LMFDB - Embedded newform 784.2.x.p.165.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.16
Character	$\chi$	$=$	784.165
Dual form			784.2.x.p.765.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.581133 + 1.28930i) q^{2} +(0.554865 + 2.07078i) q^{3} +(-1.32457 + 1.49850i) q^{4} +(0.213735 - 0.797669i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} +(-1.38220 + 0.798013i) q^{9} +O(q^{10})$	\(q+(0.581133 + 1.28930i) q^{2} +(0.554865 + 2.07078i) q^{3} +(-1.32457 + 1.49850i) q^{4} +(0.213735 - 0.797669i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} +(-1.38220 + 0.798013i) q^{9} +(1.15264 - 0.187984i) q^{10} +(-1.03115 + 0.276295i) q^{11} +(-3.83804 - 1.91143i) q^{12} +(-2.93078 + 2.93078i) q^{13} +1.77039 q^{15} +(-0.491033 - 3.96975i) q^{16} +(-2.45215 + 4.24726i) q^{17} +(-1.83212 - 1.31831i) q^{18} +(-6.43542 - 1.72437i) q^{19} +(0.912204 + 1.37685i) q^{20} +(-0.955458 - 1.16889i) q^{22} +(-5.11212 + 2.95149i) q^{23} +(0.233988 - 6.05916i) q^{24} +(3.73953 + 2.15902i) q^{25} +(-5.48182 - 2.07547i) q^{26} +(2.12831 + 2.12831i) q^{27} +(3.32371 - 3.32371i) q^{29} +(1.02883 + 2.28256i) q^{30} +(-1.74230 + 3.01775i) q^{31} +(4.83282 - 2.94004i) q^{32} +(-1.14429 - 1.98197i) q^{33} +(-6.90100 - 0.693333i) q^{34} +(0.634992 - 3.12825i) q^{36} +(1.82174 - 6.79882i) q^{37} +(-1.51662 - 9.29925i) q^{38} +(-7.69520 - 4.44283i) q^{39} +(-1.24506 + 1.97623i) q^{40} +3.86206i q^{41} +(5.89641 + 5.89641i) q^{43} +(0.951795 - 1.91115i) q^{44} +(0.341126 + 1.27310i) q^{45} +(-6.77616 - 4.87584i) q^{46} +(3.10648 + 5.38058i) q^{47} +(7.94803 - 3.21950i) q^{48} +(-0.610451 + 6.07604i) q^{50} +(-10.1558 - 2.72123i) q^{51} +(-0.509767 - 8.27381i) q^{52} +(12.8748 - 3.44980i) q^{53} +(-1.50719 + 3.98086i) q^{54} +0.881566i q^{55} -14.2832i q^{57} +(6.21677 + 2.35373i) q^{58} +(5.82851 - 1.56174i) q^{59} +(-2.34501 + 2.65294i) q^{60} +(9.40542 + 2.52017i) q^{61} +(-4.90328 - 0.492626i) q^{62} +(6.59909 + 4.52239i) q^{64} +(1.71138 + 2.96420i) q^{65} +(1.89037 - 2.62712i) q^{66} +(3.19457 + 11.9223i) q^{67} +(-3.11649 - 9.30035i) q^{68} +(-8.94843 - 8.94843i) q^{69} +0.135373i q^{71} +(4.40226 - 0.999239i) q^{72} +(-6.55413 - 3.78403i) q^{73} +(9.82436 - 1.60226i) q^{74} +(-2.39593 + 8.94174i) q^{75} +(11.1081 - 7.35947i) q^{76} +(1.25618 - 12.5033i) q^{78} +(-3.39649 - 5.88289i) q^{79} +(-3.27149 - 0.456791i) q^{80} +(-5.62039 + 9.73480i) q^{81} +(-4.97934 + 2.24437i) q^{82} +(-5.63027 + 5.63027i) q^{83} +(2.86379 + 2.86379i) q^{85} +(-4.17562 + 11.0288i) q^{86} +(8.72690 + 5.03848i) q^{87} +(3.01715 + 0.116514i) q^{88} +(4.83608 - 2.79211i) q^{89} +(-1.44316 + 1.17965i) q^{90} +(2.34855 - 11.5700i) q^{92} +(-7.21586 - 1.93348i) q^{93} +(-5.13189 + 7.13201i) q^{94} +(-2.75095 + 4.76478i) q^{95} +(8.76975 + 8.37641i) q^{96} -6.15204 q^{97} +(1.20476 - 1.20476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.581133	+	1.28930i	0.410923	+	0.911670i
$2$	0.581133	+	1.28930i	0.410923	+	0.911670i
$3$	0.554865	+	2.07078i	0.320352	+	1.19557i	0.918903	+	0.394484i	$0.129077\pi$
$3$	0.554865	+	2.07078i	0.320352	+	1.19557i	−0.598551	+	0.801084i	$0.704257\pi$
$4$	−1.32457	+	1.49850i	−0.662285	+	0.749252i
$5$	0.213735	−	0.797669i	0.0955851	−	0.356728i	−0.901522	−	0.432732i	$-0.857550\pi$
$5$	0.213735	−	0.797669i	0.0955851	−	0.356728i	0.997108	+	0.0760040i	$0.0242162\pi$
$6$	−2.34740	+	1.91879i	−0.958324	+	0.783341i
$7$		0			0
$7$		0			0
$8$	−2.70177	−	0.836931i	−0.955219	−	0.295900i
$9$	−1.38220	+	0.798013i	−0.460733	+	0.266004i
$10$	1.15264	−	0.187984i	0.364497	−	0.0594458i
$11$	−1.03115	+	0.276295i	−0.310902	+	0.0833060i	−0.410896	−	0.911682i	$-0.634784\pi$
$11$	−1.03115	+	0.276295i	−0.310902	+	0.0833060i	0.0999943	+	0.994988i	$0.468118\pi$
$12$	−3.83804	−	1.91143i	−1.10795	−	0.551782i
$13$	−2.93078	+	2.93078i	−0.812852	+	0.812852i	−0.985061	−	0.172208i	$-0.944910\pi$
$13$	−2.93078	+	2.93078i	−0.812852	+	0.812852i	0.172208	+	0.985061i	$0.444910\pi$
$14$		0			0
$15$	1.77039			0.457114
$16$	−0.491033	−	3.96975i	−0.122758	−	0.992437i
$17$	−2.45215	+	4.24726i	−0.594735	+	1.03011i	0.398849	+	0.917016i	$0.369410\pi$
$17$	−2.45215	+	4.24726i	−0.594735	+	1.03011i	−0.993584	+	0.113095i	$0.963924\pi$
$18$	−1.83212	−	1.31831i	−0.431834	−	0.310729i
$19$	−6.43542	−	1.72437i	−1.47639	−	0.395597i	−0.571271	−	0.820761i	$-0.693549\pi$
$19$	−6.43542	−	1.72437i	−1.47639	−	0.395597i	−0.905116	+	0.425165i	$0.860216\pi$
$20$	0.912204	+	1.37685i	0.203975	+	0.307873i
$21$		0			0
$22$	−0.955458	−	1.16889i	−0.203704	−	0.249208i
$23$	−5.11212	+	2.95149i	−1.06595	+	0.615427i	−0.927073	−	0.374882i	$-0.877683\pi$
$23$	−5.11212	+	2.95149i	−1.06595	+	0.615427i	−0.138879	+	0.990309i	$0.544350\pi$
$24$	0.233988	−	6.05916i	0.0477627	−	1.23682i
$25$	3.73953	+	2.15902i	0.747907	+	0.431804i
$26$	−5.48182	−	2.07547i	−1.07507	−	0.407033i
$27$	2.12831	+	2.12831i	0.409594	+	0.409594i
$28$		0			0
$29$	3.32371	−	3.32371i	0.617198	−	0.617198i	−0.327614	−	0.944812i	$-0.606245\pi$
$29$	3.32371	−	3.32371i	0.617198	−	0.617198i	0.944812	+	0.327614i	$0.106245\pi$
$30$	1.02883	+	2.28256i	0.187839	+	0.416737i
$31$	−1.74230	+	3.01775i	−0.312926	+	0.542004i	−0.978995	−	0.203887i	$-0.934643\pi$
$31$	−1.74230	+	3.01775i	−0.312926	+	0.542004i	0.666068	+	0.745891i	$0.267976\pi$
$32$	4.83282	−	2.94004i	0.854330	−	0.519730i
$33$	−1.14429	−	1.98197i	−0.199196	−	0.345017i
$34$	−6.90100	−	0.693333i	−1.18351	−	0.118906i
$35$		0			0
$36$	0.634992	−	3.12825i	0.105832	−	0.521376i
$37$	1.82174	−	6.79882i	0.299492	−	1.11772i	−0.638092	−	0.769960i	$-0.720276\pi$
$37$	1.82174	−	6.79882i	0.299492	−	1.11772i	0.937584	−	0.347759i	$-0.113057\pi$
$38$	−1.51662	−	9.29925i	−0.246028	−	1.50854i
$39$	−7.69520	−	4.44283i	−1.23222	−	0.711422i
$40$	−1.24506	+	1.97623i	−0.196861	+	0.312470i
$41$			3.86206i			0.603152i	0.953442	+	0.301576i	$0.0975127\pi$
$41$			3.86206i			0.603152i	−0.953442	+	0.301576i	$0.902487\pi$
$42$		0			0
$43$	5.89641	+	5.89641i	0.899194	+	0.899194i	0.995365	−	0.0961708i	$-0.0306595\pi$
$43$	5.89641	+	5.89641i	0.899194	+	0.899194i	−0.0961708	+	0.995365i	$0.530659\pi$
$44$	0.951795	−	1.91115i	0.143488	−	0.288116i
$45$	0.341126	+	1.27310i	0.0508521	+	0.189783i
$46$	−6.77616	−	4.87584i	−0.999091	−	0.718903i
$47$	3.10648	+	5.38058i	0.453127	+	0.784839i	0.998578	−	0.0533036i	$-0.0169751\pi$
$47$	3.10648	+	5.38058i	0.453127	+	0.784839i	−0.545451	+	0.838142i	$0.683642\pi$
$48$	7.94803	−	3.21950i	1.14720	−	0.464695i
$49$		0			0
$50$	−0.610451	+	6.07604i	−0.0863308	+	0.859283i
$51$	−10.1558	−	2.72123i	−1.42209	−	0.381049i
$52$	−0.509767	−	8.27381i	−0.0706920	−	1.14737i
$53$	12.8748	−	3.44980i	1.76850	−	0.473867i	0.780086	−	0.625673i	$-0.215175\pi$
$53$	12.8748	−	3.44980i	1.76850	−	0.473867i	0.988410	+	0.151806i	$0.0485088\pi$
$54$	−1.50719	+	3.98086i	−0.205103	+	0.541726i
$55$			0.881566i			0.118870i
$56$		0			0
$57$		−	14.2832i		−	1.89185i
$58$	6.21677	+	2.35373i	0.816301	+	0.309060i
$59$	5.82851	−	1.56174i	0.758807	−	0.203322i	0.141386	−	0.989955i	$-0.454844\pi$
$59$	5.82851	−	1.56174i	0.758807	−	0.203322i	0.617421	+	0.786633i	$0.288178\pi$
$60$	−2.34501	+	2.65294i	−0.302739	+	0.342494i
$61$	9.40542	+	2.52017i	1.20424	+	0.322675i	0.804500	−	0.593953i	$-0.202434\pi$
$61$	9.40542	+	2.52017i	1.20424	+	0.322675i	0.399741	+	0.916628i	$0.369100\pi$
$62$	−4.90328	−	0.492626i	−0.622718	−	0.0625635i
$63$		0			0
$64$	6.59909	+	4.52239i	0.824886	+	0.565298i
$65$	1.71138	+	2.96420i	0.212271	+	0.367664i
$66$	1.89037	−	2.62712i	0.232688	−	0.323377i
$67$	3.19457	+	11.9223i	0.390278	+	1.45654i	0.829676	+	0.558245i	$0.188525\pi$
$67$	3.19457	+	11.9223i	0.390278	+	1.45654i	−0.439398	+	0.898293i	$0.644808\pi$
$68$	−3.11649	−	9.30035i	−0.377929	−	1.12783i
$69$	−8.94843	−	8.94843i	−1.07726	−	1.07726i
$70$		0			0
$71$			0.135373i			0.0160659i	0.999968	+	0.00803293i	$0.00255699\pi$
$71$			0.135373i			0.0160659i	−0.999968	+	0.00803293i	$0.997443\pi$
$72$	4.40226	−	0.999239i	0.518812	−	0.117762i
$73$	−6.55413	−	3.78403i	−0.767103	−	0.442887i	0.0647370	−	0.997902i	$-0.479379\pi$
$73$	−6.55413	−	3.78403i	−0.767103	−	0.442887i	−0.831840	+	0.555015i	$0.812712\pi$
$74$	9.82436	−	1.60226i	1.14206	−	0.186259i
$75$	−2.39593	+	8.94174i	−0.276658	+	1.03250i
$76$	11.1081	−	7.35947i	1.27419	−	0.844189i
$77$		0			0
$78$	1.25618	−	12.5033i	0.142235	−	1.41572i
$79$	−3.39649	−	5.88289i	−0.382135	−	0.661877i	0.609232	−	0.792992i	$-0.291478\pi$
$79$	−3.39649	−	5.88289i	−0.382135	−	0.661877i	−0.991367	+	0.131115i	$0.958144\pi$
$80$	−3.27149	−	0.456791i	−0.365764	−	0.0510707i
$81$	−5.62039	+	9.73480i	−0.624488	+	1.08164i
$82$	−4.97934	+	2.24437i	−0.549876	+	0.247849i
$83$	−5.63027	+	5.63027i	−0.618003	+	0.618003i	−0.945019	−	0.327016i	$-0.893957\pi$
$83$	−5.63027	+	5.63027i	−0.618003	+	0.618003i	0.327016	+	0.945019i	$0.393957\pi$
$84$		0			0
$85$	2.86379	+	2.86379i	0.310622	+	0.310622i
$86$	−4.17562	+	11.0288i	−0.450269	+	1.18927i
$87$	8.72690	+	5.03848i	0.935622	+	0.540182i
$88$	3.01715	+	0.116514i	0.321630	+	0.0124205i
$89$	4.83608	−	2.79211i	0.512623	−	0.295963i	−0.221288	−	0.975208i	$-0.571026\pi$
$89$	4.83608	−	2.79211i	0.512623	−	0.295963i	0.733911	+	0.679245i	$0.237693\pi$
$90$	−1.44316	+	1.17965i	−0.152123	+	0.124346i
$91$		0			0
$92$	2.34855	−	11.5700i	0.244853	−	1.20625i
$93$	−7.21586	−	1.93348i	−0.748249	−	0.200493i
$94$	−5.13189	+	7.13201i	−0.529314	+	0.735611i
$95$	−2.75095	+	4.76478i	−0.282241	+	0.488856i
$96$	8.76975	+	8.37641i	0.895059	+	0.854914i
$97$	−6.15204			−0.624645			−0.312322	−	0.949976i	$-0.601107\pi$
$97$	−6.15204			−0.624645			−0.312322	+	0.949976i	$0.601107\pi$
$98$		0			0
$99$	1.20476	−	1.20476i	0.121083	−	0.121083i
$100$	−8.18857	+	2.74394i	−0.818857	+	0.274394i
$101$	7.08585	−	1.89865i	0.705069	−	0.188923i	0.111569	−	0.993757i	$-0.464412\pi$
$101$	7.08585	−	1.89865i	0.705069	−	0.188923i	0.593500	+	0.804834i	$0.297746\pi$
$102$	−2.39338	−	14.6752i	−0.236980	−	1.45306i
$103$	12.1464	−	7.01271i	1.19682	−	0.690983i	0.236974	−	0.971516i	$-0.423844\pi$
$103$	12.1464	−	7.01271i	1.19682	−	0.690983i	0.959844	+	0.280533i	$0.0905111\pi$
$104$	10.3711	−	5.46542i	1.01697	−	0.535929i
$105$		0			0
$106$	11.9298	+	14.5947i	1.15873	+	1.41756i
$107$	1.24077	−	4.63060i	0.119949	−	0.447657i	−0.879660	−	0.475603i	$-0.842230\pi$
$107$	1.24077	−	4.63060i	0.119949	−	0.447657i	0.999609	+	0.0279457i	$0.00889655\pi$
$108$	−6.00838	+	0.370190i	−0.578157	+	0.0356215i
$109$	1.48011	+	5.52385i	0.141769	+	0.529089i	0.999878	+	0.0156216i	$0.00497270\pi$
$109$	1.48011	+	5.52385i	0.141769	+	0.529089i	−0.858109	+	0.513468i	$0.828361\pi$
$110$	−1.13660	+	0.512307i	−0.108371	+	0.0488466i
$111$	15.0897			1.43225
$112$		0			0
$113$	−18.9549			−1.78313			−0.891565	−	0.452893i	$-0.850392\pi$
$113$	−18.9549			−1.78313			−0.891565	+	0.452893i	$0.850392\pi$
$114$	18.4152	−	8.30042i	1.72474	−	0.777405i
$115$	1.26167	+	4.70862i	0.117651	+	0.439081i
$116$	0.578112	+	9.38308i	0.0536764	+	0.871197i
$117$	1.71212	−	6.38972i	0.158286	−	0.590730i
$118$	5.40069	+	6.60709i	0.497174	+	0.608232i
$119$		0			0
$120$	−4.78319	−	1.48170i	−0.436644	−	0.135260i
$121$	−8.53936	+	4.93020i	−0.776305	+	0.448200i
$122$	2.21655	+	13.5909i	0.200677	+	1.23046i
$123$	−7.99749	+	2.14292i	−0.721109	+	0.193221i
$124$	−2.21432	−	6.60807i	−0.198852	−	0.593422i
$125$	5.44112	−	5.44112i	0.486669	−	0.486669i
$126$		0			0
$127$	−13.0124			−1.15467			−0.577333	−	0.816509i	$-0.695907\pi$
$127$	−13.0124			−1.15467			−0.577333	+	0.816509i	$0.695907\pi$
$128$	−1.99575	+	11.1363i	−0.176401	+	0.984318i
$129$	−8.93848	+	15.4819i	−0.786990	+	1.36311i
$130$	−2.82719	+	3.92907i	−0.247961	+	0.344603i
$131$	−11.9616	−	3.20510i	−1.04509	−	0.280031i	−0.304868	−	0.952394i	$-0.598613\pi$
$131$	−11.9616	−	3.20510i	−1.04509	−	0.280031i	−0.740221	+	0.672364i	$0.765279\pi$
$132$	4.48569	+	0.910533i	0.390430	+	0.0792517i
$133$		0			0
$134$	−13.5149	+	11.0472i	−1.16751	+	0.954330i
$135$	2.15258	−	1.24279i	0.185265	−	0.106963i
$136$	10.1798	−	9.42281i	0.872912	−	0.808000i
$137$	9.24765	+	5.33913i	0.790080	+	0.456153i	0.839991	−	0.542601i	$-0.182560\pi$
$137$	9.24765	+	5.33913i	0.790080	+	0.456153i	−0.0499109	+	0.998754i	$0.515894\pi$
$138$	6.33695	−	16.7374i	0.539437	−	1.42478i
$139$	−0.564966	−	0.564966i	−0.0479198	−	0.0479198i	0.682741	−	0.730661i	$-0.260788\pi$
$139$	−0.564966	−	0.564966i	−0.0479198	−	0.0479198i	−0.730661	+	0.682741i	$0.760788\pi$
$140$		0			0
$141$	−9.41835	+	9.41835i	−0.793169	+	0.793169i
$142$	−0.174536	+	0.0786699i	−0.0146468	+	0.00660183i
$143$	2.21230	−	3.83182i	0.185002	−	0.320433i
$144$	3.84661	+	5.09513i	0.320551	+	0.424594i
$145$	−1.94083	−	3.36161i	−0.161177	−	0.279167i
$146$	1.06991	−	10.6492i	0.0885467	−	0.881338i
$147$		0			0
$148$	7.77504	+	11.7354i	0.639105	+	0.964643i
$149$	1.76514	−	6.58760i	0.144606	−	0.539677i	−0.855167	−	0.518353i	$-0.826545\pi$
$149$	1.76514	−	6.58760i	0.144606	−	0.539677i	0.999773	−	0.0213237i	$-0.00678807\pi$
$150$	−12.9209	+	2.10727i	−1.05499	+	0.172058i
$151$	−16.1165	−	9.30487i	−1.31154	−	0.757220i	−0.329191	−	0.944263i	$-0.606776\pi$
$151$	−16.1165	−	9.30487i	−1.31154	−	0.757220i	−0.982352	+	0.187044i	$0.940109\pi$
$152$	15.9438	+	10.0448i	1.29322	+	0.814744i
$153$		−	7.82741i		−	0.632808i
$154$		0			0
$155$	2.03478	+	2.03478i	0.163437	+	0.163437i
$156$	16.8504	−	5.64647i	1.34911	−	0.452079i
$157$	0.178169	+	0.664936i	0.0142194	+	0.0530677i	0.972671	−	0.232188i	$-0.0745883\pi$
$157$	0.178169	+	0.664936i	0.0142194	+	0.0530677i	−0.958452	+	0.285255i	$0.907922\pi$
$158$	5.61098	−	7.79782i	0.446385	−	0.620361i
$159$	14.2876	+	24.7469i	1.13308	+	1.96255i
$160$	−1.31223	−	4.48338i	−0.103741	−	0.354442i
$161$		0			0
$162$	−15.8172	−	1.58913i	−1.24272	−	0.124854i
$163$	11.9341	+	3.19773i	0.934749	+	0.250465i	0.693879	−	0.720092i	$-0.255900\pi$
$163$	11.9341	+	3.19773i	0.934749	+	0.250465i	0.240871	+	0.970557i	$0.422567\pi$
$164$	−5.78731	−	5.11556i	−0.451913	−	0.399458i
$165$	−1.82553	+	0.489150i	−0.142118	+	0.0380803i
$166$	−10.5310	−	3.98715i	−0.817366	−	0.309463i
$167$			18.6633i			1.44421i	0.691783	+	0.722106i	$0.256826\pi$
$167$			18.6633i			1.44421i	−0.691783	+	0.722106i	$0.743174\pi$
$168$		0			0
$169$		−	4.17895i		−	0.321457i
$170$	−2.02803	+	5.35652i	−0.155543	+	0.410827i
$171$	10.2711	−	2.75213i	0.785451	−	0.210461i
$172$	−16.6460	+	1.02560i	−1.26925	+	0.0782010i
$173$	8.97435	+	2.40467i	0.682307	+	0.182824i	0.583292	−	0.812262i	$-0.301764\pi$
$173$	8.97435	+	2.40467i	0.682307	+	0.182824i	0.0990149	+	0.995086i	$0.468431\pi$
$174$	−1.42460	+	14.1796i	−0.107999	+	1.07495i
$175$		0			0
$176$	1.60315	+	3.95772i	0.120842	+	0.298324i
$177$	6.46807	+	11.2030i	0.486170	+	0.842071i
$178$	6.41026	+	4.61255i	0.480470	+	0.345725i
$179$	0.0920684	+	0.343604i	0.00688152	+	0.0256822i	0.969281	−	0.245955i	$-0.0791016\pi$
$179$	0.0920684	+	0.343604i	0.00688152	+	0.0256822i	−0.962400	+	0.271637i	$0.912435\pi$
$180$	−2.35959	−	1.17513i	−0.175874	−	0.0875890i
$181$	−16.5200	−	16.5200i	−1.22792	−	1.22792i	−0.964750	−	0.263170i	$-0.915232\pi$
$181$	−16.5200	−	16.5200i	−1.22792	−	1.22792i	−0.263170	−	0.964750i	$-0.584768\pi$
$182$		0			0
$183$			20.8750i			1.54312i
$184$	16.2820	−	3.69573i	1.20032	−	0.272453i
$185$	−5.03384	−	2.90629i	−0.370095	−	0.213674i
$186$	−1.70054	−	10.4270i	−0.124690	−	0.764544i
$187$	1.35503	−	5.05706i	0.0990899	−	0.369809i
$188$	−12.1776	−	2.47188i	−0.888141	−	0.180280i
$189$		0			0
$190$	−7.74188	−	0.777815i	−0.561655	−	0.0564286i
$191$	10.1926	+	17.6541i	0.737511	+	1.27741i	0.953613	+	0.301036i	$0.0973325\pi$
$191$	10.1926	+	17.6541i	0.737511	+	1.27741i	−0.216101	+	0.976371i	$0.569334\pi$
$192$	−5.70329	+	16.1746i	−0.411599	+	1.16730i
$193$	9.55624	−	16.5519i	0.687873	−	1.19143i	−0.284652	−	0.958631i	$-0.591878\pi$
$193$	9.55624	−	16.5519i	0.687873	−	1.19143i	0.972525	−	0.232800i	$-0.0747888\pi$
$194$	−3.57515	−	7.93180i	−0.256681	−	0.569470i
$195$	−5.18864	+	5.18864i	−0.371566	+	0.371566i
$196$		0			0
$197$	6.69173	+	6.69173i	0.476766	+	0.476766i	0.904096	−	0.427330i	$-0.140546\pi$
$197$	6.69173	+	6.69173i	0.476766	+	0.476766i	−0.427330	+	0.904096i	$0.640546\pi$
$198$	2.25342	+	0.853168i	0.160144	+	0.0606320i
$199$	−6.89757	−	3.98231i	−0.488956	−	0.282299i	0.235185	−	0.971951i	$-0.424430\pi$
$199$	−6.89757	−	3.98231i	−0.488956	−	0.282299i	−0.724141	+	0.689652i	$0.757764\pi$
$200$	−8.29640	−	8.96291i	−0.586644	−	0.633773i
$201$	−22.9159	+	13.2305i	−1.61636	+	0.933209i
$202$	6.56574	+	8.03240i	0.461964	+	0.565157i
$203$		0			0
$204$	17.5298	−	11.6140i	1.22733	−	0.813144i
$205$	3.08064	+	0.825456i	0.215161	+	0.0576523i
$206$	16.1001	+	11.5850i	1.12175	+	0.807162i
$207$	4.71065	−	8.15908i	0.327413	−	0.567095i
$208$	13.0736	+	10.1953i	0.906489	+	0.706920i
$209$	7.11229			0.491967
$210$		0			0
$211$	9.30887	−	9.30887i	0.640849	−	0.640849i	−0.309915	−	0.950764i	$-0.600301\pi$
$211$	9.30887	−	9.30887i	0.640849	−	0.640849i	0.950764	+	0.309915i	$0.100301\pi$
$212$	−11.8841	+	23.8625i	−0.816202	+	1.63888i
$213$	−0.280329	+	0.0751139i	−0.0192078	+	0.00514672i
$214$	6.69127	−	1.09128i	0.457406	−	0.0745984i
$215$	5.96365	−	3.44311i	0.406718	−	0.234818i
$216$	−3.96895	−	7.53146i	−0.270053	−	0.512451i
$217$		0			0
$218$	−6.26174	+	5.11840i	−0.424099	+	0.346662i
$219$	4.19925	−	15.6718i	0.283759	−	1.05900i
$220$	−1.32103	−	1.16770i	−0.0890639	−	0.0787260i
$221$	−5.26105	−	19.6345i	−0.353897	−	1.32076i
$222$	8.76913	+	19.4551i	0.588545	+	1.30574i
$223$	3.87218			0.259301			0.129650	−	0.991560i	$-0.458615\pi$
$223$	3.87218			0.259301			0.129650	+	0.991560i	$0.458615\pi$
$224$		0			0
$225$	−6.89171			−0.459447
$226$	−11.0153	−	24.4385i	−0.732729	−	1.62563i
$227$	−1.58523	−	5.91615i	−0.105215	−	0.392668i	0.893154	−	0.449750i	$-0.148487\pi$
$227$	−1.58523	−	5.91615i	−0.105215	−	0.392668i	−0.998369	+	0.0570819i	$0.981820\pi$
$228$	21.4034	+	18.9190i	1.41747	+	1.25294i
$229$	6.97424	−	26.0282i	0.460871	−	1.71999i	−0.209358	−	0.977839i	$-0.567138\pi$
$229$	6.97424	−	26.0282i	0.460871	−	1.71999i	0.670229	−	0.742154i	$-0.266196\pi$
$230$	−5.33760	+	4.36300i	−0.351951	+	0.287688i
$231$		0			0
$232$	−11.7616	+	6.19818i	−0.772188	+	0.406930i
$233$	−11.8630	+	6.84909i	−0.777169	+	0.448699i	−0.835426	−	0.549603i	$-0.814779\pi$
$233$	−11.8630	+	6.84909i	−0.777169	+	0.448699i	0.0582572	+	0.998302i	$0.481446\pi$
$234$	9.23321	−	1.50585i	0.603594	−	0.0984403i
$235$	4.95589	−	1.32793i	0.323286	−	0.0866243i
$236$	−5.37998	+	10.8027i	−0.350207	+	0.703195i
$237$	10.2976	−	10.2976i	0.668901	−	0.668901i
$238$		0			0
$239$	−1.05904			−0.0685033			−0.0342517	−	0.999413i	$-0.510905\pi$
$239$	−1.05904			−0.0685033			−0.0342517	+	0.999413i	$0.510905\pi$
$240$	−0.869323	−	7.02802i	−0.0561146	−	0.453657i
$241$	2.47862	−	4.29309i	0.159662	−	0.276542i	−0.775085	−	0.631857i	$-0.782293\pi$
$241$	2.47862	−	4.29309i	0.159662	−	0.276542i	0.934747	+	0.355315i	$0.115626\pi$
$242$	−11.3190	−	8.14466i	−0.727612	−	0.523558i
$243$	−14.5553	−	3.90007i	−0.933720	−	0.250189i
$244$	−16.2346	+	10.7559i	−1.03932	+	0.688577i
$245$		0			0
$246$	−7.41046	−	9.06581i	−0.472474	−	0.578015i
$247$	23.9145	−	13.8071i	1.52165	−	0.878523i
$248$	7.23294	−	6.69508i	0.459292	−	0.425138i
$249$	−14.7831	−	8.53505i	−0.936843	−	0.540887i
$250$	10.1772	+	3.85320i	0.643665	+	0.243698i
$251$	20.0251	+	20.0251i	1.26397	+	1.26397i	0.949151	+	0.314822i	$0.101945\pi$
$251$	20.0251	+	20.0251i	1.26397	+	1.26397i	0.314822	+	0.949151i	$0.398055\pi$
$252$		0			0
$253$	4.45586	−	4.45586i	0.280138	−	0.280138i
$254$	−7.56195	−	16.7769i	−0.474479	−	1.05267i
$255$	−4.34128	+	7.51932i	−0.271862	+	0.470878i
$256$	−15.5178	+	3.89856i	−0.969861	+	0.243660i
$257$	10.4559	+	18.1101i	0.652220	+	1.12968i	0.982583	+	0.185824i	$0.0594954\pi$
$257$	10.4559	+	18.1101i	0.652220	+	1.12968i	−0.330363	+	0.943854i	$0.607171\pi$
$258$	−25.1552	−	2.52731i	−1.56610	−	0.157343i
$259$		0			0
$260$	−6.70871	−	1.36177i	−0.416057	−	0.0844537i
$261$	−1.94167	+	7.24640i	−0.120186	+	0.448541i
$262$	−2.81895	−	17.2846i	−0.174156	−	1.06785i
$263$	10.5699	+	6.10253i	0.651768	+	0.376298i	0.789133	−	0.614222i	$-0.210530\pi$
$263$	10.5699	+	6.10253i	0.651768	+	0.376298i	−0.137365	+	0.990520i	$0.543863\pi$
$264$	1.43284	+	6.31253i	0.0881851	+	0.388509i
$265$		−	11.0072i		−	0.676167i
$266$		0			0
$267$	8.46523	+	8.46523i	0.518064	+	0.518064i
$268$	−22.0970	−	11.0048i	−1.34979	−	0.672226i
$269$	1.46849	+	5.48048i	0.0895354	+	0.334151i	0.996134	−	0.0878427i	$-0.0279973\pi$
$269$	1.46849	+	5.48048i	0.0895354	+	0.334151i	−0.906599	+	0.421993i	$0.861331\pi$
$270$	2.85327	+	2.05309i	0.173644	+	0.124947i
$271$	1.47292	+	2.55118i	0.0894737	+	0.154973i	0.907289	−	0.420508i	$-0.138148\pi$
$271$	1.47292	+	2.55118i	0.0894737	+	0.154973i	−0.817815	+	0.575481i	$0.804815\pi$
$272$	18.0646	+	7.64889i	1.09533	+	0.463782i
$273$		0			0
$274$	−1.50961	+	15.0257i	−0.0911988	+	0.907736i
$275$	−4.45253	−	1.19305i	−0.268498	−	0.0719437i
$276$	25.2621	−	1.55645i	1.52060	−	0.0936874i
$277$	12.9118	−	3.45970i	0.775793	−	0.207873i	0.150864	−	0.988555i	$-0.451794\pi$
$277$	12.9118	−	3.45970i	0.775793	−	0.207873i	0.624929	+	0.780681i	$0.285128\pi$
$278$	0.400088	−	1.05673i	0.0239957	−	0.0633784i
$279$		−	5.56151i		−	0.332959i
$280$		0			0
$281$		−	5.24743i		−	0.313036i	−0.987675	−	0.156518i	$-0.949973\pi$
$281$		−	5.24743i		−	0.313036i	0.987675	−	0.156518i	$-0.0500269\pi$
$282$	−17.6164	−	6.66973i	−1.04904	−	0.397177i
$283$	−5.21685	+	1.39785i	−0.310110	+	0.0830936i	−0.410517	−	0.911853i	$-0.634652\pi$
$283$	−5.21685	+	1.39785i	−0.310110	+	0.0830936i	0.100408	+	0.994946i	$0.467985\pi$
$284$	−0.202858	−	0.179311i	−0.0120374	−	0.0106402i
$285$	−11.3932	−	3.05281i	−0.674877	−	0.180833i
$286$	6.22599	+	0.625516i	0.368151	+	0.0369875i
$287$		0			0
$288$	−4.33373	+	7.92037i	−0.255368	+	0.466712i
$289$	−3.52613	−	6.10743i	−0.207419	−	0.359261i
$290$	3.20624	−	4.45585i	0.188277	−	0.261656i
$291$	−3.41355	−	12.7395i	−0.200106	−	0.746806i
$292$	14.3518	−	4.80919i	0.839875	−	0.281437i
$293$	1.49974	+	1.49974i	0.0876160	+	0.0876160i	0.749556	−	0.661940i	$-0.230267\pi$
$293$	1.49974	+	1.49974i	0.0876160	+	0.0876160i	−0.661940	+	0.749556i	$0.730267\pi$
$294$		0			0
$295$		−	4.98302i		−	0.290122i
$296$	−10.6121	+	16.8442i	−0.616813	+	0.979046i
$297$	−2.78264	−	1.60656i	−0.161465	−	0.0932220i
$298$	9.51914	−	1.55248i	0.551429	−	0.0899327i
$299$	6.33235	−	23.6327i	0.366210	−	1.36671i
$300$	−10.2257	−	15.4343i	−0.590379	−	0.891098i
$301$		0			0
$302$	2.63090	−	26.1863i	0.151391	−	1.50685i
$303$	7.86339	+	13.6198i	0.451740	+	0.782436i
$304$	−3.68529	+	26.3937i	−0.211366	+	1.51378i
$305$	4.02053	−	6.96376i	0.230215	−	0.398744i
$306$	10.0918	−	4.54876i	0.576912	−	0.260035i
$307$	−6.27283	+	6.27283i	−0.358010	+	0.358010i	−0.863079	−	0.505069i	$-0.831467\pi$
$307$	−6.27283	+	6.27283i	−0.358010	+	0.358010i	0.505069	+	0.863079i	$0.331467\pi$
$308$		0			0
$309$	21.2614	+	21.2614i	1.20952	+	1.20952i
$310$	−1.44095	+	3.80590i	−0.0818407	+	0.216161i
$311$	9.59468	+	5.53949i	0.544065	+	0.314116i	0.746725	−	0.665133i	$-0.231625\pi$
$311$	9.59468	+	5.53949i	0.544065	+	0.314116i	−0.202660	+	0.979249i	$0.564959\pi$
$312$	17.0723	+	18.4438i	0.966529	+	1.04418i
$313$	−11.0653	+	6.38853i	−0.625445	+	0.361101i	−0.778986	−	0.627041i	$-0.784266\pi$
$313$	−11.0653	+	6.38853i	−0.625445	+	0.361101i	0.153541	+	0.988142i	$0.450932\pi$
$314$	−0.753760	+	0.616129i	−0.0425371	+	0.0347702i
$315$		0			0
$316$	13.3144	+	2.70264i	0.748995	+	0.152035i
$317$	22.2221	+	5.95440i	1.24812	+	0.334432i	0.821610	−	0.570051i	$-0.193076\pi$
$317$	22.2221	+	5.95440i	1.24812	+	0.334432i	0.426509	+	0.904483i	$0.359743\pi$
$318$	−23.6030	+	32.8022i	−1.32359	+	1.83945i
$319$	−2.50891	+	4.34555i	−0.140472	+	0.243304i
$320$	5.01782	−	4.29730i	0.280505	−	0.240226i
$321$	10.2774			0.573631
$322$		0			0
$323$	23.1045	−	23.1045i	1.28557	−	1.28557i
$324$	−7.14305	−	21.3166i	−0.396836	−	1.18426i
$325$	−17.2874	+	4.63214i	−0.958931	+	0.256945i
$326$	2.81247	+	17.2449i	0.155768	+	0.955105i
$327$	−10.6175	+	6.12999i	−0.587146	+	0.338989i
$328$	3.23228	−	10.4344i	0.178473	−	0.576142i
$329$		0			0
$330$	−1.69154	−	2.06939i	−0.0931161	−	0.113916i
$331$	−2.91186	+	10.8672i	−0.160050	+	0.597316i	0.838569	+	0.544795i	$0.183392\pi$
$331$	−2.91186	+	10.8672i	−0.160050	+	0.597316i	−0.998620	+	0.0525215i	$0.983274\pi$
$332$	−0.979306	−	15.8947i	−0.0537464	−	0.872334i
$333$	2.90754	+	10.8511i	0.159332	+	0.594636i
$334$	−24.0625	+	10.8459i	−1.31664	+	0.593460i
$335$	10.1928			0.556893
$336$		0			0
$337$	1.61885			0.0881844			0.0440922	−	0.999027i	$-0.485960\pi$
$337$	1.61885			0.0881844			0.0440922	+	0.999027i	$0.485960\pi$
$338$	5.38790	−	2.42852i	0.293063	−	0.132094i
$339$	−10.5174	−	39.2516i	−0.571228	−	2.13185i
$340$	−8.08470	+	0.498116i	−0.438454	+	0.0270141i
$341$	0.962776	−	3.59313i	0.0521372	−	0.194579i
$342$	9.51719	+	11.6431i	0.514631	+	0.629589i
$343$		0			0
$344$	−10.9958	−	20.8656i	−0.592856	−	1.12500i
$345$	−9.05048	+	5.22529i	−0.487261	+	0.281320i
$346$	2.11496	+	12.9680i	0.113701	+	0.697166i
$347$	−12.5306	+	3.35756i	−0.672676	+	0.180243i	−0.578960	−	0.815356i	$-0.696541\pi$
$347$	−12.5306	+	3.35756i	−0.672676	+	0.180243i	−0.0937162	+	0.995599i	$0.529875\pi$
$348$	−19.1096	+	6.40349i	−1.02438	+	0.343263i
$349$	0.267623	−	0.267623i	0.0143255	−	0.0143255i	−0.699908	−	0.714233i	$-0.746776\pi$
$349$	0.267623	−	0.267623i	0.0143255	−	0.0143255i	0.714233	+	0.699908i	$0.246776\pi$
$350$		0			0
$351$	−12.4752			−0.665879
$352$	−4.17103	+	4.36689i	−0.222316	+	0.232756i
$353$	16.9920	−	29.4309i	0.904391	−	1.56645i	0.0826573	−	0.996578i	$-0.473659\pi$
$353$	16.9920	−	29.4309i	0.904391	−	1.56645i	0.821733	−	0.569872i	$-0.193007\pi$
$354$	−10.6852	+	14.8497i	−0.567913	+	0.789253i
$355$	0.107983	+	0.0289340i	0.00573115	+	0.00153566i
$356$	−2.22173	+	10.9452i	−0.117751	+	0.580096i
$357$		0			0
$358$	−0.389503	+	0.318383i	−0.0205859	+	0.0168271i
$359$	2.23306	−	1.28926i	0.117856	−	0.0680444i	−0.439913	−	0.898040i	$-0.644991\pi$
$359$	2.23306	−	1.28926i	0.117856	−	0.0680444i	0.557769	+	0.829996i	$0.311657\pi$
$360$	0.143854	−	3.72512i	0.00758177	−	0.196331i
$361$	21.9867	+	12.6940i	1.15720	+	0.668108i
$362$	11.6988	−	30.8994i	0.614877	−	1.62404i
$363$	−14.9476	−	14.9476i	−0.784544	−	0.784544i
$364$		0			0
$365$	−4.41925	+	4.41925i	−0.231314	+	0.231314i
$366$	−26.9140	+	12.1311i	−1.40682	+	0.634104i
$367$	−4.64642	+	8.04784i	−0.242541	+	0.420094i	−0.961437	−	0.275024i	$-0.911314\pi$
$367$	−4.64642	+	8.04784i	−0.242541	+	0.420094i	0.718896	+	0.695117i	$0.244648\pi$
$368$	14.2269	+	18.8446i	0.741627	+	0.982340i
$369$	−3.08197	−	5.33813i	−0.160441	−	0.277892i
$370$	0.821736	−	8.17904i	0.0427200	−	0.425208i
$371$		0			0
$372$	12.4552	−	8.25196i	0.645774	−	0.427844i
$373$	2.84650	−	10.6233i	0.147386	−	0.550053i	−0.852251	−	0.523133i	$-0.824763\pi$
$373$	2.84650	−	10.6233i	0.147386	−	0.550053i	0.999638	−	0.0269206i	$-0.00857012\pi$
$374$	7.30750	−	1.19178i	0.377862	−	0.0616256i
$375$	14.2865	+	8.24831i	0.737751	+	0.425941i
$376$	−3.88981	−	17.1370i	−0.200602	−	0.883773i
$377$			19.4821i			1.00338i
$378$		0			0
$379$	−13.2670	−	13.2670i	−0.681482	−	0.681482i	0.278852	−	0.960334i	$-0.410046\pi$
$379$	−13.2670	−	13.2670i	−0.681482	−	0.681482i	−0.960334	+	0.278852i	$0.910046\pi$
$380$	−3.49623	−	10.4336i	−0.179353	−	0.535232i
$381$	−7.22014	−	26.9459i	−0.369899	−	1.38048i
$382$	−16.8381	+	23.4007i	−0.861513	+	1.19728i
$383$	−9.28982	−	16.0904i	−0.474687	−	0.822183i	0.524892	−	0.851169i	$-0.324106\pi$
$383$	−9.28982	−	16.0904i	−0.474687	−	0.822183i	−0.999580	+	0.0289859i	$0.990772\pi$
$384$	−24.1682	+	2.04638i	−1.23333	+	0.104429i
$385$		0			0
$386$	26.8937	+	2.70197i	1.36885	+	0.137527i
$387$	−12.8554	−	3.44460i	−0.653478	−	0.175099i
$388$	8.14880	−	9.21886i	0.413693	−	0.468017i
$389$	−30.0299	+	8.04649i	−1.52258	+	0.407973i	−0.920589	−	0.390532i	$-0.872291\pi$
$389$	−30.0299	+	8.04649i	−1.52258	+	0.407973i	−0.601988	+	0.798505i	$0.705624\pi$
$390$	−9.70498	−	3.67440i	−0.491431	−	0.186061i
$391$		−	28.9500i		−	1.46406i
$392$		0			0
$393$		−	26.5483i		−	1.33918i
$394$	−4.73884	+	12.5164i	−0.238739	+	0.630567i
$395$	−5.41854	+	1.45189i	−0.272637	+	0.0730527i
$396$	0.209551	+	3.40113i	0.0105303	+	0.170913i
$397$	−29.8799	−	8.00628i	−1.49963	−	0.401824i	−0.586652	−	0.809839i	$-0.699554\pi$
$397$	−29.8799	−	8.00628i	−1.49963	−	0.401824i	−0.912975	+	0.408015i	$0.866221\pi$
$398$	1.12598	−	11.2073i	0.0564401	−	0.561769i
$399$		0			0
$400$	6.73453	−	15.9052i	0.336726	−	0.795258i
$401$	3.55546	+	6.15824i	0.177551	+	0.307528i	0.941041	−	0.338292i	$-0.109849\pi$
$401$	3.55546	+	6.15824i	0.177551	+	0.307528i	−0.763490	+	0.645820i	$0.776516\pi$
$402$	−30.3752	−	21.8567i	−1.51498	−	1.09011i
$403$	−3.73807	−	13.9507i	−0.186206	−	0.694932i
$404$	−6.54057	+	13.1331i	−0.325405	+	0.653395i
$405$	6.56387	+	6.56387i	0.326162	+	0.326162i
$406$		0			0
$407$			7.51391i			0.372451i
$408$	25.1610	+	15.8518i	1.24566	+	0.784782i
$409$	−30.1624	−	17.4143i	−1.49144	−	0.861081i	−0.491484	−	0.870887i	$-0.663545\pi$
$409$	−30.1624	−	17.4143i	−1.49144	−	0.861081i	−0.999952	+	0.00980587i	$0.996879\pi$
$410$	0.726006	+	4.45156i	0.0358549	+	0.219847i
$411$	−5.92499	+	22.1124i	−0.292258	+	1.09072i
$412$	−5.58013	+	27.4902i	−0.274913	+	1.35435i
$413$		0			0
$414$	13.2570	+	1.33191i	0.651545	+	0.0654598i
$415$	3.28771	+	5.69448i	0.161387	+	0.279531i
$416$	−5.54734	+	22.7805i	−0.271981	+	1.11691i
$417$	0.856443	−	1.48340i	0.0419402	−	0.0726426i
$418$	4.13319	+	9.16985i	0.202161	+	0.448512i
$419$	0.653529	−	0.653529i	0.0319270	−	0.0319270i	−0.690963	−	0.722890i	$-0.742813\pi$
$419$	0.653529	−	0.653529i	0.0319270	−	0.0319270i	0.722890	+	0.690963i	$0.242813\pi$
$420$		0			0
$421$	−9.48036	−	9.48036i	−0.462045	−	0.462045i	0.437280	−	0.899325i	$-0.355942\pi$
$421$	−9.48036	−	9.48036i	−0.462045	−	0.462045i	−0.899325	+	0.437280i	$0.855942\pi$
$422$	17.4116	+	6.59220i	0.847582	+	0.320903i
$423$	−8.58755	−	4.95802i	−0.417541	−	0.241067i
$424$	−37.6721	−	1.45479i	−1.82952	−	0.0706510i
$425$	−18.3398	+	10.5885i	−0.889613	+	0.513618i
$426$	−0.259753	−	0.317776i	−0.0125851	−	0.0153963i
$427$		0			0
$428$	5.29550	+	7.99285i	0.255968	+	0.386349i
$429$	9.16240	+	2.45506i	0.442365	+	0.118531i
$430$	7.90487	+	5.68800i	0.381207	+	0.274300i
$431$	−6.79706	+	11.7729i	−0.327403	+	0.567079i	−0.981996	−	0.188903i	$-0.939507\pi$
$431$	−6.79706	+	11.7729i	−0.327403	+	0.567079i	0.654593	+	0.755982i	$0.272840\pi$
$432$	7.40379	−	9.49393i	0.356215	−	0.456777i
$433$	−6.65932			−0.320027			−0.160013	−	0.987115i	$-0.551154\pi$
$433$	−6.65932			−0.320027			−0.160013	+	0.987115i	$0.551154\pi$
$434$		0			0
$435$	5.88428	−	5.88428i	0.282130	−	0.282130i
$436$	−10.2380	−	5.09877i	−0.490313	−	0.244187i
$437$	37.9881	−	10.1789i	1.81722	−	0.486922i
$438$	22.6460	−	3.69333i	1.08207	−	0.176474i
$439$	−5.26579	+	3.04021i	−0.251323	+	0.145101i	−0.620370	−	0.784310i	$-0.713017\pi$
$439$	−5.26579	+	3.04021i	−0.251323	+	0.145101i	0.369047	+	0.929411i	$0.379684\pi$
$440$	0.737810	−	2.38179i	0.0351737	−	0.113547i
$441$		0			0
$442$	22.2573	−	18.1933i	1.05867	−	0.865367i
$443$	−5.02775	+	18.7638i	−0.238876	+	0.891497i	0.737487	+	0.675361i	$0.236012\pi$
$443$	−5.02775	+	18.7638i	−0.238876	+	0.891497i	−0.976363	+	0.216136i	$0.930655\pi$
$444$	−19.9874	+	22.6120i	−0.948558	+	1.07312i
$445$	−1.19354	−	4.45436i	−0.0565793	−	0.211157i
$446$	2.25025	+	4.99239i	0.106553	+	0.236397i
$447$	14.6209			0.691545
$448$		0			0
$449$	16.7810			0.791946			0.395973	−	0.918262i	$-0.370407\pi$
$449$	16.7810			0.791946			0.395973	+	0.918262i	$0.370407\pi$
$450$	−4.00500	−	8.88545i	−0.188797	−	0.418864i
$451$	−1.06707	−	3.98234i	−0.0502462	−	0.187521i
$452$	25.1071	−	28.4041i	1.18094	−	1.33601i
$453$	10.3259	−	38.5368i	0.485153	−	1.81062i
$454$	6.70644	−	5.48189i	0.314749	−	0.257278i
$455$		0			0
$456$	−11.9540	+	38.5898i	−0.559799	+	1.80713i
$457$	34.1832	−	19.7357i	1.59902	−	0.923197i	0.607348	−	0.794436i	$-0.292233\pi$
$457$	34.1832	−	19.7357i	1.59902	−	0.923197i	0.991676	−	0.128761i	$-0.0410999\pi$
$458$	37.6110	−	6.13399i	1.75745	−	0.286623i
$459$	−14.2584	+	3.82054i	−0.665527	+	0.178327i
$460$	−8.72705	−	4.34627i	−0.406901	−	0.202646i
$461$	1.46832	−	1.46832i	0.0683865	−	0.0683865i	−0.672086	−	0.740473i	$-0.734602\pi$
$461$	1.46832	−	1.46832i	0.0683865	−	0.0683865i	0.740473	+	0.672086i	$0.234602\pi$
$462$		0			0
$463$	−23.8476			−1.10829			−0.554145	−	0.832420i	$-0.686955\pi$
$463$	−23.8476			−1.10829			−0.554145	+	0.832420i	$0.686955\pi$
$464$	−14.8263	−	11.5622i	−0.688296	−	0.536763i
$465$	−3.08456	+	5.34261i	−0.143043	+	0.247758i
$466$	−15.7245	−	11.3146i	−0.728422	−	0.524141i
$467$	−34.3174	−	9.19531i	−1.58802	−	0.425508i	−0.646622	−	0.762811i	$-0.723819\pi$
$467$	−34.3174	−	9.19531i	−1.58802	−	0.425508i	−0.941396	+	0.337302i	$0.890486\pi$
$468$	7.30721	+	11.0292i	0.337776	+	0.509827i
$469$		0			0
$470$	4.59212	+	5.61790i	0.211819	+	0.259135i
$471$	−1.27808	+	0.737900i	−0.0588908	+	0.0340006i
$472$	−17.0543	−	0.658592i	−0.784990	−	0.0303142i
$473$	−7.70920	−	4.45091i	−0.354470	−	0.204653i
$474$	19.2609	+	7.29239i	0.884684	+	0.334950i
$475$	−20.3425	−	20.3425i	−0.933380	−	0.933380i
$476$		0			0
$477$	−15.0426	+	15.0426i	−0.688754	+	0.688754i
$478$	−0.615441	−	1.36541i	−0.0281496	−	0.0624525i
$479$	13.4563	−	23.3070i	0.614834	−	1.06492i	−0.375579	−	0.926790i	$-0.622556\pi$
$479$	13.4563	−	23.3070i	0.614834	−	1.06492i	0.990414	−	0.138134i	$-0.0441104\pi$
$480$	8.55600	−	5.20503i	0.390526	−	0.237576i
$481$	14.5867	+	25.2650i	0.665098	+	1.15198i
$482$	6.97547	+	0.700815i	0.317724	+	0.0319212i
$483$		0			0
$484$	3.92304	−	19.3267i	0.178320	−	0.878484i
$485$	−1.31490	+	4.90729i	−0.0597067	+	0.222828i
$486$	−3.43019	−	21.0325i	−0.155597	−	0.954053i
$487$	23.1882	+	13.3877i	1.05076	+	0.606654i	0.922861	−	0.385133i	$-0.125845\pi$
$487$	23.1882	+	13.3877i	1.05076	+	0.606654i	0.127895	+	0.991788i	$0.459178\pi$
$488$	−23.3020	−	14.6806i	−1.05483	−	0.664560i
$489$			26.4872i			1.19779i
$490$		0			0
$491$	6.87914	+	6.87914i	0.310451	+	0.310451i	0.845084	−	0.534633i	$-0.179550\pi$
$491$	6.87914	+	6.87914i	0.310451	+	0.310451i	−0.534633	+	0.845084i	$0.679550\pi$
$492$	7.38205	−	14.8227i	0.332809	−	0.668260i
$493$	5.96640	+	22.2669i	0.268713	+	1.00285i
$494$	31.6989	+	22.8092i	1.42620	+	1.02623i
$495$	−0.703501	−	1.21850i	−0.0316200	−	0.0547675i
$496$	12.8352	+	5.43467i	0.576319	+	0.244024i
$497$		0			0
$498$	2.41324	−	24.0198i	0.108140	−	1.07635i
$499$	−20.1108	−	5.38868i	−0.900284	−	0.241230i	−0.221146	−	0.975241i	$-0.570980\pi$
$499$	−20.1108	−	5.38868i	−0.900284	−	0.241230i	−0.679138	+	0.734010i	$0.737646\pi$
$500$	0.946406	+	15.3607i	0.0423245	+	0.686951i
$501$	−38.6477	+	10.3556i	−1.72665	+	0.462655i
$502$	−14.1810	+	37.4555i	−0.632931	+	1.67172i
$503$		−	19.2528i		−	0.858438i	−0.903200	−	0.429219i	$-0.858789\pi$
$503$		−	19.2528i		−	0.858438i	0.903200	−	0.429219i	$-0.141211\pi$
$504$		0			0
$505$		−	6.05797i		−	0.269576i
$506$	8.33438	+	3.15548i	0.370508	+	0.140278i
$507$	8.65370	−	2.31875i	0.384324	−	0.102979i
$508$	17.2359	−	19.4992i	0.764717	−	0.865136i
$509$	32.0506	+	8.58792i	1.42062	+	0.380653i	0.885702	−	0.464254i	$-0.153677\pi$
$509$	32.0506	+	8.58792i	1.42062	+	0.380653i	0.534914	+	0.844907i	$0.320344\pi$
$510$	−12.2175	−	1.22747i	−0.541000	−	0.0543534i
$511$		0			0
$512$	−14.0443	−	17.7414i	−0.620675	−	0.784068i
$513$	−10.0266	−	17.3666i	−0.442685	−	0.766753i
$514$	−17.2730	+	24.0051i	−0.761881	+	1.05882i
$515$	−2.99772	−	11.1876i	−0.132095	−	0.492987i
$516$	−11.3601	−	33.9012i	−0.500099	−	1.49242i
$517$	−4.68986	−	4.68986i	−0.206260	−	0.206260i
$518$		0			0
$519$			19.9182i			0.874313i
$520$	−2.14292	−	9.44089i	−0.0939734	−	0.414010i
$521$	28.3618	+	16.3747i	1.24255	+	0.717389i	0.969613	−	0.244642i	$-0.0786704\pi$
$521$	28.3618	+	16.3747i	1.24255	+	0.717389i	0.272941	+	0.962031i	$0.412004\pi$
$522$	−10.4711	+	1.70774i	−0.458308	+	0.0747456i
$523$	9.91430	−	37.0007i	0.433522	−	1.61793i	−0.311056	−	0.950392i	$-0.600683\pi$
$523$	9.91430	−	37.0007i	0.433522	−	1.61793i	0.744578	−	0.667535i	$-0.232651\pi$
$524$	20.6468	−	13.6791i	0.901960	−	0.597576i
$525$		0			0
$526$	−1.72546	+	17.1741i	−0.0752335	+	0.748827i
$527$	−8.54478	−	14.8000i	−0.372216	−	0.644698i
$528$	−7.30605	+	5.51577i	−0.317955	+	0.240043i
$529$	5.92254	−	10.2581i	0.257502	−	0.446006i
$530$	14.1915	−	6.39665i	0.616441	−	0.277853i
$531$	−6.80986	+	6.80986i	−0.295523	+	0.295523i
$532$		0			0
$533$	−11.3188	−	11.3188i	−0.490273	−	0.490273i
$534$	−5.99477	+	15.8336i	−0.259419	+	0.685188i
$535$	−3.42849	−	1.97944i	−0.148227	−	0.0855787i
$536$	1.34716	−	34.8849i	0.0581884	−	1.50680i
$537$	−0.660445	+	0.381308i	−0.0285003	+	0.0164547i
$538$	−6.21257	+	5.07820i	−0.267843	+	0.218937i
$539$		0			0
$540$	−0.988911	+	4.87182i	−0.0425560	+	0.209650i
$541$	−29.4876	−	7.90119i	−1.26777	−	0.339699i	−0.438596	−	0.898685i	$-0.644524\pi$
$541$	−29.4876	−	7.90119i	−1.26777	−	0.339699i	−0.829177	+	0.558986i	$0.811191\pi$
$542$	−2.43326	+	3.38161i	−0.104517	+	0.145253i
$543$	25.0429	−	43.3756i	1.07470	−	1.86143i
$544$	0.636265	+	27.7357i	0.0272796	+	1.18916i
$545$	4.72256			0.202292
$546$		0			0
$547$	−10.1273	+	10.1273i	−0.433010	+	0.433010i	−0.889651	−	0.456641i	$-0.849052\pi$
$547$	−10.1273	+	10.1273i	−0.433010	+	0.433010i	0.456641	+	0.889651i	$0.349052\pi$
$548$	−20.2499	+	6.78559i	−0.865031	+	0.289866i
$549$	−15.0113	+	4.02226i	−0.640666	+	0.171666i
$550$	−1.04931	−	6.43395i	−0.0447429	−	0.274345i
$551$	−27.1208	+	15.6582i	−1.15538	+	0.667061i
$552$	16.6874	+	31.6658i	0.710261	+	1.34779i
$553$		0			0
$554$	11.9640	+	14.6366i	0.508303	+	0.621848i
$555$	3.22519	−	12.0366i	0.136902	−	0.510925i
$556$	1.59494	−	0.0982678i	0.0676406	−	0.00416748i
$557$	5.92462	+	22.1110i	0.251034	+	0.936872i	0.970254	+	0.242090i	$0.0778328\pi$
$557$	5.92462	+	22.1110i	0.251034	+	0.936872i	−0.719220	+	0.694783i	$0.755501\pi$
$558$	7.17043	−	3.23198i	0.303549	−	0.136820i
$559$	−34.5622			−1.46182
$560$		0			0
$561$	11.2239			0.473875
$562$	6.76550	−	3.04946i	0.285385	−	0.128634i
$563$	−2.30767	−	8.61234i	−0.0972567	−	0.362967i	0.900095	−	0.435693i	$-0.143497\pi$
$563$	−2.30767	−	8.61234i	−0.0972567	−	0.362967i	−0.997352	+	0.0727263i	$0.976830\pi$
$564$	−1.63819	−	26.5887i	−0.0689802	−	1.11959i
$565$	−4.05133	+	15.1198i	−0.170441	+	0.636093i
$566$	−4.83393	−	5.91373i	−0.203185	−	0.248572i
$567$		0			0
$568$	0.113298	−	0.365747i	0.00475389	−	0.0153464i
$569$	−2.25931	+	1.30441i	−0.0947150	+	0.0546837i	−0.546609	−	0.837388i	$-0.684082\pi$
$569$	−2.25931	+	1.30441i	−0.0947150	+	0.0546837i	0.451894	+	0.892071i	$0.350748\pi$
$570$	−2.68501	−	16.4633i	−0.112463	−	0.689573i
$571$	28.8897	−	7.74098i	1.20900	−	0.323950i	0.402629	−	0.915363i	$-0.368096\pi$
$571$	28.8897	−	7.74098i	1.20900	−	0.323950i	0.806369	+	0.591413i	$0.201430\pi$
$572$	2.81165	+	8.39066i	0.117561	+	0.350831i
$573$	−30.9024	+	30.9024i	−1.29096	+	1.29096i
$574$		0			0
$575$	−25.4893			−1.06298
$576$	−12.7302	−	0.984678i	−0.530424	−	0.0410283i
$577$	14.9838	−	25.9527i	0.623785	−	1.08043i	−0.364990	−	0.931011i	$-0.618928\pi$
$577$	14.9838	−	25.9527i	0.623785	−	1.08043i	0.988775	−	0.149415i	$-0.0477391\pi$
$578$	5.82514	−	8.09545i	0.242294	−	0.336726i
$579$	39.5778	+	10.6048i	1.64480	+	0.440722i
$580$	7.60816	+	1.54435i	0.315911	+	0.0641256i
$581$		0			0
$582$	14.4413	−	11.8044i	0.598612	−	0.489310i
$583$	−12.3227	+	7.11450i	−0.510353	+	0.294653i
$584$	14.5408	+	15.7089i	0.601701	+	0.650040i
$585$	−4.73094	−	2.73141i	−0.195600	−	0.112930i
$586$	−1.06206	+	2.80517i	−0.0438735	+	0.115880i
$587$	−6.58566	−	6.58566i	−0.271819	−	0.271819i	0.558013	−	0.829832i	$-0.311564\pi$
$587$	−6.58566	−	6.58566i	−0.271819	−	0.271819i	−0.829832	+	0.558013i	$0.811564\pi$
$588$		0			0
$589$	16.4161	−	16.4161i	0.676415	−	0.676415i
$590$	6.42458	−	2.89579i	0.264496	−	0.119218i
$591$	−10.1441	+	17.5701i	−0.417273	+	0.722739i
$592$	−27.8841	−	3.89339i	−1.14603	−	0.160017i
$593$	9.25485	+	16.0299i	0.380051	+	0.658268i	0.991069	−	0.133349i	$-0.0425731\pi$
$593$	9.25485	+	16.0299i	0.380051	+	0.658268i	−0.611018	+	0.791617i	$0.709240\pi$
$594$	0.454245	−	4.52127i	0.0186379	−	0.185510i
$595$		0			0
$596$	7.53349	+	11.3708i	0.308584	+	0.465766i
$597$	4.41929	−	16.4930i	0.180870	−	0.675015i
$598$	34.1494	−	5.56944i	1.39647	−	0.227751i
$599$	−14.2600	−	8.23300i	−0.582647	−	0.336391i	0.179538	−	0.983751i	$-0.442540\pi$
$599$	−14.2600	−	8.23300i	−0.582647	−	0.336391i	−0.762184	+	0.647360i	$0.775873\pi$
$600$	13.9569	−	22.1533i	0.569787	−	0.904403i
$601$			41.7312i			1.70225i	0.524962	+	0.851126i	$0.324079\pi$
$601$			41.7312i			1.70225i	−0.524962	+	0.851126i	$0.675921\pi$
$602$		0			0
$603$	−13.9297	−	13.9297i	−0.567259	−	0.567259i
$604$	35.2908	−	11.8257i	1.43596	−	0.481182i
$605$	2.10751	+	7.86533i	0.0856825	+	0.319771i
$606$	−12.9903	+	18.0531i	−0.527693	+	0.733359i
$607$	16.8167	+	29.1274i	0.682569	+	1.18224i	0.974194	+	0.225712i	$0.0724707\pi$
$607$	16.8167	+	29.1274i	0.682569	+	1.18224i	−0.291625	+	0.956533i	$0.594196\pi$
$608$	−36.1710	+	10.5868i	−1.46693	+	0.429353i
$609$		0			0
$610$	11.3148	+	1.13678i	0.458123	+	0.0460270i
$611$	−24.8737	−	6.66489i	−1.00628	−	0.269633i
$612$	11.7294	+	10.3679i	0.474133	+	0.419099i
$613$	−14.8284	+	3.97327i	−0.598915	+	0.160479i	−0.545524	−	0.838095i	$-0.683670\pi$
$613$	−14.8284	+	3.97327i	−0.598915	+	0.160479i	−0.0533906	+	0.998574i	$0.517003\pi$
$614$	−11.7329	−	4.44219i	−0.473501	−	0.179272i
$615$			6.83737i			0.275709i
$616$		0			0
$617$			46.1375i			1.85743i	0.370797	+	0.928714i	$0.379085\pi$
$617$			46.1375i			1.85743i	−0.370797	+	0.928714i	$0.620915\pi$
$618$	−15.0566	+	39.7680i	−0.605664	+	1.59970i
$619$	−20.1997	+	5.41249i	−0.811893	+	0.217546i	−0.640799	−	0.767708i	$-0.721397\pi$
$619$	−20.1997	+	5.41249i	−0.811893	+	0.217546i	−0.171094	+	0.985255i	$0.554730\pi$
$620$	−5.74432	+	0.353920i	−0.230698	+	0.0142138i
$621$	−17.1619	−	4.59851i	−0.688683	−	0.184532i
$622$	−1.56626	+	15.5896i	−0.0628013	+	0.625085i
$623$		0			0
$624$	−13.8583	+	32.7296i	−0.554776	+	1.31023i
$625$	7.61785	+	13.1945i	0.304714	+	0.527780i
$626$	−14.6671	−	10.5538i	−0.586215	−	0.421815i
$627$	3.94636	+	14.7280i	0.157602	+	0.588181i
$628$	−1.23241	−	0.613767i	−0.0491784	−	0.0244919i
$629$	24.4091	+	24.4091i	0.973256	+	0.973256i
$630$		0			0
$631$		−	6.87207i		−	0.273573i	−0.990601	−	0.136786i	$-0.956323\pi$
$631$		−	6.87207i		−	0.273573i	0.990601	−	0.136786i	$-0.0436774\pi$
$632$	4.25294	+	18.7368i	0.169173	+	0.745311i
$633$	24.4418	+	14.1115i	0.971476	+	0.560882i
$634$	5.23702	+	32.1112i	0.207989	+	1.27530i
$635$	−2.78121	+	10.3796i	−0.110369	+	0.411902i
$636$	−56.0082	−	11.3689i	−2.22087	−	0.450805i
$637$		0			0
$638$	−7.06071	−	0.709379i	−0.279536	−	0.0280846i
$639$	−0.108030	−	0.187113i	−0.00427359	−	0.00740207i
$640$	8.45651	+	3.97216i	0.334273	+	0.157013i
$641$	6.85975	−	11.8814i	0.270944	−	0.469288i	−0.698160	−	0.715942i	$-0.745998\pi$
$641$	6.85975	−	11.8814i	0.270944	−	0.469288i	0.969104	+	0.246653i	$0.0793309\pi$
$642$	5.97256	+	13.2507i	0.235718	+	0.522962i
$643$	22.2363	−	22.2363i	0.876913	−	0.876913i	−0.116301	−	0.993214i	$-0.537104\pi$
$643$	22.2363	−	22.2363i	0.876913	−	0.876913i	0.993214	+	0.116301i	$0.0371039\pi$
$644$		0			0
$645$	10.4390	+	10.4390i	0.411034	+	0.411034i
$646$	43.2153	+	16.3617i	1.70028	+	0.643744i
$647$	31.3065	+	18.0748i	1.23079	+	0.710595i	0.967194	−	0.254038i	$-0.0817590\pi$
$647$	31.3065	+	18.0748i	1.23079	+	0.710595i	0.263593	+	0.964634i	$0.415092\pi$
$648$	23.3323	−	21.5973i	0.916581	−	0.848421i
$649$	−5.57854	+	3.22077i	−0.218977	+	0.126426i
$650$	−16.0185	−	19.5967i	−0.628295	−	0.768644i
$651$		0			0
$652$	−20.5993	+	13.6477i	−0.806732	+	0.534484i
$653$	47.9908	+	12.8591i	1.87802	+	0.503215i	0.999683	+	0.0251813i	$0.00801629\pi$
$653$	47.9908	+	12.8591i	1.87802	+	0.503215i	0.878341	+	0.478034i	$0.158650\pi$
$654$	−14.0735	−	10.1267i	−0.550318	−	0.395985i
$655$	−5.11322	+	8.85635i	−0.199790	+	0.346046i
$656$	15.3314	−	1.89640i	0.598590	−	0.0740420i
$657$	12.0788			0.471240
$658$		0			0
$659$	4.01002	−	4.01002i	0.156208	−	0.156208i	−0.624676	−	0.780884i	$-0.714769\pi$
$659$	4.01002	−	4.01002i	0.156208	−	0.156208i	0.780884	+	0.624676i	$0.214769\pi$
$660$	1.68505	−	3.38349i	0.0655906	−	0.131702i
$661$	8.38969	−	2.24801i	0.326321	−	0.0874375i	−0.0919393	−	0.995765i	$-0.529307\pi$
$661$	8.38969	−	2.24801i	0.326321	−	0.0874375i	0.418260	+	0.908327i	$0.362640\pi$
$662$	−15.7032	+	2.56105i	−0.610324	+	0.0995378i
$663$	37.7397	−	21.7890i	1.46569	−	0.846215i
$664$	19.9238	−	10.4995i	0.773195	−	0.407461i
$665$		0			0
$666$	−12.3006	+	10.0546i	−0.476639	+	0.389608i
$667$	−7.18134	+	26.8011i	−0.278062	+	1.03774i
$668$	−27.9671	−	24.7209i	−1.08208	−	0.956479i
$669$	2.14854	+	8.01846i	0.0830673	+	0.310011i
$670$	5.92338	+	13.1416i	0.228840	+	0.507703i
$671$	−10.3947			−0.401282
$672$		0			0
$673$	−17.2802			−0.666105			−0.333052	−	0.942908i	$-0.608079\pi$
$673$	−17.2802			−0.666105			−0.333052	+	0.942908i	$0.608079\pi$
$674$	0.940768	+	2.08718i	0.0362370	+	0.0803951i
$675$	3.36383	+	12.5540i	0.129474	+	0.483202i
$676$	6.26217	+	5.53530i	0.240853	+	0.212896i
$677$	1.13041	−	4.21875i	0.0434452	−	0.162140i	−0.940795	−	0.338976i	$-0.889920\pi$
$677$	1.13041	−	4.21875i	0.0434452	−	0.162140i	0.984240	+	0.176836i	$0.0565862\pi$
$678$	44.4949	−	36.3705i	1.70882	−	1.39680i
$679$		0			0
$680$	−5.34051	−	10.1341i	−0.204799	−	0.388625i
$681$	11.3715	−	6.56533i	0.435756	−	0.251584i
$682$	5.19211	−	0.846782i	0.198816	−	0.0324250i
$683$	13.7619	−	3.68749i	0.526585	−	0.141098i	0.0142741	−	0.999898i	$-0.495456\pi$
$683$	13.7619	−	3.68749i	0.526585	−	0.141098i	0.512311	+	0.858800i	$0.328790\pi$
$684$	−9.48070	+	19.0367i	−0.362503	+	0.727886i
$685$	6.23540	−	6.23540i	0.238242	−	0.238242i
$686$		0			0
$687$	57.7686			2.20401
$688$	20.5119	−	26.3026i	0.782010	−	1.00278i
$689$	−27.6227	+	47.8440i	−1.05234	+	1.82271i
$690$	−11.9965	−	8.63215i	−0.456698	−	0.328620i
$691$	18.0089	+	4.82548i	0.685092	+	0.183570i	0.584544	−	0.811362i	$-0.301274\pi$
$691$	18.0089	+	4.82548i	0.685092	+	0.183570i	0.100548	+	0.994932i	$0.467940\pi$
$692$	−15.4906	+	10.2630i	−0.588863	+	0.390139i
$693$		0			0
$694$	−11.6108	−	14.2044i	−0.440740	−	0.539193i
$695$	−0.571409	+	0.329903i	−0.0216748	+	0.0125139i
$696$	−19.3612	−	20.9166i	−0.733884	−	0.792842i
$697$	−16.4032	−	9.47036i	−0.621314	−	0.358716i
$698$	0.500570	+	0.189521i	0.0189469	+	0.00717347i
$699$	−20.7653	−	20.7653i	−0.785417	−	0.785417i
$700$		0			0
$701$	−5.24919	+	5.24919i	−0.198259	+	0.198259i	−0.799253	−	0.600994i	$-0.794771\pi$
$701$	−5.24919	+	5.24919i	−0.198259	+	0.198259i	0.600994	+	0.799253i	$0.294771\pi$
$702$	−7.24977	−	16.0843i	−0.273625	−	0.607062i
$703$	−23.4473	+	40.6119i	−0.884332	+	1.53171i
$704$	−8.05413	−	2.83995i	−0.303552	−	0.107034i
$705$	5.49970	+	9.52576i	0.207131	+	0.358761i
$706$	47.8198	+	4.80438i	1.79972	+	0.180815i
$707$		0			0
$708$	−25.3552	−	5.14675i	−0.952907	−	0.193427i
$709$	−1.29134	+	4.81933i	−0.0484972	+	0.180994i	−0.985926	−	0.167184i	$-0.946533\pi$
$709$	−1.29134	+	4.81933i	−0.0484972	+	0.180994i	0.937429	+	0.348178i	$0.113199\pi$
$710$	0.0254481	+	0.156037i	0.000955048	+	0.00585595i
$711$	9.38924	+	5.42088i	0.352124	+	0.203299i
$712$	−15.4028	+	3.49617i	−0.577243	+	0.131024i
$713$		−	20.5695i		−	0.770334i
$714$		0			0
$715$	−2.58368	−	2.58368i	−0.0966240	−	0.0966240i
$716$	−0.636843	−	0.317162i	−0.0238000	−	0.0118529i
$717$	−0.587622	−	2.19304i	−0.0219452	−	0.0819004i
$718$	2.95994	+	2.12984i	0.110464	+	0.0794851i
$719$	−19.6724	−	34.0736i	−0.733657	−	1.27073i	−0.955310	−	0.295605i	$-0.904479\pi$
$719$	−19.6724	−	34.0736i	−0.733657	−	1.27073i	0.221654	−	0.975125i	$-0.428855\pi$
$720$	4.88638	−	1.97932i	0.182105	−	0.0737649i
$721$		0			0
$722$	−3.58917	+	35.7243i	−0.133575	+	1.32952i
$723$	10.2654	+	2.75060i	0.381773	+	0.102296i
$724$	46.6371	−	2.87341i	1.73325	−	0.106790i
$725$	19.6051	−	5.25317i	0.728115	−	0.195098i
$726$	10.5853	−	27.9584i	0.392858	−	1.03763i
$727$		−	44.4513i		−	1.64861i	−0.566148	−	0.824304i	$-0.691567\pi$
$727$		−	44.4513i		−	1.64861i	0.566148	−	0.824304i	$-0.308433\pi$
$728$		0			0
$729$			1.41753i			0.0525012i
$730$	−8.26589	−	3.12955i	−0.305934	−	0.115830i
$731$	−39.5025	+	10.5847i	−1.46105	+	0.391488i
$732$	−31.2812	−	27.6503i	−1.15619	−	1.02199i
$733$	39.5628	+	10.6008i	1.46128	+	0.391550i	0.899933	−	0.436028i	$-0.143615\pi$
$733$	39.5628	+	10.6008i	1.46128	+	0.391550i	0.561351	+	0.827578i	$0.310282\pi$
$734$	−13.0762	−	1.31375i	−0.482652	−	0.0484914i
$735$		0			0
$736$	−16.0285	+	29.2938i	−0.590819	+	1.07979i
$737$	−6.58812	−	11.4110i	−0.242677	−	0.420328i
$738$	5.09140	−	7.07574i	0.187417	−	0.260462i
$739$	−1.46775	−	5.47770i	−0.0539919	−	0.201501i	0.933661	−	0.358158i	$-0.116595\pi$
$739$	−1.46775	−	5.47770i	−0.0539919	−	0.201501i	−0.987653	+	0.156657i	$0.949928\pi$
$740$	11.0227	−	3.69365i	0.405204	−	0.135781i
$741$	41.8608	+	41.8608i	1.53780	+	1.53780i
$742$		0			0
$743$		−	41.4130i		−	1.51930i	−0.650335	−	0.759648i	$-0.725371\pi$
$743$		−	41.4130i		−	1.51930i	0.650335	−	0.759648i	$-0.274629\pi$
$744$	17.8774	+	11.2630i	0.655416	+	0.412921i
$745$	−4.87745	−	2.81600i	−0.178696	−	0.103170i
$746$	15.3508	−	2.50356i	0.562032	−	0.0916618i
$747$	3.28913	−	12.2752i	0.120343	−	0.449126i
$748$	5.78319	+	8.72895i	0.211454	+	0.319162i
$749$		0			0
$750$	−2.33216	+	23.2129i	−0.0851585	+	0.847614i
$751$	15.3377	+	26.5656i	0.559680	+	0.969394i	0.997523	+	0.0703424i	$0.0224092\pi$
$751$	15.3377	+	26.5656i	0.559680	+	0.969394i	−0.437843	+	0.899051i	$0.644257\pi$
$752$	19.8342	−	14.9740i	0.723278	−	0.546045i
$753$	−30.3564	+	52.5789i	−1.10625	+	1.91608i
$754$	−25.1182	+	11.3217i	−0.914752	+	0.412312i
$755$	−10.8669	+	10.8669i	−0.395486	+	0.395486i
$756$		0			0
$757$	14.1660	+	14.1660i	0.514873	+	0.514873i	0.916016	−	0.401143i	$-0.131387\pi$
$757$	14.1660	+	14.1660i	0.514873	+	0.514873i	−0.401143	+	0.916016i	$0.631387\pi$
$758$	9.39522	−	24.8150i	0.341250	−	0.901323i
$759$	11.6995	+	6.75473i	0.424666	+	0.245181i
$760$	11.4202	−	10.5710i	0.414254	−	0.383449i
$761$	33.5826	−	19.3889i	1.21737	−	0.702847i	0.253013	−	0.967463i	$-0.418578\pi$
$761$	33.5826	−	19.3889i	1.21737	−	0.702847i	0.964354	+	0.264615i	$0.0852450\pi$
$762$	30.5454	−	24.9681i	1.10654	−	0.904498i
$763$		0			0
$764$	−39.9556	−	8.11042i	−1.44554	−	0.293425i
$765$	−6.24368	−	1.67299i	−0.225741	−	0.0604870i
$766$	15.3467	−	21.3280i	0.554499	−	0.770612i
$767$	−12.5049	+	21.6592i	−0.451527	+	0.782068i
$768$	−16.6833	−	29.9708i	−0.602008	−	1.08148i
$769$	−0.129416			−0.00466687			−0.00233344	−	0.999997i	$-0.500743\pi$
$769$	−0.129416			−0.00466687			−0.00233344	+	0.999997i	$0.500743\pi$
$770$		0			0
$771$	−31.7005	+	31.7005i	−1.14167	+	1.14167i
$772$	12.1452	+	36.2442i	0.437115	+	1.30446i
$773$	−4.21166	+	1.12851i	−0.151483	+	0.0405897i	−0.333764	−	0.942657i	$-0.608319\pi$
$773$	−4.21166	+	1.12851i	−0.151483	+	0.0405897i	0.182281	+	0.983247i	$0.441652\pi$
$774$	−3.02960	−	18.5762i	−0.108897	−	0.667708i
$775$	−13.0308	+	7.52332i	−0.468079	+	0.270246i
$776$	16.6214	+	5.14883i	0.596673	+	0.184832i
$777$		0			0
$778$	−27.8257	−	34.0414i	−0.997599	−	1.22044i
$779$	6.65960	−	24.8540i	0.238605	−	0.890486i
$780$	−0.902489	−	14.6479i	−0.0323143	−	0.524479i
$781$	−0.0374029	−	0.139590i	−0.00133838	−	0.00499491i
$782$	37.3251	−	16.8238i	1.33474	−	0.601618i
$783$	14.1478			0.505601
$784$		0			0
$785$	0.568480			0.0202899
$786$	34.2286	−	15.4281i	1.22089	−	0.550302i
$787$	11.0354	+	41.1845i	0.393368	+	1.46807i	0.824542	+	0.565801i	$0.191433\pi$
$787$	11.0354	+	41.1845i	0.393368	+	1.46807i	−0.431173	+	0.902269i	$0.641900\pi$
$788$	−18.8912	+	1.16393i	−0.672973	+	0.0414633i
$789$	−6.77217	+	25.2741i	−0.241095	+	0.899781i
$790$	−5.02082	−	6.14236i	−0.178633	−	0.218536i
$791$		0			0
$792$	−4.26329	+	2.24668i	−0.151489	+	0.0798324i
$793$	−34.9513	+	20.1791i	−1.24116	+	0.716582i
$794$	−7.04170	−	43.1767i	−0.249900	−	1.53228i
$795$	22.7936	−	6.10751i	0.808404	−	0.216611i
$796$	15.1038	−	5.06119i	0.535341	−	0.179389i
$797$	18.9375	−	18.9375i	0.670800	−	0.670800i	−0.287100	−	0.957901i	$-0.592691\pi$
$797$	18.9375	−	18.9375i	0.670800	−	0.670800i	0.957901	+	0.287100i	$0.0926913\pi$
$798$		0			0
$799$	−30.4703			−1.07796
$800$	24.4201	−	0.560205i	0.863381	−	0.0198062i
$801$	−4.45628	+	7.71851i	−0.157455	+	0.272720i
$802$	−5.87360	+	8.16280i	−0.207404	+	0.288238i
$803$	7.80377	+	2.09101i	0.275389	+	0.0737903i
$804$	10.5277	−	51.8644i	0.371285	−	1.82911i
$805$		0			0
$806$	15.8142	−	12.9267i	0.557032	−	0.455322i
$807$	−10.5341	+	6.08185i	−0.370817	+	0.214091i
$808$	−20.7334	−	0.800666i	−0.729397	−	0.0281673i
$809$	−4.94829	−	2.85690i	−0.173973	−	0.100443i	0.410485	−	0.911867i	$-0.365359\pi$
$809$	−4.94829	−	2.85690i	−0.173973	−	0.100443i	−0.584458	+	0.811424i	$0.698693\pi$
$810$	−4.64829	+	12.2773i	−0.163324	+	0.431379i
$811$	20.8976	+	20.8976i	0.733815	+	0.733815i	0.971373	−	0.237559i	$-0.0763472\pi$
$811$	20.8976	+	20.8976i	0.733815	+	0.733815i	−0.237559	+	0.971373i	$0.576347\pi$
$812$		0			0
$813$	−4.46567	+	4.46567i	−0.156618	+	0.156618i
$814$	−9.68765	+	4.36658i	−0.339552	+	0.153048i
$815$	5.10145	−	8.83598i	0.178696	−	0.309511i
$816$	−5.81577	+	41.6521i	−0.203593	+	1.45811i
$817$	−27.7783	−	48.1135i	−0.971840	−	1.68328i
$818$	4.92379	−	49.0083i	0.172156	−	1.71354i
$819$		0			0
$820$	−5.31747	+	3.52298i	−0.185694	+	0.123028i
$821$	1.84034	−	6.86823i	0.0642282	−	0.239703i	−0.926347	−	0.376670i	$-0.877069\pi$
$821$	1.84034	−	6.86823i	0.0642282	−	0.239703i	0.990576	+	0.136968i	$0.0437356\pi$
$822$	−31.9526	+	5.21116i	−1.11448	+	0.181760i
$823$	22.7514	+	13.1355i	0.793065	+	0.457876i	0.841040	−	0.540972i	$-0.181944\pi$
$823$	22.7514	+	13.1355i	0.793065	+	0.457876i	−0.0479755	+	0.998849i	$0.515277\pi$
$824$	−38.6858	+	8.78104i	−1.34769	+	0.305902i
$825$		−	9.88221i		−	0.344055i
$826$		0			0
$827$	9.59215	+	9.59215i	0.333552	+	0.333552i	0.853934	−	0.520382i	$-0.174210\pi$
$827$	9.59215	+	9.59215i	0.333552	+	0.333552i	−0.520382	+	0.853934i	$0.674210\pi$
$828$	5.98684	+	17.8662i	0.208057	+	0.620893i
$829$	7.61117	+	28.4053i	0.264347	+	0.986556i	0.962649	+	0.270753i	$0.0872726\pi$
$829$	7.61117	+	28.4053i	0.264347	+	0.986556i	−0.698302	+	0.715803i	$0.746061\pi$
$830$	−5.43127	+	7.54808i	−0.188522	+	0.261998i
$831$	14.3286	+	24.8178i	0.497053	+	0.860921i
$832$	−32.5946	+	6.08636i	−1.13001	+	0.211007i
$833$		0			0
$834$	2.41025	+	0.242155i	0.0834603	+	0.00838513i
$835$	14.8871	+	3.98900i	0.515191	+	0.138045i
$836$	−9.42072	+	10.6578i	−0.325822	+	0.368608i
$837$	−10.1309	+	2.71456i	−0.350174	+	0.0938289i
$838$	1.22238	+	0.462805i	0.0422264	+	0.0159873i
$839$			9.21526i			0.318146i	0.987267	+	0.159073i	$0.0508505\pi$
$839$			9.21526i			0.318146i	−0.987267	+	0.159073i	$0.949149\pi$
$840$		0			0
$841$			6.90588i			0.238134i
$842$	6.71365	−	17.7323i	0.231368	−	0.611097i
$843$	10.8663	−	2.91162i	0.374255	−	0.100281i
$844$	1.61914	+	26.2796i	0.0557333	+	0.904582i
$845$	−3.33342	−	0.893186i	−0.114673	−	0.0307265i
$846$	1.40185	−	13.9532i	0.0481967	−	0.479720i
$847$		0			0
$848$	−20.0168	−	49.4159i	−0.687381	−	1.69695i
$849$	−5.78930	−	10.0274i	−0.198688	−	0.344138i
$850$	−24.3096	−	17.4921i	−0.833813	−	0.599976i
$851$	10.7537	+	40.1332i	0.368631	+	1.37575i
$852$	0.258757	−	0.519568i	0.00886485	−	0.0178001i
$853$	−27.5443	−	27.5443i	−0.943099	−	0.943099i	0.0553669	−	0.998466i	$-0.482367\pi$
$853$	−27.5443	−	27.5443i	−0.943099	−	0.943099i	−0.998466	+	0.0553669i	$0.982367\pi$
$854$		0			0
$855$		−	8.78116i		−	0.300309i
$856$	−7.22776	+	11.4724i	−0.247040	+	0.392118i
$857$	−0.698639	−	0.403360i	−0.0238651	−	0.0137785i	0.488020	−	0.872832i	$-0.337719\pi$
$857$	−0.698639	−	0.403360i	−0.0238651	−	0.0137785i	−0.511885	+	0.859054i	$0.671053\pi$
$858$	2.15928	+	13.2398i	0.0737165	+	0.451998i
$859$	−0.0819615	+	0.305884i	−0.00279649	+	0.0104366i	−0.967310	−	0.253597i	$-0.918386\pi$
$859$	−0.0819615	+	0.305884i	−0.00279649	+	0.0104366i	0.964513	+	0.264034i	$0.0850530\pi$
$860$	−2.73974	+	13.4972i	−0.0934244	+	0.460251i
$861$		0			0
$862$	−19.1287	−	1.92183i	−0.651526	−	0.0654578i
$863$	−12.9097	−	22.3603i	−0.439452	−	0.761154i	0.558195	−	0.829710i	$-0.311494\pi$
$863$	−12.9097	−	22.3603i	−0.439452	−	0.761154i	−0.997647	+	0.0685559i	$0.978161\pi$
$864$	16.5431	+	4.02844i	0.562807	+	0.137050i
$865$	3.83626	−	6.64460i	0.130437	−	0.225923i
$866$	−3.86995	−	8.58584i	−0.131506	−	0.291759i
$867$	10.6907	−	10.6907i	0.363074	−	0.363074i
$868$		0			0
$869$	5.12768	+	5.12768i	0.173945	+	0.173945i
$870$	11.0061	+	4.16703i	0.373143	+	0.141276i
$871$	−44.3041	−	25.5790i	−1.50119	−	0.866712i
$872$	0.624168	−	16.1629i	0.0211370	−	0.547345i
$873$	8.50334	−	4.90941i	0.287794	−	0.166158i
$874$	35.1997	+	43.0626i	1.19065	+	1.45662i
$875$		0			0
$876$	17.9221	+	27.0510i	0.605532	+	0.913969i
$877$	−47.4737	−	12.7205i	−1.60307	−	0.429542i	−0.657104	−	0.753800i	$-0.728219\pi$
$877$	−47.4737	−	12.7205i	−1.60307	−	0.429542i	−0.945969	+	0.324258i	$0.894886\pi$
$878$	−6.97985	−	5.02240i	−0.235559	−	0.169498i
$879$	−2.27349	+	3.93780i	−0.0766830	+	0.132819i
$880$	3.49959	−	0.432879i	0.117971	−	0.0145923i
$881$	29.7995			1.00397			0.501985	−	0.864876i	$-0.332603\pi$
$881$	29.7995			1.00397			0.501985	+	0.864876i	$0.332603\pi$
$882$		0			0
$883$	18.4638	−	18.4638i	0.621356	−	0.621356i	−0.324522	−	0.945878i	$-0.605203\pi$
$883$	18.4638	−	18.4638i	0.621356	−	0.621356i	0.945878	+	0.324522i	$0.105203\pi$
$884$	36.3910	+	18.1235i	1.22396	+	0.609561i
$885$	10.3188	−	2.76490i	0.346861	−	0.0929412i
$886$	−27.1139	+	4.42202i	−0.910910	+	0.148561i
$887$	47.2046	−	27.2536i	1.58497	−	0.915086i	0.590858	−	0.806776i	$-0.298790\pi$
$887$	47.2046	−	27.2536i	1.58497	−	0.915086i	0.994117	−	0.108310i	$-0.0345438\pi$
$888$	−40.7689	−	12.6290i	−1.36811	−	0.423803i
$889$		0			0
$890$	5.04938	−	4.12740i	0.169256	−	0.138351i
$891$	3.10577	−	11.5909i	0.104047	−	0.388309i
$892$	−5.12897	+	5.80248i	−0.171731	+	0.194282i
$893$	−10.7134	−	39.9830i	−0.358511	−	1.33798i
$894$	8.49669	+	18.8507i	0.284172	+	0.630461i
$895$	0.293760			0.00981933
$896$		0			0
$897$	52.4518			1.75131
$898$	9.75202	+	21.6357i	0.325429	+	0.721994i
$899$	4.23923	+	15.8210i	0.141386	+	0.527661i
$900$	9.12854	−	10.3273i	0.304285	−	0.344242i
$901$	−16.9189	+	63.1422i	−0.563651	+	2.10357i
$902$	4.51431	−	3.69003i	0.150310	−	0.122865i
$903$		0			0
$904$	51.2118	+	15.8640i	1.70328	+	0.527628i
$905$	−16.7083	+	9.64657i	−0.555404	+	0.320663i
$906$	55.6860	−	9.08185i	1.85004	−	0.301724i
$907$	26.0185	−	6.97164i	0.863930	−	0.231489i	0.200469	−	0.979700i	$-0.435753\pi$
$907$	26.0185	−	6.97164i	0.863930	−	0.231489i	0.663461	+	0.748211i	$0.269087\pi$
$908$	10.9651	+	5.46088i	0.363890	+	0.181226i
$909$	−8.27891	+	8.27891i	−0.274594	+	0.274594i
$910$		0			0
$911$	38.1287			1.26326			0.631629	−	0.775270i	$-0.282386\pi$
$911$	38.1287			1.26326			0.631629	+	0.775270i	$0.282386\pi$
$912$	−56.7005	+	7.01351i	−1.87754	+	0.232241i
$913$	4.25002	−	7.36125i	0.140655	−	0.243622i
$914$	45.3101	+	32.6032i	1.49873	+	1.07842i
$915$	16.6513	+	4.46170i	0.550475	+	0.147499i
$916$	29.7656	+	44.9271i	0.983481	+	1.48443i
$917$		0			0
$918$	−13.2119	−	16.1631i	−0.436056	−	0.533462i
$919$	13.9817	−	8.07235i	0.461215	−	0.266282i	−0.251340	−	0.967899i	$-0.580871\pi$
$919$	13.9817	−	8.07235i	0.461215	−	0.266282i	0.712555	+	0.701616i	$0.247538\pi$
$920$	0.532050	−	13.7775i	0.0175412	−	0.454231i
$921$	−16.4703	−	9.50911i	−0.542714	−	0.313336i
$922$	2.74639	+	1.03981i	0.0904475	+	0.0342443i
$923$	−0.396749	−	0.396749i	−0.0130592	−	0.0130592i
$924$		0			0
$925$	21.4912	−	21.4912i	0.706628	−	0.706628i
$926$	−13.8586	−	30.7466i	−0.455422	−	1.01040i
$927$	−11.1925	+	19.3859i	−0.367609	+	0.636718i
$928$	6.29107	−	25.8347i	0.206515	−	0.848067i
$929$	14.1904	+	24.5784i	0.465571	+	0.806393i	0.999227	−	0.0393090i	$-0.0125157\pi$
$929$	14.1904	+	24.5784i	0.465571	+	0.806393i	−0.533656	+	0.845702i	$0.679182\pi$
$930$	−8.68075	−	0.872142i	−0.284653	−	0.0285986i
$931$		0			0
$932$	5.44993	−	26.8488i	0.178518	−	0.879462i
$933$	−6.14734	+	22.9422i	−0.201255	+	0.751094i
$934$	−8.08747	−	49.5889i	−0.264630	−	1.62260i
$935$	−3.74424	−	2.16174i	−0.122450	−	0.0706964i
$936$	−9.97351	+	15.8306i	−0.325994	+	0.517440i
$937$		−	18.2863i		−	0.597387i	−0.954349	−	0.298693i	$-0.903449\pi$
$937$		−	18.2863i		−	0.597387i	0.954349	−	0.298693i	$-0.0965508\pi$
$938$		0			0
$939$	−19.3690	−	19.3690i	−0.632083	−	0.632083i
$940$	−4.57451	+	9.18535i	−0.149204	+	0.299593i
$941$	3.54336	+	13.2240i	0.115510	+	0.431090i	0.999325	−	0.0367479i	$-0.0116998\pi$
$941$	3.54336	+	13.2240i	0.115510	+	0.431090i	−0.883814	+	0.467838i	$0.845033\pi$
$942$	−1.69411	−	1.21901i	−0.0551969	−	0.0397173i
$943$	−11.3988	−	19.7433i	−0.371196	−	0.642931i
$944$	−9.06172	−	22.3708i	−0.294934	−	0.728108i
$945$		0			0
$946$	1.25847	−	12.5260i	0.0409164	−	0.407256i
$947$	12.6829	+	3.39838i	0.412139	+	0.110432i	0.458930	−	0.888472i	$-0.348233\pi$
$947$	12.6829	+	3.39838i	0.412139	+	0.110432i	−0.0467909	+	0.998905i	$0.514899\pi$
$948$	1.79112	+	29.0709i	0.0581729	+	0.944179i
$949$	30.2989	−	8.11856i	0.983544	−	0.263540i
$950$	14.4058	−	38.0493i	0.467387	−	1.23448i
$951$			49.3211i			1.59935i
$952$		0			0
$953$			28.4500i			0.921586i	0.887508	+	0.460793i	$0.152435\pi$
$953$			28.4500i			0.921586i	−0.887508	+	0.460793i	$0.847565\pi$
$954$	−28.1361	−	10.6526i	−0.910941	−	0.344891i
$955$	16.2607	−	4.35703i	0.526182	−	0.140990i
$956$	1.40277	−	1.58697i	0.0453687	−	0.0513263i
$957$	−10.3908	−	2.78421i	−0.335887	−	0.0900007i
$958$	37.8695	+	3.80469i	1.22351	+	0.122924i
$959$		0			0
$960$	11.6830	+	8.00641i	0.377067	+	0.258406i
$961$	9.42878	+	16.3311i	0.304154	+	0.526811i
$962$	−24.0972	+	33.4889i	−0.776924	+	1.07973i
$963$	1.98030	+	7.39056i	0.0638141	+	0.238158i
$964$	3.15012	+	9.40071i	0.101458	+	0.302777i
$965$	−11.1604	−	11.1604i	−0.359267	−	0.359267i
$966$		0			0
$967$			4.34118i			0.139603i	0.997561	+	0.0698015i	$0.0222366\pi$
$967$			4.34118i			0.139603i	−0.997561	+	0.0698015i	$0.977763\pi$
$968$	27.1976	−	6.17340i	0.874164	−	0.198421i
$969$	60.6643	+	35.0245i	1.94882	+	1.12515i
$970$	−7.09108	+	1.15649i	−0.227681	+	0.0371325i
$971$	−1.60086	+	5.97449i	−0.0513741	+	0.191731i	−0.986844	−	0.161676i	$-0.948310\pi$
$971$	−1.60086	+	5.97449i	−0.0513741	+	0.191731i	0.935470	+	0.353407i	$0.114977\pi$
$972$	25.1237	−	16.6452i	0.805843	−	0.533895i
$973$		0			0
$974$	−3.78530	+	37.6765i	−0.121289	+	1.20723i
$975$	−19.1843	−	33.2282i	−0.614390	−	1.06415i
$976$	5.38608	−	38.5746i	0.172404	−	1.23474i
$977$	−21.6145	+	37.4374i	−0.691509	+	1.19773i	0.279834	+	0.960048i	$0.409721\pi$
$977$	−21.6145	+	37.4374i	−0.691509	+	1.19773i	−0.971343	+	0.237681i	$0.923613\pi$
$978$	−34.1499	+	15.3926i	−1.09199	+	0.492201i
$979$	−4.21526	+	4.21526i	−0.134720	+	0.134720i
$980$		0			0
$981$	−6.45392	−	6.45392i	−0.206058	−	0.206058i
$982$	−4.87155	+	12.8669i	−0.155457	+	0.410600i
$983$	−27.7494	−	16.0211i	−0.885068	−	0.510994i	−0.0127419	−	0.999919i	$-0.504056\pi$
$983$	−27.7494	−	16.0211i	−0.885068	−	0.510994i	−0.872326	+	0.488925i	$0.837389\pi$
$984$	23.4008	+	0.903677i	0.745991	+	0.0288082i
$985$	6.76804	−	3.90753i	0.215648	−	0.124504i
$986$	−25.2414	+	20.6325i	−0.803849	+	0.657072i
$987$		0			0
$988$	−10.9865	+	54.1245i	−0.349527	+	1.72193i
$989$	−47.5463	−	12.7400i	−1.51189	−	0.405109i
$990$	1.16218	−	1.61513i	0.0369365	−	0.0513323i
$991$	5.34937	−	9.26538i	0.169928	−	0.294324i	−0.768466	−	0.639890i	$-0.778980\pi$
$991$	5.34937	−	9.26538i	0.169928	−	0.294324i	0.938394	+	0.345566i	$0.112313\pi$
$992$	0.452078	+	19.7067i	0.0143535	+	0.625688i
$993$	−24.1194			−0.765405
$994$		0			0
$995$	−4.65082	+	4.65082i	−0.147441	+	0.147441i
$996$	32.3711	−	10.8473i	1.02572	−	0.343711i
$997$	26.3865	−	7.07025i	0.835670	−	0.223917i	0.184484	−	0.982835i	$-0.440939\pi$
$997$	26.3865	−	7.07025i	0.835670	−	0.223917i	0.651186	+	0.758918i	$0.274272\pi$
$998$	−4.73946	−	29.0603i	−0.150025	−	0.919889i
$999$	18.3472	−	10.5928i	0.580481	−	0.335141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.165.16		96
7.2	even	3	inner	784.2.x.p.373.17		96
7.3	odd	6		784.2.m.l.197.1	✓	48
7.4	even	3		784.2.m.l.197.2	yes	48
7.5	odd	6	inner	784.2.x.p.373.18		96
7.6	odd	2	inner	784.2.x.p.165.15		96
16.13	even	4	inner	784.2.x.p.557.17		96
112.13	odd	4	inner	784.2.x.p.557.18		96
112.45	odd	12		784.2.m.l.589.1	yes	48
112.61	odd	12	inner	784.2.x.p.765.15		96
112.93	even	12	inner	784.2.x.p.765.16		96
112.109	even	12		784.2.m.l.589.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.1	✓	48	7.3	odd	6
784.2.m.l.197.2	yes	48	7.4	even	3
784.2.m.l.589.1	yes	48	112.45	odd	12
784.2.m.l.589.2	yes	48	112.109	even	12
784.2.x.p.165.15		96	7.6	odd	2	inner
784.2.x.p.165.16		96	1.1	even	1	trivial
784.2.x.p.373.17		96	7.2	even	3	inner
784.2.x.p.373.18		96	7.5	odd	6	inner
784.2.x.p.557.17		96	16.13	even	4	inner
784.2.x.p.557.18		96	112.13	odd	4	inner
784.2.x.p.765.15		96	112.61	odd	12	inner
784.2.x.p.765.16		96	112.93	even	12	inner

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.581133 + 1.28930i) q^{2} +(0.554865 + 2.07078i) q^{3} +(-1.32457 + 1.49850i) q^{4} +(0.213735 - 0.797669i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} +(-1.38220 + 0.798013i) q^{9} +O(q^{10})\)	\(q+(0.581133 + 1.28930i) q^{2} +(0.554865 + 2.07078i) q^{3} +(-1.32457 + 1.49850i) q^{4} +(0.213735 - 0.797669i) q^{5} +(-2.34740 + 1.91879i) q^{6} +(-2.70177 - 0.836931i) q^{8} +(-1.38220 + 0.798013i) q^{9} +(1.15264 - 0.187984i) q^{10} +(-1.03115 + 0.276295i) q^{11} +(-3.83804 - 1.91143i) q^{12} +(-2.93078 + 2.93078i) q^{13} +1.77039 q^{15} +(-0.491033 - 3.96975i) q^{16} +(-2.45215 + 4.24726i) q^{17} +(-1.83212 - 1.31831i) q^{18} +(-6.43542 - 1.72437i) q^{19} +(0.912204 + 1.37685i) q^{20} +(-0.955458 - 1.16889i) q^{22} +(-5.11212 + 2.95149i) q^{23} +(0.233988 - 6.05916i) q^{24} +(3.73953 + 2.15902i) q^{25} +(-5.48182 - 2.07547i) q^{26} +(2.12831 + 2.12831i) q^{27} +(3.32371 - 3.32371i) q^{29} +(1.02883 + 2.28256i) q^{30} +(-1.74230 + 3.01775i) q^{31} +(4.83282 - 2.94004i) q^{32} +(-1.14429 - 1.98197i) q^{33} +(-6.90100 - 0.693333i) q^{34} +(0.634992 - 3.12825i) q^{36} +(1.82174 - 6.79882i) q^{37} +(-1.51662 - 9.29925i) q^{38} +(-7.69520 - 4.44283i) q^{39} +(-1.24506 + 1.97623i) q^{40} +3.86206i q^{41} +(5.89641 + 5.89641i) q^{43} +(0.951795 - 1.91115i) q^{44} +(0.341126 + 1.27310i) q^{45} +(-6.77616 - 4.87584i) q^{46} +(3.10648 + 5.38058i) q^{47} +(7.94803 - 3.21950i) q^{48} +(-0.610451 + 6.07604i) q^{50} +(-10.1558 - 2.72123i) q^{51} +(-0.509767 - 8.27381i) q^{52} +(12.8748 - 3.44980i) q^{53} +(-1.50719 + 3.98086i) q^{54} +0.881566i q^{55} -14.2832i q^{57} +(6.21677 + 2.35373i) q^{58} +(5.82851 - 1.56174i) q^{59} +(-2.34501 + 2.65294i) q^{60} +(9.40542 + 2.52017i) q^{61} +(-4.90328 - 0.492626i) q^{62} +(6.59909 + 4.52239i) q^{64} +(1.71138 + 2.96420i) q^{65} +(1.89037 - 2.62712i) q^{66} +(3.19457 + 11.9223i) q^{67} +(-3.11649 - 9.30035i) q^{68} +(-8.94843 - 8.94843i) q^{69} +0.135373i q^{71} +(4.40226 - 0.999239i) q^{72} +(-6.55413 - 3.78403i) q^{73} +(9.82436 - 1.60226i) q^{74} +(-2.39593 + 8.94174i) q^{75} +(11.1081 - 7.35947i) q^{76} +(1.25618 - 12.5033i) q^{78} +(-3.39649 - 5.88289i) q^{79} +(-3.27149 - 0.456791i) q^{80} +(-5.62039 + 9.73480i) q^{81} +(-4.97934 + 2.24437i) q^{82} +(-5.63027 + 5.63027i) q^{83} +(2.86379 + 2.86379i) q^{85} +(-4.17562 + 11.0288i) q^{86} +(8.72690 + 5.03848i) q^{87} +(3.01715 + 0.116514i) q^{88} +(4.83608 - 2.79211i) q^{89} +(-1.44316 + 1.17965i) q^{90} +(2.34855 - 11.5700i) q^{92} +(-7.21586 - 1.93348i) q^{93} +(-5.13189 + 7.13201i) q^{94} +(-2.75095 + 4.76478i) q^{95} +(8.76975 + 8.37641i) q^{96} -6.15204 q^{97} +(1.20476 - 1.20476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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