LMFDB - Embedded newform 231.2.e.a.188.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(188,231)]

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, 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("231.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.e (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:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.7
Character	$\chi$	$=$	231.188
Dual form			231.2.e.a.188.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68989i q^{2} +(-1.02930 + 1.39303i) q^{3} -0.855732 q^{4} -1.45819 q^{5} +(2.35408 + 1.73940i) q^{6} +(0.366782 - 2.62020i) q^{7} -1.93369i q^{8} +(-0.881093 - 2.86770i) q^{9} +O(q^{10})$	\(q-1.68989i q^{2} +(-1.02930 + 1.39303i) q^{3} -0.855732 q^{4} -1.45819 q^{5} +(2.35408 + 1.73940i) q^{6} +(0.366782 - 2.62020i) q^{7} -1.93369i q^{8} +(-0.881093 - 2.86770i) q^{9} +2.46419i q^{10} -1.00000i q^{11} +(0.880803 - 1.19207i) q^{12} -3.51679i q^{13} +(-4.42786 - 0.619821i) q^{14} +(1.50091 - 2.03131i) q^{15} -4.97919 q^{16} +2.75133 q^{17} +(-4.84609 + 1.48895i) q^{18} -4.07921i q^{19} +1.24782 q^{20} +(3.27251 + 3.20791i) q^{21} -1.68989 q^{22} +4.35116i q^{23} +(2.69369 + 1.99034i) q^{24} -2.87368 q^{25} -5.94299 q^{26} +(4.90171 + 1.72432i) q^{27} +(-0.313867 + 2.24219i) q^{28} +1.86171i q^{29} +(-3.43270 - 2.53638i) q^{30} +5.81906i q^{31} +4.54691i q^{32} +(1.39303 + 1.02930i) q^{33} -4.64944i q^{34} +(-0.534838 + 3.82076i) q^{35} +(0.753980 + 2.45398i) q^{36} +7.59266 q^{37} -6.89341 q^{38} +(4.89901 + 3.61982i) q^{39} +2.81969i q^{40} +0.863985 q^{41} +(5.42102 - 5.53018i) q^{42} +2.11779 q^{43} +0.855732i q^{44} +(1.28480 + 4.18165i) q^{45} +7.35299 q^{46} +0.483798 q^{47} +(5.12507 - 6.93618i) q^{48} +(-6.73094 - 1.92209i) q^{49} +4.85620i q^{50} +(-2.83193 + 3.83270i) q^{51} +3.00943i q^{52} -13.8100i q^{53} +(2.91391 - 8.28335i) q^{54} +1.45819i q^{55} +(-5.06666 - 0.709241i) q^{56} +(5.68248 + 4.19872i) q^{57} +3.14609 q^{58} -5.87555 q^{59} +(-1.28438 + 1.73826i) q^{60} -5.37692i q^{61} +9.83358 q^{62} +(-7.83712 + 1.25683i) q^{63} -2.27459 q^{64} +5.12815i q^{65} +(1.73940 - 2.35408i) q^{66} +12.5438 q^{67} -2.35440 q^{68} +(-6.06132 - 4.47864i) q^{69} +(6.45667 + 0.903818i) q^{70} +10.0663i q^{71} +(-5.54523 + 1.70376i) q^{72} +12.0605i q^{73} -12.8308i q^{74} +(2.95787 - 4.00313i) q^{75} +3.49071i q^{76} +(-2.62020 - 0.366782i) q^{77} +(6.11710 - 8.27879i) q^{78} +8.75956 q^{79} +7.26061 q^{80} +(-7.44735 + 5.05341i) q^{81} -1.46004i q^{82} +7.13853 q^{83} +(-2.80039 - 2.74511i) q^{84} -4.01196 q^{85} -3.57884i q^{86} +(-2.59343 - 1.91626i) q^{87} -1.93369 q^{88} +15.2657 q^{89} +(7.06653 - 2.17118i) q^{90} +(-9.21470 - 1.28989i) q^{91} -3.72343i q^{92} +(-8.10615 - 5.98954i) q^{93} -0.817566i q^{94} +5.94826i q^{95} +(-6.33400 - 4.68012i) q^{96} -11.7571i q^{97} +(-3.24812 + 11.3746i) q^{98} +(-2.86770 + 0.881093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

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 $

$2$		−	1.68989i		−	1.19493i	−0.801894	−	0.597467i	$-0.796174\pi$
$2$		−	1.68989i		−	1.19493i	0.801894	−	0.597467i	$-0.203826\pi$
$3$	−1.02930	+	1.39303i	−0.594265	+	0.804269i
$3$	−1.02930	+	1.39303i	−0.594265	+	0.804269i
$4$	−0.855732			−0.427866
$5$	−1.45819			−0.652123			−0.326062	−	0.945349i	$-0.605722\pi$
$5$	−1.45819			−0.652123			−0.326062	+	0.945349i	$0.605722\pi$
$6$	2.35408	+	1.73940i	0.961048	+	0.710108i
$7$	0.366782	−	2.62020i	0.138630	−	0.990344i
$7$	0.366782	−	2.62020i	0.138630	−	0.990344i
$8$		−	1.93369i		−	0.683662i
$9$	−0.881093	−	2.86770i	−0.293698	−	0.955898i
$10$			2.46419i			0.779244i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	0.880803	−	1.19207i	0.254266	−	0.344120i
$13$		−	3.51679i		−	0.975381i	−0.873017	−	0.487691i	$-0.837839\pi$
$13$		−	3.51679i		−	0.975381i	0.873017	−	0.487691i	$-0.162161\pi$
$14$	−4.42786	−	0.619821i	−1.18340	−	0.165654i
$15$	1.50091	−	2.03131i	0.387534	−	0.524483i
$16$	−4.97919			−1.24480
$17$	2.75133			0.667295			0.333647	−	0.942698i	$-0.391720\pi$
$17$	2.75133			0.667295			0.333647	+	0.942698i	$0.391720\pi$
$18$	−4.84609	+	1.48895i	−1.14224	+	0.350949i
$19$		−	4.07921i		−	0.935834i	−0.883772	−	0.467917i	$-0.845005\pi$
$19$		−	4.07921i		−	0.935834i	0.883772	−	0.467917i	$-0.154995\pi$
$20$	1.24782			0.279022
$21$	3.27251	+	3.20791i	0.714120	+	0.700023i
$22$	−1.68989			−0.360286
$23$			4.35116i			0.907280i	0.891185	+	0.453640i	$0.149875\pi$
$23$			4.35116i			0.907280i	−0.891185	+	0.453640i	$0.850125\pi$
$24$	2.69369	+	1.99034i	0.549848	+	0.406277i
$25$	−2.87368			−0.574735
$26$	−5.94299			−1.16552
$27$	4.90171	+	1.72432i	0.943334	+	0.331845i
$28$	−0.313867	+	2.24219i	−0.0593153	+	0.423735i
$29$			1.86171i			0.345712i	0.984947	+	0.172856i	$0.0552995\pi$
$29$			1.86171i			0.345712i	−0.984947	+	0.172856i	$0.944701\pi$
$30$	−3.43270	−	2.53638i	−0.626722	−	0.463078i
$31$			5.81906i			1.04513i	0.852598	+	0.522567i	$0.175026\pi$
$31$			5.81906i			1.04513i	−0.852598	+	0.522567i	$0.824974\pi$
$32$			4.54691i			0.803788i
$33$	1.39303	+	1.02930i	0.242496	+	0.179178i
$34$		−	4.64944i		−	0.797373i
$35$	−0.534838	+	3.82076i	−0.0904041	+	0.645827i
$36$	0.753980	+	2.45398i	0.125663	+	0.408997i
$37$	7.59266			1.24823			0.624113	−	0.781334i	$-0.285461\pi$
$37$	7.59266			1.24823			0.624113	+	0.781334i	$0.285461\pi$
$38$	−6.89341			−1.11826
$39$	4.89901	+	3.61982i	0.784469	+	0.579635i
$40$			2.81969i			0.445832i
$41$	0.863985			0.134932			0.0674659	−	0.997722i	$-0.478509\pi$
$41$	0.863985			0.134932			0.0674659	+	0.997722i	$0.478509\pi$
$42$	5.42102	−	5.53018i	0.836481	−	0.853326i
$43$	2.11779			0.322960			0.161480	−	0.986876i	$-0.448373\pi$
$43$	2.11779			0.322960			0.161480	+	0.986876i	$0.448373\pi$
$44$			0.855732i			0.129007i
$45$	1.28480	+	4.18165i	0.191527	+	0.623364i
$46$	7.35299			1.08414
$47$	0.483798			0.0705692			0.0352846	−	0.999377i	$-0.488766\pi$
$47$	0.483798			0.0705692			0.0352846	+	0.999377i	$0.488766\pi$
$48$	5.12507	−	6.93618i	0.739739	−	1.00115i
$49$	−6.73094	−	1.92209i	−0.961563	−	0.274584i
$50$			4.85620i			0.686770i
$51$	−2.83193	+	3.83270i	−0.396550	+	0.536685i
$52$			3.00943i			0.417333i
$53$		−	13.8100i		−	1.89695i	−0.316857	−	0.948473i	$-0.602628\pi$
$53$		−	13.8100i		−	1.89695i	0.316857	−	0.948473i	$-0.397372\pi$
$54$	2.91391	−	8.28335i	0.396533	−	1.12722i
$55$			1.45819i			0.196623i
$56$	−5.06666	−	0.709241i	−0.677061	−	0.0947763i
$57$	5.68248	+	4.19872i	0.752662	+	0.556134i
$58$	3.14609			0.413102
$59$	−5.87555			−0.764932			−0.382466	−	0.923970i	$-0.624925\pi$
$59$	−5.87555			−0.764932			−0.382466	+	0.923970i	$0.624925\pi$
$60$	−1.28438	+	1.73826i	−0.165813	+	0.224408i
$61$		−	5.37692i		−	0.688444i	−0.938888	−	0.344222i	$-0.888143\pi$
$61$		−	5.37692i		−	0.688444i	0.938888	−	0.344222i	$-0.111857\pi$
$62$	9.83358			1.24887
$63$	−7.83712	+	1.25683i	−0.987384	+	0.158345i
$64$	−2.27459			−0.284324
$65$			5.12815i			0.636069i
$66$	1.73940	−	2.35408i	0.214105	−	0.289767i
$67$	12.5438			1.53246			0.766232	−	0.642564i	$-0.222129\pi$
$67$	12.5438			1.53246			0.766232	+	0.642564i	$0.222129\pi$
$68$	−2.35440			−0.285513
$69$	−6.06132	−	4.47864i	−0.729697	−	0.539165i
$70$	6.45667	+	0.903818i	0.771720	+	0.108027i
$71$			10.0663i			1.19465i	0.802000	+	0.597324i	$0.203769\pi$
$71$			10.0663i			1.19465i	−0.802000	+	0.597324i	$0.796231\pi$
$72$	−5.54523	+	1.70376i	−0.653511	+	0.200790i
$73$			12.0605i			1.41157i	0.708425	+	0.705786i	$0.249406\pi$
$73$			12.0605i			1.41157i	−0.708425	+	0.705786i	$0.750594\pi$
$74$		−	12.8308i		−	1.49155i
$75$	2.95787	−	4.00313i	0.341545	−	0.462242i
$76$			3.49071i			0.400412i
$77$	−2.62020	−	0.366782i	−0.298600	−	0.0417986i
$78$	6.11710	−	8.27879i	0.692626	−	0.937388i
$79$	8.75956			0.985528			0.492764	−	0.870163i	$-0.335987\pi$
$79$	8.75956			0.985528			0.492764	+	0.870163i	$0.335987\pi$
$80$	7.26061			0.811761
$81$	−7.44735	+	5.05341i	−0.827483	+	0.561490i
$82$		−	1.46004i		−	0.161234i
$83$	7.13853			0.783555			0.391777	−	0.920060i	$-0.371860\pi$
$83$	7.13853			0.783555			0.391777	+	0.920060i	$0.371860\pi$
$84$	−2.80039	−	2.74511i	−0.305548	−	0.299516i
$85$	−4.01196			−0.435159
$86$		−	3.57884i		−	0.385916i
$87$	−2.59343	−	1.91626i	−0.278045	−	0.205444i
$88$	−1.93369			−0.206132
$89$	15.2657			1.61817			0.809083	−	0.587695i	$-0.199964\pi$
$89$	15.2657			1.61817			0.809083	+	0.587695i	$0.199964\pi$
$90$	7.06653	−	2.17118i	0.744878	−	0.228862i
$91$	−9.21470	−	1.28989i	−0.965963	−	0.135217i
$92$		−	3.72343i		−	0.388194i
$93$	−8.10615	−	5.98954i	−0.840569	−	0.621087i
$94$		−	0.817566i		−	0.0843255i
$95$			5.94826i			0.610279i
$96$	−6.33400	−	4.68012i	−0.646461	−	0.477663i
$97$		−	11.7571i		−	1.19375i	−0.802335	−	0.596874i	$-0.796409\pi$
$97$		−	11.7571i		−	1.19375i	0.802335	−	0.596874i	$-0.203591\pi$
$98$	−3.24812	+	11.3746i	−0.328109	+	1.14900i
$99$	−2.86770	+	0.881093i	−0.288214	+	0.0885532i
$100$	2.45910			0.245910
$101$	−6.38633			−0.635464			−0.317732	−	0.948181i	$-0.602921\pi$
$101$	−6.38633			−0.635464			−0.317732	+	0.948181i	$0.602921\pi$
$102$	6.47684	+	4.78566i	0.641303	+	0.473851i
$103$			16.9062i			1.66581i	0.553413	+	0.832907i	$0.313325\pi$
$103$			16.9062i			1.66581i	−0.553413	+	0.832907i	$0.686675\pi$
$104$	−6.80037			−0.666831
$105$	−4.77195	−	4.67775i	−0.465694	−	0.456502i
$106$	−23.3374			−2.26673
$107$			5.41669i			0.523651i	0.965115	+	0.261825i	$0.0843245\pi$
$107$			5.41669i			0.523651i	−0.965115	+	0.261825i	$0.915676\pi$
$108$	−4.19455	−	1.47556i	−0.403621	−	0.141985i
$109$	−20.0350			−1.91901			−0.959504	−	0.281694i	$-0.909104\pi$
$109$	−20.0350			−1.91901			−0.959504	+	0.281694i	$0.909104\pi$
$110$	2.46419			0.234951
$111$	−7.81510	+	10.5768i	−0.741777	+	1.00391i
$112$	−1.82627	+	13.0465i	−0.172567	+	1.23278i
$113$		−	11.5983i		−	1.09108i	−0.838085	−	0.545539i	$-0.816325\pi$
$113$		−	11.5983i		−	1.09108i	0.838085	−	0.545539i	$-0.183675\pi$
$114$	7.09537	−	9.60277i	0.664543	−	0.899381i
$115$		−	6.34483i		−	0.591658i
$116$		−	1.59313i		−	0.147918i
$117$	−10.0851	+	3.09862i	−0.932365	+	0.286467i
$118$			9.92905i			0.914043i
$119$	1.00914	−	7.20904i	0.0925074	−	0.660852i
$120$	−3.92792	−	2.90230i	−0.358569	−	0.264942i
$121$	−1.00000			−0.0909091
$122$	−9.08641			−0.822645
$123$	−0.889297	+	1.20356i	−0.0801852	+	0.108521i
$124$		−	4.97956i		−	0.447177i
$125$	11.4813			1.02692
$126$	2.12390	+	13.2439i	0.189212	+	1.17986i
$127$	3.27840			0.290911			0.145456	−	0.989365i	$-0.453535\pi$
$127$	3.27840			0.290911			0.145456	+	0.989365i	$0.453535\pi$
$128$			12.9376i			1.14354i
$129$	−2.17984	+	2.95016i	−0.191924	+	0.259747i
$130$	8.66602			0.760060
$131$	12.5297			1.09473			0.547364	−	0.836894i	$-0.315631\pi$
$131$	12.5297			1.09473			0.547364	+	0.836894i	$0.315631\pi$
$132$	−1.19207	−	0.880803i	−0.103756	−	0.0766641i
$133$	−10.6884	−	1.49618i	−0.926798	−	0.129735i
$134$		−	21.1976i		−	1.83119i
$135$	−7.14763	−	2.51439i	−0.615170	−	0.216404i
$136$		−	5.32021i		−	0.456204i
$137$			0.178787i			0.0152748i	0.999971	+	0.00763740i	$0.00243108\pi$
$137$			0.178787i			0.0152748i	−0.999971	+	0.00763740i	$0.997569\pi$
$138$	−7.56841	+	10.2430i	−0.644266	+	0.871939i
$139$		−	9.62340i		−	0.816246i	−0.912927	−	0.408123i	$-0.866183\pi$
$139$		−	9.62340i		−	0.816246i	0.912927	−	0.408123i	$-0.133817\pi$
$140$	0.457678	−	3.26955i	0.0386809	−	0.276327i
$141$	−0.497972	+	0.673948i	−0.0419368	+	0.0567566i
$142$	17.0109			1.42752
$143$	−3.51679			−0.294089
$144$	4.38713	+	14.2788i	0.365594	+	1.18990i
$145$		−	2.71474i		−	0.225447i
$146$	20.3809			1.68673
$147$	9.60568	−	7.39804i	0.792263	−	0.610180i
$148$	−6.49728			−0.534073
$149$		−	12.3604i		−	1.01260i	−0.862356	−	0.506302i	$-0.831012\pi$
$149$		−	12.3604i		−	1.01260i	0.862356	−	0.506302i	$-0.168988\pi$
$150$	−6.76486	−	4.99848i	−0.552348	−	0.408124i
$151$	−4.94666			−0.402553			−0.201277	−	0.979534i	$-0.564509\pi$
$151$	−4.94666			−0.402553			−0.201277	+	0.979534i	$0.564509\pi$
$152$	−7.88791			−0.639794
$153$	−2.42417	−	7.88997i	−0.195983	−	0.637866i
$154$	−0.619821	+	4.42786i	−0.0499466	+	0.356807i
$155$		−	8.48531i		−	0.681556i
$156$	−4.19224	−	3.09760i	−0.335648	−	0.248006i
$157$		−	1.59035i		−	0.126924i	−0.997984	−	0.0634620i	$-0.979786\pi$
$157$		−	1.59035i		−	0.126924i	0.997984	−	0.0634620i	$-0.0202142\pi$
$158$		−	14.8027i		−	1.17764i
$159$	19.2378	+	14.2146i	1.52566	+	1.12729i
$160$		−	6.63027i		−	0.524169i
$161$	11.4009	+	1.59593i	0.898519	+	0.125777i
$162$	8.53971	+	12.5852i	0.670943	+	0.988788i
$163$	17.0776			1.33762			0.668812	−	0.743432i	$-0.266803\pi$
$163$	17.0776			1.33762			0.668812	+	0.743432i	$0.266803\pi$
$164$	−0.739340			−0.0577327
$165$	−2.03131	−	1.50091i	−0.158137	−	0.116846i
$166$		−	12.0633i		−	0.936296i
$167$	−19.4712			−1.50673			−0.753364	−	0.657604i	$-0.771570\pi$
$167$	−19.4712			−1.50673			−0.753364	+	0.657604i	$0.771570\pi$
$168$	6.20310	−	6.32801i	0.478579	−	0.488217i
$169$	0.632207			0.0486313
$170$			6.77978i			0.519986i
$171$	−11.6979	+	3.59416i	−0.894562	+	0.274852i
$172$	−1.81226			−0.138184
$173$	23.0744			1.75431			0.877156	−	0.480206i	$-0.159438\pi$
$173$	23.0744			1.75431			0.877156	+	0.480206i	$0.159438\pi$
$174$	−3.23827	+	4.38262i	−0.245492	+	0.332246i
$175$	−1.05401	+	7.52962i	−0.0796758	+	0.569186i
$176$			4.97919i			0.375320i
$177$	6.04769	−	8.18485i	0.454573	−	0.615211i
$178$		−	25.7974i		−	1.93360i
$179$			3.07484i			0.229824i	0.993376	+	0.114912i	$0.0366586\pi$
$179$			3.07484i			0.229824i	−0.993376	+	0.114912i	$0.963341\pi$
$180$	−1.09945	−	3.57837i	−0.0819479	−	0.266716i
$181$		−	11.3295i		−	0.842113i	−0.907034	−	0.421057i	$-0.861659\pi$
$181$		−	11.3295i		−	0.842113i	0.907034	−	0.421057i	$-0.138341\pi$
$182$	−2.17978	+	15.5718i	−0.161576	+	1.15426i
$183$	7.49024	+	5.53445i	0.553694	+	0.409118i
$184$	8.41379			0.620272
$185$	−11.0716			−0.813997
$186$	−10.1217	+	13.6985i	−0.742157	+	1.00442i
$187$		−	2.75133i		−	0.201197i
$188$	−0.414002			−0.0301942
$189$	6.31592	−	12.2110i	0.459416	−	0.888221i
$190$	10.0519			0.729243
$191$			11.0831i			0.801944i	0.916090	+	0.400972i	$0.131328\pi$
$191$			11.0831i			0.801944i	−0.916090	+	0.400972i	$0.868672\pi$
$192$	2.34123	−	3.16859i	0.168964	−	0.228673i
$193$	1.41790			0.102063			0.0510313	−	0.998697i	$-0.483749\pi$
$193$	1.41790			0.102063			0.0510313	+	0.998697i	$0.483749\pi$
$194$	−19.8681			−1.42645
$195$	−7.14369	−	5.27839i	−0.511571	−	0.377994i
$196$	5.75989	+	1.64479i	0.411420	+	0.117485i
$197$		−	12.3840i		−	0.882322i	−0.897428	−	0.441161i	$-0.854567\pi$
$197$		−	12.3840i		−	0.882322i	0.897428	−	0.441161i	$-0.145433\pi$
$198$	1.48895	+	4.84609i	0.105815	+	0.344397i
$199$		−	15.3346i		−	1.08704i	−0.839396	−	0.543521i	$-0.817091\pi$
$199$		−	15.3346i		−	1.08704i	0.839396	−	0.543521i	$-0.182909\pi$
$200$			5.55679i			0.392925i
$201$	−12.9113	+	17.4739i	−0.910691	+	1.23251i
$202$			10.7922i			0.759337i
$203$	4.87807	+	0.682842i	0.342374	+	0.0479261i
$204$	2.42338	−	3.27976i	0.169670	−	0.229629i
$205$	−1.25986			−0.0879921
$206$	28.5696			1.99054
$207$	12.4778	−	3.83378i	0.867267	−	0.266466i
$208$			17.5107i			1.21415i
$209$	−4.07921			−0.282165
$210$	−7.90489	+	8.06407i	−0.545489	+	0.556474i
$211$	−1.20919			−0.0832442			−0.0416221	−	0.999133i	$-0.513253\pi$
$211$	−1.20919			−0.0832442			−0.0416221	+	0.999133i	$0.513253\pi$
$212$			11.8176i			0.811639i
$213$	−14.0227	−	10.3612i	−0.960818	−	0.709938i
$214$	9.15361			0.625728
$215$	−3.08815			−0.210610
$216$	3.33429	−	9.47837i	0.226870	−	0.644921i
$217$	15.2471	+	2.13432i	1.03504	+	0.144887i
$218$			33.8570i			2.29309i
$219$	−16.8007	−	12.4138i	−1.13528	−	0.838848i
$220$		−	1.24782i		−	0.0841282i
$221$		−	9.67583i		−	0.650867i
$222$	17.8737	+	13.2067i	1.19960	+	0.886374i
$223$			1.60414i			0.107421i	0.998557	+	0.0537106i	$0.0171048\pi$
$223$			1.60414i			0.107421i	−0.998557	+	0.0537106i	$0.982895\pi$
$224$	11.9138	+	1.66772i	0.796026	+	0.111429i
$225$	2.53197	+	8.24083i	0.168798	+	0.549388i
$226$	−19.5999			−1.30377
$227$	15.1868			1.00798			0.503992	−	0.863708i	$-0.331864\pi$
$227$	15.1868			1.00798			0.503992	+	0.863708i	$0.331864\pi$
$228$	−4.86268	−	3.59298i	−0.322039	−	0.237951i
$229$			21.7042i			1.43426i	0.696942	+	0.717128i	$0.254544\pi$
$229$			21.7042i			1.43426i	−0.696942	+	0.717128i	$0.745456\pi$
$230$	−10.7221			−0.706992
$231$	3.20791	−	3.27251i	0.211065	−	0.215315i
$232$	3.59997			0.236350
$233$		−	0.456992i		−	0.0299385i	−0.999888	−	0.0149693i	$-0.995235\pi$
$233$		−	0.456992i		−	0.0299385i	0.999888	−	0.0149693i	$-0.00476504\pi$
$234$	5.23632	+	17.0427i	0.342309	+	1.11411i
$235$	−0.705471			−0.0460198
$236$	5.02790			0.327289
$237$	−9.01620	+	12.2024i	−0.585665	+	0.792630i
$238$	−12.1825	−	1.70533i	−0.789674	−	0.110540i
$239$			22.8862i			1.48038i	0.672396	+	0.740192i	$0.265265\pi$
$239$			22.8862i			1.48038i	−0.672396	+	0.740192i	$0.734735\pi$
$240$	−7.47333	+	10.1143i	−0.482401	+	0.652874i
$241$			19.8304i			1.27739i	0.769461	+	0.638693i	$0.220525\pi$
$241$			19.8304i			1.27739i	−0.769461	+	0.638693i	$0.779475\pi$
$242$			1.68989i			0.108630i
$243$	0.625963	−	15.5759i	0.0401556	−	0.999193i
$244$			4.60120i			0.294562i
$245$	9.81501	+	2.80277i	0.627058	+	0.179062i
$246$	2.03389	+	1.50282i	0.129676	+	0.0958160i
$247$	−14.3457			−0.912795
$248$	11.2522			0.714518
$249$	−7.34767	+	9.94422i	−0.465640	+	0.630189i
$250$		−	19.4022i		−	1.22710i
$251$	0.885000			0.0558607			0.0279304	−	0.999610i	$-0.491108\pi$
$251$	0.885000			0.0558607			0.0279304	+	0.999610i	$0.491108\pi$
$252$	6.70647	−	1.07551i	0.422468	−	0.0677505i
$253$	4.35116			0.273555
$254$		−	5.54014i		−	0.347619i
$255$	4.12951	−	5.58881i	0.258600	−	0.349985i
$256$	17.3140			1.08213
$257$	−19.1067			−1.19184			−0.595921	−	0.803043i	$-0.703213\pi$
$257$	−19.1067			−1.19184			−0.595921	+	0.803043i	$0.703213\pi$
$258$	4.98545	+	3.68369i	0.310381	+	0.229337i
$259$	2.78485	−	19.8943i	0.173042	−	1.23617i
$260$		−	4.38833i		−	0.272152i
$261$	5.33883	−	1.64034i	0.330465	−	0.101535i
$262$		−	21.1739i		−	1.30813i
$263$		−	21.0776i		−	1.29970i	−0.760061	−	0.649851i	$-0.774831\pi$
$263$		−	21.0776i		−	1.29970i	0.760061	−	0.649851i	$-0.225169\pi$
$264$	1.99034	−	2.69369i	0.122497	−	0.165785i
$265$			20.1376i			1.23704i
$266$	−2.52838	+	18.0622i	−0.155025	+	1.10746i
$267$	−15.7130	+	21.2657i	−0.961620	+	1.30144i
$268$	−10.7341			−0.655690
$269$	−19.5822			−1.19395			−0.596974	−	0.802261i	$-0.703630\pi$
$269$	−19.5822			−1.19395			−0.596974	+	0.802261i	$0.703630\pi$
$270$	−4.24904	+	12.0787i	−0.258588	+	0.735087i
$271$		−	8.26071i		−	0.501803i	−0.968013	−	0.250901i	$-0.919273\pi$
$271$		−	8.26071i		−	0.501803i	0.968013	−	0.250901i	$-0.0807270\pi$
$272$	−13.6994			−0.830647
$273$	11.2815	−	11.5087i	0.682790	−	0.696539i
$274$	0.302130			0.0182524
$275$			2.87368i			0.173289i
$276$	5.18687	+	3.83252i	0.312213	+	0.230690i
$277$	−8.38977			−0.504092			−0.252046	−	0.967715i	$-0.581103\pi$
$277$	−8.38977			−0.504092			−0.252046	+	0.967715i	$0.581103\pi$
$278$	−16.2625			−0.975360
$279$	16.6873	−	5.12713i	0.999042	−	0.306953i
$280$	7.38816	+	1.03421i	0.441527	+	0.0618058i
$281$		−	24.9821i		−	1.49031i	−0.666892	−	0.745154i	$-0.732376\pi$
$281$		−	24.9821i		−	1.49031i	0.666892	−	0.745154i	$-0.267624\pi$
$282$	1.13890	+	0.841519i	0.0678204	+	0.0501117i
$283$			12.2954i			0.730888i	0.930833	+	0.365444i	$0.119083\pi$
$283$			12.2954i			0.730888i	−0.930833	+	0.365444i	$0.880917\pi$
$284$		−	8.61404i		−	0.511149i
$285$	−8.28614	−	6.12253i	−0.490829	−	0.362668i
$286$			5.94299i			0.351416i
$287$	0.316894	−	2.26382i	0.0187056	−	0.133629i
$288$	13.0391	−	4.00625i	0.768339	−	0.236070i
$289$	−9.43020			−0.554717
$290$	−4.58761			−0.269394
$291$	16.3780	+	12.1015i	0.960095	+	0.709403i
$292$		−	10.3205i		−	0.603964i
$293$	−9.65664			−0.564147			−0.282074	−	0.959393i	$-0.591022\pi$
$293$	−9.65664			−0.564147			−0.282074	+	0.959393i	$0.591022\pi$
$294$	−12.5019	−	16.2325i	−0.729125	−	0.946701i
$295$	8.56769			0.498830
$296$		−	14.6818i		−	0.853364i
$297$	1.72432	−	4.90171i	0.100055	−	0.284426i
$298$	−20.8878			−1.21000
$299$	15.3021			0.884944
$300$	−2.53114	+	3.42561i	−0.146136	+	0.197778i
$301$	0.776767	−	5.54905i	0.0447721	−	0.319842i
$302$			8.35932i			0.481025i
$303$	6.57344	−	8.89639i	0.377634	−	0.511084i
$304$			20.3111i			1.16492i
$305$			7.84058i			0.448950i
$306$	−13.3332	+	4.09659i	−0.762208	+	0.234187i
$307$			5.92838i			0.338350i	0.985586	+	0.169175i	$0.0541104\pi$
$307$			5.92838i			0.338350i	−0.985586	+	0.169175i	$0.945890\pi$
$308$	2.24219	+	0.313867i	0.127761	+	0.0178842i
$309$	−23.5509	−	17.4015i	−1.33976	−	0.989936i
$310$	−14.3392			−0.814414
$311$	−3.45749			−0.196056			−0.0980281	−	0.995184i	$-0.531254\pi$
$311$	−3.45749			−0.196056			−0.0980281	+	0.995184i	$0.531254\pi$
$312$	6.99960	−	9.47315i	0.396275	−	0.536312i
$313$			8.41263i			0.475510i	0.971325	+	0.237755i	$0.0764115\pi$
$313$			8.41263i			0.475510i	−0.971325	+	0.237755i	$0.923588\pi$
$314$	−2.68753			−0.151666
$315$	11.4280	−	1.83269i	0.643896	−	0.103261i
$316$	−7.49584			−0.421674
$317$			14.8191i			0.832325i	0.909290	+	0.416162i	$0.136625\pi$
$317$			14.8191i			0.832325i	−0.909290	+	0.416162i	$0.863375\pi$
$318$	24.0211	−	32.5098i	1.34704	−	1.82306i
$319$	1.86171			0.104236
$320$	3.31679			0.185414
$321$	−7.54563	−	5.57538i	−0.421156	−	0.311188i
$322$	2.69694	−	19.2663i	0.150295	−	1.07367i
$323$		−	11.2232i		−	0.624477i
$324$	6.37294	−	4.32437i	0.354052	−	0.240243i
$325$			10.1061i			0.560586i
$326$		−	28.8593i		−	1.59837i
$327$	20.6220	−	27.9095i	1.14040	−	1.54340i
$328$		−	1.67068i		−	0.0922477i
$329$	0.177448	−	1.26765i	0.00978304	−	0.0698878i
$330$	−2.53638	+	3.43270i	−0.139623	+	0.188964i
$331$	−3.46613			−0.190516			−0.0952580	−	0.995453i	$-0.530368\pi$
$331$	−3.46613			−0.190516			−0.0952580	+	0.995453i	$0.530368\pi$
$332$	−6.10867			−0.335257
$333$	−6.68983	−	21.7734i	−0.366601	−	1.19318i
$334$			32.9042i			1.80044i
$335$	−18.2912			−0.999356
$336$	−16.2944	−	15.9728i	−0.888934	−	0.871387i
$337$	26.1356			1.42370			0.711849	−	0.702332i	$-0.247858\pi$
$337$	26.1356			1.42370			0.711849	+	0.702332i	$0.247858\pi$
$338$		−	1.06836i		−	0.0581112i
$339$	16.1569	+	11.9381i	0.877520	+	0.648390i
$340$	3.43317			0.186190
$341$	5.81906			0.315120
$342$	6.07374	+	19.7682i	0.328430	+	1.06894i
$343$	−7.50504	+	16.9315i	−0.405234	+	0.914213i
$344$		−	4.09515i		−	0.220796i
$345$	8.83857	+	6.53072i	0.475852	+	0.351602i
$346$		−	38.9932i		−	2.09629i
$347$			6.04785i			0.324665i	0.986736	+	0.162333i	$0.0519018\pi$
$347$			6.04785i			0.324665i	−0.986736	+	0.162333i	$0.948098\pi$
$348$	2.21928	+	1.63980i	0.118966	+	0.0879027i
$349$			33.6712i			1.80238i	0.433424	+	0.901190i	$0.357305\pi$
$349$			33.6712i			1.80238i	−0.433424	+	0.901190i	$0.642695\pi$
$350$	12.7242	+	1.78116i	0.680139	+	0.0952072i
$351$	6.06406	−	17.2383i	0.323676	−	0.920110i
$352$	4.54691			0.242351
$353$	26.7944			1.42612			0.713061	−	0.701102i	$-0.247308\pi$
$353$	26.7944			1.42612			0.713061	+	0.701102i	$0.247308\pi$
$354$	−13.8315	−	10.2199i	−0.735137	−	0.543184i
$355$		−	14.6786i		−	0.779058i
$356$	−13.0634			−0.692358
$357$	9.00374	+	8.82601i	0.476529	+	0.467122i
$358$	5.19614			0.274625
$359$		−	11.6784i		−	0.616364i	−0.951327	−	0.308182i	$-0.900279\pi$
$359$		−	11.6784i		−	0.616364i	0.951327	−	0.308182i	$-0.0997206\pi$
$360$	8.08601	−	2.48441i	0.426170	−	0.130940i
$361$	2.36008			0.124215
$362$	−19.1456			−1.00627
$363$	1.02930	−	1.39303i	0.0540241	−	0.0731154i
$364$	7.88532	+	1.10380i	0.413303	+	0.0578550i
$365$		−	17.5865i		−	0.920519i
$366$	9.35262	−	12.6577i	0.488869	−	0.661628i
$367$			11.9966i			0.626217i	0.949717	+	0.313109i	$0.101370\pi$
$367$			11.9966i			0.626217i	−0.949717	+	0.313109i	$0.898630\pi$
$368$		−	21.6652i		−	1.12938i
$369$	−0.761251	−	2.47764i	−0.0396291	−	0.128981i
$370$			18.7097i			0.972672i
$371$	−36.1850	−	5.06525i	−1.87863	−	0.262974i
$372$	6.93670	+	5.12545i	0.359651	+	0.265742i
$373$	−11.1248			−0.576019			−0.288009	−	0.957628i	$-0.592993\pi$
$373$	−11.1248			−0.576019			−0.288009	+	0.957628i	$0.592993\pi$
$374$	−4.64944			−0.240417
$375$	−11.8177	+	15.9939i	−0.610264	+	0.825921i
$376$		−	0.935515i		−	0.0482455i
$377$	6.54725			0.337201
$378$	−20.6353	−	10.6732i	−1.06137	−	0.548971i
$379$	−0.528289			−0.0271364			−0.0135682	−	0.999908i	$-0.504319\pi$
$379$	−0.528289			−0.0271364			−0.0135682	+	0.999908i	$0.504319\pi$
$380$		−	5.09012i		−	0.261118i
$381$	−3.37445	+	4.56693i	−0.172878	+	0.233971i
$382$	18.7292			0.958270
$383$	−15.9107			−0.812998			−0.406499	−	0.913651i	$-0.633251\pi$
$383$	−15.9107			−0.812998			−0.406499	+	0.913651i	$0.633251\pi$
$384$	−18.0226	−	13.3167i	−0.919711	−	0.679564i
$385$	3.82076	+	0.534838i	0.194724	+	0.0272579i
$386$		−	2.39610i		−	0.121958i
$387$	−1.86597	−	6.07319i	−0.0948527	−	0.308717i
$388$			10.0609i			0.510765i
$389$			21.7159i			1.10104i	0.834822	+	0.550520i	$0.185570\pi$
$389$			21.7159i			1.10104i	−0.834822	+	0.550520i	$0.814430\pi$
$390$	−8.91991	+	12.0721i	−0.451677	+	0.611293i
$391$			11.9715i			0.605423i
$392$	−3.71671	+	13.0155i	−0.187722	+	0.657384i
$393$	−12.8968	+	17.4544i	−0.650559	+	0.880457i
$394$	−20.9276			−1.05432
$395$	−12.7731			−0.642686
$396$	2.45398	−	0.753980i	0.123317	−	0.0378889i
$397$		−	15.2832i		−	0.767043i	−0.923532	−	0.383522i	$-0.874711\pi$
$397$		−	15.2832i		−	0.767043i	0.923532	−	0.383522i	$-0.125289\pi$
$398$	−25.9138			−1.29894
$399$	13.0857	−	13.3492i	0.655106	−	0.668298i
$400$	14.3086			0.715428
$401$			20.2500i			1.01124i	0.862758	+	0.505618i	$0.168735\pi$
$401$			20.2500i			1.01124i	−0.862758	+	0.505618i	$0.831265\pi$
$402$	29.5290	+	21.8186i	1.47277	+	1.08821i
$403$	20.4644			1.01940
$404$	5.46499			0.271894
$405$	10.8597	−	7.36884i	0.539621	−	0.366161i
$406$	1.15393	−	8.24341i	0.0572686	−	0.409114i
$407$		−	7.59266i		−	0.376354i
$408$	7.41124	+	5.47608i	0.366911	+	0.271106i
$409$		−	0.450101i		−	0.0222561i	−0.999938	−	0.0111280i	$-0.996458\pi$
$409$		−	0.450101i		−	0.0222561i	0.999938	−	0.0111280i	$-0.00354224\pi$
$410$			2.12902i			0.105145i
$411$	−0.249056	−	0.184025i	−0.0122850	−	0.00907728i
$412$		−	14.4672i		−	0.712746i
$413$	−2.15504	+	15.3952i	−0.106043	+	0.757546i
$414$	−6.47866	−	21.0861i	−0.318409	−	1.03633i
$415$	−10.4093			−0.510974
$416$	15.9905			0.783999
$417$	13.4057	+	9.90534i	0.656481	+	0.485067i
$418$			6.89341i			0.337168i
$419$	−39.4106			−1.92533			−0.962667	−	0.270689i	$-0.912748\pi$
$419$	−39.4106			−1.92533			−0.962667	+	0.270689i	$0.912748\pi$
$420$	4.08351	+	4.00290i	0.199255	+	0.195322i
$421$	−17.0494			−0.830937			−0.415468	−	0.909608i	$-0.636382\pi$
$421$	−17.0494			−0.830937			−0.415468	+	0.909608i	$0.636382\pi$
$422$			2.04340i			0.0994713i
$423$	−0.426271	−	1.38739i	−0.0207260	−	0.0674570i
$424$	−26.7042			−1.29687
$425$	−7.90642			−0.383518
$426$	−17.5093	+	23.6968i	−0.848328	+	1.14811i
$427$	−14.0886	−	1.97215i	−0.681796	−	0.0954393i
$428$		−	4.63523i		−	0.224053i
$429$	3.61982	−	4.89901i	0.174767	−	0.236526i
$430$			5.21864i			0.251665i
$431$			31.4958i			1.51710i	0.651616	+	0.758549i	$0.274091\pi$
$431$			31.4958i			1.51710i	−0.651616	+	0.758549i	$0.725909\pi$
$432$	−24.4065	−	8.58571i	−1.17426	−	0.413080i
$433$		−	18.0607i		−	0.867943i	−0.900927	−	0.433971i	$-0.857112\pi$
$433$		−	18.0607i		−	0.867943i	0.900927	−	0.433971i	$-0.142888\pi$
$434$	3.60677	−	25.7660i	0.173131	−	1.23681i
$435$	3.78172	+	2.79427i	0.181320	+	0.133975i
$436$	17.1446			0.821079
$437$	17.7493			0.849063
$438$	−20.9780	+	28.3913i	−1.00237	+	1.35659i
$439$		−	11.4461i		−	0.546294i	−0.961972	−	0.273147i	$-0.911935\pi$
$439$		−	11.4461i		−	0.546294i	0.961972	−	0.273147i	$-0.0880645\pi$
$440$	2.81969			0.134423
$441$	0.418630	+	20.9958i	0.0199348	+	0.999801i
$442$	−16.3511			−0.777743
$443$			10.3278i			0.490690i	0.969436	+	0.245345i	$0.0789012\pi$
$443$			10.3278i			0.490690i	−0.969436	+	0.245345i	$0.921099\pi$
$444$	6.68764	−	9.05094i	0.317381	−	0.429539i
$445$	−22.2604			−1.05524
$446$	2.71082			0.128361
$447$	17.2185	+	12.7225i	0.814407	+	0.601756i
$448$	−0.834279	+	5.95990i	−0.0394160	+	0.281579i
$449$			15.4000i			0.726770i	0.931639	+	0.363385i	$0.118379\pi$
$449$			15.4000i			0.726770i	−0.931639	+	0.363385i	$0.881621\pi$
$450$	13.9261	−	4.27876i	0.656483	−	0.201703i
$451$		−	0.863985i		−	0.0406834i
$452$			9.92506i			0.466835i
$453$	5.09158	−	6.89087i	0.239224	−	0.323761i
$454$		−	25.6641i		−	1.20447i
$455$	13.4368	+	1.88091i	0.629927	+	0.0881785i
$456$	8.11901	−	10.9881i	0.380207	−	0.514567i
$457$	18.0431			0.844020			0.422010	−	0.906591i	$-0.361325\pi$
$457$	18.0431			0.844020			0.422010	+	0.906591i	$0.361325\pi$
$458$	36.6778			1.71384
$459$	13.4862	+	4.74417i	0.629482	+	0.221439i
$460$			5.42947i			0.253151i
$461$	41.0255			1.91075			0.955374	−	0.295399i	$-0.0954527\pi$
$461$	41.0255			1.91075			0.955374	+	0.295399i	$0.0954527\pi$
$462$	−5.53018	−	5.42102i	−0.257287	−	0.252209i
$463$	8.69880			0.404267			0.202134	−	0.979358i	$-0.435212\pi$
$463$	8.69880			0.404267			0.202134	+	0.979358i	$0.435212\pi$
$464$		−	9.26982i		−	0.430341i
$465$	11.8203	+	8.73390i	0.548155	+	0.405025i
$466$	−0.772267			−0.0357746
$467$	2.83763			0.131310			0.0656549	−	0.997842i	$-0.479086\pi$
$467$	2.83763			0.131310			0.0656549	+	0.997842i	$0.479086\pi$
$468$	8.63012	−	2.65159i	0.398928	−	0.122570i
$469$	4.60082	−	32.8672i	0.212446	−	1.51767i
$470$			1.19217i			0.0549906i
$471$	2.21542	+	1.63695i	0.102081	+	0.0754266i
$472$			11.3615i			0.522955i
$473$		−	2.11779i		−	0.0973762i
$474$	20.6207	+	15.2364i	0.947140	+	0.699831i
$475$			11.7223i			0.537857i
$476$	−0.863551	+	6.16901i	−0.0395808	+	0.282756i
$477$	−39.6028	+	12.1679i	−1.81329	+	0.557129i
$478$	38.6751			1.76896
$479$	2.89906			0.132461			0.0662307	−	0.997804i	$-0.478903\pi$
$479$	2.89906			0.132461			0.0662307	+	0.997804i	$0.478903\pi$
$480$	9.23619	+	6.82452i	0.421573	+	0.311495i
$481$		−	26.7018i		−	1.21750i
$482$	33.5112			1.52639
$483$	−13.9581	+	14.2392i	−0.635117	+	0.647907i
$484$	0.855732			0.0388969
$485$			17.1440i			0.778471i
$486$	−26.3216	−	1.05781i	−1.19397	−	0.0479832i
$487$	−13.7638			−0.623698			−0.311849	−	0.950132i	$-0.600948\pi$
$487$	−13.7638			−0.623698			−0.311849	+	0.950132i	$0.600948\pi$
$488$	−10.3973			−0.470663
$489$	−17.5780	+	23.7897i	−0.794903	+	1.07581i
$490$	4.73638	−	16.5863i	0.213968	−	0.749292i
$491$			8.92839i			0.402933i	0.979495	+	0.201466i	$0.0645707\pi$
$491$			8.92839i			0.402933i	−0.979495	+	0.201466i	$0.935429\pi$
$492$	0.761001	−	1.02993i	0.0343086	−	0.0464327i
$493$			5.12219i			0.230692i
$494$			24.2427i			1.09073i
$495$	4.18165	−	1.28480i	0.187951	−	0.0577476i
$496$		−	28.9742i		−	1.30098i
$497$	26.3757	+	3.69213i	1.18311	+	0.165614i
$498$	16.8046	+	12.4168i	0.753034	+	0.556408i
$499$	−37.9058			−1.69689			−0.848447	−	0.529280i	$-0.822462\pi$
$499$	−37.9058			−1.69689			−0.848447	+	0.529280i	$0.822462\pi$
$500$	−9.82495			−0.439385
$501$	20.0417	−	27.1241i	0.895396	−	1.21181i
$502$		−	1.49555i		−	0.0667498i
$503$	−38.2037			−1.70342			−0.851709	−	0.524016i	$-0.824433\pi$
$503$	−38.2037			−1.70342			−0.851709	+	0.524016i	$0.824433\pi$
$504$	2.43031	+	15.1545i	0.108255	+	0.675037i
$505$	9.31250			0.414401
$506$		−	7.35299i		−	0.326880i
$507$	−0.650729	+	0.880686i	−0.0288999	+	0.0391126i
$508$	−2.80543			−0.124471
$509$	−36.4703			−1.61652			−0.808259	−	0.588827i	$-0.799590\pi$
$509$	−36.4703			−1.61652			−0.808259	+	0.588827i	$0.799590\pi$
$510$	−9.44447	−	6.97841i	−0.418208	−	0.309009i
$511$	31.6009	+	4.42356i	1.39794	+	0.195687i
$512$		−	3.38352i		−	0.149532i
$513$	7.03385	−	19.9951i	0.310552	−	0.882804i
$514$			32.2882i			1.42417i
$515$		−	24.6524i		−	1.08632i
$516$	1.86536	−	2.52455i	0.0821179	−	0.111137i
$517$		−	0.483798i		−	0.0212774i
$518$	−33.6192	−	4.70609i	−1.47714	−	0.206774i
$519$	−23.7504	+	32.1434i	−1.04253	+	1.41094i
$520$	9.91624			0.434856
$521$	−10.7999			−0.473151			−0.236576	−	0.971613i	$-0.576025\pi$
$521$	−10.7999			−0.473151			−0.236576	+	0.971613i	$0.576025\pi$
$522$	−2.77200	−	9.02204i	−0.121327	−	0.394884i
$523$		−	16.5059i		−	0.721751i	−0.932614	−	0.360875i	$-0.882478\pi$
$523$		−	16.5059i		−	0.721751i	0.932614	−	0.360875i	$-0.117522\pi$
$524$	−10.7221			−0.468397
$525$	−9.40413	−	9.21849i	−0.410430	−	0.402328i
$526$	−35.6189			−1.55306
$527$			16.0101i			0.697413i
$528$	−6.93618	−	5.12507i	−0.301859	−	0.223040i
$529$	4.06741			0.176844
$530$	34.0304			1.47818
$531$	5.17691	+	16.8493i	0.224659	+	0.731197i
$532$	9.14637	+	1.28033i	0.396545	+	0.0555092i
$533$		−	3.03845i		−	0.131610i
$534$	35.9367	+	26.5533i	1.55514	+	1.14907i
$535$		−	7.89857i		−	0.341485i
$536$		−	24.2557i		−	1.04769i
$537$	−4.28336	−	3.16492i	−0.184840	−	0.136577i
$538$			33.0918i			1.42669i
$539$	−1.92209	+	6.73094i	−0.0827901	+	0.289922i
$540$	6.11646	+	2.15164i	0.263210	+	0.0925920i
$541$	43.4115			1.86641			0.933203	−	0.359349i	$-0.117001\pi$
$541$	43.4115			1.86641			0.933203	+	0.359349i	$0.117001\pi$
$542$	−13.9597			−0.599621
$543$	15.7824	+	11.6614i	0.677286	+	0.500439i
$544$			12.5100i			0.536363i
$545$	29.2149			1.25143
$546$	−19.4485	−	19.0646i	−0.832318	−	0.815888i
$547$	1.13100			0.0483579			0.0241789	−	0.999708i	$-0.492303\pi$
$547$	1.13100			0.0483579			0.0241789	+	0.999708i	$0.492303\pi$
$548$		−	0.152994i		−	0.00653557i
$549$	−15.4194	+	4.73756i	−0.658082	+	0.202194i
$550$	4.85620			0.207069
$551$	7.59432			0.323529
$552$	−8.66029	+	11.7207i	−0.368606	+	0.498866i
$553$	3.21285	−	22.9519i	0.136624	−	0.976012i
$554$			14.1778i			0.602357i
$555$	11.3959	−	15.4231i	0.483730	−	0.654672i
$556$			8.23505i			0.349244i
$557$			2.69594i			0.114230i	0.998368	+	0.0571152i	$0.0181902\pi$
$557$			2.69594i			0.114230i	−0.998368	+	0.0571152i	$0.981810\pi$
$558$	−8.66429	−	28.1997i	−0.366789	−	1.19379i
$559$		−	7.44783i		−	0.315010i
$560$	2.66306	−	19.0243i	0.112535	−	0.803923i
$561$	3.83270	+	2.83193i	0.161817	+	0.119564i
$562$	−42.2171			−1.78082
$563$	−1.54693			−0.0651951			−0.0325976	−	0.999469i	$-0.510378\pi$
$563$	−1.54693			−0.0651951			−0.0325976	+	0.999469i	$0.510378\pi$
$564$	0.426131	−	0.576719i	0.0179434	−	0.0242843i
$565$			16.9126i			0.711517i
$566$	20.7780			0.873363
$567$	10.5094	+	21.3671i	0.441354	+	0.897333i
$568$	19.4650			0.816735
$569$			20.8296i			0.873222i	0.899650	+	0.436611i	$0.143821\pi$
$569$			20.8296i			0.873222i	−0.899650	+	0.436611i	$0.856179\pi$
$570$	−10.3464	+	14.0027i	−0.433364	+	0.586508i
$571$	42.0434			1.75946			0.879731	−	0.475472i	$-0.157723\pi$
$571$	42.0434			1.75946			0.879731	+	0.475472i	$0.157723\pi$
$572$	3.00943			0.125831
$573$	−15.4391	−	11.4078i	−0.644979	−	0.476568i
$574$	−3.82560	−	0.535516i	−0.159678	−	0.0223520i
$575$		−	12.5038i		−	0.521446i
$576$	2.00413	+	6.52284i	0.0835053	+	0.271785i
$577$		−	45.5882i		−	1.89786i	−0.315487	−	0.948930i	$-0.602168\pi$
$577$		−	45.5882i		−	1.89786i	0.315487	−	0.948930i	$-0.397832\pi$
$578$			15.9360i			0.662851i
$579$	−1.45944	+	1.97518i	−0.0606523	+	0.0820858i
$580$			2.32309i			0.0964610i
$581$	2.61828	−	18.7044i	0.108625	−	0.775989i
$582$	20.4502	−	27.6770i	0.847690	−	1.14725i
$583$	−13.8100			−0.571951
$584$	23.3212			0.965038
$585$	14.7060	−	4.51838i	0.608017	−	0.186812i
$586$			16.3187i			0.674118i
$587$	17.4054			0.718397			0.359199	−	0.933261i	$-0.383050\pi$
$587$	17.4054			0.718397			0.359199	+	0.933261i	$0.383050\pi$
$588$	−8.21989	+	6.33074i	−0.338982	+	0.261075i
$589$	23.7371			0.978072
$590$		−	14.4785i		−	0.596069i
$591$	17.2513	+	12.7468i	0.709624	+	0.524333i
$592$	−37.8053			−1.55379
$593$	−1.16298			−0.0477580			−0.0238790	−	0.999715i	$-0.507602\pi$
$593$	−1.16298			−0.0477580			−0.0238790	+	0.999715i	$0.507602\pi$
$594$	−8.28335	−	2.91391i	−0.339870	−	0.119559i
$595$	−1.47151	+	10.5122i	−0.0603262	+	0.430957i
$596$			10.5772i			0.433259i
$597$	21.3617	+	15.7839i	0.874274	+	0.645991i
$598$		−	25.8589i		−	1.05745i
$599$		−	34.7781i		−	1.42099i	−0.703700	−	0.710497i	$-0.748470\pi$
$599$		−	34.7781i		−	1.42099i	0.703700	−	0.710497i	$-0.251530\pi$
$600$	−7.74081	−	5.71959i	−0.316017	−	0.233501i
$601$		−	16.1517i		−	0.658841i	−0.944183	−	0.329420i	$-0.893147\pi$
$601$		−	16.1517i		−	0.658841i	0.944183	−	0.329420i	$-0.106853\pi$
$602$	−9.37729	−	1.31265i	−0.382190	−	0.0534997i
$603$	−11.0522	−	35.9717i	−0.450081	−	1.46488i
$604$	4.23302			0.172239
$605$	1.45819			0.0592839
$606$	−15.0339	−	11.1084i	−0.610711	−	0.451248i
$607$			0.757029i			0.0307269i	0.999882	+	0.0153634i	$0.00489053\pi$
$607$			0.757029i			0.0307269i	−0.999882	+	0.0153634i	$0.995109\pi$
$608$	18.5478			0.752212
$609$	−5.97221	+	6.09248i	−0.242006	+	0.246880i
$610$	13.2497			0.536466
$611$		−	1.70142i		−	0.0688319i
$612$	2.07444	+	6.75170i	0.0838545	+	0.272921i
$613$	−18.2996			−0.739112			−0.369556	−	0.929208i	$-0.620490\pi$
$613$	−18.2996			−0.739112			−0.369556	+	0.929208i	$0.620490\pi$
$614$	10.0183			0.404306
$615$	1.29677	−	1.75502i	0.0522907	−	0.0707694i
$616$	−0.709241	+	5.06666i	−0.0285761	+	0.204141i
$617$			48.9521i			1.97074i	0.170439	+	0.985368i	$0.445482\pi$
$617$			48.9521i			1.97074i	−0.170439	+	0.985368i	$0.554518\pi$
$618$	−29.4066	+	39.7984i	−1.18291	+	1.60093i
$619$			37.7204i			1.51611i	0.652191	+	0.758055i	$0.273850\pi$
$619$			37.7204i			1.51611i	−0.652191	+	0.758055i	$0.726150\pi$
$620$			7.26115i			0.291615i
$621$	−7.50279	+	21.3281i	−0.301077	+	0.855868i
$622$			5.84278i			0.234274i
$623$	5.59919	−	39.9994i	0.224327	−	1.60254i
$624$	−24.3931	−	18.0238i	−0.976504	−	0.721528i
$625$	−2.37361			−0.0949443
$626$	14.2164			0.568203
$627$	4.19872	−	5.68248i	0.167681	−	0.226936i
$628$			1.36092i			0.0543065i
$629$	20.8899			0.832934
$630$	−3.09705	−	19.3121i	−0.123389	−	0.769413i
$631$	3.50668			0.139599			0.0697993	−	0.997561i	$-0.477764\pi$
$631$	3.50668			0.139599			0.0697993	+	0.997561i	$0.477764\pi$
$632$		−	16.9383i		−	0.673768i
$633$	1.24462	−	1.68445i	0.0494692	−	0.0669508i
$634$	25.0427			0.994573
$635$	−4.78054			−0.189710
$636$	−16.4624	−	12.1639i	−0.652776	−	0.482329i
$637$	−6.75956	+	23.6713i	−0.267824	+	0.937891i
$638$		−	3.14609i		−	0.124555i
$639$	28.8670	−	8.86933i	1.14196	−	0.350865i
$640$		−	18.8656i		−	0.745726i
$641$			4.33625i			0.171271i	0.996327	+	0.0856357i	$0.0272921\pi$
$641$			4.33625i			0.171271i	−0.996327	+	0.0856357i	$0.972708\pi$
$642$	−9.42179	+	12.7513i	−0.371848	+	0.503254i
$643$		−	3.54931i		−	0.139971i	−0.997548	−	0.0699856i	$-0.977705\pi$
$643$		−	3.54931i		−	0.139971i	0.997548	−	0.0699856i	$-0.0222953\pi$
$644$	−9.75614	−	1.36568i	−0.384446	−	0.0538155i
$645$	3.17862	−	4.30190i	0.125158	−	0.169387i
$646$	−18.9660			−0.746209
$647$	−25.1464			−0.988605			−0.494303	−	0.869290i	$-0.664577\pi$
$647$	−25.1464			−0.988605			−0.494303	+	0.869290i	$0.664577\pi$
$648$	9.77172	+	14.4009i	0.383869	+	0.565719i
$649$			5.87555i			0.230636i
$650$	17.0782			0.669863
$651$	−18.6670	+	19.0429i	−0.731618	+	0.746351i
$652$	−14.6139			−0.572324
$653$		−	22.5809i		−	0.883657i	−0.897099	−	0.441829i	$-0.854330\pi$
$653$		−	22.5809i		−	0.883657i	0.897099	−	0.441829i	$-0.145670\pi$
$654$	−47.1640	−	34.8490i	−1.84426	−	1.36270i
$655$	−18.2708			−0.713898
$656$	−4.30194			−0.167963
$657$	34.5858	−	10.6264i	1.34932	−	0.414575i
$658$	−2.14219	−	0.299868i	−0.0835113	−	0.0116901i
$659$			31.6426i			1.23262i	0.787504	+	0.616310i	$0.211373\pi$
$659$			31.6426i			1.23262i	−0.787504	+	0.616310i	$0.788627\pi$
$660$	1.73826	+	1.28438i	0.0676617	+	0.0499944i
$661$		−	6.23184i		−	0.242390i	−0.992629	−	0.121195i	$-0.961327\pi$
$661$		−	6.23184i		−	0.242390i	0.992629	−	0.121195i	$-0.0386727\pi$
$662$			5.85739i			0.227654i
$663$	13.4788	+	9.95931i	0.523472	+	0.386788i
$664$		−	13.8037i		−	0.535687i
$665$	15.5857	+	2.18171i	0.604386	+	0.0846032i
$666$	−36.7947	+	11.3051i	−1.42577	+	0.438063i
$667$	−8.10062			−0.313657
$668$	16.6622			0.644678
$669$	−2.23462	−	1.65114i	−0.0863956	−	0.0638367i
$670$			30.9102i			1.19416i
$671$	−5.37692			−0.207574
$672$	−14.5861	+	14.8798i	−0.562670	+	0.574001i
$673$	10.7998			0.416301			0.208151	−	0.978097i	$-0.433256\pi$
$673$	10.7998			0.416301			0.208151	+	0.978097i	$0.433256\pi$
$674$		−	44.1664i		−	1.70122i
$675$	−14.0859	−	4.95513i	−0.542167	−	0.190723i
$676$	−0.541000			−0.0208077
$677$	−46.0148			−1.76849			−0.884247	−	0.467019i	$-0.845328\pi$
$677$	−46.0148			−1.76849			−0.884247	+	0.467019i	$0.845328\pi$
$678$	20.1741	−	27.3033i	0.774783	−	1.04858i
$679$	−30.8059	−	4.31227i	−1.18222	−	0.165490i
$680$			7.75789i			0.297501i
$681$	−15.6318	+	21.1558i	−0.599010	+	0.810691i
$682$		−	9.83358i		−	0.376547i
$683$		−	20.9248i		−	0.800665i	−0.916370	−	0.400333i	$-0.868895\pi$
$683$		−	20.9248i		−	0.800665i	0.916370	−	0.400333i	$-0.131105\pi$
$684$	10.0103	−	3.07564i	0.382753	−	0.117600i
$685$		−	0.260706i		−	0.00996105i
$686$	28.6123	+	12.6827i	1.09242	+	0.484228i
$687$	−30.2347	−	22.3401i	−1.15353	−	0.852328i
$688$	−10.5449			−0.402020
$689$	−48.5668			−1.85025
$690$	11.0362	−	14.9362i	0.420141	−	0.568612i
$691$			24.6653i			0.938313i	0.883115	+	0.469156i	$0.155442\pi$
$691$			24.6653i			0.938313i	−0.883115	+	0.469156i	$0.844558\pi$
$692$	−19.7455			−0.750611
$693$	1.25683	+	7.83712i	0.0477428	+	0.297707i
$694$	10.2202			0.387954
$695$			14.0328i			0.532293i
$696$	−3.70545	+	5.01489i	−0.140455	+	0.190089i
$697$	2.37710			0.0900393
$698$	56.9007			2.15372
$699$	0.636606	+	0.470381i	0.0240786	+	0.0177914i
$700$	0.901952	−	6.44334i	0.0340906	−	0.243535i
$701$		−	46.1898i		−	1.74456i	−0.489004	−	0.872282i	$-0.662640\pi$
$701$		−	46.1898i		−	1.74456i	0.489004	−	0.872282i	$-0.337360\pi$
$702$	−29.1308	−	10.2476i	−1.09947	−	0.386771i
$703$		−	30.9720i		−	1.16813i
$704$			2.27459i			0.0857269i
$705$	0.726139	−	0.982745i	0.0273480	−	0.0370123i
$706$		−	45.2796i		−	1.70412i
$707$	−2.34239	+	16.7335i	−0.0880946	+	0.629328i
$708$	−5.17521	+	7.00404i	−0.194496	+	0.263228i
$709$	−2.12583			−0.0798371			−0.0399185	−	0.999203i	$-0.512710\pi$
$709$	−2.12583			−0.0798371			−0.0399185	+	0.999203i	$0.512710\pi$
$710$	−24.8052			−0.930922
$711$	−7.71799	−	25.1198i	−0.289447	−	0.942065i
$712$		−	29.5192i		−	1.10628i
$713$	−25.3197			−0.948229
$714$	14.9150	−	15.2153i	0.558180	−	0.569420i
$715$	5.12815			0.191782
$716$		−	2.63124i		−	0.0983340i
$717$	−31.8812	−	23.5567i	−1.19063	−	0.879740i
$718$	−19.7353			−0.736515
$719$	26.6268			0.993013			0.496507	−	0.868033i	$-0.334616\pi$
$719$	26.6268			0.993013			0.496507	+	0.868033i	$0.334616\pi$
$720$	−6.39727	−	20.8212i	−0.238412	−	0.775961i
$721$	44.2976	+	6.20087i	1.64973	+	0.230932i
$722$		−	3.98828i		−	0.148429i
$723$	−27.6244	−	20.4114i	−1.02736	−	0.759107i
$724$			9.69500i			0.360312i
$725$		−	5.34996i		−	0.198693i
$726$	−2.35408	−	1.73940i	−0.0873680	−	0.0645552i
$727$			36.4042i			1.35016i	0.737745	+	0.675079i	$0.235890\pi$
$727$			36.4042i			1.35016i	−0.737745	+	0.675079i	$0.764110\pi$
$728$	−2.49425	+	17.8184i	−0.0924430	+	0.660392i
$729$	21.0534	+	16.9042i	0.779757	+	0.626082i
$730$	−29.7192			−1.09996
$731$	5.82674			0.215510
$732$	−6.40964	−	4.73601i	−0.236907	−	0.175048i
$733$			16.7068i			0.617078i	0.951212	+	0.308539i	$0.0998400\pi$
$733$			16.7068i			0.617078i	−0.951212	+	0.308539i	$0.900160\pi$
$734$	20.2729			0.748288
$735$	−14.0069	+	10.7878i	−0.516653	+	0.397913i
$736$	−19.7843			−0.729260
$737$		−	12.5438i		−	0.462055i
$738$	−4.18695	+	1.28643i	−0.154124	+	0.0473542i
$739$	−20.1718			−0.742032			−0.371016	−	0.928626i	$-0.620991\pi$
$739$	−20.1718			−0.742032			−0.371016	+	0.928626i	$0.620991\pi$
$740$	9.47429			0.348282
$741$	14.7660	−	19.9841i	0.542442	−	0.734133i
$742$	−8.55971	+	61.1487i	−0.314237	+	2.24484i
$743$		−	17.2512i		−	0.632884i	−0.948612	−	0.316442i	$-0.897512\pi$
$743$		−	17.2512i		−	0.632884i	0.948612	−	0.316442i	$-0.102488\pi$
$744$	−11.5819	+	15.6748i	−0.424613	+	0.574665i
$745$			18.0239i			0.660343i
$746$			18.7996i			0.688304i
$747$	−6.28970	−	20.4711i	−0.230128	−	0.748999i
$748$			2.35440i			0.0860854i
$749$	14.1928	+	1.98674i	0.518595	+	0.0725939i
$750$	27.0279	+	19.9706i	0.986921	+	0.729225i
$751$	−21.4620			−0.783160			−0.391580	−	0.920144i	$-0.628071\pi$
$751$	−21.4620			−0.783160			−0.391580	+	0.920144i	$0.628071\pi$
$752$	−2.40892			−0.0878443
$753$	−0.910928	+	1.23284i	−0.0331961	+	0.0449270i
$754$		−	11.0641i		−	0.402932i
$755$	7.21318			0.262514
$756$	−5.40474	+	10.4494i	−0.196569	+	0.380040i
$757$	−31.1462			−1.13203			−0.566014	−	0.824395i	$-0.691515\pi$
$757$	−31.1462			−1.13203			−0.566014	+	0.824395i	$0.691515\pi$
$758$			0.892750i			0.0324261i
$759$	−4.47864	+	6.06132i	−0.162564	+	0.220012i
$760$	11.5021			0.417225
$761$	39.7189			1.43981			0.719905	−	0.694073i	$-0.244185\pi$
$761$	39.7189			1.43981			0.719905	+	0.694073i	$0.244185\pi$
$762$	7.71761	+	5.70245i	0.279580	+	0.206578i
$763$	−7.34848	+	52.4959i	−0.266033	+	1.90048i
$764$		−	9.48416i		−	0.343125i
$765$	3.53491	+	11.5051i	0.127805	+	0.415967i
$766$			26.8873i			0.971479i
$767$			20.6631i			0.746100i
$768$	−17.8213	+	24.1190i	−0.643069	+	0.870320i
$769$		−	23.5141i		−	0.847939i	−0.905677	−	0.423969i	$-0.860636\pi$
$769$		−	23.5141i		−	0.847939i	0.905677	−	0.423969i	$-0.139364\pi$
$770$	0.903818	−	6.45667i	0.0325713	−	0.232682i
$771$	19.6665	−	26.6163i	0.708270	−	0.958561i
$772$	−1.21334			−0.0436692
$773$	11.3070			0.406684			0.203342	−	0.979108i	$-0.434820\pi$
$773$	11.3070			0.406684			0.203342	+	0.979108i	$0.434820\pi$
$774$	−10.2630	+	3.15329i	−0.368897	+	0.113343i
$775$		−	16.7221i		−	0.600675i
$776$	−22.7345			−0.816120
$777$	24.8470	+	24.3566i	0.891383	+	0.873787i
$778$	36.6975			1.31567
$779$		−	3.52437i		−	0.126274i
$780$	6.11309	+	4.51689i	0.218884	+	0.161731i
$781$	10.0663			0.360200
$782$	20.2305			0.723440
$783$	−3.21019	+	9.12558i	−0.114723	+	0.326122i
$784$	33.5146	+	9.57042i	1.19695	+	0.341801i
$785$			2.31904i			0.0827702i
$786$	29.4960	+	21.7943i	1.05209	+	0.777375i
$787$		−	8.67136i		−	0.309100i	−0.987985	−	0.154550i	$-0.950607\pi$
$787$		−	8.67136i		−	0.309100i	0.987985	−	0.154550i	$-0.0493928\pi$
$788$			10.5974i			0.377516i
$789$	29.3619	+	21.6952i	1.04531	+	0.772368i
$790$			21.5852i			0.767967i
$791$	−30.3900	−	4.25405i	−1.08054	−	0.151257i
$792$	1.70376	+	5.54523i	0.0605404	+	0.197041i
$793$	−18.9095			−0.671495
$794$	−25.8270			−0.916566
$795$	−28.0524	−	20.7276i	−0.994916	−	0.735132i
$796$			13.1223i			0.465109i
$797$	5.56607			0.197160			0.0985801	−	0.995129i	$-0.468570\pi$
$797$	5.56607			0.197160			0.0985801	+	0.995129i	$0.468570\pi$
$798$	−22.5588	−	22.1134i	−0.798571	−	0.782808i
$799$	1.33109			0.0470905
$800$		−	13.0663i		−	0.461965i
$801$	−13.4505	−	43.7775i	−0.475251	−	1.54680i
$802$	34.2203			1.20836
$803$	12.0605			0.425605
$804$	11.0486	−	14.9530i	0.389654	−	0.527351i
$805$	−16.6247	−	2.32717i	−0.585945	−	0.0820218i
$806$		−	34.5826i		−	1.21812i
$807$	20.1559	−	27.2787i	0.709522	−	0.960255i
$808$			12.3492i			0.434442i
$809$			16.2308i			0.570644i	0.958432	+	0.285322i	$0.0921005\pi$
$809$			16.2308i			0.570644i	−0.958432	+	0.285322i	$0.907900\pi$
$810$	−12.4525	−	18.3517i	−0.437538	−	0.644812i
$811$		−	10.8313i		−	0.380340i	−0.981751	−	0.190170i	$-0.939096\pi$
$811$		−	10.8313i		−	0.380340i	0.981751	−	0.190170i	$-0.0609039\pi$
$812$	−4.17432	−	0.584330i	−0.146490	−	0.0205060i
$813$	11.5075	+	8.50273i	0.403584	+	0.298204i
$814$	−12.8308			−0.449718
$815$	−24.9025			−0.872295
$816$	14.1007	−	19.0837i	0.493624	−	0.668063i
$817$		−	8.63891i		−	0.302237i
$818$	−0.760622			−0.0265945
$819$	4.41999	+	27.5615i	0.154447	+	0.963076i
$820$	1.07810			0.0376489
$821$		−	21.3847i		−	0.746332i	−0.927765	−	0.373166i	$-0.878272\pi$
$821$		−	21.3847i		−	0.746332i	0.927765	−	0.373166i	$-0.121728\pi$
$822$	−0.310982	+	0.420878i	−0.0108467	+	0.0146798i
$823$	22.2162			0.774408			0.387204	−	0.921994i	$-0.373441\pi$
$823$	22.2162			0.774408			0.387204	+	0.921994i	$0.373441\pi$
$824$	32.6913			1.13885
$825$	−4.00313	−	2.95787i	−0.139371	−	0.102980i
$826$	26.0161	+	3.64179i	0.905217	+	0.126714i
$827$		−	47.5182i		−	1.65237i	−0.563400	−	0.826184i	$-0.690507\pi$
$827$		−	47.5182i		−	1.65237i	0.563400	−	0.826184i	$-0.309493\pi$
$828$	−10.6777	+	3.28069i	−0.371074	+	0.114012i
$829$			23.6060i			0.819871i	0.912115	+	0.409935i	$0.134449\pi$
$829$			23.6060i			0.819871i	−0.912115	+	0.409935i	$0.865551\pi$
$830$			17.5907i			0.610581i
$831$	8.63557	−	11.6872i	0.299564	−	0.405426i
$832$			7.99926i			0.277324i
$833$	−18.5190	−	5.28829i	−0.641646	−	0.183228i
$834$	16.7389	−	22.6542i	0.579622	−	0.784452i
$835$	28.3928			0.982573
$836$	3.49071			0.120729
$837$	−10.0339	+	28.5233i	−0.346823	+	0.985910i
$838$			66.5996i			2.30065i
$839$	8.39883			0.289960			0.144980	−	0.989435i	$-0.453688\pi$
$839$	8.39883			0.289960			0.144980	+	0.989435i	$0.453688\pi$
$840$	−9.04531	+	9.22745i	−0.312093	+	0.318377i
$841$	25.5340			0.880483
$842$			28.8116i			0.992914i
$843$	34.8010	+	25.7140i	1.19861	+	0.885638i
$844$	1.03474			0.0356174
$845$	−0.921879			−0.0317136
$846$	−2.34453	+	0.720352i	−0.0806066	+	0.0247662i
$847$	−0.366782	+	2.62020i	−0.0126028	+	0.0900313i
$848$			68.7625i			2.36131i
$849$	−17.1280	−	12.6557i	−0.587831	−	0.434342i
$850$			13.3610i			0.458278i
$851$			33.0369i			1.13249i
$852$	11.9997	+	8.86641i	0.411102	+	0.303758i
$853$		−	33.4361i		−	1.14483i	−0.819963	−	0.572416i	$-0.806006\pi$
$853$		−	33.4361i		−	1.14483i	0.819963	−	0.572416i	$-0.193994\pi$
$854$	−3.33273	+	23.8082i	−0.114044	+	0.814701i
$855$	17.0578	−	5.24097i	0.583365	−	0.179237i
$856$	10.4742			0.358000
$857$	−17.6528			−0.603010			−0.301505	−	0.953465i	$-0.597489\pi$
$857$	−17.6528			−0.603010			−0.301505	+	0.953465i	$0.597489\pi$
$858$	−8.27879	−	6.11710i	−0.282633	−	0.208834i
$859$		−	30.3759i		−	1.03641i	−0.855255	−	0.518207i	$-0.826600\pi$
$859$		−	30.3759i		−	1.03641i	0.855255	−	0.518207i	$-0.173400\pi$
$860$	2.64263			0.0901129
$861$	2.82740	+	2.77158i	0.0963575	+	0.0944554i
$862$	53.2244			1.81283
$863$		−	17.3523i		−	0.590678i	−0.955393	−	0.295339i	$-0.904567\pi$
$863$		−	17.3523i		−	0.590678i	0.955393	−	0.295339i	$-0.0954325\pi$
$864$	−7.84032	+	22.2876i	−0.266733	+	0.758240i
$865$	−33.6469			−1.14403
$866$	−30.5207			−1.03713
$867$	9.70648	−	13.1366i	0.329649	−	0.446142i
$868$	−13.0475	−	1.82641i	−0.442860	−	0.0619924i
$869$		−	8.75956i		−	0.297148i
$870$	4.72202	−	6.39070i	0.160091	−	0.216665i
$871$		−	44.1137i		−	1.49474i
$872$			38.7415i			1.31195i
$873$	−33.7157	+	10.3591i	−1.14110	+	0.350601i
$874$		−	29.9943i		−	1.01457i
$875$	4.21114	−	30.0834i	0.142363	−	1.01701i
$876$	14.3769	+	10.6229i	0.485749	+	0.358915i
$877$	19.0234			0.642375			0.321187	−	0.947016i	$-0.395918\pi$
$877$	19.0234			0.642375			0.321187	+	0.947016i	$0.395918\pi$
$878$	−19.3427			−0.652785
$879$	9.93956	−	13.4520i	0.335253	−	0.453726i
$880$		−	7.26061i		−	0.244755i
$881$	25.9732			0.875061			0.437530	−	0.899204i	$-0.355853\pi$
$881$	25.9732			0.875061			0.437530	+	0.899204i	$0.355853\pi$
$882$	35.4807	−	0.707439i	1.19470	−	0.0238207i
$883$	7.05819			0.237527			0.118764	−	0.992923i	$-0.462107\pi$
$883$	7.05819			0.237527			0.118764	+	0.992923i	$0.462107\pi$
$884$			8.27992i			0.278484i
$885$	−8.81870	+	11.9351i	−0.296437	+	0.401194i
$886$	17.4529			0.586342
$887$	−41.3253			−1.38757			−0.693785	−	0.720183i	$-0.744058\pi$
$887$	−41.3253			−1.38757			−0.693785	+	0.720183i	$0.744058\pi$
$888$	20.4523	+	15.1120i	0.686334	+	0.507125i
$889$	1.20246	−	8.59008i	0.0403291	−	0.288102i
$890$			37.6176i			1.26095i
$891$	5.05341	+	7.44735i	0.169296	+	0.249496i
$892$		−	1.37272i		−	0.0459619i
$893$		−	1.97351i		−	0.0660411i
$894$	21.4997	−	29.0974i	0.719058	−	0.973162i
$895$		−	4.48370i		−	0.149874i
$896$	33.8992	+	4.74528i	1.13249	+	0.158529i
$897$	−15.7504	+	21.3164i	−0.525891	+	0.711733i
$898$	26.0243			0.868442
$899$	−10.8334			−0.361315
$900$	−2.16669	−	7.05194i	−0.0722231	−	0.235065i
$901$		−	37.9958i		−	1.26582i
$902$	−1.46004			−0.0486140
$903$	6.93050	+	6.79369i	0.230633	+	0.226080i
$904$	−22.4275			−0.745928
$905$			16.5206i			0.549162i
$906$	−11.6448	−	8.60422i	−0.386873	−	0.285856i
$907$	−42.9161			−1.42500			−0.712502	−	0.701670i	$-0.752438\pi$
$907$	−42.9161			−1.42500			−0.712502	+	0.701670i	$0.752438\pi$
$908$	−12.9959			−0.431282
$909$	5.62695	+	18.3141i	0.186634	+	0.607439i
$910$	3.17854	−	22.7067i	0.105367	−	0.752721i
$911$			19.6193i			0.650018i	0.945711	+	0.325009i	$0.105367\pi$
$911$			19.6193i			0.650018i	−0.945711	+	0.325009i	$0.894633\pi$
$912$	−28.2941	−	20.9062i	−0.936912	−	0.692273i
$913$		−	7.13853i		−	0.236251i
$914$		−	30.4908i		−	1.00855i
$915$	−10.9222	−	8.07029i	−0.361077	−	0.266796i
$916$		−	18.5730i		−	0.613670i
$917$	4.59568	−	32.8305i	0.151763	−	1.08416i
$918$	8.01712	−	22.7902i	0.264605	−	0.752189i
$919$	−6.36026			−0.209806			−0.104903	−	0.994482i	$-0.533453\pi$
$919$	−6.36026			−0.209806			−0.104903	+	0.994482i	$0.533453\pi$
$920$	−12.2689			−0.404494
$921$	−8.25844	−	6.10206i	−0.272125	−	0.201070i
$922$		−	69.3286i		−	2.28322i
$923$	35.4010			1.16524
$924$	−2.74511	+	2.80039i	−0.0903076	+	0.0921261i
$925$	−21.8188			−0.717399
$926$		−	14.7000i		−	0.483073i
$927$	48.4817	−	14.8959i	1.59235	−	0.489246i
$928$	−8.46505			−0.277879
$929$	11.9445			0.391885			0.195942	−	0.980615i	$-0.437223\pi$
$929$	11.9445			0.391885			0.195942	+	0.980615i	$0.437223\pi$
$930$	14.7593	−	19.9751i	0.483978	−	0.655008i
$931$	−7.84058	+	27.4569i	−0.256965	+	0.899863i
$932$			0.391063i			0.0128097i
$933$	3.55879	−	4.81640i	0.116509	−	0.157682i
$934$		−	4.79529i		−	0.156907i
$935$			4.01196i			0.131205i
$936$	5.99176	+	19.5014i	0.195847	+	0.637423i
$937$			46.7121i			1.52602i	0.646388	+	0.763009i	$0.276279\pi$
$937$			46.7121i			1.52602i	−0.646388	+	0.763009i	$0.723721\pi$
$938$	−55.5420	−	7.77489i	−1.81351	−	0.253859i
$939$	−11.7191	−	8.65910i	−0.382438	−	0.282579i
$940$	0.603694			0.0196903
$941$	49.6376			1.61814			0.809070	−	0.587712i	$-0.199971\pi$
$941$	49.6376			1.61814			0.809070	+	0.587712i	$0.199971\pi$
$942$	2.76626	−	3.74382i	0.0901298	−	0.121980i
$943$			3.75934i			0.122421i
$944$	29.2555			0.952185
$945$	−9.20983	+	17.8060i	−0.299596	+	0.579230i
$946$	−3.57884			−0.116358
$947$			6.58429i			0.213961i	0.994261	+	0.106980i	$0.0341182\pi$
$947$			6.58429i			0.213961i	−0.994261	+	0.106980i	$0.965882\pi$
$948$	7.71545	−	10.4420i	0.250586	−	0.339139i
$949$	42.4141			1.37682
$950$	19.8094			0.642703
$951$	−20.6436	−	15.2533i	−0.669413	−	0.494622i
$952$	−13.9400	−	1.95135i	−0.451799	−	0.0632438i
$953$			14.5012i			0.469741i	0.972027	+	0.234871i	$0.0754667\pi$
$953$			14.5012i			0.469741i	−0.972027	+	0.234871i	$0.924533\pi$
$954$	20.5624	+	66.9244i	0.665732	+	2.16676i
$955$		−	16.1613i		−	0.522967i
$956$		−	19.5844i		−	0.633406i
$957$	−1.91626	+	2.59343i	−0.0619438	+	0.0838338i
$958$		−	4.89909i		−	0.158282i
$959$	0.468458	+	0.0655757i	0.0151273	+	0.00211755i
$960$	−3.41397	+	4.62041i	−0.110185	+	0.149123i
$961$	−2.86145			−0.0923048
$962$	−45.1231			−1.45483
$963$	15.5334	−	4.77260i	0.500557	−	0.153795i
$964$		−	16.9695i		−	0.546551i
$965$	−2.06757			−0.0665574
$966$	24.0627	+	23.5877i	0.774205	+	0.758922i
$967$	−3.74566			−0.120452			−0.0602262	−	0.998185i	$-0.519182\pi$
$967$	−3.74566			−0.120452			−0.0602262	+	0.998185i	$0.519182\pi$
$968$			1.93369i			0.0621511i
$969$	15.6344	+	11.5520i	0.502248	+	0.371105i
$970$	28.9716			0.930221
$971$	12.8433			0.412162			0.206081	−	0.978535i	$-0.433929\pi$
$971$	12.8433			0.412162			0.206081	+	0.978535i	$0.433929\pi$
$972$	−0.535657	+	13.3288i	−0.0171812	+	0.427521i
$973$	−25.2153	−	3.52968i	−0.808364	−	0.113156i
$974$			23.2594i			0.745278i
$975$	−14.0782	−	10.4022i	−0.450862	−	0.333137i
$976$			26.7727i			0.856973i
$977$			21.0624i			0.673845i	0.941532	+	0.336923i	$0.109386\pi$
$977$			21.0624i			0.673845i	−0.941532	+	0.336923i	$0.890614\pi$
$978$	40.2021	+	29.7048i	1.28552	+	0.949856i
$979$		−	15.2657i		−	0.487895i
$980$	−8.39902	−	2.39842i	−0.268297	−	0.0766147i
$981$	17.6527	+	57.4544i	0.563608	+	1.83438i
$982$	15.0880			0.481478
$983$	−8.69359			−0.277282			−0.138641	−	0.990343i	$-0.544273\pi$
$983$	−8.69359			−0.277282			−0.138641	+	0.990343i	$0.544273\pi$
$984$	2.32731	+	1.71962i	0.0741920	+	0.0548196i
$985$			18.0582i			0.575383i
$986$	8.65594			0.275661
$987$	1.58323	+	1.55198i	0.0503949	+	0.0494001i
$988$	12.2761			0.390554
$989$			9.21486i			0.293015i
$990$	−2.17118	−	7.06653i	−0.0690045	−	0.224589i
$991$	−3.59873			−0.114318			−0.0571588	−	0.998365i	$-0.518204\pi$
$991$	−3.59873			−0.114318			−0.0571588	+	0.998365i	$0.518204\pi$
$992$	−26.4587			−0.840066
$993$	3.56768	−	4.82845i	0.113217	−	0.153226i
$994$	6.23929	−	44.5721i	0.197898	−	1.41374i
$995$			22.3608i			0.708885i
$996$	6.28764	−	8.50959i	0.199231	−	0.269637i
$997$		−	3.11530i		−	0.0986626i	−0.998782	−	0.0493313i	$-0.984291\pi$
$997$		−	3.11530i		−	0.0986626i	0.998782	−	0.0493313i	$-0.0157090\pi$
$998$			64.0566i			2.02768i
$999$	37.2170	+	13.0922i	1.17749	+	0.414218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.e.a.188.7	✓	28
3.2	odd	2	inner	231.2.e.a.188.22	yes	28
7.6	odd	2	inner	231.2.e.a.188.8	yes	28
21.20	even	2	inner	231.2.e.a.188.21	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.e.a.188.7	✓	28	1.1	even	1	trivial
231.2.e.a.188.8	yes	28	7.6	odd	2	inner
231.2.e.a.188.21	yes	28	21.20	even	2	inner
231.2.e.a.188.22	yes	28	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.68989i q^{2} +(-1.02930 + 1.39303i) q^{3} -0.855732 q^{4} -1.45819 q^{5} +(2.35408 + 1.73940i) q^{6} +(0.366782 - 2.62020i) q^{7} -1.93369i q^{8} +(-0.881093 - 2.86770i) q^{9} +O(q^{10})\)	\(q-1.68989i q^{2} +(-1.02930 + 1.39303i) q^{3} -0.855732 q^{4} -1.45819 q^{5} +(2.35408 + 1.73940i) q^{6} +(0.366782 - 2.62020i) q^{7} -1.93369i q^{8} +(-0.881093 - 2.86770i) q^{9} +2.46419i q^{10} -1.00000i q^{11} +(0.880803 - 1.19207i) q^{12} -3.51679i q^{13} +(-4.42786 - 0.619821i) q^{14} +(1.50091 - 2.03131i) q^{15} -4.97919 q^{16} +2.75133 q^{17} +(-4.84609 + 1.48895i) q^{18} -4.07921i q^{19} +1.24782 q^{20} +(3.27251 + 3.20791i) q^{21} -1.68989 q^{22} +4.35116i q^{23} +(2.69369 + 1.99034i) q^{24} -2.87368 q^{25} -5.94299 q^{26} +(4.90171 + 1.72432i) q^{27} +(-0.313867 + 2.24219i) q^{28} +1.86171i q^{29} +(-3.43270 - 2.53638i) q^{30} +5.81906i q^{31} +4.54691i q^{32} +(1.39303 + 1.02930i) q^{33} -4.64944i q^{34} +(-0.534838 + 3.82076i) q^{35} +(0.753980 + 2.45398i) q^{36} +7.59266 q^{37} -6.89341 q^{38} +(4.89901 + 3.61982i) q^{39} +2.81969i q^{40} +0.863985 q^{41} +(5.42102 - 5.53018i) q^{42} +2.11779 q^{43} +0.855732i q^{44} +(1.28480 + 4.18165i) q^{45} +7.35299 q^{46} +0.483798 q^{47} +(5.12507 - 6.93618i) q^{48} +(-6.73094 - 1.92209i) q^{49} +4.85620i q^{50} +(-2.83193 + 3.83270i) q^{51} +3.00943i q^{52} -13.8100i q^{53} +(2.91391 - 8.28335i) q^{54} +1.45819i q^{55} +(-5.06666 - 0.709241i) q^{56} +(5.68248 + 4.19872i) q^{57} +3.14609 q^{58} -5.87555 q^{59} +(-1.28438 + 1.73826i) q^{60} -5.37692i q^{61} +9.83358 q^{62} +(-7.83712 + 1.25683i) q^{63} -2.27459 q^{64} +5.12815i q^{65} +(1.73940 - 2.35408i) q^{66} +12.5438 q^{67} -2.35440 q^{68} +(-6.06132 - 4.47864i) q^{69} +(6.45667 + 0.903818i) q^{70} +10.0663i q^{71} +(-5.54523 + 1.70376i) q^{72} +12.0605i q^{73} -12.8308i q^{74} +(2.95787 - 4.00313i) q^{75} +3.49071i q^{76} +(-2.62020 - 0.366782i) q^{77} +(6.11710 - 8.27879i) q^{78} +8.75956 q^{79} +7.26061 q^{80} +(-7.44735 + 5.05341i) q^{81} -1.46004i q^{82} +7.13853 q^{83} +(-2.80039 - 2.74511i) q^{84} -4.01196 q^{85} -3.57884i q^{86} +(-2.59343 - 1.91626i) q^{87} -1.93369 q^{88} +15.2657 q^{89} +(7.06653 - 2.17118i) q^{90} +(-9.21470 - 1.28989i) q^{91} -3.72343i q^{92} +(-8.10615 - 5.98954i) q^{93} -0.817566i q^{94} +5.94826i q^{95} +(-6.33400 - 4.68012i) q^{96} -11.7571i q^{97} +(-3.24812 + 11.3746i) q^{98} +(-2.86770 + 0.881093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

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