LMFDB - Embedded newform 231.2.g.a.197.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(197,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("231.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.g (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.7
Character	$\chi$	$=$	231.197
Dual form			231.2.g.a.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36666 q^{2} +(-0.859522 - 1.50374i) q^{3} -0.132249 q^{4} -3.05646i q^{5} +(1.17467 + 2.05509i) q^{6} -1.00000i q^{7} +2.91405 q^{8} +(-1.52244 + 2.58499i) q^{9} +O(q^{10})$	\(q-1.36666 q^{2} +(-0.859522 - 1.50374i) q^{3} -0.132249 q^{4} -3.05646i q^{5} +(1.17467 + 2.05509i) q^{6} -1.00000i q^{7} +2.91405 q^{8} +(-1.52244 + 2.58499i) q^{9} +4.17714i q^{10} +(-2.29803 - 2.39145i) q^{11} +(0.113671 + 0.198867i) q^{12} +3.62292i q^{13} +1.36666i q^{14} +(-4.59611 + 2.62710i) q^{15} -3.71801 q^{16} -4.38517 q^{17} +(2.08066 - 3.53279i) q^{18} -1.58576i q^{19} +0.404213i q^{20} +(-1.50374 + 0.859522i) q^{21} +(3.14062 + 3.26829i) q^{22} +2.62350i q^{23} +(-2.50469 - 4.38197i) q^{24} -4.34196 q^{25} -4.95129i q^{26} +(5.19571 + 0.0674985i) q^{27} +0.132249i q^{28} -8.41328 q^{29} +(6.28131 - 3.59034i) q^{30} +7.15507 q^{31} -0.746857 q^{32} +(-1.62090 + 5.51114i) q^{33} +5.99302 q^{34} -3.05646 q^{35} +(0.201341 - 0.341862i) q^{36} -7.41499 q^{37} +2.16720i q^{38} +(5.44791 - 3.11398i) q^{39} -8.90669i q^{40} +8.17745 q^{41} +(2.05509 - 1.17467i) q^{42} -5.36300i q^{43} +(0.303912 + 0.316267i) q^{44} +(7.90092 + 4.65329i) q^{45} -3.58543i q^{46} +4.01434i q^{47} +(3.19571 + 5.59091i) q^{48} -1.00000 q^{49} +5.93398 q^{50} +(3.76915 + 6.59414i) q^{51} -0.479127i q^{52} -6.53391i q^{53} +(-7.10076 - 0.0922472i) q^{54} +(-7.30938 + 7.02385i) q^{55} -2.91405i q^{56} +(-2.38457 + 1.36300i) q^{57} +11.4981 q^{58} -9.19809i q^{59} +(0.607830 - 0.347430i) q^{60} -7.21990i q^{61} -9.77853 q^{62} +(2.58499 + 1.52244i) q^{63} +8.45672 q^{64} +11.0733 q^{65} +(2.21522 - 7.53184i) q^{66} -2.55762 q^{67} +0.579933 q^{68} +(3.94505 - 2.25496i) q^{69} +4.17714 q^{70} +1.54245i q^{71} +(-4.43648 + 7.53279i) q^{72} +7.32344i q^{73} +10.1337 q^{74} +(3.73201 + 6.52917i) q^{75} +0.209715i q^{76} +(-2.39145 + 2.29803i) q^{77} +(-7.44543 + 4.25574i) q^{78} -16.5934i q^{79} +11.3640i q^{80} +(-4.36433 - 7.87100i) q^{81} -11.1758 q^{82} -4.26394 q^{83} +(0.198867 - 0.113671i) q^{84} +13.4031i q^{85} +7.32938i q^{86} +(7.23140 + 12.6513i) q^{87} +(-6.69659 - 6.96882i) q^{88} -6.22274i q^{89} +(-10.7978 - 6.35945i) q^{90} +3.62292 q^{91} -0.346955i q^{92} +(-6.14994 - 10.7593i) q^{93} -5.48623i q^{94} -4.84683 q^{95} +(0.641940 + 1.12308i) q^{96} -15.0918 q^{97} +1.36666 q^{98} +(9.68050 - 2.29954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.36666			−0.966372			−0.483186	−	0.875518i	$-0.660521\pi$
$2$	−1.36666			−0.966372			−0.483186	+	0.875518i	$0.660521\pi$
$3$	−0.859522	−	1.50374i	−0.496245	−	0.868182i
$3$	−0.859522	−	1.50374i	−0.496245	−	0.868182i
$4$	−0.132249			−0.0661244
$5$		−	3.05646i		−	1.36689i	−0.730001	−	0.683446i	$-0.760481\pi$
$5$		−	3.05646i		−	1.36689i	0.730001	−	0.683446i	$-0.239519\pi$
$6$	1.17467	+	2.05509i	0.479558	+	0.838987i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.91405			1.03027
$9$	−1.52244	+	2.58499i	−0.507481	+	0.861663i
$10$			4.17714i			1.32093i
$11$	−2.29803	−	2.39145i	−0.692883	−	0.721050i
$11$	−2.29803	−	2.39145i	−0.692883	−	0.721050i
$12$	0.113671	+	0.198867i	0.0328139	+	0.0574080i
$13$			3.62292i			1.00482i	0.864630	+	0.502409i	$0.167553\pi$
$13$			3.62292i			1.00482i	−0.864630	+	0.502409i	$0.832447\pi$
$14$			1.36666i			0.365254i
$15$	−4.59611	+	2.62710i	−1.18671	+	0.678314i
$16$	−3.71801			−0.929503
$17$	−4.38517			−1.06356			−0.531780	−	0.846883i	$-0.678477\pi$
$17$	−4.38517			−1.06356			−0.531780	+	0.846883i	$0.678477\pi$
$18$	2.08066	−	3.53279i	0.490416	−	0.832687i
$19$		−	1.58576i		−	0.363799i	−0.983317	−	0.181900i	$-0.941775\pi$
$19$		−	1.58576i		−	0.363799i	0.983317	−	0.181900i	$-0.0582246\pi$
$20$			0.404213i			0.0903849i
$21$	−1.50374	+	0.859522i	−0.328142	+	0.187563i
$22$	3.14062	+	3.26829i	0.669583	+	0.696803i
$23$			2.62350i			0.547038i	0.961867	+	0.273519i	$0.0881876\pi$
$23$			2.62350i			0.547038i	−0.961867	+	0.273519i	$0.911812\pi$
$24$	−2.50469	−	4.38197i	−0.511268	−	0.894465i
$25$	−4.34196			−0.868393
$26$		−	4.95129i		−	0.971028i
$27$	5.19571	+	0.0674985i	0.999916	+	0.0129901i
$28$			0.132249i			0.0249927i
$29$	−8.41328			−1.56231			−0.781153	−	0.624339i	$-0.785368\pi$
$29$	−8.41328			−1.56231			−0.781153	+	0.624339i	$0.785368\pi$
$30$	6.28131	−	3.59034i	1.14680	−	0.655504i
$31$	7.15507			1.28509			0.642544	−	0.766249i	$-0.277879\pi$
$31$	7.15507			1.28509			0.642544	+	0.766249i	$0.277879\pi$
$32$	−0.746857			−0.132027
$33$	−1.62090	+	5.51114i	−0.282163	+	0.959366i
$34$	5.99302			1.02780
$35$	−3.05646			−0.516636
$36$	0.201341	−	0.341862i	0.0335569	−	0.0569769i
$37$	−7.41499			−1.21902			−0.609508	−	0.792780i	$-0.708633\pi$
$37$	−7.41499			−1.21902			−0.609508	+	0.792780i	$0.708633\pi$
$38$			2.16720i			0.351565i
$39$	5.44791	−	3.11398i	0.872365	−	0.498636i
$40$		−	8.90669i		−	1.40827i
$41$	8.17745			1.27710			0.638551	−	0.769579i	$-0.279534\pi$
$41$	8.17745			1.27710			0.638551	+	0.769579i	$0.279534\pi$
$42$	2.05509	−	1.17467i	0.317107	−	0.181256i
$43$		−	5.36300i		−	0.817850i	−0.912568	−	0.408925i	$-0.865904\pi$
$43$		−	5.36300i		−	0.817850i	0.912568	−	0.408925i	$-0.134096\pi$
$44$	0.303912	+	0.316267i	0.0458165	+	0.0476790i
$45$	7.90092	+	4.65329i	1.17780	+	0.693672i
$46$		−	3.58543i		−	0.528642i
$47$			4.01434i			0.585552i	0.956181	+	0.292776i	$0.0945791\pi$
$47$			4.01434i			0.585552i	−0.956181	+	0.292776i	$0.905421\pi$
$48$	3.19571	+	5.59091i	0.461262	+	0.806978i
$49$	−1.00000			−0.142857
$50$	5.93398			0.839191
$51$	3.76915	+	6.59414i	0.527787	+	0.923364i
$52$		−	0.479127i		−	0.0664429i
$53$		−	6.53391i		−	0.897502i	−0.893657	−	0.448751i	$-0.851869\pi$
$53$		−	6.53391i		−	0.897502i	0.893657	−	0.448751i	$-0.148131\pi$
$54$	−7.10076	−	0.0922472i	−0.966291	−	0.0125533i
$55$	−7.30938	+	7.02385i	−0.985597	+	0.947096i
$56$		−	2.91405i		−	0.389407i
$57$	−2.38457	+	1.36300i	−0.315844	+	0.180534i
$58$	11.4981			1.50977
$59$		−	9.19809i		−	1.19749i	−0.800940	−	0.598744i	$-0.795667\pi$
$59$		−	9.19809i		−	1.19749i	0.800940	−	0.598744i	$-0.204333\pi$
$60$	0.607830	−	0.347430i	0.0784706	−	0.0448531i
$61$		−	7.21990i		−	0.924413i	−0.886772	−	0.462207i	$-0.847058\pi$
$61$		−	7.21990i		−	0.924413i	0.886772	−	0.462207i	$-0.152942\pi$
$62$	−9.77853			−1.24187
$63$	2.58499	+	1.52244i	0.325678	+	0.191810i
$64$	8.45672			1.05709
$65$	11.0733			1.37348
$66$	2.21522	−	7.53184i	0.272674	−	0.927105i
$67$	−2.55762			−0.312464			−0.156232	−	0.987720i	$-0.549935\pi$
$67$	−2.55762			−0.312464			−0.156232	+	0.987720i	$0.549935\pi$
$68$	0.579933			0.0703273
$69$	3.94505	−	2.25496i	0.474929	−	0.271465i
$70$	4.17714			0.499263
$71$			1.54245i			0.183056i	0.995803	+	0.0915278i	$0.0291750\pi$
$71$			1.54245i			0.183056i	−0.995803	+	0.0915278i	$0.970825\pi$
$72$	−4.43648	+	7.53279i	−0.522844	+	0.887748i
$73$			7.32344i			0.857144i	0.903508	+	0.428572i	$0.140983\pi$
$73$			7.32344i			0.857144i	−0.903508	+	0.428572i	$0.859017\pi$
$74$	10.1337			1.17802
$75$	3.73201	+	6.52917i	0.430936	+	0.753923i
$76$			0.209715i			0.0240560i
$77$	−2.39145	+	2.29803i	−0.272531	+	0.261885i
$78$	−7.44543	+	4.25574i	−0.843029	+	0.481868i
$79$		−	16.5934i		−	1.86691i	−0.358696	−	0.933454i	$-0.616779\pi$
$79$		−	16.5934i		−	1.86691i	0.358696	−	0.933454i	$-0.383221\pi$
$80$			11.3640i			1.27053i
$81$	−4.36433	−	7.87100i	−0.484926	−	0.874555i
$82$	−11.1758			−1.23416
$83$	−4.26394			−0.468028			−0.234014	−	0.972233i	$-0.575186\pi$
$83$	−4.26394			−0.468028			−0.234014	+	0.972233i	$0.575186\pi$
$84$	0.198867	−	0.113671i	0.0216982	−	0.0124025i
$85$			13.4031i			1.45377i
$86$			7.32938i			0.790347i
$87$	7.23140	+	12.6513i	0.775287	+	1.35637i
$88$	−6.69659	−	6.96882i	−0.713859	−	0.742878i
$89$		−	6.22274i		−	0.659609i	−0.944049	−	0.329804i	$-0.893017\pi$
$89$		−	6.22274i		−	0.659609i	0.944049	−	0.329804i	$-0.106983\pi$
$90$	−10.7978	−	6.35945i	−1.13819	−	0.670345i
$91$	3.62292			0.379785
$92$		−	0.346955i		−	0.0361725i
$93$	−6.14994	−	10.7593i	−0.637719	−	1.11569i
$94$		−	5.48623i		−	0.565862i
$95$	−4.84683			−0.497274
$96$	0.641940	+	1.12308i	0.0655178	+	0.114623i
$97$	−15.0918			−1.53234			−0.766171	−	0.642637i	$-0.777840\pi$
$97$	−15.0918			−1.53234			−0.766171	+	0.642637i	$0.777840\pi$
$98$	1.36666			0.138053
$99$	9.68050	−	2.29954i	0.972927	−	0.231112i
$100$	0.574219			0.0574219
$101$	−12.5118			−1.24497			−0.622487	−	0.782630i	$-0.713878\pi$
$101$	−12.5118			−1.24497			−0.622487	+	0.782630i	$0.713878\pi$
$102$	−5.15114	−	9.01192i	−0.510038	−	0.892313i
$103$	2.69091			0.265143			0.132571	−	0.991173i	$-0.457677\pi$
$103$	2.69091			0.265143			0.132571	+	0.991173i	$0.457677\pi$
$104$			10.5574i			1.03524i
$105$	2.62710	+	4.59611i	0.256378	+	0.448535i
$106$			8.92961i			0.867321i
$107$	−8.74541			−0.845450			−0.422725	−	0.906258i	$-0.638926\pi$
$107$	−8.74541			−0.845450			−0.422725	+	0.906258i	$0.638926\pi$
$108$	−0.687127	−	0.00892659i	−0.0661188	−	0.000858962i
$109$		−	1.99794i		−	0.191368i	−0.995412	−	0.0956838i	$-0.969496\pi$
$109$		−	1.99794i		−	0.191368i	0.995412	−	0.0956838i	$-0.0305038\pi$
$110$	9.98942	−	9.59920i	0.952454	−	0.915247i
$111$	6.37335	+	11.1502i	0.604931	+	1.05833i
$112$			3.71801i			0.351319i
$113$		−	1.40705i		−	0.132364i	−0.997808	−	0.0661819i	$-0.978918\pi$
$113$		−	1.40705i		−	0.132364i	0.997808	−	0.0661819i	$-0.0210818\pi$
$114$	3.25889	−	1.86275i	0.305223	−	0.174463i
$115$	8.01863			0.747742
$116$	1.11265			0.103307
$117$	−9.36521	−	5.51569i	−0.865814	−	0.509926i
$118$			12.5706i			1.15722i
$119$			4.38517i			0.401988i
$120$	−13.3933	+	7.65550i	−1.22264	+	0.698848i
$121$	−0.438088	+	10.9913i	−0.0398262	+	0.999207i
$122$			9.86713i			0.893328i
$123$	−7.02870	−	12.2967i	−0.633756	−	1.10876i
$124$	−0.946249			−0.0849757
$125$		−	2.01126i		−	0.179893i
$126$	−3.53279	−	2.08066i	−0.314726	−	0.185360i
$127$		−	17.9230i		−	1.59040i	−0.606344	−	0.795202i	$-0.707365\pi$
$127$		−	17.9230i		−	1.59040i	0.606344	−	0.795202i	$-0.292635\pi$
$128$	−10.0637			−0.889516
$129$	−8.06453	+	4.60962i	−0.710043	+	0.405854i
$130$	−15.1334			−1.32729
$131$	12.9974			1.13559			0.567793	−	0.823172i	$-0.307798\pi$
$131$	12.9974			1.13559			0.567793	+	0.823172i	$0.307798\pi$
$132$	0.214362	−	0.728842i	0.0186579	−	0.0634375i
$133$	−1.58576			−0.137503
$134$	3.49540			0.301956
$135$	0.206307	−	15.8805i	0.0177560	−	1.36678i
$136$	−12.7786			−1.09576
$137$			11.0714i			0.945890i	0.881092	+	0.472945i	$0.156809\pi$
$137$			11.0714i			0.945890i	−0.881092	+	0.472945i	$0.843191\pi$
$138$	−5.39154	+	3.08175i	−0.458958	+	0.262336i
$139$		−	8.22036i		−	0.697242i	−0.937264	−	0.348621i	$-0.886650\pi$
$139$		−	8.22036i		−	0.697242i	0.937264	−	0.348621i	$-0.113350\pi$
$140$	0.404213			0.0341623
$141$	6.03651	−	3.45042i	0.508366	−	0.290578i
$142$		−	2.10801i		−	0.176900i
$143$	8.66404	−	8.32559i	0.724523	−	0.696221i
$144$	5.66046	−	9.61102i	0.471705	−	0.800918i
$145$			25.7149i			2.13550i
$146$		−	10.0086i		−	0.828320i
$147$	0.859522	+	1.50374i	0.0708922	+	0.124026i
$148$	0.980623			0.0806068
$149$	−3.17248			−0.259900			−0.129950	−	0.991521i	$-0.541482\pi$
$149$	−3.17248			−0.259900			−0.129950	+	0.991521i	$0.541482\pi$
$150$	−5.10038	−	8.92313i	−0.416445	−	0.728571i
$151$			5.80853i			0.472691i	0.971669	+	0.236346i	$0.0759498\pi$
$151$			5.80853i			0.472691i	−0.971669	+	0.236346i	$0.924050\pi$
$152$		−	4.62100i		−	0.374813i
$153$	6.67617	−	11.3356i	0.539737	−	0.916430i
$154$	3.26829	−	3.14062i	0.263367	−	0.253079i
$155$		−	21.8692i		−	1.75658i
$156$	−0.720480	+	0.411820i	−0.0576846	+	0.0329720i
$157$	−15.0850			−1.20391			−0.601957	−	0.798529i	$-0.705612\pi$
$157$	−15.0850			−1.20391			−0.601957	+	0.798529i	$0.705612\pi$
$158$			22.6776i			1.80413i
$159$	−9.82528	+	5.61604i	−0.779195	+	0.445381i
$160$			2.28274i			0.180467i
$161$	2.62350			0.206761
$162$	5.96454	+	10.7570i	0.468619	+	0.845146i
$163$	18.3595			1.43802			0.719012	−	0.694997i	$-0.244595\pi$
$163$	18.3595			1.43802			0.719012	+	0.694997i	$0.244595\pi$
$164$	−1.08146			−0.0844477
$165$	16.8446	+	4.95423i	1.31135	+	0.385686i
$166$	5.82734			0.452289
$167$	8.75738			0.677667			0.338833	−	0.940846i	$-0.389968\pi$
$167$	8.75738			0.677667			0.338833	+	0.940846i	$0.389968\pi$
$168$	−4.38197	+	2.50469i	−0.338076	+	0.193241i
$169$	−0.125549			−0.00965763
$170$		−	18.3175i		−	1.40488i
$171$	4.09918	+	2.41424i	0.313472	+	0.184621i
$172$			0.709250i			0.0540798i
$173$	17.8412			1.35644			0.678222	−	0.734857i	$-0.262751\pi$
$173$	17.8412			1.35644			0.678222	+	0.734857i	$0.262751\pi$
$174$	−9.88284	−	17.2901i	−0.749216	−	1.31076i
$175$			4.34196i			0.328222i
$176$	8.54412	+	8.89145i	0.644037	+	0.670218i
$177$	−13.8315	+	7.90596i	−1.03964	+	0.594248i
$178$			8.50435i			0.637428i
$179$			17.7420i			1.32610i	0.748576	+	0.663049i	$0.230738\pi$
$179$			17.7420i			1.32610i	−0.748576	+	0.663049i	$0.769262\pi$
$180$	−1.04489	−	0.615392i	−0.0778813	−	0.0458686i
$181$	20.5862			1.53016			0.765079	−	0.643936i	$-0.222700\pi$
$181$	20.5862			1.53016			0.765079	+	0.643936i	$0.222700\pi$
$182$	−4.95129			−0.367014
$183$	−10.8568	+	6.20566i	−0.802559	+	0.458736i
$184$			7.64502i			0.563598i
$185$			22.6636i			1.66626i
$186$	8.40486	+	14.7043i	0.616274	+	1.07817i
$187$	10.0773	+	10.4869i	0.736923	+	0.766880i
$188$		−	0.530892i		−	0.0387193i
$189$	0.0674985	−	5.19571i	0.00490979	−	0.377933i
$190$	6.62395			0.480552
$191$			0.508199i			0.0367720i	0.999831	+	0.0183860i	$0.00585277\pi$
$191$			0.508199i			0.0367720i	−0.999831	+	0.0183860i	$0.994147\pi$
$192$	−7.26874	−	12.7167i	−0.524576	−	0.917747i
$193$		−	0.620253i		−	0.0446468i	−0.999751	−	0.0223234i	$-0.992894\pi$
$193$		−	0.620253i		−	0.0446468i	0.999751	−	0.0223234i	$-0.00710635\pi$
$194$	20.6253			1.48081
$195$	−9.51776	−	16.6513i	−0.681581	−	1.19243i
$196$	0.132249			0.00944634
$197$	17.1228			1.21995			0.609976	−	0.792420i	$-0.291179\pi$
$197$	17.1228			1.21995			0.609976	+	0.792420i	$0.291179\pi$
$198$	−13.2299	+	3.14268i	−0.940210	+	0.223340i
$199$	17.0929			1.21168			0.605841	−	0.795586i	$-0.292837\pi$
$199$	17.0929			1.21168			0.605841	+	0.795586i	$0.292837\pi$
$200$	−12.6527			−0.894682
$201$	2.19833	+	3.84599i	0.155059	+	0.271275i
$202$	17.0994			1.20311
$203$			8.41328i			0.590496i
$204$	−0.498466	−	0.872067i	−0.0348996	−	0.0610569i
$205$		−	24.9941i		−	1.74566i
$206$	−3.67754			−0.256227
$207$	−6.78172	−	3.99413i	−0.471362	−	0.277611i
$208$		−	13.4701i		−	0.933981i
$209$	−3.79228	+	3.64414i	−0.262317	+	0.252070i
$210$	−3.59034	−	6.28131i	−0.247757	−	0.433452i
$211$		−	21.5139i		−	1.48108i	−0.672013	−	0.740539i	$-0.734570\pi$
$211$		−	21.5139i		−	1.48108i	0.672013	−	0.740539i	$-0.265430\pi$
$212$			0.864102i			0.0593468i
$213$	2.31944	−	1.32577i	0.158926	−	0.0908405i
$214$	11.9520			0.817020
$215$	−16.3918			−1.11791
$216$	15.1406	+	0.196694i	1.03019	+	0.0133833i
$217$		−	7.15507i		−	0.485718i
$218$			2.73049i			0.184932i
$219$	11.0125	−	6.29466i	0.744157	−	0.425354i
$220$	0.966657	−	0.928896i	0.0651720	−	0.0626262i
$221$		−	15.8871i		−	1.06868i
$222$	−8.71018	−	15.2385i	−0.584589	−	1.02274i
$223$	−13.4616			−0.901458			−0.450729	−	0.892661i	$-0.648836\pi$
$223$	−13.4616			−0.901458			−0.450729	+	0.892661i	$0.648836\pi$
$224$			0.746857i			0.0499015i
$225$	6.61040	−	11.2239i	0.440693	−	0.748262i
$226$			1.92295i			0.127913i
$227$	5.53708			0.367509			0.183754	−	0.982972i	$-0.441175\pi$
$227$	5.53708			0.367509			0.183754	+	0.982972i	$0.441175\pi$
$228$	0.315357	−	0.180255i	0.0208850	−	0.0119377i
$229$	5.01119			0.331149			0.165574	−	0.986197i	$-0.447052\pi$
$229$	5.01119			0.331149			0.165574	+	0.986197i	$0.447052\pi$
$230$	−10.9587			−0.722597
$231$	5.51114	+	1.62090i	0.362606	+	0.106648i
$232$	−24.5167			−1.60960
$233$	−22.0175			−1.44241			−0.721207	−	0.692720i	$-0.756412\pi$
$233$	−22.0175			−1.44241			−0.721207	+	0.692720i	$0.756412\pi$
$234$	12.7990	+	7.53806i	0.836698	+	0.492778i
$235$	12.2697			0.800386
$236$			1.21644i			0.0791832i
$237$	−24.9522	+	14.2624i	−1.62082	+	0.926445i
$238$		−	5.99302i		−	0.388470i
$239$	−15.8377			−1.02446			−0.512228	−	0.858849i	$-0.671180\pi$
$239$	−15.8377			−1.02446			−0.512228	+	0.858849i	$0.671180\pi$
$240$	17.0884	−	9.76758i	1.10305	−	0.630495i
$241$		−	13.7548i		−	0.886022i	−0.896516	−	0.443011i	$-0.853910\pi$
$241$		−	13.7548i		−	0.886022i	0.896516	−	0.443011i	$-0.146090\pi$
$242$	0.598716	−	15.0213i	0.0384870	−	0.965606i
$243$	−8.08466	+	13.3281i	−0.518631	+	0.854998i
$244$			0.954823i			0.0611263i
$245$			3.05646i			0.195270i
$246$	9.60582	+	16.8054i	0.612445	+	1.07147i
$247$	5.74510			0.365552
$248$	20.8502			1.32399
$249$	3.66495	+	6.41184i	0.232257	+	0.406334i
$250$			2.74871i			0.173843i
$251$		−	22.6110i		−	1.42720i	−0.700555	−	0.713598i	$-0.747064\pi$
$251$		−	22.6110i		−	1.42720i	0.700555	−	0.713598i	$-0.252936\pi$
$252$	−0.341862	−	0.201341i	−0.0215353	−	0.0126833i
$253$	6.27398	−	6.02889i	0.394442	−	0.379033i
$254$			24.4945i			1.53692i
$255$	20.1547	−	11.5203i	1.26214	−	0.721427i
$256$	−3.15979			−0.197487
$257$			0.881475i			0.0549849i	0.999622	+	0.0274925i	$0.00875222\pi$
$257$			0.881475i			0.0549849i	−0.999622	+	0.0274925i	$0.991248\pi$
$258$	11.0215	−	6.29976i	0.686166	−	0.392206i
$259$			7.41499i			0.460745i
$260$	−1.46443			−0.0908203
$261$	12.8087	−	21.7482i	0.792841	−	1.34618i
$262$	−17.7629			−1.09740
$263$	0.948250			0.0584716			0.0292358	−	0.999573i	$-0.490693\pi$
$263$	0.948250			0.0584716			0.0292358	+	0.999573i	$0.490693\pi$
$264$	−4.72340	+	16.0598i	−0.290705	+	0.988410i
$265$	−19.9707			−1.22679
$266$	2.16720			0.132879
$267$	−9.35735	+	5.34858i	−0.572661	+	0.327328i
$268$	0.338243			0.0206615
$269$			22.5642i			1.37577i	0.725822	+	0.687883i	$0.241460\pi$
$269$			22.5642i			1.37577i	−0.725822	+	0.687883i	$0.758540\pi$
$270$	−0.281950	+	21.7032i	−0.0171589	+	1.32081i
$271$		−	12.2874i		−	0.746408i	−0.927749	−	0.373204i	$-0.878259\pi$
$271$		−	12.2874i		−	0.746408i	0.927749	−	0.373204i	$-0.121741\pi$
$272$	16.3041			0.988582
$273$	−3.11398	−	5.44791i	−0.188467	−	0.329723i
$274$		−	15.1307i		−	0.914082i
$275$	9.97798	+	10.3836i	0.601695	+	0.626155i
$276$	−0.521729	+	0.298215i	−0.0314044	+	0.0179505i
$277$			18.3424i			1.10209i	0.834477	+	0.551043i	$0.185770\pi$
$277$			18.3424i			1.10209i	−0.834477	+	0.551043i	$0.814230\pi$
$278$			11.2344i			0.673796i
$279$	−10.8932	+	18.4958i	−0.652158	+	1.10731i
$280$	−8.90669			−0.532277
$281$	−12.7812			−0.762463			−0.381232	−	0.924480i	$-0.624500\pi$
$281$	−12.7812			−0.762463			−0.381232	+	0.924480i	$0.624500\pi$
$282$	−8.24984	+	4.71554i	−0.491271	+	0.280806i
$283$			7.23858i			0.430289i	0.976582	+	0.215145i	$0.0690223\pi$
$283$			7.23858i			0.430289i	−0.976582	+	0.215145i	$0.930978\pi$
$284$		−	0.203988i		−	0.0121044i
$285$	4.16596	+	7.28835i	0.246770	+	0.431725i
$286$	−11.8408	+	11.3782i	−0.700159	+	0.672809i
$287$		−	8.17745i		−	0.482700i
$288$	1.13705	−	1.93062i	0.0670012	−	0.113763i
$289$	2.22972			0.131160
$290$		−	35.1434i		−	2.06369i
$291$	12.9717	+	22.6941i	0.760417	+	1.33035i
$292$		−	0.968516i		−	0.0566781i
$293$	16.2038			0.946636			0.473318	−	0.880892i	$-0.343056\pi$
$293$	16.2038			0.946636			0.473318	+	0.880892i	$0.343056\pi$
$294$	−1.17467	−	2.05509i	−0.0685083	−	0.119855i
$295$	−28.1136			−1.63684
$296$	−21.6077			−1.25592
$297$	−11.7785	−	12.5804i	−0.683458	−	0.729990i
$298$	4.33569			0.251160
$299$	−9.50474			−0.549673
$300$	−0.493554	−	0.863474i	−0.0284954	−	0.0498527i
$301$	−5.36300			−0.309118
$302$		−	7.93827i		−	0.456796i
$303$	10.7542	+	18.8145i	0.617813	+	1.08086i
$304$			5.89589i			0.338153i
$305$	−22.0674			−1.26357
$306$	−9.12404	+	15.4919i	−0.521587	+	0.885613i
$307$			6.65169i			0.379632i	0.981820	+	0.189816i	$0.0607891\pi$
$307$			6.65169i			0.379632i	−0.981820	+	0.189816i	$0.939211\pi$
$308$	0.316267	−	0.303912i	0.0180210	−	0.0173170i
$309$	−2.31289	−	4.04641i	−0.131576	−	0.230192i
$310$			29.8877i			1.69751i
$311$			0.464509i			0.0263399i	0.999913	+	0.0131699i	$0.00419224\pi$
$311$			0.464509i			0.0263399i	−0.999913	+	0.0131699i	$0.995808\pi$
$312$	15.8755	−	9.07430i	0.898774	−	0.513731i
$313$	6.04240			0.341537			0.170768	−	0.985311i	$-0.445375\pi$
$313$	6.04240			0.341537			0.170768	+	0.985311i	$0.445375\pi$
$314$	20.6160			1.16343
$315$	4.65329	−	7.90092i	0.262183	−	0.445166i
$316$			2.19446i			0.123448i
$317$		−	2.43510i		−	0.136769i	−0.997659	−	0.0683844i	$-0.978216\pi$
$317$		−	2.43510i		−	0.136769i	0.997659	−	0.0683844i	$-0.0217844\pi$
$318$	13.4278	−	7.67520i	0.752993	−	0.430404i
$319$	19.3340	+	20.1200i	1.08250	+	1.12650i
$320$		−	25.8477i		−	1.44493i
$321$	7.51687	+	13.1508i	0.419551	+	0.734005i
$322$	−3.58543			−0.199808
$323$			6.95384i			0.386922i
$324$	0.577177	+	1.04093i	0.0320654	+	0.0578294i
$325$		−	15.7306i		−	0.872576i
$326$	−25.0911			−1.38967
$327$	−3.00437	+	1.71727i	−0.166142	+	0.0949653i
$328$	23.8295			1.31576
$329$	4.01434			0.221318
$330$	−23.0208	−	6.77073i	−1.26725	−	0.372716i
$331$	−30.5708			−1.68032			−0.840161	−	0.542337i	$-0.817540\pi$
$331$	−30.5708			−1.68032			−0.840161	+	0.542337i	$0.817540\pi$
$332$	0.563901			0.0309481
$333$	11.2889	−	19.1677i	0.618628	−	1.05038i
$334$	−11.9683			−0.654878
$335$			7.81728i			0.427104i
$336$	5.59091	−	3.19571i	0.305009	−	0.174340i
$337$			32.5515i			1.77319i	0.462542	+	0.886597i	$0.346937\pi$
$337$			32.5515i			1.77319i	−0.462542	+	0.886597i	$0.653063\pi$
$338$	0.171583			0.00933286
$339$	−2.11583	+	1.20939i	−0.114916	+	0.0656849i
$340$		−	1.77254i		−	0.0961297i
$341$	−16.4426	−	17.1110i	−0.890416	−	0.926613i
$342$	−5.60217	−	3.29943i	−0.302931	−	0.178413i
$343$			1.00000i			0.0539949i
$344$		−	15.6281i		−	0.842609i
$345$	−6.89219	−	12.0579i	−0.371063	−	0.649176i
$346$	−24.3829			−1.31083
$347$	−1.67153			−0.0897324			−0.0448662	−	0.998993i	$-0.514286\pi$
$347$	−1.67153			−0.0897324			−0.0448662	+	0.998993i	$0.514286\pi$
$348$	−0.956344	−	1.67313i	−0.0512654	−	0.0896889i
$349$		−	25.3053i		−	1.35456i	−0.735724	−	0.677281i	$-0.763158\pi$
$349$		−	25.3053i		−	1.35456i	0.735724	−	0.677281i	$-0.236842\pi$
$350$		−	5.93398i		−	0.317184i
$351$	−0.244542	+	18.8237i	−0.0130527	+	1.00473i
$352$	1.71630	+	1.78607i	0.0914793	+	0.0951981i
$353$		−	20.3271i		−	1.08190i	−0.841053	−	0.540952i	$-0.818064\pi$
$353$		−	20.3271i		−	1.08190i	0.841053	−	0.540952i	$-0.181936\pi$
$354$	18.9029	−	10.8047i	1.00468	−	0.574265i
$355$	4.71445			0.250217
$356$			0.822949i			0.0436162i
$357$	6.59414	−	3.76915i	0.348999	−	0.199485i
$358$		−	24.2472i		−	1.28150i
$359$	25.5904			1.35061			0.675305	−	0.737539i	$-0.264012\pi$
$359$	25.5904			1.35061			0.675305	+	0.737539i	$0.264012\pi$
$360$	23.0237	+	13.5599i	1.21346	+	0.714671i
$361$	16.4854			0.867650
$362$	−28.1342			−1.47870
$363$	16.9045	−	8.78847i	0.887257	−	0.461275i
$364$	−0.479127			−0.0251131
$365$	22.3838			1.17162
$366$	14.8376	−	8.48101i	0.775571	−	0.443310i
$367$	6.55667			0.342255			0.171128	−	0.985249i	$-0.445259\pi$
$367$	6.55667			0.342255			0.171128	+	0.985249i	$0.445259\pi$
$368$		−	9.75421i		−	0.508473i
$369$	−12.4497	+	21.1386i	−0.648106	+	1.10043i
$370$		−	30.9734i		−	1.61023i
$371$	−6.53391			−0.339224
$372$	0.813322	+	1.42291i	0.0421688	+	0.0737744i
$373$			10.1725i			0.526710i	0.964699	+	0.263355i	$0.0848290\pi$
$373$			10.1725i			0.526710i	−0.964699	+	0.263355i	$0.915171\pi$
$374$	−13.7722	−	14.3320i	−0.712142	−	0.741092i
$375$	−3.02441	+	1.72872i	−0.156180	+	0.0892709i
$376$			11.6980i			0.603279i
$377$		−	30.4806i		−	1.56983i
$378$	−0.0922472	+	7.10076i	−0.00474469	+	0.365224i
$379$	−24.3893			−1.25280			−0.626398	−	0.779504i	$-0.715471\pi$
$379$	−24.3893			−1.25280			−0.626398	+	0.779504i	$0.715471\pi$
$380$	0.640987			0.0328819
$381$	−26.9514	+	15.4052i	−1.38076	+	0.789231i
$382$		−	0.694533i		−	0.0355354i
$383$			8.47410i			0.433006i	0.976282	+	0.216503i	$0.0694652\pi$
$383$			8.47410i			0.433006i	−0.976282	+	0.216503i	$0.930535\pi$
$384$	8.64999	+	15.1332i	0.441418	+	0.772262i
$385$	7.02385	+	7.30938i	0.357969	+	0.372521i
$386$			0.847673i			0.0431454i
$387$	13.8633	+	8.16486i	0.704711	+	0.415043i
$388$	1.99587			0.101325
$389$			20.7583i			1.05249i	0.850334	+	0.526244i	$0.176400\pi$
$389$			20.7583i			1.05249i	−0.850334	+	0.526244i	$0.823600\pi$
$390$	13.0075	+	22.7567i	0.658661	+	1.15233i
$391$		−	11.5045i		−	0.581808i
$392$	−2.91405			−0.147182
$393$	−11.1715	−	19.5446i	−0.563529	−	0.985895i
$394$	−23.4010			−1.17893
$395$	−50.7173			−2.55186
$396$	−1.28023	+	0.304111i	−0.0643342	+	0.0152822i
$397$	6.79065			0.340813			0.170406	−	0.985374i	$-0.445492\pi$
$397$	6.79065			0.340813			0.170406	+	0.985374i	$0.445492\pi$
$398$	−23.3601			−1.17094
$399$	1.36300	+	2.38457i	0.0682353	+	0.119378i
$400$	16.1435			0.807174
$401$		−	9.60506i		−	0.479654i	−0.970816	−	0.239827i	$-0.922909\pi$
$401$		−	9.60506i		−	0.479654i	0.970816	−	0.239827i	$-0.0770907\pi$
$402$	−3.00437	−	5.25615i	−0.149844	−	0.262153i
$403$			25.9222i			1.29128i
$404$	1.65468			0.0823232
$405$	−24.0574	+	13.3394i	−1.19542	+	0.662841i
$406$		−	11.4981i		−	0.570639i
$407$	17.0399	+	17.7326i	0.844636	+	0.878972i
$408$	10.9835	+	19.2157i	0.543764	+	0.951317i
$409$		−	11.1975i		−	0.553679i	−0.960916	−	0.276840i	$-0.910713\pi$
$409$		−	11.1975i		−	0.553679i	0.960916	−	0.276840i	$-0.0892871\pi$
$410$			34.1583i			1.68696i
$411$	16.6484	−	9.51607i	0.821205	−	0.469393i
$412$	−0.355869			−0.0175324
$413$	−9.19809			−0.452608
$414$	9.26829	+	5.45861i	0.455511	+	0.268276i
$415$			13.0326i			0.639743i
$416$		−	2.70580i		−	0.132663i
$417$	−12.3613	+	7.06558i	−0.605333	+	0.346003i
$418$	5.18274	−	4.98029i	0.253496	−	0.243594i
$419$			0.341835i			0.0166998i	0.999965	+	0.00834988i	$0.00265788\pi$
$419$			0.341835i			0.0166998i	−0.999965	+	0.00834988i	$0.997342\pi$
$420$	−0.347430	−	0.607830i	−0.0169529	−	0.0296591i
$421$	24.5743			1.19768			0.598839	−	0.800869i	$-0.295629\pi$
$421$	24.5743			1.19768			0.598839	+	0.800869i	$0.295629\pi$
$422$			29.4021i			1.43127i
$423$	−10.3770	−	6.11161i	−0.504549	−	0.297157i
$424$		−	19.0402i		−	0.924672i
$425$	19.0403			0.923588
$426$	−3.16988	+	1.81188i	−0.153581	+	0.0877858i
$427$	−7.21990			−0.349395
$428$	1.15657			0.0559049
$429$	−19.9664	−	5.87240i	−0.963988	−	0.283522i
$430$	22.4020			1.08032
$431$	19.7655			0.952071			0.476035	−	0.879426i	$-0.342073\pi$
$431$	19.7655			0.952071			0.476035	+	0.879426i	$0.342073\pi$
$432$	−19.3177	−	0.250960i	−0.929425	−	0.0120743i
$433$	−7.41259			−0.356226			−0.178113	−	0.984010i	$-0.556999\pi$
$433$	−7.41259			−0.356226			−0.178113	+	0.984010i	$0.556999\pi$
$434$			9.77853i			0.469384i
$435$	38.6684	−	22.1025i	1.85401	−	1.05973i
$436$			0.264225i			0.0126541i
$437$	4.16025			0.199012
$438$	−15.0503	+	8.60264i	−0.719133	+	0.411050i
$439$			3.19709i			0.152589i	0.997085	+	0.0762944i	$0.0243089\pi$
$439$			3.19709i			0.152589i	−0.997085	+	0.0762944i	$0.975691\pi$
$440$	−21.2999	+	20.4679i	−1.01543	+	0.975768i
$441$	1.52244	−	2.58499i	0.0724973	−	0.123095i
$442$			21.7122i			1.03275i
$443$		−	34.1507i		−	1.62255i	−0.584666	−	0.811274i	$-0.698774\pi$
$443$		−	34.1507i		−	1.62255i	0.584666	−	0.811274i	$-0.301226\pi$
$444$	−0.842868	−	1.47460i	−0.0400007	−	0.0699814i
$445$	−19.0196			−0.901614
$446$	18.3974			0.871144
$447$	2.72682	+	4.77057i	0.128974	+	0.225640i
$448$		−	8.45672i		−	0.399543i
$449$		−	36.5324i		−	1.72407i	−0.506848	−	0.862036i	$-0.669189\pi$
$449$		−	36.5324i		−	1.72407i	0.506848	−	0.862036i	$-0.330811\pi$
$450$	−9.03414	+	15.3393i	−0.425874	+	0.723100i
$451$	−18.7920	−	19.5560i	−0.884883	−	0.920855i
$452$			0.186080i			0.00875248i
$453$	8.73449	−	4.99256i	0.410382	−	0.234571i
$454$	−7.56729			−0.355151
$455$		−	11.0733i		−	0.519125i
$456$	−6.94876	+	3.97185i	−0.325406	+	0.185999i
$457$		−	16.0589i		−	0.751205i	−0.926781	−	0.375602i	$-0.877436\pi$
$457$		−	16.0589i		−	0.751205i	0.926781	−	0.375602i	$-0.122564\pi$
$458$	−6.84858			−0.320013
$459$	−22.7841	−	0.295992i	−1.06347	−	0.0138157i
$460$	−1.06045			−0.0494440
$461$	20.2965			0.945302			0.472651	−	0.881250i	$-0.343297\pi$
$461$	20.2965			0.945302			0.472651	+	0.881250i	$0.343297\pi$
$462$	−7.53184	−	2.21522i	−0.350413	−	0.103061i
$463$	15.5973			0.724868			0.362434	−	0.932009i	$-0.381946\pi$
$463$	15.5973			0.724868			0.362434	+	0.932009i	$0.381946\pi$
$464$	31.2807			1.45217
$465$	−32.8855	+	18.7971i	−1.52503	+	0.871693i
$466$	30.0904			1.39391
$467$		−	19.4868i		−	0.901744i	−0.892589	−	0.450872i	$-0.851113\pi$
$467$		−	19.4868i		−	0.901744i	0.892589	−	0.450872i	$-0.148887\pi$
$468$	1.23854	+	0.729443i	0.0572514	+	0.0337185i
$469$			2.55762i			0.118100i
$470$	−16.7685			−0.773471
$471$	12.9659	+	22.6839i	0.597437	+	1.04522i
$472$		−	26.8037i		−	1.23374i
$473$	−12.8254	+	12.3243i	−0.589711	+	0.566674i
$474$	34.1010	−	19.4919i	1.56631	−	0.895291i
$475$			6.88533i			0.315921i
$476$		−	0.579933i		−	0.0265812i
$477$	16.8901	+	9.94751i	0.773344	+	0.455465i
$478$	21.6447			0.990007
$479$	18.2551			0.834096			0.417048	−	0.908885i	$-0.363065\pi$
$479$	18.2551			0.834096			0.417048	+	0.908885i	$0.363065\pi$
$480$	3.43264	−	1.96207i	0.156678	−	0.0895557i
$481$		−	26.8639i		−	1.22489i
$482$			18.7980i			0.856227i
$483$	−2.25496	−	3.94505i	−0.102604	−	0.179506i
$484$	0.0579366	−	1.45358i	0.00263348	−	0.0660719i
$485$			46.1276i			2.09454i
$486$	11.0490	−	18.2149i	0.501191	−	0.826246i
$487$	−2.65848			−0.120467			−0.0602335	−	0.998184i	$-0.519185\pi$
$487$	−2.65848			−0.120467			−0.0602335	+	0.998184i	$0.519185\pi$
$488$		−	21.0392i		−	0.952398i
$489$	−15.7804	−	27.6078i	−0.713613	−	1.24847i
$490$		−	4.17714i		−	0.188704i
$491$	−8.83789			−0.398848			−0.199424	−	0.979913i	$-0.563907\pi$
$491$	−8.83789			−0.398848			−0.199424	+	0.979913i	$0.563907\pi$
$492$	0.929537	+	1.62623i	0.0419068	+	0.0733160i
$493$	36.8937			1.66161
$494$	−7.85158			−0.353259
$495$	−7.02845	−	29.5881i	−0.315905	−	1.32989i
$496$	−26.6026			−1.19449
$497$	1.54245			0.0691885
$498$	−5.00873	−	8.76278i	−0.224446	−	0.392670i
$499$	−25.9990			−1.16387			−0.581937	−	0.813234i	$-0.697705\pi$
$499$	−25.9990			−1.16387			−0.581937	+	0.813234i	$0.697705\pi$
$500$			0.265987i			0.0118953i
$501$	−7.52716	−	13.1688i	−0.336289	−	0.588338i
$502$			30.9015i			1.37920i
$503$	−3.26893			−0.145754			−0.0728771	−	0.997341i	$-0.523218\pi$
$503$	−3.26893			−0.145754			−0.0728771	+	0.997341i	$0.523218\pi$
$504$	7.53279	+	4.43648i	0.335537	+	0.197617i
$505$			38.2420i			1.70175i
$506$	−8.57438	+	8.23943i	−0.381178	+	0.366287i
$507$	0.107912	+	0.188793i	0.00479255	+	0.00838458i
$508$			2.37029i			0.105165i
$509$			34.8035i			1.54264i	0.636449	+	0.771319i	$0.280403\pi$
$509$			34.8035i			1.54264i	−0.636449	+	0.771319i	$0.719597\pi$
$510$	−27.5446	+	15.7443i	−1.21970	+	0.697167i
$511$	7.32344			0.323970
$512$	24.4458			1.08036
$513$	0.107037	−	8.23918i	0.00472578	−	0.363768i
$514$		−	1.20467i		−	0.0531359i
$515$		−	8.22465i		−	0.362421i
$516$	1.06652	−	0.609616i	0.0469511	−	0.0268369i
$517$	9.60011	−	9.22509i	0.422212	−	0.405719i
$518$		−	10.1337i		−	0.445251i
$519$	−15.3349	−	26.8285i	−0.673129	−	1.17764i
$520$	32.2682			1.41506
$521$		−	6.88923i		−	0.301823i	−0.988547	−	0.150911i	$-0.951779\pi$
$521$		−	6.88923i		−	0.301823i	0.988547	−	0.150911i	$-0.0482208\pi$
$522$	−17.5052	+	29.7224i	−0.766180	+	1.30091i
$523$			33.0848i			1.44670i	0.690483	+	0.723348i	$0.257398\pi$
$523$			33.0848i			1.44670i	−0.690483	+	0.723348i	$0.742602\pi$
$524$	−1.71889			−0.0750899
$525$	6.52917	−	3.73201i	0.284956	−	0.162878i
$526$	−1.29593			−0.0565053
$527$	−31.3762			−1.36677
$528$	6.02654	−	20.4905i	0.262271	−	0.891734i
$529$	16.1172			0.700750
$530$	27.2930			1.18553
$531$	23.7769	+	14.0036i	1.03183	+	0.607703i
$532$	0.209715			0.00909231
$533$			29.6262i			1.28326i
$534$	12.7883	−	7.30967i	0.553404	−	0.316321i
$535$			26.7300i			1.15564i
$536$	−7.45305			−0.321923
$537$	26.6792	−	15.2496i	1.15129	−	0.658070i
$538$		−	30.8376i		−	1.32950i
$539$	2.29803	+	2.39145i	0.0989833	+	0.103007i
$540$	−0.0272838	+	2.10018i	−0.00117411	+	0.0903773i
$541$			8.08502i			0.347602i	0.984781	+	0.173801i	$0.0556050\pi$
$541$			8.08502i			0.347602i	−0.984781	+	0.173801i	$0.944395\pi$
$542$			16.7927i			0.721308i
$543$	−17.6943	−	30.9562i	−0.759334	−	1.32846i
$544$	3.27510			0.140419
$545$	−6.10662			−0.261579
$546$	4.25574	+	7.44543i	0.182129	+	0.318635i
$547$			36.2406i			1.54954i	0.632246	+	0.774768i	$0.282133\pi$
$547$			36.2406i			1.54954i	−0.632246	+	0.774768i	$0.717867\pi$
$548$		−	1.46417i		−	0.0625464i
$549$	18.6634	+	10.9919i	0.796533	+	0.469122i
$550$	−13.6365	−	14.1908i	−0.581461	−	0.605099i
$551$			13.3415i			0.568366i
$552$	11.4961	−	6.57107i	0.489306	−	0.279683i
$553$	−16.5934			−0.705625
$554$		−	25.0677i		−	1.06503i
$555$	34.0801	−	19.4799i	1.44662	−	0.826876i
$556$			1.08713i			0.0461047i
$557$	16.1400			0.683873			0.341937	−	0.939723i	$-0.388917\pi$
$557$	16.1400			0.683873			0.341937	+	0.939723i	$0.388917\pi$
$558$	14.8873	−	25.2774i	0.630228	−	1.07008i
$559$	19.4297			0.821789
$560$	11.3640			0.480215
$561$	7.10793	−	24.1673i	0.300097	−	1.02034i
$562$	17.4675			0.736823
$563$	14.4249			0.607935			0.303968	−	0.952682i	$-0.401689\pi$
$563$	14.4249			0.607935			0.303968	+	0.952682i	$0.401689\pi$
$564$	−0.798322	+	0.456313i	−0.0336154	+	0.0192143i
$565$	−4.30059			−0.180927
$566$		−	9.89266i		−	0.415819i
$567$	−7.87100	+	4.36433i	−0.330551	+	0.183285i
$568$			4.49479i			0.188597i
$569$	0.166098			0.00696317			0.00348159	−	0.999994i	$-0.498892\pi$
$569$	0.166098			0.00696317			0.00348159	+	0.999994i	$0.498892\pi$
$570$	−5.69343	−	9.96067i	−0.238472	−	0.417207i
$571$		−	23.6347i		−	0.989081i	−0.869155	−	0.494540i	$-0.835336\pi$
$571$		−	23.6347i		−	0.989081i	0.869155	−	0.494540i	$-0.164664\pi$
$572$	−1.14581	+	1.10105i	−0.0479087	+	0.0460372i
$573$	0.764196	−	0.436808i	0.0319248	−	0.0182479i
$574$			11.1758i			0.466468i
$575$		−	11.3912i		−	0.475044i
$576$	−12.8749	+	21.8605i	−0.536453	+	0.910856i
$577$	−6.86762			−0.285903			−0.142951	−	0.989730i	$-0.545659\pi$
$577$	−6.86762			−0.285903			−0.142951	+	0.989730i	$0.545659\pi$
$578$	−3.04726			−0.126749
$579$	−0.932696	+	0.533121i	−0.0387615	+	0.0221558i
$580$		−	3.40076i		−	0.141209i
$581$			4.26394i			0.176898i
$582$	−17.7279	−	31.0151i	−0.734846	−	1.28562i
$583$	−15.6255	+	15.0151i	−0.647144	+	0.621864i
$584$			21.3409i			0.883093i
$585$	−16.8585	+	28.6244i	−0.697013	+	1.18347i
$586$	−22.1450			−0.914803
$587$		−	18.0785i		−	0.746179i	−0.927795	−	0.373089i	$-0.878298\pi$
$587$		−	18.0785i		−	0.746179i	0.927795	−	0.373089i	$-0.121702\pi$
$588$	−0.113671	−	0.198867i	−0.00468770	−	0.00820115i
$589$		−	11.3463i		−	0.467514i
$590$	38.4217			1.58179
$591$	−14.7175	−	25.7482i	−0.605395	−	1.05914i
$592$	27.5690			1.13308
$593$	30.7957			1.26463			0.632315	−	0.774711i	$-0.282105\pi$
$593$	30.7957			1.26463			0.632315	+	0.774711i	$0.282105\pi$
$594$	16.0972	+	17.1931i	0.660475	+	0.705442i
$595$	13.4031			0.549474
$596$	0.419557			0.0171857
$597$	−14.6917	−	25.7032i	−0.601292	−	1.05196i
$598$	12.9897			0.531189
$599$		−	33.1828i		−	1.35581i	−0.735148	−	0.677906i	$-0.762887\pi$
$599$		−	33.1828i		−	1.35581i	0.735148	−	0.677906i	$-0.237113\pi$
$600$	10.8753	+	19.0263i	0.443982	+	0.776747i
$601$		−	6.64582i		−	0.271089i	−0.990771	−	0.135544i	$-0.956722\pi$
$601$		−	6.64582i		−	0.271089i	0.990771	−	0.135544i	$-0.0432783\pi$
$602$	7.32938			0.298723
$603$	3.89384	−	6.61143i	0.158569	−	0.269238i
$604$		−	0.768171i		−	0.0312564i
$605$	33.5944	+	1.33900i	1.36581	+	0.0544381i
$606$	−14.6973	−	25.7130i	−0.597037	−	1.04452i
$607$		−	25.2480i		−	1.02479i	−0.858751	−	0.512393i	$-0.828759\pi$
$607$		−	25.2480i		−	1.02479i	0.858751	−	0.512393i	$-0.171241\pi$
$608$			1.18434i			0.0480313i
$609$	12.6513	−	7.23140i	0.512659	−	0.293031i
$610$	30.1585			1.22108
$611$	−14.5436			−0.588373
$612$	−0.882916	+	1.49912i	−0.0356898	+	0.0605984i
$613$		−	6.24677i		−	0.252305i	−0.992011	−	0.126152i	$-0.959737\pi$
$613$		−	6.24677i		−	0.252305i	0.992011	−	0.126152i	$-0.0402628\pi$
$614$		−	9.09057i		−	0.366866i
$615$	−37.5845	+	21.4830i	−1.51555	+	0.866276i
$616$	−6.96882	+	6.69659i	−0.280782	+	0.269813i
$617$			42.2569i			1.70120i	0.525815	+	0.850599i	$0.323760\pi$
$617$			42.2569i			1.70120i	−0.525815	+	0.850599i	$0.676240\pi$
$618$	3.16093	+	5.53006i	0.127151	+	0.222451i
$619$	−3.89940			−0.156730			−0.0783651	−	0.996925i	$-0.524970\pi$
$619$	−3.89940			−0.156730			−0.0783651	+	0.996925i	$0.524970\pi$
$620$			2.89218i			0.116153i
$621$	−0.177082	+	13.6310i	−0.00710607	+	0.546992i
$622$		−	0.634824i		−	0.0254541i
$623$	−6.22274			−0.249309
$624$	−20.2554	+	11.5778i	−0.810866	+	0.463484i
$625$	−27.8572			−1.11429
$626$	−8.25789			−0.330051
$627$	8.73937	+	2.57037i	0.349017	+	0.102651i
$628$	1.99497			0.0796081
$629$	32.5160			1.29650
$630$	−6.35945	+	10.7978i	−0.253367	+	0.430197i
$631$	−31.7360			−1.26339			−0.631695	−	0.775217i	$-0.717641\pi$
$631$	−31.7360			−1.26339			−0.631695	+	0.775217i	$0.717641\pi$
$632$		−	48.3542i		−	1.92343i
$633$	−32.3512	+	18.4917i	−1.28585	+	0.734978i
$634$			3.32794i			0.132170i
$635$	−54.7808			−2.17391
$636$	1.29938	−	0.742715i	0.0515238	−	0.0294505i
$637$		−	3.62292i		−	0.143545i
$638$	−26.4229	−	27.4971i	−1.04609	−	1.08862i
$639$	−3.98723	−	2.34830i	−0.157732	−	0.0928973i
$640$			30.7594i			1.21587i
$641$			11.5220i			0.455091i	0.973767	+	0.227545i	$0.0730700\pi$
$641$			11.5220i			0.455091i	−0.973767	+	0.227545i	$0.926930\pi$
$642$	−10.2730	−	17.9726i	−0.405442	−	0.709322i
$643$	−2.47464			−0.0975904			−0.0487952	−	0.998809i	$-0.515538\pi$
$643$	−2.47464			−0.0975904			−0.0487952	+	0.998809i	$0.515538\pi$
$644$	−0.346955			−0.0136719
$645$	14.0891	+	24.6489i	0.554759	+	0.970551i
$646$		−	9.50352i		−	0.373911i
$647$			21.8387i			0.858568i	0.903170	+	0.429284i	$0.141234\pi$
$647$			21.8387i			0.858568i	−0.903170	+	0.429284i	$0.858766\pi$
$648$	−12.7179	−	22.9365i	−0.499606	−	0.901031i
$649$	−21.9968	+	21.1375i	−0.863449	+	0.829720i
$650$			21.4983i			0.843233i
$651$	−10.7593	+	6.14994i	−0.421692	+	0.241035i
$652$	−2.42802			−0.0950885
$653$			11.4888i			0.449590i	0.974406	+	0.224795i	$0.0721712\pi$
$653$			11.4888i			0.449590i	−0.974406	+	0.224795i	$0.927829\pi$
$654$	4.10594	−	2.34692i	0.160555	−	0.0917718i
$655$		−	39.7260i		−	1.55222i
$656$	−30.4039			−1.18707
$657$	−18.9310	−	11.1495i	−0.738569	−	0.434985i
$658$	−5.48623			−0.213876
$659$	3.68630			0.143598			0.0717990	−	0.997419i	$-0.477126\pi$
$659$	3.68630			0.143598			0.0717990	+	0.997419i	$0.477126\pi$
$660$	−2.22768	−	0.655191i	−0.0867122	−	0.0255033i
$661$	−14.8911			−0.579196			−0.289598	−	0.957148i	$-0.593522\pi$
$661$	−14.8911			−0.579196			−0.289598	+	0.957148i	$0.593522\pi$
$662$	41.7798			1.62382
$663$	−23.8900	+	13.6553i	−0.927812	+	0.530329i
$664$	−12.4253			−0.482197
$665$			4.84683i			0.187952i
$666$	−15.4281	+	26.1956i	−0.597825	+	1.01506i
$667$		−	22.0722i		−	0.854641i
$668$	−1.15815			−0.0448103
$669$	11.5706	+	20.2427i	0.447344	+	0.782630i
$670$		−	10.6835i		−	0.412741i
$671$	−17.2660	+	16.5916i	−0.666548	+	0.640510i
$672$	1.12308	−	0.641940i	0.0433236	−	0.0247634i
$673$			4.58983i			0.176925i	0.996080	+	0.0884624i	$0.0281953\pi$
$673$			4.58983i			0.176925i	−0.996080	+	0.0884624i	$0.971805\pi$
$674$		−	44.4868i		−	1.71357i
$675$	−22.5596	−	0.293076i	−0.868320	−	0.0112805i
$676$	0.0166037			0.000638605
$677$	1.73217			0.0665728			0.0332864	−	0.999446i	$-0.489403\pi$
$677$	1.73217			0.0665728			0.0332864	+	0.999446i	$0.489403\pi$
$678$	2.89161	−	1.65282i	0.111052	−	0.0634761i
$679$			15.0918i			0.579171i
$680$			39.0574i			1.49778i
$681$	−4.75924	−	8.32631i	−0.182375	−	0.319065i
$682$	22.4714	+	23.3849i	0.860473	+	0.895453i
$683$		−	19.9482i		−	0.763296i	−0.924308	−	0.381648i	$-0.875357\pi$
$683$		−	19.9482i		−	0.763296i	0.924308	−	0.381648i	$-0.124643\pi$
$684$	−0.542112	−	0.319280i	−0.0207282	−	0.0122080i
$685$	33.8392			1.29293
$686$		−	1.36666i		−	0.0521792i
$687$	−4.30723	−	7.53551i	−0.164331	−	0.287498i
$688$			19.9397i			0.760194i
$689$	23.6718			0.901825
$690$	9.41926	+	16.4790i	0.358585	+	0.627346i
$691$	−21.4439			−0.815765			−0.407882	−	0.913034i	$-0.633733\pi$
$691$	−21.4439			−0.815765			−0.407882	+	0.913034i	$0.633733\pi$
$692$	−2.35948			−0.0896941
$693$	−2.29954	−	9.68050i	−0.0873522	−	0.367732i
$694$	2.28441			0.0867149
$695$	−25.1252			−0.953055
$696$	21.0727	+	36.8667i	0.798758	+	1.39743i
$697$	−35.8595			−1.35828
$698$			34.5837i			1.30901i
$699$	18.9245	+	33.1085i	0.715791	+	1.25228i
$700$		−	0.574219i		−	0.0217035i
$701$	−1.02260			−0.0386231			−0.0193116	−	0.999814i	$-0.506147\pi$
$701$	−1.02260			−0.0386231			−0.0193116	+	0.999814i	$0.506147\pi$
$702$	0.334204	−	25.7255i	0.0126137	−	0.970946i
$703$			11.7584i			0.443477i
$704$	−19.4338	−	20.2239i	−0.732440	−	0.762215i
$705$	−10.5461	−	18.4504i	−0.397188	−	0.694881i
$706$			27.7802i			1.04552i
$707$			12.5118i			0.470556i
$708$	1.82920	−	1.04555i	0.0687455	−	0.0392943i
$709$	5.26348			0.197674			0.0988370	−	0.995104i	$-0.468488\pi$
$709$	5.26348			0.197674			0.0988370	+	0.995104i	$0.468488\pi$
$710$	−6.44304			−0.241803
$711$	42.8939	+	25.2626i	1.60865	+	0.947421i
$712$		−	18.1334i		−	0.679577i
$713$			18.7713i			0.702992i
$714$	−9.01192	+	5.15114i	−0.337263	+	0.192776i
$715$	−25.4469	−	26.4813i	−0.951658	−	0.990345i
$716$		−	2.34635i		−	0.0876874i
$717$	13.6129	+	23.8157i	0.508382	+	0.889415i
$718$	−34.9733			−1.30519
$719$			45.7225i			1.70516i	0.522594	+	0.852581i	$0.324964\pi$
$719$			45.7225i			1.70516i	−0.522594	+	0.852581i	$0.675036\pi$
$720$	−29.3757	−	17.3010i	−1.09477	−	0.644770i
$721$		−	2.69091i		−	0.100215i
$722$	−22.5298			−0.838473
$723$	−20.6835	+	11.8225i	−0.769229	+	0.439684i
$724$	−2.72250			−0.101181
$725$	36.5302			1.35670
$726$	−23.1027	+	12.0108i	−0.857421	+	0.445764i
$727$	10.5337			0.390673			0.195336	−	0.980736i	$-0.437420\pi$
$727$	10.5337			0.390673			0.195336	+	0.980736i	$0.437420\pi$
$728$	10.5574			0.391283
$729$	26.9909	+	0.701405i	0.999663	+	0.0259780i
$730$	−30.5910			−1.13222
$731$			23.5177i			0.869832i
$732$	1.43580	−	0.820691i	0.0530688	−	0.0303336i
$733$		−	48.1500i		−	1.77846i	−0.457458	−	0.889231i	$-0.651240\pi$
$733$		−	48.1500i		−	1.77846i	0.457458	−	0.889231i	$-0.348760\pi$
$734$	−8.96072			−0.330746
$735$	4.59611	−	2.62710i	0.169530	−	0.0969019i
$736$		−	1.95938i		−	0.0722238i
$737$	5.87751	+	6.11644i	0.216501	+	0.225302i
$738$	17.0145	−	28.8892i	0.626311	−	1.06343i
$739$			15.1302i			0.556575i	0.960498	+	0.278287i	$0.0897668\pi$
$739$			15.1302i			0.556575i	−0.960498	+	0.278287i	$0.910233\pi$
$740$		−	2.99724i		−	0.110181i
$741$	−4.93804	−	8.63911i	−0.181403	−	0.317366i
$742$	8.92961			0.327816
$743$	−4.66492			−0.171139			−0.0855697	−	0.996332i	$-0.527271\pi$
$743$	−4.66492			−0.171139			−0.0855697	+	0.996332i	$0.527271\pi$
$744$	−17.9212	−	31.3533i	−0.657025	−	1.14947i
$745$			9.69656i			0.355255i
$746$		−	13.9023i		−	0.508998i
$747$	6.49160	−	11.0222i	0.237515	−	0.403282i
$748$	−1.33271	−	1.38688i	−0.0487286	−	0.0507095i
$749$			8.74541i			0.319550i
$750$	4.13333	−	2.36257i	0.150928	−	0.0862690i
$751$	32.0810			1.17065			0.585326	−	0.810798i	$-0.300967\pi$
$751$	32.0810			1.17065			0.585326	+	0.810798i	$0.300967\pi$
$752$		−	14.9254i		−	0.544273i
$753$	−34.0010	+	19.4347i	−1.23907	+	0.708239i
$754$			41.6566i			1.51704i
$755$	17.7536			0.646118
$756$	−0.00892659	+	0.687127i	−0.000324657	+	0.0249906i
$757$	−16.7783			−0.609819			−0.304909	−	0.952381i	$-0.598626\pi$
$757$	−16.7783			−0.609819			−0.304909	+	0.952381i	$0.598626\pi$
$758$	33.3318			1.21067
$759$	−14.4585	−	4.25244i	−0.524810	−	0.154354i
$760$	−14.1239			−0.512328
$761$	−34.8438			−1.26309			−0.631543	−	0.775341i	$-0.717578\pi$
$761$	−34.8438			−1.26309			−0.631543	+	0.775341i	$0.717578\pi$
$762$	36.8333	−	21.0536i	1.33433	−	0.762691i
$763$	−1.99794			−0.0723302
$764$		−	0.0672086i		−	0.00243152i
$765$	−34.6469	−	20.4055i	−1.25266	−	0.737762i
$766$		−	11.5812i		−	0.418445i
$767$	33.3239			1.20326
$768$	2.71591	+	4.75149i	0.0980018	+	0.171454i
$769$			4.74762i			0.171204i	0.996329	+	0.0856018i	$0.0272813\pi$
$769$			4.74762i			0.171204i	−0.996329	+	0.0856018i	$0.972719\pi$
$770$	−9.59920	−	9.98942i	−0.345931	−	0.359994i
$771$	1.32551	−	0.757647i	0.0477369	−	0.0272860i
$772$			0.0820277i			0.00295224i
$773$			6.02917i			0.216854i	0.994104	+	0.108427i	$0.0345814\pi$
$773$			6.02917i			0.216854i	−0.994104	+	0.108427i	$0.965419\pi$
$774$	−18.9464	−	11.1586i	−0.681013	−	0.401086i
$775$	−31.0671			−1.11596
$776$	−43.9783			−1.57873
$777$	11.1502	−	6.37335i	0.400011	−	0.228643i
$778$		−	28.3695i		−	1.01709i
$779$		−	12.9675i		−	0.464609i
$780$	1.25871	+	2.20212i	0.0450691	+	0.0788486i
$781$	3.68871	−	3.54461i	0.131992	−	0.126836i
$782$			15.7227i			0.562243i
$783$	−43.7130	−	0.567883i	−1.56217	−	0.0202945i
$784$	3.71801			0.132786
$785$			46.1067i			1.64562i
$786$	15.2676	+	26.7108i	0.544579	+	0.952742i
$787$		−	10.9767i		−	0.391278i	−0.980676	−	0.195639i	$-0.937322\pi$
$787$		−	10.9767i		−	0.391278i	0.980676	−	0.195639i	$-0.0626781\pi$
$788$	−2.26447			−0.0806686
$789$	−0.815041	−	1.42592i	−0.0290162	−	0.0507640i
$790$	69.3131			2.46605
$791$	−1.40705			−0.0500288
$792$	28.2095	−	6.70097i	1.00238	−	0.238109i
$793$	26.1571			0.928867
$794$	−9.28049			−0.329352
$795$	17.1652	+	30.0306i	0.608788	+	1.06508i
$796$	−2.26051			−0.0801218
$797$		−	50.2802i		−	1.78102i	−0.454966	−	0.890509i	$-0.650349\pi$
$797$		−	50.2802i		−	1.78102i	0.454966	−	0.890509i	$-0.349651\pi$
$798$	−1.86275	−	3.25889i	−0.0659407	−	0.115363i
$799$		−	17.6036i		−	0.622770i
$800$	3.24283			0.114651
$801$	16.0857	+	9.47377i	0.568360	+	0.334739i
$802$			13.1268i			0.463524i
$803$	17.5137	−	16.8295i	0.618044	−	0.593901i
$804$	−0.290727	−	0.508628i	−0.0102532	−	0.0179379i
$805$		−	8.01863i		−	0.282620i
$806$		−	35.4268i		−	1.24786i
$807$	33.9307	−	19.3945i	1.19442	−	0.682717i
$808$	−36.4602			−1.28266
$809$	10.6479			0.374360			0.187180	−	0.982326i	$-0.440065\pi$
$809$	10.6479			0.374360			0.187180	+	0.982326i	$0.440065\pi$
$810$	32.8782	−	18.2304i	1.15522	−	0.640551i
$811$		−	0.696259i		−	0.0244490i	−0.999925	−	0.0122245i	$-0.996109\pi$
$811$		−	0.696259i		−	0.0244490i	0.999925	−	0.0122245i	$-0.00389127\pi$
$812$		−	1.11265i		−	0.0390462i
$813$	−18.4770	+	10.5613i	−0.648018	+	0.370401i
$814$	−23.2877	−	24.2344i	−0.816233	−	0.849414i
$815$		−	56.1150i		−	1.96562i
$816$	−14.0137	−	24.5171i	−0.490579	−	0.858270i
$817$	−8.50445			−0.297533
$818$			15.3031i			0.535060i
$819$	−5.51569	+	9.36521i	−0.192734	+	0.327247i
$820$			3.30544i			0.115431i
$821$	7.39068			0.257936			0.128968	−	0.991649i	$-0.458833\pi$
$821$	7.39068			0.257936			0.128968	+	0.991649i	$0.458833\pi$
$822$	−22.7526	+	13.0052i	−0.793590	+	0.453609i
$823$	−15.7003			−0.547279			−0.273639	−	0.961832i	$-0.588227\pi$
$823$	−15.7003			−0.547279			−0.273639	+	0.961832i	$0.588227\pi$
$824$	7.84144			0.273169
$825$	7.03790	−	23.9292i	0.245028	−	0.833107i
$826$	12.5706			0.437388
$827$	23.9181			0.831715			0.415857	−	0.909430i	$-0.363482\pi$
$827$	23.9181			0.831715			0.415857	+	0.909430i	$0.363482\pi$
$828$	0.896874	+	0.528219i	0.0311685	+	0.0183569i
$829$	50.3456			1.74857			0.874287	−	0.485409i	$-0.161329\pi$
$829$	50.3456			1.74857			0.874287	+	0.485409i	$0.161329\pi$
$830$		−	17.8110i		−	0.618230i
$831$	27.5821	−	15.7657i	0.956812	−	0.546905i
$832$			30.6380i			1.06218i
$833$	4.38517			0.151937
$834$	16.8936	−	9.65623i	0.584977	−	0.334368i
$835$		−	26.7666i		−	0.926297i
$836$	0.501524	−	0.481933i	0.0173456	−	0.0166680i
$837$	37.1757	+	0.482956i	1.28498	+	0.0166934i
$838$		−	0.467172i		−	0.0161382i
$839$		−	26.5226i		−	0.915661i	−0.889039	−	0.457831i	$-0.848627\pi$
$839$		−	26.5226i		−	0.915661i	0.889039	−	0.457831i	$-0.151373\pi$
$840$	7.65550	+	13.3933i	0.264140	+	0.462113i
$841$	41.7833			1.44080
$842$	−33.5846			−1.15740
$843$	10.9857	+	19.2196i	0.378369	+	0.661957i
$844$			2.84519i			0.0979354i
$845$			0.383736i			0.0132009i
$846$	14.1818	+	8.35248i	0.487582	+	0.287164i
$847$	10.9913	+	0.438088i	0.377665	+	0.0150529i
$848$			24.2932i			0.834231i
$849$	10.8849	−	6.22172i	0.373569	−	0.213529i
$850$	−26.0215			−0.892530
$851$		−	19.4532i		−	0.666848i
$852$	−0.306744	+	0.175332i	−0.0105089	+	0.00600677i
$853$			45.1252i			1.54506i	0.634979	+	0.772529i	$0.281009\pi$
$853$			45.1252i			1.54506i	−0.634979	+	0.772529i	$0.718991\pi$
$854$	9.86713			0.337646
$855$	7.37902	−	12.5290i	0.252357	−	0.428483i
$856$	−25.4846			−0.871045
$857$	31.7037			1.08298			0.541489	−	0.840708i	$-0.317861\pi$
$857$	31.7037			1.08298			0.541489	+	0.840708i	$0.317861\pi$
$858$	27.2873	+	8.02556i	0.931571	+	0.273988i
$859$	40.6660			1.38751			0.693753	−	0.720213i	$-0.255956\pi$
$859$	40.6660			1.38751			0.693753	+	0.720213i	$0.255956\pi$
$860$	2.16780			0.0739212
$861$	−12.2967	+	7.02870i	−0.419071	+	0.239537i
$862$	−27.0127			−0.920055
$863$			12.7841i			0.435176i	0.976041	+	0.217588i	$0.0698189\pi$
$863$			12.7841i			0.435176i	−0.976041	+	0.217588i	$0.930181\pi$
$864$	−3.88046	−	0.0504117i	−0.132016	−	0.00171504i
$865$		−	54.5311i		−	1.85411i
$866$	10.1305			0.344247
$867$	−1.91649	−	3.35291i	−0.0650874	−	0.113871i
$868$			0.946249i			0.0321178i
$869$	−39.6824	+	38.1323i	−1.34613	+	1.29355i
$870$	−52.8464	+	30.2065i	−1.79166	+	1.02410i
$871$		−	9.26607i		−	0.313969i
$872$		−	5.82209i		−	0.197161i
$873$	22.9764	−	39.0122i	0.777635	−	1.32036i
$874$	−5.68564			−0.192320
$875$	−2.01126			−0.0679931
$876$	−1.45639	+	0.832461i	−0.0492070	+	0.0281263i
$877$		−	40.5779i		−	1.37022i	−0.728440	−	0.685109i	$-0.759754\pi$
$877$		−	40.5779i		−	1.37022i	0.728440	−	0.685109i	$-0.240246\pi$
$878$		−	4.36933i		−	0.147458i
$879$	−13.9275	−	24.3662i	−0.469764	−	0.821853i
$880$	27.1764	−	26.1148i	0.916116	−	0.880329i
$881$			23.6130i			0.795542i	0.917485	+	0.397771i	$0.130216\pi$
$881$			23.6130i			0.795542i	−0.917485	+	0.397771i	$0.869784\pi$
$882$	−2.08066	+	3.53279i	−0.0700594	+	0.118955i
$883$	−8.68143			−0.292153			−0.146077	−	0.989273i	$-0.546665\pi$
$883$	−8.68143			−0.292153			−0.146077	+	0.989273i	$0.546665\pi$
$884$			2.10105i			0.0706660i
$885$	24.1643	+	42.2754i	0.812273	+	1.42107i
$886$			46.6723i			1.56799i
$887$	17.9370			0.602264			0.301132	−	0.953582i	$-0.402635\pi$
$887$	17.9370			0.602264			0.301132	+	0.953582i	$0.402635\pi$
$888$	18.5723	+	32.4922i	0.623245	+	1.09037i
$889$	−17.9230			−0.601116
$890$	25.9932			0.871295
$891$	−8.79374	+	28.5249i	−0.294601	+	0.955620i
$892$	1.78029			0.0596084
$893$	6.36580			0.213023
$894$	−3.72662	−	6.51973i	−0.124637	−	0.218053i
$895$	54.2277			1.81263
$896$			10.0637i			0.336205i
$897$	8.16953	+	14.2926i	0.272773	+	0.477216i
$898$			49.9273i			1.66609i
$899$	−60.1976			−2.00770
$900$	−0.874217	+	1.48435i	−0.0291406	+	0.0494784i
$901$			28.6523i			0.954547i
$902$	25.6823	+	26.7263i	0.855126	+	0.889889i
$903$	4.60962	+	8.06453i	0.153398	+	0.268371i
$904$		−	4.10021i		−	0.136371i
$905$		−	62.9209i		−	2.09156i
$906$	−11.9371	+	6.82312i	−0.396582	+	0.226683i
$907$	−16.2204			−0.538588			−0.269294	−	0.963058i	$-0.586790\pi$
$907$	−16.2204			−0.538588			−0.269294	+	0.963058i	$0.586790\pi$
$908$	−0.732272			−0.0243013
$909$	19.0486	−	32.3430i	0.631801	−	1.07275i
$910$			15.1334i			0.501668i
$911$		−	10.9935i		−	0.364232i	−0.983277	−	0.182116i	$-0.941705\pi$
$911$		−	10.9935i		−	0.364232i	0.983277	−	0.182116i	$-0.0582946\pi$
$912$	8.86586	−	5.06765i	0.293578	−	0.167807i
$913$	9.79867	+	10.1970i	0.324289	+	0.337472i
$914$			21.9470i			0.725943i
$915$	18.9674	+	33.1835i	0.627042	+	1.09701i
$916$	−0.662724			−0.0218970
$917$		−	12.9974i		−	0.429211i
$918$	31.1380	+	0.404520i	1.02771	+	0.0133511i
$919$		−	26.5465i		−	0.875687i	−0.899051	−	0.437844i	$-0.855742\pi$
$919$		−	26.5465i		−	0.875687i	0.899051	−	0.437844i	$-0.144258\pi$
$920$	23.3667			0.770378
$921$	10.0024	−	5.71727i	0.329590	−	0.188390i
$922$	−27.7383			−0.913513
$923$	−5.58819			−0.183937
$924$	−0.728842	−	0.214362i	−0.0239771	−	0.00705201i
$925$	32.1956			1.05859
$926$	−21.3162			−0.700493
$927$	−4.09675	+	6.95596i	−0.134555	+	0.228464i
$928$	6.28352			0.206267
$929$			1.71987i			0.0564271i	0.999602	+	0.0282135i	$0.00898184\pi$
$929$			1.71987i			0.0564271i	−0.999602	+	0.0282135i	$0.991018\pi$
$930$	44.9432	−	25.6891i	1.47375	−	0.842380i
$931$			1.58576i			0.0519713i
$932$	2.91179			0.0953787
$933$	0.698499	−	0.399256i	0.0228678	−	0.0130710i
$934$			26.6318i			0.871420i
$935$	32.0529	−	30.8008i	1.04824	−	1.00729i
$936$	−27.2907	−	16.0730i	−0.892025	−	0.525363i
$937$		−	14.4933i		−	0.473475i	−0.971574	−	0.236737i	$-0.923922\pi$
$937$		−	14.4933i		−	0.473475i	0.971574	−	0.236737i	$-0.0760781\pi$
$938$		−	3.49540i		−	0.114129i
$939$	−5.19357	−	9.08617i	−0.169486	−	0.296516i
$940$	−1.62265			−0.0529251
$941$	4.85563			0.158289			0.0791444	−	0.996863i	$-0.474781\pi$
$941$	4.85563			0.158289			0.0791444	+	0.996863i	$0.474781\pi$
$942$	−17.7199	−	31.0010i	−0.577346	−	1.01007i
$943$			21.4536i			0.698624i
$944$			34.1986i			1.11307i
$945$	−15.8805	−	0.206307i	−0.516593	−	0.00671115i
$946$	17.5279	−	16.8432i	0.569880	−	0.547618i
$947$			45.1780i			1.46809i	0.679102	+	0.734044i	$0.262369\pi$
$947$			45.1780i			1.46809i	−0.679102	+	0.734044i	$0.737631\pi$
$948$	3.29989	−	1.88619i	0.107176	−	0.0612606i
$949$	−26.5322			−0.861273
$950$		−	9.40988i		−	0.305297i
$951$	−3.66175	+	2.09302i	−0.118740	+	0.0678709i
$952$			12.7786i			0.414157i
$953$	−46.3328			−1.50087			−0.750433	−	0.660947i	$-0.770155\pi$
$953$	−46.3328			−1.50087			−0.750433	+	0.660947i	$0.770155\pi$
$954$	−23.0830	−	13.5948i	−0.747338	−	0.440149i
$955$	1.55329			0.0502633
$956$	2.09452			0.0677416
$957$	13.6371	−	46.3668i	0.440825	−	1.49882i
$958$	−24.9484			−0.806047
$959$	11.0714			0.357513
$960$	−38.8681	+	22.2166i	−1.25446	+	0.717039i
$961$	20.1950			0.651452
$962$			36.7138i			1.18370i
$963$	13.3144	−	22.6068i	0.429050	−	0.728493i
$964$			1.81905i			0.0585877i
$965$	−1.89578			−0.0610273
$966$	3.08175	+	5.39154i	0.0991538	+	0.173470i
$967$		−	27.4045i		−	0.881268i	−0.897687	−	0.440634i	$-0.854754\pi$
$967$		−	27.4045i		−	0.881268i	0.897687	−	0.440634i	$-0.145246\pi$
$968$	−1.27661	+	32.0291i	−0.0410319	+	1.02946i
$969$	10.4567	−	5.97698i	0.335919	−	0.192008i
$970$		−	63.0406i		−	2.02411i
$971$			20.6866i			0.663865i	0.943303	+	0.331932i	$0.107701\pi$
$971$			20.6866i			0.663865i	−0.943303	+	0.331932i	$0.892299\pi$
$972$	1.06919	−	1.76262i	0.0342942	−	0.0565362i
$973$	−8.22036			−0.263533
$974$	3.63322			0.116416
$975$	−23.6547	+	13.5208i	−0.757555	+	0.433012i
$976$			26.8437i			0.859245i
$977$			12.7288i			0.407231i	0.979051	+	0.203616i	$0.0652693\pi$
$977$			12.7288i			0.407231i	−0.979051	+	0.203616i	$0.934731\pi$
$978$	21.5663	+	37.7304i	0.689616	+	1.20648i
$979$	−14.8814	+	14.3001i	−0.475611	+	0.457032i
$980$		−	0.404213i		−	0.0129121i
$981$	5.16464	+	3.04175i	0.164894	+	0.0971155i
$982$	12.0784			0.385436
$983$			24.8277i			0.791880i	0.918276	+	0.395940i	$0.129581\pi$
$983$			24.8277i			0.791880i	−0.918276	+	0.395940i	$0.870419\pi$
$984$	−20.4820	−	35.8333i	−0.652942	−	1.14232i
$985$		−	52.3353i		−	1.66754i
$986$	−50.4210			−1.60573
$987$	−3.45042	−	6.03651i	−0.109828	−	0.192144i
$988$	−0.759782			−0.0241719
$989$	14.0698			0.447395
$990$	9.60548	+	40.4368i	0.305282	+	1.28517i
$991$	−51.3902			−1.63246			−0.816232	−	0.577724i	$-0.803941\pi$
$991$	−51.3902			−1.63246			−0.816232	+	0.577724i	$0.803941\pi$
$992$	−5.34382			−0.169666
$993$	26.2763	+	45.9704i	0.833852	+	1.45883i
$994$	−2.10801			−0.0668619
$995$		−	52.2438i		−	1.65624i
$996$	−0.484685	−	0.847958i	−0.0153578	−	0.0268686i
$997$		−	34.9659i		−	1.10738i	−0.832723	−	0.553690i	$-0.813219\pi$
$997$		−	34.9659i		−	1.10738i	0.832723	−	0.553690i	$-0.186781\pi$
$998$	35.5317			1.12473
$999$	−38.5262	−	0.500500i	−1.21891	−	0.0158351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.g.a.197.7	✓	24
3.2	odd	2	inner	231.2.g.a.197.18	yes	24
11.10	odd	2	inner	231.2.g.a.197.17	yes	24
33.32	even	2	inner	231.2.g.a.197.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.g.a.197.7	✓	24	1.1	even	1	trivial
231.2.g.a.197.8	yes	24	33.32	even	2	inner
231.2.g.a.197.17	yes	24	11.10	odd	2	inner
231.2.g.a.197.18	yes	24	3.2	odd	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.36666 q^{2} +(-0.859522 - 1.50374i) q^{3} -0.132249 q^{4} -3.05646i q^{5} +(1.17467 + 2.05509i) q^{6} -1.00000i q^{7} +2.91405 q^{8} +(-1.52244 + 2.58499i) q^{9} +O(q^{10})\)	\(q-1.36666 q^{2} +(-0.859522 - 1.50374i) q^{3} -0.132249 q^{4} -3.05646i q^{5} +(1.17467 + 2.05509i) q^{6} -1.00000i q^{7} +2.91405 q^{8} +(-1.52244 + 2.58499i) q^{9} +4.17714i q^{10} +(-2.29803 - 2.39145i) q^{11} +(0.113671 + 0.198867i) q^{12} +3.62292i q^{13} +1.36666i q^{14} +(-4.59611 + 2.62710i) q^{15} -3.71801 q^{16} -4.38517 q^{17} +(2.08066 - 3.53279i) q^{18} -1.58576i q^{19} +0.404213i q^{20} +(-1.50374 + 0.859522i) q^{21} +(3.14062 + 3.26829i) q^{22} +2.62350i q^{23} +(-2.50469 - 4.38197i) q^{24} -4.34196 q^{25} -4.95129i q^{26} +(5.19571 + 0.0674985i) q^{27} +0.132249i q^{28} -8.41328 q^{29} +(6.28131 - 3.59034i) q^{30} +7.15507 q^{31} -0.746857 q^{32} +(-1.62090 + 5.51114i) q^{33} +5.99302 q^{34} -3.05646 q^{35} +(0.201341 - 0.341862i) q^{36} -7.41499 q^{37} +2.16720i q^{38} +(5.44791 - 3.11398i) q^{39} -8.90669i q^{40} +8.17745 q^{41} +(2.05509 - 1.17467i) q^{42} -5.36300i q^{43} +(0.303912 + 0.316267i) q^{44} +(7.90092 + 4.65329i) q^{45} -3.58543i q^{46} +4.01434i q^{47} +(3.19571 + 5.59091i) q^{48} -1.00000 q^{49} +5.93398 q^{50} +(3.76915 + 6.59414i) q^{51} -0.479127i q^{52} -6.53391i q^{53} +(-7.10076 - 0.0922472i) q^{54} +(-7.30938 + 7.02385i) q^{55} -2.91405i q^{56} +(-2.38457 + 1.36300i) q^{57} +11.4981 q^{58} -9.19809i q^{59} +(0.607830 - 0.347430i) q^{60} -7.21990i q^{61} -9.77853 q^{62} +(2.58499 + 1.52244i) q^{63} +8.45672 q^{64} +11.0733 q^{65} +(2.21522 - 7.53184i) q^{66} -2.55762 q^{67} +0.579933 q^{68} +(3.94505 - 2.25496i) q^{69} +4.17714 q^{70} +1.54245i q^{71} +(-4.43648 + 7.53279i) q^{72} +7.32344i q^{73} +10.1337 q^{74} +(3.73201 + 6.52917i) q^{75} +0.209715i q^{76} +(-2.39145 + 2.29803i) q^{77} +(-7.44543 + 4.25574i) q^{78} -16.5934i q^{79} +11.3640i q^{80} +(-4.36433 - 7.87100i) q^{81} -11.1758 q^{82} -4.26394 q^{83} +(0.198867 - 0.113671i) q^{84} +13.4031i q^{85} +7.32938i q^{86} +(7.23140 + 12.6513i) q^{87} +(-6.69659 - 6.96882i) q^{88} -6.22274i q^{89} +(-10.7978 - 6.35945i) q^{90} +3.62292 q^{91} -0.346955i q^{92} +(-6.14994 - 10.7593i) q^{93} -5.48623i q^{94} -4.84683 q^{95} +(0.641940 + 1.12308i) q^{96} -15.0918 q^{97} +1.36666 q^{98} +(9.68050 - 2.29954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

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