LMFDB - Embedded newform 460.2.s.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	460.29
Dual form			460.2.s.a.349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.545020 + 1.85617i) q^{3} +(2.03988 - 0.915906i) q^{5} +(3.48084 + 0.500469i) q^{7} +(-0.624547 - 0.401372i) q^{9} +O(q^{10})$	\(q+(-0.545020 + 1.85617i) q^{3} +(2.03988 - 0.915906i) q^{5} +(3.48084 + 0.500469i) q^{7} +(-0.624547 - 0.401372i) q^{9} +(-2.73032 - 5.97856i) q^{11} +(4.92515 - 0.708129i) q^{13} +(0.588298 + 4.28555i) q^{15} +(-3.57985 - 3.10196i) q^{17} +(4.08843 + 4.71830i) q^{19} +(-2.82608 + 6.18824i) q^{21} +(-2.66660 + 3.98613i) q^{23} +(3.32223 - 3.73668i) q^{25} +(-3.30065 + 2.86003i) q^{27} +(-0.210877 + 0.243365i) q^{29} +(-4.13895 + 1.21531i) q^{31} +(12.5853 - 1.80949i) q^{33} +(7.55887 - 2.16722i) q^{35} +(-0.714105 + 1.11117i) q^{37} +(-1.36990 + 9.52784i) q^{39} +(3.12238 - 2.00663i) q^{41} +(-0.00210803 + 0.00717928i) q^{43} +(-1.64162 - 0.246725i) q^{45} +10.7443i q^{47} +(5.14930 + 1.51197i) q^{49} +(7.70884 - 4.95417i) q^{51} +(-5.87268 - 0.844364i) q^{53} +(-11.0453 - 9.69484i) q^{55} +(-10.9862 + 5.01724i) q^{57} +(0.615479 + 4.28075i) q^{59} +(2.54449 - 0.747130i) q^{61} +(-1.97307 - 1.70968i) q^{63} +(9.39814 - 5.95547i) q^{65} +(-11.0846 - 5.06216i) q^{67} +(-5.94557 - 7.12218i) q^{69} +(-0.804883 + 1.76245i) q^{71} +(-4.61309 + 3.99726i) q^{73} +(5.12521 + 8.20318i) q^{75} +(-6.51170 - 22.1768i) q^{77} +(-0.998355 - 6.94371i) q^{79} +(-4.43499 - 9.71127i) q^{81} +(1.02912 - 1.60134i) q^{83} +(-10.1436 - 3.04882i) q^{85} +(-0.336793 - 0.524061i) q^{87} +(-10.5233 - 3.08993i) q^{89} +17.4980 q^{91} -8.34496i q^{93} +(12.6614 + 5.88015i) q^{95} +(-3.42753 - 5.33334i) q^{97} +(-0.694415 + 4.82976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{11}\right)$

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			0
$2$		0			0
$3$	−0.545020	+	1.85617i	−0.314667	+	1.07166i	0.638602	+	0.769537i	$0.279513\pi$
$3$	−0.545020	+	1.85617i	−0.314667	+	1.07166i	−0.953270	+	0.302121i	$0.902305\pi$
$4$		0			0
$5$	2.03988	−	0.915906i	0.912263	−	0.409605i
$5$	2.03988	−	0.915906i	0.912263	−	0.409605i
$6$		0			0
$7$	3.48084	+	0.500469i	1.31563	+	0.189159i	0.764156	−	0.645031i	$-0.223156\pi$
$7$	3.48084	+	0.500469i	1.31563	+	0.189159i	0.551476	+	0.834191i	$0.314065\pi$
$8$		0			0
$9$	−0.624547	−	0.401372i	−0.208182	−	0.133791i
$10$		0			0
$11$	−2.73032	−	5.97856i	−0.823221	−	1.80260i	−0.534436	−	0.845209i	$-0.679476\pi$
$11$	−2.73032	−	5.97856i	−0.823221	−	1.80260i	−0.288785	−	0.957394i	$-0.593251\pi$
$12$		0			0
$13$	4.92515	−	0.708129i	1.36599	−	0.196400i	0.579989	−	0.814625i	$-0.303057\pi$
$13$	4.92515	−	0.708129i	1.36599	−	0.196400i	0.786001	+	0.618225i	$0.212148\pi$
$14$		0			0
$15$	0.588298	+	4.28555i	0.151898	+	1.10652i
$16$		0			0
$17$	−3.57985	−	3.10196i	−0.868241	−	0.752335i	0.101921	−	0.994793i	$-0.467501\pi$
$17$	−3.57985	−	3.10196i	−0.868241	−	0.752335i	−0.970162	+	0.242457i	$0.922047\pi$
$18$		0			0
$19$	4.08843	+	4.71830i	0.937950	+	1.08245i	0.996452	+	0.0841642i	$0.0268220\pi$
$19$	4.08843	+	4.71830i	0.937950	+	1.08245i	−0.0585024	+	0.998287i	$0.518633\pi$
$20$		0			0
$21$	−2.82608	+	6.18824i	−0.616701	+	1.35039i
$22$		0			0
$23$	−2.66660	+	3.98613i	−0.556025	+	0.831165i
$23$	−2.66660	+	3.98613i	−0.556025	+	0.831165i
$24$		0			0
$25$	3.32223	−	3.73668i	0.664447	−	0.747336i
$26$		0			0
$27$	−3.30065	+	2.86003i	−0.635211	+	0.550414i
$28$		0			0
$29$	−0.210877	+	0.243365i	−0.0391588	+	0.0451917i	−0.774991	−	0.631972i	$-0.782246\pi$
$29$	−0.210877	+	0.243365i	−0.0391588	+	0.0451917i	0.735832	+	0.677164i	$0.236791\pi$
$30$		0			0
$31$	−4.13895	+	1.21531i	−0.743378	+	0.218276i	−0.631424	−	0.775438i	$-0.717529\pi$
$31$	−4.13895	+	1.21531i	−0.743378	+	0.218276i	−0.111954	+	0.993713i	$0.535711\pi$
$32$		0			0
$33$	12.5853	−	1.80949i	2.19081	−	0.314992i
$34$		0			0
$35$	7.55887	−	2.16722i	1.27768	−	0.366327i
$36$		0			0
$37$	−0.714105	+	1.11117i	−0.117398	+	0.182675i	−0.894980	−	0.446107i	$-0.852810\pi$
$37$	−0.714105	+	1.11117i	−0.117398	+	0.182675i	0.777581	+	0.628782i	$0.216446\pi$
$38$		0			0
$39$	−1.36990	+	9.52784i	−0.219359	+	1.52567i
$40$		0			0
$41$	3.12238	−	2.00663i	0.487634	−	0.313383i	−0.273619	−	0.961838i	$-0.588221\pi$
$41$	3.12238	−	2.00663i	0.487634	−	0.313383i	0.761253	+	0.648455i	$0.224584\pi$
$42$		0			0
$43$	−0.00210803	+	0.00717928i	−0.000321471	+	0.00109483i	−0.959654	−	0.281185i	$-0.909273\pi$
$43$	−0.00210803	+	0.00717928i	−0.000321471	+	0.00109483i	0.959332	+	0.282280i	$0.0910907\pi$
$44$		0			0
$45$	−1.64162	−	0.246725i	−0.244718	−	0.0367796i
$46$		0			0
$47$			10.7443i			1.56721i	0.621258	+	0.783606i	$0.286622\pi$
$47$			10.7443i			1.56721i	−0.621258	+	0.783606i	$0.713378\pi$
$48$		0			0
$49$	5.14930	+	1.51197i	0.735614	+	0.215996i
$50$		0			0
$51$	7.70884	−	4.95417i	1.07945	−	0.693723i
$52$		0			0
$53$	−5.87268	−	0.844364i	−0.806674	−	0.115982i	−0.273374	−	0.961908i	$-0.588140\pi$
$53$	−5.87268	−	0.844364i	−0.806674	−	0.115982i	−0.533301	+	0.845926i	$0.679049\pi$
$54$		0			0
$55$	−11.0453	−	9.69484i	−1.48935	−	1.30725i
$56$		0			0
$57$	−10.9862	+	5.01724i	−1.45516	+	0.664549i
$58$		0			0
$59$	0.615479	+	4.28075i	0.0801286	+	0.557306i	0.989853	+	0.142094i	$0.0453836\pi$
$59$	0.615479	+	4.28075i	0.0801286	+	0.557306i	−0.909725	+	0.415212i	$0.863707\pi$
$60$		0			0
$61$	2.54449	−	0.747130i	0.325789	−	0.0956602i	−0.114748	−	0.993395i	$-0.536606\pi$
$61$	2.54449	−	0.747130i	0.325789	−	0.0956602i	0.440537	+	0.897734i	$0.354788\pi$
$62$		0			0
$63$	−1.97307	−	1.70968i	−0.248584	−	0.215399i
$64$		0			0
$65$	9.39814	−	5.95547i	1.16570	−	0.738685i
$66$		0			0
$67$	−11.0846	−	5.06216i	−1.35420	−	0.618442i	−0.399697	−	0.916647i	$-0.630885\pi$
$67$	−11.0846	−	5.06216i	−1.35420	−	0.618442i	−0.954502	+	0.298206i	$0.903612\pi$
$68$		0			0
$69$	−5.94557	−	7.12218i	−0.715762	−	0.857410i
$70$		0			0
$71$	−0.804883	+	1.76245i	−0.0955221	+	0.209164i	−0.951361	−	0.308078i	$-0.900314\pi$
$71$	−0.804883	+	1.76245i	−0.0955221	+	0.209164i	0.855839	+	0.517242i	$0.173041\pi$
$72$		0			0
$73$	−4.61309	+	3.99726i	−0.539921	+	0.467844i	−0.881617	−	0.471966i	$-0.843544\pi$
$73$	−4.61309	+	3.99726i	−0.539921	+	0.467844i	0.341695	+	0.939811i	$0.388999\pi$
$74$		0			0
$75$	5.12521	+	8.20318i	0.591809	+	0.947222i
$76$		0			0
$77$	−6.51170	−	22.1768i	−0.742077	−	2.52728i
$78$		0			0
$79$	−0.998355	−	6.94371i	−0.112324	−	0.781228i	−0.965649	−	0.259850i	$-0.916327\pi$
$79$	−0.998355	−	6.94371i	−0.112324	−	0.781228i	0.853325	−	0.521379i	$-0.174582\pi$
$80$		0			0
$81$	−4.43499	−	9.71127i	−0.492776	−	1.07903i
$82$		0			0
$83$	1.02912	−	1.60134i	0.112960	−	0.175769i	−0.780170	−	0.625567i	$-0.784868\pi$
$83$	1.02912	−	1.60134i	0.112960	−	0.175769i	0.893130	+	0.449798i	$0.148504\pi$
$84$		0			0
$85$	−10.1436	−	3.04882i	−1.10022	−	0.330691i
$86$		0			0
$87$	−0.336793	−	0.524061i	−0.0361080	−	0.0561852i
$88$		0			0
$89$	−10.5233	−	3.08993i	−1.11547	−	0.327532i	−0.328489	−	0.944508i	$-0.606539\pi$
$89$	−10.5233	−	3.08993i	−1.11547	−	0.327532i	−0.786982	+	0.616976i	$0.788358\pi$
$90$		0			0
$91$	17.4980			1.83429
$92$		0			0
$93$		−	8.34496i		−	0.865332i
$94$		0			0
$95$	12.6614	+	5.88015i	1.29903	+	0.603291i
$96$		0			0
$97$	−3.42753	−	5.33334i	−0.348013	−	0.541519i	0.622484	−	0.782633i	$-0.286124\pi$
$97$	−3.42753	−	5.33334i	−0.348013	−	0.541519i	−0.970497	+	0.241114i	$0.922487\pi$
$98$		0			0
$99$	−0.694415	+	4.82976i	−0.0697913	+	0.485409i
$100$		0			0
$101$	11.3551	+	7.29746i	1.12987	+	0.726124i	0.965533	−	0.260280i	$-0.0838149\pi$
$101$	11.3551	+	7.29746i	1.12987	+	0.726124i	0.164338	+	0.986404i	$0.447451\pi$
$102$		0			0
$103$	8.17430	−	3.73308i	0.805438	−	0.367831i	0.0302344	−	0.999543i	$-0.490375\pi$
$103$	8.17430	−	3.73308i	0.805438	−	0.367831i	0.775203	+	0.631712i	$0.217647\pi$
$104$		0			0
$105$	−0.0970132	+	15.2117i	−0.00946752	+	1.48451i
$106$		0			0
$107$	−5.36192	−	18.2610i	−0.518356	−	1.76536i	−0.635349	−	0.772225i	$-0.719144\pi$
$107$	−5.36192	−	18.2610i	−0.518356	−	1.76536i	0.116993	−	0.993133i	$-0.462675\pi$
$108$		0			0
$109$	3.18973	−	3.68115i	0.305521	−	0.352590i	−0.582139	−	0.813089i	$-0.697784\pi$
$109$	3.18973	−	3.68115i	0.305521	−	0.352590i	0.887660	+	0.460499i	$0.152330\pi$
$110$		0			0
$111$	−1.67331	−	1.93111i	−0.158824	−	0.183293i
$112$		0			0
$113$	−7.41961	−	3.38842i	−0.697978	−	0.318756i	0.0346363	−	0.999400i	$-0.488973\pi$
$113$	−7.41961	−	3.38842i	−0.697978	−	0.318756i	−0.732614	+	0.680644i	$0.761700\pi$
$114$		0			0
$115$	−1.78864	+	10.5736i	−0.166791	+	0.985992i
$116$		0			0
$117$	−3.36021	−	1.53456i	−0.310651	−	0.141870i
$118$		0			0
$119$	−10.9084	−	12.5890i	−0.999975	−	1.15403i
$120$		0			0
$121$	−21.0851	+	24.3334i	−1.91682	+	2.21213i
$122$		0			0
$123$	2.02288	+	6.88931i	0.182397	+	0.621188i
$124$		0			0
$125$	3.35452	−	10.6652i	0.300037	−	0.953927i
$126$		0			0
$127$	−14.0573	+	6.41976i	−1.24738	+	0.569661i	−0.926084	−	0.377316i	$-0.876847\pi$
$127$	−14.0573	+	6.41976i	−1.24738	+	0.569661i	−0.321300	+	0.946978i	$0.604120\pi$
$128$		0			0
$129$	−0.0121770	−	0.00782570i	−0.00107213	−	0.000689014i
$130$		0			0
$131$	−0.697477	+	4.85106i	−0.0609389	+	0.423839i	0.936400	+	0.350934i	$0.114136\pi$
$131$	−0.697477	+	4.85106i	−0.0609389	+	0.423839i	−0.997339	+	0.0729048i	$0.976773\pi$
$132$		0			0
$133$	11.8698	+	18.4697i	1.02924	+	1.60153i
$134$		0			0
$135$	−4.11342	+	8.85722i	−0.354027	+	0.762308i
$136$		0			0
$137$			8.15523i			0.696748i	0.937356	+	0.348374i	$0.113266\pi$
$137$			8.15523i			0.696748i	−0.937356	+	0.348374i	$0.886734\pi$
$138$		0			0
$139$	13.5220			1.14692			0.573459	−	0.819234i	$-0.305601\pi$
$139$	13.5220			1.14692			0.573459	+	0.819234i	$0.305601\pi$
$140$		0			0
$141$	−19.9431	−	5.85584i	−1.67952	−	0.493150i
$142$		0			0
$143$	−17.6808	−	27.5119i	−1.47854	−	2.30066i
$144$		0			0
$145$	−0.207264	+	0.689578i	−0.0172124	+	0.0572664i
$146$		0			0
$147$	−5.61294	+	8.73390i	−0.462947	+	0.720360i
$148$		0			0
$149$	6.66904	+	14.6032i	0.546349	+	1.19634i	0.958466	+	0.285207i	$0.0920622\pi$
$149$	6.66904	+	14.6032i	0.546349	+	1.19634i	−0.412117	+	0.911131i	$0.635210\pi$
$150$		0			0
$151$	−2.02439	−	14.0800i	−0.164743	−	1.14581i	−0.889543	−	0.456852i	$-0.848977\pi$
$151$	−2.02439	−	14.0800i	−0.164743	−	1.14581i	0.724800	−	0.688960i	$-0.241932\pi$
$152$		0			0
$153$	0.990745	+	3.37417i	0.0800970	+	0.272785i
$154$		0			0
$155$	−7.32987	+	6.26997i	−0.588749	+	0.503616i
$156$		0			0
$157$	9.23978	−	8.00631i	0.737415	−	0.638973i	−0.202931	−	0.979193i	$-0.565047\pi$
$157$	9.23978	−	8.00631i	0.737415	−	0.638973i	0.940346	+	0.340219i	$0.110501\pi$
$158$		0			0
$159$	4.76800	−	10.4405i	0.378127	−	0.827983i
$160$		0			0
$161$	−11.2769	+	12.5405i	−0.888748	+	0.988330i
$162$		0			0
$163$	19.6346	+	8.96681i	1.53790	+	0.702335i	0.990875	−	0.134782i	$-0.0430334\pi$
$163$	19.6346	+	8.96681i	1.53790	+	0.702335i	0.547024	+	0.837117i	$0.315761\pi$
$164$		0			0
$165$	24.0151	−	15.2181i	1.86958	−	1.18472i
$166$		0			0
$167$	0.601956	+	0.521598i	0.0465808	+	0.0403625i	0.677840	−	0.735209i	$-0.262916\pi$
$167$	0.601956	+	0.521598i	0.0465808	+	0.0403625i	−0.631259	+	0.775572i	$0.717462\pi$
$168$		0			0
$169$	11.2822	−	3.31276i	0.867863	−	0.254828i
$170$		0			0
$171$	−0.659623	−	4.58778i	−0.0504426	−	0.350836i
$172$		0			0
$173$	4.83648	−	2.20875i	0.367711	−	0.167928i	−0.222986	−	0.974822i	$-0.571580\pi$
$173$	4.83648	−	2.20875i	0.367711	−	0.167928i	0.590697	+	0.806894i	$0.298853\pi$
$174$		0			0
$175$	13.4342	−	11.3441i	1.01553	−	0.857533i
$176$		0			0
$177$	−8.28124	−	1.19066i	−0.622456	−	0.0894956i
$178$		0			0
$179$	5.57425	−	3.58235i	0.416639	−	0.267758i	−0.315483	−	0.948931i	$-0.602167\pi$
$179$	5.57425	−	3.58235i	0.416639	−	0.267758i	0.732122	+	0.681174i	$0.238530\pi$
$180$		0			0
$181$	11.4545	+	3.36333i	0.851404	+	0.249995i	0.678187	−	0.734889i	$-0.262766\pi$
$181$	11.4545	+	3.36333i	0.851404	+	0.249995i	0.173216	+	0.984884i	$0.444584\pi$
$182$		0			0
$183$			5.13020i			0.379235i
$184$		0			0
$185$	−0.438964	+	2.92071i	−0.0322732	+	0.214735i
$186$		0			0
$187$	−8.77111	+	29.8717i	−0.641407	+	2.18443i
$188$		0			0
$189$	−12.9204	+	8.30343i	−0.939820	+	0.603986i
$190$		0			0
$191$	−2.92693	+	20.3573i	−0.211785	+	1.47300i	0.555405	+	0.831580i	$0.312563\pi$
$191$	−2.92693	+	20.3573i	−0.211785	+	1.47300i	−0.767191	+	0.641419i	$0.778346\pi$
$192$		0			0
$193$	−3.18512	+	4.95614i	−0.229270	+	0.356751i	−0.936760	−	0.349972i	$-0.886191\pi$
$193$	−3.18512	+	4.95614i	−0.229270	+	0.356751i	0.707490	+	0.706723i	$0.249827\pi$
$194$		0			0
$195$	5.93217	+	20.6904i	0.424812	+	1.48167i
$196$		0			0
$197$	7.06478	−	1.01576i	0.503345	−	0.0723700i	0.114034	−	0.993477i	$-0.463623\pi$
$197$	7.06478	−	1.01576i	0.503345	−	0.0723700i	0.389310	+	0.921107i	$0.372713\pi$
$198$		0			0
$199$	−14.7723	+	4.33754i	−1.04718	+	0.307480i	−0.759677	−	0.650300i	$-0.774643\pi$
$199$	−14.7723	+	4.33754i	−1.04718	+	0.307480i	−0.287503	+	0.957780i	$0.592825\pi$
$200$		0			0
$201$	15.4375	−	17.8159i	1.08888	−	1.25663i
$202$		0			0
$203$	−0.855824	+	0.741575i	−0.0600670	+	0.0520484i
$204$		0			0
$205$	4.53140	−	6.95310i	0.316487	−	0.485625i
$206$		0			0
$207$	3.26534	−	1.41922i	0.226957	−	0.0986429i
$208$		0			0
$209$	17.0459	−	37.3253i	1.17909	−	2.58185i
$210$		0			0
$211$	−7.36870	−	8.50394i	−0.507283	−	0.585435i	0.443118	−	0.896463i	$-0.353872\pi$
$211$	−7.36870	−	8.50394i	−0.507283	−	0.585435i	−0.950401	+	0.311028i	$0.899327\pi$
$212$		0			0
$213$	−2.83272	−	2.45457i	−0.194095	−	0.168184i
$214$		0			0
$215$	0.00227542	+	0.0165756i	0.000155182	+	0.00113045i
$216$		0			0
$217$	−15.0152	+	2.15887i	−1.01930	+	0.146553i
$218$		0			0
$219$	−4.90536	−	10.7412i	−0.331474	−	0.725826i
$220$		0			0
$221$	−19.8279	−	12.7426i	−1.33377	−	0.857160i
$222$		0			0
$223$	−5.84909	−	0.840972i	−0.391684	−	0.0563156i	−0.0563405	−	0.998412i	$-0.517943\pi$
$223$	−5.84909	−	0.840972i	−0.391684	−	0.0563156i	−0.335343	+	0.942096i	$0.608852\pi$
$224$		0			0
$225$	−3.57469	+	1.00028i	−0.238313	+	0.0666853i
$226$		0			0
$227$	3.89851	−	13.2771i	0.258753	−	0.881233i	−0.722963	−	0.690886i	$-0.757220\pi$
$227$	3.89851	−	13.2771i	0.258753	−	0.881233i	0.981717	−	0.190347i	$-0.0609613\pi$
$228$		0			0
$229$	−8.51412			−0.562629			−0.281314	−	0.959616i	$-0.590770\pi$
$229$	−8.51412			−0.562629			−0.281314	+	0.959616i	$0.590770\pi$
$230$		0			0
$231$	44.7129			2.94189
$232$		0			0
$233$	1.58297	−	5.39110i	0.103704	−	0.353183i	−0.891251	−	0.453511i	$-0.850171\pi$
$233$	1.58297	−	5.39110i	0.103704	−	0.353183i	0.994954	+	0.100329i	$0.0319894\pi$
$234$		0			0
$235$	9.84073	+	21.9170i	0.641939	+	1.42971i
$236$		0			0
$237$	13.4328	+	1.93135i	0.872554	+	0.125454i
$238$		0			0
$239$	−6.34638	−	4.07857i	−0.410513	−	0.263821i	0.319045	−	0.947740i	$-0.396638\pi$
$239$	−6.34638	−	4.07857i	−0.410513	−	0.263821i	−0.729558	+	0.683919i	$0.760274\pi$
$240$		0			0
$241$	0.669372	+	1.46572i	0.0431180	+	0.0944153i	0.929965	−	0.367648i	$-0.119837\pi$
$241$	0.669372	+	1.46572i	0.0431180	+	0.0944153i	−0.886847	+	0.462063i	$0.847109\pi$
$242$		0			0
$243$	7.47408	−	1.07461i	0.479462	−	0.0689363i
$244$		0			0
$245$	11.8888	−	1.63203i	0.759546	−	0.104267i
$246$		0			0
$247$	23.4773	+	20.3432i	1.49382	+	1.29440i
$248$		0			0
$249$	2.41146	+	2.78297i	0.152820	+	0.176364i
$250$		0			0
$251$	−3.10251	+	6.79354i	−0.195829	+	0.428805i	−0.981918	−	0.189309i	$-0.939375\pi$
$251$	−3.10251	+	6.79354i	−0.195829	+	0.428805i	0.786089	+	0.618113i	$0.212103\pi$
$252$		0			0
$253$	31.1120	+	5.05906i	1.95599	+	0.318060i
$254$		0			0
$255$	11.1876	−	17.1665i	0.700593	−	1.07501i
$256$		0			0
$257$	−18.1183	+	15.6996i	−1.13019	+	0.979316i	−0.999926	−	0.0121629i	$-0.996128\pi$
$257$	−18.1183	+	15.6996i	−1.13019	+	0.979316i	−0.130265	+	0.991479i	$0.541583\pi$
$258$		0			0
$259$	−3.04179	+	3.51041i	−0.189007	+	0.218126i
$260$		0			0
$261$	0.229382	−	0.0673527i	0.0141984	−	0.00416903i
$262$		0			0
$263$	19.3375	−	2.78031i	1.19240	−	0.171442i	0.482599	−	0.875842i	$-0.339693\pi$
$263$	19.3375	−	2.78031i	1.19240	−	0.171442i	0.709803	+	0.704400i	$0.248784\pi$
$264$		0			0
$265$	−12.7529	+	3.65642i	−0.783406	+	0.224612i
$266$		0			0
$267$	11.4708	−	17.8490i	0.702004	−	1.09234i
$268$		0			0
$269$	1.44634	−	10.0595i	0.0881846	−	0.613338i	−0.897024	−	0.441981i	$-0.854276\pi$
$269$	1.44634	−	10.0595i	0.0881846	−	0.613338i	0.985209	−	0.171357i	$-0.0548150\pi$
$270$		0			0
$271$	−15.0873	+	9.69600i	−0.916487	+	0.588990i	−0.911636	−	0.410998i	$-0.865180\pi$
$271$	−15.0873	+	9.69600i	−0.916487	+	0.588990i	−0.00485037	+	0.999988i	$0.501544\pi$
$272$		0			0
$273$	−9.53677	+	32.4792i	−0.577191	+	1.96573i
$274$		0			0
$275$	−31.4107	−	9.65985i	−1.89414	−	0.582511i
$276$		0			0
$277$		−	5.01429i		−	0.301280i	−0.988589	−	0.150640i	$-0.951867\pi$
$277$		−	5.01429i		−	0.301280i	0.988589	−	0.150640i	$-0.0481334\pi$
$278$		0			0
$279$	3.07276	+	0.902244i	0.183961	+	0.0540159i
$280$		0			0
$281$	3.62194	−	2.32768i	0.216067	−	0.138858i	−0.428131	−	0.903717i	$-0.640828\pi$
$281$	3.62194	−	2.32768i	0.216067	−	0.138858i	0.644198	+	0.764859i	$0.277191\pi$
$282$		0			0
$283$	−11.5854	−	1.66572i	−0.688678	−	0.0990170i	−0.210913	−	0.977505i	$-0.567644\pi$
$283$	−11.5854	−	1.66572i	−0.688678	−	0.0990170i	−0.477765	+	0.878488i	$0.658553\pi$
$284$		0			0
$285$	−17.8153	+	20.2969i	−1.05529	+	1.20229i
$286$		0			0
$287$	11.8727	−	5.42210i	0.700826	−	0.320057i
$288$		0			0
$289$	0.773833	+	5.38213i	0.0455196	+	0.316596i
$290$		0			0
$291$	11.7676	−	3.45529i	0.689831	−	0.202553i
$292$		0			0
$293$	−2.93827	−	2.54603i	−0.171656	−	0.148740i	0.564796	−	0.825230i	$-0.308955\pi$
$293$	−2.93827	−	2.54603i	−0.171656	−	0.148740i	−0.736452	+	0.676490i	$0.763500\pi$
$294$		0			0
$295$	5.17627	+	8.16851i	0.301374	+	0.475589i
$296$		0			0
$297$	26.1107	+	11.9244i	1.51510	+	0.691921i
$298$		0			0
$299$	−10.3107	+	21.5206i	−0.596285	+	1.24457i
$300$		0			0
$301$	−0.0109307	+	0.0239349i	−0.000630035	+	0.00137958i
$302$		0			0
$303$	−19.7340	+	17.0996i	−1.13369	+	0.982348i
$304$		0			0
$305$	4.50616	−	3.85457i	0.258022	−	0.220712i
$306$		0			0
$307$	−5.60884	−	19.1020i	−0.320114	−	1.09021i	−0.949670	−	0.313252i	$-0.898581\pi$
$307$	−5.60884	−	19.1020i	−0.320114	−	1.09021i	0.629556	−	0.776955i	$-0.283237\pi$
$308$		0			0
$309$	2.47406	+	17.2075i	0.140744	+	0.978898i
$310$		0			0
$311$	−2.79562	−	6.12155i	−0.158525	−	0.347121i	0.813658	−	0.581344i	$-0.197473\pi$
$311$	−2.79562	−	6.12155i	−0.158525	−	0.347121i	−0.972183	+	0.234223i	$0.924746\pi$
$312$		0			0
$313$	−5.19660	+	8.08607i	−0.293729	+	0.457051i	−0.956484	−	0.291785i	$-0.905751\pi$
$313$	−5.19660	+	8.08607i	−0.293729	+	0.457051i	0.662755	+	0.748836i	$0.269387\pi$
$314$		0			0
$315$	−5.59073	−	1.68039i	−0.315002	−	0.0946792i
$316$		0			0
$317$	−3.29500	−	5.12712i	−0.185066	−	0.287968i	0.736307	−	0.676647i	$-0.236568\pi$
$317$	−3.29500	−	5.12712i	−0.185066	−	0.287968i	−0.921373	+	0.388679i	$0.872931\pi$
$318$		0			0
$319$	2.03073	+	0.596276i	0.113699	+	0.0333850i
$320$		0			0
$321$	36.8178			2.05497
$322$		0			0
$323$		−	29.5729i		−	1.64548i
$324$		0			0
$325$	13.7164	−	20.7563i	0.760851	−	1.15135i
$326$		0			0
$327$	5.09435	+	7.92697i	0.281718	+	0.438362i
$328$		0			0
$329$	−5.37717	+	37.3990i	−0.296453	+	2.06187i
$330$		0			0
$331$	−25.0834	−	16.1201i	−1.37871	−	0.886042i	−0.379476	−	0.925202i	$-0.623896\pi$
$331$	−25.0834	−	16.1201i	−1.37871	−	0.886042i	−0.999233	+	0.0391593i	$0.987532\pi$
$332$		0			0
$333$	0.891984	−	0.407355i	0.0488804	−	0.0223229i
$334$		0			0
$335$	−27.2477	−	0.173773i	−1.48870	−	0.00949425i
$336$		0			0
$337$	2.42540	+	8.26015i	0.132120	+	0.449959i	0.998804	−	0.0488986i	$-0.0155711\pi$
$337$	2.42540	+	8.26015i	0.132120	+	0.449959i	−0.866684	+	0.498858i	$0.833753\pi$
$338$		0			0
$339$	10.3333	−	11.9253i	0.561228	−	0.647692i
$340$		0			0
$341$	18.5664	+	21.4268i	1.00543	+	1.16033i
$342$		0			0
$343$	−5.22471	−	2.38605i	−0.282108	−	0.128834i
$344$		0			0
$345$	−18.6515	−	9.08283i	−1.00416	−	0.489003i
$346$		0			0
$347$	14.2353	+	6.50106i	0.764192	+	0.348995i	0.759085	−	0.650992i	$-0.225647\pi$
$347$	14.2353	+	6.50106i	0.764192	+	0.348995i	0.00510781	+	0.999987i	$0.498374\pi$
$348$		0			0
$349$	5.01714	+	5.79009i	0.268562	+	0.309937i	0.873971	−	0.485977i	$-0.161536\pi$
$349$	5.01714	+	5.79009i	0.268562	+	0.309937i	−0.605410	+	0.795914i	$0.706991\pi$
$350$		0			0
$351$	−14.2309	+	16.4234i	−0.759591	+	0.876615i
$352$		0			0
$353$	5.46405	+	18.6088i	0.290822	+	0.990449i	0.967226	+	0.253918i	$0.0817192\pi$
$353$	5.46405	+	18.6088i	0.290822	+	0.990449i	−0.676404	+	0.736531i	$0.736463\pi$
$354$		0			0
$355$	−0.0276299	+	4.33238i	−0.00146644	+	0.229939i
$356$		0			0
$357$	29.3126	−	13.3866i	1.55139	−	0.708495i
$358$		0			0
$359$	−16.0826	−	10.3357i	−0.848808	−	0.545496i	0.0423945	−	0.999101i	$-0.486501\pi$
$359$	−16.0826	−	10.3357i	−0.848808	−	0.545496i	−0.891203	+	0.453605i	$0.850138\pi$
$360$		0			0
$361$	−2.84310	+	19.7742i	−0.149637	+	1.04075i
$362$		0			0
$363$	−33.6752	−	52.3996i	−1.76749	−	2.75026i
$364$		0			0
$365$	−5.74904	+	12.3791i	−0.300918	+	0.647952i
$366$		0			0
$367$		−	25.0604i		−	1.30814i	−0.756433	−	0.654071i	$-0.773060\pi$
$367$		−	25.0604i		−	1.30814i	0.756433	−	0.654071i	$-0.226940\pi$
$368$		0			0
$369$	−2.75548			−0.143444
$370$		0			0
$371$	−20.0192	−	5.87818i	−1.03935	−	0.305180i
$372$		0			0
$373$	9.16889	+	14.2671i	0.474747	+	0.738721i	0.993204	−	0.116383i	$-0.0371299\pi$
$373$	9.16889	+	14.2671i	0.474747	+	0.738721i	−0.518457	+	0.855103i	$0.673494\pi$
$374$		0			0
$375$	17.9682	+	12.0393i	0.927872	+	0.621707i
$376$		0			0
$377$	−0.866265	+	1.34793i	−0.0446149	+	0.0694222i
$378$		0			0
$379$	12.9214	+	28.2940i	0.663729	+	1.45336i	0.879006	+	0.476811i	$0.158207\pi$
$379$	12.9214	+	28.2940i	0.663729	+	1.45336i	−0.215277	+	0.976553i	$0.569065\pi$
$380$		0			0
$381$	−4.25463	−	29.5916i	−0.217971	−	1.51602i
$382$		0			0
$383$	−5.11554	−	17.4219i	−0.261392	−	0.890220i	−0.980698	−	0.195527i	$-0.937358\pi$
$383$	−5.11554	−	17.4219i	−0.261392	−	0.890220i	0.719306	−	0.694693i	$-0.244460\pi$
$384$		0			0
$385$	−33.5950	−	39.2740i	−1.71216	−	2.00159i
$386$		0			0
$387$	0.00419812	−	0.00363770i	0.000213403	−	0.000184914i
$388$		0			0
$389$	−2.20349	+	4.82497i	−0.111721	+	0.244636i	−0.957231	−	0.289324i	$-0.906569\pi$
$389$	−2.20349	+	4.82497i	−0.111721	+	0.244636i	0.845510	+	0.533960i	$0.179297\pi$
$390$		0			0
$391$	21.9108	−	5.99805i	1.10808	−	0.303334i
$392$		0			0
$393$	−8.62424	−	3.93856i	−0.435035	−	0.198674i
$394$		0			0
$395$	−8.39631	−	13.2499i	−0.422464	−	0.666677i
$396$		0			0
$397$	−15.4155	−	13.3576i	−0.773681	−	0.670399i	0.175729	−	0.984439i	$-0.443772\pi$
$397$	−15.4155	−	13.3576i	−0.773681	−	0.670399i	−0.949410	+	0.314040i	$0.898317\pi$
$398$		0			0
$399$	−40.7522	+	11.9659i	−2.04016	+	0.599045i
$400$		0			0
$401$	−0.547517	−	3.80806i	−0.0273417	−	0.190166i	0.971573	−	0.236739i	$-0.0760788\pi$
$401$	−0.547517	−	3.80806i	−0.0273417	−	0.190166i	−0.998915	+	0.0465739i	$0.985170\pi$
$402$		0			0
$403$	−19.5244	+	8.91648i	−0.972578	+	0.444161i
$404$		0			0
$405$	−17.9415	−	15.7478i	−0.891518	−	0.782515i
$406$		0			0
$407$	8.59292	+	1.23548i	0.425935	+	0.0612402i
$408$		0			0
$409$	7.19814	−	4.62597i	0.355925	−	0.228739i	−0.350443	−	0.936584i	$-0.613969\pi$
$409$	7.19814	−	4.62597i	0.355925	−	0.228739i	0.706368	+	0.707845i	$0.250332\pi$
$410$		0			0
$411$	−15.1375	−	4.44476i	−0.746676	−	0.219244i
$412$		0			0
$413$			15.2086i			0.748367i
$414$		0			0
$415$	0.632602	−	4.20911i	0.0310532	−	0.206617i
$416$		0			0
$417$	−7.36974	+	25.0990i	−0.360898	+	1.22910i
$418$		0			0
$419$	18.1477	−	11.6628i	0.886573	−	0.569766i	−0.0162069	−	0.999869i	$-0.505159\pi$
$419$	18.1477	−	11.6628i	0.886573	−	0.569766i	0.902780	+	0.430103i	$0.141523\pi$
$420$		0			0
$421$	1.32403	−	9.20882i	0.0645292	−	0.448810i	−0.931784	−	0.363014i	$-0.881748\pi$
$421$	1.32403	−	9.20882i	0.0645292	−	0.448810i	0.996313	−	0.0857961i	$-0.0273433\pi$
$422$		0			0
$423$	4.31245	−	6.71030i	0.209678	−	0.326266i
$424$		0			0
$425$	−23.4841	+	3.07132i	−1.13915	+	0.148981i
$426$		0			0
$427$	9.23087	−	1.32720i	0.446713	−	0.0642276i
$428$		0			0
$429$	60.7030	−	17.8240i	2.93077	−	0.860551i
$430$		0			0
$431$	17.9439	−	20.7083i	0.864327	−	0.997486i	−0.135651	−	0.990757i	$-0.543313\pi$
$431$	17.9439	−	20.7083i	0.864327	−	0.997486i	0.999977	−	0.00672938i	$-0.00214204\pi$
$432$		0			0
$433$	−8.59151	+	7.44459i	−0.412882	+	0.357764i	−0.836396	−	0.548125i	$-0.815342\pi$
$433$	−8.59151	+	7.44459i	−0.412882	+	0.357764i	0.423515	+	0.905889i	$0.360796\pi$
$434$		0			0
$435$	−1.16701	−	0.760551i	−0.0559538	−	0.0364656i
$436$		0			0
$437$	−29.7100	+	3.71517i	−1.42122	+	0.177721i
$438$		0			0
$439$	−4.56098	+	9.98715i	−0.217684	+	0.476661i	−0.986697	−	0.162573i	$-0.948021\pi$
$439$	−4.56098	+	9.98715i	−0.217684	+	0.476661i	0.769013	+	0.639233i	$0.220748\pi$
$440$		0			0
$441$	−2.60911	−	3.01108i	−0.124244	−	0.143385i
$442$		0			0
$443$	−11.4737	−	9.94203i	−0.545133	−	0.472360i	0.338221	−	0.941067i	$-0.390175\pi$
$443$	−11.4737	−	9.94203i	−0.545133	−	0.472360i	−0.883354	+	0.468707i	$0.844720\pi$
$444$		0			0
$445$	−24.2964	+	3.33529i	−1.15176	+	0.158108i
$446$		0			0
$447$	−30.7407	+	4.41984i	−1.45398	+	0.209051i
$448$		0			0
$449$	9.38716	+	20.5550i	0.443008	+	0.970051i	0.991036	+	0.133592i	$0.0426511\pi$
$449$	9.38716	+	20.5550i	0.443008	+	0.970051i	−0.548029	+	0.836459i	$0.684622\pi$
$450$		0			0
$451$	−20.5218	−	13.1886i	−0.966336	−	0.621026i
$452$		0			0
$453$	27.2381	+	3.91625i	1.27976	+	0.184001i
$454$		0			0
$455$	35.6939	−	16.0265i	1.67336	−	0.751336i
$456$		0			0
$457$	0.590292	−	2.01035i	0.0276127	−	0.0940402i	−0.944534	−	0.328414i	$-0.893486\pi$
$457$	0.590292	−	2.01035i	0.0276127	−	0.0940402i	0.972147	+	0.234374i	$0.0753040\pi$
$458$		0			0
$459$	20.6875			0.965612
$460$		0			0
$461$	−13.5277			−0.630050			−0.315025	−	0.949083i	$-0.602013\pi$
$461$	−13.5277			−0.630050			−0.315025	+	0.949083i	$0.602013\pi$
$462$		0			0
$463$	3.87685	−	13.2033i	0.180172	−	0.613611i	−0.819033	−	0.573747i	$-0.805489\pi$
$463$	3.87685	−	13.2033i	0.180172	−	0.613611i	0.999205	−	0.0398639i	$-0.0126924\pi$
$464$		0			0
$465$	−7.64319	−	17.0227i	−0.354445	−	0.789410i
$466$		0			0
$467$	27.4112	+	3.94114i	1.26844	+	0.182374i	0.743483	−	0.668754i	$-0.233172\pi$
$467$	27.4112	+	3.94114i	1.26844	+	0.182374i	0.524957	+	0.851129i	$0.324081\pi$
$468$		0			0
$469$	−36.0502	−	23.1680i	−1.66464	−	1.06980i
$470$		0			0
$471$	9.82519	+	21.5142i	0.452721	+	0.991321i
$472$		0			0
$473$	0.0486773	−	0.00699874i	0.00223819	−	0.000321803i
$474$		0			0
$475$	31.2135	+	0.398146i	1.43217	+	0.0182682i
$476$		0			0
$477$	3.32886	+	2.88447i	0.152418	+	0.132071i
$478$		0			0
$479$	15.6784	+	18.0939i	0.716366	+	0.826731i	0.990865	−	0.134857i	$-0.0430574\pi$
$479$	15.6784	+	18.0939i	0.716366	+	0.826731i	−0.274499	+	0.961587i	$0.588512\pi$
$480$		0			0
$481$	−2.73022	+	5.97835i	−0.124487	+	0.272589i
$482$		0			0
$483$	−17.1311	−	27.7667i	−0.779493	−	1.26343i
$484$		0			0
$485$	−11.8766	−	7.74009i	−0.539288	−	0.351459i
$486$		0			0
$487$	−3.23543	+	2.80352i	−0.146611	+	0.127039i	−0.725079	−	0.688666i	$-0.758197\pi$
$487$	−3.23543	+	2.80352i	−0.146611	+	0.127039i	0.578467	+	0.815706i	$0.303651\pi$
$488$		0			0
$489$	−27.3451	+	31.5580i	−1.23659	+	1.42710i
$490$		0			0
$491$	−4.75219	+	1.39537i	−0.214463	+	0.0629722i	−0.387199	−	0.921996i	$-0.626557\pi$
$491$	−4.75219	+	1.39537i	−0.214463	+	0.0629722i	0.172736	+	0.984968i	$0.444739\pi$
$492$		0			0
$493$	1.50981	−	0.217078i	0.0679986	−	0.00977672i
$494$		0			0
$495$	3.00708	+	10.4882i	0.135158	+	0.471408i
$496$		0			0
$497$	−3.68372	+	5.73197i	−0.165237	+	0.257114i
$498$		0			0
$499$	2.17093	−	15.0992i	0.0971842	−	0.675931i	−0.881744	−	0.471728i	$-0.843630\pi$
$499$	2.17093	−	15.0992i	0.0971842	−	0.675931i	0.978928	−	0.204203i	$-0.0654604\pi$
$500$		0			0
$501$	−1.29625	+	0.833050i	−0.0579122	+	0.0372179i
$502$		0			0
$503$	4.82554	−	16.4343i	0.215160	−	0.732769i	−0.779206	−	0.626768i	$-0.784377\pi$
$503$	4.82554	−	16.4343i	0.215160	−	0.732769i	0.994366	−	0.106001i	$-0.0338046\pi$
$504$		0			0
$505$	29.8468	+	4.48578i	1.32816	+	0.199615i
$506$		0			0
$507$			22.7472i			1.01024i
$508$		0			0
$509$	3.18407	+	0.934926i	0.141131	+	0.0414399i	0.351535	−	0.936175i	$-0.385660\pi$
$509$	3.18407	+	0.934926i	0.141131	+	0.0414399i	−0.210404	+	0.977615i	$0.567478\pi$
$510$		0			0
$511$	−18.0579	+	11.6051i	−0.798835	+	0.513380i
$512$		0			0
$513$	−26.9890	−	3.88043i	−1.19159	−	0.171325i
$514$		0			0
$515$	13.2555	−	15.1019i	0.584105	−	0.665470i
$516$		0			0
$517$	64.2352	−	29.3352i	2.82506	−	1.29016i
$518$		0			0
$519$	1.46383	+	10.1811i	0.0642548	+	0.446902i
$520$		0			0
$521$	2.33918	−	0.686845i	0.102481	−	0.0300912i	−0.230090	−	0.973169i	$-0.573902\pi$
$521$	2.33918	−	0.686845i	0.102481	−	0.0300912i	0.332571	+	0.943078i	$0.392084\pi$
$522$		0			0
$523$	3.60146	+	3.12069i	0.157481	+	0.136458i	0.730037	−	0.683407i	$-0.239503\pi$
$523$	3.60146	+	3.12069i	0.157481	+	0.136458i	−0.572556	+	0.819865i	$0.694048\pi$
$524$		0			0
$525$	13.7346	+	31.1189i	0.599427	+	1.35814i
$526$		0			0
$527$	18.5867	+	8.48825i	0.809648	+	0.369754i
$528$		0			0
$529$	−8.77844	−	21.2589i	−0.381671	−	0.924298i
$530$		0			0
$531$	1.33378	−	2.92057i	0.0578810	−	0.126742i
$532$		0			0
$533$	13.9572	−	12.0940i	0.604555	−	0.523850i
$534$		0			0
$535$	−27.6630	−	32.3393i	−1.19598	−	1.39815i
$536$		0			0
$537$	3.61137	+	12.2992i	0.155842	+	0.530749i
$538$		0			0
$539$	−5.01981	−	34.9135i	−0.216218	−	1.50383i
$540$		0			0
$541$	6.32705	+	13.8543i	0.272021	+	0.595643i	0.995506	−	0.0946970i	$-0.0301882\pi$
$541$	6.32705	+	13.8543i	0.272021	+	0.595643i	−0.723485	+	0.690340i	$0.757461\pi$
$542$		0			0
$543$	−12.4858	+	19.4283i	−0.535818	+	0.833749i
$544$		0			0
$545$	3.13509	−	10.4306i	0.134293	−	0.446798i
$546$		0			0
$547$	7.54722	+	11.7437i	0.322696	+	0.502124i	0.964265	−	0.264941i	$-0.0853525\pi$
$547$	7.54722	+	11.7437i	0.322696	+	0.502124i	−0.641569	+	0.767065i	$0.721716\pi$
$548$		0			0
$549$	−1.88903	−	0.554669i	−0.0806218	−	0.0236727i
$550$		0			0
$551$	−2.01042			−0.0856468
$552$		0			0
$553$		−	24.6696i		−	1.04906i
$554$		0			0
$555$	−5.18207	−	2.40663i	−0.219967	−	0.102156i
$556$		0			0
$557$	11.9415	+	18.5814i	0.505979	+	0.787319i	0.996454	−	0.0841365i	$-0.0268132\pi$
$557$	11.9415	+	18.5814i	0.505979	+	0.787319i	−0.490475	+	0.871455i	$0.663177\pi$
$558$		0			0
$559$	−0.00529849	+	0.0368518i	−0.000224102	+	0.00155866i
$560$		0			0
$561$	−50.6663	−	32.5613i	−2.13913	−	1.37474i
$562$		0			0
$563$	−28.5769	+	13.0506i	−1.20437	+	0.550019i	−0.913538	−	0.406754i	$-0.866661\pi$
$563$	−28.5769	+	13.0506i	−1.20437	+	0.550019i	−0.290836	+	0.956773i	$0.593933\pi$
$564$		0			0
$565$	−18.2386	−	0.116317i	−0.767303	−	0.00489350i
$566$		0			0
$567$	−10.5773	−	36.0229i	−0.444204	−	1.51282i
$568$		0			0
$569$	−27.4899	+	31.7251i	−1.15244	+	1.32998i	−0.217132	+	0.976142i	$0.569670\pi$
$569$	−27.4899	+	31.7251i	−1.15244	+	1.32998i	−0.935305	+	0.353842i	$0.884875\pi$
$570$		0			0
$571$	12.2172	+	14.0994i	0.511273	+	0.590040i	0.951424	−	0.307883i	$-0.0996207\pi$
$571$	12.2172	+	14.0994i	0.511273	+	0.590040i	−0.440151	+	0.897924i	$0.645075\pi$
$572$		0			0
$573$	−36.1912	−	16.5280i	−1.51191	−	0.690466i
$574$		0			0
$575$	6.03580	+	23.2071i	0.251710	+	0.967803i
$576$		0			0
$577$	8.46988	+	3.86807i	0.352606	+	0.161030i	0.583841	−	0.811868i	$-0.301549\pi$
$577$	8.46988	+	3.86807i	0.352606	+	0.161030i	−0.231235	+	0.972898i	$0.574277\pi$
$578$		0			0
$579$	−7.46347	−	8.61330i	−0.310171	−	0.357957i
$580$		0			0
$581$	4.38360	−	5.05895i	0.181862	−	0.209880i
$582$		0			0
$583$	10.9862	+	37.4155i	0.455001	+	1.54959i
$584$		0			0
$585$	−8.25993	−	0.0526780i	−0.341506	−	0.00217797i
$586$		0			0
$587$	−15.0938	+	6.89313i	−0.622990	+	0.284510i	−0.701794	−	0.712380i	$-0.747617\pi$
$587$	−15.0938	+	6.89313i	−0.622990	+	0.284510i	0.0788040	+	0.996890i	$0.474890\pi$
$588$		0			0
$589$	−22.6560	−	14.5601i	−0.933524	−	0.599939i
$590$		0			0
$591$	−1.96502	+	13.6670i	−0.0808301	+	0.562186i
$592$		0			0
$593$	19.1142	+	29.7422i	0.784925	+	1.22137i	0.971058	+	0.238843i	$0.0767681\pi$
$593$	19.1142	+	29.7422i	0.784925	+	1.22137i	−0.186133	+	0.982525i	$0.559596\pi$
$594$		0			0
$595$	−33.7823	−	15.6890i	−1.38494	−	0.643186i
$596$		0			0
$597$		−	29.7839i		−	1.21897i
$598$		0			0
$599$	26.2065			1.07077			0.535385	−	0.844608i	$-0.320167\pi$
$599$	26.2065			1.07077			0.535385	+	0.844608i	$0.320167\pi$
$600$		0			0
$601$	−7.21608	−	2.11883i	−0.294350	−	0.0864290i	0.131223	−	0.991353i	$-0.458109\pi$
$601$	−7.21608	−	2.11883i	−0.294350	−	0.0864290i	−0.425574	+	0.904924i	$0.639928\pi$
$602$		0			0
$603$	4.89104	+	7.61060i	0.199178	+	0.309928i
$604$		0			0
$605$	−20.7239	+	68.9493i	−0.842545	+	2.80319i
$606$		0			0
$607$	20.4498	−	31.8205i	0.830033	−	1.29156i	−0.124130	−	0.992266i	$-0.539614\pi$
$607$	20.4498	−	31.8205i	0.830033	−	1.29156i	0.954162	−	0.299290i	$-0.0967498\pi$
$608$		0			0
$609$	−0.910047	−	1.99272i	−0.0368769	−	0.0807493i
$610$		0			0
$611$	7.60833	+	52.9171i	0.307800	+	2.14080i
$612$		0			0
$613$	12.0750	+	41.1237i	0.487705	+	1.66097i	0.724396	+	0.689384i	$0.242119\pi$
$613$	12.0750	+	41.1237i	0.487705	+	1.66097i	−0.236691	+	0.971585i	$0.576063\pi$
$614$		0			0
$615$	10.4364	+	12.2006i	0.420836	+	0.491976i
$616$		0			0
$617$	10.0116	−	8.67506i	0.403050	−	0.349245i	−0.429624	−	0.903008i	$-0.641354\pi$
$617$	10.0116	−	8.67506i	0.403050	−	0.349245i	0.832674	+	0.553763i	$0.186809\pi$
$618$		0			0
$619$	−4.61220	+	10.0993i	−0.185380	+	0.405926i	−0.979390	−	0.201979i	$-0.935263\pi$
$619$	−4.61220	+	10.0993i	−0.185380	+	0.405926i	0.794010	+	0.607905i	$0.207990\pi$
$620$		0			0
$621$	−2.59892	−	20.7834i	−0.104291	−	0.834009i
$622$		0			0
$623$	−35.0836	−	16.0221i	−1.40559	−	0.641913i
$624$		0			0
$625$	−2.92553	−	24.8282i	−0.117021	−	0.993129i
$626$		0			0
$627$	59.9917	+	51.9831i	2.39584	+	2.07600i
$628$		0			0
$629$	6.00319	−	1.76270i	0.239363	−	0.0702833i
$630$		0			0
$631$	5.79413	+	40.2990i	0.230660	+	1.60428i	0.695260	+	0.718758i	$0.255289\pi$
$631$	5.79413	+	40.2990i	0.230660	+	1.60428i	−0.464600	+	0.885521i	$0.653802\pi$
$632$		0			0
$633$	19.8008	−	9.04273i	0.787012	−	0.359416i
$634$		0			0
$635$	−22.7954	+	25.9707i	−0.904606	+	1.03062i
$636$		0			0
$637$	26.4317	+	3.80031i	1.04726	+	0.150574i
$638$		0			0
$639$	1.21008	−	0.777674i	0.0478702	−	0.0307643i
$640$		0			0
$641$	29.5180	+	8.66727i	1.16589	+	0.342337i	0.806719	−	0.590935i	$-0.201241\pi$
$641$	29.5180	+	8.66727i	1.16589	+	0.342337i	0.359172	+	0.933271i	$0.383059\pi$
$642$		0			0
$643$			19.6823i			0.776192i	0.921619	+	0.388096i	$0.126867\pi$
$643$			19.6823i			0.776192i	−0.921619	+	0.388096i	$0.873133\pi$
$644$		0			0
$645$	−0.0320073	−	0.00481049i	−0.00126029	−	0.000189413i
$646$		0			0
$647$	12.5210	−	42.6425i	0.492250	−	1.67645i	−0.220787	−	0.975322i	$-0.570863\pi$
$647$	12.5210	−	42.6425i	0.492250	−	1.67645i	0.713037	−	0.701127i	$-0.247319\pi$
$648$		0			0
$649$	23.9123	−	15.3675i	0.938639	−	0.603226i
$650$		0			0
$651$	4.17639	−	29.0474i	0.163686	−	1.13846i
$652$		0			0
$653$	−14.0822	+	21.9123i	−0.551078	+	0.857494i	−0.999337	−	0.0364096i	$-0.988408\pi$
$653$	−14.0822	+	21.9123i	−0.551078	+	0.857494i	0.448259	+	0.893904i	$0.352044\pi$
$654$		0			0
$655$	3.02034	+	10.5344i	0.118015	+	0.411614i
$656$		0			0
$657$	4.48548	−	0.644915i	0.174995	−	0.0251605i
$658$		0			0
$659$	29.9965	−	8.80777i	1.16850	−	0.343102i	0.360769	−	0.932655i	$-0.382514\pi$
$659$	29.9965	−	8.80777i	1.16850	−	0.343102i	0.807730	+	0.589553i	$0.200696\pi$
$660$		0			0
$661$	28.4279	−	32.8075i	1.10572	−	1.27606i	0.147800	−	0.989017i	$-0.452781\pi$
$661$	28.4279	−	32.8075i	1.10572	−	1.27606i	0.957916	−	0.287047i	$-0.0926737\pi$
$662$		0			0
$663$	34.4590	−	29.8589i	1.33828	−	1.15962i
$664$		0			0
$665$	41.1295	+	26.8045i	1.59493	+	1.03943i
$666$		0			0
$667$	−0.407758	−	1.48954i	−0.0157885	−	0.0576752i
$668$		0			0
$669$	4.74885	−	10.3985i	0.183601	−	0.402031i
$670$		0			0
$671$	−11.4140	−	13.1725i	−0.440633	−	0.508518i
$672$		0			0
$673$	37.3585	+	32.3713i	1.44006	+	1.24782i	0.918972	+	0.394322i	$0.129020\pi$
$673$	37.3585	+	32.3713i	1.44006	+	1.24782i	0.521091	+	0.853501i	$0.325525\pi$
$674$		0			0
$675$	−0.278520	+	21.8352i	−0.0107203	+	0.840436i
$676$		0			0
$677$	−19.7234	+	2.83579i	−0.758031	+	0.108988i	−0.510484	−	0.859888i	$-0.670534\pi$
$677$	−19.7234	+	2.83579i	−0.758031	+	0.108988i	−0.247547	+	0.968876i	$0.579624\pi$
$678$		0			0
$679$	−9.26150	−	20.2798i	−0.355424	−	0.778269i
$680$		0			0
$681$	22.5198	+	14.4726i	0.862960	+	0.554591i
$682$		0			0
$683$	6.73838	+	0.968833i	0.257837	+	0.0370714i	0.270021	−	0.962854i	$-0.412969\pi$
$683$	6.73838	+	0.968833i	0.257837	+	0.0370714i	−0.0121841	+	0.999926i	$0.503878\pi$
$684$		0			0
$685$	7.46942	+	16.6357i	0.285392	+	0.635617i
$686$		0			0
$687$	4.64036	−	15.8036i	0.177041	−	0.602946i
$688$		0			0
$689$	−29.5217			−1.12469
$690$		0			0
$691$	39.7191			1.51099			0.755493	−	0.655156i	$-0.227397\pi$
$691$	39.7191			1.51099			0.755493	+	0.655156i	$0.227397\pi$
$692$		0			0
$693$	−4.83429	+	16.4641i	−0.183639	+	0.625418i
$694$		0			0
$695$	27.5832	−	12.3848i	1.04629	−	0.469784i
$696$		0			0
$697$	−17.4021	−	2.50205i	−0.659153	−	0.0947719i
$698$		0			0
$699$	9.14403	+	5.87651i	0.345859	+	0.222270i
$700$		0			0
$701$	6.35331	+	13.9118i	0.239961	+	0.525442i	0.990847	−	0.134991i	$-0.0431004\pi$
$701$	6.35331	+	13.9118i	0.239961	+	0.525442i	−0.750886	+	0.660432i	$0.770373\pi$
$702$		0			0
$703$	−8.16239	+	1.17357i	−0.307850	+	0.0442622i
$704$		0			0
$705$	−46.0450	+	6.32083i	−1.73416	+	0.238056i
$706$		0			0
$707$	35.8730	+	31.0841i	1.34914	+	1.16904i
$708$		0			0
$709$	6.68818	+	7.71857i	0.251180	+	0.289877i	0.867311	−	0.497767i	$-0.165846\pi$
$709$	6.68818	+	7.71857i	0.251180	+	0.289877i	−0.616131	+	0.787643i	$0.711301\pi$
$710$		0			0
$711$	−2.16349	+	4.73738i	−0.0811372	+	0.177666i
$712$		0			0
$713$	6.19259	−	19.7391i	0.231914	−	0.739237i
$714$		0			0
$715$	−61.2650	−	39.9270i	−2.29118	−	1.49318i
$716$		0			0
$717$	11.0294	−	9.55704i	0.411901	−	0.356914i
$718$		0			0
$719$	11.0499	−	12.7523i	0.412092	−	0.475579i	−0.511320	−	0.859391i	$-0.670843\pi$
$719$	11.0499	−	12.7523i	0.412092	−	0.475579i	0.923412	+	0.383811i	$0.125389\pi$
$720$		0			0
$721$	30.3217	−	8.90325i	1.12924	−	0.331574i
$722$		0			0
$723$	−3.08544	+	0.443619i	−0.114749	+	0.0164984i
$724$		0			0
$725$	0.208794	+	1.59649i	0.00775441	+	0.0592923i
$726$		0			0
$727$	−28.1424	+	43.7905i	−1.04374	+	1.62410i	−0.302137	+	0.953264i	$0.597700\pi$
$727$	−28.1424	+	43.7905i	−1.04374	+	1.62410i	−0.741608	+	0.670834i	$0.765936\pi$
$728$		0			0
$729$	2.47921	−	17.2433i	0.0918227	−	0.638641i
$730$		0			0
$731$	0.0298163	−	0.0191617i	0.00110279	−	0.000708723i
$732$		0			0
$733$	11.8632	−	40.4023i	0.438177	−	1.49229i	−0.384147	−	0.923272i	$-0.625504\pi$
$733$	11.8632	−	40.4023i	0.438177	−	1.49229i	0.822323	−	0.569021i	$-0.192678\pi$
$734$		0			0
$735$	−3.45030	+	22.9570i	−0.127266	+	0.846783i
$736$		0			0
$737$			80.0912i			2.95020i
$738$		0			0
$739$	−24.6312	−	7.23238i	−0.906074	−	0.266047i	−0.204687	−	0.978828i	$-0.565618\pi$
$739$	−24.6312	−	7.23238i	−0.906074	−	0.266047i	−0.701388	+	0.712780i	$0.747436\pi$
$740$		0			0
$741$	−50.5559	+	32.4903i	−1.85722	+	1.19356i
$742$		0			0
$743$	16.1439	+	2.32115i	0.592263	+	0.0851546i	0.431928	−	0.901908i	$-0.357833\pi$
$743$	16.1439	+	2.32115i	0.592263	+	0.0851546i	0.160335	+	0.987063i	$0.448743\pi$
$744$		0			0
$745$	26.9792	+	23.6805i	0.988440	+	0.867587i
$746$		0			0
$747$	−1.28546	+	0.587051i	−0.0470326	+	0.0214791i
$748$		0			0
$749$	−9.52489	−	66.2470i	−0.348032	−	2.42061i
$750$		0			0
$751$	17.5226	−	5.14511i	0.639410	−	0.187748i	0.0540721	−	0.998537i	$-0.482780\pi$
$751$	17.5226	−	5.14511i	0.639410	−	0.187748i	0.585338	+	0.810789i	$0.300962\pi$
$752$		0			0
$753$	−10.9190	−	9.46138i	−0.397911	−	0.344792i
$754$		0			0
$755$	−17.0255	−	26.8673i	−0.619620	−	0.977802i
$756$		0			0
$757$	−39.1981	−	17.9012i	−1.42468	−	0.650629i	−0.453998	−	0.891003i	$-0.650003\pi$
$757$	−39.1981	−	17.9012i	−1.42468	−	0.650629i	−0.970680	+	0.240374i	$0.922730\pi$
$758$		0			0
$759$	−26.3471	+	54.9917i	−0.956339	+	1.99607i
$760$		0			0
$761$	18.6793	−	40.9019i	0.677124	−	1.48269i	−0.188539	−	0.982066i	$-0.560375\pi$
$761$	18.6793	−	40.9019i	0.677124	−	1.48269i	0.865662	−	0.500628i	$-0.166898\pi$
$762$		0			0
$763$	12.9452	−	11.2171i	0.468649	−	0.406086i
$764$		0			0
$765$	5.11142	+	5.97548i	0.184804	+	0.216044i
$766$		0			0
$767$	6.06265	+	20.6475i	0.218910	+	0.745538i
$768$		0			0
$769$	−4.77011	−	33.1769i	−0.172015	−	1.19639i	−0.874620	−	0.484809i	$-0.838889\pi$
$769$	−4.77011	−	33.1769i	−0.172015	−	1.19639i	0.702606	−	0.711579i	$-0.252020\pi$
$770$		0			0
$771$	−19.2663	−	42.1873i	−0.693858	−	1.51934i
$772$		0			0
$773$	−14.2686	+	22.2024i	−0.513206	+	0.798564i	−0.997063	−	0.0765826i	$-0.975599\pi$
$773$	−14.2686	+	22.2024i	−0.513206	+	0.798564i	0.483857	+	0.875147i	$0.339235\pi$
$774$		0			0
$775$	−9.20936	+	19.5035i	−0.330810	+	0.700586i
$776$		0			0
$777$	−4.85807	−	7.55931i	−0.174282	−	0.271189i
$778$		0			0
$779$	22.2335	+	6.52835i	0.796598	+	0.233902i
$780$		0			0
$781$	12.7345			0.455676
$782$		0			0
$783$		−	1.40638i		−	0.0502598i
$784$		0			0
$785$	11.5150	−	24.7947i	0.410989	−	0.884961i
$786$		0			0
$787$	−10.7330	−	16.7009i	−0.382592	−	0.595324i	0.595536	−	0.803328i	$-0.296940\pi$
$787$	−10.7330	−	16.7009i	−0.382592	−	0.595324i	−0.978128	+	0.208004i	$0.933303\pi$
$788$		0			0
$789$	−5.37860	+	37.4090i	−0.191483	+	1.33179i
$790$		0			0
$791$	−24.1306	−	15.5078i	−0.857986	−	0.551394i
$792$		0			0
$793$	12.0029	−	5.48155i	0.426236	−	0.194656i
$794$		0			0
$795$	0.163675	−	25.6644i	0.00580497	−	0.910221i
$796$		0			0
$797$	−4.02087	−	13.6938i	−0.142426	−	0.485060i	0.857122	−	0.515114i	$-0.172250\pi$
$797$	−4.02087	−	13.6938i	−0.142426	−	0.485060i	−0.999548	+	0.0300538i	$0.990432\pi$
$798$		0			0
$799$	33.3283	−	38.4629i	1.17907	−	1.36072i
$800$		0			0
$801$	5.33210	+	6.15357i	0.188401	+	0.217426i
$802$		0			0
$803$	36.4931	+	16.6658i	1.28781	+	0.588124i
$804$		0			0
$805$	−11.5177	+	35.9098i	−0.405946	+	1.26565i
$806$		0			0
$807$	17.8838	+	8.16726i	0.629539	+	0.287501i
$808$		0			0
$809$	−2.14146	−	2.47138i	−0.0752897	−	0.0868889i	0.716855	−	0.697222i	$-0.245581\pi$
$809$	−2.14146	−	2.47138i	−0.0752897	−	0.0868889i	−0.792145	+	0.610333i	$0.791035\pi$
$810$		0			0
$811$	−16.5784	+	19.1325i	−0.582146	+	0.671832i	−0.968065	−	0.250701i	$-0.919339\pi$
$811$	−16.5784	+	19.1325i	−0.582146	+	0.671832i	0.385919	+	0.922533i	$0.373884\pi$
$812$		0			0
$813$	−9.77453	−	33.2890i	−0.342808	−	1.16750i
$814$		0			0
$815$	48.2650	+	0.307811i	1.69065	+	0.0107822i
$816$		0			0
$817$	−0.0424925	+	0.0194057i	−0.00148662	+	0.000678919i
$818$		0			0
$819$	−10.9283	−	7.02321i	−0.381867	−	0.245411i
$820$		0			0
$821$	−0.0312117	+	0.217082i	−0.00108930	+	0.00757623i	−0.990359	−	0.138526i	$-0.955764\pi$
$821$	−0.0312117	+	0.217082i	−0.00108930	+	0.00757623i	0.989270	+	0.146102i	$0.0466727\pi$
$822$		0			0
$823$	9.68091	+	15.0638i	0.337455	+	0.525090i	0.967963	−	0.251092i	$-0.0807898\pi$
$823$	9.68091	+	15.0638i	0.337455	+	0.525090i	−0.630508	+	0.776183i	$0.717153\pi$
$824$		0			0
$825$	35.0497	−	53.0387i	1.22028	−	1.84657i
$826$		0			0
$827$		−	20.3212i		−	0.706638i	−0.935503	−	0.353319i	$-0.885053\pi$
$827$		−	20.3212i		−	0.706638i	0.935503	−	0.353319i	$-0.114947\pi$
$828$		0			0
$829$	27.7287			0.963059			0.481529	−	0.876430i	$-0.340081\pi$
$829$	27.7287			0.963059			0.481529	+	0.876430i	$0.340081\pi$
$830$		0			0
$831$	9.30736	+	2.73289i	0.322869	+	0.0948028i
$832$		0			0
$833$	−13.7436	−	21.3855i	−0.476189	−	0.740965i
$834$		0			0
$835$	1.70565	+	0.512663i	0.0590266	+	0.0177414i
$836$		0			0
$837$	10.1854	−	15.8489i	0.352060	−	0.547817i
$838$		0			0
$839$	−12.2392	−	26.8001i	−0.422544	−	0.925242i	−0.994478	−	0.104943i	$-0.966534\pi$
$839$	−12.2392	−	26.8001i	−0.422544	−	0.925242i	0.571934	−	0.820300i	$-0.306193\pi$
$840$		0			0
$841$	4.11237	+	28.6022i	0.141806	+	0.986282i
$842$		0			0
$843$	2.34653	+	7.99155i	0.0808188	+	0.275243i
$844$		0			0
$845$	19.9802	−	17.0911i	0.687340	−	0.587951i
$846$		0			0
$847$	−85.5717	+	74.1483i	−2.94028	+	2.54777i
$848$		0			0
$849$	9.40611	−	20.5965i	0.322817	−	0.706870i
$850$		0			0
$851$	−2.52503	−	5.80956i	−0.0865568	−	0.199149i
$852$		0			0
$853$	−33.6529	−	15.3688i	−1.15225	−	0.526217i	−0.254656	−	0.967032i	$-0.581962\pi$
$853$	−33.6529	−	15.3688i	−1.15225	−	0.526217i	−0.897598	+	0.440815i	$0.854690\pi$
$854$		0			0
$855$	−5.54752	−	8.75437i	−0.189721	−	0.299393i
$856$		0			0
$857$	11.8888	+	10.3017i	0.406112	+	0.351898i	0.833837	−	0.552011i	$-0.186139\pi$
$857$	11.8888	+	10.3017i	0.406112	+	0.351898i	−0.427725	+	0.903909i	$0.640685\pi$
$858$		0			0
$859$	2.23917	−	0.657481i	0.0763996	−	0.0224329i	−0.243309	−	0.969949i	$-0.578233\pi$
$859$	2.23917	−	0.657481i	0.0763996	−	0.0224329i	0.319709	+	0.947516i	$0.396415\pi$
$860$		0			0
$861$	3.59344	+	24.9929i	0.122464	+	0.851757i
$862$		0			0
$863$	13.2059	−	6.03093i	0.449534	−	0.205295i	−0.177766	−	0.984073i	$-0.556887\pi$
$863$	13.2059	−	6.03093i	0.449534	−	0.205295i	0.627300	+	0.778777i	$0.284160\pi$
$864$		0			0
$865$	7.84285	−	8.93535i	0.266665	−	0.303811i
$866$		0			0
$867$	−10.4119	−	1.49700i	−0.353606	−	0.0508408i
$868$		0			0
$869$	−38.7875	+	24.9272i	−1.31578	+	0.845599i
$870$		0			0
$871$	−58.1779	−	17.0826i	−1.97128	−	0.578821i
$872$		0			0
$873$			4.70663i			0.159295i
$874$		0			0
$875$	17.0141	−	35.4451i	0.575183	−	1.19826i
$876$		0			0
$877$	8.82943	−	30.0703i	0.298149	−	1.01540i	−0.665092	−	0.746761i	$-0.731608\pi$
$877$	8.82943	−	30.0703i	0.298149	−	1.01540i	0.963241	−	0.268640i	$-0.0865741\pi$
$878$		0			0
$879$	6.32726	−	4.06628i	0.213413	−	0.137152i
$880$		0			0
$881$	−1.57689	+	10.9675i	−0.0531267	+	0.369504i	0.945863	+	0.324566i	$0.105218\pi$
$881$	−1.57689	+	10.9675i	−0.0531267	+	0.369504i	−0.998990	+	0.0449384i	$0.985691\pi$
$882$		0			0
$883$	21.7623	−	33.8628i	0.732360	−	1.13957i	−0.252730	−	0.967537i	$-0.581328\pi$
$883$	21.7623	−	33.8628i	0.732360	−	1.13957i	0.985090	−	0.172038i	$-0.0550352\pi$
$884$		0			0
$885$	−17.9833	+	5.15602i	−0.604501	+	0.173318i
$886$		0			0
$887$	22.0600	−	3.17175i	0.740703	−	0.106497i	0.238374	−	0.971173i	$-0.423386\pi$
$887$	22.0600	−	3.17175i	0.740703	−	0.106497i	0.502329	+	0.864676i	$0.332477\pi$
$888$		0			0
$889$	−52.1441	+	15.3109i	−1.74886	+	0.513510i
$890$		0			0
$891$	−45.9505	+	53.0297i	−1.53940	+	1.77656i
$892$		0			0
$893$	−50.6946	+	43.9271i	−1.69643	+	1.46997i
$894$		0			0
$895$	8.08971	−	12.4131i	0.270409	−	0.414923i
$896$		0			0
$897$	−34.3262	−	30.8676i	−1.14612	−	1.03064i
$898$		0			0
$899$	0.577046	−	1.26356i	0.0192456	−	0.0421419i
$900$		0			0
$901$	18.4041	+	21.2395i	0.613130	+	0.707590i
$902$		0			0
$903$	−0.0384697	−	0.0333342i	−0.00128019	−	0.00110929i
$904$		0			0
$905$	26.4462	−	3.63041i	0.879103	−	0.120679i
$906$		0			0
$907$	−10.6025	+	1.52441i	−0.352052	+	0.0506174i	−0.316072	−	0.948735i	$-0.602364\pi$
$907$	−10.6025	+	1.52441i	−0.352052	+	0.0506174i	−0.0359794	+	0.999353i	$0.511455\pi$
$908$		0			0
$909$	−4.16278	−	9.11521i	−0.138071	−	0.302332i
$910$		0			0
$911$	15.9957	+	10.2798i	0.529960	+	0.340584i	0.778101	−	0.628139i	$-0.216183\pi$
$911$	15.9957	+	10.2798i	0.529960	+	0.340584i	−0.248141	+	0.968724i	$0.579820\pi$
$912$		0			0
$913$	−12.3835	−	1.78048i	−0.409834	−	0.0589252i
$914$		0			0
$915$	4.69878	+	10.4650i	0.155337	+	0.345962i
$916$		0			0
$917$	−4.85561	+	16.5367i	−0.160346	+	0.546089i
$918$		0			0
$919$	−5.15507			−0.170050			−0.0850251	−	0.996379i	$-0.527097\pi$
$919$	−5.15507			−0.170050			−0.0850251	+	0.996379i	$0.527097\pi$
$920$		0			0
$921$	38.5134			1.26906
$922$		0			0
$923$	−2.71613	+	9.25028i	−0.0894024	+	0.304477i
$924$		0			0
$925$	1.77966	+	6.35994i	0.0585148	+	0.209114i
$926$		0			0
$927$	−6.60359	−	0.949452i	−0.216890	−	0.0311841i
$928$		0			0
$929$	29.6498	+	19.0548i	0.972780	+	0.625168i	0.927507	−	0.373807i	$-0.121948\pi$
$929$	29.6498	+	19.0548i	0.972780	+	0.625168i	0.0452734	+	0.998975i	$0.485584\pi$
$930$		0			0
$931$	13.9186	+	30.4775i	0.456164	+	0.998859i
$932$		0			0
$933$	12.8863	−	1.85277i	0.421878	−	0.0606568i
$934$		0			0
$935$	9.46760	+	68.9682i	0.309624	+	2.25550i
$936$		0			0
$937$	−35.4708	−	30.7356i	−1.15878	−	1.00409i	−0.999859	−	0.0167983i	$-0.994653\pi$
$937$	−35.4708	−	30.7356i	−1.15878	−	1.00409i	−0.158922	−	0.987291i	$-0.550802\pi$
$938$		0			0
$939$	−12.1768	−	14.0528i	−0.397376	−	0.458596i
$940$		0			0
$941$	14.2933	−	31.2980i	0.465949	−	1.02029i	−0.520141	−	0.854080i	$-0.674121\pi$
$941$	14.2933	−	31.2980i	0.465949	−	1.02029i	0.986091	−	0.166207i	$-0.0531520\pi$
$942$		0			0
$943$	−0.327460	+	17.7971i	−0.0106636	+	0.579553i
$944$		0			0
$945$	−18.7509	+	28.7719i	−0.609967	+	0.935949i
$946$		0			0
$947$	−7.77145	+	6.73400i	−0.252538	+	0.218826i	−0.771925	−	0.635714i	$-0.780706\pi$
$947$	−7.77145	+	6.73400i	−0.252538	+	0.218826i	0.519387	+	0.854539i	$0.326160\pi$
$948$		0			0
$949$	−19.8896	+	22.9538i	−0.645642	+	0.745111i
$950$		0			0
$951$	11.3126	−	3.32169i	0.366837	−	0.107713i
$952$		0			0
$953$	−51.2395	+	7.36713i	−1.65981	+	0.238645i	−0.907466	−	0.420126i	$-0.861986\pi$
$953$	−51.2395	+	7.36713i	−1.65981	+	0.238645i	−0.752344	+	0.658771i	$0.771077\pi$
$954$		0			0
$955$	12.6747	+	44.2072i	0.410145	+	1.43051i
$956$		0			0
$957$	−2.21358	+	3.44439i	−0.0715547	+	0.111341i
$958$		0			0
$959$	−4.08144	+	28.3870i	−0.131796	+	0.916664i
$960$		0			0
$961$	−10.4249	+	6.69967i	−0.336287	+	0.216118i
$962$		0			0
$963$	−3.98069	+	13.5570i	−0.128276	+	0.436867i
$964$		0			0
$965$	−1.95791	+	13.0272i	−0.0630272	+	0.419361i
$966$		0			0
$967$		−	24.4155i		−	0.785151i	−0.919720	−	0.392575i	$-0.871584\pi$
$967$		−	24.4155i		−	0.785151i	0.919720	−	0.392575i	$-0.128416\pi$
$968$		0			0
$969$	54.8923	+	16.1178i	1.76339	+	0.517779i
$970$		0			0
$971$	−26.6095	+	17.1009i	−0.853939	+	0.548793i	−0.892801	−	0.450451i	$-0.851263\pi$
$971$	−26.6095	+	17.1009i	−0.853939	+	0.548793i	0.0388620	+	0.999245i	$0.487627\pi$
$972$		0			0
$973$	47.0678	+	6.76732i	1.50892	+	0.216950i
$974$		0			0
$975$	31.0513	+	36.7726i	0.994439	+	1.17766i
$976$		0			0
$977$	43.1882	−	19.7234i	1.38171	−	0.631007i	0.420620	−	0.907237i	$-0.361812\pi$
$977$	43.1882	−	19.7234i	1.38171	−	0.631007i	0.961092	+	0.276230i	$0.0890852\pi$
$978$		0			0
$979$	10.2587	+	71.3508i	0.327869	+	2.28038i
$980$		0			0
$981$	−3.46964	+	1.01878i	−0.110777	+	0.0325271i
$982$		0			0
$983$	−38.4421	−	33.3103i	−1.22611	−	1.06243i	−0.996008	−	0.0892679i	$-0.971547\pi$
$983$	−38.4421	−	33.3103i	−1.22611	−	1.06243i	−0.230106	−	0.973166i	$-0.573907\pi$
$984$		0			0
$985$	13.4810	−	8.54270i	0.429539	−	0.272193i
$986$		0			0
$987$	−66.4881	−	30.3641i	−2.11634	−	0.966501i
$988$		0			0
$989$	−0.0229963	−	0.0275472i	−0.000731239	−	0.000875949i
$990$		0			0
$991$	20.3286	−	44.5134i	0.645760	−	1.41402i	−0.249457	−	0.968386i	$-0.580252\pi$
$991$	20.3286	−	44.5134i	0.645760	−	1.41402i	0.895217	−	0.445631i	$-0.147020\pi$
$992$		0			0
$993$	43.5926	−	37.7732i	1.38337	−	1.19870i
$994$		0			0
$995$	−26.1610	+	22.3781i	−0.829358	+	0.709433i
$996$		0			0
$997$	−5.77068	−	19.6531i	−0.182759	−	0.622421i	−0.999000	−	0.0447092i	$-0.985764\pi$
$997$	−5.77068	−	19.6531i	−0.182759	−	0.622421i	0.816241	−	0.577712i	$-0.196054\pi$
$998$		0			0
$999$	−0.820967	−	5.70995i	−0.0259742	−	0.180655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.29.3	✓	120
5.4	even	2	inner	460.2.s.a.29.10	yes	120
23.4	even	11	inner	460.2.s.a.349.10	yes	120
115.4	even	22	inner	460.2.s.a.349.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.29.3	✓	120	1.1	even	1	trivial
460.2.s.a.29.10	yes	120	5.4	even	2	inner
460.2.s.a.349.3	yes	120	115.4	even	22	inner
460.2.s.a.349.10	yes	120	23.4	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.545020 + 1.85617i) q^{3} +(2.03988 - 0.915906i) q^{5} +(3.48084 + 0.500469i) q^{7} +(-0.624547 - 0.401372i) q^{9} +O(q^{10})\)	\(q+(-0.545020 + 1.85617i) q^{3} +(2.03988 - 0.915906i) q^{5} +(3.48084 + 0.500469i) q^{7} +(-0.624547 - 0.401372i) q^{9} +(-2.73032 - 5.97856i) q^{11} +(4.92515 - 0.708129i) q^{13} +(0.588298 + 4.28555i) q^{15} +(-3.57985 - 3.10196i) q^{17} +(4.08843 + 4.71830i) q^{19} +(-2.82608 + 6.18824i) q^{21} +(-2.66660 + 3.98613i) q^{23} +(3.32223 - 3.73668i) q^{25} +(-3.30065 + 2.86003i) q^{27} +(-0.210877 + 0.243365i) q^{29} +(-4.13895 + 1.21531i) q^{31} +(12.5853 - 1.80949i) q^{33} +(7.55887 - 2.16722i) q^{35} +(-0.714105 + 1.11117i) q^{37} +(-1.36990 + 9.52784i) q^{39} +(3.12238 - 2.00663i) q^{41} +(-0.00210803 + 0.00717928i) q^{43} +(-1.64162 - 0.246725i) q^{45} +10.7443i q^{47} +(5.14930 + 1.51197i) q^{49} +(7.70884 - 4.95417i) q^{51} +(-5.87268 - 0.844364i) q^{53} +(-11.0453 - 9.69484i) q^{55} +(-10.9862 + 5.01724i) q^{57} +(0.615479 + 4.28075i) q^{59} +(2.54449 - 0.747130i) q^{61} +(-1.97307 - 1.70968i) q^{63} +(9.39814 - 5.95547i) q^{65} +(-11.0846 - 5.06216i) q^{67} +(-5.94557 - 7.12218i) q^{69} +(-0.804883 + 1.76245i) q^{71} +(-4.61309 + 3.99726i) q^{73} +(5.12521 + 8.20318i) q^{75} +(-6.51170 - 22.1768i) q^{77} +(-0.998355 - 6.94371i) q^{79} +(-4.43499 - 9.71127i) q^{81} +(1.02912 - 1.60134i) q^{83} +(-10.1436 - 3.04882i) q^{85} +(-0.336793 - 0.524061i) q^{87} +(-10.5233 - 3.08993i) q^{89} +17.4980 q^{91} -8.34496i q^{93} +(12.6614 + 5.88015i) q^{95} +(-3.42753 - 5.33334i) q^{97} +(-0.694415 + 4.82976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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