LMFDB - Embedded newform 368.3.k.b.45.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,3,Mod(45,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("368.45");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$368 = 2^{4} \cdot 23$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	368.k (of order $4$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.0272737285$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$88$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			45.11
Character	$\chi$	$=$	368.45
Dual form			368.3.k.b.229.11

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88889 - 0.657339i) q^{2} +(-0.875057 - 0.875057i) q^{3} +(3.13581 + 2.48328i) q^{4} +(-6.27246 - 6.27246i) q^{5} +(1.07768 + 2.22809i) q^{6} -13.5040 q^{7} +(-4.29085 - 6.75194i) q^{8} -7.46855i q^{9} +(7.72485 + 15.9711i) q^{10} +(-9.24750 - 9.24750i) q^{11} +(-0.571000 - 4.91702i) q^{12} +(5.06345 + 5.06345i) q^{13} +(25.5076 + 8.87670i) q^{14} +10.9775i q^{15} +(3.66662 + 15.5742i) q^{16} +11.9217i q^{17} +(-4.90937 + 14.1073i) q^{18} +(21.6286 - 21.6286i) q^{19} +(-4.09296 - 35.2455i) q^{20} +(11.8168 + 11.8168i) q^{21} +(11.3888 + 23.5463i) q^{22} +(-9.25829 - 21.0543i) q^{23} +(-2.15359 + 9.66306i) q^{24} +53.6875i q^{25} +(-6.23590 - 12.8927i) q^{26} +(-14.4109 + 14.4109i) q^{27} +(-42.3460 - 33.5342i) q^{28} +(-1.84906 - 1.84906i) q^{29} +(7.21595 - 20.7353i) q^{30} -32.8551 q^{31} +(3.31168 - 31.8282i) q^{32} +16.1842i q^{33} +(7.83662 - 22.5188i) q^{34} +(84.7032 + 84.7032i) q^{35} +(18.5465 - 23.4200i) q^{36} +(23.1273 + 23.1273i) q^{37} +(-55.0712 + 26.6367i) q^{38} -8.86161i q^{39} +(-15.4371 + 69.2654i) q^{40} -61.1238i q^{41} +(-14.5529 - 30.0882i) q^{42} +(-4.44257 - 4.44257i) q^{43} +(-6.03427 - 51.9626i) q^{44} +(-46.8462 + 46.8462i) q^{45} +(3.64806 + 45.8551i) q^{46} +6.23398 q^{47} +(10.4198 - 16.8368i) q^{48} +133.358 q^{49} +(35.2909 - 101.410i) q^{50} +(10.4322 - 10.4322i) q^{51} +(3.30405 + 28.4520i) q^{52} +(6.69376 + 6.69376i) q^{53} +(36.6935 - 17.7478i) q^{54} +116.009i q^{55} +(57.9435 + 91.1781i) q^{56} -37.8524 q^{57} +(2.27721 + 4.70812i) q^{58} +(-24.5447 + 24.5447i) q^{59} +(-27.2603 + 34.4234i) q^{60} +(-35.7487 + 35.7487i) q^{61} +(62.0597 + 21.5970i) q^{62} +100.855i q^{63} +(-27.1773 + 57.9430i) q^{64} -63.5205i q^{65} +(10.6385 - 30.5701i) q^{66} +(27.6456 - 27.6456i) q^{67} +(-29.6050 + 37.3843i) q^{68} +(-10.3222 + 26.5252i) q^{69} +(-104.316 - 215.674i) q^{70} +0.0223440i q^{71} +(-50.4272 + 32.0464i) q^{72} +19.3177i q^{73} +(-28.4824 - 58.8874i) q^{74} +(46.9796 - 46.9796i) q^{75} +(121.533 - 14.1133i) q^{76} +(124.878 + 124.878i) q^{77} +(-5.82508 + 16.7386i) q^{78} -73.1520i q^{79} +(74.6898 - 120.687i) q^{80} -41.9962 q^{81} +(-40.1791 + 115.456i) q^{82} +(26.2318 - 26.2318i) q^{83} +(7.71078 + 66.3995i) q^{84} +(74.7786 - 74.7786i) q^{85} +(5.47125 + 11.3118i) q^{86} +3.23606i q^{87} +(-22.7589 + 102.118i) q^{88} +64.1708 q^{89} +(119.281 - 57.6935i) q^{90} +(-68.3768 - 68.3768i) q^{91} +(23.2516 - 89.0133i) q^{92} +(28.7501 + 28.7501i) q^{93} +(-11.7753 - 4.09784i) q^{94} -271.328 q^{95} +(-30.7494 + 24.9535i) q^{96} -142.243i q^{97} +(-251.898 - 87.6613i) q^{98} +(-69.0654 + 69.0654i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$176 q - 4 q^{2} - 4 q^{3} - 16 q^{4} - 64 q^{6} - 4 q^{8} - 28 q^{12} - 4 q^{13} - 80 q^{16} + 72 q^{18} + 68 q^{24} + 96 q^{26} + 212 q^{27} + 28 q^{29} - 8 q^{31} + 136 q^{32} - 104 q^{35} - 264 q^{36}+ \cdots - 240 q^{98}+O(q^{100})$ 176 * q - 4 * q^2 - 4 * q^3 - 16 * q^4 - 64 * q^6 - 4 * q^8 - 28 * q^12 - 4 * q^13 - 80 * q^16 + 72 * q^18 + 68 * q^24 + 96 * q^26 + 212 * q^27 + 28 * q^29 - 8 * q^31 + 136 * q^32 - 104 * q^35 - 264 * q^36 - 32 * q^46 - 8 * q^47 - 520 * q^48 + 1728 * q^49 + 88 * q^50 - 56 * q^52 - 148 * q^54 + 540 * q^58 + 296 * q^59 - 812 * q^62 - 352 * q^64 - 80 * q^69 + 124 * q^70 + 712 * q^72 + 132 * q^75 + 24 * q^77 - 320 * q^78 - 440 * q^81 - 844 * q^82 + 416 * q^85 - 492 * q^92 - 1084 * q^93 - 596 * q^94 - 8 * q^95 + 664 * q^96 - 240 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$ .

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	−1.88889	−	0.657339i	−0.944445	−	0.328669i
$2$	−1.88889	−	0.657339i	−0.944445	−	0.328669i
$3$	−0.875057	−	0.875057i	−0.291686	−	0.291686i	0.546060	−	0.837746i	$-0.316127\pi$
$3$	−0.875057	−	0.875057i	−0.291686	−	0.291686i	−0.837746	+	0.546060i	$0.816127\pi$
$4$	3.13581	+	2.48328i	0.783953	+	0.620820i
$5$	−6.27246	−	6.27246i	−1.25449	−	1.25449i	−0.953685	−	0.300806i	$-0.902744\pi$
$5$	−6.27246	−	6.27246i	−1.25449	−	1.25449i	−0.300806	−	0.953685i	$-0.597256\pi$
$6$	1.07768	+	2.22809i	0.179613	+	0.371349i
$7$	−13.5040			−1.92914			−0.964571	−	0.263824i	$-0.915016\pi$
$7$	−13.5040			−1.92914			−0.964571	+	0.263824i	$0.915016\pi$
$8$	−4.29085	−	6.75194i	−0.536356	−	0.843992i
$9$		−	7.46855i		−	0.829839i
$10$	7.72485	+	15.9711i	0.772485	+	1.59711i
$11$	−9.24750	−	9.24750i	−0.840682	−	0.840682i	0.148266	−	0.988948i	$-0.452631\pi$
$11$	−9.24750	−	9.24750i	−0.840682	−	0.840682i	−0.988948	+	0.148266i	$0.952631\pi$
$12$	−0.571000	−	4.91702i	−0.0475834	−	0.409752i
$13$	5.06345	+	5.06345i	0.389496	+	0.389496i	0.874508	−	0.485012i	$-0.161185\pi$
$13$	5.06345	+	5.06345i	0.389496	+	0.389496i	−0.485012	+	0.874508i	$0.661185\pi$
$14$	25.5076	+	8.87670i	1.82197	+	0.634050i
$15$			10.9775i			0.731834i
$16$	3.66662	+	15.5742i	0.229164	+	0.973388i
$17$			11.9217i			0.701278i	0.936511	+	0.350639i	$0.114036\pi$
$17$			11.9217i			0.701278i	−0.936511	+	0.350639i	$0.885964\pi$
$18$	−4.90937	+	14.1073i	−0.272743	+	0.783737i
$19$	21.6286	−	21.6286i	1.13834	−	1.13834i	0.149598	−	0.988747i	$-0.452202\pi$
$19$	21.6286	−	21.6286i	1.13834	−	1.13834i	0.988747	−	0.149598i	$-0.0477979\pi$
$20$	−4.09296	−	35.2455i	−0.204648	−	1.76228i
$21$	11.8168	+	11.8168i	0.562703	+	0.562703i
$22$	11.3888	+	23.5463i	0.517671	+	1.07028i
$23$	−9.25829	−	21.0543i	−0.402534	−	0.915405i
$23$	−9.25829	−	21.0543i	−0.402534	−	0.915405i
$24$	−2.15359	+	9.66306i	−0.0897331	+	0.402627i
$25$			53.6875i			2.14750i
$26$	−6.23590	−	12.8927i	−0.239842	−	0.495873i
$27$	−14.4109	+	14.4109i	−0.533738	+	0.533738i
$28$	−42.3460	−	33.5342i	−1.51236	−	1.19765i
$29$	−1.84906	−	1.84906i	−0.0637606	−	0.0637606i	0.674507	−	0.738268i	$-0.264356\pi$
$29$	−1.84906	−	1.84906i	−0.0637606	−	0.0637606i	−0.738268	+	0.674507i	$0.764356\pi$
$30$	7.21595	−	20.7353i	0.240532	−	0.691177i
$31$	−32.8551			−1.05984			−0.529922	−	0.848047i	$-0.677779\pi$
$31$	−32.8551			−1.05984			−0.529922	+	0.848047i	$0.677779\pi$
$32$	3.31168	−	31.8282i	0.103490	−	0.994630i
$33$			16.1842i			0.490429i
$34$	7.83662	−	22.5188i	0.230489	−	0.662319i
$35$	84.7032	+	84.7032i	2.42009	+	2.42009i
$36$	18.5465	−	23.4200i	0.515181	−	0.650555i
$37$	23.1273	+	23.1273i	0.625062	+	0.625062i	0.946821	−	0.321760i	$-0.104274\pi$
$37$	23.1273	+	23.1273i	0.625062	+	0.625062i	−0.321760	+	0.946821i	$0.604274\pi$
$38$	−55.0712	+	26.6367i	−1.44924	+	0.700965i
$39$		−	8.86161i		−	0.227221i
$40$	−15.4371	+	69.2654i	−0.385927	+	1.73163i
$41$		−	61.1238i		−	1.49083i	−0.666603	−	0.745413i	$-0.732252\pi$
$41$		−	61.1238i		−	1.49083i	0.666603	−	0.745413i	$-0.267748\pi$
$42$	−14.5529	−	30.0882i	−0.346499	−	0.716385i
$43$	−4.44257	−	4.44257i	−0.103315	−	0.103315i	0.653560	−	0.756875i	$-0.273275\pi$
$43$	−4.44257	−	4.44257i	−0.103315	−	0.103315i	−0.756875	+	0.653560i	$0.773275\pi$
$44$	−6.03427	−	51.9626i	−0.137142	−	1.18097i
$45$	−46.8462	+	46.8462i	−1.04103	+	1.04103i
$46$	3.64806	+	45.8551i	0.0793057	+	0.996850i
$47$	6.23398			0.132638			0.0663189	−	0.997798i	$-0.478875\pi$
$47$	6.23398			0.132638			0.0663189	+	0.997798i	$0.478875\pi$
$48$	10.4198	−	16.8368i	0.217079	−	0.350767i
$49$	133.358			2.72159
$50$	35.2909	−	101.410i	0.705817	−	2.02819i
$51$	10.4322	−	10.4322i	0.204553	−	0.204553i
$52$	3.30405	+	28.4520i	0.0635394	+	0.547154i
$53$	6.69376	+	6.69376i	0.126297	+	0.126297i	0.767430	−	0.641133i	$-0.221535\pi$
$53$	6.69376	+	6.69376i	0.126297	+	0.126297i	−0.641133	+	0.767430i	$0.721535\pi$
$54$	36.6935	−	17.7478i	0.679509	−	0.328663i
$55$			116.009i			2.10926i
$56$	57.9435	+	91.1781i	1.03471	+	1.62818i
$57$	−37.8524			−0.664077
$58$	2.27721	+	4.70812i	0.0392622	+	0.0811745i
$59$	−24.5447	+	24.5447i	−0.416012	+	0.416012i	−0.883826	−	0.467815i	$-0.845041\pi$
$59$	−24.5447	+	24.5447i	−0.416012	+	0.416012i	0.467815	+	0.883826i	$0.345041\pi$
$60$	−27.2603	+	34.4234i	−0.454338	+	0.573723i
$61$	−35.7487	+	35.7487i	−0.586044	+	0.586044i	−0.936558	−	0.350513i	$-0.886007\pi$
$61$	−35.7487	+	35.7487i	−0.586044	+	0.586044i	0.350513	+	0.936558i	$0.386007\pi$
$62$	62.0597	+	21.5970i	1.00096	+	0.348338i
$63$			100.855i			1.60088i
$64$	−27.1773	+	57.9430i	−0.424645	+	0.905360i
$65$		−	63.5205i		−	0.977239i
$66$	10.6385	−	30.5701i	0.161189	−	0.463184i
$67$	27.6456	−	27.6456i	0.412621	−	0.412621i	−0.470030	−	0.882651i	$-0.655757\pi$
$67$	27.6456	−	27.6456i	0.412621	−	0.412621i	0.882651	+	0.470030i	$0.155757\pi$
$68$	−29.6050	+	37.3843i	−0.435368	+	0.549769i
$69$	−10.3222	+	26.5252i	−0.149597	+	0.384424i
$70$	−104.316	−	215.674i	−1.49023	−	3.08105i
$71$			0.0223440i			0.000314704i	1.00000		0.000157352i	$5.00867e-5\pi$
$71$			0.0223440i			0.000314704i	−1.00000		0.000157352i	$0.999950\pi$
$72$	−50.4272	+	32.0464i	−0.700378	+	0.445089i
$73$			19.3177i			0.264625i	0.991208	+	0.132313i	$0.0422403\pi$
$73$			19.3177i			0.264625i	−0.991208	+	0.132313i	$0.957760\pi$
$74$	−28.4824	−	58.8874i	−0.384898	−	0.795775i
$75$	46.9796	−	46.9796i	0.626394	−	0.626394i
$76$	121.533	−	14.1133i	1.59912	−	0.185701i
$77$	124.878	+	124.878i	1.62179	+	1.62179i
$78$	−5.82508	+	16.7386i	−0.0746805	+	0.214597i
$79$		−	73.1520i		−	0.925975i	−0.886365	−	0.462987i	$-0.846778\pi$
$79$		−	73.1520i		−	0.925975i	0.886365	−	0.462987i	$-0.153222\pi$
$80$	74.6898	−	120.687i	0.933623	−	1.50859i
$81$	−41.9962			−0.518472
$82$	−40.1791	+	115.456i	−0.489989	+	1.40800i
$83$	26.2318	−	26.2318i	0.316046	−	0.316046i	−0.531201	−	0.847246i	$-0.678259\pi$
$83$	26.2318	−	26.2318i	0.316046	−	0.316046i	0.847246	+	0.531201i	$0.178259\pi$
$84$	7.71078	+	66.3995i	0.0917950	+	0.790470i
$85$	74.7786	−	74.7786i	0.879748	−	0.879748i
$86$	5.47125	+	11.3118i	0.0636192	+	0.131532i
$87$			3.23606i			0.0371961i
$88$	−22.7589	+	102.118i	−0.258624	+	1.16043i
$89$	64.1708			0.721020			0.360510	−	0.932755i	$-0.382603\pi$
$89$	64.1708			0.721020			0.360510	+	0.932755i	$0.382603\pi$
$90$	119.281	−	57.6935i	1.32535	−	0.641038i
$91$	−68.3768	−	68.3768i	−0.751393	−	0.751393i
$92$	23.2516	−	89.0133i	0.252734	−	0.967536i
$93$	28.7501	+	28.7501i	0.309141	+	0.309141i
$94$	−11.7753	−	4.09784i	−0.125269	−	0.0435940i
$95$	−271.328			−2.85609
$96$	−30.7494	+	24.9535i	−0.320306	+	0.259933i
$97$		−	142.243i		−	1.46642i	−0.680002	−	0.733210i	$-0.738021\pi$
$97$		−	142.243i		−	1.46642i	0.680002	−	0.733210i	$-0.261979\pi$
$98$	−251.898	−	87.6613i	−2.57039	−	0.894503i
$99$	−69.0654	+	69.0654i	−0.697631	+	0.697631i
$100$	−133.321	+	168.354i	−1.33321	+	1.68354i
$101$	75.6336	−	75.6336i	0.748848	−	0.748848i	−0.225415	−	0.974263i	$-0.572374\pi$
$101$	75.6336	−	75.6336i	0.748848	−	0.748848i	0.974263	+	0.225415i	$0.0723738\pi$
$102$	−26.5627	+	12.8478i	−0.260419	+	0.125959i
$103$	−175.282			−1.70177			−0.850886	−	0.525351i	$-0.823934\pi$
$103$	−175.282			−1.70177			−0.850886	+	0.525351i	$0.823934\pi$
$104$	12.4616	−	55.9146i	0.119823	−	0.537640i
$105$		−	148.240i		−	1.41181i
$106$	−8.24371	−	17.0439i	−0.0777709	−	0.160791i
$107$	75.8520	+	75.8520i	0.708898	+	0.708898i	0.966303	−	0.257406i	$-0.0828677\pi$
$107$	75.8520	+	75.8520i	0.708898	+	0.708898i	−0.257406	+	0.966303i	$0.582868\pi$
$108$	−80.9763	+	9.40355i	−0.749780	+	0.0870699i
$109$	−41.9915	+	41.9915i	−0.385243	+	0.385243i	−0.872987	−	0.487744i	$-0.837820\pi$
$109$	−41.9915	+	41.9915i	−0.385243	+	0.385243i	0.487744	+	0.872987i	$0.337820\pi$
$110$	76.2573	−	219.128i	0.693248	−	1.99208i
$111$		−	40.4754i		−	0.364643i
$112$	−49.5141	−	210.314i	−0.442090	−	1.87780i
$113$			109.643i			0.970290i	0.874434	+	0.485145i	$0.161233\pi$
$113$			109.643i			0.970290i	−0.874434	+	0.485145i	$0.838767\pi$
$114$	71.4991	+	24.8819i	0.627185	+	0.218262i
$115$	−73.9901	+	190.135i	−0.643392	+	1.65334i
$116$	−1.20656	−	10.3900i	−0.0104014	−	0.0895691i
$117$	37.8166	−	37.8166i	0.323219	−	0.323219i
$118$	62.4964	−	30.2280i	0.529630	−	0.256170i
$119$		−	160.991i		−	1.35287i
$120$	74.1195	−	47.1028i	0.617662	−	0.392523i
$121$			50.0325i			0.413492i
$122$	91.0244	−	44.0264i	0.746101	−	0.360872i
$123$	−53.4868	+	53.4868i	−0.434852	+	0.434852i
$124$	−103.027	−	81.5886i	−0.830867	−	0.657972i
$125$	179.941	−	179.941i	1.43953	−	1.43953i
$126$	66.2961	−	190.505i	0.526159	−	1.51194i
$127$	−107.647			−0.847616			−0.423808	−	0.905752i	$-0.639307\pi$
$127$	−107.647			−0.847616			−0.423808	+	0.905752i	$0.639307\pi$
$128$	89.4231	−	91.5833i	0.698618	−	0.715495i
$129$			7.77499i			0.0602713i
$130$	−41.7545	+	119.983i	−0.321189	+	0.922948i
$131$	−152.448	−	152.448i	−1.16372	−	1.16372i	−0.983654	−	0.180068i	$-0.942368\pi$
$131$	−152.448	−	152.448i	−1.16372	−	1.16372i	−0.180068	−	0.983654i	$-0.557632\pi$
$132$	−40.1899	+	50.7505i	−0.304469	+	0.384474i
$133$	−292.072	+	292.072i	−2.19603	+	2.19603i
$134$	−70.3920	+	34.0470i	−0.525314	+	0.254082i
$135$	180.784			1.33914
$136$	80.4948	−	51.1543i	0.591873	−	0.376135i
$137$	−84.7818			−0.618845			−0.309423	−	0.950925i	$-0.600136\pi$
$137$	−84.7818			−0.618845			−0.309423	+	0.950925i	$0.600136\pi$
$138$	36.9336	−	43.3181i	0.267634	−	0.313899i
$139$	−46.6363	+	46.6363i	−0.335513	+	0.335513i	−0.854675	−	0.519163i	$-0.826244\pi$
$139$	−46.6363	+	46.6363i	−0.335513	+	0.335513i	0.519163	+	0.854675i	$0.326244\pi$
$140$	55.2714	+	475.955i	0.394795	+	3.39968i
$141$	−5.45508	−	5.45508i	−0.0386885	−	0.0386885i
$142$	0.0146876	−	0.0422053i	0.000103434	−	0.000297221i
$143$		−	93.6485i		−	0.654884i
$144$	116.317	−	27.3844i	0.807755	−	0.190169i
$145$			23.1963i			0.159974i
$146$	12.6982	−	36.4889i	0.0869743	−	0.249924i
$147$	−116.696	−	116.696i	−0.793848	−	0.793848i
$148$	15.0912	+	129.954i	0.101968	+	0.878070i
$149$	−30.8347	−	30.8347i	−0.206944	−	0.206944i	0.596023	−	0.802967i	$-0.296747\pi$
$149$	−30.8347	−	30.8347i	−0.206944	−	0.206944i	−0.802967	+	0.596023i	$0.796747\pi$
$150$	−119.621	+	57.8577i	−0.797471	+	0.385718i
$151$		−	152.378i		−	1.00912i	−0.863376	−	0.504561i	$-0.831654\pi$
$151$		−	152.378i		−	1.00912i	0.863376	−	0.504561i	$-0.168346\pi$
$152$	−238.839	−	53.2299i	−1.57131	−	0.350196i
$153$	89.0381			0.581948
$154$	−153.794	−	317.968i	−0.998661	−	2.06473i
$155$	206.082	+	206.082i	1.32956	+	1.32956i
$156$	22.0059	−	27.7883i	0.141063	−	0.178130i
$157$	34.5790	−	34.5790i	0.220249	−	0.220249i	−0.588355	−	0.808603i	$-0.700224\pi$
$157$	34.5790	−	34.5790i	0.220249	−	0.220249i	0.808603	+	0.588355i	$0.200224\pi$
$158$	−48.0856	+	138.176i	−0.304340	+	0.874532i
$159$		−	11.7148i		−	0.0736783i
$160$	−220.413	+	178.869i	−1.37758	+	1.11793i
$161$	125.024	+	284.317i	0.776545	+	1.76595i
$162$	79.3263	+	27.6058i	0.489668	+	0.170406i
$163$	−1.27838	−	1.27838i	−0.00784279	−	0.00784279i	0.703175	−	0.711017i	$-0.251765\pi$
$163$	−1.27838	−	1.27838i	−0.00784279	−	0.00784279i	−0.711017	+	0.703175i	$0.751765\pi$
$164$	151.788	−	191.673i	0.925535	−	1.16874i
$165$	101.515	−	101.515i	0.615240	−	0.615240i
$166$	−66.7921	+	32.3058i	−0.402362	+	0.194613i
$167$			310.909i			1.86173i	0.365361	+	0.930866i	$0.380945\pi$
$167$			310.909i			1.86173i	−0.365361	+	0.930866i	$0.619055\pi$
$168$	29.0821	−	130.490i	0.173108	−	0.776725i
$169$		−	117.723i		−	0.696586i
$170$	−190.403	+	92.0936i	−1.12002	+	0.541727i
$171$	−161.534	−	161.534i	−0.944643	−	0.944643i
$172$	−2.89891	−	24.9632i	−0.0168541	−	0.145135i
$173$	101.807	+	101.807i	0.588477	+	0.588477i	0.937219	−	0.348742i	$-0.113391\pi$
$173$	101.807	+	101.807i	0.588477	+	0.588477i	−0.348742	+	0.937219i	$0.613391\pi$
$174$	2.12719	−	6.11256i	0.0122252	−	0.0351296i
$175$		−	724.995i		−	4.14283i
$176$	110.115	−	177.930i	0.625655	−	1.01096i
$177$	42.9560			0.242689
$178$	−121.212	−	42.1819i	−0.680964	−	0.236977i
$179$	140.985	+	140.985i	0.787625	+	0.787625i	0.981104	−	0.193480i	$-0.0619774\pi$
$179$	140.985	+	140.985i	0.787625	+	0.787625i	−0.193480	+	0.981104i	$0.561977\pi$
$180$	−263.233	+	30.5685i	−1.46241	+	0.169825i
$181$	127.844	+	127.844i	0.706319	+	0.706319i	0.965759	−	0.259440i	$-0.0835379\pi$
$181$	127.844	+	127.844i	0.706319	+	0.706319i	−0.259440	+	0.965759i	$0.583538\pi$
$182$	84.2095	+	174.103i	0.462689	+	0.956609i
$183$	62.5643			0.341881
$184$	−102.432	+	152.852i	−0.556693	+	0.830718i
$185$		−	290.130i		−	1.56827i
$186$	−35.4072	−	73.2043i	−0.190361	−	0.393572i
$187$	110.246	−	110.246i	0.589552	−	0.589552i
$188$	19.5486	+	15.4807i	0.103982	+	0.0823443i
$189$	194.605	−	194.605i	1.02966	−	1.02966i
$190$	512.509	+	178.355i	2.69742	+	0.938709i
$191$		−	28.2910i		−	0.148121i	−0.997254	−	0.0740603i	$-0.976404\pi$
$191$		−	28.2910i		−	0.148121i	0.997254	−	0.0740603i	$-0.0235957\pi$
$192$	74.4851	−	26.9218i	0.387943	−	0.140217i
$193$	−114.005			−0.590701			−0.295350	−	0.955389i	$-0.595436\pi$
$193$	−114.005			−0.590701			−0.295350	+	0.955389i	$0.595436\pi$
$194$	−93.5017	+	268.681i	−0.481967	+	1.38495i
$195$	−55.5841	+	55.5841i	−0.285046	+	0.285046i
$196$	418.185	+	331.165i	2.13360	+	1.68962i
$197$	54.3132	−	54.3132i	0.275701	−	0.275701i	−0.555689	−	0.831390i	$-0.687545\pi$
$197$	54.3132	−	54.3132i	0.275701	−	0.275701i	0.831390	+	0.555689i	$0.187545\pi$
$198$	175.856	−	85.0576i	0.888164	−	0.429584i
$199$	219.466			1.10285			0.551423	−	0.834226i	$-0.314085\pi$
$199$	219.466			1.10285			0.551423	+	0.834226i	$0.314085\pi$
$200$	362.494	−	230.365i	1.81247	−	1.15182i
$201$	−48.3829			−0.240711
$202$	−192.581	+	93.1467i	−0.953369	+	0.461122i
$203$	24.9696	+	24.9696i	0.123003	+	0.123003i
$204$	58.6194	−	6.80731i	0.287350	−	0.0333692i
$205$	−383.397	+	383.397i	−1.87023	+	1.87023i
$206$	331.089	+	115.220i	1.60723	+	0.559320i
$207$	−157.245	+	69.1460i	−0.759639	+	0.334039i
$208$	−60.2934	+	97.4249i	−0.289872	+	0.468389i
$209$	−400.020			−1.91397
$210$	−97.4441	+	280.009i	−0.464019	+	1.33338i
$211$	111.383	+	111.383i	0.527882	+	0.527882i	0.919940	−	0.392059i	$-0.128237\pi$
$211$	111.383	+	111.383i	0.527882	+	0.527882i	−0.392059	+	0.919940i	$0.628237\pi$
$212$	4.36788	+	37.6129i	0.0206032	+	0.177419i
$213$	0.0195523	−	0.0195523i	9.17946e−5	−	9.17946e-5i
$214$	−93.4157	−	193.137i	−0.436522	−	0.902508i
$215$			55.7316i			0.259217i
$216$	159.137	+	35.4666i	0.736743	+	0.164197i
$217$	443.675			2.04459
$218$	106.920	−	51.7147i	0.490459	−	0.237223i
$219$	16.9040	−	16.9040i	0.0771874	−	0.0771874i
$220$	−288.083	+	363.783i	−1.30947	+	1.65356i
$221$	−60.3651	+	60.3651i	−0.273145	+	0.273145i
$222$	−26.6060	+	76.4535i	−0.119847	+	0.344385i
$223$	158.502			0.710772			0.355386	−	0.934720i	$-0.384349\pi$
$223$	158.502			0.710772			0.355386	+	0.934720i	$0.384349\pi$
$224$	−44.7209	+	429.807i	−0.199647	+	1.91878i
$225$	400.968			1.78208
$226$	72.0725	−	207.103i	0.318905	−	0.916386i
$227$	−186.887	+	186.887i	−0.823292	+	0.823292i	−0.986579	−	0.163287i	$-0.947790\pi$
$227$	−186.887	+	186.887i	−0.823292	+	0.823292i	0.163287	+	0.986579i	$0.447790\pi$
$228$	−118.698	−	93.9982i	−0.520605	−	0.412273i
$229$	75.6971	+	75.6971i	0.330555	+	0.330555i	0.852797	−	0.522242i	$-0.174904\pi$
$229$	75.6971	+	75.6971i	0.330555	+	0.330555i	−0.522242	+	0.852797i	$0.674904\pi$
$230$	264.742	−	310.507i	1.15105	−	1.35003i
$231$		−	218.551i		−	0.946108i
$232$	−4.55070	+	20.4187i	−0.0196151	+	0.0880117i
$233$		−	200.737i		−	0.861532i	−0.902464	−	0.430766i	$-0.858243\pi$
$233$		−	200.737i		−	0.861532i	0.902464	−	0.430766i	$-0.141757\pi$
$234$	−96.2898	+	46.5731i	−0.411495	+	0.199030i
$235$	−39.1024	−	39.1024i	−0.166393	−	0.166393i
$236$	−137.919	+	16.0161i	−0.584402	+	0.0678650i
$237$	−64.0121	+	64.0121i	−0.270093	+	0.270093i
$238$	−105.826	+	304.094i	−0.444645	+	1.27771i
$239$	−127.508			−0.533507			−0.266754	−	0.963765i	$-0.585951\pi$
$239$	−127.508			−0.533507			−0.266754	+	0.963765i	$0.585951\pi$
$240$	−170.966	+	40.2504i	−0.712358	+	0.167710i
$241$			228.352i			0.947518i	0.880655	+	0.473759i	$0.157103\pi$
$241$			228.352i			0.947518i	−0.880655	+	0.473759i	$0.842897\pi$
$242$	32.8883	−	94.5059i	0.135902	−	0.390520i
$243$	166.447	+	166.447i	0.684968	+	0.684968i
$244$	−200.875	+	23.3271i	−0.823259	+	0.0956028i
$245$	−836.481	−	836.481i	−3.41421	−	3.41421i
$246$	136.190	−	65.8718i	0.553617	−	0.267771i
$247$	219.030			0.886762
$248$	140.976	+	221.836i	0.568453	+	0.894499i
$249$	−45.9086			−0.184372
$250$	−458.171	+	221.606i	−1.83268	+	0.886426i
$251$	136.585	+	136.585i	0.544162	+	0.544162i	0.924746	−	0.380584i	$-0.124277\pi$
$251$	136.585	+	136.585i	0.544162	+	0.544162i	−0.380584	+	0.924746i	$0.624277\pi$
$252$	−250.452	+	316.263i	−0.993857	+	1.25501i
$253$	−109.084	+	280.316i	−0.431161	+	1.10797i
$254$	203.334	+	70.7607i	0.800527	+	0.278585i
$255$	−130.871			−0.513219
$256$	−229.112	+	114.210i	−0.894968	+	0.446131i
$257$	−48.2818			−0.187867			−0.0939334	−	0.995578i	$-0.529944\pi$
$257$	−48.2818			−0.187867			−0.0939334	+	0.995578i	$0.529944\pi$
$258$	5.11081	−	14.6861i	0.0198093	−	0.0569229i
$259$	−312.311	−	312.311i	−1.20583	−	1.20583i
$260$	157.739	−	199.188i	0.606690	−	0.766109i
$261$	−13.8098	+	13.8098i	−0.0529110	+	0.0529110i
$262$	187.747	+	388.167i	0.716592	+	1.48155i
$263$	−220.965			−0.840171			−0.420086	−	0.907484i	$-0.638000\pi$
$263$	−220.965			−0.840171			−0.420086	+	0.907484i	$0.638000\pi$
$264$	109.275	−	69.4438i	0.413919	−	0.263045i
$265$		−	83.9727i		−	0.316878i
$266$	743.682	−	359.701i	2.79580	−	1.35226i
$267$	−56.1531	−	56.1531i	−0.210311	−	0.210311i
$268$	155.343	−	18.0396i	0.579639	−	0.0673118i
$269$	−270.861	−	270.861i	−1.00692	−	1.00692i	−0.999976	−	0.00694234i	$-0.997790\pi$
$269$	−270.861	−	270.861i	−1.00692	−	1.00692i	−0.00694234	−	0.999976i	$-0.502210\pi$
$270$	−341.481	−	118.836i	−1.26474	−	0.440134i
$271$	−247.486			−0.913232			−0.456616	−	0.889664i	$-0.650939\pi$
$271$	−247.486			−0.913232			−0.456616	+	0.889664i	$0.650939\pi$
$272$	−185.671	+	43.7125i	−0.682616	+	0.160708i
$273$			119.667i			0.438341i
$274$	160.144	+	55.7304i	0.584466	+	0.203396i
$275$	496.475	−	496.475i	1.80536	−	1.80536i
$276$	−98.2381	+	57.5452i	−0.355935	+	0.208497i
$277$	−151.298	+	151.298i	−0.546201	+	0.546201i	−0.925340	−	0.379139i	$-0.876220\pi$
$277$	−151.298	+	151.298i	−0.546201	+	0.546201i	0.379139	+	0.925340i	$0.376220\pi$
$278$	118.747	−	57.4349i	0.427146	−	0.206600i
$279$			245.380i			0.879499i
$280$	208.462	−	935.359i	0.744509	−	3.34057i
$281$	−136.441			−0.485556			−0.242778	−	0.970082i	$-0.578059\pi$
$281$	−136.441			−0.485556			−0.242778	+	0.970082i	$0.578059\pi$
$282$	6.71821	+	13.8899i	0.0238235	+	0.0492549i
$283$	−142.308	−	142.308i	−0.502856	−	0.502856i	0.409468	−	0.912324i	$-0.365714\pi$
$283$	−142.308	−	142.308i	−0.502856	−	0.502856i	−0.912324	+	0.409468i	$0.865714\pi$
$284$	−0.0554864	+	0.0700665i	−0.000195375	+	0.000246713i
$285$	237.428	+	237.428i	0.833080	+	0.833080i
$286$	−61.5588	+	176.892i	−0.215241	+	0.618502i
$287$			825.416i			2.87601i
$288$	−237.710	−	24.7335i	−0.825383	−	0.0858801i
$289$	146.872			0.508209
$290$	15.2478	−	43.8152i	0.0525786	−	0.151087i
$291$	−124.470	+	124.470i	−0.427734	+	0.427734i
$292$	−47.9712	+	60.5765i	−0.164285	+	0.207454i
$293$	−68.2180	−	68.2180i	−0.232826	−	0.232826i	0.581045	−	0.813871i	$-0.302644\pi$
$293$	−68.2180	−	68.2180i	−0.232826	−	0.232826i	−0.813871	+	0.581045i	$0.802644\pi$
$294$	143.717	+	297.134i	0.488832	+	1.01066i
$295$	307.911			1.04377
$296$	56.9184	−	255.390i	0.192292	−	0.862803i
$297$	266.530			0.897407
$298$	37.9745	+	78.5121i	0.127431	+	0.263464i
$299$	59.7286	−	153.486i	0.199761	−	0.513332i
$300$	263.983	−	30.6556i	0.879942	−	0.102185i
$301$	59.9924	+	59.9924i	0.199310	+	0.199310i
$302$	−100.164	+	287.824i	−0.331668	+	0.953061i
$303$	−132.367			−0.436856
$304$	416.151	+	257.544i	1.36892	+	0.847183i
$305$	448.464			1.47038
$306$	−168.183	−	58.5282i	−0.549618	−	0.191269i
$307$	302.327	+	302.327i	0.984777	+	0.984777i	0.999886	−	0.0151088i	$-0.00480945\pi$
$307$	302.327	+	302.327i	0.984777	+	0.984777i	−0.0151088	+	0.999886i	$0.504809\pi$
$308$	81.4867	+	701.702i	0.264567	+	2.27825i
$309$	153.382	+	153.382i	0.496382	+	0.496382i
$310$	−253.801	−	524.733i	−0.818713	−	1.69269i
$311$		−	244.971i		−	0.787690i	−0.919177	−	0.393845i	$-0.871145\pi$
$311$		−	244.971i		−	0.787690i	0.919177	−	0.393845i	$-0.128855\pi$
$312$	−59.8330	+	38.0238i	−0.191772	+	0.121871i
$313$	516.407			1.64986			0.824932	−	0.565232i	$-0.191213\pi$
$313$	516.407			1.64986			0.824932	+	0.565232i	$0.191213\pi$
$314$	−88.0461	+	42.5858i	−0.280402	+	0.135624i
$315$	632.610	−	632.610i	2.00829	−	2.00829i
$316$	181.657	−	229.391i	0.574864	−	0.725920i
$317$	−235.214	−	235.214i	−0.742001	−	0.742001i	0.230962	−	0.972963i	$-0.425813\pi$
$317$	−235.214	−	235.214i	−0.742001	−	0.742001i	−0.972963	+	0.230962i	$0.925813\pi$
$318$	−7.70062	+	22.1281i	−0.0242158	+	0.0695851i
$319$			34.1983i			0.107205i
$320$	533.914	−	192.977i	1.66848	−	0.603052i
$321$		−	132.750i		−	0.413550i
$322$	−49.2634	−	619.227i	−0.152992	−	1.92307i
$323$	257.850	+	257.850i	0.798297	+	0.798297i
$324$	−131.692	−	104.288i	−0.406458	−	0.321878i
$325$	−271.844	+	271.844i	−0.836442	+	0.836442i
$326$	1.57438	+	3.25504i	0.00482940	+	0.00998477i
$327$	73.4899			0.224740
$328$	−412.704	+	262.273i	−1.25824	+	0.799613i
$329$	−84.1836			−0.255877
$330$	−258.479	+	125.020i	−0.783270	+	0.378850i
$331$	63.9148	−	63.9148i	0.193096	−	0.193096i	−0.603936	−	0.797033i	$-0.706402\pi$
$331$	63.9148	−	63.9148i	0.193096	−	0.193096i	0.797033	+	0.603936i	$0.206402\pi$
$332$	147.399	−	17.1170i	0.443972	−	0.0515573i
$333$	172.727	−	172.727i	0.518701	−	0.518701i
$334$	204.373	−	587.273i	0.611894	−	1.75830i
$335$	−346.812			−1.03526
$336$	−140.709	+	227.364i	−0.418777	+	0.676679i
$337$		−	364.246i		−	1.08085i	−0.841392	−	0.540425i	$-0.818263\pi$
$337$		−	364.246i		−	1.08085i	0.841392	−	0.540425i	$-0.181737\pi$
$338$	−77.3839	+	222.366i	−0.228946	+	0.657887i
$339$	95.9437	−	95.9437i	0.283020	−	0.283020i
$340$	420.188	−	48.7952i	1.23585	−	0.143515i
$341$	303.828	+	303.828i	0.890991	+	0.890991i
$342$	198.937	+	411.302i	0.581688	+	1.20264i
$343$	−1139.17			−3.32119
$344$	−10.9336	+	49.0583i	−0.0317836	+	0.142611i
$345$	231.124	−	101.633i	0.669925	−	0.294588i
$346$	−125.380	−	259.223i	−0.362370	−	0.749199i
$347$	−185.323	+	185.323i	−0.534072	+	0.534072i	−0.921782	−	0.387709i	$-0.873266\pi$
$347$	−185.323	+	185.323i	−0.534072	+	0.534072i	0.387709	+	0.921782i	$0.373266\pi$
$348$	−8.03604	+	10.1477i	−0.0230921	+	0.0291600i
$349$	188.541	+	188.541i	0.540232	+	0.540232i	0.923597	−	0.383365i	$-0.125235\pi$
$349$	188.541	+	188.541i	0.540232	+	0.540232i	−0.383365	+	0.923597i	$0.625235\pi$
$350$	−476.567	+	1369.44i	−1.36162	+	3.91267i
$351$	−145.938			−0.415777
$352$	−324.956	+	263.706i	−0.923170	+	0.749166i
$353$	−405.785			−1.14953			−0.574766	−	0.818317i	$-0.694907\pi$
$353$	−405.785			−1.14953			−0.574766	+	0.818317i	$0.694907\pi$
$354$	−81.1391	−	28.2366i	−0.229207	−	0.0797645i
$355$	0.140152	−	0.140152i	0.000394794	−	0.000394794i
$356$	201.227	+	159.354i	0.565246	+	0.447624i
$357$	−140.876	+	140.876i	−0.394611	+	0.394611i
$358$	−173.630	−	358.980i	−0.485000	−	1.00274i
$359$	43.5284			0.121249			0.0606245	−	0.998161i	$-0.480691\pi$
$359$	43.5284			0.121249			0.0606245	+	0.998161i	$0.480691\pi$
$360$	517.312	+	115.293i	1.43698	+	0.320258i
$361$		−	574.589i		−	1.59166i
$362$	−157.446	−	325.520i	−0.434934	−	0.899225i
$363$	43.7813	−	43.7813i	0.120610	−	0.120610i
$364$	−44.6179	−	384.215i	−0.122577	−	1.05554i
$365$	121.169	−	121.169i	0.331970	−	0.331970i
$366$	−118.177	−	41.1259i	−0.322888	−	0.112366i
$367$			51.3496i			0.139917i	0.997550	+	0.0699585i	$0.0222867\pi$
$367$			51.3496i			0.139917i	−0.997550	+	0.0699585i	$0.977713\pi$
$368$	293.958	−	221.389i	0.798798	−	0.601600i
$369$	−456.507			−1.23715
$370$	−190.714	+	548.023i	−0.515442	+	1.48114i
$371$	−90.3925	−	90.3925i	−0.243646	−	0.243646i
$372$	18.7603	+	161.549i	0.0504309	+	0.434273i
$373$	−20.6559	−	20.6559i	−0.0553779	−	0.0553779i	0.678876	−	0.734253i	$-0.262468\pi$
$373$	−20.6559	−	20.6559i	−0.0553779	−	0.0553779i	−0.734253	+	0.678876i	$0.762468\pi$
$374$	−280.712	+	135.774i	−0.750567	+	0.363032i
$375$	−314.917			−0.839778
$376$	−26.7490	−	42.0914i	−0.0711410	−	0.111945i
$377$		−	18.7252i		−	0.0496690i
$378$	−495.509	+	239.666i	−1.31087	+	0.634037i
$379$	148.912	+	148.912i	0.392909	+	0.392909i	0.875723	−	0.482814i	$-0.160385\pi$
$379$	148.912	+	148.912i	0.392909	+	0.392909i	−0.482814	+	0.875723i	$0.660385\pi$
$380$	−850.835	−	673.785i	−2.23904	−	1.77312i
$381$	94.1974	+	94.1974i	0.247237	+	0.247237i
$382$	−18.5968	+	53.4386i	−0.0486827	+	0.139892i
$383$		−	67.6650i		−	0.176671i	−0.996091	−	0.0883355i	$-0.971845\pi$
$383$		−	67.6650i		−	0.176671i	0.996091	−	0.0883355i	$-0.0281548\pi$
$384$	−158.391	+	1.89028i	−0.412476	+	0.00492261i
$385$		−	1566.59i		−	4.06905i
$386$	215.343	+	74.9401i	0.557884	+	0.194145i
$387$	−33.1795	+	33.1795i	−0.0857352	+	0.0857352i
$388$	353.229	−	446.046i	0.910384	−	1.14960i
$389$	142.032	+	142.032i	0.365120	+	0.365120i	0.865694	−	0.500574i	$-0.166878\pi$
$389$	142.032	+	142.032i	0.365120	+	0.365120i	−0.500574	+	0.865694i	$0.666878\pi$
$390$	141.530	−	68.4546i	0.362897	−	0.175525i
$391$	251.004	−	110.375i	0.641954	−	0.282288i
$392$	−572.218	−	900.423i	−1.45974	−	2.29700i
$393$			266.801i			0.678882i
$394$	−138.294	+	66.8895i	−0.350999	+	0.169770i
$395$	−458.843	+	458.843i	−1.16163	+	1.16163i
$396$	−388.085	+	45.0672i	−0.980013	+	0.113806i
$397$	128.831	+	128.831i	0.324510	+	0.324510i	0.850494	−	0.525984i	$-0.176303\pi$
$397$	128.831	+	128.831i	0.324510	+	0.324510i	−0.525984	+	0.850494i	$0.676303\pi$
$398$	−414.548	−	144.264i	−1.04158	−	0.362472i
$399$	511.159			1.28110
$400$	−836.139	+	196.852i	−2.09035	+	0.492129i
$401$			265.047i			0.660965i	0.943812	+	0.330482i	$0.107211\pi$
$401$			265.047i			0.660965i	−0.943812	+	0.330482i	$0.892789\pi$
$402$	91.3900	+	31.8040i	0.227338	+	0.0791144i
$403$	−166.360	−	166.360i	−0.412805	−	0.412805i
$404$	424.992	−	49.3532i	1.05196	−	0.122161i
$405$	263.420	+	263.420i	0.650419	+	0.650419i
$406$	−30.7514	−	63.5784i	−0.0757423	−	0.156597i
$407$		−	427.739i		−	1.05096i
$408$	−115.200	−	25.6746i	−0.282354	−	0.0629279i
$409$			490.325i			1.19884i	0.800435	+	0.599420i	$0.204602\pi$
$409$			490.325i			1.19884i	−0.800435	+	0.599420i	$0.795398\pi$
$410$	976.216	−	472.173i	2.38101	−	1.15164i
$411$	74.1889	+	74.1889i	0.180508	+	0.180508i
$412$	−549.653	−	435.276i	−1.33411	−	1.05649i
$413$	331.451	−	331.451i	0.802545	−	0.802545i
$414$	342.471	−	27.2458i	0.827225	−	0.0658110i
$415$	−329.076			−0.792953
$416$	177.929	−	144.392i	0.427714	−	0.347096i
$417$	81.6187			0.195728
$418$	755.594	+	262.949i	1.80764	+	0.629064i
$419$	−205.235	+	205.235i	−0.489822	+	0.489822i	−0.908250	−	0.418428i	$-0.862581\pi$
$419$	−205.235	+	205.235i	−0.489822	+	0.489822i	0.418428	+	0.908250i	$0.362581\pi$
$420$	368.122	−	464.853i	0.876482	−	1.10679i
$421$	278.850	+	278.850i	0.662352	+	0.662352i	0.955934	−	0.293582i	$-0.0948472\pi$
$421$	278.850	+	278.850i	0.662352	+	0.662352i	−0.293582	+	0.955934i	$0.594847\pi$
$422$	−137.174	−	283.607i	−0.325057	−	0.672054i
$423$		−	46.5588i		−	0.110068i
$424$	16.4740	−	73.9178i	0.0388537	−	0.174334i
$425$	−640.047			−1.50599
$426$	−0.0497845	+	0.0240796i	−0.000116865	+	5.65249e-5i
$427$	482.750	−	482.750i	1.13056	−	1.13056i
$428$	49.4957	+	426.220i	0.115644	+	0.995840i
$429$	−81.9477	+	81.9477i	−0.191020	+	0.191020i
$430$	36.6346	−	105.271i	0.0851966	−	0.244816i
$431$			329.470i			0.764431i	0.924073	+	0.382216i	$0.124839\pi$
$431$			329.470i			0.764431i	−0.924073	+	0.382216i	$0.875161\pi$
$432$	−277.278	−	171.599i	−0.641847	−	0.397220i
$433$			561.046i			1.29572i	0.761760	+	0.647859i	$0.224335\pi$
$433$			561.046i			1.29572i	−0.761760	+	0.647859i	$0.775665\pi$
$434$	−838.054	−	291.645i	−1.93100	−	0.671993i
$435$	20.2980	−	20.2980i	0.0466622	−	0.0466622i
$436$	−235.954	+	27.4007i	−0.541180	+	0.0628457i
$437$	−655.618	−	255.131i	−1.50027	−	0.583824i
$438$	−43.0416	+	20.8182i	−0.0982684	+	0.0475301i
$439$			534.808i			1.21824i	0.793078	+	0.609121i	$0.208477\pi$
$439$			534.808i			1.21824i	−0.793078	+	0.609121i	$0.791523\pi$
$440$	783.286	−	497.777i	1.78020	−	1.13131i
$441$		−	995.990i		−	2.25848i
$442$	153.703	−	74.3427i	0.347745	−	0.168196i
$443$	−195.027	+	195.027i	−0.440241	+	0.440241i	−0.892093	−	0.451852i	$-0.850764\pi$
$443$	−195.027	+	195.027i	−0.440241	+	0.440241i	0.451852	+	0.892093i	$0.350764\pi$
$444$	100.512	−	126.923i	0.226378	−	0.285863i
$445$	−402.508	−	402.508i	−0.904513	−	0.904513i
$446$	−299.393	−	104.190i	−0.671285	−	0.233609i
$447$			53.9642i			0.120725i
$448$	367.002	−	782.462i	0.819201	−	1.74657i
$449$	−154.215			−0.343463			−0.171731	−	0.985144i	$-0.554936\pi$
$449$	−154.215			−0.343463			−0.171731	+	0.985144i	$0.554936\pi$
$450$	−757.384	−	263.572i	−1.68307	−	0.585715i
$451$	−565.243	+	565.243i	−1.25331	+	1.25331i
$452$	−272.274	+	343.819i	−0.602376	+	0.760662i
$453$	−133.339	+	133.339i	−0.294346	+	0.294346i
$454$	475.858	−	230.161i	1.04815	−	0.506963i
$455$			857.781i			1.88523i
$456$	162.419	+	255.577i	0.356182	+	0.560476i
$457$	−378.638			−0.828530			−0.414265	−	0.910156i	$-0.635961\pi$
$457$	−378.638			−0.828530			−0.414265	+	0.910156i	$0.635961\pi$
$458$	−93.2248	−	192.742i	−0.203548	−	0.420834i
$459$	−171.803	−	171.803i	−0.374299	−	0.374299i
$460$	−704.177	+	412.488i	−1.53082	+	0.896712i
$461$	305.291	+	305.291i	0.662236	+	0.662236i	0.955907	−	0.293671i	$-0.0948770\pi$
$461$	305.291	+	305.291i	0.662236	+	0.662236i	−0.293671	+	0.955907i	$0.594877\pi$
$462$	−143.662	+	412.819i	−0.310957	+	0.893547i
$463$	536.251			1.15821			0.579104	−	0.815253i	$-0.303402\pi$
$463$	536.251			1.15821			0.579104	+	0.815253i	$0.303402\pi$
$464$	22.0178	−	35.5774i	0.0474521	−	0.0766754i
$465$		−	360.668i		−	0.775629i
$466$	−131.952	+	379.170i	−0.283159	+	0.813670i
$467$	326.848	−	326.848i	0.699888	−	0.699888i	−0.264498	−	0.964386i	$-0.585206\pi$
$467$	326.848	−	326.848i	0.699888	−	0.699888i	0.964386	+	0.264498i	$0.0852064\pi$
$468$	212.495	−	24.6765i	0.454049	−	0.0527275i
$469$	−373.326	+	373.326i	−0.796004	+	0.796004i
$470$	48.1566	+	99.5636i	0.102461	+	0.211837i
$471$	−60.5172			−0.128487
$472$	271.042	+	60.4067i	0.574241	+	0.127980i
$473$			82.1653i			0.173711i
$474$	162.990	−	78.8342i	0.343860	−	0.166317i
$475$	1161.18	+	1161.18i	2.44459	+	2.44459i
$476$	399.786	−	504.837i	0.839886	−	1.06058i
$477$	49.9927	−	49.9927i	0.104807	−	0.104807i
$478$	240.849	+	83.8162i	0.503868	+	0.175348i
$479$		−	462.127i		−	0.964774i	−0.875958	−	0.482387i	$-0.839770\pi$
$479$		−	462.127i		−	0.964774i	0.875958	−	0.482387i	$-0.160230\pi$
$480$	349.394	+	36.3540i	0.727905	+	0.0757375i
$481$			234.208i			0.486918i
$482$	150.105	−	431.331i	0.311420	−	0.894878i
$483$	139.391	−	358.197i	0.288594	−	0.741608i
$484$	−124.245	+	156.893i	−0.256704	+	0.324158i
$485$	−892.212	+	892.212i	−1.83961	+	1.83961i
$486$	−204.988	−	423.813i	−0.421787	−	0.872043i
$487$		−	373.680i		−	0.767310i	−0.923476	−	0.383655i	$-0.874665\pi$
$487$		−	373.680i		−	0.767310i	0.923476	−	0.383655i	$-0.125335\pi$
$488$	394.765	+	87.9808i	0.808945	+	0.180289i
$489$			2.23730i			0.00457526i
$490$	1030.17	+	2129.87i	2.10239	+	4.34668i
$491$	517.615	−	517.615i	1.05421	−	1.05421i	0.0557624	−	0.998444i	$-0.482241\pi$
$491$	517.615	−	517.615i	1.05421	−	1.05421i	0.998444	−	0.0557624i	$-0.0177589\pi$
$492$	−300.547	+	34.9017i	−0.610869	+	0.0709385i
$493$	22.0440	−	22.0440i	0.0447139	−	0.0447139i
$494$	−413.724	−	143.977i	−0.837498	−	0.291451i
$495$	866.420			1.75034
$496$	−120.467	−	511.693i	−0.242878	−	1.03164i
$497$		−	0.301733i		−	0.000607109i
$498$	86.7163	+	30.1775i	0.174129	+	0.0605974i
$499$	269.165	+	269.165i	0.539409	+	0.539409i	0.923355	−	0.383947i	$-0.125435\pi$
$499$	269.165	+	269.165i	0.539409	+	0.539409i	−0.383947	+	0.923355i	$0.625435\pi$
$500$	1011.10	−	117.417i	2.02221	−	0.234833i
$501$	272.063	−	272.063i	0.543040	−	0.543040i
$502$	−168.211	−	347.776i	−0.335081	−	0.692780i
$503$	83.3763			0.165758			0.0828790	−	0.996560i	$-0.473588\pi$
$503$	83.3763			0.165758			0.0828790	+	0.996560i	$0.473588\pi$
$504$	680.968	−	432.754i	1.35113	−	0.858640i
$505$	−948.818			−1.87885
$506$	390.310	−	457.781i	0.771363	−	0.904705i
$507$	−103.014	+	103.014i	−0.203184	+	0.203184i
$508$	−337.561	−	267.318i	−0.664491	−	0.526217i
$509$	376.327	+	376.327i	0.739346	+	0.739346i	0.972451	−	0.233106i	$-0.0748888\pi$
$509$	376.327	+	376.327i	0.739346	+	0.739346i	−0.233106	+	0.972451i	$0.574889\pi$
$510$	247.201	+	86.0266i	0.484708	+	0.168680i
$511$		−	260.865i		−	0.510500i
$512$	507.841	−	65.1252i	0.991877	−	0.127198i
$513$			623.374i			1.21515i
$514$	91.1989	+	31.7375i	0.177430	+	0.0617461i
$515$	1099.45	+	1099.45i	2.13486	+	2.13486i
$516$	−19.3075	+	24.3809i	−0.0374176	+	0.0472498i
$517$	−57.6487	−	57.6487i	−0.111506	−	0.111506i
$518$	384.627	+	795.215i	0.742522	+	1.53516i
$519$		−	178.173i		−	0.343300i
$520$	−428.887	+	272.557i	−0.824782	+	0.524148i
$521$	195.384			0.375017			0.187508	−	0.982263i	$-0.439959\pi$
$521$	195.384			0.375017			0.187508	+	0.982263i	$0.439959\pi$
$522$	35.1628	−	17.0074i	0.0673618	−	0.0325813i
$523$	530.989	+	530.989i	1.01528	+	1.01528i	0.999881	+	0.0153946i	$0.00490044\pi$
$523$	530.989	+	530.989i	1.01528	+	1.01528i	0.0153946	+	0.999881i	$0.495100\pi$
$524$	−99.4766	−	856.617i	−0.189841	−	1.63477i
$525$	−634.412	+	634.412i	−1.20840	+	1.20840i
$526$	417.379	+	145.249i	0.793496	+	0.276139i
$527$		−	391.690i		−	0.743245i
$528$	−252.056	+	59.3413i	−0.477378	+	0.112389i
$529$	−357.568	+	389.854i	−0.675933	+	0.736964i
$530$	−55.1985	+	158.615i	−0.104148	+	0.299274i
$531$	183.313	+	183.313i	0.345223	+	0.345223i
$532$	−1641.18	+	190.585i	−3.08492	+	0.358243i
$533$	309.497	−	309.497i	0.580671	−	0.580671i
$534$	69.1554	+	142.979i	0.129504	+	0.267750i
$535$		−	951.558i		−	1.77861i
$536$	−305.284	−	68.0384i	−0.569560	−	0.126937i
$537$		−	246.739i		−	0.459477i
$538$	333.579	+	689.674i	0.620036	+	1.28192i
$539$	−1233.23	−	1233.23i	−2.28799	−	2.28799i
$540$	566.904	+	448.937i	1.04982	+	0.831365i
$541$	−706.134	−	706.134i	−1.30524	−	1.30524i	−0.924811	−	0.380427i	$-0.875777\pi$
$541$	−706.134	−	706.134i	−1.30524	−	1.30524i	−0.380427	−	0.924811i	$-0.624223\pi$
$542$	467.474	+	162.682i	0.862497	+	0.300151i
$543$		−	223.741i		−	0.412046i
$544$	379.447	+	39.4810i	0.697513	+	0.0725753i
$545$	526.780			0.966569
$546$	78.6618	−	226.038i	0.144069	−	0.413989i
$547$	−336.508	−	336.508i	−0.615188	−	0.615188i	0.329105	−	0.944293i	$-0.393253\pi$
$547$	−336.508	−	336.508i	−0.615188	−	0.615188i	−0.944293	+	0.329105i	$0.893253\pi$
$548$	−265.860	−	210.537i	−0.485146	−	0.384192i
$549$	266.991	+	266.991i	0.486322	+	0.486322i
$550$	−1264.14	+	611.434i	−2.29843	+	1.11170i
$551$	−79.9848			−0.145163
$552$	223.388	−	44.1209i	0.404688	−	0.0799292i
$553$			987.844i			1.78634i
$554$	385.238	−	186.331i	0.695376	−	0.336337i
$555$	−253.880	+	253.880i	−0.457442	+	0.457442i
$556$	−262.053	+	30.4315i	−0.471319	+	0.0547330i
$557$	303.865	−	303.865i	0.545539	−	0.545539i	−0.379608	−	0.925147i	$-0.623941\pi$
$557$	303.865	−	303.865i	0.545539	−	0.545539i	0.925147	+	0.379608i	$0.123941\pi$
$558$	161.298	−	463.496i	0.289065	−	0.830639i
$559$		−	44.9894i		−	0.0804819i
$560$	−1008.61	+	1629.76i	−1.80109	+	2.91029i
$561$	−192.943			−0.343928
$562$	257.722	+	89.6880i	0.458580	+	0.159587i
$563$	487.003	−	487.003i	0.865015	−	0.865015i	−0.126901	−	0.991915i	$-0.540503\pi$
$563$	487.003	−	487.003i	0.865015	−	0.865015i	0.991915	+	0.126901i	$0.0405029\pi$
$564$	−3.55960	−	30.6526i	−0.00631135	−	0.0543486i
$565$	687.730	−	687.730i	1.21722	−	1.21722i
$566$	175.260	+	362.349i	0.309646	+	0.640193i
$567$	567.117			1.00021
$568$	0.150865	−	0.0958746i	0.000265608	−	0.000168793i
$569$	−1119.37			−1.96727			−0.983633	−	0.180185i	$-0.942330\pi$
$569$	−1119.37			−1.96727			−0.983633	+	0.180185i	$0.942330\pi$
$570$	−292.404	−	604.545i	−0.512990	−	1.06061i
$571$	150.035	+	150.035i	0.262758	+	0.262758i	0.826174	−	0.563416i	$-0.190513\pi$
$571$	150.035	+	150.035i	0.262758	+	0.262758i	−0.563416	+	0.826174i	$0.690513\pi$
$572$	232.556	−	293.664i	0.406566	−	0.513399i
$573$	−24.7563	+	24.7563i	−0.0432046	+	0.0432046i
$574$	542.578	−	1559.12i	0.945258	−	2.71624i
$575$	1130.35	−	497.054i	1.96583	−	0.864441i
$576$	432.751	+	202.975i	0.751303	+	0.352387i
$577$	804.212			1.39378			0.696891	−	0.717177i	$-0.254566\pi$
$577$	804.212			1.39378			0.696891	+	0.717177i	$0.254566\pi$
$578$	−277.426	−	96.5449i	−0.479975	−	0.167033i
$579$	99.7610	+	99.7610i	0.172299	+	0.172299i
$580$	−57.6028	+	72.7391i	−0.0993152	+	0.125412i
$581$	−354.234	+	354.234i	−0.609697	+	0.609697i
$582$	316.930	−	153.292i	0.544554	−	0.263388i
$583$		−	123.801i		−	0.212352i
$584$	130.432	−	82.8890i	0.223342	−	0.141933i
$585$	−474.406			−0.810951
$586$	84.0139	+	173.699i	0.143368	+	0.296414i
$587$	437.230	−	437.230i	0.744855	−	0.744855i	−0.228653	−	0.973508i	$-0.573432\pi$
$587$	437.230	−	437.230i	0.744855	−	0.744855i	0.973508	+	0.228653i	$0.0734322\pi$
$588$	−76.1473	−	655.724i	−0.129502	−	1.11518i
$589$	−710.609	+	710.609i	−1.20647	+	1.20647i
$590$	−581.610	−	202.402i	−0.985780	−	0.343054i
$591$	−95.0542			−0.160836
$592$	−275.390	+	444.988i	−0.465186	+	0.751669i
$593$	−1084.67			−1.82912			−0.914561	−	0.404449i	$-0.867463\pi$
$593$	−1084.67			−1.82912			−0.914561	+	0.404449i	$0.867463\pi$
$594$	−503.446	−	175.200i	−0.847552	−	0.294950i
$595$	−1009.81	+	1009.81i	−1.69716	+	1.69716i
$596$	−20.1205	−	173.263i	−0.0337593	−	0.290710i
$597$	−192.045	−	192.045i	−0.321684	−	0.321684i
$598$	−213.713	+	250.657i	−0.357380	+	0.419159i
$599$			266.048i			0.444154i	0.975029	+	0.222077i	$0.0712836\pi$
$599$			266.048i			0.444154i	−0.975029	+	0.222077i	$0.928716\pi$
$600$	−518.785	−	115.621i	−0.864642	−	0.192702i
$601$			1140.44i			1.89757i	0.315924	+	0.948784i	$0.397685\pi$
$601$			1140.44i			1.89757i	−0.315924	+	0.948784i	$0.602315\pi$
$602$	−73.8837	−	152.754i	−0.122730	−	0.253745i
$603$	−206.473	−	206.473i	−0.342409	−	0.342409i
$604$	378.396	−	477.827i	0.626484	−	0.791105i
$605$	313.827	−	313.827i	0.518722	−	0.518722i
$606$	250.027	+	87.0102i	0.412587	+	0.143581i
$607$	−35.5662			−0.0585934			−0.0292967	−	0.999571i	$-0.509327\pi$
$607$	−35.5662			−0.0585934			−0.0292967	+	0.999571i	$0.509327\pi$
$608$	−616.771	−	760.024i	−1.01443	−	1.25004i
$609$		−	43.6997i		−	0.0717565i
$610$	−847.100	−	294.793i	−1.38869	−	0.483267i
$611$	31.5654	+	31.5654i	0.0516619	+	0.0516619i
$612$	279.207	+	221.107i	0.456220	+	0.361285i
$613$	−558.143	−	558.143i	−0.910510	−	0.910510i	0.0858021	−	0.996312i	$-0.472655\pi$
$613$	−558.143	−	558.143i	−0.910510	−	0.910510i	−0.996312	+	0.0858021i	$0.972655\pi$
$614$	−372.331	−	769.793i	−0.606402	−	1.25373i
$615$	670.988			1.09104
$616$	307.337	−	1379.00i	0.498923	−	2.23864i
$617$	−838.248			−1.35859			−0.679293	−	0.733867i	$-0.737714\pi$
$617$	−838.248			−1.35859			−0.679293	+	0.733867i	$0.737714\pi$
$618$	−188.898	−	390.546i	−0.305660	−	0.631951i
$619$	−155.904	−	155.904i	−0.251865	−	0.251865i	0.569870	−	0.821735i	$-0.306994\pi$
$619$	−155.904	−	155.904i	−0.251865	−	0.251865i	−0.821735	+	0.569870i	$0.806994\pi$
$620$	134.475	+	1158.00i	0.216895	+	1.86774i
$621$	436.832	+	169.992i	0.703434	+	0.273738i
$622$	−161.029	+	462.724i	−0.258889	+	0.743929i
$623$	−866.562			−1.39095
$624$	138.012	−	32.4922i	0.221174	−	0.0520708i
$625$	−915.157			−1.46425
$626$	−975.437	−	339.455i	−1.55821	−	0.542260i
$627$	350.040	+	350.040i	0.558278	+	0.558278i
$628$	194.303	−	22.5638i	0.309399	−	0.0359297i
$629$	−275.717	+	275.717i	−0.438342	+	0.438342i
$630$	−1610.77	+	779.092i	−2.55678	+	1.23665i
$631$	325.044			0.515126			0.257563	−	0.966262i	$-0.417081\pi$
$631$	325.044			0.515126			0.257563	+	0.966262i	$0.417081\pi$
$632$	−493.918	+	313.884i	−0.781515	+	0.496652i
$633$		−	194.933i		−	0.307951i
$634$	289.678	+	598.909i	0.456906	+	0.944652i
$635$	675.213	+	675.213i	1.06333	+	1.06333i
$636$	29.0913	−	36.7355i	0.0457410	−	0.0577603i
$637$	675.250	+	675.250i	1.06005	+	1.06005i
$638$	22.4799	−	64.5968i	0.0352349	−	0.101249i
$639$	0.166877			0.000261154
$640$	−1135.36	+	13.5497i	−1.77399	+	0.0211714i
$641$		−	353.421i		−	0.551359i	−0.961250	−	0.275680i	$-0.911097\pi$
$641$		−	353.421i		−	0.551359i	0.961250	−	0.275680i	$-0.0889029\pi$
$642$	−87.2615	+	250.750i	−0.135921	+	0.390576i
$643$	733.825	−	733.825i	1.14125	−	1.14125i	0.153031	−	0.988221i	$-0.451097\pi$
$643$	733.825	−	733.825i	1.14125	−	1.14125i	0.988221	−	0.153031i	$-0.0489033\pi$
$644$	−313.989	+	1202.03i	−0.487560	+	1.86651i
$645$	48.7683	−	48.7683i	0.0756098	−	0.0756098i
$646$	−317.555	−	656.545i	−0.491572	−	1.01632i
$647$			158.817i			0.245467i	0.992440	+	0.122733i	$0.0391660\pi$
$647$			158.817i			0.245467i	−0.992440	+	0.122733i	$0.960834\pi$
$648$	180.199	+	283.556i	0.278085	+	0.437586i
$649$	453.954			0.699467
$650$	692.176	−	334.789i	1.06489	−	0.515061i
$651$	−388.241	−	388.241i	−0.596377	−	0.596377i
$652$	−0.834178	−	7.18331i	−0.00127941	−	0.0110173i
$653$	−669.245	−	669.245i	−1.02488	−	1.02488i	−0.999683	−	0.0251947i	$-0.991979\pi$
$653$	−669.245	−	669.245i	−1.02488	−	1.02488i	−0.0251947	−	0.999683i	$-0.508021\pi$
$654$	−138.814	−	48.3078i	−0.212254	−	0.0738651i
$655$			1912.44i			2.91976i
$656$	951.955	−	224.118i	1.45115	−	0.341644i
$657$	144.275			0.219596
$658$	159.014	+	55.3371i	0.241662	+	0.0840990i
$659$	−405.338	+	405.338i	−0.615081	+	0.615081i	−0.944266	−	0.329185i	$-0.893226\pi$
$659$	−405.338	+	405.338i	−0.615081	+	0.615081i	0.329185	+	0.944266i	$0.393226\pi$
$660$	570.420	−	66.2412i	0.864272	−	0.100366i
$661$	−324.045	−	324.045i	−0.490235	−	0.490235i	0.418145	−	0.908380i	$-0.362680\pi$
$661$	−324.045	−	324.045i	−0.490235	−	0.490235i	−0.908380	+	0.418145i	$0.862680\pi$
$662$	−162.742	+	78.7144i	−0.245833	+	0.118904i
$663$	105.646			0.159345
$664$	−289.672	−	64.5588i	−0.436253	−	0.0972271i
$665$	3664.02			5.50980
$666$	−439.803	+	212.723i	−0.660365	+	0.319403i
$667$	−21.8115	+	56.0497i	−0.0327009	+	0.0840325i
$668$	−772.075	+	974.952i	−1.15580	+	1.45951i
$669$	−138.698	−	138.698i	−0.207322	−	0.207322i
$670$	655.089	+	227.973i	0.977745	+	0.340258i
$671$	661.172			0.985354
$672$	415.239	−	336.973i	0.617915	−	0.501447i
$673$	−488.918			−0.726475			−0.363238	−	0.931697i	$-0.618329\pi$
$673$	−488.918			−0.726475			−0.363238	+	0.931697i	$0.618329\pi$
$674$	−239.433	+	688.021i	−0.355242	+	1.02080i
$675$	−773.685	−	773.685i	−1.14620	−	1.14620i
$676$	292.339	−	369.157i	0.432455	−	0.546090i
$677$	346.064	+	346.064i	0.511173	+	0.511173i	0.914886	−	0.403713i	$-0.132281\pi$
$677$	346.064	+	346.064i	0.511173	+	0.511173i	−0.403713	+	0.914886i	$0.632281\pi$
$678$	−244.295	+	118.160i	−0.360316	+	0.174277i
$679$			1920.84i			2.82893i
$680$	−825.763	−	184.037i	−1.21436	−	0.270642i
$681$	327.074			0.480285
$682$	−374.180	−	773.615i	−0.548650	−	1.13433i
$683$	−235.665	+	235.665i	−0.345045	+	0.345045i	−0.858260	−	0.513215i	$-0.828454\pi$
$683$	−235.665	+	235.665i	−0.345045	+	0.345045i	0.513215	+	0.858260i	$0.328454\pi$
$684$	−105.406	−	907.674i	−0.154102	−	1.32701i
$685$	531.790	+	531.790i	0.776336	+	0.776336i
$686$	2151.76	+	748.819i	3.13668	+	1.09157i
$687$		−	132.478i		−	0.192836i
$688$	52.9002	−	85.4787i	0.0768898	−	0.124242i
$689$			67.7871i			0.0983847i
$690$	−503.375	+	40.0467i	−0.729529	+	0.0580386i
$691$	−448.303	−	448.303i	−0.648774	−	0.648774i	0.303923	−	0.952697i	$-0.401704\pi$
$691$	−448.303	−	448.303i	−0.648774	−	0.648774i	−0.952697	+	0.303923i	$0.901704\pi$
$692$	66.4318	+	572.060i	0.0959997	+	0.826677i
$693$	932.659	−	932.659i	1.34583	−	1.34583i
$694$	471.875	−	228.235i	0.679935	−	0.328869i
$695$	585.048			0.841795
$696$	21.8497	−	13.8854i	0.0313932	−	0.0199503i
$697$	728.702			1.04548
$698$	−232.198	−	480.069i	−0.332662	−	0.687778i
$699$	−175.656	+	175.656i	−0.251296	+	0.251296i
$700$	1800.37	−	2273.45i	2.57195	−	3.24778i
$701$	601.042	−	601.042i	0.857406	−	0.857406i	−0.133626	−	0.991032i	$-0.542662\pi$
$701$	601.042	−	601.042i	0.857406	−	0.857406i	0.991032	+	0.133626i	$0.0426620\pi$
$702$	275.661	+	95.9306i	0.392679	+	0.136653i
$703$	1000.42			1.42307
$704$	787.150	−	284.506i	1.11811	−	0.404128i
$705$			68.4336i			0.0970689i
$706$	766.484	+	266.738i	1.08567	+	0.377816i
$707$	−1021.36	+	1021.36i	−1.44463	+	1.44463i
$708$	134.702	+	106.672i	0.190257	+	0.150666i
$709$	431.081	+	431.081i	0.608012	+	0.608012i	0.942426	−	0.334414i	$-0.108538\pi$
$709$	431.081	+	431.081i	0.608012	+	0.608012i	−0.334414	+	0.942426i	$0.608538\pi$
$710$	−0.356858	+	0.172604i	−0.000502617	+	0.000243104i
$711$	−546.339			−0.768410
$712$	−275.347	−	433.277i	−0.386723	−	0.608535i
$713$	304.182	+	691.742i	0.426623	+	0.970186i
$714$	358.703	−	173.496i	0.502385	−	0.242992i
$715$	−587.406	+	587.406i	−0.821547	+	0.821547i
$716$	91.9967	+	792.207i	0.128487	+	1.10643i
$717$	111.577	+	111.577i	0.155616	+	0.155616i
$718$	−82.2204	−	28.6129i	−0.114513	−	0.0398508i
$719$	−770.221			−1.07124			−0.535620	−	0.844459i	$-0.679922\pi$
$719$	−770.221			−1.07124			−0.535620	+	0.844459i	$0.679922\pi$
$720$	−901.359	−	557.825i	−1.25189	−	0.774756i
$721$	2367.01			3.28296
$722$	−377.699	+	1085.33i	−0.523129	+	1.50323i
$723$	199.821	−	199.821i	0.276377	−	0.276377i
$724$	83.4219	+	718.366i	0.115224	+	0.992219i
$725$	99.2711	−	99.2711i	0.136926	−	0.136926i
$726$	−111.477	+	53.9189i	−0.153550	+	0.0742684i
$727$	−453.890			−0.624333			−0.312166	−	0.950027i	$-0.601055\pi$
$727$	−453.890			−0.624333			−0.312166	+	0.950027i	$0.601055\pi$
$728$	−168.281	+	755.070i	−0.231156	+	1.03718i
$729$			86.6644i			0.118881i
$730$	−308.524	+	149.226i	−0.422636	+	0.204419i
$731$	52.9631	−	52.9631i	0.0724529	−	0.0724529i
$732$	196.190	+	155.365i	0.268019	+	0.212247i
$733$	300.003	−	300.003i	0.409281	−	0.409281i	−0.472207	−	0.881488i	$-0.656542\pi$
$733$	300.003	−	300.003i	0.409281	−	0.409281i	0.881488	+	0.472207i	$0.156542\pi$
$734$	33.7541	−	96.9937i	0.0459865	−	0.132144i
$735$			1463.94i			1.99175i
$736$	−700.781	+	224.949i	−0.952148	+	0.305637i
$737$	−511.305			−0.693766
$738$	862.291	+	300.080i	1.16842	+	0.406612i
$739$	−675.318	−	675.318i	−0.913827	−	0.913827i	0.0827442	−	0.996571i	$-0.473632\pi$
$739$	−675.318	−	675.318i	−0.913827	−	0.913827i	−0.996571	+	0.0827442i	$0.973632\pi$
$740$	720.474	−	909.792i	0.973614	−	1.22945i
$741$	−191.664	−	191.664i	−0.258656	−	0.258656i
$742$	111.323	+	230.160i	0.150031	+	0.310189i
$743$	−1008.64			−1.35753			−0.678765	−	0.734356i	$-0.737484\pi$
$743$	−1008.64			−1.35753			−0.678765	+	0.734356i	$0.737484\pi$
$744$	70.7566	−	317.481i	0.0951030	−	0.426722i
$745$			386.818i			0.519219i
$746$	25.4389	+	52.5948i	0.0341003	+	0.0705024i
$747$	−195.913	−	195.913i	−0.262267	−	0.262267i
$748$	619.484	−	71.9389i	0.828187	−	0.0961750i
$749$	−1024.31	−	1024.31i	−1.36756	−	1.36756i
$750$	594.843	+	207.007i	0.793125	+	0.276009i
$751$		−	180.767i		−	0.240701i	−0.992731	−	0.120351i	$-0.961598\pi$
$751$		−	180.767i		−	0.240701i	0.992731	−	0.120351i	$-0.0384019\pi$
$752$	22.8577	+	97.0892i	0.0303958	+	0.129108i
$753$		−	239.038i		−	0.317448i
$754$	−12.3088	+	35.3698i	−0.0163247	+	0.0469096i
$755$	−955.782	+	955.782i	−1.26594	+	1.26594i
$756$	1093.50	−	126.985i	1.44643	−	0.167970i
$757$	−977.765	−	977.765i	−1.29163	−	1.29163i	−0.933778	−	0.357854i	$-0.883509\pi$
$757$	−977.765	−	977.765i	−1.29163	−	1.29163i	−0.357854	−	0.933778i	$-0.616491\pi$
$758$	−183.393	−	379.165i	−0.241944	−	0.500218i
$759$	340.747	−	149.838i	0.448942	−	0.197415i
$760$	1164.23	+	1831.99i	1.53188	+	2.41052i
$761$			989.507i			1.30027i	0.759818	+	0.650136i	$0.225288\pi$
$761$			989.507i			1.30027i	−0.759818	+	0.650136i	$0.774712\pi$
$762$	−116.009	−	239.848i	−0.152243	−	0.314761i
$763$	567.053	−	567.053i	0.743189	−	0.743189i
$764$	70.2546	−	88.7153i	0.0919563	−	0.116120i
$765$	−558.488	−	558.488i	−0.730049	−	0.730049i
$766$	−44.4788	+	127.812i	−0.0580664	+	0.166856i
$767$	−248.562			−0.324070
$768$	300.426	+	100.546i	0.391179	+	0.130919i
$769$		−	80.4319i		−	0.104593i	−0.998632	−	0.0522964i	$-0.983346\pi$
$769$		−	80.4319i		−	0.104593i	0.998632	−	0.0522964i	$-0.0166541\pi$
$770$	−1029.78	+	2959.11i	−1.33737	+	3.84300i
$771$	42.2493	+	42.2493i	0.0547980	+	0.0547980i
$772$	−357.499	−	283.107i	−0.463081	−	0.366719i
$773$	178.335	+	178.335i	0.230705	+	0.230705i	0.812987	−	0.582282i	$-0.197840\pi$
$773$	178.335	+	178.335i	0.230705	+	0.230705i	−0.582282	+	0.812987i	$0.697840\pi$
$774$	84.4827	−	40.8623i	0.109151	−	0.0527937i
$775$		−	1763.91i		−	2.27601i
$776$	−960.414	+	610.342i	−1.23765	+	0.786523i
$777$			546.579i			0.703448i
$778$	−174.920	−	361.646i	−0.224832	−	0.464840i
$779$	−1322.02	−	1322.02i	−1.69707	−	1.69707i
$780$	−312.332	+	36.2702i	−0.400426	+	0.0465003i
$781$	0.206626	−	0.206626i	0.000264566	−	0.000264566i
$782$	−546.672	+	43.4912i	−0.699070	+	0.0556154i
$783$	53.2932			0.0680628
$784$	488.973	+	2076.94i	0.623690	+	2.64916i
$785$	−433.791			−0.552600
$786$	175.378	−	503.957i	0.223128	−	0.641167i
$787$	−386.055	+	386.055i	−0.490541	+	0.490541i	−0.908477	−	0.417936i	$-0.862754\pi$
$787$	−386.055	+	386.055i	−0.490541	+	0.490541i	0.417936	+	0.908477i	$0.362754\pi$
$788$	305.191	−	35.4410i	0.387298	−	0.0449758i
$789$	193.357	+	193.357i	0.245066	+	0.245066i
$790$	1168.32	−	565.088i	1.47888	−	0.715302i
$791$		−	1480.62i		−	1.87183i
$792$	762.675	+	169.976i	0.962973	+	0.214617i
$793$	−362.023			−0.456524
$794$	−158.661	−	328.032i	−0.199825	−	0.413139i
$795$	−73.4809	+	73.4809i	−0.0924288	+	0.0924288i
$796$	688.205	+	544.996i	0.864579	+	0.684669i
$797$	−162.290	+	162.290i	−0.203626	+	0.203626i	−0.801552	−	0.597926i	$-0.795992\pi$
$797$	−162.290	+	162.290i	−0.203626	+	0.203626i	0.597926	+	0.801552i	$0.295992\pi$
$798$	−965.523	−	336.005i	−1.20993	−	0.421058i
$799$			74.3198i			0.0930160i
$800$	1708.77	+	177.796i	2.13597	+	0.222245i
$801$		−	479.263i		−	0.598331i
$802$	174.226	−	500.644i	0.217239	−	0.624245i
$803$	178.640	−	178.640i	0.222466	−	0.222466i
$804$	−151.720	−	120.148i	−0.188706	−	0.149438i
$805$	999.162	−	2567.57i	1.24119	−	3.18953i
$806$	204.881	+	423.591i	0.254195	+	0.525548i
$807$			474.037i			0.587407i
$808$	−835.206	−	186.141i	−1.03367	−	0.230373i
$809$			1355.76i			1.67584i	0.545791	+	0.837921i	$0.316229\pi$
$809$			1355.76i			1.67584i	−0.545791	+	0.837921i	$0.683771\pi$
$810$	−324.415	−	670.727i	−0.400512	−	0.828058i
$811$	643.692	−	643.692i	0.793702	−	0.793702i	−0.188392	−	0.982094i	$-0.560327\pi$
$811$	643.692	−	643.692i	0.793702	−	0.793702i	0.982094	+	0.188392i	$0.0603275\pi$
$812$	16.2934	+	140.307i	0.0200658	+	0.172792i
$813$	216.564	+	216.564i	0.266377	+	0.266377i
$814$	−281.170	+	807.952i	−0.345417	+	0.992570i
$815$			16.0371i			0.0196774i
$816$	200.724	+	124.222i	0.245985	+	0.152233i
$817$	−192.173			−0.235217
$818$	322.310	−	926.171i	0.394022	−	1.13224i
$819$	−510.675	+	510.675i	−0.623535	+	0.623535i
$820$	−2154.34	+	250.178i	−2.62725	+	0.305095i
$821$	826.135	−	826.135i	1.00625	−	1.00625i	0.00627455	−	0.999980i	$-0.498003\pi$
$821$	826.135	−	826.135i	1.00625	−	1.00625i	0.999980	−	0.00627455i	$-0.00199726\pi$
$822$	−91.3674	−	188.902i	−0.111153	−	0.229808i
$823$		−	1360.74i		−	1.65339i	−0.562647	−	0.826697i	$-0.690217\pi$
$823$		−	1360.74i		−	1.65339i	0.562647	−	0.826697i	$-0.309783\pi$
$824$	752.110	+	1183.50i	0.912755	+	1.43628i
$825$	−868.887			−1.05320
$826$	−843.951	+	408.199i	−1.02173	+	0.494188i
$827$	−446.717	−	446.717i	−0.540166	−	0.540166i	0.383412	−	0.923578i	$-0.374749\pi$
$827$	−446.717	−	446.717i	−0.540166	−	0.540166i	−0.923578	+	0.383412i	$0.874749\pi$
$828$	−664.800	−	173.655i	−0.802899	−	0.209729i
$829$	−233.334	−	233.334i	−0.281464	−	0.281464i	0.552229	−	0.833693i	$-0.313778\pi$
$829$	−233.334	−	233.334i	−0.281464	−	0.281464i	−0.833693	+	0.552229i	$0.813778\pi$
$830$	621.587	+	216.314i	0.748901	+	0.260619i
$831$	264.788			0.318638
$832$	−431.002	+	155.781i	−0.518032	+	0.187236i
$833$			1589.86i			1.90859i
$834$	−154.169	−	53.6512i	−0.184855	−	0.0643299i
$835$	1950.16	−	1950.16i	2.33553	−	2.33553i
$836$	−1254.39	−	993.363i	−1.50046	−	1.18823i
$837$	473.473	−	473.473i	0.565678	−	0.565678i
$838$	522.576	−	252.758i	0.623600	−	0.301620i
$839$	212.932			0.253793			0.126896	−	0.991916i	$-0.459498\pi$
$839$	212.932			0.253793			0.126896	+	0.991916i	$0.459498\pi$
$840$	−1000.91	+	636.076i	−1.19156	+	0.757233i
$841$		−	834.162i		−	0.991869i
$842$	−343.419	−	710.017i	−0.407860	−	0.843250i
$843$	119.394	+	119.394i	0.141630	+	0.141630i
$844$	72.6807	+	625.872i	0.0861146	+	0.741554i
$845$	−738.412	+	738.412i	−0.873861	+	0.873861i
$846$	−30.6049	+	87.9444i	−0.0361760	+	0.103953i
$847$		−	675.639i		−	0.797684i
$848$	−79.7065	+	128.794i	−0.0939936	+	0.151879i
$849$			249.056i			0.293352i
$850$	1208.98	+	420.728i	1.42233	+	0.494974i
$851$	272.810	−	701.048i	0.320576	−	0.823793i
$852$	0.109866	−	0.0127584i	0.000128951	−	1.49747e-5i
$853$	319.516	−	319.516i	0.374579	−	0.374579i	−0.494563	−	0.869142i	$-0.664672\pi$
$853$	319.516	−	319.516i	0.374579	−	0.374579i	0.869142	+	0.494563i	$0.164672\pi$
$854$	−1229.19	+	594.532i	−1.43934	+	0.696173i
$855$			2026.43i			2.37009i
$856$	186.679	−	837.618i	0.218083	−	0.978525i
$857$		−	1427.30i		−	1.66547i	−0.553674	−	0.832733i	$-0.686775\pi$
$857$		−	1427.30i		−	1.66547i	0.553674	−	0.832733i	$-0.313225\pi$
$858$	208.658	−	100.923i	0.243191	−	0.117626i
$859$	−281.675	+	281.675i	−0.327911	+	0.327911i	−0.851792	−	0.523881i	$-0.824484\pi$
$859$	−281.675	+	281.675i	−0.327911	+	0.327911i	0.523881	+	0.851792i	$0.324484\pi$
$860$	−138.397	+	174.764i	−0.160927	+	0.203214i
$861$	722.286	−	722.286i	0.838892	−	0.838892i
$862$	216.573	−	622.333i	0.251245	−	0.721963i
$863$	−1210.34			−1.40248			−0.701240	−	0.712925i	$-0.747370\pi$
$863$	−1210.34			−1.40248			−0.701240	+	0.712925i	$0.747370\pi$
$864$	410.949	+	506.397i	0.475635	+	0.586108i
$865$		−	1277.15i		−	1.47648i
$866$	368.797	−	1059.75i	0.425863	−	1.22373i
$867$	−128.522	−	128.522i	−0.148237	−	0.148237i
$868$	1391.28	+	1101.77i	1.60286	+	1.26932i
$869$	−676.473	+	676.473i	−0.778450	+	0.778450i
$870$	−51.6834	+	24.9981i	−0.0594063	+	0.0287334i
$871$	279.964			0.321428
$872$	463.703	+	103.345i	0.531770	+	0.118515i
$873$	−1062.35			−1.21689
$874$	1070.68	+	912.877i	1.22504	+	1.04448i
$875$	−2429.92	+	2429.92i	−2.77705	+	2.77705i
$876$	94.9854	−	11.0304i	0.108431	−	0.0125918i
$877$	−427.618	−	427.618i	−0.487592	−	0.487592i	0.419954	−	0.907546i	$-0.362046\pi$
$877$	−427.618	−	427.618i	−0.487592	−	0.487592i	−0.907546	+	0.419954i	$0.862046\pi$
$878$	351.550	−	1010.19i	0.400399	−	1.15056i
$879$			119.389i			0.135824i
$880$	−1806.75	+	425.362i	−2.05312	+	0.483366i
$881$			609.490i			0.691816i	0.938269	+	0.345908i	$0.112429\pi$
$881$			609.490i			0.691816i	−0.938269	+	0.345908i	$0.887571\pi$
$882$	−654.703	+	1881.31i	−0.742293	+	2.13301i
$883$	−737.504	−	737.504i	−0.835225	−	0.835225i	0.153001	−	0.988226i	$-0.451106\pi$
$883$	−737.504	−	737.504i	−0.835225	−	0.835225i	−0.988226	+	0.153001i	$0.951106\pi$
$884$	−339.197	+	39.3900i	−0.383707	+	0.0445588i
$885$	−269.440	−	269.440i	−0.304452	−	0.304452i
$886$	496.583	−	240.186i	0.560478	−	0.271090i
$887$			1110.67i			1.25216i	0.779759	+	0.626080i	$0.215342\pi$
$887$			1110.67i			1.25216i	−0.779759	+	0.626080i	$0.784658\pi$
$888$	−273.287	+	173.674i	−0.307756	+	0.195578i
$889$	1453.67			1.63517
$890$	495.710	+	1024.88i	0.556977	+	1.15155i
$891$	388.360	+	388.360i	0.435870	+	0.435870i
$892$	497.033	+	393.605i	0.557211	+	0.441262i
$893$	134.832	−	134.832i	0.150988	−	0.150988i
$894$	35.4728	−	101.932i	0.0396787	−	0.114018i
$895$		−	1768.64i		−	1.97614i
$896$	−1207.57	+	1236.74i	−1.34773	+	1.38029i
$897$	−186.575	+	82.0433i	−0.207999	+	0.0914641i
$898$	291.295	+	101.371i	0.324382	+	0.112886i
$899$	60.7510	+	60.7510i	0.0675762	+	0.0675762i
$900$	1257.36	+	995.715i	1.39707	+	1.10635i
$901$	−79.8013	+	79.8013i	−0.0885696	+	0.0885696i
$902$	1439.24	−	696.125i	1.59561	−	0.771758i
$903$		−	104.993i		−	0.116272i
$904$	740.301	−	470.460i	0.818917	−	0.520421i
$905$		−	1603.79i		−	1.77214i
$906$	339.512	−	164.214i	0.374737	−	0.181251i
$907$	743.443	+	743.443i	0.819672	+	0.819672i	0.986060	−	0.166388i	$-0.0532104\pi$
$907$	743.443	+	743.443i	0.819672	+	0.819672i	−0.166388	+	0.986060i	$0.553210\pi$
$908$	−1050.14	+	121.949i	−1.15654	+	0.134306i
$909$	−564.874	−	564.874i	−0.621423	−	0.621423i
$910$	563.853	−	1620.25i	0.619618	−	1.78050i
$911$		−	1154.54i		−	1.26733i	−0.773607	−	0.633665i	$-0.781550\pi$
$911$		−	1154.54i		−	1.26733i	0.773607	−	0.633665i	$-0.218450\pi$
$912$	−138.791	−	589.521i	−0.152183	−	0.646405i
$913$	−485.157			−0.531388
$914$	715.206	+	248.894i	0.782501	+	0.272313i
$915$	−392.432	−	392.432i	−0.428887	−	0.428887i
$916$	49.3946	+	425.349i	0.0539242	+	0.464355i
$917$	2058.65	+	2058.65i	2.24499	+	2.24499i
$918$	211.584	+	437.450i	0.230484	+	0.476525i
$919$	1153.62			1.25530			0.627649	−	0.778497i	$-0.284017\pi$
$919$	1153.62			1.25530			0.627649	+	0.778497i	$0.284017\pi$
$920$	1601.26	−	316.261i	1.74050	−	0.343762i
$921$		−	529.106i		−	0.574490i
$922$	−375.981	−	777.340i	−0.407789	−	0.843102i
$923$	−0.113138	+	0.113138i	−0.000122576	+	0.000122576i
$924$	542.724	−	685.334i	0.587363	−	0.741704i
$925$	−1241.65	+	1241.65i	−1.34232	+	1.34232i
$926$	−1012.92	−	352.498i	−1.09386	−	0.380668i
$927$			1309.11i			1.41220i
$928$	−64.9756	+	52.7286i	−0.0700168	+	0.0568196i
$929$	841.858			0.906199			0.453099	−	0.891460i	$-0.350318\pi$
$929$	841.858			0.906199			0.453099	+	0.891460i	$0.350318\pi$
$930$	−237.081	+	681.261i	−0.254926	+	0.732539i
$931$	2884.34	−	2884.34i	3.09811	−	3.09811i
$932$	498.486	−	629.473i	0.534857	−	0.675401i
$933$	−214.364	+	214.364i	−0.229758	+	0.229758i
$934$	−832.229	+	402.530i	−0.891037	+	0.430974i
$935$	−1383.03			−1.47918
$936$	−417.601	−	93.0702i	−0.446155	−	0.0994340i
$937$	−1678.33			−1.79118			−0.895588	−	0.444884i	$-0.853245\pi$
$937$	−1678.33			−1.79118			−0.895588	+	0.444884i	$0.853245\pi$
$938$	950.573	−	459.770i	1.01340	−	0.490160i
$939$	−451.886	−	451.886i	−0.481241	−	0.481241i
$940$	−25.5154	−	219.720i	−0.0271441	−	0.233744i
$941$	579.610	−	579.610i	0.615951	−	0.615951i	−0.328539	−	0.944490i	$-0.606556\pi$
$941$	579.610	−	579.610i	0.615951	−	0.615951i	0.944490	+	0.328539i	$0.106556\pi$
$942$	114.310	+	39.7803i	0.121349	+	0.0422296i
$943$	−1286.92	+	565.902i	−1.36471	+	0.600108i
$944$	−472.260	−	292.268i	−0.500276	−	0.309606i
$945$	−2441.30			−2.58339
$946$	54.0104	−	155.201i	0.0570935	−	0.164060i
$947$	−463.504	−	463.504i	−0.489445	−	0.489445i	0.418686	−	0.908131i	$-0.362491\pi$
$947$	−463.504	−	463.504i	−0.489445	−	0.489445i	−0.908131	+	0.418686i	$0.862491\pi$
$948$	−359.690	+	41.7698i	−0.379420	+	0.0440610i
$949$	−97.8139	+	97.8139i	−0.103071	+	0.103071i
$950$	−1430.06	−	2956.64i	−1.50532	−	3.11225i
$951$			411.652i			0.432862i
$952$	−1087.00	+	690.787i	−1.14181	+	0.725617i
$953$	−1575.01			−1.65268			−0.826342	−	0.563169i	$-0.809582\pi$
$953$	−1575.01			−1.65268			−0.826342	+	0.563169i	$0.809582\pi$
$954$	−127.293	+	61.5686i	−0.133431	+	0.0645373i
$955$	−177.454	+	177.454i	−0.185816	+	0.185816i
$956$	−399.842	−	316.639i	−0.418245	−	0.331212i
$957$	29.9254	−	29.9254i	0.0312701	−	0.0312701i
$958$	−303.774	+	872.907i	−0.317092	+	0.911176i
$959$	1144.89			1.19384
$960$	−636.070	−	298.339i	−0.662573	−	0.310770i
$961$	118.460			0.123267
$962$	153.954	−	442.392i	0.160035	−	0.459867i
$963$	566.505	−	566.505i	0.588271	−	0.588271i
$964$	−567.062	+	716.068i	−0.588238	+	0.742809i
$965$	715.093	+	715.093i	0.741029	+	0.741029i
$966$	−498.751	+	584.967i	−0.516305	+	0.605556i
$967$			28.9033i			0.0298897i	0.999888	+	0.0149448i	$0.00475727\pi$
$967$			28.9033i			0.0298897i	−0.999888	+	0.0149448i	$0.995243\pi$
$968$	337.816	−	214.682i	0.348984	−	0.221779i
$969$		−	451.266i		−	0.465703i
$970$	2271.78	−	1098.80i	2.34204	−	1.13279i
$971$	944.362	+	944.362i	0.972567	+	0.972567i	0.999634	−	0.0270668i	$-0.00861670\pi$
$971$	944.362	+	944.362i	0.972567	+	0.972567i	−0.0270668	+	0.999634i	$0.508617\pi$
$972$	108.612	+	935.283i	0.111741	+	0.962225i
$973$	629.776	−	629.776i	0.647251	−	0.647251i
$974$	−245.634	+	705.841i	−0.252191	+	0.724682i
$975$	475.757			0.487956
$976$	−687.835	−	425.681i	−0.704749	−	0.436148i
$977$		−	527.542i		−	0.539961i	−0.962866	−	0.269981i	$-0.912983\pi$
$977$		−	527.542i		−	0.539961i	0.962866	−	0.269981i	$-0.0870173\pi$
$978$	1.47067	−	4.22602i	0.00150375	−	0.00432108i
$979$	−593.419	−	593.419i	−0.606148	−	0.606148i
$980$	−545.829	−	4700.27i	−0.556968	−	4.79619i
$981$	313.616	+	313.616i	0.319690	+	0.319690i
$982$	−1317.97	+	637.470i	−1.34213	+	0.649155i
$983$	361.383			0.367633			0.183816	−	0.982961i	$-0.441155\pi$
$983$	361.383			0.367633			0.183816	+	0.982961i	$0.441155\pi$
$984$	590.643	+	131.636i	0.600247	+	0.133776i
$985$	−681.354			−0.691730
$986$	−56.1290	+	27.1483i	−0.0569259	+	0.0275337i
$987$	73.6654	+	73.6654i	0.0746357	+	0.0746357i
$988$	686.837	+	543.913i	0.695179	+	0.550520i
$989$	−52.4046	+	134.666i	−0.0529875	+	0.136164i
$990$	−1636.57	−	569.532i	−1.65310	−	0.575284i
$991$	193.580			0.195338			0.0976690	−	0.995219i	$-0.468861\pi$
$991$	193.580			0.195338			0.0976690	+	0.995219i	$0.468861\pi$
$992$	−108.806	+	1045.72i	−0.109683	+	1.05415i
$993$	−111.858			−0.112647
$994$	−0.198341	+	0.569941i	−0.000199538	+	0.000573381i
$995$	−1376.59	−	1376.59i	−1.38351	−	1.38351i
$996$	−143.961	−	114.004i	−0.144539	−	0.114462i
$997$	963.584	−	963.584i	0.966484	−	0.966484i	−0.0329724	−	0.999456i	$-0.510497\pi$
$997$	963.584	−	963.584i	0.966484	−	0.966484i	0.999456	+	0.0329724i	$0.0104973\pi$
$998$	−331.490	−	685.356i	−0.332155	−	0.686729i
$999$	−666.571			−0.667238

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.3.k.b.45.11	✓	176
16.5	even	4	inner	368.3.k.b.229.12	yes	176
23.22	odd	2	inner	368.3.k.b.45.12	yes	176
368.229	odd	4	inner	368.3.k.b.229.11	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.3.k.b.45.11	✓	176	1.1	even	1	trivial
368.3.k.b.45.12	yes	176	23.22	odd	2	inner
368.3.k.b.229.11	yes	176	368.229	odd	4	inner
368.3.k.b.229.12	yes	176	16.5	even	4	inner

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	368.3.k.b.45.11

Level	$368$
Weight	$3$
Character	368.45
Analytic conductor	$10.027$
Analytic rank	$0$
Dimension	$176$
Inner twists	$4$