LMFDB - Embedded newform 380.2.r.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(49,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("380.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-1.08802 + 0.628167i$ of defining polynomial
Character	$\chi$	$=$	380.49
Dual form			380.2.r.a.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08802 - 0.628167i) q^{3} +(1.87507 + 1.21824i) q^{5} +4.97100i q^{7} +(-0.710812 - 1.23116i) q^{9} -3.85491 q^{11} +(-2.31178 + 1.33470i) q^{13} +(-1.27486 - 2.50332i) q^{15} +(2.24337 + 1.29521i) q^{17} +(1.24479 + 4.17738i) q^{19} +(3.12262 - 5.40854i) q^{21} +(-1.88243 + 1.08682i) q^{23} +(2.03180 + 4.56857i) q^{25} +5.55504i q^{27} +(1.29432 + 2.24183i) q^{29} +7.76610 q^{31} +(4.19421 + 2.42153i) q^{33} +(-6.05586 + 9.32100i) q^{35} -2.75768i q^{37} +3.35367 q^{39} +(3.66243 - 6.34351i) q^{41} +(-1.55033 - 0.895083i) q^{43} +(0.167024 - 3.17445i) q^{45} +(-1.47942 + 0.854141i) q^{47} -17.7109 q^{49} +(-1.62722 - 2.81842i) q^{51} +(6.89738 - 3.98220i) q^{53} +(-7.22823 - 4.69619i) q^{55} +(1.26974 - 5.32700i) q^{57} +(-0.127300 + 0.220490i) q^{59} +(-1.66702 - 2.88737i) q^{61} +(6.12011 - 3.53345i) q^{63} +(-5.96073 - 0.313624i) q^{65} +(-11.4356 + 6.60237i) q^{67} +2.73082 q^{69} +(3.85760 - 6.68156i) q^{71} +(3.90558 + 2.25489i) q^{73} +(0.659195 - 6.24699i) q^{75} -19.1628i q^{77} +(5.52715 - 9.57330i) q^{79} +(1.35706 - 2.35050i) q^{81} +3.04360i q^{83} +(2.62861 + 5.16157i) q^{85} -3.25221i q^{87} +(4.76212 + 8.24824i) q^{89} +(-6.63482 - 11.4918i) q^{91} +(-8.44966 - 4.87841i) q^{93} +(-2.75497 + 9.34934i) q^{95} +(9.72851 + 5.61676i) q^{97} +(2.74011 + 4.74601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65}+ \cdots - 20 q^{99}+O(q^{100}) $ 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	−1.08802	−	0.628167i	−0.628167	−	0.362673i	0.151875	−	0.988400i	$-0.451469\pi$
$3$	−1.08802	−	0.628167i	−0.628167	−	0.362673i	−0.780042	+	0.625727i	$0.784802\pi$
$4$		0			0
$5$	1.87507	+	1.21824i	0.838558	+	0.544812i
$5$	1.87507	+	1.21824i	0.838558	+	0.544812i
$6$		0			0
$7$			4.97100i			1.87886i	0.342736	+	0.939432i	$0.388646\pi$
$7$			4.97100i			1.87886i	−0.342736	+	0.939432i	$0.611354\pi$
$8$		0			0
$9$	−0.710812	−	1.23116i	−0.236937	−	0.410387i
$10$		0			0
$11$	−3.85491			−1.16230			−0.581149	−	0.813797i	$-0.697397\pi$
$11$	−3.85491			−1.16230			−0.581149	+	0.813797i	$0.697397\pi$
$12$		0			0
$13$	−2.31178	+	1.33470i	−0.641171	+	0.370180i	−0.785066	−	0.619413i	$-0.787371\pi$
$13$	−2.31178	+	1.33470i	−0.641171	+	0.370180i	0.143894	+	0.989593i	$0.454037\pi$
$14$		0			0
$15$	−1.27486	−	2.50332i	−0.329166	−	0.646355i
$16$		0			0
$17$	2.24337	+	1.29521i	0.544097	+	0.314135i	0.746738	−	0.665118i	$-0.231619\pi$
$17$	2.24337	+	1.29521i	0.544097	+	0.314135i	−0.202641	+	0.979253i	$0.564952\pi$
$18$		0			0
$19$	1.24479	+	4.17738i	0.285574	+	0.958357i
$19$	1.24479	+	4.17738i	0.285574	+	0.958357i
$20$		0			0
$21$	3.12262	−	5.40854i	0.681412	−	1.18024i
$22$		0			0
$23$	−1.88243	+	1.08682i	−0.392514	+	0.226618i	−0.683249	−	0.730186i	$-0.739434\pi$
$23$	−1.88243	+	1.08682i	−0.392514	+	0.226618i	0.290735	+	0.956804i	$0.406100\pi$
$24$		0			0
$25$	2.03180	+	4.56857i	0.406359	+	0.913713i
$26$		0			0
$27$			5.55504i			1.06907i
$28$		0			0
$29$	1.29432	+	2.24183i	0.240350	+	0.416298i	0.960814	−	0.277194i	$-0.0894045\pi$
$29$	1.29432	+	2.24183i	0.240350	+	0.416298i	−0.720464	+	0.693492i	$0.756071\pi$
$30$		0			0
$31$	7.76610			1.39483			0.697417	−	0.716666i	$-0.254333\pi$
$31$	7.76610			1.39483			0.697417	+	0.716666i	$0.254333\pi$
$32$		0			0
$33$	4.19421	+	2.42153i	0.730117	+	0.421533i
$34$		0			0
$35$	−6.05586	+	9.32100i	−1.02363	+	1.57554i
$36$		0			0
$37$		−	2.75768i		−	0.453359i	−0.973969	−	0.226680i	$-0.927213\pi$
$37$		−	2.75768i		−	0.453359i	0.973969	−	0.226680i	$-0.0727870\pi$
$38$		0			0
$39$	3.35367			0.537017
$40$		0			0
$41$	3.66243	−	6.34351i	0.571975	−	0.990690i	−0.424388	−	0.905481i	$-0.639511\pi$
$41$	3.66243	−	6.34351i	0.571975	−	0.990690i	0.996363	−	0.0852097i	$-0.0271560\pi$
$42$		0			0
$43$	−1.55033	−	0.895083i	−0.236423	−	0.136499i	0.377109	−	0.926169i	$-0.376918\pi$
$43$	−1.55033	−	0.895083i	−0.236423	−	0.136499i	−0.613532	+	0.789670i	$0.710252\pi$
$44$		0			0
$45$	0.167024	−	3.17445i	0.0248984	−	0.473220i
$46$		0			0
$47$	−1.47942	+	0.854141i	−0.215795	+	0.124589i	−0.604002	−	0.796983i	$-0.706428\pi$
$47$	−1.47942	+	0.854141i	−0.215795	+	0.124589i	0.388207	+	0.921572i	$0.373095\pi$
$48$		0			0
$49$	−17.7109			−2.53013
$50$		0			0
$51$	−1.62722	−	2.81842i	−0.227856	−	0.394658i
$52$		0			0
$53$	6.89738	−	3.98220i	0.947428	−	0.546998i	0.0551469	−	0.998478i	$-0.482437\pi$
$53$	6.89738	−	3.98220i	0.947428	−	0.546998i	0.892281	+	0.451480i	$0.149104\pi$
$54$		0			0
$55$	−7.22823	−	4.69619i	−0.974654	−	0.633234i
$56$		0			0
$57$	1.26974	−	5.32700i	0.168182	−	0.705578i
$58$		0			0
$59$	−0.127300	+	0.220490i	−0.0165730	+	0.0287053i	−0.874193	−	0.485579i	$-0.838609\pi$
$59$	−0.127300	+	0.220490i	−0.0165730	+	0.0287053i	0.857620	+	0.514284i	$0.171942\pi$
$60$		0			0
$61$	−1.66702	−	2.88737i	−0.213441	−	0.369690i	0.739349	−	0.673323i	$-0.235134\pi$
$61$	−1.66702	−	2.88737i	−0.213441	−	0.369690i	−0.952789	+	0.303633i	$0.901800\pi$
$62$		0			0
$63$	6.12011	−	3.53345i	0.771062	−	0.445173i
$64$		0			0
$65$	−5.96073	−	0.313624i	−0.739338	−	0.0389002i
$66$		0			0
$67$	−11.4356	+	6.60237i	−1.39708	+	0.806607i	−0.994086	−	0.108593i	$-0.965365\pi$
$67$	−11.4356	+	6.60237i	−1.39708	+	0.806607i	−0.402999	+	0.915201i	$0.632032\pi$
$68$		0			0
$69$	2.73082			0.328752
$70$		0			0
$71$	3.85760	−	6.68156i	0.457813	−	0.792955i	−0.541032	−	0.841002i	$-0.681966\pi$
$71$	3.85760	−	6.68156i	0.457813	−	0.792955i	0.998845	+	0.0480468i	$0.0152997\pi$
$72$		0			0
$73$	3.90558	+	2.25489i	0.457114	+	0.263915i	0.710830	−	0.703364i	$-0.248320\pi$
$73$	3.90558	+	2.25489i	0.457114	+	0.263915i	−0.253716	+	0.967279i	$0.581653\pi$
$74$		0			0
$75$	0.659195	−	6.24699i	0.0761173	−	0.721340i
$76$		0			0
$77$		−	19.1628i		−	2.18380i
$78$		0			0
$79$	5.52715	−	9.57330i	0.621852	−	1.07708i	−0.367288	−	0.930107i	$-0.619714\pi$
$79$	5.52715	−	9.57330i	0.621852	−	1.07708i	0.989141	−	0.146973i	$-0.0469530\pi$
$80$		0			0
$81$	1.35706	−	2.35050i	0.150784	−	0.261166i
$82$		0			0
$83$			3.04360i			0.334079i	0.985950	+	0.167040i	$0.0534207\pi$
$83$			3.04360i			0.334079i	−0.985950	+	0.167040i	$0.946579\pi$
$84$		0			0
$85$	2.62861	+	5.16157i	0.285113	+	0.559851i
$86$		0			0
$87$		−	3.25221i		−	0.348673i
$88$		0			0
$89$	4.76212	+	8.24824i	0.504784	+	0.874311i	0.999985	+	0.00553277i	$0.00176114\pi$
$89$	4.76212	+	8.24824i	0.504784	+	0.874311i	−0.495201	+	0.868779i	$0.664906\pi$
$90$		0			0
$91$	−6.63482	−	11.4918i	−0.695518	−	1.20467i
$92$		0			0
$93$	−8.44966	−	4.87841i	−0.876189	−	0.505868i
$94$		0			0
$95$	−2.75497	+	9.34934i	−0.282654	+	0.959222i
$96$		0			0
$97$	9.72851	+	5.61676i	0.987780	+	0.570295i	0.904610	−	0.426240i	$-0.140162\pi$
$97$	9.72851	+	5.61676i	0.987780	+	0.570295i	0.0831703	+	0.996535i	$0.473495\pi$
$98$		0			0
$99$	2.74011	+	4.74601i	0.275392	+	0.476992i
$100$		0			0
$101$	5.45345	+	9.44564i	0.542638	+	0.939877i	0.998751	+	0.0499550i	$0.0159078\pi$
$101$	5.45345	+	9.44564i	0.542638	+	0.939877i	−0.456113	+	0.889922i	$0.650759\pi$
$102$		0			0
$103$		−	11.4532i		−	1.12852i	−0.825597	−	0.564260i	$-0.809161\pi$
$103$		−	11.4532i		−	1.12852i	0.825597	−	0.564260i	$-0.190839\pi$
$104$		0			0
$105$	12.4440	−	6.33731i	1.21441	−	0.618458i
$106$		0			0
$107$		−	18.3401i		−	1.77300i	−0.462725	−	0.886502i	$-0.653128\pi$
$107$		−	18.3401i		−	1.77300i	0.462725	−	0.886502i	$-0.346872\pi$
$108$		0			0
$109$	−6.55467	+	11.3530i	−0.627824	+	1.08742i	0.360164	+	0.932889i	$0.382721\pi$
$109$	−6.55467	+	11.3530i	−0.627824	+	1.08742i	−0.987988	+	0.154533i	$0.950613\pi$
$110$		0			0
$111$	−1.73228	+	3.00040i	−0.164421	+	0.284785i
$112$		0			0
$113$		−	0.696954i		−	0.0655640i	−0.999463	−	0.0327820i	$-0.989563\pi$
$113$		−	0.696954i		−	0.0655640i	0.999463	−	0.0327820i	$-0.0104367\pi$
$114$		0			0
$115$	−4.85370	−	0.255377i	−0.452610	−	0.0238140i
$116$		0			0
$117$	3.28647	+	1.89745i	0.303835	+	0.175419i
$118$		0			0
$119$	−6.43850	+	11.1518i	−0.590216	+	1.02228i
$120$		0			0
$121$	3.86029			0.350936
$122$		0			0
$123$	−7.96957	+	4.60124i	−0.718592	+	0.414879i
$124$		0			0
$125$	−1.75583	+	11.0416i	−0.157047	+	0.987591i
$126$		0			0
$127$	−11.9968	+	6.92636i	−1.06454	+	0.614615i	−0.926686	−	0.375837i	$-0.877355\pi$
$127$	−11.9968	+	6.92636i	−1.06454	+	0.614615i	−0.137859	+	0.990452i	$0.544022\pi$
$128$		0			0
$129$	1.12452	+	1.94773i	0.0990088	+	0.171488i
$130$		0			0
$131$	6.11533	−	10.5921i	0.534299	−	0.925433i	−0.464898	−	0.885364i	$-0.653909\pi$
$131$	6.11533	−	10.5921i	0.534299	−	0.925433i	0.999197	−	0.0400690i	$-0.0127578\pi$
$132$		0			0
$133$	−20.7658	+	6.18785i	−1.80062	+	0.536554i
$134$		0			0
$135$	−6.76736	+	10.4161i	−0.582441	+	0.896475i
$136$		0			0
$137$	7.96493	−	4.59855i	0.680490	−	0.392881i	−0.119550	−	0.992828i	$-0.538145\pi$
$137$	7.96493	−	4.59855i	0.680490	−	0.392881i	0.800039	+	0.599947i	$0.204812\pi$
$138$		0			0
$139$	−3.22178	−	5.58028i	−0.273267	−	0.473313i	0.696429	−	0.717626i	$-0.254771\pi$
$139$	−3.22178	−	5.58028i	−0.273267	−	0.473313i	−0.969697	+	0.244312i	$0.921438\pi$
$140$		0			0
$141$	2.14617			0.180741
$142$		0			0
$143$	8.91168	−	5.14516i	0.745232	−	0.430260i
$144$		0			0
$145$	−0.304135	+	5.78039i	−0.0252570	+	0.480036i
$146$		0			0
$147$	19.2698	+	11.1254i	1.58934	+	0.917608i
$148$		0			0
$149$	11.5381	−	19.9846i	0.945239	−	1.63720i	0.189966	−	0.981791i	$-0.439162\pi$
$149$	11.5381	−	19.9846i	0.945239	−	1.63720i	0.755272	−	0.655411i	$-0.227505\pi$
$150$		0			0
$151$	20.1613			1.64071			0.820353	−	0.571858i	$-0.193777\pi$
$151$	20.1613			1.64071			0.820353	+	0.571858i	$0.193777\pi$
$152$		0			0
$153$		−	3.68260i		−	0.297721i
$154$		0			0
$155$	14.5620	+	9.46096i	1.16965	+	0.759922i
$156$		0			0
$157$	−10.2803	−	5.93532i	−0.820456	−	0.473690i	0.0301179	−	0.999546i	$-0.490412\pi$
$157$	−10.2803	−	5.93532i	−0.820456	−	0.473690i	−0.850574	+	0.525856i	$0.823745\pi$
$158$		0			0
$159$	−10.0060			−0.793524
$160$		0			0
$161$	−5.40259	−	9.35757i	−0.425784	−	0.737480i
$162$		0			0
$163$			13.1763i			1.03205i	0.856575	+	0.516023i	$0.172588\pi$
$163$			13.1763i			1.03205i	−0.856575	+	0.516023i	$0.827412\pi$
$164$		0			0
$165$	4.91445	+	9.65007i	0.382589	+	0.751257i
$166$		0			0
$167$	3.17459	−	1.83285i	0.245657	−	0.141830i	−0.372117	−	0.928186i	$-0.621368\pi$
$167$	3.17459	−	1.83285i	0.245657	−	0.141830i	0.617774	+	0.786356i	$0.288035\pi$
$168$		0			0
$169$	−2.93713	+	5.08726i	−0.225933	+	0.391327i
$170$		0			0
$171$	4.25822	−	4.50186i	0.325634	−	0.344266i
$172$		0			0
$173$	0.0739334	+	0.0426855i	0.00562105	+	0.00324532i	0.502808	−	0.864398i	$-0.332300\pi$
$173$	0.0739334	+	0.0426855i	0.00562105	+	0.00324532i	−0.497187	+	0.867644i	$0.665634\pi$
$174$		0			0
$175$	−22.7104	+	10.1001i	−1.71674	+	0.763493i
$176$		0			0
$177$	0.277009	−	0.159931i	0.0208212	−	0.0120212i
$178$		0			0
$179$	16.2256			1.21276			0.606380	−	0.795175i	$-0.292621\pi$
$179$	16.2256			1.21276			0.606380	+	0.795175i	$0.292621\pi$
$180$		0			0
$181$	−10.1549	−	17.5888i	−0.754808	−	1.30737i	−0.945470	−	0.325710i	$-0.894397\pi$
$181$	−10.1549	−	17.5888i	−0.754808	−	1.30737i	0.190662	−	0.981656i	$-0.438937\pi$
$182$		0			0
$183$			4.18868i			0.309636i
$184$		0			0
$185$	3.35950	−	5.17084i	0.246996	−	0.380168i
$186$		0			0
$187$	−8.64798	−	4.99291i	−0.632403	−	0.365118i
$188$		0			0
$189$	−27.6141			−2.00863
$190$		0			0
$191$	−21.9157			−1.58576			−0.792881	−	0.609377i	$-0.791420\pi$
$191$	−21.9157			−1.58576			−0.792881	+	0.609377i	$0.791420\pi$
$192$		0			0
$193$	4.35575	+	2.51480i	0.313534	+	0.181019i	0.648507	−	0.761209i	$-0.275394\pi$
$193$	4.35575	+	2.51480i	0.313534	+	0.181019i	−0.334973	+	0.942228i	$0.608727\pi$
$194$		0			0
$195$	6.28838	+	4.08557i	0.450320	+	0.292574i
$196$		0			0
$197$			19.1189i			1.36217i	0.732205	+	0.681084i	$0.238491\pi$
$197$			19.1189i			1.36217i	−0.732205	+	0.681084i	$0.761509\pi$
$198$		0			0
$199$	9.04425	+	15.6651i	0.641130	+	1.11047i	0.985181	+	0.171518i	$0.0548672\pi$
$199$	9.04425	+	15.6651i	0.641130	+	1.11047i	−0.344051	+	0.938951i	$0.611799\pi$
$200$		0			0
$201$	16.5896			1.17014
$202$		0			0
$203$	−11.1442	+	6.43409i	−0.782167	+	0.451584i
$204$		0			0
$205$	14.5952	−	7.43284i	1.01937	−	0.519132i
$206$		0			0
$207$	2.67611	+	1.54505i	0.186002	+	0.107388i
$208$		0			0
$209$	−4.79854	−	16.1034i	−0.331922	−	1.11390i
$210$		0			0
$211$	−8.03757	+	13.9215i	−0.553329	+	0.958394i	0.444702	+	0.895678i	$0.353309\pi$
$211$	−8.03757	+	13.9215i	−0.553329	+	0.958394i	−0.998031	+	0.0627157i	$0.980024\pi$
$212$		0			0
$213$	−8.39427	+	4.84644i	−0.575166	+	0.332072i
$214$		0			0
$215$	−1.81656	−	3.56702i	−0.123888	−	0.243268i
$216$		0			0
$217$			38.6053i			2.62070i
$218$		0			0
$219$	−2.83289	−	4.90672i	−0.191429	−	0.331565i
$220$		0			0
$221$	−6.91489			−0.465146
$222$		0			0
$223$	15.0002	+	8.66036i	1.00449	+	0.579941i	0.909573	−	0.415545i	$-0.136409\pi$
$223$	15.0002	+	8.66036i	1.00449	+	0.579941i	0.0949140	+	0.995485i	$0.469742\pi$
$224$		0			0
$225$	4.18042	−	5.74886i	0.278695	−	0.383257i
$226$		0			0
$227$		−	23.7579i		−	1.57687i	−0.615120	−	0.788434i	$-0.710892\pi$
$227$		−	23.7579i		−	1.57687i	0.615120	−	0.788434i	$-0.289108\pi$
$228$		0			0
$229$	−0.732245			−0.0483881			−0.0241941	−	0.999707i	$-0.507702\pi$
$229$	−0.732245			−0.0483881			−0.0241941	+	0.999707i	$0.507702\pi$
$230$		0			0
$231$	−12.0374	+	20.8494i	−0.792004	+	1.37179i
$232$		0			0
$233$	17.2328	+	9.94933i	1.12896	+	0.651803i	0.943672	−	0.330883i	$-0.107346\pi$
$233$	17.2328	+	9.94933i	1.12896	+	0.651803i	0.185283	+	0.982685i	$0.440680\pi$
$234$		0			0
$235$	−3.81456	−	0.200703i	−0.248834	−	0.0130924i
$236$		0			0
$237$	−12.0273	+	6.94394i	−0.781255	+	0.451058i
$238$		0			0
$239$	28.9063			1.86979			0.934897	−	0.354919i	$-0.115492\pi$
$239$	28.9063			1.86979			0.934897	+	0.354919i	$0.115492\pi$
$240$		0			0
$241$	11.8979	+	20.6077i	0.766409	+	1.32746i	0.939499	+	0.342553i	$0.111292\pi$
$241$	11.8979	+	20.6077i	0.766409	+	1.32746i	−0.173090	+	0.984906i	$0.555375\pi$
$242$		0			0
$243$	11.4794	−	6.62764i	0.736404	−	0.425163i
$244$		0			0
$245$	−33.2092	−	21.5761i	−2.12166	−	1.37844i
$246$		0			0
$247$	−8.45324	−	7.99574i	−0.537867	−	0.508757i
$248$		0			0
$249$	1.91189	−	3.31150i	0.121161	−	0.209858i
$250$		0			0
$251$	3.44694	+	5.97028i	0.217569	+	0.376840i	0.954064	−	0.299602i	$-0.0968540\pi$
$251$	3.44694	+	5.97028i	0.217569	+	0.376840i	−0.736495	+	0.676443i	$0.763521\pi$
$252$		0			0
$253$	7.25659	−	4.18959i	0.456218	−	0.263397i
$254$		0			0
$255$	0.382357	−	7.26709i	0.0239441	−	0.455083i
$256$		0			0
$257$	−10.9617	+	6.32874i	−0.683772	+	0.394776i	−0.801275	−	0.598296i	$-0.795845\pi$
$257$	−10.9617	+	6.32874i	−0.683772	+	0.394776i	0.117502	+	0.993073i	$0.462511\pi$
$258$		0			0
$259$	13.7084			0.851800
$260$		0			0
$261$	1.84004	−	3.18704i	0.113896	−	0.197273i
$262$		0			0
$263$	21.6062	+	12.4743i	1.33229	+	0.769200i	0.985651	−	0.168797i	$-0.0539883\pi$
$263$	21.6062	+	12.4743i	1.33229	+	0.769200i	0.346643	+	0.937997i	$0.387322\pi$
$264$		0			0
$265$	17.7844	+	0.935723i	1.09248	+	0.0574810i
$266$		0			0
$267$		−	11.9656i		−	0.732285i
$268$		0			0
$269$	−9.54155	+	16.5265i	−0.581759	+	1.00764i	0.413512	+	0.910499i	$0.364302\pi$
$269$	−9.54155	+	16.5265i	−0.581759	+	1.00764i	−0.995271	+	0.0971371i	$0.969031\pi$
$270$		0			0
$271$	−1.48490	+	2.57192i	−0.0902012	+	0.156233i	−0.907596	−	0.419845i	$-0.862084\pi$
$271$	−1.48490	+	2.57192i	−0.0902012	+	0.156233i	0.817395	+	0.576078i	$0.195418\pi$
$272$		0			0
$273$			16.6711i			1.00898i
$274$		0			0
$275$	−7.83238	−	17.6114i	−0.472310	−	1.06201i
$276$		0			0
$277$		−	5.51535i		−	0.331385i	−0.986177	−	0.165693i	$-0.947014\pi$
$277$		−	5.51535i		−	0.331385i	0.986177	−	0.165693i	$-0.0529860\pi$
$278$		0			0
$279$	−5.52024	−	9.56133i	−0.330488	−	0.572422i
$280$		0			0
$281$	12.4800	+	21.6159i	0.744493	+	1.28950i	0.950431	+	0.310934i	$0.100642\pi$
$281$	12.4800	+	21.6159i	0.744493	+	1.28950i	−0.205939	+	0.978565i	$0.566025\pi$
$282$		0			0
$283$	−11.6526	−	6.72761i	−0.692673	−	0.399915i	0.111939	−	0.993715i	$-0.464294\pi$
$283$	−11.6526	−	6.72761i	−0.692673	−	0.399915i	−0.804613	+	0.593800i	$0.797627\pi$
$284$		0			0
$285$	8.87041	−	8.44166i	0.525438	−	0.500041i
$286$		0			0
$287$	31.5336	+	18.2060i	1.86137	+	1.07466i
$288$		0			0
$289$	−5.14486	−	8.91116i	−0.302639	−	0.524186i
$290$		0			0
$291$	−7.05653	−	12.2223i	−0.413661	−	0.716482i
$292$		0			0
$293$		−	23.7710i		−	1.38871i	−0.719630	−	0.694357i	$-0.755689\pi$
$293$		−	23.7710i		−	1.38871i	0.719630	−	0.694357i	$-0.244311\pi$
$294$		0			0
$295$	−0.507305	+	0.258353i	−0.0295364	+	0.0150419i
$296$		0			0
$297$		−	21.4141i		−	1.24257i
$298$		0			0
$299$	2.90117	−	5.02497i	0.167779	−	0.290602i
$300$		0			0
$301$	4.44946	−	7.70670i	0.256463	−	0.444207i
$302$		0			0
$303$		−	13.7027i		−	0.787200i
$304$		0			0
$305$	0.391711	−	7.44486i	0.0224293	−	0.426291i
$306$		0			0
$307$	−5.84122	−	3.37243i	−0.333376	−	0.192475i	0.323963	−	0.946070i	$-0.394985\pi$
$307$	−5.84122	−	3.37243i	−0.333376	−	0.192475i	−0.657339	+	0.753595i	$0.728318\pi$
$308$		0			0
$309$	−7.19455	+	12.4613i	−0.409284	+	0.708900i
$310$		0			0
$311$	−11.6908			−0.662924			−0.331462	−	0.943468i	$-0.607542\pi$
$311$	−11.6908			−0.662924			−0.331462	+	0.943468i	$0.607542\pi$
$312$		0			0
$313$	−15.2101	+	8.78157i	−0.859727	+	0.496364i	−0.863921	−	0.503628i	$-0.831998\pi$
$313$	−15.2101	+	8.78157i	−0.859727	+	0.496364i	0.00419387	+	0.999991i	$0.498665\pi$
$314$		0			0
$315$	15.7802	+	0.830276i	0.889115	+	0.0467807i
$316$		0			0
$317$	−28.5399	+	16.4775i	−1.60296	+	0.925469i	−0.612067	+	0.790806i	$0.709662\pi$
$317$	−28.5399	+	16.4775i	−1.60296	+	0.925469i	−0.990891	+	0.134663i	$0.957005\pi$
$318$		0			0
$319$	−4.98949	−	8.64206i	−0.279358	−	0.483862i
$320$		0			0
$321$	−11.5206	+	19.9543i	−0.643020	+	1.11374i
$322$		0			0
$323$	−2.61807	+	10.9837i	−0.145673	+	0.611148i
$324$		0			0
$325$	−10.7947	−	7.84966i	−0.598785	−	0.435421i
$326$		0			0
$327$	14.2632	−	8.23486i	0.788757	−	0.455389i
$328$		0			0
$329$	−4.24594	−	7.35418i	−0.234086	−	0.405449i
$330$		0			0
$331$	−4.54726			−0.249940			−0.124970	−	0.992161i	$-0.539883\pi$
$331$	−4.54726			−0.249940			−0.124970	+	0.992161i	$0.539883\pi$
$332$		0			0
$333$	−3.39515	+	1.96019i	−0.186053	+	0.107418i
$334$		0			0
$335$	−29.4859	−	1.55140i	−1.61099	−	0.0847619i
$336$		0			0
$337$	19.0180	+	10.9801i	1.03598	+	0.598122i	0.918691	−	0.394976i	$-0.129247\pi$
$337$	19.0180	+	10.9801i	1.03598	+	0.598122i	0.117286	+	0.993098i	$0.462581\pi$
$338$		0			0
$339$	−0.437804	+	0.758299i	−0.0237783	+	0.0411851i
$340$		0			0
$341$	−29.9376			−1.62121
$342$		0			0
$343$		−	53.2439i		−	2.87490i
$344$		0			0
$345$	5.12049	+	3.32679i	0.275678	+	0.179108i
$346$		0			0
$347$	−6.28915	−	3.63104i	−0.337619	−	0.194925i	0.321599	−	0.946876i	$-0.395780\pi$
$347$	−6.28915	−	3.63104i	−0.337619	−	0.194925i	−0.659219	+	0.751951i	$0.729113\pi$
$348$		0			0
$349$	16.0910			0.861329			0.430665	−	0.902512i	$-0.358279\pi$
$349$	16.0910			0.861329			0.430665	+	0.902512i	$0.358279\pi$
$350$		0			0
$351$	−7.41433	−	12.8420i	−0.395748	−	0.685455i
$352$		0			0
$353$		−	33.4331i		−	1.77947i	−0.456481	−	0.889733i	$-0.650890\pi$
$353$		−	33.4331i		−	1.77947i	0.456481	−	0.889733i	$-0.349110\pi$
$354$		0			0
$355$	15.3730	−	7.82894i	0.815914	−	0.415517i
$356$		0			0
$357$	14.0104	−	8.08891i	0.741509	−	0.428110i
$358$		0			0
$359$	9.97814	−	17.2826i	0.526626	−	0.912143i	−0.472893	−	0.881120i	$-0.656790\pi$
$359$	9.97814	−	17.2826i	0.526626	−	0.912143i	0.999519	−	0.0310231i	$-0.00987655\pi$
$360$		0			0
$361$	−15.9010	+	10.3999i	−0.836895	+	0.547363i
$362$		0			0
$363$	−4.20007	−	2.42491i	−0.220446	−	0.127275i
$364$		0			0
$365$	4.57626	+	8.98600i	0.239532	+	0.470349i
$366$		0			0
$367$	6.60735	−	3.81476i	0.344901	−	0.199129i	−0.317536	−	0.948246i	$-0.602856\pi$
$367$	6.60735	−	3.81476i	0.344901	−	0.199129i	0.662437	+	0.749117i	$0.269522\pi$
$368$		0			0
$369$	−10.4132			−0.542089
$370$		0			0
$371$	19.7956	+	34.2869i	1.02773	+	1.78009i
$372$		0			0
$373$			2.22095i			0.114996i	0.998346	+	0.0574982i	$0.0183123\pi$
$373$			2.22095i			0.114996i	−0.998346	+	0.0574982i	$0.981688\pi$
$374$		0			0
$375$	8.84635	−	10.9105i	0.456824	−	0.563416i
$376$		0			0
$377$	−5.98437	−	3.45508i	−0.308211	−	0.177946i
$378$		0			0
$379$	−6.92717			−0.355825			−0.177912	−	0.984046i	$-0.556934\pi$
$379$	−6.92717			−0.355825			−0.177912	+	0.984046i	$0.556934\pi$
$380$		0			0
$381$	17.4037			0.891616
$382$		0			0
$383$	−16.6386	−	9.60631i	−0.850193	−	0.490859i	0.0105227	−	0.999945i	$-0.496650\pi$
$383$	−16.6386	−	9.60631i	−0.850193	−	0.490859i	−0.860716	+	0.509085i	$0.829984\pi$
$384$		0			0
$385$	23.3448	−	35.9316i	1.18976	−	1.83124i
$386$		0			0
$387$			2.54494i			0.129367i
$388$		0			0
$389$	13.4261	+	23.2547i	0.680730	+	1.17906i	0.974758	+	0.223262i	$0.0716706\pi$
$389$	13.4261	+	23.2547i	0.680730	+	1.17906i	−0.294029	+	0.955797i	$0.594996\pi$
$390$		0			0
$391$	−5.63065			−0.284754
$392$		0			0
$393$	−13.3072	+	7.68291i	−0.671259	+	0.387551i
$394$		0			0
$395$	22.0263	−	11.2173i	1.10827	−	0.564401i
$396$		0			0
$397$	−6.42312	−	3.70839i	−0.322367	−	0.186119i	0.330080	−	0.943953i	$-0.392924\pi$
$397$	−6.42312	−	3.70839i	−0.322367	−	0.186119i	−0.652447	+	0.757834i	$0.726258\pi$
$398$		0			0
$399$	26.4805	+	6.31190i	1.32568	+	0.315990i
$400$		0			0
$401$	2.66556	−	4.61689i	0.133112	−	0.230557i	−0.791763	−	0.610829i	$-0.790836\pi$
$401$	2.66556	−	4.61689i	0.133112	−	0.230557i	0.924875	+	0.380272i	$0.124170\pi$
$402$		0			0
$403$	−17.9535	+	10.3655i	−0.894327	+	0.516340i
$404$		0			0
$405$	5.40805	−	2.75413i	0.268728	−	0.136854i
$406$		0			0
$407$			10.6306i			0.526938i
$408$		0			0
$409$	−5.70960	−	9.88933i	−0.282322	−	0.488996i	0.689634	−	0.724158i	$-0.257771\pi$
$409$	−5.70960	−	9.88933i	−0.282322	−	0.488996i	−0.971956	+	0.235162i	$0.924438\pi$
$410$		0			0
$411$	−11.5546			−0.569948
$412$		0			0
$413$	−1.09605	−	0.632807i	−0.0539333	−	0.0311384i
$414$		0			0
$415$	−3.70783	+	5.70698i	−0.182010	+	0.280145i
$416$		0			0
$417$			8.09526i			0.396426i
$418$		0			0
$419$	12.2311			0.597529			0.298765	−	0.954327i	$-0.403425\pi$
$419$	12.2311			0.597529			0.298765	+	0.954327i	$0.403425\pi$
$420$		0			0
$421$	6.63359	−	11.4897i	0.323301	−	0.559974i	−0.657866	−	0.753135i	$-0.728541\pi$
$421$	6.63359	−	11.4897i	0.323301	−	0.559974i	0.981167	+	0.193161i	$0.0618739\pi$
$422$		0			0
$423$	2.10317	+	1.21427i	0.102260	+	0.0590397i
$424$		0			0
$425$	−1.35919	+	12.8806i	−0.0659302	+	0.624801i
$426$		0			0
$427$	14.3531	−	8.28678i	0.694597	−	0.401026i
$428$		0			0
$429$	−12.9281			−0.624174
$430$		0			0
$431$	−8.19094	−	14.1871i	−0.394544	−	0.683370i	0.598499	−	0.801124i	$-0.295764\pi$
$431$	−8.19094	−	14.1871i	−0.394544	−	0.683370i	−0.993043	+	0.117754i	$0.962431\pi$
$432$		0			0
$433$	13.0054	−	7.50864i	0.624997	−	0.360842i	−0.153815	−	0.988100i	$-0.549156\pi$
$433$	13.0054	−	7.50864i	0.624997	−	0.360842i	0.778812	+	0.627257i	$0.215823\pi$
$434$		0			0
$435$	3.96196	−	6.09812i	0.189961	−	0.292383i
$436$		0			0
$437$	−6.88329	−	6.51076i	−0.329272	−	0.311452i
$438$		0			0
$439$	7.68192	−	13.3055i	0.366638	−	0.635035i	−0.622400	−	0.782700i	$-0.713842\pi$
$439$	7.68192	−	13.3055i	0.366638	−	0.635035i	0.989038	+	0.147664i	$0.0471755\pi$
$440$		0			0
$441$	12.5891	+	21.8050i	0.599481	+	1.03833i
$442$		0			0
$443$	20.9890	−	12.1180i	0.997219	−	0.575745i	0.0897946	−	0.995960i	$-0.471379\pi$
$443$	20.9890	−	12.1180i	0.997219	−	0.575745i	0.907424	+	0.420216i	$0.138046\pi$
$444$		0			0
$445$	−1.11898	+	21.2674i	−0.0530450	+	1.00817i
$446$		0			0
$447$	−25.1073	+	14.4957i	−1.18754	+	0.685624i
$448$		0			0
$449$	−16.8854			−0.796873			−0.398436	−	0.917196i	$-0.630447\pi$
$449$	−16.8854			−0.796873			−0.398436	+	0.917196i	$0.630447\pi$
$450$		0			0
$451$	−14.1183	+	24.4536i	−0.664805	+	1.15148i
$452$		0			0
$453$	−21.9359	−	12.6647i	−1.03064	−	0.595039i
$454$		0			0
$455$	1.55902	−	29.6308i	0.0730882	−	1.38912i
$456$		0			0
$457$		−	29.1914i		−	1.36551i	−0.730645	−	0.682757i	$-0.760781\pi$
$457$		−	29.1914i		−	1.36551i	0.730645	−	0.682757i	$-0.239219\pi$
$458$		0			0
$459$	−7.19495	+	12.4620i	−0.335831	+	0.581677i
$460$		0			0
$461$	−1.87254	+	3.24333i	−0.0872127	+	0.151057i	−0.906332	−	0.422566i	$-0.861129\pi$
$461$	−1.87254	+	3.24333i	−0.0872127	+	0.151057i	0.819119	+	0.573623i	$0.194463\pi$
$462$		0			0
$463$			21.4714i			0.997860i	0.866642	+	0.498930i	$0.166273\pi$
$463$			21.4714i			0.997860i	−0.866642	+	0.498930i	$0.833727\pi$
$464$		0			0
$465$	−9.90066	−	19.4411i	−0.459132	−	0.901558i
$466$		0			0
$467$			29.1079i			1.34695i	0.739209	+	0.673476i	$0.235200\pi$
$467$			29.1079i			1.34695i	−0.739209	+	0.673476i	$0.764800\pi$
$468$		0			0
$469$	−32.8204	−	56.8466i	−1.51550	−	2.62493i
$470$		0			0
$471$	7.45675	+	12.9155i	0.343589	+	0.595114i
$472$		0			0
$473$	5.97637	+	3.45046i	0.274794	+	0.158652i
$474$		0			0
$475$	−16.5555	+	14.1745i	−0.759618	+	0.650370i
$476$		0			0
$477$	−9.80547	−	5.66119i	−0.448962	−	0.259208i
$478$		0			0
$479$	−0.258348	−	0.447471i	−0.0118042	−	0.0204455i	0.860063	−	0.510188i	$-0.170424\pi$
$479$	−0.258348	−	0.447471i	−0.0118042	−	0.0204455i	−0.871867	+	0.489742i	$0.837091\pi$
$480$		0			0
$481$	3.68068	+	6.37513i	0.167825	+	0.290681i
$482$		0			0
$483$			13.5749i			0.617681i
$484$		0			0
$485$	11.3991	+	22.3835i	0.517607	+	1.01638i
$486$		0			0
$487$		−	10.6668i		−	0.483358i	−0.970356	−	0.241679i	$-0.922302\pi$
$487$		−	10.6668i		−	0.483358i	0.970356	−	0.241679i	$-0.0776981\pi$
$488$		0			0
$489$	8.27691	−	14.3360i	0.374295	−	0.648298i
$490$		0			0
$491$	−12.0852	+	20.9322i	−0.545398	+	0.944656i	0.453184	+	0.891417i	$0.350288\pi$
$491$	−12.0852	+	20.9322i	−0.545398	+	0.944656i	−0.998582	+	0.0532395i	$0.983045\pi$
$492$		0			0
$493$			6.70569i			0.302009i
$494$		0			0
$495$	−0.643861	+	12.2372i	−0.0289394	+	0.550022i
$496$		0			0
$497$	33.2141	+	19.1761i	1.48985	+	0.860168i
$498$		0			0
$499$	−2.38934	+	4.13846i	−0.106962	+	0.185263i	−0.914538	−	0.404500i	$-0.867446\pi$
$499$	−2.38934	+	4.13846i	−0.106962	+	0.185263i	0.807576	+	0.589763i	$0.200779\pi$
$500$		0			0
$501$	−4.60535			−0.205752
$502$		0			0
$503$	−15.4577	+	8.92453i	−0.689227	+	0.397925i	−0.803322	−	0.595545i	$-0.796936\pi$
$503$	−15.4577	+	8.92453i	−0.689227	+	0.397925i	0.114096	+	0.993470i	$0.463603\pi$
$504$		0			0
$505$	−1.28143	+	24.3549i	−0.0570229	+	1.08378i
$506$		0			0
$507$	6.39130	−	3.69002i	0.283847	−	0.163879i
$508$		0			0
$509$	3.57492	+	6.19194i	0.158455	+	0.274453i	0.934312	−	0.356457i	$-0.116015\pi$
$509$	3.57492	+	6.19194i	0.158455	+	0.274453i	−0.775856	+	0.630909i	$0.782682\pi$
$510$		0			0
$511$	−11.2091	+	19.4147i	−0.495860	+	0.858854i
$512$		0			0
$513$	−23.2055	+	6.91484i	−1.02455	+	0.305298i
$514$		0			0
$515$	13.9528	−	21.4757i	0.614832	−	0.946330i
$516$		0			0
$517$	5.70301	−	3.29263i	0.250818	−	0.144810i
$518$		0			0
$519$	−0.0536272	−	0.0928851i	−0.00235397	−	0.00407720i
$520$		0			0
$521$	−19.7280			−0.864301			−0.432151	−	0.901801i	$-0.642245\pi$
$521$	−19.7280			−0.864301			−0.432151	+	0.901801i	$0.642245\pi$
$522$		0			0
$523$	31.4070	−	18.1328i	1.37333	−	0.792894i	0.381986	−	0.924168i	$-0.375240\pi$
$523$	31.4070	−	18.1328i	1.37333	−	0.792894i	0.991346	+	0.131274i	$0.0419069\pi$
$524$		0			0
$525$	31.0538	+	3.27686i	1.35530	+	0.143014i
$526$		0			0
$527$	17.4222	+	10.0587i	0.758925	+	0.438166i
$528$		0			0
$529$	−9.13764	+	15.8269i	−0.397289	+	0.688124i
$530$		0			0
$531$	0.361944			0.0157070
$532$		0			0
$533$			19.5530i			0.846936i
$534$		0			0
$535$	22.3426	−	34.3890i	0.965954	−	1.48677i
$536$		0			0
$537$	−17.6538	−	10.1924i	−0.761816	−	0.439835i
$538$		0			0
$539$	68.2738			2.94076
$540$		0			0
$541$	11.4419	+	19.8180i	0.491927	+	0.852043i	0.999957	−	0.00929658i	$-0.00295924\pi$
$541$	11.4419	+	19.8180i	0.491927	+	0.852043i	−0.508029	+	0.861340i	$0.669626\pi$
$542$		0			0
$543$			25.5159i			1.09499i
$544$		0			0
$545$	−26.1212	+	13.3026i	−1.11891	+	0.569821i
$546$		0			0
$547$	−11.0134	+	6.35861i	−0.470901	+	0.271875i	−0.716617	−	0.697467i	$-0.754310\pi$
$547$	−11.0134	+	6.35861i	−0.470901	+	0.271875i	0.245716	+	0.969342i	$0.420977\pi$
$548$		0			0
$549$	−2.36988	+	4.10475i	−0.101144	+	0.175187i
$550$		0			0
$551$	−7.75383	+	8.19749i	−0.330324	+	0.349225i
$552$		0			0
$553$	47.5889	+	27.4755i	2.02369	+	1.16838i
$554$		0			0
$555$	−6.90335	+	3.51564i	−0.293031	+	0.149231i
$556$		0			0
$557$	−19.3648	+	11.1803i	−0.820511	+	0.473722i	−0.850593	−	0.525825i	$-0.823757\pi$
$557$	−19.3648	+	11.1803i	−0.820511	+	0.473722i	0.0300814	+	0.999547i	$0.490423\pi$
$558$		0			0
$559$	4.77869			0.202117
$560$		0			0
$561$	6.27277	+	10.8648i	0.264837	+	0.458710i
$562$		0			0
$563$		−	10.6447i		−	0.448619i	−0.974518	−	0.224310i	$-0.927987\pi$
$563$		−	10.6447i		−	0.448619i	0.974518	−	0.224310i	$-0.0720127\pi$
$564$		0			0
$565$	0.849056	−	1.30684i	0.0357201	−	0.0549792i
$566$		0			0
$567$	11.6843	+	6.74595i	0.490696	+	0.283303i
$568$		0			0
$569$	3.13498			0.131425			0.0657126	−	0.997839i	$-0.479068\pi$
$569$	3.13498			0.131425			0.0657126	+	0.997839i	$0.479068\pi$
$570$		0			0
$571$	1.29260			0.0540938			0.0270469	−	0.999634i	$-0.491390\pi$
$571$	1.29260			0.0540938			0.0270469	+	0.999634i	$0.491390\pi$
$572$		0			0
$573$	23.8446	+	13.7667i	0.996124	+	0.575112i
$574$		0			0
$575$	−8.78993	−	6.39181i	−0.366565	−	0.266557i
$576$		0			0
$577$		−	8.18544i		−	0.340764i	−0.985378	−	0.170382i	$-0.945500\pi$
$577$		−	8.18544i		−	0.340764i	0.985378	−	0.170382i	$-0.0545002\pi$
$578$		0			0
$579$	−3.15943	−	5.47229i	−0.131301	−	0.227420i
$580$		0			0
$581$	−15.1298			−0.627689
$582$		0			0
$583$	−26.5887	+	15.3510i	−1.10119	+	0.635774i
$584$		0			0
$585$	3.85084	+	7.56156i	0.159213	+	0.312632i
$586$		0			0
$587$	−15.7359	−	9.08512i	−0.649490	−	0.374983i	0.138771	−	0.990325i	$-0.455685\pi$
$587$	−15.7359	−	9.08512i	−0.649490	−	0.374983i	−0.788261	+	0.615341i	$0.789018\pi$
$588$		0			0
$589$	9.66715	+	32.4420i	0.398328	+	1.33675i
$590$		0			0
$591$	12.0099	−	20.8017i	0.494021	−	0.855669i
$592$		0			0
$593$	7.69621	−	4.44341i	0.316046	−	0.182469i	−0.333583	−	0.942721i	$-0.608258\pi$
$593$	7.69621	−	4.44341i	0.316046	−	0.182469i	0.649629	+	0.760252i	$0.274924\pi$
$594$		0			0
$595$	−25.6582	+	13.0668i	−1.05188	+	0.535688i
$596$		0			0
$597$		−	22.7252i		−	0.930081i
$598$		0			0
$599$	−2.18264	−	3.78044i	−0.0891801	−	0.154465i	0.817985	−	0.575240i	$-0.195091\pi$
$599$	−2.18264	−	3.78044i	−0.0891801	−	0.154465i	−0.907165	+	0.420775i	$0.861758\pi$
$600$		0			0
$601$	−4.25303			−0.173485			−0.0867424	−	0.996231i	$-0.527646\pi$
$601$	−4.25303			−0.173485			−0.0867424	+	0.996231i	$0.527646\pi$
$602$		0			0
$603$	16.2572	+	9.38608i	0.662043	+	0.382231i
$604$		0			0
$605$	7.23833	+	4.70275i	0.294280	+	0.191194i
$606$		0			0
$607$		−	23.5995i		−	0.957876i	−0.877849	−	0.478938i	$-0.841022\pi$
$607$		−	23.5995i		−	0.957876i	0.877849	−	0.478938i	$-0.158978\pi$
$608$		0			0
$609$	16.1667			0.655109
$610$		0			0
$611$	2.28005	−	3.94917i	0.0922410	−	0.159766i
$612$		0			0
$613$	17.6090	+	10.1665i	0.711220	+	0.410623i	0.811512	−	0.584335i	$-0.198645\pi$
$613$	17.6090	+	10.1665i	0.711220	+	0.410623i	−0.100293	+	0.994958i	$0.531978\pi$
$614$		0			0
$615$	−20.5489	−	1.08118i	−0.828613	−	0.0435974i
$616$		0			0
$617$	−27.0932	+	15.6422i	−1.09073	+	0.629733i	−0.933771	−	0.357872i	$-0.883502\pi$
$617$	−27.0932	+	15.6422i	−1.09073	+	0.629733i	−0.156959	+	0.987605i	$0.550169\pi$
$618$		0			0
$619$	−25.7635			−1.03552			−0.517761	−	0.855525i	$-0.673234\pi$
$619$	−25.7635			−1.03552			−0.517761	+	0.855525i	$0.673234\pi$
$620$		0			0
$621$	−6.03733	−	10.4570i	−0.242270	−	0.419624i
$622$		0			0
$623$	−41.0020	+	23.6725i	−1.64271	+	0.948420i
$624$		0			0
$625$	−16.7436	+	18.5648i	−0.669744	+	0.742592i
$626$		0			0
$627$	−4.89474	+	20.5351i	−0.195477	+	0.820092i
$628$		0			0
$629$	3.57177	−	6.18649i	0.142416	−	0.246671i
$630$		0			0
$631$	−10.6458	−	18.4391i	−0.423804	−	0.734050i	0.572504	−	0.819902i	$-0.305972\pi$
$631$	−10.6458	−	18.4391i	−0.423804	−	0.734050i	−0.996308	+	0.0858517i	$0.972639\pi$
$632$		0			0
$633$	17.4900	−	10.0979i	0.695167	−	0.401355i
$634$		0			0
$635$	−30.9328	−	1.62753i	−1.22753	−	0.0645865i
$636$		0			0
$637$	40.9436	−	23.6388i	1.62224	−	0.936603i
$638$		0			0
$639$	−10.9681			−0.433891
$640$		0			0
$641$	16.5525	−	28.6698i	0.653785	−	1.13239i	−0.328412	−	0.944535i	$-0.606513\pi$
$641$	16.5525	−	28.6698i	0.653785	−	1.13239i	0.982197	−	0.187854i	$-0.0601533\pi$
$642$		0			0
$643$	26.1024	+	15.0702i	1.02938	+	0.594311i	0.916806	−	0.399333i	$-0.130758\pi$
$643$	26.1024	+	15.0702i	1.02938	+	0.594311i	0.112570	+	0.993644i	$0.464092\pi$
$644$		0			0
$645$	−0.264236	+	5.02208i	−0.0104043	+	0.197744i
$646$		0			0
$647$			10.5273i			0.413870i	0.978355	+	0.206935i	$0.0663489\pi$
$647$			10.5273i			0.413870i	−0.978355	+	0.206935i	$0.933651\pi$
$648$		0			0
$649$	0.490728	−	0.849966i	0.0192628	−	0.0333641i
$650$		0			0
$651$	24.2506	−	42.0033i	0.950456	−	1.64624i
$652$		0			0
$653$		−	14.9511i		−	0.585081i	−0.956253	−	0.292540i	$-0.905499\pi$
$653$		−	14.9511i		−	0.585081i	0.956253	−	0.292540i	$-0.0945006\pi$
$654$		0			0
$655$	24.3703	−	12.4110i	0.952228	−	0.484937i
$656$		0			0
$657$		−	6.41120i		−	0.250125i
$658$		0			0
$659$	−16.6909	−	28.9094i	−0.650184	−	1.12615i	−0.983078	−	0.183187i	$-0.941359\pi$
$659$	−16.6909	−	28.9094i	−0.650184	−	1.12615i	0.332894	−	0.942964i	$-0.391975\pi$
$660$		0			0
$661$	−12.7433	−	22.0720i	−0.495655	−	0.858501i	0.504332	−	0.863510i	$-0.331739\pi$
$661$	−12.7433	−	22.0720i	−0.495655	−	0.858501i	−0.999987	+	0.00500935i	$0.998405\pi$
$662$		0			0
$663$	7.52353	+	4.34371i	0.292190	+	0.168696i
$664$		0			0
$665$	−46.4756	−	13.6950i	−1.80225	−	0.531069i
$666$		0			0
$667$	−4.87295	−	2.81340i	−0.188681	−	0.108935i
$668$		0			0
$669$	−10.8803	−	18.8453i	−0.420657	−	0.728600i
$670$		0			0
$671$	6.42622	+	11.1305i	0.248081	+	0.429690i
$672$		0			0
$673$		−	9.87133i		−	0.380512i	−0.981735	−	0.190256i	$-0.939068\pi$
$673$		−	9.87133i		−	0.380512i	0.981735	−	0.190256i	$-0.0609318\pi$
$674$		0			0
$675$	−25.3786	+	11.2867i	−0.976821	+	0.434425i
$676$		0			0
$677$			11.8367i			0.454922i	0.973787	+	0.227461i	$0.0730424\pi$
$677$			11.8367i			0.454922i	−0.973787	+	0.227461i	$0.926958\pi$
$678$		0			0
$679$	−27.9209	+	48.3605i	−1.07151	+	1.85590i
$680$		0			0
$681$	−14.9239	+	25.8490i	−0.571887	+	0.990537i
$682$		0			0
$683$			29.6716i			1.13535i	0.823253	+	0.567675i	$0.192157\pi$
$683$			29.6716i			1.13535i	−0.823253	+	0.567675i	$0.807843\pi$
$684$		0			0
$685$	20.5369	+	1.08055i	0.784676	+	0.0412857i
$686$		0			0
$687$	0.796696	+	0.459972i	0.0303958	+	0.0175490i
$688$		0			0
$689$	−10.6301	+	18.4119i	−0.404976	+	0.701438i
$690$		0			0
$691$	9.73437			0.370313			0.185156	−	0.982709i	$-0.440721\pi$
$691$	9.73437			0.370313			0.185156	+	0.982709i	$0.440721\pi$
$692$		0			0
$693$	−23.5924	+	13.6211i	−0.896203	+	0.517423i
$694$		0			0
$695$	0.757040	−	14.3883i	0.0287162	−	0.545780i
$696$		0			0
$697$	16.4324	−	9.48723i	0.622420	−	0.359355i
$698$		0			0
$699$	−12.4997	−	21.6501i	−0.472782	−	0.818882i
$700$		0			0
$701$	10.3345	−	17.8999i	0.390329	−	0.676070i	−0.602164	−	0.798373i	$-0.705695\pi$
$701$	10.3345	−	17.8999i	0.390329	−	0.676070i	0.992493	+	0.122303i	$0.0390279\pi$
$702$		0			0
$703$	11.5199	−	3.43272i	0.434480	−	0.129468i
$704$		0			0
$705$	4.02423	+	2.61455i	0.151561	+	0.0984696i
$706$		0			0
$707$	−46.9543	+	27.1091i	−1.76590	+	1.01954i
$708$		0			0
$709$	10.0066	+	17.3319i	0.375806	+	0.650915i	0.990447	−	0.137892i	$-0.0440326\pi$
$709$	10.0066	+	17.3319i	0.375806	+	0.650915i	−0.614641	+	0.788807i	$0.710699\pi$
$710$		0			0
$711$	−15.7150			−0.589360
$712$		0			0
$713$	−14.6191	+	8.44037i	−0.547491	+	0.316094i
$714$		0			0
$715$	22.9781	+	1.20899i	0.859331	+	0.0452136i
$716$		0			0
$717$	−31.4506	−	18.1580i	−1.17454	−	0.678123i
$718$		0			0
$719$	11.2807	−	19.5387i	0.420698	−	0.728671i	−0.575309	−	0.817936i	$-0.695118\pi$
$719$	11.2807	−	19.5387i	0.420698	−	0.728671i	0.996008	+	0.0892647i	$0.0284517\pi$
$720$		0			0
$721$	56.9341			2.12034
$722$		0			0
$723$		−	29.8954i		−	1.11182i
$724$		0			0
$725$	−7.61217	+	10.4682i	−0.282709	+	0.388777i
$726$		0			0
$727$	4.81051	+	2.77735i	0.178412	+	0.103006i	0.586546	−	0.809916i	$-0.300487\pi$
$727$	4.81051	+	2.77735i	0.178412	+	0.103006i	−0.408134	+	0.912922i	$0.633821\pi$
$728$		0			0
$729$	−24.7954			−0.918349
$730$		0			0
$731$	−2.31864	−	4.01601i	−0.0857581	−	0.148537i
$732$		0			0
$733$		−	45.3490i		−	1.67500i	−0.546436	−	0.837501i	$-0.684016\pi$
$733$		−	45.3490i		−	1.67500i	0.546436	−	0.837501i	$-0.315984\pi$
$734$		0			0
$735$	22.5788	+	44.3361i	0.832833	+	1.63536i
$736$		0			0
$737$	44.0833	−	25.4515i	1.62383	−	0.937518i
$738$		0			0
$739$	−9.01081	+	15.6072i	−0.331468	+	0.574119i	−0.982800	−	0.184674i	$-0.940877\pi$
$739$	−9.01081	+	15.6072i	−0.331468	+	0.574119i	0.651332	+	0.758793i	$0.274211\pi$
$740$		0			0
$741$	4.17461	+	14.0096i	0.153358	+	0.514654i
$742$		0			0
$743$	−36.9333	−	21.3235i	−1.35495	−	0.782282i	−0.366013	−	0.930610i	$-0.619277\pi$
$743$	−36.9333	−	21.3235i	−1.35495	−	0.782282i	−0.988938	+	0.148328i	$0.952611\pi$
$744$		0			0
$745$	45.9808	−	23.4164i	1.68461	−	0.857911i
$746$		0			0
$747$	3.74717	−	2.16343i	0.137102	−	0.0791557i
$748$		0			0
$749$	91.1687			3.33123
$750$		0			0
$751$	−2.45338	−	4.24938i	−0.0895252	−	0.155062i	0.817785	−	0.575523i	$-0.195202\pi$
$751$	−2.45338	−	4.24938i	−0.0895252	−	0.155062i	−0.907311	+	0.420461i	$0.861868\pi$
$752$		0			0
$753$		−	8.66102i		−	0.315625i
$754$		0			0
$755$	37.8040	+	24.5613i	1.37583	+	0.893876i
$756$		0			0
$757$	24.2213	+	13.9842i	0.880339	+	0.508264i	0.870770	−	0.491690i	$-0.163621\pi$
$757$	24.2213	+	13.9842i	0.880339	+	0.508264i	0.00956884	+	0.999954i	$0.496954\pi$
$758$		0			0
$759$	−10.5271			−0.382108
$760$		0			0
$761$	−11.7443			−0.425731			−0.212866	−	0.977081i	$-0.568280\pi$
$761$	−11.7443			−0.425731			−0.212866	+	0.977081i	$0.568280\pi$
$762$		0			0
$763$	−56.4359	−	32.5833i	−2.04312	−	1.17959i
$764$		0			0
$765$	4.48628	−	6.90515i	0.162202	−	0.249656i
$766$		0			0
$767$		−	0.679630i		−	0.0245400i
$768$		0			0
$769$	8.22905	+	14.2531i	0.296747	+	0.513981i	0.975390	−	0.220488i	$-0.0707648\pi$
$769$	8.22905	+	14.2531i	0.296747	+	0.513981i	−0.678643	+	0.734469i	$0.737432\pi$
$770$		0			0
$771$	15.9020			0.572698
$772$		0			0
$773$	39.7578	−	22.9542i	1.42999	−	0.825605i	0.432871	−	0.901456i	$-0.357501\pi$
$773$	39.7578	−	22.9542i	1.42999	−	0.825605i	0.997119	+	0.0758511i	$0.0241674\pi$
$774$		0			0
$775$	15.7791	+	35.4800i	0.566803	+	1.27448i
$776$		0			0
$777$	−14.9150	−	8.61118i	−0.535073	−	0.308924i
$778$		0			0
$779$	31.0582	+	7.40303i	1.11278	+	0.265241i
$780$		0			0
$781$	−14.8707	+	25.7568i	−0.532115	+	0.921650i
$782$		0			0
$783$	−12.4535	+	7.19002i	−0.445051	+	0.256950i
$784$		0			0
$785$	−12.0456	−	23.6530i	−0.429927	−	0.844211i
$786$		0			0
$787$		−	28.1763i		−	1.00438i	−0.864758	−	0.502189i	$-0.832528\pi$
$787$		−	28.1763i		−	1.00438i	0.864758	−	0.502189i	$-0.167472\pi$
$788$		0			0
$789$	−15.6719	−	27.1446i	−0.557936	−	0.966373i
$790$		0			0
$791$	3.46456			0.123186
$792$		0			0
$793$	7.70757	+	4.44997i	0.273704	+	0.158023i
$794$		0			0
$795$	−18.7619	−	12.1896i	−0.665416	−	0.432322i
$796$		0			0
$797$			1.18117i			0.0418394i	0.999781	+	0.0209197i	$0.00665943\pi$
$797$			1.18117i			0.0418394i	−0.999781	+	0.0209197i	$0.993341\pi$
$798$		0			0
$799$	−4.42517			−0.156551
$800$		0			0
$801$	6.76994	−	11.7259i	0.239204	−	0.414314i
$802$		0			0
$803$	−15.0556	−	8.69238i	−0.531302	−	0.306747i
$804$		0			0
$805$	1.26948	−	24.1278i	0.0447433	−	0.850392i
$806$		0			0
$807$	20.7628	−	11.9874i	0.730884	−	0.421976i
$808$		0			0
$809$	−4.72471			−0.166112			−0.0830561	−	0.996545i	$-0.526468\pi$
$809$	−4.72471			−0.166112			−0.0830561	+	0.996545i	$0.526468\pi$
$810$		0			0
$811$	18.7800	+	32.5280i	0.659456	+	1.14221i	0.980757	+	0.195234i	$0.0625465\pi$
$811$	18.7800	+	32.5280i	0.659456	+	1.14221i	−0.321301	+	0.946977i	$0.604120\pi$
$812$		0			0
$813$	3.23119	−	1.86553i	0.113323	−	0.0654270i
$814$		0			0
$815$	−16.0518	+	24.7065i	−0.562272	+	0.865431i
$816$		0			0
$817$	1.80927	−	7.59050i	0.0632984	−	0.265558i
$818$		0			0
$819$	−9.43222	+	16.3371i	−0.329588	+	0.570864i
$820$		0			0
$821$	−17.3453	−	30.0430i	−0.605357	−	1.04851i	−0.991995	−	0.126277i	$-0.959697\pi$
$821$	−17.3453	−	30.0430i	−0.605357	−	1.04851i	0.386638	−	0.922231i	$-0.373636\pi$
$822$		0			0
$823$	2.19067	−	1.26478i	0.0763620	−	0.0440876i	−0.461333	−	0.887227i	$-0.652629\pi$
$823$	2.19067	−	1.26478i	0.0763620	−	0.0440876i	0.537695	+	0.843140i	$0.319295\pi$
$824$		0			0
$825$	−2.54113	+	24.0816i	−0.0884709	+	0.838412i
$826$		0			0
$827$	18.0721	−	10.4339i	0.628428	−	0.362823i	−0.151715	−	0.988424i	$-0.548480\pi$
$827$	18.0721	−	10.4339i	0.628428	−	0.362823i	0.780143	+	0.625601i	$0.215146\pi$
$828$		0			0
$829$	−26.1170			−0.907081			−0.453540	−	0.891236i	$-0.649839\pi$
$829$	−26.1170			−0.907081			−0.453540	+	0.891236i	$0.649839\pi$
$830$		0			0
$831$	−3.46456	+	6.00080i	−0.120184	+	0.208165i
$832$		0			0
$833$	−39.7321	−	22.9393i	−1.37664	−	0.794801i
$834$		0			0
$835$	8.18544	+	0.430676i	0.283269	+	0.0149042i
$836$		0			0
$837$			43.1410i			1.49117i
$838$		0			0
$839$	−5.69792	+	9.86908i	−0.196714	+	0.340719i	−0.947461	−	0.319871i	$-0.896360\pi$
$839$	−5.69792	+	9.86908i	−0.196714	+	0.340719i	0.750747	+	0.660590i	$0.229694\pi$
$840$		0			0
$841$	11.1495	−	19.3114i	0.384464	−	0.665911i
$842$		0			0
$843$		−	31.3580i		−	1.08003i
$844$		0			0
$845$	−11.7048	+	5.96086i	−0.402658	+	0.205060i
$846$		0			0
$847$			19.1895i			0.659360i
$848$		0			0
$849$	8.45213	+	14.6395i	0.290077	+	0.502427i
$850$		0			0
$851$	2.99710	+	5.19113i	0.102739	+	0.177950i
$852$		0			0
$853$	5.39521	+	3.11493i	0.184728	+	0.106653i	0.589512	−	0.807759i	$-0.299320\pi$
$853$	5.39521	+	3.11493i	0.184728	+	0.106653i	−0.404784	+	0.914412i	$0.632653\pi$
$854$		0			0
$855$	13.4688	−	3.25380i	0.460624	−	0.111278i
$856$		0			0
$857$	−43.9606	−	25.3807i	−1.50166	−	0.866987i	−0.999998	−	0.00192568i	$-0.999387\pi$
$857$	−43.9606	−	25.3807i	−1.50166	−	0.866987i	−0.501667	−	0.865061i	$-0.667280\pi$
$858$		0			0
$859$	−4.07445	−	7.05715i	−0.139018	−	0.240787i	0.788107	−	0.615538i	$-0.211061\pi$
$859$	−4.07445	−	7.05715i	−0.139018	−	0.240787i	−0.927125	+	0.374751i	$0.877728\pi$
$860$		0			0
$861$	−22.8728	−	39.6168i	−0.779502	−	1.35014i
$862$		0			0
$863$			1.20591i			0.0410498i	0.999789	+	0.0205249i	$0.00653373\pi$
$863$			1.20591i			0.0410498i	−0.999789	+	0.0205249i	$0.993466\pi$
$864$		0			0
$865$	0.0866295	+	0.170107i	0.00294549	+	0.00578380i
$866$		0			0
$867$			12.9273i			0.439035i
$868$		0			0
$869$	−21.3066	+	36.9041i	−0.722778	+	1.25189i
$870$		0			0
$871$	17.6244	−	30.5264i	0.597180	−	1.03435i
$872$		0			0
$873$		−	15.9698i		−	0.540497i
$874$		0			0
$875$	−54.8879	−	8.72826i	−1.85555	−	0.295069i
$876$		0			0
$877$	14.2958	+	8.25368i	0.482735	+	0.278707i	0.721555	−	0.692357i	$-0.243428\pi$
$877$	14.2958	+	8.25368i	0.482735	+	0.278707i	−0.238821	+	0.971064i	$0.576761\pi$
$878$		0			0
$879$	−14.9321	+	25.8632i	−0.503649	+	0.872345i
$880$		0			0
$881$	−22.9549			−0.773370			−0.386685	−	0.922212i	$-0.626380\pi$
$881$	−22.9549			−0.773370			−0.386685	+	0.922212i	$0.626380\pi$
$882$		0			0
$883$	24.9234	−	14.3895i	0.838739	−	0.484246i	−0.0180963	−	0.999836i	$-0.505761\pi$
$883$	24.9234	−	14.3895i	0.838739	−	0.484246i	0.856835	+	0.515590i	$0.172427\pi$
$884$		0			0
$885$	0.714245	+	0.0375800i	0.0240091	+	0.00126324i
$886$		0			0
$887$	26.4482	−	15.2699i	0.888044	−	0.512712i	0.0147418	−	0.999891i	$-0.495307\pi$
$887$	26.4482	−	15.2699i	0.888044	−	0.512712i	0.873302	+	0.487179i	$0.161974\pi$
$888$		0			0
$889$	−34.4310	−	59.6362i	−1.15478	−	2.00013i
$890$		0			0
$891$	−5.23133	+	9.06094i	−0.175256	+	0.303553i
$892$		0			0
$893$	−5.40963	−	5.11686i	−0.181026	−	0.171229i
$894$		0			0
$895$	30.4242	+	19.7667i	1.01697	+	0.660727i
$896$		0			0
$897$	−6.31305	+	3.64484i	−0.210787	+	0.121698i
$898$		0			0
$899$	10.0518	+	17.4103i	0.335248	+	0.580666i
$900$		0			0
$901$	20.6312			0.687324
$902$		0			0
$903$	−9.68219	+	5.59001i	−0.322203	+	0.186024i
$904$		0			0
$905$	2.38616	−	45.3514i	0.0793186	−	1.50753i
$906$		0			0
$907$	−15.1811	−	8.76481i	−0.504080	−	0.291031i	0.226317	−	0.974054i	$-0.427332\pi$
$907$	−15.1811	−	8.76481i	−0.504080	−	0.291031i	−0.730397	+	0.683023i	$0.760665\pi$
$908$		0			0
$909$	7.75274	−	13.4281i	0.257142	−	0.445383i
$910$		0			0
$911$	1.25152			0.0414648			0.0207324	−	0.999785i	$-0.493400\pi$
$911$	1.25152			0.0414648			0.0207324	+	0.999785i	$0.493400\pi$
$912$		0			0
$913$		−	11.7328i		−	0.388299i
$914$		0			0
$915$	−5.10281	+	7.85408i	−0.168694	+	0.259648i
$916$		0			0
$917$	52.6532	+	30.3994i	1.73876	+	1.00388i
$918$		0			0
$919$	−17.4588			−0.575912			−0.287956	−	0.957644i	$-0.592976\pi$
$919$	−17.4588			−0.575912			−0.287956	+	0.957644i	$0.592976\pi$
$920$		0			0
$921$	4.23690	+	7.33853i	0.139611	+	0.241813i
$922$		0			0
$923$			20.5950i			0.677893i
$924$		0			0
$925$	12.5986	−	5.60303i	0.414240	−	0.184227i
$926$		0			0
$927$	−14.1008	+	8.14109i	−0.463131	+	0.267389i
$928$		0			0
$929$	28.6100	−	49.5540i	0.938665	−	1.62582i	0.170701	−	0.985323i	$-0.445397\pi$
$929$	28.6100	−	49.5540i	0.938665	−	1.62582i	0.767964	−	0.640493i	$-0.221270\pi$
$930$		0			0
$931$	−22.0463	−	73.9851i	−0.722538	−	2.42476i
$932$		0			0
$933$	12.7198	+	7.34378i	0.416428	+	0.240425i
$934$		0			0
$935$	−10.1330	−	19.8974i	−0.331386	−	0.650714i
$936$		0			0
$937$	−8.38001	+	4.83820i	−0.273763	+	0.158057i	−0.630596	−	0.776111i	$-0.717190\pi$
$937$	−8.38001	+	4.83820i	−0.273763	+	0.158057i	0.356834	+	0.934168i	$0.383856\pi$
$938$		0			0
$939$	22.0652			0.720070
$940$		0			0
$941$	−14.0336	−	24.3069i	−0.457482	−	0.792383i	0.541345	−	0.840801i	$-0.317915\pi$
$941$	−14.0336	−	24.3069i	−0.457482	−	0.792383i	−0.998827	+	0.0484179i	$0.984582\pi$
$942$		0			0
$943$			15.9216i			0.518479i
$944$		0			0
$945$	−51.7785	−	33.6406i	−1.68435	−	1.09433i
$946$		0			0
$947$	−26.2228	−	15.1397i	−0.852125	−	0.491975i	0.00924220	−	0.999957i	$-0.497058\pi$
$947$	−26.2228	−	15.1397i	−0.852125	−	0.491975i	−0.861367	+	0.507983i	$0.830391\pi$
$948$		0			0
$949$	−12.0384			−0.390784
$950$		0			0
$951$	41.4025			1.34257
$952$		0			0
$953$	5.82020	+	3.36029i	0.188535	+	0.108851i	0.591296	−	0.806454i	$-0.298616\pi$
$953$	5.82020	+	3.36029i	0.188535	+	0.108851i	−0.402762	+	0.915305i	$0.631950\pi$
$954$		0			0
$955$	−41.0935	−	26.6985i	−1.32975	−	0.863942i
$956$		0			0
$957$			12.5369i			0.405262i
$958$		0			0
$959$	22.8594	+	39.5937i	0.738169	+	1.27855i
$960$		0			0
$961$	29.3124			0.945560
$962$		0			0
$963$	−22.5796	+	13.0364i	−0.727618	+	0.420091i
$964$		0			0
$965$	5.10374	+	10.0218i	0.164295	+	0.322612i
$966$		0			0
$967$	−34.3960	−	19.8585i	−1.10610	−	0.638607i	−0.168284	−	0.985739i	$-0.553823\pi$
$967$	−34.3960	−	19.8585i	−1.10610	−	0.638607i	−0.937817	+	0.347131i	$0.887156\pi$
$968$		0			0
$969$	9.74809	−	10.3058i	0.313154	−	0.331072i
$970$		0			0
$971$	−7.09379	+	12.2868i	−0.227651	+	0.394302i	−0.957111	−	0.289720i	$-0.906438\pi$
$971$	−7.09379	+	12.2868i	−0.227651	+	0.394302i	0.729461	+	0.684023i	$0.239771\pi$
$972$		0			0
$973$	27.7396	−	16.0155i	0.889291	−	0.513432i
$974$		0			0
$975$	6.81397	+	15.3215i	0.218222	+	0.490680i
$976$		0			0
$977$		−	5.49394i		−	0.175767i	−0.996131	−	0.0878833i	$-0.971990\pi$
$977$		−	5.49394i		−	0.175767i	0.996131	−	0.0878833i	$-0.0280103\pi$
$978$		0			0
$979$	−18.3575	−	31.7962i	−0.586709	−	1.01621i
$980$		0			0
$981$	18.6365			0.595019
$982$		0			0
$983$	−32.7834	−	18.9275i	−1.04563	−	0.603695i	−0.124207	−	0.992256i	$-0.539639\pi$
$983$	−32.7834	−	18.9275i	−1.04563	−	0.603695i	−0.921423	+	0.388562i	$0.872972\pi$
$984$		0			0
$985$	−23.2914	+	35.8494i	−0.742126	+	1.14226i
$986$		0			0
$987$			10.6686i			0.339587i
$988$		0			0
$989$	3.89118			0.123732
$990$		0			0
$991$	22.6116	−	39.1645i	0.718282	−	1.24410i	−0.243398	−	0.969927i	$-0.578262\pi$
$991$	22.6116	−	39.1645i	0.718282	−	1.24410i	0.961680	−	0.274175i	$-0.0884047\pi$
$992$		0			0
$993$	4.94750	+	2.85644i	0.157004	+	0.0906464i
$994$		0			0
$995$	−2.12518	+	40.3912i	−0.0673728	+	1.28049i
$996$		0			0
$997$	42.8135	−	24.7184i	1.35592	−	0.782840i	0.366848	−	0.930281i	$-0.380437\pi$
$997$	42.8135	−	24.7184i	1.35592	−	0.782840i	0.989071	+	0.147441i	$0.0471037\pi$
$998$		0			0
$999$	15.3190			0.484672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.r.a.49.4	✓	20
3.2	odd	2		3420.2.bj.c.1189.2		20
5.2	odd	4		1900.2.i.g.201.4		20
5.3	odd	4		1900.2.i.g.201.7		20
5.4	even	2	inner	380.2.r.a.49.7	yes	20
15.14	odd	2		3420.2.bj.c.1189.9		20
19.7	even	3	inner	380.2.r.a.349.7	yes	20
57.26	odd	6		3420.2.bj.c.2629.9		20
95.7	odd	12		1900.2.i.g.501.4		20
95.64	even	6	inner	380.2.r.a.349.4	yes	20
95.83	odd	12		1900.2.i.g.501.7		20
285.254	odd	6		3420.2.bj.c.2629.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.4	✓	20	1.1	even	1	trivial
380.2.r.a.49.7	yes	20	5.4	even	2	inner
380.2.r.a.349.4	yes	20	95.64	even	6	inner
380.2.r.a.349.7	yes	20	19.7	even	3	inner
1900.2.i.g.201.4		20	5.2	odd	4
1900.2.i.g.201.7		20	5.3	odd	4
1900.2.i.g.501.4		20	95.7	odd	12
1900.2.i.g.501.7		20	95.83	odd	12
3420.2.bj.c.1189.2		20	3.2	odd	2
3420.2.bj.c.1189.9		20	15.14	odd	2
3420.2.bj.c.2629.2		20	285.254	odd	6
3420.2.bj.c.2629.9		20	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08802 - 0.628167i) q^{3} +(1.87507 + 1.21824i) q^{5} +4.97100i q^{7} +(-0.710812 - 1.23116i) q^{9} -3.85491 q^{11} +(-2.31178 + 1.33470i) q^{13} +(-1.27486 - 2.50332i) q^{15} +(2.24337 + 1.29521i) q^{17} +(1.24479 + 4.17738i) q^{19} +(3.12262 - 5.40854i) q^{21} +(-1.88243 + 1.08682i) q^{23} +(2.03180 + 4.56857i) q^{25} +5.55504i q^{27} +(1.29432 + 2.24183i) q^{29} +7.76610 q^{31} +(4.19421 + 2.42153i) q^{33} +(-6.05586 + 9.32100i) q^{35} -2.75768i q^{37} +3.35367 q^{39} +(3.66243 - 6.34351i) q^{41} +(-1.55033 - 0.895083i) q^{43} +(0.167024 - 3.17445i) q^{45} +(-1.47942 + 0.854141i) q^{47} -17.7109 q^{49} +(-1.62722 - 2.81842i) q^{51} +(6.89738 - 3.98220i) q^{53} +(-7.22823 - 4.69619i) q^{55} +(1.26974 - 5.32700i) q^{57} +(-0.127300 + 0.220490i) q^{59} +(-1.66702 - 2.88737i) q^{61} +(6.12011 - 3.53345i) q^{63} +(-5.96073 - 0.313624i) q^{65} +(-11.4356 + 6.60237i) q^{67} +2.73082 q^{69} +(3.85760 - 6.68156i) q^{71} +(3.90558 + 2.25489i) q^{73} +(0.659195 - 6.24699i) q^{75} -19.1628i q^{77} +(5.52715 - 9.57330i) q^{79} +(1.35706 - 2.35050i) q^{81} +3.04360i q^{83} +(2.62861 + 5.16157i) q^{85} -3.25221i q^{87} +(4.76212 + 8.24824i) q^{89} +(-6.63482 - 11.4918i) q^{91} +(-8.44966 - 4.87841i) q^{93} +(-2.75497 + 9.34934i) q^{95} +(9.72851 + 5.61676i) q^{97} +(2.74011 + 4.74601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65}+ \cdots - 20 q^{99}+O(q^{100}) \) 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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