LMFDB - Embedded newform 756.2.ck.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.671662 + 1.59652i) q^{3} +(-0.158784 + 0.900507i) q^{5} +(-0.241705 - 2.63469i) q^{7} +(-2.09774 + 2.14464i) q^{9} +O(q^{10})$	\(q+(0.671662 + 1.59652i) q^{3} +(-0.158784 + 0.900507i) q^{5} +(-0.241705 - 2.63469i) q^{7} +(-2.09774 + 2.14464i) q^{9} +(-3.68787 + 0.650271i) q^{11} +(-2.48376 + 2.96003i) q^{13} +(-1.54432 + 0.351336i) q^{15} -6.10539 q^{17} +5.56765i q^{19} +(4.04398 - 2.15551i) q^{21} +(-1.03164 + 1.22946i) q^{23} +(3.91276 + 1.42413i) q^{25} +(-4.83293 - 1.90860i) q^{27} +(4.21794 + 5.02674i) q^{29} +(-0.823531 - 2.26263i) q^{31} +(-3.51517 - 5.45099i) q^{33} +(2.41093 + 0.200688i) q^{35} +(1.21795 + 2.10956i) q^{37} +(-6.39400 - 1.97723i) q^{39} +(-4.95635 - 4.15887i) q^{41} +(7.68736 + 2.79797i) q^{43} +(-1.59818 - 2.22956i) q^{45} +(4.31905 + 1.57200i) q^{47} +(-6.88316 + 1.27364i) q^{49} +(-4.10076 - 9.74737i) q^{51} +(-9.92435 + 5.72983i) q^{53} -3.42420i q^{55} +(-8.88885 + 3.73958i) q^{57} +(0.682613 + 0.572780i) q^{59} +(4.21480 - 11.5801i) q^{61} +(6.15750 + 5.00852i) q^{63} +(-2.27115 - 2.70665i) q^{65} +(2.26341 - 12.8364i) q^{67} +(-2.65578 - 0.821252i) q^{69} +(11.1044 + 6.41115i) q^{71} +(-4.20689 - 2.42885i) q^{73} +(0.354408 + 7.20333i) q^{75} +(2.60464 + 9.55921i) q^{77} +(-0.979078 - 5.55263i) q^{79} +(-0.198980 - 8.99780i) q^{81} +(-6.26479 + 5.25678i) q^{83} +(0.969437 - 5.49795i) q^{85} +(-5.19226 + 10.1103i) q^{87} +4.08655 q^{89} +(8.39910 + 5.82848i) q^{91} +(3.05920 - 2.83451i) q^{93} +(-5.01371 - 0.884052i) q^{95} +(-4.13766 + 11.3681i) q^{97} +(6.34159 - 9.27326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	0.671662	+	1.59652i	0.387784	+	0.921750i
$3$	0.671662	+	1.59652i	0.387784	+	0.921750i
$4$		0			0
$5$	−0.158784	+	0.900507i	−0.0710102	+	0.402719i	0.928497	+	0.371339i	$0.121101\pi$
$5$	−0.158784	+	0.900507i	−0.0710102	+	0.402719i	−0.999508	+	0.0313798i	$0.990010\pi$
$6$		0			0
$7$	−0.241705	−	2.63469i	−0.0913560	−	0.995818i
$7$	−0.241705	−	2.63469i	−0.0913560	−	0.995818i
$8$		0			0
$9$	−2.09774	+	2.14464i	−0.699246	+	0.714881i
$10$		0			0
$11$	−3.68787	+	0.650271i	−1.11193	+	0.196064i	−0.699297	−	0.714831i	$-0.746503\pi$
$11$	−3.68787	+	0.650271i	−1.11193	+	0.196064i	−0.412637	+	0.910895i	$0.635392\pi$
$12$		0			0
$13$	−2.48376	+	2.96003i	−0.688872	+	0.820965i	−0.991219	−	0.132233i	$-0.957785\pi$
$13$	−2.48376	+	2.96003i	−0.688872	+	0.820965i	0.302347	+	0.953198i	$0.402230\pi$
$14$		0			0
$15$	−1.54432	+	0.351336i	−0.398743	+	0.0907145i
$16$		0			0
$17$	−6.10539			−1.48078			−0.740388	−	0.672180i	$-0.765358\pi$
$17$	−6.10539			−1.48078			−0.740388	+	0.672180i	$0.765358\pi$
$18$		0			0
$19$			5.56765i			1.27731i	0.769495	+	0.638653i	$0.220508\pi$
$19$			5.56765i			1.27731i	−0.769495	+	0.638653i	$0.779492\pi$
$20$		0			0
$21$	4.04398	−	2.15551i	0.882469	−	0.470370i
$22$		0			0
$23$	−1.03164	+	1.22946i	−0.215113	+	0.256361i	−0.862800	−	0.505545i	$-0.831292\pi$
$23$	−1.03164	+	1.22946i	−0.215113	+	0.256361i	0.647688	+	0.761906i	$0.275736\pi$
$24$		0			0
$25$	3.91276	+	1.42413i	0.782553	+	0.284826i
$26$		0			0
$27$	−4.83293	−	1.90860i	−0.930098	−	0.367311i
$28$		0			0
$29$	4.21794	+	5.02674i	0.783251	+	0.933443i	0.999076	−	0.0429895i	$-0.0136882\pi$
$29$	4.21794	+	5.02674i	0.783251	+	0.933443i	−0.215824	+	0.976432i	$0.569244\pi$
$30$		0			0
$31$	−0.823531	−	2.26263i	−0.147911	−	0.406381i	0.843506	−	0.537119i	$-0.180487\pi$
$31$	−0.823531	−	2.26263i	−0.147911	−	0.406381i	−0.991417	+	0.130738i	$0.958265\pi$
$32$		0			0
$33$	−3.51517	−	5.45099i	−0.611913	−	0.948895i
$34$		0			0
$35$	2.41093	+	0.200688i	0.407522	+	0.0339225i
$36$		0			0
$37$	1.21795	+	2.10956i	0.200230	+	0.346809i	0.948603	−	0.316470i	$-0.102498\pi$
$37$	1.21795	+	2.10956i	0.200230	+	0.346809i	−0.748372	+	0.663279i	$0.769164\pi$
$38$		0			0
$39$	−6.39400	−	1.97723i	−1.02386	−	0.316610i
$40$		0			0
$41$	−4.95635	−	4.15887i	−0.774052	−	0.649506i	0.167691	−	0.985840i	$-0.446369\pi$
$41$	−4.95635	−	4.15887i	−0.774052	−	0.649506i	−0.941743	+	0.336333i	$0.890813\pi$
$42$		0			0
$43$	7.68736	+	2.79797i	1.17231	+	0.426686i	0.853480	−	0.521125i	$-0.174488\pi$
$43$	7.68736	+	2.79797i	1.17231	+	0.426686i	0.318831	+	0.947812i	$0.396710\pi$
$44$		0			0
$45$	−1.59818	−	2.22956i	−0.238242	−	0.332364i
$46$		0			0
$47$	4.31905	+	1.57200i	0.629998	+	0.229300i	0.637230	−	0.770673i	$-0.280080\pi$
$47$	4.31905	+	1.57200i	0.629998	+	0.229300i	−0.00723267	+	0.999974i	$0.502302\pi$
$48$		0			0
$49$	−6.88316	+	1.27364i	−0.983308	+	0.181948i
$50$		0			0
$51$	−4.10076	−	9.74737i	−0.574222	−	1.36490i
$52$		0			0
$53$	−9.92435	+	5.72983i	−1.36321	+	0.787052i	−0.990050	−	0.140713i	$-0.955060\pi$
$53$	−9.92435	+	5.72983i	−1.36321	+	0.787052i	−0.373164	+	0.927765i	$0.621727\pi$
$54$		0			0
$55$		−	3.42420i		−	0.461720i
$56$		0			0
$57$	−8.88885	+	3.73958i	−1.17736	+	0.495319i
$58$		0			0
$59$	0.682613	+	0.572780i	0.0888687	+	0.0745697i	0.686140	−	0.727470i	$-0.259304\pi$
$59$	0.682613	+	0.572780i	0.0888687	+	0.0745697i	−0.597271	+	0.802039i	$0.703748\pi$
$60$		0			0
$61$	4.21480	−	11.5801i	0.539650	−	1.48268i	−0.307617	−	0.951510i	$-0.599531\pi$
$61$	4.21480	−	11.5801i	0.539650	−	1.48268i	0.847267	−	0.531167i	$-0.178246\pi$
$62$		0			0
$63$	6.15750	+	5.00852i	0.775772	+	0.631014i
$64$		0			0
$65$	−2.27115	−	2.70665i	−0.281701	−	0.335719i
$66$		0			0
$67$	2.26341	−	12.8364i	0.276520	−	1.56822i	−0.457574	−	0.889172i	$-0.651281\pi$
$67$	2.26341	−	12.8364i	0.276520	−	1.56822i	0.734093	−	0.679049i	$-0.237607\pi$
$68$		0			0
$69$	−2.65578	−	0.821252i	−0.319718	−	0.0988671i
$70$		0			0
$71$	11.1044	+	6.41115i	1.31785	+	0.760864i	0.983383	−	0.181542i	$-0.0581089\pi$
$71$	11.1044	+	6.41115i	1.31785	+	0.760864i	0.334471	+	0.942406i	$0.391442\pi$
$72$		0			0
$73$	−4.20689	−	2.42885i	−0.492379	−	0.284275i	0.233182	−	0.972433i	$-0.425086\pi$
$73$	−4.20689	−	2.42885i	−0.492379	−	0.284275i	−0.725561	+	0.688158i	$0.758420\pi$
$74$		0			0
$75$	0.354408	+	7.20333i	0.0409235	+	0.831769i
$76$		0			0
$77$	2.60464	+	9.55921i	0.296826	+	1.08937i
$78$		0			0
$79$	−0.979078	−	5.55263i	−0.110155	−	0.624719i	−0.989036	−	0.147678i	$-0.952820\pi$
$79$	−0.979078	−	5.55263i	−0.110155	−	0.624719i	0.878881	−	0.477042i	$-0.158291\pi$
$80$		0			0
$81$	−0.198980	−	8.99780i	−0.0221089	−	0.999756i
$82$		0			0
$83$	−6.26479	+	5.25678i	−0.687650	+	0.577006i	−0.918230	−	0.396047i	$-0.870382\pi$
$83$	−6.26479	+	5.25678i	−0.687650	+	0.577006i	0.230581	+	0.973053i	$0.425937\pi$
$84$		0			0
$85$	0.969437	−	5.49795i	0.105150	−	0.596336i
$86$		0			0
$87$	−5.19226	+	10.1103i	−0.556668	+	1.08394i
$88$		0			0
$89$	4.08655			0.433174			0.216587	−	0.976263i	$-0.430508\pi$
$89$	4.08655			0.433174			0.216587	+	0.976263i	$0.430508\pi$
$90$		0			0
$91$	8.39910	+	5.82848i	0.880465	+	0.610991i
$92$		0			0
$93$	3.05920	−	2.83451i	0.317224	−	0.293925i
$94$		0			0
$95$	−5.01371	−	0.884052i	−0.514395	−	0.0907018i
$96$		0			0
$97$	−4.13766	+	11.3681i	−0.420115	+	1.15426i	0.531525	+	0.847043i	$0.321619\pi$
$97$	−4.13766	+	11.3681i	−0.420115	+	1.15426i	−0.951640	+	0.307215i	$0.900603\pi$
$98$		0			0
$99$	6.34159	−	9.27326i	0.637354	−	0.931998i
$100$		0			0
$101$	−2.27509	+	1.90902i	−0.226380	+	0.189955i	−0.748922	−	0.662658i	$-0.769428\pi$
$101$	−2.27509	+	1.90902i	−0.226380	+	0.189955i	0.522542	+	0.852613i	$0.324984\pi$
$102$		0			0
$103$	8.96723	+	1.58117i	0.883568	+	0.155797i	0.596979	−	0.802257i	$-0.296368\pi$
$103$	8.96723	+	1.58117i	0.883568	+	0.155797i	0.286589	+	0.958054i	$0.407479\pi$
$104$		0			0
$105$	1.29893	+	3.98389i	0.126763	+	0.388788i
$106$		0			0
$107$	12.5146	+	7.22532i	1.20983	+	0.698498i	0.962723	−	0.270489i	$-0.0871855\pi$
$107$	12.5146	+	7.22532i	1.20983	+	0.698498i	0.247111	+	0.968987i	$0.420519\pi$
$108$		0			0
$109$	4.51287	+	7.81653i	0.432255	+	0.748688i	0.997067	−	0.0765319i	$-0.0243847\pi$
$109$	4.51287	+	7.81653i	0.432255	+	0.748688i	−0.564812	+	0.825220i	$0.691051\pi$
$110$		0			0
$111$	−2.54989	+	3.36139i	−0.242025	+	0.319049i
$112$		0			0
$113$	−3.84867	−	10.5741i	−0.362053	−	0.994732i	−0.978303	−	0.207181i	$-0.933571\pi$
$113$	−3.84867	−	10.5741i	−0.362053	−	0.994732i	0.616250	−	0.787551i	$-0.288651\pi$
$114$		0			0
$115$	−0.943333	−	1.12422i	−0.0879663	−	0.104834i
$116$		0			0
$117$	−1.13793	−	11.5362i	−0.105201	−	1.06652i
$118$		0			0
$119$	1.47571	+	16.0858i	0.135278	+	1.47458i
$120$		0			0
$121$	2.84091	−	1.03401i	0.258264	−	0.0940005i
$122$		0			0
$123$	3.31072	−	10.7063i	0.298517	−	0.965351i
$124$		0			0
$125$	−4.18972	+	7.25680i	−0.374740	+	0.649068i
$126$		0			0
$127$	1.76290	+	3.05343i	0.156432	+	0.270948i	0.933579	−	0.358370i	$-0.116668\pi$
$127$	1.76290	+	3.05343i	0.156432	+	0.270948i	−0.777148	+	0.629318i	$0.783334\pi$
$128$		0			0
$129$	0.696301	+	14.1523i	0.0613059	+	1.24604i
$130$		0			0
$131$	−8.87289	−	7.44524i	−0.775228	−	0.650493i	0.166814	−	0.985988i	$-0.446652\pi$
$131$	−8.87289	−	7.44524i	−0.775228	−	0.650493i	−0.942042	+	0.335495i	$0.891096\pi$
$132$		0			0
$133$	14.6690	−	1.34573i	1.27196	−	0.116690i
$134$		0			0
$135$	2.48610	−	4.04903i	0.213969	−	0.348485i
$136$		0			0
$137$	1.59066	−	4.37031i	0.135899	−	0.373381i	−0.853011	−	0.521893i	$-0.825226\pi$
$137$	1.59066	−	4.37031i	0.135899	−	0.373381i	0.988911	+	0.148512i	$0.0474484\pi$
$138$		0			0
$139$	20.6952	+	3.64913i	1.75535	+	0.309515i	0.956438	−	0.291935i	$-0.0942992\pi$
$139$	20.6952	+	3.64913i	1.75535	+	0.309515i	0.798910	+	0.601450i	$0.205410\pi$
$140$		0			0
$141$	0.391208	+	7.95129i	0.0329457	+	0.669619i
$142$		0			0
$143$	7.23497	−	12.5313i	0.605018	−	1.04792i
$144$		0			0
$145$	−5.19636	+	3.00012i	−0.431534	+	0.249146i
$146$		0			0
$147$	−6.65654	−	10.1336i	−0.549022	−	0.835808i
$148$		0			0
$149$	4.58792	+	12.6052i	0.375857	+	1.03266i	0.973057	+	0.230566i	$0.0740576\pi$
$149$	4.58792	+	12.6052i	0.375857	+	1.03266i	−0.597200	+	0.802092i	$0.703720\pi$
$150$		0			0
$151$	−1.81633	−	10.3009i	−0.147811	−	0.838279i	−0.965067	−	0.262004i	$-0.915617\pi$
$151$	−1.81633	−	10.3009i	−0.147811	−	0.838279i	0.817256	−	0.576275i	$-0.195494\pi$
$152$		0			0
$153$	12.8075	−	13.0939i	1.03543	−	1.05858i
$154$		0			0
$155$	2.16828	−	0.382326i	0.174160	−	0.0307092i
$156$		0			0
$157$	−12.7728	+	15.2220i	−1.01938	+	1.21485i	−0.0429337	+	0.999078i	$0.513670\pi$
$157$	−12.7728	+	15.2220i	−1.01938	+	1.21485i	−0.976444	+	0.215770i	$0.930774\pi$
$158$		0			0
$159$	−15.8136	−	11.9959i	−1.25410	−	0.951336i
$160$		0			0
$161$	3.48861	+	2.42089i	0.274941	+	0.190793i
$162$		0			0
$163$	7.01252	−	12.1460i	0.549263	−	0.951352i	−0.449062	−	0.893501i	$-0.648242\pi$
$163$	7.01252	−	12.1460i	0.549263	−	0.951352i	0.998325	−	0.0578512i	$-0.0184249\pi$
$164$		0			0
$165$	5.46680	−	2.29991i	0.425590	−	0.179048i
$166$		0			0
$167$	−2.12777	+	0.774444i	−0.164652	+	0.0599283i	−0.423031	−	0.906115i	$-0.639034\pi$
$167$	−2.12777	+	0.774444i	−0.164652	+	0.0599283i	0.258379	+	0.966044i	$0.416812\pi$
$168$		0			0
$169$	−0.335292	−	1.90154i	−0.0257917	−	0.146272i
$170$		0			0
$171$	−11.9406	−	11.6795i	−0.913121	−	0.893152i
$172$		0			0
$173$	−19.4358	+	16.3086i	−1.47768	+	1.23992i	−0.569057	+	0.822298i	$0.692692\pi$
$173$	−19.4358	+	16.3086i	−1.47768	+	1.23992i	−0.908621	+	0.417621i	$0.862864\pi$
$174$		0			0
$175$	2.80640	−	10.6531i	0.212144	−	0.805301i
$176$		0			0
$177$	−0.455969	+	1.47452i	−0.0342727	+	0.110832i
$178$		0			0
$179$			4.35026i			0.325154i	0.986696	+	0.162577i	$0.0519805\pi$
$179$			4.35026i			0.325154i	−0.986696	+	0.162577i	$0.948019\pi$
$180$		0			0
$181$	−2.32397	+	1.34175i	−0.172740	+	0.0997313i	−0.583877	−	0.811842i	$-0.698465\pi$
$181$	−2.32397	+	1.34175i	−0.172740	+	0.0997313i	0.411137	+	0.911573i	$0.365132\pi$
$182$		0			0
$183$	21.3187	−	1.04889i	1.57593	−	0.0775364i
$184$		0			0
$185$	−2.09306	+	0.761812i	−0.153885	+	0.0560095i
$186$		0			0
$187$	22.5159	−	3.97016i	1.64653	−	0.290327i
$188$		0			0
$189$	−3.86043	+	13.1946i	−0.280805	+	0.959765i
$190$		0			0
$191$	−16.2247	+	2.86085i	−1.17398	+	0.207004i	−0.726419	−	0.687252i	$-0.758817\pi$
$191$	−16.2247	+	2.86085i	−1.17398	+	0.207004i	−0.447557	+	0.894256i	$0.647706\pi$
$192$		0			0
$193$	−9.52163	+	3.46559i	−0.685382	+	0.249459i	−0.661157	−	0.750248i	$-0.729934\pi$
$193$	−9.52163	+	3.46559i	−0.685382	+	0.249459i	−0.0242252	+	0.999707i	$0.507712\pi$
$194$		0			0
$195$	2.79577	−	5.44389i	0.200209	−	0.389845i
$196$		0			0
$197$	23.3394	−	13.4750i	1.66286	−	0.960054i	0.691524	−	0.722353i	$-0.256939\pi$
$197$	23.3394	−	13.4750i	1.66286	−	0.960054i	0.971338	−	0.237701i	$-0.0763939\pi$
$198$		0			0
$199$			12.5565i			0.890107i	0.895504	+	0.445053i	$0.146815\pi$
$199$			12.5565i			0.890107i	−0.895504	+	0.445053i	$0.853185\pi$
$200$		0			0
$201$	22.0138	−	5.00818i	1.55274	−	0.353250i
$202$		0			0
$203$	12.2244	−	12.3279i	0.857985	−	0.865252i
$204$		0			0
$205$	4.53208	−	3.80287i	0.316534	−	0.265604i
$206$		0			0
$207$	−0.472643	−	4.79160i	−0.0328510	−	0.333039i
$208$		0			0
$209$	−3.62048	−	20.5328i	−0.250434	−	1.42028i
$210$		0			0
$211$	4.63971	−	1.68871i	0.319411	−	0.116256i	−0.177339	−	0.984150i	$-0.556749\pi$
$211$	4.63971	−	1.68871i	0.319411	−	0.116256i	0.496750	+	0.867894i	$0.334527\pi$
$212$		0			0
$213$	−2.77708	+	22.0346i	−0.190283	+	1.50978i
$214$		0			0
$215$	−3.74022	+	6.47825i	−0.255081	+	0.441813i
$216$		0			0
$217$	−5.76228	+	2.71664i	−0.391169	+	0.184417i
$218$		0			0
$219$	1.05209	−	8.34775i	0.0710938	−	0.564088i
$220$		0			0
$221$	15.1643	−	18.0722i	1.02006	−	1.21567i
$222$		0			0
$223$	12.8650	−	2.26844i	0.861502	−	0.151906i	0.274595	−	0.961560i	$-0.411456\pi$
$223$	12.8650	−	2.26844i	0.861502	−	0.151906i	0.586908	+	0.809654i	$0.300345\pi$
$224$		0			0
$225$	−11.2622	+	5.40402i	−0.750814	+	0.360268i
$226$		0			0
$227$	2.66067	+	15.0894i	0.176595	+	1.00152i	0.936287	+	0.351237i	$0.114239\pi$
$227$	2.66067	+	15.0894i	0.176595	+	1.00152i	−0.759692	+	0.650284i	$0.774650\pi$
$228$		0			0
$229$	3.17798	+	8.73143i	0.210007	+	0.576989i	0.999315	−	0.0370081i	$-0.0117827\pi$
$229$	3.17798	+	8.73143i	0.210007	+	0.576989i	−0.789308	+	0.613997i	$0.789561\pi$
$230$		0			0
$231$	−13.5120	+	10.5789i	−0.889025	+	0.696041i
$232$		0			0
$233$	8.13366	−	4.69597i	0.532854	−	0.307643i	−0.209324	−	0.977846i	$-0.567126\pi$
$233$	8.13366	−	4.69597i	0.532854	−	0.307643i	0.742178	+	0.670203i	$0.233793\pi$
$234$		0			0
$235$	−2.10139	+	3.63972i	−0.137080	+	0.237429i
$236$		0			0
$237$	8.20726	−	5.29261i	0.533119	−	0.343792i
$238$		0			0
$239$	−8.59351	−	1.51527i	−0.555868	−	0.0980145i	−0.111345	−	0.993782i	$-0.535516\pi$
$239$	−8.59351	−	1.51527i	−0.555868	−	0.0980145i	−0.444523	+	0.895767i	$0.646627\pi$
$240$		0			0
$241$	−1.93208	+	5.30834i	−0.124456	+	0.341940i	−0.986236	−	0.165342i	$-0.947127\pi$
$241$	−1.93208	+	5.30834i	−0.124456	+	0.341940i	0.861780	+	0.507282i	$0.169350\pi$
$242$		0			0
$243$	14.2315	−	6.36116i	0.912951	−	0.408069i
$244$		0			0
$245$	−0.0539848	−	6.40056i	−0.00344896	−	0.408917i
$246$		0			0
$247$	−16.4804	−	13.8287i	−1.04862	−	0.879900i
$248$		0			0
$249$	−12.6004	−	6.47106i	−0.798516	−	0.410087i
$250$		0			0
$251$	0.593298	+	1.02762i	0.0374487	+	0.0648630i	0.884142	−	0.467218i	$-0.154744\pi$
$251$	0.593298	+	1.02762i	0.0374487	+	0.0648630i	−0.846694	+	0.532081i	$0.821410\pi$
$252$		0			0
$253$	3.00508	−	5.20495i	0.188928	−	0.327233i
$254$		0			0
$255$	9.42871	−	2.14504i	0.590449	−	0.134328i
$256$		0			0
$257$	11.3769	−	4.14085i	0.709672	−	0.258299i	0.0381371	−	0.999273i	$-0.487858\pi$
$257$	11.3769	−	4.14085i	0.709672	−	0.258299i	0.671535	+	0.740973i	$0.265635\pi$
$258$		0			0
$259$	5.26363	−	3.71882i	0.327066	−	0.231076i
$260$		0			0
$261$	−19.6287	−	1.49883i	−1.21499	−	0.0927751i
$262$		0			0
$263$	−0.921965	−	1.09875i	−0.0568508	−	0.0677521i	0.736870	−	0.676035i	$-0.236303\pi$
$263$	−0.921965	−	1.09875i	−0.0568508	−	0.0677521i	−0.793720	+	0.608283i	$0.791859\pi$
$264$		0			0
$265$	−3.58392	−	9.84675i	−0.220159	−	0.604881i
$266$		0			0
$267$	2.74478	+	6.52425i	0.167978	+	0.399278i
$268$		0			0
$269$	5.22031	+	9.04184i	0.318288	+	0.551291i	0.980131	−	0.198352i	$-0.0635588\pi$
$269$	5.22031	+	9.04184i	0.318288	+	0.551291i	−0.661843	+	0.749642i	$0.730225\pi$
$270$		0			0
$271$	11.2170	+	6.47615i	0.681386	+	0.393398i	0.800377	−	0.599497i	$-0.204633\pi$
$271$	11.2170	+	6.47615i	0.681386	+	0.393398i	−0.118991	+	0.992895i	$0.537966\pi$
$272$		0			0
$273$	−3.66392	+	17.3241i	−0.221750	+	1.04850i
$274$		0			0
$275$	−15.3558	−	2.70765i	−0.925991	−	0.163277i
$276$		0			0
$277$	−15.4923	+	12.9996i	−0.930842	+	0.781069i	−0.975968	−	0.217912i	$-0.930075\pi$
$277$	−15.4923	+	12.9996i	−0.930842	+	0.781069i	0.0451263	+	0.998981i	$0.485631\pi$
$278$		0			0
$279$	6.58009	+	2.98024i	0.393940	+	0.178422i
$280$		0			0
$281$	−9.35867	+	25.7127i	−0.558291	+	1.53389i	0.263824	+	0.964571i	$0.415016\pi$
$281$	−9.35867	+	25.7127i	−0.558291	+	1.53389i	−0.822115	+	0.569322i	$0.807206\pi$
$282$		0			0
$283$	−21.6032	−	3.80923i	−1.28418	−	0.226435i	−0.510426	−	0.859922i	$-0.670512\pi$
$283$	−21.6032	−	3.80923i	−1.28418	−	0.226435i	−0.773754	+	0.633486i	$0.781623\pi$
$284$		0			0
$285$	−1.95611	−	8.59825i	−0.115870	−	0.509317i
$286$		0			0
$287$	−9.75935	+	14.0637i	−0.576076	+	0.830151i
$288$		0			0
$289$	20.2758			1.19270
$290$		0			0
$291$	−20.9285	+	1.02969i	−1.22685	+	0.0603618i
$292$		0			0
$293$	2.68082	−	15.2037i	0.156615	−	0.888209i	−0.800679	−	0.599094i	$-0.795528\pi$
$293$	2.68082	−	15.2037i	0.156615	−	0.888209i	0.957294	−	0.289116i	$-0.0933612\pi$
$294$		0			0
$295$	−0.624181	+	0.523750i	−0.0363412	+	0.0304939i
$296$		0			0
$297$	19.0643	+	3.89596i	1.10622	+	0.226067i
$298$		0			0
$299$	−1.07690	−	6.10740i	−0.0622787	−	0.353200i
$300$		0			0
$301$	5.51370	−	20.9301i	0.317804	−	1.20639i
$302$		0			0
$303$	−4.57588	−	2.35000i	−0.262877	−	0.135004i
$304$		0			0
$305$	9.75870	+	5.63419i	0.558781	+	0.322613i
$306$		0			0
$307$	−22.4632	−	12.9691i	−1.28204	−	0.740187i	−0.304820	−	0.952410i	$-0.598596\pi$
$307$	−22.4632	−	12.9691i	−1.28204	−	0.740187i	−0.977221	+	0.212223i	$0.931930\pi$
$308$		0			0
$309$	3.49860	+	15.3784i	0.199028	+	0.874844i
$310$		0			0
$311$	−0.161417	+	0.915442i	−0.00915313	+	0.0519100i	−0.989042	−	0.147633i	$-0.952835\pi$
$311$	−0.161417	+	0.915442i	−0.00915313	+	0.0519100i	0.979889	+	0.199543i	$0.0639457\pi$
$312$		0			0
$313$	3.09257	+	3.68558i	0.174802	+	0.208321i	0.846331	−	0.532657i	$-0.178807\pi$
$313$	3.09257	+	3.68558i	0.174802	+	0.208321i	−0.671529	+	0.740978i	$0.734362\pi$
$314$		0			0
$315$	−5.48791	+	4.74960i	−0.309209	+	0.267610i
$316$		0			0
$317$	4.48170	−	12.3134i	0.251718	−	0.691588i	−0.747897	−	0.663815i	$-0.768936\pi$
$317$	4.48170	−	12.3134i	0.251718	−	0.691588i	0.999614	−	0.0277732i	$-0.00884162\pi$
$318$		0			0
$319$	−18.8239	−	15.7952i	−1.05394	−	0.884360i
$320$		0			0
$321$	−3.12975	+	24.8328i	−0.174686	+	1.38603i
$322$		0			0
$323$		−	33.9927i		−	1.89140i
$324$		0			0
$325$	−13.9338	+	8.04471i	−0.772910	+	0.446240i
$326$		0			0
$327$	−9.44810	+	12.4550i	−0.522481	+	0.688761i
$328$		0			0
$329$	3.09780	−	11.7593i	0.170787	−	0.648311i
$330$		0			0
$331$	17.2491	+	6.27817i	0.948098	+	0.345079i	0.769359	−	0.638817i	$-0.220576\pi$
$331$	17.2491	+	6.27817i	0.948098	+	0.345079i	0.178739	+	0.983896i	$0.442798\pi$
$332$		0			0
$333$	−7.07919	−	1.81323i	−0.387937	−	0.0993641i
$334$		0			0
$335$	11.1999	+	4.07643i	0.611916	+	0.222719i
$336$		0			0
$337$	−19.7150	−	16.5428i	−1.07394	−	0.901145i	−0.0785390	−	0.996911i	$-0.525026\pi$
$337$	−19.7150	−	16.5428i	−1.07394	−	0.901145i	−0.995404	+	0.0957659i	$0.969470\pi$
$338$		0			0
$339$	14.2968	−	13.2467i	0.776496	−	0.719464i
$340$		0			0
$341$	4.50840	+	7.80878i	0.244144	+	0.422869i
$342$		0			0
$343$	5.01933	+	17.8271i	0.271018	+	0.962574i
$344$		0			0
$345$	1.16124	−	2.26115i	0.0625189	−	0.121736i
$346$		0			0
$347$	−6.60870	−	18.1573i	−0.354774	−	0.974733i	−0.980815	−	0.194942i	$-0.937548\pi$
$347$	−6.60870	−	18.1573i	−0.354774	−	0.974733i	0.626041	−	0.779790i	$-0.284674\pi$
$348$		0			0
$349$	−5.91691	−	7.05150i	−0.316725	−	0.377458i	0.584070	−	0.811704i	$-0.301459\pi$
$349$	−5.91691	−	7.05150i	−0.316725	−	0.377458i	−0.900795	+	0.434245i	$0.857015\pi$
$350$		0			0
$351$	17.6534	−	9.56512i	0.942268	−	0.510548i
$352$		0			0
$353$	−24.3476	−	8.86179i	−1.29589	−	0.471666i	−0.400234	−	0.916413i	$-0.631071\pi$
$353$	−24.3476	−	8.86179i	−1.29589	−	0.471666i	−0.895656	+	0.444747i	$0.853293\pi$
$354$		0			0
$355$	−7.53649	+	8.98164i	−0.399995	+	0.476696i
$356$		0			0
$357$	−24.6901	+	13.1602i	−1.30674	+	0.696513i
$358$		0			0
$359$			21.7705i			1.14901i	0.818503	+	0.574503i	$0.194805\pi$
$359$			21.7705i			1.14901i	−0.818503	+	0.574503i	$0.805195\pi$
$360$		0			0
$361$	−11.9987			−0.631511
$362$		0			0
$363$	3.55894	+	3.84106i	0.186796	+	0.201603i
$364$		0			0
$365$	2.85518	−	3.40267i	0.149447	−	0.178104i
$366$		0			0
$367$	−15.3983	+	2.71514i	−0.803787	+	0.141729i	−0.560424	−	0.828206i	$-0.689362\pi$
$367$	−15.3983	+	2.71514i	−0.803787	+	0.141729i	−0.243363	+	0.969935i	$0.578251\pi$
$368$		0			0
$369$	19.3164	−	1.90537i	1.00557	−	0.0991896i
$370$		0			0
$371$	17.4951	+	24.7626i	0.908299	+	1.28561i
$372$		0			0
$373$	−4.12582	+	23.3987i	−0.213627	+	1.21154i	0.669647	+	0.742680i	$0.266446\pi$
$373$	−4.12582	+	23.3987i	−0.213627	+	1.21154i	−0.883273	+	0.468858i	$0.844666\pi$
$374$		0			0
$375$	−14.3997	−	1.81484i	−0.743597	−	0.0937178i
$376$		0			0
$377$	−25.3557			−1.30588
$378$		0			0
$379$	−2.22199			−0.114136			−0.0570680	−	0.998370i	$-0.518175\pi$
$379$	−2.22199			−0.114136			−0.0570680	+	0.998370i	$0.518175\pi$
$380$		0			0
$381$	−3.69078	+	4.86537i	−0.189084	+	0.249260i
$382$		0			0
$383$	−3.59378	+	20.3814i	−0.183634	+	1.04144i	0.744065	+	0.668108i	$0.232895\pi$
$383$	−3.59378	+	20.3814i	−0.183634	+	1.04144i	−0.927698	+	0.373331i	$0.878216\pi$
$384$		0			0
$385$	−9.02171	+	0.827648i	−0.459789	+	0.0421809i
$386$		0			0
$387$	−22.1267	+	10.6172i	−1.12476	+	0.539704i
$388$		0			0
$389$	−28.8767	+	5.09173i	−1.46410	+	0.258161i	−0.848207	−	0.529665i	$-0.822318\pi$
$389$	−28.8767	+	5.09173i	−1.46410	+	0.258161i	−0.615898	+	0.787826i	$0.711207\pi$
$390$		0			0
$391$	6.29859	−	7.50637i	0.318533	−	0.379613i
$392$		0			0
$393$	5.92687	−	19.1664i	0.298971	−	0.966817i
$394$		0			0
$395$	5.15564			0.259408
$396$		0			0
$397$			31.8885i			1.60044i	0.599707	+	0.800220i	$0.295284\pi$
$397$			31.8885i			1.60044i	−0.599707	+	0.800220i	$0.704716\pi$
$398$		0			0
$399$	12.0011	+	22.5155i	0.600807	+	1.12718i
$400$		0			0
$401$	6.72607	−	8.01582i	0.335884	−	0.400291i	−0.571494	−	0.820606i	$-0.693636\pi$
$401$	6.72607	−	8.01582i	0.335884	−	0.400291i	0.907378	+	0.420315i	$0.138080\pi$
$402$		0			0
$403$	8.74293	+	3.18216i	0.435516	+	0.158515i
$404$		0			0
$405$	8.13418	+	1.24952i	0.404190	+	0.0620892i
$406$		0			0
$407$	−5.86343	−	6.98777i	−0.290640	−	0.346371i
$408$		0			0
$409$	0.336606	+	0.924817i	0.0166441	+	0.0457293i	0.947736	−	0.319054i	$-0.103365\pi$
$409$	0.336606	+	0.924817i	0.0166441	+	0.0457293i	−0.931092	+	0.364784i	$0.881143\pi$
$410$		0			0
$411$	8.04566	−	0.395851i	0.396863	−	0.0195259i
$412$		0			0
$413$	1.34411	−	1.93692i	0.0661392	−	0.0953094i
$414$		0			0
$415$	−3.73902	−	6.47617i	−0.183541	−	0.317903i
$416$		0			0
$417$	8.07432	+	35.4913i	0.395401	+	1.73802i
$418$		0			0
$419$	10.6223	+	8.91314i	0.518931	+	0.435435i	0.864259	−	0.503047i	$-0.167788\pi$
$419$	10.6223	+	8.91314i	0.518931	+	0.435435i	−0.345328	+	0.938482i	$0.612232\pi$
$420$		0			0
$421$	6.03019	+	2.19481i	0.293893	+	0.106968i	0.484759	−	0.874648i	$-0.338907\pi$
$421$	6.03019	+	2.19481i	0.293893	+	0.106968i	−0.190866	+	0.981616i	$0.561130\pi$
$422$		0			0
$423$	−12.4316	+	5.96515i	−0.604446	+	0.290036i
$424$		0			0
$425$	−23.8890	−	8.69487i	−1.15878	−	0.421763i
$426$		0			0
$427$	−31.5286	−	8.30573i	−1.52578	−	0.401942i
$428$		0			0
$429$	24.8660	+	3.13393i	1.20054	+	0.151308i
$430$		0			0
$431$	8.73432	−	5.04276i	0.420717	−	0.242901i	−0.274667	−	0.961539i	$-0.588568\pi$
$431$	8.73432	−	5.04276i	0.420717	−	0.242901i	0.695384	+	0.718638i	$0.255234\pi$
$432$		0			0
$433$			15.6232i			0.750805i	0.926862	+	0.375403i	$0.122496\pi$
$433$			15.6232i			0.750805i	−0.926862	+	0.375403i	$0.877504\pi$
$434$		0			0
$435$	−8.27994	−	6.28101i	−0.396993	−	0.301151i
$436$		0			0
$437$	−6.84523	−	5.74383i	−0.327452	−	0.274765i
$438$		0			0
$439$	−9.20653	+	25.2947i	−0.439404	+	1.20725i	0.500477	+	0.865750i	$0.333158\pi$
$439$	−9.20653	+	25.2947i	−0.439404	+	1.20725i	−0.939881	+	0.341502i	$0.889064\pi$
$440$		0			0
$441$	11.7076	−	17.4337i	0.557504	−	0.830175i
$442$		0			0
$443$	21.9759	+	26.1899i	1.04411	+	1.24432i	0.968978	+	0.247146i	$0.0794927\pi$
$443$	21.9759	+	26.1899i	1.04411	+	1.24432i	0.0751299	+	0.997174i	$0.476063\pi$
$444$		0			0
$445$	−0.648878	+	3.67997i	−0.0307597	+	0.174447i
$446$		0			0
$447$	−17.0429	+	15.7911i	−0.806101	+	0.746895i
$448$		0			0
$449$	21.9379	+	12.6659i	1.03531	+	0.597739i	0.918502	−	0.395415i	$-0.129399\pi$
$449$	21.9379	+	12.6659i	1.03531	+	0.597739i	0.116812	+	0.993154i	$0.462733\pi$
$450$		0			0
$451$	20.9828	+	12.1144i	0.988040	+	0.570445i
$452$		0			0
$453$	15.2257	−	9.81857i	0.715365	−	0.461316i
$454$		0			0
$455$	−6.58223	+	6.63798i	−0.308580	+	0.311193i
$456$		0			0
$457$	−5.22960	−	29.6585i	−0.244630	−	1.38737i	−0.821350	−	0.570425i	$-0.806779\pi$
$457$	−5.22960	−	29.6585i	−0.244630	−	1.38737i	0.576720	−	0.816942i	$-0.304333\pi$
$458$		0			0
$459$	29.5070	+	11.6528i	1.37727	+	0.543905i
$460$		0			0
$461$	16.9479	−	14.2210i	0.789344	−	0.662338i	−0.156239	−	0.987719i	$-0.549937\pi$
$461$	16.9479	−	14.2210i	0.789344	−	0.662338i	0.945583	+	0.325381i	$0.105493\pi$
$462$		0			0
$463$	−6.48204	+	36.7614i	−0.301246	+	1.70845i	0.339425	+	0.940633i	$0.389768\pi$
$463$	−6.48204	+	36.7614i	−0.301246	+	1.70845i	−0.640670	+	0.767816i	$0.721343\pi$
$464$		0			0
$465$	2.06674	+	3.20490i	0.0958429	+	0.148624i
$466$		0			0
$467$	−17.6269			−0.815678			−0.407839	−	0.913054i	$-0.633717\pi$
$467$	−17.6269			−0.815678			−0.407839	+	0.913054i	$0.633717\pi$
$468$		0			0
$469$	−34.3671	−	2.86074i	−1.58692	−	0.132097i
$470$		0			0
$471$	−32.8812	−	10.1679i	−1.51508	−	0.468513i
$472$		0			0
$473$	−30.1694	−	5.31968i	−1.38719	−	0.244599i
$474$		0			0
$475$	−7.92905	+	21.7849i	−0.363810	+	0.999559i
$476$		0			0
$477$	8.53027	−	33.3039i	0.390574	−	1.52488i
$478$		0			0
$479$	19.9841	−	16.7687i	0.913098	−	0.766180i	−0.0596077	−	0.998222i	$-0.518985\pi$
$479$	19.9841	−	16.7687i	0.913098	−	0.766180i	0.972706	+	0.232042i	$0.0745405\pi$
$480$		0			0
$481$	−9.26946	−	1.63446i	−0.422651	−	0.0745248i
$482$		0			0
$483$	−1.52183	+	7.19565i	−0.0692455	+	0.327413i
$484$		0			0
$485$	−9.58008	−	5.53106i	−0.435009	−	0.251153i
$486$		0			0
$487$	1.88377	+	3.26279i	0.0853619	+	0.147851i	0.905545	−	0.424249i	$-0.139462\pi$
$487$	1.88377	+	3.26279i	0.0853619	+	0.147851i	−0.820183	+	0.572101i	$0.806129\pi$
$488$		0			0
$489$	24.1014	+	3.03758i	1.08990	+	0.137364i
$490$		0			0
$491$	−10.2584	−	28.1847i	−0.462955	−	1.27196i	−0.923253	−	0.384193i	$-0.874480\pi$
$491$	−10.2584	−	28.1847i	−0.462955	−	1.27196i	0.460298	−	0.887764i	$-0.347743\pi$
$492$		0			0
$493$	−25.7522	−	30.6902i	−1.15982	−	1.38222i
$494$		0			0
$495$	7.34369	+	7.18309i	0.330074	+	0.322856i
$496$		0			0
$497$	14.2074	−	30.8063i	0.637288	−	1.38185i
$498$		0			0
$499$	17.4946	−	6.36751i	0.783166	−	0.285049i	0.0806736	−	0.996741i	$-0.474293\pi$
$499$	17.4946	−	6.36751i	0.783166	−	0.285049i	0.702492	+	0.711692i	$0.252071\pi$
$500$		0			0
$501$	−2.66555	−	2.87685i	−0.119088	−	0.128528i
$502$		0			0
$503$	21.0298	−	36.4246i	0.937670	−	1.62409i	0.167869	−	0.985809i	$-0.446311\pi$
$503$	21.0298	−	36.4246i	0.937670	−	1.62409i	0.769801	−	0.638284i	$-0.220355\pi$
$504$		0			0
$505$	−1.35784	−	2.35185i	−0.0604232	−	0.104656i
$506$		0			0
$507$	2.81063	−	1.81249i	0.124825	−	0.0804955i
$508$		0			0
$509$	−18.7068	−	15.6968i	−0.829162	−	0.695750i	0.125936	−	0.992038i	$-0.459807\pi$
$509$	−18.7068	−	15.6968i	−0.829162	−	0.695750i	−0.955098	+	0.296289i	$0.904251\pi$
$510$		0			0
$511$	−5.38243	+	11.6709i	−0.238105	+	0.516291i
$512$		0			0
$513$	10.6264	−	26.9081i	0.469168	−	1.18802i
$514$		0			0
$515$	−2.84770	+	7.82399i	−0.125485	+	0.344766i
$516$		0			0
$517$	−16.9503	−	2.98880i	−0.745474	−	0.131447i
$518$		0			0
$519$	−39.0913	−	20.0758i	−1.71592	−	0.881229i
$520$		0			0
$521$	8.33631	−	14.4389i	0.365220	−	0.632580i	−0.623591	−	0.781751i	$-0.714327\pi$
$521$	8.33631	−	14.4389i	0.365220	−	0.632580i	0.988812	+	0.149170i	$0.0476603\pi$
$522$		0			0
$523$	−8.45882	+	4.88370i	−0.369878	+	0.213549i	−0.673405	−	0.739273i	$-0.735169\pi$
$523$	−8.45882	+	4.88370i	−0.369878	+	0.213549i	0.303527	+	0.952823i	$0.401836\pi$
$524$		0			0
$525$	18.8929	−	2.67484i	0.824552	−	0.116739i
$526$		0			0
$527$	5.02798	+	13.8143i	0.219022	+	0.601759i
$528$		0			0
$529$	3.54661	+	20.1138i	0.154201	+	0.874515i
$530$		0			0
$531$	−2.66035	+	0.262417i	−0.115450	+	0.0113879i
$532$		0			0
$533$	24.6208	−	4.34131i	1.06644	−	0.188043i
$534$		0			0
$535$	−8.49357	+	10.1222i	−0.367209	+	0.437623i
$536$		0			0
$537$	−6.94527	+	2.92191i	−0.299710	+	0.126090i
$538$		0			0
$539$	24.5560	−	9.17292i	1.05770	−	0.395106i
$540$		0			0
$541$	15.0773	−	26.1147i	0.648224	−	1.12276i	−0.335322	−	0.942103i	$-0.608845\pi$
$541$	15.0773	−	26.1147i	0.648224	−	1.12276i	0.983547	−	0.180654i	$-0.0578214\pi$
$542$		0			0
$543$	−3.70305	−	2.80907i	−0.158913	−	0.120549i
$544$		0			0
$545$	−7.75541	+	2.82274i	−0.332205	+	0.120913i
$546$		0			0
$547$	−8.06550	−	45.7417i	−0.344856	−	1.95578i	−0.288970	−	0.957338i	$-0.593313\pi$
$547$	−8.06550	−	45.7417i	−0.344856	−	1.95578i	−0.0558860	−	0.998437i	$-0.517798\pi$
$548$		0			0
$549$	15.9936	+	33.3312i	0.682589	+	1.42254i
$550$		0			0
$551$	−27.9871	+	23.4840i	−1.19229	+	1.00045i
$552$		0			0
$553$	−14.3928	+	3.92166i	−0.612044	+	0.166766i
$554$		0			0
$555$	−2.62208	−	2.82993i	−0.111301	−	0.120124i
$556$		0			0
$557$		−	34.1214i		−	1.44577i	−0.690968	−	0.722886i	$-0.742815\pi$
$557$		−	34.1214i		−	1.44577i	0.690968	−	0.722886i	$-0.257185\pi$
$558$		0			0
$559$	−27.3756	+	15.8053i	−1.15787	+	0.668494i
$560$		0			0
$561$	21.4615	+	33.2804i	0.906106	+	1.40510i
$562$		0			0
$563$	−5.11849	+	1.86298i	−0.215719	+	0.0785151i	−0.447619	−	0.894224i	$-0.647728\pi$
$563$	−5.11849	+	1.86298i	−0.215719	+	0.0785151i	0.231900	+	0.972740i	$0.425506\pi$
$564$		0			0
$565$	10.1332	−	1.78676i	0.426307	−	0.0751694i
$566$		0			0
$567$	−23.6583	+	2.69907i	−0.993555	+	0.113350i
$568$		0			0
$569$	1.00282	−	0.176824i	0.0420403	−	0.00741284i	−0.152588	−	0.988290i	$-0.548761\pi$
$569$	1.00282	−	0.176824i	0.0420403	−	0.00741284i	0.194629	+	0.980877i	$0.437650\pi$
$570$		0			0
$571$	−3.36592	+	1.22509i	−0.140859	+	0.0512686i	−0.411488	−	0.911415i	$-0.634991\pi$
$571$	−3.36592	+	1.22509i	−0.140859	+	0.0512686i	0.270629	+	0.962684i	$0.412768\pi$
$572$		0			0
$573$	−15.4649	−	23.9814i	−0.646055	−	1.00184i
$574$		0			0
$575$	−5.78749	+	3.34141i	−0.241355	+	0.139346i
$576$		0			0
$577$			23.0893i			0.961218i	0.876935	+	0.480609i	$0.159584\pi$
$577$			23.0893i			0.961218i	−0.876935	+	0.480609i	$0.840416\pi$
$578$		0			0
$579$	−11.9282	−	12.8737i	−0.495719	−	0.535014i
$580$		0			0
$581$	15.3642	+	15.2352i	0.637414	+	0.632061i
$582$		0			0
$583$	32.8738	−	27.5844i	1.36149	−	1.14243i
$584$		0			0
$585$	10.5691	+	0.807044i	0.436977	+	0.0333672i
$586$		0			0
$587$	−0.0818717	−	0.464317i	−0.00337921	−	0.0191644i	0.983072	−	0.183222i	$-0.0586528\pi$
$587$	−0.0818717	−	0.464317i	−0.00337921	−	0.0191644i	−0.986451	+	0.164058i	$0.947542\pi$
$588$		0			0
$589$	12.5975	−	4.58513i	0.519073	−	0.188927i
$590$		0			0
$591$	37.1893	+	28.2111i	1.52976	+	1.16045i
$592$		0			0
$593$	19.0760	−	33.0406i	0.783357	−	1.35681i	−0.146619	−	0.989193i	$-0.546839\pi$
$593$	19.0760	−	33.0406i	0.783357	−	1.35681i	0.929976	−	0.367621i	$-0.119828\pi$
$594$		0			0
$595$	−14.7197	−	1.22528i	−0.603449	−	0.0502316i
$596$		0			0
$597$	−20.0467	+	8.43373i	−0.820456	+	0.345170i
$598$		0			0
$599$	17.1655	−	20.4570i	0.701362	−	0.835850i	−0.291318	−	0.956626i	$-0.594094\pi$
$599$	17.1655	−	20.4570i	0.701362	−	0.835850i	0.992680	+	0.120776i	$0.0385382\pi$
$600$		0			0
$601$	26.0201	−	4.58804i	1.06138	−	0.187150i	0.384412	−	0.923162i	$-0.374404\pi$
$601$	26.0201	−	4.58804i	1.06138	−	0.187150i	0.676969	+	0.736012i	$0.263293\pi$
$602$		0			0
$603$	22.7815	+	31.7817i	0.927735	+	1.29425i
$604$		0			0
$605$	0.480040	+	2.72244i	0.0195164	+	0.110683i
$606$		0			0
$607$	−2.40611	−	6.61074i	−0.0976611	−	0.268322i	0.881236	−	0.472677i	$-0.156712\pi$
$607$	−2.40611	−	6.61074i	−0.0976611	−	0.268322i	−0.978897	+	0.204356i	$0.934490\pi$
$608$		0			0
$609$	27.8924	+	11.2363i	1.13026	+	0.455316i
$610$		0			0
$611$	−15.3807	+	8.88003i	−0.622235	+	0.359248i
$612$		0			0
$613$	10.6152	−	18.3860i	0.428743	−	0.742604i	−0.568019	−	0.823015i	$-0.692290\pi$
$613$	10.6152	−	18.3860i	0.428743	−	0.742604i	0.996762	+	0.0804113i	$0.0256234\pi$
$614$		0			0
$615$	9.11537	+	4.68130i	0.367567	+	0.188768i
$616$		0			0
$617$	−16.1973	−	2.85602i	−0.652079	−	0.114979i	−0.162184	−	0.986761i	$-0.551854\pi$
$617$	−16.1973	−	2.85602i	−0.652079	−	0.114979i	−0.489895	+	0.871782i	$0.662965\pi$
$618$		0			0
$619$	9.90984	−	27.2271i	0.398310	−	1.09435i	−0.564797	−	0.825230i	$-0.691045\pi$
$619$	9.90984	−	27.2271i	0.398310	−	1.09435i	0.963107	−	0.269118i	$-0.0867323\pi$
$620$		0			0
$621$	7.33242	−	3.97292i	0.294240	−	0.159428i
$622$		0			0
$623$	−0.987741	−	10.7668i	−0.0395730	−	0.431362i
$624$		0			0
$625$	10.0790	+	8.45731i	0.403161	+	0.338292i
$626$		0			0
$627$	30.3492	−	19.5712i	1.21203	−	0.781600i
$628$		0			0
$629$	−7.43608	−	12.8797i	−0.296496	−	0.513546i
$630$		0			0
$631$	−7.51188	+	13.0110i	−0.299043	+	0.517958i	−0.975917	−	0.218141i	$-0.930001\pi$
$631$	−7.51188	+	13.0110i	−0.299043	+	0.517958i	0.676874	+	0.736099i	$0.263334\pi$
$632$		0			0
$633$	5.81238	+	6.27313i	0.231021	+	0.249334i
$634$		0			0
$635$	−3.02955	+	1.10267i	−0.120224	+	0.0437580i
$636$		0			0
$637$	13.3261	−	23.5378i	0.528000	−	0.932601i
$638$		0			0
$639$	−37.0438	+	10.3661i	−1.46543	+	0.410078i
$640$		0			0
$641$	5.13002	+	6.11372i	0.202624	+	0.241478i	0.857781	−	0.514015i	$-0.171842\pi$
$641$	5.13002	+	6.11372i	0.202624	+	0.241478i	−0.655158	+	0.755492i	$0.727398\pi$
$642$		0			0
$643$	−10.8529	−	29.8181i	−0.427996	−	1.17591i	−0.947027	−	0.321154i	$-0.895929\pi$
$643$	−10.8529	−	29.8181i	−0.427996	−	1.17591i	0.519031	−	0.854756i	$-0.326293\pi$
$644$		0			0
$645$	−12.8548	−	1.62013i	−0.506157	−	0.0637925i
$646$		0			0
$647$	−0.285978	−	0.495329i	−0.0112430	−	0.0194734i	0.860349	−	0.509705i	$-0.170245\pi$
$647$	−0.285978	−	0.495329i	−0.0112430	−	0.0194734i	−0.871592	+	0.490232i	$0.836912\pi$
$648$		0			0
$649$	−2.88985	−	1.66846i	−0.113437	−	0.0654926i
$650$		0			0
$651$	−8.20747	−	7.37492i	−0.321676	−	0.289046i
$652$		0			0
$653$	40.4916	+	7.13976i	1.58456	+	0.279400i	0.895417	−	0.445228i	$-0.146877\pi$
$653$	40.4916	+	7.13976i	1.58456	+	0.279400i	0.689140	+	0.724628i	$0.257988\pi$
$654$		0			0
$655$	8.11335	−	6.80791i	0.317015	−	0.266007i
$656$		0			0
$657$	14.0340	−	3.92718i	0.547518	−	0.153214i
$658$		0			0
$659$	−4.33314	+	11.9052i	−0.168795	+	0.463761i	−0.995031	−	0.0995628i	$-0.968256\pi$
$659$	−4.33314	+	11.9052i	−0.168795	+	0.463761i	0.826236	+	0.563324i	$0.190478\pi$
$660$		0			0
$661$	8.08600	+	1.42578i	0.314509	+	0.0554564i	0.328674	−	0.944443i	$-0.393398\pi$
$661$	8.08600	+	1.42578i	0.314509	+	0.0554564i	−0.0141656	+	0.999900i	$0.504509\pi$
$662$		0			0
$663$	39.0379	+	12.0718i	1.51610	+	0.468828i
$664$		0			0
$665$	−1.11736	+	13.4232i	−0.0433294	+	0.520530i
$666$		0			0
$667$	−10.5316			−0.407786
$668$		0			0
$669$	12.2625	+	19.0155i	0.474097	+	0.735183i
$670$		0			0
$671$	−8.01346	+	45.4466i	−0.309356	+	1.75445i
$672$		0			0
$673$	−33.8139	+	28.3732i	−1.30343	+	1.09371i	−0.313889	+	0.949460i	$0.601632\pi$
$673$	−33.8139	+	28.3732i	−1.30343	+	1.09371i	−0.989542	+	0.144248i	$0.953924\pi$
$674$		0			0
$675$	−16.1920	−	14.3506i	−0.623231	−	0.552356i
$676$		0			0
$677$	−3.91905	−	22.2260i	−0.150621	−	0.854216i	−0.962680	−	0.270641i	$-0.912764\pi$
$677$	−3.91905	−	22.2260i	−0.150621	−	0.854216i	0.812059	−	0.583575i	$-0.198347\pi$
$678$		0			0
$679$	30.9515	+	8.15370i	1.18781	+	0.312910i
$680$		0			0
$681$	−22.3035	+	14.3828i	−0.854671	+	0.551151i
$682$		0			0
$683$	10.1811	+	5.87807i	0.389569	+	0.224918i	0.681974	−	0.731377i	$-0.261122\pi$
$683$	10.1811	+	5.87807i	0.389569	+	0.224918i	−0.292404	+	0.956295i	$0.594455\pi$
$684$		0			0
$685$	3.68292	+	2.12634i	0.140717	+	0.0812431i
$686$		0			0
$687$	−11.8054	+	10.9383i	−0.450403	+	0.417321i
$688$		0			0
$689$	7.68925	−	43.6079i	0.292937	−	1.66133i
$690$		0			0
$691$	11.6847	+	13.9253i	0.444506	+	0.529742i	0.941049	−	0.338270i	$-0.109842\pi$
$691$	11.6847	+	13.9253i	0.444506	+	0.529742i	−0.496543	+	0.868012i	$0.665397\pi$
$692$		0			0
$693$	−25.9649	−	14.4667i	−0.986326	−	0.549545i
$694$		0			0
$695$	−6.57213	+	18.0568i	−0.249295	+	0.684933i
$696$		0			0
$697$	30.2605	+	25.3915i	1.14620	+	0.961773i
$698$		0			0
$699$	12.9603	+	9.83142i	0.490202	+	0.371859i
$700$		0			0
$701$			10.7142i			0.404669i	0.979317	+	0.202334i	$0.0648527\pi$
$701$			10.7142i			0.404669i	−0.979317	+	0.202334i	$0.935147\pi$
$702$		0			0
$703$	−11.7453	+	6.78113i	−0.442981	+	0.255755i
$704$		0			0
$705$	−7.22231	−	0.910250i	−0.272008	−	0.0342820i
$706$		0			0
$707$	5.57958	+	5.53272i	0.209842	+	0.208079i
$708$		0			0
$709$	−6.72909	−	2.44919i	−0.252716	−	0.0919812i	0.212556	−	0.977149i	$-0.431821\pi$
$709$	−6.72909	−	2.44919i	−0.252716	−	0.0919812i	−0.465272	+	0.885168i	$0.654043\pi$
$710$		0			0
$711$	13.9622	+	9.54819i	0.523625	+	0.358085i
$712$		0			0
$713$	3.63142	+	1.32173i	0.135998	+	0.0494991i
$714$		0			0
$715$	10.1358	+	8.50491i	0.379056	+	0.318066i
$716$		0			0
$717$	−3.35279	−	14.7374i	−0.125212	−	0.550380i
$718$		0			0
$719$	6.42531	+	11.1290i	0.239624	+	0.415040i	0.960606	−	0.277913i	$-0.0896426\pi$
$719$	6.42531	+	11.1290i	0.239624	+	0.415040i	−0.720983	+	0.692953i	$0.756309\pi$
$720$		0			0
$721$	1.99845	−	24.0080i	0.0744261	−	0.894106i
$722$		0			0
$723$	−9.77256	+	0.480815i	−0.363445	+	0.0178817i
$724$		0			0
$725$	9.34506	+	25.6753i	0.347067	+	0.953558i
$726$		0			0
$727$	25.2662	+	30.1111i	0.937071	+	1.11676i	0.992975	+	0.118322i	$0.0377514\pi$
$727$	25.2662	+	30.1111i	0.937071	+	1.11676i	−0.0559043	+	0.998436i	$0.517804\pi$
$728$		0			0
$729$	19.7145	+	18.4483i	0.730166	+	0.683270i
$730$		0			0
$731$	−46.9343	−	17.0827i	−1.73593	−	0.631827i
$732$		0			0
$733$	4.42383	−	5.27212i	0.163398	−	0.194730i	−0.678133	−	0.734939i	$-0.737211\pi$
$733$	4.42383	−	5.27212i	0.163398	−	0.194730i	0.841531	+	0.540209i	$0.181655\pi$
$734$		0			0
$735$	10.1824	−	4.38521i	0.375582	−	0.161751i
$736$		0			0
$737$			48.8109i			1.79797i
$738$		0			0
$739$	16.2662			0.598360			0.299180	−	0.954197i	$-0.403287\pi$
$739$	16.2662			0.598360			0.299180	+	0.954197i	$0.403287\pi$
$740$		0			0
$741$	11.0085	−	35.5995i	0.404408	−	1.30778i
$742$		0			0
$743$	−4.66918	+	5.56451i	−0.171296	+	0.204142i	−0.844862	−	0.534985i	$-0.820317\pi$
$743$	−4.66918	+	5.56451i	−0.171296	+	0.204142i	0.673566	+	0.739127i	$0.264762\pi$
$744$		0			0
$745$	−12.0796	+	2.12995i	−0.442561	+	0.0780354i
$746$		0			0
$747$	1.86798	−	24.4631i	0.0683456	−	0.895057i
$748$		0			0
$749$	16.0116	−	34.7185i	0.585051	−	1.26859i
$750$		0			0
$751$	5.09362	−	28.8874i	0.185869	−	1.05411i	−0.738965	−	0.673744i	$-0.764685\pi$
$751$	5.09362	−	28.8874i	0.185869	−	1.05411i	0.924834	−	0.380371i	$-0.124204\pi$
$752$		0			0
$753$	−1.24212	+	1.63743i	−0.0452654	+	0.0596711i
$754$		0			0
$755$	9.56447			0.348087
$756$		0			0
$757$	20.1619			0.732796			0.366398	−	0.930458i	$-0.380591\pi$
$757$	20.1619			0.732796			0.366398	+	0.930458i	$0.380591\pi$
$758$		0			0
$759$	10.3282	+	1.30169i	0.374890	+	0.0472485i
$760$		0			0
$761$	7.77530	−	44.0959i	0.281855	−	1.59848i	−0.434455	−	0.900694i	$-0.643059\pi$
$761$	7.77530	−	44.0959i	0.281855	−	1.59848i	0.716309	−	0.697783i	$-0.245830\pi$
$762$		0			0
$763$	19.5033	−	13.7793i	0.706068	−	0.498845i
$764$		0			0
$765$	9.75751	+	13.6124i	0.352783	+	0.492156i
$766$		0			0
$767$	−3.39090	+	0.597907i	−0.122438	+	0.0215892i
$768$		0			0
$769$	−7.23057	+	8.61705i	−0.260741	+	0.310739i	−0.880493	−	0.474058i	$-0.842789\pi$
$769$	−7.23057	+	8.61705i	−0.260741	+	0.310739i	0.619752	+	0.784797i	$0.287233\pi$
$770$		0			0
$771$	14.2524	+	15.3822i	0.513287	+	0.553976i
$772$		0			0
$773$	20.3371			0.731475			0.365737	−	0.930718i	$-0.380817\pi$
$773$	20.3371			0.731475			0.365737	+	0.930718i	$0.380817\pi$
$774$		0			0
$775$		−	10.0260i		−	0.360143i
$776$		0			0
$777$	9.47254	+	5.90570i	0.339826	+	0.211866i
$778$		0			0
$779$	23.1551	−	27.5952i	0.829619	−	0.988701i
$780$		0			0
$781$	−45.1207	−	16.4226i	−1.61455	−	0.587647i
$782$		0			0
$783$	−10.7910	−	32.3443i	−0.385637	−	1.15589i
$784$		0			0
$785$	−11.6794	−	13.9190i	−0.416856	−	0.496789i
$786$		0			0
$787$	−7.59217	−	20.8593i	−0.270631	−	0.743554i	−0.998336	−	0.0576632i	$-0.981635\pi$
$787$	−7.59217	−	20.8593i	−0.270631	−	0.743554i	0.727705	−	0.685891i	$-0.240587\pi$
$788$		0			0
$789$	1.13493	−	2.20993i	0.0404047	−	0.0786754i
$790$		0			0
$791$	−26.9293	+	12.6959i	−0.957497	+	0.451414i
$792$		0			0
$793$	23.8088	+	41.2381i	0.845477	+	1.46441i
$794$		0			0
$795$	13.3133	−	12.3355i	0.472175	−	0.437495i
$796$		0			0
$797$	2.21466	+	1.85832i	0.0784473	+	0.0658251i	0.681168	−	0.732127i	$-0.261472\pi$
$797$	2.21466	+	1.85832i	0.0784473	+	0.0658251i	−0.602721	+	0.797952i	$0.705917\pi$
$798$		0			0
$799$	−26.3695	−	9.59770i	−0.932885	−	0.339542i
$800$		0			0
$801$	−8.57252	+	8.76419i	−0.302895	+	0.309667i
$802$		0			0
$803$	17.0939	+	6.22166i	0.603230	+	0.219558i
$804$		0			0
$805$	−2.73396	+	2.75712i	−0.0963595	+	0.0971757i
$806$		0			0
$807$	−10.9292	+	14.4074i	−0.384725	+	0.507164i
$808$		0			0
$809$	−13.6590	+	7.88602i	−0.480224	+	0.277258i	−0.720510	−	0.693445i	$-0.756092\pi$
$809$	−13.6590	+	7.88602i	−0.480224	+	0.277258i	0.240286	+	0.970702i	$0.422759\pi$
$810$		0			0
$811$			14.4836i			0.508589i	0.967127	+	0.254294i	$0.0818432\pi$
$811$			14.4836i			0.508589i	−0.967127	+	0.254294i	$0.918157\pi$
$812$		0			0
$813$	−2.80524	+	22.2580i	−0.0983841	+	0.780621i
$814$		0			0
$815$	9.82412	+	8.24342i	0.344124	+	0.288754i
$816$		0			0
$817$	−15.5781	+	42.8005i	−0.545009	+	1.49740i
$818$		0			0
$819$	−30.1191	+	5.78643i	−1.05245	+	0.202194i
$820$		0			0
$821$	21.7942	+	25.9733i	0.760623	+	0.906475i	0.997887	−	0.0649703i	$-0.0206953\pi$
$821$	21.7942	+	25.9733i	0.760623	+	0.906475i	−0.237265	+	0.971445i	$0.576251\pi$
$822$		0			0
$823$	−1.58964	+	9.01531i	−0.0554115	+	0.314254i	−0.999898	−	0.0142966i	$-0.995449\pi$
$823$	−1.58964	+	9.01531i	−0.0554115	+	0.314254i	0.944486	+	0.328551i	$0.106560\pi$
$824$		0			0
$825$	−5.99113	−	26.3345i	−0.208584	−	0.916849i
$826$		0			0
$827$	−10.4030	−	6.00615i	−0.361746	−	0.208854i	0.308100	−	0.951354i	$-0.400307\pi$
$827$	−10.4030	−	6.00615i	−0.361746	−	0.208854i	−0.669846	+	0.742500i	$0.733640\pi$
$828$		0			0
$829$	0.0480247	+	0.0277270i	0.00166797	+	0.000963000i	0.500834	−	0.865544i	$-0.333027\pi$
$829$	0.0480247	+	0.0277270i	0.00166797	+	0.000963000i	−0.499166	+	0.866507i	$0.666360\pi$
$830$		0			0
$831$	−31.1597	−	16.0024i	−1.08092	−	0.555117i
$832$		0			0
$833$	42.0244	−	7.77605i	1.45606	−	0.269424i
$834$		0			0
$835$	−0.359537	−	2.03904i	−0.0124423	−	0.0705638i
$836$		0			0
$837$	−0.338398	+	12.5069i	−0.0116967	+	0.432303i
$838$		0			0
$839$	35.6042	−	29.8755i	1.22919	−	1.03142i	0.230903	−	0.972977i	$-0.425832\pi$
$839$	35.6042	−	29.8755i	1.22919	−	1.03142i	0.998291	−	0.0584391i	$-0.0186123\pi$
$840$		0			0
$841$	−2.44135	+	13.8456i	−0.0841843	+	0.477433i
$842$		0			0
$843$	−47.3367	+	2.32899i	−1.63036	+	0.0802147i
$844$		0			0
$845$	1.76558			0.0607380
$846$		0			0
$847$	−3.41094	−	7.23498i	−0.117201	−	0.248597i
$848$		0			0
$849$	−8.42857	−	37.0485i	−0.289268	−	1.27150i
$850$		0			0
$851$	−3.85012	−	0.678880i	−0.131980	−	0.0232717i
$852$		0			0
$853$	−13.7813	+	37.8638i	−0.471862	+	1.29643i	0.444391	+	0.895833i	$0.353420\pi$
$853$	−13.7813	+	37.8638i	−0.471862	+	1.29643i	−0.916254	+	0.400599i	$0.868802\pi$
$854$		0			0
$855$	12.4134	−	8.89809i	0.424530	−	0.304308i
$856$		0			0
$857$	43.2434	−	36.2855i	1.47717	−	1.23949i	0.568021	−	0.823014i	$-0.307709\pi$
$857$	43.2434	−	36.2855i	1.47717	−	1.23949i	0.909147	−	0.416476i	$-0.136735\pi$
$858$		0			0
$859$	9.52329	+	1.67921i	0.324930	+	0.0572940i	0.333734	−	0.942667i	$-0.391691\pi$
$859$	9.52329	+	1.67921i	0.324930	+	0.0572940i	−0.00880372	+	0.999961i	$0.502802\pi$
$860$		0			0
$861$	−29.0079	−	6.13495i	−0.988585	−	0.209079i
$862$		0			0
$863$	7.71069	+	4.45177i	0.262475	+	0.151540i	0.625463	−	0.780254i	$-0.284910\pi$
$863$	7.71069	+	4.45177i	0.262475	+	0.151540i	−0.362988	+	0.931794i	$0.618243\pi$
$864$		0			0
$865$	−11.5999	−	20.0916i	−0.394409	−	0.683136i
$866$		0			0
$867$	13.6185	+	32.3707i	0.462509	+	1.09937i
$868$		0			0
$869$	7.22142	+	19.8407i	0.244970	+	0.673049i
$870$		0			0
$871$	32.3745	+	38.5824i	1.09697	+	1.30732i
$872$		0			0
$873$	−15.7008	−	32.7211i	−0.531392	−	1.10744i
$874$		0			0
$875$	20.1321	+	9.28459i	0.680589	+	0.313876i
$876$		0			0
$877$	−21.3509	+	7.77111i	−0.720970	+	0.262412i	−0.676337	−	0.736592i	$-0.736434\pi$
$877$	−21.3509	+	7.77111i	−0.720970	+	0.262412i	−0.0446324	+	0.999003i	$0.514212\pi$
$878$		0			0
$879$	26.0736	−	5.93177i	0.879440	−	0.200074i
$880$		0			0
$881$	−20.5916	+	35.6656i	−0.693748	+	1.20161i	0.276854	+	0.960912i	$0.410708\pi$
$881$	−20.5916	+	35.6656i	−0.693748	+	1.20161i	−0.970601	+	0.240694i	$0.922625\pi$
$882$		0			0
$883$	−22.4947	−	38.9620i	−0.757008	−	1.31118i	−0.944370	−	0.328886i	$-0.893327\pi$
$883$	−22.4947	−	38.9620i	−0.757008	−	1.31118i	0.187361	−	0.982291i	$-0.440006\pi$
$884$		0			0
$885$	−1.25541	−	0.644733i	−0.0422003	−	0.0216724i
$886$		0			0
$887$	−21.8955	−	18.3725i	−0.735178	−	0.616888i	0.196360	−	0.980532i	$-0.437088\pi$
$887$	−21.8955	−	18.3725i	−0.735178	−	0.616888i	−0.931538	+	0.363644i	$0.881532\pi$
$888$		0			0
$889$	7.61873	−	5.38271i	0.255524	−	0.180530i
$890$		0			0
$891$	6.58482	+	33.0533i	0.220600	+	1.10733i
$892$		0			0
$893$	−8.75237	+	24.0469i	−0.292887	+	0.804700i
$894$		0			0
$895$	−3.91744	−	0.690750i	−0.130946	−	0.0230892i
$896$		0			0
$897$	9.02726	−	5.82140i	0.301411	−	0.194371i
$898$		0			0
$899$	7.90007	−	13.6833i	0.263482	−	0.456365i
$900$		0			0
$901$	60.5921	−	34.9828i	2.01861	−	1.16545i
$902$		0			0
$903$	37.1186	−	5.25522i	1.23523	−	0.174883i
$904$		0			0
$905$	−0.839243	−	2.30580i	−0.0278974	−	0.0766475i
$906$		0			0
$907$	−3.55945	−	20.1866i	−0.118190	−	0.670286i	−0.985121	−	0.171859i	$-0.945022\pi$
$907$	−3.55945	−	20.1866i	−0.118190	−	0.670286i	0.866932	−	0.498426i	$-0.166089\pi$
$908$		0			0
$909$	0.678364	−	8.88388i	0.0224999	−	0.294660i
$910$		0			0
$911$	26.1535	−	4.61157i	0.866505	−	0.152788i	0.277311	−	0.960780i	$-0.410557\pi$
$911$	26.1535	−	4.61157i	0.866505	−	0.152788i	0.589193	+	0.807992i	$0.299446\pi$
$912$		0			0
$913$	19.6854	−	23.4601i	0.651491	−	0.776417i
$914$		0			0
$915$	−2.44053	+	19.3642i	−0.0806814	+	0.640161i
$916$		0			0
$917$	−17.4712	+	25.1768i	−0.576951	+	0.831412i
$918$		0			0
$919$	−6.74735	+	11.6868i	−0.222575	+	0.385511i	−0.955589	−	0.294702i	$-0.904779\pi$
$919$	−6.74735	+	11.6868i	−0.222575	+	0.385511i	0.733014	+	0.680213i	$0.238113\pi$
$920$		0			0
$921$	5.61776	−	44.5737i	0.185112	−	1.46875i
$922$		0			0
$923$	−46.5580	+	16.9457i	−1.53248	+	0.557775i
$924$		0			0
$925$	1.76128	+	9.98871i	0.0579105	+	0.328427i
$926$		0			0
$927$	−22.2020	+	15.9146i	−0.729208	+	0.522705i
$928$		0			0
$929$	−21.1568	+	17.7527i	−0.694133	+	0.582447i	−0.920098	−	0.391689i	$-0.871891\pi$
$929$	−21.1568	+	17.7527i	−0.694133	+	0.582447i	0.225965	+	0.974136i	$0.427447\pi$
$930$		0			0
$931$	−7.09115	−	38.3230i	−0.232403	−	1.25599i
$932$		0			0
$933$	−1.56994	+	0.357163i	−0.0513975	+	0.0116930i
$934$		0			0
$935$			20.9061i			0.683703i
$936$		0			0
$937$	−22.1137	+	12.7673i	−0.722423	+	0.417091i	−0.815644	−	0.578554i	$-0.803617\pi$
$937$	−22.1137	+	12.7673i	−0.722423	+	0.417091i	0.0932208	+	0.995645i	$0.470284\pi$
$938$		0			0
$939$	−3.80693	+	7.41280i	−0.124234	+	0.241908i
$940$		0			0
$941$	14.5954	−	5.31230i	0.475797	−	0.173176i	−0.0929794	−	0.995668i	$-0.529639\pi$
$941$	14.5954	−	5.31230i	0.475797	−	0.173176i	0.568777	+	0.822492i	$0.307417\pi$
$942$		0			0
$943$	10.2264	−	1.80319i	0.333016	−	0.0587198i
$944$		0			0
$945$	−11.2688	−	5.57143i	−0.366575	−	0.181238i
$946$		0			0
$947$	−48.3156	+	8.51934i	−1.57005	+	0.276841i	−0.889872	−	0.456210i	$-0.849207\pi$
$947$	−48.3156	+	8.51934i	−1.57005	+	0.276841i	−0.680173	+	0.733051i	$0.738096\pi$
$948$		0			0
$949$	17.6384	−	6.41985i	0.572567	−	0.208397i
$950$		0			0
$951$	22.6687	−	1.11531i	0.735084	−	0.0361665i
$952$		0			0
$953$	−16.1052	+	9.29833i	−0.521698	+	0.301202i	−0.737629	−	0.675206i	$-0.764055\pi$
$953$	−16.1052	+	9.29833i	−0.521698	+	0.301202i	0.215931	+	0.976409i	$0.430721\pi$
$954$		0			0
$955$		−	15.0647i		−	0.487482i
$956$		0			0
$957$	12.5739	−	40.6618i	0.406457	−	1.31441i
$958$		0			0
$959$	−11.8989	−	3.13457i	−0.384234	−	0.101221i
$960$		0			0
$961$	19.3061	−	16.1997i	0.622776	−	0.522572i
$962$		0			0
$963$	−41.7481	+	11.6825i	−1.34531	+	0.376465i
$964$		0			0
$965$	−1.60891	−	9.12457i	−0.0517926	−	0.293730i
$966$		0			0
$967$	18.0291	−	6.56204i	0.579775	−	0.211021i	−0.0354510	−	0.999371i	$-0.511287\pi$
$967$	18.0291	−	6.56204i	0.579775	−	0.211021i	0.615226	+	0.788350i	$0.289065\pi$
$968$		0			0
$969$	54.2699	−	22.8316i	1.74340	−	0.733457i
$970$		0			0
$971$	−21.5511	+	37.3275i	−0.691606	+	1.19790i	0.279705	+	0.960086i	$0.409763\pi$
$971$	−21.5511	+	37.3275i	−0.691606	+	1.19790i	−0.971311	+	0.237811i	$0.923570\pi$
$972$		0			0
$973$	4.61217	−	55.4075i	0.147859	−	1.77628i
$974$		0			0
$975$	−22.2024	−	16.8423i	−0.711045	−	0.539385i
$976$		0			0
$977$	−1.14854	+	1.36878i	−0.0367452	+	0.0437912i	−0.784104	−	0.620629i	$-0.786877\pi$
$977$	−1.14854	+	1.36878i	−0.0367452	+	0.0437912i	0.747359	+	0.664421i	$0.231322\pi$
$978$		0			0
$979$	−15.0707	+	2.65737i	−0.481661	+	0.0849298i
$980$		0			0
$981$	−26.2305	−	6.71854i	−0.837475	−	0.214506i
$982$		0			0
$983$	2.04856	+	11.6180i	0.0653390	+	0.370556i	0.999891	+	0.0147307i	$0.00468908\pi$
$983$	2.04856	+	11.6180i	0.0653390	+	0.370556i	−0.934552	+	0.355825i	$0.884200\pi$
$984$		0			0
$985$	8.42842	+	23.1569i	0.268552	+	0.737840i
$986$		0			0
$987$	20.8546	−	2.95258i	0.663810	−	0.0939816i
$988$		0			0
$989$	−11.3706	+	6.56483i	−0.361565	+	0.208749i
$990$		0			0
$991$	−5.04929	+	8.74562i	−0.160396	+	0.277814i	−0.935011	−	0.354620i	$-0.884610\pi$
$991$	−5.04929	+	8.74562i	−0.160396	+	0.277814i	0.774615	+	0.632433i	$0.217944\pi$
$992$		0			0
$993$	1.56238	+	31.7554i	0.0495807	+	1.00773i
$994$		0			0
$995$	−11.3072	−	1.99377i	−0.358463	−	0.0632067i
$996$		0			0
$997$	0.420611	−	1.15562i	0.0133209	−	0.0365989i	−0.932854	−	0.360255i	$-0.882690\pi$
$997$	0.420611	−	1.15562i	0.0133209	−	0.0365989i	0.946175	+	0.323656i	$0.104912\pi$
$998$		0			0
$999$	−1.85998	−	12.5199i	−0.0588471	−	0.396113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.15	yes	144
7.3	odd	6		756.2.ca.a.437.8	yes	144
27.11	odd	18		756.2.ca.a.173.8	✓	144
189.38	even	18	inner	756.2.ck.a.605.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.8	✓	144	27.11	odd	18
756.2.ca.a.437.8	yes	144	7.3	odd	6
756.2.ck.a.5.15	yes	144	1.1	even	1	trivial
756.2.ck.a.605.15	yes	144	189.38	even	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.671662 + 1.59652i) q^{3} +(-0.158784 + 0.900507i) q^{5} +(-0.241705 - 2.63469i) q^{7} +(-2.09774 + 2.14464i) q^{9} +O(q^{10})\)	\(q+(0.671662 + 1.59652i) q^{3} +(-0.158784 + 0.900507i) q^{5} +(-0.241705 - 2.63469i) q^{7} +(-2.09774 + 2.14464i) q^{9} +(-3.68787 + 0.650271i) q^{11} +(-2.48376 + 2.96003i) q^{13} +(-1.54432 + 0.351336i) q^{15} -6.10539 q^{17} +5.56765i q^{19} +(4.04398 - 2.15551i) q^{21} +(-1.03164 + 1.22946i) q^{23} +(3.91276 + 1.42413i) q^{25} +(-4.83293 - 1.90860i) q^{27} +(4.21794 + 5.02674i) q^{29} +(-0.823531 - 2.26263i) q^{31} +(-3.51517 - 5.45099i) q^{33} +(2.41093 + 0.200688i) q^{35} +(1.21795 + 2.10956i) q^{37} +(-6.39400 - 1.97723i) q^{39} +(-4.95635 - 4.15887i) q^{41} +(7.68736 + 2.79797i) q^{43} +(-1.59818 - 2.22956i) q^{45} +(4.31905 + 1.57200i) q^{47} +(-6.88316 + 1.27364i) q^{49} +(-4.10076 - 9.74737i) q^{51} +(-9.92435 + 5.72983i) q^{53} -3.42420i q^{55} +(-8.88885 + 3.73958i) q^{57} +(0.682613 + 0.572780i) q^{59} +(4.21480 - 11.5801i) q^{61} +(6.15750 + 5.00852i) q^{63} +(-2.27115 - 2.70665i) q^{65} +(2.26341 - 12.8364i) q^{67} +(-2.65578 - 0.821252i) q^{69} +(11.1044 + 6.41115i) q^{71} +(-4.20689 - 2.42885i) q^{73} +(0.354408 + 7.20333i) q^{75} +(2.60464 + 9.55921i) q^{77} +(-0.979078 - 5.55263i) q^{79} +(-0.198980 - 8.99780i) q^{81} +(-6.26479 + 5.25678i) q^{83} +(0.969437 - 5.49795i) q^{85} +(-5.19226 + 10.1103i) q^{87} +4.08655 q^{89} +(8.39910 + 5.82848i) q^{91} +(3.05920 - 2.83451i) q^{93} +(-5.01371 - 0.884052i) q^{95} +(-4.13766 + 11.3681i) q^{97} +(6.34159 - 9.27326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more