LMFDB - Embedded newform 567.2.h.h.352.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.h.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.760877 q^{2} -1.42107 q^{4} +(1.59097 + 2.75564i) q^{5} +(0.710533 + 2.54856i) q^{7} +2.60301 q^{8} +(-1.21053 - 2.09671i) q^{10} +(1.11956 - 1.93914i) q^{11} +(-1.85185 + 3.20750i) q^{13} +(-0.540628 - 1.93914i) q^{14} +0.861564 q^{16} +(-2.80150 - 4.85235i) q^{17} +(-2.21053 + 3.82876i) q^{19} +(-2.26088 - 3.91595i) q^{20} +(-0.851848 + 1.47544i) q^{22} +(-0.471410 - 0.816506i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(1.40903 - 2.44051i) q^{26} +(-1.00972 - 3.62167i) q^{28} +(5.06238 + 8.76830i) q^{29} -5.70370 q^{31} -5.86156 q^{32} +(2.13160 + 3.69204i) q^{34} +(-5.89248 + 6.01266i) q^{35} +(-1.56238 + 2.70612i) q^{37} +(1.68194 - 2.91321i) q^{38} +(4.14132 + 7.17297i) q^{40} +(1.99316 - 3.45226i) q^{41} +(1.64132 + 2.84284i) q^{43} +(-1.59097 + 2.75564i) q^{44} +(0.358685 + 0.621261i) q^{46} +0.225450 q^{47} +(-5.99028 + 3.62167i) q^{49} +(1.94966 - 3.37690i) q^{50} +(2.63160 - 4.55806i) q^{52} +(5.33009 + 9.23200i) q^{53} +7.12476 q^{55} +(1.84953 + 6.63392i) q^{56} +(-3.85185 - 6.67160i) q^{58} +2.05718 q^{59} -5.84213 q^{61} +4.33981 q^{62} +2.73680 q^{64} -11.7850 q^{65} +7.42107 q^{67} +(3.98113 + 6.89551i) q^{68} +(4.48345 - 4.57489i) q^{70} -7.26320 q^{71} +(-3.77975 - 6.54672i) q^{73} +(1.18878 - 2.05903i) q^{74} +(3.14132 - 5.44092i) q^{76} +(5.73749 + 1.47544i) q^{77} -6.82846 q^{79} +(1.37072 + 2.37416i) q^{80} +(-1.51655 + 2.62674i) q^{82} +(-4.05555 - 7.02441i) q^{83} +(8.91423 - 15.4399i) q^{85} +(-1.24884 - 2.16305i) q^{86} +(2.91423 - 5.04759i) q^{88} +(4.86389 - 8.42450i) q^{89} +(-9.49028 - 2.44051i) q^{91} +(0.669905 + 1.16031i) q^{92} -0.171540 q^{94} -14.0676 q^{95} +(-0.421067 - 0.729309i) q^{97} +(4.55787 - 2.75564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{2} + 8 q^{4} + q^{5} - 4 q^{7} - 18 q^{8} + q^{10} + 7 q^{11} - 2 q^{13} + 13 q^{14} + 20 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) $ 6 * q - 4 * q^2 + 8 * q^4 + q^5 - 4 * q^7 - 18 * q^8 + q^10 + 7 * q^11 - 2 * q^13 + 13 * q^14 + 20 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 - 16 * q^31 - 50 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 - 7 * q^38 + 24 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 - 18 * q^47 - 12 * q^49 + 4 * q^50 - 9 * q^52 + 24 * q^53 + 8 * q^55 + 51 * q^56 - 14 * q^58 + 30 * q^59 - 2 * q^61 + 42 * q^62 + 66 * q^64 - 20 * q^65 + 28 * q^67 + 39 * q^68 - 7 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 - 10 * q^77 + 12 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 - 32 * q^86 - 9 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 - 54 * q^94 - 32 * q^95 + 14 * q^97 - 49 * q^98

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 $

$2$	−0.760877			−0.538021			−0.269011	−	0.963137i	$-0.586697\pi$
$2$	−0.760877			−0.538021			−0.269011	+	0.963137i	$0.586697\pi$
$3$		0			0
$3$		0			0
$4$	−1.42107			−0.710533
$5$	1.59097	+	2.75564i	0.711504	+	1.23236i	0.964292	+	0.264840i	$0.0853191\pi$
$5$	1.59097	+	2.75564i	0.711504	+	1.23236i	−0.252788	+	0.967522i	$0.581348\pi$
$6$		0			0
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$8$	2.60301			0.920303
$9$		0			0
$10$	−1.21053	−	2.09671i	−0.382804	−	0.663036i
$11$	1.11956	−	1.93914i	0.337561	−	0.584672i	−0.646413	−	0.762988i	$-0.723732\pi$
$11$	1.11956	−	1.93914i	0.337561	−	0.584672i	0.983973	+	0.178316i	$0.0570649\pi$
$12$		0			0
$13$	−1.85185	+	3.20750i	−0.513610	+	0.889599i	0.486265	+	0.873811i	$0.338359\pi$
$13$	−1.85185	+	3.20750i	−0.513610	+	0.889599i	−0.999875	+	0.0157878i	$0.994974\pi$
$14$	−0.540628	−	1.93914i	−0.144489	−	0.518256i
$15$		0			0
$16$	0.861564			0.215391
$17$	−2.80150	−	4.85235i	−0.679465	−	1.17687i	−0.975142	−	0.221580i	$-0.928879\pi$
$17$	−2.80150	−	4.85235i	−0.679465	−	1.17687i	0.295678	−	0.955288i	$-0.404455\pi$
$18$		0			0
$19$	−2.21053	+	3.82876i	−0.507131	+	0.878377i	0.492835	+	0.870123i	$0.335961\pi$
$19$	−2.21053	+	3.82876i	−0.507131	+	0.878377i	−0.999966	+	0.00825398i	$0.997373\pi$
$20$	−2.26088	−	3.91595i	−0.505547	−	0.875634i
$21$		0			0
$22$	−0.851848	+	1.47544i	−0.181615	+	0.314566i
$23$	−0.471410	−	0.816506i	−0.0982958	−	0.170253i	0.812684	−	0.582705i	$-0.198006\pi$
$23$	−0.471410	−	0.816506i	−0.0982958	−	0.170253i	−0.910979	+	0.412452i	$0.864672\pi$
$24$		0			0
$25$	−2.56238	+	4.43818i	−0.512476	+	0.887635i
$26$	1.40903	−	2.44051i	0.276333	−	0.478623i
$27$		0			0
$28$	−1.00972	−	3.62167i	−0.190818	−	0.684431i
$29$	5.06238	+	8.76830i	0.940061	+	1.62823i	0.765351	+	0.643613i	$0.222565\pi$
$29$	5.06238	+	8.76830i	0.940061	+	1.62823i	0.174709	+	0.984620i	$0.444101\pi$
$30$		0			0
$31$	−5.70370			−1.02441			−0.512207	−	0.858862i	$-0.671172\pi$
$31$	−5.70370			−1.02441			−0.512207	+	0.858862i	$0.671172\pi$
$32$	−5.86156			−1.03619
$33$		0			0
$34$	2.13160	+	3.69204i	0.365566	+	0.633180i
$35$	−5.89248	+	6.01266i	−0.996010	+	1.01632i
$36$		0			0
$37$	−1.56238	+	2.70612i	−0.256854	+	0.444884i	−0.965397	−	0.260783i	$-0.916019\pi$
$37$	−1.56238	+	2.70612i	−0.256854	+	0.444884i	0.708543	+	0.705667i	$0.249353\pi$
$38$	1.68194	−	2.91321i	0.272847	−	0.472585i
$39$		0			0
$40$	4.14132	+	7.17297i	0.654799	+	1.13415i
$41$	1.99316	−	3.45226i	0.311280	−	0.539152i	−0.667360	−	0.744735i	$-0.732576\pi$
$41$	1.99316	−	3.45226i	0.311280	−	0.539152i	0.978640	+	0.205583i	$0.0659090\pi$
$42$		0			0
$43$	1.64132	+	2.84284i	0.250298	+	0.433529i	0.963608	−	0.267320i	$-0.0861380\pi$
$43$	1.64132	+	2.84284i	0.250298	+	0.433529i	−0.713310	+	0.700849i	$0.752805\pi$
$44$	−1.59097	+	2.75564i	−0.239848	+	0.415429i
$45$		0			0
$46$	0.358685	+	0.621261i	0.0528852	+	0.0915999i
$47$	0.225450			0.0328853			0.0164426	−	0.999865i	$-0.494766\pi$
$47$	0.225450			0.0328853			0.0164426	+	0.999865i	$0.494766\pi$
$48$		0			0
$49$	−5.99028	+	3.62167i	−0.855755	+	0.517381i
$50$	1.94966	−	3.37690i	0.275723	−	0.477566i
$51$		0			0
$52$	2.63160	−	4.55806i	0.364937	−	0.632090i
$53$	5.33009	+	9.23200i	0.732145	+	1.26811i	0.955965	+	0.293482i	$0.0948139\pi$
$53$	5.33009	+	9.23200i	0.732145	+	1.26811i	−0.223820	+	0.974631i	$0.571853\pi$
$54$		0			0
$55$	7.12476			0.960703
$56$	1.84953	+	6.63392i	0.247153	+	0.886495i
$57$		0			0
$58$	−3.85185	−	6.67160i	−0.505772	−	0.876024i
$59$	2.05718			0.267822			0.133911	−	0.990993i	$-0.457246\pi$
$59$	2.05718			0.267822			0.133911	+	0.990993i	$0.457246\pi$
$60$		0			0
$61$	−5.84213			−0.748009			−0.374004	−	0.927427i	$-0.622015\pi$
$61$	−5.84213			−0.748009			−0.374004	+	0.927427i	$0.622015\pi$
$62$	4.33981			0.551156
$63$		0			0
$64$	2.73680			0.342100
$65$	−11.7850			−1.46174
$66$		0			0
$67$	7.42107			0.906628			0.453314	−	0.891351i	$-0.350242\pi$
$67$	7.42107			0.906628			0.453314	+	0.891351i	$0.350242\pi$
$68$	3.98113	+	6.89551i	0.482782	+	0.836204i
$69$		0			0
$70$	4.48345	−	4.57489i	0.535875	−	0.546804i
$71$	−7.26320			−0.861983			−0.430992	−	0.902356i	$-0.641836\pi$
$71$	−7.26320			−0.861983			−0.430992	+	0.902356i	$0.641836\pi$
$72$		0			0
$73$	−3.77975	−	6.54672i	−0.442386	−	0.766236i	0.555480	−	0.831530i	$-0.312535\pi$
$73$	−3.77975	−	6.54672i	−0.442386	−	0.766236i	−0.997866	+	0.0652944i	$0.979201\pi$
$74$	1.18878	−	2.05903i	0.138193	−	0.239357i
$75$		0			0
$76$	3.14132	−	5.44092i	0.360334	−	0.624116i
$77$	5.73749	+	1.47544i	0.653847	+	0.168143i
$78$		0			0
$79$	−6.82846			−0.768262			−0.384131	−	0.923279i	$-0.625499\pi$
$79$	−6.82846			−0.768262			−0.384131	+	0.923279i	$0.625499\pi$
$80$	1.37072	+	2.37416i	0.153252	+	0.265439i
$81$		0			0
$82$	−1.51655	+	2.62674i	−0.167475	+	0.290075i
$83$	−4.05555	−	7.02441i	−0.445154	−	0.771029i	0.552909	−	0.833242i	$-0.313518\pi$
$83$	−4.05555	−	7.02441i	−0.445154	−	0.771029i	−0.998063	+	0.0622124i	$0.980184\pi$
$84$		0			0
$85$	8.91423	−	15.4399i	0.966884	−	1.67469i
$86$	−1.24884	−	2.16305i	−0.134666	−	0.233248i
$87$		0			0
$88$	2.91423	−	5.04759i	0.310658	−	0.538075i
$89$	4.86389	−	8.42450i	0.515571	−	0.892995i	−0.484266	−	0.874921i	$-0.660913\pi$
$89$	4.86389	−	8.42450i	0.515571	−	0.892995i	0.999837	−	0.0180741i	$-0.00575348\pi$
$90$		0			0
$91$	−9.49028	−	2.44051i	−0.994852	−	0.255835i
$92$	0.669905	+	1.16031i	0.0698424	+	0.120971i
$93$		0			0
$94$	−0.171540			−0.0176930
$95$	−14.0676			−1.44330
$96$		0			0
$97$	−0.421067	−	0.729309i	−0.0427528	−	0.0740501i	0.843857	−	0.536568i	$-0.180279\pi$
$97$	−0.421067	−	0.729309i	−0.0427528	−	0.0740501i	−0.886610	+	0.462518i	$0.846946\pi$
$98$	4.55787	−	2.75564i	0.460414	−	0.278362i
$99$		0			0
$100$	3.64132	−	6.30694i	0.364132	−	0.630694i
$101$	−3.87360	+	6.70928i	−0.385438	+	0.667598i	−0.991830	−	0.127568i	$-0.959283\pi$
$101$	−3.87360	+	6.70928i	−0.385438	+	0.667598i	0.606392	+	0.795166i	$0.292616\pi$
$102$		0			0
$103$	1.21737	+	2.10855i	0.119951	+	0.207761i	0.919748	−	0.392509i	$-0.128393\pi$
$103$	1.21737	+	2.10855i	0.119951	+	0.207761i	−0.799797	+	0.600271i	$0.795060\pi$
$104$	−4.82038	+	8.34914i	−0.472677	+	0.818701i
$105$		0			0
$106$	−4.05555	−	7.02441i	−0.393909	−	0.682271i
$107$	5.73229	−	9.92861i	0.554161	−	0.959835i	−0.443807	−	0.896122i	$-0.646372\pi$
$107$	5.73229	−	9.92861i	0.554161	−	0.959835i	0.997968	−	0.0637128i	$-0.0202942\pi$
$108$		0			0
$109$	9.12476	+	15.8046i	0.873994	+	1.51380i	0.857831	+	0.513932i	$0.171812\pi$
$109$	9.12476	+	15.8046i	0.873994	+	1.51380i	0.0161631	+	0.999869i	$0.494855\pi$
$110$	−5.42107			−0.516878
$111$		0			0
$112$	0.612170	+	2.19574i	0.0578446	+	0.207478i
$113$	−2.62476	+	4.54622i	−0.246917	+	0.427673i	−0.962669	−	0.270682i	$-0.912751\pi$
$113$	−2.62476	+	4.54622i	−0.246917	+	0.427673i	0.715752	+	0.698355i	$0.246084\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−7.19398	−	12.4603i	−0.667944	−	1.15691i
$117$		0			0
$118$	−1.56526			−0.144094
$119$	10.3759	−	10.5876i	0.951159	−	0.970559i
$120$		0			0
$121$	2.99316	+	5.18431i	0.272106	+	0.471301i
$122$	4.44514			0.402444
$123$		0			0
$124$	8.10533			0.727880
$125$	−0.396990			−0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	9.64076			0.852131
$129$		0			0
$130$	8.96690			0.786449
$131$	−2.04063	−	3.53447i	−0.178291	−	0.308808i	0.763005	−	0.646393i	$-0.223723\pi$
$131$	−2.04063	−	3.53447i	−0.178291	−	0.308808i	−0.941295	+	0.337585i	$0.890390\pi$
$132$		0			0
$133$	−11.3285	−	2.91321i	−0.982302	−	0.252607i
$134$	−5.64652			−0.487785
$135$		0			0
$136$	−7.29235	−	12.6307i	−0.625313	−	1.08307i
$137$	−0.942820	+	1.63301i	−0.0805506	+	0.139518i	−0.903487	−	0.428616i	$-0.859001\pi$
$137$	−0.942820	+	1.63301i	−0.0805506	+	0.139518i	0.822936	+	0.568134i	$0.192335\pi$
$138$		0			0
$139$	6.39768	−	11.0811i	0.542644	−	0.939887i	−0.456107	−	0.889925i	$-0.650757\pi$
$139$	6.39768	−	11.0811i	0.542644	−	0.939887i	0.998751	−	0.0499621i	$-0.0159101\pi$
$140$	8.37360	−	8.54439i	0.707699	−	0.722133i
$141$		0			0
$142$	5.52640			0.463765
$143$	4.14652	+	7.18198i	0.346749	+	0.600587i
$144$		0			0
$145$	−16.1082	+	27.9002i	−1.33771	+	2.31699i
$146$	2.87592	+	4.98125i	0.238013	+	0.412251i
$147$		0			0
$148$	2.22025	−	3.84558i	0.182503	−	0.316105i
$149$	4.02859	+	6.97772i	0.330035	+	0.571637i	0.982518	−	0.186166i	$-0.0596061\pi$
$149$	4.02859	+	6.97772i	0.330035	+	0.571637i	−0.652483	+	0.757803i	$0.726273\pi$
$150$		0			0
$151$	3.14132	−	5.44092i	0.255637	−	0.442776i	−0.709432	−	0.704774i	$-0.751048\pi$
$151$	3.14132	−	5.44092i	0.255637	−	0.442776i	0.965068	+	0.261999i	$0.0843816\pi$
$152$	−5.75404	+	9.96629i	−0.466714	+	0.808373i
$153$		0			0
$154$	−4.36552	−	1.12263i	−0.351784	−	0.0904642i
$155$	−9.07442	−	15.7174i	−0.728875	−	1.26245i
$156$		0			0
$157$	0.703697			0.0561611			0.0280806	−	0.999606i	$-0.491061\pi$
$157$	0.703697			0.0561611			0.0280806	+	0.999606i	$0.491061\pi$
$158$	5.19562			0.413341
$159$		0			0
$160$	−9.32558	−	16.1524i	−0.737252	−	1.27696i
$161$	1.74596	−	1.78157i	0.137601	−	0.140407i
$162$		0			0
$163$	9.61793	−	16.6587i	0.753334	−	1.30481i	−0.192864	−	0.981225i	$-0.561778\pi$
$163$	9.61793	−	16.6587i	0.753334	−	1.30481i	0.946198	−	0.323588i	$-0.104889\pi$
$164$	−2.83242	+	4.90589i	−0.221175	+	0.383086i
$165$		0			0
$166$	3.08577	+	5.34471i	0.239502	+	0.414830i
$167$	11.6940	−	20.2546i	0.904907	−	1.56735i	0.0838661	−	0.996477i	$-0.473273\pi$
$167$	11.6940	−	20.2546i	0.904907	−	1.56735i	0.821041	−	0.570869i	$-0.193393\pi$
$168$		0			0
$169$	−0.358685	−	0.621261i	−0.0275911	−	0.0477893i
$170$	−6.78263	+	11.7479i	−0.520204	+	0.901020i
$171$		0			0
$172$	−2.33242	−	4.03987i	−0.177845	−	0.308037i
$173$	8.23912			0.626409			0.313204	−	0.949686i	$-0.398597\pi$
$173$	8.23912			0.626409			0.313204	+	0.949686i	$0.398597\pi$
$174$		0			0
$175$	−13.1316	−	3.37690i	−0.992656	−	0.255270i
$176$	0.964574	−	1.67069i	0.0727075	−	0.125933i
$177$		0			0
$178$	−3.70082	+	6.41001i	−0.277388	+	0.480450i
$179$	4.95486	+	8.58207i	0.370344	+	0.641454i	0.989618	−	0.143721i	$-0.0459066\pi$
$179$	4.95486	+	8.58207i	0.370344	+	0.641454i	−0.619275	+	0.785174i	$0.712573\pi$
$180$		0			0
$181$	−9.38796			−0.697802			−0.348901	−	0.937160i	$-0.613445\pi$
$181$	−9.38796			−0.697802			−0.348901	+	0.937160i	$0.613445\pi$
$182$	7.22094	+	1.85693i	0.535251	+	0.137645i
$183$		0			0
$184$	−1.22708	−	2.12537i	−0.0904619	−	0.156685i
$185$	−9.94282			−0.731011
$186$		0			0
$187$	−12.5458			−0.917442
$188$	−0.320380			−0.0233661
$189$		0			0
$190$	10.7037			0.776528
$191$	24.7382			1.78999			0.894996	−	0.446075i	$-0.147178\pi$
$191$	24.7382			1.78999			0.894996	+	0.446075i	$0.147178\pi$
$192$		0			0
$193$	−0.828460			−0.0596339			−0.0298169	−	0.999555i	$-0.509492\pi$
$193$	−0.828460			−0.0596339			−0.0298169	+	0.999555i	$0.509492\pi$
$194$	0.320380	+	0.554914i	0.0230019	+	0.0398405i
$195$		0			0
$196$	8.51259	−	5.14663i	0.608042	−	0.367617i
$197$	−5.86156			−0.417619			−0.208810	−	0.977956i	$-0.566959\pi$
$197$	−5.86156			−0.417619			−0.208810	+	0.977956i	$0.566959\pi$
$198$		0			0
$199$	4.62476	+	8.01033i	0.327841	+	0.567837i	0.982083	−	0.188448i	$-0.0603457\pi$
$199$	4.62476	+	8.01033i	0.327841	+	0.567837i	−0.654242	+	0.756285i	$0.727012\pi$
$200$	−6.66991	+	11.5526i	−0.471634	+	0.816893i
$201$		0			0
$202$	2.94733	−	5.10493i	0.207374	−	0.359182i
$203$	−18.7495	+	19.1319i	−1.31596	+	1.34280i
$204$		0			0
$205$	12.6843			0.885908
$206$	−0.926268	−	1.60434i	−0.0645362	−	0.111780i
$207$		0			0
$208$	−1.59549	+	2.76346i	−0.110627	+	0.191612i
$209$	4.94966	+	8.57306i	0.342375	+	0.593011i
$210$		0			0
$211$	6.27975	−	10.8768i	0.432316	−	0.748793i	−0.564756	−	0.825258i	$-0.691030\pi$
$211$	6.27975	−	10.8768i	0.432316	−	0.748793i	0.997072	+	0.0764645i	$0.0243632\pi$
$212$	−7.57442	−	13.1193i	−0.520213	−	0.901036i
$213$		0			0
$214$	−4.36156	+	7.55445i	−0.298150	+	0.516412i
$215$	−5.22257	+	9.04576i	−0.356176	+	0.616916i
$216$		0			0
$217$	−4.05267	−	14.5362i	−0.275113	−	0.986781i
$218$	−6.94282	−	12.0253i	−0.470227	−	0.814457i
$219$		0			0
$220$	−10.1248			−0.682611
$221$	20.7518			1.39592
$222$		0			0
$223$	10.6940	+	18.5225i	0.716122	+	1.24036i	0.962525	+	0.271192i	$0.0874179\pi$
$223$	10.6940	+	18.5225i	0.716122	+	1.24036i	−0.246403	+	0.969167i	$0.579249\pi$
$224$	−4.16484	−	14.9385i	−0.278275	−	0.998122i
$225$		0			0
$226$	1.99712	−	3.45912i	0.132847	−	0.230097i
$227$	−6.31122	+	10.9314i	−0.418890	+	0.725539i	−0.995828	−	0.0912487i	$-0.970914\pi$
$227$	−6.31122	+	10.9314i	−0.418890	+	0.725539i	0.576938	+	0.816788i	$0.304248\pi$
$228$		0			0
$229$	14.4601	+	25.0456i	0.955548	+	1.65506i	0.733110	+	0.680110i	$0.238068\pi$
$229$	14.4601	+	25.0456i	0.955548	+	1.65506i	0.222438	+	0.974947i	$0.428599\pi$
$230$	−1.14132	+	1.97682i	−0.0752561	+	0.130347i
$231$		0			0
$232$	13.1774	+	22.8240i	0.865141	+	1.49847i
$233$	10.7255	−	18.5770i	0.702648	−	1.21702i	−0.264886	−	0.964280i	$-0.585334\pi$
$233$	10.7255	−	18.5770i	0.702648	−	1.21702i	0.967534	−	0.252742i	$-0.0813323\pi$
$234$		0			0
$235$	0.358685	+	0.621261i	0.0233980	+	0.0405266i
$236$	−2.92339			−0.190296
$237$		0			0
$238$	−7.89480	+	8.05582i	−0.511744	+	0.522181i
$239$	−3.86840	+	6.70027i	−0.250226	+	0.433404i	−0.963588	−	0.267392i	$-0.913838\pi$
$239$	−3.86840	+	6.70027i	−0.250226	+	0.433404i	0.713362	+	0.700796i	$0.247172\pi$
$240$		0			0
$241$	−3.04583	+	5.27553i	−0.196199	+	0.339827i	−0.947293	−	0.320369i	$-0.896193\pi$
$241$	−3.04583	+	5.27553i	−0.196199	+	0.339827i	0.751094	+	0.660195i	$0.229527\pi$
$242$	−2.27743	−	3.94462i	−0.146399	−	0.253570i
$243$		0			0
$244$	8.30206			0.531485
$245$	−19.5104	−	10.7451i	−1.24647	−	0.686480i
$246$		0			0
$247$	−8.18715	−	14.1806i	−0.520936	−	0.902287i
$248$	−14.8468			−0.942771
$249$		0			0
$250$	0.302060			0.0191040
$251$	1.40164			0.0884705			0.0442352	−	0.999021i	$-0.485915\pi$
$251$	1.40164			0.0884705			0.0442352	+	0.999021i	$0.485915\pi$
$252$		0			0
$253$	−2.11109			−0.132723
$254$	−15.2977			−0.959862
$255$		0			0
$256$	−12.8090			−0.800564
$257$	−8.97825	−	15.5508i	−0.560048	−	0.970031i	−0.997492	−	0.0707853i	$-0.977449\pi$
$257$	−8.97825	−	15.5508i	−0.560048	−	0.970031i	0.437444	−	0.899246i	$-0.355884\pi$
$258$		0			0
$259$	−8.00684	−	2.05903i	−0.497521	−	0.127942i
$260$	16.7472			1.03862
$261$		0			0
$262$	1.55267	+	2.68930i	0.0959241	+	0.166145i
$263$	−3.58809	+	6.21476i	−0.221251	+	0.383218i	−0.955188	−	0.295999i	$-0.904347\pi$
$263$	−3.58809	+	6.21476i	−0.221251	+	0.383218i	0.733937	+	0.679218i	$0.237681\pi$
$264$		0			0
$265$	−16.9601	+	29.3757i	−1.04185	+	1.80453i
$266$	8.61956	+	2.21659i	0.528499	+	0.135908i
$267$		0			0
$268$	−10.5458			−0.644189
$269$	1.69850	+	2.94188i	0.103559	+	0.179370i	0.913149	−	0.407627i	$-0.133644\pi$
$269$	1.69850	+	2.94188i	0.103559	+	0.179370i	−0.809590	+	0.586996i	$0.800310\pi$
$270$		0			0
$271$	5.11793	−	8.86451i	0.310892	−	0.538481i	−0.667664	−	0.744463i	$-0.732706\pi$
$271$	5.11793	−	8.86451i	0.310892	−	0.538481i	0.978556	+	0.205982i	$0.0660389\pi$
$272$	−2.41367	−	4.18061i	−0.146351	−	0.253487i
$273$		0			0
$274$	0.717370	−	1.24252i	0.0433379	−	0.0750634i
$275$	5.73749	+	9.93762i	0.345984	+	0.599261i
$276$		0			0
$277$	1.77975	−	3.08262i	0.106935	−	0.185217i	−0.807592	−	0.589741i	$-0.799230\pi$
$277$	1.77975	−	3.08262i	0.106935	−	0.185217i	0.914527	+	0.404525i	$0.132563\pi$
$278$	−4.86784	+	8.43135i	−0.291954	+	0.505679i
$279$		0			0
$280$	−15.3382	+	15.6510i	−0.916631	+	0.935327i
$281$	3.49316	+	6.05034i	0.208385	+	0.360933i	0.951206	−	0.308557i	$-0.0998461\pi$
$281$	3.49316	+	6.05034i	0.208385	+	0.360933i	−0.742821	+	0.669490i	$0.766513\pi$
$282$		0			0
$283$	−30.2164			−1.79618			−0.898090	−	0.439812i	$-0.855045\pi$
$283$	−30.2164			−1.79618			−0.898090	+	0.439812i	$0.855045\pi$
$284$	10.3215			0.612468
$285$		0			0
$286$	−3.15499	−	5.46460i	−0.186558	−	0.323129i
$287$	10.2145	+	2.62674i	0.602942	+	0.155052i
$288$		0			0
$289$	−7.19686	+	12.4653i	−0.423345	+	0.733255i
$290$	12.2564	−	21.2286i	0.719718	−	1.24659i
$291$		0			0
$292$	5.37128	+	9.30333i	0.314330	+	0.544436i
$293$	−7.61793	+	13.1946i	−0.445044	+	0.770839i	−0.998055	−	0.0623349i	$-0.980145\pi$
$293$	−7.61793	+	13.1946i	−0.445044	+	0.770839i	0.553011	+	0.833174i	$0.313479\pi$
$294$		0			0
$295$	3.27292	+	5.66886i	0.190556	+	0.330054i
$296$	−4.06690	+	7.04407i	−0.236383	+	0.409428i
$297$		0			0
$298$	−3.06526	−	5.30919i	−0.177566	−	0.307553i
$299$	3.49192			0.201943
$300$		0			0
$301$	−6.07893	+	6.20292i	−0.350384	+	0.357530i
$302$	−2.39015	+	4.13987i	−0.137538	+	0.238223i
$303$		0			0
$304$	−1.90451	+	3.29872i	−0.109231	+	0.189194i
$305$	−9.29467	−	16.0988i	−0.532211	−	0.921817i
$306$		0			0
$307$	−1.03310			−0.0589623			−0.0294812	−	0.999565i	$-0.509386\pi$
$307$	−1.03310			−0.0589623			−0.0294812	+	0.999565i	$0.509386\pi$
$308$	−8.15335	−	2.09671i	−0.464580	−	0.119471i
$309$		0			0
$310$	6.90451	+	11.9590i	0.392150	+	0.679224i
$311$	9.32038			0.528510			0.264255	−	0.964453i	$-0.414874\pi$
$311$	9.32038			0.528510			0.264255	+	0.964453i	$0.414874\pi$
$312$		0			0
$313$	6.09166			0.344321			0.172160	−	0.985069i	$-0.444925\pi$
$313$	6.09166			0.344321			0.172160	+	0.985069i	$0.444925\pi$
$314$	−0.535426			−0.0302159
$315$		0			0
$316$	9.70370			0.545876
$317$	−23.3009			−1.30871			−0.654356	−	0.756187i	$-0.727060\pi$
$317$	−23.3009			−1.30871			−0.654356	+	0.756187i	$0.727060\pi$
$318$		0			0
$319$	22.6706			1.26931
$320$	4.35417	+	7.54165i	0.243406	+	0.421591i
$321$		0			0
$322$	−1.32846	+	1.35556i	−0.0740322	+	0.0755421i
$323$	24.7713			1.37831
$324$		0			0
$325$	−9.49028	−	16.4377i	−0.526426	−	0.911797i
$326$	−7.31806	+	12.6752i	−0.405310	+	0.702017i
$327$		0			0
$328$	5.18822	−	8.98627i	0.286472	−	0.496184i
$329$	0.160190	+	0.574573i	0.00883155	+	0.0316772i
$330$		0			0
$331$	14.6764			0.806685			0.403343	−	0.915049i	$-0.367848\pi$
$331$	14.6764			0.806685			0.403343	+	0.915049i	$0.367848\pi$
$332$	5.76320	+	9.98215i	0.316297	+	0.547842i
$333$		0			0
$334$	−8.89768	+	15.4112i	−0.486859	+	0.843265i
$335$	11.8067	+	20.4498i	0.645069	+	1.11729i
$336$		0			0
$337$	−12.8119	+	22.1909i	−0.697909	+	1.20881i	0.271281	+	0.962500i	$0.412553\pi$
$337$	−12.8119	+	22.1909i	−0.697909	+	1.20881i	−0.969190	+	0.246314i	$0.920781\pi$
$338$	0.272915	+	0.472703i	0.0148446	+	0.0257116i
$339$		0			0
$340$	−12.6677	+	21.9411i	−0.687003	+	1.18992i
$341$	−6.38564	+	11.0603i	−0.345802	+	0.598946i
$342$		0			0
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$	4.27236	+	7.39994i	0.230350	+	0.398978i
$345$		0			0
$346$	−6.26896			−0.337021
$347$	11.2930			0.606242			0.303121	−	0.952952i	$-0.401971\pi$
$347$	11.2930			0.606242			0.303121	+	0.952952i	$0.401971\pi$
$348$		0			0
$349$	5.64815	+	9.78289i	0.302339	+	0.523666i	0.976665	−	0.214767i	$-0.0688993\pi$
$349$	5.64815	+	9.78289i	0.302339	+	0.523666i	−0.674327	+	0.738433i	$0.735566\pi$
$350$	9.99153	+	2.56941i	0.534070	+	0.137341i
$351$		0			0
$352$	−6.56238	+	11.3664i	−0.349776	+	0.605830i
$353$	9.25116	−	16.0235i	0.492390	−	0.852844i	−0.507572	−	0.861609i	$-0.669457\pi$
$353$	9.25116	−	16.0235i	0.492390	−	0.852844i	0.999962	+	0.00876550i	$0.00279018\pi$
$354$		0			0
$355$	−11.5555	−	20.0148i	−0.613305	−	1.06227i
$356$	−6.91191	+	11.9718i	−0.366330	+	0.634503i
$357$		0			0
$358$	−3.77004	−	6.52989i	−0.199253	−	0.345116i
$359$	−9.94802	+	17.2305i	−0.525037	+	0.909390i	0.474538	+	0.880235i	$0.342615\pi$
$359$	−9.94802	+	17.2305i	−0.525037	+	0.909390i	−0.999575	+	0.0291551i	$0.990718\pi$
$360$		0			0
$361$	−0.272915	−	0.472703i	−0.0143639	−	0.0248791i
$362$	7.14308			0.375432
$363$		0			0
$364$	13.4863	+	3.46813i	0.706876	+	0.181779i
$365$	12.0270	−	20.8313i	0.629520	−	1.09036i
$366$		0			0
$367$	−2.87524	+	4.98006i	−0.150086	+	0.259957i	−0.931259	−	0.364358i	$-0.881288\pi$
$367$	−2.87524	+	4.98006i	−0.150086	+	0.259957i	0.781173	+	0.624315i	$0.214622\pi$
$368$	−0.406150	−	0.703472i	−0.0211720	−	0.0366710i
$369$		0			0
$370$	7.56526			0.393299
$371$	−19.7411	+	20.1437i	−1.02490	+	1.04581i
$372$		0			0
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	0.838975	−	0.544170i	$-0.183156\pi$
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	−0.890753	+	0.454488i	$0.849822\pi$
$374$	9.54583			0.493603
$375$		0			0
$376$	0.586849			0.0302644
$377$	−37.4991			−1.93130
$378$		0			0
$379$	8.95322			0.459896			0.229948	−	0.973203i	$-0.426144\pi$
$379$	8.95322			0.459896			0.229948	+	0.973203i	$0.426144\pi$
$380$	19.9910			1.02552
$381$		0			0
$382$	−18.8227			−0.963053
$383$	−10.0825	−	17.4634i	−0.515192	−	0.892338i	−0.999845	−	0.0176316i	$-0.994387\pi$
$383$	−10.0825	−	17.4634i	−0.515192	−	0.892338i	0.484653	−	0.874707i	$-0.338946\pi$
$384$		0			0
$385$	5.06238	+	18.1579i	0.258003	+	0.925410i
$386$	0.630356			0.0320843
$387$		0			0
$388$	0.598364	+	1.03640i	0.0303773	+	0.0526151i
$389$	16.7999	−	29.0982i	0.851787	−	1.47534i	−0.0278066	−	0.999613i	$-0.508852\pi$
$389$	16.7999	−	29.0982i	0.851787	−	1.47534i	0.879594	−	0.475725i	$-0.157814\pi$
$390$		0			0
$391$	−2.64132	+	4.57489i	−0.133577	+	0.231362i
$392$	−15.5928	+	9.42724i	−0.787554	+	0.476148i
$393$		0			0
$394$	4.45993			0.224688
$395$	−10.8639	−	18.8168i	−0.546621	−	0.946776i
$396$		0			0
$397$	2.06922	−	3.58399i	0.103851	−	0.179875i	−0.809417	−	0.587234i	$-0.800217\pi$
$397$	2.06922	−	3.58399i	0.103851	−	0.179875i	0.913268	+	0.407359i	$0.133550\pi$
$398$	−3.51887	−	6.09487i	−0.176385	−	0.305508i
$399$		0			0
$400$	−2.20765	+	3.82377i	−0.110383	+	0.191189i
$401$	−7.73461	−	13.3967i	−0.386248	−	0.669001i	0.605693	−	0.795698i	$-0.292896\pi$
$401$	−7.73461	−	13.3967i	−0.386248	−	0.669001i	−0.991941	+	0.126697i	$0.959562\pi$
$402$		0			0
$403$	10.5624	−	18.2946i	0.526150	−	0.911318i
$404$	5.50465	−	9.53433i	0.273866	−	0.474350i
$405$		0			0
$406$	14.2661	−	14.5570i	0.708014	−	0.722454i
$407$	3.49837	+	6.05935i	0.173408	+	0.300351i
$408$		0			0
$409$	27.3937			1.35453			0.677266	−	0.735738i	$-0.263165\pi$
$409$	27.3937			1.35453			0.677266	+	0.735738i	$0.263165\pi$
$410$	−9.65116			−0.476637
$411$		0			0
$412$	−1.72996	−	2.99638i	−0.0852292	−	0.147621i
$413$	1.46169	+	5.24284i	0.0719253	+	0.257983i
$414$		0			0
$415$	12.9045	−	22.3513i	0.633458	−	1.09718i
$416$	10.8547	−	18.8009i	0.532197	−	0.921792i
$417$		0			0
$418$	−3.76608	−	6.52304i	−0.184205	−	0.319052i
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	−0.486928	−	0.873442i	$-0.661883\pi$
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	0.999887	−	0.0150285i	$-0.00478389\pi$
$420$		0			0
$421$	−9.97949	−	17.2850i	−0.486371	−	0.842419i	0.513507	−	0.858086i	$-0.328346\pi$
$421$	−9.97949	−	17.2850i	−0.486371	−	0.842419i	−0.999877	+	0.0156670i	$0.995013\pi$
$422$	−4.77812	+	8.27594i	−0.232595	+	0.402867i
$423$		0			0
$424$	13.8743	+	24.0310i	0.673795	+	1.16705i
$425$	28.7141			1.39284
$426$		0			0
$427$	−4.15103	−	14.8890i	−0.200882	−	0.720530i
$428$	−8.14596	+	14.1092i	−0.393750	+	0.681995i
$429$		0			0
$430$	3.97373	−	6.88271i	0.191630	−	0.331914i
$431$	−10.0647	−	17.4326i	−0.484800	−	0.839698i	0.515048	−	0.857162i	$-0.327774\pi$
$431$	−10.0647	−	17.4326i	−0.484800	−	0.839698i	−0.999847	+	0.0174637i	$0.994441\pi$
$432$		0			0
$433$	11.8558			0.569754			0.284877	−	0.958564i	$-0.408047\pi$
$433$	11.8558			0.569754			0.284877	+	0.958564i	$0.408047\pi$
$434$	3.08358	+	11.0603i	0.148017	+	0.530909i
$435$		0			0
$436$	−12.9669	−	22.4593i	−0.621002	−	1.07561i
$437$	4.16827			0.199395
$438$		0			0
$439$	−2.15787			−0.102989			−0.0514947	−	0.998673i	$-0.516399\pi$
$439$	−2.15787			−0.102989			−0.0514947	+	0.998673i	$0.516399\pi$
$440$	18.5458			0.884138
$441$		0			0
$442$	−15.7896			−0.751035
$443$	1.96225			0.0932293			0.0466147	−	0.998913i	$-0.485157\pi$
$443$	1.96225			0.0932293			0.0466147	+	0.998913i	$0.485157\pi$
$444$		0			0
$445$	30.9532			1.46732
$446$	−8.13680	−	14.0934i	−0.385289	−	0.667340i
$447$		0			0
$448$	1.94459	+	6.97489i	0.0918731	+	0.329533i
$449$	−2.15211			−0.101564			−0.0507822	−	0.998710i	$-0.516171\pi$
$449$	−2.15211			−0.101564			−0.0507822	+	0.998710i	$0.516171\pi$
$450$		0			0
$451$	−4.46294	−	7.73004i	−0.210152	−	0.363993i
$452$	3.72996	−	6.46049i	0.175443	−	0.303876i
$453$		0			0
$454$	4.80206	−	8.31741i	0.225372	−	0.390356i
$455$	−8.37360	−	30.0346i	−0.392561	−	1.40804i
$456$		0			0
$457$	−13.1053			−0.613042			−0.306521	−	0.951864i	$-0.599165\pi$
$457$	−13.1053			−0.613042			−0.306521	+	0.951864i	$0.599165\pi$
$458$	−11.0023	−	19.0566i	−0.514105	−	0.890456i
$459$		0			0
$460$	−2.13160	+	3.69204i	−0.0993864	+	0.172142i
$461$	−2.74364	−	4.75212i	−0.127784	−	0.221328i	0.795034	−	0.606565i	$-0.207453\pi$
$461$	−2.74364	−	4.75212i	−0.127784	−	0.221328i	−0.922818	+	0.385237i	$0.874120\pi$
$462$		0			0
$463$	10.2495	−	17.7527i	0.476336	−	0.825038i	−0.523296	−	0.852151i	$-0.675298\pi$
$463$	10.2495	−	17.7527i	0.476336	−	0.825038i	0.999632	+	0.0271127i	$0.00863130\pi$
$464$	4.36156	+	7.55445i	0.202481	+	0.350707i
$465$		0			0
$466$	−8.16075	+	14.1348i	−0.378039	+	0.654783i
$467$	19.6758	−	34.0795i	0.910487	−	1.57701i	0.0971099	−	0.995274i	$-0.469040\pi$
$467$	19.6758	−	34.0795i	0.910487	−	1.57701i	0.813377	−	0.581736i	$-0.197626\pi$
$468$		0			0
$469$	5.27292	+	18.9130i	0.243481	+	0.873322i
$470$	−0.272915	−	0.472703i	−0.0125886	−	0.0218041i
$471$		0			0
$472$	5.35486			0.246477
$473$	7.35021			0.337963
$474$		0			0
$475$	−11.3285	−	19.6215i	−0.519785	−	0.900295i
$476$	−14.7449	+	15.0456i	−0.675830	+	0.689615i
$477$		0			0
$478$	2.94338	−	5.09808i	0.134627	−	0.233181i
$479$	−8.37360	+	14.5035i	−0.382600	+	0.662682i	−0.991433	−	0.130616i	$-0.958304\pi$
$479$	−8.37360	+	14.5035i	−0.382600	+	0.662682i	0.608833	+	0.793298i	$0.291638\pi$
$480$		0			0
$481$	−5.78659	−	10.0227i	−0.263846	−	0.456994i
$482$	2.31750	−	4.01403i	0.105559	−	0.182834i
$483$		0			0
$484$	−4.25348	−	7.36725i	−0.193340	−	0.334875i
$485$	1.33981	−	2.32062i	0.0608376	−	0.105374i
$486$		0			0
$487$	−2.00288	−	3.46909i	−0.0907591	−	0.157199i	0.817072	−	0.576536i	$-0.195596\pi$
$487$	−2.00288	−	3.46909i	−0.0907591	−	0.157199i	−0.907831	+	0.419337i	$0.862263\pi$
$488$	−15.2071			−0.688394
$489$		0			0
$490$	14.8450	+	8.17571i	0.670629	+	0.369341i
$491$	−12.3256	+	21.3485i	−0.556246	+	0.963446i	0.441560	+	0.897232i	$0.354425\pi$
$491$	−12.3256	+	21.3485i	−0.556246	+	0.963446i	−0.997805	+	0.0662140i	$0.978908\pi$
$492$		0			0
$493$	28.3646	−	49.1289i	1.27748	−	2.21265i
$494$	6.22941	+	10.7897i	0.280274	+	0.485449i
$495$		0			0
$496$	−4.91410			−0.220649
$497$	−5.16075	−	18.5107i	−0.231491	−	0.830317i
$498$		0			0
$499$	12.2798	+	21.2692i	0.549717	+	0.952138i	0.998294	+	0.0583936i	$0.0185978\pi$
$499$	12.2798	+	21.2692i	0.549717	+	0.952138i	−0.448576	+	0.893744i	$0.648069\pi$
$500$	0.564149			0.0252295
$501$		0			0
$502$	−1.06647			−0.0475990
$503$	−12.3743			−0.551742			−0.275871	−	0.961195i	$-0.588966\pi$
$503$	−12.3743			−0.551742			−0.275871	+	0.961195i	$0.588966\pi$
$504$		0			0
$505$	−24.6512			−1.09696
$506$	1.60628			0.0714078
$507$		0			0
$508$	−28.5710			−1.26763
$509$	5.59781	+	9.69569i	0.248118	+	0.429754i	0.963004	−	0.269488i	$-0.0868544\pi$
$509$	5.59781	+	9.69569i	0.248118	+	0.429754i	−0.714885	+	0.699242i	$0.753521\pi$
$510$		0			0
$511$	13.9991	−	14.2846i	0.619282	−	0.631912i
$512$	−9.53543			−0.421410
$513$		0			0
$514$	6.83134	+	11.8322i	0.301317	+	0.521897i
$515$	−3.87360	+	6.70928i	−0.170691	+	0.295646i
$516$		0			0
$517$	0.252405	−	0.437179i	0.0111008	−	0.0192271i
$518$	6.09222	+	1.56667i	0.267677	+	0.0688353i
$519$		0			0
$520$	−30.6764			−1.34525
$521$	15.8096	+	27.3830i	0.692631	+	1.19967i	0.970973	+	0.239189i	$0.0768817\pi$
$521$	15.8096	+	27.3830i	0.692631	+	1.19967i	−0.278342	+	0.960482i	$0.589785\pi$
$522$		0			0
$523$	14.1179	−	24.4530i	0.617334	−	1.06925i	−0.372636	−	0.927977i	$-0.621546\pi$
$523$	14.1179	−	24.4530i	0.617334	−	1.06925i	0.989970	−	0.141276i	$-0.0451205\pi$
$524$	2.89987	+	5.02272i	0.126681	+	0.219419i
$525$		0			0
$526$	2.73010	−	4.72867i	0.119038	−	0.206180i
$527$	15.9789	+	27.6763i	0.696053	+	1.20560i
$528$		0			0
$529$	11.0555	−	19.1488i	0.480676	−	0.832555i
$530$	12.9045	−	22.3513i	0.560536	−	0.970877i
$531$		0			0
$532$	16.0985	+	4.13987i	0.697958	+	0.179486i
$533$	7.38207	+	12.7861i	0.319753	+	0.553829i
$534$		0			0
$535$	36.4796			1.57715
$536$	19.3171			0.834372
$537$		0			0
$538$	−1.29235	−	2.23841i	−0.0557170	−	0.0965046i
$539$	0.316422	+	15.6707i	0.0136293	+	0.674983i
$540$		0			0
$541$	−21.4045	+	37.0737i	−0.920252	+	1.59392i	−0.121227	+	0.992625i	$0.538683\pi$
$541$	−21.4045	+	37.0737i	−0.920252	+	1.59392i	−0.799025	+	0.601298i	$0.794650\pi$
$542$	−3.89411	+	6.74480i	−0.167266	+	0.289714i
$543$		0			0
$544$	16.4212	+	28.4424i	0.704053	+	1.21946i
$545$	−29.0345	+	50.2892i	−1.24370	+	2.15415i
$546$		0			0
$547$	−6.77579	−	11.7360i	−0.289712	−	0.501796i	0.684029	−	0.729455i	$-0.260226\pi$
$547$	−6.77579	−	11.7360i	−0.289712	−	0.501796i	−0.973741	+	0.227659i	$0.926893\pi$
$548$	1.33981	−	2.32062i	0.0572339	−	0.0991319i
$549$		0			0
$550$	−4.36552	−	7.56130i	−0.186146	−	0.322415i
$551$	−44.7623			−1.90694
$552$		0			0
$553$	−4.85185	−	17.4027i	−0.206322	−	0.740039i
$554$	−1.35417	+	2.34549i	−0.0575332	+	0.0996505i
$555$		0			0
$556$	−9.09153	+	15.7470i	−0.385567	+	0.667821i
$557$	16.3925	+	28.3926i	0.694572	+	1.20303i	0.970325	+	0.241805i	$0.0777394\pi$
$557$	16.3925	+	28.3926i	0.694572	+	1.20303i	−0.275753	+	0.961228i	$0.588927\pi$
$558$		0			0
$559$	−12.1579			−0.514223
$560$	−5.07674	+	5.18029i	−0.214532	+	0.218907i
$561$		0			0
$562$	−2.65787	−	4.60356i	−0.112115	−	0.194189i
$563$	17.1546			0.722980			0.361490	−	0.932376i	$-0.382268\pi$
$563$	17.1546			0.722980			0.361490	+	0.932376i	$0.382268\pi$
$564$		0			0
$565$	−16.7037			−0.702730
$566$	22.9910			0.966383
$567$		0			0
$568$	−18.9062			−0.793286
$569$	−12.8993			−0.540767			−0.270384	−	0.962753i	$-0.587151\pi$
$569$	−12.8993			−0.540767			−0.270384	+	0.962753i	$0.587151\pi$
$570$		0			0
$571$	−0.282630			−0.0118277			−0.00591385	−	0.999983i	$-0.501882\pi$
$571$	−0.282630			−0.0118277			−0.00591385	+	0.999983i	$0.501882\pi$
$572$	−5.89248	−	10.2061i	−0.246377	−	0.426737i
$573$		0			0
$574$	−7.77197	−	1.99863i	−0.324396	−	0.0834212i
$575$	4.83173			0.201497
$576$		0			0
$577$	1.08289	+	1.87562i	0.0450814	+	0.0780832i	0.887686	−	0.460450i	$-0.152312\pi$
$577$	1.08289	+	1.87562i	0.0450814	+	0.0780832i	−0.842604	+	0.538533i	$0.818979\pi$
$578$	5.47592	−	9.48458i	0.227768	−	0.394506i
$579$		0			0
$580$	22.8908	−	39.6481i	0.950490	−	1.64630i
$581$	15.0205	−	15.3269i	0.623156	−	0.635866i
$582$		0			0
$583$	23.8695			0.988573
$584$	−9.83873	−	17.0412i	−0.407130	−	0.705169i
$585$		0			0
$586$	5.79630	−	10.0395i	0.239443	−	0.414728i
$587$	−8.38796	−	14.5284i	−0.346208	−	0.599650i	0.639364	−	0.768904i	$-0.279198\pi$
$587$	−8.38796	−	14.5284i	−0.346208	−	0.599650i	−0.985573	+	0.169254i	$0.945864\pi$
$588$		0			0
$589$	12.6082	−	21.8381i	0.519512	−	0.899822i
$590$	−2.49028	−	4.31330i	−0.102523	−	0.177576i
$591$		0			0
$592$	−1.34609	+	2.33150i	−0.0553240	+	0.0958240i
$593$	−12.5933	+	21.8122i	−0.517145	+	0.895721i	0.482657	+	0.875809i	$0.339672\pi$
$593$	−12.5933	+	21.8122i	−0.517145	+	0.895721i	−0.999802	+	0.0199114i	$0.993662\pi$
$594$		0			0
$595$	45.6833	+	11.7479i	1.87283	+	0.481615i
$596$	−5.72489	−	9.91581i	−0.234501	−	0.406167i
$597$		0			0
$598$	−2.65692			−0.108650
$599$	−28.7324			−1.17397			−0.586987	−	0.809596i	$-0.699686\pi$
$599$	−28.7324			−1.17397			−0.586987	+	0.809596i	$0.699686\pi$
$600$		0			0
$601$	18.3977	+	31.8657i	0.750457	+	1.29983i	0.947601	+	0.319455i	$0.103500\pi$
$601$	18.3977	+	31.8657i	0.750457	+	1.29983i	−0.197144	+	0.980374i	$0.563167\pi$
$602$	4.62532	−	4.71966i	0.188514	−	0.192359i
$603$		0			0
$604$	−4.46402	+	7.73191i	−0.181638	+	0.314607i
$605$	−9.52408	+	16.4962i	−0.387209	+	0.670665i
$606$		0			0
$607$	−18.9503	−	32.8230i	−0.769171	−	1.33224i	−0.938013	−	0.346600i	$-0.887336\pi$
$607$	−18.9503	−	32.8230i	−0.769171	−	1.33224i	0.168842	−	0.985643i	$-0.445997\pi$
$608$	12.9572	−	22.4425i	0.525483	−	0.910163i
$609$		0			0
$610$	7.07210	+	12.2492i	0.286341	+	0.495957i
$611$	−0.417500	+	0.723131i	−0.0168902	+	0.0292547i
$612$		0			0
$613$	−19.0196	−	32.9428i	−0.768193	−	1.33055i	−0.938542	−	0.345165i	$-0.887823\pi$
$613$	−19.0196	−	32.9428i	−0.768193	−	1.33055i	0.170349	−	0.985384i	$-0.445511\pi$
$614$	0.786064			0.0317230
$615$		0			0
$616$	14.9347	+	3.84060i	0.601738	+	0.154742i
$617$	13.2632	−	22.9725i	0.533956	−	0.924839i	−0.465257	−	0.885176i	$-0.654038\pi$
$617$	13.2632	−	22.9725i	0.533956	−	0.924839i	0.999213	−	0.0396637i	$-0.0126287\pi$
$618$		0			0
$619$	−6.35185	+	11.0017i	−0.255302	+	0.442197i	−0.964978	−	0.262332i	$-0.915508\pi$
$619$	−6.35185	+	11.0017i	−0.255302	+	0.442197i	0.709675	+	0.704529i	$0.248842\pi$
$620$	12.8954	+	22.3354i	0.517890	+	0.897012i
$621$		0			0
$622$	−7.09166			−0.284350
$623$	24.9263	+	6.41001i	0.998650	+	0.256811i
$624$		0			0
$625$	12.1803	+	21.0969i	0.487212	+	0.843877i
$626$	−4.63500			−0.185252
$627$		0			0
$628$	−1.00000			−0.0399043
$629$	17.5081			0.698093
$630$		0			0
$631$	20.6764			0.823113			0.411556	−	0.911384i	$-0.364985\pi$
$631$	20.6764			0.823113			0.411556	+	0.911384i	$0.364985\pi$
$632$	−17.7745			−0.707034
$633$		0			0
$634$	17.7292			0.704114
$635$	31.9870	+	55.4031i	1.26937	+	2.19861i
$636$		0			0
$637$	−0.523388	−	25.9206i	−0.0207374	−	1.02701i
$638$	−17.2495			−0.682915
$639$		0			0
$640$	15.3382	+	26.5665i	0.606295	+	1.05013i
$641$	13.9870	−	24.2262i	0.552454	−	0.956878i	−0.445643	−	0.895211i	$-0.647025\pi$
$641$	13.9870	−	24.2262i	0.552454	−	0.956878i	0.998097	−	0.0616674i	$-0.0196418\pi$
$642$		0			0
$643$	−13.9903	+	24.2319i	−0.551723	+	0.955612i	0.446427	+	0.894820i	$0.352696\pi$
$643$	−13.9903	+	24.2319i	−0.551723	+	0.955612i	−0.998150	+	0.0607924i	$0.980637\pi$
$644$	−2.48113	+	2.53173i	−0.0977700	+	0.0997641i
$645$		0			0
$646$	−18.8479			−0.741560
$647$	−2.30834	−	3.99816i	−0.0907503	−	0.157184i	0.817077	−	0.576529i	$-0.195593\pi$
$647$	−2.30834	−	3.99816i	−0.0907503	−	0.157184i	−0.907827	+	0.419345i	$0.862260\pi$
$648$		0			0
$649$	2.30314	−	3.98916i	0.0904061	−	0.156588i
$650$	7.22094	+	12.5070i	0.283228	+	0.490566i
$651$		0			0
$652$	−13.6677	+	23.6732i	−0.535269	+	0.927113i
$653$	−5.79016	−	10.0288i	−0.226586	−	0.392459i	0.730208	−	0.683225i	$-0.239423\pi$
$653$	−5.79016	−	10.0288i	−0.226586	−	0.392459i	−0.956794	+	0.290766i	$0.906090\pi$
$654$		0			0
$655$	6.49316	−	11.2465i	0.253709	−	0.439437i
$656$	1.71724	−	2.97434i	0.0670468	−	0.116129i
$657$		0			0
$658$	−0.121885	−	0.437179i	−0.00475156	−	0.0170430i
$659$	−2.36840	−	4.10219i	−0.0922598	−	0.159799i	0.816202	−	0.577767i	$-0.196076\pi$
$659$	−2.36840	−	4.10219i	−0.0922598	−	0.159799i	−0.908462	+	0.417968i	$0.862742\pi$
$660$		0			0
$661$	−13.8227			−0.537641			−0.268820	−	0.963190i	$-0.586634\pi$
$661$	−13.8227			−0.537641			−0.268820	+	0.963190i	$0.586634\pi$
$662$	−11.1669			−0.434014
$663$		0			0
$664$	−10.5566	−	18.2846i	−0.409676	−	0.709580i
$665$	−9.99549	−	35.8520i	−0.387608	−	1.39028i
$666$		0			0
$667$	4.77292	−	8.26693i	0.184808	−	0.320097i
$668$	−16.6179	+	28.7831i	−0.642967	+	1.11365i
$669$		0			0
$670$	−8.98345	−	15.5598i	−0.347061	−	0.601127i
$671$	−6.54063	+	11.3287i	−0.252498	+	0.437340i
$672$		0			0
$673$	−3.01367	−	5.21983i	−0.116169	−	0.201210i	0.802078	−	0.597220i	$-0.203728\pi$
$673$	−3.01367	−	5.21983i	−0.116169	−	0.201210i	−0.918246	+	0.396010i	$0.870395\pi$
$674$	9.74828	−	16.8845i	0.375490	−	0.650367i
$675$		0			0
$676$	0.509715	+	0.882853i	0.0196044	+	0.0339559i
$677$	−22.8856			−0.879567			−0.439783	−	0.898104i	$-0.644945\pi$
$677$	−22.8856			−0.879567			−0.439783	+	0.898104i	$0.644945\pi$
$678$		0			0
$679$	1.55950	−	1.59131i	0.0598482	−	0.0610689i
$680$	23.2038	−	40.1902i	0.889826	−	1.54122i
$681$		0			0
$682$	4.85868	−	8.41549i	0.186049	−	0.322246i
$683$	−5.14940	−	8.91901i	−0.197036	−	0.341277i	0.750530	−	0.660836i	$-0.229798\pi$
$683$	−5.14940	−	8.91901i	−0.197036	−	0.341277i	−0.947566	+	0.319560i	$0.896465\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	10.2614	+	9.65801i	0.391783	+	0.368745i
$687$		0			0
$688$	1.41410	+	2.44929i	0.0539120	+	0.0933782i
$689$	−39.4821			−1.50415
$690$		0			0
$691$	29.0722			1.10596			0.552980	−	0.833195i	$-0.313491\pi$
$691$	29.0722			1.10596			0.552980	+	0.833195i	$0.313491\pi$
$692$	−11.7083			−0.445084
$693$		0			0
$694$	−8.59261			−0.326171
$695$	40.7141			1.54437
$696$		0			0
$697$	−22.3354			−0.846015
$698$	−4.29755	−	7.44357i	−0.162665	−	0.281743i
$699$		0			0
$700$	18.6609	+	4.79881i	0.705315	+	0.181378i
$701$	−27.4153			−1.03546			−0.517731	−	0.855543i	$-0.673223\pi$
$701$	−27.4153			−1.03546			−0.517731	+	0.855543i	$0.673223\pi$
$702$		0			0
$703$	−6.90739	−	11.9640i	−0.260517	−	0.451229i
$704$	3.06402	−	5.30703i	0.115479	−	0.200016i
$705$		0			0
$706$	−7.03899	+	12.1919i	−0.264916	+	0.458848i
$707$	−19.8513	−	5.10493i	−0.746585	−	0.191991i
$708$		0			0
$709$	−36.9669			−1.38832			−0.694160	−	0.719820i	$-0.744224\pi$
$709$	−36.9669			−1.38832			−0.694160	+	0.719820i	$0.744224\pi$
$710$	8.79235	+	15.2288i	0.329971	+	0.571526i
$711$		0			0
$712$	12.6607	−	21.9291i	0.474481	−	0.821826i
$713$	2.68878	+	4.65710i	0.100696	+	0.174410i
$714$		0			0
$715$	−13.1940	+	22.8526i	−0.493427	+	0.854641i
$716$	−7.04118	−	12.1957i	−0.263141	−	0.455774i
$717$		0			0
$718$	7.56922	−	13.1103i	0.282481	−	0.489271i
$719$	−20.2599	+	35.0912i	−0.755568	+	1.30868i	0.189524	+	0.981876i	$0.439306\pi$
$719$	−20.2599	+	35.0912i	−0.755568	+	1.30868i	−0.945092	+	0.326806i	$0.894028\pi$
$720$		0			0
$721$	−4.50877	+	4.60073i	−0.167915	+	0.171340i
$722$	0.207655	+	0.359668i	0.00772811	+	0.0133855i
$723$		0			0
$724$	13.3409			0.495811
$725$	−51.8870			−1.92704
$726$		0			0
$727$	7.62081	+	13.1996i	0.282640	+	0.489547i	0.972034	−	0.234840i	$-0.0754565\pi$
$727$	7.62081	+	13.1996i	0.282640	+	0.489547i	−0.689394	+	0.724386i	$0.742123\pi$
$728$	−24.7033	−	6.35267i	−0.915565	−	0.235446i
$729$		0			0
$730$	−9.15103	+	15.8500i	−0.338695	+	0.586637i
$731$	9.19630	−	15.9285i	0.340138	−	0.589136i
$732$		0			0
$733$	−16.2895	−	28.2142i	−0.601665	−	1.04211i	−0.992569	−	0.121683i	$-0.961171\pi$
$733$	−16.2895	−	28.2142i	−0.601665	−	1.04211i	0.390904	−	0.920432i	$-0.372163\pi$
$734$	2.18770	−	3.78921i	0.0807495	−	0.139862i
$735$		0			0
$736$	2.76320	+	4.78600i	0.101853	+	0.176414i
$737$	8.30834	−	14.3905i	0.306042	−	0.530080i
$738$		0			0
$739$	−3.50684	−	6.07402i	−0.129001	−	0.223436i	0.794289	−	0.607540i	$-0.207844\pi$
$739$	−3.50684	−	6.07402i	−0.129001	−	0.223436i	−0.923290	+	0.384104i	$0.874510\pi$
$740$	14.1294			0.519407
$741$		0			0
$742$	15.0205	−	15.3269i	0.551420	−	0.562667i
$743$	17.5059	−	30.3211i	0.642229	−	1.11237i	−0.342705	−	0.939443i	$-0.611343\pi$
$743$	17.5059	−	30.3211i	0.642229	−	1.11237i	0.984934	−	0.172930i	$-0.0553234\pi$
$744$		0			0
$745$	−12.8187	+	22.2027i	−0.469642	+	0.813445i
$746$	0.760877	+	1.31788i	0.0278577	+	0.0482509i
$747$		0			0
$748$	17.8285			0.651873
$749$	29.3766	+	7.55445i	1.07340	+	0.276034i
$750$		0			0
$751$	2.13844	+	3.70388i	0.0780327	+	0.135157i	0.902401	−	0.430897i	$-0.141803\pi$
$751$	2.13844	+	3.70388i	0.0780327	+	0.135157i	−0.824368	+	0.566054i	$0.808469\pi$
$752$	0.194240			0.00708319
$753$		0			0
$754$	28.5322			1.03908
$755$	19.9910			0.727546
$756$		0			0
$757$	−34.9611			−1.27068			−0.635342	−	0.772231i	$-0.719141\pi$
$757$	−34.9611			−1.27068			−0.635342	+	0.772231i	$0.719141\pi$
$758$	−6.81230			−0.247434
$759$		0			0
$760$	−36.6181			−1.32828
$761$	2.29179	+	3.96950i	0.0830773	+	0.143894i	0.904570	−	0.426324i	$-0.140192\pi$
$761$	2.29179	+	3.96950i	0.0830773	+	0.143894i	−0.821493	+	0.570219i	$0.806858\pi$
$762$		0			0
$763$	−33.7954	+	34.4846i	−1.22347	+	1.24843i
$764$	−35.1546			−1.27185
$765$		0			0
$766$	7.67154	+	13.2875i	0.277184	+	0.480097i
$767$	−3.80959	+	6.59840i	−0.137556	+	0.238254i
$768$		0			0
$769$	−8.47949	+	14.6869i	−0.305778	+	0.529623i	−0.977434	−	0.211240i	$-0.932250\pi$
$769$	−8.47949	+	14.6869i	−0.305778	+	0.529623i	0.671656	+	0.740863i	$0.265583\pi$
$770$	−3.85185	−	13.8159i	−0.138811	−	0.497890i
$771$		0			0
$772$	1.17730			0.0423718
$773$	20.1420	+	34.8870i	0.724458	+	1.25480i	0.959197	+	0.282739i	$0.0912430\pi$
$773$	20.1420	+	34.8870i	0.724458	+	1.25480i	−0.234739	+	0.972058i	$0.575424\pi$
$774$		0			0
$775$	14.6150	−	25.3140i	0.524988	−	0.909306i
$776$	−1.09604	−	1.89840i	−0.0393456	−	0.0681485i
$777$		0			0
$778$	−12.7826	+	22.1402i	−0.458279	+	0.793763i
$779$	8.81191	+	15.2627i	0.315719	+	0.546842i
$780$		0			0
$781$	−8.13160	+	14.0843i	−0.290972	+	0.503977i
$782$	2.00972	−	3.48093i	0.0718673	−	0.124478i
$783$		0			0
$784$	−5.16101	+	3.12030i	−0.184322	+	0.111439i
$785$	1.11956	+	1.93914i	0.0399589	+	0.0692108i
$786$		0			0
$787$	47.2107			1.68288			0.841439	−	0.540352i	$-0.181709\pi$
$787$	47.2107			1.68288			0.841439	+	0.540352i	$0.181709\pi$
$788$	8.32967			0.296732
$789$		0			0
$790$	8.26608	+	14.3173i	0.294094	+	0.509386i
$791$	−13.4513	−	3.45912i	−0.478273	−	0.122992i
$792$		0			0
$793$	10.8187	−	18.7386i	0.384185	−	0.665428i
$794$	−1.57442	+	2.72698i	−0.0558741	+	0.0967767i
$795$		0			0
$796$	−6.57210	−	11.3832i	−0.232942	−	0.403467i
$797$	−2.01367	+	3.48778i	−0.0713280	+	0.123544i	−0.899484	−	0.436955i	$-0.856057\pi$
$797$	−2.01367	+	3.48778i	−0.0713280	+	0.123544i	0.828156	+	0.560498i	$0.189390\pi$
$798$		0			0
$799$	−0.631600	−	1.09396i	−0.0223444	−	0.0387016i
$800$	15.0196	−	26.0146i	0.531022	−	0.919757i
$801$		0			0
$802$	5.88508	+	10.1933i	0.207810	+	0.359937i
$803$	−16.9267			−0.597329
$804$		0			0
$805$	7.68715	+	1.97682i	0.270936	+	0.0696736i
$806$	−8.03667	+	13.9199i	−0.283080	+	0.490308i
$807$		0			0
$808$	−10.0830	+	17.4643i	−0.354720	+	0.614392i
$809$	5.94119	+	10.2904i	0.208881	+	0.361792i	0.951362	−	0.308074i	$-0.0996845\pi$
$809$	5.94119	+	10.2904i	0.208881	+	0.361792i	−0.742481	+	0.669867i	$0.766351\pi$
$810$		0			0
$811$	−21.1111			−0.741311			−0.370655	−	0.928770i	$-0.620867\pi$
$811$	−21.1111			−0.741311			−0.370655	+	0.928770i	$0.620867\pi$
$812$	26.6443	−	27.1878i	0.935033	−	0.954103i
$813$		0			0
$814$	−2.66182	−	4.61042i	−0.0932969	−	0.161595i
$815$	61.2074			2.14400
$816$		0			0
$817$	−14.5127			−0.507736
$818$	−20.8432			−0.728767
$819$		0			0
$820$	−18.0252			−0.629467
$821$	37.2919			1.30150			0.650749	−	0.759293i	$-0.274455\pi$
$821$	37.2919			1.30150			0.650749	+	0.759293i	$0.274455\pi$
$822$		0			0
$823$	−21.4523			−0.747779			−0.373890	−	0.927473i	$-0.621976\pi$
$823$	−21.4523			−0.747779			−0.373890	+	0.927473i	$0.621976\pi$
$824$	3.16883	+	5.48857i	0.110391	+	0.191203i
$825$		0			0
$826$	−1.11217	−	3.98916i	−0.0386973	−	0.138800i
$827$	28.6375			0.995823			0.497912	−	0.867228i	$-0.334100\pi$
$827$	28.6375			0.995823			0.497912	+	0.867228i	$0.334100\pi$
$828$		0			0
$829$	19.8646	+	34.4065i	0.689925	+	1.19499i	0.971862	+	0.235552i	$0.0756899\pi$
$829$	19.8646	+	34.4065i	0.689925	+	1.19499i	−0.281936	+	0.959433i	$0.590977\pi$
$830$	−9.81875	+	17.0066i	−0.340814	+	0.590306i
$831$		0			0
$832$	−5.06814	+	8.77827i	−0.175706	+	0.304332i
$833$	34.3554	+	18.9208i	1.19034	+	0.655568i
$834$		0			0
$835$	74.4192			2.57538
$836$	−7.03379	−	12.1829i	−0.243269	−	0.421354i
$837$		0			0
$838$	−7.98921	+	13.8377i	−0.275983	+	0.478016i
$839$	−17.1803	−	29.7572i	−0.593130	−	1.02733i	−0.993808	−	0.111112i	$-0.964559\pi$
$839$	−17.1803	−	29.7572i	−0.593130	−	1.02733i	0.400678	−	0.916219i	$-0.368775\pi$
$840$		0			0
$841$	−36.7554	+	63.6622i	−1.26743	+	2.19525i
$842$	7.59316	+	13.1517i	0.261678	+	0.453239i
$843$		0			0
$844$	−8.92395	+	15.4567i	−0.307175	+	0.532042i
$845$	1.14132	−	1.97682i	0.0392624	−	0.0680045i
$846$		0			0
$847$	−11.0858	+	11.3119i	−0.380912	+	0.388681i
$848$	4.59222	+	7.95395i	0.157697	+	0.273140i
$849$		0			0
$850$	−21.8479			−0.749376
$851$	2.94609			0.100991
$852$		0			0
$853$	0.757310	+	1.31170i	0.0259298	+	0.0449117i	0.878699	−	0.477376i	$-0.158412\pi$
$853$	0.757310	+	1.31170i	0.0259298	+	0.0449117i	−0.852769	+	0.522288i	$0.825079\pi$
$854$	3.15842	+	11.3287i	0.108079	+	0.387660i
$855$		0			0
$856$	14.9212	−	25.8443i	0.509996	−	0.883339i
$857$	−2.25473	+	3.90530i	−0.0770201	+	0.133403i	−0.901963	−	0.431813i	$-0.857874\pi$
$857$	−2.25473	+	3.90530i	−0.0770201	+	0.133403i	0.824943	+	0.565216i	$0.191207\pi$
$858$		0			0
$859$	−6.30314	−	10.9174i	−0.215060	−	0.372495i	0.738231	−	0.674548i	$-0.235661\pi$
$859$	−6.30314	−	10.9174i	−0.215060	−	0.372495i	−0.953291	+	0.302053i	$0.902328\pi$
$860$	7.42162	−	12.8546i	0.253075	−	0.438339i
$861$		0			0
$862$	7.65800	+	13.2640i	0.260833	+	0.451775i
$863$	−5.33009	+	9.23200i	−0.181439	+	0.314261i	−0.942371	−	0.334571i	$-0.891409\pi$
$863$	−5.33009	+	9.23200i	−0.181439	+	0.314261i	0.760932	+	0.648832i	$0.224742\pi$
$864$		0			0
$865$	13.1082	+	22.7041i	0.445693	+	0.771962i
$866$	−9.02081			−0.306540
$867$		0			0
$868$	5.75911	+	20.6569i	0.195477	+	0.701141i
$869$	−7.64488	+	13.2413i	−0.259335	+	0.449181i
$870$		0			0
$871$	−13.7427	+	23.8030i	−0.465653	+	0.806535i
$872$	23.7518	+	41.1394i	0.804339	+	1.39316i
$873$		0			0
$874$	−3.17154			−0.107279
$875$	−0.282075	−	1.01175i	−0.00953586	−	0.0342035i
$876$		0			0
$877$	16.1190	+	27.9189i	0.544300	+	0.942756i	0.998651	+	0.0519325i	$0.0165381\pi$
$877$	16.1190	+	27.9189i	0.544300	+	0.942756i	−0.454350	+	0.890823i	$0.650129\pi$
$878$	1.64187			0.0554104
$879$		0			0
$880$	6.13844			0.206927
$881$	55.6375			1.87447			0.937237	−	0.348692i	$-0.113374\pi$
$881$	55.6375			1.87447			0.937237	+	0.348692i	$0.113374\pi$
$882$		0			0
$883$	−42.4854			−1.42975			−0.714873	−	0.699254i	$-0.753516\pi$
$883$	−42.4854			−1.42975			−0.714873	+	0.699254i	$0.753516\pi$
$884$	−29.4898			−0.991848
$885$		0			0
$886$	−1.49303			−0.0501593
$887$	−4.47825	−	7.75655i	−0.150365	−	0.260439i	0.780997	−	0.624535i	$-0.214711\pi$
$887$	−4.47825	−	7.75655i	−0.150365	−	0.260439i	−0.931362	+	0.364096i	$0.881378\pi$
$888$		0			0
$889$	14.2855	+	51.2396i	0.479121	+	1.71852i
$890$	−23.5516			−0.789451
$891$		0			0
$892$	−15.1969	−	26.3217i	−0.508829	−	0.881317i
$893$	−0.498365	+	0.863194i	−0.0166772	+	0.0288857i
$894$		0			0
$895$	−15.7661	+	27.3076i	−0.527002	+	0.912794i
$896$	6.85008	+	24.5700i	0.228845	+	0.820827i
$897$		0			0
$898$	1.63749			0.0546437
$899$	−28.8743	−	50.0117i	−0.963011	−	1.66798i
$900$		0			0
$901$	29.8646	−	51.7270i	0.994933	−	1.72327i
$902$	3.39575	+	5.88160i	0.113066	+	0.195836i
$903$		0			0
$904$	−6.83229	+	11.8339i	−0.227238	+	0.393589i
$905$	−14.9360	−	25.8699i	−0.496489	−	0.859944i
$906$		0			0
$907$	−5.39372	+	9.34220i	−0.179096	+	0.310203i	−0.941571	−	0.336815i	$-0.890650\pi$
$907$	−5.39372	+	9.34220i	−0.179096	+	0.310203i	0.762475	+	0.647017i	$0.223984\pi$
$908$	8.96866	−	15.5342i	0.297636	−	0.515520i
$909$		0			0
$910$	6.37128	+	22.8526i	0.211206	+	0.757558i
$911$	−23.7427	−	41.1235i	−0.786630	−	1.36248i	−0.928020	−	0.372530i	$-0.878490\pi$
$911$	−23.7427	−	41.1235i	−0.786630	−	1.36248i	0.141390	−	0.989954i	$-0.454843\pi$
$912$		0			0
$913$	−18.1617			−0.601066
$914$	9.97154			0.329829
$915$		0			0
$916$	−20.5487	−	35.5914i	−0.678948	−	1.17597i
$917$	7.55787	−	7.71202i	0.249583	−	0.254673i
$918$		0			0
$919$	−28.1375	+	48.7356i	−0.928170	+	1.60764i	−0.141788	+	0.989897i	$0.545285\pi$
$919$	−28.1375	+	48.7356i	−0.928170	+	1.60764i	−0.786382	+	0.617741i	$0.788048\pi$
$920$	3.90451	−	6.76282i	0.128728	−	0.222964i
$921$		0			0
$922$	2.08757	+	3.61578i	0.0687504	+	0.119079i
$923$	13.4503	−	23.2967i	0.442723	−	0.766820i
$924$		0			0
$925$	−8.00684	−	13.8682i	−0.263263	−	0.455985i
$926$	−7.79863	+	13.5076i	−0.256279	+	0.443888i
$927$		0			0
$928$	−29.6735	−	51.3960i	−0.974079	−	1.68716i
$929$	−0.760877			−0.0249636			−0.0124818	−	0.999922i	$-0.503973\pi$
$929$	−0.760877			−0.0249636			−0.0124818	+	0.999922i	$0.503973\pi$
$930$		0			0
$931$	−0.624763	−	30.9412i	−0.0204758	−	1.01406i
$932$	−15.2416	+	26.3992i	−0.499255	+	0.864734i
$933$		0			0
$934$	−14.9709	+	25.9303i	−0.489861	+	0.848465i
$935$	−19.9601	−	34.5718i	−0.652764	−	1.13062i
$936$		0			0
$937$	−30.3218			−0.990569			−0.495284	−	0.868731i	$-0.664936\pi$
$937$	−30.3218			−0.990569			−0.495284	+	0.868731i	$0.664936\pi$
$938$	−4.01204	−	14.3905i	−0.130998	−	0.469865i
$939$		0			0
$940$	−0.509715	−	0.882853i	−0.0166251	−	0.0287955i
$941$	−55.0813			−1.79560			−0.897799	−	0.440406i	$-0.854835\pi$
$941$	−55.0813			−1.79560			−0.897799	+	0.440406i	$0.854835\pi$
$942$		0			0
$943$	−3.75839			−0.122390
$944$	1.77239			0.0576864
$945$		0			0
$946$	−5.59261			−0.181831
$947$	−30.6205			−0.995034			−0.497517	−	0.867454i	$-0.665755\pi$
$947$	−30.6205			−0.995034			−0.497517	+	0.867454i	$0.665755\pi$
$948$		0			0
$949$	27.9981			0.908857
$950$	8.61956	+	14.9295i	0.279656	+	0.484378i
$951$		0			0
$952$	27.0086	−	27.5595i	0.875355	−	0.893209i
$953$	−7.83422			−0.253775			−0.126888	−	0.991917i	$-0.540499\pi$
$953$	−7.83422			−0.253775			−0.126888	+	0.991917i	$0.540499\pi$
$954$		0			0
$955$	39.3577	+	68.1696i	1.27359	+	2.20592i
$956$	5.49725	−	9.52152i	0.177794	−	0.307948i
$957$		0			0
$958$	6.37128	−	11.0354i	0.205847	−	0.356537i
$959$	−4.83173	−	1.24252i	−0.156025	−	0.0401231i
$960$		0			0
$961$	1.53216			0.0494244
$962$	4.40288	+	7.62601i	0.141955	+	0.245872i
$963$		0			0
$964$	4.32833	−	7.49688i	0.139406	−	0.241458i
$965$	−1.31806	−	2.28294i	−0.0424297	−	0.0734905i
$966$		0			0
$967$	2.64815	−	4.58673i	0.0851588	−	0.147499i	−0.820300	−	0.571933i	$-0.806194\pi$
$967$	2.64815	−	4.58673i	0.0851588	−	0.147499i	0.905459	+	0.424434i	$0.139527\pi$
$968$	7.79123	+	13.4948i	0.250420	+	0.433740i
$969$		0			0
$970$	−1.01943	+	1.76571i	−0.0327319	+	0.0566934i
$971$	26.1202	−	45.2416i	0.838239	−	1.45187i	−0.0531273	−	0.998588i	$-0.516919\pi$
$971$	26.1202	−	45.2416i	0.838239	−	1.45187i	0.891366	−	0.453284i	$-0.149748\pi$
$972$		0			0
$973$	32.7866	+	8.43135i	1.05109	+	0.270297i
$974$	1.52394	+	2.63955i	0.0488303	+	0.0845766i
$975$		0			0
$976$	−5.03337			−0.161114
$977$	5.94609			0.190232			0.0951161	−	0.995466i	$-0.469678\pi$
$977$	5.94609			0.190232			0.0951161	+	0.995466i	$0.469678\pi$
$978$		0			0
$979$	−10.8908	−	18.8635i	−0.348073	−	0.602880i
$980$	27.7256	+	15.2695i	0.885661	+	0.487767i
$981$		0			0
$982$	9.37825	−	16.2436i	0.299272	−	0.518354i
$983$	−9.28207	+	16.0770i	−0.296052	+	0.512777i	−0.975229	−	0.221197i	$-0.929004\pi$
$983$	−9.28207	+	16.0770i	−0.296052	+	0.512777i	0.679177	+	0.733975i	$0.262337\pi$
$984$		0			0
$985$	−9.32558	−	16.1524i	−0.297138	−	0.514658i
$986$	−21.5819	+	37.3810i	−0.687309	+	1.19045i
$987$		0			0
$988$	11.6345	+	20.1515i	0.370142	+	0.641105i
$989$	1.54746	−	2.68029i	0.0492065	−	0.0852282i
$990$		0			0
$991$	−9.31875	−	16.1405i	−0.296020	−	0.512721i	0.679202	−	0.733951i	$-0.262326\pi$
$991$	−9.31875	−	16.1405i	−0.296020	−	0.512721i	−0.975222	+	0.221230i	$0.928993\pi$
$992$	33.4326			1.06149
$993$		0			0
$994$	3.92669	+	14.0843i	0.124547	+	0.446728i
$995$	−14.7157	+	25.4884i	−0.466520	+	0.808037i
$996$		0			0
$997$	15.2798	−	26.4653i	0.483915	−	0.838165i	−0.515915	−	0.856640i	$-0.672548\pi$
$997$	15.2798	−	26.4653i	0.483915	−	0.838165i	0.999829	+	0.0184753i	$0.00588120\pi$
$998$	−9.34338	−	16.1832i	−0.295759	−	0.512270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.h.352.2		6
3.2	odd	2		567.2.h.i.352.2		6
7.4	even	3		567.2.g.i.109.2		6
9.2	odd	6		567.2.g.h.541.2		6
9.4	even	3		189.2.e.f.163.2	yes	6
9.5	odd	6		189.2.e.e.163.2	yes	6
9.7	even	3		567.2.g.i.541.2		6
21.11	odd	6		567.2.g.h.109.2		6
63.4	even	3		189.2.e.f.109.2	yes	6
63.5	even	6		1323.2.a.z.1.2		3
63.11	odd	6		567.2.h.i.298.2		6
63.23	odd	6		1323.2.a.ba.1.2		3
63.25	even	3	inner	567.2.h.h.298.2		6
63.32	odd	6		189.2.e.e.109.2	✓	6
63.40	odd	6		1323.2.a.y.1.2		3
63.58	even	3		1323.2.a.x.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.2	✓	6	63.32	odd	6
189.2.e.e.163.2	yes	6	9.5	odd	6
189.2.e.f.109.2	yes	6	63.4	even	3
189.2.e.f.163.2	yes	6	9.4	even	3
567.2.g.h.109.2		6	21.11	odd	6
567.2.g.h.541.2		6	9.2	odd	6
567.2.g.i.109.2		6	7.4	even	3
567.2.g.i.541.2		6	9.7	even	3
567.2.h.h.298.2		6	63.25	even	3	inner
567.2.h.h.352.2		6	1.1	even	1	trivial
567.2.h.i.298.2		6	63.11	odd	6
567.2.h.i.352.2		6	3.2	odd	2
1323.2.a.x.1.2		3	63.58	even	3
1323.2.a.y.1.2		3	63.40	odd	6
1323.2.a.z.1.2		3	63.5	even	6
1323.2.a.ba.1.2		3	63.23	odd	6

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)

\(f(q)\)	\(=\)	\(q-0.760877 q^{2} -1.42107 q^{4} +(1.59097 + 2.75564i) q^{5} +(0.710533 + 2.54856i) q^{7} +2.60301 q^{8} +(-1.21053 - 2.09671i) q^{10} +(1.11956 - 1.93914i) q^{11} +(-1.85185 + 3.20750i) q^{13} +(-0.540628 - 1.93914i) q^{14} +0.861564 q^{16} +(-2.80150 - 4.85235i) q^{17} +(-2.21053 + 3.82876i) q^{19} +(-2.26088 - 3.91595i) q^{20} +(-0.851848 + 1.47544i) q^{22} +(-0.471410 - 0.816506i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(1.40903 - 2.44051i) q^{26} +(-1.00972 - 3.62167i) q^{28} +(5.06238 + 8.76830i) q^{29} -5.70370 q^{31} -5.86156 q^{32} +(2.13160 + 3.69204i) q^{34} +(-5.89248 + 6.01266i) q^{35} +(-1.56238 + 2.70612i) q^{37} +(1.68194 - 2.91321i) q^{38} +(4.14132 + 7.17297i) q^{40} +(1.99316 - 3.45226i) q^{41} +(1.64132 + 2.84284i) q^{43} +(-1.59097 + 2.75564i) q^{44} +(0.358685 + 0.621261i) q^{46} +0.225450 q^{47} +(-5.99028 + 3.62167i) q^{49} +(1.94966 - 3.37690i) q^{50} +(2.63160 - 4.55806i) q^{52} +(5.33009 + 9.23200i) q^{53} +7.12476 q^{55} +(1.84953 + 6.63392i) q^{56} +(-3.85185 - 6.67160i) q^{58} +2.05718 q^{59} -5.84213 q^{61} +4.33981 q^{62} +2.73680 q^{64} -11.7850 q^{65} +7.42107 q^{67} +(3.98113 + 6.89551i) q^{68} +(4.48345 - 4.57489i) q^{70} -7.26320 q^{71} +(-3.77975 - 6.54672i) q^{73} +(1.18878 - 2.05903i) q^{74} +(3.14132 - 5.44092i) q^{76} +(5.73749 + 1.47544i) q^{77} -6.82846 q^{79} +(1.37072 + 2.37416i) q^{80} +(-1.51655 + 2.62674i) q^{82} +(-4.05555 - 7.02441i) q^{83} +(8.91423 - 15.4399i) q^{85} +(-1.24884 - 2.16305i) q^{86} +(2.91423 - 5.04759i) q^{88} +(4.86389 - 8.42450i) q^{89} +(-9.49028 - 2.44051i) q^{91} +(0.669905 + 1.16031i) q^{92} -0.171540 q^{94} -14.0676 q^{95} +(-0.421067 - 0.729309i) q^{97} +(4.55787 - 2.75564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{2} + 8 q^{4} + q^{5} - 4 q^{7} - 18 q^{8} + q^{10} + 7 q^{11} - 2 q^{13} + 13 q^{14} + 20 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) \) 6 * q - 4 * q^2 + 8 * q^4 + q^5 - 4 * q^7 - 18 * q^8 + q^10 + 7 * q^11 - 2 * q^13 + 13 * q^14 + 20 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 - 16 * q^31 - 50 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 - 7 * q^38 + 24 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 - 18 * q^47 - 12 * q^49 + 4 * q^50 - 9 * q^52 + 24 * q^53 + 8 * q^55 + 51 * q^56 - 14 * q^58 + 30 * q^59 - 2 * q^61 + 42 * q^62 + 66 * q^64 - 20 * q^65 + 28 * q^67 + 39 * q^68 - 7 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 - 10 * q^77 + 12 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 - 32 * q^86 - 9 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 - 54 * q^94 - 32 * q^95 + 14 * q^97 - 49 * q^98

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