LMFDB - Embedded newform 429.2.f.a.131.14

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			131.14
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67217 q^{2} +(-1.56232 + 0.747762i) q^{3} +0.796163 q^{4} +2.44281i q^{5} +(2.61247 - 1.25039i) q^{6} -0.956855i q^{7} +2.01302 q^{8} +(1.88170 - 2.33649i) q^{9} +O(q^{10})$	\(q-1.67217 q^{2} +(-1.56232 + 0.747762i) q^{3} +0.796163 q^{4} +2.44281i q^{5} +(2.61247 - 1.25039i) q^{6} -0.956855i q^{7} +2.01302 q^{8} +(1.88170 - 2.33649i) q^{9} -4.08480i q^{10} +(3.19482 + 0.890587i) q^{11} +(-1.24386 + 0.595340i) q^{12} -1.00000i q^{13} +1.60003i q^{14} +(-1.82664 - 3.81646i) q^{15} -4.95845 q^{16} +2.79470 q^{17} +(-3.14653 + 3.90702i) q^{18} -1.65665i q^{19} +1.94487i q^{20} +(0.715500 + 1.49492i) q^{21} +(-5.34229 - 1.48922i) q^{22} +7.92262i q^{23} +(-3.14499 + 1.50526i) q^{24} -0.967318 q^{25} +1.67217i q^{26} +(-1.19269 + 5.05742i) q^{27} -0.761812i q^{28} -4.85674 q^{29} +(3.05446 + 6.38178i) q^{30} +6.88106 q^{31} +4.26534 q^{32} +(-5.65728 + 0.997578i) q^{33} -4.67323 q^{34} +2.33742 q^{35} +(1.49814 - 1.86023i) q^{36} -2.79242 q^{37} +2.77021i q^{38} +(0.747762 + 1.56232i) q^{39} +4.91744i q^{40} -5.64350 q^{41} +(-1.19644 - 2.49976i) q^{42} +11.8989i q^{43} +(2.54359 + 0.709052i) q^{44} +(5.70760 + 4.59664i) q^{45} -13.2480i q^{46} +6.25171i q^{47} +(7.74670 - 3.70774i) q^{48} +6.08443 q^{49} +1.61752 q^{50} +(-4.36623 + 2.08977i) q^{51} -0.796163i q^{52} -7.02720i q^{53} +(1.99438 - 8.45688i) q^{54} +(-2.17554 + 7.80433i) q^{55} -1.92617i q^{56} +(1.23878 + 2.58822i) q^{57} +8.12131 q^{58} +6.12712i q^{59} +(-1.45430 - 3.03852i) q^{60} -1.79174i q^{61} -11.5063 q^{62} +(-2.23568 - 1.80052i) q^{63} +2.78452 q^{64} +2.44281 q^{65} +(9.45995 - 1.66812i) q^{66} -13.7435 q^{67} +2.22504 q^{68} +(-5.92423 - 12.3777i) q^{69} -3.90856 q^{70} +8.11341i q^{71} +(3.78792 - 4.70341i) q^{72} +8.25258i q^{73} +4.66941 q^{74} +(1.51126 - 0.723324i) q^{75} -1.31896i q^{76} +(0.852163 - 3.05698i) q^{77} +(-1.25039 - 2.61247i) q^{78} -11.8497i q^{79} -12.1125i q^{80} +(-1.91838 - 8.79317i) q^{81} +9.43692 q^{82} -11.5546 q^{83} +(0.569654 + 1.19020i) q^{84} +6.82692i q^{85} -19.8970i q^{86} +(7.58779 - 3.63169i) q^{87} +(6.43124 + 1.79277i) q^{88} -5.15763i q^{89} +(-9.54410 - 7.68638i) q^{90} -0.956855 q^{91} +6.30769i q^{92} +(-10.7504 + 5.14540i) q^{93} -10.4539i q^{94} +4.04688 q^{95} +(-6.66383 + 3.18946i) q^{96} +7.74783 q^{97} -10.1742 q^{98} +(8.09255 - 5.78884i) 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 $

$2$	−1.67217			−1.18240			−0.591202	−	0.806523i	$-0.701347\pi$
$2$	−1.67217			−1.18240			−0.591202	+	0.806523i	$0.701347\pi$
$3$	−1.56232	+	0.747762i	−0.902007	+	0.431721i
$3$	−1.56232	+	0.747762i	−0.902007	+	0.431721i
$4$	0.796163			0.398081
$5$			2.44281i			1.09246i	0.837636	+	0.546229i	$0.183937\pi$
$5$			2.44281i			1.09246i	−0.837636	+	0.546229i	$0.816063\pi$
$6$	2.61247	−	1.25039i	1.06654	−	0.510469i
$7$		−	0.956855i		−	0.361657i	−0.983515	−	0.180829i	$-0.942122\pi$
$7$		−	0.956855i		−	0.361657i	0.983515	−	0.180829i	$-0.0578779\pi$
$8$	2.01302			0.711712
$9$	1.88170	−	2.33649i	0.627235	−	0.778830i
$10$		−	4.08480i		−	1.29173i
$11$	3.19482	+	0.890587i	0.963273	+	0.268522i
$11$	3.19482	+	0.890587i	0.963273	+	0.268522i
$12$	−1.24386	+	0.595340i	−0.359072	+	0.171860i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$			1.60003i			0.427625i
$15$	−1.82664	−	3.81646i	−0.471636	−	0.985405i
$16$	−4.95845			−1.23961
$17$	2.79470			0.677815			0.338907	−	0.940820i	$-0.389943\pi$
$17$	2.79470			0.677815			0.338907	+	0.940820i	$0.389943\pi$
$18$	−3.14653	+	3.90702i	−0.741645	+	0.920893i
$19$		−	1.65665i		−	0.380062i	−0.981778	−	0.190031i	$-0.939141\pi$
$19$		−	1.65665i		−	0.380062i	0.981778	−	0.190031i	$-0.0608588\pi$
$20$			1.94487i			0.434887i
$21$	0.715500	+	1.49492i	0.156135	+	0.326218i
$22$	−5.34229	−	1.48922i	−1.13898	−	0.317502i
$23$			7.92262i			1.65198i	0.563685	+	0.825990i	$0.309383\pi$
$23$			7.92262i			1.65198i	−0.563685	+	0.825990i	$0.690617\pi$
$24$	−3.14499	+	1.50526i	−0.641969	+	0.307261i
$25$	−0.967318			−0.193464
$26$			1.67217i			0.327940i
$27$	−1.19269	+	5.05742i	−0.229533	+	0.973301i
$28$		−	0.761812i		−	0.143969i
$29$	−4.85674			−0.901874			−0.450937	−	0.892556i	$-0.648910\pi$
$29$	−4.85674			−0.901874			−0.450937	+	0.892556i	$0.648910\pi$
$30$	3.05446	+	6.38178i	0.557665	+	1.16515i
$31$	6.88106			1.23587			0.617937	−	0.786227i	$-0.287968\pi$
$31$	6.88106			1.23587			0.617937	+	0.786227i	$0.287968\pi$
$32$	4.26534			0.754012
$33$	−5.65728	+	0.997578i	−0.984806	+	0.173656i
$34$	−4.67323			−0.801452
$35$	2.33742			0.395095
$36$	1.49814	−	1.86023i	0.249690	−	0.310038i
$37$	−2.79242			−0.459071			−0.229535	−	0.973300i	$-0.573721\pi$
$37$	−2.79242			−0.459071			−0.229535	+	0.973300i	$0.573721\pi$
$38$			2.77021i			0.449387i
$39$	0.747762	+	1.56232i	0.119738	+	0.250172i
$40$			4.91744i			0.777515i
$41$	−5.64350			−0.881367			−0.440684	−	0.897662i	$-0.645264\pi$
$41$	−5.64350			−0.881367			−0.440684	+	0.897662i	$0.645264\pi$
$42$	−1.19644	−	2.49976i	−0.184615	−	0.385721i
$43$			11.8989i			1.81457i	0.420518	+	0.907284i	$0.361848\pi$
$43$			11.8989i			1.81457i	−0.420518	+	0.907284i	$0.638152\pi$
$44$	2.54359	+	0.709052i	0.383461	+	0.106894i
$45$	5.70760	+	4.59664i	0.850839	+	0.685227i
$46$		−	13.2480i		−	1.95331i
$47$			6.25171i			0.911905i	0.890004	+	0.455952i	$0.150701\pi$
$47$			6.25171i			0.911905i	−0.890004	+	0.455952i	$0.849299\pi$
$48$	7.74670	−	3.70774i	1.11814	−	0.535166i
$49$	6.08443			0.869204
$50$	1.61752			0.228752
$51$	−4.36623	+	2.08977i	−0.611394	+	0.292627i
$52$		−	0.796163i		−	0.110408i
$53$		−	7.02720i		−	0.965260i	−0.875824	−	0.482630i	$-0.839682\pi$
$53$		−	7.02720i		−	0.965260i	0.875824	−	0.482630i	$-0.160318\pi$
$54$	1.99438	−	8.45688i	0.271401	−	1.15084i
$55$	−2.17554	+	7.80433i	−0.293349	+	1.05234i
$56$		−	1.92617i		−	0.257396i
$57$	1.23878	+	2.58822i	0.164080	+	0.342818i
$58$	8.12131			1.06638
$59$			6.12712i			0.797683i	0.917020	+	0.398841i	$0.130588\pi$
$59$			6.12712i			0.797683i	−0.917020	+	0.398841i	$0.869412\pi$
$60$	−1.45430	−	3.03852i	−0.187750	−	0.392271i
$61$		−	1.79174i		−	0.229409i	−0.993400	−	0.114705i	$-0.963408\pi$
$61$		−	1.79174i		−	0.229409i	0.993400	−	0.114705i	$-0.0365922\pi$
$62$	−11.5063			−1.46130
$63$	−2.23568	−	1.80052i	−0.281670	−	0.226844i
$64$	2.78452			0.348065
$65$	2.44281			0.302993
$66$	9.45995	−	1.66812i	1.16444	−	0.205332i
$67$	−13.7435			−1.67904			−0.839520	−	0.543329i	$-0.817164\pi$
$67$	−13.7435			−1.67904			−0.839520	+	0.543329i	$0.817164\pi$
$68$	2.22504			0.269825
$69$	−5.92423	−	12.3777i	−0.713194	−	1.49010i
$70$	−3.90856			−0.467163
$71$			8.11341i			0.962885i	0.876478	+	0.481442i	$0.159887\pi$
$71$			8.11341i			0.962885i	−0.876478	+	0.481442i	$0.840113\pi$
$72$	3.78792	−	4.70341i	0.446410	−	0.554303i
$73$			8.25258i			0.965892i	0.875650	+	0.482946i	$0.160433\pi$
$73$			8.25258i			0.965892i	−0.875650	+	0.482946i	$0.839567\pi$
$74$	4.66941			0.542807
$75$	1.51126	−	0.723324i	0.174506	−	0.0835222i
$76$		−	1.31896i		−	0.151295i
$77$	0.852163	−	3.05698i	0.0971130	−	0.348375i
$78$	−1.25039	−	2.61247i	−0.141579	−	0.295804i
$79$		−	11.8497i		−	1.33320i	−0.745416	−	0.666600i	$-0.767749\pi$
$79$		−	11.8497i		−	1.33320i	0.745416	−	0.666600i	$-0.232251\pi$
$80$		−	12.1125i		−	1.35422i
$81$	−1.91838	−	8.79317i	−0.213154	−	0.977019i
$82$	9.43692			1.04213
$83$	−11.5546			−1.26829			−0.634143	−	0.773216i	$-0.718647\pi$
$83$	−11.5546			−1.26829			−0.634143	+	0.773216i	$0.718647\pi$
$84$	0.569654	+	1.19020i	0.0621544	+	0.129861i
$85$			6.82692i			0.740484i
$86$		−	19.8970i		−	2.14555i
$87$	7.58779	−	3.63169i	0.813497	−	0.389358i
$88$	6.43124	+	1.79277i	0.685573	+	0.191110i
$89$		−	5.15763i		−	0.546707i	−0.961914	−	0.273354i	$-0.911867\pi$
$89$		−	5.15763i		−	0.546707i	0.961914	−	0.273354i	$-0.0881329\pi$
$90$	−9.54410	−	7.68638i	−1.00604	−	0.810216i
$91$	−0.956855			−0.100306
$92$			6.30769i			0.657622i
$93$	−10.7504	+	5.14540i	−1.11477	+	0.533553i
$94$		−	10.4539i		−	1.07824i
$95$	4.04688			0.415201
$96$	−6.66383	+	3.18946i	−0.680125	+	0.325523i
$97$	7.74783			0.786673			0.393337	−	0.919395i	$-0.371321\pi$
$97$	7.74783			0.786673			0.393337	+	0.919395i	$0.371321\pi$
$98$	−10.1742			−1.02775
$99$	8.09255	−	5.78884i	0.813332	−	0.581800i
$100$	−0.770142			−0.0770142
$101$	7.64718			0.760923			0.380461	−	0.924797i	$-0.375765\pi$
$101$	7.64718			0.760923			0.380461	+	0.924797i	$0.375765\pi$
$102$	7.30109	−	3.49446i	0.722915	−	0.346003i
$103$	11.0857			1.09230			0.546152	−	0.837686i	$-0.316092\pi$
$103$	11.0857			1.09230			0.546152	+	0.837686i	$0.316092\pi$
$104$		−	2.01302i		−	0.197393i
$105$	−3.65180	+	1.74783i	−0.356379	+	0.170571i
$106$			11.7507i			1.14133i
$107$	9.33701			0.902643			0.451321	−	0.892361i	$-0.350953\pi$
$107$	9.33701			0.902643			0.451321	+	0.892361i	$0.350953\pi$
$108$	−0.949574	+	4.02653i	−0.0913728	+	0.387453i
$109$		−	11.6545i		−	1.11630i	−0.829741	−	0.558148i	$-0.811512\pi$
$109$		−	11.6545i		−	1.11630i	0.829741	−	0.558148i	$-0.188488\pi$
$110$	3.63787	−	13.0502i	0.346857	−	1.24429i
$111$	4.36266	−	2.08806i	0.414085	−	0.198190i
$112$			4.74452i			0.448315i
$113$			15.9736i			1.50267i	0.659922	+	0.751334i	$0.270589\pi$
$113$			15.9736i			1.50267i	−0.659922	+	0.751334i	$0.729411\pi$
$114$	−2.07145	−	4.32795i	−0.194010	−	0.405350i
$115$	−19.3534			−1.80472
$116$	−3.86675			−0.359019
$117$	−2.33649	−	1.88170i	−0.216009	−	0.173964i
$118$		−	10.2456i		−	0.943184i
$119$		−	2.67413i		−	0.245137i
$120$	−3.67707	−	7.68262i	−0.335669	−	0.701324i
$121$	9.41371	+	5.69053i	0.855792	+	0.517321i
$122$			2.99611i			0.271255i
$123$	8.81697	−	4.22000i	0.795000	−	0.380504i
$124$	5.47844			0.491979
$125$			9.85107i			0.881107i
$126$	3.73845	+	3.01078i	0.333048	+	0.268221i
$127$			2.59691i			0.230439i	0.993340	+	0.115219i	$0.0367571\pi$
$127$			2.59691i			0.230439i	−0.993340	+	0.115219i	$0.963243\pi$
$128$	−13.1869			−1.16557
$129$	−8.89756	−	18.5899i	−0.783386	−	1.63675i
$130$	−4.08480			−0.358261
$131$	−2.57323			−0.224824			−0.112412	−	0.993662i	$-0.535858\pi$
$131$	−2.57323			−0.224824			−0.112412	+	0.993662i	$0.535858\pi$
$132$	−4.50412	+	0.794234i	−0.392033	+	0.0691292i
$133$	−1.58517			−0.137452
$134$	22.9816			1.98530
$135$	−12.3543	−	2.91351i	−1.06329	−	0.250755i
$136$	5.62580			0.482409
$137$			2.23850i			0.191248i	0.995418	+	0.0956238i	$0.0304846\pi$
$137$			2.23850i			0.191248i	−0.995418	+	0.0956238i	$0.969515\pi$
$138$	9.90634	+	20.6976i	0.843284	+	1.76190i
$139$			16.7903i			1.42413i	0.702111	+	0.712067i	$0.252241\pi$
$139$			16.7903i			1.42413i	−0.702111	+	0.712067i	$0.747759\pi$
$140$	1.86096			0.157280
$141$	−4.67479	−	9.76718i	−0.393688	−	0.822545i
$142$		−	13.5670i		−	1.13852i
$143$	0.890587	−	3.19482i	0.0744747	−	0.267164i
$144$	−9.33033	+	11.5854i	−0.777528	+	0.965448i
$145$		−	11.8641i		−	0.985259i
$146$		−	13.7997i		−	1.14208i
$147$	−9.50584	+	4.54970i	−0.784028	+	0.375253i
$148$	−2.22322			−0.182747
$149$	5.98667			0.490447			0.245224	−	0.969467i	$-0.421139\pi$
$149$	5.98667			0.490447			0.245224	+	0.969467i	$0.421139\pi$
$150$	−2.52709	+	1.20952i	−0.206336	+	0.0987571i
$151$		−	7.57509i		−	0.616452i	−0.951313	−	0.308226i	$-0.900265\pi$
$151$		−	7.57509i		−	0.616452i	0.951313	−	0.308226i	$-0.0997353\pi$
$152$		−	3.33488i		−	0.270494i
$153$	5.25880	−	6.52980i	0.425149	−	0.527903i
$154$	−1.42496	+	5.11179i	−0.114827	+	0.411920i
$155$			16.8091i			1.35014i
$156$	0.595340	+	1.24386i	0.0476654	+	0.0995887i
$157$	−2.55353			−0.203794			−0.101897	−	0.994795i	$-0.532491\pi$
$157$	−2.55353			−0.203794			−0.101897	+	0.994795i	$0.532491\pi$
$158$			19.8148i			1.57638i
$159$	5.25467	+	10.9788i	0.416723	+	0.870672i
$160$			10.4194i			0.823726i
$161$	7.58080			0.597450
$162$	3.20787	+	14.7037i	0.252034	+	1.15523i
$163$	−18.1994			−1.42549			−0.712745	−	0.701423i	$-0.752548\pi$
$163$	−18.1994			−1.42549			−0.712745	+	0.701423i	$0.752548\pi$
$164$	−4.49315			−0.350856
$165$	−2.43689	−	13.8197i	−0.189712	−	1.07586i
$166$	19.3213			1.49963
$167$	5.12010			0.396205			0.198103	−	0.980181i	$-0.436522\pi$
$167$	5.12010			0.396205			0.198103	+	0.980181i	$0.436522\pi$
$168$	1.44032	+	3.00930i	0.111123	+	0.232173i
$169$	−1.00000			−0.0769231
$170$		−	11.4158i		−	0.875552i
$171$	−3.87075	−	3.11732i	−0.296004	−	0.238388i
$172$			9.47347i			0.722346i
$173$	4.67564			0.355482			0.177741	−	0.984077i	$-0.443121\pi$
$173$	4.67564			0.355482			0.177741	+	0.984077i	$0.443121\pi$
$174$	−12.6881	+	6.07281i	−0.961883	+	0.460378i
$175$			0.925583i			0.0699675i
$176$	−15.8413	−	4.41593i	−1.19409	−	0.332864i
$177$	−4.58163	−	9.57253i	−0.344376	−	0.719516i
$178$			8.62444i			0.646429i
$179$			7.37290i			0.551077i	0.961290	+	0.275538i	$0.0888561\pi$
$179$			7.37290i			0.551077i	−0.961290	+	0.275538i	$0.911144\pi$
$180$	4.54418	+	3.65968i	0.338703	+	0.272776i
$181$	9.13199			0.678776			0.339388	−	0.940647i	$-0.389780\pi$
$181$	9.13199			0.678776			0.339388	+	0.940647i	$0.389780\pi$
$182$	1.60003			0.118602
$183$	1.33980	+	2.79928i	0.0990408	+	0.206929i
$184$			15.9484i			1.17573i
$185$		−	6.82135i		−	0.501515i
$186$	17.9766	−	8.60399i	1.31811	−	0.630875i
$187$	8.92856	+	2.48893i	0.652921	+	0.182008i
$188$			4.97737i			0.363012i
$189$	4.83922	+	1.14123i	0.352001	+	0.0830123i
$190$	−6.76708			−0.490936
$191$		−	1.41800i		−	0.102603i	−0.998683	−	0.0513014i	$-0.983663\pi$
$191$		−	1.41800i		−	0.102603i	0.998683	−	0.0513014i	$-0.0163369\pi$
$192$	−4.35032	+	2.08216i	−0.313957	+	0.150267i
$193$			19.9375i			1.43513i	0.696491	+	0.717566i	$0.254744\pi$
$193$			19.9375i			1.43513i	−0.696491	+	0.717566i	$0.745256\pi$
$194$	−12.9557			−0.930166
$195$	−3.81646	+	1.82664i	−0.273302	+	0.130808i
$196$	4.84419			0.346014
$197$	−14.5869			−1.03928			−0.519638	−	0.854387i	$-0.673933\pi$
$197$	−14.5869			−1.03928			−0.519638	+	0.854387i	$0.673933\pi$
$198$	−13.5321	+	9.67994i	−0.961687	+	0.687923i
$199$	6.23407			0.441922			0.220961	−	0.975283i	$-0.429081\pi$
$199$	6.23407			0.441922			0.220961	+	0.975283i	$0.429081\pi$
$200$	−1.94723			−0.137690
$201$	21.4718	−	10.2769i	1.51451	−	0.724876i
$202$	−12.7874			−0.899719
$203$			4.64720i			0.326169i
$204$	−3.47623	+	1.66380i	−0.243384	+	0.116489i
$205$		−	13.7860i		−	0.962856i
$206$	−18.5372			−1.29155
$207$	18.5111	+	14.9080i	1.28661	+	1.03618i
$208$			4.95845i			0.343807i
$209$	1.47539	−	5.29269i	0.102055	−	0.366103i
$210$	6.10644	−	2.92267i	0.421384	−	0.201684i
$211$			27.9531i			1.92437i	0.272391	+	0.962187i	$0.412185\pi$
$211$			27.9531i			1.92437i	−0.272391	+	0.962187i	$0.587815\pi$
$212$		−	5.59479i		−	0.384252i
$213$	−6.06690	−	12.6758i	−0.415697	−	0.868529i
$214$	−15.6131			−1.06729
$215$	−29.0668			−1.98234
$216$	−2.40091	+	10.1807i	−0.163361	+	0.692710i
$217$		−	6.58418i		−	0.446963i
$218$			19.4883i			1.31991i
$219$	−6.17097	−	12.8932i	−0.416995	−	0.871241i
$220$	−1.73208	+	6.21351i	−0.116777	+	0.418915i
$221$		−	2.79470i		−	0.187992i
$222$	−7.29512	+	3.49160i	−0.489616	+	0.234341i
$223$	−3.35865			−0.224912			−0.112456	−	0.993657i	$-0.535872\pi$
$223$	−3.35865			−0.224912			−0.112456	+	0.993657i	$0.535872\pi$
$224$		−	4.08131i		−	0.272694i
$225$	−1.82021	+	2.26013i	−0.121347	+	0.150675i
$226$		−	26.7106i		−	1.77676i
$227$	21.3741			1.41865			0.709324	−	0.704882i	$-0.249000\pi$
$227$	21.3741			1.41865			0.709324	+	0.704882i	$0.249000\pi$
$228$	0.986270	+	2.06065i	0.0653173	+	0.136470i
$229$	8.23806			0.544386			0.272193	−	0.962243i	$-0.412251\pi$
$229$	8.23806			0.544386			0.272193	+	0.962243i	$0.412251\pi$
$230$	32.3623			2.13391
$231$	0.954538	+	5.41320i	0.0628040	+	0.356162i
$232$	−9.77673			−0.641874
$233$	−1.52934			−0.100190			−0.0500952	−	0.998744i	$-0.515952\pi$
$233$	−1.52934			−0.100190			−0.0500952	+	0.998744i	$0.515952\pi$
$234$	3.90702	+	3.14653i	0.255410	+	0.205695i
$235$	−15.2717			−0.996217
$236$			4.87818i			0.317542i
$237$	8.86078	+	18.5131i	0.575570	+	1.20256i
$238$			4.47160i			0.289851i
$239$	2.44996			0.158475			0.0792375	−	0.996856i	$-0.474751\pi$
$239$	2.44996			0.158475			0.0792375	+	0.996856i	$0.474751\pi$
$240$	9.05731	+	18.9237i	0.584647	+	1.22152i
$241$		−	4.27165i		−	0.275161i	−0.990491	−	0.137581i	$-0.956067\pi$
$241$		−	4.27165i		−	0.275161i	0.990491	−	0.137581i	$-0.0439326\pi$
$242$	−15.7413	−	9.51555i	−1.01189	−	0.611683i
$243$	9.57233	+	12.3033i	0.614065	+	0.789255i
$244$		−	1.42652i		−	0.0913236i
$245$			14.8631i			0.949568i
$246$	−14.7435	+	7.05657i	−0.940012	+	0.449910i
$247$	−1.65665			−0.105410
$248$	13.8517			0.879587
$249$	18.0521	−	8.64011i	1.14400	−	0.547545i
$250$		−	16.4727i		−	1.04183i
$251$		−	9.05319i		−	0.571432i	−0.958314	−	0.285716i	$-0.907769\pi$
$251$		−	9.05319i		−	0.571432i	0.958314	−	0.285716i	$-0.0922315\pi$
$252$	−1.77997	−	1.43351i	−0.112127	−	0.0903023i
$253$	−7.05578	+	25.3113i	−0.443593	+	1.59131i
$254$		−	4.34249i		−	0.272472i
$255$	−5.10492	−	10.6659i	−0.319682	−	0.667922i
$256$	16.4817			1.03011
$257$		−	13.1868i		−	0.822567i	−0.911507	−	0.411283i	$-0.865081\pi$
$257$		−	13.1868i		−	0.822567i	0.911507	−	0.411283i	$-0.134919\pi$
$258$	14.8783	+	31.0856i	0.926280	+	1.93531i
$259$			2.67194i			0.166026i
$260$	1.94487			0.120616
$261$	−9.13894	+	11.3477i	−0.565686	+	0.702407i
$262$	4.30288			0.265833
$263$	27.0586			1.66850			0.834252	−	0.551384i	$-0.185900\pi$
$263$	27.0586			1.66850			0.834252	+	0.551384i	$0.185900\pi$
$264$	−11.3882	+	2.00815i	−0.700898	+	0.123593i
$265$	17.1661			1.05451
$266$	2.65069			0.162524
$267$	3.85668	+	8.05787i	0.236025	+	0.493134i
$268$	−10.9421			−0.668394
$269$		−	21.1927i		−	1.29214i	−0.763279	−	0.646069i	$-0.776412\pi$
$269$		−	21.1927i		−	1.29214i	0.763279	−	0.646069i	$-0.223588\pi$
$270$	20.6585	+	4.87189i	1.25724	+	0.296494i
$271$		−	5.00130i		−	0.303807i	−0.988395	−	0.151904i	$-0.951460\pi$
$271$		−	5.00130i		−	0.303807i	0.988395	−	0.151904i	$-0.0485403\pi$
$272$	−13.8574			−0.840228
$273$	1.49492	−	0.715500i	0.0904765	−	0.0433040i
$274$		−	3.74315i		−	0.226132i
$275$	−3.09040	−	0.861481i	−0.186358	−	0.0519493i
$276$	−4.71665	−	9.85465i	−0.283909	−	0.593180i
$277$		−	32.2299i		−	1.93651i	−0.249971	−	0.968253i	$-0.580421\pi$
$277$		−	32.2299i		−	1.93651i	0.249971	−	0.968253i	$-0.419579\pi$
$278$		−	28.0763i		−	1.68390i
$279$	12.9481	−	16.0775i	0.775183	−	0.962537i
$280$	4.70527			0.281194
$281$	−9.67607			−0.577226			−0.288613	−	0.957446i	$-0.593194\pi$
$281$	−9.67607			−0.577226			−0.288613	+	0.957446i	$0.593194\pi$
$282$	7.81706	+	16.3324i	0.465499	+	0.972581i
$283$		−	10.9404i		−	0.650339i	−0.945656	−	0.325170i	$-0.894579\pi$
$283$		−	10.9404i		−	0.650339i	0.945656	−	0.325170i	$-0.105421\pi$
$284$			6.45959i			0.383306i
$285$	−6.32253	+	3.02610i	−0.374515	+	0.179251i
$286$	−1.48922	+	5.34229i	−0.0880592	+	0.315896i
$287$			5.40002i			0.318753i
$288$	8.02610	−	9.96592i	0.472943	−	0.587248i
$289$	−9.18964			−0.540567
$290$			19.8388i			1.16497i
$291$	−12.1046	+	5.79354i	−0.709585	+	0.339623i
$292$			6.57040i			0.384503i
$293$	−12.7932			−0.747385			−0.373692	−	0.927553i	$-0.621908\pi$
$293$	−12.7932			−0.747385			−0.373692	+	0.927553i	$0.621908\pi$
$294$	15.8954	−	7.60789i	0.927039	−	0.443701i
$295$	−14.9674			−0.871434
$296$	−5.62121			−0.326726
$297$	−8.31450	+	15.0953i	−0.482456	+	0.875920i
$298$	−10.0107			−0.579907
$299$	7.92262			0.458177
$300$	1.20321	−	0.575883i	0.0694674	−	0.0332486i
$301$	11.3855			0.656252
$302$			12.6669i			0.728896i
$303$	−11.9474	+	5.71827i	−0.686358	+	0.328506i
$304$			8.21442i			0.471129i
$305$	4.37689			0.250620
$306$	−8.79363	+	10.9190i	−0.502698	+	0.624195i
$307$		−	30.3716i		−	1.73340i	−0.498828	−	0.866701i	$-0.666236\pi$
$307$		−	30.3716i		−	1.73340i	0.498828	−	0.866701i	$-0.333764\pi$
$308$	0.678461	−	2.43385i	0.0386589	−	0.138682i
$309$	−17.3194	+	8.28945i	−0.985266	+	0.471570i
$310$		−	28.1078i		−	1.59641i
$311$			0.609897i			0.0345841i	0.999850	+	0.0172920i	$0.00550450\pi$
$311$			0.609897i			0.0345841i	−0.999850	+	0.0172920i	$0.994496\pi$
$312$	1.50526	+	3.14499i	0.0852188	+	0.178050i
$313$	1.67027			0.0944092			0.0472046	−	0.998885i	$-0.484969\pi$
$313$	1.67027			0.0944092			0.0472046	+	0.998885i	$0.484969\pi$
$314$	4.26995			0.240967
$315$	4.39832	−	5.46135i	0.247817	−	0.307712i
$316$		−	9.43431i		−	0.530722i
$317$		−	6.78095i		−	0.380856i	−0.981701	−	0.190428i	$-0.939012\pi$
$317$		−	6.78095i		−	0.380856i	0.981701	−	0.190428i	$-0.0609876\pi$
$318$	−8.78672	−	18.3584i	−0.492735	−	1.02949i
$319$	−15.5164	−	4.32535i	−0.868751	−	0.242173i
$320$			6.80205i			0.380246i
$321$	−14.5874	+	6.98186i	−0.814190	+	0.389690i
$322$	−12.6764			−0.706428
$323$		−	4.62984i		−	0.257611i
$324$	−1.52734	−	7.00079i	−0.0848525	−	0.388933i
$325$			0.967318i			0.0536571i
$326$	30.4326			1.68551
$327$	8.71478	+	18.2081i	0.481928	+	1.00691i
$328$	−11.3605			−0.627279
$329$	5.98198			0.329797
$330$	4.07491	+	23.1089i	0.224316	+	1.27210i
$331$	−14.7976			−0.813350			−0.406675	−	0.913573i	$-0.633312\pi$
$331$	−14.7976			−0.813350			−0.406675	+	0.913573i	$0.633312\pi$
$332$	−9.19936			−0.504881
$333$	−5.25450	+	6.52446i	−0.287945	+	0.357538i
$334$	−8.56170			−0.468475
$335$		−	33.5728i		−	1.83428i
$336$	−3.54777	−	7.41247i	−0.193547	−	0.404383i
$337$		−	3.65994i		−	0.199370i	−0.995019	−	0.0996848i	$-0.968217\pi$
$337$		−	3.65994i		−	0.199370i	0.995019	−	0.0996848i	$-0.0317835\pi$
$338$	1.67217			0.0909542
$339$	−11.9444	−	24.9559i	−0.648733	−	1.35542i
$340$			5.43534i			0.294773i
$341$	21.9837	+	6.12819i	1.19049	+	0.331860i
$342$	6.47256	+	5.21271i	0.349996	+	0.281871i
$343$		−	12.5199i		−	0.676011i
$344$			23.9528i			1.29145i
$345$	30.2363	−	14.4718i	1.62787	−	0.779134i
$346$	−7.81848			−0.420324
$347$	−32.4885			−1.74407			−0.872037	−	0.489441i	$-0.837201\pi$
$347$	−32.4885			−1.74407			−0.872037	+	0.489441i	$0.837201\pi$
$348$	6.04112	−	2.89141i	0.323838	−	0.154996i
$349$		−	24.2952i		−	1.30049i	−0.759723	−	0.650247i	$-0.774666\pi$
$349$		−	24.2952i		−	1.30049i	0.759723	−	0.650247i	$-0.225334\pi$
$350$		−	1.54774i		−	0.0827299i
$351$	5.05742	+	1.19269i	0.269945	+	0.0636610i
$352$	13.6270	+	3.79866i	0.726320	+	0.202469i
$353$		−	20.8180i		−	1.10803i	−0.832507	−	0.554014i	$-0.813095\pi$
$353$		−	20.8180i		−	1.10803i	0.832507	−	0.554014i	$-0.186905\pi$
$354$	7.66127	+	16.0069i	0.407192	+	0.850759i
$355$	−19.8195			−1.05191
$356$		−	4.10631i		−	0.217634i
$357$	1.99961	+	4.17785i	0.105831	+	0.221115i
$358$		−	12.3288i		−	0.651596i
$359$	−15.0226			−0.792864			−0.396432	−	0.918064i	$-0.629752\pi$
$359$	−15.0226			−0.792864			−0.396432	+	0.918064i	$0.629752\pi$
$360$	11.4895	+	9.25316i	0.605552	+	0.487684i
$361$	16.2555			0.855553
$362$	−15.2703			−0.802588
$363$	−18.9624	−	1.85123i	−0.995268	−	0.0971642i
$364$	−0.761812			−0.0399298
$365$	−20.1595			−1.05520
$366$	−2.24038	−	4.68089i	−0.117106	−	0.244674i
$367$	36.9783			1.93025			0.965126	−	0.261785i	$-0.0843112\pi$
$367$	36.9783			1.93025			0.965126	+	0.261785i	$0.0843112\pi$
$368$		−	39.2839i		−	2.04781i
$369$	−10.6194	+	13.1860i	−0.552824	+	0.686436i
$370$			11.4065i			0.592994i
$371$	−6.72401			−0.349093
$372$	−8.55909	+	4.09657i	−0.443768	+	0.212397i
$373$			19.7390i			1.02204i	0.859567	+	0.511022i	$0.170733\pi$
$373$			19.7390i			1.02204i	−0.859567	+	0.511022i	$0.829267\pi$
$374$	−14.9301	−	4.16192i	−0.772017	−	0.215208i
$375$	−7.36626	−	15.3906i	−0.380392	−	0.794765i
$376$			12.5848i			0.649013i
$377$			4.85674i			0.250135i
$378$	−8.09201	−	1.90833i	−0.416208	−	0.0981541i
$379$	9.91387			0.509241			0.254621	−	0.967041i	$-0.418049\pi$
$379$	9.91387			0.509241			0.254621	+	0.967041i	$0.418049\pi$
$380$	3.22197			0.165284
$381$	−1.94187	−	4.05721i	−0.0994851	−	0.207857i
$382$			2.37114i			0.121318i
$383$		−	0.614861i		−	0.0314179i	−0.999877	−	0.0157090i	$-0.994999\pi$
$383$		−	0.614861i		−	0.0314179i	0.999877	−	0.0157090i	$-0.00500052\pi$
$384$	20.6021	−	9.86064i	1.05135	−	0.503199i
$385$	7.46761	+	2.08167i	0.380585	+	0.106092i
$386$		−	33.3389i		−	1.69691i
$387$	27.8017	+	22.3902i	1.41324	+	1.13816i
$388$	6.16853			0.313160
$389$			12.3785i			0.627613i	0.949487	+	0.313806i	$0.101604\pi$
$389$			12.3785i			0.627613i	−0.949487	+	0.313806i	$0.898396\pi$
$390$	6.38178	−	3.05446i	0.323154	−	0.154669i
$391$			22.1414i			1.11974i
$392$	12.2481			0.618623
$393$	4.02021	−	1.92416i	0.202793	−	0.0970611i
$394$	24.3919			1.22884
$395$	28.9466			1.45646
$396$	6.44298	−	4.60886i	0.323772	−	0.231604i
$397$	8.94213			0.448793			0.224396	−	0.974498i	$-0.427959\pi$
$397$	8.94213			0.448793			0.224396	+	0.974498i	$0.427959\pi$
$398$	−10.4244			−0.522530
$399$	2.47655	−	1.18533i	0.123983	−	0.0593409i
$400$	4.79640			0.239820
$401$		−	27.3727i		−	1.36693i	−0.729984	−	0.683465i	$-0.760472\pi$
$401$		−	27.3727i		−	1.36693i	0.729984	−	0.683465i	$-0.239528\pi$
$402$	−35.9046	+	17.1847i	−1.79076	+	0.857097i
$403$		−	6.88106i		−	0.342770i
$404$	6.08840			0.302909
$405$	21.4800	−	4.68624i	1.06735	−	0.232861i
$406$		−	7.77092i		−	0.385664i
$407$	−8.92126	−	2.48689i	−0.442211	−	0.123271i
$408$	−8.78932	+	4.20676i	−0.435136	+	0.208266i
$409$		−	8.59187i		−	0.424841i	−0.977178	−	0.212420i	$-0.931865\pi$
$409$		−	8.59187i		−	0.424841i	0.977178	−	0.212420i	$-0.0681346\pi$
$410$			23.0526i			1.13849i
$411$	−1.67386	−	3.49725i	−0.0825655	−	0.172507i
$412$	8.82600			0.434826
$413$	5.86276			0.288488
$414$	−30.9538	−	24.9288i	−1.52130	−	1.22518i
$415$		−	28.2258i		−	1.38555i
$416$		−	4.26534i		−	0.209125i
$417$	−12.5551	−	26.2319i	−0.614828	−	1.28458i
$418$	−2.46711	+	8.85030i	−0.120670	+	0.432882i
$419$		−	17.6612i		−	0.862808i	−0.902159	−	0.431404i	$-0.858018\pi$
$419$		−	17.6612i		−	0.862808i	0.902159	−	0.431404i	$-0.141982\pi$
$420$	−2.90742	+	1.39156i	−0.141868	+	0.0679010i
$421$	25.2339			1.22982			0.614911	−	0.788596i	$-0.289192\pi$
$421$	25.2339			1.22982			0.614911	+	0.788596i	$0.289192\pi$
$422$		−	46.7425i		−	2.27539i
$423$	14.6071	+	11.7639i	0.710219	+	0.571978i
$424$		−	14.1459i		−	0.686987i
$425$	−2.70337			−0.131132
$426$	10.1449	+	21.1961i	0.491522	+	1.02695i
$427$	−1.71444			−0.0829676
$428$	7.43378			0.359325
$429$	0.997578	+	5.65728i	0.0481635	+	0.273136i
$430$	48.6047			2.34393
$431$	−33.2417			−1.60119			−0.800597	−	0.599203i	$-0.795484\pi$
$431$	−33.2417			−1.60119			−0.800597	+	0.599203i	$0.795484\pi$
$432$	5.91389	−	25.0770i	0.284532	−	1.20652i
$433$	15.2594			0.733319			0.366659	−	0.930355i	$-0.380501\pi$
$433$	15.2594			0.733319			0.366659	+	0.930355i	$0.380501\pi$
$434$			11.0099i			0.528491i
$435$	8.87152	+	18.5355i	0.425357	+	0.888711i
$436$		−	9.27886i		−	0.444377i
$437$	13.1250			0.627854
$438$	10.3189	+	21.5597i	0.493057	+	1.03016i
$439$			19.4561i			0.928589i	0.885681	+	0.464294i	$0.153692\pi$
$439$			19.4561i			0.928589i	−0.885681	+	0.464294i	$0.846308\pi$
$440$	−4.37941	+	15.7103i	−0.208780	+	0.748959i
$441$	11.4491	−	14.2162i	0.545195	−	0.676963i
$442$			4.67323i			0.222283i
$443$			30.9276i			1.46942i	0.678384	+	0.734708i	$0.262681\pi$
$443$			30.9276i			1.46942i	−0.678384	+	0.734708i	$0.737319\pi$
$444$	3.47338	−	1.66244i	0.164840	−	0.0788958i
$445$	12.5991			0.597254
$446$	5.61624			0.265937
$447$	−9.35311	+	4.47661i	−0.442387	+	0.211736i
$448$		−	2.66438i		−	0.125880i
$449$		−	12.8333i		−	0.605642i	−0.953047	−	0.302821i	$-0.902072\pi$
$449$		−	12.8333i		−	0.605642i	0.953047	−	0.302821i	$-0.0979284\pi$
$450$	3.04370	−	3.77933i	0.143481	−	0.178159i
$451$	−18.0300	−	5.02603i	−0.848998	−	0.236667i
$452$			12.7176i			0.598184i
$453$	5.66436	+	11.8347i	0.266135	+	0.556044i
$454$	−35.7412			−1.67742
$455$		−	2.33742i		−	0.109580i
$456$	2.49369	+	5.21015i	0.116778	+	0.243988i
$457$		−	15.4057i		−	0.720648i	−0.932827	−	0.360324i	$-0.882666\pi$
$457$		−	15.4057i		−	0.720648i	0.932827	−	0.360324i	$-0.117334\pi$
$458$	−13.7755			−0.643685
$459$	−3.33321	+	14.1340i	−0.155581	+	0.659718i
$460$	−15.4085			−0.718424
$461$	−30.6984			−1.42977			−0.714883	−	0.699244i	$-0.753520\pi$
$461$	−30.6984			−1.42977			−0.714883	+	0.699244i	$0.753520\pi$
$462$	−1.59615	−	9.05181i	−0.0742597	−	0.421128i
$463$	13.9293			0.647350			0.323675	−	0.946168i	$-0.395082\pi$
$463$	13.9293			0.647350			0.323675	+	0.946168i	$0.395082\pi$
$464$	24.0819			1.11797
$465$	−12.5692	−	26.2613i	−0.582884	−	1.21784i
$466$	2.55732			0.118465
$467$		−	34.2201i		−	1.58352i	−0.610833	−	0.791759i	$-0.709165\pi$
$467$		−	34.2201i		−	1.58352i	0.610833	−	0.791759i	$-0.290835\pi$
$468$	−1.86023	−	1.49814i	−0.0859890	−	0.0692516i
$469$			13.1506i			0.607237i
$470$	25.5370			1.17793
$471$	3.98944	−	1.90944i	0.183824	−	0.0879822i
$472$			12.3340i			0.567720i
$473$	−10.5970	+	38.0149i	−0.487252	+	1.74793i
$474$	−14.8168	−	30.9571i	−0.680556	−	1.42191i
$475$			1.60251i			0.0735281i
$476$		−	2.12904i		−	0.0975843i
$477$	−16.4190	−	13.2231i	−0.751774	−	0.605444i
$478$	−4.09676			−0.187382
$479$	−3.65218			−0.166872			−0.0834361	−	0.996513i	$-0.526589\pi$
$479$	−3.65218			−0.166872			−0.0834361	+	0.996513i	$0.526589\pi$
$480$	−7.79124	−	16.2785i	−0.355620	−	0.743007i
$481$			2.79242i			0.127323i
$482$			7.14294i			0.325352i
$483$	−11.8436	+	5.66863i	−0.538905	+	0.257932i
$484$	7.49484	+	4.53058i	0.340675	+	0.205936i
$485$			18.9265i			0.859407i
$486$	−16.0066	−	20.5732i	−0.726074	−	0.933219i
$487$	−9.73004			−0.440910			−0.220455	−	0.975397i	$-0.570754\pi$
$487$	−9.73004			−0.440910			−0.220455	+	0.975397i	$0.570754\pi$
$488$		−	3.60683i		−	0.163273i
$489$	28.4334	−	13.6089i	1.28580	−	0.615414i
$490$		−	24.8537i		−	1.12277i
$491$	−38.8236			−1.75208			−0.876042	−	0.482234i	$-0.839825\pi$
$491$	−38.8236			−1.75208			−0.876042	+	0.482234i	$0.839825\pi$
$492$	7.01974	−	3.35980i	0.316475	−	0.151472i
$493$	−13.5731			−0.611303
$494$	2.77021			0.124637
$495$	14.1410	+	19.7686i	0.635592	+	0.888530i
$496$	−34.1194			−1.53201
$497$	7.76336			0.348234
$498$	−30.1862	+	14.4478i	−1.35267	+	0.647420i
$499$	26.3756			1.18073			0.590366	−	0.807136i	$-0.298983\pi$
$499$	26.3756			1.18073			0.590366	+	0.807136i	$0.298983\pi$
$500$			7.84306i			0.350752i
$501$	−7.99925	+	3.82862i	−0.357380	+	0.171050i
$502$			15.1385i			0.675665i
$503$	35.6490			1.58951			0.794756	−	0.606930i	$-0.207599\pi$
$503$	35.6490			1.58951			0.794756	+	0.606930i	$0.207599\pi$
$504$	−4.50049	−	3.62449i	−0.200468	−	0.161447i
$505$			18.6806i			0.831276i
$506$	11.7985	−	42.3249i	0.524507	−	1.88157i
$507$	1.56232	−	0.747762i	0.0693852	−	0.0332093i
$508$			2.06756i			0.0917333i
$509$			27.6810i			1.22694i	0.789718	+	0.613469i	$0.210227\pi$
$509$			27.6810i			1.22694i	−0.789718	+	0.613469i	$0.789773\pi$
$510$	8.53630	+	17.8352i	0.377994	+	0.789754i
$511$	7.89653			0.349322
$512$	−1.18650			−0.0524364
$513$	8.37837	+	1.97587i	0.369914	+	0.0872367i
$514$			22.0505i			0.972607i
$515$			27.0802i			1.19330i
$516$	−7.08390	−	14.8006i	−0.311851	−	0.651561i
$517$	−5.56769	+	19.9731i	−0.244867	+	0.878414i
$518$		−	4.46795i		−	0.196310i
$519$	−7.30486	+	3.49627i	−0.320648	+	0.153469i
$520$	4.91744			0.215644
$521$			7.78321i			0.340988i	0.985359	+	0.170494i	$0.0545364\pi$
$521$			7.78321i			0.340988i	−0.985359	+	0.170494i	$0.945464\pi$
$522$	15.2819	−	18.9754i	0.668870	−	0.830529i
$523$			39.9284i			1.74595i	0.487766	+	0.872975i	$0.337812\pi$
$523$			39.9284i			1.74595i	−0.487766	+	0.872975i	$0.662188\pi$
$524$	−2.04871			−0.0894982
$525$	−0.692116	−	1.44606i	−0.0302064	−	0.0631112i
$526$	−45.2466			−1.97285
$527$	19.2305			0.837694
$528$	28.0514	−	4.94644i	1.22078	−	0.215266i
$529$	−39.7678			−1.72904
$530$	−28.7047			−1.24685
$531$	14.3160	+	11.5294i	0.621259	+	0.500334i
$532$	−1.26206			−0.0547171
$533$			5.64350i			0.244447i
$534$	−6.44903	−	13.4742i	−0.279077	−	0.583084i
$535$			22.8085i			0.986099i
$536$	−27.6661			−1.19499
$537$	−5.51318	−	11.5189i	−0.237911	−	0.497075i
$538$			35.4378i			1.52783i
$539$	19.4386	+	5.41872i	0.837281	+	0.233401i
$540$	−9.83604	−	2.31963i	−0.423276	−	0.0998209i
$541$			29.7871i			1.28065i	0.768106	+	0.640323i	$0.221199\pi$
$541$			29.7871i			1.28065i	−0.768106	+	0.640323i	$0.778801\pi$
$542$			8.36303i			0.359223i
$543$	−14.2671	+	6.82856i	−0.612261	+	0.293041i
$544$	11.9203			0.511081
$545$	28.4697			1.21951
$546$	−2.49976	+	1.19644i	−0.106980	+	0.0512029i
$547$		−	20.3656i		−	0.870769i	−0.900245	−	0.435384i	$-0.856613\pi$
$547$		−	20.3656i		−	0.870769i	0.900245	−	0.435384i	$-0.143387\pi$
$548$			1.78221i			0.0761321i
$549$	−4.18640	−	3.37153i	−0.178671	−	0.143893i
$550$	5.16769	+	1.44055i	0.220351	+	0.0614251i
$551$			8.04592i			0.342768i
$552$	−11.9256	−	24.9166i	−0.507588	−	1.06052i
$553$	−11.3385			−0.482161
$554$			53.8940i			2.28973i
$555$	5.10074	+	10.6571i	0.216515	+	0.452370i
$556$			13.3678i			0.566921i
$557$	20.3081			0.860480			0.430240	−	0.902715i	$-0.358429\pi$
$557$	20.3081			0.860480			0.430240	+	0.902715i	$0.358429\pi$
$558$	−21.6515	+	26.8844i	−0.916581	+	1.13811i
$559$	11.8989			0.503271
$560$	−11.5900			−0.489765
$561$	−15.8104	+	2.78793i	−0.667516	+	0.117707i
$562$	16.1801			0.682515
$563$	3.32261			0.140031			0.0700156	−	0.997546i	$-0.477695\pi$
$563$	3.32261			0.140031			0.0700156	+	0.997546i	$0.477695\pi$
$564$	−3.72189	−	7.77626i	−0.156720	−	0.327440i
$565$	−39.0204			−1.64160
$566$			18.2942i			0.768964i
$567$	−8.41379	+	1.83561i	−0.353346	+	0.0770886i
$568$			16.3325i			0.685296i
$569$	13.1106			0.549624			0.274812	−	0.961498i	$-0.411384\pi$
$569$	13.1106			0.549624			0.274812	+	0.961498i	$0.411384\pi$
$570$	10.5724	−	5.06017i	0.442828	−	0.211947i
$571$			11.6888i			0.489159i	0.969629	+	0.244580i	$0.0786500\pi$
$571$			11.6888i			0.489159i	−0.969629	+	0.244580i	$0.921350\pi$
$572$	0.709052	−	2.54359i	0.0296470	−	0.106353i
$573$	1.06033	+	2.21537i	0.0442957	+	0.0925485i
$574$		−	9.02976i		−	0.376895i
$575$		−	7.66369i		−	0.319598i
$576$	5.23964	−	6.50600i	0.218318	−	0.271083i
$577$	−21.1831			−0.881864			−0.440932	−	0.897541i	$-0.645352\pi$
$577$	−21.1831			−0.881864			−0.440932	+	0.897541i	$0.645352\pi$
$578$	15.3667			0.639169
$579$	−14.9085	−	31.1488i	−0.619576	−	1.29450i
$580$		−	9.44574i		−	0.392213i
$581$			11.0561i			0.458685i
$582$	20.2410	−	9.68779i	0.839017	−	0.401572i
$583$	6.25834	−	22.4506i	0.259194	−	0.929809i
$584$			16.6127i			0.687436i
$585$	4.59664	−	5.70760i	0.190048	−	0.235980i
$586$	21.3924			0.883711
$587$			25.5244i			1.05350i	0.850019	+	0.526752i	$0.176590\pi$
$587$			25.5244i			1.05350i	−0.850019	+	0.526752i	$0.823410\pi$
$588$	−7.56819	+	3.62230i	−0.312107	+	0.149381i
$589$		−	11.3995i		−	0.469709i
$590$	25.0280			1.03039
$591$	22.7895	−	10.9075i	0.937434	−	0.448677i
$592$	13.8461			0.569070
$593$	−46.4883			−1.90905			−0.954523	−	0.298138i	$-0.903635\pi$
$593$	−46.4883			−1.90905			−0.954523	+	0.298138i	$0.903635\pi$
$594$	13.9033	−	25.2420i	0.570458	−	1.03569i
$595$	6.53238			0.267801
$596$	4.76636			0.195238
$597$	−9.73963	+	4.66160i	−0.398617	+	0.190787i
$598$	−13.2480			−0.541750
$599$		−	46.8352i		−	1.91363i	−0.290690	−	0.956817i	$-0.593885\pi$
$599$		−	46.8352i		−	1.91363i	0.290690	−	0.956817i	$-0.406115\pi$
$600$	3.04221	−	1.45607i	0.124198	−	0.0594437i
$601$		−	33.4730i		−	1.36539i	−0.730702	−	0.682696i	$-0.760807\pi$
$601$		−	33.4730i		−	1.36539i	0.730702	−	0.682696i	$-0.239193\pi$
$602$	−19.0386			−0.775955
$603$	−25.8613	+	32.1116i	−1.05315	+	1.30769i
$604$		−	6.03100i		−	0.245398i
$605$	−13.9009	+	22.9959i	−0.565151	+	0.934916i
$606$	19.9781	−	9.56194i	0.811553	−	0.388427i
$607$		−	25.6162i		−	1.03973i	−0.854249	−	0.519865i	$-0.825982\pi$
$607$		−	25.6162i		−	1.03973i	0.854249	−	0.519865i	$-0.174018\pi$
$608$		−	7.06617i		−	0.286571i
$609$	−3.47500	−	7.26042i	−0.140814	−	0.294207i
$610$	−7.31892			−0.296334
$611$	6.25171			0.252917
$612$	4.18686	−	5.19878i	0.169244	−	0.210148i
$613$		−	20.0936i		−	0.811573i	−0.913968	−	0.405787i	$-0.866998\pi$
$613$		−	20.0936i		−	0.811573i	0.913968	−	0.405787i	$-0.133002\pi$
$614$			50.7867i			2.04958i
$615$	10.3087	+	21.5382i	0.415685	+	0.868504i
$616$	1.71543	−	6.15377i	0.0691165	−	0.247942i
$617$			5.16918i			0.208104i	0.994572	+	0.104052i	$0.0331808\pi$
$617$			5.16918i			0.208104i	−0.994572	+	0.104052i	$0.966819\pi$
$618$	28.9610	−	13.8614i	1.16498	−	0.557587i
$619$	46.0353			1.85031			0.925157	−	0.379584i	$-0.123933\pi$
$619$	46.0353			1.85031			0.925157	+	0.379584i	$0.123933\pi$
$620$			13.3828i			0.537466i
$621$	−40.0680	−	9.44921i	−1.60787	−	0.379184i
$622$		−	1.01985i		−	0.0408924i
$623$	−4.93510			−0.197721
$624$	−3.70774	−	7.74670i	−0.148428	−	0.310116i
$625$	−28.9009			−1.15604
$626$	−2.79298			−0.111630
$627$	1.65264	+	9.37214i	0.0660000	+	0.374287i
$628$	−2.03303			−0.0811267
$629$	−7.80398			−0.311165
$630$	−7.35476	+	9.13232i	−0.293020	+	0.363840i
$631$	−30.9152			−1.23071			−0.615357	−	0.788249i	$-0.710988\pi$
$631$	−30.9152			−1.23071			−0.615357	+	0.788249i	$0.710988\pi$
$632$		−	23.8538i		−	0.948853i
$633$	−20.9023	−	43.6718i	−0.830792	−	1.73580i
$634$			11.3389i			0.450326i
$635$	−6.34376			−0.251744
$636$	4.18357	+	8.74087i	0.165890	+	0.346598i
$637$		−	6.08443i		−	0.241074i
$638$	25.9461	+	7.23274i	1.02722	+	0.286347i
$639$	18.9569	+	15.2670i	0.749924	+	0.603954i
$640$		−	32.2130i		−	1.27333i
$641$		−	3.33389i		−	0.131681i	−0.997830	−	0.0658404i	$-0.979027\pi$
$641$		−	3.33389i		−	0.131681i	0.997830	−	0.0658404i	$-0.0209728\pi$
$642$	24.3927	−	11.6749i	0.962703	−	0.460771i
$643$	27.7206			1.09319			0.546596	−	0.837396i	$-0.315923\pi$
$643$	27.7206			1.09319			0.546596	+	0.837396i	$0.315923\pi$
$644$	6.03555			0.237834
$645$	45.4117	−	21.7350i	1.78808	−	0.855817i
$646$			7.74190i			0.304601i
$647$		−	16.3539i		−	0.642938i	−0.946920	−	0.321469i	$-0.895823\pi$
$647$		−	16.3539i		−	0.642938i	0.946920	−	0.321469i	$-0.104177\pi$
$648$	−3.86175	−	17.7009i	−0.151704	−	0.695356i
$649$	−5.45673	+	19.5750i	−0.214195	+	0.768386i
$650$		−	1.61752i		−	0.0634445i
$651$	4.92340	+	10.2866i	0.192963	+	0.403164i
$652$	−14.4897			−0.567461
$653$		−	14.3167i		−	0.560256i	−0.959963	−	0.280128i	$-0.909623\pi$
$653$		−	14.3167i		−	0.560256i	0.959963	−	0.280128i	$-0.0903769\pi$
$654$	−14.5726	−	30.4470i	−0.569834	−	1.19057i
$655$		−	6.28590i		−	0.245611i
$656$	27.9830			1.09255
$657$	19.2821	+	15.5289i	0.752266	+	0.605841i
$658$	−10.0029			−0.389954
$659$	30.9225			1.20457			0.602285	−	0.798281i	$-0.294257\pi$
$659$	30.9225			1.20457			0.602285	+	0.798281i	$0.294257\pi$
$660$	−1.94016	−	11.0027i	−0.0755207	−	0.428279i
$661$	−11.9456			−0.464629			−0.232315	−	0.972641i	$-0.574630\pi$
$661$	−11.9456			−0.464629			−0.232315	+	0.972641i	$0.574630\pi$
$662$	24.7442			0.961709
$663$	2.08977	+	4.36623i	0.0811600	+	0.169570i
$664$	−23.2598			−0.902653
$665$		−	3.87228i		−	0.150161i
$666$	8.78644	−	10.9100i	0.340468	−	0.422755i
$667$		−	38.4781i		−	1.48988i
$668$	4.07643			0.157722
$669$	5.24730	−	2.51147i	0.202872	−	0.0970991i
$670$			56.1396i			2.16886i
$671$	1.59571	−	5.72430i	0.0616015	−	0.220984i
$672$	3.05185	+	6.37632i	0.117728	+	0.245972i
$673$			21.3227i			0.821930i	0.911651	+	0.410965i	$0.134808\pi$
$673$			21.3227i			0.821930i	−0.911651	+	0.410965i	$0.865192\pi$
$674$			6.12005i			0.235736i
$675$	1.15371	−	4.89213i	0.0444063	−	0.188298i
$676$	−0.796163			−0.0306216
$677$	26.8575			1.03222			0.516108	−	0.856523i	$-0.327380\pi$
$677$	26.8575			1.03222			0.516108	+	0.856523i	$0.327380\pi$
$678$	19.9732	+	41.7306i	0.767065	+	1.60265i
$679$		−	7.41356i		−	0.284506i
$680$			13.7428i			0.527011i
$681$	−33.3932	+	15.9827i	−1.27963	+	0.612460i
$682$	−36.7606	−	10.2474i	−1.40764	−	0.392393i
$683$		−	1.82341i		−	0.0697708i	−0.999391	−	0.0348854i	$-0.988893\pi$
$683$		−	1.82341i		−	0.0697708i	0.999391	−	0.0348854i	$-0.0111066\pi$
$684$	−3.08174	−	2.48190i	−0.117833	−	0.0948977i
$685$	−5.46822			−0.208930
$686$			20.9354i			0.799319i
$687$	−12.8705	+	6.16011i	−0.491040	+	0.235023i
$688$		−	59.0002i		−	2.24936i
$689$	−7.02720			−0.267715
$690$	−50.5603	+	24.1993i	−1.92480	+	0.921252i
$691$	50.0336			1.90337			0.951684	−	0.307079i	$-0.0993515\pi$
$691$	50.0336			1.90337			0.951684	+	0.307079i	$0.0993515\pi$
$692$	3.72257			0.141511
$693$	−5.53908	−	7.74340i	−0.210412	−	0.294147i
$694$	54.3264			2.06220
$695$	−41.0155			−1.55581
$696$	15.2744	−	7.31067i	0.578975	−	0.277110i
$697$	−15.7719			−0.597404
$698$			40.6258i			1.53771i
$699$	2.38932	−	1.14358i	0.0903724	−	0.0432542i
$700$			0.736915i			0.0278528i
$701$	13.2586			0.500771			0.250386	−	0.968146i	$-0.419443\pi$
$701$	13.2586			0.500771			0.250386	+	0.968146i	$0.419443\pi$
$702$	−8.45688	−	1.99438i	−0.319184	−	0.0752731i
$703$			4.62606i			0.174475i
$704$	8.89602	+	2.47986i	0.335282	+	0.0934631i
$705$	23.8594	−	11.4196i	0.898596	−	0.430088i
$706$			34.8113i			1.31014i
$707$		−	7.31724i		−	0.275193i
$708$	−3.64772	−	7.62129i	−0.137090	−	0.286426i
$709$	21.1030			0.792539			0.396270	−	0.918134i	$-0.370305\pi$
$709$	21.1030			0.792539			0.396270	+	0.918134i	$0.370305\pi$
$710$	33.1417			1.24378
$711$	−27.6868	−	22.2977i	−1.03834	−	0.836229i
$712$		−	10.3824i		−	0.389098i
$713$			54.5160i			2.04164i
$714$	−3.34369	−	6.98608i	−0.125135	−	0.261448i
$715$	7.80433	+	2.17554i	0.291865	+	0.0813604i
$716$			5.87003i			0.219373i
$717$	−3.82763	+	1.83199i	−0.142946	+	0.0684169i
$718$	25.1204			0.937487
$719$			23.1214i			0.862282i	0.902285	+	0.431141i	$0.141889\pi$
$719$			23.1214i			0.862282i	−0.902285	+	0.431141i	$0.858111\pi$
$720$	−28.3009	−	22.7922i	−1.05471	−	0.849416i
$721$		−	10.6074i		−	0.395040i
$722$	−27.1820			−1.01161
$723$	3.19418	+	6.67370i	0.118793	+	0.248197i
$724$	7.27055			0.270208
$725$	4.69801			0.174480
$726$	31.7084	+	3.09557i	1.17681	+	0.114887i
$727$	−19.3306			−0.716934			−0.358467	−	0.933542i	$-0.616700\pi$
$727$	−19.3306			−0.716934			−0.358467	+	0.933542i	$0.616700\pi$
$728$	−1.92617			−0.0713887
$729$	−24.1550	−	12.0639i	−0.894629	−	0.446809i
$730$	33.7101			1.24767
$731$			33.2539i			1.22994i
$732$	1.06670	+	2.22868i	0.0394263	+	0.0823745i
$733$			26.0122i			0.960784i	0.877054	+	0.480392i	$0.159506\pi$
$733$			26.0122i			0.960784i	−0.877054	+	0.480392i	$0.840494\pi$
$734$	−61.8341			−2.28234
$735$	−11.1141	−	23.2210i	−0.409948	−	0.856518i
$736$			33.7926i			1.24561i
$737$	−43.9081	−	12.2398i	−1.61737	−	0.450859i
$738$	17.7575	−	22.0493i	0.653662	−	0.811645i
$739$			23.6091i			0.868474i	0.900799	+	0.434237i	$0.142982\pi$
$739$			23.6091i			0.868474i	−0.900799	+	0.434237i	$0.857018\pi$
$740$		−	5.43090i		−	0.199644i
$741$	2.58822	−	1.23878i	0.0950807	−	0.0455077i
$742$	11.2437			0.412770
$743$	0.483591			0.0177412			0.00887062	−	0.999961i	$-0.497176\pi$
$743$	0.483591			0.0177412			0.00887062	+	0.999961i	$0.497176\pi$
$744$	−21.6409	+	10.3578i	−0.793394	+	0.379736i
$745$			14.6243i			0.535793i
$746$		−	33.0070i		−	1.20847i
$747$	−21.7424	+	26.9973i	−0.795512	+	0.987779i
$748$	7.10859	+	1.98159i	0.259916	+	0.0724541i
$749$		−	8.93417i		−	0.326447i
$750$	12.3177	+	25.7357i	0.449777	+	0.939734i
$751$	8.14907			0.297364			0.148682	−	0.988885i	$-0.452497\pi$
$751$	8.14907			0.297364			0.148682	+	0.988885i	$0.452497\pi$
$752$		−	30.9988i		−	1.13041i
$753$	6.76963	+	14.1440i	0.246699	+	0.515436i
$754$		−	8.12131i		−	0.295761i
$755$	18.5045			0.673447
$756$	3.85280	+	0.908605i	0.140125	+	0.0330456i
$757$	−10.3591			−0.376508			−0.188254	−	0.982120i	$-0.560283\pi$
$757$	−10.3591			−0.376508			−0.188254	+	0.982120i	$0.560283\pi$
$758$	−16.5777			−0.602130
$759$	−7.90343	−	44.8205i	−0.286876	−	1.62688i
$760$	8.14647			0.295504
$761$	30.3528			1.10029			0.550145	−	0.835069i	$-0.314573\pi$
$761$	30.3528			1.10029			0.550145	+	0.835069i	$0.314573\pi$
$762$	3.24715	+	6.78436i	0.117632	+	0.245772i
$763$	−11.1516			−0.403717
$764$		−	1.12896i		−	0.0408442i
$765$	15.9510	+	12.8462i	0.576711	+	0.464457i
$766$			1.02815i			0.0371487i
$767$	6.12712			0.221237
$768$	−25.7497	+	12.3244i	−0.929163	+	0.444718i
$769$		−	51.5710i		−	1.85970i	−0.367940	−	0.929850i	$-0.619937\pi$
$769$		−	51.5710i		−	1.85970i	0.367940	−	0.929850i	$-0.380063\pi$
$770$	−12.4871	−	3.48092i	−0.450005	−	0.125444i
$771$	9.86055	+	20.6020i	0.355119	+	0.741961i
$772$			15.8735i			0.571299i
$773$		−	25.1008i		−	0.902813i	−0.892318	−	0.451407i	$-0.850922\pi$
$773$		−	25.1008i		−	0.902813i	0.892318	−	0.451407i	$-0.149078\pi$
$774$	−46.4893	−	37.4404i	−1.67102	−	1.34577i
$775$	−6.65617			−0.239097
$776$	15.5966			0.559885
$777$	−1.99798	−	4.17443i	−0.0716770	−	0.149757i
$778$		−	20.6989i		−	0.742093i
$779$			9.34931i			0.334974i
$780$	−3.03852	+	1.45430i	−0.108796	+	0.0520724i
$781$	−7.22570	+	25.9209i	−0.258556	+	0.927521i
$782$		−	37.0242i		−	1.32398i
$783$	5.79258	−	24.5626i	0.207010	−	0.877795i
$784$	−30.1693			−1.07748
$785$		−	6.23780i		−	0.222637i
$786$	−6.72249	+	3.21753i	−0.239783	+	0.114766i
$787$		−	38.8457i		−	1.38470i	−0.721562	−	0.692350i	$-0.756576\pi$
$787$		−	38.8457i		−	1.38470i	0.721562	−	0.692350i	$-0.243424\pi$
$788$	−11.6136			−0.413716
$789$	−42.2742	+	20.2334i	−1.50500	+	0.720327i
$790$	−48.4038			−1.72213
$791$	15.2844			0.543451
$792$	16.2905	−	11.6531i	0.578858	−	0.414074i
$793$	−1.79174			−0.0636267
$794$	−14.9528			−0.530655
$795$	−26.8190	+	12.8362i	−0.951172	+	0.455252i
$796$	4.96333			0.175921
$797$			6.93286i			0.245574i	0.992433	+	0.122787i	$0.0391833\pi$
$797$			6.93286i			0.245574i	−0.992433	+	0.122787i	$0.960817\pi$
$798$	−4.14123	+	1.98208i	−0.146598	+	0.0701650i
$799$			17.4717i			0.618103i
$800$	−4.12594			−0.145874
$801$	−12.0507	−	9.70512i	−0.425792	−	0.342914i
$802$			45.7719i			1.61626i
$803$	−7.34965	+	26.3655i	−0.259363	+	0.930418i
$804$	17.0951	−	8.18208i	0.602896	−	0.288560i
$805$			18.5184i			0.652689i
$806$			11.5063i			0.405293i
$807$	15.8471	+	33.1098i	0.557843	+	1.16552i
$808$	15.3940			0.541558
$809$	17.7195			0.622983			0.311492	−	0.950249i	$-0.399171\pi$
$809$	17.7195			0.622983			0.311492	+	0.950249i	$0.399171\pi$
$810$	−35.9183	+	7.83621i	−1.26204	+	0.275336i
$811$		−	18.8184i		−	0.660803i	−0.943841	−	0.330401i	$-0.892816\pi$
$811$		−	18.8184i		−	0.660803i	0.943841	−	0.330401i	$-0.107184\pi$
$812$			3.69992i			0.129842i
$813$	3.73978	+	7.81364i	0.131160	+	0.274036i
$814$	14.9179	+	4.15851i	0.522872	+	0.145756i
$815$		−	44.4578i		−	1.55729i
$816$	21.6497	−	10.3620i	0.757892	−	0.362744i
$817$	19.7123			0.689648
$818$			14.3671i			0.502334i
$819$	−1.80052	+	2.23568i	−0.0629152	+	0.0781211i
$820$		−	10.9759i		−	0.383295i
$821$	27.0834			0.945218			0.472609	−	0.881272i	$-0.343312\pi$
$821$	27.0834			0.945218			0.472609	+	0.881272i	$0.343312\pi$
$822$	2.79899	+	5.84801i	0.0976259	+	0.203973i
$823$	4.92473			0.171665			0.0858326	−	0.996310i	$-0.472645\pi$
$823$	4.92473			0.171665			0.0858326	+	0.996310i	$0.472645\pi$
$824$	22.3157			0.777406
$825$	5.47239	−	0.964975i	0.190524	−	0.0335961i
$826$	−9.80355			−0.341109
$827$	−2.60413			−0.0905546			−0.0452773	−	0.998974i	$-0.514417\pi$
$827$	−2.60413			−0.0905546			−0.0452773	+	0.998974i	$0.514417\pi$
$828$	14.7379	+	11.8692i	0.512176	+	0.412483i
$829$	11.5682			0.401779			0.200889	−	0.979614i	$-0.435617\pi$
$829$	11.5682			0.401779			0.200889	+	0.979614i	$0.435617\pi$
$830$			47.1984i			1.63828i
$831$	24.1003	+	50.3535i	0.836030	+	1.74674i
$832$		−	2.78452i		−	0.0965358i
$833$	17.0042			0.589159
$834$	20.9944	+	43.8642i	0.726976	+	1.51889i
$835$			12.5074i			0.432838i
$836$	1.17465	−	4.21384i	0.0406262	−	0.145739i
$837$	−8.20696	+	34.8004i	−0.283674	+	1.20288i
$838$			29.5327i			1.02019i
$839$			0.127340i			0.00439627i	0.999998	+	0.00219813i	$0.000699689\pi$
$839$			0.127340i			0.00439627i	−0.999998	+	0.00219813i	$0.999300\pi$
$840$	−7.35116	+	3.51843i	−0.253639	+	0.121397i
$841$	−5.41209			−0.186624
$842$	−42.1954			−1.45415
$843$	15.1171	−	7.23540i	0.520662	−	0.249200i
$844$			22.2552i			0.766057i
$845$		−	2.44281i		−	0.0840352i
$846$	−24.4255	−	19.6712i	−0.839767	−	0.676310i
$847$	5.44501	−	9.00756i	0.187093	−	0.309503i
$848$			34.8440i			1.19655i
$849$	8.18082	+	17.0924i	0.280765	+	0.586611i
$850$	4.52049			0.155052
$851$		−	22.1233i		−	0.758375i
$852$	−4.83024	−	10.0920i	−0.165481	−	0.345745i
$853$		−	10.4257i		−	0.356970i	−0.983943	−	0.178485i	$-0.942880\pi$
$853$		−	10.4257i		−	0.356970i	0.983943	−	0.178485i	$-0.0571196\pi$
$854$	2.86684			0.0981013
$855$	7.61503	−	9.45550i	0.260429	−	0.323371i
$856$	18.7956			0.642421
$857$	29.5617			1.00981			0.504904	−	0.863175i	$-0.331528\pi$
$857$	29.5617			1.00981			0.504904	+	0.863175i	$0.331528\pi$
$858$	−1.66812	−	9.45995i	−0.0569488	−	0.322958i
$859$	−14.4871			−0.494295			−0.247147	−	0.968978i	$-0.579493\pi$
$859$	−14.4871			−0.494295			−0.247147	+	0.968978i	$0.579493\pi$
$860$	−23.1419			−0.789132
$861$	−4.03793	−	8.43657i	−0.137612	−	0.287517i
$862$	55.5858			1.89326
$863$		−	38.3825i		−	1.30656i	−0.757118	−	0.653278i	$-0.773393\pi$
$863$		−	38.3825i		−	1.30656i	0.757118	−	0.653278i	$-0.226607\pi$
$864$	−5.08722	+	21.5716i	−0.173071	+	0.733881i
$865$			11.4217i			0.388349i
$866$	−25.5163			−0.867080
$867$	14.3572	−	6.87166i	0.487595	−	0.233374i
$868$		−	5.24208i		−	0.177928i
$869$	10.5532	−	37.8577i	0.357994	−	1.28424i
$870$	−14.8347	−	30.9946i	−0.502944	−	1.05082i
$871$			13.7435i			0.465682i
$872$		−	23.4608i		−	0.794481i
$873$	14.5791	−	18.1027i	0.493429	−	0.612685i
$874$	−21.9473			−0.742378
$875$	9.42605			0.318659
$876$	−4.91309	−	10.2651i	−0.165998	−	0.346825i
$877$		−	12.1589i		−	0.410576i	−0.978702	−	0.205288i	$-0.934187\pi$
$877$		−	12.1589i		−	0.410576i	0.978702	−	0.205288i	$-0.0658130\pi$
$878$		−	32.5340i		−	1.09797i
$879$	19.9871	−	9.56624i	0.674146	−	0.322661i
$880$	10.7873	−	38.6974i	0.363639	−	1.30449i
$881$			41.7038i			1.40504i	0.711666	+	0.702518i	$0.247941\pi$
$881$			41.7038i			1.40504i	−0.711666	+	0.702518i	$0.752059\pi$
$882$	−19.1449	+	23.7720i	−0.644641	+	0.800444i
$883$	−6.91994			−0.232874			−0.116437	−	0.993198i	$-0.537147\pi$
$883$	−6.91994			−0.232874			−0.116437	+	0.993198i	$0.537147\pi$
$884$		−	2.22504i		−	0.0748361i
$885$	23.3839	−	11.1920i	0.786040	−	0.376216i
$886$		−	51.7163i		−	1.73744i
$887$	−8.79731			−0.295385			−0.147692	−	0.989033i	$-0.547185\pi$
$887$	−8.79731			−0.295385			−0.147692	+	0.989033i	$0.547185\pi$
$888$	8.78214	−	4.20332i	0.294709	−	0.141054i
$889$	2.48487			0.0833398
$890$	−21.0679			−0.706197
$891$	1.70220	−	29.8010i	0.0570260	−	0.998373i
$892$	−2.67403			−0.0895332
$893$	10.3569			0.346580
$894$	15.6400	−	7.48566i	0.523080	−	0.250358i
$895$	−18.0106			−0.602028
$896$			12.6179i			0.421535i
$897$	−12.3777	+	5.92423i	−0.413279	+	0.197804i
$898$			21.4595i			0.716114i
$899$	−33.4195			−1.11460
$900$	−1.44918	+	1.79943i	−0.0483060	+	0.0599810i
$901$		−	19.6389i		−	0.654268i
$902$	30.1492	+	8.40440i	1.00386	+	0.279836i
$903$	−17.7879	+	8.51368i	−0.591944	+	0.283317i
$904$			32.1552i			1.06947i
$905$			22.3077i			0.741534i
$906$	−9.47179	−	19.7897i	−0.314679	−	0.657469i
$907$	−42.9906			−1.42748			−0.713739	−	0.700412i	$-0.753000\pi$
$907$	−42.9906			−1.42748			−0.713739	+	0.700412i	$0.753000\pi$
$908$	17.0173			0.564738
$909$	14.3897	−	17.8676i	0.477277	−	0.592630i
$910$			3.90856i			0.129568i
$911$		−	37.3688i		−	1.23808i	−0.785358	−	0.619041i	$-0.787521\pi$
$911$		−	37.3688i		−	1.23808i	0.785358	−	0.619041i	$-0.212479\pi$
$912$	−6.14243	−	12.8336i	−0.203396	−	0.424962i
$913$	−36.9149	−	10.2904i	−1.22171	−	0.340563i
$914$			25.7610i			0.852098i
$915$	−6.83811	+	3.27287i	−0.226061	+	0.108198i
$916$	6.55883			0.216710
$917$			2.46221i			0.0813092i
$918$	5.57370	−	23.6345i	0.183960	−	0.780054i
$919$			34.0165i			1.12210i	0.827782	+	0.561050i	$0.189603\pi$
$919$			34.0165i			1.12210i	−0.827782	+	0.561050i	$0.810397\pi$
$920$	−38.9589			−1.28444
$921$	22.7108	+	47.4503i	0.748345	+	1.56354i
$922$	51.3330			1.69056
$923$	8.11341			0.267056
$924$	0.759967	+	4.30979i	0.0250011	+	0.141782i
$925$	2.70116			0.0888135
$926$	−23.2922			−0.765430
$927$	20.8600	−	25.9016i	0.685131	−	0.850720i
$928$	−20.7156			−0.680024
$929$			31.5249i			1.03430i	0.855896	+	0.517149i	$0.173007\pi$
$929$			31.5249i			1.03430i	−0.855896	+	0.517149i	$0.826993\pi$
$930$	21.0179	+	43.9134i	0.689205	+	1.43998i
$931$		−	10.0798i		−	0.330351i
$932$	−1.21760			−0.0398839
$933$	−0.456058	−	0.952855i	−0.0149307	−	0.0311951i
$934$			57.2220i			1.87236i
$935$	−6.07997	+	21.8108i	−0.198836	+	0.713289i
$936$	−4.70341	−	3.78792i	−0.153736	−	0.123812i
$937$		−	32.6255i		−	1.06583i	−0.846169	−	0.532915i	$-0.821097\pi$
$937$		−	32.6255i		−	1.06583i	0.846169	−	0.532915i	$-0.178903\pi$
$938$		−	21.9900i		−	0.718000i
$939$	−2.60950	+	1.24896i	−0.0851578	+	0.0407584i
$940$	−12.1588			−0.396576
$941$	3.31307			0.108003			0.0540016	−	0.998541i	$-0.482802\pi$
$941$	3.31307			0.108003			0.0540016	+	0.998541i	$0.482802\pi$
$942$	−6.67104	+	3.19291i	−0.217354	+	0.104031i
$943$		−	44.7113i		−	1.45600i
$944$		−	30.3810i		−	0.988817i
$945$	−2.78781	+	11.8213i	−0.0906874	+	0.384547i
$946$	17.7201	−	63.5674i	0.576129	−	2.06676i
$947$		−	22.4215i		−	0.728601i	−0.931281	−	0.364301i	$-0.881308\pi$
$947$		−	22.4215i		−	0.728601i	0.931281	−	0.364301i	$-0.118692\pi$
$948$	7.05462	+	14.7394i	0.229123	+	0.478715i
$949$	8.25258			0.267890
$950$		−	2.67967i		−	0.0869399i
$951$	5.07053	+	10.5940i	0.164423	+	0.343535i
$952$		−	5.38308i		−	0.174467i
$953$	−4.66356			−0.151068			−0.0755338	−	0.997143i	$-0.524066\pi$
$953$	−4.66356			−0.151068			−0.0755338	+	0.997143i	$0.524066\pi$
$954$	27.4554	+	22.1113i	0.888901	+	0.715880i
$955$	3.46390			0.112089
$956$	1.95057			0.0630859
$957$	27.4759	−	4.84498i	0.888171	−	0.156616i
$958$	6.10707			0.197311
$959$	2.14192			0.0691661
$960$	−5.08631	−	10.6270i	−0.164160	−	0.342985i
$961$	16.3490			0.527387
$962$		−	4.66941i		−	0.150548i
$963$	17.5695	−	21.8158i	0.566169	−	0.703006i
$964$		−	3.40093i		−	0.109537i
$965$	−48.7035			−1.56782
$966$	19.8046	−	9.47893i	0.637204	−	0.304980i
$967$		−	0.319454i		−	0.0102729i	−0.999987	−	0.00513647i	$-0.998365\pi$
$967$		−	0.319454i		−	0.0102729i	0.999987	−	0.00513647i	$-0.00163500\pi$
$968$	18.9500	+	11.4552i	0.609077	+	0.368183i
$969$	3.46202	+	7.23331i	0.111216	+	0.232367i
$970$		−	31.6483i		−	1.01617i
$971$		−	8.75348i		−	0.280912i	−0.990087	−	0.140456i	$-0.955143\pi$
$971$		−	8.75348i		−	0.280912i	0.990087	−	0.140456i	$-0.0448569\pi$
$972$	7.62113	+	9.79540i	0.244448	+	0.314188i
$973$	16.0659			0.515049
$974$	16.2703			0.521335
$975$	−0.723324	−	1.51126i	−0.0231649	−	0.0483991i
$976$			8.88428i			0.284379i
$977$			24.3314i			0.778431i	0.921147	+	0.389216i	$0.127254\pi$
$977$			24.3314i			0.778431i	−0.921147	+	0.389216i	$0.872746\pi$
$978$	−47.5456	+	22.7564i	−1.52034	+	0.727668i
$979$	4.59332	−	16.4777i	0.146803	−	0.526629i
$980$			11.8334i			0.378005i
$981$	−27.2306	−	21.9303i	−0.869406	−	0.700180i
$982$	64.9198			2.07167
$983$		−	55.1939i		−	1.76041i	−0.474592	−	0.880206i	$-0.657404\pi$
$983$		−	55.1939i		−	1.76041i	0.474592	−	0.880206i	$-0.342596\pi$
$984$	17.7488	−	8.49496i	0.565811	−	0.270809i
$985$		−	35.6331i		−	1.13536i
$986$	22.6966			0.722808
$987$	−9.34578	+	4.47310i	−0.297479	+	0.142380i
$988$	−1.31896			−0.0419618
$989$	−94.2706			−2.99763
$990$	−23.6463	−	33.0564i	−0.751527	−	1.05060i
$991$	−26.4780			−0.841102			−0.420551	−	0.907269i	$-0.638163\pi$
$991$	−26.4780			−0.841102			−0.420551	+	0.907269i	$0.638163\pi$
$992$	29.3500			0.931865
$993$	23.1186	−	11.0651i	0.733648	−	0.351140i
$994$	−12.9817			−0.411754
$995$			15.2287i			0.482781i
$996$	14.3724	−	6.87894i	0.455406	−	0.217967i
$997$		−	35.2898i		−	1.11764i	−0.829289	−	0.558820i	$-0.811254\pi$
$997$		−	35.2898i		−	1.11764i	0.829289	−	0.558820i	$-0.188746\pi$
$998$	−44.1045			−1.39610
$999$	3.33049	−	14.1224i	0.105372	−	0.446814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.14	yes	48
3.2	odd	2	inner	429.2.f.a.131.35	yes	48
11.10	odd	2	inner	429.2.f.a.131.36	yes	48
33.32	even	2	inner	429.2.f.a.131.13	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.13	✓	48	33.32	even	2	inner
429.2.f.a.131.14	yes	48	1.1	even	1	trivial
429.2.f.a.131.35	yes	48	3.2	odd	2	inner
429.2.f.a.131.36	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)

\(f(q)\)	\(=\)	\(q-1.67217 q^{2} +(-1.56232 + 0.747762i) q^{3} +0.796163 q^{4} +2.44281i q^{5} +(2.61247 - 1.25039i) q^{6} -0.956855i q^{7} +2.01302 q^{8} +(1.88170 - 2.33649i) q^{9} +O(q^{10})\)	\(q-1.67217 q^{2} +(-1.56232 + 0.747762i) q^{3} +0.796163 q^{4} +2.44281i q^{5} +(2.61247 - 1.25039i) q^{6} -0.956855i q^{7} +2.01302 q^{8} +(1.88170 - 2.33649i) q^{9} -4.08480i q^{10} +(3.19482 + 0.890587i) q^{11} +(-1.24386 + 0.595340i) q^{12} -1.00000i q^{13} +1.60003i q^{14} +(-1.82664 - 3.81646i) q^{15} -4.95845 q^{16} +2.79470 q^{17} +(-3.14653 + 3.90702i) q^{18} -1.65665i q^{19} +1.94487i q^{20} +(0.715500 + 1.49492i) q^{21} +(-5.34229 - 1.48922i) q^{22} +7.92262i q^{23} +(-3.14499 + 1.50526i) q^{24} -0.967318 q^{25} +1.67217i q^{26} +(-1.19269 + 5.05742i) q^{27} -0.761812i q^{28} -4.85674 q^{29} +(3.05446 + 6.38178i) q^{30} +6.88106 q^{31} +4.26534 q^{32} +(-5.65728 + 0.997578i) q^{33} -4.67323 q^{34} +2.33742 q^{35} +(1.49814 - 1.86023i) q^{36} -2.79242 q^{37} +2.77021i q^{38} +(0.747762 + 1.56232i) q^{39} +4.91744i q^{40} -5.64350 q^{41} +(-1.19644 - 2.49976i) q^{42} +11.8989i q^{43} +(2.54359 + 0.709052i) q^{44} +(5.70760 + 4.59664i) q^{45} -13.2480i q^{46} +6.25171i q^{47} +(7.74670 - 3.70774i) q^{48} +6.08443 q^{49} +1.61752 q^{50} +(-4.36623 + 2.08977i) q^{51} -0.796163i q^{52} -7.02720i q^{53} +(1.99438 - 8.45688i) q^{54} +(-2.17554 + 7.80433i) q^{55} -1.92617i q^{56} +(1.23878 + 2.58822i) q^{57} +8.12131 q^{58} +6.12712i q^{59} +(-1.45430 - 3.03852i) q^{60} -1.79174i q^{61} -11.5063 q^{62} +(-2.23568 - 1.80052i) q^{63} +2.78452 q^{64} +2.44281 q^{65} +(9.45995 - 1.66812i) q^{66} -13.7435 q^{67} +2.22504 q^{68} +(-5.92423 - 12.3777i) q^{69} -3.90856 q^{70} +8.11341i q^{71} +(3.78792 - 4.70341i) q^{72} +8.25258i q^{73} +4.66941 q^{74} +(1.51126 - 0.723324i) q^{75} -1.31896i q^{76} +(0.852163 - 3.05698i) q^{77} +(-1.25039 - 2.61247i) q^{78} -11.8497i q^{79} -12.1125i q^{80} +(-1.91838 - 8.79317i) q^{81} +9.43692 q^{82} -11.5546 q^{83} +(0.569654 + 1.19020i) q^{84} +6.82692i q^{85} -19.8970i q^{86} +(7.58779 - 3.63169i) q^{87} +(6.43124 + 1.79277i) q^{88} -5.15763i q^{89} +(-9.54410 - 7.68638i) q^{90} -0.956855 q^{91} +6.30769i q^{92} +(-10.7504 + 5.14540i) q^{93} -10.4539i q^{94} +4.04688 q^{95} +(-6.66383 + 3.18946i) q^{96} +7.74783 q^{97} -10.1742 q^{98} +(8.09255 - 5.78884i) 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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