LMFDB - Embedded newform 175.4.x.a.103.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.22
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59880 - 0.0837897i) q^{2} +(-4.11426 - 5.08068i) q^{3} +(-5.40702 - 0.568301i) q^{4} +(-9.89445 + 5.20575i) q^{5} +(6.15218 + 8.46775i) q^{6} +(-14.4655 + 11.5650i) q^{7} +(21.2474 + 3.36526i) q^{8} +(-3.27262 + 15.3965i) q^{9} +(16.2555 - 7.49391i) q^{10} +(-56.8321 + 12.0800i) q^{11} +(19.3585 + 29.8095i) q^{12} +(-10.5262 - 5.36337i) q^{13} +(24.0965 - 17.2781i) q^{14} +(67.1571 + 28.8528i) q^{15} +(8.85550 + 1.88230i) q^{16} +(-7.45196 - 19.4130i) q^{17} +(6.52235 - 24.3417i) q^{18} +(-8.62650 - 82.0756i) q^{19} +(56.4580 - 22.5246i) q^{20} +(118.273 + 25.9131i) q^{21} +(91.8755 - 14.5516i) q^{22} +(-0.885668 + 16.8995i) q^{23} +(-70.3196 - 121.797i) q^{24} +(70.8004 - 103.016i) q^{25} +(16.3799 + 9.45696i) q^{26} +(-65.5876 + 33.4185i) q^{27} +(84.7877 - 54.3116i) q^{28} +(93.2324 - 128.323i) q^{29} +(-104.953 - 51.7570i) q^{30} +(2.66569 - 5.98724i) q^{31} +(-180.235 - 48.2937i) q^{32} +(295.197 + 239.045i) q^{33} +(10.2876 + 31.6620i) q^{34} +(82.9235 - 189.733i) q^{35} +(26.4450 - 81.3893i) q^{36} +(-210.297 + 136.568i) q^{37} +(6.91498 + 131.946i) q^{38} +(16.0579 + 75.5466i) q^{39} +(-227.751 + 77.3113i) q^{40} +(262.447 - 85.2743i) q^{41} +(-186.924 - 51.3400i) q^{42} +(313.362 + 313.362i) q^{43} +(314.158 - 33.0193i) q^{44} +(-47.7694 - 169.376i) q^{45} +(2.83202 - 26.9448i) q^{46} +(305.246 + 117.173i) q^{47} +(-26.8705 - 52.7363i) q^{48} +(75.5007 - 334.587i) q^{49} +(-121.828 + 158.770i) q^{50} +(-67.9721 + 117.731i) q^{51} +(53.8674 + 34.9819i) q^{52} +(-371.801 + 301.079i) q^{53} +(107.662 - 47.9341i) q^{54} +(499.437 - 415.379i) q^{55} +(-346.274 + 197.047i) q^{56} +(-381.509 + 381.509i) q^{57} +(-159.812 + 197.352i) q^{58} +(-376.703 + 418.371i) q^{59} +(-346.723 - 194.173i) q^{60} +(32.2969 - 29.0802i) q^{61} +(-4.76358 + 9.34906i) q^{62} +(-130.721 - 260.566i) q^{63} +(215.231 + 69.9329i) q^{64} +(132.071 - 1.72914i) q^{65} +(-451.932 - 406.921i) q^{66} +(-160.644 + 61.6656i) q^{67} +(29.2605 + 109.202i) q^{68} +(89.5051 - 65.0293i) q^{69} +(-148.476 + 296.398i) q^{70} +(-212.013 - 154.036i) q^{71} +(-121.348 + 316.123i) q^{72} +(332.465 - 511.951i) q^{73} +(347.666 - 200.725i) q^{74} +(-814.683 + 64.1198i) q^{75} +448.687i q^{76} +(682.398 - 832.008i) q^{77} +(-19.3434 - 122.130i) q^{78} +(-105.641 - 237.273i) q^{79} +(-97.4191 + 27.4752i) q^{80} +(827.883 + 368.597i) q^{81} +(-426.747 + 114.346i) q^{82} +(-200.723 + 1267.31i) q^{83} +(-624.778 - 207.327i) q^{84} +(174.792 + 153.288i) q^{85} +(-474.747 - 527.260i) q^{86} +(-1035.55 + 54.2710i) q^{87} +(-1248.19 + 65.4148i) q^{88} +(-621.305 - 690.029i) q^{89} +(62.1818 + 274.802i) q^{90} +(214.294 - 44.1520i) q^{91} +(14.3929 - 90.8729i) q^{92} +(-41.3866 + 11.0895i) q^{93} +(-478.211 - 212.913i) q^{94} +(512.619 + 767.186i) q^{95} +(496.167 + 1114.41i) q^{96} +(-160.176 - 1011.31i) q^{97} +(-148.746 + 528.613i) q^{98} -914.548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−1.59880	−	0.0837897i	−0.565262	−	0.0296241i	−0.232435	−	0.972612i	$-0.574669\pi$
$2$	−1.59880	−	0.0837897i	−0.565262	−	0.0296241i	−0.332827	+	0.942988i	$0.608003\pi$
$3$	−4.11426	−	5.08068i	−0.791789	−	0.977778i	0.208211	−	0.978084i	$-0.433236\pi$
$3$	−4.11426	−	5.08068i	−0.791789	−	0.977778i	−1.00000		0.000305959i	$0.999903\pi$
$4$	−5.40702	−	0.568301i	−0.675878	−	0.0710376i
$5$	−9.89445	+	5.20575i	−0.884987	+	0.465616i
$5$	−9.89445	+	5.20575i	−0.884987	+	0.465616i
$6$	6.15218	+	8.46775i	0.418603	+	0.576157i
$7$	−14.4655	+	11.5650i	−0.781063	+	0.624452i
$7$	−14.4655	+	11.5650i	−0.781063	+	0.624452i
$8$	21.2474	+	3.36526i	0.939013	+	0.148725i
$9$	−3.27262	+	15.3965i	−0.121208	+	0.570240i
$10$	16.2555	−	7.49391i	0.514043	−	0.236978i
$11$	−56.8321	+	12.0800i	−1.55777	+	0.331115i	−0.904657	−	0.426141i	$-0.859873\pi$
$11$	−56.8321	+	12.0800i	−1.55777	+	0.331115i	−0.653118	+	0.757256i	$0.726539\pi$
$12$	19.3585	+	29.8095i	0.465694	+	0.717105i
$13$	−10.5262	−	5.36337i	−0.224573	−	0.114425i	0.338085	−	0.941116i	$-0.390221\pi$
$13$	−10.5262	−	5.36337i	−0.224573	−	0.114425i	−0.562657	+	0.826690i	$0.690221\pi$
$14$	24.0965	−	17.2781i	0.460004	−	0.329841i
$15$	67.1571	+	28.8528i	1.15599	+	0.496651i
$16$	8.85550	+	1.88230i	0.138367	+	0.0294109i
$17$	−7.45196	−	19.4130i	−0.106316	−	0.276962i	0.870095	−	0.492884i	$-0.164057\pi$
$17$	−7.45196	−	19.4130i	−0.106316	−	0.276962i	−0.976410	+	0.215923i	$0.930724\pi$
$18$	6.52235	−	24.3417i	0.0854073	−	0.318745i
$19$	−8.62650	−	82.0756i	−0.104161	−	0.991023i	−0.914369	−	0.404881i	$-0.867313\pi$
$19$	−8.62650	−	82.0756i	−0.104161	−	0.991023i	0.810208	−	0.586142i	$-0.199354\pi$
$20$	56.4580	−	22.5246i	0.631219	−	0.251832i
$21$	118.273	+	25.9131i	1.22901	+	0.269272i
$22$	91.8755	−	14.5516i	0.890360	−	0.141019i
$23$	−0.885668	+	16.8995i	−0.00802932	+	0.153209i	0.991672	+	0.128786i	$0.0411081\pi$
$23$	−0.885668	+	16.8995i	−0.00802932	+	0.153209i	−0.999702	+	0.0244226i	$0.992225\pi$
$24$	−70.3196	−	121.797i	−0.598080	−	1.03591i
$25$	70.8004	−	103.016i	0.566403	−	0.824128i
$26$	16.3799	+	9.45696i	0.123553	+	0.0713331i
$27$	−65.5876	+	33.4185i	−0.467494	+	0.238200i
$28$	84.7877	−	54.3116i	0.572263	−	0.366569i
$29$	93.2324	−	128.323i	0.596994	−	0.821692i	−0.398435	−	0.917197i	$-0.630447\pi$
$29$	93.2324	−	128.323i	0.596994	−	0.821692i	0.995429	+	0.0955048i	$0.0304465\pi$
$30$	−104.953	−	51.7570i	−0.638726	−	0.314983i
$31$	2.66569	−	5.98724i	0.0154443	−	0.0346884i	−0.905659	−	0.424008i	$-0.860623\pi$
$31$	2.66569	−	5.98724i	0.0154443	−	0.0346884i	0.921103	+	0.389319i	$0.127290\pi$
$32$	−180.235	−	48.2937i	−0.995666	−	0.266788i
$33$	295.197	+	239.045i	1.55719	+	1.26098i
$34$	10.2876	+	31.6620i	0.0518914	+	0.159705i
$35$	82.9235	−	189.733i	0.400475	−	0.916308i
$36$	26.4450	−	81.3893i	0.122431	−	0.376802i
$37$	−210.297	+	136.568i	−0.934395	+	0.606803i	−0.919502	−	0.393086i	$-0.871407\pi$
$37$	−210.297	+	136.568i	−0.934395	+	0.606803i	−0.0148931	+	0.999889i	$0.504741\pi$
$38$	6.91498	+	131.946i	0.0295199	+	0.563274i
$39$	16.0579	+	75.5466i	0.0659314	+	0.310183i
$40$	−227.751	+	77.3113i	−0.900263	+	0.305600i
$41$	262.447	−	85.2743i	0.999693	−	0.324820i	0.236950	−	0.971522i	$-0.423852\pi$
$41$	262.447	−	85.2743i	0.999693	−	0.324820i	0.762743	+	0.646702i	$0.223852\pi$
$42$	−186.924	−	51.3400i	−0.686738	−	0.188618i
$43$	313.362	+	313.362i	1.11133	+	1.11133i	0.992971	+	0.118360i	$0.0377638\pi$
$43$	313.362	+	313.362i	1.11133	+	1.11133i	0.118360	+	0.992971i	$0.462236\pi$
$44$	314.158	−	33.0193i	1.07639	−	0.113133i
$45$	−47.7694	−	169.376i	−0.158245	−	0.561091i
$46$	2.83202	−	26.9448i	0.00907735	−	0.0863652i
$47$	305.246	+	117.173i	0.947336	+	0.363648i	0.782484	−	0.622670i	$-0.213952\pi$
$47$	305.246	+	117.173i	0.947336	+	0.363648i	0.164851	+	0.986318i	$0.447286\pi$
$48$	−26.8705	−	52.7363i	−0.0808004	−	0.158580i
$49$	75.5007	−	334.587i	0.220119	−	0.975473i
$50$	−121.828	+	158.770i	−0.344581	+	0.449069i
$51$	−67.9721	+	117.731i	−0.186627	+	0.323248i
$52$	53.8674	+	34.9819i	0.143655	+	0.0932907i
$53$	−371.801	+	301.079i	−0.963601	+	0.780309i	−0.975586	−	0.219619i	$-0.929518\pi$
$53$	−371.801	+	301.079i	−0.963601	+	0.780309i	0.0119845	+	0.999928i	$0.496185\pi$
$54$	107.662	−	47.9341i	0.271313	−	0.120796i
$55$	499.437	−	415.379i	1.22444	−	1.01836i
$56$	−346.274	+	197.047i	−0.826300	+	0.470205i
$57$	−381.509	+	381.509i	−0.886527	+	0.886527i
$58$	−159.812	+	197.352i	−0.361800	+	0.446786i
$59$	−376.703	+	418.371i	−0.831230	+	0.923174i	−0.998025	−	0.0628172i	$-0.979991\pi$
$59$	−376.703	+	418.371i	−0.831230	+	0.923174i	0.166795	+	0.985992i	$0.446658\pi$
$60$	−346.723	−	194.173i	−0.746029	−	0.417794i
$61$	32.2969	−	29.0802i	0.0677900	−	0.0610384i	−0.634539	−	0.772891i	$-0.718810\pi$
$61$	32.2969	−	29.0802i	0.0677900	−	0.0610384i	0.702329	+	0.711852i	$0.252143\pi$
$62$	−4.76358	+	9.34906i	−0.00975767	+	0.0191505i
$63$	−130.721	−	260.566i	−0.261416	−	0.521082i
$64$	215.231	+	69.9329i	0.420374	+	0.136588i
$65$	132.071	−	1.72914i	0.252022	−	0.00329960i
$66$	−451.932	−	406.921i	−0.842863	−	0.758917i
$67$	−160.644	+	61.6656i	−0.292923	+	0.112443i	−0.500392	−	0.865799i	$-0.666811\pi$
$67$	−160.644	+	61.6656i	−0.292923	+	0.112443i	0.207469	+	0.978242i	$0.433477\pi$
$68$	29.2605	+	109.202i	0.0521817	+	0.194745i
$69$	89.5051	−	65.0293i	0.156162	−	0.113458i
$70$	−148.476	+	296.398i	−0.253518	+	0.506090i
$71$	−212.013	−	154.036i	−0.354384	−	0.257475i	0.396322	−	0.918112i	$-0.370286\pi$
$71$	−212.013	−	154.036i	−0.354384	−	0.257475i	−0.750706	+	0.660637i	$0.770286\pi$
$72$	−121.348	+	316.123i	−0.198625	+	0.517436i
$73$	332.465	−	511.951i	0.533042	−	0.820813i	−0.464872	−	0.885378i	$-0.653900\pi$
$73$	332.465	−	511.951i	0.533042	−	0.820813i	0.997913	+	0.0645656i	$0.0205662\pi$
$74$	347.666	−	200.725i	0.546154	−	0.315322i
$75$	−814.683	+	64.1198i	−1.25429	+	0.0987190i
$76$			448.687i			0.677210i
$77$	682.398	−	832.008i	1.00995	−	1.23138i
$78$	−19.3434	−	122.130i	−0.0280796	−	0.177288i
$79$	−105.641	−	237.273i	−0.150450	−	0.337916i	0.822560	−	0.568678i	$-0.192545\pi$
$79$	−105.641	−	237.273i	−0.150450	−	0.337916i	−0.973010	+	0.230762i	$0.925878\pi$
$80$	−97.4191	+	27.4752i	−0.136147	+	0.0383978i
$81$	827.883	+	368.597i	1.13564	+	0.505620i
$82$	−426.747	+	114.346i	−0.574711	+	0.153993i
$83$	−200.723	+	1267.31i	−0.265448	+	1.67597i	0.390066	+	0.920787i	$0.372452\pi$
$83$	−200.723	+	1267.31i	−0.265448	+	1.67597i	−0.655513	+	0.755184i	$0.727548\pi$
$84$	−624.778	−	207.327i	−0.811534	−	0.269301i
$85$	174.792	+	153.288i	0.223046	+	0.195605i
$86$	−474.747	−	527.260i	−0.595271	−	0.661116i
$87$	−1035.55	+	54.2710i	−1.27613	+	0.0668789i
$88$	−1248.19	+	65.4148i	−1.51202	+	0.0792414i
$89$	−621.305	−	690.029i	−0.739980	−	0.821831i	0.249213	−	0.968449i	$-0.419828\pi$
$89$	−621.305	−	690.029i	−0.739980	−	0.821831i	−0.989193	+	0.146617i	$0.953161\pi$
$90$	62.1818	+	274.802i	0.0728282	+	0.321852i
$91$	214.294	−	44.1520i	0.246859	−	0.0508614i
$92$	14.3929	−	90.8729i	0.0163104	−	0.102980i
$93$	−41.3866	+	11.0895i	−0.0461461	+	0.0123648i
$94$	−478.211	−	212.913i	−0.524720	−	0.233621i
$95$	512.619	+	767.186i	0.553617	+	0.828544i
$96$	496.167	+	1114.41i	0.527498	+	1.18478i
$97$	−160.176	−	1011.31i	−0.167664	−	1.05859i	−0.917724	−	0.397219i	$-0.869975\pi$
$97$	−160.176	−	1011.31i	−0.167664	−	1.05859i	0.750060	−	0.661370i	$-0.230025\pi$
$98$	−148.746	+	528.613i	−0.153322	+	0.544877i
$99$		−	914.548i		−	0.928439i
$100$	−441.364	+	516.774i	−0.441364	+	0.516774i
$101$	1542.76	−	890.715i	1.51991	−	0.877519i	0.520183	−	0.854055i	$-0.325864\pi$
$101$	1542.76	−	890.715i	1.51991	−	0.877519i	0.999725	−	0.0234640i	$-0.00746950\pi$
$102$	118.539	−	182.534i	0.115069	−	0.177191i
$103$	469.914	−	1224.17i	0.449534	−	1.17108i	−0.502363	−	0.864657i	$-0.667536\pi$
$103$	469.914	−	1224.17i	0.449534	−	1.17108i	0.951897	−	0.306419i	$-0.0991308\pi$
$104$	−205.606	−	149.381i	−0.193859	−	0.140847i
$105$	−1305.14	+	359.303i	−1.21304	+	0.333946i
$106$	619.665	−	450.213i	0.567803	−	0.412533i
$107$	496.211	+	1851.88i	0.448323	+	1.67316i	0.707012	+	0.707202i	$0.250043\pi$
$107$	496.211	+	1851.88i	0.448323	+	1.67316i	−0.258689	+	0.965961i	$0.583290\pi$
$108$	373.625	−	143.421i	0.332890	−	0.127784i
$109$	−254.267	−	228.943i	−0.223435	−	0.201182i	0.549809	−	0.835290i	$-0.314700\pi$
$109$	−254.267	−	228.943i	−0.223435	−	0.201182i	−0.773244	+	0.634109i	$0.781367\pi$
$110$	−833.306	+	622.261i	−0.722296	+	0.539366i
$111$	1559.08	+	506.575i	1.33316	+	0.433171i
$112$	−149.868	+	75.1857i	−0.126439	+	0.0634320i
$113$	−941.369	+	1847.54i	−0.783686	+	1.53807i	0.0581311	+	0.998309i	$0.481486\pi$
$113$	−941.369	+	1847.54i	−0.783686	+	1.53807i	−0.841818	+	0.539762i	$0.818514\pi$
$114$	641.924	−	577.991i	0.527383	−	0.474858i
$115$	−79.2115	−	171.822i	−0.0642306	−	0.139326i
$116$	−577.036	+	640.864i	−0.461866	+	0.512954i
$117$	117.025	−	144.514i	0.0924700	−	0.114191i
$118$	637.329	−	637.329i	0.497211	−	0.497211i
$119$	332.308	+	194.637i	0.255988	+	0.149935i
$120$	1329.82	+	839.050i	1.01163	+	0.638287i
$121$	1868.03	−	831.700i	1.40348	−	0.624869i
$122$	−54.0730	+	43.7874i	−0.0401273	+	0.0324945i
$123$	−1513.03	−	982.572i	−1.10915	−	0.720289i
$124$	−17.8160	+	30.8582i	−0.0129026	+	0.0223480i
$125$	−164.256	+	1387.86i	−0.117532	+	0.993069i
$126$	187.164	+	427.546i	0.132332	+	0.302292i
$127$	−526.571	−	1033.45i	−0.367918	−	0.722081i	0.630622	−	0.776090i	$-0.282800\pi$
$127$	−526.571	−	1033.45i	−0.367918	−	0.722081i	−0.998540	+	0.0540095i	$0.982800\pi$
$128$	1055.34	+	405.108i	0.728749	+	0.279741i
$129$	302.841	−	2881.34i	0.206695	−	1.96657i
$130$	−211.301	−	8.30166i	−0.142556	−	0.00560080i
$131$	2037.01	−	214.098i	1.35858	−	0.142793i	0.602945	−	0.797783i	$-0.293994\pi$
$131$	2037.01	−	214.098i	1.35858	−	0.142793i	0.755637	+	0.654990i	$0.227327\pi$
$132$	−1460.29	−	1460.29i	−0.962890	−	0.962890i
$133$	1073.99	+	1087.50i	0.700203	+	0.709008i
$134$	262.006	−	85.1309i	0.168909	−	0.0548820i
$135$	474.985	−	672.090i	0.302816	−	0.428476i
$136$	−93.0051	−	437.555i	−0.0586406	−	0.275882i
$137$	9.08466	+	173.346i	0.00566536	+	0.108102i	0.999998	+	0.00179153i	$0.000570263\pi$
$137$	9.08466	+	173.346i	0.00566536	+	0.108102i	−0.994333	+	0.106310i	$0.966096\pi$
$138$	−148.550	+	96.4694i	−0.0916333	+	0.0595074i
$139$	−574.008	+	1766.62i	−0.350264	+	1.07800i	0.608440	+	0.793600i	$0.291796\pi$
$139$	−574.008	+	1766.62i	−0.350264	+	1.07800i	−0.958705	+	0.284403i	$0.908204\pi$
$140$	−556.195	+	978.766i	−0.335765	+	0.590863i
$141$	−660.543	−	2032.94i	−0.394523	−	1.21422i
$142$	326.060	+	264.038i	0.192693	+	0.156039i
$143$	663.016	+	177.655i	0.387721	+	0.103890i
$144$	−57.9615	+	130.184i	−0.0335425	+	0.0753377i
$145$	−254.465	+	1755.03i	−0.145739	+	1.00516i
$146$	−574.442	+	790.652i	−0.325624	+	0.448183i
$147$	−2010.56	+	992.983i	−1.12808	+	0.557142i
$148$	1214.69	−	618.917i	0.674643	−	0.343748i
$149$	1221.32	+	705.128i	0.671505	+	0.387694i	0.796647	−	0.604445i	$-0.206605\pi$
$149$	1221.32	+	705.128i	0.671505	+	0.387694i	−0.125142	+	0.992139i	$0.539939\pi$
$150$	1307.89	−	34.2530i	0.711925	−	0.0186450i
$151$	500.718	+	867.269i	0.269853	+	0.467400i	0.968824	−	0.247751i	$-0.0796914\pi$
$151$	500.718	+	867.269i	0.269853	+	0.467400i	−0.698970	+	0.715151i	$0.746358\pi$
$152$	92.9152	−	1772.93i	0.0495817	−	0.946075i
$153$	323.280	−	51.2025i	0.170821	−	0.0270554i
$154$	−1160.73	+	1273.04i	−0.607368	+	0.666132i
$155$	4.79250	+	73.1174i	0.00248350	+	0.0378899i
$156$	−43.8924	−	417.608i	−0.0225269	−	0.214329i
$157$	795.322	−	2968.18i	0.404291	−	1.50883i	−0.401070	−	0.916047i	$-0.631362\pi$
$157$	795.322	−	2968.18i	0.404291	−	1.50883i	0.805360	−	0.592785i	$-0.201972\pi$
$158$	149.018	+	388.205i	0.0750331	+	0.195468i
$159$	3059.37	+	650.290i	1.52594	+	0.324348i
$160$	2034.73	−	460.416i	1.00537	−	0.227494i
$161$	−182.632	−	254.703i	−0.0894001	−	0.124680i
$162$	−1292.74	−	658.682i	−0.626957	−	0.319450i
$163$	−1551.28	−	2388.76i	−0.745434	−	1.14787i	−0.984246	−	0.176802i	$-0.943425\pi$
$163$	−1551.28	−	2388.76i	−0.745434	−	1.14787i	0.238813	−	0.971066i	$-0.423242\pi$
$164$	−1467.52	+	311.931i	−0.698745	+	0.148523i
$165$	−4165.22	−	828.506i	−1.96522	−	0.390904i
$166$	427.103	−	2009.36i	0.199697	−	0.939499i
$167$	2060.93	+	326.420i	0.954968	+	0.151252i	0.614424	−	0.788976i	$-0.289389\pi$
$167$	2060.93	+	326.420i	0.954968	+	0.151252i	0.340545	+	0.940228i	$0.389389\pi$
$168$	2425.79	+	948.607i	1.11401	+	0.435635i
$169$	−1209.33	−	1664.50i	−0.550446	−	0.757623i
$170$	−266.614	−	259.723i	−0.120285	−	0.117176i
$171$	1291.91	+	135.785i	0.577746	+	0.0607236i
$172$	−1516.27	−	1872.44i	−0.672178	−	0.830071i
$173$	3027.32	+	158.655i	1.33042	+	0.0697244i	0.704245	−	0.709957i	$-0.251286\pi$
$173$	3027.32	+	158.655i	1.33042	+	0.0697244i	0.626176	+	0.779682i	$0.284619\pi$
$174$	1660.19			0.723327
$175$	167.220	+	2308.99i	0.0722321	+	0.997388i
$176$	−526.015			−0.225283
$177$	3675.46	+	192.623i	1.56082	+	0.0817990i
$178$	935.527	+	1155.28i	0.393937	+	0.486471i
$179$	−2026.17	−	212.959i	−0.846052	−	0.0889237i	−0.328425	−	0.944530i	$-0.606518\pi$
$179$	−2026.17	−	212.959i	−0.846052	−	0.0889237i	−0.517627	+	0.855606i	$0.673185\pi$
$180$	162.033	+	942.969i	0.0670959	+	0.390471i
$181$	−361.179	−	497.120i	−0.148322	−	0.204147i	0.728391	−	0.685162i	$-0.240268\pi$
$181$	−361.179	−	497.120i	−0.148322	−	0.204147i	−0.876713	+	0.481014i	$0.840268\pi$
$182$	−346.314	+	52.6347i	−0.141047	+	0.0214370i
$183$	−280.625	−	44.4466i	−0.113357	−	0.0179540i
$184$	−75.6896	+	356.092i	−0.0303256	+	0.142671i
$185$	1369.83	−	2446.02i	0.544390	−	0.972082i
$186$	67.0982	−	14.2622i	0.0264510	−	0.00562233i
$187$	658.020	+	1013.26i	0.257322	+	0.396241i
$188$	−1583.89	−	807.030i	−0.614451	−	0.313078i
$189$	562.270	−	1241.94i	0.216398	−	0.477977i
$190$	−755.295	−	1269.53i	−0.288394	−	0.484745i
$191$	−1945.21	−	413.468i	−0.736914	−	0.156636i	−0.175860	−	0.984415i	$-0.556271\pi$
$191$	−1945.21	−	413.468i	−0.736914	−	0.156636i	−0.561054	+	0.827779i	$0.689604\pi$
$192$	−530.210	−	1381.24i	−0.199295	−	0.519181i
$193$	−3.09030	+	11.5331i	−0.00115256	+	0.00430142i	−0.966500	−	0.256668i	$-0.917375\pi$
$193$	−3.09030	+	11.5331i	−0.00115256	+	0.00430142i	0.965347	+	0.260969i	$0.0840421\pi$
$194$	171.352	+	1630.31i	0.0634144	+	0.603347i
$195$	−552.161	−	663.899i	−0.202775	−	0.243809i
$196$	−598.380	+	1766.21i	−0.218069	+	0.643664i
$197$	−568.813	+	90.0912i	−0.205717	+	0.0325824i	−0.258442	−	0.966027i	$-0.583209\pi$
$197$	−568.813	+	90.0912i	−0.205717	+	0.0325824i	0.0527253	+	0.998609i	$0.483209\pi$
$198$	−76.6297	+	1462.18i	−0.0275042	+	0.524812i
$199$	−448.040	−	776.028i	−0.159602	−	0.276438i	0.775123	−	0.631810i	$-0.217688\pi$
$199$	−448.040	−	776.028i	−0.159602	−	0.276438i	−0.934725	+	0.355372i	$0.884354\pi$
$200$	1851.00	−	1950.56i	0.654429	−	0.689629i
$201$	974.236	+	562.475i	0.341877	+	0.197383i
$202$	−2541.21	+	1294.81i	−0.885142	+	0.451002i
$203$	135.410	+	2934.50i	0.0468174	+	1.01459i
$204$	434.434	−	597.947i	0.149100	−	0.205219i
$205$	−2152.86	+	2209.98i	−0.733474	+	0.752934i
$206$	−853.872	+	1917.83i	−0.288797	+	0.648648i
$207$	−257.295	−	68.9420i	−0.0863925	−	0.0231488i
$208$	−83.1194	−	67.3087i	−0.0277081	−	0.0224376i
$209$	1481.74	+	4560.32i	0.490402	+	1.50930i
$210$	2116.77	−	465.097i	0.695577	−	0.152832i
$211$	−716.387	+	2204.81i	−0.233735	+	0.719363i	0.763551	+	0.645747i	$0.223454\pi$
$211$	−716.387	+	2204.81i	−0.233735	+	0.719363i	−0.997287	+	0.0736160i	$0.976546\pi$
$212$	2181.44	−	1416.65i	0.706708	−	0.458942i
$213$	89.6652	+	1710.91i	0.0288439	+	0.550375i
$214$	−638.175	−	3002.38i	−0.203854	−	0.959057i
$215$	−4731.83	−	1469.26i	−1.50097	−	0.466060i
$216$	−1506.03	+	489.339i	−0.474409	+	0.154145i
$217$	30.6820	+	117.437i	0.00959830	+	0.0367380i
$218$	387.340	+	387.340i	0.120339	+	0.120339i
$219$	−3968.91	+	417.149i	−1.22463	+	0.128714i
$220$	−2936.53	+	1962.13i	−0.899912	+	0.601304i
$221$	−25.6783	+	244.313i	−0.00781589	+	0.0743632i
$222$	−2450.21	−	940.548i	−0.740754	−	0.284349i
$223$	1072.80	+	2105.49i	0.322153	+	0.632262i	0.994116	−	0.108324i	$-0.0345483\pi$
$223$	1072.80	+	2105.49i	0.322153	+	0.632262i	−0.671962	+	0.740585i	$0.734548\pi$
$224$	3165.70	−	1385.83i	0.944274	−	0.413368i
$225$	1354.38	+	1427.21i	0.401298	+	0.422877i
$226$	1659.87	−	2874.98i	0.488552	−	0.846198i
$227$	−568.367	−	369.102i	−0.166184	−	0.107921i	0.458867	−	0.888505i	$-0.348255\pi$
$227$	−568.367	−	369.102i	−0.166184	−	0.107921i	−0.625051	+	0.780584i	$0.714922\pi$
$228$	2279.64	−	1846.02i	0.662161	−	0.536208i
$229$	−1925.40	+	857.243i	−0.555607	+	0.247372i	−0.665278	−	0.746596i	$-0.731687\pi$
$229$	−1925.40	+	857.243i	−0.555607	+	0.247372i	0.109671	+	0.993968i	$0.465020\pi$
$230$	112.247	+	281.347i	0.0321797	+	0.0806586i
$231$	−7034.73	−	43.9557i	−2.00368	−	0.0125198i
$232$	2412.79	−	2412.79i	0.682791	−	0.682791i
$233$	−2575.09	+	3179.97i	−0.724033	+	0.894106i	−0.997705	−	0.0677173i	$-0.978428\pi$
$233$	−2575.09	+	3179.97i	−0.724033	+	0.894106i	0.273672	+	0.961823i	$0.411762\pi$
$234$	−199.209	+	221.244i	−0.0556526	+	0.0618085i
$235$	−3630.22	+	429.672i	−1.00770	+	0.119271i
$236$	2274.60	−	2048.06i	0.627390	−	0.564905i
$237$	−770.877	+	1512.93i	−0.211282	+	0.414664i
$238$	−514.987	−	339.030i	−0.140259	−	0.0923363i
$239$	−3409.00	−	1107.65i	−0.922636	−	0.299782i	−0.191088	−	0.981573i	$-0.561202\pi$
$239$	−3409.00	−	1107.65i	−0.922636	−	0.299782i	−0.731548	+	0.681790i	$0.761202\pi$
$240$	540.400	+	381.916i	0.145344	+	0.102719i
$241$	3192.20	+	2874.27i	0.853227	+	0.768249i	0.974504	−	0.224370i	$-0.0720323\pi$
$241$	3192.20	+	2874.27i	0.853227	+	0.768249i	−0.121277	+	0.992619i	$0.538699\pi$
$242$	−3056.30	+	1173.20i	−0.811845	+	0.311638i
$243$	−1019.00	−	3802.95i	−0.269007	−	1.00395i
$244$	−191.156	+	138.883i	−0.0501538	+	0.0364389i
$245$	994.738	+	3703.60i	0.259394	+	0.965772i
$246$	2336.70	+	1697.72i	0.605621	+	0.440010i
$247$	−349.398	+	910.212i	−0.0900066	+	0.234475i
$248$	76.7877	−	118.243i	0.0196614	−	0.0302759i
$249$	7264.63	−	4194.24i	1.84891	−	1.06747i
$250$	378.901	−	2205.15i	0.0958553	−	0.557863i
$251$			1721.08i			0.432803i	0.976304	+	0.216402i	$0.0694321\pi$
$251$			1721.08i			0.432803i	−0.976304	+	0.216402i	$0.930568\pi$
$252$	558.729	+	1483.17i	0.139669	+	0.370758i
$253$	−153.813	−	971.135i	−0.0382218	−	0.241323i
$254$	755.291	+	1696.41i	0.186579	+	0.419064i
$255$	59.6684	−	1518.73i	0.0146533	−	0.372967i
$256$	−3307.28	−	1472.50i	−0.807441	−	0.359496i
$257$	−14.2025	+	3.80556i	−0.00344720	+	0.000923674i	−0.260542	−	0.965462i	$-0.583901\pi$
$257$	−14.2025	+	3.80556i	−0.00344720	+	0.000923674i	0.257095	+	0.966386i	$0.417235\pi$
$258$	−725.611	+	4581.33i	−0.175095	+	1.10551i
$259$	1462.63	−	4407.62i	0.350902	−	1.05744i
$260$	−715.096	−	65.7068i	−0.170571	−	0.0156729i
$261$	1670.61	+	1855.41i	0.396201	+	0.440026i
$262$	−3274.71	+	171.620i	−0.772185	+	0.0404685i
$263$	735.597	−	38.5510i	0.172467	−	0.00903862i	0.0340931	−	0.999419i	$-0.489146\pi$
$263$	735.597	−	38.5510i	0.172467	−	0.00903862i	0.138374	+	0.990380i	$0.455812\pi$
$264$	5467.72	+	6072.52i	1.27468	+	1.41567i
$265$	2111.43	−	4914.52i	0.489450	−	1.13923i
$266$	−1625.98	−	1828.69i	−0.374795	−	0.421518i
$267$	−949.612	+	5995.61i	−0.217660	+	1.37425i
$268$	903.653	−	242.133i	0.205968	−	0.0551889i
$269$	−2658.03	−	1183.43i	−0.602464	−	0.268234i	0.0827568	−	0.996570i	$-0.473628\pi$
$269$	−2658.03	−	1183.43i	−0.602464	−	0.268234i	−0.685221	+	0.728336i	$0.740294\pi$
$270$	−815.721	+	1034.74i	−0.183864	+	0.233231i
$271$	−2789.26	−	6264.79i	−0.625224	−	1.40428i	−0.897050	−	0.441929i	$-0.854294\pi$
$271$	−2789.26	−	6264.79i	−0.625224	−	1.40428i	0.271826	−	0.962346i	$-0.412372\pi$
$272$	−29.4498	−	185.939i	−0.00656492	−	0.0414492i
$273$	−1105.98	−	907.108i	−0.245191	−	0.201101i
$274$		−	277.907i		−	0.0612736i
$275$	−2779.30	+	6709.89i	−0.609447	+	1.47135i
$276$	−520.912	+	300.749i	−0.113606	+	0.0655904i
$277$	211.379	−	325.496i	0.0458504	−	0.0706034i	−0.815002	−	0.579458i	$-0.803264\pi$
$277$	211.379	−	325.496i	0.0458504	−	0.0706034i	0.860852	+	0.508855i	$0.169931\pi$
$278$	1065.75	−	2776.38i	0.229926	−	0.598978i
$279$	83.4586	+	60.6362i	0.0179087	+	0.0130115i
$280$	2400.42	−	3752.29i	0.512330	−	0.800864i
$281$	1842.94	−	1338.97i	0.391248	−	0.284258i	−0.374719	−	0.927138i	$-0.622261\pi$
$281$	1842.94	−	1338.97i	0.391248	−	0.284258i	0.765967	+	0.642880i	$0.222261\pi$
$282$	885.738	+	3305.62i	0.187039	+	0.698038i
$283$	5213.85	−	2001.41i	1.09516	−	0.420394i	0.257332	−	0.966323i	$-0.417157\pi$
$283$	5213.85	−	2001.41i	1.09516	−	0.420394i	0.837831	+	0.545929i	$0.183823\pi$
$284$	1058.82	+	953.365i	0.221230	+	0.199196i
$285$	1788.78	−	5760.86i	0.371784	−	1.19735i
$286$	−1045.15	−	339.588i	−0.216087	−	0.0702108i
$287$	−2810.23	+	4268.74i	−0.577988	+	0.877965i
$288$	1333.39	−	2616.93i	0.272816	−	0.535432i
$289$	3329.74	−	2998.11i	0.677740	−	0.610240i
$290$	553.893	−	2784.63i	0.112158	−	0.563860i
$291$	−4479.15	+	4974.60i	−0.902310	+	1.00212i
$292$	−2088.59	+	2579.19i	−0.418580	+	0.516903i
$293$	3119.86	−	3119.86i	0.622062	−	0.622062i	−0.323996	−	0.946058i	$-0.605026\pi$
$293$	3119.86	−	3119.86i	0.622062	−	0.622062i	0.946058	+	0.323996i	$0.105026\pi$
$294$	3297.69	−	1419.12i	0.654168	−	0.281513i
$295$	1549.34	−	6100.57i	0.305783	−	1.20403i
$296$	−4927.86	+	2194.03i	−0.967656	+	0.430828i
$297$	3323.78	−	2691.54i	0.649378	−	0.525856i
$298$	−1893.56	−	1229.70i	−0.368091	−	0.239041i
$299$	99.9612	−	173.138i	0.0193341	−	0.0334877i
$300$	4441.45	+	116.288i	0.854757	+	0.0223796i
$301$	−8156.97	−	908.897i	−1.56199	−	0.174046i
$302$	−727.882	−	1428.55i	−0.138692	−	0.272198i
$303$	−10872.8	−	4173.66i	−2.06146	−	0.791322i
$304$	78.0986	−	743.059i	0.0147344	−	0.140189i
$305$	−168.176	+	455.862i	−0.0315728	+	0.0855823i
$306$	−521.151	+	54.7751i	−0.0973601	+	0.0102330i
$307$	1516.00	+	1516.00i	0.281834	+	0.281834i	0.833840	−	0.552006i	$-0.186138\pi$
$307$	1516.00	+	1516.00i	0.281834	+	0.281834i	−0.552006	+	0.833840i	$0.686138\pi$
$308$	−4162.57	+	4110.88i	−0.770080	+	0.760516i
$309$	−8152.95	+	2649.05i	−1.50099	+	0.487701i
$310$	−1.53577	−	117.302i	−0.000281374	−	0.0214913i
$311$	268.894	+	1265.05i	0.0490276	+	0.230657i	0.995839	−	0.0911331i	$-0.0290489\pi$
$311$	268.894	+	1265.05i	0.0490276	+	0.230657i	−0.946811	+	0.321790i	$0.895716\pi$
$312$	86.9555	+	1659.21i	0.0157785	+	0.301071i
$313$	−2110.09	+	1370.31i	−0.381053	+	0.247458i	−0.720925	−	0.693013i	$-0.756283\pi$
$313$	−2110.09	+	1370.31i	−0.381053	+	0.247458i	0.339872	+	0.940472i	$0.389616\pi$
$314$	−1520.27	+	4678.90i	−0.273228	+	0.840909i
$315$	2649.85	+	1897.66i	0.473974	+	0.339431i
$316$	436.360	+	1342.98i	0.0776809	+	0.239077i
$317$	3340.08	+	2704.74i	0.591791	+	0.479223i	0.877815	−	0.479000i	$-0.159000\pi$
$317$	3340.08	+	2704.74i	0.591791	+	0.479223i	−0.286024	+	0.958222i	$0.592334\pi$
$318$	−4836.85	−	1296.03i	−0.852946	−	0.228546i
$319$	−3748.44	+	8419.14i	−0.657907	+	1.47768i
$320$	−2493.65	+	428.492i	−0.435623	+	0.0748545i
$321$	7367.30	−	10140.2i	1.28100	−	1.76315i
$322$	270.651	+	422.522i	0.0468410	+	0.0731250i
$323$	−1529.05	+	779.090i	−0.263401	+	0.134210i
$324$	−4266.91	−	2463.50i	−0.731637	−	0.422411i
$325$	−1297.77	+	704.639i	−0.221500	+	0.120266i
$326$	2280.04	+	3949.14i	0.387361	+	0.670929i
$327$	−117.068	+	2233.78i	−0.0197977	+	0.377763i
$328$	5863.31	−	928.657i	0.987033	−	0.156331i
$329$	−5770.65	+	1835.21i	−0.967010	+	0.307534i
$330$	6589.95	+	1673.62i	1.09929	+	0.279181i
$331$	−1017.61	−	9681.94i	−0.168982	−	1.60776i	−0.670028	−	0.742336i	$-0.733718\pi$
$331$	−1017.61	−	9681.94i	−0.168982	−	1.60776i	0.501046	−	0.865421i	$-0.332949\pi$
$332$	1805.53	−	6738.32i	0.298467	−	1.11389i
$333$	−1414.45	−	3684.77i	−0.232767	−	0.606379i
$334$	−3267.67	−	694.566i	−0.535327	−	0.113787i
$335$	1268.47	−	1446.42i	0.206878	−	0.235900i
$336$	998.590	+	452.098i	0.162136	+	0.0734047i
$337$	8673.94	+	4419.60i	1.40208	+	0.714394i	0.981249	−	0.192747i	$-0.0617395\pi$
$337$	8673.94	+	4419.60i	1.40208	+	0.714394i	0.420828	+	0.907140i	$0.361740\pi$
$338$	1794.01	+	2762.53i	0.288702	+	0.444562i
$339$	13259.8	−	2818.46i	2.12441	−	0.451557i
$340$	−857.992	−	928.167i	−0.136856	−	0.148050i
$341$	−79.1707	+	372.469i	−0.0125728	+	0.0591505i
$342$	−2054.13	−	325.342i	−0.324779	−	0.0514400i
$343$	2777.35	+	5713.14i	0.437210	+	0.899360i
$344$	5603.59	+	7712.68i	0.878272	+	1.20884i
$345$	−547.078	+	1109.37i	−0.0853730	+	0.173120i
$346$	−4826.79	−	507.317i	−0.749971	−	0.0788252i
$347$	1493.94	+	1844.86i	0.231121	+	0.285411i	0.879492	−	0.475914i	$-0.157883\pi$
$347$	1493.94	+	1844.86i	0.231121	+	0.285411i	−0.648371	+	0.761325i	$0.724549\pi$
$348$	5630.10	+	295.061i	0.867256	+	0.0454510i
$349$	7509.60			1.15180			0.575902	−	0.817519i	$-0.304651\pi$
$349$	7509.60			1.15180			0.575902	+	0.817519i	$0.304651\pi$
$350$	−73.8821	−	3705.62i	−0.0112833	−	0.565926i
$351$	869.624			0.132242
$352$	10826.5	+	567.393i	1.63936	+	0.0859152i
$353$	4899.89	+	6050.85i	0.738795	+	0.912336i	0.998577	−	0.0533316i	$-0.0169840\pi$
$353$	4899.89	+	6050.85i	0.738795	+	0.912336i	−0.259782	+	0.965667i	$0.583651\pi$
$354$	−5860.20	−	615.932i	−0.879848	−	0.0924758i
$355$	2899.62	+	420.420i	0.433510	+	0.0628552i
$356$	2967.27	+	4084.09i	0.441755	+	0.608024i
$357$	−378.313	−	2489.14i	−0.0560853	−	0.369017i
$358$	3221.61	+	510.253i	0.475607	+	0.0753288i
$359$	1829.21	−	8605.74i	0.268919	−	1.26516i	−0.611606	−	0.791163i	$-0.709476\pi$
$359$	1829.21	−	8605.74i	0.268919	−	1.26516i	0.880524	−	0.474001i	$-0.157191\pi$
$360$	−444.981	−	3759.57i	−0.0651460	−	0.550407i
$361$	47.1204	−	10.0158i	0.00686987	−	0.00146023i
$362$	535.801	+	825.061i	0.0777930	+	0.119791i
$363$	−11911.2	−	6069.04i	−1.72224	−	0.877526i
$364$	−1183.78	+	116.947i	−0.170459	+	0.0168398i
$365$	−624.471	+	6796.20i	−0.0895515	+	0.974601i
$366$	444.940	+	94.5749i	0.0635448	+	0.0135069i
$367$	−968.106	−	2522.00i	−0.137697	−	0.358712i	0.847341	−	0.531049i	$-0.178202\pi$
$367$	−968.106	−	2522.00i	−0.137697	−	0.358712i	−0.985038	+	0.172336i	$0.944868\pi$
$368$	−39.6530	+	147.987i	−0.00561699	+	0.0209629i
$369$	454.033	+	4319.84i	0.0640543	+	0.609436i
$370$	−2395.04	+	3795.93i	−0.336520	+	0.533354i
$371$	1896.31	−	8655.14i	0.265368	−	1.21119i
$372$	230.081	−	36.4412i	0.0320675	−	0.00507900i
$373$	197.470	−	3767.95i	0.0274118	−	0.523048i	−0.950071	−	0.312033i	$-0.898990\pi$
$373$	197.470	−	3767.95i	0.0274118	−	0.523048i	0.977483	−	0.211015i	$-0.0676768\pi$
$374$	−967.144	−	1675.14i	−0.133716	−	0.231603i
$375$	7727.05	−	4875.46i	1.06406	−	0.671381i
$376$	6091.39	+	3516.86i	0.835477	+	0.482363i
$377$	−1669.63	+	850.719i	−0.228091	+	0.116218i
$378$	−1003.02	+	1938.50i	−0.136481	+	0.263772i
$379$	−6672.84	+	9184.37i	−0.904381	+	1.24477i	0.0646680	+	0.997907i	$0.479401\pi$
$379$	−6672.84	+	9184.37i	−0.904381	+	1.24477i	−0.969049	+	0.246867i	$0.920599\pi$
$380$	−2335.75	−	4439.52i	−0.315320	−	0.599322i
$381$	−3084.21	+	6927.24i	−0.414721	+	0.931478i
$382$	3075.37	+	824.042i	0.411910	+	0.110371i
$383$	−7646.93	−	6192.36i	−1.02021	−	0.826149i	−0.0353267	−	0.999376i	$-0.511247\pi$
$383$	−7646.93	−	6192.36i	−1.02021	−	0.826149i	−0.984882	+	0.173227i	$0.944581\pi$
$384$	−2283.72	−	7028.57i	−0.303491	−	0.934050i
$385$	−2420.74	+	11784.7i	−0.320447	+	1.56000i
$386$	5.90714	−	18.1803i	0.000778926	−	0.00239729i
$387$	−5850.19	+	3799.15i	−0.768428	+	0.499023i
$388$	291.346	+	5559.21i	0.0381208	+	0.727388i
$389$	1548.15	+	7283.47i	0.201785	+	0.949323i	0.956152	+	0.292870i	$0.0946104\pi$
$389$	1548.15	+	7283.47i	0.201785	+	0.949323i	−0.754367	+	0.656452i	$0.772056\pi$
$390$	827.168	+	1107.71i	0.107398	+	0.143823i
$391$	334.671	−	108.741i	0.0432866	−	0.0140647i
$392$	2730.17	−	6855.04i	0.351772	−	0.883245i
$393$	−9468.54	−	9468.54i	−1.21533	−	1.21533i
$394$	916.969	−	96.3773i	0.117249	−	0.0123234i
$395$	2280.44	+	1797.75i	0.290485	+	0.228999i
$396$	−519.738	+	4944.98i	−0.0659541	+	0.627512i
$397$	6305.95	+	2420.63i	0.797195	+	0.306015i	0.722660	−	0.691204i	$-0.242919\pi$
$397$	6305.95	+	2420.63i	0.797195	+	0.306015i	0.0745354	+	0.997218i	$0.476253\pi$
$398$	651.305	+	1278.26i	0.0820275	+	0.160988i
$399$	1106.55	−	9930.87i	0.138840	−	1.24603i
$400$	820.880	−	778.991i	0.102610	−	0.0973739i
$401$	−2975.74	+	5154.14i	−0.370577	+	0.641859i	−0.989654	−	0.143471i	$-0.954174\pi$
$401$	−2975.74	+	5154.14i	−0.370577	+	0.641859i	0.619077	+	0.785330i	$0.287507\pi$
$402$	−1510.48	−	980.919i	−0.187403	−	0.121701i
$403$	−60.1714	+	48.7258i	−0.00743759	+	0.00602284i
$404$	−8847.95	+	3939.36i	−1.08961	+	0.485125i
$405$	−10110.3	+	662.680i	−1.24045	+	0.0813058i
$406$	29.3864	−	4703.03i	0.00359217	−	0.574895i
$407$	10301.9	−	10301.9i	1.25465	−	1.25465i
$408$	−1840.43	+	2272.74i	−0.223321	+	0.275778i
$409$	−7116.13	+	7903.26i	−0.860318	+	0.955479i	−0.999394	−	0.0348021i	$-0.988920\pi$
$409$	−7116.13	+	7903.26i	−0.860318	+	0.955479i	0.139077	+	0.990282i	$0.455587\pi$
$410$	3627.17	−	3352.93i	0.436910	−	0.403877i
$411$	843.337	−	759.344i	0.101214	−	0.0911331i
$412$	−3236.53	+	6352.05i	−0.387020	+	0.759570i
$413$	610.724	−	10408.5i	0.0727646	−	1.24012i
$414$	405.588	+	131.783i	0.0481486	+	0.0156444i
$415$	−4611.27	−	13584.3i	−0.545441	−	1.60681i
$416$	1638.17	+	1475.01i	0.193072	+	0.173843i
$417$	11337.2	−	4351.96i	1.33138	−	0.511070i
$418$	−1986.90	−	7415.21i	−0.232494	−	0.867679i
$419$	7296.77	−	5301.41i	0.850765	−	0.618117i	−0.0745919	−	0.997214i	$-0.523765\pi$
$419$	7296.77	−	5301.41i	0.850765	−	0.618117i	0.925357	+	0.379097i	$0.123765\pi$
$420$	7261.13	−	1201.04i	0.843588	−	0.139536i
$421$	10111.3	+	7346.28i	1.17053	+	0.850441i	0.991073	−	0.133324i	$-0.0425650\pi$
$421$	10111.3	+	7346.28i	1.17053	+	0.850441i	0.179460	+	0.983765i	$0.442565\pi$
$422$	1330.10	−	3465.04i	0.153432	−	0.399705i
$423$	−2803.01	+	4316.26i	−0.322192	+	0.496132i
$424$	−8913.04	+	5145.95i	−1.02089	+	0.589409i
$425$	−2527.45	−	606.778i	−0.288469	−	0.0692543i
$426$		−	2742.93i		−	0.311961i
$427$	−130.877	+	794.174i	−0.0148327	+	0.0900064i
$428$	−1630.60	−	10295.2i	−0.184154	−	1.16270i
$429$	−1825.21	−	4099.49i	−0.205413	−	0.461364i
$430$	7442.15	+	2745.54i	0.834633	+	0.307911i
$431$	13542.5	+	6029.51i	1.51350	+	0.673854i	0.984599	−	0.174828i	$-0.0559371\pi$
$431$	13542.5	+	6029.51i	1.51350	+	0.673854i	0.528902	+	0.848683i	$0.322604\pi$
$432$	−643.714	+	172.483i	−0.0716915	+	0.0192097i
$433$	880.875	−	5561.63i	0.0977648	−	0.617263i	−0.889347	−	0.457232i	$-0.848841\pi$
$433$	880.875	−	5561.63i	0.0977648	−	0.617263i	0.987112	−	0.160030i	$-0.0511592\pi$
$434$	−39.2145	−	190.330i	−0.00433722	−	0.0210510i
$435$	9963.71	−	5927.81i	1.09821	−	0.653372i
$436$	1244.72	+	1382.40i	0.136723	+	0.151847i
$437$	1394.68	−	73.0921i	0.152670	−	0.00800108i
$438$	6380.45	−	334.385i	0.696050	−	0.0364784i
$439$	7122.47	+	7910.31i	0.774344	+	0.859996i	0.993279	−	0.115743i	$-0.0369250\pi$
$439$	7122.47	+	7910.31i	0.774344	+	0.859996i	−0.218935	+	0.975739i	$0.570258\pi$
$440$	12009.6	−	7145.00i	1.30122	−	0.774146i
$441$	4904.38	+	2257.42i	0.529574	+	0.243756i
$442$	61.5255	−	388.457i	0.00662097	−	0.0418032i
$443$	3500.15	−	937.861i	0.375388	−	0.100585i	−0.0661917	−	0.997807i	$-0.521085\pi$
$443$	3500.15	−	937.861i	0.375388	−	0.100585i	0.441580	+	0.897222i	$0.354418\pi$
$444$	−8142.08	−	3625.09i	−0.870284	−	0.387475i
$445$	9739.59	+	3593.11i	1.03753	+	0.382763i
$446$	−1538.78	−	3456.16i	−0.163371	−	0.366937i
$447$	−1442.28	−	9106.21i	−0.152612	−	0.963555i
$448$	−3922.20	+	1477.54i	−0.413631	+	0.155820i
$449$			12149.7i			1.27702i	0.769614	+	0.638509i	$0.220449\pi$
$449$			12149.7i			1.27702i	−0.769614	+	0.638509i	$0.779551\pi$
$450$	−2045.80	−	2395.31i	−0.214311	−	0.250925i
$451$	−13885.3	+	8016.69i	−1.44974	+	0.837010i
$452$	6139.97	−	9454.72i	0.638937	−	0.983877i
$453$	2346.24	−	6112.16i	0.243346	−	0.633939i
$454$	877.780	+	637.744i	0.0907406	+	0.0659269i
$455$	−1890.48	+	1552.42i	−0.194785	+	0.159953i
$456$	−9389.96	+	6822.21i	−0.964310	+	0.700612i
$457$	1142.86	+	4265.23i	0.116982	+	0.436584i	0.999428	−	0.0338312i	$-0.0107709\pi$
$457$	1142.86	+	4265.23i	0.116982	+	0.436584i	−0.882445	+	0.470415i	$0.844104\pi$
$458$	3150.16	−	1209.23i	0.321392	−	0.123371i
$459$	1137.51	+	1024.22i	0.115674	+	0.104153i
$460$	330.652	+	974.063i	0.0335146	+	0.0987303i
$461$	−3281.50	−	1066.22i	−0.331528	−	0.107720i	0.138523	−	0.990359i	$-0.455765\pi$
$461$	−3281.50	−	1066.22i	−0.331528	−	0.107720i	−0.470051	+	0.882639i	$0.655765\pi$
$462$	11243.5	+	659.715i	1.13224	+	0.0664344i
$463$	324.120	−	636.121i	0.0325337	−	0.0638511i	−0.874168	−	0.485625i	$-0.838592\pi$
$463$	324.120	−	636.121i	0.0325337	−	0.0638511i	0.906701	+	0.421773i	$0.138592\pi$
$464$	1067.16	−	960.878i	0.106771	−	0.0961371i
$465$	351.769	−	325.173i	0.0350815	−	0.0324291i
$466$	4383.51	−	4868.38i	0.435755	−	0.483955i
$467$	−9416.38	+	11628.3i	−0.933058	+	1.15223i	0.0550526	+	0.998483i	$0.482467\pi$
$467$	−9416.38	+	11628.3i	−0.933058	+	1.15223i	−0.988110	+	0.153747i	$0.950866\pi$
$468$	−714.886	+	714.886i	−0.0706103	+	0.0706103i
$469$	1610.64	−	2749.88i	0.158576	−	0.270741i
$470$	5840.01	−	382.785i	0.573148	−	0.0375671i
$471$	−18352.6	+	8171.08i	−1.79542	+	0.799371i
$472$	−9411.91	+	7621.61i	−0.917835	+	0.743248i
$473$	−21594.4	−	14023.6i	−2.09918	−	1.36322i
$474$	1359.25	−	2354.29i	0.131714	−	0.228135i
$475$	−9065.87	−	4922.32i	−0.875727	−	0.475477i
$476$	−1686.19	−	1241.26i	−0.162366	−	0.119523i
$477$	−3418.79	−	6709.75i	−0.328167	−	0.644064i
$478$	5357.51	+	2056.56i	0.512650	+	0.196788i
$479$	−63.7240	+	606.293i	−0.00607854	+	0.0578335i	−0.997141	−	0.0755675i	$-0.975923\pi$
$479$	−63.7240	+	606.293i	−0.00607854	+	0.0578335i	0.991062	+	0.133401i	$0.0425898\pi$
$480$	−10710.6	−	8443.54i	−1.01848	−	0.802903i
$481$	2946.09	−	309.647i	0.279273	−	0.0293528i
$482$	−4862.87	−	4862.87i	−0.459538	−	0.459538i
$483$	−542.670	+	1975.81i	−0.0511229	+	0.186133i
$484$	−10573.1	+	3435.42i	−0.992969	+	0.322635i
$485$	6849.49	+	9172.54i	0.641277	+	0.858770i
$486$	1310.53	+	6165.55i	0.122318	+	0.575463i
$487$	601.379	+	11475.0i	0.0559570	+	1.06772i	0.871929	+	0.489632i	$0.162869\pi$
$487$	601.379	+	11475.0i	0.0559570	+	1.06772i	−0.815972	+	0.578091i	$0.803798\pi$
$488$	784.088	−	509.193i	0.0727336	−	0.0472338i
$489$	−5754.18	+	17709.6i	−0.532133	+	1.63774i
$490$	−1280.07	−	6004.67i	−0.118015	−	0.553599i
$491$	−4291.00	−	13206.3i	−0.394400	−	1.21384i	−0.929428	−	0.369003i	$-0.879699\pi$
$491$	−4291.00	−	13206.3i	−0.394400	−	1.21384i	0.535029	−	0.844834i	$-0.320301\pi$
$492$	7622.58	+	6172.65i	0.698481	+	0.565619i
$493$	−3185.91	−	853.662i	−0.291047	−	0.0779858i
$494$	634.884	−	1425.97i	0.0578235	−	0.129874i
$495$	4760.90	+	9048.95i	0.432296	+	0.821657i
$496$	34.8758	−	48.0024i	0.00315719	−	0.00434551i
$497$	4848.30	−	223.721i	0.437577	−	0.0201917i
$498$	−11966.2	+	6097.06i	−1.07674	+	0.548626i
$499$	13730.2	+	7927.13i	1.23176	+	0.711157i	0.967397	−	0.253267i	$-0.0815050\pi$
$499$	13730.2	+	7927.13i	1.23176	+	0.711157i	0.264363	+	0.964423i	$0.414838\pi$
$500$	1676.86	−	7410.83i	0.149983	−	0.662844i
$501$	−6820.77	−	11813.9i	−0.608243	−	1.05351i
$502$	144.209	−	2751.67i	0.0128214	−	0.244647i
$503$	−5927.34	+	938.799i	−0.525422	+	0.0832186i	−0.413510	−	0.910500i	$-0.635697\pi$
$503$	−5927.34	+	938.799i	−0.525422	+	0.0832186i	−0.111912	+	0.993718i	$0.535697\pi$
$504$	−1900.60	−	5976.26i	−0.167975	−	0.528182i
$505$	−10628.0	+	16844.4i	−0.936511	+	1.48429i
$506$	164.545	+	1565.54i	0.0144564	+	0.137543i
$507$	−3481.30	+	12992.4i	−0.304951	+	1.13809i
$508$	2259.87	+	5887.16i	0.197373	+	0.514175i
$509$	−15093.1	−	3208.13i	−1.31432	−	0.279367i	−0.503160	−	0.864193i	$-0.667829\pi$
$509$	−15093.1	−	3208.13i	−1.31432	−	0.279367i	−0.811158	+	0.584826i	$0.801163\pi$
$510$	−222.652	+	2423.15i	−0.0193318	+	0.210390i
$511$	1111.46	+	11250.6i	0.0962190	+	0.973965i
$512$	−2893.41	−	1474.27i	−0.249750	−	0.127254i
$513$	3308.64	+	5094.86i	0.284756	+	0.438486i
$514$	23.0259	−	4.89431i	0.00197593	−	0.000419998i
$515$	1723.16	+	14558.7i	0.147440	+	1.24570i
$516$	−3274.94	+	15407.4i	−0.279402	+	1.31448i
$517$	−18763.3	−	2971.81i	−1.59614	−	0.252804i
$518$	−2707.77	+	6924.36i	−0.229677	+	0.587334i
$519$	−11649.1	−	16033.6i	−0.985238	−	1.35606i
$520$	2812.00	+	407.715i	0.237143	+	0.0343836i
$521$	14433.3	+	1517.00i	1.21370	+	0.127565i	0.689661	−	0.724132i	$-0.257759\pi$
$521$	14433.3	+	1517.00i	1.21370	+	0.127565i	0.524035	+	0.851697i	$0.324426\pi$
$522$	−2515.52	−	3106.41i	−0.210922	−	0.260467i
$523$	8543.88	+	447.766i	0.714336	+	0.0374368i	0.406042	−	0.913854i	$-0.366909\pi$
$523$	8543.88	+	447.766i	0.714336	+	0.0374368i	0.308294	+	0.951291i	$0.400242\pi$
$524$	−11135.8			−0.928379
$525$	11043.2	−	10349.3i	0.918031	−	0.860348i
$526$	−1179.31			−0.0977570
$527$	−136.095	−	7.13243i	−0.0112493	−	0.000589552i
$528$	2164.16	+	2672.52i	0.178377	+	0.220277i
$529$	11815.5	+	1241.86i	0.971113	+	0.102068i
$530$	−3787.55	+	7680.43i	−0.310416	+	0.629465i
$531$	−5208.64	−	7169.07i	−0.425679	−	0.585897i
$532$	−5189.08	−	6490.48i	−0.422885	−	0.528944i
$533$	−3219.93	−	509.987i	−0.261671	−	0.0414446i
$534$	2020.61	−	9506.24i	0.163746	−	0.770365i
$535$	−14550.2	−	15740.2i	−1.17581	−	1.27198i
$536$	−3620.81	+	769.626i	−0.291782	+	0.0620201i
$537$	7254.22	+	11170.5i	0.582947	+	0.897660i
$538$	4150.50	+	2114.79i	0.332604	+	0.169470i
$539$	−249.037	+	19927.3i	−0.0199013	+	1.59245i
$540$	−2950.20	+	3364.07i	−0.235105	+	0.268086i
$541$	−885.961	−	188.317i	−0.0704075	−	0.0149656i	0.172573	−	0.984997i	$-0.444792\pi$
$541$	−885.961	−	188.317i	−0.0704075	−	0.0149656i	−0.242981	+	0.970031i	$0.578125\pi$
$542$	3934.56	+	10249.9i	0.311815	+	0.812306i
$543$	−1039.73	+	3880.32i	−0.0821712	+	0.306667i
$544$	405.574	+	3858.78i	0.0319648	+	0.304125i
$545$	3707.66	+	941.618i	0.291410	+	0.0740082i
$546$	1692.24	+	1542.96i	0.132640	+	0.120939i
$547$	−17456.2	+	2764.80i	−1.36449	+	0.216114i	−0.795361	−	0.606136i	$-0.792719\pi$
$547$	−17456.2	+	2764.80i	−1.36449	+	0.216114i	−0.569127	+	0.822250i	$0.692719\pi$
$548$	49.3915	−	942.447i	0.00385019	−	0.0734659i
$549$	342.038	+	592.427i	0.0265898	+	0.0460549i
$550$	5005.77	−	10494.9i	0.388085	−	0.813645i
$551$	−11336.5	−	6545.13i	−0.876499	−	0.506047i
$552$	2120.59	−	1080.50i	0.163512	−	0.0833134i
$553$	4272.22	+	2210.54i	0.328523	+	0.169985i
$554$	−365.227	+	502.692i	−0.0280091	+	0.0385512i
$555$	−18063.3	+	3103.88i	−1.38152	+	0.237391i
$556$	4107.65	−	9225.93i	0.313315	−	0.703717i
$557$	5596.40	+	1499.55i	0.425722	+	0.114072i	0.465317	−	0.885144i	$-0.345940\pi$
$557$	5596.40	+	1499.55i	0.425722	+	0.114072i	−0.0395956	+	0.999216i	$0.512607\pi$
$558$	−128.353	−	103.938i	−0.00973768	−	0.00788542i
$559$	−1617.84	−	4979.18i	−0.122410	−	0.376739i
$560$	1091.46	−	1524.10i	0.0823621	−	0.115009i
$561$	2440.80	−	7512.01i	0.183691	−	0.565343i
$562$	−3058.69	+	1986.34i	−0.229578	+	0.149090i
$563$	792.070	+	15113.6i	0.0592926	+	1.13137i	0.852605	+	0.522556i	$0.175021\pi$
$563$	792.070	+	15113.6i	0.0592926	+	1.13137i	−0.793312	+	0.608815i	$0.791645\pi$
$564$	2416.25	+	11367.5i	0.180394	+	0.848688i
$565$	−303.496	−	23180.9i	−0.0225986	−	1.72607i
$566$	−8503.62	+	2762.99i	−0.631508	+	0.205190i
$567$	−16238.6	+	4242.54i	−1.20274	+	0.314233i
$568$	−3986.35	−	3986.35i	−0.294478	−	0.294478i
$569$	18804.5	−	1976.43i	1.38546	−	0.145617i	0.617728	−	0.786392i	$-0.288053\pi$
$569$	18804.5	−	1976.43i	1.38546	−	0.145617i	0.767729	+	0.640775i	$0.221387\pi$
$570$	−3342.61	+	9060.60i	−0.245626	+	0.665801i
$571$	740.722	−	7047.50i	0.0542876	−	0.516512i	−0.933261	−	0.359199i	$-0.883050\pi$
$571$	740.722	−	7047.50i	0.0542876	−	0.516512i	0.987549	−	0.157314i	$-0.0502833\pi$
$572$	−3483.98	−	1337.37i	−0.254672	−	0.0977595i
$573$	5902.40	+	11584.1i	0.430325	+	0.844561i
$574$	4850.68	−	6589.41i	0.352724	−	0.479158i
$575$	1678.22	+	1287.73i	0.121716	+	0.0933951i
$576$	−1781.09	+	3084.94i	−0.128841	+	0.223158i
$577$	−9839.38	−	6389.77i	−0.709911	−	0.461022i	0.138498	−	0.990363i	$-0.455773\pi$
$577$	−9839.38	−	6389.77i	−0.709911	−	0.461022i	−0.848409	+	0.529341i	$0.822439\pi$
$578$	−5574.80	+	4514.39i	−0.401179	+	0.324868i
$579$	71.3105	−	31.7495i	0.00511842	−	0.00227887i
$580$	2373.29	−	9344.90i	0.169906	−	0.669010i
$581$	−11752.9	−	20653.6i	−0.839232	−	1.47480i
$582$	7578.10	−	7578.10i	0.539729	−	0.539729i
$583$	17493.2	−	21602.3i	1.24270	−	1.53461i
$584$	8786.88	−	9758.81i	0.622609	−	0.691477i
$585$	−405.597	+	2039.09i	−0.0286656	+	0.144113i
$586$	−5249.46	+	4726.63i	−0.370056	+	0.333200i
$587$	918.769	−	1803.19i	0.0646025	−	0.126790i	−0.856447	−	0.516235i	$-0.827333\pi$
$587$	918.769	−	1803.19i	0.0646025	−	0.126790i	0.921050	+	0.389445i	$0.127333\pi$
$588$	11435.5	−	4226.48i	0.802025	−	0.296423i
$589$	−514.402	−	167.139i	−0.0359857	−	0.0116925i
$590$	−2988.25	+	9623.80i	−0.208516	+	0.671535i
$591$	2797.97	+	2519.30i	0.194743	+	0.175347i
$592$	−2119.35	+	813.541i	−0.147136	+	0.0564803i
$593$	1791.11	+	6684.51i	0.124034	+	0.462900i	0.999803	−	0.0198289i	$-0.00631215\pi$
$593$	1791.11	+	6684.51i	0.124034	+	0.462900i	−0.875770	+	0.482729i	$0.839645\pi$
$594$	−5539.60	+	4024.75i	−0.382647	+	0.278009i
$595$	−4301.24	−	195.912i	−0.296359	−	0.0134985i
$596$	−6202.97	−	4506.72i	−0.426315	−	0.309736i
$597$	−2099.40	+	5469.13i	−0.143924	+	0.374935i
$598$	−174.325	+	268.438i	−0.0119209	+	0.0183566i
$599$	21991.4	−	12696.8i	1.50008	−	0.866069i	0.500076	−	0.865982i	$-0.333305\pi$
$599$	21991.4	−	12696.8i	1.50008	−	0.866069i	1.00000		8.76916e-5i	$-2.79131e-5\pi$
$600$	−17525.7	−	1379.24i	−1.19247	−	0.0938454i
$601$		−	12370.1i		−	0.839577i	−0.907622	−	0.419788i	$-0.862104\pi$
$601$		−	12370.1i		−	0.839577i	0.907622	−	0.419788i	$-0.137896\pi$
$602$	12965.2	+	2136.62i	0.877780	+	0.144654i
$603$	−423.705	−	2675.17i	−0.0286146	−	0.180665i
$604$	−2214.53	−	4973.91i	−0.149185	−	0.335075i
$605$	−14153.5	+	17953.7i	−0.951111	+	1.20648i
$606$	17033.7	+	7583.89i	1.14183	+	0.508374i
$607$	8772.24	−	2350.52i	0.586580	−	0.157174i	0.0466905	−	0.998909i	$-0.485133\pi$
$607$	8772.24	−	2350.52i	0.586580	−	0.157174i	0.539890	+	0.841736i	$0.318466\pi$
$608$	−2408.95	+	15209.5i	−0.160684	+	1.01452i
$609$	14352.1	−	12761.2i	0.954972	−	0.849116i
$610$	307.076	−	714.743i	0.0203822	−	0.0474411i
$611$	−2584.64	−	2870.54i	−0.171135	−	0.190065i
$612$	−1777.08	+	93.1328i	−0.117376	+	0.00615142i
$613$	20122.3	−	1054.57i	1.32583	−	0.0694838i	0.623773	−	0.781605i	$-0.285599\pi$
$613$	20122.3	−	1054.57i	1.32583	−	0.0694838i	0.702056	+	0.712121i	$0.252265\pi$
$614$	−2296.77	−	2550.82i	−0.150961	−	0.167659i
$615$	20085.6	+	1845.57i	1.31696	+	0.121009i
$616$	17299.1	−	15381.6i	1.13150	−	1.00607i
$617$	3100.38	−	19575.0i	0.202296	−	1.27725i	−0.652304	−	0.757958i	$-0.726197\pi$
$617$	3100.38	−	19575.0i	0.202296	−	1.27725i	0.854599	−	0.519288i	$-0.173803\pi$
$618$	13256.9	−	3552.18i	0.862900	−	0.231213i
$619$	10861.1	+	4835.68i	0.705242	+	0.313994i	0.727836	−	0.685751i	$-0.240526\pi$
$619$	10861.1	+	4835.68i	0.705242	+	0.313994i	−0.0225944	+	0.999745i	$0.507193\pi$
$620$	15.6395	−	398.071i	0.00101306	−	0.0257853i
$621$	−506.669	−	1138.00i	−0.0327406	−	0.0735367i
$622$	−323.911	−	2045.09i	−0.0208805	−	0.131834i
$623$	16967.7	+	2796.21i	1.09117	+	0.179820i
$624$			699.229i			0.0448582i
$625$	−5599.60	−	14587.2i	−0.358375	−	0.933578i
$626$	3488.44	−	2014.05i	0.222725	−	0.128591i
$627$	17073.3	−	26290.6i	1.08747	−	1.67455i
$628$	−5987.15	+	15597.1i	−0.380435	+	0.991067i
$629$	4218.33	+	3064.80i	0.267402	+	0.194279i
$630$	−4077.58	−	3256.01i	−0.257864	−	0.205909i
$631$	6777.69	−	4924.28i	0.427600	−	0.310669i	−0.353089	−	0.935590i	$-0.614869\pi$
$631$	6777.69	−	4924.28i	0.427600	−	0.310669i	0.780688	+	0.624920i	$0.214869\pi$
$632$	−1446.11	−	5396.96i	−0.0910178	−	0.339683i
$633$	14149.4	−	5431.43i	0.888446	−	0.341043i
$634$	−5113.50	−	4604.22i	−0.320320	−	0.288418i
$635$	10590.0	+	7484.27i	0.661815	+	0.467723i
$636$	−16172.5	−	5254.78i	−1.00831	−	0.327619i
$637$	−2589.25	+	3117.00i	−0.161052	+	0.193877i
$638$	6698.46	−	13146.5i	0.415665	−	0.815789i
$639$	3065.45	−	2760.15i	0.189777	−	0.170876i
$640$	−12550.9	+	1485.52i	−0.775185	+	0.0917506i
$641$	−14003.0	+	15551.9i	−0.862848	+	0.958290i	−0.999477	−	0.0323327i	$-0.989706\pi$
$641$	−14003.0	+	15551.9i	−0.862848	+	0.958290i	0.136629	+	0.990622i	$0.456373\pi$
$642$	−12628.5	+	15594.9i	−0.776336	+	0.958695i
$643$	−18582.6	+	18582.6i	−1.13970	+	1.13970i	−0.151194	+	0.988504i	$0.548312\pi$
$643$	−18582.6	+	18582.6i	−1.13970	+	1.13970i	−0.988504	+	0.151194i	$0.951688\pi$
$644$	842.747	+	1480.97i	0.0515666	+	0.0906189i
$645$	12003.1	+	30085.8i	0.732746	+	1.83663i
$646$	2509.93	−	1117.49i	0.152867	−	0.0680607i
$647$	21456.4	−	17375.0i	1.30377	−	1.05577i	0.309274	−	0.950973i	$-0.399914\pi$
$647$	21456.4	−	17375.0i	1.30377	−	1.05577i	0.994494	−	0.104797i	$-0.0334192\pi$
$648$	16350.0	+	10617.8i	0.991184	+	0.643682i
$649$	16354.9	−	28327.5i	0.989192	−	1.71333i
$650$	2133.92	−	1017.84i	0.128768	−	0.0614199i
$651$	470.427	−	639.052i	0.0283218	−	0.0384738i
$652$	7030.28	+	13797.7i	0.422281	+	0.828772i
$653$	−10900.2	−	4184.18i	−0.653226	−	0.250750i	0.00910839	−	0.999959i	$-0.497101\pi$
$653$	−10900.2	−	4184.18i	−0.653226	−	0.250750i	−0.662334	+	0.749209i	$0.730434\pi$
$654$	374.336	−	3561.57i	0.0223818	−	0.212949i
$655$	−19040.5	+	12722.5i	−1.13584	+	0.758947i
$656$	2484.62	−	261.144i	0.147878	−	0.0155426i
$657$	6794.21	+	6794.21i	0.403451	+	0.403451i
$658$	9379.90	−	2450.63i	0.555725	−	0.145190i
$659$	−4770.63	+	1550.07i	−0.281999	+	0.0916270i	−0.446602	−	0.894733i	$-0.647366\pi$
$659$	−4770.63	+	1550.07i	−0.281999	+	0.0916270i	0.164603	+	0.986360i	$0.447366\pi$
$660$	22050.6	+	6846.85i	1.30048	+	0.403808i
$661$	−121.584	−	572.008i	−0.00715442	−	0.0336589i	0.974426	−	0.224710i	$-0.0721436\pi$
$661$	−121.584	−	572.008i	−0.00715442	−	0.0336589i	−0.981580	+	0.191051i	$0.938810\pi$
$662$	815.715	+	15564.8i	0.0478907	+	0.913810i
$663$	1346.92	−	874.702i	0.0788992	−	0.0512377i
$664$	−8529.68	+	26251.7i	−0.498518	+	1.53428i
$665$	−16287.8	−	5169.27i	−0.949796	−	0.301437i
$666$	1952.68	+	6009.74i	0.113611	+	0.349659i
$667$	2086.03	+	1689.24i	0.121097	+	0.0980623i
$668$	−10958.0	−	2936.19i	−0.634698	−	0.170067i
$669$	6283.56	−	14113.1i	0.363134	−	0.815612i
$670$	−2149.23	+	2206.26i	−0.123929	+	0.127217i
$671$	−1484.21	+	2042.84i	−0.0853908	+	0.117530i
$672$	−20065.4	−	10382.3i	−1.15185	−	0.595990i
$673$	20844.9	−	10621.0i	1.19392	−	0.608334i	0.259930	−	0.965627i	$-0.416300\pi$
$673$	20844.9	−	10621.0i	1.19392	−	0.608334i	0.933992	+	0.357293i	$0.116300\pi$
$674$	−13497.6	−	7792.85i	−0.771378	−	0.445355i
$675$	−1200.98	+	9122.62i	−0.0684827	+	0.520192i
$676$	5592.93	+	9687.25i	0.318214	+	0.551163i
$677$	1066.63	−	20352.5i	0.0605522	−	1.15540i	−0.784292	−	0.620392i	$-0.786974\pi$
$677$	1066.63	−	20352.5i	0.0605522	−	1.15540i	0.844844	−	0.535012i	$-0.179693\pi$
$678$	−21436.0	+	3395.13i	−1.21422	+	0.192314i
$679$	14012.9	+	12776.7i	0.791994	+	0.722126i
$680$	3198.03	+	3845.20i	0.180351	+	0.216848i
$681$	463.118	+	4406.27i	0.0260598	+	0.247942i
$682$	157.787	−	588.871i	0.00885923	−	0.0330631i
$683$	−6272.69	−	16340.9i	−0.351417	−	0.915472i	−0.989373	−	0.145400i	$-0.953553\pi$
$683$	−6272.69	−	16340.9i	−0.351417	−	0.915472i	0.637956	−	0.770073i	$-0.279780\pi$
$684$	−6908.21	−	1468.38i	−0.386172	−	0.0820835i
$685$	−992.281	−	1667.87i	−0.0553476	−	0.0930306i
$686$	−3961.74	−	9366.89i	−0.220495	−	0.521326i
$687$	12277.0	+	6255.42i	0.681798	+	0.347394i
$688$	2185.14	+	3364.82i	0.121087	+	0.186457i
$689$	5528.45	−	1175.11i	0.305686	−	0.0649755i
$690$	967.624	−	1727.82i	0.0533867	−	0.0953292i
$691$	442.836	−	2083.38i	0.0243795	−	0.114697i	−0.964275	−	0.264902i	$-0.914660\pi$
$691$	442.836	−	2083.38i	0.0243795	−	0.114697i	0.988655	+	0.150206i	$0.0479936\pi$
$692$	−16278.6	−	2578.28i	−0.894249	−	0.141635i
$693$	10576.8	+	13229.4i	0.579766	+	0.725170i
$694$	−2233.94	−	3074.75i	−0.122189	−	0.168179i
$695$	−3517.06	−	20467.8i	−0.191956	−	1.11711i
$696$	−22185.5	−	2331.79i	−1.20825	−	0.126992i
$697$	−3611.18	−	4459.43i	−0.196246	−	0.242343i
$698$	−12006.4	−	629.227i	−0.651071	−	0.0341212i
$699$	26751.0			1.44752
$700$	408.038	−	12579.8i	0.0220320	−	0.679244i
$701$	31870.7			1.71717			0.858587	−	0.512667i	$-0.171343\pi$
$701$	31870.7			1.71717			0.858587	+	0.512667i	$0.171343\pi$
$702$	−1390.36	−	72.8655i	−0.0747516	−	0.00391757i
$703$	13023.1	+	16082.1i	0.698683	+	0.862802i
$704$	−13076.8	−	1374.43i	−0.700074	−	0.0735807i
$705$	17118.7	+	16676.2i	0.914506	+	0.890869i
$706$	−7326.95	−	10084.7i	−0.390586	−	0.537595i
$707$	−12015.7	+	30726.7i	−0.639175	+	1.63451i
$708$	−19763.9	−	3130.29i	−1.04911	−	0.166163i
$709$	−4309.66	+	20275.4i	−0.228283	+	1.07399i	0.703422	+	0.710772i	$0.251654\pi$
$709$	−4309.66	+	20275.4i	−0.228283	+	1.07399i	−0.931705	+	0.363215i	$0.881679\pi$
$710$	−4600.70	−	915.128i	−0.243185	−	0.0483720i
$711$	3998.90	−	849.992i	0.210929	−	0.0448343i
$712$	−10879.0	−	16752.2i	−0.572624	−	0.881764i
$713$	98.8207	+	50.3517i	0.00519055	+	0.00264472i
$714$	396.284	+	4011.34i	0.0207711	+	0.210253i
$715$	−7485.00	+	1693.70i	−0.391501	+	0.0885884i
$716$	10834.5	+	2302.95i	0.565511	+	0.120203i
$717$	8397.88	+	21877.2i	0.437412	+	1.13950i
$718$	−3645.62	+	13605.6i	−0.189489	+	0.707183i
$719$	−945.252	−	8993.48i	−0.0490292	−	0.466481i	−0.991299	−	0.131627i	$-0.957980\pi$
$719$	−945.252	−	8993.48i	−0.0490292	−	0.466481i	0.942270	−	0.334854i	$-0.108687\pi$
$720$	−104.206	−	1589.83i	−0.00539377	−	0.0822908i
$721$	7359.98	+	23142.7i	0.380167	+	1.19540i
$722$	−76.1755	+	12.0650i	−0.00392653	+	0.000621902i
$723$	1469.73	−	28044.0i	0.0756013	−	1.44256i
$724$	1670.39	+	2893.20i	0.0857452	+	0.148515i
$725$	−6618.48	−	18689.8i	−0.339040	−	0.957409i
$726$	18535.1	+	10701.2i	0.947522	+	0.547052i
$727$	−4962.69	+	2528.62i	−0.253172	+	0.128998i	−0.575971	−	0.817470i	$-0.695376\pi$
$727$	−4962.69	+	2528.62i	−0.253172	+	0.128998i	0.322800	+	0.946467i	$0.395376\pi$
$728$	4701.78	−	216.960i	0.239368	−	0.0110455i
$729$	−747.099	+	1028.29i	−0.0379566	+	0.0522427i
$730$	1567.86	−	10813.5i	0.0794918	−	0.548252i
$731$	3748.14	−	8418.46i	0.189644	−	0.425948i
$732$	1492.09	+	399.804i	0.0753403	+	0.0201874i
$733$	−28540.3	−	23111.5i	−1.43814	−	1.16459i	−0.957775	−	0.287519i	$-0.907170\pi$
$733$	−28540.3	−	23111.5i	−1.43814	−	1.16459i	−0.480368	−	0.877067i	$-0.659497\pi$
$734$	1336.49	+	4113.30i	0.0672083	+	0.206846i
$735$	14724.2	−	20291.5i	0.738925	−	1.01832i
$736$	975.770	−	3003.11i	0.0488687	−	0.150402i
$737$	8384.84	−	5445.18i	0.419077	−	0.272152i
$738$	−363.952	−	6944.61i	−0.0181535	−	0.346389i
$739$	5304.01	+	24953.4i	0.264021	+	1.24212i	0.887694	+	0.460434i	$0.152306\pi$
$739$	5304.01	+	24953.4i	0.264021	+	1.24212i	−0.623673	+	0.781685i	$0.714360\pi$
$740$	−8796.80	+	12447.2i	−0.436996	+	0.618337i
$741$	6062.01	−	1969.67i	0.300531	−	0.0976484i
$742$	−3757.03	+	13679.0i	−0.185883	+	0.676781i
$743$	11098.2	+	11098.2i	0.547985	+	0.547985i	0.925858	−	0.377873i	$-0.123344\pi$
$743$	11098.2	+	11098.2i	0.547985	+	0.547985i	−0.377873	+	0.925858i	$0.623344\pi$
$744$	−916.678	+	96.3468i	−0.0451708	+	0.00474764i
$745$	−15755.0	−	618.987i	−0.774790	−	0.0304402i
$746$	−631.431	+	6007.66i	−0.0309897	+	0.294847i
$747$	−18855.3	−	7237.86i	−0.923531	−	0.354510i
$748$	−2982.09	−	5852.69i	−0.145770	−	0.286090i
$749$	−28595.0	−	21049.7i	−1.39498	−	1.02689i
$750$	−12762.5	+	7147.46i	−0.621363	+	0.347984i
$751$	−11452.3	+	19836.0i	−0.556461	+	0.963818i	0.441328	+	0.897346i	$0.354508\pi$
$751$	−11452.3	+	19836.0i	−0.556461	+	0.963818i	−0.997788	+	0.0664719i	$0.978826\pi$
$752$	2482.56	+	1612.19i	0.120385	+	0.0781789i
$753$	8744.26	−	7080.97i	0.423185	−	0.342689i
$754$	2740.69	−	1220.23i	0.132374	−	0.0589367i
$755$	−9469.12	−	5974.54i	−0.456446	−	0.287995i
$756$	−3746.00	+	6395.64i	−0.180213	+	0.307682i
$757$	3527.14	−	3527.14i	0.169347	−	0.169347i	−0.617345	−	0.786693i	$-0.711792\pi$
$757$	3527.14	−	3527.14i	0.169347	−	0.169347i	0.786693	+	0.617345i	$0.211792\pi$
$758$	11438.1	−	14124.9i	0.548088	−	0.676832i
$759$	−4301.21	+	4776.97i	−0.205697	+	0.228449i
$760$	8310.07	+	18025.8i	0.396629	+	0.860350i
$761$	10249.7	−	9228.88i	0.488241	−	0.439614i	−0.387877	−	0.921711i	$-0.626791\pi$
$761$	10249.7	−	9228.88i	0.488241	−	0.439614i	0.876118	+	0.482097i	$0.160125\pi$
$762$	5511.47	−	10816.9i	0.262020	−	0.514244i
$763$	6325.84	+	371.171i	0.300145	+	0.0176111i
$764$	10282.8	+	3341.10i	0.486937	+	0.158215i
$765$	−2932.13	+	2189.53i	−0.138577	+	0.103481i
$766$	11707.1	+	10541.1i	0.552211	+	0.497213i
$767$	6209.13	−	2383.46i	0.292306	−	0.112206i
$768$	6125.71	+	22861.5i	0.287816	+	1.07414i
$769$	22642.7	−	16450.9i	1.06179	−	0.771434i	0.0873700	−	0.996176i	$-0.472154\pi$
$769$	22642.7	−	16450.9i	1.06179	−	0.771434i	0.974418	+	0.224741i	$0.0721538\pi$
$770$	4857.71	−	18638.5i	0.227350	−	0.872318i
$771$	77.7677	+	56.5015i	0.00363260	+	0.00263924i
$772$	23.2636	−	60.6038i	0.00108455	−	0.00282536i
$773$	−19298.6	+	29717.2i	−0.897958	+	1.38273i	0.0257634	+	0.999668i	$0.491798\pi$
$773$	−19298.6	+	29717.2i	−0.897958	+	1.38273i	−0.923721	+	0.383066i	$0.874868\pi$
$774$	9671.63	−	5583.92i	0.449146	−	0.259315i
$775$	−428.050	−	698.508i	−0.0198400	−	0.0323757i
$776$		−	22026.8i		−	1.01896i
$777$	−28411.3	+	10702.9i	−1.31178	+	0.494163i
$778$	−1864.91	−	11774.6i	−0.0859385	−	0.542594i
$779$	−9262.95	−	20804.9i	−0.426033	−	0.956885i
$780$	2608.25	+	3903.51i	0.119731	+	0.179190i
$781$	13909.9	+	6193.08i	0.637305	+	0.283746i
$782$	−544.184	+	145.814i	−0.0248849	+	0.00666789i
$783$	−1826.51	+	11532.1i	−0.0833640	+	0.526340i
$784$	1298.39	−	2820.82i	0.0591467	−	0.128500i
$785$	7582.33	+	33508.8i	0.344745	+	1.52354i
$786$	14345.0	+	15931.7i	0.650977	+	0.722983i
$787$	−29737.8	+	1558.49i	−1.34694	+	0.0705899i	−0.712111	−	0.702067i	$-0.752261\pi$
$787$	−29737.8	+	1558.49i	−1.34694	+	0.0705899i	−0.634824	+	0.772657i	$0.718927\pi$
$788$	3126.79	−	163.868i	0.141354	−	0.00740806i
$789$	−3222.30	−	3578.73i	−0.145395	−	0.161478i
$790$	−3495.35	−	3065.33i	−0.157416	−	0.138050i
$791$	−7749.48	−	37612.5i	−0.348344	−	1.69071i
$792$	3077.69	−	19431.8i	0.138082	−	0.871817i
$793$	−495.931	+	132.884i	−0.0222081	+	0.00595065i
$794$	−9879.15	−	4398.48i	−0.441559	−	0.196595i
$795$	−33656.1	+	9492.06i	−1.50146	+	0.423457i
$796$	1981.55	+	4450.62i	0.0882337	+	0.198176i
$797$	−4122.57	−	26028.9i	−0.183223	−	1.15683i	−0.892216	−	0.451610i	$-0.850850\pi$
$797$	−4122.57	−	26028.9i	−0.183223	−	1.15683i	0.708992	−	0.705216i	$-0.249150\pi$
$798$	−2601.27	+	15784.8i	−0.115393	+	0.700220i
$799$		−	6798.92i		−	0.301037i
$800$	−17735.7	+	15147.8i	−0.783816	+	0.669447i
$801$	12657.3	−	7307.71i	0.558333	−	0.322354i
$802$	5189.49	−	7991.12i	0.228488	−	0.351841i
$803$	−12710.3	+	33111.4i	−0.558576	+	1.45514i
$804$	−4948.06	−	3594.98i	−0.217046	−	0.157693i
$805$	3132.96	+	1569.41i	0.137171	+	0.0687136i
$806$	100.285	−	72.8612i	0.00438261	−	0.00318415i
$807$	4923.17	+	18373.5i	0.214751	+	0.801461i
$808$	35777.3	−	13733.6i	1.55772	−	0.597953i
$809$	−26983.3	−	24295.8i	−1.17266	−	1.05587i	−0.997452	−	0.0713346i	$-0.977274\pi$
$809$	−26983.3	−	24295.8i	−1.17266	−	1.05587i	−0.175206	−	0.984532i	$-0.556059\pi$
$810$	16219.9	−	212.358i	0.703590	−	0.00921175i
$811$	11411.4	+	3707.79i	0.494093	+	0.160540i	0.545456	−	0.838140i	$-0.316357\pi$
$811$	11411.4	+	3707.79i	0.494093	+	0.160540i	−0.0513632	+	0.998680i	$0.516357\pi$
$812$	935.511	−	15943.8i	0.0404310	−	0.689063i
$813$	−20353.7	+	39946.3i	−0.878024	+	1.72322i
$814$	−17333.8	+	15607.5i	−0.746377	+	0.672041i
$815$	27784.4	+	15559.9i	1.19416	+	0.668761i
$816$	−823.532	+	914.625i	−0.0353301	+	0.0392381i
$817$	23016.2	−	28422.6i	0.985598	−	1.21711i
$818$	12039.5	−	12039.5i	0.514610	−	0.514610i
$819$	−21.5186	+	3443.87i	−0.000918098	+	0.146933i
$820$	12896.5	−	10725.9i	0.549225	−	0.456788i
$821$	13813.3	−	6150.08i	0.587196	−	0.261437i	−0.0915609	−	0.995799i	$-0.529186\pi$
$821$	13813.3	−	6150.08i	0.587196	−	0.261437i	0.678757	+	0.734363i	$0.262519\pi$
$822$	−1411.96	+	1143.38i	−0.0599119	+	0.0485157i
$823$	−2735.02	−	1776.15i	−0.115841	−	0.0752279i	0.485418	−	0.874282i	$-0.338667\pi$
$823$	−2735.02	−	1776.15i	−0.115841	−	0.0752279i	−0.601259	+	0.799054i	$0.705334\pi$
$824$	14104.1	−	24429.0i	0.596286	−	1.03280i
$825$	45525.6	−	13485.5i	1.92121	−	0.569095i
$826$	−1848.55	+	16590.0i	−0.0778686	+	0.698838i
$827$	−13207.6	−	25921.4i	−0.555349	−	1.08993i	−0.982588	−	0.185796i	$-0.940514\pi$
$827$	−13207.6	−	25921.4i	−0.555349	−	1.08993i	0.427239	−	0.904139i	$-0.359486\pi$
$828$	1352.02	+	518.992i	0.0567463	+	0.0217829i
$829$	1638.26	−	15587.0i	0.0686359	−	0.653027i	−0.905077	−	0.425248i	$-0.860187\pi$
$829$	1638.26	−	15587.0i	0.0686359	−	0.653027i	0.973713	−	0.227779i	$-0.0731463\pi$
$830$	6234.28	+	22105.0i	0.260717	+	0.924427i
$831$	−2523.41	+	265.221i	−0.105338	+	0.0110715i
$832$	−1890.49	−	1890.49i	−0.0787753	−	0.0787753i
$833$	−7057.98	+	1027.63i	−0.293571	+	0.0427436i
$834$	−18490.7	+	6007.98i	−0.767721	+	0.249448i
$835$	−22091.1	+	7498.95i	−0.915560	+	0.310793i
$836$	−5420.16	−	25499.8i	−0.224235	−	1.05494i
$837$	25.2486	+	481.772i	0.00104268	+	0.0198954i
$838$	−12110.3	+	7864.52i	−0.499217	+	0.324195i
$839$	2041.12	−	6281.92i	0.0839895	−	0.258493i	−0.900239	−	0.435397i	$-0.856608\pi$
$839$	2041.12	−	6281.92i	0.0839895	−	0.258493i	0.984228	+	0.176904i	$0.0566081\pi$
$840$	−28940.1	+	3242.11i	−1.18872	+	0.133171i
$841$	−238.002	−	732.493i	−0.00975856	−	0.0300338i
$842$	−15550.4	−	12592.5i	−0.636464	−	0.515398i
$843$	−14385.2	−	3854.51i	−0.587727	−	0.157481i
$844$	5126.52	−	11514.4i	0.209078	−	0.469598i
$845$	20630.6	+	10173.8i	0.839899	+	0.414190i
$846$	4843.12	−	6665.98i	0.196820	−	0.270900i
$847$	−17403.3	+	33634.8i	−0.706004	+	1.36447i
$848$	−3859.21	+	1966.36i	−0.156280	+	0.0796288i
$849$	−31619.7	−	18255.6i	−1.27819	−	0.737964i
$850$	3990.06	+	1181.89i	0.161009	+	0.0476925i
$851$	−2121.69	−	3674.88i	−0.0854649	−	0.148030i
$852$	487.492	−	9301.91i	0.0196024	−	0.374035i
$853$	−30917.2	+	4896.81i	−1.24101	+	0.196557i	−0.742216	−	0.670160i	$-0.766225\pi$
$853$	−30917.2	+	4896.81i	−1.24101	+	0.196557i	−0.498799	+	0.866718i	$0.666225\pi$
$854$	275.789	−	1258.76i	0.0110507	−	0.0504378i
$855$	−13489.6	+	5381.82i	−0.539572	+	0.215268i
$856$	4311.13	+	41017.7i	0.172140	+	1.63780i
$857$	−7256.63	+	27082.1i	−0.289244	+	1.07947i	0.656439	+	0.754379i	$0.272062\pi$
$857$	−7256.63	+	27082.1i	−0.289244	+	1.07947i	−0.945682	+	0.325092i	$0.894605\pi$
$858$	2574.66	+	6707.21i	0.102444	+	0.266877i
$859$	−30187.9	−	6416.63i	−1.19907	−	0.254869i	−0.435254	−	0.900308i	$-0.643341\pi$
$859$	−30187.9	−	6416.63i	−1.19907	−	0.254869i	−0.763812	+	0.645439i	$0.776675\pi$
$860$	24750.1	+	10633.4i	0.981363	+	0.421625i
$861$	33250.1	−	3284.81i	1.31610	−	0.130019i
$862$	−21146.6	−	10774.7i	−0.835563	−	0.425741i
$863$	15781.2	+	24300.8i	0.622476	+	0.958529i	0.999478	+	0.0323164i	$0.0102884\pi$
$863$	15781.2	+	24300.8i	0.622476	+	0.958529i	−0.377002	+	0.926213i	$0.623045\pi$
$864$	13435.1	−	2855.71i	0.529016	−	0.112446i
$865$	−30779.6	+	14189.7i	−1.20987	+	0.557760i
$866$	−1874.35	+	8818.14i	−0.0735486	+	0.346019i
$867$	−28931.8	−	4582.35i	−1.13331	−	0.179498i
$868$	−99.1587	−	652.422i	−0.00387750	−	0.0255123i
$869$	8870.06	+	12208.6i	0.346256	+	0.476580i
$870$	−16426.7	+	8642.54i	−0.640135	+	0.336793i
$871$	2021.71	+	212.490i	0.0786488	+	0.00826632i
$872$	−4632.08	−	5720.14i	−0.179888	−	0.222143i
$873$	16094.8	+	843.495i	0.623972	+	0.0327010i
$874$	−2235.94			−0.0865354
$875$	−13674.5	−	21975.6i	−0.528324	−	0.849043i
$876$	21697.0			0.836843
$877$	−26988.6	−	1414.41i	−1.03916	−	0.0544598i	−0.474884	−	0.880049i	$-0.657510\pi$
$877$	−26988.6	−	1414.41i	−1.03916	−	0.0544598i	−0.564272	+	0.825589i	$0.690843\pi$
$878$	−10724.6	−	13243.8i	−0.412231	−	0.509063i
$879$	−28686.9	−	3015.12i	−1.10078	−	0.115697i
$880$	5204.63	−	2738.30i	0.199373	−	0.104896i
$881$	13186.0	+	18149.0i	0.504254	+	0.694046i	0.982937	−	0.183942i	$-0.0588858\pi$
$881$	13186.0	+	18149.0i	0.504254	+	0.694046i	−0.478683	+	0.877988i	$0.658886\pi$
$882$	−7651.99	−	4020.11i	−0.292127	−	0.153474i
$883$	−14996.4	−	2375.19i	−0.571537	−	0.0905226i	−0.136025	−	0.990705i	$-0.543433\pi$
$883$	−14996.4	−	2375.19i	−0.571537	−	0.0905226i	−0.435512	+	0.900183i	$0.643433\pi$
$884$	277.687	−	1306.41i	0.0105652	−	0.0497052i
$885$	−37369.5	+	17227.6i	−1.41939	+	0.654351i
$886$	−5674.63	+	1206.18i	−0.215173	+	0.0457363i
$887$	310.407	+	477.984i	0.0117502	+	0.0180937i	0.844497	−	0.535560i	$-0.179900\pi$
$887$	310.407	+	477.984i	0.0117502	+	0.0180937i	−0.832747	+	0.553654i	$0.813233\pi$
$888$	31421.6	+	16010.1i	1.18743	+	0.605028i
$889$	19569.0	+	8859.62i	0.738272	+	0.334243i
$890$	−15270.6	−	6560.75i	−0.575138	−	0.247097i
$891$	−51503.0	−	10947.3i	−1.93649	−	0.411614i
$892$	−4604.12	−	11994.1i	−0.172822	−	0.450217i
$893$	6983.85	−	26064.1i	0.261709	−	0.976710i
$894$	1542.92	+	14679.9i	0.0577214	+	0.549182i
$895$	21156.5	−	8440.63i	0.790149	−	0.315239i
$896$	−19951.1	+	6344.96i	−0.743884	+	0.236574i
$897$	−1290.92	+	204.462i	−0.0480521	+	0.00761070i
$898$	1018.02	−	19425.0i	0.0378306	−	0.721850i
$899$	−519.774	−	900.275i	−0.0192830	−	0.0333992i
$900$	−6512.09	−	8486.66i	−0.241188	−	0.314321i
$901$	8615.50	+	4974.16i	0.318561	+	0.183922i
$902$	22871.6	−	11653.7i	0.844281	−	0.430183i
$903$	28942.0	+	45182.4i	1.06659	+	1.66509i
$904$	−26219.1	+	36087.6i	−0.964642	+	1.32772i
$905$	6161.55	+	3038.53i	0.226317	+	0.111607i
$906$	−4263.31	+	9575.55i	−0.156334	+	0.351133i
$907$	34034.3	+	9119.46i	1.24597	+	0.333855i	0.820777	−	0.571249i	$-0.193541\pi$
$907$	34034.3	+	9119.46i	1.24597	+	0.333855i	0.425189	+	0.905105i	$0.360208\pi$
$908$	2863.41	+	2318.75i	0.104654	+	0.0847470i
$909$	8664.99	+	26668.1i	0.316171	+	0.973075i
$910$	3152.58	−	2323.61i	0.114843	−	0.0846450i
$911$	6991.24	−	21516.8i	0.254259	−	0.782529i	−0.739716	−	0.672919i	$-0.765040\pi$
$911$	6991.24	−	21516.8i	0.254259	−	0.782529i	0.993975	−	0.109609i	$-0.0349600\pi$
$912$	−4096.56	+	2660.34i	−0.148740	+	0.0965928i
$913$	−3901.69	−	74448.7i	−0.141432	−	2.69868i
$914$	−1469.83	−	6915.02i	−0.0531923	−	0.250250i
$915$	3008.01	−	1021.09i	0.108679	−	0.0368919i
$916$	10897.8	−	3540.93i	0.393095	−	0.127724i
$917$	−26990.3	+	26655.1i	−0.971971	+	0.959900i
$918$	−1732.84	−	1732.84i	−0.0623008	−	0.0623008i
$919$	−49344.1	+	5186.28i	−1.77118	+	0.186158i	−0.933155	−	0.359475i	$-0.882956\pi$
$919$	−49344.1	+	5186.28i	−1.77118	+	0.186158i	−0.838024	+	0.545634i	$0.816289\pi$
$920$	−1104.82	−	3917.35i	−0.0395920	−	0.140382i
$921$	1465.11	−	13939.6i	0.0524179	−	0.498723i
$922$	5157.13	+	1979.64i	0.184209	+	0.0707114i
$923$	1405.54	+	2758.52i	0.0501232	+	0.0983724i
$924$	38012.0	+	4235.51i	1.35336	+	0.150799i
$925$	−820.373	+	31333.1i	−0.0291608	+	1.11376i
$926$	−571.504	+	989.874i	−0.0202816	+	0.0351288i
$927$	17310.0	+	11241.3i	0.613307	+	0.398286i
$928$	−23000.9	+	18625.8i	−0.813624	+	0.658860i
$929$	−44368.8	+	19754.3i	−1.56695	+	0.697650i	−0.992653	−	0.120999i	$-0.961390\pi$
$929$	−44368.8	+	19754.3i	−1.56695	+	0.697650i	−0.574295	+	0.818649i	$0.694724\pi$
$930$	−589.655	+	490.413i	−0.0207909	+	0.0172917i
$931$	−28112.8	−	3310.45i	−0.989644	−	0.116537i
$932$	15730.7	−	15730.7i	0.552873	−	0.552873i
$933$	5321.01	−	6570.90i	0.186712	−	0.230570i
$934$	16029.3	−	17802.3i	0.561556	−	0.623671i
$935$	−11785.5	−	6600.19i	−0.412223	−	0.230855i
$936$	2972.82	−	2676.74i	0.103814	−	0.0934742i
$937$	12605.4	−	24739.5i	0.439489	−	0.862545i	−0.559933	−	0.828538i	$-0.689173\pi$
$937$	12605.4	−	24739.5i	0.439489	−	0.862545i	0.999422	−	0.0340071i	$-0.0108269\pi$
$938$	−2805.50	+	4261.56i	−0.0976577	+	0.148342i
$939$	15643.6	+	5082.90i	0.543673	+	0.176650i
$940$	19872.9	−	260.186i	0.689555	−	0.00902800i
$941$	22876.8	+	20598.4i	0.792522	+	0.713590i	0.962329	−	0.271887i	$-0.0876478\pi$
$941$	22876.8	+	20598.4i	0.792522	+	0.713590i	−0.169807	+	0.985477i	$0.554314\pi$
$942$	30026.8	−	11526.2i	1.03856	−	0.398667i
$943$	1208.66	+	4510.77i	0.0417383	+	0.155770i
$944$	−4123.39	+	2995.82i	−0.142166	+	0.103290i
$945$	901.851	+	15215.3i	0.0310447	+	0.523761i
$946$	33350.2	+	24230.3i	1.14620	+	0.832766i
$947$	4881.58	−	12717.0i	0.167508	−	0.436373i	−0.823972	−	0.566630i	$-0.808247\pi$
$947$	4881.58	−	12717.0i	0.167508	−	0.436373i	0.991480	+	0.130257i	$0.0415802\pi$
$948$	5027.95	−	7742.37i	0.172258	−	0.265254i
$949$	−6245.37	+	3605.77i	−0.213628	+	0.123338i
$950$	14082.1	+	8629.45i	0.480930	+	0.294712i
$951$		−	28097.9i		−	0.958083i
$952$	6405.69	+	5253.84i	0.218077	+	0.178863i
$953$	−4234.42	−	26735.0i	−0.143931	−	0.908744i	−0.948934	−	0.315474i	$-0.897837\pi$
$953$	−4234.42	−	26735.0i	−0.143931	−	0.908744i	0.805003	−	0.593270i	$-0.202163\pi$
$954$	4903.76	+	11014.0i	0.166421	+	0.373787i
$955$	21399.2	−	6035.24i	0.725091	−	0.204498i
$956$	17803.1	+	7926.44i	0.602293	+	0.268158i
$957$	58197.0	−	15593.8i	1.96577	−	0.526727i
$958$	152.683	−	964.004i	0.00514924	−	0.0325110i
$959$	−2136.16	−	2402.46i	−0.0719293	−	0.0808964i
$960$	12436.5	+	10906.5i	0.418112	+	0.366673i
$961$	19905.3	+	22107.1i	0.668166	+	0.742073i
$962$	−4736.17	+	248.212i	−0.158732	+	0.00831880i
$963$	−30136.4	+	1579.38i	−1.00844	+	0.0528504i
$964$	−15626.9	−	17355.4i	−0.522103	−	0.579854i
$965$	−29.4618	−	130.201i	−0.000982808	−	0.00434335i
$966$	1033.18	−	3113.46i	0.0344119	−	0.103700i
$967$	−6136.26	+	38742.8i	−0.204063	+	1.28840i	0.646656	+	0.762782i	$0.276167\pi$
$967$	−6136.26	+	38742.8i	−0.204063	+	1.28840i	−0.850719	+	0.525621i	$0.823833\pi$
$968$	42489.7	−	11385.1i	1.41082	−	0.378028i
$969$	10249.2	+	4563.25i	0.339786	+	0.151282i
$970$	−10182.4	−	15239.0i	−0.337049	−	0.504428i
$971$	−91.9967	−	206.628i	−0.00304049	−	0.00682905i	0.912019	−	0.410148i	$-0.134523\pi$
$971$	−91.9967	−	206.628i	−0.00304049	−	0.00682905i	−0.915059	+	0.403319i	$0.867856\pi$
$972$	3348.52	+	21141.7i	0.110498	+	0.697656i
$973$	−12127.6	−	32193.4i	−0.399583	−	1.06071i
$974$		−	18396.6i		−	0.605202i
$975$	8919.41	+	3694.51i	0.292974	+	0.121353i
$976$	340.743	−	196.728i	0.0111751	−	0.00645195i
$977$	−18407.8	+	28345.5i	−0.602782	+	0.928202i	0.397164	+	0.917748i	$0.369994\pi$
$977$	−18407.8	+	28345.5i	−0.602782	+	0.928202i	−0.999945	+	0.0104545i	$0.996672\pi$
$978$	10683.7	−	27831.9i	0.349311	−	0.909987i
$979$	43645.7	+	31710.4i	1.42484	+	1.03521i
$980$	−3273.82	−	20590.7i	−0.106712	−	0.671171i
$981$	4357.04	−	3165.58i	0.141804	−	0.103027i
$982$	5753.91	+	21473.9i	0.186980	+	0.697820i
$983$	−31373.6	+	12043.2i	−1.01797	+	0.390761i	−0.809407	−	0.587248i	$-0.800211\pi$
$983$	−31373.6	+	12043.2i	−1.01797	+	0.390761i	−0.208561	+	0.978009i	$0.566878\pi$
$984$	−28841.4	−	25968.9i	−0.934379	−	0.841319i
$985$	5159.10	−	3852.50i	0.166886	−	0.124620i
$986$	5022.11	+	1631.78i	0.162208	+	0.0527044i
$987$	33066.1	+	21768.3i	1.06637	+	0.702019i
$988$	2406.48	−	4722.97i	0.0774901	−	0.152083i
$989$	−5573.21	+	5018.14i	−0.179189	+	0.161342i
$990$	−6853.54	−	14866.4i	−0.220020	−	0.477258i
$991$	−4961.21	+	5509.98i	−0.159029	+	0.176620i	−0.817394	−	0.576079i	$-0.804582\pi$
$991$	−4961.21	+	5509.98i	−0.159029	+	0.176620i	0.658364	+	0.752699i	$0.271249\pi$
$992$	−769.596	+	950.372i	−0.0246318	+	0.0304177i
$993$	−45004.1	+	45004.1i	−1.43823	+	1.43823i
$994$	−7770.22	−	48.5514i	−0.247944	−	0.00154925i
$995$	8472.92	+	5345.99i	0.269959	+	0.170331i
$996$	−41663.6	+	18549.9i	−1.32547	+	0.590135i
$997$	−15483.9	+	12538.6i	−0.491857	+	0.398298i	−0.842907	−	0.538059i	$-0.819158\pi$
$997$	−15483.9	+	12538.6i	−0.491857	+	0.398298i	0.351050	+	0.936357i	$0.385825\pi$
$998$	−21287.7	−	13824.4i	−0.675200	−	0.438480i
$999$	9228.95	−	15985.0i	0.292283	−	0.506249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.103.22	yes	928
7.3	odd	6	inner	175.4.x.a.3.37	✓	928
25.17	odd	20	inner	175.4.x.a.117.37	yes	928
175.17	even	60	inner	175.4.x.a.17.22	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.37	✓	928	7.3	odd	6	inner
175.4.x.a.17.22	yes	928	175.17	even	60	inner
175.4.x.a.103.22	yes	928	1.1	even	1	trivial
175.4.x.a.117.37	yes	928	25.17	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59880 - 0.0837897i) q^{2} +(-4.11426 - 5.08068i) q^{3} +(-5.40702 - 0.568301i) q^{4} +(-9.89445 + 5.20575i) q^{5} +(6.15218 + 8.46775i) q^{6} +(-14.4655 + 11.5650i) q^{7} +(21.2474 + 3.36526i) q^{8} +(-3.27262 + 15.3965i) q^{9} +(16.2555 - 7.49391i) q^{10} +(-56.8321 + 12.0800i) q^{11} +(19.3585 + 29.8095i) q^{12} +(-10.5262 - 5.36337i) q^{13} +(24.0965 - 17.2781i) q^{14} +(67.1571 + 28.8528i) q^{15} +(8.85550 + 1.88230i) q^{16} +(-7.45196 - 19.4130i) q^{17} +(6.52235 - 24.3417i) q^{18} +(-8.62650 - 82.0756i) q^{19} +(56.4580 - 22.5246i) q^{20} +(118.273 + 25.9131i) q^{21} +(91.8755 - 14.5516i) q^{22} +(-0.885668 + 16.8995i) q^{23} +(-70.3196 - 121.797i) q^{24} +(70.8004 - 103.016i) q^{25} +(16.3799 + 9.45696i) q^{26} +(-65.5876 + 33.4185i) q^{27} +(84.7877 - 54.3116i) q^{28} +(93.2324 - 128.323i) q^{29} +(-104.953 - 51.7570i) q^{30} +(2.66569 - 5.98724i) q^{31} +(-180.235 - 48.2937i) q^{32} +(295.197 + 239.045i) q^{33} +(10.2876 + 31.6620i) q^{34} +(82.9235 - 189.733i) q^{35} +(26.4450 - 81.3893i) q^{36} +(-210.297 + 136.568i) q^{37} +(6.91498 + 131.946i) q^{38} +(16.0579 + 75.5466i) q^{39} +(-227.751 + 77.3113i) q^{40} +(262.447 - 85.2743i) q^{41} +(-186.924 - 51.3400i) q^{42} +(313.362 + 313.362i) q^{43} +(314.158 - 33.0193i) q^{44} +(-47.7694 - 169.376i) q^{45} +(2.83202 - 26.9448i) q^{46} +(305.246 + 117.173i) q^{47} +(-26.8705 - 52.7363i) q^{48} +(75.5007 - 334.587i) q^{49} +(-121.828 + 158.770i) q^{50} +(-67.9721 + 117.731i) q^{51} +(53.8674 + 34.9819i) q^{52} +(-371.801 + 301.079i) q^{53} +(107.662 - 47.9341i) q^{54} +(499.437 - 415.379i) q^{55} +(-346.274 + 197.047i) q^{56} +(-381.509 + 381.509i) q^{57} +(-159.812 + 197.352i) q^{58} +(-376.703 + 418.371i) q^{59} +(-346.723 - 194.173i) q^{60} +(32.2969 - 29.0802i) q^{61} +(-4.76358 + 9.34906i) q^{62} +(-130.721 - 260.566i) q^{63} +(215.231 + 69.9329i) q^{64} +(132.071 - 1.72914i) q^{65} +(-451.932 - 406.921i) q^{66} +(-160.644 + 61.6656i) q^{67} +(29.2605 + 109.202i) q^{68} +(89.5051 - 65.0293i) q^{69} +(-148.476 + 296.398i) q^{70} +(-212.013 - 154.036i) q^{71} +(-121.348 + 316.123i) q^{72} +(332.465 - 511.951i) q^{73} +(347.666 - 200.725i) q^{74} +(-814.683 + 64.1198i) q^{75} +448.687i q^{76} +(682.398 - 832.008i) q^{77} +(-19.3434 - 122.130i) q^{78} +(-105.641 - 237.273i) q^{79} +(-97.4191 + 27.4752i) q^{80} +(827.883 + 368.597i) q^{81} +(-426.747 + 114.346i) q^{82} +(-200.723 + 1267.31i) q^{83} +(-624.778 - 207.327i) q^{84} +(174.792 + 153.288i) q^{85} +(-474.747 - 527.260i) q^{86} +(-1035.55 + 54.2710i) q^{87} +(-1248.19 + 65.4148i) q^{88} +(-621.305 - 690.029i) q^{89} +(62.1818 + 274.802i) q^{90} +(214.294 - 44.1520i) q^{91} +(14.3929 - 90.8729i) q^{92} +(-41.3866 + 11.0895i) q^{93} +(-478.211 - 212.913i) q^{94} +(512.619 + 767.186i) q^{95} +(496.167 + 1114.41i) q^{96} +(-160.176 - 1011.31i) q^{97} +(-148.746 + 528.613i) q^{98} -914.548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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