LMFDB - Embedded newform 184.4.j.a.11.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,4,Mod(11,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.11"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 9])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	184.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8563514411$
Analytic rank:	$0$
Dimension:	$700$
Relative dimension:	$70$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	184.11
Dual form			184.4.j.a.67.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.64482 - 1.00245i) q^{2} +(0.730695 - 5.08210i) q^{3} +(5.99019 + 5.30260i) q^{4} +(14.1524 - 4.15552i) q^{5} +(-7.02710 + 12.7088i) q^{6} +(-11.2898 - 13.0291i) q^{7} +(-10.5274 - 20.0293i) q^{8} +(0.612524 + 0.179853i) q^{9} +(-41.5964 - 3.19643i) q^{10} +(15.9098 - 24.7561i) q^{11} +(31.3253 - 26.5682i) q^{12} +(27.8279 + 24.1130i) q^{13} +(16.7985 + 45.7771i) q^{14} +(-10.7777 - 74.9604i) q^{15} +(7.76486 + 63.5272i) q^{16} +(61.2777 - 27.9846i) q^{17} +(-1.43973 - 1.08970i) q^{18} +(73.3374 + 33.4921i) q^{19} +(106.811 + 50.1522i) q^{20} +(-74.4645 + 47.8554i) q^{21} +(-66.8954 + 49.5269i) q^{22} +(-74.9087 - 80.9672i) q^{23} +(-109.483 + 38.8661i) q^{24} +(77.8658 - 50.0413i) q^{25} +(-49.4279 - 91.6708i) q^{26} +(58.9496 - 129.082i) q^{27} +(1.46014 - 137.912i) q^{28} +(-123.688 + 56.4864i) q^{29} +(-46.6388 + 209.061i) q^{30} +(-179.925 + 25.8694i) q^{31} +(43.1461 - 175.802i) q^{32} +(-114.188 - 98.9444i) q^{33} +(-190.122 + 12.5866i) q^{34} +(-213.920 - 137.478i) q^{35} +(2.71545 + 4.32533i) q^{36} +(-126.554 - 37.1597i) q^{37} +(-160.390 - 162.098i) q^{38} +(142.879 - 123.805i) q^{39} +(-232.221 - 239.716i) q^{40} +(113.198 - 33.2381i) q^{41} +(244.918 - 51.9224i) q^{42} +(-194.601 - 27.9794i) q^{43} +(226.575 - 63.9308i) q^{44} +9.41609 q^{45} +(116.955 + 289.236i) q^{46} +111.728i q^{47} +(328.525 + 6.95727i) q^{48} +(6.51572 - 45.3179i) q^{49} +(-256.105 + 54.2941i) q^{50} +(-97.4451 - 331.868i) q^{51} +(38.8329 + 292.002i) q^{52} +(165.182 + 190.630i) q^{53} +(-285.309 + 282.304i) q^{54} +(122.287 - 416.473i) q^{55} +(-142.111 + 363.289i) q^{56} +(223.797 - 348.235i) q^{57} +(383.758 - 25.4058i) q^{58} +(-317.617 + 366.549i) q^{59} +(332.924 - 506.177i) q^{60} +(-76.8738 - 534.669i) q^{61} +(501.804 + 111.946i) q^{62} +(-4.57193 - 10.0111i) q^{63} +(-290.346 + 421.714i) q^{64} +(494.035 + 225.618i) q^{65} +(202.820 + 376.158i) q^{66} +(-201.714 - 313.874i) q^{67} +(515.457 + 157.298i) q^{68} +(-466.219 + 321.531i) q^{69} +(427.967 + 578.050i) q^{70} +(495.207 + 770.557i) q^{71} +(-2.84597 - 14.1618i) q^{72} +(-90.8848 + 199.010i) q^{73} +(297.464 + 225.145i) q^{74} +(-197.419 - 432.287i) q^{75} +(261.710 + 589.503i) q^{76} +(-502.168 + 72.2009i) q^{77} +(-501.997 + 184.214i) q^{78} +(138.703 - 160.072i) q^{79} +(373.880 + 866.797i) q^{80} +(-598.431 - 384.588i) q^{81} +(-332.709 - 25.5667i) q^{82} +(249.387 - 849.333i) q^{83} +(-699.815 - 108.192i) q^{84} +(750.937 - 650.691i) q^{85} +(486.638 + 269.079i) q^{86} +(196.691 + 669.869i) q^{87} +(-663.338 - 58.0439i) q^{88} +(394.947 + 56.7848i) q^{89} +(-24.9039 - 9.43914i) q^{90} -634.803i q^{91} +(-19.3808 - 882.220i) q^{92} +933.300i q^{93} +(112.001 - 295.500i) q^{94} +(1177.08 + 169.238i) q^{95} +(-861.917 - 347.730i) q^{96} +(463.485 + 1578.49i) q^{97} +(-62.6618 + 113.326i) q^{98} +(14.1976 - 12.3023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 700 q - 7 q^{2} - 18 q^{3} - 11 q^{4} + 10 q^{6} - 40 q^{8} - 612 q^{9} - 11 q^{10} - 22 q^{11} + 6 q^{12} - 11 q^{14} - 27 q^{16} - 22 q^{17} + 244 q^{18} - 22 q^{19} - 11 q^{20} - 194 q^{24} - 1568 q^{25}+ \cdots - 22 q^{99}+O(q^{100}) $ 700 * q - 7 * q^2 - 18 * q^3 - 11 * q^4 + 10 * q^6 - 40 * q^8 - 612 * q^9 - 11 * q^10 - 22 * q^11 + 6 * q^12 - 11 * q^14 - 27 * q^16 - 22 * q^17 + 244 * q^18 - 22 * q^19 - 11 * q^20 - 194 * q^24 - 1568 * q^25 + 380 * q^26 + 222 * q^27 - 11 * q^28 - 11 * q^30 - 427 * q^32 - 22 * q^33 + 1903 * q^34 + 482 * q^35 - 1329 * q^36 + 594 * q^38 + 1309 * q^40 - 18 * q^41 - 3641 * q^42 - 22 * q^43 + 3300 * q^44 - 2727 * q^46 + 3204 * q^48 - 2860 * q^49 - 80 * q^50 - 22 * q^51 + 934 * q^52 + 2088 * q^54 - 3586 * q^56 - 22 * q^57 + 6159 * q^58 + 1002 * q^59 - 3641 * q^60 - 618 * q^62 + 1666 * q^64 - 22 * q^65 + 286 * q^66 - 22 * q^67 - 1474 * q^70 + 89 * q^72 - 18 * q^73 + 2354 * q^74 + 590 * q^75 + 8184 * q^76 + 10268 * q^78 + 4048 * q^80 - 5516 * q^81 - 4052 * q^82 - 22 * q^83 - 5401 * q^84 - 6721 * q^86 - 6963 * q^88 - 22 * q^89 - 18700 * q^90 - 4776 * q^92 - 8575 * q^94 - 5643 * q^96 - 22 * q^97 - 3995 * q^98 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	−2.64482	−	1.00245i	−0.935087	−	0.354419i
$2$	−2.64482	−	1.00245i	−0.935087	−	0.354419i
$3$	0.730695	−	5.08210i	0.140622	−	0.978050i	−0.790271	−	0.612758i	$-0.790060\pi$
$3$	0.730695	−	5.08210i	0.140622	−	0.978050i	0.930893	−	0.365292i	$-0.119031\pi$
$4$	5.99019	+	5.30260i	0.748774	+	0.662825i
$5$	14.1524	−	4.15552i	1.26583	−	0.371681i	0.421169	−	0.906982i	$-0.361620\pi$
$5$	14.1524	−	4.15552i	1.26583	−	0.371681i	0.844662	+	0.535301i	$0.179802\pi$
$6$	−7.02710	+	12.7088i	−0.478134	+	0.864722i
$7$	−11.2898	−	13.0291i	−0.609590	−	0.703505i	0.364105	−	0.931358i	$-0.381375\pi$
$7$	−11.2898	−	13.0291i	−0.609590	−	0.703505i	−0.973696	+	0.227853i	$0.926829\pi$
$8$	−10.5274	−	20.0293i	−0.465251	−	0.885179i
$9$	0.612524	+	0.179853i	0.0226861	+	0.00666124i
$10$	−41.5964	−	3.19643i	−1.31539	−	0.101080i
$11$	15.9098	−	24.7561i	0.436090	−	0.678569i	−0.551756	−	0.834006i	$-0.686042\pi$
$11$	15.9098	−	24.7561i	0.436090	−	0.678569i	0.987846	+	0.155437i	$0.0496784\pi$
$12$	31.3253	−	26.5682i	0.753570	−	0.639131i
$13$	27.8279	+	24.1130i	0.593698	+	0.514443i	0.899078	−	0.437788i	$-0.144238\pi$
$13$	27.8279	+	24.1130i	0.593698	+	0.514443i	−0.305380	+	0.952231i	$0.598783\pi$
$14$	16.7985	+	45.7771i	0.320684	+	0.873888i
$15$	−10.7777	−	74.9604i	−0.185519	−	1.29031i
$16$	7.76486	+	63.5272i	0.121326	+	0.992613i
$17$	61.2777	−	27.9846i	0.874237	−	0.399251i	0.0728121	−	0.997346i	$-0.476803\pi$
$17$	61.2777	−	27.9846i	0.874237	−	0.399251i	0.801425	+	0.598095i	$0.204075\pi$
$18$	−1.43973	−	1.08970i	−0.0188526	−	0.0142692i
$19$	73.3374	+	33.4921i	0.885513	+	0.404400i	0.805640	−	0.592405i	$-0.201821\pi$
$19$	73.3374	+	33.4921i	0.885513	+	0.404400i	0.0798725	+	0.996805i	$0.474549\pi$
$20$	106.811	+	50.1522i	1.19418	+	0.560719i
$21$	−74.4645	+	47.8554i	−0.773785	+	0.497281i
$22$	−66.8954	+	49.5269i	−0.648280	+	0.479962i
$23$	−74.9087	−	80.9672i	−0.679110	−	0.734036i
$23$	−74.9087	−	80.9672i	−0.679110	−	0.734036i
$24$	−109.483	+	38.8661i	−0.931174	+	0.330563i
$25$	77.8658	−	50.0413i	0.622927	−	0.400331i
$26$	−49.4279	−	91.6708i	−0.372831	−	0.691466i
$27$	58.9496	−	129.082i	0.420180	−	0.920065i
$28$	1.46014	−	137.912i	0.00985499	−	0.930818i
$29$	−123.688	+	56.4864i	−0.792010	+	0.361699i	−0.769988	−	0.638059i	$-0.779738\pi$
$29$	−123.688	+	56.4864i	−0.792010	+	0.361699i	−0.0220221	+	0.999757i	$0.507010\pi$
$30$	−46.6388	+	209.061i	−0.283835	+	1.27231i
$31$	−179.925	+	25.8694i	−1.04244	+	0.149880i	−0.642204	−	0.766534i	$-0.721980\pi$
$31$	−179.925	+	25.8694i	−1.04244	+	0.149880i	−0.400233	+	0.916414i	$0.631071\pi$
$32$	43.1461	−	175.802i	0.238351	−	0.971179i
$33$	−114.188	−	98.9444i	−0.602350	−	0.521940i
$34$	−190.122	+	12.5866i	−0.958990	+	0.0634878i
$35$	−213.920	−	137.478i	−1.03312	−	0.663944i
$36$	2.71545	+	4.32533i	0.0125715	+	0.0200247i
$37$	−126.554	−	37.1597i	−0.562309	−	0.165109i	−0.0117883	−	0.999931i	$-0.503752\pi$
$37$	−126.554	−	37.1597i	−0.562309	−	0.165109i	−0.550520	+	0.834822i	$0.685571\pi$
$38$	−160.390	−	162.098i	−0.684704	−	0.691992i
$39$	142.879	−	123.805i	0.586638	−	0.508324i
$40$	−232.221	−	239.716i	−0.917934	−	0.947561i
$41$	113.198	−	33.2381i	0.431186	−	0.126608i	−0.0589355	−	0.998262i	$-0.518771\pi$
$41$	113.198	−	33.2381i	0.431186	−	0.126608i	0.490121	+	0.871654i	$0.336952\pi$
$42$	244.918	−	51.9224i	0.899802	−	0.190757i
$43$	−194.601	−	27.9794i	−0.690149	−	0.0992285i	−0.211688	−	0.977337i	$-0.567896\pi$
$43$	−194.601	−	27.9794i	−0.690149	−	0.0992285i	−0.478461	+	0.878109i	$0.658805\pi$
$44$	226.575	−	63.9308i	0.776305	−	0.219044i
$45$	9.41609			0.0311926
$46$	116.955	+	289.236i	0.374871	+	0.927077i
$47$			111.728i			0.346748i	0.984856	+	0.173374i	$0.0554670\pi$
$47$			111.728i			0.346748i	−0.984856	+	0.173374i	$0.944533\pi$
$48$	328.525	+	6.95727i	0.987886	+	0.0209207i
$49$	6.51572	−	45.3179i	0.0189963	−	0.132122i
$50$	−256.105	+	54.2941i	−0.724375	+	0.153567i
$51$	−97.4451	−	331.868i	−0.267550	−	0.911191i
$52$	38.8329	+	292.002i	0.103561	+	0.778720i
$53$	165.182	+	190.630i	0.428103	+	0.494057i	0.928288	−	0.371861i	$-0.121280\pi$
$53$	165.182	+	190.630i	0.428103	+	0.494057i	−0.500186	+	0.865918i	$0.666735\pi$
$54$	−285.309	+	282.304i	−0.718993	+	0.711421i
$55$	122.287	−	416.473i	0.299804	−	1.02104i
$56$	−142.111	+	363.289i	−0.339115	+	0.866903i
$57$	223.797	−	348.235i	0.520046	−	0.809208i
$58$	383.758	−	25.4058i	0.868791	−	0.0575164i
$59$	−317.617	+	366.549i	−0.700850	+	0.808824i	−0.988867	−	0.148801i	$-0.952459\pi$
$59$	−317.617	+	366.549i	−0.700850	+	0.808824i	0.288017	+	0.957625i	$0.407004\pi$
$60$	332.924	−	506.177i	0.716339	−	1.08912i
$61$	−76.8738	−	534.669i	−0.161356	−	1.12225i	−0.896082	−	0.443889i	$-0.853599\pi$
$61$	−76.8738	−	534.669i	−0.161356	−	1.12225i	0.734726	−	0.678364i	$-0.237311\pi$
$62$	501.804	+	111.946i	1.02789	+	0.229309i
$63$	−4.57193	−	10.0111i	−0.00914301	−	0.0200204i
$64$	−290.346	+	421.714i	−0.567083	+	0.823661i
$65$	494.035	+	225.618i	0.942730	+	0.430531i
$66$	202.820	+	376.158i	0.378265	+	0.701543i
$67$	−201.714	−	313.874i	−0.367811	−	0.572325i	0.607181	−	0.794563i	$-0.292300\pi$
$67$	−201.714	−	313.874i	−0.367811	−	0.572325i	−0.974992	+	0.222238i	$0.928664\pi$
$68$	515.457	+	157.298i	0.919240	+	0.280518i
$69$	−466.219	+	321.531i	−0.813422	+	0.560982i
$70$	427.967	+	578.050i	0.730740	+	0.987002i
$71$	495.207	+	770.557i	0.827750	+	1.28800i	0.955141	+	0.296151i	$0.0957032\pi$
$71$	495.207	+	770.557i	0.827750	+	1.28800i	−0.127392	+	0.991853i	$0.540660\pi$
$72$	−2.84597	−	14.1618i	−0.00465834	−	0.0231804i
$73$	−90.8848	+	199.010i	−0.145716	+	0.319074i	−0.968390	−	0.249439i	$-0.919754\pi$
$73$	−90.8848	+	199.010i	−0.145716	+	0.319074i	0.822674	+	0.568513i	$0.192481\pi$
$74$	297.464	+	225.145i	0.467290	+	0.353684i
$75$	−197.419	−	432.287i	−0.303946	−	0.665549i
$76$	261.710	+	589.503i	0.395003	+	0.889745i
$77$	−502.168	+	72.2009i	−0.743213	+	0.106858i
$78$	−501.997	+	184.214i	−0.728717	+	0.267412i
$79$	138.703	−	160.072i	0.197536	−	0.227968i	−0.648337	−	0.761354i	$-0.724535\pi$
$79$	138.703	−	160.072i	0.197536	−	0.227968i	0.845872	+	0.533386i	$0.179080\pi$
$80$	373.880	+	866.797i	0.522514	+	1.21139i
$81$	−598.431	−	384.588i	−0.820893	−	0.527556i
$82$	−332.709	−	25.5667i	−0.448068	−	0.0344314i
$83$	249.387	−	849.333i	0.329804	−	1.12321i	−0.613061	−	0.790035i	$-0.710062\pi$
$83$	249.387	−	849.333i	0.329804	−	1.12321i	0.942865	−	0.333174i	$-0.108120\pi$
$84$	−699.815	−	108.192i	−0.909001	−	0.140532i
$85$	750.937	−	650.691i	0.958242	−	0.830322i
$86$	486.638	+	269.079i	0.610181	+	0.337389i
$87$	196.691	+	669.869i	0.242385	+	0.825488i
$88$	−663.338	−	58.0439i	−0.803546	−	0.0703125i
$89$	394.947	+	56.7848i	0.470386	+	0.0676313i	0.373432	−	0.927658i	$-0.378181\pi$
$89$	394.947	+	56.7848i	0.470386	+	0.0676313i	0.0969539	+	0.995289i	$0.469090\pi$
$90$	−24.9039	−	9.43914i	−0.0291678	−	0.0110553i
$91$		−	634.803i		−	0.731269i
$92$	−19.3808	−	882.220i	−0.0219629	−	0.999759i
$93$			933.300i			1.04063i
$94$	112.001	−	295.500i	0.122894	−	0.324240i
$95$	1177.08	+	169.238i	1.27122	+	0.182773i
$96$	−861.917	−	347.730i	−0.916344	−	0.369688i
$97$	463.485	+	1578.49i	0.485152	+	1.65228i	0.730554	+	0.682855i	$0.239262\pi$
$97$	463.485	+	1578.49i	0.485152	+	1.65228i	−0.245401	+	0.969422i	$0.578920\pi$
$98$	−62.6618	+	113.326i	−0.0645897	+	0.116813i
$99$	14.1976	−	12.3023i	0.0144133	−	0.0124892i
$100$	731.781	+	113.134i	0.731781	+	0.113134i
$101$	−507.560	+	1728.59i	−0.500041	+	1.70298i	0.192233	+	0.981349i	$0.438427\pi$
$101$	−507.560	+	1728.59i	−0.500041	+	1.70298i	−0.692274	+	0.721634i	$0.743391\pi$
$102$	−74.9549	+	975.415i	−0.0727612	+	0.946868i
$103$	−285.432	−	183.436i	−0.273053	−	0.175481i	0.396947	−	0.917841i	$-0.370070\pi$
$103$	−285.432	−	183.436i	−0.273053	−	0.175481i	−0.670000	+	0.742361i	$0.733706\pi$
$104$	190.011	−	811.223i	0.179155	−	0.764874i
$105$	−854.988	+	986.709i	−0.794650	+	0.917075i
$106$	−245.780	−	669.768i	−0.225210	−	0.613714i
$107$	2050.66	−	294.841i	1.85276	−	0.266387i	0.876249	−	0.481858i	$-0.160038\pi$
$107$	2050.66	−	294.841i	1.85276	−	0.266387i	0.976510	+	0.215472i	$0.0691289\pi$
$108$	1037.59	−	460.638i	0.924462	−	0.410416i
$109$	−374.820	−	820.742i	−0.329369	−	0.721218i	0.670415	−	0.741986i	$-0.266116\pi$
$109$	−374.820	−	820.742i	−0.329369	−	0.721218i	−0.999784	+	0.0207681i	$0.993389\pi$
$110$	−740.922	+	978.911i	−0.642219	+	0.848505i
$111$	−281.322	+	616.009i	−0.240558	+	0.526748i
$112$	740.038	−	818.377i	0.624349	−	0.690440i
$113$	833.114	+	1296.35i	0.693564	+	1.07921i	0.992178	+	0.124833i	$0.0398394\pi$
$113$	833.114	+	1296.35i	0.693564	+	1.07921i	−0.298614	+	0.954374i	$0.596524\pi$
$114$	−940.992	+	696.676i	−0.773087	+	0.572365i
$115$	−1396.60	−	834.597i	−1.13247	−	0.676753i
$116$	−1040.44	−	317.503i	−0.832780	−	0.254133i
$117$	12.7085	+	19.7748i	0.0100419	+	0.0156255i
$118$	1207.49	−	651.064i	0.942018	−	0.507926i
$119$	−1056.43	−	482.453i	−0.813802	−	0.371651i
$120$	−1387.94	+	1005.01i	−1.05584	+	0.764537i
$121$	193.173	+	422.989i	0.145133	+	0.317798i
$122$	−332.661	+	1491.17i	−0.246866	+	1.10659i
$123$	−86.2055	−	599.572i	−0.0631942	−	0.439525i
$124$	−1214.96	−	799.110i	−0.879894	−	0.578727i
$125$	−313.349	+	361.624i	−0.224214	+	0.258757i
$126$	2.05631	+	31.0608i	0.00145390	+	0.0219613i
$127$	1269.88	−	1975.97i	0.887270	−	1.38062i	−0.0371773	−	0.999309i	$-0.511837\pi$
$127$	1269.88	−	1975.97i	0.887270	−	1.38062i	0.924447	−	0.381310i	$-0.124527\pi$
$128$	1190.66	−	824.303i	0.822193	−	0.569209i
$129$	−284.389	+	968.538i	−0.194101	+	0.661047i
$130$	−1080.46	−	1091.96i	−0.728946	−	0.736705i
$131$	1271.09	+	1466.92i	0.847754	+	0.978360i	0.999950	−	0.00999011i	$-0.00318000\pi$
$131$	1271.09	+	1466.92i	0.847754	+	0.978360i	−0.152196	+	0.988350i	$0.548635\pi$
$132$	−159.345	−	1198.19i	−0.105070	−	0.790068i
$133$	−391.591	−	1333.64i	−0.255303	−	0.869481i
$134$	218.857	+	1032.35i	0.141092	+	0.665533i
$135$	297.877	−	2071.78i	0.189905	−	1.32082i
$136$	−1205.61	−	932.745i	−0.760148	−	0.588104i
$137$		−	2667.82i		−	1.66370i	−0.554998	−	0.831852i	$-0.687281\pi$
$137$		−	2667.82i		−	1.66370i	0.554998	−	0.831852i	$-0.312719\pi$
$138$	1555.38	−	383.032i	0.959443	−	0.236275i
$139$	1042.06			0.635873			0.317937	−	0.948112i	$-0.397010\pi$
$139$	1042.06			0.635873			0.317937	+	0.948112i	$0.397010\pi$
$140$	−552.432	−	1957.85i	−0.333493	−	1.18192i
$141$	567.811	+	81.6389i	0.339137	+	0.0487606i
$142$	−537.292	−	2534.41i	−0.317525	−	1.49777i
$143$	1039.68	−	305.278i	0.607991	−	0.178522i
$144$	−6.66942	+	40.3085i	−0.00385962	+	0.0233267i
$145$	−1515.75	+	1313.41i	−0.868114	+	0.752225i
$146$	439.872	−	435.239i	0.249343	−	0.246717i
$147$	−225.549	−	66.2271i	−0.126551	−	0.0371586i
$148$	−561.042	−	893.661i	−0.311604	−	0.496341i
$149$	−1293.18	−	831.077i	−0.711017	−	0.456943i	0.134485	−	0.990916i	$-0.457062\pi$
$149$	−1293.18	−	831.077i	−0.711017	−	0.456943i	−0.845502	+	0.533973i	$0.820699\pi$
$150$	88.7928	+	1341.22i	0.0483327	+	0.730070i
$151$	833.230	+	721.998i	0.449055	+	0.389108i	0.849820	−	0.527072i	$-0.176710\pi$
$151$	833.230	+	721.998i	0.449055	+	0.389108i	−0.400765	+	0.916181i	$0.631256\pi$
$152$	−101.231	−	1821.48i	−0.0540194	−	0.971985i
$153$	42.5672	−	6.12025i	0.0224925	−	0.00323394i
$154$	1400.52	+	312.439i	0.732841	+	0.163487i
$155$	−2438.88	+	1113.80i	−1.26384	+	0.577177i
$156$	1512.36	+	16.0120i	0.776189	+	0.00821787i
$157$	−67.0498	+	146.819i	−0.0340838	+	0.0746331i	−0.925908	−	0.377749i	$-0.876698\pi$
$157$	−67.0498	+	146.819i	−0.0340838	+	0.0746331i	0.891824	+	0.452382i	$0.149426\pi$
$158$	−527.309	+	284.319i	−0.265509	+	0.143160i
$159$	1089.50	−	700.177i	0.543413	−	0.349230i
$160$	−119.929	−	2667.32i	−0.0592578	−	1.31794i
$161$	−209.227	+	1890.09i	−0.102419	+	0.925219i
$162$	1197.21	+	1617.06i	0.580630	+	0.784250i
$163$	−1677.49	+	1078.06i	−0.806082	+	0.518037i	−0.877595	−	0.479402i	$-0.840853\pi$
$163$	−1677.49	+	1078.06i	−0.806082	+	0.518037i	0.0715135	+	0.997440i	$0.477217\pi$
$164$	854.329	+	401.144i	0.406780	+	0.191000i
$165$	−2027.20	−	925.792i	−0.956469	−	0.436805i
$166$	−1511.00	+	1996.34i	−0.706482	+	0.933409i
$167$	−175.819	+	80.2940i	−0.0814689	+	0.0372056i	−0.455733	−	0.890117i	$-0.650623\pi$
$167$	−175.819	+	80.2940i	−0.0814689	+	0.0372056i	0.374264	+	0.927322i	$0.377895\pi$
$168$	1742.43	+	987.677i	0.800187	+	0.453577i
$169$	−119.711	−	832.606i	−0.0544882	−	0.378974i
$170$	−2638.38	+	968.188i	−1.19032	+	0.436803i
$171$	38.8973	+	33.7047i	0.0173950	+	0.0150729i
$172$	−1017.34	−	1199.50i	−0.450995	−	0.531748i
$173$	−244.370	+	380.248i	−0.107394	+	0.167108i	−0.890791	−	0.454414i	$-0.849849\pi$
$173$	−244.370	+	380.248i	−0.107394	+	0.167108i	0.783397	+	0.621522i	$0.213485\pi$
$174$	151.295	−	1968.86i	0.0659175	−	0.857809i
$175$	−1531.08	−	449.566i	−0.661365	−	0.194194i
$176$	1696.23	+	818.478i	0.726465	+	0.350540i
$177$	1630.76	+	1881.99i	0.692515	+	0.799205i
$178$	−987.642	−	546.100i	−0.415882	−	0.229955i
$179$	−3207.76	+	941.883i	−1.33944	+	0.393294i	−0.871468	−	0.490452i	$-0.836832\pi$
$179$	−3207.76	+	941.883i	−1.33944	+	0.393294i	−0.467968	+	0.883746i	$0.655014\pi$
$180$	56.4042	+	49.9297i	0.0233562	+	0.0206752i
$181$	−200.672	+	1395.70i	−0.0824079	+	0.573160i	0.906223	+	0.422799i	$0.138952\pi$
$181$	−200.672	+	1395.70i	−0.0824079	+	0.573160i	−0.988631	+	0.150360i	$0.951957\pi$
$182$	−636.358	+	1678.94i	−0.259176	+	0.683800i
$183$	−2773.41			−1.12031
$184$	−833.121	+	2352.75i	−0.333796	+	0.942645i
$185$	−1945.47			−0.773155
$186$	935.586	−	2468.42i	0.368820	−	0.973081i
$187$	282.126	−	1962.23i	0.110327	−	0.767340i
$188$	−592.448	+	669.271i	−0.229833	+	0.259636i
$189$	−2347.34	+	689.242i	−0.903408	+	0.265265i
$190$	−2943.51	−	1627.57i	−1.12392	−	0.621453i
$191$	2230.95	+	2574.66i	0.845163	+	0.975370i	0.999921	−	0.0125821i	$-0.00400510\pi$
$191$	2230.95	+	2574.66i	0.845163	+	0.975370i	−0.154758	+	0.987952i	$0.549460\pi$
$192$	1931.04	+	1783.71i	0.725837	+	0.670460i
$193$	3890.53	+	1142.36i	1.45102	+	0.426057i	0.909878	−	0.414875i	$-0.136175\pi$
$193$	3890.53	+	1142.36i	1.45102	+	0.426057i	0.541140	+	0.840932i	$0.317993\pi$
$194$	356.513	−	4639.44i	0.131939	−	1.71697i
$195$	1507.60	−	2345.87i	0.553649	−	0.861495i
$196$	279.333	−	236.913i	0.101798	−	0.0863384i
$197$	3600.21	+	3119.60i	1.30205	+	1.12824i	0.983613	+	0.180293i	$0.0577046\pi$
$197$	3600.21	+	3119.60i	1.30205	+	1.12824i	0.318441	+	0.947943i	$0.396841\pi$
$198$	−49.8827	+	18.3051i	−0.0179041	+	0.00657013i
$199$	445.341	+	3097.41i	0.158640	+	1.10337i	0.901143	+	0.433522i	$0.142729\pi$
$199$	445.341	+	3097.41i	0.158640	+	1.10337i	−0.742503	+	0.669843i	$0.766361\pi$
$200$	−1822.02	−	1032.79i	−0.644181	−	0.365147i
$201$	−1742.53	+	795.786i	−0.611485	+	0.279256i
$202$	3075.23	−	4063.02i	1.07115	−	1.41521i
$203$	2132.38	+	973.823i	0.737258	+	0.336695i
$204$	1176.05	−	2504.66i	0.403626	−	0.859615i
$205$	1463.91	−	940.798i	0.498751	−	0.320528i
$206$	571.033	+	771.287i	0.193135	+	0.260865i
$207$	−31.3212	−	63.0670i	−0.0105168	−	0.0211761i
$208$	−1315.75	+	1955.07i	−0.438611	+	0.651728i
$209$	1995.92	−	1282.70i	0.660577	−	0.424527i
$210$	3250.42	−	1752.59i	1.06810	−	0.575906i
$211$	−1805.00	+	3952.40i	−0.588917	+	1.28955i	0.347177	+	0.937799i	$0.387140\pi$
$211$	−1805.00	+	3952.40i	−0.588917	+	1.28955i	−0.936094	+	0.351749i	$0.885587\pi$
$212$	−21.3634	+	2017.80i	−0.00692095	+	0.653694i
$213$	4277.89	−	1953.65i	1.37613	−	0.628458i
$214$	−5719.21	−	1275.88i	−1.82690	−	0.407559i
$215$	−2870.35	+	412.694i	−0.910494	+	0.130909i
$216$	−3206.00	+	178.178i	−1.00991	+	0.0561272i
$217$	2368.37	+	2052.20i	0.740901	+	0.641994i
$218$	168.582	+	2546.46i	0.0523754	+	0.791136i
$219$	944.979	+	607.301i	0.291579	+	0.187386i
$220$	2940.92	−	1846.31i	0.901257	−	0.565811i
$221$	2380.03	+	698.839i	0.724425	+	0.212710i
$222$	1361.56	−	1347.23i	0.411632	−	0.407297i
$223$	279.839	−	242.482i	0.0840332	−	0.0728152i	−0.611831	−	0.790988i	$-0.709567\pi$
$223$	279.839	−	242.482i	0.0840332	−	0.0728152i	0.695864	+	0.718173i	$0.255021\pi$
$224$	−2777.65	+	1422.61i	−0.828525	+	0.424341i
$225$	56.6948	−	16.6471i	0.0167985	−	0.00493248i
$226$	−903.915	−	4263.77i	−0.266051	−	1.25496i
$227$	−3527.06	−	507.115i	−1.03127	−	0.148275i	−0.394158	−	0.919043i	$-0.628964\pi$
$227$	−3527.06	−	507.115i	−1.03127	−	0.148275i	−0.637116	+	0.770768i	$0.719873\pi$
$228$	3187.14	−	899.289i	0.925761	−	0.261214i
$229$	−218.488			−0.0630485			−0.0315242	−	0.999503i	$-0.510036\pi$
$229$	−218.488			−0.0630485			−0.0315242	+	0.999503i	$0.510036\pi$
$230$	2857.12	+	3607.38i	0.819100	+	1.03419i
$231$			2604.82i			0.741926i
$232$	2433.50	+	1882.73i	0.688651	+	0.532790i
$233$	878.388	−	6109.32i	0.246975	−	1.71775i	−0.368532	−	0.929615i	$-0.620139\pi$
$233$	878.388	−	6109.32i	0.246975	−	1.71775i	0.615506	−	0.788132i	$-0.288952\pi$
$234$	−13.7885	−	65.0404i	−0.00385206	−	0.0181702i
$235$	464.287	+	1581.22i	0.128880	+	0.438925i
$236$	−3846.25	+	511.506i	−1.06089	+	0.141086i
$237$	−712.151	−	821.866i	−0.195186	−	0.225257i
$238$	2310.43	+	2335.02i	0.629255	+	0.635952i
$239$	1291.82	−	4399.54i	0.349627	−	1.19072i	−0.577630	−	0.816298i	$-0.696022\pi$
$239$	1291.82	−	4399.54i	0.349627	−	1.19072i	0.927258	−	0.374423i	$-0.122159\pi$
$240$	4678.34	−	1266.73i	1.25827	−	0.340697i
$241$	3325.76	−	5174.99i	0.888926	−	1.38320i	−0.0344942	−	0.999405i	$-0.510982\pi$
$241$	3325.76	−	5174.99i	0.888926	−	1.38320i	0.923420	−	0.383791i	$-0.125382\pi$
$242$	−86.8830	−	1312.38i	−0.0230787	−	0.348607i
$243$	117.277	−	135.345i	0.0309603	−	0.0357301i
$244$	2374.65	−	3610.40i	0.623038	−	0.947264i
$245$	−96.1062	−	668.434i	−0.0250612	−	0.174305i
$246$	−373.042	+	1672.18i	−0.0966840	+	0.433391i
$247$	1233.23	+	2700.40i	0.317687	+	0.695637i
$248$	2412.30	+	3331.44i	0.617665	+	0.853011i
$249$	−4134.17	−	1888.01i	−1.05218	−	0.480513i
$250$	1191.26	−	642.316i	0.301368	−	0.162494i
$251$	2256.21	+	3510.74i	0.567375	+	0.882852i	0.999823	−	0.0188065i	$-0.00598665\pi$
$251$	2256.21	+	3510.74i	0.567375	+	0.882852i	−0.432449	+	0.901659i	$0.642350\pi$
$252$	25.6983	−	84.2118i	0.00642397	−	0.0210510i
$253$	−3196.22	+	566.277i	−0.794247	+	0.140718i
$254$	−5339.40	+	3953.10i	−1.31899	+	0.976533i
$255$	−2758.17	−	4291.79i	−0.677346	−	1.05397i
$256$	−3975.41	+	986.560i	−0.970560	+	0.240859i
$257$	−2947.06	+	6453.15i	−0.715301	+	1.56629i	0.105074	+	0.994464i	$0.466492\pi$
$257$	−2947.06	+	6453.15i	−0.715301	+	1.56629i	−0.820375	+	0.571826i	$0.806235\pi$
$258$	1723.07	−	2276.53i	0.415789	−	0.549343i
$259$	944.613	+	2068.41i	0.226623	+	0.496235i
$260$	1763.00	+	3971.17i	0.420526	+	0.947235i
$261$	−85.9212	+	12.3536i	−0.0203770	+	0.00292977i
$262$	−1891.30	−	5153.94i	−0.445974	−	1.21531i
$263$	350.045	−	403.974i	0.0820712	−	0.0947152i	−0.713229	−	0.700931i	$-0.752768\pi$
$263$	350.045	−	403.974i	0.0820712	−	0.0947152i	0.795300	+	0.606216i	$0.207313\pi$
$264$	−779.682	+	3328.73i	−0.181766	+	0.776021i
$265$	3129.89	+	2011.46i	0.725537	+	0.466275i
$266$	−301.212	+	3919.79i	−0.0694305	+	0.903524i
$267$	577.172	−	1965.67i	0.132293	−	0.450550i
$268$	456.039	−	2949.78i	0.103944	−	0.672337i
$269$	2037.07	−	1765.13i	0.461718	−	0.400081i	−0.392701	−	0.919666i	$-0.628459\pi$
$269$	2037.07	−	1765.13i	0.461718	−	0.400081i	0.854418	+	0.519586i	$0.173914\pi$
$270$	−2864.69	+	5180.90i	−0.645702	+	1.16778i
$271$	−1575.09	−	5364.28i	−0.353063	−	1.20242i	−0.924309	−	0.381644i	$-0.875358\pi$
$271$	−1575.09	−	5364.28i	−0.353063	−	1.20242i	0.571246	−	0.820779i	$-0.306460\pi$
$272$	2253.60	+	3675.51i	0.502369	+	0.819340i
$273$	−3226.13	−	463.848i	−0.715217	−	0.102833i
$274$	−2674.35	+	7055.92i	−0.589648	+	1.55571i
$275$		−	2723.81i		−	0.597279i
$276$	−4497.69	−	546.139i	−0.980902	−	0.119108i
$277$		−	723.925i		−	0.157027i	−0.996913	−	0.0785135i	$-0.974983\pi$
$277$		−	723.925i		−	0.157027i	0.996913	−	0.0785135i	$-0.0250174\pi$
$278$	−2756.07	−	1044.61i	−0.594596	−	0.225366i
$279$	−114.861	−	16.5146i	−0.0246472	−	0.00354373i
$280$	−501.563	+	5731.97i	−0.107050	+	1.22339i
$281$	−1007.40	−	3430.88i	−0.213866	−	0.728359i	−0.994626	−	0.103529i	$-0.966986\pi$
$281$	−1007.40	−	3430.88i	−0.213866	−	0.728359i	0.780761	−	0.624830i	$-0.214832\pi$
$282$	−1419.92	−	785.122i	−0.299841	−	0.165792i
$283$	−5195.40	+	4501.84i	−1.09129	+	0.945606i	−0.998744	−	0.0501030i	$-0.984045\pi$
$283$	−5195.40	+	4501.84i	−1.09129	+	0.945606i	−0.0925430	+	0.995709i	$0.529500\pi$
$284$	−1119.57	+	7241.67i	−0.233923	+	1.51308i
$285$	1720.17	−	5858.36i	0.357523	−	1.21761i
$286$	−3055.81	−	234.821i	−0.631796	−	0.0485498i
$287$	−1711.05	−	1099.62i	−0.351916	−	0.226163i
$288$	58.0466	−	99.9232i	0.0118765	−	0.0204445i
$289$	−245.507	+	283.330i	−0.0499709	+	0.0576695i
$290$	5325.53	−	1954.27i	1.07836	−	0.395719i
$291$	8360.68	−	1202.08i	1.68423	−	0.242156i
$292$	−1599.69	+	710.183i	−0.320598	+	0.142330i
$293$	3482.31	+	7625.20i	0.694331	+	1.52037i	0.846713	+	0.532050i	$0.178578\pi$
$293$	3482.31	+	7625.20i	0.694331	+	1.52037i	−0.152382	+	0.988322i	$0.548694\pi$
$294$	530.148	+	401.260i	0.105166	+	0.0795985i
$295$	−2971.84	+	6507.42i	−0.586533	+	1.28433i
$296$	588.009	+	2925.99i	0.115464	+	0.574561i
$297$	−2257.69	−	3513.03i	−0.441092	−	0.686352i
$298$	2587.13	+	3494.40i	0.502913	+	0.679279i
$299$	−132.188	−	4059.43i	−0.0255673	−	0.785159i
$300$	1109.67	−	3636.31i	0.213555	−	0.699809i
$301$	1832.46	+	2851.36i	0.350901	+	0.546012i
$302$	−1479.98	−	2744.83i	−0.281998	−	0.523004i
$303$	8414.00	+	3842.55i	1.59529	+	0.728543i
$304$	−1558.20	+	4918.98i	−0.293977	+	0.928036i
$305$	−3309.78	−	7247.41i	−0.621369	−	1.36061i
$306$	−118.718	−	26.4845i	−0.0221786	−	0.00494777i
$307$	−211.652	−	1472.07i	−0.0393474	−	0.273667i	0.960644	−	0.277782i	$-0.0895992\pi$
$307$	−211.652	−	1472.07i	−0.0393474	−	0.273667i	−0.999992	+	0.00411498i	$0.998690\pi$
$308$	−3390.94	−	2230.30i	−0.627327	−	0.412608i
$309$	−1140.80	+	1316.56i	−0.210026	+	0.242383i
$310$	7566.93	−	500.952i	1.38636	−	0.0917811i
$311$	300.918	−	468.238i	0.0548666	−	0.0853740i	−0.812737	−	0.582631i	$-0.802023\pi$
$311$	300.918	−	468.238i	0.0548666	−	0.0853740i	0.867603	+	0.497257i	$0.165660\pi$
$312$	−3983.87	−	1558.41i	−0.722892	−	0.282781i
$313$	−77.2003	+	262.920i	−0.0139413	+	0.0474796i	−0.966170	−	0.257907i	$-0.916967\pi$
$313$	−77.2003	+	262.920i	−0.0139413	+	0.0474796i	0.952229	+	0.305386i	$0.0987855\pi$
$314$	324.513	−	321.095i	0.0583227	−	0.0577085i
$315$	−106.305	−	122.683i	−0.0190147	−	0.0219441i
$316$	1679.66	−	223.375i	0.299013	−	0.0397652i
$317$	−2371.24	−	8075.71i	−0.420133	−	1.43084i	−0.849441	−	0.527684i	$-0.823060\pi$
$317$	−2371.24	−	8075.71i	−0.420133	−	1.43084i	0.429307	−	0.903158i	$-0.358758\pi$
$318$	−3583.42	+	759.681i	−0.631912	+	0.133965i
$319$	−569.467	+	3960.73i	−0.0999499	+	0.695166i
$320$	−2356.66	+	7174.82i	−0.411691	+	1.25339i
$321$		−	10637.1i		−	1.84955i
$322$	2448.09	−	4789.23i	0.423686	−	0.828861i
$323$	5431.21			0.935606
$324$	−1545.40	−	5477.00i	−0.264986	−	0.939128i
$325$	3373.49	+	485.035i	0.575778	+	0.0827843i
$326$	5517.37	−	1169.68i	0.937359	−	0.198719i
$327$	−4444.97	+	1305.16i	−0.751704	+	0.220720i
$328$	−1857.42	−	1917.37i	−0.312680	−	0.322772i
$329$	1455.71	−	1261.38i	0.243939	−	0.211374i
$330$	4433.53	+	4480.72i	0.739569	+	0.747441i
$331$	−4973.12	−	1460.24i	−0.825823	−	0.242484i	−0.158602	−	0.987343i	$-0.550699\pi$
$331$	−4973.12	−	1460.24i	−0.825823	−	0.242484i	−0.667222	+	0.744859i	$0.732517\pi$
$332$	5997.55	−	3765.27i	0.991440	−	0.622428i
$333$	−70.8344	−	45.5225i	−0.0116568	−	0.00749134i
$334$	545.502	−	36.1137i	0.0893669	−	0.00591634i
$335$	−4159.06	−	3603.84i	−0.678309	−	0.587758i
$336$	−3618.33	−	4358.93i	−0.587488	−	0.707735i
$337$	−5562.32	+	799.740i	−0.899106	+	0.129272i	−0.576343	−	0.817208i	$-0.695521\pi$
$337$	−5562.32	+	799.740i	−0.899106	+	0.129272i	−0.322763	+	0.946480i	$0.604612\pi$
$338$	−518.031	+	2322.10i	−0.0833644	+	0.373685i
$339$	7196.93	−	3286.73i	1.15305	−	0.526580i
$340$	7948.62	+	84.1555i	1.26787	+	0.0134235i
$341$	−2222.15	+	4865.83i	−0.352892	+	0.772726i
$342$	−69.0893	−	128.135i	−0.0109237	−	0.0202596i
$343$	−5638.60	+	3623.71i	−0.887626	+	0.570443i
$344$	1488.24	+	4192.28i	0.233258	+	0.657072i
$345$	−5261.99	+	6487.82i	−0.821148	+	1.01244i
$346$	1027.50	−	760.720i	0.159649	−	0.118198i
$347$	307.321	−	197.503i	0.0475443	−	0.0305549i	−0.516653	−	0.856195i	$-0.672822\pi$
$347$	307.321	−	197.503i	0.0475443	−	0.0305549i	0.564197	+	0.825640i	$0.309186\pi$
$348$	−2373.83	+	5055.62i	−0.365662	+	0.778763i
$349$	−5118.38	−	2337.49i	−0.785045	−	0.358518i	−0.0177747	−	0.999842i	$-0.505658\pi$
$349$	−5118.38	−	2337.49i	−0.785045	−	0.358518i	−0.767270	+	0.641324i	$0.778385\pi$
$350$	3598.77	+	2723.85i	0.549607	+	0.415989i
$351$	4753.00	−	2170.62i	0.722781	−	0.330083i
$352$	−3665.74	−	3865.11i	−0.555070	−	0.585259i
$353$	−392.586	−	2730.49i	−0.0591933	−	0.411698i	−0.997777	−	0.0666458i	$-0.978770\pi$
$353$	−392.586	−	2730.49i	−0.0591933	−	0.411698i	0.938583	−	0.345052i	$-0.112139\pi$
$354$	−2426.46	−	6612.29i	−0.364308	−	0.992766i
$355$	10210.4	+	8847.40i	1.52652	+	1.32274i
$356$	2064.70	+	2434.40i	0.307385	+	0.362424i
$357$	−3223.80	+	5016.33i	−0.477932	+	0.743676i
$358$	9428.15	+	724.497i	1.39188	+	0.106958i
$359$	−3320.40	−	974.958i	−0.488145	−	0.143332i	0.0283925	−	0.999597i	$-0.490961\pi$
$359$	−3320.40	−	974.958i	−0.488145	−	0.143332i	−0.516538	+	0.856265i	$0.672779\pi$
$360$	−99.1272	−	188.598i	−0.0145124	−	0.0276110i
$361$	−235.038	−	271.248i	−0.0342671	−	0.0395463i
$362$	1929.86	−	3490.23i	0.280197	−	0.506747i
$363$	2290.82	−	672.646i	0.331231	−	0.0972582i
$364$	3366.11	−	3802.60i	0.484703	−	0.547555i
$365$	−459.249	+	3194.15i	−0.0658581	+	0.458053i
$366$	7335.19	+	2780.20i	1.04759	+	0.397059i
$367$	993.018			0.141240			0.0706200	−	0.997503i	$-0.477502\pi$
$367$	993.018			0.141240			0.0706200	+	0.997503i	$0.477502\pi$
$368$	4561.97	−	5387.44i	0.646220	−	0.763151i
$369$	75.3148			0.0106253
$370$	5145.42	+	1950.23i	0.722967	+	0.274021i
$371$	618.870	−	4304.33i	0.0866041	−	0.602345i
$372$	−4948.92	+	5590.65i	−0.689757	+	0.779198i
$373$	6033.36	−	1771.55i	0.837521	−	0.245918i	0.165276	−	0.986247i	$-0.447148\pi$
$373$	6033.36	−	1771.55i	0.837521	−	0.245918i	0.672245	+	0.740329i	$0.265330\pi$
$374$	−2713.21	+	4906.94i	−0.375125	+	0.678427i
$375$	1608.84	+	1856.71i	0.221548	+	0.255680i
$376$	2237.83	−	1176.21i	0.306934	−	0.161325i
$377$	−4804.04	−	1410.59i	−0.656288	−	0.192704i
$378$	6899.24	+	530.166i	0.938780	+	0.0721397i
$379$	−655.064	+	1019.30i	−0.0887820	+	0.138148i	−0.882804	−	0.469742i	$-0.844347\pi$
$379$	−655.064	+	1019.30i	−0.0887820	+	0.138148i	0.794022	+	0.607889i	$0.207983\pi$
$380$	6153.52	+	7255.34i	0.830708	+	0.979451i
$381$	−9114.15	−	7897.46i	−1.22554	−	1.06194i
$382$	−3319.52	−	9045.94i	−0.444611	−	1.21160i
$383$	1320.88	+	9186.95i	0.176225	+	1.22567i	0.865403	+	0.501077i	$0.167063\pi$
$383$	1320.88	+	9186.95i	0.176225	+	1.22567i	−0.689178	+	0.724592i	$0.742028\pi$
$384$	−3319.18	−	6653.37i	−0.441096	−	0.884189i
$385$	−6806.86	+	3108.59i	−0.901064	+	0.411502i
$386$	−9144.61	−	6921.41i	−1.20583	−	0.912669i
$387$	−114.166	−	52.1378i	−0.0149958	−	0.00684836i
$388$	−5593.71	+	11913.1i	−0.731901	+	1.55875i
$389$	10786.1	−	6931.83i	1.40586	−	0.903490i	0.405913	−	0.913912i	$-0.366954\pi$
$389$	10786.1	−	6931.83i	1.40586	−	0.903490i	0.999946	+	0.0104215i	$0.00331733\pi$
$390$	−6338.96	+	4693.13i	−0.823040	+	0.609349i
$391$	−6856.07	−	2865.20i	−0.886768	−	0.370586i
$392$	−976.279	+	346.575i	−0.125790	+	0.0446548i
$393$	8383.80	−	5387.94i	1.07610	−	0.691566i
$394$	−6394.69	−	11859.8i	−0.817665	−	1.51647i
$395$	1297.80	−	2841.79i	0.165315	−	0.361990i
$396$	150.281	+	1.59109i	0.0190704	+	0.000201907i
$397$	1108.54	−	506.254i	0.140141	−	0.0640004i	−0.344110	−	0.938929i	$-0.611819\pi$
$397$	1108.54	−	506.254i	0.140141	−	0.0640004i	0.484251	+	0.874929i	$0.339092\pi$
$398$	1927.15	−	8638.54i	0.242712	−	1.08797i
$399$	−7063.80	+	1015.62i	−0.886297	+	0.127430i
$400$	3783.60	+	4558.04i	0.472950	+	0.569754i
$401$	5355.80	+	4640.83i	0.666973	+	0.577935i	0.921143	−	0.389224i	$-0.127257\pi$
$401$	5355.80	+	4640.83i	0.666973	+	0.577935i	−0.254170	+	0.967159i	$0.581802\pi$
$402$	5406.42	−	357.920i	0.670765	−	0.0444065i
$403$	−5630.74	−	3618.66i	−0.695998	−	0.447291i
$404$	−12206.4	+	7663.21i	−1.50320	+	0.943711i
$405$	−10067.4	−	2956.06i	−1.23519	−	0.362686i
$406$	−4663.55	−	4713.19i	−0.570069	−	0.576137i
$407$	−2933.39	+	2541.80i	−0.357255	+	0.309563i
$408$	−5621.23	+	5445.47i	−0.682089	+	0.660762i
$409$	6855.64	−	2013.00i	0.828826	−	0.243365i	0.160313	−	0.987066i	$-0.448750\pi$
$409$	6855.64	−	2013.00i	0.828826	−	0.243365i	0.668512	+	0.743701i	$0.266931\pi$
$410$	−4814.88	+	1020.75i	−0.579976	+	0.122954i
$411$	−13558.1	−	1949.36i	−1.62719	−	0.233954i
$412$	−737.106	−	2612.35i	−0.0881422	−	0.312382i
$413$	8361.62			0.996243
$414$	19.6176	+	198.199i	0.00232887	+	0.0235289i
$415$		−	13056.4i		−	1.54438i
$416$	5439.79	−	3851.83i	0.641124	−	0.453970i
$417$	761.428	−	5295.85i	0.0894180	−	0.621916i
$418$	−6564.69	+	1391.71i	−0.768157	+	0.162848i
$419$	109.047	+	371.379i	0.0127143	+	0.0433008i	0.965606	−	0.260010i	$-0.0837260\pi$
$419$	109.047	+	371.379i	0.0127143	+	0.0433008i	−0.952892	+	0.303311i	$0.901908\pi$
$420$	−10353.7	+	1376.92i	−1.20287	+	0.159968i
$421$	−660.484	−	762.239i	−0.0764608	−	0.0882405i	0.716230	−	0.697864i	$-0.245866\pi$
$421$	−660.484	−	762.239i	−0.0764608	−	0.0882405i	−0.792691	+	0.609624i	$0.791321\pi$
$422$	8736.00	−	8643.99i	1.00773	−	0.997116i
$423$	−20.0946	+	68.4360i	−0.00230977	+	0.00786636i
$424$	2079.24	−	5315.32i	0.238153	−	0.608808i
$425$	3371.06	−	5245.46i	0.384753	−	0.598688i
$426$	−13272.7	+	878.689i	−1.50954	+	0.0999357i
$427$	−6098.37	+	7037.89i	−0.691149	+	0.797629i
$428$	13847.3	+	9107.70i	1.56387	+	1.02859i
$429$	−791.763	−	5506.83i	−0.0891065	−	0.619749i
$430$	8005.27	+	1785.87i	0.897787	+	0.200285i
$431$	3049.78	+	6678.09i	0.340842	+	0.746340i	0.999984	−	0.00567879i	$-0.00180762\pi$
$431$	3049.78	+	6678.09i	0.340842	+	0.746340i	−0.659142	+	0.752019i	$0.729080\pi$
$432$	8657.93	+	2742.60i	0.964247	+	0.305448i
$433$	−5080.11	−	2320.01i	−0.563821	−	0.257488i	0.113051	−	0.993589i	$-0.463938\pi$
$433$	−5080.11	−	2320.01i	−0.563821	−	0.257488i	−0.676872	+	0.736101i	$0.736665\pi$
$434$	−4206.69	−	7801.89i	−0.465271	−	0.862909i
$435$	5567.31	+	8662.91i	0.613637	+	0.954838i
$436$	2106.82	−	6903.92i	0.231418	−	0.758344i
$437$	−2781.85	−	8446.77i	−0.304517	−	0.924631i
$438$	−1890.52	−	2553.50i	−0.206238	−	0.278564i
$439$	−2050.88	−	3191.24i	−0.222969	−	0.346946i	0.711689	−	0.702495i	$-0.247930\pi$
$439$	−2050.88	−	3191.24i	−0.222969	−	0.346946i	−0.934658	+	0.355548i	$0.884294\pi$
$440$	−9629.04	+	1935.06i	−1.04329	+	0.209659i
$441$	12.1416	−	26.5864i	0.00131105	−	0.00287079i
$442$	−5594.20	−	4234.16i	−0.602012	−	0.455653i
$443$	2044.16	+	4476.09i	0.219235	+	0.480058i	0.987009	−	0.160662i	$-0.0513631\pi$
$443$	2044.16	+	4476.09i	0.219235	+	0.480058i	−0.767774	+	0.640720i	$0.778636\pi$
$444$	−4951.62	+	2198.28i	−0.529265	+	0.234968i
$445$	5825.43	−	837.570i	0.620566	−	0.0892239i
$446$	−983.201	+	360.798i	−0.104385	+	0.0383055i
$447$	−5168.54	+	5964.81i	−0.546898	+	0.631154i
$448$	8772.50	−	978.108i	0.925137	−	0.103150i
$449$	1445.21	+	928.782i	0.151902	+	0.0976212i	0.614384	−	0.789007i	$-0.289405\pi$
$449$	1445.21	+	928.782i	0.151902	+	0.0976212i	−0.462482	+	0.886629i	$0.653041\pi$
$450$	−166.636	−	12.8050i	−0.0174562	−	0.00134140i
$451$	978.119	−	3331.17i	0.102124	−	0.347802i
$452$	−1883.51	+	12183.1i	−0.196002	+	1.26779i
$453$	4278.10	−	3707.00i	0.443715	−	0.384481i
$454$	8820.10	+	4876.92i	0.911779	+	0.504153i
$455$	−2637.94	−	8984.00i	−0.271799	−	0.925663i
$456$	−9330.92	−	816.481i	−0.958246	−	0.0838491i
$457$	−4653.87	−	669.126i	−0.476365	−	0.0684910i	−0.100050	−	0.994982i	$-0.531900\pi$
$457$	−4653.87	−	669.126i	−0.476365	−	0.0684910i	−0.376316	+	0.926491i	$0.622809\pi$
$458$	577.863	+	219.023i	0.0589558	+	0.0223456i
$459$		−	9559.51i		−	0.972113i
$460$	−3940.37	−	12405.0i	−0.399393	−	1.25736i
$461$		−	9102.56i		−	0.919628i	−0.888015	−	0.459814i	$-0.847916\pi$
$461$		−	9102.56i		−	0.919628i	0.888015	−	0.459814i	$-0.152084\pi$
$462$	2611.20	−	6889.30i	0.262953	−	0.693765i
$463$	11585.9	+	1665.79i	1.16294	+	0.167205i	0.696639	−	0.717422i	$-0.254678\pi$
$463$	11585.9	+	1665.79i	1.16294	+	0.167205i	0.466299	+	0.884627i	$0.345587\pi$
$464$	−4548.84	−	7418.94i	−0.455118	−	0.742276i
$465$	3878.35	+	13208.5i	0.386783	+	1.31726i
$466$	−8447.46	+	15277.6i	−0.839745	+	1.51871i
$467$	−12248.9	+	10613.7i	−1.21373	+	1.05170i	−0.216576	+	0.976266i	$0.569489\pi$
$467$	−12248.9	+	10613.7i	−1.21373	+	1.05170i	−0.997151	+	0.0754344i	$0.975966\pi$
$468$	−28.7315	+	185.843i	−0.00283785	+	0.0183559i
$469$	−1812.18	+	6171.72i	−0.178419	+	0.607641i
$470$	357.130	−	4647.47i	0.0350494	−	0.456110i
$471$	697.153	+	448.033i	0.0682019	+	0.0438307i
$472$	10685.4	+	2502.82i	1.04203	+	0.244071i
$473$	−3788.73	+	4372.43i	−0.368301	+	0.425042i
$474$	1059.64	+	2887.59i	0.102681	+	0.279813i
$475$	7386.46	−	1062.01i	0.713503	−	0.102586i
$476$	−3769.94	−	8491.79i	−0.363014	−	0.817691i
$477$	66.8924	+	146.474i	0.00642095	+	0.0140599i
$478$	−7826.95	+	10341.0i	−0.748946	+	0.989513i
$479$	−340.858	+	746.375i	−0.0325140	+	0.0711957i	−0.925192	−	0.379499i	$-0.876096\pi$
$479$	−340.858	+	746.375i	−0.0325140	+	0.0711957i	0.892678	+	0.450695i	$0.148824\pi$
$480$	−13643.2	−	1339.51i	−1.29734	−	0.127375i
$481$	−2625.71	−	4085.69i	−0.248903	−	0.387300i
$482$	−13983.7	+	10353.0i	−1.32145	+	0.978356i
$483$	9452.75	+	2444.40i	0.890508	+	0.230277i
$484$	−1085.80	+	3558.10i	−0.101972	+	0.334157i
$485$	13118.9	+	20413.4i	1.22824	+	1.91118i
$486$	−445.855	+	240.400i	−0.0416140	+	0.0224378i
$487$	11944.0	+	5454.64i	1.11136	+	0.507543i	0.884574	−	0.466401i	$-0.154450\pi$
$487$	11944.0	+	5454.64i	1.11136	+	0.507543i	0.226790	+	0.973944i	$0.427177\pi$
$488$	−9899.77	+	7168.42i	−0.918323	+	0.664958i
$489$	4253.06	+	9312.91i	0.393313	+	0.861236i
$490$	−415.886	+	1864.23i	−0.0383425	+	0.171872i
$491$	2785.57	+	19374.0i	0.256030	+	1.78073i	0.560447	+	0.828190i	$0.310629\pi$
$491$	2785.57	+	19374.0i	0.256030	+	1.78073i	−0.304417	+	0.952539i	$0.598461\pi$
$492$	2662.90	−	4048.67i	0.244010	−	0.370992i
$493$	−5998.57	+	6922.72i	−0.547996	+	0.632421i
$494$	−554.669	−	8378.34i	−0.0505177	−	0.763075i
$495$	149.808	−	233.106i	0.0136028	−	0.0211663i
$496$	−3040.50	−	11229.3i	−0.275247	−	1.01655i
$497$	4448.88	−	15151.5i	0.401528	−	1.36748i
$498$	9041.51	+	9137.74i	0.813574	+	0.822233i
$499$	−2462.16	−	2841.49i	−0.220885	−	0.254915i	0.634482	−	0.772938i	$-0.281214\pi$
$499$	−2462.16	−	2841.49i	−0.220885	−	0.254915i	−0.855367	+	0.518023i	$0.826668\pi$
$500$	−3794.57	+	504.633i	−0.339396	+	0.0451358i
$501$	279.592	+	952.201i	0.0249326	+	0.0849126i
$502$	−2447.96	−	11547.0i	−0.217645	−	1.02663i
$503$	1462.47	−	10171.7i	0.129638	−	0.901655i	−0.816374	−	0.577524i	$-0.804019\pi$
$503$	1462.47	−	10171.7i	0.129638	−	0.901655i	0.946012	−	0.324131i	$-0.105072\pi$
$504$	−152.385	+	196.964i	−0.0134678	+	0.0174077i
$505$			26572.9i			2.34154i
$506$	9021.10	+	1706.34i	0.792563	+	0.149913i
$507$	−4318.86			−0.378318
$508$	18084.6	−	5102.77i	1.57947	−	0.445667i
$509$	−11319.2	−	1627.46i	−0.985690	−	0.141721i	−0.369426	−	0.929260i	$-0.620446\pi$
$509$	−11319.2	−	1627.46i	−0.985690	−	0.141721i	−0.616264	+	0.787539i	$0.711355\pi$
$510$	2992.57	+	14116.0i	0.259830	+	1.22562i
$511$	3618.99	−	1062.63i	0.313297	−	0.0919922i
$512$	11503.2	+	1375.87i	0.992923	+	0.118761i
$513$	8646.42	−	7492.16i	0.744149	−	0.644809i
$514$	14263.4	−	14113.2i	1.22399	−	1.21110i
$515$	−4801.83	−	1409.94i	−0.410862	−	0.120640i
$516$	−6839.31	+	4293.73i	−0.583496	+	0.366320i
$517$	2765.95	+	1777.57i	0.235293	+	0.151213i
$518$	−424.857	−	6417.52i	−0.0360370	−	0.544343i
$519$	1753.90	+	1519.76i	0.148338	+	0.128536i
$520$	−681.942	−	12270.4i	−0.0575099	−	1.03479i
$521$	20294.5	−	2917.91i	1.70656	−	0.245367i	0.781154	−	0.624338i	$-0.214631\pi$
$521$	20294.5	−	2917.91i	1.70656	−	0.245367i	0.925408	+	0.378972i	$0.123722\pi$
$522$	239.630	+	53.4585i	0.0200926	+	0.00448240i
$523$	12358.2	−	5643.79i	1.03324	−	0.471866i	0.174707	−	0.984620i	$-0.444102\pi$
$523$	12358.2	−	5643.79i	1.03324	−	0.471866i	0.858535	+	0.512754i	$0.171375\pi$
$524$	−164.394	+	15527.2i	−0.0137053	+	1.29448i
$525$	−3403.49	+	7452.60i	−0.282934	+	0.619539i
$526$	−1330.77	+	717.538i	−0.110313	+	0.0594793i
$527$	−10301.5	+	6620.36i	−0.851498	+	0.547224i
$528$	5399.01	−	8022.33i	0.445003	−	0.661225i
$529$	−944.380	+	12130.3i	−0.0776181	+	0.996983i
$530$	−6261.62	−	8457.50i	−0.513184	−	0.693151i
$531$	−260.473	+	167.396i	−0.0212873	+	0.0136805i
$532$	4726.04	−	10065.2i	0.385150	−	0.820266i
$533$	3951.55	+	1804.61i	0.321127	+	0.146654i
$534$	−3497.00	+	4620.26i	−0.283389	+	0.374416i
$535$	27796.6	−	12694.3i	2.24627	−	1.02584i
$536$	−4163.14	+	7344.49i	−0.335486	+	0.591854i
$537$	2442.85	+	16990.4i	0.196306	+	1.36534i
$538$	−7157.13	+	2626.40i	−0.573542	+	0.210469i
$539$	−1018.23	−	882.303i	−0.0813698	−	0.0705074i
$540$	12770.2	−	10830.9i	1.01767	−	0.863122i
$541$	−11201.3	+	17429.6i	−0.890170	+	1.38513i	0.0324719	+	0.999473i	$0.489662\pi$
$541$	−11201.3	+	17429.6i	−0.890170	+	1.38513i	−0.922642	+	0.385658i	$0.873974\pi$
$542$	−1211.56	+	15766.5i	−0.0960168	+	1.24950i
$543$	6946.47	+	2039.67i	0.548990	+	0.161198i
$544$	−2275.86	−	11980.2i	−0.179369	−	0.944203i
$545$	−8715.22	−	10057.9i	−0.684989	−	0.790520i
$546$	8067.57	+	4460.83i	0.632344	+	0.349644i
$547$	−22731.3	+	6674.51i	−1.77682	+	0.521721i	−0.994829	−	0.101568i	$-0.967614\pi$
$547$	−22731.3	+	6674.51i	−1.77682	+	0.521721i	−0.781991	+	0.623289i	$0.785796\pi$
$548$	14146.4	−	15980.8i	1.10274	−	1.24574i
$549$	49.0750	−	341.324i	0.00381506	−	0.0265343i
$550$	−2730.48	+	7203.99i	−0.211687	+	0.558508i
$551$	−10962.8			−0.847606
$552$	11348.1	+	5953.14i	0.875015	+	0.459026i
$553$	−3651.52			−0.280793
$554$	−725.698	+	1914.66i	−0.0556533	+	0.146834i
$555$	−1421.54	+	9887.06i	−0.108723	+	0.756184i
$556$	6242.14	+	5525.63i	0.476125	+	0.421473i
$557$	8016.30	−	2353.80i	0.609805	−	0.179055i	0.0377734	−	0.999286i	$-0.487974\pi$
$557$	8016.30	−	2353.80i	0.609805	−	0.179055i	0.572032	+	0.820231i	$0.306155\pi$
$558$	287.233	+	158.821i	0.0217913	+	0.0120491i
$559$	−4740.68	−	5471.04i	−0.358693	−	0.413954i
$560$	7072.55	−	14657.3i	0.533696	−	1.10604i
$561$	−9766.10	−	2867.58i	−0.734982	−	0.215810i
$562$	−774.890	+	10083.9i	−0.0581615	+	0.756877i
$563$	−6762.97	+	10523.4i	−0.506262	+	0.787759i	−0.996479	−	0.0838415i	$-0.973281\pi$
$563$	−6762.97	+	10523.4i	−0.506262	+	0.787759i	0.490217	+	0.871600i	$0.336917\pi$
$564$	2968.40	+	3499.91i	0.221617	+	0.261299i
$565$	17177.6	+	14884.5i	1.27906	+	1.10831i
$566$	18253.8	−	6698.45i	1.35559	−	0.497450i
$567$	1745.31	+	12138.9i	0.129270	+	0.899095i
$568$	10220.5	−	18030.6i	0.755002	−	1.33195i
$569$	−4359.57	+	1990.95i	−0.321200	+	0.146687i	−0.569489	−	0.821999i	$-0.692859\pi$
$569$	−4359.57	+	1990.95i	−0.321200	+	0.146687i	0.248289	+	0.968686i	$0.420132\pi$
$570$	−10422.3	+	13770.0i	−0.765860	+	1.01186i
$571$	3572.16	+	1631.35i	0.261804	+	0.119562i	0.541993	−	0.840383i	$-0.317670\pi$
$571$	3572.16	+	1631.35i	0.261804	+	0.119562i	−0.280189	+	0.959945i	$0.590397\pi$
$572$	7846.67	+	3684.35i	0.573577	+	0.269319i
$573$	14714.8	−	9456.63i	1.07281	−	0.689453i
$574$	3423.10	+	4623.54i	0.248915	+	0.336207i
$575$	−9884.53	−	2556.05i	−0.716893	−	0.185382i
$576$	−253.691	+	206.091i	−0.0183515	+	0.0149082i
$577$	−979.533	+	629.508i	−0.0706733	+	0.0454190i	−0.575500	−	0.817802i	$-0.695193\pi$
$577$	−979.533	+	629.508i	−0.0706733	+	0.0454190i	0.504827	+	0.863221i	$0.331556\pi$
$578$	933.348	−	503.251i	0.0671663	−	0.0362154i
$579$	8648.39	−	18937.3i	0.620751	−	1.35926i
$580$	−16044.1	−	169.866i	−1.14861	−	0.0121609i
$581$	−13881.6	+	6339.49i	−0.991229	+	0.452679i
$582$	−23317.6	−	5201.85i	−1.66073	−	0.370487i
$583$	7347.27	−	1056.38i	0.521943	−	0.0750441i
$584$	4942.82	−	274.704i	0.350232	−	0.0194646i
$585$	262.030	+	227.050i	0.0185190	+	0.0160468i
$586$	−1566.24	−	23658.2i	−0.110411	−	1.66776i
$587$	−2602.52	−	1672.54i	−0.182994	−	0.117603i	0.445937	−	0.895064i	$-0.352871\pi$
$587$	−2602.52	−	1672.54i	−0.182994	−	0.117603i	−0.628931	+	0.777462i	$0.716507\pi$
$588$	−999.905	−	1592.71i	−0.0701282	−	0.111704i
$589$	−14061.7	−	4128.88i	−0.983703	−	0.288841i
$590$	14383.3	−	14231.9i	1.00365	−	0.993079i
$591$	18484.8	−	16017.2i	1.28657	−	1.11482i
$592$	1377.98	−	8328.19i	0.0956664	−	0.578187i
$593$	−3094.32	+	908.575i	−0.214281	+	0.0629186i	−0.387111	−	0.922033i	$-0.626527\pi$
$593$	−3094.32	+	908.575i	−0.214281	+	0.0629186i	0.172830	+	0.984952i	$0.444709\pi$
$594$	2449.55	+	11554.6i	0.169203	+	0.798130i
$595$	−16955.8	−	2437.88i	−1.16827	−	0.167972i
$596$	−3339.54	−	11835.5i	−0.229518	−	0.813427i
$597$	16066.8			1.10145
$598$	−3719.75	+	10869.0i	−0.254368	+	0.743254i
$599$			12746.4i			0.869455i	0.900562	+	0.434728i	$0.143155\pi$
$599$			12746.4i			0.869455i	−0.900562	+	0.434728i	$0.856845\pi$
$600$	−6580.09	+	8505.03i	−0.447718	+	0.578694i
$601$	−3520.19	+	24483.4i	−0.238921	+	1.66173i	0.418506	+	0.908214i	$0.362554\pi$
$601$	−3520.19	+	24483.4i	−0.238921	+	1.66173i	−0.657427	+	0.753518i	$0.728355\pi$
$602$	−1988.19	−	9378.29i	−0.134605	−	0.634935i
$603$	−67.1038	−	228.534i	−0.00453180	−	0.0154339i
$604$	1162.74	+	8743.19i	0.0783301	+	0.588999i
$605$	4491.60	+	5183.58i	0.301834	+	0.348335i
$606$	−18401.6	−	18597.5i	−1.23352	−	1.24665i
$607$	108.928	−	370.975i	0.00728378	−	0.0248063i	−0.955771	−	0.294112i	$-0.904976\pi$
$607$	108.928	−	370.975i	0.00728378	−	0.0248063i	0.963055	+	0.269306i	$0.0867943\pi$
$608$	9052.20	−	11447.8i	0.603808	−	0.763603i
$609$	6507.18	−	10125.4i	0.432979	−	0.673729i
$610$	1488.64	+	22486.0i	0.0988084	+	1.49251i
$611$	−2694.10	+	3109.15i	−0.178382	+	0.205864i
$612$	287.439	+	189.056i	0.0189854	+	0.0124871i
$613$	2346.21	+	16318.2i	0.154588	+	1.07518i	0.908403	+	0.418096i	$0.137302\pi$
$613$	2346.21	+	16318.2i	0.154588	+	1.07518i	−0.753815	+	0.657087i	$0.771789\pi$
$614$	−915.895	+	4105.55i	−0.0601996	+	0.269848i
$615$	−3711.55	−	8127.17i	−0.243356	−	0.532876i
$616$	6732.67	+	9297.99i	0.440369	+	0.608160i
$617$	−22230.9	−	10152.5i	−1.45054	−	0.662439i	−0.474544	−	0.880232i	$-0.657387\pi$
$617$	−22230.9	−	10152.5i	−1.45054	−	0.662439i	−0.975995	+	0.217793i	$0.930114\pi$
$618$	4337.01	−	2338.47i	0.282298	−	0.152212i
$619$	219.508	+	341.561i	0.0142533	+	0.0221785i	0.848307	−	0.529505i	$-0.177622\pi$
$619$	219.508	+	341.561i	0.0142533	+	0.0221785i	−0.834054	+	0.551683i	$0.813986\pi$
$620$	−20515.4	−	6260.53i	−1.32890	−	0.405530i
$621$	−14867.2	+	4896.35i	−0.960710	+	0.316399i
$622$	−1265.26	+	936.752i	−0.0815632	+	0.0603864i
$623$	−3719.01	−	5786.89i	−0.239164	−	0.372146i
$624$	8974.41	+	8115.35i	0.575744	+	0.520631i
$625$	−7738.22	+	16944.3i	−0.495246	+	1.08444i
$626$	467.745	−	617.988i	0.0298640	−	0.0394565i
$627$	−5060.39	−	11080.7i	−0.322317	−	0.705775i
$628$	−1180.16	+	523.933i	−0.0749897	+	0.0332917i
$629$	−8794.87	+	1264.51i	−0.557511	+	0.0801580i
$630$	158.176	+	431.041i	0.0100030	+	0.0272589i
$631$	−11497.4	+	13268.7i	−0.725362	+	0.837112i	−0.991941	−	0.126701i	$-0.959561\pi$
$631$	−11497.4	+	13268.7i	−0.725362	+	0.837112i	0.266579	+	0.963813i	$0.414107\pi$
$632$	−4666.32	−	1092.98i	−0.293696	−	0.0687919i
$633$	18767.6	+	12061.2i	1.17843	+	0.757330i
$634$	−1823.96	+	23735.9i	−0.114257	+	1.48687i
$635$	9760.64	−	33241.7i	0.609983	−	2.07741i
$636$	10239.1	+	1582.97i	0.638372	+	0.0986931i
$637$	1274.07	−	1103.99i	0.0792473	−	0.0686681i
$638$	5476.56	−	9904.57i	0.339842	−	0.614617i
$639$	164.739	+	561.049i	0.0101987	+	0.0347336i
$640$	13425.3	−	16613.7i	0.829192	−	1.02612i
$641$	24006.5	+	3451.61i	1.47925	+	0.212684i	0.834202	−	0.551460i	$-0.185929\pi$
$641$	24006.5	+	3451.61i	1.47925	+	0.212684i	0.645046	+	0.764143i	$0.276838\pi$
$642$	−10663.2	+	28133.3i	−0.655516	+	1.72949i
$643$			15132.6i			0.928107i	0.885807	+	0.464053i	$0.153605\pi$
$643$			15132.6i			0.928107i	−0.885807	+	0.464053i	$0.846395\pi$
$644$	−11275.7	+	10212.6i	−0.689947	+	0.624894i
$645$			14888.9i			0.908917i
$646$	−14364.6	−	5444.51i	−0.874872	−	0.331596i
$647$	−16428.3	−	2362.04i	−0.998244	−	0.143526i	−0.376225	−	0.926528i	$-0.622778\pi$
$647$	−16428.3	−	2362.04i	−0.998244	−	0.143526i	−0.622019	+	0.783002i	$0.713687\pi$
$648$	−1403.10	+	16034.9i	−0.0850599	+	0.972083i
$649$	4021.12	+	13694.7i	0.243209	+	0.828295i
$650$	−8436.08	−	4664.59i	−0.509062	−	0.281477i
$651$	12160.1	−	10536.7i	0.732089	−	0.634359i
$652$	−15765.0	−	2437.29i	−0.946941	−	0.146398i
$653$	6431.41	−	21903.4i	0.385422	−	1.31263i	−0.507203	−	0.861826i	$-0.669321\pi$
$653$	6431.41	−	21903.4i	0.385422	−	1.31263i	0.892625	−	0.450800i	$-0.148861\pi$
$654$	13064.5	+	1003.93i	0.781136	+	0.0600257i
$655$	24084.8	+	15478.4i	1.43675	+	0.923344i
$656$	2990.49	+	6933.09i	0.177986	+	0.412640i
$657$	−91.4618	+	105.553i	−0.00543115	+	0.00626788i
$658$	−5114.57	+	1876.86i	−0.303019	+	0.111197i
$659$	−2095.72	+	301.318i	−0.123881	+	0.0178114i	−0.203976	−	0.978976i	$-0.565387\pi$
$659$	−2095.72	+	301.318i	−0.123881	+	0.0178114i	0.0800955	+	0.996787i	$0.474477\pi$
$660$	−7234.22	−	16295.1i	−0.426654	−	0.961040i
$661$	−12270.0	−	26867.6i	−0.722009	−	1.58098i	−0.811067	−	0.584953i	$-0.801113\pi$
$661$	−12270.0	−	26867.6i	−0.722009	−	1.58098i	0.0890578	−	0.996026i	$-0.471614\pi$
$662$	11689.2	+	8847.38i	0.686276	+	0.519431i
$663$	5290.64	−	11584.9i	0.309912	−	0.678612i
$664$	−19637.0	+	3946.25i	−1.14768	+	0.230639i
$665$	−11083.9	−	17246.9i	−0.646340	−	1.00572i
$666$	141.711	+	191.407i	0.00824500	+	0.0111364i
$667$	13838.9	+	5783.35i	0.803362	+	0.335730i
$668$	−1478.96	−	451.323i	−0.0856626	−	0.0261410i
$669$	−1027.84	−	1599.35i	−0.0593999	−	0.0924281i
$670$	7387.31	+	13700.8i	0.425965	+	0.790011i
$671$	−14459.4	−	6603.39i	−0.831891	−	0.379912i
$672$	5200.24	+	15155.8i	0.298517	+	0.870011i
$673$	−5846.38	−	12801.8i	−0.334861	−	0.733243i	0.665047	−	0.746801i	$-0.268411\pi$
$673$	−5846.38	−	12801.8i	−0.334861	−	0.733243i	−0.999908	+	0.0135586i	$0.995684\pi$
$674$	15513.0	+	3460.76i	0.886558	+	0.197780i
$675$	−1869.26	−	13001.0i	−0.106589	−	0.741344i
$676$	3697.89	−	5622.25i	0.210394	−	0.319882i
$677$	−6877.89	+	7937.51i	−0.390456	+	0.450610i	−0.916612	−	0.399778i	$-0.869087\pi$
$677$	−6877.89	+	7937.51i	−0.390456	+	0.450610i	0.526156	+	0.850388i	$0.323633\pi$
$678$	−22329.4	+	1478.27i	−1.26483	+	0.0837353i
$679$	15333.6	−	23859.5i	0.866641	−	1.34852i
$680$	−20938.3	−	8190.65i	−1.18081	−	0.461908i
$681$	−5154.41	+	17554.3i	−0.290040	+	0.987786i
$682$	10755.0	−	10641.7i	0.603854	−	0.597494i
$683$	−10058.5	−	11608.2i	−0.563512	−	0.650328i	0.400465	−	0.916312i	$-0.368849\pi$
$683$	−10058.5	−	11608.2i	−0.563512	−	0.650328i	−0.963977	+	0.265984i	$0.914303\pi$
$684$	54.2798	+	408.154i	0.00303427	+	0.0228160i
$685$	−11086.2	−	37756.1i	−0.618368	−	2.10597i
$686$	18545.7	−	3931.67i	1.03218	−	0.218822i
$687$	−159.648	+	1110.38i	−0.00886602	+	0.0616645i
$688$	266.404	−	12579.7i	0.0147625	−	0.697090i
$689$			9287.86i			0.513555i
$690$	20420.7	−	11884.3i	1.12667	−	0.655691i
$691$	−3256.24			−0.179267			−0.0896333	−	0.995975i	$-0.528570\pi$
$691$	−3256.24			−0.179267			−0.0896333	+	0.995975i	$0.528570\pi$
$692$	−3480.13	+	981.960i	−0.191177	+	0.0539429i
$693$	−320.576	−	46.0919i	−0.0175724	−	0.00252653i
$694$	−1010.80	+	214.288i	−0.0552872	+	0.0117208i
$695$	14747.7	−	4330.31i	0.804908	−	0.236342i
$696$	11346.4	−	10991.6i	0.617934	−	0.598613i
$697$	6006.39	−	5204.57i	0.326411	−	0.282836i
$698$	11194.0	+	11313.2i	0.607019	+	0.613480i
$699$	−30406.3	−	8928.11i	−1.64531	−	0.483107i
$700$	−6787.60	−	10811.7i	−0.366496	−	0.583777i
$701$	−28077.9	−	18044.6i	−1.51282	−	0.972232i	−0.993020	−	0.117946i	$-0.962369\pi$
$701$	−28077.9	−	18044.6i	−1.51282	−	0.972232i	−0.519803	−	0.854286i	$-0.673994\pi$
$702$	−14746.8	+	976.277i	−0.792851	+	0.0524889i
$703$	−8036.61	−	6963.76i	−0.431162	−	0.373604i
$704$	5820.67	+	13897.3i	0.311612	+	0.743995i
$705$	8375.15	−	1204.17i	0.447414	−	0.0643284i
$706$	−1698.86	+	7615.22i	−0.0905628	+	0.405953i
$707$	28252.2	−	12902.4i	1.50288	−	0.686341i
$708$	−210.910	+	19920.8i	−0.0111956	+	1.05744i
$709$	−3335.79	+	7304.37i	−0.176697	+	0.386913i	−0.977171	−	0.212455i	$-0.931854\pi$
$709$	−3335.79	+	7304.37i	−0.176697	+	0.386913i	0.800474	+	0.599368i	$0.204581\pi$
$710$	−18135.8	−	33635.2i	−0.958624	−	1.77790i
$711$	113.749	−	73.1017i	0.00599986	−	0.00385588i
$712$	−3020.42	−	8508.32i	−0.158982	−	0.447841i
$713$	15572.5	+	12630.2i	0.817947	+	0.663401i
$714$	13555.0	−	10035.6i	0.710480	−	0.526014i
$715$	13445.4	−	8640.86i	0.703260	−	0.451958i
$716$	−24209.5	−	11367.4i	−1.26362	−	0.593323i
$717$	−21415.0	−	9779.88i	−1.11542	−	0.509395i
$718$	7804.53	+	5907.12i	0.405658	+	0.307036i
$719$	−603.940	+	275.810i	−0.0313257	+	0.0143060i	−0.431016	−	0.902344i	$-0.641845\pi$
$719$	−603.940	+	275.810i	−0.0313257	+	0.0143060i	0.399691	+	0.916650i	$0.369118\pi$
$720$	73.1146	+	598.178i	0.00378447	+	0.0309622i
$721$	832.458	+	5789.87i	0.0429991	+	0.299065i
$722$	349.722	+	953.018i	0.0180267	+	0.0491242i
$723$	−23869.7	−	20683.2i	−1.22783	−	1.06392i
$724$	−8602.93	+	7296.46i	−0.441610	+	0.374545i
$725$	−6804.41	+	10587.9i	−0.348565	+	0.542378i
$726$	−6733.11	−	517.400i	−0.344200	−	0.0264497i
$727$	−4467.06	−	1311.65i	−0.227887	−	0.0669137i	0.165795	−	0.986160i	$-0.446981\pi$
$727$	−4467.06	−	1311.65i	−0.227887	−	0.0669137i	−0.393682	+	0.919246i	$0.628799\pi$
$728$	−12714.7	+	6682.85i	−0.647304	+	0.340224i
$729$	−13179.8	−	15210.3i	−0.669603	−	0.772763i
$730$	4416.60	−	7987.59i	0.223926	−	0.404978i
$731$	−12707.7	+	3731.32i	−0.642972	+	0.188793i
$732$	−16613.3	−	14706.3i	−0.838859	−	0.742569i
$733$	1468.43	−	10213.2i	0.0739943	−	0.514642i	−0.918792	−	0.394743i	$-0.870834\pi$
$733$	1468.43	−	10213.2i	0.0739943	−	0.514642i	0.992786	−	0.119899i	$-0.0382571\pi$
$734$	−2626.36	−	995.449i	−0.132072	−	0.0500582i
$735$	−3467.27			−0.174003
$736$	−17466.2	+	9675.69i	−0.874747	+	0.484580i
$737$	−10979.5			−0.548761
$738$	−199.194	−	75.4992i	−0.00993556	−	0.00376580i
$739$	3490.98	−	24280.3i	0.173772	−	1.20861i	−0.697052	−	0.717020i	$-0.745505\pi$
$739$	3490.98	−	24280.3i	0.173772	−	1.20861i	0.870825	−	0.491594i	$-0.163586\pi$
$740$	−11653.7	−	10316.0i	−0.578919	−	0.512467i
$741$	14624.8	−	4294.23i	0.725042	−	0.212891i
$742$	−5951.67	+	10763.8i	−0.294465	+	0.532550i
$743$	26398.1	+	30465.0i	1.30344	+	1.50424i	0.725673	+	0.688040i	$0.241529\pi$
$743$	26398.1	+	30465.0i	1.30344	+	1.50424i	0.577763	+	0.816205i	$0.303926\pi$
$744$	18693.4	−	9825.26i	0.921145	−	0.484155i
$745$	−21755.2	−	6387.91i	−1.06986	−	0.314141i
$746$	−17733.1	−	1362.68i	−0.870313	−	0.0668784i
$747$	305.511	−	475.384i	0.0149639	−	0.0232843i
$748$	12094.9	−	10258.1i	0.591222	−	0.501437i
$749$	−26993.0	−	23389.6i	−1.31683	−	1.14104i
$750$	−2393.86	−	6523.44i	−0.116549	−	0.317603i
$751$	343.604	+	2389.82i	0.0166955	+	0.116119i	0.996465	−	0.0840101i	$-0.0267728\pi$
$751$	343.604	+	2389.82i	0.0166955	+	0.116119i	−0.979769	+	0.200130i	$0.935864\pi$
$752$	−7097.75	+	867.550i	−0.344187	+	0.0420696i
$753$	19490.5	−	8901.02i	0.943259	−	0.430772i
$754$	11291.8	+	8546.57i	0.545389	+	0.412796i
$755$	14792.5	+	6755.51i	0.713052	+	0.325640i
$756$	−17715.8	−	8318.33i	−0.852273	−	0.400178i
$757$	−26205.2	+	16841.1i	−1.25818	+	0.808586i	−0.988035	−	0.154232i	$-0.950710\pi$
$757$	−26205.2	+	16841.1i	−1.25818	+	0.808586i	−0.270150	+	0.962818i	$0.587073\pi$
$758$	2754.33	−	2039.20i	0.131981	−	0.0977139i
$759$	542.414	+	16657.3i	0.0259399	+	0.796602i
$760$	−9001.88	−	25357.7i	−0.429648	−	1.21029i
$761$	32950.3	−	21175.9i	1.56958	−	1.00871i	0.590058	−	0.807361i	$-0.299105\pi$
$761$	32950.3	−	21175.9i	1.56958	−	1.00871i	0.979520	−	0.201346i	$-0.0645316\pi$
$762$	16188.5	+	30023.9i	0.769618	+	1.42736i
$763$	−6461.88	+	14149.5i	−0.306600	+	0.671361i
$764$	−288.535	+	27252.6i	−0.0136634	+	1.29053i
$765$	576.997	−	263.505i	0.0272697	−	0.0124537i
$766$	5715.93	−	25622.0i	0.269615	−	1.20856i
$767$	−17677.2	+	2541.60i	−0.832187	+	0.119650i
$768$	2108.98	+	20924.3i	0.0990900	+	0.983126i
$769$	12250.2	+	10614.9i	0.574454	+	0.497767i	0.892949	−	0.450157i	$-0.148632\pi$
$769$	12250.2	+	10614.9i	0.574454	+	0.497767i	−0.318495	+	0.947924i	$0.603177\pi$
$770$	21119.2	−	1398.15i	0.988418	−	0.0654360i
$771$	30642.1	+	19692.5i	1.43132	+	0.919855i
$772$	17247.5	+	27472.9i	0.804084	+	1.28079i
$773$	30445.6	+	8939.64i	1.41663	+	0.415959i	0.898360	−	0.439260i	$-0.144759\pi$
$773$	30445.6	+	8939.64i	1.41663	+	0.415959i	0.518267	+	0.855219i	$0.326578\pi$
$774$	249.683	+	252.341i	0.0115952	+	0.0117186i
$775$	−12715.5	+	11018.0i	−0.589360	+	0.510684i
$776$	26736.7	−	25900.7i	1.23684	−	1.19817i
$777$	11202.1	−	3289.23i	0.517211	−	0.151867i
$778$	−35476.2	+	7520.93i	−1.63481	+	0.346579i
$779$	9414.88	+	1353.66i	0.433021	+	0.0622590i
$780$	21470.1	−	6058.03i	0.985579	−	0.278093i
$781$	26954.7			1.23497
$782$	15260.9	+	14450.8i	0.697862	+	0.660818i
$783$			19295.7i			0.880679i
$784$	2929.51	+	62.0390i	0.133451	+	0.00282612i
$785$	−338.808	+	2356.46i	−0.0154046	+	0.107141i
$786$	−27574.8	+	5845.83i	−1.25135	+	0.265285i
$787$	−7442.05	−	25345.3i	−0.337078	−	1.14798i	−0.937409	−	0.348231i	$-0.886783\pi$
$787$	−7442.05	−	25345.3i	−0.337078	−	1.14798i	0.600331	−	0.799752i	$-0.295036\pi$
$788$	5023.97	+	37777.5i	0.227121	+	1.70783i
$789$	−1797.26	−	2074.15i	−0.0810952	−	0.0935888i
$790$	−6281.20	+	6215.05i	−0.282880	+	0.279901i
$791$	7484.60	−	25490.2i	0.336437	−	1.14580i
$792$	−395.871	−	154.857i	−0.0177610	−	0.00694773i
$793$	10753.3	−	16732.4i	0.481538	−	0.749288i
$794$	−3439.39	+	227.697i	−0.153727	+	0.0101772i
$795$	12509.4	−	14436.6i	0.558067	−	0.644043i
$796$	−13756.7	+	20915.6i	−0.612553	+	0.931322i
$797$	141.643	+	985.148i	0.00629517	+	0.0437839i	0.992727	−	0.120388i	$-0.0384139\pi$
$797$	141.643	+	985.148i	0.00629517	+	0.0437839i	−0.986432	+	0.164172i	$0.947505\pi$
$798$	19700.6	+	4394.96i	0.873928	+	0.194962i
$799$	3126.66	+	6846.42i	0.138440	+	0.303140i
$800$	−5437.77	−	15848.1i	−0.240318	−	0.700392i
$801$	231.702	+	105.815i	0.0102207	+	0.00466764i
$802$	−9512.97	−	17643.1i	−0.418846	−	0.776807i
$803$	3480.76	+	5416.17i	0.152968	+	0.238023i
$804$	−14657.8	−	4473.02i	−0.642962	−	0.196208i
$805$	4893.26	+	27618.8i	0.214242	+	1.20924i
$806$	11264.8	+	15215.2i	0.492290	+	0.664930i
$807$	−7482.07	−	11642.3i	−0.326371	−	0.507843i
$808$	39965.8	−	8031.55i	1.74009	−	0.349689i
$809$	10059.8	−	22027.9i	0.437187	−	0.957307i	−0.554918	−	0.831905i	$-0.687251\pi$
$809$	10059.8	−	22027.9i	0.437187	−	0.957307i	0.992106	−	0.125402i	$-0.0400222\pi$
$810$	23663.2	+	17910.3i	1.02647	+	0.776919i
$811$	9688.02	+	21213.8i	0.419473	+	0.918517i	0.994919	+	0.100678i	$0.0321011\pi$
$811$	9688.02	+	21213.8i	0.419473	+	0.918517i	−0.575446	+	0.817840i	$0.695172\pi$
$812$	7609.55	+	17140.5i	0.328870	+	0.740782i
$813$	−28412.7	+	4085.13i	−1.22568	+	0.176226i
$814$	10306.3	−	3782.03i	0.443779	−	0.162850i
$815$	−19260.7	+	22228.0i	−0.827818	+	0.955353i
$816$	20326.0	−	8767.32i	0.871999	−	0.376125i
$817$	−13334.5	−	8569.54i	−0.571008	−	0.366965i
$818$	−20149.9	−	1548.40i	−0.861277	−	0.0661841i
$819$	114.172	−	388.833i	0.00487116	−	0.0165896i
$820$	13757.8	+	2126.97i	0.585905	+	0.0905816i
$821$	19111.2	−	16559.9i	0.812406	−	0.703954i	−0.146024	−	0.989281i	$-0.546648\pi$
$821$	19111.2	−	16559.9i	0.812406	−	0.703954i	0.958430	+	0.285327i	$0.0921023\pi$
$822$	33904.7	+	18747.1i	1.43864	+	0.795473i
$823$	−6480.37	−	22070.1i	−0.274473	−	0.934770i	−0.975197	−	0.221338i	$-0.928958\pi$
$823$	−6480.37	−	22070.1i	−0.274473	−	0.934770i	0.700724	−	0.713432i	$-0.252860\pi$
$824$	−669.231	+	7648.12i	−0.0282934	+	0.323343i
$825$	−13842.6	−	1990.27i	−0.584169	−	0.0839908i
$826$	−22115.0	−	8382.09i	−0.931574	−	0.353087i
$827$			4467.47i			0.187847i	0.995579	+	0.0939233i	$0.0299409\pi$
$827$			4467.47i			0.187847i	−0.995579	+	0.0939233i	$0.970059\pi$
$828$	146.799	−	543.867i	0.00616138	−	0.0228269i
$829$			20542.6i			0.860645i	0.902675	+	0.430323i	$0.141600\pi$
$829$			20542.6i			0.860645i	−0.902675	+	0.430323i	$0.858400\pi$
$830$	−13088.4	+	34532.0i	−0.547356	+	1.44412i
$831$	−3679.06	−	528.969i	−0.153580	−	0.0220815i
$832$	−18248.6	+	4734.30i	−0.760402	+	0.197274i
$833$	−868.934	−	2959.32i	−0.0361426	−	0.123090i
$834$	−7322.66	+	13243.3i	−0.304032	+	0.549854i
$835$	−2154.61	+	1866.98i	−0.0892972	+	0.0773765i
$836$	18757.6	+	2899.94i	0.776010	+	0.119972i
$837$	−7267.27	+	24750.0i	−0.300112	+	1.02209i
$838$	83.8788	−	1091.55i	0.00345769	−	0.0449962i
$839$	30789.4	+	19787.1i	1.26695	+	0.814217i	0.989219	−	0.146443i	$-0.0467824\pi$
$839$	30789.4	+	19787.1i	1.26695	+	0.814217i	0.277727	+	0.960660i	$0.410419\pi$
$840$	28763.9	+	6737.31i	1.18149	+	0.276737i
$841$	−3863.39	+	4458.59i	−0.158407	+	0.182812i
$842$	982.759	+	2678.09i	0.0402234	+	0.109612i
$843$	−18172.1	+	2612.76i	−0.742446	+	0.106748i
$844$	−31770.3	+	14104.5i	−1.29571	+	0.575232i
$845$	−5154.11	−	11285.9i	−0.209830	−	0.459465i
$846$	121.750	−	160.857i	0.00494783	−	0.00653710i
$847$	3330.29	−	7292.31i	0.135100	−	0.295829i
$848$	−10827.6	+	11973.7i	−0.438467	+	0.484882i
$849$	19082.5	+	29693.0i	0.771390	+	1.20031i
$850$	−14174.2	+	10494.0i	−0.571964	+	0.423461i
$851$	6471.30	+	13030.3i	0.260674	+	0.524882i
$852$	35984.8	+	10981.2i	1.44697	+	0.441561i
$853$	12694.0	+	19752.3i	0.509537	+	0.792855i	0.996761	−	0.0804222i	$-0.0256269\pi$
$853$	12694.0	+	19752.3i	0.509537	+	0.792855i	−0.487224	+	0.873277i	$0.661991\pi$
$854$	23184.2	−	12500.7i	0.928979	−	0.500895i
$855$	690.551	+	315.364i	0.0276215	+	0.0126143i
$856$	−27493.7	−	37969.5i	−1.09780	−	1.51609i
$857$	−16407.9	−	35928.4i	−0.654008	−	1.43208i	−0.888002	−	0.459840i	$-0.847907\pi$
$857$	−16407.9	−	35928.4i	−0.654008	−	1.43208i	0.233994	−	0.972238i	$-0.424820\pi$
$858$	−3426.24	+	15358.3i	−0.136329	+	0.611100i
$859$	−5670.35	−	39438.2i	−0.225227	−	1.56649i	−0.717820	−	0.696228i	$-0.754860\pi$
$859$	−5670.35	−	39438.2i	−0.225227	−	1.56649i	0.492594	−	0.870260i	$-0.336049\pi$
$860$	−19382.3	−	12748.2i	−0.768524	−	0.505477i
$861$	−6838.64	+	7892.21i	−0.270685	+	0.312388i
$862$	−1371.70	−	20719.6i	−0.0541998	−	0.818693i
$863$	13255.7	−	20626.3i	0.522863	−	0.813590i	−0.474928	−	0.880025i	$-0.657526\pi$
$863$	13255.7	−	20626.3i	0.522863	−	0.813590i	0.997791	+	0.0664344i	$0.0211623\pi$
$864$	−20149.4	−	15932.8i	−0.793398	−	0.627368i
$865$	−1878.30	+	6396.91i	−0.0738315	+	0.251447i
$866$	11110.3	+	11228.6i	0.435963	+	0.440603i
$867$	1260.52	+	1454.72i	0.0493767	+	0.0569837i
$868$	3304.98	+	24851.6i	0.129238	+	0.971796i
$869$	−1756.02	−	5980.47i	−0.0685489	−	0.233456i
$870$	−6040.45	−	28492.8i	−0.235391	−	1.11034i
$871$	1955.16	−	13598.4i	0.0760596	−	0.529006i
$872$	−12493.0	+	16147.7i	−0.485168	+	0.627098i
$873$			1050.22i			0.0407154i
$874$	−1109.95	+	25128.9i	−0.0429573	+	0.972537i
$875$	8249.27			0.318716
$876$	2440.33	+	8648.70i	0.0941224	+	0.333576i
$877$	22935.6	+	3297.63i	0.883100	+	0.126971i	0.568920	−	0.822393i	$-0.307361\pi$
$877$	22935.6	+	3297.63i	0.883100	+	0.126971i	0.314180	+	0.949363i	$0.398270\pi$
$878$	2225.18	+	10496.2i	0.0855308	+	0.403449i
$879$	41296.5	−	12125.7i	1.58464	−	0.465292i
$880$	27406.9	+	4534.73i	1.04987	+	0.173711i
$881$	−6869.37	+	5952.34i	−0.262696	+	0.227627i	−0.776242	−	0.630435i	$-0.782877\pi$
$881$	−6869.37	+	5952.34i	−0.262696	+	0.227627i	0.513547	+	0.858062i	$0.328331\pi$
$882$	−58.7640	+	58.1451i	−0.00224341	+	0.00221978i
$883$	−41485.6	−	12181.3i	−1.58109	−	0.464250i	−0.630886	−	0.775876i	$-0.717308\pi$
$883$	−41485.6	−	12181.3i	−1.58109	−	0.464250i	−0.950205	+	0.311626i	$0.899126\pi$
$884$	10551.2	+	16806.5i	0.401441	+	0.639439i
$885$	30899.8	+	19858.1i	1.17366	+	0.754263i
$886$	−919.401	−	13887.7i	−0.0348622	−	0.526597i
$887$	−5199.60	−	4505.48i	−0.196827	−	0.170551i	0.550871	−	0.834590i	$-0.314296\pi$
$887$	−5199.60	−	4505.48i	−0.196827	−	0.170551i	−0.747698	+	0.664039i	$0.768841\pi$
$888$	15299.8	−	850.309i	0.578186	−	0.0321335i
$889$	−40081.6	+	5762.87i	−1.51214	+	0.217413i
$890$	−16246.9	−	3624.47i	−0.611906	−	0.136508i
$891$	−19041.8	+	8696.12i	−0.715966	+	0.326971i
$892$	2962.07	+	31.3608i	0.111186	+	0.00117717i
$893$	−3741.99	+	8193.82i	−0.140225	+	0.307050i
$894$	19649.3	−	10594.7i	0.735090	−	0.396353i
$895$	−41483.5	+	26659.8i	−1.54932	+	0.995687i
$896$	−24182.2	−	6207.05i	−0.901642	−	0.231432i
$897$	−20727.0	−	2294.41i	−0.771520	−	0.0854049i
$898$	−2891.28	−	3905.22i	−0.107442	−	0.145121i
$899$	20793.3	−	13363.1i	0.771409	−	0.495754i
$900$	427.886	+	200.911i	0.0158476	+	0.00744113i
$901$	15456.7	+	7058.82i	0.571516	+	0.261003i
$902$	−5926.28	+	7829.84i	−0.218762	+	0.289030i
$903$	15829.9	−	7229.25i	0.583372	−	0.266417i
$904$	17194.5	−	30333.9i	0.632610	−	1.11603i
$905$	2959.89	+	20586.5i	0.108718	+	0.756153i
$906$	−15030.9	+	5515.78i	−0.551179	+	0.202262i
$907$	4092.93	+	3546.54i	0.149838	+	0.129836i	0.726554	−	0.687109i	$-0.241121\pi$
$907$	4092.93	+	3546.54i	0.149838	+	0.129836i	−0.576716	+	0.816945i	$0.695666\pi$
$908$	−18438.7	−	21740.3i	−0.673911	−	0.794578i
$909$	−621.786	+	967.519i	−0.0226880	+	0.0353032i
$910$	−2029.11	+	26405.5i	−0.0739167	+	0.961905i
$911$	−34986.6	−	10273.0i	−1.27240	−	0.373611i	−0.425305	−	0.905050i	$-0.639833\pi$
$911$	−34986.6	−	10273.0i	−1.27240	−	0.373611i	−0.847097	+	0.531439i	$0.821651\pi$
$912$	23860.2	+	11513.2i	0.866325	+	0.418027i
$913$	−17058.5	−	19686.6i	−0.618351	−	0.713615i
$914$	11637.9	+	6434.99i	0.421168	+	0.232878i
$915$	−39250.5	+	11525.0i	−1.41812	+	0.416398i
$916$	−1308.79	−	1158.55i	−0.0472091	−	0.0417901i
$917$	4762.27	−	33122.3i	0.171498	−	1.19280i
$918$	−9582.92	+	25283.2i	−0.344535	+	0.909010i
$919$	17068.8			0.612673			0.306336	−	0.951923i	$-0.400897\pi$
$919$	17068.8			0.612673			0.306336	+	0.951923i	$0.400897\pi$
$920$	−2013.79	+	36759.1i	−0.0721659	+	1.31730i
$921$	−7635.88			−0.273193
$922$	−9124.85	+	24074.7i	−0.325934	+	0.859932i
$923$	−4799.88	+	33383.9i	−0.171170	+	1.19052i
$924$	−13812.3	+	15603.4i	−0.491767	+	0.555535i
$925$	−11713.8	+	3439.48i	−0.416375	+	0.122259i
$926$	−28972.7	−	16020.0i	−1.02819	−	0.568519i
$927$	−141.843	−	163.695i	−0.00502559	−	0.00579984i
$928$	4593.79	+	24181.8i	0.162498	+	0.855395i
$929$	−1225.37	−	359.801i	−0.0432756	−	0.0127069i	0.260023	−	0.965602i	$-0.416270\pi$
$929$	−1225.37	−	359.801i	−0.0432756	−	0.0127069i	−0.303299	+	0.952896i	$0.598088\pi$
$930$	2983.23	−	38821.9i	0.105187	−	1.36884i
$931$	1995.63	−	3105.27i	0.0702516	−	0.109314i
$932$	37657.0	−	31938.3i	1.32349	−	1.12250i
$933$	−2159.75	−	1871.43i	−0.0757846	−	0.0656677i
$934$	43035.8	−	15792.5i	1.50768	−	0.553263i
$935$	−4161.33	−	28942.7i	−0.145551	−	1.01233i
$936$	262.287	−	462.720i	0.00915933	−	0.0161586i
$937$	4231.15	−	1932.30i	0.147519	−	0.0673699i	−0.340287	−	0.940322i	$-0.610524\pi$
$937$	4231.15	−	1932.30i	0.147519	−	0.0673699i	0.487807	+	0.872952i	$0.337797\pi$
$938$	10979.7	−	14506.5i	0.382197	−	0.504962i
$939$	1279.78	+	584.454i	0.0444770	+	0.0203120i
$940$	−5603.39	+	11933.7i	−0.194428	+	0.414080i
$941$	36261.3	−	23303.7i	1.25620	−	0.807312i	0.268442	−	0.963296i	$-0.413491\pi$
$941$	36261.3	−	23303.7i	1.25620	−	0.807312i	0.987760	+	0.155984i	$0.0498549\pi$
$942$	−1394.72	−	1883.83i	−0.0482403	−	0.0651576i
$943$	−11170.7	−	6675.54i	−0.385757	−	0.230525i
$944$	−25752.1	−	17331.1i	−0.887880	−	0.597541i
$945$	−30356.4	+	19508.9i	−1.04497	+	0.671560i
$946$	14403.7	−	7766.31i	0.495036	−	0.266918i
$947$	−9584.40	+	20986.9i	−0.328882	+	0.720151i	−0.999771	−	0.0214070i	$-0.993185\pi$
$947$	−9584.40	+	20986.9i	−0.328882	+	0.720151i	0.670889	+	0.741558i	$0.265913\pi$
$948$	92.1043	−	8699.39i	0.00315550	−	0.298041i
$949$	−7327.87	+	3346.53i	−0.250656	+	0.114471i
$950$	−20600.5	−	4595.71i	−0.703546	−	0.156952i
$951$	−42774.2	+	6150.00i	−1.45852	+	0.209703i
$952$	1458.24	+	26238.5i	0.0496447	+	0.893271i
$953$	−24955.1	−	21623.7i	−0.848242	−	0.735006i	0.117897	−	0.993026i	$-0.462385\pi$
$953$	−24955.1	−	21623.7i	−0.848242	−	0.735006i	−0.966140	+	0.258020i	$0.916930\pi$
$954$	−30.0861	−	454.454i	−0.00102104	−	0.0154229i
$955$	42272.5	+	27166.9i	1.43236	+	0.920522i
$956$	31067.3	−	19504.1i	1.05103	−	0.659840i
$957$	19712.7	+	5788.17i	0.665852	+	0.195512i
$958$	1649.71	−	1632.34i	0.0556365	−	0.0550506i
$959$	−34759.3	+	30119.1i	−1.17042	+	1.01418i
$960$	34741.1	+	17219.4i	1.16798	+	0.578909i
$961$	3119.64	−	916.010i	0.104718	−	0.0307479i
$962$	2848.86	+	13438.1i	0.0954791	+	0.450375i
$963$	1309.11	+	188.222i	0.0438063	+	0.00629840i
$964$	47362.8	−	13364.0i	1.58242	−	0.446499i
$965$	59807.5			1.99510
$966$	−22550.5	−	15940.9i	−0.751087	−	0.530942i
$967$			4259.48i			0.141650i	0.997489	+	0.0708251i	$0.0225632\pi$
$967$			4259.48i			0.141650i	−0.997489	+	0.0708251i	$0.977437\pi$
$968$	6438.56	−	8322.10i	0.213784	−	0.276325i
$969$	3968.56	−	27601.9i	0.131567	−	0.915069i
$970$	−14233.8	−	67140.7i	−0.471153	−	2.22243i
$971$	5417.54	+	18450.4i	0.179049	+	0.609787i	0.999287	+	0.0377631i	$0.0120232\pi$
$971$	5417.54	+	18450.4i	0.179049	+	0.609787i	−0.820237	+	0.572023i	$0.806159\pi$
$972$	1420.20	−	188.870i	0.0468651	−	0.00623251i
$973$	−11764.6	−	13577.1i	−0.387622	−	0.447340i
$974$	−26121.8	−	26399.8i	−0.859339	−	0.868485i
$975$	4929.99	−	16790.0i	0.161934	−	0.551498i
$976$	33369.1	−	9035.21i	1.09439	−	0.296322i
$977$	15025.5	−	23380.1i	0.492024	−	0.765605i	−0.503101	−	0.864228i	$-0.667807\pi$
$977$	15025.5	−	23380.1i	0.492024	−	0.765605i	0.995125	+	0.0986231i	$0.0314438\pi$
$978$	−1912.90	−	28894.5i	−0.0625436	−	0.944728i
$979$	7689.31	−	8873.94i	0.251023	−	0.289696i
$980$	2968.74	−	4513.66i	0.0967683	−	0.147126i
$981$	−81.9733	−	570.137i	−0.00266790	−	0.0185556i
$982$	12054.1	−	54033.3i	0.391714	−	1.75588i
$983$	−24421.6	−	53475.9i	−0.792400	−	1.73511i	−0.669650	−	0.742677i	$-0.733556\pi$
$983$	−24421.6	−	53475.9i	−0.792400	−	1.73511i	−0.122751	−	0.992438i	$-0.539172\pi$
$984$	−11101.5	+	8038.59i	−0.359657	+	0.260428i
$985$	63915.3	+	29189.1i	2.06752	+	0.944206i
$986$	22804.8	−	12296.1i	0.736566	−	0.397148i
$987$	−5346.78	−	8319.75i	−0.172431	−	0.268309i
$988$	−6931.85	+	22715.3i	−0.223210	+	0.731446i
$989$	12311.9	+	17852.2i	0.395850	+	0.573982i
$990$	−629.893	+	466.350i	−0.0202215	+	0.0149713i
$991$	975.286	+	1517.57i	0.0312623	+	0.0486451i	0.856533	−	0.516092i	$-0.172614\pi$
$991$	975.286	+	1517.57i	0.0312623	+	0.0486451i	−0.825271	+	0.564737i	$0.808977\pi$
$992$	−3215.18	+	32747.4i	−0.102905	+	1.04812i
$993$	−11054.9	+	24206.9i	−0.353290	+	0.773598i
$994$	−26955.1	+	35613.3i	−0.860125	+	1.13640i
$995$	19174.0	+	41985.2i	0.610912	+	1.33771i
$996$	−14753.1	−	33231.4i	−0.469347	−	1.05721i
$997$	−488.071	+	70.1740i	−0.0155039	+	0.00222912i	−0.150062	−	0.988677i	$-0.547947\pi$
$997$	−488.071	+	70.1740i	−0.0155039	+	0.00222912i	0.134559	+	0.990906i	$0.457038\pi$
$998$	3663.54	+	9983.43i	0.116200	+	0.316653i
$999$	−12257.0	+	14145.3i	−0.388182	+	0.447985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.j.a.11.8	✓	700
8.3	odd	2	inner	184.4.j.a.11.34	yes	700
23.21	odd	22	inner	184.4.j.a.67.34	yes	700
184.67	even	22	inner	184.4.j.a.67.8	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.j.a.11.8	✓	700	1.1	even	1	trivial
184.4.j.a.11.34	yes	700	8.3	odd	2	inner
184.4.j.a.67.8	yes	700	184.67	even	22	inner
184.4.j.a.67.34	yes	700	23.21	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	184.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.64482 - 1.00245i) q^{2} +(0.730695 - 5.08210i) q^{3} +(5.99019 + 5.30260i) q^{4} +(14.1524 - 4.15552i) q^{5} +(-7.02710 + 12.7088i) q^{6} +(-11.2898 - 13.0291i) q^{7} +(-10.5274 - 20.0293i) q^{8} +(0.612524 + 0.179853i) q^{9} +(-41.5964 - 3.19643i) q^{10} +(15.9098 - 24.7561i) q^{11} +(31.3253 - 26.5682i) q^{12} +(27.8279 + 24.1130i) q^{13} +(16.7985 + 45.7771i) q^{14} +(-10.7777 - 74.9604i) q^{15} +(7.76486 + 63.5272i) q^{16} +(61.2777 - 27.9846i) q^{17} +(-1.43973 - 1.08970i) q^{18} +(73.3374 + 33.4921i) q^{19} +(106.811 + 50.1522i) q^{20} +(-74.4645 + 47.8554i) q^{21} +(-66.8954 + 49.5269i) q^{22} +(-74.9087 - 80.9672i) q^{23} +(-109.483 + 38.8661i) q^{24} +(77.8658 - 50.0413i) q^{25} +(-49.4279 - 91.6708i) q^{26} +(58.9496 - 129.082i) q^{27} +(1.46014 - 137.912i) q^{28} +(-123.688 + 56.4864i) q^{29} +(-46.6388 + 209.061i) q^{30} +(-179.925 + 25.8694i) q^{31} +(43.1461 - 175.802i) q^{32} +(-114.188 - 98.9444i) q^{33} +(-190.122 + 12.5866i) q^{34} +(-213.920 - 137.478i) q^{35} +(2.71545 + 4.32533i) q^{36} +(-126.554 - 37.1597i) q^{37} +(-160.390 - 162.098i) q^{38} +(142.879 - 123.805i) q^{39} +(-232.221 - 239.716i) q^{40} +(113.198 - 33.2381i) q^{41} +(244.918 - 51.9224i) q^{42} +(-194.601 - 27.9794i) q^{43} +(226.575 - 63.9308i) q^{44} +9.41609 q^{45} +(116.955 + 289.236i) q^{46} +111.728i q^{47} +(328.525 + 6.95727i) q^{48} +(6.51572 - 45.3179i) q^{49} +(-256.105 + 54.2941i) q^{50} +(-97.4451 - 331.868i) q^{51} +(38.8329 + 292.002i) q^{52} +(165.182 + 190.630i) q^{53} +(-285.309 + 282.304i) q^{54} +(122.287 - 416.473i) q^{55} +(-142.111 + 363.289i) q^{56} +(223.797 - 348.235i) q^{57} +(383.758 - 25.4058i) q^{58} +(-317.617 + 366.549i) q^{59} +(332.924 - 506.177i) q^{60} +(-76.8738 - 534.669i) q^{61} +(501.804 + 111.946i) q^{62} +(-4.57193 - 10.0111i) q^{63} +(-290.346 + 421.714i) q^{64} +(494.035 + 225.618i) q^{65} +(202.820 + 376.158i) q^{66} +(-201.714 - 313.874i) q^{67} +(515.457 + 157.298i) q^{68} +(-466.219 + 321.531i) q^{69} +(427.967 + 578.050i) q^{70} +(495.207 + 770.557i) q^{71} +(-2.84597 - 14.1618i) q^{72} +(-90.8848 + 199.010i) q^{73} +(297.464 + 225.145i) q^{74} +(-197.419 - 432.287i) q^{75} +(261.710 + 589.503i) q^{76} +(-502.168 + 72.2009i) q^{77} +(-501.997 + 184.214i) q^{78} +(138.703 - 160.072i) q^{79} +(373.880 + 866.797i) q^{80} +(-598.431 - 384.588i) q^{81} +(-332.709 - 25.5667i) q^{82} +(249.387 - 849.333i) q^{83} +(-699.815 - 108.192i) q^{84} +(750.937 - 650.691i) q^{85} +(486.638 + 269.079i) q^{86} +(196.691 + 669.869i) q^{87} +(-663.338 - 58.0439i) q^{88} +(394.947 + 56.7848i) q^{89} +(-24.9039 - 9.43914i) q^{90} -634.803i q^{91} +(-19.3808 - 882.220i) q^{92} +933.300i q^{93} +(112.001 - 295.500i) q^{94} +(1177.08 + 169.238i) q^{95} +(-861.917 - 347.730i) q^{96} +(463.485 + 1578.49i) q^{97} +(-62.6618 + 113.326i) q^{98} +(14.1976 - 12.3023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 700 q - 7 q^{2} - 18 q^{3} - 11 q^{4} + 10 q^{6} - 40 q^{8} - 612 q^{9} - 11 q^{10} - 22 q^{11} + 6 q^{12} - 11 q^{14} - 27 q^{16} - 22 q^{17} + 244 q^{18} - 22 q^{19} - 11 q^{20} - 194 q^{24} - 1568 q^{25}+ \cdots - 22 q^{99}+O(q^{100}) \) 700 * q - 7 * q^2 - 18 * q^3 - 11 * q^4 + 10 * q^6 - 40 * q^8 - 612 * q^9 - 11 * q^10 - 22 * q^11 + 6 * q^12 - 11 * q^14 - 27 * q^16 - 22 * q^17 + 244 * q^18 - 22 * q^19 - 11 * q^20 - 194 * q^24 - 1568 * q^25 + 380 * q^26 + 222 * q^27 - 11 * q^28 - 11 * q^30 - 427 * q^32 - 22 * q^33 + 1903 * q^34 + 482 * q^35 - 1329 * q^36 + 594 * q^38 + 1309 * q^40 - 18 * q^41 - 3641 * q^42 - 22 * q^43 + 3300 * q^44 - 2727 * q^46 + 3204 * q^48 - 2860 * q^49 - 80 * q^50 - 22 * q^51 + 934 * q^52 + 2088 * q^54 - 3586 * q^56 - 22 * q^57 + 6159 * q^58 + 1002 * q^59 - 3641 * q^60 - 618 * q^62 + 1666 * q^64 - 22 * q^65 + 286 * q^66 - 22 * q^67 - 1474 * q^70 + 89 * q^72 - 18 * q^73 + 2354 * q^74 + 590 * q^75 + 8184 * q^76 + 10268 * q^78 + 4048 * q^80 - 5516 * q^81 - 4052 * q^82 - 22 * q^83 - 5401 * q^84 - 6721 * q^86 - 6963 * q^88 - 22 * q^89 - 18700 * q^90 - 4776 * q^92 - 8575 * q^94 - 5643 * q^96 - 22 * q^97 - 3995 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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