LMFDB - Embedded newform 572.2.p.a.309.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(309,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("572.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.p (of order $6$, degree $2$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.10
Character	$\chi$	$=$	572.309
Dual form			572.2.p.a.485.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.994483 + 1.72249i) q^{3} -2.64929i q^{5} +(-0.165013 - 0.0952705i) q^{7} +(-0.477992 + 0.827907i) q^{9} +O(q^{10})$	\(q+(0.994483 + 1.72249i) q^{3} -2.64929i q^{5} +(-0.165013 - 0.0952705i) q^{7} +(-0.477992 + 0.827907i) q^{9} +(0.866025 - 0.500000i) q^{11} +(2.36507 + 2.72148i) q^{13} +(4.56339 - 2.63467i) q^{15} +(1.73845 - 3.01108i) q^{17} +(7.06684 + 4.08004i) q^{19} -0.378979i q^{21} +(-1.64923 - 2.85655i) q^{23} -2.01875 q^{25} +4.06548 q^{27} +(-2.33338 - 4.04153i) q^{29} +2.17098i q^{31} +(1.72249 + 0.994483i) q^{33} +(-0.252399 + 0.437168i) q^{35} +(-6.49487 + 3.74981i) q^{37} +(-2.33571 + 6.78028i) q^{39} +(-1.57935 + 0.911838i) q^{41} +(4.88739 - 8.46522i) q^{43} +(2.19337 + 1.26634i) q^{45} +12.0728i q^{47} +(-3.48185 - 6.03074i) q^{49} +6.91544 q^{51} -2.84991 q^{53} +(-1.32465 - 2.29435i) q^{55} +16.2301i q^{57} +(6.41710 + 3.70492i) q^{59} +(-5.30941 + 9.19617i) q^{61} +(0.157750 - 0.0910771i) q^{63} +(7.20999 - 6.26576i) q^{65} +(-8.95316 + 5.16911i) q^{67} +(3.28027 - 5.68159i) q^{69} +(-11.1563 - 6.44112i) q^{71} -10.7491i q^{73} +(-2.00761 - 3.47728i) q^{75} -0.190541 q^{77} +1.21943 q^{79} +(5.47702 + 9.48648i) q^{81} -7.54640i q^{83} +(-7.97724 - 4.60566i) q^{85} +(4.64101 - 8.03846i) q^{87} +(-7.99487 + 4.61584i) q^{89} +(-0.130991 - 0.674401i) q^{91} +(-3.73951 + 2.15901i) q^{93} +(10.8092 - 18.7221i) q^{95} +(7.71339 + 4.45333i) q^{97} +0.955984i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.994483	+	1.72249i	0.574165	+	0.994483i	0.996132	+	0.0878716i	$0.0280065\pi$
$3$	0.994483	+	1.72249i	0.574165	+	0.994483i	−0.421967	+	0.906611i	$0.638660\pi$
$4$		0			0
$5$		−	2.64929i		−	1.18480i	−0.805644	−	0.592400i	$-0.798181\pi$
$5$		−	2.64929i		−	1.18480i	0.805644	−	0.592400i	$-0.201819\pi$
$6$		0			0
$7$	−0.165013	−	0.0952705i	−0.0623692	−	0.0360089i	0.468491	−	0.883468i	$-0.344798\pi$
$7$	−0.165013	−	0.0952705i	−0.0623692	−	0.0360089i	−0.530860	+	0.847459i	$0.678131\pi$
$8$		0			0
$9$	−0.477992	+	0.827907i	−0.159331	+	0.275969i
$10$		0			0
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$		0			0
$13$	2.36507	+	2.72148i	0.655952	+	0.754802i
$13$	2.36507	+	2.72148i	0.655952	+	0.754802i
$14$		0			0
$15$	4.56339	−	2.63467i	1.17826	−	0.680270i
$16$		0			0
$17$	1.73845	−	3.01108i	0.421636	−	0.730295i	−0.574464	−	0.818530i	$-0.694789\pi$
$17$	1.73845	−	3.01108i	0.421636	−	0.730295i	0.996100	+	0.0882349i	$0.0281226\pi$
$18$		0			0
$19$	7.06684	+	4.08004i	1.62124	+	0.936026i	0.986588	+	0.163232i	$0.0521919\pi$
$19$	7.06684	+	4.08004i	1.62124	+	0.936026i	0.634657	+	0.772794i	$0.281141\pi$
$20$		0			0
$21$		−	0.378979i		−	0.0827001i
$22$		0			0
$23$	−1.64923	−	2.85655i	−0.343889	−	0.595633i	0.641263	−	0.767322i	$-0.278411\pi$
$23$	−1.64923	−	2.85655i	−0.343889	−	0.595633i	−0.985151	+	0.171689i	$0.945078\pi$
$24$		0			0
$25$	−2.01875			−0.403749
$26$		0			0
$27$	4.06548			0.782401
$28$		0			0
$29$	−2.33338	−	4.04153i	−0.433297	−	0.750493i	0.563858	−	0.825872i	$-0.309317\pi$
$29$	−2.33338	−	4.04153i	−0.433297	−	0.750493i	−0.997155	+	0.0753790i	$0.975983\pi$
$30$		0			0
$31$			2.17098i			0.389920i	0.980811	+	0.194960i	$0.0624578\pi$
$31$			2.17098i			0.389920i	−0.980811	+	0.194960i	$0.937542\pi$
$32$		0			0
$33$	1.72249	+	0.994483i	0.299848	+	0.173117i
$34$		0			0
$35$	−0.252399	+	0.437168i	−0.0426633	+	0.0738949i
$36$		0			0
$37$	−6.49487	+	3.74981i	−1.06775	+	0.616465i	−0.927566	−	0.373660i	$-0.878103\pi$
$37$	−6.49487	+	3.74981i	−1.06775	+	0.616465i	−0.140184	+	0.990126i	$0.544769\pi$
$38$		0			0
$39$	−2.33571	+	6.78028i	−0.374013	+	1.08571i
$40$		0			0
$41$	−1.57935	+	0.911838i	−0.246653	+	0.142405i	−0.618231	−	0.785997i	$-0.712150\pi$
$41$	−1.57935	+	0.911838i	−0.246653	+	0.142405i	0.371578	+	0.928402i	$0.378817\pi$
$42$		0			0
$43$	4.88739	−	8.46522i	0.745321	−	1.29093i	−0.204724	−	0.978820i	$-0.565630\pi$
$43$	4.88739	−	8.46522i	0.745321	−	1.29093i	0.950045	−	0.312114i	$-0.101037\pi$
$44$		0			0
$45$	2.19337	+	1.26634i	0.326968	+	0.188775i
$46$		0			0
$47$			12.0728i			1.76099i	0.474051	+	0.880497i	$0.342791\pi$
$47$			12.0728i			1.76099i	−0.474051	+	0.880497i	$0.657209\pi$
$48$		0			0
$49$	−3.48185	−	6.03074i	−0.497407	−	0.861534i
$50$		0			0
$51$	6.91544			0.968355
$52$		0			0
$53$	−2.84991			−0.391466			−0.195733	−	0.980657i	$-0.562709\pi$
$53$	−2.84991			−0.391466			−0.195733	+	0.980657i	$0.562709\pi$
$54$		0			0
$55$	−1.32465	−	2.29435i	−0.178615	−	0.309371i
$56$		0			0
$57$			16.2301i			2.14973i
$58$		0			0
$59$	6.41710	+	3.70492i	0.835436	+	0.482339i	0.855710	−	0.517455i	$-0.173121\pi$
$59$	6.41710	+	3.70492i	0.835436	+	0.482339i	−0.0202743	+	0.999794i	$0.506454\pi$
$60$		0			0
$61$	−5.30941	+	9.19617i	−0.679801	+	1.17745i	0.295240	+	0.955423i	$0.404600\pi$
$61$	−5.30941	+	9.19617i	−0.679801	+	1.17745i	−0.975041	+	0.222026i	$0.928733\pi$
$62$		0			0
$63$	0.157750	−	0.0910771i	0.0198746	−	0.0114746i
$64$		0			0
$65$	7.20999	−	6.26576i	0.894289	−	0.777172i
$66$		0			0
$67$	−8.95316	+	5.16911i	−1.09380	+	0.631507i	−0.934586	−	0.355736i	$-0.884230\pi$
$67$	−8.95316	+	5.16911i	−1.09380	+	0.631507i	−0.159217	+	0.987244i	$0.550897\pi$
$68$		0			0
$69$	3.28027	−	5.68159i	0.394898	−	0.683983i
$70$		0			0
$71$	−11.1563	−	6.44112i	−1.32401	−	0.764420i	−0.339648	−	0.940553i	$-0.610308\pi$
$71$	−11.1563	−	6.44112i	−1.32401	−	0.764420i	−0.984366	+	0.176133i	$0.943641\pi$
$72$		0			0
$73$		−	10.7491i		−	1.25809i	−0.777369	−	0.629045i	$-0.783446\pi$
$73$		−	10.7491i		−	1.25809i	0.777369	−	0.629045i	$-0.216554\pi$
$74$		0			0
$75$	−2.00761	−	3.47728i	−0.231819	−	0.401521i
$76$		0			0
$77$	−0.190541			−0.0217142
$78$		0			0
$79$	1.21943			0.137197			0.0685985	−	0.997644i	$-0.478147\pi$
$79$	1.21943			0.137197			0.0685985	+	0.997644i	$0.478147\pi$
$80$		0			0
$81$	5.47702	+	9.48648i	0.608558	+	1.05405i
$82$		0			0
$83$		−	7.54640i		−	0.828326i	−0.910203	−	0.414163i	$-0.864074\pi$
$83$		−	7.54640i		−	0.828326i	0.910203	−	0.414163i	$-0.135926\pi$
$84$		0			0
$85$	−7.97724	−	4.60566i	−0.865253	−	0.499554i
$86$		0			0
$87$	4.64101	−	8.03846i	0.497568	−	0.861814i
$88$		0			0
$89$	−7.99487	+	4.61584i	−0.847454	+	0.489278i	−0.859791	−	0.510646i	$-0.829406\pi$
$89$	−7.99487	+	4.61584i	−0.847454	+	0.489278i	0.0123370	+	0.999924i	$0.496073\pi$
$90$		0			0
$91$	−0.130991	−	0.674401i	−0.0137316	−	0.0706965i
$92$		0			0
$93$	−3.73951	+	2.15901i	−0.387769	+	0.223879i
$94$		0			0
$95$	10.8092	−	18.7221i	1.10900	−	1.92085i
$96$		0			0
$97$	7.71339	+	4.45333i	0.783176	+	0.452167i	0.837555	−	0.546353i	$-0.183984\pi$
$97$	7.71339	+	4.45333i	0.783176	+	0.452167i	−0.0543785	+	0.998520i	$0.517318\pi$
$98$		0			0
$99$			0.955984i			0.0960800i
$100$		0			0
$101$	0.273962	+	0.474517i	0.0272603	+	0.0472162i	0.879334	−	0.476206i	$-0.157988\pi$
$101$	0.273962	+	0.474517i	0.0272603	+	0.0472162i	−0.852073	+	0.523422i	$0.824655\pi$
$102$		0			0
$103$	4.10775			0.404749			0.202374	−	0.979308i	$-0.435134\pi$
$103$	4.10775			0.404749			0.202374	+	0.979308i	$0.435134\pi$
$104$		0			0
$105$	−1.00403			−0.0979830
$106$		0			0
$107$	−9.48568	−	16.4297i	−0.917015	−	1.58832i	−0.803924	−	0.594732i	$-0.797258\pi$
$107$	−9.48568	−	16.4297i	−0.917015	−	1.58832i	−0.113091	−	0.993585i	$-0.536075\pi$
$108$		0			0
$109$			3.76372i			0.360499i	0.983621	+	0.180250i	$0.0576905\pi$
$109$			3.76372i			0.360499i	−0.983621	+	0.180250i	$0.942309\pi$
$110$		0			0
$111$	−12.9181	−	7.45825i	−1.22613	−	0.707906i
$112$		0			0
$113$	−3.74900	+	6.49346i	−0.352677	+	0.610854i	−0.986717	−	0.162446i	$-0.948062\pi$
$113$	−3.74900	+	6.49346i	−0.352677	+	0.610854i	0.634041	+	0.773300i	$0.281395\pi$
$114$		0			0
$115$	−7.56784	+	4.36930i	−0.705705	+	0.407439i
$116$		0			0
$117$	−3.38362	+	0.657212i	−0.312815	+	0.0607592i
$118$		0			0
$119$	−0.573735	+	0.331246i	−0.0525942	+	0.0303653i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	−3.14127	−	1.81361i	−0.283239	−	0.163528i
$124$		0			0
$125$		−	7.89821i		−	0.706438i
$126$		0			0
$127$	−4.35454	−	7.54228i	−0.386403	−	0.669269i	0.605560	−	0.795800i	$-0.292949\pi$
$127$	−4.35454	−	7.54228i	−0.386403	−	0.669269i	−0.991963	+	0.126531i	$0.959616\pi$
$128$		0			0
$129$	19.4417			1.71175
$130$		0			0
$131$	−0.0899845			−0.00786198			−0.00393099	−	0.999992i	$-0.501251\pi$
$131$	−0.0899845			−0.00786198			−0.00393099	+	0.999992i	$0.501251\pi$
$132$		0			0
$133$	−0.777415	−	1.34652i	−0.0674104	−	0.116758i
$134$		0			0
$135$		−	10.7706i		−	0.926988i
$136$		0			0
$137$	−0.0288239	−	0.0166415i	−0.00246259	−	0.00142178i	0.498768	−	0.866735i	$-0.333786\pi$
$137$	−0.0288239	−	0.0166415i	−0.00246259	−	0.00142178i	−0.501231	+	0.865314i	$0.667119\pi$
$138$		0			0
$139$	−4.65590	+	8.06426i	−0.394908	+	0.684002i	−0.993090	−	0.117359i	$-0.962557\pi$
$139$	−4.65590	+	8.06426i	−0.394908	+	0.684002i	0.598181	+	0.801361i	$0.295890\pi$
$140$		0			0
$141$	−20.7953	+	12.0062i	−1.75128	+	1.01110i
$142$		0			0
$143$	3.40895	+	1.17433i	0.285071	+	0.0982028i
$144$		0			0
$145$	−10.7072	+	6.18180i	−0.889183	+	0.513370i
$146$		0			0
$147$	6.92527	−	11.9949i	0.571187	−	0.989325i
$148$		0			0
$149$	5.18058	+	2.99101i	0.424409	+	0.245033i	0.696962	−	0.717108i	$-0.254535\pi$
$149$	5.18058	+	2.99101i	0.424409	+	0.245033i	−0.272553	+	0.962141i	$0.587868\pi$
$150$		0			0
$151$			16.7393i			1.36223i	0.732179	+	0.681113i	$0.238504\pi$
$151$			16.7393i			1.36223i	−0.732179	+	0.681113i	$0.761496\pi$
$152$		0			0
$153$	1.66193	+	2.87855i	0.134359	+	0.232717i
$154$		0			0
$155$	5.75157			0.461977
$156$		0			0
$157$	−23.9964			−1.91512			−0.957560	−	0.288235i	$-0.906932\pi$
$157$	−23.9964			−1.91512			−0.957560	+	0.288235i	$0.906932\pi$
$158$		0			0
$159$	−2.83419	−	4.90896i	−0.224766	−	0.389306i
$160$		0			0
$161$			0.628492i			0.0495321i
$162$		0			0
$163$	4.36893	+	2.52240i	0.342201	+	0.197570i	0.661245	−	0.750170i	$-0.270028\pi$
$163$	4.36893	+	2.52240i	0.342201	+	0.197570i	−0.319044	+	0.947740i	$0.603362\pi$
$164$		0			0
$165$	2.63467	−	4.56339i	0.205109	−	0.355259i
$166$		0			0
$167$	−7.09291	+	4.09509i	−0.548866	+	0.316888i	−0.748664	−	0.662949i	$-0.769305\pi$
$167$	−7.09291	+	4.09509i	−0.548866	+	0.316888i	0.199799	+	0.979837i	$0.435971\pi$
$168$		0			0
$169$	−1.81289	+	12.8730i	−0.139453	+	0.990229i
$170$		0			0
$171$	−6.75579	+	3.90046i	−0.516628	+	0.298275i
$172$		0			0
$173$	−0.668866	+	1.15851i	−0.0508530	+	0.0880799i	−0.890331	−	0.455313i	$-0.849527\pi$
$173$	−0.668866	+	1.15851i	−0.0508530	+	0.0880799i	0.839478	+	0.543393i	$0.182861\pi$
$174$		0			0
$175$	0.333120	+	0.192327i	0.0251815	+	0.0145385i
$176$		0			0
$177$			14.7379i			1.10777i
$178$		0			0
$179$	5.78274	+	10.0160i	0.432222	+	0.748631i	0.997064	−	0.0765681i	$-0.0243963\pi$
$179$	5.78274	+	10.0160i	0.432222	+	0.748631i	−0.564842	+	0.825199i	$0.691063\pi$
$180$		0			0
$181$	−18.5975			−1.38234			−0.691170	−	0.722693i	$-0.742904\pi$
$181$	−18.5975			−1.38234			−0.691170	+	0.722693i	$0.742904\pi$
$182$		0			0
$183$	−21.1205			−1.56127
$184$		0			0
$185$	9.93435	+	17.2068i	0.730388	+	1.26507i
$186$		0			0
$187$		−	3.47690i		−	0.254256i
$188$		0			0
$189$	−0.670858	−	0.387320i	−0.0487977	−	0.0281734i
$190$		0			0
$191$	−2.62620	+	4.54872i	−0.190025	+	0.329134i	−0.945258	−	0.326323i	$-0.894190\pi$
$191$	−2.62620	+	4.54872i	−0.190025	+	0.329134i	0.755233	+	0.655456i	$0.227524\pi$
$192$		0			0
$193$	−3.37407	+	1.94802i	−0.242871	+	0.140222i	−0.616496	−	0.787358i	$-0.711448\pi$
$193$	−3.37407	+	1.94802i	−0.242871	+	0.140222i	0.373625	+	0.927580i	$0.378115\pi$
$194$		0			0
$195$	17.9629	+	6.18798i	1.28635	+	0.443131i
$196$		0			0
$197$	17.4966	−	10.1017i	1.24658	−	0.719715i	0.276156	−	0.961113i	$-0.410939\pi$
$197$	17.4966	−	10.1017i	1.24658	−	0.719715i	0.970426	+	0.241398i	$0.0776060\pi$
$198$		0			0
$199$	−5.68321	+	9.84361i	−0.402872	+	0.697795i	−0.994071	−	0.108731i	$-0.965321\pi$
$199$	−5.68321	+	9.84361i	−0.402872	+	0.697795i	0.591199	+	0.806526i	$0.298655\pi$
$200$		0			0
$201$	−17.8075	−	10.2812i	−1.25605	−	0.725179i
$202$		0			0
$203$			0.889208i			0.0624102i
$204$		0			0
$205$	2.41572	+	4.18416i	0.168721	+	0.292234i
$206$		0			0
$207$	3.15328			0.219168
$208$		0			0
$209$	8.16009			0.564445
$210$		0			0
$211$	−1.63748	−	2.83620i	−0.112729	−	0.195252i	0.804141	−	0.594439i	$-0.202626\pi$
$211$	−1.63748	−	2.83620i	−0.112729	−	0.195252i	−0.916870	+	0.399187i	$0.869292\pi$
$212$		0			0
$213$		−	25.6223i		−	1.75561i
$214$		0			0
$215$	−22.4268	−	12.9481i	−1.52950	−	0.883055i
$216$		0			0
$217$	0.206831	−	0.358241i	0.0140406	−	0.0243190i
$218$		0			0
$219$	18.5153	−	10.6898i	1.25115	−	0.722351i
$220$		0			0
$221$	12.3062	−	2.39027i	0.827802	−	0.160787i
$222$		0			0
$223$	14.3962	−	8.31164i	0.964039	−	0.556588i	0.0666254	−	0.997778i	$-0.478777\pi$
$223$	14.3962	−	8.31164i	0.964039	−	0.556588i	0.897414	+	0.441190i	$0.145443\pi$
$224$		0			0
$225$	0.964944	−	1.67133i	0.0643296	−	0.111422i
$226$		0			0
$227$	13.8397	+	7.99037i	0.918575	+	0.530340i	0.883180	−	0.469034i	$-0.155398\pi$
$227$	13.8397	+	7.99037i	0.918575	+	0.530340i	0.0353951	+	0.999373i	$0.488731\pi$
$228$		0			0
$229$		−	0.675351i		−	0.0446284i	−0.999751	−	0.0223142i	$-0.992897\pi$
$229$		−	0.675351i		−	0.0446284i	0.999751	−	0.0223142i	$-0.00710342\pi$
$230$		0			0
$231$	−0.189490	−	0.328206i	−0.0124675	−	0.0215944i
$232$		0			0
$233$	−1.05661			−0.0692206			−0.0346103	−	0.999401i	$-0.511019\pi$
$233$	−1.05661			−0.0692206			−0.0346103	+	0.999401i	$0.511019\pi$
$234$		0			0
$235$	31.9843			2.08642
$236$		0			0
$237$	1.21271	+	2.10047i	0.0787737	+	0.136440i
$238$		0			0
$239$		−	12.9873i		−	0.840080i	−0.907506	−	0.420040i	$-0.862016\pi$
$239$		−	12.9873i		−	0.840080i	0.907506	−	0.420040i	$-0.137984\pi$
$240$		0			0
$241$	−6.10803	−	3.52647i	−0.393453	−	0.227160i	0.290202	−	0.956965i	$-0.406277\pi$
$241$	−6.10803	−	3.52647i	−0.393453	−	0.227160i	−0.683655	+	0.729805i	$0.739611\pi$
$242$		0			0
$243$	−4.79540	+	8.30587i	−0.307625	+	0.532822i
$244$		0			0
$245$	−15.9772	+	9.22443i	−1.02074	+	0.589327i
$246$		0			0
$247$	5.60982	+	28.8818i	0.356944	+	1.83771i
$248$		0			0
$249$	12.9986	−	7.50477i	0.823756	−	0.475595i
$250$		0			0
$251$	4.54309	−	7.86886i	0.286757	−	0.496678i	−0.686277	−	0.727341i	$-0.740756\pi$
$251$	4.54309	−	7.86886i	0.286757	−	0.496678i	0.973034	+	0.230663i	$0.0740893\pi$
$252$		0			0
$253$	−2.85655	−	1.64923i	−0.179590	−	0.103686i
$254$		0			0
$255$		−	18.3210i		−	1.14731i
$256$		0			0
$257$	−0.967458	−	1.67569i	−0.0603484	−	0.104526i	0.834273	−	0.551352i	$-0.185888\pi$
$257$	−0.967458	−	1.67569i	−0.0603484	−	0.104526i	−0.894621	+	0.446825i	$0.852554\pi$
$258$		0			0
$259$	1.42899			0.0887928
$260$		0			0
$261$	4.46135			0.276150
$262$		0			0
$263$	6.66256	+	11.5399i	0.410831	+	0.711580i	0.994981	−	0.100066i	$-0.0319054\pi$
$263$	6.66256	+	11.5399i	0.410831	+	0.711580i	−0.584150	+	0.811646i	$0.698572\pi$
$264$		0			0
$265$			7.55025i			0.463808i
$266$		0			0
$267$	−15.9015	−	9.18074i	−0.973157	−	0.561852i
$268$		0			0
$269$	8.13891	−	14.0970i	0.496238	−	0.859510i	−0.503752	−	0.863848i	$-0.668048\pi$
$269$	8.13891	−	14.0970i	0.496238	−	0.859510i	0.999991	+	0.00433832i	$0.00138093\pi$
$270$		0			0
$271$	−0.103866	+	0.0599672i	−0.00630942	+	0.00364275i	−0.503151	−	0.864198i	$-0.667826\pi$
$271$	−0.103866	+	0.0599672i	−0.00630942	+	0.00364275i	0.496842	+	0.867841i	$0.334493\pi$
$272$		0			0
$273$	1.03138	−	0.896313i	0.0624222	−	0.0542473i
$274$		0			0
$275$	−1.74828	+	1.00937i	−0.105426	+	0.0608675i
$276$		0			0
$277$	11.9471	−	20.6930i	0.717831	−	1.24332i	−0.244026	−	0.969769i	$-0.578468\pi$
$277$	11.9471	−	20.6930i	0.717831	−	1.24332i	0.961857	−	0.273552i	$-0.0881985\pi$
$278$		0			0
$279$	−1.79737	−	1.03771i	−0.107606	−	0.0621263i
$280$		0			0
$281$			24.2316i			1.44554i	0.691091	+	0.722768i	$0.257130\pi$
$281$			24.2316i			1.44554i	−0.691091	+	0.722768i	$0.742870\pi$
$282$		0			0
$283$	−7.94913	−	13.7683i	−0.472527	−	0.818440i	0.526979	−	0.849878i	$-0.323325\pi$
$283$	−7.94913	−	13.7683i	−0.472527	−	0.818440i	−0.999506	+	0.0314379i	$0.989991\pi$
$284$		0			0
$285$	42.9983			2.54700
$286$		0			0
$287$	0.347485			0.0205114
$288$		0			0
$289$	2.45558	+	4.25319i	0.144446	+	0.250188i
$290$		0			0
$291$			17.7150i			1.03847i
$292$		0			0
$293$	15.9061	+	9.18337i	0.929242	+	0.536498i	0.886572	−	0.462591i	$-0.153080\pi$
$293$	15.9061	+	9.18337i	0.929242	+	0.536498i	0.0426704	+	0.999089i	$0.486413\pi$
$294$		0			0
$295$	9.81541	−	17.0008i	0.571475	−	0.989824i
$296$		0			0
$297$	3.52081	−	2.03274i	0.204298	−	0.117951i
$298$		0			0
$299$	3.87350	−	11.2443i	0.224010	−	0.650275i
$300$		0			0
$301$	−1.61297	+	0.931249i	−0.0929701	+	0.0536763i
$302$		0			0
$303$	−0.544902	+	0.943798i	−0.0313038	+	0.0542198i
$304$		0			0
$305$	24.3633	+	14.0662i	1.39504	+	0.805427i
$306$		0			0
$307$			20.2829i			1.15760i	0.815468	+	0.578802i	$0.196480\pi$
$307$			20.2829i			1.15760i	−0.815468	+	0.578802i	$0.803520\pi$
$308$		0			0
$309$	4.08509	+	7.07558i	0.232393	+	0.402516i
$310$		0			0
$311$	27.6230			1.56636			0.783179	−	0.621797i	$-0.213597\pi$
$311$	27.6230			1.56636			0.783179	+	0.621797i	$0.213597\pi$
$312$		0			0
$313$	−33.5385			−1.89571			−0.947853	−	0.318708i	$-0.896751\pi$
$313$	−33.5385			−1.89571			−0.947853	+	0.318708i	$0.896751\pi$
$314$		0			0
$315$	−0.241290	−	0.417926i	−0.0135951	−	0.0235475i
$316$		0			0
$317$		−	27.6904i		−	1.55525i	−0.628728	−	0.777625i	$-0.716424\pi$
$317$		−	27.6904i		−	1.55525i	0.628728	−	0.777625i	$-0.283576\pi$
$318$		0			0
$319$	−4.04153	−	2.33338i	−0.226282	−	0.130644i
$320$		0			0
$321$	18.8667	−	32.6781i	1.05304	−	1.82391i
$322$		0			0
$323$	24.5707	−	14.1859i	1.36715	−	0.789325i
$324$		0			0
$325$	−4.77447	−	5.49397i	−0.264840	−	0.304751i
$326$		0			0
$327$	−6.48299	+	3.74296i	−0.358510	+	0.206986i
$328$		0			0
$329$	1.15018	−	1.99217i	0.0634114	−	0.109832i
$330$		0			0
$331$	−6.47684	−	3.73941i	−0.356000	−	0.205536i	0.311325	−	0.950304i	$-0.399227\pi$
$331$	−6.47684	−	3.73941i	−0.356000	−	0.205536i	−0.667324	+	0.744767i	$0.732561\pi$
$332$		0			0
$333$		−	7.16952i		−	0.392887i
$334$		0			0
$335$	13.6945	+	23.7195i	0.748209	+	1.29594i
$336$		0			0
$337$	−19.2210			−1.04704			−0.523518	−	0.852015i	$-0.675381\pi$
$337$	−19.2210			−1.04704			−0.523518	+	0.852015i	$0.675381\pi$
$338$		0			0
$339$	−14.9133			−0.809978
$340$		0			0
$341$	1.08549	+	1.88013i	0.0587827	+	0.101815i
$342$		0			0
$343$			2.66066i			0.143662i
$344$		0			0
$345$	−15.0522	−	8.69038i	−0.810382	−	0.467874i
$346$		0			0
$347$	−4.55069	+	7.88202i	−0.244294	+	0.423129i	−0.961933	−	0.273286i	$-0.911889\pi$
$347$	−4.55069	+	7.88202i	−0.244294	+	0.423129i	0.717639	+	0.696415i	$0.245223\pi$
$348$		0			0
$349$	10.6147	−	6.12843i	0.568194	−	0.328047i	−0.188234	−	0.982124i	$-0.560276\pi$
$349$	10.6147	−	6.12843i	0.568194	−	0.328047i	0.756428	+	0.654077i	$0.226943\pi$
$350$		0			0
$351$	9.61514	+	11.0641i	0.513218	+	0.590558i
$352$		0			0
$353$	−27.2920	+	15.7570i	−1.45260	+	0.838662i	−0.998629	−	0.0523522i	$-0.983328\pi$
$353$	−27.2920	+	15.7570i	−1.45260	+	0.838662i	−0.453976	+	0.891014i	$0.649995\pi$
$354$		0			0
$355$	−17.0644	+	29.5564i	−0.905684	+	1.56869i
$356$		0			0
$357$	−1.14114	−	0.658837i	−0.0603955	−	0.0348693i
$358$		0			0
$359$			28.7885i			1.51940i	0.650275	+	0.759699i	$0.274654\pi$
$359$			28.7885i			1.51940i	−0.650275	+	0.759699i	$0.725346\pi$
$360$		0			0
$361$	23.7935	+	41.2115i	1.25229	+	2.16903i
$362$		0			0
$363$	1.98897			0.104394
$364$		0			0
$365$	−28.4776			−1.49058
$366$		0			0
$367$	18.2963	+	31.6901i	0.955059	+	1.65421i	0.734232	+	0.678899i	$0.237542\pi$
$367$	18.2963	+	31.6901i	0.955059	+	1.65421i	0.220827	+	0.975313i	$0.429124\pi$
$368$		0			0
$369$		−	1.74341i		−	0.0907581i
$370$		0			0
$371$	0.470274	+	0.271513i	0.0244154	+	0.0140962i
$372$		0			0
$373$	9.34752	−	16.1904i	0.483996	−	0.838306i	−0.515835	−	0.856688i	$-0.672518\pi$
$373$	9.34752	−	16.1904i	0.483996	−	0.838306i	0.999831	+	0.0183818i	$0.00585145\pi$
$374$		0			0
$375$	13.6046	−	7.85464i	0.702540	−	0.405612i
$376$		0			0
$377$	5.48033	−	15.9087i	0.282252	−	0.819341i
$378$		0			0
$379$	−21.5281	+	12.4293i	−1.10582	+	0.638448i	−0.937745	−	0.347325i	$-0.887090\pi$
$379$	−21.5281	+	12.4293i	−1.10582	+	0.638448i	−0.168080	+	0.985773i	$0.553757\pi$
$380$		0			0
$381$	8.66102	−	15.0013i	0.443718	−	0.768542i
$382$		0			0
$383$	−15.4627	−	8.92737i	−0.790105	−	0.456167i	0.0498946	−	0.998754i	$-0.484111\pi$
$383$	−15.4627	−	8.92737i	−0.790105	−	0.456167i	−0.839999	+	0.542587i	$0.817445\pi$
$384$		0			0
$385$			0.504798i			0.0257269i
$386$		0			0
$387$	4.67227	+	8.09261i	0.237505	+	0.411371i
$388$		0			0
$389$	17.2194			0.873060			0.436530	−	0.899690i	$-0.356207\pi$
$389$	17.2194			0.873060			0.436530	+	0.899690i	$0.356207\pi$
$390$		0			0
$391$	−11.4684			−0.579984
$392$		0			0
$393$	−0.0894880	−	0.154998i	−0.00451407	−	0.00781860i
$394$		0			0
$395$		−	3.23064i		−	0.162551i
$396$		0			0
$397$	−11.0684	−	6.39036i	−0.555509	−	0.320723i	0.195832	−	0.980637i	$-0.437259\pi$
$397$	−11.0684	−	6.39036i	−0.555509	−	0.320723i	−0.751341	+	0.659914i	$0.770593\pi$
$398$		0			0
$399$	1.54625	−	2.67819i	0.0774094	−	0.134077i
$400$		0			0
$401$	−14.4557	+	8.34600i	−0.721883	+	0.416779i	−0.815445	−	0.578834i	$-0.803508\pi$
$401$	−14.4557	+	8.34600i	−0.721883	+	0.416779i	0.0935622	+	0.995613i	$0.470175\pi$
$402$		0			0
$403$	−5.90829	+	5.13453i	−0.294313	+	0.255769i
$404$		0			0
$405$	25.1325	−	14.5102i	1.24884	−	0.721019i
$406$		0			0
$407$	−3.74981	+	6.49487i	−0.185871	+	0.321939i
$408$		0			0
$409$	26.1493	+	15.0973i	1.29300	+	0.746514i	0.979185	−	0.202970i	$-0.0650595\pi$
$409$	26.1493	+	15.0973i	1.29300	+	0.746514i	0.313815	+	0.949484i	$0.398393\pi$
$410$		0			0
$411$		−	0.0661987i		−	0.00326534i
$412$		0			0
$413$	−0.705938	−	1.22272i	−0.0347370	−	0.0601662i
$414$		0			0
$415$	−19.9926			−0.981399
$416$		0			0
$417$	−18.5209			−0.906970
$418$		0			0
$419$	−8.31981	−	14.4103i	−0.406450	−	0.703991i	0.588039	−	0.808832i	$-0.299900\pi$
$419$	−8.31981	−	14.4103i	−0.406450	−	0.703991i	−0.994489	+	0.104841i	$0.966567\pi$
$420$		0			0
$421$		−	13.8517i		−	0.675088i	−0.941310	−	0.337544i	$-0.890404\pi$
$421$		−	13.8517i		−	0.675088i	0.941310	−	0.337544i	$-0.109596\pi$
$422$		0			0
$423$	−9.99513	−	5.77069i	−0.485980	−	0.280581i
$424$		0			0
$425$	−3.50949	+	6.07861i	−0.170235	+	0.294856i
$426$		0			0
$427$	1.75225	−	1.01166i	0.0847972	−	0.0489577i
$428$		0			0
$429$	1.36736	+	7.03975i	0.0660166	+	0.339883i
$430$		0			0
$431$	−17.0454	+	9.84117i	−0.821049	+	0.474033i	−0.850778	−	0.525525i	$-0.823869\pi$
$431$	−17.0454	+	9.84117i	−0.821049	+	0.474033i	0.0297294	+	0.999558i	$0.490535\pi$
$432$		0			0
$433$	16.6442	−	28.8286i	0.799871	−	1.38542i	−0.119829	−	0.992794i	$-0.538235\pi$
$433$	16.6442	−	28.8286i	0.799871	−	1.38542i	0.919700	−	0.392622i	$-0.128432\pi$
$434$		0			0
$435$	−21.2962	−	12.2954i	−1.02108	−	0.589518i
$436$		0			0
$437$		−	26.9158i		−	1.28755i
$438$		0			0
$439$	15.4736	+	26.8011i	0.738515	+	1.27915i	0.953164	+	0.302455i	$0.0978061\pi$
$439$	15.4736	+	26.8011i	0.738515	+	1.27915i	−0.214648	+	0.976691i	$0.568861\pi$
$440$		0			0
$441$	6.65718			0.317009
$442$		0			0
$443$	−18.5217			−0.879991			−0.439995	−	0.898000i	$-0.645020\pi$
$443$	−18.5217			−0.879991			−0.439995	+	0.898000i	$0.645020\pi$
$444$		0			0
$445$	12.2287	+	21.1807i	0.579696	+	1.00406i
$446$		0			0
$447$			11.8980i			0.562757i
$448$		0			0
$449$	−2.35182	−	1.35782i	−0.110989	−	0.0640796i	0.443478	−	0.896285i	$-0.353745\pi$
$449$	−2.35182	−	1.35782i	−0.110989	−	0.0640796i	−0.554467	+	0.832206i	$0.687078\pi$
$450$		0			0
$451$	−0.911838	+	1.57935i	−0.0429368	+	0.0743686i
$452$		0			0
$453$	−28.8334	+	16.6469i	−1.35471	+	0.782142i
$454$		0			0
$455$	−1.78669	+	0.347034i	−0.0837611	+	0.0162692i
$456$		0			0
$457$	5.30068	−	3.06035i	0.247955	−	0.143157i	−0.370872	−	0.928684i	$-0.620941\pi$
$457$	5.30068	−	3.06035i	0.247955	−	0.143157i	0.618828	+	0.785527i	$0.287608\pi$
$458$		0			0
$459$	7.06763	−	12.2415i	0.329889	−	0.571384i
$460$		0			0
$461$	−16.6803	−	9.63036i	−0.776878	−	0.448531i	0.0584447	−	0.998291i	$-0.481386\pi$
$461$	−16.6803	−	9.63036i	−0.776878	−	0.448531i	−0.835323	+	0.549760i	$0.814719\pi$
$462$		0			0
$463$		−	1.62227i		−	0.0753935i	−0.999289	−	0.0376967i	$-0.987998\pi$
$463$		−	1.62227i		−	0.0753935i	0.999289	−	0.0376967i	$-0.0120021\pi$
$464$		0			0
$465$	5.71984	+	9.90705i	0.265251	+	0.459428i
$466$		0			0
$467$	−16.6992			−0.772746			−0.386373	−	0.922343i	$-0.626272\pi$
$467$	−16.6992			−0.772746			−0.386373	+	0.922343i	$0.626272\pi$
$468$		0			0
$469$	1.96985			0.0909594
$470$		0			0
$471$	−23.8640	−	41.3336i	−1.09959	−	1.90455i
$472$		0			0
$473$		−	9.77479i		−	0.449445i
$474$		0			0
$475$	−14.2662	−	8.23657i	−0.654576	−	0.377920i
$476$		0			0
$477$	1.36224	−	2.35946i	0.0623725	−	0.108032i
$478$		0			0
$479$	22.3425	−	12.8994i	1.02085	−	0.589390i	0.106502	−	0.994312i	$-0.466035\pi$
$479$	22.3425	−	12.8994i	1.02085	−	0.589390i	0.914351	+	0.404923i	$0.132702\pi$
$480$		0			0
$481$	−25.5658	−	8.80707i	−1.16570	−	0.401568i
$482$		0			0
$483$	−1.08258	+	0.625025i	−0.0492589	+	0.0284396i
$484$		0			0
$485$	11.7982	−	20.4350i	0.535727	−	0.927907i
$486$		0			0
$487$	5.47569	+	3.16139i	0.248127	+	0.143256i	0.618906	−	0.785465i	$-0.287576\pi$
$487$	5.47569	+	3.16139i	0.248127	+	0.143256i	−0.370779	+	0.928721i	$0.620909\pi$
$488$		0			0
$489$			10.0339i			0.453751i
$490$		0			0
$491$	8.10401	+	14.0366i	0.365729	+	0.633461i	0.988893	−	0.148630i	$-0.0474864\pi$
$491$	8.10401	+	14.0366i	0.365729	+	0.633461i	−0.623164	+	0.782091i	$0.714153\pi$
$492$		0			0
$493$	−16.2258			−0.730775
$494$		0			0
$495$	2.53268			0.113836
$496$		0			0
$497$	1.22730	+	2.12574i	0.0550518	+	0.0953525i
$498$		0			0
$499$		−	26.6520i		−	1.19311i	−0.802573	−	0.596554i	$-0.796536\pi$
$499$		−	26.6520i		−	1.19311i	0.802573	−	0.596554i	$-0.203464\pi$
$500$		0			0
$501$	−14.1076	−	8.14500i	−0.630279	−	0.363892i
$502$		0			0
$503$	−5.70555	+	9.88231i	−0.254398	+	0.440630i	−0.964732	−	0.263235i	$-0.915211\pi$
$503$	−5.70555	+	9.88231i	−0.254398	+	0.440630i	0.710334	+	0.703865i	$0.248544\pi$
$504$		0			0
$505$	1.25713	−	0.725806i	0.0559417	−	0.0322980i
$506$		0			0
$507$	−23.9765	+	9.67925i	−1.06483	+	0.429871i
$508$		0			0
$509$	−8.10812	+	4.68122i	−0.359386	+	0.207492i	−0.668811	−	0.743432i	$-0.733197\pi$
$509$	−8.10812	+	4.68122i	−0.359386	+	0.207492i	0.309425	+	0.950924i	$0.399863\pi$
$510$		0			0
$511$	−1.02407	+	1.77375i	−0.0453024	+	0.0784660i
$512$		0			0
$513$	28.7301	+	16.5873i	1.26846	+	0.732348i
$514$		0			0
$515$		−	10.8826i		−	0.479546i
$516$		0			0
$517$	6.03639	+	10.4553i	0.265480	+	0.459825i
$518$		0			0
$519$	−2.66070			−0.116792
$520$		0			0
$521$	15.9092			0.696995			0.348497	−	0.937310i	$-0.386692\pi$
$521$	15.9092			0.696995			0.348497	+	0.937310i	$0.386692\pi$
$522$		0			0
$523$	12.0735	+	20.9119i	0.527936	+	0.914412i	0.999470	+	0.0325637i	$0.0103672\pi$
$523$	12.0735	+	20.9119i	0.527936	+	0.914412i	−0.471534	+	0.881848i	$0.656299\pi$
$524$		0			0
$525$			0.765063i			0.0333901i
$526$		0			0
$527$	6.53702	+	3.77415i	0.284757	+	0.164404i
$528$		0			0
$529$	6.06007	−	10.4963i	0.263481	−	0.456363i
$530$		0			0
$531$	−6.13465	+	3.54184i	−0.266221	+	0.153703i
$532$		0			0
$533$	−6.21682	−	2.14161i	−0.269280	−	0.0927632i
$534$		0			0
$535$	−43.5270	+	25.1303i	−1.88184	+	1.08648i
$536$		0			0
$537$	−11.5017	+	19.9215i	−0.496334	+	0.859675i
$538$		0			0
$539$	−6.03074	−	3.48185i	−0.259762	−	0.149974i
$540$		0			0
$541$			0.761896i			0.0327565i	0.999866	+	0.0163782i	$0.00521358\pi$
$541$			0.761896i			0.0327565i	−0.999866	+	0.0163782i	$0.994786\pi$
$542$		0			0
$543$	−18.4949	−	32.0340i	−0.793691	−	1.37471i
$544$		0			0
$545$	9.97119			0.427119
$546$		0			0
$547$	26.3836			1.12808			0.564040	−	0.825747i	$-0.309246\pi$
$547$	26.3836			1.12808			0.564040	+	0.825747i	$0.309246\pi$
$548$		0			0
$549$	−5.07571	−	8.79140i	−0.216626	−	0.375208i
$550$		0			0
$551$		−	38.0811i		−	1.62231i
$552$		0			0
$553$	−0.201223	−	0.116176i	−0.00855686	−	0.00494031i
$554$		0			0
$555$	−19.7591	+	34.2237i	−0.838726	+	1.45272i
$556$		0			0
$557$	−8.05383	+	4.64988i	−0.341252	+	0.197022i	−0.660825	−	0.750540i	$-0.729794\pi$
$557$	−8.05383	+	4.64988i	−0.341252	+	0.197022i	0.319574	+	0.947561i	$0.396460\pi$
$558$		0			0
$559$	34.5969	−	6.71988i	1.46329	−	0.284221i
$560$		0			0
$561$	5.98894	−	3.45772i	0.252853	−	0.145985i
$562$		0			0
$563$	4.09815	−	7.09820i	0.172716	−	0.299154i	−0.766652	−	0.642063i	$-0.778079\pi$
$563$	4.09815	−	7.09820i	0.172716	−	0.299154i	0.939369	+	0.342909i	$0.111412\pi$
$564$		0			0
$565$	17.2031	+	9.93220i	0.723739	+	0.417851i
$566$		0			0
$567$		−	2.08719i		−	0.0876539i
$568$		0			0
$569$	8.18070	+	14.1694i	0.342953	+	0.594012i	0.984980	−	0.172670i	$-0.0552396\pi$
$569$	8.18070	+	14.1694i	0.342953	+	0.594012i	−0.642027	+	0.766682i	$0.721906\pi$
$570$		0			0
$571$	−13.2551			−0.554710			−0.277355	−	0.960768i	$-0.589458\pi$
$571$	−13.2551			−0.554710			−0.277355	+	0.960768i	$0.589458\pi$
$572$		0			0
$573$	−10.4469			−0.436424
$574$		0			0
$575$	3.32938	+	5.76665i	0.138845	+	0.240486i
$576$		0			0
$577$		−	40.1367i		−	1.67091i	−0.549557	−	0.835456i	$-0.685204\pi$
$577$		−	40.1367i		−	1.67091i	0.549557	−	0.835456i	$-0.314796\pi$
$578$		0			0
$579$	−6.71091	−	3.87455i	−0.278896	−	0.161021i
$580$		0			0
$581$	−0.718950	+	1.24526i	−0.0298271	+	0.0516620i
$582$		0			0
$583$	−2.46810	+	1.42496i	−0.102218	+	0.0590157i
$584$		0			0
$585$	1.74115	+	8.96418i	0.0719875	+	0.370623i
$586$		0			0
$587$	−32.9237	+	19.0085i	−1.35891	+	0.784566i	−0.989477	−	0.144693i	$-0.953781\pi$
$587$	−32.9237	+	19.0085i	−1.35891	+	0.784566i	−0.369431	+	0.929258i	$0.620447\pi$
$588$		0			0
$589$	−8.85771	+	15.3420i	−0.364976	+	0.632156i
$590$		0			0
$591$	34.8002	+	20.0919i	1.43149	+	0.826470i
$592$		0			0
$593$		−	21.9059i		−	0.899569i	−0.893137	−	0.449785i	$-0.851501\pi$
$593$		−	21.9059i		−	0.899569i	0.893137	−	0.449785i	$-0.148499\pi$
$594$		0			0
$595$	0.877567	+	1.51999i	0.0359767	+	0.0623136i
$596$		0			0
$597$	−22.6074			−0.925260
$598$		0			0
$599$	26.4065			1.07894			0.539470	−	0.842005i	$-0.318625\pi$
$599$	26.4065			1.07894			0.539470	+	0.842005i	$0.318625\pi$
$600$		0			0
$601$	−15.2316	−	26.3820i	−0.621312	−	1.07614i	−0.989242	−	0.146290i	$-0.953267\pi$
$601$	−15.2316	−	26.3820i	−0.621312	−	1.07614i	0.367930	−	0.929853i	$-0.380067\pi$
$602$		0			0
$603$		−	9.88318i		−	0.402474i
$604$		0			0
$605$	−2.29435	−	1.32465i	−0.0932787	−	0.0538545i
$606$		0			0
$607$	13.2057	−	22.8729i	0.536002	−	0.928382i	−0.463112	−	0.886300i	$-0.653267\pi$
$607$	13.2057	−	22.8729i	0.536002	−	0.928382i	0.999114	−	0.0420828i	$-0.0133993\pi$
$608$		0			0
$609$	−1.53166	+	0.884302i	−0.0620658	+	0.0358337i
$610$		0			0
$611$	−32.8558	+	28.5529i	−1.32920	+	1.15513i
$612$		0			0
$613$	23.7384	−	13.7054i	0.958785	−	0.553555i	0.0629863	−	0.998014i	$-0.479938\pi$
$613$	23.7384	−	13.7054i	0.958785	−	0.553555i	0.895799	+	0.444459i	$0.146604\pi$
$614$		0			0
$615$	−4.80479	+	8.32214i	−0.193748	+	0.335581i
$616$		0			0
$617$	−33.8441	−	19.5399i	−1.36251	−	0.786647i	−0.372555	−	0.928010i	$-0.621518\pi$
$617$	−33.8441	−	19.5399i	−1.36251	−	0.786647i	−0.989958	+	0.141363i	$0.954851\pi$
$618$		0			0
$619$			19.5639i			0.786339i	0.919466	+	0.393170i	$0.128621\pi$
$619$			19.5639i			0.786339i	−0.919466	+	0.393170i	$0.871379\pi$
$620$		0			0
$621$	−6.70491	−	11.6133i	−0.269059	−	0.466024i
$622$		0			0
$623$	1.75901			0.0704733
$624$		0			0
$625$	−31.0184			−1.24074
$626$		0			0
$627$	8.11506	+	14.0557i	0.324084	+	0.561331i
$628$		0			0
$629$			26.0754i			1.03970i
$630$		0			0
$631$	−10.2509	−	5.91838i	−0.408084	−	0.235607i	0.281882	−	0.959449i	$-0.409041\pi$
$631$	−10.2509	−	5.91838i	−0.408084	−	0.235607i	−0.689966	+	0.723842i	$0.742375\pi$
$632$		0			0
$633$	3.25689	−	5.64110i	0.129450	−	0.224214i
$634$		0			0
$635$	−19.9817	+	11.5364i	−0.792949	+	0.457810i
$636$		0			0
$637$	8.17771	−	23.7389i	0.324013	−	0.940569i
$638$		0			0
$639$	10.6653	−	6.15761i	0.421912	−	0.243591i
$640$		0			0
$641$	−5.50106	+	9.52812i	−0.217279	+	0.376338i	−0.953975	−	0.299886i	$-0.903051\pi$
$641$	−5.50106	+	9.52812i	−0.217279	+	0.376338i	0.736696	+	0.676224i	$0.236385\pi$
$642$		0			0
$643$	13.0583	+	7.53924i	0.514971	+	0.297318i	0.734875	−	0.678203i	$-0.237241\pi$
$643$	13.0583	+	7.53924i	0.514971	+	0.297318i	−0.219904	+	0.975522i	$0.570574\pi$
$644$		0			0
$645$		−	51.5068i		−	2.02808i
$646$		0			0
$647$	−9.55002	−	16.5411i	−0.375450	−	0.650299i	0.614944	−	0.788571i	$-0.289179\pi$
$647$	−9.55002	−	16.5411i	−0.375450	−	0.650299i	−0.990394	+	0.138272i	$0.955845\pi$
$648$		0			0
$649$	7.40983			0.290861
$650$		0			0
$651$	0.822758			0.0322464
$652$		0			0
$653$	−13.0657	−	22.6304i	−0.511299	−	0.885596i	−0.999914	−	0.0130963i	$-0.995831\pi$
$653$	−13.0657	−	22.6304i	−0.511299	−	0.885596i	0.488615	−	0.872499i	$-0.337502\pi$
$654$		0			0
$655$			0.238395i			0.00931487i
$656$		0			0
$657$	8.89927	+	5.13800i	0.347194	+	0.200452i
$658$		0			0
$659$	23.4770	−	40.6634i	0.914535	−	1.58402i	0.106954	−	0.994264i	$-0.465890\pi$
$659$	23.4770	−	40.6634i	0.914535	−	1.58402i	0.807581	−	0.589757i	$-0.200776\pi$
$660$		0			0
$661$	14.4811	−	8.36064i	0.563248	−	0.325191i	−0.191200	−	0.981551i	$-0.561238\pi$
$661$	14.4811	−	8.36064i	0.563248	−	0.325191i	0.754448	+	0.656360i	$0.227905\pi$
$662$		0			0
$663$	16.3555	+	18.8202i	0.635195	+	0.730916i
$664$		0			0
$665$	−3.56733	+	2.05960i	−0.138335	+	0.0798678i
$666$		0			0
$667$	−7.69656	+	13.3308i	−0.298012	+	0.516172i
$668$		0			0
$669$	28.6335	+	16.5316i	1.10704	+	0.639147i
$670$		0			0
$671$			10.6188i			0.409935i
$672$		0			0
$673$	7.87251	+	13.6356i	0.303463	+	0.525613i	0.976918	−	0.213615i	$-0.0685238\pi$
$673$	7.87251	+	13.6356i	0.303463	+	0.525613i	−0.673455	+	0.739228i	$0.735190\pi$
$674$		0			0
$675$	−8.20716			−0.315894
$676$		0			0
$677$	29.8791			1.14835			0.574174	−	0.818733i	$-0.305323\pi$
$677$	29.8791			1.14835			0.574174	+	0.818733i	$0.305323\pi$
$678$		0			0
$679$	−0.848541	−	1.46972i	−0.0325640	−	0.0564026i
$680$		0			0
$681$			31.7852i			1.21801i
$682$		0			0
$683$	−4.20036	−	2.42508i	−0.160722	−	0.0927930i	0.417482	−	0.908685i	$-0.362913\pi$
$683$	−4.20036	−	2.42508i	−0.160722	−	0.0927930i	−0.578204	+	0.815892i	$0.696246\pi$
$684$		0			0
$685$	−0.0440882	+	0.0763629i	−0.00168452	+	0.00291768i
$686$		0			0
$687$	1.16329	−	0.671625i	0.0443822	−	0.0256241i
$688$		0			0
$689$	−6.74024	−	7.75598i	−0.256783	−	0.295479i
$690$		0			0
$691$	19.7551	−	11.4056i	0.751518	−	0.433889i	−0.0747243	−	0.997204i	$-0.523808\pi$
$691$	19.7551	−	11.4056i	0.751518	−	0.433889i	0.826242	+	0.563315i	$0.190474\pi$
$692$		0			0
$693$	0.0910771	−	0.157750i	0.00345973	−	0.00599243i
$694$		0			0
$695$	21.3646	+	12.3348i	0.810404	+	0.467887i
$696$		0			0
$697$			6.34074i			0.240173i
$698$		0			0
$699$	−1.05078	−	1.82000i	−0.0397441	−	0.0688387i
$700$		0			0
$701$	−50.4218			−1.90441			−0.952203	−	0.305466i	$-0.901188\pi$
$701$	−50.4218			−1.90441			−0.952203	+	0.305466i	$0.901188\pi$
$702$		0			0
$703$	−61.1976			−2.30811
$704$		0			0
$705$	31.8078	+	55.0928i	1.19795	+	2.07491i
$706$		0			0
$707$		−	0.104402i		−	0.00392645i
$708$		0			0
$709$	−20.9118	−	12.0734i	−0.785359	−	0.453427i	0.0529671	−	0.998596i	$-0.483132\pi$
$709$	−20.9118	−	12.0734i	−0.785359	−	0.453427i	−0.838326	+	0.545169i	$0.816465\pi$
$710$		0			0
$711$	−0.582880	+	1.00958i	−0.0218597	+	0.0378621i
$712$		0			0
$713$	6.20153	−	3.58046i	0.232249	−	0.134089i
$714$		0			0
$715$	3.11116	−	9.03130i	0.116351	−	0.337752i
$716$		0			0
$717$	22.3706	−	12.9157i	0.835445	−	0.482345i
$718$		0			0
$719$	7.44700	−	12.8986i	0.277726	−	0.481036i	−0.693093	−	0.720848i	$-0.743753\pi$
$719$	7.44700	−	12.8986i	0.277726	−	0.481036i	0.970819	+	0.239812i	$0.0770858\pi$
$720$		0			0
$721$	−0.677834	−	0.391347i	−0.0252438	−	0.0145745i
$722$		0			0
$723$		−	14.0281i		−	0.521709i
$724$		0			0
$725$	4.71049	+	8.15882i	0.174943	+	0.303011i
$726$		0			0
$727$	19.1909			0.711752			0.355876	−	0.934533i	$-0.384183\pi$
$727$	19.1909			0.711752			0.355876	+	0.934533i	$0.384183\pi$
$728$		0			0
$729$	13.7864			0.510607
$730$		0			0
$731$	−16.9930	−	29.4327i	−0.628508	−	1.08861i
$732$		0			0
$733$			22.7418i			0.839988i	0.907527	+	0.419994i	$0.137968\pi$
$733$			22.7418i			0.839988i	−0.907527	+	0.419994i	$0.862032\pi$
$734$		0			0
$735$	−31.7781	−	18.3471i	−1.17215	−	0.676742i
$736$		0			0
$737$	−5.16911	+	8.95316i	−0.190407	+	0.329794i
$738$		0			0
$739$	17.7095	−	10.2246i	0.651454	−	0.376117i	−0.137559	−	0.990494i	$-0.543926\pi$
$739$	17.7095	−	10.2246i	0.651454	−	0.376117i	0.789013	+	0.614376i	$0.210592\pi$
$740$		0			0
$741$	−44.1700	+	38.3854i	−1.62262	+	1.41012i
$742$		0			0
$743$	−41.6256	+	24.0325i	−1.52709	+	0.881669i	−0.527613	+	0.849485i	$0.676913\pi$
$743$	−41.6256	+	24.0325i	−1.52709	+	0.881669i	−0.999482	+	0.0321838i	$0.989754\pi$
$744$		0			0
$745$	7.92405	−	13.7249i	0.290315	−	0.502840i
$746$		0			0
$747$	6.24772	+	3.60712i	0.228592	+	0.131978i
$748$		0			0
$749$			3.61482i			0.132083i
$750$		0			0
$751$	3.29374	+	5.70492i	0.120190	+	0.208175i	0.919843	−	0.392288i	$-0.128316\pi$
$751$	3.29374	+	5.70492i	0.120190	+	0.208175i	−0.799652	+	0.600463i	$0.794983\pi$
$752$		0			0
$753$	18.0721			0.658584
$754$		0			0
$755$	44.3473			1.61396
$756$		0			0
$757$	−1.61864	−	2.80357i	−0.0588304	−	0.101897i	0.835110	−	0.550083i	$-0.185404\pi$
$757$	−1.61864	−	2.80357i	−0.0588304	−	0.101897i	−0.893941	+	0.448185i	$0.852070\pi$
$758$		0			0
$759$		−	6.56053i		−	0.238132i
$760$		0			0
$761$	36.3104	+	20.9638i	1.31625	+	0.759938i	0.983123	−	0.182944i	$-0.0585628\pi$
$761$	36.3104	+	20.9638i	1.31625	+	0.759938i	0.333127	+	0.942882i	$0.391896\pi$
$762$		0			0
$763$	0.358572	−	0.621064i	0.0129812	−	0.0224840i
$764$		0			0
$765$	7.62612	−	4.40294i	0.275723	−	0.159189i
$766$		0			0
$767$	5.09405	+	26.2264i	0.183935	+	0.946980i
$768$		0			0
$769$	3.61022	−	2.08436i	0.130188	−	0.0751640i	−0.433492	−	0.901158i	$-0.642719\pi$
$769$	3.61022	−	2.08436i	0.130188	−	0.0751640i	0.563680	+	0.825994i	$0.309385\pi$
$770$		0			0
$771$	1.92424	−	3.33288i	0.0692998	−	0.120031i
$772$		0			0
$773$	−19.0663	−	11.0080i	−0.685769	−	0.395929i	0.116256	−	0.993219i	$-0.462911\pi$
$773$	−19.0663	−	11.0080i	−0.685769	−	0.395929i	−0.802025	+	0.597291i	$0.796244\pi$
$774$		0			0
$775$		−	4.38266i		−	0.157430i
$776$		0			0
$777$	1.42110	+	2.46142i	0.0509817	+	0.0883030i
$778$		0			0
$779$	−14.8813			−0.533180
$780$		0			0
$781$	−12.8822			−0.460963
$782$		0			0
$783$	−9.48629	−	16.4307i	−0.339012	−	0.587187i
$784$		0			0
$785$			63.5734i			2.26903i
$786$		0			0
$787$	3.60246	+	2.07988i	0.128414	+	0.0741397i	0.562831	−	0.826572i	$-0.309712\pi$
$787$	3.60246	+	2.07988i	0.128414	+	0.0741397i	−0.434417	+	0.900712i	$0.643046\pi$
$788$		0			0
$789$	−13.2516	+	22.9524i	−0.471769	+	0.817128i
$790$		0			0
$791$	1.23727	−	0.714339i	0.0439923	−	0.0253990i
$792$		0			0
$793$	−37.5843	+	7.30013i	−1.33466	+	0.259235i
$794$		0			0
$795$	−13.0053	+	7.50860i	−0.461249	+	0.266302i
$796$		0			0
$797$	23.6862	−	41.0257i	0.839009	−	1.45321i	−0.0517149	−	0.998662i	$-0.516469\pi$
$797$	23.6862	−	41.0257i	0.839009	−	1.45321i	0.890724	−	0.454545i	$-0.150198\pi$
$798$		0			0
$799$	36.3521	+	20.9879i	1.28605	+	0.742499i
$800$		0			0
$801$		−	8.82534i		−	0.311828i
$802$		0			0
$803$	−5.37456	−	9.30901i	−0.189664	−	0.328508i
$804$		0			0
$805$	1.66506			0.0586856
$806$		0			0
$807$	32.3760			1.13969
$808$		0			0
$809$	24.1795	+	41.8801i	0.850106	+	1.47243i	0.881112	+	0.472908i	$0.156796\pi$
$809$	24.1795	+	41.8801i	0.850106	+	1.47243i	−0.0310052	+	0.999519i	$0.509871\pi$
$810$		0			0
$811$		−	12.6854i		−	0.445446i	−0.974882	−	0.222723i	$-0.928506\pi$
$811$		−	12.6854i		−	0.445446i	0.974882	−	0.222723i	$-0.0714945\pi$
$812$		0			0
$813$	−0.206586	−	0.119273i	−0.00724530	−	0.00418308i
$814$		0			0
$815$	6.68258	−	11.5746i	0.234081	−	0.405440i
$816$		0			0
$817$	69.0769	−	39.8816i	2.41669	−	1.39528i
$818$		0			0
$819$	0.620954	+	0.213910i	0.0216979	+	0.00747462i
$820$		0			0
$821$	4.75307	−	2.74419i	0.165883	−	0.0957728i	−0.414760	−	0.909931i	$-0.636134\pi$
$821$	4.75307	−	2.74419i	0.165883	−	0.0957728i	0.580643	+	0.814158i	$0.302801\pi$
$822$		0			0
$823$	−9.64477	+	16.7052i	−0.336196	+	0.582308i	−0.983714	−	0.179742i	$-0.942474\pi$
$823$	−9.64477	+	16.7052i	−0.336196	+	0.582308i	0.647518	+	0.762050i	$0.275807\pi$
$824$		0			0
$825$	−3.47728	−	2.00761i	−0.121063	−	0.0698959i
$826$		0			0
$827$		−	15.3225i		−	0.532815i	−0.963861	−	0.266407i	$-0.914163\pi$
$827$		−	15.3225i		−	0.532815i	0.963861	−	0.266407i	$-0.0858367\pi$
$828$		0			0
$829$	−0.123205	−	0.213398i	−0.00427909	−	0.00741160i	0.863878	−	0.503701i	$-0.168029\pi$
$829$	−0.123205	−	0.213398i	−0.00427909	−	0.00741160i	−0.868157	+	0.496290i	$0.834695\pi$
$830$		0			0
$831$	47.5247			1.64861
$832$		0			0
$833$	−24.2121			−0.838899
$834$		0			0
$835$	10.8491	+	18.7912i	0.375449	+	0.650296i
$836$		0			0
$837$			8.82609i			0.305074i
$838$		0			0
$839$	3.57543	+	2.06428i	0.123438	+	0.0712668i	0.560448	−	0.828190i	$-0.310629\pi$
$839$	3.57543	+	2.06428i	0.123438	+	0.0712668i	−0.437010	+	0.899457i	$0.643962\pi$
$840$		0			0
$841$	3.61070	−	6.25391i	0.124507	−	0.215652i
$842$		0			0
$843$	−41.7388	+	24.0979i	−1.43756	+	0.829976i
$844$		0			0
$845$	34.1043	+	4.80288i	1.17322	+	0.165224i
$846$		0			0
$847$	−0.165013	+	0.0952705i	−0.00566992	+	0.00327353i
$848$		0			0
$849$	15.8105	−	27.3847i	0.542617	−	0.939840i
$850$		0			0
$851$	21.4231	+	12.3686i	0.734374	+	0.423991i
$852$		0			0
$853$		−	0.871461i		−	0.0298382i	−0.999889	−	0.0149191i	$-0.995251\pi$
$853$		−	0.871461i		−	0.0298382i	0.999889	−	0.0149191i	$-0.00474908\pi$
$854$		0			0
$855$	10.3334	+	17.8981i	0.353396	+	0.612101i
$856$		0			0
$857$	18.4913			0.631652			0.315826	−	0.948817i	$-0.397718\pi$
$857$	18.4913			0.631652			0.315826	+	0.948817i	$0.397718\pi$
$858$		0			0
$859$	16.3878			0.559146			0.279573	−	0.960124i	$-0.409807\pi$
$859$	16.3878			0.559146			0.279573	+	0.960124i	$0.409807\pi$
$860$		0			0
$861$	0.345568	+	0.598541i	0.0117769	+	0.0203982i
$862$		0			0
$863$			8.73163i			0.297228i	0.988895	+	0.148614i	$0.0474812\pi$
$863$			8.73163i			0.297228i	−0.988895	+	0.148614i	$0.952519\pi$
$864$		0			0
$865$	3.06923	+	1.77202i	0.104357	+	0.0602505i
$866$		0			0
$867$	−4.88407	+	8.45945i	−0.165872	+	0.287298i
$868$		0			0
$869$	1.05606	−	0.609717i	0.0358244	−	0.0206832i
$870$		0			0
$871$	−35.2425	−	12.1405i	−1.19415	−	0.411366i
$872$		0			0
$873$	−7.37388	+	4.25731i	−0.249568	+	0.144088i
$874$		0			0
$875$	−0.752466	+	1.30331i	−0.0254380	+	0.0440599i
$876$		0			0
$877$	−21.5990	−	12.4702i	−0.729347	−	0.421089i	0.0888359	−	0.996046i	$-0.471685\pi$
$877$	−21.5990	−	12.4702i	−0.729347	−	0.421089i	−0.818183	+	0.574957i	$0.805019\pi$
$878$		0			0
$879$			36.5308i			1.23215i
$880$		0			0
$881$	−26.9355	−	46.6537i	−0.907481	−	1.57180i	−0.817552	−	0.575855i	$-0.804669\pi$
$881$	−26.9355	−	46.6537i	−0.907481	−	1.57180i	−0.0899292	−	0.995948i	$-0.528664\pi$
$882$		0			0
$883$	4.59752			0.154719			0.0773595	−	0.997003i	$-0.475351\pi$
$883$	4.59752			0.154719			0.0773595	+	0.997003i	$0.475351\pi$
$884$		0			0
$885$	39.0450			1.31248
$886$		0			0
$887$	−10.0032	−	17.3260i	−0.335873	−	0.581750i	0.647779	−	0.761828i	$-0.275698\pi$
$887$	−10.0032	−	17.3260i	−0.335873	−	0.581750i	−0.983652	+	0.180079i	$0.942365\pi$
$888$		0			0
$889$			1.65944i			0.0556557i
$890$		0			0
$891$	9.48648	+	5.47702i	0.317809	+	0.183487i
$892$		0			0
$893$	−49.2574	+	85.3164i	−1.64834	+	2.85500i
$894$		0			0
$895$	26.5353	−	15.3202i	0.886977	−	0.512097i
$896$		0			0
$897$	23.2204	−	4.51018i	0.775306	−	0.150590i
$898$		0			0
$899$	8.77409	−	5.06573i	0.292632	−	0.168951i
$900$		0			0
$901$	−4.95443	+	8.58133i	−0.165056	+	0.285886i
$902$		0			0
$903$	−3.20814	−	1.85222i	−0.106760	−	0.0616381i
$904$		0			0
$905$			49.2701i			1.63779i
$906$		0			0
$907$	−14.4316	−	24.9962i	−0.479192	−	0.829985i	0.520523	−	0.853847i	$-0.325737\pi$
$907$	−14.4316	−	24.9962i	−0.479192	−	0.829985i	−0.999715	+	0.0238629i	$0.992403\pi$
$908$		0			0
$909$	−0.523808			−0.0173736
$910$		0			0
$911$	24.5946			0.814855			0.407428	−	0.913237i	$-0.366426\pi$
$911$	24.5946			0.814855			0.407428	+	0.913237i	$0.366426\pi$
$912$		0			0
$913$	−3.77320	−	6.53538i	−0.124875	−	0.216289i
$914$		0			0
$915$			55.9543i			1.84979i
$916$		0			0
$917$	0.0148486	+	0.00857286i	0.000490345	+	0.000283101i
$918$		0			0
$919$	23.2713	−	40.3071i	0.767651	−	1.32961i	−0.171183	−	0.985239i	$-0.554759\pi$
$919$	23.2713	−	40.3071i	0.767651	−	1.32961i	0.938834	−	0.344371i	$-0.111908\pi$
$920$		0			0
$921$	−34.9371	+	20.1710i	−1.15122	+	0.664656i
$922$		0			0
$923$	−8.85616	−	45.5954i	−0.291504	−	1.50079i
$924$		0			0
$925$	13.1115	−	7.56992i	0.431103	−	0.248897i
$926$		0			0
$927$	−1.96347	+	3.40084i	−0.0644889	+	0.111698i
$928$		0			0
$929$	41.2799	+	23.8330i	1.35435	+	0.781935i	0.988856	−	0.148878i	$-0.0475662\pi$
$929$	41.2799	+	23.8330i	1.35435	+	0.781935i	0.365495	+	0.930813i	$0.380900\pi$
$930$		0			0
$931$		−	56.8243i		−	1.86234i
$932$		0			0
$933$	27.4706	+	47.5805i	0.899347	+	1.55772i
$934$		0			0
$935$	−9.21132			−0.301242
$936$		0			0
$937$	−44.3595			−1.44916			−0.724581	−	0.689190i	$-0.757967\pi$
$937$	−44.3595			−1.44916			−0.724581	+	0.689190i	$0.757967\pi$
$938$		0			0
$939$	−33.3534	−	57.7698i	−1.08845	−	1.88525i
$940$		0			0
$941$		−	45.1446i		−	1.47167i	−0.677159	−	0.735836i	$-0.736789\pi$
$941$		−	45.1446i		−	1.47167i	0.677159	−	0.735836i	$-0.263211\pi$
$942$		0			0
$943$	5.20943	+	3.00766i	0.169642	+	0.0979430i
$944$		0			0
$945$	−1.02612	+	1.77730i	−0.0333798	+	0.0578155i
$946$		0			0
$947$	1.64500	−	0.949740i	0.0534552	−	0.0308624i	−0.473034	−	0.881044i	$-0.656841\pi$
$947$	1.64500	−	0.949740i	0.0534552	−	0.0308624i	0.526489	+	0.850182i	$0.323508\pi$
$948$		0			0
$949$	29.2535	−	25.4224i	0.949609	−	0.825247i
$950$		0			0
$951$	47.6967	−	27.5377i	1.54667	−	0.892970i
$952$		0			0
$953$	25.2628	−	43.7565i	0.818343	−	1.41741i	−0.0885599	−	0.996071i	$-0.528226\pi$
$953$	25.2628	−	43.7565i	0.818343	−	1.41741i	0.906903	−	0.421340i	$-0.138440\pi$
$954$		0			0
$955$	12.0509	+	6.95758i	0.389957	+	0.225142i
$956$		0			0
$957$		−	9.28202i		−	0.300045i
$958$		0			0
$959$	0.00317089	+	0.00549213i	0.000102393	+	0.000177350i
$960$		0			0
$961$	26.2868			0.847962
$962$		0			0
$963$	18.1363			0.584435
$964$		0			0
$965$	5.16087	+	8.93889i	0.166134	+	0.287753i
$966$		0			0
$967$			4.86827i			0.156553i	0.996932	+	0.0782765i	$0.0249417\pi$
$967$			4.86827i			0.156553i	−0.996932	+	0.0782765i	$0.975058\pi$
$968$		0			0
$969$	48.8703	+	28.2153i	1.56994	+	0.906405i
$970$		0			0
$971$	29.9548	−	51.8832i	0.961295	−	1.66501i	0.242038	−	0.970267i	$-0.422184\pi$
$971$	29.9548	−	51.8832i	0.961295	−	1.66501i	0.719256	−	0.694745i	$-0.244483\pi$
$972$		0			0
$973$	1.53657	−	0.887140i	0.0492602	−	0.0284404i
$974$		0			0
$975$	4.71521	−	13.6877i	0.151007	−	0.438356i
$976$		0			0
$977$	−22.2933	+	12.8710i	−0.713225	+	0.411780i	−0.812254	−	0.583304i	$-0.801760\pi$
$977$	−22.2933	+	12.8710i	−0.713225	+	0.411780i	0.0990292	+	0.995085i	$0.468426\pi$
$978$		0			0
$979$	−4.61584	+	7.99487i	−0.147523	+	0.255517i
$980$		0			0
$981$	−3.11601	−	1.79903i	−0.0994866	−	0.0574386i
$982$		0			0
$983$			24.9613i			0.796142i	0.917355	+	0.398071i	$0.130320\pi$
$983$			24.9613i			0.796142i	−0.917355	+	0.398071i	$0.869680\pi$
$984$		0			0
$985$	−26.7623	−	46.3536i	−0.852717	−	1.47695i
$986$		0			0
$987$	4.57533			0.145634
$988$		0			0
$989$	−32.2418			−1.02523
$990$		0			0
$991$	21.0530	+	36.4649i	0.668770	+	1.15834i	0.978248	+	0.207438i	$0.0665124\pi$
$991$	21.0530	+	36.4649i	0.668770	+	1.15834i	−0.309478	+	0.950907i	$0.600154\pi$
$992$		0			0
$993$		−	14.8751i		−	0.472047i
$994$		0			0
$995$	26.0786	+	15.0565i	0.826747	+	0.477323i
$996$		0			0
$997$	24.5725	−	42.5608i	0.778218	−	1.34791i	−0.154750	−	0.987954i	$-0.549457\pi$
$997$	24.5725	−	42.5608i	0.778218	−	1.34791i	0.932968	−	0.359960i	$-0.117210\pi$
$998$		0			0
$999$	−26.4047	+	15.2448i	−0.835408	+	0.482323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.p.a.309.10	✓	24
13.2	odd	12		7436.2.a.u.1.3		12
13.4	even	6	inner	572.2.p.a.485.10	yes	24
13.11	odd	12		7436.2.a.v.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.p.a.309.10	✓	24	1.1	even	1	trivial
572.2.p.a.485.10	yes	24	13.4	even	6	inner
7436.2.a.u.1.3		12	13.2	odd	12
7436.2.a.v.1.3		12	13.11	odd	12

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.994483 + 1.72249i) q^{3} -2.64929i q^{5} +(-0.165013 - 0.0952705i) q^{7} +(-0.477992 + 0.827907i) q^{9} +O(q^{10})\)	\(q+(0.994483 + 1.72249i) q^{3} -2.64929i q^{5} +(-0.165013 - 0.0952705i) q^{7} +(-0.477992 + 0.827907i) q^{9} +(0.866025 - 0.500000i) q^{11} +(2.36507 + 2.72148i) q^{13} +(4.56339 - 2.63467i) q^{15} +(1.73845 - 3.01108i) q^{17} +(7.06684 + 4.08004i) q^{19} -0.378979i q^{21} +(-1.64923 - 2.85655i) q^{23} -2.01875 q^{25} +4.06548 q^{27} +(-2.33338 - 4.04153i) q^{29} +2.17098i q^{31} +(1.72249 + 0.994483i) q^{33} +(-0.252399 + 0.437168i) q^{35} +(-6.49487 + 3.74981i) q^{37} +(-2.33571 + 6.78028i) q^{39} +(-1.57935 + 0.911838i) q^{41} +(4.88739 - 8.46522i) q^{43} +(2.19337 + 1.26634i) q^{45} +12.0728i q^{47} +(-3.48185 - 6.03074i) q^{49} +6.91544 q^{51} -2.84991 q^{53} +(-1.32465 - 2.29435i) q^{55} +16.2301i q^{57} +(6.41710 + 3.70492i) q^{59} +(-5.30941 + 9.19617i) q^{61} +(0.157750 - 0.0910771i) q^{63} +(7.20999 - 6.26576i) q^{65} +(-8.95316 + 5.16911i) q^{67} +(3.28027 - 5.68159i) q^{69} +(-11.1563 - 6.44112i) q^{71} -10.7491i q^{73} +(-2.00761 - 3.47728i) q^{75} -0.190541 q^{77} +1.21943 q^{79} +(5.47702 + 9.48648i) q^{81} -7.54640i q^{83} +(-7.97724 - 4.60566i) q^{85} +(4.64101 - 8.03846i) q^{87} +(-7.99487 + 4.61584i) q^{89} +(-0.130991 - 0.674401i) q^{91} +(-3.73951 + 2.15901i) q^{93} +(10.8092 - 18.7221i) q^{95} +(7.71339 + 4.45333i) q^{97} +0.955984i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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