LMFDB - Embedded newform 2646.2.m.c.1763.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.m (of order $6$, degree $2$, not 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1763.11
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.c.881.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.220087 - 0.381202i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.220087 - 0.381202i) q^{5} -1.00000i q^{8} +0.440174i q^{10} +(0.450580 + 0.260142i) q^{11} +(-5.55020 + 3.20441i) q^{13} +(-0.500000 + 0.866025i) q^{16} -0.327345 q^{17} +4.23981i q^{19} +(0.220087 - 0.381202i) q^{20} +(-0.260142 - 0.450580i) q^{22} +(-1.25636 + 0.725359i) q^{23} +(2.40312 - 4.16233i) q^{25} +6.40882 q^{26} +(-5.74668 - 3.31785i) q^{29} +(6.07157 - 3.50542i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.283489 + 0.163672i) q^{34} +3.68230 q^{37} +(2.11990 - 3.67178i) q^{38} +(-0.381202 + 0.220087i) q^{40} +(-2.96701 - 5.13902i) q^{41} +(5.21400 - 9.03091i) q^{43} +0.520285i q^{44} +1.45072 q^{46} +(4.02633 - 6.97382i) q^{47} +(-4.16233 + 2.40312i) q^{50} +(-5.55020 - 3.20441i) q^{52} +7.95672i q^{53} -0.229016i q^{55} +(3.31785 + 5.74668i) q^{58} +(2.45205 + 4.24708i) q^{59} +(1.33678 + 0.771791i) q^{61} -7.01085 q^{62} -1.00000 q^{64} +(2.44305 + 1.41050i) q^{65} +(-3.26206 - 5.65005i) q^{67} +(-0.163672 - 0.283489i) q^{68} -16.2646i q^{71} -4.12648i q^{73} +(-3.18897 - 1.84115i) q^{74} +(-3.67178 + 2.11990i) q^{76} +(0.662324 - 1.14718i) q^{79} +0.440174 q^{80} +5.93403i q^{82} +(-8.55240 + 14.8132i) q^{83} +(0.0720443 + 0.124784i) q^{85} +(-9.03091 + 5.21400i) q^{86} +(0.260142 - 0.450580i) q^{88} +11.7248 q^{89} +(-1.25636 - 0.725359i) q^{92} +(-6.97382 + 4.02633i) q^{94} +(1.61622 - 0.933127i) q^{95} +(-10.6061 - 6.12344i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 - 48 * q^11 - 24 * q^16 - 48 * q^23 - 24 * q^25 + 48 * q^50 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 96 * q^86 - 48 * q^92 + 192 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.220087	−	0.381202i	−0.0984259	−	0.170479i	0.812607	−	0.582812i	$-0.198047\pi$
$5$	−0.220087	−	0.381202i	−0.0984259	−	0.170479i	−0.911033	+	0.412333i	$0.864714\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			0.440174i			0.139195i
$11$	0.450580	+	0.260142i	0.135855	+	0.0784359i	0.566387	−	0.824139i	$-0.308341\pi$
$11$	0.450580	+	0.260142i	0.135855	+	0.0784359i	−0.430532	+	0.902575i	$0.641674\pi$
$12$		0			0
$13$	−5.55020	+	3.20441i	−1.53935	+	0.888743i	−0.540471	+	0.841362i	$0.681754\pi$
$13$	−5.55020	+	3.20441i	−1.53935	+	0.888743i	−0.998877	+	0.0473809i	$0.984913\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.327345			−0.0793927			−0.0396964	−	0.999212i	$-0.512639\pi$
$17$	−0.327345			−0.0793927			−0.0396964	+	0.999212i	$0.512639\pi$
$18$		0			0
$19$			4.23981i			0.972679i	0.873770	+	0.486339i	$0.161668\pi$
$19$			4.23981i			0.972679i	−0.873770	+	0.486339i	$0.838332\pi$
$20$	0.220087	−	0.381202i	0.0492130	−	0.0852394i
$21$		0			0
$22$	−0.260142	−	0.450580i	−0.0554625	−	0.0960639i
$23$	−1.25636	+	0.725359i	−0.261969	+	0.151248i	−0.625232	−	0.780439i	$-0.714996\pi$
$23$	−1.25636	+	0.725359i	−0.261969	+	0.151248i	0.363263	+	0.931686i	$0.381662\pi$
$24$		0			0
$25$	2.40312	−	4.16233i	0.480625	−	0.832466i
$26$	6.40882			1.25687
$27$		0			0
$28$		0			0
$29$	−5.74668	−	3.31785i	−1.06713	−	0.616109i	−0.139735	−	0.990189i	$-0.544625\pi$
$29$	−5.74668	−	3.31785i	−1.06713	−	0.616109i	−0.927396	+	0.374080i	$0.877958\pi$
$30$		0			0
$31$	6.07157	−	3.50542i	1.09049	−	0.629593i	0.156781	−	0.987633i	$-0.449888\pi$
$31$	6.07157	−	3.50542i	1.09049	−	0.629593i	0.933706	+	0.358041i	$0.116555\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	0.283489	+	0.163672i	0.0486179	+	0.0280696i
$35$		0			0
$36$		0			0
$37$	3.68230			0.605367			0.302684	−	0.953091i	$-0.402117\pi$
$37$	3.68230			0.605367			0.302684	+	0.953091i	$0.402117\pi$
$38$	2.11990	−	3.67178i	0.343894	−	0.595642i
$39$		0			0
$40$	−0.381202	+	0.220087i	−0.0602733	+	0.0347988i
$41$	−2.96701	−	5.13902i	−0.463370	−	0.802580i	0.535757	−	0.844372i	$-0.320026\pi$
$41$	−2.96701	−	5.13902i	−0.463370	−	0.802580i	−0.999126	+	0.0417927i	$0.986693\pi$
$42$		0			0
$43$	5.21400	−	9.03091i	0.795127	−	1.37720i	−0.127631	−	0.991822i	$-0.540737\pi$
$43$	5.21400	−	9.03091i	0.795127	−	1.37720i	0.922758	−	0.385379i	$-0.125929\pi$
$44$			0.520285i			0.0784359i
$45$		0			0
$46$	1.45072			0.213897
$47$	4.02633	−	6.97382i	0.587301	−	1.01724i	−0.407283	−	0.913302i	$-0.633524\pi$
$47$	4.02633	−	6.97382i	0.587301	−	1.01724i	0.994584	−	0.103934i	$-0.0331429\pi$
$48$		0			0
$49$		0			0
$50$	−4.16233	+	2.40312i	−0.588643	+	0.339853i
$51$		0			0
$52$	−5.55020	−	3.20441i	−0.769674	−	0.444372i
$53$			7.95672i			1.09294i	0.837479	+	0.546470i	$0.184029\pi$
$53$			7.95672i			1.09294i	−0.837479	+	0.546470i	$0.815971\pi$
$54$		0			0
$55$		−	0.229016i		−	0.0308805i
$56$		0			0
$57$		0			0
$58$	3.31785	+	5.74668i	0.435655	+	0.754576i
$59$	2.45205	+	4.24708i	0.319230	+	0.552922i	0.980328	−	0.197377i	$-0.0632424\pi$
$59$	2.45205	+	4.24708i	0.319230	+	0.552922i	−0.661098	+	0.750300i	$0.729909\pi$
$60$		0			0
$61$	1.33678	+	0.771791i	0.171157	+	0.0988177i	0.583131	−	0.812378i	$-0.301827\pi$
$61$	1.33678	+	0.771791i	0.171157	+	0.0988177i	−0.411974	+	0.911196i	$0.635161\pi$
$62$	−7.01085			−0.890379
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.44305	+	1.41050i	0.303024	+	0.174951i
$66$		0			0
$67$	−3.26206	−	5.65005i	−0.398524	−	0.690264i	0.595020	−	0.803711i	$-0.297144\pi$
$67$	−3.26206	−	5.65005i	−0.398524	−	0.690264i	−0.993544	+	0.113447i	$0.963811\pi$
$68$	−0.163672	−	0.283489i	−0.0198482	−	0.0343781i
$69$		0			0
$70$		0			0
$71$		−	16.2646i		−	1.93026i	−0.261774	−	0.965129i	$-0.584307\pi$
$71$		−	16.2646i		−	1.93026i	0.261774	−	0.965129i	$-0.415693\pi$
$72$		0			0
$73$		−	4.12648i		−	0.482968i	−0.970405	−	0.241484i	$-0.922366\pi$
$73$		−	4.12648i		−	0.482968i	0.970405	−	0.241484i	$-0.0776341\pi$
$74$	−3.18897	−	1.84115i	−0.370710	−	0.214030i
$75$		0			0
$76$	−3.67178	+	2.11990i	−0.421182	+	0.243170i
$77$		0			0
$78$		0			0
$79$	0.662324	−	1.14718i	0.0745173	−	0.129068i	−0.826359	−	0.563144i	$-0.809592\pi$
$79$	0.662324	−	1.14718i	0.0745173	−	0.129068i	0.900876	+	0.434076i	$0.142925\pi$
$80$	0.440174			0.0492130
$81$		0			0
$82$			5.93403i			0.655304i
$83$	−8.55240	+	14.8132i	−0.938748	+	1.62596i	−0.170938	+	0.985282i	$0.554680\pi$
$83$	−8.55240	+	14.8132i	−0.938748	+	1.62596i	−0.767810	+	0.640677i	$0.778654\pi$
$84$		0			0
$85$	0.0720443	+	0.124784i	0.00781430	+	0.0135348i
$86$	−9.03091	+	5.21400i	−0.973828	+	0.562240i
$87$		0			0
$88$	0.260142	−	0.450580i	0.0277313	−	0.0480320i
$89$	11.7248			1.24283			0.621413	−	0.783484i	$-0.286559\pi$
$89$	11.7248			1.24283			0.621413	+	0.783484i	$0.286559\pi$
$90$		0			0
$91$		0			0
$92$	−1.25636	−	0.725359i	−0.130984	−	0.0756239i
$93$		0			0
$94$	−6.97382	+	4.02633i	−0.719294	+	0.415285i
$95$	1.61622	−	0.933127i	0.165821	−	0.0957368i
$96$		0			0
$97$	−10.6061	−	6.12344i	−1.07689	−	0.621741i	−0.146832	−	0.989161i	$-0.546908\pi$
$97$	−10.6061	−	6.12344i	−1.07689	−	0.621741i	−0.930055	+	0.367421i	$0.880241\pi$
$98$		0			0
$99$		0			0
$100$	4.80625			0.480625
$101$	−5.40492	+	9.36159i	−0.537809	+	0.931513i	0.461212	+	0.887290i	$0.347415\pi$
$101$	−5.40492	+	9.36159i	−0.537809	+	0.931513i	−0.999022	+	0.0442233i	$0.985919\pi$
$102$		0			0
$103$	9.69122	−	5.59523i	0.954904	−	0.551314i	0.0603031	−	0.998180i	$-0.480793\pi$
$103$	9.69122	−	5.59523i	0.954904	−	0.551314i	0.894601	+	0.446866i	$0.147460\pi$
$104$	3.20441	+	5.55020i	0.314218	+	0.544242i
$105$		0			0
$106$	3.97836	−	6.89072i	0.386412	−	0.669286i
$107$			0.678721i			0.0656145i	0.999462	+	0.0328072i	$0.0104447\pi$
$107$			0.678721i			0.0656145i	−0.999462	+	0.0328072i	$0.989555\pi$
$108$		0			0
$109$	18.2203			1.74519			0.872595	−	0.488445i	$-0.162436\pi$
$109$	18.2203			1.74519			0.872595	+	0.488445i	$0.162436\pi$
$110$	−0.114508	+	0.198334i	−0.0109179	+	0.0189104i
$111$		0			0
$112$		0			0
$113$	9.18833	−	5.30488i	0.864365	−	0.499041i	−0.00110649	−	0.999999i	$-0.500352\pi$
$113$	9.18833	−	5.30488i	0.864365	−	0.499041i	0.865472	+	0.500958i	$0.167019\pi$
$114$		0			0
$115$	0.553017	+	0.319284i	0.0515691	+	0.0297734i
$116$		−	6.63569i		−	0.616109i
$117$		0			0
$118$		−	4.90410i		−	0.451459i
$119$		0			0
$120$		0			0
$121$	−5.36465	−	9.29185i	−0.487696	−	0.844714i
$122$	−0.771791	−	1.33678i	−0.0698746	−	0.121026i
$123$		0			0
$124$	6.07157	+	3.50542i	0.545243	+	0.314796i
$125$	−4.31646			−0.386076
$126$		0			0
$127$	−2.88189			−0.255726			−0.127863	−	0.991792i	$-0.540812\pi$
$127$	−2.88189			−0.255726			−0.127863	+	0.991792i	$0.540812\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.41050	−	2.44305i	−0.123709	−	0.214270i
$131$	−8.34798	−	14.4591i	−0.729367	−	1.26330i	−0.957151	−	0.289589i	$-0.906481\pi$
$131$	−8.34798	−	14.4591i	−0.729367	−	1.26330i	0.227784	−	0.973712i	$-0.426852\pi$
$132$		0			0
$133$		0			0
$134$			6.52412i			0.563598i
$135$		0			0
$136$			0.327345i			0.0280696i
$137$	−14.2714	−	8.23961i	−1.21929	−	0.703957i	−0.254524	−	0.967066i	$-0.581919\pi$
$137$	−14.2714	−	8.23961i	−1.21929	−	0.703957i	−0.964766	+	0.263109i	$0.915252\pi$
$138$		0			0
$139$	−1.71999	+	0.993034i	−0.145887	+	0.0842281i	−0.571167	−	0.820834i	$-0.693509\pi$
$139$	−1.71999	+	0.993034i	−0.145887	+	0.0842281i	0.425280	+	0.905062i	$0.360176\pi$
$140$		0			0
$141$		0			0
$142$	−8.13232	+	14.0856i	−0.682449	+	1.18204i
$143$	−3.33441			−0.278837
$144$		0			0
$145$			2.92086i			0.242564i
$146$	−2.06324	+	3.57364i	−0.170755	+	0.295756i
$147$		0			0
$148$	1.84115	+	3.18897i	0.151342	+	0.262132i
$149$	14.6722	−	8.47103i	1.20200	−	0.693973i	0.240998	−	0.970526i	$-0.422525\pi$
$149$	14.6722	−	8.47103i	1.20200	−	0.693973i	0.960999	+	0.276552i	$0.0891918\pi$
$150$		0			0
$151$	−4.54082	+	7.86493i	−0.369527	+	0.640039i	−0.989492	−	0.144591i	$-0.953813\pi$
$151$	−4.54082	+	7.86493i	−0.369527	+	0.640039i	0.619965	+	0.784630i	$0.287147\pi$
$152$	4.23981			0.343894
$153$		0			0
$154$		0			0
$155$	−2.67255	−	1.54300i	−0.214664	−	0.123937i
$156$		0			0
$157$	8.55567	−	4.93962i	0.682817	−	0.394224i	−0.118099	−	0.993002i	$-0.537680\pi$
$157$	8.55567	−	4.93962i	0.682817	−	0.394224i	0.800915	+	0.598777i	$0.204347\pi$
$158$	−1.14718	+	0.662324i	−0.0912646	+	0.0526917i
$159$		0			0
$160$	−0.381202	−	0.220087i	−0.0301367	−	0.0173994i
$161$		0			0
$162$		0			0
$163$	5.26969			0.412754			0.206377	−	0.978473i	$-0.433833\pi$
$163$	5.26969			0.412754			0.206377	+	0.978473i	$0.433833\pi$
$164$	2.96701	−	5.13902i	0.231685	−	0.401290i
$165$		0			0
$166$	14.8132	−	8.55240i	1.14973	−	0.663795i
$167$	−6.69964	−	11.6041i	−0.518433	−	0.897953i	−0.999771	−	0.0214174i	$-0.993182\pi$
$167$	−6.69964	−	11.6041i	−0.518433	−	0.897953i	0.481337	−	0.876535i	$-0.340151\pi$
$168$		0			0
$169$	14.0365	−	24.3119i	1.07973	−	1.87015i
$170$		−	0.144089i		−	0.0110511i
$171$		0			0
$172$	10.4280			0.795127
$173$	−7.57707	+	13.1239i	−0.576074	+	0.997790i	0.419850	+	0.907594i	$0.362083\pi$
$173$	−7.57707	+	13.1239i	−0.576074	+	0.997790i	−0.995924	+	0.0901962i	$0.971251\pi$
$174$		0			0
$175$		0			0
$176$	−0.450580	+	0.260142i	−0.0339637	+	0.0196090i
$177$		0			0
$178$	−10.1540	−	5.86239i	−0.761072	−	0.439405i
$179$		−	20.9184i		−	1.56351i	−0.623585	−	0.781756i	$-0.714324\pi$
$179$		−	20.9184i		−	1.56351i	0.623585	−	0.781756i	$-0.285676\pi$
$180$		0			0
$181$		−	14.5567i		−	1.08199i	−0.841026	−	0.540995i	$-0.818048\pi$
$181$		−	14.5567i		−	1.08199i	0.841026	−	0.540995i	$-0.181952\pi$
$182$		0			0
$183$		0			0
$184$	0.725359	+	1.25636i	0.0534742	+	0.0926200i
$185$	−0.810428	−	1.40370i	−0.0595838	−	0.103202i
$186$		0			0
$187$	−0.147495	−	0.0851562i	−0.0107859	−	0.00622724i
$188$	8.05267			0.587301
$189$		0			0
$190$	−1.86625			−0.135392
$191$	17.0163	+	9.82435i	1.23125	+	0.710865i	0.967291	−	0.253668i	$-0.0816371\pi$
$191$	17.0163	+	9.82435i	1.23125	+	0.710865i	0.263963	+	0.964533i	$0.414970\pi$
$192$		0			0
$193$	−5.87861	−	10.1820i	−0.423151	−	0.732920i	0.573094	−	0.819489i	$-0.305743\pi$
$193$	−5.87861	−	10.1820i	−0.423151	−	0.732920i	−0.996246	+	0.0865696i	$0.972410\pi$
$194$	6.12344	+	10.6061i	0.439637	+	0.761474i
$195$		0			0
$196$		0			0
$197$		−	12.6642i		−	0.902290i	−0.892451	−	0.451145i	$-0.851016\pi$
$197$		−	12.6642i		−	0.902290i	0.892451	−	0.451145i	$-0.148984\pi$
$198$		0			0
$199$			17.8214i			1.26333i	0.775243	+	0.631663i	$0.217627\pi$
$199$			17.8214i			1.26333i	−0.775243	+	0.631663i	$0.782373\pi$
$200$	−4.16233	−	2.40312i	−0.294321	−	0.169926i
$201$		0			0
$202$	9.36159	−	5.40492i	0.658679	−	0.380289i
$203$		0			0
$204$		0			0
$205$	−1.30600	+	2.26206i	−0.0912152	+	0.157989i
$206$	−11.1905			−0.779676
$207$		0			0
$208$		−	6.40882i		−	0.444372i
$209$	−1.10295	+	1.91037i	−0.0762929	+	0.132143i
$210$		0			0
$211$	−0.975723	−	1.69000i	−0.0671715	−	0.116344i	0.830484	−	0.557043i	$-0.188064\pi$
$211$	−0.975723	−	1.69000i	−0.0671715	−	0.116344i	−0.897655	+	0.440698i	$0.854731\pi$
$212$	−6.89072	+	3.97836i	−0.473257	+	0.273235i
$213$		0			0
$214$	0.339361	−	0.587790i	0.0231982	−	0.0401805i
$215$	−4.59013			−0.313045
$216$		0			0
$217$		0			0
$218$	−15.7793	−	9.11016i	−1.06871	−	0.617018i
$219$		0			0
$220$	0.198334	−	0.114508i	0.0133716	−	0.00772012i
$221$	1.81683	−	1.04895i	0.122213	−	0.0705597i
$222$		0			0
$223$	3.44154	+	1.98697i	0.230463	+	0.133058i	0.610785	−	0.791796i	$-0.290854\pi$
$223$	3.44154	+	1.98697i	0.230463	+	0.133058i	−0.380323	+	0.924854i	$0.624187\pi$
$224$		0			0
$225$		0			0
$226$	−10.6098			−0.705751
$227$	−3.63558	+	6.29701i	−0.241302	+	0.417947i	−0.961085	−	0.276251i	$-0.910908\pi$
$227$	−3.63558	+	6.29701i	−0.241302	+	0.417947i	0.719783	+	0.694199i	$0.244241\pi$
$228$		0			0
$229$	1.51483	−	0.874590i	0.100103	−	0.0577945i	−0.449113	−	0.893475i	$-0.648260\pi$
$229$	1.51483	−	0.874590i	0.100103	−	0.0577945i	0.549216	+	0.835681i	$0.314927\pi$
$230$	−0.319284	−	0.553017i	−0.0210530	−	0.0364648i
$231$		0			0
$232$	−3.31785	+	5.74668i	−0.217827	+	0.377288i
$233$		−	6.89073i		−	0.451427i	−0.974194	−	0.225713i	$-0.927529\pi$
$233$		−	6.89073i		−	0.451427i	0.974194	−	0.225713i	$-0.0724713\pi$
$234$		0			0
$235$	−3.54458			−0.231223
$236$	−2.45205	+	4.24708i	−0.159615	+	0.276461i
$237$		0			0
$238$		0			0
$239$	−16.3611	+	9.44606i	−1.05831	+	0.611015i	−0.924964	−	0.380055i	$-0.875905\pi$
$239$	−16.3611	+	9.44606i	−1.05831	+	0.611015i	−0.133345	+	0.991070i	$0.542572\pi$
$240$		0			0
$241$	−14.1951	−	8.19555i	−0.914387	−	0.527922i	−0.0325469	−	0.999470i	$-0.510362\pi$
$241$	−14.1951	−	8.19555i	−0.914387	−	0.527922i	−0.881840	+	0.471549i	$0.843695\pi$
$242$			10.7293i			0.689706i
$243$		0			0
$244$			1.54358i			0.0988177i
$245$		0			0
$246$		0			0
$247$	−13.5861	−	23.5318i	−0.864462	−	1.49729i
$248$	−3.50542	−	6.07157i	−0.222595	−	0.385545i
$249$		0			0
$250$	3.73816	+	2.15823i	0.236422	+	0.136498i
$251$	−0.663086			−0.0418536			−0.0209268	−	0.999781i	$-0.506662\pi$
$251$	−0.663086			−0.0418536			−0.0209268	+	0.999781i	$0.506662\pi$
$252$		0			0
$253$	−0.754786			−0.0474530
$254$	2.49579	+	1.44094i	0.156600	+	0.0904129i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.83784	−	4.91529i	−0.177020	−	0.306607i	0.763839	−	0.645407i	$-0.223312\pi$
$257$	−2.83784	−	4.91529i	−0.177020	−	0.306607i	−0.940858	+	0.338800i	$0.889979\pi$
$258$		0			0
$259$		0			0
$260$			2.82100i			0.174951i
$261$		0			0
$262$			16.6960i			1.03148i
$263$	−8.73855	−	5.04520i	−0.538842	−	0.311101i	0.205767	−	0.978601i	$-0.434031\pi$
$263$	−8.73855	−	5.04520i	−0.538842	−	0.311101i	−0.744610	+	0.667500i	$0.767364\pi$
$264$		0			0
$265$	3.03312	−	1.75117i	0.186323	−	0.107574i
$266$		0			0
$267$		0			0
$268$	3.26206	−	5.65005i	0.199262	−	0.345132i
$269$	19.3340			1.17881			0.589406	−	0.807837i	$-0.299362\pi$
$269$	19.3340			1.17881			0.589406	+	0.807837i	$0.299362\pi$
$270$		0			0
$271$			12.2930i			0.746749i	0.927681	+	0.373374i	$0.121799\pi$
$271$			12.2930i			0.746749i	−0.927681	+	0.373374i	$0.878201\pi$
$272$	0.163672	−	0.283489i	0.00992409	−	0.0171890i
$273$		0			0
$274$	8.23961	+	14.2714i	0.497773	+	0.862168i
$275$	2.16560	−	1.25031i	0.130590	−	0.0753964i
$276$		0			0
$277$	4.08322	−	7.07235i	0.245337	−	0.424936i	−0.716889	−	0.697187i	$-0.754435\pi$
$277$	4.08322	−	7.07235i	0.245337	−	0.424936i	0.962226	+	0.272251i	$0.0877680\pi$
$278$	1.98607			0.119116
$279$		0			0
$280$		0			0
$281$	27.6901	+	15.9869i	1.65185	+	0.953697i	0.976310	+	0.216375i	$0.0694232\pi$
$281$	27.6901	+	15.9869i	1.65185	+	0.953697i	0.675541	+	0.737322i	$0.263910\pi$
$282$		0			0
$283$	8.71809	−	5.03339i	0.518237	−	0.299204i	−0.217976	−	0.975954i	$-0.569946\pi$
$283$	8.71809	−	5.03339i	0.518237	−	0.299204i	0.736213	+	0.676750i	$0.236612\pi$
$284$	14.0856	−	8.13232i	0.835826	−	0.482565i
$285$		0			0
$286$	2.88768	+	1.66720i	0.170752	+	0.0985839i
$287$		0			0
$288$		0			0
$289$	−16.8928			−0.993697
$290$	1.46043	−	2.52954i	0.0857594	−	0.148540i
$291$		0			0
$292$	3.57364	−	2.06324i	0.209131	−	0.120742i
$293$	6.64697	+	11.5129i	0.388320	+	0.672590i	0.992224	−	0.124467i	$-0.0397221\pi$
$293$	6.64697	+	11.5129i	0.388320	+	0.672590i	−0.603904	+	0.797057i	$0.706389\pi$
$294$		0			0
$295$	1.07933	−	1.86945i	0.0628410	−	0.108844i
$296$		−	3.68230i		−	0.214030i
$297$		0			0
$298$	−16.9421			−0.981427
$299$	4.64869	−	8.05177i	0.268841	−	0.465646i
$300$		0			0
$301$		0			0
$302$	7.86493	−	4.54082i	0.452576	−	0.261295i
$303$		0			0
$304$	−3.67178	−	2.11990i	−0.210591	−	0.121585i
$305$		−	0.679445i		−	0.0389049i
$306$		0			0
$307$			5.44565i			0.310799i	0.987852	+	0.155400i	$0.0496665\pi$
$307$			5.44565i			0.310799i	−0.987852	+	0.155400i	$0.950333\pi$
$308$		0			0
$309$		0			0
$310$	1.54300	+	2.67255i	0.0876364	+	0.151791i
$311$	0.129774	+	0.224774i	0.00735878	+	0.0127458i	0.869681	−	0.493614i	$-0.164324\pi$
$311$	0.129774	+	0.224774i	0.00735878	+	0.0127458i	−0.862323	+	0.506359i	$0.830991\pi$
$312$		0			0
$313$	−26.6757	−	15.4012i	−1.50780	−	0.870528i	−0.999959	−	0.00907611i	$-0.997111\pi$
$313$	−26.6757	−	15.4012i	−1.50780	−	0.870528i	−0.507840	−	0.861452i	$-0.669556\pi$
$314$	−9.87924			−0.557518
$315$		0			0
$316$	1.32465			0.0745173
$317$	−13.8977	−	8.02382i	−0.780570	−	0.450662i	0.0560621	−	0.998427i	$-0.482146\pi$
$317$	−13.8977	−	8.02382i	−0.780570	−	0.450662i	−0.836632	+	0.547765i	$0.815479\pi$
$318$		0			0
$319$	−1.72622	−	2.98991i	−0.0966500	−	0.167403i
$320$	0.220087	+	0.381202i	0.0123032	+	0.0213098i
$321$		0			0
$322$		0			0
$323$		−	1.38788i		−	0.0772236i
$324$		0			0
$325$			30.8024i			1.70861i
$326$	−4.56369	−	2.63485i	−0.252759	−	0.145931i
$327$		0			0
$328$	−5.13902	+	2.96701i	−0.283755	+	0.163826i
$329$		0			0
$330$		0			0
$331$	13.6069	−	23.5678i	0.747901	−	1.29540i	−0.200926	−	0.979606i	$-0.564395\pi$
$331$	13.6069	−	23.5678i	0.747901	−	1.29540i	0.948827	−	0.315796i	$-0.102272\pi$
$332$	−17.1048			−0.938748
$333$		0			0
$334$			13.3993i			0.733175i
$335$	−1.43587	+	2.48701i	−0.0784502	+	0.135880i
$336$		0			0
$337$	−2.35738	−	4.08310i	−0.128415	−	0.222421i	0.794648	−	0.607071i	$-0.207656\pi$
$337$	−2.35738	−	4.08310i	−0.128415	−	0.222421i	−0.923063	+	0.384650i	$0.874322\pi$
$338$	−24.3119	+	14.0365i	−1.32239	+	0.763484i
$339$		0			0
$340$	−0.0720443	+	0.124784i	−0.00390715	+	0.00676738i
$341$	3.64764			0.197531
$342$		0			0
$343$		0			0
$344$	−9.03091	−	5.21400i	−0.486914	−	0.281120i
$345$		0			0
$346$	13.1239	−	7.57707i	0.705544	−	0.407346i
$347$	−4.84197	+	2.79551i	−0.259930	+	0.150071i	−0.624303	−	0.781182i	$-0.714617\pi$
$347$	−4.84197	+	2.79551i	−0.259930	+	0.150071i	0.364372	+	0.931253i	$0.381284\pi$
$348$		0			0
$349$	−3.38689	−	1.95542i	−0.181296	−	0.104671i	0.406605	−	0.913604i	$-0.366712\pi$
$349$	−3.38689	−	1.95542i	−0.181296	−	0.104671i	−0.587902	+	0.808932i	$0.700046\pi$
$350$		0			0
$351$		0			0
$352$	0.520285			0.0277313
$353$	−0.359707	+	0.623031i	−0.0191453	+	0.0331606i	−0.875439	−	0.483328i	$-0.839428\pi$
$353$	−0.359707	+	0.623031i	−0.0191453	+	0.0331606i	0.856294	+	0.516489i	$0.172761\pi$
$354$		0			0
$355$	−6.20012	+	3.57964i	−0.329068	+	0.189988i
$356$	5.86239	+	10.1540i	0.310706	+	0.538159i
$357$		0			0
$358$	−10.4592	+	18.1158i	−0.552785	+	0.957451i
$359$		−	19.6045i		−	1.03469i	−0.855778	−	0.517343i	$-0.826921\pi$
$359$		−	19.6045i		−	1.03469i	0.855778	−	0.517343i	$-0.173079\pi$
$360$		0			0
$361$	1.02402			0.0538959
$362$	−7.27834	+	12.6065i	−0.382541	+	0.662581i
$363$		0			0
$364$		0			0
$365$	−1.57302	+	0.908185i	−0.0823358	+	0.0475366i
$366$		0			0
$367$	−12.1913	−	7.03862i	−0.636378	−	0.367413i	0.146840	−	0.989160i	$-0.453090\pi$
$367$	−12.1913	−	7.03862i	−0.636378	−	0.367413i	−0.783218	+	0.621747i	$0.786423\pi$
$368$		−	1.45072i		−	0.0756239i
$369$		0			0
$370$			1.62086i			0.0842643i
$371$		0			0
$372$		0			0
$373$	6.40178	+	11.0882i	0.331471	+	0.574125i	0.982801	−	0.184670i	$-0.0591216\pi$
$373$	6.40178	+	11.0882i	0.331471	+	0.574125i	−0.651329	+	0.758795i	$0.725788\pi$
$374$	0.0851562	+	0.147495i	0.00440332	+	0.00762678i
$375$		0			0
$376$	−6.97382	−	4.02633i	−0.359647	−	0.207642i
$377$	42.5269			2.19025
$378$		0			0
$379$	−33.3624			−1.71371			−0.856856	−	0.515556i	$-0.827585\pi$
$379$	−33.3624			−1.71371			−0.856856	+	0.515556i	$0.827585\pi$
$380$	1.61622	+	0.933127i	0.0829105	+	0.0478684i
$381$		0			0
$382$	−9.82435	−	17.0163i	−0.502657	−	0.870628i
$383$	−4.03360	−	6.98639i	−0.206107	−	0.356988i	0.744378	−	0.667759i	$-0.232746\pi$
$383$	−4.03360	−	6.98639i	−0.206107	−	0.356988i	−0.950485	+	0.310771i	$0.899413\pi$
$384$		0			0
$385$		0			0
$386$			11.7572i			0.598427i
$387$		0			0
$388$		−	12.2469i		−	0.621741i
$389$	29.8901	+	17.2571i	1.51549	+	0.874968i	0.999835	+	0.0181720i	$0.00578465\pi$
$389$	29.8901	+	17.2571i	1.51549	+	0.874968i	0.515655	+	0.856796i	$0.327549\pi$
$390$		0			0
$391$	0.411262	−	0.237442i	0.0207984	−	0.0120080i
$392$		0			0
$393$		0			0
$394$	−6.33212	+	10.9676i	−0.319008	+	0.552538i
$395$	−0.583076			−0.0293377
$396$		0			0
$397$			19.2184i			0.964544i	0.876022	+	0.482272i	$0.160188\pi$
$397$			19.2184i			0.964544i	−0.876022	+	0.482272i	$0.839812\pi$
$398$	8.91071	−	15.4338i	0.446653	−	0.773626i
$399$		0			0
$400$	2.40312	+	4.16233i	0.120156	+	0.208117i
$401$	13.8907	−	8.01983i	0.693671	−	0.400491i	−0.111315	−	0.993785i	$-0.535506\pi$
$401$	13.8907	−	8.01983i	0.693671	−	0.400491i	0.804986	+	0.593294i	$0.202173\pi$
$402$		0			0
$403$	−22.4656	+	38.9116i	−1.11909	+	1.93833i
$404$	−10.8098			−0.537809
$405$		0			0
$406$		0			0
$407$	1.65917	+	0.957923i	0.0822421	+	0.0474825i
$408$		0			0
$409$	20.7630	−	11.9875i	1.02666	−	0.592745i	0.110637	−	0.993861i	$-0.464711\pi$
$409$	20.7630	−	11.9875i	1.02666	−	0.592745i	0.916027	+	0.401116i	$0.131377\pi$
$410$	2.26206	−	1.30600i	0.111715	−	0.0644989i
$411$		0			0
$412$	9.69122	+	5.59523i	0.477452	+	0.275657i
$413$		0			0
$414$		0			0
$415$	7.52909			0.369589
$416$	−3.20441	+	5.55020i	−0.157109	+	0.272121i
$417$		0			0
$418$	1.91037	−	1.10295i	0.0934393	−	0.0539472i
$419$	−13.9896	−	24.2307i	−0.683436	−	1.18375i	−0.973926	−	0.226868i	$-0.927151\pi$
$419$	−13.9896	−	24.2307i	−0.683436	−	1.18375i	0.290490	−	0.956878i	$-0.406182\pi$
$420$		0			0
$421$	4.45075	−	7.70893i	0.216916	−	0.375710i	−0.736947	−	0.675950i	$-0.763733\pi$
$421$	4.45075	−	7.70893i	0.216916	−	0.375710i	0.953864	+	0.300240i	$0.0970668\pi$
$422$			1.95145i			0.0949949i
$423$		0			0
$424$	7.95672			0.386412
$425$	−0.786649	+	1.36252i	−0.0381581	+	0.0660918i
$426$		0			0
$427$		0			0
$428$	−0.587790	+	0.339361i	−0.0284119	+	0.0164036i
$429$		0			0
$430$	3.97517	+	2.29507i	0.191700	+	0.110678i
$431$			2.25785i			0.108757i	0.998520	+	0.0543785i	$0.0173177\pi$
$431$			2.25785i			0.108757i	−0.998520	+	0.0543785i	$0.982682\pi$
$432$		0			0
$433$		−	12.6020i		−	0.605612i	−0.953052	−	0.302806i	$-0.902077\pi$
$433$		−	12.6020i		−	0.605612i	0.953052	−	0.302806i	$-0.0979234\pi$
$434$		0			0
$435$		0			0
$436$	9.11016	+	15.7793i	0.436297	+	0.755689i
$437$	−3.07538	−	5.32672i	−0.147116	−	0.254812i
$438$		0			0
$439$	−24.4195	−	14.0986i	−1.16548	−	0.672888i	−0.212866	−	0.977081i	$-0.568280\pi$
$439$	−24.4195	−	14.0986i	−1.16548	−	0.672888i	−0.952610	+	0.304193i	$0.901613\pi$
$440$	−0.229016			−0.0109179
$441$		0			0
$442$	−2.09789			−0.0997865
$443$	−27.2756	−	15.7476i	−1.29590	−	0.748190i	−0.316209	−	0.948689i	$-0.602410\pi$
$443$	−27.2756	−	15.7476i	−1.29590	−	0.748190i	−0.979694	+	0.200499i	$0.935744\pi$
$444$		0			0
$445$	−2.58047	−	4.46951i	−0.122326	−	0.211875i
$446$	−1.98697	−	3.44154i	−0.0940860	−	0.162962i
$447$		0			0
$448$		0			0
$449$			24.8151i			1.17110i	0.810638	+	0.585548i	$0.199120\pi$
$449$			24.8151i			1.17110i	−0.810638	+	0.585548i	$0.800880\pi$
$450$		0			0
$451$		−	3.08738i		−	0.145379i
$452$	9.18833	+	5.30488i	0.432183	+	0.249521i
$453$		0			0
$454$	6.29701	−	3.63558i	0.295533	−	0.170626i
$455$		0			0
$456$		0			0
$457$	−8.04092	+	13.9273i	−0.376138	+	0.651491i	−0.990497	−	0.137536i	$-0.956082\pi$
$457$	−8.04092	+	13.9273i	−0.376138	+	0.651491i	0.614358	+	0.789027i	$0.289415\pi$
$458$	−1.74918			−0.0817338
$459$		0			0
$460$			0.638569i			0.0297734i
$461$	11.7250	−	20.3083i	0.546089	−	0.945853i	−0.452449	−	0.891790i	$-0.649450\pi$
$461$	11.7250	−	20.3083i	0.546089	−	0.945853i	0.998538	−	0.0540628i	$-0.0172171\pi$
$462$		0			0
$463$	8.40381	+	14.5558i	0.390558	+	0.676467i	0.992523	−	0.122056i	$-0.0389486\pi$
$463$	8.40381	+	14.5558i	0.390558	+	0.676467i	−0.601965	+	0.798523i	$0.705615\pi$
$464$	5.74668	−	3.31785i	0.266783	−	0.154027i
$465$		0			0
$466$	−3.44537	+	5.96755i	−0.159603	+	0.276441i
$467$	−6.41671			−0.296930			−0.148465	−	0.988918i	$-0.547433\pi$
$467$	−6.41671			−0.296930			−0.148465	+	0.988918i	$0.547433\pi$
$468$		0			0
$469$		0			0
$470$	3.06969	+	1.77229i	0.141594	+	0.0817496i
$471$		0			0
$472$	4.24708	−	2.45205i	0.195488	−	0.112865i
$473$	4.69864	−	2.71276i	0.216044	−	0.124733i
$474$		0			0
$475$	17.6475	+	10.1888i	0.809722	+	0.467493i
$476$		0			0
$477$		0			0
$478$	18.8921			0.864105
$479$	6.35492	−	11.0070i	0.290364	−	0.502925i	−0.683532	−	0.729921i	$-0.739557\pi$
$479$	6.35492	−	11.0070i	0.290364	−	0.502925i	0.973896	+	0.226996i	$0.0728904\pi$
$480$		0			0
$481$	−20.4375	+	11.7996i	−0.931871	+	0.538016i
$482$	8.19555	+	14.1951i	0.373297	+	0.646569i
$483$		0			0
$484$	5.36465	−	9.29185i	0.243848	−	0.422357i
$485$			5.39076i			0.244782i
$486$		0			0
$487$	−2.62592			−0.118992			−0.0594960	−	0.998229i	$-0.518949\pi$
$487$	−2.62592			−0.118992			−0.0594960	+	0.998229i	$0.518949\pi$
$488$	0.771791	−	1.33678i	0.0349373	−	0.0605132i
$489$		0			0
$490$		0			0
$491$	4.13045	−	2.38472i	0.186405	−	0.107621i	−0.403894	−	0.914806i	$-0.632343\pi$
$491$	4.13045	−	2.38472i	0.186405	−	0.107621i	0.590298	+	0.807185i	$0.299010\pi$
$492$		0			0
$493$	1.88114	+	1.08608i	0.0847225	+	0.0489145i
$494$			27.1722i			1.22253i
$495$		0			0
$496$			7.01085i			0.314796i
$497$		0			0
$498$		0			0
$499$	9.73459	+	16.8608i	0.435780	+	0.754793i	0.997359	−	0.0726299i	$-0.0231392\pi$
$499$	9.73459	+	16.8608i	0.435780	+	0.754793i	−0.561579	+	0.827423i	$0.689806\pi$
$500$	−2.15823	−	3.73816i	−0.0965189	−	0.167176i
$501$		0			0
$502$	0.574249	+	0.331543i	0.0256300	+	0.0147975i
$503$	9.40949			0.419549			0.209774	−	0.977750i	$-0.432727\pi$
$503$	9.40949			0.419549			0.209774	+	0.977750i	$0.432727\pi$
$504$		0			0
$505$	4.75821			0.211738
$506$	0.653664	+	0.377393i	0.0290589	+	0.0167772i
$507$		0			0
$508$	−1.44094	−	2.49579i	−0.0639316	−	0.110733i
$509$	9.40879	+	16.2965i	0.417037	+	0.722330i	0.995640	−	0.0932799i	$-0.0297351\pi$
$509$	9.40879	+	16.2965i	0.417037	+	0.722330i	−0.578603	+	0.815610i	$0.696402\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$			5.67569i			0.250344i
$515$	−4.26582	−	2.46287i	−0.187975	−	0.108527i
$516$		0			0
$517$	3.62837	−	2.09484i	0.159576	−	0.0921310i
$518$		0			0
$519$		0			0
$520$	1.41050	−	2.44305i	0.0618544	−	0.107135i
$521$	16.7044			0.731834			0.365917	−	0.930647i	$-0.380755\pi$
$521$	16.7044			0.731834			0.365917	+	0.930647i	$0.380755\pi$
$522$		0			0
$523$		−	15.4855i		−	0.677135i	−0.940942	−	0.338568i	$-0.890058\pi$
$523$		−	15.4855i		−	0.677135i	0.940942	−	0.338568i	$-0.109942\pi$
$524$	8.34798	−	14.4591i	0.364683	−	0.631650i
$525$		0			0
$526$	5.04520	+	8.73855i	0.219981	+	0.381019i
$527$	−1.98750	+	1.14748i	−0.0865767	+	0.0499851i
$528$		0			0
$529$	−10.4477	+	18.0960i	−0.454248	+	0.786781i
$530$	−3.50234			−0.152132
$531$		0			0
$532$		0			0
$533$	32.9350	+	19.0150i	1.42657	+	0.823633i
$534$		0			0
$535$	0.258730	−	0.149378i	0.0111859	−	0.00645817i
$536$	−5.65005	+	3.26206i	−0.244045	+	0.140900i
$537$		0			0
$538$	−16.7437	−	9.66698i	−0.721872	−	0.416773i
$539$		0			0
$540$		0			0
$541$	22.7051			0.976168			0.488084	−	0.872797i	$-0.337696\pi$
$541$	22.7051			0.976168			0.488084	+	0.872797i	$0.337696\pi$
$542$	6.14652	−	10.6461i	0.264016	−	0.457288i
$543$		0			0
$544$	−0.283489	+	0.163672i	−0.0121545	+	0.00701739i
$545$	−4.01006	−	6.94562i	−0.171772	−	0.297518i
$546$		0			0
$547$	−22.2991	+	38.6232i	−0.953441	+	1.65141i	−0.215546	+	0.976494i	$0.569153\pi$
$547$	−22.2991	+	38.6232i	−0.953441	+	1.65141i	−0.737895	+	0.674915i	$0.764180\pi$
$548$		−	16.4792i		−	0.703957i
$549$		0			0
$550$	−2.50062			−0.106627
$551$	14.0670	−	24.3648i	0.599276	−	1.03798i
$552$		0			0
$553$		0			0
$554$	−7.07235	+	4.08322i	−0.300475	+	0.173480i
$555$		0			0
$556$	−1.71999	−	0.993034i	−0.0729436	−	0.0421140i
$557$			25.2720i			1.07081i	0.844596	+	0.535405i	$0.179841\pi$
$557$			25.2720i			1.07081i	−0.844596	+	0.535405i	$0.820159\pi$
$558$		0			0
$559$			66.8311i			2.82666i
$560$		0			0
$561$		0			0
$562$	−15.9869	−	27.6901i	−0.674366	−	1.16804i
$563$	13.5727	+	23.5086i	0.572020	+	0.990767i	0.996358	+	0.0852637i	$0.0271733\pi$
$563$	13.5727	+	23.5086i	0.572020	+	0.990767i	−0.424339	+	0.905504i	$0.639493\pi$
$564$		0			0
$565$	−4.04446	−	2.33507i	−0.170152	−	0.0982372i
$566$	−10.0668			−0.423139
$567$		0			0
$568$	−16.2646			−0.682449
$569$	13.4182	+	7.74698i	0.562519	+	0.324770i	0.754156	−	0.656695i	$-0.228046\pi$
$569$	13.4182	+	7.74698i	0.562519	+	0.324770i	−0.191637	+	0.981466i	$0.561380\pi$
$570$		0			0
$571$	0.784829	+	1.35936i	0.0328441	+	0.0568876i	0.881980	−	0.471286i	$-0.156210\pi$
$571$	0.784829	+	1.35936i	0.0328441	+	0.0568876i	−0.849136	+	0.528174i	$0.822877\pi$
$572$	−1.66720	−	2.88768i	−0.0697093	−	0.120740i
$573$		0			0
$574$		0			0
$575$			6.97251i			0.290774i
$576$		0			0
$577$			12.2773i			0.511113i	0.966794	+	0.255556i	$0.0822586\pi$
$577$			12.2773i			0.511113i	−0.966794	+	0.255556i	$0.917741\pi$
$578$	14.6296	+	8.44642i	0.608513	+	0.351325i
$579$		0			0
$580$	−2.52954	+	1.46043i	−0.105033	+	0.0606411i
$581$		0			0
$582$		0			0
$583$	−2.06988	+	3.58514i	−0.0857256	+	0.148481i
$584$	−4.12648			−0.170755
$585$		0			0
$586$		−	13.2939i		−	0.549168i
$587$	−7.79739	+	13.5055i	−0.321833	+	0.557431i	−0.980866	−	0.194683i	$-0.937632\pi$
$587$	−7.79739	+	13.5055i	−0.321833	+	0.557431i	0.659033	+	0.752114i	$0.270966\pi$
$588$		0			0
$589$	14.8623	+	25.7423i	0.612392	+	1.06069i
$590$	−1.86945	+	1.07933i	−0.0769642	+	0.0444353i
$591$		0			0
$592$	−1.84115	+	3.18897i	−0.0756709	+	0.131066i
$593$	−23.6898			−0.972825			−0.486412	−	0.873729i	$-0.661695\pi$
$593$	−23.6898			−0.972825			−0.486412	+	0.873729i	$0.661695\pi$
$594$		0			0
$595$		0			0
$596$	14.6722	+	8.47103i	0.600999	+	0.346987i
$597$		0			0
$598$	−8.05177	+	4.64869i	−0.329262	+	0.190099i
$599$	1.89981	−	1.09686i	0.0776242	−	0.0448164i	−0.460686	−	0.887563i	$-0.652396\pi$
$599$	1.89981	−	1.09686i	0.0776242	−	0.0448164i	0.538310	+	0.842747i	$0.319063\pi$
$600$		0			0
$601$	−4.26683	−	2.46345i	−0.174047	−	0.100486i	0.410445	−	0.911885i	$-0.365373\pi$
$601$	−4.26683	−	2.46345i	−0.174047	−	0.100486i	−0.584493	+	0.811399i	$0.698707\pi$
$602$		0			0
$603$		0			0
$604$	−9.08164			−0.369527
$605$	−2.36138	+	4.09003i	−0.0960038	+	0.166283i
$606$		0			0
$607$	−5.09255	+	2.94018i	−0.206700	+	0.119338i	−0.599777	−	0.800167i	$-0.704744\pi$
$607$	−5.09255	+	2.94018i	−0.206700	+	0.119338i	0.393077	+	0.919506i	$0.371411\pi$
$608$	2.11990	+	3.67178i	0.0859735	+	0.148910i
$609$		0			0
$610$	−0.339722	+	0.588416i	−0.0137550	+	0.0238243i
$611$			51.6081i			2.08784i
$612$		0			0
$613$	26.4873			1.06981			0.534906	−	0.844912i	$-0.320347\pi$
$613$	26.4873			1.06981			0.534906	+	0.844912i	$0.320347\pi$
$614$	2.72282	−	4.71607i	0.109884	−	0.190325i
$615$		0			0
$616$		0			0
$617$	17.9549	−	10.3663i	0.722839	−	0.417331i	−0.0929578	−	0.995670i	$-0.529632\pi$
$617$	17.9549	−	10.3663i	0.722839	−	0.417331i	0.815797	+	0.578339i	$0.196299\pi$
$618$		0			0
$619$	−5.47577	−	3.16144i	−0.220090	−	0.127069i	0.385902	−	0.922540i	$-0.373890\pi$
$619$	−5.47577	−	3.16144i	−0.220090	−	0.127069i	−0.605992	+	0.795471i	$0.707224\pi$
$620$		−	3.08599i		−	0.123937i
$621$		0			0
$622$		−	0.259547i		−	0.0104069i
$623$		0			0
$624$		0			0
$625$	−11.0656	−	19.1662i	−0.442625	−	0.766649i
$626$	15.4012	+	26.6757i	0.615556	+	1.06617i
$627$		0			0
$628$	8.55567	+	4.93962i	0.341408	+	0.197112i
$629$	−1.20538			−0.0480617
$630$		0			0
$631$	−9.24859			−0.368180			−0.184090	−	0.982909i	$-0.558934\pi$
$631$	−9.24859			−0.368180			−0.184090	+	0.982909i	$0.558934\pi$
$632$	−1.14718	−	0.662324i	−0.0456323	−	0.0263458i
$633$		0			0
$634$	8.02382	+	13.8977i	0.318666	+	0.551946i
$635$	0.634266	+	1.09858i	0.0251701	+	0.0435959i
$636$		0			0
$637$		0			0
$638$			3.45245i			0.136684i
$639$		0			0
$640$		−	0.440174i		−	0.0173994i
$641$	39.0779	+	22.5616i	1.54349	+	0.891132i	0.998615	+	0.0526111i	$0.0167544\pi$
$641$	39.0779	+	22.5616i	1.54349	+	0.891132i	0.544870	+	0.838520i	$0.316579\pi$
$642$		0			0
$643$	10.5183	−	6.07274i	0.414801	−	0.239486i	−0.278049	−	0.960567i	$-0.589688\pi$
$643$	10.5183	−	6.07274i	0.414801	−	0.239486i	0.692851	+	0.721081i	$0.256355\pi$
$644$		0			0
$645$		0			0
$646$	−0.693939	+	1.20194i	−0.0273027	+	0.0472896i
$647$	16.0283			0.630139			0.315070	−	0.949069i	$-0.397972\pi$
$647$	16.0283			0.630139			0.315070	+	0.949069i	$0.397972\pi$
$648$		0			0
$649$			2.55153i			0.100156i
$650$	15.4012	−	26.6756i	0.604084	−	1.04630i
$651$		0			0
$652$	2.63485	+	4.56369i	0.103189	+	0.178728i
$653$	−1.92426	+	1.11097i	−0.0753020	+	0.0434756i	−0.537178	−	0.843469i	$-0.680510\pi$
$653$	−1.92426	+	1.11097i	−0.0753020	+	0.0434756i	0.461876	+	0.886944i	$0.347176\pi$
$654$		0			0
$655$	−3.67457	+	6.36454i	−0.143577	+	0.248683i
$656$	5.93403			0.231685
$657$		0			0
$658$		0			0
$659$	−2.93978	−	1.69728i	−0.114518	−	0.0661168i	0.441647	−	0.897189i	$-0.354394\pi$
$659$	−2.93978	−	1.69728i	−0.114518	−	0.0661168i	−0.556165	+	0.831072i	$0.687728\pi$
$660$		0			0
$661$	−2.27818	+	1.31531i	−0.0886110	+	0.0511596i	−0.543651	−	0.839312i	$-0.682958\pi$
$661$	−2.27818	+	1.31531i	−0.0886110	+	0.0511596i	0.455040	+	0.890471i	$0.349625\pi$
$662$	−23.5678	+	13.6069i	−0.915988	+	0.528846i
$663$		0			0
$664$	14.8132	+	8.55240i	0.574863	+	0.331898i
$665$		0			0
$666$		0			0
$667$	9.62652			0.372740
$668$	6.69964	−	11.6041i	0.259217	−	0.448976i
$669$		0			0
$670$	2.48701	−	1.43587i	0.0960815	−	0.0554727i
$671$	0.401551	+	0.695507i	0.0155017	+	0.0268497i
$672$		0			0
$673$	−9.02538	+	15.6324i	−0.347903	+	0.602585i	−0.985877	−	0.167473i	$-0.946439\pi$
$673$	−9.02538	+	15.6324i	−0.347903	+	0.602585i	0.637974	+	0.770058i	$0.279773\pi$
$674$			4.71476i			0.181606i
$675$		0			0
$676$	28.0730			1.07973
$677$	−19.8417	+	34.3668i	−0.762578	+	1.32082i	0.178940	+	0.983860i	$0.442733\pi$
$677$	−19.8417	+	34.3668i	−0.762578	+	1.32082i	−0.941518	+	0.336963i	$0.890600\pi$
$678$		0			0
$679$		0			0
$680$	0.124784	−	0.0720443i	0.00478526	−	0.00276277i
$681$		0			0
$682$	−3.15895	−	1.82382i	−0.120962	−	0.0698376i
$683$			29.9509i			1.14604i	0.819541	+	0.573020i	$0.194228\pi$
$683$			29.9509i			1.14604i	−0.819541	+	0.573020i	$0.805772\pi$
$684$		0			0
$685$			7.25373i			0.277151i
$686$		0			0
$687$		0			0
$688$	5.21400	+	9.03091i	0.198782	+	0.344300i
$689$	−25.4966	−	44.1614i	−0.971342	−	1.68241i
$690$		0			0
$691$	−19.4916	−	11.2535i	−0.741496	−	0.428103i	0.0811172	−	0.996705i	$-0.474151\pi$
$691$	−19.4916	−	11.2535i	−0.741496	−	0.428103i	−0.822613	+	0.568602i	$0.807485\pi$
$692$	−15.1541			−0.576074
$693$		0			0
$694$	5.59102			0.212232
$695$	0.757093	+	0.437108i	0.0287182	+	0.0165805i
$696$		0			0
$697$	0.971236	+	1.68223i	0.0367882	+	0.0637190i
$698$	1.95542	+	3.38689i	0.0740139	+	0.128196i
$699$		0			0
$700$		0			0
$701$			6.00423i			0.226777i	0.993551	+	0.113388i	$0.0361704\pi$
$701$			6.00423i			0.226777i	−0.993551	+	0.113388i	$0.963830\pi$
$702$		0			0
$703$			15.6123i			0.588828i
$704$	−0.450580	−	0.260142i	−0.0169819	−	0.00980448i
$705$		0			0
$706$	0.623031	−	0.359707i	0.0234481	−	0.0135378i
$707$		0			0
$708$		0			0
$709$	−5.99791	+	10.3887i	−0.225256	+	0.390155i	−0.956396	−	0.292072i	$-0.905655\pi$
$709$	−5.99791	+	10.3887i	−0.225256	+	0.390155i	0.731140	+	0.682227i	$0.238989\pi$
$710$	7.15928			0.268683
$711$		0			0
$712$		−	11.7248i		−	0.439405i
$713$	−5.08538	+	8.80814i	−0.190449	+	0.329867i
$714$		0			0
$715$	0.733861	+	1.27108i	0.0274448	+	0.0475358i
$716$	18.1158	−	10.4592i	0.677020	−	0.390878i
$717$		0			0
$718$	−9.80225	+	16.9780i	−0.365817	+	0.633613i
$719$	−34.9738			−1.30430			−0.652151	−	0.758089i	$-0.726133\pi$
$719$	−34.9738			−1.30430			−0.652151	+	0.758089i	$0.726133\pi$
$720$		0			0
$721$		0			0
$722$	−0.886830	−	0.512011i	−0.0330044	−	0.0190551i
$723$		0			0
$724$	12.6065	−	7.27834i	0.468515	−	0.270497i
$725$	−27.6200	+	15.9464i	−1.02578	+	0.592234i
$726$		0			0
$727$	37.2435	+	21.5026i	1.38129	+	0.797486i	0.992312	−	0.123763i	$-0.0394963\pi$
$727$	37.2435	+	21.5026i	1.38129	+	0.797486i	0.388974	+	0.921249i	$0.372830\pi$
$728$		0			0
$729$		0			0
$730$	1.81637			0.0672269
$731$	−1.70677	+	2.95622i	−0.0631273	+	0.109340i
$732$		0			0
$733$	41.5096	−	23.9656i	1.53319	−	0.885188i	0.533979	−	0.845498i	$-0.320696\pi$
$733$	41.5096	−	23.9656i	1.53319	−	0.885188i	0.999212	−	0.0396905i	$-0.0126372\pi$
$734$	7.03862	+	12.1913i	0.259800	+	0.449987i
$735$		0			0
$736$	−0.725359	+	1.25636i	−0.0267371	+	0.0463100i
$737$		−	3.39440i		−	0.125034i
$738$		0			0
$739$	−9.24019			−0.339906			−0.169953	−	0.985452i	$-0.554362\pi$
$739$	−9.24019			−0.339906			−0.169953	+	0.985452i	$0.554362\pi$
$740$	0.810428	−	1.40370i	0.0297919	−	0.0516011i
$741$		0			0
$742$		0			0
$743$	−39.7222	+	22.9336i	−1.45726	+	0.841352i	−0.998876	−	0.0473999i	$-0.984906\pi$
$743$	−39.7222	+	22.9336i	−1.45726	+	0.841352i	−0.458389	+	0.888752i	$0.651573\pi$
$744$		0			0
$745$	−6.45834	−	3.72873i	−0.236615	−	0.136610i
$746$		−	12.8036i		−	0.468771i
$747$		0			0
$748$		−	0.170312i		−	0.00622724i
$749$		0			0
$750$		0			0
$751$	11.0946	+	19.2165i	0.404849	+	0.701219i	0.994304	−	0.106582i	$-0.0339908\pi$
$751$	11.0946	+	19.2165i	0.404849	+	0.701219i	−0.589455	+	0.807801i	$0.700657\pi$
$752$	4.02633	+	6.97382i	0.146825	+	0.254309i
$753$		0			0
$754$	−36.8294	−	21.2635i	−1.34125	−	0.774370i
$755$	3.99750			0.145484
$756$		0			0
$757$	−0.971966			−0.0353267			−0.0176633	−	0.999844i	$-0.505623\pi$
$757$	−0.971966			−0.0353267			−0.0176633	+	0.999844i	$0.505623\pi$
$758$	28.8927	+	16.6812i	1.04943	+	0.605889i
$759$		0			0
$760$	−0.933127	−	1.61622i	−0.0338481	−	0.0586266i
$761$	11.9307	+	20.6646i	0.432488	+	0.749091i	0.997087	−	0.0762743i	$-0.0243025\pi$
$761$	11.9307	+	20.6646i	0.432488	+	0.749091i	−0.564599	+	0.825365i	$0.690969\pi$
$762$		0			0
$763$		0			0
$764$			19.6487i			0.710865i
$765$		0			0
$766$			8.06719i			0.291480i
$767$	−27.2188	−	15.7148i	−0.982812	−	0.567427i
$768$		0			0
$769$	−2.29392	+	1.32440i	−0.0827209	+	0.0477589i	−0.540790	−	0.841158i	$-0.681875\pi$
$769$	−2.29392	+	1.32440i	−0.0827209	+	0.0477589i	0.458069	+	0.888917i	$0.348541\pi$
$770$		0			0
$771$		0			0
$772$	5.87861	−	10.1820i	0.211576	−	0.366460i
$773$	35.5698			1.27936			0.639678	−	0.768643i	$-0.279068\pi$
$773$	35.5698			1.27936			0.639678	+	0.768643i	$0.279068\pi$
$774$		0			0
$775$		−	33.6959i		−	1.21039i
$776$	−6.12344	+	10.6061i	−0.219819	+	0.380737i
$777$		0			0
$778$	−17.2571	−	29.8901i	−0.618696	−	1.07161i
$779$	21.7885	−	12.5796i	0.780652	−	0.450710i
$780$		0			0
$781$	4.23112	−	7.32852i	0.151402	−	0.262235i
$782$	−0.474885			−0.0169818
$783$		0			0
$784$		0			0
$785$	−3.76598	−	2.17429i	−0.134414	−	0.0776038i
$786$		0			0
$787$	24.6483	−	14.2307i	0.878616	−	0.507269i	0.00841411	−	0.999965i	$-0.497322\pi$
$787$	24.6483	−	14.2307i	0.878616	−	0.507269i	0.870202	+	0.492695i	$0.163988\pi$
$788$	10.9676	−	6.33212i	0.390703	−	0.225573i
$789$		0			0
$790$	0.504958	+	0.291538i	0.0179656	+	0.0103725i
$791$		0			0
$792$		0			0
$793$	−9.89253			−0.351294
$794$	9.60920	−	16.6436i	0.341018	−	0.590660i
$795$		0			0
$796$	−15.4338	+	8.91071i	−0.547036	+	0.315832i
$797$	−25.5890	−	44.3214i	−0.906408	−	1.56995i	−0.819015	−	0.573772i	$-0.805480\pi$
$797$	−25.5890	−	44.3214i	−0.906408	−	1.56995i	−0.0873931	−	0.996174i	$-0.527854\pi$
$798$		0			0
$799$	−1.31800	+	2.28284i	−0.0466274	+	0.0807611i
$800$		−	4.80625i		−	0.169926i
$801$		0			0
$802$	−16.0397			−0.566380
$803$	1.07347	−	1.85931i	0.0378820	−	0.0656136i
$804$		0			0
$805$		0			0
$806$	38.9116	−	22.4656i	1.37060	−	0.791318i
$807$		0			0
$808$	9.36159	+	5.40492i	0.329340	+	0.190144i
$809$		−	31.7896i		−	1.11766i	−0.829281	−	0.558832i	$-0.811250\pi$
$809$		−	31.7896i		−	1.11766i	0.829281	−	0.558832i	$-0.188750\pi$
$810$		0			0
$811$		−	42.1668i		−	1.48068i	−0.672235	−	0.740338i	$-0.734666\pi$
$811$		−	42.1668i		−	1.48068i	0.672235	−	0.740338i	$-0.265334\pi$
$812$		0			0
$813$		0			0
$814$	−0.957923	−	1.65917i	−0.0335752	−	0.0581539i
$815$	−1.15979	−	2.00882i	−0.0406257	−	0.0703658i
$816$		0			0
$817$	38.2893	+	22.1064i	1.33957	+	0.773403i
$818$	−23.9751			−0.838268
$819$		0			0
$820$	−2.61201			−0.0912152
$821$	−8.54339	−	4.93253i	−0.298166	−	0.172146i	0.343452	−	0.939170i	$-0.388404\pi$
$821$	−8.54339	−	4.93253i	−0.298166	−	0.172146i	−0.641619	+	0.767024i	$0.721737\pi$
$822$		0			0
$823$	20.2834	+	35.1319i	0.707035	+	1.22462i	0.965952	+	0.258721i	$0.0833011\pi$
$823$	20.2834	+	35.1319i	0.707035	+	1.22462i	−0.258917	+	0.965900i	$0.583366\pi$
$824$	−5.59523	−	9.69122i	−0.194919	−	0.337610i
$825$		0			0
$826$		0			0
$827$		−	3.24077i		−	0.112693i	−0.998411	−	0.0563463i	$-0.982055\pi$
$827$		−	3.24077i		−	0.112693i	0.998411	−	0.0563463i	$-0.0179451\pi$
$828$		0			0
$829$		−	47.6536i		−	1.65508i	−0.561409	−	0.827539i	$-0.689740\pi$
$829$		−	47.6536i		−	1.65508i	0.561409	−	0.827539i	$-0.310260\pi$
$830$	−6.52038	−	3.76455i	−0.226326	−	0.130669i
$831$		0			0
$832$	5.55020	−	3.20441i	0.192419	−	0.111093i
$833$		0			0
$834$		0			0
$835$	−2.94901	+	5.10783i	−0.102055	+	0.176764i
$836$	−2.20591			−0.0762929
$837$		0			0
$838$			27.9792i			0.966525i
$839$	3.12066	−	5.40514i	0.107737	−	0.186606i	−0.807116	−	0.590393i	$-0.798973\pi$
$839$	3.12066	−	5.40514i	0.107737	−	0.186606i	0.914853	+	0.403787i	$0.132306\pi$
$840$		0			0
$841$	7.51621	+	13.0185i	0.259180	+	0.448912i
$842$	−7.70893	+	4.45075i	−0.265667	+	0.153383i
$843$		0			0
$844$	0.975723	−	1.69000i	0.0335858	−	0.0581722i
$845$	−12.3570			−0.425093
$846$		0			0
$847$		0			0
$848$	−6.89072	−	3.97836i	−0.236628	−	0.136617i
$849$		0			0
$850$	1.36252	−	0.786649i	0.0467339	−	0.0269819i
$851$	−4.62630	+	2.67099i	−0.158587	+	0.0915605i
$852$		0			0
$853$	−14.6158	−	8.43842i	−0.500435	−	0.288926i	0.228458	−	0.973554i	$-0.426632\pi$
$853$	−14.6158	−	8.43842i	−0.500435	−	0.288926i	−0.728893	+	0.684628i	$0.759965\pi$
$854$		0			0
$855$		0			0
$856$	0.678721			0.0231982
$857$	−12.3709	+	21.4270i	−0.422581	+	0.731932i	−0.996191	−	0.0871967i	$-0.972209\pi$
$857$	−12.3709	+	21.4270i	−0.422581	+	0.731932i	0.573610	+	0.819128i	$0.305542\pi$
$858$		0			0
$859$	36.8928	−	21.3001i	1.25877	−	0.726749i	0.285932	−	0.958250i	$-0.407697\pi$
$859$	36.8928	−	21.3001i	1.25877	−	0.726749i	0.972835	+	0.231500i	$0.0743635\pi$
$860$	−2.29507	−	3.97517i	−0.0782611	−	0.135552i
$861$		0			0
$862$	1.12893	−	1.95536i	0.0384514	−	0.0665998i
$863$			45.9445i			1.56397i	0.623297	+	0.781985i	$0.285793\pi$
$863$			45.9445i			1.56397i	−0.623297	+	0.781985i	$0.714207\pi$
$864$		0			0
$865$	6.67046			0.226803
$866$	−6.30098	+	10.9136i	−0.214116	+	0.370860i
$867$		0			0
$868$		0			0
$869$	0.596859	−	0.344597i	0.0202471	−	0.0116897i
$870$		0			0
$871$	36.2102	+	20.9059i	1.22693	+	0.708371i
$872$		−	18.2203i		−	0.617018i
$873$		0			0
$874$			6.15077i			0.208053i
$875$		0			0
$876$		0			0
$877$	−2.28391	−	3.95585i	−0.0771222	−	0.133580i	0.824885	−	0.565301i	$-0.191240\pi$
$877$	−2.28391	−	3.95585i	−0.0771222	−	0.133580i	−0.902007	+	0.431721i	$0.857907\pi$
$878$	14.0986	+	24.4195i	0.475804	+	0.824117i
$879$		0			0
$880$	0.198334	+	0.114508i	0.00668582	+	0.00386006i
$881$	13.8959			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$881$	13.8959			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$882$		0			0
$883$	−37.2914			−1.25495			−0.627477	−	0.778635i	$-0.715912\pi$
$883$	−37.2914			−1.25495			−0.627477	+	0.778635i	$0.715912\pi$
$884$	1.81683	+	1.04895i	0.0611065	+	0.0352799i
$885$		0			0
$886$	15.7476	+	27.2756i	0.529050	+	0.916342i
$887$	21.1209	+	36.5825i	0.709171	+	1.22832i	0.965165	+	0.261642i	$0.0842641\pi$
$887$	21.1209	+	36.5825i	0.709171	+	1.22832i	−0.255993	+	0.966679i	$0.582403\pi$
$888$		0			0
$889$		0			0
$890$			5.16095i			0.172995i
$891$		0			0
$892$			3.97395i			0.133058i
$893$	29.5676	+	17.0709i	0.989443	+	0.571255i
$894$		0			0
$895$	−7.97412	+	4.60386i	−0.266545	+	0.153890i
$896$		0			0
$897$		0			0
$898$	12.4075	−	21.4905i	0.414045	−	0.717146i
$899$	−46.5218			−1.55159
$900$		0			0
$901$		−	2.60459i		−	0.0867714i
$902$	−1.54369	+	2.67375i	−0.0513993	+	0.0890262i
$903$		0			0
$904$	−5.30488	−	9.18833i	−0.176438	−	0.305599i
$905$	−5.54904	+	3.20374i	−0.184456	+	0.106496i
$906$		0			0
$907$	12.9784	−	22.4792i	0.430939	−	0.746409i	−0.566015	−	0.824395i	$-0.691516\pi$
$907$	12.9784	−	22.4792i	0.430939	−	0.746409i	0.996954	+	0.0779859i	$0.0248489\pi$
$908$	−7.27116			−0.241302
$909$		0			0
$910$		0			0
$911$	−11.2478	−	6.49395i	−0.372658	−	0.215154i	0.301961	−	0.953320i	$-0.402359\pi$
$911$	−11.2478	−	6.49395i	−0.372658	−	0.215154i	−0.674619	+	0.738166i	$0.735692\pi$
$912$		0			0
$913$	−7.70708	+	4.44968i	−0.255067	+	0.147263i
$914$	13.9273	−	8.04092i	0.460674	−	0.265970i
$915$		0			0
$916$	1.51483	+	0.874590i	0.0500515	+	0.0288973i
$917$		0			0
$918$		0			0
$919$	−33.9718			−1.12063			−0.560313	−	0.828281i	$-0.689319\pi$
$919$	−33.9718			−1.12063			−0.560313	+	0.828281i	$0.689319\pi$
$920$	0.319284	−	0.553017i	0.0105265	−	0.0182324i
$921$		0			0
$922$	−20.3083	+	11.7250i	−0.668819	+	0.386143i
$923$	52.1186	+	90.2720i	1.71550	+	2.97134i
$924$		0			0
$925$	8.84903	−	15.3270i	0.290954	−	0.503948i
$926$		−	16.8076i		−	0.552333i
$927$		0			0
$928$	−6.63569			−0.217827
$929$	−10.0804	+	17.4598i	−0.330727	+	0.572836i	−0.982655	−	0.185445i	$-0.940627\pi$
$929$	−10.0804	+	17.4598i	−0.330727	+	0.572836i	0.651928	+	0.758281i	$0.273961\pi$
$930$		0			0
$931$		0			0
$932$	5.96755	−	3.44537i	0.195474	−	0.112857i
$933$		0			0
$934$	5.55704	+	3.20836i	0.181832	+	0.104981i
$935$			0.0749671i			0.00245169i
$936$		0			0
$937$		−	44.7538i		−	1.46204i	−0.682354	−	0.731022i	$-0.739044\pi$
$937$		−	44.7538i		−	1.46204i	0.682354	−	0.731022i	$-0.260956\pi$
$938$		0			0
$939$		0			0
$940$	−1.77229	−	3.06969i	−0.0578057	−	0.100122i
$941$	−11.6135	−	20.1152i	−0.378590	−	0.655737i	0.612267	−	0.790651i	$-0.290258\pi$
$941$	−11.6135	−	20.1152i	−0.378590	−	0.655737i	−0.990857	+	0.134914i	$0.956924\pi$
$942$		0			0
$943$	7.45527	+	4.30430i	0.242777	+	0.140167i
$944$	−4.90410			−0.159615
$945$		0			0
$946$	−5.42553			−0.176399
$947$	−47.1601	−	27.2279i	−1.53250	−	0.884788i	−0.999246	−	0.0388309i	$-0.987637\pi$
$947$	−47.1601	−	27.2279i	−1.53250	−	0.884788i	−0.533251	−	0.845957i	$-0.679030\pi$
$948$		0			0
$949$	13.2229	+	22.9028i	0.429235	+	0.743456i
$950$	−10.1888	−	17.6475i	−0.330568	−	0.572560i
$951$		0			0
$952$		0			0
$953$			47.2143i			1.52942i	0.644373	+	0.764711i	$0.277118\pi$
$953$			47.2143i			1.52942i	−0.644373	+	0.764711i	$0.722882\pi$
$954$		0			0
$955$		−	8.64885i		−	0.279870i
$956$	−16.3611	−	9.44606i	−0.529154	−	0.305507i
$957$		0			0
$958$	−11.0070	+	6.35492i	−0.355621	+	0.205318i
$959$		0			0
$960$		0			0
$961$	9.07600	−	15.7201i	0.292774	−	0.507100i
$962$	23.5992			0.760869
$963$		0			0
$964$		−	16.3911i		−	0.527922i
$965$	−2.58761	+	4.48187i	−0.0832982	+	0.144277i
$966$		0			0
$967$	4.23256	+	7.33101i	0.136110	+	0.235749i	0.926021	−	0.377472i	$-0.123207\pi$
$967$	4.23256	+	7.33101i	0.136110	+	0.235749i	−0.789911	+	0.613222i	$0.789873\pi$
$968$	−9.29185	+	5.36465i	−0.298651	+	0.172426i
$969$		0			0
$970$	2.69538	−	4.66853i	0.0865434	−	0.149898i
$971$	30.4435			0.976978			0.488489	−	0.872570i	$-0.337548\pi$
$971$	30.4435			0.976978			0.488489	+	0.872570i	$0.337548\pi$
$972$		0			0
$973$		0			0
$974$	2.27412	+	1.31296i	0.0728674	+	0.0420700i
$975$		0			0
$976$	−1.33678	+	0.771791i	−0.0427893	+	0.0247044i
$977$	−18.9382	+	10.9340i	−0.605886	+	0.349808i	−0.771354	−	0.636407i	$-0.780420\pi$
$977$	−18.9382	+	10.9340i	−0.605886	+	0.349808i	0.165468	+	0.986215i	$0.447087\pi$
$978$		0			0
$979$	5.28295	+	3.05011i	0.168844	+	0.0974821i
$980$		0			0
$981$		0			0
$982$	−4.76943			−0.152199
$983$	−8.24949	+	14.2885i	−0.263118	+	0.455734i	−0.967069	−	0.254515i	$-0.918084\pi$
$983$	−8.24949	+	14.2885i	−0.263118	+	0.455734i	0.703951	+	0.710249i	$0.251418\pi$
$984$		0			0
$985$	−4.82764	+	2.78724i	−0.153821	+	0.0888088i
$986$	−1.08608	−	1.88114i	−0.0345878	−	0.0599078i
$987$		0			0
$988$	13.5861	−	23.5318i	0.432231	−	0.748646i
$989$			15.1281i			0.481045i
$990$		0			0
$991$	−30.2641			−0.961370			−0.480685	−	0.876893i	$-0.659612\pi$
$991$	−30.2641			−0.961370			−0.480685	+	0.876893i	$0.659612\pi$
$992$	3.50542	−	6.07157i	0.111297	−	0.192773i
$993$		0			0
$994$		0			0
$995$	6.79356	−	3.92226i	0.215370	−	0.124344i
$996$		0			0
$997$	−35.1065	−	20.2688i	−1.11184	−	0.641919i	−0.172531	−	0.985004i	$-0.555195\pi$
$997$	−35.1065	−	20.2688i	−1.11184	−	0.641919i	−0.939304	+	0.343086i	$0.888528\pi$
$998$		−	19.4692i		−	0.616286i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.c.1763.11		48
3.2	odd	2		882.2.m.c.587.21	yes	48
7.2	even	3		2646.2.l.c.521.3		48
7.3	odd	6		2646.2.t.c.1979.15		48
7.4	even	3		2646.2.t.c.1979.16		48
7.5	odd	6		2646.2.l.c.521.4		48
7.6	odd	2	inner	2646.2.m.c.1763.12		48
9.4	even	3		882.2.m.c.293.16	✓	48
9.5	odd	6	inner	2646.2.m.c.881.12		48
21.2	odd	6		882.2.l.c.227.1		48
21.5	even	6		882.2.l.c.227.12		48
21.11	odd	6		882.2.t.c.803.7		48
21.17	even	6		882.2.t.c.803.6		48
21.20	even	2		882.2.m.c.587.16	yes	48
63.4	even	3		882.2.l.c.509.24		48
63.5	even	6		2646.2.t.c.2285.16		48
63.13	odd	6		882.2.m.c.293.21	yes	48
63.23	odd	6		2646.2.t.c.2285.15		48
63.31	odd	6		882.2.l.c.509.13		48
63.32	odd	6		2646.2.l.c.1097.4		48
63.40	odd	6		882.2.t.c.815.7		48
63.41	even	6	inner	2646.2.m.c.881.11		48
63.58	even	3		882.2.t.c.815.6		48
63.59	even	6		2646.2.l.c.1097.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.1		48	21.2	odd	6
882.2.l.c.227.12		48	21.5	even	6
882.2.l.c.509.13		48	63.31	odd	6
882.2.l.c.509.24		48	63.4	even	3
882.2.m.c.293.16	✓	48	9.4	even	3
882.2.m.c.293.21	yes	48	63.13	odd	6
882.2.m.c.587.16	yes	48	21.20	even	2
882.2.m.c.587.21	yes	48	3.2	odd	2
882.2.t.c.803.6		48	21.17	even	6
882.2.t.c.803.7		48	21.11	odd	6
882.2.t.c.815.6		48	63.58	even	3
882.2.t.c.815.7		48	63.40	odd	6
2646.2.l.c.521.3		48	7.2	even	3
2646.2.l.c.521.4		48	7.5	odd	6
2646.2.l.c.1097.3		48	63.59	even	6
2646.2.l.c.1097.4		48	63.32	odd	6
2646.2.m.c.881.11		48	63.41	even	6	inner
2646.2.m.c.881.12		48	9.5	odd	6	inner
2646.2.m.c.1763.11		48	1.1	even	1	trivial
2646.2.m.c.1763.12		48	7.6	odd	2	inner
2646.2.t.c.1979.15		48	7.3	odd	6
2646.2.t.c.1979.16		48	7.4	even	3
2646.2.t.c.2285.15		48	63.23	odd	6
2646.2.t.c.2285.16		48	63.5	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.220087 - 0.381202i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.220087 - 0.381202i) q^{5} -1.00000i q^{8} +0.440174i q^{10} +(0.450580 + 0.260142i) q^{11} +(-5.55020 + 3.20441i) q^{13} +(-0.500000 + 0.866025i) q^{16} -0.327345 q^{17} +4.23981i q^{19} +(0.220087 - 0.381202i) q^{20} +(-0.260142 - 0.450580i) q^{22} +(-1.25636 + 0.725359i) q^{23} +(2.40312 - 4.16233i) q^{25} +6.40882 q^{26} +(-5.74668 - 3.31785i) q^{29} +(6.07157 - 3.50542i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.283489 + 0.163672i) q^{34} +3.68230 q^{37} +(2.11990 - 3.67178i) q^{38} +(-0.381202 + 0.220087i) q^{40} +(-2.96701 - 5.13902i) q^{41} +(5.21400 - 9.03091i) q^{43} +0.520285i q^{44} +1.45072 q^{46} +(4.02633 - 6.97382i) q^{47} +(-4.16233 + 2.40312i) q^{50} +(-5.55020 - 3.20441i) q^{52} +7.95672i q^{53} -0.229016i q^{55} +(3.31785 + 5.74668i) q^{58} +(2.45205 + 4.24708i) q^{59} +(1.33678 + 0.771791i) q^{61} -7.01085 q^{62} -1.00000 q^{64} +(2.44305 + 1.41050i) q^{65} +(-3.26206 - 5.65005i) q^{67} +(-0.163672 - 0.283489i) q^{68} -16.2646i q^{71} -4.12648i q^{73} +(-3.18897 - 1.84115i) q^{74} +(-3.67178 + 2.11990i) q^{76} +(0.662324 - 1.14718i) q^{79} +0.440174 q^{80} +5.93403i q^{82} +(-8.55240 + 14.8132i) q^{83} +(0.0720443 + 0.124784i) q^{85} +(-9.03091 + 5.21400i) q^{86} +(0.260142 - 0.450580i) q^{88} +11.7248 q^{89} +(-1.25636 - 0.725359i) q^{92} +(-6.97382 + 4.02633i) q^{94} +(1.61622 - 0.933127i) q^{95} +(-10.6061 - 6.12344i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 - 48 * q^11 - 24 * q^16 - 48 * q^23 - 24 * q^25 + 48 * q^50 - 48 * q^64 + 48 * q^79 + 48 * q^85 - 96 * q^86 - 48 * q^92 + 192 * q^95

Introduction

L-functions

Modular forms

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Representations

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Database

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