LMFDB - Embedded newform 315.2.r.b.184.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			184.3
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61386i q^{2} +(1.67535 - 0.439552i) q^{3} -4.83226 q^{4} +(2.17617 + 0.514103i) q^{5} +(-1.14893 - 4.37913i) q^{6} +(1.37276 - 2.26175i) q^{7} +7.40313i q^{8} +(2.61359 - 1.47280i) q^{9} +O(q^{10})$	\(q-2.61386i q^{2} +(1.67535 - 0.439552i) q^{3} -4.83226 q^{4} +(2.17617 + 0.514103i) q^{5} +(-1.14893 - 4.37913i) q^{6} +(1.37276 - 2.26175i) q^{7} +7.40313i q^{8} +(2.61359 - 1.47280i) q^{9} +(1.34379 - 5.68819i) q^{10} +(0.0393440 - 0.0681458i) q^{11} +(-8.09573 + 2.12403i) q^{12} +(0.00542028 + 0.00312940i) q^{13} +(-5.91190 - 3.58821i) q^{14} +(3.87181 - 0.0952351i) q^{15} +9.68623 q^{16} +(-4.87614 + 2.81524i) q^{17} +(-3.84971 - 6.83155i) q^{18} +(-3.83039 + 6.63444i) q^{19} +(-10.5158 - 2.48428i) q^{20} +(1.30570 - 4.39262i) q^{21} +(-0.178124 - 0.102840i) q^{22} +(-1.90325 + 1.09884i) q^{23} +(3.25406 + 12.4028i) q^{24} +(4.47140 + 2.23755i) q^{25} +(0.00817982 - 0.0141679i) q^{26} +(3.73130 - 3.61627i) q^{27} +(-6.63356 + 10.9294i) q^{28} +(-3.13943 - 5.43765i) q^{29} +(-0.248931 - 10.1204i) q^{30} +3.71536 q^{31} -10.5122i q^{32} +(0.0359613 - 0.131462i) q^{33} +(7.35864 + 12.7455i) q^{34} +(4.15014 - 4.21620i) q^{35} +(-12.6295 + 7.11698i) q^{36} +(2.76672 + 1.59737i) q^{37} +(17.3415 + 10.0121i) q^{38} +(0.0104564 + 0.00286035i) q^{39} +(-3.80597 + 16.1104i) q^{40} +(-5.37251 + 9.30547i) q^{41} +(-11.4817 - 3.41293i) q^{42} +(7.17523 - 4.14262i) q^{43} +(-0.190121 + 0.329299i) q^{44} +(6.44478 - 1.86141i) q^{45} +(2.87221 + 4.97482i) q^{46} -2.86094i q^{47} +(16.2278 - 4.25760i) q^{48} +(-3.23103 - 6.20970i) q^{49} +(5.84863 - 11.6876i) q^{50} +(-6.93179 + 6.85982i) q^{51} +(-0.0261922 - 0.0151221i) q^{52} +(-1.29201 + 0.745945i) q^{53} +(-9.45242 - 9.75309i) q^{54} +(0.120653 - 0.128070i) q^{55} +(16.7440 + 10.1628i) q^{56} +(-3.50107 + 12.7987i) q^{57} +(-14.2133 + 8.20603i) q^{58} +1.71502 q^{59} +(-18.7096 + 0.460201i) q^{60} -7.49303 q^{61} -9.71142i q^{62} +(0.256725 - 7.93310i) q^{63} -8.10489 q^{64} +(0.0101866 + 0.00959668i) q^{65} +(-0.343623 - 0.0939979i) q^{66} +0.465791i q^{67} +(23.5628 - 13.6040i) q^{68} +(-2.70561 + 2.67752i) q^{69} +(-11.0206 - 10.8479i) q^{70} -2.56819 q^{71} +(10.9034 + 19.3487i) q^{72} +(5.20158 - 3.00313i) q^{73} +(4.17529 - 7.23181i) q^{74} +(8.47467 + 1.78326i) q^{75} +(18.5095 - 32.0593i) q^{76} +(-0.100119 - 0.182535i) q^{77} +(0.00747654 - 0.0273316i) q^{78} +7.70542 q^{79} +(21.0788 + 4.97972i) q^{80} +(4.66169 - 7.69861i) q^{81} +(24.3232 + 14.0430i) q^{82} +(-2.83357 + 1.63597i) q^{83} +(-6.30950 + 21.2263i) q^{84} +(-12.0586 + 3.61959i) q^{85} +(-10.8282 - 18.7551i) q^{86} +(-7.64977 - 7.73003i) q^{87} +(0.504493 + 0.291269i) q^{88} +(4.45339 - 7.71349i) q^{89} +(-4.86547 - 16.8457i) q^{90} +(0.0145187 - 0.00796340i) q^{91} +(9.19699 - 5.30988i) q^{92} +(6.22452 - 1.63309i) q^{93} -7.47810 q^{94} +(-11.7464 + 12.4684i) q^{95} +(-4.62064 - 17.6116i) q^{96} +(-3.75004 + 2.16509i) q^{97} +(-16.2313 + 8.44547i) q^{98} +(0.00246356 - 0.236051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.61386i		−	1.84828i	−0.382057	−	0.924139i	$-0.624784\pi$
$2$		−	2.61386i		−	1.84828i	0.382057	−	0.924139i	$-0.375216\pi$
$3$	1.67535	−	0.439552i	0.967263	−	0.253775i
$3$	1.67535	−	0.439552i	0.967263	−	0.253775i
$4$	−4.83226			−2.41613
$5$	2.17617	+	0.514103i	0.973211	+	0.229914i
$5$	2.17617	+	0.514103i	0.973211	+	0.229914i
$6$	−1.14893	−	4.37913i	−0.469047	−	1.78777i
$7$	1.37276	−	2.26175i	0.518856	−	0.854861i
$7$	1.37276	−	2.26175i	0.518856	−	0.854861i
$8$			7.40313i			2.61740i
$9$	2.61359	−	1.47280i	0.871196	−	0.490935i
$10$	1.34379	−	5.68819i	0.424945	−	1.79876i
$11$	0.0393440	−	0.0681458i	0.0118627	−	0.0205467i	−0.860033	−	0.510238i	$-0.829557\pi$
$11$	0.0393440	−	0.0681458i	0.0118627	−	0.0205467i	0.871896	+	0.489691i	$0.162891\pi$
$12$	−8.09573	+	2.12403i	−2.33703	+	0.613154i
$13$	0.00542028	+	0.00312940i	0.00150332	+	0.000867940i	0.500751	−	0.865591i	$-0.333057\pi$
$13$	0.00542028	+	0.00312940i	0.00150332	+	0.000867940i	−0.499248	+	0.866459i	$0.666390\pi$
$14$	−5.91190	−	3.58821i	−1.58002	−	0.958991i
$15$	3.87181	−	0.0952351i	0.999698	−	0.0245896i
$16$	9.68623			2.42156
$17$	−4.87614	+	2.81524i	−1.18264	+	0.682796i	−0.956623	−	0.291329i	$-0.905903\pi$
$17$	−4.87614	+	2.81524i	−1.18264	+	0.682796i	−0.226013	+	0.974124i	$0.572569\pi$
$18$	−3.84971	−	6.83155i	−0.907384	−	1.61021i
$19$	−3.83039	+	6.63444i	−0.878752	+	1.52204i	−0.0260415	+	0.999661i	$0.508290\pi$
$19$	−3.83039	+	6.63444i	−0.878752	+	1.52204i	−0.852711	+	0.522383i	$0.825043\pi$
$20$	−10.5158	−	2.48428i	−2.35141	−	0.555502i
$21$	1.30570	−	4.39262i	0.284928	−	0.958549i
$22$	−0.178124	−	0.102840i	−0.0379761	−	0.0219255i
$23$	−1.90325	+	1.09884i	−0.396854	+	0.229124i	−0.685126	−	0.728425i	$-0.740253\pi$
$23$	−1.90325	+	1.09884i	−0.396854	+	0.229124i	0.288271	+	0.957549i	$0.406919\pi$
$24$	3.25406	+	12.4028i	0.664232	+	2.53172i
$25$	4.47140	+	2.23755i	0.894279	+	0.447509i
$26$	0.00817982	−	0.0141679i	0.00160419	−	0.00277855i
$27$	3.73130	−	3.61627i	0.718089	−	0.695951i
$28$	−6.63356	+	10.9294i	−1.25362	+	2.06546i
$29$	−3.13943	−	5.43765i	−0.582978	−	1.00975i	−0.995124	−	0.0986293i	$-0.968554\pi$
$29$	−3.13943	−	5.43765i	−0.582978	−	1.00975i	0.412147	−	0.911118i	$-0.364779\pi$
$30$	−0.248931	−	10.1204i	−0.0454484	−	1.84772i
$31$	3.71536			0.667298			0.333649	−	0.942697i	$-0.391720\pi$
$31$	3.71536			0.667298			0.333649	+	0.942697i	$0.391720\pi$
$32$		−	10.5122i		−	1.85831i
$33$	0.0359613	−	0.131462i	0.00626007	−	0.0228846i
$34$	7.35864	+	12.7455i	1.26200	+	2.18584i
$35$	4.15014	−	4.21620i	0.701501	−	0.712668i
$36$	−12.6295	+	7.11698i	−2.10492	+	1.18616i
$37$	2.76672	+	1.59737i	0.454846	+	0.262605i	0.709875	−	0.704328i	$-0.248752\pi$
$37$	2.76672	+	1.59737i	0.454846	+	0.262605i	−0.255029	+	0.966933i	$0.582085\pi$
$38$	17.3415	+	10.0121i	2.81316	+	1.62418i
$39$	0.0104564	+	0.00286035i	0.00167436	+	0.000458022i
$40$	−3.80597	+	16.1104i	−0.601777	+	2.54729i
$41$	−5.37251	+	9.30547i	−0.839046	+	1.45327i	0.0516475	+	0.998665i	$0.483553\pi$
$41$	−5.37251	+	9.30547i	−0.839046	+	1.45327i	−0.890693	+	0.454605i	$0.849781\pi$
$42$	−11.4817	−	3.41293i	−1.77166	−	0.526626i
$43$	7.17523	−	4.14262i	1.09421	−	0.631744i	0.159518	−	0.987195i	$-0.449006\pi$
$43$	7.17523	−	4.14262i	1.09421	−	0.631744i	0.934695	+	0.355451i	$0.115673\pi$
$44$	−0.190121	+	0.329299i	−0.0286618	+	0.0496436i
$45$	6.44478	−	1.86141i	0.960731	−	0.277483i
$46$	2.87221	+	4.97482i	0.423485	+	0.733497i
$47$		−	2.86094i		−	0.417312i	−0.977989	−	0.208656i	$-0.933091\pi$
$47$		−	2.86094i		−	0.417312i	0.977989	−	0.208656i	$-0.0669088\pi$
$48$	16.2278	−	4.25760i	2.34228	−	0.614531i
$49$	−3.23103	−	6.20970i	−0.461576	−	0.887101i
$50$	5.84863	−	11.6876i	0.827122	−	1.65288i
$51$	−6.93179	+	6.85982i	−0.970644	+	0.960567i
$52$	−0.0261922	−	0.0151221i	−0.00363221	−	0.00209706i
$53$	−1.29201	+	0.745945i	−0.177472	+	0.102463i	−0.586104	−	0.810236i	$-0.699339\pi$
$53$	−1.29201	+	0.745945i	−0.177472	+	0.102463i	0.408632	+	0.912699i	$0.366006\pi$
$54$	−9.45242	−	9.75309i	−1.28631	−	1.32723i
$55$	0.120653	−	0.128070i	0.0162689	−	0.0172689i
$56$	16.7440	+	10.1628i	2.23752	+	1.35806i
$57$	−3.50107	+	12.7987i	−0.463728	+	1.69522i
$58$	−14.2133	+	8.20603i	−1.86629	+	1.07750i
$59$	1.71502			0.223277			0.111638	−	0.993749i	$-0.464390\pi$
$59$	1.71502			0.223277			0.111638	+	0.993749i	$0.464390\pi$
$60$	−18.7096	+	0.460201i	−2.41540	+	0.0594117i
$61$	−7.49303			−0.959385			−0.479692	−	0.877437i	$-0.659252\pi$
$61$	−7.49303			−0.959385			−0.479692	+	0.877437i	$0.659252\pi$
$62$		−	9.71142i		−	1.23335i
$63$	0.256725	−	7.93310i	0.0323443	−	0.999477i
$64$	−8.10489			−1.01311
$65$	0.0101866	+	0.00959668i	0.00126349	+	0.00119032i
$66$	−0.343623	−	0.0939979i	−0.0422970	−	0.0115703i
$67$			0.465791i			0.0569054i	0.999595	+	0.0284527i	$0.00905800\pi$
$67$			0.465791i			0.0569054i	−0.999595	+	0.0284527i	$0.990942\pi$
$68$	23.5628	−	13.6040i	2.85740	−	1.64972i
$69$	−2.70561	+	2.67752i	−0.325717	+	0.322335i
$70$	−11.0206	−	10.8479i	−1.31721	−	1.29657i
$71$	−2.56819			−0.304788			−0.152394	−	0.988320i	$-0.548698\pi$
$71$	−2.56819			−0.304788			−0.152394	+	0.988320i	$0.548698\pi$
$72$	10.9034	+	19.3487i	1.28497	+	2.28027i
$73$	5.20158	−	3.00313i	0.608799	−	0.351490i	−0.163696	−	0.986511i	$-0.552342\pi$
$73$	5.20158	−	3.00313i	0.608799	−	0.351490i	0.772495	+	0.635020i	$0.219008\pi$
$74$	4.17529	−	7.23181i	0.485367	−	0.840681i
$75$	8.47467	+	1.78326i	0.978570	+	0.205914i
$76$	18.5095	−	32.0593i	2.12318	−	3.67746i
$77$	−0.100119	−	0.182535i	−0.0114096	−	0.0208017i
$78$	0.00747654	−	0.0273316i	0.000846552	−	0.00309469i
$79$	7.70542			0.866928			0.433464	−	0.901171i	$-0.357291\pi$
$79$	7.70542			0.866928			0.433464	+	0.901171i	$0.357291\pi$
$80$	21.0788	+	4.97972i	2.35669	+	0.556750i
$81$	4.66169	−	7.69861i	0.517966	−	0.855401i
$82$	24.3232	+	14.0430i	2.68605	+	1.55079i
$83$	−2.83357	+	1.63597i	−0.311025	+	0.179571i	−0.647385	−	0.762163i	$-0.724137\pi$
$83$	−2.83357	+	1.63597i	−0.311025	+	0.179571i	0.336360	+	0.941734i	$0.390804\pi$
$84$	−6.30950	+	21.2263i	−0.688423	+	2.31598i
$85$	−12.0586	+	3.61959i	−1.30794	+	0.392599i
$86$	−10.8282	−	18.7551i	−1.16764	−	2.02241i
$87$	−7.64977	−	7.73003i	−0.820142	−	0.828746i
$88$	0.504493	+	0.291269i	0.0537791	+	0.0310494i
$89$	4.45339	−	7.71349i	0.472058	−	0.817628i	−0.527431	−	0.849598i	$-0.676845\pi$
$89$	4.45339	−	7.71349i	0.472058	−	0.817628i	0.999489	+	0.0319696i	$0.0101780\pi$
$90$	−4.86547	−	16.8457i	−0.512866	−	1.77570i
$91$	0.0145187	−	0.00796340i	0.00152197	−	0.000834791i
$92$	9.19699	−	5.30988i	0.958852	−	0.553594i
$93$	6.22452	−	1.63309i	0.645452	−	0.169344i
$94$	−7.47810			−0.771308
$95$	−11.7464	+	12.4684i	−1.20515	+	1.27923i
$96$	−4.62064	−	17.6116i	−0.471593	−	1.79747i
$97$	−3.75004	+	2.16509i	−0.380759	+	0.219831i	−0.678148	−	0.734925i	$-0.737217\pi$
$97$	−3.75004	+	2.16509i	−0.380759	+	0.219831i	0.297389	+	0.954756i	$0.403884\pi$
$98$	−16.2313	+	8.44547i	−1.63961	+	0.853121i
$99$	0.00246356	−	0.236051i	0.000247597	−	0.0237240i
$100$	−21.6070	−	10.8124i	−2.16070	−	1.08124i
$101$	−5.10327	+	8.83913i	−0.507795	+	0.879526i	0.492165	+	0.870502i	$0.336206\pi$
$101$	−5.10327	+	8.83913i	−0.507795	+	0.879526i	−0.999959	+	0.00902410i	$0.997128\pi$
$102$	17.9306	+	18.1187i	1.77539	+	1.79402i
$103$	13.4952	−	7.79146i	1.32972	−	0.767715i	0.344465	−	0.938799i	$-0.388060\pi$
$103$	13.4952	−	7.79146i	1.32972	−	0.767715i	0.985256	+	0.171084i	$0.0547270\pi$
$104$	−0.0231674	+	0.0401271i	−0.00227175	+	0.00393478i
$105$	5.09969	−	8.88781i	0.497679	−	0.867361i
$106$	1.94980	+	3.37714i	0.189381	+	0.328017i
$107$	1.42036	+	0.820043i	0.137311	+	0.0792765i	0.567082	−	0.823661i	$-0.308072\pi$
$107$	1.42036	+	0.820043i	0.137311	+	0.0792765i	−0.429771	+	0.902938i	$0.641406\pi$
$108$	−18.0306	+	17.4748i	−1.73500	+	1.68151i
$109$	1.86832	+	3.23602i	0.178952	+	0.309955i	0.941522	−	0.336952i	$-0.109396\pi$
$109$	1.86832	+	3.23602i	0.178952	+	0.309955i	−0.762570	+	0.646906i	$0.776063\pi$
$110$	−0.334756	−	0.315370i	−0.0319178	−	0.0300694i
$111$	5.33734	+	1.46003i	0.506598	+	0.138580i
$112$	13.2969	−	21.9078i	1.25644	−	2.07010i
$113$	−15.3589	−	8.86747i	−1.44484	−	0.834182i	−0.446677	−	0.894695i	$-0.647393\pi$
$113$	−15.3589	−	8.86747i	−1.44484	−	0.834182i	−0.998167	+	0.0605135i	$0.980726\pi$
$114$	33.4539	+	9.15130i	3.13324	+	0.857098i
$115$	−4.70670	+	1.41279i	−0.438902	+	0.131744i
$116$	15.1706	+	26.2762i	1.40855	+	2.43968i
$117$	0.0187754		0.000195950i	0.00173579		1.81156e-5i
$118$		−	4.48282i		−	0.412677i
$119$	−0.326420	+	14.8933i	−0.0299229	+	1.36526i
$120$	0.705038	+	28.6635i	0.0643609	+	2.61661i
$121$	5.49690	+	9.52092i	0.499719	+	0.865538i
$122$			19.5857i			1.77321i
$123$	−4.91060	+	17.9514i	−0.442774	+	1.61862i
$124$	−17.9536			−1.61228
$125$	8.58017	+	7.16803i	0.767434	+	0.641128i
$126$	−20.7360	−	0.671043i	−1.84731	−	0.0597813i
$127$		−	6.65281i		−	0.590341i	−0.955445	−	0.295171i	$-0.904624\pi$
$127$		−	6.65281i		−	0.590341i	0.955445	−	0.295171i	$-0.0953765\pi$
$128$			0.160697i			0.0142038i
$129$	10.2001	−	10.0942i	0.898071	−	0.888747i
$130$	0.0250844	−	0.0266263i	0.00220005	−	0.00233528i
$131$	5.09355	+	8.82229i	0.445026	+	0.770807i	0.998054	−	0.0623555i	$-0.0198613\pi$
$131$	5.09355	+	8.82229i	0.445026	+	0.770807i	−0.553028	+	0.833162i	$0.686528\pi$
$132$	−0.173775	+	0.635258i	−0.0151251	+	0.0552921i
$133$	9.74721	+	17.7709i	0.845190	+	1.54093i
$134$	1.21751			0.105177
$135$	9.97906	−	5.95133i	0.858861	−	0.512209i
$136$	−20.8416	−	36.0987i	−1.78715	−	3.09544i
$137$	−9.26692	−	5.35026i	−0.791726	−	0.457103i	0.0488437	−	0.998806i	$-0.484446\pi$
$137$	−9.26692	−	5.35026i	−0.791726	−	0.457103i	−0.840570	+	0.541703i	$0.817780\pi$
$138$	6.99865	+	7.07207i	0.595765	+	0.602015i
$139$	−1.01823	+	1.76362i	−0.0863649	+	0.149588i	−0.905972	−	0.423338i	$-0.860858\pi$
$139$	−1.01823	+	1.76362i	−0.0863649	+	0.149588i	0.819607	+	0.572926i	$0.194192\pi$
$140$	−20.0545	+	20.3738i	−1.69492	+	1.72190i
$141$	−1.25753	−	4.79308i	−0.105903	−	0.403650i
$142$			6.71288i			0.563332i
$143$	0.000426511	0	0.000246246i	3.56667e−5	0	2.05922e-5i
$144$	25.3158	−	14.2659i	2.10965	−	1.18883i
$145$	−4.03641	−	13.4472i	−0.335205	−	1.11673i
$146$	−7.84977	−	13.5962i	−0.649652	−	1.12523i
$147$	−8.14259	−	8.98322i	−0.671590	−	0.740923i
$148$	−13.3695	−	7.71889i	−1.09897	−	0.634489i
$149$	1.83122	+	3.17177i	0.150020	+	0.259841i	0.931234	−	0.364421i	$-0.118733\pi$
$149$	1.83122	+	3.17177i	0.150020	+	0.259841i	−0.781215	+	0.624262i	$0.785400\pi$
$150$	4.66120	−	22.1516i	0.380585	−	1.80867i
$151$	−8.61647	+	14.9242i	−0.701198	+	1.21451i	0.266848	+	0.963739i	$0.414018\pi$
$151$	−8.61647	+	14.9242i	−0.701198	+	1.21451i	−0.968046	+	0.250772i	$0.919315\pi$
$152$	−49.1156	−	28.3569i	−3.98380	−	2.30005i
$153$	−8.59792	+	14.5395i	−0.695100	+	1.17545i
$154$	−0.477120	+	0.261697i	−0.0384474	+	0.0210881i
$155$	8.08523	+	1.91008i	0.649421	+	0.153421i
$156$	−0.0505281	−	0.0138219i	−0.00404548	−	0.00110664i
$157$		−	11.4921i		−	0.917172i	−0.888650	−	0.458586i	$-0.848356\pi$
$157$		−	11.4921i		−	0.917172i	0.888650	−	0.458586i	$-0.151644\pi$
$158$		−	20.1409i		−	1.60232i
$159$	−1.83669	+	1.81763i	−0.145659	+	0.144147i
$160$	5.40434	−	22.8762i	0.427251	−	1.80853i
$161$	−0.127408	+	5.81312i	−0.0100412	+	0.458138i
$162$	−20.1231	−	12.1850i	−1.58102	−	0.957345i
$163$	−7.60286	−	4.38952i	−0.595502	−	0.343813i	0.171768	−	0.985137i	$-0.445052\pi$
$163$	−7.60286	−	4.38952i	−0.595502	−	0.343813i	−0.767270	+	0.641324i	$0.778385\pi$
$164$	25.9614	−	44.9665i	2.02724	−	3.51129i
$165$	0.145843	−	0.267595i	0.0113538	−	0.0208322i
$166$	4.27618	+	7.40657i	0.331896	+	0.574861i
$167$	3.66245	+	2.11451i	0.283409	+	0.163626i	0.634965	−	0.772540i	$-0.281014\pi$
$167$	3.66245	+	2.11451i	0.283409	+	0.163626i	−0.351557	+	0.936167i	$0.614348\pi$
$168$	32.5192	+	9.66630i	2.50891	+	0.745771i
$169$	−6.49998	−	11.2583i	−0.499998	−	0.866023i
$170$	9.46110	+	31.5195i	0.725633	+	2.41743i
$171$	−0.239843	+	22.9811i	−0.0183413	+	1.75741i
$172$	−34.6726	+	20.0182i	−2.64376	+	1.52638i
$173$			6.57154i			0.499625i	0.968294	+	0.249812i	$0.0803689\pi$
$173$			6.57154i			0.499625i	−0.968294	+	0.249812i	$0.919631\pi$
$174$	−20.2052	+	19.9954i	−1.53175	+	1.51585i
$175$	11.1989	−	7.04156i	0.846561	−	0.532292i
$176$	0.381095	−	0.660076i	0.0287261	−	0.0497551i
$177$	2.87326	−	0.753840i	0.215967	−	0.0566621i
$178$	−20.1620	−	11.6405i	−1.51120	−	0.872494i
$179$	−11.1663	−	19.3407i	−0.834612	−	1.44559i	−0.894346	−	0.447375i	$-0.852359\pi$
$179$	−11.1663	−	19.3407i	−0.834612	−	1.44559i	0.0597347	−	0.998214i	$-0.480975\pi$
$180$	−31.1428	+	8.99484i	−2.32125	+	0.670436i
$181$	−15.0918			−1.12177			−0.560884	−	0.827895i	$-0.689539\pi$
$181$	−15.0918			−1.12177			−0.560884	+	0.827895i	$0.689539\pi$
$182$	−0.0208152	−	0.0379498i	−0.00154293	−	0.00281303i
$183$	−12.5534	+	3.29357i	−0.927977	+	0.243468i
$184$	−8.13486	−	14.0900i	−0.599710	−	1.03873i
$185$	5.19963	+	4.89851i	0.382284	+	0.360146i
$186$	−4.26867	−	16.2700i	−0.312994	−	1.19298i
$187$			0.443051i			0.0323991i
$188$			13.8248i			1.00828i
$189$	−3.05690	−	13.4036i	−0.222357	−	0.974965i
$190$	32.5907	+	30.7033i	2.36438	+	2.22745i
$191$	−4.86589			−0.352083			−0.176042	−	0.984383i	$-0.556329\pi$
$191$	−4.86589			−0.352083			−0.176042	+	0.984383i	$0.556329\pi$
$192$	−13.5785	+	3.56252i	−0.979945	+	0.257103i
$193$			9.20057i			0.662271i	0.943583	+	0.331136i	$0.107432\pi$
$193$			9.20057i			0.662271i	−0.943583	+	0.331136i	$0.892568\pi$
$194$	5.65923	+	9.80208i	0.406309	+	0.703748i
$195$	0.0212843	+	0.0116003i	0.00152420	+	0.000830711i
$196$	15.6132	+	30.0069i	1.11523	+	2.14335i
$197$		−	3.28084i		−	0.233750i	−0.993147	−	0.116875i	$-0.962712\pi$
$197$		−	3.28084i		−	0.233750i	0.993147	−	0.116875i	$-0.0372877\pi$
$198$	−0.617005	−	0.00643940i	−0.0438486	−	0.000457628i
$199$	−0.0653504	−	0.113190i	−0.00463257	−	0.00802384i	0.863700	−	0.504007i	$-0.168141\pi$
$199$	−0.0653504	−	0.113190i	−0.00463257	−	0.00802384i	−0.868332	+	0.495983i	$0.834808\pi$
$200$	−16.5649	+	33.1023i	−1.17131	+	2.34069i
$201$	0.204739	+	0.780362i	0.0144412	+	0.0550425i
$202$	23.1042	+	13.3392i	1.62561	+	0.938546i
$203$	−16.6083	−	0.364010i	−1.16568	−	0.0255485i
$204$	33.4962	−	33.1484i	2.34520	−	2.32086i
$205$	−16.4755	+	17.4882i	−1.15070	+	1.22143i
$206$	−20.3658	−	35.2746i	−1.41895	−	2.45769i
$207$	−3.35593	+	5.67503i	−0.233253	+	0.394442i
$208$	0.0525021	+	0.0303121i	0.00364037	+	0.00210177i
$209$	0.301406	+	0.522051i	0.0208487	+	0.0361110i
$210$	−23.2315	−	13.3299i	−1.60312	−	0.919849i
$211$	−1.44799	+	2.50799i	−0.0996838	+	0.172657i	−0.911554	−	0.411181i	$-0.865116\pi$
$211$	−1.44799	+	2.50799i	−0.0996838	+	0.172657i	0.811870	+	0.583838i	$0.198450\pi$
$212$	6.24335	−	3.60460i	0.428795	−	0.247565i
$213$	−4.30261	+	1.12885i	−0.294810	+	0.0773476i
$214$	2.14348	−	3.71261i	0.146525	−	0.253789i
$215$	17.7442	−	5.32623i	1.21015	−	0.363246i
$216$	26.7717	+	27.6233i	1.82159	+	1.87953i
$217$	5.10031	−	8.40321i	0.346232	−	0.570447i
$218$	8.45851	−	4.88352i	0.572882	−	0.330754i
$219$	7.39443	−	7.31766i	0.499669	−	0.494482i
$220$	−0.583027	+	0.618867i	−0.0393077	+	0.0417240i
$221$	−0.0352400			−0.00237050
$222$	3.81631	−	13.9511i	0.256134	−	0.936334i
$223$	15.5532	−	8.97964i	1.04152	−	0.601321i	0.121255	−	0.992621i	$-0.461308\pi$
$223$	15.5532	−	8.97964i	1.04152	−	0.601321i	0.920263	+	0.391300i	$0.127975\pi$
$224$	−23.7759	−	14.4307i	−1.58860	−	0.964195i
$225$	14.9819	−	0.737465i	0.998791	−	0.0491643i
$226$	−23.1783	+	40.1460i	−1.54180	+	2.67047i
$227$	−3.22762	−	1.86347i	−0.214224	−	0.123683i	0.389049	−	0.921217i	$-0.372804\pi$
$227$	−3.22762	−	1.86347i	−0.214224	−	0.123683i	−0.603273	+	0.797535i	$0.706137\pi$
$228$	16.9181	−	61.8464i	1.12043	−	4.09588i
$229$	1.92393	+	3.33235i	0.127137	+	0.220208i	0.922566	−	0.385839i	$-0.126088\pi$
$229$	1.92393	+	3.33235i	0.127137	+	0.220208i	−0.795429	+	0.606047i	$0.792754\pi$
$230$	3.69284	+	12.3026i	0.243499	+	0.811213i
$231$	−0.247967	−	0.261802i	−0.0163151	−	0.0172253i
$232$	40.2557	−	23.2416i	2.64291	−	1.52589i
$233$	6.97761	+	4.02853i	0.457119	+	0.263918i	0.710832	−	0.703362i	$-0.248319\pi$
$233$	6.97761	+	4.02853i	0.457119	+	0.263918i	−0.253713	+	0.967279i	$0.581652\pi$
$234$	0.000512186	−	0.0490762i	3.34827e−5	−	0.00320821i
$235$	1.47082	−	6.22589i	0.0959457	−	0.406132i
$236$	−8.28743			−0.539465
$237$	12.9093	−	3.38693i	0.838547	−	0.220005i
$238$	38.9289	+	0.853217i	2.52339	+	0.0553058i
$239$	−5.23027	+	9.05909i	−0.338318	+	0.585984i	−0.984116	−	0.177524i	$-0.943191\pi$
$239$	−5.23027	+	9.05909i	−0.338318	+	0.585984i	0.645798	+	0.763508i	$0.276525\pi$
$240$	37.5033	−	0.922469i	2.42083	−	0.0595451i
$241$	4.15257	−	7.19246i	0.267490	−	0.463307i	−0.700723	−	0.713434i	$-0.747139\pi$
$241$	4.15257	−	7.19246i	0.267490	−	0.463307i	0.968213	+	0.250127i	$0.0804723\pi$
$242$	24.8863	−	14.3681i	1.59975	−	0.923619i
$243$	4.42602	−	14.9469i	0.283930	−	0.958845i
$244$	36.2083			2.31800
$245$	−3.83884	−	15.1744i	−0.245254	−	0.969459i
$246$	46.9225	+	12.8356i	2.99167	+	0.818370i
$247$	−0.0415236	+	0.0239737i	−0.00264208	+	0.00152541i
$248$			27.5053i			1.74659i
$249$	−4.02814	+	3.98632i	−0.255273	+	0.252622i
$250$	18.7362	−	22.4274i	1.18498	−	1.41843i
$251$	−1.16808			−0.0737287			−0.0368644	−	0.999320i	$-0.511737\pi$
$251$	−1.16808			−0.0737287			−0.0368644	+	0.999320i	$0.511737\pi$
$252$	−1.24056	+	38.3348i	−0.0781481	+	2.41487i
$253$			0.172931i			0.0108721i
$254$	−17.3895			−1.09111
$255$	−18.6114	+	11.3645i	−1.16549	+	0.711670i
$256$	−15.7897			−0.986859
$257$	−19.2510	+	11.1146i	−1.20084	+	0.693307i	−0.960743	−	0.277442i	$-0.910513\pi$
$257$	−19.2510	+	11.1146i	−1.20084	+	0.693307i	−0.240100	+	0.970748i	$0.577180\pi$
$258$	−26.3849	−	26.6617i	−1.64265	−	1.65988i
$259$	7.41090	−	4.06482i	0.460491	−	0.252576i
$260$	−0.0492243	−	0.0463737i	−0.00305276	−	0.00287597i
$261$	−16.2138	−	9.58802i	−1.00361	−	0.593484i
$262$	23.0602	−	13.3138i	1.42467	−	0.822531i
$263$	17.2010	+	9.93100i	1.06066	+	0.612372i	0.925614	−	0.378468i	$-0.123549\pi$
$263$	17.2010	+	9.93100i	1.06066	+	0.612372i	0.135044	+	0.990840i	$0.456882\pi$
$264$	0.973229	+	0.266227i	0.0598981	+	0.0163851i
$265$	−3.19513	+	0.959071i	−0.196275	+	0.0589153i
$266$	46.4507	−	25.4778i	2.84807	−	1.56215i
$267$	4.07050	−	14.8803i	0.249110	−	0.910658i
$268$		−	2.25082i		−	0.137491i
$269$	11.4230	+	19.7853i	0.696475	+	1.20633i	0.969681	+	0.244375i	$0.0785828\pi$
$269$	11.4230	+	19.7853i	0.696475	+	1.20633i	−0.273205	+	0.961956i	$0.588084\pi$
$270$	−15.5559	−	26.0839i	−0.946704	−	1.58741i
$271$	−1.22023	+	2.11350i	−0.0741237	+	0.128386i	−0.900705	−	0.434432i	$-0.856949\pi$
$271$	−1.22023	+	2.11350i	−0.0741237	+	0.128386i	0.826581	+	0.562818i	$0.190283\pi$
$272$	−47.2314	+	27.2690i	−2.86382	+	1.65343i
$273$	0.0208236	−	0.0197232i	0.00126030	−	0.00119370i
$274$	−13.9848	+	24.2224i	−0.844854	+	1.46333i
$275$	0.328402	−	0.216673i	0.0198034	−	0.0130659i
$276$	13.0742	−	12.9385i	0.786974	−	0.778804i
$277$	−26.4943	−	15.2965i	−1.59189	−	0.919075i	−0.992984	−	0.118253i	$-0.962271\pi$
$277$	−26.4943	−	15.2965i	−1.59189	−	0.919075i	−0.598902	−	0.800823i	$-0.704396\pi$
$278$	4.60986	+	2.66150i	0.276481	+	0.159626i
$279$	9.71041	−	5.47199i	0.581347	−	0.327600i
$280$	31.2131	+	30.7240i	1.86534	+	1.83611i
$281$	−14.5211	−	25.1513i	−0.866256	−	1.50040i	−0.865795	−	0.500399i	$-0.833187\pi$
$281$	−14.5211	−	25.1513i	−0.866256	−	1.50040i	−0.000460513	−	1.00000i	$-0.500147\pi$
$282$	−12.5284	+	3.28701i	−0.746057	+	0.195739i
$283$			28.5899i			1.69949i	0.527192	+	0.849746i	$0.323245\pi$
$283$			28.5899i			1.69949i	−0.527192	+	0.849746i	$0.676755\pi$
$284$	12.4102			0.736407
$285$	−14.1987	+	26.0521i	−0.841060	+	1.54319i
$286$	−0.000643654	−	0.00111484i	−3.80600e−5	−	6.59219e-5i
$287$	13.6715	+	24.9255i	0.807000	+	1.47131i
$288$	−15.4824	−	27.4745i	−0.912308	−	1.61895i
$289$	7.35113	−	12.7325i	0.432419	−	0.748972i
$290$	−35.1492	+	10.5506i	−2.06403	+	0.619553i
$291$	−5.33096	+	5.27561i	−0.312506	+	0.309262i
$292$	−25.1354	+	14.5119i	−1.47094	+	0.849247i
$293$	−0.357409	−	0.206350i	−0.0208801	−	0.0120551i	0.489524	−	0.871990i	$-0.337171\pi$
$293$	−0.357409	−	0.206350i	−0.0208801	−	0.0120551i	−0.510404	+	0.859935i	$0.670504\pi$
$294$	−23.4809	+	21.2836i	−1.36943	+	1.24128i
$295$	3.73217	+	0.881697i	0.217295	+	0.0513344i
$296$	−11.8255	+	20.4824i	−0.687344	+	1.19051i
$297$	−0.0996294	−	0.396551i	−0.00578108	−	0.0230102i
$298$	8.29056	−	4.78656i	0.480259	−	0.277278i
$299$	−0.0137548			−0.000795463
$300$	−40.9518	−	8.61720i	−2.36435	−	0.497514i
$301$	0.480327	−	21.9154i	0.0276856	−	1.26318i
$302$	39.0097	+	22.5222i	2.24475	+	1.29601i
$303$	−4.66451	+	17.0518i	−0.267969	+	0.979599i
$304$	−37.1021	+	64.2627i	−2.12795	+	3.68572i
$305$	−16.3061	−	3.85219i	−0.933684	−	0.220576i
$306$	38.0041	+	22.4737i	2.17255	+	1.28474i
$307$			9.52628i			0.543693i	0.962341	+	0.271847i	$0.0876344\pi$
$307$			9.52628i			0.543693i	−0.962341	+	0.271847i	$0.912366\pi$
$308$	0.483800	+	0.882055i	0.0275671	+	0.0502597i
$309$	19.1844	−	18.9852i	1.09136	−	1.08003i
$310$	4.99267	−	21.1337i	0.283565	−	1.20031i
$311$	23.8703			1.35356			0.676780	−	0.736185i	$-0.263375\pi$
$311$	23.8703			1.35356			0.676780	+	0.736185i	$0.263375\pi$
$312$	−0.0211755	+	0.0774101i	−0.00119883	+	0.00438249i
$313$		−	30.8689i		−	1.74482i	−0.488779	−	0.872408i	$-0.662558\pi$
$313$		−	30.8689i		−	1.74482i	0.488779	−	0.872408i	$-0.337442\pi$
$314$	−30.0388			−1.69519
$315$	4.63711	−	17.1318i	0.261271	−	0.965265i
$316$	−37.2346			−2.09461
$317$		−	22.8634i		−	1.28414i	−0.766648	−	0.642068i	$-0.778077\pi$
$317$		−	22.8634i		−	1.28414i	0.766648	−	0.642068i	$-0.221923\pi$
$318$	4.75102	+	4.80086i	0.266424	+	0.269219i
$319$	−0.494071			−0.0276627
$320$	−17.6376	−	4.16675i	−0.985971	−	0.232928i
$321$	2.74004	+	0.749538i	0.152934	+	0.0418351i
$322$	15.1947	+	0.333026i	0.846766	+	0.0185588i
$323$		−	43.1339i		−	2.40003i
$324$	−22.5265	+	37.2017i	−1.25147	+	2.06676i
$325$	0.0172340	+	0.0261209i	0.000955973	+	0.00144893i
$326$	−11.4736	+	19.8728i	−0.635463	+	1.10065i
$327$	4.55248	+	4.60024i	0.251753	+	0.254394i
$328$	−68.8896	−	39.7734i	−3.80379	−	2.19612i
$329$	−6.47074	−	3.92740i	−0.356744	−	0.216525i
$330$	−0.699455	−	0.381213i	−0.0385037	−	0.0209851i
$331$	26.1163			1.43548			0.717741	−	0.696310i	$-0.245176\pi$
$331$	26.1163			1.43548			0.717741	+	0.696310i	$0.245176\pi$
$332$	13.6926	−	7.90541i	0.751478	−	0.433866i
$333$	9.58367	+	0.100020i	0.525182	+	0.00548109i
$334$	5.52704	−	9.57312i	0.302426	−	0.523818i
$335$	−0.239465	+	1.01364i	−0.0130833	+	0.0553810i
$336$	12.6473	−	42.5480i	0.689969	−	2.32118i
$337$	−19.4080	−	11.2052i	−1.05722	−	0.610388i	−0.132561	−	0.991175i	$-0.542320\pi$
$337$	−19.4080	−	11.2052i	−1.05722	−	0.610388i	−0.924663	+	0.380786i	$0.875653\pi$
$338$	−29.4276	+	16.9900i	−1.60065	+	0.924136i
$339$	−29.6292	−	8.10508i	−1.60924	−	0.440207i
$340$	58.2703	−	17.4908i	3.16015	−	0.948572i
$341$	0.146177	−	0.253186i	0.00791593	−	0.0137108i
$342$	60.0694	+	0.626917i	3.24818	+	0.0338998i
$343$	−18.4803	−	1.21667i	−0.997840	−	0.0656941i
$344$	30.6684	+	53.1192i	1.65353	+	2.86400i
$345$	−7.26437	+	4.43576i	−0.391100	+	0.238813i
$346$	17.1771			0.923445
$347$		−	22.1089i		−	1.18687i	−0.804884	−	0.593433i	$-0.797772\pi$
$347$		−	22.1089i		−	1.18687i	0.804884	−	0.593433i	$-0.202228\pi$
$348$	36.9657	+	37.3535i	1.98157	+	2.00236i
$349$	−8.79455	−	15.2326i	−0.470762	−	0.815383i	0.528679	−	0.848822i	$-0.322688\pi$
$349$	−8.79455	−	15.2326i	−0.470762	−	0.815383i	−0.999441	+	0.0334386i	$0.989354\pi$
$350$	−18.4056	−	29.2725i	−0.983823	−	1.56468i
$351$	0.0315415	−	0.00792447i	0.00168356	−	0.000422977i
$352$	−0.716361	−	0.413591i	−0.0381822	−	0.0220445i
$353$	−26.0458	−	15.0376i	−1.38628	−	0.800368i	−0.393385	−	0.919374i	$-0.628696\pi$
$353$	−26.0458	−	15.0376i	−1.38628	−	0.800368i	−0.992894	+	0.119005i	$0.962029\pi$
$354$	−1.97043	−	7.51029i	−0.104727	−	0.399167i
$355$	−5.58880	−	1.32031i	−0.296623	−	0.0700749i
$356$	−21.5199	+	37.2736i	−1.14055	+	1.97550i
$357$	5.99949	+	25.0949i	0.317527	+	1.32816i
$358$	−50.5538	+	29.1872i	−2.67185	+	1.54259i
$359$	1.72687	−	2.99102i	0.0911405	−	0.157860i	−0.816851	−	0.576849i	$-0.804282\pi$
$359$	1.72687	−	2.99102i	0.0911405	−	0.157860i	0.907991	+	0.418989i	$0.137615\pi$
$360$	13.7803	+	47.7115i	0.726285	+	2.51462i
$361$	−19.8438	−	34.3705i	−1.04441	−	1.80897i
$362$			39.4479i			2.07334i
$363$	13.3942	+	13.5347i	0.703011	+	0.710387i
$364$	−0.0701582	+	0.0384812i	−0.00367729	+	0.00201696i
$365$	12.8634	−	3.86117i	0.673302	−	0.202103i
$366$	8.60894	+	32.8129i	0.449997	+	1.71516i
$367$	17.2042	+	9.93286i	0.898053	+	0.518491i	0.876568	−	0.481278i	$-0.159827\pi$
$367$	17.2042	+	9.93286i	0.898053	+	0.518491i	0.0214849	+	0.999769i	$0.493161\pi$
$368$	−18.4353	+	10.6436i	−0.961006	+	0.554837i
$369$	−0.336405	+	32.2333i	−0.0175125	+	1.67800i
$370$	12.8040	−	13.5911i	0.665649	−	0.706567i
$371$	−0.0864906	+	3.94622i	−0.00449037	+	0.204878i
$372$	−30.0785	+	7.89152i	−1.55950	+	0.409156i
$373$	19.2818	−	11.1324i	0.998374	−	0.576411i	0.0906071	−	0.995887i	$-0.471119\pi$
$373$	19.2818	−	11.1324i	0.998374	−	0.576411i	0.907767	+	0.419475i	$0.137786\pi$
$374$	1.15807			0.0598825
$375$	17.5255	+	8.23753i	0.905013	+	0.425384i
$376$	21.1799			1.09227
$377$		−	0.0392982i		−	0.00202396i
$378$	−35.0350	+	7.99032i	−1.80201	+	0.410978i
$379$	−10.2046			−0.524173			−0.262086	−	0.965044i	$-0.584411\pi$
$379$	−10.2046			−0.524173			−0.262086	+	0.965044i	$0.584411\pi$
$380$	56.7615	−	60.2506i	2.91180	−	3.09079i
$381$	−2.92425	−	11.1458i	−0.149814	−	0.571015i
$382$			12.7188i			0.650748i
$383$	11.8711	−	6.85380i	0.606587	−	0.350213i	−0.165042	−	0.986287i	$-0.552776\pi$
$383$	11.8711	−	6.85380i	0.606587	−	0.350213i	0.771628	+	0.636074i	$0.219443\pi$
$384$	0.0706347	+	0.269224i	0.00360456	+	0.0137388i
$385$	−0.124034	−	0.448697i	−0.00632134	−	0.0228677i
$386$	24.0490			1.22406
$387$	12.6518	−	21.3948i	0.643129	−	1.08756i
$388$	18.1212	−	10.4623i	0.919963	−	0.531141i
$389$	−18.6949	+	32.3804i	−0.947867	+	1.64175i	−0.197960	+	0.980210i	$0.563432\pi$
$389$	−18.6949	+	32.3804i	−0.947867	+	1.64175i	−0.749907	+	0.661543i	$0.769902\pi$
$390$	0.0303214	−	0.0556343i	0.00153539	−	0.00281715i
$391$	6.18699	−	10.7162i	0.312890	−	0.541941i
$392$	45.9713	−	23.9198i	2.32190	−	1.20813i
$393$	12.4113	+	12.5415i	0.626069	+	0.632637i
$394$	−8.57564			−0.432035
$395$	16.7683	+	3.96138i	0.843704	+	0.199319i
$396$	−0.0119046	+	1.14066i	−0.000598227	+	0.0573204i
$397$	−1.68317	−	0.971776i	−0.0844756	−	0.0487720i	0.457167	−	0.889381i	$-0.348864\pi$
$397$	−1.68317	−	0.971776i	−0.0844756	−	0.0487720i	−0.541643	+	0.840609i	$0.682197\pi$
$398$	−0.295863	+	0.170817i	−0.0148303	+	0.00856227i
$399$	24.1412	+	25.4881i	1.20857	+	1.27600i
$400$	43.3110	+	21.6734i	2.16555	+	1.08367i
$401$	3.41829	+	5.92065i	0.170701	+	0.295663i	0.938665	−	0.344830i	$-0.112063\pi$
$401$	3.41829	+	5.92065i	0.170701	+	0.295663i	−0.767964	+	0.640493i	$0.778730\pi$
$402$	2.03976	−	0.535159i	0.101734	−	0.0266913i
$403$	0.0201383	+	0.0116268i	0.00100316	+	0.000579174i
$404$	24.6604	−	42.7130i	1.22690	−	2.12505i
$405$	14.1025	−	14.3569i	0.700759	−	0.713398i
$406$	−0.951470	+	43.4118i	−0.0472207	+	2.15449i
$407$	0.217708	−	0.125694i	0.0107914	−	0.00623040i
$408$	−50.7842	−	51.3169i	−2.51419	−	2.54057i
$409$	−6.20176			−0.306657			−0.153329	−	0.988175i	$-0.548999\pi$
$409$	−6.20176			−0.306657			−0.153329	+	0.988175i	$0.548999\pi$
$410$	45.7117	+	43.0645i	2.25754	+	2.12681i
$411$	−17.8770	−	4.89026i	−0.881809	−	0.241219i
$412$	−65.2123	+	37.6504i	−3.21278	+	1.85490i
$413$	2.35432	−	3.87895i	0.115848	−	0.190871i
$414$	14.8337	+	8.77192i	0.729038	+	0.431117i
$415$	−7.00738	+	2.10338i	−0.343979	+	0.103251i
$416$	0.0328968	−	0.0569790i	0.00161290	−	0.00279362i
$417$	−0.930684	+	3.40225i	−0.0455758	+	0.166609i
$418$	1.36457	−	0.787833i	0.0667432	−	0.0385342i
$419$	10.3308	−	17.8934i	0.504691	−	0.874150i	−0.495295	−	0.868725i	$-0.664940\pi$
$419$	10.3308	−	17.8934i	0.504691	−	0.874150i	0.999985	−	0.00542492i	$-0.00172681\pi$
$420$	−24.6430	+	42.9482i	−1.20246	+	2.09566i
$421$	8.45803	+	14.6497i	0.412219	+	0.713985i	0.995132	−	0.0985499i	$-0.0314204\pi$
$421$	8.45803	+	14.6497i	0.412219	+	0.713985i	−0.582913	+	0.812535i	$0.698087\pi$
$422$	6.55555	+	3.78485i	0.319119	+	0.184243i
$423$	−4.21361	−	7.47733i	−0.204873	−	0.363560i
$424$	−5.52233	−	9.56496i	−0.268188	−	0.464515i
$425$	−28.1024	+	1.67746i	−1.36316	+	0.0813688i
$426$	2.95066	+	11.2464i	0.142960	+	0.544891i
$427$	−10.2862	+	16.9474i	−0.497783	+	0.820141i
$428$	−6.86353	−	3.96266i	−0.331761	−	0.191542i
$429$	0.000606317	0	0.000600022i	2.92733e−5	0	2.89694e-5i
$430$	−13.9220	−	46.3809i	−0.671379	−	2.23669i
$431$	3.57938	+	6.19967i	0.172413	+	0.298627i	0.939263	−	0.343199i	$-0.111510\pi$
$431$	3.57938	+	6.19967i	0.172413	+	0.298627i	−0.766850	+	0.641826i	$0.778177\pi$
$432$	36.1422	−	35.0280i	1.73889	−	1.68529i
$433$			19.0591i			0.915923i	0.888972	+	0.457961i	$0.151420\pi$
$433$			19.0591i			0.915923i	−0.888972	+	0.457961i	$0.848580\pi$
$434$	−21.9648	−	13.3315i	−1.05434	−	0.639932i
$435$	−12.6731	−	20.7546i	−0.607631	−	0.995106i
$436$	−9.02820	−	15.6373i	−0.432373	−	0.748891i
$437$		−	16.8360i		−	0.805373i
$438$	−19.1273	−	19.3280i	−0.913940	−	0.923528i
$439$	−15.3897			−0.734512			−0.367256	−	0.930120i	$-0.619703\pi$
$439$	−15.3897			−0.734512			−0.367256	+	0.930120i	$0.619703\pi$
$440$	0.948118	+	0.893211i	0.0451997	+	0.0425822i
$441$	−17.5903	−	11.4709i	−0.837632	−	0.546235i
$442$			0.0921125i			0.00438135i
$443$		−	0.0510054i		−	0.00242334i	−0.999999	−	0.00121167i	$-0.999614\pi$
$443$		−	0.0510054i		−	0.00242334i	0.999999	−	0.00121167i	$-0.000385686\pi$
$444$	−25.7914	−	7.05524i	−1.22401	−	0.334827i
$445$	13.6568	−	14.4963i	0.647396	−	0.687192i
$446$	−23.4715	−	40.6538i	−1.11141	−	1.92502i
$447$	4.46209	+	4.50890i	0.211050	+	0.213264i
$448$	−11.1261	+	18.3312i	−0.525659	+	0.866070i
$449$	16.4622			0.776901			0.388450	−	0.921470i	$-0.373010\pi$
$449$	16.4622			0.776901			0.388450	+	0.921470i	$0.373010\pi$
$450$	−1.92763	−	39.1605i	−0.0908694	−	1.84604i
$451$	0.422753	+	0.732229i	0.0199066	+	0.0344793i
$452$	74.2183	+	42.8499i	3.49093	+	2.01549i
$453$	−7.87565	+	28.7906i	−0.370030	+	1.35270i
$454$	−4.87084	+	8.43654i	−0.228600	+	0.395946i
$455$	0.0356891	−	0.00986556i	0.00167313	−	0.000462505i
$456$	−94.7501	−	25.9189i	−4.43708	−	1.21376i
$457$		−	13.4836i		−	0.630737i	−0.948969	−	0.315369i	$-0.897872\pi$
$457$		−	13.4836i		−	0.630737i	0.948969	−	0.315369i	$-0.102128\pi$
$458$	8.71030	−	5.02889i	0.407006	−	0.234985i
$459$	−8.01366	+	28.1379i	−0.374046	+	1.31337i
$460$	22.7440	−	6.82699i	1.06044	−	0.318310i
$461$	4.33126	+	7.50196i	0.201727	+	0.349401i	0.949085	−	0.315020i	$-0.102011\pi$
$461$	4.33126	+	7.50196i	0.201727	+	0.349401i	−0.747358	+	0.664422i	$0.768678\pi$
$462$	−0.684313	+	0.648152i	−0.0318371	+	0.0301547i
$463$	−4.00270	−	2.31096i	−0.186021	−	0.107399i	0.404097	−	0.914716i	$-0.367586\pi$
$463$	−4.00270	−	2.31096i	−0.186021	−	0.107399i	−0.590119	+	0.807317i	$0.700919\pi$
$464$	−30.4092	−	52.6704i	−1.41171	−	2.44516i
$465$	14.3852	−	0.353832i	0.667096	−	0.0164086i
$466$	10.5300	−	18.2385i	0.487793	−	0.844882i
$467$	24.0472	+	13.8837i	1.11277	+	0.642459i	0.939546	−	0.342423i	$-0.111248\pi$
$467$	24.0472	+	13.8837i	1.11277	+	0.642459i	0.173226	+	0.984882i	$0.444581\pi$
$468$	−0.0907276		0.000946883i	−0.00419388		4.37697e-5i
$469$	1.05350	+	0.639421i	0.0486463	+	0.0295257i
$470$	−16.2736	−	3.84452i	−0.750645	−	0.177334i
$471$	−5.05139	−	19.2533i	−0.232756	−	0.887147i
$472$			12.6965i			0.584405i
$473$		−	0.651950i		−	0.0299767i
$474$	−8.85296	−	33.7430i	−0.406630	−	1.54987i
$475$	−31.9721	+	21.0945i	−1.46698	+	0.967882i
$476$	1.57735	−	71.9681i	0.0722976	−	3.29865i
$477$	−2.27816	+	3.85248i	−0.104310	+	0.176393i
$478$	23.6792	+	13.6712i	1.08306	+	0.625306i
$479$	9.56012	−	16.5586i	0.436813	−	0.756582i	−0.560629	−	0.828067i	$-0.689440\pi$
$479$	9.56012	−	16.5586i	0.436813	−	0.756582i	0.997442	+	0.0714851i	$0.0227738\pi$
$480$	−1.00113	−	40.7012i	−0.0456951	−	1.85775i
$481$	0.00999760	+	0.0173163i	0.000455851	+	0.000789557i
$482$	−18.8001	−	10.8542i	−0.856320	−	0.494397i
$483$	2.34171	+	9.79501i	0.106552	+	0.445688i
$484$	−26.5625	−	46.0076i	−1.20739	−	2.09125i
$485$	−9.27379	+	2.78368i	−0.421101	+	0.126400i
$486$	−39.0691	−	11.5690i	−1.77221	−	0.524781i
$487$	−33.2053	+	19.1711i	−1.50468	+	0.868726i	−0.504692	+	0.863299i	$0.668394\pi$
$487$	−33.2053	+	19.1711i	−1.50468	+	0.868726i	−0.999985	+	0.00542631i	$0.998273\pi$
$488$		−	55.4719i		−	2.51110i
$489$	−14.6669	−	4.01212i	−0.663259	−	0.181434i
$490$	−39.6638	+	10.0342i	−1.79183	+	0.453298i
$491$	−11.2096	+	19.4155i	−0.505880	+	0.876210i	0.494097	+	0.869407i	$0.335499\pi$
$491$	−11.2096	+	19.4155i	−0.505880	+	0.876210i	−0.999977	+	0.00680296i	$0.997835\pi$
$492$	23.7293	−	86.7459i	1.06980	−	3.91081i
$493$	30.6166	+	17.6765i	1.37890	+	0.796109i
$494$	0.0626638	+	0.108537i	0.00281938	+	0.00488331i
$495$	0.126716	−	0.512420i	0.00569545	−	0.0230316i
$496$	35.9878			1.61590
$497$	−3.52552	+	5.80860i	−0.158141	+	0.260551i
$498$	10.4197	+	10.5290i	0.466917	+	0.471815i
$499$	5.28162	+	9.14804i	0.236438	+	0.409522i	0.959690	−	0.281062i	$-0.0906867\pi$
$499$	5.28162	+	9.14804i	0.236438	+	0.409522i	−0.723252	+	0.690585i	$0.757353\pi$
$500$	−41.4616	−	34.6378i	−1.85422	−	1.54905i
$501$	7.06531	+	1.93271i	0.315655	+	0.0863473i
$502$			3.05320i			0.136271i
$503$		−	27.4063i		−	1.22199i	−0.791636	−	0.610993i	$-0.790771\pi$
$503$		−	27.4063i		−	1.22199i	0.791636	−	0.610993i	$-0.209229\pi$
$504$	58.7298	+	1.90057i	2.61603	+	0.0846581i
$505$	−15.6498	+	16.6118i	−0.696407	+	0.739216i
$506$	0.452018			0.0200946
$507$	−15.8383	−	16.0045i	−0.703405	−	0.710785i
$508$			32.1481i			1.42634i
$509$	8.34654	+	14.4566i	0.369954	+	0.640779i	0.989558	−	0.144135i	$-0.0460401\pi$
$509$	8.34654	+	14.4566i	0.369954	+	0.640779i	−0.619604	+	0.784915i	$0.712707\pi$
$510$	29.7051	+	48.6475i	1.31536	+	2.15415i
$511$	0.348206	−	15.8873i	0.0154037	−	0.702812i
$512$			41.5936i			1.83819i
$513$	9.69956	+	38.6068i	0.428246	+	1.70453i
$514$	29.0519	+	50.3193i	1.28142	+	2.21949i
$515$	33.3734	−	10.0176i	1.47061	−	0.441427i
$516$	−49.2897	+	48.7779i	−2.16986	+	2.14733i
$517$	−0.194961	−	0.112561i	−0.00857439	−	0.00495043i
$518$	−10.6249	−	19.3710i	−0.466830	−	0.851115i
$519$	2.88853	+	11.0096i	0.126792	+	0.483269i
$520$	−0.0710455	+	0.0754128i	−0.00311555	+	0.00330707i
$521$	6.22446	+	10.7811i	0.272699	+	0.472328i	0.969552	−	0.244886i	$-0.0787505\pi$
$521$	6.22446	+	10.7811i	0.272699	+	0.472328i	−0.696853	+	0.717214i	$0.745417\pi$
$522$	−25.0617	+	42.3806i	−1.09692	+	1.85495i
$523$	−0.196990	−	0.113732i	−0.00861378	−	0.00497317i	0.495687	−	0.868501i	$-0.334916\pi$
$523$	−0.196990	−	0.113732i	−0.00861378	−	0.00497317i	−0.504301	+	0.863528i	$0.668250\pi$
$524$	−24.6134	−	42.6316i	−1.07524	−	1.86237i
$525$	15.6670	−	16.7196i	0.683765	−	0.729702i
$526$	25.9582	−	44.9610i	1.13183	−	1.96039i
$527$	−18.1166	+	10.4596i	−0.789170	+	0.455628i
$528$	0.348330	−	1.27337i	0.0151591	−	0.0554163i
$529$	−9.08510	+	15.7359i	−0.395004	+	0.684168i
$530$	2.50688	+	8.35162i	0.108892	+	0.362771i
$531$	4.48236	−	2.52589i	0.194518	−	0.109614i
$532$	−47.1011	−	85.8737i	−2.04209	−	3.72310i
$533$	−0.0582411	+	0.0336255i	−0.00252270	+	0.00145648i
$534$	−38.8950	−	10.6397i	−1.68315	−	0.460425i
$535$	2.66934	+	2.51476i	0.115406	+	0.108722i
$536$	−3.44831			−0.148944
$537$	−27.2087	−	27.4942i	−1.17414	−	1.18646i
$538$	51.7160	−	29.8582i	2.22963	−	1.28728i
$539$	−0.550287	−	0.0241332i	−0.0237026	−	0.00103949i
$540$	−48.2214	+	28.7584i	−2.07512	+	1.23756i
$541$	16.3403	−	28.3022i	0.702523	−	1.21681i	−0.265055	−	0.964233i	$-0.585390\pi$
$541$	16.3403	−	28.3022i	0.702523	−	1.21681i	0.967578	−	0.252573i	$-0.0812766\pi$
$542$	5.52439	+	3.18951i	0.237293	+	0.137001i
$543$	−25.2841	+	6.63364i	−1.08504	+	0.284677i
$544$	29.5943	+	51.2588i	1.26884	+	2.19770i
$545$	2.40212	+	8.00263i	0.102896	+	0.342795i
$546$	−0.0515536	−	0.0544299i	−0.00220629	−	0.00232938i
$547$	−23.4381	+	13.5320i	−1.00214	+	0.578586i	−0.908881	−	0.417055i	$-0.863062\pi$
$547$	−23.4381	+	13.5320i	−1.00214	+	0.578586i	−0.0932600	+	0.995642i	$0.529729\pi$
$548$	44.7802	+	25.8538i	1.91291	+	1.10442i
$549$	−19.5837	+	11.0358i	−0.835812	+	0.470995i
$550$	−0.566353	−	0.858397i	−0.0241494	−	0.0366022i
$551$	48.1010			2.04917
$552$	−19.8220	−	20.0300i	−0.843681	−	0.852532i
$553$	10.5777	−	17.4277i	0.449811	−	0.741103i
$554$	−39.9828	+	69.2522i	−1.69871	+	2.94225i
$555$	10.8643	+	5.92121i	0.461165	+	0.251341i
$556$	4.92034	−	8.52228i	0.208669	−	0.361425i
$557$	−0.714474	+	0.412502i	−0.0302732	+	0.0174783i	−0.515060	−	0.857154i	$-0.672230\pi$
$557$	−0.714474	+	0.412502i	−0.0302732	+	0.0174783i	0.484787	+	0.874632i	$0.338897\pi$
$558$	−14.3030	−	25.3817i	−0.605495	−	1.07449i
$559$	0.0518557			0.00219326
$560$	40.1992	−	40.8391i	1.69873	−	1.72577i
$561$	0.194744	+	0.742265i	0.00822209	+	0.0313385i
$562$	−65.7419	+	37.9561i	−2.77315	+	1.60108i
$563$		−	16.3272i		−	0.688110i	−0.938949	−	0.344055i	$-0.888199\pi$
$563$		−	16.3272i		−	0.688110i	0.938949	−	0.344055i	$-0.111801\pi$
$564$	6.07673	+	23.1614i	0.255876	+	0.975271i
$565$	−28.8647	−	27.1932i	−1.21435	−	1.14402i
$566$	74.7299			3.14113
$567$	−11.0129	−	21.1120i	−0.462500	−	0.886619i
$568$		−	19.0126i		−	0.797752i
$569$	14.9066			0.624918			0.312459	−	0.949931i	$-0.398847\pi$
$569$	14.9066			0.624918			0.312459	+	0.949931i	$0.398847\pi$
$570$	68.0965	+	37.1135i	2.85225	+	1.55451i
$571$	18.9285			0.792134			0.396067	−	0.918222i	$-0.370375\pi$
$571$	18.9285			0.792134			0.396067	+	0.918222i	$0.370375\pi$
$572$	−0.00206101	+	0.00118993i	−8.61753e−5	+	4.97534e-5i
$573$	−8.15206	+	2.13881i	−0.340557	+	0.0893501i
$574$	65.1518	−	35.7353i	2.71938	−	1.49156i
$575$	−10.9689	+	0.654744i	−0.457434	+	0.0273047i
$576$	−21.1829	+	11.9369i	−0.882619	+	0.497372i
$577$	−31.9513	+	18.4471i	−1.33015	+	0.767963i	−0.985323	−	0.170702i	$-0.945396\pi$
$577$	−31.9513	+	18.4471i	−1.33015	+	0.767963i	−0.344829	+	0.938666i	$0.612063\pi$
$578$	−33.2810	−	19.2148i	−1.38431	−	0.799231i
$579$	4.04413	+	15.4142i	0.168068	+	0.640591i
$580$	19.5050	+	64.9805i	0.809900	+	2.69817i
$581$	−0.189686	+	8.65464i	−0.00786951	+	0.359055i
$582$	13.7897	+	13.9344i	0.571602	+	0.577599i
$583$			0.117394i			0.00486196i
$584$	22.2326	+	38.5080i	0.919992	+	1.59347i
$585$	0.0407576	+	0.0100789i	0.00168512	+	0.000416711i
$586$	−0.539371	+	0.934217i	−0.0222812	+	0.0385922i
$587$	17.1035	−	9.87469i	0.705936	−	0.407572i	−0.103619	−	0.994617i	$-0.533042\pi$
$587$	17.1035	−	9.87469i	0.705936	−	0.407572i	0.809554	+	0.587045i	$0.199709\pi$
$588$	39.3471	+	43.4092i	1.62265	+	1.79017i
$589$	−14.2313	+	24.6493i	−0.586389	+	1.01566i
$590$	2.30463	−	9.75536i	0.0948802	−	0.401622i
$591$	−1.44210	−	5.49654i	−0.0593199	−	0.226098i
$592$	26.7991	+	15.4724i	1.10143	+	0.635914i
$593$	13.3709	+	7.71968i	0.549076	+	0.317009i	0.748749	−	0.662853i	$-0.230655\pi$
$593$	13.3709	+	7.71968i	0.549076	+	0.317009i	−0.199673	+	0.979863i	$0.563988\pi$
$594$	−1.03653	+	0.260417i	−0.0425293	+	0.0106850i
$595$	−8.36702	+	32.2424i	−0.343014	+	1.32181i
$596$	−8.84894	−	15.3268i	−0.362467	−	0.627811i
$597$	−0.159238	−	0.160908i	−0.00651716	−	0.00658554i
$598$			0.0359532i			0.00147024i
$599$	41.3447			1.68930			0.844648	−	0.535322i	$-0.179810\pi$
$599$	41.3447			1.68930			0.844648	+	0.535322i	$0.179810\pi$
$600$	−13.2017	+	62.7391i	−0.538959	+	2.56131i
$601$	20.4247	+	35.3766i	0.833142	+	1.44304i	0.895535	+	0.444992i	$0.146793\pi$
$601$	20.4247	+	35.3766i	0.833142	+	1.44304i	−0.0623931	+	0.998052i	$0.519873\pi$
$602$	−57.2839	−	1.25551i	−2.33472	−	0.0511707i
$603$	0.686019	+	1.21739i	0.0279369	+	0.0495758i
$604$	41.6370	−	72.1175i	1.69419	−	2.93442i
$605$	7.06744	+	23.5451i	0.287332	+	0.957243i
$606$	44.5710	+	12.1924i	1.81057	+	0.495281i
$607$	10.7492	−	6.20602i	0.436295	−	0.251895i	−0.265730	−	0.964047i	$-0.585613\pi$
$607$	10.7492	−	6.20602i	0.436295	−	0.251895i	0.702025	+	0.712153i	$0.252280\pi$
$608$	69.7424	+	40.2658i	2.82843	+	1.63299i
$609$	−27.9847	+	6.69037i	−1.13400	+	0.271107i
$610$	−10.0691	+	42.6218i	−0.407685	+	1.72571i
$611$	0.00895304	−	0.0155071i	0.000362201	−	0.000627351i
$612$	41.5474	−	70.2585i	1.67945	−	2.84003i
$613$	30.6258	−	17.6818i	1.23696	−	0.714162i	0.268492	−	0.963282i	$-0.413475\pi$
$613$	30.6258	−	17.6818i	1.23696	−	0.714162i	0.968473	+	0.249120i	$0.0801414\pi$
$614$	24.9003			1.00490
$615$	−19.9152	+	36.5407i	−0.803057	+	1.47346i
$616$	1.35133	−	0.741193i	0.0544466	−	0.0298635i
$617$	18.3285	+	10.5820i	0.737878	+	0.426014i	0.821297	−	0.570501i	$-0.193251\pi$
$617$	18.3285	+	10.5820i	0.737878	+	0.426014i	−0.0834195	+	0.996515i	$0.526584\pi$
$618$	−49.6248	−	50.1454i	−1.99620	−	2.01714i
$619$	0.736601	−	1.27583i	0.0296065	−	0.0512800i	−0.850843	−	0.525421i	$-0.823908\pi$
$619$	0.736601	−	1.27583i	0.0296065	−	0.0512800i	0.880449	+	0.474141i	$0.157241\pi$
$620$	−39.0699	−	9.22999i	−1.56909	−	0.370685i
$621$	−3.12788	+	10.9828i	−0.125518	+	0.440723i
$622$		−	62.3936i		−	2.50176i
$623$	−11.3325	−	20.6613i	−0.454029	−	0.827776i
$624$	0.101283	+	0.0277060i	0.00405457	+	0.00110913i
$625$	14.9868	+	20.0099i	0.599471	+	0.800397i
$626$	−80.6871			−3.22490
$627$	0.734429	+	0.742134i	0.0293303	+	0.0296380i
$628$			55.5330i			2.21601i
$629$	−17.9879			−0.717223
$630$	−44.7800	−	12.1208i	−1.78408	−	0.482902i
$631$	38.7917			1.54427			0.772137	−	0.635456i	$-0.219188\pi$
$631$	38.7917			1.54427			0.772137	+	0.635456i	$0.219188\pi$
$632$			57.0443i			2.26910i
$633$	−1.32350	+	4.83823i	−0.0526043	+	0.192303i
$634$	−59.7617			−2.37344
$635$	3.42023	−	14.4776i	0.135728	−	0.574527i
$636$	8.87539	−	8.78324i	0.351932	−	0.348278i
$637$	0.00191954	−	0.0437695i	7.60551e−5	−	0.00173421i
$638$			1.29143i			0.0511283i
$639$	−6.71218	+	3.78244i	−0.265530	+	0.149631i
$640$	−0.0826149	+	0.349704i	−0.00326564	+	0.0138232i
$641$	6.73857	−	11.6715i	0.266157	−	0.460998i	−0.701709	−	0.712464i	$-0.747579\pi$
$641$	6.73857	−	11.6715i	0.266157	−	0.460998i	0.967866	+	0.251466i	$0.0809126\pi$
$642$	1.95919	−	7.16209i	0.0773230	−	0.282665i
$643$	−15.2182	−	8.78621i	−0.600146	−	0.346494i	0.168953	−	0.985624i	$-0.445961\pi$
$643$	−15.2182	−	8.78621i	−0.600146	−	0.346494i	−0.769099	+	0.639130i	$0.779295\pi$
$644$	0.615669	−	28.0905i	0.0242607	−	1.10692i
$645$	27.3866	−	16.7228i	1.07835	−	0.658459i
$646$	−112.746			−4.43593
$647$	−26.9455	+	15.5570i	−1.05934	+	0.611608i	−0.925248	−	0.379362i	$-0.876144\pi$
$647$	−26.9455	+	15.5570i	−1.05934	+	0.611608i	−0.134087	+	0.990970i	$0.542810\pi$
$648$	56.9939	+	34.5111i	2.23893	+	1.35573i
$649$	0.0674758	−	0.116871i	0.00264866	−	0.00458761i
$650$	0.0682764	−	0.0450474i	0.00267802	−	0.00176690i
$651$	4.85115	−	16.3202i	0.190132	−	0.639637i
$652$	36.7390	+	21.2113i	1.43881	+	0.830698i
$653$	−22.9926	+	13.2748i	−0.899771	+	0.519483i	−0.877126	−	0.480261i	$-0.840542\pi$
$653$	−22.9926	+	13.2748i	−0.899771	+	0.519483i	−0.0226450	+	0.999744i	$0.507209\pi$
$654$	12.0244	−	11.8996i	0.470191	−	0.465309i
$655$	6.54884	+	21.8174i	0.255885	+	0.852475i
$656$	−52.0394	+	90.1349i	−2.03180	+	3.51918i
$657$	9.17176	−	15.5099i	0.357825	−	0.605098i
$658$	−10.2657	+	16.9136i	−0.400198	+	0.659361i
$659$	−8.86820	−	15.3602i	−0.345456	−	0.598347i	0.639981	−	0.768391i	$-0.278942\pi$
$659$	−8.86820	−	15.3602i	−0.345456	−	0.598347i	−0.985436	+	0.170044i	$0.945609\pi$
$660$	−0.704750	+	1.29309i	−0.0274324	+	0.0503334i
$661$	5.95663			0.231686			0.115843	−	0.993268i	$-0.463043\pi$
$661$	5.95663			0.231686			0.115843	+	0.993268i	$0.463043\pi$
$662$		−	68.2644i		−	2.65317i
$663$	−0.0590394	+	0.0154898i	−0.00229290	+	0.000601575i
$664$	−12.1113	−	20.9773i	−0.470008	−	0.814079i
$665$	12.0755	+	43.6835i	0.468266	+	1.69397i
$666$	0.261439	−	25.0504i	0.0101306	−	0.970682i
$667$	11.9502	+	6.89947i	0.462715	+	0.267148i
$668$	−17.6979	−	10.2179i	−0.684752	−	0.395342i
$669$	22.1100	−	21.8805i	0.854822	−	0.845947i
$670$	2.64951	+	0.625927i	0.102359	+	0.0241817i
$671$	−0.294806	+	0.510619i	−0.0113809	+	0.0197122i
$672$	−46.1760	−	13.7258i	−1.78128	−	0.529484i
$673$	1.13022	−	0.652531i	0.0435666	−	0.0251532i	−0.478058	−	0.878328i	$-0.658659\pi$
$673$	1.13022	−	0.652531i	0.0435666	−	0.0251532i	0.521625	+	0.853175i	$0.325326\pi$
$674$	−29.2889	+	50.7299i	−1.12817	+	1.95404i
$675$	24.7757	−	7.82081i	0.953617	−	0.301023i
$676$	31.4096	+	54.4030i	1.20806	+	2.09242i
$677$			24.4666i			0.940326i	0.882579	+	0.470163i	$0.155805\pi$
$677$			24.4666i			0.940326i	−0.882579	+	0.470163i	$0.844195\pi$
$678$	−21.1855	+	77.4467i	−0.813625	+	2.97432i
$679$	−0.251037	+	11.4538i	−0.00963391	+	0.439557i
$680$	−26.7963	−	89.2715i	−1.02759	−	3.42340i
$681$	−6.22647	−	1.70325i	−0.238599	−	0.0652687i
$682$	−0.661793	−	0.382086i	−0.0253414	−	0.0146308i
$683$	2.99256	−	1.72775i	0.114507	−	0.0661107i	−0.441653	−	0.897186i	$-0.645608\pi$
$683$	2.99256	−	1.72775i	0.114507	−	0.0661107i	0.556160	+	0.831075i	$0.312274\pi$
$684$	1.15899	−	111.051i	0.0443149	−	4.24613i
$685$	−17.4158	−	16.4072i	−0.665422	−	0.626887i
$686$	−3.18021	+	48.3048i	−0.121421	+	1.84429i
$687$	4.68800	+	4.73718i	0.178858	+	0.180735i
$688$	69.5010	−	40.1264i	2.64970	−	1.52980i
$689$	−0.00933745			−0.000355728
$690$	11.5945	+	18.9880i	0.441393	+	0.722862i
$691$	4.33136			0.164773			0.0823863	−	0.996600i	$-0.473746\pi$
$691$	4.33136			0.164773			0.0823863	+	0.996600i	$0.473746\pi$
$692$		−	31.7554i		−	1.20716i
$693$	−0.530507	−	0.329615i	−0.0201523	−	0.0125210i
$694$	−57.7894			−2.19366
$695$	−3.12252	+	3.31446i	−0.118444	+	0.125725i
$696$	57.2264	−	56.6323i	2.16916	−	2.14664i
$697$		−	60.4996i		−	2.29159i
$698$	−39.8159	+	22.9877i	−1.50705	+	0.870098i
$699$	13.4607	+	3.68217i	0.509130	+	0.139272i
$700$	−54.1163	+	34.0266i	−2.04540	+	1.28609i
$701$	−9.31122			−0.351680			−0.175840	−	0.984419i	$-0.556264\pi$
$701$	−9.31122			−0.351680			−0.175840	+	0.984419i	$0.556264\pi$
$702$	−0.0207134	−	0.0824449i	−0.000781779	−	0.00311168i
$703$	−21.1952	+	12.2371i	−0.799393	+	0.461530i
$704$	−0.318879	+	0.552315i	−0.0120182	+	0.0208161i
$705$	−0.272462	−	11.0770i	−0.0102615	−	0.417185i
$706$	−39.3061	+	68.0801i	−1.47930	+	2.56223i
$707$	12.9863	+	23.6764i	0.488401	+	0.890442i
$708$	−13.8843	+	3.64275i	−0.521805	+	0.136903i
$709$	34.0294			1.27800			0.639000	−	0.769207i	$-0.279349\pi$
$709$	34.0294			1.27800			0.639000	+	0.769207i	$0.279349\pi$
$710$	−3.45111	+	14.6083i	−0.129518	+	0.548241i
$711$	20.1388	−	11.3486i	0.755264	−	0.425605i
$712$	57.1040	+	32.9690i	2.14006	+	1.23557i
$713$	−7.07124	+	4.08258i	−0.264820	+	0.152894i
$714$	65.5945	−	15.6818i	2.45481	−	0.586878i
$715$	0.00105476		0.000316602i	3.94456e−5		1.18403e-5i
$716$	53.9587	+	93.4592i	2.01653	+	3.49273i
$717$	−4.78059	+	17.4761i	−0.178534	+	0.652658i
$718$	−7.81811	−	4.51379i	−0.291769	−	0.168453i
$719$	−7.15099	+	12.3859i	−0.266687	+	0.461915i	−0.968004	−	0.250934i	$-0.919262\pi$
$719$	−7.15099	+	12.3859i	−0.266687	+	0.461915i	0.701317	+	0.712849i	$0.252596\pi$
$720$	62.4256	−	18.0301i	2.32646	−	0.671941i
$721$	0.903401	−	41.2186i	0.0336444	−	1.53506i
$722$	−89.8397	+	51.8690i	−3.34349	+	1.93036i
$723$	3.79554	−	13.8752i	0.141158	−	0.516022i
$724$	72.9277			2.71034
$725$	−1.87063	−	31.3385i	−0.0694735	−	1.16388i
$726$	35.3778	−	35.0105i	1.31299	−	1.29936i
$727$	21.4064	−	12.3590i	0.793919	−	0.458369i	−0.0474217	−	0.998875i	$-0.515100\pi$
$727$	21.4064	−	12.3590i	0.793919	−	0.458369i	0.841340	+	0.540506i	$0.181767\pi$
$728$	0.0589541	+	0.107484i	0.00218498	+	0.00398362i
$729$	0.845192	−	26.9868i	0.0313034	−	0.999510i
$730$	−10.0926	−	33.6232i	−0.373542	−	1.24445i
$731$	−23.3249	+	40.4000i	−0.862704	+	1.49425i
$732$	60.6615	−	15.9154i	2.24211	−	0.588251i
$733$	14.8627	−	8.58099i	0.548967	−	0.316946i	−0.199738	−	0.979849i	$-0.564009\pi$
$733$	14.8627	−	8.58099i	0.548967	−	0.316946i	0.748705	+	0.662903i	$0.230676\pi$
$734$	25.9631	−	44.9694i	0.958315	−	1.65985i
$735$	−13.1013	−	23.7351i	−0.483250	−	0.875482i
$736$	11.5512	+	20.0073i	0.425783	+	0.737478i
$737$	0.0317417	+	0.0183261i	0.00116922	+	0.000675050i
$738$	84.2534	+	0.879315i	3.10141	+	0.0323680i
$739$	23.1349	+	40.0708i	0.851030	+	1.47403i	0.880280	+	0.474455i	$0.157355\pi$
$739$	23.1349	+	40.0708i	0.851030	+	1.47403i	−0.0292493	+	0.999572i	$0.509312\pi$
$740$	−25.1260	−	23.6709i	−0.923649	−	0.870159i
$741$	−0.0590289	+	0.0584161i	−0.00216848	+	0.00214597i
$742$	10.3149	+	0.226074i	0.378671	+	0.00829944i
$743$	14.3911	+	8.30873i	0.527960	+	0.304818i	0.740185	−	0.672403i	$-0.234738\pi$
$743$	14.3911	+	8.30873i	0.527960	+	0.304818i	−0.212226	+	0.977221i	$0.568071\pi$
$744$	12.0900	+	46.0809i	0.443241	+	1.68941i
$745$	2.35443	+	7.84373i	0.0862595	+	0.287372i
$746$	−29.0984	−	50.3999i	−1.06537	−	1.84527i
$747$	−4.99634	+	8.44904i	−0.182807	+	0.309134i
$748$		−	2.14094i		−	0.0782805i
$749$	3.80455	−	2.08677i	0.139015	−	0.0762487i
$750$	21.5317	−	45.8092i	0.786228	−	1.67272i
$751$	−5.93708	−	10.2833i	−0.216647	−	0.375244i	0.737134	−	0.675747i	$-0.236179\pi$
$751$	−5.93708	−	10.2833i	−0.216647	−	0.375244i	−0.953781	+	0.300503i	$0.902845\pi$
$752$		−	27.7118i		−	1.01054i
$753$	−1.95695	+	0.513433i	−0.0713151	+	0.0187105i
$754$	−0.102720			−0.00374084
$755$	−26.4234	+	28.0477i	−0.961647	+	1.02076i
$756$	14.7718	+	64.7695i	0.537244	+	2.35564i
$757$			0.189629i			0.00689218i	0.999994	+	0.00344609i	$0.00109693\pi$
$757$			0.189629i			0.00689218i	−0.999994	+	0.00344609i	$0.998903\pi$
$758$			26.6733i			0.968817i
$759$	0.0760122	+	0.289720i	0.00275907	+	0.0105162i
$760$	−92.3054	−	86.9598i	−3.34827	−	3.15437i
$761$	−14.9798	−	25.9458i	−0.543018	−	0.940535i	−0.998729	−	0.0504071i	$-0.983948\pi$
$761$	−14.9798	−	25.9458i	−0.543018	−	0.940535i	0.455711	−	0.890128i	$-0.349385\pi$
$762$	−29.1335	+	7.64359i	−1.05540	+	0.276898i
$763$	9.88384	+	0.216627i	0.357819	+	0.00784243i
$764$	23.5133			0.850680
$765$	−26.1853	+	27.2201i	−0.946731	+	0.984144i
$766$	−17.9149	−	31.0295i	−0.647291	−	1.12114i
$767$	0.00929589	+	0.00536699i	0.000335655	+	0.000193791i
$768$	−26.4533	+	6.94041i	−0.954552	+	0.250440i
$769$	7.95632	−	13.7808i	0.286912	−	0.496947i	−0.686159	−	0.727452i	$-0.740704\pi$
$769$	7.95632	−	13.7808i	0.286912	−	0.496947i	0.973071	+	0.230505i	$0.0740378\pi$
$770$	−1.17283	+	0.324206i	−0.0422659	+	0.0116836i
$771$	−27.3667	+	27.0825i	−0.985586	+	0.975354i
$772$		−	44.4596i		−	1.60013i
$773$	5.19871	−	3.00147i	0.186984	−	0.107956i	−0.403586	−	0.914942i	$-0.632236\pi$
$773$	5.19871	−	3.00147i	0.186984	−	0.107956i	0.590570	+	0.806986i	$0.298903\pi$
$774$	−55.9231	−	33.0701i	−2.01011	−	1.18868i
$775$	16.6128	+	8.31328i	0.596750	+	0.298622i
$776$	−16.0284	−	27.7621i	−0.575387	−	0.996600i
$777$	10.6291	−	10.0675i	0.381318	−	0.361168i
$778$	84.6379	+	48.8657i	3.03442	+	1.75192i
$779$	−41.1577	−	71.2872i	−1.47463	−	2.55413i
$780$	−0.102852	−	0.0560555i	−0.00368268	−	0.00200711i
$781$	−0.101043	+	0.175011i	−0.00361560	+	0.00626239i
$782$	−28.0106	−	16.1719i	−1.00166	−	0.578307i
$783$	−31.3782	−	8.93649i	−1.12136	−	0.319364i
$784$	−31.2965	−	60.1486i	−1.11773	−	2.14817i
$785$	5.90814	−	25.0088i	0.210871	−	0.892602i
$786$	32.7818	−	32.4415i	1.16929	−	1.15715i
$787$			18.8179i			0.670786i	0.942078	+	0.335393i	$0.108869\pi$
$787$			18.8179i			0.670786i	−0.942078	+	0.335393i	$0.891131\pi$
$788$			15.8539i			0.564770i
$789$	33.1829	+	9.07716i	1.18134	+	0.323156i
$790$	10.3545	−	43.8299i	0.368396	−	1.55940i
$791$	−41.1402	+	22.5651i	−1.46278	+	0.802322i
$792$	1.74752	+	0.0182381i	0.0620954	+	0.000648061i
$793$	−0.0406144	−	0.0234487i	−0.00144226	−	0.000832688i
$794$	−2.54009	+	4.39956i	−0.0901443	+	0.156134i
$795$	−4.93140	+	3.01120i	−0.174899	+	0.106796i
$796$	0.315790	+	0.546965i	0.0111929	+	0.0193867i
$797$	30.7524	+	17.7549i	1.08931	+	0.628912i	0.933392	−	0.358859i	$-0.116834\pi$
$797$	30.7524	+	17.7549i	1.08931	+	0.628912i	0.155915	+	0.987770i	$0.450167\pi$
$798$	66.6223	−	63.1017i	2.35840	−	2.23378i
$799$	8.05424	+	13.9503i	0.284938	+	0.493528i
$800$	23.5215	−	47.0041i	0.831610	−	1.66185i
$801$	0.278853	−	26.7189i	0.00985277	−	0.944064i
$802$	15.4757	−	8.93492i	0.546467	−	0.315503i
$803$		−	0.472622i		−	0.0166785i
$804$	−0.989353	−	3.77092i	−0.0348918	−	0.132990i
$805$	−3.26580	+	12.5848i	−0.115104	+	0.443556i
$806$	0.0303909	−	0.0526386i	0.00107047	−	0.00185412i
$807$	27.8342	+	28.1263i	0.979812	+	0.990091i
$808$	−65.4373	−	37.7802i	−2.30207	−	1.32910i
$809$	−10.1501	−	17.5805i	−0.356858	−	0.618096i	0.630576	−	0.776127i	$-0.282819\pi$
$809$	−10.1501	−	17.5805i	−0.356858	−	0.618096i	−0.987434	+	0.158031i	$0.949485\pi$
$810$	−37.5268	−	36.8619i	−1.31856	−	1.29520i
$811$	16.6110			0.583293			0.291646	−	0.956526i	$-0.405797\pi$
$811$	16.6110			0.583293			0.291646	+	0.956526i	$0.405797\pi$
$812$	80.2557	+	1.75899i	2.81642	+	0.0617284i
$813$	−1.11532	+	4.07721i	−0.0391159	+	0.142994i
$814$	−0.328545	−	0.569057i	−0.0115155	−	0.0199454i
$815$	−14.2884	−	13.4610i	−0.500502	−	0.471517i
$816$	−67.1429	+	66.4458i	−2.35047	+	2.32607i
$817$			63.4715i			2.22059i
$818$			16.2105i			0.566788i
$819$	0.0262174	−	0.0421963i	0.000916109	−	0.00147446i
$820$	79.6137	−	84.5076i	2.78023	−	2.95113i
$821$	29.1853			1.01857			0.509286	−	0.860597i	$-0.329909\pi$
$821$	29.1853			1.01857			0.509286	+	0.860597i	$0.329909\pi$
$822$	−12.7825	+	46.7281i	−0.445839	+	1.62983i
$823$			32.0384i			1.11679i	0.829575	+	0.558395i	$0.188583\pi$
$823$			32.0384i			1.11679i	−0.829575	+	0.558395i	$0.811417\pi$
$824$	57.6812	+	99.9068i	2.00942	+	3.48042i
$825$	0.454949	−	0.507352i	0.0158393	−	0.0176637i
$826$	−10.1390	−	6.15386i	−0.352782	−	0.214120i
$827$		−	27.6068i		−	0.959983i	−0.877273	−	0.479991i	$-0.840640\pi$
$827$		−	27.6068i		−	0.959983i	0.877273	−	0.479991i	$-0.159360\pi$
$828$	16.2167	−	27.4232i	0.563570	−	0.953023i
$829$	24.5776	+	42.5696i	0.853615	+	1.47851i	0.877924	+	0.478801i	$0.158928\pi$
$829$	24.5776	+	42.5696i	0.853615	+	1.47851i	−0.0243084	+	0.999705i	$0.507738\pi$
$830$	5.49795	+	18.3163i	0.190836	+	0.635769i
$831$	−51.1107	−	13.9813i	−1.77301	−	0.485007i
$832$	−0.0439308	−	0.0253635i	−0.00152303	−	0.000879320i
$833$	33.2368	+	21.1832i	1.15159	+	0.733955i
$834$	8.89299	+	2.43268i	0.307939	+	0.0842367i
$835$	6.88301	+	6.48441i	0.238196	+	0.224402i
$836$	−1.45647	−	2.52269i	−0.0503732	−	0.0872489i
$837$	13.8631	−	13.4357i	0.479179	−	0.464407i
$838$	−46.7708	−	27.0032i	−1.61567	−	0.932809i
$839$	−15.4451	−	26.7516i	−0.533222	−	0.923568i	−0.999247	−	0.0387965i	$-0.987648\pi$
$839$	−15.4451	−	26.7516i	−0.533222	−	0.923568i	0.466025	−	0.884772i	$-0.345686\pi$
$840$	65.7977	+	37.7537i	2.27023	+	1.30263i
$841$	−5.21205	+	9.02753i	−0.179726	+	0.311294i
$842$	38.2924	−	22.1081i	1.31964	−	0.761896i
$843$	−35.3832	−	35.7544i	−1.21866	−	1.23145i
$844$	6.99707	−	12.1193i	0.240849	−	0.417163i
$845$	−8.35711	−	27.8416i	−0.287493	−	0.957779i
$846$	−19.5447	+	11.0138i	−0.671960	+	0.378662i
$847$	29.0799	+	0.637353i	0.999197	+	0.0218997i
$848$	−12.5148	+	7.22539i	−0.429758	+	0.248121i
$849$	12.5667	+	47.8980i	0.431289	+	1.64386i
$850$	4.38465	+	73.4556i	0.150392	+	2.51951i
$851$	−7.02100			−0.240677
$852$	20.7913	−	5.45490i	0.712299	−	0.186882i
$853$	−21.0313	+	12.1424i	−0.720097	+	0.415748i	−0.814788	−	0.579758i	$-0.803147\pi$
$853$	−21.0313	+	12.1424i	−0.720097	+	0.415748i	0.0946913	+	0.995507i	$0.469814\pi$
$854$	44.2981	+	26.8866i	1.51585	+	0.920041i
$855$	−12.3366	+	49.8874i	−0.421903	+	1.70611i
$856$	−6.07089	+	10.5151i	−0.207499	+	0.359398i
$857$	−12.0819	−	6.97547i	−0.412709	−	0.238277i	0.279244	−	0.960220i	$-0.409916\pi$
$857$	−12.0819	−	6.97547i	−0.412709	−	0.238277i	−0.691953	+	0.721943i	$0.743249\pi$
$858$	−0.00156837	−	0.00158483i	−5.35434e−5	−	5.41051e-5i
$859$	−19.6418	−	34.0207i	−0.670171	−	1.16077i	−0.977855	−	0.209282i	$-0.932887\pi$
$859$	−19.6418	−	34.0207i	−0.670171	−	1.16077i	0.307684	−	0.951489i	$-0.400446\pi$
$860$	−85.7448	+	25.7377i	−2.92387	+	0.877649i
$861$	33.8605	+	35.7496i	1.15396	+	1.21834i
$862$	16.2051	−	9.35599i	0.551946	−	0.318666i
$863$	−35.2788	−	20.3682i	−1.20091	−	0.693343i	−0.240149	−	0.970736i	$-0.577196\pi$
$863$	−35.2788	−	20.3682i	−1.20091	−	0.693343i	−0.960757	+	0.277393i	$0.910530\pi$
$864$	−38.0149	−	39.2241i	−1.29329	−	1.33443i
$865$	−3.37845	+	14.3008i	−0.114871	+	0.486240i
$866$	49.8179			1.69288
$867$	6.71910	−	24.5626i	0.228193	−	0.834191i
$868$	−24.6460	+	40.6065i	−0.836541	+	1.37827i
$869$	0.303162	−	0.525092i	0.0102841	−	0.0178125i
$870$	−54.2496	+	33.1258i	−1.83923	+	1.12307i
$871$	−0.00145765	+	0.00252472i	−4.93905e−5	+	8.55468e-5i
$872$	−23.9567	+	13.8314i	−0.811277	+	0.468391i
$873$	−6.61231	+	11.1817i	−0.223793	+	0.378444i
$874$	−44.0068			−1.48855
$875$	27.9909	−	9.56618i	0.946264	−	0.323396i
$876$	−35.7318	+	35.3609i	−1.20727	+	1.19473i
$877$	19.5650	−	11.2959i	0.660664	−	0.381434i	−0.131866	−	0.991268i	$-0.542097\pi$
$877$	19.5650	−	11.2959i	0.660664	−	0.381434i	0.792530	+	0.609833i	$0.208764\pi$
$878$			40.2266i			1.35758i
$879$	−0.689487	−	0.188609i	−0.0232558	−	0.00636162i
$880$	1.16867	−	1.24051i	0.0393960	−	0.0418177i
$881$	8.90837			0.300131			0.150065	−	0.988676i	$-0.452052\pi$
$881$	8.90837			0.300131			0.150065	+	0.988676i	$0.452052\pi$
$882$	−29.9834	+	45.9785i	−1.00959	+	1.54818i
$883$		−	17.9788i		−	0.605033i	−0.953144	−	0.302517i	$-0.902173\pi$
$883$		−	17.9788i		−	0.605033i	0.953144	−	0.302517i	$-0.0978268\pi$
$884$	0.170289			0.00572744
$885$	6.64024	−	0.163330i	0.223209	−	0.00549028i
$886$	−0.133321			−0.00447900
$887$	6.02195	−	3.47677i	0.202197	−	0.116739i	−0.395483	−	0.918473i	$-0.629423\pi$
$887$	6.02195	−	3.47677i	0.202197	−	0.116739i	0.597680	+	0.801735i	$0.296089\pi$
$888$	−10.8088	+	39.5131i	−0.362719	+	1.32597i
$889$	−15.0470	−	9.13274i	−0.504660	−	0.306302i
$890$	−37.8914	−	35.6970i	−1.27012	−	1.19657i
$891$	−0.341219	−	0.620569i	−0.0114313	−	0.0207899i
$892$	−75.1571	+	43.3920i	−2.51644	+	1.45287i
$893$	18.9807	+	10.9585i	0.635166	+	0.366714i
$894$	11.7856	−	11.6633i	0.394171	−	0.390079i
$895$	−14.3567	−	47.8292i	−0.479892	−	1.59875i
$896$	0.363457	+	0.220599i	0.0121422	+	0.00736971i
$897$	−0.0230442	+	0.00604597i	−0.000769423	+	0.000201869i
$898$		−	43.0300i		−	1.43593i
$899$	−11.6641	−	20.2028i	−0.389020	−	0.673802i
$900$	−72.3963	+	3.56362i	−2.41321	+	0.118787i
$901$	4.20003	−	7.27466i	0.139923	−	0.242354i
$902$	1.91394	−	1.10502i	0.0637274	−	0.0367930i
$903$	−8.82825	−	36.9271i	−0.293786	−	1.22886i
$904$	65.6471	−	113.704i	2.18339	−	3.78174i
$905$	−32.8423	−	7.75876i	−1.09172	−	0.257910i
$906$	75.2545	+	20.5859i	2.50016	+	0.683919i
$907$	−2.82154	−	1.62902i	−0.0936877	−	0.0540906i	0.452424	−	0.891803i	$-0.350559\pi$
$907$	−2.82154	−	1.62902i	−0.0936877	−	0.0540906i	−0.546112	+	0.837712i	$0.683893\pi$
$908$	15.5967	+	9.00475i	0.517594	+	0.298833i
$909$	−0.319546	+	30.6180i	−0.0105987	+	1.01553i
$910$	−0.0257872	−	0.0932863i	−0.000854837	−	0.00309241i
$911$	−23.2286	−	40.2331i	−0.769599	−	1.33298i	−0.937781	−	0.347228i	$-0.887123\pi$
$911$	−23.2286	−	40.2331i	−0.769599	−	1.33298i	0.168182	−	0.985756i	$-0.446210\pi$
$912$	−33.9122	+	123.971i	−1.12294	+	4.10508i
$913$			0.257462i			0.00852074i
$914$	−35.2443			−1.16578
$915$	−29.0116	+	0.713600i	−0.959094	+	0.0235909i
$916$	−9.29696	−	16.1028i	−0.307180	−	0.532051i
$917$	26.9461	+	0.590585i	0.889837	+	0.0195028i
$918$	73.5486	+	20.9466i	2.42746	+	0.691340i
$919$	−22.2884	+	38.6046i	−0.735226	+	1.27345i	0.219399	+	0.975635i	$0.429590\pi$
$919$	−22.2884	+	38.6046i	−0.735226	+	1.27345i	−0.954624	+	0.297813i	$0.903743\pi$
$920$	−10.4591	−	34.8443i	−0.344826	−	1.14878i
$921$	4.18729	+	15.9598i	0.137976	+	0.525895i
$922$	19.6091	−	11.3213i	0.645791	−	0.372847i
$923$	−0.0139203	−	0.00803689i	−0.000458192	−	0.000264537i
$924$	1.19824	+	1.26509i	0.0394193	+	0.0416186i
$925$	8.79691	+	13.3331i	0.289241	+	0.438390i
$926$	−6.04053	+	10.4625i	−0.198504	+	0.343819i
$927$	23.7956	−	40.2395i	0.781550	−	1.32164i
$928$	−57.1616	+	33.0022i	−1.87642	+	1.08335i
$929$	−2.82613			−0.0927222			−0.0463611	−	0.998925i	$-0.514762\pi$
$929$	−2.82613			−0.0927222			−0.0463611	+	0.998925i	$0.514762\pi$
$930$	−0.924868	−	37.6008i	−0.0303276	−	1.23298i
$931$	53.5740	+	2.34952i	1.75582	+	0.0770026i
$932$	−33.7177	−	19.4669i	−1.10446	−	0.637659i
$933$	39.9911	−	10.4922i	1.30925	−	0.343500i
$934$	36.2899	−	62.8560i	1.18744	−	2.05671i
$935$	−0.227774	+	0.964153i	−0.00744900	+	0.0315312i
$936$	−0.00145065	+	0.138997i	−4.74158e−5	+	0.00454325i
$937$		−	29.8049i		−	0.973683i	−0.873490	−	0.486841i	$-0.838149\pi$
$937$		−	29.8049i		−	0.973683i	0.873490	−	0.486841i	$-0.161851\pi$
$938$	1.67136	−	2.75371i	0.0545718	−	0.0899118i
$939$	−13.5685	−	51.7162i	−0.442791	−	1.68770i
$940$	−7.10739	+	30.0851i	−0.231817	+	0.981268i
$941$	38.0384			1.24002			0.620009	−	0.784595i	$-0.287129\pi$
$941$	38.0384			1.24002			0.620009	+	0.784595i	$0.287129\pi$
$942$	−50.3255	+	13.2036i	−1.63969	+	0.430197i
$943$		−	23.6141i		−	0.768982i
$944$	16.6121			0.540677
$945$	0.238482	−	30.7399i	0.00775781	−	0.999970i
$946$	−1.70411			−0.0554052
$947$			15.6306i			0.507927i	0.967214	+	0.253963i	$0.0817343\pi$
$947$			15.6306i			0.507927i	−0.967214	+	0.253963i	$0.918266\pi$
$948$	−62.3810	+	16.3665i	−2.02604	+	0.531560i
$949$	0.0375921			0.00122029
$950$	55.1381	+	83.5705i	1.78892	+	2.71138i
$951$	−10.0496	−	38.3041i	−0.325882	−	1.24210i
$952$	−110.257	−	2.41653i	−3.57344	−	0.0783203i
$953$			2.66056i			0.0861840i	0.999071	+	0.0430920i	$0.0137209\pi$
$953$			2.66056i			0.0861840i	−0.999071	+	0.0430920i	$0.986279\pi$
$954$	10.0698	+	5.95480i	0.326023	+	0.192794i
$955$	−10.5890	−	2.50157i	−0.342651	−	0.0809489i
$956$	25.2740	−	43.7759i	0.817421	−	1.41581i
$957$	−0.827742	+	0.217170i	−0.0267571	+	0.00702010i
$958$	−43.2819	−	24.9888i	−1.39837	−	0.807352i
$959$	−24.8222	+	13.6148i	−0.801552	+	0.439645i
$960$	−31.3806	+	0.771870i	−1.01281	+	0.0249120i
$961$	−17.1961			−0.554714
$962$	0.0452625	−	0.0261323i	0.00145932	−	0.000842540i
$963$	4.91999	+	0.0513477i	0.158544	+	0.00165466i
$964$	−20.0663	+	34.7559i	−0.646292	+	1.11941i
$965$	−4.73004	+	20.0220i	−0.152265	+	0.644530i
$966$	25.6028	−	6.12091i	0.823756	−	0.196937i
$967$	−8.98158	−	5.18552i	−0.288828	−	0.166755i	0.348585	−	0.937277i	$-0.386662\pi$
$967$	−8.98158	−	5.18552i	−0.288828	−	0.166755i	−0.637413	+	0.770522i	$0.719996\pi$
$968$	−70.4846	+	40.6943i	−2.26546	+	1.30796i
$969$	−18.9596	−	72.2643i	−0.609069	−	2.32146i
$970$	7.27615	+	24.2404i	0.233623	+	0.778312i
$971$	24.8401	−	43.0243i	0.797157	−	1.38072i	−0.124303	−	0.992244i	$-0.539670\pi$
$971$	24.8401	−	43.0243i	0.797157	−	1.38072i	0.921460	−	0.388472i	$-0.126997\pi$
$972$	−21.3877	+	72.2274i	−0.686011	+	2.31670i
$973$	2.59109	+	4.72402i	0.0830664	+	0.151445i
$974$	50.1106	+	86.7941i	1.60565	+	2.78106i
$975$	0.0403545	+	0.0361864i	0.00129238	+	0.00115889i
$976$	−72.5792			−2.32320
$977$		−	5.31918i		−	0.170176i	−0.996373	−	0.0850879i	$-0.972883\pi$
$977$		−	5.31918i		−	0.170176i	0.996373	−	0.0850879i	$-0.0271171\pi$
$978$	−10.4871	+	38.3371i	−0.335341	+	1.22589i
$979$	−0.350428	−	0.606959i	−0.0111997	−	0.0193985i
$980$	18.5503	+	73.3268i	0.592566	+	2.34234i
$981$	9.64905	+	5.70596i	0.308070	+	0.182177i
$982$	50.7494	+	29.3002i	1.61948	+	0.935007i
$983$	33.9526	+	19.6026i	1.08292	+	0.625225i	0.931683	−	0.363273i	$-0.118341\pi$
$983$	33.9526	+	19.6026i	1.08292	+	0.625225i	0.151238	+	0.988497i	$0.451674\pi$
$984$	−132.897	−	36.3539i	−4.23659	−	1.15892i
$985$	1.68669	−	7.13964i	0.0537423	−	0.227488i
$986$	46.2039	−	80.0274i	1.47143	−	2.54859i
$987$	−12.5670	−	3.73555i	−0.400014	−	0.118904i
$988$	0.200653	−	0.115847i	0.00638362	−	0.00368559i
$989$	−9.10416	+	15.7689i	−0.289496	+	0.501421i
$990$	−1.33939	−	0.331217i	−0.0425687	−	0.0105268i
$991$	−9.00485	−	15.5969i	−0.286048	−	0.495450i	0.686814	−	0.726833i	$-0.259008\pi$
$991$	−9.00485	−	15.5969i	−0.286048	−	0.495450i	−0.972863	+	0.231382i	$0.925675\pi$
$992$		−	39.0565i		−	1.24004i
$993$	43.7540	−	11.4795i	1.38849	−	0.364290i
$994$	15.1829	+	9.21521i	0.481571	+	0.292289i
$995$	−0.0840219	−	0.279918i	−0.00266367	−	0.00887398i
$996$	19.4650	−	19.2629i	0.616772	−	0.610369i
$997$	47.8336	+	27.6167i	1.51490	+	0.874630i	0.999847	+	0.0174739i	$0.00556240\pi$
$997$	47.8336	+	27.6167i	1.51490	+	0.874630i	0.515057	+	0.857156i	$0.327771\pi$
$998$	23.9117	−	13.8054i	0.756911	−	0.437003i
$999$	16.1000	−	4.04495i	0.509380	−	0.127977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.3	✓	84
3.2	odd	2		945.2.r.b.604.40		84
5.4	even	2	inner	315.2.r.b.184.40	yes	84
7.4	even	3		315.2.bo.b.4.40	yes	84
9.2	odd	6		945.2.bo.b.289.40		84
9.7	even	3		315.2.bo.b.79.3	yes	84
15.14	odd	2		945.2.r.b.604.3		84
21.11	odd	6		945.2.bo.b.739.3		84
35.4	even	6		315.2.bo.b.4.3	yes	84
45.29	odd	6		945.2.bo.b.289.3		84
45.34	even	6		315.2.bo.b.79.40	yes	84
63.11	odd	6		945.2.r.b.424.40		84
63.25	even	3	inner	315.2.r.b.214.3	yes	84
105.74	odd	6		945.2.bo.b.739.40		84
315.74	odd	6		945.2.r.b.424.3		84
315.214	even	6	inner	315.2.r.b.214.40	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.3	✓	84	1.1	even	1	trivial
315.2.r.b.184.40	yes	84	5.4	even	2	inner
315.2.r.b.214.3	yes	84	63.25	even	3	inner
315.2.r.b.214.40	yes	84	315.214	even	6	inner
315.2.bo.b.4.3	yes	84	35.4	even	6
315.2.bo.b.4.40	yes	84	7.4	even	3
315.2.bo.b.79.3	yes	84	9.7	even	3
315.2.bo.b.79.40	yes	84	45.34	even	6
945.2.r.b.424.3		84	315.74	odd	6
945.2.r.b.424.40		84	63.11	odd	6
945.2.r.b.604.3		84	15.14	odd	2
945.2.r.b.604.40		84	3.2	odd	2
945.2.bo.b.289.3		84	45.29	odd	6
945.2.bo.b.289.40		84	9.2	odd	6
945.2.bo.b.739.3		84	21.11	odd	6
945.2.bo.b.739.40		84	105.74	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.61386i q^{2} +(1.67535 - 0.439552i) q^{3} -4.83226 q^{4} +(2.17617 + 0.514103i) q^{5} +(-1.14893 - 4.37913i) q^{6} +(1.37276 - 2.26175i) q^{7} +7.40313i q^{8} +(2.61359 - 1.47280i) q^{9} +O(q^{10})\)	\(q-2.61386i q^{2} +(1.67535 - 0.439552i) q^{3} -4.83226 q^{4} +(2.17617 + 0.514103i) q^{5} +(-1.14893 - 4.37913i) q^{6} +(1.37276 - 2.26175i) q^{7} +7.40313i q^{8} +(2.61359 - 1.47280i) q^{9} +(1.34379 - 5.68819i) q^{10} +(0.0393440 - 0.0681458i) q^{11} +(-8.09573 + 2.12403i) q^{12} +(0.00542028 + 0.00312940i) q^{13} +(-5.91190 - 3.58821i) q^{14} +(3.87181 - 0.0952351i) q^{15} +9.68623 q^{16} +(-4.87614 + 2.81524i) q^{17} +(-3.84971 - 6.83155i) q^{18} +(-3.83039 + 6.63444i) q^{19} +(-10.5158 - 2.48428i) q^{20} +(1.30570 - 4.39262i) q^{21} +(-0.178124 - 0.102840i) q^{22} +(-1.90325 + 1.09884i) q^{23} +(3.25406 + 12.4028i) q^{24} +(4.47140 + 2.23755i) q^{25} +(0.00817982 - 0.0141679i) q^{26} +(3.73130 - 3.61627i) q^{27} +(-6.63356 + 10.9294i) q^{28} +(-3.13943 - 5.43765i) q^{29} +(-0.248931 - 10.1204i) q^{30} +3.71536 q^{31} -10.5122i q^{32} +(0.0359613 - 0.131462i) q^{33} +(7.35864 + 12.7455i) q^{34} +(4.15014 - 4.21620i) q^{35} +(-12.6295 + 7.11698i) q^{36} +(2.76672 + 1.59737i) q^{37} +(17.3415 + 10.0121i) q^{38} +(0.0104564 + 0.00286035i) q^{39} +(-3.80597 + 16.1104i) q^{40} +(-5.37251 + 9.30547i) q^{41} +(-11.4817 - 3.41293i) q^{42} +(7.17523 - 4.14262i) q^{43} +(-0.190121 + 0.329299i) q^{44} +(6.44478 - 1.86141i) q^{45} +(2.87221 + 4.97482i) q^{46} -2.86094i q^{47} +(16.2278 - 4.25760i) q^{48} +(-3.23103 - 6.20970i) q^{49} +(5.84863 - 11.6876i) q^{50} +(-6.93179 + 6.85982i) q^{51} +(-0.0261922 - 0.0151221i) q^{52} +(-1.29201 + 0.745945i) q^{53} +(-9.45242 - 9.75309i) q^{54} +(0.120653 - 0.128070i) q^{55} +(16.7440 + 10.1628i) q^{56} +(-3.50107 + 12.7987i) q^{57} +(-14.2133 + 8.20603i) q^{58} +1.71502 q^{59} +(-18.7096 + 0.460201i) q^{60} -7.49303 q^{61} -9.71142i q^{62} +(0.256725 - 7.93310i) q^{63} -8.10489 q^{64} +(0.0101866 + 0.00959668i) q^{65} +(-0.343623 - 0.0939979i) q^{66} +0.465791i q^{67} +(23.5628 - 13.6040i) q^{68} +(-2.70561 + 2.67752i) q^{69} +(-11.0206 - 10.8479i) q^{70} -2.56819 q^{71} +(10.9034 + 19.3487i) q^{72} +(5.20158 - 3.00313i) q^{73} +(4.17529 - 7.23181i) q^{74} +(8.47467 + 1.78326i) q^{75} +(18.5095 - 32.0593i) q^{76} +(-0.100119 - 0.182535i) q^{77} +(0.00747654 - 0.0273316i) q^{78} +7.70542 q^{79} +(21.0788 + 4.97972i) q^{80} +(4.66169 - 7.69861i) q^{81} +(24.3232 + 14.0430i) q^{82} +(-2.83357 + 1.63597i) q^{83} +(-6.30950 + 21.2263i) q^{84} +(-12.0586 + 3.61959i) q^{85} +(-10.8282 - 18.7551i) q^{86} +(-7.64977 - 7.73003i) q^{87} +(0.504493 + 0.291269i) q^{88} +(4.45339 - 7.71349i) q^{89} +(-4.86547 - 16.8457i) q^{90} +(0.0145187 - 0.00796340i) q^{91} +(9.19699 - 5.30988i) q^{92} +(6.22452 - 1.63309i) q^{93} -7.47810 q^{94} +(-11.7464 + 12.4684i) q^{95} +(-4.62064 - 17.6116i) q^{96} +(-3.75004 + 2.16509i) q^{97} +(-16.2313 + 8.44547i) q^{98} +(0.00246356 - 0.236051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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