LMFDB - Embedded newform 363.3.h.k.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.23612624896000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 5 x^{14} + 20 x^{13} + 19 x^{12} + 88 x^{11} - 497 x^{10} + 10 x^{9} + 3711 x^{8} + \cdots + 16 $ x^16 - 2x^15 - 5x^14 + 20x^13 + 19x^12 + 88x^11 - 497x^10 + 10x^9 + 3711x^8 - 3712x^7 + 2758x^6 - 1816x^5 + 1084x^4 - 464x^3 + 184x^2 - 64*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			251.3
Root			$-2.75764 + 0.370279i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.k.269.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.51626 + 0.817582i) q^{2} +(-0.853491 - 2.87603i) q^{3} +(2.42705 + 1.76336i) q^{4} +(-2.68999 + 0.874032i) q^{5} +(0.203788 - 7.93464i) q^{6} +(-6.05413 - 4.39858i) q^{7} +(-1.55513 - 2.14046i) q^{8} +(-7.54311 + 4.90933i) q^{9} -7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +(-6.93741 + 21.3512i) q^{13} +(-11.6376 - 16.0177i) q^{14} +(4.80963 + 6.99053i) q^{15} +(-5.87132 - 18.0701i) q^{16} +(-20.1301 + 6.54066i) q^{17} +(-22.9942 + 6.18604i) q^{18} +(12.1083 - 8.79716i) q^{19} +(-8.06998 - 2.62210i) q^{20} +(-7.48331 + 21.1660i) q^{21} -31.1127i q^{23} +(-4.82873 + 6.29947i) q^{24} +(-13.7533 + 9.99235i) q^{25} +(-34.9127 + 48.0532i) q^{26} +(20.5574 + 17.5041i) q^{27} +(-6.93741 - 21.3512i) q^{28} +(12.4411 - 17.1237i) q^{29} +(6.38694 + 21.5222i) q^{30} +(9.27051 - 28.5317i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(20.1301 + 6.54066i) q^{35} +(-26.9644 - 1.38598i) q^{36} +(8.09017 + 5.87785i) q^{37} +(37.6599 - 12.2364i) q^{38} +(67.3276 + 1.72920i) q^{39} +(6.05413 + 4.39858i) q^{40} +(-24.8821 - 34.2473i) q^{41} +(-36.1349 + 47.1409i) q^{42} +14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} +(25.4372 - 78.2876i) q^{46} +(-21.6126 - 29.7472i) q^{47} +(-46.9590 + 32.3087i) q^{48} +(2.16312 + 6.65740i) q^{49} +(-42.7764 + 13.8989i) q^{50} +(35.9920 + 52.3123i) q^{51} +(-54.4872 + 39.5872i) q^{52} +(-40.3499 - 13.1105i) q^{53} +(37.4166 + 60.8523i) q^{54} +19.7990i q^{56} +(-35.6352 - 27.3154i) q^{57} +(45.3050 - 32.9160i) q^{58} +(19.9501 - 27.4589i) q^{59} +(-0.653574 + 25.4475i) q^{60} +(30.0621 + 92.5217i) q^{61} +(46.6540 - 64.2137i) q^{62} +(67.2610 + 3.45725i) q^{63} +(8.96149 - 27.5806i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(-60.3902 - 19.6220i) q^{68} +(-89.4811 + 26.5544i) q^{69} +(45.3050 + 32.9160i) q^{70} +(-61.8699 + 20.1027i) q^{71} +(22.2388 + 8.51104i) q^{72} +(60.5413 + 43.9858i) q^{73} +(15.5513 + 21.4046i) q^{74} +(40.4766 + 31.0265i) q^{75} +44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +(-6.93741 + 21.3512i) q^{79} +(31.5876 + 43.4767i) q^{80} +(32.7969 - 74.0632i) q^{81} +(-34.6099 - 106.518i) q^{82} +(-20.1301 + 6.54066i) q^{83} +(-55.4856 + 38.1752i) q^{84} +(48.4330 - 35.1887i) q^{85} +(37.6599 + 12.2364i) q^{86} +(-59.8665 - 21.1660i) q^{87} -62.2254i q^{89} +(56.4474 - 36.7381i) q^{90} +(135.915 - 98.7479i) q^{91} +(54.8628 - 75.5121i) q^{92} +(-89.9703 - 2.31073i) q^{93} +(-30.0621 - 92.5217i) q^{94} +(-24.8821 + 34.2473i) q^{95} +(-114.139 + 33.8719i) q^{96} +(22.8673 - 70.3782i) q^{97} +18.5203i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 12 q^{4} + 28 q^{9} + 48 q^{12} + 32 q^{15} + 76 q^{16} - 68 q^{25} - 92 q^{27} - 120 q^{31} - 896 q^{34} - 84 q^{36} + 40 q^{37} + 224 q^{42} + 256 q^{45} - 76 q^{48} - 28 q^{49} + 224 q^{58}+ \cdots - 296 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 + 12 * q^4 + 28 * q^9 + 48 * q^12 + 32 * q^15 + 76 * q^16 - 68 * q^25 - 92 * q^27 - 120 * q^31 - 896 * q^34 - 84 * q^36 + 40 * q^37 + 224 * q^42 + 256 * q^45 - 76 * q^48 - 28 * q^49 + 224 * q^58 - 96 * q^60 - 116 * q^64 - 672 * q^67 - 352 * q^69 + 224 * q^70 + 68 * q^75 + 2688 * q^78 - 68 * q^81 + 448 * q^82 + 672 * q^91 + 120 * q^93 - 296 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.51626	+	0.817582i	1.25813	+	0.408791i	0.860828	−	0.508897i	$-0.169947\pi$
$2$	2.51626	+	0.817582i	1.25813	+	0.408791i	0.397302	+	0.917688i	$0.369947\pi$
$3$	−0.853491	−	2.87603i	−0.284497	−	0.958677i
$3$	−0.853491	−	2.87603i	−0.284497	−	0.958677i
$4$	2.42705	+	1.76336i	0.606763	+	0.440839i
$5$	−2.68999	+	0.874032i	−0.537999	+	0.174806i	−0.565398	−	0.824818i	$-0.691277\pi$
$5$	−2.68999	+	0.874032i	−0.537999	+	0.174806i	0.0273993	+	0.999625i	$0.491277\pi$
$6$	0.203788	−	7.93464i	0.0339646	−	1.32244i
$7$	−6.05413	−	4.39858i	−0.864876	−	0.628369i	0.0643314	−	0.997929i	$-0.479509\pi$
$7$	−6.05413	−	4.39858i	−0.864876	−	0.628369i	−0.929207	+	0.369560i	$0.879509\pi$
$8$	−1.55513	−	2.14046i	−0.194392	−	0.267557i
$9$	−7.54311	+	4.90933i	−0.838123	+	0.545481i
$10$	−7.48331			−0.748331
$11$		0			0
$11$		0			0
$12$	3.00000	−	8.48528i	0.250000	−	0.707107i
$13$	−6.93741	+	21.3512i	−0.533647	+	1.64240i	0.212907	+	0.977073i	$0.431707\pi$
$13$	−6.93741	+	21.3512i	−0.533647	+	1.64240i	−0.746554	+	0.665325i	$0.768293\pi$
$14$	−11.6376	−	16.0177i	−0.831254	−	1.14412i
$15$	4.80963	+	6.99053i	0.320642	+	0.466035i
$16$	−5.87132	−	18.0701i	−0.366958	−	1.12938i
$17$	−20.1301	+	6.54066i	−1.18412	+	0.384745i	−0.833896	−	0.551921i	$-0.813895\pi$
$17$	−20.1301	+	6.54066i	−1.18412	+	0.384745i	−0.350225	+	0.936665i	$0.613895\pi$
$18$	−22.9942	+	6.18604i	−1.27746	+	0.343669i
$19$	12.1083	−	8.79716i	0.637277	−	0.463009i	−0.221637	−	0.975129i	$-0.571140\pi$
$19$	12.1083	−	8.79716i	0.637277	−	0.463009i	0.858914	+	0.512121i	$0.171140\pi$
$20$	−8.06998	−	2.62210i	−0.403499	−	0.131105i
$21$	−7.48331	+	21.1660i	−0.356348	+	1.00791i
$22$		0			0
$23$		−	31.1127i		−	1.35273i	−0.736568	−	0.676363i	$-0.763555\pi$
$23$		−	31.1127i		−	1.35273i	0.736568	−	0.676363i	$-0.236445\pi$
$24$	−4.82873	+	6.29947i	−0.201197	+	0.262478i
$25$	−13.7533	+	9.99235i	−0.550132	+	0.399694i
$26$	−34.9127	+	48.0532i	−1.34279	+	1.84820i
$27$	20.5574	+	17.5041i	0.761384	+	0.648301i
$28$	−6.93741	−	21.3512i	−0.247765	−	0.762542i
$29$	12.4411	−	17.1237i	0.429002	−	0.590471i	−0.538722	−	0.842484i	$-0.681093\pi$
$29$	12.4411	−	17.1237i	0.429002	−	0.590471i	0.967724	+	0.252013i	$0.0810925\pi$
$30$	6.38694	+	21.5222i	0.212898	+	0.717408i
$31$	9.27051	−	28.5317i	0.299049	−	0.920377i	−0.682783	−	0.730622i	$-0.739230\pi$
$31$	9.27051	−	28.5317i	0.299049	−	0.920377i	0.981831	−	0.189756i	$-0.0607696\pi$
$32$		−	39.6863i		−	1.24020i
$33$		0			0
$34$	−56.0000			−1.64706
$35$	20.1301	+	6.54066i	0.575145	+	0.186876i
$36$	−26.9644	−	1.38598i	−0.749011	−	0.0384995i
$37$	8.09017	+	5.87785i	0.218653	+	0.158861i	0.691720	−	0.722166i	$-0.256853\pi$
$37$	8.09017	+	5.87785i	0.218653	+	0.158861i	−0.473067	+	0.881026i	$0.656853\pi$
$38$	37.6599	−	12.2364i	0.991050	−	0.322012i
$39$	67.3276	+	1.72920i	1.72635	+	0.0443383i
$40$	6.05413	+	4.39858i	0.151353	+	0.109965i
$41$	−24.8821	−	34.2473i	−0.606881	−	0.835301i	0.389435	−	0.921054i	$-0.372670\pi$
$41$	−24.8821	−	34.2473i	−0.606881	−	0.835301i	−0.996316	+	0.0857534i	$0.972670\pi$
$42$	−36.1349	+	47.1409i	−0.860355	+	1.12240i
$43$	14.9666			0.348061			0.174031	−	0.984740i	$-0.444321\pi$
$43$	14.9666			0.348061			0.174031	+	0.984740i	$0.444321\pi$
$44$		0			0
$45$	16.0000	−	19.7990i	0.355556	−	0.439978i
$46$	25.4372	−	78.2876i	0.552982	−	1.70190i
$47$	−21.6126	−	29.7472i	−0.459843	−	0.632919i	0.514634	−	0.857410i	$-0.327928\pi$
$47$	−21.6126	−	29.7472i	−0.459843	−	0.632919i	−0.974476	+	0.224491i	$0.927928\pi$
$48$	−46.9590	+	32.3087i	−0.978312	+	0.673099i
$49$	2.16312	+	6.65740i	0.0441453	+	0.135865i
$50$	−42.7764	+	13.8989i	−0.855528	+	0.277978i
$51$	35.9920	+	52.3123i	0.705725	+	1.02573i
$52$	−54.4872	+	39.5872i	−1.04783	+	0.761293i
$53$	−40.3499	−	13.1105i	−0.761319	−	0.247368i	−0.0974744	−	0.995238i	$-0.531076\pi$
$53$	−40.3499	−	13.1105i	−0.761319	−	0.247368i	−0.663845	+	0.747870i	$0.731076\pi$
$54$	37.4166	+	60.8523i	0.692900	+	1.12689i
$55$		0			0
$56$			19.7990i			0.353553i
$57$	−35.6352	−	27.3154i	−0.625179	−	0.479218i
$58$	45.3050	−	32.9160i	0.781120	−	0.567517i
$59$	19.9501	−	27.4589i	0.338137	−	0.465406i	−0.605759	−	0.795648i	$-0.707130\pi$
$59$	19.9501	−	27.4589i	0.338137	−	0.465406i	0.943896	+	0.330242i	$0.107130\pi$
$60$	−0.653574	+	25.4475i	−0.0108929	+	0.424124i
$61$	30.0621	+	92.5217i	0.492822	+	1.51675i	0.820324	+	0.571899i	$0.193793\pi$
$61$	30.0621	+	92.5217i	0.492822	+	1.51675i	−0.327502	+	0.944850i	$0.606207\pi$
$62$	46.6540	−	64.2137i	0.752484	−	1.03571i
$63$	67.2610	+	3.45725i	1.06764	+	0.0548770i
$64$	8.96149	−	27.5806i	0.140023	−	0.430947i
$65$		−	63.4980i		−	0.976893i
$66$		0			0
$67$	−42.0000			−0.626866			−0.313433	−	0.949610i	$-0.601479\pi$
$67$	−42.0000			−0.626866			−0.313433	+	0.949610i	$0.601479\pi$
$68$	−60.3902	−	19.6220i	−0.888091	−	0.288558i
$69$	−89.4811	+	26.5544i	−1.29683	+	0.384846i
$70$	45.3050	+	32.9160i	0.647214	+	0.470228i
$71$	−61.8699	+	20.1027i	−0.871407	+	0.283137i	−0.710385	−	0.703814i	$-0.751479\pi$
$71$	−61.8699	+	20.1027i	−0.871407	+	0.283137i	−0.161022	+	0.986951i	$0.551479\pi$
$72$	22.2388	+	8.51104i	0.308872	+	0.118209i
$73$	60.5413	+	43.9858i	0.829333	+	0.602545i	0.919370	−	0.393393i	$-0.128699\pi$
$73$	60.5413	+	43.9858i	0.829333	+	0.602545i	−0.0900377	+	0.995938i	$0.528699\pi$
$74$	15.5513	+	21.4046i	0.210153	+	0.289251i
$75$	40.4766	+	31.0265i	0.539688	+	0.413687i
$76$	44.8999			0.590788
$77$		0			0
$78$	168.000	+	59.3970i	2.15385	+	0.761500i
$79$	−6.93741	+	21.3512i	−0.0878154	+	0.270268i	−0.985315	−	0.170748i	$-0.945382\pi$
$79$	−6.93741	+	21.3512i	−0.0878154	+	0.270268i	0.897499	+	0.441016i	$0.145382\pi$
$80$	31.5876	+	43.4767i	0.394846	+	0.543458i
$81$	32.7969	−	74.0632i	0.404900	−	0.914361i
$82$	−34.6099	−	106.518i	−0.422072	−	1.29900i
$83$	−20.1301	+	6.54066i	−0.242531	+	0.0788031i	−0.427760	−	0.903892i	$-0.640697\pi$
$83$	−20.1301	+	6.54066i	−0.242531	+	0.0788031i	0.185229	+	0.982695i	$0.440697\pi$
$84$	−55.4856	+	38.1752i	−0.660543	+	0.454467i
$85$	48.4330	−	35.1887i	0.569800	−	0.413984i
$86$	37.6599	+	12.2364i	0.437906	+	0.142284i
$87$	−59.8665	−	21.1660i	−0.688121	−	0.243287i
$88$		0			0
$89$		−	62.2254i		−	0.699162i	−0.936906	−	0.349581i	$-0.886324\pi$
$89$		−	62.2254i		−	0.699162i	0.936906	−	0.349581i	$-0.113676\pi$
$90$	56.4474	−	36.7381i	0.627194	−	0.408201i
$91$	135.915	−	98.7479i	1.49357	−	1.08514i
$92$	54.8628	−	75.5121i	0.596334	−	0.820784i
$93$	−89.9703	−	2.31073i	−0.967423	−	0.0248466i
$94$	−30.0621	−	92.5217i	−0.319810	−	0.984274i
$95$	−24.8821	+	34.2473i	−0.261917	+	0.360498i
$96$	−114.139	+	33.8719i	−1.18895	+	0.352832i
$97$	22.8673	−	70.3782i	0.235745	−	0.725548i	−0.761277	−	0.648427i	$-0.775427\pi$
$97$	22.8673	−	70.3782i	0.235745	−	0.725548i	0.997022	−	0.0771212i	$-0.0245728\pi$
$98$			18.5203i			0.188982i
$99$		0			0
$100$	−51.0000			−0.510000
$101$	140.911	+	45.7846i	1.39515	+	0.453313i	0.907620	−	0.419792i	$-0.137897\pi$
$101$	140.911	+	45.7846i	1.39515	+	0.453313i	0.487533	+	0.873105i	$0.337897\pi$
$102$	47.7955	+	161.058i	0.468583	+	1.57900i
$103$	−27.5066	−	19.9847i	−0.267054	−	0.194026i	0.446197	−	0.894935i	$-0.352778\pi$
$103$	−27.5066	−	19.9847i	−0.267054	−	0.194026i	−0.713251	+	0.700909i	$0.752778\pi$
$104$	56.4899	−	18.3547i	0.543172	−	0.176487i
$105$	1.63030	−	63.4771i	0.0155267	−	0.604544i
$106$	−90.8119	−	65.9787i	−0.856716	−	0.622441i
$107$	−24.8821	−	34.2473i	−0.232543	−	0.320068i	0.676759	−	0.736205i	$-0.263384\pi$
$107$	−24.8821	−	34.2473i	−0.232543	−	0.320068i	−0.909302	+	0.416136i	$0.863384\pi$
$108$	19.0277	+	78.7334i	0.176183	+	0.729013i
$109$	−67.3498			−0.617888			−0.308944	−	0.951080i	$-0.599976\pi$
$109$	−67.3498			−0.617888			−0.308944	+	0.951080i	$0.599976\pi$
$110$		0			0
$111$	10.0000	−	28.2843i	0.0900901	−	0.254813i
$112$	−43.9370	+	135.224i	−0.392294	+	1.20736i
$113$	69.8253	+	96.1063i	0.617923	+	0.850498i	0.997200	−	0.0747850i	$-0.0238271\pi$
$113$	69.8253	+	96.1063i	0.617923	+	0.850498i	−0.379276	+	0.925283i	$0.623827\pi$
$114$	−67.3348	−	97.8674i	−0.590656	−	0.858486i
$115$	27.1935	+	83.6930i	0.236465	+	0.727765i
$116$	60.3902	−	19.6220i	0.520605	−	0.169155i
$117$	−52.4903	−	195.112i	−0.448635	−	1.66763i
$118$	72.6495	−	52.7830i	0.615674	−	0.447313i
$119$	150.640	+	48.9458i	1.26588	+	0.411309i
$120$	7.48331	−	21.1660i	0.0623610	−	0.176383i
$121$		0			0
$122$			257.387i			2.10973i
$123$	−77.2597	+	100.792i	−0.628128	+	0.819444i
$124$	72.8115	−	52.9007i	0.587190	−	0.426618i
$125$	69.8253	−	96.1063i	0.558603	−	0.768851i
$126$	166.420	+	63.6908i	1.32079	+	0.505482i
$127$	−20.8122	−	64.0535i	−0.163876	−	0.504358i	0.835076	−	0.550135i	$-0.185424\pi$
$127$	−20.8122	−	64.0535i	−0.163876	−	0.504358i	−0.998952	+	0.0457767i	$0.985424\pi$
$128$	−48.2091	+	66.3542i	−0.376634	+	0.518392i
$129$	−12.7739	−	43.0445i	−0.0990223	−	0.333678i
$130$	51.9149	−	159.777i	0.399345	−	1.22906i
$131$			232.826i			1.77730i	0.458587	+	0.888649i	$0.348356\pi$
$131$			232.826i			1.77730i	−0.458587	+	0.888649i	$0.651644\pi$
$132$		0			0
$133$	−112.000			−0.842105
$134$	−105.683	−	34.3384i	−0.788678	−	0.256257i
$135$	−70.5984	−	29.1182i	−0.522951	−	0.215691i
$136$	45.3050	+	32.9160i	0.333125	+	0.242029i
$137$	−150.640	+	48.9458i	−1.09956	+	0.357269i	−0.801933	−	0.597414i	$-0.796195\pi$
$137$	−150.640	+	48.9458i	−1.09956	+	0.357269i	−0.297626	+	0.954682i	$0.596195\pi$
$138$	−246.868	−	6.34038i	−1.78890	−	0.0459448i
$139$	−72.6495	−	52.7830i	−0.522659	−	0.379734i	0.294946	−	0.955514i	$-0.404698\pi$
$139$	−72.6495	−	52.7830i	−0.522659	−	0.379734i	−0.817604	+	0.575780i	$0.804698\pi$
$140$	37.3232	+	51.3710i	0.266594	+	0.366936i
$141$	−67.1077	+	87.5475i	−0.475941	+	0.620904i
$142$	−172.116			−1.21209
$143$		0			0
$144$	133.000	+	107.480i	0.923611	+	0.746390i
$145$	−18.4998	+	56.9364i	−0.127585	+	0.392665i
$146$	116.376	+	160.177i	0.797093	+	1.09710i
$147$	17.3007	−	11.9032i	0.117692	−	0.0809743i
$148$	9.27051	+	28.5317i	0.0626386	+	0.192782i
$149$	−20.1301	+	6.54066i	−0.135101	+	0.0438970i	−0.375787	−	0.926706i	$-0.622628\pi$
$149$	−20.1301	+	6.54066i	−0.135101	+	0.0438970i	0.240686	+	0.970603i	$0.422628\pi$
$150$	76.4829	+	111.164i	0.509886	+	0.741091i
$151$	−54.4872	+	39.5872i	−0.360842	+	0.262167i	−0.753403	−	0.657559i	$-0.771589\pi$
$151$	−54.4872	+	39.5872i	−0.360842	+	0.262167i	0.392561	+	0.919726i	$0.371589\pi$
$152$	−37.6599	−	12.2364i	−0.247763	−	0.0805030i
$153$	119.733	−	148.162i	0.782569	−	0.968380i
$154$		0			0
$155$			84.8528i			0.547438i
$156$	160.358	+	122.919i	1.02794	+	0.787945i
$157$	−69.5755	+	50.5495i	−0.443156	+	0.321972i	−0.786888	−	0.617096i	$-0.788309\pi$
$157$	−69.5755	+	50.5495i	−0.443156	+	0.321972i	0.343732	+	0.939068i	$0.388309\pi$
$158$	−34.9127	+	48.0532i	−0.220966	+	0.304134i
$159$	−3.26787	+	127.237i	−0.0205527	+	0.800234i
$160$	34.6871	+	106.756i	0.216794	+	0.667224i
$161$	−136.852	+	188.360i	−0.850011	+	1.16994i
$162$	143.078	−	159.548i	0.883200	−	0.984865i
$163$	−4.32624	+	13.3148i	−0.0265413	+	0.0816858i	−0.963450	−	0.267889i	$-0.913674\pi$
$163$	−4.32624	+	13.3148i	−0.0265413	+	0.0816858i	0.936908	+	0.349575i	$0.113674\pi$
$164$		−	126.996i		−	0.774366i
$165$		0			0
$166$	−56.0000			−0.337349
$167$	−80.5203	−	26.1626i	−0.482157	−	0.156662i	0.0578456	−	0.998326i	$-0.481577\pi$
$167$	−80.5203	−	26.1626i	−0.482157	−	0.156662i	−0.540003	+	0.841663i	$0.681577\pi$
$168$	56.9425	−	16.8983i	0.338943	−	0.100585i
$169$	−271.021	−	196.908i	−1.60367	−	1.16514i
$170$	150.640	−	48.9458i	0.886116	−	0.287916i
$171$	−48.1457	+	125.801i	−0.281554	+	0.735681i
$172$	36.3248	+	26.3915i	0.211191	+	0.153439i
$173$	111.970	+	154.113i	0.647223	+	0.890826i	0.998975	−	0.0452670i	$-0.0144139\pi$
$173$	111.970	+	154.113i	0.647223	+	0.890826i	−0.351752	+	0.936093i	$0.614414\pi$
$174$	−133.335	−	102.205i	−0.766291	−	0.587385i
$175$	127.216			0.726951
$176$		0			0
$177$	−96.0000	−	33.9411i	−0.542373	−	0.191758i
$178$	50.8744	−	156.575i	0.285811	−	0.879636i
$179$	−186.201	−	256.284i	−1.04023	−	1.43175i	−0.896983	−	0.442064i	$-0.854246\pi$
$179$	−186.201	−	256.284i	−1.04023	−	1.43175i	−0.143245	−	0.989687i	$-0.545754\pi$
$180$	73.7455	−	19.8395i	0.409697	−	0.110219i
$181$	−80.9625	−	249.177i	−0.447306	−	1.37667i	−0.879935	−	0.475095i	$-0.842414\pi$
$181$	−80.9625	−	249.177i	−0.447306	−	1.37667i	0.432628	−	0.901572i	$-0.357586\pi$
$182$	422.732	−	137.354i	2.32270	−	0.754691i
$183$	240.438	−	165.426i	1.31387	−	0.903967i
$184$	−66.5954	+	48.3844i	−0.361932	+	0.262959i
$185$	−26.8999	−	8.74032i	−0.145405	−	0.0472450i
$186$	−224.499	−	79.3725i	−1.20699	−	0.426734i
$187$		0			0
$188$		−	110.309i		−	0.586748i
$189$	−47.4635	−	196.396i	−0.251130	−	1.03913i
$190$	−90.6099	+	65.8319i	−0.476894	+	0.346484i
$191$	−34.9127	+	48.0532i	−0.182789	+	0.251587i	−0.890572	−	0.454843i	$-0.849695\pi$
$191$	−34.9127	+	48.0532i	−0.182789	+	0.251587i	0.707783	+	0.706430i	$0.249695\pi$
$192$	−86.9713	−	2.23371i	−0.452976	−	0.0116339i
$193$	−46.2494	−	142.341i	−0.239634	−	0.737519i	−0.996473	−	0.0839167i	$-0.973257\pi$
$193$	−46.2494	−	142.341i	−0.239634	−	0.737519i	0.756838	−	0.653602i	$-0.226743\pi$
$194$	115.080	−	158.394i	0.593195	−	0.816463i
$195$	−182.622	+	54.1950i	−0.936525	+	0.277923i
$196$	−6.48936	+	19.9722i	−0.0331090	+	0.101899i
$197$			232.826i			1.18186i	0.806723	+	0.590929i	$0.201239\pi$
$197$			232.826i			1.18186i	−0.806723	+	0.590929i	$0.798761\pi$
$198$		0			0
$199$	222.000			1.11558			0.557789	−	0.829983i	$-0.311650\pi$
$199$	222.000			1.11558			0.557789	+	0.829983i	$0.311650\pi$
$200$	42.7764	+	13.8989i	0.213882	+	0.0694945i
$201$	35.8466	+	120.793i	0.178341	+	0.600962i
$202$	317.135	+	230.412i	1.56997	+	1.14065i
$203$	−150.640	+	48.9458i	−0.742067	+	0.241112i
$204$	−4.89090	+	190.431i	−0.0239750	+	0.933487i
$205$	96.8661	+	70.3773i	0.472517	+	0.343304i
$206$	−52.8745	−	72.7756i	−0.256673	−	0.353279i
$207$	152.743	+	234.686i	0.737887	+	1.13375i
$208$	426.549			2.05072
$209$		0			0
$210$	56.0000	−	158.392i	0.266667	−	0.754247i
$211$	120.249	−	370.087i	0.569898	−	1.75397i	−0.0830307	−	0.996547i	$-0.526460\pi$
$211$	120.249	−	370.087i	0.569898	−	1.75397i	0.652929	−	0.757419i	$-0.273540\pi$
$212$	−74.8128	−	102.971i	−0.352891	−	0.485713i
$213$	110.621	+	160.782i	0.519350	+	0.754846i
$214$	−34.6099	−	106.518i	−0.161729	−	0.497749i
$215$	−40.2601	+	13.0813i	−0.187256	+	0.0608433i
$216$	5.49743	−	71.2234i	0.0254511	−	0.329738i
$217$	−181.624	+	131.957i	−0.836976	+	0.608099i
$218$	−169.470	−	55.0640i	−0.777384	−	0.252587i
$219$	74.8331	−	211.660i	0.341704	−	0.966484i
$220$		0			0
$221$		−	475.176i		−	2.15012i
$222$	48.2873	−	62.9947i	0.217510	−	0.283760i
$223$	37.2148	−	27.0381i	0.166882	−	0.121247i	−0.501209	−	0.865326i	$-0.667111\pi$
$223$	37.2148	−	27.0381i	0.166882	−	0.121247i	0.668092	+	0.744079i	$0.267111\pi$
$224$	−174.563	+	240.266i	−0.779301	+	1.07262i
$225$	54.6868	−	142.893i	0.243052	−	0.635079i
$226$	97.1238	+	298.916i	0.429751	+	1.32264i
$227$	−124.411	+	171.237i	−0.548065	+	0.754346i	−0.989748	−	0.142825i	$-0.954381\pi$
$227$	−124.411	+	171.237i	−0.548065	+	0.754346i	0.441683	+	0.897171i	$0.354381\pi$
$228$	−38.3216	−	129.133i	−0.168077	−	0.566375i
$229$	36.4640	−	112.225i	0.159231	−	0.490064i	−0.839334	−	0.543617i	$-0.817055\pi$
$229$	36.4640	−	112.225i	0.159231	−	0.490064i	0.998565	+	0.0535527i	$0.0170545\pi$
$230$			232.826i			1.01229i
$231$		0			0
$232$	−56.0000			−0.241379
$233$	−80.5203	−	26.1626i	−0.345581	−	0.112286i	0.131084	−	0.991371i	$-0.458154\pi$
$233$	−80.5203	−	26.1626i	−0.345581	−	0.112286i	−0.476664	+	0.879085i	$0.658154\pi$
$234$	27.4411	−	533.868i	0.117270	−	2.28149i
$235$	84.1378	+	61.1297i	0.358033	+	0.260126i
$236$	96.8398	−	31.4652i	0.410338	−	0.133327i
$237$	67.3276	+	1.72920i	0.284083	+	0.00729618i
$238$	339.031	+	246.321i	1.42450	+	1.03496i
$239$	−24.8821	−	34.2473i	−0.104109	−	0.143294i	0.753784	−	0.657123i	$-0.228227\pi$
$239$	−24.8821	−	34.2473i	−0.104109	−	0.143294i	−0.857893	+	0.513829i	$0.828227\pi$
$240$	98.0805	−	127.954i	0.408669	−	0.533142i
$241$	−149.666			−0.621022			−0.310511	−	0.950570i	$-0.600500\pi$
$241$	−149.666			−0.621022			−0.310511	+	0.950570i	$0.600500\pi$
$242$		0			0
$243$	−241.000	−	31.1127i	−0.991770	−	0.128036i
$244$	−90.1864	+	277.565i	−0.369616	+	1.13756i
$245$	−11.6376	−	16.0177i	−0.0475002	−	0.0653784i
$246$	−276.811	+	190.452i	−1.12525	+	0.774193i
$247$	103.830	+	319.555i	0.420363	+	1.29374i
$248$	−75.4878	+	24.5275i	−0.304386	+	0.0989011i
$249$	35.9920	+	52.3123i	0.144546	+	0.210090i
$250$	254.273	−	184.740i	1.01709	−	0.738962i
$251$	48.4199	+	15.7326i	0.192908	+	0.0626796i	0.403878	−	0.914813i	$-0.367662\pi$
$251$	48.4199	+	15.7326i	0.192908	+	0.0626796i	−0.210970	+	0.977493i	$0.567662\pi$
$252$	157.150	+	126.996i	0.623610	+	0.503953i
$253$		0			0
$254$		−	178.191i		−	0.701539i
$255$	−142.541	−	109.262i	−0.558984	−	0.428477i
$256$	−269.403	+	195.732i	−1.05235	+	0.764580i
$257$	56.5253	−	77.8004i	0.219943	−	0.302725i	−0.684760	−	0.728769i	$-0.740093\pi$
$257$	56.5253	−	77.8004i	0.219943	−	0.302725i	0.904703	+	0.426044i	$0.140093\pi$
$258$	3.05001	−	118.755i	0.0118218	−	0.460290i
$259$	−23.1247	−	71.1706i	−0.0892846	−	0.274790i
$260$	111.970	−	154.113i	0.430652	−	0.592742i
$261$	−9.77858	+	190.243i	−0.0374658	+	0.728900i
$262$	−190.354	+	585.851i	−0.726544	+	2.23607i
$263$		−	465.652i		−	1.77054i	−0.465077	−	0.885270i	$-0.653973\pi$
$263$		−	465.652i		−	1.77054i	0.465077	−	0.885270i	$-0.346027\pi$
$264$		0			0
$265$	120.000			0.452830
$266$	−281.821	−	91.5692i	−1.05948	−	0.344245i
$267$	−178.962	+	53.1088i	−0.670270	+	0.198909i
$268$	−101.936	−	74.0609i	−0.380359	−	0.276347i
$269$	352.389	−	114.498i	1.31000	−	0.425644i	0.430949	−	0.902376i	$-0.358179\pi$
$269$	352.389	−	114.498i	1.31000	−	0.425644i	0.879048	+	0.476733i	$0.158179\pi$
$270$	−153.837	−	130.989i	−0.569767	−	0.485144i
$271$	−272.436	−	197.936i	−1.00530	−	0.730392i	−0.0420805	−	0.999114i	$-0.513399\pi$
$271$	−272.436	−	197.936i	−1.00530	−	0.730392i	−0.963218	+	0.268722i	$0.913399\pi$
$272$	236.380	+	325.350i	0.869045	+	1.19614i
$273$	−400.004	−	306.615i	−1.46522	−	1.12313i
$274$	−419.066			−1.52944
$275$		0			0
$276$	−264.000	−	93.3381i	−0.956522	−	0.338182i
$277$	−6.93741	+	21.3512i	−0.0250448	+	0.0770800i	−0.962798	−	0.270223i	$-0.912903\pi$
$277$	−6.93741	+	21.3512i	−0.0250448	+	0.0770800i	0.937753	+	0.347303i	$0.112903\pi$
$278$	−139.651	−	192.213i	−0.502340	−	0.691412i
$279$	70.1431	+	260.730i	0.251409	+	0.934515i
$280$	−17.3050	−	53.2592i	−0.0618034	−	0.190211i
$281$	−20.1301	+	6.54066i	−0.0716373	+	0.0232764i	−0.344616	−	0.938744i	$-0.611991\pi$
$281$	−20.1301	+	6.54066i	−0.0716373	+	0.0232764i	0.272979	+	0.962020i	$0.411991\pi$
$282$	−240.438	+	165.426i	−0.852615	+	0.586617i
$283$	145.299	−	105.566i	0.513424	−	0.373025i	−0.300697	−	0.953720i	$-0.597219\pi$
$283$	145.299	−	105.566i	0.513424	−	0.373025i	0.814121	+	0.580695i	$0.197219\pi$
$284$	−185.610	−	60.3082i	−0.653555	−	0.212353i
$285$	119.733	+	42.3320i	0.420116	+	0.148533i
$286$		0			0
$287$			316.784i			1.10378i
$288$	194.833	+	299.358i	0.676504	+	1.03944i
$289$	128.634	−	93.4579i	0.445099	−	0.323384i
$290$	−93.1004	+	128.142i	−0.321036	+	0.441868i
$291$	−221.927	−	5.69981i	−0.762635	−	0.0195870i
$292$	69.3741	+	213.512i	0.237583	+	0.731204i
$293$	12.4411	−	17.1237i	0.0424610	−	0.0584425i	−0.787259	−	0.616623i	$-0.788500\pi$
$293$	12.4411	−	17.1237i	0.0424610	−	0.0584425i	0.829720	+	0.558180i	$0.188500\pi$
$294$	53.2648	−	15.8069i	0.181173	−	0.0537649i
$295$	−29.6656	+	91.3014i	−0.100561	+	0.309496i
$296$		−	26.4575i		−	0.0893835i
$297$		0			0
$298$	−56.0000			−0.187919
$299$	664.292	+	215.842i	2.22171	+	0.721879i
$300$	43.5280	+	146.678i	0.145093	+	0.488925i
$301$	−90.6099	−	65.8319i	−0.301030	−	0.218711i
$302$	−169.470	+	55.0640i	−0.561158	+	0.182331i
$303$	11.4121	−	444.340i	0.0376637	−	1.46647i
$304$	−230.057	−	167.146i	−0.756766	−	0.549823i
$305$	−161.734	−	222.608i	−0.530275	−	0.729861i
$306$	422.414	−	274.923i	1.38044	−	0.898440i
$307$	−149.666			−0.487512			−0.243756	−	0.969837i	$-0.578380\pi$
$307$	−149.666			−0.487512			−0.243756	+	0.969837i	$0.578380\pi$
$308$		0			0
$309$	−34.0000	+	96.1665i	−0.110032	+	0.311219i
$310$	−69.3741	+	213.512i	−0.223788	+	0.688747i
$311$	14.9626	+	20.5942i	0.0481112	+	0.0662193i	0.832395	−	0.554183i	$-0.186969\pi$
$311$	14.9626	+	20.5942i	0.0481112	+	0.0662193i	−0.784284	+	0.620402i	$0.786969\pi$
$312$	−101.002	−	146.801i	−0.323725	−	0.470516i
$313$	122.989	+	378.520i	0.392935	+	1.20933i	0.930558	+	0.366145i	$0.119323\pi$
$313$	122.989	+	378.520i	0.392935	+	1.20933i	−0.537622	+	0.843186i	$0.680677\pi$
$314$	−216.398	+	70.3121i	−0.689166	+	0.223924i
$315$	−183.954	+	49.4883i	−0.583980	+	0.157106i
$316$	−54.4872	+	39.5872i	−0.172428	+	0.125276i
$317$	−395.429	−	128.483i	−1.24741	−	0.405308i	−0.390418	−	0.920638i	$-0.627670\pi$
$317$	−395.429	−	128.483i	−1.24741	−	0.405308i	−0.856992	+	0.515329i	$0.827670\pi$
$318$	−112.250	+	317.490i	−0.352987	+	0.998397i
$319$		0			0
$320$			82.0244i			0.256326i
$321$	−77.2597	+	100.792i	−0.240684	+	0.313992i
$322$	−498.354	+	362.076i	−1.54768	+	1.12446i
$323$	−186.201	+	256.284i	−0.576473	+	0.793447i
$324$	210.200	−	121.923i	0.648764	−	0.376304i
$325$	−117.936	−	362.970i	−0.362880	−	1.11683i
$326$	−21.7719	+	29.9664i	−0.0667849	+	0.0919215i
$327$	57.4825	+	193.700i	0.175787	+	0.592355i
$328$	−34.6099	+	106.518i	−0.105518	+	0.324751i
$329$			275.158i			0.836347i
$330$		0			0
$331$	178.000			0.537764			0.268882	−	0.963173i	$-0.413346\pi$
$331$	178.000			0.537764			0.268882	+	0.963173i	$0.413346\pi$
$332$	−60.3902	−	19.6220i	−0.181898	−	0.0591023i
$333$	−89.8813	−	4.61994i	−0.269914	−	0.0138737i
$334$	−181.220	−	131.664i	−0.542574	−	0.394203i
$335$	112.980	−	36.7093i	0.337253	−	0.109580i
$336$	426.408	+	10.9516i	1.26907	+	0.0325940i
$337$	−205.840	−	149.552i	−0.610802	−	0.443774i	0.238894	−	0.971046i	$-0.423215\pi$
$337$	−205.840	−	149.552i	−0.610802	−	0.443774i	−0.849697	+	0.527272i	$0.823215\pi$
$338$	−520.970	−	717.053i	−1.54133	−	2.12146i
$339$	216.809	−	282.846i	0.639556	−	0.834353i
$340$	179.600			0.528234
$341$		0			0
$342$	−224.000	+	277.186i	−0.654971	+	0.810485i
$343$	−97.1238	+	298.916i	−0.283160	+	0.871476i
$344$	−23.2751	−	32.0354i	−0.0676602	−	0.0931263i
$345$	217.494	−	149.641i	0.630418	−	0.433741i
$346$	155.745	+	479.332i	0.450129	+	1.38535i
$347$	−462.992	+	150.435i	−1.33427	+	0.433531i	−0.887372	−	0.461054i	$-0.847471\pi$
$347$	−462.992	+	150.435i	−1.33427	+	0.433531i	−0.446898	+	0.894585i	$0.647471\pi$
$348$	−107.976	−	156.937i	−0.310276	−	0.450968i
$349$	−54.4872	+	39.5872i	−0.156124	+	0.113430i	−0.663104	−	0.748527i	$-0.730761\pi$
$349$	−54.4872	+	39.5872i	−0.156124	+	0.113430i	0.506981	+	0.861957i	$0.330761\pi$
$350$	320.109	+	104.010i	0.914598	+	0.297171i
$351$	−516.349	+	317.490i	−1.47108	+	0.904530i
$352$		0			0
$353$			124.451i			0.352552i	0.984341	+	0.176276i	$0.0564051\pi$
$353$			124.451i			0.352552i	−0.984341	+	0.176276i	$0.943595\pi$
$354$	−213.811	−	163.893i	−0.603986	−	0.462973i
$355$	148.859	−	108.152i	0.419321	−	0.304655i
$356$	109.726	−	151.024i	0.308218	−	0.424225i
$357$	12.2001	−	475.019i	0.0341738	−	1.33059i
$358$	−258.997	−	797.110i	−0.723455	−	2.22656i
$359$	149.293	−	205.484i	0.415857	−	0.572379i	−0.548777	−	0.835969i	$-0.684907\pi$
$359$	149.293	−	205.484i	0.415857	−	0.572379i	0.964635	+	0.263590i	$0.0849065\pi$
$360$	−67.2610	−	3.45725i	−0.186836	−	0.00960347i
$361$	−42.3353	+	130.295i	−0.117272	+	0.360927i
$362$		−	693.187i		−	1.91488i
$363$		0			0
$364$	504.000			1.38462
$365$	−201.301	−	65.4066i	−0.551509	−	0.179196i
$366$	740.253	−	219.677i	2.02255	−	0.600211i
$367$	114.880	+	83.4655i	0.313026	+	0.227426i	0.733194	−	0.680020i	$-0.238029\pi$
$367$	114.880	+	83.4655i	0.313026	+	0.227426i	−0.420168	+	0.907446i	$0.638029\pi$
$368$	−562.209	+	182.673i	−1.52774	+	0.496393i
$369$	355.820	+	136.177i	0.964282	+	0.369042i
$370$	−60.5413	−	43.9858i	−0.163625	−	0.118881i
$371$	186.616	+	256.855i	0.503008	+	0.692331i
$372$	−214.288	−	164.258i	−0.576043	−	0.441554i
$373$	426.549			1.14356			0.571781	−	0.820406i	$-0.306253\pi$
$373$	426.549			1.14356			0.571781	+	0.820406i	$0.306253\pi$
$374$		0			0
$375$	−336.000	−	118.794i	−0.896000	−	0.316784i
$376$	−30.0621	+	92.5217i	−0.0799525	+	0.246068i
$377$	279.301	+	384.425i	0.740852	+	1.01970i
$378$	41.1390	−	532.987i	0.108833	−	1.41002i
$379$	−108.156	−	332.870i	−0.285372	−	0.878284i	−0.986287	−	0.165040i	$-0.947225\pi$
$379$	−108.156	−	332.870i	−0.285372	−	0.878284i	0.700915	−	0.713245i	$-0.252775\pi$
$380$	−120.780	+	39.2439i	−0.317843	+	0.103274i
$381$	−166.457	+	114.526i	−0.436894	+	0.300592i
$382$	−127.137	+	92.3702i	−0.332819	+	0.241807i
$383$	492.269	+	159.948i	1.28530	+	0.417618i	0.870443	−	0.492269i	$-0.163832\pi$
$383$	492.269	+	159.948i	1.28530	+	0.417618i	0.414854	+	0.909888i	$0.363832\pi$
$384$	231.983	+	82.0183i	0.604122	+	0.213589i
$385$		0			0
$386$		−	395.980i		−	1.02585i
$387$	−112.895	+	73.4761i	−0.291718	+	0.189861i
$388$	179.602	−	130.488i	0.462891	−	0.336310i
$389$	257.689	−	354.678i	0.662439	−	0.911769i	−0.337120	−	0.941462i	$-0.609453\pi$
$389$	257.689	−	354.678i	0.662439	−	0.911769i	0.999559	+	0.0296928i	$0.00945289\pi$
$390$	−503.834	−	12.9401i	−1.29188	−	0.0331798i
$391$	203.497	+	626.301i	0.520454	+	1.60179i
$392$	10.8859	−	14.9832i	0.0277702	−	0.0382225i
$393$	669.615	−	198.715i	1.70386	−	0.505636i
$394$	−190.354	+	585.851i	−0.483133	+	1.48693i
$395$		−	63.4980i		−	0.160755i
$396$		0			0
$397$	442.000			1.11335			0.556675	−	0.830730i	$-0.312077\pi$
$397$	442.000			1.11335			0.556675	+	0.830730i	$0.312077\pi$
$398$	558.610	+	181.503i	1.40354	+	0.456038i
$399$	95.5910	+	322.115i	0.239576	+	0.807307i
$400$	261.312	+	189.855i	0.653281	+	0.474637i
$401$	500.339	−	162.570i	1.24773	−	0.405411i	0.390622	−	0.920551i	$-0.372260\pi$
$401$	500.339	−	162.570i	1.24773	−	0.405411i	0.857106	+	0.515140i	$0.172260\pi$
$402$	−8.55908	+	333.255i	−0.0212912	+	0.828992i
$403$	544.872	+	395.872i	1.35204	+	0.982314i
$404$	261.262	+	359.597i	0.646689	+	0.890091i
$405$	−23.4899	+	227.895i	−0.0579998	+	0.562704i
$406$	−419.066			−1.03218
$407$		0			0
$408$	56.0000	−	158.392i	0.137255	−	0.388215i
$409$	69.3741	−	213.512i	0.169619	−	0.522033i	−0.829728	−	0.558168i	$-0.811504\pi$
$409$	69.3741	−	213.512i	0.169619	−	0.522033i	0.999347	+	0.0361345i	$0.0115045\pi$
$410$	186.201	+	256.284i	0.454148	+	0.625082i
$411$	269.339	+	391.470i	0.655326	+	0.952481i
$412$	−31.5197	−	97.0078i	−0.0765042	−	0.235456i
$413$	−241.561	+	78.4879i	−0.584893	+	0.190043i
$414$	192.464	+	715.411i	0.464890	+	1.72805i
$415$	48.4330	−	35.1887i	0.116706	−	0.0847919i
$416$	847.348	+	275.320i	2.03689	+	0.661827i
$417$	−89.7998	+	253.992i	−0.215347	+	0.609094i
$418$		0			0
$419$			684.479i			1.63360i	0.576919	+	0.816801i	$0.304255\pi$
$419$			684.479i			1.63360i	−0.576919	+	0.816801i	$0.695745\pi$
$420$	115.890	−	151.187i	0.275927	−	0.359970i
$421$	215.199	−	156.351i	0.511160	−	0.371380i	−0.302103	−	0.953275i	$-0.597689\pi$
$421$	215.199	−	156.351i	0.511160	−	0.371380i	0.813264	+	0.581895i	$0.197689\pi$
$422$	605.153	−	832.921i	1.43401	−	1.97375i
$423$	309.065	+	118.283i	0.730650	+	0.279628i
$424$	34.6871	+	106.756i	0.0818091	+	0.251783i
$425$	211.498	−	291.102i	0.497643	−	0.684946i
$426$	146.900	+	495.012i	0.344835	+	1.16200i
$427$	224.964	−	692.369i	0.526849	−	1.62147i
$428$		−	126.996i		−	0.296720i
$429$		0			0
$430$	−112.000			−0.260465
$431$	−523.382	−	170.057i	−1.21434	−	0.394564i	−0.369324	−	0.929301i	$-0.620411\pi$
$431$	−523.382	−	170.057i	−1.21434	−	0.394564i	−0.845019	+	0.534737i	$0.820411\pi$
$432$	195.602	−	474.245i	0.452783	−	1.09779i
$433$	−597.055	−	433.786i	−1.37888	−	1.00181i	−0.996984	−	0.0776084i	$-0.975272\pi$
$433$	−597.055	−	433.786i	−1.37888	−	1.00181i	−0.381895	−	0.924206i	$-0.624728\pi$
$434$	−564.899	+	183.547i	−1.30161	+	0.422919i
$435$	179.540	+	4.61119i	0.412736	+	0.0106004i
$436$	−163.461	−	118.762i	−0.374912	−	0.272389i
$437$	−273.704	−	376.721i	−0.626324	−	0.862061i
$438$	361.349	−	471.409i	0.824998	−	1.07628i
$439$	426.549			0.971638			0.485819	−	0.874060i	$-0.338521\pi$
$439$	426.549			0.971638			0.485819	+	0.874060i	$0.338521\pi$
$440$		0			0
$441$	−49.0000	−	39.5980i	−0.111111	−	0.0897913i
$442$	388.495	−	1195.67i	0.878948	−	2.70513i
$443$	69.8253	+	96.1063i	0.157619	+	0.216944i	0.880522	−	0.474006i	$-0.157192\pi$
$443$	69.8253	+	96.1063i	0.157619	+	0.216944i	−0.722902	+	0.690950i	$0.757192\pi$
$444$	74.1457	−	51.0138i	0.166995	−	0.114896i
$445$	54.3870	+	167.386i	0.122218	+	0.376148i
$446$	115.748	−	37.6088i	0.259524	−	0.0843246i
$447$	35.9920	+	52.3123i	0.0805189	+	0.117030i
$448$	−175.570	+	127.559i	−0.391897	+	0.284730i
$449$	−484.199	−	157.326i	−1.07839	−	0.350391i	−0.284643	−	0.958634i	$-0.591875\pi$
$449$	−484.199	−	157.326i	−1.07839	−	0.350391i	−0.793751	+	0.608242i	$0.791875\pi$
$450$	254.433	−	314.844i	0.565406	−	0.699654i
$451$		0			0
$452$			356.382i			0.788455i
$453$	160.358	+	122.919i	0.353992	+	0.271345i
$454$	−453.050	+	329.160i	−0.997906	+	0.725021i
$455$	−279.301	+	384.425i	−0.613849	+	0.844891i
$456$	−3.05001	+	118.755i	−0.00668863	+	0.260427i
$457$	208.122	+	640.535i	0.455410	+	1.40161i	0.870653	+	0.491898i	$0.163697\pi$
$457$	208.122	+	640.535i	0.455410	+	1.40161i	−0.415243	+	0.909711i	$0.636303\pi$
$458$	183.506	−	252.574i	0.400668	−	0.551472i
$459$	−528.310	−	217.901i	−1.15100	−	0.474730i
$460$	−81.5805	+	251.079i	−0.177349	+	0.545824i
$461$		−	698.478i		−	1.51514i	−0.652755	−	0.757569i	$-0.726387\pi$
$461$		−	698.478i		−	1.51514i	0.652755	−	0.757569i	$-0.273613\pi$
$462$		0			0
$463$	882.000			1.90497			0.952484	−	0.304589i	$-0.0985192\pi$
$463$	882.000			1.90497			0.952484	+	0.304589i	$0.0985192\pi$
$464$	−382.471	−	124.272i	−0.824292	−	0.267829i
$465$	244.039	−	72.4211i	0.524816	−	0.155744i
$466$	−181.220	−	131.664i	−0.388884	−	0.282541i
$467$	−505.719	+	164.318i	−1.08291	+	0.351859i	−0.795503	−	0.605950i	$-0.792793\pi$
$467$	−505.719	+	164.318i	−1.08291	+	0.351859i	−0.287407	+	0.957809i	$0.592793\pi$
$468$	216.656	−	566.106i	0.462939	−	1.20963i
$469$	254.273	+	184.740i	0.542161	+	0.393903i
$470$	161.734	+	222.608i	0.344115	+	0.473633i
$471$	204.764	+	156.958i	0.434743	+	0.333243i
$472$	−89.7998			−0.190254
$473$		0			0
$474$	168.000	+	59.3970i	0.354430	+	0.125310i
$475$	−78.6240	+	241.980i	−0.165524	+	0.509431i
$476$	279.301	+	384.425i	0.586767	+	0.807616i
$477$	368.727	−	99.1973i	0.773013	−	0.207961i
$478$	−34.6099	−	106.518i	−0.0724057	−	0.222842i
$479$	644.162	−	209.301i	1.34481	−	0.436954i	0.453864	−	0.891071i	$-0.350045\pi$
$479$	644.162	−	209.301i	1.34481	−	0.436954i	0.890942	+	0.454117i	$0.150045\pi$
$480$	277.428	−	190.876i	0.577975	−	0.397659i
$481$	−181.624	+	131.957i	−0.377596	+	0.274340i
$482$	−376.599	−	122.364i	−0.781326	−	0.253868i
$483$	658.532	+	232.826i	1.36342	+	0.482042i
$484$		0			0
$485$			209.304i			0.431554i
$486$	−580.981	−	275.325i	−1.19543	−	0.566512i
$487$	−283.156	+	205.725i	−0.581429	+	0.422433i	−0.839239	−	0.543763i	$-0.816999\pi$
$487$	−283.156	+	205.725i	−0.581429	+	0.422433i	0.257810	+	0.966196i	$0.416999\pi$
$488$	151.288	−	208.230i	0.310017	−	0.426702i
$489$	41.9862	+	1.07834i	0.0858613	+	0.00220520i
$490$	−16.1873	−	49.8194i	−0.0330353	−	0.101672i
$491$	149.293	−	205.484i	0.304059	−	0.418501i	−0.629458	−	0.777034i	$-0.716723\pi$
$491$	149.293	−	205.484i	0.304059	−	0.418501i	0.933517	+	0.358533i	$0.116723\pi$
$492$	−365.245	+	108.390i	−0.742367	+	0.220305i
$493$	−138.440	+	426.073i	−0.280811	+	0.864246i
$494$			888.972i			1.79954i
$495$		0			0
$496$	−570.000			−1.14919
$497$	462.992	+	150.435i	0.931573	+	0.302686i
$498$	47.7955	+	161.058i	0.0959749	+	0.323409i
$499$	79.2837	+	57.6030i	0.158885	+	0.115437i	0.664387	−	0.747389i	$-0.268693\pi$
$499$	79.2837	+	57.6030i	0.158885	+	0.115437i	−0.505502	+	0.862825i	$0.668693\pi$
$500$	338.939	−	110.128i	0.677879	−	0.220256i
$501$	−6.52120	+	253.908i	−0.0130164	+	0.506803i
$502$	108.974	+	79.1745i	0.217080	+	0.157718i
$503$	−298.586	−	410.968i	−0.593610	−	0.817034i	0.401495	−	0.915861i	$-0.368491\pi$
$503$	−298.586	−	410.968i	−0.593610	−	0.817034i	−0.995105	+	0.0988277i	$0.968491\pi$
$504$	−97.1998	−	149.346i	−0.192857	−	0.296321i
$505$	−419.066			−0.829833
$506$		0			0
$507$	−335.000	+	947.523i	−0.660750	+	1.86888i
$508$	62.4367	−	192.160i	0.122907	−	0.378269i
$509$	−94.7629	−	130.430i	−0.186175	−	0.256248i	0.705720	−	0.708491i	$-0.250624\pi$
$509$	−94.7629	−	130.430i	−0.186175	−	0.256248i	−0.891894	+	0.452244i	$0.850624\pi$
$510$	−269.339	−	391.470i	−0.528116	−	0.767587i
$511$	−173.050	−	532.592i	−0.338649	−	1.04225i
$512$	−525.898	+	170.875i	−1.02714	+	0.333740i
$513$	402.901	+	31.0982i	0.785381	+	0.0606202i
$514$	205.840	−	149.552i	0.400468	−	0.290957i
$515$	91.4598	+	29.7171i	0.177592	+	0.0577031i
$516$	44.8999	−	126.996i	0.0870153	−	0.246116i
$517$		0			0
$518$		−	197.990i		−	0.382220i
$519$	347.669	−	453.562i	0.669882	−	0.873915i
$520$	−135.915	+	98.7479i	−0.261375	+	0.189900i
$521$	−89.7754	+	123.565i	−0.172314	+	0.237169i	−0.886436	−	0.462852i	$-0.846826\pi$
$521$	−89.7754	+	123.565i	−0.172314	+	0.237169i	0.714122	+	0.700021i	$0.246826\pi$
$522$	−180.145	+	470.706i	−0.345105	+	0.901735i
$523$	4.62494	+	14.2341i	0.00884310	+	0.0272163i	0.955381	−	0.295377i	$-0.0954453\pi$
$523$	4.62494	+	14.2341i	0.00884310	+	0.0272163i	−0.946538	+	0.322593i	$0.895445\pi$
$524$	−410.555	+	565.081i	−0.783502	+	1.07840i
$525$	−108.578	−	365.878i	−0.206815	−	0.696911i
$526$	380.709	−	1171.70i	0.723781	−	2.22757i
$527$			634.980i			1.20490i
$528$		0			0
$529$	−439.000			−0.829868
$530$	301.951	+	98.1099i	0.569719	+	0.185113i
$531$	−15.6806	+	305.067i	−0.0295303	+	0.574515i
$532$	−271.830	−	197.496i	−0.510958	−	0.371233i
$533$	903.838	−	293.675i	1.69576	−	0.550985i
$534$	−493.736	−	12.6808i	−0.924599	−	0.0237467i
$535$	96.8661	+	70.3773i	0.181058	+	0.131546i
$536$	65.3156	+	89.8992i	0.121857	+	0.167722i
$537$	−578.159	+	754.255i	−1.07665	+	1.40457i
$538$	980.314			1.82215
$539$		0			0
$540$	−120.000	−	195.161i	−0.222222	−	0.361410i
$541$	−159.561	+	491.077i	−0.294936	+	0.907721i	0.688307	+	0.725420i	$0.258354\pi$
$541$	−159.561	+	491.077i	−0.294936	+	0.907721i	−0.983243	+	0.182301i	$0.941646\pi$
$542$	−523.690	−	720.797i	−0.966218	−	1.32988i
$543$	−647.539	+	445.521i	−1.19252	+	0.820480i
$544$	259.574	+	798.887i	0.477159	+	1.46854i
$545$	181.171	−	58.8659i	0.332423	−	0.108011i
$546$	−755.831	−	1098.56i	−1.38431	−	2.01201i
$547$	544.872	−	395.872i	0.996109	−	0.723716i	0.0348585	−	0.999392i	$-0.488902\pi$
$547$	544.872	−	395.872i	0.996109	−	0.723716i	0.961250	+	0.275677i	$0.0889019\pi$
$548$	−451.919	−	146.837i	−0.824670	−	0.267951i
$549$	−680.982	−	550.316i	−1.24040	−	1.00240i
$550$		0			0
$551$		−	316.784i		−	0.574925i
$552$	195.994	+	150.235i	0.355061	+	0.272165i
$553$	135.915	−	98.7479i	0.245777	−	0.178568i
$554$	−34.9127	+	48.0532i	−0.0630192	+	0.0867386i
$555$	−2.17858	+	84.8248i	−0.00392537	+	0.152838i
$556$	−83.2490	−	256.214i	−0.149728	−	0.460817i
$557$	−261.262	+	359.597i	−0.469053	+	0.645596i	−0.976355	−	0.216172i	$-0.930643\pi$
$557$	−261.262	+	359.597i	−0.469053	+	0.645596i	0.507302	+	0.861768i	$0.330643\pi$
$558$	−36.6697	+	713.411i	−0.0657163	+	1.27851i
$559$	−103.830	+	319.555i	−0.185742	+	0.571655i
$560$		−	402.154i		−	0.718132i
$561$		0			0
$562$	−56.0000			−0.0996441
$563$	−523.382	−	170.057i	−0.929630	−	0.302055i	−0.195219	−	0.980760i	$-0.562542\pi$
$563$	−523.382	−	170.057i	−0.929630	−	0.302055i	−0.734411	+	0.678704i	$0.762542\pi$
$564$	−317.251	+	94.1474i	−0.562502	+	0.166928i
$565$	−271.830	−	197.496i	−0.481115	−	0.349550i
$566$	451.919	−	146.837i	0.798443	−	0.259430i
$567$	−524.330	+	304.128i	−0.924744	+	0.536382i
$568$	139.245	+	101.167i	0.245150	+	0.178112i
$569$	659.377	+	907.554i	1.15883	+	1.59500i	0.715445	+	0.698669i	$0.246224\pi$
$569$	659.377	+	907.554i	1.15883	+	1.59500i	0.443389	+	0.896329i	$0.353776\pi$
$570$	266.669	+	204.410i	0.467841	+	0.358614i
$571$	−808.198			−1.41541			−0.707704	−	0.706509i	$-0.750269\pi$
$571$	−808.198			−1.41541			−0.707704	+	0.706509i	$0.750269\pi$
$572$		0			0
$573$	168.000	+	59.3970i	0.293194	+	0.103660i
$574$	−258.997	+	797.110i	−0.451214	+	1.38869i
$575$	310.889	+	427.902i	0.540676	+	0.744177i
$576$	67.8050	+	252.039i	0.117717	+	0.437567i
$577$	95.7953	+	294.828i	0.166023	+	0.510966i	0.999110	−	0.0421754i	$-0.0134288\pi$
$577$	95.7953	+	294.828i	0.166023	+	0.510966i	−0.833087	+	0.553142i	$0.813429\pi$
$578$	400.085	−	129.996i	0.692189	−	0.224906i
$579$	−369.904	+	254.502i	−0.638867	+	0.439554i
$580$	−145.299	+	105.566i	−0.250516	+	0.182010i
$581$	150.640	+	48.9458i	0.259277	+	0.0842441i
$582$	−553.765	−	195.786i	−0.951487	−	0.336401i
$583$		0			0
$584$		−	197.990i		−	0.339024i
$585$	311.733	+	478.972i	0.532877	+	0.818756i
$586$	45.3050	−	32.9160i	0.0773122	−	0.0561706i
$587$	−565.253	+	778.004i	−0.962952	+	1.32539i	−0.0174238	+	0.999848i	$0.505546\pi$
$587$	−565.253	+	778.004i	−0.962952	+	1.32539i	−0.945528	+	0.325541i	$0.894454\pi$
$588$	62.9792	+	1.61751i	0.107108	+	0.00275087i
$589$	−138.748	−	427.023i	−0.235566	−	0.724997i
$590$	−149.293	+	205.484i	−0.253039	+	0.348278i
$591$	669.615	−	198.715i	1.13302	−	0.336235i
$592$	58.7132	−	180.701i	0.0991778	−	0.305238i
$593$		−	232.826i		−	0.392624i	−0.980541	−	0.196312i	$-0.937103\pi$
$593$		−	232.826i		−	0.392624i	0.980541	−	0.196312i	$-0.0628966\pi$
$594$		0			0
$595$	−448.000			−0.752941
$596$	−60.3902	−	19.6220i	−0.101326	−	0.0329228i
$597$	−189.475	−	638.479i	−0.317378	−	1.06948i
$598$	1495.06	+	1086.23i	2.50011	+	1.81643i
$599$	−831.208	+	270.076i	−1.38766	+	0.450878i	−0.905180	−	0.425029i	$-0.860264\pi$
$599$	−831.208	+	270.076i	−1.38766	+	0.450878i	−0.482480	+	0.875907i	$0.660264\pi$
$600$	3.46439	−	134.889i	0.00577398	−	0.224815i
$601$	−472.222	−	343.089i	−0.785727	−	0.570864i	0.120965	−	0.992657i	$-0.461401\pi$
$601$	−472.222	−	343.089i	−0.785727	−	0.570864i	−0.906692	+	0.421793i	$0.861401\pi$
$602$	−174.175	−	239.731i	−0.289327	−	0.398225i
$603$	316.810	−	206.192i	0.525391	−	0.341943i
$604$	−202.049			−0.334519
$605$		0			0
$606$	392.000	−	1108.74i	0.646865	−	1.82961i
$607$	−261.309	+	804.227i	−0.430493	+	1.32492i	0.467142	+	0.884182i	$0.345284\pi$
$607$	−261.309	+	804.227i	−0.430493	+	1.32492i	−0.897635	+	0.440739i	$0.854716\pi$
$608$	−349.127	−	480.532i	−0.574221	−	0.790348i
$609$	269.339	+	391.470i	0.442265	+	0.642807i
$610$	−224.964	−	692.369i	−0.368794	−	1.13503i
$611$	785.073	−	255.086i	1.28490	−	0.417489i
$612$	551.861	−	148.465i	0.901733	−	0.242590i
$613$	478.276	−	347.488i	0.780222	−	0.566865i	−0.124824	−	0.992179i	$-0.539836\pi$
$613$	478.276	−	347.488i	0.780222	−	0.566865i	0.905046	+	0.425314i	$0.139836\pi$
$614$	−376.599	−	122.364i	−0.613354	−	0.199291i
$615$	119.733	−	338.656i	0.194688	−	0.550660i
$616$		0			0
$617$		−	435.578i		−	0.705961i	−0.935631	−	0.352980i	$-0.885168\pi$
$617$		−	435.578i		−	0.705961i	0.935631	−	0.352980i	$-0.114832\pi$
$618$	−164.177	+	214.182i	−0.265658	+	0.346573i
$619$	677.956	−	492.564i	1.09524	−	0.795742i	0.114967	−	0.993369i	$-0.463324\pi$
$619$	677.956	−	492.564i	1.09524	−	0.795742i	0.980277	+	0.197628i	$0.0633237\pi$
$620$	−149.626	+	205.942i	−0.241332	+	0.332165i
$621$	544.601	−	639.595i	0.876974	−	1.02994i
$622$	20.8122	+	64.0535i	0.0334602	+	0.102980i
$623$	−273.704	+	376.721i	−0.439331	+	0.604688i
$624$	−364.056	−	1226.77i	−0.583422	−	1.96597i
$625$	27.5025	−	84.6440i	0.0440040	−	0.135430i
$626$			1053.01i			1.68212i
$627$		0			0
$628$	−258.000			−0.410828
$629$	−201.301	−	65.4066i	−0.320033	−	0.103985i
$630$	−503.336	−	25.8717i	−0.798945	−	0.0410662i
$631$	−205.490	−	149.297i	−0.325658	−	0.236605i	0.412928	−	0.910764i	$-0.364506\pi$
$631$	−205.490	−	149.297i	−0.325658	−	0.236605i	−0.738586	+	0.674159i	$0.764506\pi$
$632$	56.4899	−	18.3547i	0.0893827	−	0.0290422i
$633$	−1167.01	−	29.9727i	−1.84362	−	0.0473503i
$634$	−889.957	−	646.592i	−1.40372	−	1.01986i
$635$	111.970	+	154.113i	0.176330	+	0.242698i
$636$	−232.296	+	303.049i	−0.365245	+	0.476492i
$637$	−157.150			−0.246703
$638$		0			0
$639$	368.000	−	455.377i	0.575900	−	0.712640i
$640$	71.6866	−	220.629i	0.112010	−	0.344732i
$641$	69.8253	+	96.1063i	0.108932	+	0.149932i	0.860002	−	0.510290i	$-0.170462\pi$
$641$	69.8253	+	96.1063i	0.108932	+	0.149932i	−0.751070	+	0.660222i	$0.770462\pi$
$642$	−276.811	+	190.452i	−0.431169	+	0.296654i
$643$	−135.349	−	416.563i	−0.210497	−	0.647843i	−0.999443	−	0.0333799i	$-0.989373\pi$
$643$	−135.349	−	416.563i	−0.210497	−	0.647843i	0.788946	−	0.614463i	$-0.210627\pi$
$644$	−664.292	+	215.842i	−1.03151	+	0.335158i
$645$	71.9839	+	104.625i	0.111603	+	0.162209i
$646$	−678.062	+	492.641i	−1.04963	+	0.762602i
$647$	314.729	+	102.262i	0.486444	+	0.158055i	0.541963	−	0.840402i	$-0.317681\pi$
$647$	314.729	+	102.262i	0.486444	+	0.158055i	−0.0555189	+	0.998458i	$0.517681\pi$
$648$	−209.533	+	44.9778i	−0.323353	+	0.0694101i
$649$		0			0
$650$		−	1009.75i		−	1.55346i
$651$	534.528	+	409.731i	0.821088	+	0.629388i
$652$	−33.9787	+	24.6870i	−0.0521146	+	0.0378635i
$653$	367.414	−	505.702i	0.562656	−	0.774429i	−0.429005	−	0.903302i	$-0.641136\pi$
$653$	367.414	−	505.702i	0.562656	−	0.774429i	0.991661	+	0.128873i	$0.0411359\pi$
$654$	−13.7251	+	534.397i	−0.0209863	+	0.817120i
$655$	−203.497	−	626.301i	−0.310683	−	0.956185i
$656$	−472.761	+	650.699i	−0.720672	+	0.991919i
$657$	−672.610	−	34.5725i	−1.02376	−	0.0526218i
$658$	−224.964	+	692.369i	−0.341891	+	1.05223i
$659$			465.652i			0.706604i	0.935509	+	0.353302i	$0.114941\pi$
$659$			465.652i			0.706604i	−0.935509	+	0.353302i	$0.885059\pi$
$660$		0			0
$661$	−394.000			−0.596067			−0.298033	−	0.954555i	$-0.596331\pi$
$661$	−394.000			−0.596067			−0.298033	+	0.954555i	$0.596331\pi$
$662$	447.894	+	145.530i	0.676577	+	0.219833i
$663$	−1366.62	+	405.558i	−2.06127	+	0.611702i
$664$	45.3050	+	32.9160i	0.0682303	+	0.0495723i
$665$	301.279	−	97.8916i	0.453052	−	0.147205i
$666$	−222.388	−	85.1104i	−0.333915	−	0.127793i
$667$	−532.763	−	387.075i	−0.798746	−	0.580323i
$668$	−149.293	−	205.484i	−0.223492	−	0.307611i
$669$	−109.525	−	83.9541i	−0.163714	−	0.125492i
$670$	314.299			0.469103
$671$		0			0
$672$	840.000	+	296.985i	1.25000	+	0.441942i
$673$	272.872	−	839.813i	0.405456	−	1.24786i	−0.515059	−	0.857155i	$-0.672230\pi$
$673$	272.872	−	839.813i	0.405456	−	1.24786i	0.920514	−	0.390709i	$-0.127770\pi$
$674$	−395.677	−	544.602i	−0.587058	−	0.808016i
$675$	−457.639	−	35.3232i	−0.677983	−	0.0523306i
$676$	−310.562	−	955.812i	−0.459411	−	1.41392i
$677$	865.593	−	281.248i	1.27857	−	0.415433i	0.410495	−	0.911863i	$-0.365356\pi$
$677$	865.593	−	281.248i	1.27857	−	0.415433i	0.868077	+	0.496430i	$0.165356\pi$
$678$	776.798	−	534.453i	1.14572	−	0.788279i
$679$	−448.006	+	325.495i	−0.659802	+	0.479374i
$680$	−150.640	−	48.9458i	−0.221529	−	0.0719791i
$681$	598.665	+	211.660i	0.879097	+	0.310808i
$682$		0			0
$683$			435.578i			0.637742i	0.947798	+	0.318871i	$0.103304\pi$
$683$			435.578i			0.637742i	−0.947798	+	0.318871i	$0.896696\pi$
$684$	−338.685	+	220.428i	−0.495153	+	0.322264i
$685$	362.440	−	263.328i	0.529109	−	0.384420i
$686$	−488.777	+	672.744i	−0.712503	+	0.980677i
$687$	−353.883	−	9.08889i	−0.515114	−	0.0132298i
$688$	−87.8739	−	270.448i	−0.127724	−	0.393093i
$689$	559.848	−	770.565i	0.812552	−	1.11838i
$690$	669.615	−	198.715i	0.970457	−	0.287993i
$691$	131.641	−	405.150i	0.190508	−	0.586324i	−0.809491	−	0.587132i	$-0.800257\pi$
$691$	131.641	−	405.150i	0.190508	−	0.586324i	1.00000		0.000807501i	$0.000257036\pi$
$692$			571.482i			0.825841i
$693$		0			0
$694$	−1288.00			−1.85591
$695$	241.561	+	78.4879i	0.347570	+	0.112932i
$696$	47.7955	+	161.058i	0.0686717	+	0.231405i
$697$	724.879	+	526.656i	1.04000	+	0.755603i
$698$	−169.470	+	55.0640i	−0.242793	+	0.0788883i
$699$	−6.52120	+	253.908i	−0.00932933	+	0.363245i
$700$	308.761	+	224.328i	0.441087	+	0.320468i
$701$	−161.734	−	222.608i	−0.230719	−	0.317557i	0.677924	−	0.735132i	$-0.262880\pi$
$701$	−161.734	−	222.608i	−0.230719	−	0.317557i	−0.908642	+	0.417575i	$0.862880\pi$
$702$	−1558.84	+	376.730i	−2.22057	+	0.536652i
$703$	149.666			0.212897
$704$		0			0
$705$	104.000	−	294.156i	0.147518	−	0.417243i
$706$	−101.749	+	313.150i	−0.144120	+	0.443556i
$707$	−651.703	−	896.992i	−0.921786	−	1.26873i
$708$	−173.147	−	251.659i	−0.244557	−	0.355451i
$709$	−12.9787	−	39.9444i	−0.0183057	−	0.0563390i	0.941486	−	0.337051i	$-0.109429\pi$
$709$	−12.9787	−	39.9444i	−0.0183057	−	0.0563390i	−0.959792	+	0.280712i	$0.909429\pi$
$710$	462.992	−	150.435i	0.652101	−	0.211880i
$711$	−52.4903	−	195.112i	−0.0738260	−	0.274419i
$712$	−133.191	+	96.7688i	−0.187066	+	0.135911i
$713$	−887.698	−	288.431i	−1.24502	−	0.404531i
$714$	419.066	−	1185.30i	0.586927	−	1.66008i
$715$		0			0
$716$		−	950.352i		−	1.32731i
$717$	−77.2597	+	100.792i	−0.107754	+	0.140574i
$718$	543.659	−	394.992i	0.757186	−	0.550128i
$719$	−254.364	+	350.102i	−0.353774	+	0.486928i	−0.948401	−	0.317073i	$-0.897300\pi$
$719$	−254.364	+	350.102i	−0.353774	+	0.486928i	0.594627	+	0.804002i	$0.297300\pi$
$720$	−451.710	−	172.875i	−0.627376	−	0.240104i
$721$	78.6240	+	241.980i	0.109049	+	0.335617i
$722$	−213.053	+	293.243i	−0.295088	+	0.406153i
$723$	127.739	+	430.445i	0.176679	+	0.595359i
$724$	242.887	−	747.530i	0.335480	−	1.03250i
$725$			359.822i			0.496306i
$726$		0			0
$727$	1102.00			1.51582			0.757909	−	0.652360i	$-0.226221\pi$
$727$	1102.00			1.51582			0.757909	+	0.652360i	$0.226221\pi$
$728$	−422.732	−	137.354i	−0.580675	−	0.188673i
$729$	116.210	+	719.678i	0.159410	+	0.987212i
$730$	−453.050	−	329.160i	−0.620616	−	0.450904i
$731$	−301.279	+	97.8916i	−0.412147	+	0.133915i
$732$	875.259	+	22.4795i	1.19571	+	0.0307097i
$733$	393.518	+	285.908i	0.536860	+	0.390052i	0.822918	−	0.568161i	$-0.192345\pi$
$733$	393.518	+	285.908i	0.536860	+	0.390052i	−0.286058	+	0.958212i	$0.592345\pi$
$734$	220.829	+	303.945i	0.300857	+	0.414094i
$735$	−36.1349	+	47.1409i	−0.0491631	+	0.0641373i
$736$	−1234.75			−1.67765
$737$		0			0
$738$	784.000	+	633.568i	1.06233	+	0.858493i
$739$	323.746	−	996.388i	0.438087	−	1.34829i	−0.451804	−	0.892117i	$-0.649219\pi$
$739$	323.746	−	996.388i	0.438087	−	1.34829i	0.889890	−	0.456175i	$-0.150781\pi$
$740$	−49.8752	−	68.6474i	−0.0673990	−	0.0927667i
$741$	830.432	−	571.355i	1.12069	−	0.771059i
$742$	259.574	+	798.887i	0.349831	+	1.07667i
$743$	−241.561	+	78.4879i	−0.325116	+	0.105636i	−0.467027	−	0.884243i	$-0.654675\pi$
$743$	−241.561	+	78.4879i	−0.325116	+	0.105636i	0.141912	+	0.989879i	$0.454675\pi$
$744$	134.970	+	196.171i	0.181411	+	0.263671i
$745$	48.4330	−	35.1887i	0.0650108	−	0.0472331i
$746$	1073.31	+	348.739i	1.43875	+	0.467478i
$747$	119.733	−	148.162i	0.160285	−	0.198343i
$748$		0			0
$749$			316.784i			0.422942i
$750$	−748.339	−	573.624i	−0.997786	−	0.764832i
$751$	−283.156	+	205.725i	−0.377039	+	0.273935i	−0.760124	−	0.649779i	$-0.774862\pi$
$751$	−283.156	+	205.725i	−0.377039	+	0.273935i	0.383085	+	0.923713i	$0.374862\pi$
$752$	−410.639	+	565.197i	−0.546063	+	0.751591i
$753$	3.92145	−	152.685i	0.00520776	−	0.202769i
$754$	388.495	+	1195.67i	0.515246	+	1.58576i
$755$	111.970	−	154.113i	0.148304	−	0.204123i
$756$	231.119	−	560.357i	0.305713	−	0.741213i
$757$	90.8510	−	279.611i	0.120015	−	0.369367i	−0.872945	−	0.487818i	$-0.837793\pi$
$757$	90.8510	−	279.611i	0.120015	−	0.369367i	0.992960	+	0.118451i	$0.0377930\pi$
$758$		−	926.013i		−	1.22165i
$759$		0			0
$760$	112.000			0.147368
$761$	−744.813	−	242.004i	−0.978729	−	0.318008i	−0.224394	−	0.974498i	$-0.572040\pi$
$761$	−744.813	−	242.004i	−0.978729	−	0.318008i	−0.754335	+	0.656490i	$0.772040\pi$
$762$	−512.483	+	152.084i	−0.672549	+	0.199586i
$763$	407.745	+	296.244i	0.534397	+	0.388262i
$764$	−169.470	+	55.0640i	−0.221819	+	0.0720733i
$765$	−192.583	+	503.206i	−0.251742	+	0.657785i
$766$	1107.91	+	804.941i	1.44635	+	1.05084i
$767$	447.878	+	616.452i	0.583935	+	0.803718i
$768$	792.865	+	607.754i	1.03238	+	0.791347i
$769$	838.131			1.08990			0.544949	−	0.838469i	$-0.316549\pi$
$769$	838.131			1.08990			0.544949	+	0.838469i	$0.316549\pi$
$770$		0			0
$771$	−272.000	−	96.1665i	−0.352789	−	0.124730i
$772$	138.748	−	427.023i	0.179726	−	0.553139i
$773$	−241.064	−	331.796i	−0.311855	−	0.429231i	0.624104	−	0.781341i	$-0.285464\pi$
$773$	−241.064	−	331.796i	−0.311855	−	0.429231i	−0.935959	+	0.352110i	$0.885464\pi$
$774$	−344.146	+	92.5842i	−0.444633	+	0.119618i
$775$	157.599	+	485.039i	0.203353	+	0.625857i
$776$	−186.203	+	60.5011i	−0.239953	+	0.0779653i
$777$	−184.952	+	127.251i	−0.238033	+	0.163772i
$778$	938.390	−	681.780i	1.20616	−	0.876324i
$779$	−602.559	−	195.783i	−0.773503	−	0.251326i
$780$	−538.799	−	190.494i	−0.690768	−	0.244223i
$781$		0			0
$782$			1742.31i			2.22802i
$783$	555.491	−	134.247i	0.709439	−	0.171452i
$784$	107.599	−	78.1754i	0.137244	−	0.0997136i
$785$	142.976	−	196.789i	0.182135	−	0.250687i
$786$	1847.39	+	47.4471i	2.35037	+	0.0603652i
$787$	−97.1238	−	298.916i	−0.123410	−	0.379817i	0.870198	−	0.492702i	$-0.163991\pi$
$787$	−97.1238	−	298.916i	−0.123410	−	0.379817i	−0.993608	+	0.112885i	$0.963991\pi$
$788$	−410.555	+	565.081i	−0.521009	+	0.717108i
$789$	−1339.23	+	397.430i	−1.69738	+	0.503713i
$790$	51.9149	−	159.777i	0.0657150	−	0.202250i
$791$		−	888.972i		−	1.12386i
$792$		0			0
$793$	−2184.00			−2.75410
$794$	1112.19	+	361.371i	1.40074	+	0.455128i
$795$	−102.419	−	345.124i	−0.128829	−	0.434118i
$796$	538.805	+	391.465i	0.676891	+	0.491790i
$797$	234.029	−	76.0408i	0.293638	−	0.0954088i	−0.158494	−	0.987360i	$-0.550664\pi$
$797$	234.029	−	76.0408i	0.293638	−	0.0954088i	0.452132	+	0.891951i	$0.350664\pi$
$798$	−22.8242	+	888.679i	−0.0286018	+	1.11363i
$799$	629.629	+	457.453i	0.788022	+	0.572531i
$800$	396.559	+	545.817i	0.495699	+	0.682271i
$801$	305.485	+	469.373i	0.381380	+	0.585984i
$802$	1391.90			1.73553
$803$		0			0
$804$	−126.000	+	356.382i	−0.156716	+	0.443261i
$805$	203.497	−	626.301i	0.252792	−	0.778013i
$806$	1047.38	+	1441.59i	1.29948	+	1.78858i
$807$	−630.061	−	915.759i	−0.780745	−	1.13477i
$808$	−121.135	−	372.814i	−0.149919	−	0.461404i
$809$	−241.561	+	78.4879i	−0.298592	+	0.0970184i	−0.454482	−	0.890756i	$-0.650176\pi$
$809$	−241.561	+	78.4879i	−0.298592	+	0.0970184i	0.155890	+	0.987774i	$0.450176\pi$
$810$	−245.430	+	554.238i	−0.303000	+	0.684245i
$811$	−787.037	+	571.816i	−0.970452	+	0.705075i	−0.955555	−	0.294814i	$-0.904742\pi$
$811$	−787.037	+	571.816i	−0.970452	+	0.705075i	−0.0148976	+	0.999889i	$0.504742\pi$
$812$	−451.919	−	146.837i	−0.556550	−	0.180834i
$813$	−336.749	+	952.470i	−0.414206	+	1.17155i
$814$		0			0
$815$		−	39.5980i		−	0.0485865i
$816$	733.967	−	957.520i	0.899469	−	1.17343i
$817$	181.220	−	131.664i	0.221811	−	0.161155i
$818$	349.127	−	480.532i	0.426805	−	0.587447i
$819$	−540.434	+	1412.12i	−0.659871	+	1.72420i
$820$	110.999	+	341.619i	0.135364	+	0.416608i
$821$	286.145	−	393.844i	0.348532	−	0.479713i	−0.598377	−	0.801215i	$-0.704188\pi$
$821$	286.145	−	393.844i	0.348532	−	0.479713i	0.946909	+	0.321502i	$0.104188\pi$
$822$	357.669	+	1205.25i	0.435120	+	1.46624i
$823$	321.996	−	991.001i	0.391246	−	1.20413i	−0.540600	−	0.841280i	$-0.681803\pi$
$823$	321.996	−	991.001i	0.391246	−	1.20413i	0.931847	−	0.362853i	$-0.118197\pi$
$824$			89.9555i			0.109169i
$825$		0			0
$826$	−672.000			−0.813559
$827$	−1187.67	−	385.899i	−1.43612	−	0.466625i	−0.515437	−	0.856927i	$-0.672370\pi$
$827$	−1187.67	−	385.899i	−1.43612	−	0.466625i	−0.920687	+	0.390303i	$0.872370\pi$
$828$	−43.1217	+	838.935i	−0.0520793	+	1.01321i
$829$	−953.022	−	692.411i	−1.14960	−	0.835236i	−0.161176	−	0.986926i	$-0.551529\pi$
$829$	−953.022	−	692.411i	−1.14960	−	0.835236i	−0.988428	+	0.151689i	$0.951529\pi$
$830$	150.640	−	48.9458i	0.181494	−	0.0589708i
$831$	67.3276	+	1.72920i	0.0810200	+	0.00208086i
$832$	526.709	+	382.677i	0.633064	+	0.459948i
$833$	−87.0875	−	119.866i	−0.104547	−	0.143896i
$834$	−433.619	+	565.691i	−0.519927	+	0.678287i
$835$	239.466			0.286786
$836$		0			0
$837$	690.000	−	424.264i	0.824373	−	0.506887i
$838$	−559.618	+	1722.33i	−0.667802	+	2.05528i
$839$	600.165	+	826.057i	0.715334	+	0.984573i	0.999666	+	0.0258470i	$0.00822826\pi$
$839$	600.165	+	826.057i	0.715334	+	0.984573i	−0.284332	+	0.958726i	$0.591772\pi$
$840$	−138.405	+	95.2258i	−0.164768	+	0.113364i
$841$	121.444	+	373.765i	0.144404	+	0.444430i
$842$	669.325	−	217.477i	0.794923	−	0.258286i
$843$	35.9920	+	52.3123i	0.0426951	+	0.0620549i
$844$	944.444	−	686.179i	1.11901	−	0.813008i
$845$	901.148	+	292.801i	1.06645	+	0.346510i
$846$	680.982	+	550.316i	0.804943	+	0.650492i
$847$		0			0
$848$			806.102i			0.950592i
$849$	−427.622	−	327.785i	−0.503678	−	0.386084i
$850$	770.184	−	559.572i	0.906099	−	0.658319i
$851$	182.876	−	251.707i	0.214895	−	0.295778i
$852$	−15.0322	+	585.291i	−0.0176434	+	0.686962i
$853$	182.685	+	562.247i	0.214168	+	0.659141i	0.999212	+	0.0397007i	$0.0126405\pi$
$853$	182.685	+	562.247i	0.214168	+	0.659141i	−0.785044	+	0.619440i	$0.787360\pi$
$854$	1132.14	−	1558.25i	1.32569	−	1.82465i
$855$	19.5572	−	380.486i	0.0228739	−	0.445013i
$856$	−34.6099	+	106.518i	−0.0404321	+	0.124437i
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	706.000			0.821886			0.410943	−	0.911661i	$-0.365200\pi$
$859$	706.000			0.821886			0.410943	+	0.911661i	$0.365200\pi$
$860$	−120.780	−	39.2439i	−0.140442	−	0.0456325i
$861$	911.080	−	270.372i	1.05817	−	0.314021i
$862$	−1177.93	−	855.815i	−1.36651	−	0.992825i
$863$	470.749	−	152.956i	0.545480	−	0.177237i	−0.0232978	−	0.999729i	$-0.507417\pi$
$863$	470.749	−	152.956i	0.545480	−	0.177237i	0.568777	+	0.822491i	$0.307417\pi$
$864$	694.674	−	815.845i	0.804021	−	0.944265i
$865$	−435.897	−	316.698i	−0.503927	−	0.366125i
$866$	−1147.69	−	1579.66i	−1.32528	−	1.82409i
$867$	−378.575	−	290.189i	−0.436650	−	0.334705i
$868$	−673.498			−0.775920
$869$		0			0
$870$	448.000	+	158.392i	0.514943	+	0.182060i
$871$	291.371	−	896.749i	0.334525	−	1.02956i
$872$	104.738	+	144.159i	0.120112	+	0.165320i
$873$	173.020	+	643.133i	0.198190	+	0.736693i
$874$	−380.709	−	1171.70i	−0.435594	−	1.34062i
$875$	−845.463	+	274.708i	−0.966243	+	0.313952i
$876$	554.856	−	381.752i	0.633397	−	0.435790i
$877$	78.7037	−	57.1816i	0.0897419	−	0.0652013i	−0.542010	−	0.840372i	$-0.682336\pi$
$877$	78.7037	−	57.1816i	0.0897419	−	0.0652013i	0.631751	+	0.775171i	$0.282336\pi$
$878$	1073.31	+	348.739i	1.22245	+	0.397197i
$879$	−59.8665	−	21.1660i	−0.0681075	−	0.0240796i
$880$		0			0
$881$		−	1493.41i		−	1.69513i	−0.530692	−	0.847565i	$-0.678068\pi$
$881$		−	1493.41i		−	1.69513i	0.530692	−	0.847565i	$-0.321932\pi$
$882$	−90.9221	−	139.700i	−0.103086	−	0.158390i
$883$	−69.5755	+	50.5495i	−0.0787944	+	0.0572475i	−0.626485	−	0.779433i	$-0.715507\pi$
$883$	−69.5755	+	50.5495i	−0.0787944	+	0.0572475i	0.547691	+	0.836681i	$0.315507\pi$
$884$	837.904	−	1153.28i	0.947855	−	1.30461i
$885$	287.905	+	7.39435i	0.325316	+	0.00835520i
$886$	97.1238	+	298.916i	0.109621	+	0.337377i
$887$	149.293	−	205.484i	0.168312	−	0.231662i	−0.716526	−	0.697560i	$-0.754269\pi$
$887$	149.293	−	205.484i	0.168312	−	0.231662i	0.884838	+	0.465899i	$0.154269\pi$
$888$	−76.0926	+	22.5812i	−0.0856899	+	0.0254293i
$889$	−155.745	+	479.332i	−0.175191	+	0.539182i
$890$			465.652i			0.523205i
$891$		0			0
$892$	138.000			0.154709
$893$	−523.382	−	170.057i	−0.586094	−	0.190433i
$894$	47.7955	+	161.058i	0.0534625	+	0.180154i
$895$	724.879	+	526.656i	0.809921	+	0.588442i
$896$	583.729	−	189.665i	0.651483	−	0.211680i
$897$	53.7999	−	2094.74i	0.0599776	−	2.33528i
$898$	−1089.74	−	791.745i	−1.21352	−	0.881676i
$899$	−373.232	−	513.710i	−0.415164	−	0.571424i
$900$	384.698	−	250.376i	0.427443	−	0.278195i
$901$	897.998			0.996668
$902$		0			0
$903$	−112.000	+	316.784i	−0.124031	+	0.350813i
$904$	97.1238	−	298.916i	0.107438	−	0.330660i
$905$	435.577	+	599.520i	0.481301	+	0.662453i
$906$	303.007	+	440.403i	0.334444	+	0.486096i
$907$	−298.510	−	918.721i	−0.329118	−	1.01292i	−0.969547	−	0.244905i	$-0.921243\pi$
$907$	−298.510	−	918.721i	−0.329118	−	1.01292i	0.640429	−	0.768018i	$-0.278757\pi$
$908$	−603.902	+	196.220i	−0.665090	+	0.216101i
$909$	−1287.67	+	346.418i	−1.41658	+	0.381098i
$910$	−1017.09	+	738.962i	−1.11769	+	0.812046i
$911$	1379.97	+	448.378i	1.51478	+	0.492183i	0.944288	−	0.329119i	$-0.106752\pi$
$911$	1379.97	+	448.378i	1.51478	+	0.492183i	0.570494	+	0.821302i	$0.306752\pi$
$912$	−284.366	+	804.308i	−0.311805	+	0.881917i
$913$		0			0
$914$			1781.91i			1.94957i
$915$	−502.188	+	655.145i	−0.548839	+	0.716006i
$916$	286.392	−	208.076i	0.312655	−	0.227157i
$917$	1024.10	−	1409.56i	1.11680	−	1.53714i
$918$	−1151.21	−	980.232i	−1.25404	−	1.06779i
$919$	−122.561	−	377.204i	−0.133363	−	0.410450i	0.861968	−	0.506962i	$-0.169232\pi$
$919$	−122.561	−	377.204i	−0.133363	−	0.410450i	−0.995332	+	0.0965115i	$0.969232\pi$
$920$	136.852	−	188.360i	0.148752	−	0.204739i
$921$	127.739	+	430.445i	0.138696	+	0.467367i
$922$	571.063	−	1757.55i	0.619375	−	1.90624i
$923$		−	1460.45i		−	1.58229i
$924$		0			0
$925$	−170.000			−0.183784
$926$	2219.34	+	721.107i	2.39670	+	0.778734i
$927$	305.597	+	15.7078i	0.329662	+	0.0169448i
$928$	−679.574	−	493.740i	−0.732300	−	0.532047i
$929$	−1452.60	+	471.977i	−1.56361	+	0.508049i	−0.957770	−	0.287535i	$-0.907164\pi$
$929$	−1452.60	+	471.977i	−1.56361	+	0.508049i	−0.605843	+	0.795584i	$0.707164\pi$
$930$	673.276	+	17.2920i	0.723953	+	0.0185935i
$931$	84.7578	+	61.5801i	0.0910395	+	0.0661441i
$932$	−149.293	−	205.484i	−0.160185	−	0.220476i
$933$	46.4592	−	60.6098i	0.0497955	−	0.0649623i
$934$	−1406.86			−1.50628
$935$		0			0
$936$	−336.000	+	415.779i	−0.358974	+	0.444208i
$937$	−388.495	+	1195.67i	−0.414616	+	1.27606i	0.497978	+	0.867190i	$0.334076\pi$
$937$	−388.495	+	1195.67i	−0.414616	+	1.27606i	−0.912594	+	0.408867i	$0.865924\pi$
$938$	488.777	+	672.744i	0.521085	+	0.717211i
$939$	983.667	−	676.783i	1.04757	−	0.720749i
$940$	96.4133	+	296.730i	0.102567	+	0.315670i
$941$	−462.992	+	150.435i	−0.492021	+	0.159867i	−0.544510	−	0.838754i	$-0.683284\pi$
$941$	−462.992	+	150.435i	−0.492021	+	0.159867i	0.0524893	+	0.998621i	$0.483284\pi$
$942$	386.914	+	562.357i	0.410736	+	0.596982i
$943$	−1065.53	+	774.150i	−1.12993	+	0.820944i
$944$	−613.319	−	199.279i	−0.649702	−	0.211101i
$945$	299.333	+	486.818i	0.316754	+	0.515152i
$946$		0			0
$947$		−	435.578i		−	0.459955i	−0.973196	−	0.229978i	$-0.926135\pi$
$947$		−	435.578i		−	0.459955i	0.973196	−	0.229978i	$-0.0738653\pi$
$948$	160.358	+	122.919i	0.169154	+	0.129662i
$949$	−1359.15	+	987.479i	−1.43219	+	1.04055i
$950$	−395.677	+	544.602i	−0.416502	+	0.573266i
$951$	−32.0251	+	1246.93i	−0.0336752	+	1.31117i
$952$	−129.498	−	398.555i	−0.136028	−	0.418650i
$953$	−945.521	+	1301.40i	−0.992152	+	1.36558i	−0.0621339	+	0.998068i	$0.519791\pi$
$953$	−945.521	+	1301.40i	−0.992152	+	1.36558i	−0.930018	+	0.367513i	$0.880209\pi$
$954$	1008.92	+	51.8587i	1.05756	+	0.0543593i
$955$	51.9149	−	159.777i	0.0543611	−	0.167306i
$956$		−	126.996i		−	0.132841i
$957$		0			0
$958$	1792.00			1.87056
$959$	1127.28	+	366.277i	1.17548	+	0.381936i
$960$	235.905	−	70.0071i	0.245734	−	0.0729240i
$961$	49.3500	+	35.8549i	0.0513528	+	0.0373100i
$962$	−564.899	+	183.547i	−0.587213	+	0.190797i
$963$	355.820	+	136.177i	0.369491	+	0.141409i
$964$	−363.248	−	263.915i	−0.376813	−	0.273771i
$965$	248.821	+	342.473i	0.257846	+	0.354895i
$966$	1466.68	+	1124.25i	1.51830	+	1.16382i
$967$	−1055.15			−1.09116			−0.545578	−	0.838060i	$-0.683690\pi$
$967$	−1055.15			−1.09116			−0.545578	+	0.838060i	$0.683690\pi$
$968$		0			0
$969$	896.000	+	316.784i	0.924665	+	0.326918i
$970$	−171.123	+	526.662i	−0.176415	+	0.542951i
$971$	−149.626	−	205.942i	−0.154094	−	0.212093i	0.724989	−	0.688760i	$-0.241845\pi$
$971$	−149.626	−	205.942i	−0.154094	−	0.212093i	−0.879084	+	0.476667i	$0.841845\pi$
$972$	−530.057	−	500.481i	−0.545326	−	0.514898i
$973$	207.659	+	639.110i	0.213422	+	0.656845i
$974$	−880.691	+	286.154i	−0.904200	+	0.293792i
$975$	−943.255	+	648.979i	−0.967441	+	0.665620i
$976$	1495.37	−	1086.45i	1.53214	−	1.11317i
$977$	−1371.90	−	445.756i	−1.40419	−	0.456250i	−0.493649	−	0.869661i	$-0.664337\pi$
$977$	−1371.90	−	445.756i	−1.40419	−	0.456250i	−0.910544	+	0.413411i	$0.864337\pi$
$978$	104.766	+	37.0405i	0.107123	+	0.0378737i
$979$		0			0
$980$		−	59.3970i		−	0.0606092i
$981$	508.027	−	330.643i	0.517866	−	0.337047i
$982$	543.659	−	394.992i	0.553625	−	0.402232i
$983$	403.989	−	556.044i	0.410976	−	0.565660i	−0.552480	−	0.833526i	$-0.686318\pi$
$983$	403.989	−	556.044i	0.410976	−	0.565660i	0.963456	+	0.267866i	$0.0863185\pi$
$984$	335.889	+	8.62674i	0.341351	+	0.00876701i
$985$	−203.497	−	626.301i	−0.206596	−	0.635838i
$986$	−696.700	+	958.925i	−0.706592	+	0.972541i
$987$	791.363	−	234.845i	0.801787	−	0.237938i
$988$	−311.489	+	958.665i	−0.315272	+	0.970309i
$989$		−	465.652i		−	0.470831i
$990$		0			0
$991$	574.000			0.579213			0.289606	−	0.957146i	$-0.406476\pi$
$991$	574.000			0.579213			0.289606	+	0.957146i	$0.406476\pi$
$992$	−1132.32	−	367.912i	−1.14145	−	0.370879i
$993$	−151.921	−	511.933i	−0.152992	−	0.515542i
$994$	1042.01	+	757.067i	1.04830	+	0.761637i
$995$	−597.179	+	194.035i	−0.600180	+	0.195010i
$996$	−4.89090	+	190.431i	−0.00491054	+	0.191196i
$997$	−1071.58	−	778.549i	−1.07481	−	0.780892i	−0.0980354	−	0.995183i	$-0.531256\pi$
$997$	−1071.58	−	778.549i	−1.07481	−	0.780892i	−0.976770	+	0.214291i	$0.931256\pi$
$998$	152.403	+	209.765i	0.152709	+	0.210185i
$999$	63.4258	+	262.445i	0.0634893	+	0.262707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.k.251.3		16
3.2	odd	2	inner	363.3.h.k.251.2		16
11.2	odd	10	inner	363.3.h.k.245.3		16
11.3	even	5	inner	363.3.h.k.323.4		16
11.4	even	5		363.3.b.i.122.4	yes	4
11.5	even	5	inner	363.3.h.k.269.2		16
11.6	odd	10	inner	363.3.h.k.269.4		16
11.7	odd	10		363.3.b.i.122.2	yes	4
11.8	odd	10	inner	363.3.h.k.323.2		16
11.9	even	5	inner	363.3.h.k.245.1		16
11.10	odd	2	inner	363.3.h.k.251.1		16
33.2	even	10	inner	363.3.h.k.245.2		16
33.5	odd	10	inner	363.3.h.k.269.3		16
33.8	even	10	inner	363.3.h.k.323.3		16
33.14	odd	10	inner	363.3.h.k.323.1		16
33.17	even	10	inner	363.3.h.k.269.1		16
33.20	odd	10	inner	363.3.h.k.245.4		16
33.26	odd	10		363.3.b.i.122.1	✓	4
33.29	even	10		363.3.b.i.122.3	yes	4
33.32	even	2	inner	363.3.h.k.251.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.i.122.1	✓	4	33.26	odd	10
363.3.b.i.122.2	yes	4	11.7	odd	10
363.3.b.i.122.3	yes	4	33.29	even	10
363.3.b.i.122.4	yes	4	11.4	even	5
363.3.h.k.245.1		16	11.9	even	5	inner
363.3.h.k.245.2		16	33.2	even	10	inner
363.3.h.k.245.3		16	11.2	odd	10	inner
363.3.h.k.245.4		16	33.20	odd	10	inner
363.3.h.k.251.1		16	11.10	odd	2	inner
363.3.h.k.251.2		16	3.2	odd	2	inner
363.3.h.k.251.3		16	1.1	even	1	trivial
363.3.h.k.251.4		16	33.32	even	2	inner
363.3.h.k.269.1		16	33.17	even	10	inner
363.3.h.k.269.2		16	11.5	even	5	inner
363.3.h.k.269.3		16	33.5	odd	10	inner
363.3.h.k.269.4		16	11.6	odd	10	inner
363.3.h.k.323.1		16	33.14	odd	10	inner
363.3.h.k.323.2		16	11.8	odd	10	inner
363.3.h.k.323.3		16	33.8	even	10	inner
363.3.h.k.323.4		16	11.3	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.51626 + 0.817582i) q^{2} +(-0.853491 - 2.87603i) q^{3} +(2.42705 + 1.76336i) q^{4} +(-2.68999 + 0.874032i) q^{5} +(0.203788 - 7.93464i) q^{6} +(-6.05413 - 4.39858i) q^{7} +(-1.55513 - 2.14046i) q^{8} +(-7.54311 + 4.90933i) q^{9} -7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +(-6.93741 + 21.3512i) q^{13} +(-11.6376 - 16.0177i) q^{14} +(4.80963 + 6.99053i) q^{15} +(-5.87132 - 18.0701i) q^{16} +(-20.1301 + 6.54066i) q^{17} +(-22.9942 + 6.18604i) q^{18} +(12.1083 - 8.79716i) q^{19} +(-8.06998 - 2.62210i) q^{20} +(-7.48331 + 21.1660i) q^{21} -31.1127i q^{23} +(-4.82873 + 6.29947i) q^{24} +(-13.7533 + 9.99235i) q^{25} +(-34.9127 + 48.0532i) q^{26} +(20.5574 + 17.5041i) q^{27} +(-6.93741 - 21.3512i) q^{28} +(12.4411 - 17.1237i) q^{29} +(6.38694 + 21.5222i) q^{30} +(9.27051 - 28.5317i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(20.1301 + 6.54066i) q^{35} +(-26.9644 - 1.38598i) q^{36} +(8.09017 + 5.87785i) q^{37} +(37.6599 - 12.2364i) q^{38} +(67.3276 + 1.72920i) q^{39} +(6.05413 + 4.39858i) q^{40} +(-24.8821 - 34.2473i) q^{41} +(-36.1349 + 47.1409i) q^{42} +14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} +(25.4372 - 78.2876i) q^{46} +(-21.6126 - 29.7472i) q^{47} +(-46.9590 + 32.3087i) q^{48} +(2.16312 + 6.65740i) q^{49} +(-42.7764 + 13.8989i) q^{50} +(35.9920 + 52.3123i) q^{51} +(-54.4872 + 39.5872i) q^{52} +(-40.3499 - 13.1105i) q^{53} +(37.4166 + 60.8523i) q^{54} +19.7990i q^{56} +(-35.6352 - 27.3154i) q^{57} +(45.3050 - 32.9160i) q^{58} +(19.9501 - 27.4589i) q^{59} +(-0.653574 + 25.4475i) q^{60} +(30.0621 + 92.5217i) q^{61} +(46.6540 - 64.2137i) q^{62} +(67.2610 + 3.45725i) q^{63} +(8.96149 - 27.5806i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(-60.3902 - 19.6220i) q^{68} +(-89.4811 + 26.5544i) q^{69} +(45.3050 + 32.9160i) q^{70} +(-61.8699 + 20.1027i) q^{71} +(22.2388 + 8.51104i) q^{72} +(60.5413 + 43.9858i) q^{73} +(15.5513 + 21.4046i) q^{74} +(40.4766 + 31.0265i) q^{75} +44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +(-6.93741 + 21.3512i) q^{79} +(31.5876 + 43.4767i) q^{80} +(32.7969 - 74.0632i) q^{81} +(-34.6099 - 106.518i) q^{82} +(-20.1301 + 6.54066i) q^{83} +(-55.4856 + 38.1752i) q^{84} +(48.4330 - 35.1887i) q^{85} +(37.6599 + 12.2364i) q^{86} +(-59.8665 - 21.1660i) q^{87} -62.2254i q^{89} +(56.4474 - 36.7381i) q^{90} +(135.915 - 98.7479i) q^{91} +(54.8628 - 75.5121i) q^{92} +(-89.9703 - 2.31073i) q^{93} +(-30.0621 - 92.5217i) q^{94} +(-24.8821 + 34.2473i) q^{95} +(-114.139 + 33.8719i) q^{96} +(22.8673 - 70.3782i) q^{97} +18.5203i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 12 q^{4} + 28 q^{9} + 48 q^{12} + 32 q^{15} + 76 q^{16} - 68 q^{25} - 92 q^{27} - 120 q^{31} - 896 q^{34} - 84 q^{36} + 40 q^{37} + 224 q^{42} + 256 q^{45} - 76 q^{48} - 28 q^{49} + 224 q^{58}+ \cdots - 296 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 + 12 * q^4 + 28 * q^9 + 48 * q^12 + 32 * q^15 + 76 * q^16 - 68 * q^25 - 92 * q^27 - 120 * q^31 - 896 * q^34 - 84 * q^36 + 40 * q^37 + 224 * q^42 + 256 * q^45 - 76 * q^48 - 28 * q^49 + 224 * q^58 - 96 * q^60 - 116 * q^64 - 672 * q^67 - 352 * q^69 + 224 * q^70 + 68 * q^75 + 2688 * q^78 - 68 * q^81 + 448 * q^82 + 672 * q^91 + 120 * q^93 - 296 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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