LMFDB - Embedded newform 644.2.i.a.93.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 13 x^{12} - 8 x^{11} + 130 x^{10} - 78 x^{9} + 505 x^{8} - 519 x^{7} + 1508 x^{6} - 955 x^{5} + \cdots + 1 $ x^14 + 13x^12 - 8x^11 + 130x^10 - 78x^9 + 505x^8 - 519x^7 + 1508x^6 - 955x^5 + 1023x^4 + 156x^3 + 107x^2 - 9x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.6
Root			$0.725556 + 1.25670i$ of defining polynomial
Character	$\chi$	$=$	644.93
Dual form			644.2.i.a.277.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04242 + 1.80553i) q^{3} +(-1.94126 + 3.36236i) q^{5} +(-2.32824 + 1.25670i) q^{7} +(-0.673281 + 1.16616i) q^{9} +O(q^{10})$	\(q+(1.04242 + 1.80553i) q^{3} +(-1.94126 + 3.36236i) q^{5} +(-2.32824 + 1.25670i) q^{7} +(-0.673281 + 1.16616i) q^{9} +(-2.28623 - 3.95986i) q^{11} +2.58017 q^{13} -8.09442 q^{15} +(2.22435 + 3.85269i) q^{17} +(-1.93728 + 3.35547i) q^{19} +(-4.69601 - 2.89369i) q^{21} +(0.500000 - 0.866025i) q^{23} +(-5.03696 - 8.72427i) q^{25} +3.44716 q^{27} -6.62079 q^{29} +(-2.51523 - 4.35651i) q^{31} +(4.76642 - 8.25567i) q^{33} +(0.294241 - 10.2680i) q^{35} +(-3.14732 + 5.45131i) q^{37} +(2.68962 + 4.65856i) q^{39} -3.21229 q^{41} +7.89902 q^{43} +(-2.61402 - 4.52762i) q^{45} +(-4.74241 + 8.21410i) q^{47} +(3.84141 - 5.85180i) q^{49} +(-4.63742 + 8.03224i) q^{51} +(5.34517 + 9.25811i) q^{53} +17.7526 q^{55} -8.07785 q^{57} +(-0.915931 - 1.58644i) q^{59} +(-1.14021 + 1.97491i) q^{61} +(0.102051 - 3.56120i) q^{63} +(-5.00877 + 8.67544i) q^{65} +(0.962260 + 1.66668i) q^{67} +2.08484 q^{69} -1.37812 q^{71} +(0.660816 + 1.14457i) q^{73} +(10.5013 - 18.1887i) q^{75} +(10.2992 + 6.34640i) q^{77} +(2.22376 - 3.85167i) q^{79} +(5.61323 + 9.72240i) q^{81} -7.87643 q^{83} -17.2721 q^{85} +(-6.90165 - 11.9540i) q^{87} +(-5.50761 + 9.53946i) q^{89} +(-6.00725 + 3.24250i) q^{91} +(5.24386 - 9.08264i) q^{93} +(-7.52152 - 13.0277i) q^{95} +13.8660 q^{97} +6.15708 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	1.04242	+	1.80553i	0.601842	+	1.04242i	0.992542	+	0.121902i	$0.0388995\pi$
$3$	1.04242	+	1.80553i	0.601842	+	1.04242i	−0.390700	+	0.920518i	$0.627767\pi$
$4$		0			0
$5$	−1.94126	+	3.36236i	−0.868157	+	1.50369i	−0.00427815	+	0.999991i	$0.501362\pi$
$5$	−1.94126	+	3.36236i	−0.868157	+	1.50369i	−0.863878	+	0.503700i	$0.831972\pi$
$6$		0			0
$7$	−2.32824	+	1.25670i	−0.879992	+	0.474988i
$7$	−2.32824	+	1.25670i	−0.879992	+	0.474988i
$8$		0			0
$9$	−0.673281	+	1.16616i	−0.224427	+	0.388719i
$10$		0			0
$11$	−2.28623	−	3.95986i	−0.689323	−	1.19394i	−0.972057	−	0.234744i	$-0.924575\pi$
$11$	−2.28623	−	3.95986i	−0.689323	−	1.19394i	0.282734	−	0.959198i	$-0.408759\pi$
$12$		0			0
$13$	2.58017			0.715610			0.357805	−	0.933796i	$-0.383525\pi$
$13$	2.58017			0.715610			0.357805	+	0.933796i	$0.383525\pi$
$14$		0			0
$15$	−8.09442			−2.08997
$16$		0			0
$17$	2.22435	+	3.85269i	0.539484	+	0.934414i	0.998932	+	0.0462092i	$0.0147141\pi$
$17$	2.22435	+	3.85269i	0.539484	+	0.934414i	−0.459448	+	0.888205i	$0.651953\pi$
$18$		0			0
$19$	−1.93728	+	3.35547i	−0.444443	+	0.769798i	−0.998013	−	0.0630048i	$-0.979932\pi$
$19$	−1.93728	+	3.35547i	−0.444443	+	0.769798i	0.553570	+	0.832802i	$0.313265\pi$
$20$		0			0
$21$	−4.69601	−	2.89369i	−1.02475	−	0.631454i
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$		0			0
$25$	−5.03696	−	8.72427i	−1.00739	−	1.74485i
$26$		0			0
$27$	3.44716			0.663406
$28$		0			0
$29$	−6.62079			−1.22945			−0.614725	−	0.788741i	$-0.710733\pi$
$29$	−6.62079			−1.22945			−0.614725	+	0.788741i	$0.710733\pi$
$30$		0			0
$31$	−2.51523	−	4.35651i	−0.451749	−	0.782453i	0.546745	−	0.837299i	$-0.315867\pi$
$31$	−2.51523	−	4.35651i	−0.451749	−	0.782453i	−0.998495	+	0.0548459i	$0.982533\pi$
$32$		0			0
$33$	4.76642	−	8.25567i	0.829727	−	1.43713i
$34$		0			0
$35$	0.294241	−	10.2680i	0.0497358	−	1.73560i
$36$		0			0
$37$	−3.14732	+	5.45131i	−0.517416	+	0.896190i	0.482380	+	0.875962i	$0.339772\pi$
$37$	−3.14732	+	5.45131i	−0.517416	+	0.896190i	−0.999795	+	0.0202278i	$0.993561\pi$
$38$		0			0
$39$	2.68962	+	4.65856i	0.430684	+	0.745966i
$40$		0			0
$41$	−3.21229			−0.501675			−0.250838	−	0.968029i	$-0.580706\pi$
$41$	−3.21229			−0.501675			−0.250838	+	0.968029i	$0.580706\pi$
$42$		0			0
$43$	7.89902			1.20459			0.602294	−	0.798274i	$-0.294253\pi$
$43$	7.89902			1.20459			0.602294	+	0.798274i	$0.294253\pi$
$44$		0			0
$45$	−2.61402	−	4.52762i	−0.389675	−	0.674937i
$46$		0			0
$47$	−4.74241	+	8.21410i	−0.691752	+	1.19815i	0.279512	+	0.960142i	$0.409827\pi$
$47$	−4.74241	+	8.21410i	−0.691752	+	1.19815i	−0.971263	+	0.238007i	$0.923506\pi$
$48$		0			0
$49$	3.84141	−	5.85180i	0.548773	−	0.835971i
$50$		0			0
$51$	−4.63742	+	8.03224i	−0.649368	+	1.12474i
$52$		0			0
$53$	5.34517	+	9.25811i	0.734216	+	1.27170i	0.955066	+	0.296392i	$0.0957834\pi$
$53$	5.34517	+	9.25811i	0.734216	+	1.27170i	−0.220851	+	0.975308i	$0.570883\pi$
$54$		0			0
$55$	17.7526			2.39376
$56$		0			0
$57$	−8.07785			−1.06994
$58$		0			0
$59$	−0.915931	−	1.58644i	−0.119244	−	0.206537i	0.800224	−	0.599701i	$-0.204714\pi$
$59$	−0.915931	−	1.58644i	−0.119244	−	0.206537i	−0.919468	+	0.393164i	$0.871380\pi$
$60$		0			0
$61$	−1.14021	+	1.97491i	−0.145989	+	0.252861i	−0.929742	−	0.368212i	$-0.879970\pi$
$61$	−1.14021	+	1.97491i	−0.145989	+	0.252861i	0.783752	+	0.621074i	$0.213303\pi$
$62$		0			0
$63$	0.102051	−	3.56120i	0.0128572	−	0.448670i
$64$		0			0
$65$	−5.00877	+	8.67544i	−0.621261	+	1.07606i
$66$		0			0
$67$	0.962260	+	1.66668i	0.117559	+	0.203618i	0.918800	−	0.394724i	$-0.129160\pi$
$67$	0.962260	+	1.66668i	0.117559	+	0.203618i	−0.801241	+	0.598342i	$0.795826\pi$
$68$		0			0
$69$	2.08484			0.250985
$70$		0			0
$71$	−1.37812			−0.163552			−0.0817762	−	0.996651i	$-0.526059\pi$
$71$	−1.37812			−0.163552			−0.0817762	+	0.996651i	$0.526059\pi$
$72$		0			0
$73$	0.660816	+	1.14457i	0.0773427	+	0.133961i	0.902103	−	0.431522i	$-0.142023\pi$
$73$	0.660816	+	1.14457i	0.0773427	+	0.133961i	−0.824760	+	0.565483i	$0.808690\pi$
$74$		0			0
$75$	10.5013	−	18.1887i	1.21258	−	2.10025i
$76$		0			0
$77$	10.2992	+	6.34640i	1.17371	+	0.723240i
$78$		0			0
$79$	2.22376	−	3.85167i	0.250193	−	0.433347i	−0.713386	−	0.700771i	$-0.752839\pi$
$79$	2.22376	−	3.85167i	0.250193	−	0.433347i	0.963579	+	0.267425i	$0.0861726\pi$
$80$		0			0
$81$	5.61323	+	9.72240i	0.623692	+	1.08027i
$82$		0			0
$83$	−7.87643			−0.864551			−0.432275	−	0.901742i	$-0.642289\pi$
$83$	−7.87643			−0.864551			−0.432275	+	0.901742i	$0.642289\pi$
$84$		0			0
$85$	−17.2721			−1.87343
$86$		0			0
$87$	−6.90165	−	11.9540i	−0.739935	−	1.28160i
$88$		0			0
$89$	−5.50761	+	9.53946i	−0.583806	+	1.01118i	0.411218	+	0.911537i	$0.365104\pi$
$89$	−5.50761	+	9.53946i	−0.583806	+	1.01118i	−0.995023	+	0.0996438i	$0.968230\pi$
$90$		0			0
$91$	−6.00725	+	3.24250i	−0.629731	+	0.339906i
$92$		0			0
$93$	5.24386	−	9.08264i	0.543763	−	0.941826i
$94$		0			0
$95$	−7.52152	−	13.0277i	−0.771692	−	1.33661i
$96$		0			0
$97$	13.8660			1.40788			0.703938	−	0.710261i	$-0.251423\pi$
$97$	13.8660			1.40788			0.703938	+	0.710261i	$0.251423\pi$
$98$		0			0
$99$	6.15708			0.618810
$100$		0			0
$101$	7.74638	+	13.4171i	0.770794	+	1.33505i	0.937129	+	0.348984i	$0.113473\pi$
$101$	7.74638	+	13.4171i	0.770794	+	1.33505i	−0.166335	+	0.986069i	$0.553193\pi$
$102$		0			0
$103$	−7.67882	+	13.3001i	−0.756617	+	1.31050i	0.187950	+	0.982179i	$0.439816\pi$
$103$	−7.67882	+	13.3001i	−0.756617	+	1.31050i	−0.944567	+	0.328320i	$0.893518\pi$
$104$		0			0
$105$	18.8458	−	10.1723i	1.83916	−	0.992711i
$106$		0			0
$107$	−0.736748	+	1.27608i	−0.0712241	+	0.123364i	−0.899438	−	0.437048i	$-0.856024\pi$
$107$	−0.736748	+	1.27608i	−0.0712241	+	0.123364i	0.828214	+	0.560412i	$0.189357\pi$
$108$		0			0
$109$	7.88630	+	13.6595i	0.755370	+	1.30834i	0.945190	+	0.326520i	$0.105876\pi$
$109$	7.88630	+	13.6595i	0.755370	+	1.30834i	−0.189820	+	0.981819i	$0.560790\pi$
$110$		0			0
$111$	−13.1233			−1.24561
$112$		0			0
$113$	−12.9257			−1.21595			−0.607975	−	0.793956i	$-0.708018\pi$
$113$	−12.9257			−1.21595			−0.607975	+	0.793956i	$0.708018\pi$
$114$		0			0
$115$	1.94126	+	3.36236i	0.181023	+	0.313541i
$116$		0			0
$117$	−1.73718	+	3.00888i	−0.160602	+	0.278171i
$118$		0			0
$119$	−10.0205	−	6.17464i	−0.918577	−	0.566029i
$120$		0			0
$121$	−4.95365	+	8.57998i	−0.450332	+	0.779998i
$122$		0			0
$123$	−3.34855	−	5.79987i	−0.301929	−	0.522956i
$124$		0			0
$125$	19.6996			1.76198
$126$		0			0
$127$	16.2802			1.44463			0.722316	−	0.691563i	$-0.243077\pi$
$127$	16.2802			1.44463			0.722316	+	0.691563i	$0.243077\pi$
$128$		0			0
$129$	8.23409	+	14.2619i	0.724972	+	1.25569i
$130$		0			0
$131$	4.83995	−	8.38304i	0.422868	−	0.732429i	−0.573350	−	0.819310i	$-0.694357\pi$
$131$	4.83995	−	8.38304i	0.422868	−	0.732429i	0.996219	+	0.0868809i	$0.0276900\pi$
$132$		0			0
$133$	0.293638	−	10.2469i	0.0254617	−	0.888521i
$134$		0			0
$135$	−6.69182	+	11.5906i	−0.575940	+	0.997557i
$136$		0			0
$137$	0.846372	+	1.46596i	0.0723105	+	0.125245i	0.899914	−	0.436068i	$-0.143629\pi$
$137$	0.846372	+	1.46596i	0.0723105	+	0.125245i	−0.827603	+	0.561314i	$0.810296\pi$
$138$		0			0
$139$	14.6043			1.23872			0.619362	−	0.785106i	$-0.287392\pi$
$139$	14.6043			1.23872			0.619362	+	0.785106i	$0.287392\pi$
$140$		0			0
$141$	−19.7743			−1.66530
$142$		0			0
$143$	−5.89884	−	10.2171i	−0.493286	−	0.854396i
$144$		0			0
$145$	12.8527	−	22.2615i	1.06736	−	1.84871i
$146$		0			0
$147$	14.5699	+	0.835726i	1.20171	+	0.0689295i
$148$		0			0
$149$	3.59520	−	6.22707i	0.294530	−	0.510141i	−0.680345	−	0.732892i	$-0.738170\pi$
$149$	3.59520	−	6.22707i	0.294530	−	0.510141i	0.974876	+	0.222750i	$0.0715035\pi$
$150$		0			0
$151$	−5.45856	−	9.45450i	−0.444211	−	0.769397i	0.553786	−	0.832659i	$-0.313183\pi$
$151$	−5.45856	−	9.45450i	−0.444211	−	0.769397i	−0.997997	+	0.0632627i	$0.979849\pi$
$152$		0			0
$153$	−5.99045			−0.484299
$154$		0			0
$155$	19.5309			1.56876
$156$		0			0
$157$	−3.46236	−	5.99698i	−0.276326	−	0.478611i	0.694143	−	0.719838i	$-0.255784\pi$
$157$	−3.46236	−	5.99698i	−0.276326	−	0.478611i	−0.970469	+	0.241226i	$0.922450\pi$
$158$		0			0
$159$	−11.1438	+	19.3017i	−0.883764	+	1.53072i
$160$		0			0
$161$	−0.0757862	+	2.64467i	−0.00597279	+	0.208429i
$162$		0			0
$163$	10.3504	−	17.9275i	0.810709	−	1.40419i	−0.101660	−	0.994819i	$-0.532415\pi$
$163$	10.3504	−	17.9275i	0.810709	−	1.40419i	0.912369	−	0.409370i	$-0.134251\pi$
$164$		0			0
$165$	18.5057	+	32.0528i	1.44067	+	2.49531i
$166$		0			0
$167$	−19.7120			−1.52536			−0.762681	−	0.646775i	$-0.776117\pi$
$167$	−19.7120			−1.52536			−0.762681	+	0.646775i	$0.776117\pi$
$168$		0			0
$169$	−6.34274			−0.487903
$170$		0			0
$171$	−2.60867	−	4.51835i	−0.199490	−	0.345527i
$172$		0			0
$173$	−5.88837	+	10.1990i	−0.447685	+	0.775413i	−0.998235	−	0.0593894i	$-0.981085\pi$
$173$	−5.88837	+	10.1990i	−0.447685	+	0.775413i	0.550550	+	0.834802i	$0.314418\pi$
$174$		0			0
$175$	22.6910	+	13.9822i	1.71528	+	1.05696i
$176$		0			0
$177$	1.90957	−	3.30747i	0.143532	−	0.248605i
$178$		0			0
$179$	12.3182	+	21.3358i	0.920707	+	1.59471i	0.798324	+	0.602228i	$0.205720\pi$
$179$	12.3182	+	21.3358i	0.920707	+	1.59471i	0.122382	+	0.992483i	$0.460947\pi$
$180$		0			0
$181$	15.1888			1.12897			0.564486	−	0.825443i	$-0.309074\pi$
$181$	15.1888			1.12897			0.564486	+	0.825443i	$0.309074\pi$
$182$		0			0
$183$	−4.75433			−0.351450
$184$		0			0
$185$	−12.2195	−	21.1648i	−0.898395	−	1.55607i
$186$		0			0
$187$	10.1707	−	17.6162i	0.743758	−	1.28823i
$188$		0			0
$189$	−8.02581	+	4.33204i	−0.583792	+	0.315110i
$190$		0			0
$191$	8.55623	−	14.8198i	0.619107	−	1.07232i	−0.370542	−	0.928816i	$-0.620828\pi$
$191$	8.55623	−	14.8198i	0.619107	−	1.07232i	0.989649	−	0.143509i	$-0.0458386\pi$
$192$		0			0
$193$	−3.83273	−	6.63848i	−0.275886	−	0.477848i	0.694473	−	0.719519i	$-0.255638\pi$
$193$	−3.83273	−	6.63848i	−0.275886	−	0.477848i	−0.970358	+	0.241671i	$0.922304\pi$
$194$		0			0
$195$	−20.8850			−1.49560
$196$		0			0
$197$	25.3434			1.80564			0.902820	−	0.430019i	$-0.141493\pi$
$197$	25.3434			1.80564			0.902820	+	0.430019i	$0.141493\pi$
$198$		0			0
$199$	−3.32936	−	5.76661i	−0.236012	−	0.408784i	0.723554	−	0.690267i	$-0.242507\pi$
$199$	−3.32936	−	5.76661i	−0.236012	−	0.408784i	−0.959566	+	0.281483i	$0.909174\pi$
$200$		0			0
$201$	−2.00616	+	3.47477i	−0.141504	+	0.245091i
$202$		0			0
$203$	15.4148	−	8.32035i	1.08191	−	0.583974i
$204$		0			0
$205$	6.23588	−	10.8009i	0.435532	−	0.754364i
$206$		0			0
$207$	0.673281	+	1.16616i	0.0467962	+	0.0810535i
$208$		0			0
$209$	17.7162			1.22546
$210$		0			0
$211$	−13.7185			−0.944419			−0.472209	−	0.881486i	$-0.656543\pi$
$211$	−13.7185			−0.944419			−0.472209	+	0.881486i	$0.656543\pi$
$212$		0			0
$213$	−1.43658	−	2.48822i	−0.0984326	−	0.170490i
$214$		0			0
$215$	−15.3340	+	26.5593i	−1.04577	+	1.81133i
$216$		0			0
$217$	11.3309	+	6.98212i	0.769192	+	0.473977i
$218$		0			0
$219$	−1.37770	+	2.38624i	−0.0930961	+	0.161247i
$220$		0			0
$221$	5.73920	+	9.94058i	0.386060	+	0.668676i
$222$		0			0
$223$	−10.5912			−0.709242			−0.354621	−	0.935010i	$-0.615390\pi$
$223$	−10.5912			−0.709242			−0.354621	+	0.935010i	$0.615390\pi$
$224$		0			0
$225$	13.5651			0.904343
$226$		0			0
$227$	−3.76104	−	6.51432i	−0.249629	−	0.432370i	0.713794	−	0.700356i	$-0.246975\pi$
$227$	−3.76104	−	6.51432i	−0.249629	−	0.432370i	−0.963423	+	0.267986i	$0.913642\pi$
$228$		0			0
$229$	3.89960	−	6.75430i	0.257693	−	0.446337i	−0.707931	−	0.706282i	$-0.750371\pi$
$229$	3.89960	−	6.75430i	0.257693	−	0.446337i	0.965623	+	0.259945i	$0.0837045\pi$
$230$		0			0
$231$	−0.722457	+	25.2112i	−0.0475342	+	1.65877i
$232$		0			0
$233$	−3.78452	+	6.55498i	−0.247932	+	0.429431i	−0.962952	−	0.269673i	$-0.913084\pi$
$233$	−3.78452	+	6.55498i	−0.247932	+	0.429431i	0.715020	+	0.699104i	$0.246418\pi$
$234$		0			0
$235$	−18.4125	−	31.8913i	−1.20110	−	2.08036i
$236$		0			0
$237$	9.27238			0.602306
$238$		0			0
$239$	17.3822			1.12436			0.562179	−	0.827015i	$-0.309963\pi$
$239$	17.3822			1.12436			0.562179	+	0.827015i	$0.309963\pi$
$240$		0			0
$241$	−4.87972	−	8.45193i	−0.314331	−	0.544437i	0.664964	−	0.746875i	$-0.268447\pi$
$241$	−4.87972	−	8.45193i	−0.314331	−	0.544437i	−0.979295	+	0.202438i	$0.935113\pi$
$242$		0			0
$243$	−6.53195	+	11.3137i	−0.419025	+	0.725772i
$244$		0			0
$245$	12.2187	+	24.2760i	0.780622	+	1.55094i
$246$		0			0
$247$	−4.99851	+	8.65767i	−0.318048	+	0.550875i
$248$		0			0
$249$	−8.21055	−	14.2211i	−0.520323	−	0.901225i
$250$		0			0
$251$	7.02466			0.443393			0.221696	−	0.975116i	$-0.428841\pi$
$251$	7.02466			0.443393			0.221696	+	0.975116i	$0.428841\pi$
$252$		0			0
$253$	−4.57245			−0.287468
$254$		0			0
$255$	−18.0048	−	31.1853i	−1.12751	−	1.95290i
$256$		0			0
$257$	−13.0623	+	22.6246i	−0.814807	+	1.41129i	0.0946602	+	0.995510i	$0.469824\pi$
$257$	−13.0623	+	22.6246i	−0.814807	+	1.41129i	−0.909467	+	0.415777i	$0.863510\pi$
$258$		0			0
$259$	0.477046	−	16.6472i	0.0296422	−	1.03441i
$260$		0			0
$261$	4.45765	−	7.72088i	0.275922	−	0.477910i
$262$		0			0
$263$	−13.8455	−	23.9811i	−0.853749	−	1.47874i	−0.877801	−	0.479026i	$-0.840990\pi$
$263$	−13.8455	−	23.9811i	−0.853749	−	1.47874i	0.0240522	−	0.999711i	$-0.492343\pi$
$264$		0			0
$265$	−41.5054			−2.54966
$266$		0			0
$267$	−22.9650			−1.40543
$268$		0			0
$269$	−7.24960	−	12.5567i	−0.442016	−	0.765594i	0.555823	−	0.831301i	$-0.312403\pi$
$269$	−7.24960	−	12.5567i	−0.442016	−	0.765594i	−0.997839	+	0.0657066i	$0.979070\pi$
$270$		0			0
$271$	6.01655	−	10.4210i	0.365480	−	0.633029i	−0.623373	−	0.781924i	$-0.714238\pi$
$271$	6.01655	−	10.4210i	0.365480	−	0.633029i	0.988853	+	0.148895i	$0.0475716\pi$
$272$		0			0
$273$	−12.1165	−	7.46620i	−0.733323	−	0.451875i
$274$		0			0
$275$	−23.0312	+	39.8913i	−1.38884	+	2.40553i
$276$		0			0
$277$	9.55840	+	16.5556i	0.574308	+	0.994731i	0.996116	+	0.0880462i	$0.0280623\pi$
$277$	9.55840	+	16.5556i	0.574308	+	0.994731i	−0.421808	+	0.906685i	$0.638604\pi$
$278$		0			0
$279$	6.77383			0.405539
$280$		0			0
$281$	−3.47518			−0.207312			−0.103656	−	0.994613i	$-0.533054\pi$
$281$	−3.47518			−0.207312			−0.103656	+	0.994613i	$0.533054\pi$
$282$		0			0
$283$	−14.5468	−	25.1957i	−0.864716	−	1.49773i	−0.867329	−	0.497735i	$-0.834165\pi$
$283$	−14.5468	−	25.1957i	−0.864716	−	1.49773i	0.00261327	−	0.999997i	$-0.499168\pi$
$284$		0			0
$285$	15.6812	−	27.1606i	0.928873	−	1.60885i
$286$		0			0
$287$	7.47898	−	4.03688i	0.441470	−	0.238290i
$288$		0			0
$289$	−1.39547	+	2.41703i	−0.0820865	+	0.142178i
$290$		0			0
$291$	14.4542	+	25.0354i	0.847319	+	1.46760i
$292$		0			0
$293$	28.0826			1.64060			0.820301	−	0.571931i	$-0.193806\pi$
$293$	28.0826			1.64060			0.820301	+	0.571931i	$0.193806\pi$
$294$		0			0
$295$	7.11223			0.414090
$296$		0			0
$297$	−7.88098	−	13.6503i	−0.457301	−	0.792068i
$298$		0			0
$299$	1.29008	−	2.23449i	0.0746074	−	0.129224i
$300$		0			0
$301$	−18.3908	+	9.92669i	−1.06003	+	0.572165i
$302$		0			0
$303$	−16.1500	+	27.9726i	−0.927792	+	1.60698i
$304$		0			0
$305$	−4.42690	−	7.66761i	−0.253483	−	0.439046i
$306$		0			0
$307$	30.4403			1.73732			0.868659	−	0.495410i	$-0.164982\pi$
$307$	30.4403			1.73732			0.868659	+	0.495410i	$0.164982\pi$
$308$		0			0
$309$	−32.0182			−1.82145
$310$		0			0
$311$	4.53419	+	7.85345i	0.257110	+	0.445328i	0.965467	−	0.260527i	$-0.0838963\pi$
$311$	4.53419	+	7.85345i	0.257110	+	0.445328i	−0.708356	+	0.705855i	$0.750563\pi$
$312$		0			0
$313$	11.0038	−	19.0592i	0.621972	−	1.07729i	−0.367146	−	0.930163i	$-0.619665\pi$
$313$	11.0038	−	19.0592i	0.621972	−	1.07729i	0.989118	−	0.147124i	$-0.0470017\pi$
$314$		0			0
$315$	11.7759	+	7.25634i	0.663498	+	0.408849i
$316$		0			0
$317$	−5.67774	+	9.83414i	−0.318894	+	0.552340i	−0.980257	−	0.197725i	$-0.936645\pi$
$317$	−5.67774	+	9.83414i	−0.318894	+	0.552340i	0.661364	+	0.750065i	$0.269978\pi$
$318$		0			0
$319$	15.1366	+	26.2174i	0.847488	+	1.46789i
$320$		0			0
$321$	−3.07200			−0.171462
$322$		0			0
$323$	−17.2368			−0.959080
$324$		0			0
$325$	−12.9962	−	22.5101i	−0.720899	−	1.24863i
$326$		0			0
$327$	−16.4417	+	28.4778i	−0.909226	+	1.57483i
$328$		0			0
$329$	0.718819	−	25.0842i	0.0396298	−	1.38294i
$330$		0			0
$331$	−4.63478	+	8.02768i	−0.254751	+	0.441241i	−0.964828	−	0.262883i	$-0.915327\pi$
$331$	−4.63478	+	8.02768i	−0.254751	+	0.441241i	0.710077	+	0.704124i	$0.248660\pi$
$332$		0			0
$333$	−4.23805	−	7.34052i	−0.232244	−	0.402258i
$334$		0			0
$335$	−7.47198			−0.408238
$336$		0			0
$337$	4.15289			0.226223			0.113111	−	0.993582i	$-0.463918\pi$
$337$	4.15289			0.226223			0.113111	+	0.993582i	$0.463918\pi$
$338$		0			0
$339$	−13.4740	−	23.3377i	−0.731809	−	1.26753i
$340$		0			0
$341$	−11.5008	+	19.9199i	−0.622802	+	1.07873i
$342$		0			0
$343$	−1.58977	+	18.4519i	−0.0858395	+	0.996309i
$344$		0			0
$345$	−4.04721	+	7.00998i	−0.217895	+	0.377404i
$346$		0			0
$347$	−5.93157	−	10.2738i	−0.318423	−	0.551525i	0.661736	−	0.749737i	$-0.269820\pi$
$347$	−5.93157	−	10.2738i	−0.318423	−	0.551525i	−0.980159	+	0.198212i	$0.936487\pi$
$348$		0			0
$349$	−5.69943			−0.305084			−0.152542	−	0.988297i	$-0.548746\pi$
$349$	−5.69943			−0.305084			−0.152542	+	0.988297i	$0.548746\pi$
$350$		0			0
$351$	8.89424			0.474739
$352$		0			0
$353$	9.27338	+	16.0620i	0.493572	+	0.854892i	0.999973	−	0.00740636i	$-0.00235754\pi$
$353$	9.27338	+	16.0620i	0.493572	+	0.854892i	−0.506400	+	0.862298i	$0.669024\pi$
$354$		0			0
$355$	2.67528	−	4.63372i	0.141989	−	0.245932i
$356$		0			0
$357$	0.702905	−	24.5288i	0.0372017	−	1.29820i
$358$		0			0
$359$	−17.1608	+	29.7233i	−0.905711	+	1.56874i	−0.0857506	+	0.996317i	$0.527329\pi$
$359$	−17.1608	+	29.7233i	−0.905711	+	1.56874i	−0.819960	+	0.572421i	$0.806004\pi$
$360$		0			0
$361$	1.99388	+	3.45350i	0.104941	+	0.181763i
$362$		0			0
$363$	−20.6552			−1.08411
$364$		0			0
$365$	−5.13126			−0.268582
$366$		0			0
$367$	5.87678	+	10.1789i	0.306766	+	0.531334i	0.977653	−	0.210226i	$-0.0674199\pi$
$367$	5.87678	+	10.1789i	0.306766	+	0.531334i	−0.670887	+	0.741559i	$0.734087\pi$
$368$		0			0
$369$	2.16277	−	3.74603i	0.112589	−	0.195010i
$370$		0			0
$371$	−24.0795	−	14.8378i	−1.25015	−	0.770342i
$372$		0			0
$373$	−18.1699	+	31.4711i	−0.940800	+	1.62951i	−0.176851	+	0.984238i	$0.556591\pi$
$373$	−18.1699	+	31.4711i	−0.940800	+	1.62951i	−0.763949	+	0.645277i	$0.776742\pi$
$374$		0			0
$375$	20.5352	+	35.5680i	1.06043	+	1.83673i
$376$		0			0
$377$	−17.0828			−0.879807
$378$		0			0
$379$	−7.22166			−0.370952			−0.185476	−	0.982649i	$-0.559383\pi$
$379$	−7.22166			−0.370952			−0.185476	+	0.982649i	$0.559383\pi$
$380$		0			0
$381$	16.9708	+	29.3943i	0.869440	+	1.50591i
$382$		0			0
$383$	5.11952	−	8.86728i	0.261595	−	0.453097i	−0.705071	−	0.709137i	$-0.749085\pi$
$383$	5.11952	−	8.86728i	0.261595	−	0.453097i	0.966666	+	0.256040i	$0.0824180\pi$
$384$		0			0
$385$	−41.3323	+	22.3097i	−2.10649	+	1.13701i
$386$		0			0
$387$	−5.31825	+	9.21149i	−0.270342	+	0.468246i
$388$		0			0
$389$	−15.7234	−	27.2337i	−0.797209	−	1.38081i	−0.921427	−	0.388551i	$-0.872976\pi$
$389$	−15.7234	−	27.2337i	−0.797209	−	1.38081i	0.124219	−	0.992255i	$-0.460358\pi$
$390$		0			0
$391$	4.44870			0.224980
$392$		0			0
$393$	20.1810			1.01800
$394$		0			0
$395$	8.63379	+	14.9542i	0.434413	+	0.752426i
$396$		0			0
$397$	10.7848	−	18.6799i	0.541275	−	0.937515i	−0.457557	−	0.889181i	$-0.651275\pi$
$397$	10.7848	−	18.6799i	0.541275	−	0.937515i	0.998831	−	0.0483347i	$-0.0153914\pi$
$398$		0			0
$399$	18.8072	−	10.1514i	0.941536	−	0.508207i
$400$		0			0
$401$	0.345213	−	0.597927i	0.0172391	−	0.0298591i	−0.857277	−	0.514855i	$-0.827846\pi$
$401$	0.345213	−	0.597927i	0.0172391	−	0.0298591i	0.874516	+	0.484996i	$0.161179\pi$
$402$		0			0
$403$	−6.48972	−	11.2405i	−0.323276	−	0.559931i
$404$		0			0
$405$	−43.5869			−2.16585
$406$		0			0
$407$	28.7819			1.42667
$408$		0			0
$409$	3.98033	+	6.89413i	0.196815	+	0.340893i	0.947494	−	0.319774i	$-0.103607\pi$
$409$	3.98033	+	6.89413i	0.196815	+	0.340893i	−0.750679	+	0.660667i	$0.770274\pi$
$410$		0			0
$411$	−1.76455	+	3.05629i	−0.0870389	+	0.150756i
$412$		0			0
$413$	4.12619	+	2.54256i	0.203036	+	0.125111i
$414$		0			0
$415$	15.2902	−	26.4834i	0.750565	−	1.30002i
$416$		0			0
$417$	15.2239	+	26.3685i	0.745515	+	1.29127i
$418$		0			0
$419$	−8.41952			−0.411321			−0.205660	−	0.978623i	$-0.565934\pi$
$419$	−8.41952			−0.411321			−0.205660	+	0.978623i	$0.565934\pi$
$420$		0			0
$421$	−14.1326			−0.688779			−0.344390	−	0.938827i	$-0.611914\pi$
$421$	−14.1326			−0.688779			−0.344390	+	0.938827i	$0.611914\pi$
$422$		0			0
$423$	−6.38595	−	11.0608i	−0.310495	−	0.537794i
$424$		0			0
$425$	22.4079	−	38.8117i	1.08694	−	1.88264i
$426$		0			0
$427$	0.172825	−	6.03097i	0.00836359	−	0.291859i
$428$		0			0
$429$	12.2981	−	21.3010i	0.593760	−	1.02842i
$430$		0			0
$431$	2.22025	+	3.84558i	0.106945	+	0.185235i	0.914531	−	0.404515i	$-0.132560\pi$
$431$	2.22025	+	3.84558i	0.106945	+	0.185235i	−0.807586	+	0.589750i	$0.799226\pi$
$432$		0			0
$433$	−6.28996			−0.302276			−0.151138	−	0.988513i	$-0.548294\pi$
$433$	−6.28996			−0.302276			−0.151138	+	0.988513i	$0.548294\pi$
$434$		0			0
$435$	53.5915			2.56952
$436$		0			0
$437$	1.93728	+	3.35547i	0.0926727	+	0.160514i
$438$		0			0
$439$	−0.0570405	+	0.0987970i	−0.00272239	+	0.00471532i	−0.867383	−	0.497640i	$-0.834200\pi$
$439$	−0.0570405	+	0.0987970i	−0.00272239	+	0.00471532i	0.864661	+	0.502356i	$0.167533\pi$
$440$		0			0
$441$	4.23777	+	8.41959i	0.201798	+	0.400933i
$442$		0			0
$443$	6.24955	−	10.8245i	0.296925	−	0.514289i	−0.678506	−	0.734595i	$-0.737372\pi$
$443$	6.24955	−	10.8245i	0.296925	−	0.514289i	0.975431	+	0.220306i	$0.0707055\pi$
$444$		0			0
$445$	−21.3834	−	37.0371i	−1.01367	−	1.75573i
$446$		0			0
$447$	14.9908			0.709042
$448$		0			0
$449$	22.0637			1.04125			0.520626	−	0.853785i	$-0.325699\pi$
$449$	22.0637			1.04125			0.520626	+	0.853785i	$0.325699\pi$
$450$		0			0
$451$	7.34401	+	12.7202i	0.345816	+	0.598971i
$452$		0			0
$453$	11.3802	−	19.7111i	0.534690	−	0.926110i
$454$		0			0
$455$	0.759191	−	26.4930i	0.0355914	−	1.24201i
$456$		0			0
$457$	16.6200	−	28.7867i	0.777451	−	1.34659i	−0.155955	−	0.987764i	$-0.549845\pi$
$457$	16.6200	−	28.7867i	0.777451	−	1.34659i	0.933406	−	0.358821i	$-0.116821\pi$
$458$		0			0
$459$	7.66768	+	13.2808i	0.357897	+	0.619896i
$460$		0			0
$461$	−13.4759			−0.627635			−0.313817	−	0.949483i	$-0.601608\pi$
$461$	−13.4759			−0.627635			−0.313817	+	0.949483i	$0.601608\pi$
$462$		0			0
$463$	1.80006			0.0836559			0.0418279	−	0.999125i	$-0.486682\pi$
$463$	1.80006			0.0836559			0.0418279	+	0.999125i	$0.486682\pi$
$464$		0			0
$465$	20.3594	+	35.2635i	0.944143	+	1.63530i
$466$		0			0
$467$	3.97572	−	6.88615i	0.183974	−	0.318653i	−0.759256	−	0.650792i	$-0.774437\pi$
$467$	3.97572	−	6.88615i	0.183974	−	0.318653i	0.943230	+	0.332139i	$0.107770\pi$
$468$		0			0
$469$	−4.33489	−	2.67117i	−0.200167	−	0.123343i
$470$		0			0
$471$	7.21847	−	12.5028i	0.332609	−	0.576096i
$472$		0			0
$473$	−18.0589	−	31.2790i	−0.830350	−	1.43821i
$474$		0			0
$475$	39.0320			1.79091
$476$		0			0
$477$	−14.3952			−0.659111
$478$		0			0
$479$	8.36344	+	14.4859i	0.382135	+	0.661878i	0.991367	−	0.131114i	$-0.0418554\pi$
$479$	8.36344	+	14.4859i	0.382135	+	0.661878i	−0.609232	+	0.792992i	$0.708522\pi$
$480$		0			0
$481$	−8.12060	+	14.0653i	−0.370267	+	0.641322i
$482$		0			0
$483$	−4.85401	+	2.62002i	−0.220865	+	0.119215i
$484$		0			0
$485$	−26.9174	+	46.6224i	−1.22226	+	2.11701i
$486$		0			0
$487$	−8.31086	−	14.3948i	−0.376601	−	0.652292i	0.613964	−	0.789334i	$-0.289574\pi$
$487$	−8.31086	−	14.3948i	−0.376601	−	0.652292i	−0.990565	+	0.137042i	$0.956241\pi$
$488$		0			0
$489$	43.1580			1.95167
$490$		0			0
$491$	31.2160			1.40876			0.704380	−	0.709823i	$-0.251225\pi$
$491$	31.2160			1.40876			0.704380	+	0.709823i	$0.251225\pi$
$492$		0			0
$493$	−14.7270	−	25.5079i	−0.663269	−	1.14882i
$494$		0			0
$495$	−11.9525	+	20.7023i	−0.537224	+	0.930500i
$496$		0			0
$497$	3.20859	−	1.73188i	0.143925	−	0.0776854i
$498$		0			0
$499$	−11.8648	+	20.5504i	−0.531140	+	0.919962i	0.468199	+	0.883623i	$0.344903\pi$
$499$	−11.8648	+	20.5504i	−0.531140	+	0.919962i	−0.999340	+	0.0363389i	$0.988430\pi$
$500$		0			0
$501$	−20.5482	−	35.5905i	−0.918026	−	1.59007i
$502$		0			0
$503$	10.1328			0.451800			0.225900	−	0.974150i	$-0.427468\pi$
$503$	10.1328			0.451800			0.225900	+	0.974150i	$0.427468\pi$
$504$		0			0
$505$	−60.1509			−2.67668
$506$		0			0
$507$	−6.61180	−	11.4520i	−0.293640	−	0.508600i
$508$		0			0
$509$	16.1956	−	28.0515i	0.717856	−	1.24336i	−0.243992	−	0.969777i	$-0.578457\pi$
$509$	16.1956	−	28.0515i	0.717856	−	1.24336i	0.961848	−	0.273585i	$-0.0882096\pi$
$510$		0			0
$511$	−2.97692	−	1.83438i	−0.131691	−	0.0811482i
$512$		0			0
$513$	−6.67811	+	11.5668i	−0.294846	+	0.510688i
$514$		0			0
$515$	−29.8131	−	51.6378i	−1.31372	−	2.27544i
$516$		0			0
$517$	43.3689			1.90736
$518$		0			0
$519$	−24.5526			−1.07774
$520$		0			0
$521$	−8.88549	−	15.3901i	−0.389280	−	0.674253i	0.603073	−	0.797686i	$-0.293943\pi$
$521$	−8.88549	−	15.3901i	−0.389280	−	0.674253i	−0.992353	+	0.123433i	$0.960610\pi$
$522$		0			0
$523$	−1.00291	+	1.73708i	−0.0438540	+	0.0759573i	−0.887119	−	0.461540i	$-0.847297\pi$
$523$	−1.00291	+	1.73708i	−0.0438540	+	0.0759573i	0.843265	+	0.537498i	$0.180630\pi$
$524$		0			0
$525$	−1.59170	+	55.5446i	−0.0694675	+	2.42417i
$526$		0			0
$527$	11.1895	−	19.3808i	0.487423	−	0.844242i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	2.46671			0.107046
$532$		0			0
$533$	−8.28824			−0.359003
$534$		0			0
$535$	−2.86043	−	4.95442i	−0.123667	−	0.214198i
$536$		0			0
$537$	−25.6815	+	44.4817i	−1.10824	+	1.91953i
$538$		0			0
$539$	−31.9546	−	1.83291i	−1.37638	−	0.0789488i
$540$		0			0
$541$	−16.8490	+	29.1834i	−0.724396	+	1.25469i	0.234826	+	0.972037i	$0.424548\pi$
$541$	−16.8490	+	29.1834i	−0.724396	+	1.25469i	−0.959222	+	0.282653i	$0.908786\pi$
$542$		0			0
$543$	15.8331	+	27.4237i	0.679463	+	1.17686i
$544$		0			0
$545$	−61.2373			−2.62312
$546$		0			0
$547$	33.7802			1.44434			0.722169	−	0.691716i	$-0.243145\pi$
$547$	33.7802			1.44434			0.722169	+	0.691716i	$0.243145\pi$
$548$		0			0
$549$	−1.53537	−	2.65934i	−0.0655279	−	0.113498i
$550$		0			0
$551$	12.8263	−	22.2159i	0.546421	−	0.946428i
$552$		0			0
$553$	−0.337061	+	11.7622i	−0.0143333	+	0.500180i
$554$		0			0
$555$	25.4757	−	44.1252i	1.08138	−	1.87301i
$556$		0			0
$557$	4.86127	+	8.41997i	0.205979	+	0.356766i	0.950444	−	0.310895i	$-0.100629\pi$
$557$	4.86127	+	8.41997i	0.205979	+	0.356766i	−0.744465	+	0.667661i	$0.767296\pi$
$558$		0			0
$559$	20.3808			0.862015
$560$		0			0
$561$	42.4087			1.79050
$562$		0			0
$563$	18.9953	+	32.9009i	0.800557	+	1.38661i	0.919250	+	0.393675i	$0.128796\pi$
$563$	18.9953	+	32.9009i	0.800557	+	1.38661i	−0.118693	+	0.992931i	$0.537870\pi$
$564$		0			0
$565$	25.0922	−	43.4609i	1.05563	−	1.82841i
$566$		0			0
$567$	−25.2871	−	15.5819i	−1.06196	−	0.654380i
$568$		0			0
$569$	−8.96917	+	15.5351i	−0.376007	+	0.651263i	−0.990477	−	0.137677i	$-0.956037\pi$
$569$	−8.96917	+	15.5351i	−0.376007	+	0.651263i	0.614470	+	0.788940i	$0.289370\pi$
$570$		0			0
$571$	0.663795	+	1.14973i	0.0277790	+	0.0481146i	0.879581	−	0.475750i	$-0.157823\pi$
$571$	0.663795	+	1.14973i	0.0277790	+	0.0481146i	−0.851802	+	0.523864i	$0.824490\pi$
$572$		0			0
$573$	35.6767			1.49042
$574$		0			0
$575$	−10.0739			−0.420111
$576$		0			0
$577$	13.8627	+	24.0110i	0.577113	+	0.999590i	0.995808	+	0.0914630i	$0.0291543\pi$
$577$	13.8627	+	24.0110i	0.577113	+	0.999590i	−0.418695	+	0.908127i	$0.637512\pi$
$578$		0			0
$579$	7.99062	−	13.8402i	0.332079	−	0.575178i
$580$		0			0
$581$	18.3382	−	9.89831i	0.760798	−	0.410651i
$582$		0			0
$583$	24.4405	−	42.3323i	1.01222	−	1.75322i
$584$		0			0
$585$	−6.74461	−	11.6820i	−0.278855	−	0.482992i
$586$		0			0
$587$	−21.8286			−0.900962			−0.450481	−	0.892786i	$-0.648748\pi$
$587$	−21.8286			−0.900962			−0.450481	+	0.892786i	$0.648748\pi$
$588$		0			0
$589$	19.4909			0.803107
$590$		0			0
$591$	26.4184	+	45.7581i	1.08671	+	1.88224i
$592$		0			0
$593$	−10.0984	+	17.4909i	−0.414691	+	0.718266i	−0.995396	−	0.0958479i	$-0.969444\pi$
$593$	−10.0984	+	17.4909i	−0.414691	+	0.718266i	0.580705	+	0.814114i	$0.302777\pi$
$594$		0			0
$595$	40.2137	−	21.7059i	1.64860	−	0.889855i
$596$		0			0
$597$	6.94118	−	12.0225i	0.284084	−	0.492047i
$598$		0			0
$599$	13.3302	+	23.0886i	0.544658	+	0.943376i	0.998628	+	0.0523590i	$0.0166740\pi$
$599$	13.3302	+	23.0886i	0.544658	+	0.943376i	−0.453970	+	0.891017i	$0.649993\pi$
$600$		0			0
$601$	39.1464			1.59681			0.798407	−	0.602118i	$-0.205676\pi$
$601$	39.1464			1.59681			0.798407	+	0.602118i	$0.205676\pi$
$602$		0			0
$603$	−2.59148			−0.105533
$604$		0			0
$605$	−19.2326	−	33.3119i	−0.781918	−	1.35432i
$606$		0			0
$607$	−23.6194	+	40.9099i	−0.958680	+	1.66048i	−0.232969	+	0.972484i	$0.574844\pi$
$607$	−23.6194	+	40.9099i	−0.958680	+	1.66048i	−0.725712	+	0.687999i	$0.758489\pi$
$608$		0			0
$609$	31.0913	+	19.1585i	1.25988	+	0.776342i
$610$		0			0
$611$	−12.2362	+	21.1937i	−0.495024	+	0.857407i
$612$		0			0
$613$	11.0345	+	19.1123i	0.445678	+	0.771937i	0.998099	−	0.0616282i	$-0.0196293\pi$
$613$	11.0345	+	19.1123i	0.445678	+	0.771937i	−0.552421	+	0.833565i	$0.686296\pi$
$614$		0			0
$615$	26.0016			1.04849
$616$		0			0
$617$	−4.11131			−0.165515			−0.0827576	−	0.996570i	$-0.526373\pi$
$617$	−4.11131			−0.165515			−0.0827576	+	0.996570i	$0.526373\pi$
$618$		0			0
$619$	3.48109	+	6.02942i	0.139917	+	0.242343i	0.927465	−	0.373910i	$-0.121983\pi$
$619$	3.48109	+	6.02942i	0.139917	+	0.242343i	−0.787548	+	0.616253i	$0.788650\pi$
$620$		0			0
$621$	1.72358	−	2.98533i	0.0691648	−	0.119797i
$622$		0			0
$623$	0.834802	−	29.1316i	0.0334456	−	1.16713i
$624$		0			0
$625$	−13.0571	+	22.6156i	−0.522284	+	0.904623i
$626$		0			0
$627$	18.4678	+	31.9871i	0.737532	+	1.27744i
$628$		0			0
$629$	−28.0029			−1.11655
$630$		0			0
$631$	−8.79811			−0.350247			−0.175124	−	0.984546i	$-0.556033\pi$
$631$	−8.79811			−0.350247			−0.175124	+	0.984546i	$0.556033\pi$
$632$		0			0
$633$	−14.3004	−	24.7690i	−0.568390	−	0.984481i
$634$		0			0
$635$	−31.6040	+	54.7398i	−1.25417	+	2.17228i
$636$		0			0
$637$	9.91148	−	15.0986i	0.392707	−	0.598229i
$638$		0			0
$639$	0.927859	−	1.60710i	0.0367055	−	0.0635759i
$640$		0			0
$641$	−0.582417	−	1.00878i	−0.0230041	−	0.0398443i	0.854294	−	0.519790i	$-0.173990\pi$
$641$	−0.582417	−	1.00878i	−0.0230041	−	0.0398443i	−0.877298	+	0.479946i	$0.840656\pi$
$642$		0			0
$643$	26.8643			1.05942			0.529712	−	0.848177i	$-0.322300\pi$
$643$	26.8643			1.05942			0.529712	+	0.848177i	$0.322300\pi$
$644$		0			0
$645$	−63.9380			−2.51756
$646$		0			0
$647$	12.8421	+	22.2431i	0.504874	+	0.874468i	0.999984	+	0.00563734i	$0.00179443\pi$
$647$	12.8421	+	22.2431i	0.504874	+	0.874468i	−0.495110	+	0.868830i	$0.664872\pi$
$648$		0			0
$649$	−4.18805	+	7.25392i	−0.164395	+	0.284741i
$650$		0			0
$651$	−0.794825	+	27.7365i	−0.0311517	+	1.08708i
$652$		0			0
$653$	22.2425	−	38.5252i	0.870417	−	1.50761i	0.00885190	−	0.999961i	$-0.497182\pi$
$653$	22.2425	−	38.5252i	0.870417	−	1.50761i	0.861566	−	0.507646i	$-0.169484\pi$
$654$		0			0
$655$	18.7912	+	32.5473i	0.734232	+	1.27173i
$656$		0			0
$657$	−1.77966			−0.0694311
$658$		0			0
$659$	−6.95241			−0.270828			−0.135414	−	0.990789i	$-0.543236\pi$
$659$	−6.95241			−0.270828			−0.135414	+	0.990789i	$0.543236\pi$
$660$		0			0
$661$	14.3241	+	24.8100i	0.557142	+	0.964998i	0.997733	+	0.0672900i	$0.0214353\pi$
$661$	14.3241	+	24.8100i	0.557142	+	0.964998i	−0.440592	+	0.897708i	$0.645231\pi$
$662$		0			0
$663$	−11.9653	+	20.7245i	−0.464694	+	0.804874i
$664$		0			0
$665$	33.8838	+	20.8792i	1.31396	+	0.809662i
$666$		0			0
$667$	−3.31040	+	5.73378i	−0.128179	+	0.222013i
$668$		0			0
$669$	−11.0405	−	19.1228i	−0.426852	−	0.739329i
$670$		0			0
$671$	10.4271			0.402536
$672$		0			0
$673$	23.6585			0.911970			0.455985	−	0.889988i	$-0.349287\pi$
$673$	23.6585			0.911970			0.455985	+	0.889988i	$0.349287\pi$
$674$		0			0
$675$	−17.3632	−	30.0739i	−0.668309	−	1.15755i
$676$		0			0
$677$	−10.7421	+	18.6059i	−0.412854	+	0.715084i	−0.995201	−	0.0978566i	$-0.968801\pi$
$677$	−10.7421	+	18.6059i	−0.412854	+	0.715084i	0.582347	+	0.812941i	$0.302135\pi$
$678$		0			0
$679$	−32.2833	+	17.4254i	−1.23892	+	0.668725i
$680$		0			0
$681$	7.84118	−	13.5813i	0.300474	−	0.520437i
$682$		0			0
$683$	−3.65709	−	6.33427i	−0.139935	−	0.242374i	0.787537	−	0.616267i	$-0.211356\pi$
$683$	−3.65709	−	6.33427i	−0.139935	−	0.242374i	−0.927472	+	0.373893i	$0.878023\pi$
$684$		0			0
$685$	−6.57210			−0.251107
$686$		0			0
$687$	16.2601			0.620360
$688$		0			0
$689$	13.7914	+	23.8875i	0.525412	+	0.910040i
$690$		0			0
$691$	−13.2516	+	22.9525i	−0.504116	+	0.873155i	0.495872	+	0.868396i	$0.334848\pi$
$691$	−13.2516	+	22.9525i	−0.504116	+	0.873155i	−0.999989	+	0.00475986i	$0.998485\pi$
$692$		0			0
$693$	−14.3352	+	7.73761i	−0.544548	+	0.293927i
$694$		0			0
$695$	−28.3508	+	49.1050i	−1.07541	+	1.86266i
$696$		0			0
$697$	−7.14525	−	12.3759i	−0.270646	−	0.468772i
$698$		0			0
$699$	−15.7802			−0.596864
$700$		0			0
$701$	−3.33588			−0.125994			−0.0629972	−	0.998014i	$-0.520066\pi$
$701$	−3.33588			−0.125994			−0.0629972	+	0.998014i	$0.520066\pi$
$702$		0			0
$703$	−12.1945	−	21.1214i	−0.459923	−	0.796610i
$704$		0			0
$705$	38.3871	−	66.4884i	1.44574	−	2.50410i
$706$		0			0
$707$	−34.8967	−	21.5034i	−1.31243	−	0.808719i
$708$		0			0
$709$	20.6294	−	35.7311i	0.774752	−	1.34191i	−0.160182	−	0.987088i	$-0.551208\pi$
$709$	20.6294	−	35.7311i	0.774752	−	1.34191i	0.934934	−	0.354822i	$-0.115459\pi$
$710$		0			0
$711$	2.99443	+	5.18651i	0.112300	+	0.194509i
$712$		0			0
$713$	−5.03047			−0.188393
$714$		0			0
$715$	45.8047			1.71300
$716$		0			0
$717$	18.1195	+	31.3839i	0.676686	+	1.17205i
$718$		0			0
$719$	12.1009	−	20.9593i	0.451287	−	0.781652i	−0.547179	−	0.837015i	$-0.684298\pi$
$719$	12.1009	−	20.9593i	0.451287	−	0.781652i	0.998466	+	0.0553636i	$0.0176318\pi$
$720$		0			0
$721$	1.16390	−	40.6158i	0.0433458	−	1.51261i
$722$		0			0
$723$	10.1734	−	17.6209i	0.378355	−	0.655329i
$724$		0			0
$725$	33.3487	+	57.7616i	1.23854	+	2.14521i
$726$		0			0
$727$	−25.4449			−0.943700			−0.471850	−	0.881679i	$-0.656414\pi$
$727$	−25.4449			−0.943700			−0.471850	+	0.881679i	$0.656414\pi$
$728$		0			0
$729$	6.44321			0.238637
$730$		0			0
$731$	17.5702	+	30.4324i	0.649857	+	1.12558i
$732$		0			0
$733$	14.1224	−	24.4606i	0.521621	−	0.903474i	−0.478063	−	0.878326i	$-0.658661\pi$
$733$	14.1224	−	24.4606i	0.521621	−	0.903474i	0.999684	−	0.0251483i	$-0.00800579\pi$
$734$		0			0
$735$	−31.0940	+	47.3670i	−1.14692	+	1.74716i
$736$		0			0
$737$	4.39989	−	7.62083i	0.162072	−	0.280717i
$738$		0			0
$739$	13.7522	+	23.8195i	0.505882	+	0.876213i	0.999977	+	0.00680507i	$0.00216614\pi$
$739$	13.7522	+	23.8195i	0.505882	+	0.876213i	−0.494095	+	0.869408i	$0.664501\pi$
$740$		0			0
$741$	−20.8422			−0.765657
$742$		0			0
$743$	−20.3578			−0.746857			−0.373428	−	0.927659i	$-0.621818\pi$
$743$	−20.3578			−0.746857			−0.373428	+	0.927659i	$0.621818\pi$
$744$		0			0
$745$	13.9584	+	24.1767i	0.511397	+	0.885765i
$746$		0			0
$747$	5.30305	−	9.18515i	0.194028	−	0.336067i
$748$		0			0
$749$	0.111671	−	3.89690i	0.00408036	−	0.142390i
$750$		0			0
$751$	20.7186	−	35.8857i	0.756034	−	1.30949i	−0.188825	−	0.982011i	$-0.560468\pi$
$751$	20.7186	−	35.8857i	0.756034	−	1.30949i	0.944859	−	0.327478i	$-0.106199\pi$
$752$		0			0
$753$	7.32265	+	12.6832i	0.266852	+	0.462202i
$754$		0			0
$755$	42.3859			1.54258
$756$		0			0
$757$	−42.4986			−1.54464			−0.772319	−	0.635235i	$-0.780903\pi$
$757$	−42.4986			−1.54464			−0.772319	+	0.635235i	$0.780903\pi$
$758$		0			0
$759$	−4.76642	−	8.25567i	−0.173010	−	0.299662i
$760$		0			0
$761$	8.93559	−	15.4769i	0.323915	−	0.561037i	−0.657377	−	0.753562i	$-0.728334\pi$
$761$	8.93559	−	15.4769i	0.323915	−	0.561037i	0.981292	+	0.192525i	$0.0616675\pi$
$762$		0			0
$763$	−35.5270	−	21.8918i	−1.28617	−	0.792537i
$764$		0			0
$765$	11.6290	−	20.1420i	0.420447	−	0.728236i
$766$		0			0
$767$	−2.36326	−	4.09328i	−0.0853322	−	0.147800i
$768$		0			0
$769$	6.92176			0.249605			0.124803	−	0.992182i	$-0.460170\pi$
$769$	6.92176			0.249605			0.124803	+	0.992182i	$0.460170\pi$
$770$		0			0
$771$	−54.4658			−1.96154
$772$		0			0
$773$	−23.8258	−	41.2676i	−0.856956	−	1.48429i	−0.874818	−	0.484451i	$-0.839019\pi$
$773$	−23.8258	−	41.2676i	−0.856956	−	1.48429i	0.0178625	−	0.999840i	$-0.494314\pi$
$774$		0			0
$775$	−25.3383	+	43.8872i	−0.910177	+	1.57647i
$776$		0			0
$777$	30.5542	−	16.4921i	1.09613	−	0.591649i
$778$		0			0
$779$	6.22311	−	10.7787i	0.222966	−	0.386188i
$780$		0			0
$781$	3.15069	+	5.45715i	0.112740	+	0.195272i
$782$		0			0
$783$	−22.8229			−0.815624
$784$		0			0
$785$	26.8853			0.959578
$786$		0			0
$787$	6.41935	+	11.1186i	0.228825	+	0.396337i	0.957460	−	0.288566i	$-0.0931783\pi$
$787$	6.41935	+	11.1186i	0.228825	+	0.396337i	−0.728635	+	0.684902i	$0.759845\pi$
$788$		0			0
$789$	28.8656	−	49.9967i	1.02764	−	1.77993i
$790$		0			0
$791$	30.0942	−	16.2438i	1.07003	−	0.577562i
$792$		0			0
$793$	−2.94194	+	5.09560i	−0.104471	+	0.180950i
$794$		0			0
$795$	−43.2661	−	74.9391i	−1.53449	−	2.65782i
$796$		0			0
$797$	−7.53780			−0.267003			−0.133501	−	0.991049i	$-0.542622\pi$
$797$	−7.53780			−0.267003			−0.133501	+	0.991049i	$0.542622\pi$
$798$		0			0
$799$	−42.1951			−1.49276
$800$		0			0
$801$	−7.41634	−	12.8455i	−0.262043	−	0.453872i
$802$		0			0
$803$	3.02155	−	5.23348i	0.106628	−	0.184685i
$804$		0			0
$805$	−8.74519	−	5.38880i	−0.308227	−	0.189930i
$806$		0			0
$807$	15.1143	−	26.1787i	0.532047	−	0.921533i
$808$		0			0
$809$	−8.99432	−	15.5786i	−0.316223	−	0.547715i	0.663473	−	0.748200i	$-0.269082\pi$
$809$	−8.99432	−	15.5786i	−0.316223	−	0.547715i	−0.979697	+	0.200485i	$0.935748\pi$
$810$		0			0
$811$	−2.50253			−0.0878757			−0.0439379	−	0.999034i	$-0.513990\pi$
$811$	−2.50253			−0.0878757			−0.0439379	+	0.999034i	$0.513990\pi$
$812$		0			0
$813$	25.0871			0.879844
$814$		0			0
$815$	40.1857	+	69.6037i	1.40764	+	2.43811i
$816$		0			0
$817$	−15.3026	+	26.5049i	−0.535371	+	0.927289i
$818$		0			0
$819$	0.263308	−	9.18850i	0.00920073	−	0.321072i
$820$		0			0
$821$	24.9201	−	43.1629i	0.869719	−	1.50640i	0.00743478	−	0.999972i	$-0.497633\pi$
$821$	24.9201	−	43.1629i	0.869719	−	1.50640i	0.862284	−	0.506425i	$-0.169033\pi$
$822$		0			0
$823$	−7.22941	−	12.5217i	−0.252001	−	0.436479i	0.712075	−	0.702103i	$-0.247755\pi$
$823$	−7.22941	−	12.5217i	−0.252001	−	0.436479i	−0.964077	+	0.265624i	$0.914422\pi$
$824$		0			0
$825$	−96.0329			−3.34344
$826$		0			0
$827$	−15.9813			−0.555726			−0.277863	−	0.960621i	$-0.589626\pi$
$827$	−15.9813			−0.555726			−0.277863	+	0.960621i	$0.589626\pi$
$828$		0			0
$829$	−4.17374	−	7.22913i	−0.144960	−	0.251078i	0.784398	−	0.620258i	$-0.212972\pi$
$829$	−4.17374	−	7.22913i	−0.144960	−	0.251078i	−0.929358	+	0.369180i	$0.879639\pi$
$830$		0			0
$831$	−19.9277	+	34.5159i	−0.691286	+	1.19734i
$832$		0			0
$833$	31.0898	+	1.78330i	1.07720	+	0.0617877i
$834$		0			0
$835$	38.2661	−	66.2788i	1.32425	−	2.29367i
$836$		0			0
$837$	−8.67041	−	15.0176i	−0.299693	−	0.519084i
$838$		0			0
$839$	−34.2684			−1.18308			−0.591538	−	0.806277i	$-0.701479\pi$
$839$	−34.2684			−1.18308			−0.591538	+	0.806277i	$0.701479\pi$
$840$		0			0
$841$	14.8349			0.511549
$842$		0			0
$843$	−3.62260	−	6.27453i	−0.124769	−	0.216106i
$844$		0			0
$845$	12.3129	−	21.3265i	0.423576	−	0.733655i
$846$		0			0
$847$	0.750837	−	26.2015i	0.0257991	−	0.900295i
$848$		0			0
$849$	30.3277	−	52.5291i	1.04084	−	1.80279i
$850$		0			0
$851$	3.14732	+	5.45131i	0.107889	+	0.186869i
$852$		0			0
$853$	9.09261			0.311325			0.155663	−	0.987810i	$-0.450249\pi$
$853$	9.09261			0.311325			0.155663	+	0.987810i	$0.450249\pi$
$854$		0			0
$855$	20.2564			0.692754
$856$		0			0
$857$	1.31755	+	2.28206i	0.0450066	+	0.0779537i	0.887651	−	0.460517i	$-0.152336\pi$
$857$	1.31755	+	2.28206i	0.0450066	+	0.0779537i	−0.842645	+	0.538470i	$0.819002\pi$
$858$		0			0
$859$	−13.2512	+	22.9517i	−0.452124	+	0.783102i	−0.998518	−	0.0544267i	$-0.982667\pi$
$859$	−13.2512	+	22.9517i	−0.452124	+	0.783102i	0.546394	+	0.837528i	$0.316000\pi$
$860$		0			0
$861$	15.0849	+	9.29536i	0.514093	+	0.316785i
$862$		0			0
$863$	20.6843	−	35.8263i	0.704102	−	1.21954i	−0.262913	−	0.964820i	$-0.584683\pi$
$863$	20.6843	−	35.8263i	0.704102	−	1.21954i	0.967015	−	0.254721i	$-0.0819836\pi$
$864$		0			0
$865$	−22.8617	−	39.5976i	−0.777321	−	1.34636i
$866$		0			0
$867$	−5.81867			−0.197612
$868$		0			0
$869$	−20.3361			−0.689855
$870$		0			0
$871$	2.48279	+	4.30032i	0.0841262	+	0.145711i
$872$		0			0
$873$	−9.33569	+	16.1699i	−0.315965	+	0.547268i
$874$		0			0
$875$	−45.8653	+	24.7564i	−1.55053	+	0.836920i
$876$		0			0
$877$	−6.77324	+	11.7316i	−0.228716	+	0.396148i	−0.957428	−	0.288673i	$-0.906786\pi$
$877$	−6.77324	+	11.7316i	−0.228716	+	0.396148i	0.728712	+	0.684820i	$0.240119\pi$
$878$		0			0
$879$	29.2739	+	50.7038i	0.987383	+	1.71020i
$880$		0			0
$881$	−31.0312			−1.04547			−0.522734	−	0.852496i	$-0.675088\pi$
$881$	−31.0312			−1.04547			−0.522734	+	0.852496i	$0.675088\pi$
$882$		0			0
$883$	−57.2715			−1.92734			−0.963670	−	0.267096i	$-0.913936\pi$
$883$	−57.2715			−1.92734			−0.963670	+	0.267096i	$0.913936\pi$
$884$		0			0
$885$	7.41394	+	12.8413i	0.249217	+	0.431656i
$886$		0			0
$887$	1.13928	−	1.97330i	0.0382534	−	0.0662568i	−0.846265	−	0.532762i	$-0.821154\pi$
$887$	1.13928	−	1.97330i	0.0382534	−	0.0662568i	0.884518	+	0.466506i	$0.154487\pi$
$888$		0			0
$889$	−37.9042	+	20.4593i	−1.27127	+	0.686183i
$890$		0			0
$891$	25.6662	−	44.4552i	0.859850	−	1.48930i
$892$		0			0
$893$	−18.3748	−	31.8260i	−0.614888	−	1.06502i
$894$		0			0
$895$	−95.6513			−3.19727
$896$		0			0
$897$	5.37924			0.179607
$898$		0			0
$899$	16.6528	+	28.8436i	0.555404	+	0.961987i
$900$		0			0
$901$	−23.7791	+	41.1866i	−0.792196	+	1.37212i
$902$		0			0
$903$	−37.0938	−	22.8573i	−1.23441	−	0.760643i
$904$		0			0
$905$	−29.4853	+	51.0700i	−0.980125	+	1.69763i
$906$		0			0
$907$	3.78555	+	6.55677i	0.125697	+	0.217714i	0.922005	−	0.387177i	$-0.126550\pi$
$907$	3.78555	+	6.55677i	0.125697	+	0.217714i	−0.796308	+	0.604891i	$0.793217\pi$
$908$		0			0
$909$	−20.8619			−0.691947
$910$		0			0
$911$	−24.7906			−0.821349			−0.410674	−	0.911782i	$-0.634707\pi$
$911$	−24.7906			−0.821349			−0.410674	+	0.911782i	$0.634707\pi$
$912$		0			0
$913$	18.0073	+	31.1895i	0.595954	+	1.03222i
$914$		0			0
$915$	9.22938	−	15.9858i	0.305114	−	0.528473i
$916$		0			0
$917$	−0.733603	+	25.6001i	−0.0242257	+	0.845390i
$918$		0			0
$919$	0.608674	−	1.05425i	0.0200783	−	0.0347767i	−0.855812	−	0.517288i	$-0.826942\pi$
$919$	0.608674	−	1.05425i	0.0200783	−	0.0347767i	0.875890	+	0.482511i	$0.160275\pi$
$920$		0			0
$921$	31.7316	+	54.9607i	1.04559	+	1.81102i
$922$		0			0
$923$	−3.55577			−0.117040
$924$		0			0
$925$	63.4116			2.08496
$926$		0			0
$927$	−10.3400	−	17.9094i	−0.339610	−	0.588222i
$928$		0			0
$929$	23.0757	−	39.9683i	0.757090	−	1.31132i	−0.187239	−	0.982314i	$-0.559954\pi$
$929$	23.0757	−	39.9683i	0.757090	−	1.31132i	0.944329	−	0.329003i	$-0.106713\pi$
$930$		0			0
$931$	12.1936	+	24.2263i	0.399631	+	0.793986i
$932$		0			0
$933$	−9.45307	+	16.3732i	−0.309480	+	0.536034i
$934$		0			0
$935$	39.4880	+	68.3952i	1.29140	+	2.23676i
$936$		0			0
$937$	36.5284			1.19333			0.596666	−	0.802490i	$-0.296492\pi$
$937$	36.5284			1.19333			0.596666	+	0.802490i	$0.296492\pi$
$938$		0			0
$939$	45.8824			1.49732
$940$		0			0
$941$	20.3164	+	35.1890i	0.662296	+	1.14713i	0.980011	+	0.198944i	$0.0637511\pi$
$941$	20.3164	+	35.1890i	0.662296	+	1.14713i	−0.317715	+	0.948186i	$0.602916\pi$
$942$		0			0
$943$	−1.60614	+	2.78192i	−0.0523032	+	0.0905919i
$944$		0			0
$945$	1.01430	−	35.3952i	0.0329950	−	1.15141i
$946$		0			0
$947$	−14.1945	+	24.5855i	−0.461258	+	0.798922i	−0.999024	−	0.0441718i	$-0.985935\pi$
$947$	−14.1945	+	24.5855i	−0.461258	+	0.798922i	0.537766	+	0.843094i	$0.319268\pi$
$948$		0			0
$949$	1.70502	+	2.95317i	0.0553471	+	0.0958641i
$950$		0			0
$951$	−23.6744			−0.767694
$952$		0			0
$953$	9.80179			0.317511			0.158756	−	0.987318i	$-0.449252\pi$
$953$	9.80179			0.317511			0.158756	+	0.987318i	$0.449252\pi$
$954$		0			0
$955$	33.2197	+	57.5382i	1.07496	+	1.86189i
$956$		0			0
$957$	−31.5575	+	54.6591i	−1.02011	+	1.76688i
$958$		0			0
$959$	−3.81283	−	2.34947i	−0.123123	−	0.0758684i
$960$		0			0
$961$	2.84719	−	4.93148i	0.0918449	−	0.159080i
$962$		0			0
$963$	−0.992076	−	1.71833i	−0.0319692	−	0.0553723i
$964$		0			0
$965$	29.7612			0.958048
$966$		0			0
$967$	13.9541			0.448734			0.224367	−	0.974505i	$-0.427969\pi$
$967$	13.9541			0.448734			0.224367	+	0.974505i	$0.427969\pi$
$968$		0			0
$969$	−17.9680	−	31.1214i	−0.577214	−	0.999764i
$970$		0			0
$971$	27.3395	−	47.3533i	0.877365	−	1.51964i	0.0231430	−	0.999732i	$-0.492633\pi$
$971$	27.3395	−	47.3533i	0.877365	−	1.51964i	0.854222	−	0.519909i	$-0.174034\pi$
$972$		0			0
$973$	−34.0024	+	18.3533i	−1.09007	+	0.588379i
$974$		0			0
$975$	27.0950	−	46.9299i	0.867734	−	1.50296i
$976$		0			0
$977$	−17.6879	−	30.6364i	−0.565887	−	0.980145i	−0.996967	−	0.0778313i	$-0.975200\pi$
$977$	−17.6879	−	30.6364i	−0.565887	−	0.980145i	0.431079	−	0.902314i	$-0.358133\pi$
$978$		0			0
$979$	50.3666			1.60972
$980$		0			0
$981$	−21.2388			−0.678101
$982$		0			0
$983$	−18.7671	−	32.5056i	−0.598577	−	1.03677i	−0.993031	−	0.117850i	$-0.962400\pi$
$983$	−18.7671	−	32.5056i	−0.598577	−	1.03677i	0.394454	−	0.918916i	$-0.370934\pi$
$984$		0			0
$985$	−49.1980	+	85.2134i	−1.56758	+	2.71512i
$986$		0			0
$987$	46.0394	−	24.8504i	1.46545	−	0.790997i
$988$		0			0
$989$	3.94951	−	6.84075i	0.125587	−	0.217523i
$990$		0			0
$991$	−12.6278	−	21.8719i	−0.401134	−	0.694785i	0.592729	−	0.805402i	$-0.298051\pi$
$991$	−12.6278	−	21.8719i	−0.401134	−	0.694785i	−0.993863	+	0.110617i	$0.964717\pi$
$992$		0			0
$993$	−19.3256			−0.613278
$994$		0			0
$995$	25.8525			0.819581
$996$		0			0
$997$	−2.40169	−	4.15985i	−0.0760623	−	0.131744i	0.825485	−	0.564423i	$-0.190901\pi$
$997$	−2.40169	−	4.15985i	−0.0760623	−	0.131744i	−0.901548	+	0.432680i	$0.857568\pi$
$998$		0			0
$999$	−10.8493	+	18.7915i	−0.343256	+	0.594537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.i.a.93.6	✓	14
7.2	even	3		4508.2.a.m.1.2		7
7.4	even	3	inner	644.2.i.a.277.6	yes	14
7.5	odd	6		4508.2.a.l.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.i.a.93.6	✓	14	1.1	even	1	trivial
644.2.i.a.277.6	yes	14	7.4	even	3	inner
4508.2.a.l.1.6		7	7.5	odd	6
4508.2.a.m.1.2		7	7.2	even	3

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04242 + 1.80553i) q^{3} +(-1.94126 + 3.36236i) q^{5} +(-2.32824 + 1.25670i) q^{7} +(-0.673281 + 1.16616i) q^{9} +O(q^{10})\)	\(q+(1.04242 + 1.80553i) q^{3} +(-1.94126 + 3.36236i) q^{5} +(-2.32824 + 1.25670i) q^{7} +(-0.673281 + 1.16616i) q^{9} +(-2.28623 - 3.95986i) q^{11} +2.58017 q^{13} -8.09442 q^{15} +(2.22435 + 3.85269i) q^{17} +(-1.93728 + 3.35547i) q^{19} +(-4.69601 - 2.89369i) q^{21} +(0.500000 - 0.866025i) q^{23} +(-5.03696 - 8.72427i) q^{25} +3.44716 q^{27} -6.62079 q^{29} +(-2.51523 - 4.35651i) q^{31} +(4.76642 - 8.25567i) q^{33} +(0.294241 - 10.2680i) q^{35} +(-3.14732 + 5.45131i) q^{37} +(2.68962 + 4.65856i) q^{39} -3.21229 q^{41} +7.89902 q^{43} +(-2.61402 - 4.52762i) q^{45} +(-4.74241 + 8.21410i) q^{47} +(3.84141 - 5.85180i) q^{49} +(-4.63742 + 8.03224i) q^{51} +(5.34517 + 9.25811i) q^{53} +17.7526 q^{55} -8.07785 q^{57} +(-0.915931 - 1.58644i) q^{59} +(-1.14021 + 1.97491i) q^{61} +(0.102051 - 3.56120i) q^{63} +(-5.00877 + 8.67544i) q^{65} +(0.962260 + 1.66668i) q^{67} +2.08484 q^{69} -1.37812 q^{71} +(0.660816 + 1.14457i) q^{73} +(10.5013 - 18.1887i) q^{75} +(10.2992 + 6.34640i) q^{77} +(2.22376 - 3.85167i) q^{79} +(5.61323 + 9.72240i) q^{81} -7.87643 q^{83} -17.2721 q^{85} +(-6.90165 - 11.9540i) q^{87} +(-5.50761 + 9.53946i) q^{89} +(-6.00725 + 3.24250i) q^{91} +(5.24386 - 9.08264i) q^{93} +(-7.52152 - 13.0277i) q^{95} +13.8660 q^{97} +6.15708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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