LMFDB - Embedded newform 483.2.d.d.461.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (of order $2$, degree $1$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.18
Character	$\chi$	$=$	483.461
Dual form			483.2.d.d.461.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.714425i q^{2} +(0.852976 + 1.50746i) q^{3} +1.48960 q^{4} +0.589252 q^{5} +(1.07697 - 0.609388i) q^{6} +(2.38371 + 1.14801i) q^{7} -2.49306i q^{8} +(-1.54486 + 2.57165i) q^{9} +O(q^{10})$	\(q-0.714425i q^{2} +(0.852976 + 1.50746i) q^{3} +1.48960 q^{4} +0.589252 q^{5} +(1.07697 - 0.609388i) q^{6} +(2.38371 + 1.14801i) q^{7} -2.49306i q^{8} +(-1.54486 + 2.57165i) q^{9} -0.420976i q^{10} -3.80761i q^{11} +(1.27059 + 2.24551i) q^{12} -2.33263i q^{13} +(0.820166 - 1.70298i) q^{14} +(0.502618 + 0.888273i) q^{15} +1.19809 q^{16} -1.72994 q^{17} +(1.83725 + 1.10369i) q^{18} +5.00069i q^{19} +0.877748 q^{20} +(0.302674 + 4.57257i) q^{21} -2.72025 q^{22} +1.00000i q^{23} +(3.75818 - 2.12652i) q^{24} -4.65278 q^{25} -1.66649 q^{26} +(-5.19439 - 0.135258i) q^{27} +(3.55077 + 1.71007i) q^{28} +2.26408i q^{29} +(0.634604 - 0.359083i) q^{30} +0.103052i q^{31} -5.84206i q^{32} +(5.73981 - 3.24780i) q^{33} +1.23591i q^{34} +(1.40461 + 0.676466i) q^{35} +(-2.30122 + 3.83073i) q^{36} -3.37451 q^{37} +3.57262 q^{38} +(3.51635 - 1.98968i) q^{39} -1.46904i q^{40} -2.26913 q^{41} +(3.26676 - 0.216238i) q^{42} -3.75912 q^{43} -5.67180i q^{44} +(-0.910314 + 1.51535i) q^{45} +0.714425 q^{46} +11.4813 q^{47} +(1.02194 + 1.80608i) q^{48} +(4.36416 + 5.47304i) q^{49} +3.32406i q^{50} +(-1.47560 - 2.60781i) q^{51} -3.47469i q^{52} +6.67999i q^{53} +(-0.0966317 + 3.71100i) q^{54} -2.24364i q^{55} +(2.86205 - 5.94272i) q^{56} +(-7.53833 + 4.26547i) q^{57} +1.61751 q^{58} -11.3353 q^{59} +(0.748698 + 1.32317i) q^{60} -8.82935i q^{61} +0.0736227 q^{62} +(-6.63478 + 4.35656i) q^{63} -1.77753 q^{64} -1.37451i q^{65} +(-2.32031 - 4.10067i) q^{66} +13.1667 q^{67} -2.57691 q^{68} +(-1.50746 + 0.852976i) q^{69} +(0.483284 - 1.00349i) q^{70} -7.24300i q^{71} +(6.41127 + 3.85143i) q^{72} -8.17140i q^{73} +2.41083i q^{74} +(-3.96871 - 7.01388i) q^{75} +7.44901i q^{76} +(4.37117 - 9.07624i) q^{77} +(-1.42148 - 2.51217i) q^{78} -1.35694 q^{79} +0.705979 q^{80} +(-4.22680 - 7.94570i) q^{81} +1.62112i q^{82} -17.1845 q^{83} +(0.450863 + 6.81128i) q^{84} -1.01937 q^{85} +2.68561i q^{86} +(-3.41300 + 1.93120i) q^{87} -9.49258 q^{88} -2.13449 q^{89} +(1.08261 + 0.650351i) q^{90} +(2.67788 - 5.56033i) q^{91} +1.48960i q^{92} +(-0.155346 + 0.0879006i) q^{93} -8.20256i q^{94} +2.94667i q^{95} +(8.80666 - 4.98314i) q^{96} +8.67299i q^{97} +(3.91008 - 3.11786i) q^{98} +(9.79185 + 5.88223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	0.714425i		−	0.505175i	−0.967574	−	0.252587i	$-0.918718\pi$
$2$		−	0.714425i		−	0.505175i	0.967574	−	0.252587i	$-0.0812815\pi$
$3$	0.852976	+	1.50746i	0.492466	+	0.870332i
$3$	0.852976	+	1.50746i	0.492466	+	0.870332i
$4$	1.48960			0.744798
$5$	0.589252			0.263522			0.131761	−	0.991282i	$-0.457937\pi$
$5$	0.589252			0.263522			0.131761	+	0.991282i	$0.457937\pi$
$6$	1.07697	−	0.609388i	0.439670	−	0.248781i
$7$	2.38371	+	1.14801i	0.900958	+	0.433906i
$7$	2.38371	+	1.14801i	0.900958	+	0.433906i
$8$		−	2.49306i		−	0.881428i
$9$	−1.54486	+	2.57165i	−0.514954	+	0.857218i
$10$		−	0.420976i		−	0.133124i
$11$		−	3.80761i		−	1.14804i	−0.818842	−	0.574019i	$-0.805384\pi$
$11$		−	3.80761i		−	1.14804i	0.818842	−	0.574019i	$-0.194616\pi$
$12$	1.27059	+	2.24551i	0.366788	+	0.648222i
$13$		−	2.33263i		−	0.646956i	−0.946236	−	0.323478i	$-0.895148\pi$
$13$		−	2.33263i		−	0.646956i	0.946236	−	0.323478i	$-0.104852\pi$
$14$	0.820166	−	1.70298i	0.219198	−	0.455141i
$15$	0.502618	+	0.888273i	0.129775	+	0.229351i
$16$	1.19809			0.299523
$17$	−1.72994			−0.419572			−0.209786	−	0.977747i	$-0.567277\pi$
$17$	−1.72994			−0.419572			−0.209786	+	0.977747i	$0.567277\pi$
$18$	1.83725	+	1.10369i	0.433045	+	0.260142i
$19$			5.00069i			1.14724i	0.819123	+	0.573618i	$0.194461\pi$
$19$			5.00069i			1.14724i	−0.819123	+	0.573618i	$0.805539\pi$
$20$	0.877748			0.196270
$21$	0.302674	+	4.57257i	0.0660490	+	0.997816i
$22$	−2.72025			−0.579960
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	3.75818	−	2.12652i	0.767135	−	0.434073i
$25$	−4.65278			−0.930556
$26$	−1.66649			−0.326826
$27$	−5.19439	−	0.135258i	−0.999661	−	0.0260304i
$28$	3.55077	+	1.71007i	0.671032	+	0.323173i
$29$			2.26408i			0.420428i	0.977655	+	0.210214i	$0.0674161\pi$
$29$			2.26408i			0.420428i	−0.977655	+	0.210214i	$0.932584\pi$
$30$	0.634604	−	0.359083i	0.115862	−	0.0655593i
$31$			0.103052i			0.0185086i	0.999957	+	0.00925431i	$0.00294578\pi$
$31$			0.103052i			0.0185086i	−0.999957	+	0.00925431i	$0.997054\pi$
$32$		−	5.84206i		−	1.03274i
$33$	5.73981	−	3.24780i	0.999173	−	0.565369i
$34$			1.23591i			0.211957i
$35$	1.40461	+	0.676466i	0.237422	+	0.114344i
$36$	−2.30122	+	3.83073i	−0.383537	+	0.638454i
$37$	−3.37451			−0.554766			−0.277383	−	0.960759i	$-0.589467\pi$
$37$	−3.37451			−0.554766			−0.277383	+	0.960759i	$0.589467\pi$
$38$	3.57262			0.579555
$39$	3.51635	−	1.98968i	0.563067	−	0.318604i
$40$		−	1.46904i		−	0.232275i
$41$	−2.26913			−0.354378			−0.177189	−	0.984177i	$-0.556700\pi$
$41$	−2.26913			−0.354378			−0.177189	+	0.984177i	$0.556700\pi$
$42$	3.26676	−	0.216238i	0.504072	−	0.0333663i
$43$	−3.75912			−0.573260			−0.286630	−	0.958041i	$-0.592535\pi$
$43$	−3.75912			−0.573260			−0.286630	+	0.958041i	$0.592535\pi$
$44$		−	5.67180i		−	0.855056i
$45$	−0.910314	+	1.51535i	−0.135702	+	0.225895i
$46$	0.714425			0.105336
$47$	11.4813			1.67473			0.837363	−	0.546647i	$-0.184096\pi$
$47$	11.4813			1.67473			0.837363	+	0.546647i	$0.184096\pi$
$48$	1.02194	+	1.80608i	0.147505	+	0.260684i
$49$	4.36416	+	5.47304i	0.623451	+	0.781863i
$50$			3.32406i			0.470094i
$51$	−1.47560	−	2.60781i	−0.206625	−	0.365167i
$52$		−	3.47469i		−	0.481852i
$53$			6.67999i			0.917567i	0.888548	+	0.458783i	$0.151715\pi$
$53$			6.67999i			0.917567i	−0.888548	+	0.458783i	$0.848285\pi$
$54$	−0.0966317	+	3.71100i	−0.0131499	+	0.505004i
$55$		−	2.24364i		−	0.302533i
$56$	2.86205	−	5.94272i	0.382457	−	0.794130i
$57$	−7.53833	+	4.26547i	−0.998476	+	0.564975i
$58$	1.61751			0.212390
$59$	−11.3353			−1.47573			−0.737865	−	0.674949i	$-0.764166\pi$
$59$	−11.3353			−1.47573			−0.737865	+	0.674949i	$0.764166\pi$
$60$	0.748698	+	1.32317i	0.0966565	+	0.170820i
$61$		−	8.82935i		−	1.13048i	−0.824926	−	0.565241i	$-0.808783\pi$
$61$		−	8.82935i		−	1.13048i	0.824926	−	0.565241i	$-0.191217\pi$
$62$	0.0736227			0.00935009
$63$	−6.63478	+	4.35656i	−0.835904	+	0.548875i
$64$	−1.77753			−0.222191
$65$		−	1.37451i		−	0.170487i
$66$	−2.32031	−	4.10067i	−0.285610	−	0.504757i
$67$	13.1667			1.60856			0.804282	−	0.594247i	$-0.202550\pi$
$67$	13.1667			1.60856			0.804282	+	0.594247i	$0.202550\pi$
$68$	−2.57691			−0.312497
$69$	−1.50746	+	0.852976i	−0.181477	+	0.102686i
$70$	0.483284	−	1.00349i	0.0577635	−	0.119940i
$71$		−	7.24300i		−	0.859585i	−0.902928	−	0.429793i	$-0.858587\pi$
$71$		−	7.24300i		−	0.859585i	0.902928	−	0.429793i	$-0.141413\pi$
$72$	6.41127	+	3.85143i	0.755576	+	0.453895i
$73$		−	8.17140i		−	0.956390i	−0.878254	−	0.478195i	$-0.841291\pi$
$73$		−	8.17140i		−	0.956390i	0.878254	−	0.478195i	$-0.158709\pi$
$74$			2.41083i			0.280254i
$75$	−3.96871	−	7.01388i	−0.458267	−	0.809893i
$76$			7.44901i			0.854460i
$77$	4.37117	−	9.07624i	0.498141	−	1.03433i
$78$	−1.42148	−	2.51217i	−0.160951	−	0.284447i
$79$	−1.35694			−0.152667			−0.0763337	−	0.997082i	$-0.524321\pi$
$79$	−1.35694			−0.152667			−0.0763337	+	0.997082i	$0.524321\pi$
$80$	0.705979			0.0789308
$81$	−4.22680	−	7.94570i	−0.469644	−	0.882856i
$82$			1.62112i			0.179023i
$83$	−17.1845			−1.88625			−0.943124	−	0.332442i	$-0.892127\pi$
$83$	−17.1845			−1.88625			−0.943124	+	0.332442i	$0.892127\pi$
$84$	0.450863	+	6.81128i	0.0491932	+	0.743172i
$85$	−1.01937			−0.110566
$86$			2.68561i			0.289597i
$87$	−3.41300	+	1.93120i	−0.365912	+	0.207047i
$88$	−9.49258			−1.01191
$89$	−2.13449			−0.226256			−0.113128	−	0.993580i	$-0.536087\pi$
$89$	−2.13449			−0.226256			−0.113128	+	0.993580i	$0.536087\pi$
$90$	1.08261	+	0.650351i	0.114117	+	0.0685530i
$91$	2.67788	−	5.56033i	0.280718	−	0.582881i
$92$			1.48960i			0.155301i
$93$	−0.155346	+	0.0879006i	−0.0161086	+	0.00911487i
$94$		−	8.20256i		−	0.846029i
$95$			2.94667i			0.302322i
$96$	8.80666	−	4.98314i	0.898826	−	0.508589i
$97$			8.67299i			0.880609i	0.897848	+	0.440305i	$0.145130\pi$
$97$			8.67299i			0.880609i	−0.897848	+	0.440305i	$0.854870\pi$
$98$	3.91008	−	3.11786i	0.394977	−	0.314952i
$99$	9.79185	+	5.88223i	0.984118	+	0.591187i
$100$	−6.93077			−0.693077
$101$	−16.8756			−1.67918			−0.839592	−	0.543218i	$-0.817206\pi$
$101$	−16.8756			−1.67918			−0.839592	+	0.543218i	$0.817206\pi$
$102$	−1.86309	+	1.05420i	−0.184473	+	0.104382i
$103$		−	6.57408i		−	0.647763i	−0.946098	−	0.323882i	$-0.895012\pi$
$103$		−	6.57408i		−	0.647763i	0.946098	−	0.323882i	$-0.104988\pi$
$104$	−5.81539			−0.570246
$105$	0.178352	+	2.69440i	0.0174053	+	0.262946i
$106$	4.77235			0.463532
$107$			11.3501i			1.09726i	0.836065	+	0.548630i	$0.184850\pi$
$107$			11.3501i			1.09726i	−0.836065	+	0.548630i	$0.815150\pi$
$108$	−7.73755	−	0.201480i	−0.744546	−	0.0193874i
$109$	12.6901			1.21549			0.607747	−	0.794131i	$-0.292073\pi$
$109$	12.6901			1.21549			0.607747	+	0.794131i	$0.292073\pi$
$110$	−1.60291			−0.152832
$111$	−2.87838	−	5.08693i	−0.273203	−	0.482830i
$112$	2.85591	+	1.37542i	0.269858	+	0.129965i
$113$			1.93164i			0.181713i	0.995864	+	0.0908565i	$0.0289605\pi$
$113$			1.93164i			0.181713i	−0.995864	+	0.0908565i	$0.971040\pi$
$114$	3.04736	+	5.38557i	0.285411	+	0.504405i
$115$			0.589252i			0.0549480i
$116$			3.37256i			0.313134i
$117$	5.99873	+	3.60360i	0.554583	+	0.333153i
$118$			8.09822i			0.745501i
$119$	−4.12368	−	1.98599i	−0.378017	−	0.182055i
$120$	2.21451	−	1.25305i	0.202157	−	0.114388i
$121$	−3.49789			−0.317990
$122$	−6.30791			−0.571091
$123$	−1.93551	−	3.42062i	−0.174519	−	0.308427i
$124$			0.153505i			0.0137852i
$125$	−5.68792			−0.508743
$126$	3.11244	+	4.74006i	0.277278	+	0.422278i
$127$	−13.9350			−1.23653			−0.618265	−	0.785969i	$-0.712164\pi$
$127$	−13.9350			−1.23653			−0.618265	+	0.785969i	$0.712164\pi$
$128$		−	10.4142i		−	0.920494i
$129$	−3.20644	−	5.66672i	−0.282311	−	0.498927i
$130$	−0.981984			−0.0861257
$131$	−0.439094			−0.0383638			−0.0191819	−	0.999816i	$-0.506106\pi$
$131$	−0.439094			−0.0383638			−0.0191819	+	0.999816i	$0.506106\pi$
$132$	8.55001	−	4.83791i	0.744183	−	0.421086i
$133$	−5.74083	+	11.9202i	−0.497793	+	1.03361i
$134$		−	9.40660i		−	0.812606i
$135$	−3.06081	−	0.0797010i	−0.263432	−	0.00685957i
$136$			4.31284i			0.369823i
$137$			10.9573i			0.936148i	0.883689	+	0.468074i	$0.155052\pi$
$137$			10.9573i			0.936148i	−0.883689	+	0.468074i	$0.844948\pi$
$138$	0.609388	+	1.07697i	0.0518745	+	0.0916774i
$139$		−	19.9994i		−	1.69632i	−0.529737	−	0.848162i	$-0.677709\pi$
$139$		−	19.9994i		−	1.69632i	0.529737	−	0.848162i	$-0.322291\pi$
$140$	2.09230	+	1.00766i	0.176831	+	0.0851630i
$141$	9.79331	+	17.3077i	0.824746	+	1.45757i
$142$	−5.17458			−0.434241
$143$	−8.88176			−0.742730
$144$	−1.85089	+	3.08108i	−0.154241	+	0.256757i
$145$			1.33411i			0.110792i
$146$	−5.83785			−0.483144
$147$	−4.52786	+	11.2472i	−0.373451	+	0.927650i
$148$	−5.02666			−0.413189
$149$			10.5399i			0.863459i	0.902003	+	0.431729i	$0.142096\pi$
$149$			10.5399i			0.863459i	−0.902003	+	0.431729i	$0.857904\pi$
$150$	−5.01089	+	2.83535i	−0.409137	+	0.231505i
$151$	−10.3664			−0.843605			−0.421803	−	0.906688i	$-0.638602\pi$
$151$	−10.3664			−0.843605			−0.421803	+	0.906688i	$0.638602\pi$
$152$	12.4670			1.01121
$153$	2.67252	−	4.44881i	0.216061	−	0.359665i
$154$	−6.48429	−	3.12287i	−0.522519	−	0.251648i
$155$			0.0607234i			0.00487742i
$156$	5.23794	−	2.96382i	0.419371	−	0.237296i
$157$			1.65236i			0.131872i	0.997824	+	0.0659361i	$0.0210034\pi$
$157$			1.65236i			0.131872i	−0.997824	+	0.0659361i	$0.978997\pi$
$158$			0.969430i			0.0771237i
$159$	−10.0698	+	5.69787i	−0.798588	+	0.451871i
$160$		−	3.44244i		−	0.272149i
$161$	−1.14801	+	2.38371i	−0.0904757	+	0.187863i
$162$	−5.67661	+	3.01973i	−0.445996	+	0.237252i
$163$	5.40626			0.423451			0.211725	−	0.977329i	$-0.432092\pi$
$163$	5.40626			0.423451			0.211725	+	0.977329i	$0.432092\pi$
$164$	−3.38009			−0.263940
$165$	3.38220	−	1.91377i	0.263304	−	0.148987i
$166$			12.2771i			0.952885i
$167$	14.3296			1.10886			0.554430	−	0.832230i	$-0.312936\pi$
$167$	14.3296			1.10886			0.554430	+	0.832230i	$0.312936\pi$
$168$	11.3997	−	0.754584i	0.879503	−	0.0582174i
$169$	7.55881			0.581447
$170$			0.728264i			0.0558553i
$171$	−12.8600	−	7.72538i	−0.983432	−	0.590774i
$172$	−5.59957			−0.426963
$173$	23.9675			1.82221			0.911107	−	0.412169i	$-0.135229\pi$
$173$	23.9675			1.82221			0.911107	+	0.412169i	$0.135229\pi$
$174$	1.37970	+	2.43833i	0.104595	+	0.184850i
$175$	−11.0909	−	5.34143i	−0.838392	−	0.403774i
$176$		−	4.56187i		−	0.343864i
$177$	−9.66874	−	17.0875i	−0.726747	−	1.28437i
$178$			1.52494i			0.114299i
$179$		−	9.27872i		−	0.693524i	−0.937953	−	0.346762i	$-0.887281\pi$
$179$		−	9.27872i		−	0.693524i	0.937953	−	0.346762i	$-0.112719\pi$
$180$	−1.35600	+	2.25726i	−0.101070	+	0.168246i
$181$			6.46612i			0.480623i	0.970696	+	0.240311i	$0.0772496\pi$
$181$			6.46612i			0.480623i	−0.970696	+	0.240311i	$0.922750\pi$
$182$	−3.97244	−	1.91315i	−0.294457	−	0.141812i
$183$	13.3099	−	7.53122i	0.983894	−	0.556724i
$184$	2.49306			0.183790
$185$	−1.98844			−0.146193
$186$	0.0627984	+	0.110983i	0.00460460	+	0.00813768i
$187$			6.58694i			0.481685i
$188$	17.1026			1.24733
$189$	−12.2267	−	6.28562i	−0.889358	−	0.457211i
$190$	2.10517			0.152725
$191$			2.01200i			0.145584i	0.997347	+	0.0727918i	$0.0231908\pi$
$191$			2.01200i			0.145584i	−0.997347	+	0.0727918i	$0.976809\pi$
$192$	−1.51619	−	2.67955i	−0.109421	−	0.193380i
$193$	9.52142			0.685367			0.342684	−	0.939451i	$-0.388664\pi$
$193$	9.52142			0.685367			0.342684	+	0.939451i	$0.388664\pi$
$194$	6.19620			0.444862
$195$	2.07202	−	1.17242i	0.148380	−	0.0839590i
$196$	6.50083	+	8.15262i	0.464345	+	0.582330i
$197$		−	16.4450i		−	1.17166i	−0.810435	−	0.585828i	$-0.800769\pi$
$197$		−	16.4450i		−	1.17166i	0.810435	−	0.585828i	$-0.199231\pi$
$198$	4.20242	−	6.99554i	0.298653	−	0.497152i
$199$		−	6.26097i		−	0.443829i	−0.975066	−	0.221914i	$-0.928769\pi$
$199$		−	6.26097i		−	0.443829i	0.975066	−	0.221914i	$-0.0712305\pi$
$200$			11.5996i			0.820219i
$201$	11.2309	+	19.8482i	0.792163	+	1.39998i
$202$			12.0563i			0.848281i
$203$	−2.59918	+	5.39690i	−0.182426	+	0.378788i
$204$	−2.19805	−	3.88459i	−0.153894	−	0.271976i
$205$	−1.33709			−0.0933863
$206$	−4.69669			−0.327234
$207$	−2.57165	−	1.54486i	−0.178742	−	0.107375i
$208$		−	2.79471i		−	0.193778i
$209$	19.0407			1.31707
$210$	1.92494	−	0.127419i	0.132834	−	0.00879273i
$211$	−1.70149			−0.117135			−0.0585676	−	0.998283i	$-0.518653\pi$
$211$	−1.70149			−0.117135			−0.0585676	+	0.998283i	$0.518653\pi$
$212$			9.95049i			0.683402i
$213$	10.9185	−	6.17810i	0.748124	−	0.423317i
$214$	8.10883			0.554308
$215$	−2.21507			−0.151066
$216$	−0.337206	+	12.9499i	−0.0229439	+	0.881129i
$217$	−0.118304	+	0.245645i	−0.00803101	+	0.0166755i
$218$		−	9.06615i		−	0.614037i
$219$	12.3180	−	6.97001i	0.832377	−	0.470990i
$220$		−	3.34212i		−	0.225326i
$221$			4.03532i			0.271445i
$222$	−3.63423	+	2.05638i	−0.243914	+	0.138015i
$223$		−	24.4313i		−	1.63604i	−0.575188	−	0.818021i	$-0.695071\pi$
$223$		−	24.4313i		−	1.63604i	0.575188	−	0.818021i	$-0.304929\pi$
$224$	6.70673	−	13.9258i	0.448112	−	0.930455i
$225$	7.18791	−	11.9653i	0.479194	−	0.797689i
$226$	1.38001			0.0917969
$227$	10.7631			0.714372			0.357186	−	0.934033i	$-0.383736\pi$
$227$	10.7631			0.714372			0.357186	+	0.934033i	$0.383736\pi$
$228$	−11.2291	+	6.35383i	−0.743664	+	0.420793i
$229$			27.2548i			1.80105i	0.434805	+	0.900525i	$0.356817\pi$
$229$			27.2548i			1.80105i	−0.434805	+	0.900525i	$0.643183\pi$
$230$	0.420976			0.0277584
$231$	17.4106	−	1.15247i	1.14553	−	0.0758267i
$232$	5.64447			0.370577
$233$		−	15.1992i		−	0.995734i	−0.867253	−	0.497867i	$-0.834117\pi$
$233$		−	15.1992i		−	0.995734i	0.867253	−	0.497867i	$-0.165883\pi$
$234$	2.57450	−	4.28564i	0.168301	−	0.280161i
$235$	6.76541			0.441326
$236$	−16.8850			−1.09912
$237$	−1.15743	−	2.04553i	−0.0751835	−	0.132871i
$238$	−1.41884	+	2.94606i	−0.0919696	+	0.190965i
$239$			5.78576i			0.374250i	0.982336	+	0.187125i	$0.0599169\pi$
$239$			5.78576i			0.374250i	−0.982336	+	0.187125i	$0.940083\pi$
$240$	0.602183	+	1.06423i	0.0388707	+	0.0686960i
$241$		−	19.8063i		−	1.27584i	−0.770104	−	0.637918i	$-0.779796\pi$
$241$		−	19.8063i		−	1.27584i	0.770104	−	0.637918i	$-0.220204\pi$
$242$			2.49898i			0.160640i
$243$	8.37246	−	13.1492i	0.537094	−	0.843523i
$244$		−	13.1522i		−	0.841981i
$245$	2.57159	+	3.22500i	0.164293	+	0.206038i
$246$	−2.44377	+	1.38278i	−0.155809	+	0.0881627i
$247$	11.6648			0.742212
$248$	0.256913			0.0163140
$249$	−14.6580	−	25.9050i	−0.928913	−	1.64166i
$250$			4.06359i			0.257004i
$251$	−21.4519			−1.35403			−0.677015	−	0.735970i	$-0.736727\pi$
$251$	−21.4519			−1.35403			−0.677015	+	0.735970i	$0.736727\pi$
$252$	−9.88315	+	6.48952i	−0.622580	+	0.408801i
$253$	3.80761			0.239382
$254$			9.95551i			0.624664i
$255$	−0.869499	−	1.53666i	−0.0544502	−	0.0962294i
$256$	−10.9952			−0.687201
$257$	28.3004			1.76533			0.882666	−	0.470001i	$-0.155746\pi$
$257$	28.3004			1.76533			0.882666	+	0.470001i	$0.155746\pi$
$258$	−4.04844	+	2.29076i	−0.252045	+	0.142617i
$259$	−8.04386	−	3.87396i	−0.499821	−	0.240716i
$260$		−	2.04747i		−	0.126978i
$261$	−5.82242	−	3.49769i	−0.360399	−	0.216501i
$262$			0.313699i			0.0193804i
$263$			10.6761i			0.658316i	0.944275	+	0.329158i	$0.106765\pi$
$263$			10.6761i			0.658316i	−0.944275	+	0.329158i	$0.893235\pi$
$264$	−8.09695	−	14.3097i	−0.498333	−	0.880699i
$265$			3.93620i			0.241799i
$266$	8.51609	+	4.10139i	0.522155	+	0.251473i
$267$	−1.82067	−	3.21766i	−0.111423	−	0.196918i
$268$	19.6130			1.19806
$269$	13.0441			0.795310			0.397655	−	0.917535i	$-0.369824\pi$
$269$	13.0441			0.795310			0.397655	+	0.917535i	$0.369824\pi$
$270$	−0.0569404	+	2.18672i	−0.00346528	+	0.133079i
$271$			9.61813i			0.584260i	0.956379	+	0.292130i	$0.0943639\pi$
$271$			9.61813i			0.584260i	−0.956379	+	0.292130i	$0.905636\pi$
$272$	−2.07263			−0.125672
$273$	10.6661	−	0.706029i	0.645544	−	0.0427308i
$274$	7.82819			0.472918
$275$			17.7160i			1.06831i
$276$	−2.24551	+	1.27059i	−0.135164	+	0.0764806i
$277$	−7.57171			−0.454940			−0.227470	−	0.973785i	$-0.573045\pi$
$277$	−7.57171			−0.454940			−0.227470	+	0.973785i	$0.573045\pi$
$278$	−14.2881			−0.856940
$279$	−0.265013	−	0.159201i	−0.0158659	−	0.00953109i
$280$	1.68647	−	3.50176i	0.100786	−	0.209270i
$281$			0.0198510i			0.00118421i	1.00000		0.000592106i	$0.000188473\pi$
$281$			0.0198510i			0.00118421i	−1.00000		0.000592106i	$0.999812\pi$
$282$	12.3650	−	6.99659i	0.736326	−	0.416641i
$283$		−	7.50666i		−	0.446225i	−0.974793	−	0.223112i	$-0.928378\pi$
$283$		−	7.50666i		−	0.446225i	0.974793	−	0.223112i	$-0.0716217\pi$
$284$		−	10.7891i		−	0.640218i
$285$	−4.44198	+	2.51344i	−0.263120	+	0.148883i
$286$			6.34535i			0.375209i
$287$	−5.40895	−	2.60498i	−0.319280	−	0.153767i
$288$	15.0237	+	9.02518i	0.885283	+	0.531814i
$289$	−14.0073			−0.823959
$290$	0.953122			0.0559693
$291$	−13.0742	+	7.39786i	−0.766422	+	0.433670i
$292$		−	12.1721i		−	0.712318i
$293$	20.1806			1.17896			0.589481	−	0.807782i	$-0.299332\pi$
$293$	20.1806			1.17896			0.589481	+	0.807782i	$0.299332\pi$
$294$	8.03525	+	3.23481i	0.468625	+	0.188658i
$295$	−6.67934			−0.388886
$296$			8.41284i			0.488986i
$297$	−0.515010	+	19.7782i	−0.0298839	+	1.14765i
$298$	7.52994			0.436197
$299$	2.33263			0.134900
$300$	−5.91178	−	10.4478i	−0.341317	−	0.603207i
$301$	−8.96065	−	4.31550i	−0.516483	−	0.248741i
$302$			7.40601i			0.426168i
$303$	−14.3945	−	25.4392i	−0.826941	−	1.46145i
$304$			5.99129i			0.343624i
$305$		−	5.20271i		−	0.297906i
$306$	−3.17834	−	1.90932i	−0.181694	−	0.109148i
$307$			20.1367i			1.14926i	0.818413	+	0.574631i	$0.194854\pi$
$307$			20.1367i			1.14926i	−0.818413	+	0.574631i	$0.805146\pi$
$308$	6.51127	−	13.5199i	0.371014	−	0.770370i
$309$	9.91015	−	5.60753i	0.563769	−	0.319001i
$310$	0.0433823			0.00246395
$311$	−10.4395			−0.591972			−0.295986	−	0.955192i	$-0.595648\pi$
$311$	−10.4395			−0.591972			−0.295986	+	0.955192i	$0.595648\pi$
$312$	−4.96039	−	8.76646i	−0.280827	−	0.496303i
$313$			19.6359i			1.10988i	0.831889	+	0.554942i	$0.187260\pi$
$313$			19.6359i			1.10988i	−0.831889	+	0.554942i	$0.812740\pi$
$314$	1.18048			0.0666186
$315$	−3.90956	+	2.56711i	−0.220279	+	0.144640i
$316$	−2.02129			−0.113706
$317$			24.9222i			1.39977i	0.714254	+	0.699886i	$0.246766\pi$
$317$			24.9222i			1.39977i	−0.714254	+	0.699886i	$0.753234\pi$
$318$	4.07070	+	7.19412i	0.228274	+	0.403426i
$319$	8.62071			0.482667
$320$	−1.04741			−0.0585521
$321$	−17.1099	+	9.68140i	−0.954980	+	0.540363i
$322$	1.70298	+	0.820166i	0.0949035	+	0.0457060i
$323$		−	8.65090i		−	0.481349i
$324$	−6.29622	−	11.8359i	−0.349790	−	0.657550i
$325$			10.8532i			0.602030i
$326$		−	3.86237i		−	0.213917i
$327$	10.8244	+	19.1298i	0.598590	+	1.05788i
$328$			5.65706i			0.312359i
$329$	27.3682	+	13.1807i	1.50886	+	0.726674i
$330$	−1.36725	−	2.41633i	−0.0752645	−	0.133014i
$331$	22.5759			1.24088			0.620441	−	0.784253i	$-0.286953\pi$
$331$	22.5759			1.24088			0.620441	+	0.784253i	$0.286953\pi$
$332$	−25.5980			−1.40487
$333$	5.21315	−	8.67807i	0.285679	−	0.475555i
$334$		−	10.2374i		−	0.560168i
$335$	7.75849			0.423891
$336$	0.362632	+	5.47836i	0.0197832	+	0.298869i
$337$	21.3122			1.16095			0.580475	−	0.814278i	$-0.302867\pi$
$337$	21.3122			1.16095			0.580475	+	0.814278i	$0.302867\pi$
$338$		−	5.40021i		−	0.293733i
$339$	−2.91186	+	1.64764i	−0.158151	+	0.0894875i
$340$	−1.51845			−0.0823496
$341$	0.392380			0.0212486
$342$	−5.51920	+	9.18753i	−0.298444	+	0.496805i
$343$	4.11979	+	18.0562i	0.222448	+	0.974945i
$344$			9.37169i			0.505288i
$345$	−0.888273	+	0.502618i	−0.0478230	+	0.0270600i
$346$		−	17.1230i		−	0.920537i
$347$			8.72533i			0.468400i	0.972188	+	0.234200i	$0.0752471\pi$
$347$			8.72533i			0.468400i	−0.972188	+	0.234200i	$0.924753\pi$
$348$	−5.08399	+	2.87671i	−0.272531	+	0.154208i
$349$			4.28010i			0.229108i	0.993417	+	0.114554i	$0.0365439\pi$
$349$			4.28010i			0.229108i	−0.993417	+	0.114554i	$0.963456\pi$
$350$	−3.81605	+	7.92361i	−0.203977	+	0.423535i
$351$	−0.315507	+	12.1166i	−0.0168405	+	0.646737i
$352$	−22.2443			−1.18562
$353$	22.9746			1.22281			0.611406	−	0.791317i	$-0.290604\pi$
$353$	22.9746			1.22281			0.611406	+	0.791317i	$0.290604\pi$
$354$	−12.2077	+	6.90759i	−0.648833	+	0.367134i
$355$		−	4.26795i		−	0.226519i
$356$	−3.17954			−0.168515
$357$	−0.523609	−	7.91027i	−0.0277123	−	0.418656i
$358$	−6.62895			−0.350351
$359$			1.37812i			0.0727342i	0.999338	+	0.0363671i	$0.0115786\pi$
$359$			1.37812i			0.0727342i	−0.999338	+	0.0363671i	$0.988421\pi$
$360$	3.77786	+	2.26946i	0.199110	+	0.119611i
$361$	−6.00689			−0.316152
$362$	4.61956			0.242799
$363$	−2.98362	−	5.27292i	−0.156599	−	0.276757i
$364$	3.98897	−	8.28265i	0.209079	−	0.434129i
$365$		−	4.81501i		−	0.252029i
$366$	−5.38049	−	9.50891i	−0.281243	−	0.497039i
$367$			24.3540i			1.27127i	0.771991	+	0.635634i	$0.219261\pi$
$367$			24.3540i			1.27127i	−0.771991	+	0.635634i	$0.780739\pi$
$368$			1.19809i			0.0624549i
$369$	3.50549	−	5.83541i	0.182489	−	0.303779i
$370$			1.42059i			0.0738529i
$371$	−7.66868	+	15.9232i	−0.398138	+	0.826689i
$372$	−0.231403	+	0.130936i	−0.0119977	+	0.00678874i
$373$	−4.05282			−0.209847			−0.104923	−	0.994480i	$-0.533460\pi$
$373$	−4.05282			−0.209847			−0.104923	+	0.994480i	$0.533460\pi$
$374$	4.70587			0.243335
$375$	−4.85166	−	8.57431i	−0.250539	−	0.442775i
$376$		−	28.6236i		−	1.47615i
$377$	5.28126			0.271999
$378$	−4.49060	+	8.73503i	−0.230972	+	0.449281i
$379$	−22.0977			−1.13509			−0.567543	−	0.823344i	$-0.692106\pi$
$379$	−22.0977			−1.13509			−0.567543	+	0.823344i	$0.692106\pi$
$380$			4.38934i			0.225169i
$381$	−11.8862	−	21.0064i	−0.608950	−	1.07619i
$382$	1.43743			0.0735451
$383$	−1.79067			−0.0914991			−0.0457495	−	0.998953i	$-0.514568\pi$
$383$	−1.79067			−0.0914991			−0.0457495	+	0.998953i	$0.514568\pi$
$384$	15.6990	−	8.88307i	0.801135	−	0.453312i
$385$	2.57572	−	5.34819i	0.131271	−	0.272569i
$386$		−	6.80234i		−	0.346230i
$387$	5.80732	−	9.66715i	0.295203	−	0.491409i
$388$			12.9193i			0.655876i
$389$			14.6327i			0.741906i	0.928652	+	0.370953i	$0.120969\pi$
$389$			14.6327i			0.741906i	−0.928652	+	0.370953i	$0.879031\pi$
$390$	−0.837609	−	1.48030i	−0.0424140	−	0.0749579i
$391$		−	1.72994i		−	0.0874869i
$392$	13.6446	−	10.8801i	0.689156	−	0.549527i
$393$	−0.374536	−	0.661915i	−0.0188929	−	0.0333892i
$394$	−11.7487			−0.591891
$395$	−0.799578			−0.0402311
$396$	14.5859	+	8.76216i	0.732969	+	0.440315i
$397$		−	7.77702i		−	0.390318i	−0.980772	−	0.195159i	$-0.937478\pi$
$397$		−	7.77702i		−	0.390318i	0.980772	−	0.195159i	$-0.0625222\pi$
$398$	−4.47300			−0.224211
$399$	−22.8660	+	1.51358i	−1.14473	+	0.0757738i
$400$	−5.57446			−0.278723
$401$			34.9157i			1.74361i	0.489856	+	0.871803i	$0.337049\pi$
$401$			34.9157i			1.74361i	−0.489856	+	0.871803i	$0.662951\pi$
$402$	14.1801	−	8.02360i	0.707237	−	0.400181i
$403$	0.240382			0.0119743
$404$	−25.1378			−1.25065
$405$	−2.49065	−	4.68202i	−0.123761	−	0.232651i
$406$	3.85568	+	1.85692i	0.191354	+	0.0921572i
$407$			12.8488i			0.636892i
$408$	−6.50143	+	3.67875i	−0.321869	+	0.182125i
$409$			4.78603i			0.236654i	0.992975	+	0.118327i	$0.0377531\pi$
$409$			4.78603i			0.236654i	−0.992975	+	0.118327i	$0.962247\pi$
$410$			0.955249i			0.0471764i
$411$	−16.5177	+	9.34634i	−0.814759	+	0.461021i
$412$		−	9.79273i		−	0.482453i
$413$	−27.0201	−	13.0130i	−1.32957	−	0.640328i
$414$	−1.10369	+	1.83725i	−0.0542433	+	0.0902961i
$415$	−10.1260			−0.497067
$416$	−13.6274			−0.668138
$417$	30.1482	−	17.0590i	1.47636	−	0.835382i
$418$		−	13.6031i		−	0.665351i
$419$	−11.8305			−0.577959			−0.288980	−	0.957335i	$-0.593316\pi$
$419$	−11.8305			−0.577959			−0.288980	+	0.957335i	$0.593316\pi$
$420$	0.265672	+	4.01356i	0.0129635	+	0.195842i
$421$	−16.5949			−0.808787			−0.404393	−	0.914585i	$-0.632517\pi$
$421$	−16.5949			−0.808787			−0.404393	+	0.914585i	$0.632517\pi$
$422$			1.21558i			0.0591737i
$423$	−17.7371	+	29.5260i	−0.862407	+	1.43560i
$424$	16.6536			0.808769
$425$	8.04904			0.390436
$426$	−4.41379	−	7.80046i	−0.213849	−	0.377934i
$427$	10.1362	−	21.0466i	0.490523	−	1.01852i
$428$			16.9071i			0.817237i
$429$	−7.57593	−	13.3889i	−0.365769	−	0.646422i
$430$			1.58250i			0.0763149i
$431$			15.5316i			0.748130i	0.927403	+	0.374065i	$0.122036\pi$
$431$			15.5316i			0.748130i	−0.927403	+	0.374065i	$0.877964\pi$
$432$	−6.22336	−	0.162052i	−0.299422	−	0.00779671i
$433$		−	31.4475i		−	1.51127i	−0.654992	−	0.755636i	$-0.727328\pi$
$433$		−	31.4475i		−	1.51127i	0.654992	−	0.755636i	$-0.272672\pi$
$434$	0.175495	+	0.0845194i	0.00842404	+	0.00405706i
$435$	−2.01112	+	1.13797i	−0.0964257	+	0.0545612i
$436$	18.9032			0.905298
$437$	−5.00069			−0.239215
$438$	−4.97955	−	8.80032i	−0.237932	−	0.420496i
$439$			8.77600i			0.418856i	0.977824	+	0.209428i	$0.0671601\pi$
$439$			8.77600i			0.418856i	−0.977824	+	0.209428i	$0.932840\pi$
$440$	−5.59352			−0.266661
$441$	−20.8168	+	2.76800i	−0.991275	+	0.131810i
$442$	2.88293			0.137127
$443$			17.8387i			0.847540i	0.905770	+	0.423770i	$0.139294\pi$
$443$			17.8387i			0.847540i	−0.905770	+	0.423770i	$0.860706\pi$
$444$	−4.28762	−	7.57748i	−0.203481	−	0.359611i
$445$	−1.25775			−0.0596233
$446$	−17.4544			−0.826488
$447$	−15.8884	+	8.99025i	−0.751495	+	0.425224i
$448$	−4.23711	−	2.04062i	−0.200185	−	0.0964100i
$449$		−	32.8107i		−	1.54843i	−0.632921	−	0.774216i	$-0.718144\pi$
$449$		−	32.8107i		−	1.54843i	0.632921	−	0.774216i	$-0.281856\pi$
$450$	−8.54834	−	5.13522i	−0.402973	−	0.242077i
$451$			8.63995i			0.406839i
$452$			2.87736i			0.135340i
$453$	−8.84229	−	15.6269i	−0.415447	−	0.734216i
$454$		−	7.68943i		−	0.360883i
$455$	1.57795	−	3.27643i	0.0739753	−	0.153602i
$456$	10.6341	+	18.7935i	0.497985	+	0.880085i
$457$	31.1665			1.45791			0.728953	−	0.684564i	$-0.240007\pi$
$457$	31.1665			1.45791			0.728953	+	0.684564i	$0.240007\pi$
$458$	19.4715			0.909845
$459$	8.98599	+	0.233988i	0.419430	+	0.0109216i
$460$			0.877748i			0.0409252i
$461$	−0.159956			−0.00744991			−0.00372495	−	0.999993i	$-0.501186\pi$
$461$	−0.159956			−0.00744991			−0.00372495	+	0.999993i	$0.501186\pi$
$462$	−0.823351	−	12.4385i	−0.0383057	−	0.578693i
$463$	16.1044			0.748434			0.374217	−	0.927341i	$-0.377911\pi$
$463$	16.1044			0.748434			0.374217	+	0.927341i	$0.377911\pi$
$464$			2.71257i			0.125928i
$465$	−0.0915380	+	0.0517956i	−0.00424497	+	0.00240196i
$466$	−10.8587			−0.503020
$467$	−7.45279			−0.344874			−0.172437	−	0.985021i	$-0.555164\pi$
$467$	−7.45279			−0.344874			−0.172437	+	0.985021i	$0.555164\pi$
$468$	8.93569	+	5.36791i	0.413052	+	0.248132i
$469$	31.3855	+	15.1154i	1.44925	+	0.697966i
$470$		−	4.83337i		−	0.222947i
$471$	−2.49086	+	1.40942i	−0.114773	+	0.0649426i
$472$			28.2595i			1.30075i
$473$			14.3133i			0.658124i
$474$	−1.46137	+	0.826900i	−0.0671232	+	0.0379808i
$475$		−	23.2671i		−	1.06757i
$476$	−6.14262	−	2.95832i	−0.281547	−	0.135594i
$477$	−17.1786	−	10.3197i	−0.786555	−	0.472505i
$478$	4.13349			0.189062
$479$	25.2388			1.15319			0.576595	−	0.817030i	$-0.304381\pi$
$479$	25.2388			1.15319			0.576595	+	0.817030i	$0.304381\pi$
$480$	5.18934	−	2.93632i	0.236860	−	0.134024i
$481$			7.87150i			0.358909i
$482$	−14.1501			−0.644520
$483$	−4.57257	+	0.302674i	−0.208059	+	0.0137722i
$484$	−5.21044			−0.236838
$485$			5.11058i			0.232059i
$486$	−9.39413	−	5.98149i	−0.426126	−	0.271326i
$487$	−20.7089			−0.938410			−0.469205	−	0.883089i	$-0.655459\pi$
$487$	−20.7089			−0.938410			−0.469205	+	0.883089i	$0.655459\pi$
$488$	−22.0121			−0.996439
$489$	4.61141	+	8.14971i	0.208535	+	0.368543i
$490$	2.30402	−	1.83721i	0.104085	−	0.0829965i
$491$		−	11.1874i		−	0.504882i	−0.967612	−	0.252441i	$-0.918767\pi$
$491$		−	11.1874i		−	0.504882i	0.967612	−	0.252441i	$-0.0812334\pi$
$492$	−2.88313	−	5.09534i	−0.129982	−	0.229716i
$493$		−	3.91672i		−	0.176400i
$494$		−	8.33361i		−	0.374947i
$495$	5.76987	+	3.46612i	0.259336	+	0.155790i
$496$			0.123465i			0.00554376i
$497$	8.31502	−	17.2652i	0.372979	−	0.774450i
$498$	−18.5072	+	10.4720i	−0.829326	+	0.469263i
$499$	−32.4277			−1.45166			−0.725831	−	0.687873i	$-0.758544\pi$
$499$	−32.4277			−1.45166			−0.725831	+	0.687873i	$0.758544\pi$
$500$	−8.47271			−0.378911
$501$	12.2228	+	21.6013i	0.546076	+	0.965076i
$502$			15.3257i			0.684021i
$503$	−19.8267			−0.884030			−0.442015	−	0.897008i	$-0.645736\pi$
$503$	−19.8267			−0.884030			−0.442015	+	0.897008i	$0.645736\pi$
$504$	10.8612	+	16.5409i	0.483794	+	0.736790i
$505$	−9.94397			−0.442501
$506$		−	2.72025i		−	0.120930i
$507$	6.44749	+	11.3946i	0.286343	+	0.506052i
$508$	−20.7575			−0.920966
$509$	−6.73238			−0.298407			−0.149204	−	0.988806i	$-0.547671\pi$
$509$	−6.73238			−0.298407			−0.149204	+	0.988806i	$0.547671\pi$
$510$	−1.09783	+	0.621192i	−0.0486127	+	0.0275069i
$511$	9.38083	−	19.4783i	0.414984	−	0.861667i
$512$		−	12.9731i		−	0.573338i
$513$	0.676383	−	25.9755i	0.0298630	−	1.14685i
$514$		−	20.2185i		−	0.891801i
$515$		−	3.87379i		−	0.170700i
$516$	−4.77630	−	8.44112i	−0.210265	−	0.371600i
$517$		−	43.7165i		−	1.92265i
$518$	−2.76766	+	5.74673i	−0.121604	+	0.252497i
$519$	20.4437	+	36.1300i	0.897379	+	1.58593i
$520$	−3.42673			−0.150272
$521$	8.69062			0.380743			0.190372	−	0.981712i	$-0.439031\pi$
$521$	8.69062			0.380743			0.190372	+	0.981712i	$0.439031\pi$
$522$	−2.49883	+	4.15968i	−0.109371	+	0.182064i
$523$		−	35.0416i		−	1.53226i	−0.642685	−	0.766131i	$-0.722179\pi$
$523$		−	35.0416i		−	1.53226i	0.642685	−	0.766131i	$-0.277821\pi$
$524$	−0.654073			−0.0285733
$525$	−1.40828	−	21.2752i	−0.0614623	−	0.928524i
$526$	7.62727			0.332565
$527$		−	0.178273i		−	0.00776570i
$528$	6.87683	−	3.89117i	0.299276	−	0.169341i
$529$	−1.00000			−0.0434783
$530$	2.81212			0.122151
$531$	17.5115	−	29.1504i	0.759933	−	1.26502i
$532$	−8.55152	+	17.7563i	−0.370756	+	0.769833i
$533$			5.29305i			0.229267i
$534$	−2.29878	+	1.30073i	−0.0994778	+	0.0562883i
$535$			6.68809i			0.289152i
$536$		−	32.8252i		−	1.41783i
$537$	13.9873	−	7.91453i	0.603596	−	0.341537i
$538$		−	9.31900i		−	0.401771i
$539$	20.8392	−	16.6170i	0.897607	−	0.715745i
$540$	−4.55937	−	0.118722i	−0.196204	−	0.00510900i
$541$	−15.5248			−0.667461			−0.333731	−	0.942668i	$-0.608308\pi$
$541$	−15.5248			−0.667461			−0.333731	+	0.942668i	$0.608308\pi$
$542$	6.87143			0.295153
$543$	−9.74741	+	5.51545i	−0.418301	+	0.236690i
$544$			10.1064i			0.433309i
$545$	7.47768			0.320309
$546$	−0.504405	−	7.62015i	−0.0215865	−	0.326112i
$547$	4.31304			0.184412			0.0922061	−	0.995740i	$-0.470608\pi$
$547$	4.31304			0.184412			0.0922061	+	0.995740i	$0.470608\pi$
$548$			16.3220i			0.697242i
$549$	22.7060	+	13.6401i	0.969069	+	0.582147i
$550$	12.6567			0.539685
$551$	−11.3219			−0.482331
$552$	2.12652	+	3.75818i	0.0905106	+	0.159959i
$553$	−3.23455	−	1.55777i	−0.137547	−	0.0662433i
$554$			5.40942i			0.229824i
$555$	−1.69609	−	2.99749i	−0.0719950	−	0.127236i
$556$		−	29.7910i		−	1.26342i
$557$		−	37.7042i		−	1.59758i	−0.601612	−	0.798788i	$-0.705475\pi$
$557$		−	37.7042i		−	1.59758i	0.601612	−	0.798788i	$-0.294525\pi$
$558$	−0.113737	+	0.189332i	−0.00481487	+	0.00801506i
$559$			8.76865i			0.370874i
$560$	1.68285	+	0.810469i	0.0711133	+	0.0342486i
$561$	−9.92954	+	5.61850i	−0.419225	+	0.237213i
$562$	0.0141821			0.000598234
$563$	38.4472			1.62036			0.810178	−	0.586184i	$-0.199371\pi$
$563$	38.4472			1.62036			0.810178	+	0.586184i	$0.199371\pi$
$564$	14.5881	+	25.7814i	0.614269	+	1.08559i
$565$			1.13822i			0.0478853i
$566$	−5.36295			−0.225421
$567$	−0.953733	−	23.7927i	−0.0400530	−	0.999198i
$568$	−18.0572			−0.757663
$569$			8.91183i			0.373604i	0.982398	+	0.186802i	$0.0598122\pi$
$569$			8.91183i			0.373604i	−0.982398	+	0.186802i	$0.940188\pi$
$570$	1.79566	+	3.17346i	0.0752120	+	0.132922i
$571$	24.6909			1.03328			0.516640	−	0.856203i	$-0.327183\pi$
$571$	24.6909			1.03328			0.516640	+	0.856203i	$0.327183\pi$
$572$	−13.2302			−0.553184
$573$	−3.03301	+	1.71619i	−0.126706	+	0.0716949i
$574$	−1.86106	+	3.86429i	−0.0776792	+	0.161292i
$575$		−	4.65278i		−	0.194034i
$576$	2.74604	−	4.57118i	0.114418	−	0.190466i
$577$			20.5780i			0.856673i	0.903619	+	0.428336i	$0.140900\pi$
$577$			20.5780i			0.856673i	−0.903619	+	0.428336i	$0.859100\pi$
$578$			10.0072i			0.416243i
$579$	8.12155	+	14.3532i	0.337520	+	0.596497i
$580$			1.98729i			0.0825176i
$581$	−40.9630	−	19.7280i	−1.69943	−	0.818454i
$582$	5.28522	+	9.34052i	0.219079	+	0.387177i
$583$	25.4348			1.05340
$584$	−20.3718			−0.842989
$585$	3.53476	+	2.12343i	0.146144	+	0.0877930i
$586$		−	14.4175i		−	0.595582i
$587$	−8.40152			−0.346768			−0.173384	−	0.984854i	$-0.555470\pi$
$587$	−8.40152			−0.346768			−0.173384	+	0.984854i	$0.555470\pi$
$588$	−6.74468	+	16.7537i	−0.278146	+	0.690912i
$589$	−0.515329			−0.0212338
$590$			4.77189i			0.196456i
$591$	24.7901	−	14.0272i	1.01973	−	0.577001i
$592$	−4.04298			−0.166165
$593$	−9.19884			−0.377751			−0.188876	−	0.982001i	$-0.560484\pi$
$593$	−9.19884			−0.377751			−0.188876	+	0.982001i	$0.560484\pi$
$594$	14.1301	+	0.367936i	0.579763	+	0.0150966i
$595$	−2.42989	−	1.17025i	−0.0996156	−	0.0479754i
$596$			15.7001i			0.643103i
$597$	9.43816	−	5.34046i	0.386278	−	0.218571i
$598$		−	1.66649i		−	0.0681480i
$599$		−	24.1985i		−	0.988725i	−0.869256	−	0.494362i	$-0.835402\pi$
$599$		−	24.1985i		−	0.988725i	0.869256	−	0.494362i	$-0.164598\pi$
$600$	−17.4860	+	9.89422i	−0.713862	+	0.403930i
$601$			47.3489i			1.93140i	0.259656	+	0.965701i	$0.416391\pi$
$601$			47.3489i			1.93140i	−0.259656	+	0.965701i	$0.583609\pi$
$602$	−3.08310	+	6.40171i	−0.125658	+	0.260914i
$603$	−20.3407	+	33.8601i	−0.828337	+	1.37889i
$604$	−15.4418			−0.628316
$605$	−2.06114			−0.0837972
$606$	−18.1744	+	10.2838i	−0.738286	+	0.417750i
$607$			19.1419i			0.776947i	0.921460	+	0.388474i	$0.126998\pi$
$607$			19.1419i			0.776947i	−0.921460	+	0.388474i	$0.873002\pi$
$608$	29.2143			1.18480
$609$	−10.3526	+	0.685278i	−0.419510	+	0.0277689i
$610$	−3.71695			−0.150495
$611$		−	26.7818i		−	1.08347i
$612$	3.98098	−	6.62693i	0.160922	−	0.267878i
$613$	2.35025			0.0949258			0.0474629	−	0.998873i	$-0.484886\pi$
$613$	2.35025			0.0949258			0.0474629	+	0.998873i	$0.484886\pi$
$614$	14.3862			0.580578
$615$	−1.14050	−	2.01561i	−0.0459896	−	0.0812770i
$616$	−22.6276	−	10.8976i	−0.911691	−	0.439075i
$617$			8.92348i			0.359246i	0.983736	+	0.179623i	$0.0574878\pi$
$617$			8.92348i			0.359246i	−0.983736	+	0.179623i	$0.942512\pi$
$618$	−4.00616	−	7.08006i	−0.161151	−	0.284802i
$619$			43.9160i			1.76513i	0.470188	+	0.882567i	$0.344186\pi$
$619$			43.9160i			1.76513i	−0.470188	+	0.882567i	$0.655814\pi$
$620$			0.0904534i			0.00363269i
$621$	0.135258	−	5.19439i	0.00542772	−	0.208444i
$622$			7.45826i			0.299049i
$623$	−5.08802	−	2.45042i	−0.203847	−	0.0981738i
$624$	4.21291	−	2.38382i	0.168652	−	0.0954293i
$625$	19.9123			0.796492
$626$	14.0284			0.560686
$627$	16.2412	+	28.7030i	0.648613	+	1.14629i
$628$			2.46134i			0.0982183i
$629$	5.83770			0.232764
$630$	1.83401	+	2.79309i	0.0730687	+	0.111279i
$631$	−39.0172			−1.55325			−0.776624	−	0.629964i	$-0.783070\pi$
$631$	−39.0172			−1.55325			−0.776624	+	0.629964i	$0.783070\pi$
$632$			3.38292i			0.134565i
$633$	−1.45133	−	2.56492i	−0.0576851	−	0.101946i
$634$	17.8051			0.707130
$635$	−8.21122			−0.325852
$636$	−15.0000	+	8.48753i	−0.594787	+	0.336553i
$637$	12.7666	−	10.1800i	0.505831	−	0.403346i
$638$		−	6.15885i		−	0.243831i
$639$	18.6265	+	11.1894i	0.736852	+	0.442647i
$640$		−	6.13659i		−	0.242570i
$641$			43.7720i			1.72889i	0.502728	+	0.864445i	$0.332330\pi$
$641$			43.7720i			1.72889i	−0.502728	+	0.864445i	$0.667670\pi$
$642$	6.91664	+	12.2237i	0.272978	+	0.482432i
$643$			38.2852i			1.50982i	0.655827	+	0.754911i	$0.272320\pi$
$643$			38.2852i			1.50982i	−0.655827	+	0.754911i	$0.727680\pi$
$644$	−1.71007	+	3.55077i	−0.0673862	+	0.139920i
$645$	−1.88940	−	3.33912i	−0.0743951	−	0.131478i
$646$	−6.18042			−0.243165
$647$	2.41742			0.0950384			0.0475192	−	0.998870i	$-0.484868\pi$
$647$	2.41742			0.0950384			0.0475192	+	0.998870i	$0.484868\pi$
$648$	−19.8091	+	10.5376i	−0.778174	+	0.413958i
$649$			43.1604i			1.69419i
$650$	7.75383			0.304130
$651$	−0.471211	+	0.0311911i	−0.0184682	+	0.00122248i
$652$	8.05315			0.315386
$653$			43.0154i			1.68332i	0.540004	+	0.841662i	$0.318423\pi$
$653$			43.0154i			1.68332i	−0.540004	+	0.841662i	$0.681577\pi$
$654$	13.6668	−	7.73321i	0.534416	−	0.302392i
$655$	−0.258737			−0.0101097
$656$	−2.71863			−0.106144
$657$	21.0140	+	12.6237i	0.819835	+	0.492497i
$658$	9.41660	−	19.5525i	0.367097	−	0.762237i
$659$		−	50.9518i		−	1.98480i	−0.123052	−	0.992400i	$-0.539268\pi$
$659$		−	50.9518i		−	1.98480i	0.123052	−	0.992400i	$-0.460732\pi$
$660$	5.03811	−	2.85075i	0.196108	−	0.110965i
$661$		−	6.33426i		−	0.246374i	−0.992383	−	0.123187i	$-0.960688\pi$
$661$		−	6.33426i		−	0.246374i	0.992383	−	0.123187i	$-0.0393115\pi$
$662$		−	16.1288i		−	0.626863i
$663$	−6.08308	+	3.44203i	−0.236247	+	0.133677i
$664$			42.8420i			1.66259i
$665$	−3.38280	+	7.02400i	−0.131179	+	0.272379i
$666$	−6.19983	−	3.72441i	−0.240238	−	0.144318i
$667$	−2.26408			−0.0876654
$668$	21.3454			0.825877
$669$	36.8292	−	20.8393i	1.42390	−	0.805696i
$670$		−	5.54286i		−	0.214139i
$671$	−33.6187			−1.29784
$672$	26.7132	−	1.76824i	1.03048	−	0.0682114i
$673$	−4.08201			−0.157350			−0.0786750	−	0.996900i	$-0.525069\pi$
$673$	−4.08201			−0.157350			−0.0786750	+	0.996900i	$0.525069\pi$
$674$		−	15.2260i		−	0.586483i
$675$	24.1684	+	0.629326i	0.930241	+	0.0242228i
$676$	11.2596			0.433061
$677$	18.9983			0.730163			0.365082	−	0.930976i	$-0.381041\pi$
$677$	18.9983			0.730163			0.365082	+	0.930976i	$0.381041\pi$
$678$	1.17712	+	2.08031i	0.0452068	+	0.0798937i
$679$	−9.95667	+	20.6739i	−0.382102	+	0.793392i
$680$			2.54135i			0.0974563i
$681$	9.18067	+	16.2249i	0.351804	+	0.621741i
$682$		−	0.280326i		−	0.0107343i
$683$		−	46.9805i		−	1.79766i	−0.438300	−	0.898829i	$-0.644419\pi$
$683$		−	46.9805i		−	1.79766i	0.438300	−	0.898829i	$-0.355581\pi$
$684$	−19.1563	−	11.5077i	−0.732458	−	0.440008i
$685$			6.45663i			0.246695i
$686$	12.8998	−	2.94328i	0.492517	−	0.112375i
$687$	−41.0855	+	23.2477i	−1.56751	+	0.886956i
$688$	−4.50377			−0.171705
$689$	15.5820			0.593626
$690$	0.359083	+	0.634604i	0.0136701	+	0.0241590i
$691$		−	20.5154i		−	0.780441i	−0.920721	−	0.390221i	$-0.872399\pi$
$691$		−	20.5154i		−	0.780441i	0.920721	−	0.390221i	$-0.127601\pi$
$692$	35.7019			1.35718
$693$	16.5881	+	25.2627i	0.630129	+	0.959649i
$694$	6.23359			0.236624
$695$		−	11.7847i		−	0.447018i
$696$	4.81460	+	8.50880i	0.182497	+	0.322525i
$697$	3.92546			0.148687
$698$	3.05781			0.115740
$699$	22.9122	−	12.9646i	0.866619	−	0.490365i
$700$	−16.5210	−	7.95658i	−0.624433	−	0.300730i
$701$		−	30.3312i		−	1.14559i	−0.819698	−	0.572796i	$-0.805859\pi$
$701$		−	30.3312i		−	1.14559i	0.819698	−	0.572796i	$-0.194141\pi$
$702$	8.65642	+	0.225406i	0.326715	+	0.00850742i
$703$		−	16.8749i		−	0.636448i
$704$			6.76813i			0.255083i
$705$	5.77073	+	10.1986i	0.217338	+	0.384100i
$706$		−	16.4136i		−	0.617734i
$707$	−40.2265	−	19.3733i	−1.51287	−	0.728608i
$708$	−14.4025	−	25.4535i	−0.541280	−	0.956600i
$709$	−38.1580			−1.43305			−0.716526	−	0.697560i	$-0.754269\pi$
$709$	−38.1580			−1.43305			−0.716526	+	0.697560i	$0.754269\pi$
$710$	−3.04913			−0.114432
$711$	2.09628	−	3.48957i	0.0786167	−	0.130869i
$712$			5.32141i			0.199428i
$713$	−0.103052			−0.00385931
$714$	−5.65130	+	0.374079i	−0.211495	+	0.0139996i
$715$	−5.23360			−0.195725
$716$		−	13.8216i		−	0.516536i
$717$	−8.72179	+	4.93512i	−0.325721	+	0.184305i
$718$	0.984560			0.0367435
$719$	−10.9700			−0.409113			−0.204557	−	0.978855i	$-0.565575\pi$
$719$	−10.9700			−0.409113			−0.204557	+	0.978855i	$0.565575\pi$
$720$	−1.09064	+	1.81553i	−0.0406458	+	0.0676609i
$721$	7.54709	−	15.6707i	0.281068	−	0.583607i
$722$			4.29147i			0.159712i
$723$	29.8572	−	16.8943i	1.11040	−	0.628306i
$724$			9.63191i			0.357967i
$725$		−	10.5342i		−	0.391232i
$726$	−3.76711	+	2.13157i	−0.139810	+	0.0791100i
$727$		−	14.2922i		−	0.530070i	−0.964239	−	0.265035i	$-0.914616\pi$
$727$		−	14.2922i		−	0.530070i	0.964239	−	0.265035i	$-0.0853835\pi$
$728$	−13.8622	−	6.67611i	−0.513767	−	0.247433i
$729$	26.9634	+	1.40517i	0.998645	+	0.0520432i
$730$	−3.43997			−0.127319
$731$	6.50305			0.240524
$732$	19.8263	−	11.2185i	0.732803	−	0.414647i
$733$		−	30.6915i		−	1.13362i	−0.823849	−	0.566809i	$-0.808178\pi$
$733$		−	30.6915i		−	1.13362i	0.823849	−	0.566809i	$-0.191822\pi$
$734$	17.3991			0.642213
$735$	−2.66805	+	6.62741i	−0.0984125	+	0.244456i
$736$	5.84206			0.215341
$737$		−	50.1335i		−	1.84669i
$738$	−4.16896	−	2.50441i	−0.153462	−	0.0921886i
$739$	−13.2877			−0.488795			−0.244397	−	0.969675i	$-0.578590\pi$
$739$	−13.2877			−0.488795			−0.244397	+	0.969675i	$0.578590\pi$
$740$	−2.96197			−0.108884
$741$	9.94978	+	17.5842i	0.365514	+	0.645971i
$742$	11.3759	+	5.47870i	0.417623	+	0.201129i
$743$			30.9960i			1.13713i	0.822637	+	0.568566i	$0.192502\pi$
$743$			30.9960i			1.13713i	−0.822637	+	0.568566i	$0.807498\pi$
$744$	0.219141	+	0.387286i	0.00803410	+	0.0141986i
$745$			6.21063i			0.227540i
$746$			2.89543i			0.106009i
$747$	26.5477	−	44.1927i	0.971331	−	1.61692i
$748$			9.81188i			0.358758i
$749$	−13.0301	+	27.0555i	−0.476108	+	0.988585i
$750$	−6.12570	+	3.46615i	−0.223679	+	0.126566i
$751$	−10.0563			−0.366961			−0.183480	−	0.983023i	$-0.558736\pi$
$751$	−10.0563			−0.366961			−0.183480	+	0.983023i	$0.558736\pi$
$752$	13.7557			0.501619
$753$	−18.2979	−	32.3378i	−0.666813	−	1.17845i
$754$		−	3.77307i		−	0.137407i
$755$	−6.10842			−0.222308
$756$	−18.2128	−	9.36304i	−0.662392	−	0.340530i
$757$	47.3551			1.72115			0.860574	−	0.509325i	$-0.170105\pi$
$757$	47.3551			1.72115			0.860574	+	0.509325i	$0.170105\pi$
$758$			15.7872i			0.573416i
$759$	3.24780	+	5.73981i	0.117888	+	0.208342i
$760$	7.34620			0.266475
$761$	32.2692			1.16976			0.584878	−	0.811121i	$-0.301142\pi$
$761$	32.2692			1.16976			0.584878	+	0.811121i	$0.301142\pi$
$762$	−15.0075	+	8.49181i	−0.543665	+	0.307626i
$763$	30.2496	+	14.5684i	1.09511	+	0.527410i
$764$			2.99708i			0.108430i
$765$	1.57479	−	2.62147i	0.0569366	−	0.0947794i
$766$			1.27930i			0.0462230i
$767$			26.4411i			0.954733i
$768$	−9.37867	−	16.5748i	−0.338423	−	0.598093i
$769$			25.7219i			0.927557i	0.885951	+	0.463778i	$0.153507\pi$
$769$			25.7219i			0.927557i	−0.885951	+	0.463778i	$0.846493\pi$
$770$	−3.82088	−	1.84016i	−0.137695	−	0.0663147i
$771$	24.1396	+	42.6617i	0.869366	+	1.53642i
$772$	14.1831			0.510460
$773$	−12.7135			−0.457274			−0.228637	−	0.973512i	$-0.573427\pi$
$773$	−12.7135			−0.457274			−0.228637	+	0.973512i	$0.573427\pi$
$774$	−6.90645	−	4.14890i	−0.248247	−	0.149129i
$775$		−	0.479477i		−	0.0172233i
$776$	21.6223			0.776194
$777$	−1.02138	−	15.4302i	−0.0366417	−	0.553555i
$778$	10.4539			0.374792
$779$		−	11.3472i		−	0.406556i
$780$	3.08647	−	1.74644i	0.110513	−	0.0625326i
$781$	−27.5785			−0.986836
$782$	−1.23591			−0.0441962
$783$	0.306234	−	11.7605i	0.0109439	−	0.420286i
$784$	5.22866	+	6.55721i	0.186738	+	0.234186i
$785$			0.973654i			0.0347512i
$786$	−0.472889	+	0.267578i	−0.0168674	+	0.00954420i
$787$			0.0221991i			0.000791314i	1.00000		0.000395657i	$0.000125942\pi$
$787$			0.0221991i			0.000791314i	−1.00000		0.000395657i	$0.999874\pi$
$788$		−	24.4964i		−	0.872648i
$789$	−16.0938	+	9.10646i	−0.572953	+	0.324198i
$790$			0.571238i			0.0203237i
$791$	−2.21753	+	4.60446i	−0.0788464	+	0.163716i
$792$	14.6647	−	24.4116i	0.521089	−	0.867429i
$793$	−20.5956			−0.731373
$794$	−5.55610			−0.197179
$795$	−5.93365	+	3.35748i	−0.210445	+	0.119078i
$796$		−	9.32633i		−	0.330563i
$797$	12.1365			0.429896			0.214948	−	0.976625i	$-0.431042\pi$
$797$	12.1365			0.429896			0.214948	+	0.976625i	$0.431042\pi$
$798$	1.08134	+	16.3360i	0.0382790	+	0.578290i
$799$	−19.8620			−0.702669
$800$			27.1818i			0.961023i
$801$	3.29750	−	5.48918i	0.116511	−	0.193951i
$802$	24.9447			0.880826
$803$	−31.1135			−1.09797
$804$	16.7294	+	29.5658i	0.590002	+	1.04271i
$805$	−0.676466	+	1.40461i	−0.0238423	+	0.0495059i
$806$		−	0.171735i		−	0.00604910i
$807$	11.1263	+	19.6634i	0.391663	+	0.692184i
$808$			42.0718i			1.48008i
$809$		−	22.0337i		−	0.774663i	−0.921940	−	0.387332i	$-0.873397\pi$
$809$		−	22.0337i		−	0.774663i	0.921940	−	0.387332i	$-0.126603\pi$
$810$	−3.34495	+	1.77938i	−0.117530	+	0.0625211i
$811$			7.58907i			0.266488i	0.991083	+	0.133244i	$0.0425394\pi$
$811$			7.58907i			0.266488i	−0.991083	+	0.133244i	$0.957461\pi$
$812$	−3.87173	+	8.03921i	−0.135871	+	0.282121i
$813$	−14.4989	+	8.20404i	−0.508500	+	0.287728i
$814$	9.17951			0.321742
$815$	3.18565			0.111588
$816$	−1.76790	−	3.12440i	−0.0618890	−	0.109376i
$817$		−	18.7982i		−	0.657665i
$818$	3.41926			0.119552
$819$	10.1623	+	15.4765i	0.355098	+	0.540794i
$820$	−1.99172			−0.0695540
$821$			26.5571i			0.926850i	0.886136	+	0.463425i	$0.153380\pi$
$821$			26.5571i			0.926850i	−0.886136	+	0.463425i	$0.846620\pi$
$822$	6.67726	+	11.8007i	0.232896	+	0.411596i
$823$	−25.1311			−0.876016			−0.438008	−	0.898971i	$-0.644316\pi$
$823$	−25.1311			−0.876016			−0.438008	+	0.898971i	$0.644316\pi$
$824$	−16.3895			−0.570957
$825$	−26.7061	+	15.1113i	−0.929787	+	0.526108i
$826$	−9.29682	+	19.3038i	−0.323478	+	0.671665i
$827$		−	47.7797i		−	1.66146i	−0.556674	−	0.830731i	$-0.687923\pi$
$827$		−	47.7797i		−	1.66146i	0.556674	−	0.830731i	$-0.312077\pi$
$828$	−3.83073	−	2.30122i	−0.133127	−	0.0799730i
$829$			8.46712i			0.294075i	0.989131	+	0.147038i	$0.0469738\pi$
$829$			8.46712i			0.294075i	−0.989131	+	0.147038i	$0.953026\pi$
$830$			7.23428i			0.251106i
$831$	−6.45849	−	11.4140i	−0.224043	−	0.395949i
$832$			4.14632i			0.143748i
$833$	−7.54973	−	9.46803i	−0.261583	−	0.328048i
$834$	−12.1874	−	21.5386i	−0.422014	−	0.745822i
$835$	8.44376			0.292209
$836$	28.3629			0.980952
$837$	0.0139386	−	0.535291i	0.000481787	−	0.0185023i
$838$			8.45203i			0.291971i
$839$	15.9034			0.549045			0.274522	−	0.961581i	$-0.411480\pi$
$839$	15.9034			0.549045			0.274522	+	0.961581i	$0.411480\pi$
$840$	6.71728	−	0.444640i	0.231768	−	0.0153415i
$841$	23.8740			0.823240
$842$			11.8558i			0.408579i
$843$	−0.0299246	+	0.0169324i	−0.00103066	+	0.000583184i
$844$	−2.53453			−0.0872421
$845$	4.45405			0.153224
$846$	21.0941	+	12.6718i	0.725231	+	0.435666i
$847$	−8.33796	−	4.01560i	−0.286496	−	0.137978i
$848$			8.00325i			0.274833i
$849$	11.3160	−	6.40300i	0.388363	−	0.219750i
$850$		−	5.75043i		−	0.197238i
$851$		−	3.37451i		−	0.115677i
$852$	16.2642	−	9.20288i	0.557202	−	0.315286i
$853$		−	20.5840i		−	0.704783i	−0.935853	−	0.352391i	$-0.885369\pi$
$853$		−	20.5840i		−	0.704783i	0.935853	−	0.352391i	$-0.114631\pi$
$854$	−15.0362	−	7.24153i	−0.514529	−	0.247800i
$855$	−7.57780	−	4.55219i	−0.259155	−	0.155682i
$856$	28.2965			0.967156
$857$	24.4914			0.836611			0.418306	−	0.908306i	$-0.362624\pi$
$857$	24.4914			0.836611			0.418306	+	0.908306i	$0.362624\pi$
$858$	−9.56536	+	5.41244i	−0.326556	+	0.184778i
$859$		−	49.9041i		−	1.70271i	−0.524592	−	0.851354i	$-0.675782\pi$
$859$		−	49.9041i		−	1.70271i	0.524592	−	0.851354i	$-0.324218\pi$
$860$	−3.29956			−0.112514
$861$	−0.686807	−	10.3757i	−0.0234063	−	0.353604i
$862$	11.0961			0.377936
$863$			36.1396i			1.23021i	0.788446	+	0.615104i	$0.210886\pi$
$863$			36.1396i			1.23021i	−0.788446	+	0.615104i	$0.789114\pi$
$864$	−0.790185	+	30.3459i	−0.0268826	+	1.03239i
$865$	14.1229			0.480193
$866$	−22.4669			−0.763457
$867$	−11.9479	−	21.1154i	−0.405772	−	0.717118i
$868$	−0.176225	+	0.365912i	−0.00598148	+	0.0124199i
$869$			5.16669i			0.175268i
$870$	0.812991	+	1.43679i	0.0275630	+	0.0487118i
$871$		−	30.7130i		−	1.04067i
$872$		−	31.6372i		−	1.07137i
$873$	−22.3039	−	13.3986i	−0.754874	−	0.453473i
$874$			3.57262i			0.120846i
$875$	−13.5584	−	6.52978i	−0.458356	−	0.220747i
$876$	18.3489	−	10.3825i	0.619953	−	0.350792i
$877$	−47.6521			−1.60910			−0.804548	−	0.593888i	$-0.797592\pi$
$877$	−47.6521			−1.60910			−0.804548	+	0.593888i	$0.797592\pi$
$878$	6.26979			0.211595
$879$	17.2136	+	30.4214i	0.580599	+	1.02609i
$880$		−	2.68809i		−	0.0906155i
$881$	−5.48534			−0.184806			−0.0924029	−	0.995722i	$-0.529455\pi$
$881$	−5.48534			−0.184806			−0.0924029	+	0.995722i	$0.529455\pi$
$882$	1.97753	+	14.8720i	0.0665868	+	0.500767i
$883$	29.8240			1.00366			0.501828	−	0.864967i	$-0.332661\pi$
$883$	29.8240			1.00366			0.501828	+	0.864967i	$0.332661\pi$
$884$			6.01100i			0.202172i
$885$	−5.69732	−	10.0688i	−0.191513	−	0.338460i
$886$	12.7444			0.428156
$887$	54.1497			1.81817			0.909085	−	0.416611i	$-0.136782\pi$
$887$	54.1497			1.81817			0.909085	+	0.416611i	$0.136782\pi$
$888$	−12.6820	+	7.17595i	−0.425580	+	0.240809i
$889$	−33.2170	−	15.9975i	−1.11406	−	0.536538i
$890$			0.898572i			0.0301202i
$891$	−30.2541	+	16.0940i	−1.01355	+	0.539169i
$892$		−	36.3928i		−	1.21852i
$893$			57.4146i			1.92131i
$894$	6.42286	+	11.3511i	0.214812	+	0.379636i
$895$		−	5.46750i		−	0.182758i
$896$	11.9556	−	24.8245i	0.399408	−	0.829327i
$897$	1.98968	+	3.51635i	0.0664336	+	0.117408i
$898$	−23.4408			−0.782229
$899$	−0.233317			−0.00778155
$900$	10.7071	−	17.8235i	0.356903	−	0.594118i
$901$		−	11.5560i		−	0.384986i
$902$	6.17260			0.205525
$903$	−1.13779	−	17.1888i	−0.0378633	−	0.572008i
$904$	4.81568			0.160167
$905$			3.81017i			0.126654i
$906$	−11.1643	+	6.31715i	−0.370908	+	0.209873i
$907$	−24.0258			−0.797762			−0.398881	−	0.917003i	$-0.630601\pi$
$907$	−24.0258			−0.797762			−0.398881	+	0.917003i	$0.630601\pi$
$908$	16.0327			0.532063
$909$	26.0705	−	43.3981i	0.864703	−	1.43943i
$910$	−2.34077	−	1.12733i	−0.0775956	−	0.0373705i
$911$		−	41.7599i		−	1.38357i	−0.722104	−	0.691784i	$-0.756825\pi$
$911$		−	41.7599i		−	1.38357i	0.722104	−	0.691784i	$-0.243175\pi$
$912$	−9.03162	+	5.11043i	−0.299067	+	0.169223i
$913$			65.4320i			2.16548i
$914$		−	22.2661i		−	0.736497i
$915$	7.84287	−	4.43779i	0.259277	−	0.146709i
$916$			40.5987i			1.34142i
$917$	−1.04667	−	0.504083i	−0.0345642	−	0.0166463i
$918$	0.167167	−	6.41982i	0.00551734	−	0.211886i
$919$	27.4659			0.906015			0.453007	−	0.891507i	$-0.350351\pi$
$919$	27.4659			0.906015			0.453007	+	0.891507i	$0.350351\pi$
$920$	1.46904			0.0484327
$921$	−30.3552	+	17.1761i	−1.00024	+	0.565972i
$922$			0.114277i			0.00376350i
$923$	−16.8953			−0.556114
$924$	25.9347	−	1.71671i	0.853189	−	0.0564756i
$925$	15.7009			0.516241
$926$		−	11.5054i		−	0.378090i
$927$	16.9062	+	10.1561i	0.555274	+	0.333568i
$928$	13.2269			0.434193
$929$	19.8053			0.649791			0.324895	−	0.945750i	$-0.394671\pi$
$929$	19.8053			0.649791			0.324895	+	0.945750i	$0.394671\pi$
$930$	0.0370041	+	0.0653970i	0.00121341	+	0.00214445i
$931$	−27.3690	+	21.8238i	−0.896981	+	0.715246i
$932$		−	22.6407i		−	0.741621i
$933$	−8.90467	−	15.7372i	−0.291526	−	0.515212i
$934$			5.32446i			0.174222i
$935$			3.88137i			0.126934i
$936$	8.98398	−	14.9552i	0.293650	−	0.488825i
$937$		−	24.1653i		−	0.789446i	−0.918800	−	0.394723i	$-0.870841\pi$
$937$		−	24.1653i		−	0.789446i	0.918800	−	0.394723i	$-0.129159\pi$
$938$	10.7988	−	22.4226i	0.352595	−	0.732124i
$939$	−29.6003	+	16.7489i	−0.965968	+	0.546581i
$940$	10.0777			0.328699
$941$	−60.0391			−1.95722			−0.978609	−	0.205728i	$-0.934044\pi$
$941$	−60.0391			−1.95722			−0.978609	+	0.205728i	$0.934044\pi$
$942$	1.00692	+	1.77953i	0.0328074	+	0.0579802i
$943$		−	2.26913i		−	0.0738930i
$944$	−13.5807			−0.442015
$945$	−7.20458	−	3.70381i	−0.234365	−	0.120485i
$946$	10.2257			0.332468
$947$		−	46.3747i		−	1.50697i	−0.657463	−	0.753487i	$-0.728370\pi$
$947$		−	46.3747i		−	1.50697i	0.657463	−	0.753487i	$-0.271630\pi$
$948$	−1.72411	−	3.04701i	−0.0559965	−	0.0989623i
$949$	−19.0609			−0.618743
$950$	−16.6226			−0.539309
$951$	−37.5692	+	21.2581i	−1.21827	+	0.689340i
$952$	−4.95117	+	10.2806i	−0.160468	+	0.333195i
$953$		−	9.35443i		−	0.303020i	−0.988456	−	0.151510i	$-0.951586\pi$
$953$		−	9.35443i		−	0.303020i	0.988456	−	0.151510i	$-0.0484135\pi$
$954$	−7.37263	+	12.2728i	−0.238698	+	0.397348i
$955$			1.18558i			0.0383644i
$956$			8.61845i			0.278741i
$957$	7.35327	+	12.9954i	0.237697	+	0.420081i
$958$		−	18.0312i		−	0.582563i
$959$	−12.5791	+	26.1191i	−0.406200	+	0.843430i
$960$	−0.893417	−	1.57893i	−0.0288349	−	0.0509597i
$961$	30.9894			0.999657
$962$	5.62360			0.181312
$963$	−29.1886	−	17.5344i	−0.940590	−	0.565039i
$964$		−	29.5034i		−	0.950241i
$965$	5.61052			0.180609
$966$	0.216238	+	3.26676i	0.00695735	+	0.105106i
$967$	−47.8338			−1.53823			−0.769116	−	0.639109i	$-0.779303\pi$
$967$	−47.8338			−1.53823			−0.769116	+	0.639109i	$0.779303\pi$
$968$			8.72043i			0.280285i
$969$	13.0409	−	7.37901i	0.418933	−	0.237048i
$970$	3.65113			0.117231
$971$	−8.28347			−0.265829			−0.132915	−	0.991128i	$-0.542434\pi$
$971$	−8.28347			−0.265829			−0.132915	+	0.991128i	$0.542434\pi$
$972$	12.4716	−	19.5870i	0.400026	−	0.628254i
$973$	22.9594	−	47.6727i	0.736046	−	1.52832i
$974$			14.7950i			0.474061i
$975$	−16.3608	+	9.25756i	−0.523965	+	0.296479i
$976$		−	10.5784i		−	0.338606i
$977$			32.4947i			1.03960i	0.854289	+	0.519798i	$0.173993\pi$
$977$			32.4947i			1.03960i	−0.854289	+	0.519798i	$0.826007\pi$
$978$	5.82236	−	3.29451i	0.186179	−	0.105347i
$979$			8.12732i			0.259750i
$980$	3.83063	+	4.80395i	0.122365	+	0.153456i
$981$	−19.6045	+	32.6346i	−0.625924	+	1.04194i
$982$	−7.99259			−0.255054
$983$	0.586963			0.0187212			0.00936061	−	0.999956i	$-0.497020\pi$
$983$	0.586963			0.0187212			0.00936061	+	0.999956i	$0.497020\pi$
$984$	−8.52779	+	4.82534i	−0.271856	+	0.153826i
$985$		−	9.69024i		−	0.308757i
$986$	−2.79820			−0.0891129
$987$	3.47511	+	52.4992i	0.110614	+	1.67107i
$988$	17.3758			0.552799
$989$		−	3.75912i		−	0.119533i
$990$	2.47628	−	4.12214i	0.0787014	−	0.131010i
$991$	−46.0427			−1.46259			−0.731297	−	0.682059i	$-0.761085\pi$
$991$	−46.0427			−1.46259			−0.731297	+	0.682059i	$0.761085\pi$
$992$	0.602034			0.0191146
$993$	19.2567	+	34.0322i	0.611093	+	1.07998i
$994$	−12.3347	−	5.94046i	−0.391233	−	0.188420i
$995$		−	3.68929i		−	0.116958i
$996$	−21.8345	−	38.5880i	−0.691853	−	1.22271i
$997$		−	33.2130i		−	1.05187i	−0.850526	−	0.525933i	$-0.823716\pi$
$997$		−	33.2130i		−	1.05187i	0.850526	−	0.525933i	$-0.176284\pi$
$998$			23.1671i			0.733343i
$999$	17.5285	+	0.456429i	0.554578	+	0.0144408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.d.461.18	yes	44
3.2	odd	2	inner	483.2.d.d.461.27	yes	44
7.6	odd	2	inner	483.2.d.d.461.17	✓	44
21.20	even	2	inner	483.2.d.d.461.28	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.d.461.17	✓	44	7.6	odd	2	inner
483.2.d.d.461.18	yes	44	1.1	even	1	trivial
483.2.d.d.461.27	yes	44	3.2	odd	2	inner
483.2.d.d.461.28	yes	44	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.714425i q^{2} +(0.852976 + 1.50746i) q^{3} +1.48960 q^{4} +0.589252 q^{5} +(1.07697 - 0.609388i) q^{6} +(2.38371 + 1.14801i) q^{7} -2.49306i q^{8} +(-1.54486 + 2.57165i) q^{9} +O(q^{10})\)	\(q-0.714425i q^{2} +(0.852976 + 1.50746i) q^{3} +1.48960 q^{4} +0.589252 q^{5} +(1.07697 - 0.609388i) q^{6} +(2.38371 + 1.14801i) q^{7} -2.49306i q^{8} +(-1.54486 + 2.57165i) q^{9} -0.420976i q^{10} -3.80761i q^{11} +(1.27059 + 2.24551i) q^{12} -2.33263i q^{13} +(0.820166 - 1.70298i) q^{14} +(0.502618 + 0.888273i) q^{15} +1.19809 q^{16} -1.72994 q^{17} +(1.83725 + 1.10369i) q^{18} +5.00069i q^{19} +0.877748 q^{20} +(0.302674 + 4.57257i) q^{21} -2.72025 q^{22} +1.00000i q^{23} +(3.75818 - 2.12652i) q^{24} -4.65278 q^{25} -1.66649 q^{26} +(-5.19439 - 0.135258i) q^{27} +(3.55077 + 1.71007i) q^{28} +2.26408i q^{29} +(0.634604 - 0.359083i) q^{30} +0.103052i q^{31} -5.84206i q^{32} +(5.73981 - 3.24780i) q^{33} +1.23591i q^{34} +(1.40461 + 0.676466i) q^{35} +(-2.30122 + 3.83073i) q^{36} -3.37451 q^{37} +3.57262 q^{38} +(3.51635 - 1.98968i) q^{39} -1.46904i q^{40} -2.26913 q^{41} +(3.26676 - 0.216238i) q^{42} -3.75912 q^{43} -5.67180i q^{44} +(-0.910314 + 1.51535i) q^{45} +0.714425 q^{46} +11.4813 q^{47} +(1.02194 + 1.80608i) q^{48} +(4.36416 + 5.47304i) q^{49} +3.32406i q^{50} +(-1.47560 - 2.60781i) q^{51} -3.47469i q^{52} +6.67999i q^{53} +(-0.0966317 + 3.71100i) q^{54} -2.24364i q^{55} +(2.86205 - 5.94272i) q^{56} +(-7.53833 + 4.26547i) q^{57} +1.61751 q^{58} -11.3353 q^{59} +(0.748698 + 1.32317i) q^{60} -8.82935i q^{61} +0.0736227 q^{62} +(-6.63478 + 4.35656i) q^{63} -1.77753 q^{64} -1.37451i q^{65} +(-2.32031 - 4.10067i) q^{66} +13.1667 q^{67} -2.57691 q^{68} +(-1.50746 + 0.852976i) q^{69} +(0.483284 - 1.00349i) q^{70} -7.24300i q^{71} +(6.41127 + 3.85143i) q^{72} -8.17140i q^{73} +2.41083i q^{74} +(-3.96871 - 7.01388i) q^{75} +7.44901i q^{76} +(4.37117 - 9.07624i) q^{77} +(-1.42148 - 2.51217i) q^{78} -1.35694 q^{79} +0.705979 q^{80} +(-4.22680 - 7.94570i) q^{81} +1.62112i q^{82} -17.1845 q^{83} +(0.450863 + 6.81128i) q^{84} -1.01937 q^{85} +2.68561i q^{86} +(-3.41300 + 1.93120i) q^{87} -9.49258 q^{88} -2.13449 q^{89} +(1.08261 + 0.650351i) q^{90} +(2.67788 - 5.56033i) q^{91} +1.48960i q^{92} +(-0.155346 + 0.0879006i) q^{93} -8.20256i q^{94} +2.94667i q^{95} +(8.80666 - 4.98314i) q^{96} +8.67299i q^{97} +(3.91008 - 3.11786i) q^{98} +(9.79185 + 5.88223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

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