LMFDB - Embedded newform 644.2.bc.a.425.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			425.10
Character	$\chi$	$=$	644.425
Dual form			644.2.bc.a.297.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.296529 + 0.740692i) q^{3} +(0.842227 - 3.47171i) q^{5} +(2.64401 + 0.0960306i) q^{7} +(1.71051 - 1.63096i) q^{9} +O(q^{10})$	\(q+(0.296529 + 0.740692i) q^{3} +(0.842227 - 3.47171i) q^{5} +(2.64401 + 0.0960306i) q^{7} +(1.71051 - 1.63096i) q^{9} +(-0.318362 - 0.0151655i) q^{11} +(-2.83875 - 2.45979i) q^{13} +(2.82121 - 0.405629i) q^{15} +(-4.24312 + 5.95862i) q^{17} +(-3.76758 - 5.29082i) q^{19} +(0.712895 + 1.98687i) q^{21} +(3.85192 - 2.85704i) q^{23} +(-6.89922 - 3.55680i) q^{25} +(3.89249 + 1.77764i) q^{27} +(-3.48906 - 7.63997i) q^{29} +(4.90092 + 6.23203i) q^{31} +(-0.0831705 - 0.240305i) q^{33} +(2.56024 - 9.09834i) q^{35} +(3.87478 + 4.06375i) q^{37} +(0.980178 - 2.83204i) q^{39} +(0.796014 + 2.71098i) q^{41} +(5.56374 + 0.799945i) q^{43} +(-4.22159 - 7.31202i) q^{45} +(0.648688 + 0.374520i) q^{47} +(6.98156 + 0.507811i) q^{49} +(-5.67171 - 1.37594i) q^{51} +(1.83865 + 0.636364i) q^{53} +(-0.320783 + 1.09249i) q^{55} +(2.80168 - 4.35950i) q^{57} +(0.0111021 - 0.0576032i) q^{59} +(7.86409 + 3.14831i) q^{61} +(4.67921 - 4.14802i) q^{63} +(-10.9305 + 7.78360i) q^{65} +(-0.819131 + 1.58889i) q^{67} +(3.25840 + 2.00590i) q^{69} +(-4.64332 + 2.98408i) q^{71} +(1.33543 + 13.9853i) q^{73} +(0.588676 - 6.16490i) q^{75} +(-0.840296 - 0.0706701i) q^{77} +(4.97898 - 1.72324i) q^{79} +(0.174921 - 3.67205i) q^{81} +(-3.72466 - 1.09366i) q^{83} +(17.1129 + 19.7494i) q^{85} +(4.62426 - 4.84979i) q^{87} +(-3.37838 - 2.65679i) q^{89} +(-7.26946 - 6.77631i) q^{91} +(-3.16276 + 5.47805i) q^{93} +(-21.5413 + 8.62385i) q^{95} +(-6.58069 + 1.93226i) q^{97} +(-0.569295 + 0.493297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.296529	+	0.740692i	0.171201	+	0.427639i	0.989010	−	0.147851i	$-0.0472356\pi$
$3$	0.296529	+	0.740692i	0.171201	+	0.427639i	−0.817809	+	0.575490i	$0.804811\pi$
$4$		0			0
$5$	0.842227	−	3.47171i	0.376655	−	1.55259i	−0.396292	−	0.918124i	$-0.629703\pi$
$5$	0.842227	−	3.47171i	0.376655	−	1.55259i	0.772947	−	0.634470i	$-0.218782\pi$
$6$		0			0
$7$	2.64401	+	0.0960306i	0.999341	+	0.0362961i
$7$	2.64401	+	0.0960306i	0.999341	+	0.0362961i
$8$		0			0
$9$	1.71051	−	1.63096i	0.570169	−	0.543655i
$10$		0			0
$11$	−0.318362	−	0.0151655i	−0.0959898	−	0.00457256i	−0.000467936	−	1.00000i	$-0.500149\pi$
$11$	−0.318362	−	0.0151655i	−0.0959898	−	0.00457256i	−0.0955219	+	0.995427i	$0.530452\pi$
$12$		0			0
$13$	−2.83875	−	2.45979i	−0.787327	−	0.682223i	0.165340	−	0.986237i	$-0.447128\pi$
$13$	−2.83875	−	2.45979i	−0.787327	−	0.682223i	−0.952668	+	0.304014i	$0.901673\pi$
$14$		0			0
$15$	2.82121	−	0.405629i	0.728434	−	0.104733i
$16$		0			0
$17$	−4.24312	+	5.95862i	−1.02911	+	1.44518i	−0.138523	+	0.990359i	$0.544235\pi$
$17$	−4.24312	+	5.95862i	−1.02911	+	1.44518i	−0.890584	+	0.454819i	$0.849704\pi$
$18$		0			0
$19$	−3.76758	−	5.29082i	−0.864342	−	1.21380i	−0.975501	−	0.219996i	$-0.929396\pi$
$19$	−3.76758	−	5.29082i	−0.864342	−	1.21380i	0.111159	−	0.993803i	$-0.464544\pi$
$20$		0			0
$21$	0.712895	+	1.98687i	0.155566	+	0.433571i
$22$		0			0
$23$	3.85192	−	2.85704i	0.803181	−	0.595735i
$23$	3.85192	−	2.85704i	0.803181	−	0.595735i
$24$		0			0
$25$	−6.89922	−	3.55680i	−1.37984	−	0.711359i
$26$		0			0
$27$	3.89249	+	1.77764i	0.749110	+	0.342107i
$28$		0			0
$29$	−3.48906	−	7.63997i	−0.647902	−	1.41871i	−0.893379	−	0.449304i	$-0.851672\pi$
$29$	−3.48906	−	7.63997i	−0.647902	−	1.41871i	0.245477	−	0.969402i	$-0.421055\pi$
$30$		0			0
$31$	4.90092	+	6.23203i	0.880232	+	1.11931i	0.992083	+	0.125581i	$0.0400795\pi$
$31$	4.90092	+	6.23203i	0.880232	+	1.11931i	−0.111851	+	0.993725i	$0.535678\pi$
$32$		0			0
$33$	−0.0831705	−	0.240305i	−0.0144781	−	0.0418318i
$34$		0			0
$35$	2.56024	−	9.09834i	0.432760	−	1.53790i
$36$		0			0
$37$	3.87478	+	4.06375i	0.637010	+	0.668077i	0.960540	−	0.278141i	$-0.0897183\pi$
$37$	3.87478	+	4.06375i	0.637010	+	0.668077i	−0.323530	+	0.946218i	$0.604870\pi$
$38$		0			0
$39$	0.980178	−	2.83204i	0.156954	−	0.453489i
$40$		0			0
$41$	0.796014	+	2.71098i	0.124317	+	0.423383i	0.998007	−	0.0630984i	$-0.0200982\pi$
$41$	0.796014	+	2.71098i	0.124317	+	0.423383i	−0.873691	+	0.486482i	$0.838280\pi$
$42$		0			0
$43$	5.56374	+	0.799945i	0.848462	+	0.121990i	0.552812	−	0.833306i	$-0.313555\pi$
$43$	5.56374	+	0.799945i	0.848462	+	0.121990i	0.295650	+	0.955296i	$0.404464\pi$
$44$		0			0
$45$	−4.22159	−	7.31202i	−0.629318	−	1.09001i
$46$		0			0
$47$	0.648688	+	0.374520i	0.0946209	+	0.0546294i	0.546564	−	0.837417i	$-0.315936\pi$
$47$	0.648688	+	0.374520i	0.0946209	+	0.0546294i	−0.451943	+	0.892047i	$0.649269\pi$
$48$		0			0
$49$	6.98156	+	0.507811i	0.997365	+	0.0725445i
$50$		0			0
$51$	−5.67171	−	1.37594i	−0.794198	−	0.192670i
$52$		0			0
$53$	1.83865	+	0.636364i	0.252558	+	0.0874113i	0.450414	−	0.892820i	$-0.351276\pi$
$53$	1.83865	+	0.636364i	0.252558	+	0.0874113i	−0.197856	+	0.980231i	$0.563398\pi$
$54$		0			0
$55$	−0.320783	+	1.09249i	−0.0432544	+	0.147311i
$56$		0			0
$57$	2.80168	−	4.35950i	0.371091	−	0.577430i
$58$		0			0
$59$	0.0111021	−	0.0576032i	0.00144537	−	0.00749930i	−0.981199	−	0.193000i	$-0.938178\pi$
$59$	0.0111021	−	0.0576032i	0.00144537	−	0.00749930i	0.982644	+	0.185500i	$0.0593905\pi$
$60$		0			0
$61$	7.86409	+	3.14831i	1.00689	+	0.403100i	0.815714	−	0.578456i	$-0.196344\pi$
$61$	7.86409	+	3.14831i	1.00689	+	0.403100i	0.191180	+	0.981555i	$0.438769\pi$
$62$		0			0
$63$	4.67921	−	4.14802i	0.589526	−	0.522602i
$64$		0			0
$65$	−10.9305	+	7.78360i	−1.35577	+	0.965437i
$66$		0			0
$67$	−0.819131	+	1.58889i	−0.100073	+	0.194114i	−0.933557	−	0.358429i	$-0.883312\pi$
$67$	−0.819131	+	1.58889i	−0.100073	+	0.194114i	0.833484	+	0.552544i	$0.186343\pi$
$68$		0			0
$69$	3.25840	+	2.00590i	0.392265	+	0.241481i
$70$		0			0
$71$	−4.64332	+	2.98408i	−0.551061	+	0.354146i	−0.786351	−	0.617780i	$-0.788032\pi$
$71$	−4.64332	+	2.98408i	−0.551061	+	0.354146i	0.235290	+	0.971925i	$0.424396\pi$
$72$		0			0
$73$	1.33543	+	13.9853i	0.156300	+	1.63685i	0.644846	+	0.764312i	$0.276921\pi$
$73$	1.33543	+	13.9853i	0.156300	+	1.63685i	−0.488546	+	0.872538i	$0.662473\pi$
$74$		0			0
$75$	0.588676	−	6.16490i	0.0679745	−	0.711861i
$76$		0			0
$77$	−0.840296	−	0.0706701i	−0.0957606	−	0.00805360i
$78$		0			0
$79$	4.97898	−	1.72324i	0.560179	−	0.193880i	−0.0322823	−	0.999479i	$-0.510278\pi$
$79$	4.97898	−	1.72324i	0.560179	−	0.193880i	0.592461	+	0.805599i	$0.298156\pi$
$80$		0			0
$81$	0.174921	−	3.67205i	0.0194357	−	0.408005i
$82$		0			0
$83$	−3.72466	−	1.09366i	−0.408834	−	0.120045i	0.0708474	−	0.997487i	$-0.477430\pi$
$83$	−3.72466	−	1.09366i	−0.408834	−	0.120045i	−0.479682	+	0.877443i	$0.659248\pi$
$84$		0			0
$85$	17.1129	+	19.7494i	1.85616	+	2.14212i
$86$		0			0
$87$	4.62426	−	4.84979i	0.495773	−	0.519952i
$88$		0			0
$89$	−3.37838	−	2.65679i	−0.358107	−	0.281619i	0.422854	−	0.906198i	$-0.361028\pi$
$89$	−3.37838	−	2.65679i	−0.358107	−	0.281619i	−0.780962	+	0.624579i	$0.785271\pi$
$90$		0			0
$91$	−7.26946	−	6.77631i	−0.762046	−	0.710350i
$92$		0			0
$93$	−3.16276	+	5.47805i	−0.327962	+	0.568048i
$94$		0			0
$95$	−21.5413	+	8.62385i	−2.21010	+	0.884789i
$96$		0			0
$97$	−6.58069	+	1.93226i	−0.668168	+	0.196192i	−0.598187	−	0.801357i	$-0.704112\pi$
$97$	−6.58069	+	1.93226i	−0.668168	+	0.196192i	−0.0699808	+	0.997548i	$0.522294\pi$
$98$		0			0
$99$	−0.569295	+	0.493297i	−0.0572163	+	0.0495782i
$100$		0			0
$101$	−6.11110	+	1.48254i	−0.608077	+	0.147518i	−0.527963	−	0.849268i	$-0.677044\pi$
$101$	−6.11110	+	1.48254i	−0.608077	+	0.147518i	−0.0801148	+	0.996786i	$0.525529\pi$
$102$		0			0
$103$	2.44225	−	1.25907i	0.240642	−	0.124059i	−0.333688	−	0.942684i	$-0.608293\pi$
$103$	2.44225	−	1.25907i	0.240642	−	0.124059i	0.574329	+	0.818624i	$0.305263\pi$
$104$		0			0
$105$	7.49826	−	0.801564i	0.731755	−	0.0782246i
$106$		0			0
$107$	2.79295	−	6.97645i	0.270005	−	0.674439i	−0.729954	−	0.683496i	$-0.760459\pi$
$107$	2.79295	−	6.97645i	0.270005	−	0.674439i	0.999959	+	0.00905692i	$0.00288295\pi$
$108$		0			0
$109$	−1.58603	−	1.12941i	−0.151914	−	0.108178i	0.501572	−	0.865116i	$-0.332755\pi$
$109$	−1.58603	−	1.12941i	−0.151914	−	0.108178i	−0.653487	+	0.756938i	$0.726695\pi$
$110$		0			0
$111$	−1.86101	+	4.07504i	−0.176639	+	0.386785i
$112$		0			0
$113$	−3.73000	−	5.80399i	−0.350889	−	0.545993i	0.620282	−	0.784379i	$-0.287018\pi$
$113$	−3.73000	−	5.80399i	−0.350889	−	0.545993i	−0.971171	+	0.238386i	$0.923382\pi$
$114$		0			0
$115$	−6.67462	−	15.7790i	−0.622412	−	1.47140i
$116$		0			0
$117$	−8.86753	+	0.422412i	−0.819803	+	0.0390520i
$118$		0			0
$119$	−11.7910	+	15.3472i	−1.08088	+	1.40687i
$120$		0			0
$121$	−10.8491	−	1.03596i	−0.986279	−	0.0941782i
$122$		0			0
$123$	−1.77196	+	1.39348i	−0.159772	+	0.125646i
$124$		0			0
$125$	−6.46172	+	7.45723i	−0.577954	+	0.666995i
$126$		0			0
$127$	14.8675	+	9.55478i	1.31928	+	0.847849i	0.995170	−	0.0981704i	$-0.0312990\pi$
$127$	14.8675	+	9.55478i	1.31928	+	0.847849i	0.324110	+	0.946020i	$0.394935\pi$
$128$		0			0
$129$	1.05729	+	4.35823i	0.0930896	+	0.383721i
$130$		0			0
$131$	−2.50796	−	13.0125i	−0.219122	−	1.13691i	−0.910212	−	0.414143i	$-0.864081\pi$
$131$	−2.50796	−	13.0125i	−0.219122	−	1.13691i	0.691090	−	0.722768i	$-0.257131\pi$
$132$		0			0
$133$	−9.45343	−	14.3508i	−0.819716	−	1.24437i
$134$		0			0
$135$	9.44980	−	12.0164i	0.813310	−	1.03421i
$136$		0			0
$137$	16.8712	−	9.74059i	1.44140	−	0.832195i	0.443460	−	0.896294i	$-0.353751\pi$
$137$	16.8712	−	9.74059i	1.44140	−	0.832195i	0.997943	+	0.0640997i	$0.0204176\pi$
$138$		0			0
$139$			16.3425i			1.38615i	0.720865	+	0.693076i	$0.243745\pi$
$139$			16.3425i			1.38615i	−0.720865	+	0.693076i	$0.756255\pi$
$140$		0			0
$141$	−0.0850498	+	0.591534i	−0.00716248	+	0.0498162i
$142$		0			0
$143$	0.866446	+	0.826155i	0.0724559	+	0.0690865i
$144$		0			0
$145$	−29.4623	+	5.67840i	−2.44671	+	0.471565i
$146$		0			0
$147$	1.69410	+	5.32177i	0.139727	+	0.438932i
$148$		0			0
$149$	5.46159	+	10.5940i	0.447431	+	0.867895i	0.999420	+	0.0340437i	$0.0108385\pi$
$149$	5.46159	+	10.5940i	0.447431	+	0.867895i	−0.551990	+	0.833851i	$0.686131\pi$
$150$		0			0
$151$	−2.98374	−	0.575070i	−0.242814	−	0.0467985i	0.0663923	−	0.997794i	$-0.478851\pi$
$151$	−2.98374	−	0.575070i	−0.242814	−	0.0467985i	−0.309206	+	0.950995i	$0.600063\pi$
$152$		0			0
$153$	2.46042	+	17.1126i	0.198914	+	1.38347i
$154$		0			0
$155$	25.7635	−	11.7658i	2.06937	−	0.945051i
$156$		0			0
$157$	−16.4252	+	1.56842i	−1.31087	+	0.125173i	−0.726981	−	0.686657i	$-0.759077\pi$
$157$	−16.4252	+	1.56842i	−1.31087	+	0.125173i	−0.583893	+	0.811831i	$0.698471\pi$
$158$		0			0
$159$	0.0738630	+	1.55058i	0.00585772	+	0.122969i
$160$		0			0
$161$	10.4589	−	7.18414i	0.824275	−	0.566190i
$162$		0			0
$163$	0.569436	+	11.9539i	0.0446016	+	0.936304i	0.904667	+	0.426119i	$0.140120\pi$
$163$	0.569436	+	11.9539i	0.0446016	+	0.936304i	−0.860065	+	0.510184i	$0.829577\pi$
$164$		0			0
$165$	−0.904318	+	0.0863519i	−0.0704011	+	0.00672249i
$166$		0			0
$167$	−15.3468	+	7.00866i	−1.18757	+	0.542347i	−0.908485	−	0.417919i	$-0.862760\pi$
$167$	−15.3468	+	7.00866i	−1.18757	+	0.542347i	−0.279089	+	0.960265i	$0.590032\pi$
$168$		0			0
$169$	0.157836	+	1.09777i	0.0121412	+	0.0844439i
$170$		0			0
$171$	−15.0736	−	2.90520i	−1.15271	−	0.222166i
$172$		0			0
$173$	8.28126	+	16.0634i	0.629612	+	1.22128i	0.960677	+	0.277669i	$0.0895619\pi$
$173$	8.28126	+	16.0634i	0.629612	+	1.22128i	−0.331064	+	0.943608i	$0.607408\pi$
$174$		0			0
$175$	−17.9000	−	10.0667i	−1.35312	−	0.760974i
$176$		0			0
$177$	0.0459584	−	0.00885775i	0.00345444	−	0.000665789i
$178$		0			0
$179$	13.0476	+	12.4409i	0.975226	+	0.929876i	0.997556	−	0.0698743i	$-0.0222598\pi$
$179$	13.0476	+	12.4409i	0.975226	+	0.929876i	−0.0223295	+	0.999751i	$0.507108\pi$
$180$		0			0
$181$	−3.42675	+	23.8336i	−0.254708	+	1.77154i	0.314416	+	0.949285i	$0.398191\pi$
$181$	−3.42675	+	23.8336i	−0.254708	+	1.77154i	−0.569125	+	0.822251i	$0.692718\pi$
$182$		0			0
$183$			6.75844i			0.499598i
$184$		0			0
$185$	17.3716	−	10.0295i	1.27719	−	0.737383i
$186$		0			0
$187$	1.44121	−	1.83265i	0.105392	−	0.134017i
$188$		0			0
$189$	10.1211	+	5.07389i	0.736199	+	0.369071i
$190$		0			0
$191$	1.75181	+	9.08926i	0.126757	+	0.657676i	0.988608	+	0.150515i	$0.0480931\pi$
$191$	1.75181	+	9.08926i	0.126757	+	0.657676i	−0.861851	+	0.507161i	$0.830695\pi$
$192$		0			0
$193$	2.57008	+	10.5940i	0.184998	+	0.762573i	0.986389	+	0.164431i	$0.0525789\pi$
$193$	2.57008	+	10.5940i	0.184998	+	0.762573i	−0.801390	+	0.598142i	$0.795906\pi$
$194$		0			0
$195$	−9.00647	−	5.78811i	−0.644967	−	0.414495i
$196$		0			0
$197$	−2.64244	+	3.04954i	−0.188266	+	0.217271i	−0.842034	−	0.539424i	$-0.818642\pi$
$197$	−2.64244	+	3.04954i	−0.188266	+	0.217271i	0.653768	+	0.756695i	$0.273187\pi$
$198$		0			0
$199$	17.1432	−	13.4815i	1.21525	−	0.955682i	0.215465	−	0.976512i	$-0.430873\pi$
$199$	17.1432	−	13.4815i	1.21525	−	0.955682i	0.999783	+	0.0208299i	$0.00663084\pi$
$200$		0			0
$201$	−1.41978	−	0.135572i	−0.100143	−	0.00956253i
$202$		0			0
$203$	−8.49142	−	20.5352i	−0.595981	−	1.44129i
$204$		0			0
$205$	10.0821	−	0.480271i	0.704167	−	0.0335436i
$206$		0			0
$207$	1.92900	−	11.1693i	0.134075	−	0.776323i
$208$		0			0
$209$	1.11922	+	1.74153i	0.0774178	+	0.120464i
$210$		0			0
$211$	−10.1066	+	22.1304i	−0.695769	+	1.52352i	0.149257	+	0.988798i	$0.452312\pi$
$211$	−10.1066	+	22.1304i	−0.695769	+	1.52352i	−0.845027	+	0.534724i	$0.820416\pi$
$212$		0			0
$213$	−3.58717	−	2.55441i	−0.245789	−	0.175025i
$214$		0			0
$215$	7.46311	−	18.6419i	0.508980	−	1.27137i
$216$		0			0
$217$	12.3596	+	16.9482i	0.839025	+	1.15052i
$218$		0			0
$219$	−9.96278	+	5.13617i	−0.673222	+	0.347070i
$220$		0			0
$221$	26.7021	−	6.47786i	1.79618	−	0.435748i
$222$		0			0
$223$	11.4235	−	9.89852i	0.764974	−	0.662854i	−0.182313	−	0.983241i	$-0.558358\pi$
$223$	11.4235	−	9.89852i	0.764974	−	0.662854i	0.947287	+	0.320387i	$0.103813\pi$
$224$		0			0
$225$	−17.6022	+	5.16846i	−1.17348	+	0.344564i
$226$		0			0
$227$	−0.283487	+	0.113491i	−0.0188157	+	0.00753267i	−0.381051	−	0.924554i	$-0.624438\pi$
$227$	−0.283487	+	0.113491i	−0.0188157	+	0.00753267i	0.362236	+	0.932087i	$0.382014\pi$
$228$		0			0
$229$	−0.325231	+	0.563317i	−0.0214919	+	0.0372250i	−0.876571	−	0.481272i	$-0.840175\pi$
$229$	−0.325231	+	0.563317i	−0.0214919	+	0.0372250i	0.855079	+	0.518497i	$0.173508\pi$
$230$		0			0
$231$	−0.196827	−	0.643356i	−0.0129503	−	0.0423297i
$232$		0			0
$233$	−5.85113	−	4.60138i	−0.383320	−	0.301447i	0.407842	−	0.913052i	$-0.366281\pi$
$233$	−5.85113	−	4.60138i	−0.383320	−	0.301447i	−0.791163	+	0.611606i	$0.790524\pi$
$234$		0			0
$235$	1.84657	−	1.93662i	0.120457	−	0.126331i
$236$		0			0
$237$	2.75280	+	3.17690i	0.178814	+	0.206362i
$238$		0			0
$239$	10.4487	+	3.06802i	0.675871	+	0.198454i	0.601616	−	0.798786i	$-0.294524\pi$
$239$	10.4487	+	3.06802i	0.675871	+	0.198454i	0.0742552	+	0.997239i	$0.476342\pi$
$240$		0			0
$241$	0.440204	−	9.24101i	0.0283560	−	0.595266i	−0.939316	−	0.343053i	$-0.888539\pi$
$241$	0.440204	−	9.24101i	0.0283560	−	0.595266i	0.967672	−	0.252212i	$-0.0811582\pi$
$242$		0			0
$243$	14.9032	−	5.15806i	0.956044	−	0.330890i
$244$		0			0
$245$	7.64303	−	23.8102i	0.488295	−	1.52118i
$246$		0			0
$247$	−2.31911	+	24.2868i	−0.147561	+	1.54533i
$248$		0			0
$249$	−0.294403	−	3.08313i	−0.0186570	−	0.195385i
$250$		0			0
$251$	6.11214	−	3.92804i	0.385795	−	0.247935i	−0.333339	−	0.942807i	$-0.608175\pi$
$251$	6.11214	−	3.92804i	0.385795	−	0.247935i	0.719134	+	0.694872i	$0.244539\pi$
$252$		0			0
$253$	−1.26963	+	0.851158i	−0.0798212	+	0.0535118i
$254$		0			0
$255$	−9.55374	+	18.5317i	−0.598278	+	1.16050i
$256$		0			0
$257$	−22.3052	+	15.8835i	−1.39136	+	0.990785i	−0.393932	+	0.919139i	$0.628886\pi$
$257$	−22.3052	+	15.8835i	−1.39136	+	0.990785i	−0.997430	+	0.0716453i	$0.977175\pi$
$258$		0			0
$259$	9.85470	+	11.1167i	0.612341	+	0.690757i
$260$		0			0
$261$	−18.4286	−	7.37769i	−1.14070	−	0.456667i
$262$		0			0
$263$	−0.0782270	+	0.405880i	−0.00482368	+	0.0250276i	−0.984261	−	0.176722i	$-0.943451\pi$
$263$	−0.0782270	+	0.405880i	−0.00482368	+	0.0250276i	0.979437	+	0.201750i	$0.0646627\pi$
$264$		0			0
$265$	3.75783	−	5.84730i	0.230842	−	0.359197i
$266$		0			0
$267$	0.966075	−	3.29015i	0.0591229	−	0.201354i
$268$		0			0
$269$	−22.6892	−	7.85282i	−1.38339	−	0.478795i	−0.468843	−	0.883281i	$-0.655329\pi$
$269$	−22.6892	−	7.85282i	−1.38339	−	0.478795i	−0.914544	+	0.404486i	$0.867450\pi$
$270$		0			0
$271$	−20.8671	−	5.06232i	−1.26759	−	0.307514i	−0.455074	−	0.890454i	$-0.650387\pi$
$271$	−20.8671	−	5.06232i	−1.26759	−	0.307514i	−0.812515	+	0.582940i	$0.801902\pi$
$272$		0			0
$273$	2.86356	−	7.39380i	0.173311	−	0.447493i
$274$		0			0
$275$	2.14251	+	1.23698i	0.129198	+	0.0745927i
$276$		0			0
$277$	−2.02848	−	3.51343i	−0.121880	−	0.211102i	0.798629	−	0.601823i	$-0.205559\pi$
$277$	−2.02848	−	3.51343i	−0.121880	−	0.211102i	−0.920509	+	0.390722i	$0.872226\pi$
$278$		0			0
$279$	18.5473	+	2.66670i	1.11040	+	0.159651i
$280$		0			0
$281$	−5.56454	−	18.9511i	−0.331952	−	1.13053i	−0.941285	−	0.337612i	$-0.890381\pi$
$281$	−5.56454	−	18.9511i	−0.331952	−	1.13053i	0.609333	−	0.792914i	$-0.291437\pi$
$282$		0			0
$283$	2.16374	−	6.25172i	0.128621	−	0.371626i	−0.862242	−	0.506496i	$-0.830940\pi$
$283$	2.16374	−	6.25172i	0.128621	−	0.371626i	0.990863	+	0.134870i	$0.0430617\pi$
$284$		0			0
$285$	−12.7752	−	13.3983i	−0.756740	−	0.793646i
$286$		0			0
$287$	1.84433	+	7.24428i	0.108867	+	0.427617i
$288$		0			0
$289$	−11.9410	−	34.5012i	−0.702411	−	2.02948i
$290$		0			0
$291$	−3.38258	−	4.30129i	−0.198290	−	0.252146i
$292$		0			0
$293$	−13.8208	−	30.2632i	−0.807418	−	1.76800i	−0.618130	−	0.786076i	$-0.712109\pi$
$293$	−13.8208	−	30.2632i	−0.807418	−	1.76800i	−0.189288	−	0.981922i	$-0.560618\pi$
$294$		0			0
$295$	−0.190631	−	0.0870583i	−0.0110990	−	0.00506873i
$296$		0			0
$297$	−1.21226	−	0.624965i	−0.0703426	−	0.0362641i
$298$		0			0
$299$	−17.9624	−	1.36449i	−1.03879	−	0.0789106i
$300$		0			0
$301$	14.6338	+	2.64935i	0.843476	+	0.152706i
$302$		0			0
$303$	−2.91022	−	4.08683i	−0.167188	−	0.234782i
$304$		0			0
$305$	17.5534	−	24.6502i	1.00510	−	1.41147i
$306$		0			0
$307$	21.2609	−	3.05686i	1.21342	−	0.174464i	0.494266	−	0.869311i	$-0.335437\pi$
$307$	21.2609	−	3.05686i	1.21342	−	0.174464i	0.719158	+	0.694847i	$0.244528\pi$
$308$		0			0
$309$	1.65678	+	1.43560i	0.0942507	+	0.0816687i
$310$		0			0
$311$	−19.8842	−	0.947200i	−1.12753	−	0.0537108i	−0.524485	−	0.851420i	$-0.675742\pi$
$311$	−19.8842	−	0.947200i	−1.12753	−	0.0537108i	−0.603043	+	0.797709i	$0.706045\pi$
$312$		0			0
$313$	5.49427	−	5.23877i	0.310554	−	0.296113i	−0.518732	−	0.854937i	$-0.673596\pi$
$313$	5.49427	−	5.23877i	0.310554	−	0.296113i	0.829286	+	0.558824i	$0.188747\pi$
$314$		0			0
$315$	−10.4598	−	19.7384i	−0.589340	−	1.11213i
$316$		0			0
$317$	−2.48321	+	10.2359i	−0.139471	+	0.574907i	0.858590	+	0.512663i	$0.171341\pi$
$317$	−2.48321	+	10.2359i	−0.139471	+	0.574907i	−0.998061	+	0.0622441i	$0.980174\pi$
$318$		0			0
$319$	0.994920	+	2.48519i	0.0557048	+	0.139144i
$320$		0			0
$321$	5.99559			0.334641
$322$		0			0
$323$	47.5123			2.64365
$324$		0			0
$325$	10.8362	+	27.0675i	0.601084	+	1.50143i
$326$		0			0
$327$	0.366241	−	1.50967i	0.0202532	−	0.0834847i
$328$		0			0
$329$	1.67917	+	1.05253i	0.0925757	+	0.0580278i
$330$		0			0
$331$	13.0211	−	12.4156i	0.715704	−	0.682422i	−0.241968	−	0.970284i	$-0.577793\pi$
$331$	13.0211	−	12.4156i	0.715704	−	0.682422i	0.957672	+	0.287862i	$0.0929445\pi$
$332$		0			0
$333$	13.2557	+	0.631445i	0.726406	+	0.0346030i
$334$		0			0
$335$	4.82627	+	4.18199i	0.263688	+	0.228487i
$336$		0			0
$337$	−25.1771	+	3.61991i	−1.37148	+	0.197189i	−0.788369	−	0.615202i	$-0.789074\pi$
$337$	−25.1771	+	3.61991i	−1.37148	+	0.197189i	−0.583112	+	0.812392i	$0.698165\pi$
$338$		0			0
$339$	3.19292	−	4.48383i	0.173416	−	0.243528i
$340$		0			0
$341$	−1.46576	−	2.05837i	−0.0793752	−	0.111467i
$342$		0			0
$343$	18.4105	+	2.01310i	0.994075	+	0.108697i
$344$		0			0
$345$	9.70819	−	9.62277i	0.522671	−	0.518073i
$346$		0			0
$347$	−30.5133	−	15.7307i	−1.63804	−	0.844470i	−0.997036	−	0.0769337i	$-0.975487\pi$
$347$	−30.5133	−	15.7307i	−1.63804	−	0.844470i	−0.641006	−	0.767536i	$-0.721483\pi$
$348$		0			0
$349$	1.43869	+	0.657026i	0.0770111	+	0.0351698i	0.453548	−	0.891232i	$-0.350158\pi$
$349$	1.43869	+	0.657026i	0.0770111	+	0.0351698i	−0.376537	+	0.926402i	$0.622885\pi$
$350$		0			0
$351$	−6.67718	−	14.6210i	−0.356401	−	0.780410i
$352$		0			0
$353$	13.5084	+	17.1773i	0.718980	+	0.914257i	0.998953	−	0.0457505i	$-0.0145679\pi$
$353$	13.5084	+	17.1773i	0.718980	+	0.914257i	−0.279973	+	0.960008i	$0.590325\pi$
$354$		0			0
$355$	6.44913	+	18.6335i	0.342284	+	0.988965i
$356$		0			0
$357$	−14.8639	−	4.18266i	−0.786682	−	0.221370i
$358$		0			0
$359$	8.14766	+	8.54502i	0.430017	+	0.450989i	0.902717	−	0.430235i	$-0.141569\pi$
$359$	8.14766	+	8.54502i	0.430017	+	0.450989i	−0.472700	+	0.881223i	$0.656721\pi$
$360$		0			0
$361$	−7.58388	+	21.9122i	−0.399151	+	1.15327i
$362$		0			0
$363$	−2.44973	−	8.34301i	−0.128577	−	0.437895i
$364$		0			0
$365$	49.6774	+	7.14254i	2.60024	+	0.373858i
$366$		0			0
$367$	4.51439	+	7.81915i	0.235649	+	0.408156i	0.959461	−	0.281841i	$-0.0909450\pi$
$367$	4.51439	+	7.81915i	0.235649	+	0.408156i	−0.723812	+	0.689997i	$0.757612\pi$
$368$		0			0
$369$	5.78309	+	3.33887i	0.301056	+	0.173815i
$370$		0			0
$371$	4.80030	+	1.85912i	0.249219	+	0.0965206i
$372$		0			0
$373$	−2.29330	−	0.556349i	−0.118743	−	0.0288066i	0.175947	−	0.984400i	$-0.443701\pi$
$373$	−2.29330	−	0.556349i	−0.118743	−	0.0288066i	−0.294690	+	0.955593i	$0.595216\pi$
$374$		0			0
$375$	−7.43960	−	2.57487i	−0.384179	−	0.132966i
$376$		0			0
$377$	−8.88816	+	30.2703i	−0.457764	+	1.55900i
$378$		0			0
$379$	8.97128	−	13.9596i	0.460824	−	0.717056i	−0.530617	−	0.847612i	$-0.678040\pi$
$379$	8.97128	−	13.9596i	0.460824	−	0.717056i	0.991441	+	0.130556i	$0.0416761\pi$
$380$		0			0
$381$	−2.66851	+	13.8455i	−0.136712	+	0.709328i
$382$		0			0
$383$	−15.4560	−	6.18766i	−0.789766	−	0.316174i	−0.0585177	−	0.998286i	$-0.518637\pi$
$383$	−15.4560	−	6.18766i	−0.789766	−	0.316174i	−0.731248	+	0.682112i	$0.761062\pi$
$384$		0			0
$385$	−0.953065	+	2.85774i	−0.0485727	+	0.145644i
$386$		0			0
$387$	10.8215	−	7.70595i	0.550087	−	0.391715i
$388$		0			0
$389$	0.658282	−	1.27689i	0.0333762	−	0.0647409i	−0.871558	−	0.490293i	$-0.836890\pi$
$389$	0.658282	−	1.27689i	0.0333762	−	0.0647409i	0.904934	+	0.425552i	$0.139920\pi$
$390$		0			0
$391$	0.679887	+	35.0749i	0.0343834	+	1.77381i
$392$		0			0
$393$	8.89461	−	5.71622i	0.448674	−	0.288345i
$394$		0			0
$395$	−1.78916	−	18.7369i	−0.0900223	−	0.942757i
$396$		0			0
$397$	2.06132	−	21.5871i	0.103455	−	1.08343i	−0.783444	−	0.621463i	$-0.786539\pi$
$397$	2.06132	−	21.5871i	0.103455	−	1.08343i	0.886898	−	0.461965i	$-0.152855\pi$
$398$		0			0
$399$	7.82631	−	11.2575i	0.391805	−	0.563580i
$400$		0			0
$401$	10.1361	−	3.50815i	0.506175	−	0.175189i	−0.0620326	−	0.998074i	$-0.519758\pi$
$401$	10.1361	−	3.50815i	0.506175	−	0.175189i	0.568208	+	0.822885i	$0.307637\pi$
$402$		0			0
$403$	1.41700	−	29.7464i	0.0705856	−	1.48177i
$404$		0			0
$405$	−12.6009	−	3.69997i	−0.626146	−	0.183853i
$406$		0			0
$407$	−1.17195	−	1.35251i	−0.0580916	−	0.0670413i
$408$		0			0
$409$	−6.66393	+	6.98892i	−0.329510	+	0.345580i	−0.867560	−	0.497333i	$-0.834313\pi$
$409$	−6.66393	+	6.98892i	−0.329510	+	0.345580i	0.538050	+	0.842913i	$0.319161\pi$
$410$		0			0
$411$	12.2176	+	9.60800i	0.602648	+	0.473928i
$412$		0			0
$413$	0.0348857	−	0.151237i	0.00171662	−	0.00744190i
$414$		0			0
$415$	−6.93387	+	12.0098i	−0.340370	+	0.589538i
$416$		0			0
$417$	−12.1048	+	4.84601i	−0.592773	+	0.237310i
$418$		0			0
$419$	−16.4759	+	4.83776i	−0.804901	+	0.236340i	−0.658202	−	0.752841i	$-0.728683\pi$
$419$	−16.4759	+	4.83776i	−0.804901	+	0.236340i	−0.146699	+	0.989181i	$0.546865\pi$
$420$		0			0
$421$	−4.97748	+	4.31301i	−0.242588	+	0.210203i	−0.767665	−	0.640851i	$-0.778582\pi$
$421$	−4.97748	+	4.31301i	−0.242588	+	0.210203i	0.525078	+	0.851054i	$0.324036\pi$
$422$		0			0
$423$	1.72041	−	0.417368i	0.0836494	−	0.0202931i
$424$		0			0
$425$	50.4678	−	26.0180i	2.44805	−	1.26206i
$426$		0			0
$427$	20.4904	+	9.07934i	0.991599	+	0.439380i
$428$		0			0
$429$	−0.355001	+	0.886749i	−0.0171396	+	0.0428126i
$430$		0			0
$431$	6.62447	+	4.71726i	0.319089	+	0.227222i	0.728367	−	0.685188i	$-0.240280\pi$
$431$	6.62447	+	4.71726i	0.319089	+	0.227222i	−0.409277	+	0.912410i	$0.634219\pi$
$432$		0			0
$433$	14.2119	−	31.1197i	0.682981	−	1.49552i	−0.176473	−	0.984305i	$-0.556469\pi$
$433$	14.2119	−	31.1197i	0.682981	−	1.49552i	0.859454	−	0.511214i	$-0.170804\pi$
$434$		0			0
$435$	−12.9424	−	20.1387i	−0.620539	−	0.965577i
$436$		0			0
$437$	−29.6285	−	9.61571i	−1.41732	−	0.459982i
$438$		0			0
$439$	−24.8546	+	1.18397i	−1.18625	+	0.0565078i	−0.631408	−	0.775451i	$-0.717523\pi$
$439$	−24.8546	+	1.18397i	−1.18625	+	0.0565078i	−0.554838	+	0.831959i	$0.687220\pi$
$440$		0			0
$441$	12.7702	−	10.5181i	0.608105	−	0.500860i
$442$		0			0
$443$	22.0523	+	2.10574i	1.04774	+	0.100047i	0.604698	−	0.796455i	$-0.293294\pi$
$443$	22.0523	+	2.10574i	1.04774	+	0.100047i	0.443040	+	0.896502i	$0.353900\pi$
$444$		0			0
$445$	−12.0689	+	9.49112i	−0.572123	+	0.449922i
$446$		0			0
$447$	−6.22738	+	7.18678i	−0.294545	+	0.339923i
$448$		0			0
$449$	−7.95010	−	5.10922i	−0.375188	−	0.241119i	0.339433	−	0.940630i	$-0.389765\pi$
$449$	−7.95010	−	5.10922i	−0.375188	−	0.241119i	−0.714622	+	0.699511i	$0.753401\pi$
$450$		0			0
$451$	−0.212308	−	0.875144i	−0.00999717	−	0.0412089i
$452$		0			0
$453$	−0.458816	−	2.38056i	−0.0215570	−	0.111849i
$454$		0			0
$455$	−29.6479	+	19.5302i	−1.38991	+	0.915592i
$456$		0			0
$457$	10.4233	−	13.2542i	0.487579	−	0.620007i	−0.478552	−	0.878059i	$-0.658838\pi$
$457$	10.4233	−	13.2542i	0.487579	−	0.620007i	0.966131	+	0.258052i	$0.0830806\pi$
$458$		0			0
$459$	−27.1086	+	15.6511i	−1.26532	+	0.730533i
$460$		0			0
$461$		−	32.2246i		−	1.50085i	−0.660956	−	0.750424i	$-0.729849\pi$
$461$		−	32.2246i		−	1.50085i	0.660956	−	0.750424i	$-0.270151\pi$
$462$		0			0
$463$	−4.38091	+	30.4699i	−0.203598	+	1.41606i	0.589896	+	0.807479i	$0.299169\pi$
$463$	−4.38091	+	30.4699i	−0.203598	+	1.41606i	−0.793494	+	0.608578i	$0.791740\pi$
$464$		0			0
$465$	16.3544	+	15.5939i	0.758419	+	0.723151i
$466$		0			0
$467$	15.2939	−	2.94766i	0.707717	−	0.136401i	0.177323	−	0.984153i	$-0.443256\pi$
$467$	15.2939	−	2.94766i	0.707717	−	0.136401i	0.530394	+	0.847751i	$0.322044\pi$
$468$		0			0
$469$	−2.31837	+	4.12238i	−0.107052	+	0.190354i
$470$		0			0
$471$	−6.03226	−	11.7009i	−0.277952	−	0.539151i
$472$		0			0
$473$	−1.75915	−	0.339049i	−0.0808859	−	0.0155895i
$474$		0			0
$475$	7.17498	+	49.9031i	0.329211	+	2.28971i
$476$		0			0
$477$	4.18291	−	1.91027i	0.191522	−	0.0874653i
$478$		0			0
$479$	7.24778	−	0.692079i	0.331160	−	0.0316219i	0.0718479	−	0.997416i	$-0.477110\pi$
$479$	7.24778	−	0.692079i	0.331160	−	0.0316219i	0.259312	+	0.965794i	$0.416504\pi$
$480$		0			0
$481$	−1.00355	−	21.0671i	−0.0457579	−	0.960577i
$482$		0			0
$483$	8.42260	+	5.61651i	0.383241	+	0.255560i
$484$		0			0
$485$	1.16582	+	24.4736i	0.0529373	+	1.11129i
$486$		0			0
$487$	−0.203922	+	0.0194721i	−0.00924057	+	0.000882367i	−0.0996753	−	0.995020i	$-0.531780\pi$
$487$	−0.203922	+	0.0194721i	−0.00924057	+	0.000882367i	0.0904347	+	0.995902i	$0.471174\pi$
$488$		0			0
$489$	−8.68533	+	3.96646i	−0.392764	+	0.179369i
$490$		0			0
$491$	−5.75189	−	40.0053i	−0.259579	−	1.80541i	−0.535830	−	0.844326i	$-0.680001\pi$
$491$	−5.75189	−	40.0053i	−0.259579	−	1.80541i	0.276251	−	0.961086i	$-0.410908\pi$
$492$		0			0
$493$	60.3282	+	11.6273i	2.71704	+	0.523667i
$494$		0			0
$495$	1.23311	+	2.39189i	0.0554240	+	0.107508i
$496$		0			0
$497$	−12.5636	+	7.44404i	−0.563552	+	0.333911i
$498$		0			0
$499$	−42.1619	+	8.12604i	−1.88743	+	0.363772i	−0.995997	−	0.0893872i	$-0.971509\pi$
$499$	−42.1619	+	8.12604i	−1.88743	+	0.363772i	−0.891430	+	0.453159i	$0.850297\pi$
$500$		0			0
$501$	−9.74204	−	9.28901i	−0.435242	−	0.415003i
$502$		0			0
$503$	−0.202255	+	1.40672i	−0.00901813	+	0.0627225i	−0.993834	−	0.110882i	$-0.964632\pi$
$503$	−0.202255	+	1.40672i	−0.00901813	+	0.0627225i	0.984815	+	0.173605i	$0.0555415\pi$
$504$		0			0
$505$			22.4646i			0.999661i
$506$		0			0
$507$	−0.766307	+	0.442428i	−0.0340329	+	0.0196489i
$508$		0			0
$509$	−11.8321	+	15.0457i	−0.524449	+	0.666891i	−0.974049	−	0.226339i	$-0.927324\pi$
$509$	−11.8321	+	15.0457i	−0.524449	+	0.666891i	0.449600	+	0.893230i	$0.351567\pi$
$510$		0			0
$511$	2.18788	+	37.1054i	0.0967859	+	1.64145i
$512$		0			0
$513$	−5.26008	−	27.2919i	−0.232238	−	1.20497i
$514$		0			0
$515$	−2.31418	−	9.53918i	−0.101975	−	0.420347i
$516$		0			0
$517$	−0.200838	−	0.129071i	−0.00883284	−	0.00567652i
$518$		0			0
$519$	−9.44241	+	10.8971i	−0.414476	+	0.478330i
$520$		0			0
$521$	−15.3949	+	12.1067i	−0.674464	+	0.530404i	−0.895612	−	0.444836i	$-0.853262\pi$
$521$	−15.3949	+	12.1067i	−0.674464	+	0.530404i	0.221148	+	0.975240i	$0.429020\pi$
$522$		0			0
$523$	7.75975	+	0.740966i	0.339310	+	0.0324002i	0.263320	−	0.964708i	$-0.415182\pi$
$523$	7.75975	+	0.740966i	0.339310	+	0.0324002i	0.0759896	+	0.997109i	$0.475788\pi$
$524$		0			0
$525$	2.14848	−	16.2435i	0.0937675	−	0.708925i
$526$		0			0
$527$	−57.9295	+	2.75952i	−2.52345	+	0.120207i
$528$		0			0
$529$	6.67461	−	22.0102i	0.290200	−	0.956966i
$530$		0			0
$531$	−0.0749586	−	0.116638i	−0.00325293	−	0.00506165i
$532$		0			0
$533$	4.40875	−	9.65381i	0.190964	−	0.418153i
$534$		0			0
$535$	−21.8679	−	15.5721i	−0.945432	−	0.673239i
$536$		0			0
$537$	−5.34588	+	13.3534i	−0.230692	+	0.576240i
$538$		0			0
$539$	−2.21496	−	0.267546i	−0.0954052	−	0.0115240i
$540$		0			0
$541$	−7.38326	+	3.80634i	−0.317431	+	0.163647i	−0.609578	−	0.792726i	$-0.708661\pi$
$541$	−7.38326	+	3.80634i	−0.317431	+	0.163647i	0.292146	+	0.956374i	$0.405631\pi$
$542$		0			0
$543$	−18.6695	+	4.52917i	−0.801184	+	0.194365i
$544$		0			0
$545$	−5.25678	+	4.55502i	−0.225176	+	0.195116i
$546$		0			0
$547$	2.92487	−	0.858819i	0.125058	−	0.0367204i	−0.218604	−	0.975814i	$-0.570150\pi$
$547$	2.92487	−	0.858819i	0.125058	−	0.0367204i	0.343663	+	0.939093i	$0.388332\pi$
$548$		0			0
$549$	18.5864	−	7.44085i	0.793246	−	0.317568i
$550$		0			0
$551$	−27.2764	+	47.2442i	−1.16202	+	2.01267i
$552$		0			0
$553$	13.3299	−	4.07813i	0.566847	−	0.173420i
$554$		0			0
$555$	12.5799	+	9.89298i	0.533989	+	0.419934i
$556$		0			0
$557$	15.6048	−	16.3658i	0.661195	−	0.693442i	−0.304678	−	0.952455i	$-0.598549\pi$
$557$	15.6048	−	16.3658i	0.661195	−	0.693442i	0.965874	+	0.259014i	$0.0833975\pi$
$558$		0			0
$559$	−13.8264	−	15.9565i	−0.584793	−	0.674887i
$560$		0			0
$561$	1.78479	+	0.524062i	0.0753539	+	0.0221259i
$562$		0			0
$563$	−1.11480	+	23.4024i	−0.0469830	+	0.986295i	0.845152	+	0.534526i	$0.179510\pi$
$563$	−1.11480	+	23.4024i	−0.0469830	+	0.986295i	−0.892135	+	0.451769i	$0.850793\pi$
$564$		0			0
$565$	−23.2912	+	8.06118i	−0.979870	+	0.339136i
$566$		0			0
$567$	0.815122	−	9.69212i	0.0342319	−	0.407031i
$568$		0			0
$569$	−0.489531	+	5.12660i	−0.0205222	+	0.214918i	0.979394	+	0.201960i	$0.0647310\pi$
$569$	−0.489531	+	5.12660i	−0.0205222	+	0.214918i	−0.999916	+	0.0129586i	$0.995875\pi$
$570$		0			0
$571$	2.39519	+	25.0836i	0.100236	+	1.04972i	0.895984	+	0.444087i	$0.146472\pi$
$571$	2.39519	+	25.0836i	0.100236	+	1.04972i	−0.795748	+	0.605628i	$0.792922\pi$
$572$		0			0
$573$	−6.21289	+	3.99278i	−0.259547	+	0.166801i
$574$		0			0
$575$	−36.7372	+	6.01087i	−1.53205	+	0.250671i
$576$		0			0
$577$	9.46517	−	18.3599i	0.394040	−	0.764331i	−0.605462	−	0.795874i	$-0.707012\pi$
$577$	9.46517	−	18.3599i	0.394040	−	0.764331i	0.999502	+	0.0315429i	$0.0100421\pi$
$578$		0			0
$579$	−7.08480	+	5.04506i	−0.294434	+	0.209666i
$580$		0			0
$581$	−9.74300	−	3.24932i	−0.404208	−	0.134805i
$582$		0			0
$583$	−0.575706	−	0.230478i	−0.0238433	−	0.00954543i
$584$		0			0
$585$	−6.00198	+	31.1412i	−0.248151	+	1.28753i
$586$		0			0
$587$	24.4406	−	38.0304i	1.00877	−	1.56968i	0.201513	−	0.979486i	$-0.435414\pi$
$587$	24.4406	−	38.0304i	1.00877	−	1.56968i	0.807260	−	0.590196i	$-0.200949\pi$
$588$		0			0
$589$	14.5080	−	49.4096i	0.597790	−	2.03589i
$590$		0			0
$591$	−3.04233	−	1.05296i	−0.125145	−	0.0433130i
$592$		0			0
$593$	11.6332	+	2.82218i	0.477718	+	0.115893i	0.467386	−	0.884054i	$-0.345196\pi$
$593$	11.6332	+	2.82218i	0.477718	+	0.115893i	0.0103322	+	0.999947i	$0.496711\pi$
$594$		0			0
$595$	43.3502	+	53.8608i	1.77718	+	2.20808i
$596$		0			0
$597$	15.0691	+	8.70016i	0.616738	+	0.356074i
$598$		0			0
$599$	20.5477	+	35.5897i	0.839558	+	1.45416i	0.890265	+	0.455443i	$0.150519\pi$
$599$	20.5477	+	35.5897i	0.839558	+	1.45416i	−0.0507071	+	0.998714i	$0.516148\pi$
$600$		0			0
$601$	−35.1514	−	5.05400i	−1.43385	−	0.206157i	−0.618803	−	0.785546i	$-0.712382\pi$
$601$	−35.1514	−	5.05400i	−1.43385	−	0.206157i	−0.815051	+	0.579389i	$0.803291\pi$
$602$		0			0
$603$	1.19030	+	4.05378i	0.0484727	+	0.165083i
$604$		0			0
$605$	−12.7339	+	36.7923i	−0.517708	+	1.49582i
$606$		0			0
$607$	25.4637	+	26.7055i	1.03354	+	1.08394i	0.996412	+	0.0846340i	$0.0269721\pi$
$607$	25.4637	+	26.7055i	1.03354	+	1.08394i	0.0371269	+	0.999311i	$0.488179\pi$
$608$		0			0
$609$	12.6923	−	12.3788i	0.514319	−	0.501615i
$610$		0			0
$611$	−0.920221	−	2.65880i	−0.0372282	−	0.107564i
$612$		0			0
$613$	6.98231	+	8.87873i	0.282013	+	0.358609i	0.906336	−	0.422558i	$-0.138868\pi$
$613$	6.98231	+	8.87873i	0.282013	+	0.358609i	−0.624323	+	0.781166i	$0.714625\pi$
$614$		0			0
$615$	3.34537	+	7.32535i	0.134899	+	0.295387i
$616$		0			0
$617$	10.4420	+	4.76872i	0.420381	+	0.191981i	0.614363	−	0.789024i	$-0.289413\pi$
$617$	10.4420	+	4.76872i	0.420381	+	0.191981i	−0.193982	+	0.981005i	$0.562140\pi$
$618$		0			0
$619$	26.2226	+	13.5187i	1.05398	+	0.543362i	0.895988	−	0.444079i	$-0.146469\pi$
$619$	26.2226	+	13.5187i	1.05398	+	0.543362i	0.157988	+	0.987441i	$0.449499\pi$
$620$		0			0
$621$	20.0724	−	4.27368i	0.805476	−	0.171497i
$622$		0			0
$623$	−8.67732	−	7.34899i	−0.347650	−	0.294431i
$624$		0			0
$625$	−2.06522	−	2.90019i	−0.0826086	−	0.116008i
$626$		0			0
$627$	−0.958062	+	1.34541i	−0.0382613	+	0.0537305i
$628$		0			0
$629$	−40.6555	+	5.84538i	−1.62104	+	0.233070i
$630$		0			0
$631$	−6.45013	−	5.58907i	−0.256776	−	0.222497i	0.516954	−	0.856013i	$-0.327066\pi$
$631$	−6.45013	−	5.58907i	−0.256776	−	0.222497i	−0.773730	+	0.633516i	$0.781611\pi$
$632$		0			0
$633$	−19.3888	−	0.923600i	−0.770634	−	0.0367098i
$634$		0			0
$635$	45.6932	−	43.5684i	1.81328	−	1.72896i
$636$		0			0
$637$	−18.5698	−	18.6147i	−0.735761	−	0.737542i
$638$		0			0
$639$	−3.07550	+	12.6774i	−0.121665	+	0.501510i
$640$		0			0
$641$	2.27484	+	5.68227i	0.0898507	+	0.224436i	0.966486	−	0.256719i	$-0.0826416\pi$
$641$	2.27484	+	5.68227i	0.0898507	+	0.224436i	−0.876635	+	0.481155i	$0.840217\pi$
$642$		0			0
$643$	18.2375			0.719217			0.359609	−	0.933103i	$-0.382910\pi$
$643$	18.2375			0.719217			0.359609	+	0.933103i	$0.382910\pi$
$644$		0			0
$645$	16.0210			0.630825
$646$		0			0
$647$	−7.08866	−	17.7066i	−0.278684	−	0.696119i	−0.999994	−	0.00350643i	$-0.998884\pi$
$647$	−7.08866	−	17.7066i	−0.278684	−	0.696119i	0.721310	−	0.692612i	$-0.243540\pi$
$648$		0			0
$649$	−0.00440807	+	0.0181703i	−0.000173032	+	0.000713247i
$650$		0			0
$651$	−8.88841	+	14.1803i	−0.348364	+	0.555770i
$652$		0			0
$653$	26.9321	−	25.6797i	1.05393	−	1.00492i	0.0539541	−	0.998543i	$-0.482818\pi$
$653$	26.9321	−	25.6797i	1.05393	−	1.00492i	0.999980	−	0.00638034i	$-0.00203094\pi$
$654$		0			0
$655$	−47.2880	−	2.25260i	−1.84769	−	0.0880166i
$656$		0			0
$657$	25.0937	+	21.7438i	0.978999	+	0.848308i
$658$		0			0
$659$	−40.1248	+	5.76908i	−1.56304	+	0.224731i	−0.868856	−	0.495065i	$-0.835144\pi$
$659$	−40.1248	+	5.76908i	−1.56304	+	0.224731i	−0.694185	+	0.719797i	$0.744235\pi$
$660$		0			0
$661$	−0.335486	+	0.471125i	−0.0130489	+	0.0183246i	−0.821049	−	0.570858i	$-0.806611\pi$
$661$	−0.335486	+	0.471125i	−0.0130489	+	0.0183246i	0.808000	+	0.589183i	$0.200550\pi$
$662$		0			0
$663$	12.7160	+	17.8572i	0.493850	+	0.693515i
$664$		0			0
$665$	−57.7836	+	20.7329i	−2.24075	+	0.803988i
$666$		0			0
$667$	−35.2673	−	19.4602i	−1.36556	−	0.753501i
$668$		0			0
$669$	10.7191	+	5.52611i	0.414426	+	0.213652i
$670$		0			0
$671$	−2.45588	−	1.12156i	−0.0948083	−	0.0432975i
$672$		0			0
$673$	−0.696920	−	1.52604i	−0.0268643	−	0.0588246i	0.895724	−	0.444610i	$-0.146658\pi$
$673$	−0.696920	−	1.52604i	−0.0268643	−	0.0588246i	−0.922589	+	0.385785i	$0.873930\pi$
$674$		0			0
$675$	−20.5324	−	26.1091i	−0.790294	−	1.00494i
$676$		0			0
$677$	11.9974	+	34.6643i	0.461099	+	1.33226i	0.900847	+	0.434137i	$0.142947\pi$
$677$	11.9974	+	34.6643i	0.461099	+	1.33226i	−0.439748	+	0.898121i	$0.644932\pi$
$678$		0			0
$679$	−17.5849	+	4.47698i	−0.674848	+	0.171811i
$680$		0			0
$681$	−0.168124	−	0.176323i	−0.00644253	−	0.00675673i
$682$		0			0
$683$	6.08338	−	17.5768i	0.232774	−	0.672556i	−0.766757	−	0.641937i	$-0.778131\pi$
$683$	6.08338	−	17.5768i	0.232774	−	0.672556i	0.999531	−	0.0306191i	$-0.00974789\pi$
$684$		0			0
$685$	−19.6071	−	66.7756i	−0.749148	−	2.55137i
$686$		0			0
$687$	−0.513685	−	0.0738567i	−0.0195983	−	0.00281781i
$688$		0			0
$689$	−3.65415	−	6.32917i	−0.139212	−	0.241122i
$690$		0			0
$691$	17.5212	+	10.1159i	0.666537	+	0.384825i	0.794763	−	0.606920i	$-0.207595\pi$
$691$	17.5212	+	10.1159i	0.666537	+	0.384825i	−0.128226	+	0.991745i	$0.540928\pi$
$692$		0			0
$693$	−1.55259	+	1.24961i	−0.0589781	+	0.0474688i
$694$		0			0
$695$	56.7363	+	13.7641i	2.15213	+	0.522102i
$696$		0			0
$697$	−19.5313	−	6.75983i	−0.739799	−	0.256047i
$698$		0			0
$699$	1.67318	−	5.69833i	0.0632855	−	0.215531i
$700$		0			0
$701$	−20.7390	+	32.2705i	−0.783300	+	1.21884i	0.188277	+	0.982116i	$0.439710\pi$
$701$	−20.7390	+	32.2705i	−0.783300	+	1.21884i	−0.971577	+	0.236723i	$0.923927\pi$
$702$		0			0
$703$	6.90206	−	35.8113i	0.260316	−	1.35065i
$704$		0			0
$705$	1.98200	+	0.793474i	0.0746465	+	0.0298840i
$706$		0			0
$707$	−16.3002	+	3.33299i	−0.613031	+	0.125350i
$708$		0			0
$709$	−7.96498	+	5.67183i	−0.299131	+	0.213010i	−0.719761	−	0.694222i	$-0.755749\pi$
$709$	−7.96498	+	5.67183i	−0.299131	+	0.213010i	0.420630	+	0.907232i	$0.361809\pi$
$710$		0			0
$711$	5.70603	−	11.0682i	0.213993	−	0.415088i
$712$		0			0
$713$	36.6832	+	10.0032i	1.37380	+	0.374621i
$714$		0			0
$715$	3.59791	−	2.31224i	0.134554	−	0.0864728i
$716$		0			0
$717$	0.825883	+	8.64904i	0.0308432	+	0.323004i
$718$		0			0
$719$	−2.07970	+	21.7796i	−0.0775598	+	0.812243i	0.870082	+	0.492907i	$0.164066\pi$
$719$	−2.07970	+	21.7796i	−0.0775598	+	0.812243i	−0.947642	+	0.319336i	$0.896540\pi$
$720$		0			0
$721$	6.57823	−	3.09445i	0.244986	−	0.115243i
$722$		0			0
$723$	6.97528	−	2.41417i	0.259413	−	0.0897839i
$724$		0			0
$725$	−3.10204	+	65.1197i	−0.115207	+	2.41849i
$726$		0			0
$727$	17.4520	+	5.12437i	0.647259	+	0.190052i	0.588853	−	0.808240i	$-0.299580\pi$
$727$	17.4520	+	5.12437i	0.647259	+	0.190052i	0.0584066	+	0.998293i	$0.481398\pi$
$728$		0			0
$729$	1.01756	+	1.17432i	0.0376873	+	0.0434934i
$730$		0			0
$731$	−28.3742	+	29.7580i	−1.04946	+	1.10064i
$732$		0			0
$733$	−6.75149	−	5.30943i	−0.249372	−	0.196108i	0.485647	−	0.874155i	$-0.338584\pi$
$733$	−6.75149	−	5.30943i	−0.249372	−	0.196108i	−0.735019	+	0.678047i	$0.762827\pi$
$734$		0			0
$735$	19.9024	−	1.39928i	0.734112	−	0.0516132i
$736$		0			0
$737$	0.284877	−	0.493421i	0.0104936	−	0.0181754i
$738$		0			0
$739$	29.8577	−	11.9532i	1.09833	−	0.439707i	0.249505	−	0.968374i	$-0.419732\pi$
$739$	29.8577	−	11.9532i	1.09833	−	0.439707i	0.848829	+	0.528667i	$0.177308\pi$
$740$		0			0
$741$	−18.6767	+	5.48398i	−0.686106	+	0.201459i
$742$		0			0
$743$	−10.4711	+	9.07323i	−0.384146	+	0.332864i	−0.825431	−	0.564502i	$-0.809068\pi$
$743$	−10.4711	+	9.07323i	−0.384146	+	0.332864i	0.441285	+	0.897367i	$0.354523\pi$
$744$		0			0
$745$	41.3792	−	10.0385i	1.51602	−	0.367781i
$746$		0			0
$747$	−8.15477	+	4.20407i	−0.298367	+	0.153819i
$748$		0			0
$749$	8.05453	−	18.1776i	0.294306	−	0.664194i
$750$		0			0
$751$	−9.33624	+	23.3208i	−0.340684	+	0.850988i	0.654777	+	0.755822i	$0.272763\pi$
$751$	−9.33624	+	23.3208i	−0.340684	+	0.850988i	−0.995461	+	0.0951663i	$0.969662\pi$
$752$		0			0
$753$	4.72189	+	3.36244i	0.172075	+	0.122534i
$754$		0			0
$755$	−4.50946	+	9.87435i	−0.164116	+	0.359364i
$756$		0			0
$757$	3.52084	+	5.47854i	0.127967	+	0.199121i	0.899325	−	0.437281i	$-0.144058\pi$
$757$	3.52084	+	5.47854i	0.127967	+	0.199121i	−0.771358	+	0.636402i	$0.780422\pi$
$758$		0			0
$759$	−1.00693	−	0.688016i	−0.0365492	−	0.0249734i
$760$		0			0
$761$	−13.5936	+	0.647541i	−0.492766	+	0.0234733i	−0.292495	−	0.956267i	$-0.594485\pi$
$761$	−13.5936	+	0.647541i	−0.492766	+	0.0234733i	−0.200271	+	0.979740i	$0.564182\pi$
$762$		0			0
$763$	−4.08503	−	3.13848i	−0.147888	−	0.113620i
$764$		0			0
$765$	61.4823	+	5.87084i	2.22290	+	0.212261i
$766$		0			0
$767$	−0.173208	+	0.136212i	−0.00625418	+	0.00491834i
$768$		0			0
$769$	19.6682	−	22.6983i	0.709254	−	0.818522i	−0.280718	−	0.959790i	$-0.590573\pi$
$769$	19.6682	−	22.6983i	0.709254	−	0.818522i	0.989971	+	0.141268i	$0.0451180\pi$
$770$		0			0
$771$	−18.3789	−	11.8114i	−0.661901	−	0.425378i
$772$		0			0
$773$	−11.0913	−	45.7191i	−0.398928	−	1.64440i	−0.717539	−	0.696518i	$-0.754732\pi$
$773$	−11.0913	−	45.7191i	−0.398928	−	1.64440i	0.318611	−	0.947885i	$-0.396783\pi$
$774$		0			0
$775$	−11.6465	−	60.4278i	−0.418355	−	2.17063i
$776$		0			0
$777$	−5.31185	+	10.5957i	−0.190561	+	0.380119i
$778$		0			0
$779$	11.3442	−	14.4254i	0.406450	−	0.516843i
$780$		0			0
$781$	1.52351	−	0.879601i	0.0545156	−	0.0314746i
$782$		0			0
$783$		−	35.9408i		−	1.28442i
$784$		0			0
$785$	−8.38867	+	58.3445i	−0.299404	+	2.08240i
$786$		0			0
$787$	−2.33408	−	2.22554i	−0.0832009	−	0.0793319i	0.647338	−	0.762203i	$-0.275882\pi$
$787$	−2.33408	−	2.22554i	−0.0832009	−	0.0793319i	−0.730539	+	0.682872i	$0.760731\pi$
$788$		0			0
$789$	−0.323829	+	0.0624129i	−0.0115286	+	0.00222196i
$790$		0			0
$791$	−9.30478	−	15.7040i	−0.330840	−	0.558369i
$792$		0			0
$793$	−14.5800	−	28.2813i	−0.517751	−	1.00430i
$794$		0			0
$795$	5.44535	+	1.04951i	0.193127	+	0.0372221i
$796$		0			0
$797$	−5.88929	−	40.9609i	−0.208609	−	1.45091i	−0.777700	−	0.628635i	$-0.783614\pi$
$797$	−5.88929	−	40.9609i	−0.208609	−	1.45091i	0.569091	−	0.822274i	$-0.307295\pi$
$798$		0			0
$799$	−4.98408	+	2.27615i	−0.176324	+	0.0805245i
$800$		0			0
$801$	−10.1119	+	0.965565i	−0.357285	+	0.0341166i
$802$		0			0
$803$	−0.213058	−	4.47263i	−0.00751864	−	0.157836i
$804$		0			0
$805$	−16.1325	−	42.3608i	−0.568595	−	1.49302i
$806$		0			0
$807$	−0.911481	−	19.1343i	−0.0320856	−	0.673560i
$808$		0			0
$809$	−34.4946	+	3.29383i	−1.21276	+	0.115805i	−0.681768	−	0.731569i	$-0.738788\pi$
$809$	−34.4946	+	3.29383i	−1.21276	+	0.115805i	−0.530997	+	0.847374i	$0.678182\pi$
$810$		0			0
$811$	−19.8568	+	9.06828i	−0.697265	+	0.318430i	−0.732326	−	0.680955i	$-0.761565\pi$
$811$	−19.8568	+	9.06828i	−0.697265	+	0.318430i	0.0350600	+	0.999385i	$0.488838\pi$
$812$		0			0
$813$	−2.43809	−	16.9573i	−0.0855074	−	0.594717i
$814$		0			0
$815$	41.9801	+	8.09100i	1.47050	+	0.283415i
$816$		0			0
$817$	−16.7295	−	32.4506i	−0.585290	−	1.13530i
$818$		0			0
$819$	−23.4864	+	0.265308i	−0.820680	+	0.00927061i
$820$		0			0
$821$	−16.9911	+	3.27476i	−0.592992	+	0.114290i	−0.476913	−	0.878950i	$-0.658245\pi$
$821$	−16.9911	+	3.27476i	−0.592992	+	0.114290i	−0.116078	+	0.993240i	$0.537032\pi$
$822$		0			0
$823$	6.06464	+	5.78262i	0.211400	+	0.201570i	0.788380	−	0.615189i	$-0.210920\pi$
$823$	6.06464	+	5.78262i	0.211400	+	0.201570i	−0.576980	+	0.816759i	$0.695769\pi$
$824$		0			0
$825$	−0.280906	+	1.95374i	−0.00977988	+	0.0680205i
$826$		0			0
$827$			29.8931i			1.03949i	0.854323	+	0.519743i	$0.173972\pi$
$827$			29.8931i			1.03949i	−0.854323	+	0.519743i	$0.826028\pi$
$828$		0			0
$829$	−22.7546	+	13.1374i	−0.790301	+	0.456280i	−0.840068	−	0.542481i	$-0.817485\pi$
$829$	−22.7546	+	13.1374i	−0.790301	+	0.456280i	0.0497677	+	0.998761i	$0.484152\pi$
$830$		0			0
$831$	2.00087	−	2.54431i	0.0694094	−	0.0882612i
$832$		0			0
$833$	−32.6494	+	39.4458i	−1.13123	+	1.36671i
$834$		0			0
$835$	11.4065	+	59.1826i	0.394739	+	2.04810i
$836$		0			0
$837$	7.99848	+	32.9702i	0.276468	+	1.13962i
$838$		0			0
$839$	19.9599	+	12.8274i	0.689092	+	0.442852i	0.837763	−	0.546034i	$-0.183863\pi$
$839$	19.9599	+	12.8274i	0.689092	+	0.442852i	−0.148671	+	0.988887i	$0.547500\pi$
$840$		0			0
$841$	−27.2047	+	31.3958i	−0.938092	+	1.08262i
$842$		0			0
$843$	12.3869	−	9.74114i	0.426627	−	0.335503i
$844$		0			0
$845$	3.94407	+	0.376613i	0.135680	+	0.0129559i
$846$		0			0
$847$	−28.5855	−	3.78093i	−0.982211	−	0.129914i
$848$		0			0
$849$	5.27221	−	0.251146i	0.180942	−	0.00861932i
$850$		0			0
$851$	26.5357	+	4.58284i	0.909631	+	0.157098i
$852$		0			0
$853$	−6.04261	−	9.40249i	−0.206895	−	0.321935i	0.722262	−	0.691619i	$-0.243102\pi$
$853$	−6.04261	−	9.40249i	−0.206895	−	0.321935i	−0.929158	+	0.369684i	$0.879466\pi$
$854$		0			0
$855$	−22.7814	+	49.8843i	−0.779108	+	1.70601i
$856$		0			0
$857$	−6.07691	−	4.32735i	−0.207583	−	0.147819i	0.471537	−	0.881846i	$-0.343699\pi$
$857$	−6.07691	−	4.32735i	−0.207583	−	0.147819i	−0.679121	+	0.734027i	$0.737639\pi$
$858$		0			0
$859$	−6.37352	+	15.9203i	−0.217462	+	0.543193i	−0.996482	−	0.0838053i	$-0.973293\pi$
$859$	−6.37352	+	15.9203i	−0.217462	+	0.543193i	0.779020	+	0.626999i	$0.215717\pi$
$860$		0			0
$861$	−4.81889	+	3.51422i	−0.164227	+	0.119764i
$862$		0			0
$863$	−16.9508	+	8.73877i	−0.577013	+	0.297471i	−0.721922	−	0.691974i	$-0.756741\pi$
$863$	−16.9508	+	8.73877i	−0.577013	+	0.297471i	0.144909	+	0.989445i	$0.453711\pi$
$864$		0			0
$865$	62.7421	−	15.2211i	2.13330	−	0.517532i
$866$		0			0
$867$	22.0140	−	19.0752i	0.747633	−	0.647828i
$868$		0			0
$869$	−1.61125	+	0.473106i	−0.0546580	+	0.0160490i
$870$		0			0
$871$	6.23365	−	2.49558i	0.211219	−	0.0845594i
$872$		0			0
$873$	−8.10485	+	14.0380i	−0.274308	+	0.475115i
$874$		0			0
$875$	−17.8010	+	19.0964i	−0.601783	+	0.645578i
$876$		0			0
$877$	−29.0141	−	22.8170i	−0.979738	−	0.770474i	−0.00643018	−	0.999979i	$-0.502047\pi$
$877$	−29.0141	−	22.8170i	−0.979738	−	0.770474i	−0.973307	+	0.229505i	$0.926289\pi$
$878$		0			0
$879$	18.3175	−	19.2109i	0.617834	−	0.647966i
$880$		0			0
$881$	−9.12254	−	10.5280i	−0.307346	−	0.354696i	0.580973	−	0.813923i	$-0.302672\pi$
$881$	−9.12254	−	10.5280i	−0.307346	−	0.354696i	−0.888319	+	0.459226i	$0.848127\pi$
$882$		0			0
$883$	−37.1436	−	10.9063i	−1.24998	−	0.367028i	−0.411225	−	0.911534i	$-0.634899\pi$
$883$	−37.1436	−	10.9063i	−1.24998	−	0.367028i	−0.838757	+	0.544506i	$0.816717\pi$
$884$		0			0
$885$	0.00795587	−	0.167014i	0.000267434	−	0.00561412i
$886$		0			0
$887$	34.9368	−	12.0917i	1.17306	−	0.406001i	0.330085	−	0.943951i	$-0.392922\pi$
$887$	34.9368	−	12.0917i	1.17306	−	0.406001i	0.842976	+	0.537950i	$0.180801\pi$
$888$		0			0
$889$	38.3923	+	26.6906i	1.28764	+	0.895175i
$890$		0			0
$891$	−0.111377	+	1.16639i	−0.00373125	+	0.0390755i
$892$		0			0
$893$	−0.462463	−	4.84313i	−0.0154757	−	0.162069i
$894$		0			0
$895$	54.1802	−	34.8195i	1.81105	−	1.16389i
$896$		0			0
$897$	−4.31568	−	13.7092i	−0.144097	−	0.457737i
$898$		0			0
$899$	30.5129	−	59.1868i	1.01766	−	1.97399i
$900$		0			0
$901$	−11.5935	+	8.25567i	−0.386234	+	0.275036i
$902$		0			0
$903$	2.37697	+	11.6247i	0.0791007	+	0.386846i
$904$		0			0
$905$	79.8571	+	31.9700i	2.65454	+	1.06272i
$906$		0			0
$907$	−1.56985	+	8.14518i	−0.0521261	+	0.270456i	−0.998636	−	0.0522199i	$-0.983370\pi$
$907$	−1.56985	+	8.14518i	−0.0521261	+	0.270456i	0.946509	+	0.322676i	$0.104582\pi$
$908$		0			0
$909$	−8.03511	+	12.5029i	−0.266508	+	0.414694i
$910$		0			0
$911$	12.7800	−	43.5248i	0.423421	−	1.44204i	−0.421342	−	0.906902i	$-0.638441\pi$
$911$	12.7800	−	43.5248i	0.423421	−	1.44204i	0.844764	−	0.535139i	$-0.179741\pi$
$912$		0			0
$913$	1.16920	+	0.404665i	0.0386950	+	0.0133925i
$914$		0			0
$915$	23.4633	+	5.69214i	0.775673	+	0.188176i
$916$		0			0
$917$	−5.38147	−	34.6461i	−0.177712	−	1.14412i
$918$		0			0
$919$	13.2332	+	7.64018i	0.436522	+	0.252026i	0.702121	−	0.712057i	$-0.252236\pi$
$919$	13.2332	+	7.64018i	0.436522	+	0.252026i	−0.265599	+	0.964084i	$0.585570\pi$
$920$		0			0
$921$	8.56865	+	14.8413i	0.282347	+	0.489039i
$922$		0			0
$923$	20.5214	+	2.95054i	0.675472	+	0.0971182i
$924$		0			0
$925$	−12.2790	−	41.8185i	−0.403732	−	1.37498i
$926$		0			0
$927$	2.12399	−	6.13685i	0.0697608	−	0.201561i
$928$		0			0
$929$	−20.3476	−	21.3399i	−0.667582	−	0.700140i	0.299646	−	0.954051i	$-0.403132\pi$
$929$	−20.3476	−	21.3399i	−0.667582	−	0.700140i	−0.967228	+	0.253911i	$0.918283\pi$
$930$		0			0
$931$	−23.6168	−	38.8514i	−0.774010	−	1.27330i
$932$		0			0
$933$	−5.19464	−	15.0089i	−0.170065	−	0.491370i
$934$		0			0
$935$	−5.14860	−	6.54697i	−0.168377	−	0.214109i
$936$		0			0
$937$	13.8513	+	30.3301i	0.452503	+	0.990842i	0.989133	+	0.147025i	$0.0469697\pi$
$937$	13.8513	+	30.3301i	0.452503	+	0.990842i	−0.536630	+	0.843817i	$0.680303\pi$
$938$		0			0
$939$	5.50953	+	2.51612i	0.179797	+	0.0821104i
$940$		0			0
$941$	8.54738	+	4.40648i	0.278637	+	0.143647i	0.591881	−	0.806025i	$-0.298386\pi$
$941$	8.54738	+	4.40648i	0.278637	+	0.143647i	−0.313244	+	0.949673i	$0.601416\pi$
$942$		0			0
$943$	10.8116	+	8.16822i	0.352073	+	0.265994i
$944$		0			0
$945$	26.1393	−	30.8640i	0.850312	−	1.00401i
$946$		0			0
$947$	−6.07245	−	8.52757i	−0.197328	−	0.277109i	0.704042	−	0.710159i	$-0.251377\pi$
$947$	−6.07245	−	8.52757i	−0.197328	−	0.277109i	−0.901370	+	0.433050i	$0.857437\pi$
$948$		0			0
$949$	30.6098	−	42.9855i	0.993638	−	1.39537i
$950$		0			0
$951$	−8.31802	+	1.19595i	−0.269730	+	0.0387813i
$952$		0			0
$953$	−12.0851	−	10.4718i	−0.391475	−	0.339215i	0.436778	−	0.899569i	$-0.356119\pi$
$953$	−12.0851	−	10.4718i	−0.391475	−	0.339215i	−0.828253	+	0.560355i	$0.810665\pi$
$954$		0			0
$955$	33.0307	+	1.57345i	1.06885	+	0.0509155i
$956$		0			0
$957$	−1.54574	+	1.47386i	−0.0499667	+	0.0476431i
$958$		0			0
$959$	45.5430	−	24.1340i	1.47066	−	0.779329i
$960$		0			0
$961$	−7.51064	+	30.9593i	−0.242279	+	0.998686i
$962$		0			0
$963$	−6.60098	−	16.4885i	−0.212714	−	0.531333i
$964$		0			0
$965$	38.9439			1.25365
$966$		0			0
$967$	51.9067			1.66921			0.834603	−	0.550852i	$-0.185697\pi$
$967$	51.9067			1.66921			0.834603	+	0.550852i	$0.185697\pi$
$968$		0			0
$969$	14.0887	+	35.1920i	0.452596	+	1.13053i
$970$		0			0
$971$	1.06800	−	4.40237i	0.0342739	−	0.141279i	−0.952104	−	0.305775i	$-0.901085\pi$
$971$	1.06800	−	4.40237i	0.0342739	−	0.141279i	0.986378	+	0.164496i	$0.0525997\pi$
$972$		0			0
$973$	−1.56938	+	43.2097i	−0.0503120	+	1.38524i
$974$		0			0
$975$	−16.8354	+	16.0526i	−0.539166	+	0.514094i
$976$		0			0
$977$	38.9472	+	1.85528i	1.24603	+	0.0593557i	0.660207	−	0.751084i	$-0.270468\pi$
$977$	38.9472	+	1.85528i	1.24603	+	0.0593557i	0.585823	+	0.810439i	$0.300772\pi$
$978$		0			0
$979$	1.03526	+	0.897054i	0.0330869	+	0.0286700i
$980$		0			0
$981$	−4.55495	+	0.654902i	−0.145428	+	0.0209094i
$982$		0			0
$983$	18.8103	−	26.4154i	0.599956	−	0.842521i	−0.397212	−	0.917727i	$-0.630022\pi$
$983$	18.8103	−	26.4154i	0.599956	−	0.842521i	0.997168	+	0.0752063i	$0.0239615\pi$
$984$		0			0
$985$	8.36157	+	11.7422i	0.266422	+	0.374137i
$986$		0			0
$987$	−0.281678	+	1.55585i	−0.00896590	+	0.0495234i
$988$		0			0
$989$	23.7166	−	12.8145i	0.754143	−	0.407478i
$990$		0			0
$991$	43.1275	+	22.2338i	1.36999	+	0.706280i	0.976995	−	0.213261i	$-0.0684083\pi$
$991$	43.1275	+	22.2338i	1.36999	+	0.706280i	0.392996	+	0.919540i	$0.371439\pi$
$992$		0			0
$993$	13.0572	+	5.96305i	0.414359	+	0.189232i
$994$		0			0
$995$	−32.3655	−	70.8706i	−1.02606	−	2.24675i
$996$		0			0
$997$	−7.61868	−	9.68794i	−0.241286	−	0.306820i	0.650295	−	0.759682i	$-0.274645\pi$
$997$	−7.61868	−	9.68794i	−0.241286	−	0.306820i	−0.891581	+	0.452862i	$0.850403\pi$
$998$		0			0
$999$	7.85865	+	22.7061i	0.248637	+	0.718388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.425.10	yes	320
7.3	odd	6	inner	644.2.bc.a.241.7	✓	320
23.21	odd	22	inner	644.2.bc.a.481.7	yes	320
161.136	even	66	inner	644.2.bc.a.297.10	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.241.7	✓	320	7.3	odd	6	inner
644.2.bc.a.297.10	yes	320	161.136	even	66	inner
644.2.bc.a.425.10	yes	320	1.1	even	1	trivial
644.2.bc.a.481.7	yes	320	23.21	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.296529 + 0.740692i) q^{3} +(0.842227 - 3.47171i) q^{5} +(2.64401 + 0.0960306i) q^{7} +(1.71051 - 1.63096i) q^{9} +O(q^{10})\)	\(q+(0.296529 + 0.740692i) q^{3} +(0.842227 - 3.47171i) q^{5} +(2.64401 + 0.0960306i) q^{7} +(1.71051 - 1.63096i) q^{9} +(-0.318362 - 0.0151655i) q^{11} +(-2.83875 - 2.45979i) q^{13} +(2.82121 - 0.405629i) q^{15} +(-4.24312 + 5.95862i) q^{17} +(-3.76758 - 5.29082i) q^{19} +(0.712895 + 1.98687i) q^{21} +(3.85192 - 2.85704i) q^{23} +(-6.89922 - 3.55680i) q^{25} +(3.89249 + 1.77764i) q^{27} +(-3.48906 - 7.63997i) q^{29} +(4.90092 + 6.23203i) q^{31} +(-0.0831705 - 0.240305i) q^{33} +(2.56024 - 9.09834i) q^{35} +(3.87478 + 4.06375i) q^{37} +(0.980178 - 2.83204i) q^{39} +(0.796014 + 2.71098i) q^{41} +(5.56374 + 0.799945i) q^{43} +(-4.22159 - 7.31202i) q^{45} +(0.648688 + 0.374520i) q^{47} +(6.98156 + 0.507811i) q^{49} +(-5.67171 - 1.37594i) q^{51} +(1.83865 + 0.636364i) q^{53} +(-0.320783 + 1.09249i) q^{55} +(2.80168 - 4.35950i) q^{57} +(0.0111021 - 0.0576032i) q^{59} +(7.86409 + 3.14831i) q^{61} +(4.67921 - 4.14802i) q^{63} +(-10.9305 + 7.78360i) q^{65} +(-0.819131 + 1.58889i) q^{67} +(3.25840 + 2.00590i) q^{69} +(-4.64332 + 2.98408i) q^{71} +(1.33543 + 13.9853i) q^{73} +(0.588676 - 6.16490i) q^{75} +(-0.840296 - 0.0706701i) q^{77} +(4.97898 - 1.72324i) q^{79} +(0.174921 - 3.67205i) q^{81} +(-3.72466 - 1.09366i) q^{83} +(17.1129 + 19.7494i) q^{85} +(4.62426 - 4.84979i) q^{87} +(-3.37838 - 2.65679i) q^{89} +(-7.26946 - 6.77631i) q^{91} +(-3.16276 + 5.47805i) q^{93} +(-21.5413 + 8.62385i) q^{95} +(-6.58069 + 1.93226i) q^{97} +(-0.569295 + 0.493297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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