LMFDB - Embedded newform 950.2.u.f.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.1
Character	$\chi$	$=$	950.99
Dual form			950.2.u.f.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 + 0.939693i) q^{2} +(-2.25357 + 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(2.39766 + 1.38429i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +O(q^{10})$	\(q+(-0.342020 + 0.939693i) q^{2} +(-2.25357 + 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(2.39766 + 1.38429i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +(-1.21064 - 2.09689i) q^{11} +(1.98176 + 1.14417i) q^{12} +(-1.70381 - 0.300428i) q^{13} +(-2.12086 + 1.77961i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-1.38022 + 3.79213i) q^{17} +2.23649i q^{18} +(-0.0664727 - 4.35839i) q^{19} +(-5.95337 - 2.16685i) q^{21} +(2.38450 - 0.420451i) q^{22} +(-5.74414 + 6.84561i) q^{23} +(-1.75297 + 1.47092i) q^{24} +(0.865049 - 1.49831i) q^{26} +(1.51309 - 0.873583i) q^{27} +(-0.946910 - 2.60161i) q^{28} +(-4.18479 + 1.52314i) q^{29} +(0.953372 - 1.65129i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(3.56150 + 4.24443i) q^{33} +(-3.09138 - 2.59397i) q^{34} +(-2.10161 - 0.764925i) q^{36} -2.89348i q^{37} +(4.11828 + 1.42819i) q^{38} +3.95905 q^{39} +(-0.808735 - 4.58656i) q^{41} +(4.07235 - 4.85323i) q^{42} +(-1.91317 - 2.28003i) q^{43} +(-0.420451 + 2.38450i) q^{44} +(-4.46815 - 7.73907i) q^{46} +(-3.39608 - 9.33064i) q^{47} +(-0.782658 - 2.15033i) q^{48} +(0.332517 + 0.575937i) q^{49} +(1.60357 - 9.09430i) q^{51} +(1.11209 + 1.32533i) q^{52} +(7.18700 - 8.56514i) q^{53} +(0.303392 + 1.72062i) q^{54} +2.76858 q^{56} +(1.88168 + 9.79554i) q^{57} -4.45336i q^{58} +(1.89474 + 0.689630i) q^{59} +(6.66844 + 5.59549i) q^{61} +(1.22563 + 1.46065i) q^{62} +(6.09783 + 1.07521i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.20657 + 1.89504i) q^{66} +(-4.61495 - 12.6795i) q^{67} +(3.49485 - 2.01775i) q^{68} +(10.2246 - 17.7096i) q^{69} +(10.2246 - 8.57949i) q^{71} +(1.43759 - 1.71325i) q^{72} +(-5.62193 + 0.991298i) q^{73} +(2.71898 + 0.989627i) q^{74} +(-2.75060 + 3.38145i) q^{76} -6.70352i q^{77} +(-1.35407 + 3.72029i) q^{78} +(-1.16772 - 6.62249i) q^{79} +(-8.20248 + 6.88270i) q^{81} +(4.58656 + 0.808735i) q^{82} +(-14.6821 - 8.47670i) q^{83} +(3.16772 + 5.48666i) q^{84} +(2.79687 - 1.01798i) q^{86} +(8.82549 - 5.09540i) q^{87} +(-2.09689 - 1.21064i) q^{88} +(-0.964193 + 5.46821i) q^{89} +(-3.66929 - 3.07890i) q^{91} +(8.80054 - 1.55177i) q^{92} +(-1.49233 + 4.10014i) q^{93} +9.92946 q^{94} +2.28834 q^{96} +(-2.63009 + 7.22610i) q^{97} +(-0.654931 + 0.115482i) q^{98} +(-4.14827 - 3.48081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 18 * q^9	$ 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	−2.25357	+	0.397366i	−1.30110	+	0.229419i	−0.780917	−	0.624635i	$-0.785248\pi$
$3$	−2.25357	+	0.397366i	−1.30110	+	0.229419i	−0.520184	+	0.854054i	$0.674137\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	0.397366	−	2.25357i	0.162224	−	0.920017i
$7$	2.39766	+	1.38429i	0.906230	+	0.523212i	0.879216	−	0.476423i	$-0.158067\pi$
$7$	2.39766	+	1.38429i	0.906230	+	0.523212i	0.0270141	+	0.999635i	$0.491400\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	2.10161	−	0.764925i	0.700538	−	0.254975i
$10$		0			0
$11$	−1.21064	−	2.09689i	−0.365022	−	0.632237i	0.623758	−	0.781618i	$-0.285605\pi$
$11$	−1.21064	−	2.09689i	−0.365022	−	0.632237i	−0.988780	+	0.149381i	$0.952272\pi$
$12$	1.98176	+	1.14417i	0.572085	+	0.330293i
$13$	−1.70381	−	0.300428i	−0.472553	−	0.0833238i	−0.0677001	−	0.997706i	$-0.521566\pi$
$13$	−1.70381	−	0.300428i	−0.472553	−	0.0833238i	−0.404853	+	0.914382i	$0.632677\pi$
$14$	−2.12086	+	1.77961i	−0.566822	+	0.475620i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.38022	+	3.79213i	−0.334753	+	0.919728i	0.652103	+	0.758130i	$0.273887\pi$
$17$	−1.38022	+	3.79213i	−0.334753	+	0.919728i	−0.986857	+	0.161597i	$0.948335\pi$
$18$			2.23649i			0.527146i
$19$	−0.0664727	−	4.35839i	−0.0152499	−	0.999884i
$19$	−0.0664727	−	4.35839i	−0.0152499	−	0.999884i
$20$		0			0
$21$	−5.95337	−	2.16685i	−1.29913	−	0.472846i
$22$	2.38450	−	0.420451i	0.508377	−	0.0896406i
$23$	−5.74414	+	6.84561i	−1.19774	+	1.42741i	−0.320568	+	0.947225i	$0.603874\pi$
$23$	−5.74414	+	6.84561i	−1.19774	+	1.42741i	−0.877169	+	0.480182i	$0.840571\pi$
$24$	−1.75297	+	1.47092i	−0.357823	+	0.300249i
$25$		0			0
$26$	0.865049	−	1.49831i	0.169650	−	0.293842i
$27$	1.51309	−	0.873583i	0.291194	−	0.168121i
$28$	−0.946910	−	2.60161i	−0.178949	−	0.491659i
$29$	−4.18479	+	1.52314i	−0.777096	+	0.282840i	−0.699961	−	0.714181i	$-0.746799\pi$
$29$	−4.18479	+	1.52314i	−0.777096	+	0.282840i	−0.0771351	+	0.997021i	$0.524577\pi$
$30$		0			0
$31$	0.953372	−	1.65129i	0.171231	−	0.296580i	−0.767620	−	0.640906i	$-0.778559\pi$
$31$	0.953372	−	1.65129i	0.171231	−	0.296580i	0.938850	+	0.344325i	$0.111892\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	3.56150	+	4.24443i	0.619978	+	0.738861i
$34$	−3.09138	−	2.59397i	−0.530167	−	0.444863i
$35$		0			0
$36$	−2.10161	−	0.764925i	−0.350269	−	0.127487i
$37$		−	2.89348i		−	0.475685i	−0.971304	−	0.237842i	$-0.923560\pi$
$37$		−	2.89348i		−	0.475685i	0.971304	−	0.237842i	$-0.0764402\pi$
$38$	4.11828	+	1.42819i	0.668074	+	0.231684i
$39$	3.95905			0.633955
$40$		0			0
$41$	−0.808735	−	4.58656i	−0.126303	−	0.716301i	−0.980525	−	0.196393i	$-0.937077\pi$
$41$	−0.808735	−	4.58656i	−0.126303	−	0.716301i	0.854222	−	0.519908i	$-0.174034\pi$
$42$	4.07235	−	4.85323i	0.628377	−	0.748870i
$43$	−1.91317	−	2.28003i	−0.291756	−	0.347702i	0.600178	−	0.799866i	$-0.295096\pi$
$43$	−1.91317	−	2.28003i	−0.291756	−	0.347702i	−0.891934	+	0.452165i	$0.850652\pi$
$44$	−0.420451	+	2.38450i	−0.0633854	+	0.359477i
$45$		0			0
$46$	−4.46815	−	7.73907i	−0.658793	−	1.14106i
$47$	−3.39608	−	9.33064i	−0.495369	−	1.36101i	−0.895706	−	0.444646i	$-0.853329\pi$
$47$	−3.39608	−	9.33064i	−0.495369	−	1.36101i	0.400338	−	0.916368i	$-0.368893\pi$
$48$	−0.782658	−	2.15033i	−0.112967	−	0.310374i
$49$	0.332517	+	0.575937i	0.0475025	+	0.0822767i
$50$		0			0
$51$	1.60357	−	9.09430i	0.224545	−	1.27346i
$52$	1.11209	+	1.32533i	0.154218	+	0.183790i
$53$	7.18700	−	8.56514i	0.987211	−	1.17651i	0.00291297	−	0.999996i	$-0.499073\pi$
$53$	7.18700	−	8.56514i	0.987211	−	1.17651i	0.984298	−	0.176516i	$-0.0564828\pi$
$54$	0.303392	+	1.72062i	0.0412865	+	0.234147i
$55$		0			0
$56$	2.76858			0.369967
$57$	1.88168	+	9.79554i	0.249234	+	1.29745i
$58$		−	4.45336i		−	0.584755i
$59$	1.89474	+	0.689630i	0.246674	+	0.0897821i	0.462399	−	0.886672i	$-0.346989\pi$
$59$	1.89474	+	0.689630i	0.246674	+	0.0897821i	−0.215724	+	0.976454i	$0.569211\pi$
$60$		0			0
$61$	6.66844	+	5.59549i	0.853806	+	0.716429i	0.960624	−	0.277850i	$-0.0896218\pi$
$61$	6.66844	+	5.59549i	0.853806	+	0.716429i	−0.106818	+	0.994279i	$0.534066\pi$
$62$	1.22563	+	1.46065i	0.155655	+	0.185503i
$63$	6.09783	+	1.07521i	0.768255	+	0.135464i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−5.20657	+	1.89504i	−0.640884	+	0.233263i
$67$	−4.61495	−	12.6795i	−0.563805	−	1.54904i	−0.814011	−	0.580850i	$-0.802720\pi$
$67$	−4.61495	−	12.6795i	−0.563805	−	1.54904i	0.250205	−	0.968193i	$-0.419502\pi$
$68$	3.49485	−	2.01775i	0.423813	−	0.244688i
$69$	10.2246	−	17.7096i	1.23090	−	2.13199i
$70$		0			0
$71$	10.2246	−	8.57949i	1.21344	−	1.01820i	0.214300	−	0.976768i	$-0.431253\pi$
$71$	10.2246	−	8.57949i	1.21344	−	1.01820i	0.999141	−	0.0414306i	$-0.0131916\pi$
$72$	1.43759	−	1.71325i	0.169421	−	0.201909i
$73$	−5.62193	+	0.991298i	−0.657997	+	0.116023i	−0.492670	−	0.870216i	$-0.663979\pi$
$73$	−5.62193	+	0.991298i	−0.657997	+	0.116023i	−0.165327	+	0.986239i	$0.552868\pi$
$74$	2.71898	+	0.989627i	0.316075	+	0.115042i
$75$		0			0
$76$	−2.75060	+	3.38145i	−0.315515	+	0.387879i
$77$		−	6.70352i		−	0.763937i
$78$	−1.35407	+	3.72029i	−0.153319	+	0.421240i
$79$	−1.16772	−	6.62249i	−0.131379	−	0.745088i	−0.977313	−	0.211800i	$-0.932067\pi$
$79$	−1.16772	−	6.62249i	−0.131379	−	0.745088i	0.845934	−	0.533288i	$-0.179044\pi$
$80$		0			0
$81$	−8.20248	+	6.88270i	−0.911387	+	0.764744i
$82$	4.58656	+	0.808735i	0.506501	+	0.0893098i
$83$	−14.6821	−	8.47670i	−1.61157	−	0.930439i	−0.989007	−	0.147866i	$-0.952760\pi$
$83$	−14.6821	−	8.47670i	−1.61157	−	0.930439i	−0.622559	−	0.782573i	$-0.713907\pi$
$84$	3.16772	+	5.48666i	0.345627	+	0.598643i
$85$		0			0
$86$	2.79687	−	1.01798i	0.301595	−	0.109771i
$87$	8.82549	−	5.09540i	0.946192	−	0.546284i
$88$	−2.09689	−	1.21064i	−0.223530	−	0.129055i
$89$	−0.964193	+	5.46821i	−0.102204	+	0.579629i	0.890096	+	0.455773i	$0.150637\pi$
$89$	−0.964193	+	5.46821i	−0.102204	+	0.579629i	−0.992300	+	0.123856i	$0.960474\pi$
$90$		0			0
$91$	−3.66929	−	3.07890i	−0.384646	−	0.322756i
$92$	8.80054	−	1.55177i	0.917520	−	0.161783i
$93$	−1.49233	+	4.10014i	−0.154747	+	0.425165i
$94$	9.92946			1.02415
$95$		0			0
$96$	2.28834			0.233553
$97$	−2.63009	+	7.22610i	−0.267045	+	0.733699i	0.731604	+	0.681730i	$0.238772\pi$
$97$	−2.63009	+	7.22610i	−0.267045	+	0.733699i	−0.998649	+	0.0519694i	$0.983450\pi$
$98$	−0.654931	+	0.115482i	−0.0661580	+	0.0116654i
$99$	−4.14827	−	3.48081i	−0.416917	−	0.349835i
$100$		0			0
$101$	−1.82471	+	10.3484i	−0.181565	+	1.02971i	0.748724	+	0.662882i	$0.230667\pi$
$101$	−1.82471	+	10.3484i	−0.181565	+	1.02971i	−0.930289	+	0.366826i	$0.880444\pi$
$102$	7.99740	+	4.61730i	0.791860	+	0.457181i
$103$	8.92940	−	5.15539i	0.879840	−	0.507976i	0.00923425	−	0.999957i	$-0.497061\pi$
$103$	8.92940	−	5.15539i	0.879840	−	0.507976i	0.870606	+	0.491982i	$0.163727\pi$
$104$	−1.62576	+	0.591728i	−0.159419	+	0.0580237i
$105$		0			0
$106$	5.59050	+	9.68302i	0.542997	+	0.940498i
$107$	6.09138	+	3.51686i	0.588876	+	0.339987i	0.764653	−	0.644442i	$-0.222910\pi$
$107$	6.09138	+	3.51686i	0.588876	+	0.339987i	−0.175777	+	0.984430i	$0.556244\pi$
$108$	−1.72062	−	0.303392i	−0.165567	−	0.0291939i
$109$	−4.78492	+	4.01503i	−0.458312	+	0.384570i	−0.842510	−	0.538681i	$-0.818923\pi$
$109$	−4.78492	+	4.01503i	−0.458312	+	0.384570i	0.384197	+	0.923251i	$0.374478\pi$
$110$		0			0
$111$	1.14977	+	6.52066i	0.109131	+	0.618914i
$112$	−0.946910	+	2.60161i	−0.0894746	+	0.245829i
$113$		−	7.50521i		−	0.706031i	−0.935618	−	0.353015i	$-0.885156\pi$
$113$		−	7.50521i		−	0.706031i	0.935618	−	0.353015i	$-0.114844\pi$
$114$	−9.84837	−	1.58207i	−0.922384	−	0.148175i
$115$		0			0
$116$	4.18479	+	1.52314i	0.388548	+	0.141420i
$117$	−3.81056	+	0.671905i	−0.352287	+	0.0621177i
$118$	−1.29608	+	1.54461i	−0.119314	+	0.142193i
$119$	−8.55872	+	7.18162i	−0.784577	+	0.658338i
$120$		0			0
$121$	2.56869	−	4.44911i	0.233518	−	0.404464i
$122$	−7.53878	+	4.35252i	−0.682529	+	0.394058i
$123$	3.64509	+	10.0148i	0.328666	+	0.903003i
$124$	−1.79175	+	0.652145i	−0.160904	+	0.0585644i
$125$		0			0
$126$	−3.09595	+	5.36235i	−0.275809	+	0.477716i
$127$	−12.8097	−	2.25870i	−1.13668	−	0.200427i	−0.426526	−	0.904476i	$-0.640263\pi$
$127$	−12.8097	−	2.25870i	−1.13668	−	0.200427i	−0.710152	+	0.704049i	$0.751374\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	5.21748	+	4.37799i	0.459374	+	0.385460i
$130$		0			0
$131$	−4.41978	−	1.60867i	−0.386158	−	0.140550i	0.141643	−	0.989918i	$-0.454761\pi$
$131$	−4.41978	−	1.60867i	−0.386158	−	0.140550i	−0.527802	+	0.849368i	$0.676984\pi$
$132$		−	5.54072i		−	0.482257i
$133$	5.87390	−	10.5420i	0.509332	−	0.914104i
$134$	13.4932			1.16564
$135$		0			0
$136$	0.700758	+	3.97420i	0.0600895	+	0.340785i
$137$	−14.1629	+	16.8787i	−1.21002	+	1.44204i	−0.346258	+	0.938139i	$0.612548\pi$
$137$	−14.1629	+	16.8787i	−1.21002	+	1.44204i	−0.863760	+	0.503903i	$0.831897\pi$
$138$	13.1445	+	15.6651i	1.11894	+	1.33350i
$139$	2.26902	−	12.8682i	0.192456	−	1.09147i	−0.723540	−	0.690282i	$-0.757486\pi$
$139$	2.26902	−	12.8682i	0.192456	−	1.09147i	0.915996	−	0.401188i	$-0.131403\pi$
$140$		0			0
$141$	11.3610	+	19.6778i	0.956767	+	1.65717i
$142$	4.56505	+	12.5424i	0.383091	+	1.05253i
$143$	1.43274	+	3.93643i	0.119812	+	0.329180i
$144$	1.11825	+	1.93686i	0.0931871	+	0.161405i
$145$		0			0
$146$	0.991298	−	5.62193i	0.0820404	−	0.465274i
$147$	−0.978209	−	1.16578i	−0.0806813	−	0.0961523i
$148$	−1.85989	+	2.21653i	−0.152882	+	0.182198i
$149$	−0.359724	−	2.04010i	−0.0294697	−	0.167131i	0.966521	−	0.256587i	$-0.0825982\pi$
$149$	−0.359724	−	2.04010i	−0.0294697	−	0.167131i	−0.995991	+	0.0894563i	$0.971487\pi$
$150$		0			0
$151$	−3.55532			−0.289328			−0.144664	−	0.989481i	$-0.546210\pi$
$151$	−3.55532			−0.289328			−0.144664	+	0.989481i	$0.546210\pi$
$152$	−2.23676	−	3.74124i	−0.181425	−	0.303455i
$153$			9.02537i			0.729658i
$154$	6.29925	+	2.29274i	0.507608	+	0.184754i
$155$		0			0
$156$	−3.03281	−	2.54483i	−0.242819	−	0.203749i
$157$	−5.92056	−	7.05585i	−0.472512	−	0.563118i	0.476168	−	0.879354i	$-0.342025\pi$
$157$	−5.92056	−	7.05585i	−0.472512	−	0.563118i	−0.948681	+	0.316236i	$0.897581\pi$
$158$	6.62249	+	1.16772i	0.526857	+	0.0928991i
$159$	−12.7929	+	22.1580i	−1.01455	+	1.75725i
$160$		0			0
$161$	−23.2488	+	8.46188i	−1.83226	+	0.666889i
$162$	−3.66221	−	10.0618i	−0.287730	−	0.790532i
$163$	17.5880	−	10.1545i	1.37760	−	0.795359i	0.385731	−	0.922611i	$-0.373949\pi$
$163$	17.5880	−	10.1545i	1.37760	−	0.795359i	0.991870	+	0.127253i	$0.0406159\pi$
$164$	−2.32866	+	4.03336i	−0.181838	+	0.314952i
$165$		0			0
$166$	12.9871	−	10.8974i	1.00799	−	0.845805i
$167$	−7.00352	+	8.34647i	−0.541949	+	0.645869i	−0.965623	−	0.259945i	$-0.916296\pi$
$167$	−7.00352	+	8.34647i	−0.541949	+	0.645869i	0.423675	+	0.905814i	$0.360740\pi$
$168$	−6.23920	+	1.10014i	−0.481364	+	0.0848775i
$169$	−9.40328	−	3.42251i	−0.723329	−	0.263270i
$170$		0			0
$171$	−3.47354	−	9.10881i	−0.265628	−	0.696568i
$172$			2.97637i			0.226946i
$173$	−5.71759	+	15.7089i	−0.434700	+	1.19433i	0.508196	+	0.861242i	$0.330313\pi$
$173$	−5.71759	+	15.7089i	−0.434700	+	1.19433i	−0.942896	+	0.333087i	$0.891910\pi$
$174$	1.76961	+	10.0360i	0.134154	+	0.760826i
$175$		0			0
$176$	1.85481	−	1.55637i	0.139812	−	0.117316i
$177$	−4.54397	−	0.801225i	−0.341546	−	0.0602238i
$178$	−4.80866	−	2.77628i	−0.360424	−	0.208091i
$179$	−12.7705	−	22.1191i	−0.954510	−	1.65326i	−0.735486	−	0.677540i	$-0.763046\pi$
$179$	−12.7705	−	22.1191i	−0.954510	−	1.65326i	−0.219024	−	0.975719i	$-0.570287\pi$
$180$		0			0
$181$	−1.96483	+	0.715139i	−0.146044	+	0.0531558i	−0.414008	−	0.910273i	$-0.635872\pi$
$181$	−1.96483	+	0.715139i	−0.146044	+	0.0531558i	0.267964	+	0.963429i	$0.413649\pi$
$182$	4.14819	−	2.39496i	0.307484	−	0.177526i
$183$	−17.2513	−	9.96003i	−1.27525	−	0.736266i
$184$	−1.55177	+	8.80054i	−0.114398	+	0.648784i
$185$		0			0
$186$	−3.34246	−	2.80466i	−0.245081	−	0.205648i
$187$	9.62266	−	1.69673i	0.703678	−	0.124077i
$188$	−3.39608	+	9.33064i	−0.247684	+	0.680507i
$189$	4.83717			0.351852
$190$		0			0
$191$	12.9071			0.933924			0.466962	−	0.884278i	$-0.345349\pi$
$191$	12.9071			0.933924			0.466962	+	0.884278i	$0.345349\pi$
$192$	−0.782658	+	2.15033i	−0.0564835	+	0.155187i
$193$	21.1670	−	3.73231i	1.52363	−	0.268657i	0.651772	−	0.758415i	$-0.274026\pi$
$193$	21.1670	−	3.73231i	1.52363	−	0.268657i	0.871859	+	0.489757i	$0.162915\pi$
$194$	−5.89077	−	4.94294i	−0.422933	−	0.354883i
$195$		0			0
$196$	0.115482	−	0.654931i	0.00824871	−	0.0467808i
$197$	−9.82570	−	5.67287i	−0.700052	−	0.404175i	0.107315	−	0.994225i	$-0.465775\pi$
$197$	−9.82570	−	5.67287i	−0.700052	−	0.404175i	−0.807367	+	0.590050i	$0.799108\pi$
$198$	4.68968	−	2.70759i	0.333281	−	0.192420i
$199$	−12.7763	+	4.65019i	−0.905688	+	0.329643i	−0.752530	−	0.658558i	$-0.771167\pi$
$199$	−12.7763	+	4.65019i	−0.905688	+	0.329643i	−0.153158	+	0.988202i	$0.548944\pi$
$200$		0			0
$201$	15.4385	+	26.7403i	1.08895	+	1.88611i
$202$	−9.10027	−	5.25404i	−0.640292	−	0.369673i
$203$	−12.1422	−	2.14099i	−0.852214	−	0.150268i
$204$	−7.07411	+	5.93589i	−0.495287	+	0.415595i
$205$		0			0
$206$	1.79045	+	10.1541i	0.124746	+	0.707472i
$207$	−6.83560	+	18.7807i	−0.475107	+	1.30535i
$208$		−	1.73010i		−	0.119961i
$209$	−9.05861	+	5.41584i	−0.626597	+	0.374621i
$210$		0			0
$211$	−4.18459	−	1.52307i	−0.288079	−	0.104852i	0.193939	−	0.981014i	$-0.437874\pi$
$211$	−4.18459	−	1.52307i	−0.288079	−	0.104852i	−0.482018	+	0.876161i	$0.660096\pi$
$212$	−11.0111	+	1.94156i	−0.756247	+	0.133347i
$213$	−19.6328	+	23.3974i	−1.34522	+	1.60317i
$214$	−5.38814	+	4.52119i	−0.368326	+	0.309062i
$215$		0			0
$216$	0.873583	−	1.51309i	0.0594398	−	0.102953i
$217$	4.57173	−	2.63949i	0.310349	−	0.179180i
$218$	−2.13635	−	5.86958i	−0.144692	−	0.397538i
$219$	12.2755	−	4.46792i	0.829503	−	0.301914i
$220$		0			0
$221$	3.49091	−	6.04643i	0.234824	−	0.406727i
$222$	−6.52066	−	1.14977i	−0.437638	−	0.0771674i
$223$	−12.7480	−	15.1924i	−0.853667	−	1.01736i	−0.999606	−	0.0280676i	$-0.991065\pi$
$223$	−12.7480	−	15.1924i	−0.853667	−	1.01736i	0.145939	−	0.989294i	$-0.453380\pi$
$224$	−2.12086	−	1.77961i	−0.141706	−	0.118905i
$225$		0			0
$226$	7.05259	+	2.56693i	0.469131	+	0.170750i
$227$			12.8345i			0.851857i	0.904757	+	0.425928i	$0.140052\pi$
$227$			12.8345i			0.851857i	−0.904757	+	0.425928i	$0.859948\pi$
$228$	4.85500	−	8.71334i	0.321531	−	0.577055i
$229$	11.4892			0.759230			0.379615	−	0.925145i	$-0.376056\pi$
$229$	11.4892			0.759230			0.379615	+	0.925145i	$0.376056\pi$
$230$		0			0
$231$	2.66375	+	15.1069i	0.175262	+	0.993959i
$232$	−2.86257	+	3.41147i	−0.187937	+	0.223974i
$233$	−1.75412	−	2.09048i	−0.114916	−	0.136952i	0.705520	−	0.708690i	$-0.250714\pi$
$233$	−1.75412	−	2.09048i	−0.114916	−	0.136952i	−0.820436	+	0.571738i	$0.806269\pi$
$234$	0.671905	−	3.81056i	0.0439238	−	0.249104i
$235$		0			0
$236$	−1.00817	−	1.74620i	−0.0656264	−	0.113668i
$237$	5.26310	+	14.4602i	0.341875	+	0.939294i
$238$	−3.82126	−	10.4988i	−0.247696	−	0.680538i
$239$	12.5128	+	21.6728i	0.809386	+	1.40190i	0.913290	+	0.407310i	$0.133533\pi$
$239$	12.5128	+	21.6728i	0.809386	+	1.40190i	−0.103904	+	0.994587i	$0.533133\pi$
$240$		0			0
$241$	4.37954	−	24.8376i	0.282111	−	1.59993i	−0.433316	−	0.901242i	$-0.642656\pi$
$241$	4.37954	−	24.8376i	0.282111	−	1.59993i	0.715426	−	0.698688i	$-0.246232\pi$
$242$	3.30225	+	3.93547i	0.212277	+	0.252981i
$243$	12.3808	−	14.7548i	0.794227	−	0.946523i
$244$	−1.51161	−	8.57278i	−0.0967711	−	0.548816i
$245$		0			0
$246$	−10.6575			−0.679499
$247$	−1.19613	+	7.44586i	−0.0761077	+	0.473769i
$248$		−	1.90674i		−	0.121078i
$249$	36.4555	+	13.2687i	2.31027	+	0.840870i
$250$		0			0
$251$	−2.55784	−	2.14629i	−0.161450	−	0.135472i	0.558484	−	0.829515i	$-0.311383\pi$
$251$	−2.55784	−	2.14629i	−0.161450	−	0.135472i	−0.719933	+	0.694043i	$0.755828\pi$
$252$	−3.98008	−	4.74327i	−0.250721	−	0.298798i
$253$	21.3086	+	3.75728i	1.33966	+	0.236218i
$254$	6.50366	−	11.2647i	0.408076	−	0.706808i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−3.24404	−	8.91294i	−0.202358	−	0.555974i	0.796454	−	0.604699i	$-0.206706\pi$
$257$	−3.24404	−	8.91294i	−0.202358	−	0.555974i	−0.998812	+	0.0487248i	$0.984484\pi$
$258$	−5.89845	+	3.40547i	−0.367221	+	0.212015i
$259$	4.00541	−	6.93758i	0.248884	−	0.431080i
$260$		0			0
$261$	−7.62973	+	6.40210i	−0.472268	+	0.396280i
$262$	3.02331	−	3.60304i	0.186781	−	0.222597i
$263$	−27.8496	+	4.91064i	−1.71728	+	0.302803i	−0.943677	−	0.330868i	$-0.892659\pi$
$263$	−27.8496	+	4.91064i	−1.71728	+	0.302803i	−0.773603	+	0.633671i	$0.781547\pi$
$264$	5.20657	+	1.89504i	0.320442	+	0.116631i
$265$		0			0
$266$	7.89721	+	9.12522i	0.484209	+	0.559503i
$267$		−	12.7061i		−	0.777603i
$268$	−4.61495	+	12.6795i	−0.281903	+	0.774521i
$269$	0.907359	+	5.14589i	0.0553227	+	0.313750i	0.999894	−	0.0145556i	$-0.00463336\pi$
$269$	0.907359	+	5.14589i	0.0553227	+	0.313750i	−0.944571	+	0.328306i	$0.893522\pi$
$270$		0			0
$271$	0.277215	−	0.232611i	0.0168396	−	0.0141301i	−0.634329	−	0.773063i	$-0.718724\pi$
$271$	0.277215	−	0.232611i	0.0168396	−	0.0141301i	0.651169	+	0.758933i	$0.274279\pi$
$272$	−3.97420	−	0.700758i	−0.240971	−	0.0424897i
$273$	9.49245	+	5.48047i	0.574509	+	0.331693i
$274$	−11.0168	−	19.0816i	−0.665548	−	1.15276i
$275$		0			0
$276$	−19.2160	+	6.99407i	−1.15667	+	0.420993i
$277$	11.3195	−	6.53530i	0.680121	−	0.392668i	−0.119779	−	0.992801i	$-0.538219\pi$
$277$	11.3195	−	6.53530i	0.680121	−	0.392668i	0.799901	+	0.600132i	$0.204885\pi$
$278$	11.3161	+	6.53338i	0.678697	+	0.391846i
$279$	0.740508	−	4.19963i	0.0443331	−	0.251425i
$280$		0			0
$281$	7.77732	+	6.52595i	0.463956	+	0.389305i	0.844584	−	0.535423i	$-0.179848\pi$
$281$	7.77732	+	6.52595i	0.463956	+	0.389305i	−0.380628	+	0.924728i	$0.624292\pi$
$282$	−22.3768	+	3.94563i	−1.33252	+	0.234959i
$283$	−3.51037	+	9.64467i	−0.208670	+	0.573316i	−0.999237	−	0.0390595i	$-0.987564\pi$
$283$	−3.51037	+	9.64467i	−0.208670	+	0.573316i	0.790567	+	0.612376i	$0.209786\pi$
$284$	−13.3473			−0.792018
$285$		0			0
$286$	−4.18906			−0.247704
$287$	4.41006	−	12.1165i	0.260318	−	0.715217i
$288$	−2.20251	+	0.388363i	−0.129784	+	0.0228845i
$289$	0.547493	+	0.459401i	0.0322054	+	0.0270236i
$290$		0			0
$291$	3.05568	−	17.3296i	0.179127	−	1.01588i
$292$	4.94384	+	2.85433i	0.289316	+	0.167037i
$293$	−6.18499	+	3.57090i	−0.361331	+	0.208614i	−0.669664	−	0.742664i	$-0.733562\pi$
$293$	−6.18499	+	3.57090i	−0.361331	+	0.208614i	0.308334	+	0.951278i	$0.400229\pi$
$294$	1.43005	−	0.520494i	0.0834020	−	0.0303558i
$295$		0			0
$296$	−1.44674	−	2.50582i	−0.0840900	−	0.145648i
$297$	−3.66362	−	2.11519i	−0.212585	−	0.122736i
$298$	2.04010	+	0.359724i	0.118180	+	0.0208383i
$299$	11.8436	−	9.93793i	0.684931	−	0.574725i
$300$		0			0
$301$	−1.43092	−	8.11513i	−0.0824766	−	0.467748i
$302$	1.21599	−	3.34091i	0.0699725	−	0.192248i
$303$		−	24.0460i		−	1.38141i
$304$	4.28064	−	0.822290i	0.245511	−	0.0471615i
$305$		0			0
$306$	−8.48107	−	3.08686i	−0.484831	−	0.176464i
$307$	−10.6573	+	1.87916i	−0.608242	+	0.107250i	−0.469282	−	0.883048i	$-0.655487\pi$
$307$	−10.6573	+	1.87916i	−0.608242	+	0.107250i	−0.138960	+	0.990298i	$0.544376\pi$
$308$	−4.30894	+	5.13519i	−0.245524	+	0.292605i
$309$	−18.0745	+	15.1663i	−1.02822	+	0.862780i
$310$		0			0
$311$	−13.1789	+	22.8265i	−0.747307	+	1.29437i	0.201802	+	0.979426i	$0.435320\pi$
$311$	−13.1789	+	22.8265i	−0.747307	+	1.29437i	−0.949109	+	0.314947i	$0.898013\pi$
$312$	3.42864	−	1.97952i	0.194108	−	0.112068i
$313$	10.3207	+	28.3558i	0.583358	+	1.60276i	0.782403	+	0.622772i	$0.213994\pi$
$313$	10.3207	+	28.3558i	0.583358	+	1.60276i	−0.199046	+	0.979990i	$0.563784\pi$
$314$	8.65528	−	3.15027i	0.488446	−	0.177780i
$315$		0			0
$316$	−3.36233	+	5.82372i	−0.189146	+	0.327610i
$317$	11.7732	+	2.07593i	0.661248	+	0.116596i	0.494194	−	0.869352i	$-0.335463\pi$
$317$	11.7732	+	2.07593i	0.661248	+	0.116596i	0.167054	+	0.985948i	$0.446575\pi$
$318$	−16.4463	−	19.5999i	−0.922262	−	1.09911i
$319$	8.26015	+	6.93109i	0.462479	+	0.388066i
$320$		0			0
$321$	−15.1248	−	5.50499i	−0.844186	−	0.307259i
$322$		−	24.7409i		−	1.37875i
$323$	16.6194	+	5.76348i	0.924726	+	0.320689i
$324$	10.7076			0.594866
$325$		0			0
$326$	3.52661	+	20.0004i	0.195321	+	1.10772i
$327$	9.18774	−	10.9495i	0.508083	−	0.605510i
$328$	−2.99367	−	3.56771i	−0.165298	−	0.196994i
$329$	4.77368	−	27.0729i	0.263181	−	1.49258i
$330$		0			0
$331$	14.4811	+	25.0820i	0.795954	+	1.37863i	0.922232	+	0.386638i	$0.126364\pi$
$331$	14.4811	+	25.0820i	0.795954	+	1.37863i	−0.126277	+	0.991995i	$0.540303\pi$
$332$	5.79840	+	15.9310i	0.318229	+	0.874326i
$333$	−2.21329	−	6.08097i	−0.121288	−	0.333235i
$334$	−5.44777	−	9.43582i	−0.298089	−	0.516305i
$335$		0			0
$336$	1.10014	−	6.23920i	0.0600175	−	0.340376i
$337$	2.86591	+	3.41545i	0.156116	+	0.186052i	0.838433	−	0.545005i	$-0.183472\pi$
$337$	2.86591	+	3.41545i	0.156116	+	0.186052i	−0.682317	+	0.731056i	$0.739028\pi$
$338$	6.43222	−	7.66562i	0.349867	−	0.416955i
$339$	2.98231	+	16.9135i	0.161977	+	0.918617i
$340$		0			0
$341$	−4.61677			−0.250012
$342$	9.74750	−	0.148666i	0.527085	−	0.00803892i
$343$		−	17.5389i		−	0.947009i
$344$	−2.79687	−	1.01798i	−0.150797	−	0.0548857i
$345$		0			0
$346$	−12.8061	−	10.7456i	−0.688458	−	0.577684i
$347$	−16.6023	−	19.7859i	−0.891260	−	1.06216i	−0.997696	−	0.0678428i	$-0.978388\pi$
$347$	−16.6023	−	19.7859i	−0.891260	−	1.06216i	0.106436	−	0.994320i	$-0.466056\pi$
$348$	−10.0360	−	1.76961i	−0.537985	−	0.0948613i
$349$	−10.9499	+	18.9659i	−0.586137	+	1.01522i	0.408595	+	0.912716i	$0.366019\pi$
$349$	−10.9499	+	18.9659i	−0.586137	+	1.01522i	−0.994733	+	0.102504i	$0.967315\pi$
$350$		0			0
$351$	−2.84047	+	1.03385i	−0.151613	+	0.0551827i
$352$	0.828128	+	2.27526i	0.0441394	+	0.121272i
$353$	−11.0320	+	6.36930i	−0.587172	+	0.339004i	−0.763978	−	0.645242i	$-0.776757\pi$
$353$	−11.0320	+	6.36930i	−0.587172	+	0.339004i	0.176807	+	0.984246i	$0.443423\pi$
$354$	2.30704	−	3.99590i	0.122618	−	0.212380i
$355$		0			0
$356$	4.25351	−	3.56912i	0.225436	−	0.189163i
$357$	16.4340	−	19.5852i	0.869778	−	1.03656i
$358$	25.1529	−	4.43514i	1.32937	−	0.234404i
$359$	23.3776	+	8.50877i	1.23382	+	0.449075i	0.874906	−	0.484293i	$-0.160923\pi$
$359$	23.3776	+	8.50877i	1.23382	+	0.449075i	0.358919	+	0.933369i	$0.383145\pi$
$360$		0			0
$361$	−18.9912	+	0.579428i	−0.999535	+	0.0304962i
$362$		−	2.09093i		−	0.109897i
$363$	−4.02081	+	11.0471i	−0.211038	+	0.579822i
$364$	0.831760	+	4.71714i	0.0435961	+	0.247246i
$365$		0			0
$366$	15.2596	−	12.8044i	0.797635	−	0.669295i
$367$	10.9168	+	1.92492i	0.569851	+	0.100480i	0.451147	−	0.892450i	$-0.351015\pi$
$367$	10.9168	+	1.92492i	0.569851	+	0.100480i	0.118704	+	0.992930i	$0.462126\pi$
$368$	−7.73907	−	4.46815i	−0.403427	−	0.232919i
$369$	−5.20803	−	9.02056i	−0.271119	−	0.469592i
$370$		0			0
$371$	29.0886	−	10.5874i	1.51021	−	0.549670i
$372$	3.77871	−	2.18164i	0.195917	−	0.113113i
$373$	29.0060	+	16.7466i	1.50188	+	0.867108i	0.999998	+	0.00216955i	$0.000690590\pi$
$373$	29.0060	+	16.7466i	1.50188	+	0.867108i	0.501878	+	0.864939i	$0.332643\pi$
$374$	−1.69673	+	9.62266i	−0.0877360	+	0.497576i
$375$		0			0
$376$	−7.60641	−	6.38254i	−0.392271	−	0.329154i
$377$	7.58770	−	1.33792i	0.390786	−	0.0689062i
$378$	−1.65441	+	4.54545i	−0.0850937	+	0.233793i
$379$	−13.5486			−0.695946			−0.347973	−	0.937504i	$-0.613130\pi$
$379$	−13.5486			−0.695946			−0.347973	+	0.937504i	$0.613130\pi$
$380$		0			0
$381$	29.7651			1.52491
$382$	−4.41448	+	12.1287i	−0.225865	+	0.620558i
$383$	−37.7833	+	6.66222i	−1.93064	+	0.340423i	−0.999694	−	0.0247406i	$-0.992124\pi$
$383$	−37.7833	+	6.66222i	−1.93064	+	0.340423i	−0.930943	+	0.365164i	$0.881013\pi$
$384$	−1.75297	−	1.47092i	−0.0894558	−	0.0750623i
$385$		0			0
$386$	−3.73231	+	21.1670i	−0.189969	+	1.07737i
$387$	−5.76481	−	3.32831i	−0.293042	−	0.169188i
$388$	6.65961	−	3.84493i	0.338090	−	0.195197i
$389$	12.5980	−	4.58528i	0.638742	−	0.232483i	−0.00228971	−	0.999997i	$-0.500729\pi$
$389$	12.5980	−	4.58528i	0.638742	−	0.232483i	0.641032	+	0.767514i	$0.278507\pi$
$390$		0			0
$391$	−18.0312	−	31.2310i	−0.911879	−	1.57942i
$392$	0.575937	+	0.332517i	0.0290892	+	0.0167947i
$393$	10.5995	+	1.86898i	0.534676	+	0.0942778i
$394$	8.69134	−	7.29290i	0.437863	−	0.367411i
$395$		0			0
$396$	0.940336	+	5.33291i	0.0472537	+	0.267989i
$397$	10.3175	−	28.3472i	0.517822	−	1.42270i	−0.355094	−	0.934831i	$-0.615551\pi$
$397$	10.3175	−	28.3472i	0.517822	−	1.42270i	0.872915	−	0.487872i	$-0.162227\pi$
$398$		−	13.5963i		−	0.681519i
$399$	−9.04825	+	26.0912i	−0.452979	+	1.30619i
$400$		0			0
$401$	−9.60460	−	3.49579i	−0.479631	−	0.174571i	0.0908794	−	0.995862i	$-0.471032\pi$
$401$	−9.60460	−	3.49579i	−0.479631	−	0.174571i	−0.570510	+	0.821291i	$0.693254\pi$
$402$	−30.4079	+	5.36174i	−1.51661	+	0.267419i
$403$	−2.12046	+	2.52707i	−0.105628	+	0.125882i
$404$	8.04966	−	6.75447i	0.400485	−	0.336047i
$405$		0			0
$406$	6.16475	−	10.6777i	0.305951	−	0.529923i
$407$	−6.06731	+	3.50296i	−0.300745	+	0.173635i
$408$	−3.15842	−	8.67768i	−0.156365	−	0.429609i
$409$	−23.6095	+	8.59314i	−1.16741	+	0.424904i	−0.851740	−	0.523964i	$-0.824452\pi$
$409$	−23.6095	+	8.59314i	−1.16741	+	0.424904i	−0.315673	+	0.948868i	$0.602230\pi$
$410$		0			0
$411$	25.2101	−	43.6652i	1.24352	−	2.15384i
$412$	−10.1541	−	1.79045i	−0.500258	−	0.0882091i
$413$	3.58830	+	4.27637i	0.176569	+	0.210426i
$414$	−15.3101	−	12.8467i	−0.752452	−	0.631382i
$415$		0			0
$416$	1.62576	+	0.591728i	0.0797094	+	0.0290119i
$417$			29.9012i			1.46427i
$418$	−1.99100	−	10.3646i	−0.0973828	−	0.506951i
$419$	4.75112			0.232107			0.116054	−	0.993243i	$-0.462976\pi$
$419$	4.75112			0.232107			0.116054	+	0.993243i	$0.462976\pi$
$420$		0			0
$421$	2.00373	+	11.3637i	0.0976559	+	0.553834i	0.993901	+	0.110275i	$0.0351732\pi$
$421$	2.00373	+	11.3637i	0.0976559	+	0.553834i	−0.896245	+	0.443559i	$0.853716\pi$
$422$	2.86243	−	3.41131i	0.139341	−	0.166060i
$423$	−14.2745	−	17.0117i	−0.694049	−	0.827136i
$424$	1.94156	−	11.0111i	0.0942904	−	0.534748i
$425$		0			0
$426$	−15.2716	−	26.4512i	−0.739911	−	1.28156i
$427$	8.24288	+	22.6471i	0.398901	+	1.09597i
$428$	−2.40567	−	6.60953i	−0.116283	−	0.319484i
$429$	−4.79299	−	8.30170i	−0.231408	−	0.400810i
$430$		0			0
$431$	1.50718	−	8.54765i	0.0725984	−	0.411726i	−0.926752	−	0.375675i	$-0.877411\pi$
$431$	1.50718	−	8.54765i	0.0725984	−	0.411726i	0.999350	−	0.0360511i	$-0.0114779\pi$
$432$	1.12306	+	1.33841i	0.0540331	+	0.0643942i
$433$	−0.838704	+	0.999529i	−0.0403056	+	0.0480343i	−0.785821	−	0.618454i	$-0.787759\pi$
$433$	−0.838704	+	0.999529i	−0.0403056	+	0.0480343i	0.745515	+	0.666489i	$0.232204\pi$
$434$	0.916684	+	5.19878i	0.0440023	+	0.249549i
$435$		0			0
$436$	6.24627			0.299142
$437$	30.2177	+	24.5802i	1.44551	+	1.17583i
$438$			13.0633i			0.624190i
$439$	−21.7294	−	7.90886i	−1.03709	−	0.377469i	−0.233313	−	0.972402i	$-0.574957\pi$
$439$	−21.7294	−	7.90886i	−1.03709	−	0.377469i	−0.803776	+	0.594932i	$0.797179\pi$
$440$		0			0
$441$	1.13937	+	0.956046i	0.0542558	+	0.0455260i
$442$	4.48783	+	5.34838i	0.213464	+	0.254397i
$443$	31.3712	+	5.53159i	1.49049	+	0.262814i	0.858762	−	0.512375i	$-0.171234\pi$
$443$	31.3712	+	5.53159i	1.49049	+	0.262814i	0.631730	+	0.775189i	$0.282345\pi$
$444$	3.31063	−	5.73417i	0.157115	−	0.272132i
$445$		0			0
$446$	18.6363	−	6.78306i	0.882454	−	0.321187i
$447$	1.62133	+	4.45456i	0.0766862	+	0.210694i
$448$	2.39766	−	1.38429i	0.113279	−	0.0654016i
$449$	−16.7627	+	29.0338i	−0.791080	+	1.37019i	0.134218	+	0.990952i	$0.457148\pi$
$449$	−16.7627	+	29.0338i	−0.791080	+	1.37019i	−0.925298	+	0.379240i	$0.876186\pi$
$450$		0			0
$451$	−8.63844	+	7.24852i	−0.406768	+	0.341319i
$452$	−4.82426	+	5.74932i	−0.226914	+	0.270425i
$453$	8.01218	−	1.41276i	0.376445	−	0.0663774i
$454$	−12.0605	−	4.38966i	−0.566027	−	0.206017i
$455$		0			0
$456$	6.52735	+	7.54235i	0.305671	+	0.353203i
$457$		−	2.81534i		−	0.131696i	−0.997830	−	0.0658479i	$-0.979025\pi$
$457$		−	2.81534i		−	0.131696i	0.997830	−	0.0658479i	$-0.0209752\pi$
$458$	−3.92955	+	10.7963i	−0.183616	+	0.504480i
$459$	1.22434	+	6.94358i	0.0571474	+	0.324099i
$460$		0			0
$461$	−6.64940	+	5.57951i	−0.309693	+	0.259864i	−0.784365	−	0.620299i	$-0.787011\pi$
$461$	−6.64940	+	5.57951i	−0.309693	+	0.259864i	0.474672	+	0.880163i	$0.342567\pi$
$462$	−15.1069	−	2.66375i	−0.702835	−	0.123929i
$463$	16.4040	+	9.47085i	0.762358	+	0.440148i	0.830142	−	0.557552i	$-0.188259\pi$
$463$	16.4040	+	9.47085i	0.762358	+	0.440148i	−0.0677837	+	0.997700i	$0.521593\pi$
$464$	−2.22668	−	3.85673i	−0.103371	−	0.179044i
$465$		0			0
$466$	2.56436	−	0.933350i	0.118792	−	0.0432366i
$467$	−4.27919	+	2.47059i	−0.198017	+	0.114325i	−0.595730	−	0.803184i	$-0.703137\pi$
$467$	−4.27919	+	2.47059i	−0.198017	+	0.114325i	0.397713	+	0.917510i	$0.369804\pi$
$468$	3.35095	+	1.93467i	0.154898	+	0.0894303i
$469$	6.48698	−	36.7895i	0.299541	−	1.69878i
$470$		0			0
$471$	16.1462	+	13.5482i	0.743976	+	0.624270i
$472$	1.98571	−	0.350134i	0.0913997	−	0.0161162i
$473$	−2.46481	+	6.77202i	−0.113332	+	0.311378i
$474$	−15.3883			−0.706807
$475$		0			0
$476$	11.1726			0.512096
$477$	8.55262	−	23.4981i	0.391598	−	1.07591i
$478$	−24.6454	+	4.34565i	−1.12725	+	0.198765i
$479$	19.4138	+	16.2901i	0.887038	+	0.744313i	0.967614	−	0.252435i	$-0.0812314\pi$
$479$	19.4138	+	16.2901i	0.887038	+	0.744313i	−0.0805757	+	0.996748i	$0.525676\pi$
$480$		0			0
$481$	−0.869282	+	4.92995i	−0.0396359	+	0.224786i
$482$	21.8418	+	12.6104i	0.994867	+	0.574387i
$483$	49.0304	−	28.3077i	2.23096	−	1.28805i
$484$	−4.82756	+	1.75709i	−0.219435	+	0.0798677i
$485$		0			0
$486$	9.63053	+	16.6806i	0.436850	+	0.756646i
$487$	17.2918	+	9.98344i	0.783567	+	0.452393i	0.837693	−	0.546141i	$-0.183904\pi$
$487$	17.2918	+	9.98344i	0.783567	+	0.452393i	−0.0541258	+	0.998534i	$0.517237\pi$
$488$	8.57278	+	1.51161i	0.388072	+	0.0684275i
$489$	−35.6009	+	29.8727i	−1.60993	+	1.35089i
$490$		0			0
$491$	−2.43814	−	13.8274i	−0.110032	−	0.624020i	−0.989091	−	0.147308i	$-0.952939\pi$
$491$	−2.43814	−	13.8274i	−0.110032	−	0.624020i	0.879059	−	0.476713i	$-0.158172\pi$
$492$	3.64509	−	10.0148i	0.164333	−	0.451502i
$493$		−	17.9716i		−	0.809399i
$494$	−6.58772	−	3.67063i	−0.296395	−	0.165149i
$495$		0			0
$496$	1.79175	+	0.652145i	0.0804521	+	0.0292822i
$497$	36.3917	−	6.41684i	1.63239	−	0.287835i
$498$	−24.9370	+	29.7188i	−1.11745	+	1.33173i
$499$	14.2758	−	11.9788i	0.639072	−	0.536245i	−0.264661	−	0.964341i	$-0.585260\pi$
$499$	14.2758	−	11.9788i	0.639072	−	0.536245i	0.903733	+	0.428097i	$0.140816\pi$
$500$		0			0
$501$	12.4663	−	21.5923i	0.556955	−	0.964674i
$502$	2.89168	−	1.66951i	0.129062	−	0.0745140i
$503$	2.81271	+	7.72785i	0.125412	+	0.344568i	0.986470	−	0.163939i	$-0.0524200\pi$
$503$	2.81271	+	7.72785i	0.125412	+	0.344568i	−0.861058	+	0.508507i	$0.830198\pi$
$504$	5.81849	−	2.11776i	0.259176	−	0.0943323i
$505$		0			0
$506$	−10.8187	+	18.7385i	−0.480948	+	0.833027i
$507$	22.5510	+	3.97634i	1.00152	+	0.176596i
$508$	8.36094	+	9.96418i	0.370957	+	0.442089i
$509$	−20.2854	−	17.0215i	−0.899136	−	0.754465i	0.0708852	−	0.997484i	$-0.477418\pi$
$509$	−20.2854	−	17.0215i	−0.899136	−	0.754465i	−0.970021	+	0.243020i	$0.921862\pi$
$510$		0			0
$511$	−14.8517	−	5.40558i	−0.657001	−	0.239129i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.90800	−	6.53657i	−0.172542	−	0.288597i
$514$	9.48495			0.418363
$515$		0			0
$516$	−1.18271	−	6.70747i	−0.0520658	−	0.295280i
$517$	−15.4539	+	18.4173i	−0.679663	+	0.809991i
$518$	5.14926	+	6.13665i	0.226245	+	0.269629i
$519$	6.64281	−	37.6732i	0.291587	−	1.65367i
$520$		0			0
$521$	−14.7837	−	25.6061i	−0.647686	−	1.12183i	−0.983674	−	0.179959i	$-0.942404\pi$
$521$	−14.7837	−	25.6061i	−0.647686	−	1.12183i	0.335988	−	0.941866i	$-0.390930\pi$
$522$	−3.40649	−	9.35925i	−0.149098	−	0.409643i
$523$	0.839597	+	2.30677i	0.0367130	+	0.100868i	0.956695	−	0.291093i	$-0.0940189\pi$
$523$	0.839597	+	2.30677i	0.0367130	+	0.100868i	−0.919982	+	0.391961i	$0.871797\pi$
$524$	2.35172	+	4.07330i	0.102735	+	0.177943i
$525$		0			0
$526$	4.91064	−	27.8496i	0.214114	−	1.21430i
$527$	4.94604	+	5.89447i	0.215453	+	0.256767i
$528$	−3.56150	+	4.24443i	−0.154995	+	0.184715i
$529$	−9.87320	−	55.9937i	−0.429270	−	2.43451i
$530$		0			0
$531$	4.50953			0.195697
$532$	−11.2759	+	4.29994i	−0.488873	+	0.186426i
$533$			8.05761i			0.349014i
$534$	11.9399	+	4.34576i	0.516689	+	0.188059i
$535$		0			0
$536$	−10.3364	−	8.67326i	−0.446464	−	0.374628i
$537$	37.5686	+	44.7725i	1.62120	+	1.93207i
$538$	−5.14589	−	0.907359i	−0.221855	−	0.0391190i
$539$	0.805118	−	1.39451i	0.0346789	−	0.0600656i
$540$		0			0
$541$	−35.2607	+	12.8338i	−1.51597	+	0.551769i	−0.960139	−	0.279523i	$-0.909824\pi$
$541$	−35.2607	+	12.8338i	−1.51597	+	0.551769i	−0.555835	+	0.831293i	$0.687601\pi$
$542$	0.123770	+	0.340055i	0.00531637	+	0.0146066i
$543$	4.14371	−	2.39237i	0.177824	−	0.102667i
$544$	2.01775	−	3.49485i	0.0865104	−	0.149840i
$545$		0			0
$546$	−8.39657	+	7.04556i	−0.359340	+	0.301522i
$547$	2.45730	−	2.92850i	0.105067	−	0.125213i	−0.710949	−	0.703244i	$-0.751734\pi$
$547$	2.45730	−	2.92850i	0.105067	−	0.125213i	0.816015	+	0.578031i	$0.196179\pi$
$548$	21.6988	−	3.82609i	0.926927	−	0.163442i
$549$	18.2946	+	6.65870i	0.780795	+	0.284186i
$550$		0			0
$551$	6.91662	+	18.1377i	0.294658	+	0.772693i
$552$		−	20.4493i		−	0.870379i
$553$	6.36764	−	17.4949i	0.270780	−	0.743961i
$554$	2.26969	+	12.8720i	0.0964298	+	0.546880i
$555$		0			0
$556$	−10.0097	+	8.39915i	−0.424507	+	0.356203i
$557$	2.33736	+	0.412140i	0.0990373	+	0.0174629i	0.222947	−	0.974831i	$-0.428432\pi$
$557$	2.33736	+	0.412140i	0.0990373	+	0.0174629i	−0.123910	+	0.992293i	$0.539543\pi$
$558$	3.69309	+	2.13221i	0.156341	+	0.0902636i
$559$	2.57470	+	4.45952i	0.108898	+	0.188618i
$560$		0			0
$561$	−21.0111	+	7.64743i	−0.887091	+	0.322875i
$562$	−8.79238	+	5.07629i	−0.370884	+	0.214130i
$563$	−15.9054	−	9.18301i	−0.670335	−	0.387018i	0.125869	−	0.992047i	$-0.459828\pi$
$563$	−15.9054	−	9.18301i	−0.670335	−	0.387018i	−0.796203	+	0.605029i	$0.793162\pi$
$564$	3.94563	−	22.3768i	0.166141	−	0.942232i
$565$		0			0
$566$	−7.86241	−	6.59734i	−0.330482	−	0.277307i
$567$	−29.1944	+	5.14776i	−1.22605	+	0.216186i
$568$	4.56505	−	12.5424i	0.191545	−	0.526267i
$569$	−3.09691			−0.129829			−0.0649146	−	0.997891i	$-0.520678\pi$
$569$	−3.09691			−0.129829			−0.0649146	+	0.997891i	$0.520678\pi$
$570$		0			0
$571$	−21.1742			−0.886113			−0.443056	−	0.896494i	$-0.646106\pi$
$571$	−21.1742			−0.886113			−0.443056	+	0.896494i	$0.646106\pi$
$572$	1.43274	−	3.93643i	0.0599059	−	0.164590i
$573$	−29.0870	+	5.12883i	−1.21513	+	0.214260i
$574$	9.87750	+	8.28820i	0.412279	+	0.345943i
$575$		0			0
$576$	0.388363	−	2.20251i	0.0161818	−	0.0917714i
$577$	−15.6935	−	9.06063i	−0.653328	−	0.377199i	0.136402	−	0.990654i	$-0.456446\pi$
$577$	−15.6935	−	9.06063i	−0.653328	−	0.377199i	−0.789730	+	0.613455i	$0.789779\pi$
$578$	−0.618949	+	0.357350i	−0.0257449	+	0.0148638i
$579$	−46.2182	+	16.8220i	−1.92076	+	0.699100i
$580$		0			0
$581$	−23.4684	−	40.6485i	−0.973634	−	1.68638i
$582$	15.2394	+	8.79849i	0.631695	+	0.364709i
$583$	−26.6611	−	4.70106i	−1.10419	−	0.194698i
$584$	−4.37308	+	3.66945i	−0.180960	+	0.151843i
$585$		0			0
$586$	−1.24016	−	7.03331i	−0.0512306	−	0.290543i
$587$	−2.62190	+	7.20361i	−0.108217	+	0.297325i	−0.981967	−	0.189051i	$-0.939459\pi$
$587$	−2.62190	+	7.20361i	−0.108217	+	0.297325i	0.873750	+	0.486375i	$0.161681\pi$
$588$			1.52182i			0.0627589i
$589$	−7.26034	−	4.04540i	−0.299157	−	0.166688i
$590$		0			0
$591$	24.3971	+	8.87983i	1.00356	+	0.365267i
$592$	2.84952	−	0.502447i	0.117114	−	0.0206504i
$593$	0.814183	−	0.970306i	0.0334345	−	0.0398457i	−0.749068	−	0.662493i	$-0.769498\pi$
$593$	0.814183	−	0.970306i	0.0334345	−	0.0398457i	0.782503	+	0.622647i	$0.213943\pi$
$594$	3.24066	−	2.71924i	0.132966	−	0.111572i
$595$		0			0
$596$	−1.03578	+	1.79403i	−0.0424274	+	0.0734864i
$597$	26.9445	−	15.5564i	1.10277	−	0.636682i
$598$	5.28786	+	14.5283i	0.216237	+	0.594106i
$599$	6.46096	−	2.35160i	0.263987	−	0.0960836i	−0.206636	−	0.978418i	$-0.566251\pi$
$599$	6.46096	−	2.35160i	0.263987	−	0.0960836i	0.470623	+	0.882334i	$0.344029\pi$
$600$		0			0
$601$	10.4282	−	18.0622i	0.425376	−	0.736772i	−0.571080	−	0.820895i	$-0.693475\pi$
$601$	10.4282	−	18.0622i	0.425376	−	0.736772i	0.996455	+	0.0841223i	$0.0268086\pi$
$602$	8.11513	+	1.43092i	0.330748	+	0.0583198i
$603$	−19.3977	−	23.1172i	−0.789934	−	0.941407i
$604$	2.72354	+	2.28532i	0.110819	+	0.0929883i
$605$		0			0
$606$	22.5959	+	8.22423i	0.917895	+	0.334087i
$607$		−	8.73323i		−	0.354471i	−0.984168	−	0.177235i	$-0.943285\pi$
$607$		−	8.73323i		−	0.354471i	0.984168	−	0.177235i	$-0.0567154\pi$
$608$	−0.691364	+	4.30372i	−0.0280385	+	0.174539i
$609$	28.2140			1.14329
$610$		0			0
$611$	2.98309	+	16.9180i	0.120683	+	0.684427i
$612$	5.80140	−	6.91383i	0.234508	−	0.279475i
$613$	−13.9291	−	16.6001i	−0.562591	−	0.670470i	0.407501	−	0.913205i	$-0.366400\pi$
$613$	−13.9291	−	16.6001i	−0.562591	−	0.670470i	−0.970093	+	0.242734i	$0.921956\pi$
$614$	1.87916	−	10.6573i	0.0758369	−	0.430092i
$615$		0			0
$616$	−3.35176	−	5.80542i	−0.135046	−	0.233907i
$617$	−4.07342	−	11.1916i	−0.163990	−	0.450559i	0.830294	−	0.557325i	$-0.188172\pi$
$617$	−4.07342	−	11.1916i	−0.163990	−	0.450559i	−0.994284	+	0.106767i	$0.965950\pi$
$618$	−8.06981	−	22.1716i	−0.324615	−	0.891874i
$619$	4.19167	+	7.26019i	0.168478	+	0.291812i	0.937885	−	0.346947i	$-0.112782\pi$
$619$	4.19167	+	7.26019i	0.168478	+	0.291812i	−0.769407	+	0.638759i	$0.779448\pi$
$620$		0			0
$621$	−2.71121	+	15.3760i	−0.108797	+	0.617018i
$622$	−16.9425	−	20.1912i	−0.679331	−	0.809595i
$623$	−9.88139	+	11.7762i	−0.395890	+	0.471803i
$624$	0.687481	+	3.89890i	0.0275213	+	0.156081i
$625$		0			0
$626$	−30.1756			−1.20606
$627$	18.2622	−	15.8046i	0.729321	−	0.631174i
$628$			9.21076i			0.367549i
$629$	10.9725	+	3.99365i	0.437500	+	0.159237i
$630$		0			0
$631$	34.4895	+	28.9401i	1.37301	+	1.15209i	0.971720	+	0.236135i	$0.0758807\pi$
$631$	34.4895	+	28.9401i	1.37301	+	1.15209i	0.401285	+	0.915953i	$0.368564\pi$
$632$	−4.32252	−	5.15138i	−0.171941	−	0.204911i
$633$	10.0355	+	1.76953i	0.398875	+	0.0703324i
$634$	−5.97740	+	10.3532i	−0.237393	+	0.411177i
$635$		0			0
$636$	24.0429	−	8.75089i	0.953362	−	0.346995i
$637$	−0.393520	−	1.08119i	−0.0155918	−	0.0428382i
$638$	−9.33823	+	5.39143i	−0.369704	+	0.213449i
$639$	14.9256	−	25.8519i	0.590447	−	1.02268i
$640$		0			0
$641$	−0.336944	+	0.282730i	−0.0133085	+	0.0111672i	−0.649418	−	0.760432i	$-0.724987\pi$
$641$	−0.336944	+	0.282730i	−0.0133085	+	0.0111672i	0.636109	+	0.771599i	$0.280543\pi$
$642$	10.3460	−	12.3299i	0.408324	−	0.486622i
$643$	−5.39224	+	0.950798i	−0.212649	+	0.0374958i	−0.278958	−	0.960303i	$-0.589989\pi$
$643$	−5.39224	+	0.950798i	−0.212649	+	0.0374958i	0.0663085	+	0.997799i	$0.478878\pi$
$644$	23.2488	+	8.46188i	0.916132	+	0.333445i
$645$		0			0
$646$	−11.1001	+	13.6459i	−0.436726	+	0.536889i
$647$		−	20.1149i		−	0.790797i	−0.918510	−	0.395398i	$-0.870607\pi$
$647$		−	20.1149i		−	0.790797i	0.918510	−	0.395398i	$-0.129393\pi$
$648$	−3.66221	+	10.0618i	−0.143865	+	0.395266i
$649$	−0.847774	−	4.80797i	−0.0332780	−	0.188729i
$650$		0			0
$651$	−9.25388	+	7.76493i	−0.362688	+	0.304331i
$652$	−20.0004	−	3.52661i	−0.783275	−	0.138113i
$653$	−22.5556	−	13.0225i	−0.882671	−	0.509610i	−0.0111325	−	0.999938i	$-0.503544\pi$
$653$	−22.5556	−	13.0225i	−0.882671	−	0.509610i	−0.871538	+	0.490328i	$0.836877\pi$
$654$	7.14679	+	12.3786i	0.279462	+	0.484042i
$655$		0			0
$656$	4.37645	−	1.59290i	0.170872	−	0.0621922i
$657$	−11.0569	+	6.38368i	−0.431369	+	0.249051i
$658$	23.8075	+	13.7453i	0.928112	+	0.535846i
$659$	0.984194	−	5.58164i	0.0383387	−	0.217430i	−0.959619	−	0.281302i	$-0.909234\pi$
$659$	0.984194	−	5.58164i	0.0383387	−	0.217430i	0.997958	+	0.0638720i	$0.0203449\pi$
$660$		0			0
$661$	−10.2769	−	8.62333i	−0.399724	−	0.335409i	0.420663	−	0.907217i	$-0.361798\pi$
$661$	−10.2769	−	8.62333i	−0.399724	−	0.335409i	−0.820387	+	0.571809i	$0.806242\pi$
$662$	−28.5222	+	5.02924i	−1.10855	+	0.195467i
$663$	−5.46437	+	15.0132i	−0.212219	+	0.583066i
$664$	−16.9534			−0.657919
$665$		0			0
$666$	6.47124			0.250755
$667$	13.6112	−	37.3966i	0.527029	−	1.44800i
$668$	10.7300	−	1.89199i	0.415157	−	0.0732033i
$669$	34.7654	+	29.1717i	1.34411	+	1.12784i
$670$		0			0
$671$	3.66004	−	20.7571i	0.141294	−	0.801320i
$672$	5.48666	+	3.16772i	0.211652	+	0.122198i
$673$	26.5220	−	15.3125i	1.02235	−	0.590252i	0.107564	−	0.994198i	$-0.465695\pi$
$673$	26.5220	−	15.3125i	1.02235	−	0.590252i	0.914783	+	0.403946i	$0.132362\pi$
$674$	−4.18967	+	1.52492i	−0.161380	+	0.0587376i
$675$		0			0
$676$	5.00338	+	8.66611i	0.192438	+	0.333312i
$677$	−11.5683	−	6.67895i	−0.444605	−	0.256693i	0.260944	−	0.965354i	$-0.415966\pi$
$677$	−11.5683	−	6.67895i	−0.444605	−	0.256693i	−0.705549	+	0.708661i	$0.749300\pi$
$678$	−16.9135	−	2.98231i	−0.649561	−	0.114535i
$679$	−16.3091	+	13.6849i	−0.625885	+	0.525179i
$680$		0			0
$681$	−5.10000	−	28.9235i	−0.195432	−	1.10835i
$682$	1.57903	−	4.33834i	0.0604641	−	0.166124i
$683$			9.75308i			0.373191i	0.982437	+	0.186596i	$0.0597454\pi$
$683$			9.75308i			0.373191i	−0.982437	+	0.186596i	$0.940255\pi$
$684$	−3.19414	+	9.21050i	−0.122131	+	0.352172i
$685$		0			0
$686$	16.4811	+	5.99864i	0.629253	+	0.229029i
$687$	−25.8918	+	4.56543i	−0.987835	+	0.174182i
$688$	1.91317	−	2.28003i	0.0729391	−	0.0869254i
$689$	−14.8185	+	12.4342i	−0.564541	+	0.473706i
$690$		0			0
$691$	−1.80854	+	3.13248i	−0.0688001	+	0.119165i	−0.898373	−	0.439233i	$-0.855250\pi$
$691$	−1.80854	+	3.13248i	−0.0688001	+	0.119165i	0.829573	+	0.558398i	$0.188584\pi$
$692$	14.4774	−	8.35856i	0.550350	−	0.317745i
$693$	−5.12769	−	14.0882i	−0.194785	−	0.535167i
$694$	24.2710	−	8.83392i	0.921314	−	0.335331i
$695$		0			0
$696$	5.09540	−	8.82549i	0.193141	−	0.334529i
$697$	18.5091	+	3.26365i	0.701082	+	0.123620i
$698$	−14.0770	−	16.7763i	−0.532822	−	0.634992i
$699$	4.78373	+	4.01403i	0.180937	+	0.151825i
$700$		0			0
$701$	−16.7716	−	6.10435i	−0.633453	−	0.230558i	0.00528040	−	0.999986i	$-0.498319\pi$
$701$	−16.7716	−	6.10435i	−0.633453	−	0.230558i	−0.638734	+	0.769428i	$0.720541\pi$
$702$		−	3.02277i		−	0.114087i
$703$	−12.6109	+	0.192337i	−0.475629	+	0.00725414i
$704$	−2.42128			−0.0912556
$705$		0			0
$706$	−2.21203	−	12.5451i	−0.0832510	−	0.472140i
$707$	−18.7003	+	22.2861i	−0.703296	+	0.838156i
$708$	2.96587	+	3.53458i	0.111464	+	0.132838i
$709$	6.05271	−	34.3266i	0.227314	−	1.28916i	−0.630897	−	0.775867i	$-0.717313\pi$
$709$	6.05271	−	34.3266i	0.227314	−	1.28916i	0.858211	−	0.513297i	$-0.171576\pi$
$710$		0			0
$711$	−7.51981	−	13.0247i	−0.282015	−	0.488464i
$712$	1.89909	+	5.21770i	0.0711714	+	0.195542i
$713$	5.82777	+	16.0117i	0.218252	+	0.599641i
$714$	12.7834	+	22.1414i	0.478405	+	0.828622i
$715$		0			0
$716$	−4.43514	+	25.1529i	−0.165749	+	0.940009i
$717$	−36.8105	−	43.8691i	−1.37472	−	1.63832i
$718$	−15.9912	+	19.0576i	−0.596788	+	0.711224i
$719$	3.64425	+	20.6676i	0.135908	+	0.770771i	0.974223	+	0.225586i	$0.0724296\pi$
$719$	3.64425	+	20.6676i	0.135908	+	0.770771i	−0.838316	+	0.545185i	$0.816459\pi$
$720$		0			0
$721$	28.5462			1.06312
$722$	5.95088	−	18.0440i	0.221469	−	0.671529i
$723$			57.7136i			2.14639i
$724$	1.96483	+	0.715139i	0.0730222	+	0.0265779i
$725$		0			0
$726$	−9.00568	−	7.55666i	−0.334232	−	0.280454i
$727$	5.39689	+	6.43176i	0.200159	+	0.238541i	0.856782	−	0.515678i	$-0.172460\pi$
$727$	5.39689	+	6.43176i	0.200159	+	0.238541i	−0.656623	+	0.754219i	$0.728016\pi$
$728$	−4.71714	−	0.831760i	−0.174829	−	0.0308271i
$729$	−5.97654	+	10.3517i	−0.221353	+	0.383395i
$730$		0			0
$731$	11.2868	−	4.10806i	0.417457	−	0.151942i
$732$	6.81306	+	18.7187i	0.251818	+	0.691864i
$733$	7.51610	−	4.33942i	0.277614	−	0.160280i	−0.354729	−	0.934969i	$-0.615427\pi$
$733$	7.51610	−	4.33942i	0.277614	−	0.160280i	0.632343	+	0.774689i	$0.282094\pi$
$734$	−5.54259	+	9.60005i	−0.204581	+	0.354344i
$735$		0			0
$736$	6.84561	−	5.74414i	0.252332	−	0.211732i
$737$	−21.0004	+	25.0273i	−0.773561	+	0.921894i
$738$	10.2578	−	1.80873i	0.377595	−	0.0665802i
$739$	9.63552	+	3.50704i	0.354448	+	0.129009i	0.513107	−	0.858325i	$-0.328495\pi$
$739$	9.63552	+	3.50704i	0.354448	+	0.129009i	−0.158658	+	0.987334i	$0.550717\pi$
$740$		0			0
$741$	−0.263169	−	17.2551i	−0.00966774	−	0.633881i
$742$			30.9555i			1.13641i
$743$	11.7681	−	32.3326i	0.431730	−	1.18617i	−0.513020	−	0.858377i	$-0.671473\pi$
$743$	11.7681	−	32.3326i	0.431730	−	1.18617i	0.944750	−	0.327792i	$-0.106305\pi$
$744$	0.757675	+	4.29699i	0.0277777	+	0.157535i
$745$		0			0
$746$	−25.6573	+	21.5291i	−0.939382	+	0.788235i
$747$	−37.3401	−	6.58407i	−1.36620	−	0.240898i
$748$	−8.46202	−	4.88555i	−0.309402	−	0.178633i
$749$	9.73670	+	16.8645i	0.355771	+	0.616214i
$750$		0			0
$751$	−3.94631	+	1.43634i	−0.144003	+	0.0524127i	−0.413016	−	0.910724i	$-0.635525\pi$
$751$	−3.94631	+	1.43634i	−0.144003	+	0.0524127i	0.269013	+	0.963136i	$0.413302\pi$
$752$	8.59917	−	4.96473i	0.313579	−	0.181045i
$753$	6.61715	+	3.82041i	0.241142	+	0.139224i
$754$	−1.33792	+	7.58770i	−0.0487240	+	0.276328i
$755$		0			0
$756$	−3.70549	−	3.10927i	−0.134767	−	0.113083i
$757$	−14.1076	+	2.48755i	−0.512749	+	0.0904115i	−0.424035	−	0.905646i	$-0.639387\pi$
$757$	−14.1076	+	2.48755i	−0.512749	+	0.0904115i	−0.0887138	+	0.996057i	$0.528276\pi$
$758$	4.63390	−	12.7315i	0.168311	−	0.462431i
$759$	−49.5135			−1.79723
$760$		0			0
$761$	15.6963			0.568992			0.284496	−	0.958677i	$-0.408174\pi$
$761$	15.6963			0.568992			0.284496	+	0.958677i	$0.408174\pi$
$762$	−10.1803	+	27.9701i	−0.368792	+	1.01325i
$763$	−17.0306	+	3.00295i	−0.616548	+	0.108714i
$764$	−9.88740	−	8.29651i	−0.357713	−	0.300157i
$765$		0			0
$766$	6.66222	−	37.7833i	0.240716	−	1.36517i
$767$	−3.02110	−	1.74423i	−0.109086	−	0.0629807i
$768$	1.98176	−	1.14417i	0.0715106	−	0.0412866i
$769$	−17.9278	+	6.52518i	−0.646492	+	0.235304i	−0.644394	−	0.764694i	$-0.722890\pi$
$769$	−17.9278	+	6.52518i	−0.646492	+	0.235304i	−0.00209836	+	0.999998i	$0.500668\pi$
$770$		0			0
$771$	10.8524	+	18.7969i	0.390839	+	0.676953i
$772$	−18.6139	−	10.7467i	−0.669929	−	0.386784i
$773$	45.3434	+	7.99526i	1.63089	+	0.287570i	0.912807	−	0.408390i	$-0.133910\pi$
$773$	45.3434	+	7.99526i	1.63089	+	0.287570i	0.718081	+	0.695960i	$0.245021\pi$
$774$	5.09927	−	4.27880i	0.183289	−	0.153798i
$775$		0			0
$776$	1.33533	+	7.57303i	0.0479355	+	0.271856i
$777$	−6.26973	+	17.2259i	−0.224925	+	0.617977i
$778$			13.4065i			0.480645i
$779$	−19.9363	+	3.82966i	−0.714291	+	0.137212i
$780$		0			0
$781$	−30.3687	−	11.0533i	−1.08668	−	0.395518i
$782$	35.5146	−	6.26219i	1.27000	−	0.223935i
$783$	−5.00138	+	5.96041i	−0.178735	+	0.213008i
$784$	−0.509446	+	0.427476i	−0.0181945	+	0.0152670i
$785$		0			0
$786$	−5.38153	+	9.32108i	−0.191953	+	0.332472i
$787$	−45.8391	+	26.4652i	−1.63399	+	0.943383i	−0.651141	+	0.758956i	$0.725710\pi$
$787$	−45.8391	+	26.4652i	−1.63399	+	0.943383i	−0.982846	+	0.184427i	$0.940957\pi$
$788$	3.88047	+	10.6615i	0.138236	+	0.379800i
$789$	60.8098	−	22.1330i	2.16489	−	0.787954i
$790$		0			0
$791$	10.3894	−	17.9949i	0.369404	−	0.639827i
$792$	−5.33291	−	0.940336i	−0.189497	−	0.0334134i
$793$	−9.68074	−	11.5371i	−0.343773	−	0.409693i
$794$	23.1088	+	19.3906i	0.820101	+	0.688146i
$795$		0			0
$796$	12.7763	+	4.65019i	0.452844	+	0.164822i
$797$		−	40.6890i		−	1.44128i	−0.693311	−	0.720639i	$-0.743849\pi$
$797$		−	40.6890i		−	1.44128i	0.693311	−	0.720639i	$-0.256151\pi$
$798$	−21.4230	−	17.4263i	−0.758366	−	0.616883i
$799$	40.0704			1.41759
$800$		0			0
$801$	2.15641	+	12.2296i	0.0761929	+	0.432112i
$802$	6.56993	−	7.82974i	0.231992	−	0.276478i
$803$	8.88479	+	10.5885i	0.313537	+	0.373659i
$804$	5.36174	−	30.4079i	0.189094	−	1.07240i
$805$		0			0
$806$	−1.64943	−	2.85689i	−0.0580986	−	0.100630i
$807$	−4.08960	−	11.2361i	−0.143961	−	0.395529i
$808$	3.59398	+	9.87437i	0.126436	+	0.347379i
$809$	−2.30197	−	3.98714i	−0.0809331	−	0.140180i	0.822718	−	0.568450i	$-0.192457\pi$
$809$	−2.30197	−	3.98714i	−0.0809331	−	0.140180i	−0.903651	+	0.428270i	$0.859123\pi$
$810$		0			0
$811$	−5.75399	+	32.6325i	−0.202050	+	1.14588i	0.699965	+	0.714177i	$0.253199\pi$
$811$	−5.75399	+	32.6325i	−0.202050	+	1.14588i	−0.902015	+	0.431705i	$0.857912\pi$
$812$	7.92524	+	9.44494i	0.278122	+	0.331452i
$813$	−0.532293	+	0.634362i	−0.0186683	+	0.0222481i
$814$	−1.21657	−	6.89949i	−0.0426406	−	0.241827i
$815$		0			0
$816$	9.23460			0.323276
$817$	−9.81010	+	8.48992i	−0.343212	+	0.297025i
$818$		−	25.1247i		−	0.878464i
$819$	−10.0665	−	3.66392i	−0.351754	−	0.128028i
$820$		0			0
$821$	16.3258	+	13.6990i	0.569774	+	0.478098i	0.881571	−	0.472051i	$-0.156486\pi$
$821$	16.3258	+	13.6990i	0.569774	+	0.478098i	−0.311797	+	0.950149i	$0.600931\pi$
$822$	32.4095	+	38.6241i	1.13041	+	1.34717i
$823$	47.1791	+	8.31895i	1.64456	+	0.289980i	0.917839	−	0.396952i	$-0.129932\pi$
$823$	47.1791	+	8.31895i	1.64456	+	0.289980i	0.726721	+	0.686933i	$0.241043\pi$
$824$	5.15539	−	8.92940i	0.179597	−	0.311070i
$825$		0			0
$826$	−5.24574	+	1.90929i	−0.182523	+	0.0664329i
$827$	−4.93122	−	13.5484i	−0.171475	−	0.471125i	0.823950	−	0.566662i	$-0.191765\pi$
$827$	−4.93122	−	13.5484i	−0.171475	−	0.471125i	−0.995426	+	0.0955370i	$0.969543\pi$
$828$	17.3084	−	9.99298i	0.601507	−	0.347280i
$829$	−3.14956	+	5.45520i	−0.109389	+	0.189467i	−0.915523	−	0.402266i	$-0.868223\pi$
$829$	−3.14956	+	5.45520i	−0.109389	+	0.189467i	0.806134	+	0.591733i	$0.201556\pi$
$830$		0			0
$831$	−22.9124	+	19.2258i	−0.794821	+	0.666934i
$832$	−1.11209	+	1.32533i	−0.0385546	+	0.0459476i
$833$	−2.64298	+	0.466028i	−0.0915737	+	0.0161469i
$834$	−28.0979	−	10.2268i	−0.972951	−	0.354125i
$835$		0			0
$836$	10.4205	+	1.67399i	0.360402	+	0.0578961i
$837$		−	3.33140i		−	0.115150i
$838$	−1.62498	+	4.46459i	−0.0561339	+	0.154227i
$839$	2.58965	+	14.6867i	0.0894048	+	0.507040i	0.996319	+	0.0857242i	$0.0273204\pi$
$839$	2.58965	+	14.6867i	0.0894048	+	0.507040i	−0.906914	+	0.421316i	$0.861568\pi$
$840$		0			0
$841$	−7.02276	+	5.89279i	−0.242164	+	0.203200i
$842$	−11.3637	−	2.00373i	−0.391620	−	0.0690532i
$843$	−20.1199	−	11.6163i	−0.692968	−	0.400085i
$844$	2.22657	+	3.85654i	0.0766418	+	0.132747i
$845$		0			0
$846$	20.8679	−	7.59529i	0.717453	−	0.261132i
$847$	12.3177	−	7.11163i	0.423241	−	0.244359i
$848$	9.68302	+	5.59050i	0.332516	+	0.191978i
$849$	4.07842	−	23.1299i	0.139971	−	0.793815i
$850$		0			0
$851$	19.8076	+	16.6206i	0.678996	+	0.569745i
$852$	30.0792	−	5.30377i	1.03050	−	0.181704i
$853$	−19.6098	+	53.8776i	−0.671428	+	1.84473i	−0.156100	+	0.987741i	$0.549892\pi$
$853$	−19.6098	+	53.8776i	−0.671428	+	1.84473i	−0.515328	+	0.856993i	$0.672330\pi$
$854$	−24.1006			−0.824705
$855$		0			0
$856$	7.03372			0.240407
$857$	−7.80367	+	21.4404i	−0.266568	+	0.732390i	0.732120	+	0.681176i	$0.238531\pi$
$857$	−7.80367	+	21.4404i	−0.266568	+	0.732390i	−0.998688	+	0.0512138i	$0.983691\pi$
$858$	9.44034	−	1.66459i	0.322288	−	0.0568281i
$859$	18.2941	+	15.3506i	0.624188	+	0.523756i	0.899117	−	0.437709i	$-0.144210\pi$
$859$	18.2941	+	15.3506i	0.624188	+	0.523756i	−0.274929	+	0.961465i	$0.588654\pi$
$860$		0			0
$861$	−5.12370	+	29.0579i	−0.174615	+	0.990291i
$862$	7.51668	+	4.33976i	0.256019	+	0.147813i
$863$	1.71748	−	0.991588i	0.0584637	−	0.0337540i	−0.470483	−	0.882409i	$-0.655920\pi$
$863$	1.71748	−	0.991588i	0.0584637	−	0.0337540i	0.528947	+	0.848655i	$0.322587\pi$
$864$	−1.64180	+	0.597566i	−0.0558552	+	0.0203296i
$865$		0			0
$866$	−0.652396	−	1.12998i	−0.0221693	−	0.0383984i
$867$	−1.41636	−	0.817739i	−0.0481023	−	0.0277719i
$868$	−5.19878	−	0.916684i	−0.176458	−	0.0311143i
$869$	−12.4730	+	10.4661i	−0.423116	+	0.355036i
$870$		0			0
$871$	4.05374	+	22.9899i	0.137356	+	0.778983i
$872$	−2.13635	+	5.86958i	−0.0723460	+	0.198769i
$873$			17.1983i			0.582074i
$874$	−33.4329	+	19.9884i	−1.13088	+	0.676117i
$875$		0			0
$876$	−12.2755	−	4.46792i	−0.414751	−	0.150957i
$877$	−8.80479	+	1.55252i	−0.297317	+	0.0524250i	−0.320317	−	0.947311i	$-0.603789\pi$
$877$	−8.80479	+	1.55252i	−0.297317	+	0.0524250i	0.0230000	+	0.999735i	$0.492678\pi$
$878$	14.8638	−	17.7140i	0.501629	−	0.597818i
$879$	12.5194	−	10.5050i	0.422268	−	0.354325i
$880$		0			0
$881$	−17.8638	+	30.9409i	−0.601845	+	1.04243i	0.390696	+	0.920520i	$0.372234\pi$
$881$	−17.8638	+	30.9409i	−0.601845	+	1.04243i	−0.992542	+	0.121907i	$0.961099\pi$
$882$	−1.28808	+	0.743672i	−0.0433718	+	0.0250407i
$883$	−16.3514	−	44.9250i	−0.550268	−	1.51185i	−0.833346	−	0.552751i	$-0.813578\pi$
$883$	−16.3514	−	44.9250i	−0.550268	−	1.51185i	0.283079	−	0.959097i	$-0.408644\pi$
$884$	−6.56076	+	2.38792i	−0.220662	+	0.0803145i
$885$		0			0
$886$	−15.9276	+	27.5874i	−0.535098	+	0.926816i
$887$	14.4771	+	2.55270i	0.486093	+	0.0857112i	0.411323	−	0.911490i	$-0.365067\pi$
$887$	14.4771	+	2.55270i	0.486093	+	0.0857112i	0.0747695	+	0.997201i	$0.476178\pi$
$888$	4.25606	+	5.07217i	0.142824	+	0.170211i
$889$	−27.5866	−	23.1479i	−0.925226	−	0.776357i
$890$		0			0
$891$	24.3626	+	8.86724i	0.816176	+	0.297064i
$892$			19.8323i			0.664035i
$893$	−40.4409	+	15.4217i	−1.35330	+	0.516066i
$894$	−4.74045			−0.158544
$895$		0			0
$896$	0.480759	+	2.72652i	0.0160610	+	0.0910866i
$897$	−22.7413	+	27.1021i	−0.759311	+	0.904912i
$898$	−21.5497	−	25.6819i	−0.719123	−	0.857017i
$899$	−1.47452	+	8.36242i	−0.0491780	+	0.278902i
$900$		0			0
$901$	22.5605	+	39.0759i	0.751598	+	1.30181i
$902$	−3.85685	−	10.5966i	−0.128419	−	0.352829i
$903$	6.44935	+	17.7194i	0.214621	+	0.589666i
$904$	−3.75261	−	6.49970i	−0.124810	−	0.216177i
$905$		0			0
$906$	−1.41276	+	8.01218i	−0.0469359	+	0.266187i
$907$	31.1582	+	37.1329i	1.03459	+	1.23298i	0.972011	+	0.234936i	$0.0754882\pi$
$907$	31.1582	+	37.1329i	1.03459	+	1.23298i	0.0625793	+	0.998040i	$0.480067\pi$
$908$	8.24987	−	9.83181i	0.273782	−	0.326280i
$909$	4.08095	+	23.1442i	0.135356	+	0.767644i
$910$		0			0
$911$	−1.23529			−0.0409271			−0.0204635	−	0.999791i	$-0.506514\pi$
$911$	−1.23529			−0.0409271			−0.0204635	+	0.999791i	$0.506514\pi$
$912$	−9.31997	+	3.55407i	−0.308615	+	0.117687i
$913$			41.0490i			1.35852i
$914$	2.64555	+	0.962902i	0.0875070	+	0.0318500i
$915$		0			0
$916$	−8.80126	−	7.38514i	−0.290802	−	0.244012i
$917$	−8.37028	−	9.97531i	−0.276411	−	0.329414i
$918$	−6.94358	−	1.22434i	−0.229172	−	0.0404093i
$919$	−2.15131	+	3.72618i	−0.0709652	+	0.122915i	−0.899325	−	0.437282i	$-0.855941\pi$
$919$	−2.15131	+	3.72618i	−0.0709652	+	0.122915i	0.828359	+	0.560197i	$0.189275\pi$
$920$		0			0
$921$	23.2702	−	8.46966i	0.766780	−	0.279085i
$922$	−2.96880	−	8.15670i	−0.0977721	−	0.268627i
$923$	−19.9984	+	11.5461i	−0.658255	+	0.380044i
$924$	7.66996	−	13.2848i	0.252323	−	0.437036i
$925$		0			0
$926$	−14.5102	+	12.1755i	−0.476834	+	0.400111i
$927$	14.8227	−	17.6650i	0.486840	−	0.580193i
$928$	4.38571	−	0.773318i	0.143968	−	0.0253854i
$929$	32.8280	+	11.9484i	1.07705	+	0.392015i	0.818810	−	0.574065i	$-0.194634\pi$
$929$	32.8280	+	11.9484i	1.07705	+	0.392015i	0.258242	+	0.966080i	$0.416857\pi$
$930$		0			0
$931$	2.48805	−	1.48752i	0.0815427	−	0.0487516i
$932$			2.72893i			0.0893892i
$933$	20.6291	−	56.6781i	0.675368	−	1.85556i
$934$	−0.858028	−	4.86612i	−0.0280755	−	0.159224i
$935$		0			0
$936$	−2.96409	+	2.48717i	−0.0968844	+	0.0812956i
$937$	−2.50293	−	0.441335i	−0.0817673	−	0.0144178i	0.132615	−	0.991168i	$-0.457663\pi$
$937$	−2.50293	−	0.441335i	−0.0817673	−	0.0144178i	−0.214382	+	0.976750i	$0.568774\pi$
$938$	32.3521	+	18.6785i	1.05633	+	0.609875i
$939$	−34.5260	−	59.8007i	−1.12671	−	1.95152i
$940$		0			0
$941$	−19.8302	+	7.21759i	−0.646445	+	0.235287i	−0.644373	−	0.764711i	$-0.722882\pi$
$941$	−19.8302	+	7.21759i	−0.646445	+	0.235287i	−0.00207156	+	0.999998i	$0.500659\pi$
$942$	−18.2535	+	10.5387i	−0.594731	+	0.343368i
$943$	36.0433	+	20.8096i	1.17373	+	0.677654i
$944$	−0.350134	+	1.98571i	−0.0113959	+	0.0646293i
$945$		0			0
$946$	−5.52060	−	4.63234i	−0.179490	−	0.150610i
$947$	−38.3965	+	6.77033i	−1.24772	+	0.220006i	−0.758220	−	0.651999i	$-0.773931\pi$
$947$	−38.3965	+	6.77033i	−1.24772	+	0.220006i	−0.489497	+	0.872005i	$0.662820\pi$
$948$	5.26310	−	14.4602i	0.170938	−	0.469647i
$949$	9.87653			0.320606
$950$		0			0
$951$	−27.3566			−0.887099
$952$	−3.82126	+	10.4988i	−0.123848	+	0.340269i
$953$	−21.5051	+	3.79192i	−0.696618	+	0.122832i	−0.510733	−	0.859739i	$-0.670626\pi$
$953$	−21.5051	+	3.79192i	−0.696618	+	0.122832i	−0.185884	+	0.982572i	$0.559515\pi$
$954$	19.1558	+	16.0737i	0.620194	+	0.520404i
$955$		0			0
$956$	4.34565	−	24.6454i	0.140548	−	0.797090i
$957$	−21.3690	−	12.3374i	−0.690762	−	0.398812i
$958$	−21.9476	+	12.6714i	−0.709094	+	0.409396i
$959$	−57.3228	+	20.8638i	−1.85105	+	0.673727i
$960$		0			0
$961$	13.6822	+	23.6982i	0.441360	+	0.764458i
$962$	−4.33532	−	2.50300i	−0.139776	−	0.0806999i
$963$	15.4919	+	2.73163i	0.499218	+	0.0880256i
$964$	−19.3202	+	16.2116i	−0.622262	+	0.522140i
$965$		0			0
$966$	9.83117	+	55.7554i	0.316313	+	1.79390i
$967$	−3.40380	+	9.35186i	−0.109459	+	0.300736i	−0.982313	−	0.187245i	$-0.940044\pi$
$967$	−3.40380	+	9.35186i	−0.109459	+	0.300736i	0.872854	+	0.487981i	$0.162266\pi$
$968$		−	5.13739i		−	0.165122i
$969$	−39.7431	−	6.38447i	−1.27673	−	0.205099i
$970$		0			0
$971$	17.9288	+	6.52554i	0.575362	+	0.209415i	0.613279	−	0.789866i	$-0.289850\pi$
$971$	17.9288	+	6.52554i	0.575362	+	0.209415i	−0.0379172	+	0.999281i	$0.512072\pi$
$972$	−18.9684	+	3.34465i	−0.608413	+	0.107280i
$973$	23.2537	−	27.7127i	0.745480	−	0.888429i
$974$	−15.2955	+	12.8345i	−0.490100	+	0.411243i
$975$		0			0
$976$	−4.35252	+	7.53878i	−0.139321	+	0.241310i
$977$	9.54886	−	5.51304i	0.305495	−	0.176378i	−0.339414	−	0.940637i	$-0.610229\pi$
$977$	9.54886	−	5.51304i	0.305495	−	0.176378i	0.644909	+	0.764260i	$0.276895\pi$
$978$	−15.8949	−	43.6710i	−0.508264	−	1.39644i
$979$	12.6335	−	4.59823i	0.403770	−	0.146960i
$980$		0			0
$981$	−6.98487	+	12.0981i	−0.223010	+	0.386264i
$982$	13.8274	+	2.43814i	0.441249	+	0.0778041i
$983$	−3.23425	−	3.85443i	−0.103157	−	0.122937i	0.711996	−	0.702184i	$-0.247791\pi$
$983$	−3.23425	−	3.85443i	−0.103157	−	0.122937i	−0.815153	+	0.579246i	$0.803347\pi$
$984$	8.16413	+	6.85052i	0.260263	+	0.218387i
$985$		0			0
$986$	16.8878	+	6.14664i	0.537816	+	0.195749i
$987$			62.9076i			2.00237i
$988$	5.70239	−	4.93500i	0.181417	−	0.157003i
$989$	26.5977			0.845759
$990$		0			0
$991$	−8.36382	−	47.4336i	−0.265686	−	1.50678i	−0.767076	−	0.641556i	$-0.778289\pi$
$991$	−8.36382	−	47.4336i	−0.265686	−	1.50678i	0.501390	−	0.865221i	$-0.332822\pi$
$992$	−1.22563	+	1.46065i	−0.0389139	+	0.0463757i
$993$	−42.6010	−	50.7699i	−1.35190	−	1.61113i
$994$	−6.41684	+	36.3917i	−0.203530	+	1.15428i
$995$		0			0
$996$	−19.3976	−	33.5975i	−0.614635	−	1.06458i
$997$	10.4731	+	28.7745i	0.331685	+	0.911298i	0.987674	+	0.156527i	$0.0500298\pi$
$997$	10.4731	+	28.7745i	0.331685	+	0.911298i	−0.655988	+	0.754771i	$0.727748\pi$
$998$	6.37379	+	17.5118i	0.201759	+	0.554327i
$999$	−2.52769	−	4.37809i	−0.0799727	−	0.138517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.f.99.1		24
5.2	odd	4		190.2.k.c.61.2	✓	12
5.3	odd	4		950.2.l.g.251.1		12
5.4	even	2	inner	950.2.u.f.99.4		24
19.5	even	9	inner	950.2.u.f.499.4		24
95.24	even	18	inner	950.2.u.f.499.1		24
95.43	odd	36		950.2.l.g.651.1		12
95.47	odd	36		3610.2.a.bf.1.5		6
95.62	odd	36		190.2.k.c.81.2	yes	12
95.67	even	36		3610.2.a.bd.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.61.2	✓	12	5.2	odd	4
190.2.k.c.81.2	yes	12	95.62	odd	36
950.2.l.g.251.1		12	5.3	odd	4
950.2.l.g.651.1		12	95.43	odd	36
950.2.u.f.99.1		24	1.1	even	1	trivial
950.2.u.f.99.4		24	5.4	even	2	inner
950.2.u.f.499.1		24	95.24	even	18	inner
950.2.u.f.499.4		24	19.5	even	9	inner
3610.2.a.bd.1.2		6	95.67	even	36
3610.2.a.bf.1.5		6	95.47	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-2.25357 + 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(2.39766 + 1.38429i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +O(q^{10})\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-2.25357 + 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(2.39766 + 1.38429i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +(-1.21064 - 2.09689i) q^{11} +(1.98176 + 1.14417i) q^{12} +(-1.70381 - 0.300428i) q^{13} +(-2.12086 + 1.77961i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-1.38022 + 3.79213i) q^{17} +2.23649i q^{18} +(-0.0664727 - 4.35839i) q^{19} +(-5.95337 - 2.16685i) q^{21} +(2.38450 - 0.420451i) q^{22} +(-5.74414 + 6.84561i) q^{23} +(-1.75297 + 1.47092i) q^{24} +(0.865049 - 1.49831i) q^{26} +(1.51309 - 0.873583i) q^{27} +(-0.946910 - 2.60161i) q^{28} +(-4.18479 + 1.52314i) q^{29} +(0.953372 - 1.65129i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(3.56150 + 4.24443i) q^{33} +(-3.09138 - 2.59397i) q^{34} +(-2.10161 - 0.764925i) q^{36} -2.89348i q^{37} +(4.11828 + 1.42819i) q^{38} +3.95905 q^{39} +(-0.808735 - 4.58656i) q^{41} +(4.07235 - 4.85323i) q^{42} +(-1.91317 - 2.28003i) q^{43} +(-0.420451 + 2.38450i) q^{44} +(-4.46815 - 7.73907i) q^{46} +(-3.39608 - 9.33064i) q^{47} +(-0.782658 - 2.15033i) q^{48} +(0.332517 + 0.575937i) q^{49} +(1.60357 - 9.09430i) q^{51} +(1.11209 + 1.32533i) q^{52} +(7.18700 - 8.56514i) q^{53} +(0.303392 + 1.72062i) q^{54} +2.76858 q^{56} +(1.88168 + 9.79554i) q^{57} -4.45336i q^{58} +(1.89474 + 0.689630i) q^{59} +(6.66844 + 5.59549i) q^{61} +(1.22563 + 1.46065i) q^{62} +(6.09783 + 1.07521i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.20657 + 1.89504i) q^{66} +(-4.61495 - 12.6795i) q^{67} +(3.49485 - 2.01775i) q^{68} +(10.2246 - 17.7096i) q^{69} +(10.2246 - 8.57949i) q^{71} +(1.43759 - 1.71325i) q^{72} +(-5.62193 + 0.991298i) q^{73} +(2.71898 + 0.989627i) q^{74} +(-2.75060 + 3.38145i) q^{76} -6.70352i q^{77} +(-1.35407 + 3.72029i) q^{78} +(-1.16772 - 6.62249i) q^{79} +(-8.20248 + 6.88270i) q^{81} +(4.58656 + 0.808735i) q^{82} +(-14.6821 - 8.47670i) q^{83} +(3.16772 + 5.48666i) q^{84} +(2.79687 - 1.01798i) q^{86} +(8.82549 - 5.09540i) q^{87} +(-2.09689 - 1.21064i) q^{88} +(-0.964193 + 5.46821i) q^{89} +(-3.66929 - 3.07890i) q^{91} +(8.80054 - 1.55177i) q^{92} +(-1.49233 + 4.10014i) q^{93} +9.92946 q^{94} +2.28834 q^{96} +(-2.63009 + 7.22610i) q^{97} +(-0.654931 + 0.115482i) q^{98} +(-4.14827 - 3.48081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 18 * q^9	\( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

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