LMFDB - Embedded newform 429.2.y.a.233.2

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			233.2
Character	$\chi$	$=$	429.233
Dual form			429.2.y.a.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06579 - 0.671217i) q^{2} +(1.40126 - 1.01807i) q^{3} +(2.19893 + 1.59762i) q^{4} +(-0.710253 - 2.18593i) q^{5} +(-3.57806 + 1.16258i) q^{6} +(-0.916732 - 1.26177i) q^{8} +(0.927051 - 2.85317i) q^{9} +O(q^{10})$	\(q+(-2.06579 - 0.671217i) q^{2} +(1.40126 - 1.01807i) q^{3} +(2.19893 + 1.59762i) q^{4} +(-0.710253 - 2.18593i) q^{5} +(-3.57806 + 1.16258i) q^{6} +(-0.916732 - 1.26177i) q^{8} +(0.927051 - 2.85317i) q^{9} +4.99242i q^{10} +(2.94009 - 1.53488i) q^{11} +4.70777 q^{12} +(-3.42908 - 1.11418i) q^{13} +(-3.22069 - 2.33997i) q^{15} +(-0.632981 - 1.94811i) q^{16} +(-3.83019 + 5.27180i) q^{18} +(1.93049 - 5.94144i) q^{20} +(-7.10386 + 1.19731i) q^{22} +(-2.56916 - 0.834770i) q^{24} +(-0.228763 + 0.166206i) q^{25} +(6.33592 + 4.60332i) q^{26} +(-1.60570 - 4.94183i) q^{27} +(5.08265 + 6.99567i) q^{30} +7.56854i q^{32} +(2.55720 - 5.14400i) q^{33} +(6.59680 - 4.79286i) q^{36} +(-5.93935 + 1.92981i) q^{39} +(-2.10704 + 2.90009i) q^{40} +(-4.59885 - 6.32977i) q^{41} +7.75348i q^{43} +(8.91722 + 1.32204i) q^{44} -6.89528 q^{45} +(-5.39703 + 3.92117i) q^{47} +(-2.87029 - 2.08539i) q^{48} +(-2.16312 - 6.65740i) q^{49} +(0.584137 - 0.189798i) q^{50} +(-5.76030 - 7.92837i) q^{52} +11.2866i q^{54} +(-5.44336 - 5.33669i) q^{55} +(-4.20012 - 3.05156i) q^{59} +(-3.34371 - 10.2909i) q^{60} +(-10.4139 + 3.38370i) q^{61} +(3.81417 - 11.7388i) q^{64} +8.28710i q^{65} +(-8.73539 + 8.91000i) q^{66} +(-1.52081 - 4.68057i) q^{71} +(-4.44991 + 1.44586i) q^{72} +(-0.151346 + 0.465795i) q^{75} +13.5648 q^{78} +(13.6385 + 4.43142i) q^{79} +(-3.80887 + 2.76731i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(5.25162 + 16.1628i) q^{82} +(17.0554 - 5.54164i) q^{83} +(5.20426 - 16.0171i) q^{86} +(-4.63195 - 2.30265i) q^{88} +18.3671 q^{89} +(14.2442 + 4.62823i) q^{90} +(13.7811 - 4.47775i) q^{94} +(7.70534 + 10.6055i) q^{96} +15.2047i q^{98} +(-1.65367 - 9.81149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.06579	−	0.671217i	−1.46074	−	0.474622i	−0.532441	−	0.846467i	$-0.678725\pi$
$2$	−2.06579	−	0.671217i	−1.46074	−	0.474622i	−0.928295	+	0.371845i	$0.878725\pi$
$3$	1.40126	−	1.01807i	0.809017	−	0.587785i
$3$	1.40126	−	1.01807i	0.809017	−	0.587785i
$4$	2.19893	+	1.59762i	1.09947	+	0.798809i
$5$	−0.710253	−	2.18593i	−0.317635	−	0.977579i	−0.974656	−	0.223708i	$-0.928184\pi$
$5$	−0.710253	−	2.18593i	−0.317635	−	0.977579i	0.657022	−	0.753872i	$-0.271816\pi$
$6$	−3.57806	+	1.16258i	−1.46074	+	0.474622i
$7$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$7$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$8$	−0.916732	−	1.26177i	−0.324114	−	0.446104i
$9$	0.927051	−	2.85317i	0.309017	−	0.951057i
$10$			4.99242i			1.57874i
$11$	2.94009	−	1.53488i	0.886471	−	0.462785i
$11$	2.94009	−	1.53488i	0.886471	−	0.462785i
$12$	4.70777			1.35902
$13$	−3.42908	−	1.11418i	−0.951057	−	0.309017i
$13$	−3.42908	−	1.11418i	−0.951057	−	0.309017i
$14$		0			0
$15$	−3.22069	−	2.33997i	−0.831579	−	0.604177i
$16$	−0.632981	−	1.94811i	−0.158245	−	0.487029i
$17$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$17$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$18$	−3.83019	+	5.27180i	−0.902785	+	1.24258i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	1.93049	−	5.94144i	0.431671	−	1.32855i
$21$		0			0
$22$	−7.10386	+	1.19731i	−1.51455	+	0.255268i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−2.56916	−	0.834770i	−0.524427	−	0.170397i
$25$	−0.228763	+	0.166206i	−0.0457526	+	0.0332412i
$26$	6.33592	+	4.60332i	1.24258	+	0.902785i
$27$	−1.60570	−	4.94183i	−0.309017	−	0.951057i
$28$		0			0
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$	5.08265	+	6.99567i	0.927961	+	1.27723i
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$			7.56854i			1.33794i
$33$	2.55720	−	5.14400i	0.445152	−	0.895455i
$34$		0			0
$35$		0			0
$36$	6.59680	−	4.79286i	1.09947	−	0.798809i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$		0			0
$39$	−5.93935	+	1.92981i	−0.951057	+	0.309017i
$40$	−2.10704	+	2.90009i	−0.333153	+	0.458545i
$41$	−4.59885	−	6.32977i	−0.718219	−	0.988544i	−0.999581	−	0.0289423i	$-0.990786\pi$
$41$	−4.59885	−	6.32977i	−0.718219	−	0.988544i	0.281362	−	0.959602i	$-0.409214\pi$
$42$		0			0
$43$			7.75348i			1.18239i	0.806527	+	0.591197i	$0.201344\pi$
$43$			7.75348i			1.18239i	−0.806527	+	0.591197i	$0.798656\pi$
$44$	8.91722	+	1.32204i	1.34432	+	0.199304i
$45$	−6.89528			−1.02789
$46$		0			0
$47$	−5.39703	+	3.92117i	−0.787238	+	0.571962i	−0.907142	−	0.420824i	$-0.861741\pi$
$47$	−5.39703	+	3.92117i	−0.787238	+	0.571962i	0.119905	+	0.992785i	$0.461741\pi$
$48$	−2.87029	−	2.08539i	−0.414291	−	0.301000i
$49$	−2.16312	−	6.65740i	−0.309017	−	0.951057i
$50$	0.584137	−	0.189798i	0.0826094	−	0.0268414i
$51$		0			0
$52$	−5.76030	−	7.92837i	−0.798809	−	1.09947i
$53$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$53$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$54$			11.2866i			1.53591i
$55$	−5.44336	−	5.33669i	−0.733983	−	0.719599i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.20012	−	3.05156i	−0.546808	−	0.397280i	0.279799	−	0.960059i	$-0.409732\pi$
$59$	−4.20012	−	3.05156i	−0.546808	−	0.397280i	−0.826607	+	0.562779i	$0.809732\pi$
$60$	−3.34371	−	10.2909i	−0.431671	−	1.32855i
$61$	−10.4139	+	3.38370i	−1.33337	+	0.433238i	−0.887066	−	0.461644i	$-0.847260\pi$
$61$	−10.4139	+	3.38370i	−1.33337	+	0.433238i	−0.446304	+	0.894881i	$0.647260\pi$
$62$		0			0
$63$		0			0
$64$	3.81417	−	11.7388i	0.476771	−	1.46735i
$65$			8.28710i			1.02789i
$66$	−8.73539	+	8.91000i	−1.07525	+	1.09675i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.52081	−	4.68057i	−0.180487	−	0.555481i	0.819355	−	0.573287i	$-0.194332\pi$
$71$	−1.52081	−	4.68057i	−0.180487	−	0.555481i	−0.999841	+	0.0178059i	$0.994332\pi$
$72$	−4.44991	+	1.44586i	−0.524427	+	0.170397i
$73$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$73$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$74$		0			0
$75$	−0.151346	+	0.465795i	−0.0174759	+	0.0537854i
$76$		0			0
$77$		0			0
$78$	13.5648			1.53591
$79$	13.6385	+	4.43142i	1.53445	+	0.498574i	0.949839	−	0.312739i	$-0.101246\pi$
$79$	13.6385	+	4.43142i	1.53445	+	0.498574i	0.584613	+	0.811312i	$0.301246\pi$
$80$	−3.80887	+	2.76731i	−0.425845	+	0.309394i
$81$	−7.28115	−	5.29007i	−0.809017	−	0.587785i
$82$	5.25162	+	16.1628i	0.579944	+	1.78488i
$83$	17.0554	−	5.54164i	1.87207	−	0.608274i	0.881336	−	0.472489i	$-0.156644\pi$
$83$	17.0554	−	5.54164i	1.87207	−	0.608274i	0.990738	−	0.135785i	$-0.0433556\pi$
$84$		0			0
$85$		0			0
$86$	5.20426	−	16.0171i	0.561190	−	1.72717i
$87$		0			0
$88$	−4.63195	−	2.30265i	−0.493768	−	0.245463i
$89$	18.3671			1.94690			0.973452	−	0.228892i	$-0.0735101\pi$
$89$	18.3671			1.94690			0.973452	+	0.228892i	$0.0735101\pi$
$90$	14.2442	+	4.62823i	1.50147	+	0.487858i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	13.7811	−	4.47775i	1.42141	−	0.461845i
$95$		0			0
$96$	7.70534	+	10.6055i	0.786423	+	1.08242i
$97$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$97$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$98$			15.2047i			1.53591i
$99$	−1.65367	−	9.81149i	−0.166200	−	0.986092i
$100$	−0.768568			−0.0768568
$101$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$101$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$102$		0			0
$103$	16.4115	+	11.9236i	1.61707	+	1.17487i	0.828808	+	0.559533i	$0.189020\pi$
$103$	16.4115	+	11.9236i	1.61707	+	1.17487i	0.788263	+	0.615338i	$0.210980\pi$
$104$	1.73771	+	5.34813i	0.170397	+	0.524427i
$105$		0			0
$106$		0			0
$107$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$107$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$108$	4.36434	−	13.4321i	0.419959	−	1.29250i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	7.66279	+	14.6782i	0.730618	+	1.39951i
$111$		0			0
$112$		0			0
$113$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$113$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−6.35787	+	8.75086i	−0.587785	+	0.809017i
$118$	6.62831	+	9.12308i	0.610185	+	0.839848i
$119$		0			0
$120$			6.20891i			0.566793i
$121$	6.28826	−	9.02540i	0.571660	−	0.820491i
$122$	23.7843			2.15332
$123$	−12.8883	−	4.18768i	−1.16210	−	0.377590i
$124$		0			0
$125$	−8.77154	−	6.37290i	−0.784550	−	0.570009i
$126$		0			0
$127$	−1.41429	+	0.459530i	−0.125498	+	0.0407767i	−0.371093	−	0.928596i	$-0.621017\pi$
$127$	−1.41429	+	0.459530i	−0.125498	+	0.0407767i	0.245595	+	0.969373i	$0.421017\pi$
$128$	−6.86122	+	9.44366i	−0.606452	+	0.834709i
$129$	7.89361	+	10.8646i	0.694994	+	0.956577i
$130$	5.56244	−	17.1194i	0.487858	−	1.50147i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	13.8413	−	7.22588i	1.20473	−	0.628932i
$133$		0			0
$134$		0			0
$135$	−9.66207	+	7.01991i	−0.831579	+	0.604177i
$136$		0			0
$137$	6.77919	+	20.8642i	0.579186	+	1.78255i	0.621463	+	0.783444i	$0.286539\pi$
$137$	6.77919	+	20.8642i	0.579186	+	1.78255i	−0.0422769	+	0.999106i	$0.513461\pi$
$138$		0			0
$139$	13.4490	−	18.5109i	1.14073	−	1.57008i	0.374853	−	0.927084i	$-0.377693\pi$
$139$	13.4490	−	18.5109i	1.14073	−	1.57008i	0.765874	−	0.642991i	$-0.222307\pi$
$140$		0			0
$141$	−3.57059	+	10.9891i	−0.300698	+	0.925453i
$142$			10.6899i			0.897074i
$143$	−11.7919	+	1.98747i	−0.986092	+	0.166200i
$144$	−6.14511			−0.512092
$145$		0			0
$146$		0			0
$147$	−9.80881	−	7.12652i	−0.809017	−	0.587785i
$148$		0			0
$149$	18.9477	−	6.15649i	1.55226	−	0.504359i	0.597531	−	0.801846i	$-0.296148\pi$
$149$	18.9477	−	6.15649i	1.55226	−	0.504359i	0.954726	+	0.297487i	$0.0961483\pi$
$150$	0.625299	−	0.860650i	0.0510554	−	0.0702718i
$151$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$151$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−16.1433	−	5.24529i	−1.29250	−	0.419959i
$157$	18.7201	−	13.6010i	1.49403	−	1.08548i	0.521344	−	0.853347i	$-0.325431\pi$
$157$	18.7201	−	13.6010i	1.49403	−	1.08548i	0.972685	−	0.232129i	$-0.0745691\pi$
$158$	−25.1999	−	18.3088i	−2.00480	−	1.45657i
$159$		0			0
$160$	16.5443	−	5.37558i	1.30794	−	0.424977i
$161$		0			0
$162$	11.4906	+	15.8154i	0.902785	+	1.24258i
$163$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$163$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$164$		−	21.2659i		−	1.66059i
$165$	−13.0607	−	1.93633i	−1.01677	−	0.150743i
$166$	−38.9526			−3.02331
$167$	−24.2443	−	7.87744i	−1.87608	−	0.609575i	−0.988991	−	0.147973i	$-0.952725\pi$
$167$	−24.2443	−	7.87744i	−1.87608	−	0.609575i	−0.887087	−	0.461602i	$-0.847275\pi$
$168$		0			0
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$		0			0
$171$		0			0
$172$	−12.3871	+	17.0494i	−0.944508	+	1.30000i
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$		0			0
$176$	−4.85115	−	4.75608i	−0.365669	−	0.358503i
$177$	−8.99216			−0.675892
$178$	−37.9425	−	12.3283i	−2.84391	−	0.924043i
$179$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$179$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$180$	−15.1623	−	11.0160i	−1.13013	−	0.821086i
$181$	7.03726	+	21.6584i	0.523075	+	1.60986i	0.768091	+	0.640341i	$0.221207\pi$
$181$	7.03726	+	21.6584i	0.523075	+	1.60986i	−0.245016	+	0.969519i	$0.578793\pi$
$182$		0			0
$183$	−11.1478	+	15.3436i	−0.824068	+	1.13423i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−18.1322			−1.32243
$189$		0			0
$190$		0			0
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$	−6.60634	−	20.3322i	−0.476771	−	1.46735i
$193$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$193$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$194$		0			0
$195$	8.43688	+	11.6124i	0.604177	+	0.831579i
$196$	5.87943	−	18.0950i	0.419959	−	1.29250i
$197$			18.9032i			1.34680i	0.739278	+	0.673400i	$0.235167\pi$
$197$			18.9032i			1.34680i	−0.739278	+	0.673400i	$0.764833\pi$
$198$	−3.16950	+	21.3785i	−0.225246	+	1.51930i
$199$	21.2096			1.50351			0.751754	−	0.659443i	$-0.229208\pi$
$199$	21.2096			1.50351			0.751754	+	0.659443i	$0.229208\pi$
$200$	0.419429	+	0.136281i	0.0296581	+	0.00963649i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−10.5701	+	14.5485i	−0.738249	+	1.01611i
$206$	−25.8994	−	35.6474i	−1.80449	−	2.48367i
$207$		0			0
$208$			7.38550i			0.512092i
$209$		0			0
$210$		0			0
$211$	−24.1300	−	7.84031i	−1.66118	−	0.539749i	−0.680058	−	0.733158i	$-0.738046\pi$
$211$	−24.1300	−	7.84031i	−1.66118	−	0.539749i	−0.981118	+	0.193409i	$0.938046\pi$
$212$		0			0
$213$	−6.89621	−	5.01039i	−0.472520	−	0.343306i
$214$		0			0
$215$	16.9486	−	5.50693i	1.15588	−	0.375570i
$216$	−4.76348	+	6.55637i	−0.324114	+	0.446104i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−3.44360	−	20.4314i	−0.232168	−	1.37749i
$221$		0			0
$222$		0			0
$223$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$223$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$224$		0			0
$225$	0.262139	+	0.806781i	0.0174759	+	0.0537854i
$226$		0			0
$227$	15.5338	−	21.3804i	1.03101	−	1.41907i	0.126828	−	0.991925i	$-0.459520\pi$
$227$	15.5338	−	21.3804i	1.03101	−	1.41907i	0.904184	−	0.427143i	$-0.140480\pi$
$228$		0			0
$229$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$229$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$233$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$234$	19.0078	−	13.8099i	1.24258	−	0.902785i
$235$	12.4047	+	9.01252i	0.809192	+	0.587912i
$236$	−4.36054	−	13.4204i	−0.283847	−	0.873591i
$237$	23.6226	−	7.67544i	1.53445	−	0.498574i
$238$		0			0
$239$	−0.798759	−	1.09940i	−0.0516674	−	0.0711141i	0.782402	−	0.622774i	$-0.213995\pi$
$239$	−0.798759	−	1.09940i	−0.0516674	−	0.0711141i	−0.834069	+	0.551660i	$0.813995\pi$
$240$	−2.51989	+	7.75543i	−0.162658	+	0.500611i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−19.0482	+	14.4238i	−1.22447	+	0.927198i
$243$	−15.5885			−1.00000
$244$	−28.3054	−	9.19699i	−1.81207	−	0.588777i
$245$	−13.0163	+	9.45687i	−0.831579	+	0.604177i
$246$	23.8138	+	17.3018i	1.51831	+	1.10312i
$247$		0			0
$248$		0			0
$249$	18.2572	−	25.1289i	1.15701	−	1.59248i
$250$	13.8426	+	19.0527i	0.875482	+	1.20500i
$251$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$251$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$252$		0			0
$253$		0			0
$254$	3.23007			0.202673
$255$		0			0
$256$	0.541336	−	0.393304i	0.0338335	−	0.0245815i
$257$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$257$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$258$	−9.01405	−	27.7424i	−0.561190	−	1.72717i
$259$		0			0
$260$	−13.2396	+	18.2228i	−0.821086	+	1.13013i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−8.83483	+	1.48906i	−0.543746	+	0.0916453i
$265$		0			0
$266$		0			0
$267$	25.7370	−	18.6990i	1.57508	−	1.14436i
$268$		0			0
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$	24.6717	−	8.01633i	1.50147	−	0.487858i
$271$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$271$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$272$		0			0
$273$		0			0
$274$		−	47.6514i		−	2.87873i
$275$	−0.417477	+	0.839785i	−0.0251748	+	0.0506409i
$276$		0			0
$277$	−23.7574	−	7.71924i	−1.42744	−	0.463804i	−0.509484	−	0.860480i	$-0.670164\pi$
$277$	−23.7574	−	7.71924i	−1.42744	−	0.463804i	−0.917959	+	0.396676i	$0.870164\pi$
$278$	−40.2076	+	29.2125i	−2.41149	+	1.75205i
$279$		0			0
$280$		0			0
$281$	3.66582	−	1.19110i	0.218685	−	0.0710550i	−0.197626	−	0.980278i	$-0.563323\pi$
$281$	3.66582	−	1.19110i	0.218685	−	0.0710550i	0.416310	+	0.909223i	$0.363323\pi$
$282$	14.7522	−	20.3047i	0.878481	−	1.20912i
$283$	−4.44329	−	6.11566i	−0.264126	−	0.363538i	0.656270	−	0.754526i	$-0.272133\pi$
$283$	−4.44329	−	6.11566i	−0.264126	−	0.363538i	−0.920396	+	0.390988i	$0.872133\pi$
$284$	4.13360	−	12.7219i	0.245284	−	0.754907i
$285$		0			0
$286$	25.6937	+	3.80926i	1.51930	+	0.225246i
$287$		0			0
$288$	21.5943	+	7.01643i	1.27246	+	0.413447i
$289$	13.7533	−	9.99235i	0.809017	−	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−16.2106	+	22.3120i	−0.947034	+	1.30348i	0.00579779	+	0.999983i	$0.498154\pi$
$293$	−16.2106	+	22.3120i	−0.947034	+	1.30348i	−0.952832	+	0.303498i	$0.901846\pi$
$294$	15.4795	+	21.3057i	0.902785	+	1.24258i
$295$	−3.68737	+	11.3486i	−0.214687	+	0.660738i
$296$		0			0
$297$	−12.3060	−	12.0649i	−0.714069	−	0.700075i
$298$	−43.2744			−2.50682
$299$		0			0
$300$	−1.07696	+	0.782459i	−0.0621785	+	0.0451753i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	14.7931	+	20.3609i	0.847049	+	1.16586i
$306$		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	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$	7.87977	+	5.72499i	0.446104	+	0.324114i
$313$	9.97005	+	30.6847i	0.563540	+	1.73440i	0.672249	+	0.740325i	$0.265329\pi$
$313$	9.97005	+	30.6847i	0.563540	+	1.73440i	−0.108708	+	0.994074i	$0.534671\pi$
$314$	−47.8011	+	15.5315i	−2.69757	+	0.876494i
$315$		0			0
$316$	22.9105	+	31.5335i	1.28881	+	1.77390i
$317$	−9.89558	+	30.4555i	−0.555791	+	1.71055i	0.138053	+	0.990425i	$0.455916\pi$
$317$	−9.89558	+	30.4555i	−0.555791	+	1.71055i	−0.693844	+	0.720125i	$0.744084\pi$
$318$		0			0
$319$		0			0
$320$	−28.3693			−1.58589
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−7.55926	−	23.2650i	−0.419959	−	1.29250i
$325$	0.969630	−	0.315052i	0.0537854	−	0.0174759i
$326$		0			0
$327$		0			0
$328$	−3.77083	+	11.6054i	−0.208209	+	0.640801i
$329$		0			0
$330$	25.6810	+	12.7666i	1.41369	+	0.702779i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	46.3571	+	15.0624i	2.54418	+	0.826654i
$333$		0			0
$334$	44.7962	+	32.5463i	2.45114	+	1.78086i
$335$		0			0
$336$		0			0
$337$	−10.4219	+	14.3446i	−0.567720	+	0.781399i	−0.992282	−	0.123999i	$-0.960428\pi$
$337$	−10.4219	+	14.3446i	−0.567720	+	0.781399i	0.424563	+	0.905399i	$0.360428\pi$
$338$	−16.5975	−	22.8445i	−0.902785	−	1.24258i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	9.78313	−	7.10786i	0.527471	−	0.383230i
$345$		0			0
$346$		0			0
$347$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$347$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$348$		0			0
$349$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$349$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$350$		0			0
$351$			18.7350i			1.00000i
$352$	11.6168	+	22.2522i	0.619179	+	1.18605i
$353$	24.0608			1.28063			0.640314	−	0.768114i	$-0.278804\pi$
$353$	24.0608			1.28063			0.640314	+	0.768114i	$0.278804\pi$
$354$	18.5759	+	6.03569i	0.987300	+	0.320793i
$355$	−9.15125	+	6.64877i	−0.485698	+	0.352880i
$356$	40.3879	+	29.3435i	2.14056	+	1.55521i
$357$		0			0
$358$		0			0
$359$	−1.23226	+	1.69606i	−0.0650361	+	0.0895145i	−0.840296	−	0.542128i	$-0.817619\pi$
$359$	−1.23226	+	1.69606i	−0.0650361	+	0.0895145i	0.775260	+	0.631642i	$0.217619\pi$
$360$	6.32113	+	8.70028i	0.333153	+	0.458545i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$		−	49.4654i		−	2.59984i
$363$	−0.377040	−	19.0488i	−0.0197895	−	0.999804i
$364$		0			0
$365$		0			0
$366$	33.3279	−	24.2141i	1.74208	−	1.26569i
$367$	−30.8302	−	22.3994i	−1.60932	−	1.16924i	−0.865572	−	0.500785i	$-0.833045\pi$
$367$	−30.8302	−	22.3994i	−1.60932	−	1.16924i	−0.743751	−	0.668457i	$-0.766955\pi$
$368$		0			0
$369$	−22.3233	+	7.25327i	−1.16210	+	0.377590i
$370$		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
$375$	−18.7793			−0.969757
$376$	9.89526	+	3.21516i	0.510309	+	0.165809i
$377$		0			0
$378$		0			0
$379$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$379$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$380$		0			0
$381$	−1.51395	+	2.08377i	−0.0775619	+	0.106755i
$382$		0			0
$383$	8.74548	−	26.9158i	0.446873	−	1.37533i	−0.433543	−	0.901133i	$-0.642737\pi$
$383$	8.74548	−	26.9158i	0.446873	−	1.37533i	0.880416	−	0.474202i	$-0.157263\pi$
$384$			20.2182i			1.03176i
$385$		0			0
$386$		0			0
$387$	22.1220	+	7.18787i	1.12452	+	0.365380i
$388$		0			0
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$	−9.63442	−	29.6517i	−0.487858	−	1.50147i
$391$		0			0
$392$	−6.41713	+	8.83242i	−0.324114	+	0.446104i
$393$		0			0
$394$	12.6882	−	39.0502i	0.639221	−	1.96732i
$395$		−	32.9603i		−	1.65841i
$396$	12.0387	−	24.2168i	0.604968	−	1.21694i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−43.8146	−	14.2362i	−2.19623	−	0.713598i
$399$		0			0
$400$	0.468591	+	0.340451i	0.0234295	+	0.0170226i
$401$	12.3560	+	38.0278i	0.617028	+	1.89902i	0.362761	+	0.931882i	$0.381834\pi$
$401$	12.3560	+	38.0278i	0.617028	+	1.89902i	0.254267	+	0.967134i	$0.418166\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−6.39228	+	19.6734i	−0.317635	+	0.977579i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$409$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$410$	31.6009	−	22.9594i	1.56066	−	1.13388i
$411$	30.7407	+	22.3344i	1.51633	+	1.10168i
$412$	17.0383	+	52.4386i	0.839418	+	2.58346i
$413$		0			0
$414$		0			0
$415$	−24.2273	−	33.3460i	−1.18927	−	1.63689i
$416$	8.43269	−	25.9532i	0.413447	−	1.27246i
$417$		−	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	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$	44.5850	+	32.3929i	2.17036	+	1.57686i
$423$	6.18444	+	19.0338i	0.300698	+	0.925453i
$424$		0			0
$425$		0			0
$426$	10.8831	+	14.9793i	0.527287	+	0.725748i
$427$		0			0
$428$		0			0
$429$	−14.5002	+	14.7900i	−0.700075	+	0.714069i
$430$	−38.7086			−1.86670
$431$	39.4464	+	12.8169i	1.90007	+	0.617369i	0.964364	+	0.264578i	$0.0852325\pi$
$431$	39.4464	+	12.8169i	1.90007	+	0.617369i	0.935702	+	0.352791i	$0.114767\pi$
$432$	−8.61088	+	6.25617i	−0.414291	+	0.301000i
$433$	−30.7491	−	22.3405i	−1.47771	−	1.07362i	−0.978286	−	0.207259i	$-0.933546\pi$
$433$	−30.7491	−	22.3405i	−1.47771	−	1.07362i	−0.499422	−	0.866359i	$-0.666454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$			33.6160i			1.60441i	0.597052	+	0.802203i	$0.296339\pi$
$439$			33.6160i			1.60441i	−0.597052	+	0.802203i	$0.703661\pi$
$440$	−1.74358	+	11.7606i	−0.0831221	+	0.560665i
$441$	−21.0000			−1.00000
$442$		0			0
$443$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$443$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$	−13.0453	−	40.1492i	−0.618404	−	1.90325i
$446$		0			0
$447$	20.2829	−	27.9170i	0.959348	−	1.32043i
$448$		0			0
$449$	−11.0247	+	33.9304i	−0.520286	+	1.60127i	0.253168	+	0.967422i	$0.418527\pi$
$449$	−11.0247	+	33.9304i	−0.520286	+	1.60127i	−0.773454	+	0.633853i	$0.781473\pi$
$450$		−	1.84259i		−	0.0868607i
$451$	−23.2365	−	11.5514i	−1.09416	−	0.543934i
$452$		0			0
$453$		0			0
$454$	−46.4404	+	33.7410i	−2.17956	+	1.58354i
$455$		0			0
$456$		0			0
$457$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$457$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	34.9272i		−	1.62672i	−0.581758	−	0.813362i	$-0.697635\pi$
$461$		−	34.9272i		−	1.62672i	0.581758	−	0.813362i	$-0.302365\pi$
$462$		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	$-0.600000\pi$
$467$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$468$	−27.9611	+	9.08510i	−1.29250	+	0.419959i
$469$		0			0
$470$	−19.5761	−	26.9442i	−0.902980	−	1.24284i
$471$	12.3849	−	38.1169i	0.570668	−	1.75634i
$472$			8.09706i			0.372697i
$473$	11.9007	+	22.7959i	0.547194	+	1.04816i
$474$	−53.9513			−2.47806
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.912137	+	2.80727i	0.0417202	+	0.128401i
$479$	−3.05803	+	0.993613i	−0.139725	+	0.0453993i	−0.378045	−	0.925787i	$-0.623403\pi$
$479$	−3.05803	+	0.993613i	−0.139725	+	0.0453993i	0.238320	+	0.971187i	$0.423403\pi$
$480$	17.7102	−	24.3759i	0.808354	−	1.11260i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	28.2466	−	9.80000i	1.28394	−	0.445455i
$485$		0			0
$486$	32.2025	+	10.4632i	1.46074	+	0.474622i
$487$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$487$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$488$	13.8163	+	10.0381i	0.625433	+	0.454403i
$489$		0			0
$490$	33.2365	−	10.7992i	1.50147	−	0.487858i
$491$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$491$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$492$	−21.6503	−	29.7991i	−0.976071	−	1.34345i
$493$		0			0
$494$		0			0
$495$	−20.2727	+	10.5835i	−0.911192	+	0.475691i
$496$		0			0
$497$		0			0
$498$	−54.5826	+	39.6566i	−2.44591	+	1.77706i
$499$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$499$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$500$	−9.10657	−	28.0271i	−0.407258	−	1.25341i
$501$	−41.9923	+	13.6441i	−1.87608	+	0.609575i
$502$		0			0
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.5167			1.00000
$508$	−3.84408	−	1.24902i	−0.170553	−	0.0554161i
$509$	−13.0242	+	9.46264i	−0.577288	+	0.419424i	−0.837745	−	0.546061i	$-0.816127\pi$
$509$	−13.0242	+	9.46264i	−0.577288	+	0.419424i	0.260457	+	0.965485i	$0.416127\pi$
$510$		0			0
$511$		0			0
$512$	20.8211	−	6.76518i	0.920171	−	0.298982i
$513$		0			0
$514$		0			0
$515$	14.4080	−	44.3432i	0.634892	−	1.95400i
$516$			36.5016i			1.60689i
$517$	−9.84921	+	19.8124i	−0.433168	+	0.871349i
$518$		0			0
$519$		0			0
$520$	10.4564	−	7.59705i	0.458545	−	0.333153i
$521$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$521$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$522$		0			0
$523$	−11.8787	+	3.85962i	−0.519419	+	0.168769i	−0.556982	−	0.830525i	$-0.688041\pi$
$523$	−11.8787	+	3.85962i	−0.519419	+	0.168769i	0.0375627	+	0.999294i	$0.488041\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−11.6398	−	1.72567i	−0.506555	−	0.0751001i
$529$	23.0000			1.00000
$530$		0			0
$531$	−12.6003	+	9.15469i	−0.546808	+	0.397280i
$532$		0			0
$533$	8.71735	+	26.8292i	0.377590	+	1.16210i
$534$	−65.7184	+	21.3532i	−2.84391	+	0.924043i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−16.5781	−	16.2532i	−0.714069	−	0.700075i
$540$	−32.4614			−1.39692
$541$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$541$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$542$		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	0.955121	−	0.296217i	$-0.0957252\pi$
$547$	8.84659	+	12.1763i	0.378253	+	0.520620i	−0.576868	+	0.816838i	$0.695725\pi$
$548$	−18.4261	+	56.7096i	−0.787122	+	2.42251i
$549$			32.8496i			1.40199i
$550$	1.42610	−	1.45460i	0.0608090	−	0.0620245i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	43.8965	+	31.8927i	1.86499	+	1.35499i
$555$		0			0
$556$	59.1468	−	19.2180i	2.50838	−	0.815023i
$557$	6.57984	−	9.05637i	0.278797	−	0.383731i	−0.646538	−	0.762882i	$-0.723784\pi$
$557$	6.57984	−	9.05637i	0.278797	−	0.383731i	0.925335	+	0.379151i	$0.123784\pi$
$558$		0			0
$559$	8.63874	−	26.5873i	0.365380	−	1.12452i
$560$		0			0
$561$		0			0
$562$	−8.37232			−0.353165
$563$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$563$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$564$	−25.4080	+	18.4600i	−1.06987	+	0.777305i
$565$		0			0
$566$	5.07398	+	15.6161i	0.213275	+	0.656393i
$567$		0			0
$568$	−4.51164	+	6.20974i	−0.189304	+	0.260555i
$569$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$569$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$570$		0			0
$571$		−	28.8444i		−	1.20710i	−0.797325	−	0.603550i	$-0.793752\pi$
$571$		−	28.8444i		−	1.20710i	0.797325	−	0.603550i	$-0.206248\pi$
$572$	−29.1049	−	14.4687i	−1.21694	−	0.604968i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−29.9569	−	21.7650i	−1.24820	−	0.906873i
$577$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$577$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$578$	−35.1185	+	11.4107i	−1.46074	+	0.474622i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	23.6445	+	7.68256i	0.977579	+	0.317635i
$586$	48.4640	−	35.2111i	2.00203	−	1.45456i
$587$	−33.7000	−	24.4845i	−1.39095	−	1.01058i	−0.995760	−	0.0919844i	$-0.970679\pi$
$587$	−33.7000	−	24.4845i	−1.39095	−	1.01058i	−0.395189	−	0.918600i	$-0.629321\pi$
$588$	−10.1835	−	31.3415i	−0.419959	−	1.29250i
$589$		0			0
$590$	15.2347	−	20.9687i	0.627202	−	0.863269i
$591$	19.2449	+	26.4883i	0.791630	+	1.08958i
$592$		0			0
$593$			28.3972i			1.16613i	0.812425	+	0.583066i	$0.198147\pi$
$593$			28.3972i			1.16613i	−0.812425	+	0.583066i	$0.801853\pi$
$594$	17.3236	+	33.1836i	0.710795	+	1.36154i
$595$		0			0
$596$	51.5005	+	16.7335i	2.10954	+	0.685432i
$597$	29.7201	−	21.5929i	1.21636	−	0.883740i
$598$		0			0
$599$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$599$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$600$	0.726472	−	0.236045i	0.0296581	−	0.00963649i
$601$	−20.1845	+	27.7816i	−0.823344	+	1.13324i	0.165781	+	0.986163i	$0.446985\pi$
$601$	−20.1845	+	27.7816i	−0.823344	+	1.13324i	−0.989126	+	0.147074i	$0.953015\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.1952	−	7.33541i	−0.983674	−	0.298227i
$606$		0			0
$607$	46.7187	+	15.1798i	1.89625	+	0.616131i	0.972361	+	0.233481i	$0.0750118\pi$
$607$	46.7187	+	15.1798i	1.89625	+	0.616131i	0.923894	+	0.382649i	$0.124988\pi$
$608$		0			0
$609$		0			0
$610$	−16.8928	−	51.9908i	−0.683971	−	2.10505i
$611$	22.8757	−	7.43278i	0.925453	−	0.300698i
$612$		0			0
$613$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$613$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$614$		0			0
$615$			31.1474i			1.25598i
$616$		0			0
$617$	1.17142			0.0471595			0.0235798	−	0.999722i	$-0.492494\pi$
$617$	1.17142			0.0471595			0.0235798	+	0.999722i	$0.492494\pi$
$618$	−72.5834	−	23.5838i	−2.91973	−	0.948679i
$619$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$619$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	7.51898	+	10.3490i	0.301000	+	0.414291i
$625$	−8.13762	+	25.0450i	−0.325505	+	1.00180i
$626$		−	70.0802i		−	2.80097i
$627$		0			0
$628$	62.8935			2.50972
$629$		0			0
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$	−6.91141	−	21.2711i	−0.274921	−	0.846120i
$633$	−41.7944	+	13.5798i	−1.66118	+	0.539749i
$634$	40.8844	−	56.2726i	1.62373	−	2.23487i
$635$	2.00900	+	2.76516i	0.0797249	+	0.109732i
$636$		0			0
$637$			25.2389i			1.00000i
$638$		0			0
$639$	−14.7643			−0.584067
$640$	25.5164	+	8.29079i	1.00862	+	0.327722i
$641$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$641$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$642$		0			0
$643$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$643$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$644$		0			0
$645$	18.1429	−	24.9716i	0.714376	−	0.983254i
$646$		0			0
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$			14.0367i			0.551415i
$649$	−17.0325	−	2.52518i	−0.668585	−	0.0991219i
$650$	−2.21452			−0.0868607
$651$		0			0
$652$		0			0
$653$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$653$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$654$		0			0
$655$		0			0
$656$	−9.42013	+	12.9657i	−0.367794	+	0.506226i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	−25.6261	−	25.1239i	−0.997494	−	0.977946i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−22.6275	−	16.4399i	−0.878119	−	0.637991i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−40.7264	−	56.0551i	−1.57575	−	2.16884i
$669$		0			0
$670$		0			0
$671$	−25.4244	+	25.9326i	−0.981497	+	1.00112i
$672$		0			0
$673$	27.3460	+	8.88525i	1.05411	+	0.342501i	0.784280	−	0.620407i	$-0.213032\pi$
$673$	27.3460	+	8.88525i	1.05411	+	0.342501i	0.269830	+	0.962908i	$0.413032\pi$
$674$	31.1579	−	22.6375i	1.20016	−	0.871966i
$675$	1.18869	+	0.863632i	0.0457526	+	0.0332412i
$676$	10.9189	+	33.6050i	0.419959	+	1.29250i
$677$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$677$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		−	45.7740i		−	1.75406i
$682$		0			0
$683$	51.3398			1.96446			0.982231	−	0.187674i	$-0.0600949\pi$
$683$	51.3398			1.96446			0.982231	+	0.187674i	$0.0600949\pi$
$684$		0			0
$685$	40.7928	−	29.6377i	1.55861	−	1.13240i
$686$		0			0
$687$		0			0
$688$	15.1047	−	4.90780i	0.575860	−	0.187108i
$689$		0			0
$690$		0			0
$691$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$691$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−50.0158	−	16.2511i	−1.89721	−	0.616440i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$701$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$702$	12.5752	−	38.7026i	0.474622	−	1.46074i
$703$		0			0
$704$	−6.80371	−	40.3675i	−0.256424	−	1.52141i
$705$	26.5576			1.00022
$706$	−49.7046	−	16.1500i	−1.87066	−	0.607814i
$707$		0			0
$708$	−19.7732	−	14.3660i	−0.743121	−	0.539909i
$709$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$709$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$710$	23.3673	−	7.59251i	0.876961	−	0.284942i
$711$	25.2872	−	34.8048i	0.948343	−	1.30528i
$712$	−16.8377	−	23.1751i	−0.631018	−	0.868522i
$713$		0			0
$714$		0			0
$715$	12.7197	+	24.3648i	0.475691	+	0.911192i
$716$		0			0
$717$	−2.23854	−	0.727344i	−0.0835997	−	0.0271632i
$718$	3.68401	−	2.67659i	0.137486	−	0.0998895i
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$	4.36458	+	13.4328i	0.162658	+	0.500611i
$721$		0			0
$722$	24.2579	−	33.3881i	0.902785	−	1.24258i
$723$		0			0
$724$	−19.1275	+	58.8683i	−0.710867	+	2.18782i
$725$		0			0
$726$	−12.0070	+	39.6040i	−0.445622	+	1.46984i
$727$	−2.34066			−0.0868103			−0.0434052	−	0.999058i	$-0.513821\pi$
$727$	−2.34066			−0.0868103			−0.0434052	+	0.999058i	$0.513821\pi$
$728$		0			0
$729$	−21.8435	+	15.8702i	−0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$	−49.0265	+	15.9297i	−1.81207	+	0.588777i
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$	48.6539	+	66.9664i	1.79585	+	2.47177i
$735$	−8.61136	+	26.5030i	−0.317635	+	0.977579i
$736$		0			0
$737$		0			0
$738$	50.9838			1.87674
$739$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$739$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−47.6652	+	15.4874i	−1.74867	+	0.568177i	−0.995929	−	0.0901418i	$-0.971268\pi$
$743$	−47.6652	+	15.4874i	−1.74867	+	0.568177i	−0.752739	+	0.658319i	$0.771268\pi$
$744$		0			0
$745$	−26.9153	−	37.0458i	−0.986102	−	1.35725i
$746$	−25.0459	+	77.0832i	−0.916994	+	2.82222i
$747$		−	53.7994i		−	1.96842i
$748$		0			0
$749$		0			0
$750$	38.7941	+	12.6050i	1.41656	+	0.460268i
$751$	−8.36230	+	6.07557i	−0.305145	+	0.221701i	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−8.36230	+	6.07557i	−0.305145	+	0.221701i	0.424666	+	0.905350i	$0.360392\pi$
$752$	11.0551	+	8.03200i	0.403138	+	0.292897i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−14.5660	+	44.8294i	−0.529409	+	1.62935i	0.226021	+	0.974122i	$0.427428\pi$
$757$	−14.5660	+	44.8294i	−0.529409	+	1.62935i	−0.755429	+	0.655230i	$0.772572\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10.4810	+	3.40548i	0.379935	+	0.123448i	0.492757	−	0.870167i	$-0.335989\pi$
$761$	10.4810	+	3.40548i	0.379935	+	0.123448i	−0.112822	+	0.993615i	$0.535989\pi$
$762$	4.52616	−	3.28845i	0.163966	−	0.119128i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−36.1327	+	49.7324i	−1.30553	+	1.79690i
$767$	11.0026	+	15.1437i	0.397280	+	0.546808i
$768$	0.358140	−	1.10224i	0.0129233	−	0.0397737i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−44.8442	+	32.5813i	−1.61294	+	1.17187i	−0.759842	+	0.650108i	$0.774724\pi$
$773$	−44.8442	+	32.5813i	−1.61294	+	1.17187i	−0.853093	+	0.521758i	$0.825276\pi$
$774$	−40.8748	−	29.6973i	−1.46922	−	1.06745i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			39.0137i			1.39692i
$781$	−11.6554	−	11.4270i	−0.417064	−	0.408891i
$782$		0			0
$783$		0			0
$784$	−11.6002	+	8.42800i	−0.414291	+	0.301000i
$785$	−43.0268	−	31.2608i	−1.53569	−	1.11575i
$786$		0			0
$787$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$787$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$788$	−30.2002	+	41.5670i	−1.07584	+	1.48076i
$789$		0			0
$790$	−22.1235	+	68.0892i	−0.787119	+	2.42250i
$791$		0			0
$792$	−10.8639	+	11.0811i	−0.386032	+	0.393749i
$793$	39.4803			1.40199
$794$		0			0
$795$		0			0
$796$	46.6385	+	33.8848i	1.65306	+	1.20102i
$797$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$		0			0
$800$	−1.25794	−	1.73140i	−0.0444748	−	0.0612143i
$801$	17.0272	−	52.4043i	0.601626	−	1.85162i
$802$		−	86.8510i		−	3.06682i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$809$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$810$	26.4102	−	36.3506i	0.927961	−	1.27723i
$811$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$811$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−46.4860	+	15.1042i	−1.62336	+	0.527462i
$821$	32.0122	−	44.0610i	1.11723	−	1.53774i	0.306928	−	0.951733i	$-0.400699\pi$
$821$	32.0122	−	44.0610i	1.11723	−	1.53774i	0.810306	−	0.586007i	$-0.199301\pi$
$822$	−48.5127	−	66.7720i	−1.69207	−	2.32894i
$823$	−1.67681	+	5.16068i	−0.0584498	+	0.179890i	−0.976019	−	0.217687i	$-0.930149\pi$
$823$	−1.67681	+	5.16068i	−0.0584498	+	0.179890i	0.917569	+	0.397577i	$0.130149\pi$
$824$		−	31.6384i		−	1.10217i
$825$	0.269971	+	1.60178i	0.00939917	+	0.0557668i
$826$		0			0
$827$	−53.7586	−	17.4672i	−1.86937	−	0.607395i	−0.991775	−	0.127995i	$-0.959146\pi$
$827$	−53.7586	−	17.4672i	−1.86937	−	0.607395i	−0.877596	−	0.479401i	$-0.840854\pi$
$828$		0			0
$829$	−45.7668	−	33.2515i	−1.58955	−	1.15487i	−0.904584	−	0.426296i	$-0.859818\pi$
$829$	−45.7668	−	33.2515i	−1.58955	−	1.15487i	−0.684964	−	0.728577i	$-0.740182\pi$
$830$	27.6662	+	85.1478i	0.960308	+	2.95552i
$831$	−41.1490	+	13.3701i	−1.42744	+	0.463804i
$832$	−26.1582	+	36.0037i	−0.906873	+	1.24820i
$833$		0			0
$834$	−26.6007	+	81.8687i	−0.921108	+	2.83488i
$835$			58.5914i			2.02764i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	39.6964	−	28.8411i	1.37047	−	0.995707i	0.372773	−	0.927923i	$-0.378407\pi$
$839$	39.6964	−	28.8411i	1.37047	−	0.995707i	0.997700	−	0.0677843i	$-0.0215930\pi$
$840$		0			0
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$		0			0
$843$	3.92414	−	5.40112i	0.135155	−	0.186024i
$844$	−40.5344	−	55.7908i	−1.39525	−	1.92040i
$845$	9.23329	−	28.4171i	0.317635	−	0.977579i
$846$		−	43.4709i		−	1.49456i
$847$		0			0
$848$		0			0
$849$	−12.4524	−	4.04602i	−0.427365	−	0.138859i
$850$		0			0
$851$		0			0
$852$	−7.15961	−	22.0350i	−0.245284	−	0.754907i
$853$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$853$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	39.8817	−	20.8204i	1.36154	−	0.710795i
$859$	−42.3162			−1.44381			−0.721905	−	0.691992i	$-0.756733\pi$
$859$	−42.3162			−1.44381			−0.721905	+	0.691992i	$0.756733\pi$
$860$	46.0668	+	14.9680i	1.57086	+	0.510405i
$861$		0			0
$862$	−72.8852	−	52.9542i	−2.48248	−	1.80363i
$863$	−5.53688	−	17.0408i	−0.188478	−	0.580074i	0.811513	−	0.584334i	$-0.198644\pi$
$863$	−5.53688	−	17.0408i	−0.188478	−	0.580074i	−0.999991	+	0.00425952i	$0.998644\pi$
$864$	37.4025	−	12.1528i	1.27246	−	0.413447i
$865$		0			0
$866$	48.5260	+	66.7903i	1.64898	+	2.26963i
$867$	9.09896	−	28.0037i	0.309017	−	0.951057i
$868$		0			0
$869$	46.9002	−	7.90476i	1.59098	−	0.268150i
$870$		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	$-0.700000\pi$
$877$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$878$	22.5636	−	69.4437i	0.761486	−	2.34361i
$879$			47.7685i			1.61119i
$880$	−6.95093	+	13.9823i	−0.234316	+	0.471344i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	43.3816	+	14.0956i	1.46074	+	0.474622i
$883$	20.2929	−	14.7437i	0.682911	−	0.496164i	−0.191411	−	0.981510i	$-0.561306\pi$
$883$	20.2929	−	14.7437i	0.682911	−	0.496164i	0.874322	+	0.485346i	$0.161306\pi$
$884$		0			0
$885$	6.38671	+	19.6563i	0.214687	+	0.660738i
$886$		0			0
$887$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$887$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$		0			0
$890$			91.6960i			3.07366i
$891$	−29.5269	−	4.37755i	−0.989188	−	0.146653i
$892$		0			0
$893$		0			0
$894$	−60.6386	+	44.0565i	−2.02806	+	1.47347i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	45.5493	−	62.6932i	1.52000	−	2.09210i
$899$		0			0
$900$	−0.712502	+	2.19286i	−0.0237501	+	0.0730952i
$901$		0			0
$902$	40.2483	+	39.4595i	1.34012	+	1.31386i
$903$		0			0
$904$		0			0
$905$	42.3457	−	30.7660i	1.40762	−	1.02269i
$906$		0			0
$907$	15.3004	+	47.0897i	0.508040	+	1.56359i	0.795599	+	0.605824i	$0.207156\pi$
$907$	15.3004	+	47.0897i	0.508040	+	1.56359i	−0.287559	+	0.957763i	$0.592844\pi$
$908$	68.3155	−	22.1970i	2.26713	−	0.736635i
$909$		0			0
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$	41.6387	−	42.4710i	1.37804	−	1.40559i
$914$		0			0
$915$	41.4578	+	13.4705i	1.37055	+	0.445320i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−44.0171	+	14.3020i	−1.45199	+	0.471780i	−0.925613	−	0.378471i	$-0.876450\pi$
$919$	−44.0171	+	14.3020i	−1.45199	+	0.471780i	−0.526377	+	0.850251i	$0.676450\pi$
$920$		0			0
$921$		0			0
$922$	−23.4438	+	72.1525i	−0.772079	+	2.37621i
$923$			17.7445i			0.584067i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	49.2344	−	35.7709i	1.61707	−	1.17487i
$928$		0			0
$929$	−17.2767	−	53.1724i	−0.566832	−	1.74453i	−0.662445	−	0.749110i	$-0.730481\pi$
$929$	−17.2767	−	53.1724i	−0.566832	−	1.74453i	0.0956136	−	0.995419i	$-0.469519\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	16.8701			0.551415
$937$	58.2035	+	18.9115i	1.90143	+	0.617811i	0.959016	+	0.283352i	$0.0914466\pi$
$937$	58.2035	+	18.9115i	1.90143	+	0.617811i	0.942410	+	0.334458i	$0.108553\pi$
$938$		0			0
$939$	45.2099	+	32.8469i	1.47537	+	1.07192i
$940$	12.8785	+	39.6359i	0.420050	+	1.29278i
$941$	−2.21781	+	0.720610i	−0.0722985	+	0.0234912i	−0.344943	−	0.938624i	$-0.612102\pi$
$941$	−2.21781	+	0.720610i	−0.0722985	+	0.0234912i	0.272644	+	0.962115i	$0.412102\pi$
$942$	−51.1695	+	70.4287i	−1.66719	+	2.29469i
$943$		0			0
$944$	−3.28620	+	10.1139i	−0.106957	+	0.329179i
$945$		0			0
$946$	−9.28335	−	55.0796i	−0.301828	−	1.79079i
$947$	50.8682			1.65300			0.826498	−	0.562940i	$-0.190330\pi$
$947$	50.8682			1.65300			0.826498	+	0.562940i	$0.190330\pi$
$948$	64.2069	+	20.8621i	2.08534	+	0.677569i
$949$		0			0
$950$		0			0
$951$	17.1397	+	52.7504i	0.555791	+	1.71055i
$952$		0			0
$953$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$953$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$954$		0			0
$955$		0			0
$956$		−	3.69361i		−	0.119460i
$957$		0			0
$958$	6.98418			0.225649
$959$		0			0
$960$	−39.7527	+	28.8820i	−1.28301	+	0.932164i
$961$	−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	$0.5\pi$
$968$	−17.1527	+	0.339509i	−0.551307	+	0.0109122i
$969$		0			0
$970$		0			0
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$	−34.2780	−	24.9044i	−1.09947	−	0.798809i
$973$		0			0
$974$		0			0
$975$	1.03796	−	1.42862i	0.0332412	−	0.0457526i
$976$	13.1837	+	18.1457i	0.421998	+	0.580831i
$977$	−10.9440	+	33.6821i	−0.350128	+	1.07758i	0.608652	+	0.793437i	$0.291711\pi$
$977$	−10.9440	+	33.6821i	−0.350128	+	1.07758i	−0.958781	+	0.284147i	$0.908289\pi$
$978$		0			0
$979$	54.0008	−	28.1913i	1.72587	−	0.900998i
$980$	−43.7304			−1.39692
$981$		0			0
$982$		0			0
$983$	−37.4343	−	27.1976i	−1.19397	−	0.867470i	−0.200292	−	0.979736i	$-0.564189\pi$
$983$	−37.4343	−	27.1976i	−1.19397	−	0.867470i	−0.993678	+	0.112267i	$0.964189\pi$
$984$	6.53126	+	20.1012i	0.208209	+	0.640801i
$985$	41.3212	−	13.4261i	1.31660	−	0.427791i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	48.9831	−	8.25582i	1.55678	−	0.262387i
$991$	−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
$995$	−15.0642	−	46.3628i	−0.477567	−	1.46980i
$996$	80.2929	−	26.0888i	2.54418	−	0.826654i
$997$	−31.9172	+	43.9303i	−1.01083	+	1.39129i	−0.0923886	+	0.995723i	$0.529450\pi$
$997$	−31.9172	+	43.9303i	−1.01083	+	1.39129i	−0.918439	+	0.395562i	$0.870550\pi$
$998$		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.233.2	yes	32
3.2	odd	2	inner	429.2.y.a.233.7	yes	32
11.6	odd	10	inner	429.2.y.a.116.2	✓	32
13.12	even	2	inner	429.2.y.a.233.7	yes	32
33.17	even	10	inner	429.2.y.a.116.7	yes	32
39.38	odd	2	CM	429.2.y.a.233.2	yes	32
143.116	odd	10	inner	429.2.y.a.116.7	yes	32
429.116	even	10	inner	429.2.y.a.116.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.116.2	✓	32	11.6	odd	10	inner
429.2.y.a.116.2	✓	32	429.116	even	10	inner
429.2.y.a.116.7	yes	32	33.17	even	10	inner
429.2.y.a.116.7	yes	32	143.116	odd	10	inner
429.2.y.a.233.2	yes	32	1.1	even	1	trivial
429.2.y.a.233.2	yes	32	39.38	odd	2	CM
429.2.y.a.233.7	yes	32	3.2	odd	2	inner
429.2.y.a.233.7	yes	32	13.12	even	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.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06579 - 0.671217i) q^{2} +(1.40126 - 1.01807i) q^{3} +(2.19893 + 1.59762i) q^{4} +(-0.710253 - 2.18593i) q^{5} +(-3.57806 + 1.16258i) q^{6} +(-0.916732 - 1.26177i) q^{8} +(0.927051 - 2.85317i) q^{9} +O(q^{10})\)	\(q+(-2.06579 - 0.671217i) q^{2} +(1.40126 - 1.01807i) q^{3} +(2.19893 + 1.59762i) q^{4} +(-0.710253 - 2.18593i) q^{5} +(-3.57806 + 1.16258i) q^{6} +(-0.916732 - 1.26177i) q^{8} +(0.927051 - 2.85317i) q^{9} +4.99242i q^{10} +(2.94009 - 1.53488i) q^{11} +4.70777 q^{12} +(-3.42908 - 1.11418i) q^{13} +(-3.22069 - 2.33997i) q^{15} +(-0.632981 - 1.94811i) q^{16} +(-3.83019 + 5.27180i) q^{18} +(1.93049 - 5.94144i) q^{20} +(-7.10386 + 1.19731i) q^{22} +(-2.56916 - 0.834770i) q^{24} +(-0.228763 + 0.166206i) q^{25} +(6.33592 + 4.60332i) q^{26} +(-1.60570 - 4.94183i) q^{27} +(5.08265 + 6.99567i) q^{30} +7.56854i q^{32} +(2.55720 - 5.14400i) q^{33} +(6.59680 - 4.79286i) q^{36} +(-5.93935 + 1.92981i) q^{39} +(-2.10704 + 2.90009i) q^{40} +(-4.59885 - 6.32977i) q^{41} +7.75348i q^{43} +(8.91722 + 1.32204i) q^{44} -6.89528 q^{45} +(-5.39703 + 3.92117i) q^{47} +(-2.87029 - 2.08539i) q^{48} +(-2.16312 - 6.65740i) q^{49} +(0.584137 - 0.189798i) q^{50} +(-5.76030 - 7.92837i) q^{52} +11.2866i q^{54} +(-5.44336 - 5.33669i) q^{55} +(-4.20012 - 3.05156i) q^{59} +(-3.34371 - 10.2909i) q^{60} +(-10.4139 + 3.38370i) q^{61} +(3.81417 - 11.7388i) q^{64} +8.28710i q^{65} +(-8.73539 + 8.91000i) q^{66} +(-1.52081 - 4.68057i) q^{71} +(-4.44991 + 1.44586i) q^{72} +(-0.151346 + 0.465795i) q^{75} +13.5648 q^{78} +(13.6385 + 4.43142i) q^{79} +(-3.80887 + 2.76731i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(5.25162 + 16.1628i) q^{82} +(17.0554 - 5.54164i) q^{83} +(5.20426 - 16.0171i) q^{86} +(-4.63195 - 2.30265i) q^{88} +18.3671 q^{89} +(14.2442 + 4.62823i) q^{90} +(13.7811 - 4.47775i) q^{94} +(7.70534 + 10.6055i) q^{96} +15.2047i q^{98} +(-1.65367 - 9.81149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more