LMFDB - Embedded newform 360.2.x.a.53.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(53,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("360.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.x (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.13
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.159967 - 1.40514i) q^{2} +(-1.94882 - 0.449551i) q^{4} +(0.215413 + 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-0.943427 + 2.66645i) q^{8} +O(q^{10})$	\(q+(0.159967 - 1.40514i) q^{2} +(-1.94882 - 0.449551i) q^{4} +(0.215413 + 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-0.943427 + 2.66645i) q^{8} +(3.16183 + 0.0533477i) q^{10} +5.57646 q^{11} +(1.79226 - 1.79226i) q^{13} +(2.88958 + 3.63203i) q^{14} +(3.59581 + 1.75219i) q^{16} +(5.56203 + 5.56203i) q^{17} -2.61960 q^{19} +(0.580749 - 4.43427i) q^{20} +(0.892049 - 7.83569i) q^{22} +(-4.44948 + 4.44948i) q^{23} +(-4.90719 + 0.958877i) q^{25} +(-2.23167 - 2.80507i) q^{26} +(5.56573 - 3.47925i) q^{28} -2.12491i q^{29} -4.52171 q^{31} +(3.03728 - 4.77231i) q^{32} +(8.70516 - 6.92568i) q^{34} +(-5.66484 - 4.66506i) q^{35} +(5.02845 + 5.02845i) q^{37} +(-0.419049 + 3.68090i) q^{38} +(-6.13785 - 1.52537i) q^{40} -1.73215i q^{41} +(1.19790 - 1.19790i) q^{43} +(-10.8675 - 2.50690i) q^{44} +(5.54036 + 6.96390i) q^{46} +(-0.849681 - 0.849681i) q^{47} -3.77064i q^{49} +(0.562366 + 7.04867i) q^{50} +(-4.29850 + 2.68708i) q^{52} +(4.22906 + 4.22906i) q^{53} +(1.20124 + 12.4113i) q^{55} +(-3.99849 - 8.37718i) q^{56} +(-2.98580 - 0.339916i) q^{58} -8.08999i q^{59} -3.13786i q^{61} +(-0.723323 + 6.35362i) q^{62} +(-6.21989 - 5.03120i) q^{64} +(4.37505 + 3.60290i) q^{65} +(-1.86836 - 1.86836i) q^{67} +(-8.33899 - 13.3398i) q^{68} +(-7.46123 + 7.21363i) q^{70} -6.95452i q^{71} +(-5.86607 - 5.86607i) q^{73} +(7.87005 - 6.26128i) q^{74} +(5.10513 + 1.17764i) q^{76} +(-12.9409 + 12.9409i) q^{77} -2.52204i q^{79} +(-3.12520 + 8.38052i) q^{80} +(-2.43390 - 0.277086i) q^{82} +(0.694298 + 0.694298i) q^{83} +(-11.1811 + 13.5774i) q^{85} +(-1.49159 - 1.87484i) q^{86} +(-5.26099 + 14.8693i) q^{88} +12.1475 q^{89} +8.31834i q^{91} +(10.6715 - 6.67097i) q^{92} +(-1.32984 + 1.05800i) q^{94} +(-0.564297 - 5.83036i) q^{95} +(4.09526 - 4.09526i) q^{97} +(-5.29827 - 0.603178i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) $ 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.159967	−	1.40514i	0.113114	−	0.993582i
$2$	0.159967	−	1.40514i	0.113114	−	0.993582i
$3$		0			0
$3$		0			0
$4$	−1.94882	−	0.449551i	−0.974411	−	0.224775i
$5$	0.215413	+	2.22567i	0.0963358	+	0.995349i
$5$	0.215413	+	2.22567i	0.0963358	+	0.995349i
$6$		0			0
$7$	−2.32063	+	2.32063i	−0.877115	+	0.877115i	−0.993235	−	0.116120i	$-0.962954\pi$
$7$	−2.32063	+	2.32063i	−0.877115	+	0.877115i	0.116120	+	0.993235i	$0.462954\pi$
$8$	−0.943427	+	2.66645i	−0.333552	+	0.942732i
$9$		0			0
$10$	3.16183	+	0.0533477i	0.999858	+	0.0168700i
$11$	5.57646			1.68137			0.840683	−	0.541528i	$-0.182154\pi$
$11$	5.57646			1.68137			0.840683	+	0.541528i	$0.182154\pi$
$12$		0			0
$13$	1.79226	−	1.79226i	0.497083	−	0.497083i	−0.413446	−	0.910529i	$-0.635675\pi$
$13$	1.79226	−	1.79226i	0.497083	−	0.497083i	0.910529	+	0.413446i	$0.135675\pi$
$14$	2.88958	+	3.63203i	0.772272	+	0.970700i
$15$		0			0
$16$	3.59581	+	1.75219i	0.898952	+	0.438047i
$17$	5.56203	+	5.56203i	1.34899	+	1.34899i	0.886758	+	0.462233i	$0.152952\pi$
$17$	5.56203	+	5.56203i	1.34899	+	1.34899i	0.462233	+	0.886758i	$0.347048\pi$
$18$		0			0
$19$	−2.61960			−0.600978			−0.300489	−	0.953785i	$-0.597150\pi$
$19$	−2.61960			−0.600978			−0.300489	+	0.953785i	$0.597150\pi$
$20$	0.580749	−	4.43427i	0.129859	−	0.991532i
$21$		0			0
$22$	0.892049	−	7.83569i	0.190185	−	1.67058i
$23$	−4.44948	+	4.44948i	−0.927781	+	0.927781i	−0.997562	−	0.0697816i	$-0.977770\pi$
$23$	−4.44948	+	4.44948i	−0.927781	+	0.927781i	0.0697816	+	0.997562i	$0.477770\pi$
$24$		0			0
$25$	−4.90719	+	0.958877i	−0.981439	+	0.191775i
$26$	−2.23167	−	2.80507i	−0.437666	−	0.550120i
$27$		0			0
$28$	5.56573	−	3.47925i	1.05182	−	0.657517i
$29$		−	2.12491i		−	0.394587i	−0.980345	−	0.197293i	$-0.936785\pi$
$29$		−	2.12491i		−	0.394587i	0.980345	−	0.197293i	$-0.0632151\pi$
$30$		0			0
$31$	−4.52171			−0.812123			−0.406061	−	0.913846i	$-0.633098\pi$
$31$	−4.52171			−0.812123			−0.406061	+	0.913846i	$0.633098\pi$
$32$	3.03728	−	4.77231i	0.536919	−	0.843634i
$33$		0			0
$34$	8.70516	−	6.92568i	1.49292	−	1.18774i
$35$	−5.66484	−	4.66506i	−0.957534	−	0.788538i
$36$		0			0
$37$	5.02845	+	5.02845i	0.826673	+	0.826673i	0.987055	−	0.160382i	$-0.0512727\pi$
$37$	5.02845	+	5.02845i	0.826673	+	0.826673i	−0.160382	+	0.987055i	$0.551273\pi$
$38$	−0.419049	+	3.68090i	−0.0679788	+	0.597121i
$39$		0			0
$40$	−6.13785	−	1.52537i	−0.970480	−	0.241182i
$41$		−	1.73215i		−	0.270516i	−0.990810	−	0.135258i	$-0.956814\pi$
$41$		−	1.73215i		−	0.270516i	0.990810	−	0.135258i	$-0.0431863\pi$
$42$		0			0
$43$	1.19790	−	1.19790i	0.182678	−	0.182678i	−0.609844	−	0.792522i	$-0.708768\pi$
$43$	1.19790	−	1.19790i	0.182678	−	0.182678i	0.792522	+	0.609844i	$0.208768\pi$
$44$	−10.8675	−	2.50690i	−1.63834	−	0.377930i
$45$		0			0
$46$	5.54036	+	6.96390i	0.816882	+	1.02677i
$47$	−0.849681	−	0.849681i	−0.123939	−	0.123939i	0.642417	−	0.766355i	$-0.277932\pi$
$47$	−0.849681	−	0.849681i	−0.123939	−	0.123939i	−0.766355	+	0.642417i	$0.777932\pi$
$48$		0			0
$49$		−	3.77064i		−	0.538663i
$50$	0.562366	+	7.04867i	0.0795305	+	0.996832i
$51$		0			0
$52$	−4.29850	+	2.68708i	−0.596095	+	0.372631i
$53$	4.22906	+	4.22906i	0.580906	+	0.580906i	0.935152	−	0.354246i	$-0.115263\pi$
$53$	4.22906	+	4.22906i	0.580906	+	0.580906i	−0.354246	+	0.935152i	$0.615263\pi$
$54$		0			0
$55$	1.20124	+	12.4113i	0.161976	+	1.67355i
$56$	−3.99849	−	8.37718i	−0.534321	−	1.11945i
$57$		0			0
$58$	−2.98580	−	0.339916i	−0.392054	−	0.0446331i
$59$		−	8.08999i		−	1.05323i	−0.850105	−	0.526614i	$-0.823461\pi$
$59$		−	8.08999i		−	1.05323i	0.850105	−	0.526614i	$-0.176539\pi$
$60$		0			0
$61$		−	3.13786i		−	0.401762i	−0.979616	−	0.200881i	$-0.935620\pi$
$61$		−	3.13786i		−	0.401762i	0.979616	−	0.200881i	$-0.0643805\pi$
$62$	−0.723323	+	6.35362i	−0.0918622	+	0.806910i
$63$		0			0
$64$	−6.21989	−	5.03120i	−0.777486	−	0.628900i
$65$	4.37505	+	3.60290i	0.542658	+	0.446884i
$66$		0			0
$67$	−1.86836	−	1.86836i	−0.228256	−	0.228256i	0.583708	−	0.811964i	$-0.301601\pi$
$67$	−1.86836	−	1.86836i	−0.228256	−	0.228256i	−0.811964	+	0.583708i	$0.801601\pi$
$68$	−8.33899	−	13.3398i	−1.01125	−	1.61769i
$69$		0			0
$70$	−7.46123	+	7.21363i	−0.891788	+	0.862194i
$71$		−	6.95452i		−	0.825350i	−0.910878	−	0.412675i	$-0.864595\pi$
$71$		−	6.95452i		−	0.825350i	0.910878	−	0.412675i	$-0.135405\pi$
$72$		0			0
$73$	−5.86607	−	5.86607i	−0.686572	−	0.686572i	0.274901	−	0.961473i	$-0.411355\pi$
$73$	−5.86607	−	5.86607i	−0.686572	−	0.686572i	−0.961473	+	0.274901i	$0.911355\pi$
$74$	7.87005	−	6.26128i	0.914875	−	0.727859i
$75$		0			0
$76$	5.10513	+	1.17764i	0.585599	+	0.135085i
$77$	−12.9409	+	12.9409i	−1.47475	+	1.47475i
$78$		0			0
$79$		−	2.52204i		−	0.283752i	−0.989884	−	0.141876i	$-0.954687\pi$
$79$		−	2.52204i		−	0.283752i	0.989884	−	0.141876i	$-0.0453134\pi$
$80$	−3.12520	+	8.38052i	−0.349408	+	0.936971i
$81$		0			0
$82$	−2.43390	−	0.277086i	−0.268780	−	0.0305990i
$83$	0.694298	+	0.694298i	0.0762091	+	0.0762091i	0.744184	−	0.667975i	$-0.232839\pi$
$83$	0.694298	+	0.694298i	0.0762091	+	0.0762091i	−0.667975	+	0.744184i	$0.732839\pi$
$84$		0			0
$85$	−11.1811	+	13.5774i	−1.21276	+	1.47267i
$86$	−1.49159	−	1.87484i	−0.160842	−	0.202169i
$87$		0			0
$88$	−5.26099	+	14.8693i	−0.560823	+	1.58508i
$89$	12.1475			1.28763			0.643816	−	0.765180i	$-0.277350\pi$
$89$	12.1475			1.28763			0.643816	+	0.765180i	$0.277350\pi$
$90$		0			0
$91$			8.31834i			0.871999i
$92$	10.6715	−	6.67097i	1.11258	−	0.695497i
$93$		0			0
$94$	−1.32984	+	1.05800i	−0.137162	+	0.109124i
$95$	−0.564297	−	5.83036i	−0.0578957	−	0.598183i
$96$		0			0
$97$	4.09526	−	4.09526i	0.415811	−	0.415811i	−0.467946	−	0.883757i	$-0.655006\pi$
$97$	4.09526	−	4.09526i	0.415811	−	0.415811i	0.883757	+	0.467946i	$0.155006\pi$
$98$	−5.29827	−	0.603178i	−0.535206	−	0.0609301i
$99$		0			0
$100$	9.99431	+	0.337353i	0.999431	+	0.0337353i
$101$	0.617937			0.0614871			0.0307435	−	0.999527i	$-0.490212\pi$
$101$	0.617937			0.0614871			0.0307435	+	0.999527i	$0.490212\pi$
$102$		0			0
$103$	−2.59696	−	2.59696i	−0.255886	−	0.255886i	0.567493	−	0.823379i	$-0.307914\pi$
$103$	−2.59696	−	2.59696i	−0.255886	−	0.255886i	−0.823379	+	0.567493i	$0.807914\pi$
$104$	3.08810	+	6.46983i	0.302813	+	0.634419i
$105$		0			0
$106$	6.61892	−	5.26590i	0.642886	−	0.511469i
$107$	−1.74306	+	1.74306i	−0.168508	+	0.168508i	−0.786323	−	0.617815i	$-0.788018\pi$
$107$	−1.74306	+	1.74306i	−0.168508	+	0.168508i	0.617815	+	0.786323i	$0.288018\pi$
$108$		0			0
$109$	15.1487			1.45098			0.725491	−	0.688231i	$-0.241613\pi$
$109$	15.1487			1.45098			0.725491	+	0.688231i	$0.241613\pi$
$110$	17.6318	+	0.297491i	1.68113	+	0.0283647i
$111$		0			0
$112$	−12.4107	+	4.27836i	−1.17270	+	0.404267i
$113$	−2.41591	+	2.41591i	−0.227270	+	0.227270i	−0.811551	−	0.584281i	$-0.801376\pi$
$113$	−2.41591	+	2.41591i	−0.227270	+	0.227270i	0.584281	+	0.811551i	$0.301376\pi$
$114$		0			0
$115$	−10.8615	−	8.94459i	−1.01284	−	0.834087i
$116$	−0.955257	+	4.14108i	−0.0886934	+	0.384489i
$117$		0			0
$118$	−11.3675	−	1.29413i	−1.04647	−	0.119134i
$119$	−25.8148			−2.36644
$120$		0			0
$121$	20.0969			1.82699
$122$	−4.40913	−	0.501954i	−0.399184	−	0.0454448i
$123$		0			0
$124$	8.81200	+	2.03274i	0.791341	+	0.182545i
$125$	−3.19122	−	10.7152i	−0.285431	−	0.958399i
$126$		0			0
$127$	−1.40304	+	1.40304i	−0.124500	+	0.124500i	−0.766611	−	0.642112i	$-0.778059\pi$
$127$	−1.40304	+	1.40304i	−0.124500	+	0.124500i	0.642112	+	0.766611i	$0.278059\pi$
$128$	−8.06450	+	7.93497i	−0.712808	+	0.701359i
$129$		0			0
$130$	5.76243	−	5.57120i	0.505398	−	0.488627i
$131$	7.14182			0.623984			0.311992	−	0.950085i	$-0.399004\pi$
$131$	7.14182			0.623984			0.311992	+	0.950085i	$0.399004\pi$
$132$		0			0
$133$	6.07912	−	6.07912i	0.527127	−	0.527127i
$134$	−2.92417	+	2.32642i	−0.252610	+	0.200972i
$135$		0			0
$136$	−20.0783	+	9.58350i	−1.72170	+	0.821778i
$137$	−6.58546	−	6.58546i	−0.562634	−	0.562634i	0.367421	−	0.930055i	$-0.380241\pi$
$137$	−6.58546	−	6.58546i	−0.562634	−	0.562634i	−0.930055	+	0.367421i	$0.880241\pi$
$138$		0			0
$139$	−15.1568			−1.28558			−0.642791	−	0.766042i	$-0.722224\pi$
$139$	−15.1568			−1.28558			−0.642791	+	0.766042i	$0.722224\pi$
$140$	8.94259	+	11.6380i	0.755787	+	0.983590i
$141$		0			0
$142$	−9.77206	−	1.11249i	−0.820053	−	0.0933583i
$143$	9.99446	−	9.99446i	0.835779	−	0.835779i
$144$		0			0
$145$	4.72935	−	0.457735i	0.392751	−	0.0380128i
$146$	−9.18101	+	7.30426i	−0.759826	+	0.604505i
$147$		0			0
$148$	−7.53901	−	12.0601i	−0.619703	−	0.991334i
$149$		−	5.51376i		−	0.451705i	−0.974162	−	0.225852i	$-0.927483\pi$
$149$		−	5.51376i		−	0.451705i	0.974162	−	0.225852i	$-0.0725167\pi$
$150$		0			0
$151$	14.7042			1.19661			0.598307	−	0.801267i	$-0.295840\pi$
$151$	14.7042			1.19661			0.598307	+	0.801267i	$0.295840\pi$
$152$	2.47140	−	6.98503i	0.200457	−	0.566561i
$153$		0			0
$154$	16.1136	+	20.2539i	1.29847	+	1.63210i
$155$	−0.974036	−	10.0638i	−0.0782365	−	0.808345i
$156$		0			0
$157$	−11.3534	−	11.3534i	−0.906103	−	0.906103i	0.0898521	−	0.995955i	$-0.471361\pi$
$157$	−11.3534	−	11.3534i	−0.906103	−	0.906103i	−0.995955	+	0.0898521i	$0.971361\pi$
$158$	−3.54381	−	0.403443i	−0.281931	−	0.0320962i
$159$		0			0
$160$	11.2759	+	5.73195i	0.891434	+	0.453150i
$161$		−	20.6512i		−	1.62754i
$162$		0			0
$163$	11.7245	−	11.7245i	0.918331	−	0.918331i	−0.0785768	−	0.996908i	$-0.525038\pi$
$163$	11.7245	−	11.7245i	0.918331	−	0.918331i	0.996908	+	0.0785768i	$0.0250376\pi$
$164$	−0.778688	+	3.37564i	−0.0608053	+	0.263594i
$165$		0			0
$166$	1.08665	−	0.864519i	0.0843402	−	0.0670997i
$167$	7.91997	+	7.91997i	0.612865	+	0.612865i	0.943692	−	0.330826i	$-0.107327\pi$
$167$	7.91997	+	7.91997i	0.612865	+	0.612865i	−0.330826	+	0.943692i	$0.607327\pi$
$168$		0			0
$169$			6.57562i			0.505817i
$170$	17.2895	+	17.8829i	1.32604	+	1.37156i
$171$		0			0
$172$	−2.87301	+	1.79598i	−0.219065	+	0.136942i
$173$	7.22597	+	7.22597i	0.549380	+	0.549380i	0.926262	−	0.376881i	$-0.123004\pi$
$173$	7.22597	+	7.22597i	0.549380	+	0.549380i	−0.376881	+	0.926262i	$0.623004\pi$
$174$		0			0
$175$	9.16258	−	13.6130i	0.692626	−	1.02904i
$176$	20.0519	+	9.77101i	1.51147	+	0.736517i
$177$		0			0
$178$	1.94320	−	17.0689i	0.145649	−	1.27937i
$179$			13.7942i			1.03103i	0.856880	+	0.515515i	$0.172399\pi$
$179$			13.7942i			1.03103i	−0.856880	+	0.515515i	$0.827601\pi$
$180$		0			0
$181$		−	18.3310i		−	1.36254i	−0.732034	−	0.681268i	$-0.761429\pi$
$181$		−	18.3310i		−	1.36254i	0.732034	−	0.681268i	$-0.238571\pi$
$182$	11.6884	+	1.33066i	0.866402	+	0.0986349i
$183$		0			0
$184$	−7.66655	−	16.0621i	−0.565185	−	1.18411i
$185$	−10.1085	+	12.2749i	−0.743190	+	0.902466i
$186$		0			0
$187$	31.0165	+	31.0165i	2.26815	+	2.26815i
$188$	1.27390	+	2.03785i	0.0929088	+	0.148626i
$189$		0			0
$190$	−8.28273	−	0.139750i	−0.600892	−	0.0101385i
$191$			12.2206i			0.884251i	0.896953	+	0.442125i	$0.145775\pi$
$191$			12.2206i			0.884251i	−0.896953	+	0.442125i	$0.854225\pi$
$192$		0			0
$193$	−1.67882	−	1.67882i	−0.120844	−	0.120844i	0.644099	−	0.764943i	$-0.277233\pi$
$193$	−1.67882	−	1.67882i	−0.120844	−	0.120844i	−0.764943	+	0.644099i	$0.777233\pi$
$194$	−5.09930	−	6.40951i	−0.366108	−	0.460176i
$195$		0			0
$196$	−1.69509	+	7.34831i	−0.121078	+	0.524879i
$197$	−4.43727	+	4.43727i	−0.316143	+	0.316143i	−0.847283	−	0.531141i	$-0.821763\pi$
$197$	−4.43727	+	4.43727i	−0.316143	+	0.316143i	0.531141	+	0.847283i	$0.321763\pi$
$198$		0			0
$199$		−	16.2067i		−	1.14886i	−0.818553	−	0.574432i	$-0.805223\pi$
$199$		−	16.2067i		−	1.14886i	0.818553	−	0.574432i	$-0.194777\pi$
$200$	2.07278	−	13.9894i	0.146568	−	0.989201i
$201$		0			0
$202$	0.0988495	−	0.868287i	0.00695503	−	0.0610924i
$203$	4.93114	+	4.93114i	0.346098	+	0.346098i
$204$		0			0
$205$	3.85518	−	0.373128i	0.269258	−	0.0260604i
$206$	−4.06451	+	3.23366i	−0.283188	+	0.225300i
$207$		0			0
$208$	9.58499	−	3.30424i	0.664600	−	0.229108i
$209$	−14.6081			−1.01046
$210$		0			0
$211$		−	22.6302i		−	1.55793i	−0.627068	−	0.778964i	$-0.715745\pi$
$211$		−	22.6302i		−	1.55793i	0.627068	−	0.778964i	$-0.284255\pi$
$212$	−6.34050	−	10.1429i	−0.435467	−	0.696614i
$213$		0			0
$214$	2.17041	+	2.72807i	0.148366	+	0.186487i
$215$	2.92417	+	2.40808i	0.199427	+	0.164230i
$216$		0			0
$217$	10.4932	−	10.4932i	0.712325	−	0.712325i
$218$	2.42329	−	21.2860i	0.164126	−	1.44167i
$219$		0			0
$220$	3.23852	−	24.7275i	0.218341	−	1.66713i
$221$	19.9372			1.34112
$222$		0			0
$223$	10.8423	+	10.8423i	0.726057	+	0.726057i	0.969832	−	0.243775i	$-0.0783859\pi$
$223$	10.8423	+	10.8423i	0.726057	+	0.726057i	−0.243775	+	0.969832i	$0.578386\pi$
$224$	4.02638	+	18.1232i	0.269024	+	1.21090i
$225$		0			0
$226$	3.00822	+	3.78115i	0.200104	+	0.251518i
$227$	−12.6177	+	12.6177i	−0.837465	+	0.837465i	−0.988525	−	0.151059i	$-0.951732\pi$
$227$	−12.6177	+	12.6177i	−0.837465	+	0.837465i	0.151059	+	0.988525i	$0.451732\pi$
$228$		0			0
$229$	−0.594060			−0.0392566			−0.0196283	−	0.999807i	$-0.506248\pi$
$229$	−0.594060			−0.0392566			−0.0196283	+	0.999807i	$0.506248\pi$
$230$	−14.3059	+	13.8311i	−0.943300	+	0.911997i
$231$		0			0
$232$	5.66597	+	2.00470i	0.371989	+	0.131615i
$233$	5.12779	−	5.12779i	0.335933	−	0.335933i	−0.518901	−	0.854834i	$-0.673659\pi$
$233$	5.12779	−	5.12779i	0.335933	−	0.335933i	0.854834	+	0.518901i	$0.173659\pi$
$234$		0			0
$235$	1.70807	−	2.07414i	0.111423	−	0.135302i
$236$	−3.63686	+	15.7659i	−0.236740	+	1.02628i
$237$		0			0
$238$	−4.12952	+	36.2734i	−0.267677	+	2.35126i
$239$	11.1582			0.721763			0.360881	−	0.932612i	$-0.382476\pi$
$239$	11.1582			0.721763			0.360881	+	0.932612i	$0.382476\pi$
$240$		0			0
$241$	−19.9706			−1.28642			−0.643209	−	0.765691i	$-0.722397\pi$
$241$	−19.9706			−1.28642			−0.643209	+	0.765691i	$0.722397\pi$
$242$	3.21484	−	28.2389i	0.206658	−	1.81527i
$243$		0			0
$244$	−1.41063	+	6.11513i	−0.0903062	+	0.391481i
$245$	8.39219	−	0.812247i	0.536158	−	0.0518925i
$246$		0			0
$247$	−4.69500	+	4.69500i	−0.298736	+	0.298736i
$248$	4.26590	−	12.0569i	0.270885	−	0.765614i
$249$		0			0
$250$	−15.5669	+	2.77002i	−0.984534	+	0.175191i
$251$	20.4134			1.28848			0.644240	−	0.764823i	$-0.277174\pi$
$251$	20.4134			1.28848			0.644240	+	0.764823i	$0.277174\pi$
$252$		0			0
$253$	−24.8123	+	24.8123i	−1.55994	+	1.55994i
$254$	1.74703	+	2.19591i	0.109618	+	0.137783i
$255$		0			0
$256$	9.85967	+	12.6011i	0.616230	+	0.787567i
$257$	−13.9742	−	13.9742i	−0.871688	−	0.871688i	0.120968	−	0.992656i	$-0.461400\pi$
$257$	−13.9742	−	13.9742i	−0.871688	−	0.871688i	−0.992656	+	0.120968i	$0.961400\pi$
$258$		0			0
$259$	−23.3384			−1.45017
$260$	−6.90650	−	8.98821i	−0.428323	−	0.557425i
$261$		0			0
$262$	1.14246	−	10.0352i	0.0705811	−	0.619979i
$263$	10.4243	−	10.4243i	0.642788	−	0.642788i	−0.308452	−	0.951240i	$-0.599811\pi$
$263$	10.4243	−	10.4243i	0.642788	−	0.642788i	0.951240	+	0.308452i	$0.0998109\pi$
$264$		0			0
$265$	−8.50148	+	10.3235i	−0.522242	+	0.634166i
$266$	−7.56954	−	9.51446i	−0.464119	−	0.583369i
$267$		0			0
$268$	2.80117	+	4.48101i	0.171109	+	0.273721i
$269$		−	29.5007i		−	1.79869i	−0.437241	−	0.899345i	$-0.644044\pi$
$269$		−	29.5007i		−	1.79869i	0.437241	−	0.899345i	$-0.355956\pi$
$270$		0			0
$271$	−19.3447			−1.17511			−0.587554	−	0.809185i	$-0.699909\pi$
$271$	−19.3447			−1.17511			−0.587554	+	0.809185i	$0.699909\pi$
$272$	10.2543	+	29.7457i	0.621757	+	1.80360i
$273$		0			0
$274$	−10.3069	+	8.20002i	−0.622664	+	0.495381i
$275$	−27.3648	+	5.34714i	−1.65016	+	0.322445i
$276$		0			0
$277$	1.44346	+	1.44346i	0.0867293	+	0.0867293i	0.749140	−	0.662411i	$-0.230467\pi$
$277$	1.44346	+	1.44346i	0.0867293	+	0.0867293i	−0.662411	+	0.749140i	$0.730467\pi$
$278$	−2.42458	+	21.2974i	−0.145417	+	1.27733i
$279$		0			0
$280$	17.7835	−	10.7039i	1.06277	−	0.639679i
$281$			23.9276i			1.42740i	0.700450	+	0.713702i	$0.252983\pi$
$281$			23.9276i			1.42740i	−0.700450	+	0.713702i	$0.747017\pi$
$282$		0			0
$283$	7.90740	−	7.90740i	0.470046	−	0.470046i	−0.431883	−	0.901930i	$-0.642151\pi$
$283$	7.90740	−	7.90740i	0.470046	−	0.470046i	0.901930	+	0.431883i	$0.142151\pi$
$284$	−3.12641	+	13.5531i	−0.185518	+	0.804229i
$285$		0			0
$286$	−12.4448	−	15.6424i	−0.735877	−	0.924953i
$287$	4.01967	+	4.01967i	0.237274	+	0.237274i
$288$		0			0
$289$			44.8725i			2.63956i
$290$	0.113359	−	6.71861i	0.00665669	−	0.394530i
$291$		0			0
$292$	8.79483	+	14.0690i	0.514678	+	0.823327i
$293$	−5.38544	−	5.38544i	−0.314621	−	0.314621i	0.532076	−	0.846697i	$-0.321412\pi$
$293$	−5.38544	−	5.38544i	−0.314621	−	0.314621i	−0.846697	+	0.532076i	$0.821412\pi$
$294$		0			0
$295$	18.0056	−	1.74269i	1.04833	−	0.101463i
$296$	−18.1521	+	8.66413i	−1.05507	+	0.503592i
$297$		0			0
$298$	−7.74758	−	0.882018i	−0.448806	−	0.0510940i
$299$			15.9492i			0.922368i
$300$		0			0
$301$			5.55977i			0.320460i
$302$	2.35219	−	20.6615i	0.135353	−	1.18893i
$303$		0			0
$304$	−9.41958	−	4.59003i	−0.540250	−	0.263257i
$305$	6.98384	−	0.675938i	0.399893	−	0.0387041i
$306$		0			0
$307$	0.116076	+	0.116076i	0.00662479	+	0.00662479i	0.710411	−	0.703787i	$-0.248509\pi$
$307$	0.116076	+	0.116076i	0.00662479	+	0.00662479i	−0.703787	+	0.710411i	$0.748509\pi$
$308$	31.0371	−	19.4019i	1.76850	−	1.10553i
$309$		0			0
$310$	−14.2969	−	0.241223i	−0.812007	−	0.0137005i
$311$		−	1.42835i		−	0.0809944i	−0.999180	−	0.0404972i	$-0.987106\pi$
$311$		−	1.42835i		−	0.0809944i	0.999180	−	0.0404972i	$-0.0128942\pi$
$312$		0			0
$313$	−6.59396	−	6.59396i	−0.372712	−	0.372712i	0.495752	−	0.868464i	$-0.334893\pi$
$313$	−6.59396	−	6.59396i	−0.372712	−	0.372712i	−0.868464	+	0.495752i	$0.834893\pi$
$314$	−17.7693	+	14.1370i	−1.00278	+	0.797795i
$315$		0			0
$316$	−1.13379	+	4.91500i	−0.0637804	+	0.276491i
$317$	−11.2572	+	11.2572i	−0.632269	+	0.632269i	−0.948637	−	0.316367i	$-0.897537\pi$
$317$	−11.2572	+	11.2572i	−0.632269	+	0.632269i	0.316367	+	0.948637i	$0.397537\pi$
$318$		0			0
$319$		−	11.8495i		−	0.663444i
$320$	9.85793	−	14.9272i	0.551075	−	0.834456i
$321$		0			0
$322$	−29.0178	−	3.30351i	−1.61710	−	0.184097i
$323$	−14.5703	−	14.5703i	−0.810714	−	0.810714i
$324$		0			0
$325$	−7.07640	+	10.5135i	−0.392528	+	0.583185i
$326$	−14.5990	−	18.3500i	−0.808562	−	1.01631i
$327$		0			0
$328$	4.61868	+	1.63415i	0.255024	+	0.0902311i
$329$	3.94359			0.217417
$330$		0			0
$331$			35.0445i			1.92622i	0.269113	+	0.963109i	$0.413270\pi$
$331$			35.0445i			1.92622i	−0.269113	+	0.963109i	$0.586730\pi$
$332$	−1.04094	−	1.66518i	−0.0571290	−	0.0913888i
$333$		0			0
$334$	12.3956	−	9.86171i	0.678256	−	0.539609i
$335$	3.75587	−	4.56081i	0.205205	−	0.249184i
$336$		0			0
$337$	1.94865	−	1.94865i	0.106150	−	0.106150i	−0.652037	−	0.758187i	$-0.726085\pi$
$337$	1.94865	−	1.94865i	0.106150	−	0.106150i	0.758187	+	0.652037i	$0.226085\pi$
$338$	9.23965	+	1.05188i	0.502570	+	0.0572148i
$339$		0			0
$340$	27.8937	−	21.4334i	1.51275	−	1.16239i
$341$	−25.2151			−1.36548
$342$		0			0
$343$	−7.49415	−	7.49415i	−0.404646	−	0.404646i
$344$	2.06401	+	4.32427i	0.111284	+	0.233149i
$345$		0			0
$346$	11.3094	−	8.99756i	0.607997	−	0.483712i
$347$	18.0347	−	18.0347i	0.968151	−	0.968151i	−0.0313569	−	0.999508i	$-0.509983\pi$
$347$	18.0347	−	18.0347i	0.968151	−	0.968151i	0.999508	+	0.0313569i	$0.00998286\pi$
$348$		0			0
$349$	1.54696			0.0828069			0.0414035	−	0.999143i	$-0.486817\pi$
$349$	1.54696			0.0828069			0.0414035	+	0.999143i	$0.486817\pi$
$350$	−17.6624	−	15.0523i	−0.944095	−	0.804580i
$351$		0			0
$352$	16.9372	−	26.6126i	0.902758	−	1.41846i
$353$	−13.4669	+	13.4669i	−0.716770	+	0.716770i	−0.967942	−	0.251172i	$-0.919184\pi$
$353$	−13.4669	+	13.4669i	−0.716770	+	0.716770i	0.251172	+	0.967942i	$0.419184\pi$
$354$		0			0
$355$	15.4785	−	1.49810i	0.821511	−	0.0795107i
$356$	−23.6733	−	5.46092i	−1.25468	−	0.289428i
$357$		0			0
$358$	19.3828	+	2.20662i	1.02441	+	0.116624i
$359$	32.2230			1.70067			0.850334	−	0.526244i	$-0.176400\pi$
$359$	32.2230			1.70067			0.850334	+	0.526244i	$0.176400\pi$
$360$		0			0
$361$	−12.1377			−0.638826
$362$	−25.7576	−	2.93236i	−1.35379	−	0.154121i
$363$		0			0
$364$	3.73951	−	16.2109i	0.196004	−	0.849685i
$365$	11.7923	−	14.3196i	0.617237	−	0.749520i
$366$		0			0
$367$	−7.07186	+	7.07186i	−0.369148	+	0.369148i	−0.867167	−	0.498018i	$-0.834061\pi$
$367$	−7.07186	+	7.07186i	−0.369148	+	0.369148i	0.498018	+	0.867167i	$0.334061\pi$
$368$	−23.7958	+	8.20315i	−1.24044	+	0.427619i
$369$		0			0
$370$	15.6308	+	16.1674i	0.812609	+	0.840501i
$371$	−19.6282			−1.01904
$372$		0			0
$373$	5.32291	−	5.32291i	0.275610	−	0.275610i	−0.555744	−	0.831354i	$-0.687566\pi$
$373$	5.32291	−	5.32291i	0.275610	−	0.275610i	0.831354	+	0.555744i	$0.187566\pi$
$374$	48.5440	−	38.6208i	2.51015	−	1.99703i
$375$		0			0
$376$	3.06724	−	1.46402i	0.158181	−	0.0755010i
$377$	−3.80839	−	3.80839i	−0.196142	−	0.196142i
$378$		0			0
$379$	19.7611			1.01506			0.507529	−	0.861635i	$-0.330559\pi$
$379$	19.7611			1.01506			0.507529	+	0.861635i	$0.330559\pi$
$380$	−1.52133	+	11.6160i	−0.0780426	+	0.595889i
$381$		0			0
$382$	17.1716	+	1.95489i	0.878575	+	0.100021i
$383$	−13.2191	+	13.2191i	−0.675466	+	0.675466i	−0.958971	−	0.283505i	$-0.908503\pi$
$383$	−13.2191	+	13.2191i	−0.675466	+	0.675466i	0.283505	+	0.958971i	$0.408503\pi$
$384$		0			0
$385$	−31.5898	−	26.0145i	−1.60996	−	1.32582i
$386$	−2.62753	+	2.09041i	−0.133738	+	0.106399i
$387$		0			0
$388$	−9.82197	+	6.13991i	−0.498635	+	0.311707i
$389$		−	27.1107i		−	1.37457i	−0.726389	−	0.687284i	$-0.758803\pi$
$389$		−	27.1107i		−	1.37457i	0.726389	−	0.687284i	$-0.241197\pi$
$390$		0			0
$391$	−49.4963			−2.50314
$392$	10.0542	+	3.55733i	0.507815	+	0.179672i
$393$		0			0
$394$	5.52516	+	6.94479i	0.278354	+	0.349874i
$395$	5.61322	−	0.543281i	0.282432	−	0.0273354i
$396$		0			0
$397$	−8.68567	−	8.68567i	−0.435921	−	0.435921i	0.454715	−	0.890637i	$-0.349741\pi$
$397$	−8.68567	−	8.68567i	−0.435921	−	0.435921i	−0.890637	+	0.454715i	$0.849741\pi$
$398$	−22.7727	−	2.59254i	−1.14149	−	0.129952i
$399$		0			0
$400$	−19.3255	−	5.15039i	−0.966273	−	0.257519i
$401$		−	3.09967i		−	0.154790i	−0.997000	−	0.0773951i	$-0.975340\pi$
$401$		−	3.09967i		−	0.154790i	0.997000	−	0.0773951i	$-0.0246603\pi$
$402$		0			0
$403$	−8.10407	+	8.10407i	−0.403692	+	0.403692i
$404$	−1.20425	−	0.277794i	−0.0599136	−	0.0138208i
$405$		0			0
$406$	7.71774	−	6.14011i	0.383025	−	0.304728i
$407$	28.0410	+	28.0410i	1.38994	+	1.38994i
$408$		0			0
$409$			14.1083i			0.697610i	0.937195	+	0.348805i	$0.113412\pi$
$409$			14.1083i			0.697610i	−0.937195	+	0.348805i	$0.886588\pi$
$410$	0.0924061	−	5.47675i	0.00456361	−	0.270477i
$411$		0			0
$412$	3.89354	+	6.22847i	0.191821	+	0.306855i
$413$	18.7739	+	18.7739i	0.923802	+	0.923802i
$414$		0			0
$415$	−1.39571	+	1.69484i	−0.0685129	+	0.0831963i
$416$	−3.10963	−	13.9968i	−0.152462	−	0.686250i
$417$		0			0
$418$	−2.33681	+	20.5264i	−0.114297	+	1.00398i
$419$			30.4747i			1.48878i	0.667743	+	0.744392i	$0.267261\pi$
$419$			30.4747i			1.48878i	−0.667743	+	0.744392i	$0.732739\pi$
$420$		0			0
$421$		−	38.0605i		−	1.85496i	−0.373878	−	0.927478i	$-0.621972\pi$
$421$		−	38.0605i		−	1.85496i	0.373878	−	0.927478i	$-0.378028\pi$
$422$	−31.7986	−	3.62008i	−1.54793	−	0.176223i
$423$		0			0
$424$	−15.2664	+	7.28675i	−0.741401	+	0.353876i
$425$	−32.6273	−	21.9607i	−1.58266	−	1.06525i
$426$		0			0
$427$	7.28181	+	7.28181i	0.352392	+	0.352392i
$428$	4.18051	−	2.61332i	0.202073	−	0.126320i
$429$		0			0
$430$	3.85146	−	3.72365i	0.185734	−	0.179570i
$431$			30.0050i			1.44529i	0.691220	+	0.722644i	$0.257073\pi$
$431$			30.0050i			1.44529i	−0.691220	+	0.722644i	$0.742927\pi$
$432$		0			0
$433$	20.6496	+	20.6496i	0.992355	+	0.992355i	0.999971	−	0.00761624i	$-0.00242435\pi$
$433$	20.6496	+	20.6496i	0.992355	+	0.992355i	−0.00761624	+	0.999971i	$0.502424\pi$
$434$	−13.0658	−	16.4230i	−0.627180	−	0.788327i
$435$		0			0
$436$	−29.5221	−	6.81011i	−1.41385	−	0.326145i
$437$	11.6559	−	11.6559i	0.557576	−	0.557576i
$438$		0			0
$439$		−	0.227040i		−	0.0108360i	−0.999985	−	0.00541802i	$-0.998275\pi$
$439$		−	0.227040i		−	0.0108360i	0.999985	−	0.00541802i	$-0.00172462\pi$
$440$	−34.2275	−	8.50615i	−1.63173	−	0.405515i
$441$		0			0
$442$	3.18929	−	28.0145i	0.151699	−	1.33251i
$443$	16.3406	+	16.3406i	0.776364	+	0.776364i	0.979211	−	0.202846i	$-0.0650192\pi$
$443$	16.3406	+	16.3406i	0.776364	+	0.776364i	−0.202846	+	0.979211i	$0.565019\pi$
$444$		0			0
$445$	2.61673	+	27.0363i	0.124045	+	1.28164i
$446$	16.9694	−	13.5006i	0.803524	−	0.639270i
$447$		0			0
$448$	26.1096	−	2.75851i	1.23356	−	0.130327i
$449$	21.4698			1.01322			0.506611	−	0.862175i	$-0.330898\pi$
$449$	21.4698			1.01322			0.506611	+	0.862175i	$0.330898\pi$
$450$		0			0
$451$		−	9.65925i		−	0.454836i
$452$	5.79425	−	3.62210i	0.272539	−	0.170369i
$453$		0			0
$454$	15.7112	+	19.7480i	0.737362	+	0.926819i
$455$	−18.5139	+	1.79188i	−0.867943	+	0.0840047i
$456$		0			0
$457$	−19.4509	+	19.4509i	−0.909876	+	0.909876i	−0.996262	−	0.0863855i	$-0.972468\pi$
$457$	−19.4509	+	19.4509i	−0.909876	+	0.909876i	0.0863855	+	0.996262i	$0.472468\pi$
$458$	−0.0950299	+	0.834736i	−0.00444046	+	0.0390046i
$459$		0			0
$460$	17.1462	+	22.3142i	0.799444	+	1.04041i
$461$	−19.2557			−0.896828			−0.448414	−	0.893826i	$-0.648011\pi$
$461$	−19.2557			−0.896828			−0.448414	+	0.893826i	$0.648011\pi$
$462$		0			0
$463$	10.6135	+	10.6135i	0.493250	+	0.493250i	0.909329	−	0.416079i	$-0.136596\pi$
$463$	10.6135	+	10.6135i	0.493250	+	0.493250i	−0.416079	+	0.909329i	$0.636596\pi$
$464$	3.72325	−	7.64078i	0.172847	−	0.354714i
$465$		0			0
$466$	−6.38497	−	8.02552i	−0.295778	−	0.371775i
$467$	−1.94796	+	1.94796i	−0.0901407	+	0.0901407i	−0.750739	−	0.660599i	$-0.770303\pi$
$467$	−1.94796	+	1.94796i	−0.0901407	+	0.0901407i	0.660599	+	0.750739i	$0.270303\pi$
$468$		0			0
$469$	8.67152			0.400414
$470$	−2.64122	−	2.73187i	−0.121830	−	0.126012i
$471$		0			0
$472$	21.5715	+	7.63232i	0.992911	+	0.351306i
$473$	6.68004	−	6.68004i	0.307149	−	0.307149i
$474$		0			0
$475$	12.8549	−	2.51188i	0.589823	−	0.115253i
$476$	50.3085	+	11.6051i	2.30589	+	0.531918i
$477$		0			0
$478$	1.78494	−	15.6788i	0.0816412	−	0.717131i
$479$	−19.9363			−0.910911			−0.455456	−	0.890258i	$-0.650524\pi$
$479$	−19.9363			−0.910911			−0.455456	+	0.890258i	$0.650524\pi$
$480$		0			0
$481$	18.0246			0.821850
$482$	−3.19463	+	28.0614i	−0.145511	+	1.27816i
$483$		0			0
$484$	−39.1653	−	9.03458i	−1.78024	−	0.410663i
$485$	9.99687	+	8.23252i	0.453935	+	0.373820i
$486$		0			0
$487$	18.5407	−	18.5407i	0.840161	−	0.840161i	−0.148719	−	0.988880i	$-0.547515\pi$
$487$	18.5407	−	18.5407i	0.840161	−	0.840161i	0.988880	+	0.148719i	$0.0475149\pi$
$488$	8.36695	+	2.96034i	0.378754	+	0.134009i
$489$		0			0
$490$	0.201155	−	11.9221i	0.00908726	−	0.538586i
$491$	−1.08218			−0.0488379			−0.0244189	−	0.999702i	$-0.507774\pi$
$491$	−1.08218			−0.0488379			−0.0244189	+	0.999702i	$0.507774\pi$
$492$		0			0
$493$	11.8188	−	11.8188i	0.532294	−	0.532294i
$494$	5.84608	+	7.34817i	0.263028	+	0.330610i
$495$		0			0
$496$	−16.2592	−	7.92288i	−0.730059	−	0.355748i
$497$	16.1389	+	16.1389i	0.723927	+	0.723927i
$498$		0			0
$499$	−16.6371			−0.744779			−0.372390	−	0.928076i	$-0.621461\pi$
$499$	−16.6371			−0.744779			−0.372390	+	0.928076i	$0.621461\pi$
$500$	1.40207	+	22.3167i	0.0627026	+	0.998032i
$501$		0			0
$502$	3.26546	−	28.6836i	0.145745	−	1.28021i
$503$	23.0316	−	23.0316i	1.02693	−	1.02693i	0.0273024	−	0.999627i	$-0.491308\pi$
$503$	23.0316	−	23.0316i	1.02693	−	1.02693i	0.999627	−	0.0273024i	$-0.00869169\pi$
$504$		0			0
$505$	0.133112	+	1.37532i	0.00592341	+	0.0612011i
$506$	30.8956	+	38.8339i	1.37348	+	1.72638i
$507$		0			0
$508$	3.36501	−	2.10354i	0.149298	−	0.0933294i
$509$			25.0494i			1.11030i	0.831751	+	0.555148i	$0.187338\pi$
$509$			25.0494i			1.11030i	−0.831751	+	0.555148i	$0.812662\pi$
$510$		0			0
$511$	27.2260			1.20441
$512$	19.2834	−	11.8384i	0.852216	−	0.523190i
$513$		0			0
$514$	−21.8711	+	17.4003i	−0.964694	+	0.767494i
$515$	5.22055	−	6.33939i	0.230045	−	0.279347i
$516$		0			0
$517$	−4.73821	−	4.73821i	−0.208386	−	0.208386i
$518$	−3.73336	+	32.7936i	−0.164035	+	1.44087i
$519$		0			0
$520$	−13.7345	+	8.26677i	−0.602297	+	0.362522i
$521$		−	12.1278i		−	0.531327i	−0.964066	−	0.265663i	$-0.914409\pi$
$521$		−	12.1278i		−	0.531327i	0.964066	−	0.265663i	$-0.0855909\pi$
$522$		0			0
$523$	−15.8272	+	15.8272i	−0.692077	+	0.692077i	−0.962689	−	0.270611i	$-0.912774\pi$
$523$	−15.8272	+	15.8272i	−0.692077	+	0.692077i	0.270611	+	0.962689i	$0.412774\pi$
$524$	−13.9181	−	3.21061i	−0.608017	−	0.140256i
$525$		0			0
$526$	−12.9800	−	16.3151i	−0.565954	−	0.711371i
$527$	−25.1499	−	25.1499i	−1.09555	−	1.09555i
$528$		0			0
$529$		−	16.5957i		−	0.721554i
$530$	13.1459	+	13.5972i	0.571023	+	0.590623i
$531$		0			0
$532$	−14.5800	+	9.11425i	−0.632123	+	0.395153i
$533$	−3.10446	−	3.10446i	−0.134469	−	0.134469i
$534$		0			0
$535$	−4.25496	−	3.50400i	−0.183958	−	0.151491i
$536$	6.74453	−	3.21922i	0.291319	−	0.139049i
$537$		0			0
$538$	−41.4525	−	4.71913i	−1.78715	−	0.203456i
$539$		−	21.0268i		−	0.905690i
$540$		0			0
$541$			9.09722i			0.391120i	0.980692	+	0.195560i	$0.0626524\pi$
$541$			9.09722i			0.391120i	−0.980692	+	0.195560i	$0.937348\pi$
$542$	−3.09452	+	27.1820i	−0.132921	+	1.16757i
$543$		0			0
$544$	43.4372	−	9.65033i	1.86235	−	0.413755i
$545$	3.26323	+	33.7160i	0.139782	+	1.44423i
$546$		0			0
$547$	−28.5935	−	28.5935i	−1.22257	−	1.22257i	−0.966715	−	0.255856i	$-0.917643\pi$
$547$	−28.5935	−	28.5935i	−1.22257	−	1.22257i	−0.255856	−	0.966715i	$-0.582357\pi$
$548$	9.87338	+	15.7944i	0.421770	+	0.674703i
$549$		0			0
$550$	3.13601	+	39.3066i	0.133720	+	1.67604i
$551$			5.56643i			0.237138i
$552$		0			0
$553$	5.85272	+	5.85272i	0.248883	+	0.248883i
$554$	2.25917	−	1.79736i	0.0959829	−	0.0763624i
$555$		0			0
$556$	29.5379	+	6.81375i	1.25268	+	0.288967i
$557$	27.5733	−	27.5733i	1.16832	−	1.16832i	0.185716	−	0.982604i	$-0.440540\pi$
$557$	27.5733	−	27.5733i	1.16832	−	1.16832i	0.982604	−	0.185716i	$-0.0594603\pi$
$558$		0			0
$559$		−	4.29389i		−	0.181612i
$560$	−12.1956	−	26.7005i	−0.515360	−	1.12830i
$561$		0			0
$562$	33.6216	+	3.82763i	1.41824	+	0.161459i
$563$	10.6071	+	10.6071i	0.447036	+	0.447036i	0.894368	−	0.447332i	$-0.147626\pi$
$563$	10.6071	+	10.6071i	0.447036	+	0.447036i	−0.447332	+	0.894368i	$0.647626\pi$
$564$		0			0
$565$	−5.89743	−	4.85659i	−0.248107	−	0.204318i
$566$	−9.84606	−	12.3759i	−0.413861	−	0.520198i
$567$		0			0
$568$	18.5439	+	6.56108i	0.778083	+	0.275297i
$569$	13.8127			0.579060			0.289530	−	0.957169i	$-0.406501\pi$
$569$	13.8127			0.579060			0.289530	+	0.957169i	$0.406501\pi$
$570$		0			0
$571$			27.2118i			1.13878i	0.822068	+	0.569390i	$0.192821\pi$
$571$			27.2118i			1.13878i	−0.822068	+	0.569390i	$0.807179\pi$
$572$	−23.9704	+	14.9844i	−1.00225	+	0.626529i
$573$		0			0
$574$	6.29120	−	5.00517i	0.262590	−	0.208912i
$575$	17.5680	−	26.1010i	0.732634	−	1.08849i
$576$		0			0
$577$	23.7851	−	23.7851i	0.990188	−	0.990188i	−0.00976420	−	0.999952i	$-0.503108\pi$
$577$	23.7851	−	23.7851i	0.990188	−	0.990188i	0.999952	+	0.00976420i	$0.00310809\pi$
$578$	63.0520	+	7.17811i	2.62262	+	0.298570i
$579$		0			0
$580$	−9.42244	−	1.23404i	−0.391245	−	0.0512407i
$581$	−3.22241			−0.133688
$582$		0			0
$583$	23.5832	+	23.5832i	0.976715	+	0.976715i
$584$	21.1758	−	10.1074i	0.876260	−	0.418246i
$585$		0			0
$586$	−8.42877	+	6.70579i	−0.348189	+	0.277014i
$587$	20.8981	−	20.8981i	0.862557	−	0.862557i	−0.129077	−	0.991635i	$-0.541202\pi$
$587$	20.8981	−	20.8981i	0.862557	−	0.862557i	0.991635	+	0.129077i	$0.0412016\pi$
$588$		0			0
$589$	11.8451			0.488068
$590$	0.431583	−	25.5792i	0.0177680	−	1.05308i
$591$		0			0
$592$	9.27056	+	26.8922i	0.381018	+	1.10526i
$593$	−15.5965	+	15.5965i	−0.640471	+	0.640471i	−0.950671	−	0.310200i	$-0.899604\pi$
$593$	−15.5965	+	15.5965i	−0.640471	+	0.640471i	0.310200	+	0.950671i	$0.399604\pi$
$594$		0			0
$595$	−5.56086	−	57.4553i	−0.227973	−	2.35544i
$596$	−2.47871	+	10.7453i	−0.101532	+	0.440146i
$597$		0			0
$598$	22.4109	+	2.55135i	0.916448	+	0.104332i
$599$	−17.7577			−0.725558			−0.362779	−	0.931875i	$-0.618172\pi$
$599$	−17.7577			−0.725558			−0.362779	+	0.931875i	$0.618172\pi$
$600$		0			0
$601$	10.1083			0.412325			0.206163	−	0.978518i	$-0.433902\pi$
$601$	10.1083			0.412325			0.206163	+	0.978518i	$0.433902\pi$
$602$	7.81223	+	0.889378i	0.318403	+	0.0362484i
$603$		0			0
$604$	−28.6560	−	6.61031i	−1.16599	−	0.268970i
$605$	4.32914	+	44.7290i	0.176005	+	1.81849i
$606$		0			0
$607$	−15.9642	+	15.9642i	−0.647966	+	0.647966i	−0.952501	−	0.304535i	$-0.901499\pi$
$607$	−15.9642	+	15.9642i	−0.647966	+	0.647966i	0.304535	+	0.952501i	$0.401499\pi$
$608$	−7.95645	+	12.5016i	−0.322677	+	0.507005i
$609$		0			0
$610$	0.167398	−	9.92138i	0.00677774	−	0.401705i
$611$	−3.04570			−0.123216
$612$		0			0
$613$	−16.9357	+	16.9357i	−0.684026	+	0.684026i	−0.960905	−	0.276878i	$-0.910700\pi$
$613$	−16.9357	+	16.9357i	−0.684026	+	0.684026i	0.276878	+	0.960905i	$0.410700\pi$
$614$	0.181671	−	0.144534i	0.00733163	−	0.00583292i
$615$		0			0
$616$	−22.2974	−	46.7150i	−0.898389	−	1.88220i
$617$	−8.84335	−	8.84335i	−0.356020	−	0.356020i	0.506324	−	0.862344i	$-0.331004\pi$
$617$	−8.84335	−	8.84335i	−0.356020	−	0.356020i	−0.862344	+	0.506324i	$0.831004\pi$
$618$		0			0
$619$	−7.27180			−0.292278			−0.146139	−	0.989264i	$-0.546685\pi$
$619$	−7.27180			−0.292278			−0.146139	+	0.989264i	$0.546685\pi$
$620$	−2.62597	+	20.0505i	−0.105462	+	0.805246i
$621$		0			0
$622$	−2.00703	−	0.228489i	−0.0804746	−	0.00916157i
$623$	−28.1898	+	28.1898i	−1.12940	+	1.12940i
$624$		0			0
$625$	23.1611	−	9.41079i	0.926444	−	0.376432i
$626$	−10.3202	+	8.21060i	−0.412479	+	0.328161i
$627$		0			0
$628$	17.0219	+	27.2298i	0.679247	+	1.08659i
$629$			55.9369i			2.23035i
$630$		0			0
$631$	−13.2389			−0.527031			−0.263515	−	0.964655i	$-0.584882\pi$
$631$	−13.2389			−0.527031			−0.263515	+	0.964655i	$0.584882\pi$
$632$	6.72489	+	2.37936i	0.267502	+	0.0946459i
$633$		0			0
$634$	14.0172	+	17.6187i	0.556693	+	0.699730i
$635$	−3.42494	−	2.82047i	−0.135914	−	0.111927i
$636$		0			0
$637$	−6.75796	−	6.75796i	−0.267760	−	0.267760i
$638$	−16.6502	−	1.89553i	−0.659186	−	0.0750446i
$639$		0			0
$640$	−19.3978	−	16.2396i	−0.766766	−	0.641927i
$641$		−	16.7648i		−	0.662171i	−0.943601	−	0.331086i	$-0.892585\pi$
$641$		−	16.7648i		−	0.662171i	0.943601	−	0.331086i	$-0.107415\pi$
$642$		0			0
$643$	35.3834	−	35.3834i	1.39538	−	1.39538i	0.582690	−	0.812695i	$-0.302000\pi$
$643$	35.3834	−	35.3834i	1.39538	−	1.39538i	0.812695	−	0.582690i	$-0.198000\pi$
$644$	−9.28376	+	40.2455i	−0.365831	+	1.58589i
$645$		0			0
$646$	−22.8041	+	18.1425i	−0.897214	+	0.713808i
$647$	−23.0431	−	23.0431i	−0.905919	−	0.905919i	0.0900206	−	0.995940i	$-0.471307\pi$
$647$	−23.0431	−	23.0431i	−0.905919	−	0.905919i	−0.995940	+	0.0900206i	$0.971307\pi$
$648$		0			0
$649$		−	45.1135i		−	1.77086i
$650$	13.6409	+	11.6251i	0.535042	+	0.455975i
$651$		0			0
$652$	−28.1196	+	17.5781i	−1.10125	+	0.688413i
$653$	−31.6390	−	31.6390i	−1.23813	−	1.23813i	−0.960765	−	0.277365i	$-0.910539\pi$
$653$	−31.6390	−	31.6390i	−1.23813	−	1.23813i	−0.277365	−	0.960765i	$-0.589461\pi$
$654$		0			0
$655$	1.53844	+	15.8953i	0.0601120	+	0.621082i
$656$	3.03505	−	6.22847i	0.118499	−	0.243181i
$657$		0			0
$658$	0.630844	−	5.54128i	0.0245928	−	0.216022i
$659$		−	20.2093i		−	0.787242i	−0.919273	−	0.393621i	$-0.871222\pi$
$659$		−	20.2093i		−	0.787242i	0.919273	−	0.393621i	$-0.128778\pi$
$660$		0			0
$661$			44.1882i			1.71872i	0.511369	+	0.859361i	$0.329139\pi$
$661$			44.1882i			1.71872i	−0.511369	+	0.859361i	$0.670861\pi$
$662$	49.2423	+	5.60595i	1.91386	+	0.217882i
$663$		0			0
$664$	−2.50633	+	1.19629i	−0.0972644	+	0.0464250i
$665$	14.8396	+	12.2206i	0.575456	+	0.473894i
$666$		0			0
$667$	9.45476	+	9.45476i	0.366090	+	0.366090i
$668$	−11.8742	−	18.9950i	−0.459426	−	0.734940i
$669$		0			0
$670$	−5.80775	−	6.00709i	−0.224373	−	0.232074i
$671$		−	17.4982i		−	0.675509i
$672$		0			0
$673$	−23.8238	−	23.8238i	−0.918340	−	0.918340i	0.0785687	−	0.996909i	$-0.474965\pi$
$673$	−23.8238	−	23.8238i	−0.918340	−	0.918340i	−0.996909	+	0.0785687i	$0.974965\pi$
$674$	−2.42640	−	3.04984i	−0.0934615	−	0.117475i
$675$		0			0
$676$	2.95607	−	12.8147i	0.113695	−	0.492873i
$677$	−5.72866	+	5.72866i	−0.220170	+	0.220170i	−0.808570	−	0.588400i	$-0.799758\pi$
$677$	−5.72866	+	5.72866i	−0.220170	+	0.220170i	0.588400	+	0.808570i	$0.299758\pi$
$678$		0			0
$679$			19.0072i			0.729429i
$680$	−25.6548	−	42.6231i	−0.983817	−	1.63452i
$681$		0			0
$682$	−4.03358	+	35.4307i	−0.154454	+	1.35671i
$683$	−33.0998	−	33.0998i	−1.26653	−	1.26653i	−0.947869	−	0.318659i	$-0.896768\pi$
$683$	−33.0998	−	33.0998i	−1.26653	−	1.26653i	−0.318659	−	0.947869i	$-0.603232\pi$
$684$		0			0
$685$	13.2384	−	16.0756i	0.505815	−	0.614219i
$686$	−11.7291	+	9.33149i	−0.447820	+	0.356278i
$687$		0			0
$688$	6.40637	−	2.20847i	0.244240	−	0.0841972i
$689$	15.1591			0.577517
$690$		0			0
$691$			0.570988i			0.0217214i	0.999941	+	0.0108607i	$0.00345714\pi$
$691$			0.570988i			0.0217214i	−0.999941	+	0.0108607i	$0.996543\pi$
$692$	−10.8337	−	17.3306i	−0.411835	−	0.658809i
$693$		0			0
$694$	−22.4562	−	28.2261i	−0.852427	−	1.07145i
$695$	−3.26498	−	33.7340i	−0.123848	−	1.27960i
$696$		0			0
$697$	9.63426	−	9.63426i	0.364924	−	0.364924i
$698$	0.247462	−	2.17369i	0.00936659	−	0.0822755i
$699$		0			0
$700$	−23.9760	+	22.4102i	−0.906206	+	0.847026i
$701$	−25.9738			−0.981018			−0.490509	−	0.871436i	$-0.663189\pi$
$701$	−25.9738			−0.981018			−0.490509	+	0.871436i	$0.663189\pi$
$702$		0			0
$703$	−13.1725	−	13.1725i	−0.496812	−	0.496812i
$704$	−34.6850	−	28.0563i	−1.30724	−	1.05741i
$705$		0			0
$706$	16.7686	+	21.0771i	0.631093	+	0.793246i
$707$	−1.43400	+	1.43400i	−0.0539313	+	0.0539313i
$708$		0			0
$709$	35.8807			1.34753			0.673764	−	0.738947i	$-0.264677\pi$
$709$	35.8807			1.34753			0.673764	+	0.738947i	$0.264677\pi$
$710$	0.371008	−	21.9890i	0.0139237	−	0.825232i
$711$		0			0
$712$	−11.4603	+	32.3907i	−0.429492	+	1.21389i
$713$	20.1192	−	20.1192i	0.753472	−	0.753472i
$714$		0			0
$715$	24.3973	+	20.0914i	0.912407	+	0.751376i
$716$	6.20121	−	26.8825i	0.231750	−	1.00465i
$717$		0			0
$718$	5.15462	−	45.2778i	0.192369	−	1.68975i
$719$	−24.2588			−0.904699			−0.452350	−	0.891841i	$-0.649414\pi$
$719$	−24.2588			−0.904699			−0.452350	+	0.891841i	$0.649414\pi$
$720$		0			0
$721$	12.0532			0.448883
$722$	−1.94163	+	17.0551i	−0.0722599	+	0.634726i
$723$		0			0
$724$	−8.24073	+	35.7239i	−0.306264	+	1.32767i
$725$	2.03753	+	10.4274i	0.0756720	+	0.387263i
$726$		0			0
$727$	23.7764	−	23.7764i	0.881819	−	0.881819i	−0.111900	−	0.993719i	$-0.535694\pi$
$727$	23.7764	−	23.7764i	0.881819	−	0.881819i	0.993719	+	0.111900i	$0.0356936\pi$
$728$	−22.1804	−	7.84775i	−0.822061	−	0.290857i
$729$		0			0
$730$	−18.2346	−	18.8604i	−0.674892	−	0.698057i
$731$	13.3255			0.492862
$732$		0			0
$733$	1.58667	−	1.58667i	0.0586051	−	0.0586051i	−0.677197	−	0.735802i	$-0.736805\pi$
$733$	1.58667	−	1.58667i	0.0586051	−	0.0586051i	0.735802	+	0.677197i	$0.236805\pi$
$734$	8.80567	+	11.0682i	0.325023	+	0.408535i
$735$		0			0
$736$	7.72001	+	34.7486i	0.284563	+	1.28085i
$737$	−10.4188	−	10.4188i	−0.383782	−	0.383782i
$738$		0			0
$739$	−25.6836			−0.944786			−0.472393	−	0.881388i	$-0.656610\pi$
$739$	−25.6836			−0.944786			−0.472393	+	0.881388i	$0.656610\pi$
$740$	25.2178	−	19.3772i	0.927024	−	0.712322i
$741$		0			0
$742$	−3.13985	+	27.5802i	−0.115268	+	1.01250i
$743$	−0.375129	+	0.375129i	−0.0137622	+	0.0137622i	−0.713954	−	0.700192i	$-0.753098\pi$
$743$	−0.375129	+	0.375129i	−0.0137622	+	0.0137622i	0.700192	+	0.713954i	$0.253098\pi$
$744$		0			0
$745$	12.2718	−	1.18774i	0.449604	−	0.0435153i
$746$	−6.62793	−	8.33091i	−0.242666	−	0.305016i
$747$		0			0
$748$	−46.5021	−	74.3890i	−1.70028	−	2.71993i
$749$		−	8.09000i		−	0.295602i
$750$		0			0
$751$	50.4813			1.84209			0.921045	−	0.389457i	$-0.127337\pi$
$751$	50.4813			1.84209			0.921045	+	0.389457i	$0.127337\pi$
$752$	−1.56649	−	4.54409i	−0.0571240	−	0.165706i
$753$		0			0
$754$	−5.96053	+	4.74210i	−0.217070	+	0.172697i
$755$	3.16749	+	32.7268i	0.115277	+	1.19105i
$756$		0			0
$757$	−7.30248	−	7.30248i	−0.265413	−	0.265413i	0.561836	−	0.827249i	$-0.310095\pi$
$757$	−7.30248	−	7.30248i	−0.265413	−	0.265413i	−0.827249	+	0.561836i	$0.810095\pi$
$758$	3.16112	−	27.7670i	0.114817	−	1.00854i
$759$		0			0
$760$	16.0787	+	3.99585i	0.583237	+	0.144945i
$761$			13.1137i			0.475371i	0.971342	+	0.237685i	$0.0763887\pi$
$761$			13.1137i			0.475371i	−0.971342	+	0.237685i	$0.923611\pi$
$762$		0			0
$763$	−35.1545	+	35.1545i	−1.27268	+	1.27268i
$764$	5.49377	−	23.8157i	0.198758	−	0.861623i
$765$		0			0
$766$	16.4601	+	20.6893i	0.594726	+	0.747535i
$767$	−14.4994	−	14.4994i	−0.523541	−	0.523541i
$768$		0			0
$769$			16.1276i			0.581577i	0.956787	+	0.290788i	$0.0939175\pi$
$769$			16.1276i			0.581577i	−0.956787	+	0.290788i	$0.906082\pi$
$770$	−41.6073	+	40.2265i	−1.49942	+	1.44966i
$771$		0			0
$772$	2.51700	+	4.02643i	0.0905889	+	0.144914i
$773$	−7.60986	−	7.60986i	−0.273708	−	0.273708i	0.556883	−	0.830591i	$-0.311997\pi$
$773$	−7.60986	−	7.60986i	−0.273708	−	0.273708i	−0.830591	+	0.556883i	$0.811997\pi$
$774$		0			0
$775$	22.1889	−	4.33576i	0.797049	−	0.155745i
$776$	7.05622	+	14.7834i	0.253304	+	0.530693i
$777$		0			0
$778$	−38.0943	−	4.33682i	−1.36575	−	0.155482i
$779$			4.53753i			0.162574i
$780$		0			0
$781$		−	38.7816i		−	1.38771i
$782$	−7.91777	+	69.5491i	−0.283139	+	2.48707i
$783$		0			0
$784$	6.60687	−	13.5585i	0.235960	−	0.484232i
$785$	22.8233	−	27.7147i	0.814598	−	0.989179i
$786$		0			0
$787$	−24.1198	−	24.1198i	−0.859779	−	0.859779i	0.131533	−	0.991312i	$-0.458010\pi$
$787$	−24.1198	−	24.1198i	−0.859779	−	0.859779i	−0.991312	+	0.131533i	$0.958010\pi$
$788$	10.6422	−	6.65267i	0.379114	−	0.236992i
$789$		0			0
$790$	0.134545	−	7.97426i	0.00478690	−	0.283711i
$791$		−	11.2129i		−	0.398683i
$792$		0			0
$793$	−5.62386	−	5.62386i	−0.199709	−	0.199709i
$794$	−13.5940	+	10.8151i	−0.482432	+	0.383815i
$795$		0			0
$796$	−7.28574	+	31.5840i	−0.258236	+	1.11946i
$797$	−9.34128	+	9.34128i	−0.330885	+	0.330885i	−0.852923	−	0.522037i	$-0.825172\pi$
$797$	−9.34128	+	9.34128i	−0.330885	+	0.330885i	0.522037	+	0.852923i	$0.325172\pi$
$798$		0			0
$799$		−	9.45191i		−	0.334385i
$800$	−10.3284	+	26.3310i	−0.365165	+	0.930943i
$801$		0			0
$802$	−4.35547	−	0.495845i	−0.153797	−	0.0175089i
$803$	−32.7119	−	32.7119i	−1.15438	−	1.15438i
$804$		0			0
$805$	45.9627	−	4.44854i	1.61997	−	0.156791i
$806$	10.0909	+	12.6837i	0.355438	+	0.446765i
$807$		0			0
$808$	−0.582979	+	1.64770i	−0.0205091	+	0.0579658i
$809$	−8.47429			−0.297940			−0.148970	−	0.988842i	$-0.547596\pi$
$809$	−8.47429			−0.297940			−0.148970	+	0.988842i	$0.547596\pi$
$810$		0			0
$811$		−	2.25683i		−	0.0792481i	−0.999215	−	0.0396240i	$-0.987384\pi$
$811$		−	2.25683i		−	0.0792481i	0.999215	−	0.0396240i	$-0.0126160\pi$
$812$	−7.39311	−	11.8267i	−0.259447	−	0.415036i
$813$		0			0
$814$	43.8870	−	34.9158i	1.53824	−	1.22380i
$815$	28.6204	+	23.5692i	1.00253	+	0.825592i
$816$		0			0
$817$	−3.13802	+	3.13802i	−0.109785	+	0.109785i
$818$	19.8241	+	2.25686i	0.693132	+	0.0789092i
$819$		0			0
$820$	−7.68080	−	1.00594i	−0.268225	−	0.0351290i
$821$	25.8885			0.903515			0.451757	−	0.892141i	$-0.350797\pi$
$821$	25.8885			0.903515			0.451757	+	0.892141i	$0.350797\pi$
$822$		0			0
$823$	−32.4100	−	32.4100i	−1.12974	−	1.12974i	−0.990219	−	0.139522i	$-0.955443\pi$
$823$	−32.4100	−	32.4100i	−1.12974	−	1.12974i	−0.139522	−	0.990219i	$-0.544557\pi$
$824$	9.37470	−	4.47461i	0.326583	−	0.155881i
$825$		0			0
$826$	29.3831	−	23.3767i	1.02237	−	0.813378i
$827$	18.2295	−	18.2295i	0.633901	−	0.633901i	−0.315143	−	0.949044i	$-0.602053\pi$
$827$	18.2295	−	18.2295i	0.633901	−	0.633901i	0.949044	+	0.315143i	$0.102053\pi$
$828$		0			0
$829$	−14.3355			−0.497894			−0.248947	−	0.968517i	$-0.580085\pi$
$829$	−14.3355			−0.497894			−0.248947	+	0.968517i	$0.580085\pi$
$830$	2.15821	+	2.23229i	0.0749126	+	0.0774839i
$831$		0			0
$832$	−20.1649	+	2.13044i	−0.699091	+	0.0738597i
$833$	20.9724	−	20.9724i	0.726652	−	0.726652i
$834$		0			0
$835$	−15.9211	+	19.3333i	−0.550974	+	0.669056i
$836$	28.4686	+	6.56708i	0.984606	+	0.227127i
$837$		0			0
$838$	42.8211	+	4.87493i	1.47923	+	0.168402i
$839$	−29.2314			−1.00918			−0.504590	−	0.863359i	$-0.668356\pi$
$839$	−29.2314			−1.00918			−0.504590	+	0.863359i	$0.668356\pi$
$840$		0			0
$841$	24.4847			0.844301
$842$	−53.4802	−	6.08842i	−1.84305	−	0.209821i
$843$		0			0
$844$	−10.1734	+	44.1022i	−0.350184	+	1.51806i
$845$	−14.6351	+	1.41648i	−0.503464	+	0.0487283i
$846$		0			0
$847$	−46.6375	+	46.6375i	−1.60248	+	1.60248i
$848$	7.79678	+	22.6170i	0.267742	+	0.776671i
$849$		0			0
$850$	−36.0770	+	42.3328i	−1.23743	+	1.45200i
$851$	−44.7480			−1.53394
$852$		0			0
$853$	−28.2054	+	28.2054i	−0.965735	+	0.965735i	−0.999432	−	0.0336967i	$-0.989272\pi$
$853$	−28.2054	+	28.2054i	−0.965735	+	0.965735i	0.0336967	+	0.999432i	$0.489272\pi$
$854$	11.3968	−	9.06710i	0.389990	−	0.310270i
$855$		0			0
$856$	−3.00333	−	6.29224i	−0.102652	−	0.215064i
$857$	12.8982	+	12.8982i	0.440593	+	0.440593i	0.892211	−	0.451619i	$-0.149153\pi$
$857$	12.8982	+	12.8982i	0.440593	+	0.440593i	−0.451619	+	0.892211i	$0.649153\pi$
$858$		0			0
$859$	14.2270			0.485421			0.242710	−	0.970099i	$-0.421964\pi$
$859$	14.2270			0.485421			0.242710	+	0.970099i	$0.421964\pi$
$860$	−4.61613	−	6.00749i	−0.157409	−	0.204854i
$861$		0			0
$862$	42.1611	+	4.79980i	1.43601	+	0.163482i
$863$	−3.78453	+	3.78453i	−0.128827	+	0.128827i	−0.768580	−	0.639753i	$-0.779036\pi$
$863$	−3.78453	+	3.78453i	−0.128827	+	0.128827i	0.639753	+	0.768580i	$0.279036\pi$
$864$		0			0
$865$	−14.5260	+	17.6392i	−0.493900	+	0.599750i
$866$	32.3187	−	25.7122i	1.09823	−	0.873737i
$867$		0			0
$868$	−25.1666	+	15.7322i	−0.854210	+	0.533984i
$869$		−	14.0641i		−	0.477090i
$870$		0			0
$871$	−6.69716			−0.226924
$872$	−14.2917	+	40.3932i	−0.483978	+	1.36789i
$873$		0			0
$874$	−14.5135	−	18.2426i	−0.490928	−	0.617066i
$875$	32.2717	+	17.4604i	1.09098	+	0.590271i
$876$		0			0
$877$	18.4253	+	18.4253i	0.622177	+	0.622177i	0.946088	−	0.323910i	$-0.104998\pi$
$877$	18.4253	+	18.4253i	0.622177	+	0.622177i	−0.323910	+	0.946088i	$0.604998\pi$
$878$	−0.319023	−	0.0363189i	−0.0107665	−	0.00122571i
$879$		0			0
$880$	−17.4276	+	46.7336i	−0.587483	+	1.57539i
$881$			2.06935i			0.0697181i	0.999392	+	0.0348591i	$0.0110982\pi$
$881$			2.06935i			0.0697181i	−0.999392	+	0.0348591i	$0.988902\pi$
$882$		0			0
$883$	−37.3458	+	37.3458i	−1.25679	+	1.25679i	−0.304170	+	0.952618i	$0.598379\pi$
$883$	−37.3458	+	37.3458i	−1.25679	+	1.25679i	−0.952618	+	0.304170i	$0.901621\pi$
$884$	−38.8541	−	8.96279i	−1.30680	−	0.301451i
$885$		0			0
$886$	25.5747	−	20.3468i	0.859199	−	0.683564i
$887$	20.7113	+	20.7113i	0.695418	+	0.695418i	0.963419	−	0.268001i	$-0.0863629\pi$
$887$	20.7113	+	20.7113i	0.695418	+	0.695418i	−0.268001	+	0.963419i	$0.586363\pi$
$888$		0			0
$889$		−	6.51188i		−	0.218401i
$890$	38.4083	+	0.648041i	1.28745	+	0.0217224i
$891$		0			0
$892$	−16.2556	−	26.0040i	−0.544278	−	0.870677i
$893$	2.22583	+	2.22583i	0.0744844	+	0.0744844i
$894$		0			0
$895$	−30.7014	+	2.97147i	−1.02623	+	0.0993251i
$896$	0.300591	−	37.1289i	0.0100420	−	1.24039i
$897$		0			0
$898$	3.43446	−	30.1680i	0.114609	−	1.00672i
$899$			9.60824i			0.320453i
$900$		0			0
$901$			47.0443i			1.56727i
$902$	−13.5726	−	1.54516i	−0.451917	−	0.0514482i
$903$		0			0
$904$	−4.16266	−	8.72113i	−0.138448	−	0.290061i
$905$	40.7988	−	3.94875i	1.35620	−	0.131261i
$906$		0			0
$907$	−10.5449	−	10.5449i	−0.350139	−	0.350139i	0.510022	−	0.860161i	$-0.329637\pi$
$907$	−10.5449	−	10.5449i	−0.350139	−	0.350139i	−0.860161	+	0.510022i	$0.829637\pi$
$908$	30.2619	−	18.9173i	1.00428	−	0.627794i
$909$		0			0
$910$	−0.443764	+	26.3011i	−0.0147106	+	0.871874i
$911$		−	26.8997i		−	0.891226i	−0.895226	−	0.445613i	$-0.852986\pi$
$911$		−	26.8997i		−	0.891226i	0.895226	−	0.445613i	$-0.147014\pi$
$912$		0			0
$913$	3.87172	+	3.87172i	0.128135	+	0.128135i
$914$	24.2197	+	30.4427i	0.801117	+	1.00696i
$915$		0			0
$916$	1.15772	+	0.267060i	0.0382520	+	0.00882392i
$917$	−16.5735	+	16.5735i	−0.547306	+	0.547306i
$918$		0			0
$919$			30.3696i			1.00180i	0.865505	+	0.500900i	$0.166998\pi$
$919$			30.3696i			1.00180i	−0.865505	+	0.500900i	$0.833002\pi$
$920$	34.0973	−	20.5232i	1.12416	−	0.676629i
$921$		0			0
$922$	−3.08028	+	27.0569i	−0.101443	+	0.891072i
$923$	−12.4643	−	12.4643i	−0.410267	−	0.410267i
$924$		0			0
$925$	−29.4973	−	19.8539i	−0.969864	−	0.652793i
$926$	16.6112	−	13.2156i	0.545878	−	0.434291i
$927$		0			0
$928$	−10.1408	−	6.45395i	−0.332886	−	0.211861i
$929$	−31.6162			−1.03729			−0.518646	−	0.854989i	$-0.673564\pi$
$929$	−31.6162			−1.03729			−0.518646	+	0.854989i	$0.673564\pi$
$930$		0			0
$931$			9.87758i			0.323724i
$932$	−12.2983	+	7.68794i	−0.402846	+	0.251827i
$933$		0			0
$934$	2.42554	+	3.04876i	0.0793660	+	0.0997583i
$935$	−62.3510	+	75.7137i	−2.03910	+	2.47610i
$936$		0			0
$937$	−3.51188	+	3.51188i	−0.114728	+	0.114728i	−0.762140	−	0.647412i	$-0.775851\pi$
$937$	−3.51188	+	3.51188i	−0.114728	+	0.114728i	0.647412	+	0.762140i	$0.275851\pi$
$938$	1.38716	−	12.1847i	0.0452923	−	0.397844i
$939$		0			0
$940$	−4.26116	+	3.27426i	−0.138984	+	0.106795i
$941$	−24.7342			−0.806312			−0.403156	−	0.915131i	$-0.632087\pi$
$941$	−24.7342			−0.806312			−0.403156	+	0.915131i	$0.632087\pi$
$942$		0			0
$943$	7.70715	+	7.70715i	0.250979	+	0.250979i
$944$	14.1752	−	29.0901i	0.461363	−	0.946801i
$945$		0			0
$946$	−8.31779	−	10.4550i	−0.270435	−	0.339920i
$947$	23.0920	−	23.0920i	0.750389	−	0.750389i	−0.224163	−	0.974552i	$-0.571965\pi$
$947$	23.0920	−	23.0920i	0.750389	−	0.750389i	0.974552	+	0.224163i	$0.0719648\pi$
$948$		0			0
$949$	−21.0270			−0.682566
$950$	−1.47317	−	18.4647i	−0.0477961	−	0.599074i
$951$		0			0
$952$	24.3544	−	68.8339i	0.789332	−	2.23092i
$953$	−32.1149	+	32.1149i	−1.04030	+	1.04030i	−0.0411513	+	0.999153i	$0.513103\pi$
$953$	−32.1149	+	32.1149i	−1.04030	+	1.04030i	−0.999153	+	0.0411513i	$0.986897\pi$
$954$		0			0
$955$	−27.1990	+	2.63248i	−0.880138	+	0.0851850i
$956$	−21.7453	−	5.01617i	−0.703293	−	0.162235i
$957$		0			0
$958$	−3.18914	+	28.0132i	−0.103037	+	0.905065i
$959$	30.5648			0.986990
$960$		0			0
$961$	−10.5542			−0.340457
$962$	2.88334	−	25.3270i	0.0929625	−	0.816575i
$963$		0			0
$964$	38.9191	+	8.97779i	1.25350	+	0.289155i
$965$	3.37485	−	4.09813i	0.108640	−	0.131924i
$966$		0			0
$967$	−29.3972	+	29.3972i	−0.945349	+	0.945349i	−0.998582	−	0.0532327i	$-0.983047\pi$
$967$	−29.3972	+	29.3972i	−0.945349	+	0.945349i	0.0532327	+	0.998582i	$0.483047\pi$
$968$	−18.9600	+	53.5874i	−0.609397	+	1.72236i
$969$		0			0
$970$	13.1670	−	12.7300i	0.422767	−	0.408737i
$971$	40.7956			1.30919			0.654596	−	0.755979i	$-0.272839\pi$
$971$	40.7956			1.30919			0.654596	+	0.755979i	$0.272839\pi$
$972$		0			0
$973$	35.1733	−	35.1733i	1.12760	−	1.12760i
$974$	−23.0864	−	29.0182i	−0.739735	−	0.929802i
$975$		0			0
$976$	5.49813	−	11.2831i	0.175991	−	0.361165i
$977$	8.32380	+	8.32380i	0.266302	+	0.266302i	0.827608	−	0.561306i	$-0.189701\pi$
$977$	8.32380	+	8.32380i	0.266302	+	0.266302i	−0.561306	+	0.827608i	$0.689701\pi$
$978$		0			0
$979$	67.7400			2.16498
$980$	−16.7200	−	2.18979i	−0.534102	−	0.0699504i
$981$		0			0
$982$	−0.173112	+	1.52061i	−0.00552423	+	0.0485245i
$983$	16.0382	−	16.0382i	0.511539	−	0.511539i	−0.403458	−	0.914998i	$-0.632192\pi$
$983$	16.0382	−	16.0382i	0.511539	−	0.511539i	0.914998	+	0.403458i	$0.132192\pi$
$984$		0			0
$985$	−10.8317	−	8.92005i	−0.345128	−	0.284216i
$986$	−14.7165	−	18.4977i	−0.468668	−	0.589087i
$987$		0			0
$988$	11.2604	−	7.03908i	0.358240	−	0.223943i
$989$			10.6601i			0.338970i
$990$		0			0
$991$	23.7160			0.753362			0.376681	−	0.926343i	$-0.377065\pi$
$991$	23.7160			0.753362			0.376681	+	0.926343i	$0.377065\pi$
$992$	−13.7337	+	21.5790i	−0.436044	+	0.685134i
$993$		0			0
$994$	25.2590	−	20.0956i	0.801167	−	0.637395i
$995$	36.0708	−	3.49114i	1.14352	−	0.110677i
$996$		0			0
$997$	−22.4793	−	22.4793i	−0.711926	−	0.711926i	0.255012	−	0.966938i	$-0.417921\pi$
$997$	−22.4793	−	22.4793i	−0.711926	−	0.711926i	−0.966938	+	0.255012i	$0.917921\pi$
$998$	−2.66139	+	23.3774i	−0.0842447	+	0.739999i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.x.a.53.13	yes	48
3.2	odd	2	inner	360.2.x.a.53.12	yes	48
4.3	odd	2		1440.2.bj.a.593.14		48
5.2	odd	4	inner	360.2.x.a.197.24	yes	48
8.3	odd	2		1440.2.bj.a.593.11		48
8.5	even	2	inner	360.2.x.a.53.1	✓	48
12.11	even	2		1440.2.bj.a.593.12		48
15.2	even	4	inner	360.2.x.a.197.1	yes	48
20.7	even	4		1440.2.bj.a.17.13		48
24.5	odd	2	inner	360.2.x.a.53.24	yes	48
24.11	even	2		1440.2.bj.a.593.13		48
40.27	even	4		1440.2.bj.a.17.12		48
40.37	odd	4	inner	360.2.x.a.197.12	yes	48
60.47	odd	4		1440.2.bj.a.17.11		48
120.77	even	4	inner	360.2.x.a.197.13	yes	48
120.107	odd	4		1440.2.bj.a.17.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.x.a.53.1	✓	48	8.5	even	2	inner
360.2.x.a.53.12	yes	48	3.2	odd	2	inner
360.2.x.a.53.13	yes	48	1.1	even	1	trivial
360.2.x.a.53.24	yes	48	24.5	odd	2	inner
360.2.x.a.197.1	yes	48	15.2	even	4	inner
360.2.x.a.197.12	yes	48	40.37	odd	4	inner
360.2.x.a.197.13	yes	48	120.77	even	4	inner
360.2.x.a.197.24	yes	48	5.2	odd	4	inner
1440.2.bj.a.17.11		48	60.47	odd	4
1440.2.bj.a.17.12		48	40.27	even	4
1440.2.bj.a.17.13		48	20.7	even	4
1440.2.bj.a.17.14		48	120.107	odd	4
1440.2.bj.a.593.11		48	8.3	odd	2
1440.2.bj.a.593.12		48	12.11	even	2
1440.2.bj.a.593.13		48	24.11	even	2
1440.2.bj.a.593.14		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.159967 - 1.40514i) q^{2} +(-1.94882 - 0.449551i) q^{4} +(0.215413 + 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-0.943427 + 2.66645i) q^{8} +O(q^{10})\)	\(q+(0.159967 - 1.40514i) q^{2} +(-1.94882 - 0.449551i) q^{4} +(0.215413 + 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-0.943427 + 2.66645i) q^{8} +(3.16183 + 0.0533477i) q^{10} +5.57646 q^{11} +(1.79226 - 1.79226i) q^{13} +(2.88958 + 3.63203i) q^{14} +(3.59581 + 1.75219i) q^{16} +(5.56203 + 5.56203i) q^{17} -2.61960 q^{19} +(0.580749 - 4.43427i) q^{20} +(0.892049 - 7.83569i) q^{22} +(-4.44948 + 4.44948i) q^{23} +(-4.90719 + 0.958877i) q^{25} +(-2.23167 - 2.80507i) q^{26} +(5.56573 - 3.47925i) q^{28} -2.12491i q^{29} -4.52171 q^{31} +(3.03728 - 4.77231i) q^{32} +(8.70516 - 6.92568i) q^{34} +(-5.66484 - 4.66506i) q^{35} +(5.02845 + 5.02845i) q^{37} +(-0.419049 + 3.68090i) q^{38} +(-6.13785 - 1.52537i) q^{40} -1.73215i q^{41} +(1.19790 - 1.19790i) q^{43} +(-10.8675 - 2.50690i) q^{44} +(5.54036 + 6.96390i) q^{46} +(-0.849681 - 0.849681i) q^{47} -3.77064i q^{49} +(0.562366 + 7.04867i) q^{50} +(-4.29850 + 2.68708i) q^{52} +(4.22906 + 4.22906i) q^{53} +(1.20124 + 12.4113i) q^{55} +(-3.99849 - 8.37718i) q^{56} +(-2.98580 - 0.339916i) q^{58} -8.08999i q^{59} -3.13786i q^{61} +(-0.723323 + 6.35362i) q^{62} +(-6.21989 - 5.03120i) q^{64} +(4.37505 + 3.60290i) q^{65} +(-1.86836 - 1.86836i) q^{67} +(-8.33899 - 13.3398i) q^{68} +(-7.46123 + 7.21363i) q^{70} -6.95452i q^{71} +(-5.86607 - 5.86607i) q^{73} +(7.87005 - 6.26128i) q^{74} +(5.10513 + 1.17764i) q^{76} +(-12.9409 + 12.9409i) q^{77} -2.52204i q^{79} +(-3.12520 + 8.38052i) q^{80} +(-2.43390 - 0.277086i) q^{82} +(0.694298 + 0.694298i) q^{83} +(-11.1811 + 13.5774i) q^{85} +(-1.49159 - 1.87484i) q^{86} +(-5.26099 + 14.8693i) q^{88} +12.1475 q^{89} +8.31834i q^{91} +(10.6715 - 6.67097i) q^{92} +(-1.32984 + 1.05800i) q^{94} +(-0.564297 - 5.83036i) q^{95} +(4.09526 - 4.09526i) q^{97} +(-5.29827 - 0.603178i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more