LMFDB - Embedded newform 1216.2.t.d.1185.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(353,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1216.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1185.4
Character	$\chi$	$=$	1216.1185
Dual form			1216.2.t.d.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80664 + 1.04307i) q^{3} +(-1.98453 + 1.14577i) q^{5} +1.72665 q^{7} +(0.675970 - 1.17081i) q^{9} +O(q^{10})$	\(q+(-1.80664 + 1.04307i) q^{3} +(-1.98453 + 1.14577i) q^{5} +1.72665 q^{7} +(0.675970 - 1.17081i) q^{9} -2.75349i q^{11} +(-1.45195 - 0.838282i) q^{13} +(2.39022 - 4.13999i) q^{15} +(0.0573903 + 0.0994029i) q^{17} +(-3.55541 - 2.52172i) q^{19} +(-3.11944 + 1.80101i) q^{21} +(2.20718 - 3.82295i) q^{23} +(0.125574 - 0.217501i) q^{25} -3.43807i q^{27} +(3.68908 + 2.12989i) q^{29} +1.36057 q^{31} +(2.87207 + 4.97457i) q^{33} +(-3.42659 + 1.97834i) q^{35} +4.06828i q^{37} +3.49753 q^{39} +(-0.293039 - 0.507558i) q^{41} +(1.28837 - 0.743841i) q^{43} +3.09802i q^{45} +(3.00520 - 5.20516i) q^{47} -4.01867 q^{49} +(-0.207367 - 0.119724i) q^{51} +(7.48006 + 4.31861i) q^{53} +(3.15486 + 5.46439i) q^{55} +(9.05367 + 0.847330i) q^{57} +(12.0808 - 6.97487i) q^{59} +(10.2645 + 5.92622i) q^{61} +(1.16716 - 2.02159i) q^{63} +3.84191 q^{65} +(3.72538 + 2.15085i) q^{67} +9.20894i q^{69} +(-0.0279764 - 0.0484565i) q^{71} +(-5.91641 - 10.2475i) q^{73} +0.523929i q^{75} -4.75432i q^{77} +(7.04401 + 12.2006i) q^{79} +(5.61404 + 9.72380i) q^{81} +1.36295i q^{83} +(-0.227785 - 0.131512i) q^{85} -8.88647 q^{87} +(7.48611 - 12.9663i) q^{89} +(-2.50701 - 1.44742i) q^{91} +(-2.45806 + 1.41916i) q^{93} +(9.94513 + 0.930761i) q^{95} +(-0.462808 - 0.801606i) q^{97} +(-3.22382 - 1.86128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) $ 24 * q - 6 * q^5 + 8 * q^9	$ 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) $ 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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			0
$2$		0			0
$3$	−1.80664	+	1.04307i	−1.04307	+	0.602214i	−0.920700	−	0.390271i	$-0.872381\pi$
$3$	−1.80664	+	1.04307i	−1.04307	+	0.602214i	−0.122365	+	0.992485i	$0.539048\pi$
$4$		0			0
$5$	−1.98453	+	1.14577i	−0.887509	+	0.512404i	−0.873127	−	0.487493i	$-0.837911\pi$
$5$	−1.98453	+	1.14577i	−0.887509	+	0.512404i	−0.0143821	+	0.999897i	$0.504578\pi$
$6$		0			0
$7$	1.72665			0.652613			0.326307	−	0.945264i	$-0.394196\pi$
$7$	1.72665			0.652613			0.326307	+	0.945264i	$0.394196\pi$
$8$		0			0
$9$	0.675970	−	1.17081i	0.225323	−	0.390271i
$10$		0			0
$11$		−	2.75349i		−	0.830209i	−0.909774	−	0.415104i	$-0.863745\pi$
$11$		−	2.75349i		−	0.830209i	0.909774	−	0.415104i	$-0.136255\pi$
$12$		0			0
$13$	−1.45195	−	0.838282i	−0.402697	−	0.232497i	0.284950	−	0.958542i	$-0.408023\pi$
$13$	−1.45195	−	0.838282i	−0.402697	−	0.232497i	−0.687647	+	0.726045i	$0.741356\pi$
$14$		0			0
$15$	2.39022	−	4.13999i	0.617153	−	1.06894i
$16$		0			0
$17$	0.0573903	+	0.0994029i	0.0139192	+	0.0241087i	0.872901	−	0.487897i	$-0.162236\pi$
$17$	0.0573903	+	0.0994029i	0.0139192	+	0.0241087i	−0.858982	+	0.512006i	$0.828903\pi$
$18$		0			0
$19$	−3.55541	−	2.52172i	−0.815666	−	0.578523i
$19$	−3.55541	−	2.52172i	−0.815666	−	0.578523i
$20$		0			0
$21$	−3.11944	+	1.80101i	−0.680718	+	0.393013i
$22$		0			0
$23$	2.20718	−	3.82295i	0.460230	−	0.797141i	−0.538743	−	0.842470i	$-0.681100\pi$
$23$	2.20718	−	3.82295i	0.460230	−	0.797141i	0.998972	+	0.0453295i	$0.0144338\pi$
$24$		0			0
$25$	0.125574	−	0.217501i	0.0251149	−	0.0435003i
$26$		0			0
$27$		−	3.43807i		−	0.661657i
$28$		0			0
$29$	3.68908	+	2.12989i	0.685046	+	0.395511i	0.801753	−	0.597655i	$-0.203901\pi$
$29$	3.68908	+	2.12989i	0.685046	+	0.395511i	−0.116708	+	0.993166i	$0.537234\pi$
$30$		0			0
$31$	1.36057			0.244366			0.122183	−	0.992508i	$-0.461011\pi$
$31$	1.36057			0.244366			0.122183	+	0.992508i	$0.461011\pi$
$32$		0			0
$33$	2.87207	+	4.97457i	0.499963	+	0.865962i
$34$		0			0
$35$	−3.42659	+	1.97834i	−0.579200	+	0.334401i
$36$		0			0
$37$			4.06828i			0.668821i	0.942428	+	0.334411i	$0.108537\pi$
$37$			4.06828i			0.668821i	−0.942428	+	0.334411i	$0.891463\pi$
$38$		0			0
$39$	3.49753			0.560053
$40$		0			0
$41$	−0.293039	−	0.507558i	−0.0457649	−	0.0792672i	0.842236	−	0.539110i	$-0.181239\pi$
$41$	−0.293039	−	0.507558i	−0.0457649	−	0.0792672i	−0.888000	+	0.459843i	$0.847906\pi$
$42$		0			0
$43$	1.28837	−	0.743841i	0.196475	−	0.113435i	−0.398535	−	0.917153i	$-0.630481\pi$
$43$	1.28837	−	0.743841i	0.196475	−	0.113435i	0.595010	+	0.803718i	$0.297148\pi$
$44$		0			0
$45$			3.09802i			0.461826i
$46$		0			0
$47$	3.00520	−	5.20516i	0.438353	−	0.759250i	−0.559209	−	0.829027i	$-0.688895\pi$
$47$	3.00520	−	5.20516i	0.438353	−	0.759250i	0.997563	+	0.0697762i	$0.0222285\pi$
$48$		0			0
$49$	−4.01867			−0.574096
$50$		0			0
$51$	−0.207367	−	0.119724i	−0.0290372	−	0.0167647i
$52$		0			0
$53$	7.48006	+	4.31861i	1.02746	+	0.593207i	0.916257	−	0.400590i	$-0.131195\pi$
$53$	7.48006	+	4.31861i	1.02746	+	0.593207i	0.111208	+	0.993797i	$0.464528\pi$
$54$		0			0
$55$	3.15486	+	5.46439i	0.425402	+	0.736818i
$56$		0			0
$57$	9.05367	+	0.847330i	1.19919	+	0.112232i
$58$		0			0
$59$	12.0808	−	6.97487i	1.57279	−	0.908050i	0.576964	−	0.816770i	$-0.304237\pi$
$59$	12.0808	−	6.97487i	1.57279	−	0.908050i	0.995825	−	0.0912807i	$-0.0290960\pi$
$60$		0			0
$61$	10.2645	+	5.92622i	1.31424	+	0.758774i	0.982795	−	0.184702i	$-0.0591319\pi$
$61$	10.2645	+	5.92622i	1.31424	+	0.758774i	0.331441	+	0.943476i	$0.392465\pi$
$62$		0			0
$63$	1.16716	−	2.02159i	0.147049	−	0.254696i
$64$		0			0
$65$	3.84191			0.476530
$66$		0			0
$67$	3.72538	+	2.15085i	0.455128	+	0.262768i	0.709993	−	0.704208i	$-0.248698\pi$
$67$	3.72538	+	2.15085i	0.455128	+	0.262768i	−0.254866	+	0.966977i	$0.582031\pi$
$68$		0			0
$69$			9.20894i			1.10863i
$70$		0			0
$71$	−0.0279764	−	0.0484565i	−0.00332018	−	0.00575072i	0.864361	−	0.502873i	$-0.167724\pi$
$71$	−0.0279764	−	0.0484565i	−0.00332018	−	0.00575072i	−0.867681	+	0.497122i	$0.834390\pi$
$72$		0			0
$73$	−5.91641	−	10.2475i	−0.692464	−	1.19938i	−0.971028	−	0.238965i	$-0.923192\pi$
$73$	−5.91641	−	10.2475i	−0.692464	−	1.19938i	0.278564	−	0.960418i	$-0.410141\pi$
$74$		0			0
$75$			0.523929i			0.0604981i
$76$		0			0
$77$		−	4.75432i		−	0.541805i
$78$		0			0
$79$	7.04401	+	12.2006i	0.792513	+	1.37267i	0.924406	+	0.381409i	$0.124561\pi$
$79$	7.04401	+	12.2006i	0.792513	+	1.37267i	−0.131893	+	0.991264i	$0.542106\pi$
$80$		0			0
$81$	5.61404	+	9.72380i	0.623782	+	1.08042i
$82$		0			0
$83$			1.36295i			0.149603i	0.997198	+	0.0748017i	$0.0238324\pi$
$83$			1.36295i			0.149603i	−0.997198	+	0.0748017i	$0.976168\pi$
$84$		0			0
$85$	−0.227785	−	0.131512i	−0.0247068	−	0.0142645i
$86$		0			0
$87$	−8.88647			−0.952729
$88$		0			0
$89$	7.48611	−	12.9663i	0.793526	−	1.37443i	−0.130245	−	0.991482i	$-0.541576\pi$
$89$	7.48611	−	12.9663i	0.793526	−	1.37443i	0.923771	−	0.382945i	$-0.125090\pi$
$90$		0			0
$91$	−2.50701	−	1.44742i	−0.262806	−	0.151731i
$92$		0			0
$93$	−2.45806	+	1.41916i	−0.254889	+	0.147160i
$94$		0			0
$95$	9.94513	+	0.930761i	1.02035	+	0.0954941i
$96$		0			0
$97$	−0.462808	−	0.801606i	−0.0469910	−	0.0813908i	0.841573	−	0.540143i	$-0.181630\pi$
$97$	−0.462808	−	0.801606i	−0.0469910	−	0.0813908i	−0.888564	+	0.458752i	$0.848297\pi$
$98$		0			0
$99$	−3.22382	−	1.86128i	−0.324007	−	0.187065i
$100$		0			0
$101$	4.65814	+	2.68938i	0.463503	+	0.267603i	0.713516	−	0.700639i	$-0.247102\pi$
$101$	4.65814	+	2.68938i	0.463503	+	0.267603i	−0.250013	+	0.968242i	$0.580435\pi$
$102$		0			0
$103$	4.99242			0.491917			0.245959	−	0.969280i	$-0.420897\pi$
$103$	4.99242			0.491917			0.245959	+	0.969280i	$0.420897\pi$
$104$		0			0
$105$	4.12708	−	7.14832i	0.402762	−	0.697605i
$106$		0			0
$107$		−	7.93812i		−	0.767407i	−0.923456	−	0.383704i	$-0.874648\pi$
$107$		−	7.93812i		−	0.767407i	0.923456	−	0.383704i	$-0.125352\pi$
$108$		0			0
$109$	6.74128	−	3.89208i	0.645697	−	0.372793i	−0.141109	−	0.989994i	$-0.545067\pi$
$109$	6.74128	−	3.89208i	0.645697	−	0.372793i	0.786806	+	0.617201i	$0.211733\pi$
$110$		0			0
$111$	−4.24348	−	7.34992i	−0.402773	−	0.697624i
$112$		0			0
$113$	−6.60777			−0.621607			−0.310803	−	0.950474i	$-0.600598\pi$
$113$	−6.60777			−0.621607			−0.310803	+	0.950474i	$0.600598\pi$
$114$		0			0
$115$			10.1157i			0.943293i
$116$		0			0
$117$	−1.96294	+	1.13331i	−0.181474	+	0.104774i
$118$		0			0
$119$	0.0990930	+	0.171634i	0.00908384	+	0.0157337i
$120$		0			0
$121$	3.41829			0.310754
$122$		0			0
$123$	1.05883	+	0.611317i	0.0954716	+	0.0551206i
$124$		0			0
$125$		−	10.8822i		−	0.973331i
$126$		0			0
$127$	−7.08870	+	12.2780i	−0.629020	+	1.08950i	0.358728	+	0.933442i	$0.383210\pi$
$127$	−7.08870	+	12.2780i	−0.629020	+	1.08950i	−0.987749	+	0.156053i	$0.950123\pi$
$128$		0			0
$129$	−1.55175	+	2.68771i	−0.136624	+	0.236639i
$130$		0			0
$131$	−9.32823	+	5.38565i	−0.815011	+	0.470547i	−0.848693	−	0.528886i	$-0.822610\pi$
$131$	−9.32823	+	5.38565i	−0.815011	+	0.470547i	0.0336821	+	0.999433i	$0.489277\pi$
$132$		0			0
$133$	−6.13895	−	4.35414i	−0.532314	−	0.377552i
$134$		0			0
$135$	3.93923	+	6.82295i	0.339035	+	0.587226i
$136$		0			0
$137$	1.42012	−	2.45973i	0.121329	−	0.210149i	−0.798963	−	0.601380i	$-0.794618\pi$
$137$	1.42012	−	2.45973i	0.121329	−	0.210149i	0.920292	+	0.391232i	$0.127951\pi$
$138$		0			0
$139$	−7.36126	−	4.25003i	−0.624374	−	0.360483i	0.154196	−	0.988040i	$-0.450721\pi$
$139$	−7.36126	−	4.25003i	−0.624374	−	0.360483i	−0.778570	+	0.627558i	$0.784055\pi$
$140$		0			0
$141$			12.5385i			1.05593i
$142$		0			0
$143$	−2.30820	+	3.99792i	−0.193021	+	0.334323i
$144$		0			0
$145$	−9.76146			−0.810645
$146$		0			0
$147$	7.26030	−	4.19174i	0.598820	−	0.345729i
$148$		0			0
$149$	19.1965	−	11.0831i	1.57264	−	0.907964i	0.576796	−	0.816888i	$-0.304303\pi$
$149$	19.1965	−	11.0831i	1.57264	−	0.907964i	0.995844	−	0.0910754i	$-0.0290304\pi$
$150$		0			0
$151$	−0.622274			−0.0506400			−0.0253200	−	0.999679i	$-0.508060\pi$
$151$	−0.622274			−0.0506400			−0.0253200	+	0.999679i	$0.508060\pi$
$152$		0			0
$153$	0.155176			0.0125453
$154$		0			0
$155$	−2.70009	+	1.55890i	−0.216877	+	0.125214i
$156$		0			0
$157$	−18.7694	+	10.8365i	−1.49796	+	0.864848i	−0.999997	−	0.00235058i	$-0.999252\pi$
$157$	−18.7694	+	10.8365i	−1.49796	+	0.864848i	−0.497963	+	0.867198i	$0.665918\pi$
$158$		0			0
$159$	−18.0184			−1.42895
$160$		0			0
$161$	3.81104	−	6.60091i	0.300352	−	0.520225i
$162$		0			0
$163$			5.42805i			0.425158i	0.977144	+	0.212579i	$0.0681862\pi$
$163$			5.42805i			0.425158i	−0.977144	+	0.212579i	$0.931814\pi$
$164$		0			0
$165$	−11.3994	−	6.58146i	−0.887444	−	0.512366i
$166$		0			0
$167$	10.8403	−	18.7760i	0.838850	−	1.45293i	−0.0520065	−	0.998647i	$-0.516562\pi$
$167$	10.8403	−	18.7760i	0.838850	−	1.45293i	0.890857	−	0.454284i	$-0.150105\pi$
$168$		0			0
$169$	−5.09457	−	8.82405i	−0.391890	−	0.678773i
$170$		0			0
$171$	−5.35581	+	2.45811i	−0.409569	+	0.187976i
$172$		0			0
$173$	−6.00578	+	3.46744i	−0.456611	+	0.263625i	−0.710618	−	0.703578i	$-0.751585\pi$
$173$	−6.00578	+	3.46744i	−0.456611	+	0.263625i	0.254007	+	0.967202i	$0.418251\pi$
$174$		0			0
$175$	0.216823	−	0.375549i	0.0163903	−	0.0283888i
$176$		0			0
$177$	−14.5505	+	25.2022i	−1.09368	+	1.89431i
$178$		0			0
$179$		−	12.0175i		−	0.898227i	−0.893475	−	0.449114i	$-0.851740\pi$
$179$		−	12.0175i		−	0.898227i	0.893475	−	0.449114i	$-0.148260\pi$
$180$		0			0
$181$	−12.8795	−	7.43597i	−0.957324	−	0.552711i	−0.0619756	−	0.998078i	$-0.519740\pi$
$181$	−12.8795	−	7.43597i	−0.957324	−	0.552711i	−0.895348	+	0.445366i	$0.853073\pi$
$182$		0			0
$183$	−24.7257			−1.82778
$184$		0			0
$185$	−4.66131	−	8.07362i	−0.342706	−	0.593585i
$186$		0			0
$187$	0.273705	−	0.158024i	0.0200153	−	0.0115558i
$188$		0			0
$189$		−	5.93635i		−	0.431806i
$190$		0			0
$191$	−4.55482			−0.329575			−0.164788	−	0.986329i	$-0.552694\pi$
$191$	−4.55482			−0.329575			−0.164788	+	0.986329i	$0.552694\pi$
$192$		0			0
$193$	12.3127	+	21.3262i	0.886286	+	1.53509i	0.844232	+	0.535978i	$0.180057\pi$
$193$	12.3127	+	21.3262i	0.886286	+	1.53509i	0.0420542	+	0.999115i	$0.486610\pi$
$194$		0			0
$195$	−6.94095	+	4.00736i	−0.497052	+	0.286973i
$196$		0			0
$197$		−	0.170380i		−	0.0121391i	−0.999982	−	0.00606953i	$-0.998068\pi$
$197$		−	0.170380i		−	0.0121391i	0.999982	−	0.00606953i	$-0.00193200\pi$
$198$		0			0
$199$	8.35142	−	14.4651i	0.592017	−	1.02540i	−0.401944	−	0.915664i	$-0.631665\pi$
$199$	8.35142	−	14.4651i	0.592017	−	1.02540i	0.993960	−	0.109739i	$-0.0350014\pi$
$200$		0			0
$201$	−8.97391			−0.632971
$202$		0			0
$203$	6.36976	+	3.67758i	0.447070	+	0.258116i
$204$		0			0
$205$	1.16309	+	0.671509i	0.0812336	+	0.0469002i
$206$		0			0
$207$	−2.98398	−	5.16840i	−0.207401	−	0.359229i
$208$		0			0
$209$	−6.94354	+	9.78978i	−0.480295	+	0.677173i
$210$		0			0
$211$	12.6866	−	7.32460i	0.873380	−	0.504246i	0.00491007	−	0.999988i	$-0.498437\pi$
$211$	12.6866	−	7.32460i	0.873380	−	0.504246i	0.868470	+	0.495742i	$0.165104\pi$
$212$		0			0
$213$	0.101086	+	0.0583623i	0.00692633	+	0.00399892i
$214$		0			0
$215$	−1.70454	+	2.95235i	−0.116249	+	0.201349i
$216$		0			0
$217$	2.34923			0.159476
$218$		0			0
$219$	21.3777	+	12.3424i	1.44457	+	0.834023i
$220$		0			0
$221$		−	0.192437i		−	0.0129447i
$222$		0			0
$223$	−7.11122	−	12.3170i	−0.476203	−	0.824807i	0.523426	−	0.852071i	$-0.324654\pi$
$223$	−7.11122	−	12.3170i	−0.476203	−	0.824807i	−0.999628	+	0.0272643i	$0.991320\pi$
$224$		0			0
$225$	−0.169769	−	0.294048i	−0.0113179	−	0.0196032i
$226$		0			0
$227$			7.11325i			0.472123i	0.971738	+	0.236062i	$0.0758567\pi$
$227$			7.11325i			0.472123i	−0.971738	+	0.236062i	$0.924143\pi$
$228$		0			0
$229$		−	26.7173i		−	1.76553i	−0.469815	−	0.882765i	$-0.655679\pi$
$229$		−	26.7173i		−	1.76553i	0.469815	−	0.882765i	$-0.344321\pi$
$230$		0			0
$231$	4.95906	+	8.58935i	0.326282	+	0.565138i
$232$		0			0
$233$	8.14440	+	14.1065i	0.533558	+	0.924149i	0.999232	+	0.0391927i	$0.0124786\pi$
$233$	8.14440	+	14.1065i	0.533558	+	0.924149i	−0.465674	+	0.884956i	$0.654188\pi$
$234$		0			0
$235$			13.7731i			0.898455i
$236$		0			0
$237$	−25.4520	−	14.6947i	−1.65329	−	0.954525i
$238$		0			0
$239$	7.17158			0.463891			0.231946	−	0.972729i	$-0.425491\pi$
$239$	7.17158			0.463891			0.231946	+	0.972729i	$0.425491\pi$
$240$		0			0
$241$	−13.5251	+	23.4262i	−0.871230	+	1.50901i	−0.0105051	+	0.999945i	$0.503344\pi$
$241$	−13.5251	+	23.4262i	−0.871230	+	1.50901i	−0.860725	+	0.509070i	$0.829989\pi$
$242$		0			0
$243$	−11.3527	−	6.55451i	−0.728279	−	0.420472i
$244$		0			0
$245$	7.97518	−	4.60447i	0.509516	−	0.294169i
$246$		0			0
$247$	3.04834	+	6.64184i	0.193962	+	0.422610i
$248$		0			0
$249$	−1.42165	−	2.46237i	−0.0900933	−	0.156046i
$250$		0			0
$251$	−12.6195	−	7.28585i	−0.796534	−	0.459879i	0.0457241	−	0.998954i	$-0.485440\pi$
$251$	−12.6195	−	7.28585i	−0.796534	−	0.459879i	−0.842258	+	0.539075i	$0.818774\pi$
$252$		0			0
$253$	−10.5265	−	6.07746i	−0.661793	−	0.382087i
$254$		0			0
$255$	0.548702			0.0343611
$256$		0			0
$257$	2.78684	−	4.82695i	0.173838	−	0.301097i	−0.765920	−	0.642935i	$-0.777716\pi$
$257$	2.78684	−	4.82695i	0.173838	−	0.301097i	0.939759	+	0.341839i	$0.111050\pi$
$258$		0			0
$259$			7.02450i			0.436481i
$260$		0			0
$261$	4.98742	−	2.87949i	0.308713	−	0.178236i
$262$		0			0
$263$	−11.9584	−	20.7126i	−0.737388	−	1.27719i	−0.953668	−	0.300862i	$-0.902726\pi$
$263$	−11.9584	−	20.7126i	−0.737388	−	1.27719i	0.216280	−	0.976331i	$-0.430608\pi$
$264$		0			0
$265$	−19.7925			−1.21585
$266$		0			0
$267$			31.2340i			1.91149i
$268$		0			0
$269$	24.7898	−	14.3124i	1.51146	−	0.872643i	0.511552	−	0.859252i	$-0.329071\pi$
$269$	24.7898	−	14.3124i	1.51146	−	0.872643i	0.999910	−	0.0133906i	$-0.00426250\pi$
$270$		0			0
$271$	5.03561	+	8.72194i	0.305892	+	0.529820i	0.977459	−	0.211123i	$-0.0677121\pi$
$271$	5.03561	+	8.72194i	0.305892	+	0.529820i	−0.671568	+	0.740943i	$0.734379\pi$
$272$		0			0
$273$	6.03902			0.365498
$274$		0			0
$275$	−0.598888	−	0.345768i	−0.0361143	−	0.0208506i
$276$		0			0
$277$		−	22.3860i		−	1.34504i	−0.740077	−	0.672522i	$-0.765211\pi$
$277$		−	22.3860i		−	1.34504i	0.740077	−	0.672522i	$-0.234789\pi$
$278$		0			0
$279$	0.919705	−	1.59298i	0.0550613	−	0.0953689i
$280$		0			0
$281$	4.78468	−	8.28732i	0.285430	−	0.494380i	−0.687283	−	0.726390i	$-0.741197\pi$
$281$	4.78468	−	8.28732i	0.285430	−	0.494380i	0.972713	+	0.232010i	$0.0745301\pi$
$282$		0			0
$283$	−0.384719	+	0.222118i	−0.0228692	+	0.0132035i	−0.511391	−	0.859348i	$-0.670870\pi$
$283$	−0.384719	+	0.222118i	−0.0228692	+	0.0132035i	0.488522	+	0.872552i	$0.337536\pi$
$284$		0			0
$285$	−18.9381	+	8.69186i	−1.12180	+	0.514861i
$286$		0			0
$287$	−0.505976	−	0.876376i	−0.0298668	−	0.0517308i
$288$		0			0
$289$	8.49341	−	14.7110i	0.499613	−	0.865354i
$290$		0			0
$291$	1.67226	+	0.965477i	0.0980293	+	0.0565973i
$292$		0			0
$293$			16.9075i			0.987748i	0.869534	+	0.493874i	$0.164420\pi$
$293$			16.9075i			0.987748i	−0.869534	+	0.493874i	$0.835580\pi$
$294$		0			0
$295$	−15.9832	+	27.6837i	−0.930576	+	1.61181i
$296$		0			0
$297$	−9.46669			−0.549313
$298$		0			0
$299$	−6.40942	+	3.70048i	−0.370667	+	0.214004i
$300$		0			0
$301$	2.22457	−	1.28435i	0.128222	−	0.0740289i
$302$		0			0
$303$	−11.2208			−0.644618
$304$		0			0
$305$	−27.1603			−1.55519
$306$		0			0
$307$	27.9473	−	16.1354i	1.59504	−	0.920895i	0.602613	−	0.798034i	$-0.294126\pi$
$307$	27.9473	−	16.1354i	1.59504	−	0.920895i	0.992424	−	0.122861i	$-0.0392070\pi$
$308$		0			0
$309$	−9.01951	+	5.20742i	−0.513102	+	0.296239i
$310$		0			0
$311$	−31.6176			−1.79287			−0.896436	−	0.443174i	$-0.853852\pi$
$311$	−31.6176			−1.79287			−0.896436	+	0.443174i	$0.853852\pi$
$312$		0			0
$313$	11.5063	−	19.9295i	0.650374	−	1.12648i	−0.332658	−	0.943048i	$-0.607945\pi$
$313$	11.5063	−	19.9295i	0.650374	−	1.12648i	0.983032	−	0.183433i	$-0.0587212\pi$
$314$		0			0
$315$			5.34920i			0.301393i
$316$		0			0
$317$	3.38678	+	1.95536i	0.190220	+	0.109824i	0.592086	−	0.805875i	$-0.298305\pi$
$317$	3.38678	+	1.95536i	0.190220	+	0.109824i	−0.401865	+	0.915699i	$0.631638\pi$
$318$		0			0
$319$	5.86464	−	10.1579i	0.328357	−	0.568731i
$320$		0			0
$321$	8.27998	+	14.3413i	0.462143	+	0.800456i
$322$		0			0
$323$	0.0466208	−	0.498140i	0.00259405	−	0.0277172i
$324$		0			0
$325$	−0.364655	+	0.210533i	−0.0202274	+	0.0116783i
$326$		0			0
$327$	−8.11938	+	14.0632i	−0.449003	+	0.777696i
$328$		0			0
$329$	5.18893	−	8.98750i	0.286075	−	0.495497i
$330$		0			0
$331$			0.495996i			0.0272624i	0.999907	+	0.0136312i	$0.00433908\pi$
$331$			0.495996i			0.0272624i	−0.999907	+	0.0136312i	$0.995661\pi$
$332$		0			0
$333$	4.76320	+	2.75003i	0.261022	+	0.150701i
$334$		0			0
$335$	−9.85751			−0.538574
$336$		0			0
$337$	−3.03198	−	5.25154i	−0.165162	−	0.286070i	0.771550	−	0.636168i	$-0.219482\pi$
$337$	−3.03198	−	5.25154i	−0.165162	−	0.286070i	−0.936713	+	0.350098i	$0.886148\pi$
$338$		0			0
$339$	11.9379	−	6.89234i	0.648376	−	0.374340i
$340$		0			0
$341$		−	3.74632i		−	0.202875i
$342$		0			0
$343$	−19.0254			−1.02728
$344$		0			0
$345$	−10.5513	−	18.2754i	−0.568064	−	0.983916i
$346$		0			0
$347$	−17.4753	+	10.0894i	−0.938124	+	0.541626i	−0.889372	−	0.457185i	$-0.848858\pi$
$347$	−17.4753	+	10.0894i	−0.938124	+	0.541626i	−0.0487522	+	0.998811i	$0.515524\pi$
$348$		0			0
$349$		−	10.6014i		−	0.567478i	−0.958902	−	0.283739i	$-0.908425\pi$
$349$		−	10.6014i		−	0.567478i	0.958902	−	0.283739i	$-0.0915749\pi$
$350$		0			0
$351$	−2.88207	+	4.99189i	−0.153834	+	0.266447i
$352$		0			0
$353$	−1.29301			−0.0688197			−0.0344099	−	0.999408i	$-0.510955\pi$
$353$	−1.29301			−0.0688197			−0.0344099	+	0.999408i	$0.510955\pi$
$354$		0			0
$355$	0.111040	+	0.0641089i	0.00589338	+	0.00340255i
$356$		0			0
$357$	−0.358051	−	0.206721i	−0.0189501	−	0.0109408i
$358$		0			0
$359$	11.2574	+	19.4984i	0.594143	+	1.02909i	0.993667	+	0.112363i	$0.0358418\pi$
$359$	11.2574	+	19.4984i	0.594143	+	1.02909i	−0.399525	+	0.916722i	$0.630825\pi$
$360$		0			0
$361$	6.28183	+	17.9315i	0.330622	+	0.943763i
$362$		0			0
$363$	−6.17563	+	3.56550i	−0.324136	+	0.187140i
$364$		0			0
$365$	23.4826	+	13.5577i	1.22914	+	0.709642i
$366$		0			0
$367$	−6.24160	+	10.8108i	−0.325809	+	0.564318i	−0.981676	−	0.190559i	$-0.938970\pi$
$367$	−6.24160	+	10.8108i	−0.325809	+	0.564318i	0.655867	+	0.754877i	$0.272303\pi$
$368$		0			0
$369$	−0.792341			−0.0412476
$370$		0			0
$371$	12.9155	+	7.45674i	0.670537	+	0.387135i
$372$		0			0
$373$			20.6854i			1.07105i	0.844520	+	0.535524i	$0.179886\pi$
$373$			20.6854i			1.07105i	−0.844520	+	0.535524i	$0.820114\pi$
$374$		0			0
$375$	11.3508	+	19.6602i	0.586154	+	1.01525i
$376$		0			0
$377$	−3.57090	−	6.18498i	−0.183911	−	0.318543i
$378$		0			0
$379$		−	19.1303i		−	0.982658i	−0.870974	−	0.491329i	$-0.836511\pi$
$379$		−	19.1303i		−	0.982658i	0.870974	−	0.491329i	$-0.163489\pi$
$380$		0			0
$381$		−	29.5759i		−	1.51522i
$382$		0			0
$383$	7.52196	+	13.0284i	0.384354	+	0.665721i	0.991679	−	0.128733i	$-0.0410909\pi$
$383$	7.52196	+	13.0284i	0.384354	+	0.665721i	−0.607325	+	0.794453i	$0.707758\pi$
$384$		0			0
$385$	5.44735	+	9.43509i	0.277623	+	0.480857i
$386$		0			0
$387$		−	2.01125i		−	0.102238i
$388$		0			0
$389$	23.7662	+	13.7214i	1.20499	+	0.695704i	0.961662	−	0.274239i	$-0.0884258\pi$
$389$	23.7662	+	13.7214i	1.20499	+	0.695704i	0.243333	+	0.969943i	$0.421759\pi$
$390$		0			0
$391$	0.506683			0.0256241
$392$		0			0
$393$	11.2352	−	19.4599i	0.566740	−	0.981622i
$394$		0			0
$395$	−27.9581	−	16.1416i	−1.40672	−	0.812173i
$396$		0			0
$397$	−1.45672	+	0.841040i	−0.0731109	+	0.0422106i	−0.536110	−	0.844148i	$-0.680107\pi$
$397$	−1.45672	+	0.841040i	−0.0731109	+	0.0422106i	0.462999	+	0.886359i	$0.346773\pi$
$398$		0			0
$399$	15.6325	+	1.46304i	0.782605	+	0.0732438i
$400$		0			0
$401$	−11.8622	−	20.5459i	−0.592370	−	1.02602i	−0.993912	−	0.110175i	$-0.964859\pi$
$401$	−11.8622	−	20.5459i	−0.592370	−	1.02602i	0.401542	−	0.915841i	$-0.368474\pi$
$402$		0			0
$403$	−1.97548	−	1.14054i	−0.0984055	−	0.0568144i
$404$		0			0
$405$	−22.2825	−	12.8648i	−1.10722	−	0.639256i
$406$		0			0
$407$	11.2020			0.555261
$408$		0			0
$409$	−2.44741	+	4.23903i	−0.121016	+	0.209607i	−0.920169	−	0.391522i	$-0.871949\pi$
$409$	−2.44741	+	4.23903i	−0.121016	+	0.209607i	0.799152	+	0.601129i	$0.205282\pi$
$410$		0			0
$411$			5.92512i			0.292265i
$412$		0			0
$413$	20.8594	−	12.0432i	1.02642	−	0.592605i
$414$		0			0
$415$	−1.56163	−	2.70482i	−0.0766574	−	0.132774i
$416$		0			0
$417$	17.7322			0.868350
$418$		0			0
$419$			13.8392i			0.676088i	0.941130	+	0.338044i	$0.109765\pi$
$419$			13.8392i			0.676088i	−0.941130	+	0.338044i	$0.890235\pi$
$420$		0			0
$421$	11.0032	−	6.35272i	0.536265	−	0.309613i	−0.207299	−	0.978278i	$-0.566467\pi$
$421$	11.0032	−	6.35272i	0.536265	−	0.309613i	0.743564	+	0.668665i	$0.233134\pi$
$422$		0			0
$423$	−4.06285	−	7.03706i	−0.197542	−	0.342153i
$424$		0			0
$425$	0.0288270			0.00139831
$426$		0			0
$427$	17.7232	+	10.2325i	0.857687	+	0.495186i
$428$		0			0
$429$		−	9.63041i		−	0.464961i
$430$		0			0
$431$	9.66652	−	16.7429i	0.465620	−	0.806478i	−0.533609	−	0.845731i	$-0.679165\pi$
$431$	9.66652	−	16.7429i	0.465620	−	0.806478i	0.999229	+	0.0392535i	$0.0124980\pi$
$432$		0			0
$433$	−9.31161	+	16.1282i	−0.447487	+	0.775071i	−0.998222	−	0.0596098i	$-0.981014\pi$
$433$	−9.31161	+	16.1282i	−0.447487	+	0.775071i	0.550734	+	0.834681i	$0.314348\pi$
$434$		0			0
$435$	17.6355	−	10.1818i	0.845556	−	0.488182i
$436$		0			0
$437$	−17.4879	+	8.02625i	−0.836558	+	0.383948i
$438$		0			0
$439$	13.4326	+	23.2660i	0.641105	+	1.11043i	0.985186	+	0.171487i	$0.0548571\pi$
$439$	13.4326	+	23.2660i	0.641105	+	1.11043i	−0.344081	+	0.938940i	$0.611810\pi$
$440$		0			0
$441$	−2.71650	+	4.70512i	−0.129357	+	0.224053i
$442$		0			0
$443$	−10.4454	−	6.03065i	−0.496275	−	0.286525i	0.230899	−	0.972978i	$-0.425833\pi$
$443$	−10.4454	−	6.03065i	−0.496275	−	0.286525i	−0.727174	+	0.686453i	$0.759167\pi$
$444$		0			0
$445$			34.3094i			1.62642i
$446$		0			0
$447$	−23.1208	+	40.0464i	−1.09358	+	1.89413i
$448$		0			0
$449$	4.81822			0.227386			0.113693	−	0.993516i	$-0.463732\pi$
$449$	4.81822			0.227386			0.113693	+	0.993516i	$0.463732\pi$
$450$		0			0
$451$	−1.39756	+	0.806879i	−0.0658083	+	0.0379944i
$452$		0			0
$453$	1.12423	−	0.649073i	0.0528208	−	0.0304961i
$454$		0			0
$455$	6.63364			0.310990
$456$		0			0
$457$	8.37673			0.391847			0.195923	−	0.980619i	$-0.437230\pi$
$457$	8.37673			0.391847			0.195923	+	0.980619i	$0.437230\pi$
$458$		0			0
$459$	0.341754	−	0.197312i	0.0159517	−	0.00920972i
$460$		0			0
$461$	−16.5657	+	9.56420i	−0.771541	+	0.445449i	−0.833424	−	0.552634i	$-0.813623\pi$
$461$	−16.5657	+	9.56420i	−0.771541	+	0.445449i	0.0618832	+	0.998083i	$0.480289\pi$
$462$		0			0
$463$	−28.6639			−1.33212			−0.666062	−	0.745896i	$-0.732021\pi$
$463$	−28.6639			−1.33212			−0.666062	+	0.745896i	$0.732021\pi$
$464$		0			0
$465$	3.25207	−	5.63275i	0.150811	−	0.261213i
$466$		0			0
$467$		−	26.6155i		−	1.23162i	−0.787895	−	0.615810i	$-0.788829\pi$
$467$		−	26.6155i		−	1.23162i	0.787895	−	0.615810i	$-0.211171\pi$
$468$		0			0
$469$	6.43244	+	3.71377i	0.297022	+	0.171486i
$470$		0			0
$471$	22.6064	−	39.1554i	1.04165	−	1.80418i
$472$		0			0
$473$	−2.04816	−	3.54751i	−0.0941744	−	0.163115i
$474$		0			0
$475$	−0.994946	+	0.456641i	−0.0456513	+	0.0209521i
$476$		0			0
$477$	10.1126	−	5.83850i	0.463023	−	0.267327i
$478$		0			0
$479$	17.0776	−	29.5792i	0.780294	−	1.35151i	−0.151477	−	0.988461i	$-0.548403\pi$
$479$	17.0776	−	29.5792i	0.780294	−	1.35151i	0.931770	−	0.363048i	$-0.118264\pi$
$480$		0			0
$481$	3.41036	−	5.90692i	0.155499	−	0.269333i
$482$		0			0
$483$			15.9006i			0.723504i
$484$		0			0
$485$	1.83691	+	1.06054i	0.0834099	+	0.0481567i
$486$		0			0
$487$	−9.73523			−0.441146			−0.220573	−	0.975371i	$-0.570793\pi$
$487$	−9.73523			−0.441146			−0.220573	+	0.975371i	$0.570793\pi$
$488$		0			0
$489$	−5.66181	−	9.80654i	−0.256036	−	0.443467i
$490$		0			0
$491$	−13.4614	+	7.77195i	−0.607505	+	0.350743i	−0.771988	−	0.635637i	$-0.780738\pi$
$491$	−13.4614	+	7.77195i	−0.607505	+	0.350743i	0.164483	+	0.986380i	$0.447404\pi$
$492$		0			0
$493$			0.488941i			0.0220208i
$494$		0			0
$495$	8.53037			0.383412
$496$		0			0
$497$	−0.0483054	−	0.0836675i	−0.00216679	−	0.00375300i
$498$		0			0
$499$	27.4467	−	15.8464i	1.22868	−	0.709381i	0.261929	−	0.965087i	$-0.415641\pi$
$499$	27.4467	−	15.8464i	1.22868	−	0.709381i	0.966754	+	0.255707i	$0.0823081\pi$
$500$		0			0
$501$			45.2287i			2.02067i
$502$		0			0
$503$	19.9459	−	34.5473i	0.889343	−	1.54039i	0.0486889	−	0.998814i	$-0.484496\pi$
$503$	19.9459	−	34.5473i	0.889343	−	1.54039i	0.840654	−	0.541573i	$-0.182171\pi$
$504$		0			0
$505$	−12.3256			−0.548484
$506$		0			0
$507$	18.4081	+	10.6279i	0.817533	+	0.472003i
$508$		0			0
$509$	14.1562	+	8.17306i	0.627461	+	0.362265i	0.779768	−	0.626069i	$-0.215337\pi$
$509$	14.1562	+	8.17306i	0.627461	+	0.362265i	−0.152307	+	0.988333i	$0.548670\pi$
$510$		0			0
$511$	−10.2156	−	17.6939i	−0.451911	−	0.782733i
$512$		0			0
$513$	−8.66986	+	12.2237i	−0.382784	+	0.539691i
$514$		0			0
$515$	−9.90760	+	5.72016i	−0.436581	+	0.252060i
$516$		0			0
$517$	−14.3324	−	8.27479i	−0.630336	−	0.363925i
$518$		0			0
$519$	7.23353	−	12.5288i	0.317517	−	0.549955i
$520$		0			0
$521$	25.9028			1.13482			0.567411	−	0.823434i	$-0.307945\pi$
$521$	25.9028			1.13482			0.567411	+	0.823434i	$0.307945\pi$
$522$		0			0
$523$	3.63933	+	2.10117i	0.159137	+	0.0918776i	0.577453	−	0.816424i	$-0.304046\pi$
$523$	3.63933	+	2.10117i	0.159137	+	0.0918776i	−0.418317	+	0.908301i	$0.637380\pi$
$524$		0			0
$525$			0.904643i			0.0394819i
$526$		0			0
$527$	0.0780835	+	0.135245i	0.00340137	+	0.00589135i
$528$		0			0
$529$	1.75668	+	3.04266i	0.0763775	+	0.132290i
$530$		0			0
$531$		−	18.8592i		−	0.818419i
$532$		0			0
$533$			0.982596i			0.0425609i
$534$		0			0
$535$	9.09526	+	15.7534i	0.393222	+	0.681081i
$536$		0			0
$537$	12.5350	+	21.7112i	0.540925	+	0.936909i
$538$		0			0
$539$			11.0654i			0.476620i
$540$		0			0
$541$	7.51752	+	4.34024i	0.323203	+	0.186602i	0.652820	−	0.757513i	$-0.273586\pi$
$541$	7.51752	+	4.34024i	0.323203	+	0.186602i	−0.329616	+	0.944115i	$0.606919\pi$
$542$		0			0
$543$	31.0248			1.33140
$544$		0			0
$545$	−8.91885	+	15.4479i	−0.382041	+	0.661715i
$546$		0			0
$547$	−5.23717	−	3.02368i	−0.223925	−	0.129283i	0.383841	−	0.923399i	$-0.374601\pi$
$547$	−5.23717	−	3.02368i	−0.223925	−	0.129283i	−0.607767	+	0.794116i	$0.707934\pi$
$548$		0			0
$549$	13.8770	−	8.01189i	0.592256	−	0.341939i
$550$		0			0
$551$	−7.74519	−	16.8755i	−0.329956	−	0.718920i
$552$		0			0
$553$	12.1626	+	21.0662i	0.517204	+	0.895824i
$554$		0			0
$555$	16.8426	+	9.72410i	0.714930	+	0.412765i
$556$		0			0
$557$	−11.5458	−	6.66599i	−0.489212	−	0.282447i	0.235035	−	0.971987i	$-0.424479\pi$
$557$	−11.5458	−	6.66599i	−0.489212	−	0.282447i	−0.724248	+	0.689540i	$0.757813\pi$
$558$		0			0
$559$	−2.49419			−0.105493
$560$		0			0
$561$	−0.329658	+	0.570984i	−0.0139182	+	0.0241070i
$562$		0			0
$563$			23.3883i			0.985701i	0.870114	+	0.492850i	$0.164045\pi$
$563$			23.3883i			0.985701i	−0.870114	+	0.492850i	$0.835955\pi$
$564$		0			0
$565$	13.1133	−	7.57098i	0.551682	−	0.318514i
$566$		0			0
$567$	9.69349	+	16.7896i	0.407088	+	0.705098i
$568$		0			0
$569$	0.626034			0.0262447			0.0131224	−	0.999914i	$-0.495823\pi$
$569$	0.626034			0.0262447			0.0131224	+	0.999914i	$0.495823\pi$
$570$		0			0
$571$		−	25.4590i		−	1.06542i	−0.846296	−	0.532712i	$-0.821173\pi$
$571$		−	25.4590i		−	1.06542i	0.846296	−	0.532712i	$-0.178827\pi$
$572$		0			0
$573$	8.22892	−	4.75097i	0.343768	−	0.198475i
$574$		0			0
$575$	−0.554332	−	0.960130i	−0.0231172	−	0.0400402i
$576$		0			0
$577$	23.0720			0.960500			0.480250	−	0.877132i	$-0.340546\pi$
$577$	23.0720			0.960500			0.480250	+	0.877132i	$0.340546\pi$
$578$		0			0
$579$	−44.4892	−	25.6859i	−1.84891	−	1.06747i
$580$		0			0
$581$			2.35334i			0.0976332i
$582$		0			0
$583$	11.8913	−	20.5963i	0.492486	−	0.853010i
$584$		0			0
$585$	2.59701	−	4.49816i	0.107373	−	0.185976i
$586$		0			0
$587$	−6.63487	+	3.83064i	−0.273850	+	0.158108i	−0.630636	−	0.776079i	$-0.717206\pi$
$587$	−6.63487	+	3.83064i	−0.273850	+	0.158108i	0.356786	+	0.934186i	$0.383873\pi$
$588$		0			0
$589$	−4.83738	−	3.43098i	−0.199321	−	0.141371i
$590$		0			0
$591$	0.177717	+	0.307815i	0.00731031	+	0.0126618i
$592$		0			0
$593$	21.2842	−	36.8653i	0.874037	−	1.51388i	0.0162526	−	0.999868i	$-0.494826\pi$
$593$	21.2842	−	36.8653i	0.874037	−	1.51388i	0.857785	−	0.514009i	$-0.171840\pi$
$594$		0			0
$595$	−0.393306	−	0.227075i	−0.0161240	−	0.00930919i
$596$		0			0
$597$			34.8443i			1.42608i
$598$		0			0
$599$	17.5983	−	30.4812i	0.719049	−	1.24543i	−0.242329	−	0.970194i	$-0.577911\pi$
$599$	17.5983	−	30.4812i	0.719049	−	1.24543i	0.961377	−	0.275234i	$-0.0887555\pi$
$600$		0			0
$601$	34.6748			1.41442			0.707208	−	0.707005i	$-0.249954\pi$
$601$	34.6748			1.41442			0.707208	+	0.707005i	$0.249954\pi$
$602$		0			0
$603$	5.03649	−	2.90782i	0.205102	−	0.118416i
$604$		0			0
$605$	−6.78370	+	3.91657i	−0.275797	+	0.159231i
$606$		0			0
$607$	32.9098			1.33577			0.667883	−	0.744266i	$-0.267201\pi$
$607$	32.9098			1.33577			0.667883	+	0.744266i	$0.267201\pi$
$608$		0			0
$609$	−15.3438			−0.621764
$610$		0			0
$611$	−8.72678	+	5.03841i	−0.353048	+	0.203832i
$612$		0			0
$613$	−41.0920	+	23.7245i	−1.65969	+	0.958223i	−0.686833	+	0.726815i	$0.741000\pi$
$613$	−41.0920	+	23.7245i	−1.65969	+	0.958223i	−0.972857	+	0.231407i	$0.925667\pi$
$614$		0			0
$615$	−2.80171			−0.112976
$616$		0			0
$617$	−21.9776	+	38.0664i	−0.884786	+	1.53249i	−0.0388272	+	0.999246i	$0.512362\pi$
$617$	−21.9776	+	38.0664i	−0.884786	+	1.53249i	−0.845959	+	0.533248i	$0.820971\pi$
$618$		0			0
$619$		−	14.4299i		−	0.579986i	−0.957029	−	0.289993i	$-0.906347\pi$
$619$		−	14.4299i		−	0.579986i	0.957029	−	0.289993i	$-0.0936530\pi$
$620$		0			0
$621$	−13.1436	−	7.58845i	−0.527434	−	0.304514i
$622$		0			0
$623$	12.9259	−	22.3883i	0.517865	−	0.896969i
$624$		0			0
$625$	13.0963	+	22.6835i	0.523853	+	0.907341i
$626$		0			0
$627$	2.33311	−	24.9292i	0.0931756	−	0.995576i
$628$		0			0
$629$	−0.404399	+	0.233480i	−0.0161244	+	0.00930944i
$630$		0			0
$631$	−11.9535	+	20.7041i	−0.475862	+	0.824217i	−0.999618	−	0.0276512i	$-0.991197\pi$
$631$	−11.9535	+	20.7041i	−0.475862	+	0.824217i	0.523755	+	0.851869i	$0.324531\pi$
$632$		0			0
$633$	−15.2801	+	26.4659i	−0.607328	+	1.05192i
$634$		0			0
$635$		−	32.4881i		−	1.28925i
$636$		0			0
$637$	5.83490	+	3.36878i	0.231187	+	0.133476i
$638$		0			0
$639$	−0.0756447			−0.00299246
$640$		0			0
$641$	−10.9605	−	18.9841i	−0.432913	−	0.749828i	0.564210	−	0.825632i	$-0.309181\pi$
$641$	−10.9605	−	18.9841i	−0.432913	−	0.749828i	−0.997123	+	0.0758040i	$0.975848\pi$
$642$		0			0
$643$	−38.7175	+	22.3535i	−1.52687	+	0.881538i	−0.527378	+	0.849631i	$0.676825\pi$
$643$	−38.7175	+	22.3535i	−1.52687	+	0.881538i	−0.999491	+	0.0319070i	$0.989842\pi$
$644$		0			0
$645$		−	7.11178i		−	0.280026i
$646$		0			0
$647$	−27.0393			−1.06302			−0.531512	−	0.847051i	$-0.678376\pi$
$647$	−27.0393			−1.06302			−0.531512	+	0.847051i	$0.678376\pi$
$648$		0			0
$649$	−19.2052	−	33.2644i	−0.753871	−	1.30574i
$650$		0			0
$651$	−4.24422	+	2.45040i	−0.166344	+	0.0960389i
$652$		0			0
$653$			43.0102i			1.68312i	0.540166	+	0.841559i	$0.318362\pi$
$653$			43.0102i			1.68312i	−0.540166	+	0.841559i	$0.681638\pi$
$654$		0			0
$655$	12.3414	−	21.3760i	0.482220	−	0.835229i
$656$		0			0
$657$	−15.9973			−0.624113
$658$		0			0
$659$	−16.9791	−	9.80289i	−0.661412	−	0.381866i	0.131403	−	0.991329i	$-0.458052\pi$
$659$	−16.9791	−	9.80289i	−0.661412	−	0.381866i	−0.792815	+	0.609463i	$0.791385\pi$
$660$		0			0
$661$	−27.8225	−	16.0633i	−1.08217	−	0.624791i	−0.150689	−	0.988581i	$-0.548149\pi$
$661$	−27.8225	−	16.0633i	−1.08217	−	0.624791i	−0.931481	+	0.363790i	$0.881483\pi$
$662$		0			0
$663$	0.200724	+	0.347664i	0.00779548	+	0.0135022i
$664$		0			0
$665$	17.1718	+	1.60710i	0.665893	+	0.0623207i
$666$		0			0
$667$	16.2850	−	9.40213i	0.630556	−	0.364052i
$668$		0			0
$669$	25.6949	+	14.8349i	0.993420	+	0.573552i
$670$		0			0
$671$	16.3178	−	28.2632i	0.629941	−	1.09109i
$672$		0			0
$673$	32.8077			1.26464			0.632321	−	0.774706i	$-0.282102\pi$
$673$	32.8077			1.26464			0.632321	+	0.774706i	$0.282102\pi$
$674$		0			0
$675$	−0.747784	−	0.431734i	−0.0287822	−	0.0166174i
$676$		0			0
$677$			14.2719i			0.548513i	0.961657	+	0.274256i	$0.0884317\pi$
$677$			14.2719i			0.548513i	−0.961657	+	0.274256i	$0.911568\pi$
$678$		0			0
$679$	−0.799108	−	1.38410i	−0.0306669	−	0.0531167i
$680$		0			0
$681$	−7.41959	−	12.8511i	−0.284319	−	0.492455i
$682$		0			0
$683$		−	19.4957i		−	0.745981i	−0.927835	−	0.372990i	$-0.878332\pi$
$683$		−	19.4957i		−	0.745981i	0.927835	−	0.372990i	$-0.121668\pi$
$684$		0			0
$685$			6.50853i			0.248678i
$686$		0			0
$687$	27.8679	+	48.2686i	1.06323	+	1.84156i
$688$		0			0
$689$	−7.24043	−	12.5408i	−0.275838	−	0.477766i
$690$		0			0
$691$			44.3432i			1.68690i	0.537211	+	0.843448i	$0.319478\pi$
$691$			44.3432i			1.68690i	−0.537211	+	0.843448i	$0.680522\pi$
$692$		0			0
$693$	−5.56642	−	3.21378i	−0.211451	−	0.122081i
$694$		0			0
$695$	19.4782			0.738850
$696$		0			0
$697$	0.0336351	−	0.0582578i	0.00127402	−	0.00220667i
$698$		0			0
$699$	−29.4280	−	16.9903i	−1.11307	−	0.642632i
$700$		0			0
$701$	−9.06906	+	5.23602i	−0.342534	+	0.197762i	−0.661392	−	0.750041i	$-0.730034\pi$
$701$	−9.06906	+	5.23602i	−0.342534	+	0.197762i	0.318858	+	0.947802i	$0.396701\pi$
$702$		0			0
$703$	10.2591	−	14.4644i	0.386928	−	0.545535i
$704$		0			0
$705$	−14.3662	−	24.8830i	−0.541062	−	0.937147i
$706$		0			0
$707$	8.04299	+	4.64362i	0.302488	+	0.174641i
$708$		0			0
$709$	−3.00363	−	1.73415i	−0.112804	−	0.0651273i	0.442537	−	0.896750i	$-0.354079\pi$
$709$	−3.00363	−	1.73415i	−0.112804	−	0.0651273i	−0.555340	+	0.831623i	$0.687412\pi$
$710$		0			0
$711$	19.0461			0.714286
$712$		0			0
$713$	3.00303	−	5.20140i	0.112464	−	0.194794i
$714$		0			0
$715$		−	10.5787i		−	0.395619i
$716$		0			0
$717$	−12.9565	+	7.48043i	−0.483869	+	0.279362i
$718$		0			0
$719$	−0.352088	−	0.609834i	−0.0131307	−	0.0227430i	0.859385	−	0.511328i	$-0.170846\pi$
$719$	−0.352088	−	0.609834i	−0.0131307	−	0.0227430i	−0.872516	+	0.488585i	$0.837513\pi$
$720$		0			0
$721$	8.62017			0.321032
$722$		0			0
$723$		−	56.4304i		−	2.09867i
$724$		0			0
$725$	0.926509	−	0.534920i	0.0344097	−	0.0198664i
$726$		0			0
$727$	−15.0322	−	26.0365i	−0.557512	−	0.965640i	−0.997703	−	0.0677354i	$-0.978423\pi$
$727$	−15.0322	−	26.0365i	−0.557512	−	0.965640i	0.440191	−	0.897904i	$-0.354911\pi$
$728$		0			0
$729$	−6.33710			−0.234707
$730$		0			0
$731$	0.147880	+	0.0853784i	0.00546953	+	0.00315784i
$732$		0			0
$733$			5.98434i			0.221037i	0.993874	+	0.110518i	$0.0352511\pi$
$733$			5.98434i			0.221037i	−0.993874	+	0.110518i	$0.964749\pi$
$734$		0			0
$735$	−9.60553	+	16.6373i	−0.354305	+	0.613675i
$736$		0			0
$737$	5.92235	−	10.2578i	0.218152	−	0.377851i
$738$		0			0
$739$	−7.49057	+	4.32468i	−0.275545	+	0.159086i	−0.631405	−	0.775453i	$-0.717521\pi$
$739$	−7.49057	+	4.32468i	−0.275545	+	0.159086i	0.355860	+	0.934539i	$0.384188\pi$
$740$		0			0
$741$	−12.4351	−	8.81980i	−0.456816	−	0.324003i
$742$		0			0
$743$	3.88211	+	6.72402i	0.142421	+	0.246680i	0.928408	−	0.371563i	$-0.121178\pi$
$743$	3.88211	+	6.72402i	0.142421	+	0.246680i	−0.785987	+	0.618243i	$0.787845\pi$
$744$		0			0
$745$	−25.3974	+	43.9895i	−0.930488	+	1.61165i
$746$		0			0
$747$	1.59576	+	0.921314i	0.0583859	+	0.0337091i
$748$		0			0
$749$		−	13.7064i		−	0.500820i
$750$		0			0
$751$	−25.7459	+	44.5932i	−0.939481	+	1.62723i	−0.173040	+	0.984915i	$0.555359\pi$
$751$	−25.7459	+	44.5932i	−0.939481	+	1.62723i	−0.766441	+	0.642314i	$0.777974\pi$
$752$		0			0
$753$	30.3985			1.10778
$754$		0			0
$755$	1.23492	−	0.712983i	0.0449434	−	0.0259481i
$756$		0			0
$757$	18.6041	−	10.7411i	0.676179	−	0.390392i	−0.122235	−	0.992501i	$-0.539006\pi$
$757$	18.6041	−	10.7411i	0.676179	−	0.390392i	0.798414	+	0.602109i	$0.205673\pi$
$758$		0			0
$759$	25.3567			0.920391
$760$		0			0
$761$	19.7421			0.715652			0.357826	−	0.933788i	$-0.383518\pi$
$761$	19.7421			0.715652			0.357826	+	0.933788i	$0.383518\pi$
$762$		0			0
$763$	11.6398	−	6.72026i	0.421390	−	0.243290i
$764$		0			0
$765$	−0.307952	+	0.177796i	−0.0111340	+	0.00642824i
$766$		0			0
$767$	−23.3876			−0.844478
$768$		0			0
$769$	1.12881	−	1.95516i	0.0407060	−	0.0705049i	−0.844955	−	0.534838i	$-0.820373\pi$
$769$	1.12881	−	1.95516i	0.0407060	−	0.0705049i	0.885661	+	0.464333i	$0.153706\pi$
$770$		0			0
$771$			11.6274i			0.418751i
$772$		0			0
$773$	21.9907	+	12.6963i	0.790951	+	0.456656i	0.840297	−	0.542126i	$-0.182380\pi$
$773$	21.9907	+	12.6963i	0.790951	+	0.456656i	−0.0493464	+	0.998782i	$0.515714\pi$
$774$		0			0
$775$	0.170853	−	0.295926i	0.00613722	−	0.0106300i
$776$		0			0
$777$	−7.32701	−	12.6908i	−0.262855	−	0.455278i
$778$		0			0
$779$	−0.238049	+	2.54354i	−0.00852898	+	0.0911316i
$780$		0			0
$781$	−0.133424	+	0.0770326i	−0.00477430	+	0.00275644i
$782$		0			0
$783$	7.32272	−	12.6833i	0.261693	−	0.453265i
$784$		0			0
$785$	24.8323	−	43.0108i	0.886302	−	1.53512i
$786$		0			0
$787$			12.7147i			0.453230i	0.973984	+	0.226615i	$0.0727659\pi$
$787$			12.7147i			0.453230i	−0.973984	+	0.226615i	$0.927234\pi$
$788$		0			0
$789$	43.2092	+	24.9468i	1.53829	+	0.888130i
$790$		0			0
$791$	−11.4093			−0.405669
$792$		0			0
$793$	−9.93568	−	17.2091i	−0.352826	−	0.611113i
$794$		0			0
$795$	35.7580	−	20.6449i	1.26821	−	0.732199i
$796$		0			0
$797$		−	36.6076i		−	1.29671i	−0.761339	−	0.648354i	$-0.775458\pi$
$797$		−	36.6076i		−	1.29671i	0.761339	−	0.648354i	$-0.224542\pi$
$798$		0			0
$799$	0.689877			0.0244061
$800$		0			0
$801$	−10.1208	−	17.5297i	−0.357600	−	0.619381i
$802$		0			0
$803$	−28.2165	+	16.2908i	−0.995738	+	0.574889i
$804$		0			0
$805$			17.4663i			0.615605i
$806$		0			0
$807$	−29.8576	+	51.7148i	−1.05104	+	1.82045i
$808$		0			0
$809$	16.7198			0.587837			0.293919	−	0.955830i	$-0.405041\pi$
$809$	16.7198			0.587837			0.293919	+	0.955830i	$0.405041\pi$
$810$		0			0
$811$	−20.8152	−	12.0177i	−0.730921	−	0.421998i	0.0878379	−	0.996135i	$-0.472004\pi$
$811$	−20.8152	−	12.0177i	−0.730921	−	0.421998i	−0.818759	+	0.574137i	$0.805338\pi$
$812$		0			0
$813$	−18.1951	−	10.5049i	−0.638130	−	0.368425i
$814$		0			0
$815$	−6.21929	−	10.7721i	−0.217852	−	0.377331i
$816$		0			0
$817$	−6.45644	−	0.604256i	−0.225882	−	0.0211402i
$818$		0			0
$819$	−3.38932	+	1.95682i	−0.118432	+	0.0683770i
$820$		0			0
$821$	37.7904	+	21.8183i	1.31890	+	0.761464i	0.983551	−	0.180631i	$-0.0578141\pi$
$821$	37.7904	+	21.8183i	1.31890	+	0.761464i	0.335344	+	0.942096i	$0.391147\pi$
$822$		0			0
$823$	13.6517	−	23.6455i	0.475869	−	0.824229i	−0.523749	−	0.851873i	$-0.675467\pi$
$823$	13.6517	−	23.6455i	0.475869	−	0.824229i	0.999618	+	0.0276434i	$0.00880030\pi$
$824$		0			0
$825$	1.44263			0.0502261
$826$		0			0
$827$	20.0572	+	11.5800i	0.697458	+	0.402677i	0.806400	−	0.591371i	$-0.201413\pi$
$827$	20.0572	+	11.5800i	0.697458	+	0.402677i	−0.108942	+	0.994048i	$0.534746\pi$
$828$		0			0
$829$			16.9838i			0.589871i	0.955517	+	0.294936i	$0.0952982\pi$
$829$			16.9838i			0.589871i	−0.955517	+	0.294936i	$0.904702\pi$
$830$		0			0
$831$	23.3500	+	40.4435i	0.810004	+	1.40297i
$832$		0			0
$833$	−0.230633	−	0.399468i	−0.00799095	−	0.0138407i
$834$		0			0
$835$			49.6821i			1.71932i
$836$		0			0
$837$		−	4.67774i		−	0.161686i
$838$		0			0
$839$	7.13821	+	12.3637i	0.246438	+	0.426844i	0.962535	−	0.271157i	$-0.0874064\pi$
$839$	7.13821	+	12.3637i	0.246438	+	0.426844i	−0.716097	+	0.698001i	$0.754073\pi$
$840$		0			0
$841$	−5.42711	−	9.40003i	−0.187142	−	0.324139i
$842$		0			0
$843$			19.9630i			0.687561i
$844$		0			0
$845$	20.2207	+	11.6744i	0.695612	+	0.401612i
$846$		0			0
$847$	5.90220			0.202802
$848$		0			0
$849$	0.463366	−	0.802574i	0.0159027	−	0.0275443i
$850$		0			0
$851$	15.5528	+	8.97944i	0.533145	+	0.307811i
$852$		0			0
$853$	−4.96947	+	2.86913i	−0.170152	+	0.0982370i	−0.582657	−	0.812718i	$-0.697987\pi$
$853$	−4.96947	+	2.86913i	−0.170152	+	0.0982370i	0.412506	+	0.910955i	$0.364654\pi$
$854$		0			0
$855$	7.81235	−	11.0147i	0.267177	−	0.376696i
$856$		0			0
$857$	25.5734	+	44.2945i	0.873571	+	1.51307i	0.858277	+	0.513187i	$0.171535\pi$
$857$	25.5734	+	44.2945i	0.873571	+	1.51307i	0.0152941	+	0.999883i	$0.495132\pi$
$858$		0			0
$859$	14.2087	+	8.20342i	0.484796	+	0.279897i	0.722413	−	0.691462i	$-0.243033\pi$
$859$	14.2087	+	8.20342i	0.484796	+	0.279897i	−0.237617	+	0.971359i	$0.576366\pi$
$860$		0			0
$861$	1.82823	+	1.05553i	0.0623060	+	0.0359724i
$862$		0			0
$863$	−38.3169			−1.30432			−0.652161	−	0.758081i	$-0.726137\pi$
$863$	−38.3169			−1.30432			−0.652161	+	0.758081i	$0.726137\pi$
$864$		0			0
$865$	7.94578	−	13.7625i	0.270164	−	0.467939i
$866$		0			0
$867$			35.4367i			1.20349i
$868$		0			0
$869$	33.5942	−	19.3956i	1.13960	−	0.657951i
$870$		0			0
$871$	−3.60604	−	6.24584i	−0.122186	−	0.211632i
$872$		0			0
$873$	−1.25138			−0.0423526
$874$		0			0
$875$		−	18.7897i		−	0.635209i
$876$		0			0
$877$	−3.40345	+	1.96498i	−0.114926	+	0.0663528i	−0.556361	−	0.830940i	$-0.687803\pi$
$877$	−3.40345	+	1.96498i	−0.114926	+	0.0663528i	0.441435	+	0.897293i	$0.354470\pi$
$878$		0			0
$879$	−17.6356	−	30.5458i	−0.594835	−	1.03029i
$880$		0			0
$881$	20.3758			0.686479			0.343240	−	0.939248i	$-0.388476\pi$
$881$	20.3758			0.686479			0.343240	+	0.939248i	$0.388476\pi$
$882$		0			0
$883$	−7.45189	−	4.30235i	−0.250776	−	0.144786i	0.369344	−	0.929293i	$-0.379583\pi$
$883$	−7.45189	−	4.30235i	−0.250776	−	0.144786i	−0.620120	+	0.784507i	$0.712916\pi$
$884$		0			0
$885$		−	66.6860i		−	2.24162i
$886$		0			0
$887$	−11.8329	+	20.4952i	−0.397311	+	0.688162i	−0.993393	−	0.114761i	$-0.963390\pi$
$887$	−11.8329	+	20.4952i	−0.397311	+	0.688162i	0.596082	+	0.802923i	$0.296723\pi$
$888$		0			0
$889$	−12.2397	+	21.1998i	−0.410507	+	0.711019i
$890$		0			0
$891$	26.7744	−	15.4582i	0.896976	−	0.517869i
$892$		0			0
$893$	−23.8107	+	10.9282i	−0.796794	+	0.365697i
$894$		0			0
$895$	13.7692	+	23.8490i	0.460255	+	0.797185i
$896$		0			0
$897$	7.71969	−	13.3709i	0.257753	−	0.446441i
$898$		0			0
$899$	5.01926	+	2.89787i	0.167402	+	0.0966494i
$900$		0			0
$901$			0.991386i			0.0330278i
$902$		0			0
$903$	−2.67933	+	4.64073i	−0.0891625	+	0.154434i
$904$		0			0
$905$	34.0796			1.13285
$906$		0			0
$907$	8.45834	−	4.88343i	0.280855	−	0.162152i	−0.352956	−	0.935640i	$-0.614823\pi$
$907$	8.45834	−	4.88343i	0.280855	−	0.162152i	0.633810	+	0.773489i	$0.281490\pi$
$908$		0			0
$909$	6.29753	−	3.63588i	0.208876	−	0.120595i
$910$		0			0
$911$	−20.0731			−0.665051			−0.332526	−	0.943094i	$-0.607901\pi$
$911$	−20.0731			−0.665051			−0.332526	+	0.943094i	$0.607901\pi$
$912$		0			0
$913$	3.75288			0.124202
$914$		0			0
$915$	49.0689	−	28.3300i	1.62217	−	0.936560i
$916$		0			0
$917$	−16.1066	+	9.29915i	−0.531887	+	0.307085i
$918$		0			0
$919$	−6.24809			−0.206105			−0.103053	−	0.994676i	$-0.532861\pi$
$919$	−6.24809			−0.206105			−0.103053	+	0.994676i	$0.532861\pi$
$920$		0			0
$921$	−33.6605	+	58.3017i	−1.10915	+	1.92111i
$922$		0			0
$923$			0.0938082i			0.00308774i
$924$		0			0
$925$	0.884856	+	0.510872i	0.0290939	+	0.0167974i
$926$		0			0
$927$	3.37472	−	5.84519i	0.110840	−	0.191981i
$928$		0			0
$929$	−19.8790	−	34.4315i	−0.652210	−	1.12966i	−0.982585	−	0.185811i	$-0.940509\pi$
$929$	−19.8790	−	34.4315i	−0.652210	−	1.12966i	0.330376	−	0.943850i	$-0.392825\pi$
$930$		0			0
$931$	14.2880	+	10.1340i	0.468271	+	0.332128i
$932$		0			0
$933$	57.1217	−	32.9792i	1.87008	−	1.07969i
$934$		0			0
$935$	−0.362117	+	0.627205i	−0.0118425	+	0.0205118i
$936$		0			0
$937$	−24.0407	+	41.6396i	−0.785374	+	1.36031i	0.143402	+	0.989665i	$0.454196\pi$
$937$	−24.0407	+	41.6396i	−0.785374	+	1.36031i	−0.928775	+	0.370643i	$0.879137\pi$
$938$		0			0
$939$			48.0072i			1.56666i
$940$		0			0
$941$	34.2936	+	19.7994i	1.11794	+	0.645443i	0.940874	−	0.338756i	$-0.110006\pi$
$941$	34.2936	+	19.7994i	1.11794	+	0.645443i	0.177066	+	0.984199i	$0.443340\pi$
$942$		0			0
$943$	−2.58716			−0.0842495
$944$		0			0
$945$	6.80169	+	11.7809i	0.221259	+	0.383232i
$946$		0			0
$947$	4.77965	−	2.75953i	0.155318	−	0.0896728i	−0.420327	−	0.907373i	$-0.638085\pi$
$947$	4.77965	−	2.75953i	0.155318	−	0.0896728i	0.575645	+	0.817700i	$0.304751\pi$
$948$		0			0
$949$			19.8385i			0.643984i
$950$		0			0
$951$	−8.15826			−0.264550
$952$		0			0
$953$	−23.9689	−	41.5153i	−0.776428	−	1.34481i	−0.933988	−	0.357303i	$-0.883696\pi$
$953$	−23.9689	−	41.5153i	−0.776428	−	1.34481i	0.157561	−	0.987509i	$-0.449637\pi$
$954$		0			0
$955$	9.03918	−	5.21877i	0.292501	−	0.168875i
$956$		0			0
$957$			24.4688i			0.790964i
$958$		0			0
$959$	2.45206	−	4.24709i	0.0791811	−	0.137146i
$960$		0			0
$961$	−29.1488			−0.940285
$962$		0			0
$963$	−9.29406	−	5.36593i	−0.299497	−	0.172915i
$964$		0			0
$965$	−48.8698	−	28.2150i	−1.57317	−	0.908273i
$966$		0			0
$967$	21.7457	+	37.6646i	0.699294	+	1.21121i	0.968711	+	0.248190i	$0.0798356\pi$
$967$	21.7457	+	37.6646i	0.699294	+	1.21121i	−0.269417	+	0.963024i	$0.586831\pi$
$968$		0			0
$969$	0.435365	+	0.948589i	0.0139860	+	0.0304731i
$970$		0			0
$971$	22.6824	−	13.0957i	0.727912	−	0.420260i	−0.0897457	−	0.995965i	$-0.528605\pi$
$971$	22.6824	−	13.0957i	0.727912	−	0.420260i	0.817658	+	0.575704i	$0.195272\pi$
$972$		0			0
$973$	−12.7103	−	7.33832i	−0.407475	−	0.235256i
$974$		0			0
$975$	0.439200	−	0.760717i	0.0140657	−	0.0243624i
$976$		0			0
$977$	−30.0644			−0.961844			−0.480922	−	0.876763i	$-0.659698\pi$
$977$	−30.0644			−0.961844			−0.480922	+	0.876763i	$0.659698\pi$
$978$		0			0
$979$	−35.7026	−	20.6129i	−1.14106	−	0.658792i
$980$		0			0
$981$		−	10.5237i		−	0.335996i
$982$		0			0
$983$	10.9332	+	18.9368i	0.348714	+	0.603991i	0.986021	−	0.166619i	$-0.0532850\pi$
$983$	10.9332	+	18.9368i	0.348714	+	0.603991i	−0.637307	+	0.770610i	$0.719952\pi$
$984$		0			0
$985$	0.195216	+	0.338124i	0.00622010	+	0.0107735i
$986$		0			0
$987$			21.6496i			0.689114i
$988$		0			0
$989$		−	6.56717i		−	0.208824i
$990$		0			0
$991$	−10.2273	−	17.7142i	−0.324881	−	0.562710i	0.656608	−	0.754232i	$-0.271991\pi$
$991$	−10.2273	−	17.7142i	−0.324881	−	0.562710i	−0.981488	+	0.191523i	$0.938657\pi$
$992$		0			0
$993$	−0.517356	−	0.896088i	−0.0164178	−	0.0284365i
$994$		0			0
$995$			38.2752i			1.21341i
$996$		0			0
$997$	−25.5676	−	14.7614i	−0.809733	−	0.467499i	0.0371304	−	0.999310i	$-0.488178\pi$
$997$	−25.5676	−	14.7614i	−0.809733	−	0.467499i	−0.846863	+	0.531811i	$0.821512\pi$
$998$		0			0
$999$	13.9870			0.442530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.t.d.1185.4	yes	24
4.3	odd	2	inner	1216.2.t.d.1185.10	yes	24
8.3	odd	2		1216.2.t.e.1185.4	yes	24
8.5	even	2		1216.2.t.e.1185.10	yes	24
19.11	even	3		1216.2.t.e.353.10	yes	24
76.11	odd	6		1216.2.t.e.353.4	yes	24
152.11	odd	6	inner	1216.2.t.d.353.10	yes	24
152.125	even	6	inner	1216.2.t.d.353.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.d.353.4	✓	24	152.125	even	6	inner
1216.2.t.d.353.10	yes	24	152.11	odd	6	inner
1216.2.t.d.1185.4	yes	24	1.1	even	1	trivial
1216.2.t.d.1185.10	yes	24	4.3	odd	2	inner
1216.2.t.e.353.4	yes	24	76.11	odd	6
1216.2.t.e.353.10	yes	24	19.11	even	3
1216.2.t.e.1185.4	yes	24	8.3	odd	2
1216.2.t.e.1185.10	yes	24	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80664 + 1.04307i) q^{3} +(-1.98453 + 1.14577i) q^{5} +1.72665 q^{7} +(0.675970 - 1.17081i) q^{9} +O(q^{10})\)	\(q+(-1.80664 + 1.04307i) q^{3} +(-1.98453 + 1.14577i) q^{5} +1.72665 q^{7} +(0.675970 - 1.17081i) q^{9} -2.75349i q^{11} +(-1.45195 - 0.838282i) q^{13} +(2.39022 - 4.13999i) q^{15} +(0.0573903 + 0.0994029i) q^{17} +(-3.55541 - 2.52172i) q^{19} +(-3.11944 + 1.80101i) q^{21} +(2.20718 - 3.82295i) q^{23} +(0.125574 - 0.217501i) q^{25} -3.43807i q^{27} +(3.68908 + 2.12989i) q^{29} +1.36057 q^{31} +(2.87207 + 4.97457i) q^{33} +(-3.42659 + 1.97834i) q^{35} +4.06828i q^{37} +3.49753 q^{39} +(-0.293039 - 0.507558i) q^{41} +(1.28837 - 0.743841i) q^{43} +3.09802i q^{45} +(3.00520 - 5.20516i) q^{47} -4.01867 q^{49} +(-0.207367 - 0.119724i) q^{51} +(7.48006 + 4.31861i) q^{53} +(3.15486 + 5.46439i) q^{55} +(9.05367 + 0.847330i) q^{57} +(12.0808 - 6.97487i) q^{59} +(10.2645 + 5.92622i) q^{61} +(1.16716 - 2.02159i) q^{63} +3.84191 q^{65} +(3.72538 + 2.15085i) q^{67} +9.20894i q^{69} +(-0.0279764 - 0.0484565i) q^{71} +(-5.91641 - 10.2475i) q^{73} +0.523929i q^{75} -4.75432i q^{77} +(7.04401 + 12.2006i) q^{79} +(5.61404 + 9.72380i) q^{81} +1.36295i q^{83} +(-0.227785 - 0.131512i) q^{85} -8.88647 q^{87} +(7.48611 - 12.9663i) q^{89} +(-2.50701 - 1.44742i) q^{91} +(-2.45806 + 1.41916i) q^{93} +(9.94513 + 0.930761i) q^{95} +(-0.462808 - 0.801606i) q^{97} +(-3.22382 - 1.86128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 24 * q - 6 * q^5 + 8 * q^9	\( 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) \) 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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