LMFDB - Embedded newform 429.2.y.a.116.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(116,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 5]))

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

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

chi := DirichletCharacter("429.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.y (of order $10$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			116.3
Character	$\chi$	$=$	429.116
Dual form			429.2.y.a.233.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72295 + 0.559822i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(1.03713 - 0.753522i) q^{4} +(1.18548 - 3.64854i) q^{5} +(2.98424 + 0.969639i) q^{6} +(0.764591 - 1.05237i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})$	\(q+(-1.72295 + 0.559822i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(1.03713 - 0.753522i) q^{4} +(1.18548 - 3.64854i) q^{5} +(2.98424 + 0.969639i) q^{6} +(0.764591 - 1.05237i) q^{8} +(0.927051 + 2.85317i) q^{9} +6.94993i q^{10} +(1.53488 - 2.94009i) q^{11} -2.22043 q^{12} +(3.42908 - 1.11418i) q^{13} +(-5.37565 + 3.90564i) q^{15} +(-1.52052 + 4.67967i) q^{16} +(-3.19453 - 4.39690i) q^{18} +(-1.51975 - 4.67732i) q^{20} +(-0.998608 + 5.92490i) q^{22} +(-2.14278 + 0.696231i) q^{24} +(-7.86141 - 5.71165i) q^{25} +(-5.28441 + 3.83935i) q^{26} +(1.60570 - 4.94183i) q^{27} +(7.07554 - 9.73865i) q^{30} -6.31247i q^{32} +(-5.14400 + 2.55720i) q^{33} +(3.11140 + 2.26057i) q^{36} +(-5.93935 - 1.92981i) q^{39} +(-2.93320 - 4.03721i) q^{40} +(5.95913 - 8.20204i) q^{41} -7.75348i q^{43} +(-0.623542 - 4.20584i) q^{44} +11.5089 q^{45} +(-9.69122 - 7.04108i) q^{47} +(6.89488 - 5.00943i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(16.7423 + 5.43992i) q^{50} +(2.71686 - 3.73944i) q^{52} +9.41346i q^{54} +(-8.90746 - 9.08552i) q^{55} +(-11.6971 + 8.49847i) q^{59} +(-2.63229 + 8.10135i) q^{60} +(10.4139 + 3.38370i) q^{61} +(0.492822 + 1.51675i) q^{64} -13.8320i q^{65} +(7.43129 - 7.28566i) q^{66} +(-4.98064 + 15.3288i) q^{71} +(3.71140 + 1.20591i) q^{72} +(5.20099 + 16.0070i) q^{75} +11.3136 q^{78} +(-13.6385 + 4.43142i) q^{79} +(15.2714 + 11.0953i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-5.67562 + 17.4678i) q^{82} +(-3.06752 - 0.996699i) q^{83} +(4.34056 + 13.3589i) q^{86} +(-1.92050 - 3.86323i) q^{88} +4.31872 q^{89} +(-19.8293 + 6.44294i) q^{90} +(20.6393 + 6.70610i) q^{94} +(-6.42656 + 8.84540i) q^{96} -12.6813i q^{98} +(9.81149 + 1.65367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 24 * q^9	$ 32 q + 16 q^{4} - 24 q^{9} - 24 q^{12} - 92 q^{16} + 28 q^{22} - 40 q^{25} + 180 q^{30} + 48 q^{36} - 72 q^{48} + 56 q^{49} - 260 q^{52} + 32 q^{55} + 184 q^{64} - 60 q^{66} - 144 q^{75} - 72 q^{81} + 204 q^{82} - 40 q^{88} + 60 q^{90}+O(q^{100}) $ 32 * q + 16 * q^4 - 24 * q^9 - 24 * q^12 - 92 * q^16 + 28 * q^22 - 40 * q^25 + 180 * q^30 + 48 * q^36 - 72 * q^48 + 56 * q^49 - 260 * q^52 + 32 * q^55 + 184 * q^64 - 60 * q^66 - 144 * q^75 - 72 * q^81 + 204 * q^82 - 40 * q^88 + 60 * q^90

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−1.72295	+	0.559822i	−1.21831	+	0.395854i	−0.846467	−	0.532441i	$-0.821275\pi$
$2$	−1.72295	+	0.559822i	−1.21831	+	0.395854i	−0.371845	+	0.928295i	$0.621275\pi$
$3$	−1.40126	−	1.01807i	−0.809017	−	0.587785i
$3$	−1.40126	−	1.01807i	−0.809017	−	0.587785i
$4$	1.03713	−	0.753522i	0.518567	−	0.376761i
$5$	1.18548	−	3.64854i	0.530164	−	1.63168i	−0.223708	−	0.974656i	$-0.571816\pi$
$5$	1.18548	−	3.64854i	0.530164	−	1.63168i	0.753872	−	0.657022i	$-0.228184\pi$
$6$	2.98424	+	0.969639i	1.21831	+	0.395854i
$7$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$7$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$8$	0.764591	−	1.05237i	0.270324	−	0.372069i
$9$	0.927051	+	2.85317i	0.309017	+	0.951057i
$10$			6.94993i			2.19776i
$11$	1.53488	−	2.94009i	0.462785	−	0.886471i
$11$	1.53488	−	2.94009i	0.462785	−	0.886471i
$12$	−2.22043			−0.640984
$13$	3.42908	−	1.11418i	0.951057	−	0.309017i
$13$	3.42908	−	1.11418i	0.951057	−	0.309017i
$14$		0			0
$15$	−5.37565	+	3.90564i	−1.38799	+	1.00843i
$16$	−1.52052	+	4.67967i	−0.380129	+	1.16992i
$17$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$17$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$18$	−3.19453	−	4.39690i	−0.752958	−	1.03636i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	−1.51975	−	4.67732i	−0.339827	−	1.04588i
$21$		0			0
$22$	−0.998608	+	5.92490i	−0.212904	+	1.26319i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−2.14278	+	0.696231i	−0.437393	+	0.142118i
$25$	−7.86141	−	5.71165i	−1.57228	−	1.14233i
$26$	−5.28441	+	3.83935i	−1.03636	+	0.752958i
$27$	1.60570	−	4.94183i	0.309017	−	0.951057i
$28$		0			0
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$	7.07554	−	9.73865i	1.29181	−	1.77803i
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$		−	6.31247i		−	1.11590i
$33$	−5.14400	+	2.55720i	−0.895455	+	0.445152i
$34$		0			0
$35$		0			0
$36$	3.11140	+	2.26057i	0.518567	+	0.376761i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$	−5.93935	−	1.92981i	−0.951057	−	0.309017i
$40$	−2.93320	−	4.03721i	−0.463780	−	0.638339i
$41$	5.95913	−	8.20204i	0.930659	−	1.28094i	−0.0289423	−	0.999581i	$-0.509214\pi$
$41$	5.95913	−	8.20204i	0.930659	−	1.28094i	0.959602	−	0.281362i	$-0.0907861\pi$
$42$		0			0
$43$		−	7.75348i		−	1.18239i	−0.806527	−	0.591197i	$-0.798656\pi$
$43$		−	7.75348i		−	1.18239i	0.806527	−	0.591197i	$-0.201344\pi$
$44$	−0.623542	−	4.20584i	−0.0940025	−	0.634054i
$45$	11.5089			1.71565
$46$		0			0
$47$	−9.69122	−	7.04108i	−1.41361	−	1.02705i	−0.992785	−	0.119905i	$-0.961741\pi$
$47$	−9.69122	−	7.04108i	−1.41361	−	1.02705i	−0.420824	−	0.907142i	$-0.638259\pi$
$48$	6.89488	−	5.00943i	0.995191	−	0.723048i
$49$	−2.16312	+	6.65740i	−0.309017	+	0.951057i
$50$	16.7423	+	5.43992i	2.36772	+	0.769320i
$51$		0			0
$52$	2.71686	−	3.73944i	0.376761	−	0.518567i
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$			9.41346i			1.28101i
$55$	−8.90746	−	9.08552i	−1.20108	−	1.22509i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−11.6971	+	8.49847i	−1.52284	+	1.10641i	−0.562779	+	0.826607i	$0.690268\pi$
$59$	−11.6971	+	8.49847i	−1.52284	+	1.10641i	−0.960059	+	0.279799i	$0.909732\pi$
$60$	−2.63229	+	8.10135i	−0.339827	+	1.04588i
$61$	10.4139	+	3.38370i	1.33337	+	0.433238i	0.887066	−	0.461644i	$-0.152740\pi$
$61$	10.4139	+	3.38370i	1.33337	+	0.433238i	0.446304	+	0.894881i	$0.352740\pi$
$62$		0			0
$63$		0			0
$64$	0.492822	+	1.51675i	0.0616028	+	0.189594i
$65$		−	13.8320i		−	1.71565i
$66$	7.43129	−	7.28566i	0.914729	−	0.896803i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.98064	+	15.3288i	−0.591093	+	1.81920i	−0.0178059	+	0.999841i	$0.505668\pi$
$71$	−4.98064	+	15.3288i	−0.591093	+	1.81920i	−0.573287	+	0.819355i	$0.694332\pi$
$72$	3.71140	+	1.20591i	0.437393	+	0.142118i
$73$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$73$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$74$		0			0
$75$	5.20099	+	16.0070i	0.600558	+	1.84833i
$76$		0			0
$77$		0			0
$78$	11.3136			1.28101
$79$	−13.6385	+	4.43142i	−1.53445	+	0.498574i	−0.949839	−	0.312739i	$-0.898754\pi$
$79$	−13.6385	+	4.43142i	−1.53445	+	0.498574i	−0.584613	+	0.811312i	$0.698754\pi$
$80$	15.2714	+	11.0953i	1.70740	+	1.24050i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$	−5.67562	+	17.4678i	−0.626768	+	1.92899i
$83$	−3.06752	−	0.996699i	−0.336705	−	0.109402i	0.135785	−	0.990738i	$-0.456644\pi$
$83$	−3.06752	−	0.996699i	−0.336705	−	0.109402i	−0.472489	+	0.881336i	$0.656644\pi$
$84$		0			0
$85$		0			0
$86$	4.34056	+	13.3589i	0.468055	+	1.44053i
$87$		0			0
$88$	−1.92050	−	3.86323i	−0.204726	−	0.411822i
$89$	4.31872			0.457783			0.228892	−	0.973452i	$-0.426490\pi$
$89$	4.31872			0.457783			0.228892	+	0.973452i	$0.426490\pi$
$90$	−19.8293	+	6.44294i	−2.09019	+	0.679145i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	20.6393	+	6.70610i	2.12878	+	0.691682i
$95$		0			0
$96$	−6.42656	+	8.84540i	−0.655908	+	0.902780i
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$		−	12.6813i		−	1.28101i
$99$	9.81149	+	1.65367i	0.986092	+	0.166200i
$100$	−12.4572			−1.24572
$101$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$101$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$102$		0			0
$103$	16.4115	−	11.9236i	1.61707	−	1.17487i	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.4115	−	11.9236i	1.61707	−	1.17487i	0.828808	−	0.559533i	$-0.189020\pi$
$104$	1.44932	−	4.46055i	0.142118	−	0.437393i
$105$		0			0
$106$		0			0
$107$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$107$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$108$	−2.05846	−	6.33528i	−0.198075	−	0.609612i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	20.4334	+	10.6673i	1.94825	+	1.01709i
$111$		0			0
$112$		0			0
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.35787	+	8.75086i	0.587785	+	0.809017i
$118$	15.3960	−	21.1908i	1.41732	−	1.95077i
$119$		0			0
$120$			8.64339i			0.789030i
$121$	−6.28826	−	9.02540i	−0.571660	−	0.820491i
$122$	−19.8370			−1.79596
$123$	−16.7006	+	5.42634i	−1.50584	+	0.489277i
$124$		0			0
$125$	−14.6406	+	10.6370i	−1.30949	+	0.951402i
$126$		0			0
$127$	1.41429	+	0.459530i	0.125498	+	0.0407767i	0.371093	−	0.928596i	$-0.378983\pi$
$127$	1.41429	+	0.459530i	0.125498	+	0.0407767i	−0.245595	+	0.969373i	$0.578983\pi$
$128$	5.72253	+	7.87639i	0.505805	+	0.696181i
$129$	−7.89361	+	10.8646i	−0.694994	+	0.956577i
$130$	7.74345	+	23.8319i	0.679145	+	2.09019i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−3.40811	+	6.52828i	−0.296638	+	0.568214i
$133$		0			0
$134$		0			0
$135$	−16.1270	−	11.7169i	−1.38799	−	1.00843i
$136$		0			0
$137$	2.52426	−	7.76887i	0.215662	−	0.663739i	−0.783444	−	0.621463i	$-0.786539\pi$
$137$	2.52426	−	7.76887i	0.215662	−	0.663739i	0.999106	−	0.0422769i	$-0.0134612\pi$
$138$		0			0
$139$	13.4490	+	18.5109i	1.14073	+	1.57008i	0.765874	+	0.642991i	$0.222307\pi$
$139$	13.4490	+	18.5109i	1.14073	+	1.57008i	0.374853	+	0.927084i	$0.377693\pi$
$140$		0			0
$141$	6.41156	+	19.7327i	0.539951	+	1.66180i
$142$		−	29.1991i		−	2.45033i
$143$	1.98747	−	11.7919i	0.166200	−	0.986092i
$144$	−14.7615			−1.23012
$145$		0			0
$146$		0			0
$147$	9.80881	−	7.12652i	0.809017	−	0.587785i
$148$		0			0
$149$	−13.4191	−	4.36012i	−1.09933	−	0.357195i	−0.297487	−	0.954726i	$-0.596148\pi$
$149$	−13.4191	−	4.36012i	−1.09933	−	0.357195i	−0.801846	+	0.597531i	$0.796148\pi$
$150$	−17.9221	−	24.6677i	−1.46333	−	2.01411i
$151$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$151$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−7.61406	+	2.47396i	−0.609612	+	0.198075i
$157$	18.7201	+	13.6010i	1.49403	+	1.08548i	0.972685	+	0.232129i	$0.0745691\pi$
$157$	18.7201	+	13.6010i	1.49403	+	1.08548i	0.521344	+	0.853347i	$0.325431\pi$
$158$	21.0177	−	15.2703i	1.67208	−	1.21484i
$159$		0			0
$160$	−23.0313	−	7.48332i	−1.82078	−	0.591609i
$161$		0			0
$162$	9.58359	−	13.1907i	0.752958	−	1.03636i
$163$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$163$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$164$		−	12.9970i		−	1.01489i
$165$	3.23193	+	21.7996i	0.251606	+	1.69710i
$166$	5.84317			0.453518
$167$	4.05298	−	1.31689i	0.313629	−	0.101904i	−0.147973	−	0.988991i	$-0.547275\pi$
$167$	4.05298	−	1.31689i	0.313629	−	0.101904i	0.461602	+	0.887087i	$0.347275\pi$
$168$		0			0
$169$	10.5172	−	7.64121i	0.809017	−	0.587785i
$170$		0			0
$171$		0			0
$172$	−5.84242	−	8.04140i	−0.445480	−	0.613151i
$173$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$173$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$174$		0			0
$175$		0			0
$176$	11.4248	+	11.6532i	0.861179	+	0.878393i
$177$	25.0428			1.88233
$178$	−7.44095	+	2.41771i	−0.557723	+	0.181215i
$179$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$179$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$180$	11.9363	−	8.67222i	0.889679	−	0.646389i
$181$	7.03726	−	21.6584i	0.523075	−	1.60986i	−0.245016	−	0.969519i	$-0.578793\pi$
$181$	7.03726	−	21.6584i	0.523075	−	1.60986i	0.768091	−	0.640341i	$-0.221207\pi$
$182$		0			0
$183$	−11.1478	−	15.3436i	−0.824068	−	1.13423i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−15.3567			−1.12000
$189$		0			0
$190$		0			0
$191$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$191$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$192$	0.853593	−	2.62709i	0.0616028	−	0.189594i
$193$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$193$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$194$		0			0
$195$	−14.0820	+	19.3822i	−1.00843	+	1.38799i
$196$	2.77305	+	8.53457i	0.198075	+	0.609612i
$197$		−	20.7525i		−	1.47856i	−0.673400	−	0.739278i	$-0.735167\pi$
$197$		−	20.7525i		−	1.47856i	0.673400	−	0.739278i	$-0.264833\pi$
$198$	−17.8305	+	2.64349i	−1.26716	+	0.187864i
$199$	−21.2096			−1.50351			−0.751754	−	0.659443i	$-0.770792\pi$
$199$	−21.2096			−1.50351			−0.751754	+	0.659443i	$0.770792\pi$
$200$	−12.0215	+	3.90603i	−0.850050	+	0.276198i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−22.8610	−	31.4655i	−1.59668	−	2.19765i
$206$	−21.6011	+	29.7314i	−1.50502	+	2.07148i
$207$		0			0
$208$			17.7411i			1.23012i
$209$		0			0
$210$		0			0
$211$	24.1300	−	7.84031i	1.66118	−	0.539749i	0.680058	−	0.733158i	$-0.261954\pi$
$211$	24.1300	−	7.84031i	1.66118	−	0.539749i	0.981118	+	0.193409i	$0.0619544\pi$
$212$		0			0
$213$	22.5850	−	16.4090i	1.54750	−	1.12433i
$214$		0			0
$215$	−28.2889	−	9.19162i	−1.92929	−	0.626863i
$216$	−3.97293	−	5.46827i	−0.270324	−	0.372069i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−16.0844	−	2.71093i	−1.08441	−	0.182771i
$221$		0			0
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$		0			0
$225$	9.00837	−	27.7249i	0.600558	−	1.84833i
$226$		0			0
$227$	8.50930	+	11.7120i	0.564782	+	0.777356i	0.991925	−	0.126828i	$-0.0404798\pi$
$227$	8.50930	+	11.7120i	0.564782	+	0.777356i	−0.427143	+	0.904184i	$0.640480\pi$
$228$		0			0
$229$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$229$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$233$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$234$	−15.8532	−	11.5180i	−1.03636	−	0.752958i
$235$	−37.1785	+	27.0117i	−2.42526	+	1.76205i
$236$	−5.72772	+	17.6281i	−0.372843	+	1.14749i
$237$	23.6226	+	7.67544i	1.53445	+	0.498574i
$238$		0			0
$239$	18.1563	−	24.9900i	1.17443	−	1.61647i	0.551660	−	0.834069i	$-0.313995\pi$
$239$	18.1563	−	24.9900i	1.17443	−	1.61647i	0.622774	−	0.782402i	$-0.286005\pi$
$240$	−10.1033	−	31.0949i	−0.652167	−	2.00717i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	15.8870	+	12.0300i	1.02125	+	0.773320i
$243$	15.5885			1.00000
$244$	13.3504	−	4.33779i	0.854669	−	0.277699i
$245$	21.7254	+	15.7845i	1.38799	+	1.00843i
$246$	25.7365	−	18.6987i	1.64090	−	1.19218i
$247$		0			0
$248$		0			0
$249$	3.28368	+	4.51960i	0.208095	+	0.286418i
$250$	19.2702	−	26.5232i	1.21875	−	1.67747i
$251$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$251$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$252$		0			0
$253$		0			0
$254$	−2.69401			−0.169037
$255$		0			0
$256$	−16.8495	−	12.2419i	−1.05309	−	0.765116i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$	7.51808	−	23.1383i	0.468055	−	1.44053i
$259$		0			0
$260$	−10.4227	−	14.3456i	−0.646389	−	0.889679i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−1.24194	+	7.36860i	−0.0764359	+	0.453506i
$265$		0			0
$266$		0			0
$267$	−6.05164	−	4.39677i	−0.370354	−	0.269078i
$268$		0			0
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$	34.3454	+	11.1595i	2.09019	+	0.679145i
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$			14.7985i			0.894012i
$275$	−28.8591	+	14.3465i	−1.74027	+	0.865128i
$276$		0			0
$277$	−23.7574	+	7.71924i	−1.42744	+	0.463804i	−0.917959	−	0.396676i	$-0.870164\pi$
$277$	−23.7574	+	7.71924i	−1.42744	+	0.463804i	−0.509484	+	0.860480i	$0.670164\pi$
$278$	−33.5348	−	24.3644i	−2.01128	−	1.46128i
$279$		0			0
$280$		0			0
$281$	31.6738	+	10.2914i	1.88950	+	0.613936i	0.980278	+	0.197626i	$0.0633230\pi$
$281$	31.6738	+	10.2914i	1.88950	+	0.613936i	0.909223	+	0.416310i	$0.136677\pi$
$282$	−22.0936	−	30.4093i	−1.31566	−	1.81085i
$283$	4.44329	−	6.11566i	0.264126	−	0.363538i	−0.656270	−	0.754526i	$-0.727867\pi$
$283$	4.44329	−	6.11566i	0.264126	−	0.363538i	0.920396	+	0.390988i	$0.127867\pi$
$284$	6.38502	+	19.6511i	0.378881	+	1.16608i
$285$		0			0
$286$	3.17707	+	21.4296i	0.187864	+	1.26716i
$287$		0			0
$288$	18.0105	−	5.85198i	1.06128	−	0.344831i
$289$	13.7533	+	9.99235i	0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	11.9219	+	16.4091i	0.696485	+	0.958630i	0.999983	+	0.00579779i	$0.00184550\pi$
$293$	11.9219	+	16.4091i	0.696485	+	0.958630i	−0.303498	+	0.952832i	$0.598154\pi$
$294$	−12.9105	+	17.7698i	−0.752958	+	1.03636i
$295$	17.1403	+	52.7523i	0.997945	+	3.07136i
$296$		0			0
$297$	−12.0649	−	12.3060i	−0.700075	−	0.714069i
$298$	25.5613			1.48073
$299$		0			0
$300$	17.4557	+	12.6823i	1.00781	+	0.732215i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	24.6911	−	33.9844i	1.41381	−	1.94594i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	−35.1359			−1.99881
$310$		0			0
$311$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$311$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$312$	−6.57205	+	4.77487i	−0.372069	+	0.270324i
$313$	−9.97005	+	30.6847i	−0.563540	+	1.73440i	0.108708	+	0.994074i	$0.465329\pi$
$313$	−9.97005	+	30.6847i	−0.563540	+	1.73440i	−0.672249	+	0.740325i	$0.734671\pi$
$314$	−39.8680	−	12.9539i	−2.24988	−	0.731031i
$315$		0			0
$316$	−10.8058	+	14.8729i	−0.607873	+	0.836666i
$317$	4.81255	+	14.8115i	0.270300	+	0.831897i	0.990425	+	0.138053i	$0.0440844\pi$
$317$	4.81255	+	14.8115i	0.270300	+	0.831897i	−0.720125	+	0.693844i	$0.755916\pi$
$318$		0			0
$319$		0			0
$320$	6.11816			0.342016
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−3.56535	+	10.9730i	−0.198075	+	0.609612i
$325$	−33.3212	−	10.8267i	−1.84833	−	0.600558i
$326$		0			0
$327$		0			0
$328$	−4.07528	−	12.5424i	−0.225019	−	0.692539i
$329$		0			0
$330$	−17.7724	−	35.7504i	−0.978336	−	1.96800i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−3.93247	+	1.27774i	−0.215822	+	0.0701249i
$333$		0			0
$334$	−6.24586	+	4.53789i	−0.341758	+	0.248302i
$335$		0			0
$336$		0			0
$337$	10.4219	+	14.3446i	0.567720	+	0.781399i	0.992282	−	0.123999i	$-0.0395721\pi$
$337$	10.4219	+	14.3446i	0.567720	+	0.781399i	−0.424563	+	0.905399i	$0.639572\pi$
$338$	−13.8430	+	19.0532i	−0.752958	+	1.03636i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−8.15952	−	5.92824i	−0.439932	−	0.319629i
$345$		0			0
$346$		0			0
$347$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$347$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$348$		0			0
$349$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$349$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$350$		0			0
$351$		−	18.7350i		−	1.00000i
$352$	−18.5592	−	9.68890i	−0.989210	−	0.516420i
$353$	−28.8631			−1.53623			−0.768114	−	0.640314i	$-0.778804\pi$
$353$	−28.8631			−1.53623			−0.768114	+	0.640314i	$0.778804\pi$
$354$	−43.1475	+	14.0195i	−2.29327	+	0.745127i
$355$	50.0234	+	36.3441i	2.65497	+	1.92895i
$356$	4.47909	−	3.25425i	0.237391	−	0.172475i
$357$		0			0
$358$		0			0
$359$	22.2398	+	30.6104i	1.17377	+	1.61556i	0.631642	+	0.775260i	$0.282381\pi$
$359$	22.2398	+	30.6104i	1.17377	+	1.61556i	0.542128	+	0.840296i	$0.317619\pi$
$360$	8.79961	−	12.1116i	0.463780	−	0.638339i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$			41.2561i			2.16837i
$363$	−0.377040	+	19.0488i	−0.0197895	+	0.999804i
$364$		0			0
$365$		0			0
$366$	27.7968	+	20.1955i	1.45296	+	1.05564i
$367$	−30.8302	+	22.3994i	−1.60932	+	1.16924i	−0.743751	+	0.668457i	$0.766955\pi$
$367$	−30.8302	+	22.3994i	−1.60932	+	1.16924i	−0.865572	+	0.500785i	$0.833045\pi$
$368$		0			0
$369$	28.9262	+	9.39870i	1.50584	+	0.489277i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		−	37.3141i		−	1.93205i	−0.258446	−	0.966026i	$-0.583210\pi$
$373$		−	37.3141i		−	1.93205i	0.258446	−	0.966026i	$-0.416790\pi$
$374$		0			0
$375$	31.3445			1.61862
$376$	−14.8196	+	4.81519i	−0.764264	+	0.248325i
$377$		0			0
$378$		0			0
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$	−1.51395	−	2.08377i	−0.0775619	−	0.106755i
$382$		0			0
$383$	−8.35521	−	25.7147i	−0.426931	−	1.31396i	−0.901133	−	0.433543i	$-0.857263\pi$
$383$	−8.35521	−	25.7147i	−0.426931	−	1.31396i	0.474202	−	0.880416i	$-0.342737\pi$
$384$		−	16.8628i		−	0.860527i
$385$		0			0
$386$		0			0
$387$	22.1220	−	7.18787i	1.12452	−	0.365380i
$388$		0			0
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$	13.4120	−	41.2780i	0.679145	−	2.09019i
$391$		0			0
$392$	5.35214	+	7.36659i	0.270324	+	0.372069i
$393$		0			0
$394$	11.6177	+	35.7556i	0.585292	+	1.80134i
$395$			55.0141i			2.76806i
$396$	11.4219	−	5.67810i	0.573973	−	0.285335i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	36.5431	−	11.8736i	1.83174	−	0.595169i
$399$		0			0
$400$	38.6820	−	28.1041i	1.93410	−	1.40521i
$401$	−0.705916	+	2.17259i	−0.0352518	+	0.108494i	−0.967134	−	0.254267i	$-0.918166\pi$
$401$	−0.705916	+	2.17259i	−0.0352518	+	0.108494i	0.931882	+	0.362761i	$0.118166\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	10.6694	+	32.8369i	0.530164	+	1.63168i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$	57.0036	+	41.4155i	2.81521	+	2.04537i
$411$	−11.4464	+	8.31631i	−0.564610	+	0.410214i
$412$	8.03619	−	24.7328i	0.395914	−	1.21850i
$413$		0			0
$414$		0			0
$415$	−7.27300	+	10.0104i	−0.357017	+	0.491392i
$416$	−7.03320	−	21.6460i	−0.344831	−	1.06128i
$417$		−	39.6306i		−	1.94072i
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$	−37.1857	+	27.0170i	−1.81017	+	1.31517i
$423$	11.1051	−	34.1781i	0.539951	−	1.66180i
$424$		0			0
$425$		0			0
$426$	−29.7269	+	40.9155i	−1.44027	+	1.98236i
$427$		0			0
$428$		0			0
$429$	−14.7900	+	14.5002i	−0.714069	+	0.700075i
$430$	53.8861			2.59862
$431$	1.83137	−	0.595047i	0.0882138	−	0.0286624i	−0.264578	−	0.964364i	$-0.585233\pi$
$431$	1.83137	−	0.595047i	0.0882138	−	0.0286624i	0.352791	+	0.935702i	$0.385233\pi$
$432$	20.6847	+	15.0283i	0.995191	+	0.723048i
$433$	30.7491	−	22.3405i	1.47771	−	1.07362i	0.499422	−	0.866359i	$-0.333546\pi$
$433$	30.7491	−	22.3405i	1.47771	−	1.07362i	0.978286	−	0.207259i	$-0.0664544\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		−	33.6160i		−	1.60441i	−0.597052	−	0.802203i	$-0.703661\pi$
$439$		−	33.6160i		−	1.60441i	0.597052	−	0.802203i	$-0.296339\pi$
$440$	−16.3719	+	2.42724i	−0.780499	+	0.115714i
$441$	−21.0000			−1.00000
$442$		0			0
$443$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$443$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$444$		0			0
$445$	5.11977	−	15.7570i	0.242700	−	0.746955i
$446$		0			0
$447$	14.3646	+	19.7712i	0.679425	+	0.935148i
$448$		0			0
$449$	−7.06822	−	21.7537i	−0.333570	−	1.02662i	−0.967422	−	0.253168i	$-0.918527\pi$
$449$	−7.06822	−	21.7537i	−0.333570	−	1.02662i	0.633853	−	0.773454i	$-0.281473\pi$
$450$			52.8118i			2.48957i
$451$	−14.9682	−	30.1096i	−0.704823	−	1.41780i
$452$		0			0
$453$		0			0
$454$	−21.2178	−	15.4156i	−0.995800	−	0.723491i
$455$		0			0
$456$		0			0
$457$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$457$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			24.9817i			1.16352i	0.813362	+	0.581758i	$0.197635\pi$
$461$			24.9817i			1.16352i	−0.813362	+	0.581758i	$0.802365\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	13.1879	+	4.28502i	0.609612	+	0.198075i
$469$		0			0
$470$	48.9350	−	67.3533i	2.25720	−	3.10677i
$471$	−12.3849	−	38.1169i	−0.570668	−	1.75634i
$472$			18.8076i			0.865688i
$473$	−22.7959	−	11.9007i	−1.04816	−	0.547194i
$474$	−44.9975			−2.06680
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−17.2925	+	53.2209i	−0.790942	+	2.43427i
$479$	41.5173	+	13.4898i	1.89697	+	0.616364i	0.971187	+	0.238320i	$0.0765966\pi$
$479$	41.5173	+	13.4898i	1.89697	+	0.616364i	0.925787	+	0.378045i	$0.123403\pi$
$480$	24.6542	+	33.9336i	1.12531	+	1.54885i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−13.3226	−	4.62220i	−0.605573	−	0.210100i
$485$		0			0
$486$	−26.8582	+	8.72675i	−1.21831	+	0.395854i
$487$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$487$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$488$	11.5233	−	8.37218i	0.521636	−	0.378991i
$489$		0			0
$490$	−46.2684	−	15.0335i	−2.09019	−	0.679145i
$491$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$491$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$492$	−13.2319	+	18.2121i	−0.596538	+	0.821064i
$493$		0			0
$494$		0			0
$495$	17.6648	−	33.8372i	0.793976	−	1.52087i
$496$		0			0
$497$		0			0
$498$	−8.18780	−	5.94878i	−0.366904	−	0.266571i
$499$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$499$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$500$	−7.16903	+	22.0640i	−0.320609	+	0.986732i
$501$	−7.01996	−	2.28092i	−0.313629	−	0.101904i
$502$		0			0
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−22.5167			−1.00000
$508$	1.81307	−	0.589103i	0.0804421	−	0.0261372i
$509$	34.1020	+	24.7766i	1.51155	+	1.09820i	0.965485	+	0.260457i	$0.0838733\pi$
$509$	34.1020	+	24.7766i	1.51155	+	1.09820i	0.546061	+	0.837745i	$0.316127\pi$
$510$		0			0
$511$		0			0
$512$	17.3656	+	5.64243i	0.767459	+	0.249363i
$513$		0			0
$514$		0			0
$515$	−24.0484	−	74.0133i	−1.05970	−	3.26141i
$516$			17.2161i			0.757896i
$517$	−35.5763	+	17.6858i	−1.56464	+	0.777821i
$518$		0			0
$519$		0			0
$520$	−14.5564	−	10.5758i	−0.638339	−	0.463780i
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$		0			0
$523$	−11.8787	−	3.85962i	−0.519419	−	0.168769i	0.0375627	−	0.999294i	$-0.488041\pi$
$523$	−11.8787	−	3.85962i	−0.519419	−	0.168769i	−0.556982	+	0.830525i	$0.688041\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−4.14532	−	27.9605i	−0.180402	−	1.21682i
$529$	23.0000			1.00000
$530$		0			0
$531$	−35.0914	−	25.4954i	−1.52284	−	1.10641i
$532$		0			0
$533$	11.2958	−	34.7650i	0.489277	−	1.50584i
$534$	12.8881	+	4.18760i	0.557723	+	0.181215i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	16.2532	+	16.5781i	0.700075	+	0.714069i
$540$	−25.5548			−1.09970
$541$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$541$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$542$		0			0
$543$	−31.9109	+	23.1846i	−1.36943	+	0.994948i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	8.84659	−	12.1763i	0.378253	−	0.520620i	−0.576868	−	0.816838i	$-0.695725\pi$
$547$	8.84659	−	12.1763i	0.378253	−	0.520620i	0.955121	+	0.296217i	$0.0957252\pi$
$548$	−3.23602	−	9.95945i	−0.138236	−	0.425447i
$549$			32.8496i			1.40199i
$550$	41.6914	−	40.8744i	1.77773	−	1.74289i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	36.6115	−	26.5998i	1.55547	−	1.13012i
$555$		0			0
$556$	27.8968	+	9.06421i	1.18309	+	0.384408i
$557$	−26.9529	−	37.0975i	−1.14203	−	1.57187i	−0.762882	−	0.646538i	$-0.776216\pi$
$557$	−26.9529	−	37.0975i	−1.14203	−	1.57187i	−0.379151	−	0.925335i	$-0.623784\pi$
$558$		0			0
$559$	−8.63874	−	26.5873i	−0.365380	−	1.12452i
$560$		0			0
$561$		0			0
$562$	−60.3338			−2.54503
$563$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$563$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$564$	21.5187	+	15.6343i	0.906101	+	0.658321i
$565$		0			0
$566$	−4.23190	+	13.0244i	−0.177880	+	0.547458i
$567$		0			0
$568$	12.3234	+	16.9617i	0.517080	+	0.711699i
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$		−	28.8444i		−	1.20710i	−0.797325	−	0.603550i	$-0.793752\pi$
$571$		−	28.8444i		−	1.20710i	0.797325	−	0.603550i	$-0.206248\pi$
$572$	−6.82422	−	13.7274i	−0.285335	−	0.573973i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−3.87068	+	2.81221i	−0.161278	+	0.117175i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	−29.2902	−	9.51697i	−1.21831	−	0.395854i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	39.4650	−	12.8230i	1.63168	−	0.530164i
$586$	−29.7271	−	21.5980i	−1.22801	−	0.892204i
$587$	−20.0273	+	14.5507i	−0.826615	+	0.600571i	−0.918600	−	0.395189i	$-0.870679\pi$
$587$	−20.0273	+	14.5507i	−0.826615	+	0.600571i	0.0919844	+	0.995760i	$0.470679\pi$
$588$	4.80306	−	14.7823i	0.198075	−	0.609612i
$589$		0			0
$590$	−59.0637	−	81.2943i	−2.43162	−	3.34683i
$591$	−21.1276	+	29.0797i	−0.869073	+	1.19618i
$592$		0			0
$593$			39.5677i			1.62485i	0.583066	+	0.812425i	$0.301853\pi$
$593$			39.5677i			1.62485i	−0.583066	+	0.812425i	$0.698147\pi$
$594$	27.6764	+	14.4486i	1.13558	+	0.592832i
$595$		0			0
$596$	−17.2028	+	5.58953i	−0.704655	+	0.228956i
$597$	29.7201	+	21.5929i	1.21636	+	0.883740i
$598$		0			0
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	20.8219	+	6.76544i	0.850050	+	0.276198i
$601$	20.1845	+	27.7816i	0.823344	+	1.13324i	0.989126	+	0.147074i	$0.0469854\pi$
$601$	20.1845	+	27.7816i	0.823344	+	1.13324i	−0.165781	+	0.986163i	$0.553015\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−40.3842	+	12.2435i	−1.64185	+	0.497770i
$606$		0			0
$607$	46.7187	−	15.1798i	1.89625	−	0.616131i	0.923894	−	0.382649i	$-0.124988\pi$
$607$	46.7187	−	15.1798i	1.89625	−	0.616131i	0.972361	−	0.233481i	$-0.0750118\pi$
$608$		0			0
$609$		0			0
$610$	−23.5164	+	72.3762i	−0.952153	+	2.93043i
$611$	−41.0770	−	13.3467i	−1.66180	−	0.539951i
$612$		0			0
$613$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$613$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$614$		0			0
$615$			67.3655i			2.71644i
$616$		0			0
$617$	−49.6652			−1.99944			−0.999722	−	0.0235798i	$-0.992494\pi$
$617$	−49.6652			−1.99944			−0.999722	+	0.0235798i	$0.992494\pi$
$618$	60.5375	−	19.6698i	2.43517	−	0.791236i
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	18.0617	−	24.8599i	0.723048	−	0.995191i
$625$	6.43944	+	19.8186i	0.257578	+	0.792742i
$626$		−	58.4497i		−	2.33612i
$627$		0			0
$628$	29.6639			1.18372
$629$		0			0
$630$		0			0
$631$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$631$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$632$	−5.76439	+	17.7410i	−0.229295	+	0.705698i
$633$	−41.7944	−	13.5798i	−1.66118	−	0.539749i
$634$	−16.5836	−	22.8254i	−0.658619	−	0.906511i
$635$	3.35323	−	4.61532i	0.133069	−	0.183154i
$636$		0			0
$637$			25.2389i			1.00000i
$638$		0			0
$639$	−48.3530			−1.91282
$640$	35.5213	−	11.5416i	1.40410	−	0.456221i
$641$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$641$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$642$		0			0
$643$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$643$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$644$		0			0
$645$	30.2823	+	41.6800i	1.19236	+	1.64115i
$646$		0			0
$647$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$647$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$648$			11.7072i			0.459902i
$649$	7.03251	+	47.4348i	0.276050	+	1.86198i
$650$	63.4719			2.48957
$651$		0			0
$652$		0			0
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$		0			0
$656$	29.3219	+	40.3581i	1.14483	+	1.57572i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	19.7784	+	20.1738i	0.769875	+	0.785264i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−3.39430	+	2.46610i	−0.131724	+	0.0957033i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	3.21117	−	4.41980i	0.124244	−	0.171007i
$669$		0			0
$670$		0			0
$671$	25.9326	−	25.4244i	1.00112	−	0.981497i
$672$		0			0
$673$	27.3460	−	8.88525i	1.05411	−	0.342501i	0.269830	−	0.962908i	$-0.413032\pi$
$673$	27.3460	−	8.88525i	1.05411	−	0.342501i	0.784280	+	0.620407i	$0.213032\pi$
$674$	−25.9869	−	18.8806i	−1.00098	−	0.727254i
$675$	−40.8491	+	29.6786i	−1.57228	+	1.14233i
$676$	5.14995	−	15.8499i	0.198075	−	0.609612i
$677$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$677$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		−	25.0747i		−	0.960865i
$682$		0			0
$683$	9.80945			0.375348			0.187674	−	0.982231i	$-0.439905\pi$
$683$	9.80945			0.375348			0.187674	+	0.982231i	$0.439905\pi$
$684$		0			0
$685$	−25.3526	−	18.4197i	−0.968673	−	0.703782i
$686$		0			0
$687$		0			0
$688$	36.2837	+	11.7893i	1.38330	+	0.449462i
$689$		0			0
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	83.4814	−	27.1247i	3.16663	−	1.02890i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$701$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$702$	10.4883	+	32.2795i	0.395854	+	1.21831i
$703$		0			0
$704$	5.21581	+	0.879095i	0.196578	+	0.0331321i
$705$	79.5966			2.99778
$706$	49.7298	−	16.1582i	1.87160	−	0.608121i
$707$		0			0
$708$	25.9727	−	18.8703i	0.976115	−	0.709189i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$	−106.534	−	34.6151i	−3.99816	−	1.29908i
$711$	−25.2872	−	34.8048i	−0.948343	−	1.30528i
$712$	3.30205	−	4.54489i	0.123750	−	0.170327i
$713$		0			0
$714$		0			0
$715$	−40.6673	−	21.2305i	−1.52087	−	0.793976i
$716$		0			0
$717$	−50.8834	+	16.5330i	−1.90028	+	0.617437i
$718$	−55.4545	−	40.2900i	−2.06954	−	1.50361i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$	−17.4995	+	53.8579i	−0.652167	+	2.00717i
$721$		0			0
$722$	20.2320	+	27.8470i	0.752958	+	1.03636i
$723$		0			0
$724$	−9.02154	−	27.7655i	−0.335283	−	1.03189i
$725$		0			0
$726$	−10.0143	−	33.0313i	−0.371666	−	1.22591i
$727$	2.34066			0.0868103			0.0434052	−	0.999058i	$-0.486179\pi$
$727$	2.34066			0.0868103			0.0434052	+	0.999058i	$0.486179\pi$
$728$		0			0
$729$	−21.8435	−	15.8702i	−0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$	−23.1235	−	7.51328i	−0.854669	−	0.277699i
$733$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$733$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$734$	40.5793	−	55.8526i	1.49781	−	2.06156i
$735$	−14.3732	−	44.2362i	−0.530164	−	1.63168i
$736$		0			0
$737$		0			0
$738$	−55.1001			−2.02826
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.4016	+	6.62887i	0.748460	+	0.243190i	0.658319	−	0.752739i	$-0.271268\pi$
$743$	20.4016	+	6.62887i	0.748460	+	0.243190i	0.0901418	+	0.995929i	$0.471268\pi$
$744$		0			0
$745$	−31.8161	+	43.7912i	−1.16565	+	1.60438i
$746$	20.8892	+	64.2905i	0.764810	+	2.35384i
$747$		−	9.67616i		−	0.354032i
$748$		0			0
$749$		0			0
$750$	−54.0051	+	17.5473i	−1.97199	+	0.640737i
$751$	−8.36230	−	6.07557i	−0.305145	−	0.221701i	0.424666	−	0.905350i	$-0.360392\pi$
$751$	−8.36230	−	6.07557i	−0.305145	−	0.221701i	−0.729810	+	0.683650i	$0.760392\pi$
$752$	47.6856	−	34.6456i	1.73891	−	1.26339i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	14.5660	+	44.8294i	0.529409	+	1.62935i	0.755429	+	0.655230i	$0.227428\pi$
$757$	14.5660	+	44.8294i	0.529409	+	1.62935i	−0.226021	+	0.974122i	$0.572572\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−51.4147	+	16.7057i	−1.86378	+	0.605579i	−0.870167	+	0.492757i	$0.835989\pi$
$761$	−51.4147	+	16.7057i	−1.86378	+	0.605579i	−0.993615	+	0.112822i	$0.964011\pi$
$762$	3.77500	+	2.74270i	0.136754	+	0.0993574i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	28.7913	+	39.6278i	1.04027	+	1.43181i
$767$	−30.6417	+	42.1746i	−1.10641	+	1.52284i
$768$	11.1474	+	34.3080i	0.402245	+	1.23798i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.56849	+	2.59266i	0.128350	+	0.0932514i	0.650108	−	0.759842i	$-0.274724\pi$
$773$	3.56849	+	2.59266i	0.128350	+	0.0932514i	−0.521758	+	0.853093i	$0.674724\pi$
$774$	−34.0912	+	24.7687i	−1.22538	+	0.890294i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			30.7130i			1.09970i
$781$	37.4234	+	38.1715i	1.33912	+	1.36588i
$782$		0			0
$783$		0			0
$784$	−27.8653	−	20.2454i	−0.995191	−	0.723048i
$785$	71.8161	−	52.1775i	2.56323	−	1.86229i
$786$		0			0
$787$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$787$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$788$	−15.6375	−	21.5232i	−0.557062	−	0.766731i
$789$		0			0
$790$	−30.7980	−	94.7866i	−1.09575	−	3.37236i
$791$		0			0
$792$	9.24205	−	9.06093i	0.328402	−	0.321966i
$793$	39.4803			1.40199
$794$		0			0
$795$		0			0
$796$	−21.9972	+	15.9819i	−0.779670	+	0.566464i
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	−36.0546	+	49.6249i	−1.27472	+	1.75450i
$801$	4.00367	+	12.3220i	0.141463	+	0.435378i
$802$		−	4.13845i		−	0.146134i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	−36.7656	−	50.6035i	−1.29181	−	1.77803i
$811$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$811$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−47.4199	−	15.4077i	−1.65598	−	0.538059i
$821$	−10.4792	−	14.4233i	−0.365725	−	0.503378i	0.586007	−	0.810306i	$-0.300699\pi$
$821$	−10.4792	−	14.4233i	−0.365725	−	0.503378i	−0.951733	+	0.306928i	$0.900699\pi$
$822$	15.0660	−	20.7366i	0.525487	−	0.723271i
$823$	−1.67681	−	5.16068i	−0.0584498	−	0.179890i	0.917569	−	0.397577i	$-0.130149\pi$
$823$	−1.67681	−	5.16068i	−0.0584498	−	0.179890i	−0.976019	+	0.217687i	$0.930149\pi$
$824$		−	26.3877i		−	0.919257i
$825$	55.0449	+	9.27750i	1.91642	+	0.323001i
$826$		0			0
$827$	10.1056	−	3.28351i	0.351406	−	0.114179i	−0.127995	−	0.991775i	$-0.540854\pi$
$827$	10.1056	−	3.28351i	0.351406	−	0.114179i	0.479401	+	0.877596i	$0.340854\pi$
$828$		0			0
$829$	45.7668	−	33.2515i	1.58955	−	1.15487i	0.684964	−	0.728577i	$-0.259818\pi$
$829$	45.7668	−	33.2515i	1.58955	−	1.15487i	0.904584	−	0.426296i	$-0.140182\pi$
$830$	6.92699	−	21.3191i	0.240439	−	0.739996i
$831$	41.1490	+	13.3701i	1.42744	+	0.463804i
$832$	3.37986	+	4.65197i	0.117175	+	0.161278i
$833$		0			0
$834$	22.1861	+	68.2817i	0.768241	+	2.36440i
$835$		−	16.3486i		−	0.565767i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	24.9143	+	18.1013i	0.860138	+	0.624927i	0.927923	−	0.372773i	$-0.121593\pi$
$839$	24.9143	+	18.1013i	0.860138	+	0.624927i	−0.0677843	+	0.997700i	$0.521593\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$		0			0
$843$	−33.9057	−	46.6672i	−1.16778	−	1.60730i
$844$	19.1182	−	26.3139i	0.658075	−	0.905763i
$845$	−15.4113	−	47.4311i	−0.530164	−	1.63168i
$846$			65.1042i			2.23833i
$847$		0			0
$848$		0			0
$849$	−12.4524	+	4.04602i	−0.427365	+	0.138859i
$850$		0			0
$851$		0			0
$852$	11.0592	−	34.0366i	0.378881	−	1.16608i
$853$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$853$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	17.3650	−	33.2629i	0.592832	−	1.13558i
$859$	42.3162			1.44381			0.721905	−	0.691992i	$-0.243267\pi$
$859$	42.3162			1.44381			0.721905	+	0.691992i	$0.243267\pi$
$860$	−36.2655	+	11.7834i	−1.23664	+	0.401810i
$861$		0			0
$862$	−2.82224	+	2.05048i	−0.0961258	+	0.0698395i
$863$	17.2910	−	53.2163i	0.588593	−	1.81150i	0.00425952	−	0.999991i	$-0.498644\pi$
$863$	17.2910	−	53.2163i	0.588593	−	1.81150i	0.584334	−	0.811513i	$-0.301356\pi$
$864$	−31.1952	−	10.1359i	−1.06128	−	0.344831i
$865$		0			0
$866$	−40.4726	+	55.7057i	−1.37531	+	1.89296i
$867$	−9.09896	−	28.0037i	−0.309017	−	0.951057i
$868$		0			0
$869$	−7.90476	+	46.9002i	−0.268150	+	1.59098i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$877$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$878$	18.8190	+	57.9189i	0.635110	+	1.95467i
$879$		−	35.1308i		−	1.18493i
$880$	56.0611	−	27.8693i	1.88982	−	0.939474i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	36.1820	−	11.7563i	1.21831	−	0.395854i
$883$	−20.2929	−	14.7437i	−0.682911	−	0.496164i	0.191411	−	0.981510i	$-0.438694\pi$
$883$	−20.2929	−	14.7437i	−0.682911	−	0.496164i	−0.874322	+	0.485346i	$0.838694\pi$
$884$		0			0
$885$	29.6878	−	91.3697i	0.997945	−	3.07136i
$886$		0			0
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$		0			0
$889$		0			0
$890$			30.0148i			1.00610i
$891$	4.37755	+	29.5269i	0.146653	+	0.989188i
$892$		0			0
$893$		0			0
$894$	−35.8180	−	26.0233i	−1.19793	−	0.870349i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	24.3564	+	33.5237i	0.812784	+	1.11870i
$899$		0			0
$900$	−11.5484	−	35.5425i	−0.384948	−	1.18475i
$901$		0			0
$902$	42.6454	+	43.4979i	1.41994	+	1.44832i
$903$		0			0
$904$		0			0
$905$	−70.6792	−	51.3515i	−2.34946	−	1.70698i
$906$		0			0
$907$	−15.3004	+	47.0897i	−0.508040	+	1.56359i	0.287559	+	0.957763i	$0.407156\pi$
$907$	−15.3004	+	47.0897i	−0.508040	+	1.56359i	−0.795599	+	0.605824i	$0.792844\pi$
$908$	17.6506	+	5.73502i	0.585755	+	0.190323i
$909$		0			0
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$		0			0
$913$	−7.63868	+	7.48898i	−0.252803	+	0.247849i
$914$		0			0
$915$	−69.1973	+	22.4836i	−2.28759	+	0.743284i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	44.0171	+	14.3020i	1.45199	+	0.471780i	0.925613	−	0.378471i	$-0.123550\pi$
$919$	44.0171	+	14.3020i	1.45199	+	0.471780i	0.526377	+	0.850251i	$0.323550\pi$
$920$		0			0
$921$		0			0
$922$	−13.9853	−	43.0424i	−0.460582	−	1.41753i
$923$			58.1131i			1.91282i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	49.2344	+	35.7709i	1.61707	+	1.17487i
$928$		0			0
$929$	−7.50735	+	23.1053i	−0.246308	+	0.758059i	0.749110	+	0.662445i	$0.230481\pi$
$929$	−7.50735	+	23.1053i	−0.246308	+	0.758059i	−0.995419	+	0.0956136i	$0.969519\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	14.0703			0.459902
$937$	−58.2035	+	18.9115i	−1.90143	+	0.617811i	−0.942410	+	0.334458i	$0.891447\pi$
$937$	−58.2035	+	18.9115i	−1.90143	+	0.617811i	−0.959016	+	0.283352i	$0.908553\pi$
$938$		0			0
$939$	45.2099	−	32.8469i	1.47537	−	1.07192i
$940$	−18.2051	+	56.0296i	−0.593786	+	1.82748i
$941$	58.3065	+	18.9449i	1.90074	+	0.617587i	0.962115	+	0.272644i	$0.0878983\pi$
$941$	58.3065	+	18.9449i	1.90074	+	0.617587i	0.938624	+	0.344943i	$0.112102\pi$
$942$	42.6774	+	58.7404i	1.39050	+	1.91386i
$943$		0			0
$944$	−21.9843	−	67.6608i	−0.715529	−	2.20217i
$945$		0			0
$946$	45.9386	+	7.74269i	1.49359	+	0.251736i
$947$	34.6471			1.12588			0.562940	−	0.826498i	$-0.309670\pi$
$947$	34.6471			1.12588			0.562940	+	0.826498i	$0.309670\pi$
$948$	30.2834	−	9.83968i	0.983560	−	0.319578i
$949$		0			0
$950$		0			0
$951$	8.33558	−	25.6543i	0.270300	−	0.831897i
$952$		0			0
$953$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$953$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$954$		0			0
$955$		0			0
$956$		−	39.5992i		−	1.28073i
$957$		0			0
$958$	−79.0843			−2.55510
$959$		0			0
$960$	−8.57313	−	6.22874i	−0.276696	−	0.201032i
$961$	−25.0795	+	18.2213i	−0.809017	+	0.587785i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−14.3060	−	0.283164i	−0.459812	−	0.00910123i
$969$		0			0
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$	16.1673	−	11.7462i	0.518567	−	0.376761i
$973$		0			0
$974$		0			0
$975$	35.6692	+	49.0945i	1.14233	+	1.57228i
$976$	−31.6692	+	43.5888i	−1.01370	+	1.39524i
$977$	15.9189	+	48.9932i	0.509290	+	1.56743i	0.793437	+	0.608652i	$0.208289\pi$
$977$	15.9189	+	48.9932i	0.509290	+	1.56743i	−0.284147	+	0.958781i	$0.591711\pi$
$978$		0			0
$979$	6.62873	−	12.6974i	0.211855	−	0.405811i
$980$	34.4262			1.09970
$981$		0			0
$982$		0			0
$983$	−34.2374	+	24.8749i	−1.09200	+	0.793387i	−0.979736	−	0.200292i	$-0.935811\pi$
$983$	−34.2374	+	24.8749i	−1.09200	+	0.793387i	−0.112267	+	0.993678i	$0.535811\pi$
$984$	−7.05858	+	21.7241i	−0.225019	+	0.692539i
$985$	−75.7165	−	24.6018i	−2.41253	−	0.783878i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−11.4929	+	68.1892i	−0.365268	+	2.16719i
$991$	−30.2350			−0.960448			−0.480224	−	0.877146i	$-0.659445\pi$
$991$	−30.2350			−0.960448			−0.480224	+	0.877146i	$0.659445\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−25.1436	+	77.3841i	−0.797106	+	2.45324i
$996$	6.81124	+	2.21311i	0.215822	+	0.0701249i
$997$	−31.9172	−	43.9303i	−1.01083	−	1.39129i	−0.918439	−	0.395562i	$-0.870550\pi$
$997$	−31.9172	−	43.9303i	−1.01083	−	1.39129i	−0.0923886	−	0.995723i	$-0.529450\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.y.a.116.3	✓	32
3.2	odd	2	inner	429.2.y.a.116.6	yes	32
11.2	odd	10	inner	429.2.y.a.233.3	yes	32
13.12	even	2	inner	429.2.y.a.116.6	yes	32
33.2	even	10	inner	429.2.y.a.233.6	yes	32
39.38	odd	2	CM	429.2.y.a.116.3	✓	32
143.90	odd	10	inner	429.2.y.a.233.6	yes	32
429.233	even	10	inner	429.2.y.a.233.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.116.3	✓	32	1.1	even	1	trivial
429.2.y.a.116.3	✓	32	39.38	odd	2	CM
429.2.y.a.116.6	yes	32	3.2	odd	2	inner
429.2.y.a.116.6	yes	32	13.12	even	2	inner
429.2.y.a.233.3	yes	32	11.2	odd	10	inner
429.2.y.a.233.3	yes	32	429.233	even	10	inner
429.2.y.a.233.6	yes	32	33.2	even	10	inner
429.2.y.a.233.6	yes	32	143.90	odd	10	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.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72295 + 0.559822i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(1.03713 - 0.753522i) q^{4} +(1.18548 - 3.64854i) q^{5} +(2.98424 + 0.969639i) q^{6} +(0.764591 - 1.05237i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})\)	\(q+(-1.72295 + 0.559822i) q^{2} +(-1.40126 - 1.01807i) q^{3} +(1.03713 - 0.753522i) q^{4} +(1.18548 - 3.64854i) q^{5} +(2.98424 + 0.969639i) q^{6} +(0.764591 - 1.05237i) q^{8} +(0.927051 + 2.85317i) q^{9} +6.94993i q^{10} +(1.53488 - 2.94009i) q^{11} -2.22043 q^{12} +(3.42908 - 1.11418i) q^{13} +(-5.37565 + 3.90564i) q^{15} +(-1.52052 + 4.67967i) q^{16} +(-3.19453 - 4.39690i) q^{18} +(-1.51975 - 4.67732i) q^{20} +(-0.998608 + 5.92490i) q^{22} +(-2.14278 + 0.696231i) q^{24} +(-7.86141 - 5.71165i) q^{25} +(-5.28441 + 3.83935i) q^{26} +(1.60570 - 4.94183i) q^{27} +(7.07554 - 9.73865i) q^{30} -6.31247i q^{32} +(-5.14400 + 2.55720i) q^{33} +(3.11140 + 2.26057i) q^{36} +(-5.93935 - 1.92981i) q^{39} +(-2.93320 - 4.03721i) q^{40} +(5.95913 - 8.20204i) q^{41} -7.75348i q^{43} +(-0.623542 - 4.20584i) q^{44} +11.5089 q^{45} +(-9.69122 - 7.04108i) q^{47} +(6.89488 - 5.00943i) q^{48} +(-2.16312 + 6.65740i) q^{49} +(16.7423 + 5.43992i) q^{50} +(2.71686 - 3.73944i) q^{52} +9.41346i q^{54} +(-8.90746 - 9.08552i) q^{55} +(-11.6971 + 8.49847i) q^{59} +(-2.63229 + 8.10135i) q^{60} +(10.4139 + 3.38370i) q^{61} +(0.492822 + 1.51675i) q^{64} -13.8320i q^{65} +(7.43129 - 7.28566i) q^{66} +(-4.98064 + 15.3288i) q^{71} +(3.71140 + 1.20591i) q^{72} +(5.20099 + 16.0070i) q^{75} +11.3136 q^{78} +(-13.6385 + 4.43142i) q^{79} +(15.2714 + 11.0953i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-5.67562 + 17.4678i) q^{82} +(-3.06752 - 0.996699i) q^{83} +(4.34056 + 13.3589i) q^{86} +(-1.92050 - 3.86323i) q^{88} +4.31872 q^{89} +(-19.8293 + 6.44294i) q^{90} +(20.6393 + 6.70610i) q^{94} +(-6.42656 + 8.84540i) q^{96} -12.6813i q^{98} +(9.81149 + 1.65367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 24 * q^9	\( 32 q + 16 q^{4} - 24 q^{9} - 24 q^{12} - 92 q^{16} + 28 q^{22} - 40 q^{25} + 180 q^{30} + 48 q^{36} - 72 q^{48} + 56 q^{49} - 260 q^{52} + 32 q^{55} + 184 q^{64} - 60 q^{66} - 144 q^{75} - 72 q^{81} + 204 q^{82} - 40 q^{88} + 60 q^{90}+O(q^{100}) \) 32 * q + 16 * q^4 - 24 * q^9 - 24 * q^12 - 92 * q^16 + 28 * q^22 - 40 * q^25 + 180 * q^30 + 48 * q^36 - 72 * q^48 + 56 * q^49 - 260 * q^52 + 32 * q^55 + 184 * q^64 - 60 * q^66 - 144 * q^75 - 72 * q^81 + 204 * q^82 - 40 * q^88 + 60 * q^90

Introduction

L-functions

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