2.08458	−	2.19410i
$391$	1.09561	+	0.632550i	0.0554073	+	0.0319894i
$392$	−4.30454	−	0.169550i	−0.217412	−	0.00856355i
$393$	8.21922	+	46.6135i	0.414605	+	2.35134i
$394$	6.43179	−	16.9747i	0.324029	−	0.855175i
$395$	−2.88675	+	28.8476i	−0.145248	+	1.45148i
$396$	11.7620	−	6.38527i	0.591065	−	0.320872i
$397$	7.24010	+	19.8920i	0.363370	+	0.998351i	0.977829	+	0.209403i	$0.0671520\pi$
$397$	7.24010	+	19.8920i	0.363370	+	0.998351i	−0.614459	+	0.788948i	$0.710626\pi$
$398$	0.260839	+	0.747008i	0.0130747	+	0.0374441i
$399$	−11.4738	+	30.9105i	−0.574407	+	1.54746i
$400$	−19.3685	−	4.98615i	−0.968424	−	0.249307i
$401$	−0.365563	−	1.00438i	−0.0182554	−	0.0501562i	0.930230	−	0.366976i	$-0.119607\pi$
$401$	−0.365563	−	1.00438i	−0.0182554	−	0.0501562i	−0.948486	+	0.316820i	$0.897385\pi$
$402$	−1.91969	−	11.7898i	−0.0957453	−	0.588020i
$403$	19.0767	−	16.0073i	0.950280	−	0.797380i
$404$	−13.8962	−	0.364797i	−0.691364	−	0.0181493i
$405$	−43.7799	−	31.4759i	−2.17544	−	1.56405i
$406$	20.1528	−	23.3870i	1.00017	−	1.16068i
$407$	−2.63619	−	1.52201i	−0.130671	−	0.0754431i
$408$	−4.64805	+	3.59818i	−0.230113	+	0.178136i
$409$	8.11558	−	22.2974i	0.401289	−	1.10253i	−0.560359	−	0.828250i	$-0.689337\pi$
$409$	8.11558	−	22.2974i	0.401289	−	1.10253i	0.961649	−	0.274284i	$-0.0884409\pi$
$410$	16.9174	−	11.2116i	0.835489	−	0.553703i
$411$	21.5987	+	37.4101i	1.06539	+	1.84531i
$412$	−6.56678	+	7.42141i	−0.323522	+	0.365627i
$413$	13.8590	+	11.6291i	0.681957	+	0.572230i
$414$	−10.5951	+	17.8074i	−0.520720	+	0.875186i
$415$	5.61934	+	8.24213i	0.275843	+	0.404590i
$416$	−14.6257	−	29.6701i	−0.717082	−	1.45470i
$417$	−33.7686			−1.65365
$418$	−4.74239	−	2.86265i	−0.231958	−	0.140017i
$419$		−	2.45023i		−	0.119702i	−0.998207	−	0.0598508i	$-0.980938\pi$
$419$		−	2.45023i		−	0.119702i	0.998207	−	0.0598508i	$-0.0190625\pi$
$420$	32.9896	−	7.48400i	1.60973	−	0.365182i
$421$	7.83524	+	1.38156i	0.381866	+	0.0673333i	0.361286	−	0.932455i	$-0.382338\pi$
$421$	7.83524	+	1.38156i	0.381866	+	0.0673333i	0.0205798	+	0.999788i	$0.493449\pi$
$422$	−5.91208	+	9.93658i	−0.287796	+	0.483705i
$423$	33.9595	+	28.4954i	1.65117	+	1.38549i
$424$	−19.9890	−	8.17999i	−0.970750	−	0.397256i
$425$	−1.53751	−	2.82340i	−0.0745803	−	0.136955i
$426$	−21.6343	−	4.10813i	−1.04818	−	0.199040i
$427$	−2.92334	−	1.06401i	−0.141470	−	0.0514910i
$428$	5.98235	+	17.8833i	0.289168	+	0.864420i
$429$	−8.49202	+	14.7086i	−0.409999	+	0.710138i
$430$	−21.5841	+	1.33285i	−1.04088	+	0.0642758i
$431$	3.37820	+	19.1587i	0.162722	+	0.922843i	0.951382	+	0.308013i	$0.0996642\pi$
$431$	3.37820	+	19.1587i	0.162722	+	0.922843i	−0.788660	+	0.614830i	$0.789225\pi$
$432$	−34.5925	−	45.9183i	−1.66433	−	2.20925i
$433$	−5.62003	+	4.71576i	−0.270081	+	0.226625i	−0.767762	−	0.640735i	$-0.778630\pi$
$433$	−5.62003	+	4.71576i	−0.270081	+	0.226625i	0.497681	+	0.867360i	$0.334185\pi$
$434$	2.26516	+	13.9115i	0.108731	+	0.667772i
$435$	29.2506	−	60.7390i	1.40246	−	2.91221i
$436$	−5.82340	−	7.32200i	−0.278890	−	0.350660i
$437$	8.57623	+	0.0545725i	0.410257	+	0.00261056i
$438$	1.63261	−	0.570074i	0.0780092	−	0.0272392i
$439$	−16.1824	+	5.88991i	−0.772344	+	0.281110i	−0.697976	−	0.716121i	$-0.745916\pi$
$439$	−16.1824	+	5.88991i	−0.772344	+	0.281110i	−0.0743675	+	0.997231i	$0.523694\pi$
$440$	0.201305	+	5.67975i	0.00959684	+	0.270771i
$441$	8.68840	−	7.29044i	0.413733	−	0.347164i
$442$	1.88403	−	4.97232i	0.0896142	−	0.236509i
$443$	−0.658914	−	3.73689i	−0.0313060	−	0.177545i	0.965146	−	0.261714i	$-0.0842876\pi$
$443$	−0.658914	−	3.73689i	−0.0313060	−	0.177545i	−0.996452	+	0.0841688i	$0.973177\pi$
$444$	−8.02682	+	20.3734i	−0.380936	+	0.966877i
$445$	1.77191	−	0.451177i	0.0839967	−	0.0213878i
$446$	0.177481	−	13.5240i	0.00840398	−	0.640378i
$447$	5.11407	−	14.0508i	0.241887	−	0.664579i
$448$	18.6643	+	1.47260i	0.881804	+	0.0695739i
$449$	−8.91088	+	5.14470i	−0.420531	+	0.242793i	−0.695304	−	0.718715i	$-0.744730\pi$
$449$	−8.91088	+	5.14470i	−0.420531	+	0.242793i	0.274774	+	0.961509i	$0.411397\pi$
$450$	46.5708	−	24.5738i	2.19537	−	1.15842i
$451$	−4.41794	−	3.70710i	−0.208033	−	0.174560i
$452$	2.09341	−	10.2860i	0.0984657	−	0.483812i
$453$	73.1182	+	12.8927i	3.43539	+	0.605752i
$454$	17.6814	+	21.6424i	0.829828	+	1.01573i
$455$	−21.9062	+	21.3665i	−1.02698	+	1.00168i
$456$	−15.3266	+	36.7832i	−0.717733	+	1.72253i
$457$			15.9912i			0.748039i	0.927421	+	0.374019i	$0.122021\pi$
$457$			15.9912i			0.748039i	−0.927421	+	0.374019i	$0.877979\pi$
$458$	−20.2275	+	16.5255i	−0.945171	+	0.772185i
$459$	1.60473	−	9.10085i	0.0749022	−	0.424791i
$460$	−4.76424	−	7.39783i	−0.222134	−	0.344926i
$461$	−10.8446	−	9.09972i	−0.505085	−	0.423816i	0.354311	−	0.935128i	$-0.384715\pi$
$461$	−10.8446	−	9.09972i	−0.505085	−	0.423816i	−0.859396	+	0.511311i	$0.829160\pi$
$462$	−4.69670	−	8.38721i	−0.218510	−	0.390208i
$463$	1.72660	+	2.99056i	0.0802419	+	0.138983i	0.903354	−	0.428896i	$-0.141097\pi$
$463$	1.72660	+	2.99056i	0.0802419	+	0.138983i	−0.823112	+	0.567879i	$0.807764\pi$
$464$	25.4500	−	27.2846i	1.18148	−	1.26665i
$465$	12.6587	+	28.0548i	0.587033	+	1.30101i
$466$	−0.477550	+	36.3890i	−0.0221221	+	1.68569i
$467$	14.6341	−	25.3470i	0.677185	−	1.17292i	−0.298640	−	0.954366i	$-0.596533\pi$
$467$	14.6341	−	25.3470i	0.677185	−	1.17292i	0.975825	−	0.218553i	$-0.0701337\pi$
$468$	81.0294	+	31.9245i	3.74559	+	1.47571i
$469$	−6.02284	+	1.06199i	−0.278109	+	0.0490381i
$470$	−17.2594	+	7.51666i	−0.796118	+	0.346718i
$471$	43.3841	−	36.4036i	1.99903	−	1.67739i
$472$	16.1836	+	14.7030i	0.744910	+	0.676763i
$473$	2.10176	+	5.77455i	0.0966391	+	0.265514i
$474$	−19.5371	−	55.9516i	−0.897369	−	2.56994i
$475$	−18.5243	−	11.4827i	−0.849952	−	0.526861i
$476$	1.87331	+	2.35539i	0.0858629	+	0.107959i
$477$	53.4343	−	19.4485i	2.44659	−	0.890486i
$478$	−3.61543	+	0.588689i	−0.165366	+	0.0269260i
$479$	−15.7756	−	18.8006i	−0.720804	−	0.859020i	0.273905	−	0.961757i	$-0.411685\pi$
$479$	−15.7756	−	18.8006i	−0.720804	−	0.859020i	−0.994709	+	0.102736i	$0.967240\pi$
$480$	40.1958	−	7.46879i	1.83468	−	0.340902i
$481$	−3.43973	−	19.5077i	−0.156838	−	0.889473i
$482$	0.445444	−	0.516928i	0.0202894	−	0.0235454i
$483$	12.8890	+	7.44145i	0.586469	+	0.338598i
$484$	−19.3320	+	6.46699i	−0.878727	+	0.293954i
$485$	−12.5853	+	5.67867i	−0.571471	+	0.257855i
$486$	48.3812	+	9.18710i	2.19462	+	0.416736i
$487$	−17.2452	+	9.95654i	−0.781456	+	0.451174i	−0.836946	−	0.547285i	$-0.815661\pi$
$487$	−17.2452	+	9.95654i	−0.781456	+	0.451174i	0.0554898	+	0.998459i	$0.482328\pi$
$488$	−3.47975	−	1.42400i	−0.157521	−	0.0644616i
$489$	−14.6869	+	17.5031i	−0.664164	+	0.791519i
$490$	1.12710	+	4.68262i	0.0509174	+	0.211539i
$491$	−12.6512	−	2.23076i	−0.570943	−	0.100673i	−0.119279	−	0.992861i	$-0.538058\pi$
$491$	−12.6512	−	2.23076i	−0.570943	−	0.100673i	−0.451664	+	0.892188i	$0.649169\pi$
$492$	−21.6794	+	35.3723i	−0.977382	+	1.59471i
$493$	5.99762			0.270119
$494$	−5.56663	−	35.6147i	−0.250455	−	1.60238i
$495$	−10.4478	−	10.7117i	−0.469594	−	0.481454i
$496$	2.07378	+	16.9079i	0.0931154	+	0.759186i
$497$	−1.95780	+	11.1032i	−0.0878193	+	0.498048i
$498$	−17.5244	−	10.4267i	−0.785288	−	0.467232i
$499$	20.0321	−	23.8733i	0.896758	−	1.06871i	−0.100517	−	0.994935i	$-0.532050\pi$
$499$	20.0321	−	23.8733i	0.896758	−	1.06871i	0.997275	−	0.0737792i	$-0.0235060\pi$
$500$	0.527874	+	22.3544i	0.0236072	+	0.999721i
$501$	1.11722	+	1.93509i	0.0499139	+	0.0864534i
$502$	6.23587	+	1.18413i	0.278321	+	0.0528503i
$503$	−0.859347	−	0.312777i	−0.0383164	−	0.0139460i	0.322791	−	0.946470i	$-0.395379\pi$
$503$	−0.859347	−	0.312777i	−0.0383164	−	0.0139460i	−0.361107	+	0.932524i	$0.617601\pi$
$504$	−38.9780	+	30.1739i	−1.73622	+	1.34405i
$505$	3.83500	+	15.0612i	0.170655	+	0.670217i
$506$	−1.63224	+	1.89419i	−0.0725620	+	0.0842068i
$507$	−67.4632	+	11.8956i	−2.99615	+	0.528302i
$508$	0.505996	−	19.2750i	0.0224500	−	0.855188i
$509$	8.31018	+	9.90368i	0.368342	+	0.438973i	0.918099	−	0.396352i	$-0.129724\pi$
$509$	8.31018	+	9.90368i	0.368342	+	0.438973i	−0.549757	+	0.835325i	$0.685280\pi$
$510$	5.28511	+	3.90598i	0.234029	+	0.172960i
$511$	−0.302817	−	0.831982i	−0.0133958	−	0.0368047i
$512$	22.4698	+	2.66619i	0.993034	+	0.117830i
$513$	−21.0520	−	59.0055i	−0.929470	−	2.60516i
$514$	−35.9709	+	12.5603i	−1.58661	+	0.554010i
$515$	9.98204	+	4.80715i	0.439861	+	0.211828i
$516$	38.8504	−	21.0907i	1.71029	−	0.928468i
$517$	3.43858	+	4.09794i	0.151228	+	0.180227i
$518$	10.4840	+	3.97243i	0.460641	+	0.174539i
$519$	−20.6385	+	3.63912i	−0.905928	+	0.159740i
$520$	−27.4712	+	24.7611i	−1.20469	+	1.08585i
$521$	−31.0141	−	17.9060i	−1.35875	−	0.784477i	−0.369298	−	0.929311i	$-0.620402\pi$
$521$	−31.0141	−	17.9060i	−1.35875	−	0.784477i	−0.989456	+	0.144834i	$0.953735\pi$
$522$	−1.28907	+	98.2262i	−0.0564211	+	4.29925i
$523$	−13.9660	+	38.3713i	−0.610691	+	1.67786i	0.117998	+	0.993014i	$0.462352\pi$
$523$	−13.9660	+	38.3713i	−0.610691	+	1.67786i	−0.728689	+	0.684845i	$0.759870\pi$
$524$	28.9672	−	4.32724i	1.26544	−	0.189037i
$525$	−18.0876	−	33.2151i	−0.789409	−	1.44963i
$526$	5.86062	+	10.4657i	0.255535	+	0.456326i
$527$	−1.76009	+	2.09760i	−0.0766708	+	0.0913727i
$528$	−5.27300	−	10.3522i	−0.229478	−	0.450521i
$529$	−3.32166	+	18.8381i	−0.144420	+	0.819048i
$530$	−2.71947	+	23.9936i	−0.118126	+	1.04222i
$531$	−57.5674			−2.49821
$532$	18.9340	+	7.59928i	0.820895	+	0.329471i
$533$		−	37.5295i		−	1.62559i
$534$	−2.89452	+	2.36477i	−0.125258	+	0.102333i
$535$	17.4198	−	11.8765i	0.753122	−	0.513466i
$536$	−7.32398	+	0.996017i	−0.316348	+	0.0430214i
$537$	15.2914	−	18.2236i	0.659872	−	0.786405i
$538$	24.9501	−	13.9716i	1.07567	−	0.602360i
$539$	1.18528	−	0.684322i	0.0510536	−	0.0294758i
$540$	−38.8776	+	51.1854i	−1.67302	+	2.20267i
$541$	−10.1932	−	3.71003i	−0.438241	−	0.159507i	0.113471	−	0.993541i	$-0.463803\pi$
$541$	−10.1932	−	3.71003i	−0.438241	−	0.159507i	−0.551712	+	0.834035i	$0.686025\pi$
$542$	−0.389741	+	29.6980i	−0.0167408	+	1.27564i
$543$	21.2950	−	36.8840i	0.913856	−	1.58285i
$544$	2.15025	+	2.93358i	0.0921913	+	0.125776i
$545$	−6.10579	+	8.49257i	−0.261543	+	0.363782i
$546$	22.1641	−	58.4955i	0.948538	−	2.50337i
$547$	−11.5230	−	13.7326i	−0.492690	−	0.587165i	0.461210	−	0.887291i	$-0.347416\pi$
$547$	−11.5230	−	13.7326i	−0.492690	−	0.587165i	−0.953899	+	0.300127i	$0.902971\pi$
$548$	23.4915	−	12.7529i	1.00351	−	0.544776i
$549$	9.30204	−	3.38567i	0.397001	−	0.144497i
$550$	6.04931	−	1.94445i	0.257944	−	0.0829115i
$551$	35.3406	−	20.1052i	1.50556	−	0.856509i
$552$	15.2114	+	9.59974i	0.647438	+	0.408592i
$553$	−28.5130	+	10.3779i	−1.21250	+	0.441313i
$554$	41.9252	−	6.82654i	1.78123	−	0.290032i
$555$	24.3606	+	2.43774i	1.03405	+	0.103476i
$556$	−0.548348	+	20.8883i	−0.0232551	+	0.885860i
$557$	4.50207	−	0.793836i	0.190759	−	0.0336359i	−0.0774525	−	0.996996i	$-0.524679\pi$
$557$	4.50207	−	0.793836i	0.190759	−	0.0336359i	0.268211	+	0.963360i	$0.413568\pi$
$558$	−33.9752	−	29.2768i	−1.43828	−	1.23939i
$559$	−19.9944	+	34.6314i	−0.845674	+	1.46475i
$560$	−4.09369	−	20.5279i	−0.172990	−	0.867464i
$561$	0.638720	−	1.75487i	0.0269668	−	0.0740906i
$562$	−15.3934	−	2.92306i	−0.649333	−	0.123302i
$563$	30.3535	−	17.5246i	1.27925	−	0.738574i	0.302538	−	0.953137i	$-0.402166\pi$
$563$	30.3535	−	17.5246i	1.27925	−	0.738574i	0.976710	+	0.214563i	$0.0688329\pi$
$564$	25.5010	−	28.8198i	1.07379	−	1.21353i
$565$	−11.7030	+	0.876975i	−0.492350	+	0.0368946i
$566$	−21.9803	+	36.9428i	−0.923901	+	1.55282i
$567$	9.79957	−	55.5761i	0.411543	−	2.33398i
$568$	−2.89248	+	13.3156i	−0.121366	+	0.558712i
$569$			2.16166i			0.0906214i	0.998973	+	0.0453107i	$0.0144278\pi$
$569$			2.16166i			0.0906214i	−0.998973	+	0.0453107i	$0.985572\pi$
$570$	44.2358	+	5.29905i	1.85283	+	0.221953i
$571$			0.651598i			0.0272685i	0.999907	+	0.0136343i	$0.00434005\pi$
$571$			0.651598i			0.0272685i	−0.999907	+	0.0136343i	$0.995660\pi$
$572$	8.96042	+	5.49176i	0.374654	+	0.229622i
$573$	−0.608719	+	3.45222i	−0.0254296	+	0.144218i
$574$	18.2544	+	10.8611i	0.761926	+	0.453332i
$575$	−6.50960	+	7.37615i	−0.271469	+	0.307607i
$576$	−48.5070	+	34.5853i	−2.02112	+	1.44105i
$577$	8.05852	−	4.65259i	0.335481	−	0.193690i	−0.322791	−	0.946470i	$-0.604621\pi$
$577$	8.05852	−	4.65259i	0.335481	−	0.193690i	0.658272	+	0.752780i	$0.271288\pi$
$578$	4.37604	−	23.0452i	0.182019	−	0.958552i
$579$	7.32208	−	20.1173i	0.304295	−	0.836045i
$580$	−37.0964	−	19.0799i	−1.54034	−	0.792250i
$581$	−5.22019	+	9.04164i	−0.216570	+	0.375110i
$582$	18.4245	−	21.3813i	0.763720	−	0.886282i
$583$	6.75757	−	1.19154i	0.279870	−	0.0493486i
$584$	−0.326120	−	1.01914i	−0.0134949	−	0.0421725i
$585$	9.69543	−	96.8874i	0.400857	−	4.00580i
$586$	3.72554	+	22.8804i	0.153901	+	0.945181i
$587$	−0.463800	+	0.168809i	−0.0191431	+	0.00696751i	−0.351574	−	0.936160i	$-0.614353\pi$
$587$	−0.463800	+	0.168809i	−0.0191431	+	0.00696751i	0.332431	+	0.943128i	$0.392131\pi$
$588$	−6.12849	−	7.70560i	−0.252735	−	0.317774i
$589$	−3.33969	+	18.2601i	−0.137610	+	0.752395i
$590$	10.8949	−	21.8840i	0.448538	−	0.900951i
$591$	38.9848	−	14.1893i	1.60362	−	0.583671i
$592$	12.4720	+	5.29599i	0.512597	+	0.217664i
$593$	19.5741	+	23.3275i	0.803812	+	0.957946i	0.999743	−	0.0226716i	$-0.00721722\pi$
$593$	19.5741	+	23.3275i	0.803812	+	0.957946i	−0.195931	+	0.980618i	$0.562773\pi$
$594$	17.0801	+	6.47170i	0.700804	+	0.265537i
$595$	1.96415	−	2.73194i	0.0805223	−	0.111999i
$596$	−8.60836	−	3.39158i	−0.352612	−	0.138924i
$597$	−0.904176	+	1.56608i	−0.0370055	+	0.0640953i
$598$	−16.2699	−	0.213518i	−0.665325	−	0.00873138i
$599$	−20.0725	−	7.30579i	−0.820140	−	0.298507i	−0.102334	−	0.994750i	$-0.532631\pi$
$599$	−20.0725	−	7.30579i	−0.820140	−	0.298507i	−0.717806	+	0.696243i	$0.754853\pi$
$600$	−20.2635	−	40.9725i	−0.827254	−	1.67269i
$601$	8.07048	−	4.65949i	0.329202	−	0.190065i	−0.326285	−	0.945271i	$-0.605797\pi$
$601$	8.07048	−	4.65949i	0.329202	−	0.190065i	0.655487	+	0.755207i	$0.272464\pi$
$602$	−11.0584	−	19.7477i	−0.450706	−	0.804854i
$603$	12.5088	−	14.9074i	0.509398	−	0.607077i
$604$	9.16238	−	45.0195i	0.372812	−	1.83182i
$605$	12.8386	+	18.8310i	0.521964	+	0.765587i
$606$	−20.1005	−	24.6034i	−0.816527	−	0.999446i
$607$			11.8349i			0.480365i	0.970728	+	0.240182i	$0.0772072\pi$
$607$			11.8349i			0.480365i	−0.970728	+	0.240182i	$0.922793\pi$
$608$	22.5041	+	10.0779i	0.912663	+	0.408712i
$609$	70.5573			2.85913
$610$	−0.473415	+	4.17689i	−0.0191680	+	0.169117i
$611$	−6.04489	+	34.2823i	−0.244550	+	1.38691i
$612$	−9.38384	−	1.90980i	−0.379319	−	0.0771992i
$613$	−15.8478	+	18.8867i	−0.640089	+	0.762828i	−0.984384	−	0.176033i	$-0.943673\pi$
$613$	−15.8478	+	18.8867i	−0.640089	+	0.762828i	0.344296	+	0.938861i	$0.388118\pi$
$614$	14.7756	−	8.27412i	0.596296	−	0.333916i
$615$	44.6505	+	12.5629i	1.80048	+	0.506585i
$616$	−5.26435	+	2.76905i	−0.212107	+	0.111568i
$617$	−7.18902	+	19.7517i	−0.289419	+	0.795172i	0.706729	+	0.707484i	$0.250170\pi$
$617$	−7.18902	+	19.7517i	−0.289419	+	0.795172i	−0.996148	+	0.0876877i	$0.972052\pi$
$618$	−22.6461	−	0.297196i	−0.910961	−	0.0119550i
$619$	41.3672	+	23.8833i	1.66269	+	0.959953i	0.971424	+	0.237349i	$0.0762786\pi$
$619$	41.3672	+	23.8833i	1.66269	+	0.959953i	0.691263	+	0.722604i	$0.257055\pi$
$620$	17.5595	−	7.37473i	0.705205	−	0.296176i
$621$	−27.8493	+	4.91058i	−1.11755	+	0.197055i
$622$	−6.65185	+	17.5555i	−0.266715	+	0.703913i
$623$	1.23008	+	1.46596i	0.0492822	+	0.0587323i
$624$	29.5489	−	69.5875i	1.18290	−	2.78573i
$625$	23.8894	−	7.36851i	0.955577	−	0.294740i
$626$	2.44834	+	7.01170i	0.0978552	+	0.280244i
$627$	−2.11903	−	12.4816i	−0.0846261	−	0.498465i
$628$	−21.8137	−	27.4273i	−0.870463	−	1.09447i
$629$	0.744943	+	2.04671i	0.0297028	+	0.0816078i
$630$	44.3203	+	32.7551i	1.76576	+	1.30499i
$631$	2.31893	+	2.76359i	0.0923150	+	0.110017i	0.810224	−	0.586120i	$-0.199345\pi$
$631$	2.31893	+	2.76359i	0.0923150	+	0.110017i	−0.717909	+	0.696137i	$0.754901\pi$
$632$	−34.9273	+	11.1765i	−1.38933	+	0.444579i
$633$	−26.0240	+	4.58873i	−1.03436	+	0.182386i
$634$	−18.8026	−	16.2025i	−0.746748	−	0.643482i
$635$	−20.8909	+	5.31939i	−0.829030	+	0.211093i
$636$	−15.6596	−	46.8117i	−0.620942	−	1.85620i
$637$	8.36919	+	3.04613i	0.331599	+	0.120692i
$638$	−2.21146	+	11.6460i	−0.0875525	+	0.461070i
$639$	−17.9377	−	31.0690i	−0.709604	−	1.22907i
$640$	−3.96726	−	24.9852i	−0.156820	−	0.987627i
$641$	29.2460	−	34.8541i	1.15515	−	1.37665i	0.241374	−	0.970432i	$-0.422402\pi$
$641$	29.2460	−	34.8541i	1.15515	−	1.37665i	0.913775	−	0.406221i	$-0.133154\pi$
$642$	−22.0369	+	37.0379i	−0.869727	+	1.46177i
$643$	−8.26463	+	46.8710i	−0.325925	+	1.84841i	0.177167	+	0.984181i	$0.443307\pi$
$643$	−8.26463	+	46.8710i	−0.325925	+	1.84841i	−0.503092	+	0.864233i	$0.667804\pi$
$644$	4.81237	−	7.85191i	0.189634	−	0.309409i
$645$	−34.5094	−	35.3810i	−1.35881	−	1.39313i
$646$	1.28280	+	3.75026i	0.0504710	+	0.147552i
$647$	7.59214			0.298478			0.149239	−	0.988801i	$-0.452318\pi$
$647$	7.59214			0.298478			0.149239	+	0.988801i	$0.452318\pi$
$648$	14.4780	−	66.6501i	0.568750	−	2.61826i
$649$	−6.84120	−	1.20629i	−0.268541	−	0.0473509i
$650$	34.9965	+	22.0222i	1.37267	+	0.863780i
$651$	−20.7061	+	24.6766i	−0.811536	+	0.967152i
$652$	10.5884	+	9.36910i	0.414675	+	0.366922i
$653$	−7.38806	+	4.26550i	−0.289117	+	0.166922i	−0.637544	−	0.770414i	$-0.720049\pi$
$653$	−7.38806	+	4.26550i	−0.289117	+	0.166922i	0.348427	+	0.937336i	$0.386716\pi$
$654$	3.98885	−	21.0061i	0.155976	−	0.821405i
$655$	−13.4678	−	29.8480i	−0.526230	−	1.16626i
$656$	21.5283	+	13.9846i	0.840538	+	0.546008i
$657$	2.43982	+	1.40863i	0.0951863	+	0.0549559i
$658$	−14.9256	−	12.8615i	−0.581859	−	0.501395i
$659$	−7.92304	−	44.9338i	−0.308638	−	1.75037i	−0.605867	−	0.795566i	$-0.707174\pi$
$659$	−7.92304	−	44.9338i	−0.308638	−	1.75037i	0.297230	−	0.954806i	$-0.403937\pi$
$660$	−9.53327	+	8.82226i	−0.371082	+	0.343406i
$661$	6.55296	+	7.80951i	0.254881	+	0.303755i	0.878278	−	0.478150i	$-0.158693\pi$
$661$	6.55296	+	7.80951i	0.254881	+	0.303755i	−0.623397	+	0.781905i	$0.714248\pi$
$662$	−5.22593	−	32.0950i	−0.203112	−	1.24741i
$663$	11.4196	−	4.15640i	0.443501	−	0.161421i
$664$	−6.73423	+	10.6708i	−0.261339	+	0.414107i
$665$	2.41564	−	22.6820i	0.0936743	−	0.879571i
$666$	−33.6802	+	11.7604i	−1.30508	+	0.455707i
$667$	−6.27715	−	17.2463i	−0.243052	−	0.667781i
$668$	1.21513	−	0.659660i	0.0470149	−	0.0255230i
$669$	23.6794	−	19.8694i	0.915499	−	0.768195i
$670$	3.29964	+	7.57649i	0.127476	+	0.292705i
$671$	1.17638	−	0.207428i	0.0454137	−	0.00800766i
$672$	25.2960	+	34.5113i	0.975816	+	1.33130i
$673$	11.7153	−	20.2914i	0.451590	−	0.782177i	−0.546895	−	0.837201i	$-0.684190\pi$
$673$	11.7153	−	20.2914i	0.451590	−	0.782177i	0.998485	+	0.0550244i	$0.0175237\pi$
$674$	−7.65928	−	0.100516i	−0.295024	−	0.00387175i
$675$	66.8950	+	26.2550i	2.57479	+	1.01055i
$676$	6.26277	+	41.9240i	0.240876	+	1.61246i
$677$	18.4252	+	31.9133i	0.708137	+	1.22653i	0.965548	+	0.260227i	$0.0837973\pi$
$677$	18.4252	+	31.9133i	0.708137	+	1.22653i	−0.257411	+	0.966302i	$0.582869\pi$
$678$	20.9318	−	11.7215i	0.803881	−	0.450160i
$679$	−11.0699	−	9.28873i	−0.424823	−	0.356469i
$680$	2.50195	−	3.20579i	0.0959454	−	0.122936i
$681$	−11.0912	+	62.9012i	−0.425015	+	2.41038i
$682$	−3.42407	−	4.19113i	−0.131114	−	0.160487i
$683$		−	17.2295i		−	0.659267i	−0.944109	−	0.329633i	$-0.893075\pi$
$683$		−	17.2295i		−	0.659267i	0.944109	−	0.329633i	$-0.106925\pi$
$684$	−61.6957	+	20.2030i	−2.35899	+	0.772481i
$685$	−20.8667	−	21.3937i	−0.797275	−	0.817413i
$686$	−21.8450	+	17.8469i	−0.834047	+	0.681399i
$687$	−58.7892	−	10.3661i	−2.24295	−	0.395492i
$688$	−12.4153	−	24.3742i	−0.473327	−	0.929257i
$689$	34.2058	+	28.7021i	1.30314	+	1.09346i
$690$	5.70033	−	19.2855i	0.217008	−	0.734187i
$691$	−15.2902	+	8.82782i	−0.581668	+	0.335826i	−0.761796	−	0.647817i	$-0.775682\pi$
$691$	−15.2902	+	8.82782i	−0.581668	+	0.335826i	0.180128	+	0.983643i	$0.442349\pi$
$692$	1.91592	+	12.8255i	0.0728323	+	0.487551i
$693$	5.35623	−	14.7161i	0.203466	−	0.559019i
$694$	37.6376	+	0.493937i	1.42871	+	0.0187496i
$695$	22.6394	−	5.76462i	0.858763	−	0.218664i
$696$	85.2083	+	3.35623i	3.22981	+	0.127218i
$697$	0.716574	+	4.06390i	0.0271422	+	0.153931i
$698$	36.5301	+	13.8414i	1.38268	+	0.523904i
$699$	−63.7143	+	53.4626i	−2.40989	+	2.02214i
$700$	−20.8396	+	10.6491i	−0.787663	+	0.402499i
$701$	−4.56008	+	1.65973i	−0.172232	+	0.0626873i	−0.426697	−	0.904395i	$-0.640323\pi$
$701$	−4.56008	+	1.65973i	−0.172232	+	0.0626873i	0.254465	+	0.967082i	$0.418101\pi$
$702$	39.1827	+	112.214i	1.47885	+	4.23523i
$703$	11.2505	+	9.56294i	0.424321	+	0.360673i
$704$	−6.48919	+	3.09362i	−0.244571	+	0.116595i
$705$	−38.7636	−	18.6678i	−1.45992	−	0.703069i
$706$	6.57175	−	1.07006i	0.247331	−	0.0402721i
$707$	−12.4606	+	10.4557i	−0.468630	+	0.393227i
$708$	−1.31140	+	49.9552i	−0.0492853	+	1.87743i
$709$	0.673721	+	3.82086i	0.0253021	+	0.143496i	0.994842	−	0.101439i	$-0.0323447\pi$
$709$	0.673721	+	3.82086i	0.0253021	+	0.143496i	−0.969540	+	0.244934i	$0.921234\pi$
$710$	15.2056	−	0.938967i	0.570655	−	0.0352388i
$711$	48.2754	−	83.6155i	1.81047	−	3.13583i
$712$	1.41577	+	1.82887i	0.0530583	+	0.0685397i
$713$	7.87382	+	2.86584i	0.294877	+	0.107326i
$714$	−1.28316	+	6.75739i	−0.0480210	+	0.252889i
$715$	3.18240	−	11.3108i	0.119015	−	0.422998i
$716$	−11.0243	−	9.75474i	−0.411996	−	0.364552i
$717$	−6.41316	−	5.38128i	−0.239504	−	0.200968i
$718$	28.9777	+	17.2412i	1.08144	+	0.643436i
$719$	32.2678	+	5.68969i	1.20339	+	0.212190i	0.739162	−	0.673528i	$-0.235222\pi$
$719$	32.2678	+	5.68969i	1.20339	+	0.212190i	0.464225	+	0.885717i	$0.346333\pi$
$720$	51.9652	+	41.6648i	1.93663	+	1.55275i
$721$			11.5956i			0.431844i
$722$	20.1304	+	17.7980i	0.749175	+	0.662372i
$723$	1.55955			0.0580002
$724$	−22.4696	−	13.7714i	−0.835076	−	0.511810i
$725$	−9.24177	+	45.7146i	−0.343231	+	1.69780i
$726$	−40.0384	−	23.8221i	−1.48596	−	0.884122i
$727$	−32.8750	−	27.5854i	−1.21927	−	1.02309i	−0.998863	−	0.0476764i	$-0.984818\pi$
$727$	−32.8750	−	27.5854i	−1.21927	−	1.02309i	−0.220403	−	0.975409i	$-0.570737\pi$
$728$	−35.8237	−	14.6600i	−1.32771	−	0.543335i
$729$	20.1040	+	34.8211i	0.744593	+	1.28967i
$730$	−0.997234	+	0.660897i	−0.0369093	+	0.0244609i
$731$	1.50386	−	4.13183i	0.0556224	−	0.152821i
$732$	−2.72607	−	8.14914i	−0.100759	−	0.301201i
$733$	−17.3626	−	10.0243i	−0.641303	−	0.370256i	0.143814	−	0.989605i	$-0.454063\pi$
$733$	−17.3626	−	10.0243i	−0.641303	−	0.370256i	−0.785116	+	0.619349i	$0.787397\pi$
$734$	−10.8286	−	9.33115i	−0.399691	−	0.344419i
$735$	−6.42568	+	8.93750i	−0.237015	+	0.329665i
$736$	6.18513	−	9.25342i	0.227987	−	0.341085i
$737$	1.79890	−	1.50946i	0.0662633	−	0.0556015i
$738$	−66.7106	+	10.8623i	−2.45565	+	0.399846i
$739$	−1.91541	−	5.26255i	−0.0704596	−	0.193586i	0.899464	−	0.436994i	$-0.143957\pi$
$739$	−1.91541	−	5.26255i	−0.0704596	−	0.193586i	−0.969924	+	0.243408i	$0.921735\pi$
$740$	1.90349	−	15.0291i	0.0699737	−	0.552483i
$741$	53.3563	−	62.7721i	1.96009	−	2.30599i
$742$	−23.8599	+	8.33138i	−0.875925	+	0.305855i
$743$	9.24172	+	25.3914i	0.339046	+	0.931521i	0.985666	+	0.168709i	$0.0539598\pi$
$743$	9.24172	+	25.3914i	0.339046	+	0.931521i	−0.646620	+	0.762812i	$0.723818\pi$
$744$	−26.1795	+	28.8156i	−0.959785	+	1.05643i
$745$	−1.03002	+	10.2931i	−0.0377370	+	0.377109i
$746$	−32.2719	−	12.2279i	−1.18156	−	0.447697i
$747$	−5.76880	−	32.7165i	−0.211069	−	1.19703i
$748$	−1.07514	−	0.423590i	−0.0393110	−	0.0154880i
$749$	19.1095	+	11.0329i	0.698247	+	0.403133i
$750$	−37.9157	+	34.2650i	−1.38449	+	1.25118i
$751$	−27.2871	−	9.93170i	−0.995722	−	0.362413i	−0.207788	−	0.978174i	$-0.566627\pi$
$751$	−27.2871	−	9.93170i	−0.995722	−	0.362413i	−0.787933	+	0.615761i	$0.788849\pi$
$752$	−17.4130	−	16.2422i	−0.634987	−	0.592291i
$753$	7.25329	+	12.5631i	0.264325	+	0.457824i
$754$	−67.3051	+	37.6898i	−2.45111	+	1.37258i
$755$	−51.2215	+	3.83832i	−1.86414	+	0.139691i
$756$	−65.9204	−	13.4162i	−2.39750	−	0.487941i
$757$	−8.36120	−	1.47430i	−0.303893	−	0.0535845i	0.0196224	−	0.999807i	$-0.493754\pi$
$757$	−8.36120	−	1.47430i	−0.303893	−	0.0535845i	−0.323515	+	0.946223i	$0.604865\pi$
$758$	25.0860	−	20.4947i	0.911164	−	0.744403i
$759$	−5.71466			−0.207429
$760$	3.99616	−	27.2769i	0.144956	−	0.989438i
$761$	16.7553			0.607381			0.303690	−	0.952771i	$-0.401781\pi$
$761$	16.7553			0.607381			0.303690	+	0.952771i	$0.401781\pi$
$762$	34.1265	−	27.8807i	1.23627	−	1.01001i
$763$	−10.7808	−	1.90095i	−0.390293	−	0.0688191i
$764$	2.12556	+	0.432594i	0.0768999	+	0.0156507i
$765$	0.800058	+	10.6766i	0.0289262	+	0.386013i
$766$	−44.4078	+	24.8676i	−1.60452	+	0.898505i
$767$	−22.6026	−	39.1488i	−0.816131	−	1.41358i
$768$	28.9070	+	42.8807i	1.04309	+	1.54732i
$769$	31.0490	+	11.3009i	1.11966	+	0.407521i	0.834526	−	0.550968i	$-0.185741\pi$
$769$	31.0490	+	11.3009i	1.11966	+	0.407521i	0.285129	+	0.958489i	$0.407964\pi$
$770$	4.58058	+	4.82126i	0.165073	+	0.173746i
$771$	−75.4118	−	43.5390i	−2.71589	−	1.56802i
$772$	−12.3251	−	4.85590i	−0.443588	−	0.174768i
$773$	2.99266	+	16.9722i	0.107638	+	0.610448i	0.990134	+	0.140127i	$0.0447510\pi$
$773$	2.99266	+	16.9722i	0.107638	+	0.610448i	−0.882495	+	0.470322i	$0.844138\pi$
$774$	67.3460	+	25.5176i	2.42070	+	0.917212i
$775$	−13.2760	−	16.6478i	−0.476887	−	0.598007i
$776$	−12.9266	−	11.7441i	−0.464040	−	0.421587i
$777$	8.76367	+	24.0780i	0.314395	+	0.863793i
$778$	29.1809	−	10.1894i	1.04619	−	0.365306i
$779$	17.8453	+	21.5441i	0.639375	+	0.771899i
$780$	−83.8550	−	10.6205i	−3.00249	−	0.380275i
$781$	−1.48065	−	4.06805i	−0.0529818	−	0.145566i
$782$	1.76587	−	0.287530i	0.0631472	−	0.0102821i
$783$	−102.700	+	86.1756i	−3.67020	+	3.07967i
$784$	−4.86598	+	3.66578i	−0.173785	+	0.130921i
$785$	−22.8716	+	31.8121i	−0.816321	+	1.13542i
$786$	50.7088	+	43.6964i	1.80872	+	1.55860i
$787$	−23.8404	−	13.7642i	−0.849818	−	0.490642i	0.0107717	−	0.999942i	$-0.496571\pi$
$787$	−23.8404	−	13.7642i	−0.849818	−	0.490642i	−0.860589	+	0.509300i	$0.829905\pi$
$788$	−8.14405	−	24.3453i	−0.290120	−	0.867266i
$789$	−9.37614	+	25.7607i	−0.333799	+	0.917106i
$790$	22.6497	+	34.1764i	0.805841	+	1.21594i
$791$	−6.14141	−	10.6372i	−0.218363	−	0.378216i
$792$	7.16844	−	17.5171i	0.254719	−	0.622442i
$793$	5.95467	+	4.99656i	0.211457	+	0.177433i
$794$	25.7275	+	15.3074i	0.913036	+	0.543240i
$795$	−45.5984	+	31.0882i	−1.61721	+	1.10259i
$796$	0.954049	+	0.584728i	0.0338154	+	0.0207251i
$797$	30.0582			1.06472			0.532359	−	0.846519i	$-0.321306\pi$
$797$	30.0582			1.06472			0.532359	+	0.846519i	$0.321306\pi$
$798$	15.0911	+	44.1189i	0.534219	+	1.56179i
$799$		−	3.82768i		−	0.135414i
$800$	−25.6734	+	11.8691i	−0.907693	+	0.419636i
$801$	−5.99676	−	1.05739i	−0.211885	−	0.0373611i
$802$	−1.29902	−	0.772894i	−0.0458700	−	0.0272918i
$803$	0.260426	+	0.218524i	0.00919025	+	0.00771153i
$804$	−12.6512	−	11.1943i	−0.446175	−	0.394794i
$805$	−9.91148	−	2.78870i	−0.349334	−	0.0982887i
$806$	6.57014	−	34.5998i	0.231423	−	1.21872i
$807$	61.4132	+	22.3526i	2.16185	+	0.786848i
$808$	−15.5454	+	12.0341i	−0.546884	+	0.423357i
$809$	−13.2894	+	23.0179i	−0.467231	+	0.809267i	−0.999299	−	0.0374340i	$-0.988082\pi$
$809$	−13.2894	+	23.0179i	−0.467231	+	0.809267i	0.532068	+	0.846701i	$0.321415\pi$
$810$	−76.1100	+	4.69991i	−2.67423	+	0.165138i
$811$	−6.95932	−	39.4683i	−0.244375	−	1.38592i	−0.821940	−	0.569574i	$-0.807108\pi$
$811$	−6.95932	−	39.4683i	−0.244375	−	1.38592i	0.577565	−	0.816344i	$-0.304003\pi$
$812$	1.14574	−	43.6447i	0.0402076	−	1.53163i
$813$	−51.9989	+	43.6322i	−1.82368	+	1.53025i
$814$	−4.24893	+	0.691839i	−0.148925	+	0.0242489i
$815$	6.85856	−	14.2418i	0.240245	−	0.498869i
$816$	−1.87103	+	8.09950i	−0.0654993	+	0.283539i
$817$	−4.98926	−	29.3878i	−0.174552	−	1.02815i
$818$	−11.0624	−	31.6811i	−0.386787	−	1.10770i
$819$	95.7636	−	34.8551i	3.34625	−	1.21794i
$820$	8.49610	−	27.4155i	0.296697	−	0.957392i
$821$	−36.8467	+	30.9181i	−1.28596	+	1.07905i	−0.293566	+	0.955939i	$0.594842\pi$
$821$	−36.8467	+	30.9181i	−1.28596	+	1.07905i	−0.992393	+	0.123109i	$0.960714\pi$
$822$	57.1271	+	21.6457i	1.99254	+	0.754980i
$823$	5.61077	+	31.8203i	0.195579	+	1.10919i	0.911591	+	0.411097i	$0.134854\pi$
$823$	5.61077	+	31.8203i	0.195579	+	1.10919i	−0.716012	+	0.698088i	$0.754035\pi$
$824$	−0.551574	+	14.0034i	−0.0192150	+	0.487832i
$825$	12.3916	+	7.57248i	0.431420	+	0.263640i
$826$	25.5832	+	0.335741i	0.890155	+	0.0116819i
$827$	−5.18112	+	14.2350i	−0.180165	+	0.495000i	−0.996596	−	0.0824436i	$-0.973728\pi$
$827$	−5.18112	+	14.2350i	−0.180165	+	0.495000i	0.816430	+	0.577444i	$0.195950\pi$
$828$	4.32949	+	28.9823i	0.150460	+	1.00721i
$829$	−21.0512	+	12.1539i	−0.731137	+	0.422122i	−0.818838	−	0.574025i	$-0.805381\pi$
$829$	−21.0512	+	12.1539i	−0.731137	+	0.422122i	0.0877009	+	0.996147i	$0.472048\pi$
$830$	13.5288	+	3.99879i	0.469592	+	0.138800i
$831$	74.3681	+	62.4022i	2.57980	+	2.16471i
$832$	−42.5650	−	19.4081i	−1.47568	−	0.672855i
$833$	−0.964421	−	0.170053i	−0.0334152	−	0.00589200i
$834$	−36.9829	+	30.2142i	−1.28061	+	1.04623i
$835$	−1.07936	−	1.10662i	−0.0373527	−	0.0382962i
$836$	−7.75514	+	1.10809i	−0.268217	+	0.0383242i
$837$		−	61.2077i		−	2.11565i
$838$	−2.19233	−	2.68346i	−0.0757327	−	0.0926984i
$839$	−2.97631	+	16.8795i	−0.102754	+	0.582745i	0.889340	+	0.457246i	$0.151164\pi$
$839$	−2.97631	+	16.8795i	−0.102754	+	0.582745i	−0.992094	+	0.125499i	$0.959947\pi$
$840$	29.4335	−	37.7136i	1.01555	−	1.30124i
$841$	−44.4377	−	37.2876i	−1.53233	−	1.28578i
$842$	9.81719	−	5.49747i	0.338323	−	0.189455i
$843$	−17.9050	−	31.0123i	−0.616679	−	1.06812i
$844$	2.41587	+	16.1722i	0.0831576	+	0.556670i
$845$	43.1986	−	19.4918i	1.48608	−	0.670537i
$846$	62.6880	+	0.822685i	2.15526	+	0.0282845i
$847$	−11.9267	+	20.6576i	−0.409805	+	0.709804i
$848$	−29.2106	+	8.92640i	−1.00310	+	0.306534i
$849$	−96.7535	+	17.0603i	−3.32057	+	0.585507i
$850$	−4.21008	−	1.71647i	−0.144405	−	0.0588743i
$851$	5.10572	−	4.28421i	0.175022	−	0.146861i
$852$	−27.3693	+	14.8580i	−0.937657	+	0.509027i
$853$	−14.6106	−	40.1422i	−0.500257	−	1.37444i	−0.891025	−	0.453955i	$-0.850013\pi$
$853$	−14.6106	−	40.1422i	−0.500257	−	1.37444i	0.390768	−	0.920489i	$-0.372210\pi$
$854$	−4.15362	+	1.45036i	−0.142134	+	0.0496302i
$855$	40.5043	+	60.2292i	1.38522	+	2.05979i
$856$	22.5527	+	14.2328i	0.770837	+	0.486468i
$857$	−29.0654	+	10.5789i	−0.992855	+	0.361370i	−0.786825	−	0.617176i	$-0.788277\pi$
$857$	−29.0654	+	10.5789i	−0.992855	+	0.361370i	−0.206030	+	0.978546i	$0.566054\pi$
$858$	3.86011	+	23.7069i	0.131782	+	0.809339i
$859$	26.9109	+	32.0711i	0.918187	+	1.09425i	0.995262	+	0.0972276i	$0.0309975\pi$
$859$	26.9109	+	32.0711i	0.918187	+	1.09425i	−0.0770750	+	0.997025i	$0.524558\pi$
$860$	−22.4460	+	20.7720i	−0.765404	+	0.708319i
$861$	8.42994	+	47.8086i	0.287292	+	1.62931i
$862$	20.8419	+	17.9597i	0.709879	+	0.611711i
$863$	−36.6287	−	21.1476i	−1.24686	−	0.719873i	−0.276375	−	0.961050i	$-0.589133\pi$
$863$	−36.6287	−	21.1476i	−1.24686	−	0.719873i	−0.970481	+	0.241177i	$0.922466\pi$
$864$	−78.9703	−	19.3376i	−2.68663	−	0.657880i
$865$	13.2154	−	5.96296i	0.449337	−	0.202747i
$866$	−1.93557	+	10.1931i	−0.0657734	+	0.346377i
$867$	46.4278	−	26.8051i	1.57677	−	0.910349i
$868$	14.9280	+	13.2089i	0.506689	+	0.448340i
$869$	7.48907	−	8.92513i	0.254049	−	0.302764i
$870$	−22.3110	−	92.6923i	−0.756413	−	3.14256i
$871$	15.0491	+	2.65357i	0.509920	+	0.0899127i
$872$	−12.9290	−	2.80849i	−0.437832	−	0.0951076i
$873$	45.9819			1.55625
$874$	9.44139	−	7.61377i	0.319360	−	0.257539i
$875$	17.7966	+	19.1806i	0.601636	+	0.648424i
$876$	1.27794	−	2.08511i	0.0431777	−	0.0704493i
$877$	1.37264	−	7.78464i	0.0463508	−	0.262869i	−0.952822	−	0.303529i	$-0.901835\pi$
$877$	1.37264	−	7.78464i	0.0463508	−	0.262869i	0.999173	+	0.0406604i	$0.0129462\pi$
$878$	−12.4528	+	20.9297i	−0.420261	+	0.706342i
$879$	−34.0556	+	40.5859i	−1.14867	+	1.36893i
$880$	5.30239	+	6.04026i	0.178743	+	0.203617i
$881$	−19.0188	−	32.9416i	−0.640761	−	1.10983i	−0.985263	−	0.171045i	$-0.945286\pi$
$881$	−19.0188	−	32.9416i	−0.640761	−	1.10983i	0.344502	−	0.938786i	$-0.388048\pi$
$882$	2.99234	−	15.7583i	0.100757	−	0.530609i
$883$	25.0602	+	9.12116i	0.843342	+	0.306951i	0.727323	−	0.686296i	$-0.240764\pi$
$883$	25.0602	+	9.12116i	0.843342	+	0.306951i	0.116019	+	0.993247i	$0.462987\pi$
$884$	−2.38559	−	7.13134i	−0.0802362	−	0.239853i
$885$	54.1432	−	13.7863i	1.82000	−	0.463422i
$886$	−4.06519	−	3.50303i	−0.136573	−	0.117687i
$887$	40.5230	−	7.14530i	1.36063	−	0.239916i	0.554760	−	0.832010i	$-0.312810\pi$
$887$	40.5230	−	7.14530i	1.36063	−	0.239916i	0.805869	+	0.592094i	$0.201699\pi$
$888$	9.43809	+	29.4946i	0.316721	+	0.989773i
$889$	−14.5027	−	17.2837i	−0.486405	−	0.579675i
$890$	1.53688	−	2.07953i	0.0515165	−	0.0697060i
$891$	7.41125	+	20.3622i	0.248286	+	0.682160i
$892$	−11.9061	−	14.9700i	−0.398646	−	0.501234i
$893$	−12.8311	−	22.5544i	−0.429377	−	0.754753i
$894$	−6.97101	−	19.9640i	−0.233145	−	0.667696i
$895$	−7.14086	+	14.8280i	−0.238693	+	0.495646i
$896$	21.7585	−	15.0870i	0.726899	−	0.504021i
$897$	−23.9037	−	28.4873i	−0.798122	−	0.951164i
$898$	−5.15588	+	13.6074i	−0.172054	+	0.454084i
$899$	39.1206	−	6.89802i	1.30475	−	0.230062i
$900$	29.0163	−	68.5819i	0.967212	−	2.28606i
$901$	−4.25201	−	2.45490i	−0.141655	−	0.0817846i
$902$	−8.15537	−	0.107027i	−0.271544	−	0.00356360i
$903$	17.6918	−	48.6078i	0.588746	−	1.61757i
$904$	−6.91066	−	13.1381i	−0.229845	−	0.436968i
$905$	−7.98034	+	28.3634i	−0.265276	+	0.942831i
$906$	91.6137	−	51.3022i	3.04366	−	1.70440i
$907$	1.95885	−	2.33446i	0.0650424	−	0.0775145i	−0.732542	−	0.680722i	$-0.761666\pi$
$907$	1.95885	−	2.33446i	0.0650424	−	0.0775145i	0.797585	+	0.603207i	$0.206111\pi$
$908$	38.7288	+	7.88210i	1.28526	+	0.261577i
$909$	8.98782	−	50.9725i	0.298107	−	1.69065i
$910$	−4.87376	+	43.0007i	−0.161564	+	1.42546i
$911$	39.4840			1.30816			0.654081	−	0.756424i	$-0.273055\pi$
$911$	39.4840			1.30816			0.654081	+	0.756424i	$0.273055\pi$
$912$	16.1261	+	53.9978i	0.533988	+	1.78805i
$913$		−	4.00885i		−	0.132673i
$914$	14.3081	+	17.5134i	0.473269	+	0.579291i
$915$	−7.93794	+	5.41195i	−0.262420	+	0.178913i
$916$	−7.36682	+	36.1970i	−0.243407	+	1.19598i
$917$	22.0296	−	26.2538i	0.727480	−	0.866977i
$918$	−6.38547	−	11.4029i	−0.210752	−	0.376353i
$919$	−35.6271	+	20.5693i	−1.17523	+	0.678520i	−0.954906	−	0.296907i	$-0.904045\pi$
$919$	−35.6271	+	20.5693i	−1.17523	+	0.678520i	−0.220324	+	0.975427i	$0.570712\pi$
$920$	−11.8369	−	3.83922i	−0.390251	−	0.126575i
$921$	36.3694	+	13.2374i	1.19841	+	0.436187i
$922$	−20.0188	−	0.262716i	−0.659284	−	0.00865210i
$923$	14.0857	−	24.3971i	0.463636	−	0.803040i
$924$	−12.6482	−	4.98320i	−0.416094	−	0.163935i
$925$	−16.7482	+	2.52425i	−0.550677	+	0.0829968i
$926$	4.56674	+	1.73035i	0.150072	+	0.0568629i
$927$	−23.7170	−	28.2649i	−0.778969	−	0.928340i
$928$	3.45971	−	52.6529i	0.113571	−	1.72842i
$929$	50.9286	−	18.5365i	1.67091	−	0.608162i	0.678891	−	0.734239i	$-0.262461\pi$
$929$	50.9286	−	18.5365i	1.67091	−	0.608162i	0.992020	+	0.126077i	$0.0402386\pi$
$930$	38.9655	+	19.3990i	1.27773	+	0.636117i
$931$	−6.25284	+	2.23089i	−0.204928	+	0.0731145i
$932$	32.0358	+	40.2800i	1.04937	+	1.31941i
$933$	−40.3187	+	14.6748i	−1.31998	+	0.480432i
$934$	−6.65203	−	40.8534i	−0.217661	−	1.33677i
$935$	−0.128644	+	1.28555i	−0.00420710	+	0.0420420i
$936$	117.306	−	37.5374i	3.83428	−	1.22695i
$937$	−2.74961	+	0.484831i	−0.0898259	+	0.0158387i	−0.218380	−	0.975864i	$-0.570077\pi$
$937$	−2.74961	+	0.484831i	−0.0898259	+	0.0158387i	0.128555	+	0.991702i	$0.458966\pi$
$938$	−5.64592	+	6.55198i	−0.184346	+	0.213930i
$939$	−8.48694	+	14.6998i	−0.276961	+	0.479710i
$940$	−12.1768	+	23.6749i	−0.397163	+	0.772191i
$941$	12.3812	−	34.0170i	0.403615	−	1.10892i	−0.556872	−	0.830599i	$-0.687998\pi$
$941$	12.3812	−	34.0170i	0.403615	−	1.10892i	0.960487	−	0.278325i	$-0.0897793\pi$
$942$	14.9418	−	78.6864i	0.486829	−	2.56374i
$943$	10.9359	−	6.31383i	0.356121	−	0.205607i
$944$	30.8795	+	1.62238i	1.00504	+	0.0528041i
$945$	5.62032	+	75.0019i	0.182829	+	2.43981i
$946$	7.46856	+	4.44366i	0.242824	+	0.144476i
$947$	−1.37865	+	7.81871i	−0.0448001	+	0.254074i	−0.998980	−	0.0451604i	$-0.985620\pi$
$947$	−1.37865	+	7.81871i	−0.0448001	+	0.254074i	0.954180	+	0.299234i	$0.0967312\pi$
$948$	−71.4592	−	43.7967i	−2.32089	−	1.42245i
$949$			2.21227i			0.0718133i
$950$	−30.5616	+	3.99883i	−0.991548	+	0.129739i
$951$		−	56.7266i		−	1.83949i
$952$	4.15909	+	0.903455i	0.134797	+	0.0292811i
$953$	7.57025	−	42.9330i	0.245225	−	1.39074i	−0.574746	−	0.818332i	$-0.694899\pi$
$953$	7.57025	−	42.9330i	0.245225	−	1.39074i	0.819970	−	0.572406i	$-0.193990\pi$
$954$	41.1191	−	69.1098i	1.33128	−	2.23751i
$955$	−0.181223	−	2.41838i	−0.00586424	−	0.0782570i
$956$	−3.43285	+	3.87962i	−0.111026	+	0.125476i
$957$	−23.4626	+	13.5461i	−0.758437	+	0.437884i
$958$	−34.0989	−	6.47503i	−1.10168	−	0.209199i
$959$	10.6976	−	29.3915i	0.345445	−	0.949102i
$960$	37.3392	−	44.1446i	1.20512	−	1.42476i
$961$	6.43197	−	11.1405i	0.207483	−	0.359371i
$962$	−21.2215	−	18.2868i	−0.684209	−	0.589591i
$963$	−69.1464	+	12.1924i	−2.22821	+	0.392894i
$964$	0.0253246	−	0.964691i	0.000815649	−	0.0310706i
$965$	−1.47473	+	14.7372i	−0.0474733	+	0.474406i
$966$	20.7740	−	3.38257i	0.668393	−	0.108832i
$967$	−1.51273	+	0.550589i	−0.0486462	+	0.0177058i	−0.366229	−	0.930525i	$-0.619351\pi$
$967$	−1.51273	+	0.550589i	−0.0486462	+	0.0177058i	0.317582	+	0.948231i	$0.397129\pi$
$968$	−15.3858	+	24.3798i	−0.494519	+	0.783595i
$969$	−4.57916	+	7.81605i	−0.147104	+	0.251088i
$970$	−8.70234	+	17.4799i	−0.279415	+	0.561245i
$971$	−5.01116	+	1.82391i	−0.160816	+	0.0585322i	−0.421174	−	0.906980i	$-0.638382\pi$
$971$	−5.01116	+	1.82391i	−0.160816	+	0.0585322i	0.260358	+	0.965512i	$0.416159\pi$
$972$	61.2065	−	33.2273i	1.96320	−	1.06576i
$973$	15.7166	+	18.7303i	0.503851	+	0.600466i
$974$	−9.97818	+	26.3344i	−0.319721	+	0.843807i
$975$	14.0840	+	93.4463i	0.451049	+	2.99268i
$976$	−5.08509	+	1.55394i	−0.162770	+	0.0497404i
$977$	22.5629	−	39.0800i	0.721850	−	1.25028i	−0.238408	−	0.971165i	$-0.576626\pi$
$977$	22.5629	−	39.0800i	0.721850	−	1.25028i	0.960258	−	0.279115i	$-0.0900412\pi$
$978$	−0.424022	+	32.3102i	−0.0135587	+	1.03317i
$979$	−0.690487	−	0.251317i	−0.0220681	−	0.00803212i
$980$	5.42414	+	4.11987i	0.173268	+	0.131604i
$981$	30.1669	−	17.4169i	0.963154	−	0.556077i
$982$	−15.8514	+	8.87654i	−0.505839	+	0.283262i
$983$	27.8251	−	33.1606i	0.887482	−	1.05766i	−0.110482	−	0.993878i	$-0.535239\pi$
$983$	27.8251	−	33.1606i	0.887482	−	1.05766i	0.997964	−	0.0637818i	$-0.0203162\pi$
$984$	7.90625	+	58.1368i	0.252042	+	1.85333i
$985$	−23.7143	+	16.1680i	−0.755601	+	0.515156i
$986$	6.56851	−	5.36634i	0.209184	−	0.170899i
$987$		−	45.0297i		−	1.43331i
$988$	−37.9626	−	34.0240i	−1.20775	−	1.08245i
$989$	−13.4552			−0.427849
$990$	−21.0265	−	2.38317i	−0.668266	−	0.0757422i
$991$	−5.46820	+	31.0117i	−0.173703	+	0.985120i	0.765927	+	0.642928i	$0.222280\pi$
$991$	−5.46820	+	31.0117i	−0.173703	+	0.985120i	−0.939630	+	0.342192i	$0.888831\pi$
$992$	17.3994	+	16.6618i	0.552432	+	0.529012i
$993$	47.7709	−	56.9311i	1.51596	−	1.80665i
$994$	7.79040	+	13.9118i	0.247096	+	0.441256i
$995$	0.338842	−	1.20430i	0.0107420	−	0.0381788i
$996$	−28.5217	+	4.26069i	−0.903746	+	0.135005i
$997$	8.07184	−	22.1772i	0.255638	−	0.702359i	−0.743786	−	0.668418i	$-0.766972\pi$
$997$	8.07184	−	22.1772i	0.255638	−	0.702359i	0.999424	−	0.0339413i	$-0.0108059\pi$
$998$	0.578342	−	44.0692i	0.0183071	−	1.39499i
$999$	−42.1638	−	24.3433i	−1.33400	−	0.770188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.299.45	yes	336
4.3	odd	2	inner	380.2.bb.a.299.56	yes	336
5.4	even	2	inner	380.2.bb.a.299.12	yes	336
19.15	odd	18	inner	380.2.bb.a.319.1	yes	336
20.19	odd	2	inner	380.2.bb.a.299.1	✓	336
76.15	even	18	inner	380.2.bb.a.319.12	yes	336
95.34	odd	18	inner	380.2.bb.a.319.56	yes	336
380.319	even	18	inner	380.2.bb.a.319.45	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.299.1	✓	336	20.19	odd	2	inner
380.2.bb.a.299.12	yes	336	5.4	even	2	inner
380.2.bb.a.299.45	yes	336	1.1	even	1	trivial
380.2.bb.a.299.56	yes	336	4.3	odd	2	inner
380.2.bb.a.319.1	yes	336	19.15	odd	18	inner
380.2.bb.a.319.12	yes	336	76.15	even	18	inner
380.2.bb.a.319.45	yes	336	380.319	even	18	inner
380.2.bb.a.319.56	yes	336	95.34	odd	18	inner

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.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09519 - 0.894745i) q^{2} +(3.18304 + 0.561256i) q^{3} +(0.398864 - 1.95982i) q^{4} +(-2.22982 + 0.167093i) q^{5} +(3.98820 - 2.23333i) q^{6} +(-1.17014 - 2.02675i) q^{7} +(-1.31671 - 2.50325i) q^{8} +(6.99766 + 2.54694i) q^{9} +O(q^{10})\)	\(q+(1.09519 - 0.894745i) q^{2} +(3.18304 + 0.561256i) q^{3} +(0.398864 - 1.95982i) q^{4} +(-2.22982 + 0.167093i) q^{5} +(3.98820 - 2.23333i) q^{6} +(-1.17014 - 2.02675i) q^{7} +(-1.31671 - 2.50325i) q^{8} +(6.99766 + 2.54694i) q^{9} +(-2.29256 + 2.17811i) q^{10} +(0.778220 + 0.449305i) q^{11} +(2.36956 - 6.01433i) q^{12} +(1.01543 + 5.75878i) q^{13} +(-3.09494 - 1.17269i) q^{14} +(-7.19138 - 0.719634i) q^{15} +(-3.68181 - 1.56341i) q^{16} +(-0.219912 - 0.604202i) q^{17} +(9.94260 - 3.47175i) q^{18} +(-3.32121 - 2.82304i) q^{19} +(-0.561921 + 4.43669i) q^{20} +(-2.58709 - 7.10797i) q^{21} +(1.25431 - 0.204235i) q^{22} +(-1.50724 + 1.26472i) q^{23} +(-2.78618 - 8.70697i) q^{24} +(4.94416 - 0.745173i) q^{25} +(6.26471 + 5.39838i) q^{26} +(12.4470 + 7.18628i) q^{27} +(-4.43879 + 1.48488i) q^{28} +(-3.19032 + 8.76534i) q^{29} +(-8.51978 + 5.64631i) q^{30} +(-2.12932 - 3.68810i) q^{31} +(-5.43112 + 1.58206i) q^{32} +(2.22493 + 1.86694i) q^{33} +(-0.781451 - 0.464949i) q^{34} +(2.94786 + 4.32375i) q^{35} +(7.78267 - 12.6983i) q^{36} -3.38747 q^{37} +(-6.16324 - 0.120111i) q^{38} +18.9003i q^{39} +(3.35430 + 5.36178i) q^{40} +(-6.32042 - 1.11446i) q^{41} +(-9.19316 - 5.46976i) q^{42} +(5.23859 + 4.39570i) q^{43} +(1.19096 - 1.34596i) q^{44} +(-16.0291 - 4.50995i) q^{45} +(-0.519102 + 2.73370i) q^{46} +(5.59404 + 2.03606i) q^{47} +(-10.8419 - 7.04283i) q^{48} +(0.761533 - 1.31901i) q^{49} +(4.74803 - 5.23986i) q^{50} +(-0.360875 - 2.04663i) q^{51} +(11.6912 + 0.306911i) q^{52} +(5.84953 - 4.90834i) q^{53} +(20.0617 - 3.26658i) q^{54} +(-1.81036 - 0.871833i) q^{55} +(-3.53272 + 5.59780i) q^{56} +(-8.98711 - 10.8499i) q^{57} +(4.34874 + 12.4542i) q^{58} +(-7.26432 + 2.64400i) q^{59} +(-4.27874 + 13.8068i) q^{60} +(1.01831 - 0.854462i) q^{61} +(-5.63191 - 2.13395i) q^{62} +(-3.02626 - 17.1628i) q^{63} +(-4.53255 + 6.59212i) q^{64} +(-3.22647 - 12.6713i) q^{65} +(4.10714 + 0.0539000i) q^{66} +(0.893785 - 2.45565i) q^{67} +(-1.27184 + 0.189993i) q^{68} +(-5.50744 + 3.17972i) q^{69} +(7.09710 + 2.09773i) q^{70} +(-3.69048 - 3.09668i) q^{71} +(-2.83826 - 20.8705i) q^{72} +(0.372573 + 0.0656946i) q^{73} +(-3.70991 + 3.03092i) q^{74} +(16.1557 + 0.403024i) q^{75} +(-6.85737 + 5.38298i) q^{76} -2.10301i q^{77} +(16.9110 + 20.6994i) q^{78} +(2.25143 - 12.7685i) q^{79} +(8.47100 + 2.87090i) q^{80} +(18.4723 + 15.5001i) q^{81} +(-7.91920 + 4.43462i) q^{82} +(-2.23058 - 3.86348i) q^{83} +(-14.9623 + 2.23512i) q^{84} +(0.591320 + 1.31051i) q^{85} +(9.67026 + 0.126907i) q^{86} +(-15.0745 + 26.1098i) q^{87} +(0.100034 - 2.53969i) q^{88} +(-0.805285 + 0.141993i) q^{89} +(-21.5901 + 9.40270i) q^{90} +(10.4834 - 8.79660i) q^{91} +(1.87745 + 3.45838i) q^{92} +(-4.70776 - 12.9345i) q^{93} +(7.94827 - 2.77537i) q^{94} +(7.87741 + 5.73990i) q^{95} +(-18.1754 + 1.98752i) q^{96} +(5.80238 - 2.11189i) q^{97} +(-0.346160 - 2.12594i) q^{98} +(4.30137 + 5.12617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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