LMFDB - Embedded newform 429.2.f.a.131.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(131,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, 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("429.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.8
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96237 q^{2} +(-1.16712 + 1.27978i) q^{3} +1.85089 q^{4} -3.33889i q^{5} +(2.29031 - 2.51140i) q^{6} +4.49805i q^{7} +0.292612 q^{8} +(-0.275676 - 2.98731i) q^{9} +O(q^{10})$	\(q-1.96237 q^{2} +(-1.16712 + 1.27978i) q^{3} +1.85089 q^{4} -3.33889i q^{5} +(2.29031 - 2.51140i) q^{6} +4.49805i q^{7} +0.292612 q^{8} +(-0.275676 - 2.98731i) q^{9} +6.55213i q^{10} +(-3.20831 + 0.840687i) q^{11} +(-2.16020 + 2.36873i) q^{12} -1.00000i q^{13} -8.82684i q^{14} +(4.27305 + 3.89688i) q^{15} -4.27599 q^{16} +0.227302 q^{17} +(0.540978 + 5.86220i) q^{18} -4.91986i q^{19} -6.17991i q^{20} +(-5.75652 - 5.24976i) q^{21} +(6.29588 - 1.64974i) q^{22} -0.962301i q^{23} +(-0.341513 + 0.374479i) q^{24} -6.14820 q^{25} +1.96237i q^{26} +(4.14484 + 3.13373i) q^{27} +8.32540i q^{28} +0.116406 q^{29} +(-8.38529 - 7.64711i) q^{30} +9.05538 q^{31} +7.80584 q^{32} +(2.66858 - 5.08711i) q^{33} -0.446051 q^{34} +15.0185 q^{35} +(-0.510246 - 5.52917i) q^{36} +10.9916 q^{37} +9.65458i q^{38} +(1.27978 + 1.16712i) q^{39} -0.977001i q^{40} +5.48470 q^{41} +(11.2964 + 10.3020i) q^{42} -2.48713i q^{43} +(-5.93822 + 1.55602i) q^{44} +(-9.97429 + 0.920452i) q^{45} +1.88839i q^{46} -2.09661i q^{47} +(4.99058 - 5.47233i) q^{48} -13.2325 q^{49} +12.0650 q^{50} +(-0.265288 + 0.290897i) q^{51} -1.85089i q^{52} -11.2171i q^{53} +(-8.13371 - 6.14953i) q^{54} +(2.80696 + 10.7122i) q^{55} +1.31619i q^{56} +(6.29634 + 5.74205i) q^{57} -0.228431 q^{58} +5.88710i q^{59} +(7.90893 + 7.21268i) q^{60} -10.6796i q^{61} -17.7700 q^{62} +(13.4371 - 1.24001i) q^{63} -6.76595 q^{64} -3.33889 q^{65} +(-5.23673 + 9.98278i) q^{66} +8.34904 q^{67} +0.420711 q^{68} +(1.23153 + 1.12312i) q^{69} -29.4719 q^{70} -11.2854i q^{71} +(-0.0806662 - 0.874123i) q^{72} -4.41695i q^{73} -21.5696 q^{74} +(7.17566 - 7.86834i) q^{75} -9.10611i q^{76} +(-3.78146 - 14.4311i) q^{77} +(-2.51140 - 2.29031i) q^{78} -0.735929i q^{79} +14.2771i q^{80} +(-8.84801 + 1.64706i) q^{81} -10.7630 q^{82} +9.78001 q^{83} +(-10.6547 - 9.71671i) q^{84} -0.758938i q^{85} +4.88065i q^{86} +(-0.135859 + 0.148974i) q^{87} +(-0.938790 + 0.245995i) q^{88} +11.4346i q^{89} +(19.5732 - 1.80627i) q^{90} +4.49805 q^{91} -1.78111i q^{92} +(-10.5687 + 11.5889i) q^{93} +4.11431i q^{94} -16.4269 q^{95} +(-9.11033 + 9.98976i) q^{96} -6.53254 q^{97} +25.9670 q^{98} +(3.39584 + 9.35245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.96237			−1.38760			−0.693802	−	0.720166i	$-0.744066\pi$
$2$	−1.96237			−1.38760			−0.693802	+	0.720166i	$0.744066\pi$
$3$	−1.16712	+	1.27978i	−0.673835	+	0.738882i
$3$	−1.16712	+	1.27978i	−0.673835	+	0.738882i
$4$	1.85089			0.925444
$5$		−	3.33889i		−	1.49320i	−0.665275	−	0.746599i	$-0.731686\pi$
$5$		−	3.33889i		−	1.49320i	0.665275	−	0.746599i	$-0.268314\pi$
$6$	2.29031	−	2.51140i	0.935016	−	1.02527i
$7$			4.49805i			1.70010i	0.526698	+	0.850052i	$0.323430\pi$
$7$			4.49805i			1.70010i	−0.526698	+	0.850052i	$0.676570\pi$
$8$	0.292612			0.103454
$9$	−0.275676	−	2.98731i	−0.0918920	−	0.995769i
$10$			6.55213i			2.07197i
$11$	−3.20831	+	0.840687i	−0.967341	+	0.253477i
$11$	−3.20831	+	0.840687i	−0.967341	+	0.253477i
$12$	−2.16020	+	2.36873i	−0.623597	+	0.683794i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$		−	8.82684i		−	2.35907i
$15$	4.27305	+	3.89688i	1.10330	+	1.00617i
$16$	−4.27599			−1.06900
$17$	0.227302			0.0551289			0.0275645	−	0.999620i	$-0.491225\pi$
$17$	0.227302			0.0551289			0.0275645	+	0.999620i	$0.491225\pi$
$18$	0.540978	+	5.86220i	0.127510	+	1.38173i
$19$		−	4.91986i		−	1.12869i	−0.825538	−	0.564347i	$-0.809128\pi$
$19$		−	4.91986i		−	1.12869i	0.825538	−	0.564347i	$-0.190872\pi$
$20$		−	6.17991i		−	1.38187i
$21$	−5.75652	−	5.24976i	−1.25618	−	1.14559i
$22$	6.29588	−	1.64974i	1.34229	−	0.351725i
$23$		−	0.962301i		−	0.200654i	−0.994955	−	0.100327i	$-0.968011\pi$
$23$		−	0.962301i		−	0.200654i	0.994955	−	0.100327i	$-0.0319888\pi$
$24$	−0.341513	+	0.374479i	−0.0697110	+	0.0764403i
$25$	−6.14820			−1.22964
$26$			1.96237i			0.384852i
$27$	4.14484	+	3.13373i	0.797675	+	0.603087i
$28$			8.32540i			1.57335i
$29$	0.116406			0.0216161			0.0108080	−	0.999942i	$-0.496560\pi$
$29$	0.116406			0.0216161			0.0108080	+	0.999942i	$0.496560\pi$
$30$	−8.38529	−	7.64711i	−1.53094	−	1.39616i
$31$	9.05538			1.62639			0.813197	−	0.581989i	$-0.197725\pi$
$31$	9.05538			1.62639			0.813197	+	0.581989i	$0.197725\pi$
$32$	7.80584			1.37989
$33$	2.66858	−	5.08711i	0.464540	−	0.885552i
$34$	−0.446051			−0.0764971
$35$	15.0185			2.53859
$36$	−0.510246	−	5.52917i	−0.0850409	−	0.921529i
$37$	10.9916			1.80701			0.903504	−	0.428581i	$-0.140986\pi$
$37$	10.9916			1.80701			0.903504	+	0.428581i	$0.140986\pi$
$38$			9.65458i			1.56618i
$39$	1.27978	+	1.16712i	0.204929	+	0.186888i
$40$		−	0.977001i		−	0.154477i
$41$	5.48470			0.856566			0.428283	−	0.903645i	$-0.359119\pi$
$41$	5.48470			0.856566			0.428283	+	0.903645i	$0.359119\pi$
$42$	11.2964	+	10.3020i	1.74307	+	1.58963i
$43$		−	2.48713i		−	0.379283i	−0.981853	−	0.189642i	$-0.939267\pi$
$43$		−	2.48713i		−	0.379283i	0.981853	−	0.189642i	$-0.0607326\pi$
$44$	−5.93822	+	1.55602i	−0.895220	+	0.234578i
$45$	−9.97429	+	0.920452i	−1.48688	+	0.137213i
$46$			1.88839i			0.278428i
$47$		−	2.09661i		−	0.305821i	−0.988240	−	0.152911i	$-0.951135\pi$
$47$		−	2.09661i		−	0.305821i	0.988240	−	0.152911i	$-0.0488647\pi$
$48$	4.99058	−	5.47233i	0.720328	−	0.789862i
$49$	−13.2325			−1.89036
$50$	12.0650			1.70625
$51$	−0.265288	+	0.290897i	−0.0371478	+	0.0407337i
$52$		−	1.85089i		−	0.256672i
$53$		−	11.2171i		−	1.54078i	−0.637570	−	0.770392i	$-0.720060\pi$
$53$		−	11.2171i		−	1.54078i	0.637570	−	0.770392i	$-0.279940\pi$
$54$	−8.13371	−	6.14953i	−1.10686	−	0.836846i
$55$	2.80696	+	10.7122i	0.378491	+	1.44443i
$56$			1.31619i			0.175883i
$57$	6.29634	+	5.74205i	0.833971	+	0.760553i
$58$	−0.228431			−0.0299945
$59$			5.88710i			0.766435i	0.923658	+	0.383217i	$0.125184\pi$
$59$			5.88710i			0.766435i	−0.923658	+	0.383217i	$0.874816\pi$
$60$	7.90893	+	7.21268i	1.02104	+	0.931153i
$61$		−	10.6796i		−	1.36738i	−0.729771	−	0.683692i	$-0.760373\pi$
$61$		−	10.6796i		−	1.36738i	0.729771	−	0.683692i	$-0.239627\pi$
$62$	−17.7700			−2.25679
$63$	13.4371	−	1.24001i	1.69291	−	0.156226i
$64$	−6.76595			−0.845744
$65$	−3.33889			−0.414138
$66$	−5.23673	+	9.98278i	−0.644597	+	1.22880i
$67$	8.34904			1.02000			0.509999	−	0.860175i	$-0.329646\pi$
$67$	8.34904			1.02000			0.509999	+	0.860175i	$0.329646\pi$
$68$	0.420711			0.0510187
$69$	1.23153	+	1.12312i	0.148259	+	0.135208i
$70$	−29.4719			−3.52256
$71$		−	11.2854i		−	1.33933i	−0.742665	−	0.669663i	$-0.766439\pi$
$71$		−	11.2854i		−	1.33933i	0.742665	−	0.669663i	$-0.233561\pi$
$72$	−0.0806662	−	0.874123i	−0.00950660	−	0.103016i
$73$		−	4.41695i		−	0.516965i	−0.966016	−	0.258482i	$-0.916778\pi$
$73$		−	4.41695i		−	0.516965i	0.966016	−	0.258482i	$-0.0832224\pi$
$74$	−21.5696			−2.50741
$75$	7.17566	−	7.86834i	0.828574	−	0.908558i
$76$		−	9.10611i		−	1.04454i
$77$	−3.78146	−	14.4311i	−0.430937	−	1.64458i
$78$	−2.51140	−	2.29031i	−0.284360	−	0.259327i
$79$		−	0.735929i		−	0.0827985i	−0.999143	−	0.0413993i	$-0.986818\pi$
$79$		−	0.735929i		−	0.0827985i	0.999143	−	0.0413993i	$-0.0131816\pi$
$80$			14.2771i			1.59622i
$81$	−8.84801	+	1.64706i	−0.983112	+	0.183006i
$82$	−10.7630			−1.18857
$83$	9.78001			1.07350			0.536748	−	0.843743i	$-0.319653\pi$
$83$	9.78001			1.07350			0.536748	+	0.843743i	$0.319653\pi$
$84$	−10.6547	−	9.71671i	−1.16252	−	1.06018i
$85$		−	0.758938i		−	0.0823184i
$86$			4.88065i			0.526295i
$87$	−0.135859	+	0.148974i	−0.0145657	+	0.0159717i
$88$	−0.938790	+	0.245995i	−0.100075	+	0.0262232i
$89$			11.4346i			1.21206i	0.795441	+	0.606032i	$0.207239\pi$
$89$			11.4346i			1.21206i	−0.795441	+	0.606032i	$0.792761\pi$
$90$	19.5732	−	1.80627i	2.06320	−	0.190397i
$91$	4.49805			0.471524
$92$		−	1.78111i		−	0.185694i
$93$	−10.5687	+	11.5889i	−1.09592	+	1.20171i
$94$			4.11431i			0.424359i
$95$	−16.4269			−1.68536
$96$	−9.11033	+	9.98976i	−0.929819	+	1.01958i
$97$	−6.53254			−0.663279			−0.331639	−	0.943406i	$-0.607602\pi$
$97$	−6.53254			−0.663279			−0.331639	+	0.943406i	$0.607602\pi$
$98$	25.9670			2.62307
$99$	3.39584	+	9.35245i	0.341295	+	0.939956i
$100$	−11.3796			−1.13796
$101$	7.80905			0.777030			0.388515	−	0.921442i	$-0.372988\pi$
$101$	7.80905			0.777030			0.388515	+	0.921442i	$0.372988\pi$
$102$	0.520594	−	0.570847i	0.0515464	−	0.0565223i
$103$	7.98701			0.786984			0.393492	−	0.919328i	$-0.371267\pi$
$103$	7.98701			0.786984			0.393492	+	0.919328i	$0.371267\pi$
$104$		−	0.292612i		−	0.0286930i
$105$	−17.5284	+	19.2204i	−1.71059	+	1.87572i
$106$			22.0120i			2.13800i
$107$	−13.7718			−1.33137			−0.665685	−	0.746233i	$-0.731860\pi$
$107$	−13.7718			−1.33137			−0.665685	+	0.746233i	$0.731860\pi$
$108$	7.67164	+	5.80019i	0.738204	+	0.558123i
$109$		−	6.73699i		−	0.645286i	−0.946521	−	0.322643i	$-0.895429\pi$
$109$		−	6.73699i		−	0.645286i	0.946521	−	0.322643i	$-0.104571\pi$
$110$	−5.50829	−	21.0213i	−0.525195	−	2.00430i
$111$	−12.8285	+	14.0668i	−1.21763	+	1.33516i
$112$		−	19.2336i		−	1.81741i
$113$			6.19992i			0.583239i	0.956534	+	0.291620i	$0.0941941\pi$
$113$			6.19992i			0.583239i	−0.956534	+	0.291620i	$0.905806\pi$
$114$	−12.3557	−	11.2680i	−1.15722	−	1.05535i
$115$	−3.21302			−0.299616
$116$	0.215455			0.0200045
$117$	−2.98731	+	0.275676i	−0.276177	+	0.0254863i
$118$		−	11.5526i		−	1.06351i
$119$			1.02242i			0.0937249i
$120$	1.25035	+	1.14027i	0.114140	+	0.104092i
$121$	9.58649	−	5.39437i	0.871499	−	0.490397i
$122$			20.9573i			1.89739i
$123$	−6.40128	+	7.01921i	−0.577184	+	0.632901i
$124$	16.7605			1.50514
$125$			3.83370i			0.342896i
$126$	−26.3685	+	2.43335i	−2.34909	+	0.216780i
$127$			2.13256i			0.189234i	0.995514	+	0.0946171i	$0.0301627\pi$
$127$			2.13256i			0.189234i	−0.995514	+	0.0946171i	$0.969837\pi$
$128$	−2.33439			−0.206333
$129$	3.18297	+	2.90277i	0.280245	+	0.255574i
$130$	6.55213			0.574660
$131$	−10.7199			−0.936603			−0.468302	−	0.883569i	$-0.655134\pi$
$131$	−10.7199			−0.936603			−0.468302	+	0.883569i	$0.655134\pi$
$132$	4.93924	−	9.41567i	0.429905	−	0.819529i
$133$	22.1298			1.91890
$134$	−16.3839			−1.41535
$135$	10.4632	−	13.8392i	0.900528	−	1.19109i
$136$	0.0665115			0.00570331
$137$			6.69062i			0.571618i	0.958287	+	0.285809i	$0.0922623\pi$
$137$			6.69062i			0.571618i	−0.958287	+	0.285809i	$0.907738\pi$
$138$	−2.41672	−	2.20397i	−0.205725	−	0.187614i
$139$			4.14860i			0.351880i	0.984401	+	0.175940i	$0.0562964\pi$
$139$			4.14860i			0.351880i	−0.984401	+	0.175940i	$0.943704\pi$
$140$	27.7976			2.34933
$141$	2.68320	+	2.44698i	0.225966	+	0.206073i
$142$			22.1460i			1.85845i
$143$	0.840687	+	3.20831i	0.0703018	+	0.268292i
$144$	1.17879	+	12.7737i	0.0982323	+	1.06447i
$145$		−	0.388667i		−	0.0322770i
$146$			8.66768i			0.717342i
$147$	15.4439	−	16.9347i	1.27379	−	1.39675i
$148$	20.3442			1.67228
$149$	−1.69786			−0.139094			−0.0695471	−	0.997579i	$-0.522155\pi$
$149$	−1.69786			−0.139094			−0.0695471	+	0.997579i	$0.522155\pi$
$150$	−14.0813	+	15.4406i	−1.14973	+	1.26072i
$151$			5.24695i			0.426991i	0.976944	+	0.213495i	$0.0684849\pi$
$151$			5.24695i			0.426991i	−0.976944	+	0.213495i	$0.931515\pi$
$152$		−	1.43961i		−	0.116768i
$153$	−0.0626618	−	0.679022i	−0.00506591	−	0.0548957i
$154$	7.42061	+	28.3192i	0.597970	+	2.28203i
$155$		−	30.2349i		−	2.42853i
$156$	2.36873	+	2.16020i	0.189650	+	0.172955i
$157$	5.66483			0.452102			0.226051	−	0.974115i	$-0.427418\pi$
$157$	5.66483			0.452102			0.226051	+	0.974115i	$0.427418\pi$
$158$			1.44416i			0.114892i
$159$	14.3554	+	13.0916i	1.13846	+	1.03824i
$160$		−	26.0629i		−	2.06045i
$161$	4.32848			0.341132
$162$	17.3630	−	3.23213i	1.36417	−	0.253940i
$163$	2.44110			0.191201			0.0956007	−	0.995420i	$-0.469523\pi$
$163$	2.44110			0.191201			0.0956007	+	0.995420i	$0.469523\pi$
$164$	10.1516			0.792704
$165$	−16.9853	−	8.91009i	−1.32230	−	0.693649i
$166$	−19.1920			−1.48959
$167$	−11.1382			−0.861897			−0.430949	−	0.902376i	$-0.641821\pi$
$167$	−11.1382			−0.861897			−0.430949	+	0.902376i	$0.641821\pi$
$168$	−1.68443	−	1.53614i	−0.129957	−	0.118516i
$169$	−1.00000			−0.0769231
$170$			1.48932i			0.114225i
$171$	−14.6971	+	1.35629i	−1.12392	+	0.103718i
$172$		−	4.60339i		−	0.351005i
$173$	16.9158			1.28608			0.643041	−	0.765832i	$-0.277672\pi$
$173$	16.9158			1.28608			0.643041	+	0.765832i	$0.277672\pi$
$174$	0.266606	−	0.292342i	0.0202114	−	0.0221624i
$175$		−	27.6549i		−	2.09052i
$176$	13.7187	−	3.59477i	1.03409	−	0.270966i
$177$	−7.53419	−	6.87093i	−0.566304	−	0.516451i
$178$		−	22.4389i		−	1.68186i
$179$		−	7.83508i		−	0.585621i	−0.956170	−	0.292811i	$-0.905409\pi$
$179$		−	7.83508i		−	0.585621i	0.956170	−	0.292811i	$-0.0945905\pi$
$180$	−18.4613	+	1.70365i	−1.37602	+	0.126983i
$181$	−22.0579			−1.63955			−0.819777	−	0.572683i	$-0.805903\pi$
$181$	−22.0579			−1.63955			−0.819777	+	0.572683i	$0.805903\pi$
$182$	−8.82684			−0.654289
$183$	13.6675	+	12.4643i	1.01033	+	0.921391i
$184$		−	0.281581i		−	0.0207584i
$185$		−	36.6997i		−	2.69822i
$186$	20.7396	−	22.7417i	1.52070	−	1.66750i
$187$	−0.729256	+	0.191090i	−0.0533285	+	0.0139739i
$188$		−	3.88058i		−	0.283021i
$189$	−14.0957	+	18.6437i	−1.02531	+	1.35613i
$190$	32.2356			2.33861
$191$			0.327169i			0.0236731i	0.999930	+	0.0118366i	$0.00376778\pi$
$191$			0.327169i			0.0236731i	−0.999930	+	0.0118366i	$0.996232\pi$
$192$	7.89666	−	8.65893i	0.569892	−	0.624905i
$193$		−	4.26158i		−	0.306755i	−0.988168	−	0.153378i	$-0.950985\pi$
$193$		−	4.26158i		−	0.306755i	0.988168	−	0.153378i	$-0.0490151\pi$
$194$	12.8192			0.920368
$195$	3.89688	−	4.27305i	0.279061	−	0.305999i
$196$	−24.4919			−1.74942
$197$	11.4288			0.814269			0.407135	−	0.913368i	$-0.366528\pi$
$197$	11.4288			0.814269			0.407135	+	0.913368i	$0.366528\pi$
$198$	−6.66390	−	18.3529i	−0.473582	−	1.30429i
$199$	−13.1261			−0.930482			−0.465241	−	0.885184i	$-0.654032\pi$
$199$	−13.1261			−0.930482			−0.465241	+	0.885184i	$0.654032\pi$
$200$	−1.79904			−0.127211
$201$	−9.74430	+	10.6849i	−0.687310	+	0.753657i
$202$	−15.3242			−1.07821
$203$			0.523601i			0.0367496i
$204$	−0.491019	+	0.538418i	−0.0343782	+	0.0376968i
$205$		−	18.3128i		−	1.27902i
$206$	−15.6735			−1.09202
$207$	−2.87469	+	0.265283i	−0.199805	+	0.0184385i
$208$			4.27599i			0.296487i
$209$	4.13606	+	15.7844i	0.286097	+	1.09183i
$210$	34.3971	−	37.7175i	2.37363	−	2.60275i
$211$		−	27.3780i		−	1.88478i	−0.334519	−	0.942389i	$-0.608574\pi$
$211$		−	27.3780i		−	1.88478i	0.334519	−	0.942389i	$-0.391426\pi$
$212$		−	20.7616i		−	1.42591i
$213$	14.4428	+	13.1713i	0.989603	+	0.902485i
$214$	27.0253			1.84741
$215$	−8.30424			−0.566344
$216$	1.21283	+	0.916968i	0.0825228	+	0.0623918i
$217$			40.7316i			2.76504i
$218$			13.2204i			0.895402i
$219$	5.65273	+	5.15510i	0.381976	+	0.348349i
$220$	5.19537	+	19.8271i	0.350272	+	1.33674i
$221$		−	0.227302i		−	0.0152900i
$222$	25.1742	−	27.6043i	1.68958	−	1.85268i
$223$	−14.3982			−0.964177			−0.482088	−	0.876123i	$-0.660122\pi$
$223$	−14.3982			−0.964177			−0.482088	+	0.876123i	$0.660122\pi$
$224$			35.1111i			2.34596i
$225$	1.69491	+	18.3665i	0.112994	+	1.22444i
$226$		−	12.1665i		−	0.809305i
$227$	13.7608			0.913334			0.456667	−	0.889638i	$-0.349043\pi$
$227$	13.7608			0.913334			0.456667	+	0.889638i	$0.349043\pi$
$228$	11.6538	+	10.6279i	0.771793	+	0.703850i
$229$	−0.633774			−0.0418809			−0.0209405	−	0.999781i	$-0.506666\pi$
$229$	−0.633774			−0.0418809			−0.0209405	+	0.999781i	$0.506666\pi$
$230$	6.30513			0.415748
$231$	22.8821	+	12.0034i	1.50553	+	0.789766i
$232$	0.0340618			0.00223627
$233$	15.2340			0.998011			0.499005	−	0.866599i	$-0.333699\pi$
$233$	15.2340			0.998011			0.499005	+	0.866599i	$0.333699\pi$
$234$	5.86220	−	0.540978i	0.383224	−	0.0353648i
$235$	−7.00034			−0.456652
$236$			10.8964i			0.709292i
$237$	0.941828	+	0.858916i	0.0611783	+	0.0557926i
$238$		−	2.00636i		−	0.130053i
$239$	−1.36608			−0.0883645			−0.0441822	−	0.999023i	$-0.514068\pi$
$239$	−1.36608			−0.0883645			−0.0441822	+	0.999023i	$0.514068\pi$
$240$	−18.2715	−	16.6630i	−1.17942	−	1.07559i
$241$			10.0558i			0.647754i	0.946099	+	0.323877i	$0.104986\pi$
$241$			10.0558i			0.647754i	−0.946099	+	0.323877i	$0.895014\pi$
$242$	−18.8122	+	10.5857i	−1.20930	+	0.680477i
$243$	8.21878	−	13.2458i	0.527235	−	0.849719i
$244$		−	19.7668i		−	1.26544i
$245$			44.1819i			2.82268i
$246$	12.5617	−	13.7743i	0.800903	−	0.878216i
$247$	−4.91986			−0.313043
$248$	2.64971			0.168257
$249$	−11.4144	+	12.5163i	−0.723359	+	0.793186i
$250$		−	7.52313i		−	0.475804i
$251$		−	1.70629i		−	0.107700i	−0.998549	−	0.0538502i	$-0.982851\pi$
$251$		−	1.70629i		−	0.107700i	0.998549	−	0.0538502i	$-0.0171493\pi$
$252$	24.8705	−	2.29511i	1.56670	−	0.144578i
$253$	0.808994	+	3.08736i	0.0508610	+	0.194101i
$254$		−	4.18487i		−	0.262582i
$255$	0.971274	+	0.885769i	0.0608235	+	0.0554690i
$256$	18.1128			1.13205
$257$			5.96976i			0.372383i	0.982513	+	0.186192i	$0.0596146\pi$
$257$			5.96976i			0.372383i	−0.982513	+	0.186192i	$0.940385\pi$
$258$	−6.24617	−	5.69629i	−0.388869	−	0.354636i
$259$			49.4408i			3.07210i
$260$	−6.17991			−0.383262
$261$	−0.0320904	−	0.347741i	−0.00198634	−	0.0215246i
$262$	21.0364			1.29963
$263$	−11.8881			−0.733054			−0.366527	−	0.930407i	$-0.619453\pi$
$263$	−11.8881			−0.733054			−0.366527	+	0.930407i	$0.619453\pi$
$264$	0.780858	−	1.48855i	0.0480585	−	0.0916140i
$265$	−37.4526			−2.30070
$266$	−43.4268			−2.66267
$267$	−14.6338	−	13.3455i	−0.895571	−	0.816731i
$268$	15.4531			0.943950
$269$		−	13.2715i		−	0.809178i	−0.914499	−	0.404589i	$-0.867415\pi$
$269$		−	13.2715i		−	0.809178i	0.914499	−	0.404589i	$-0.132585\pi$
$270$	−20.5326	+	27.1576i	−1.24958	+	1.65276i
$271$		−	6.71550i		−	0.407938i	−0.978977	−	0.203969i	$-0.934616\pi$
$271$		−	6.71550i		−	0.407938i	0.978977	−	0.203969i	$-0.0653842\pi$
$272$	−0.971942			−0.0589327
$273$	−5.24976	+	5.75652i	−0.317730	+	0.348401i
$274$		−	13.1295i		−	0.793179i
$275$	19.7253	−	5.16871i	1.18948	−	0.311685i
$276$	2.27943	+	2.07877i	0.137206	+	0.125127i
$277$			23.4113i			1.40665i	0.710869	+	0.703324i	$0.248302\pi$
$277$			23.4113i			1.40665i	−0.710869	+	0.703324i	$0.751698\pi$
$278$		−	8.14108i		−	0.488270i
$279$	−2.49635	−	27.0512i	−0.149453	−	1.61951i
$280$	4.39460			0.262628
$281$	18.4345			1.09971			0.549856	−	0.835259i	$-0.314683\pi$
$281$	18.4345			1.09971			0.549856	+	0.835259i	$0.314683\pi$
$282$	−5.26542	−	4.80188i	−0.313551	−	0.285948i
$283$		−	13.5318i		−	0.804383i	−0.915556	−	0.402191i	$-0.868249\pi$
$283$		−	13.5318i		−	0.804383i	0.915556	−	0.402191i	$-0.131751\pi$
$284$		−	20.8879i		−	1.23947i
$285$	19.1721	−	21.0228i	1.13566	−	1.24528i
$286$	−1.64974	−	6.29588i	−0.0975510	−	0.372283i
$287$			24.6705i			1.45625i
$288$	−2.15188	−	23.3184i	−0.126801	−	1.37405i
$289$	−16.9483			−0.996961
$290$			0.762708i			0.0447877i
$291$	7.62424	−	8.36022i	0.446941	−	0.490085i
$292$		−	8.17528i		−	0.478422i
$293$	−16.3288			−0.953940			−0.476970	−	0.878920i	$-0.658265\pi$
$293$	−16.3288			−0.953940			−0.476970	+	0.878920i	$0.658265\pi$
$294$	−30.3066	+	33.2321i	−1.76751	+	1.93813i
$295$	19.6564			1.14444
$296$	3.21628			0.186942
$297$	−15.9324	−	6.56946i	−0.924493	−	0.381199i
$298$	3.33183			0.193008
$299$	−0.962301			−0.0556513
$300$	13.2813	−	14.5634i	0.766799	−	0.840819i
$301$	11.1872			0.644821
$302$		−	10.2965i		−	0.592494i
$303$	−9.11408	+	9.99387i	−0.523590	+	0.574133i
$304$			21.0373i			1.20657i
$305$	−35.6580			−2.04177
$306$	0.122966	+	1.33249i	0.00702947	+	0.0761734i
$307$			18.4165i			1.05109i	0.850766	+	0.525544i	$0.176138\pi$
$307$			18.4165i			1.05109i	−0.850766	+	0.525544i	$0.823862\pi$
$308$	−6.99905	−	26.7104i	−0.398808	−	1.52197i
$309$	−9.32178	+	10.2216i	−0.530297	+	0.581488i
$310$			59.3320i			3.36983i
$311$			3.10855i			0.176270i	0.996109	+	0.0881350i	$0.0280907\pi$
$311$			3.10855i			0.176270i	−0.996109	+	0.0881350i	$0.971909\pi$
$312$	0.374479	+	0.341513i	0.0212007	+	0.0193344i
$313$	24.4427			1.38158			0.690791	−	0.723054i	$-0.257262\pi$
$313$	24.4427			1.38158			0.690791	+	0.723054i	$0.257262\pi$
$314$	−11.1165			−0.627339
$315$	−4.14025	−	44.8649i	−0.233276	−	2.52785i
$316$		−	1.36212i		−	0.0766254i
$317$			1.71125i			0.0961134i	0.998845	+	0.0480567i	$0.0153028\pi$
$317$			1.71125i			0.0961134i	−0.998845	+	0.0480567i	$0.984697\pi$
$318$	−28.1706	−	25.6906i	−1.57973	−	1.44066i
$319$	−0.373466	+	0.0978610i	−0.0209101	+	0.00547917i
$320$			22.5908i			1.26286i
$321$	16.0733	−	17.6249i	0.897124	−	0.983724i
$322$	−8.49408			−0.473356
$323$		−	1.11830i		−	0.0622236i
$324$	−16.3767	+	3.04852i	−0.909815	+	0.169362i
$325$			6.14820i			0.341041i
$326$	−4.79033			−0.265312
$327$	8.62186	+	7.86285i	0.476790	+	0.434817i
$328$	1.60489			0.0886152
$329$	9.43065			0.519928
$330$	33.3314	+	17.4849i	1.83483	+	0.962510i
$331$	12.0422			0.661897			0.330948	−	0.943649i	$-0.392631\pi$
$331$	12.0422			0.661897			0.330948	+	0.943649i	$0.392631\pi$
$332$	18.1017			0.993461
$333$	−3.03012	−	32.8353i	−0.166050	−	1.79936i
$334$	21.8572			1.19597
$335$		−	27.8765i		−	1.52306i
$336$	24.6148	+	22.4479i	1.34285	+	1.22463i
$337$		−	16.1234i		−	0.878296i	−0.898415	−	0.439148i	$-0.855280\pi$
$337$		−	16.1234i		−	0.878296i	0.898415	−	0.439148i	$-0.144720\pi$
$338$	1.96237			0.106739
$339$	−7.93453	−	7.23603i	−0.430945	−	0.393007i
$340$		−	1.40471i		−	0.0761810i
$341$	−29.0524	+	7.61274i	−1.57328	+	0.412253i
$342$	28.8412	−	2.66154i	1.55955	−	0.143919i
$343$		−	28.0341i		−	1.51370i
$344$		−	0.727763i		−	0.0392384i
$345$	3.74997	−	4.11196i	0.201892	−	0.221380i
$346$	−33.1950			−1.78457
$347$	−30.6912			−1.64759			−0.823794	−	0.566889i	$-0.808147\pi$
$347$	−30.6912			−1.64759			−0.823794	+	0.566889i	$0.808147\pi$
$348$	−0.251461	+	0.275735i	−0.0134797	+	0.0147809i
$349$		−	11.9009i		−	0.637041i	−0.947916	−	0.318521i	$-0.896814\pi$
$349$		−	11.9009i		−	0.637041i	0.947916	−	0.318521i	$-0.103186\pi$
$350$			54.2691i			2.90081i
$351$	3.13373	−	4.14484i	0.167266	−	0.221235i
$352$	−25.0435	+	6.56227i	−1.33483	+	0.349770i
$353$		−	2.73796i		−	0.145727i	−0.997342	−	0.0728635i	$-0.976786\pi$
$353$		−	2.73796i		−	0.145727i	0.997342	−	0.0728635i	$-0.0232137\pi$
$354$	14.7849	+	13.4833i	0.785806	+	0.716629i
$355$	−37.6806			−1.99988
$356$			21.1641i			1.12170i
$357$	−1.30847	−	1.19328i	−0.0692516	−	0.0631552i
$358$			15.3753i			0.812610i
$359$	23.5356			1.24216			0.621081	−	0.783746i	$-0.286694\pi$
$359$	23.5356			1.24216			0.621081	+	0.783746i	$0.286694\pi$
$360$	−2.91860	+	0.269336i	−0.153824	+	0.0141952i
$361$	−5.20502			−0.273948
$362$	43.2858			2.27505
$363$	−4.28495	+	18.5645i	−0.224902	+	0.974381i
$364$	8.32540			0.436369
$365$	−14.7477			−0.771931
$366$	−26.8208	−	24.4596i	−1.40194	−	1.27853i
$367$	−22.8577			−1.19316			−0.596581	−	0.802553i	$-0.703475\pi$
$367$	−22.8577			−1.19316			−0.596581	+	0.802553i	$0.703475\pi$
$368$			4.11479i			0.214498i
$369$	−1.51200	−	16.3845i	−0.0787116	−	0.852942i
$370$			72.0184i			3.74406i
$371$	50.4551			2.61950
$372$	−19.5615	+	21.4497i	−1.01421	+	1.11212i
$373$			26.1875i			1.35594i	0.735091	+	0.677968i	$0.237139\pi$
$373$			26.1875i			1.35594i	−0.735091	+	0.677968i	$0.762861\pi$
$374$	1.43107	−	0.374989i	0.0739988	−	0.0193902i
$375$	−4.90629	−	4.47437i	−0.253360	−	0.231056i
$376$		−	0.613493i		−	0.0316385i
$377$		−	0.116406i		−	0.00599522i
$378$	27.6609	−	36.5859i	1.42273	−	1.88177i
$379$	−4.56799			−0.234642			−0.117321	−	0.993094i	$-0.537431\pi$
$379$	−4.56799			−0.234642			−0.117321	+	0.993094i	$0.537431\pi$
$380$	−30.4043			−1.55971
$381$	−2.72921	−	2.48895i	−0.139822	−	0.127513i
$382$		−	0.642026i		−	0.0328489i
$383$			35.9644i			1.83769i	0.394615	+	0.918846i	$0.370878\pi$
$383$			35.9644i			1.83769i	−0.394615	+	0.918846i	$0.629122\pi$
$384$	2.72451	−	2.98751i	0.139034	−	0.152456i
$385$	−48.1840	+	12.6259i	−2.45569	+	0.643474i
$386$			8.36279i			0.425655i
$387$	−7.42981	+	0.685641i	−0.377678	+	0.0348531i
$388$	−12.0910			−0.613828
$389$			2.88440i			0.146245i	0.997323	+	0.0731225i	$0.0232964\pi$
$389$			2.88440i			0.146245i	−0.997323	+	0.0731225i	$0.976704\pi$
$390$	−7.64711	+	8.38529i	−0.387226	+	0.424606i
$391$		−	0.218733i		−	0.0110618i
$392$	−3.87199			−0.195565
$393$	12.5114	−	13.7191i	0.631116	−	0.692039i
$394$	−22.4275			−1.12988
$395$	−2.45719			−0.123635
$396$	6.28533	+	17.3103i	0.315850	+	0.869877i
$397$	16.1879			0.812448			0.406224	−	0.913773i	$-0.366845\pi$
$397$	16.1879			0.812448			0.406224	+	0.913773i	$0.366845\pi$
$398$	25.7582			1.29114
$399$	−25.8281	+	28.3213i	−1.29302	+	1.41784i
$400$	26.2896			1.31448
$401$		−	25.7848i		−	1.28763i	−0.765180	−	0.643816i	$-0.777350\pi$
$401$		−	25.7848i		−	1.28763i	0.765180	−	0.643816i	$-0.222650\pi$
$402$	19.1219	−	20.9678i	0.953714	−	1.04578i
$403$		−	9.05538i		−	0.451080i
$404$	14.4537			0.719098
$405$	5.49935	+	29.5425i	0.273265	+	1.46798i
$406$		−	1.02750i		−	0.0509938i
$407$	−35.2644	+	9.24049i	−1.74799	+	0.458034i
$408$	−0.0776266	+	0.0851201i	−0.00384309	+	0.00421407i
$409$		−	31.5453i		−	1.55982i	−0.625894	−	0.779908i	$-0.715266\pi$
$409$		−	31.5453i		−	1.55982i	0.625894	−	0.779908i	$-0.284734\pi$
$410$			35.9365i			1.77478i
$411$	−8.56252	−	7.80873i	−0.422358	−	0.385176i
$412$	14.7831			0.728310
$413$	−26.4805			−1.30302
$414$	5.64120	−	0.520584i	0.277250	−	0.0255853i
$415$		−	32.6544i		−	1.60294i
$416$		−	7.80584i		−	0.382713i
$417$	−5.30930	−	4.84190i	−0.259997	−	0.237109i
$418$	−8.11648	−	30.9749i	−0.396990	−	1.51503i
$419$		−	9.75874i		−	0.476746i	−0.971174	−	0.238373i	$-0.923386\pi$
$419$		−	9.75874i		−	0.476746i	0.971174	−	0.238373i	$-0.0766140\pi$
$420$	−32.4430	+	35.5748i	−1.58306	+	1.73587i
$421$	−10.2968			−0.501833			−0.250916	−	0.968009i	$-0.580732\pi$
$421$	−10.2968			−0.501833			−0.250916	+	0.968009i	$0.580732\pi$
$422$			53.7257i			2.61533i
$423$	−6.26321	+	0.577984i	−0.304527	+	0.0281025i
$424$		−	3.28226i		−	0.159400i
$425$	−1.39750			−0.0677887
$426$	−28.3420	−	25.8470i	−1.37318	−	1.25229i
$427$	48.0374			2.32469
$428$	−25.4900			−1.23211
$429$	−5.08711	−	2.66858i	−0.245608	−	0.128840i
$430$	16.2960			0.785862
$431$	8.65767			0.417025			0.208513	−	0.978020i	$-0.433138\pi$
$431$	8.65767			0.417025			0.208513	+	0.978020i	$0.433138\pi$
$432$	−17.7233	−	13.3998i	−0.852713	−	0.644698i
$433$	7.29053			0.350361			0.175180	−	0.984536i	$-0.443949\pi$
$433$	7.29053			0.350361			0.175180	+	0.984536i	$0.443949\pi$
$434$		−	79.9303i		−	3.83678i
$435$	0.497409	+	0.453620i	0.0238489	+	0.0217494i
$436$		−	12.4694i		−	0.597176i
$437$	−4.73439			−0.226476
$438$	−11.0927	−	10.1162i	−0.530031	−	0.483371i
$439$		−	3.03896i		−	0.145042i	−0.997367	−	0.0725209i	$-0.976896\pi$
$439$		−	3.03896i		−	0.145042i	0.997367	−	0.0725209i	$-0.0231044\pi$
$440$	0.821352	+	3.13452i	0.0391564	+	0.149432i
$441$	3.64788	+	39.5295i	0.173709	+	1.88236i
$442$			0.446051i			0.0212165i
$443$			0.971646i			0.0461643i	0.999734	+	0.0230821i	$0.00734793\pi$
$443$			0.971646i			0.0461643i	−0.999734	+	0.0230821i	$0.992652\pi$
$444$	−23.7441	+	26.0361i	−1.12684	+	1.23562i
$445$	38.1788			1.80985
$446$	28.2546			1.33790
$447$	1.98160	−	2.17289i	0.0937266	−	0.102774i
$448$		−	30.4336i		−	1.43785i
$449$		−	13.4661i		−	0.635506i	−0.948174	−	0.317753i	$-0.897072\pi$
$449$		−	13.4661i		−	0.635506i	0.948174	−	0.317753i	$-0.102928\pi$
$450$	−3.32604	−	36.0419i	−0.156791	−	1.69903i
$451$	−17.5966	+	4.61091i	−0.828592	+	0.217120i
$452$			11.4754i			0.539755i
$453$	−6.71495	−	6.12381i	−0.315496	−	0.287722i
$454$	−27.0037			−1.26735
$455$		−	15.0185i		−	0.704079i
$456$	1.84239	+	1.68019i	0.0862776	+	0.0786823i
$457$		−	18.5457i		−	0.867532i	−0.901025	−	0.433766i	$-0.857184\pi$
$457$		−	18.5457i		−	0.867532i	0.901025	−	0.433766i	$-0.142816\pi$
$458$	1.24370			0.0581142
$459$	0.942133	+	0.712305i	0.0439750	+	0.0332475i
$460$	−5.94694			−0.277277
$461$	4.20525			0.195858			0.0979290	−	0.995193i	$-0.468778\pi$
$461$	4.20525			0.195858			0.0979290	+	0.995193i	$0.468778\pi$
$462$	−44.9031	−	23.5551i	−2.08908	−	1.09588i
$463$	35.1489			1.63351			0.816753	−	0.576987i	$-0.195772\pi$
$463$	35.1489			1.63351			0.816753	+	0.576987i	$0.195772\pi$
$464$	−0.497751			−0.0231075
$465$	38.6941	+	35.2877i	1.79439	+	1.63643i
$466$	−29.8947			−1.38484
$467$			15.9155i			0.736482i	0.929730	+	0.368241i	$0.120040\pi$
$467$			15.9155i			0.736482i	−0.929730	+	0.368241i	$0.879960\pi$
$468$	−5.52917	+	0.510246i	−0.255586	+	0.0235861i
$469$			37.5544i			1.73410i
$470$	13.7372			0.633652
$471$	−6.61152	+	7.24974i	−0.304643	+	0.334050i
$472$			1.72264i			0.0792908i
$473$	2.09089	+	7.97947i	0.0961394	+	0.366896i
$474$	−1.84821	−	1.68551i	−0.0848913	−	0.0774180i
$475$			30.2483i			1.38789i
$476$			1.89238i			0.0867372i
$477$	−33.5089	+	3.09228i	−1.53427	+	0.141586i
$478$	2.68076			0.122615
$479$	−18.7119			−0.854971			−0.427485	−	0.904022i	$-0.640600\pi$
$479$	−18.7119			−0.854971			−0.427485	+	0.904022i	$0.640600\pi$
$480$	33.3547	+	30.4184i	1.52243	+	1.38840i
$481$		−	10.9916i		−	0.501174i
$482$		−	19.7333i		−	0.898826i
$483$	−5.05185	+	5.53951i	−0.229867	+	0.252056i
$484$	17.7435	−	9.98437i	0.806524	−	0.453835i
$485$			21.8114i			0.990406i
$486$	−16.1283	+	25.9932i	−0.731594	+	1.17907i
$487$	−13.4584			−0.609858			−0.304929	−	0.952375i	$-0.598633\pi$
$487$	−13.4584			−0.609858			−0.304929	+	0.952375i	$0.598633\pi$
$488$		−	3.12498i		−	0.141461i
$489$	−2.84905	+	3.12407i	−0.128838	+	0.141275i
$490$		−	86.7011i		−	3.91676i
$491$	39.8220			1.79714			0.898571	−	0.438828i	$-0.144606\pi$
$491$	39.8220			1.79714			0.898571	+	0.438828i	$0.144606\pi$
$492$	−11.8481	+	12.9918i	−0.534152	+	0.585714i
$493$	0.0264594			0.00119167
$494$	9.65458			0.434380
$495$	31.2268	−	11.3384i	1.40354	−	0.509621i
$496$	−38.7207			−1.73861
$497$	50.7622			2.27699
$498$	22.3993	−	24.5615i	1.00374	−	1.10063i
$499$	−28.7427			−1.28670			−0.643350	−	0.765572i	$-0.722456\pi$
$499$	−28.7427			−1.28670			−0.643350	+	0.765572i	$0.722456\pi$
$500$			7.09575i			0.317331i
$501$	12.9995	−	14.2544i	0.580777	−	0.636840i
$502$			3.34838i			0.149445i
$503$	16.2333			0.723805			0.361903	−	0.932216i	$-0.382127\pi$
$503$	16.2333			0.723805			0.361903	+	0.932216i	$0.382127\pi$
$504$	3.93185	−	0.362841i	0.175139	−	0.0161622i
$505$		−	26.0736i		−	1.16026i
$506$	−1.58754	−	6.05854i	−0.0705750	−	0.269335i
$507$	1.16712	−	1.27978i	0.0518335	−	0.0568370i
$508$			3.94713i			0.175126i
$509$			23.7473i			1.05258i	0.850305	+	0.526291i	$0.176418\pi$
$509$			23.7473i			1.05258i	−0.850305	+	0.526291i	$0.823582\pi$
$510$	−1.90600	−	1.73821i	−0.0843990	−	0.0769690i
$511$	19.8677			0.878894
$512$	−30.8753			−1.36451
$513$	15.4175	−	20.3920i	0.680700	−	0.900331i
$514$		−	11.7149i		−	0.516721i
$515$		−	26.6678i		−	1.17512i
$516$	5.89133	+	5.37270i	0.259351	+	0.236520i
$517$	1.76259	+	6.72656i	0.0775186	+	0.295834i
$518$		−	97.0210i		−	4.26286i
$519$	−19.7427	+	21.6485i	−0.866608	+	0.950263i
$520$	−0.977001			−0.0428443
$521$		−	6.08284i		−	0.266494i	−0.991083	−	0.133247i	$-0.957460\pi$
$521$		−	6.08284i		−	0.266494i	0.991083	−	0.133247i	$-0.0425403\pi$
$522$	0.0629731	+	0.682395i	0.00275626	+	0.0298676i
$523$			15.4461i			0.675409i	0.941252	+	0.337705i	$0.109651\pi$
$523$			15.4461i			0.675409i	−0.941252	+	0.337705i	$0.890349\pi$
$524$	−19.8414			−0.866774
$525$	35.3922	+	32.2765i	1.54464	+	1.40866i
$526$	23.3289			1.01719
$527$	2.05831			0.0896613
$528$	−11.4108	+	21.7524i	−0.496592	+	0.946653i
$529$	22.0740			0.959738
$530$	73.4958			3.19245
$531$	17.5866	−	1.62293i	0.763192	−	0.0704292i
$532$	40.9598			1.77583
$533$		−	5.48470i		−	0.237569i
$534$	28.7168	+	26.1888i	1.24270	+	1.13330i
$535$			45.9825i			1.98800i
$536$	2.44303			0.105523
$537$	10.0272	+	9.14445i	0.432705	+	0.394612i
$538$			26.0436i			1.12282i
$539$	42.4539	−	11.1244i	1.82862	−	0.479161i
$540$	19.3662	−	25.6148i	0.833388	−	1.10228i
$541$			13.4203i			0.576986i	0.957482	+	0.288493i	$0.0931542\pi$
$541$			13.4203i			0.576986i	−0.957482	+	0.288493i	$0.906846\pi$
$542$			13.1783i			0.566056i
$543$	25.7442	−	28.2293i	1.10479	−	1.21144i
$544$	1.77429			0.0760719
$545$	−22.4941			−0.963540
$546$	10.3020	−	11.2964i	0.440883	−	0.483442i
$547$		−	18.2678i		−	0.781074i	−0.920587	−	0.390537i	$-0.872289\pi$
$547$		−	18.2678i		−	0.781074i	0.920587	−	0.390537i	$-0.127711\pi$
$548$			12.3836i			0.529001i
$549$	−31.9033	+	2.94411i	−1.36160	+	0.125652i
$550$	−38.7083	+	10.1429i	−1.65053	+	0.432495i
$551$		−	0.572701i		−	0.0243979i
$552$	0.360362	+	0.328638i	0.0153380	+	0.0139878i
$553$	3.31025			0.140766
$554$		−	45.9416i		−	1.95187i
$555$	46.9676	+	42.8329i	1.99366	+	1.81815i
$556$			7.67860i			0.325645i
$557$	31.2064			1.32226			0.661129	−	0.750272i	$-0.270078\pi$
$557$	31.2064			1.32226			0.661129	+	0.750272i	$0.270078\pi$
$558$	4.89876	+	53.0844i	0.207381	+	2.24724i
$559$	−2.48713			−0.105194
$560$	−64.2190			−2.71375
$561$	0.606574	−	1.15631i	0.0256096	−	0.0488195i
$562$	−36.1753			−1.52596
$563$	−17.7519			−0.748152			−0.374076	−	0.927398i	$-0.622040\pi$
$563$	−17.7519			−0.748152			−0.374076	+	0.927398i	$0.622040\pi$
$564$	4.96629	+	4.52909i	0.209119	+	0.190709i
$565$	20.7009			0.870891
$566$			26.5544i			1.11616i
$567$	−7.40856	−	39.7988i	−0.311130	−	1.67139i
$568$		−	3.30223i		−	0.138559i
$569$	−27.2072			−1.14059			−0.570293	−	0.821441i	$-0.693170\pi$
$569$	−27.2072			−1.14059			−0.570293	+	0.821441i	$0.693170\pi$
$570$	−37.6227	+	41.2545i	−1.57584	+	1.72796i
$571$			6.36586i			0.266403i	0.991089	+	0.133201i	$0.0425257\pi$
$571$			6.36586i			0.266403i	−0.991089	+	0.133201i	$0.957474\pi$
$572$	1.55602	+	5.93822i	0.0650604	+	0.248289i
$573$	−0.418705	−	0.381845i	−0.0174916	−	0.0159518i
$574$		−	48.4125i		−	2.02070i
$575$			5.91642i			0.246732i
$576$	1.86521	+	20.2120i	0.0777171	+	0.842166i
$577$	−46.5370			−1.93736			−0.968680	−	0.248314i	$-0.920124\pi$
$577$	−46.5370			−1.93736			−0.968680	+	0.248314i	$0.920124\pi$
$578$	33.2589			1.38339
$579$	5.45389	+	4.97376i	0.226656	+	0.206703i
$580$		−	0.719379i		−	0.0298706i
$581$			43.9910i			1.82506i
$582$	−14.9616	+	16.4058i	−0.620177	+	0.680043i
$583$	9.43006	+	35.9879i	0.390553	+	1.49047i
$584$		−	1.29245i		−	0.0534821i
$585$	0.920452	+	9.97429i	0.0380560	+	0.412386i
$586$	32.0431			1.32369
$587$		−	40.4692i		−	1.67034i	−0.549989	−	0.835172i	$-0.685368\pi$
$587$		−	40.4692i		−	1.67034i	0.549989	−	0.835172i	$-0.314632\pi$
$588$	28.5849	−	31.3442i	1.17882	−	1.29261i
$589$		−	44.5512i		−	1.83570i
$590$	−38.5730			−1.58803
$591$	−13.3388	+	14.6264i	−0.548683	+	0.601648i
$592$	−46.9999			−1.93169
$593$	−18.7098			−0.768320			−0.384160	−	0.923266i	$-0.625509\pi$
$593$	−18.7098			−0.768320			−0.384160	+	0.923266i	$0.625509\pi$
$594$	31.2653	+	12.8917i	1.28283	+	0.528953i
$595$	3.41374			0.139950
$596$	−3.14255			−0.128724
$597$	15.3197	−	16.7985i	0.626992	−	0.687516i
$598$	1.88839			0.0772220
$599$			24.3812i			0.996188i	0.867123	+	0.498094i	$0.165967\pi$
$599$			24.3812i			0.996188i	−0.867123	+	0.498094i	$0.834033\pi$
$600$	2.09969	−	2.30237i	0.0857194	−	0.0939940i
$601$		−	20.6198i		−	0.841099i	−0.907270	−	0.420550i	$-0.861837\pi$
$601$		−	20.6198i		−	0.841099i	0.907270	−	0.420550i	$-0.138163\pi$
$602$	−21.9535			−0.894756
$603$	−2.30163	−	24.9411i	−0.0937296	−	1.01568i
$604$			9.71152i			0.395156i
$605$	−18.0112	−	32.0083i	−0.732260	−	1.30132i
$606$	17.8852	−	19.6117i	0.726536	−	0.796669i
$607$			14.9862i			0.608271i	0.952629	+	0.304136i	$0.0983676\pi$
$607$			14.9862i			0.608271i	−0.952629	+	0.304136i	$0.901632\pi$
$608$		−	38.4036i		−	1.55747i
$609$	−0.670094	−	0.611103i	−0.0271536	−	0.0247632i
$610$	69.9742			2.83317
$611$	−2.09661			−0.0848196
$612$	−0.115980	−	1.25679i	−0.00468821	−	0.0508029i
$613$		−	35.9070i		−	1.45027i	−0.688606	−	0.725136i	$-0.741777\pi$
$613$		−	35.9070i		−	1.45027i	0.688606	−	0.725136i	$-0.258223\pi$
$614$		−	36.1400i		−	1.45849i
$615$	23.4364	+	21.3732i	0.945046	+	0.861850i
$616$	−1.10650	−	4.22273i	−0.0445822	−	0.170139i
$617$		−	17.3461i		−	0.698326i	−0.937062	−	0.349163i	$-0.886466\pi$
$617$		−	17.3461i		−	0.698326i	0.937062	−	0.349163i	$-0.113534\pi$
$618$	18.2928	−	20.0586i	0.735843	−	0.806875i
$619$	−3.44227			−0.138356			−0.0691782	−	0.997604i	$-0.522038\pi$
$619$	−3.44227			−0.138356			−0.0691782	+	0.997604i	$0.522038\pi$
$620$		−	55.9614i		−	2.24747i
$621$	3.01559	−	3.98859i	0.121012	−	0.160057i
$622$		−	6.10013i		−	0.244593i
$623$	−51.4334			−2.06063
$624$	−5.47233	−	4.99058i	−0.219068	−	0.199783i
$625$	−17.9407			−0.717627
$626$	−47.9655			−1.91709
$627$	−25.0279	−	13.1290i	−0.999517	−	0.524323i
$628$	10.4850			0.418396
$629$	2.49842			0.0996184
$630$	8.12468	+	88.0415i	0.323695	+	3.50766i
$631$	10.8671			0.432612			0.216306	−	0.976326i	$-0.430599\pi$
$631$	10.8671			0.432612			0.216306	+	0.976326i	$0.430599\pi$
$632$		−	0.215342i		−	0.00856584i
$633$	35.0378	+	31.9533i	1.39263	+	1.27003i
$634$		−	3.35810i		−	0.133367i
$635$	7.12039			0.282564
$636$	26.5702	+	24.2312i	1.05358	+	0.960829i
$637$			13.2325i			0.524291i
$638$	0.732879	−	0.192039i	0.0290149	−	0.00760291i
$639$	−33.7128	+	3.11110i	−1.33366	+	0.123073i
$640$			7.79428i			0.308096i
$641$		−	42.4990i		−	1.67861i	−0.543662	−	0.839304i	$-0.682963\pi$
$641$		−	42.4990i		−	1.67861i	0.543662	−	0.839304i	$-0.317037\pi$
$642$	−31.5417	+	34.5865i	−1.24485	+	1.36502i
$643$	39.0292			1.53916			0.769581	−	0.638549i	$-0.220465\pi$
$643$	39.0292			1.53916			0.769581	+	0.638549i	$0.220465\pi$
$644$	8.01154			0.315699
$645$	9.69202	−	10.6276i	0.381623	−	0.418462i
$646$			2.19451i			0.0863417i
$647$			49.8914i			1.96143i	0.195439	+	0.980716i	$0.437387\pi$
$647$			49.8914i			1.96143i	−0.195439	+	0.980716i	$0.562613\pi$
$648$	−2.58903	+	0.481949i	−0.101707	+	0.0189328i
$649$	−4.94921	−	18.8876i	−0.194273	−	0.741404i
$650$		−	12.0650i		−	0.473229i
$651$	−52.1275	−	47.5385i	−2.04304	−	1.86318i
$652$	4.51820			0.176946
$653$			24.7317i			0.967827i	0.875116	+	0.483913i	$0.160785\pi$
$653$			24.7317i			0.967827i	−0.875116	+	0.483913i	$0.839215\pi$
$654$	−16.9193	−	15.4298i	−0.661596	−	0.603353i
$655$			35.7926i			1.39853i
$656$	−23.4525			−0.915667
$657$	−13.1948	+	1.21765i	−0.514778	+	0.0475049i
$658$	−18.5064			−0.721455
$659$	3.82795			0.149116			0.0745578	−	0.997217i	$-0.476245\pi$
$659$	3.82795			0.149116			0.0745578	+	0.997217i	$0.476245\pi$
$660$	−31.4379	−	16.4916i	−1.22372	−	0.641934i
$661$	−9.96741			−0.387687			−0.193844	−	0.981032i	$-0.562095\pi$
$661$	−9.96741			−0.387687			−0.193844	+	0.981032i	$0.562095\pi$
$662$	−23.6311			−0.918450
$663$	0.290897	+	0.265288i	0.0112975	+	0.0103029i
$664$	2.86175			0.111058
$665$		−	73.8890i		−	2.86529i
$666$	5.94621	+	64.4349i	0.230411	+	2.49680i
$667$		−	0.112018i		−	0.00433734i
$668$	−20.6155			−0.797638
$669$	16.8044	−	18.4266i	0.649696	−	0.712413i
$670$			54.7040i			2.11340i
$671$	8.97820	+	34.2635i	0.346600	+	1.32273i
$672$	−44.9345	−	40.9788i	−1.73339	−	1.58079i
$673$			50.8102i			1.95859i	0.202439	+	0.979295i	$0.435113\pi$
$673$			50.8102i			1.95859i	−0.202439	+	0.979295i	$0.564887\pi$
$674$			31.6400i			1.21873i
$675$	−25.4833	−	19.2668i	−0.980853	−	0.741579i
$676$	−1.85089			−0.0711880
$677$	9.94541			0.382233			0.191117	−	0.981567i	$-0.438789\pi$
$677$	9.94541			0.382233			0.191117	+	0.981567i	$0.438789\pi$
$678$	15.5705	+	14.1998i	0.597980	+	0.545338i
$679$		−	29.3837i		−	1.12764i
$680$		−	0.222075i		−	0.00851617i
$681$	−16.0604	+	17.6108i	−0.615436	+	0.674845i
$682$	57.0116	−	14.9390i	2.18309	−	0.572044i
$683$			29.2703i			1.12000i	0.828493	+	0.559999i	$0.189199\pi$
$683$			29.2703i			1.12000i	−0.828493	+	0.559999i	$0.810801\pi$
$684$	−27.2027	+	2.51034i	−1.04012	+	0.0959851i
$685$	22.3392			0.853539
$686$			55.0132i			2.10041i
$687$	0.739688	−	0.811091i	0.0282209	−	0.0309451i
$688$			10.6349i			0.405453i
$689$	−11.2171			−0.427337
$690$	−7.35882	+	8.06918i	−0.280145	+	0.307188i
$691$	−3.66671			−0.139488			−0.0697441	−	0.997565i	$-0.522218\pi$
$691$	−3.66671			−0.139488			−0.0697441	+	0.997565i	$0.522218\pi$
$692$	31.3092			1.19020
$693$	−42.0678	+	15.2747i	−1.59802	+	0.580238i
$694$	60.2274			2.28620
$695$	13.8517			0.525426
$696$	−0.0397541	+	0.0435917i	−0.00150688	+	0.00165234i
$697$	1.24668			0.0472216
$698$			23.3540i			0.883961i
$699$	−17.7798	+	19.4961i	−0.672495	+	0.737412i
$700$		−	51.1862i		−	1.93465i
$701$	10.3199			0.389778			0.194889	−	0.980825i	$-0.437565\pi$
$701$	10.3199			0.389778			0.194889	+	0.980825i	$0.437565\pi$
$702$	−6.14953	+	8.13371i	−0.232099	+	0.306987i
$703$		−	54.0771i		−	2.03956i
$704$	21.7073	−	5.68805i	0.818123	−	0.214376i
$705$	8.17021	−	8.95890i	0.307708	−	0.337412i
$706$			5.37289i			0.202211i
$707$			35.1255i			1.32103i
$708$	−13.9449	−	12.7173i	−0.524083	−	0.477946i
$709$	46.3537			1.74085			0.870425	−	0.492301i	$-0.163844\pi$
$709$	46.3537			1.74085			0.870425	+	0.492301i	$0.163844\pi$
$710$	73.9432			2.77504
$711$	−2.19845	+	0.202878i	−0.0824482	+	0.00760852i
$712$			3.34590i			0.125393i
$713$		−	8.71400i		−	0.326342i
$714$	2.56770	+	2.34166i	0.0960938	+	0.0876344i
$715$	10.7122	−	2.80696i	0.400613	−	0.104974i
$716$		−	14.5019i		−	0.541960i
$717$	1.59438	−	1.74828i	0.0595431	−	0.0652909i
$718$	−46.1855			−1.72363
$719$			29.8196i			1.11208i	0.831154	+	0.556042i	$0.187681\pi$
$719$			29.8196i			1.11208i	−0.831154	+	0.556042i	$0.812319\pi$
$720$	42.6500	−	3.93584i	1.58947	−	0.146680i
$721$			35.9260i			1.33795i
$722$	10.2142			0.380132
$723$	−12.8693	−	11.7364i	−0.478614	−	0.436480i
$724$	−40.8268			−1.51732
$725$	−0.715687			−0.0265799
$726$	8.40865	−	36.4303i	0.312074	−	1.35206i
$727$	−24.9030			−0.923601			−0.461801	−	0.886984i	$-0.652796\pi$
$727$	−24.9030			−0.923601			−0.461801	+	0.886984i	$0.652796\pi$
$728$	1.31619			0.0487811
$729$	7.35945	+	25.9777i	0.272572	+	0.962135i
$730$	28.9404			1.07113
$731$		−	0.565329i		−	0.0209095i
$732$	25.2971	+	23.0701i	0.935008	+	0.852696i
$733$			26.0707i			0.962945i	0.876461	+	0.481472i	$0.159898\pi$
$733$			26.0707i			0.962945i	−0.876461	+	0.481472i	$0.840102\pi$
$734$	44.8552			1.65564
$735$	−56.5431	−	51.5654i	−2.08562	−	1.90202i
$736$		−	7.51157i		−	0.276880i
$737$	−26.7863	+	7.01893i	−0.986686	+	0.258545i
$738$	2.96710	+	32.1524i	0.109220	+	1.18355i
$739$			14.9215i			0.548895i	0.961602	+	0.274447i	$0.0884949\pi$
$739$			14.9215i			0.548895i	−0.961602	+	0.274447i	$0.911505\pi$
$740$		−	67.9271i		−	2.49705i
$741$	5.74205	−	6.29634i	0.210940	−	0.231302i
$742$	−99.0114			−3.63482
$743$	43.1870			1.58438			0.792188	−	0.610277i	$-0.208942\pi$
$743$	43.1870			1.58438			0.792188	+	0.610277i	$0.208942\pi$
$744$	−3.09253	+	3.39105i	−0.113378	+	0.124322i
$745$			5.66897i			0.207695i
$746$		−	51.3895i		−	1.88150i
$747$	−2.69612	−	29.2159i	−0.0986457	−	1.06895i
$748$	−1.34977	+	0.353686i	−0.0493525	+	0.0129321i
$749$		−	61.9463i		−	2.26347i
$750$	9.62795	+	8.78037i	0.351563	+	0.320614i
$751$	−9.93547			−0.362551			−0.181275	−	0.983432i	$-0.558022\pi$
$751$	−9.93547			−0.362551			−0.181275	+	0.983432i	$0.558022\pi$
$752$			8.96506i			0.326922i
$753$	2.18368	+	1.99145i	0.0795778	+	0.0725723i
$754$			0.228431i			0.00831898i
$755$	17.5190			0.637582
$756$	−26.0896	+	34.5075i	−0.948868	+	1.25502i
$757$	−10.3121			−0.374799			−0.187400	−	0.982284i	$-0.560006\pi$
$757$	−10.3121			−0.374799			−0.187400	+	0.982284i	$0.560006\pi$
$758$	8.96407			0.325590
$759$	−4.89533	−	2.56797i	−0.177689	−	0.0932116i
$760$	−4.80671			−0.174358
$761$	24.8011			0.899039			0.449520	−	0.893270i	$-0.351595\pi$
$761$	24.8011			0.899039			0.449520	+	0.893270i	$0.351595\pi$
$762$	5.35571	+	4.88423i	0.194017	+	0.176937i
$763$	30.3033			1.09705
$764$			0.605554i			0.0219082i
$765$	−2.26718	+	0.209221i	−0.0819701	+	0.00756440i
$766$		−	70.5753i		−	2.54999i
$767$	5.88710			0.212571
$768$	−21.1398	+	23.1805i	−0.762817	+	0.836453i
$769$		−	2.42597i		−	0.0874829i	−0.999043	−	0.0437414i	$-0.986072\pi$
$769$		−	2.42597i		−	0.0874829i	0.999043	−	0.0437414i	$-0.0139278\pi$
$770$	94.5548	−	24.7766i	3.40752	−	0.892887i
$771$	−7.63998	−	6.96741i	−0.275147	−	0.250925i
$772$		−	7.88771i		−	0.283885i
$773$		−	2.75882i		−	0.0992280i	−0.998768	−	0.0496140i	$-0.984201\pi$
$773$		−	2.75882i		−	0.0992280i	0.998768	−	0.0496140i	$-0.0157991\pi$
$774$	14.5800	−	1.34548i	0.524068	−	0.0483623i
$775$	−55.6742			−1.99988
$776$	−1.91150			−0.0686189
$777$	−63.2734	−	57.7032i	−2.26992	−	2.07009i
$778$		−	5.66026i		−	0.202930i
$779$		−	26.9839i		−	0.966800i
$780$	7.21268	−	7.90893i	0.258255	−	0.283185i
$781$	9.48745	+	36.2069i	0.339488	+	1.29559i
$782$			0.429235i			0.0153494i
$783$	0.482485	+	0.364785i	0.0172426	+	0.0130364i
$784$	56.5820			2.02079
$785$		−	18.9142i		−	0.675078i
$786$	−24.5520	+	26.9220i	−0.875739	+	0.960276i
$787$		−	25.6255i		−	0.913451i	−0.889608	−	0.456726i	$-0.849022\pi$
$787$		−	25.6255i		−	0.913451i	0.889608	−	0.456726i	$-0.150978\pi$
$788$	21.1535			0.753561
$789$	13.8748	−	15.2142i	0.493958	−	0.541640i
$790$	4.82191			0.171556
$791$	−27.8876			−0.991568
$792$	0.993666	+	2.73664i	0.0353084	+	0.0972423i
$793$	−10.6796			−0.379244
$794$	−31.7667			−1.12736
$795$	43.7116	−	47.9311i	1.55029	−	1.69994i
$796$	−24.2949			−0.861109
$797$		−	53.7276i		−	1.90313i	−0.307451	−	0.951564i	$-0.599476\pi$
$797$		−	53.7276i		−	1.90313i	0.307451	−	0.951564i	$-0.400524\pi$
$798$	50.6842	−	55.5768i	1.79420	−	1.96740i
$799$		−	0.476563i		−	0.0168596i
$800$	−47.9918			−1.69677
$801$	34.1586	−	3.15224i	1.20693	−	0.111379i
$802$			50.5993i			1.78672i
$803$	3.71327	+	14.1709i	0.131039	+	0.500081i
$804$	−18.0356	+	19.7766i	−0.636067	+	0.697468i
$805$		−	14.4523i		−	0.509378i
$806$			17.7700i			0.625921i
$807$	16.9846	+	15.4894i	0.597886	+	0.545252i
$808$	2.28502			0.0803869
$809$	−21.2337			−0.746538			−0.373269	−	0.927723i	$-0.621763\pi$
$809$	−21.2337			−0.746538			−0.373269	+	0.927723i	$0.621763\pi$
$810$	−10.7917	−	57.9733i	−0.379183	−	2.03697i
$811$		−	34.6958i		−	1.21834i	−0.793041	−	0.609168i	$-0.791504\pi$
$811$		−	34.6958i		−	1.21834i	0.793041	−	0.609168i	$-0.208496\pi$
$812$			0.969126i			0.0340097i
$813$	8.59437	+	7.83778i	0.301418	+	0.274883i
$814$	69.2018	−	18.1332i	2.42552	−	0.635570i
$815$		−	8.15056i		−	0.285502i
$816$	1.13437	−	1.24387i	0.0397109	−	0.0435443i
$817$	−12.2363			−0.428094
$818$			61.9035i			2.16441i
$819$	−1.24001	−	13.4371i	−0.0433293	−	0.469529i
$820$		−	33.8950i		−	1.18366i
$821$	45.3844			1.58393			0.791964	−	0.610568i	$-0.209059\pi$
$821$	45.3844			1.58393			0.791964	+	0.610568i	$0.209059\pi$
$822$	16.8028	+	15.3236i	0.586066	+	0.534472i
$823$	18.2089			0.634721			0.317361	−	0.948305i	$-0.397203\pi$
$823$	18.2089			0.634721			0.317361	+	0.948305i	$0.397203\pi$
$824$	2.33710			0.0814167
$825$	−16.4069	+	31.2766i	−0.571216	+	1.08891i
$826$	51.9644			1.80807
$827$	−35.2704			−1.22647			−0.613236	−	0.789900i	$-0.710133\pi$
$827$	−35.2704			−1.22647			−0.613236	+	0.789900i	$0.710133\pi$
$828$	−5.32073	+	0.491010i	−0.184908	+	0.0170638i
$829$	−42.2297			−1.46670			−0.733349	−	0.679852i	$-0.762044\pi$
$829$	−42.2297			−1.46670			−0.733349	+	0.679852i	$0.762044\pi$
$830$			64.0800i			2.22425i
$831$	−29.9613	−	27.3237i	−1.03935	−	0.947849i
$832$			6.76595i			0.234567i
$833$	−3.00778			−0.104213
$834$	10.4188	+	9.50159i	0.360773	+	0.329013i
$835$			37.1891i			1.28698i
$836$	7.65539	+	29.2152i	0.264767	+	1.01043i
$837$	37.5331	+	28.3771i	1.29733	+	0.980857i
$838$			19.1502i			0.661534i
$839$			35.3752i			1.22129i	0.791905	+	0.610644i	$0.209089\pi$
$839$			35.3752i			1.22129i	−0.791905	+	0.610644i	$0.790911\pi$
$840$	−5.12901	+	5.62413i	−0.176968	+	0.194051i
$841$	−28.9864			−0.999533
$842$	20.2060			0.696345
$843$	−21.5153	+	23.5922i	−0.741025	+	0.812557i
$844$		−	50.6736i		−	1.74426i
$845$			3.33889i			0.114861i
$846$	12.2907	−	1.13422i	0.422563	−	0.0389952i
$847$	24.2642	+	43.1206i	0.833726	+	1.48164i
$848$			47.9641i			1.64709i
$849$	17.3178	+	15.7932i	0.594344	+	0.542022i
$850$	2.74241			0.0940638
$851$		−	10.5772i		−	0.362583i
$852$	26.7320	+	24.3787i	0.915822	+	0.835199i
$853$			1.80344i			0.0617487i	0.999523	+	0.0308743i	$0.00982917\pi$
$853$			1.80344i			0.0617487i	−0.999523	+	0.0308743i	$0.990171\pi$
$854$	−94.2671			−3.22576
$855$	4.52850	+	49.0721i	0.154871	+	1.67823i
$856$	−4.02979			−0.137736
$857$	40.5768			1.38608			0.693038	−	0.720901i	$-0.256272\pi$
$857$	40.5768			1.38608			0.693038	+	0.720901i	$0.256272\pi$
$858$	9.98278	+	5.23673i	0.340807	+	0.178779i
$859$	34.7071			1.18419			0.592095	−	0.805868i	$-0.298301\pi$
$859$	34.7071			1.18419			0.592095	+	0.805868i	$0.298301\pi$
$860$	−15.3702			−0.524120
$861$	−31.5728	−	28.7933i	−1.07600	−	0.981274i
$862$	−16.9895			−0.578666
$863$		−	15.5300i		−	0.528646i	−0.964434	−	0.264323i	$-0.914852\pi$
$863$		−	15.5300i		−	0.528646i	0.964434	−	0.264323i	$-0.0851485\pi$
$864$	32.3540	+	24.4614i	1.10070	+	0.832194i
$865$		−	56.4799i		−	1.92038i
$866$	−14.3067			−0.486162
$867$	19.7807	−	21.6901i	0.671787	−	0.736636i
$868$			75.3896i			2.55889i
$869$	0.618686	+	2.36109i	0.0209875	+	0.0800945i
$870$	−0.976099	−	0.890169i	−0.0330928	−	0.0301796i
$871$		−	8.34904i		−	0.282896i
$872$		−	1.97133i		−	0.0667575i
$873$	1.80086	+	19.5147i	0.0609500	+	0.660473i
$874$	9.29061			0.314260
$875$	−17.2442			−0.582960
$876$	10.4626	+	9.54151i	0.353497	+	0.322378i
$877$			49.4532i			1.66992i	0.550313	+	0.834958i	$0.314508\pi$
$877$			49.4532i			1.66992i	−0.550313	+	0.834958i	$0.685492\pi$
$878$			5.96356i			0.201260i
$879$	19.0576	−	20.8973i	0.642798	−	0.704848i
$880$	−12.0025	−	45.8052i	−0.404606	−	1.54409i
$881$		−	0.920835i		−	0.0310237i	−0.999880	−	0.0155119i	$-0.995062\pi$
$881$		−	0.920835i		−	0.0310237i	0.999880	−	0.0155119i	$-0.00493778\pi$
$882$	−7.15849	−	77.5715i	−0.241039	−	2.61197i
$883$	40.3332			1.35732			0.678661	−	0.734452i	$-0.262561\pi$
$883$	40.3332			1.35732			0.678661	+	0.734452i	$0.262561\pi$
$884$		−	0.420711i		−	0.0141501i
$885$	−22.9413	+	25.1558i	−0.771163	+	0.845604i
$886$		−	1.90673i		−	0.0640577i
$887$	13.9977			0.469998			0.234999	−	0.971996i	$-0.424491\pi$
$887$	13.9977			0.469998			0.234999	+	0.971996i	$0.424491\pi$
$888$	−3.75377	+	4.11613i	−0.125968	+	0.138128i
$889$	−9.59238			−0.321718
$890$	−74.9209			−2.51135
$891$	27.0025	−	12.7227i	0.904617	−	0.426226i
$892$	−26.6495			−0.892292
$893$	−10.3150			−0.345179
$894$	−3.88863	+	4.26401i	−0.130055	+	0.142610i
$895$	−26.1605			−0.874448
$896$		−	10.5002i		−	0.350788i
$897$	1.12312	−	1.23153i	0.0374998	−	0.0411197i
$898$			26.4255i			0.881831i
$899$	1.05410			0.0351562
$900$	3.13709	+	33.9944i	0.104570	+	1.13315i
$901$		−	2.54967i		−	0.0849418i
$902$	34.5310	−	9.04831i	1.14976	−	0.301276i
$903$	−13.0568	+	14.3172i	−0.434503	+	0.476446i
$904$			1.81417i			0.0603385i
$905$			73.6491i			2.44818i
$906$	13.1772	+	12.0172i	0.437783	+	0.399244i
$907$	21.3742			0.709718			0.354859	−	0.934920i	$-0.384529\pi$
$907$	21.3742			0.709718			0.354859	+	0.934920i	$0.384529\pi$
$908$	25.4696			0.845239
$909$	−2.15277	−	23.3280i	−0.0714028	−	0.773742i
$910$			29.4719i			0.976982i
$911$			14.2183i			0.471072i	0.971866	+	0.235536i	$0.0756846\pi$
$911$			14.2183i			0.471072i	−0.971866	+	0.235536i	$0.924315\pi$
$912$	−26.9231	−	24.5530i	−0.891512	−	0.813029i
$913$	−31.3773	+	8.22193i	−1.03844	+	0.272106i
$914$			36.3935i			1.20379i
$915$	41.6171	−	45.6345i	1.37582	−	1.50863i
$916$	−1.17304			−0.0387585
$917$		−	48.2188i		−	1.59232i
$918$	−1.84881	−	1.39780i	−0.0610199	−	0.0461344i
$919$		−	22.1420i		−	0.730397i	−0.930930	−	0.365198i	$-0.881001\pi$
$919$		−	22.1420i		−	0.730397i	0.930930	−	0.365198i	$-0.118999\pi$
$920$	−0.940169			−0.0309964
$921$	−23.5691	−	21.4943i	−0.776630	−	0.708260i
$922$	−8.25225			−0.271773
$923$	−11.2854			−0.371462
$924$	42.3522	+	22.2170i	1.39329	+	0.730884i
$925$	−67.5785			−2.22197
$926$	−68.9750			−2.26666
$927$	−2.20183	−	23.8597i	−0.0723175	−	0.783654i
$928$	0.908647			0.0298278
$929$			0.717200i			0.0235306i	0.999931	+	0.0117653i	$0.00374509\pi$
$929$			0.717200i			0.0235306i	−0.999931	+	0.0117653i	$0.996255\pi$
$930$	−75.9320	−	69.2474i	−2.48991	−	2.27071i
$931$			65.1020i			2.13363i
$932$	28.1964			0.923603
$933$	−3.97827	−	3.62805i	−0.130243	−	0.118777i
$934$		−	31.2321i		−	1.02195i
$935$	0.638029	+	2.43491i	0.0208658	+	0.0796300i
$936$	−0.874123	+	0.0806662i	−0.0285716	+	0.00263666i
$937$			36.5868i			1.19524i	0.801780	+	0.597619i	$0.203887\pi$
$937$			36.5868i			1.19524i	−0.801780	+	0.597619i	$0.796113\pi$
$938$		−	73.6956i		−	2.40625i
$939$	−28.5275	+	31.2813i	−0.930959	+	1.02083i
$940$	−12.9568			−0.422606
$941$	−31.0674			−1.01277			−0.506384	−	0.862308i	$-0.669018\pi$
$941$	−31.0674			−1.01277			−0.506384	+	0.862308i	$0.669018\pi$
$942$	12.9742	−	14.2266i	0.422723	−	0.463529i
$943$		−	5.27793i		−	0.171873i
$944$		−	25.1732i		−	0.819317i
$945$	62.2494	+	47.0640i	2.02497	+	1.53099i
$946$	−4.10310	−	15.6586i	−0.133403	−	0.509107i
$947$			9.70964i			0.315521i	0.987477	+	0.157760i	$0.0504274\pi$
$947$			9.70964i			0.315521i	−0.987477	+	0.157760i	$0.949573\pi$
$948$	1.74322	+	1.58976i	0.0566171	+	0.0516329i
$949$	−4.41695			−0.143380
$950$		−	59.3582i		−	1.92583i
$951$	−2.19003	−	1.99723i	−0.0710165	−	0.0647646i
$952$			0.299172i			0.00969623i
$953$	34.3642			1.11317			0.556583	−	0.830792i	$-0.312112\pi$
$953$	34.3642			1.11317			0.556583	+	0.830792i	$0.312112\pi$
$954$	65.7567	−	6.06819i	2.12895	−	0.196465i
$955$	1.09238			0.0353487
$956$	−2.52846			−0.0817764
$957$	0.310638	−	0.592170i	0.0100415	−	0.0191422i
$958$	36.7197			1.18636
$959$	−30.0948			−0.971811
$960$	−28.9112	−	26.3661i	−0.933106	−	0.850962i
$961$	50.9998			1.64516
$962$			21.5696i			0.695430i
$963$	3.79655	+	41.1406i	0.122342	+	1.32574i
$964$			18.6123i			0.599460i
$965$	−14.2290			−0.458046
$966$	9.91358	−	10.8706i	0.318964	−	0.349754i
$967$			38.8785i			1.25025i	0.780525	+	0.625125i	$0.214952\pi$
$967$			38.8785i			1.25025i	−0.780525	+	0.625125i	$0.785048\pi$
$968$	2.80512	−	1.57846i	0.0901601	−	0.0507336i
$969$	1.43117	+	1.30518i	0.0459759	+	0.0419285i
$970$		−	42.8021i		−	1.37429i
$971$		−	18.2938i		−	0.587075i	−0.955948	−	0.293537i	$-0.905167\pi$
$971$		−	18.2938i		−	0.587075i	0.955948	−	0.293537i	$-0.0948325\pi$
$972$	15.2121	−	24.5165i	0.487927	−	0.786368i
$973$	−18.6606			−0.598232
$974$	26.4103			0.846241
$975$	−7.86834	−	7.17566i	−0.251989	−	0.229805i
$976$			45.6659i			1.46173i
$977$			25.0670i			0.801964i	0.916086	+	0.400982i	$0.131331\pi$
$977$			25.0670i			0.801964i	−0.916086	+	0.400982i	$0.868669\pi$
$978$	5.59088	−	6.13057i	0.178777	−	0.196034i
$979$	−9.61290	−	36.6857i	−0.307230	−	1.17248i
$980$			81.7757i			2.61223i
$981$	−20.1254	+	1.85723i	−0.642556	+	0.0592967i
$982$	−78.1455			−2.49372
$983$		−	26.0237i		−	0.830027i	−0.909815	−	0.415013i	$-0.863777\pi$
$983$		−	26.0237i		−	0.830027i	0.909815	−	0.415013i	$-0.136223\pi$
$984$	−1.87309	+	2.05391i	−0.0597121	+	0.0654762i
$985$		−	38.1596i		−	1.21586i
$986$	−0.0519230			−0.00165357
$987$	−11.0067	+	12.0692i	−0.350346	+	0.384166i
$988$	−9.10611			−0.289704
$989$	−2.39336			−0.0761045
$990$	−61.2785	+	22.2500i	−1.94756	+	0.707152i
$991$	8.67920			0.275704			0.137852	−	0.990453i	$-0.455980\pi$
$991$	8.67920			0.275704			0.137852	+	0.990453i	$0.455980\pi$
$992$	70.6848			2.24425
$993$	−14.0546	+	15.4113i	−0.446009	+	0.489063i
$994$	−99.6140			−3.15956
$995$			43.8265i			1.38939i
$996$	−21.1268	+	23.1662i	−0.669429	+	0.734050i
$997$			28.3476i			0.897776i	0.893588	+	0.448888i	$0.148180\pi$
$997$			28.3476i			0.897776i	−0.893588	+	0.448888i	$0.851820\pi$
$998$	56.4038			1.78543
$999$	45.5584	+	34.4447i	1.44141	+	1.08978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.8	yes	48
3.2	odd	2	inner	429.2.f.a.131.41	yes	48
11.10	odd	2	inner	429.2.f.a.131.42	yes	48
33.32	even	2	inner	429.2.f.a.131.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.7	✓	48	33.32	even	2	inner
429.2.f.a.131.8	yes	48	1.1	even	1	trivial
429.2.f.a.131.41	yes	48	3.2	odd	2	inner
429.2.f.a.131.42	yes	48	11.10	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.96237 q^{2} +(-1.16712 + 1.27978i) q^{3} +1.85089 q^{4} -3.33889i q^{5} +(2.29031 - 2.51140i) q^{6} +4.49805i q^{7} +0.292612 q^{8} +(-0.275676 - 2.98731i) q^{9} +O(q^{10})\)	\(q-1.96237 q^{2} +(-1.16712 + 1.27978i) q^{3} +1.85089 q^{4} -3.33889i q^{5} +(2.29031 - 2.51140i) q^{6} +4.49805i q^{7} +0.292612 q^{8} +(-0.275676 - 2.98731i) q^{9} +6.55213i q^{10} +(-3.20831 + 0.840687i) q^{11} +(-2.16020 + 2.36873i) q^{12} -1.00000i q^{13} -8.82684i q^{14} +(4.27305 + 3.89688i) q^{15} -4.27599 q^{16} +0.227302 q^{17} +(0.540978 + 5.86220i) q^{18} -4.91986i q^{19} -6.17991i q^{20} +(-5.75652 - 5.24976i) q^{21} +(6.29588 - 1.64974i) q^{22} -0.962301i q^{23} +(-0.341513 + 0.374479i) q^{24} -6.14820 q^{25} +1.96237i q^{26} +(4.14484 + 3.13373i) q^{27} +8.32540i q^{28} +0.116406 q^{29} +(-8.38529 - 7.64711i) q^{30} +9.05538 q^{31} +7.80584 q^{32} +(2.66858 - 5.08711i) q^{33} -0.446051 q^{34} +15.0185 q^{35} +(-0.510246 - 5.52917i) q^{36} +10.9916 q^{37} +9.65458i q^{38} +(1.27978 + 1.16712i) q^{39} -0.977001i q^{40} +5.48470 q^{41} +(11.2964 + 10.3020i) q^{42} -2.48713i q^{43} +(-5.93822 + 1.55602i) q^{44} +(-9.97429 + 0.920452i) q^{45} +1.88839i q^{46} -2.09661i q^{47} +(4.99058 - 5.47233i) q^{48} -13.2325 q^{49} +12.0650 q^{50} +(-0.265288 + 0.290897i) q^{51} -1.85089i q^{52} -11.2171i q^{53} +(-8.13371 - 6.14953i) q^{54} +(2.80696 + 10.7122i) q^{55} +1.31619i q^{56} +(6.29634 + 5.74205i) q^{57} -0.228431 q^{58} +5.88710i q^{59} +(7.90893 + 7.21268i) q^{60} -10.6796i q^{61} -17.7700 q^{62} +(13.4371 - 1.24001i) q^{63} -6.76595 q^{64} -3.33889 q^{65} +(-5.23673 + 9.98278i) q^{66} +8.34904 q^{67} +0.420711 q^{68} +(1.23153 + 1.12312i) q^{69} -29.4719 q^{70} -11.2854i q^{71} +(-0.0806662 - 0.874123i) q^{72} -4.41695i q^{73} -21.5696 q^{74} +(7.17566 - 7.86834i) q^{75} -9.10611i q^{76} +(-3.78146 - 14.4311i) q^{77} +(-2.51140 - 2.29031i) q^{78} -0.735929i q^{79} +14.2771i q^{80} +(-8.84801 + 1.64706i) q^{81} -10.7630 q^{82} +9.78001 q^{83} +(-10.6547 - 9.71671i) q^{84} -0.758938i q^{85} +4.88065i q^{86} +(-0.135859 + 0.148974i) q^{87} +(-0.938790 + 0.245995i) q^{88} +11.4346i q^{89} +(19.5732 - 1.80627i) q^{90} +4.49805 q^{91} -1.78111i q^{92} +(-10.5687 + 11.5889i) q^{93} +4.11431i q^{94} -16.4269 q^{95} +(-9.11033 + 9.98976i) q^{96} -6.53254 q^{97} +25.9670 q^{98} +(3.39584 + 9.35245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

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