LMFDB - Embedded newform 360.2.x.a.53.1

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			53.1
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40514 + 0.159967i) q^{2} +(1.94882 - 0.449551i) q^{4} +(-0.215413 - 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-2.66645 + 0.943427i) q^{8} +O(q^{10})$	\(q+(-1.40514 + 0.159967i) q^{2} +(1.94882 - 0.449551i) q^{4} +(-0.215413 - 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-2.66645 + 0.943427i) q^{8} +(0.658719 + 3.09291i) q^{10} -5.57646 q^{11} +(-1.79226 + 1.79226i) q^{13} +(2.88958 - 3.63203i) q^{14} +(3.59581 - 1.75219i) q^{16} +(5.56203 + 5.56203i) q^{17} +2.61960 q^{19} +(-1.42035 - 4.24059i) q^{20} +(7.83569 - 0.892049i) q^{22} +(-4.44948 + 4.44948i) q^{23} +(-4.90719 + 0.958877i) q^{25} +(2.23167 - 2.80507i) q^{26} +(-3.47925 + 5.56573i) q^{28} +2.12491i q^{29} -4.52171 q^{31} +(-4.77231 + 3.03728i) q^{32} +(-8.70516 - 6.92568i) q^{34} +(5.66484 + 4.66506i) q^{35} +(-5.02845 - 5.02845i) q^{37} +(-3.68090 + 0.419049i) q^{38} +(2.67414 + 5.73140i) q^{40} -1.73215i q^{41} +(-1.19790 + 1.19790i) q^{43} +(-10.8675 + 2.50690i) q^{44} +(5.54036 - 6.96390i) q^{46} +(-0.849681 - 0.849681i) q^{47} -3.77064i q^{49} +(6.74189 - 2.13234i) q^{50} +(-2.68708 + 4.29850i) q^{52} +(-4.22906 - 4.22906i) q^{53} +(1.20124 + 12.4113i) q^{55} +(3.99849 - 8.37718i) q^{56} +(-0.339916 - 2.98580i) q^{58} +8.08999i q^{59} +3.13786i q^{61} +(6.35362 - 0.723323i) q^{62} +(6.21989 - 5.03120i) q^{64} +(4.37505 + 3.60290i) q^{65} +(1.86836 + 1.86836i) q^{67} +(13.3398 + 8.33899i) q^{68} +(-8.70614 - 5.64886i) q^{70} -6.95452i q^{71} +(-5.86607 - 5.86607i) q^{73} +(7.87005 + 6.26128i) q^{74} +(5.10513 - 1.17764i) q^{76} +(12.9409 - 12.9409i) q^{77} -2.52204i q^{79} +(-4.67437 - 7.62563i) q^{80} +(0.277086 + 2.43390i) q^{82} +(-0.694298 - 0.694298i) q^{83} +(11.1811 - 13.5774i) q^{85} +(1.49159 - 1.87484i) q^{86} +(14.8693 - 5.26099i) q^{88} +12.1475 q^{89} -8.31834i q^{91} +(-6.67097 + 10.6715i) q^{92} +(1.32984 + 1.05800i) q^{94} +(-0.564297 - 5.83036i) q^{95} +(4.09526 - 4.09526i) q^{97} +(0.603178 + 5.29827i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.40514	+	0.159967i	−0.993582	+	0.113114i
$2$	−1.40514	+	0.159967i	−0.993582	+	0.113114i
$3$		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	$0.462954\pi$
$8$	−2.66645	+	0.943427i	−0.942732	+	0.333552i
$9$		0			0
$10$	0.658719	+	3.09291i	0.208305	+	0.978064i
$11$	−5.57646			−1.68137			−0.840683	−	0.541528i	$-0.817846\pi$
$11$	−5.57646			−1.68137			−0.840683	+	0.541528i	$0.817846\pi$
$12$		0			0
$13$	−1.79226	+	1.79226i	−0.497083	+	0.497083i	−0.910529	−	0.413446i	$-0.864325\pi$
$13$	−1.79226	+	1.79226i	−0.497083	+	0.497083i	0.413446	+	0.910529i	$0.364325\pi$
$14$	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	$-0.402850\pi$
$19$	2.61960			0.600978			0.300489	+	0.953785i	$0.402850\pi$
$20$	−1.42035	−	4.24059i	−0.317601	−	0.948225i
$21$		0			0
$22$	7.83569	−	0.892049i	1.67058	−	0.190185i
$23$	−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
$28$	−3.47925	+	5.56573i	−0.657517	+	1.05182i
$29$			2.12491i			0.394587i	0.980345	+	0.197293i	$0.0632151\pi$
$29$			2.12491i			0.394587i	−0.980345	+	0.197293i	$0.936785\pi$
$30$		0			0
$31$	−4.52171			−0.812123			−0.406061	−	0.913846i	$-0.633098\pi$
$31$	−4.52171			−0.812123			−0.406061	+	0.913846i	$0.633098\pi$
$32$	−4.77231	+	3.03728i	−0.843634	+	0.536919i
$33$		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	0.160382	−	0.987055i	$-0.448727\pi$
$37$	−5.02845	−	5.02845i	−0.826673	−	0.826673i	−0.987055	+	0.160382i	$0.948727\pi$
$38$	−3.68090	+	0.419049i	−0.597121	+	0.0679788i
$39$		0			0
$40$	2.67414	+	5.73140i	0.422819	+	0.906214i
$41$		−	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	−0.792522	−	0.609844i	$-0.791232\pi$
$43$	−1.19790	+	1.19790i	−0.182678	+	0.182678i	0.609844	+	0.792522i	$0.291232\pi$
$44$	−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
$50$	6.74189	−	2.13234i	0.953448	−	0.301559i
$51$		0			0
$52$	−2.68708	+	4.29850i	−0.372631	+	0.596095i
$53$	−4.22906	−	4.22906i	−0.580906	−	0.580906i	0.354246	−	0.935152i	$-0.384737\pi$
$53$	−4.22906	−	4.22906i	−0.580906	−	0.580906i	−0.935152	+	0.354246i	$0.884737\pi$
$54$		0			0
$55$	1.20124	+	12.4113i	0.161976	+	1.67355i
$56$	3.99849	−	8.37718i	0.534321	−	1.11945i
$57$		0			0
$58$	−0.339916	−	2.98580i	−0.0446331	−	0.392054i
$59$			8.08999i			1.05323i	0.850105	+	0.526614i	$0.176539\pi$
$59$			8.08999i			1.05323i	−0.850105	+	0.526614i	$0.823461\pi$
$60$		0			0
$61$			3.13786i			0.401762i	0.979616	+	0.200881i	$0.0643805\pi$
$61$			3.13786i			0.401762i	−0.979616	+	0.200881i	$0.935620\pi$
$62$	6.35362	−	0.723323i	0.806910	−	0.0918622i
$63$		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	0.811964	−	0.583708i	$-0.198399\pi$
$67$	1.86836	+	1.86836i	0.228256	+	0.228256i	−0.583708	+	0.811964i	$0.698399\pi$
$68$	13.3398	+	8.33899i	1.61769	+	1.01125i
$69$		0			0
$70$	−8.70614	−	5.64886i	−1.04058	−	0.675167i
$71$		−	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	$-0.0453134\pi$
$80$	−4.67437	−	7.62563i	−0.522611	−	0.852571i
$81$		0			0
$82$	0.277086	+	2.43390i	0.0305990	+	0.268780i
$83$	−0.694298	−	0.694298i	−0.0762091	−	0.0762091i	0.667975	−	0.744184i	$-0.267161\pi$
$83$	−0.694298	−	0.694298i	−0.0762091	−	0.0762091i	−0.744184	+	0.667975i	$0.767161\pi$
$84$		0			0
$85$	11.1811	−	13.5774i	1.21276	−	1.47267i
$86$	1.49159	−	1.87484i	0.160842	−	0.202169i
$87$		0			0
$88$	14.8693	−	5.26099i	1.58508	−	0.560823i
$89$	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
$92$	−6.67097	+	10.6715i	−0.695497	+	1.11258i
$93$		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	$0.155006\pi$
$98$	0.603178	+	5.29827i	0.0609301	+	0.535206i
$99$		0			0
$100$	−9.13218	+	4.07471i	−0.913218	+	0.407471i
$101$	−0.617937			−0.0614871			−0.0307435	−	0.999527i	$-0.509788\pi$
$101$	−0.617937			−0.0614871			−0.0307435	+	0.999527i	$0.509788\pi$
$102$		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	−0.617815	−	0.786323i	$-0.711982\pi$
$107$	1.74306	−	1.74306i	0.168508	−	0.168508i	0.786323	+	0.617815i	$0.211982\pi$
$108$		0			0
$109$	−15.1487			−1.45098			−0.725491	−	0.688231i	$-0.758387\pi$
$109$	−15.1487			−1.45098			−0.725491	+	0.688231i	$0.758387\pi$
$110$	−3.67332	−	17.2475i	−0.350237	−	1.64448i
$111$		0			0
$112$	−4.27836	+	12.4107i	−0.404267	+	1.17270i
$113$	−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
$118$	−1.29413	−	11.3675i	−0.119134	−	1.04647i
$119$	−25.8148			−2.36644
$120$		0			0
$121$	20.0969			1.82699
$122$	−0.501954	−	4.40913i	−0.0454448	−	0.399184i
$123$		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	$0.278059\pi$
$128$	−7.93497	+	8.06450i	−0.701359	+	0.712808i
$129$		0			0
$130$	−6.72389	−	4.36270i	−0.589724	−	0.382634i
$131$	−7.14182			−0.623984			−0.311992	−	0.950085i	$-0.600996\pi$
$131$	−7.14182			−0.623984			−0.311992	+	0.950085i	$0.600996\pi$
$132$		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	$-0.277776\pi$
$139$	15.1568			1.28558			0.642791	+	0.766042i	$0.277776\pi$
$140$	13.1369	+	6.54472i	1.11027	+	0.553130i
$141$		0			0
$142$	1.11249	+	9.77206i	0.0933583	+	0.820053i
$143$	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
$148$	−12.0601	−	7.53901i	−0.991334	−	0.619703i
$149$			5.51376i			0.451705i	0.974162	+	0.225852i	$0.0725167\pi$
$149$			5.51376i			0.451705i	−0.974162	+	0.225852i	$0.927483\pi$
$150$		0			0
$151$	14.7042			1.19661			0.598307	−	0.801267i	$-0.295840\pi$
$151$	14.7042			1.19661			0.598307	+	0.801267i	$0.295840\pi$
$152$	−6.98503	+	2.47140i	−0.566561	+	0.200457i
$153$		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	0.995955	−	0.0898521i	$-0.0286394\pi$
$157$	11.3534	+	11.3534i	0.906103	+	0.906103i	−0.0898521	+	0.995955i	$0.528639\pi$
$158$	0.403443	+	3.54381i	0.0320962	+	0.281931i
$159$		0			0
$160$	7.78799	+	9.96731i	0.615694	+	0.787985i
$161$		−	20.6512i		−	1.62754i
$162$		0			0
$163$	−11.7245	+	11.7245i	−0.918331	+	0.918331i	−0.996908	−	0.0785768i	$-0.974962\pi$
$163$	−11.7245	+	11.7245i	−0.918331	+	0.918331i	0.0785768	+	0.996908i	$0.474962\pi$
$164$	−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
$170$	−13.5391	+	20.8667i	−1.03840	+	1.60040i
$171$		0			0
$172$	−1.79598	+	2.87301i	−0.136942	+	0.219065i
$173$	−7.22597	−	7.22597i	−0.549380	−	0.549380i	0.376881	−	0.926262i	$-0.376996\pi$
$173$	−7.22597	−	7.22597i	−0.549380	−	0.549380i	−0.926262	+	0.376881i	$0.876996\pi$
$174$		0			0
$175$	9.16258	−	13.6130i	0.692626	−	1.02904i
$176$	−20.0519	+	9.77101i	−1.51147	+	0.736517i
$177$		0			0
$178$	−17.0689	+	1.94320i	−1.27937	+	0.145649i
$179$		−	13.7942i		−	1.03103i	−0.856880	−	0.515515i	$-0.827601\pi$
$179$		−	13.7942i		−	1.03103i	0.856880	−	0.515515i	$-0.172399\pi$
$180$		0			0
$181$			18.3310i			1.36254i	0.732034	+	0.681268i	$0.238571\pi$
$181$			18.3310i			1.36254i	−0.732034	+	0.681268i	$0.761429\pi$
$182$	1.33066	+	11.6884i	0.0986349	+	0.866402i
$183$		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
$188$	−2.03785	−	1.27390i	−0.148626	−	0.0929088i
$189$		0			0
$190$	1.72558	+	8.10219i	0.125187	+	0.587795i
$191$			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	−0.531141	−	0.847283i	$-0.678237\pi$
$197$	4.43727	−	4.43727i	0.316143	−	0.316143i	0.847283	+	0.531141i	$0.178237\pi$
$198$		0			0
$199$		−	16.2067i		−	1.14886i	−0.818553	−	0.574432i	$-0.805223\pi$
$199$		−	16.2067i		−	1.14886i	0.818553	−	0.574432i	$-0.194777\pi$
$200$	12.1801	−	7.18638i	0.861266	−	0.508154i
$201$		0			0
$202$	0.868287	−	0.0988495i	0.0610924	−	0.00695503i
$203$	−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
$208$	−3.30424	+	9.58499i	−0.229108	+	0.664600i
$209$	−14.6081			−1.01046
$210$		0			0
$211$			22.6302i			1.55793i	0.627068	+	0.778964i	$0.284255\pi$
$211$			22.6302i			1.55793i	−0.627068	+	0.778964i	$0.715745\pi$
$212$	−10.1429	−	6.34050i	−0.696614	−	0.435467i
$213$		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
$218$	21.2860	−	2.42329i	1.44167	−	0.164126i
$219$		0			0
$220$	7.92054	+	23.6475i	0.534003	+	1.59431i
$221$	−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	−0.151059	−	0.988525i	$-0.548268\pi$
$227$	12.6177	−	12.6177i	0.837465	−	0.837465i	0.988525	+	0.151059i	$0.0482685\pi$
$228$		0			0
$229$	0.594060			0.0392566			0.0196283	−	0.999807i	$-0.493752\pi$
$229$	0.594060			0.0392566			0.0196283	+	0.999807i	$0.493752\pi$
$230$	−16.6928	−	10.8309i	−1.10069	−	0.714167i
$231$		0			0
$232$	−2.00470	−	5.66597i	−0.131615	−	0.371989i
$233$	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
$238$	36.2734	−	4.12952i	2.35126	−	0.267677i
$239$	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	$0.722397\pi$
$242$	−28.2389	+	3.21484i	−1.81527	+	0.206658i
$243$		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
$248$	12.0569	−	4.26590i	0.765614	−	0.270885i
$249$		0			0
$250$	−6.19818	−	14.5459i	−0.392007	−	0.919962i
$251$	−20.4134			−1.28848			−0.644240	−	0.764823i	$-0.722826\pi$
$251$	−20.4134			−1.28848			−0.644240	+	0.764823i	$0.722826\pi$
$252$		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
$260$	10.1459	+	5.05459i	0.629220	+	0.313473i
$261$		0			0
$262$	10.0352	−	1.14246i	0.619979	−	0.0705811i
$263$	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
$268$	4.48101	+	2.80117i	0.273721	+	0.171109i
$269$			29.5007i			1.79869i	0.437241	+	0.899345i	$0.355956\pi$
$269$			29.5007i			1.79869i	−0.437241	+	0.899345i	$0.644044\pi$
$270$		0			0
$271$	−19.3447			−1.17511			−0.587554	−	0.809185i	$-0.699909\pi$
$271$	−19.3447			−1.17511			−0.587554	+	0.809185i	$0.699909\pi$
$272$	29.7457	+	10.2543i	1.80360	+	0.621757i
$273$		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	0.662411	−	0.749140i	$-0.269533\pi$
$277$	−1.44346	−	1.44346i	−0.0867293	−	0.0867293i	−0.749140	+	0.662411i	$0.769533\pi$
$278$	−21.2974	+	2.42458i	−1.27733	+	0.145417i
$279$		0			0
$280$	−19.5062	−	7.09476i	−1.16572	−	0.423993i
$281$			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	−0.901930	−	0.431883i	$-0.857849\pi$
$283$	−7.90740	+	7.90740i	−0.470046	+	0.470046i	0.431883	+	0.901930i	$0.357849\pi$
$284$	−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
$290$	−6.57217	+	1.39972i	−0.385931	+	0.0821944i
$291$		0			0
$292$	−14.0690	−	8.79483i	−0.823327	−	0.514678i
$293$	5.38544	+	5.38544i	0.314621	+	0.314621i	0.846697	−	0.532076i	$-0.178588\pi$
$293$	5.38544	+	5.38544i	0.314621	+	0.314621i	−0.532076	+	0.846697i	$0.678588\pi$
$294$		0			0
$295$	18.0056	−	1.74269i	1.04833	−	0.101463i
$296$	18.1521	+	8.66413i	1.05507	+	0.503592i
$297$		0			0
$298$	−0.882018	−	7.74758i	−0.0510940	−	0.448806i
$299$		−	15.9492i		−	0.922368i
$300$		0			0
$301$		−	5.55977i		−	0.320460i
$302$	−20.6615	+	2.35219i	−1.18893	+	0.135353i
$303$		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	0.703787	−	0.710411i	$-0.251491\pi$
$307$	−0.116076	−	0.116076i	−0.00662479	−	0.00662479i	−0.710411	+	0.703787i	$0.751491\pi$
$308$	19.4019	−	31.0371i	1.10553	−	1.76850i
$309$		0			0
$310$	−2.97853	−	13.9852i	−0.169169	−	0.794308i
$311$		−	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	−0.316367	−	0.948637i	$-0.602463\pi$
$317$	11.2572	−	11.2572i	0.632269	−	0.632269i	0.948637	+	0.316367i	$0.102463\pi$
$318$		0			0
$319$		−	11.8495i		−	0.663444i
$320$	−12.5376	−	12.7596i	−0.700875	−	0.713284i
$321$		0			0
$322$	3.30351	+	29.0178i	0.184097	+	1.61710i
$323$	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
$328$	1.63415	+	4.61868i	0.0902311	+	0.255024i
$329$	3.94359			0.217417
$330$		0			0
$331$		−	35.0445i		−	1.92622i	−0.269113	−	0.963109i	$-0.586730\pi$
$331$		−	35.0445i		−	1.92622i	0.269113	−	0.963109i	$-0.413270\pi$
$332$	−1.66518	−	1.04094i	−0.0913888	−	0.0571290i
$333$		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	$0.226085\pi$
$338$	−1.05188	−	9.23965i	−0.0572148	−	0.502570i
$339$		0			0
$340$	15.6863	−	31.4864i	0.850706	−	1.70759i
$341$	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	−0.999508	−	0.0313569i	$-0.990017\pi$
$347$	−18.0347	+	18.0347i	−0.968151	+	0.968151i	0.0313569	+	0.999508i	$0.490017\pi$
$348$		0			0
$349$	−1.54696			−0.0828069			−0.0414035	−	0.999143i	$-0.513183\pi$
$349$	−1.54696			−0.0828069			−0.0414035	+	0.999143i	$0.513183\pi$
$350$	−10.6971	+	20.5938i	−0.571782	+	1.10079i
$351$		0			0
$352$	26.6126	−	16.9372i	1.41846	−	0.902758i
$353$	−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
$358$	2.20662	+	19.3828i	0.116624	+	1.02441i
$359$	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
$362$	−2.93236	−	25.7576i	−0.154121	−	1.35379i
$363$		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	$0.334061\pi$
$368$	−8.20315	+	23.7958i	−0.427619	+	1.24044i
$369$		0			0
$370$	12.2402	−	18.8649i	0.636339	−	0.980739i
$371$	19.6282			1.01904
$372$		0			0
$373$	−5.32291	+	5.32291i	−0.275610	+	0.275610i	−0.831354	−	0.555744i	$-0.812434\pi$
$373$	−5.32291	+	5.32291i	−0.275610	+	0.275610i	0.555744	+	0.831354i	$0.312434\pi$
$374$	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	$-0.669441\pi$
$379$	−19.7611			−1.01506			−0.507529	+	0.861635i	$0.669441\pi$
$380$	−3.72076	−	11.1087i	−0.190871	−	0.569862i
$381$		0			0
$382$	−1.95489	−	17.1716i	−0.100021	−	0.878575i
$383$	−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
$388$	6.13991	−	9.82197i	0.311707	−	0.498635i
$389$			27.1107i			1.37457i	0.726389	+	0.687284i	$0.241197\pi$
$389$			27.1107i			1.37457i	−0.726389	+	0.687284i	$0.758803\pi$
$390$		0			0
$391$	−49.4963			−2.50314
$392$	3.55733	+	10.0542i	0.179672	+	0.507815i
$393$		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	0.890637	−	0.454715i	$-0.150259\pi$
$397$	8.68567	+	8.68567i	0.435921	+	0.435921i	−0.454715	+	0.890637i	$0.650259\pi$
$398$	2.59254	+	22.7727i	0.129952	+	1.14149i
$399$		0			0
$400$	−15.9652	+	12.0463i	−0.798260	+	0.602313i
$401$		−	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	$0.886588\pi$
$410$	5.35737	−	1.14100i	0.264582	−	0.0563498i
$411$		0			0
$412$	−6.22847	−	3.89354i	−0.306855	−	0.191821i
$413$	−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
$418$	20.5264	−	2.33681i	1.00398	−	0.114297i
$419$		−	30.4747i		−	1.48878i	−0.667743	−	0.744392i	$-0.732739\pi$
$419$		−	30.4747i		−	1.48878i	0.667743	−	0.744392i	$-0.267261\pi$
$420$		0			0
$421$			38.0605i			1.85496i	0.373878	+	0.927478i	$0.378028\pi$
$421$			38.0605i			1.85496i	−0.373878	+	0.927478i	$0.621972\pi$
$422$	−3.62008	−	31.7986i	−0.176223	−	1.54793i
$423$		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
$428$	2.61332	−	4.18051i	0.126320	−	0.202073i
$429$		0			0
$430$	−4.49408	−	2.91592i	−0.216724	−	0.140618i
$431$			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	$-0.00172462\pi$
$440$	−14.9123	−	31.9609i	−0.710914	−	1.52368i
$441$		0			0
$442$	28.0145	−	3.18929i	1.33251	−	0.151699i
$443$	−16.3406	−	16.3406i	−0.776364	−	0.776364i	0.202846	−	0.979211i	$-0.434981\pi$
$443$	−16.3406	−	16.3406i	−0.776364	−	0.776364i	−0.979211	+	0.202846i	$0.934981\pi$
$444$		0			0
$445$	−2.61673	−	27.0363i	−0.124045	−	1.28164i
$446$	−16.9694	−	13.5006i	−0.803524	−	0.639270i
$447$		0			0
$448$	−2.75851	+	26.1096i	−0.130327	+	1.23356i
$449$	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
$452$	−3.62210	+	5.79425i	−0.170369	+	0.272539i
$453$		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	$0.472468\pi$
$458$	−0.834736	+	0.0950299i	−0.0390046	+	0.00444046i
$459$		0			0
$460$	25.1882	+	12.5486i	1.17441	+	0.585081i
$461$	19.2557			0.896828			0.448414	−	0.893826i	$-0.351989\pi$
$461$	19.2557			0.896828			0.448414	+	0.893826i	$0.351989\pi$
$462$		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	−0.660599	−	0.750739i	$-0.729697\pi$
$467$	1.94796	−	1.94796i	0.0901407	−	0.0901407i	0.750739	+	0.660599i	$0.229697\pi$
$468$		0			0
$469$	−8.67152			−0.400414
$470$	2.06829	−	3.18769i	0.0954029	−	0.147037i
$471$		0			0
$472$	−7.63232	−	21.5715i	−0.351306	−	0.992911i
$473$	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
$478$	−15.6788	+	1.78494i	−0.717131	+	0.0816412i
$479$	−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
$482$	28.0614	−	3.19463i	1.27816	−	0.145511i
$483$		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	$0.0475149\pi$
$488$	−2.96034	−	8.36695i	−0.134009	−	0.378754i
$489$		0			0
$490$	11.6623	−	2.48379i	0.526847	−	0.112206i
$491$	1.08218			0.0488379			0.0244189	−	0.999702i	$-0.492226\pi$
$491$	1.08218			0.0488379			0.0244189	+	0.999702i	$0.492226\pi$
$492$		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	$-0.378539\pi$
$499$	16.6371			0.744779			0.372390	+	0.928076i	$0.378539\pi$
$500$	11.0362	+	19.4475i	0.493552	+	0.869716i
$501$		0			0
$502$	28.6836	−	3.26546i	1.28021	−	0.145745i
$503$	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
$508$	−2.10354	+	3.36501i	−0.0933294	+	0.149298i
$509$		−	25.0494i		−	1.11030i	−0.831751	−	0.555148i	$-0.812662\pi$
$509$		−	25.0494i		−	1.11030i	0.831751	−	0.555148i	$-0.187338\pi$
$510$		0			0
$511$	27.2260			1.20441
$512$	−11.8384	+	19.2834i	−0.523190	+	0.852216i
$513$		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
$518$	−32.7936	+	3.73336i	−1.44087	+	0.164035i
$519$		0			0
$520$	−15.0649	−	5.47939i	−0.660640	−	0.240287i
$521$		−	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	−0.270611	−	0.962689i	$-0.587226\pi$
$523$	15.8272	−	15.8272i	0.692077	−	0.692077i	0.962689	+	0.270611i	$0.0872259\pi$
$524$	−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
$530$	10.2943	−	15.8659i	0.447157	−	0.689169i
$531$		0			0
$532$	−9.11425	+	14.5800i	−0.395153	+	0.632123i
$533$	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
$538$	−4.71913	−	41.4525i	−0.203456	−	1.78715i
$539$			21.0268i			0.905690i
$540$		0			0
$541$		−	9.09722i		−	0.391120i	−0.980692	−	0.195560i	$-0.937348\pi$
$541$		−	9.09722i		−	0.391120i	0.980692	−	0.195560i	$-0.0626524\pi$
$542$	27.1820	−	3.09452i	1.16757	−	0.132921i
$543$		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	$0.0823573\pi$
$547$	28.5935	+	28.5935i	1.22257	+	1.22257i	0.255856	+	0.966715i	$0.417643\pi$
$548$	−15.7944	−	9.87338i	−0.674703	−	0.421770i
$549$		0			0
$550$	−37.5959	+	11.8909i	−1.60309	+	0.507031i
$551$			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	$0.559460\pi$
$557$	−27.5733	+	27.5733i	−1.16832	+	1.16832i	−0.982604	+	0.185716i	$0.940540\pi$
$558$		0			0
$559$		−	4.29389i		−	0.181612i
$560$	28.5437	+	6.84877i	1.20619	+	0.289413i
$561$		0			0
$562$	−3.82763	−	33.6216i	−0.161459	−	1.41824i
$563$	−10.6071	−	10.6071i	−0.447036	−	0.447036i	0.447332	−	0.894368i	$-0.352374\pi$
$563$	−10.6071	−	10.6071i	−0.447036	−	0.447036i	−0.894368	+	0.447332i	$0.852374\pi$
$564$		0			0
$565$	5.89743	+	4.85659i	0.248107	+	0.204318i
$566$	9.84606	−	12.3759i	0.413861	−	0.520198i
$567$		0			0
$568$	6.56108	+	18.5439i	0.275297	+	0.778083i
$569$	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	$-0.807179\pi$
$571$		−	27.2118i		−	1.13878i	0.822068	−	0.569390i	$-0.192821\pi$
$572$	14.9844	−	23.9704i	0.626529	−	1.00225i
$573$		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	$0.00310809\pi$
$578$	−7.17811	−	63.0520i	−0.298570	−	2.62262i
$579$		0			0
$580$	9.01089	−	3.01813i	0.374157	−	0.125321i
$581$	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	−0.991635	−	0.129077i	$-0.958798\pi$
$587$	−20.8981	+	20.8981i	−0.862557	+	0.862557i	0.129077	+	0.991635i	$0.458798\pi$
$588$		0			0
$589$	−11.8451			−0.488068
$590$	−25.0216	+	5.32903i	−1.03012	+	0.219393i
$591$		0			0
$592$	−26.8922	−	9.27056i	−1.10526	−	0.381018i
$593$	−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
$598$	2.55135	+	22.4109i	0.104332	+	0.916448i
$599$	−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	$0.433902\pi$
$602$	0.889378	+	7.81223i	0.0362484	+	0.318403i
$603$		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	$0.401499\pi$
$608$	−12.5016	+	7.95645i	−0.507005	+	0.322677i
$609$		0			0
$610$	−9.70512	+	2.06697i	−0.392949	+	0.0836891i
$611$	3.04570			0.123216
$612$		0			0
$613$	16.9357	−	16.9357i	0.684026	−	0.684026i	−0.276878	−	0.960905i	$-0.589300\pi$
$613$	16.9357	−	16.9357i	0.684026	−	0.684026i	0.960905	+	0.276878i	$0.0892999\pi$
$614$	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	$-0.453315\pi$
$619$	7.27180			0.292278			0.146139	+	0.989264i	$0.453315\pi$
$620$	6.42242	+	19.1747i	0.257931	+	0.770075i
$621$		0			0
$622$	0.228489	+	2.00703i	0.00916157	+	0.0804746i
$623$	−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
$628$	27.2298	+	17.0219i	1.08659	+	0.679247i
$629$		−	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	$0.584882\pi$
$632$	2.37936	+	6.72489i	0.0946459	+	0.267502i
$633$		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
$638$	1.89553	+	16.6502i	0.0750446	+	0.659186i
$639$		0			0
$640$	19.6582	+	15.9234i	0.777059	+	0.629428i
$641$		−	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	$0.698000\pi$
$643$	−35.3834	+	35.3834i	−1.39538	+	1.39538i	−0.812695	+	0.582690i	$0.802000\pi$
$644$	−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
$650$	−8.26151	+	15.9049i	−0.324043	+	0.623842i
$651$		0			0
$652$	−17.5781	+	28.1196i	−0.688413	+	1.10125i
$653$	31.6390	+	31.6390i	1.23813	+	1.23813i	0.960765	+	0.277365i	$0.0894612\pi$
$653$	31.6390	+	31.6390i	1.23813	+	1.23813i	0.277365	+	0.960765i	$0.410539\pi$
$654$		0			0
$655$	1.53844	+	15.8953i	0.0601120	+	0.621082i
$656$	−3.03505	−	6.22847i	−0.118499	−	0.243181i
$657$		0			0
$658$	−5.54128	+	0.630844i	−0.216022	+	0.0245928i
$659$			20.2093i			0.787242i	0.919273	+	0.393621i	$0.128778\pi$
$659$			20.2093i			0.787242i	−0.919273	+	0.393621i	$0.871222\pi$
$660$		0			0
$661$		−	44.1882i		−	1.71872i	−0.511369	−	0.859361i	$-0.670861\pi$
$661$		−	44.1882i		−	1.71872i	0.511369	−	0.859361i	$-0.329139\pi$
$662$	5.60595	+	49.2423i	0.217882	+	1.91386i
$663$		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
$668$	18.9950	+	11.8742i	0.734940	+	0.459426i
$669$		0			0
$670$	−4.54794	+	7.00938i	−0.175702	+	0.270796i
$671$		−	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	−0.588400	−	0.808570i	$-0.700242\pi$
$677$	5.72866	−	5.72866i	0.220170	−	0.220170i	0.808570	+	0.588400i	$0.200242\pi$
$678$		0			0
$679$			19.0072i			0.729429i
$680$	−17.0046	+	46.7519i	−0.652095	+	1.79285i
$681$		0			0
$682$	−35.4307	+	4.03358i	−1.35671	+	0.154454i
$683$	33.0998	+	33.0998i	1.26653	+	1.26653i	0.947869	+	0.318659i	$0.103232\pi$
$683$	33.0998	+	33.0998i	1.26653	+	1.26653i	0.318659	+	0.947869i	$0.396768\pi$
$684$		0			0
$685$	−13.2384	+	16.0756i	−0.505815	+	0.614219i
$686$	11.7291	+	9.33149i	0.447820	+	0.356278i
$687$		0			0
$688$	−2.20847	+	6.40637i	−0.0841972	+	0.244240i
$689$	15.1591			0.577517
$690$		0			0
$691$		−	0.570988i		−	0.0217214i	−0.999941	−	0.0108607i	$-0.996543\pi$
$691$		−	0.570988i		−	0.0217214i	0.999941	−	0.0108607i	$-0.00345714\pi$
$692$	−17.3306	−	10.8337i	−0.658809	−	0.411835i
$693$		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
$698$	2.17369	−	0.247462i	0.0822755	−	0.00936659i
$699$		0			0
$700$	11.7365	−	30.6483i	0.443598	−	1.15840i
$701$	25.9738			0.981018			0.490509	−	0.871436i	$-0.336811\pi$
$701$	25.9738			0.981018			0.490509	+	0.871436i	$0.336811\pi$
$702$		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	$-0.735323\pi$
$709$	−35.8807			−1.34753			−0.673764	+	0.738947i	$0.735323\pi$
$710$	21.5097	−	4.58107i	0.807245	−	0.171925i
$711$		0			0
$712$	−32.3907	+	11.4603i	−1.21389	+	0.429492i
$713$	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
$718$	−45.2778	+	5.15462i	−1.68975	+	0.192369i
$719$	−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
$722$	17.0551	−	1.94163i	0.634726	−	0.0722599i
$723$		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	$0.0356936\pi$
$728$	7.84775	+	22.1804i	0.290857	+	0.822061i
$729$		0			0
$730$	14.2791	−	22.0073i	0.528495	−	0.814527i
$731$	−13.3255			−0.492862
$732$		0			0
$733$	−1.58667	+	1.58667i	−0.0586051	+	0.0586051i	−0.735802	−	0.677197i	$-0.763195\pi$
$733$	−1.58667	+	1.58667i	−0.0586051	+	0.0586051i	0.677197	+	0.735802i	$0.263195\pi$
$734$	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	$-0.343390\pi$
$739$	25.6836			0.944786			0.472393	+	0.881388i	$0.343390\pi$
$740$	−14.1814	+	28.4658i	−0.521320	+	1.04642i
$741$		0			0
$742$	−27.5802	+	3.13985i	−1.01250	+	0.115268i
$743$	−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
$748$	−74.3890	−	46.5021i	−2.71993	−	1.70028i
$749$			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	$0.127337\pi$
$752$	−4.54409	−	1.56649i	−0.165706	−	0.0571240i
$753$		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	0.827249	−	0.561836i	$-0.189905\pi$
$757$	7.30248	+	7.30248i	0.265413	+	0.265413i	−0.561836	+	0.827249i	$0.689905\pi$
$758$	27.7670	−	3.16112i	1.00854	−	0.114817i
$759$		0			0
$760$	7.00519	+	15.0140i	0.254105	+	0.544614i
$761$			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	$0.906082\pi$
$770$	48.5494	+	31.5006i	1.74960	+	1.13520i
$771$		0			0
$772$	−4.02643	−	2.51700i	−0.144914	−	0.0905889i
$773$	7.60986	+	7.60986i	0.273708	+	0.273708i	0.830591	−	0.556883i	$-0.188003\pi$
$773$	7.60986	+	7.60986i	0.273708	+	0.273708i	−0.556883	+	0.830591i	$0.688003\pi$
$774$		0			0
$775$	22.1889	−	4.33576i	0.797049	−	0.155745i
$776$	−7.05622	+	14.7834i	−0.253304	+	0.530693i
$777$		0			0
$778$	−4.33682	−	38.0943i	−0.155482	−	1.36575i
$779$		−	4.53753i		−	0.162574i
$780$		0			0
$781$			38.7816i			1.38771i
$782$	69.5491	−	7.91777i	2.48707	−	0.283139i
$783$		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	0.991312	−	0.131533i	$-0.0419899\pi$
$787$	24.1198	+	24.1198i	0.859779	+	0.859779i	−0.131533	+	0.991312i	$0.541990\pi$
$788$	6.65267	−	10.6422i	0.236992	−	0.379114i
$789$		0			0
$790$	7.80044	−	1.66131i	0.277527	−	0.0591069i
$791$		−	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	−0.522037	−	0.852923i	$-0.674828\pi$
$797$	9.34128	−	9.34128i	0.330885	−	0.330885i	0.852923	+	0.522037i	$0.174828\pi$
$798$		0			0
$799$		−	9.45191i		−	0.334385i
$800$	20.5063	−	19.4806i	0.725007	−	0.688742i
$801$		0			0
$802$	0.495845	+	4.35547i	0.0175089	+	0.153797i
$803$	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
$808$	1.64770	−	0.582979i	0.0579658	−	0.0205091i
$809$	−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	$0.0126160\pi$
$811$			2.25683i			0.0792481i	−0.999215	+	0.0396240i	$0.987384\pi$
$812$	−11.8267	−	7.39311i	−0.415036	−	0.259447i
$813$		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
$818$	−2.25686	−	19.8241i	−0.0789092	−	0.693132i
$819$		0			0
$820$	−7.34532	+	2.46026i	−0.256510	+	0.0859160i
$821$	−25.8885			−0.903515			−0.451757	−	0.892141i	$-0.649203\pi$
$821$	−25.8885			−0.903515			−0.451757	+	0.892141i	$0.649203\pi$
$822$		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	−0.949044	−	0.315143i	$-0.897947\pi$
$827$	−18.2295	+	18.2295i	−0.633901	+	0.633901i	0.315143	+	0.949044i	$0.397947\pi$
$828$		0			0
$829$	14.3355			0.497894			0.248947	−	0.968517i	$-0.419915\pi$
$829$	14.3355			0.497894			0.248947	+	0.968517i	$0.419915\pi$
$830$	1.69005	−	2.60475i	0.0586626	−	0.0904121i
$831$		0			0
$832$	−2.13044	+	20.1649i	−0.0738597	+	0.699091i
$833$	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
$838$	4.87493	+	42.8211i	0.168402	+	1.47923i
$839$	−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
$842$	−6.08842	−	53.4802i	−0.209821	−	1.84305i
$843$		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
$848$	−22.6170	−	7.79678i	−0.776671	−	0.267742i
$849$		0			0
$850$	49.3588	+	25.6385i	1.69299	+	0.879392i
$851$	44.7480			1.53394
$852$		0			0
$853$	28.2054	−	28.2054i	0.965735	−	0.965735i	−0.0336967	−	0.999432i	$-0.510728\pi$
$853$	28.2054	−	28.2054i	0.965735	−	0.965735i	0.999432	+	0.0336967i	$0.0107280\pi$
$854$	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	$-0.578036\pi$
$859$	−14.2270			−0.485421			−0.242710	+	0.970099i	$0.578036\pi$
$860$	6.78124	+	3.37836i	0.231239	+	0.115201i
$861$		0			0
$862$	−4.79980	−	42.1611i	−0.163482	−	1.43601i
$863$	−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
$868$	15.7322	−	25.1666i	0.533984	−	0.854210i
$869$			14.0641i			0.477090i
$870$		0			0
$871$	−6.69716			−0.226924
$872$	40.3932	−	14.2917i	1.36789	−	0.483978i
$873$		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	0.323910	−	0.946088i	$-0.395002\pi$
$877$	−18.4253	−	18.4253i	−0.622177	−	0.622177i	−0.946088	+	0.323910i	$0.895002\pi$
$878$	0.0363189	+	0.319023i	0.00122571	+	0.0107665i
$879$		0			0
$880$	26.0665	+	42.5240i	0.878700	+	1.43348i
$881$			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	$-0.401621\pi$
$883$	37.3458	−	37.3458i	1.25679	−	1.25679i	0.952618	−	0.304170i	$-0.0983790\pi$
$884$	−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
$890$	8.00178	+	37.5711i	0.268220	+	1.25939i
$891$		0			0
$892$	26.0040	+	16.2556i	0.870677	+	0.544278i
$893$	−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
$898$	−30.1680	+	3.43446i	−1.00672	+	0.114609i
$899$		−	9.60824i		−	0.320453i
$900$		0			0
$901$		−	47.0443i		−	1.56727i
$902$	−1.54516	−	13.5726i	−0.0514482	−	0.451917i
$903$		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	0.860161	−	0.510022i	$-0.170363\pi$
$907$	10.5449	+	10.5449i	0.350139	+	0.350139i	−0.510022	+	0.860161i	$0.670363\pi$
$908$	18.9173	−	30.2619i	0.627794	−	1.00428i
$909$		0			0
$910$	25.7279	−	5.47944i	0.852870	−	0.181642i
$911$		−	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	$0.833002\pi$
$920$	−37.4003	−	13.6032i	−1.23305	−	0.448484i
$921$		0			0
$922$	−27.0569	+	3.08028i	−0.891072	+	0.101443i
$923$	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
$928$	−6.45395	−	10.1408i	−0.211861	−	0.332886i
$929$	−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
$932$	7.68794	−	12.2983i	0.251827	−	0.402846i
$933$		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	$0.275851\pi$
$938$	12.1847	−	1.38716i	0.397844	−	0.0452923i
$939$		0			0
$940$	−2.39630	+	4.81000i	−0.0781587	+	0.156885i
$941$	24.7342			0.806312			0.403156	−	0.915131i	$-0.367913\pi$
$941$	24.7342			0.806312			0.403156	+	0.915131i	$0.367913\pi$
$942$		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	−0.974552	−	0.224163i	$-0.928035\pi$
$947$	−23.0920	+	23.0920i	−0.750389	+	0.750389i	0.224163	+	0.974552i	$0.428035\pi$
$948$		0			0
$949$	21.0270			0.682566
$950$	17.6611	−	5.58589i	0.573001	−	0.181230i
$951$		0			0
$952$	68.8339	−	24.3544i	2.23092	−	0.789332i
$953$	−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
$958$	28.0132	−	3.18914i	0.905065	−	0.103037i
$959$	30.5648			0.986990
$960$		0			0
$961$	−10.5542			−0.340457
$962$	−25.3270	+	2.88334i	−0.816575	+	0.0929625i
$963$		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	$0.483047\pi$
$968$	−53.5874	+	18.9600i	−1.72236	+	0.609397i
$969$		0			0
$970$	15.3639	+	9.96866i	0.493305	+	0.320074i
$971$	−40.7956			−1.30919			−0.654596	−	0.755979i	$-0.727161\pi$
$971$	−40.7956			−1.30919			−0.654596	+	0.755979i	$0.727161\pi$
$972$		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
$980$	−15.9897	+	5.35564i	−0.510774	+	0.171080i
$981$		0			0
$982$	−1.52061	+	0.173112i	−0.0485245	+	0.00552423i
$983$	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
$988$	−7.03908	+	11.2604i	−0.223943	+	0.358240i
$989$		−	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	$0.377065\pi$
$992$	21.5790	−	13.7337i	0.685134	−	0.436044i
$993$		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	0.966938	−	0.255012i	$-0.0820793\pi$
$997$	22.4793	+	22.4793i	0.711926	+	0.711926i	−0.255012	+	0.966938i	$0.582079\pi$
$998$	−23.3774	+	2.66139i	−0.739999	+	0.0842447i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.40514 + 0.159967i) q^{2} +(1.94882 - 0.449551i) q^{4} +(-0.215413 - 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-2.66645 + 0.943427i) q^{8} +O(q^{10})\)	\(q+(-1.40514 + 0.159967i) q^{2} +(1.94882 - 0.449551i) q^{4} +(-0.215413 - 2.22567i) q^{5} +(-2.32063 + 2.32063i) q^{7} +(-2.66645 + 0.943427i) q^{8} +(0.658719 + 3.09291i) q^{10} -5.57646 q^{11} +(-1.79226 + 1.79226i) q^{13} +(2.88958 - 3.63203i) q^{14} +(3.59581 - 1.75219i) q^{16} +(5.56203 + 5.56203i) q^{17} +2.61960 q^{19} +(-1.42035 - 4.24059i) q^{20} +(7.83569 - 0.892049i) q^{22} +(-4.44948 + 4.44948i) q^{23} +(-4.90719 + 0.958877i) q^{25} +(2.23167 - 2.80507i) q^{26} +(-3.47925 + 5.56573i) q^{28} +2.12491i q^{29} -4.52171 q^{31} +(-4.77231 + 3.03728i) q^{32} +(-8.70516 - 6.92568i) q^{34} +(5.66484 + 4.66506i) q^{35} +(-5.02845 - 5.02845i) q^{37} +(-3.68090 + 0.419049i) q^{38} +(2.67414 + 5.73140i) q^{40} -1.73215i q^{41} +(-1.19790 + 1.19790i) q^{43} +(-10.8675 + 2.50690i) q^{44} +(5.54036 - 6.96390i) q^{46} +(-0.849681 - 0.849681i) q^{47} -3.77064i q^{49} +(6.74189 - 2.13234i) q^{50} +(-2.68708 + 4.29850i) q^{52} +(-4.22906 - 4.22906i) q^{53} +(1.20124 + 12.4113i) q^{55} +(3.99849 - 8.37718i) q^{56} +(-0.339916 - 2.98580i) q^{58} +8.08999i q^{59} +3.13786i q^{61} +(6.35362 - 0.723323i) q^{62} +(6.21989 - 5.03120i) q^{64} +(4.37505 + 3.60290i) q^{65} +(1.86836 + 1.86836i) q^{67} +(13.3398 + 8.33899i) q^{68} +(-8.70614 - 5.64886i) q^{70} -6.95452i q^{71} +(-5.86607 - 5.86607i) q^{73} +(7.87005 + 6.26128i) q^{74} +(5.10513 - 1.17764i) q^{76} +(12.9409 - 12.9409i) q^{77} -2.52204i q^{79} +(-4.67437 - 7.62563i) q^{80} +(0.277086 + 2.43390i) q^{82} +(-0.694298 - 0.694298i) q^{83} +(11.1811 - 13.5774i) q^{85} +(1.49159 - 1.87484i) q^{86} +(14.8693 - 5.26099i) q^{88} +12.1475 q^{89} -8.31834i q^{91} +(-6.67097 + 10.6715i) q^{92} +(1.32984 + 1.05800i) q^{94} +(-0.564297 - 5.83036i) q^{95} +(4.09526 - 4.09526i) q^{97} +(0.603178 + 5.29827i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

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