LMFDB - Embedded newform 912.2.bb.e.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(31,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bb (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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	912.31
Dual form			912.2.bb.e.559.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} +1.45735i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} +1.45735i q^{7} +(-0.500000 + 0.866025i) q^{9} +3.18940i q^{11} +(-2.23419 - 1.28991i) q^{13} +(-0.675970 + 1.17081i) q^{15} +(2.08613 + 3.61328i) q^{17} +(2.43807 + 3.61328i) q^{19} +(1.26210 - 0.728674i) q^{21} +(6.49629 + 3.75064i) q^{23} +(1.58613 - 2.74726i) q^{25} +1.00000 q^{27} +(-0.734191 - 0.423885i) q^{29} -0.351939 q^{31} +(2.76210 - 1.59470i) q^{33} +(1.70628 - 0.985122i) q^{35} -6.89169i q^{37} +2.57982i q^{39} +(-4.05582 + 2.34163i) q^{41} +(-6.52791 + 3.76889i) q^{43} +1.35194 q^{45} +(8.04840 + 4.64675i) q^{47} +4.87614 q^{49} +(2.08613 - 3.61328i) q^{51} +(8.76210 + 5.05880i) q^{53} +(3.73419 - 2.15594i) q^{55} +(1.91016 - 3.91807i) q^{57} +(0.675970 + 1.17081i) q^{59} +(4.29001 - 7.43051i) q^{61} +(-1.26210 - 0.728674i) q^{63} +3.48776i q^{65} +(1.08984 - 1.88766i) q^{67} -7.50127i q^{69} +(0.438069 + 0.758758i) q^{71} +(6.67226 + 11.5567i) q^{73} -3.17226 q^{75} -4.64806 q^{77} +(2.52791 + 4.37847i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.22657i q^{83} +(2.82032 - 4.88494i) q^{85} +0.847771i q^{87} +(-3.81792 - 2.20428i) q^{89} +(1.87985 - 3.25599i) q^{91} +(0.175970 + 0.304788i) q^{93} +(2.58242 - 5.29699i) q^{95} +(-7.79001 + 4.49756i) q^{97} +(-2.76210 - 1.59470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9	$ 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9} - 3 q^{13} - 2 q^{15} - 2 q^{17} - 4 q^{19} - 9 q^{21} + 12 q^{23} - 5 q^{25} + 6 q^{27} + 6 q^{29} + 2 q^{31} + 6 q^{35} - 12 q^{41} - 33 q^{43} + 4 q^{45} - 18 q^{47} - 8 q^{49} - 2 q^{51} + 36 q^{53} + 12 q^{55} - q^{57} + 2 q^{59} + 3 q^{61} + 9 q^{63} + 19 q^{67} - 16 q^{71} + 11 q^{73} + 10 q^{75} - 32 q^{77} + 9 q^{79} - 3 q^{81} - 8 q^{85} + 6 q^{89} + q^{91} - q^{93} - 26 q^{95} - 24 q^{97}+O(q^{100}) $ 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9 - 3 * q^13 - 2 * q^15 - 2 * q^17 - 4 * q^19 - 9 * q^21 + 12 * q^23 - 5 * q^25 + 6 * q^27 + 6 * q^29 + 2 * q^31 + 6 * q^35 - 12 * q^41 - 33 * q^43 + 4 * q^45 - 18 * q^47 - 8 * q^49 - 2 * q^51 + 36 * q^53 + 12 * q^55 - q^57 + 2 * q^59 + 3 * q^61 + 9 * q^63 + 19 * q^67 - 16 * q^71 + 11 * q^73 + 10 * q^75 - 32 * q^77 + 9 * q^79 - 3 * q^81 - 8 * q^85 + 6 * q^89 + q^91 - q^93 - 26 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	−0.675970	−	1.17081i	−0.302303	−	0.523604i	0.674354	−	0.738408i	$-0.264422\pi$
$5$	−0.675970	−	1.17081i	−0.302303	−	0.523604i	−0.976657	+	0.214804i	$0.931089\pi$
$6$		0			0
$7$			1.45735i			0.550826i	0.961326	+	0.275413i	$0.0888145\pi$
$7$			1.45735i			0.550826i	−0.961326	+	0.275413i	$0.911185\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$			3.18940i			0.961640i	0.876819	+	0.480820i	$0.159661\pi$
$11$			3.18940i			0.961640i	−0.876819	+	0.480820i	$0.840339\pi$
$12$		0			0
$13$	−2.23419	−	1.28991i	−0.619653	−	0.357757i	0.157081	−	0.987586i	$-0.449792\pi$
$13$	−2.23419	−	1.28991i	−0.619653	−	0.357757i	−0.776734	+	0.629829i	$0.783125\pi$
$14$		0			0
$15$	−0.675970	+	1.17081i	−0.174535	+	0.302303i
$16$		0			0
$17$	2.08613	+	3.61328i	0.505961	+	0.876350i	0.999976	+	0.00689678i	$0.00219533\pi$
$17$	2.08613	+	3.61328i	0.505961	+	0.876350i	−0.494015	+	0.869453i	$0.664471\pi$
$18$		0			0
$19$	2.43807	+	3.61328i	0.559331	+	0.828944i
$19$	2.43807	+	3.61328i	0.559331	+	0.828944i
$20$		0			0
$21$	1.26210	−	0.728674i	0.275413	−	0.159010i
$22$		0			0
$23$	6.49629	+	3.75064i	1.35457	+	0.782062i	0.988886	−	0.148677i	$-0.0475016\pi$
$23$	6.49629	+	3.75064i	1.35457	+	0.782062i	0.365685	+	0.930739i	$0.380835\pi$
$24$		0			0
$25$	1.58613	−	2.74726i	0.317226	−	0.549452i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.734191	−	0.423885i	−0.136336	−	0.0787135i	0.430281	−	0.902695i	$-0.358415\pi$
$29$	−0.734191	−	0.423885i	−0.136336	−	0.0787135i	−0.566617	+	0.823982i	$0.691748\pi$
$30$		0			0
$31$	−0.351939			−0.0632101			−0.0316051	−	0.999500i	$-0.510062\pi$
$31$	−0.351939			−0.0632101			−0.0316051	+	0.999500i	$0.510062\pi$
$32$		0			0
$33$	2.76210	−	1.59470i	0.480820	−	0.277601i
$34$		0			0
$35$	1.70628	−	0.985122i	0.288414	−	0.166516i
$36$		0			0
$37$		−	6.89169i		−	1.13299i	−0.824066	−	0.566494i	$-0.808300\pi$
$37$		−	6.89169i		−	1.13299i	0.824066	−	0.566494i	$-0.191700\pi$
$38$		0			0
$39$			2.57982i			0.413102i
$40$		0			0
$41$	−4.05582	+	2.34163i	−0.633412	+	0.365701i	−0.782072	−	0.623188i	$-0.785837\pi$
$41$	−4.05582	+	2.34163i	−0.633412	+	0.365701i	0.148660	+	0.988888i	$0.452504\pi$
$42$		0			0
$43$	−6.52791	+	3.76889i	−0.995497	+	0.574750i	−0.906913	−	0.421318i	$-0.861567\pi$
$43$	−6.52791	+	3.76889i	−0.995497	+	0.574750i	−0.0885840	+	0.996069i	$0.528234\pi$
$44$		0			0
$45$	1.35194			0.201535
$46$		0			0
$47$	8.04840	+	4.64675i	1.17398	+	0.677797i	0.954614	−	0.297845i	$-0.0962679\pi$
$47$	8.04840	+	4.64675i	1.17398	+	0.677797i	0.219366	+	0.975643i	$0.429601\pi$
$48$		0			0
$49$	4.87614			0.696591
$50$		0			0
$51$	2.08613	−	3.61328i	0.292117	−	0.505961i
$52$		0			0
$53$	8.76210	+	5.05880i	1.20357	+	0.694880i	0.961346	−	0.275342i	$-0.0887909\pi$
$53$	8.76210	+	5.05880i	1.20357	+	0.694880i	0.242220	+	0.970221i	$0.422124\pi$
$54$		0			0
$55$	3.73419	−	2.15594i	0.503518	−	0.290706i
$56$		0			0
$57$	1.91016	−	3.91807i	0.253007	−	0.518961i
$58$		0			0
$59$	0.675970	+	1.17081i	0.0880037	+	0.152427i	0.906667	−	0.421847i	$-0.138618\pi$
$59$	0.675970	+	1.17081i	0.0880037	+	0.152427i	−0.818663	+	0.574274i	$0.805285\pi$
$60$		0			0
$61$	4.29001	−	7.43051i	0.549279	−	0.951380i	−0.449045	−	0.893509i	$-0.648236\pi$
$61$	4.29001	−	7.43051i	0.549279	−	0.951380i	0.998324	−	0.0578704i	$-0.0184310\pi$
$62$		0			0
$63$	−1.26210	−	0.728674i	−0.159010	−	0.0918043i
$64$		0			0
$65$			3.48776i			0.432604i
$66$		0			0
$67$	1.08984	−	1.88766i	0.133145	−	0.230614i	−0.791742	−	0.610855i	$-0.790826\pi$
$67$	1.08984	−	1.88766i	0.133145	−	0.230614i	0.924887	+	0.380241i	$0.124159\pi$
$68$		0			0
$69$		−	7.50127i		−	0.903047i
$70$		0			0
$71$	0.438069	+	0.758758i	0.0519893	+	0.0900481i	0.890849	−	0.454300i	$-0.150111\pi$
$71$	0.438069	+	0.758758i	0.0519893	+	0.0900481i	−0.838860	+	0.544348i	$0.816777\pi$
$72$		0			0
$73$	6.67226	+	11.5567i	0.780929	+	1.35261i	0.931401	+	0.363994i	$0.118587\pi$
$73$	6.67226	+	11.5567i	0.780929	+	1.35261i	−0.150472	+	0.988614i	$0.548079\pi$
$74$		0			0
$75$	−3.17226			−0.366301
$76$		0			0
$77$	−4.64806			−0.529696
$78$		0			0
$79$	2.52791	+	4.37847i	0.284412	+	0.492616i	0.972466	−	0.233043i	$-0.0748683\pi$
$79$	2.52791	+	4.37847i	0.284412	+	0.492616i	−0.688054	+	0.725659i	$0.741535\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			7.22657i			0.793219i	0.917987	+	0.396609i	$0.129813\pi$
$83$			7.22657i			0.793219i	−0.917987	+	0.396609i	$0.870187\pi$
$84$		0			0
$85$	2.82032	−	4.88494i	0.305907	−	0.529846i
$86$		0			0
$87$			0.847771i			0.0908906i
$88$		0			0
$89$	−3.81792	−	2.20428i	−0.404698	−	0.233653i	0.283811	−	0.958880i	$-0.408401\pi$
$89$	−3.81792	−	2.20428i	−0.404698	−	0.233653i	−0.688509	+	0.725228i	$0.741735\pi$
$90$		0			0
$91$	1.87985	−	3.25599i	0.197062	−	0.341321i
$92$		0			0
$93$	0.175970	+	0.304788i	0.0182472	+	0.0316051i
$94$		0			0
$95$	2.58242	−	5.29699i	0.264951	−	0.543460i
$96$		0			0
$97$	−7.79001	+	4.49756i	−0.790956	+	0.456658i	−0.840299	−	0.542123i	$-0.817620\pi$
$97$	−7.79001	+	4.49756i	−0.790956	+	0.456658i	0.0493433	+	0.998782i	$0.484287\pi$
$98$		0			0
$99$	−2.76210	−	1.59470i	−0.277601	−	0.160273i
$100$		0			0
$101$	−3.73419	+	6.46781i	−0.371566	+	0.643571i	−0.989807	−	0.142418i	$-0.954512\pi$
$101$	−3.73419	+	6.46781i	−0.371566	+	0.643571i	0.618241	+	0.785989i	$0.287846\pi$
$102$		0			0
$103$	−11.5726			−1.14028			−0.570141	−	0.821547i	$-0.693111\pi$
$103$	−11.5726			−1.14028			−0.570141	+	0.821547i	$0.693111\pi$
$104$		0			0
$105$	−1.70628	−	0.985122i	−0.166516	−	0.0961381i
$106$		0			0
$107$	−10.1723			−0.983390			−0.491695	−	0.870768i	$-0.663622\pi$
$107$	−10.1723			−0.983390			−0.491695	+	0.870768i	$0.663622\pi$
$108$		0			0
$109$	7.31421	−	4.22286i	0.700574	−	0.404477i	−0.106987	−	0.994260i	$-0.534120\pi$
$109$	7.31421	−	4.22286i	0.700574	−	0.404477i	0.807561	+	0.589784i	$0.200787\pi$
$110$		0			0
$111$	−5.96838	+	3.44585i	−0.566494	+	0.327065i
$112$		0			0
$113$			12.4829i			1.17429i	0.809481	+	0.587146i	$0.199748\pi$
$113$			12.4829i			1.17429i	−0.809481	+	0.587146i	$0.800252\pi$
$114$		0			0
$115$		−	10.1413i		−	0.945678i
$116$		0			0
$117$	2.23419	−	1.28991i	0.206551	−	0.119252i
$118$		0			0
$119$	−5.26581	+	3.04022i	−0.482716	+	0.278696i
$120$		0			0
$121$	0.827740			0.0752491
$122$		0			0
$123$	4.05582	+	2.34163i	0.365701	+	0.211137i
$124$		0			0
$125$	−11.0484			−0.988199
$126$		0			0
$127$	3.52420	−	6.10409i	0.312722	−	0.541651i	−0.666229	−	0.745748i	$-0.732092\pi$
$127$	3.52420	−	6.10409i	0.312722	−	0.541651i	0.978951	+	0.204097i	$0.0654258\pi$
$128$		0			0
$129$	6.52791	+	3.76889i	0.574750	+	0.331832i
$130$		0			0
$131$	2.74161	−	1.58287i	0.239536	−	0.138296i	−0.375428	−	0.926852i	$-0.622504\pi$
$131$	2.74161	−	1.58287i	0.239536	−	0.138296i	0.614963	+	0.788556i	$0.289171\pi$
$132$		0			0
$133$	−5.26581	+	3.55311i	−0.456604	+	0.308094i
$134$		0			0
$135$	−0.675970	−	1.17081i	−0.0581782	−	0.100768i
$136$		0			0
$137$	−3.25839	+	5.64370i	−0.278383	+	0.482174i	−0.970983	−	0.239148i	$-0.923132\pi$
$137$	−3.25839	+	5.64370i	−0.278383	+	0.482174i	0.692600	+	0.721322i	$0.256465\pi$
$138$		0			0
$139$	12.4647	+	7.19648i	1.05724	+	0.610398i	0.924667	−	0.380776i	$-0.124343\pi$
$139$	12.4647	+	7.19648i	1.05724	+	0.610398i	0.132572	+	0.991173i	$0.457676\pi$
$140$		0			0
$141$		−	9.29349i		−	0.782653i
$142$		0			0
$143$	4.11404	−	7.12572i	0.344033	−	0.595883i
$144$		0			0
$145$			1.14613i			0.0951813i
$146$		0			0
$147$	−2.43807	−	4.22286i	−0.201089	−	0.348296i
$148$		0			0
$149$	−3.20017	−	5.54286i	−0.262168	−	0.454088i	0.704650	−	0.709555i	$-0.251104\pi$
$149$	−3.20017	−	5.54286i	−0.262168	−	0.454088i	−0.966818	+	0.255467i	$0.917771\pi$
$150$		0			0
$151$	−9.64064			−0.784544			−0.392272	−	0.919849i	$-0.628311\pi$
$151$	−9.64064			−0.784544			−0.392272	+	0.919849i	$0.628311\pi$
$152$		0			0
$153$	−4.17226			−0.337307
$154$		0			0
$155$	0.237900	+	0.412055i	0.0191086	+	0.0330971i
$156$		0			0
$157$	−11.7281	−	20.3136i	−0.936003	−	1.62120i	−0.772836	−	0.634605i	$-0.781163\pi$
$157$	−11.7281	−	20.3136i	−0.936003	−	1.62120i	−0.163166	−	0.986599i	$-0.552171\pi$
$158$		0			0
$159$		−	10.1176i		−	0.802378i
$160$		0			0
$161$	−5.46598	+	9.46735i	−0.430779	+	0.746132i
$162$		0			0
$163$		−	3.15289i		−	0.246953i	−0.992347	−	0.123477i	$-0.960596\pi$
$163$		−	3.15289i		−	0.246953i	0.992347	−	0.123477i	$-0.0394044\pi$
$164$		0			0
$165$	−3.73419	−	2.15594i	−0.290706	−	0.167839i
$166$		0			0
$167$	3.49629	−	6.05575i	0.270551	−	0.468608i	−0.698452	−	0.715657i	$-0.746127\pi$
$167$	3.49629	−	6.05575i	0.270551	−	0.468608i	0.969003	+	0.247049i	$0.0794608\pi$
$168$		0			0
$169$	−3.17226	−	5.49452i	−0.244020	−	0.422655i
$170$		0			0
$171$	−4.34823	+	0.304788i	−0.332517	+	0.0233077i
$172$		0			0
$173$	−17.3068	+	9.99208i	−1.31581	+	0.759684i	−0.983052	−	0.183328i	$-0.941313\pi$
$173$	−17.3068	+	9.99208i	−1.31581	+	0.759684i	−0.332759	+	0.943012i	$0.607980\pi$
$174$		0			0
$175$	4.00371	+	2.31154i	0.302652	+	0.174736i
$176$		0			0
$177$	0.675970	−	1.17081i	0.0508090	−	0.0880037i
$178$		0			0
$179$	15.6965			1.17321			0.586604	−	0.809874i	$-0.300464\pi$
$179$	15.6965			1.17321			0.586604	+	0.809874i	$0.300464\pi$
$180$		0			0
$181$	13.3142	+	7.68696i	0.989637	+	0.571367i	0.905166	−	0.425059i	$-0.139746\pi$
$181$	13.3142	+	7.68696i	0.989637	+	0.571367i	0.0844714	+	0.996426i	$0.473080\pi$
$182$		0			0
$183$	−8.58002			−0.634253
$184$		0			0
$185$	−8.06889	+	4.65858i	−0.593237	+	0.342505i
$186$		0			0
$187$	−11.5242	+	6.65350i	−0.842733	+	0.486552i
$188$		0			0
$189$			1.45735i			0.106006i
$190$		0			0
$191$		−	3.85914i		−	0.279238i	−0.990205	−	0.139619i	$-0.955412\pi$
$191$		−	3.85914i		−	0.279238i	0.990205	−	0.139619i	$-0.0445878\pi$
$192$		0			0
$193$	−11.8142	+	6.82094i	−0.850405	+	0.490982i	−0.860788	−	0.508964i	$-0.830028\pi$
$193$	−11.8142	+	6.82094i	−0.850405	+	0.490982i	0.0103823	+	0.999946i	$0.496695\pi$
$194$		0			0
$195$	3.02049	−	1.74388i	0.216302	−	0.124882i
$196$		0			0
$197$	23.7571			1.69262			0.846311	−	0.532689i	$-0.178818\pi$
$197$	23.7571			1.69262			0.846311	+	0.532689i	$0.178818\pi$
$198$		0			0
$199$	−19.5205	−	11.2702i	−1.38377	−	0.798920i	−0.391167	−	0.920320i	$-0.627929\pi$
$199$	−19.5205	−	11.2702i	−1.38377	−	0.798920i	−0.992604	+	0.121399i	$0.961262\pi$
$200$		0			0
$201$	−2.17968			−0.153743
$202$		0			0
$203$	0.617748	−	1.06997i	0.0433574	−	0.0750973i
$204$		0			0
$205$	5.48322	+	3.16574i	0.382965	+	0.221105i
$206$		0			0
$207$	−6.49629	+	3.75064i	−0.451523	+	0.260687i
$208$		0			0
$209$	−11.5242	+	7.77597i	−0.797146	+	0.537875i
$210$		0			0
$211$	−11.0521	−	19.1428i	−0.760859	−	1.31785i	−0.942409	−	0.334464i	$-0.891445\pi$
$211$	−11.0521	−	19.1428i	−0.760859	−	1.31785i	0.181550	−	0.983382i	$-0.441889\pi$
$212$		0			0
$213$	0.438069	−	0.758758i	0.0300160	−	0.0519893i
$214$		0			0
$215$	8.82534	+	5.09531i	0.601883	+	0.347497i
$216$		0			0
$217$		−	0.512898i		−	0.0348178i
$218$		0			0
$219$	6.67226	−	11.5567i	0.450870	−	0.780929i
$220$		0			0
$221$		−	10.7637i		−	0.724044i
$222$		0			0
$223$	−2.87985	−	4.98804i	−0.192849	−	0.334024i	0.753344	−	0.657626i	$-0.228439\pi$
$223$	−2.87985	−	4.98804i	−0.192849	−	0.334024i	−0.946193	+	0.323602i	$0.895106\pi$
$224$		0			0
$225$	1.58613	+	2.74726i	0.105742	+	0.183151i
$226$		0			0
$227$	−23.5242			−1.56136			−0.780678	−	0.624934i	$-0.785126\pi$
$227$	−23.5242			−1.56136			−0.780678	+	0.624934i	$0.785126\pi$
$228$		0			0
$229$	−5.76450			−0.380929			−0.190465	−	0.981694i	$-0.560999\pi$
$229$	−5.76450			−0.380929			−0.190465	+	0.981694i	$0.560999\pi$
$230$		0			0
$231$	2.32403	+	4.02534i	0.152910	+	0.264848i
$232$		0			0
$233$	−0.321627	−	0.557074i	−0.0210705	−	0.0364951i	0.855298	−	0.518137i	$-0.173374\pi$
$233$	−0.321627	−	0.557074i	−0.0210705	−	0.0364951i	−0.876368	+	0.481641i	$0.840041\pi$
$234$		0			0
$235$		−	12.5642i		−	0.819600i
$236$		0			0
$237$	2.52791	−	4.37847i	0.164205	−	0.284412i
$238$		0			0
$239$			6.65350i			0.430379i	0.976572	+	0.215190i	$0.0690369\pi$
$239$			6.65350i			0.430379i	−0.976572	+	0.215190i	$0.930963\pi$
$240$		0			0
$241$	0.548399	+	0.316618i	0.0353255	+	0.0203952i	0.517559	−	0.855648i	$-0.326841\pi$
$241$	0.548399	+	0.316618i	0.0353255	+	0.0203952i	−0.482233	+	0.876043i	$0.660174\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−3.29612	−	5.70905i	−0.210581	−	0.364738i
$246$		0			0
$247$	−0.786299	−	11.2177i	−0.0500310	−	0.713762i
$248$		0			0
$249$	6.25839	−	3.61328i	0.396609	−	0.228983i
$250$		0			0
$251$	−6.10422	−	3.52427i	−0.385295	−	0.222450i	0.294825	−	0.955551i	$-0.404739\pi$
$251$	−6.10422	−	3.52427i	−0.385295	−	0.222450i	−0.680119	+	0.733101i	$0.738072\pi$
$252$		0			0
$253$	−11.9623	+	20.7193i	−0.752061	+	1.30261i
$254$		0			0
$255$	−5.64064			−0.353231
$256$		0			0
$257$	21.7547	+	12.5601i	1.35702	+	0.783476i	0.989221	−	0.146430i	$-0.0467782\pi$
$257$	21.7547	+	12.5601i	1.35702	+	0.783476i	0.367799	+	0.929905i	$0.380112\pi$
$258$		0			0
$259$	10.0436			0.624078
$260$		0			0
$261$	0.734191	−	0.423885i	0.0454453	−	0.0262378i
$262$		0			0
$263$	12.3216	−	7.11389i	0.759784	−	0.438662i	−0.0694342	−	0.997587i	$-0.522119\pi$
$263$	12.3216	−	7.11389i	0.759784	−	0.438662i	0.829218	+	0.558925i	$0.188786\pi$
$264$		0			0
$265$		−	13.6784i		−	0.840256i
$266$		0			0
$267$			4.40855i			0.269799i
$268$		0			0
$269$	−1.18950	+	0.686759i	−0.0725252	+	0.0418724i	−0.535824	−	0.844330i	$-0.679999\pi$
$269$	−1.18950	+	0.686759i	−0.0725252	+	0.0418724i	0.463299	+	0.886202i	$0.346666\pi$
$270$		0			0
$271$	−10.4684	+	6.04392i	−0.635909	+	0.367142i	−0.783037	−	0.621975i	$-0.786330\pi$
$271$	−10.4684	+	6.04392i	−0.635909	+	0.367142i	0.147128	+	0.989117i	$0.452997\pi$
$272$		0			0
$273$	−3.75970			−0.227547
$274$		0			0
$275$	8.76210	+	5.05880i	0.528374	+	0.305057i
$276$		0			0
$277$	5.58002			0.335271			0.167635	−	0.985849i	$-0.446387\pi$
$277$	5.58002			0.335271			0.167635	+	0.985849i	$0.446387\pi$
$278$		0			0
$279$	0.175970	−	0.304788i	0.0105350	−	0.0182472i
$280$		0			0
$281$	11.6079	+	6.70184i	0.692471	+	0.399798i	0.804537	−	0.593903i	$-0.202414\pi$
$281$	11.6079	+	6.70184i	0.692471	+	0.399798i	−0.112066	+	0.993701i	$0.535747\pi$
$282$		0			0
$283$	−7.88095	+	4.55007i	−0.468474	+	0.270473i	−0.715601	−	0.698510i	$-0.753847\pi$
$283$	−7.88095	+	4.55007i	−0.468474	+	0.270473i	0.247127	+	0.968983i	$0.420514\pi$
$284$		0			0
$285$	−5.87854	+	0.412055i	−0.348215	+	0.0244080i
$286$		0			0
$287$	−3.41256	−	5.91073i	−0.201437	−	0.348900i
$288$		0			0
$289$	−0.203878	+	0.353128i	−0.0119928	+	0.0207722i
$290$		0			0
$291$	7.79001	+	4.49756i	0.456658	+	0.263652i
$292$		0			0
$293$		−	5.70905i		−	0.333526i	−0.985997	−	0.166763i	$-0.946668\pi$
$293$		−	5.70905i		−	0.333526i	0.985997	−	0.166763i	$-0.0533315\pi$
$294$		0			0
$295$	0.913870	−	1.58287i	0.0532076	−	0.0921582i
$296$		0			0
$297$			3.18940i			0.185068i
$298$		0			0
$299$	−9.67597	−	16.7593i	−0.559576	−	0.969214i
$300$		0			0
$301$	−5.49258	−	9.51343i	−0.316587	−	0.548345i
$302$		0			0
$303$	7.46838			0.429047
$304$		0			0
$305$	−11.5997			−0.664195
$306$		0			0
$307$	11.1419	+	19.2984i	0.635905	+	1.10142i	0.986323	+	0.164826i	$0.0527061\pi$
$307$	11.1419	+	19.2984i	0.635905	+	1.10142i	−0.350418	+	0.936593i	$0.613961\pi$
$308$		0			0
$309$	5.78630	+	10.0222i	0.329171	+	0.570141i
$310$		0			0
$311$		−	20.9286i		−	1.18675i	−0.804925	−	0.593376i	$-0.797795\pi$
$311$		−	20.9286i		−	1.18675i	0.804925	−	0.593376i	$-0.202205\pi$
$312$		0			0
$313$	0.561931	−	0.973292i	0.0317622	−	0.0550137i	−0.849707	−	0.527255i	$-0.823221\pi$
$313$	0.561931	−	0.973292i	0.0317622	−	0.0550137i	0.881470	+	0.472241i	$0.156555\pi$
$314$		0			0
$315$			1.97024i			0.111011i
$316$		0			0
$317$	−15.0205	−	8.67208i	−0.843635	−	0.487073i	0.0148633	−	0.999890i	$-0.495269\pi$
$317$	−15.0205	−	8.67208i	−0.843635	−	0.487073i	−0.858498	+	0.512817i	$0.828602\pi$
$318$		0			0
$319$	1.35194	−	2.34163i	0.0756941	−	0.131106i
$320$		0			0
$321$	5.08613	+	8.80944i	0.283880	+	0.491695i
$322$		0			0
$323$	−7.96969	+	16.3472i	−0.443445	+	0.909583i
$324$		0			0
$325$	−7.08744	+	4.09193i	−0.393140	+	0.226980i
$326$		0			0
$327$	−7.31421	−	4.22286i	−0.404477	−	0.233525i
$328$		0			0
$329$	−6.77192	+	11.7293i	−0.373348	+	0.646658i
$330$		0			0
$331$	0.584825			0.0321449			0.0160724	−	0.999871i	$-0.494884\pi$
$331$	0.584825			0.0321449			0.0160724	+	0.999871i	$0.494884\pi$
$332$		0			0
$333$	5.96838	+	3.44585i	0.327065	+	0.188831i
$334$		0			0
$335$	−2.94679			−0.161001
$336$		0			0
$337$	23.8142	−	13.7491i	1.29724	−	0.748963i	0.317316	−	0.948320i	$-0.397219\pi$
$337$	23.8142	−	13.7491i	1.29724	−	0.748963i	0.979927	+	0.199357i	$0.0638852\pi$
$338$		0			0
$339$	10.8105	−	6.24144i	0.587146	−	0.338989i
$340$		0			0
$341$		−	1.12247i		−	0.0607854i
$342$		0			0
$343$			17.3077i			0.934526i
$344$		0			0
$345$	−8.78259	+	5.07063i	−0.472839	+	0.272994i
$346$		0			0
$347$	−22.8105	+	13.1696i	−1.22453	+	0.706984i	−0.965881	−	0.258987i	$-0.916611\pi$
$347$	−22.8105	+	13.1696i	−1.22453	+	0.706984i	−0.258651	+	0.965971i	$0.583278\pi$
$348$		0			0
$349$	9.53162			0.510216			0.255108	−	0.966913i	$-0.417889\pi$
$349$	9.53162			0.510216			0.255108	+	0.966913i	$0.417889\pi$
$350$		0			0
$351$	−2.23419	−	1.28991i	−0.119252	−	0.0688503i
$352$		0			0
$353$	7.94418			0.422826			0.211413	−	0.977397i	$-0.432193\pi$
$353$	7.94418			0.422826			0.211413	+	0.977397i	$0.432193\pi$
$354$		0			0
$355$	0.592243	−	1.02580i	0.0314330	−	0.0544436i
$356$		0			0
$357$	5.26581	+	3.04022i	0.278696	+	0.160905i
$358$		0			0
$359$	15.9293	−	9.19681i	0.840719	−	0.485389i	−0.0167898	−	0.999859i	$-0.505345\pi$
$359$	15.9293	−	9.19681i	0.840719	−	0.485389i	0.857508	+	0.514470i	$0.172011\pi$
$360$		0			0
$361$	−7.11164	+	17.6189i	−0.374297	+	0.927309i
$362$		0			0
$363$	−0.413870	−	0.716844i	−0.0217225	−	0.0376245i
$364$		0			0
$365$	9.02049	−	15.6239i	0.472154	−	0.817795i
$366$		0			0
$367$	7.41627	+	4.28179i	0.387126	+	0.223507i	0.680914	−	0.732363i	$-0.261583\pi$
$367$	7.41627	+	4.28179i	0.387126	+	0.223507i	−0.293788	+	0.955871i	$0.594916\pi$
$368$		0			0
$369$		−	4.68325i		−	0.243801i
$370$		0			0
$371$	−7.37243	+	12.7694i	−0.382757	+	0.662955i
$372$		0			0
$373$		−	25.0965i		−	1.29945i	−0.760171	−	0.649723i	$-0.774885\pi$
$373$		−	25.0965i		−	1.29945i	0.760171	−	0.649723i	$-0.225115\pi$
$374$		0			0
$375$	5.52420	+	9.56819i	0.285268	+	0.494099i
$376$		0			0
$377$	1.09355	+	1.89408i	0.0563206	+	0.0975502i
$378$		0			0
$379$	34.6816			1.78148			0.890738	−	0.454518i	$-0.150188\pi$
$379$	34.6816			1.78148			0.890738	+	0.454518i	$0.150188\pi$
$380$		0			0
$381$	−7.04840			−0.361100
$382$		0			0
$383$	−4.58984	−	7.94984i	−0.234530	−	0.406218i	0.724606	−	0.689163i	$-0.242022\pi$
$383$	−4.58984	−	7.94984i	−0.234530	−	0.406218i	−0.959136	+	0.282946i	$0.908688\pi$
$384$		0			0
$385$	3.14195	+	5.44201i	0.160128	+	0.277351i
$386$		0			0
$387$		−	7.53778i		−	0.383167i
$388$		0			0
$389$	11.4660	−	19.8597i	0.581348	−	1.00692i	−0.413972	−	0.910290i	$-0.635859\pi$
$389$	11.4660	−	19.8597i	0.581348	−	1.00692i	0.995320	−	0.0966348i	$-0.0308079\pi$
$390$		0			0
$391$			31.2973i			1.58277i
$392$		0			0
$393$	−2.74161	−	1.58287i	−0.138296	−	0.0798452i
$394$		0			0
$395$	3.41758	−	5.91942i	0.171957	−	0.297838i
$396$		0			0
$397$	−0.593549	−	1.02806i	−0.0297894	−	0.0515967i	0.850746	−	0.525576i	$-0.176150\pi$
$397$	−0.593549	−	1.02806i	−0.0297894	−	0.0515967i	−0.880536	+	0.473980i	$0.842817\pi$
$398$		0			0
$399$	5.70999	+	2.78377i	0.285857	+	0.139363i
$400$		0			0
$401$	29.3273	−	16.9321i	1.46453	−	0.845549i	0.465319	−	0.885143i	$-0.345940\pi$
$401$	29.3273	−	16.9321i	1.46453	−	0.845549i	0.999216	+	0.0395939i	$0.0126064\pi$
$402$		0			0
$403$	0.786299	+	0.453970i	0.0391684	+	0.0226139i
$404$		0			0
$405$	−0.675970	+	1.17081i	−0.0335892	+	0.0581782i
$406$		0			0
$407$	21.9804			1.08953
$408$		0			0
$409$	−19.8310	−	11.4494i	−0.980579	−	0.566138i	−0.0781343	−	0.996943i	$-0.524896\pi$
$409$	−19.8310	−	11.4494i	−0.980579	−	0.566138i	−0.902445	+	0.430805i	$0.858230\pi$
$410$		0			0
$411$	6.51678			0.321449
$412$		0			0
$413$	−1.70628	+	0.985122i	−0.0839607	+	0.0484747i
$414$		0			0
$415$	8.46096	−	4.88494i	0.415332	−	0.239792i
$416$		0			0
$417$		−	14.3930i		−	0.704826i
$418$		0			0
$419$			13.7020i			0.669389i	0.942327	+	0.334694i	$0.108633\pi$
$419$			13.7020i			0.669389i	−0.942327	+	0.334694i	$0.891367\pi$
$420$		0			0
$421$	12.3216	−	7.11389i	0.600519	−	0.346710i	−0.168727	−	0.985663i	$-0.553965\pi$
$421$	12.3216	−	7.11389i	0.600519	−	0.346710i	0.769246	+	0.638953i	$0.220632\pi$
$422$		0			0
$423$	−8.04840	+	4.64675i	−0.391327	+	0.225932i
$424$		0			0
$425$	13.2355			0.642016
$426$		0			0
$427$	10.8288	+	6.25203i	0.524044	+	0.302557i
$428$		0			0
$429$	−8.22808			−0.397255
$430$		0			0
$431$	−8.04840	+	13.9402i	−0.387678	+	0.671478i	−0.992137	−	0.125159i	$-0.960056\pi$
$431$	−8.04840	+	13.9402i	−0.387678	+	0.671478i	0.604459	+	0.796636i	$0.293389\pi$
$432$		0			0
$433$	33.1635	+	19.1470i	1.59374	+	0.920145i	0.992658	+	0.120956i	$0.0385960\pi$
$433$	33.1635	+	19.1470i	1.59374	+	0.920145i	0.601080	+	0.799189i	$0.294737\pi$
$434$		0			0
$435$	0.992582	−	0.573067i	0.0475906	−	0.0274765i
$436$		0			0
$437$	2.28630	+	32.6172i	0.109369	+	1.56029i
$438$		0			0
$439$	6.95856	+	12.0526i	0.332114	+	0.575238i	0.982926	−	0.184001i	$-0.0589048\pi$
$439$	6.95856	+	12.0526i	0.332114	+	0.575238i	−0.650812	+	0.759239i	$0.725571\pi$
$440$		0			0
$441$	−2.43807	+	4.22286i	−0.116099	+	0.201089i
$442$		0			0
$443$	2.16159	+	1.24800i	0.102700	+	0.0592941i	0.550470	−	0.834855i	$-0.314448\pi$
$443$	2.16159	+	1.24800i	0.102700	+	0.0592941i	−0.447770	+	0.894149i	$0.647782\pi$
$444$		0			0
$445$			5.96009i			0.282536i
$446$		0			0
$447$	−3.20017	+	5.54286i	−0.151363	+	0.262168i
$448$		0			0
$449$		−	39.4766i		−	1.86302i	−0.363721	−	0.931508i	$-0.618494\pi$
$449$		−	39.4766i		−	1.86302i	0.363721	−	0.931508i	$-0.381506\pi$
$450$		0			0
$451$	−7.46838	−	12.9356i	−0.351672	−	0.609114i
$452$		0			0
$453$	4.82032	+	8.34904i	0.226478	+	0.392272i
$454$		0			0
$455$	−5.08288			−0.238289
$456$		0			0
$457$	−38.2207			−1.78789			−0.893944	−	0.448180i	$-0.852072\pi$
$457$	−38.2207			−1.78789			−0.893944	+	0.448180i	$0.852072\pi$
$458$		0			0
$459$	2.08613	+	3.61328i	0.0973722	+	0.168654i
$460$		0			0
$461$	−13.3469	−	23.1176i	−0.621628	−	1.07669i	−0.989183	−	0.146690i	$-0.953138\pi$
$461$	−13.3469	−	23.1176i	−0.621628	−	1.07669i	0.367554	−	0.930002i	$-0.380195\pi$
$462$		0			0
$463$			4.96877i			0.230918i	0.993312	+	0.115459i	$0.0368339\pi$
$463$			4.96877i			0.230918i	−0.993312	+	0.115459i	$0.963166\pi$
$464$		0			0
$465$	0.237900	−	0.412055i	0.0110324	−	0.0191086i
$466$		0			0
$467$			24.1757i			1.11872i	0.828926	+	0.559359i	$0.188953\pi$
$467$			24.1757i			1.11872i	−0.828926	+	0.559359i	$0.811047\pi$
$468$		0			0
$469$	2.75097	+	1.58827i	0.127028	+	0.0733397i
$470$		0			0
$471$	−11.7281	+	20.3136i	−0.540401	+	0.936003i
$472$		0			0
$473$	−12.0205	−	20.8201i	−0.552703	−	0.957309i
$474$		0			0
$475$	13.7937	−	0.966868i	0.632899	−	0.0443629i
$476$		0			0
$477$	−8.76210	+	5.05880i	−0.401189	+	0.231627i
$478$		0			0
$479$	32.9500	+	19.0237i	1.50553	+	0.869216i	0.999979	+	0.00641641i	$0.00204242\pi$
$479$	32.9500	+	19.0237i	1.50553	+	0.869216i	0.505546	+	0.862799i	$0.331291\pi$
$480$		0			0
$481$	−8.88967	+	15.3974i	−0.405334	+	0.702059i
$482$		0			0
$483$	10.9320			0.497421
$484$		0			0
$485$	10.5316	+	6.08043i	0.478216	+	0.276098i
$486$		0			0
$487$	0.344521			0.0156117			0.00780586	−	0.999970i	$-0.497515\pi$
$487$	0.344521			0.0156117			0.00780586	+	0.999970i	$0.497515\pi$
$488$		0			0
$489$	−2.73048	+	1.57644i	−0.123477	+	0.0712893i
$490$		0			0
$491$	−0.838408	+	0.484055i	−0.0378368	+	0.0218451i	−0.518799	−	0.854896i	$-0.673621\pi$
$491$	−0.838408	+	0.484055i	−0.0378368	+	0.0218451i	0.480962	+	0.876741i	$0.340287\pi$
$492$		0			0
$493$		−	3.53712i		−	0.159304i
$494$		0			0
$495$			4.31187i			0.193804i
$496$		0			0
$497$	−1.10577	+	0.638419i	−0.0496008	+	0.0286370i
$498$		0			0
$499$	−12.2695	+	7.08381i	−0.549259	+	0.317115i	−0.748823	−	0.662770i	$-0.769381\pi$
$499$	−12.2695	+	7.08381i	−0.549259	+	0.317115i	0.199564	+	0.979885i	$0.436047\pi$
$500$		0			0
$501$	−6.99258			−0.312406
$502$		0			0
$503$	−36.7752	−	21.2322i	−1.63972	−	0.946695i	−0.980928	−	0.194374i	$-0.937733\pi$
$503$	−36.7752	−	21.2322i	−1.63972	−	0.946695i	−0.658796	−	0.752321i	$-0.728934\pi$
$504$		0			0
$505$	10.0968			0.449302
$506$		0			0
$507$	−3.17226	+	5.49452i	−0.140885	+	0.244020i
$508$		0			0
$509$	15.4758	+	8.93496i	0.685953	+	0.396035i	0.802094	−	0.597198i	$-0.203719\pi$
$509$	15.4758	+	8.93496i	0.685953	+	0.396035i	−0.116141	+	0.993233i	$0.537053\pi$
$510$		0			0
$511$	−16.8421	+	9.72380i	−0.745051	+	0.430156i
$512$		0			0
$513$	2.43807	+	3.61328i	0.107643	+	0.159530i
$514$		0			0
$515$	7.82272	+	13.5494i	0.344710	+	0.597056i
$516$		0			0
$517$	−14.8203	+	25.6695i	−0.651797	+	1.12895i
$518$		0			0
$519$	17.3068	+	9.99208i	0.759684	+	0.438604i
$520$		0			0
$521$		−	11.0384i		−	0.483601i	−0.970326	−	0.241800i	$-0.922262\pi$
$521$		−	11.0384i		−	0.483601i	0.970326	−	0.241800i	$-0.0777379\pi$
$522$		0			0
$523$	11.0824	−	19.1953i	0.484600	−	0.839353i	−0.515243	−	0.857044i	$-0.672298\pi$
$523$	11.0824	−	19.1953i	0.484600	−	0.839353i	0.999843	+	0.0176915i	$0.00563168\pi$
$524$		0			0
$525$		−	4.62309i		−	0.201768i
$526$		0			0
$527$	−0.734191	−	1.27166i	−0.0319819	−	0.0553942i
$528$		0			0
$529$	16.6345	+	28.8119i	0.723240	+	1.25269i
$530$		0			0
$531$	−1.35194			−0.0586692
$532$		0			0
$533$	12.0820			0.523328
$534$		0			0
$535$	6.87614	+	11.9098i	0.297281	+	0.514906i
$536$		0			0
$537$	−7.84823	−	13.5935i	−0.338676	−	0.586604i
$538$		0			0
$539$			15.5519i			0.669870i
$540$		0			0
$541$	−12.4245	+	21.5199i	−0.534173	+	0.925214i	0.465030	+	0.885295i	$0.346043\pi$
$541$	−12.4245	+	21.5199i	−0.534173	+	0.925214i	−0.999203	+	0.0399193i	$0.987290\pi$
$542$		0			0
$543$		−	15.3739i		−	0.659758i
$544$		0			0
$545$	−9.88836	−	5.70905i	−0.423571	−	0.244549i
$546$		0			0
$547$	15.8798	−	27.5047i	0.678973	−	1.17602i	−0.296317	−	0.955090i	$-0.595759\pi$
$547$	15.8798	−	27.5047i	0.678973	−	1.17602i	0.975290	−	0.220927i	$-0.0709081\pi$
$548$		0			0
$549$	4.29001	+	7.43051i	0.183093	+	0.317127i
$550$		0			0
$551$	−0.258391	−	3.68630i	−0.0110078	−	0.157042i
$552$		0			0
$553$	−6.38095	+	3.68404i	−0.271345	+	0.156661i
$554$		0			0
$555$	8.06889	+	4.65858i	0.342505	+	0.197746i
$556$		0			0
$557$	4.72677	−	8.18701i	0.200280	−	0.346895i	−0.748339	−	0.663317i	$-0.769148\pi$
$557$	4.72677	−	8.18701i	0.200280	−	0.346895i	0.948619	+	0.316422i	$0.102482\pi$
$558$		0			0
$559$	19.4461			0.822484
$560$		0			0
$561$	11.5242	+	6.65350i	0.486552	+	0.280911i
$562$		0			0
$563$	−43.5503			−1.83543			−0.917714	−	0.397242i	$-0.869968\pi$
$563$	−43.5503			−1.83543			−0.917714	+	0.397242i	$0.869968\pi$
$564$		0			0
$565$	14.6151	−	8.43805i	0.614863	−	0.354992i
$566$		0			0
$567$	1.26210	−	0.728674i	0.0530032	−	0.0306014i
$568$		0			0
$569$		−	46.3471i		−	1.94297i	−0.237097	−	0.971486i	$-0.576196\pi$
$569$		−	46.3471i		−	1.94297i	0.237097	−	0.971486i	$-0.423804\pi$
$570$		0			0
$571$			38.0346i			1.59170i	0.605495	+	0.795849i	$0.292975\pi$
$571$			38.0346i			1.59170i	−0.605495	+	0.795849i	$0.707025\pi$
$572$		0			0
$573$	−3.34212	+	1.92957i	−0.139619	+	0.0806090i
$574$		0			0
$575$	20.6079	−	11.8980i	0.859410	−	0.496181i
$576$		0			0
$577$	22.8761			0.952346			0.476173	−	0.879352i	$-0.342024\pi$
$577$	22.8761			0.952346			0.476173	+	0.879352i	$0.342024\pi$
$578$		0			0
$579$	11.8142	+	6.82094i	0.490982	+	0.283468i
$580$		0			0
$581$	−10.5316			−0.436925
$582$		0			0
$583$	−16.1345	+	27.9458i	−0.668224	+	1.15740i
$584$		0			0
$585$	−3.02049	−	1.74388i	−0.124882	−	0.0721006i
$586$		0			0
$587$	17.6079	−	10.1659i	0.726757	−	0.419593i	−0.0904777	−	0.995898i	$-0.528839\pi$
$587$	17.6079	−	10.1659i	0.726757	−	0.419593i	0.817235	+	0.576305i	$0.195506\pi$
$588$		0			0
$589$	−0.858052	−	1.27166i	−0.0353554	−	0.0523977i
$590$		0			0
$591$	−11.8785	−	20.5742i	−0.488618	−	0.846311i
$592$		0			0
$593$	−3.81792	+	6.61283i	−0.156783	+	0.271556i	−0.933707	−	0.358038i	$-0.883446\pi$
$593$	−3.81792	+	6.61283i	−0.156783	+	0.271556i	0.776924	+	0.629595i	$0.216779\pi$
$594$		0			0
$595$	7.11905	+	4.11019i	0.291853	+	0.168501i
$596$		0			0
$597$			22.5403i			0.922514i
$598$		0			0
$599$	−5.94178	+	10.2915i	−0.242774	+	0.420498i	−0.961504	−	0.274792i	$-0.911391\pi$
$599$	−5.94178	+	10.2915i	−0.242774	+	0.420498i	0.718729	+	0.695290i	$0.244724\pi$
$600$		0			0
$601$		−	35.0962i		−	1.43161i	−0.698303	−	0.715803i	$-0.746061\pi$
$601$		−	35.0962i		−	1.43161i	0.698303	−	0.715803i	$-0.253939\pi$
$602$		0			0
$603$	1.08984	+	1.88766i	0.0443817	+	0.0768713i
$604$		0			0
$605$	−0.559527	−	0.969129i	−0.0227480	−	0.0394007i
$606$		0			0
$607$	−32.9293			−1.33656			−0.668280	−	0.743909i	$-0.732969\pi$
$607$	−32.9293			−1.33656			−0.668280	+	0.743909i	$0.732969\pi$
$608$		0			0
$609$	−1.23550			−0.0500648
$610$		0			0
$611$	−11.9878	−	20.7634i	−0.484973	−	0.839999i
$612$		0			0
$613$	14.8310	+	25.6880i	0.599018	+	1.03753i	0.992966	+	0.118397i	$0.0377756\pi$
$613$	14.8310	+	25.6880i	0.599018	+	1.03753i	−0.393948	+	0.919133i	$0.628891\pi$
$614$		0			0
$615$		−	6.33148i		−	0.255310i
$616$		0			0
$617$	13.2560	−	22.9600i	0.533666	−	0.924337i	−0.465561	−	0.885016i	$-0.654147\pi$
$617$	13.2560	−	22.9600i	0.533666	−	0.924337i	0.999227	−	0.0393206i	$-0.0125194\pi$
$618$		0			0
$619$		−	19.8510i		−	0.797878i	−0.916977	−	0.398939i	$-0.869379\pi$
$619$		−	19.8510i		−	0.797878i	0.916977	−	0.398939i	$-0.130621\pi$
$620$		0			0
$621$	6.49629	+	3.75064i	0.260687	+	0.150508i
$622$		0			0
$623$	3.21240	−	5.56403i	0.128702	−	0.222918i
$624$		0			0
$625$	−0.462269	−	0.800673i	−0.0184908	−	0.0320269i
$626$		0			0
$627$	12.4963	+	6.09226i	0.499054	+	0.243302i
$628$		0			0
$629$	24.9016	−	14.3770i	0.992894	−	0.573247i
$630$		0			0
$631$	20.3179	+	11.7306i	0.808844	+	0.466986i	0.846554	−	0.532303i	$-0.178673\pi$
$631$	20.3179	+	11.7306i	0.808844	+	0.466986i	−0.0377106	+	0.999289i	$0.512006\pi$
$632$		0			0
$633$	−11.0521	+	19.1428i	−0.439282	+	0.760859i
$634$		0			0
$635$	−9.52901			−0.378147
$636$		0			0
$637$	−10.8942	−	6.28978i	−0.431645	−	0.249210i
$638$		0			0
$639$	−0.876139			−0.0346595
$640$		0			0
$641$	42.4535	−	24.5106i	1.67681	−	0.968109i	0.713143	−	0.701019i	$-0.247271\pi$
$641$	42.4535	−	24.5106i	1.67681	−	0.968109i	0.963672	−	0.267090i	$-0.0860622\pi$
$642$		0			0
$643$	−12.8495	+	7.41868i	−0.506736	+	0.292564i	−0.731491	−	0.681851i	$-0.761175\pi$
$643$	−12.8495	+	7.41868i	−0.506736	+	0.292564i	0.224755	+	0.974415i	$0.427842\pi$
$644$		0			0
$645$		−	10.1906i		−	0.401255i
$646$		0			0
$647$		−	25.8135i		−	1.01484i	−0.861700	−	0.507418i	$-0.830600\pi$
$647$		−	25.8135i		−	1.01484i	0.861700	−	0.507418i	$-0.169400\pi$
$648$		0			0
$649$	−3.73419	+	2.15594i	−0.146580	+	0.0846279i
$650$		0			0
$651$	−0.444182	+	0.256449i	−0.0174089	+	0.0100510i
$652$		0			0
$653$	24.6433			0.964365			0.482183	−	0.876071i	$-0.339844\pi$
$653$	24.6433			0.964365			0.482183	+	0.876071i	$0.339844\pi$
$654$		0			0
$655$	−3.70649	−	2.13994i	−0.144825	−	0.0836145i
$656$		0			0
$657$	−13.3445			−0.520619
$658$		0			0
$659$	0.0582214	−	0.100842i	0.00226798	−	0.00392826i	−0.864889	−	0.501963i	$-0.832611\pi$
$659$	0.0582214	−	0.100842i	0.00226798	−	0.00392826i	0.867157	+	0.498035i	$0.165945\pi$
$660$		0			0
$661$	5.35675	+	3.09272i	0.208353	+	0.120293i	0.600546	−	0.799590i	$-0.294950\pi$
$661$	5.35675	+	3.09272i	0.208353	+	0.120293i	−0.392193	+	0.919883i	$0.628283\pi$
$662$		0			0
$663$	−9.32163	+	5.38184i	−0.362022	+	0.209013i
$664$		0			0
$665$	7.71956	+	3.76348i	0.299352	+	0.145942i
$666$		0			0
$667$	−3.17968	−	5.50737i	−0.123118	−	0.213246i
$668$		0			0
$669$	−2.87985	+	4.98804i	−0.111341	+	0.192849i
$670$		0			0
$671$	23.6989	+	13.6825i	0.914884	+	0.528209i
$672$		0			0
$673$		−	18.6082i		−	0.717292i	−0.933474	−	0.358646i	$-0.883239\pi$
$673$		−	18.6082i		−	0.717292i	0.933474	−	0.358646i	$-0.116761\pi$
$674$		0			0
$675$	1.58613	−	2.74726i	0.0610502	−	0.105742i
$676$		0			0
$677$			28.9793i			1.11376i	0.830591	+	0.556882i	$0.188003\pi$
$677$			28.9793i			1.11376i	−0.830591	+	0.556882i	$0.811997\pi$
$678$		0			0
$679$	−6.55451	−	11.3527i	−0.251539	−	0.435678i
$680$		0			0
$681$	11.7621	+	20.3726i	0.450725	+	0.780678i
$682$		0			0
$683$	−43.8687			−1.67859			−0.839295	−	0.543676i	$-0.817032\pi$
$683$	−43.8687			−1.67859			−0.839295	+	0.543676i	$0.817032\pi$
$684$		0			0
$685$	8.81029			0.336624
$686$		0			0
$687$	2.88225	+	4.99221i	0.109965	+	0.190465i
$688$		0			0
$689$	−13.0508	−	22.6047i	−0.497196	−	0.861169i
$690$		0			0
$691$		−	27.2837i		−	1.03792i	−0.854798	−	0.518961i	$-0.826319\pi$
$691$		−	27.2837i		−	1.03792i	0.854798	−	0.518961i	$-0.173681\pi$
$692$		0			0
$693$	2.32403	−	4.02534i	0.0882826	−	0.152910i
$694$		0			0
$695$		−	19.4584i		−	0.738100i
$696$		0			0
$697$	−16.9219	−	9.76988i	−0.640964	−	0.370061i
$698$		0			0
$699$	−0.321627	+	0.557074i	−0.0121650	+	0.0210705i
$700$		0			0
$701$	5.44047	+	9.42318i	0.205484	+	0.355908i	0.950287	−	0.311376i	$-0.100790\pi$
$701$	5.44047	+	9.42318i	0.205484	+	0.355908i	−0.744803	+	0.667284i	$0.767457\pi$
$702$		0			0
$703$	24.9016	−	16.8024i	0.939183	−	0.633716i
$704$		0			0
$705$	−10.8809	+	6.28212i	−0.409800	+	0.236598i
$706$		0			0
$707$	−9.42584	−	5.44201i	−0.354495	−	0.204668i
$708$		0			0
$709$	−24.8626	+	43.0633i	−0.933735	+	1.61728i	−0.156860	+	0.987621i	$0.550137\pi$
$709$	−24.8626	+	43.0633i	−0.933735	+	1.61728i	−0.776875	+	0.629655i	$0.783196\pi$
$710$		0			0
$711$	−5.05582			−0.189608
$712$		0			0
$713$	−2.28630	−	1.32000i	−0.0856226	−	0.0494342i
$714$		0			0
$715$	−11.1239			−0.416009
$716$		0			0
$717$	5.76210	−	3.32675i	0.215190	−	0.124240i
$718$		0			0
$719$	26.6079	−	15.3621i	0.992308	−	0.572909i	0.0863447	−	0.996265i	$-0.472481\pi$
$719$	26.6079	−	15.3621i	0.992308	−	0.572909i	0.905963	+	0.423356i	$0.139148\pi$
$720$		0			0
$721$		−	16.8653i		−	0.628096i
$722$		0			0
$723$		−	0.633237i		−	0.0235503i
$724$		0			0
$725$	−2.32905	+	1.34467i	−0.0864986	+	0.0499400i
$726$		0			0
$727$	25.9963	−	15.0090i	0.964149	−	0.556652i	0.0667015	−	0.997773i	$-0.478752\pi$
$727$	25.9963	−	15.0090i	0.964149	−	0.556652i	0.897448	+	0.441121i	$0.145419\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−27.2361	−	15.7248i	−1.00736	−	0.581602i
$732$		0			0
$733$	−47.3026			−1.74716			−0.873581	−	0.486679i	$-0.838208\pi$
$733$	−47.3026			−1.74716			−0.873581	+	0.486679i	$0.838208\pi$
$734$		0			0
$735$	−3.29612	+	5.70905i	−0.121579	+	0.210581i
$736$		0			0
$737$	6.02049	+	3.47593i	0.221768	+	0.128038i
$738$		0			0
$739$	27.3515	−	15.7914i	1.00614	−	0.580895i	0.0960811	−	0.995374i	$-0.469369\pi$
$739$	27.3515	−	15.7914i	1.00614	−	0.580895i	0.910059	+	0.414478i	$0.136036\pi$
$740$		0			0
$741$	−9.32163	+	6.28978i	−0.342439	+	0.231061i
$742$		0			0
$743$	16.7063	+	28.9361i	0.612894	+	1.06156i	0.990750	+	0.135699i	$0.0433281\pi$
$743$	16.7063	+	28.9361i	0.612894	+	1.06156i	−0.377856	+	0.925864i	$0.623339\pi$
$744$		0			0
$745$	−4.32643	+	7.49360i	−0.158508	+	0.274544i
$746$		0			0
$747$	−6.25839	−	3.61328i	−0.228983	−	0.132203i
$748$		0			0
$749$		−	14.8245i		−	0.541676i
$750$		0			0
$751$	9.84212	−	17.0470i	0.359144	−	0.622056i	−0.628674	−	0.777669i	$-0.716402\pi$
$751$	9.84212	−	17.0470i	0.359144	−	0.622056i	0.987818	+	0.155613i	$0.0497354\pi$
$752$		0			0
$753$			7.04854i			0.256863i
$754$		0			0
$755$	6.51678	+	11.2874i	0.237170	+	0.410790i
$756$		0			0
$757$	16.5181	+	28.6102i	0.600360	+	1.03985i	0.992766	+	0.120062i	$0.0383094\pi$
$757$	16.5181	+	28.6102i	0.600360	+	1.03985i	−0.392406	+	0.919792i	$0.628357\pi$
$758$		0			0
$759$	23.9245			0.868406
$760$		0			0
$761$	−46.5726			−1.68826			−0.844128	−	0.536142i	$-0.819881\pi$
$761$	−46.5726			−1.68826			−0.844128	+	0.536142i	$0.819881\pi$
$762$		0			0
$763$	6.15417	+	10.6593i	0.222796	+	0.385894i
$764$		0			0
$765$	2.82032	+	4.88494i	0.101969	+	0.176615i
$766$		0			0
$767$		−	3.48776i		−	0.125936i
$768$		0			0
$769$	15.9562	−	27.6369i	0.575394	−	0.996611i	−0.420605	−	0.907244i	$-0.638182\pi$
$769$	15.9562	−	27.6369i	0.575394	−	0.996611i	0.995999	−	0.0893673i	$-0.0284845\pi$
$770$		0			0
$771$		−	25.1201i		−	0.904680i
$772$		0			0
$773$	−13.0558	−	7.53778i	−0.469585	−	0.271115i	0.246481	−	0.969148i	$-0.420726\pi$
$773$	−13.0558	−	7.53778i	−0.469585	−	0.271115i	−0.716066	+	0.698033i	$0.754059\pi$
$774$		0			0
$775$	−0.558221	+	0.966868i	−0.0200519	+	0.0347309i
$776$		0			0
$777$	−5.02180	−	8.69801i	−0.180156	−	0.312039i
$778$		0			0
$779$	−18.3493	−	8.94577i	−0.657433	−	0.320515i
$780$		0			0
$781$	−2.41998	+	1.39718i	−0.0865938	+	0.0499949i
$782$		0			0
$783$	−0.734191	−	0.423885i	−0.0262378	−	0.0151484i
$784$		0			0
$785$	−15.8556	+	27.4628i	−0.565912	+	0.980189i
$786$		0			0
$787$	−37.9023			−1.35107			−0.675535	−	0.737328i	$-0.736087\pi$
$787$	−37.9023			−1.35107			−0.675535	+	0.737328i	$0.736087\pi$
$788$		0			0
$789$	−12.3216	−	7.11389i	−0.438662	−	0.253261i
$790$		0			0
$791$	−18.1919			−0.646830
$792$		0			0
$793$	−19.1694	+	11.0675i	−0.680725	+	0.393017i
$794$		0			0
$795$	−11.8458	+	6.83919i	−0.420128	+	0.242561i
$796$		0			0
$797$			2.06692i			0.0732142i	0.999330	+	0.0366071i	$0.0116550\pi$
$797$			2.06692i			0.0732142i	−0.999330	+	0.0366071i	$0.988345\pi$
$798$		0			0
$799$			38.7749i			1.37176i
$800$		0			0
$801$	3.81792	−	2.20428i	0.134899	−	0.0778843i
$802$		0			0
$803$	−36.8589	+	21.2805i	−1.30072	+	0.750972i
$804$		0			0
$805$	14.7793			0.520903
$806$		0			0
$807$	1.18950	+	0.686759i	0.0418724	+	0.0241751i
$808$		0			0
$809$	−19.2255			−0.675931			−0.337966	−	0.941158i	$-0.609739\pi$
$809$	−19.2255			−0.675931			−0.337966	+	0.941158i	$0.609739\pi$
$810$		0			0
$811$	−5.94418	+	10.2956i	−0.208728	+	0.361528i	−0.951314	−	0.308223i	$-0.900266\pi$
$811$	−5.94418	+	10.2956i	−0.208728	+	0.361528i	0.742586	+	0.669751i	$0.233599\pi$
$812$		0			0
$813$	10.4684	+	6.04392i	0.367142	+	0.211970i
$814$		0			0
$815$	−3.69145	+	2.13126i	−0.129306	+	0.0746547i
$816$		0			0
$817$	−29.5336	−	14.3984i	−1.03325	−	0.503735i
$818$		0			0
$819$	1.87985	+	3.25599i	0.0656872	+	0.113774i
$820$		0			0
$821$	−5.26581	+	9.12065i	−0.183778	+	0.318313i	−0.943164	−	0.332327i	$-0.892166\pi$
$821$	−5.26581	+	9.12065i	−0.183778	+	0.318313i	0.759386	+	0.650640i	$0.225499\pi$
$822$		0			0
$823$	−20.0894	−	11.5986i	−0.700272	−	0.404302i	0.107177	−	0.994240i	$-0.465819\pi$
$823$	−20.0894	−	11.5986i	−0.700272	−	0.404302i	−0.807449	+	0.589938i	$0.799152\pi$
$824$		0			0
$825$		−	10.1176i		−	0.352250i
$826$		0			0
$827$	20.6029	−	35.6853i	0.716433	−	1.24090i	−0.245971	−	0.969277i	$-0.579107\pi$
$827$	20.6029	−	35.6853i	0.716433	−	1.24090i	0.962404	−	0.271622i	$-0.0875600\pi$
$828$		0			0
$829$		−	3.00889i		−	0.104503i	−0.998634	−	0.0522515i	$-0.983360\pi$
$829$		−	3.00889i		−	0.104503i	0.998634	−	0.0522515i	$-0.0166398\pi$
$830$		0			0
$831$	−2.79001	−	4.83244i	−0.0967843	−	0.167635i
$832$		0			0
$833$	10.1723	+	17.6189i	0.352448	+	0.610458i
$834$		0			0
$835$	−9.45355			−0.327153
$836$		0			0
$837$	−0.351939			−0.0121648
$838$		0			0
$839$	−15.1747	−	26.2833i	−0.523888	−	0.907400i	−0.999613	−	0.0278063i	$-0.991148\pi$
$839$	−15.1747	−	26.2833i	−0.523888	−	0.907400i	0.475726	−	0.879594i	$-0.342185\pi$
$840$		0			0
$841$	−14.1406	−	24.4923i	−0.487608	−	0.844562i
$842$		0			0
$843$		−	13.4037i		−	0.461647i
$844$		0			0
$845$	−4.28870	+	7.42825i	−0.147536	+	0.255540i
$846$		0			0
$847$			1.20630i			0.0414491i
$848$		0			0
$849$	7.88095	+	4.55007i	0.270473	+	0.156158i
$850$		0			0
$851$	25.8482	−	44.7704i	0.886066	−	1.53471i
$852$		0			0
$853$	3.61644	+	6.26386i	0.123825	+	0.214471i	0.921273	−	0.388917i	$-0.127151\pi$
$853$	3.61644	+	6.26386i	0.123825	+	0.214471i	−0.797448	+	0.603387i	$0.793817\pi$
$854$		0			0
$855$	3.29612	+	4.88494i	0.112725	+	0.167061i
$856$		0			0
$857$	−6.10422	+	3.52427i	−0.208516	+	0.120387i	−0.600622	−	0.799533i	$-0.705080\pi$
$857$	−6.10422	+	3.52427i	−0.208516	+	0.120387i	0.392105	+	0.919920i	$0.371747\pi$
$858$		0			0
$859$	−14.6263	−	8.44448i	−0.499042	−	0.288122i	0.229276	−	0.973361i	$-0.426364\pi$
$859$	−14.6263	−	8.44448i	−0.499042	−	0.288122i	−0.728318	+	0.685240i	$0.759697\pi$
$860$		0			0
$861$	−3.41256	+	5.91073i	−0.116300	+	0.201437i
$862$		0			0
$863$	−32.5530			−1.10812			−0.554058	−	0.832478i	$-0.686921\pi$
$863$	−32.5530			−1.10812			−0.554058	+	0.832478i	$0.686921\pi$
$864$		0			0
$865$	23.3977	+	13.5087i	0.795547	+	0.459309i
$866$		0			0
$867$	0.407757			0.0138481
$868$		0			0
$869$	−13.9647	+	8.06251i	−0.473719	+	0.273502i
$870$		0			0
$871$	−4.86982	+	2.81159i	−0.165008	+	0.0952671i
$872$		0			0
$873$		−	8.99513i		−	0.304439i
$874$		0			0
$875$		−	16.1014i		−	0.544325i
$876$		0			0
$877$	18.7791	−	10.8421i	0.634125	−	0.366112i	−0.148223	−	0.988954i	$-0.547355\pi$
$877$	18.7791	−	10.8421i	0.634125	−	0.366112i	0.782348	+	0.622842i	$0.214022\pi$
$878$		0			0
$879$	−4.94418	+	2.85453i	−0.166763	+	0.0962807i
$880$		0			0
$881$	40.0558			1.34951			0.674757	−	0.738040i	$-0.264248\pi$
$881$	40.0558			1.34951			0.674757	+	0.738040i	$0.264248\pi$
$882$		0			0
$883$	1.10793	+	0.639661i	0.0372847	+	0.0215263i	0.518526	−	0.855062i	$-0.326481\pi$
$883$	1.10793	+	0.639661i	0.0372847	+	0.0215263i	−0.481242	+	0.876588i	$0.659814\pi$
$884$		0			0
$885$	−1.82774			−0.0614388
$886$		0			0
$887$	11.8408	−	20.5089i	0.397576	−	0.688621i	−0.595851	−	0.803095i	$-0.703185\pi$
$887$	11.8408	−	20.5089i	0.397576	−	0.688621i	0.993426	+	0.114474i	$0.0365183\pi$
$888$		0			0
$889$	8.89578	+	5.13598i	0.298355	+	0.172255i
$890$		0			0
$891$	2.76210	−	1.59470i	0.0925338	−	0.0534244i
$892$		0			0
$893$	2.83255	+	40.4102i	0.0947876	+	1.35228i
$894$		0			0
$895$	−10.6103	−	18.3776i	−0.354664	−	0.614296i
$896$		0			0
$897$	−9.67597	+	16.7593i	−0.323071	+	0.559576i
$898$		0			0
$899$	0.258391	+	0.149182i	0.00861781	+	0.00497549i
$900$		0			0
$901$			42.2133i			1.40633i
$902$		0			0
$903$	−5.49258	+	9.51343i	−0.182782	+	0.316587i
$904$		0			0
$905$		−	20.7846i		−	0.690904i
$906$		0			0
$907$	10.9926	+	19.0397i	0.365003	+	0.632203i	0.988777	−	0.149402i	$-0.0477347\pi$
$907$	10.9926	+	19.0397i	0.365003	+	0.632203i	−0.623774	+	0.781605i	$0.714401\pi$
$908$		0			0
$909$	−3.73419	−	6.46781i	−0.123855	−	0.214524i
$910$		0			0
$911$	−51.5046			−1.70642			−0.853211	−	0.521566i	$-0.825348\pi$
$911$	−51.5046			−1.70642			−0.853211	+	0.521566i	$0.825348\pi$
$912$		0			0
$913$	−23.0484			−0.762791
$914$		0			0
$915$	5.79983	+	10.0456i	0.191736	+	0.332097i
$916$		0			0
$917$	2.30679	+	3.99548i	0.0761769	+	0.131942i
$918$		0			0
$919$		−	34.8792i		−	1.15056i	−0.817957	−	0.575279i	$-0.804893\pi$
$919$		−	34.8792i		−	1.15056i	0.817957	−	0.575279i	$-0.195107\pi$
$920$		0			0
$921$	11.1419	−	19.2984i	0.367140	−	0.635905i
$922$		0			0
$923$		−	2.26028i		−	0.0743981i
$924$		0			0
$925$	−18.9333	−	10.9311i	−0.622522	−	0.359413i
$926$		0			0
$927$	5.78630	−	10.0222i	0.190047	−	0.329171i
$928$		0			0
$929$	−23.7244	−	41.0918i	−0.778371	−	1.34818i	−0.932880	−	0.360187i	$-0.882713\pi$
$929$	−23.7244	−	41.0918i	−0.778371	−	1.34818i	0.154509	−	0.987991i	$-0.450621\pi$
$930$		0			0
$931$	11.8884	+	17.6189i	0.389625	+	0.577435i
$932$		0			0
$933$	−18.1247	+	10.4643i	−0.593376	+	0.342586i
$934$		0			0
$935$	15.5800	+	8.99513i	0.509521	+	0.294172i
$936$		0			0
$937$	−12.0545	+	20.8790i	−0.393804	+	0.682088i	−0.992948	−	0.118553i	$-0.962174\pi$
$937$	−12.0545	+	20.8790i	−0.393804	+	0.682088i	0.599144	+	0.800641i	$0.295508\pi$
$938$		0			0
$939$	−1.12386			−0.0366758
$940$		0			0
$941$	−7.16003	−	4.13385i	−0.233410	−	0.134760i	0.378734	−	0.925506i	$-0.376360\pi$
$941$	−7.16003	−	4.13385i	−0.233410	−	0.134760i	−0.612144	+	0.790746i	$0.709693\pi$
$942$		0			0
$943$	−35.1304			−1.14400
$944$		0			0
$945$	1.70628	−	0.985122i	0.0555054	−	0.0320460i
$946$		0			0
$947$	−1.66354	+	0.960443i	−0.0540577	+	0.0312102i	−0.526785	−	0.849998i	$-0.676603\pi$
$947$	−1.66354	+	0.960443i	−0.0540577	+	0.0312102i	0.472728	+	0.881209i	$0.343269\pi$
$948$		0			0
$949$		−	34.4265i		−	1.11753i
$950$		0			0
$951$			17.3442i			0.562423i
$952$		0			0
$953$	−16.9014	+	9.75805i	−0.547491	+	0.316094i	−0.748110	−	0.663575i	$-0.769038\pi$
$953$	−16.9014	+	9.75805i	−0.547491	+	0.316094i	0.200618	+	0.979669i	$0.435705\pi$
$954$		0			0
$955$	−4.51834	+	2.60866i	−0.146210	+	0.0844144i
$956$		0			0
$957$	−2.70388			−0.0874040
$958$		0			0
$959$	−8.22483	−	4.74861i	−0.265594	−	0.153341i
$960$		0			0
$961$	−30.8761			−0.996004
$962$		0			0
$963$	5.08613	−	8.80944i	0.163898	−	0.283880i
$964$		0			0
$965$	15.9721	+	9.22149i	0.514160	+	0.296850i
$966$		0			0
$967$	−34.1079	+	19.6922i	−1.09684	+	0.633259i	−0.935388	−	0.353622i	$-0.884950\pi$
$967$	−34.1079	+	19.6922i	−1.09684	+	0.633259i	−0.161449	+	0.986881i	$0.551617\pi$
$968$		0			0
$969$	18.1419	−	1.27166i	0.582803	−	0.0408515i
$970$		0			0
$971$	28.3519	+	49.1070i	0.909857	+	1.57592i	0.814261	+	0.580498i	$0.197142\pi$
$971$	28.3519	+	49.1070i	0.909857	+	1.57592i	0.0955956	+	0.995420i	$0.469524\pi$
$972$		0			0
$973$	−10.4878	+	18.1654i	−0.336223	+	0.582355i
$974$		0			0
$975$	7.08744	+	4.09193i	0.226980	+	0.131047i
$976$		0			0
$977$			26.5410i			0.849121i	0.905400	+	0.424561i	$0.139571\pi$
$977$			26.5410i			0.849121i	−0.905400	+	0.424561i	$0.860429\pi$
$978$		0			0
$979$	7.03031	−	12.1769i	0.224690	−	0.389174i
$980$		0			0
$981$			8.44572i			0.269651i
$982$		0			0
$983$	−26.2108	−	45.3985i	−0.835996	−	1.44799i	−0.893217	−	0.449626i	$-0.851557\pi$
$983$	−26.2108	−	45.3985i	−0.835996	−	1.44799i	0.0572211	−	0.998362i	$-0.481776\pi$
$984$		0			0
$985$	−16.0591	−	27.8151i	−0.511684	−	0.886263i
$986$		0			0
$987$	13.5438			0.431105
$988$		0			0
$989$	−56.5429			−1.79796
$990$		0			0
$991$	−28.3334	−	49.0749i	−0.900040	−	1.55891i	−0.827440	−	0.561554i	$-0.810204\pi$
$991$	−28.3334	−	49.0749i	−0.900040	−	1.55891i	−0.0725996	−	0.997361i	$-0.523130\pi$
$992$		0			0
$993$	−0.292412	−	0.506473i	−0.00927943	−	0.0160724i
$994$		0			0
$995$			30.4731i			0.966064i
$996$		0			0
$997$	4.44418	−	7.69755i	0.140749	−	0.243784i	−0.787030	−	0.616915i	$-0.788382\pi$
$997$	4.44418	−	7.69755i	0.140749	−	0.243784i	0.927779	+	0.373131i	$0.121716\pi$
$998$		0			0
$999$		−	6.89169i		−	0.218044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bb.e.31.2	✓	6
3.2	odd	2		2736.2.bm.n.1855.2		6
4.3	odd	2		912.2.bb.f.31.2	yes	6
12.11	even	2		2736.2.bm.o.1855.2		6
19.8	odd	6		912.2.bb.f.559.2	yes	6
57.8	even	6		2736.2.bm.o.559.2		6
76.27	even	6	inner	912.2.bb.e.559.2	yes	6
228.179	odd	6		2736.2.bm.n.559.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.e.31.2	✓	6	1.1	even	1	trivial
912.2.bb.e.559.2	yes	6	76.27	even	6	inner
912.2.bb.f.31.2	yes	6	4.3	odd	2
912.2.bb.f.559.2	yes	6	19.8	odd	6
2736.2.bm.n.559.2		6	228.179	odd	6
2736.2.bm.n.1855.2		6	3.2	odd	2
2736.2.bm.o.559.2		6	57.8	even	6
2736.2.bm.o.1855.2		6	12.11	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} +1.45735i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} +1.45735i q^{7} +(-0.500000 + 0.866025i) q^{9} +3.18940i q^{11} +(-2.23419 - 1.28991i) q^{13} +(-0.675970 + 1.17081i) q^{15} +(2.08613 + 3.61328i) q^{17} +(2.43807 + 3.61328i) q^{19} +(1.26210 - 0.728674i) q^{21} +(6.49629 + 3.75064i) q^{23} +(1.58613 - 2.74726i) q^{25} +1.00000 q^{27} +(-0.734191 - 0.423885i) q^{29} -0.351939 q^{31} +(2.76210 - 1.59470i) q^{33} +(1.70628 - 0.985122i) q^{35} -6.89169i q^{37} +2.57982i q^{39} +(-4.05582 + 2.34163i) q^{41} +(-6.52791 + 3.76889i) q^{43} +1.35194 q^{45} +(8.04840 + 4.64675i) q^{47} +4.87614 q^{49} +(2.08613 - 3.61328i) q^{51} +(8.76210 + 5.05880i) q^{53} +(3.73419 - 2.15594i) q^{55} +(1.91016 - 3.91807i) q^{57} +(0.675970 + 1.17081i) q^{59} +(4.29001 - 7.43051i) q^{61} +(-1.26210 - 0.728674i) q^{63} +3.48776i q^{65} +(1.08984 - 1.88766i) q^{67} -7.50127i q^{69} +(0.438069 + 0.758758i) q^{71} +(6.67226 + 11.5567i) q^{73} -3.17226 q^{75} -4.64806 q^{77} +(2.52791 + 4.37847i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.22657i q^{83} +(2.82032 - 4.88494i) q^{85} +0.847771i q^{87} +(-3.81792 - 2.20428i) q^{89} +(1.87985 - 3.25599i) q^{91} +(0.175970 + 0.304788i) q^{93} +(2.58242 - 5.29699i) q^{95} +(-7.79001 + 4.49756i) q^{97} +(-2.76210 - 1.59470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9	\( 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9} - 3 q^{13} - 2 q^{15} - 2 q^{17} - 4 q^{19} - 9 q^{21} + 12 q^{23} - 5 q^{25} + 6 q^{27} + 6 q^{29} + 2 q^{31} + 6 q^{35} - 12 q^{41} - 33 q^{43} + 4 q^{45} - 18 q^{47} - 8 q^{49} - 2 q^{51} + 36 q^{53} + 12 q^{55} - q^{57} + 2 q^{59} + 3 q^{61} + 9 q^{63} + 19 q^{67} - 16 q^{71} + 11 q^{73} + 10 q^{75} - 32 q^{77} + 9 q^{79} - 3 q^{81} - 8 q^{85} + 6 q^{89} + q^{91} - q^{93} - 26 q^{95} - 24 q^{97}+O(q^{100}) \) 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9 - 3 * q^13 - 2 * q^15 - 2 * q^17 - 4 * q^19 - 9 * q^21 + 12 * q^23 - 5 * q^25 + 6 * q^27 + 6 * q^29 + 2 * q^31 + 6 * q^35 - 12 * q^41 - 33 * q^43 + 4 * q^45 - 18 * q^47 - 8 * q^49 - 2 * q^51 + 36 * q^53 + 12 * q^55 - q^57 + 2 * q^59 + 3 * q^61 + 9 * q^63 + 19 * q^67 - 16 * q^71 + 11 * q^73 + 10 * q^75 - 32 * q^77 + 9 * q^79 - 3 * q^81 - 8 * q^85 + 6 * q^89 + q^91 - q^93 - 26 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more