LMFDB - Embedded newform 289.3.e.q.75.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,3,Mod(40,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([15]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("289.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			75.4
Character	$\chi$	$=$	289.75
Dual form			289.3.e.q.158.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453400 + 1.09461i) q^{2} +(3.10496 - 4.64690i) q^{3} +(1.83584 + 1.83584i) q^{4} +(-0.0407565 - 0.204897i) q^{5} +(3.67873 + 5.50561i) q^{6} +(0.784602 - 3.94446i) q^{7} +(-7.22031 + 2.99075i) q^{8} +(-8.50875 - 20.5419i) q^{9} +O(q^{10})$	\(q+(-0.453400 + 1.09461i) q^{2} +(3.10496 - 4.64690i) q^{3} +(1.83584 + 1.83584i) q^{4} +(-0.0407565 - 0.204897i) q^{5} +(3.67873 + 5.50561i) q^{6} +(0.784602 - 3.94446i) q^{7} +(-7.22031 + 2.99075i) q^{8} +(-8.50875 - 20.5419i) q^{9} +(0.242760 + 0.0482880i) q^{10} +(8.17283 - 5.46091i) q^{11} +(14.2311 - 2.83075i) q^{12} +(6.06272 - 6.06272i) q^{13} +(3.96189 + 2.64725i) q^{14} +(-1.07868 - 0.446804i) q^{15} +1.12567i q^{16} +26.3432 q^{18} +(-6.63138 + 16.0096i) q^{19} +(0.301335 - 0.450979i) q^{20} +(-15.8933 - 15.8933i) q^{21} +(2.27198 + 11.4220i) q^{22} +(-8.38804 - 12.5536i) q^{23} +(-8.52105 + 42.8382i) q^{24} +(23.0567 - 9.55038i) q^{25} +(3.88745 + 9.38512i) q^{26} +(-72.5430 - 14.4297i) q^{27} +(8.68179 - 5.80099i) q^{28} +(16.8075 - 3.34322i) q^{29} +(0.978149 - 0.978149i) q^{30} +(12.0354 + 8.04177i) q^{31} +(-30.1134 - 12.4734i) q^{32} -54.9342i q^{33} -0.840185 q^{35} +(22.0910 - 53.3323i) q^{36} +(-29.1586 + 43.6389i) q^{37} +(-14.5175 - 14.5175i) q^{38} +(-9.34835 - 46.9973i) q^{39} +(0.907069 + 1.35753i) q^{40} +(1.86180 - 9.35988i) q^{41} +(24.6030 - 10.1909i) q^{42} +(0.125047 + 0.301889i) q^{43} +(25.0293 + 4.97864i) q^{44} +(-3.86219 + 2.58063i) q^{45} +(17.5444 - 3.48979i) q^{46} +(35.1236 - 35.1236i) q^{47} +(5.23086 + 3.49515i) q^{48} +(30.3269 + 12.5618i) q^{49} +29.5681i q^{50} +22.2603 q^{52} +(-27.5780 + 66.5792i) q^{53} +(48.6859 - 72.8636i) q^{54} +(-1.45202 - 1.45202i) q^{55} +(6.13183 + 30.8268i) q^{56} +(53.8047 + 80.5244i) q^{57} +(-3.96103 + 19.9134i) q^{58} +(-65.1792 + 26.9981i) q^{59} +(-1.16002 - 2.80054i) q^{60} +(76.9122 + 15.2988i) q^{61} +(-14.2594 + 9.52783i) q^{62} +(-87.7028 + 17.4452i) q^{63} +(24.1230 - 24.1230i) q^{64} +(-1.48933 - 0.995136i) q^{65} +(60.1313 + 24.9072i) q^{66} +84.8560i q^{67} -84.3798 q^{69} +(0.380940 - 0.919671i) q^{70} +(10.4732 - 15.6743i) q^{71} +(122.872 + 122.872i) q^{72} +(-3.90441 - 19.6288i) q^{73} +(-34.5468 - 51.7030i) q^{74} +(27.2103 - 136.796i) q^{75} +(-41.5651 + 17.2168i) q^{76} +(-15.1279 - 36.5220i) q^{77} +(55.6821 + 11.0759i) q^{78} +(72.9102 - 48.7170i) q^{79} +(0.230646 - 0.0458782i) q^{80} +(-150.797 + 150.797i) q^{81} +(9.40124 + 6.28171i) q^{82} +(-46.1534 - 19.1173i) q^{83} -58.3552i q^{84} -0.387146 q^{86} +(36.6510 - 88.4834i) q^{87} +(-42.6781 + 63.8723i) q^{88} +(-37.5364 - 37.5364i) q^{89} +(-1.07366 - 5.39763i) q^{90} +(-19.1573 - 28.6710i) q^{91} +(7.64728 - 38.4455i) q^{92} +(74.7386 - 30.9577i) q^{93} +(22.5214 + 54.3716i) q^{94} +(3.55058 + 0.706254i) q^{95} +(-151.463 + 101.205i) q^{96} +(-27.1595 + 5.40237i) q^{97} +(-27.5005 + 27.5005i) q^{98} +(-181.718 - 121.420i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 432 q^{18} + 144 q^{35} - 720 q^{52} - 432 q^{69}+O(q^{100}) $ 48 * q + 432 * q^18 + 144 * q^35 - 720 * q^52 - 432 * q^69

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{16}\right)$

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 $

$2$	−0.453400	+	1.09461i	−0.226700	+	0.547303i	−0.995772	−	0.0918597i	$-0.970719\pi$
$2$	−0.453400	+	1.09461i	−0.226700	+	0.547303i	0.769072	+	0.639162i	$0.220719\pi$
$3$	3.10496	−	4.64690i	1.03499	−	1.54897i	0.214974	−	0.976620i	$-0.431033\pi$
$3$	3.10496	−	4.64690i	1.03499	−	1.54897i	0.820012	−	0.572346i	$-0.193967\pi$
$4$	1.83584	+	1.83584i	0.458959	+	0.458959i
$5$	−0.0407565	−	0.204897i	−0.00815130	−	0.0409793i	0.976496	−	0.215537i	$-0.0691503\pi$
$5$	−0.0407565	−	0.204897i	−0.00815130	−	0.0409793i	−0.984647	+	0.174558i	$0.944150\pi$
$6$	3.67873	+	5.50561i	0.613122	+	0.917602i
$7$	0.784602	−	3.94446i	0.112086	−	0.563494i	−0.883403	−	0.468615i	$-0.844753\pi$
$7$	0.784602	−	3.94446i	0.112086	−	0.563494i	0.995489	−	0.0948798i	$-0.0302467\pi$
$8$	−7.22031	+	2.99075i	−0.902539	+	0.373844i
$9$	−8.50875	−	20.5419i	−0.945416	−	2.28244i
$10$	0.242760	+	0.0482880i	0.0242760	+	0.00482880i
$11$	8.17283	−	5.46091i	0.742984	−	0.496446i	−0.125543	−	0.992088i	$-0.540067\pi$
$11$	8.17283	−	5.46091i	0.742984	−	0.496446i	0.868527	+	0.495642i	$0.165067\pi$
$12$	14.2311	−	2.83075i	1.18593	−	0.235896i
$13$	6.06272	−	6.06272i	0.466363	−	0.466363i	−0.434371	−	0.900734i	$-0.643029\pi$
$13$	6.06272	−	6.06272i	0.466363	−	0.466363i	0.900734	+	0.434371i	$0.143029\pi$
$14$	3.96189	+	2.64725i	0.282992	+	0.189089i
$15$	−1.07868	−	0.446804i	−0.0719121	−	0.0297870i
$16$			1.12567i			0.0703542i
$17$		0			0
$17$		0			0
$18$	26.3432			1.46351
$19$	−6.63138	+	16.0096i	−0.349020	+	0.842609i	0.647716	+	0.761882i	$0.275724\pi$
$19$	−6.63138	+	16.0096i	−0.349020	+	0.842609i	−0.996736	+	0.0807271i	$0.974276\pi$
$20$	0.301335	−	0.450979i	0.0150667	−	0.0225490i
$21$	−15.8933	−	15.8933i	−0.756826	−	0.756826i
$22$	2.27198	+	11.4220i	0.103272	+	0.519182i
$23$	−8.38804	−	12.5536i	−0.364698	−	0.545809i	0.603059	−	0.797697i	$-0.293948\pi$
$23$	−8.38804	−	12.5536i	−0.364698	−	0.545809i	−0.967756	+	0.251888i	$0.918948\pi$
$24$	−8.52105	+	42.8382i	−0.355044	+	1.78492i
$25$	23.0567	−	9.55038i	0.922267	−	0.382015i
$26$	3.88745	+	9.38512i	0.149517	+	0.360966i
$27$	−72.5430	−	14.4297i	−2.68678	−	0.534434i
$28$	8.68179	−	5.80099i	0.310064	−	0.207178i
$29$	16.8075	−	3.34322i	0.579570	−	0.115284i	0.103404	−	0.994639i	$-0.467026\pi$
$29$	16.8075	−	3.34322i	0.579570	−	0.115284i	0.476165	+	0.879356i	$0.342026\pi$
$30$	0.978149	−	0.978149i	0.0326050	−	0.0326050i
$31$	12.0354	+	8.04177i	0.388237	+	0.259412i	0.734336	−	0.678786i	$-0.237494\pi$
$31$	12.0354	+	8.04177i	0.388237	+	0.259412i	−0.346099	+	0.938198i	$0.612494\pi$
$32$	−30.1134	−	12.4734i	−0.941044	−	0.389793i
$33$		−	54.9342i		−	1.66467i
$34$		0			0
$35$	−0.840185			−0.0240053
$36$	22.0910	−	53.3323i	0.613638	−	1.48145i
$37$	−29.1586	+	43.6389i	−0.788069	+	1.17943i	0.192121	+	0.981371i	$0.438463\pi$
$37$	−29.1586	+	43.6389i	−0.788069	+	1.17943i	−0.980190	+	0.198057i	$0.936537\pi$
$38$	−14.5175	−	14.5175i	−0.382039	−	0.382039i
$39$	−9.34835	−	46.9973i	−0.239701	−	1.20506i
$40$	0.907069	+	1.35753i	0.0226767	+	0.0339381i
$41$	1.86180	−	9.35988i	0.0454097	−	0.228290i	−0.951416	−	0.307910i	$-0.900371\pi$
$41$	1.86180	−	9.35988i	0.0454097	−	0.228290i	0.996825	+	0.0796197i	$0.0253706\pi$
$42$	24.6030	−	10.1909i	0.585786	−	0.242640i
$43$	0.125047	+	0.301889i	0.00290806	+	0.00702068i	0.925327	−	0.379170i	$-0.123791\pi$
$43$	0.125047	+	0.301889i	0.00290806	+	0.00702068i	−0.922419	+	0.386191i	$0.873791\pi$
$44$	25.0293	+	4.97864i	0.568848	+	0.113151i
$45$	−3.86219	+	2.58063i	−0.0858264	+	0.0573474i
$46$	17.5444	−	3.48979i	0.381400	−	0.0758651i
$47$	35.1236	−	35.1236i	0.747311	−	0.747311i	−0.226662	−	0.973973i	$-0.572781\pi$
$47$	35.1236	−	35.1236i	0.747311	−	0.747311i	0.973973	+	0.226662i	$0.0727814\pi$
$48$	5.23086	+	3.49515i	0.108976	+	0.0728156i
$49$	30.3269	+	12.5618i	0.618917	+	0.256364i
$50$			29.5681i			0.591362i
$51$		0			0
$52$	22.2603			0.428083
$53$	−27.5780	+	66.5792i	−0.520340	+	1.25621i	0.417353	+	0.908745i	$0.362958\pi$
$53$	−27.5780	+	66.5792i	−0.520340	+	1.25621i	−0.937692	+	0.347466i	$0.887042\pi$
$54$	48.6859	−	72.8636i	0.901590	−	1.34933i
$55$	−1.45202	−	1.45202i	−0.0264003	−	0.0264003i
$56$	6.13183	+	30.8268i	0.109497	+	0.550478i
$57$	53.8047	+	80.5244i	0.943941	+	1.41271i
$58$	−3.96103	+	19.9134i	−0.0682935	+	0.343335i
$59$	−65.1792	+	26.9981i	−1.10473	+	0.457595i	−0.859120	−	0.511773i	$-0.828989\pi$
$59$	−65.1792	+	26.9981i	−1.10473	+	0.457595i	−0.245611	+	0.969368i	$0.578989\pi$
$60$	−1.16002	−	2.80054i	−0.0193337	−	0.0466757i
$61$	76.9122	+	15.2988i	1.26086	+	0.250800i	0.779877	−	0.625932i	$-0.215281\pi$
$61$	76.9122	+	15.2988i	1.26086	+	0.250800i	0.480979	+	0.876732i	$0.340281\pi$
$62$	−14.2594	+	9.52783i	−0.229990	+	0.153675i
$63$	−87.7028	+	17.4452i	−1.39211	+	0.276907i
$64$	24.1230	−	24.1230i	0.376922	−	0.376922i
$65$	−1.48933	−	0.995136i	−0.0229127	−	0.0153098i
$66$	60.1313	+	24.9072i	0.911080	+	0.377382i
$67$			84.8560i			1.26651i	0.773945	+	0.633253i	$0.218281\pi$
$67$			84.8560i			1.26651i	−0.773945	+	0.633253i	$0.781719\pi$
$68$		0			0
$69$	−84.3798			−1.22290
$70$	0.380940	−	0.919671i	0.00544200	−	0.0131382i
$71$	10.4732	−	15.6743i	0.147510	−	0.220765i	−0.750355	−	0.661035i	$-0.770117\pi$
$71$	10.4732	−	15.6743i	0.147510	−	0.220765i	0.897865	+	0.440270i	$0.145117\pi$
$72$	122.872	+	122.872i	1.70655	+	1.70655i
$73$	−3.90441	−	19.6288i	−0.0534850	−	0.268887i	0.944784	−	0.327692i	$-0.106271\pi$
$73$	−3.90441	−	19.6288i	−0.0534850	−	0.268887i	−0.998269	+	0.0588050i	$0.981271\pi$
$74$	−34.5468	−	51.7030i	−0.466849	−	0.698689i
$75$	27.2103	−	136.796i	0.362804	−	1.82394i
$76$	−41.5651	+	17.2168i	−0.546909	+	0.226537i
$77$	−15.1279	−	36.5220i	−0.196466	−	0.474312i
$78$	55.6821	+	11.0759i	0.713873	+	0.141998i
$79$	72.9102	−	48.7170i	0.922914	−	0.616672i	−0.000698038	−	1.00000i	$-0.500222\pi$
$79$	72.9102	−	48.7170i	0.922914	−	0.616672i	0.923612	+	0.383328i	$0.125222\pi$
$80$	0.230646	−	0.0458782i	0.00288307	−	0.000573478i
$81$	−150.797	+	150.797i	−1.86170	+	1.86170i
$82$	9.40124	+	6.28171i	0.114649	+	0.0766062i
$83$	−46.1534	−	19.1173i	−0.556065	−	0.230329i	0.0869111	−	0.996216i	$-0.472300\pi$
$83$	−46.1534	−	19.1173i	−0.556065	−	0.230329i	−0.642976	+	0.765887i	$0.722300\pi$
$84$		−	58.3552i		−	0.694705i
$85$		0			0
$86$	−0.387146			−0.00450169
$87$	36.6510	−	88.4834i	0.421276	−	1.01705i
$88$	−42.6781	+	63.8723i	−0.484979	+	0.725822i
$89$	−37.5364	−	37.5364i	−0.421757	−	0.421757i	0.464051	−	0.885808i	$-0.346395\pi$
$89$	−37.5364	−	37.5364i	−0.421757	−	0.421757i	−0.885808	+	0.464051i	$0.846395\pi$
$90$	−1.07366	−	5.39763i	−0.0119295	−	0.0599737i
$91$	−19.1573	−	28.6710i	−0.210520	−	0.315066i
$92$	7.64728	−	38.4455i	0.0831226	−	0.417885i
$93$	74.7386	−	30.9577i	0.803641	−	0.332879i
$94$	22.5214	+	54.3716i	0.239590	+	0.578421i
$95$	3.55058	+	0.706254i	0.0373745	+	0.00743425i
$96$	−151.463	+	101.205i	−1.57774	+	1.05421i
$97$	−27.1595	+	5.40237i	−0.279995	+	0.0556945i	−0.333090	−	0.942895i	$-0.608091\pi$
$97$	−27.1595	+	5.40237i	−0.279995	+	0.0556945i	0.0530950	+	0.998589i	$0.483091\pi$
$98$	−27.5005	+	27.5005i	−0.280617	+	0.280617i
$99$	−181.718	−	121.420i	−1.83554	−	1.22647i
$100$	59.8613	+	24.7953i	0.598613	+	0.247953i
$101$			114.575i			1.13441i	0.823578	+	0.567204i	$0.191975\pi$
$101$			114.575i			1.13441i	−0.823578	+	0.567204i	$0.808025\pi$
$102$		0			0
$103$	−78.8225			−0.765267			−0.382633	−	0.923900i	$-0.624983\pi$
$103$	−78.8225			−0.765267			−0.382633	+	0.923900i	$0.624983\pi$
$104$	−25.6426	+	61.9068i	−0.246564	+	0.595258i
$105$	−2.60874	+	3.90425i	−0.0248451	+	0.0371833i
$106$	−60.3741	−	60.3741i	−0.569567	−	0.569567i
$107$	35.6670	+	179.310i	0.333337	+	1.67580i	0.676438	+	0.736499i	$0.263523\pi$
$107$	35.6670	+	179.310i	0.333337	+	1.67580i	−0.343101	+	0.939298i	$0.611477\pi$
$108$	−106.687	−	159.668i	−0.987839	−	1.47841i
$109$	−29.5878	+	148.748i	−0.271448	+	1.36466i	0.568809	+	0.822470i	$0.307405\pi$
$109$	−29.5878	+	148.748i	−0.271448	+	1.36466i	−0.840256	+	0.542190i	$0.817595\pi$
$110$	2.24773	−	0.931041i	0.0204339	−	0.00846401i
$111$	112.249	+	270.994i	1.01125	+	2.44138i
$112$	4.44015	+	0.883201i	0.0396442	+	0.00788572i
$113$	−93.3279	+	62.3597i	−0.825911	+	0.551856i	−0.895161	−	0.445744i	$-0.852939\pi$
$113$	−93.3279	+	62.3597i	−0.825911	+	0.551856i	0.0692502	+	0.997599i	$0.477939\pi$
$114$	−112.537	+	22.3851i	−0.987171	+	0.196361i
$115$	−2.23032	+	2.23032i	−0.0193941	+	0.0193941i
$116$	36.9935	+	24.7183i	0.318909	+	0.213088i
$117$	−176.126	−	72.9538i	−1.50535	−	0.623537i
$118$		−	83.5864i		−	0.708360i
$119$		0			0
$120$	9.12469			0.0760391
$121$	−9.33112	+	22.5273i	−0.0771167	+	0.186176i
$122$	−51.6182	+	77.2521i	−0.423100	+	0.633214i
$123$	−37.7136	−	37.7136i	−0.306615	−	0.306615i
$124$	7.33158	+	36.8584i	0.0591257	+	0.297245i
$125$	−5.79817	−	8.67757i	−0.0463853	−	0.0694206i
$126$	20.6689	−	103.910i	0.164039	−	0.824679i
$127$	−18.6022	+	7.70528i	−0.146474	+	0.0606715i	−0.454716	−	0.890636i	$-0.650259\pi$
$127$	−18.6022	+	7.70528i	−0.146474	+	0.0606715i	0.308242	+	0.951308i	$0.400259\pi$
$128$	−34.4257	−	83.1111i	−0.268951	−	0.649305i
$129$	1.79111	+	0.356274i	0.0138846	+	0.00276182i
$130$	1.76454	−	1.17903i	0.0135734	−	0.00906946i
$131$	240.124	−	47.7636i	1.83301	−	0.364608i	0.847037	−	0.531533i	$-0.178384\pi$
$131$	240.124	−	47.7636i	1.83301	−	0.364608i	0.985970	+	0.166925i	$0.0533839\pi$
$132$	100.850	−	100.850i	0.764017	−	0.764017i
$133$	57.9461	+	38.7183i	0.435685	+	0.291115i
$134$	−92.8838	−	38.4737i	−0.693163	−	0.287117i
$135$			15.4519i			0.114459i
$136$		0			0
$137$	−137.724			−1.00528			−0.502641	−	0.864495i	$-0.667638\pi$
$137$	−137.724			−1.00528			−0.502641	+	0.864495i	$0.667638\pi$
$138$	38.2578	−	92.3626i	0.277231	−	0.669294i
$139$	−21.3364	+	31.9322i	−0.153499	+	0.229728i	−0.900247	−	0.435379i	$-0.856614\pi$
$139$	−21.3364	+	31.9322i	−0.153499	+	0.229728i	0.746748	+	0.665107i	$0.231614\pi$
$140$	−1.54244	−	1.54244i	−0.0110174	−	0.0110174i
$141$	−54.1585	−	272.273i	−0.384103	−	1.93102i
$142$	12.4086	+	18.5708i	0.0873847	+	0.130780i
$143$	16.4416	−	82.6575i	0.114976	−	0.578024i
$144$	23.1234	−	9.57802i	0.160579	−	0.0665140i
$145$	−1.37003	−	3.30755i	−0.00944849	−	0.0228107i
$146$	23.2560	+	4.62591i	0.159288	+	0.0316843i
$147$	152.537	−	101.922i	1.03767	−	0.693348i
$148$	−133.644	+	26.5835i	−0.903002	+	0.179618i
$149$	−81.5217	+	81.5217i	−0.547125	+	0.547125i	−0.925608	−	0.378483i	$-0.876446\pi$
$149$	−81.5217	+	81.5217i	−0.547125	+	0.547125i	0.378483	+	0.925608i	$0.376446\pi$
$150$	137.400	+	91.8077i	0.916000	+	0.612051i
$151$	238.866	+	98.9416i	1.58189	+	0.655242i	0.988712	−	0.149826i	$-0.0478714\pi$
$151$	238.866	+	98.9416i	1.58189	+	0.655242i	0.593182	+	0.805068i	$0.297871\pi$
$152$		−	135.427i		−	0.890966i
$153$		0			0
$154$	46.8362			0.304131
$155$	1.15721	−	2.79376i	0.00746589	−	0.0180243i
$156$	69.1174	−	103.441i	0.443060	−	0.663086i
$157$	105.070	+	105.070i	0.669234	+	0.669234i	0.957539	−	0.288304i	$-0.0930915\pi$
$157$	105.070	+	105.070i	0.669234	+	0.669234i	−0.288304	+	0.957539i	$0.593092\pi$
$158$	20.2684	+	101.896i	0.128281	+	0.644913i
$159$	223.758	+	334.878i	1.40728	+	2.10615i
$160$	−1.32844	+	6.67851i	−0.00830274	+	0.0417407i
$161$	−56.0984	+	23.2367i	−0.348437	+	0.144328i
$162$	−96.6921	−	233.435i	−0.596865	−	1.44096i
$163$	−91.5034	−	18.2012i	−0.561371	−	0.111664i	−0.0937547	−	0.995595i	$-0.529887\pi$
$163$	−91.5034	−	18.2012i	−0.561371	−	0.111664i	−0.467616	+	0.883932i	$0.654887\pi$
$164$	20.6012	−	13.7653i	0.125617	−	0.0839346i
$165$	−11.2558	+	2.23892i	−0.0682172	+	0.0135692i
$166$	41.8519	−	41.8519i	0.252120	−	0.252120i
$167$	−189.698	−	126.752i	−1.13591	−	0.758993i	−0.162197	−	0.986758i	$-0.551858\pi$
$167$	−189.698	−	126.752i	−1.13591	−	0.758993i	−0.973716	+	0.227765i	$0.926858\pi$
$168$	162.288	+	67.2219i	0.966000	+	0.400130i
$169$			95.4869i			0.565011i
$170$		0			0
$171$	385.292			2.25317
$172$	−0.324654	+	0.783784i	−0.00188752	+	0.00455689i
$173$	174.620	−	261.338i	1.00937	−	1.51062i	0.157055	−	0.987590i	$-0.449800\pi$
$173$	174.620	−	261.338i	1.00937	−	1.51062i	0.852312	−	0.523034i	$-0.175200\pi$
$174$	80.2368	+	80.2368i	0.461131	+	0.461131i
$175$	−19.5808	−	98.4393i	−0.111890	−	0.562511i
$176$	6.14717	+	9.19988i	0.0349271	+	0.0522721i
$177$	−76.9212	+	386.709i	−0.434583	+	2.18480i
$178$	58.1066	−	24.0685i	0.326442	−	0.135217i
$179$	−96.6819	−	233.411i	−0.540122	−	1.30397i	−0.924636	−	0.380851i	$-0.875631\pi$
$179$	−96.6819	−	233.411i	−0.540122	−	1.30397i	0.384514	−	0.923119i	$-0.374369\pi$
$180$	−11.8280	−	2.35273i	−0.0657109	−	0.0130707i
$181$	91.2741	−	60.9874i	0.504277	−	0.336947i	−0.277272	−	0.960792i	$-0.589430\pi$
$181$	91.2741	−	60.9874i	0.504277	−	0.336947i	0.781548	+	0.623845i	$0.214430\pi$
$182$	40.0693	−	7.97029i	0.220161	−	0.0437928i
$183$	309.901	−	309.901i	1.69345	−	1.69345i
$184$	98.1090	+	65.5543i	0.533201	+	0.356273i
$185$	10.1299	+	4.19593i	0.0547560	+	0.0226807i
$186$			95.8455i			0.515298i
$187$		0			0
$188$	128.963			0.685971
$189$	−113.835	+	274.821i	−0.602300	+	1.45408i
$190$	−2.38290	+	3.56627i	−0.0125416	+	0.0187698i
$191$	−59.1941	−	59.1941i	−0.309917	−	0.309917i	0.534960	−	0.844877i	$-0.320327\pi$
$191$	−59.1941	−	59.1941i	−0.309917	−	0.309917i	−0.844877	+	0.534960i	$0.820327\pi$
$192$	−37.1962	−	186.998i	−0.193730	−	0.973948i
$193$	29.9815	+	44.8705i	0.155345	+	0.232490i	0.900976	−	0.433869i	$-0.142852\pi$
$193$	29.9815	+	44.8705i	0.155345	+	0.232490i	−0.745631	+	0.666359i	$0.767852\pi$
$194$	6.40069	−	32.1784i	0.0329932	−	0.165868i
$195$	−9.24859	+	3.83089i	−0.0474287	+	0.0196456i
$196$	32.6139	+	78.7368i	0.166397	+	0.401718i
$197$	−40.1005	−	7.97648i	−0.203556	−	0.0404897i	0.0922592	−	0.995735i	$-0.470591\pi$
$197$	−40.1005	−	7.97648i	−0.203556	−	0.0404897i	−0.295815	+	0.955245i	$0.595591\pi$
$198$	215.298	−	143.858i	1.08736	−	0.726554i
$199$	−104.856	+	20.8572i	−0.526916	+	0.104810i	−0.451378	−	0.892333i	$-0.649067\pi$
$199$	−104.856	+	20.8572i	−0.526916	+	0.104810i	−0.0755378	+	0.997143i	$0.524067\pi$
$200$	−137.913	+	137.913i	−0.689567	+	0.689567i
$201$	394.317	+	263.474i	1.96178	+	1.31082i
$202$	−125.415	−	51.9484i	−0.620864	−	0.257170i
$203$		−	68.9197i		−	0.339506i
$204$		0			0
$205$	−1.99369			−0.00972532
$206$	35.7381	−	86.2795i	0.173486	−	0.418832i
$207$	−186.503	+	279.122i	−0.900982	+	1.34842i
$208$	6.82460	+	6.82460i	0.0328106	+	0.0328106i
$209$	33.2297	+	167.057i	0.158994	+	0.799315i
$210$	−3.09081	−	4.62573i	−0.0147182	−	0.0220273i
$211$	37.0463	−	186.245i	0.175575	−	0.882676i	−0.788090	−	0.615561i	$-0.788930\pi$
$211$	37.0463	−	186.245i	0.175575	−	0.882676i	0.963665	−	0.267115i	$-0.0860704\pi$
$212$	−172.857	+	71.5998i	−0.815365	+	0.337735i
$213$	−40.3180	−	97.3362i	−0.189286	−	0.456977i
$214$	−212.446	−	42.2581i	−0.992736	−	0.197468i
$215$	0.0567596	−	0.0379256i	0.000263998	−	0.000176398i
$216$	566.939	−	112.771i	2.62472	−	0.522089i
$217$	41.1634	−	41.1634i	0.189693	−	0.189693i
$218$	−149.405	−	99.8293i	−0.685345	−	0.457933i
$219$	−103.336	−	42.8032i	−0.471854	−	0.195448i
$220$		−	5.33134i		−	0.0242334i
$221$		0			0
$222$	−347.525			−1.56543
$223$	73.9393	−	178.505i	0.331566	−	0.800472i	−0.666902	−	0.745145i	$-0.732380\pi$
$223$	73.9393	−	178.505i	0.331566	−	0.800472i	0.998468	−	0.0553262i	$-0.0176199\pi$
$224$	−72.8278	+	108.994i	−0.325124	+	0.486582i
$225$	−392.367	−	392.367i	−1.74385	−	1.74385i
$226$	−25.9444	−	130.431i	−0.114798	−	0.577129i
$227$	−197.762	−	295.972i	−0.871200	−	1.30384i	−0.951681	−	0.307087i	$-0.900646\pi$
$227$	−197.762	−	295.972i	−0.871200	−	1.30384i	0.0804815	−	0.996756i	$-0.474354\pi$
$228$	−49.0530	+	246.606i	−0.215145	+	1.08161i
$229$	243.212	−	100.742i	1.06206	−	0.439920i	0.217879	−	0.975976i	$-0.430086\pi$
$229$	243.212	−	100.742i	1.06206	−	0.439920i	0.844183	+	0.536055i	$0.180086\pi$
$230$	−1.43009	−	3.45255i	−0.00621780	−	0.0150111i
$231$	−216.686	−	43.1015i	−0.938033	−	0.186586i
$232$	−111.357	+	74.4062i	−0.479986	+	0.320716i
$233$	40.6187	−	8.07957i	0.174329	−	0.0346763i	−0.107154	−	0.994242i	$-0.534174\pi$
$233$	40.6187	−	8.07957i	0.174329	−	0.0346763i	0.281483	+	0.959566i	$0.409174\pi$
$234$	159.711	−	159.711i	0.682527	−	0.682527i
$235$	−8.62823	−	5.76520i	−0.0367159	−	0.0245328i
$236$	−169.223	−	70.0943i	−0.717045	−	0.297010i
$237$		−	490.071i		−	2.06781i
$238$		0			0
$239$	255.897			1.07070			0.535348	−	0.844631i	$-0.320180\pi$
$239$	255.897			1.07070			0.535348	+	0.844631i	$0.320180\pi$
$240$	0.502953	−	1.21424i	0.00209564	−	0.00505932i
$241$	47.4110	−	70.9555i	0.196726	−	0.294421i	−0.719971	−	0.694004i	$-0.755845\pi$
$241$	47.4110	−	70.9555i	0.196726	−	0.294421i	0.916697	+	0.399583i	$0.130845\pi$
$242$	−20.4278	−	20.4278i	−0.0844123	−	0.0844123i
$243$	102.653	+	516.072i	0.422441	+	2.12376i
$244$	113.112	+	169.284i	0.463575	+	0.693789i
$245$	1.33786	−	6.72587i	0.00546064	−	0.0274525i
$246$	58.3809	−	24.1822i	0.237321	−	0.0983015i
$247$	56.8573	+	137.266i	0.230192	+	0.555731i
$248$	−110.950	−	22.0693i	−0.447379	−	0.0889892i
$249$	−232.141	+	155.111i	−0.932291	+	0.622937i
$250$	12.1274	−	2.41229i	0.0485096	−	0.00964917i
$251$	−195.580	+	195.580i	−0.779202	+	0.779202i	−0.979695	−	0.200493i	$-0.935746\pi$
$251$	−195.580	+	195.580i	−0.779202	+	0.779202i	0.200493	+	0.979695i	$0.435746\pi$
$252$	−193.035	−	128.982i	−0.766010	−	0.511832i
$253$	−137.108	−	56.7920i	−0.541929	−	0.224474i
$254$		−	23.8557i		−	0.0939199i
$255$		0			0
$256$	243.043			0.949386
$257$	−68.1176	+	164.451i	−0.265049	+	0.639885i	−0.999237	−	0.0390614i	$-0.987563\pi$
$257$	−68.1176	+	164.451i	−0.265049	+	0.639885i	0.734188	+	0.678947i	$0.237563\pi$
$258$	−1.20207	+	1.79903i	−0.00465919	+	0.00697297i
$259$	149.254	+	149.254i	0.576270	+	0.576270i
$260$	−0.907253	−	4.56107i	−0.00348944	−	0.0175426i
$261$	−211.687	−	316.812i	−0.811062	−	1.21384i
$262$	−56.5900	+	284.497i	−0.215992	+	1.08587i
$263$	273.067	−	113.108i	1.03828	−	0.430068i	0.202583	−	0.979265i	$-0.435066\pi$
$263$	273.067	−	113.108i	1.03828	−	0.430068i	0.835693	+	0.549197i	$0.185066\pi$
$264$	164.294	+	396.642i	0.622327	+	1.50243i
$265$	14.7658	+	2.93711i	0.0557201	+	0.0110834i
$266$	−68.6541	+	45.8732i	−0.258098	+	0.172456i
$267$	−290.977	+	57.8789i	−1.08980	+	0.216775i
$268$	−155.782	+	155.782i	−0.581275	+	0.581275i
$269$	−383.020	−	255.925i	−1.42386	−	0.951396i	−0.998934	−	0.0461701i	$-0.985298\pi$
$269$	−383.020	−	255.925i	−1.42386	−	0.951396i	−0.424931	−	0.905226i	$-0.639702\pi$
$270$	−16.9138	−	7.00591i	−0.0626436	−	0.0259478i
$271$		−	48.9996i		−	0.180810i	−0.995905	−	0.0904051i	$-0.971184\pi$
$271$		−	48.9996i		−	0.180810i	0.995905	−	0.0904051i	$-0.0288162\pi$
$272$		0			0
$273$	−192.714			−0.705911
$274$	62.4440	−	150.753i	0.227898	−	0.550194i
$275$	136.284	−	203.964i	0.495580	−	0.741687i
$276$	−154.908	−	154.908i	−0.561260	−	0.561260i
$277$	−80.2110	−	403.248i	−0.289570	−	1.45577i	−0.802147	−	0.597127i	$-0.796309\pi$
$277$	−80.2110	−	403.248i	−0.289570	−	1.45577i	0.512577	−	0.858641i	$-0.328691\pi$
$278$	−25.2792	−	37.8330i	−0.0909324	−	0.136090i
$279$	62.7877	−	315.655i	0.225045	−	1.13138i
$280$	6.06639	−	2.51278i	0.0216657	−	0.00897422i
$281$	−124.236	−	299.932i	−0.442120	−	1.06737i	−0.975203	−	0.221310i	$-0.928967\pi$
$281$	−124.236	−	299.932i	−0.442120	−	1.06737i	0.533083	−	0.846063i	$-0.321033\pi$
$282$	322.587	+	64.1666i	1.14393	+	0.227541i
$283$	−172.200	+	115.060i	−0.608479	+	0.406573i	−0.821282	−	0.570522i	$-0.806741\pi$
$283$	−172.200	+	115.060i	−0.608479	+	0.406573i	0.212803	+	0.977095i	$0.431741\pi$
$284$	48.0027	−	9.54833i	0.169024	−	0.0336209i
$285$	14.3063	−	14.3063i	0.0501975	−	0.0501975i
$286$	83.0227	+	55.4740i	0.290289	+	0.193965i
$287$	−35.4589	−	14.6876i	−0.123550	−	0.0511762i
$288$			724.720i			2.51639i
$289$		0			0
$290$	4.24163			0.0146263
$291$	−59.2250	+	142.982i	−0.203522	+	0.491346i
$292$	28.8674	−	43.2031i	0.0988610	−	0.147956i
$293$	217.944	+	217.944i	0.743837	+	0.743837i	0.973314	−	0.229477i	$-0.0737016\pi$
$293$	217.944	+	217.944i	0.743837	+	0.743837i	−0.229477	+	0.973314i	$0.573702\pi$
$294$	42.4041	+	213.180i	0.144232	+	0.725102i
$295$	8.18830	+	12.2547i	0.0277569	+	0.0415412i
$296$	80.0209	−	402.292i	0.270341	−	1.35909i
$297$	−671.681	+	278.219i	−2.26155	+	0.936765i
$298$	−52.2721	−	126.196i	−0.175410	−	0.423477i
$299$	−126.963	−	25.2546i	−0.424626	−	0.0844634i
$300$	301.088	−	201.181i	1.00363	−	0.670602i
$301$	1.28890	−	0.256378i	0.00428206	−	0.000851755i
$302$	−216.604	+	216.604i	−0.717232	+	0.717232i
$303$	532.419	+	355.751i	1.75716	+	1.17410i
$304$	−18.0214	−	7.46473i	−0.0592811	−	0.0245550i
$305$		−	16.3826i		−	0.0537134i
$306$		0			0
$307$	−314.446			−1.02426			−0.512128	−	0.858909i	$-0.671143\pi$
$307$	−314.446			−1.02426			−0.512128	+	0.858909i	$0.671143\pi$
$308$	39.2761	−	94.8209i	0.127520	−	0.307860i
$309$	−244.740	+	366.280i	−0.792040	+	1.18537i
$310$	2.53338	+	2.53338i	0.00817221	+	0.00817221i
$311$	−12.3367	−	62.0207i	−0.0396678	−	0.199424i	0.955870	−	0.293791i	$-0.0949171\pi$
$311$	−12.3367	−	62.0207i	−0.0396678	−	0.199424i	−0.995537	+	0.0943677i	$0.969917\pi$
$312$	208.055	+	311.377i	0.666844	+	0.998002i
$313$	24.7546	−	124.450i	0.0790883	−	0.397604i	−0.920882	−	0.389842i	$-0.872530\pi$
$313$	24.7546	−	124.450i	0.0790883	−	0.397604i	0.999970	−	0.00776121i	$-0.00247049\pi$
$314$	−162.649	+	67.3713i	−0.517989	+	0.214558i
$315$	7.14892	+	17.2590i	0.0226950	+	0.0547905i
$316$	223.288	+	44.4147i	0.706607	+	0.140553i
$317$	117.209	−	78.3168i	0.369746	−	0.247056i	−0.356790	−	0.934184i	$-0.616129\pi$
$317$	117.209	−	78.3168i	0.369746	−	0.247056i	0.726536	+	0.687128i	$0.241129\pi$
$318$	−468.011	+	93.0932i	−1.47173	+	0.292746i
$319$	119.108	−	119.108i	0.373379	−	0.373379i
$320$	−5.92589	−	3.95955i	−0.0185184	−	0.0123736i
$321$	943.982	+	391.010i	2.94075	+	1.21810i
$322$		−	71.9412i		−	0.223420i
$323$		0			0
$324$	−553.679			−1.70889
$325$	81.8848	−	197.687i	0.251953	−	0.608269i
$326$	61.4108	−	91.9077i	0.188377	−	0.281926i
$327$	599.347	+	599.347i	1.83287	+	1.83287i
$328$	14.5503	+	73.1494i	0.0443607	+	0.223017i
$329$	−110.986	−	166.102i	−0.337342	−	0.504869i
$330$	2.65266	−	13.3358i	0.00803837	−	0.0404116i
$331$	23.6466	−	9.79472i	0.0714397	−	0.0295913i	−0.346677	−	0.937984i	$-0.612690\pi$
$331$	23.6466	−	9.79472i	0.0714397	−	0.0295913i	0.418117	+	0.908393i	$0.362690\pi$
$332$	−49.6337	−	119.826i	−0.149499	−	0.360923i
$333$	1144.53	+	227.661i	3.43702	+	0.683667i
$334$	224.752	−	150.175i	0.672911	−	0.449625i
$335$	17.3867	−	3.45843i	0.0519006	−	0.0103237i
$336$	17.8906	−	17.8906i	0.0532459	−	0.0532459i
$337$	−300.377	−	200.706i	−0.891328	−	0.595566i	0.0233602	−	0.999727i	$-0.492564\pi$
$337$	−300.377	−	200.706i	−0.891328	−	0.595566i	−0.914688	+	0.404161i	$0.867564\pi$
$338$	−104.520	−	43.2938i	−0.309232	−	0.128088i
$339$			627.309i			1.85047i
$340$		0			0
$341$	142.278			0.417238
$342$	−174.692	+	421.743i	−0.510794	+	1.23317i
$343$	182.828	−	273.621i	0.533025	−	0.797729i
$344$	−1.80575	−	1.80575i	−0.00524927	−	0.00524927i
$345$	3.43902	+	17.2891i	0.00996819	+	0.0501135i
$346$	206.889	+	309.631i	0.597945	+	0.894888i
$347$	3.90382	−	19.6258i	0.0112502	−	0.0565586i	−0.974752	−	0.223289i	$-0.928321\pi$
$347$	3.90382	−	19.6258i	0.0112502	−	0.0565586i	0.986003	+	0.166730i	$0.0533208\pi$
$348$	229.726	−	95.1558i	0.660133	−	0.273436i
$349$	131.619	+	317.757i	0.377133	+	0.910479i	0.992501	+	0.122239i	$0.0390075\pi$
$349$	131.619	+	317.757i	0.377133	+	0.910479i	−0.615368	+	0.788240i	$0.710993\pi$
$350$	116.630	+	23.1992i	0.333229	+	0.0662834i
$351$	−527.291	+	352.325i	−1.50225	+	1.00377i
$352$	−314.228	+	62.5038i	−0.892692	+	0.177567i
$353$	−37.7408	+	37.7408i	−0.106915	+	0.106915i	−0.758540	−	0.651626i	$-0.774087\pi$
$353$	−37.7408	+	37.7408i	−0.106915	+	0.106915i	0.651626	+	0.758540i	$0.274087\pi$
$354$	−388.418	−	259.532i	−1.09723	−	0.733142i
$355$	−3.63847	−	1.50710i	−0.0102492	−	0.00424536i
$356$		−	137.822i		−	0.387139i
$357$		0			0
$358$	299.328			0.836112
$359$	−2.24744	+	5.42580i	−0.00626028	+	0.0151136i	−0.926979	−	0.375114i	$-0.877604\pi$
$359$	−2.24744	+	5.42580i	−0.00626028	+	0.0151136i	0.920718	+	0.390227i	$0.127604\pi$
$360$	20.1682	−	30.1838i	0.0560227	−	0.0838439i
$361$	42.9345	+	42.9345i	0.118932	+	0.118932i
$362$	25.3734	+	127.561i	0.0700924	+	0.352378i
$363$	75.7094	+	113.307i	0.208566	+	0.312141i
$364$	17.4655	−	87.8050i	0.0479821	−	0.241222i
$365$	−3.86274	+	1.60000i	−0.0105829	+	0.00438356i
$366$	198.710	+	479.729i	0.542924	+	1.31073i
$367$	43.8548	+	8.72326i	0.119495	+	0.0237691i	0.254476	−	0.967079i	$-0.418097\pi$
$367$	43.8548	+	8.72326i	0.119495	+	0.0237691i	−0.134980	+	0.990848i	$0.543097\pi$
$368$	14.1312	−	9.44215i	0.0383999	−	0.0256580i
$369$	−208.112	+	41.3960i	−0.563988	+	0.112184i
$370$	−9.18577	+	9.18577i	−0.0248264	+	0.0248264i
$371$	240.981	+	161.018i	0.649545	+	0.434012i
$372$	194.041	+	80.3745i	0.521616	+	0.216061i
$373$		−	488.740i		−	1.31029i	−0.755501	−	0.655147i	$-0.772607\pi$
$373$		−	488.740i		−	1.31029i	0.755501	−	0.655147i	$-0.227393\pi$
$374$		0			0
$375$	−58.3269			−0.155538
$376$	−148.557	+	358.649i	−0.395100	+	0.953855i
$377$	81.6302	−	122.168i	0.216526	−	0.324054i
$378$	−249.208	−	249.208i	−0.659281	−	0.659281i
$379$	−61.1832	−	307.589i	−0.161433	−	0.811580i	−0.973619	−	0.228181i	$-0.926722\pi$
$379$	−61.1832	−	307.589i	−0.161433	−	0.811580i	0.812185	−	0.583399i	$-0.198278\pi$
$380$	5.22172	+	7.81486i	0.0137414	+	0.0205654i
$381$	−21.9534	+	110.367i	−0.0576204	+	0.289677i
$382$	91.6328	−	37.9556i	0.239876	−	0.0993601i
$383$	76.3787	+	184.395i	0.199422	+	0.481448i	0.991678	−	0.128741i	$-0.0410936\pi$
$383$	76.3787	+	184.395i	0.199422	+	0.481448i	−0.792256	+	0.610189i	$0.791094\pi$
$384$	−493.099	−	98.0835i	−1.28411	−	0.255426i
$385$	−6.86668	+	4.58817i	−0.0178355	+	0.0119173i
$386$	−62.7092	+	12.4736i	−0.162459	+	0.0323151i
$387$	5.13739	−	5.13739i	0.0132749	−	0.0132749i
$388$	−59.7784	−	39.9426i	−0.154068	−	0.102945i
$389$	−333.774	−	138.254i	−0.858031	−	0.355408i	−0.0900941	−	0.995933i	$-0.528717\pi$
$389$	−333.774	−	138.254i	−0.858031	−	0.355408i	−0.767937	+	0.640525i	$0.778717\pi$
$390$		−	11.8605i		−	0.0304115i
$391$		0			0
$392$	−256.539			−0.654437
$393$	523.622	−	1264.14i	1.33237	−	3.21663i
$394$	26.9127	−	40.2777i	0.0683063	−	0.102228i
$395$	−12.9535	−	12.9535i	−0.0327937	−	0.0327937i
$396$	−110.697	−	556.513i	−0.279538	−	1.40533i
$397$	−226.277	−	338.648i	−0.569968	−	0.853017i	0.428761	−	0.903418i	$-0.358950\pi$
$397$	−226.277	−	338.648i	−0.569968	−	0.853017i	−0.998729	+	0.0504007i	$0.983950\pi$
$398$	24.7115	−	124.233i	0.0620891	−	0.312143i
$399$	359.840	−	149.051i	0.901856	−	0.373561i
$400$	10.7506	+	25.9541i	0.0268764	+	0.0648853i
$401$	−336.953	−	67.0241i	−0.840282	−	0.167142i	−0.243857	−	0.969811i	$-0.578413\pi$
$401$	−336.953	−	67.0241i	−0.840282	−	0.167142i	−0.596425	+	0.802669i	$0.703413\pi$
$402$	−467.184	+	312.162i	−1.16215	+	0.776523i
$403$	121.722	−	24.2120i	0.302040	−	0.0600794i
$404$	−210.341	+	210.341i	−0.520647	+	0.520647i
$405$	37.0439	+	24.7519i	0.0914663	+	0.0611159i
$406$	75.4399	+	31.2482i	0.185812	+	0.0769660i
$407$			515.885i			1.26753i
$408$		0			0
$409$	−541.811			−1.32472			−0.662361	−	0.749185i	$-0.730445\pi$
$409$	−541.811			−1.32472			−0.662361	+	0.749185i	$0.730445\pi$
$410$	0.903940	−	2.18230i	0.00220473	−	0.00532269i
$411$	−427.626	+	639.988i	−1.04045	+	1.55715i
$412$	−144.705	−	144.705i	−0.351226	−	0.351226i
$413$	55.3532	+	278.279i	0.134027	+	0.673800i
$414$	−220.968	−	330.702i	−0.533739	−	0.798796i
$415$	−2.03603	+	10.2358i	−0.00490610	+	0.0246646i
$416$	−258.192	+	106.946i	−0.620653	+	0.257083i
$417$	82.1369	+	198.296i	0.196971	+	0.475530i
$418$	−197.928	−	39.3702i	−0.473511	−	0.0941872i
$419$	−98.2911	+	65.6760i	−0.234585	+	0.156745i	−0.667307	−	0.744783i	$-0.732553\pi$
$419$	−98.2911	+	65.6760i	−0.234585	+	0.156745i	0.432722	+	0.901527i	$0.357553\pi$
$420$	−11.9568	+	2.37835i	−0.0284686	+	0.00566275i
$421$	115.542	−	115.542i	0.274447	−	0.274447i	−0.556441	−	0.830887i	$-0.687833\pi$
$421$	115.542	−	115.542i	0.274447	−	0.274447i	0.830887	+	0.556441i	$0.187833\pi$
$422$	187.068	+	124.995i	0.443288	+	0.296196i
$423$	−1020.36	−	422.649i	−2.41221	−	0.999170i
$424$		−	563.201i		−	1.32830i
$425$		0			0
$426$	124.825			0.293016
$427$	120.691	−	291.374i	0.282649	−	0.682374i
$428$	−263.706	+	394.664i	−0.616135	+	0.922111i
$429$	−333.050	−	333.050i	−0.776341	−	0.776341i
$430$	0.0157787	+	0.0793249i	3.66946e−5	+	0.000184476i
$431$	−45.2384	−	67.7040i	−0.104961	−	0.157086i	0.775271	−	0.631629i	$-0.217613\pi$
$431$	−45.2384	−	67.7040i	−0.104961	−	0.157086i	−0.880232	+	0.474543i	$0.842613\pi$
$432$	16.2430	−	81.6593i	0.0375996	−	0.189026i
$433$	−315.906	+	130.853i	−0.729575	+	0.302200i	−0.716377	−	0.697713i	$-0.754201\pi$
$433$	−315.906	+	130.853i	−0.729575	+	0.302200i	−0.0131977	+	0.999913i	$0.504201\pi$
$434$	26.3942	+	63.7212i	0.0608161	+	0.146823i
$435$	−19.6237	−	3.90340i	−0.0451120	−	0.00897334i
$436$	−327.395	+	218.759i	−0.750907	+	0.501740i
$437$	256.602	−	51.0413i	0.587190	−	0.116799i
$438$	93.7051	−	93.7051i	0.213939	−	0.213939i
$439$	285.665	+	190.875i	0.650717	+	0.434795i	0.836628	−	0.547771i	$-0.184524\pi$
$439$	285.665	+	190.875i	0.650717	+	0.434795i	−0.185911	+	0.982567i	$0.559524\pi$
$440$	14.8266	+	6.14140i	0.0336969	+	0.0139577i
$441$		−	729.859i		−	1.65501i
$442$		0			0
$443$	150.115			0.338861			0.169430	−	0.985542i	$-0.445807\pi$
$443$	150.115			0.338861			0.169430	+	0.985542i	$0.445807\pi$
$444$	−291.429	+	703.572i	−0.656372	+	1.58462i
$445$	−6.16124	+	9.22094i	−0.0138455	+	0.0207212i
$446$	161.869	+	161.869i	0.362934	+	0.362934i
$447$	125.702	+	631.944i	0.281211	+	1.41375i
$448$	−76.2252	−	114.079i	−0.170146	−	0.254641i
$449$	−148.671	+	747.419i	−0.331115	+	1.66463i	0.353279	+	0.935518i	$0.385067\pi$
$449$	−148.671	+	747.419i	−0.331115	+	1.66463i	−0.684395	+	0.729112i	$0.739933\pi$
$450$	607.386	−	251.587i	1.34975	−	0.559083i
$451$	−35.8973	−	86.6638i	−0.0795949	−	0.192159i
$452$	−285.817	−	56.8526i	−0.632339	−	0.125780i
$453$	1201.44	−	802.777i	2.65219	−	1.77213i
$454$	413.639	−	82.2778i	0.911098	−	0.181229i
$455$	−5.09380	+	5.09380i	−0.0111952	+	0.0111952i
$456$	−629.315	−	420.495i	−1.38008	−	0.922137i
$457$	75.0260	+	31.0768i	0.164171	+	0.0680017i	0.463255	−	0.886225i	$-0.346681\pi$
$457$	75.0260	+	31.0768i	0.164171	+	0.0680017i	−0.299085	+	0.954227i	$0.596681\pi$
$458$			311.898i			0.680999i
$459$		0			0
$460$	−8.18902			−0.0178022
$461$	−182.552	+	440.721i	−0.395992	+	0.956010i	0.592614	+	0.805487i	$0.298096\pi$
$461$	−182.552	+	440.721i	−0.395992	+	0.956010i	−0.988606	+	0.150524i	$0.951904\pi$
$462$	145.424	−	217.643i	0.314772	−	0.471089i
$463$	−311.442	−	311.442i	−0.672660	−	0.672660i	0.285668	−	0.958329i	$-0.407784\pi$
$463$	−311.442	−	311.442i	−0.672660	−	0.672660i	−0.958329	+	0.285668i	$0.907784\pi$
$464$	3.76336	+	18.9197i	0.00811068	+	0.0407752i
$465$	−9.38922	−	14.0520i	−0.0201919	−	0.0302193i
$466$	−9.57261	+	48.1248i	−0.0205421	+	0.103272i
$467$	530.456	−	219.722i	1.13588	−	0.470497i	0.266104	−	0.963944i	$-0.414263\pi$
$467$	530.456	−	219.722i	1.13588	−	0.470497i	0.869776	+	0.493447i	$0.164263\pi$
$468$	−189.407	−	457.270i	−0.404717	−	0.977073i
$469$	334.711	+	66.5781i	0.713669	+	0.141958i
$470$	10.2227	−	6.83057i	0.0217503	−	0.0145331i
$471$	814.486	−	162.011i	1.72927	−	0.343973i
$472$	389.869	−	389.869i	0.825994	−	0.825994i
$473$	2.67057	+	1.78442i	0.00564603	+	0.00377256i
$474$	536.434	+	222.198i	1.13172	+	0.468773i
$475$			432.459i			0.910441i
$476$		0			0
$477$	1602.32			3.35916
$478$	−116.024	+	280.106i	−0.242727	+	0.585995i
$479$	102.521	−	153.433i	0.214031	−	0.320320i	−0.708883	−	0.705326i	$-0.750801\pi$
$479$	102.521	−	153.433i	0.214031	−	0.320320i	0.922914	+	0.385006i	$0.125801\pi$
$480$	26.9096	+	26.9096i	0.0560617	+	0.0560617i
$481$	87.7900	+	441.350i	0.182516	+	0.917568i
$482$	56.1722	+	84.0676i	0.116540	+	0.174414i
$483$	−66.2045	+	332.833i	−0.137069	+	0.689095i
$484$	−58.4869	+	24.2261i	−0.120841	+	0.0500539i
$485$	2.21386	+	5.34472i	0.00456465	+	0.0110200i
$486$	−611.439	−	121.623i	−1.25810	−	0.250253i
$487$	−376.306	+	251.439i	−0.772702	+	0.516303i	−0.878302	−	0.478106i	$-0.841324\pi$
$487$	−376.306	+	251.439i	−0.772702	+	0.516303i	0.105600	+	0.994409i	$0.466324\pi$
$488$	−601.085	+	119.563i	−1.23173	+	0.245007i
$489$	−368.693	+	368.693i	−0.753974	+	0.753974i
$490$	6.75558	+	4.51394i	0.0137869	+	0.00921212i
$491$	404.453	+	167.530i	0.823734	+	0.341202i	0.754419	−	0.656393i	$-0.227919\pi$
$491$	404.453	+	167.530i	0.823734	+	0.341202i	0.0693148	+	0.997595i	$0.477919\pi$
$492$		−	138.472i		−	0.281448i
$493$		0			0
$494$	−176.031			−0.356338
$495$	−17.4724	+	42.1821i	−0.0352978	+	0.0852164i
$496$	−9.05236	+	13.5478i	−0.0182507	+	0.0273141i
$497$	−53.6094	−	53.6094i	−0.107866	−	0.107866i
$498$	−64.5331	−	324.430i	−0.129585	−	0.651466i
$499$	377.374	+	564.780i	0.756261	+	1.13182i	0.987298	+	0.158880i	$0.0507882\pi$
$499$	377.374	+	564.780i	0.756261	+	1.13182i	−0.231037	+	0.972945i	$0.574212\pi$
$500$	5.28612	−	26.5751i	0.0105722	−	0.0531502i
$501$	−1178.01	+	487.946i	−2.35131	+	0.973944i
$502$	−125.407	−	302.759i	−0.249814	−	0.603105i
$503$	317.444	+	63.1436i	0.631102	+	0.125534i	0.500268	−	0.865870i	$-0.333235\pi$
$503$	317.444	+	63.1436i	0.631102	+	0.125534i	0.130833	+	0.991404i	$0.458235\pi$
$504$	581.067	−	388.257i	1.15291	−	0.770351i
$505$	23.4761	−	4.66968i	0.0464873	−	0.00924689i
$506$	124.330	−	124.330i	0.245711	−	0.245711i
$507$	443.718	+	296.483i	0.875183	+	0.584779i
$508$	−48.2963	−	20.0050i	−0.0950714	−	0.0393799i
$509$			145.680i			0.286209i	0.989708	+	0.143105i	$0.0457085\pi$
$509$			145.680i			0.286209i	−0.989708	+	0.143105i	$0.954291\pi$
$510$		0			0
$511$	−80.4883			−0.157511
$512$	27.5072	−	66.4083i	0.0537251	−	0.129704i
$513$	712.074	−	1065.69i	1.38806	−	2.07738i
$514$	−149.124	−	149.124i	−0.290124	−	0.290124i
$515$	3.21253	+	16.1505i	0.00623792	+	0.0313601i
$516$	2.63413	+	3.94225i	0.00510490	+	0.00764002i
$517$	95.2524	−	478.866i	0.184241	−	0.926240i
$518$	−231.046	+	95.7023i	−0.446035	+	0.184754i
$519$	−672.222	−	1622.89i	−1.29522	−	3.12695i
$520$	13.7296	+	2.73099i	0.0264031	+	0.00525190i
$521$	10.4447	−	6.97892i	0.0200474	−	0.0133952i	−0.545506	−	0.838107i	$-0.683663\pi$
$521$	10.4447	−	6.97892i	0.0200474	−	0.0133952i	0.565554	+	0.824712i	$0.308663\pi$
$522$	442.763	−	88.0711i	0.848206	−	0.168719i
$523$	−68.6445	+	68.6445i	−0.131251	+	0.131251i	−0.769681	−	0.638429i	$-0.779585\pi$
$523$	−68.6445	+	68.6445i	−0.131251	+	0.131251i	0.638429	+	0.769681i	$0.279585\pi$
$524$	528.515	+	353.142i	1.00862	+	0.673936i
$525$	−518.235	−	214.660i	−0.987115	−	0.408876i
$526$			350.183i			0.665748i
$527$		0			0
$528$	61.8376			0.117117
$529$	115.206	−	278.132i	0.217781	−	0.525769i
$530$	−9.90981	+	14.8311i	−0.0186978	+	0.0279832i
$531$	1109.19	+	1109.19i	2.08886	+	2.08886i
$532$	35.2990	+	177.460i	0.0663516	+	0.333572i
$533$	−45.4588	−	68.0339i	−0.0852885	−	0.127643i
$534$	68.5745	−	344.747i	0.128417	−	0.645594i
$535$	35.2864	−	14.6161i	0.0659560	−	0.0273199i
$536$	−253.783	−	612.686i	−0.473476	−	1.14307i
$537$	−1384.83	−	275.460i	−2.57882	−	0.512960i
$538$	453.799	−	303.219i	0.843492	−	0.563603i
$539$	316.456	−	62.9470i	0.587116	−	0.116785i
$540$	−28.3672	+	28.3672i	−0.0525319	+	0.0525319i
$541$	−253.851	−	169.618i	−0.469225	−	0.313526i	0.298382	−	0.954446i	$-0.403553\pi$
$541$	−253.851	−	169.618i	−0.469225	−	0.313526i	−0.767608	+	0.640920i	$0.778553\pi$
$542$	53.6352	+	22.2164i	0.0989580	+	0.0409897i
$543$		−	613.505i		−	1.12984i
$544$		0			0
$545$	31.6839			0.0581355
$546$	87.3765	−	210.946i	0.160030	−	0.386347i
$547$	−313.463	+	469.131i	−0.573059	+	0.857644i	−0.998887	−	0.0471604i	$-0.984983\pi$
$547$	−313.463	+	469.131i	−0.573059	+	0.857644i	0.425828	+	0.904804i	$0.359983\pi$
$548$	−252.838	−	252.838i	−0.461384	−	0.461384i
$549$	−340.160	−	1710.10i	−0.619599	−	3.11493i
$550$	161.469	+	241.655i	0.293579	+	0.439373i
$551$	−57.9335	+	291.251i	−0.105142	+	0.528587i
$552$	609.248	−	252.359i	1.10371	−	0.457172i
$553$	−134.957	−	325.815i	−0.244045	−	0.589177i
$554$	477.765	+	95.0333i	0.862391	+	0.171540i
$555$	50.9508	−	34.0443i	0.0918033	−	0.0613410i
$556$	−97.7925	+	19.4521i	−0.175886	+	0.0349858i
$557$	638.055	−	638.055i	1.14552	−	1.14552i	0.158097	−	0.987424i	$-0.449464\pi$
$557$	638.055	−	638.055i	1.14552	−	1.14552i	0.987424	−	0.158097i	$-0.0505359\pi$
$558$	317.050	+	211.846i	0.568189	+	0.379652i
$559$	2.58839	+	1.07215i	0.00463039	+	0.00191797i
$560$		−	0.945768i		−	0.00168887i
$561$		0			0
$562$	384.636			0.684405
$563$	−100.343	+	242.249i	−0.178228	+	0.430282i	−0.987595	−	0.157022i	$-0.949811\pi$
$563$	−100.343	+	242.249i	−0.178228	+	0.430282i	0.809367	+	0.587304i	$0.199811\pi$
$564$	400.423	−	599.276i	0.709970	−	1.06255i
$565$	16.5810	+	16.5810i	0.0293469	+	0.0293469i
$566$	−47.8700	−	240.659i	−0.0845761	−	0.425193i
$567$	476.498	+	713.130i	0.840385	+	1.25773i
$568$	−28.7421	+	144.496i	−0.0506023	+	0.254395i
$569$	−772.154	+	319.837i	−1.35704	+	0.562103i	−0.938243	−	0.345978i	$-0.887547\pi$
$569$	−772.154	+	319.837i	−1.35704	+	0.562103i	−0.418794	+	0.908081i	$0.637547\pi$
$570$	9.17327	+	22.1462i	0.0160934	+	0.0388530i
$571$	114.660	+	22.8074i	0.200806	+	0.0399429i	0.294469	−	0.955661i	$-0.404857\pi$
$571$	114.660	+	22.8074i	0.200806	+	0.0399429i	−0.0936622	+	0.995604i	$0.529857\pi$
$572$	181.930	−	121.562i	0.318059	−	0.212520i
$573$	−458.864	+	91.2737i	−0.800810	+	0.159291i
$574$	32.1542	−	32.1542i	0.0560177	−	0.0560177i
$575$	−313.292	−	209.335i	−0.544856	−	0.364061i
$576$	−700.789	−	290.276i	−1.21665	−	0.503952i
$577$			416.487i			0.721814i	0.932602	+	0.360907i	$0.117533\pi$
$577$			416.487i			0.721814i	−0.932602	+	0.360907i	$0.882467\pi$
$578$		0			0
$579$	301.600			0.520898
$580$	3.55697	−	8.58727i	0.00613270	−	0.0148056i
$581$	−111.620	+	167.051i	−0.192116	+	0.287522i
$582$	−129.656	−	129.656i	−0.222777	−	0.222777i
$583$	138.193	+	694.741i	0.237037	+	1.19167i
$584$	86.8958	+	130.049i	0.148794	+	0.222686i
$585$	−7.76971	+	39.0610i	−0.0132816	+	0.0667709i
$586$	−337.379	+	139.747i	−0.575732	+	0.238476i
$587$	404.626	+	976.853i	0.689312	+	1.66415i	0.746163	+	0.665763i	$0.231894\pi$
$587$	404.626	+	976.853i	0.689312	+	1.66415i	−0.0568517	+	0.998383i	$0.518106\pi$
$588$	467.147	+	92.9212i	0.794467	+	0.158029i
$589$	−208.556	+	139.353i	−0.354085	+	0.236592i
$590$	−17.1266	+	3.40669i	−0.0290281	+	0.00577405i
$591$	−161.576	+	161.576i	−0.273394	+	0.273394i
$592$	−49.1228	−	32.8228i	−0.0829778	−	0.0554440i
$593$	727.272	+	301.246i	1.22643	+	0.508004i	0.899448	−	0.437027i	$-0.143969\pi$
$593$	727.272	+	301.246i	1.22643	+	0.508004i	0.326981	+	0.945031i	$0.393969\pi$
$594$		−	861.370i		−	1.45012i
$595$		0			0
$596$	−299.321			−0.502217
$597$	−228.653	+	552.017i	−0.383003	+	0.924651i
$598$	85.2090	−	127.524i	0.142490	−	0.213251i
$599$	−677.644	−	677.644i	−1.13129	−	1.13129i	−0.989963	−	0.141329i	$-0.954862\pi$
$599$	−677.644	−	677.644i	−1.13129	−	1.13129i	−0.141329	−	0.989963i	$-0.545138\pi$
$600$	212.654	+	1069.09i	0.354424	+	1.78181i
$601$	−215.839	−	323.026i	−0.359133	−	0.537480i	0.607276	−	0.794491i	$-0.292262\pi$
$601$	−215.839	−	323.026i	−0.359133	−	0.537480i	−0.966408	+	0.257011i	$0.917262\pi$
$602$	−0.303755	+	1.52708i	−0.000504577	+	0.00253668i
$603$	1743.10	−	722.018i	2.89072	−	1.19738i
$604$	256.879	+	620.160i	0.425296	+	1.02675i
$605$	4.99608	+	0.993781i	0.00825798	+	0.00164261i
$606$	−630.806	+	421.491i	−1.04093	+	0.695530i
$607$	841.563	−	167.397i	1.38643	−	0.275778i	0.555205	−	0.831714i	$-0.312640\pi$
$607$	841.563	−	167.397i	1.38643	−	0.275778i	0.831225	+	0.555936i	$0.187640\pi$
$608$	399.387	−	399.387i	0.656886	−	0.656886i
$609$	−320.263	−	213.993i	−0.525883	−	0.351384i
$610$	17.9325	+	7.42787i	0.0293975	+	0.0121768i
$611$		−	425.889i		−	0.697036i
$612$		0			0
$613$	−468.221			−0.763819			−0.381909	−	0.924200i	$-0.624733\pi$
$613$	−468.221			−0.763819			−0.381909	+	0.924200i	$0.624733\pi$
$614$	142.570	−	344.195i	0.232199	−	0.560578i
$615$	−6.19032	+	9.26447i	−0.0100656	+	0.0150642i
$616$	218.457	+	218.457i	0.354637	+	0.354637i
$617$	−25.0731	−	126.051i	−0.0406371	−	0.204297i	0.955133	−	0.296178i	$-0.0957121\pi$
$617$	−25.0731	−	126.051i	−0.0406371	−	0.204297i	−0.995770	+	0.0918810i	$0.970712\pi$
$618$	−289.967	−	433.966i	−0.469202	−	0.702210i
$619$	−20.4590	+	102.854i	−0.0330516	+	0.166162i	−0.993786	−	0.111308i	$-0.964496\pi$
$619$	−20.4590	+	102.854i	−0.0330516	+	0.166162i	0.960734	+	0.277470i	$0.0894959\pi$
$620$	7.25335	−	3.00443i	0.0116989	−	0.00484586i
$621$	427.349	+	1031.71i	0.688163	+	1.66137i
$622$	73.4817	+	14.6164i	0.118138	+	0.0234991i
$623$	−177.512	+	118.610i	−0.284931	+	0.190385i
$624$	52.9033	−	10.5231i	0.0847810	−	0.0168640i
$625$	439.629	−	439.629i	0.703406	−	0.703406i
$626$	125.000	+	83.5222i	0.199680	+	0.133422i
$627$	879.472	+	364.289i	1.40267	+	0.581004i
$628$			385.782i			0.614303i
$629$		0			0
$630$	−22.1331			−0.0351320
$631$	−224.517	+	542.031i	−0.355811	+	0.859004i	0.640069	+	0.768318i	$0.278906\pi$
$631$	−224.517	+	542.031i	−0.355811	+	0.859004i	−0.995880	+	0.0906858i	$0.971094\pi$
$632$	−380.734	+	569.808i	−0.602427	+	0.901596i
$633$	−750.432	−	750.432i	−1.18552	−	1.18552i
$634$	32.5832	+	163.807i	0.0513931	+	0.258371i
$635$	2.33695	+	3.49749i	0.00368023	+	0.00550786i
$636$	−203.998	+	1025.56i	−0.320751	+	1.61252i
$637$	260.022	−	107.705i	0.408199	−	0.169081i
$638$	76.3726	+	184.380i	0.119706	+	0.288996i
$639$	−411.095	−	81.7719i	−0.643341	−	0.127968i
$640$	−15.6261	+	10.4410i	−0.0244158	+	0.0163141i
$641$	−633.841	+	126.079i	−0.988831	+	0.196691i	−0.662904	−	0.748704i	$-0.730676\pi$
$641$	−633.841	+	126.079i	−0.988831	+	0.196691i	−0.325927	+	0.945395i	$0.605676\pi$
$642$	−856.003	+	856.003i	−1.33334	+	1.33334i
$643$	413.369	+	276.204i	0.642876	+	0.429556i	0.833813	−	0.552046i	$-0.186153\pi$
$643$	413.369	+	276.204i	0.642876	+	0.429556i	−0.190938	+	0.981602i	$0.561153\pi$
$644$	−145.646	−	60.3287i	−0.226159	−	0.0936782i
$645$		−	0.381513i		−	0.000591494i
$646$		0			0
$647$	−62.0539			−0.0959102			−0.0479551	−	0.998849i	$-0.515270\pi$
$647$	−62.0539			−0.0959102			−0.0479551	+	0.998849i	$0.515270\pi$
$648$	637.807	−	1539.80i	0.984270	−	2.37624i
$649$	−385.264	+	576.588i	−0.593627	+	0.888426i
$650$	179.263	+	179.263i	0.275789	+	0.275789i
$651$	−63.4715	−	319.093i	−0.0974985	−	0.490158i
$652$	−134.571	−	201.400i	−0.206397	−	0.308895i
$653$	−1.83835	+	9.24200i	−0.00281523	+	0.0141531i	−0.982167	−	0.188009i	$-0.939797\pi$
$653$	−1.83835	+	9.24200i	−0.00281523	+	0.0141531i	0.979352	+	0.202162i	$0.0647967\pi$
$654$	−927.793	+	384.305i	−1.41864	+	0.587622i
$655$	−19.5732	−	47.2539i	−0.0298828	−	0.0721434i
$656$	10.5361	+	2.09576i	0.0160611	+	0.00319476i
$657$	−369.991	+	247.220i	−0.563153	+	0.376287i
$658$	232.137	−	46.1749i	0.352792	−	0.0701746i
$659$	248.723	−	248.723i	0.377426	−	0.377426i	−0.492747	−	0.870173i	$-0.664007\pi$
$659$	248.723	−	248.723i	0.377426	−	0.377426i	0.870173	+	0.492747i	$0.164007\pi$
$660$	−24.7742	−	16.5536i	−0.0375366	−	0.0250812i
$661$	−1056.34	−	437.551i	−1.59810	−	0.661953i	−0.606951	−	0.794739i	$-0.707608\pi$
$661$	−1056.34	−	437.551i	−1.59810	−	0.661953i	−0.991145	+	0.132786i	$0.957608\pi$
$662$			30.3246i			0.0458075i
$663$		0			0
$664$	390.417			0.587977
$665$	5.57158	−	13.4510i	0.00837832	−	0.0202271i
$666$	−768.129	+	1149.59i	−1.15335	+	1.72611i
$667$	−182.952	−	182.952i	−0.274290	−	0.274290i
$668$	−115.558	−	580.950i	−0.172991	−	0.869685i
$669$	−599.917	−	897.839i	−0.896737	−	1.34206i
$670$	−4.09752	+	20.5996i	−0.00611571	+	0.0307457i
$671$	712.136	−	294.976i	1.06131	−	0.439607i
$672$	280.359	+	676.846i	0.417201	+	1.00721i
$673$	−62.3785	−	12.4079i	−0.0926872	−	0.0184366i	0.148529	−	0.988908i	$-0.452546\pi$
$673$	−62.3785	−	12.4079i	−0.0926872	−	0.0184366i	−0.241216	+	0.970471i	$0.577546\pi$
$674$	355.885	−	237.795i	0.528019	−	0.352811i
$675$	−1810.41	+	360.113i	−2.68209	+	0.533501i
$676$	−175.298	+	175.298i	−0.259317	+	0.259317i
$677$	248.638	+	166.135i	0.367265	+	0.245398i	0.725484	−	0.688239i	$-0.241616\pi$
$677$	248.638	+	166.135i	0.367265	+	0.245398i	−0.358219	+	0.933637i	$0.616616\pi$
$678$	−686.656	−	284.422i	−1.01277	−	0.419502i
$679$			111.368i			0.164018i
$680$		0			0
$681$	−1989.40			−2.92129
$682$	−64.5090	+	155.739i	−0.0945880	+	0.228356i
$683$	−250.557	+	374.984i	−0.366847	+	0.549025i	−0.968270	−	0.249905i	$-0.919601\pi$
$683$	−250.557	+	374.984i	−0.366847	+	0.549025i	0.601423	+	0.798931i	$0.294601\pi$
$684$	707.334	+	707.334i	1.03411	+	1.03411i
$685$	5.61314	+	28.2191i	0.00819436	+	0.0411958i
$686$	216.613	+	324.184i	0.315762	+	0.472572i
$687$	287.027	−	1442.98i	0.417797	−	2.10041i
$688$	−0.339827	+	0.140761i	−0.000493934	+	0.000204594i
$689$	236.453	+	570.848i	0.343183	+	0.828517i
$690$	−20.4841	−	4.07453i	−0.0296870	−	0.00590512i
$691$	279.537	−	186.781i	0.404539	−	0.270305i	−0.336611	−	0.941644i	$-0.609281\pi$
$691$	279.537	−	186.781i	0.404539	−	0.270305i	0.741150	+	0.671339i	$0.234281\pi$
$692$	800.349	−	159.199i	1.15657	−	0.230057i
$693$	−621.513	+	621.513i	−0.896844	+	0.896844i
$694$	19.7126	+	13.1715i	0.0284043	+	0.0189791i
$695$	7.41240	+	3.07031i	0.0106653	+	0.00441772i
$696$			748.491i			1.07542i
$697$		0			0
$698$	−407.495			−0.583804
$699$	88.5745	−	213.838i	0.126716	−	0.305920i
$700$	144.771	−	216.666i	0.206816	−	0.309523i
$701$	593.627	+	593.627i	0.846828	+	0.846828i	0.989736	−	0.142908i	$-0.0456453\pi$
$701$	593.627	+	593.627i	0.846828	+	0.846828i	−0.142908	+	0.989736i	$0.545645\pi$
$702$	−146.583	−	736.920i	−0.208807	−	1.04974i
$703$	−505.278	−	756.202i	−0.718745	−	1.07568i
$704$	65.4196	−	328.887i	0.0929256	−	0.467168i
$705$	−53.5806	+	22.1938i	−0.0760008	+	0.0314806i
$706$	−24.1996	−	58.4231i	−0.0342771	−	0.0827522i
$707$	451.937	+	89.8959i	0.639232	+	0.127151i
$708$	−851.150	+	568.720i	−1.20219	+	0.803277i
$709$	−644.968	+	128.292i	−0.909686	+	0.180948i	−0.627686	−	0.778466i	$-0.715998\pi$
$709$	−644.968	+	128.292i	−0.909686	+	0.180948i	−0.282000	+	0.959414i	$0.590998\pi$
$710$	3.29937	−	3.29937i	0.00464700	−	0.00464700i
$711$	−1621.12	−	1083.20i	−2.28005	−	1.52348i
$712$	383.287	+	158.762i	0.538324	+	0.222981i
$713$		−	218.542i		−	0.306510i
$714$		0			0
$715$	−17.6064			−0.0246243
$716$	251.012	−	605.996i	0.350575	−	0.846364i
$717$	794.548	−	1189.12i	1.10816	−	1.65847i
$718$	−4.92012	−	4.92012i	−0.00685253	−	0.00685253i
$719$	21.1301	+	106.228i	0.0293882	+	0.147744i	0.992693	−	0.120664i	$-0.0385023\pi$
$719$	21.1301	+	106.228i	0.0293882	+	0.147744i	−0.963305	+	0.268408i	$0.913502\pi$
$720$	−2.90493	−	4.34754i	−0.00403463	−	0.00603825i
$721$	−61.8442	+	310.912i	−0.0857756	+	0.431223i
$722$	−66.4629	+	27.5298i	−0.0920539	+	0.0381300i
$723$	−182.514	−	440.628i	−0.252440	−	0.609444i
$724$	279.527	+	55.6015i	0.386088	+	0.0767976i
$725$	355.596	−	237.602i	0.490478	−	0.327727i
$726$	−158.353	+	31.4984i	−0.218117	+	0.0433863i
$727$	−882.782	+	882.782i	−1.21428	+	1.21428i	−0.244676	+	0.969605i	$0.578682\pi$
$727$	−882.782	+	882.782i	−1.21428	+	1.21428i	−0.969605	+	0.244676i	$0.921318\pi$
$728$	224.070	+	149.718i	0.307788	+	0.205657i
$729$	943.633	+	390.866i	1.29442	+	0.536167i
$730$		−	4.95362i		−	0.00678578i
$731$		0			0
$732$	1137.86			1.55445
$733$	−374.956	+	905.225i	−0.511537	+	1.23496i	0.431453	+	0.902136i	$0.358001\pi$
$733$	−374.956	+	905.225i	−0.511537	+	1.23496i	−0.942989	+	0.332823i	$0.891999\pi$
$734$	−29.4323	+	44.0486i	−0.0400985	+	0.0600117i
$735$	−27.1004	−	27.1004i	−0.0368713	−	0.0368713i
$736$	96.0068	+	482.659i	0.130444	+	0.655786i
$737$	463.391	+	693.513i	0.628752	+	0.940995i
$738$	49.0456	−	246.569i	0.0664575	−	0.334104i
$739$	−430.693	+	178.399i	−0.582806	+	0.241406i	−0.654552	−	0.756017i	$-0.727143\pi$
$739$	−430.693	+	178.399i	−0.582806	+	0.241406i	0.0717465	+	0.997423i	$0.477143\pi$
$740$	10.8937	+	26.2998i	0.0147213	+	0.0355403i
$741$	814.399	+	161.994i	1.09905	+	0.218615i
$742$	−285.513	+	190.773i	−0.384788	+	0.257107i
$743$	−1043.18	+	207.502i	−1.40401	+	0.279275i	−0.838247	−	0.545291i	$-0.816419\pi$
$743$	−1043.18	+	207.502i	−1.40401	+	0.279275i	−0.565765	+	0.824566i	$0.691419\pi$
$744$	−447.049	+	447.049i	−0.600872	+	0.600872i
$745$	20.0261	+	13.3810i	0.0268806	+	0.0179611i
$746$	534.978	+	221.595i	0.717128	+	0.297044i
$747$			1110.74i			1.48694i
$748$		0			0
$749$	735.267			0.981665
$750$	26.4454	−	63.8449i	0.0352606	−	0.0851265i
$751$	318.527	−	476.709i	0.424137	−	0.634766i	−0.556443	−	0.830886i	$-0.687834\pi$
$751$	318.527	−	476.709i	0.424137	−	0.634766i	0.980580	+	0.196120i	$0.0628342\pi$
$752$	39.5375	+	39.5375i	0.0525765	+	0.0525765i
$753$	301.572	+	1516.11i	0.400494	+	2.01342i
$754$	96.7149	+	144.744i	0.128269	+	0.191968i
$755$	10.5375	−	52.9754i	0.0139569	−	0.0701661i
$756$	−713.510	+	295.545i	−0.943796	+	0.390933i
$757$	−199.233	−	480.991i	−0.263188	−	0.635391i	0.735945	−	0.677042i	$-0.236738\pi$
$757$	−199.233	−	480.991i	−0.263188	−	0.635391i	−0.999132	+	0.0416507i	$0.986738\pi$
$758$	364.429	+	72.4894i	0.480777	+	0.0956325i
$759$	−689.622	+	460.790i	−0.908592	+	0.607102i
$760$	−27.7485	+	5.51952i	−0.0365112	+	0.00726253i
$761$	577.095	−	577.095i	0.758338	−	0.758338i	−0.217682	−	0.976020i	$-0.569850\pi$
$761$	577.095	−	577.095i	0.758338	−	0.758338i	0.976020	+	0.217682i	$0.0698496\pi$
$762$	−110.855	−	74.0708i	−0.145479	−	0.0972058i
$763$	563.515	+	233.416i	0.738552	+	0.305918i
$764$		−	217.341i		−	0.284478i
$765$		0			0
$766$	−236.469			−0.308707
$767$	−231.481	+	558.845i	−0.301801	+	0.728611i
$768$	754.637	−	1129.39i	0.982601	−	1.47057i
$769$	21.1831	+	21.1831i	0.0275462	+	0.0275462i	0.720746	−	0.693200i	$-0.243800\pi$
$769$	21.1831	+	21.1831i	0.0275462	+	0.0275462i	−0.693200	+	0.720746i	$0.743800\pi$
$770$	−1.90888	−	9.59659i	−0.00247906	−	0.0124631i
$771$	552.682	+	827.148i	0.716838	+	1.07282i
$772$	−27.3338	+	137.416i	−0.0354065	+	0.178000i
$773$	768.053	−	318.138i	0.993601	−	0.411563i	0.174154	−	0.984718i	$-0.444281\pi$
$773$	768.053	−	318.138i	0.993601	−	0.411563i	0.819447	+	0.573155i	$0.194281\pi$
$774$	3.29412	+	7.95272i	0.00425597	+	0.0102748i
$775$	354.297	+	70.4741i	0.457158	+	0.0909343i
$776$	179.943	−	120.234i	0.231886	−	0.154941i
$777$	1156.99	−	230.141i	1.48905	−	0.296191i
$778$	302.667	−	302.667i	0.389032	−	0.389032i
$779$	137.501	+	91.8755i	0.176510	+	0.117940i
$780$	−24.0118	−	9.94602i	−0.0307844	−	0.0127513i
$781$		−	185.297i		−	0.237256i
$782$		0			0
$783$	−1267.51			−1.61879
$784$	−14.1404	+	34.1380i	−0.0180363	+	0.0435434i
$785$	17.2462	−	25.8107i	0.0219697	−	0.0328799i
$786$	1146.32	+	1146.32i	1.45842	+	1.45842i
$787$	−111.383	−	559.962i	−0.141529	−	0.711515i	−0.984754	−	0.173954i	$-0.944346\pi$
$787$	−111.383	−	559.962i	−0.141529	−	0.711515i	0.843225	−	0.537561i	$-0.180654\pi$
$788$	−58.9744	−	88.2615i	−0.0748406	−	0.112007i
$789$	322.260	−	1620.11i	0.408440	−	2.05337i
$790$	20.0521	−	8.30587i	0.0253825	−	0.0105138i
$791$	172.750	+	417.056i	0.218395	+	0.527251i
$792$	1675.20	+	333.218i	2.11515	+	0.420729i
$793$	559.049	−	373.545i	0.704980	−	0.471053i
$794$	473.280	−	94.1412i	0.596071	−	0.118566i
$795$	59.4957	−	59.4957i	0.0748374	−	0.0748374i
$796$	−230.789	−	154.209i	−0.289936	−	0.193729i
$797$	428.854	+	177.637i	0.538086	+	0.222882i	0.635140	−	0.772397i	$-0.280942\pi$
$797$	428.854	+	177.637i	0.538086	+	0.222882i	−0.0970548	+	0.995279i	$0.530942\pi$
$798$			461.463i			0.578274i
$799$		0			0
$800$	−813.440			−1.01680
$801$	−451.682	+	1090.46i	−0.563898	+	1.36137i
$802$	226.140	−	338.442i	0.281970	−	0.421997i
$803$	−139.101	−	139.101i	−0.173227	−	0.173227i
$804$	240.206	+	1207.60i	0.298764	+	1.50199i
$805$	7.04751	+	10.5473i	0.00875466	+	0.0131023i
$806$	−28.6862	+	144.215i	−0.0355908	+	0.178927i
$807$	−2378.52	+	985.215i	−2.94736	+	1.22084i
$808$	−342.666	−	827.268i	−0.424091	−	1.02385i
$809$	838.395	+	166.767i	1.03634	+	0.206140i	0.683808	−	0.729662i	$-0.260322\pi$
$809$	838.395	+	166.767i	1.03634	+	0.206140i	0.352527	+	0.935802i	$0.385322\pi$
$810$	−43.8893	+	29.3259i	−0.0541843	+	0.0362048i
$811$	−8.64965	+	1.72052i	−0.0106654	+	0.00212148i	−0.200420	−	0.979710i	$-0.564231\pi$
$811$	−8.64965	+	1.72052i	−0.0106654	+	0.00212148i	0.189755	+	0.981832i	$0.439231\pi$
$812$	126.525	−	126.525i	0.155819	−	0.155819i
$813$	−227.696	−	152.142i	−0.280069	−	0.187136i
$814$	−564.691	−	233.903i	−0.693723	−	0.287350i
$815$			19.4906i			0.0239148i
$816$		0			0
$817$	−5.66234			−0.00693065
$818$	245.657	−	593.069i	0.300315	−	0.725024i
$819$	−425.952	+	637.482i	−0.520088	+	0.778367i
$820$	−3.66009	−	3.66009i	−0.00446353	−	0.00446353i
$821$	−179.610	−	902.963i	−0.218770	−	1.09983i	−0.921501	−	0.388376i	$-0.873036\pi$
$821$	−179.610	−	902.963i	−0.218770	−	1.09983i	0.702730	−	0.711456i	$-0.251964\pi$
$822$	−506.648	−	758.253i	−0.616361	−	0.922449i
$823$	285.118	−	1433.39i	0.346438	−	1.74166i	−0.277996	−	0.960582i	$-0.589670\pi$
$823$	285.118	−	1433.39i	0.346438	−	1.74166i	0.624434	−	0.781078i	$-0.285330\pi$
$824$	569.123	−	235.738i	0.690683	−	0.286090i
$825$	−524.643	−	1266.60i	−0.635930	−	1.53527i
$826$	−329.703	−	65.5821i	−0.399157	−	0.0793972i
$827$	56.8333	−	37.9748i	0.0687223	−	0.0459188i	−0.520734	−	0.853719i	$-0.674342\pi$
$827$	56.8333	−	37.9748i	0.0687223	−	0.0459188i	0.589457	+	0.807800i	$0.299342\pi$
$828$	−854.812	+	170.033i	−1.03238	+	0.205354i
$829$	−932.147	+	932.147i	−1.12442	+	1.12442i	−0.133354	+	0.991068i	$0.542575\pi$
$829$	−932.147	+	932.147i	−1.12442	+	1.12442i	−0.991068	+	0.133354i	$0.957425\pi$
$830$	−10.2811	−	6.86958i	−0.0123868	−	0.00827660i
$831$	−2122.90	−	879.335i	−2.55464	−	1.05816i
$832$		−	292.502i		−	0.351565i
$833$		0			0
$834$	−254.297			−0.304912
$835$	−18.2396	+	44.0344i	−0.0218439	+	0.0527358i
$836$	−245.685	+	367.693i	−0.293881	+	0.439825i
$837$	−757.041	−	757.041i	−0.904470	−	0.904470i
$838$	−27.3241	−	137.368i	−0.0326063	−	0.163923i
$839$	619.586	+	927.277i	0.738482	+	1.10522i	0.990503	+	0.137495i	$0.0439050\pi$
$839$	619.586	+	927.277i	0.738482	+	1.10522i	−0.252021	+	0.967722i	$0.581095\pi$
$840$	7.15925	−	35.9920i	0.00852292	−	0.0428476i
$841$	−505.667	+	209.454i	−0.601269	+	0.249054i
$842$	74.0861	+	178.860i	0.0879883	+	0.212423i
$843$	−1779.50	−	353.964i	−2.11091	−	0.419887i
$844$	409.926	−	273.904i	0.485694	−	0.324530i
$845$	19.5650	−	3.89171i	0.0231538	−	0.00460558i
$846$	925.268	−	925.268i	1.09370	−	1.09370i
$847$	81.5369	+	54.4812i	0.0962655	+	0.0643225i
$848$	−74.9460	−	31.0437i	−0.0883797	−	0.0366081i
$849$			1157.45i			1.36331i
$850$		0			0
$851$	792.408			0.931149
$852$	104.676	−	252.711i	0.122859	−	0.296609i
$853$	−655.402	+	980.879i	−0.768350	+	1.14992i	0.216462	+	0.976291i	$0.430548\pi$
$853$	−655.402	+	980.879i	−0.768350	+	1.14992i	−0.984812	+	0.173625i	$0.944452\pi$
$854$	264.218	+	264.218i	0.309389	+	0.309389i
$855$	−15.7032	−	78.9451i	−0.0183663	−	0.0923334i
$856$	−793.800	−	1188.01i	−0.927336	−	1.38786i
$857$	−234.016	+	1176.48i	−0.273064	+	1.37278i	0.564044	+	0.825745i	$0.309245\pi$
$857$	−234.016	+	1176.48i	−0.273064	+	1.37278i	−0.837107	+	0.547039i	$0.815755\pi$
$858$	515.564	−	213.554i	0.600891	−	0.248897i
$859$	249.671	+	602.760i	0.290653	+	0.701699i	0.999995	−	0.00316564i	$-0.00100766\pi$
$859$	249.671	+	602.760i	0.290653	+	0.701699i	−0.709342	+	0.704865i	$0.751008\pi$
$860$	0.173827	+	0.0345763i	0.000202124	+	4.02050e-5i
$861$	−178.350	+	119.170i	−0.207143	+	0.138408i
$862$	94.6203	−	18.8211i	0.109768	−	0.0218343i
$863$	277.083	−	277.083i	0.321070	−	0.321070i	−0.528108	−	0.849177i	$-0.677098\pi$
$863$	277.083	−	277.083i	0.321070	−	0.321070i	0.849177	+	0.528108i	$0.177098\pi$
$864$	2004.53	+	1339.38i	2.32006	+	1.55021i
$865$	−60.6642	−	25.1279i	−0.0701320	−	0.0290496i
$866$		−	405.121i		−	0.467807i
$867$		0			0
$868$	151.139			0.174123
$869$	329.843	−	796.312i	0.379566	−	0.916354i
$870$	13.1701	−	19.7104i	0.0151380	−	0.0226557i
$871$	514.458	+	514.458i	0.590652	+	0.590652i
$872$	−231.235	−	1162.50i	−0.265177	−	1.33314i
$873$	342.069	+	511.942i	0.391831	+	0.586417i
$874$	−60.4733	+	304.020i	−0.0691915	+	0.347849i
$875$	−38.7776	+	16.0622i	−0.0443172	+	0.0183568i
$876$	−111.128	−	268.288i	−0.126859	−	0.306264i
$877$	−675.329	−	134.331i	−0.770044	−	0.153171i	−0.205593	−	0.978638i	$-0.565912\pi$
$877$	−675.329	−	134.331i	−0.770044	−	0.153171i	−0.564451	+	0.825466i	$0.690912\pi$
$878$	−338.454	+	226.148i	−0.385483	+	0.257571i
$879$	1689.47	−	336.057i	1.92204	−	0.382317i
$880$	1.63449	−	1.63449i	0.00185737	−	0.00185737i
$881$	−924.123	−	617.479i	−1.04895	−	0.700884i	−0.0933722	−	0.995631i	$-0.529765\pi$
$881$	−924.123	−	617.479i	−1.04895	−	0.700884i	−0.955575	+	0.294747i	$0.904765\pi$
$882$	798.908	+	330.918i	0.905791	+	0.375191i
$883$		−	248.129i		−	0.281007i	−0.990080	−	0.140503i	$-0.955128\pi$
$883$		−	248.129i		−	0.281007i	0.990080	−	0.140503i	$-0.0448721\pi$
$884$		0			0
$885$	82.3704			0.0930739
$886$	−68.0623	+	164.317i	−0.0768198	+	0.185459i
$887$	704.408	−	1054.22i	0.794147	−	1.18852i	−0.184471	−	0.982838i	$-0.559057\pi$
$887$	704.408	−	1054.22i	0.794147	−	1.18852i	0.978618	−	0.205686i	$-0.0659427\pi$
$888$	−1620.95	−	1620.95i	−1.82539	−	1.82539i
$889$	15.7979	+	79.4212i	0.0177704	+	0.0893377i
$890$	−7.29979	−	10.9249i	−0.00820201	−	0.0122752i
$891$	−408.950	+	2055.93i	−0.458979	+	2.30744i
$892$	463.447	−	191.966i	0.519559	−	0.215209i
$893$	329.396	+	795.232i	0.368864	+	0.890517i
$894$	−748.723	−	148.930i	−0.837498	−	0.166589i
$895$	−43.8847	+	29.3228i	−0.0490331	+	0.0327629i
$896$	−354.839	+	70.5818i	−0.396025	+	0.0787744i
$897$	−511.571	+	511.571i	−0.570313	+	0.570313i
$898$	−750.721	−	501.616i	−0.835993	−	0.558592i
$899$	229.170	+	94.9253i	0.254917	+	0.105590i
$900$		−	1440.64i		−	1.60071i
$901$		0			0
$902$	111.139			0.123213
$903$	2.81062	−	6.78543i	0.00311254	−	0.00751432i
$904$	487.354	−	729.377i	0.539108	−	0.806833i
$905$	−16.2161	−	16.2161i	−0.0179184	−	0.0179184i
$906$	333.990	+	1679.08i	0.368643	+	1.85329i
$907$	−699.535	−	1046.93i	−0.771262	−	1.15427i	−0.984174	−	0.177204i	$-0.943295\pi$
$907$	−699.535	−	1046.93i	−0.771262	−	1.15427i	0.212912	−	0.977071i	$-0.431705\pi$
$908$	180.298	−	906.417i	0.198566	−	0.998257i
$909$	2353.59	−	974.891i	2.58921	−	1.07249i
$910$	−3.26617	−	7.88524i	−0.00358920	−	0.00866509i
$911$	−1259.37	−	250.504i	−1.38240	−	0.274977i	−0.552792	−	0.833319i	$-0.686438\pi$
$911$	−1259.37	−	250.504i	−1.38240	−	0.274977i	−0.829611	+	0.558342i	$0.811438\pi$
$912$	−90.6436	+	60.5661i	−0.0993900	+	0.0664102i
$913$	−481.601	+	95.7965i	−0.527493	+	0.104925i
$914$	−68.0336	+	68.0336i	−0.0744351	+	0.0744351i
$915$	−76.1282	−	50.8673i	−0.0832002	−	0.0555926i
$916$	631.443	+	261.552i	0.689349	+	0.285538i
$917$		−	984.635i		−	1.07376i
$918$		0			0
$919$	1532.68			1.66777			0.833886	−	0.551937i	$-0.186111\pi$
$919$	1532.68			1.66777			0.833886	+	0.551937i	$0.186111\pi$
$920$	9.43329	−	22.7740i	0.0102536	−	0.0247543i
$921$	−976.343	+	1461.20i	−1.06009	+	1.58654i
$922$	−399.646	−	399.646i	−0.433455	−	0.433455i
$923$	−31.5326	−	158.525i	−0.0341632	−	0.171750i
$924$	−318.672	−	476.927i	−0.344884	−	0.516155i
$925$	−255.531	+	1284.64i	−0.276250	+	1.38880i
$926$	482.114	−	199.698i	0.520641	−	0.215657i
$927$	670.680	+	1619.17i	0.723495	+	1.74667i
$928$	−547.833	−	108.971i	−0.590337	−	0.117425i
$929$	−1365.77	+	912.576i	−1.47015	+	0.982321i	−0.475421	+	0.879758i	$0.657704\pi$
$929$	−1365.77	+	912.576i	−1.47015	+	0.982321i	−0.994727	+	0.102563i	$0.967296\pi$
$930$	19.6384	−	3.90633i	0.0211166	−	0.00420035i
$931$	−402.219	+	402.219i	−0.432029	+	0.432029i
$932$	89.4022	+	59.7366i	0.0959251	+	0.0640951i
$933$	−326.509	−	135.244i	−0.349956	−	0.144956i
$934$			680.262i			0.728332i
$935$		0			0
$936$	1489.87			1.59174
$937$	488.648	−	1179.70i	0.521502	−	1.25902i	−0.415468	−	0.909608i	$-0.636382\pi$
$937$	488.648	−	1179.70i	0.521502	−	1.25902i	0.936970	−	0.349410i	$-0.113618\pi$
$938$	−224.635	+	336.190i	−0.239483	+	0.358411i
$939$	−501.444	−	501.444i	−0.534019	−	0.534019i
$940$	−5.25606	−	26.4240i	−0.00559155	−	0.0281106i
$941$	940.410	+	1407.42i	0.999373	+	1.49567i	0.863123	+	0.504994i	$0.168505\pi$
$941$	940.410	+	1407.42i	0.999373	+	1.49567i	0.136250	+	0.990674i	$0.456495\pi$
$942$	−191.950	+	964.997i	−0.203768	+	1.02441i
$943$	−133.117	+	55.1389i	−0.141163	+	0.0584718i
$944$	−30.3909	−	73.3701i	−0.0321937	−	0.0777225i
$945$	60.9495	+	12.1236i	0.0644969	+	0.0128292i
$946$	−3.16407	+	2.11417i	−0.00334469	+	0.00223485i
$947$	−759.725	+	151.119i	−0.802244	+	0.159576i	−0.579150	−	0.815221i	$-0.696616\pi$
$947$	−759.725	+	151.119i	−0.802244	+	0.159576i	−0.223093	+	0.974797i	$0.571616\pi$
$948$	899.690	−	899.690i	0.949040	−	0.949040i
$949$	−142.675	−	95.3324i	−0.150343	−	0.100456i
$950$	−473.373	−	196.077i	−0.498287	−	0.206397i
$951$		−	787.831i		−	0.828423i
$952$		0			0
$953$	−103.362			−0.108460			−0.0542299	−	0.998528i	$-0.517270\pi$
$953$	−103.362			−0.108460			−0.0542299	+	0.998528i	$0.517270\pi$
$954$	−726.492	+	1753.91i	−0.761522	+	1.83848i
$955$	−9.71613	+	14.5412i	−0.0101740	+	0.0152264i
$956$	469.784	+	469.784i	0.491406	+	0.491406i
$957$	−183.657	−	923.307i	−0.191909	−	0.964793i
$958$	121.466	+	181.787i	0.126791	+	0.189757i
$959$	−108.058	+	543.246i	−0.112678	+	0.566471i
$960$	−36.7993	+	15.2428i	−0.0383326	+	0.0158779i
$961$	−287.579	−	694.277i	−0.299250	−	0.722453i
$962$	−522.908	−	104.013i	−0.543564	−	0.108122i
$963$	3379.90	−	2258.38i	3.50976	−	2.34515i
$964$	217.302	−	43.2240i	0.225417	−	0.0448382i
$965$	7.97188	−	7.97188i	0.00826102	−	0.00826102i
$966$	−334.303	−	223.374i	−0.346070	−	0.231236i
$967$	−545.336	−	225.886i	−0.563946	−	0.233594i	0.0824511	−	0.996595i	$-0.473725\pi$
$967$	−545.336	−	225.886i	−0.563946	−	0.233594i	−0.646397	+	0.763001i	$0.723725\pi$
$968$		−	190.561i		−	0.196861i
$969$		0			0
$970$	−6.85412			−0.00706611
$971$	299.758	−	723.680i	0.308711	−	0.745293i	−0.691037	−	0.722820i	$-0.742846\pi$
$971$	299.758	−	723.680i	0.308711	−	0.745293i	0.999747	−	0.0224739i	$-0.00715426\pi$
$972$	−758.971	+	1135.88i	−0.780834	+	1.16860i
$973$	109.215	+	109.215i	0.112245	+	0.112245i
$974$	−104.610	−	525.909i	−0.107402	−	0.539948i
$975$	−664.384	−	994.321i	−0.681420	−	1.01982i
$976$	−17.2214	+	86.5776i	−0.0176448	+	0.0887065i
$977$	922.512	−	382.117i	0.944229	−	0.391113i	0.143170	−	0.989698i	$-0.454270\pi$
$977$	922.512	−	382.117i	0.944229	−	0.391113i	0.801059	+	0.598586i	$0.204270\pi$
$978$	−236.408	−	570.739i	−0.241726	−	0.583578i
$979$	−511.761	−	101.796i	−0.522739	−	0.103979i
$980$	14.8037	−	9.89151i	0.0151058	−	0.0100934i
$981$	3307.32	−	657.868i	3.37138	−	0.670609i
$982$	−366.759	+	366.759i	−0.373481	+	0.373481i
$983$	1527.13	+	1020.39i	1.55354	+	1.03804i	0.974951	+	0.222421i	$0.0713960\pi$
$983$	1527.13	+	1020.39i	1.55354	+	1.03804i	0.578588	+	0.815620i	$0.303604\pi$
$984$	385.096	+	159.512i	0.391358	+	0.162106i
$985$			8.54155i			0.00867162i
$986$		0			0
$987$	−1116.46			−1.13117
$988$	−147.617	+	356.378i	−0.149410	+	0.360707i
$989$	2.74090	−	4.10204i	0.00277138	−	0.00414767i
$990$	−38.2508	−	38.2508i	−0.0386371	−	0.0386371i
$991$	−43.7286	−	219.839i	−0.0441257	−	0.221835i	0.952430	−	0.304756i	$-0.0985750\pi$
$991$	−43.7286	−	219.839i	−0.0441257	−	0.221835i	−0.996556	+	0.0829212i	$0.973575\pi$
$992$	−262.118	−	392.287i	−0.264231	−	0.395450i
$993$	27.9065	−	140.295i	0.0281032	−	0.141284i
$994$	82.9877	−	34.3746i	0.0834886	−	0.0345821i
$995$	8.54714	+	20.6346i	0.00859009	+	0.0207383i
$996$	−710.932	−	141.413i	−0.713787	−	0.141981i
$997$	868.136	−	580.070i	0.870749	−	0.581816i	−0.0379448	−	0.999280i	$-0.512081\pi$
$997$	868.136	−	580.070i	0.870749	−	0.581816i	0.908693	+	0.417464i	$0.137081\pi$
$998$	−789.313	+	157.004i	−0.790895	+	0.157319i
$999$	2744.95	−	2744.95i	2.74769	−	2.74769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.q.75.4	yes	48
17.2	even	8	inner	289.3.e.q.249.3	yes	48
17.3	odd	16	inner	289.3.e.q.131.4	yes	48
17.4	even	4	inner	289.3.e.q.214.3	yes	48
17.5	odd	16	inner	289.3.e.q.158.4	yes	48
17.6	odd	16	inner	289.3.e.q.65.4	yes	48
17.7	odd	16	inner	289.3.e.q.224.3	yes	48
17.8	even	8	inner	289.3.e.q.40.3	✓	48
17.9	even	8	inner	289.3.e.q.40.4	yes	48
17.10	odd	16	inner	289.3.e.q.224.4	yes	48
17.11	odd	16	inner	289.3.e.q.65.3	yes	48
17.12	odd	16	inner	289.3.e.q.158.3	yes	48
17.13	even	4	inner	289.3.e.q.214.4	yes	48
17.14	odd	16	inner	289.3.e.q.131.3	yes	48
17.15	even	8	inner	289.3.e.q.249.4	yes	48
17.16	even	2	inner	289.3.e.q.75.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.3.e.q.40.3	✓	48	17.8	even	8	inner
289.3.e.q.40.4	yes	48	17.9	even	8	inner
289.3.e.q.65.3	yes	48	17.11	odd	16	inner
289.3.e.q.65.4	yes	48	17.6	odd	16	inner
289.3.e.q.75.3	yes	48	17.16	even	2	inner
289.3.e.q.75.4	yes	48	1.1	even	1	trivial
289.3.e.q.131.3	yes	48	17.14	odd	16	inner
289.3.e.q.131.4	yes	48	17.3	odd	16	inner
289.3.e.q.158.3	yes	48	17.12	odd	16	inner
289.3.e.q.158.4	yes	48	17.5	odd	16	inner
289.3.e.q.214.3	yes	48	17.4	even	4	inner
289.3.e.q.214.4	yes	48	17.13	even	4	inner
289.3.e.q.224.3	yes	48	17.7	odd	16	inner
289.3.e.q.224.4	yes	48	17.10	odd	16	inner
289.3.e.q.249.3	yes	48	17.2	even	8	inner
289.3.e.q.249.4	yes	48	17.15	even	8	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453400 + 1.09461i) q^{2} +(3.10496 - 4.64690i) q^{3} +(1.83584 + 1.83584i) q^{4} +(-0.0407565 - 0.204897i) q^{5} +(3.67873 + 5.50561i) q^{6} +(0.784602 - 3.94446i) q^{7} +(-7.22031 + 2.99075i) q^{8} +(-8.50875 - 20.5419i) q^{9} +O(q^{10})\)	\(q+(-0.453400 + 1.09461i) q^{2} +(3.10496 - 4.64690i) q^{3} +(1.83584 + 1.83584i) q^{4} +(-0.0407565 - 0.204897i) q^{5} +(3.67873 + 5.50561i) q^{6} +(0.784602 - 3.94446i) q^{7} +(-7.22031 + 2.99075i) q^{8} +(-8.50875 - 20.5419i) q^{9} +(0.242760 + 0.0482880i) q^{10} +(8.17283 - 5.46091i) q^{11} +(14.2311 - 2.83075i) q^{12} +(6.06272 - 6.06272i) q^{13} +(3.96189 + 2.64725i) q^{14} +(-1.07868 - 0.446804i) q^{15} +1.12567i q^{16} +26.3432 q^{18} +(-6.63138 + 16.0096i) q^{19} +(0.301335 - 0.450979i) q^{20} +(-15.8933 - 15.8933i) q^{21} +(2.27198 + 11.4220i) q^{22} +(-8.38804 - 12.5536i) q^{23} +(-8.52105 + 42.8382i) q^{24} +(23.0567 - 9.55038i) q^{25} +(3.88745 + 9.38512i) q^{26} +(-72.5430 - 14.4297i) q^{27} +(8.68179 - 5.80099i) q^{28} +(16.8075 - 3.34322i) q^{29} +(0.978149 - 0.978149i) q^{30} +(12.0354 + 8.04177i) q^{31} +(-30.1134 - 12.4734i) q^{32} -54.9342i q^{33} -0.840185 q^{35} +(22.0910 - 53.3323i) q^{36} +(-29.1586 + 43.6389i) q^{37} +(-14.5175 - 14.5175i) q^{38} +(-9.34835 - 46.9973i) q^{39} +(0.907069 + 1.35753i) q^{40} +(1.86180 - 9.35988i) q^{41} +(24.6030 - 10.1909i) q^{42} +(0.125047 + 0.301889i) q^{43} +(25.0293 + 4.97864i) q^{44} +(-3.86219 + 2.58063i) q^{45} +(17.5444 - 3.48979i) q^{46} +(35.1236 - 35.1236i) q^{47} +(5.23086 + 3.49515i) q^{48} +(30.3269 + 12.5618i) q^{49} +29.5681i q^{50} +22.2603 q^{52} +(-27.5780 + 66.5792i) q^{53} +(48.6859 - 72.8636i) q^{54} +(-1.45202 - 1.45202i) q^{55} +(6.13183 + 30.8268i) q^{56} +(53.8047 + 80.5244i) q^{57} +(-3.96103 + 19.9134i) q^{58} +(-65.1792 + 26.9981i) q^{59} +(-1.16002 - 2.80054i) q^{60} +(76.9122 + 15.2988i) q^{61} +(-14.2594 + 9.52783i) q^{62} +(-87.7028 + 17.4452i) q^{63} +(24.1230 - 24.1230i) q^{64} +(-1.48933 - 0.995136i) q^{65} +(60.1313 + 24.9072i) q^{66} +84.8560i q^{67} -84.3798 q^{69} +(0.380940 - 0.919671i) q^{70} +(10.4732 - 15.6743i) q^{71} +(122.872 + 122.872i) q^{72} +(-3.90441 - 19.6288i) q^{73} +(-34.5468 - 51.7030i) q^{74} +(27.2103 - 136.796i) q^{75} +(-41.5651 + 17.2168i) q^{76} +(-15.1279 - 36.5220i) q^{77} +(55.6821 + 11.0759i) q^{78} +(72.9102 - 48.7170i) q^{79} +(0.230646 - 0.0458782i) q^{80} +(-150.797 + 150.797i) q^{81} +(9.40124 + 6.28171i) q^{82} +(-46.1534 - 19.1173i) q^{83} -58.3552i q^{84} -0.387146 q^{86} +(36.6510 - 88.4834i) q^{87} +(-42.6781 + 63.8723i) q^{88} +(-37.5364 - 37.5364i) q^{89} +(-1.07366 - 5.39763i) q^{90} +(-19.1573 - 28.6710i) q^{91} +(7.64728 - 38.4455i) q^{92} +(74.7386 - 30.9577i) q^{93} +(22.5214 + 54.3716i) q^{94} +(3.55058 + 0.706254i) q^{95} +(-151.463 + 101.205i) q^{96} +(-27.1595 + 5.40237i) q^{97} +(-27.5005 + 27.5005i) q^{98} +(-181.718 - 121.420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 432 q^{18} + 144 q^{35} - 720 q^{52} - 432 q^{69}+O(q^{100}) \) 48 * q + 432 * q^18 + 144 * q^35 - 720 * q^52 - 432 * q^69

Introduction

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