LMFDB - Embedded newform 380.2.d.b.379.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(379,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("380.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.d (of order $2$, degree $1$, 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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.11
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.948256 + 1.04920i) q^{2} +1.76151i q^{3} +(-0.201622 - 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 - 1.67036i) q^{6} +4.29252 q^{7} +(2.27889 + 1.67531i) q^{8} -0.102903 q^{9} +O(q^{10})$	\(q+(-0.948256 + 1.04920i) q^{2} +1.76151i q^{3} +(-0.201622 - 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 - 1.67036i) q^{6} +4.29252 q^{7} +(2.27889 + 1.67531i) q^{8} -0.102903 q^{9} +(3.06685 - 0.770986i) q^{10} +0.376641i q^{11} +(3.50506 - 0.355158i) q^{12} +0.928582 q^{13} +(-4.07040 + 4.50369i) q^{14} +(2.19011 - 3.27382i) q^{15} +(-3.91870 + 0.802380i) q^{16} +5.96697i q^{17} +(0.0975780 - 0.107965i) q^{18} +(3.61406 - 2.43692i) q^{19} +(-2.09924 + 3.94882i) q^{20} +7.56129i q^{21} +(-0.395170 - 0.357152i) q^{22} -0.352652 q^{23} +(-2.95107 + 4.01428i) q^{24} +(1.90832 + 4.62150i) q^{25} +(-0.880533 + 0.974264i) q^{26} +5.10325i q^{27} +(-0.865466 - 8.54130i) q^{28} -3.89105i q^{29} +(1.35810 + 5.40228i) q^{30} -1.06308 q^{31} +(2.87407 - 4.87234i) q^{32} -0.663455 q^{33} +(-6.26051 - 5.65821i) q^{34} +(-7.97780 - 5.33696i) q^{35} +(0.0207474 + 0.204757i) q^{36} -9.60143 q^{37} +(-0.870242 + 6.10268i) q^{38} +1.63570i q^{39} +(-2.15246 - 5.94701i) q^{40} +6.82129i q^{41} +(-7.93327 - 7.17004i) q^{42} +9.45416 q^{43} +(0.749444 - 0.0759391i) q^{44} +(0.191248 + 0.127941i) q^{45} +(0.334405 - 0.370001i) q^{46} +2.56158 q^{47} +(-1.41340 - 6.90281i) q^{48} +11.4257 q^{49} +(-6.65844 - 2.38016i) q^{50} -10.5108 q^{51} +(-0.187223 - 1.84770i) q^{52} +3.18648 q^{53} +(-5.35431 - 4.83919i) q^{54} +(0.468284 - 0.700001i) q^{55} +(9.78217 + 7.19129i) q^{56} +(4.29265 + 6.36618i) q^{57} +(4.08247 + 3.68971i) q^{58} -3.98595 q^{59} +(-6.95587 - 3.69783i) q^{60} -3.22322 q^{61} +(1.00807 - 1.11538i) q^{62} -0.441711 q^{63} +(2.38668 + 7.63569i) q^{64} +(-1.72580 - 1.15452i) q^{65} +(0.629125 - 0.696094i) q^{66} +8.75380i q^{67} +(11.8731 - 1.20307i) q^{68} -0.621199i q^{69} +(13.1645 - 3.30947i) q^{70} +10.1166 q^{71} +(-0.234504 - 0.172394i) q^{72} -5.09707i q^{73} +(9.10461 - 10.0738i) q^{74} +(-8.14081 + 3.36152i) q^{75} +(-5.57769 - 6.69995i) q^{76} +1.61674i q^{77} +(-1.71617 - 1.55106i) q^{78} +14.4968 q^{79} +(8.28066 + 3.38093i) q^{80} -9.29812 q^{81} +(-7.15687 - 6.46833i) q^{82} -3.49815 q^{83} +(15.0455 - 1.52452i) q^{84} +(7.41883 - 11.0898i) q^{85} +(-8.96496 + 9.91926i) q^{86} +6.85410 q^{87} +(-0.630990 + 0.858323i) q^{88} -10.4915i q^{89} +(-0.315587 + 0.0793365i) q^{90} +3.98595 q^{91} +(0.0711025 + 0.701712i) q^{92} -1.87262i q^{93} +(-2.42904 + 2.68760i) q^{94} +(-9.74673 + 0.0356921i) q^{95} +(8.58266 + 5.06270i) q^{96} -9.74137 q^{97} +(-10.8345 + 11.9878i) q^{98} -0.0387573i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.948256	+	1.04920i	−0.670518	+	0.741893i
$2$	−0.948256	+	1.04920i	−0.670518	+	0.741893i
$3$			1.76151i			1.01701i	0.861060	+	0.508503i	$0.169801\pi$
$3$			1.76151i			1.01701i	−0.861060	+	0.508503i	$0.830199\pi$
$4$	−0.201622	−	1.98981i	−0.100811	−	0.994906i
$5$	−1.85854	−	1.24332i	−0.831163	−	0.556028i
$5$	−1.85854	−	1.24332i	−0.831163	−	0.556028i
$6$	−1.84816	−	1.67036i	−0.754510	−	0.681921i
$7$	4.29252			1.62242			0.811209	−	0.584756i	$-0.198810\pi$
$7$	4.29252			1.62242			0.811209	+	0.584756i	$0.198810\pi$
$8$	2.27889	+	1.67531i	0.805709	+	0.592311i
$9$	−0.102903			−0.0343009
$10$	3.06685	−	0.770986i	0.969824	−	0.243807i
$11$			0.376641i			0.113562i	0.998387	+	0.0567808i	$0.0180836\pi$
$11$			0.376641i			0.113562i	−0.998387	+	0.0567808i	$0.981916\pi$
$12$	3.50506	−	0.355158i	1.01182	−	0.102525i
$13$	0.928582			0.257542			0.128771	−	0.991674i	$-0.458897\pi$
$13$	0.928582			0.257542			0.128771	+	0.991674i	$0.458897\pi$
$14$	−4.07040	+	4.50369i	−1.08786	+	1.20366i
$15$	2.19011	−	3.27382i	0.565484	−	0.845298i
$16$	−3.91870	+	0.802380i	−0.979674	+	0.200595i
$17$			5.96697i			1.44720i	0.690219	+	0.723601i	$0.257514\pi$
$17$			5.96697i			1.44720i	−0.690219	+	0.723601i	$0.742486\pi$
$18$	0.0975780	−	0.107965i	0.0229994	−	0.0254476i
$19$	3.61406	−	2.43692i	0.829122	−	0.559068i
$19$	3.61406	−	2.43692i	0.829122	−	0.559068i
$20$	−2.09924	+	3.94882i	−0.469405	+	0.882983i
$21$			7.56129i			1.65001i
$22$	−0.395170	−	0.357152i	−0.0842505	−	0.0761450i
$23$	−0.352652			−0.0735331			−0.0367666	−	0.999324i	$-0.511706\pi$
$23$	−0.352652			−0.0735331			−0.0367666	+	0.999324i	$0.511706\pi$
$24$	−2.95107	+	4.01428i	−0.602384	+	0.819411i
$25$	1.90832	+	4.62150i	0.381665	+	0.924301i
$26$	−0.880533	+	0.974264i	−0.172687	+	0.191069i
$27$			5.10325i			0.982122i
$28$	−0.865466	−	8.54130i	−0.163558	−	1.61415i
$29$		−	3.89105i		−	0.722549i	−0.932459	−	0.361275i	$-0.882342\pi$
$29$		−	3.89105i		−	0.722549i	0.932459	−	0.361275i	$-0.117658\pi$
$30$	1.35810	+	5.40228i	0.247953	+	0.986316i
$31$	−1.06308			−0.190934			−0.0954672	−	0.995433i	$-0.530435\pi$
$31$	−1.06308			−0.190934			−0.0954672	+	0.995433i	$0.530435\pi$
$32$	2.87407	−	4.87234i	0.508069	−	0.861316i
$33$	−0.663455			−0.115493
$34$	−6.26051	−	5.65821i	−1.07367	−	0.970375i
$35$	−7.97780	−	5.33696i	−1.34849	−	0.902111i
$36$	0.0207474	+	0.204757i	0.00345791	+	0.0341261i
$37$	−9.60143			−1.57846			−0.789232	−	0.614095i	$-0.789521\pi$
$37$	−9.60143			−1.57846			−0.789232	+	0.614095i	$0.789521\pi$
$38$	−0.870242	+	6.10268i	−0.141172	+	0.989985i
$39$			1.63570i			0.261922i
$40$	−2.15246	−	5.94701i	−0.340334	−	0.940305i
$41$			6.82129i			1.06531i	0.846334	+	0.532653i	$0.178805\pi$
$41$			6.82129i			1.06531i	−0.846334	+	0.532653i	$0.821195\pi$
$42$	−7.93327	−	7.17004i	−1.22413	−	1.10636i
$43$	9.45416			1.44175			0.720873	−	0.693067i	$-0.243741\pi$
$43$	9.45416			1.44175			0.720873	+	0.693067i	$0.243741\pi$
$44$	0.749444	−	0.0759391i	0.112983	−	0.0114483i
$45$	0.191248	+	0.127941i	0.0285096	+	0.0190723i
$46$	0.334405	−	0.370001i	0.0493053	−	0.0545537i
$47$	2.56158			0.373645			0.186823	−	0.982394i	$-0.440181\pi$
$47$	2.56158			0.373645			0.186823	+	0.982394i	$0.440181\pi$
$48$	−1.41340	−	6.90281i	−0.204006	−	0.996334i
$49$	11.4257			1.63224
$50$	−6.65844	−	2.38016i	−0.941646	−	0.336606i
$51$	−10.5108			−1.47181
$52$	−0.187223	−	1.84770i	−0.0259631	−	0.256230i
$53$	3.18648			0.437697			0.218848	−	0.975759i	$-0.429770\pi$
$53$	3.18648			0.437697			0.218848	+	0.975759i	$0.429770\pi$
$54$	−5.35431	−	4.83919i	−0.728629	−	0.658530i
$55$	0.468284	−	0.700001i	0.0631434	−	0.0943882i
$56$	9.78217	+	7.19129i	1.30720	+	0.960977i
$57$	4.29265	+	6.36618i	0.568576	+	0.843221i
$58$	4.08247	+	3.68971i	0.536054	+	0.484482i
$59$	−3.98595			−0.518927			−0.259463	−	0.965753i	$-0.583546\pi$
$59$	−3.98595			−0.518927			−0.259463	+	0.965753i	$0.583546\pi$
$60$	−6.95587	−	3.69783i	−0.897999	−	0.477388i
$61$	−3.22322			−0.412691			−0.206346	−	0.978479i	$-0.566157\pi$
$61$	−3.22322			−0.412691			−0.206346	+	0.978479i	$0.566157\pi$
$62$	1.00807	−	1.11538i	0.128025	−	0.141653i
$63$	−0.441711			−0.0556504
$64$	2.38668	+	7.63569i	0.298335	+	0.954461i
$65$	−1.72580	−	1.15452i	−0.214060	−	0.143201i
$66$	0.629125	−	0.696094i	0.0774400	−	0.0856833i
$67$			8.75380i			1.06945i	0.845027	+	0.534723i	$0.179584\pi$
$67$			8.75380i			1.06945i	−0.845027	+	0.534723i	$0.820416\pi$
$68$	11.8731	−	1.20307i	1.43983	−	0.145894i
$69$		−	0.621199i		−	0.0747836i
$70$	13.1645	−	3.30947i	1.57346	−	0.395557i
$71$	10.1166			1.20062			0.600308	−	0.799769i	$-0.295044\pi$
$71$	10.1166			1.20062			0.600308	+	0.799769i	$0.295044\pi$
$72$	−0.234504	−	0.172394i	−0.0276365	−	0.0203168i
$73$		−	5.09707i		−	0.596567i	−0.954477	−	0.298283i	$-0.903586\pi$
$73$		−	5.09707i		−	0.596567i	0.954477	−	0.298283i	$-0.0964141\pi$
$74$	9.10461	−	10.0738i	1.05839	−	1.17105i
$75$	−8.14081	+	3.36152i	−0.940019	+	0.388155i
$76$	−5.57769	−	6.69995i	−0.639805	−	0.768537i
$77$			1.61674i			0.184244i
$78$	−1.71617	−	1.55106i	−0.194318	−	0.175623i
$79$	14.4968			1.63102			0.815509	−	0.578745i	$-0.196457\pi$
$79$	14.4968			1.63102			0.815509	+	0.578745i	$0.196457\pi$
$80$	8.28066	+	3.38093i	0.925806	+	0.378000i
$81$	−9.29812			−1.03312
$82$	−7.15687	−	6.46833i	−0.790344	−	0.714307i
$83$	−3.49815			−0.383972			−0.191986	−	0.981398i	$-0.561493\pi$
$83$	−3.49815			−0.383972			−0.191986	+	0.981398i	$0.561493\pi$
$84$	15.0455	−	1.52452i	1.64160	−	0.166339i
$85$	7.41883	−	11.0898i	0.804686	−	1.20286i
$86$	−8.96496	+	9.91926i	−0.966716	+	1.06962i
$87$	6.85410			0.734837
$88$	−0.630990	+	0.858323i	−0.0672638	+	0.0914976i
$89$		−	10.4915i		−	1.11210i	−0.831149	−	0.556050i	$-0.812316\pi$
$89$		−	10.4915i		−	1.11210i	0.831149	−	0.556050i	$-0.187684\pi$
$90$	−0.315587	+	0.0793365i	−0.0332658	+	0.00836280i
$91$	3.98595			0.417841
$92$	0.0711025	+	0.701712i	0.00741295	+	0.0731585i
$93$		−	1.87262i		−	0.194181i
$94$	−2.42904	+	2.68760i	−0.250536	+	0.277205i
$95$	−9.74673	+	0.0356921i	−0.999993	+	0.00366193i
$96$	8.58266	+	5.06270i	0.875964	+	0.516709i
$97$	−9.74137			−0.989086			−0.494543	−	0.869153i	$-0.664665\pi$
$97$	−9.74137			−0.989086			−0.494543	+	0.869153i	$0.664665\pi$
$98$	−10.8345	+	11.9878i	−1.09445	+	1.21095i
$99$		−	0.0387573i		−	0.00389526i
$100$	8.81116	−	4.72900i	0.881116	−	0.472900i
$101$	−12.8341			−1.27704			−0.638519	−	0.769606i	$-0.720452\pi$
$101$	−12.8341			−1.27704			−0.638519	+	0.769606i	$0.720452\pi$
$102$	9.96697	−	11.0279i	0.986877	−	1.09193i
$103$		−	2.13005i		−	0.209881i	−0.994479	−	0.104940i	$-0.966535\pi$
$103$		−	2.13005i		−	0.209881i	0.994479	−	0.104940i	$-0.0334651\pi$
$104$	2.11614	+	1.55566i	0.207504	+	0.152545i
$105$	9.40109	−	14.0529i	0.917452	−	1.37143i
$106$	−3.02160	+	3.34324i	−0.293484	+	0.324724i
$107$		−	16.4182i		−	1.58721i	−0.608433	−	0.793606i	$-0.708201\pi$
$107$		−	16.4182i		−	1.58721i	0.608433	−	0.793606i	$-0.291799\pi$
$108$	10.1545	−	1.02893i	0.977118	−	0.0990087i
$109$		−	17.3936i		−	1.66600i	−0.553273	−	0.833000i	$-0.686621\pi$
$109$		−	17.3936i		−	1.66600i	0.553273	−	0.833000i	$-0.313379\pi$
$110$	0.290385	+	1.15510i	0.0276871	+	0.110135i
$111$		−	16.9130i		−	1.60531i
$112$	−16.8211	+	3.44423i	−1.58944	+	0.325449i
$113$	−12.0642			−1.13490			−0.567452	−	0.823406i	$-0.692071\pi$
$113$	−12.0642			−1.13490			−0.567452	+	0.823406i	$0.692071\pi$
$114$	−10.7499	−	1.53294i	−1.00682	−	0.143573i
$115$	0.655418	+	0.438459i	0.0611180	+	0.0408865i
$116$	−7.74245	+	0.784521i	−0.718868	+	0.0728409i
$117$	−0.0955535			−0.00883392
$118$	3.77970	−	4.18204i	0.347950	−	0.384988i
$119$			25.6133i			2.34797i
$120$	10.4757	−	3.79157i	0.956295	−	0.346122i
$121$	10.8581			0.987104
$122$	3.05644	−	3.38179i	0.276717	−	0.306173i
$123$	−12.0157			−1.08342
$124$	0.214340	+	2.11533i	0.0192483	+	0.189962i
$125$	2.19931	−	10.9619i	0.196712	−	0.980461i
$126$	0.418855	−	0.463441i	0.0373146	−	0.0412866i
$127$		−	4.18189i		−	0.371083i	−0.982636	−	0.185541i	$-0.940596\pi$
$127$		−	4.18189i		−	0.371083i	0.982636	−	0.185541i	$-0.0594039\pi$
$128$	−10.2745	−	4.73649i	−0.908147	−	0.418651i
$129$			16.6536i			1.46626i
$130$	2.84782	−	0.715924i	0.249771	−	0.0627907i
$131$		−	0.974860i		−	0.0851740i	−0.999093	−	0.0425870i	$-0.986440\pi$
$131$		−	0.974860i		−	0.0851740i	0.999093	−	0.0425870i	$-0.0135600\pi$
$132$	0.133767	+	1.32015i	0.0116429	+	0.114904i
$133$	15.5134	−	10.4605i	1.34518	−	0.907043i
$134$	−9.18445	−	8.30084i	−0.793415	−	0.717083i
$135$	6.34496	−	9.48459i	0.546088	−	0.816303i
$136$	−9.99651	+	13.5981i	−0.857194	+	1.16602i
$137$		−	3.53192i		−	0.301753i	−0.988553	−	0.150876i	$-0.951790\pi$
$137$		−	3.53192i		−	0.301753i	0.988553	−	0.150876i	$-0.0482095\pi$
$138$	0.651759	+	0.589056i	0.0554814	+	0.0501438i
$139$		−	7.20995i		−	0.611540i	−0.952105	−	0.305770i	$-0.901086\pi$
$139$		−	7.20995i		−	0.611540i	0.952105	−	0.305770i	$-0.0989139\pi$
$140$	−9.01104	+	16.9504i	−0.761572	+	1.43257i
$141$			4.51225i			0.380000i
$142$	−9.59310	+	10.6143i	−0.805035	+	0.890729i
$143$			0.349742i			0.0292469i
$144$	0.403244	−	0.0825670i	0.0336037	−	0.00688058i
$145$	−4.83781	+	7.23166i	−0.401758	+	0.600556i
$146$	5.34782	+	4.83333i	0.442589	+	0.400009i
$147$			20.1264i			1.66000i
$148$	1.93586	+	19.1050i	0.159127	+	1.57042i
$149$	3.91562			0.320780			0.160390	−	0.987054i	$-0.448725\pi$
$149$	3.91562			0.320780			0.160390	+	0.987054i	$0.448725\pi$
$150$	4.19267	−	11.7289i	0.342330	−	0.957659i
$151$	−7.22811			−0.588216			−0.294108	−	0.955772i	$-0.595022\pi$
$151$	−7.22811			−0.588216			−0.294108	+	0.955772i	$0.595022\pi$
$152$	12.3186	+	0.501183i	0.999173	+	0.0406513i
$153$		−	0.614016i		−	0.0496403i
$154$	−1.69627	−	1.53308i	−0.136690	−	0.123539i
$155$	1.97577	+	1.32174i	0.158698	+	0.106165i
$156$	3.25474	−	0.329794i	0.260588	−	0.0264046i
$157$			23.7964i			1.89916i	0.313526	+	0.949580i	$0.398490\pi$
$157$			23.7964i			1.89916i	−0.313526	+	0.949580i	$0.601510\pi$
$158$	−13.7467	+	15.2100i	−1.09363	+	1.21004i
$159$			5.61301i			0.445140i
$160$	−11.3994	+	5.48204i	−0.901205	+	0.433393i
$161$	−1.51377			−0.119301
$162$	8.81699	−	9.75554i	0.692729	−	0.766468i
$163$	−15.5139			−1.21514			−0.607571	−	0.794265i	$-0.707856\pi$
$163$	−15.5139			−1.21514			−0.607571	+	0.794265i	$0.707856\pi$
$164$	13.5731	−	1.37532i	1.05988	−	0.107395i
$165$	1.23306	+	0.824885i	0.0959933	+	0.0642172i
$166$	3.31714	−	3.67025i	0.257460	−	0.284866i
$167$		−	4.46016i		−	0.345138i	−0.984997	−	0.172569i	$-0.944793\pi$
$167$		−	4.46016i		−	0.345138i	0.984997	−	0.172569i	$-0.0552067\pi$
$168$	−12.6675	+	17.2314i	−0.977319	+	1.32943i
$169$	−12.1377			−0.933672
$170$	4.60045	+	18.2998i	0.352838	+	1.40353i
$171$	−0.371896	+	0.250766i	−0.0284396	+	0.0191765i
$172$	−1.90617	−	18.8120i	−0.145344	−	1.43440i
$173$	21.0522			1.60057			0.800283	−	0.599622i	$-0.204682\pi$
$173$	21.0522			1.60057			0.800283	+	0.599622i	$0.204682\pi$
$174$	−6.49944	+	7.19129i	−0.492721	+	0.545170i
$175$	8.19151	+	19.8379i	0.619220	+	1.49960i
$176$	−0.302209	−	1.47594i	−0.0227799	−	0.111253i
$177$		−	7.02128i		−	0.527752i
$178$	11.0077	+	9.94866i	0.825060	+	0.745684i
$179$	−19.5988			−1.46488			−0.732440	−	0.680832i	$-0.761619\pi$
$179$	−19.5988			−1.46488			−0.732440	+	0.680832i	$0.761619\pi$
$180$	0.216018	−	0.406344i	0.0161010	−	0.0302871i
$181$		−	17.6144i		−	1.30926i	−0.755947	−	0.654632i	$-0.772823\pi$
$181$		−	17.6144i		−	1.30926i	0.755947	−	0.654632i	$-0.227177\pi$
$182$	−3.77970	+	4.18204i	−0.280170	+	0.309994i
$183$		−	5.67772i		−	0.419709i
$184$	−0.803656	−	0.590802i	−0.0592463	−	0.0435545i
$185$	17.8446	+	11.9376i	1.31196	+	0.877671i
$186$	1.96474	+	1.77572i	0.144062	+	0.130202i
$187$	−2.24740			−0.164346
$188$	−0.516472	−	5.09707i	−0.0376676	−	0.371742i
$189$			21.9058i			1.59341i
$190$	9.20494	−	10.2601i	0.667797	−	0.744344i
$191$			23.4244i			1.69493i	0.530849	+	0.847467i	$0.321873\pi$
$191$			23.4244i			1.69493i	−0.530849	+	0.847467i	$0.678127\pi$
$192$	−13.4503	+	4.20415i	−0.970693	+	0.303408i
$193$	−19.0446			−1.37086			−0.685431	−	0.728137i	$-0.740386\pi$
$193$	−19.0446			−1.37086			−0.685431	+	0.728137i	$0.740386\pi$
$194$	9.23731	−	10.2206i	0.663200	−	0.733796i
$195$	2.03370	−	3.04001i	0.145636	−	0.217700i
$196$	−2.30367	−	22.7350i	−0.164548	−	1.62393i
$197$		−	19.5602i		−	1.39361i	−0.717262	−	0.696803i	$-0.754605\pi$
$197$		−	19.5602i		−	1.39361i	0.717262	−	0.696803i	$-0.245395\pi$
$198$	0.0406640	+	0.0367519i	0.00288987	+	0.00261184i
$199$		−	20.7395i		−	1.47018i	−0.677969	−	0.735091i	$-0.737140\pi$
$199$		−	20.7395i		−	1.47018i	0.677969	−	0.735091i	$-0.262860\pi$
$200$	−3.39359	+	13.7289i	−0.239963	+	0.970782i
$201$	−15.4199			−1.08763
$202$	12.1700	−	13.4654i	0.856276	−	0.947425i
$203$		−	16.7024i		−	1.17228i
$204$	2.11922	+	20.9146i	0.148375	+	1.46431i
$205$	8.48103	−	12.6776i	0.592341	−	0.885444i
$206$	2.23484	+	2.01984i	0.155709	+	0.140729i
$207$	0.0362888			0.00252225
$208$	−3.63883	+	0.745075i	−0.252308	+	0.0516617i
$209$	0.917845	+	1.36120i	0.0634887	+	0.0941563i
$210$	5.82965	+	23.1894i	0.402284	+	1.60022i
$211$	−0.0749824			−0.00516200			−0.00258100	−	0.999997i	$-0.500822\pi$
$211$	−0.0749824			−0.00516200			−0.00258100	+	0.999997i	$0.500822\pi$
$212$	−0.642465	−	6.34050i	−0.0441247	−	0.435467i
$213$			17.8204i			1.22103i
$214$	17.2259	+	15.5687i	1.17754	+	1.06425i
$215$	−17.5709	−	11.7545i	−1.19833	−	0.801651i
$216$	−8.54953	+	11.6298i	−0.581722	+	0.791305i
$217$	−4.56328			−0.309776
$218$	18.2492	+	16.4935i	1.23599	+	1.11708i
$219$	8.97852			0.606712
$220$	−1.48729	−	0.790662i	−0.100273	−	0.0533064i
$221$			5.54082i			0.372716i
$222$	17.7450	+	16.0378i	1.19097	+	1.07639i
$223$		−	1.00367i		−	0.0672104i	−0.999435	−	0.0336052i	$-0.989301\pi$
$223$		−	1.00367i		−	0.0672104i	0.999435	−	0.0336052i	$-0.0106989\pi$
$224$	12.3370	−	20.9146i	0.824301	−	1.39742i
$225$	−0.196371	−	0.475565i	−0.0130914	−	0.0317043i
$226$	11.4399	−	12.6577i	0.760974	−	0.841978i
$227$			6.78069i			0.450050i	0.974353	+	0.225025i	$0.0722464\pi$
$227$			6.78069i			0.450050i	−0.974353	+	0.225025i	$0.927754\pi$
$228$	11.8020	−	9.82513i	0.781607	−	0.650685i
$229$	−18.5264			−1.22426			−0.612129	−	0.790758i	$-0.709687\pi$
$229$	−18.5264			−1.22426			−0.612129	+	0.790758i	$0.709687\pi$
$230$	−1.08153	+	0.271890i	−0.0713142	+	0.0179279i
$231$	−2.84789			−0.187378
$232$	6.51870	−	8.86727i	0.427974	−	0.582165i
$233$		−	10.1129i		−	0.662519i	−0.943540	−	0.331259i	$-0.892527\pi$
$233$		−	10.1129i		−	0.662519i	0.943540	−	0.331259i	$-0.107473\pi$
$234$	0.0906091	−	0.100254i	0.00592331	−	0.00655383i
$235$	−4.76080	−	3.18486i	−0.310560	−	0.207758i
$236$	0.803656	+	7.93129i	0.0523136	+	0.516283i
$237$			25.5362i			1.65875i
$238$	−26.8734	−	24.2880i	−1.74194	−	1.57435i
$239$		−	18.2687i		−	1.18171i	−0.806780	−	0.590853i	$-0.798792\pi$
$239$		−	18.2687i		−	1.18171i	0.806780	−	0.590853i	$-0.201208\pi$
$240$	−5.95553	+	14.5864i	−0.384428	+	0.941550i
$241$			13.1021i			0.843981i	0.906600	+	0.421991i	$0.138668\pi$
$241$			13.1021i			0.843981i	−0.906600	+	0.421991i	$0.861332\pi$
$242$	−10.2963	+	11.3923i	−0.661871	+	0.732326i
$243$		−	1.06893i		−	0.0685718i
$244$	0.649873	+	6.41360i	0.0416038	+	0.410589i
$245$	−21.2351	−	14.2058i	−1.35666	−	0.907573i
$246$	11.3940	−	12.6069i	0.726455	−	0.803784i
$247$	3.35595	−	2.26288i	0.213534	−	0.143984i
$248$	−2.42264	−	1.78098i	−0.153838	−	0.113093i
$249$		−	6.16202i		−	0.390502i
$250$	9.41566	+	12.7022i	0.595499	+	0.803356i
$251$			12.8628i			0.811891i	0.913897	+	0.405946i	$0.133058\pi$
$251$			12.8628i			0.811891i	−0.913897	+	0.405946i	$0.866942\pi$
$252$	0.0890587	+	0.878922i	0.00561017	+	0.0553669i
$253$		−	0.132823i		−	0.00835053i
$254$	4.38762	+	3.96550i	0.275304	+	0.248818i
$255$	19.5348	+	13.0683i	1.22332	+	0.818370i
$256$	14.7124	−	6.28857i	0.919523	−	0.393035i
$257$	27.1520			1.69369			0.846847	−	0.531836i	$-0.178498\pi$
$257$	27.1520			1.69369			0.846847	+	0.531836i	$0.178498\pi$
$258$	−17.4728	−	15.7918i	−1.08781	−	0.983156i
$259$	−41.2143			−2.56093
$260$	−1.94932	+	3.66680i	−0.120892	+	0.227405i
$261$			0.400399i			0.0247841i
$262$	1.02282	+	0.924417i	0.0631900	+	0.0571107i
$263$	−18.6447			−1.14968			−0.574841	−	0.818265i	$-0.694936\pi$
$263$	−18.6447			−1.14968			−0.574841	+	0.818265i	$0.694936\pi$
$264$	−1.51194	−	1.11149i	−0.0930536	−	0.0684076i
$265$	−5.92220	−	3.96181i	−0.363798	−	0.243372i
$266$	−3.73553	+	26.1958i	−0.229040	+	1.60617i
$267$	18.4809			1.13101
$268$	17.4184	−	1.76496i	1.06400	−	0.107812i
$269$			4.51225i			0.275116i	0.990494	+	0.137558i	$0.0439254\pi$
$269$			4.51225i			0.275116i	−0.990494	+	0.137558i	$0.956075\pi$
$270$	3.93454	+	15.6509i	0.239448	+	0.952485i
$271$			12.8691i			0.781741i	0.920446	+	0.390871i	$0.127826\pi$
$271$			12.8691i			0.781741i	−0.920446	+	0.390871i	$0.872174\pi$
$272$	−4.78777	−	23.3827i	−0.290301	−	1.41779i
$273$			7.02128i			0.424947i
$274$	3.70568	+	3.34917i	0.223868	+	0.202331i
$275$	−1.74065	+	0.718753i	−0.104965	+	0.0433424i
$276$	−1.23607	+	0.125247i	−0.0744026	+	0.00753901i
$277$			4.35925i			0.261922i	0.991388	+	0.130961i	$0.0418063\pi$
$277$			4.35925i			0.261922i	−0.991388	+	0.130961i	$0.958194\pi$
$278$	7.56465	+	6.83688i	0.453697	+	0.410049i
$279$	0.109394			0.00654922
$280$	−9.23948	−	25.5276i	−0.552164	−	1.52557i
$281$		−	7.22169i		−	0.430810i	−0.976525	−	0.215405i	$-0.930893\pi$
$281$		−	7.22169i		−	0.430810i	0.976525	−	0.215405i	$-0.0691071\pi$
$282$	−4.73423	−	4.27876i	−0.281919	−	0.254797i
$283$	−4.15031			−0.246710			−0.123355	−	0.992363i	$-0.539365\pi$
$283$	−4.15031			−0.246710			−0.123355	+	0.992363i	$0.539365\pi$
$284$	−2.03973	−	20.1301i	−0.121035	−	1.19450i
$285$	−0.0628719	−	17.1689i	−0.00372421	−	1.01700i
$286$	−0.366948	−	0.331645i	−0.0216981	−	0.0196106i
$287$			29.2805i			1.72837i
$288$	−0.295750	+	0.501376i	−0.0174272	+	0.0295439i
$289$	−18.6047			−1.09439
$290$	−2.99994	−	11.9333i	−0.176163	−	0.700745i
$291$		−	17.1595i		−	1.00591i
$292$	−10.1422	+	1.02768i	−0.593528	+	0.0601405i
$293$	4.82841			0.282079			0.141039	−	0.990004i	$-0.454956\pi$
$293$	4.82841			0.282079			0.141039	+	0.990004i	$0.454956\pi$
$294$	−21.1166	−	19.0850i	−1.23154	−	1.11306i
$295$	7.40804	+	4.95580i	0.431313	+	0.288538i
$296$	−21.8806	−	16.0854i	−1.27178	−	0.934942i
$297$	−1.92209			−0.111531
$298$	−3.71301	+	4.10825i	−0.215089	+	0.237985i
$299$	−0.327467			−0.0189379
$300$	8.33016	+	15.5209i	0.480942	+	0.896100i
$301$	40.5821			2.33911
$302$	6.85410	−	7.58370i	0.394409	−	0.436393i
$303$		−	22.6073i		−	1.29875i
$304$	−12.2071	+	12.4494i	−0.700123	+	0.714023i
$305$	5.99048	+	4.00749i	0.343014	+	0.229468i
$306$	0.644223	+	0.582245i	0.0368278	+	0.0332847i
$307$		−	0.488437i		−	0.0278766i	−0.999903	−	0.0139383i	$-0.995563\pi$
$307$		−	0.488437i		−	0.0278766i	0.999903	−	0.0139383i	$-0.00443684\pi$
$308$	3.21700	−	0.325970i	0.183306	−	0.0185739i
$309$	3.75210			0.213450
$310$	−3.26030	+	0.819619i	−0.185173	+	0.0465512i
$311$		−	2.59142i		−	0.146946i	−0.997297	−	0.0734730i	$-0.976592\pi$
$311$		−	2.59142i		−	0.146946i	0.997297	−	0.0734730i	$-0.0234083\pi$
$312$	−2.74031	+	3.72759i	−0.155139	+	0.211033i
$313$		−	9.45632i		−	0.534503i	−0.963627	−	0.267251i	$-0.913885\pi$
$313$		−	9.45632i		−	0.534503i	0.963627	−	0.267251i	$-0.0861154\pi$
$314$	−24.9671	−	22.5651i	−1.40897	−	1.27342i
$315$	0.820937	+	0.549187i	0.0462545	+	0.0309432i
$316$	−2.92287	−	28.8459i	−0.164425	−	1.62271i
$317$	−23.7528			−1.33409			−0.667045	−	0.745018i	$-0.732441\pi$
$317$	−23.7528			−1.33409			−0.667045	+	0.745018i	$0.732441\pi$
$318$	−5.88914	−	5.32257i	−0.330247	−	0.298475i
$319$	1.46553			0.0820538
$320$	5.05785	−	17.1586i	0.282743	−	0.959196i
$321$	28.9208			1.61420
$322$	1.43544	−	1.58824i	0.0799938	−	0.0885090i
$323$	14.5410	+	21.5650i	0.809085	+	1.19991i
$324$	1.87471	+	18.5015i	0.104150	+	1.02786i
$325$	1.77203	+	4.29145i	0.0982948	+	0.238047i
$326$	14.7111	−	16.2771i	0.814775	−	0.901506i
$327$	30.6388			1.69433
$328$	−11.4278	+	15.5450i	−0.630993	+	0.858327i
$329$	10.9956			0.606209
$330$	−2.03472	+	0.511515i	−0.112008	+	0.0281580i
$331$	17.7390			0.975021			0.487511	−	0.873117i	$-0.337905\pi$
$331$	17.7390			0.975021			0.487511	+	0.873117i	$0.337905\pi$
$332$	0.705305	+	6.96066i	0.0387086	+	0.382016i
$333$	0.988012			0.0541427
$334$	4.67958	+	4.22938i	0.256055	+	0.231421i
$335$	10.8838	−	16.2693i	0.594643	−	0.888885i
$336$	−6.06703	−	29.6304i	−0.330983	−	1.61647i
$337$	−4.34489			−0.236681			−0.118341	−	0.992973i	$-0.537757\pi$
$337$	−4.34489			−0.236681			−0.118341	+	0.992973i	$0.537757\pi$
$338$	11.5097	−	12.7349i	0.626044	−	0.692685i
$339$		−	21.2512i		−	1.15420i
$340$	−23.5625	−	12.5261i	−1.27785	−	0.679324i
$341$		−	0.400399i		−	0.0216828i
$342$	0.0895502	−	0.627981i	0.00484232	−	0.0339573i
$343$	18.9974			1.02576
$344$	21.5450	+	15.8386i	1.16163	+	0.853962i
$345$	−0.772348	+	1.15452i	−0.0415818	+	0.0621574i
$346$	−19.9628	+	22.0878i	−1.07321	+	1.18745i
$347$	23.7679			1.27593			0.637964	−	0.770067i	$-0.279777\pi$
$347$	23.7679			1.27593			0.637964	+	0.770067i	$0.279777\pi$
$348$	−1.38194	−	13.6384i	−0.0740796	−	0.731093i
$349$	14.9933			0.802570			0.401285	−	0.915953i	$-0.368564\pi$
$349$	14.9933			0.802570			0.401285	+	0.915953i	$0.368564\pi$
$350$	−28.5815	−	10.2169i	−1.52774	−	0.546116i
$351$			4.73879i			0.252938i
$352$	1.83512	+	1.08249i	0.0978124	+	0.0576971i
$353$			3.27604i			0.174366i	0.996192	+	0.0871831i	$0.0277865\pi$
$353$			3.27604i			0.174366i	−0.996192	+	0.0871831i	$0.972213\pi$
$354$	7.36669	+	6.65797i	0.391535	+	0.353867i
$355$	−18.8020	−	12.5781i	−0.997909	−	0.667577i
$356$	−20.8762	+	2.11533i	−1.10644	+	0.112112i
$357$	−45.1180			−2.38790
$358$	18.5846	−	20.5629i	0.982228	−	1.08678i
$359$			1.83814i			0.0970133i	0.998823	+	0.0485067i	$0.0154462\pi$
$359$			1.83814i			0.0970133i	−0.998823	+	0.0485067i	$0.984554\pi$
$360$	0.221494	+	0.611963i	0.0116738	+	0.0322533i
$361$	7.12282	−	17.6144i	0.374885	−	0.927071i
$362$	18.4809	+	16.7029i	0.971335	+	0.877886i
$363$			19.1267i			1.00389i
$364$	−0.803656	−	7.93129i	−0.0421230	−	0.415713i
$365$	−6.33728	+	9.47309i	−0.331708	+	0.495844i
$366$	5.95704	+	5.38393i	0.311380	+	0.281423i
$367$	−9.82842			−0.513040			−0.256520	−	0.966539i	$-0.582576\pi$
$367$	−9.82842			−0.513040			−0.256520	+	0.966539i	$0.582576\pi$
$368$	1.38194	−	0.282961i	0.0720385	−	0.0147504i
$369$		−	0.701928i		−	0.0365409i
$370$	−29.4462	+	7.40257i	−1.53083	+	0.384841i
$371$	13.6780			0.710128
$372$	−3.72616	+	0.377561i	−0.193192	+	0.0195756i
$373$	−8.37248			−0.433510			−0.216755	−	0.976226i	$-0.569547\pi$
$373$	−8.37248			−0.433510			−0.216755	+	0.976226i	$0.569547\pi$
$374$	2.13111	−	2.35797i	0.110197	−	0.121928i
$375$	19.3094	+	3.87409i	0.997135	+	0.200057i
$376$	5.83757	+	4.29145i	0.301050	+	0.221314i
$377$		−	3.61316i		−	0.186087i
$378$	−22.9835	−	20.7723i	−1.18214	−	1.06841i
$379$	32.6382			1.67651			0.838256	−	0.545277i	$-0.183575\pi$
$379$	32.6382			1.67651			0.838256	+	0.545277i	$0.183575\pi$
$380$	2.03618	+	19.3870i	0.104454	+	0.994530i
$381$	7.36642			0.377393
$382$	−24.5768	−	22.2124i	−1.25746	−	1.13648i
$383$			6.10267i			0.311832i	0.987770	+	0.155916i	$0.0498329\pi$
$383$			6.10267i			0.311832i	−0.987770	+	0.155916i	$0.950167\pi$
$384$	8.34336	−	18.0986i	0.425770	−	0.923591i
$385$	2.01012	−	3.00477i	0.102445	−	0.153137i
$386$	18.0592	−	19.9815i	0.919188	−	1.01703i
$387$	−0.972857			−0.0494531
$388$	1.96407	+	19.3835i	0.0997108	+	0.984047i
$389$	3.65867			0.185502			0.0927510	−	0.995689i	$-0.470434\pi$
$389$	3.65867			0.185502			0.0927510	+	0.995689i	$0.470434\pi$
$390$	1.26110	+	5.01646i	0.0638585	+	0.254018i
$391$		−	2.10427i		−	0.106417i
$392$	26.0379	+	19.1416i	1.31511	+	0.966795i
$393$	1.71722			0.0866224
$394$	20.5225	+	18.5481i	1.03391	+	0.934439i
$395$	−26.9428	−	18.0241i	−1.35564	−	0.906892i
$396$	−0.0771198	+	0.00781433i	−0.00387541	+	0.000392685i
$397$			30.1641i			1.51389i	0.653478	+	0.756946i	$0.273309\pi$
$397$			30.1641i			1.51389i	−0.653478	+	0.756946i	$0.726691\pi$
$398$	21.7597	+	19.6663i	1.09072	+	0.985783i
$399$	18.4263	+	27.3269i	0.922468	+	1.36806i
$400$	−11.1863	−	16.5791i	−0.559317	−	0.828954i
$401$		−	34.6456i		−	1.73012i	−0.501670	−	0.865059i	$-0.667281\pi$
$401$		−	34.6456i		−	1.73012i	0.501670	−	0.865059i	$-0.332719\pi$
$402$	14.6220	−	16.1785i	0.729278	−	0.806908i
$403$	−0.987155			−0.0491737
$404$	2.58763	+	25.5374i	0.128739	+	1.27053i
$405$	17.2809	+	11.5605i	0.858695	+	0.574447i
$406$	17.5241	+	15.8381i	0.869705	+	0.786033i
$407$		−	3.61629i		−	0.179253i
$408$	−23.9531	−	17.6089i	−1.18585	−	0.871771i
$409$			30.5268i			1.50945i	0.656041	+	0.754726i	$0.272230\pi$
$409$			30.5268i			1.50945i	−0.656041	+	0.754726i	$0.727770\pi$
$410$	5.25912	+	20.9199i	0.259729	+	1.03316i
$411$	6.22150			0.306884
$412$	−4.23841	+	0.429466i	−0.208811	+	0.0211583i
$413$	−17.1098			−0.841917
$414$	−0.0344111	+	0.0380741i	−0.00169121	+	0.00187124i
$415$	6.50145	+	4.34931i	0.319144	+	0.213499i
$416$	2.66881	−	4.52437i	0.130849	−	0.221825i
$417$	12.7004			0.621940
$418$	−2.29852	−	0.327769i	−0.112424	−	0.0160317i
$419$		−	6.46767i		−	0.315966i	−0.987442	−	0.157983i	$-0.949501\pi$
$419$		−	6.46767i		−	0.315966i	0.987442	−	0.157983i	$-0.0504992\pi$
$420$	−29.8582	−	15.8730i	−1.45693	−	0.774523i
$421$		−	21.2039i		−	1.03341i	−0.856162	−	0.516707i	$-0.827158\pi$
$421$		−	21.2039i		−	1.03341i	0.856162	−	0.516707i	$-0.172842\pi$
$422$	0.0711025	−	0.0786712i	0.00346122	−	0.00382965i
$423$	−0.263594			−0.0128164
$424$	7.26164	+	5.33834i	0.352656	+	0.259253i
$425$	−27.5764	+	11.3869i	−1.33765	+	0.552346i
$426$	−18.6971	−	16.8983i	−0.905877	−	0.818726i
$427$	−13.8357			−0.669558
$428$	−32.6692	+	3.31028i	−1.57913	+	0.160008i
$429$	−0.616072			−0.0297443
$430$	28.9945	−	7.28902i	1.39824	−	0.351508i
$431$	7.73794			0.372723			0.186362	−	0.982481i	$-0.440330\pi$
$431$	7.73794			0.372723			0.186362	+	0.982481i	$0.440330\pi$
$432$	−4.09475	−	19.9981i	−0.197009	−	0.962159i
$433$	−23.8336			−1.14537			−0.572684	−	0.819776i	$-0.694098\pi$
$433$	−23.8336			−1.14537			−0.572684	+	0.819776i	$0.694098\pi$
$434$	4.32716	−	4.78777i	0.207710	−	0.229820i
$435$	−12.7386	−	8.52182i	−0.610769	−	0.408590i
$436$	−34.6099	+	3.50692i	−1.65751	+	0.167951i
$437$	−1.27451	+	0.859387i	−0.0609679	+	0.0411100i
$438$	−8.51393	+	9.42022i	−0.406811	+	0.450115i
$439$	10.4173			0.497193			0.248596	−	0.968607i	$-0.420031\pi$
$439$	10.4173			0.497193			0.248596	+	0.968607i	$0.420031\pi$
$440$	2.23989	−	0.810705i	0.106782	−	0.0386489i
$441$	−1.17573			−0.0559873
$442$	−5.81340	−	5.25411i	−0.276515	−	0.249913i
$443$	−5.03629			−0.239282			−0.119641	−	0.992817i	$-0.538174\pi$
$443$	−5.03629			−0.239282			−0.119641	+	0.992817i	$0.538174\pi$
$444$	−33.6536	+	3.41003i	−1.59713	+	0.161833i
$445$	−13.0443	+	19.4989i	−0.618360	+	0.924337i
$446$	1.05304	+	0.951732i	0.0498630	+	0.0450658i
$447$			6.89739i			0.326235i
$448$	10.2449	+	32.7763i	0.484024	+	1.54854i
$449$		−	27.3757i		−	1.29194i	−0.763363	−	0.645970i	$-0.776453\pi$
$449$		−	27.3757i		−	1.29194i	0.763363	−	0.645970i	$-0.223547\pi$
$450$	0.685171	+	0.244925i	0.0322993	+	0.0115459i
$451$	−2.56918			−0.120978
$452$	2.43241	+	24.0055i	0.114411	+	1.12912i
$453$		−	12.7324i		−	0.598219i
$454$	−7.11427	−	6.42983i	−0.333889	−	0.301767i
$455$	−7.40804	−	4.95580i	−0.347294	−	0.232332i
$456$	−0.882837	+	21.6994i	−0.0413426	+	1.01617i
$457$		−	8.86333i		−	0.414609i	−0.978276	−	0.207305i	$-0.933531\pi$
$457$		−	8.86333i		−	0.414609i	0.978276	−	0.207305i	$-0.0664691\pi$
$458$	17.5677	−	19.4378i	0.820887	−	0.908268i
$459$	−30.4509			−1.42133
$460$	0.740304	−	1.39256i	0.0345168	−	0.0649285i
$461$	−6.71485			−0.312742			−0.156371	−	0.987698i	$-0.549980\pi$
$461$	−6.71485			−0.312742			−0.156371	+	0.987698i	$0.549980\pi$
$462$	2.70053	−	2.98800i	0.125640	−	0.139014i
$463$	7.43802			0.345674			0.172837	−	0.984950i	$-0.444707\pi$
$463$	7.43802			0.345674			0.172837	+	0.984950i	$0.444707\pi$
$464$	3.12210	+	15.2478i	0.144940	+	0.707863i
$465$	−2.32826	+	3.48033i	−0.107970	+	0.161397i
$466$	10.6104	+	9.58962i	0.491518	+	0.444231i
$467$	−31.0421			−1.43646			−0.718228	−	0.695808i	$-0.755047\pi$
$467$	−31.0421			−1.43646			−0.718228	+	0.695808i	$0.755047\pi$
$468$	0.0192657	+	0.190133i	0.000890557	+	0.00878892i
$469$			37.5758i			1.73509i
$470$	7.85600	−	1.97495i	0.362370	−	0.0910975i
$471$	−41.9175			−1.93146
$472$	−9.08355	−	6.67770i	−0.418104	−	0.307366i
$473$			3.56082i			0.163727i
$474$	−26.7925	−	24.2148i	−1.23062	−	1.11222i
$475$	18.1590	+	12.0519i	0.833194	+	0.552981i
$476$	50.9656	−	5.16421i	2.33601	−	0.236701i
$477$	−0.327897			−0.0150134
$478$	19.1675	+	17.3234i	0.876699	+	0.792355i
$479$		−	21.0127i		−	0.960093i	−0.877243	−	0.480046i	$-0.840620\pi$
$479$		−	21.0127i		−	0.960093i	0.877243	−	0.480046i	$-0.159380\pi$
$480$	−9.65665	−	20.0802i	−0.440764	−	0.916531i
$481$	−8.91571			−0.406521
$482$	−13.7467	−	12.4242i	−0.626144	−	0.565905i
$483$		−	2.66651i		−	0.121330i
$484$	−2.18924	−	21.6057i	−0.0995110	−	0.982075i
$485$	18.1047	+	12.1116i	0.822092	+	0.549960i
$486$	1.12152	+	1.01362i	0.0508730	+	0.0459786i
$487$		−	23.9504i		−	1.08530i	−0.839960	−	0.542648i	$-0.817422\pi$
$487$		−	23.9504i		−	1.08530i	0.839960	−	0.542648i	$-0.182578\pi$
$488$	−7.34537	−	5.39989i	−0.332509	−	0.244442i
$489$		−	27.3278i		−	1.23581i
$490$	35.0409	−	8.80905i	1.58299	−	0.397952i
$491$		−	31.9941i		−	1.44387i	−0.691959	−	0.721937i	$-0.743252\pi$
$491$		−	31.9941i		−	1.44387i	0.691959	−	0.721937i	$-0.256748\pi$
$492$	2.42264	+	23.9091i	0.109221	+	1.07790i
$493$	23.2177			1.04567
$494$	−0.808091	+	5.66684i	−0.0363577	+	0.254963i
$495$	−0.0481877	+	0.0720320i	−0.00216587	+	0.00323760i
$496$	4.16588	−	0.852992i	0.187054	−	0.0383005i
$497$	43.4256			1.94790
$498$	6.46516	+	5.84317i	0.289711	+	0.261839i
$499$			29.7730i			1.33282i	0.745584	+	0.666412i	$0.232171\pi$
$499$			29.7730i			1.33282i	−0.745584	+	0.666412i	$0.767829\pi$
$500$	−22.2555	−	2.16605i	−0.995297	−	0.0968685i
$501$	7.85660			0.351007
$502$	−13.4956	−	12.1972i	−0.602337	−	0.544388i
$503$	24.3841			1.08723			0.543617	−	0.839333i	$-0.317054\pi$
$503$	24.3841			1.08723			0.543617	+	0.839333i	$0.317054\pi$
$504$	−1.00661	−	0.740003i	−0.0448380	−	0.0329623i
$505$	23.8526	+	15.9568i	1.06143	+	0.710069i
$506$	0.139358	+	0.125950i	0.00619520	+	0.00559918i
$507$		−	21.3807i		−	0.949550i
$508$	−8.32117	+	0.843161i	−0.369192	+	0.0374092i
$509$			28.9266i			1.28215i	0.767478	+	0.641075i	$0.221511\pi$
$509$			28.9266i			1.28215i	−0.767478	+	0.641075i	$0.778489\pi$
$510$	−32.2352	+	8.10372i	−1.42740	+	0.358839i
$511$		−	21.8793i		−	0.967881i
$512$	−7.35316	+	21.3993i	−0.324967	+	0.945725i
$513$	12.4362	+	18.4434i	0.549073	+	0.814298i
$514$	−25.7470	+	28.4877i	−1.13565	+	1.25654i
$515$	−2.64833	+	3.95879i	−0.116700	+	0.174445i
$516$	33.1374	−	3.35772i	1.45879	−	0.147816i
$517$			0.964797i			0.0424317i
$518$	39.0817	−	43.2418i	1.71715	−	1.89994i
$519$			37.0835i			1.62779i
$520$	−1.99874	−	5.52228i	−0.0876504	−	0.242168i
$521$		−	8.62409i		−	0.377828i	−0.981994	−	0.188914i	$-0.939503\pi$
$521$		−	8.62409i		−	0.377828i	0.981994	−	0.188914i	$-0.0604968\pi$
$522$	−0.420097	−	0.379680i	−0.0183871	−	0.0166182i
$523$			33.0172i			1.44374i	0.692028	+	0.721870i	$0.256717\pi$
$523$			33.0172i			1.44374i	−0.692028	+	0.721870i	$0.743283\pi$
$524$	−1.93979	+	0.196553i	−0.0847400	+	0.00858647i
$525$	−34.9445	+	14.4294i	−1.52510	+	0.629750i
$526$	17.6800	−	19.5620i	0.770883	−	0.852942i
$527$		−	6.34335i		−	0.276321i
$528$	2.59988	−	0.532343i	0.113145	−	0.0231673i
$529$	−22.8756			−0.994593
$530$	9.77247	−	2.45673i	0.424489	−	0.106714i
$531$	0.410165			0.0177996
$532$	−23.9423	−	28.7597i	−1.03803	−	1.24689i
$533$			6.33413i			0.274361i
$534$	−17.5246	+	19.3901i	−0.758364	+	0.839091i
$535$	−20.4131	+	30.5139i	−0.882535	+	1.31923i
$536$	−14.6653	+	19.9489i	−0.633445	+	0.861663i
$537$		−	34.5233i		−	1.48979i
$538$	−4.73423	−	4.27876i	−0.204107	−	0.184471i
$539$			4.30338i			0.185360i
$540$	−20.1518	−	10.7130i	−0.867196	−	0.461013i
$541$	−31.2615			−1.34404			−0.672018	−	0.740535i	$-0.734572\pi$
$541$	−31.2615			−1.34404			−0.672018	+	0.740535i	$0.734572\pi$
$542$	−13.5022	−	12.2032i	−0.579969	−	0.524172i
$543$	31.0278			1.33153
$544$	29.0731	+	17.1495i	1.24650	+	0.735279i
$545$	−21.6257	+	32.3266i	−0.926344	+	1.38472i
$546$	−7.36669	−	6.65797i	−0.315265	−	0.284935i
$547$			21.1292i			0.903419i	0.892165	+	0.451709i	$0.149186\pi$
$547$			21.1292i			0.903419i	−0.892165	+	0.451709i	$0.850814\pi$
$548$	−7.02786	+	0.712114i	−0.300215	+	0.0304200i
$549$	0.331678			0.0141557
$550$	0.896467	−	2.50784i	0.0382255	−	0.106935i
$551$	−9.48218	−	14.0625i	−0.403954	−	0.599081i
$552$	1.04070	−	1.41564i	0.0442952	−	0.0602538i
$553$	62.2277			2.64619
$554$	−4.57371	−	4.13369i	−0.194318	−	0.175624i
$555$	−21.0282	+	31.4334i	−0.892597	+	1.33427i
$556$	−14.3464	+	1.45369i	−0.608425	+	0.0616500i
$557$		−	8.78169i		−	0.372092i	−0.982541	−	0.186046i	$-0.940433\pi$
$557$		−	8.78169i		−	0.372092i	0.982541	−	0.186046i	$-0.0595674\pi$
$558$	−0.103733	+	0.114775i	−0.00439137	+	0.00485882i
$559$	8.77896			0.371310
$560$	35.5449	+	14.5127i	1.50204	+	0.613274i
$561$		−	3.95881i		−	0.167141i
$562$	7.57696	+	6.84801i	0.319615	+	0.288866i
$563$			17.0044i			0.716649i	0.933597	+	0.358325i	$0.116652\pi$
$563$			17.0044i			0.716649i	−0.933597	+	0.358325i	$0.883348\pi$
$564$	8.97852	−	0.909768i	0.378064	−	0.0383082i
$565$	22.4218	+	14.9996i	0.943291	+	0.631039i
$566$	3.93556	−	4.35449i	0.165424	−	0.183033i
$567$	−39.9123			−1.67616
$568$	23.0546	+	16.9484i	0.967348	+	0.711139i
$569$			15.9943i			0.670515i	0.942127	+	0.335258i	$0.108823\pi$
$569$			15.9943i			0.670515i	−0.942127	+	0.335258i	$0.891177\pi$
$570$	18.0732	+	16.2146i	0.757002	+	0.679153i
$571$			40.0149i			1.67457i	0.546765	+	0.837286i	$0.315859\pi$
$571$			40.0149i			1.67457i	−0.546765	+	0.837286i	$0.684141\pi$
$572$	0.695920	−	0.0705157i	0.0290979	−	0.00294841i
$573$	−41.2623			−1.72376
$574$	−30.7210	−	27.7654i	−1.28227	−	1.15891i
$575$	−0.672975	−	1.62978i	−0.0280650	−	0.0679667i
$576$	−0.245596	−	0.785732i	−0.0102331	−	0.0327388i
$577$			14.6674i			0.610613i	0.952254	+	0.305306i	$0.0987589\pi$
$577$			14.6674i			0.610613i	−0.952254	+	0.305306i	$0.901241\pi$
$578$	17.6420	−	19.5200i	0.733811	−	0.811923i
$579$		−	33.5472i		−	1.39418i
$580$	15.3650	+	8.16826i	0.637998	+	0.339168i
$581$	−15.0159			−0.622964
$582$	18.0036	+	16.2716i	0.746275	+	0.674478i
$583$			1.20016i			0.0497055i
$584$	8.53917	−	11.6157i	0.353353	−	0.480659i
$585$	0.177590	+	0.118803i	0.00734243	+	0.00491191i
$586$	−4.57857	+	5.06594i	−0.189139	+	0.209272i
$587$	−0.410556			−0.0169454			−0.00847272	−	0.999964i	$-0.502697\pi$
$587$	−0.410556			−0.0169454			−0.00847272	+	0.999964i	$0.502697\pi$
$588$	40.0478	−	4.05793i	1.65154	−	0.167346i
$589$	−3.84203	+	2.59064i	−0.158308	+	0.106745i
$590$	−12.2243	+	3.07311i	−0.503268	+	0.126518i
$591$	34.4554			1.41731
$592$	37.6251	−	7.70399i	1.54638	−	0.316632i
$593$		−	20.4734i		−	0.840742i	−0.907352	−	0.420371i	$-0.861900\pi$
$593$		−	20.4734i		−	0.840742i	0.907352	−	0.420371i	$-0.138100\pi$
$594$	1.82264	−	2.01665i	0.0747837	−	0.0827443i
$595$	31.8455	−	47.6033i	1.30554	−	1.95154i
$596$	−0.789476	−	7.79135i	−0.0323382	−	0.319146i
$597$	36.5327			1.49518
$598$	0.310522	−	0.343576i	0.0126982	−	0.0140499i
$599$	35.7972			1.46263			0.731317	−	0.682038i	$-0.238906\pi$
$599$	35.7972			1.46263			0.731317	+	0.682038i	$0.238906\pi$
$600$	−24.1836	−	5.97783i	−0.987291	−	0.244044i
$601$			36.5899i			1.49253i	0.665647	+	0.746267i	$0.268156\pi$
$601$			36.5899i			1.49253i	−0.665647	+	0.746267i	$0.731844\pi$
$602$	−38.4822	+	42.5786i	−1.56842	+	1.73537i
$603$		−	0.900789i		−	0.0366830i
$604$	1.45735	+	14.3826i	0.0592986	+	0.585219i
$605$	−20.1803	−	13.5001i	−0.820444	−	0.548858i
$606$	23.7195	+	21.4375i	0.963537	+	0.870838i
$607$		−	24.9730i		−	1.01362i	−0.862057	−	0.506812i	$-0.830824\pi$
$607$		−	24.9730i		−	1.01362i	0.862057	−	0.506812i	$-0.169176\pi$
$608$	−1.48645	−	24.6128i	−0.0602835	−	0.998181i
$609$	29.4213			1.19221
$610$	−9.88514	+	2.48506i	−0.400238	+	0.100617i
$611$	2.37864			0.0962295
$612$	−1.22178	+	0.123799i	−0.0493874	+	0.00500429i
$613$			19.7446i			0.797478i	0.917065	+	0.398739i	$0.130552\pi$
$613$			19.7446i			0.797478i	−0.917065	+	0.398739i	$0.869448\pi$
$614$	0.512466	+	0.463163i	0.0206814	+	0.0186917i
$615$	22.3317	+	14.9394i	0.900501	+	0.602414i
$616$	−2.70853	+	3.68437i	−0.109130	+	0.148447i
$617$		−	32.3305i		−	1.30158i	−0.759259	−	0.650788i	$-0.774439\pi$
$617$		−	32.3305i		−	1.30158i	0.759259	−	0.650788i	$-0.225561\pi$
$618$	−3.55795	+	3.93669i	−0.143122	+	0.158357i
$619$		−	7.95921i		−	0.319908i	−0.987124	−	0.159954i	$-0.948865\pi$
$619$		−	7.95921i		−	0.319908i	0.987124	−	0.159954i	$-0.0511345\pi$
$620$	2.23166	−	4.19790i	0.0896257	−	0.168592i
$621$		−	1.79967i		−	0.0722185i
$622$	2.71891	+	2.45733i	0.109018	+	0.0985300i
$623$		−	45.0351i		−	1.80429i
$624$	−1.31245	−	6.40982i	−0.0525402	−	0.256598i
$625$	−17.7166	+	17.6386i	−0.708664	+	0.705546i
$626$	9.92153	+	8.96701i	0.396544	+	0.358394i
$627$	−2.39776	+	1.61679i	−0.0957575	+	0.0645683i
$628$	47.3503	−	4.79788i	1.88948	−	0.191456i
$629$		−	57.2914i		−	2.28436i
$630$	−1.35466	+	0.340553i	−0.0539710	+	0.0135680i
$631$		−	37.9642i		−	1.51133i	−0.654957	−	0.755666i	$-0.727313\pi$
$631$		−	37.9642i		−	1.51133i	0.654957	−	0.755666i	$-0.272687\pi$
$632$	33.0366	+	24.2866i	1.31413	+	0.966070i
$633$		−	0.132082i		−	0.00524979i
$634$	22.5237	−	24.9213i	0.894531	−	0.989752i
$635$	−5.19942	+	7.77220i	−0.206333	+	0.308430i
$636$	11.1688	−	1.13171i	0.442873	−	0.0448751i
$637$	10.6097			0.420371
$638$	−1.38969	+	1.53762i	−0.0550185	+	0.0608751i
$639$	−1.04102			−0.0411822
$640$	13.2066	+	21.5774i	0.522037	+	0.852923i
$641$			22.7859i			0.899988i	0.893032	+	0.449994i	$0.148574\pi$
$641$			22.7859i			0.899988i	−0.893032	+	0.449994i	$0.851426\pi$
$642$	−27.4243	+	30.3436i	−1.08235	+	1.19757i
$643$	17.9394			0.707461			0.353731	−	0.935347i	$-0.384913\pi$
$643$	17.9394			0.707461			0.353731	+	0.935347i	$0.384913\pi$
$644$	0.305209	+	3.01211i	0.0120269	+	0.118694i
$645$	20.7057	−	30.9513i	0.815284	−	1.21870i
$646$	−36.4145	−	5.19271i	−1.43271	−	0.204304i
$647$	−21.4626			−0.843781			−0.421891	−	0.906647i	$-0.638633\pi$
$647$	−21.4626			−0.843781			−0.421891	+	0.906647i	$0.638633\pi$
$648$	−21.1894	−	15.5772i	−0.832398	−	0.611931i
$649$		−	1.50127i		−	0.0589301i
$650$	−6.18291	−	2.21018i	−0.242514	−	0.0866903i
$651$		−	8.03825i		−	0.315044i
$652$	3.12794	+	30.8697i	0.122500	+	1.20895i
$653$		−	11.7812i		−	0.461035i	−0.973068	−	0.230518i	$-0.925958\pi$
$653$		−	11.7812i		−	0.461035i	0.973068	−	0.230518i	$-0.0740420\pi$
$654$	−29.0535	+	32.1461i	−1.13608	+	1.25701i
$655$	−1.21206	+	1.81181i	−0.0473591	+	0.0707935i
$656$	−5.47326	−	26.7306i	−0.213695	−	1.04365i
$657$			0.524502i			0.0204628i
$658$	−10.4267	+	11.5366i	−0.406474	+	0.449743i
$659$	−24.3327			−0.947866			−0.473933	−	0.880561i	$-0.657166\pi$
$659$	−24.3327			−0.947866			−0.473933	+	0.880561i	$0.657166\pi$
$660$	1.39275	−	2.61986i	0.0542129	−	0.101978i
$661$			7.73106i			0.300703i	0.988633	+	0.150352i	$0.0480406\pi$
$661$			7.73106i			0.300703i	−0.988633	+	0.150352i	$0.951959\pi$
$662$	−16.8211	+	18.6116i	−0.653769	+	0.723362i
$663$	−9.76018			−0.379054
$664$	−7.97191	−	5.86049i	−0.309370	−	0.227431i
$665$	−41.8380	+	0.153209i	−1.62241	+	0.00594119i
$666$	−0.936888	+	1.03662i	−0.0363037	+	0.0401681i
$667$			1.37219i			0.0531313i
$668$	−8.87488	+	0.899267i	−0.343380	+	0.0347937i
$669$	1.76796			0.0683534
$670$	6.74906	+	26.8466i	0.260739	+	1.03717i
$671$		−	1.21400i		−	0.0468658i
$672$	36.8412	+	21.7317i	1.42118	+	0.838319i
$673$	4.63946			0.178838			0.0894190	−	0.995994i	$-0.471499\pi$
$673$	4.63946			0.178838			0.0894190	+	0.995994i	$0.471499\pi$
$674$	4.12007	−	4.55864i	0.158699	−	0.175592i
$675$	−23.5847	+	9.73866i	−0.907776	+	0.374841i
$676$	2.44724	+	24.1518i	0.0941244	+	0.928915i
$677$	−3.39362			−0.130427			−0.0652137	−	0.997871i	$-0.520773\pi$
$677$	−3.39362			−0.130427			−0.0652137	+	0.997871i	$0.520773\pi$
$678$	22.2966	+	20.1515i	0.856296	+	0.773915i
$679$	−41.8150			−1.60471
$680$	35.4856	−	12.8437i	1.36081	−	0.492532i
$681$	−11.9442			−0.457704
$682$	0.420097	+	0.379680i	0.0160863	+	0.0145387i
$683$		−	9.59176i		−	0.367018i	−0.983018	−	0.183509i	$-0.941254\pi$
$683$		−	9.59176i		−	0.367018i	0.983018	−	0.183509i	$-0.0587457\pi$
$684$	0.573959	+	0.689443i	0.0219459	+	0.0263615i
$685$	−4.39130	+	6.56421i	−0.167783	+	0.250806i
$686$	−18.0144	+	19.9320i	−0.687792	+	0.761006i
$687$		−	32.6343i		−	1.24508i
$688$	−37.0480	+	7.58582i	−1.41244	+	0.289207i
$689$	2.95891			0.112725
$690$	−0.478936	−	1.90513i	−0.0182328	−	0.0725269i
$691$			21.3675i			0.812856i	0.913683	+	0.406428i	$0.133226\pi$
$691$			21.3675i			0.812856i	−0.913683	+	0.406428i	$0.866774\pi$
$692$	−4.24458	−	41.8898i	−0.161355	−	1.59241i
$693$		−	0.166366i		−	0.00631974i
$694$	−22.5380	+	24.9372i	−0.855532	+	0.946602i
$695$	−8.96426	+	13.4000i	−0.340034	+	0.508290i
$696$	15.6197	+	11.4827i	0.592065	+	0.435252i
$697$	−40.7024			−1.54171
$698$	−14.2174	+	15.7308i	−0.538138	+	0.595421i
$699$	17.8139			0.673785
$700$	37.8221	−	20.2993i	1.42954	−	0.767242i
$701$	17.7323			0.669739			0.334869	−	0.942265i	$-0.391308\pi$
$701$	17.7323			0.669739			0.334869	+	0.942265i	$0.391308\pi$
$702$	−4.97192	−	4.49358i	−0.187653	−	0.169599i
$703$	−34.7001	+	23.3979i	−1.30874	+	0.882470i
$704$	−2.87591	+	0.898921i	−0.108390	+	0.0338794i
$705$	5.61015	−	8.38618i	0.211291	−	0.315842i
$706$	−3.43721	−	3.10653i	−0.129361	−	0.116916i
$707$	−55.0904			−2.07189
$708$	−13.9710	+	1.41564i	−0.525063	+	0.0532032i
$709$	1.60751			0.0603715			0.0301857	−	0.999544i	$-0.490390\pi$
$709$	1.60751			0.0603715			0.0301857	+	0.999544i	$0.490390\pi$
$710$	31.0260	−	7.79974i	1.16439	−	0.292719i
$711$	−1.49176			−0.0559453
$712$	17.5766	−	23.9091i	0.658710	−	0.896030i
$713$	0.374897			0.0140400
$714$	42.7834	−	47.3376i	1.60113	−	1.77156i
$715$	0.434840	−	0.650009i	0.0162621	−	0.0243089i
$716$	3.95154	+	38.9978i	0.147676	+	1.45742i
$717$	32.1804			1.20180
$718$	−1.92857	−	1.74303i	−0.0719735	−	0.0650492i
$719$			37.3717i			1.39373i	0.717203	+	0.696864i	$0.245422\pi$
$719$			37.3717i			1.39373i	−0.717203	+	0.696864i	$0.754578\pi$
$720$	−0.852101	−	0.347907i	−0.0317559	−	0.0129657i
$721$		−	9.14329i		−	0.340514i
$722$	11.7266	+	24.1761i	0.436421	+	0.899743i
$723$	−23.0794			−0.858334
$724$	−35.0492	+	3.55144i	−1.30259	+	0.131988i
$725$	17.9825	−	7.42537i	0.667853	−	0.275771i
$726$	−20.0676	−	18.1370i	−0.744779	−	0.673127i
$727$	−10.1249			−0.375514			−0.187757	−	0.982216i	$-0.560122\pi$
$727$	−10.1249			−0.375514			−0.187757	+	0.982216i	$0.560122\pi$
$728$	9.08355	+	6.67770i	0.336659	+	0.247492i
$729$	−26.0114			−0.963386
$730$	−3.92977	−	15.6320i	−0.145447	−	0.578565i
$731$			56.4126i			2.08650i
$732$	−11.2976	+	1.14475i	−0.417571	+	0.0423113i
$733$		−	26.6032i		−	0.982613i	−0.870987	−	0.491307i	$-0.836519\pi$
$733$		−	26.6032i		−	0.982613i	0.870987	−	0.491307i	$-0.163481\pi$
$734$	9.31986	−	10.3119i	0.344002	−	0.380621i
$735$	25.0235	−	37.4057i	0.923007	−	1.37973i
$736$	−1.01355	+	1.71824i	−0.0373599	+	0.0633353i
$737$	−3.29704			−0.121448
$738$	0.736460	+	0.665608i	0.0271095	+	0.0245014i
$739$		−	15.5478i		−	0.571934i	−0.958239	−	0.285967i	$-0.907685\pi$
$739$		−	15.5478i		−	0.571934i	0.958239	−	0.285967i	$-0.0923147\pi$
$740$	20.1557	−	37.9143i	0.740940	−	1.39376i
$741$	3.98608	+	5.91152i	0.146432	+	0.217165i
$742$	−12.9703	+	14.3509i	−0.476153	+	0.526839i
$743$			37.6670i			1.38187i	0.722918	+	0.690934i	$0.242801\pi$
$743$			37.6670i			1.38187i	−0.722918	+	0.690934i	$0.757199\pi$
$744$	3.13721	−	4.26749i	0.115016	−	0.156454i
$745$	−7.27733	−	4.86836i	−0.266621	−	0.178363i
$746$	7.93925	−	8.78436i	0.290677	−	0.321618i
$747$	0.359969			0.0131706
$748$	0.453126	+	4.47191i	0.0165679	+	0.163509i
$749$		−	70.4756i		−	2.57512i
$750$	−22.3750	+	16.5857i	−0.817018	+	0.605626i
$751$	−4.74210			−0.173042			−0.0865208	−	0.996250i	$-0.527575\pi$
$751$	−4.74210			−0.173042			−0.0865208	+	0.996250i	$0.527575\pi$
$752$	−10.0381	+	2.05536i	−0.366051	+	0.0749514i
$753$	−22.6579			−0.825698
$754$	3.79091	+	3.42620i	0.138057	+	0.124775i
$755$	13.4337	+	8.98684i	0.488903	+	0.327065i
$756$	43.5884	−	4.41669i	1.58529	−	0.160634i
$757$		−	15.0862i		−	0.548316i	−0.961685	−	0.274158i	$-0.911601\pi$
$757$		−	15.0862i		−	0.548316i	0.961685	−	0.274158i	$-0.0883992\pi$
$758$	−30.9494	+	34.2439i	−1.12413	+	1.24379i
$759$	0.233969			0.00849254
$760$	−22.2715	−	16.2474i	−0.807873	−	0.589357i
$761$	−24.9280			−0.903638			−0.451819	−	0.892110i	$-0.649225\pi$
$761$	−24.9280			−0.903638			−0.451819	+	0.892110i	$0.649225\pi$
$762$	−6.98525	+	7.72882i	−0.253049	+	0.279986i
$763$		−	74.6621i		−	2.70295i
$764$	46.6102	−	4.72288i	1.68630	−	0.170868i
$765$	−0.763417	+	1.14117i	−0.0276014	+	0.0412592i
$766$	−6.40289	−	5.78689i	−0.231346	−	0.209089i
$767$	−3.70128			−0.133646
$768$	11.0773	+	25.9159i	0.399719	+	0.935161i
$769$	27.1950			0.980678			0.490339	−	0.871532i	$-0.336873\pi$
$769$	27.1950			0.980678			0.490339	+	0.871532i	$0.336873\pi$
$770$	1.24648	+	4.95829i	0.0449201	+	0.178685i
$771$			47.8284i			1.72250i
$772$	3.83982	+	37.8952i	0.138198	+	1.36388i
$773$	−11.1297			−0.400308			−0.200154	−	0.979764i	$-0.564144\pi$
$773$	−11.1297			−0.400308			−0.200154	+	0.979764i	$0.564144\pi$
$774$	0.922518	−	1.02072i	0.0331592	−	0.0366889i
$775$	−2.02870	−	4.91302i	−0.0728730	−	0.176481i
$776$	−22.1995	−	16.3198i	−0.796916	−	0.585847i
$777$		−	72.5992i		−	2.60448i
$778$	−3.46936	+	3.83866i	−0.124382	+	0.137623i
$779$	16.6230	+	24.6525i	0.595579	+	0.883269i
$780$	−6.45909	−	3.43374i	−0.231273	−	0.122948i
$781$			3.81032i			0.136344i
$782$	2.20779	+	1.99538i	0.0789502	+	0.0713547i
$783$	19.8570			0.709631
$784$	−44.7738	+	9.16775i	−1.59907	+	0.327420i
$785$	29.5865	−	44.2265i	1.05599	−	1.57851i
$786$	−1.62837	+	1.80170i	−0.0580819	+	0.0642646i
$787$		−	13.2771i		−	0.473278i	−0.971598	−	0.236639i	$-0.923954\pi$
$787$		−	13.2771i		−	0.473278i	0.971598	−	0.236639i	$-0.0760459\pi$
$788$	−38.9211	+	3.94377i	−1.38651	+	0.140491i
$789$		−	32.8428i		−	1.16923i
$790$	44.4595	−	11.1768i	1.58180	−	0.397654i
$791$	−51.7858			−1.84129
$792$	0.0649305	−	0.0883237i	0.00230721	−	0.00313845i
$793$	−2.99303			−0.106285
$794$	−31.6480	−	28.6033i	−1.12315	−	1.01509i
$795$	6.97875	−	10.4320i	0.247511	−	0.369984i
$796$	−41.2676	+	4.18153i	−1.46269	+	0.148210i
$797$	−19.5604			−0.692866			−0.346433	−	0.938075i	$-0.612607\pi$
$797$	−19.5604			−0.692866			−0.346433	+	0.938075i	$0.612607\pi$
$798$	−46.1441	−	6.58016i	−1.63348	−	0.232935i
$799$			15.2849i			0.540740i
$800$	28.0022	+	3.98454i	0.990027	+	0.140875i
$801$			1.07961i			0.0381460i
$802$	36.3500	+	32.8529i	1.28356	+	1.16008i
$803$	1.91976			0.0677470
$804$	3.10899	+	30.6826i	0.109645	+	1.08209i
$805$	2.81339	+	1.88209i	0.0991590	+	0.0663350i
$806$	0.936076	−	1.03572i	0.0329719	−	0.0364816i
$807$	−7.94835			−0.279795
$808$	−29.2474	−	21.5010i	−1.02892	−	0.756403i
$809$	6.76217			0.237745			0.118873	−	0.992910i	$-0.462072\pi$
$809$	6.76217			0.237745			0.118873	+	0.992910i	$0.462072\pi$
$810$	−28.5160	+	7.16872i	−1.00195	+	0.251883i
$811$	6.17322			0.216771			0.108385	−	0.994109i	$-0.465432\pi$
$811$	6.17322			0.216771			0.108385	+	0.994109i	$0.465432\pi$
$812$	−33.2346	+	3.36757i	−1.16631	+	0.118178i
$813$	−22.6690			−0.795035
$814$	3.79419	+	3.42917i	0.132986	+	0.120192i
$815$	28.8332	+	19.2887i	1.00998	+	0.675654i
$816$	41.1888	−	8.43369i	1.44190	−	0.295238i
$817$	34.1679	−	23.0390i	1.19538	−	0.806034i
$818$	−32.0285	−	28.9472i	−1.11985	−	1.01211i
$819$	−0.410165			−0.0143323
$820$	−26.9360	−	14.3196i	−0.940647	−	0.500061i
$821$	50.4086			1.75927			0.879636	−	0.475647i	$-0.157786\pi$
$821$	50.4086			1.75927			0.879636	+	0.475647i	$0.157786\pi$
$822$	−5.89958	+	6.52757i	−0.205771	+	0.227675i
$823$	−42.0362			−1.46529			−0.732644	−	0.680612i	$-0.761714\pi$
$823$	−42.0362			−1.46529			−0.732644	+	0.680612i	$0.761714\pi$
$824$	3.56850	−	4.85416i	0.124315	−	0.169103i
$825$	−1.26609	−	3.06616i	−0.0440795	−	0.106750i
$826$	16.2244	−	17.9515i	0.564520	−	0.624612i
$827$		−	36.2488i		−	1.26050i	−0.776394	−	0.630248i	$-0.782953\pi$
$827$		−	36.2488i		−	1.26050i	0.776394	−	0.630248i	$-0.217047\pi$
$828$	−0.00731663	−	0.0722080i	−0.000254271	−	0.00250940i
$829$			30.0656i			1.04422i	0.852878	+	0.522110i	$0.174855\pi$
$829$			30.0656i			1.04422i	−0.852878	+	0.522110i	$0.825145\pi$
$830$	−10.7283	+	2.69703i	−0.372385	+	0.0936152i
$831$	−7.67885			−0.266376
$832$	2.21623	+	7.09036i	0.0768339	+	0.245814i
$833$			68.1767i			2.36218i
$834$	−12.0432	+	13.3252i	−0.417022	+	0.461413i
$835$	−5.54540	+	8.28938i	−0.191906	+	0.286866i
$836$	2.52348	−	2.10079i	0.0872763	−	0.0726572i
$837$		−	5.42516i		−	0.187521i
$838$	6.78585	+	6.13300i	0.234413	+	0.211861i
$839$	20.6881			0.714231			0.357116	−	0.934060i	$-0.383760\pi$
$839$	20.6881			0.714231			0.357116	+	0.934060i	$0.383760\pi$
$840$	44.9671	−	16.2754i	1.55151	−	0.561554i
$841$	13.8598			0.477923
$842$	22.2470	+	20.1067i	0.766682	+	0.692922i
$843$	12.7210			0.438136
$844$	0.0151181	+	0.149201i	0.000520387	+	0.00513570i
$845$	22.5584	+	15.0911i	0.776034	+	0.519148i
$846$	0.249954	−	0.276561i	0.00859360	−	0.00950837i
$847$	46.6087			1.60150
$848$	−12.4869	+	2.55677i	−0.428800	+	0.0877998i
$849$		−	7.31080i		−	0.250906i
$850$	14.2024	−	39.7307i	0.487137	−	1.36275i
$851$	3.38597			0.116069
$852$	35.4593	−	3.59299i	1.21481	−	0.123094i
$853$		−	10.3551i		−	0.354553i	−0.984161	−	0.177276i	$-0.943271\pi$
$853$		−	10.3551i		−	0.354553i	0.984161	−	0.177276i	$-0.0567286\pi$
$854$	13.1198	−	14.5164i	0.448951	−	0.496741i
$855$	1.00296	−	0.00367281i	0.0343006	−	0.000125608i
$856$	27.5056	−	37.4154i	0.940123	−	1.27883i
$857$	−8.93791			−0.305313			−0.152657	−	0.988279i	$-0.548783\pi$
$857$	−8.93791			−0.305313			−0.152657	+	0.988279i	$0.548783\pi$
$858$	0.584194	−	0.646380i	0.0199441	−	0.0220671i
$859$		−	18.8257i		−	0.642325i	−0.947024	−	0.321162i	$-0.895927\pi$
$859$		−	18.8257i		−	0.642325i	0.947024	−	0.321162i	$-0.104073\pi$
$860$	−19.8466	+	37.3328i	−0.676763	+	1.27304i
$861$	−51.5778			−1.75777
$862$	−7.33754	+	8.11861i	−0.249918	+	0.276521i
$863$		−	14.2058i		−	0.483573i	−0.970330	−	0.241786i	$-0.922267\pi$
$863$		−	14.2058i		−	0.483573i	0.970330	−	0.241786i	$-0.0777333\pi$
$864$	24.8648	+	14.6671i	0.845917	+	0.498986i
$865$	−39.1262	−	26.1745i	−1.33033	−	0.889961i
$866$	22.6003	−	25.0061i	0.767990	−	0.849741i
$867$		−	32.7723i		−	1.11300i
$868$	0.920058	+	9.08007i	0.0312288	+	0.308198i
$869$			5.46009i			0.185221i
$870$	21.0205	−	5.28442i	0.712662	−	0.179158i
$871$			8.12862i			0.275428i
$872$	29.1396	−	39.6380i	0.986791	−	1.34231i
$873$	1.00241			0.0339265
$874$	0.306893	−	2.15212i	0.0103808	−	0.0727967i
$875$	9.44056	−	47.0541i	0.319149	−	1.59072i
$876$	−1.81027	−	17.8656i	−0.0611633	−	0.603621i
$877$	52.5843			1.77565			0.887824	−	0.460184i	$-0.152217\pi$
$877$	52.5843			1.77565			0.887824	+	0.460184i	$0.152217\pi$
$878$	−9.87831	+	10.9298i	−0.333377	+	0.368864i
$879$			8.50527i			0.286876i
$880$	−1.27340	+	3.11883i	−0.0429262	+	0.105136i
$881$	7.17014			0.241568			0.120784	−	0.992679i	$-0.461459\pi$
$881$	7.17014			0.241568			0.120784	+	0.992679i	$0.461459\pi$
$882$	1.11490	−	1.23357i	0.0375405	−	0.0415366i
$883$	−23.0586			−0.775985			−0.387992	−	0.921663i	$-0.626831\pi$
$883$	−23.0586			−0.775985			−0.387992	+	0.921663i	$0.626831\pi$
$884$	11.0252	−	1.11715i	0.370817	−	0.0375739i
$885$	−8.72968	+	13.0493i	−0.293445	+	0.438648i
$886$	4.77569	−	5.28406i	0.160443	−	0.177521i
$887$			34.1642i			1.14712i	0.819163	+	0.573560i	$0.194438\pi$
$887$			34.1642i			1.14712i	−0.819163	+	0.573560i	$0.805562\pi$
$888$	28.3344	−	38.5428i	0.950842	−	1.29341i
$889$		−	17.9508i		−	0.602052i
$890$	−8.08883	−	32.1760i	−0.271138	−	1.07854i
$891$		−	3.50205i		−	0.117323i
$892$	−1.99711	+	0.202361i	−0.0668680	+	0.00677555i
$893$	9.25771	−	6.24238i	0.309798	−	0.208893i
$894$	−7.23671	−	6.54049i	−0.242032	−	0.218747i
$895$	36.4250	+	24.3675i	1.21755	+	0.814515i
$896$	−44.1035	−	20.3315i	−1.47340	−	0.679227i
$897$		−	0.576834i		−	0.0192599i
$898$	28.7225	+	25.9592i	0.958482	+	0.866269i
$899$			4.13649i			0.137960i
$900$	−0.906691	+	0.486626i	−0.0302230	+	0.0162209i
$901$			19.0136i			0.633436i
$902$	2.43624	−	2.69557i	0.0811178	−	0.0897526i
$903$			71.4856i			2.37889i
$904$	−27.4930	−	20.2113i	−0.914403	−	0.672216i
$905$	−21.9002	+	32.7369i	−0.727988	+	1.08821i
$906$	13.3587	+	12.0735i	0.443814	+	0.401116i
$907$			40.1696i			1.33381i	0.745142	+	0.666906i	$0.232382\pi$
$907$			40.1696i			1.33381i	−0.745142	+	0.666906i	$0.767618\pi$
$908$	13.4923	−	1.36714i	0.447757	−	0.0453700i
$909$	1.32066			0.0438035
$910$	12.2243	−	3.07311i	0.405232	−	0.101873i
$911$	−53.5926			−1.77560			−0.887802	−	0.460226i	$-0.847768\pi$
$911$	−53.5926			−1.77560			−0.887802	+	0.460226i	$0.847768\pi$
$912$	−21.9297	−	21.5028i	−0.726165	−	0.712029i
$913$		−	1.31755i		−	0.0436045i
$914$	9.29936	+	8.40470i	0.307596	+	0.278003i
$915$	−7.05921	+	10.5523i	−0.233370	+	0.348847i
$916$	3.73533	+	36.8640i	0.123419	+	1.21802i
$917$		−	4.18460i		−	0.138188i
$918$	28.8753	−	31.9490i	0.953026	−	1.05447i
$919$		−	36.0060i		−	1.18773i	−0.804566	−	0.593864i	$-0.797602\pi$
$919$		−	36.0060i		−	1.18773i	0.804566	−	0.593864i	$-0.202398\pi$
$920$	0.759071	+	2.09723i	0.0250258	+	0.0691435i
$921$	0.860384			0.0283506
$922$	6.36740	−	7.04519i	0.209699	−	0.232021i
$923$	9.39407			0.309210
$924$	0.574198	+	5.66677i	0.0188897	+	0.186423i
$925$	−18.3226	−	44.3730i	−0.602444	−	1.45898i
$926$	−7.05314	+	7.80393i	−0.231781	+	0.256453i
$927$			0.219188i			0.00719908i
$928$	−18.9585	−	11.1832i	−0.622343	−	0.367105i
$929$	13.0488			0.428118			0.214059	−	0.976821i	$-0.431331\pi$
$929$	13.0488			0.428118			0.214059	+	0.976821i	$0.431331\pi$
$930$	−1.44376	−	5.74304i	−0.0473428	−	0.188322i
$931$	41.2931	−	27.8435i	1.35333	−	0.912535i
$932$	−20.1228	+	2.03899i	−0.659143	+	0.0667892i
$933$	4.56481			0.149445
$934$	29.4358	−	32.5692i	0.963170	−	1.06570i
$935$	4.17688	+	2.79424i	0.136599	+	0.0913813i
$936$	−0.217756	−	0.160082i	−0.00711757	−	0.00523243i
$937$			22.0684i			0.720943i	0.932770	+	0.360471i	$0.117384\pi$
$937$			22.0684i			0.720943i	−0.932770	+	0.360471i	$0.882616\pi$
$938$	−39.4244	−	35.6315i	−1.28725	−	1.16341i
$939$	16.6574			0.543593
$940$	−5.37739	+	10.1152i	−0.175391	+	0.329923i
$941$			32.6150i			1.06322i	0.846990	+	0.531609i	$0.178413\pi$
$941$			32.6150i			1.06322i	−0.846990	+	0.531609i	$0.821587\pi$
$942$	39.7485	−	43.9796i	1.29508	−	1.43293i
$943$		−	2.40554i		−	0.0783353i
$944$	15.6197	−	3.19825i	0.508379	−	0.104094i
$945$	27.2359	−	40.7128i	0.885983	−	1.32439i
$946$	−3.73600	−	3.37657i	−0.121468	−	0.109782i
$947$	51.3144			1.66749			0.833747	−	0.552147i	$-0.186191\pi$
$947$	51.3144			1.66749			0.833747	+	0.552147i	$0.186191\pi$
$948$	50.8122	−	5.14866i	1.65030	−	0.167221i
$949$		−	4.73305i		−	0.153641i
$950$	−29.8643	+	7.62406i	−0.968924	+	0.247357i
$951$		−	41.8407i		−	1.35678i
$952$	−42.9102	+	58.3699i	−1.39073	+	1.89178i
$953$	−34.2291			−1.10879			−0.554394	−	0.832254i	$-0.687050\pi$
$953$	−34.2291			−1.10879			−0.554394	+	0.832254i	$0.687050\pi$
$954$	0.310930	−	0.344028i	0.0100667	−	0.0111383i
$955$	29.1240	−	43.5352i	0.942431	−	1.40877i
$956$	−36.3513	+	3.68338i	−1.17568	+	0.119129i
$957$			2.58153i			0.0834492i
$958$	22.0464	+	19.9254i	0.712286	+	0.643760i
$959$		−	15.1608i		−	0.489569i
$960$	30.2250	+	8.90944i	0.975508	+	0.287551i
$961$	−29.8699			−0.963544
$962$	8.45437	−	9.35432i	0.272580	−	0.301595i
$963$			1.68948i			0.0544427i
$964$	26.0707	−	2.64167i	0.839681	−	0.0850826i
$965$	35.3952	+	23.6785i	1.13941	+	0.762239i
$966$	2.79769	+	2.52853i	0.0900141	+	0.0813542i
$967$	−41.3727			−1.33046			−0.665229	−	0.746640i	$-0.731666\pi$
$967$	−41.3727			−1.33046			−0.665229	+	0.746640i	$0.731666\pi$
$968$	24.7445	+	18.1907i	0.795319	+	0.584673i
$969$	−37.9868	+	25.6141i	−1.22031	+	0.822844i
$970$	−29.8753	+	7.51046i	−0.959239	+	0.241146i
$971$	30.6284			0.982914			0.491457	−	0.870902i	$-0.336465\pi$
$971$	30.6284			0.982914			0.491457	+	0.870902i	$0.336465\pi$
$972$	−2.12697	+	0.215520i	−0.0682225	+	0.00691279i
$973$		−	30.9488i		−	0.992174i
$974$	25.1287	+	22.7111i	0.805174	+	0.727711i
$975$	−7.55941	+	3.12145i	−0.242095	+	0.0999664i
$976$	12.6308	−	2.58625i	0.404303	−	0.0827838i
$977$	31.8746			1.01976			0.509879	−	0.860246i	$-0.329690\pi$
$977$	31.8746			1.01976			0.509879	+	0.860246i	$0.329690\pi$
$978$	28.6722	+	25.9138i	0.916836	+	0.828631i
$979$	3.95154			0.126292
$980$	−23.9853	+	45.1180i	−0.766183	+	1.44124i
$981$			1.78984i			0.0571453i
$982$	33.5681	+	30.3386i	1.07120	+	0.968143i
$983$		−	11.0853i		−	0.353566i	−0.984250	−	0.176783i	$-0.943431\pi$
$983$		−	11.0853i		−	0.353566i	0.984250	−	0.176783i	$-0.0565690\pi$
$984$	−27.3826	−	20.1301i	−0.872924	−	0.641723i
$985$	−24.3195	+	36.3534i	−0.774885	+	1.15831i
$986$	−22.0164	+	24.3600i	−0.701144	+	0.775779i
$987$			19.3689i			0.616518i
$988$	−5.17934	−	6.22146i	−0.164777	−	0.197931i
$989$	−3.33403			−0.106016
$990$	−0.0298814	−	0.118863i	−0.000949692	−	0.00377771i
$991$	−17.2353			−0.547497			−0.273749	−	0.961801i	$-0.588264\pi$
$991$	−17.2353			−0.547497			−0.273749	+	0.961801i	$0.588264\pi$
$992$	−3.05537	+	5.17968i	−0.0970080	+	0.164455i
$993$			31.2473i			0.991602i
$994$	−41.1785	+	45.5619i	−1.30610	+	1.44514i
$995$	−25.7857	+	38.5451i	−0.817463	+	1.22196i
$996$	−12.2612	+	1.24240i	−0.388513	+	0.0393669i
$997$		−	11.4664i		−	0.363145i	−0.983378	−	0.181572i	$-0.941881\pi$
$997$		−	11.4664i		−	0.363145i	0.983378	−	0.181572i	$-0.0581187\pi$
$998$	−31.2377	−	28.2324i	−0.988812	−	0.893682i
$999$		−	48.9985i		−	1.55024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.d.b.379.11	yes	40
4.3	odd	2	inner	380.2.d.b.379.9	✓	40
5.4	even	2	inner	380.2.d.b.379.30	yes	40
19.18	odd	2	inner	380.2.d.b.379.29	yes	40
20.19	odd	2	inner	380.2.d.b.379.32	yes	40
76.75	even	2	inner	380.2.d.b.379.31	yes	40
95.94	odd	2	inner	380.2.d.b.379.12	yes	40
380.379	even	2	inner	380.2.d.b.379.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.9	✓	40	4.3	odd	2	inner
380.2.d.b.379.10	yes	40	380.379	even	2	inner
380.2.d.b.379.11	yes	40	1.1	even	1	trivial
380.2.d.b.379.12	yes	40	95.94	odd	2	inner
380.2.d.b.379.29	yes	40	19.18	odd	2	inner
380.2.d.b.379.30	yes	40	5.4	even	2	inner
380.2.d.b.379.31	yes	40	76.75	even	2	inner
380.2.d.b.379.32	yes	40	20.19	odd	2	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.948256 + 1.04920i) q^{2} +1.76151i q^{3} +(-0.201622 - 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 - 1.67036i) q^{6} +4.29252 q^{7} +(2.27889 + 1.67531i) q^{8} -0.102903 q^{9} +O(q^{10})\)	\(q+(-0.948256 + 1.04920i) q^{2} +1.76151i q^{3} +(-0.201622 - 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 - 1.67036i) q^{6} +4.29252 q^{7} +(2.27889 + 1.67531i) q^{8} -0.102903 q^{9} +(3.06685 - 0.770986i) q^{10} +0.376641i q^{11} +(3.50506 - 0.355158i) q^{12} +0.928582 q^{13} +(-4.07040 + 4.50369i) q^{14} +(2.19011 - 3.27382i) q^{15} +(-3.91870 + 0.802380i) q^{16} +5.96697i q^{17} +(0.0975780 - 0.107965i) q^{18} +(3.61406 - 2.43692i) q^{19} +(-2.09924 + 3.94882i) q^{20} +7.56129i q^{21} +(-0.395170 - 0.357152i) q^{22} -0.352652 q^{23} +(-2.95107 + 4.01428i) q^{24} +(1.90832 + 4.62150i) q^{25} +(-0.880533 + 0.974264i) q^{26} +5.10325i q^{27} +(-0.865466 - 8.54130i) q^{28} -3.89105i q^{29} +(1.35810 + 5.40228i) q^{30} -1.06308 q^{31} +(2.87407 - 4.87234i) q^{32} -0.663455 q^{33} +(-6.26051 - 5.65821i) q^{34} +(-7.97780 - 5.33696i) q^{35} +(0.0207474 + 0.204757i) q^{36} -9.60143 q^{37} +(-0.870242 + 6.10268i) q^{38} +1.63570i q^{39} +(-2.15246 - 5.94701i) q^{40} +6.82129i q^{41} +(-7.93327 - 7.17004i) q^{42} +9.45416 q^{43} +(0.749444 - 0.0759391i) q^{44} +(0.191248 + 0.127941i) q^{45} +(0.334405 - 0.370001i) q^{46} +2.56158 q^{47} +(-1.41340 - 6.90281i) q^{48} +11.4257 q^{49} +(-6.65844 - 2.38016i) q^{50} -10.5108 q^{51} +(-0.187223 - 1.84770i) q^{52} +3.18648 q^{53} +(-5.35431 - 4.83919i) q^{54} +(0.468284 - 0.700001i) q^{55} +(9.78217 + 7.19129i) q^{56} +(4.29265 + 6.36618i) q^{57} +(4.08247 + 3.68971i) q^{58} -3.98595 q^{59} +(-6.95587 - 3.69783i) q^{60} -3.22322 q^{61} +(1.00807 - 1.11538i) q^{62} -0.441711 q^{63} +(2.38668 + 7.63569i) q^{64} +(-1.72580 - 1.15452i) q^{65} +(0.629125 - 0.696094i) q^{66} +8.75380i q^{67} +(11.8731 - 1.20307i) q^{68} -0.621199i q^{69} +(13.1645 - 3.30947i) q^{70} +10.1166 q^{71} +(-0.234504 - 0.172394i) q^{72} -5.09707i q^{73} +(9.10461 - 10.0738i) q^{74} +(-8.14081 + 3.36152i) q^{75} +(-5.57769 - 6.69995i) q^{76} +1.61674i q^{77} +(-1.71617 - 1.55106i) q^{78} +14.4968 q^{79} +(8.28066 + 3.38093i) q^{80} -9.29812 q^{81} +(-7.15687 - 6.46833i) q^{82} -3.49815 q^{83} +(15.0455 - 1.52452i) q^{84} +(7.41883 - 11.0898i) q^{85} +(-8.96496 + 9.91926i) q^{86} +6.85410 q^{87} +(-0.630990 + 0.858323i) q^{88} -10.4915i q^{89} +(-0.315587 + 0.0793365i) q^{90} +3.98595 q^{91} +(0.0711025 + 0.701712i) q^{92} -1.87262i q^{93} +(-2.42904 + 2.68760i) q^{94} +(-9.74673 + 0.0356921i) q^{95} +(8.58266 + 5.06270i) q^{96} -9.74137 q^{97} +(-10.8345 + 11.9878i) q^{98} -0.0387573i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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