LMFDB - Embedded newform 2646.2.m.c.881.14

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			881.14
Character	$\chi$	$=$	2646.881
Dual form			2646.2.m.c.1763.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.35026 - 2.33872i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.35026 - 2.33872i) q^{5} -1.00000i q^{8} -2.70053i q^{10} +(0.205998 - 0.118933i) q^{11} +(-2.31418 - 1.33609i) q^{13} +(-0.500000 - 0.866025i) q^{16} -5.86724 q^{17} -1.15274i q^{19} +(-1.35026 - 2.33872i) q^{20} +(0.118933 - 0.205998i) q^{22} +(-7.02271 - 4.05456i) q^{23} +(-1.14642 - 1.98566i) q^{25} -2.67219 q^{26} +(-8.88796 + 5.13146i) q^{29} +(-5.21902 - 3.01320i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.08118 + 2.93362i) q^{34} +9.68488 q^{37} +(-0.576368 - 0.998299i) q^{38} +(-2.33872 - 1.35026i) q^{40} +(3.81891 - 6.61455i) q^{41} +(2.69219 + 4.66301i) q^{43} -0.237866i q^{44} -8.10913 q^{46} +(-0.221142 - 0.383029i) q^{47} +(-1.98566 - 1.14642i) q^{50} +(-2.31418 + 1.33609i) q^{52} +0.219155i q^{53} -0.642362i q^{55} +(-5.13146 + 8.88796i) q^{58} +(0.983559 - 1.70357i) q^{59} +(10.8615 - 6.27087i) q^{61} -6.02640 q^{62} -1.00000 q^{64} +(-6.24951 + 3.60816i) q^{65} +(4.48336 - 7.76541i) q^{67} +(-2.93362 + 5.08118i) q^{68} +2.24510i q^{71} -7.25634i q^{73} +(8.38735 - 4.84244i) q^{74} +(-0.998299 - 0.576368i) q^{76} +(5.43592 + 9.41528i) q^{79} -2.70053 q^{80} -7.63782i q^{82} +(0.762403 + 1.32052i) q^{83} +(-7.92232 + 13.7219i) q^{85} +(4.66301 + 2.69219i) q^{86} +(-0.118933 - 0.205998i) q^{88} -13.5277 q^{89} +(-7.02271 + 4.05456i) q^{92} +(-0.383029 - 0.221142i) q^{94} +(-2.69593 - 1.55650i) q^{95} +(1.37708 - 0.795057i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	1.35026	−	2.33872i	0.603856	−	1.04591i	−0.388375	−	0.921501i	$-0.626963\pi$
$5$	1.35026	−	2.33872i	0.603856	−	1.04591i	0.992231	−	0.124408i	$-0.0397032\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		−	2.70053i		−	0.853982i
$11$	0.205998	−	0.118933i	0.0621106	−	0.0358596i	−0.468623	−	0.883398i	$-0.655250\pi$
$11$	0.205998	−	0.118933i	0.0621106	−	0.0358596i	0.530734	+	0.847539i	$0.321916\pi$
$12$		0			0
$13$	−2.31418	−	1.33609i	−0.641839	−	0.370566i	0.143484	−	0.989653i	$-0.454169\pi$
$13$	−2.31418	−	1.33609i	−0.641839	−	0.370566i	−0.785322	+	0.619087i	$0.787503\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.86724			−1.42301			−0.711507	−	0.702679i	$-0.751987\pi$
$17$	−5.86724			−1.42301			−0.711507	+	0.702679i	$0.751987\pi$
$18$		0			0
$19$		−	1.15274i		−	0.264456i	−0.991219	−	0.132228i	$-0.957787\pi$
$19$		−	1.15274i		−	0.264456i	0.991219	−	0.132228i	$-0.0422131\pi$
$20$	−1.35026	−	2.33872i	−0.301928	−	0.522955i
$21$		0			0
$22$	0.118933	−	0.205998i	0.0253566	−	0.0439188i
$23$	−7.02271	−	4.05456i	−1.46434	−	0.845435i	−0.465129	−	0.885243i	$-0.653992\pi$
$23$	−7.02271	−	4.05456i	−1.46434	−	0.845435i	−0.999207	+	0.0398080i	$0.987325\pi$
$24$		0			0
$25$	−1.14642	−	1.98566i	−0.229284	−	0.397132i
$26$	−2.67219			−0.524059
$27$		0			0
$28$		0			0
$29$	−8.88796	+	5.13146i	−1.65045	+	0.952889i	−0.673566	+	0.739127i	$0.735238\pi$
$29$	−8.88796	+	5.13146i	−1.65045	+	0.952889i	−0.976886	+	0.213762i	$0.931428\pi$
$30$		0			0
$31$	−5.21902	−	3.01320i	−0.937364	−	0.541187i	−0.0482307	−	0.998836i	$-0.515358\pi$
$31$	−5.21902	−	3.01320i	−0.937364	−	0.541187i	−0.889133	+	0.457649i	$0.848692\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−5.08118	+	2.93362i	−0.871415	+	0.503112i
$35$		0			0
$36$		0			0
$37$	9.68488			1.59218			0.796092	−	0.605175i	$-0.206897\pi$
$37$	9.68488			1.59218			0.796092	+	0.605175i	$0.206897\pi$
$38$	−0.576368	−	0.998299i	−0.0934993	−	0.161945i
$39$		0			0
$40$	−2.33872	−	1.35026i	−0.369785	−	0.213495i
$41$	3.81891	−	6.61455i	0.596414	−	1.03302i	−0.396932	−	0.917848i	$-0.629925\pi$
$41$	3.81891	−	6.61455i	0.596414	−	1.03302i	0.993346	−	0.115171i	$-0.0367416\pi$
$42$		0			0
$43$	2.69219	+	4.66301i	0.410555	+	0.711103i	0.994951	−	0.100366i	$-0.0320015\pi$
$43$	2.69219	+	4.66301i	0.410555	+	0.711103i	−0.584395	+	0.811469i	$0.698668\pi$
$44$		−	0.237866i		−	0.0358596i
$45$		0			0
$46$	−8.10913			−1.19563
$47$	−0.221142	−	0.383029i	−0.0322568	−	0.0558705i	0.849446	−	0.527675i	$-0.176936\pi$
$47$	−0.221142	−	0.383029i	−0.0322568	−	0.0558705i	−0.881703	+	0.471805i	$0.843603\pi$
$48$		0			0
$49$		0			0
$50$	−1.98566	−	1.14642i	−0.280815	−	0.162129i
$51$		0			0
$52$	−2.31418	+	1.33609i	−0.320919	+	0.185283i
$53$			0.219155i			0.0301032i	0.999887	+	0.0150516i	$0.00479126\pi$
$53$			0.219155i			0.0301032i	−0.999887	+	0.0150516i	$0.995209\pi$
$54$		0			0
$55$		−	0.642362i		−	0.0866161i
$56$		0			0
$57$		0			0
$58$	−5.13146	+	8.88796i	−0.673794	+	1.16705i
$59$	0.983559	−	1.70357i	0.128048	−	0.221786i	−0.794872	−	0.606777i	$-0.792462\pi$
$59$	0.983559	−	1.70357i	0.128048	−	0.221786i	0.922920	+	0.384991i	$0.125795\pi$
$60$		0			0
$61$	10.8615	−	6.27087i	1.39067	−	0.802902i	0.397278	−	0.917698i	$-0.369955\pi$
$61$	10.8615	−	6.27087i	1.39067	−	0.802902i	0.993389	+	0.114796i	$0.0366214\pi$
$62$	−6.02640			−0.765354
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.24951	+	3.60816i	−0.775156	+	0.447537i
$66$		0			0
$67$	4.48336	−	7.76541i	0.547730	−	0.948696i	−0.450700	−	0.892676i	$-0.648825\pi$
$67$	4.48336	−	7.76541i	0.547730	−	0.948696i	0.998430	−	0.0560206i	$-0.0178412\pi$
$68$	−2.93362	+	5.08118i	−0.355754	+	0.616183i
$69$		0			0
$70$		0			0
$71$			2.24510i			0.266445i	0.991086	+	0.133222i	$0.0425324\pi$
$71$			2.24510i			0.266445i	−0.991086	+	0.133222i	$0.957468\pi$
$72$		0			0
$73$		−	7.25634i		−	0.849291i	−0.905360	−	0.424645i	$-0.860399\pi$
$73$		−	7.25634i		−	0.849291i	0.905360	−	0.424645i	$-0.139601\pi$
$74$	8.38735	−	4.84244i	0.975010	−	0.562922i
$75$		0			0
$76$	−0.998299	−	0.576368i	−0.114513	−	0.0661140i
$77$		0			0
$78$		0			0
$79$	5.43592	+	9.41528i	0.611588	+	1.05930i	0.990973	+	0.134063i	$0.0428024\pi$
$79$	5.43592	+	9.41528i	0.611588	+	1.05930i	−0.379385	+	0.925239i	$0.623864\pi$
$80$	−2.70053			−0.301928
$81$		0			0
$82$		−	7.63782i		−	0.843456i
$83$	0.762403	+	1.32052i	0.0836846	+	0.144946i	0.904830	−	0.425773i	$-0.139998\pi$
$83$	0.762403	+	1.32052i	0.0836846	+	0.144946i	−0.821145	+	0.570719i	$0.806665\pi$
$84$		0			0
$85$	−7.92232	+	13.7219i	−0.859296	+	1.48834i
$86$	4.66301	+	2.69219i	0.502826	+	0.290307i
$87$		0			0
$88$	−0.118933	−	0.205998i	−0.0126783	−	0.0219594i
$89$	−13.5277			−1.43393			−0.716967	−	0.697107i	$-0.754470\pi$
$89$	−13.5277			−1.43393			−0.716967	+	0.697107i	$0.754470\pi$
$90$		0			0
$91$		0			0
$92$	−7.02271	+	4.05456i	−0.732168	+	0.422717i
$93$		0			0
$94$	−0.383029	−	0.221142i	−0.0395064	−	0.0228090i
$95$	−2.69593	−	1.55650i	−0.276597	−	0.159693i
$96$		0			0
$97$	1.37708	−	0.795057i	0.139821	−	0.0807258i	−0.428458	−	0.903562i	$-0.640943\pi$
$97$	1.37708	−	0.795057i	0.139821	−	0.0807258i	0.568279	+	0.822836i	$0.307610\pi$
$98$		0			0
$99$		0			0
$100$	−2.29284			−0.229284
$101$	−6.48353	−	11.2298i	−0.645135	−	1.11741i	−0.984270	−	0.176670i	$-0.943468\pi$
$101$	−6.48353	−	11.2298i	−0.645135	−	1.11741i	0.339135	−	0.940738i	$-0.389866\pi$
$102$		0			0
$103$	−15.9765	−	9.22402i	−1.57421	−	0.908870i	−0.995644	−	0.0932327i	$-0.970280\pi$
$103$	−15.9765	−	9.22402i	−1.57421	−	0.908870i	−0.578564	−	0.815637i	$-0.696387\pi$
$104$	−1.33609	+	2.31418i	−0.131015	+	0.226924i
$105$		0			0
$106$	0.109577	+	0.189794i	0.0106431	+	0.0184344i
$107$			4.65158i			0.449686i	0.974395	+	0.224843i	$0.0721868\pi$
$107$			4.65158i			0.449686i	−0.974395	+	0.224843i	$0.927813\pi$
$108$		0			0
$109$	10.0651			0.964066			0.482033	−	0.876153i	$-0.339898\pi$
$109$	10.0651			0.964066			0.482033	+	0.876153i	$0.339898\pi$
$110$	−0.321181	−	0.556302i	−0.0306234	−	0.0530413i
$111$		0			0
$112$		0			0
$113$	8.33618	+	4.81290i	0.784202	+	0.452759i	0.837917	−	0.545797i	$-0.183773\pi$
$113$	8.33618	+	4.81290i	0.784202	+	0.452759i	−0.0537156	+	0.998556i	$0.517106\pi$
$114$		0			0
$115$	−18.9650	+	10.9495i	−1.76850	+	1.02104i
$116$			10.2629i			0.952889i
$117$		0			0
$118$		−	1.96712i		−	0.181088i
$119$		0			0
$120$		0			0
$121$	−5.47171	+	9.47728i	−0.497428	+	0.861571i
$122$	6.27087	−	10.8615i	0.567738	−	0.983350i
$123$		0			0
$124$	−5.21902	+	3.01320i	−0.468682	+	0.270594i
$125$	7.31075			0.653893
$126$		0			0
$127$	−4.69657			−0.416753			−0.208377	−	0.978049i	$-0.566818\pi$
$127$	−4.69657			−0.416753			−0.208377	+	0.978049i	$0.566818\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.60816	+	6.24951i	−0.316456	+	0.548118i
$131$	7.02151	−	12.1616i	0.613472	−	1.06257i	−0.377178	−	0.926141i	$-0.623106\pi$
$131$	7.02151	−	12.1616i	0.613472	−	1.06257i	0.990650	−	0.136424i	$-0.0435611\pi$
$132$		0			0
$133$		0			0
$134$		−	8.96673i		−	0.774607i
$135$		0			0
$136$			5.86724i			0.503112i
$137$	9.39626	−	5.42494i	0.802777	−	0.463483i	−0.0416643	−	0.999132i	$-0.513266\pi$
$137$	9.39626	−	5.42494i	0.802777	−	0.463483i	0.844441	+	0.535648i	$0.179933\pi$
$138$		0			0
$139$	19.5606	+	11.2933i	1.65911	+	0.957886i	0.973128	+	0.230266i	$0.0739597\pi$
$139$	19.5606	+	11.2933i	1.65911	+	0.957886i	0.685980	+	0.727620i	$0.259374\pi$
$140$		0			0
$141$		0			0
$142$	1.12255	+	1.94432i	0.0942024	+	0.163163i
$143$	−0.635621			−0.0531533
$144$		0			0
$145$			27.7153i			2.30163i
$146$	−3.62817	−	6.28418i	−0.300270	−	0.520082i
$147$		0			0
$148$	4.84244	−	8.38735i	0.398046	−	0.689436i
$149$	−0.236156	−	0.136345i	−0.0193467	−	0.0111698i	0.490295	−	0.871556i	$-0.336889\pi$
$149$	−0.236156	−	0.136345i	−0.0193467	−	0.0111698i	−0.509642	+	0.860386i	$0.670222\pi$
$150$		0			0
$151$	−9.42148	−	16.3185i	−0.766709	−	1.32798i	−0.939338	−	0.342992i	$-0.888560\pi$
$151$	−9.42148	−	16.3185i	−0.766709	−	1.32798i	0.172629	−	0.984987i	$-0.444774\pi$
$152$	−1.15274			−0.0934993
$153$		0			0
$154$		0			0
$155$	−14.0941	+	8.13723i	−1.13207	+	0.653598i
$156$		0			0
$157$	2.82310	+	1.62992i	0.225308	+	0.130082i	0.608406	−	0.793626i	$-0.291809\pi$
$157$	2.82310	+	1.62992i	0.225308	+	0.130082i	−0.383098	+	0.923708i	$0.625143\pi$
$158$	9.41528	+	5.43592i	0.749040	+	0.432458i
$159$		0			0
$160$	−2.33872	+	1.35026i	−0.184892	+	0.106748i
$161$		0			0
$162$		0			0
$163$	−3.13675			−0.245689			−0.122844	−	0.992426i	$-0.539202\pi$
$163$	−3.13675			−0.245689			−0.122844	+	0.992426i	$0.539202\pi$
$164$	−3.81891	−	6.61455i	−0.298207	−	0.516509i
$165$		0			0
$166$	1.32052	+	0.762403i	0.102492	+	0.0591739i
$167$	−3.19575	+	5.53520i	−0.247295	+	0.428327i	−0.962774	−	0.270307i	$-0.912875\pi$
$167$	−3.19575	+	5.53520i	−0.247295	+	0.428327i	0.715480	+	0.698634i	$0.246208\pi$
$168$		0			0
$169$	−2.92971	−	5.07440i	−0.225362	−	0.390339i
$170$			15.8446i			1.21523i
$171$		0			0
$172$	5.38438			0.410555
$173$	0.146767	+	0.254207i	0.0111585	+	0.0193270i	0.871551	−	0.490305i	$-0.163115\pi$
$173$	0.146767	+	0.254207i	0.0111585	+	0.0193270i	−0.860392	+	0.509632i	$0.829781\pi$
$174$		0			0
$175$		0			0
$176$	−0.205998	−	0.118933i	−0.0155277	−	0.00896490i
$177$		0			0
$178$	−11.7153	+	6.76386i	−0.878102	+	0.506972i
$179$		−	23.0747i		−	1.72468i	−0.506326	−	0.862342i	$-0.668997\pi$
$179$		−	23.0747i		−	1.72468i	0.506326	−	0.862342i	$-0.331003\pi$
$180$		0			0
$181$		−	10.9176i		−	0.811500i	−0.913984	−	0.405750i	$-0.867010\pi$
$181$		−	10.9176i		−	0.811500i	0.913984	−	0.405750i	$-0.132990\pi$
$182$		0			0
$183$		0			0
$184$	−4.05456	+	7.02271i	−0.298906	+	0.517721i
$185$	13.0771	−	22.6503i	0.961451	−	1.66528i
$186$		0			0
$187$	−1.20864	+	0.697807i	−0.0883843	+	0.0510287i
$188$	−0.442283			−0.0322568
$189$		0			0
$190$	−3.11300			−0.225840
$191$	−11.1456	+	6.43490i	−0.806465	+	0.465613i	−0.845727	−	0.533616i	$-0.820833\pi$
$191$	−11.1456	+	6.43490i	−0.806465	+	0.465613i	0.0392616	+	0.999229i	$0.487499\pi$
$192$		0			0
$193$	5.11771	−	8.86414i	0.368381	−	0.638054i	−0.620932	−	0.783865i	$-0.713246\pi$
$193$	5.11771	−	8.86414i	0.368381	−	0.638054i	0.989313	+	0.145810i	$0.0465789\pi$
$194$	0.795057	−	1.37708i	0.0570818	−	0.0988686i
$195$		0			0
$196$		0			0
$197$		−	3.89068i		−	0.277200i	−0.990348	−	0.138600i	$-0.955740\pi$
$197$		−	3.89068i		−	0.277200i	0.990348	−	0.138600i	$-0.0442602\pi$
$198$		0			0
$199$		−	2.33150i		−	0.165276i	−0.996580	−	0.0826378i	$-0.973666\pi$
$199$		−	2.33150i		−	0.165276i	0.996580	−	0.0826378i	$-0.0263345\pi$
$200$	−1.98566	+	1.14642i	−0.140407	+	0.0810643i
$201$		0			0
$202$	−11.2298	−	6.48353i	−0.790126	−	0.456180i
$203$		0			0
$204$		0			0
$205$	−10.3131	−	17.8628i	−0.720296	−	1.24759i
$206$	−18.4480			−1.28534
$207$		0			0
$208$			2.67219i			0.185283i
$209$	−0.137098	−	0.237461i	−0.00948328	−	0.0164255i
$210$		0			0
$211$	−7.48854	+	12.9705i	−0.515532	+	0.892928i	0.484305	+	0.874899i	$0.339072\pi$
$211$	−7.48854	+	12.9705i	−0.515532	+	0.892928i	−0.999837	+	0.0180288i	$0.994261\pi$
$212$	0.189794	+	0.109577i	0.0130351	+	0.00752581i
$213$		0			0
$214$	2.32579	+	4.02839i	0.158988	+	0.275375i
$215$	14.5407			0.991666
$216$		0			0
$217$		0			0
$218$	8.71667	−	5.03257i	0.590368	−	0.340849i
$219$		0			0
$220$	−0.556302	−	0.321181i	−0.0375059	−	0.0216540i
$221$	13.5779	+	7.83918i	0.913345	+	0.527320i
$222$		0			0
$223$	−17.5517	+	10.1335i	−1.17535	+	0.678590i	−0.954935	−	0.296816i	$-0.904075\pi$
$223$	−17.5517	+	10.1335i	−1.17535	+	0.678590i	−0.220417	+	0.975406i	$0.570742\pi$
$224$		0			0
$225$		0			0
$226$	9.62579			0.640298
$227$	5.15484	+	8.92845i	0.342139	+	0.592602i	0.984830	−	0.173524i	$-0.0555153\pi$
$227$	5.15484	+	8.92845i	0.342139	+	0.592602i	−0.642691	+	0.766126i	$0.722182\pi$
$228$		0			0
$229$	7.57314	+	4.37235i	0.500447	+	0.288933i	0.728898	−	0.684622i	$-0.240033\pi$
$229$	7.57314	+	4.37235i	0.500447	+	0.288933i	−0.228451	+	0.973555i	$0.573366\pi$
$230$	−10.9495	+	18.9650i	−0.721986	+	1.25052i
$231$		0			0
$232$	5.13146	+	8.88796i	0.336897	+	0.583523i
$233$		−	15.6014i		−	1.02208i	−0.859557	−	0.511039i	$-0.829261\pi$
$233$		−	15.6014i		−	1.02208i	0.859557	−	0.511039i	$-0.170739\pi$
$234$		0			0
$235$	−1.19440			−0.0779139
$236$	−0.983559	−	1.70357i	−0.0640242	−	0.110893i
$237$		0			0
$238$		0			0
$239$	19.2977	+	11.1415i	1.24827	+	0.720686i	0.970763	−	0.240039i	$-0.0771602\pi$
$239$	19.2977	+	11.1415i	1.24827	+	0.720686i	0.277502	+	0.960725i	$0.410494\pi$
$240$		0			0
$241$	0.568566	−	0.328262i	0.0366245	−	0.0211452i	−0.481576	−	0.876404i	$-0.659935\pi$
$241$	0.568566	−	0.328262i	0.0366245	−	0.0211452i	0.518200	+	0.855259i	$0.326602\pi$
$242$			10.9434i			0.703470i
$243$		0			0
$244$		−	12.5417i		−	0.802902i
$245$		0			0
$246$		0			0
$247$	−1.54016	+	2.66764i	−0.0979983	+	0.169738i
$248$	−3.01320	+	5.21902i	−0.191339	+	0.331408i
$249$		0			0
$250$	6.33129	−	3.65537i	0.400426	−	0.231186i
$251$	−3.48276			−0.219830			−0.109915	−	0.993941i	$-0.535058\pi$
$251$	−3.48276			−0.219830			−0.109915	+	0.993941i	$0.535058\pi$
$252$		0			0
$253$	−1.92888			−0.121268
$254$	−4.06735	+	2.34829i	−0.255208	+	0.147345i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.02515	−	1.77562i	0.0639474	−	0.110760i	−0.832279	−	0.554357i	$-0.812964\pi$
$257$	1.02515	−	1.77562i	0.0639474	−	0.110760i	0.896227	+	0.443597i	$0.146298\pi$
$258$		0			0
$259$		0			0
$260$			7.21631i			0.447537i
$261$		0			0
$262$		−	14.0430i		−	0.867581i
$263$	−8.81710	+	5.09055i	−0.543686	+	0.313897i	−0.746571	−	0.665305i	$-0.768301\pi$
$263$	−8.81710	+	5.09055i	−0.543686	+	0.313897i	0.202886	+	0.979202i	$0.434968\pi$
$264$		0			0
$265$	0.512543	+	0.295917i	0.0314853	+	0.0181780i
$266$		0			0
$267$		0			0
$268$	−4.48336	−	7.76541i	−0.273865	−	0.474348i
$269$	0.349999			0.0213398			0.0106699	−	0.999943i	$-0.496604\pi$
$269$	0.349999			0.0213398			0.0106699	+	0.999943i	$0.496604\pi$
$270$		0			0
$271$			13.9073i			0.844807i	0.906408	+	0.422403i	$0.138813\pi$
$271$			13.9073i			0.844807i	−0.906408	+	0.422403i	$0.861187\pi$
$272$	2.93362	+	5.08118i	0.177877	+	0.308092i
$273$		0			0
$274$	5.42494	−	9.39626i	0.327732	−	0.567649i
$275$	−0.472321	−	0.272694i	−0.0284820	−	0.0164441i
$276$		0			0
$277$	−7.90100	−	13.6849i	−0.474725	−	0.822248i	0.524856	−	0.851191i	$-0.324119\pi$
$277$	−7.90100	−	13.6849i	−0.474725	−	0.822248i	−0.999581	+	0.0289428i	$0.990786\pi$
$278$	22.5866			1.35466
$279$		0			0
$280$		0			0
$281$	22.2334	−	12.8365i	1.32633	−	0.765759i	0.341603	−	0.939844i	$-0.389030\pi$
$281$	22.2334	−	12.8365i	1.32633	−	0.765759i	0.984731	+	0.174086i	$0.0556970\pi$
$282$		0			0
$283$	5.73018	+	3.30832i	0.340624	+	0.196659i	0.660548	−	0.750784i	$-0.270324\pi$
$283$	5.73018	+	3.30832i	0.340624	+	0.196659i	−0.319924	+	0.947443i	$0.603657\pi$
$284$	1.94432	+	1.12255i	0.115374	+	0.0666112i
$285$		0			0
$286$	−0.550464	+	0.317811i	−0.0325496	+	0.0187925i
$287$		0			0
$288$		0			0
$289$	17.4245			1.02497
$290$	13.8577	+	24.0022i	0.813750	+	1.40946i
$291$		0			0
$292$	−6.28418	−	3.62817i	−0.367754	−	0.212323i
$293$	8.68306	−	15.0395i	0.507270	−	0.878617i	−0.492695	−	0.870202i	$-0.663988\pi$
$293$	8.68306	−	15.0395i	0.507270	−	0.878617i	0.999965	−	0.00841456i	$-0.00267847\pi$
$294$		0			0
$295$	−2.65613	−	4.60055i	−0.154646	−	0.267854i
$296$		−	9.68488i		−	0.562922i
$297$		0			0
$298$	−0.272690			−0.0157965
$299$	10.8346	+	18.7660i	0.626578	+	1.08527i
$300$		0			0
$301$		0			0
$302$	−16.3185	−	9.42148i	−0.939023	−	0.542145i
$303$		0			0
$304$	−0.998299	+	0.576368i	−0.0572564	+	0.0330570i
$305$		−	33.8693i		−	1.93935i
$306$		0			0
$307$		−	1.18328i		−	0.0675336i	−0.999430	−	0.0337668i	$-0.989250\pi$
$307$		−	1.18328i		−	0.0675336i	0.999430	−	0.0337668i	$-0.0107504\pi$
$308$		0			0
$309$		0			0
$310$	−8.13723	+	14.0941i	−0.462164	+	0.800491i
$311$	−12.6616	+	21.9306i	−0.717975	+	1.24357i	0.243825	+	0.969819i	$0.421598\pi$
$311$	−12.6616	+	21.9306i	−0.717975	+	1.24357i	−0.961801	+	0.273751i	$0.911736\pi$
$312$		0			0
$313$	−1.58789	+	0.916770i	−0.0897530	+	0.0518189i	−0.544205	−	0.838952i	$-0.683169\pi$
$313$	−1.58789	+	0.916770i	−0.0897530	+	0.0518189i	0.454452	+	0.890771i	$0.349835\pi$
$314$	3.25984			0.183963
$315$		0			0
$316$	10.8718			0.611588
$317$	−8.23307	+	4.75337i	−0.462415	+	0.266976i	−0.713059	−	0.701104i	$-0.752691\pi$
$317$	−8.23307	+	4.75337i	−0.462415	+	0.266976i	0.250644	+	0.968079i	$0.419358\pi$
$318$		0			0
$319$	−1.22060	+	2.11414i	−0.0683404	+	0.118369i
$320$	−1.35026	+	2.33872i	−0.0754820	+	0.130739i
$321$		0			0
$322$		0			0
$323$			6.76338i			0.376324i
$324$		0			0
$325$			6.12691i			0.339860i
$326$	−2.71650	+	1.56837i	−0.150453	+	0.0868642i
$327$		0			0
$328$	−6.61455	−	3.81891i	−0.365227	−	0.210864i
$329$		0			0
$330$		0			0
$331$	−9.26852	−	16.0535i	−0.509444	−	0.882382i	−0.999940	−	0.0109393i	$-0.996518\pi$
$331$	−9.26852	−	16.0535i	−0.509444	−	0.882382i	0.490496	−	0.871443i	$-0.336815\pi$
$332$	1.52481			0.0836846
$333$		0			0
$334$			6.39150i			0.349727i
$335$	−12.1074	−	20.9707i	−0.661500	−	1.14575i
$336$		0			0
$337$	4.70730	−	8.15329i	0.256423	−	0.444138i	−0.708858	−	0.705351i	$-0.750789\pi$
$337$	4.70730	−	8.15329i	0.256423	−	0.444138i	0.965281	+	0.261213i	$0.0841226\pi$
$338$	−5.07440	−	2.92971i	−0.276011	−	0.159355i
$339$		0			0
$340$	7.92232	+	13.7219i	0.429648	+	0.744172i
$341$	−1.43347			−0.0776270
$342$		0			0
$343$		0			0
$344$	4.66301	−	2.69219i	0.251413	−	0.145153i
$345$		0			0
$346$	0.254207	+	0.146767i	0.0136663	+	0.00789022i
$347$	−9.73647	−	5.62136i	−0.522681	−	0.301770i	0.215350	−	0.976537i	$-0.430911\pi$
$347$	−9.73647	−	5.62136i	−0.522681	−	0.301770i	−0.738031	+	0.674767i	$0.764244\pi$
$348$		0			0
$349$	−0.889499	+	0.513552i	−0.0476138	+	0.0274898i	−0.523618	−	0.851953i	$-0.675418\pi$
$349$	−0.889499	+	0.513552i	−0.0476138	+	0.0274898i	0.476004	+	0.879443i	$0.342085\pi$
$350$		0			0
$351$		0			0
$352$	−0.237866			−0.0126783
$353$	−12.3144	−	21.3291i	−0.655429	−	1.13524i	−0.981786	−	0.189990i	$-0.939155\pi$
$353$	−12.3144	−	21.3291i	−0.655429	−	1.13524i	0.326357	−	0.945246i	$-0.394179\pi$
$354$		0			0
$355$	5.25068	+	3.03148i	0.278677	+	0.160894i
$356$	−6.76386	+	11.7153i	−0.358484	+	0.620912i
$357$		0			0
$358$	−11.5374	−	19.9833i	−0.609768	−	1.05615i
$359$		−	10.5234i		−	0.555402i	−0.960668	−	0.277701i	$-0.910428\pi$
$359$		−	10.5234i		−	0.555402i	0.960668	−	0.277701i	$-0.0895725\pi$
$360$		0			0
$361$	17.6712			0.930063
$362$	−5.45881	−	9.45493i	−0.286908	−	0.496940i
$363$		0			0
$364$		0			0
$365$	−16.9706	−	9.79797i	−0.888281	−	0.512849i
$366$		0			0
$367$	−6.00271	+	3.46567i	−0.313339	+	0.180906i	−0.648420	−	0.761283i	$-0.724570\pi$
$367$	−6.00271	+	3.46567i	−0.313339	+	0.180906i	0.335081	+	0.942189i	$0.391236\pi$
$368$			8.10913i			0.422717i
$369$		0			0
$370$		−	26.1543i		−	1.35970i
$371$		0			0
$372$		0			0
$373$	−0.950237	+	1.64586i	−0.0492014	+	0.0852193i	−0.889577	−	0.456785i	$-0.849001\pi$
$373$	−0.950237	+	1.64586i	−0.0492014	+	0.0852193i	0.840376	+	0.542004i	$0.182334\pi$
$374$	−0.697807	+	1.20864i	−0.0360827	+	0.0624971i
$375$		0			0
$376$	−0.383029	+	0.221142i	−0.0197532	+	0.0114045i
$377$	27.4245			1.41243
$378$		0			0
$379$	37.4655			1.92447			0.962236	−	0.272217i	$-0.0877569\pi$
$379$	37.4655			1.92447			0.962236	+	0.272217i	$0.0877569\pi$
$380$	−2.69593	+	1.55650i	−0.138298	+	0.0798467i
$381$		0			0
$382$	−6.43490	+	11.1456i	−0.329238	+	0.570257i
$383$	0.740653	−	1.28285i	0.0378456	−	0.0655505i	−0.846482	−	0.532417i	$-0.821284\pi$
$383$	0.740653	−	1.28285i	0.0378456	−	0.0655505i	0.884328	+	0.466867i	$0.154617\pi$
$384$		0			0
$385$		0			0
$386$		−	10.2354i		−	0.520969i
$387$		0			0
$388$		−	1.59011i		−	0.0807258i
$389$	−11.0008	+	6.35131i	−0.557763	+	0.322024i	−0.752247	−	0.658881i	$-0.771030\pi$
$389$	−11.0008	+	6.35131i	−0.557763	+	0.322024i	0.194484	+	0.980906i	$0.437697\pi$
$390$		0			0
$391$	41.2039	+	23.7891i	2.08377	+	1.20307i
$392$		0			0
$393$		0			0
$394$	−1.94534	−	3.36943i	−0.0980049	−	0.169749i
$395$	29.3597			1.47725
$396$		0			0
$397$		−	19.3486i		−	0.971080i	−0.874215	−	0.485540i	$-0.838623\pi$
$397$		−	19.3486i		−	0.971080i	0.874215	−	0.485540i	$-0.161377\pi$
$398$	−1.16575	−	2.01914i	−0.0584338	−	0.101210i
$399$		0			0
$400$	−1.14642	+	1.98566i	−0.0573211	+	0.0992831i
$401$	9.43887	+	5.44954i	0.471355	+	0.272137i	0.716807	−	0.697272i	$-0.245603\pi$
$401$	9.43887	+	5.44954i	0.471355	+	0.272137i	−0.245452	+	0.969409i	$0.578936\pi$
$402$		0			0
$403$	8.05184	+	13.9462i	0.401091	+	0.694709i
$404$	−12.9671			−0.645135
$405$		0			0
$406$		0			0
$407$	1.99506	−	1.15185i	0.0988916	−	0.0570951i
$408$		0			0
$409$	17.7691	+	10.2590i	0.878627	+	0.507275i	0.870205	−	0.492689i	$-0.163986\pi$
$409$	17.7691	+	10.2590i	0.878627	+	0.507275i	0.00842142	+	0.999965i	$0.497319\pi$
$410$	−17.8628	−	10.3131i	−0.882179	−	0.509326i
$411$		0			0
$412$	−15.9765	+	9.22402i	−0.787104	+	0.454435i
$413$		0			0
$414$		0			0
$415$	4.11778			0.202134
$416$	1.33609	+	2.31418i	0.0655074	+	0.113462i
$417$		0			0
$418$	−0.237461	−	0.137098i	−0.0116146	−	0.00670569i
$419$	−2.73087	+	4.73000i	−0.133412	+	0.231076i	−0.924990	−	0.379993i	$-0.875927\pi$
$419$	−2.73087	+	4.73000i	−0.133412	+	0.231076i	0.791578	+	0.611068i	$0.209260\pi$
$420$		0			0
$421$	14.2759	+	24.7265i	0.695763	+	1.20510i	0.969923	+	0.243412i	$0.0782669\pi$
$421$	14.2759	+	24.7265i	0.695763	+	1.20510i	−0.274160	+	0.961684i	$0.588400\pi$
$422$			14.9771i			0.729073i
$423$		0			0
$424$	0.219155			0.0106431
$425$	6.72633	+	11.6504i	0.326275	+	0.565125i
$426$		0			0
$427$		0			0
$428$	4.02839	+	2.32579i	0.194720	+	0.112421i
$429$		0			0
$430$	12.5926	−	7.27034i	0.607269	−	0.350607i
$431$			9.55639i			0.460315i	0.973153	+	0.230157i	$0.0739241\pi$
$431$			9.55639i			0.460315i	−0.973153	+	0.230157i	$0.926076\pi$
$432$		0			0
$433$			19.7122i			0.947309i	0.880711	+	0.473654i	$0.157065\pi$
$433$			19.7122i			0.947309i	−0.880711	+	0.473654i	$0.842935\pi$
$434$		0			0
$435$		0			0
$436$	5.03257	−	8.71667i	0.241017	−	0.417453i
$437$	−4.67384	+	8.09533i	−0.223580	+	0.387252i
$438$		0			0
$439$	21.1001	−	12.1822i	1.00706	−	0.581424i	0.0967271	−	0.995311i	$-0.469163\pi$
$439$	21.1001	−	12.1822i	1.00706	−	0.581424i	0.910328	+	0.413887i	$0.135829\pi$
$440$	−0.642362			−0.0306234
$441$		0			0
$442$	15.6784			0.745743
$443$	32.4731	−	18.7483i	1.54284	−	0.890760i	0.544184	−	0.838966i	$-0.316839\pi$
$443$	32.4731	−	18.7483i	1.54284	−	0.890760i	0.998658	−	0.0517947i	$-0.0164941\pi$
$444$		0			0
$445$	−18.2660	+	31.6376i	−0.865890	+	1.49977i
$446$	−10.1335	+	17.5517i	−0.479835	+	0.831099i
$447$		0			0
$448$		0			0
$449$		−	22.6997i		−	1.07127i	−0.844451	−	0.535633i	$-0.820073\pi$
$449$		−	22.6997i		−	1.07127i	0.844451	−	0.535633i	$-0.179927\pi$
$450$		0			0
$451$		−	1.81678i		−	0.0855486i
$452$	8.33618	−	4.81290i	0.392101	−	0.226380i
$453$		0			0
$454$	8.92845	+	5.15484i	0.419033	+	0.241929i
$455$		0			0
$456$		0			0
$457$	−19.9116	−	34.4878i	−0.931424	−	1.61327i	−0.780890	−	0.624668i	$-0.785234\pi$
$457$	−19.9116	−	34.4878i	−0.931424	−	1.61327i	−0.150533	−	0.988605i	$-0.548099\pi$
$458$	8.74471			0.408613
$459$		0			0
$460$			21.8989i			1.02104i
$461$	4.33763	+	7.51299i	0.202024	+	0.349915i	0.949180	−	0.314733i	$-0.101915\pi$
$461$	4.33763	+	7.51299i	0.202024	+	0.349915i	−0.747157	+	0.664648i	$0.768582\pi$
$462$		0			0
$463$	7.06605	−	12.2388i	0.328387	−	0.568783i	−0.653805	−	0.756663i	$-0.726828\pi$
$463$	7.06605	−	12.2388i	0.328387	−	0.568783i	0.982192	+	0.187880i	$0.0601616\pi$
$464$	8.88796	+	5.13146i	0.412613	+	0.238222i
$465$		0			0
$466$	−7.80068	−	13.5112i	−0.361359	−	0.625893i
$467$	−24.6082			−1.13873			−0.569366	−	0.822084i	$-0.692811\pi$
$467$	−24.6082			−1.13873			−0.569366	+	0.822084i	$0.692811\pi$
$468$		0			0
$469$		0			0
$470$	−1.03438	+	0.597199i	−0.0477124	+	0.0275467i
$471$		0			0
$472$	−1.70357	−	0.983559i	−0.0784133	−	0.0452720i
$473$	1.10917	+	0.640380i	0.0509997	+	0.0294447i
$474$		0			0
$475$	−2.28894	+	1.32152i	−0.105024	+	0.0606356i
$476$		0			0
$477$		0			0
$478$	22.2831			1.01920
$479$	14.7674	+	25.5779i	0.674741	+	1.16869i	0.976545	+	0.215315i	$0.0690779\pi$
$479$	14.7674	+	25.5779i	0.674741	+	1.16869i	−0.301804	+	0.953370i	$0.597589\pi$
$480$		0			0
$481$	−22.4126	−	12.9399i	−1.02193	−	0.590009i
$482$	0.328262	−	0.568566i	0.0149519	−	0.0258975i
$483$		0			0
$484$	5.47171	+	9.47728i	0.248714	+	0.430785i
$485$		−	4.29415i		−	0.194987i
$486$		0			0
$487$	1.08694			0.0492538			0.0246269	−	0.999697i	$-0.492160\pi$
$487$	1.08694			0.0492538			0.0246269	+	0.999697i	$0.492160\pi$
$488$	−6.27087	−	10.8615i	−0.283869	−	0.491675i
$489$		0			0
$490$		0			0
$491$	9.43373	+	5.44657i	0.425738	+	0.245800i	0.697529	−	0.716556i	$-0.254283\pi$
$491$	9.43373	+	5.44657i	0.425738	+	0.245800i	−0.271791	+	0.962356i	$0.587616\pi$
$492$		0			0
$493$	52.1478	−	30.1075i	2.34862	−	1.35597i
$494$			3.08033i			0.138590i
$495$		0			0
$496$			6.02640i			0.270594i
$497$		0			0
$498$		0			0
$499$	−20.0342	+	34.7002i	−0.896853	+	1.55340i	−0.0653593	+	0.997862i	$0.520819\pi$
$499$	−20.0342	+	34.7002i	−0.896853	+	1.55340i	−0.831494	+	0.555534i	$0.812514\pi$
$500$	3.65537	−	6.33129i	0.163473	−	0.283144i
$501$		0			0
$502$	−3.01616	+	1.74138i	−0.134618	+	0.0777216i
$503$	27.5061			1.22644			0.613219	−	0.789913i	$-0.289874\pi$
$503$	27.5061			1.22644			0.613219	+	0.789913i	$0.289874\pi$
$504$		0			0
$505$	−35.0179			−1.55828
$506$	−1.67046	+	0.964441i	−0.0742610	+	0.0428746i
$507$		0			0
$508$	−2.34829	+	4.06735i	−0.104188	+	0.180459i
$509$	−4.17535	+	7.23192i	−0.185069	+	0.320549i	−0.943600	−	0.331088i	$-0.892584\pi$
$509$	−4.17535	+	7.23192i	−0.185069	+	0.320549i	0.758531	+	0.651637i	$0.225918\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	2.05031i		−	0.0904353i
$515$	−43.1449	+	24.9097i	−1.90119	+	1.09765i
$516$		0			0
$517$	−0.0911093	−	0.0526020i	−0.00400698	−	0.00231343i
$518$		0			0
$519$		0			0
$520$	3.60816	+	6.24951i	0.158228	+	0.274059i
$521$	8.33273			0.365064			0.182532	−	0.983200i	$-0.441571\pi$
$521$	8.33273			0.365064			0.182532	+	0.983200i	$0.441571\pi$
$522$		0			0
$523$		−	15.4297i		−	0.674694i	−0.941380	−	0.337347i	$-0.890470\pi$
$523$		−	15.4297i		−	0.674694i	0.941380	−	0.337347i	$-0.109530\pi$
$524$	−7.02151	−	12.1616i	−0.306736	−	0.531283i
$525$		0			0
$526$	−5.09055	+	8.81710i	−0.221959	+	0.384444i
$527$	30.6212	+	17.6792i	1.33388	+	0.770117i
$528$		0			0
$529$	21.3790	+	37.0295i	0.929521	+	1.60998i
$530$	0.591834			0.0257076
$531$		0			0
$532$		0			0
$533$	−17.6753	+	10.2048i	−0.765603	+	0.442021i
$534$		0			0
$535$	10.8788	+	6.28086i	0.470330	+	0.271545i
$536$	−7.76541	−	4.48336i	−0.335415	−	0.193652i
$537$		0			0
$538$	0.303108	−	0.174999i	0.0130679	−	0.00754476i
$539$		0			0
$540$		0			0
$541$	−6.27007			−0.269571			−0.134786	−	0.990875i	$-0.543035\pi$
$541$	−6.27007			−0.269571			−0.134786	+	0.990875i	$0.543035\pi$
$542$	6.95364	+	12.0441i	0.298684	+	0.517336i
$543$		0			0
$544$	5.08118	+	2.93362i	0.217854	+	0.125778i
$545$	13.5906	−	23.5396i	0.582157	−	1.00833i
$546$		0			0
$547$	−14.8501	−	25.7211i	−0.634945	−	1.09976i	−0.986527	−	0.163600i	$-0.947690\pi$
$547$	−14.8501	−	25.7211i	−0.634945	−	1.09976i	0.351582	−	0.936157i	$-0.385644\pi$
$548$		−	10.8499i		−	0.463483i
$549$		0			0
$550$	−0.545389			−0.0232555
$551$	5.91523	+	10.2455i	0.251997	+	0.436472i
$552$		0			0
$553$		0			0
$554$	−13.6849	−	7.90100i	−0.581417	−	0.335682i
$555$		0			0
$556$	19.5606	−	11.2933i	0.829554	−	0.478943i
$557$			17.9103i			0.758883i	0.925216	+	0.379442i	$0.123884\pi$
$557$			17.9103i			0.758883i	−0.925216	+	0.379442i	$0.876116\pi$
$558$		0			0
$559$		−	14.3881i		−	0.608551i
$560$		0			0
$561$		0			0
$562$	12.8365	−	22.2334i	0.541473	−	0.937859i
$563$	−21.7205	+	37.6210i	−0.915409	+	1.58553i	−0.109107	+	0.994030i	$0.534799\pi$
$563$	−21.7205	+	37.6210i	−0.915409	+	1.58553i	−0.806302	+	0.591504i	$0.798534\pi$
$564$		0			0
$565$	22.5121	−	12.9974i	0.947090	−	0.546803i
$566$	6.61664			0.278118
$567$		0			0
$568$	2.24510			0.0942024
$569$	4.14890	−	2.39537i	0.173931	−	0.100419i	−0.410507	−	0.911857i	$-0.634648\pi$
$569$	4.14890	−	2.39537i	0.173931	−	0.100419i	0.584438	+	0.811438i	$0.301315\pi$
$570$		0			0
$571$	6.69405	−	11.5944i	0.280137	−	0.485212i	−0.691281	−	0.722586i	$-0.742953\pi$
$571$	6.69405	−	11.5944i	0.280137	−	0.485212i	0.971418	+	0.237374i	$0.0762867\pi$
$572$	−0.317811	+	0.550464i	−0.0132883	+	0.0230161i
$573$		0			0
$574$		0			0
$575$			18.5930i			0.775380i
$576$		0			0
$577$		−	10.7792i		−	0.448746i	−0.974503	−	0.224373i	$-0.927967\pi$
$577$		−	10.7792i		−	0.448746i	0.974503	−	0.224373i	$-0.0720334\pi$
$578$	15.0900	−	8.71224i	0.627663	−	0.362381i
$579$		0			0
$580$	24.0022	+	13.8577i	0.996636	+	0.575408i
$581$		0			0
$582$		0			0
$583$	0.0260647	+	0.0451454i	0.00107949	+	0.00186973i
$584$	−7.25634			−0.300270
$585$		0			0
$586$		−	17.3661i		−	0.717387i
$587$	10.0173	+	17.3504i	0.413458	+	0.716130i	0.995265	−	0.0971969i	$-0.0309877\pi$
$587$	10.0173	+	17.3504i	0.413458	+	0.716130i	−0.581808	+	0.813326i	$0.697654\pi$
$588$		0			0
$589$	−3.47343	+	6.01615i	−0.143120	+	0.247891i
$590$	−4.60055	−	2.65613i	−0.189402	−	0.109351i
$591$		0			0
$592$	−4.84244	−	8.38735i	−0.199023	−	0.344718i
$593$	22.7549			0.934433			0.467217	−	0.884143i	$-0.345257\pi$
$593$	22.7549			0.934433			0.467217	+	0.884143i	$0.345257\pi$
$594$		0			0
$595$		0			0
$596$	−0.236156	+	0.136345i	−0.00967333	+	0.00558490i
$597$		0			0
$598$	18.7660	+	10.8346i	0.767399	+	0.443058i
$599$	22.0525	+	12.7320i	0.901040	+	0.520216i	0.877537	−	0.479508i	$-0.159185\pi$
$599$	22.0525	+	12.7320i	0.901040	+	0.520216i	0.0235025	+	0.999724i	$0.492518\pi$
$600$		0			0
$601$	8.94631	−	5.16515i	0.364928	−	0.210691i	−0.306313	−	0.951931i	$-0.599095\pi$
$601$	8.94631	−	5.16515i	0.364928	−	0.210691i	0.671240	+	0.741240i	$0.265762\pi$
$602$		0			0
$603$		0			0
$604$	−18.8430			−0.766709
$605$	14.7765	+	25.5936i	0.600750	+	1.04053i
$606$		0			0
$607$	−6.05553	−	3.49616i	−0.245786	−	0.141905i	0.372047	−	0.928214i	$-0.378656\pi$
$607$	−6.05553	−	3.49616i	−0.245786	−	0.141905i	−0.617833	+	0.786309i	$0.711989\pi$
$608$	−0.576368	+	0.998299i	−0.0233748	+	0.0404864i
$609$		0			0
$610$	−16.9346	−	29.3317i	−0.685664	−	1.18760i
$611$			1.18186i			0.0478131i
$612$		0			0
$613$	10.3097			0.416405			0.208203	−	0.978086i	$-0.433239\pi$
$613$	10.3097			0.416405			0.208203	+	0.978086i	$0.433239\pi$
$614$	−0.591642	−	1.02475i	−0.0238767	−	0.0413557i
$615$		0			0
$616$		0			0
$617$	−3.11226	−	1.79686i	−0.125295	−	0.0723389i	0.436043	−	0.899926i	$-0.356380\pi$
$617$	−3.11226	−	1.79686i	−0.125295	−	0.0723389i	−0.561337	+	0.827587i	$0.689713\pi$
$618$		0			0
$619$	−27.4694	+	15.8594i	−1.10409	+	0.637445i	−0.937291	−	0.348547i	$-0.886675\pi$
$619$	−27.4694	+	15.8594i	−1.10409	+	0.637445i	−0.166796	+	0.985991i	$0.553342\pi$
$620$			16.2745i			0.653598i
$621$		0			0
$622$			25.3233i			1.01537i
$623$		0			0
$624$		0			0
$625$	15.6035	−	27.0261i	0.624142	−	1.08105i
$626$	−0.916770	+	1.58789i	−0.0366415	+	0.0634649i
$627$		0			0
$628$	2.82310	−	1.62992i	0.112654	−	0.0650408i
$629$	−56.8235			−2.26570
$630$		0			0
$631$	4.92443			0.196038			0.0980192	−	0.995185i	$-0.468749\pi$
$631$	4.92443			0.196038			0.0980192	+	0.995185i	$0.468749\pi$
$632$	9.41528	−	5.43592i	0.374520	−	0.216229i
$633$		0			0
$634$	−4.75337	+	8.23307i	−0.188780	+	0.326977i
$635$	−6.34161	+	10.9840i	−0.251659	+	0.435886i
$636$		0			0
$637$		0			0
$638$			2.44120i			0.0966479i
$639$		0			0
$640$			2.70053i			0.106748i
$641$	−7.27479	+	4.20010i	−0.287337	+	0.165894i	−0.636740	−	0.771078i	$-0.719718\pi$
$641$	−7.27479	+	4.20010i	−0.287337	+	0.165894i	0.349403	+	0.936972i	$0.386384\pi$
$642$		0			0
$643$	−6.34290	−	3.66208i	−0.250140	−	0.144418i	0.369689	−	0.929156i	$-0.379464\pi$
$643$	−6.34290	−	3.66208i	−0.250140	−	0.144418i	−0.619828	+	0.784738i	$0.712798\pi$
$644$		0			0
$645$		0			0
$646$	3.38169	+	5.85726i	0.133051	+	0.230451i
$647$	−3.89938			−0.153301			−0.0766503	−	0.997058i	$-0.524422\pi$
$647$	−3.89938			−0.153301			−0.0766503	+	0.997058i	$0.524422\pi$
$648$		0			0
$649$		−	0.467910i		−	0.0183671i
$650$	3.06345	+	5.30606i	0.120159	+	0.208121i
$651$		0			0
$652$	−1.56837	+	2.71650i	−0.0614222	+	0.106386i
$653$	−20.0302	−	11.5644i	−0.783843	−	0.452552i	0.0539477	−	0.998544i	$-0.482820\pi$
$653$	−20.0302	−	11.5644i	−0.783843	−	0.452552i	−0.837790	+	0.545992i	$0.816153\pi$
$654$		0			0
$655$	−18.9618	−	32.8428i	−0.740898	−	1.28327i
$656$	−7.63782			−0.298207
$657$		0			0
$658$		0			0
$659$	28.2312	−	16.2993i	1.09973	−	0.634930i	0.163580	−	0.986530i	$-0.447696\pi$
$659$	28.2312	−	16.2993i	1.09973	−	0.634930i	0.936150	+	0.351600i	$0.114362\pi$
$660$		0			0
$661$	43.4612	+	25.0924i	1.69045	+	0.975979i	0.954154	+	0.299315i	$0.0967583\pi$
$661$	43.4612	+	25.0924i	1.69045	+	0.975979i	0.736292	+	0.676664i	$0.236575\pi$
$662$	−16.0535	−	9.26852i	−0.623939	−	0.360231i
$663$		0			0
$664$	1.32052	−	0.762403i	0.0512461	−	0.0295870i
$665$		0			0
$666$		0			0
$667$	83.2234			3.22242
$668$	3.19575	+	5.53520i	0.123647	+	0.214163i
$669$		0			0
$670$	−20.9707	−	12.1074i	−0.810169	−	0.467751i
$671$	1.49162	−	2.58357i	0.0575835	−	0.0997375i
$672$		0			0
$673$	−9.02645	−	15.6343i	−0.347944	−	0.602657i	0.637940	−	0.770086i	$-0.279787\pi$
$673$	−9.02645	−	15.6343i	−0.347944	−	0.602657i	−0.985884	+	0.167429i	$0.946453\pi$
$674$		−	9.41461i		−	0.362637i
$675$		0			0
$676$	−5.85942			−0.225362
$677$	−10.1509	−	17.5819i	−0.390131	−	0.675726i	0.602336	−	0.798243i	$-0.294237\pi$
$677$	−10.1509	−	17.5819i	−0.390131	−	0.675726i	−0.992466	+	0.122517i	$0.960903\pi$
$678$		0			0
$679$		0			0
$680$	13.7219	+	7.92232i	0.526209	+	0.303807i
$681$		0			0
$682$	−1.24142	+	0.716737i	−0.0475366	+	0.0274453i
$683$			20.0741i			0.768113i	0.923310	+	0.384056i	$0.125473\pi$
$683$			20.0741i			0.768113i	−0.923310	+	0.384056i	$0.874527\pi$
$684$		0			0
$685$		−	29.3004i		−	1.11951i
$686$		0			0
$687$		0			0
$688$	2.69219	−	4.66301i	0.102639	−	0.177776i
$689$	0.292811	−	0.507164i	0.0111552	−	0.0193214i
$690$		0			0
$691$	−21.3874	+	12.3480i	−0.813616	+	0.469742i	−0.848210	−	0.529660i	$-0.822320\pi$
$691$	−21.3874	+	12.3480i	−0.813616	+	0.469742i	0.0345939	+	0.999401i	$0.488986\pi$
$692$	0.293533			0.0111585
$693$		0			0
$694$	−11.2427			−0.426767
$695$	52.8239	−	30.4979i	2.00372	−	1.15685i
$696$		0			0
$697$	−22.4065	+	38.8091i	−0.848705	+	1.47000i
$698$	−0.513552	+	0.889499i	−0.0194382	+	0.0336680i
$699$		0			0
$700$		0			0
$701$			21.1616i			0.799263i	0.916676	+	0.399632i	$0.130862\pi$
$701$			21.1616i			0.799263i	−0.916676	+	0.399632i	$0.869138\pi$
$702$		0			0
$703$		−	11.1641i		−	0.421063i
$704$	−0.205998	+	0.118933i	−0.00776383	+	0.00448245i
$705$		0			0
$706$	−21.3291	−	12.3144i	−0.802733	−	0.463458i
$707$		0			0
$708$		0			0
$709$	−10.4861	−	18.1624i	−0.393812	−	0.682103i	0.599137	−	0.800647i	$-0.295511\pi$
$709$	−10.4861	−	18.1624i	−0.393812	−	0.682103i	−0.992949	+	0.118544i	$0.962177\pi$
$710$	6.06296			0.227539
$711$		0			0
$712$			13.5277i			0.506972i
$713$	24.4344	+	42.3217i	0.915077	+	1.58496i
$714$		0			0
$715$	−0.858256	+	1.48654i	−0.0320970	+	0.0555936i
$716$	−19.9833	−	11.5374i	−0.746810	−	0.431171i
$717$		0			0
$718$	−5.26168	−	9.11350i	−0.196364	−	0.340113i
$719$	−22.7726			−0.849273			−0.424637	−	0.905364i	$-0.639598\pi$
$719$	−22.7726			−0.849273			−0.424637	+	0.905364i	$0.639598\pi$
$720$		0			0
$721$		0			0
$722$	15.3037	−	8.83560i	0.569545	−	0.328827i
$723$		0			0
$724$	−9.45493	−	5.45881i	−0.351390	−	0.202875i
$725$	20.3787	+	11.7657i	0.756846	+	0.436965i
$726$		0			0
$727$	−15.4847	+	8.94010i	−0.574296	+	0.331570i	−0.758863	−	0.651250i	$-0.774245\pi$
$727$	−15.4847	+	8.94010i	−0.574296	+	0.331570i	0.184567	+	0.982820i	$0.440912\pi$
$728$		0			0
$729$		0			0
$730$	−19.5959			−0.725279
$731$	−15.7957	−	27.3590i	−0.584226	−	1.01191i
$732$		0			0
$733$	18.8378	+	10.8760i	0.695790	+	0.401715i	0.805778	−	0.592218i	$-0.201748\pi$
$733$	18.8378	+	10.8760i	0.695790	+	0.401715i	−0.109987	+	0.993933i	$0.535081\pi$
$734$	−3.46567	+	6.00271i	−0.127920	+	0.221564i
$735$		0			0
$736$	4.05456	+	7.02271i	0.149453	+	0.258861i
$737$		−	2.13288i		−	0.0785655i
$738$		0			0
$739$	−26.5207			−0.975578			−0.487789	−	0.872961i	$-0.662197\pi$
$739$	−26.5207			−0.975578			−0.487789	+	0.872961i	$0.662197\pi$
$740$	−13.0771	−	22.6503i	−0.480725	−	0.832641i
$741$		0			0
$742$		0			0
$743$	1.53406	+	0.885688i	0.0562791	+	0.0324927i	0.527876	−	0.849322i	$-0.322989\pi$
$743$	1.53406	+	0.885688i	0.0562791	+	0.0324927i	−0.471596	+	0.881814i	$0.656322\pi$
$744$		0			0
$745$	−0.637746	+	0.368203i	−0.0233652	+	0.0134899i
$746$			1.90047i			0.0695813i
$747$		0			0
$748$			1.39561i			0.0510287i
$749$		0			0
$750$		0			0
$751$	19.9293	−	34.5186i	0.727231	−	1.25960i	−0.230818	−	0.972997i	$-0.574140\pi$
$751$	19.9293	−	34.5186i	0.727231	−	1.25960i	0.958049	−	0.286605i	$-0.0925266\pi$
$752$	−0.221142	+	0.383029i	−0.00806421	+	0.0139676i
$753$		0			0
$754$	23.7503	−	13.7122i	0.864934	−	0.499370i
$755$	−50.8859			−1.85193
$756$		0			0
$757$	−37.2462			−1.35374			−0.676869	−	0.736104i	$-0.736663\pi$
$757$	−37.2462			−1.35374			−0.676869	+	0.736104i	$0.736663\pi$
$758$	32.4460	−	18.7327i	1.17849	−	0.680403i
$759$		0			0
$760$	−1.55650	+	2.69593i	−0.0564601	+	0.0977918i
$761$	21.6642	−	37.5235i	0.785327	−	1.36023i	−0.143477	−	0.989654i	$-0.545828\pi$
$761$	21.6642	−	37.5235i	0.785327	−	1.36023i	0.928804	−	0.370573i	$-0.120839\pi$
$762$		0			0
$763$		0			0
$764$			12.8698i			0.465613i
$765$		0			0
$766$		−	1.48131i		−	0.0535218i
$767$	−4.55227	+	2.62825i	−0.164373	+	0.0949007i
$768$		0			0
$769$	18.2010	+	10.5084i	0.656345	+	0.378941i	0.790883	−	0.611967i	$-0.209622\pi$
$769$	18.2010	+	10.5084i	0.656345	+	0.378941i	−0.134538	+	0.990908i	$0.542955\pi$
$770$		0			0
$771$		0			0
$772$	−5.11771	−	8.86414i	−0.184190	−	0.319027i
$773$	−3.08047			−0.110797			−0.0553984	−	0.998464i	$-0.517643\pi$
$773$	−3.08047			−0.110797			−0.0553984	+	0.998464i	$0.517643\pi$
$774$		0			0
$775$			13.8176i			0.496343i
$776$	−0.795057	−	1.37708i	−0.0285409	−	0.0494343i
$777$		0			0
$778$	−6.35131	+	11.0008i	−0.227706	+	0.394398i
$779$	−7.62483	−	4.40220i	−0.273188	−	0.157725i
$780$		0			0
$781$	0.267016	+	0.462486i	0.00955459	+	0.0165490i
$782$	47.5782			1.70139
$783$		0			0
$784$		0			0
$785$	7.62386	−	4.40164i	0.272107	−	0.157101i
$786$		0			0
$787$	−31.0182	−	17.9083i	−1.10568	−	0.638363i	−0.167971	−	0.985792i	$-0.553722\pi$
$787$	−31.0182	−	17.9083i	−1.10568	−	0.638363i	−0.937707	+	0.347428i	$0.887055\pi$
$788$	−3.36943	−	1.94534i	−0.120031	−	0.0692999i
$789$		0			0
$790$	25.4262	−	14.6798i	0.904624	−	0.522285i
$791$		0			0
$792$		0			0
$793$	−33.5139			−1.19011
$794$	−9.67431	−	16.7564i	−0.343328	−	0.594662i
$795$		0			0
$796$	−2.01914	−	1.16575i	−0.0715665	−	0.0413189i
$797$	−11.0878	+	19.2046i	−0.392749	+	0.680261i	−0.992811	−	0.119693i	$-0.961809\pi$
$797$	−11.0878	+	19.2046i	−0.392749	+	0.680261i	0.600062	+	0.799953i	$0.295142\pi$
$798$		0			0
$799$	1.29749	+	2.24732i	0.0459019	+	0.0795045i
$800$			2.29284i			0.0810643i
$801$		0			0
$802$	10.8991			0.384860
$803$	−0.863017	−	1.49479i	−0.0304552	−	0.0527500i
$804$		0			0
$805$		0			0
$806$	13.9462	+	8.05184i	0.491234	+	0.283614i
$807$		0			0
$808$	−11.2298	+	6.48353i	−0.395063	+	0.228090i
$809$			3.15819i			0.111036i	0.998458	+	0.0555180i	$0.0176810\pi$
$809$			3.15819i			0.111036i	−0.998458	+	0.0555180i	$0.982319\pi$
$810$		0			0
$811$		−	31.8867i		−	1.11969i	−0.828596	−	0.559847i	$-0.810860\pi$
$811$		−	31.8867i		−	1.11969i	0.828596	−	0.559847i	$-0.189140\pi$
$812$		0			0
$813$		0			0
$814$	1.15185	−	1.99506i	0.0403723	−	0.0699269i
$815$	−4.23543	+	7.33599i	−0.148361	+	0.256968i
$816$		0			0
$817$	5.37523	−	3.10339i	0.188055	−	0.108574i
$818$	20.5180			0.717396
$819$		0			0
$820$	−20.6261			−0.720296
$821$	−23.1617	+	13.3724i	−0.808348	+	0.466700i	−0.846382	−	0.532577i	$-0.821224\pi$
$821$	−23.1617	+	13.3724i	−0.808348	+	0.466700i	0.0380341	+	0.999276i	$0.487890\pi$
$822$		0			0
$823$	15.0895	−	26.1358i	0.525988	−	0.911038i	−0.473554	−	0.880765i	$-0.657029\pi$
$823$	15.0895	−	26.1358i	0.525988	−	0.911038i	0.999542	−	0.0302730i	$-0.00963766\pi$
$824$	−9.22402	+	15.9765i	−0.321334	+	0.556567i
$825$		0			0
$826$		0			0
$827$		−	23.9486i		−	0.832773i	−0.909188	−	0.416387i	$-0.863296\pi$
$827$		−	23.9486i		−	0.832773i	0.909188	−	0.416387i	$-0.136704\pi$
$828$		0			0
$829$		−	25.0860i		−	0.871273i	−0.900123	−	0.435636i	$-0.856523\pi$
$829$		−	25.0860i		−	0.871273i	0.900123	−	0.435636i	$-0.143477\pi$
$830$	3.56610	−	2.05889i	0.123781	−	0.0714651i
$831$		0			0
$832$	2.31418	+	1.33609i	0.0802298	+	0.0463207i
$833$		0			0
$834$		0			0
$835$	8.63021	+	14.9480i	0.298661	+	0.517296i
$836$	−0.274196			−0.00948328
$837$		0			0
$838$			5.46173i			0.188672i
$839$	24.0987	+	41.7402i	0.831980	+	1.44103i	0.896466	+	0.443113i	$0.146126\pi$
$839$	24.0987	+	41.7402i	0.831980	+	1.44103i	−0.0644863	+	0.997919i	$0.520541\pi$
$840$		0			0
$841$	38.1638	−	66.1017i	1.31599	−	2.27937i
$842$	24.7265	+	14.2759i	0.852132	+	0.491979i
$843$		0			0
$844$	7.48854	+	12.9705i	0.257766	+	0.446464i
$845$	−15.8235			−0.544345
$846$		0			0
$847$		0			0
$848$	0.189794	−	0.109577i	0.00651754	−	0.00376290i
$849$		0			0
$850$	11.6504	+	6.72633i	0.399604	+	0.230711i
$851$	−68.0141	−	39.2680i	−2.33149	−	1.34609i
$852$		0			0
$853$	−2.64492	+	1.52704i	−0.0905602	+	0.0522850i	−0.544596	−	0.838698i	$-0.683317\pi$
$853$	−2.64492	+	1.52704i	−0.0905602	+	0.0522850i	0.454036	+	0.890983i	$0.349984\pi$
$854$		0			0
$855$		0			0
$856$	4.65158			0.158988
$857$	−13.9460	−	24.1552i	−0.476386	−	0.825125i	0.523248	−	0.852181i	$-0.324720\pi$
$857$	−13.9460	−	24.1552i	−0.476386	−	0.825125i	−0.999634	+	0.0270556i	$0.991387\pi$
$858$		0			0
$859$	27.3959	+	15.8170i	0.934734	+	0.539669i	0.888306	−	0.459252i	$-0.151883\pi$
$859$	27.3959	+	15.8170i	0.934734	+	0.539669i	0.0464286	+	0.998922i	$0.485216\pi$
$860$	7.27034	−	12.5926i	0.247916	−	0.429404i
$861$		0			0
$862$	4.77819	+	8.27607i	0.162746	+	0.281884i
$863$			31.1120i			1.05906i	0.848290	+	0.529532i	$0.177633\pi$
$863$			31.1120i			1.05906i	−0.848290	+	0.529532i	$0.822367\pi$
$864$		0			0
$865$	0.792694			0.0269524
$866$	9.85611	+	17.0713i	0.334924	+	0.580106i
$867$		0			0
$868$		0			0
$869$	2.23957	+	1.29302i	0.0759722	+	0.0438626i
$870$		0			0
$871$	−20.7506	+	11.9804i	−0.703108	+	0.405940i
$872$		−	10.0651i		−	0.340849i
$873$		0			0
$874$			9.34769i			0.316190i
$875$		0			0
$876$		0			0
$877$	−5.94066	+	10.2895i	−0.200602	+	0.347452i	−0.948722	−	0.316110i	$-0.897623\pi$
$877$	−5.94066	+	10.2895i	−0.200602	+	0.347452i	0.748121	+	0.663563i	$0.230956\pi$
$878$	12.1822	−	21.1001i	0.411129	−	0.712096i
$879$		0			0
$880$	−0.556302	+	0.321181i	−0.0187529	+	0.0108270i
$881$	−37.0866			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$881$	−37.0866			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$882$		0			0
$883$	−7.53904			−0.253709			−0.126854	−	0.991921i	$-0.540488\pi$
$883$	−7.53904			−0.253709			−0.126854	+	0.991921i	$0.540488\pi$
$884$	13.5779	−	7.83918i	0.456673	−	0.263660i
$885$		0			0
$886$	18.7483	−	32.4731i	0.629863	−	1.09095i
$887$	26.4500	−	45.8127i	0.888103	−	1.53824i	0.0459884	−	0.998942i	$-0.485356\pi$
$887$	26.4500	−	45.8127i	0.888103	−	1.53824i	0.842115	−	0.539298i	$-0.181310\pi$
$888$		0			0
$889$		0			0
$890$			36.5319i			1.22455i
$891$		0			0
$892$			20.2670i			0.678590i
$893$	−0.441531	+	0.254918i	−0.0147753	+	0.00853051i
$894$		0			0
$895$	−53.9654	−	31.1569i	−1.80386	−	1.04146i
$896$		0			0
$897$		0			0
$898$	−11.3499	−	19.6585i	−0.378749	−	0.656013i
$899$	61.8486			2.06276
$900$		0			0
$901$		−	1.28583i		−	0.0428373i
$902$	−0.908388	−	1.57337i	−0.0302460	−	0.0523876i
$903$		0			0
$904$	4.81290	−	8.33618i	0.160075	−	0.277257i
$905$	−25.5333	−	14.7417i	−0.848755	−	0.490029i
$906$		0			0
$907$	26.1097	+	45.2233i	0.866958	+	1.50162i	0.865089	+	0.501618i	$0.167262\pi$
$907$	26.1097	+	45.2233i	0.866958	+	1.50162i	0.00186910	+	0.999998i	$0.499405\pi$
$908$	10.3097			0.342139
$909$		0			0
$910$		0			0
$911$	7.52440	−	4.34421i	0.249295	−	0.143930i	−0.370147	−	0.928973i	$-0.620693\pi$
$911$	7.52440	−	4.34421i	0.249295	−	0.143930i	0.619441	+	0.785043i	$0.287359\pi$
$912$		0			0
$913$	0.314106	+	0.181349i	0.0103954	+	0.00600179i
$914$	−34.4878	−	19.9116i	−1.14076	−	0.658616i
$915$		0			0
$916$	7.57314	−	4.37235i	0.250224	−	0.144467i
$917$		0			0
$918$		0			0
$919$	−27.6927			−0.913498			−0.456749	−	0.889596i	$-0.650986\pi$
$919$	−27.6927			−0.913498			−0.456749	+	0.889596i	$0.650986\pi$
$920$	10.9495	+	18.9650i	0.360993	+	0.625258i
$921$		0			0
$922$	7.51299	+	4.33763i	0.247427	+	0.142852i
$923$	2.99967	−	5.19557i	0.0987352	−	0.171014i
$924$		0			0
$925$	−11.1030	−	19.2309i	−0.365063	−	0.632308i
$926$		−	14.1321i		−	0.464409i
$927$		0			0
$928$	10.2629			0.336897
$929$	−16.9599	−	29.3753i	−0.556435	−	0.963774i	−0.997790	−	0.0664412i	$-0.978836\pi$
$929$	−16.9599	−	29.3753i	−0.556435	−	0.963774i	0.441355	−	0.897332i	$-0.354498\pi$
$930$		0			0
$931$		0			0
$932$	−13.5112	−	7.80068i	−0.442573	−	0.255520i
$933$		0			0
$934$	−21.3113	+	12.3041i	−0.697329	+	0.402603i
$935$			3.76889i			0.123256i
$936$		0			0
$937$		−	5.54431i		−	0.181125i	−0.995891	−	0.0905623i	$-0.971134\pi$
$937$		−	5.54431i		−	0.181125i	0.995891	−	0.0905623i	$-0.0288664\pi$
$938$		0			0
$939$		0			0
$940$	−0.597199	+	1.03438i	−0.0194785	+	0.0337377i
$941$	3.55887	−	6.16415i	0.116016	−	0.200946i	−0.802169	−	0.597096i	$-0.796321\pi$
$941$	3.55887	−	6.16415i	0.116016	−	0.200946i	0.918185	+	0.396151i	$0.129654\pi$
$942$		0			0
$943$	−53.6382	+	30.9680i	−1.74670	+	1.00846i
$944$	−1.96712			−0.0640242
$945$		0			0
$946$	1.28076			0.0416411
$947$	1.06457	−	0.614627i	0.0345937	−	0.0199727i	−0.482603	−	0.875839i	$-0.660309\pi$
$947$	1.06457	−	0.614627i	0.0345937	−	0.0199727i	0.517197	+	0.855866i	$0.326975\pi$
$948$		0			0
$949$	−9.69515	+	16.7925i	−0.314718	+	0.545108i
$950$	−1.32152	+	2.28894i	−0.0428759	+	0.0742632i
$951$		0			0
$952$		0			0
$953$		−	24.0059i		−	0.777628i	−0.921316	−	0.388814i	$-0.872885\pi$
$953$		−	24.0059i		−	0.777628i	0.921316	−	0.388814i	$-0.127115\pi$
$954$		0			0
$955$			34.7552i			1.12465i
$956$	19.2977	−	11.1415i	0.624133	−	0.360343i
$957$		0			0
$958$	25.5779	+	14.7674i	0.826385	+	0.477114i
$959$		0			0
$960$		0			0
$961$	2.65878	+	4.60514i	0.0857670	+	0.148553i
$962$	−25.8798			−0.834399
$963$		0			0
$964$		−	0.656523i		−	0.0211452i
$965$	−13.8205	−	23.9378i	−0.444898	−	0.770586i
$966$		0			0
$967$	−18.7378	+	32.4549i	−0.602568	+	1.04368i	0.389863	+	0.920873i	$0.372522\pi$
$967$	−18.7378	+	32.4549i	−0.602568	+	1.04368i	−0.992431	+	0.122805i	$0.960811\pi$
$968$	9.47728	+	5.47171i	0.304611	+	0.175867i
$969$		0			0
$970$	−2.14707	−	3.71884i	−0.0689384	−	0.119405i
$971$	−29.7244			−0.953902			−0.476951	−	0.878930i	$-0.658258\pi$
$971$	−29.7244			−0.953902			−0.476951	+	0.878930i	$0.658258\pi$
$972$		0			0
$973$		0			0
$974$	0.941315	−	0.543468i	0.0301617	−	0.0174139i
$975$		0			0
$976$	−10.8615	−	6.27087i	−0.347667	−	0.200726i
$977$	35.9649	+	20.7644i	1.15062	+	0.664310i	0.949038	−	0.315161i	$-0.102059\pi$
$977$	35.9649	+	20.7644i	1.15062	+	0.664310i	0.201581	+	0.979472i	$0.435392\pi$
$978$		0			0
$979$	−2.78668	+	1.60889i	−0.0890626	+	0.0514203i
$980$		0			0
$981$		0			0
$982$	10.8931			0.347614
$983$	6.25746	+	10.8382i	0.199582	+	0.345686i	0.948393	−	0.317098i	$-0.102708\pi$
$983$	6.25746	+	10.8382i	0.199582	+	0.345686i	−0.748811	+	0.662784i	$0.769375\pi$
$984$		0			0
$985$	−9.09923	−	5.25345i	−0.289926	−	0.167389i
$986$	30.1075	−	52.1478i	0.958819	−	1.66072i
$987$		0			0
$988$	1.54016	+	2.66764i	0.0489991	+	0.0848690i
$989$		−	43.6627i		−	1.38839i
$990$		0			0
$991$	−52.2038			−1.65831			−0.829154	−	0.559020i	$-0.811178\pi$
$991$	−52.2038			−1.65831			−0.829154	+	0.559020i	$0.811178\pi$
$992$	3.01320	+	5.21902i	0.0956693	+	0.165704i
$993$		0			0
$994$		0			0
$995$	−5.45274	−	3.14814i	−0.172863	−	0.0998027i
$996$		0			0
$997$	6.92399	−	3.99757i	0.219285	−	0.126604i	−0.386334	−	0.922359i	$-0.626259\pi$
$997$	6.92399	−	3.99757i	0.219285	−	0.126604i	0.605619	+	0.795755i	$0.292926\pi$
$998$			40.0684i			1.26834i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.c.881.14		48
3.2	odd	2		882.2.m.c.293.7	yes	48
7.2	even	3		2646.2.t.c.2285.9		48
7.3	odd	6		2646.2.l.c.1097.17		48
7.4	even	3		2646.2.l.c.1097.18		48
7.5	odd	6		2646.2.t.c.2285.10		48
7.6	odd	2	inner	2646.2.m.c.881.13		48
9.2	odd	6	inner	2646.2.m.c.1763.13		48
9.7	even	3		882.2.m.c.587.6	yes	48
21.2	odd	6		882.2.t.c.815.23		48
21.5	even	6		882.2.t.c.815.14		48
21.11	odd	6		882.2.l.c.509.3		48
21.17	even	6		882.2.l.c.509.10		48
21.20	even	2		882.2.m.c.293.6	✓	48
63.2	odd	6		2646.2.l.c.521.17		48
63.11	odd	6		2646.2.t.c.1979.10		48
63.16	even	3		882.2.l.c.227.22		48
63.20	even	6	inner	2646.2.m.c.1763.14		48
63.25	even	3		882.2.t.c.803.14		48
63.34	odd	6		882.2.m.c.587.7	yes	48
63.38	even	6		2646.2.t.c.1979.9		48
63.47	even	6		2646.2.l.c.521.18		48
63.52	odd	6		882.2.t.c.803.23		48
63.61	odd	6		882.2.l.c.227.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.15		48	63.61	odd	6
882.2.l.c.227.22		48	63.16	even	3
882.2.l.c.509.3		48	21.11	odd	6
882.2.l.c.509.10		48	21.17	even	6
882.2.m.c.293.6	✓	48	21.20	even	2
882.2.m.c.293.7	yes	48	3.2	odd	2
882.2.m.c.587.6	yes	48	9.7	even	3
882.2.m.c.587.7	yes	48	63.34	odd	6
882.2.t.c.803.14		48	63.25	even	3
882.2.t.c.803.23		48	63.52	odd	6
882.2.t.c.815.14		48	21.5	even	6
882.2.t.c.815.23		48	21.2	odd	6
2646.2.l.c.521.17		48	63.2	odd	6
2646.2.l.c.521.18		48	63.47	even	6
2646.2.l.c.1097.17		48	7.3	odd	6
2646.2.l.c.1097.18		48	7.4	even	3
2646.2.m.c.881.13		48	7.6	odd	2	inner
2646.2.m.c.881.14		48	1.1	even	1	trivial
2646.2.m.c.1763.13		48	9.2	odd	6	inner
2646.2.m.c.1763.14		48	63.20	even	6	inner
2646.2.t.c.1979.9		48	63.38	even	6
2646.2.t.c.1979.10		48	63.11	odd	6
2646.2.t.c.2285.9		48	7.2	even	3
2646.2.t.c.2285.10		48	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.35026 - 2.33872i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.35026 - 2.33872i) q^{5} -1.00000i q^{8} -2.70053i q^{10} +(0.205998 - 0.118933i) q^{11} +(-2.31418 - 1.33609i) q^{13} +(-0.500000 - 0.866025i) q^{16} -5.86724 q^{17} -1.15274i q^{19} +(-1.35026 - 2.33872i) q^{20} +(0.118933 - 0.205998i) q^{22} +(-7.02271 - 4.05456i) q^{23} +(-1.14642 - 1.98566i) q^{25} -2.67219 q^{26} +(-8.88796 + 5.13146i) q^{29} +(-5.21902 - 3.01320i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.08118 + 2.93362i) q^{34} +9.68488 q^{37} +(-0.576368 - 0.998299i) q^{38} +(-2.33872 - 1.35026i) q^{40} +(3.81891 - 6.61455i) q^{41} +(2.69219 + 4.66301i) q^{43} -0.237866i q^{44} -8.10913 q^{46} +(-0.221142 - 0.383029i) q^{47} +(-1.98566 - 1.14642i) q^{50} +(-2.31418 + 1.33609i) q^{52} +0.219155i q^{53} -0.642362i q^{55} +(-5.13146 + 8.88796i) q^{58} +(0.983559 - 1.70357i) q^{59} +(10.8615 - 6.27087i) q^{61} -6.02640 q^{62} -1.00000 q^{64} +(-6.24951 + 3.60816i) q^{65} +(4.48336 - 7.76541i) q^{67} +(-2.93362 + 5.08118i) q^{68} +2.24510i q^{71} -7.25634i q^{73} +(8.38735 - 4.84244i) q^{74} +(-0.998299 - 0.576368i) q^{76} +(5.43592 + 9.41528i) q^{79} -2.70053 q^{80} -7.63782i q^{82} +(0.762403 + 1.32052i) q^{83} +(-7.92232 + 13.7219i) q^{85} +(4.66301 + 2.69219i) q^{86} +(-0.118933 - 0.205998i) q^{88} -13.5277 q^{89} +(-7.02271 + 4.05456i) q^{92} +(-0.383029 - 0.221142i) q^{94} +(-2.69593 - 1.55650i) q^{95} +(1.37708 - 0.795057i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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