LMFDB - Embedded newform 429.2.y.a.194.5

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			194.5
Character	$\chi$	$=$	429.194
Dual form			429.2.y.a.272.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.111034 - 0.152825i) q^{2} +(0.535233 - 1.64728i) q^{3} +(0.607007 + 1.86818i) q^{4} +(2.72753 - 1.98167i) q^{5} +(-0.192316 - 0.264700i) q^{6} +(0.712214 + 0.231412i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(0.111034 - 0.152825i) q^{2} +(0.535233 - 1.64728i) q^{3} +(0.607007 + 1.86818i) q^{4} +(2.72753 - 1.98167i) q^{5} +(-0.192316 - 0.264700i) q^{6} +(0.712214 + 0.231412i) q^{8} +(-2.42705 - 1.76336i) q^{9} -0.636866i q^{10} +(2.96989 - 1.47640i) q^{11} +3.40230 q^{12} +(-2.11929 + 2.91695i) q^{13} +(-1.80449 - 5.55366i) q^{15} +(-3.06389 + 2.22604i) q^{16} +(-0.538968 + 0.175121i) q^{18} +(5.35774 + 3.89263i) q^{20} +(0.104127 - 0.617802i) q^{22} +(0.762401 - 1.04935i) q^{24} +(1.96734 - 6.05486i) q^{25} +(0.210470 + 0.647759i) q^{26} +(-4.20378 + 3.05422i) q^{27} +(-1.04910 - 0.340872i) q^{30} +2.21313i q^{32} +(-0.842460 - 5.68245i) q^{33} +(1.82102 - 5.60453i) q^{36} +(3.67072 + 5.05231i) q^{39} +(2.40117 - 0.780187i) q^{40} +(-9.64207 - 3.13290i) q^{41} +7.66385i q^{43} +(4.56092 + 4.65209i) q^{44} -10.1143 q^{45} +(4.20646 - 12.9461i) q^{47} +(2.02702 + 6.23852i) q^{48} +(5.66312 - 4.11450i) q^{49} +(-0.706890 - 0.972951i) q^{50} +(-6.73580 - 2.18860i) q^{52} +0.981562i q^{54} +(5.17473 - 9.91227i) q^{55} +(2.67163 + 8.22243i) q^{59} +(9.27988 - 6.74222i) q^{60} +(1.35819 + 1.86938i) q^{61} +(-5.78955 - 4.20635i) q^{64} +12.1558i q^{65} +(-0.961960 - 0.502195i) q^{66} +(-13.0395 + 9.47373i) q^{71} +(-1.32052 - 1.81754i) q^{72} +(-8.92105 - 6.48152i) q^{75} +1.17969 q^{78} +(-10.4486 + 14.3813i) q^{79} +(-3.94557 + 12.1432i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-1.54938 + 1.12569i) q^{82} +(9.43908 + 12.9918i) q^{83} +(1.17122 + 0.850945i) q^{86} +(2.45685 - 0.364244i) q^{88} -4.31872 q^{89} +(-1.12302 + 1.54571i) q^{90} +(-1.51143 - 2.08031i) q^{94} +(3.64565 + 1.18454i) q^{96} -1.32231i q^{98} +(-9.81149 - 1.65367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	0.111034	−	0.152825i	0.0785126	−	0.108063i	−0.767954	−	0.640505i	$-0.778725\pi$
$2$	0.111034	−	0.152825i	0.0785126	−	0.108063i	0.846467	+	0.532441i	$0.178725\pi$
$3$	0.535233	−	1.64728i	0.309017	−	0.951057i
$3$	0.535233	−	1.64728i	0.309017	−	0.951057i
$4$	0.607007	+	1.86818i	0.303504	+	0.934088i
$5$	2.72753	−	1.98167i	1.21979	−	0.886229i	0.223708	−	0.974656i	$-0.428184\pi$
$5$	2.72753	−	1.98167i	1.21979	−	0.886229i	0.996083	+	0.0884268i	$0.0281839\pi$
$6$	−0.192316	−	0.264700i	−0.0785126	−	0.108063i
$7$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$7$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$8$	0.712214	+	0.231412i	0.251806	+	0.0818166i
$9$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$10$		−	0.636866i		−	0.201395i
$11$	2.96989	−	1.47640i	0.895455	−	0.445152i
$11$	2.96989	−	1.47640i	0.895455	−	0.445152i
$12$	3.40230			0.982158
$13$	−2.11929	+	2.91695i	−0.587785	+	0.809017i
$13$	−2.11929	+	2.91695i	−0.587785	+	0.809017i
$14$		0			0
$15$	−1.80449	−	5.55366i	−0.465918	−	1.43395i
$16$	−3.06389	+	2.22604i	−0.765971	+	0.556511i
$17$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$17$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$18$	−0.538968	+	0.175121i	−0.127036	+	0.0412765i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	5.35774	+	3.89263i	1.19803	+	0.870417i
$21$		0			0
$22$	0.104127	−	0.617802i	0.0222000	−	0.131716i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	0.762401	−	1.04935i	0.155624	−	0.214199i
$25$	1.96734	−	6.05486i	0.393469	−	1.21097i
$26$	0.210470	+	0.647759i	0.0412765	+	0.127036i
$27$	−4.20378	+	3.05422i	−0.809017	+	0.587785i
$28$		0			0
$29$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$29$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$30$	−1.04910	−	0.340872i	−0.191538	−	0.0622344i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$			2.21313i			0.391231i
$33$	−0.842460	−	5.68245i	−0.146653	−	0.989188i
$34$		0			0
$35$		0			0
$36$	1.82102	−	5.60453i	0.303504	−	0.934088i
$37$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$37$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$38$		0			0
$39$	3.67072	+	5.05231i	0.587785	+	0.809017i
$40$	2.40117	−	0.780187i	0.379658	−	0.123358i
$41$	−9.64207	−	3.13290i	−1.50584	−	0.489277i	−0.564124	−	0.825690i	$-0.690786\pi$
$41$	−9.64207	−	3.13290i	−1.50584	−	0.489277i	−0.941714	+	0.336413i	$0.890786\pi$
$42$		0			0
$43$			7.66385i			1.16873i	0.811492	+	0.584363i	$0.198656\pi$
$43$			7.66385i			1.16873i	−0.811492	+	0.584363i	$0.801344\pi$
$44$	4.56092	+	4.65209i	0.687585	+	0.701329i
$45$	−10.1143			−1.50774
$46$		0			0
$47$	4.20646	−	12.9461i	0.613575	−	1.88839i	0.192751	−	0.981248i	$-0.438259\pi$
$47$	4.20646	−	12.9461i	0.613575	−	1.88839i	0.420824	−	0.907142i	$-0.361741\pi$
$48$	2.02702	+	6.23852i	0.292575	+	0.900453i
$49$	5.66312	−	4.11450i	0.809017	−	0.587785i
$50$	−0.706890	−	0.972951i	−0.0999694	−	0.137596i
$51$		0			0
$52$	−6.73580	−	2.18860i	−0.934088	−	0.303504i
$53$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$53$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$54$			0.981562i			0.133574i
$55$	5.17473	−	9.91227i	0.697761	−	1.33657i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.67163	+	8.22243i	0.347817	+	1.07047i	0.960059	+	0.279799i	$0.0902678\pi$
$59$	2.67163	+	8.22243i	0.347817	+	1.07047i	−0.612242	+	0.790670i	$0.709732\pi$
$60$	9.27988	−	6.74222i	1.19803	−	0.870417i
$61$	1.35819	+	1.86938i	0.173898	+	0.239350i	0.887066	−	0.461644i	$-0.152740\pi$
$61$	1.35819	+	1.86938i	0.173898	+	0.239350i	−0.713167	+	0.700994i	$0.752740\pi$
$62$		0			0
$63$		0			0
$64$	−5.78955	−	4.20635i	−0.723694	−	0.525794i
$65$			12.1558i			1.50774i
$66$	−0.961960	−	0.502195i	−0.118409	−	0.0618159i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.0395	+	9.47373i	−1.54750	+	1.12433i	−0.602097	+	0.798423i	$0.705668\pi$
$71$	−13.0395	+	9.47373i	−1.54750	+	1.12433i	−0.945403	+	0.325902i	$0.894332\pi$
$72$	−1.32052	−	1.81754i	−0.155624	−	0.214199i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$		0			0
$75$	−8.92105	−	6.48152i	−1.03011	−	0.748422i
$76$		0			0
$77$		0			0
$78$	1.17969			0.133574
$79$	−10.4486	+	14.3813i	−1.17556	+	1.61802i	−0.584613	+	0.811312i	$0.698754\pi$
$79$	−10.4486	+	14.3813i	−1.17556	+	1.61802i	−0.590949	+	0.806709i	$0.701246\pi$
$80$	−3.94557	+	12.1432i	−0.441128	+	1.35765i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	−1.54938	+	1.12569i	−0.171100	+	0.124312i
$83$	9.43908	+	12.9918i	1.03607	+	1.42603i	0.900288	+	0.435294i	$0.143356\pi$
$83$	9.43908	+	12.9918i	1.03607	+	1.42603i	0.135785	+	0.990738i	$0.456644\pi$
$84$		0			0
$85$		0			0
$86$	1.17122	+	0.850945i	0.126296	+	0.0917597i
$87$		0			0
$88$	2.45685	−	0.364244i	0.261901	−	0.0388286i
$89$	−4.31872			−0.457783			−0.228892	−	0.973452i	$-0.573510\pi$
$89$	−4.31872			−0.457783			−0.228892	+	0.973452i	$0.573510\pi$
$90$	−1.12302	+	1.54571i	−0.118377	+	0.162932i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−1.51143	−	2.08031i	−0.155892	−	0.214567i
$95$		0			0
$96$	3.64565	+	1.18454i	0.372082	+	0.120897i
$97$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$97$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$98$		−	1.32231i		−	0.133574i
$99$	−9.81149	−	1.65367i	−0.986092	−	0.166200i
$100$	12.5057			1.25057
$101$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$101$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$102$		0			0
$103$	−2.14285	−	6.59503i	−0.211142	−	0.649827i	−0.999405	−	0.0344892i	$-0.989020\pi$
$103$	−2.14285	−	6.59503i	−0.211142	−	0.649827i	0.788263	−	0.615338i	$-0.210980\pi$
$104$	−2.18441	+	1.58706i	−0.214199	+	0.155624i
$105$		0			0
$106$		0			0
$107$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$107$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$108$	−8.25754	−	5.99946i	−0.794583	−	0.577298i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−0.940270	−	1.89142i	−0.0896512	−	0.180340i
$111$		0			0
$112$		0			0
$113$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$113$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	10.2872	−	3.34253i	0.951057	−	0.309017i
$118$	1.55323	+	0.504675i	0.142986	+	0.0464591i
$119$		0			0
$120$		−	4.37298i		−	0.399196i
$121$	6.64048	−	8.76949i	0.603680	−	0.797227i
$122$	0.436493			0.0395182
$123$	−10.3215	+	14.2063i	−0.930659	+	1.28094i
$124$		0			0
$125$	−1.42361	−	4.38141i	−0.127331	−	0.391885i
$126$		0			0
$127$	12.3020	+	16.9323i	1.09163	+	1.50250i	0.846035	+	0.533127i	$0.178983\pi$
$127$	12.3020	+	16.9323i	1.09163	+	1.50250i	0.245595	+	0.969373i	$0.421017\pi$
$128$	−5.49530	+	1.78553i	−0.485721	+	0.157820i
$129$	12.6245	+	4.10194i	1.11152	+	0.361156i
$130$	1.85771	+	1.34970i	0.162932	+	0.118377i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	10.1044	−	5.02315i	0.879479	−	0.437209i
$133$		0			0
$134$		0			0
$135$	−5.41348	+	16.6610i	−0.465918	+	1.43395i
$136$		0			0
$137$	5.08564	−	3.69493i	0.434495	−	0.315679i	−0.348948	−	0.937142i	$-0.613461\pi$
$137$	5.08564	−	3.69493i	0.434495	−	0.315679i	0.783444	+	0.621463i	$0.213461\pi$
$138$		0			0
$139$	−20.7904	+	6.75521i	−1.76342	+	0.572970i	−0.997545	−	0.0700216i	$-0.977693\pi$
$139$	−20.7904	+	6.75521i	−1.76342	+	0.572970i	−0.765874	+	0.642991i	$0.777693\pi$
$140$		0			0
$141$	−19.0745	−	13.8584i	−1.60636	−	1.16709i
$142$			3.04466i			0.255502i
$143$	−1.98747	+	11.7919i	−0.166200	+	0.986092i
$144$	11.3615			0.946793
$145$		0			0
$146$		0			0
$147$	−3.74663	−	11.5309i	−0.309017	−	0.951057i
$148$		0			0
$149$	−13.7000	−	18.8564i	−1.12235	−	1.54478i	−0.801846	−	0.597531i	$-0.796148\pi$
$149$	−13.7000	−	18.8564i	−1.12235	−	1.54478i	−0.320502	−	0.947248i	$-0.603852\pi$
$150$	−1.98107	+	0.643689i	−0.161754	+	0.0525570i
$151$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$151$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−7.21045	+	9.92433i	−0.577298	+	0.794583i
$157$	4.03726	−	12.4254i	0.322208	−	0.991655i	−0.650477	−	0.759526i	$-0.725431\pi$
$157$	4.03726	−	12.4254i	0.322208	−	0.991655i	0.972685	−	0.232129i	$-0.0745691\pi$
$158$	1.03767	+	3.19361i	0.0825524	+	0.254070i
$159$		0			0
$160$	4.38570	+	6.03640i	0.346720	+	0.477219i
$161$		0			0
$162$	1.61691	+	0.525364i	0.127036	+	0.0412765i
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$		−	19.9148i		−	1.55508i
$165$	−13.5586	−	13.8296i	−1.05553	−	1.07663i
$166$	3.03352			0.235447
$167$	15.0245	−	20.6794i	1.16263	−	1.60022i	0.461602	−	0.887087i	$-0.347275\pi$
$167$	15.0245	−	20.6794i	1.16263	−	1.60022i	0.701027	−	0.713134i	$-0.252725\pi$
$168$		0			0
$169$	−4.01722	−	12.3637i	−0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$	−14.3174	+	4.65201i	−1.09169	+	0.354712i
$173$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$173$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$174$		0			0
$175$		0			0
$176$	−5.81287	+	11.1346i	−0.438161	+	0.839304i
$177$	14.9746			1.12556
$178$	−0.479523	+	0.660007i	−0.0359418	+	0.0494696i
$179$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$179$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$180$	−6.13942	−	18.8952i	−0.457606	−	1.40837i
$181$	−16.7201	+	12.1479i	−1.24280	+	0.902945i	−0.997781	−	0.0665740i	$-0.978793\pi$
$181$	−16.7201	+	12.1479i	−1.24280	+	0.902945i	−0.245016	+	0.969519i	$0.578793\pi$
$182$		0			0
$183$	3.80634	−	1.23676i	0.281373	−	0.0914236i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	26.7390			1.95014
$189$		0			0
$190$		0			0
$191$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$191$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$192$	−10.0278	+	7.28562i	−0.723694	+	0.525794i
$193$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$193$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$194$		0			0
$195$	20.0240	+	6.50620i	1.43395	+	0.465918i
$196$	11.1242	+	8.08217i	0.794583	+	0.577298i
$197$		−	27.9002i		−	1.98781i	−0.110256	−	0.993903i	$-0.535167\pi$
$197$		−	27.9002i		−	1.98781i	0.110256	−	0.993903i	$-0.464833\pi$
$198$	−1.34213	+	1.31582i	−0.0953808	+	0.0935116i
$199$	28.0948			1.99159			0.995793	−	0.0916309i	$-0.0292080\pi$
$199$	28.0948			1.99159			0.995793	+	0.0916309i	$0.0292080\pi$
$200$	2.80234	−	3.85709i	0.198155	−	0.272737i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−32.5074	+	10.5623i	−2.27042	+	0.737704i
$206$	−1.24581	−	0.404789i	−0.0867998	−	0.0282030i
$207$		0			0
$208$		−	13.6548i		−	0.946793i
$209$		0			0
$210$		0			0
$211$	3.30268	−	4.54575i	0.227366	−	0.312942i	−0.680058	−	0.733158i	$-0.738046\pi$
$211$	3.30268	−	4.54575i	0.227366	−	0.312942i	0.907424	+	0.420216i	$0.138046\pi$
$212$		0			0
$213$	8.62671	+	26.5503i	0.591093	+	1.81920i
$214$		0			0
$215$	15.1872	+	20.9034i	1.03576	+	1.42560i
$216$	−3.70077	+	1.20245i	−0.251806	+	0.0818166i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	21.6590	+	3.65050i	1.46025	+	0.246116i
$221$		0			0
$222$		0			0
$223$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$223$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$224$		0			0
$225$	−15.4517	+	11.2263i	−1.03011	+	0.748422i
$226$		0			0
$227$	25.9123	−	8.41942i	1.71986	−	0.558817i	0.727936	−	0.685645i	$-0.240480\pi$
$227$	25.9123	−	8.41942i	1.71986	−	0.558817i	0.991925	+	0.126828i	$0.0404798\pi$
$228$		0			0
$229$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$229$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$233$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$234$	0.631409	−	1.94328i	0.0412765	−	0.127036i
$235$	−14.1817	−	43.6469i	−0.925114	−	2.84721i
$236$	−13.7392	+	9.98215i	−0.894349	+	0.649782i
$237$	18.0975	+	24.9091i	1.17556	+	1.61802i
$238$		0			0
$239$	−7.84899	−	2.55029i	−0.507709	−	0.164965i	0.0439509	−	0.999034i	$-0.486005\pi$
$239$	−7.84899	−	2.55029i	−0.507709	−	0.164965i	−0.551660	+	0.834069i	$0.686005\pi$
$240$	17.8915	+	12.9989i	1.15489	+	0.839075i
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−0.602878	−	1.98854i	−0.0387545	−	0.127828i
$243$	15.5885			1.00000
$244$	−2.66791	+	3.67206i	−0.170795	+	0.235080i
$245$	7.29278	−	22.4449i	0.465918	−	1.43395i
$246$	1.02504	+	3.15476i	0.0653545	+	0.201140i
$247$		0			0
$248$		0			0
$249$	26.4532	−	8.59516i	1.67640	−	0.544696i
$250$	−0.827656	−	0.268922i	−0.0523455	−	0.0170081i
$251$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$251$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$252$		0			0
$253$		0			0
$254$	3.95361			0.248072
$255$		0			0
$256$	4.08553	−	12.5740i	0.255346	−	0.785873i
$257$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$257$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$258$	2.02862	−	1.47388i	0.126296	−	0.0917597i
$259$		0			0
$260$	−22.7092	+	7.37867i	−1.40837	+	0.457606i
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	0.714978	−	4.24208i	0.0440038	−	0.261082i
$265$		0			0
$266$		0			0
$267$	−2.31152	+	7.11413i	−0.141463	+	0.435378i
$268$		0			0
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$	1.94513	+	2.67724i	0.118377	+	0.162932i
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$		−	1.18747i		−	0.0717378i
$275$	−3.09661	−	20.8868i	−0.186732	−	1.25952i
$276$		0			0
$277$	14.6829	−	20.2092i	0.882208	−	1.21426i	−0.0935962	−	0.995610i	$-0.529836\pi$
$277$	14.6829	−	20.2092i	0.882208	−	1.21426i	0.975804	−	0.218645i	$-0.0701637\pi$
$278$	−1.27607	+	3.92734i	−0.0765336	+	0.235546i
$279$		0			0
$280$		0			0
$281$	−17.1686	−	23.6305i	−1.02419	−	1.40968i	−0.909223	−	0.416310i	$-0.863323\pi$
$281$	−17.1686	−	23.6305i	−1.02419	−	1.40968i	−0.114969	−	0.993369i	$-0.536677\pi$
$282$	−4.23582	+	1.37630i	−0.252239	+	0.0819575i
$283$	12.5110	+	4.06508i	0.743704	+	0.241644i	0.656270	−	0.754526i	$-0.272133\pi$
$283$	12.5110	+	4.06508i	0.743704	+	0.241644i	0.0874340	+	0.996170i	$0.472133\pi$
$284$	−25.6136	−	18.6094i	−1.51989	−	1.10427i
$285$		0			0
$286$	1.58142	+	1.61304i	0.0935116	+	0.0953808i
$287$		0			0
$288$	3.90254	−	5.37139i	0.229960	−	0.316512i
$289$	−5.25329	+	16.1680i	−0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	18.9846	−	6.16848i	1.10909	−	0.360366i	0.303498	−	0.952832i	$-0.401846\pi$
$293$	18.9846	−	6.16848i	1.10909	−	0.360366i	0.805596	+	0.592466i	$0.201846\pi$
$294$	−2.17821	−	0.707745i	−0.127036	−	0.0412765i
$295$	23.5811	+	17.1327i	1.37294	+	0.997503i
$296$		0			0
$297$	−7.97549	+	15.2772i	−0.462785	+	0.886471i
$298$	−4.40289			−0.255052
$299$		0			0
$300$	6.69348	−	20.6004i	0.386448	−	1.18937i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.40901	+	2.40733i	0.424238	+	0.137843i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	−12.0108			−0.683269
$310$		0			0
$311$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$311$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$312$	1.44517	+	4.44777i	0.0818166	+	0.251806i
$313$	−3.11188	+	2.26091i	−0.175894	+	0.127794i	−0.672249	−	0.740325i	$-0.734671\pi$
$313$	−3.11188	+	2.26091i	−0.175894	+	0.127794i	0.496355	+	0.868120i	$0.334671\pi$
$314$	−1.45064	−	1.99663i	−0.0818641	−	0.112676i
$315$		0			0
$316$	−33.2092	−	10.7903i	−1.86816	−	0.607002i
$317$	−20.7456	−	15.0725i	−1.16519	−	0.846558i	−0.174762	−	0.984611i	$-0.555916\pi$
$317$	−20.7456	−	15.0725i	−1.16519	−	0.846558i	−0.990425	+	0.138053i	$0.955916\pi$
$318$		0			0
$319$		0			0
$320$	−24.1268			−1.34873
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−14.3025	+	10.3914i	−0.794583	+	0.577298i
$325$	13.4924	+	18.5706i	0.748422	+	1.03011i
$326$		0			0
$327$		0			0
$328$	−6.14222	−	4.46259i	−0.339148	−	0.246405i
$329$		0			0
$330$	−3.61896	+	0.536534i	−0.199217	+	0.0295352i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−18.5413	+	25.5199i	−1.01759	+	1.40059i
$333$		0			0
$334$	−1.49210	−	4.59222i	−0.0816442	−	0.251275i
$335$		0			0
$336$		0			0
$337$	−31.6148	+	10.2723i	−1.72217	+	0.559567i	−0.992282	−	0.123999i	$-0.960428\pi$
$337$	−31.6148	+	10.2723i	−1.72217	+	0.559567i	−0.729888	+	0.683567i	$0.760428\pi$
$338$	−2.33553	−	0.758860i	−0.127036	−	0.0412765i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−1.77351	+	5.45830i	−0.0956212	+	0.294292i
$345$		0			0
$346$		0			0
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$		0			0
$349$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$349$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$350$		0			0
$351$		−	18.7350i		−	1.00000i
$352$	3.26747	+	6.57276i	0.174157	+	0.350329i
$353$	−13.9640			−0.743228			−0.371614	−	0.928387i	$-0.621196\pi$
$353$	−13.9640			−0.743228			−0.371614	+	0.928387i	$0.621196\pi$
$354$	1.66268	−	2.28848i	0.0883705	−	0.121632i
$355$	−16.7918	+	51.6798i	−0.891216	+	2.74288i
$356$	−2.62149	−	8.06812i	−0.138939	−	0.427610i
$357$		0			0
$358$		0			0
$359$	−35.9847	+	11.6921i	−1.89920	+	0.617087i	−0.932504	+	0.361159i	$0.882381\pi$
$359$	−35.9847	+	11.6921i	−1.89920	+	0.617087i	−0.966696	+	0.255928i	$0.917619\pi$
$360$	−7.20351	−	2.34056i	−0.379658	−	0.123358i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$			3.90407i			0.205193i
$363$	−10.8916	−	15.6324i	−0.571660	−	0.820491i
$364$		0			0
$365$		0			0
$366$	0.233625	−	0.719025i	0.0122118	−	0.0375840i
$367$	−8.80588	−	27.1017i	−0.459663	−	1.41470i	−0.865572	−	0.500785i	$-0.833045\pi$
$367$	−8.80588	−	27.1017i	−0.459663	−	1.41470i	0.405908	−	0.913914i	$-0.366955\pi$
$368$		0			0
$369$	17.8774	+	24.6061i	0.930659	+	1.28094i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		−	2.03646i		−	0.105444i	−0.998609	−	0.0527219i	$-0.983210\pi$
$373$		−	2.03646i		−	0.105444i	0.998609	−	0.0527219i	$-0.0167897\pi$
$374$		0			0
$375$	−7.97936			−0.412053
$376$	5.99180	−	8.24700i	0.309003	−	0.425307i
$377$		0			0
$378$		0			0
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$		0			0
$381$	34.4767	−	11.2022i	1.76629	−	0.573904i
$382$		0			0
$383$	31.1545	+	22.6351i	1.59192	+	1.15660i	0.901133	+	0.433543i	$0.142737\pi$
$383$	31.1545	+	22.6351i	1.59192	+	1.15660i	0.690789	+	0.723056i	$0.257263\pi$
$384$			10.0080i			0.510717i
$385$		0			0
$386$		0			0
$387$	13.5141	−	18.6005i	0.686960	−	0.945519i
$388$		0			0
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$	3.21765	−	2.33776i	0.162932	−	0.118377i
$391$		0			0
$392$	4.98550	−	1.61989i	0.251806	−	0.0818166i
$393$		0			0
$394$	−4.26384	−	3.09786i	−0.214809	−	0.156068i
$395$			59.9312i			3.01546i
$396$	−2.86630	−	19.3334i	−0.144037	−	0.971539i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	3.11946	−	4.29357i	0.156365	−	0.215217i
$399$		0			0
$400$	7.45066	+	22.9308i	0.372533	+	1.14654i
$401$	30.1940	−	21.9372i	1.50782	−	1.09549i	0.540683	−	0.841226i	$-0.318166\pi$
$401$	30.1940	−	21.9372i	1.50782	−	1.09549i	0.967134	−	0.254267i	$-0.0818342\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	24.5478	+	17.8350i	1.21979	+	0.886229i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$409$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$410$	−1.99524	+	6.14071i	−0.0985378	+	0.303268i
$411$	−3.36458	−	10.3551i	−0.165962	−	0.510780i
$412$	11.0199	−	8.00645i	0.542913	−	0.394450i
$413$		0			0
$414$		0			0
$415$	51.4908	+	16.7304i	2.52758	+	0.821262i
$416$	−6.45561	−	4.69027i	−0.316512	−	0.229960i
$417$			37.8632i			1.85417i
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$421$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$422$	−0.327994	−	1.00946i	−0.0159665	−	0.0491398i
$423$	−33.0380	+	24.0035i	−1.60636	+	1.16709i
$424$		0			0
$425$		0			0
$426$	5.01539	+	1.62960i	0.242997	+	0.0789544i
$427$		0			0
$428$		0			0
$429$	18.3609	+	9.58535i	0.886471	+	0.462785i
$430$	4.88085			0.235375
$431$	−15.2454	+	20.9835i	−0.734346	+	1.01074i	0.264578	+	0.964364i	$0.414767\pi$
$431$	−15.2454	+	20.9835i	−0.734346	+	1.01074i	−0.998924	+	0.0463767i	$0.985233\pi$
$432$	6.08106	−	18.7156i	0.292575	−	0.900453i
$433$	−8.61170	−	26.5041i	−0.413852	−	1.27370i	−0.913274	−	0.407346i	$-0.866454\pi$
$433$	−8.61170	−	26.5041i	−0.413852	−	1.27370i	0.499422	−	0.866359i	$-0.333546\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		−	34.1826i		−	1.63145i	−0.578441	−	0.815724i	$-0.696339\pi$
$439$		−	34.1826i		−	1.63145i	0.578441	−	0.815724i	$-0.303661\pi$
$440$	5.97934	−	5.86216i	0.285054	−	0.279467i
$441$	−21.0000			−1.00000
$442$		0			0
$443$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$443$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$444$		0			0
$445$	−11.7794	+	8.55827i	−0.558399	+	0.405701i
$446$		0			0
$447$	−38.3945	+	12.4751i	−1.81600	+	0.590053i
$448$		0			0
$449$	31.9359	+	23.2028i	1.50715	+	1.09501i	0.967422	+	0.253168i	$0.0814726\pi$
$449$	31.9359	+	23.2028i	1.50715	+	1.09501i	0.539727	+	0.841840i	$0.318527\pi$
$450$			3.60790i			0.170078i
$451$	−33.2613	+	4.93120i	−1.56621	+	0.232201i
$452$		0			0
$453$		0			0
$454$	1.59044	−	4.89488i	0.0746432	−	0.229728i
$455$		0			0
$456$		0			0
$457$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$457$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	24.9817i		−	1.16352i	−0.813362	−	0.581758i	$-0.802365\pi$
$461$		−	24.9817i		−	1.16352i	0.813362	−	0.581758i	$-0.197635\pi$
$462$		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		0.809017	−	0.587785i	$-0.200000\pi$
$467$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$468$	12.4889	+	17.1894i	0.577298	+	0.794583i
$469$		0			0
$470$	−8.24497	−	2.67895i	−0.380312	−	0.123571i
$471$	−18.3072	−	13.3010i	−0.843552	−	0.612876i
$472$			6.47438i			0.298007i
$473$	11.3149	+	22.7608i	0.520260	+	1.04654i
$474$	5.81616			0.267145
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.26125	+	0.916352i	−0.0576882	+	0.0419129i
$479$	9.72656	+	13.3875i	0.444418	+	0.611689i	0.971187	−	0.238320i	$-0.0765966\pi$
$479$	9.72656	+	13.3875i	0.444418	+	0.611689i	−0.526769	+	0.850009i	$0.676597\pi$
$480$	12.2910	−	3.99359i	0.561005	−	0.182282i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	20.4138	+	7.08244i	0.927899	+	0.321929i
$485$		0			0
$486$	1.73084	−	2.38230i	0.0785126	−	0.108063i
$487$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$487$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$488$	0.534721	+	1.64570i	0.0242057	+	0.0744975i
$489$		0			0
$490$	−2.62038	−	3.60665i	−0.118377	−	0.162932i
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$	−32.8052	−	10.6590i	−1.47897	−	0.480547i
$493$		0			0
$494$		0			0
$495$	−30.0382	+	14.9327i	−1.35012	+	0.671174i
$496$		0			0
$497$		0			0
$498$	1.62364	−	4.99705i	0.0727570	−	0.223923i
$499$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$499$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$500$	7.32111	−	5.31909i	0.327410	−	0.237877i
$501$	−26.0232	−	35.8178i	−1.16263	−	1.60022i
$502$		0			0
$503$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$503$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−22.5167			−1.00000
$508$	−24.1651	+	33.2604i	−1.07215	+	1.47569i
$509$	−0.706123	+	2.17322i	−0.0312983	+	0.0963264i	−0.965485	−	0.260457i	$-0.916127\pi$
$509$	−0.706123	+	2.17322i	−0.0312983	+	0.0963264i	0.934187	+	0.356784i	$0.116127\pi$
$510$		0			0
$511$		0			0
$512$	−8.26055	−	11.3697i	−0.365068	−	0.502473i
$513$		0			0
$514$		0			0
$515$	−18.9139	−	13.7417i	−0.833445	−	0.605533i
$516$			26.0747i			1.14787i
$517$	−6.62099	−	44.6590i	−0.291191	−	1.96410i
$518$		0			0
$519$		0			0
$520$	−2.81301	+	8.65754i	−0.123358	+	0.379658i
$521$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$521$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$522$		0			0
$523$	7.34144	+	10.1046i	0.321019	+	0.441844i	0.938778	−	0.344523i	$-0.111959\pi$
$523$	7.34144	+	10.1046i	0.321019	+	0.441844i	−0.617759	+	0.786367i	$0.711959\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	15.2306	+	15.5350i	0.662826	+	0.676075i
$529$	23.0000			1.00000
$530$		0			0
$531$	8.01489	−	24.6673i	0.347817	−	1.07047i
$532$		0			0
$533$	29.5729	−	21.4859i	1.28094	−	0.930659i
$534$	0.830558	+	1.14316i	0.0359418	+	0.0494696i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.7442	−	20.5806i	0.462785	−	0.886471i
$540$	−34.4117			−1.48084
$541$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$541$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$542$		0			0
$543$	11.0618	+	34.0447i	0.474706	+	1.46100i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.1777	+	4.28170i	0.563438	+	0.183072i	0.576868	−	0.816838i	$-0.304275\pi$
$547$	13.1777	+	4.28170i	0.563438	+	0.183072i	−0.0134293	+	0.999910i	$0.504275\pi$
$548$	9.98980	+	7.25802i	0.426743	+	0.310047i
$549$		−	6.93206i		−	0.295853i
$550$	−3.53585	−	1.84590i	−0.150769	−	0.0787096i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−1.45818	−	4.48781i	−0.0619520	−	0.190669i
$555$		0			0
$556$	−25.2398	−	34.7397i	−1.07041	−	1.47329i
$557$	−29.0241	+	9.43049i	−1.22979	+	0.399582i	−0.850638	−	0.525752i	$-0.823784\pi$
$557$	−29.0241	+	9.43049i	−1.22979	+	0.399582i	−0.379151	+	0.925335i	$0.623784\pi$
$558$		0			0
$559$	−22.3551	−	16.2419i	−0.945519	−	0.686960i
$560$		0			0
$561$		0			0
$562$	−5.51762			−0.232747
$563$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$563$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$564$	14.3116	−	44.0466i	0.602628	−	1.85470i
$565$		0			0
$566$	2.01039	−	1.46063i	0.0845030	−	0.0613950i
$567$		0			0
$568$	−11.4792	+	3.72983i	−0.481658	+	0.156500i
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$		−	28.8444i		−	1.20710i	−0.797325	−	0.603550i	$-0.793752\pi$
$571$		−	28.8444i		−	1.20710i	0.797325	−	0.603550i	$-0.206248\pi$
$572$	−23.2358	+	3.44486i	−0.971539	+	0.144037i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	6.63423	+	20.4181i	0.276426	+	0.850753i
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	1.88757	+	2.59802i	0.0785126	+	0.108063i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	21.4350	−	29.5028i	0.886229	−	1.21979i
$586$	1.16524	−	3.58623i	0.0481354	−	0.148146i
$587$	−7.64975	−	23.5435i	−0.315739	−	0.971745i	−0.975449	−	0.220225i	$-0.929321\pi$
$587$	−7.64975	−	23.5435i	−0.315739	−	0.971745i	0.659710	−	0.751520i	$-0.270679\pi$
$588$	19.2676	−	13.9987i	0.794583	−	0.577298i
$589$		0			0
$590$	5.23659	−	1.70147i	0.215587	−	0.0700484i
$591$	−45.9594	−	14.9331i	−1.89052	−	0.614266i
$592$		0			0
$593$			48.7024i			1.99997i	0.00582080	+	0.999983i	$0.498147\pi$
$593$			48.7024i			1.99997i	−0.00582080	+	0.999983i	$0.501853\pi$
$594$	1.44918	+	2.91513i	0.0594605	+	0.119609i
$595$		0			0
$596$	26.9111	−	37.0400i	1.10232	−	1.51722i
$597$	15.0373	−	46.2799i	0.615434	−	1.89411i
$598$		0			0
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$	−4.85379	−	6.68067i	−0.198155	−	0.272737i
$601$	41.7470	−	13.5644i	1.70290	−	0.553305i	0.713772	−	0.700378i	$-0.246985\pi$
$601$	41.7470	−	13.5644i	1.70290	−	0.553305i	0.989126	+	0.147074i	$0.0469854\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.733904	−	37.0783i	0.0298375	−	1.50745i
$606$		0			0
$607$	−11.0827	+	15.2540i	−0.449831	+	0.619140i	−0.972361	−	0.233481i	$-0.924988\pi$
$607$	−11.0827	+	15.2540i	−0.449831	+	0.619140i	0.522530	+	0.852621i	$0.324988\pi$
$608$		0			0
$609$		0			0
$610$	1.19055	−	0.864984i	0.0482039	−	0.0350222i
$611$	28.8486	+	39.7067i	1.16709	+	1.60636i
$612$		0			0
$613$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$613$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$614$		0			0
$615$			59.2021i			2.38726i
$616$		0			0
$617$	−40.8685			−1.64530			−0.822652	−	0.568545i	$-0.807506\pi$
$617$	−40.8685			−1.64530			−0.822652	+	0.568545i	$0.807506\pi$
$618$	−1.33360	+	1.83554i	−0.0536452	+	0.0738363i
$619$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$619$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−22.4933	−	7.30852i	−0.900453	−	0.292575i
$625$	13.1874	+	9.58121i	0.527496	+	0.383248i
$626$			0.726610i			0.0290412i
$627$		0			0
$628$	25.6635			1.02408
$629$		0			0
$630$		0			0
$631$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$631$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$632$	−10.7697	+	7.82461i	−0.428394	+	0.311246i
$633$	−5.72041	−	7.87347i	−0.227366	−	0.312942i
$634$	−4.60691	+	1.49688i	−0.182964	+	0.0594485i
$635$	67.1085	+	21.8049i	2.66312	+	0.865300i
$636$		0			0
$637$			25.2389i			1.00000i
$638$		0			0
$639$	48.3530			1.91282
$640$	−11.4503	+	15.7600i	−0.452612	+	0.622967i
$641$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$641$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$642$		0			0
$643$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$643$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$644$		0			0
$645$	42.5624	−	13.8294i	1.67589	−	0.544531i
$646$		0			0
$647$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$647$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$648$			6.73979i			0.264764i
$649$	20.0740	+	20.4753i	0.787975	+	0.803726i
$650$	4.33616			0.170078
$651$		0			0
$652$		0			0
$653$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$653$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$654$		0			0
$655$		0			0
$656$	36.5162	−	11.8648i	1.42572	−	0.463243i
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	17.6060	−	33.7245i	0.685312	−	1.31272i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	3.71618	+	11.4372i	0.144216	+	0.443851i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	47.7528	+	15.5158i	1.84761	+	0.600325i
$669$		0			0
$670$		0			0
$671$	6.79363	+	3.54664i	0.262265	+	0.136916i
$672$		0			0
$673$	28.5943	−	39.3566i	1.10223	−	1.51709i	0.269830	−	0.962908i	$-0.413032\pi$
$673$	28.5943	−	39.3566i	1.10223	−	1.51709i	0.832398	−	0.554179i	$-0.186968\pi$
$674$	−1.94045	+	5.97210i	−0.0747434	+	0.230037i
$675$	10.2226	+	31.4620i	0.393469	+	1.21097i
$676$	20.6591	−	15.0097i	0.794583	−	0.577298i
$677$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$677$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		−	47.1911i		−	1.80837i
$682$		0			0
$683$	38.1128			1.45835			0.729173	−	0.684330i	$-0.239905\pi$
$683$	38.1128			1.45835			0.729173	+	0.684330i	$0.239905\pi$
$684$		0			0
$685$	6.54912	−	20.1561i	0.250229	−	0.770125i
$686$		0			0
$687$		0			0
$688$	−17.0601	−	23.4811i	−0.650408	−	0.895210i
$689$		0			0
$690$		0			0
$691$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$691$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−43.3199	+	59.6248i	−1.64322	+	2.26170i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$701$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$702$	−2.86317	−	2.08021i	−0.108063	−	0.0785126i
$703$		0			0
$704$	−23.4046	−	3.94471i	−0.882093	−	0.148672i
$705$	−79.4891			−2.99373
$706$	−1.55047	+	2.13404i	−0.0583528	+	0.0803157i
$707$		0			0
$708$	9.08967	+	27.9751i	0.341611	+	1.05137i
$709$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$709$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$710$	6.03350	+	8.30440i	0.226433	+	0.311659i
$711$	50.7187	−	16.4795i	1.90210	−	0.618029i
$712$	−3.07585	−	0.999404i	−0.115272	−	0.0374543i
$713$		0			0
$714$		0			0
$715$	17.9469	+	36.1014i	0.671174	+	1.35012i
$716$		0			0
$717$	−8.40208	+	11.5645i	−0.313782	+	0.431883i
$718$	−2.20866	+	6.79757i	−0.0824266	+	0.253683i
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$	30.9889	−	22.5148i	1.15489	−	0.839075i
$721$		0			0
$722$	3.41347	−	1.10910i	0.127036	−	0.0412765i
$723$		0			0
$724$	−32.8436	−	23.8623i	−1.22062	−	0.886835i
$725$		0			0
$726$	−3.59835	−	0.0712235i	−0.133547	−	0.00264335i
$727$	−33.5606			−1.24469			−0.622347	−	0.782742i	$-0.713821\pi$
$727$	−33.5606			−1.24469			−0.622347	+	0.782742i	$0.713821\pi$
$728$		0			0
$729$	8.34346	−	25.6785i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$	4.62096	+	6.36020i	0.170795	+	0.235080i
$733$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$733$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$734$	−5.11956	−	1.66345i	−0.188966	−	0.0613989i
$735$	−33.0696	−	24.0265i	−1.21979	−	0.886229i
$736$		0			0
$737$		0			0
$738$	5.74541			0.211491
$739$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$739$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−27.5162	−	37.8728i	−1.00947	−	1.38942i	−0.919329	−	0.393489i	$-0.871268\pi$
$743$	−27.5162	−	37.8728i	−1.00947	−	1.38942i	−0.0901418	−	0.995929i	$-0.528732\pi$
$744$		0			0
$745$	−74.7344	−	24.2827i	−2.73806	−	0.889649i
$746$	−0.311221	−	0.226115i	−0.0113946	−	0.00827867i
$747$		−	48.1761i		−	1.76267i
$748$		0			0
$749$		0			0
$750$	−0.885978	+	1.21944i	−0.0323513	+	0.0445278i
$751$	−14.8318	+	45.6476i	−0.541221	+	1.66571i	0.188590	+	0.982056i	$0.439608\pi$
$751$	−14.8318	+	45.6476i	−0.541221	+	1.66571i	−0.729810	+	0.683650i	$0.760392\pi$
$752$	15.9306	+	49.0293i	0.580928	+	1.78791i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	44.3528	+	32.2242i	1.61203	+	1.17121i	0.856601	+	0.515979i	$0.172572\pi$
$757$	44.3528	+	32.2242i	1.61203	+	1.17121i	0.755429	+	0.655230i	$0.227428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	29.5148	−	40.6236i	1.06991	−	1.47261i	0.199744	−	0.979848i	$-0.435989\pi$
$761$	29.5148	−	40.6236i	1.06991	−	1.47261i	0.870167	−	0.492757i	$-0.164011\pi$
$762$	2.11611	−	6.51270i	0.0766584	−	0.235930i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	6.91840	−	2.24792i	0.249972	−	0.0812208i
$767$	−29.6464	−	9.63270i	−1.07047	−	0.347817i
$768$	−18.5261	−	13.4600i	−0.668504	−	0.485696i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−11.1709	+	34.3804i	−0.401789	+	1.23658i	0.521758	+	0.853093i	$0.325276\pi$
$773$	−11.1709	+	34.3804i	−0.401789	+	1.23658i	−0.923547	+	0.383485i	$0.874724\pi$
$774$	−1.34210	−	4.13057i	−0.0482409	−	0.148470i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			41.3577i			1.48084i
$781$	−24.7388	+	47.3874i	−0.885223	+	1.69566i
$782$		0			0
$783$		0			0
$784$	−8.19210	+	25.2127i	−0.292575	+	0.900453i
$785$	−13.6113	−	41.8912i	−0.485807	−	1.49516i
$786$		0			0
$787$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$787$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$788$	52.1225	−	16.9356i	1.85679	−	0.603306i
$789$		0			0
$790$	9.15896	+	6.65437i	0.325861	+	0.236752i
$791$		0			0
$792$	−6.60520	−	3.44827i	−0.234706	−	0.122529i
$793$	−8.33130			−0.295853
$794$		0			0
$795$		0			0
$796$	17.0537	+	52.4860i	0.604453	+	1.86032i
$797$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$797$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$798$		0			0
$799$		0			0
$800$	13.4002	+	4.35399i	0.473769	+	0.153937i
$801$	10.4817	+	7.61544i	0.370354	+	0.269078i
$802$		−	7.05016i		−	0.248950i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$809$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$810$	5.45126	−	1.77122i	0.191538	−	0.0622344i
$811$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$811$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−39.4645	−	54.3182i	−1.37816	−	1.89687i
$821$	−44.1628	+	14.3494i	−1.54129	+	0.500796i	−0.951733	−	0.306928i	$-0.900699\pi$
$821$	−44.1628	+	14.3494i	−1.54129	+	0.500796i	−0.589560	+	0.807724i	$0.700699\pi$
$822$	−1.95610	−	0.635575i	−0.0682267	−	0.0221682i
$823$	−30.7131	−	22.3144i	−1.07059	−	0.777831i	−0.0945738	−	0.995518i	$-0.530149\pi$
$823$	−30.7131	−	22.3144i	−1.07059	−	0.777831i	−0.976019	+	0.217687i	$0.930149\pi$
$824$		−	5.19295i		−	0.180905i
$825$	−36.0638	−	6.07836i	−1.25558	−	0.211621i
$826$		0			0
$827$	14.4762	−	19.9247i	0.503386	−	0.692851i	−0.479401	−	0.877596i	$-0.659146\pi$
$827$	14.4762	−	19.9247i	0.503386	−	0.692851i	0.982786	+	0.184745i	$0.0591460\pi$
$828$		0			0
$829$	16.0968	+	49.5407i	0.559063	+	1.72062i	0.684964	+	0.728577i	$0.259818\pi$
$829$	16.0968	+	49.5407i	0.559063	+	1.72062i	−0.125900	+	0.992043i	$0.540182\pi$
$830$	8.27402	−	6.01143i	0.287195	−	0.208660i
$831$	−25.4315	−	35.0034i	−0.882208	−	1.21426i
$832$	24.5395	−	7.97336i	0.850753	−	0.276426i
$833$		0			0
$834$	5.78643	+	4.20409i	0.200368	+	0.145576i
$835$		−	86.1774i		−	2.98229i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.21345	−	3.73462i	0.0418930	−	0.128933i	−0.927923	−	0.372773i	$-0.878407\pi$
$839$	1.21345	−	3.73462i	0.0418930	−	0.128933i	0.969816	+	0.243840i	$0.0784070\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$		0			0
$843$	−48.1153	+	15.6336i	−1.65718	+	0.538450i
$844$	10.4970	+	3.41069i	0.361322	+	0.117401i
$845$	−35.4579	−	25.7617i	−1.21979	−	0.886229i
$846$			7.71421i			0.265220i
$847$		0			0
$848$		0			0
$849$	13.3926	−	18.4334i	0.459634	−	0.632632i
$850$		0			0
$851$		0			0
$852$	−44.3641	+	32.2324i	−1.51989	+	1.10427i
$853$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$853$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$	3.50355	−	1.74170i	0.119609	−	0.0594605i
$859$	51.6539			1.76241			0.881205	−	0.472735i	$-0.156733\pi$
$859$	51.6539			1.76241			0.881205	+	0.472735i	$0.156733\pi$
$860$	−29.8325	+	41.0609i	−1.01728	+	1.40016i
$861$		0			0
$862$	1.51405	+	4.65975i	0.0515686	+	0.158712i
$863$	−45.1434	+	32.7986i	−1.53670	+	1.11648i	−0.584334	+	0.811513i	$0.698644\pi$
$863$	−45.1434	+	32.7986i	−1.53670	+	1.11648i	−0.952364	+	0.304963i	$0.901356\pi$
$864$	−6.75940	−	9.30352i	−0.229960	−	0.316512i
$865$		0			0
$866$	−5.00666	−	1.62676i	−0.170133	−	0.0552797i
$867$	23.8214	+	17.3073i	0.809017	+	0.587785i
$868$		0			0
$869$	−9.79869	+	58.1372i	−0.332398	+	1.97217i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$877$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$878$	−5.22395	−	3.79542i	−0.176300	−	0.128089i
$879$		−	34.5745i		−	1.16617i
$880$	6.21035	+	41.8892i	0.209351	+	1.41209i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−2.33171	+	3.20932i	−0.0785126	+	0.108063i
$883$	−13.4390	+	41.3611i	−0.452260	+	1.39191i	0.422062	+	0.906567i	$0.361306\pi$
$883$	−13.4390	+	41.3611i	−0.452260	+	1.39191i	−0.874322	+	0.485346i	$0.838694\pi$
$884$		0			0
$885$	40.8437	−	29.6747i	1.37294	−	0.997503i
$886$		0			0
$887$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$887$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$888$		0			0
$889$		0			0
$890$			2.75045i			0.0921952i
$891$	20.8970	+	21.3147i	0.700075	+	0.714069i
$892$		0			0
$893$		0			0
$894$	−2.35657	+	7.25278i	−0.0788155	+	0.242569i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	7.09192	−	2.30430i	0.236660	−	0.0768956i
$899$		0			0
$900$	−30.3520	−	22.0520i	−1.01173	−	0.735068i
$901$		0			0
$902$	−2.93951	+	5.63067i	−0.0978751	+	0.187481i
$903$		0			0
$904$		0			0
$905$	−21.5316	+	66.2675i	−0.715735	+	2.20281i
$906$		0			0
$907$	−16.0962	+	11.6946i	−0.534467	+	0.388313i	−0.822026	−	0.569450i	$-0.807156\pi$
$907$	−16.0962	+	11.6946i	−0.534467	+	0.388313i	0.287559	+	0.957763i	$0.407156\pi$
$908$	31.4579	+	43.2981i	1.04397	+	1.43690i
$909$		0			0
$910$		0			0
$911$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$911$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$912$		0			0
$913$	47.2141	+	24.6483i	1.56256	+	0.815739i
$914$		0			0
$915$	7.93109	−	10.9162i	0.262194	−	0.360879i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−30.3008	−	41.7054i	−0.999530	−	1.37574i	−0.925613	−	0.378471i	$-0.876450\pi$
$919$	−30.3008	−	41.7054i	−0.999530	−	1.37574i	−0.0739171	−	0.997264i	$-0.523550\pi$
$920$		0			0
$921$		0			0
$922$	−3.81783	−	2.77381i	−0.125733	−	0.0913506i
$923$		−	58.1131i		−	1.91282i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.42856	+	19.7851i	−0.211142	+	0.649827i
$928$		0			0
$929$	−49.0909	+	35.6666i	−1.61062	+	1.17018i	−0.749110	+	0.662445i	$0.769519\pi$
$929$	−49.0909	+	35.6666i	−1.61062	+	1.17018i	−0.861511	+	0.507739i	$0.830481\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	8.10022			0.264764
$937$	10.1964	−	14.0341i	0.333101	−	0.458474i	−0.609310	−	0.792932i	$-0.708553\pi$
$937$	10.1964	−	14.0341i	0.333101	−	0.458474i	0.942410	+	0.334458i	$0.108553\pi$
$938$		0			0
$939$	2.05877	+	6.33625i	0.0671855	+	0.206776i
$940$	72.9316	−	52.9879i	2.37877	−	1.72828i
$941$	−29.9589	−	41.2349i	−0.976633	−	1.34422i	−0.938624	−	0.344943i	$-0.887898\pi$
$941$	−29.9589	−	41.2349i	−0.976633	−	1.34422i	−0.0380096	−	0.999277i	$-0.512102\pi$
$942$	−4.06543	+	1.32094i	−0.132459	+	0.0430385i
$943$		0			0
$944$	−26.4891	−	19.2454i	−0.862145	−	0.626385i
$945$		0			0
$946$	4.73474	+	0.798014i	0.153940	+	0.0259457i
$947$	37.6720			1.22418			0.612088	−	0.790790i	$-0.290330\pi$
$947$	37.6720			1.22418			0.612088	+	0.790790i	$0.290330\pi$
$948$	−35.5493	+	48.9294i	−1.15459	+	1.58915i
$949$		0			0
$950$		0			0
$951$	−35.9324	+	26.1064i	−1.16519	+	0.846558i
$952$		0			0
$953$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$953$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$954$		0			0
$955$		0			0
$956$		−	16.2113i		−	0.524312i
$957$		0			0
$958$	3.12591			0.100994
$959$		0			0
$960$	−12.9135	+	39.7435i	−0.416780	+	1.28272i
$961$	9.57953	+	29.4828i	0.309017	+	0.951057i
$962$		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	$0.5\pi$
$968$	6.75881	−	4.70906i	0.217236	−	0.151355i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$	9.46230	+	29.1220i	0.303504	+	0.934088i
$973$		0			0
$974$		0			0
$975$	37.8126	−	12.2861i	1.21097	−	0.393469i
$976$	−8.32266	−	2.70420i	−0.266402	−	0.0865592i
$977$	41.6761	+	30.2795i	1.33334	+	0.968727i	0.999661	+	0.0260393i	$0.00828950\pi$
$977$	41.6761	+	30.2795i	1.33334	+	0.968727i	0.333677	+	0.942687i	$0.391711\pi$
$978$		0			0
$979$	−12.8261	+	6.37616i	−0.409924	+	0.203783i
$980$	46.3577			1.48084
$981$		0			0
$982$		0			0
$983$	9.55764	+	29.4154i	0.304841	+	0.938205i	0.979736	+	0.200292i	$0.0641890\pi$
$983$	9.55764	+	29.4154i	0.304841	+	0.938205i	−0.674895	+	0.737914i	$0.735811\pi$
$984$	−10.6386	+	7.72943i	−0.339148	+	0.246405i
$985$	−55.2890	−	76.0987i	−1.76165	−	2.42471i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−1.05317	+	6.24861i	−0.0334719	+	0.198594i
$991$	−61.8656			−1.96523			−0.982613	−	0.185667i	$-0.940555\pi$
$991$	−61.8656			−1.96523			−0.982613	+	0.185667i	$0.940555\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	76.6295	−	55.6746i	2.42932	−	1.76500i
$996$	32.1145	+	44.2018i	1.01759	+	1.40059i
$997$	−45.1201	+	14.6604i	−1.42897	+	0.464299i	−0.918439	−	0.395562i	$-0.870550\pi$
$997$	−45.1201	+	14.6604i	−1.42897	+	0.464299i	−0.510527	+	0.859862i	$0.670550\pi$
$998$		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.194.5	yes	32
3.2	odd	2	inner	429.2.y.a.194.4	✓	32
11.8	odd	10	inner	429.2.y.a.272.5	yes	32
13.12	even	2	inner	429.2.y.a.194.4	✓	32
33.8	even	10	inner	429.2.y.a.272.4	yes	32
39.38	odd	2	CM	429.2.y.a.194.5	yes	32
143.129	odd	10	inner	429.2.y.a.272.4	yes	32
429.272	even	10	inner	429.2.y.a.272.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.a.194.4	✓	32	3.2	odd	2	inner
429.2.y.a.194.4	✓	32	13.12	even	2	inner
429.2.y.a.194.5	yes	32	1.1	even	1	trivial
429.2.y.a.194.5	yes	32	39.38	odd	2	CM
429.2.y.a.272.4	yes	32	33.8	even	10	inner
429.2.y.a.272.4	yes	32	143.129	odd	10	inner
429.2.y.a.272.5	yes	32	11.8	odd	10	inner
429.2.y.a.272.5	yes	32	429.272	even	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)

\(f(q)\)	\(=\)	\(q+(0.111034 - 0.152825i) q^{2} +(0.535233 - 1.64728i) q^{3} +(0.607007 + 1.86818i) q^{4} +(2.72753 - 1.98167i) q^{5} +(-0.192316 - 0.264700i) q^{6} +(0.712214 + 0.231412i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(0.111034 - 0.152825i) q^{2} +(0.535233 - 1.64728i) q^{3} +(0.607007 + 1.86818i) q^{4} +(2.72753 - 1.98167i) q^{5} +(-0.192316 - 0.264700i) q^{6} +(0.712214 + 0.231412i) q^{8} +(-2.42705 - 1.76336i) q^{9} -0.636866i q^{10} +(2.96989 - 1.47640i) q^{11} +3.40230 q^{12} +(-2.11929 + 2.91695i) q^{13} +(-1.80449 - 5.55366i) q^{15} +(-3.06389 + 2.22604i) q^{16} +(-0.538968 + 0.175121i) q^{18} +(5.35774 + 3.89263i) q^{20} +(0.104127 - 0.617802i) q^{22} +(0.762401 - 1.04935i) q^{24} +(1.96734 - 6.05486i) q^{25} +(0.210470 + 0.647759i) q^{26} +(-4.20378 + 3.05422i) q^{27} +(-1.04910 - 0.340872i) q^{30} +2.21313i q^{32} +(-0.842460 - 5.68245i) q^{33} +(1.82102 - 5.60453i) q^{36} +(3.67072 + 5.05231i) q^{39} +(2.40117 - 0.780187i) q^{40} +(-9.64207 - 3.13290i) q^{41} +7.66385i q^{43} +(4.56092 + 4.65209i) q^{44} -10.1143 q^{45} +(4.20646 - 12.9461i) q^{47} +(2.02702 + 6.23852i) q^{48} +(5.66312 - 4.11450i) q^{49} +(-0.706890 - 0.972951i) q^{50} +(-6.73580 - 2.18860i) q^{52} +0.981562i q^{54} +(5.17473 - 9.91227i) q^{55} +(2.67163 + 8.22243i) q^{59} +(9.27988 - 6.74222i) q^{60} +(1.35819 + 1.86938i) q^{61} +(-5.78955 - 4.20635i) q^{64} +12.1558i q^{65} +(-0.961960 - 0.502195i) q^{66} +(-13.0395 + 9.47373i) q^{71} +(-1.32052 - 1.81754i) q^{72} +(-8.92105 - 6.48152i) q^{75} +1.17969 q^{78} +(-10.4486 + 14.3813i) q^{79} +(-3.94557 + 12.1432i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-1.54938 + 1.12569i) q^{82} +(9.43908 + 12.9918i) q^{83} +(1.17122 + 0.850945i) q^{86} +(2.45685 - 0.364244i) q^{88} -4.31872 q^{89} +(-1.12302 + 1.54571i) q^{90} +(-1.51143 - 2.08031i) q^{94} +(3.64565 + 1.18454i) q^{96} -1.32231i q^{98} +(-9.81149 - 1.65367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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