LMFDB - Embedded newform 460.2.m.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, 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:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	460.101
Dual form			460.2.m.b.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.671975 - 0.775501i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.80075 + 3.94308i) q^{7} +(0.277094 - 1.92723i) q^{9} +O(q^{10})$	\(q+(-0.671975 - 0.775501i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.80075 + 3.94308i) q^{7} +(0.277094 - 1.92723i) q^{9} +(-6.12952 - 1.79979i) q^{11} +(-0.327074 - 0.716192i) q^{13} +(0.671975 - 0.775501i) q^{15} +(-5.62371 - 3.61414i) q^{17} +(0.285753 - 0.183642i) q^{19} +(4.26792 - 1.25317i) q^{21} +(2.98491 + 3.75371i) q^{23} +(-0.959493 + 0.281733i) q^{25} +(-4.27049 + 2.74448i) q^{27} +(-3.76290 - 2.41827i) q^{29} +(-5.28851 + 6.10326i) q^{31} +(2.72315 + 5.96286i) q^{33} +(-4.15922 - 1.22126i) q^{35} +(-0.127505 + 0.886813i) q^{37} +(-0.335622 + 0.734910i) q^{39} +(0.293503 + 2.04136i) q^{41} +(2.23961 + 2.58465i) q^{43} +1.94705 q^{45} +10.6053 q^{47} +(-7.72119 - 8.91073i) q^{49} +(0.976227 + 6.78981i) q^{51} +(-3.77809 + 8.27286i) q^{53} +(0.909149 - 6.32327i) q^{55} +(-0.334433 - 0.0981985i) q^{57} +(-5.63693 - 12.3432i) q^{59} +(4.70949 - 5.43504i) q^{61} +(7.10025 + 4.56305i) q^{63} +(0.662355 - 0.425670i) q^{65} +(1.54435 - 0.453463i) q^{67} +(0.905216 - 4.83720i) q^{69} +(-5.04548 + 1.48149i) q^{71} +(1.83451 - 1.17897i) q^{73} +(0.863239 + 0.554770i) q^{75} +(18.1344 - 20.9282i) q^{77} +(0.756796 + 1.65715i) q^{79} +(-0.606531 - 0.178094i) q^{81} +(-0.323297 + 2.24858i) q^{83} +(2.77702 - 6.08082i) q^{85} +(0.653206 + 4.54315i) q^{87} +(3.41117 + 3.93670i) q^{89} +3.41298 q^{91} +8.28683 q^{93} +(0.222440 + 0.256709i) q^{95} +(1.45218 + 10.1002i) q^{97} +(-5.16706 + 11.3143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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
$3$	−0.671975	−	0.775501i	−0.387965	−	0.447736i	0.527849	−	0.849338i	$-0.322999\pi$
$3$	−0.671975	−	0.775501i	−0.387965	−	0.447736i	−0.915814	+	0.401603i	$0.868453\pi$
$4$		0			0
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$6$		0			0
$7$	−1.80075	+	3.94308i	−0.680618	+	1.49034i	0.181370	+	0.983415i	$0.441947\pi$
$7$	−1.80075	+	3.94308i	−0.680618	+	1.49034i	−0.861987	+	0.506930i	$0.830780\pi$
$8$		0			0
$9$	0.277094	−	1.92723i	0.0923646	−	0.642410i
$10$		0			0
$11$	−6.12952	−	1.79979i	−1.84812	−	0.542657i	−0.999916	−	0.0129888i	$-0.995865\pi$
$11$	−6.12952	−	1.79979i	−1.84812	−	0.542657i	−0.848205	−	0.529668i	$-0.822316\pi$
$12$		0			0
$13$	−0.327074	−	0.716192i	−0.0907140	−	0.198636i	0.858837	−	0.512249i	$-0.171188\pi$
$13$	−0.327074	−	0.716192i	−0.0907140	−	0.198636i	−0.949551	+	0.313613i	$0.898460\pi$
$14$		0			0
$15$	0.671975	−	0.775501i	0.173503	−	0.200233i
$16$		0			0
$17$	−5.62371	−	3.61414i	−1.36395	−	0.876558i	−0.365425	−	0.930841i	$-0.619076\pi$
$17$	−5.62371	−	3.61414i	−1.36395	−	0.876558i	−0.998526	+	0.0542827i	$0.982713\pi$
$18$		0			0
$19$	0.285753	−	0.183642i	0.0655562	−	0.0421304i	−0.507452	−	0.861680i	$-0.669413\pi$
$19$	0.285753	−	0.183642i	0.0655562	−	0.0421304i	0.573008	+	0.819550i	$0.305776\pi$
$20$		0			0
$21$	4.26792	−	1.25317i	0.931337	−	0.273465i
$22$		0			0
$23$	2.98491	+	3.75371i	0.622397	+	0.782702i
$23$	2.98491	+	3.75371i	0.622397	+	0.782702i
$24$		0			0
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$		0			0
$27$	−4.27049	+	2.74448i	−0.821856	+	0.528174i
$28$		0			0
$29$	−3.76290	−	2.41827i	−0.698753	−	0.449061i	0.142435	−	0.989804i	$-0.454507\pi$
$29$	−3.76290	−	2.41827i	−0.698753	−	0.449061i	−0.841188	+	0.540743i	$0.818143\pi$
$30$		0			0
$31$	−5.28851	+	6.10326i	−0.949844	+	1.09618i	0.0454202	+	0.998968i	$0.485537\pi$
$31$	−5.28851	+	6.10326i	−0.949844	+	1.09618i	−0.995264	+	0.0972101i	$0.969008\pi$
$32$		0			0
$33$	2.72315	+	5.96286i	0.474039	+	1.03800i
$34$		0			0
$35$	−4.15922	−	1.22126i	−0.703037	−	0.206430i
$36$		0			0
$37$	−0.127505	+	0.886813i	−0.0209616	+	0.145791i	−0.997614	−	0.0690328i	$-0.978009\pi$
$37$	−0.127505	+	0.886813i	−0.0209616	+	0.145791i	0.976653	+	0.214824i	$0.0689178\pi$
$38$		0			0
$39$	−0.335622	+	0.734910i	−0.0537426	+	0.117680i
$40$		0			0
$41$	0.293503	+	2.04136i	0.0458374	+	0.318806i	0.999821	+	0.0189458i	$0.00603099\pi$
$41$	0.293503	+	2.04136i	0.0458374	+	0.318806i	−0.953983	+	0.299860i	$0.903060\pi$
$42$		0			0
$43$	2.23961	+	2.58465i	0.341538	+	0.394156i	0.900370	−	0.435125i	$-0.143296\pi$
$43$	2.23961	+	2.58465i	0.341538	+	0.394156i	−0.558832	+	0.829281i	$0.688750\pi$
$44$		0			0
$45$	1.94705			0.290249
$46$		0			0
$47$	10.6053			1.54694			0.773468	−	0.633836i	$-0.218520\pi$
$47$	10.6053			1.54694			0.773468	+	0.633836i	$0.218520\pi$
$48$		0			0
$49$	−7.72119	−	8.91073i	−1.10303	−	1.27296i
$50$		0			0
$51$	0.976227	+	6.78981i	0.136699	+	0.950763i
$52$		0			0
$53$	−3.77809	+	8.27286i	−0.518960	+	1.13636i	0.450871	+	0.892589i	$0.351113\pi$
$53$	−3.77809	+	8.27286i	−0.518960	+	1.13636i	−0.969832	+	0.243776i	$0.921614\pi$
$54$		0			0
$55$	0.909149	−	6.32327i	0.122590	−	0.852629i
$56$		0			0
$57$	−0.334433	−	0.0981985i	−0.0442968	−	0.0130067i
$58$		0			0
$59$	−5.63693	−	12.3432i	−0.733866	−	1.60694i	−0.793389	−	0.608715i	$-0.791685\pi$
$59$	−5.63693	−	12.3432i	−0.733866	−	1.60694i	0.0595236	−	0.998227i	$-0.481042\pi$
$60$		0			0
$61$	4.70949	−	5.43504i	0.602989	−	0.695886i	−0.369395	−	0.929272i	$-0.620435\pi$
$61$	4.70949	−	5.43504i	0.602989	−	0.695886i	0.972384	+	0.233386i	$0.0749806\pi$
$62$		0			0
$63$	7.10025	+	4.56305i	0.894547	+	0.574891i
$64$		0			0
$65$	0.662355	−	0.425670i	0.0821550	−	0.0527978i
$66$		0			0
$67$	1.54435	−	0.453463i	0.188673	−	0.0553993i	−0.186031	−	0.982544i	$-0.559563\pi$
$67$	1.54435	−	0.453463i	0.188673	−	0.0553993i	0.374704	+	0.927145i	$0.377744\pi$
$68$		0			0
$69$	0.905216	−	4.83720i	0.108975	−	0.582330i
$70$		0			0
$71$	−5.04548	+	1.48149i	−0.598789	+	0.175820i	−0.567060	−	0.823676i	$-0.691919\pi$
$71$	−5.04548	+	1.48149i	−0.598789	+	0.175820i	−0.0317283	+	0.999497i	$0.510101\pi$
$72$		0			0
$73$	1.83451	−	1.17897i	0.214713	−	0.137988i	−0.428864	−	0.903369i	$-0.641086\pi$
$73$	1.83451	−	1.17897i	0.214713	−	0.137988i	0.643577	+	0.765381i	$0.277450\pi$
$74$		0			0
$75$	0.863239	+	0.554770i	0.0996783	+	0.0640594i
$76$		0			0
$77$	18.1344	−	20.9282i	2.06661	−	2.38500i
$78$		0			0
$79$	0.756796	+	1.65715i	0.0851462	+	0.186444i	0.947416	−	0.320006i	$-0.103685\pi$
$79$	0.756796	+	1.65715i	0.0851462	+	0.186444i	−0.862269	+	0.506450i	$0.830958\pi$
$80$		0			0
$81$	−0.606531	−	0.178094i	−0.0673923	−	0.0197882i
$82$		0			0
$83$	−0.323297	+	2.24858i	−0.0354865	+	0.246814i	−0.999842	−	0.0177974i	$-0.994335\pi$
$83$	−0.323297	+	2.24858i	−0.0354865	+	0.246814i	0.964355	+	0.264611i	$0.0852437\pi$
$84$		0			0
$85$	2.77702	−	6.08082i	0.301210	−	0.659557i
$86$		0			0
$87$	0.653206	+	4.54315i	0.0700310	+	0.487077i
$88$		0			0
$89$	3.41117	+	3.93670i	0.361583	+	0.417289i	0.907170	−	0.420765i	$-0.138238\pi$
$89$	3.41117	+	3.93670i	0.361583	+	0.417289i	−0.545586	+	0.838055i	$0.683693\pi$
$90$		0			0
$91$	3.41298			0.357778
$92$		0			0
$93$	8.28683			0.859304
$94$		0			0
$95$	0.222440	+	0.256709i	0.0228218	+	0.0263378i
$96$		0			0
$97$	1.45218	+	10.1002i	0.147447	+	1.02552i	0.920379	+	0.391028i	$0.127880\pi$
$97$	1.45218	+	10.1002i	0.147447	+	1.02552i	−0.772932	+	0.634489i	$0.781211\pi$
$98$		0			0
$99$	−5.16706	+	11.3143i	−0.519309	+	1.13713i
$100$		0			0
$101$	0.463309	−	3.22239i	0.0461010	−	0.320639i	−0.953701	−	0.300755i	$-0.902761\pi$
$101$	0.463309	−	3.22239i	0.0461010	−	0.320639i	0.999802	−	0.0198840i	$-0.00632968\pi$
$102$		0			0
$103$	−10.9026	−	3.20128i	−1.07426	−	0.315432i	−0.303681	−	0.952774i	$-0.598216\pi$
$103$	−10.9026	−	3.20128i	−1.07426	−	0.315432i	−0.770581	+	0.637342i	$0.780034\pi$
$104$		0			0
$105$	1.84781	+	4.04613i	0.180328	+	0.394862i
$106$		0			0
$107$	−1.04850	+	1.21003i	−0.101362	+	0.116978i	−0.804164	−	0.594407i	$-0.797387\pi$
$107$	−1.04850	+	1.21003i	−0.101362	+	0.116978i	0.702802	+	0.711386i	$0.251932\pi$
$108$		0			0
$109$	4.00352	+	2.57290i	0.383467	+	0.246440i	0.718146	−	0.695893i	$-0.244991\pi$
$109$	4.00352	+	2.57290i	0.383467	+	0.246440i	−0.334678	+	0.942333i	$0.608628\pi$
$110$		0			0
$111$	0.773404	−	0.497037i	0.0734083	−	0.0471766i
$112$		0			0
$113$	7.44200	−	2.18517i	0.700085	−	0.205563i	0.0877274	−	0.996145i	$-0.472040\pi$
$113$	7.44200	−	2.18517i	0.700085	−	0.205563i	0.612357	+	0.790581i	$0.290221\pi$
$114$		0			0
$115$	−3.29070	+	3.48874i	−0.306859	+	0.325326i
$116$		0			0
$117$	−1.47090	+	0.431894i	−0.135985	+	0.0399287i
$118$		0			0
$119$	24.3777	−	15.6666i	2.23470	−	1.43616i
$120$		0			0
$121$	25.0780	+	16.1167i	2.27982	+	1.46515i
$122$		0			0
$123$	1.38585	−	1.59935i	0.124958	−	0.144209i
$124$		0			0
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$		0			0
$127$	−18.9224	−	5.55611i	−1.67909	−	0.493025i	−0.703145	−	0.711046i	$-0.748222\pi$
$127$	−18.9224	−	5.55611i	−1.67909	−	0.493025i	−0.975944	+	0.218021i	$0.930040\pi$
$128$		0			0
$129$	0.499435	−	3.47365i	0.0439728	−	0.305838i
$130$		0			0
$131$	6.45716	−	14.1392i	0.564165	−	1.23535i	−0.385682	−	0.922632i	$-0.626034\pi$
$131$	6.45716	−	14.1392i	0.564165	−	1.23535i	0.949847	−	0.312716i	$-0.101239\pi$
$132$		0			0
$133$	0.209548	+	1.45744i	0.0181701	+	0.126376i
$134$		0			0
$135$	−3.32429	−	3.83644i	−0.286110	−	0.330188i
$136$		0			0
$137$	6.24950			0.533931			0.266965	−	0.963706i	$-0.413979\pi$
$137$	6.24950			0.533931			0.266965	+	0.963706i	$0.413979\pi$
$138$		0			0
$139$	−11.7737			−0.998632			−0.499316	−	0.866420i	$-0.666415\pi$
$139$	−11.7737			−0.998632			−0.499316	+	0.866420i	$0.666415\pi$
$140$		0			0
$141$	−7.12647	−	8.22439i	−0.600157	−	0.692618i
$142$		0			0
$143$	0.715812	+	4.97858i	0.0598592	+	0.416330i
$144$		0			0
$145$	1.85814	−	4.06875i	0.154310	−	0.337892i
$146$		0			0
$147$	−1.72183	+	11.9756i	−0.142014	+	0.987729i
$148$		0			0
$149$	−13.3615	−	3.92328i	−1.09461	−	0.321408i	−0.315904	−	0.948791i	$-0.602308\pi$
$149$	−13.3615	−	3.92328i	−1.09461	−	0.321408i	−0.778711	+	0.627383i	$0.784126\pi$
$150$		0			0
$151$	8.07405	+	17.6797i	0.657057	+	1.43875i	0.885239	+	0.465136i	$0.153995\pi$
$151$	8.07405	+	17.6797i	0.657057	+	1.43875i	−0.228182	+	0.973618i	$0.573278\pi$
$152$		0			0
$153$	−8.52358	+	9.83673i	−0.689090	+	0.795252i
$154$		0			0
$155$	−6.79377	−	4.36609i	−0.545689	−	0.350693i
$156$		0			0
$157$	−5.07820	+	3.26356i	−0.405284	+	0.260460i	−0.727364	−	0.686252i	$-0.759255\pi$
$157$	−5.07820	+	3.26356i	−0.405284	+	0.260460i	0.322079	+	0.946713i	$0.395618\pi$
$158$		0			0
$159$	8.95439	−	2.62925i	0.710130	−	0.208513i
$160$		0			0
$161$	−20.1762	+	5.01028i	−1.59011	+	0.394865i
$162$		0			0
$163$	−5.81932	+	1.70871i	−0.455804	+	0.133836i	−0.501572	−	0.865116i	$-0.667245\pi$
$163$	−5.81932	+	1.70871i	−0.455804	+	0.133836i	0.0457677	+	0.998952i	$0.485427\pi$
$164$		0			0
$165$	−5.51463	+	3.54404i	−0.429313	+	0.275903i
$166$		0			0
$167$	−14.1506	−	9.09402i	−1.09500	−	0.703716i	−0.137028	−	0.990567i	$-0.543755\pi$
$167$	−14.1506	−	9.09402i	−1.09500	−	0.703716i	−0.957975	+	0.286851i	$0.907392\pi$
$168$		0			0
$169$	8.10724	−	9.35625i	0.623633	−	0.719711i
$170$		0			0
$171$	−0.274740	−	0.601597i	−0.0210099	−	0.0460053i
$172$		0			0
$173$	6.26730	+	1.84024i	0.476494	+	0.139911i	0.511156	−	0.859488i	$-0.329217\pi$
$173$	6.26730	+	1.84024i	0.476494	+	0.139911i	−0.0346624	+	0.999399i	$0.511036\pi$
$174$		0			0
$175$	0.616908	−	4.29069i	0.0466338	−	0.324346i
$176$		0			0
$177$	−5.78425	+	12.6657i	−0.434771	+	0.952015i
$178$		0			0
$179$	−3.52560	−	24.5211i	−0.263516	−	1.83279i	−0.505874	−	0.862607i	$-0.668830\pi$
$179$	−3.52560	−	24.5211i	−0.263516	−	1.83279i	0.242358	−	0.970187i	$-0.422079\pi$
$180$		0			0
$181$	12.1628	+	14.0366i	0.904050	+	1.04333i	0.998855	+	0.0478338i	$0.0152318\pi$
$181$	12.1628	+	14.0366i	0.904050	+	1.04333i	−0.0948050	+	0.995496i	$0.530223\pi$
$182$		0			0
$183$	−7.37954			−0.545512
$184$		0			0
$185$	−0.895933			−0.0658703
$186$		0			0
$187$	27.9660	+	32.2745i	2.04508	+	2.36014i
$188$		0			0
$189$	−3.13163	−	21.7810i	−0.227793	−	1.58433i
$190$		0			0
$191$	2.12813	−	4.65996i	0.153986	−	0.337183i	−0.816879	−	0.576809i	$-0.804298\pi$
$191$	2.12813	−	4.65996i	0.153986	−	0.337183i	0.970865	+	0.239626i	$0.0770249\pi$
$192$		0			0
$193$	−2.02437	+	14.0798i	−0.145717	+	1.01348i	0.777411	+	0.628992i	$0.216532\pi$
$193$	−2.02437	+	14.0798i	−0.145717	+	1.01348i	−0.923128	+	0.384492i	$0.874377\pi$
$194$		0			0
$195$	−0.775194	−	0.227617i	−0.0555128	−	0.0163000i
$196$		0			0
$197$	3.91051	+	8.56283i	0.278612	+	0.610076i	0.996267	−	0.0863228i	$-0.0275117\pi$
$197$	3.91051	+	8.56283i	0.278612	+	0.610076i	−0.717655	+	0.696399i	$0.754784\pi$
$198$		0			0
$199$	−12.5249	+	14.4545i	−0.887865	+	1.02465i	0.111657	+	0.993747i	$0.464384\pi$
$199$	−12.5249	+	14.4545i	−0.887865	+	1.02465i	−0.999522	+	0.0309043i	$0.990161\pi$
$200$		0			0
$201$	−1.38943	−	0.892931i	−0.0980027	−	0.0629825i
$202$		0			0
$203$	16.3115	−	10.4827i	1.14484	−	0.735744i
$204$		0			0
$205$	−1.97881	+	0.581030i	−0.138206	+	0.0405809i
$206$		0			0
$207$	8.06135	−	4.71248i	0.560303	−	0.327540i
$208$		0			0
$209$	−2.08205	+	0.611344i	−0.144018	+	0.0422875i
$210$		0			0
$211$	16.0976	−	10.3453i	1.10820	−	0.712199i	0.147302	−	0.989092i	$-0.452941\pi$
$211$	16.0976	−	10.3453i	1.10820	−	0.712199i	0.960901	+	0.276893i	$0.0893047\pi$
$212$		0			0
$213$	4.53933	+	2.91725i	0.311030	+	0.199887i
$214$		0			0
$215$	−2.23961	+	2.58465i	−0.152740	+	0.176272i
$216$		0			0
$217$	−14.5424	−	31.8434i	−0.987203	−	2.16167i
$218$		0			0
$219$	−2.14704	−	0.630427i	−0.145083	−	0.0426003i
$220$		0			0
$221$	−0.749049	+	5.20975i	−0.0503865	+	0.350446i
$222$		0			0
$223$	−3.32169	+	7.27348i	−0.222437	+	0.487068i	−0.987644	−	0.156716i	$-0.949909\pi$
$223$	−3.32169	+	7.27348i	−0.222437	+	0.487068i	0.765207	+	0.643784i	$0.222637\pi$
$224$		0			0
$225$	0.277094	+	1.92723i	0.0184729	+	0.128482i
$226$		0			0
$227$	−5.64267	−	6.51199i	−0.374517	−	0.432216i	0.536934	−	0.843624i	$-0.319582\pi$
$227$	−5.64267	−	6.51199i	−0.374517	−	0.432216i	−0.911451	+	0.411408i	$0.865037\pi$
$228$		0			0
$229$	−18.3266			−1.21106			−0.605528	−	0.795824i	$-0.707038\pi$
$229$	−18.3266			−1.21106			−0.605528	+	0.795824i	$0.707038\pi$
$230$		0			0
$231$	−28.4158			−1.86962
$232$		0			0
$233$	−18.8139	−	21.7124i	−1.23254	−	1.42243i	−0.871870	−	0.489737i	$-0.837093\pi$
$233$	−18.8139	−	21.7124i	−1.23254	−	1.42243i	−0.360672	−	0.932693i	$-0.617453\pi$
$234$		0			0
$235$	1.50929	+	10.4973i	0.0984549	+	0.684769i
$236$		0			0
$237$	0.776575	−	1.70046i	0.0504440	−	0.110457i
$238$		0			0
$239$	−2.83537	+	19.7204i	−0.183405	+	1.27561i	0.665233	+	0.746636i	$0.268332\pi$
$239$	−2.83537	+	19.7204i	−0.183405	+	1.27561i	−0.848638	+	0.528974i	$0.822577\pi$
$240$		0			0
$241$	1.15975	+	0.340533i	0.0747061	+	0.0219357i	0.318872	−	0.947798i	$-0.396696\pi$
$241$	1.15975	+	0.340533i	0.0747061	+	0.0219357i	−0.244166	+	0.969733i	$0.578514\pi$
$242$		0			0
$243$	6.59582	+	14.4428i	0.423122	+	0.926508i
$244$		0			0
$245$	7.72119	−	8.91073i	0.493289	−	0.569285i
$246$		0			0
$247$	−0.224985	−	0.144589i	−0.0143155	−	0.00920000i
$248$		0			0
$249$	1.96103	−	1.26027i	0.124275	−	0.0798667i
$250$		0			0
$251$	−15.8409	+	4.65132i	−0.999871	+	0.293589i	−0.740403	−	0.672163i	$-0.765365\pi$
$251$	−15.8409	+	4.65132i	−0.999871	+	0.293589i	−0.259468	+	0.965752i	$0.583547\pi$
$252$		0			0
$253$	−11.5402	−	28.3806i	−0.725526	−	1.78428i
$254$		0			0
$255$	−6.58177	+	1.93258i	−0.412166	+	0.121023i
$256$		0			0
$257$	−14.5840	+	9.37257i	−0.909726	+	0.584645i	−0.909659	−	0.415355i	$-0.863657\pi$
$257$	−14.5840	+	9.37257i	−0.909726	+	0.584645i	−6.61265e−5		1.00000i	$0.500021\pi$
$258$		0			0
$259$	−3.26717	−	2.09969i	−0.203012	−	0.130468i
$260$		0			0
$261$	−5.70323	+	6.58188i	−0.353021	+	0.407408i
$262$		0			0
$263$	2.76314	+	6.05043i	0.170382	+	0.373086i	0.975490	−	0.220043i	$-0.0706198\pi$
$263$	2.76314	+	6.05043i	0.170382	+	0.373086i	−0.805108	+	0.593129i	$0.797893\pi$
$264$		0			0
$265$	−8.72633	−	2.56228i	−0.536054	−	0.157400i
$266$		0			0
$267$	0.760692	−	5.29073i	0.0465536	−	0.323787i
$268$		0			0
$269$	2.66725	−	5.84045i	0.162625	−	0.356099i	−0.810724	−	0.585429i	$-0.800926\pi$
$269$	2.66725	−	5.84045i	0.162625	−	0.356099i	0.973349	+	0.229330i	$0.0736535\pi$
$270$		0			0
$271$	−3.95587	−	27.5137i	−0.240302	−	1.67134i	−0.650626	−	0.759398i	$-0.725493\pi$
$271$	−3.95587	−	27.5137i	−0.240302	−	1.67134i	0.410324	−	0.911940i	$-0.365416\pi$
$272$		0			0
$273$	−2.29344	−	2.64677i	−0.138805	−	0.160190i
$274$		0			0
$275$	6.38829			0.385229
$276$		0			0
$277$	−8.87381			−0.533176			−0.266588	−	0.963811i	$-0.585896\pi$
$277$	−8.87381			−0.533176			−0.266588	+	0.963811i	$0.585896\pi$
$278$		0			0
$279$	10.2970	+	11.8833i	0.616464	+	0.711437i
$280$		0			0
$281$	3.41880	+	23.7783i	0.203948	+	1.41849i	0.792421	+	0.609975i	$0.208821\pi$
$281$	3.41880	+	23.7783i	0.203948	+	1.41849i	−0.588472	+	0.808517i	$0.700270\pi$
$282$		0			0
$283$	−4.92718	+	10.7890i	−0.292890	+	0.641341i	−0.997680	−	0.0680756i	$-0.978314\pi$
$283$	−4.92718	+	10.7890i	−0.292890	+	0.641341i	0.704790	+	0.709416i	$0.251041\pi$
$284$		0			0
$285$	0.0496042	−	0.345005i	0.00293830	−	0.0204363i
$286$		0			0
$287$	−8.57775	−	2.51866i	−0.506329	−	0.148672i
$288$		0			0
$289$	11.5021	+	25.1860i	0.676593	+	1.48153i
$290$		0			0
$291$	6.85685	−	7.91323i	0.401956	−	0.463882i
$292$		0			0
$293$	−13.3160	−	8.55768i	−0.777929	−	0.499945i	0.0904165	−	0.995904i	$-0.471180\pi$
$293$	−13.3160	−	8.55768i	−0.777929	−	0.499945i	−0.868346	+	0.495959i	$0.834817\pi$
$294$		0			0
$295$	11.4153	−	7.33617i	0.664624	−	0.427128i
$296$		0			0
$297$	31.1155	−	9.13634i	1.80551	−	0.530144i
$298$		0			0
$299$	1.71209	−	3.36551i	0.0990126	−	0.194633i
$300$		0			0
$301$	−14.2245	+	4.17668i	−0.819885	+	0.240740i
$302$		0			0
$303$	−2.81030	+	1.80607i	−0.161447	+	0.103756i
$304$		0			0
$305$	6.04995	+	3.88807i	0.346419	+	0.222630i
$306$		0			0
$307$	16.9113	−	19.5167i	0.965180	−	1.11388i	−0.0282687	−	0.999600i	$-0.508999\pi$
$307$	16.9113	−	19.5167i	0.965180	−	1.11388i	0.993449	−	0.114277i	$-0.0364551\pi$
$308$		0			0
$309$	4.84366	+	10.6061i	0.275546	+	0.603362i
$310$		0			0
$311$	−17.8553	−	5.24279i	−1.01248	−	0.297291i	−0.266913	−	0.963721i	$-0.586004\pi$
$311$	−17.8553	−	5.24279i	−1.01248	−	0.297291i	−0.745568	+	0.666430i	$0.767822\pi$
$312$		0			0
$313$	−2.47503	+	17.2142i	−0.139897	+	0.973005i	0.792062	+	0.610441i	$0.209008\pi$
$313$	−2.47503	+	17.2142i	−0.139897	+	0.973005i	−0.931959	+	0.362564i	$0.881901\pi$
$314$		0			0
$315$	−3.50614	+	7.67737i	−0.197548	+	0.432571i
$316$		0			0
$317$	−0.0250235	−	0.174042i	−0.00140546	−	0.00977517i	0.989107	−	0.147201i	$-0.0470263\pi$
$317$	−0.0250235	−	0.174042i	−0.00140546	−	0.00977517i	−0.990512	+	0.137426i	$0.956117\pi$
$318$		0			0
$319$	18.7124	+	21.5953i	1.04769	+	1.20910i
$320$		0			0
$321$	1.64295			0.0917005
$322$		0			0
$323$	−2.27070			−0.126345
$324$		0			0
$325$	0.515600	+	0.595034i	0.0286003	+	0.0330066i
$326$		0			0
$327$	−0.694975	−	4.83366i	−0.0384322	−	0.267302i
$328$		0			0
$329$	−19.0974	+	41.8174i	−1.05287	+	2.30547i
$330$		0			0
$331$	−1.08925	+	7.57590i	−0.0598706	+	0.416409i	0.937741	+	0.347335i	$0.112913\pi$
$331$	−1.08925	+	7.57590i	−0.0598706	+	0.416409i	−0.997612	+	0.0690736i	$0.977996\pi$
$332$		0			0
$333$	1.67376	+	0.491461i	0.0917216	+	0.0269319i
$334$		0			0
$335$	0.668631	+	1.46410i	0.0365312	+	0.0799923i
$336$		0			0
$337$	−12.4408	+	14.3575i	−0.677694	+	0.782100i	−0.985560	−	0.169329i	$-0.945840\pi$
$337$	−12.4408	+	14.3575i	−0.677694	+	0.782100i	0.307866	+	0.951430i	$0.400385\pi$
$338$		0			0
$339$	−6.69544	−	4.30290i	−0.363647	−	0.233701i
$340$		0			0
$341$	43.4006	−	27.8919i	2.35027	−	1.51043i
$342$		0			0
$343$	19.9251	−	5.85053i	1.07585	−	0.315899i
$344$		0			0
$345$	4.91679	+	0.207597i	0.264711	+	0.0111766i
$346$		0			0
$347$	14.0272	−	4.11876i	0.753020	−	0.221107i	0.117375	−	0.993088i	$-0.462552\pi$
$347$	14.0272	−	4.11876i	0.753020	−	0.221107i	0.635645	+	0.771981i	$0.280734\pi$
$348$		0			0
$349$	−4.02972	+	2.58975i	−0.215706	+	0.138626i	−0.644032	−	0.764998i	$-0.722740\pi$
$349$	−4.02972	+	2.58975i	−0.215706	+	0.138626i	0.428326	+	0.903624i	$0.359103\pi$
$350$		0			0
$351$	3.36234	+	2.16084i	0.179468	+	0.115337i
$352$		0			0
$353$	−3.89514	+	4.49523i	−0.207317	+	0.239257i	−0.849880	−	0.526976i	$-0.823326\pi$
$353$	−3.89514	+	4.49523i	−0.207317	+	0.239257i	0.642563	+	0.766233i	$0.277871\pi$
$354$		0			0
$355$	−2.18445	−	4.78329i	−0.115939	−	0.253871i
$356$		0			0
$357$	−28.5307	−	8.37737i	−1.51001	−	0.443378i
$358$		0			0
$359$	−0.400702	+	2.78694i	−0.0211482	+	0.147089i	−0.997660	−	0.0683769i	$-0.978218\pi$
$359$	−0.400702	+	2.78694i	−0.0211482	+	0.147089i	0.976511	+	0.215466i	$0.0691271\pi$
$360$		0			0
$361$	−7.84496	+	17.1781i	−0.412892	+	0.904108i
$362$		0			0
$363$	−4.35332	−	30.2780i	−0.228490	−	1.58918i
$364$		0			0
$365$	1.42805	+	1.64805i	0.0747473	+	0.0862630i
$366$		0			0
$367$	16.3681			0.854409			0.427204	−	0.904155i	$-0.359498\pi$
$367$	16.3681			0.854409			0.427204	+	0.904155i	$0.359498\pi$
$368$		0			0
$369$	4.01549			0.209038
$370$		0			0
$371$	−25.8172	−	29.7946i	−1.34036	−	1.54686i
$372$		0			0
$373$	−3.64554	−	25.3553i	−0.188759	−	1.31285i	−0.835227	−	0.549906i	$-0.814664\pi$
$373$	−3.64554	−	25.3553i	−0.188759	−	1.31285i	0.646468	−	0.762941i	$-0.276245\pi$
$374$		0			0
$375$	−0.426272	+	0.933405i	−0.0220126	+	0.0482008i
$376$		0			0
$377$	−0.501199	+	3.48591i	−0.0258130	+	0.179534i
$378$		0			0
$379$	21.0456	+	6.17954i	1.08104	+	0.317422i	0.773294	−	0.634048i	$-0.218608\pi$
$379$	21.0456	+	6.17954i	1.08104	+	0.317422i	0.307744	+	0.951469i	$0.400426\pi$
$380$		0			0
$381$	8.40660	+	18.4079i	0.430683	+	0.943065i
$382$		0			0
$383$	−2.33025	+	2.68925i	−0.119070	+	0.137414i	−0.812155	−	0.583442i	$-0.801706\pi$
$383$	−2.33025	+	2.68925i	−0.119070	+	0.137414i	0.693085	+	0.720856i	$0.256251\pi$
$384$		0			0
$385$	23.2960	+	14.9714i	1.18728	+	0.763016i
$386$		0			0
$387$	5.60180	−	3.60006i	0.284756	−	0.183001i
$388$		0			0
$389$	−19.5756	+	5.74791i	−0.992522	+	0.291431i	−0.737384	−	0.675474i	$-0.763939\pi$
$389$	−19.5756	+	5.74791i	−0.992522	+	0.291431i	−0.255138	+	0.966905i	$0.582121\pi$
$390$		0			0
$391$	−3.21986	−	31.8977i	−0.162835	−	1.61313i
$392$		0			0
$393$	−15.3040	+	4.49366i	−0.771986	+	0.226675i
$394$		0			0
$395$	−1.53258	+	0.984931i	−0.0771126	+	0.0495572i
$396$		0			0
$397$	−14.1291	−	9.08024i	−0.709121	−	0.455724i	0.135717	−	0.990748i	$-0.456666\pi$
$397$	−14.1291	−	9.08024i	−0.709121	−	0.455724i	−0.844837	+	0.535024i	$0.820303\pi$
$398$		0			0
$399$	0.989434	−	1.14187i	0.0495337	−	0.0571649i
$400$		0			0
$401$	3.37995	+	7.40106i	0.168787	+	0.369591i	0.975057	−	0.221957i	$-0.0712444\pi$
$401$	3.37995	+	7.40106i	0.168787	+	0.369591i	−0.806270	+	0.591548i	$0.798517\pi$
$402$		0			0
$403$	6.10084	+	1.79137i	0.303905	+	0.0892345i
$404$		0			0
$405$	0.0899625	−	0.625703i	0.00447027	−	0.0310914i
$406$		0			0
$407$	2.37762	−	5.20626i	0.117854	−	0.258065i
$408$		0			0
$409$	−5.53502	−	38.4969i	−0.273689	−	1.90355i	−0.408634	−	0.912698i	$-0.633995\pi$
$409$	−5.53502	−	38.4969i	−0.273689	−	1.90355i	0.134945	−	0.990853i	$-0.456914\pi$
$410$		0			0
$411$	−4.19951	−	4.84649i	−0.207147	−	0.239060i
$412$		0			0
$413$	58.8207			2.89438
$414$		0			0
$415$	−2.27171			−0.111514
$416$		0			0
$417$	7.91164	+	9.13052i	0.387435	+	0.447123i
$418$		0			0
$419$	−1.33738	−	9.30168i	−0.0653353	−	0.454417i	−0.996059	−	0.0886937i	$-0.971731\pi$
$419$	−1.33738	−	9.30168i	−0.0653353	−	0.454417i	0.930724	−	0.365723i	$-0.119178\pi$
$420$		0			0
$421$	12.1514	−	26.6079i	0.592225	−	1.29679i	−0.341864	−	0.939750i	$-0.611058\pi$
$421$	12.1514	−	26.6079i	0.592225	−	1.29679i	0.934088	−	0.357042i	$-0.116215\pi$
$422$		0			0
$423$	2.93865	−	20.4388i	0.142882	−	0.993767i
$424$		0			0
$425$	6.41413	+	1.88336i	0.311131	+	0.0913564i
$426$		0			0
$427$	12.9502	+	28.3570i	0.626706	+	1.37229i
$428$		0			0
$429$	3.37989	−	3.90060i	0.163182	−	0.188323i
$430$		0			0
$431$	13.2698	+	8.52800i	0.639185	+	0.410779i	0.819700	−	0.572793i	$-0.194140\pi$
$431$	13.2698	+	8.52800i	0.639185	+	0.410779i	−0.180515	+	0.983572i	$0.557777\pi$
$432$		0			0
$433$	0.761024	−	0.489081i	0.0365725	−	0.0235037i	−0.522227	−	0.852807i	$-0.674899\pi$
$433$	0.761024	−	0.489081i	0.0365725	−	0.0235037i	0.558799	+	0.829303i	$0.311262\pi$
$434$		0			0
$435$	−4.40394	+	1.29311i	−0.211153	+	0.0620001i
$436$		0			0
$437$	1.54229	+	0.524476i	0.0737775	+	0.0250891i
$438$		0			0
$439$	−10.0049	+	2.93771i	−0.477509	+	0.140209i	−0.511625	−	0.859209i	$-0.670956\pi$
$439$	−10.0049	+	2.93771i	−0.477509	+	0.140209i	0.0341167	+	0.999418i	$0.489138\pi$
$440$		0			0
$441$	−19.3125	+	12.4114i	−0.919643	+	0.591019i
$442$		0			0
$443$	−2.07560	−	1.33390i	−0.0986145	−	0.0633757i	0.490404	−	0.871495i	$-0.336849\pi$
$443$	−2.07560	−	1.33390i	−0.0986145	−	0.0633757i	−0.589019	+	0.808119i	$0.700486\pi$
$444$		0			0
$445$	−3.41117	+	3.93670i	−0.161705	+	0.186617i
$446$		0			0
$447$	5.93607	+	12.9982i	0.280767	+	0.614793i
$448$		0			0
$449$	32.4767	+	9.53602i	1.53267	+	0.450033i	0.935867	−	0.352354i	$-0.114619\pi$
$449$	32.4767	+	9.53602i	1.53267	+	0.450033i	0.596804	+	0.802387i	$0.296437\pi$
$450$		0			0
$451$	1.87498	−	13.0408i	0.0882894	−	0.614066i
$452$		0			0
$453$	8.28507	−	18.1418i	0.389266	−	0.852374i
$454$		0			0
$455$	0.485718	+	3.37824i	0.0227708	+	0.158375i
$456$		0			0
$457$	−12.9914	−	14.9928i	−0.607711	−	0.701336i	0.365614	−	0.930767i	$-0.380859\pi$
$457$	−12.9914	−	14.9928i	−0.607711	−	0.701336i	−0.973325	+	0.229431i	$0.926314\pi$
$458$		0			0
$459$	33.9349			1.58395
$460$		0			0
$461$	13.4425			0.626082			0.313041	−	0.949740i	$-0.398652\pi$
$461$	13.4425			0.626082			0.313041	+	0.949740i	$0.398652\pi$
$462$		0			0
$463$	19.0782	+	22.0174i	0.886638	+	1.02323i	0.999561	+	0.0296311i	$0.00943324\pi$
$463$	19.0782	+	22.0174i	0.886638	+	1.02323i	−0.112923	+	0.993604i	$0.536021\pi$
$464$		0			0
$465$	1.17934	+	8.20248i	0.0546905	+	0.380381i
$466$		0			0
$467$	−12.4094	+	27.1728i	−0.574239	+	1.25741i	0.370271	+	0.928924i	$0.379265\pi$
$467$	−12.4094	+	27.1728i	−0.574239	+	1.25741i	−0.944510	+	0.328484i	$0.893462\pi$
$468$		0			0
$469$	−0.992944	+	6.90608i	−0.0458499	+	0.318893i
$470$		0			0
$471$	5.94332	+	1.74512i	0.273854	+	0.0804107i
$472$		0			0
$473$	−9.07594	−	19.8735i	−0.417312	−	0.913786i
$474$		0			0
$475$	−0.222440	+	0.256709i	−0.0102062	+	0.0117786i
$476$		0			0
$477$	14.8968	+	9.57360i	0.682078	+	0.438345i
$478$		0			0
$479$	12.7157	−	8.17186i	0.580994	−	0.373382i	−0.216888	−	0.976197i	$-0.569591\pi$
$479$	12.7157	−	8.17186i	0.580994	−	0.373382i	0.797881	+	0.602815i	$0.205954\pi$
$480$		0			0
$481$	0.676832	−	0.198736i	0.0308609	−	0.00906158i
$482$		0			0
$483$	17.4434	+	12.2799i	0.793703	+	0.558755i
$484$		0			0
$485$	−9.79069	+	2.87481i	−0.444572	+	0.130538i
$486$		0			0
$487$	3.07095	−	1.97358i	0.139158	−	0.0894315i	−0.469209	−	0.883087i	$-0.655461\pi$
$487$	3.07095	−	1.97358i	0.139158	−	0.0894315i	0.608368	+	0.793655i	$0.291825\pi$
$488$		0			0
$489$	5.23554	+	3.36468i	0.236759	+	0.152156i
$490$		0			0
$491$	12.2321	−	14.1166i	0.552029	−	0.637075i	−0.409326	−	0.912388i	$-0.634236\pi$
$491$	12.2321	−	14.1166i	0.552029	−	0.637075i	0.961355	+	0.275313i	$0.0887816\pi$
$492$		0			0
$493$	12.4215	+	27.1993i	0.559436	+	1.22499i
$494$		0			0
$495$	−11.9345	−	3.50428i	−0.536415	−	0.157506i
$496$		0			0
$497$	3.24400	−	22.5625i	0.145513	−	1.01207i
$498$		0			0
$499$	4.66652	−	10.2182i	0.208902	−	0.457432i	−0.775958	−	0.630785i	$-0.782733\pi$
$499$	4.66652	−	10.2182i	0.208902	−	0.457432i	0.984860	+	0.173353i	$0.0554603\pi$
$500$		0			0
$501$	2.45641	+	17.0847i	0.109744	+	0.763290i
$502$		0			0
$503$	−20.2653	−	23.3874i	−0.903585	−	1.04279i	−0.998879	−	0.0473437i	$-0.984924\pi$
$503$	−20.2653	−	23.3874i	−0.903585	−	1.04279i	0.0952935	−	0.995449i	$-0.469621\pi$
$504$		0			0
$505$	3.25552			0.144869
$506$		0			0
$507$	−12.7036			−0.564188
$508$		0			0
$509$	4.38368	+	5.05904i	0.194303	+	0.224238i	0.844538	−	0.535495i	$-0.179875\pi$
$509$	4.38368	+	5.05904i	0.194303	+	0.224238i	−0.650235	+	0.759733i	$0.725330\pi$
$510$		0			0
$511$	1.34528	+	9.35664i	0.0595118	+	0.413914i
$512$		0			0
$513$	−0.716302	+	1.56848i	−0.0316255	+	0.0692502i
$514$		0			0
$515$	1.61710	−	11.2472i	0.0712580	−	0.495611i
$516$		0			0
$517$	−65.0052	−	19.0872i	−2.85892	−	0.839456i
$518$		0			0
$519$	−2.78436	−	6.09689i	−0.122220	−	0.267624i
$520$		0			0
$521$	−3.13323	+	3.61594i	−0.137269	+	0.158417i	−0.820222	−	0.572045i	$-0.806150\pi$
$521$	−3.13323	+	3.61594i	−0.137269	+	0.158417i	0.682953	+	0.730463i	$0.260696\pi$
$522$		0			0
$523$	−18.2421	−	11.7235i	−0.797672	−	0.512633i	0.0771833	−	0.997017i	$-0.475407\pi$
$523$	−18.2421	−	11.7235i	−0.797672	−	0.512633i	−0.874855	+	0.484384i	$0.839044\pi$
$524$		0			0
$525$	−3.74198	+	2.40482i	−0.163313	+	0.104955i
$526$		0			0
$527$	51.7991	−	15.2096i	2.25640	−	0.662540i
$528$		0			0
$529$	−5.18061	+	22.4090i	−0.225244	+	0.974302i
$530$		0			0
$531$	−25.3500	+	7.44344i	−1.10010	+	0.323018i
$532$		0			0
$533$	1.36601	−	0.877879i	0.0591683	−	0.0380252i
$534$		0			0
$535$	−1.34694	−	0.865623i	−0.0582331	−	0.0374241i
$536$		0			0
$537$	−16.6470	+	19.2117i	−0.718372	+	0.829046i
$538$		0			0
$539$	31.2898	+	68.5150i	1.34775	+	2.95115i
$540$		0			0
$541$	7.83668	+	2.30106i	0.336925	+	0.0989302i	0.445819	−	0.895123i	$-0.352913\pi$
$541$	7.83668	+	2.30106i	0.336925	+	0.0989302i	−0.108894	+	0.994053i	$0.534731\pi$
$542$		0			0
$543$	2.71230	−	18.8645i	0.116396	−	0.809551i
$544$		0			0
$545$	−1.97696	+	4.32893i	−0.0846835	+	0.185431i
$546$		0			0
$547$	−0.601673	−	4.18473i	−0.0257257	−	0.178926i	0.972907	−	0.231195i	$-0.0742636\pi$
$547$	−0.601673	−	4.18473i	−0.0257257	−	0.178926i	−0.998633	+	0.0522694i	$0.983355\pi$
$548$		0			0
$549$	−9.16961	−	10.5823i	−0.391349	−	0.451641i
$550$		0			0
$551$	−1.51935			−0.0647267
$552$		0			0
$553$	−7.89709			−0.335818
$554$		0			0
$555$	0.602045	+	0.694797i	0.0255554	+	0.0294925i
$556$		0			0
$557$	−2.29564	−	15.9665i	−0.0972693	−	0.676523i	−0.978863	−	0.204515i	$-0.934438\pi$
$557$	−2.29564	−	15.9665i	−0.0972693	−	0.676523i	0.881594	−	0.472008i	$-0.156471\pi$
$558$		0			0
$559$	1.11859	−	2.44937i	0.0473113	−	0.103597i
$560$		0			0
$561$	6.23642	−	43.3753i	0.263302	−	1.83131i
$562$		0			0
$563$	−36.9790	−	10.8580i	−1.55848	−	0.457610i	−0.614857	−	0.788639i	$-0.710786\pi$
$563$	−36.9790	−	10.8580i	−1.55848	−	0.457610i	−0.943621	+	0.331029i	$0.892604\pi$
$564$		0			0
$565$	3.22204	+	7.05527i	0.135552	+	0.296818i
$566$		0			0
$567$	1.79445	−	2.07090i	0.0753596	−	0.0869696i
$568$		0			0
$569$	3.97875	+	2.55699i	0.166798	+	0.107194i	0.621376	−	0.783512i	$-0.286574\pi$
$569$	3.97875	+	2.55699i	0.166798	+	0.107194i	−0.454579	+	0.890707i	$0.650210\pi$
$570$		0			0
$571$	−25.3438	+	16.2875i	−1.06060	+	0.681609i	−0.949998	−	0.312255i	$-0.898916\pi$
$571$	−25.3438	+	16.2875i	−1.06060	+	0.681609i	−0.110606	+	0.993864i	$0.535279\pi$
$572$		0			0
$573$	−5.04386	+	1.48101i	−0.210710	+	0.0618701i
$574$		0			0
$575$	−3.92154	−	2.76071i	−0.163540	−	0.115129i
$576$		0			0
$577$	−25.7761	+	7.56853i	−1.07307	+	0.315082i	−0.770104	−	0.637919i	$-0.779796\pi$
$577$	−25.7761	+	7.56853i	−1.07307	+	0.315082i	−0.302967	+	0.953001i	$0.597977\pi$
$578$		0			0
$579$	12.2792	−	7.89136i	0.510306	−	0.327954i
$580$		0			0
$581$	−8.28417	−	5.32391i	−0.343685	−	0.220873i
$582$		0			0
$583$	38.0473	−	43.9089i	1.57576	−	1.81852i
$584$		0			0
$585$	−0.636829	−	1.39446i	−0.0263296	−	0.0576539i
$586$		0			0
$587$	10.0177	+	2.94145i	0.413473	+	0.121407i	0.481852	−	0.876253i	$-0.339964\pi$
$587$	10.0177	+	2.94145i	0.413473	+	0.121407i	−0.0683787	+	0.997659i	$0.521783\pi$
$588$		0			0
$589$	−0.390389	+	2.71522i	−0.0160857	+	0.111879i
$590$		0			0
$591$	4.01271	−	8.78662i	0.165061	−	0.361433i
$592$		0			0
$593$	−1.43868	−	10.0062i	−0.0590794	−	0.410906i	−0.997804	−	0.0662376i	$-0.978900\pi$
$593$	−1.43868	−	10.0062i	−0.0590794	−	0.410906i	0.938725	−	0.344668i	$-0.112009\pi$
$594$		0			0
$595$	18.9765	+	21.9000i	0.777959	+	0.897813i
$596$		0			0
$597$	19.6259			0.803234
$598$		0			0
$599$	3.69167			0.150837			0.0754187	−	0.997152i	$-0.475971\pi$
$599$	3.69167			0.150837			0.0754187	+	0.997152i	$0.475971\pi$
$600$		0			0
$601$	−12.1303	−	13.9991i	−0.494806	−	0.571037i	0.452337	−	0.891847i	$-0.350590\pi$
$601$	−12.1303	−	13.9991i	−0.494806	−	0.571037i	−0.947143	+	0.320810i	$0.896045\pi$
$602$		0			0
$603$	−0.445996	−	3.10197i	−0.0181624	−	0.126322i
$604$		0			0
$605$	−12.3836	+	27.1164i	−0.503467	+	1.10244i
$606$		0			0
$607$	−1.30855	+	9.10120i	−0.0531126	+	0.369406i	0.945879	+	0.324518i	$0.105202\pi$
$607$	−1.30855	+	9.10120i	−0.0531126	+	0.369406i	−0.998992	+	0.0448880i	$0.985707\pi$
$608$		0			0
$609$	−19.0903	−	5.60541i	−0.773576	−	0.227143i
$610$		0			0
$611$	−3.46871	−	7.59540i	−0.140329	−	0.307277i
$612$		0			0
$613$	0.636595	−	0.734670i	0.0257118	−	0.0296731i	−0.742748	−	0.669571i	$-0.766478\pi$
$613$	0.636595	−	0.734670i	0.0257118	−	0.0296731i	0.768460	+	0.639898i	$0.221023\pi$
$614$		0			0
$615$	1.78030	+	1.14413i	0.0717886	+	0.0461357i
$616$		0			0
$617$	−4.02315	+	2.58552i	−0.161966	+	0.104089i	−0.619113	−	0.785302i	$-0.712508\pi$
$617$	−4.02315	+	2.58552i	−0.161966	+	0.104089i	0.457147	+	0.889391i	$0.348871\pi$
$618$		0			0
$619$	−22.5633	+	6.62519i	−0.906896	+	0.266289i	−0.701734	−	0.712439i	$-0.747590\pi$
$619$	−22.5633	+	6.62519i	−0.906896	+	0.266289i	−0.205162	+	0.978728i	$0.565772\pi$
$620$		0			0
$621$	−23.0490	−	7.83814i	−0.924923	−	0.314534i
$622$		0			0
$623$	−21.6654	+	6.36153i	−0.868005	+	0.254869i
$624$		0			0
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$		0			0
$627$	1.87318	+	1.20382i	0.0748076	+	0.0480759i
$628$		0			0
$629$	3.92212	−	4.52636i	0.156385	−	0.180478i
$630$		0			0
$631$	−9.32490	−	20.4187i	−0.371218	−	0.812855i	−0.999395	−	0.0347838i	$-0.988926\pi$
$631$	−9.32490	−	20.4187i	−0.371218	−	0.812855i	0.628177	−	0.778071i	$-0.283802\pi$
$632$		0			0
$633$	−18.8400	−	5.53191i	−0.748821	−	0.219874i
$634$		0			0
$635$	2.80662	−	19.5205i	0.111377	−	0.774647i
$636$		0			0
$637$	−3.85639	+	8.44433i	−0.152796	+	0.334576i
$638$		0			0
$639$	1.45709	+	10.1343i	0.0576417	+	0.400907i
$640$		0			0
$641$	24.4201	+	28.1823i	0.964535	+	1.11313i	0.993532	+	0.113553i	$0.0362232\pi$
$641$	24.4201	+	28.1823i	0.964535	+	1.11313i	−0.0289971	+	0.999579i	$0.509231\pi$
$642$		0			0
$643$	−43.0645			−1.69830			−0.849150	−	0.528152i	$-0.822885\pi$
$643$	−43.0645			−1.69830			−0.849150	+	0.528152i	$0.822885\pi$
$644$		0			0
$645$	3.50937			0.138181
$646$		0			0
$647$	−4.09815	−	4.72951i	−0.161115	−	0.185936i	0.669452	−	0.742855i	$-0.266529\pi$
$647$	−4.09815	−	4.72951i	−0.161115	−	0.185936i	−0.830567	+	0.556919i	$0.811983\pi$
$648$		0			0
$649$	12.3366	+	85.8029i	0.484254	+	3.36806i
$650$		0			0
$651$	−14.9225	+	32.6757i	−0.584858	+	1.28066i
$652$		0			0
$653$	−4.28443	+	29.7989i	−0.167663	+	1.16612i	0.716036	+	0.698064i	$0.245955\pi$
$653$	−4.28443	+	29.7989i	−0.167663	+	1.16612i	−0.883699	+	0.468056i	$0.844954\pi$
$654$		0			0
$655$	14.9142	+	4.37922i	0.582747	+	0.171110i
$656$		0			0
$657$	−1.76381	−	3.86221i	−0.0688128	−	0.150679i
$658$		0			0
$659$	−15.2306	+	17.5770i	−0.593299	+	0.684703i	−0.970410	−	0.241465i	$-0.922372\pi$
$659$	−15.2306	+	17.5770i	−0.593299	+	0.684703i	0.377111	+	0.926168i	$0.376918\pi$
$660$		0			0
$661$	10.4421	+	6.71072i	0.406150	+	0.261017i	0.727727	−	0.685867i	$-0.240577\pi$
$661$	10.4421	+	6.71072i	0.406150	+	0.261017i	−0.321577	+	0.946883i	$0.604213\pi$
$662$		0			0
$663$	4.54351	−	2.91994i	0.176455	−	0.113401i
$664$		0			0
$665$	−1.41278	+	0.414831i	−0.0547854	+	0.0160864i
$666$		0			0
$667$	−2.15445	−	21.3431i	−0.0834206	−	0.826409i
$668$		0			0
$669$	7.87268	−	2.31163i	0.304375	−	0.0893727i
$670$		0			0
$671$	−38.6489	+	24.8381i	−1.49202	+	0.958865i
$672$		0			0
$673$	−17.7566	−	11.4115i	−0.684466	−	0.439880i	0.151649	−	0.988434i	$-0.451542\pi$
$673$	−17.7566	−	11.4115i	−0.684466	−	0.439880i	−0.836115	+	0.548555i	$0.815178\pi$
$674$		0			0
$675$	3.32429	−	3.83644i	0.127952	−	0.147665i
$676$		0			0
$677$	11.7778	+	25.7898i	0.452658	+	0.991184i	0.989100	+	0.147246i	$0.0470409\pi$
$677$	11.7778	+	25.7898i	0.452658	+	0.991184i	−0.536441	+	0.843938i	$0.680232\pi$
$678$		0			0
$679$	−42.4408	−	12.4617i	−1.62873	−	0.478238i
$680$		0			0
$681$	−1.25832	+	8.75179i	−0.0482188	+	0.335369i
$682$		0			0
$683$	−11.0239	+	24.1390i	−0.421818	+	0.923651i	0.572767	+	0.819718i	$0.305870\pi$
$683$	−11.0239	+	24.1390i	−0.421818	+	0.923651i	−0.994584	+	0.103933i	$0.966857\pi$
$684$		0			0
$685$	0.889396	+	6.18589i	0.0339821	+	0.236351i
$686$		0			0
$687$	12.3150	+	14.2123i	0.469847	+	0.542233i
$688$		0			0
$689$	7.16068			0.272800
$690$		0			0
$691$	48.5261			1.84602			0.923009	−	0.384778i	$-0.125722\pi$
$691$	48.5261			1.84602			0.923009	+	0.384778i	$0.125722\pi$
$692$		0			0
$693$	−35.3086	−	40.7483i	−1.34126	−	1.54790i
$694$		0			0
$695$	−1.67557	−	11.6539i	−0.0635581	−	0.442056i
$696$		0			0
$697$	5.72717	−	12.5408i	0.216932	−	0.475015i
$698$		0			0
$699$	−4.19552	+	29.1805i	−0.158689	+	1.10371i
$700$		0			0
$701$	−19.0280	−	5.58713i	−0.718678	−	0.211023i	−0.0981103	−	0.995176i	$-0.531280\pi$
$701$	−19.0280	−	5.58713i	−0.718678	−	0.211023i	−0.620568	+	0.784153i	$0.713098\pi$
$702$		0			0
$703$	0.126422	+	0.276825i	0.00476808	+	0.0104406i
$704$		0			0
$705$	7.12647	−	8.22439i	0.268398	−	0.309748i
$706$		0			0
$707$	11.8718	+	7.62956i	0.446486	+	0.286939i
$708$		0			0
$709$	7.87812	−	5.06296i	0.295869	−	0.190143i	−0.384282	−	0.923216i	$-0.625551\pi$
$709$	7.87812	−	5.06296i	0.295869	−	0.190143i	0.680150	+	0.733073i	$0.261914\pi$
$710$		0			0
$711$	3.40342	−	0.999334i	0.127638	−	0.0374779i
$712$		0			0
$713$	−38.6956	−	1.63380i	−1.44916	−	0.0611865i
$714$		0			0
$715$	−4.82604	+	1.41705i	−0.180484	+	0.0529948i
$716$		0			0
$717$	17.1985	−	11.0528i	0.642290	−	0.412775i
$718$		0			0
$719$	−35.5520	−	22.8479i	−1.32587	−	0.852083i	−0.330095	−	0.943948i	$-0.607081\pi$
$719$	−35.5520	−	22.8479i	−1.32587	−	0.852083i	−0.995772	+	0.0918646i	$0.970717\pi$
$720$		0			0
$721$	32.2557	−	37.2250i	1.20126	−	1.38633i
$722$		0			0
$723$	−0.515240	−	1.12822i	−0.0191620	−	0.0419588i
$724$		0			0
$725$	4.29178	+	1.26018i	0.159393	+	0.0468019i
$726$		0			0
$727$	3.02378	−	21.0308i	0.112146	−	0.779990i	−0.853680	−	0.520798i	$-0.825635\pi$
$727$	3.02378	−	21.0308i	0.112146	−	0.779990i	0.965826	−	0.259192i	$-0.0834563\pi$
$728$		0			0
$729$	5.98040	−	13.0953i	0.221496	−	0.485010i
$730$		0			0
$731$	−3.25365	−	22.6296i	−0.120341	−	0.836987i
$732$		0			0
$733$	19.7365	+	22.7771i	0.728983	+	0.841291i	0.992357	−	0.123403i	$-0.0393808\pi$
$733$	19.7365	+	22.7771i	0.728983	+	0.841291i	−0.263374	+	0.964694i	$0.584835\pi$
$734$		0			0
$735$	−12.0987			−0.446268
$736$		0			0
$737$	−10.2823			−0.378753
$738$		0			0
$739$	15.0439	+	17.3616i	0.553399	+	0.638657i	0.961672	−	0.274203i	$-0.0884141\pi$
$739$	15.0439	+	17.3616i	0.553399	+	0.638657i	−0.408272	+	0.912860i	$0.633869\pi$
$740$		0			0
$741$	0.0390555	+	0.271637i	0.00143474	+	0.00997883i
$742$		0			0
$743$	9.33627	−	20.4436i	0.342514	−	0.750002i	−0.657480	−	0.753472i	$-0.728377\pi$
$743$	9.33627	−	20.4436i	0.342514	−	0.750002i	0.999994	+	0.00347042i	$0.00110467\pi$
$744$		0			0
$745$	1.98181	−	13.7838i	0.0726080	−	0.505000i
$746$		0			0
$747$	4.24395	+	1.24614i	0.155278	+	0.0455937i
$748$		0			0
$749$	−2.88318	−	6.31329i	−0.105349	−	0.230683i
$750$		0			0
$751$	7.49207	−	8.64631i	0.273390	−	0.315508i	−0.602407	−	0.798189i	$-0.705791\pi$
$751$	7.49207	−	8.64631i	0.273390	−	0.315508i	0.875796	+	0.482681i	$0.160337\pi$
$752$		0			0
$753$	14.2518	+	9.15909i	0.519365	+	0.333776i
$754$		0			0
$755$	−16.3507	+	10.5080i	−0.595063	+	0.382424i
$756$		0			0
$757$	24.7166	−	7.25743i	0.898338	−	0.263776i	0.200214	−	0.979752i	$-0.435836\pi$
$757$	24.7166	−	7.25743i	0.898338	−	0.263776i	0.698125	+	0.715976i	$0.254018\pi$
$758$		0			0
$759$	−14.2545	+	28.0205i	−0.517405	+	1.01708i
$760$		0			0
$761$	−7.54258	+	2.21470i	−0.273418	+	0.0802829i	−0.415567	−	0.909562i	$-0.636417\pi$
$761$	−7.54258	+	2.21470i	−0.273418	+	0.0802829i	0.142149	+	0.989845i	$0.454599\pi$
$762$		0			0
$763$	−17.3545	+	11.1531i	−0.628275	+	0.403768i
$764$		0			0
$765$	−10.9496	−	7.03690i	−0.395885	−	0.254420i
$766$		0			0
$767$	−6.99638	+	8.07425i	−0.252625	+	0.291544i
$768$		0			0
$769$	−10.0746	−	22.0604i	−0.363300	−	0.795517i	−0.999708	−	0.0241639i	$-0.992308\pi$
$769$	−10.0746	−	22.0604i	−0.363300	−	0.795517i	0.636408	−	0.771353i	$-0.280420\pi$
$770$		0			0
$771$	17.0685	+	5.01177i	0.614708	+	0.180495i
$772$		0			0
$773$	1.37723	−	9.57888i	0.0495357	−	0.344528i	−0.949948	−	0.312407i	$-0.898865\pi$
$773$	1.37723	−	9.57888i	0.0495357	−	0.344528i	0.999484	−	0.0321211i	$-0.0102262\pi$
$774$		0			0
$775$	3.35480	−	7.34598i	0.120508	−	0.263875i
$776$		0			0
$777$	0.567153	+	3.94463i	0.0203465	+	0.141513i
$778$		0			0
$779$	0.458748	+	0.529423i	0.0164364	+	0.0189686i
$780$		0			0
$781$	33.5928			1.20204
$782$		0			0
$783$	22.7063			0.811456
$784$		0			0
$785$	−3.95304	−	4.56206i	−0.141090	−	0.162827i
$786$		0			0
$787$	−4.11842	−	28.6442i	−0.146806	−	1.02106i	−0.921405	−	0.388604i	$-0.872957\pi$
$787$	−4.11842	−	28.6442i	−0.146806	−	1.02106i	0.774599	−	0.632453i	$-0.217952\pi$
$788$		0			0
$789$	2.83535	−	6.20856i	0.100941	−	0.221031i
$790$		0			0
$791$	−4.78485	+	33.2794i	−0.170130	+	1.18328i
$792$		0			0
$793$	−5.43289	−	1.59524i	−0.192928	−	0.0566487i
$794$		0			0
$795$	3.87683	+	8.48907i	0.137497	+	0.301076i
$796$		0			0
$797$	22.7995	−	26.3120i	0.807600	−	0.932020i	−0.191172	−	0.981557i	$-0.561229\pi$
$797$	22.7995	−	26.3120i	0.807600	−	0.932020i	0.998772	+	0.0495363i	$0.0157744\pi$
$798$		0			0
$799$	−59.6409	−	38.3289i	−2.10994	−	1.35598i
$800$		0			0
$801$	8.53214	−	5.48327i	0.301468	−	0.193742i
$802$		0			0
$803$	−13.3666	+	3.92478i	−0.471696	+	0.138502i
$804$		0			0
$805$	−7.83066	−	19.2578i	−0.275995	−	0.678749i
$806$		0			0
$807$	−6.32160	+	1.85619i	−0.222531	+	0.0653409i
$808$		0			0
$809$	27.0481	−	17.3827i	0.950959	−	0.611144i	0.0294773	−	0.999565i	$-0.490616\pi$
$809$	27.0481	−	17.3827i	0.950959	−	0.611144i	0.921482	+	0.388421i	$0.126979\pi$
$810$		0			0
$811$	−9.54208	−	6.13232i	−0.335068	−	0.215335i	0.362278	−	0.932070i	$-0.381999\pi$
$811$	−9.54208	−	6.13232i	−0.335068	−	0.215335i	−0.697345	+	0.716735i	$0.745636\pi$
$812$		0			0
$813$	−18.6786	+	21.5563i	−0.655089	+	0.756013i
$814$		0			0
$815$	−2.51949	−	5.51691i	−0.0882539	−	0.193249i
$816$		0			0
$817$	1.11463	+	0.327284i	0.0389959	+	0.0114502i
$818$		0			0
$819$	0.945716	−	6.57760i	0.0330460	−	0.229840i
$820$		0			0
$821$	−19.1739	+	41.9849i	−0.669173	+	1.46528i	0.204549	+	0.978856i	$0.434427\pi$
$821$	−19.1739	+	41.9849i	−0.669173	+	1.46528i	−0.873721	+	0.486427i	$0.838300\pi$
$822$		0			0
$823$	−1.26189	−	8.77660i	−0.0439865	−	0.305933i	−0.999924	−	0.0123614i	$-0.996065\pi$
$823$	−1.26189	−	8.77660i	−0.0439865	−	0.305933i	0.955937	−	0.293572i	$-0.0948440\pi$
$824$		0			0
$825$	−4.29278	−	4.95413i	−0.149455	−	0.172481i
$826$		0			0
$827$	−42.1335			−1.46513			−0.732563	−	0.680699i	$-0.761676\pi$
$827$	−42.1335			−1.46513			−0.732563	+	0.680699i	$0.761676\pi$
$828$		0			0
$829$	−53.4090			−1.85497			−0.927486	−	0.373857i	$-0.878035\pi$
$829$	−53.4090			−1.85497			−0.927486	+	0.373857i	$0.878035\pi$
$830$		0			0
$831$	5.96298	+	6.88165i	0.206854	+	0.238722i
$832$		0			0
$833$	11.2171	+	78.0168i	0.388650	+	2.70312i
$834$		0			0
$835$	6.98762	−	15.3007i	0.241816	−	0.529504i
$836$		0			0
$837$	5.83425	−	40.5781i	0.201661	−	1.40258i
$838$		0			0
$839$	−2.89868	−	0.851130i	−0.100074	−	0.0293843i	0.231312	−	0.972880i	$-0.425698\pi$
$839$	−2.89868	−	0.851130i	−0.100074	−	0.0293843i	−0.331386	+	0.943495i	$0.607516\pi$
$840$		0			0
$841$	−3.73565	−	8.17993i	−0.128816	−	0.282067i
$842$		0			0
$843$	16.1427	−	18.6297i	0.555985	−	0.641641i
$844$		0			0
$845$	10.4148	+	6.69318i	0.358280	+	0.230252i
$846$		0			0
$847$	−108.708	+	69.8627i	−3.73527	+	2.40051i
$848$		0			0
$849$	11.6778	−	3.42892i	0.400782	−	0.117680i
$850$		0			0
$851$	−3.70943	+	2.16844i	−0.127157	+	0.0743333i
$852$		0			0
$853$	38.9445	−	11.4351i	1.33343	−	0.391531i	0.464111	−	0.885777i	$-0.346374\pi$
$853$	38.9445	−	11.4351i	1.33343	−	0.391531i	0.869322	+	0.494246i	$0.164556\pi$
$854$		0			0
$855$	0.556374	−	0.357560i	0.0190276	−	0.0122283i
$856$		0			0
$857$	14.0063	+	9.00133i	0.478448	+	0.307480i	0.757545	−	0.652783i	$-0.226399\pi$
$857$	14.0063	+	9.00133i	0.478448	+	0.307480i	−0.279097	+	0.960263i	$0.590035\pi$
$858$		0			0
$859$	16.2272	−	18.7272i	0.553665	−	0.638964i	−0.408068	−	0.912952i	$-0.633797\pi$
$859$	16.2272	−	18.7272i	0.553665	−	0.638964i	0.961733	+	0.273988i	$0.0883428\pi$
$860$		0			0
$861$	3.81082	+	8.34453i	0.129872	+	0.284381i
$862$		0			0
$863$	45.4469	+	13.3444i	1.54703	+	0.454250i	0.940212	−	0.340590i	$-0.110627\pi$
$863$	45.4469	+	13.3444i	1.54703	+	0.454250i	0.606820	+	0.794839i	$0.292445\pi$
$864$		0			0
$865$	−0.929584	+	6.46540i	−0.0316068	+	0.219830i
$866$		0			0
$867$	11.8027	−	25.8443i	0.400840	−	0.877718i
$868$		0			0
$869$	−1.65627	−	11.5196i	−0.0561852	−	0.390777i
$870$		0			0
$871$	−0.829884	−	0.957738i	−0.0281196	−	0.0324517i
$872$		0			0
$873$	19.8677			0.672421
$874$		0			0
$875$	4.33481			0.146543
$876$		0			0
$877$	−20.3831	−	23.5234i	−0.688289	−	0.794328i	0.298831	−	0.954306i	$-0.403403\pi$
$877$	−20.3831	−	23.5234i	−0.688289	−	0.794328i	−0.987121	+	0.159978i	$0.948858\pi$
$878$		0			0
$879$	2.31154	+	16.0771i	0.0779663	+	0.542268i
$880$		0			0
$881$	2.22901	−	4.88086i	0.0750973	−	0.164440i	−0.868360	−	0.495935i	$-0.834826\pi$
$881$	2.22901	−	4.88086i	0.0750973	−	0.164440i	0.943457	+	0.331494i	$0.107553\pi$
$882$		0			0
$883$	−4.74692	+	33.0155i	−0.159746	+	1.11106i	0.739353	+	0.673318i	$0.235131\pi$
$883$	−4.74692	+	33.0155i	−0.159746	+	1.11106i	−0.899100	+	0.437744i	$0.855778\pi$
$884$		0			0
$885$	−13.3600	−	3.92285i	−0.449092	−	0.131865i
$886$		0			0
$887$	21.8754	+	47.9004i	0.734503	+	1.60834i	0.792391	+	0.610014i	$0.208836\pi$
$887$	21.8754	+	47.9004i	0.734503	+	1.60834i	−0.0578876	+	0.998323i	$0.518437\pi$
$888$		0			0
$889$	55.9826	−	64.6073i	1.87760	−	2.16686i
$890$		0			0
$891$	3.39721	+	2.18326i	0.113811	+	0.0731419i
$892$		0			0
$893$	3.03048	−	1.94757i	0.101411	−	0.0651730i
$894$		0			0
$895$	23.7698	−	6.97944i	0.794536	−	0.233297i
$896$		0			0
$897$	−3.76044	+	0.933814i	−0.125557	+	0.0311791i
$898$		0			0
$899$	34.6594	−	10.1769i	1.15596	−	0.339420i
$900$		0			0
$901$	51.1462	−	32.8696i	1.70393	−	1.09505i
$902$		0			0
$903$	12.7975	+	8.22447i	0.425875	+	0.273693i
$904$		0			0
$905$	−12.1628	+	14.0366i	−0.404304	+	0.466591i
$906$		0			0
$907$	−1.38077	−	3.02346i	−0.0458476	−	0.100392i	0.885322	−	0.464978i	$-0.153938\pi$
$907$	−1.38077	−	3.02346i	−0.0458476	−	0.100392i	−0.931170	+	0.364586i	$0.881211\pi$
$908$		0			0
$909$	−6.08190	−	1.78581i	−0.201724	−	0.0592314i
$910$		0			0
$911$	−6.65671	+	46.2984i	−0.220547	+	1.53394i	0.515432	+	0.856930i	$0.327631\pi$
$911$	−6.65671	+	46.2984i	−0.220547	+	1.53394i	−0.735979	+	0.677005i	$0.763278\pi$
$912$		0			0
$913$	6.02864	−	13.2009i	0.199519	−	0.436885i
$914$		0			0
$915$	−1.05022	−	7.30443i	−0.0347192	−	0.241477i
$916$		0			0
$917$	44.1243	+	50.9222i	1.45711	+	1.68160i
$918$		0			0
$919$	44.6697			1.47352			0.736758	−	0.676156i	$-0.236356\pi$
$919$	44.6697			1.47352			0.736758	+	0.676156i	$0.236356\pi$
$920$		0			0
$921$	−26.4992			−0.873179
$922$		0			0
$923$	2.71128	+	3.12898i	0.0892428	+	0.102992i
$924$		0			0
$925$	−0.127505	−	0.886813i	−0.00419232	−	0.0291582i
$926$		0			0
$927$	−9.19065	+	20.1247i	−0.301860	+	0.660982i
$928$		0			0
$929$	−0.642049	+	4.46555i	−0.0210649	+	0.146510i	−0.997639	−	0.0686696i	$-0.978125\pi$
$929$	−0.642049	+	4.46555i	−0.0210649	+	0.146510i	0.976575	+	0.215179i	$0.0690336\pi$
$930$		0			0
$931$	−3.84274	−	1.12833i	−0.125941	−	0.0369795i
$932$		0			0
$933$	7.93253	+	17.3698i	0.259699	+	0.568662i
$934$		0			0
$935$	−27.9660	+	32.2745i	−0.914585	+	1.05549i
$936$		0			0
$937$	20.4204	+	13.1234i	0.667106	+	0.428723i	0.829881	−	0.557940i	$-0.188408\pi$
$937$	20.4204	+	13.1234i	0.667106	+	0.428723i	−0.162775	+	0.986663i	$0.552044\pi$
$938$		0			0
$939$	15.0128	−	9.64814i	0.489924	−	0.314855i
$940$		0			0
$941$	−20.8446	+	6.12053i	−0.679515	+	0.199524i	−0.603236	−	0.797563i	$-0.706122\pi$
$941$	−20.8446	+	6.12053i	−0.679515	+	0.199524i	−0.0762791	+	0.997087i	$0.524304\pi$
$942$		0			0
$943$	−6.78657	+	7.19499i	−0.221001	+	0.234301i
$944$		0			0
$945$	21.1136	−	6.19951i	0.686826	−	0.201670i
$946$		0			0
$947$	−15.1886	+	9.76112i	−0.493563	+	0.317194i	−0.763637	−	0.645646i	$-0.776588\pi$
$947$	−15.1886	+	9.76112i	−0.493563	+	0.317194i	0.270074	+	0.962840i	$0.412952\pi$
$948$		0			0
$949$	−1.44439	−	0.928252i	−0.0468868	−	0.0301323i
$950$		0			0
$951$	−0.118155	+	0.136358i	−0.00383142	+	0.00442170i
$952$		0			0
$953$	−18.6863	−	40.9173i	−0.605308	−	1.32544i	−0.925737	−	0.378167i	$-0.876554\pi$
$953$	−18.6863	−	40.9173i	−0.605308	−	1.32544i	0.320429	−	0.947272i	$-0.396173\pi$
$954$		0			0
$955$	4.91539	+	1.44329i	0.159058	+	0.0467038i
$956$		0			0
$957$	4.17287	−	29.0230i	0.134890	−	0.938179i
$958$		0			0
$959$	−11.2538	+	24.6423i	−0.363403	+	0.795741i
$960$		0			0
$961$	−4.86974	−	33.8698i	−0.157088	−	1.09257i
$962$		0			0
$963$	2.04148	+	2.35599i	0.0657858	+	0.0759209i
$964$		0			0
$965$	−14.2246			−0.457905
$966$		0			0
$967$	35.0490			1.12710			0.563550	−	0.826082i	$-0.309435\pi$
$967$	35.0490			1.12710			0.563550	+	0.826082i	$0.309435\pi$
$968$		0			0
$969$	1.52585	+	1.76093i	0.0490175	+	0.0565692i
$970$		0			0
$971$	1.29576	+	9.01218i	0.0415828	+	0.289215i	0.999993	+	0.00381940i	$0.00121575\pi$
$971$	1.29576	+	9.01218i	0.0415828	+	0.289215i	−0.958410	+	0.285395i	$0.907875\pi$
$972$		0			0
$973$	21.2014	−	46.4247i	0.679687	−	1.48831i
$974$		0			0
$975$	0.114979	−	0.799697i	0.00368228	−	0.0256108i
$976$		0			0
$977$	55.3426	+	16.2501i	1.77057	+	0.519885i	0.993925	−	0.110058i	$-0.0351037\pi$
$977$	55.3426	+	16.2501i	1.77057	+	0.519885i	0.776641	+	0.629943i	$0.216922\pi$
$978$		0			0
$979$	−13.8236	−	30.2695i	−0.441804	−	0.967417i
$980$		0			0
$981$	6.06793	−	7.00276i	0.193734	−	0.223581i
$982$		0			0
$983$	−18.0204	−	11.5810i	−0.574761	−	0.369376i	0.220736	−	0.975334i	$-0.429154\pi$
$983$	−18.0204	−	11.5810i	−0.574761	−	0.369376i	−0.795497	+	0.605957i	$0.792790\pi$
$984$		0			0
$985$	−7.91915	+	5.08933i	−0.252325	+	0.162159i
$986$		0			0
$987$	45.2624	−	13.2902i	1.44072	−	0.423033i
$988$		0			0
$989$	−3.01698	+	16.1218i	−0.0959343	+	0.512644i
$990$		0			0
$991$	26.3051	−	7.72387i	0.835609	−	0.245357i	0.164184	−	0.986430i	$-0.447501\pi$
$991$	26.3051	−	7.72387i	0.835609	−	0.245357i	0.671425	+	0.741073i	$0.265683\pi$
$992$		0			0
$993$	6.60706	−	4.24610i	0.209669	−	0.134746i
$994$		0			0
$995$	−16.0898	−	10.3403i	−0.510082	−	0.327810i
$996$		0			0
$997$	−30.1362	+	34.7790i	−0.954423	+	1.10146i	0.0403331	+	0.999186i	$0.487158\pi$
$997$	−30.1362	+	34.7790i	−0.954423	+	1.10146i	−0.994756	+	0.102276i	$0.967387\pi$
$998$		0			0
$999$	−1.88933	−	4.13706i	−0.0597758	−	0.130891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.101.2	yes	50
23.18	even	11	inner	460.2.m.b.41.2	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.41.2	✓	50	23.18	even	11	inner
460.2.m.b.101.2	yes	50	1.1	even	1	trivial

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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.671975 - 0.775501i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.80075 + 3.94308i) q^{7} +(0.277094 - 1.92723i) q^{9} +O(q^{10})\)	\(q+(-0.671975 - 0.775501i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-1.80075 + 3.94308i) q^{7} +(0.277094 - 1.92723i) q^{9} +(-6.12952 - 1.79979i) q^{11} +(-0.327074 - 0.716192i) q^{13} +(0.671975 - 0.775501i) q^{15} +(-5.62371 - 3.61414i) q^{17} +(0.285753 - 0.183642i) q^{19} +(4.26792 - 1.25317i) q^{21} +(2.98491 + 3.75371i) q^{23} +(-0.959493 + 0.281733i) q^{25} +(-4.27049 + 2.74448i) q^{27} +(-3.76290 - 2.41827i) q^{29} +(-5.28851 + 6.10326i) q^{31} +(2.72315 + 5.96286i) q^{33} +(-4.15922 - 1.22126i) q^{35} +(-0.127505 + 0.886813i) q^{37} +(-0.335622 + 0.734910i) q^{39} +(0.293503 + 2.04136i) q^{41} +(2.23961 + 2.58465i) q^{43} +1.94705 q^{45} +10.6053 q^{47} +(-7.72119 - 8.91073i) q^{49} +(0.976227 + 6.78981i) q^{51} +(-3.77809 + 8.27286i) q^{53} +(0.909149 - 6.32327i) q^{55} +(-0.334433 - 0.0981985i) q^{57} +(-5.63693 - 12.3432i) q^{59} +(4.70949 - 5.43504i) q^{61} +(7.10025 + 4.56305i) q^{63} +(0.662355 - 0.425670i) q^{65} +(1.54435 - 0.453463i) q^{67} +(0.905216 - 4.83720i) q^{69} +(-5.04548 + 1.48149i) q^{71} +(1.83451 - 1.17897i) q^{73} +(0.863239 + 0.554770i) q^{75} +(18.1344 - 20.9282i) q^{77} +(0.756796 + 1.65715i) q^{79} +(-0.606531 - 0.178094i) q^{81} +(-0.323297 + 2.24858i) q^{83} +(2.77702 - 6.08082i) q^{85} +(0.653206 + 4.54315i) q^{87} +(3.41117 + 3.93670i) q^{89} +3.41298 q^{91} +8.28683 q^{93} +(0.222440 + 0.256709i) q^{95} +(1.45218 + 10.1002i) q^{97} +(-5.16706 + 11.3143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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