LMFDB - Embedded newform 630.2.bo.a.269.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(89,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bo (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 $ x^16 - 6x^15 + 21x^14 - 54x^13 + 113x^12 - 168x^11 + 186x^10 - 84x^9 - 6x^8 - 420x^7 + 4650x^6 - 21000x^5 + 70625x^4 - 168750x^3 + 328125x^2 - 468750*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.8
Root			$-2.11940 + 0.712845i$ of defining polynomial
Character	$\chi$	$=$	630.269
Dual form			630.2.bo.a.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.11940 + 0.712845i) q^{5} +(1.63937 - 2.07665i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.11940 + 0.712845i) q^{5} +(1.63937 - 2.07665i) q^{7} +1.00000 q^{8} +(-0.442358 - 2.19188i) q^{10} +(-5.48223 - 3.16517i) q^{11} +1.05290 q^{13} +(-2.61811 - 0.381412i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.01562 + 2.31842i) q^{17} +(5.35129 - 3.08957i) q^{19} +(-1.67704 + 1.47903i) q^{20} +6.33033i q^{22} +(-3.52236 - 6.10091i) q^{23} +(3.98371 + 3.02160i) q^{25} +(-0.526449 - 0.911836i) q^{26} +(0.978745 + 2.45806i) q^{28} +2.98101i q^{29} +(5.46948 + 3.15781i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.63684i q^{34} +(4.95481 - 3.23263i) q^{35} +(3.01361 - 1.73991i) q^{37} +(-5.35129 - 3.08957i) q^{38} +(2.11940 + 0.712845i) q^{40} -6.97007 q^{41} -2.58650i q^{43} +(5.48223 - 3.16517i) q^{44} +(-3.52236 + 6.10091i) q^{46} +(7.06176 - 4.07711i) q^{47} +(-1.62493 - 6.80879i) q^{49} +(0.624933 - 4.96079i) q^{50} +(-0.526449 + 0.911836i) q^{52} +(4.43682 - 7.68480i) q^{53} +(-9.36276 - 10.6162i) q^{55} +(1.63937 - 2.07665i) q^{56} +(2.58163 - 1.49051i) q^{58} +(0.452296 - 0.783400i) q^{59} +(-8.81047 + 5.08673i) q^{61} -6.31561i q^{62} +1.00000 q^{64} +(2.23151 + 0.750552i) q^{65} +(-8.51497 - 4.91612i) q^{67} +(-4.01562 + 2.31842i) q^{68} +(-5.27694 - 2.67467i) q^{70} +14.4282i q^{71} +(4.18333 - 7.24574i) q^{73} +(-3.01361 - 1.73991i) q^{74} +6.17914i q^{76} +(-15.5603 + 6.19578i) q^{77} +(2.73283 + 4.73340i) q^{79} +(-0.442358 - 2.19188i) q^{80} +(3.48504 + 6.03626i) q^{82} +14.6297i q^{83} +(6.85803 + 7.77617i) q^{85} +(-2.23997 + 1.29325i) q^{86} +(-5.48223 - 3.16517i) q^{88} +(1.91982 + 3.32522i) q^{89} +(1.72609 - 2.18650i) q^{91} +7.04472 q^{92} +(-7.06176 - 4.07711i) q^{94} +(13.5439 - 2.73339i) q^{95} -5.87891 q^{97} +(-5.08412 + 4.81163i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8	$ 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} - 8 q^{23} - 6 q^{25} + 12 q^{31} - 8 q^{32} + 4 q^{35} - 24 q^{38} - 6 q^{40} - 8 q^{46} + 60 q^{47} - 28 q^{49} + 12 q^{50} + 16 q^{53} + 24 q^{61} + 16 q^{64} - 20 q^{65} - 14 q^{70} - 88 q^{77} + 4 q^{79} + 6 q^{80} + 64 q^{85} - 28 q^{91} + 16 q^{92} - 60 q^{94} - 12 q^{95} + 20 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 - 8 * q^23 - 6 * q^25 + 12 * q^31 - 8 * q^32 + 4 * q^35 - 24 * q^38 - 6 * q^40 - 8 * q^46 + 60 * q^47 - 28 * q^49 + 12 * q^50 + 16 * q^53 + 24 * q^61 + 16 * q^64 - 20 * q^65 - 14 * q^70 - 88 * q^77 + 4 * q^79 + 6 * q^80 + 64 * q^85 - 28 * q^91 + 16 * q^92 - 60 * q^94 - 12 * q^95 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.11940	+	0.712845i	0.947824	+	0.318794i
$5$	2.11940	+	0.712845i	0.947824	+	0.318794i
$6$		0			0
$7$	1.63937	−	2.07665i	0.619624	−	0.784899i
$7$	1.63937	−	2.07665i	0.619624	−	0.784899i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.442358	−	2.19188i	−0.139886	−	0.693132i
$11$	−5.48223	−	3.16517i	−1.65295	−	0.954334i	−0.975849	−	0.218448i	$-0.929901\pi$
$11$	−5.48223	−	3.16517i	−1.65295	−	0.954334i	−0.677106	−	0.735886i	$-0.736766\pi$
$12$		0			0
$13$	1.05290			0.292021			0.146011	−	0.989283i	$-0.453357\pi$
$13$	1.05290			0.292021			0.146011	+	0.989283i	$0.453357\pi$
$14$	−2.61811	−	0.381412i	−0.699721	−	0.101937i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.01562	+	2.31842i	0.973931	+	0.562299i	0.900432	−	0.434996i	$-0.143250\pi$
$17$	4.01562	+	2.31842i	0.973931	+	0.562299i	0.0734985	+	0.997295i	$0.476584\pi$
$18$		0			0
$19$	5.35129	−	3.08957i	1.22767	−	0.708795i	0.261128	−	0.965304i	$-0.415906\pi$
$19$	5.35129	−	3.08957i	1.22767	−	0.708795i	0.966542	+	0.256509i	$0.0825723\pi$
$20$	−1.67704	+	1.47903i	−0.374998	+	0.330721i
$21$		0			0
$22$			6.33033i			1.34963i
$23$	−3.52236	−	6.10091i	−0.734463	−	1.27213i	−0.954959	−	0.296739i	$-0.904101\pi$
$23$	−3.52236	−	6.10091i	−0.734463	−	1.27213i	0.220496	−	0.975388i	$-0.429232\pi$
$24$		0			0
$25$	3.98371	+	3.02160i	0.796741	+	0.604321i
$26$	−0.526449	−	0.911836i	−0.103245	−	0.178826i
$27$		0			0
$28$	0.978745	+	2.45806i	0.184965	+	0.464530i
$29$			2.98101i			0.553560i	0.960933	+	0.276780i	$0.0892674\pi$
$29$			2.98101i			0.553560i	−0.960933	+	0.276780i	$0.910733\pi$
$30$		0			0
$31$	5.46948	+	3.15781i	0.982348	+	0.567159i	0.902978	−	0.429686i	$-0.141376\pi$
$31$	5.46948	+	3.15781i	0.982348	+	0.567159i	0.0793697	+	0.996845i	$0.474709\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	4.63684i		−	0.795211i
$35$	4.95481	−	3.23263i	0.837515	−	0.546414i
$36$		0			0
$37$	3.01361	−	1.73991i	0.495434	−	0.286039i	−0.231392	−	0.972861i	$-0.574328\pi$
$37$	3.01361	−	1.73991i	0.495434	−	0.286039i	0.726826	+	0.686821i	$0.240995\pi$
$38$	−5.35129	−	3.08957i	−0.868094	−	0.501194i
$39$		0			0
$40$	2.11940	+	0.712845i	0.335106	+	0.112711i
$41$	−6.97007			−1.08854			−0.544271	−	0.838909i	$-0.683194\pi$
$41$	−6.97007			−1.08854			−0.544271	+	0.838909i	$0.683194\pi$
$42$		0			0
$43$		−	2.58650i		−	0.394437i	−0.980360	−	0.197218i	$-0.936809\pi$
$43$		−	2.58650i		−	0.394437i	0.980360	−	0.197218i	$-0.0631908\pi$
$44$	5.48223	−	3.16517i	0.826477	−	0.477167i
$45$		0			0
$46$	−3.52236	+	6.10091i	−0.519344	+	0.899529i
$47$	7.06176	−	4.07711i	1.03006	−	0.594707i	0.113060	−	0.993588i	$-0.463935\pi$
$47$	7.06176	−	4.07711i	1.03006	−	0.594707i	0.917003	+	0.398881i	$0.130601\pi$
$48$		0			0
$49$	−1.62493	−	6.80879i	−0.232133	−	0.972684i
$50$	0.624933	−	4.96079i	0.0883789	−	0.701562i
$51$		0			0
$52$	−0.526449	+	0.911836i	−0.0730053	+	0.126449i
$53$	4.43682	−	7.68480i	0.609445	−	1.05559i	−0.381887	−	0.924209i	$-0.624726\pi$
$53$	4.43682	−	7.68480i	0.609445	−	1.05559i	0.991332	−	0.131380i	$-0.0419409\pi$
$54$		0			0
$55$	−9.36276	−	10.6162i	−1.26247	−	1.43149i
$56$	1.63937	−	2.07665i	0.219070	−	0.277504i
$57$		0			0
$58$	2.58163	−	1.49051i	0.338985	−	0.195713i
$59$	0.452296	−	0.783400i	0.0588839	−	0.101990i	−0.835081	−	0.550127i	$-0.814579\pi$
$59$	0.452296	−	0.783400i	0.0588839	−	0.101990i	0.893965	+	0.448137i	$0.147912\pi$
$60$		0			0
$61$	−8.81047	+	5.08673i	−1.12807	+	0.651289i	−0.943448	−	0.331522i	$-0.892438\pi$
$61$	−8.81047	+	5.08673i	−1.12807	+	0.651289i	−0.184618	+	0.982810i	$0.559105\pi$
$62$		−	6.31561i		−	0.802084i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.23151	+	0.750552i	0.276785	+	0.0930946i
$66$		0			0
$67$	−8.51497	−	4.91612i	−1.04027	−	0.600600i	−0.120360	−	0.992730i	$-0.538405\pi$
$67$	−8.51497	−	4.91612i	−1.04027	−	0.600600i	−0.919909	+	0.392131i	$0.871738\pi$
$68$	−4.01562	+	2.31842i	−0.486965	+	0.281150i
$69$		0			0
$70$	−5.27694	−	2.67467i	−0.630715	−	0.319685i
$71$			14.4282i			1.71232i	0.516713	+	0.856159i	$0.327156\pi$
$71$			14.4282i			1.71232i	−0.516713	+	0.856159i	$0.672844\pi$
$72$		0			0
$73$	4.18333	−	7.24574i	0.489622	−	0.848050i	−0.510307	−	0.859992i	$-0.670468\pi$
$73$	4.18333	−	7.24574i	0.489622	−	0.848050i	0.999929	+	0.0119423i	$0.00380146\pi$
$74$	−3.01361	−	1.73991i	−0.350325	−	0.202260i
$75$		0			0
$76$			6.17914i			0.708795i
$77$	−15.5603	+	6.19578i	−1.77327	+	0.706075i
$78$		0			0
$79$	2.73283	+	4.73340i	0.307467	+	0.532549i	0.977808	−	0.209505i	$-0.0671852\pi$
$79$	2.73283	+	4.73340i	0.307467	+	0.532549i	−0.670340	+	0.742054i	$0.733852\pi$
$80$	−0.442358	−	2.19188i	−0.0494571	−	0.245059i
$81$		0			0
$82$	3.48504	+	6.03626i	0.384858	+	0.666593i
$83$			14.6297i			1.60581i	0.596105	+	0.802907i	$0.296714\pi$
$83$			14.6297i			1.60581i	−0.596105	+	0.802907i	$0.703286\pi$
$84$		0			0
$85$	6.85803	+	7.77617i	0.743858	+	0.843444i
$86$	−2.23997	+	1.29325i	−0.241542	+	0.139455i
$87$		0			0
$88$	−5.48223	−	3.16517i	−0.584408	−	0.337408i
$89$	1.91982	+	3.32522i	0.203500	+	0.352473i	0.949654	−	0.313301i	$-0.101435\pi$
$89$	1.91982	+	3.32522i	0.203500	+	0.352473i	−0.746154	+	0.665774i	$0.768102\pi$
$90$		0			0
$91$	1.72609	−	2.18650i	0.180943	−	0.229207i
$92$	7.04472			0.734463
$93$		0			0
$94$	−7.06176	−	4.07711i	−0.728365	−	0.420522i
$95$	13.5439	−	2.73339i	1.38957	−	0.280440i
$96$		0			0
$97$	−5.87891			−0.596913			−0.298457	−	0.954423i	$-0.596472\pi$
$97$	−5.87891			−0.596913			−0.298457	+	0.954423i	$0.596472\pi$
$98$	−5.08412	+	4.81163i	−0.513573	+	0.486048i
$99$		0			0
$100$	−4.60864	+	1.93919i	−0.460864	+	0.193919i
$101$	3.35408	−	5.80944i	0.333744	−	0.578061i	−0.649499	−	0.760362i	$-0.725021\pi$
$101$	3.35408	−	5.80944i	0.333744	−	0.578061i	0.983243	+	0.182301i	$0.0583547\pi$
$102$		0			0
$103$	2.48716	+	4.30789i	0.245067	+	0.424469i	0.962151	−	0.272519i	$-0.0878566\pi$
$103$	2.48716	+	4.30789i	0.245067	+	0.424469i	−0.717083	+	0.696988i	$0.754523\pi$
$104$	1.05290			0.103245
$105$		0			0
$106$	−8.87365			−0.861885
$107$	−3.66965	−	6.35602i	−0.354759	−	0.614460i	0.632318	−	0.774709i	$-0.282104\pi$
$107$	−3.66965	−	6.35602i	−0.354759	−	0.614460i	−0.987077	+	0.160249i	$0.948770\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$	−4.51254	+	13.4165i	−0.430254	+	1.27921i
$111$		0			0
$112$	−2.61811	−	0.381412i	−0.247389	−	0.0360400i
$113$	0.184551			0.0173611			0.00868054	−	0.999962i	$-0.497237\pi$
$113$	0.184551			0.0173611			0.00868054	+	0.999962i	$0.497237\pi$
$114$		0			0
$115$	−3.11629	−	15.4411i	−0.290595	−	1.43989i
$116$	−2.58163	−	1.49051i	−0.239699	−	0.138390i
$117$		0			0
$118$	−0.904592			−0.0832745
$119$	11.3976	−	4.53828i	1.04482	−	0.416024i
$120$		0			0
$121$	14.5366	+	25.1781i	1.32151	+	2.28891i
$122$	8.81047	+	5.08673i	0.797663	+	0.460531i
$123$		0			0
$124$	−5.46948	+	3.15781i	−0.491174	+	0.283579i
$125$	6.28913	+	9.24375i	0.562517	+	0.826786i
$126$		0			0
$127$			6.70276i			0.594774i	0.954757	+	0.297387i	$0.0961151\pi$
$127$			6.70276i			0.594774i	−0.954757	+	0.297387i	$0.903885\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.465758	−	2.30782i	−0.0408497	−	0.202409i
$131$	−2.24116	−	3.88180i	−0.195811	−	0.339155i	0.751355	−	0.659898i	$-0.229401\pi$
$131$	−2.24116	−	3.88180i	−0.195811	−	0.339155i	−0.947166	+	0.320743i	$0.896067\pi$
$132$		0			0
$133$	2.35680	−	16.1777i	0.204360	−	1.40278i
$134$			9.83224i			0.849376i
$135$		0			0
$136$	4.01562	+	2.31842i	0.344337	+	0.198803i
$137$	−8.78137	+	15.2098i	−0.750243	+	1.29946i	0.197461	+	0.980311i	$0.436730\pi$
$137$	−8.78137	+	15.2098i	−0.750243	+	1.29946i	−0.947705	+	0.319149i	$0.896603\pi$
$138$		0			0
$139$		−	6.02268i		−	0.510837i	−0.966831	−	0.255418i	$-0.917787\pi$
$139$		−	6.02268i		−	0.510837i	0.966831	−	0.255418i	$-0.0822132\pi$
$140$	0.322137	+	5.90730i	0.0272255	+	0.499258i
$141$		0			0
$142$	12.4952	−	7.21412i	1.04858	−	0.605396i
$143$	−5.77223	−	3.33260i	−0.482698	−	0.278686i
$144$		0			0
$145$	−2.12500	+	6.31796i	−0.176472	+	0.524678i
$146$	−8.36666			−0.692430
$147$		0			0
$148$			3.47982i			0.286039i
$149$	6.06548	−	3.50191i	0.496903	−	0.286887i	−0.230530	−	0.973065i	$-0.574046\pi$
$149$	6.06548	−	3.50191i	0.496903	−	0.286887i	0.727434	+	0.686178i	$0.240713\pi$
$150$		0			0
$151$	−6.43540	+	11.1464i	−0.523706	+	0.907085i	0.475913	+	0.879492i	$0.342118\pi$
$151$	−6.43540	+	11.1464i	−0.523706	+	0.907085i	−0.999619	+	0.0275929i	$0.991216\pi$
$152$	5.35129	−	3.08957i	0.434047	−	0.250597i
$153$		0			0
$154$	13.1459	+	10.3778i	1.05932	+	0.836263i
$155$	9.34099	+	10.5915i	0.750286	+	0.850733i
$156$		0			0
$157$	−5.52193	+	9.56427i	−0.440698	+	0.763312i	−0.997741	−	0.0671718i	$-0.978602\pi$
$157$	−5.52193	+	9.56427i	−0.440698	+	0.763312i	0.557043	+	0.830484i	$0.311936\pi$
$158$	2.73283	−	4.73340i	0.217412	−	0.376569i
$159$		0			0
$160$	−1.67704	+	1.47903i	−0.132582	+	0.116928i
$161$	−18.4439	−	2.68694i	−1.45358	−	0.211760i
$162$		0			0
$163$	−6.27500	+	3.62287i	−0.491496	+	0.283765i	−0.725195	−	0.688544i	$-0.758250\pi$
$163$	−6.27500	+	3.62287i	−0.491496	+	0.283765i	0.233699	+	0.972309i	$0.424917\pi$
$164$	3.48504	−	6.03626i	0.272136	−	0.471353i
$165$		0			0
$166$	12.6697	−	7.31483i	0.983356	−	0.567741i
$167$			13.8606i			1.07257i	0.844038	+	0.536283i	$0.180172\pi$
$167$			13.8606i			1.07257i	−0.844038	+	0.536283i	$0.819828\pi$
$168$		0			0
$169$	−11.8914			−0.914724
$170$	3.30534	−	9.82731i	0.253508	−	0.753720i
$171$		0			0
$172$	2.23997	+	1.29325i	0.170796	+	0.0986092i
$173$	−0.830348	+	0.479402i	−0.0631302	+	0.0364482i	−0.531233	−	0.847226i	$-0.678271\pi$
$173$	−0.830348	+	0.479402i	−0.0631302	+	0.0364482i	0.468103	+	0.883674i	$0.344938\pi$
$174$		0			0
$175$	12.8056	−	3.31923i	0.968010	−	0.250910i
$176$			6.33033i			0.477167i
$177$		0			0
$178$	1.91982	−	3.32522i	0.143896	−	0.249236i
$179$	20.2531	+	11.6931i	1.51379	+	0.873984i	0.999870	+	0.0161436i	$0.00513888\pi$
$179$	20.2531	+	11.6931i	1.51379	+	0.873984i	0.513916	+	0.857841i	$0.328194\pi$
$180$		0			0
$181$			19.2865i			1.43355i	0.697303	+	0.716776i	$0.254383\pi$
$181$			19.2865i			1.43355i	−0.697303	+	0.716776i	$0.745617\pi$
$182$	−2.75661	−	0.401588i	−0.204333	−	0.0297677i
$183$		0			0
$184$	−3.52236	−	6.10091i	−0.259672	−	0.449765i
$185$	7.62733	−	1.53933i	0.560772	−	0.113173i
$186$		0			0
$187$	−14.6764	−	25.4202i	−1.07324	−	1.85891i
$188$			8.15421i			0.594707i
$189$		0			0
$190$	−9.13913	−	10.3627i	−0.663022	−	0.751787i
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	−0.585995	−	0.810315i	$-0.699296\pi$
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$192$		0			0
$193$	7.11634	+	4.10862i	0.512246	+	0.295745i	0.733756	−	0.679413i	$-0.237765\pi$
$193$	7.11634	+	4.10862i	0.512246	+	0.295745i	−0.221511	+	0.975158i	$0.571099\pi$
$194$	2.93946	+	5.09129i	0.211041	+	0.365533i
$195$		0			0
$196$	6.70905	+	1.99716i	0.479218	+	0.142654i
$197$	3.51321			0.250306			0.125153	−	0.992137i	$-0.460058\pi$
$197$	3.51321			0.250306			0.125153	+	0.992137i	$0.460058\pi$
$198$		0			0
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	0.389885	−	0.920864i	$-0.372515\pi$
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	3.98371	+	3.02160i	0.281690	+	0.213660i
$201$		0			0
$202$	−6.70816			−0.471985
$203$	6.19052	+	4.88698i	0.434489	+	0.342999i
$204$		0			0
$205$	−14.7724	−	4.96858i	−1.03175	−	0.347021i
$206$	2.48716	−	4.30789i	0.173289	−	0.300145i
$207$		0			0
$208$	−0.526449	−	0.911836i	−0.0365027	−	0.0632245i
$209$	−39.1160			−2.70571
$210$		0			0
$211$	−9.96592			−0.686082			−0.343041	−	0.939320i	$-0.611457\pi$
$211$	−9.96592			−0.686082			−0.343041	+	0.939320i	$0.611457\pi$
$212$	4.43682	+	7.68480i	0.304722	+	0.527795i
$213$		0			0
$214$	−3.66965	+	6.35602i	−0.250852	+	0.434489i
$215$	1.84377	−	5.48182i	0.125744	−	0.373857i
$216$		0			0
$217$	15.5242	−	6.18138i	1.05385	−	0.419619i
$218$	2.00000			0.135457
$219$		0			0
$220$	13.8753	−	2.80027i	0.935473	−	0.188794i
$221$	4.22804	+	2.44106i	0.284408	+	0.164203i
$222$		0			0
$223$	−11.1087			−0.743894			−0.371947	−	0.928254i	$-0.621310\pi$
$223$	−11.1087			−0.743894			−0.371947	+	0.928254i	$0.621310\pi$
$224$	0.978745	+	2.45806i	0.0653952	+	0.164236i
$225$		0			0
$226$	−0.0922754	−	0.159826i	−0.00613807	−	0.0106314i
$227$	−20.3722	−	11.7619i	−1.35215	−	0.780665i	−0.363602	−	0.931555i	$-0.618453\pi$
$227$	−20.3722	−	11.7619i	−1.35215	−	0.780665i	−0.988551	+	0.150889i	$0.951786\pi$
$228$		0			0
$229$	−8.21579	+	4.74339i	−0.542915	+	0.313452i	−0.746259	−	0.665655i	$-0.768152\pi$
$229$	−8.21579	+	4.74339i	−0.542915	+	0.313452i	0.203345	+	0.979107i	$0.434819\pi$
$230$	−11.8143	+	10.4194i	−0.779011	+	0.687032i
$231$		0			0
$232$			2.98101i			0.195713i
$233$	−5.18669	−	8.98361i	−0.339791	−	0.588536i	0.644602	−	0.764518i	$-0.277023\pi$
$233$	−5.18669	−	8.98361i	−0.339791	−	0.588536i	−0.984393	+	0.175982i	$0.943690\pi$
$234$		0			0
$235$	17.8730	−	3.60708i	1.16591	−	0.235300i
$236$	0.452296	+	0.783400i	0.0294420	+	0.0509950i
$237$		0			0
$238$	−9.62908	−	7.60149i	−0.624161	−	0.492732i
$239$		−	12.3746i		−	0.800444i	−0.916418	−	0.400222i	$-0.868933\pi$
$239$		−	12.3746i		−	0.800444i	0.916418	−	0.400222i	$-0.131067\pi$
$240$		0			0
$241$	−10.8208	−	6.24737i	−0.697027	−	0.402429i	0.109212	−	0.994018i	$-0.465167\pi$
$241$	−10.8208	−	6.24737i	−0.697027	−	0.402429i	−0.806239	+	0.591590i	$0.798501\pi$
$242$	14.5366	−	25.1781i	0.934445	−	1.61851i
$243$		0			0
$244$		−	10.1735i		−	0.651289i
$245$	1.40972	−	15.5889i	0.0900640	−	0.995936i
$246$		0			0
$247$	5.63436	−	3.25300i	0.358506	−	0.206983i
$248$	5.46948	+	3.15781i	0.347312	+	0.200521i
$249$		0			0
$250$	4.86076	−	10.0684i	0.307421	−	0.636783i
$251$	13.5304			0.854034			0.427017	−	0.904244i	$-0.359564\pi$
$251$	13.5304			0.854034			0.427017	+	0.904244i	$0.359564\pi$
$252$		0			0
$253$			44.5954i			2.80369i
$254$	5.80476	−	3.35138i	0.364223	−	0.210284i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.82609	+	2.20899i	−0.238665	+	0.137793i	−0.614563	−	0.788868i	$-0.710668\pi$
$257$	−3.82609	+	2.20899i	−0.238665	+	0.137793i	0.375898	+	0.926661i	$0.377334\pi$
$258$		0			0
$259$	1.32724	−	9.11056i	0.0824709	−	0.566103i
$260$	−1.76575	+	1.55727i	−0.109507	+	0.0965777i
$261$		0			0
$262$	−2.24116	+	3.88180i	−0.138459	+	0.239819i
$263$	3.06318	−	5.30558i	0.188884	−	0.327156i	−0.755995	−	0.654578i	$-0.772846\pi$
$263$	3.06318	−	5.30558i	0.188884	−	0.327156i	0.944878	+	0.327422i	$0.106180\pi$
$264$		0			0
$265$	14.8815	−	13.1244i	0.914162	−	0.806226i
$266$	−15.1887	+	6.04780i	−0.931278	+	0.370814i
$267$		0			0
$268$	8.51497	−	4.91612i	0.520135	−	0.300300i
$269$	2.09370	−	3.62639i	0.127655	−	0.221105i	−0.795113	−	0.606462i	$-0.792588\pi$
$269$	2.09370	−	3.62639i	0.127655	−	0.221105i	0.922768	+	0.385357i	$0.125922\pi$
$270$		0			0
$271$	0.253692	−	0.146469i	0.0154107	−	0.00889737i	−0.492275	−	0.870440i	$-0.663835\pi$
$271$	0.253692	−	0.146469i	0.0154107	−	0.00889737i	0.507686	+	0.861542i	$0.330501\pi$
$272$		−	4.63684i		−	0.281150i
$273$		0			0
$274$	17.5627			1.06100
$275$	−12.2757	−	29.1742i	−0.740253	−	1.75927i
$276$		0			0
$277$	12.6630	+	7.31099i	0.760847	+	0.439275i	0.829600	−	0.558359i	$-0.188569\pi$
$277$	12.6630	+	7.31099i	0.760847	+	0.439275i	−0.0687531	+	0.997634i	$0.521902\pi$
$278$	−5.21579	+	3.01134i	−0.312822	+	0.180608i
$279$		0			0
$280$	4.95481	−	3.23263i	0.296106	−	0.193187i
$281$			18.1691i			1.08388i	0.840419	+	0.541938i	$0.182309\pi$
$281$			18.1691i			1.08388i	−0.840419	+	0.541938i	$0.817691\pi$
$282$		0			0
$283$	−10.6066	+	18.3712i	−0.630499	+	1.09206i	0.356951	+	0.934123i	$0.383816\pi$
$283$	−10.6066	+	18.3712i	−0.630499	+	1.09206i	−0.987450	+	0.157933i	$0.949517\pi$
$284$	−12.4952	−	7.21412i	−0.741455	−	0.428079i
$285$		0			0
$286$			6.66519i			0.394121i
$287$	−11.4265	+	14.4744i	−0.674486	+	0.854396i
$288$		0			0
$289$	2.25013	+	3.89734i	0.132361	+	0.229256i
$290$	6.53401	−	1.31868i	0.383690	−	0.0774353i
$291$		0			0
$292$	4.18333	+	7.24574i	0.244811	+	0.424025i
$293$		−	7.64481i		−	0.446615i	−0.974748	−	0.223307i	$-0.928315\pi$
$293$		−	7.64481i		−	0.446615i	0.974748	−	0.223307i	$-0.0716853\pi$
$294$		0			0
$295$	1.51704	−	1.33792i	0.0883254	−	0.0778967i
$296$	3.01361	−	1.73991i	0.175163	−	0.101130i
$297$		0			0
$298$	−6.06548	−	3.50191i	−0.351364	−	0.202860i
$299$	−3.70868	−	6.42363i	−0.214479	−	0.371488i
$300$		0			0
$301$	−5.37124	−	4.24022i	−0.309593	−	0.244402i
$302$	12.8708			0.740632
$303$		0			0
$304$	−5.35129	−	3.08957i	−0.306917	−	0.177199i
$305$	−22.2990	+	4.50031i	−1.27683	+	0.257687i
$306$		0			0
$307$	−13.1561			−0.750859			−0.375429	−	0.926851i	$-0.622505\pi$
$307$	−13.1561			−0.750859			−0.375429	+	0.926851i	$0.622505\pi$
$308$	2.41446	−	16.5735i	0.137577	−	0.944365i
$309$		0			0
$310$	4.50205	−	13.3853i	0.255699	−	0.760234i
$311$	−3.13043	+	5.42207i	−0.177511	+	0.307457i	−0.941027	−	0.338331i	$-0.890138\pi$
$311$	−3.13043	+	5.42207i	−0.177511	+	0.307457i	0.763517	+	0.645788i	$0.223471\pi$
$312$		0			0
$313$	8.74065	+	15.1392i	0.494051	+	0.855721i	0.999976	−	0.00685609i	$-0.00218238\pi$
$313$	8.74065	+	15.1392i	0.494051	+	0.855721i	−0.505926	+	0.862577i	$0.668849\pi$
$314$	11.0439			0.623241
$315$		0			0
$316$	−5.46566			−0.307467
$317$	0.766906	+	1.32832i	0.0430737	+	0.0746058i	0.886758	−	0.462233i	$-0.152952\pi$
$317$	0.766906	+	1.32832i	0.0430737	+	0.0746058i	−0.843685	+	0.536839i	$0.819618\pi$
$318$		0			0
$319$	9.43540	−	16.3426i	0.528281	−	0.915010i
$320$	2.11940	+	0.712845i	0.118478	+	0.0398492i
$321$		0			0
$322$	6.89498	+	17.3163i	0.384242	+	0.965002i
$323$	28.6516			1.59422
$324$		0			0
$325$	4.19443	+	3.18144i	0.232665	+	0.176475i
$326$	6.27500	+	3.62287i	0.347540	+	0.200652i
$327$		0			0
$328$	−6.97007			−0.384858
$329$	3.11011	−	21.3487i	0.171466	−	1.17699i
$330$		0			0
$331$	0.756607	+	1.31048i	0.0415869	+	0.0720306i	0.886070	−	0.463552i	$-0.153425\pi$
$331$	0.756607	+	1.31048i	0.0415869	+	0.0720306i	−0.844483	+	0.535583i	$0.820092\pi$
$332$	−12.6697	−	7.31483i	−0.695337	−	0.401453i
$333$		0			0
$334$	12.0036	−	6.93030i	0.656810	−	0.379209i
$335$	−14.5422	−	16.4891i	−0.794525	−	0.900894i
$336$		0			0
$337$			3.14064i			0.171082i	0.996335	+	0.0855408i	$0.0272618\pi$
$337$			3.14064i			0.171082i	−0.996335	+	0.0855408i	$0.972738\pi$
$338$	5.94570	+	10.2983i	0.323404	+	0.560152i
$339$		0			0
$340$	−10.1634	+	2.05114i	−0.551186	+	0.111239i
$341$	−19.9900	−	34.6236i	−1.08252	−	1.87498i
$342$		0			0
$343$	−16.8033	−	7.78771i	−0.907294	−	0.420497i
$344$		−	2.58650i		−	0.139455i
$345$		0			0
$346$	0.830348	+	0.479402i	0.0446398	+	0.0257728i
$347$	13.7026	−	23.7336i	0.735593	−	1.27408i	−0.218870	−	0.975754i	$-0.570237\pi$
$347$	13.7026	−	23.7336i	0.735593	−	1.27408i	0.954463	−	0.298330i	$-0.0964296\pi$
$348$		0			0
$349$		−	19.5594i		−	1.04699i	−0.852028	−	0.523496i	$-0.824627\pi$
$349$		−	19.5594i		−	1.04699i	0.852028	−	0.523496i	$-0.175373\pi$
$350$	−9.27732	−	9.43034i	−0.495894	−	0.504073i
$351$		0			0
$352$	5.48223	−	3.16517i	0.292204	−	0.168704i
$353$	12.8261	+	7.40515i	0.682664	+	0.394136i	0.800858	−	0.598854i	$-0.204377\pi$
$353$	12.8261	+	7.40515i	0.682664	+	0.394136i	−0.118194	+	0.992991i	$0.537710\pi$
$354$		0			0
$355$	−10.2851	+	30.5792i	−0.545876	+	1.62298i
$356$	−3.83964			−0.203500
$357$		0			0
$358$		−	23.3862i		−	1.23600i
$359$	−14.3492	+	8.28450i	−0.757321	+	0.437239i	−0.828333	−	0.560236i	$-0.810710\pi$
$359$	−14.3492	+	8.28450i	−0.757321	+	0.437239i	0.0710122	+	0.997475i	$0.477377\pi$
$360$		0			0
$361$	9.59086	−	16.6119i	0.504782	−	0.874308i
$362$	16.7026	−	9.64324i	0.877868	−	0.506837i
$363$		0			0
$364$	1.03052	+	2.58809i	0.0540138	+	0.135653i
$365$	14.0312	−	12.3746i	0.734429	−	0.647714i
$366$		0			0
$367$	7.00655	−	12.1357i	0.365739	−	0.633479i	−0.623155	−	0.782098i	$-0.714150\pi$
$367$	7.00655	−	12.1357i	0.365739	−	0.633479i	0.988894	+	0.148619i	$0.0474829\pi$
$368$	−3.52236	+	6.10091i	−0.183616	+	0.318032i
$369$		0			0
$370$	−5.14676	−	5.83580i	−0.267567	−	0.303389i
$371$	−8.68504	−	21.8120i	−0.450905	−	1.13242i
$372$		0			0
$373$	12.6630	−	7.31099i	0.655666	−	0.378549i	−0.134958	−	0.990851i	$-0.543090\pi$
$373$	12.6630	−	7.31099i	0.655666	−	0.378549i	0.790624	+	0.612303i	$0.209757\pi$
$374$	−14.6764	+	25.4202i	−0.758897	+	1.31445i
$375$		0			0
$376$	7.06176	−	4.07711i	0.364182	−	0.210261i
$377$			3.13870i			0.161651i
$378$		0			0
$379$	−4.68145			−0.240470			−0.120235	−	0.992745i	$-0.538365\pi$
$379$	−4.68145			−0.240470			−0.120235	+	0.992745i	$0.538365\pi$
$380$	−4.40476	+	13.0961i	−0.225960	+	0.671813i
$381$		0			0
$382$	2.44949	+	1.41421i	0.125327	+	0.0723575i
$383$	10.1086	−	5.83621i	0.516526	−	0.298216i	−0.218986	−	0.975728i	$-0.570275\pi$
$383$	10.1086	−	5.83621i	0.516526	−	0.298216i	0.735512	+	0.677511i	$0.236942\pi$
$384$		0			0
$385$	−37.3952	+	2.03923i	−1.90584	+	0.103929i
$386$		−	8.21725i		−	0.418247i
$387$		0			0
$388$	2.93946	−	5.09129i	0.149228	−	0.258471i
$389$	11.3452	+	6.55018i	0.575226	+	0.332107i	0.759234	−	0.650818i	$-0.225574\pi$
$389$	11.3452	+	6.55018i	0.575226	+	0.332107i	−0.184008	+	0.982925i	$0.558907\pi$
$390$		0			0
$391$		−	32.6652i		−	1.65195i
$392$	−1.62493	−	6.80879i	−0.0820715	−	0.343896i
$393$		0			0
$394$	−1.75661	−	3.04253i	−0.0884966	−	0.153281i
$395$	2.41778	+	11.9800i	0.121652	+	0.602781i
$396$		0			0
$397$	−15.3402	−	26.5700i	−0.769903	−	1.33351i	−0.937615	−	0.347675i	$-0.886971\pi$
$397$	−15.3402	−	26.5700i	−0.769903	−	1.33351i	0.167712	−	0.985836i	$-0.446362\pi$
$398$			3.46410i			0.173640i
$399$		0			0
$400$	0.624933	−	4.96079i	0.0312467	−	0.248040i
$401$	6.88085	−	3.97266i	0.343613	−	0.198385i	−0.318255	−	0.948005i	$-0.603097\pi$
$401$	6.88085	−	3.97266i	0.343613	−	0.198385i	0.661869	+	0.749620i	$0.269764\pi$
$402$		0			0
$403$	5.75880	+	3.32485i	0.286866	+	0.165622i
$404$	3.35408	+	5.80944i	0.166872	+	0.289030i
$405$		0			0
$406$	1.13699	−	7.80464i	0.0564281	−	0.387338i
$407$	−22.0284			−1.09191
$408$		0			0
$409$	34.4957	+	19.9161i	1.70570	+	0.984789i	0.939729	+	0.341919i	$0.111077\pi$
$409$	34.4957	+	19.9161i	1.70570	+	0.984789i	0.765975	+	0.642870i	$0.222256\pi$
$410$	3.08327	+	15.2775i	0.152272	+	0.754503i
$411$		0			0
$412$	−4.97432			−0.245067
$413$	−0.885365	−	2.22354i	−0.0435660	−	0.109413i
$414$		0			0
$415$	−10.4287	+	31.0061i	−0.511923	+	1.52203i
$416$	−0.526449	+	0.911836i	−0.0258113	+	0.0447064i
$417$		0			0
$418$	19.5580	+	33.8754i	0.956613	+	1.65690i
$419$	11.0357			0.539131			0.269566	−	0.962982i	$-0.413120\pi$
$419$	11.0357			0.539131			0.269566	+	0.962982i	$0.413120\pi$
$420$		0			0
$421$	−7.78421			−0.379379			−0.189690	−	0.981844i	$-0.560748\pi$
$421$	−7.78421			−0.379379			−0.189690	+	0.981844i	$0.560748\pi$
$422$	4.98296	+	8.63074i	0.242567	+	0.420138i
$423$		0			0
$424$	4.43682	−	7.68480i	0.215471	−	0.373207i
$425$	8.99170	+	21.3695i	0.436161	+	1.03657i
$426$		0			0
$427$	−3.88028	+	26.6353i	−0.187780	+	1.28897i
$428$	7.33930			0.354759
$429$		0			0
$430$	−5.66928	+	1.14416i	−0.273397	+	0.0551762i
$431$	−8.86273	−	5.11690i	−0.426903	−	0.246472i	0.271124	−	0.962545i	$-0.412605\pi$
$431$	−8.86273	−	5.11690i	−0.426903	−	0.246472i	−0.698026	+	0.716072i	$0.745938\pi$
$432$		0			0
$433$	40.3902			1.94103			0.970513	−	0.241047i	$-0.0774909\pi$
$433$	40.3902			1.94103			0.970513	+	0.241047i	$0.0774909\pi$
$434$	−13.1153	−	10.3536i	−0.629555	−	0.496990i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−37.6983	−	21.7651i	−1.80336	−	1.04117i
$438$		0			0
$439$	−11.2331	+	6.48543i	−0.536126	+	0.309533i	−0.743508	−	0.668728i	$-0.766839\pi$
$439$	−11.2331	+	6.48543i	−0.536126	+	0.309533i	0.207381	+	0.978260i	$0.433506\pi$
$440$	−9.36276	−	10.6162i	−0.446352	−	0.506109i
$441$		0			0
$442$		−	4.88212i		−	0.232219i
$443$	4.32751	+	7.49547i	0.205606	+	0.356120i	0.950326	−	0.311257i	$-0.100750\pi$
$443$	4.32751	+	7.49547i	0.205606	+	0.356120i	−0.744720	+	0.667378i	$0.767417\pi$
$444$		0			0
$445$	1.69849	+	8.41601i	0.0805164	+	0.398957i
$446$	5.55435	+	9.62042i	0.263006	+	0.455540i
$447$		0			0
$448$	1.63937	−	2.07665i	0.0774529	−	0.0981124i
$449$			25.4407i			1.20062i	0.799768	+	0.600310i	$0.204956\pi$
$449$			25.4407i			1.20062i	−0.799768	+	0.600310i	$0.795044\pi$
$450$		0			0
$451$	38.2115	+	22.0614i	1.79931	+	1.03883i
$452$	−0.0922754	+	0.159826i	−0.00434027	+	0.00751757i
$453$		0			0
$454$			23.5238i			1.10403i
$455$	5.21690	−	3.40363i	0.244572	−	0.159565i
$456$		0			0
$457$	26.4480	−	15.2697i	1.23718	−	0.714289i	0.268666	−	0.963233i	$-0.413417\pi$
$457$	26.4480	−	15.2697i	1.23718	−	0.714289i	0.968518	+	0.248945i	$0.0800837\pi$
$458$	8.21579	+	4.74339i	0.383899	+	0.221644i
$459$		0			0
$460$	14.9306	+	5.02179i	0.696141	+	0.234142i
$461$	15.6680			0.729734			0.364867	−	0.931060i	$-0.381114\pi$
$461$	15.6680			0.729734			0.364867	+	0.931060i	$0.381114\pi$
$462$		0			0
$463$		−	32.0462i		−	1.48931i	−0.667448	−	0.744656i	$-0.732613\pi$
$463$		−	32.0462i		−	1.48931i	0.667448	−	0.744656i	$-0.267387\pi$
$464$	2.58163	−	1.49051i	0.119849	−	0.0691950i
$465$		0			0
$466$	−5.18669	+	8.98361i	−0.240269	+	0.416158i
$467$	0.605489	−	0.349579i	0.0280187	−	0.0161766i	−0.485925	−	0.874000i	$-0.661517\pi$
$467$	0.605489	−	0.349579i	0.0280187	−	0.0161766i	0.513944	+	0.857824i	$0.328184\pi$
$468$		0			0
$469$	−24.1682	+	9.62326i	−1.11599	+	0.444361i
$470$	−12.0603	−	13.6750i	−0.556302	−	0.630779i
$471$		0			0
$472$	0.452296	−	0.783400i	0.0208186	−	0.0360589i
$473$	−8.18669	+	14.1798i	−0.376424	+	0.651986i
$474$		0			0
$475$	30.6534	+	3.86155i	1.40647	+	0.177180i
$476$	−1.76855	+	12.1398i	−0.0810611	+	0.556426i
$477$		0			0
$478$	−10.7167	+	6.18728i	−0.490170	+	0.283000i
$479$	4.27280	−	7.40071i	0.195229	−	0.338147i	−0.751746	−	0.659452i	$-0.770788\pi$
$479$	4.27280	−	7.40071i	0.195229	−	0.338147i	0.946976	+	0.321305i	$0.104122\pi$
$480$		0			0
$481$	3.17302	−	1.83195i	0.144677	−	0.0835295i
$482$			12.4947i			0.569120i
$483$		0			0
$484$	−29.0731			−1.32151
$485$	−12.4598	−	4.19075i	−0.565769	−	0.190292i
$486$		0			0
$487$	20.6268	+	11.9089i	0.934689	+	0.539643i	0.888292	−	0.459280i	$-0.151892\pi$
$487$	20.6268	+	11.9089i	0.934689	+	0.539643i	0.0463978	+	0.998923i	$0.485226\pi$
$488$	−8.81047	+	5.08673i	−0.398831	+	0.230265i
$489$		0			0
$490$	−14.2052	+	6.57357i	−0.641726	+	0.296964i
$491$			12.9104i			0.582638i	0.956626	+	0.291319i	$0.0940941\pi$
$491$			12.9104i			0.582638i	−0.956626	+	0.291319i	$0.905906\pi$
$492$		0			0
$493$	−6.91124	+	11.9706i	−0.311267	+	0.539129i
$494$	−5.63436	−	3.25300i	−0.253502	−	0.146359i
$495$		0			0
$496$		−	6.31561i		−	0.283579i
$497$	29.9624	+	23.6532i	1.34400	+	1.06099i
$498$		0			0
$499$	8.16823	+	14.1478i	0.365660	+	0.633342i	0.988882	−	0.148703i	$-0.0475099\pi$
$499$	8.16823	+	14.1478i	0.365660	+	0.633342i	−0.623222	+	0.782045i	$0.714177\pi$
$500$	−11.1499	+	0.824670i	−0.498638	+	0.0368804i
$501$		0			0
$502$	−6.76522	−	11.7177i	−0.301947	−	0.522987i
$503$			28.3413i			1.26368i	0.775100	+	0.631838i	$0.217699\pi$
$503$			28.3413i			1.26368i	−0.775100	+	0.631838i	$0.782301\pi$
$504$		0			0
$505$	11.2499	−	9.92158i	0.500613	−	0.441505i
$506$	38.6208	−	22.2977i	1.71690	−	0.991254i
$507$		0			0
$508$	−5.80476	−	3.35138i	−0.257545	−	0.148693i
$509$	1.18911	+	2.05959i	0.0527062	+	0.0912898i	0.891175	−	0.453660i	$-0.149882\pi$
$509$	1.18911	+	2.05959i	0.0527062	+	0.0912898i	−0.838469	+	0.544950i	$0.816549\pi$
$510$		0			0
$511$	−8.18883	−	20.5658i	−0.362253	−	0.909776i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.82609	+	2.20899i	0.168762	+	0.0974346i
$515$	2.20043	+	10.9031i	0.0969626	+	0.480448i
$516$		0			0
$517$	−51.6189			−2.27020
$518$	−8.55360	+	3.40585i	−0.375824	+	0.149645i
$519$		0			0
$520$	2.23151	+	0.750552i	0.0978582	+	0.0329139i
$521$	−4.14185	+	7.17389i	−0.181458	+	0.314294i	−0.942377	−	0.334552i	$-0.891415\pi$
$521$	−4.14185	+	7.17389i	−0.181458	+	0.314294i	0.760919	+	0.648846i	$0.224748\pi$
$522$		0			0
$523$	−20.9308	−	36.2532i	−0.915239	−	1.58524i	−0.806550	−	0.591166i	$-0.798668\pi$
$523$	−20.9308	−	36.2532i	−0.915239	−	1.58524i	−0.108689	−	0.994076i	$-0.534665\pi$
$524$	4.48232			0.195811
$525$		0			0
$526$	−6.12635			−0.267122
$527$	14.6422	+	25.3611i	0.637826	+	1.10475i
$528$		0			0
$529$	−13.3140	+	23.0606i	−0.578871	+	1.00263i
$530$	−18.8068	−	6.32553i	−0.816915	−	0.274764i
$531$		0			0
$532$	12.8319	+	10.1299i	0.556333	+	0.439186i
$533$	−7.33877			−0.317877
$534$		0			0
$535$	−3.24660	−	16.0868i	−0.140363	−	0.695495i
$536$	−8.51497	−	4.91612i	−0.367791	−	0.212344i
$537$		0			0
$538$	−4.18740			−0.180531
$539$	−12.6427	+	42.4705i	−0.544559	+	1.82933i
$540$		0			0
$541$	−22.9652	−	39.7769i	−0.987352	−	1.71014i	−0.630978	−	0.775801i	$-0.717346\pi$
$541$	−22.9652	−	39.7769i	−0.987352	−	1.71014i	−0.356374	−	0.934343i	$-0.615987\pi$
$542$	−0.253692	−	0.146469i	−0.0108970	−	0.00629139i
$543$		0			0
$544$	−4.01562	+	2.31842i	−0.172168	+	0.0994014i
$545$	−3.35408	+	2.95806i	−0.143673	+	0.126709i
$546$		0			0
$547$			4.88688i			0.208948i	0.994528	+	0.104474i	$0.0333159\pi$
$547$			4.88688i			0.208948i	−0.994528	+	0.104474i	$0.966684\pi$
$548$	−8.78137	−	15.2098i	−0.375122	−	0.649730i
$549$		0			0
$550$	−19.1278	+	25.2182i	−0.815611	+	1.07531i
$551$	9.21004	+	15.9523i	0.392361	+	0.679589i
$552$		0			0
$553$	14.3097	+	2.08467i	0.608511	+	0.0886490i
$554$		−	14.6220i		−	0.621229i
$555$		0			0
$556$	5.21579	+	3.01134i	0.221199	+	0.127709i
$557$	−14.6839	+	25.4332i	−0.622175	+	1.07764i	0.366905	+	0.930258i	$0.380417\pi$
$557$	−14.6839	+	25.4332i	−0.622175	+	1.07764i	−0.989080	+	0.147380i	$0.952916\pi$
$558$		0			0
$559$		−	2.72332i		−	0.115184i
$560$	−5.27694	−	2.67467i	−0.222992	−	0.113026i
$561$		0			0
$562$	15.7349	−	9.08453i	0.663735	−	0.383208i
$563$	−2.37223	−	1.36961i	−0.0999775	−	0.0577220i	0.449178	−	0.893442i	$-0.351717\pi$
$563$	−2.37223	−	1.36961i	−0.0999775	−	0.0577220i	−0.549155	+	0.835720i	$0.685050\pi$
$564$		0			0
$565$	0.391137	+	0.131556i	0.0164553	+	0.00553461i
$566$	21.2133			0.891660
$567$		0			0
$568$			14.4282i			0.605396i
$569$	−0.798865	+	0.461225i	−0.0334902	+	0.0193356i	−0.516652	−	0.856196i	$-0.672822\pi$
$569$	−0.798865	+	0.461225i	−0.0334902	+	0.0193356i	0.483161	+	0.875531i	$0.339488\pi$
$570$		0			0
$571$	12.2761	−	21.2629i	0.513740	−	0.889824i	−0.486133	−	0.873885i	$-0.661593\pi$
$571$	12.2761	−	21.2629i	0.513740	−	0.889824i	0.999873	−	0.0159389i	$-0.00507372\pi$
$572$	5.77223	−	3.33260i	0.241349	−	0.139343i
$573$		0			0
$574$	18.2484	+	2.65847i	0.761675	+	0.110962i
$575$	4.40248	−	34.9474i	0.183596	−	1.45741i
$576$		0			0
$577$	−13.5667	+	23.4982i	−0.564788	+	0.978241i	0.432282	+	0.901739i	$0.357709\pi$
$577$	−13.5667	+	23.4982i	−0.564788	+	0.978241i	−0.997069	+	0.0765024i	$0.975625\pi$
$578$	2.25013	−	3.89734i	0.0935932	−	0.162108i
$579$		0			0
$580$	−4.40901	−	4.99928i	−0.183074	−	0.207584i
$581$	30.3806	+	23.9834i	1.26040	+	0.995000i
$582$		0			0
$583$	−48.6474	+	28.0866i	−2.01477	+	1.16323i
$584$	4.18333	−	7.24574i	0.173108	−	0.299831i
$585$		0			0
$586$	−6.62060	+	3.82240i	−0.273494	+	0.157902i
$587$		−	8.71353i		−	0.359646i	−0.983699	−	0.179823i	$-0.942448\pi$
$587$		−	8.71353i		−	0.359646i	0.983699	−	0.179823i	$-0.0575525\pi$
$588$		0			0
$589$	39.0250			1.60800
$590$	−1.91719	−	0.644834i	−0.0789296	−	0.0265474i
$591$		0			0
$592$	−3.01361	−	1.73991i	−0.123859	−	0.0715098i
$593$	15.8211	−	9.13432i	0.649695	−	0.375102i	−0.138644	−	0.990342i	$-0.544274\pi$
$593$	15.8211	−	9.13432i	0.649695	−	0.375102i	0.788339	+	0.615241i	$0.210941\pi$
$594$		0			0
$595$	27.3912	−	1.49370i	1.12293	−	0.0612355i
$596$			7.00381i			0.286887i
$597$		0			0
$598$	−3.70868	+	6.42363i	−0.151659	+	0.262682i
$599$	−9.94576	−	5.74219i	−0.406373	−	0.234619i	0.282857	−	0.959162i	$-0.408718\pi$
$599$	−9.94576	−	5.74219i	−0.406373	−	0.234619i	−0.689230	+	0.724543i	$0.742051\pi$
$600$		0			0
$601$			34.4022i			1.40329i	0.712525	+	0.701647i	$0.247552\pi$
$601$			34.4022i			1.40329i	−0.712525	+	0.701647i	$0.752448\pi$
$602$	−0.986520	+	6.77174i	−0.0402076	+	0.275996i
$603$		0			0
$604$	−6.43540	−	11.1464i	−0.261853	−	0.453543i
$605$	12.8607	+	63.7247i	0.522863	+	2.59078i
$606$		0			0
$607$	−22.7564	−	39.4152i	−0.923653	−	1.59981i	−0.793713	−	0.608293i	$-0.791855\pi$
$607$	−22.7564	−	39.4152i	−0.923653	−	1.59981i	−0.129941	−	0.991522i	$-0.541479\pi$
$608$			6.17914i			0.250597i
$609$		0			0
$610$	15.0469	+	17.0613i	0.609229	+	0.690792i
$611$	7.43531	−	4.29278i	0.300800	−	0.173667i
$612$		0			0
$613$	−10.1361	−	5.85205i	−0.409391	−	0.236362i	0.281137	−	0.959668i	$-0.409289\pi$
$613$	−10.1361	−	5.85205i	−0.409391	−	0.236362i	−0.690528	+	0.723306i	$0.742622\pi$
$614$	6.57805	+	11.3935i	0.265469	+	0.459805i
$615$		0			0
$616$	−15.5603	+	6.19578i	−0.626944	+	0.249635i
$617$	−24.0582			−0.968547			−0.484273	−	0.874917i	$-0.660916\pi$
$617$	−24.0582			−0.968547			−0.484273	+	0.874917i	$0.660916\pi$
$618$		0			0
$619$	3.32794	+	1.92139i	0.133761	+	0.0772271i	0.565387	−	0.824825i	$-0.308727\pi$
$619$	3.32794	+	1.92139i	0.133761	+	0.0772271i	−0.431626	+	0.902053i	$0.642060\pi$
$620$	−13.8430	+	2.79376i	−0.555950	+	0.112200i
$621$		0			0
$622$	6.26087			0.251038
$623$	10.0526	+	1.46448i	0.402749	+	0.0586733i
$624$		0			0
$625$	6.73981	+	24.0744i	0.269593	+	0.962974i
$626$	8.74065	−	15.1392i	0.349347	−	0.605086i
$627$		0			0
$628$	−5.52193	−	9.56427i	−0.220349	−	0.381656i
$629$	16.1353			0.643358
$630$		0			0
$631$	−25.4387			−1.01270			−0.506349	−	0.862328i	$-0.669005\pi$
$631$	−25.4387			−1.01270			−0.506349	+	0.862328i	$0.669005\pi$
$632$	2.73283	+	4.73340i	0.108706	+	0.188284i
$633$		0			0
$634$	0.766906	−	1.32832i	0.0304577	−	0.0527543i
$635$	−4.77803	+	14.2058i	−0.189610	+	0.563741i
$636$		0			0
$637$	−1.71089	−	7.16896i	−0.0677879	−	0.284044i
$638$	−18.8708			−0.747102
$639$		0			0
$640$	−0.442358	−	2.19188i	−0.0174857	−	0.0866415i
$641$	34.2380	+	19.7673i	1.35232	+	0.780762i	0.988574	−	0.150737i	$-0.0481647\pi$
$641$	34.2380	+	19.7673i	1.35232	+	0.780762i	0.363745	+	0.931499i	$0.381498\pi$
$642$		0			0
$643$	12.2816			0.484341			0.242170	−	0.970234i	$-0.422141\pi$
$643$	12.2816			0.484341			0.242170	+	0.970234i	$0.422141\pi$
$644$	11.5489	−	14.6294i	0.455090	−	0.576479i
$645$		0			0
$646$	−14.3258	−	24.8131i	−0.563642	−	0.976257i
$647$	−11.5956	−	6.69470i	−0.455869	−	0.263196i	0.254437	−	0.967089i	$-0.418110\pi$
$647$	−11.5956	−	6.69470i	−0.455869	−	0.263196i	−0.710306	+	0.703893i	$0.751443\pi$
$648$		0			0
$649$	−4.95918	+	2.86319i	−0.194665	+	0.112390i
$650$	0.657991	−	5.22321i	0.0258085	−	0.204871i
$651$		0			0
$652$		−	7.24574i		−	0.283765i
$653$	−24.7888	−	42.9355i	−0.970062	−	1.68020i	−0.695352	−	0.718670i	$-0.744751\pi$
$653$	−24.7888	−	42.9355i	−0.970062	−	1.68020i	−0.274710	−	0.961527i	$-0.588582\pi$
$654$		0			0
$655$	−1.98279	−	9.82469i	−0.0774741	−	0.383883i
$656$	3.48504	+	6.03626i	0.136068	+	0.235676i
$657$		0			0
$658$	−20.0435	+	7.98090i	−0.781379	+	0.311128i
$659$		−	40.7622i		−	1.58787i	−0.608002	−	0.793936i	$-0.708029\pi$
$659$		−	40.7622i		−	1.58787i	0.608002	−	0.793936i	$-0.291971\pi$
$660$		0			0
$661$	−30.9652	−	17.8778i	−1.20441	−	0.695365i	−0.242875	−	0.970057i	$-0.578091\pi$
$661$	−30.9652	−	17.8778i	−1.20441	−	0.695365i	−0.961532	+	0.274692i	$0.911424\pi$
$662$	0.756607	−	1.31048i	0.0294064	−	0.0509333i
$663$		0			0
$664$			14.6297i			0.567741i
$665$	16.5272	−	32.6069i	0.640896	−	1.26444i
$666$		0			0
$667$	18.1869	−	10.5002i	0.704199	−	0.406569i
$668$	−12.0036	−	6.93030i	−0.464435	−	0.268141i
$669$		0			0
$670$	−7.00886	+	20.8384i	−0.270776	+	0.805059i
$671$	64.4014			2.48619
$672$		0			0
$673$		−	35.1987i		−	1.35681i	−0.734687	−	0.678406i	$-0.762671\pi$
$673$		−	35.1987i		−	1.35681i	0.734687	−	0.678406i	$-0.237329\pi$
$674$	2.71987	−	1.57032i	0.104766	−	0.0604865i
$675$		0			0
$676$	5.94570	−	10.2983i	0.228681	−	0.396087i
$677$	33.2919	−	19.2211i	1.27951	−	0.738727i	0.302754	−	0.953069i	$-0.402094\pi$
$677$	33.2919	−	19.2211i	1.27951	−	0.738727i	0.976759	+	0.214341i	$0.0687605\pi$
$678$		0			0
$679$	−9.63771	+	12.2084i	−0.369862	+	0.468517i
$680$	6.85803	+	7.77617i	0.262993	+	0.298202i
$681$		0			0
$682$	−19.9900	+	34.6236i	−0.765455	+	1.32581i
$683$	−19.2012	+	33.2574i	−0.734712	+	1.27256i	0.220138	+	0.975469i	$0.429349\pi$
$683$	−19.2012	+	33.2574i	−0.734712	+	1.27256i	−0.954850	+	0.297089i	$0.903984\pi$
$684$		0			0
$685$	−29.4534	+	25.9758i	−1.12536	+	0.992486i
$686$	1.65731	+	18.4460i	0.0632764	+	0.704270i
$687$		0			0
$688$	−2.23997	+	1.29325i	−0.0853981	+	0.0493046i
$689$	4.67152	−	8.09131i	0.177971	−	0.308254i
$690$		0			0
$691$	17.6209	−	10.1735i	0.670332	−	0.387016i	−0.125870	−	0.992047i	$-0.540172\pi$
$691$	17.6209	−	10.1735i	0.670332	−	0.387016i	0.796203	+	0.605030i	$0.206839\pi$
$692$		−	0.958803i		−	0.0364482i
$693$		0			0
$694$	−27.4052			−1.04029
$695$	4.29323	−	12.7645i	0.162852	−	0.484183i
$696$		0			0
$697$	−27.9892	−	16.1595i	−1.06016	−	0.612086i
$698$	−16.9390	+	9.77972i	−0.641149	+	0.370168i
$699$		0			0
$700$	−3.52825	+	12.7496i	−0.133355	+	0.481888i
$701$			6.98574i			0.263848i	0.991260	+	0.131924i	$0.0421154\pi$
$701$			6.98574i			0.263848i	−0.991260	+	0.131924i	$0.957885\pi$
$702$		0			0
$703$	10.7511	−	18.6215i	0.405487	−	0.702323i
$704$	−5.48223	−	3.16517i	−0.206619	−	0.119292i
$705$		0			0
$706$		−	14.8103i		−	0.557393i
$707$	−6.56558	−	16.4891i	−0.246924	−	0.620135i
$708$		0			0
$709$	−6.01348	−	10.4157i	−0.225841	−	0.391168i	0.730730	−	0.682666i	$-0.239180\pi$
$709$	−6.01348	−	10.4157i	−0.225841	−	0.391168i	−0.956571	+	0.291498i	$0.905846\pi$
$710$	31.6249	−	6.38245i	1.18686	−	0.239529i
$711$		0			0
$712$	1.91982	+	3.32522i	0.0719482	+	0.124618i
$713$		−	44.4917i		−	1.66623i
$714$		0			0
$715$	−9.85803	−	11.1778i	−0.368669	−	0.418026i
$716$	−20.2531	+	11.6931i	−0.756893	+	0.436992i
$717$		0			0
$718$	14.3492	+	8.28450i	0.535507	+	0.309175i
$719$	−0.835694	−	1.44746i	−0.0311661	−	0.0539813i	0.850022	−	0.526748i	$-0.176589\pi$
$719$	−0.835694	−	1.44746i	−0.0311661	−	0.0539813i	−0.881188	+	0.472766i	$0.843255\pi$
$720$		0			0
$721$	13.0233	+	1.89727i	0.485015	+	0.0706579i
$722$	−19.1817			−0.713869
$723$		0			0
$724$	−16.7026	−	9.64324i	−0.620746	−	0.358388i
$725$	−9.00744	+	11.8755i	−0.334528	+	0.441044i
$726$		0			0
$727$	42.5043			1.57640			0.788198	−	0.615422i	$-0.211014\pi$
$727$	42.5043			1.57640			0.788198	+	0.615422i	$0.211014\pi$
$728$	1.72609	−	2.18650i	0.0639731	−	0.0810370i
$729$		0			0
$730$	−17.7323	−	5.96413i	−0.656302	−	0.220742i
$731$	5.99658	−	10.3864i	0.221792	−	0.384154i
$732$		0			0
$733$	15.9379	+	27.6053i	0.588681	+	1.01963i	0.994405	+	0.105630i	$0.0336860\pi$
$733$	15.9379	+	27.6053i	0.588681	+	1.01963i	−0.405724	+	0.913996i	$0.632981\pi$
$734$	−14.0131			−0.517233
$735$		0			0
$736$	7.04472			0.259672
$737$	31.1207	+	53.9026i	1.14634	+	1.98553i
$738$		0			0
$739$	−8.20932	+	14.2190i	−0.301985	+	0.523053i	−0.976585	−	0.215130i	$-0.930982\pi$
$739$	−8.20932	+	14.2190i	−0.301985	+	0.523053i	0.674601	+	0.738183i	$0.264316\pi$
$740$	−2.48057	+	7.37512i	−0.0911875	+	0.271115i
$741$		0			0
$742$	−14.5472	+	18.4274i	−0.534044	+	0.676493i
$743$	−4.52385			−0.165964			−0.0829821	−	0.996551i	$-0.526444\pi$
$743$	−4.52385			−0.165964			−0.0829821	+	0.996551i	$0.526444\pi$
$744$		0			0
$745$	15.3515	−	3.09819i	0.562435	−	0.113509i
$746$	−12.6630	−	7.31099i	−0.463626	−	0.267674i
$747$		0			0
$748$	29.3527			1.07324
$749$	−19.2151	−	2.79930i	−0.702106	−	0.102284i
$750$		0			0
$751$	8.69875	+	15.0667i	0.317422	+	0.549791i	0.979949	−	0.199247i	$-0.0638495\pi$
$751$	8.69875	+	15.0667i	0.317422	+	0.549791i	−0.662527	+	0.749038i	$0.730516\pi$
$752$	−7.06176	−	4.07711i	−0.257516	−	0.148677i
$753$		0			0
$754$	2.71820	−	1.56935i	0.0989908	−	0.0571524i
$755$	−21.5849	+	19.0363i	−0.785554	+	0.692803i
$756$		0			0
$757$			5.25454i			0.190980i	0.995430	+	0.0954898i	$0.0304417\pi$
$757$			5.25454i			0.190980i	−0.995430	+	0.0954898i	$0.969558\pi$
$758$	2.34072	+	4.05425i	0.0850189	+	0.147257i
$759$		0			0
$760$	13.5439	−	2.73339i	0.491289	−	0.0991505i
$761$	−7.31402	−	12.6683i	−0.265133	−	0.459224i	0.702465	−	0.711718i	$-0.252083\pi$
$761$	−7.31402	−	12.6683i	−0.265133	−	0.459224i	−0.967598	+	0.252494i	$0.918749\pi$
$762$		0			0
$763$	1.95749	+	4.91612i	0.0708659	+	0.177975i
$764$		−	2.82843i		−	0.102329i
$765$		0			0
$766$	−10.1086	−	5.83621i	−0.365239	−	0.210871i
$767$	0.476222	−	0.824840i	0.0171954	−	0.0297832i
$768$		0			0
$769$			12.4548i			0.449131i	0.974459	+	0.224566i	$0.0720963\pi$
$769$			12.4548i			0.449131i	−0.974459	+	0.224566i	$0.927904\pi$
$770$	20.4636	+	31.3656i	0.737458	+	1.13034i
$771$		0			0
$772$	−7.11634	+	4.10862i	−0.256123	+	0.147873i
$773$	−7.19300	−	4.15288i	−0.258714	−	0.149369i	0.365034	−	0.930994i	$-0.381057\pi$
$773$	−7.19300	−	4.15288i	−0.258714	−	0.149369i	−0.623748	+	0.781626i	$0.714391\pi$
$774$		0			0
$775$	12.2472	+	29.1064i	0.439931	+	1.04553i
$776$	−5.87891			−0.211041
$777$		0			0
$778$		−	13.1004i		−	0.469670i
$779$	−37.2989	+	21.5345i	−1.33637	+	0.771554i
$780$		0			0
$781$	45.6678	−	79.0990i	1.63412	−	2.83038i
$782$	−28.2889	+	16.3326i	−1.01161	+	0.584053i
$783$		0			0
$784$	−5.08412	+	4.81163i	−0.181576	+	0.171844i
$785$	−18.5210	+	16.3342i	−0.661043	+	0.582993i
$786$		0			0
$787$	−25.3036	+	43.8271i	−0.901975	+	1.56227i	−0.0770479	+	0.997027i	$0.524549\pi$
$787$	−25.3036	+	43.8271i	−0.901975	+	1.56227i	−0.824927	+	0.565239i	$0.808784\pi$
$788$	−1.75661	+	3.04253i	−0.0625765	+	0.108386i
$789$		0			0
$790$	9.16613	−	8.08388i	0.326116	−	0.287611i
$791$	0.302547	−	0.383247i	0.0107573	−	0.0136267i
$792$		0			0
$793$	−9.27652	+	5.35580i	−0.329419	+	0.190190i
$794$	−15.3402	+	26.5700i	−0.544404	+	0.942935i
$795$		0			0
$796$	3.00000	−	1.73205i	0.106332	−	0.0613909i
$797$		−	36.6354i		−	1.29769i	−0.760920	−	0.648846i	$-0.775252\pi$
$797$		−	36.6354i		−	1.29769i	0.760920	−	0.648846i	$-0.224748\pi$
$798$		0			0
$799$	37.8098			1.33761
$800$	−4.60864	+	1.93919i	−0.162940	+	0.0685606i
$801$		0			0
$802$	−6.88085	−	3.97266i	−0.242971	−	0.140280i
$803$	−45.8680	+	26.4819i	−1.61865	+	0.934525i
$804$		0			0
$805$	−37.1746	−	18.8423i	−1.31023	−	0.664104i
$806$		−	6.64969i		−	0.234225i
$807$		0			0
$808$	3.35408	−	5.80944i	0.117996	−	0.204375i
$809$	37.7055	+	21.7693i	1.32566	+	0.765368i	0.984624	−	0.174685i	$-0.0558906\pi$
$809$	37.7055	+	21.7693i	1.32566	+	0.765368i	0.341031	+	0.940052i	$0.389224\pi$
$810$		0			0
$811$		−	13.8915i		−	0.487795i	−0.969801	−	0.243897i	$-0.921574\pi$
$811$		−	13.8915i		−	0.487795i	0.969801	−	0.243897i	$-0.0784260\pi$
$812$	−7.32751	+	2.91765i	−0.257145	+	0.102390i
$813$		0			0
$814$	11.0142	+	19.0772i	0.386048	+	0.668654i
$815$	−15.8818	+	3.20521i	−0.556314	+	0.112274i
$816$		0			0
$817$	−7.99115	−	13.8411i	−0.279575	−	0.484238i
$818$		−	39.8323i		−	1.39270i
$819$		0			0
$820$	11.6891	−	10.3090i	0.408201	−	0.360004i
$821$	−8.26634	+	4.77257i	−0.288497	+	0.166564i	−0.637264	−	0.770646i	$-0.719934\pi$
$821$	−8.26634	+	4.77257i	−0.288497	+	0.166564i	0.348767	+	0.937210i	$0.386601\pi$
$822$		0			0
$823$	−9.34957	−	5.39798i	−0.325905	−	0.188162i	0.328116	−	0.944637i	$-0.393586\pi$
$823$	−9.34957	−	5.39798i	−0.325905	−	0.188162i	−0.654022	+	0.756476i	$0.726920\pi$
$824$	2.48716	+	4.30789i	0.0866444	+	0.150072i
$825$		0			0
$826$	−1.48296	+	1.87852i	−0.0515988	+	0.0653621i
$827$	10.5599			0.367204			0.183602	−	0.983001i	$-0.441224\pi$
$827$	10.5599			0.367204			0.183602	+	0.983001i	$0.441224\pi$
$828$		0			0
$829$	−30.7288	−	17.7413i	−1.06726	−	0.616181i	−0.139826	−	0.990176i	$-0.544654\pi$
$829$	−30.7288	−	17.7413i	−1.06726	−	0.616181i	−0.927431	+	0.373995i	$0.877988\pi$
$830$	32.0664	−	6.47155i	1.11304	−	0.224631i
$831$		0			0
$832$	1.05290			0.0365027
$833$	9.26051	−	31.1088i	0.320858	−	1.07786i
$834$		0			0
$835$	−9.88046	+	29.3762i	−0.341927	+	1.01660i
$836$	19.5580	−	33.8754i	0.676427	−	1.17161i
$837$		0			0
$838$	−5.51787	−	9.55723i	−0.190612	−	0.330149i
$839$	−32.5932			−1.12524			−0.562621	−	0.826715i	$-0.690207\pi$
$839$	−32.5932			−1.12524			−0.562621	+	0.826715i	$0.690207\pi$
$840$		0			0
$841$	20.1136			0.693571
$842$	3.89211	+	6.74132i	0.134131	+	0.232321i
$843$		0			0
$844$	4.98296	−	8.63074i	0.171521	−	0.297082i
$845$	−25.2026	−	8.47672i	−0.866997	−	0.291608i
$846$		0			0
$847$	76.1168	+	11.0888i	2.61540	+	0.381017i
$848$	−8.87365			−0.304722
$849$		0			0
$850$	14.0107	−	18.4718i	0.480563	−	0.633577i
$851$	−21.2300	−	12.2572i	−0.727756	−	0.420170i
$852$		0			0
$853$	−20.2310			−0.692695			−0.346347	−	0.938106i	$-0.612578\pi$
$853$	−20.2310			−0.692695			−0.346347	+	0.938106i	$0.612578\pi$
$854$	25.0070	−	9.95722i	0.855721	−	0.340729i
$855$		0			0
$856$	−3.66965	−	6.35602i	−0.125426	−	0.217244i
$857$	38.9461	+	22.4855i	1.33037	+	0.768091i	0.985357	−	0.170506i	$-0.0545402\pi$
$857$	38.9461	+	22.4855i	1.33037	+	0.768091i	0.345016	+	0.938597i	$0.387874\pi$
$858$		0			0
$859$	−37.8490	+	21.8521i	−1.29139	+	0.745585i	−0.978901	−	0.204336i	$-0.934496\pi$
$859$	−37.8490	+	21.8521i	−1.29139	+	0.745585i	−0.312490	+	0.949921i	$0.601163\pi$
$860$	3.82551	+	4.33766i	0.130449	+	0.147913i
$861$		0			0
$862$			10.2338i			0.348565i
$863$	17.8191	+	30.8636i	0.606569	+	1.05061i	0.991801	+	0.127788i	$0.0407878\pi$
$863$	17.8191	+	30.8636i	0.606569	+	1.05061i	−0.385233	+	0.922819i	$0.625879\pi$
$864$		0			0
$865$	−2.10158	+	0.424134i	−0.0714558	+	0.0144210i
$866$	−20.1951	−	34.9789i	−0.686257	−	1.18863i
$867$		0			0
$868$	−2.40885	+	16.5350i	−0.0817617	+	0.561235i
$869$		−	34.5994i		−	1.17371i
$870$		0			0
$871$	−8.96539	−	5.17617i	−0.303781	−	0.175388i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$		0			0
$874$			43.5303i			1.47243i
$875$	29.5062	+	2.09362i	0.997492	+	0.0707772i
$876$		0			0
$877$	31.6018	−	18.2453i	1.06712	−	0.616100i	0.139724	−	0.990190i	$-0.455378\pi$
$877$	31.6018	−	18.2453i	1.06712	−	0.616100i	0.927392	+	0.374091i	$0.122045\pi$
$878$	11.2331	+	6.48543i	0.379099	+	0.218873i
$879$		0			0
$880$	−4.51254	+	13.4165i	−0.152118	+	0.452270i
$881$	0.487935			0.0164390			0.00821948	−	0.999966i	$-0.497384\pi$
$881$	0.487935			0.0164390			0.00821948	+	0.999966i	$0.497384\pi$
$882$		0			0
$883$		−	6.26720i		−	0.210908i	−0.994424	−	0.105454i	$-0.966370\pi$
$883$		−	6.26720i		−	0.210908i	0.994424	−	0.105454i	$-0.0336296\pi$
$884$	−4.22804	+	2.44106i	−0.142204	+	0.0821017i
$885$		0			0
$886$	4.32751	−	7.49547i	0.145386	−	0.251815i
$887$	49.2939	−	28.4598i	1.65513	−	0.955588i	0.680210	−	0.733017i	$-0.261888\pi$
$887$	49.2939	−	28.4598i	1.65513	−	0.955588i	0.974917	−	0.222571i	$-0.0714448\pi$
$888$		0			0
$889$	13.9193	+	10.9883i	0.466838	+	0.368536i
$890$	6.43923	−	5.67894i	0.215843	−	0.190359i
$891$		0			0
$892$	5.55435	−	9.62042i	0.185973	−	0.322115i
$893$	25.1930	−	43.6356i	0.843052	−	1.46021i
$894$		0			0
$895$	34.5890	+	39.2197i	1.15618	+	1.31097i
$896$	−2.61811	−	0.381412i	−0.0874651	−	0.0127421i
$897$		0			0
$898$	22.0323	−	12.7203i	0.735226	−	0.424483i
$899$	−9.41346	+	16.3046i	−0.313957	+	0.543789i
$900$		0			0
$901$	35.6332	−	20.5728i	1.18711	−	0.685380i
$902$		−	44.1229i		−	1.46913i
$903$		0			0
$904$	0.184551			0.00613807
$905$	−13.7483	+	40.8757i	−0.457008	+	1.35876i
$906$		0			0
$907$	−14.4285	−	8.33031i	−0.479091	−	0.276603i	0.240946	−	0.970538i	$-0.422542\pi$
$907$	−14.4285	−	8.33031i	−0.479091	−	0.276603i	−0.720038	+	0.693935i	$0.755876\pi$
$908$	20.3722	−	11.7619i	0.676076	−	0.390333i
$909$		0			0
$910$	−5.55608	−	2.81616i	−0.184182	−	0.0933547i
$911$		−	8.02653i		−	0.265931i	−0.991121	−	0.132965i	$-0.957550\pi$
$911$		−	8.02653i		−	0.265931i	0.991121	−	0.132965i	$-0.0424499\pi$
$912$		0			0
$913$	46.3053	−	80.2031i	1.53248	−	2.65434i
$914$	−26.4480	−	15.2697i	−0.874821	−	0.505078i
$915$		0			0
$916$		−	9.48678i		−	0.313452i
$917$	−11.7352	−	1.70961i	−0.387532	−	0.0564563i
$918$		0			0
$919$	−6.85733	−	11.8772i	−0.226202	−	0.391794i	0.730477	−	0.682937i	$-0.239298\pi$
$919$	−6.85733	−	11.8772i	−0.226202	−	0.391794i	−0.956680	+	0.291143i	$0.905964\pi$
$920$	−3.11629	−	15.4411i	−0.102741	−	0.509080i
$921$		0			0
$922$	−7.83402	−	13.5689i	−0.258000	−	0.446869i
$923$			15.1915i			0.500033i
$924$		0			0
$925$	17.2626	+	2.17465i	0.567592	+	0.0715022i
$926$	−27.7528	+	16.0231i	−0.912014	+	0.526551i
$927$		0			0
$928$	−2.58163	−	1.49051i	−0.0847463	−	0.0489283i
$929$	−22.9480	−	39.7470i	−0.752898	−	1.30406i	−0.946413	−	0.322960i	$-0.895322\pi$
$929$	−22.9480	−	39.7470i	−0.752898	−	1.30406i	0.193515	−	0.981097i	$-0.438011\pi$
$930$		0			0
$931$	−29.7317	−	31.4154i	−0.974417	−	1.02960i
$932$	10.3734			0.339791
$933$		0			0
$934$	−0.605489	−	0.349579i	−0.0198122	−	0.0114386i
$935$	−12.9844	−	64.3375i	−0.424636	−	2.10406i
$936$		0			0
$937$	6.17552			0.201746			0.100873	−	0.994899i	$-0.467836\pi$
$937$	6.17552			0.201746			0.100873	+	0.994899i	$0.467836\pi$
$938$	20.4181	+	16.1187i	0.666675	+	0.526293i
$939$		0			0
$940$	−5.81269	+	17.2820i	−0.189589	+	0.563678i
$941$	16.7048	−	28.9335i	0.544560	−	0.943206i	−0.454074	−	0.890964i	$-0.650030\pi$
$941$	16.7048	−	28.9335i	0.544560	−	0.943206i	0.998634	−	0.0522424i	$-0.0166368\pi$
$942$		0			0
$943$	24.5511	+	42.5237i	0.799494	+	1.38476i
$944$	−0.904592			−0.0294420
$945$		0			0
$946$	16.3734			0.532345
$947$	3.27683	+	5.67563i	0.106483	+	0.184433i	0.914343	−	0.404941i	$-0.132708\pi$
$947$	3.27683	+	5.67563i	0.106483	+	0.184433i	−0.807860	+	0.589374i	$0.799375\pi$
$948$		0			0
$949$	4.40462	−	7.62903i	0.142980	−	0.247649i
$950$	−11.9825	−	28.4774i	−0.388764	−	0.923929i
$951$		0			0
$952$	11.3976	−	4.53828i	0.369399	−	0.147087i
$953$	−46.5253			−1.50710			−0.753551	−	0.657389i	$-0.771661\pi$
$953$	−46.5253			−1.50710			−0.753551	+	0.657389i	$0.771661\pi$
$954$		0			0
$955$	−6.19956	+	1.25118i	−0.200613	+	0.0404872i
$956$	10.7167	+	6.18728i	0.346602	+	0.200111i
$957$		0			0
$958$	−8.54561			−0.276096
$959$	17.1894	+	43.1703i	0.555076	+	1.39404i
$960$		0			0
$961$	4.44349	+	7.69635i	0.143338	+	0.248269i
$962$	−3.17302	−	1.83195i	−0.102302	−	0.0590643i
$963$		0			0
$964$	10.8208	−	6.24737i	0.348514	−	0.201214i
$965$	12.1536	+	13.7807i	0.391237	+	0.443615i
$966$		0			0
$967$			5.93169i			0.190750i	0.995441	+	0.0953752i	$0.0304051\pi$
$967$			5.93169i			0.190750i	−0.995441	+	0.0953752i	$0.969595\pi$
$968$	14.5366	+	25.1781i	0.467223	+	0.809253i
$969$		0			0
$970$	2.60059	+	12.8859i	0.0834998	+	0.413740i
$971$	0.170069	+	0.294568i	0.00545777	+	0.00945314i	0.868741	−	0.495266i	$-0.164929\pi$
$971$	0.170069	+	0.294568i	0.00545777	+	0.00945314i	−0.863284	+	0.504719i	$0.831596\pi$
$972$		0			0
$973$	−12.5070	−	9.87339i	−0.400955	−	0.316526i
$974$		−	23.8178i		−	0.763171i
$975$		0			0
$976$	8.81047	+	5.08673i	0.282016	+	0.162822i
$977$	10.3443	−	17.9168i	0.330943	−	0.573210i	−0.651754	−	0.758430i	$-0.725967\pi$
$977$	10.3443	−	17.9168i	0.330943	−	0.573210i	0.982697	+	0.185220i	$0.0592999\pi$
$978$		0			0
$979$		−	24.3062i		−	0.776829i
$980$	12.7955	+	9.01529i	0.408737	+	0.287983i
$981$		0			0
$982$	11.1807	−	6.45520i	0.356791	−	0.205994i
$983$	18.3821	+	10.6129i	0.586297	+	0.338499i	0.763632	−	0.645652i	$-0.223414\pi$
$983$	18.3821	+	10.6129i	0.586297	+	0.338499i	−0.177335	+	0.984151i	$0.556748\pi$
$984$		0			0
$985$	7.44590	+	2.50438i	0.237246	+	0.0797960i
$986$	13.8225			0.440197
$987$		0			0
$988$			6.50600i			0.206983i
$989$	−15.7800	+	9.11057i	−0.501774	+	0.289699i
$990$		0			0
$991$	−29.1034	+	50.4085i	−0.924499	+	1.60128i	−0.132134	+	0.991232i	$0.542183\pi$
$991$	−29.1034	+	50.4085i	−0.924499	+	1.60128i	−0.792365	+	0.610048i	$0.791150\pi$
$992$	−5.46948	+	3.15781i	−0.173656	+	0.100260i
$993$		0			0
$994$	5.50310	−	37.7748i	0.174548	−	1.19814i
$995$	−5.12351	−	5.80944i	−0.162426	−	0.184172i
$996$		0			0
$997$	−19.1416	+	33.1542i	−0.606220	+	1.05000i	0.385637	+	0.922651i	$0.373982\pi$
$997$	−19.1416	+	33.1542i	−0.606220	+	1.05000i	−0.991857	+	0.127354i	$0.959352\pi$
$998$	8.16823	−	14.1478i	0.258561	−	0.447841i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bo.a.269.8	yes	16
3.2	odd	2		630.2.bo.b.269.1	yes	16
5.2	odd	4		3150.2.bf.f.1151.14		32
5.3	odd	4		3150.2.bf.f.1151.3		32
5.4	even	2		630.2.bo.b.269.3	yes	16
7.3	odd	6		4410.2.d.b.4409.11		16
7.4	even	3		4410.2.d.b.4409.6		16
7.5	odd	6	inner	630.2.bo.a.89.6	✓	16
15.2	even	4		3150.2.bf.f.1151.4		32
15.8	even	4		3150.2.bf.f.1151.13		32
15.14	odd	2	inner	630.2.bo.a.269.6	yes	16
21.5	even	6		630.2.bo.b.89.3	yes	16
21.11	odd	6		4410.2.d.a.4409.11		16
21.17	even	6		4410.2.d.a.4409.6		16
35.4	even	6		4410.2.d.a.4409.5		16
35.12	even	12		3150.2.bf.f.1601.4		32
35.19	odd	6		630.2.bo.b.89.1	yes	16
35.24	odd	6		4410.2.d.a.4409.12		16
35.33	even	12		3150.2.bf.f.1601.15		32
105.47	odd	12		3150.2.bf.f.1601.16		32
105.59	even	6		4410.2.d.b.4409.5		16
105.68	odd	12		3150.2.bf.f.1601.3		32
105.74	odd	6		4410.2.d.b.4409.12		16
105.89	even	6	inner	630.2.bo.a.89.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.6	✓	16	7.5	odd	6	inner
630.2.bo.a.89.8	yes	16	105.89	even	6	inner
630.2.bo.a.269.6	yes	16	15.14	odd	2	inner
630.2.bo.a.269.8	yes	16	1.1	even	1	trivial
630.2.bo.b.89.1	yes	16	35.19	odd	6
630.2.bo.b.89.3	yes	16	21.5	even	6
630.2.bo.b.269.1	yes	16	3.2	odd	2
630.2.bo.b.269.3	yes	16	5.4	even	2
3150.2.bf.f.1151.3		32	5.3	odd	4
3150.2.bf.f.1151.4		32	15.2	even	4
3150.2.bf.f.1151.13		32	15.8	even	4
3150.2.bf.f.1151.14		32	5.2	odd	4
3150.2.bf.f.1601.3		32	105.68	odd	12
3150.2.bf.f.1601.4		32	35.12	even	12
3150.2.bf.f.1601.15		32	35.33	even	12
3150.2.bf.f.1601.16		32	105.47	odd	12
4410.2.d.a.4409.5		16	35.4	even	6
4410.2.d.a.4409.6		16	21.17	even	6
4410.2.d.a.4409.11		16	21.11	odd	6
4410.2.d.a.4409.12		16	35.24	odd	6
4410.2.d.b.4409.5		16	105.59	even	6
4410.2.d.b.4409.6		16	7.4	even	3
4410.2.d.b.4409.11		16	7.3	odd	6
4410.2.d.b.4409.12		16	105.74	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.11940 + 0.712845i) q^{5} +(1.63937 - 2.07665i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.11940 + 0.712845i) q^{5} +(1.63937 - 2.07665i) q^{7} +1.00000 q^{8} +(-0.442358 - 2.19188i) q^{10} +(-5.48223 - 3.16517i) q^{11} +1.05290 q^{13} +(-2.61811 - 0.381412i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.01562 + 2.31842i) q^{17} +(5.35129 - 3.08957i) q^{19} +(-1.67704 + 1.47903i) q^{20} +6.33033i q^{22} +(-3.52236 - 6.10091i) q^{23} +(3.98371 + 3.02160i) q^{25} +(-0.526449 - 0.911836i) q^{26} +(0.978745 + 2.45806i) q^{28} +2.98101i q^{29} +(5.46948 + 3.15781i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.63684i q^{34} +(4.95481 - 3.23263i) q^{35} +(3.01361 - 1.73991i) q^{37} +(-5.35129 - 3.08957i) q^{38} +(2.11940 + 0.712845i) q^{40} -6.97007 q^{41} -2.58650i q^{43} +(5.48223 - 3.16517i) q^{44} +(-3.52236 + 6.10091i) q^{46} +(7.06176 - 4.07711i) q^{47} +(-1.62493 - 6.80879i) q^{49} +(0.624933 - 4.96079i) q^{50} +(-0.526449 + 0.911836i) q^{52} +(4.43682 - 7.68480i) q^{53} +(-9.36276 - 10.6162i) q^{55} +(1.63937 - 2.07665i) q^{56} +(2.58163 - 1.49051i) q^{58} +(0.452296 - 0.783400i) q^{59} +(-8.81047 + 5.08673i) q^{61} -6.31561i q^{62} +1.00000 q^{64} +(2.23151 + 0.750552i) q^{65} +(-8.51497 - 4.91612i) q^{67} +(-4.01562 + 2.31842i) q^{68} +(-5.27694 - 2.67467i) q^{70} +14.4282i q^{71} +(4.18333 - 7.24574i) q^{73} +(-3.01361 - 1.73991i) q^{74} +6.17914i q^{76} +(-15.5603 + 6.19578i) q^{77} +(2.73283 + 4.73340i) q^{79} +(-0.442358 - 2.19188i) q^{80} +(3.48504 + 6.03626i) q^{82} +14.6297i q^{83} +(6.85803 + 7.77617i) q^{85} +(-2.23997 + 1.29325i) q^{86} +(-5.48223 - 3.16517i) q^{88} +(1.91982 + 3.32522i) q^{89} +(1.72609 - 2.18650i) q^{91} +7.04472 q^{92} +(-7.06176 - 4.07711i) q^{94} +(13.5439 - 2.73339i) q^{95} -5.87891 q^{97} +(-5.08412 + 4.81163i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8	\( 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} - 8 q^{23} - 6 q^{25} + 12 q^{31} - 8 q^{32} + 4 q^{35} - 24 q^{38} - 6 q^{40} - 8 q^{46} + 60 q^{47} - 28 q^{49} + 12 q^{50} + 16 q^{53} + 24 q^{61} + 16 q^{64} - 20 q^{65} - 14 q^{70} - 88 q^{77} + 4 q^{79} + 6 q^{80} + 64 q^{85} - 28 q^{91} + 16 q^{92} - 60 q^{94} - 12 q^{95} + 20 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 - 8 * q^23 - 6 * q^25 + 12 * q^31 - 8 * q^32 + 4 * q^35 - 24 * q^38 - 6 * q^40 - 8 * q^46 + 60 * q^47 - 28 * q^49 + 12 * q^50 + 16 * q^53 + 24 * q^61 + 16 * q^64 - 20 * q^65 - 14 * q^70 - 88 * q^77 + 4 * q^79 + 6 * q^80 + 64 * q^85 - 28 * q^91 + 16 * q^92 - 60 * q^94 - 12 * q^95 + 20 * q^98

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