LMFDB - Embedded newform 1440.2.q.j.481.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(481,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1440.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.q (of order $3$, 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.3
Root			$-0.178197 - 1.72286i$ of defining polynomial
Character	$\chi$	$=$	1440.481
Dual form			1440.2.q.j.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.178197 - 1.72286i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.178197 - 0.308646i) q^{7} +(-2.93649 - 0.614017i) q^{9} +O(q^{10})$	\(q+(0.178197 - 1.72286i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.178197 - 0.308646i) q^{7} +(-2.93649 - 0.614017i) q^{9} +(1.22474 + 2.12132i) q^{11} +(1.43649 - 2.48808i) q^{13} +(1.40294 + 1.01575i) q^{15} +0.872983 q^{17} +7.34847 q^{19} +(-0.563508 + 0.252009i) q^{21} +(-0.178197 + 0.308646i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.58114 + 4.94975i) q^{27} +(-4.37298 - 7.57423i) q^{29} +(4.38702 - 7.59855i) q^{31} +(3.87298 - 1.73205i) q^{33} +0.356394 q^{35} -6.87298 q^{37} +(-4.03063 - 2.91824i) q^{39} +(4.93649 - 8.55025i) q^{41} +(-1.22474 - 2.12132i) q^{43} +(2.00000 - 2.23607i) q^{45} +(1.75934 + 3.04726i) q^{47} +(3.43649 - 5.95218i) q^{49} +(0.155563 - 1.50403i) q^{51} -4.00000 q^{53} -2.44949 q^{55} +(1.30948 - 12.6604i) q^{57} +(0.356394 - 0.617292i) q^{59} +(0.936492 + 1.62205i) q^{61} +(0.333760 + 1.01575i) q^{63} +(1.43649 + 2.48808i) q^{65} +(-3.13964 + 5.43802i) q^{67} +(0.500000 + 0.362008i) q^{69} -3.16228 q^{71} +5.74597 q^{73} +(-1.58114 + 0.707107i) q^{75} +(0.436492 - 0.756026i) q^{77} +(-6.32456 - 10.9545i) q^{79} +(8.24597 + 3.60611i) q^{81} +(6.50275 + 11.2631i) q^{83} +(-0.436492 + 0.756026i) q^{85} +(-13.8286 + 6.18433i) q^{87} -1.25403 q^{89} -1.02391 q^{91} +(-12.3095 - 8.91226i) q^{93} +(-3.67423 + 6.36396i) q^{95} +(-6.87298 - 11.9044i) q^{97} +(-2.29393 - 6.98125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^9	$ 8 q - 4 q^{5} - 8 q^{9} - 4 q^{13} - 24 q^{17} - 20 q^{21} - 4 q^{25} - 4 q^{29} - 24 q^{37} + 24 q^{41} + 16 q^{45} + 12 q^{49} - 32 q^{53} - 36 q^{57} - 8 q^{61} - 4 q^{65} + 4 q^{69} - 16 q^{73} - 12 q^{77} + 4 q^{81} + 12 q^{85} - 72 q^{89} - 52 q^{93} - 24 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^9 - 4 * q^13 - 24 * q^17 - 20 * q^21 - 4 * q^25 - 4 * q^29 - 24 * q^37 + 24 * q^41 + 16 * q^45 + 12 * q^49 - 32 * q^53 - 36 * q^57 - 8 * q^61 - 4 * q^65 + 4 * q^69 - 16 * q^73 - 12 * q^77 + 4 * q^81 + 12 * q^85 - 72 * q^89 - 52 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.178197	−	1.72286i	0.102882	−	0.994694i
$3$	0.178197	−	1.72286i	0.102882	−	0.994694i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.178197	−	0.308646i	−0.0673521	−	0.116657i	0.830383	−	0.557193i	$-0.188122\pi$
$7$	−0.178197	−	0.308646i	−0.0673521	−	0.116657i	−0.897735	+	0.440536i	$0.854788\pi$
$8$		0			0
$9$	−2.93649	−	0.614017i	−0.978831	−	0.204672i
$10$		0			0
$11$	1.22474	+	2.12132i	0.369274	+	0.639602i	0.989452	−	0.144859i	$-0.0462729\pi$
$11$	1.22474	+	2.12132i	0.369274	+	0.639602i	−0.620178	+	0.784461i	$0.712940\pi$
$12$		0			0
$13$	1.43649	−	2.48808i	0.398411	−	0.690068i	−0.595119	−	0.803638i	$-0.702895\pi$
$13$	1.43649	−	2.48808i	0.398411	−	0.690068i	0.993530	+	0.113569i	$0.0362284\pi$
$14$		0			0
$15$	1.40294	+	1.01575i	0.362238	+	0.262266i
$16$		0			0
$17$	0.872983			0.211730			0.105865	−	0.994381i	$-0.466239\pi$
$17$	0.872983			0.211730			0.105865	+	0.994381i	$0.466239\pi$
$18$		0			0
$19$	7.34847			1.68585			0.842927	−	0.538028i	$-0.180830\pi$
$19$	7.34847			1.68585			0.842927	+	0.538028i	$0.180830\pi$
$20$		0			0
$21$	−0.563508	+	0.252009i	−0.122968	+	0.0549928i
$22$		0			0
$23$	−0.178197	+	0.308646i	−0.0371566	+	0.0643572i	−0.884006	−	0.467476i	$-0.845163\pi$
$23$	−0.178197	+	0.308646i	−0.0371566	+	0.0643572i	0.846849	+	0.531833i	$0.178497\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.58114	+	4.94975i	−0.304290	+	0.952579i
$28$		0			0
$29$	−4.37298	−	7.57423i	−0.812043	−	1.40650i	−0.911432	−	0.411450i	$-0.865022\pi$
$29$	−4.37298	−	7.57423i	−0.812043	−	1.40650i	0.0993895	−	0.995049i	$-0.468311\pi$
$30$		0			0
$31$	4.38702	−	7.59855i	0.787933	−	1.36474i	−0.139299	−	0.990250i	$-0.544485\pi$
$31$	4.38702	−	7.59855i	0.787933	−	1.36474i	0.927231	−	0.374489i	$-0.122182\pi$
$32$		0			0
$33$	3.87298	−	1.73205i	0.674200	−	0.301511i
$34$		0			0
$35$	0.356394			0.0602416
$36$		0			0
$37$	−6.87298			−1.12991			−0.564956	−	0.825121i	$-0.691107\pi$
$37$	−6.87298			−1.12991			−0.564956	+	0.825121i	$0.691107\pi$
$38$		0			0
$39$	−4.03063	−	2.91824i	−0.645417	−	0.467293i
$40$		0			0
$41$	4.93649	−	8.55025i	0.770950	−	1.33533i	−0.166092	−	0.986110i	$-0.553115\pi$
$41$	4.93649	−	8.55025i	0.770950	−	1.33533i	0.937043	−	0.349215i	$-0.113552\pi$
$42$		0			0
$43$	−1.22474	−	2.12132i	−0.186772	−	0.323498i	0.757400	−	0.652951i	$-0.226469\pi$
$43$	−1.22474	−	2.12132i	−0.186772	−	0.323498i	−0.944172	+	0.329452i	$0.893136\pi$
$44$		0			0
$45$	2.00000	−	2.23607i	0.298142	−	0.333333i
$46$		0			0
$47$	1.75934	+	3.04726i	0.256626	+	0.444488i	0.965336	−	0.261011i	$-0.0840560\pi$
$47$	1.75934	+	3.04726i	0.256626	+	0.444488i	−0.708710	+	0.705500i	$0.750723\pi$
$48$		0			0
$49$	3.43649	−	5.95218i	0.490927	−	0.850311i
$50$		0			0
$51$	0.155563	−	1.50403i	0.0217832	−	0.210606i
$52$		0			0
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	−2.44949			−0.330289
$56$		0			0
$57$	1.30948	−	12.6604i	0.173444	−	1.67691i
$58$		0			0
$59$	0.356394	−	0.617292i	0.0463985	−	0.0803646i	−0.841893	−	0.539644i	$-0.818559\pi$
$59$	0.356394	−	0.617292i	0.0463985	−	0.0803646i	0.888292	+	0.459279i	$0.151892\pi$
$60$		0			0
$61$	0.936492	+	1.62205i	0.119905	+	0.207682i	0.919730	−	0.392551i	$-0.128408\pi$
$61$	0.936492	+	1.62205i	0.119905	+	0.207682i	−0.799825	+	0.600234i	$0.795074\pi$
$62$		0			0
$63$	0.333760	+	1.01575i	0.0420498	+	0.127973i
$64$		0			0
$65$	1.43649	+	2.48808i	0.178175	+	0.308608i
$66$		0			0
$67$	−3.13964	+	5.43802i	−0.383569	+	0.664360i	−0.991569	−	0.129576i	$-0.958638\pi$
$67$	−3.13964	+	5.43802i	−0.383569	+	0.664360i	0.608001	+	0.793936i	$0.291972\pi$
$68$		0			0
$69$	0.500000	+	0.362008i	0.0601929	+	0.0435807i
$70$		0			0
$71$	−3.16228			−0.375293			−0.187647	−	0.982237i	$-0.560086\pi$
$71$	−3.16228			−0.375293			−0.187647	+	0.982237i	$0.560086\pi$
$72$		0			0
$73$	5.74597			0.672515			0.336257	−	0.941770i	$-0.390839\pi$
$73$	5.74597			0.672515			0.336257	+	0.941770i	$0.390839\pi$
$74$		0			0
$75$	−1.58114	+	0.707107i	−0.182574	+	0.0816497i
$76$		0			0
$77$	0.436492	−	0.756026i	0.0497428	−	0.0861571i
$78$		0			0
$79$	−6.32456	−	10.9545i	−0.711568	−	1.23247i	−0.964268	−	0.264927i	$-0.914652\pi$
$79$	−6.32456	−	10.9545i	−0.711568	−	1.23247i	0.252700	−	0.967545i	$-0.418681\pi$
$80$		0			0
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$		0			0
$83$	6.50275	+	11.2631i	0.713770	+	1.23629i	0.963432	+	0.267953i	$0.0863471\pi$
$83$	6.50275	+	11.2631i	0.713770	+	1.23629i	−0.249662	+	0.968333i	$0.580320\pi$
$84$		0			0
$85$	−0.436492	+	0.756026i	−0.0473442	+	0.0820025i
$86$		0			0
$87$	−13.8286	+	6.18433i	−1.48258	+	0.663030i
$88$		0			0
$89$	−1.25403			−0.132927			−0.0664636	−	0.997789i	$-0.521172\pi$
$89$	−1.25403			−0.132927			−0.0664636	+	0.997789i	$0.521172\pi$
$90$		0			0
$91$	−1.02391			−0.107335
$92$		0			0
$93$	−12.3095	−	8.91226i	−1.27643	−	0.924159i
$94$		0			0
$95$	−3.67423	+	6.36396i	−0.376969	+	0.652929i
$96$		0			0
$97$	−6.87298	−	11.9044i	−0.697846	−	1.20870i	−0.969212	−	0.246228i	$-0.920809\pi$
$97$	−6.87298	−	11.9044i	−0.697846	−	1.20870i	0.271366	−	0.962476i	$-0.412525\pi$
$98$		0			0
$99$	−2.29393	−	6.98125i	−0.230548	−	0.701642i
$100$		0			0
$101$	6.87298	+	11.9044i	0.683887	+	1.18453i	0.973785	+	0.227470i	$0.0730454\pi$
$101$	6.87298	+	11.9044i	0.683887	+	1.18453i	−0.289898	+	0.957058i	$0.593621\pi$
$102$		0			0
$103$	6.83651	−	11.8412i	0.673622	−	1.16675i	−0.303248	−	0.952912i	$-0.598071\pi$
$103$	6.83651	−	11.8412i	0.673622	−	1.16675i	0.976870	−	0.213835i	$-0.0685955\pi$
$104$		0			0
$105$	0.0635083	−	0.614017i	0.00619778	−	0.0599219i
$106$		0			0
$107$	1.78197			0.172270			0.0861348	−	0.996283i	$-0.472548\pi$
$107$	1.78197			0.172270			0.0861348	+	0.996283i	$0.472548\pi$
$108$		0			0
$109$	−8.12702			−0.778427			−0.389214	−	0.921148i	$-0.627253\pi$
$109$	−8.12702			−0.778427			−0.389214	+	0.921148i	$0.627253\pi$
$110$		0			0
$111$	−1.22474	+	11.8412i	−0.116248	+	1.12392i
$112$		0			0
$113$	2.12702	−	3.68410i	0.200093	−	0.346571i	−0.748465	−	0.663174i	$-0.769209\pi$
$113$	2.12702	−	3.68410i	0.200093	−	0.346571i	0.948558	+	0.316603i	$0.102542\pi$
$114$		0			0
$115$	−0.178197	−	0.308646i	−0.0166170	−	0.0287814i
$116$		0			0
$117$	−5.74597	+	6.42419i	−0.531215	+	0.593916i
$118$		0			0
$119$	−0.155563	−	0.269443i	−0.0142604	−	0.0246998i
$120$		0			0
$121$	2.50000	−	4.33013i	0.227273	−	0.393648i
$122$		0			0
$123$	−13.8512	−	10.0285i	−1.24892	−	0.904241i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	17.5028			1.55312			0.776562	−	0.630041i	$-0.216962\pi$
$127$	17.5028			1.55312			0.776562	+	0.630041i	$0.216962\pi$
$128$		0			0
$129$	−3.87298	+	1.73205i	−0.340997	+	0.152499i
$130$		0			0
$131$	−2.44949	+	4.24264i	−0.214013	+	0.370681i	−0.952967	−	0.303075i	$-0.901987\pi$
$131$	−2.44949	+	4.24264i	−0.214013	+	0.370681i	0.738954	+	0.673756i	$0.235320\pi$
$132$		0			0
$133$	−1.30948	−	2.26808i	−0.113546	−	0.196667i
$134$		0			0
$135$	−3.49604	−	3.84418i	−0.300891	−	0.330854i
$136$		0			0
$137$	−5.87298	−	10.1723i	−0.501763	−	0.869079i	−0.999998	−	0.00203674i	$-0.999352\pi$
$137$	−5.87298	−	10.1723i	−0.501763	−	0.869079i	0.498235	−	0.867042i	$-0.333982\pi$
$138$		0			0
$139$	2.44949	−	4.24264i	0.207763	−	0.359856i	−0.743247	−	0.669018i	$-0.766715\pi$
$139$	2.44949	−	4.24264i	0.207763	−	0.359856i	0.951010	+	0.309162i	$0.100048\pi$
$140$		0			0
$141$	5.56351	−	2.48808i	0.468532	−	0.209534i
$142$		0			0
$143$	7.03734			0.588492
$144$		0			0
$145$	8.74597			0.726313
$146$		0			0
$147$	−9.64240	−	6.98125i	−0.795291	−	0.575804i
$148$		0			0
$149$	0.936492	−	1.62205i	0.0767204	−	0.132884i	−0.825113	−	0.564968i	$-0.808888\pi$
$149$	0.936492	−	1.62205i	0.0767204	−	0.132884i	0.901833	+	0.432085i	$0.142222\pi$
$150$		0			0
$151$	2.96145	+	5.12938i	0.240999	+	0.417423i	0.960999	−	0.276551i	$-0.0891916\pi$
$151$	2.96145	+	5.12938i	0.240999	+	0.417423i	−0.720000	+	0.693974i	$0.755858\pi$
$152$		0			0
$153$	−2.56351	−	0.536026i	−0.207247	−	0.0433352i
$154$		0			0
$155$	4.38702	+	7.59855i	0.352374	+	0.610330i
$156$		0			0
$157$	0.872983	−	1.51205i	0.0696717	−	0.120675i	−0.829085	−	0.559122i	$-0.811138\pi$
$157$	0.872983	−	1.51205i	0.0696717	−	0.120675i	0.898757	+	0.438448i	$0.144472\pi$
$158$		0			0
$159$	−0.712788	+	6.89144i	−0.0565278	+	0.546527i
$160$		0			0
$161$	0.127017			0.0100103
$162$		0			0
$163$	−10.1996			−0.798896			−0.399448	−	0.916756i	$-0.630798\pi$
$163$	−10.1996			−0.798896			−0.399448	+	0.916756i	$0.630798\pi$
$164$		0			0
$165$	−0.436492	+	4.22013i	−0.0339808	+	0.328536i
$166$		0			0
$167$	−9.10781	+	15.7752i	−0.704783	+	1.22072i	0.261987	+	0.965071i	$0.415622\pi$
$167$	−9.10781	+	15.7752i	−0.704783	+	1.22072i	−0.966770	+	0.255649i	$0.917711\pi$
$168$		0			0
$169$	2.37298	+	4.11013i	0.182537	+	0.316164i
$170$		0			0
$171$	−21.5787	−	4.51208i	−1.65017	−	0.345048i
$172$		0			0
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$	−0.178197	+	0.308646i	−0.0134704	+	0.0233315i
$176$		0			0
$177$	−1.00000	−	0.724016i	−0.0751646	−	0.0544204i
$178$		0			0
$179$	24.1838			1.80758			0.903790	−	0.427976i	$-0.140773\pi$
$179$	24.1838			1.80758			0.903790	+	0.427976i	$0.140773\pi$
$180$		0			0
$181$	−0.745967			−0.0554473			−0.0277236	−	0.999616i	$-0.508826\pi$
$181$	−0.745967			−0.0554473			−0.0277236	+	0.999616i	$0.508826\pi$
$182$		0			0
$183$	2.96145	−	1.32440i	0.218916	−	0.0979024i
$184$		0			0
$185$	3.43649	−	5.95218i	0.252656	−	0.437613i
$186$		0			0
$187$	1.06918	+	1.85188i	0.0781863	+	0.135423i
$188$		0			0
$189$	1.80948	−	0.394018i	0.131620	−	0.0286606i
$190$		0			0
$191$	−1.58114	−	2.73861i	−0.114407	−	0.198159i	0.803135	−	0.595797i	$-0.203164\pi$
$191$	−1.58114	−	2.73861i	−0.114407	−	0.198159i	−0.917543	+	0.397637i	$0.869830\pi$
$192$		0			0
$193$	−8.30948	+	14.3924i	−0.598129	+	1.03599i	0.394968	+	0.918695i	$0.370756\pi$
$193$	−8.30948	+	14.3924i	−0.598129	+	1.03599i	−0.993097	+	0.117295i	$0.962578\pi$
$194$		0			0
$195$	4.54259	−	2.03151i	0.325301	−	0.145479i
$196$		0			0
$197$	−23.2379			−1.65563			−0.827816	−	0.561000i	$-0.810417\pi$
$197$	−23.2379			−1.65563			−0.827816	+	0.561000i	$0.810417\pi$
$198$		0			0
$199$	10.1996			0.723032			0.361516	−	0.932366i	$-0.382259\pi$
$199$	10.1996			0.723032			0.361516	+	0.932366i	$0.382259\pi$
$200$		0			0
$201$	8.80948	+	6.37820i	0.621372	+	0.449884i
$202$		0			0
$203$	−1.55850	+	2.69941i	−0.109386	+	0.189461i
$204$		0			0
$205$	4.93649	+	8.55025i	0.344780	+	0.597176i
$206$		0			0
$207$	0.712788	−	0.796921i	0.0495422	−	0.0553898i
$208$		0			0
$209$	9.00000	+	15.5885i	0.622543	+	1.07828i
$210$		0			0
$211$	12.4483	−	21.5611i	0.856975	−	1.48432i	−0.0178258	−	0.999841i	$-0.505674\pi$
$211$	12.4483	−	21.5611i	0.856975	−	1.48432i	0.874801	−	0.484483i	$-0.160992\pi$
$212$		0			0
$213$	−0.563508	+	5.44816i	−0.0386110	+	0.373302i
$214$		0			0
$215$	2.44949			0.167054
$216$		0			0
$217$	−3.12702			−0.212276
$218$		0			0
$219$	1.02391	−	9.89949i	0.0691897	−	0.668946i
$220$		0			0
$221$	1.25403	−	2.17205i	0.0843554	−	0.146108i
$222$		0			0
$223$	−5.99080	−	10.3764i	−0.401173	−	0.694853i	0.592694	−	0.805427i	$-0.298064\pi$
$223$	−5.99080	−	10.3764i	−0.401173	−	0.694853i	−0.993868	+	0.110575i	$0.964731\pi$
$224$		0			0
$225$	0.936492	+	2.85008i	0.0624328	+	0.190006i
$226$		0			0
$227$	6.48012	+	11.2239i	0.430101	+	0.744956i	0.996882	−	0.0789125i	$-0.0251448\pi$
$227$	6.48012	+	11.2239i	0.430101	+	0.744956i	−0.566781	+	0.823869i	$0.691811\pi$
$228$		0			0
$229$	1.62702	−	2.81808i	0.107516	−	0.186224i	−0.807247	−	0.590213i	$-0.799044\pi$
$229$	1.62702	−	2.81808i	0.107516	−	0.186224i	0.914763	+	0.403990i	$0.132377\pi$
$230$		0			0
$231$	−1.22474	−	0.886735i	−0.0805823	−	0.0583429i
$232$		0			0
$233$	−6.87298			−0.450264			−0.225132	−	0.974328i	$-0.572281\pi$
$233$	−6.87298			−0.450264			−0.225132	+	0.974328i	$0.572281\pi$
$234$		0			0
$235$	−3.51867			−0.229533
$236$		0			0
$237$	−20.0000	+	8.94427i	−1.29914	+	0.580993i
$238$		0			0
$239$	−3.51867	+	6.09452i	−0.227604	+	0.394222i	−0.957097	−	0.289766i	$-0.906422\pi$
$239$	−3.51867	+	6.09452i	−0.227604	+	0.394222i	0.729494	+	0.683988i	$0.239756\pi$
$240$		0			0
$241$	13.6825	+	23.6987i	0.881365	+	1.52657i	0.849824	+	0.527066i	$0.176708\pi$
$241$	13.6825	+	23.6987i	0.881365	+	1.52657i	0.0315402	+	0.999502i	$0.489959\pi$
$242$		0			0
$243$	7.68223	−	13.5640i	0.492815	−	0.870134i
$244$		0			0
$245$	3.43649	+	5.95218i	0.219549	+	0.380271i
$246$		0			0
$247$	10.5560	−	18.2836i	0.671663	−	1.16335i
$248$		0			0
$249$	20.5635	−	9.19628i	1.30316	−	0.582791i
$250$		0			0
$251$	10.9124			0.688785			0.344393	−	0.938826i	$-0.388085\pi$
$251$	10.9124			0.688785			0.344393	+	0.938826i	$0.388085\pi$
$252$		0			0
$253$	−0.872983			−0.0548840
$254$		0			0
$255$	1.22474	+	0.886735i	0.0766965	+	0.0555295i
$256$		0			0
$257$	6.74597	−	11.6844i	0.420802	−	0.728850i	−0.575216	−	0.818001i	$-0.695082\pi$
$257$	6.74597	−	11.6844i	0.420802	−	0.728850i	0.996018	+	0.0891512i	$0.0284154\pi$
$258$		0			0
$259$	1.22474	+	2.12132i	0.0761019	+	0.131812i
$260$		0			0
$261$	8.19052	+	24.9267i	0.506981	+	1.54293i
$262$		0			0
$263$	14.8978	+	25.8037i	0.918636	+	1.59112i	0.801489	+	0.598009i	$0.204041\pi$
$263$	14.8978	+	25.8037i	0.918636	+	1.59112i	0.117147	+	0.993115i	$0.462625\pi$
$264$		0			0
$265$	2.00000	−	3.46410i	0.122859	−	0.212798i
$266$		0			0
$267$	−0.223465	+	2.16052i	−0.0136758	+	0.132222i
$268$		0			0
$269$	−16.1270			−0.983282			−0.491641	−	0.870798i	$-0.663603\pi$
$269$	−16.1270			−0.983282			−0.491641	+	0.870798i	$0.663603\pi$
$270$		0			0
$271$	19.9976			1.21477			0.607383	−	0.794409i	$-0.292219\pi$
$271$	19.9976			1.21477			0.607383	+	0.794409i	$0.292219\pi$
$272$		0			0
$273$	−0.182458	+	1.76406i	−0.0110429	+	0.106766i
$274$		0			0
$275$	1.22474	−	2.12132i	0.0738549	−	0.127920i
$276$		0			0
$277$	10.4365	+	18.0765i	0.627068	+	1.08611i	0.988137	+	0.153575i	$0.0490785\pi$
$277$	10.4365	+	18.0765i	0.627068	+	1.08611i	−0.361069	+	0.932539i	$0.617588\pi$
$278$		0			0
$279$	−17.5481	+	19.6194i	−1.05058	+	1.17458i
$280$		0			0
$281$	13.6825	+	23.6987i	0.816227	+	1.41375i	0.908443	+	0.418008i	$0.137271\pi$
$281$	13.6825	+	23.6987i	0.816227	+	1.41375i	−0.0922164	+	0.995739i	$0.529395\pi$
$282$		0			0
$283$	−9.66503	+	16.7403i	−0.574526	+	0.995109i	0.421567	+	0.906797i	$0.361480\pi$
$283$	−9.66503	+	16.7403i	−0.574526	+	0.995109i	−0.996093	+	0.0883114i	$0.971853\pi$
$284$		0			0
$285$	10.3095	+	7.46423i	0.610681	+	0.442143i
$286$		0			0
$287$	−3.51867			−0.207701
$288$		0			0
$289$	−16.2379			−0.955171
$290$		0			0
$291$	−21.7343	+	9.71987i	−1.27409	+	0.569789i
$292$		0			0
$293$	0.436492	−	0.756026i	0.0255001	−	0.0441675i	−0.852994	−	0.521921i	$-0.825216\pi$
$293$	0.436492	−	0.756026i	0.0255001	−	0.0441675i	0.878494	+	0.477754i	$0.158549\pi$
$294$		0			0
$295$	0.356394	+	0.617292i	0.0207501	+	0.0359402i
$296$		0			0
$297$	−12.4365	+	2.70808i	−0.721638	+	0.157138i
$298$		0			0
$299$	0.511957	+	0.886735i	0.0296072	+	0.0512812i
$300$		0			0
$301$	−0.436492	+	0.756026i	−0.0251590	+	0.0435766i
$302$		0			0
$303$	21.7343	−	9.71987i	1.24860	−	0.558392i
$304$		0			0
$305$	−1.87298			−0.107247
$306$		0			0
$307$	−5.25537			−0.299940			−0.149970	−	0.988691i	$-0.547918\pi$
$307$	−5.25537			−0.299940			−0.149970	+	0.988691i	$0.547918\pi$
$308$		0			0
$309$	−19.1825	−	13.8884i	−1.09125	−	0.790084i
$310$		0			0
$311$	10.6663	−	18.4746i	0.604831	−	1.04760i	−0.387247	−	0.921976i	$-0.626574\pi$
$311$	10.6663	−	18.4746i	0.604831	−	1.04760i	0.992078	−	0.125622i	$-0.0400927\pi$
$312$		0			0
$313$	−11.3095	−	19.5886i	−0.639249	−	1.10721i	−0.985598	−	0.169106i	$-0.945912\pi$
$313$	−11.3095	−	19.5886i	−0.639249	−	1.10721i	0.346348	−	0.938106i	$-0.387421\pi$
$314$		0			0
$315$	−1.04655	−	0.218832i	−0.0589663	−	0.0123298i
$316$		0			0
$317$	5.56351	+	9.63628i	0.312478	+	0.541227i	0.978898	−	0.204349i	$-0.0655077\pi$
$317$	5.56351	+	9.63628i	0.312478	+	0.541227i	−0.666420	+	0.745576i	$0.732174\pi$
$318$		0			0
$319$	10.7116	−	18.5530i	0.599733	−	1.03877i
$320$		0			0
$321$	0.317542	−	3.07008i	0.0177234	−	0.171355i
$322$		0			0
$323$	6.41509			0.356945
$324$		0			0
$325$	−2.87298			−0.159364
$326$		0			0
$327$	−1.44821	+	14.0017i	−0.0800862	+	0.774296i
$328$		0			0
$329$	0.627017	−	1.08602i	0.0345685	−	0.0598745i
$330$		0			0
$331$	11.8911	+	20.5959i	0.653591	+	1.13205i	0.982245	+	0.187603i	$0.0600719\pi$
$331$	11.8911	+	20.5959i	0.653591	+	1.13205i	−0.328653	+	0.944451i	$0.606595\pi$
$332$		0			0
$333$	20.1825	+	4.22013i	1.10599	+	0.231262i
$334$		0			0
$335$	−3.13964	−	5.43802i	−0.171537	−	0.297111i
$336$		0			0
$337$	0.745967	−	1.29205i	0.0406354	−	0.0703826i	−0.844992	−	0.534778i	$-0.820395\pi$
$337$	0.745967	−	1.29205i	0.0406354	−	0.0703826i	0.885628	+	0.464396i	$0.153728\pi$
$338$		0			0
$339$	−5.96816	−	4.32105i	−0.324146	−	0.234687i
$340$		0			0
$341$	21.4919			1.16385
$342$		0			0
$343$	−4.94425			−0.266964
$344$		0			0
$345$	−0.563508	+	0.252009i	−0.0303383	+	0.0135677i
$346$		0			0
$347$	14.8978	−	25.8037i	0.799754	−	1.38521i	−0.120022	−	0.992771i	$-0.538296\pi$
$347$	14.8978	−	25.8037i	0.799754	−	1.38521i	0.919776	−	0.392444i	$-0.128370\pi$
$348$		0			0
$349$	−7.11895	−	12.3304i	−0.381069	−	0.660030i	0.610147	−	0.792289i	$-0.291111\pi$
$349$	−7.11895	−	12.3304i	−0.381069	−	0.660030i	−0.991215	+	0.132258i	$0.957777\pi$
$350$		0			0
$351$	10.0441	+	11.0443i	0.536112	+	0.589499i
$352$		0			0
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$		0			0
$355$	1.58114	−	2.73861i	0.0839181	−	0.145350i
$356$		0			0
$357$	−0.491933	+	0.219999i	−0.0260359	+	0.0116436i
$358$		0			0
$359$	−29.0828			−1.53493			−0.767464	−	0.641092i	$-0.778482\pi$
$359$	−29.0828			−1.53493			−0.767464	+	0.641092i	$0.778482\pi$
$360$		0			0
$361$	35.0000			1.84211
$362$		0			0
$363$	−7.01471	−	5.07877i	−0.368177	−	0.266566i
$364$		0			0
$365$	−2.87298	+	4.97615i	−0.150379	+	0.260464i
$366$		0			0
$367$	−10.7116	−	18.5530i	−0.559140	−	0.968459i	−0.997569	−	0.0696926i	$-0.977798\pi$
$367$	−10.7116	−	18.5530i	−0.559140	−	0.968459i	0.438429	−	0.898766i	$-0.355535\pi$
$368$		0			0
$369$	−19.7460	+	22.0767i	−1.02793	+	1.14927i
$370$		0			0
$371$	0.712788	+	1.23458i	0.0370061	+	0.0640965i
$372$		0			0
$373$	−7.74597	+	13.4164i	−0.401071	+	0.694675i	−0.993855	−	0.110686i	$-0.964695\pi$
$373$	−7.74597	+	13.4164i	−0.401071	+	0.694675i	0.592784	+	0.805361i	$0.298029\pi$
$374$		0			0
$375$	0.178197	−	1.72286i	0.00920205	−	0.0889681i
$376$		0			0
$377$	−25.1270			−1.29411
$378$		0			0
$379$	−8.37238			−0.430060			−0.215030	−	0.976607i	$-0.568985\pi$
$379$	−8.37238			−0.430060			−0.215030	+	0.976607i	$0.568985\pi$
$380$		0			0
$381$	3.11895	−	30.1549i	0.159789	−	1.54488i
$382$		0			0
$383$	−13.8739	+	24.0302i	−0.708921	+	1.22789i	0.256337	+	0.966588i	$0.417484\pi$
$383$	−13.8739	+	24.0302i	−0.708921	+	1.22789i	−0.965258	+	0.261300i	$0.915849\pi$
$384$		0			0
$385$	0.436492	+	0.756026i	0.0222457	+	0.0385306i
$386$		0			0
$387$	2.29393	+	6.98125i	0.116607	+	0.354877i
$388$		0			0
$389$	5.93649	+	10.2823i	0.300992	+	0.521334i	0.976361	−	0.216147i	$-0.0693489\pi$
$389$	5.93649	+	10.2823i	0.300992	+	0.521334i	−0.675369	+	0.737480i	$0.736016\pi$
$390$		0			0
$391$	−0.155563	+	0.269443i	−0.00786716	+	0.0136263i
$392$		0			0
$393$	6.87298	+	4.97615i	0.346696	+	0.251014i
$394$		0			0
$395$	12.6491			0.636446
$396$		0			0
$397$	−13.4919			−0.677141			−0.338570	−	0.940941i	$-0.609943\pi$
$397$	−13.4919			−0.677141			−0.338570	+	0.940941i	$0.609943\pi$
$398$		0			0
$399$	−4.14092	+	1.85188i	−0.207305	+	0.0927098i
$400$		0			0
$401$	−7.74597	+	13.4164i	−0.386815	+	0.669983i	−0.992019	−	0.126087i	$-0.959758\pi$
$401$	−7.74597	+	13.4164i	−0.386815	+	0.669983i	0.605204	+	0.796070i	$0.293092\pi$
$402$		0			0
$403$	−12.6038	−	21.8305i	−0.627842	−	1.08745i
$404$		0			0
$405$	−7.24597	+	5.33816i	−0.360055	+	0.265255i
$406$		0			0
$407$	−8.41765	−	14.5798i	−0.417247	−	0.722694i
$408$		0			0
$409$	−13.8730	+	24.0287i	−0.685975	+	1.18814i	0.287154	+	0.957884i	$0.407291\pi$
$409$	−13.8730	+	24.0287i	−0.685975	+	1.18814i	−0.973129	+	0.230259i	$0.926043\pi$
$410$		0			0
$411$	−18.5720	+	8.30565i	−0.916089	+	0.409688i
$412$		0			0
$413$	−0.254033			−0.0125002
$414$		0			0
$415$	−13.0055			−0.638415
$416$		0			0
$417$	−6.87298	−	4.97615i	−0.336571	−	0.243683i
$418$		0			0
$419$	−14.1850	+	24.5691i	−0.692982	+	1.20028i	0.277875	+	0.960617i	$0.410370\pi$
$419$	−14.1850	+	24.5691i	−0.692982	+	1.20028i	−0.970856	+	0.239662i	$0.922963\pi$
$420$		0			0
$421$	11.6190	+	20.1246i	0.566273	+	0.980814i	0.996930	+	0.0782979i	$0.0249485\pi$
$421$	11.6190	+	20.1246i	0.566273	+	0.980814i	−0.430657	+	0.902516i	$0.641718\pi$
$422$		0			0
$423$	−3.29521	−	10.0285i	−0.160218	−	0.487603i
$424$		0			0
$425$	−0.436492	−	0.756026i	−0.0211730	−	0.0366726i
$426$		0			0
$427$	0.333760	−	0.578089i	0.0161518	−	0.0279757i
$428$		0			0
$429$	1.25403	−	12.1244i	0.0605453	−	0.585369i
$430$		0			0
$431$	−37.9473			−1.82786			−0.913929	−	0.405873i	$-0.866967\pi$
$431$	−37.9473			−1.82786			−0.913929	+	0.405873i	$0.866967\pi$
$432$		0			0
$433$	11.1270			0.534730			0.267365	−	0.963595i	$-0.413847\pi$
$433$	11.1270			0.534730			0.267365	+	0.963595i	$0.413847\pi$
$434$		0			0
$435$	1.55850	−	15.0681i	0.0747246	−	0.722459i
$436$		0			0
$437$	−1.30948	+	2.26808i	−0.0626407	+	0.108497i
$438$		0			0
$439$	5.25537	+	9.10257i	0.250825	+	0.434442i	0.963753	−	0.266795i	$-0.0859647\pi$
$439$	5.25537	+	9.10257i	0.250825	+	0.434442i	−0.712928	+	0.701237i	$0.752631\pi$
$440$		0			0
$441$	−13.7460	+	15.3685i	−0.654570	+	0.731831i
$442$		0			0
$443$	15.4324	+	26.7296i	0.733214	+	1.26996i	0.955503	+	0.294982i	$0.0953138\pi$
$443$	15.4324	+	26.7296i	0.733214	+	1.26996i	−0.222289	+	0.974981i	$0.571353\pi$
$444$		0			0
$445$	0.627017	−	1.08602i	0.0297234	−	0.0514825i
$446$		0			0
$447$	−2.62769	−	1.90249i	−0.124285	−	0.0899846i
$448$		0			0
$449$	−30.9839			−1.46222			−0.731110	−	0.682260i	$-0.760997\pi$
$449$	−30.9839			−1.46222			−0.731110	+	0.682260i	$0.760997\pi$
$450$		0			0
$451$	24.1838			1.13877
$452$		0			0
$453$	9.36492	−	4.18812i	0.440002	−	0.196775i
$454$		0			0
$455$	0.511957	−	0.886735i	0.0240009	−	0.0415708i
$456$		0			0
$457$	−14.3095	−	24.7847i	−0.669369	−	1.15938i	−0.978081	−	0.208226i	$-0.933231\pi$
$457$	−14.3095	−	24.7847i	−0.669369	−	1.15938i	0.308712	−	0.951156i	$-0.400102\pi$
$458$		0			0
$459$	−1.38031	+	4.32105i	−0.0644273	+	0.201689i
$460$		0			0
$461$	0.627017	+	1.08602i	0.0292031	+	0.0505812i	0.880258	−	0.474496i	$-0.157370\pi$
$461$	0.627017	+	1.08602i	0.0292031	+	0.0505812i	−0.851055	+	0.525077i	$0.824036\pi$
$462$		0			0
$463$	−3.00671	+	5.20778i	−0.139734	+	0.242026i	−0.927396	−	0.374081i	$-0.877958\pi$
$463$	−3.00671	+	5.20778i	−0.139734	+	0.242026i	0.787662	+	0.616108i	$0.211291\pi$
$464$		0			0
$465$	13.8730	−	6.20419i	0.643344	−	0.287712i
$466$		0			0
$467$	−11.6252			−0.537950			−0.268975	−	0.963147i	$-0.586685\pi$
$467$	−11.6252			−0.537950			−0.268975	+	0.963147i	$0.586685\pi$
$468$		0			0
$469$	2.23790			0.103337
$470$		0			0
$471$	−2.44949	−	1.77347i	−0.112867	−	0.0817172i
$472$		0			0
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	−3.67423	−	6.36396i	−0.168585	−	0.291999i
$476$		0			0
$477$	11.7460	+	2.45607i	0.537811	+	0.112456i
$478$		0			0
$479$	4.89898	+	8.48528i	0.223840	+	0.387702i	0.955971	−	0.293462i	$-0.0948073\pi$
$479$	4.89898	+	8.48528i	0.223840	+	0.387702i	−0.732131	+	0.681164i	$0.761474\pi$
$480$		0			0
$481$	−9.87298	+	17.1005i	−0.450169	+	0.779716i
$482$		0			0
$483$	0.0226340	−	0.218832i	0.00102988	−	0.00995720i
$484$		0			0
$485$	13.7460			0.624172
$486$		0			0
$487$	15.8114			0.716482			0.358241	−	0.933629i	$-0.383377\pi$
$487$	15.8114			0.716482			0.358241	+	0.933629i	$0.383377\pi$
$488$		0			0
$489$	−1.81754	+	17.5725i	−0.0821921	+	0.794657i
$490$		0			0
$491$	9.13044	−	15.8144i	0.412051	−	0.713693i	−0.583063	−	0.812427i	$-0.698146\pi$
$491$	9.13044	−	15.8144i	0.412051	−	0.713693i	0.995114	+	0.0987338i	$0.0314792\pi$
$492$		0			0
$493$	−3.81754	−	6.61218i	−0.171933	−	0.297797i
$494$		0			0
$495$	7.19291	+	1.50403i	0.323297	+	0.0676010i
$496$		0			0
$497$	0.563508	+	0.976025i	0.0252768	+	0.0437807i
$498$		0			0
$499$	−11.5799	+	20.0570i	−0.518389	+	0.897876i	0.481383	+	0.876510i	$0.340135\pi$
$499$	−11.5799	+	20.0570i	−0.518389	+	0.897876i	−0.999772	+	0.0213654i	$0.993199\pi$
$500$		0			0
$501$	25.5554	+	18.5026i	1.14173	+	0.826633i
$502$		0			0
$503$	−9.03990			−0.403069			−0.201535	−	0.979481i	$-0.564593\pi$
$503$	−9.03990			−0.403069			−0.201535	+	0.979481i	$0.564593\pi$
$504$		0			0
$505$	−13.7460			−0.611687
$506$		0			0
$507$	7.50403	−	3.35591i	0.333266	−	0.149041i
$508$		0			0
$509$	19.2460	−	33.3350i	0.853062	−	1.47755i	−0.0253684	−	0.999678i	$-0.508076\pi$
$509$	19.2460	−	33.3350i	0.853062	−	1.47755i	0.878431	−	0.477869i	$-0.158591\pi$
$510$		0			0
$511$	−1.02391	−	1.77347i	−0.0452953	−	0.0784537i
$512$		0			0
$513$	−11.6190	+	36.3731i	−0.512989	+	1.60591i
$514$		0			0
$515$	6.83651	+	11.8412i	0.301253	+	0.521785i
$516$		0			0
$517$	−4.30948	+	7.46423i	−0.189530	+	0.328276i
$518$		0			0
$519$	6.32456	−	2.82843i	0.277617	−	0.124154i
$520$		0			0
$521$	6.74597			0.295546			0.147773	−	0.989021i	$-0.452789\pi$
$521$	6.74597			0.295546			0.147773	+	0.989021i	$0.452789\pi$
$522$		0			0
$523$	−22.4018			−0.979562			−0.489781	−	0.871845i	$-0.662923\pi$
$523$	−22.4018			−0.979562			−0.489781	+	0.871845i	$0.662923\pi$
$524$		0			0
$525$	0.500000	+	0.362008i	0.0218218	+	0.0157993i
$526$		0			0
$527$	3.82980	−	6.63340i	0.166829	−	0.288956i
$528$		0			0
$529$	11.4365	+	19.8086i	0.497239	+	0.861243i
$530$		0			0
$531$	−1.42558	+	1.59384i	−0.0618647	+	0.0691669i
$532$		0			0
$533$	−14.1825	−	24.5647i	−0.614310	−	1.06402i
$534$		0			0
$535$	−0.890985	+	1.54323i	−0.0385206	+	0.0667197i
$536$		0			0
$537$	4.30948	−	41.6652i	0.185968	−	1.79799i
$538$		0			0
$539$	16.8353			0.725148
$540$		0			0
$541$	17.9839			0.773187			0.386593	−	0.922250i	$-0.373652\pi$
$541$	17.9839			0.773187			0.386593	+	0.922250i	$0.373652\pi$
$542$		0			0
$543$	−0.132929	+	1.28520i	−0.00570453	+	0.0551530i
$544$		0			0
$545$	4.06351	−	7.03820i	0.174062	−	0.301483i
$546$		0			0
$547$	9.66503	+	16.7403i	0.413247	+	0.715765i	0.995243	−	0.0974273i	$-0.0310613\pi$
$547$	9.66503	+	16.7403i	0.413247	+	0.715765i	−0.581996	+	0.813192i	$0.697728\pi$
$548$		0			0
$549$	−1.75403	−	5.33816i	−0.0748603	−	0.227827i
$550$		0			0
$551$	−32.1347	−	55.6590i	−1.36899	−	2.37115i
$552$		0			0
$553$	−2.25403	+	3.90410i	−0.0958512	+	0.166019i
$554$		0			0
$555$	−9.64240	−	6.98125i	−0.409297	−	0.296338i
$556$		0			0
$557$	−4.25403			−0.180249			−0.0901246	−	0.995930i	$-0.528727\pi$
$557$	−4.25403			−0.180249			−0.0901246	+	0.995930i	$0.528727\pi$
$558$		0			0
$559$	−7.03734			−0.297648
$560$		0			0
$561$	3.38105	−	1.51205i	0.142748	−	0.0638389i
$562$		0			0
$563$	−8.75141	+	15.1579i	−0.368828	+	0.638829i	−0.989383	−	0.145334i	$-0.953574\pi$
$563$	−8.75141	+	15.1579i	−0.368828	+	0.638829i	0.620555	+	0.784163i	$0.286908\pi$
$564$		0			0
$565$	2.12702	+	3.68410i	0.0894843	+	0.154991i
$566$		0			0
$567$	−0.356394	−	3.18768i	−0.0149671	−	0.133870i
$568$		0			0
$569$	−6.74597	−	11.6844i	−0.282806	−	0.489834i	0.689269	−	0.724505i	$-0.257932\pi$
$569$	−6.74597	−	11.6844i	−0.282806	−	0.489834i	−0.972075	+	0.234672i	$0.924598\pi$
$570$		0			0
$571$	−10.8219	+	18.7440i	−0.452881	+	0.784413i	−0.998564	−	0.0535787i	$-0.982937\pi$
$571$	−10.8219	+	18.7440i	−0.452881	+	0.784413i	0.545682	+	0.837992i	$0.316271\pi$
$572$		0			0
$573$	−5.00000	+	2.23607i	−0.208878	+	0.0934131i
$574$		0			0
$575$	0.356394			0.0148627
$576$		0			0
$577$	−9.74597			−0.405730			−0.202865	−	0.979207i	$-0.565025\pi$
$577$	−9.74597			−0.405730			−0.202865	+	0.979207i	$0.565025\pi$
$578$		0			0
$579$	23.3154	+	16.8807i	0.968956	+	0.701540i
$580$		0			0
$581$	2.31754	−	4.01410i	0.0961478	−	0.166533i
$582$		0			0
$583$	−4.89898	−	8.48528i	−0.202895	−	0.351424i
$584$		0			0
$585$	−2.69052	−	8.18825i	−0.111240	−	0.338542i
$586$		0			0
$587$	−21.9577	−	38.0319i	−0.906293	−	1.56975i	−0.819172	−	0.573548i	$-0.805567\pi$
$587$	−21.9577	−	38.0319i	−0.906293	−	1.56975i	−0.0871213	−	0.996198i	$-0.527767\pi$
$588$		0			0
$589$	32.2379	−	55.8377i	1.32834	−	2.30075i
$590$		0			0
$591$	−4.14092	+	40.0356i	−0.170335	+	1.64685i
$592$		0			0
$593$	−9.12702			−0.374802			−0.187401	−	0.982284i	$-0.560006\pi$
$593$	−9.12702			−0.374802			−0.187401	+	0.982284i	$0.560006\pi$
$594$		0			0
$595$	0.311126			0.0127549
$596$		0			0
$597$	1.81754	−	17.5725i	0.0743870	−	0.719195i
$598$		0			0
$599$	−1.02391	+	1.77347i	−0.0418360	+	0.0724621i	−0.886185	−	0.463331i	$-0.846654\pi$
$599$	−1.02391	+	1.77347i	−0.0418360	+	0.0724621i	0.844349	+	0.535793i	$0.179987\pi$
$600$		0			0
$601$	−22.7460	−	39.3972i	−0.927827	−	1.60704i	−0.786950	−	0.617017i	$-0.788341\pi$
$601$	−22.7460	−	39.3972i	−0.927827	−	1.60704i	−0.140878	−	0.990027i	$-0.544992\pi$
$602$		0			0
$603$	12.5586	−	14.0409i	0.511425	−	0.571790i
$604$		0			0
$605$	2.50000	+	4.33013i	0.101639	+	0.176045i
$606$		0			0
$607$	21.0441	−	36.4495i	0.854155	−	1.47944i	−0.0232721	−	0.999729i	$-0.507408\pi$
$607$	21.0441	−	36.4495i	0.854155	−	1.47944i	0.877427	−	0.479710i	$-0.159258\pi$
$608$		0			0
$609$	4.37298	+	3.16611i	0.177202	+	0.128297i
$610$		0			0
$611$	10.1091			0.408970
$612$		0			0
$613$	10.6190			0.428895			0.214448	−	0.976735i	$-0.431205\pi$
$613$	10.6190			0.428895			0.214448	+	0.976735i	$0.431205\pi$
$614$		0			0
$615$	15.6106	−	6.98125i	0.629478	−	0.281511i
$616$		0			0
$617$	7.87298	−	13.6364i	0.316954	−	0.548981i	−0.662897	−	0.748711i	$-0.730673\pi$
$617$	7.87298	−	13.6364i	0.316954	−	0.548981i	0.979851	+	0.199730i	$0.0640065\pi$
$618$		0			0
$619$	12.4483	+	21.5611i	0.500339	+	0.866612i	1.00000		0.000391031i	$0.000124469\pi$
$619$	12.4483	+	21.5611i	0.500339	+	0.866612i	−0.499661	+	0.866221i	$0.666542\pi$
$620$		0			0
$621$	−1.24597	−	1.37004i	−0.0499989	−	0.0549779i
$622$		0			0
$623$	0.223465	+	0.387053i	0.00895293	+	0.0155069i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	28.4605	−	12.7279i	1.13660	−	0.508304i
$628$		0			0
$629$	−6.00000			−0.239236
$630$		0			0
$631$	34.3834			1.36878			0.684391	−	0.729116i	$-0.260068\pi$
$631$	34.3834			1.36878			0.684391	+	0.729116i	$0.260068\pi$
$632$		0			0
$633$	−34.9284	−	25.2888i	−1.38828	−	1.00514i
$634$		0			0
$635$	−8.75141	+	15.1579i	−0.347289	+	0.601522i
$636$		0			0
$637$	−9.87298	−	17.1005i	−0.391182	−	0.677547i
$638$		0			0
$639$	9.28600	+	1.94169i	0.367349	+	0.0768121i
$640$		0			0
$641$	1.06351	+	1.84205i	0.0420061	+	0.0727566i	0.886264	−	0.463180i	$-0.153292\pi$
$641$	1.06351	+	1.84205i	0.0420061	+	0.0727566i	−0.844258	+	0.535937i	$0.819958\pi$
$642$		0			0
$643$	−22.1133	+	38.3014i	−0.872064	+	1.51046i	−0.0122058	+	0.999926i	$0.503885\pi$
$643$	−22.1133	+	38.3014i	−0.872064	+	1.51046i	−0.859858	+	0.510533i	$0.829448\pi$
$644$		0			0
$645$	0.436492	−	4.22013i	0.0171868	−	0.166167i
$646$		0			0
$647$	16.7900			0.660084			0.330042	−	0.943966i	$-0.392937\pi$
$647$	16.7900			0.660084			0.330042	+	0.943966i	$0.392937\pi$
$648$		0			0
$649$	1.74597			0.0685352
$650$		0			0
$651$	−0.557225	+	5.38741i	−0.0218394	+	0.211149i
$652$		0			0
$653$	22.9284	−	39.7132i	0.897259	−	1.55410i	0.0662744	−	0.997801i	$-0.478889\pi$
$653$	22.9284	−	39.7132i	0.897259	−	1.55410i	0.830984	−	0.556296i	$-0.187778\pi$
$654$		0			0
$655$	−2.44949	−	4.24264i	−0.0957095	−	0.165774i
$656$		0			0
$657$	−16.8730	−	3.52812i	−0.658278	−	0.137645i
$658$		0			0
$659$	−18.2156	−	31.5504i	−0.709579	−	1.22903i	−0.965013	−	0.262201i	$-0.915552\pi$
$659$	−18.2156	−	31.5504i	−0.709579	−	1.22903i	0.255434	−	0.966827i	$-0.417782\pi$
$660$		0			0
$661$	17.8730	−	30.9569i	0.695178	−	1.20408i	−0.274942	−	0.961461i	$-0.588659\pi$
$661$	17.8730	−	30.9569i	0.695178	−	1.20408i	0.970120	−	0.242624i	$-0.0780080\pi$
$662$		0			0
$663$	−3.51867	−	2.54758i	−0.136654	−	0.0989397i
$664$		0			0
$665$	2.61895			0.101559
$666$		0			0
$667$	3.11701			0.120691
$668$		0			0
$669$	−18.9446	+	8.47226i	−0.732439	+	0.327557i
$670$		0			0
$671$	−2.29393	+	3.97320i	−0.0885561	+	0.153384i
$672$		0			0
$673$	5.30948	+	9.19628i	0.204665	+	0.354491i	0.950026	−	0.312171i	$-0.101056\pi$
$673$	5.30948	+	9.19628i	0.204665	+	0.354491i	−0.745361	+	0.666661i	$0.767723\pi$
$674$		0			0
$675$	5.07718	−	1.10557i	0.195421	−	0.0425533i
$676$		0			0
$677$	21.0554	+	36.4691i	0.809226	+	1.40162i	0.913400	+	0.407062i	$0.133447\pi$
$677$	21.0554	+	36.4691i	0.809226	+	1.40162i	−0.104174	+	0.994559i	$0.533220\pi$
$678$		0			0
$679$	−2.44949	+	4.24264i	−0.0940028	+	0.162818i
$680$		0			0
$681$	20.4919	−	9.16427i	0.785253	−	0.351176i
$682$		0			0
$683$	41.6413			1.59336			0.796681	−	0.604401i	$-0.206587\pi$
$683$	41.6413			1.59336			0.796681	+	0.604401i	$0.206587\pi$
$684$		0			0
$685$	11.7460			0.448790
$686$		0			0
$687$	−4.56522	−	3.30529i	−0.174174	−	0.126105i
$688$		0			0
$689$	−5.74597	+	9.95231i	−0.218904	+	0.379153i
$690$		0			0
$691$	−13.6730	−	23.6824i	−0.520146	−	0.900920i	−0.999726	−	0.0234214i	$-0.992544\pi$
$691$	−13.6730	−	23.6824i	−0.520146	−	0.900920i	0.479579	−	0.877499i	$-0.340789\pi$
$692$		0			0
$693$	−1.74597	+	1.95205i	−0.0663238	+	0.0741523i
$694$		0			0
$695$	2.44949	+	4.24264i	0.0929144	+	0.160933i
$696$		0			0
$697$	4.30948	−	7.46423i	0.163233	−	0.282728i
$698$		0			0
$699$	−1.22474	+	11.8412i	−0.0463241	+	0.447875i
$700$		0			0
$701$	−32.1270			−1.21342			−0.606710	−	0.794923i	$-0.707511\pi$
$701$	−32.1270			−1.21342			−0.606710	+	0.794923i	$0.707511\pi$
$702$		0			0
$703$	−50.5059			−1.90487
$704$		0			0
$705$	−0.627017	+	6.06218i	−0.0236148	+	0.228315i
$706$		0			0
$707$	2.44949	−	4.24264i	0.0921225	−	0.159561i
$708$		0			0
$709$	10.5000	+	18.1865i	0.394336	+	0.683010i	0.993016	−	0.117978i	$-0.0376414\pi$
$709$	10.5000	+	18.1865i	0.394336	+	0.683010i	−0.598680	+	0.800988i	$0.704308\pi$
$710$		0			0
$711$	11.8458	+	36.0510i	0.444252	+	1.35202i
$712$		0			0
$713$	1.56351	+	2.70808i	0.0585538	+	0.101418i
$714$		0			0
$715$	−3.51867	+	6.09452i	−0.131591	+	0.227922i
$716$		0			0
$717$	9.87298	+	7.14820i	0.368713	+	0.266955i
$718$		0			0
$719$	7.65960			0.285655			0.142827	−	0.989748i	$-0.454381\pi$
$719$	7.65960			0.285655			0.142827	+	0.989748i	$0.454381\pi$
$720$		0			0
$721$	−4.87298			−0.181479
$722$		0			0
$723$	43.2677	−	19.3499i	1.60914	−	0.719631i
$724$		0			0
$725$	−4.37298	+	7.57423i	−0.162409	+	0.281300i
$726$		0			0
$727$	17.1691	+	29.7377i	0.636765	+	1.10291i	0.986138	+	0.165926i	$0.0530613\pi$
$727$	17.1691	+	29.7377i	0.636765	+	1.10291i	−0.349373	+	0.936984i	$0.613605\pi$
$728$		0			0
$729$	−22.0000	−	15.6525i	−0.814815	−	0.579721i
$730$		0			0
$731$	−1.06918	−	1.85188i	−0.0395451	−	0.0684942i
$732$		0			0
$733$	9.61895	−	16.6605i	0.355284	−	0.615370i	−0.631883	−	0.775064i	$-0.717717\pi$
$733$	9.61895	−	16.6605i	0.355284	−	0.615370i	0.987167	+	0.159694i	$0.0510508\pi$
$734$		0			0
$735$	10.8671	−	4.85993i	0.400841	−	0.179261i
$736$		0			0
$737$	−15.3810			−0.566568
$738$		0			0
$739$	−25.2077			−0.927280			−0.463640	−	0.886024i	$-0.653457\pi$
$739$	−25.2077			−0.927280			−0.463640	+	0.886024i	$0.653457\pi$
$740$		0			0
$741$	−29.6190	−	21.4446i	−1.08808	−	0.787787i
$742$		0			0
$743$	10.6889	−	18.5138i	0.392139	−	0.679205i	−0.600592	−	0.799556i	$-0.705068\pi$
$743$	10.6889	−	18.5138i	0.392139	−	0.679205i	0.992731	+	0.120350i	$0.0384018\pi$
$744$		0			0
$745$	0.936492	+	1.62205i	0.0343104	+	0.0594274i
$746$		0			0
$747$	−12.1795	−	37.0668i	−0.445626	−	1.35620i
$748$		0			0
$749$	−0.317542	−	0.549998i	−0.0116027	−	0.0200965i
$750$		0			0
$751$	−19.4404	+	33.6717i	−0.709389	+	1.22870i	0.255696	+	0.966757i	$0.417696\pi$
$751$	−19.4404	+	33.6717i	−0.709389	+	1.22870i	−0.965084	+	0.261940i	$0.915638\pi$
$752$		0			0
$753$	1.94456	−	18.8006i	0.0708636	−	0.685130i
$754$		0			0
$755$	−5.92289			−0.215556
$756$		0			0
$757$	−11.3810			−0.413651			−0.206826	−	0.978378i	$-0.566313\pi$
$757$	−11.3810			−0.413651			−0.206826	+	0.978378i	$0.566313\pi$
$758$		0			0
$759$	−0.155563	+	1.50403i	−0.00564658	+	0.0545928i
$760$		0			0
$761$	12.1190	−	20.9906i	0.439312	−	0.760910i	−0.558325	−	0.829622i	$-0.688556\pi$
$761$	12.1190	−	20.9906i	0.439312	−	0.760910i	0.997637	+	0.0687124i	$0.0218891\pi$
$762$		0			0
$763$	1.44821	+	2.50837i	0.0524287	+	0.0908092i
$764$		0			0
$765$	1.74597	−	1.95205i	0.0631256	−	0.0705765i
$766$		0			0
$767$	−1.02391	−	1.77347i	−0.0369714	−	0.0640363i
$768$		0			0
$769$	−0.372983	+	0.646026i	−0.0134501	+	0.0232963i	−0.872672	−	0.488307i	$-0.837615\pi$
$769$	−0.372983	+	0.646026i	−0.0134501	+	0.0232963i	0.859222	+	0.511603i	$0.170948\pi$
$770$		0			0
$771$	−18.9284	−	13.7045i	−0.681690	−	0.493554i
$772$		0			0
$773$	−13.7460			−0.494408			−0.247204	−	0.968963i	$-0.579512\pi$
$773$	−13.7460			−0.494408			−0.247204	+	0.968963i	$0.579512\pi$
$774$		0			0
$775$	−8.77405			−0.315173
$776$		0			0
$777$	3.87298	−	1.73205i	0.138943	−	0.0621370i
$778$		0			0
$779$	36.2757	−	62.8313i	1.29971	−	2.25116i
$780$		0			0
$781$	−3.87298	−	6.70820i	−0.138586	−	0.240038i
$782$		0			0
$783$	44.4048	−	9.66926i	1.58690	−	0.345551i
$784$		0			0
$785$	0.872983	+	1.51205i	0.0311581	+	0.0539674i
$786$		0			0
$787$	−6.52539	+	11.3023i	−0.232605	+	0.402884i	−0.958574	−	0.284844i	$-0.908058\pi$
$787$	−6.52539	+	11.3023i	−0.232605	+	0.402884i	0.725969	+	0.687727i	$0.241392\pi$
$788$		0			0
$789$	47.1109	−	21.0686i	1.67719	−	0.750063i
$790$		0			0
$791$	−1.51611			−0.0539067
$792$		0			0
$793$	5.38105			0.191087
$794$		0			0
$795$	−5.61177	−	4.06301i	−0.199029	−	0.144100i
$796$		0			0
$797$	7.30948	−	12.6604i	0.258915	−	0.448454i	−0.707037	−	0.707177i	$-0.749968\pi$
$797$	7.30948	−	12.6604i	0.258915	−	0.448454i	0.965952	+	0.258723i	$0.0833017\pi$
$798$		0			0
$799$	1.53587	+	2.66021i	0.0543352	+	0.0941113i
$800$		0			0
$801$	3.68246	+	0.769998i	0.130113	+	0.0272065i
$802$		0			0
$803$	7.03734	+	12.1890i	0.248342	+	0.430142i
$804$		0			0
$805$	−0.0635083	+	0.110000i	−0.00223837	+	0.00387698i
$806$		0			0
$807$	−2.87379	+	27.7846i	−0.101162	+	0.978064i
$808$		0			0
$809$	29.7460			1.04581			0.522906	−	0.852390i	$-0.324848\pi$
$809$	29.7460			1.04581			0.522906	+	0.852390i	$0.324848\pi$
$810$		0			0
$811$	44.2719			1.55460			0.777298	−	0.629132i	$-0.216590\pi$
$811$	44.2719			1.55460			0.777298	+	0.629132i	$0.216590\pi$
$812$		0			0
$813$	3.56351	−	34.4530i	0.124978	−	1.20832i
$814$		0			0
$815$	5.09981	−	8.83313i	0.178639	−	0.309411i
$816$		0			0
$817$	−9.00000	−	15.5885i	−0.314870	−	0.545371i
$818$		0			0
$819$	3.00671	+	0.628700i	0.105063	+	0.0219686i
$820$		0			0
$821$	3.19052	+	5.52615i	0.111350	+	0.192864i	0.916315	−	0.400459i	$-0.131149\pi$
$821$	3.19052	+	5.52615i	0.111350	+	0.192864i	−0.804965	+	0.593323i	$0.797816\pi$
$822$		0			0
$823$	−10.2223	+	17.7055i	−0.356325	+	0.617174i	−0.987344	−	0.158594i	$-0.949304\pi$
$823$	−10.2223	+	17.7055i	−0.356325	+	0.617174i	0.631018	+	0.775768i	$0.282637\pi$
$824$		0			0
$825$	−3.43649	−	2.48808i	−0.119643	−	0.0866237i
$826$		0			0
$827$	−8.50819			−0.295859			−0.147929	−	0.988998i	$-0.547261\pi$
$827$	−8.50819			−0.295859			−0.147929	+	0.988998i	$0.547261\pi$
$828$		0			0
$829$	−45.6190			−1.58441			−0.792206	−	0.610254i	$-0.791067\pi$
$829$	−45.6190			−1.58441			−0.792206	+	0.610254i	$0.791067\pi$
$830$		0			0
$831$	33.0031	−	14.7594i	1.14486	−	0.511999i
$832$		0			0
$833$	3.00000	−	5.19615i	0.103944	−	0.180036i
$834$		0			0
$835$	−9.10781	−	15.7752i	−0.315189	−	0.545923i
$836$		0			0
$837$	30.6744	+	33.7290i	1.06026	+	1.16585i
$838$		0			0
$839$	0.511957	+	0.886735i	0.0176747	+	0.0306135i	0.874727	−	0.484615i	$-0.161040\pi$
$839$	0.511957	+	0.886735i	0.0176747	+	0.0306135i	−0.857053	+	0.515229i	$0.827707\pi$
$840$		0			0
$841$	−23.7460	+	41.1292i	−0.818826	+	1.41825i
$842$		0			0
$843$	43.2677	−	19.3499i	1.49022	−	0.666447i
$844$		0			0
$845$	−4.74597			−0.163266
$846$		0			0
$847$	−1.78197			−0.0612292
$848$		0			0
$849$	27.1190	+	19.6346i	0.930720	+	0.673857i
$850$		0			0
$851$	1.22474	−	2.12132i	0.0419837	−	0.0727179i
$852$		0			0
$853$	−17.3095	−	29.9809i	−0.592665	−	1.02653i	−0.993872	−	0.110539i	$-0.964742\pi$
$853$	−17.3095	−	29.9809i	−0.592665	−	1.02653i	0.401207	−	0.915988i	$-0.368591\pi$
$854$		0			0
$855$	14.6969	−	16.4317i	0.502625	−	0.561951i
$856$		0			0
$857$	−17.8014	−	30.8329i	−0.608085	−	1.05323i	−0.991556	−	0.129681i	$-0.958605\pi$
$857$	−17.8014	−	30.8329i	−0.608085	−	1.05323i	0.383471	−	0.923553i	$-0.374729\pi$
$858$		0			0
$859$	−17.3925	+	30.1247i	−0.593425	+	1.02784i	0.400342	+	0.916366i	$0.368891\pi$
$859$	−17.3925	+	30.1247i	−0.593425	+	1.02784i	−0.993767	+	0.111477i	$0.964442\pi$
$860$		0			0
$861$	−0.627017	+	6.06218i	−0.0213687	+	0.206598i
$862$		0			0
$863$	−10.4655			−0.356249			−0.178125	−	0.984008i	$-0.557003\pi$
$863$	−10.4655			−0.356249			−0.178125	+	0.984008i	$0.557003\pi$
$864$		0			0
$865$	−4.00000			−0.136004
$866$		0			0
$867$	−2.89354	+	27.9756i	−0.0982699	+	0.950102i
$868$		0			0
$869$	15.4919	−	26.8328i	0.525528	−	0.910241i
$870$		0			0
$871$	9.02014	+	15.6233i	0.305636	+	0.529377i
$872$		0			0
$873$	12.8730	+	39.1772i	0.435684	+	1.32595i
$874$		0			0
$875$	−0.178197	−	0.308646i	−0.00602416	−	0.0104341i
$876$		0			0
$877$	−8.92843	+	15.4645i	−0.301491	+	0.522199i	−0.976474	−	0.215635i	$-0.930818\pi$
$877$	−8.92843	+	15.4645i	−0.301491	+	0.522199i	0.674983	+	0.737834i	$0.264151\pi$
$878$		0			0
$879$	−1.22474	−	0.886735i	−0.0413096	−	0.0299088i
$880$		0			0
$881$	−23.6190			−0.795743			−0.397871	−	0.917441i	$-0.630251\pi$
$881$	−23.6190			−0.795743			−0.397871	+	0.917441i	$0.630251\pi$
$882$		0			0
$883$	−52.6895			−1.77314			−0.886572	−	0.462590i	$-0.846920\pi$
$883$	−52.6895			−1.77314			−0.886572	+	0.462590i	$0.846920\pi$
$884$		0			0
$885$	1.12702	−	0.504017i	0.0378843	−	0.0169424i
$886$		0			0
$887$	9.99879	−	17.3184i	0.335727	−	0.581495i	−0.647898	−	0.761727i	$-0.724352\pi$
$887$	9.99879	−	17.3184i	0.335727	−	0.581495i	0.983624	+	0.180232i	$0.0576849\pi$
$888$		0			0
$889$	−3.11895	−	5.40218i	−0.104606	−	0.181183i
$890$		0			0
$891$	2.44949	+	21.9089i	0.0820610	+	0.733976i
$892$		0			0
$893$	12.9284	+	22.3927i	0.432633	+	0.749343i
$894$		0			0
$895$	−12.0919	+	20.9438i	−0.404187	+	0.700073i
$896$		0			0
$897$	1.61895	−	0.724016i	0.0540552	−	0.0241742i
$898$		0			0
$899$	−76.7375			−2.55934
$900$		0			0
$901$	−3.49193			−0.116333
$902$		0			0
$903$	1.22474	+	0.886735i	0.0407570	+	0.0295087i
$904$		0			0
$905$	0.372983	−	0.646026i	0.0123984	−	0.0214746i
$906$		0			0
$907$	27.7251	+	48.0212i	0.920596	+	1.59452i	0.798495	+	0.602002i	$0.205630\pi$
$907$	27.7251	+	48.0212i	0.920596	+	1.59452i	0.122101	+	0.992518i	$0.461037\pi$
$908$		0			0
$909$	−12.8730	−	39.1772i	−0.426970	−	1.29942i
$910$		0			0
$911$	−22.4923	−	38.9579i	−0.745204	−	1.29073i	−0.950099	−	0.311948i	$-0.899019\pi$
$911$	−22.4923	−	38.9579i	−0.745204	−	1.29073i	0.204895	−	0.978784i	$-0.434315\pi$
$912$		0			0
$913$	−15.9284	+	27.5888i	−0.527154	+	0.913057i
$914$		0			0
$915$	−0.333760	+	3.22689i	−0.0110338	+	0.106678i
$916$		0			0
$917$	1.74597			0.0576569
$918$		0			0
$919$	27.3460			0.902063			0.451031	−	0.892508i	$-0.351056\pi$
$919$	27.3460			0.902063			0.451031	+	0.892508i	$0.351056\pi$
$920$		0			0
$921$	−0.936492	+	9.05427i	−0.0308584	+	0.298348i
$922$		0			0
$923$	−4.54259	+	7.86799i	−0.149521	+	0.258978i
$924$		0			0
$925$	3.43649	+	5.95218i	0.112991	+	0.195706i
$926$		0			0
$927$	−27.3460	+	30.5738i	−0.898162	+	1.00418i
$928$		0			0
$929$	7.87298	+	13.6364i	0.258304	+	0.447396i	0.965788	−	0.259334i	$-0.0835030\pi$
$929$	7.87298	+	13.6364i	0.258304	+	0.447396i	−0.707484	+	0.706730i	$0.750170\pi$
$930$		0			0
$931$	25.2530	−	43.7394i	0.827632	−	1.43350i
$932$		0			0
$933$	−29.9284	−	21.6687i	−0.979813	−	0.709400i
$934$		0			0
$935$	−2.13836			−0.0699320
$936$		0			0
$937$	52.9839			1.73091			0.865454	−	0.500989i	$-0.167030\pi$
$937$	52.9839			1.73091			0.865454	+	0.500989i	$0.167030\pi$
$938$		0			0
$939$	−35.7637	+	15.9940i	−1.16710	+	0.521945i
$940$		0			0
$941$	25.6109	−	44.3594i	0.834891	−	1.44607i	−0.0592283	−	0.998244i	$-0.518864\pi$
$941$	25.6109	−	44.3594i	0.834891	−	1.44607i	0.894119	−	0.447829i	$-0.147803\pi$
$942$		0			0
$943$	1.75934	+	3.04726i	0.0572919	+	0.0992324i
$944$		0			0
$945$	−0.563508	+	1.76406i	−0.0183309	+	0.0573849i
$946$		0			0
$947$	−18.9510	−	32.8242i	−0.615826	−	1.06664i	−0.990239	−	0.139380i	$-0.955489\pi$
$947$	−18.9510	−	32.8242i	−0.615826	−	1.06664i	0.374413	−	0.927262i	$-0.377844\pi$
$948$		0			0
$949$	8.25403	−	14.2964i	0.267937	−	0.464081i
$950$		0			0
$951$	17.5934	−	7.86799i	0.570504	−	0.255137i
$952$		0			0
$953$	−60.3649			−1.95541			−0.977706	−	0.209980i	$-0.932660\pi$
$953$	−60.3649			−1.95541			−0.977706	+	0.209980i	$0.932660\pi$
$954$		0			0
$955$	3.16228			0.102329
$956$		0			0
$957$	−30.0554	−	21.7606i	−0.971554	−	0.703421i
$958$		0			0
$959$	−2.09310	+	3.62535i	−0.0675896	+	0.117069i
$960$		0			0
$961$	−22.9919	−	39.8232i	−0.741675	−	1.28462i
$962$		0			0
$963$	−5.23274	−	1.09416i	−0.168623	−	0.0352588i
$964$		0			0
$965$	−8.30948	−	14.3924i	−0.267491	−	0.463309i
$966$		0			0
$967$	−16.2554	+	28.1553i	−0.522740	+	0.905412i	0.476910	+	0.878952i	$0.341757\pi$
$967$	−16.2554	+	28.1553i	−0.522740	+	0.905412i	−0.999650	+	0.0264598i	$0.991577\pi$
$968$		0			0
$969$	1.14315	−	11.0523i	0.0367233	−	0.355051i
$970$		0			0
$971$	−50.1948			−1.61083			−0.805414	−	0.592713i	$-0.798057\pi$
$971$	−50.1948			−1.61083			−0.805414	+	0.592713i	$0.798057\pi$
$972$		0			0
$973$	−1.74597			−0.0559731
$974$		0			0
$975$	−0.511957	+	4.94975i	−0.0163957	+	0.158519i
$976$		0			0
$977$	3.81754	−	6.61218i	0.122134	−	0.211542i	−0.798475	−	0.602028i	$-0.794360\pi$
$977$	3.81754	−	6.61218i	0.122134	−	0.211542i	0.920609	+	0.390486i	$0.127693\pi$
$978$		0			0
$979$	−1.53587	−	2.66021i	−0.0490866	−	0.0850206i
$980$		0			0
$981$	23.8649	+	4.99012i	0.761948	+	0.159322i
$982$		0			0
$983$	21.8672	+	37.8751i	0.697456	+	1.20803i	0.969346	+	0.245700i	$0.0790179\pi$
$983$	21.8672	+	37.8751i	0.697456	+	1.20803i	−0.271890	+	0.962328i	$0.587649\pi$
$984$		0			0
$985$	11.6190	−	20.1246i	0.370211	−	0.641223i
$986$		0			0
$987$	−1.75934	−	1.27379i	−0.0560003	−	0.0405451i
$988$		0			0
$989$	0.872983			0.0277593
$990$		0			0
$991$	−38.4790			−1.22233			−0.611164	−	0.791504i	$-0.709298\pi$
$991$	−38.4790			−1.22233			−0.611164	+	0.791504i	$0.709298\pi$
$992$		0			0
$993$	37.6028	−	16.8165i	1.19329	−	0.533655i
$994$		0			0
$995$	−5.09981	+	8.83313i	−0.161675	+	0.280029i
$996$		0			0
$997$	24.8730	+	43.0813i	0.787735	+	1.36440i	0.927351	+	0.374192i	$0.122080\pi$
$997$	24.8730	+	43.0813i	0.787735	+	1.36440i	−0.139616	+	0.990206i	$0.544587\pi$
$998$		0			0
$999$	10.8671	−	34.0195i	0.343821	−	1.07633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.q.j.481.3	yes	8
3.2	odd	2		4320.2.q.m.1441.2		8
4.3	odd	2	inner	1440.2.q.j.481.2	✓	8
9.2	odd	6		4320.2.q.m.2881.2		8
9.7	even	3	inner	1440.2.q.j.961.3	yes	8
12.11	even	2		4320.2.q.m.1441.3		8
36.7	odd	6	inner	1440.2.q.j.961.2	yes	8
36.11	even	6		4320.2.q.m.2881.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.j.481.2	✓	8	4.3	odd	2	inner
1440.2.q.j.481.3	yes	8	1.1	even	1	trivial
1440.2.q.j.961.2	yes	8	36.7	odd	6	inner
1440.2.q.j.961.3	yes	8	9.7	even	3	inner
4320.2.q.m.1441.2		8	3.2	odd	2
4320.2.q.m.1441.3		8	12.11	even	2
4320.2.q.m.2881.2		8	9.2	odd	6
4320.2.q.m.2881.3		8	36.11	even	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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.178197 - 1.72286i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.178197 - 0.308646i) q^{7} +(-2.93649 - 0.614017i) q^{9} +O(q^{10})\)	\(q+(0.178197 - 1.72286i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.178197 - 0.308646i) q^{7} +(-2.93649 - 0.614017i) q^{9} +(1.22474 + 2.12132i) q^{11} +(1.43649 - 2.48808i) q^{13} +(1.40294 + 1.01575i) q^{15} +0.872983 q^{17} +7.34847 q^{19} +(-0.563508 + 0.252009i) q^{21} +(-0.178197 + 0.308646i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.58114 + 4.94975i) q^{27} +(-4.37298 - 7.57423i) q^{29} +(4.38702 - 7.59855i) q^{31} +(3.87298 - 1.73205i) q^{33} +0.356394 q^{35} -6.87298 q^{37} +(-4.03063 - 2.91824i) q^{39} +(4.93649 - 8.55025i) q^{41} +(-1.22474 - 2.12132i) q^{43} +(2.00000 - 2.23607i) q^{45} +(1.75934 + 3.04726i) q^{47} +(3.43649 - 5.95218i) q^{49} +(0.155563 - 1.50403i) q^{51} -4.00000 q^{53} -2.44949 q^{55} +(1.30948 - 12.6604i) q^{57} +(0.356394 - 0.617292i) q^{59} +(0.936492 + 1.62205i) q^{61} +(0.333760 + 1.01575i) q^{63} +(1.43649 + 2.48808i) q^{65} +(-3.13964 + 5.43802i) q^{67} +(0.500000 + 0.362008i) q^{69} -3.16228 q^{71} +5.74597 q^{73} +(-1.58114 + 0.707107i) q^{75} +(0.436492 - 0.756026i) q^{77} +(-6.32456 - 10.9545i) q^{79} +(8.24597 + 3.60611i) q^{81} +(6.50275 + 11.2631i) q^{83} +(-0.436492 + 0.756026i) q^{85} +(-13.8286 + 6.18433i) q^{87} -1.25403 q^{89} -1.02391 q^{91} +(-12.3095 - 8.91226i) q^{93} +(-3.67423 + 6.36396i) q^{95} +(-6.87298 - 11.9044i) q^{97} +(-2.29393 - 6.98125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^9	\( 8 q - 4 q^{5} - 8 q^{9} - 4 q^{13} - 24 q^{17} - 20 q^{21} - 4 q^{25} - 4 q^{29} - 24 q^{37} + 24 q^{41} + 16 q^{45} + 12 q^{49} - 32 q^{53} - 36 q^{57} - 8 q^{61} - 4 q^{65} + 4 q^{69} - 16 q^{73} - 12 q^{77} + 4 q^{81} + 12 q^{85} - 72 q^{89} - 52 q^{93} - 24 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^9 - 4 * q^13 - 24 * q^17 - 20 * q^21 - 4 * q^25 - 4 * q^29 - 24 * q^37 + 24 * q^41 + 16 * q^45 + 12 * q^49 - 32 * q^53 - 36 * q^57 - 8 * q^61 - 4 * q^65 + 4 * q^69 - 16 * q^73 - 12 * q^77 + 4 * q^81 + 12 * q^85 - 72 * q^89 - 52 * q^93 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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