LMFDB - Embedded newform 567.2.h.l.352.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, degree $2$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 14x^12 - 39x^10 + 77x^8 - 156x^6 + 224x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.6
Root			$-0.776749 + 1.18180i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.l.298.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.27020 q^{2} -0.386601 q^{4} +(0.776749 + 1.34537i) q^{5} +(-1.15207 + 2.38175i) q^{7} -3.03145 q^{8} +O(q^{10})$	\(q+1.27020 q^{2} -0.386601 q^{4} +(0.776749 + 1.34537i) q^{5} +(-1.15207 + 2.38175i) q^{7} -3.03145 q^{8} +(0.986623 + 1.70888i) q^{10} +(-1.60500 + 2.77995i) q^{11} +(-2.39335 + 4.14540i) q^{13} +(-1.46335 + 3.02529i) q^{14} -3.07734 q^{16} +(-1.05918 - 1.83456i) q^{17} +(2.43201 - 4.21237i) q^{19} +(-0.300292 - 0.520121i) q^{20} +(-2.03867 + 3.53108i) q^{22} +(1.85379 + 3.21086i) q^{23} +(1.29332 - 2.24010i) q^{25} +(-3.04002 + 5.26547i) q^{26} +(0.445391 - 0.920788i) q^{28} +(3.68972 + 6.39078i) q^{29} +5.50418 q^{31} +2.15408 q^{32} +(-1.34537 - 2.33025i) q^{34} +(-4.09920 + 0.300067i) q^{35} +(0.0932782 - 0.161563i) q^{37} +(3.08914 - 5.35054i) q^{38} +(-2.35468 - 4.07842i) q^{40} +(-5.39860 + 9.35065i) q^{41} +(-2.43458 - 4.21681i) q^{43} +(0.620496 - 1.07473i) q^{44} +(2.35468 + 4.07842i) q^{46} -1.77187 q^{47} +(-4.34548 - 5.48788i) q^{49} +(1.64277 - 2.84537i) q^{50} +(0.925270 - 1.60261i) q^{52} +(0.834432 + 1.44528i) q^{53} -4.98674 q^{55} +(3.49244 - 7.22017i) q^{56} +(4.68667 + 8.11755i) q^{58} -5.82594 q^{59} +6.87729 q^{61} +6.99139 q^{62} +8.89078 q^{64} -7.43611 q^{65} +12.2374 q^{67} +(0.409481 + 0.709241i) q^{68} +(-5.20679 + 0.381144i) q^{70} +13.8101 q^{71} +(-5.93201 - 10.2745i) q^{73} +(0.118482 - 0.205216i) q^{74} +(-0.940219 + 1.62851i) q^{76} +(-4.77207 - 7.02540i) q^{77} -1.30926 q^{79} +(-2.39032 - 4.14015i) q^{80} +(-6.85728 + 11.8772i) q^{82} +(-0.173244 - 0.300067i) q^{83} +(1.64544 - 2.84998i) q^{85} +(-3.09239 - 5.35618i) q^{86} +(4.86549 - 8.42727i) q^{88} +(-8.70319 + 15.0744i) q^{89} +(-7.11601 - 10.4761i) q^{91} +(-0.716677 - 1.24132i) q^{92} -2.25063 q^{94} +7.55625 q^{95} +(5.28413 + 9.15238i) q^{97} +(-5.51961 - 6.97068i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 6 q^{7}+O(q^{10}) $ 16 * q + 12 * q^4 - 6 * q^7	$ 16 q + 12 q^{4} - 6 q^{7} - 14 q^{10} - 6 q^{13} + 12 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} + 40 q^{31} + 4 q^{37} - 36 q^{40} - 10 q^{43} + 36 q^{46} + 10 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} + 72 q^{61} + 76 q^{64} - 36 q^{67} - 46 q^{70} - 32 q^{73} - 58 q^{76} - 64 q^{79} + 2 q^{82} - 30 q^{85} + 72 q^{88} - 22 q^{91} + 108 q^{94} - 14 q^{97}+O(q^{100}) $ 16 * q + 12 * q^4 - 6 * q^7 - 14 * q^10 - 6 * q^13 + 12 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 + 40 * q^31 + 4 * q^37 - 36 * q^40 - 10 * q^43 + 36 * q^46 + 10 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 + 72 * q^61 + 76 * q^64 - 36 * q^67 - 46 * q^70 - 32 * q^73 - 58 * q^76 - 64 * q^79 + 2 * q^82 - 30 * q^85 + 72 * q^88 - 22 * q^91 + 108 * q^94 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.27020			0.898165			0.449082	−	0.893490i	$-0.351751\pi$
$2$	1.27020			0.898165			0.449082	+	0.893490i	$0.351751\pi$
$3$		0			0
$3$		0			0
$4$	−0.386601			−0.193301
$5$	0.776749	+	1.34537i	0.347373	+	0.601667i	0.985782	−	0.168030i	$-0.0537406\pi$
$5$	0.776749	+	1.34537i	0.347373	+	0.601667i	−0.638409	+	0.769697i	$0.720407\pi$
$6$		0			0
$7$	−1.15207	+	2.38175i	−0.435441	+	0.900217i
$7$	−1.15207	+	2.38175i	−0.435441	+	0.900217i
$8$	−3.03145			−1.07178
$9$		0			0
$10$	0.986623	+	1.70888i	0.311998	+	0.540396i
$11$	−1.60500	+	2.77995i	−0.483927	+	0.838185i	−0.999830	−	0.0184616i	$-0.994123\pi$
$11$	−1.60500	+	2.77995i	−0.483927	+	0.838185i	0.515903	+	0.856647i	$0.327456\pi$
$12$		0			0
$13$	−2.39335	+	4.14540i	−0.663795	+	1.14973i	0.315816	+	0.948820i	$0.397722\pi$
$13$	−2.39335	+	4.14540i	−0.663795	+	1.14973i	−0.979611	+	0.200905i	$0.935612\pi$
$14$	−1.46335	+	3.02529i	−0.391097	+	0.808543i
$15$		0			0
$16$	−3.07734			−0.769334
$17$	−1.05918	−	1.83456i	−0.256889	−	0.444945i	0.708518	−	0.705693i	$-0.249364\pi$
$17$	−1.05918	−	1.83456i	−0.256889	−	0.444945i	−0.965407	+	0.260748i	$0.916031\pi$
$18$		0			0
$19$	2.43201	−	4.21237i	0.557942	−	0.966384i	−0.439726	−	0.898132i	$-0.644924\pi$
$19$	2.43201	−	4.21237i	0.557942	−	0.966384i	0.997668	−	0.0682523i	$-0.0217423\pi$
$20$	−0.300292	−	0.520121i	−0.0671473	−	0.116303i
$21$		0			0
$22$	−2.03867	+	3.53108i	−0.434646	+	0.752828i
$23$	1.85379	+	3.21086i	0.386542	+	0.669510i	0.991982	−	0.126381i	$-0.0403362\pi$
$23$	1.85379	+	3.21086i	0.386542	+	0.669510i	−0.605440	+	0.795891i	$0.707003\pi$
$24$		0			0
$25$	1.29332	−	2.24010i	0.258665	−	0.448020i
$26$	−3.04002	+	5.26547i	−0.596197	+	1.03264i
$27$		0			0
$28$	0.445391	−	0.920788i	0.0841709	−	0.174013i
$29$	3.68972	+	6.39078i	0.685164	+	1.18674i	0.973385	+	0.229175i	$0.0736027\pi$
$29$	3.68972	+	6.39078i	0.685164	+	1.18674i	−0.288222	+	0.957564i	$0.593064\pi$
$30$		0			0
$31$	5.50418			0.988580			0.494290	−	0.869297i	$-0.335428\pi$
$31$	5.50418			0.988580			0.494290	+	0.869297i	$0.335428\pi$
$32$	2.15408			0.380791
$33$		0			0
$34$	−1.34537	−	2.33025i	−0.230729	−	0.399634i
$35$	−4.09920	+	0.300067i	−0.692891	+	0.0507206i
$36$		0			0
$37$	0.0932782	−	0.161563i	0.0153348	−	0.0265607i	−0.858256	−	0.513222i	$-0.828452\pi$
$37$	0.0932782	−	0.161563i	0.0153348	−	0.0265607i	0.873591	+	0.486661i	$0.161785\pi$
$38$	3.08914	−	5.35054i	0.501124	−	0.867972i
$39$		0			0
$40$	−2.35468	−	4.07842i	−0.372307	−	0.644855i
$41$	−5.39860	+	9.35065i	−0.843120	+	1.46033i	0.0441242	+	0.999026i	$0.485950\pi$
$41$	−5.39860	+	9.35065i	−0.843120	+	1.46033i	−0.887244	+	0.461300i	$0.847383\pi$
$42$		0			0
$43$	−2.43458	−	4.21681i	−0.371270	−	0.643058i	0.618491	−	0.785792i	$-0.287744\pi$
$43$	−2.43458	−	4.21681i	−0.371270	−	0.643058i	−0.989761	+	0.142734i	$0.954411\pi$
$44$	0.620496	−	1.07473i	0.0935433	−	0.162022i
$45$		0			0
$46$	2.35468	+	4.07842i	0.347178	+	0.601330i
$47$	−1.77187			−0.258455			−0.129227	−	0.991615i	$-0.541250\pi$
$47$	−1.77187			−0.258455			−0.129227	+	0.991615i	$0.541250\pi$
$48$		0			0
$49$	−4.34548	−	5.48788i	−0.620783	−	0.783983i
$50$	1.64277	−	2.84537i	0.232323	−	0.402396i
$51$		0			0
$52$	0.925270	−	1.60261i	0.128312	−	0.222243i
$53$	0.834432	+	1.44528i	0.114618	+	0.198524i	0.917627	−	0.397443i	$-0.130102\pi$
$53$	0.834432	+	1.44528i	0.114618	+	0.198524i	−0.803009	+	0.595967i	$0.796769\pi$
$54$		0			0
$55$	−4.98674			−0.672411
$56$	3.49244	−	7.22017i	0.466697	−	0.964835i
$57$		0			0
$58$	4.68667	+	8.11755i	0.615390	+	1.06589i
$59$	−5.82594			−0.758473			−0.379236	−	0.925300i	$-0.623813\pi$
$59$	−5.82594			−0.758473			−0.379236	+	0.925300i	$0.623813\pi$
$60$		0			0
$61$	6.87729			0.880547			0.440274	−	0.897864i	$-0.354881\pi$
$61$	6.87729			0.880547			0.440274	+	0.897864i	$0.354881\pi$
$62$	6.99139			0.887907
$63$		0			0
$64$	8.89078			1.11135
$65$	−7.43611			−0.922336
$66$		0			0
$67$	12.2374			1.49503			0.747516	−	0.664244i	$-0.231246\pi$
$67$	12.2374			1.49503			0.747516	+	0.664244i	$0.231246\pi$
$68$	0.409481	+	0.709241i	0.0496568	+	0.0860081i
$69$		0			0
$70$	−5.20679	+	0.381144i	−0.622330	+	0.0455554i
$71$	13.8101			1.63895			0.819477	−	0.573112i	$-0.194264\pi$
$71$	13.8101			1.63895			0.819477	+	0.573112i	$0.194264\pi$
$72$		0			0
$73$	−5.93201	−	10.2745i	−0.694290	−	1.20255i	−0.970420	−	0.241425i	$-0.922385\pi$
$73$	−5.93201	−	10.2745i	−0.694290	−	1.20255i	0.276130	−	0.961120i	$-0.410948\pi$
$74$	0.118482	−	0.205216i	0.0137732	−	0.0238559i
$75$		0			0
$76$	−0.940219	+	1.62851i	−0.107851	+	0.186803i
$77$	−4.77207	−	7.02540i	−0.543828	−	0.800619i
$78$		0			0
$79$	−1.30926			−0.147304			−0.0736518	−	0.997284i	$-0.523465\pi$
$79$	−1.30926			−0.147304			−0.0736518	+	0.997284i	$0.523465\pi$
$80$	−2.39032	−	4.14015i	−0.267246	−	0.462883i
$81$		0			0
$82$	−6.85728	+	11.8772i	−0.757260	+	1.31161i
$83$	−0.173244	−	0.300067i	−0.0190160	−	0.0329366i	0.856361	−	0.516378i	$-0.172720\pi$
$83$	−0.173244	−	0.300067i	−0.0190160	−	0.0329366i	−0.875377	+	0.483441i	$0.839387\pi$
$84$		0			0
$85$	1.64544	−	2.84998i	0.178473	−	0.309123i
$86$	−3.09239	−	5.35618i	−0.333461	−	0.577572i
$87$		0			0
$88$	4.86549	−	8.42727i	0.518663	−	0.898350i
$89$	−8.70319	+	15.0744i	−0.922537	+	1.59788i	−0.127061	+	0.991895i	$0.540554\pi$
$89$	−8.70319	+	15.0744i	−0.922537	+	1.59788i	−0.795476	+	0.605985i	$0.792779\pi$
$90$		0			0
$91$	−7.11601	−	10.4761i	−0.745960	−	1.09820i
$92$	−0.716677	−	1.24132i	−0.0747187	−	0.129417i
$93$		0			0
$94$	−2.25063			−0.232135
$95$	7.55625			0.775255
$96$		0			0
$97$	5.28413	+	9.15238i	0.536522	+	0.929283i	0.999088	+	0.0426982i	$0.0135954\pi$
$97$	5.28413	+	9.15238i	0.536522	+	0.929283i	−0.462566	+	0.886585i	$0.653071\pi$
$98$	−5.51961	−	6.97068i	−0.557565	−	0.704145i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−1.01697	+	1.76144i	−0.101192	+	0.175270i	−0.912176	−	0.409798i	$-0.865599\pi$
$101$	−1.01697	+	1.76144i	−0.101192	+	0.175270i	0.810984	+	0.585068i	$0.198932\pi$
$102$		0			0
$103$	−9.99080	−	17.3046i	−0.984423	−	1.70507i	−0.644472	−	0.764628i	$-0.722923\pi$
$103$	−9.99080	−	17.3046i	−0.984423	−	1.70507i	−0.339951	−	0.940443i	$-0.610410\pi$
$104$	7.25531	−	12.5666i	0.711442	−	1.23225i
$105$		0			0
$106$	1.05989	+	1.83579i	0.102946	+	0.178307i
$107$	8.45322	−	14.6414i	0.817204	−	1.41544i	−0.0905308	−	0.995894i	$-0.528856\pi$
$107$	8.45322	−	14.6414i	0.817204	−	1.41544i	0.907735	−	0.419545i	$-0.137810\pi$
$108$		0			0
$109$	5.34955	+	9.26569i	0.512394	+	0.887492i	0.999897	+	0.0143707i	$0.00457451\pi$
$109$	5.34955	+	9.26569i	0.512394	+	0.887492i	−0.487503	+	0.873121i	$0.662092\pi$
$110$	−6.33413			−0.603936
$111$		0			0
$112$	3.54530	−	7.32945i	0.334999	−	0.692568i
$113$	4.29236	−	7.43458i	0.403791	−	0.699386i	−0.590389	−	0.807119i	$-0.701026\pi$
$113$	4.29236	−	7.43458i	0.403791	−	0.699386i	0.994180	+	0.107733i	$0.0343590\pi$
$114$		0			0
$115$	−2.87986	+	4.98806i	−0.268548	+	0.465139i
$116$	−1.42645	−	2.47068i	−0.132442	−	0.229397i
$117$		0			0
$118$	−7.40009			−0.681233
$119$	5.58970	−	0.409174i	0.512407	−	0.0375089i
$120$		0			0
$121$	0.347932	+	0.602636i	0.0316302	+	0.0547851i
$122$	8.73551			0.790876
$123$		0			0
$124$	−2.12792			−0.191093
$125$	11.7858			1.05416
$126$		0			0
$127$	1.95162			0.173178			0.0865892	−	0.996244i	$-0.472403\pi$
$127$	1.95162			0.173178			0.0865892	+	0.996244i	$0.472403\pi$
$128$	6.98488			0.617382
$129$		0			0
$130$	−9.44532			−0.828410
$131$	−5.87214	−	10.1708i	−0.513051	−	0.888630i	−0.999885	−	0.0151361i	$-0.995182\pi$
$131$	−5.87214	−	10.1708i	−0.513051	−	0.888630i	0.486834	−	0.873494i	$-0.338151\pi$
$132$		0			0
$133$	7.23098	+	10.6454i	0.627005	+	0.923072i
$134$	15.5439			1.34278
$135$		0			0
$136$	3.21086	+	5.56137i	0.275329	+	0.476883i
$137$	−8.06604	+	13.9708i	−0.689128	+	1.19361i	0.282992	+	0.959122i	$0.408673\pi$
$137$	−8.06604	+	13.9708i	−0.689128	+	1.19361i	−0.972120	+	0.234483i	$0.924660\pi$
$138$		0			0
$139$	−6.72127	+	11.6416i	−0.570091	+	0.987426i	0.426465	+	0.904504i	$0.359759\pi$
$139$	−6.72127	+	11.6416i	−0.570091	+	0.987426i	−0.996556	+	0.0829220i	$0.973575\pi$
$140$	1.58475	−	0.116006i	0.133936	−	0.00980432i
$141$		0			0
$142$	17.5415			1.47205
$143$	−7.68265	−	13.3067i	−0.642456	−	1.11277i
$144$		0			0
$145$	−5.73197	+	9.92806i	−0.476014	+	0.824481i
$146$	−7.53482	−	13.0507i	−0.623586	−	1.08008i
$147$		0			0
$148$	−0.0360614	+	0.0624602i	−0.00296423	+	0.00513420i
$149$	−1.60587	−	2.78145i	−0.131558	−	0.227865i	0.792719	−	0.609587i	$-0.208665\pi$
$149$	−1.60587	−	2.78145i	−0.131558	−	0.227865i	−0.924277	+	0.381722i	$0.875331\pi$
$150$		0			0
$151$	−8.51610	+	14.7503i	−0.693030	+	1.20036i	0.277810	+	0.960636i	$0.410391\pi$
$151$	−8.51610	+	14.7503i	−0.693030	+	1.20036i	−0.970840	+	0.239727i	$0.922942\pi$
$152$	−7.37253	+	12.7696i	−0.597991	+	1.03575i
$153$		0			0
$154$	−6.06147	−	8.92364i	−0.488447	−	0.719088i
$155$	4.27536	+	7.40515i	0.343406	+	0.594796i
$156$		0			0
$157$	9.43418			0.752929			0.376465	−	0.926431i	$-0.377140\pi$
$157$	9.43418			0.752929			0.376465	+	0.926431i	$0.377140\pi$
$158$	−1.66302			−0.132303
$159$		0			0
$160$	1.67318	+	2.89803i	0.132276	+	0.229110i
$161$	−9.78315	+	0.716140i	−0.771021	+	0.0564398i
$162$		0			0
$163$	−1.83874	+	3.18478i	−0.144021	+	0.249452i	−0.929007	−	0.370062i	$-0.879337\pi$
$163$	−1.83874	+	3.18478i	−0.144021	+	0.249452i	0.784986	+	0.619513i	$0.212670\pi$
$164$	2.08710	−	3.61497i	0.162976	−	0.282282i
$165$		0			0
$166$	−0.220054	−	0.381144i	−0.0170795	−	0.0295825i
$167$	0.805085	−	1.39445i	0.0622994	−	0.107906i	−0.833193	−	0.552982i	$-0.813490\pi$
$167$	0.805085	−	1.39445i	0.0622994	−	0.107906i	0.895493	+	0.445076i	$0.146823\pi$
$168$		0			0
$169$	−4.95620	−	8.58440i	−0.381246	−	0.660338i
$170$	2.09003	−	3.62003i	0.160298	−	0.277644i
$171$		0			0
$172$	0.941210	+	1.63022i	0.0717666	+	0.124303i
$173$	−16.1843			−1.23047			−0.615233	−	0.788345i	$-0.710938\pi$
$173$	−16.1843			−1.23047			−0.615233	+	0.788345i	$0.710938\pi$
$174$		0			0
$175$	3.84537	+	5.66112i	0.290683	+	0.427941i
$176$	4.93914	−	8.55483i	0.372301	−	0.644845i
$177$		0			0
$178$	−11.0548	+	19.1474i	−0.828590	+	1.43516i
$179$	8.70319	+	15.0744i	0.650507	+	1.12671i	0.983000	+	0.183606i	$0.0587770\pi$
$179$	8.70319	+	15.0744i	0.650507	+	1.12671i	−0.332493	+	0.943106i	$0.607890\pi$
$180$		0			0
$181$	8.89591			0.661228			0.330614	−	0.943766i	$-0.392744\pi$
$181$	8.89591			0.661228			0.330614	+	0.943766i	$0.392744\pi$
$182$	−9.03873	−	13.3067i	−0.669995	−	0.986361i
$183$		0			0
$184$	−5.61967	−	9.73356i	−0.414288	−	0.717568i
$185$	0.289815			0.0213076
$186$		0			0
$187$	6.79996			0.497262
$188$	0.685009			0.0499594
$189$		0			0
$190$	9.59793			0.696307
$191$	14.7922			1.07033			0.535163	−	0.844749i	$-0.320250\pi$
$191$	14.7922			1.07033			0.535163	+	0.844749i	$0.320250\pi$
$192$		0			0
$193$	1.82158			0.131120			0.0655601	−	0.997849i	$-0.479117\pi$
$193$	1.82158			0.131120			0.0655601	+	0.997849i	$0.479117\pi$
$194$	6.71188	+	11.6253i	0.481885	+	0.834649i
$195$		0			0
$196$	1.67997	+	2.12162i	0.119998	+	0.151544i
$197$	7.71970			0.550006			0.275003	−	0.961443i	$-0.411321\pi$
$197$	7.71970			0.550006			0.275003	+	0.961443i	$0.411321\pi$
$198$		0			0
$199$	−1.10665	−	1.91678i	−0.0784487	−	0.135877i	0.824132	−	0.566398i	$-0.191663\pi$
$199$	−1.10665	−	1.91678i	−0.0784487	−	0.135877i	−0.902581	+	0.430521i	$0.858330\pi$
$200$	−3.92065	+	6.79076i	−0.277232	+	0.480179i
$201$		0			0
$202$	−1.29175	+	2.23738i	−0.0908872	+	0.157421i
$203$	−19.4721	+	1.42538i	−1.36667	+	0.100042i
$204$		0			0
$205$	−16.7734			−1.17151
$206$	−12.6903	−	21.9802i	−0.884174	−	1.53143i
$207$		0			0
$208$	7.36513	−	12.7568i	0.510680	−	0.884524i
$209$	7.80678	+	13.5217i	0.540006	+	0.935318i
$210$		0			0
$211$	0.906722	−	1.57049i	0.0624213	−	0.108117i	−0.833126	−	0.553083i	$-0.813451\pi$
$211$	0.906722	−	1.57049i	0.0624213	−	0.108117i	0.895547	+	0.444967i	$0.146784\pi$
$212$	−0.322592	−	0.558746i	−0.0221557	−	0.0383749i
$213$		0			0
$214$	10.7373	−	18.5975i	0.733983	−	1.27130i
$215$	3.78211	−	6.55081i	0.257938	−	0.446761i
$216$		0			0
$217$	−6.34119	+	13.1096i	−0.430468	+	0.889937i
$218$	6.79498	+	11.7692i	0.460214	+	0.797114i
$219$		0			0
$220$	1.92788			0.129977
$221$	10.1399			0.682087
$222$		0			0
$223$	−4.75308	−	8.23258i	−0.318290	−	0.551294i	0.661841	−	0.749644i	$-0.269775\pi$
$223$	−4.75308	−	8.23258i	−0.318290	−	0.551294i	−0.980131	+	0.198350i	$0.936442\pi$
$224$	−2.48165	+	5.13049i	−0.165812	+	0.342795i
$225$		0			0
$226$	5.45213	−	9.44337i	0.362671	−	0.628164i
$227$	5.41646	−	9.38158i	0.359503	−	0.622678i	−0.628375	−	0.777911i	$-0.716280\pi$
$227$	5.41646	−	9.38158i	0.359503	−	0.622678i	0.987878	+	0.155233i	$0.0496129\pi$
$228$		0			0
$229$	−6.25983	−	10.8423i	−0.413661	−	0.716482i	0.581626	−	0.813456i	$-0.302417\pi$
$229$	−6.25983	−	10.8423i	−0.413661	−	0.716482i	−0.995287	+	0.0969747i	$0.969083\pi$
$230$	−3.65798	+	6.33581i	−0.241200	+	0.417771i
$231$		0			0
$232$	−11.1852	−	19.3733i	−0.734345	−	1.27192i
$233$	−7.64044	+	13.2336i	−0.500542	+	0.866964i	0.499458	+	0.866338i	$0.333533\pi$
$233$	−7.64044	+	13.2336i	−0.500542	+	0.866964i	−1.00000		0.000625732i	$0.999801\pi$
$234$		0			0
$235$	−1.37630	−	2.38382i	−0.0897800	−	0.155504i
$236$	2.25231			0.146613
$237$		0			0
$238$	7.10002	−	0.519731i	0.460226	−	0.0336892i
$239$	−5.35791	+	9.28017i	−0.346574	+	0.600284i	−0.985638	−	0.168869i	$-0.945988\pi$
$239$	−5.35791	+	9.28017i	−0.346574	+	0.600284i	0.639064	+	0.769153i	$0.279322\pi$
$240$		0			0
$241$	7.50011	−	12.9906i	0.483125	−	0.836796i	−0.516688	−	0.856174i	$-0.672835\pi$
$241$	7.50011	−	12.9906i	0.483125	−	0.836796i	0.999812	+	0.0193775i	$0.00616845\pi$
$242$	0.441942	+	0.765467i	0.0284091	+	0.0492061i
$243$		0			0
$244$	−2.65877			−0.170210
$245$	4.00787	−	10.1090i	0.256053	−	0.645839i
$246$		0			0
$247$	11.6413	+	20.1633i	0.740718	+	1.28296i
$248$	−16.6857			−1.05954
$249$		0			0
$250$	14.9703			0.946806
$251$	−16.5665			−1.04567			−0.522833	−	0.852435i	$-0.675125\pi$
$251$	−16.5665			−1.04567			−0.522833	+	0.852435i	$0.675125\pi$
$252$		0			0
$253$	−11.9013			−0.748231
$254$	2.47894			0.155543
$255$		0			0
$256$	−8.90940			−0.556837
$257$	11.2886	+	19.5524i	0.704163	+	1.21965i	0.966993	+	0.254804i	$0.0820111\pi$
$257$	11.2886	+	19.5524i	0.704163	+	1.21965i	−0.262829	+	0.964842i	$0.584656\pi$
$258$		0			0
$259$	0.277339	+	0.408296i	0.0172330	+	0.0253703i
$260$	2.87481			0.178288
$261$		0			0
$262$	−7.45877	−	12.9190i	−0.460804	−	0.798136i
$263$	11.1730	−	19.3523i	0.688959	−	1.19331i	−0.283216	−	0.959056i	$-0.591401\pi$
$263$	11.1730	−	19.3523i	0.688959	−	1.19331i	0.972175	−	0.234256i	$-0.0752653\pi$
$264$		0			0
$265$	−1.29629	+	2.24524i	−0.0796303	+	0.137924i
$266$	9.18476	+	13.5217i	0.563154	+	0.829071i
$267$		0			0
$268$	−4.73098			−0.288990
$269$	13.9475	+	24.1577i	0.850392	+	1.47292i	0.880855	+	0.473387i	$0.156969\pi$
$269$	13.9475	+	24.1577i	0.850392	+	1.47292i	−0.0304623	+	0.999536i	$0.509698\pi$
$270$		0			0
$271$	−4.93714	+	8.55138i	−0.299910	+	0.519459i	−0.976115	−	0.217254i	$-0.930290\pi$
$271$	−4.93714	+	8.55138i	−0.299910	+	0.519459i	0.676205	+	0.736713i	$0.263623\pi$
$272$	3.25946	+	5.64555i	0.197634	+	0.342312i
$273$		0			0
$274$	−10.2455	+	17.7457i	−0.618951	+	1.07205i
$275$	4.15157	+	7.19074i	0.250349	+	0.433618i
$276$		0			0
$277$	4.35728	−	7.54704i	0.261804	−	0.453458i	−0.704917	−	0.709289i	$-0.749016\pi$
$277$	4.35728	−	7.54704i	0.261804	−	0.453458i	0.966721	+	0.255832i	$0.0823493\pi$
$278$	−8.53733	+	14.7871i	−0.512035	+	0.886871i
$279$		0			0
$280$	12.4265	−	0.909639i	0.742627	−	0.0543613i
$281$	−3.10321	−	5.37491i	−0.185122	−	0.320640i	0.758496	−	0.651678i	$-0.225935\pi$
$281$	−3.10321	−	5.37491i	−0.185122	−	0.320640i	−0.943618	+	0.331038i	$0.892601\pi$
$282$		0			0
$283$	19.6589			1.16860			0.584299	−	0.811539i	$-0.301370\pi$
$283$	19.6589			1.16860			0.584299	+	0.811539i	$0.301370\pi$
$284$	−5.33899			−0.316811
$285$		0			0
$286$	−9.75848	−	16.9022i	−0.577031	−	0.999447i
$287$	−16.0514	−	23.6307i	−0.947483	−	1.39488i
$288$		0			0
$289$	6.25627	−	10.8362i	0.368016	−	0.637422i
$290$	−7.28073	+	12.6106i	−0.427539	+	0.740519i
$291$		0			0
$292$	2.29332	+	3.97215i	0.134207	+	0.232453i
$293$	−7.24841	+	12.5546i	−0.423456	+	0.733448i	−0.996275	−	0.0862342i	$-0.972517\pi$
$293$	−7.24841	+	12.5546i	−0.423456	+	0.733448i	0.572818	+	0.819682i	$0.305850\pi$
$294$		0			0
$295$	−4.52529	−	7.83804i	−0.263473	−	0.456348i
$296$	−0.282768	+	0.489769i	−0.0164356	+	0.0284672i
$297$		0			0
$298$	−2.03977	−	3.53299i	−0.118161	−	0.204661i
$299$	−17.7470			−1.02634
$300$		0			0
$301$	12.8482	−	0.940506i	0.740558	−	0.0542099i
$302$	−10.8171	+	18.7358i	−0.622455	+	1.07812i
$303$		0			0
$304$	−7.48413	+	12.9629i	−0.429244	+	0.743473i
$305$	5.34193	+	9.25249i	0.305878	+	0.529796i
$306$		0			0
$307$	22.2776			1.27145			0.635725	−	0.771916i	$-0.280701\pi$
$307$	22.2776			1.27145			0.635725	+	0.771916i	$0.280701\pi$
$308$	1.84489	+	2.71603i	0.105122	+	0.154760i
$309$		0			0
$310$	5.43055	+	9.40599i	0.308435	+	0.534225i
$311$	−17.4005			−0.986694			−0.493347	−	0.869833i	$-0.664227\pi$
$311$	−17.4005			−0.986694			−0.493347	+	0.869833i	$0.664227\pi$
$312$		0			0
$313$	−0.200045			−0.0113072			−0.00565360	−	0.999984i	$-0.501800\pi$
$313$	−0.200045			−0.0113072			−0.00565360	+	0.999984i	$0.501800\pi$
$314$	11.9833			0.676254
$315$		0			0
$316$	0.506163			0.0284739
$317$	−8.23412			−0.462474			−0.231237	−	0.972897i	$-0.574277\pi$
$317$	−8.23412			−0.462474			−0.231237	+	0.972897i	$0.574277\pi$
$318$		0			0
$319$	−23.6880			−1.32628
$320$	6.90590	+	11.9614i	0.386052	+	0.668661i
$321$		0			0
$322$	−12.4265	+	0.909639i	−0.692503	+	0.0506922i
$323$	−10.3038			−0.573317
$324$		0			0
$325$	6.19074	+	10.7227i	0.343400	+	0.594787i
$326$	−2.33556	+	4.04530i	−0.129354	+	0.224049i
$327$		0			0
$328$	16.3656	−	28.3461i	0.903639	−	1.56515i
$329$	2.04132	−	4.22017i	0.112542	−	0.232665i
$330$		0			0
$331$	−16.6323			−0.914195			−0.457098	−	0.889417i	$-0.651111\pi$
$331$	−16.6323			−0.914195			−0.457098	+	0.889417i	$0.651111\pi$
$332$	0.0669762	+	0.116006i	0.00367580	+	0.00636667i
$333$		0			0
$334$	1.02262	−	1.77122i	0.0559551	−	0.0969170i
$335$	9.50536	+	16.4638i	0.519333	+	0.899511i
$336$		0			0
$337$	−7.95474	+	13.7780i	−0.433322	+	0.750536i	−0.997157	−	0.0753513i	$-0.975992\pi$
$337$	−7.95474	+	13.7780i	−0.433322	+	0.750536i	0.563835	+	0.825888i	$0.309326\pi$
$338$	−6.29535	−	10.9039i	−0.342422	−	0.593092i
$339$		0			0
$340$	−0.636127	+	1.10180i	−0.0344988	+	0.0597537i
$341$	−8.83422	+	15.3013i	−0.478400	+	0.828613i
$342$		0			0
$343$	18.0770	−	4.02745i	0.976069	−	0.217462i
$344$	7.38031	+	12.7831i	0.397919	+	0.689217i
$345$		0			0
$346$	−20.5572			−1.10516
$347$	−6.28925			−0.337625			−0.168812	−	0.985648i	$-0.553993\pi$
$347$	−6.28925			−0.337625			−0.168812	+	0.985648i	$0.553993\pi$
$348$		0			0
$349$	−0.809776	−	1.40257i	−0.0433463	−	0.0750781i	0.843538	−	0.537069i	$-0.180469\pi$
$349$	−0.809776	−	1.40257i	−0.0433463	−	0.0750781i	−0.886885	+	0.461991i	$0.847135\pi$
$350$	4.88437	+	7.19074i	0.261081	+	0.384361i
$351$		0			0
$352$	−3.45731	+	5.98823i	−0.184275	+	0.319174i
$353$	16.2559	−	28.1560i	0.865213	−	1.49859i	−0.00162266	−	0.999999i	$-0.500517\pi$
$353$	16.2559	−	28.1560i	0.865213	−	1.49859i	0.866836	−	0.498594i	$-0.166150\pi$
$354$		0			0
$355$	10.7270	+	18.5796i	0.569328	+	0.986104i
$356$	3.36466	−	5.82777i	0.178327	−	0.308871i
$357$		0			0
$358$	11.0548	+	19.1474i	0.584262	+	1.01197i
$359$	5.59588	−	9.69235i	0.295339	−	0.511543i	−0.679724	−	0.733468i	$-0.737901\pi$
$359$	5.59588	−	9.69235i	0.295339	−	0.511543i	0.975064	+	0.221925i	$0.0712340\pi$
$360$		0			0
$361$	−2.32938	−	4.03461i	−0.122599	−	0.212348i
$362$	11.2996			0.593891
$363$		0			0
$364$	2.75106	+	4.05008i	0.144194	+	0.212282i
$365$	9.21537	−	15.9615i	0.482354	−	0.835462i
$366$		0			0
$367$	2.59339	−	4.49188i	0.135374	−	0.234474i	−0.790366	−	0.612634i	$-0.790110\pi$
$367$	2.59339	−	4.49188i	0.135374	−	0.234474i	0.925740	+	0.378160i	$0.123443\pi$
$368$	−5.70474	−	9.88089i	−0.297380	−	0.515077i
$369$		0			0
$370$	0.368122			0.0191377
$371$	−4.40362	+	0.322351i	−0.228624	+	0.0167356i
$372$		0			0
$373$	−16.4322	−	28.4614i	−0.850825	−	1.47367i	−0.880464	−	0.474112i	$-0.842769\pi$
$373$	−16.4322	−	28.4614i	−0.850825	−	1.47367i	0.0296389	−	0.999561i	$-0.490564\pi$
$374$	8.63728			0.446623
$375$		0			0
$376$	5.37135			0.277006
$377$	−35.3231			−1.81923
$378$		0			0
$379$	13.9362			0.715856			0.357928	−	0.933749i	$-0.383483\pi$
$379$	13.9362			0.715856			0.357928	+	0.933749i	$0.383483\pi$
$380$	−2.92126			−0.149857
$381$		0			0
$382$	18.7890			0.961328
$383$	−0.857601	−	1.48541i	−0.0438214	−	0.0759008i	0.843283	−	0.537470i	$-0.180620\pi$
$383$	−0.857601	−	1.48541i	−0.0438214	−	0.0759008i	−0.887104	+	0.461569i	$0.847287\pi$
$384$		0			0
$385$	5.74506	−	11.8772i	0.292795	−	0.605316i
$386$	2.31376			0.117768
$387$		0			0
$388$	−2.04285	−	3.53832i	−0.103710	−	0.179631i
$389$	−1.57428	+	2.72673i	−0.0798191	+	0.138251i	−0.903172	−	0.429279i	$-0.858768\pi$
$389$	−1.57428	+	2.72673i	−0.0798191	+	0.138251i	0.823353	+	0.567530i	$0.192101\pi$
$390$		0			0
$391$	3.92700	−	6.80176i	0.198597	−	0.343980i
$392$	13.1731	+	16.6362i	0.665343	+	0.840257i
$393$		0			0
$394$	9.80553			0.493996
$395$	−1.01697	−	1.76144i	−0.0511693	−	0.0886277i
$396$		0			0
$397$	−13.7172	+	23.7590i	−0.688449	+	1.19243i	0.283891	+	0.958857i	$0.408375\pi$
$397$	−13.7172	+	23.7590i	−0.688449	+	1.19243i	−0.972340	+	0.233572i	$0.924959\pi$
$398$	−1.40567	−	2.43469i	−0.0704598	−	0.122040i
$399$		0			0
$400$	−3.97999	+	6.89355i	−0.199000	+	0.344677i
$401$	14.5185	+	25.1468i	0.725020	+	1.25577i	0.958966	+	0.283522i	$0.0915029\pi$
$401$	14.5185	+	25.1468i	0.725020	+	1.25577i	−0.233946	+	0.972250i	$0.575164\pi$
$402$		0			0
$403$	−13.1734	+	22.8170i	−0.656214	+	1.13660i
$404$	0.393161	−	0.680975i	0.0195605	−	0.0338798i
$405$		0			0
$406$	−24.7333	+	1.81051i	−1.22750	+	0.0898543i
$407$	0.299423	+	0.518617i	0.0148419	+	0.0257069i
$408$		0			0
$409$	−27.7300			−1.37116			−0.685581	−	0.727996i	$-0.740452\pi$
$409$	−27.7300			−1.37116			−0.685581	+	0.727996i	$0.740452\pi$
$410$	−21.3055			−1.05221
$411$		0			0
$412$	3.86246	+	6.68997i	0.190290	+	0.329591i
$413$	6.71188	−	13.8759i	0.330270	−	0.682791i
$414$		0			0
$415$	0.269134	−	0.466153i	0.0132113	−	0.0228826i
$416$	−5.15546	+	8.92952i	−0.252767	+	0.437806i
$417$		0			0
$418$	9.91614	+	17.1753i	0.485014	+	0.840070i
$419$	15.1799	−	26.2924i	0.741586	−	1.28447i	−0.210186	−	0.977661i	$-0.567407\pi$
$419$	15.1799	−	26.2924i	0.741586	−	1.28447i	0.951773	−	0.306804i	$-0.0992596\pi$
$420$		0			0
$421$	13.8868	+	24.0526i	0.676799	+	1.17225i	0.975940	+	0.218041i	$0.0699668\pi$
$421$	13.8868	+	24.0526i	0.676799	+	1.17225i	−0.299140	+	0.954209i	$0.596700\pi$
$422$	1.15171	−	1.99483i	0.0560646	−	0.0971067i
$423$		0			0
$424$	−2.52954	−	4.38129i	−0.122845	−	0.212774i
$425$	−5.47945			−0.265793
$426$		0			0
$427$	−7.92311	+	16.3800i	−0.383426	+	0.792684i
$428$	−3.26802	+	5.66038i	−0.157966	+	0.273605i
$429$		0			0
$430$	4.80402	−	8.32081i	0.231671	−	0.401265i
$431$	−3.62965	−	6.28673i	−0.174834	−	0.302821i	0.765270	−	0.643710i	$-0.222606\pi$
$431$	−3.62965	−	6.28673i	−0.174834	−	0.302821i	−0.940104	+	0.340888i	$0.889272\pi$
$432$		0			0
$433$	15.0375			0.722658			0.361329	−	0.932438i	$-0.382323\pi$
$433$	15.0375			0.722658			0.361329	+	0.932438i	$0.382323\pi$
$434$	−8.05455	+	16.6518i	−0.386631	+	0.799310i
$435$		0			0
$436$	−2.06814	−	3.58213i	−0.0990460	−	0.171553i
$437$	18.0338			0.862672
$438$		0			0
$439$	1.54119			0.0735570			0.0367785	−	0.999323i	$-0.488290\pi$
$439$	1.54119			0.0735570			0.0367785	+	0.999323i	$0.488290\pi$
$440$	15.1170			0.720677
$441$		0			0
$442$	12.8797			0.612626
$443$	20.3379			0.966281			0.483141	−	0.875543i	$-0.339496\pi$
$443$	20.3379			0.966281			0.483141	+	0.875543i	$0.339496\pi$
$444$		0			0
$445$	−27.0408			−1.28186
$446$	−6.03735	−	10.4570i	−0.285877	−	0.495153i
$447$		0			0
$448$	−10.2428	+	21.1756i	−0.483926	+	1.00045i
$449$	26.4527			1.24838			0.624190	−	0.781272i	$-0.285429\pi$
$449$	26.4527			1.24838			0.624190	+	0.781272i	$0.285429\pi$
$450$		0			0
$451$	−17.3295	−	30.0156i	−0.816016	−	1.41338i
$452$	−1.65943	+	2.87422i	−0.0780530	+	0.135192i
$453$		0			0
$454$	6.87997	−	11.9165i	0.322893	−	0.559267i
$455$	8.56690	−	17.7110i	0.401623	−	0.830303i
$456$		0			0
$457$	−6.49361			−0.303758			−0.151879	−	0.988399i	$-0.548532\pi$
$457$	−6.49361			−0.303758			−0.151879	+	0.988399i	$0.548532\pi$
$458$	−7.95121	−	13.7719i	−0.371536	−	0.643518i
$459$		0			0
$460$	1.11336	−	1.92839i	0.0519105	−	0.0899116i
$461$	−7.79582	−	13.5028i	−0.363088	−	0.628886i	0.625380	−	0.780321i	$-0.284944\pi$
$461$	−7.79582	−	13.5028i	−0.363088	−	0.628886i	−0.988467	+	0.151434i	$0.951611\pi$
$462$		0			0
$463$	−3.82792	+	6.63016i	−0.177899	+	0.308130i	−0.941161	−	0.337960i	$-0.890263\pi$
$463$	−3.82792	+	6.63016i	−0.177899	+	0.308130i	0.763262	+	0.646089i	$0.223597\pi$
$464$	−11.3545	−	19.6666i	−0.527120	−	0.912999i
$465$		0			0
$466$	−9.70486	+	16.8093i	−0.449569	+	0.778676i
$467$	20.8137	−	36.0503i	0.963142	−	1.66821i	0.248615	−	0.968602i	$-0.420024\pi$
$467$	20.8137	−	36.0503i	0.963142	−	1.66821i	0.714526	−	0.699608i	$-0.246642\pi$
$468$		0			0
$469$	−14.0983	+	29.1464i	−0.650998	+	1.34585i
$470$	−1.74817	−	3.02792i	−0.0806372	−	0.139668i
$471$		0			0
$472$	17.6611			0.812916
$473$	15.6300			0.718669
$474$		0			0
$475$	−6.29076	−	10.8959i	−0.288640	−	0.499939i
$476$	−2.16099	+	0.158187i	−0.0990486	+	0.00725050i
$477$		0			0
$478$	−6.80560	+	11.7876i	−0.311281	+	0.539154i
$479$	−1.15789	+	2.00553i	−0.0529055	+	0.0916350i	−0.891265	−	0.453482i	$-0.850182\pi$
$479$	−1.15789	+	2.00553i	−0.0529055	+	0.0916350i	0.838360	+	0.545117i	$0.183515\pi$
$480$		0			0
$481$	0.446494	+	0.773350i	0.0203584	+	0.0352617i
$482$	9.52662	−	16.5006i	0.433925	−	0.751581i
$483$		0			0
$484$	−0.134511	−	0.232980i	−0.00611414	−	0.0105900i
$485$	−8.20888	+	14.2182i	−0.372746	+	0.645615i
$486$		0			0
$487$	−9.06396	−	15.6992i	−0.410727	−	0.711401i	0.584242	−	0.811579i	$-0.301392\pi$
$487$	−9.06396	−	15.6992i	−0.410727	−	0.711401i	−0.994969	+	0.100179i	$0.968058\pi$
$488$	−20.8482			−0.943753
$489$		0			0
$490$	5.09078	−	12.8404i	0.229978	−	0.580069i
$491$	10.7972	−	18.7013i	0.487271	−	0.843978i	−0.512622	−	0.858614i	$-0.671326\pi$
$491$	10.7972	−	18.7013i	0.487271	−	0.843978i	0.999893	+	0.0146364i	$0.00465909\pi$
$492$		0			0
$493$	7.81616	−	13.5380i	0.352022	−	0.609720i
$494$	14.7867	+	25.6114i	0.665287	+	1.15231i
$495$		0			0
$496$	−16.9382			−0.760549
$497$	−15.9101	+	32.8922i	−0.713667	+	1.47541i
$498$		0			0
$499$	−13.5827	−	23.5259i	−0.608045	−	1.05316i	−0.991562	−	0.129631i	$-0.958621\pi$
$499$	−13.5827	−	23.5259i	−0.608045	−	1.05316i	0.383518	−	0.923534i	$-0.374713\pi$
$500$	−4.55642			−0.203769
$501$		0			0
$502$	−21.0427			−0.939180
$503$	−11.8850			−0.529927			−0.264964	−	0.964258i	$-0.585360\pi$
$503$	−11.8850			−0.529927			−0.264964	+	0.964258i	$0.585360\pi$
$504$		0			0
$505$	−3.15972			−0.140606
$506$	−15.1170			−0.672035
$507$		0			0
$508$	−0.754499			−0.0334755
$509$	−20.7297	−	35.9049i	−0.918829	−	1.59146i	−0.801197	−	0.598401i	$-0.795803\pi$
$509$	−20.7297	−	35.9049i	−0.918829	−	1.59146i	−0.117632	−	0.993057i	$-0.537530\pi$
$510$		0			0
$511$	31.3055	−	2.29161i	1.38487	−	0.101375i
$512$	−25.2864			−1.11751
$513$		0			0
$514$	14.3387	+	24.8354i	0.632455	+	1.09544i
$515$	15.5207	−	26.8826i	0.683923	−	1.18459i
$516$		0			0
$517$	2.84386	−	4.92572i	0.125073	−	0.216633i
$518$	0.352275	+	0.518617i	0.0154781	+	0.0227867i
$519$		0			0
$520$	22.5422			0.988542
$521$	1.65221	+	2.86171i	0.0723846	+	0.125374i	0.899946	−	0.436002i	$-0.143606\pi$
$521$	1.65221	+	2.86171i	0.0723846	+	0.125374i	−0.827561	+	0.561375i	$0.810272\pi$
$522$		0			0
$523$	1.24483	−	2.15611i	0.0544327	−	0.0942803i	−0.837525	−	0.546399i	$-0.815998\pi$
$523$	1.24483	−	2.15611i	0.0544327	−	0.0942803i	0.891958	+	0.452119i	$0.149332\pi$
$524$	2.27017	+	3.93206i	0.0991730	+	0.171773i
$525$		0			0
$526$	14.1920	−	24.5812i	0.618798	−	1.07179i
$527$	−5.82992	−	10.0977i	−0.253955	−	0.439864i
$528$		0			0
$529$	4.62693	−	8.01408i	0.201171	−	0.348438i
$530$	−1.64654	+	2.85189i	−0.0715211	+	0.123878i
$531$		0			0
$532$	−2.79550	−	4.11552i	−0.121200	−	0.178430i
$533$	−25.8414	−	44.7587i	−1.11932	−	1.93871i
$534$		0			0
$535$	26.2641			1.13550
$536$	−37.0970			−1.60235
$537$		0			0
$538$	17.7160	+	30.6851i	0.763792	+	1.32293i
$539$	22.2305	−	3.27214i	0.957536	−	0.140941i
$540$		0			0
$541$	11.2397	−	19.4677i	0.483233	−	0.836984i	−0.516582	−	0.856238i	$-0.672796\pi$
$541$	11.2397	−	19.4677i	0.483233	−	0.836984i	0.999815	+	0.0192542i	$0.00612919\pi$
$542$	−6.27114	+	10.8619i	−0.269369	+	0.466560i
$543$		0			0
$544$	−2.28156	−	3.95178i	−0.0978212	−	0.169431i
$545$	−8.31051	+	14.3942i	−0.355983	+	0.616581i
$546$		0			0
$547$	7.27727	+	12.6046i	0.311154	+	0.538934i	0.978612	−	0.205713i	$-0.0659513\pi$
$547$	7.27727	+	12.6046i	0.311154	+	0.538934i	−0.667459	+	0.744647i	$0.732618\pi$
$548$	3.11834	−	5.40112i	0.133209	−	0.230725i
$549$		0			0
$550$	5.27331	+	9.13365i	0.224855	+	0.389460i
$551$	35.8938			1.52913
$552$		0			0
$553$	1.50836	−	3.11834i	0.0641420	−	0.132605i
$554$	5.53461	−	9.58622i	0.235143	−	0.407279i
$555$		0			0
$556$	2.59845	−	4.50065i	0.110199	−	0.190870i
$557$	7.77331	+	13.4638i	0.329366	+	0.570478i	0.982386	−	0.186862i	$-0.0598318\pi$
$557$	7.77331	+	13.4638i	0.329366	+	0.570478i	−0.653021	+	0.757340i	$0.726498\pi$
$558$		0			0
$559$	23.3071			0.985787
$560$	12.6146	−	0.923408i	0.533065	−	0.0390211i
$561$		0			0
$562$	−3.94168	−	6.82719i	−0.166270	−	0.287988i
$563$	14.7383			0.621144			0.310572	−	0.950550i	$-0.399479\pi$
$563$	14.7383			0.621144			0.310572	+	0.950550i	$0.399479\pi$
$564$		0			0
$565$	13.3363			0.561063
$566$	24.9706			1.04959
$567$		0			0
$568$	−41.8646			−1.75660
$569$	−12.9708			−0.543764			−0.271882	−	0.962331i	$-0.587646\pi$
$569$	−12.9708			−0.543764			−0.271882	+	0.962331i	$0.587646\pi$
$570$		0			0
$571$	12.8586			0.538115			0.269058	−	0.963124i	$-0.413288\pi$
$571$	12.8586			0.538115			0.269058	+	0.963124i	$0.413288\pi$
$572$	2.97012	+	5.14440i	0.124187	+	0.215098i
$573$		0			0
$574$	−20.3884	−	30.0156i	−0.850995	−	1.25283i
$575$	9.59019			0.399939
$576$		0			0
$577$	5.26279	+	9.11542i	0.219093	+	0.379480i	0.954531	−	0.298112i	$-0.0963569\pi$
$577$	5.26279	+	9.11542i	0.219093	+	0.379480i	−0.735438	+	0.677592i	$0.763024\pi$
$578$	7.94669	−	13.7641i	0.330539	−	0.572510i
$579$		0			0
$580$	2.21599	−	3.83820i	0.0920138	−	0.159373i
$581$	0.914274	−	0.0669261i	0.0379305	−	0.00277656i
$582$		0			0
$583$	−5.35706			−0.221867
$584$	17.9826	+	31.1468i	0.744126	+	1.28886i
$585$		0			0
$586$	−9.20690	+	15.9468i	−0.380334	+	0.658757i
$587$	−3.10009	−	5.36951i	−0.127954	−	0.221624i	0.794930	−	0.606702i	$-0.207508\pi$
$587$	−3.10009	−	5.36951i	−0.127954	−	0.221624i	−0.922884	+	0.385078i	$0.874174\pi$
$588$		0			0
$589$	13.3862	−	23.1857i	0.551571	−	0.955348i
$590$	−5.74801	−	9.95585i	−0.236642	−	0.409876i
$591$		0			0
$592$	−0.287048	+	0.497182i	−0.0117976	+	0.0204341i
$593$	18.7629	−	32.4984i	0.770502	−	1.33455i	−0.166787	−	0.985993i	$-0.553339\pi$
$593$	18.7629	−	32.4984i	0.770502	−	1.33455i	0.937288	−	0.348555i	$-0.113327\pi$
$594$		0			0
$595$	4.89229	+	7.20239i	0.200564	+	0.295269i
$596$	0.620832	+	1.07531i	0.0254302	+	0.0440465i
$597$		0			0
$598$	−22.5422			−0.921820
$599$	35.0920			1.43382			0.716909	−	0.697166i	$-0.245556\pi$
$599$	35.0920			1.43382			0.716909	+	0.697166i	$0.245556\pi$
$600$		0			0
$601$	−13.1171	−	22.7195i	−0.535058	−	0.926748i	−0.999161	−	0.0409662i	$-0.986956\pi$
$601$	−13.1171	−	22.7195i	−0.535058	−	0.926748i	0.464102	−	0.885782i	$-0.346377\pi$
$602$	16.3197	−	1.19463i	0.665143	−	0.0486894i
$603$		0			0
$604$	3.29233	−	5.70249i	0.133963	−	0.232031i
$605$	−0.540512	+	0.936194i	−0.0219749	+	0.0380617i
$606$		0			0
$607$	1.10933	+	1.92142i	0.0450263	+	0.0779879i	0.887660	−	0.460499i	$-0.152329\pi$
$607$	1.10933	+	1.92142i	0.0450263	+	0.0779879i	−0.842634	+	0.538487i	$0.818996\pi$
$608$	5.23876	−	9.07379i	0.212460	−	0.367991i
$609$		0			0
$610$	6.78530	+	11.7525i	0.274729	+	0.475844i
$611$	4.24071	−	7.34512i	0.171561	−	0.297152i
$612$		0			0
$613$	−7.43312	−	12.8745i	−0.300221	−	0.519998i	0.675965	−	0.736934i	$-0.263727\pi$
$613$	−7.43312	−	12.8745i	−0.300221	−	0.519998i	−0.976186	+	0.216936i	$0.930394\pi$
$614$	28.2969			1.14197
$615$		0			0
$616$	14.4663	+	21.2972i	0.582864	+	0.858088i
$617$	−11.6023	+	20.0958i	−0.467091	+	0.809024i	−0.999293	−	0.0375925i	$-0.988031\pi$
$617$	−11.6023	+	20.0958i	−0.467091	+	0.809024i	0.532203	+	0.846617i	$0.321364\pi$
$618$		0			0
$619$	4.15562	−	7.19775i	0.167029	−	0.289302i	−0.770345	−	0.637627i	$-0.779916\pi$
$619$	4.15562	−	7.19775i	0.167029	−	0.289302i	0.937374	+	0.348325i	$0.113249\pi$
$620$	−1.65286	−	2.86284i	−0.0663805	−	0.114974i
$621$		0			0
$622$	−22.1021			−0.886214
$623$	−25.8767	−	38.0955i	−1.03673	−	1.52627i
$624$		0			0
$625$	2.68802	+	4.65578i	0.107521	+	0.186231i
$626$	−0.254096			−0.0101557
$627$		0			0
$628$	−3.64726			−0.145542
$629$	−0.395194			−0.0157574
$630$		0			0
$631$	−24.5415			−0.976982			−0.488491	−	0.872569i	$-0.662452\pi$
$631$	−24.5415			−0.976982			−0.488491	+	0.872569i	$0.662452\pi$
$632$	3.96897			0.157877
$633$		0			0
$634$	−10.4589			−0.415378
$635$	1.51592	+	2.62565i	0.0601574	+	0.104196i
$636$		0			0
$637$	33.1497	−	4.87935i	1.31344	−	0.193327i
$638$	−30.0885			−1.19121
$639$		0			0
$640$	5.42549	+	9.39723i	0.214461	+	0.371458i
$641$	−3.98762	+	6.90677i	−0.157502	+	0.272801i	−0.933967	−	0.357359i	$-0.883677\pi$
$641$	−3.98762	+	6.90677i	−0.157502	+	0.272801i	0.776465	+	0.630160i	$0.217011\pi$
$642$		0			0
$643$	1.56140	−	2.70442i	0.0615755	−	0.106652i	−0.833594	−	0.552377i	$-0.813721\pi$
$643$	1.56140	−	2.70442i	0.0615755	−	0.106652i	0.895170	+	0.445725i	$0.147054\pi$
$644$	3.78218	−	0.276861i	0.149039	−	0.0109098i
$645$		0			0
$646$	−13.0878			−0.514933
$647$	6.13273	+	10.6222i	0.241102	+	0.417602i	0.961029	−	0.276449i	$-0.0891577\pi$
$647$	6.13273	+	10.6222i	0.241102	+	0.417602i	−0.719926	+	0.694051i	$0.755824\pi$
$648$		0			0
$649$	9.35065	−	16.1958i	0.367045	−	0.635741i
$650$	7.86345	+	13.6199i	0.308430	+	0.534216i
$651$		0			0
$652$	0.710857	−	1.23124i	0.0278393	−	0.0482191i
$653$	−8.25476	−	14.2977i	−0.323034	−	0.559511i	0.658079	−	0.752949i	$-0.271369\pi$
$653$	−8.25476	−	14.2977i	−0.323034	−	0.559511i	−0.981112	+	0.193438i	$0.938036\pi$
$654$		0			0
$655$	9.12235	−	15.8004i	0.356440	−	0.617372i
$656$	16.6133	−	28.7751i	0.648641	−	1.12348i
$657$		0			0
$658$	2.59288	−	5.36044i	0.101081	−	0.208972i
$659$	−5.36940	−	9.30007i	−0.209162	−	0.362279i	0.742289	−	0.670080i	$-0.233740\pi$
$659$	−5.36940	−	9.30007i	−0.209162	−	0.362279i	−0.951451	+	0.307801i	$0.900407\pi$
$660$		0			0
$661$	−13.3763			−0.520280			−0.260140	−	0.965571i	$-0.583769\pi$
$661$	−13.3763			−0.520280			−0.260140	+	0.965571i	$0.583769\pi$
$662$	−21.1263			−0.821098
$663$		0			0
$664$	0.525180	+	0.909639i	0.0203810	+	0.0353008i
$665$	−8.70532	+	17.9971i	−0.337578	+	0.697898i
$666$		0			0
$667$	−13.6799	+	23.6943i	−0.529689	+	0.917448i
$668$	−0.311247	+	0.539095i	−0.0120425	+	0.0208582i
$669$		0			0
$670$	12.0737	+	20.9122i	0.466447	+	0.807909i
$671$	−11.0381	+	19.1185i	−0.426120	+	0.738062i
$672$		0			0
$673$	−20.4493	−	35.4193i	−0.788264	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$673$	−20.4493	−	35.4193i	−0.788264	−	1.36531i	0.138766	−	0.990325i	$-0.455686\pi$
$674$	−10.1041	+	17.5008i	−0.389195	+	0.674105i
$675$		0			0
$676$	1.91607	+	3.31874i	0.0736951	+	0.127644i
$677$	−21.2500			−0.816705			−0.408353	−	0.912824i	$-0.633897\pi$
$677$	−21.2500			−0.816705			−0.408353	+	0.912824i	$0.633897\pi$
$678$		0			0
$679$	−27.8864	+	2.04132i	−1.07018	+	0.0783387i
$680$	−4.98806	+	8.63957i	−0.191283	+	0.331312i
$681$		0			0
$682$	−11.2212	+	19.4357i	−0.429682	+	0.744231i
$683$	−20.6708	−	35.8029i	−0.790948	−	1.36996i	−0.925381	−	0.379039i	$-0.876255\pi$
$683$	−20.6708	−	35.8029i	−0.790948	−	1.36996i	0.134433	−	0.990923i	$-0.457079\pi$
$684$		0			0
$685$	−25.0612			−0.957537
$686$	22.9614	−	5.11565i	0.876670	−	0.195316i
$687$		0			0
$688$	7.49202	+	12.9766i	0.285631	+	0.494727i
$689$	−7.98834			−0.304331
$690$		0			0
$691$	−1.52037			−0.0578375			−0.0289187	−	0.999582i	$-0.509206\pi$
$691$	−1.52037			−0.0578375			−0.0289187	+	0.999582i	$0.509206\pi$
$692$	6.25685			0.237850
$693$		0			0
$694$	−7.98858			−0.303242
$695$	−20.8829			−0.792135
$696$		0			0
$697$	22.8724			0.866353
$698$	−1.02858	−	1.78154i	−0.0389321	−	0.0674325i
$699$		0			0
$700$	−1.48662	−	2.18860i	−0.0561891	−	0.0827211i
$701$	−32.5344			−1.22881			−0.614404	−	0.788991i	$-0.710604\pi$
$701$	−32.5344			−1.22881			−0.614404	+	0.788991i	$0.710604\pi$
$702$		0			0
$703$	−0.453708	−	0.785845i	−0.0171119	−	0.0296387i
$704$	−14.2697	+	24.7159i	−0.537811	+	0.931515i
$705$		0			0
$706$	20.6482	−	35.7637i	0.777104	−	1.34598i
$707$	−3.02370	−	4.45147i	−0.113718	−	0.167415i
$708$		0			0
$709$	22.5621			0.847337			0.423669	−	0.905817i	$-0.360742\pi$
$709$	22.5621			0.847337			0.423669	+	0.905817i	$0.360742\pi$
$710$	13.6253	+	23.5998i	0.511350	+	0.885684i
$711$		0			0
$712$	26.3833	−	45.6972i	0.988756	−	1.71258i
$713$	10.2036	+	17.6731i	0.382127	+	0.661864i
$714$		0			0
$715$	11.9350	−	20.6720i	0.446343	−	0.773089i
$716$	−3.36466	−	5.82777i	−0.125743	−	0.217794i
$717$		0			0
$718$	7.10787	−	12.3112i	0.265263	−	0.459450i
$719$	3.25084	−	5.63062i	0.121236	−	0.209987i	−0.799019	−	0.601305i	$-0.794648\pi$
$719$	3.25084	−	5.63062i	0.121236	−	0.209987i	0.920255	+	0.391319i	$0.127981\pi$
$720$		0			0
$721$	52.7253	−	3.85956i	1.96359	−	0.143738i
$722$	−2.95878	−	5.12475i	−0.110114	−	0.190723i
$723$		0			0
$724$	−3.43917			−0.127816
$725$	19.0880			0.708910
$726$		0			0
$727$	3.91607	+	6.78284i	0.145239	+	0.251562i	0.929462	−	0.368918i	$-0.120272\pi$
$727$	3.91607	+	6.78284i	0.145239	+	0.251562i	−0.784223	+	0.620479i	$0.786938\pi$
$728$	21.5718	+	31.7579i	0.799505	+	1.17703i
$729$		0			0
$730$	11.7053	−	20.2742i	0.433234	−	0.750383i
$731$	−5.15732	+	8.93274i	−0.190750	+	0.330389i
$732$		0			0
$733$	3.74780	+	6.49138i	0.138428	+	0.239764i	0.926902	−	0.375304i	$-0.122462\pi$
$733$	3.74780	+	6.49138i	0.138428	+	0.239764i	−0.788474	+	0.615068i	$0.789128\pi$
$734$	3.29411	−	5.70557i	0.121588	−	0.210597i
$735$		0			0
$736$	3.99321	+	6.91645i	0.147192	+	0.254944i
$737$	−19.6410	+	34.0192i	−0.723486	+	1.25311i
$738$		0			0
$739$	−12.0480	−	20.8678i	−0.443194	−	0.767634i	0.554731	−	0.832030i	$-0.312821\pi$
$739$	−12.0480	−	20.8678i	−0.443194	−	0.767634i	−0.997924	+	0.0643961i	$0.979488\pi$
$740$	−0.112043			−0.00411877
$741$		0			0
$742$	−5.59346	+	0.409449i	−0.205342	+	0.0150313i
$743$	−9.64411	+	16.7041i	−0.353808	+	0.612814i	−0.986913	−	0.161252i	$-0.948447\pi$
$743$	−9.64411	+	16.7041i	−0.353808	+	0.612814i	0.633105	+	0.774066i	$0.281780\pi$
$744$		0			0
$745$	2.49472	−	4.32098i	0.0913994	−	0.158308i
$746$	−20.8721	−	36.1515i	−0.764181	−	1.32360i
$747$		0			0
$748$	−2.62887			−0.0961210
$749$	25.1335	+	37.0014i	0.918359	+	1.35200i
$750$		0			0
$751$	16.6045	+	28.7598i	0.605906	+	1.04946i	0.991908	+	0.126961i	$0.0405225\pi$
$751$	16.6045	+	28.7598i	0.605906	+	1.04946i	−0.386002	+	0.922498i	$0.626144\pi$
$752$	5.45266			0.198838
$753$		0			0
$754$	−44.8673			−1.63397
$755$	−26.4595			−0.962959
$756$		0			0
$757$	9.70935			0.352892			0.176446	−	0.984310i	$-0.443540\pi$
$757$	9.70935			0.352892			0.176446	+	0.984310i	$0.443540\pi$
$758$	17.7018			0.642957
$759$		0			0
$760$	−22.9064			−0.830903
$761$	−1.36305	−	2.36086i	−0.0494104	−	0.0855813i	0.840262	−	0.542180i	$-0.182401\pi$
$761$	−1.36305	−	2.36086i	−0.0494104	−	0.0855813i	−0.889673	+	0.456599i	$0.849068\pi$
$762$		0			0
$763$	−28.2316	+	2.06659i	−1.02205	+	0.0748157i
$764$	−5.71868			−0.206894
$765$		0			0
$766$	−1.08932	−	1.88676i	−0.0393588	−	0.0681714i
$767$	13.9435	−	24.1508i	0.503470	−	0.872036i
$768$		0			0
$769$	−25.0230	+	43.3411i	−0.902352	+	1.56292i	−0.0779198	+	0.996960i	$0.524828\pi$
$769$	−25.0230	+	43.3411i	−0.902352	+	1.56292i	−0.824432	+	0.565960i	$0.808506\pi$
$770$	7.29735	−	15.0863i	0.262978	−	0.543674i
$771$		0			0
$772$	−0.704225			−0.0253456
$773$	−9.52030	−	16.4896i	−0.342421	−	0.593091i	0.642461	−	0.766319i	$-0.277914\pi$
$773$	−9.52030	−	16.4896i	−0.342421	−	0.593091i	−0.984882	+	0.173228i	$0.944580\pi$
$774$		0			0
$775$	7.11868	−	12.3299i	0.255711	−	0.442904i
$776$	−16.0186	−	27.7450i	−0.575033	−	0.995987i
$777$		0			0
$778$	−1.99964	+	3.46348i	−0.0716906	+	0.124172i
$779$	26.2589	+	45.4818i	0.940824	+	1.62956i
$780$		0			0
$781$	−22.1652	+	38.3912i	−0.793133	+	1.37375i
$782$	4.98806	−	8.63957i	0.178373	−	0.308950i
$783$		0			0
$784$	13.3725	+	16.8881i	0.477590	+	0.603145i
$785$	7.32798	+	12.6924i	0.261547	+	0.453013i
$786$		0			0
$787$	−33.2023			−1.18353			−0.591766	−	0.806110i	$-0.701569\pi$
$787$	−33.2023			−1.18353			−0.591766	+	0.806110i	$0.701569\pi$
$788$	−2.98444			−0.106316
$789$		0			0
$790$	−1.29175	−	2.23738i	−0.0459584	−	0.0796023i
$791$	12.7622	+	18.7885i	0.453773	+	0.668041i
$792$		0			0
$793$	−16.4597	+	28.5091i	−0.584502	+	1.01239i
$794$	−17.4236	+	30.1785i	−0.618340	+	1.07100i
$795$		0			0
$796$	0.427834	+	0.741030i	0.0151642	+	0.0262651i
$797$	−1.04472	+	1.80951i	−0.0370059	+	0.0640961i	−0.883935	−	0.467609i	$-0.845115\pi$
$797$	−1.04472	+	1.80951i	−0.0370059	+	0.0640961i	0.846929	+	0.531706i	$0.178449\pi$
$798$		0			0
$799$	1.87674	+	3.25060i	0.0663942	+	0.114998i
$800$	2.78592	−	4.82536i	0.0984972	−	0.170602i
$801$		0			0
$802$	18.4414	+	31.9414i	0.651187	+	1.12789i
$803$	38.0836			1.34394
$804$		0			0
$805$	−8.56253	−	12.6057i	−0.301789	−	0.444292i
$806$	−16.7328	+	28.9821i	−0.589388	+	1.02085i
$807$		0			0
$808$	3.08289	−	5.33973i	0.108456	−	0.187851i
$809$	−0.241404	−	0.418125i	−0.00848732	−	0.0147005i	0.861751	−	0.507332i	$-0.169368\pi$
$809$	−0.241404	−	0.418125i	−0.00848732	−	0.0147005i	−0.870238	+	0.492632i	$0.836035\pi$
$810$		0			0
$811$	17.1671			0.602820			0.301410	−	0.953495i	$-0.402543\pi$
$811$	17.1671			0.602820			0.301410	+	0.953495i	$0.402543\pi$
$812$	7.52792	−	0.551054i	0.264178	−	0.0193382i
$813$		0			0
$814$	0.380327	+	0.658745i	0.0133304	+	0.0230890i
$815$	−5.71294			−0.200116
$816$		0			0
$817$	−23.6837			−0.828588
$818$	−35.2226			−1.23153
$819$		0			0
$820$	6.48462			0.226453
$821$	−12.8217			−0.447481			−0.223741	−	0.974649i	$-0.571827\pi$
$821$	−12.8217			−0.447481			−0.223741	+	0.974649i	$0.571827\pi$
$822$		0			0
$823$	24.5945			0.857311			0.428655	−	0.903468i	$-0.358987\pi$
$823$	24.5945			0.857311			0.428655	+	0.903468i	$0.358987\pi$
$824$	30.2866	+	52.4580i	1.05509	+	1.82746i
$825$		0			0
$826$	8.52540	−	17.6252i	0.296637	−	0.613258i
$827$	0.527165			0.0183313			0.00916567	−	0.999958i	$-0.497082\pi$
$827$	0.527165			0.0183313			0.00916567	+	0.999958i	$0.497082\pi$
$828$		0			0
$829$	23.1015	+	40.0130i	0.802348	+	1.38971i	0.918067	+	0.396426i	$0.129750\pi$
$829$	23.1015	+	40.0130i	0.802348	+	1.38971i	−0.115718	+	0.993282i	$0.536917\pi$
$830$	0.341853	−	0.592106i	0.0118659	−	0.0205523i
$831$		0			0
$832$	−21.2787	+	36.8558i	−0.737707	+	1.27775i
$833$	−5.46517	+	13.7847i	−0.189357	+	0.477611i
$834$		0			0
$835$	2.50140			0.0865644
$836$	−3.01811	−	5.22752i	−0.104383	−	0.180797i
$837$		0			0
$838$	19.2815	−	33.3965i	0.666067	−	1.15366i
$839$	5.41289	+	9.37540i	0.186874	+	0.323675i	0.944206	−	0.329355i	$-0.106831\pi$
$839$	5.41289	+	9.37540i	0.186874	+	0.323675i	−0.757333	+	0.653029i	$0.773498\pi$
$840$		0			0
$841$	−12.7281	+	22.0456i	−0.438898	+	0.760194i
$842$	17.6389	+	30.5515i	0.607877	+	1.05287i
$843$		0			0
$844$	−0.350540	+	0.607152i	−0.0120661	+	0.0208990i
$845$	7.69945	−	13.3358i	0.264869	−	0.458767i
$846$		0			0
$847$	−1.83617	+	0.134410i	−0.0630916	+	0.00461839i
$848$	−2.56783	−	4.44761i	−0.0881796	−	0.152732i
$849$		0			0
$850$	−6.95998			−0.238725
$851$	0.691672			0.0237102
$852$		0			0
$853$	21.5961	+	37.4056i	0.739437	+	1.28074i	0.952749	+	0.303758i	$0.0982414\pi$
$853$	21.5961	+	37.4056i	0.739437	+	1.28074i	−0.213313	+	0.976984i	$0.568425\pi$
$854$	−10.0639	+	20.8058i	−0.344380	+	0.711961i
$855$		0			0
$856$	−25.6255	+	44.3847i	−0.875863	+	1.51704i
$857$	−0.787226	+	1.36352i	−0.0268911	+	0.0465768i	−0.879158	−	0.476531i	$-0.841894\pi$
$857$	−0.787226	+	1.36352i	−0.0268911	+	0.0465768i	0.852267	+	0.523108i	$0.175227\pi$
$858$		0			0
$859$	−3.41090	−	5.90786i	−0.116378	−	0.201573i	0.801951	−	0.597389i	$-0.203795\pi$
$859$	−3.41090	−	5.90786i	−0.116378	−	0.201573i	−0.918330	+	0.395816i	$0.870462\pi$
$860$	−1.46217	+	2.53255i	−0.0498595	+	0.0863592i
$861$		0			0
$862$	−4.61037	−	7.98539i	−0.157030	−	0.271983i
$863$	−4.51387	+	7.81825i	−0.153654	+	0.266136i	−0.932568	−	0.360994i	$-0.882437\pi$
$863$	−4.51387	+	7.81825i	−0.153654	+	0.266136i	0.778914	+	0.627131i	$0.215771\pi$
$864$		0			0
$865$	−12.5711	−	21.7738i	−0.427430	−	0.740331i
$866$	19.1006			0.649066
$867$		0			0
$868$	2.45151	−	5.06818i	0.0832097	−	0.172025i
$869$	2.10137	−	3.63968i	0.0712841	−	0.123468i
$870$		0			0
$871$	−29.2882	+	50.7287i	−0.992394	+	1.71888i
$872$	−16.2169	−	28.0885i	−0.549174	−	0.951196i
$873$		0			0
$874$	22.9064			0.774821
$875$	−13.5781	+	28.0709i	−0.459023	+	0.948971i
$876$		0			0
$877$	−4.83460	−	8.37377i	−0.163253	−	0.282762i	0.772781	−	0.634673i	$-0.218865\pi$
$877$	−4.83460	−	8.37377i	−0.163253	−	0.282762i	−0.936033	+	0.351911i	$0.885532\pi$
$878$	1.95761			0.0660663
$879$		0			0
$880$	15.3459			0.517309
$881$	−21.4721			−0.723415			−0.361707	−	0.932292i	$-0.617806\pi$
$881$	−21.4721			−0.723415			−0.361707	+	0.932292i	$0.617806\pi$
$882$		0			0
$883$	−26.5380			−0.893076			−0.446538	−	0.894765i	$-0.647343\pi$
$883$	−26.5380			−0.893076			−0.446538	+	0.894765i	$0.647343\pi$
$884$	−3.92011			−0.131848
$885$		0			0
$886$	25.8331			0.867880
$887$	−20.7612	−	35.9594i	−0.697091	−	1.20740i	−0.969471	−	0.245208i	$-0.921144\pi$
$887$	−20.7612	−	35.9594i	−0.697091	−	1.20740i	0.272379	−	0.962190i	$-0.412190\pi$
$888$		0			0
$889$	−2.24840	+	4.64828i	−0.0754089	+	0.155898i
$890$	−34.3471			−1.15132
$891$		0			0
$892$	1.83755	+	3.18272i	0.0615256	+	0.106565i
$893$	−4.30922	+	7.46380i	−0.144203	+	0.249766i
$894$		0			0
$895$	−13.5204	+	23.4180i	−0.451937	+	0.782777i
$896$	−8.04705	+	16.6362i	−0.268833	+	0.555778i
$897$		0			0
$898$	33.6001			1.12125
$899$	20.3089	+	35.1760i	0.677339	+	1.17319i
$900$		0			0
$901$	1.76763	−	3.06162i	0.0588883	−	0.101997i
$902$	−22.0119	−	38.1258i	−0.732917	−	1.26945i
$903$		0			0
$904$	−13.0121	+	22.5376i	−0.432775	+	0.749588i
$905$	6.90989	+	11.9683i	0.229692	+	0.397839i
$906$		0			0
$907$	2.32180	−	4.02148i	0.0770942	−	0.133531i	−0.824901	−	0.565277i	$-0.808769\pi$
$907$	2.32180	−	4.02148i	0.0770942	−	0.133531i	0.901995	+	0.431746i	$0.142102\pi$
$908$	−2.09401	+	3.62693i	−0.0694921	+	0.120364i
$909$		0			0
$910$	10.8817	−	22.4964i	0.360723	−	0.745749i
$911$	0.674054	+	1.16750i	0.0223324	+	0.0386808i	0.876976	−	0.480535i	$-0.159557\pi$
$911$	0.674054	+	1.16750i	0.0223324	+	0.0386808i	−0.854643	+	0.519216i	$0.826224\pi$
$912$		0			0
$913$	1.11223			0.0368093
$914$	−8.24816			−0.272825
$915$		0			0
$916$	2.42006	+	4.19166i	0.0799609	+	0.138496i
$917$	30.9895	−	2.26848i	1.02336	−	0.0749116i
$918$		0			0
$919$	20.2472	−	35.0692i	0.667893	−	1.15682i	−0.310599	−	0.950541i	$-0.600530\pi$
$919$	20.2472	−	35.0692i	0.667893	−	1.15682i	0.978492	−	0.206284i	$-0.0661370\pi$
$920$	8.73015	−	15.1211i	0.287824	−	0.498527i
$921$		0			0
$922$	−9.90223	−	17.1512i	−0.326112	−	0.564843i
$923$	−33.0523	+	57.2482i	−1.08793	+	1.88435i
$924$		0			0
$925$	−0.241278	−	0.417905i	−0.00793316	−	0.0137406i
$926$	−4.86221	+	8.42160i	−0.159782	+	0.276751i
$927$		0			0
$928$	7.94795	+	13.7663i	0.260904	+	0.451900i
$929$	22.3138			0.732093			0.366046	−	0.930597i	$-0.380711\pi$
$929$	22.3138			0.732093			0.366046	+	0.930597i	$0.380711\pi$
$930$		0			0
$931$	−33.6853	+	4.95818i	−1.10399	+	0.162498i
$932$	2.95380	−	5.11613i	0.0967550	−	0.167585i
$933$		0			0
$934$	26.4375	−	45.7910i	0.865060	−	1.49833i
$935$	5.28186	+	9.14844i	0.172735	+	0.299186i
$936$		0			0
$937$	−1.13943			−0.0372235			−0.0186117	−	0.999827i	$-0.505925\pi$
$937$	−1.13943			−0.0372235			−0.0186117	+	0.999827i	$0.505925\pi$
$938$	−17.9076	+	37.0216i	−0.584703	+	1.20880i
$939$		0			0
$940$	0.532080	+	0.921589i	0.0173545	+	0.0300589i
$941$	47.1875			1.53827			0.769134	−	0.639087i	$-0.220688\pi$
$941$	47.1875			1.53827			0.769134	+	0.639087i	$0.220688\pi$
$942$		0			0
$943$	−40.0315			−1.30360
$944$	17.9284			0.583519
$945$		0			0
$946$	19.8532			0.645483
$947$	24.6460			0.800888			0.400444	−	0.916321i	$-0.368856\pi$
$947$	24.6460			0.800888			0.400444	+	0.916321i	$0.368856\pi$
$948$		0			0
$949$	56.7894			1.84346
$950$	−7.99050	−	13.8400i	−0.259246	−	0.449027i
$951$		0			0
$952$	−16.9449	+	1.24039i	−0.549188	+	0.0402013i
$953$	−56.2821			−1.82316			−0.911579	−	0.411125i	$-0.865136\pi$
$953$	−56.2821			−1.82316			−0.911579	+	0.411125i	$0.865136\pi$
$954$		0			0
$955$	11.4898	+	19.9009i	0.371802	+	0.643979i
$956$	2.07137	−	3.58772i	0.0669930	−	0.116035i
$957$		0			0
$958$	−1.47075	+	2.54742i	−0.0475178	+	0.0823033i
$959$	−23.9823	−	35.3066i	−0.774430	−	1.14011i
$960$		0			0
$961$	−0.704001			−0.0227097
$962$	0.567135	+	0.982306i	0.0182852	+	0.0316708i
$963$		0			0
$964$	−2.89955	+	5.02217i	−0.0933883	+	0.161753i
$965$	1.41491	+	2.45070i	0.0455476	+	0.0788907i
$966$		0			0
$967$	29.2989	−	50.7471i	0.942188	−	1.63192i	0.180903	−	0.983501i	$-0.442098\pi$
$967$	29.2989	−	50.7471i	0.942188	−	1.63192i	0.761285	−	0.648417i	$-0.224569\pi$
$968$	−1.05474	−	1.82686i	−0.0339006	−	0.0587176i
$969$		0			0
$970$	−10.4269	+	18.0599i	−0.334787	+	0.579868i
$971$	3.04991	−	5.28260i	0.0978763	−	0.169527i	−0.812929	−	0.582363i	$-0.802128\pi$
$971$	3.04991	−	5.28260i	0.0978763	−	0.169527i	0.910805	+	0.412836i	$0.135462\pi$
$972$		0			0
$973$	−19.9840	−	29.4203i	−0.640657	−	0.943171i
$974$	−11.5130	−	19.9411i	−0.368901	−	0.638955i
$975$		0			0
$976$	−21.1638			−0.677435
$977$	−5.15976			−0.165075			−0.0825377	−	0.996588i	$-0.526302\pi$
$977$	−5.15976			−0.165075			−0.0825377	+	0.996588i	$0.526302\pi$
$978$		0			0
$979$	−27.9373	−	48.3888i	−0.892880	−	1.54651i
$980$	−1.54945	+	3.90814i	−0.0494953	+	0.124841i
$981$		0			0
$982$	13.7146	−	23.7543i	0.437649	−	0.758031i
$983$	−31.0536	+	53.7864i	−0.990455	+	1.71552i	−0.375857	+	0.926678i	$0.622652\pi$
$983$	−31.0536	+	53.7864i	−0.990455	+	1.71552i	−0.614598	+	0.788841i	$0.710682\pi$
$984$		0			0
$985$	5.99626	+	10.3858i	0.191057	+	0.330920i
$986$	9.92806	−	17.1959i	0.316174	−	0.547629i
$987$		0			0
$988$	−4.50054	−	7.79516i	−0.143181	−	0.247997i
$989$	9.02639	−	15.6342i	0.287022	−	0.497138i
$990$		0			0
$991$	10.8163	+	18.7343i	0.343590	+	0.595116i	0.985097	−	0.172002i	$-0.0550235\pi$
$991$	10.8163	+	18.7343i	0.343590	+	0.595116i	−0.641506	+	0.767118i	$0.721690\pi$
$992$	11.8565			0.376443
$993$		0			0
$994$	−20.2090	+	41.7795i	−0.640990	+	1.32517i
$995$	1.71919	−	2.97772i	0.0545018	−	0.0944000i
$996$		0			0
$997$	20.3681	−	35.2786i	0.645064	−	1.11728i	−0.339223	−	0.940706i	$-0.610164\pi$
$997$	20.3681	−	35.2786i	0.645064	−	1.11728i	0.984287	−	0.176578i	$-0.0565027\pi$
$998$	−17.2527	−	29.8825i	−0.546124	−	0.945915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.l.352.6		16
3.2	odd	2	inner	567.2.h.l.352.3		16
7.4	even	3		567.2.g.l.109.3		16
9.2	odd	6		567.2.g.l.541.6		16
9.4	even	3		567.2.e.g.163.3	✓	16
9.5	odd	6		567.2.e.g.163.6	yes	16
9.7	even	3		567.2.g.l.541.3		16
21.11	odd	6		567.2.g.l.109.6		16
63.4	even	3		567.2.e.g.487.3	yes	16
63.5	even	6		3969.2.a.bf.1.3		8
63.11	odd	6	inner	567.2.h.l.298.3		16
63.23	odd	6		3969.2.a.bg.1.3		8
63.25	even	3	inner	567.2.h.l.298.6		16
63.32	odd	6		567.2.e.g.487.6	yes	16
63.40	odd	6		3969.2.a.bf.1.6		8
63.58	even	3		3969.2.a.bg.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.3	✓	16	9.4	even	3
567.2.e.g.163.6	yes	16	9.5	odd	6
567.2.e.g.487.3	yes	16	63.4	even	3
567.2.e.g.487.6	yes	16	63.32	odd	6
567.2.g.l.109.3		16	7.4	even	3
567.2.g.l.109.6		16	21.11	odd	6
567.2.g.l.541.3		16	9.7	even	3
567.2.g.l.541.6		16	9.2	odd	6
567.2.h.l.298.3		16	63.11	odd	6	inner
567.2.h.l.298.6		16	63.25	even	3	inner
567.2.h.l.352.3		16	3.2	odd	2	inner
567.2.h.l.352.6		16	1.1	even	1	trivial
3969.2.a.bf.1.3		8	63.5	even	6
3969.2.a.bf.1.6		8	63.40	odd	6
3969.2.a.bg.1.3		8	63.23	odd	6
3969.2.a.bg.1.6		8	63.58	even	3

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.27020 q^{2} -0.386601 q^{4} +(0.776749 + 1.34537i) q^{5} +(-1.15207 + 2.38175i) q^{7} -3.03145 q^{8} +O(q^{10})\)	\(q+1.27020 q^{2} -0.386601 q^{4} +(0.776749 + 1.34537i) q^{5} +(-1.15207 + 2.38175i) q^{7} -3.03145 q^{8} +(0.986623 + 1.70888i) q^{10} +(-1.60500 + 2.77995i) q^{11} +(-2.39335 + 4.14540i) q^{13} +(-1.46335 + 3.02529i) q^{14} -3.07734 q^{16} +(-1.05918 - 1.83456i) q^{17} +(2.43201 - 4.21237i) q^{19} +(-0.300292 - 0.520121i) q^{20} +(-2.03867 + 3.53108i) q^{22} +(1.85379 + 3.21086i) q^{23} +(1.29332 - 2.24010i) q^{25} +(-3.04002 + 5.26547i) q^{26} +(0.445391 - 0.920788i) q^{28} +(3.68972 + 6.39078i) q^{29} +5.50418 q^{31} +2.15408 q^{32} +(-1.34537 - 2.33025i) q^{34} +(-4.09920 + 0.300067i) q^{35} +(0.0932782 - 0.161563i) q^{37} +(3.08914 - 5.35054i) q^{38} +(-2.35468 - 4.07842i) q^{40} +(-5.39860 + 9.35065i) q^{41} +(-2.43458 - 4.21681i) q^{43} +(0.620496 - 1.07473i) q^{44} +(2.35468 + 4.07842i) q^{46} -1.77187 q^{47} +(-4.34548 - 5.48788i) q^{49} +(1.64277 - 2.84537i) q^{50} +(0.925270 - 1.60261i) q^{52} +(0.834432 + 1.44528i) q^{53} -4.98674 q^{55} +(3.49244 - 7.22017i) q^{56} +(4.68667 + 8.11755i) q^{58} -5.82594 q^{59} +6.87729 q^{61} +6.99139 q^{62} +8.89078 q^{64} -7.43611 q^{65} +12.2374 q^{67} +(0.409481 + 0.709241i) q^{68} +(-5.20679 + 0.381144i) q^{70} +13.8101 q^{71} +(-5.93201 - 10.2745i) q^{73} +(0.118482 - 0.205216i) q^{74} +(-0.940219 + 1.62851i) q^{76} +(-4.77207 - 7.02540i) q^{77} -1.30926 q^{79} +(-2.39032 - 4.14015i) q^{80} +(-6.85728 + 11.8772i) q^{82} +(-0.173244 - 0.300067i) q^{83} +(1.64544 - 2.84998i) q^{85} +(-3.09239 - 5.35618i) q^{86} +(4.86549 - 8.42727i) q^{88} +(-8.70319 + 15.0744i) q^{89} +(-7.11601 - 10.4761i) q^{91} +(-0.716677 - 1.24132i) q^{92} -2.25063 q^{94} +7.55625 q^{95} +(5.28413 + 9.15238i) q^{97} +(-5.51961 - 6.97068i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 6 q^{7}+O(q^{10}) \) 16 * q + 12 * q^4 - 6 * q^7	\( 16 q + 12 q^{4} - 6 q^{7} - 14 q^{10} - 6 q^{13} + 12 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} + 40 q^{31} + 4 q^{37} - 36 q^{40} - 10 q^{43} + 36 q^{46} + 10 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} + 72 q^{61} + 76 q^{64} - 36 q^{67} - 46 q^{70} - 32 q^{73} - 58 q^{76} - 64 q^{79} + 2 q^{82} - 30 q^{85} + 72 q^{88} - 22 q^{91} + 108 q^{94} - 14 q^{97}+O(q^{100}) \) 16 * q + 12 * q^4 - 6 * q^7 - 14 * q^10 - 6 * q^13 + 12 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 + 40 * q^31 + 4 * q^37 - 36 * q^40 - 10 * q^43 + 36 * q^46 + 10 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 + 72 * q^61 + 76 * q^64 - 36 * q^67 - 46 * q^70 - 32 * q^73 - 58 * q^76 - 64 * q^79 + 2 * q^82 - 30 * q^85 + 72 * q^88 - 22 * q^91 + 108 * q^94 - 14 * q^97

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