LMFDB - Embedded newform 368.3.k.b.229.12

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			229.12
Character	$\chi$	$=$	368.229
Dual form			368.3.k.b.45.12

$q$-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} +(-31.3277 - 33.6835i) 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} +(-26.5252 - 10.3222i) 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} +(81.3160 + 43.0314i) 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 $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

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

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	−0.837746	−	0.546060i	$-0.816127\pi$
$3$	−0.875057	+	0.875057i	−0.291686	+	0.291686i	0.546060	+	0.837746i	$0.316127\pi$
$4$	3.13581	−	2.48328i	0.783953	−	0.620820i
$5$	6.27246	−	6.27246i	1.25449	−	1.25449i	0.300806	−	0.953685i	$-0.402744\pi$
$5$	6.27246	−	6.27246i	1.25449	−	1.25449i	0.953685	−	0.300806i	$-0.0972558\pi$
$6$	1.07768	−	2.22809i	0.179613	−	0.371349i
$7$	13.5040			1.92914			0.964571	−	0.263824i	$-0.0849838\pi$
$7$	13.5040			1.92914			0.964571	+	0.263824i	$0.0849838\pi$
$8$	−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	$-0.547369\pi$
$11$	9.24750	−	9.24750i	0.840682	−	0.840682i	0.988948	+	0.148266i	$0.0473691\pi$
$12$	−0.571000	+	4.91702i	−0.0475834	+	0.409752i
$13$	5.06345	−	5.06345i	0.389496	−	0.389496i	−0.485012	−	0.874508i	$-0.661185\pi$
$13$	5.06345	−	5.06345i	0.389496	−	0.389496i	0.874508	+	0.485012i	$0.161185\pi$
$14$	−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	−0.988747	−	0.149598i	$-0.952202\pi$
$19$	−21.6286	−	21.6286i	−1.13834	−	1.13834i	−0.149598	−	0.988747i	$-0.547798\pi$
$20$	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	−0.738268	−	0.674507i	$-0.764356\pi$
$29$	−1.84906	+	1.84906i	−0.0637606	+	0.0637606i	0.674507	+	0.738268i	$0.264356\pi$
$30$	−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	$-0.895726\pi$
$37$	−23.1273	+	23.1273i	−0.625062	+	0.625062i	0.321760	+	0.946821i	$0.395726\pi$
$38$	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	$0.267748\pi$
$41$			61.1238i			1.49083i	−0.666603	+	0.745413i	$0.732252\pi$
$42$	14.5529	−	30.0882i	0.346499	−	0.716385i
$43$	4.44257	−	4.44257i	0.103315	−	0.103315i	−0.653560	−	0.756875i	$-0.726725\pi$
$43$	4.44257	−	4.44257i	0.103315	−	0.103315i	0.756875	+	0.653560i	$0.226725\pi$
$44$	6.03427	−	51.9626i	0.137142	−	1.18097i
$45$	46.8462	+	46.8462i	1.04103	+	1.04103i
$46$	−31.3277	−	33.6835i	−0.681037	−	0.732249i
$47$	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	$-0.778465\pi$
$53$	−6.69376	+	6.69376i	−0.126297	+	0.126297i	0.641133	+	0.767430i	$0.278465\pi$
$54$	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	0.467815	−	0.883826i	$-0.345041\pi$
$59$	−24.5447	−	24.5447i	−0.416012	−	0.416012i	−0.883826	+	0.467815i	$0.845041\pi$
$60$	27.2603	+	34.4234i	0.454338	+	0.573723i
$61$	35.7487	+	35.7487i	0.586044	+	0.586044i	0.936558	−	0.350513i	$-0.113993\pi$
$61$	35.7487	+	35.7487i	0.586044	+	0.586044i	−0.350513	+	0.936558i	$0.613993\pi$
$62$	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	$-0.344243\pi$
$67$	−27.6456	−	27.6456i	−0.412621	−	0.412621i	−0.882651	+	0.470030i	$0.844243\pi$
$68$	29.6050	+	37.3843i	0.435368	+	0.549769i
$69$	−26.5252	−	10.3222i	−0.384424	−	0.149597i
$70$	−104.316	+	215.674i	−1.49023	+	3.08105i
$71$		−	0.0223440i		−	0.000314704i	−1.00000		0.000157352i	$-0.999950\pi$
$71$		−	0.0223440i		−	0.000314704i	1.00000		0.000157352i	$-5.00867e-5\pi$
$72$	−50.4272	−	32.0464i	−0.700378	−	0.445089i
$73$		−	19.3177i		−	0.264625i	−0.991208	−	0.132313i	$-0.957760\pi$
$73$		−	19.3177i		−	0.264625i	0.991208	−	0.132313i	$-0.0422403\pi$
$74$	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	$-0.321741\pi$
$83$	−26.2318	−	26.2318i	−0.316046	−	0.316046i	−0.847246	+	0.531201i	$0.821741\pi$
$84$	−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	$-0.617397\pi$
$89$	−64.1708			−0.721020			−0.360510	+	0.932755i	$0.617397\pi$
$90$	−119.281	−	57.6935i	−1.32535	−	0.641038i
$91$	68.3768	−	68.3768i	0.751393	−	0.751393i
$92$	81.3160	+	43.0314i	0.883870	+	0.467733i
$93$	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	0.974263	−	0.225415i	$-0.0723738\pi$
$101$	75.6336	+	75.6336i	0.748848	+	0.748848i	−0.225415	+	0.974263i	$0.572374\pi$
$102$	26.5627	+	12.8478i	0.260419	+	0.125959i
$103$	175.282			1.70177			0.850886	−	0.525351i	$-0.176066\pi$
$103$	175.282			1.70177			0.850886	+	0.525351i	$0.176066\pi$
$104$	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	$-0.917132\pi$
$107$	−75.8520	+	75.8520i	−0.708898	+	0.708898i	0.257406	+	0.966303i	$0.417132\pi$
$108$	−80.9763	−	9.40355i	−0.749780	−	0.0870699i
$109$	41.9915	+	41.9915i	0.385243	+	0.385243i	0.872987	−	0.487744i	$-0.162180\pi$
$109$	41.9915	+	41.9915i	0.385243	+	0.385243i	−0.487744	+	0.872987i	$0.662180\pi$
$110$	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
$115$	190.135	+	73.9901i	1.65334	+	0.643392i
$116$	−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	−0.180068	+	0.983654i	$0.557632\pi$
$131$	−152.448	+	152.448i	−1.16372	+	1.16372i	−0.983654	+	0.180068i	$0.942368\pi$
$132$	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	$-0.399864\pi$
$137$	84.7818			0.618845			0.309423	+	0.950925i	$0.399864\pi$
$138$	56.8884	+	2.06142i	0.412235	+	0.0149378i
$139$	−46.6363	−	46.6363i	−0.335513	−	0.335513i	0.519163	−	0.854675i	$-0.326244\pi$
$139$	−46.6363	−	46.6363i	−0.335513	−	0.335513i	−0.854675	+	0.519163i	$0.826244\pi$
$140$	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	$-0.703253\pi$
$149$	30.8347	−	30.8347i	0.206944	−	0.206944i	0.802967	+	0.596023i	$0.203253\pi$
$150$	−119.621	−	57.8577i	−0.797471	−	0.385718i
$151$			152.378i			1.00912i	0.863376	+	0.504561i	$0.168346\pi$
$151$			152.378i			1.00912i	−0.863376	+	0.504561i	$0.831654\pi$
$152$	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	$-0.299776\pi$
$157$	−34.5790	−	34.5790i	−0.220249	−	0.220249i	−0.808603	+	0.588355i	$0.799776\pi$
$158$	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	−0.711017	−	0.703175i	$-0.751765\pi$
$163$	−1.27838	+	1.27838i	−0.00784279	+	0.00784279i	0.703175	+	0.711017i	$0.251765\pi$
$164$	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	$-0.619055\pi$
$167$		−	310.909i		−	1.86173i	0.365361	−	0.930866i	$-0.380945\pi$
$168$	−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	−0.348742	−	0.937219i	$-0.613391\pi$
$173$	101.807	−	101.807i	0.588477	−	0.588477i	0.937219	+	0.348742i	$0.113391\pi$
$174$	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	−0.193480	−	0.981104i	$-0.561977\pi$
$179$	140.985	−	140.985i	0.787625	−	0.787625i	0.981104	+	0.193480i	$0.0619774\pi$
$180$	263.233	+	30.5685i	1.46241	+	0.169825i
$181$	−127.844	+	127.844i	−0.706319	+	0.706319i	−0.965759	−	0.259440i	$-0.916462\pi$
$181$	−127.844	+	127.844i	−0.706319	+	0.706319i	0.259440	+	0.965759i	$0.416462\pi$
$182$	−84.2095	+	174.103i	−0.462689	+	0.956609i
$183$	−62.5643			−0.341881
$184$	−181.883	−	27.8294i	−0.988496	−	0.151247i
$185$			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	0.831390	−	0.555689i	$-0.187545\pi$
$197$	54.3132	+	54.3132i	0.275701	+	0.275701i	−0.555689	+	0.831390i	$0.687545\pi$
$198$	−175.856	−	85.0576i	−0.888164	−	0.429584i
$199$	−219.466			−1.10285			−0.551423	−	0.834226i	$-0.685915\pi$
$199$	−219.466			−1.10285			−0.551423	+	0.834226i	$0.685915\pi$
$200$	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	−0.392059	−	0.919940i	$-0.628237\pi$
$211$	111.383	−	111.383i	0.527882	−	0.527882i	0.919940	+	0.392059i	$0.128237\pi$
$212$	−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	$-0.0522095\pi$
$227$	186.887	+	186.887i	0.823292	+	0.823292i	−0.163287	+	0.986579i	$0.552210\pi$
$228$	118.698	−	93.9982i	0.520605	−	0.412273i
$229$	−75.6971	+	75.6971i	−0.330555	+	0.330555i	−0.852797	−	0.522242i	$-0.825096\pi$
$229$	−75.6971	+	75.6971i	−0.330555	+	0.330555i	0.522242	+	0.852797i	$0.325096\pi$
$230$	−407.780	−	14.7764i	−1.77296	−	0.0642450i
$231$			218.551i			0.946108i
$232$	−4.55070	−	20.4187i	−0.0196151	−	0.0880117i
$233$			200.737i			0.861532i	0.902464	+	0.430766i	$0.141757\pi$
$233$			200.737i			0.861532i	−0.902464	+	0.430766i	$0.858243\pi$
$234$	−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	$-0.875723\pi$
$251$	−136.585	+	136.585i	−0.544162	+	0.544162i	0.380584	+	0.924746i	$0.375723\pi$
$252$	250.452	+	316.263i	0.993857	+	1.25501i
$253$	280.316	+	109.084i	1.10797	+	0.431161i
$254$	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	$-0.362000\pi$
$263$	220.965			0.840171			0.420086	+	0.907484i	$0.362000\pi$
$264$	−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	−0.00694234	+	0.999976i	$0.502210\pi$
$269$	−270.861	+	270.861i	−1.00692	+	1.00692i	−0.999976	+	0.00694234i	$0.997790\pi$
$270$	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
$276$	−108.811	+	33.5012i	−0.394243	+	0.121381i
$277$	−151.298	−	151.298i	−0.546201	−	0.546201i	0.379139	−	0.925340i	$-0.376220\pi$
$277$	−151.298	−	151.298i	−0.546201	−	0.546201i	−0.925340	+	0.379139i	$0.876220\pi$
$278$	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	$-0.421941\pi$
$281$	136.441			0.485556			0.242778	+	0.970082i	$0.421941\pi$
$282$	6.71821	−	13.8899i	0.0238235	−	0.0492549i
$283$	142.308	−	142.308i	0.502856	−	0.502856i	−0.409468	−	0.912324i	$-0.634286\pi$
$283$	142.308	−	142.308i	0.502856	−	0.502856i	0.912324	+	0.409468i	$0.134286\pi$
$284$	−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	$-0.697356\pi$
$293$	68.2180	−	68.2180i	0.232826	−	0.232826i	0.813871	+	0.581045i	$0.197356\pi$
$294$	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
$299$	153.486	+	59.7286i	0.513332	+	0.199761i
$300$	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	−0.0151088	−	0.999886i	$-0.504809\pi$
$307$	302.327	−	302.327i	0.984777	−	0.984777i	0.999886	+	0.0151088i	$0.00480945\pi$
$308$	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	$0.128855\pi$
$311$			244.971i			0.787690i	−0.919177	+	0.393845i	$0.871145\pi$
$312$	−59.8330	−	38.0238i	−0.191772	−	0.121871i
$313$	−516.407			−1.64986			−0.824932	−	0.565232i	$-0.808787\pi$
$313$	−516.407			−1.64986			−0.824932	+	0.565232i	$0.808787\pi$
$314$	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	−0.972963	−	0.230962i	$-0.925813\pi$
$317$	−235.214	+	235.214i	−0.742001	+	0.742001i	0.230962	+	0.972963i	$0.425813\pi$
$318$	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
$322$	−423.049	−	454.861i	−1.31382	−	1.41261i
$323$	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	0.797033	−	0.603936i	$-0.206402\pi$
$331$	63.9148	+	63.9148i	0.193096	+	0.193096i	−0.603936	+	0.797033i	$0.706402\pi$
$332$	−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	0.387709	−	0.921782i	$-0.373266\pi$
$347$	−185.323	−	185.323i	−0.534072	−	0.534072i	−0.921782	+	0.387709i	$0.873266\pi$
$348$	−8.03604	−	10.1477i	−0.0230921	−	0.0291600i
$349$	188.541	−	188.541i	0.540232	−	0.540232i	−0.383365	−	0.923597i	$-0.625235\pi$
$349$	188.541	−	188.541i	0.540232	−	0.540232i	0.923597	+	0.383365i	$0.125235\pi$
$350$	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	$-0.519309\pi$
$359$	−43.5284			−0.121249			−0.0606245	+	0.998161i	$0.519309\pi$
$360$	−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	$0.977713\pi$
$368$	361.851	−	66.9922i	0.983290	−	0.182044i
$369$	−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	$-0.737532\pi$
$373$	20.6559	−	20.6559i	0.0553779	−	0.0553779i	0.734253	+	0.678876i	$0.237532\pi$
$374$	−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	$-0.839615\pi$
$379$	−148.912	+	148.912i	−0.392909	+	0.392909i	0.482814	+	0.875723i	$0.339615\pi$
$380$	−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	$-0.833122\pi$
$389$	−142.032	+	142.032i	−0.365120	+	0.365120i	0.500574	+	0.865694i	$0.333122\pi$
$390$	−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	−0.525984	−	0.850494i	$-0.676303\pi$
$397$	128.831	−	128.831i	0.324510	−	0.324510i	0.850494	+	0.525984i	$0.176303\pi$
$398$	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	$-0.795398\pi$
$409$		−	490.325i		−	1.19884i	0.800435	−	0.599420i	$-0.204602\pi$
$410$	−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
$414$	251.567	−	233.973i	0.607649	−	0.565151i
$415$	−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	$-0.137419\pi$
$419$	205.235	+	205.235i	0.489822	+	0.489822i	−0.418428	+	0.908250i	$0.637419\pi$
$420$	368.122	+	464.853i	0.876482	+	1.10679i
$421$	−278.850	+	278.850i	−0.662352	+	0.662352i	−0.955934	−	0.293582i	$-0.905153\pi$
$421$	−278.850	+	278.850i	−0.662352	+	0.662352i	0.293582	+	0.955934i	$0.405153\pi$
$422$	−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
$437$	255.131	−	655.618i	0.583824	−	1.50027i
$438$	−43.0416	−	20.8182i	−0.0982684	−	0.0475301i
$439$		−	534.808i		−	1.21824i	−0.793078	−	0.609121i	$-0.791523\pi$
$439$		−	534.808i		−	1.21824i	0.793078	−	0.609121i	$-0.208477\pi$
$440$	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	0.451852	−	0.892093i	$-0.350764\pi$
$443$	−195.027	−	195.027i	−0.440241	−	0.440241i	−0.892093	+	0.451852i	$0.850764\pi$
$444$	−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	$-0.364039\pi$
$457$	378.638			0.828530			0.414265	+	0.910156i	$0.364039\pi$
$458$	93.2248	−	192.742i	0.203548	−	0.420834i
$459$	171.803	−	171.803i	0.374299	−	0.374299i
$460$	779.964	−	240.139i	1.69557	−	0.522040i
$461$	305.291	−	305.291i	0.662236	−	0.662236i	−0.293671	−	0.955907i	$-0.594877\pi$
$461$	305.291	−	305.291i	0.662236	−	0.662236i	0.955907	+	0.293671i	$0.0948770\pi$
$462$	−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	$-0.414794\pi$
$467$	−326.848	−	326.848i	−0.699888	−	0.699888i	−0.964386	+	0.264498i	$0.914794\pi$
$468$	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
$483$	−358.197	−	139.391i	−0.741608	−	0.288594i
$484$	−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	$0.125335\pi$
$487$			373.680i			0.767310i	−0.923476	+	0.383655i	$0.874665\pi$
$488$	−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	0.998444	+	0.0557624i	$0.0177589\pi$
$491$	517.615	+	517.615i	1.05421	+	1.05421i	0.0557624	+	0.998444i	$0.482241\pi$
$492$	−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	−0.383947	−	0.923355i	$-0.625435\pi$
$499$	269.165	−	269.165i	0.539409	−	0.539409i	0.923355	+	0.383947i	$0.125435\pi$
$500$	−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	$-0.526412\pi$
$503$	−83.3763			−0.165758			−0.0828790	+	0.996560i	$0.526412\pi$
$504$	−680.968	−	432.754i	−1.35113	−	0.858640i
$505$	948.818			1.87885
$506$	−601.191	−	21.7848i	−1.18812	−	0.0430530i
$507$	−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	−0.233106	−	0.972451i	$-0.574889\pi$
$509$	376.327	−	376.327i	0.739346	−	0.739346i	0.972451	+	0.233106i	$0.0748888\pi$
$510$	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	$-0.560041\pi$
$521$	−195.384			−0.375017			−0.187508	+	0.982263i	$0.560041\pi$
$522$	35.1628	+	17.0074i	0.0673618	+	0.0325813i
$523$	−530.989	+	530.989i	−1.01528	+	1.01528i	−0.0153946	+	0.999881i	$0.504900\pi$
$523$	−530.989	+	530.989i	−1.01528	+	1.01528i	−0.999881	+	0.0153946i	$0.995100\pi$
$524$	−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	−0.380427	+	0.924811i	$0.624223\pi$
$541$	−706.134	+	706.134i	−1.30524	+	1.30524i	−0.924811	+	0.380427i	$0.875777\pi$
$542$	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	−0.944293	−	0.329105i	$-0.893253\pi$
$547$	−336.508	+	336.508i	−0.615188	+	0.615188i	0.329105	+	0.944293i	$0.393253\pi$
$548$	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
$552$	183.510	−	134.806i	0.332447	−	0.244213i
$553$		−	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	$-0.376059\pi$
$557$	−303.865	−	303.865i	−0.545539	−	0.545539i	−0.925147	+	0.379608i	$0.876059\pi$
$558$	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	$-0.459497\pi$
$563$	−487.003	−	487.003i	−0.865015	−	0.865015i	−0.991915	+	0.126901i	$0.959497\pi$
$564$	−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	$-0.0576696\pi$
$569$	1119.37			1.96727			0.983633	+	0.180185i	$0.0576696\pi$
$570$	−292.404	+	604.545i	−0.512990	+	1.06061i
$571$	−150.035	+	150.035i	−0.262758	+	0.262758i	−0.826174	−	0.563416i	$-0.809487\pi$
$571$	−150.035	+	150.035i	−0.262758	+	0.262758i	0.563416	+	0.826174i	$0.309487\pi$
$572$	−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	0.973508	−	0.228653i	$-0.0734322\pi$
$587$	437.230	+	437.230i	0.744855	+	0.744855i	−0.228653	+	0.973508i	$0.573432\pi$
$588$	−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
$598$	−329.181	−	11.9282i	−0.550469	−	0.0199469i
$599$		−	266.048i		−	0.444154i	−0.975029	−	0.222077i	$-0.928716\pi$
$599$		−	266.048i		−	0.444154i	0.975029	−	0.222077i	$-0.0712836\pi$
$600$	−518.785	+	115.621i	−0.864642	+	0.192702i
$601$		−	1140.44i		−	1.89757i	−0.315924	−	0.948784i	$-0.602315\pi$
$601$		−	1140.44i		−	1.89757i	0.315924	−	0.948784i	$-0.397685\pi$
$602$	−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	$-0.527345\pi$
$613$	558.143	−	558.143i	0.910510	−	0.910510i	0.996312	+	0.0858021i	$0.0273453\pi$
$614$	−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	$-0.262286\pi$
$617$	838.248			1.35859			0.679293	+	0.733867i	$0.262286\pi$
$618$	188.898	−	390.546i	0.305660	−	0.631951i
$619$	155.904	−	155.904i	0.251865	−	0.251865i	−0.569870	−	0.821735i	$-0.693006\pi$
$619$	155.904	−	155.904i	0.251865	−	0.251865i	0.821735	+	0.569870i	$0.193006\pi$
$620$	−134.475	+	1158.00i	−0.216895	+	1.86774i
$621$	169.992	−	436.832i	0.273738	−	0.703434i
$622$	−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	$-0.582919\pi$
$631$	−325.044			−0.515126			−0.257563	+	0.966262i	$0.582919\pi$
$632$	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	−0.988221	−	0.153031i	$-0.951097\pi$
$643$	−733.825	−	733.825i	−1.14125	−	1.14125i	−0.153031	−	0.988221i	$-0.548903\pi$
$644$	1098.09	+	581.096i	1.70511	+	0.902323i
$645$	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	$-0.960834\pi$
$647$		−	158.817i		−	0.245467i	0.992440	−	0.122733i	$-0.0391660\pi$
$648$	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	−0.0251947	+	0.999683i	$0.508021\pi$
$653$	−669.245	+	669.245i	−1.02488	+	1.02488i	−0.999683	+	0.0251947i	$0.991979\pi$
$654$	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	$-0.106774\pi$
$659$	405.338	+	405.338i	0.615081	+	0.615081i	−0.329185	+	0.944266i	$0.606774\pi$
$660$	570.420	+	66.2412i	0.864272	+	0.100366i
$661$	324.045	−	324.045i	0.490235	−	0.490235i	−0.418145	−	0.908380i	$-0.637320\pi$
$661$	324.045	−	324.045i	0.490235	−	0.490235i	0.908380	+	0.418145i	$0.137320\pi$
$662$	−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
$667$	−56.0497	−	21.8115i	−0.0840325	−	0.0327009i
$668$	−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	$-0.867719\pi$
$677$	−346.064	+	346.064i	−0.511173	+	0.511173i	0.403713	+	0.914886i	$0.367719\pi$
$678$	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	0.513215	−	0.858260i	$-0.328454\pi$
$683$	−235.665	−	235.665i	−0.345045	−	0.345045i	−0.858260	+	0.513215i	$0.828454\pi$
$684$	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
$690$	369.761	−	343.900i	0.535885	−	0.498406i
$691$	−448.303	+	448.303i	−0.648774	+	0.648774i	−0.952697	−	0.303923i	$-0.901704\pi$
$691$	−448.303	+	448.303i	−0.648774	+	0.648774i	0.303923	+	0.952697i	$0.401704\pi$
$692$	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	$-0.457338\pi$
$701$	−601.042	−	601.042i	−0.857406	−	0.857406i	−0.991032	+	0.133626i	$0.957338\pi$
$702$	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	$-0.891462\pi$
$709$	−431.081	+	431.081i	−0.608012	+	0.608012i	0.334414	+	0.942426i	$0.391462\pi$
$710$	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	$-0.398945\pi$
$727$	453.890			0.624333			0.312166	+	0.950027i	$0.398945\pi$
$728$	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	$-0.343458\pi$
$733$	−300.003	−	300.003i	−0.409281	−	0.409281i	−0.881488	+	0.472207i	$0.843458\pi$
$734$	−33.7541	−	96.9937i	−0.0459865	−	0.132144i
$735$			1463.94i			1.99175i
$736$	−639.460	+	364.399i	−0.868831	+	0.495108i
$737$	−511.305			−0.693766
$738$	862.291	−	300.080i	1.16842	−	0.406612i
$739$	−675.318	+	675.318i	−0.913827	+	0.913827i	−0.996571	−	0.0827442i	$-0.973632\pi$
$739$	−675.318	+	675.318i	−0.913827	+	0.913827i	0.0827442	+	0.996571i	$0.473632\pi$
$740$	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	$-0.262516\pi$
$743$	1008.64			1.35753			0.678765	+	0.734356i	$0.262516\pi$
$744$	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	0.357854	−	0.933778i	$-0.383509\pi$
$757$	977.765	−	977.765i	1.29163	−	1.29163i	0.933778	−	0.357854i	$-0.116491\pi$
$758$	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	$-0.774712\pi$
$761$		−	989.507i		−	1.30027i	0.759818	−	0.650136i	$-0.225288\pi$
$762$	−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	$-0.802160\pi$
$773$	−178.335	+	178.335i	−0.230705	+	0.230705i	0.582282	+	0.812987i	$0.302160\pi$
$774$	−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
$782$	401.565	−	373.480i	0.513510	−	0.477597i
$783$	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	$-0.137246\pi$
$787$	386.055	+	386.055i	0.490541	+	0.490541i	−0.417936	+	0.908477i	$0.637246\pi$
$788$	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	$-0.204008\pi$
$797$	162.290	+	162.290i	0.203626	+	0.203626i	−0.597926	+	0.801552i	$0.704008\pi$
$798$	−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
$805$	2567.57	+	999.162i	3.18953	+	1.24119i
$806$	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	$-0.683771\pi$
$809$		−	1355.76i		−	1.67584i	0.545791	−	0.837921i	$-0.316229\pi$
$810$	324.415	−	670.727i	0.400512	−	0.828058i
$811$	643.692	+	643.692i	0.793702	+	0.793702i	0.982094	−	0.188392i	$-0.0603275\pi$
$811$	643.692	+	643.692i	0.793702	+	0.793702i	−0.188392	+	0.982094i	$0.560327\pi$
$812$	−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	0.999980	+	0.00627455i	$0.00199726\pi$
$821$	826.135	+	826.135i	1.00625	+	1.00625i	0.00627455	+	0.999980i	$0.498003\pi$
$822$	91.3674	−	188.902i	0.111153	−	0.229808i
$823$			1360.74i			1.65339i	0.562647	+	0.826697i	$0.309783\pi$
$823$			1360.74i			1.65339i	−0.562647	+	0.826697i	$0.690217\pi$
$824$	−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	$-0.625251\pi$
$827$	446.717	−	446.717i	0.540166	−	0.540166i	0.923578	+	0.383412i	$0.125251\pi$
$828$	−321.382	+	607.313i	−0.388143	+	0.733470i
$829$	−233.334	+	233.334i	−0.281464	+	0.281464i	−0.833693	−	0.552229i	$-0.813778\pi$
$829$	−233.334	+	233.334i	−0.281464	+	0.281464i	0.552229	+	0.833693i	$0.313778\pi$
$830$	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	$-0.540502\pi$
$839$	−212.932			−0.253793			−0.126896	+	0.991916i	$0.540502\pi$
$840$	−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
$851$	−701.048	−	272.810i	−0.823793	−	0.320576i
$852$	0.109866	+	0.0127584i	0.000128951	+	1.49747e-5i
$853$	319.516	+	319.516i	0.374579	+	0.374579i	0.869142	−	0.494563i	$-0.164672\pi$
$853$	319.516	+	319.516i	0.374579	+	0.374579i	−0.494563	+	0.869142i	$0.664672\pi$
$854$	−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	$0.313225\pi$
$857$			1427.30i			1.66547i	−0.553674	+	0.832733i	$0.686775\pi$
$858$	−208.658	−	100.923i	−0.243191	−	0.117626i
$859$	−281.675	−	281.675i	−0.327911	−	0.327911i	0.523881	−	0.851792i	$-0.324484\pi$
$859$	−281.675	−	281.675i	−0.327911	−	0.327911i	−0.851792	+	0.523881i	$0.824484\pi$
$860$	−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
$874$	−50.9515	+	1406.10i	−0.0582969	+	1.60881i
$875$	−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	−0.907546	−	0.419954i	$-0.862046\pi$
$877$	−427.618	+	427.618i	−0.487592	+	0.487592i	0.419954	+	0.907546i	$0.362046\pi$
$878$	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	−0.988226	−	0.153001i	$-0.951106\pi$
$883$	−737.504	+	737.504i	−0.835225	+	0.835225i	0.153001	+	0.988226i	$0.451106\pi$
$884$	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	$-0.784658\pi$
$887$		−	1110.67i		−	1.25216i	0.779759	−	0.626080i	$-0.215342\pi$
$888$	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	$-0.946790\pi$
$907$	−743.443	+	743.443i	−0.819672	+	0.819672i	0.166388	+	0.986060i	$0.446790\pi$
$908$	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	$-0.715983\pi$
$919$	−1153.62			−1.25530			−0.627649	+	0.778497i	$0.715983\pi$
$920$	−1315.41	+	966.296i	−1.42980	+	1.05032i
$921$			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	$-0.146755\pi$
$937$	1678.33			1.79118			0.895588	+	0.444884i	$0.146755\pi$
$938$	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	$-0.393444\pi$
$941$	−579.610	−	579.610i	−0.615951	−	0.615951i	−0.944490	+	0.328539i	$0.893444\pi$
$942$	−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	−0.908131	−	0.418686i	$-0.862491\pi$
$947$	−463.504	+	463.504i	−0.489445	+	0.489445i	0.418686	+	0.908131i	$0.362491\pi$
$948$	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	$-0.190418\pi$
$953$	1575.01			1.65268			0.826342	+	0.563169i	$0.190418\pi$
$954$	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
$966$	768.221	+	27.8374i	0.795260	+	0.0288171i
$967$		−	28.9033i		−	0.0298897i	−0.999888	−	0.0149448i	$-0.995243\pi$
$967$		−	28.9033i		−	0.0298897i	0.999888	−	0.0149448i	$-0.00475727\pi$
$968$	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	$-0.991383\pi$
$971$	−944.362	+	944.362i	−0.972567	+	0.972567i	0.0270668	+	0.999634i	$0.491383\pi$
$972$	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	$-0.558845\pi$
$983$	−361.383			−0.367633			−0.183816	+	0.982961i	$0.558845\pi$
$984$	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
$989$	134.666	+	52.4046i	0.136164	+	0.0529875i
$990$	−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	0.999456	−	0.0329724i	$-0.0104973\pi$
$997$	963.584	+	963.584i	0.966484	+	0.966484i	−0.0329724	+	0.999456i	$0.510497\pi$
$998$	−331.490	+	685.356i	−0.332155	+	0.686729i
$999$	666.571			0.667238

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.3.k.b.45.11	✓	176	16.13	even	4	inner
368.3.k.b.45.12	yes	176	368.45	odd	4	inner
368.3.k.b.229.11	yes	176	23.22	odd	2	inner
368.3.k.b.229.12	yes	176	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(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} +(-31.3277 - 33.6835i) 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} +(-26.5252 - 10.3222i) 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} +(81.3160 + 43.0314i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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