LMFDB - Embedded newform 184.4.p.a.13.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,4,Mod(13,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 14])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.13"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	184.p (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			13.17
Character	$\chi$	$=$	184.13
Dual form			184.4.p.a.85.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.03122 - 1.96829i) q^{2} +(4.41866 - 6.87557i) q^{3} +(0.251690 + 7.99604i) q^{4} +(-15.8545 - 7.24050i) q^{5} +(-22.5084 + 5.26859i) q^{6} +(11.0008 + 3.23011i) q^{7} +(15.2273 - 16.7371i) q^{8} +(-16.5327 - 36.2016i) q^{9} +(17.9525 + 45.9132i) q^{10} +(-46.3735 - 40.1829i) q^{11} +(56.0895 + 33.6013i) q^{12} +(14.9844 + 51.0321i) q^{13} +(-15.9871 - 28.2137i) q^{14} +(-119.838 + 77.0153i) q^{15} +(-63.8733 + 4.02504i) q^{16} +(7.97272 + 55.4515i) q^{17} +(-37.6736 + 106.075i) q^{18} +(-137.596 - 19.7833i) q^{19} +(53.9049 - 128.595i) q^{20} +(70.8175 - 61.3637i) q^{21} +(15.1033 + 172.897i) q^{22} +(93.3897 - 58.6972i) q^{23} +(-47.7930 - 178.652i) q^{24} +(117.082 + 135.120i) q^{25} +(70.0093 - 133.151i) q^{26} +(-103.534 - 14.8860i) q^{27} +(-23.0593 + 88.7755i) q^{28} +(88.3945 - 12.7092i) q^{29} +(395.006 + 79.4411i) q^{30} +(-94.0027 + 60.4119i) q^{31} +(137.663 + 117.545i) q^{32} +(-481.190 + 141.290i) q^{33} +(92.9501 - 128.327i) q^{34} +(-151.024 - 130.863i) q^{35} +(285.309 - 141.308i) q^{36} +(18.1173 - 8.27390i) q^{37} +(240.548 + 311.012i) q^{38} +(417.086 + 122.467i) q^{39} +(-362.605 + 155.105i) q^{40} +(-29.6369 + 64.8957i) q^{41} +(-264.627 - 14.7461i) q^{42} +(5.15378 - 8.01944i) q^{43} +(309.632 - 380.918i) q^{44} +693.663i q^{45} +(-305.228 - 64.5910i) q^{46} -210.440 q^{47} +(-254.560 + 456.951i) q^{48} +(-177.967 - 114.372i) q^{49} +(28.1357 - 504.909i) q^{50} +(416.490 + 190.204i) q^{51} +(-404.283 + 132.660i) q^{52} +(-113.920 + 387.976i) q^{53} +(181.001 + 234.022i) q^{54} +(444.284 + 972.847i) q^{55} +(221.574 - 134.935i) q^{56} +(-744.011 + 858.635i) q^{57} +(-204.564 - 148.171i) q^{58} +(-138.713 - 472.412i) q^{59} +(-645.980 - 938.847i) q^{60} +(-26.3818 - 41.0509i) q^{61} +(309.848 + 62.3147i) q^{62} +(-64.9372 - 451.648i) q^{63} +(-48.2607 - 509.720i) q^{64} +(131.928 - 917.581i) q^{65} +(1255.50 + 660.129i) q^{66} +(684.520 - 593.140i) q^{67} +(-441.386 + 77.7068i) q^{68} +(9.08064 - 901.471i) q^{69} +(49.1864 + 563.069i) q^{70} +(-467.724 - 539.782i) q^{71} +(-857.658 - 274.542i) q^{72} +(25.4487 - 177.000i) q^{73} +(-53.0857 - 18.8540i) q^{74} +(1446.37 - 207.957i) q^{75} +(123.557 - 1105.20i) q^{76} +(-380.349 - 591.834i) q^{77} +(-606.141 - 1069.70i) q^{78} +(-1024.50 + 300.821i) q^{79} +(1041.82 + 398.660i) q^{80} +(143.847 - 166.008i) q^{81} +(187.932 - 73.4834i) q^{82} +(-1124.41 + 513.501i) q^{83} +(508.491 + 550.815i) q^{84} +(275.093 - 936.881i) q^{85} +(-26.2530 + 6.14511i) q^{86} +(303.203 - 663.921i) q^{87} +(-1378.69 + 164.283i) q^{88} +(-1072.40 - 689.188i) q^{89} +(1365.33 - 1408.98i) q^{90} +609.793i q^{91} +(492.850 + 731.974i) q^{92} +913.262i q^{93} +(427.449 + 414.206i) q^{94} +(2038.27 + 1309.92i) q^{95} +(1416.48 - 427.119i) q^{96} +(225.825 - 494.488i) q^{97} +(136.372 + 582.605i) q^{98} +(-688.005 + 2343.13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 700 q - 7 q^{2} + 13 q^{4} - 52 q^{6} + 10 q^{7} - 46 q^{8} + 576 q^{9} + 35 q^{10} - 24 q^{12} + 77 q^{14} - 246 q^{15} - 27 q^{16} - 18 q^{17} - 230 q^{18} + 53 q^{20} + 182 q^{22} + 144 q^{23} + 154 q^{24}+ \cdots - 7727 q^{98}+O(q^{100}) $ 700 * q - 7 * q^2 + 13 * q^4 - 52 * q^6 + 10 * q^7 - 46 * q^8 + 576 * q^9 + 35 * q^10 - 24 * q^12 + 77 * q^14 - 246 * q^15 - 27 * q^16 - 18 * q^17 - 230 * q^18 + 53 * q^20 + 182 * q^22 + 144 * q^23 + 154 * q^24 + 1532 * q^25 + 50 * q^26 + 151 * q^28 + 39 * q^30 - 546 * q^31 + 53 * q^32 - 126 * q^33 - 1175 * q^34 + 2613 * q^36 + 60 * q^38 + 174 * q^39 - 1565 * q^40 - 18 * q^41 + 2983 * q^42 - 2596 * q^44 + 3645 * q^46 - 40 * q^47 - 3908 * q^48 - 2860 * q^49 + 1858 * q^50 - 1154 * q^52 - 432 * q^54 - 518 * q^55 + 4562 * q^56 - 126 * q^57 - 4499 * q^58 + 2651 * q^60 - 1540 * q^62 - 14 * q^63 - 158 * q^64 - 518 * q^65 + 2368 * q^66 - 1270 * q^68 - 2006 * q^70 - 1498 * q^71 + 2103 * q^72 - 18 * q^73 + 2216 * q^74 + 6852 * q^76 + 7956 * q^78 + 1834 * q^79 + 2362 * q^80 - 3268 * q^81 + 1098 * q^82 - 7971 * q^84 - 8759 * q^86 - 2154 * q^87 - 4495 * q^88 - 866 * q^89 - 13676 * q^90 - 10844 * q^92 - 12229 * q^94 + 722 * q^95 - 12211 * q^96 - 18 * q^97 - 7727 * q^98

Character values

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

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−2.03122	−	1.96829i	−0.718144	−	0.695895i
$2$	−2.03122	−	1.96829i	−0.718144	−	0.695895i
$3$	4.41866	−	6.87557i	0.850372	−	1.32320i	−0.0944193	−	0.995533i	$-0.530099\pi$
$3$	4.41866	−	6.87557i	0.850372	−	1.32320i	0.944791	−	0.327672i	$-0.106264\pi$
$4$	0.251690	+	7.99604i	0.0314612	+	0.999505i
$5$	−15.8545	−	7.24050i	−1.41807	−	0.647610i	−0.448803	−	0.893631i	$-0.648150\pi$
$5$	−15.8545	−	7.24050i	−1.41807	−	0.647610i	−0.969265	+	0.246021i	$0.920877\pi$
$6$	−22.5084	+	5.26859i	−1.53150	+	0.358482i
$7$	11.0008	+	3.23011i	0.593985	+	0.174410i	0.564889	−	0.825167i	$-0.308919\pi$
$7$	11.0008	+	3.23011i	0.593985	+	0.174410i	0.0290961	+	0.999577i	$0.490737\pi$
$8$	15.2273	−	16.7371i	0.672956	−	0.739682i
$9$	−16.5327	−	36.2016i	−0.612323	−	1.34080i
$10$	17.9525	+	45.9132i	0.567708	+	1.45190i
$11$	−46.3735	−	40.1829i	−1.27110	−	1.10142i	−0.989900	−	0.141771i	$-0.954720\pi$
$11$	−46.3735	−	40.1829i	−1.27110	−	1.10142i	−0.281205	−	0.959648i	$-0.590734\pi$
$12$	56.0895	+	33.6013i	1.34930	+	0.808322i
$13$	14.9844	+	51.0321i	0.319686	+	1.08875i	0.949958	+	0.312376i	$0.101125\pi$
$13$	14.9844	+	51.0321i	0.319686	+	1.08875i	−0.630273	+	0.776374i	$0.717057\pi$
$14$	−15.9871	−	28.2137i	−0.305196	−	0.538602i
$15$	−119.838	+	77.0153i	−2.06281	+	1.32568i
$16$	−63.8733	+	4.02504i	−0.998020	+	0.0628913i
$17$	7.97272	+	55.4515i	0.113745	+	0.791116i	0.964221	+	0.265101i	$0.0854052\pi$
$17$	7.97272	+	55.4515i	0.113745	+	0.791116i	−0.850475	+	0.526015i	$0.823686\pi$
$18$	−37.6736	+	106.075i	−0.493320	+	1.38900i
$19$	−137.596	−	19.7833i	−1.66140	−	0.238874i	−0.753317	−	0.657658i	$-0.771547\pi$
$19$	−137.596	−	19.7833i	−1.66140	−	0.238874i	−0.908086	+	0.418784i	$0.862456\pi$
$20$	53.9049	−	128.595i	0.602675	−	1.43774i
$21$	70.8175	−	61.3637i	0.735888	−	0.637651i
$22$	15.1033	+	172.897i	0.146365	+	1.67553i
$23$	93.3897	−	58.6972i	0.846657	−	0.532140i
$23$	93.3897	−	58.6972i	0.846657	−	0.532140i
$24$	−47.7930	−	178.652i	−0.406487	−	1.51946i
$25$	117.082	+	135.120i	0.936657	+	1.08096i
$26$	70.0093	−	133.151i	0.528075	−	1.00435i
$27$	−103.534	−	14.8860i	−0.737970	−	0.106104i
$28$	−23.0593	+	88.7755i	−0.155636	+	0.599178i
$29$	88.3945	−	12.7092i	0.566016	−	0.0813808i	0.146634	−	0.989191i	$-0.453156\pi$
$29$	88.3945	−	12.7092i	0.566016	−	0.0813808i	0.419382	+	0.907810i	$0.362247\pi$
$30$	395.006	+	79.4411i	2.40393	+	0.483463i
$31$	−94.0027	+	60.4119i	−0.544625	+	0.350009i	−0.783845	−	0.620956i	$-0.786745\pi$
$31$	−94.0027	+	60.4119i	−0.544625	+	0.350009i	0.239220	+	0.970965i	$0.423108\pi$
$32$	137.663	+	117.545i	0.760488	+	0.649352i
$33$	−481.190	+	141.290i	−2.53831	+	0.745316i
$34$	92.9501	−	128.327i	0.468848	−	0.647289i
$35$	−151.024	−	130.863i	−0.729362	−	0.631996i
$36$	285.309	−	141.308i	1.32087	−	0.654203i
$37$	18.1173	−	8.27390i	0.0804992	−	0.0367627i	−0.374759	−	0.927122i	$-0.622274\pi$
$37$	18.1173	−	8.27390i	0.0804992	−	0.0367627i	0.455258	+	0.890360i	$0.349547\pi$
$38$	240.548	+	311.012i	1.02690	+	1.32771i
$39$	417.086	+	122.467i	1.71249	+	0.502833i
$40$	−362.605	+	155.105i	−1.43332	+	0.613106i
$41$	−29.6369	+	64.8957i	−0.112890	+	0.247195i	−0.957641	−	0.287965i	$-0.907021\pi$
$41$	−29.6369	+	64.8957i	−0.112890	+	0.247195i	0.844751	+	0.535160i	$0.179749\pi$
$42$	−264.627	−	14.7461i	−0.972211	−	0.0541757i
$43$	5.15378	−	8.01944i	0.0182778	−	0.0284408i	−0.831994	−	0.554784i	$-0.812801\pi$
$43$	5.15378	−	8.01944i	0.0182778	−	0.0284408i	0.850272	+	0.526343i	$0.176437\pi$
$44$	309.632	−	380.918i	1.06088	−	1.30513i
$45$			693.663i			2.29789i
$46$	−305.228	−	64.5910i	−0.978334	−	0.207031i
$47$	−210.440			−0.653102			−0.326551	−	0.945180i	$-0.605887\pi$
$47$	−210.440			−0.653102			−0.326551	+	0.945180i	$0.605887\pi$
$48$	−254.560	+	456.951i	−0.765471	+	1.37407i
$49$	−177.967	−	114.372i	−0.518854	−	0.333447i
$50$	28.1357	−	504.909i	0.0795797	−	1.42810i
$51$	416.490	+	190.204i	1.14353	+	0.522234i
$52$	−404.283	+	132.660i	−1.07815	+	0.353781i
$53$	−113.920	+	387.976i	−0.295248	+	1.00552i	0.669602	+	0.742720i	$0.266465\pi$
$53$	−113.920	+	387.976i	−0.295248	+	1.00552i	−0.964850	+	0.262801i	$0.915354\pi$
$54$	181.001	+	234.022i	0.456132	+	0.589748i
$55$	444.284	+	972.847i	1.08922	+	2.38507i
$56$	221.574	−	134.935i	0.528734	−	0.321990i
$57$	−744.011	+	858.635i	−1.72889	+	1.99524i
$58$	−204.564	−	148.171i	−0.463113	−	0.335444i
$59$	−138.713	−	472.412i	−0.306082	−	1.04242i	−0.958626	−	0.284669i	$-0.908116\pi$
$59$	−138.713	−	472.412i	−0.306082	−	1.04242i	0.652544	−	0.757751i	$-0.273702\pi$
$60$	−645.980	−	938.847i	−1.38993	−	2.02008i
$61$	−26.3818	−	41.0509i	−0.0553744	−	0.0861643i	0.812462	−	0.583014i	$-0.198127\pi$
$61$	−26.3818	−	41.0509i	−0.0553744	−	0.0861643i	−0.867837	+	0.496849i	$0.834490\pi$
$62$	309.848	+	62.3147i	0.634689	+	0.127645i
$63$	−64.9372	−	451.648i	−0.129862	−	0.903211i
$64$	−48.2607	−	509.720i	−0.0942591	−	0.995548i
$65$	131.928	−	917.581i	0.251749	−	1.75095i
$66$	1255.50	+	660.129i	2.34154	+	1.23115i
$67$	684.520	−	593.140i	1.24817	−	1.08155i	0.254751	−	0.967007i	$-0.418006\pi$
$67$	684.520	−	593.140i	1.24817	−	1.08155i	0.993419	−	0.114539i	$-0.0365391\pi$
$68$	−441.386	+	77.7068i	−0.787145	+	0.138578i
$69$	9.08064	−	901.471i	0.0158432	−	1.57282i
$70$	49.1864	+	563.069i	0.0839843	+	0.961423i
$71$	−467.724	−	539.782i	−0.781811	−	0.902258i	0.215428	−	0.976520i	$-0.430885\pi$
$71$	−467.724	−	539.782i	−0.781811	−	0.902258i	−0.997239	+	0.0742617i	$0.976340\pi$
$72$	−857.658	−	274.542i	−1.40383	−	0.449376i
$73$	25.4487	−	177.000i	0.0408020	−	0.283784i	−0.959197	−	0.282737i	$-0.908758\pi$
$73$	25.4487	−	177.000i	0.0408020	−	0.283784i	0.999999	−	0.00104717i	$-0.000333326\pi$
$74$	−53.0857	−	18.8540i	−0.0833930	−	0.0296180i
$75$	1446.37	−	207.957i	2.22684	−	0.320171i
$76$	123.557	−	1105.20i	0.186486	−	1.66810i
$77$	−380.349	−	591.834i	−0.562919	−	0.875919i
$78$	−606.141	−	1069.70i	−0.879896	−	1.55282i
$79$	−1024.50	+	300.821i	−1.45906	+	0.428418i	−0.912525	−	0.409021i	$-0.865870\pi$
$79$	−1024.50	+	300.821i	−1.45906	+	0.428418i	−0.546531	+	0.837439i	$0.684052\pi$
$80$	1041.82	+	398.660i	1.45599	+	0.557144i
$81$	143.847	−	166.008i	0.197320	−	0.227720i
$82$	187.932	−	73.4834i	0.253093	−	0.0989619i
$83$	−1124.41	+	513.501i	−1.48699	+	0.679085i	−0.982828	−	0.184524i	$-0.940926\pi$
$83$	−1124.41	+	513.501i	−1.48699	+	0.679085i	−0.504161	+	0.863610i	$0.668198\pi$
$84$	508.491	+	550.815i	0.660487	+	0.715463i
$85$	275.093	−	936.881i	0.351036	−	1.19552i
$86$	−26.2530	+	6.14511i	−0.0329179	+	0.00770516i
$87$	303.203	−	663.921i	0.373640	−	0.818159i
$88$	−1378.69	+	164.283i	−1.67010	+	0.199007i
$89$	−1072.40	−	689.188i	−1.27724	−	0.820829i	−0.286691	−	0.958023i	$-0.592555\pi$
$89$	−1072.40	−	689.188i	−1.27724	−	0.820829i	−0.990544	+	0.137194i	$0.956192\pi$
$90$	1365.33	−	1408.98i	1.59909	−	1.65022i
$91$			609.793i			0.702458i
$92$	492.850	+	731.974i	0.558513	+	0.829496i
$93$			913.262i			1.01829i
$94$	427.449	+	414.206i	0.469021	+	0.454490i
$95$	2038.27	+	1309.92i	2.20128	+	1.41468i
$96$	1416.48	−	427.119i	1.50592	−	0.454090i
$97$	225.825	−	494.488i	0.236382	−	0.517604i	−0.753848	−	0.657049i	$-0.771804\pi$
$97$	225.825	−	494.488i	0.236382	−	0.517604i	0.990230	+	0.139445i	$0.0445318\pi$
$98$	136.372	+	582.605i	0.140568	+	0.600531i
$99$	−688.005	+	2343.13i	−0.698456	+	2.37872i
$100$	−1050.96	+	970.202i	−1.05096	+	0.970202i
$101$	−147.677	+	67.4418i	−0.145489	+	0.0664427i	−0.486829	−	0.873497i	$-0.661847\pi$
$101$	−147.677	+	67.4418i	−0.145489	+	0.0664427i	0.341340	+	0.939940i	$0.389119\pi$
$102$	−471.604	−	1206.12i	−0.457802	−	1.17082i
$103$	1224.03	−	1412.61i	1.17095	−	1.35134i	0.246911	−	0.969038i	$-0.420584\pi$
$103$	1224.03	−	1412.61i	1.17095	−	1.35134i	0.924036	−	0.382306i	$-0.124870\pi$
$104$	1082.30	+	526.284i	1.02046	+	0.496216i
$105$	−1567.08	+	460.136i	−1.45649	+	0.427664i
$106$	995.045	−	563.837i	0.911767	−	0.516648i
$107$	−160.371	−	249.542i	−0.144894	−	0.225459i	0.761219	−	0.648494i	$-0.224601\pi$
$107$	−160.371	−	249.542i	−0.144894	−	0.225459i	−0.906113	+	0.423035i	$0.860965\pi$
$108$	92.9705	−	831.612i	0.0828341	−	0.740943i
$109$	−1217.94	+	175.113i	−1.07025	+	0.153879i	−0.654850	−	0.755759i	$-0.727268\pi$
$109$	−1217.94	+	175.113i	−1.07025	+	0.153879i	−0.415402	+	0.909638i	$0.636359\pi$
$110$	1012.40	−	2850.54i	0.877536	−	2.47081i
$111$	23.1665	−	161.127i	0.0198096	−	0.137779i
$112$	−715.656	−	162.040i	−0.603778	−	0.136708i
$113$	−711.418	−	821.020i	−0.592253	−	0.683496i	0.377940	−	0.925830i	$-0.376632\pi$
$113$	−711.418	−	821.020i	−0.592253	−	0.683496i	−0.970193	+	0.242334i	$0.922087\pi$
$114$	3201.29	−	279.646i	2.63007	−	0.229748i
$115$	−1905.64	+	254.426i	−1.54524	+	0.206307i
$116$	123.871	+	703.607i	0.0991480	+	0.563175i
$117$	1599.71	−	1386.16i	1.26405	−	1.09530i
$118$	−648.087	+	1232.60i	−0.505604	+	0.961609i
$119$	−91.4087	+	635.761i	−0.0704153	+	0.489749i
$120$	−535.795	+	3178.48i	−0.407593	+	2.41795i
$121$	346.419	+	2409.40i	0.260270	+	1.81021i
$122$	−27.2127	+	135.310i	−0.0201945	+	0.100413i
$123$	315.240	+	490.522i	0.231091	+	0.359585i
$124$	−506.715	−	736.444i	−0.366971	−	0.533344i
$125$	−264.131	−	899.549i	−0.188997	−	0.643665i
$126$	−757.071	+	1045.21i	−0.535280	+	0.739006i
$127$	−154.996	+	178.875i	−0.108296	+	0.124981i	−0.807310	−	0.590128i	$-0.799077\pi$
$127$	−154.996	+	178.875i	−0.108296	+	0.124981i	0.699013	+	0.715109i	$0.253623\pi$
$128$	−905.248	+	1130.34i	−0.625105	+	0.780541i
$129$	−32.3654	−	70.8704i	−0.0220901	−	0.0483705i
$130$	−2074.04	+	1604.13i	−1.39927	+	1.08225i
$131$	394.227	−	1342.61i	0.262930	−	0.895456i	−0.717161	−	0.696907i	$-0.754559\pi$
$131$	394.227	−	1342.61i	0.262930	−	0.895456i	0.980091	−	0.198549i	$-0.0636229\pi$
$132$	−1250.87	−	3812.05i	−0.824806	−	2.51361i
$133$	−1449.76	−	662.081i	−0.945187	−	0.431652i
$134$	−2557.88	−	142.536i	−1.64901	−	0.0918896i
$135$	1533.70	+	985.650i	0.977778	+	0.628380i
$136$	1049.50	+	710.935i	0.661720	+	0.448251i
$137$	1443.58			0.900245			0.450122	−	0.892967i	$-0.351380\pi$
$137$	1443.58			0.900245			0.450122	+	0.892967i	$0.351380\pi$
$138$	−1792.80	+	1813.21i	−1.10589	+	1.11848i
$139$			551.931i			0.336792i	0.985719	+	0.168396i	$0.0538588\pi$
$139$			551.931i			0.336792i	−0.985719	+	0.168396i	$0.946141\pi$
$140$	1008.37	−	1240.53i	0.608736	−	0.748884i
$141$	−929.863	+	1446.89i	−0.555380	+	0.864188i
$142$	−112.397	+	2017.03i	−0.0664238	+	1.19201i
$143$	1355.74	−	2968.65i	0.792815	−	1.73602i
$144$	1201.71	+	2245.77i	0.695436	+	1.29964i
$145$	−1493.47	−	438.523i	−0.855352	−	0.251154i
$146$	−400.078	+	309.435i	−0.226786	+	0.175404i
$147$	−1572.75	+	718.252i	−0.882438	+	0.402996i
$148$	70.7184	+	142.784i	0.0392772	+	0.0793027i
$149$	−1775.11	−	1538.14i	−0.975991	−	0.845701i	0.0120446	−	0.999927i	$-0.496166\pi$
$149$	−1775.11	−	1538.14i	−0.975991	−	0.845701i	−0.988036	+	0.154226i	$0.950711\pi$
$150$	−3347.22	−	2424.47i	−1.82200	−	1.31972i
$151$	−101.981	+	29.9445i	−0.0549612	+	0.0161381i	−0.309098	−	0.951030i	$-0.600027\pi$
$151$	−101.981	+	29.9445i	−0.0549612	+	0.0161381i	0.254136	+	0.967168i	$0.418209\pi$
$152$	−2426.32	+	2001.71i	−1.29474	+	1.06816i
$153$	1875.62	−	1205.39i	0.991080	−	0.636928i
$154$	−392.329	+	1950.78i	−0.205291	+	1.02077i
$155$	1927.78	−	277.172i	0.998985	−	0.143632i
$156$	−874.278	+	3365.86i	−0.448707	+	1.72746i
$157$	−468.882	−	67.4150i	−0.238349	−	0.0342695i	0.0221049	−	0.999756i	$-0.492963\pi$
$157$	−468.882	−	67.4150i	−0.238349	−	0.0342695i	−0.260454	+	0.965486i	$0.583872\pi$
$158$	2673.09	+	1405.48i	1.34595	+	0.707684i
$159$	2164.18	+	2497.60i	1.07944	+	1.24574i
$160$	−1331.49	−	2860.37i	−0.657897	−	1.41332i
$161$	1216.96	−	344.054i	0.595712	−	0.168418i
$162$	−618.934	+	54.0665i	−0.300173	+	0.0262214i
$163$	2606.00	−	2258.11i	1.25225	−	1.08508i	0.259398	−	0.965771i	$-0.416476\pi$
$163$	2606.00	−	2258.11i	1.25225	−	1.08508i	0.992857	−	0.119314i	$-0.0380696\pi$
$164$	−526.368	−	220.644i	−0.250624	−	0.105057i
$165$	8652.02	+	1243.97i	4.08218	+	0.586928i
$166$	3294.64	+	1170.13i	1.54044	+	0.547107i
$167$	−147.493	−	1025.84i	−0.0683434	−	0.475339i	−0.995036	−	0.0995179i	$-0.968270\pi$
$167$	−147.493	−	1025.84i	−0.0683434	−	0.475339i	0.926692	−	0.375821i	$-0.122639\pi$
$168$	51.3067	−	2119.68i	0.0235619	−	0.973435i
$169$	−531.507	+	341.579i	−0.241924	+	0.155475i
$170$	−2402.83	+	1361.55i	−1.08405	+	0.614270i
$171$	1558.65	+	5308.27i	0.697034	+	2.37388i
$172$	65.4209	+	39.1914i	0.0290017	+	0.0173739i
$173$	1408.41	+	1220.39i	0.618954	+	0.536327i	0.906914	−	0.421316i	$-0.138432\pi$
$173$	1408.41	+	1220.39i	0.618954	+	0.536327i	−0.287960	+	0.957642i	$0.592977\pi$
$174$	−1922.66	+	751.778i	−0.837680	+	0.327541i
$175$	851.539	+	1864.61i	0.367830	+	0.805436i
$176$	3123.77	+	2379.96i	1.33786	+	1.01930i
$177$	−3861.03	−	1133.70i	−1.63962	−	0.481436i
$178$	821.753	+	3510.68i	0.346028	+	1.47830i
$179$	−661.035	−	301.885i	−0.276023	−	0.126055i	0.272594	−	0.962129i	$-0.412118\pi$
$179$	−661.035	−	301.885i	−0.276023	−	0.126055i	−0.548617	+	0.836074i	$0.684846\pi$
$180$	−5546.56	+	174.588i	−2.29676	+	0.0722946i
$181$	422.990	−	658.186i	0.173705	−	0.270290i	−0.743475	−	0.668764i	$-0.766824\pi$
$181$	422.990	−	658.186i	0.173705	−	0.270290i	0.917180	+	0.398474i	$0.130460\pi$
$182$	1200.25	−	1238.62i	0.488837	−	0.504466i
$183$	−398.820			−0.161102
$184$	439.649	−	2456.87i	0.176149	−	0.984364i
$185$	−347.148			−0.137961
$186$	1797.56	−	1855.03i	0.708622	−	0.731278i
$187$	1858.48	−	2891.85i	0.726767	−	1.13087i
$188$	−52.9656	−	1682.69i	−0.0205474	−	0.652779i
$189$	−1090.87	−	498.185i	−0.419838	−	0.191734i
$190$	−1561.88	−	6672.63i	−0.596371	−	2.54781i
$191$	1994.87	+	585.747i	0.755727	+	0.221901i	0.636829	−	0.771005i	$-0.280246\pi$
$191$	1994.87	+	585.747i	0.755727	+	0.221901i	0.118898	+	0.992906i	$0.462064\pi$
$192$	−3717.87	−	1920.46i	−1.39747	−	0.721862i
$193$	1459.52	+	3195.91i	0.544346	+	1.19195i	0.959373	+	0.282142i	$0.0910450\pi$
$193$	1459.52	+	3195.91i	0.544346	+	1.19195i	−0.415026	+	0.909809i	$0.636228\pi$
$194$	−1431.99	+	559.923i	−0.529954	+	0.207217i
$195$	−5725.95	−	4961.57i	−2.10279	−	1.82208i
$196$	869.734	−	1451.82i	0.316958	−	0.529088i
$197$	1328.67	+	4525.03i	0.480527	+	1.63652i	0.741336	+	0.671134i	$0.234193\pi$
$197$	1328.67	+	4525.03i	0.480527	+	1.63652i	−0.260809	+	0.965390i	$0.583989\pi$
$198$	6009.44	−	3405.22i	2.15693	−	1.22221i
$199$	−975.089	+	626.652i	−0.347348	+	0.223227i	−0.702668	−	0.711518i	$-0.748008\pi$
$199$	−975.089	+	626.652i	−0.347348	+	0.223227i	0.355320	+	0.934745i	$0.384372\pi$
$200$	4044.36	+	97.8934i	1.42990	+	0.0346105i
$201$	−1053.51	−	7327.35i	−0.369697	−	2.57130i
$202$	432.709	+	153.682i	0.150719	+	0.0535297i
$203$	1013.46	+	145.713i	0.350398	+	0.0503797i
$204$	−1416.06	+	3378.14i	−0.485999	+	1.15940i
$205$	939.754	−	814.301i	0.320172	−	0.277431i
$206$	−5266.70	+	460.068i	−1.78130	+	0.155604i
$207$	−3668.92	−	2410.43i	−1.23192	−	0.809356i
$208$	−1162.51	−	3199.27i	−0.387526	−	1.06649i
$209$	5585.86	+	6446.42i	1.84872	+	2.13353i
$210$	4088.76	+	2149.83i	1.34358	+	0.706439i
$211$	1639.04	+	235.659i	0.534769	+	0.0768882i	0.404409	−	0.914578i	$-0.367477\pi$
$211$	1639.04	+	235.659i	0.534769	+	0.0768882i	0.130361	+	0.991467i	$0.458386\pi$
$212$	−3130.95	−	813.260i	−1.01431	−	0.263467i
$213$	−5778.02	+	830.754i	−1.85870	+	0.267241i
$214$	−165.422	+	822.530i	−0.0528412	+	0.262743i
$215$	−139.775	+	89.8281i	−0.0443377	+	0.0284941i
$216$	−1825.69	+	1506.19i	−0.575105	+	0.474460i
$217$	−1229.24	+	360.937i	−0.384544	+	0.112912i
$218$	2818.57	+	2041.56i	0.875678	+	0.634275i
$219$	−1104.53	−	957.077i	−0.340808	−	0.295312i
$220$	−7667.10	+	3797.37i	−2.34962	+	1.16372i
$221$	−2710.34	+	1237.77i	−0.824964	+	0.376749i
$222$	−364.200	+	281.685i	−0.110106	+	0.0851597i
$223$	5896.69	+	1731.42i	1.77072	+	0.519932i	0.993949	−	0.109846i	$-0.0350358\pi$
$223$	5896.69	+	1731.42i	1.77072	+	0.519932i	0.776776	+	0.629778i	$0.216854\pi$
$224$	1134.71	+	1737.75i	0.338465	+	0.518342i
$225$	2955.88	−	6472.47i	0.875815	−	1.91777i
$226$	−170.959	+	3067.94i	−0.0503186	+	0.902994i
$227$	−899.890	+	1400.26i	−0.263118	+	0.409420i	−0.947526	−	0.319680i	$-0.896425\pi$
$227$	−899.890	+	1400.26i	−0.263118	+	0.409420i	0.684408	+	0.729100i	$0.260061\pi$
$228$	−7052.94	−	5733.03i	−2.04865	−	1.66526i
$229$		−	709.458i		−	0.204726i	−0.994747	−	0.102363i	$-0.967360\pi$
$229$		−	709.458i		−	0.204726i	0.994747	−	0.102363i	$-0.0326404\pi$
$230$	4371.56	+	3234.06i	1.25327	+	0.927163i
$231$	−5749.83			−1.63771
$232$	1133.29	−	1672.99i	0.320708	−	0.473437i
$233$	−3317.14	−	2131.79i	−0.932673	−	0.599392i	−0.0163645	−	0.999866i	$-0.505209\pi$
$233$	−3317.14	−	2131.79i	−0.932673	−	0.599392i	−0.916308	+	0.400474i	$0.868846\pi$
$234$	−5977.72	−	333.104i	−1.66998	−	0.0930584i
$235$	3336.41	+	1523.69i	0.926143	+	0.422955i
$236$	3742.51	−	1228.05i	1.03227	−	0.338726i
$237$	−2458.61	+	8373.26i	−0.673856	+	2.29494i
$238$	1437.03	−	1111.45i	0.391382	−	0.302709i
$239$	−1630.28	−	3569.81i	−0.441230	−	0.966159i	−0.991371	−	0.131087i	$-0.958153\pi$
$239$	−1630.28	−	3569.81i	−0.441230	−	0.966159i	0.550141	−	0.835072i	$-0.314574\pi$
$240$	7344.47	−	5401.58i	1.97535	−	1.45279i
$241$	−1511.39	+	1744.24i	−0.403973	+	0.466210i	−0.920888	−	0.389827i	$-0.872535\pi$
$241$	−1511.39	+	1744.24i	−0.403973	+	0.466210i	0.516915	+	0.856037i	$0.327080\pi$
$242$	4038.73	−	5575.86i	1.07281	−	1.48111i
$243$	−1301.45	−	4432.33i	−0.343573	−	1.17010i
$244$	321.604	−	221.282i	0.0843795	−	0.0580579i
$245$	1993.46	+	3101.88i	0.519826	+	0.808866i
$246$	325.169	−	1616.84i	0.0842765	−	0.419049i
$247$	−1052.20	−	7318.24i	−0.271053	−	1.88522i
$248$	−420.285	+	2493.24i	−0.107613	+	0.638391i
$249$	−1437.78	+	9999.96i	−0.365925	+	2.54507i
$250$	−1234.06	+	2347.07i	−0.312196	+	0.593766i
$251$	2605.31	−	2257.52i	0.655163	−	0.567702i	−0.262563	−	0.964915i	$-0.584568\pi$
$251$	2605.31	−	2257.52i	0.655163	−	0.567702i	0.917727	+	0.397213i	$0.130022\pi$
$252$	3595.05	−	632.915i	0.898678	−	0.158214i
$253$	−6689.44	−	1030.67i	−1.66230	−	0.256118i
$254$	666.907	−	58.2571i	0.164746	−	0.0143912i
$255$	−5226.05	−	6031.19i	−1.28340	−	1.48113i
$256$	4063.60	−	514.186i	0.992089	−	0.125534i
$257$	355.480	−	2472.42i	0.0862812	−	0.600099i	−0.900107	−	0.435668i	$-0.856512\pi$
$257$	355.480	−	2472.42i	0.0862812	−	0.600099i	0.986389	−	0.164431i	$-0.0525787\pi$
$258$	−73.7521	+	207.658i	−0.0177969	+	0.0501093i
$259$	226.030	−	32.4982i	0.0542271	−	0.00779668i
$260$	7370.22	+	823.958i	1.75801	+	0.196537i
$261$	−1921.50	−	2989.91i	−0.455700	−	0.709083i
$262$	−3443.41	+	1951.19i	−0.811965	+	0.460095i
$263$	5075.95	−	1490.43i	1.19010	−	0.349445i	0.374041	−	0.927412i	$-0.377972\pi$
$263$	5075.95	−	1490.43i	1.19010	−	0.349445i	0.816060	+	0.577967i	$0.196154\pi$
$264$	−4962.42	+	10205.2i	−1.15688	+	2.37911i
$265$	4615.28	−	5326.32i	1.06987	−	1.23469i
$266$	1641.60	+	4198.37i	0.378395	+	0.967739i
$267$	−9477.13	+	4328.06i	−2.17225	+	0.992034i
$268$	4915.06	+	5324.16i	1.12028	+	1.21353i
$269$	−497.277	+	1693.57i	−0.112712	+	0.383862i	−0.996457	−	0.0841076i	$-0.973196\pi$
$269$	−497.277	+	1693.57i	−0.112712	+	0.383862i	0.883745	+	0.467969i	$0.155014\pi$
$270$	−1175.24	−	5020.84i	−0.264899	−	1.13170i
$271$	−2995.61	+	6559.47i	−0.671477	+	1.47033i	0.199951	+	0.979806i	$0.435922\pi$
$271$	−2995.61	+	6559.47i	−0.671477	+	1.47033i	−0.871428	+	0.490524i	$0.836805\pi$
$272$	−732.439	−	3509.78i	−0.163274	−	0.782396i
$273$	4192.68	+	2694.47i	0.929495	+	0.597350i
$274$	−2932.23	−	2841.38i	−0.646505	−	0.626475i
$275$		−	10970.7i		−	2.40566i
$276$	7210.48	−	154.282i	1.57254	−	0.0336474i
$277$		−	4215.56i		−	0.914400i	−0.889364	−	0.457200i	$-0.848852\pi$
$277$		−	4215.56i		−	0.914400i	0.889364	−	0.457200i	$-0.151148\pi$
$278$	1086.36	−	1121.09i	0.234372	−	0.241865i
$279$	3741.13	+	2404.28i	0.802780	+	0.515915i
$280$	−4489.94	+	535.015i	−0.958305	+	0.114190i
$281$	−193.523	+	423.756i	−0.0410840	+	0.0899614i	−0.929061	−	0.369926i	$-0.879383\pi$
$281$	−193.523	+	423.756i	−0.0410840	+	0.0899614i	0.887977	+	0.459888i	$0.152110\pi$
$282$	4736.66	−	1108.72i	1.00023	−	0.234125i
$283$	−1945.32	+	6625.14i	−0.408612	+	1.39160i	0.456365	+	0.889793i	$0.349151\pi$
$283$	−1945.32	+	6625.14i	−0.408612	+	1.39160i	−0.864977	+	0.501811i	$0.832667\pi$
$284$	4198.40	−	3875.79i	0.877215	−	0.809810i
$285$	18012.9	−	8226.19i	3.74382	−	1.70975i
$286$	−8596.96	+	3361.50i	−1.77744	+	0.694998i
$287$	−535.648	+	618.171i	−0.110168	+	0.127141i
$288$	1979.38	−	6926.97i	0.404987	−	1.41728i
$289$	1702.68	−	499.953i	0.346567	−	0.101761i
$290$	2170.43	+	3830.31i	0.439489	+	0.775599i
$291$	−2402.04	−	3737.65i	−0.483884	−	0.752938i
$292$	1421.70	+	158.940i	0.284928	+	0.0318536i
$293$	4767.96	−	685.529i	0.950673	−	0.136686i	0.350505	−	0.936561i	$-0.386010\pi$
$293$	4767.96	−	685.529i	0.950673	−	0.136686i	0.600167	+	0.799875i	$0.295101\pi$
$294$	4608.33	+	1636.70i	0.914160	+	0.324675i
$295$	−1221.28	+	8494.19i	−0.241036	+	1.67644i
$296$	137.396	−	429.220i	0.0269797	−	0.0842835i
$297$	4203.09	+	4850.63i	0.821172	+	0.947684i
$298$	578.130	+	6618.23i	0.112383	+	1.28652i
$299$	4394.83	+	3886.33i	0.850031	+	0.751680i
$300$	2026.87	+	11512.9i	0.390072	+	2.21566i
$301$	82.5992	−	71.5726i	0.0158171	−	0.0137056i
$302$	266.086	+	139.905i	0.0507004	+	0.0266577i
$303$	−188.834	+	1313.37i	−0.0358027	+	0.249013i
$304$	8868.33	+	709.795i	1.67314	+	0.133913i
$305$	121.041	+	841.857i	0.0227239	+	0.158048i
$306$	−6182.35	−	1243.36i	−1.15497	−	0.232281i
$307$	3114.27	+	4845.91i	0.578961	+	0.900881i	0.999981	−	0.00617045i	$-0.00196413\pi$
$307$	3114.27	+	4845.91i	0.578961	+	0.900881i	−0.421020	+	0.907051i	$0.638328\pi$
$308$	4636.60	−	3190.24i	0.857775	−	0.590198i
$309$	−4303.91	−	14657.8i	−0.792365	−	2.69855i
$310$	−4461.29	−	3231.42i	−0.817368	−	0.592040i
$311$	−1502.52	+	1734.00i	−0.273955	+	0.316161i	−0.876009	−	0.482294i	$-0.839804\pi$
$311$	−1502.52	+	1734.00i	−0.273955	+	0.316161i	0.602054	+	0.798455i	$0.294349\pi$
$312$	8400.82	−	5115.96i	1.52437	−	0.928315i
$313$	−4228.94	−	9260.09i	−0.763686	−	1.67224i	−0.740081	−	0.672518i	$-0.765213\pi$
$313$	−4228.94	−	9260.09i	−0.763686	−	1.67224i	−0.0236057	−	0.999721i	$-0.507515\pi$
$314$	819.709	+	1059.83i	0.147321	+	0.190476i
$315$	−2240.61	+	7630.82i	−0.400775	+	1.36491i
$316$	−2663.23	−	8116.24i	−0.474109	−	1.44486i
$317$	106.318	+	48.5538i	0.0188373	+	0.00860270i	0.424811	−	0.905282i	$-0.360340\pi$
$317$	106.318	+	48.5538i	0.0188373	+	0.00860270i	−0.405974	+	0.913885i	$0.633068\pi$
$318$	520.069	−	9332.91i	0.0917107	−	1.64580i
$319$	−4609.86	−	2962.58i	−0.809099	−	0.519977i
$320$	−2925.48	+	8430.78i	−0.511061	+	1.47280i
$321$	−2424.37			−0.421542
$322$	−3149.10	−	1696.47i	−0.545008	−	0.293604i
$323$		−	7787.62i		−	1.34153i
$324$	1363.61	+	1108.42i	0.233815	+	0.190058i
$325$	−5141.05	+	7999.63i	−0.877459	+	1.36535i
$326$	−9737.96	−	542.640i	−1.65440	−	0.0921903i
$327$	−4177.66	+	9147.80i	−0.706499	+	1.54702i
$328$	634.877	+	1484.22i	0.106876	+	0.249854i
$329$	−2315.00	−	679.745i	−0.387933	−	0.113907i
$330$	−15125.6	−	19556.4i	−2.52315	−	3.26226i
$331$	5414.22	−	2472.59i	0.899071	−	0.410592i	0.0883941	−	0.996086i	$-0.471827\pi$
$331$	5414.22	−	2472.59i	0.899071	−	0.410592i	0.810677	+	0.585494i	$0.199099\pi$
$332$	−4388.98	−	8861.59i	−0.725532	−	1.46489i
$333$	−599.058	−	519.086i	−0.0985831	−	0.0854227i
$334$	−1719.55	+	2374.00i	−0.281705	+	0.388921i
$335$	−15147.3	+	4447.66i	−2.47041	+	0.725378i
$336$	−4276.36	+	4204.55i	−0.694329	+	0.682669i
$337$	1113.04	−	715.307i	0.179914	−	0.115624i	−0.447584	−	0.894242i	$-0.647715\pi$
$337$	1113.04	−	715.307i	0.179914	−	0.115624i	0.627498	+	0.778618i	$0.284079\pi$
$338$	1751.93	+	352.338i	0.281931	+	0.0567002i
$339$	−8788.50	+	1263.59i	−1.40804	+	0.202446i
$340$	7560.58	+	1963.85i	1.20597	+	0.313250i
$341$	6786.76	+	975.789i	1.07778	+	0.154962i
$342$	7282.24	−	13850.1i	1.15140	−	2.18985i
$343$	−4163.61	−	4805.06i	−0.655434	−	0.756411i
$344$	−55.7441	−	208.374i	−0.00873698	−	0.0326591i
$345$	−6671.07	+	14226.6i	−1.04104	+	2.22010i
$346$	−458.699	−	5251.02i	−0.0712711	−	0.815887i
$347$	−4610.91	+	3995.38i	−0.713333	+	0.618107i	−0.934013	−	0.357240i	$-0.883718\pi$
$347$	−4610.91	+	3995.38i	−0.713333	+	0.618107i	0.220680	+	0.975346i	$0.429172\pi$
$348$	5385.05	+	2257.32i	0.829509	+	0.347715i
$349$	−5251.91	−	755.111i	−0.805526	−	0.115817i	−0.272762	−	0.962081i	$-0.587937\pi$
$349$	−5251.91	−	755.111i	−0.805526	−	0.115817i	−0.532763	+	0.846264i	$0.678846\pi$
$350$	1940.43	−	5463.51i	0.296344	−	0.834390i
$351$	−791.734	−	5506.63i	−0.120398	−	0.837385i
$352$	−1660.61	−	10982.7i	−0.251451	−	1.66301i
$353$	953.749	−	612.937i	0.143804	−	0.0924175i	−0.466760	−	0.884384i	$-0.654579\pi$
$353$	953.749	−	612.937i	0.143804	−	0.0924175i	0.610565	+	0.791966i	$0.290943\pi$
$354$	5611.14	+	9902.40i	0.842454	+	1.48674i
$355$	3507.23	+	11944.5i	0.524350	+	1.78577i
$356$	5240.87	−	8748.40i	0.780240	−	1.30243i
$357$	3967.32	+	3437.70i	0.588159	+	0.509643i
$358$	748.510	+	1914.30i	0.110503	+	0.282609i
$359$	−3368.00	−	7374.90i	−0.495143	−	1.08421i	−0.978018	−	0.208523i	$-0.933135\pi$
$359$	−3368.00	−	7374.90i	−0.495143	−	1.08421i	0.482875	−	0.875690i	$-0.339593\pi$
$360$	11609.9	+	10562.6i	1.69971	+	1.54638i
$361$	11960.1	+	3511.79i	1.74370	+	0.511998i
$362$	−2154.68	+	504.352i	−0.312839	+	0.0732270i
$363$	18096.7	+	8264.48i	2.61661	+	1.19497i
$364$	−4875.93	+	153.479i	−0.702110	+	0.0221002i
$365$	−1685.04	+	2621.98i	−0.241642	+	0.376002i
$366$	810.091	+	784.993i	0.115694	+	0.112110i
$367$	−1999.65			−0.284416			−0.142208	−	0.989837i	$-0.545420\pi$
$367$	−1999.65			−0.284416			−0.142208	+	0.989837i	$0.545420\pi$
$368$	−5728.85	+	4125.08i	−0.811514	+	0.584334i
$369$	2839.31			0.400565
$370$	705.133	+	683.287i	0.0990760	+	0.0960065i
$371$	−2506.41	+	3900.06i	−0.350745	+	0.545771i
$372$	−7302.48	+	229.859i	−1.01778	+	0.0320366i
$373$	−4088.43	−	1867.12i	−0.567536	−	0.259185i	0.110916	−	0.993830i	$-0.464622\pi$
$373$	−4088.43	−	1867.12i	−0.567536	−	0.259185i	−0.678452	+	0.734645i	$0.737349\pi$
$374$	−9466.97	+	2215.96i	−1.30889	+	0.306375i
$375$	−7352.02	−	2158.75i	−1.01242	−	0.297273i
$376$	−3204.42	+	3522.15i	−0.439509	+	0.483088i
$377$	1973.11	+	4320.52i	0.269551	+	0.590233i
$378$	1235.23	+	3159.07i	0.168078	+	0.429855i
$379$	−10176.1	−	8817.65i	−1.37919	−	1.19507i	−0.957536	−	0.288313i	$-0.906906\pi$
$379$	−10176.1	−	8817.65i	−1.37919	−	1.19507i	−0.421650	−	0.906759i	$-0.638549\pi$
$380$	−9961.13	+	16627.8i	−1.34472	+	2.24470i
$381$	544.992	+	1856.07i	0.0732829	+	0.249578i
$382$	−2899.10	−	5116.26i	−0.388301	−	0.685264i
$383$	6063.20	−	3896.58i	0.808917	−	0.519859i	−0.0695977	−	0.997575i	$-0.522172\pi$
$383$	6063.20	−	3896.58i	0.808917	−	0.519859i	0.878514	+	0.477716i	$0.158535\pi$
$384$	3771.78	+	11218.7i	0.501244	+	1.49089i
$385$	1745.06	+	12137.1i	0.231004	+	1.60666i
$386$	3325.86	−	9364.35i	0.438554	−	1.23480i
$387$	−375.523	−	53.9920i	−0.0493253	−	0.00709191i
$388$	4010.78	+	1681.25i	0.524785	+	0.219980i
$389$	2308.10	−	1999.98i	0.300837	−	0.260676i	−0.491341	−	0.870968i	$-0.663493\pi$
$389$	2308.10	−	1999.98i	0.300837	−	0.260676i	0.792177	+	0.610291i	$0.208948\pi$
$390$	1864.87	+	21348.3i	0.242131	+	2.77183i
$391$	3999.42	+	4710.62i	0.517287	+	0.609275i
$392$	−4624.21	+	1237.07i	−0.595811	+	0.159392i
$393$	−7489.29	−	8643.10i	−0.961284	−	1.10938i
$394$	6207.75	−	11806.5i	0.793761	−	1.50966i
$395$	18421.0	+	2648.54i	2.34649	+	0.337374i
$396$	−18908.9	−	4911.58i	−2.39952	−	0.623273i
$397$	−7093.54	+	1019.90i	−0.896763	+	0.128935i	−0.575257	−	0.817973i	$-0.695098\pi$
$397$	−7093.54	+	1019.90i	−0.896763	+	0.128935i	−0.321506	+	0.946908i	$0.604189\pi$
$398$	3214.05	+	646.389i	0.404788	+	0.0814085i
$399$	−10958.2	+	7042.39i	−1.37492	+	0.883610i
$400$	−8022.29	−	8159.30i	−1.00279	−	1.01991i
$401$	6899.85	−	2025.98i	0.859257	−	0.252301i	0.177717	−	0.984082i	$-0.443129\pi$
$401$	6899.85	−	2025.98i	0.859257	−	0.252301i	0.681540	+	0.731781i	$0.261311\pi$
$402$	−12282.4	+	16957.1i	−1.52386	+	2.10383i
$403$	−4491.51	−	3891.92i	−0.555182	−	0.481068i
$404$	−576.436	−	1163.86i	−0.0709871	−	0.143327i
$405$	−3482.59	+	1590.45i	−0.427287	+	0.195136i
$406$	−1771.75	−	2290.75i	−0.216578	−	0.280020i
$407$	−1172.63	−	344.316i	−0.142814	−	0.0419340i
$408$	9525.47	−	4074.53i	1.15584	−	0.494410i
$409$	3205.33	−	7018.69i	0.387514	−	0.848538i	−0.610871	−	0.791730i	$-0.709181\pi$
$409$	3205.33	−	7018.69i	0.387514	−	0.848538i	0.998385	−	0.0568076i	$-0.0180922\pi$
$410$	−3511.62	−	195.682i	−0.422992	−	0.0235709i
$411$	6378.70	−	9925.45i	0.765543	−	1.19121i
$412$	11603.4	+	9431.87i	1.38751	+	1.12785i
$413$		−	5644.95i		−	0.672566i
$414$	2707.95	+	12117.6i	0.321470	+	1.43852i
$415$	21545.0			2.54843
$416$	−3935.79	+	8786.57i	−0.463865	+	1.03557i
$417$	3794.84	+	2438.80i	0.445645	+	0.286399i
$418$	1342.32	−	24088.7i	0.157070	−	2.81870i
$419$	−4067.15	−	1857.41i	−0.474209	−	0.216564i	0.163950	−	0.986469i	$-0.447576\pi$
$419$	−4067.15	−	1857.41i	−0.474209	−	0.216564i	−0.638159	+	0.769905i	$0.720304\pi$
$420$	−4073.68	−	12414.6i	−0.473275	−	1.44231i
$421$	−1422.20	+	4843.58i	−0.164641	+	0.560716i	0.835299	+	0.549796i	$0.185294\pi$
$421$	−1422.20	+	4843.58i	−0.164641	+	0.560716i	−0.999940	+	0.0109207i	$0.996524\pi$
$422$	−2865.41	−	3704.78i	−0.330535	−	0.427360i
$423$	3479.14	+	7618.26i	0.399910	+	0.875680i
$424$	4758.90	+	7814.51i	0.545077	+	0.895061i
$425$	−6559.14	+	7569.65i	−0.748624	+	0.863958i
$426$	13371.6	+	9685.37i	1.52079	+	1.10154i
$427$	−157.621	−	536.807i	−0.0178637	−	0.0608382i
$428$	1954.98	−	1345.14i	0.220789	−	0.151915i
$429$	−14420.6	−	22439.0i	−1.62293	−	2.52532i
$430$	460.722	+	92.6575i	0.0516697	+	0.0103915i
$431$	77.3935	+	538.284i	0.00864945	+	0.0601582i	0.993689	−	0.112170i	$-0.0357801\pi$
$431$	77.3935	+	538.284i	0.00864945	+	0.0601582i	−0.985040	+	0.172328i	$0.944871\pi$
$432$	6673.00	+	534.087i	0.743183	+	0.0594821i
$433$	612.435	−	4259.58i	0.0679717	−	0.472753i	−0.927197	−	0.374574i	$-0.877789\pi$
$433$	612.435	−	4259.58i	0.0679717	−	0.472753i	0.995169	−	0.0981795i	$-0.0313019\pi$
$434$	3207.28	+	1686.35i	0.354733	+	0.186515i
$435$	−9614.24	+	8330.78i	−1.05970	+	0.918231i
$436$	−1706.76	−	9694.62i	−0.187474	−	1.06488i
$437$	−14011.3	+	6228.94i	−1.53375	+	0.681854i
$438$	359.730	+	4118.06i	0.0392432	+	0.449243i
$439$	5411.10	+	6244.74i	0.588286	+	0.678918i	0.969365	−	0.245624i	$-0.0789929\pi$
$439$	5411.10	+	6244.74i	0.588286	+	0.678918i	−0.381079	+	0.924542i	$0.624447\pi$
$440$	23047.9	+	7377.77i	2.49719	+	0.799367i
$441$	−1198.19	+	8333.58i	−0.129380	+	0.899857i
$442$	7941.58	+	2820.54i	0.854620	+	0.303529i
$443$	14335.7	−	2061.17i	1.53750	−	0.221059i	0.679100	−	0.734045i	$-0.262370\pi$
$443$	14335.7	−	2061.17i	1.53750	−	0.221059i	0.858396	+	0.512987i	$0.171461\pi$
$444$	1294.21	+	144.686i	0.138334	+	0.0154651i
$445$	12012.2	+	18691.4i	1.27963	+	1.99114i
$446$	−8569.52	−	15123.3i	−0.909817	−	1.60562i
$447$	−18419.2	+	5408.37i	−1.94899	+	0.572275i
$448$	1115.55	−	5763.20i	0.117645	−	0.607780i
$449$	−1206.20	+	1392.03i	−0.126780	+	0.146311i	−0.815590	−	0.578630i	$-0.803588\pi$
$449$	−1206.20	+	1392.03i	−0.126780	+	0.146311i	0.688811	+	0.724941i	$0.258133\pi$
$450$	−18743.7	+	7328.97i	−1.96353	+	0.767758i
$451$	3982.06	−	1818.55i	0.415761	−	0.189871i
$452$	6385.85	−	5895.17i	0.664525	−	0.613463i
$453$	−244.736	+	833.496i	−0.0253835	+	0.0864482i
$454$	4583.98	−	1072.98i	0.473869	−	0.110920i
$455$	4415.20	−	9667.95i	0.454919	−	0.996133i
$456$	3041.79	+	25527.2i	0.312379	+	2.62154i
$457$	6997.80	+	4497.21i	0.716287	+	0.460330i	0.847343	−	0.531045i	$-0.178201\pi$
$457$	6997.80	+	4497.21i	0.716287	+	0.460330i	−0.131057	+	0.991375i	$0.541837\pi$
$458$	−1396.42	+	1441.06i	−0.142468	+	0.147023i
$459$		−	5859.82i		−	0.595889i
$460$	−2514.03	−	15173.6i	−0.254820	−	1.53798i
$461$		−	7344.37i		−	0.741999i	−0.928633	−	0.370999i	$-0.879015\pi$
$461$		−	7344.37i		−	0.741999i	0.928633	−	0.370999i	$-0.120985\pi$
$462$	11679.2	+	11317.3i	1.17611	+	1.13967i
$463$	7897.43	+	5075.37i	0.792710	+	0.509444i	0.873229	−	0.487309i	$-0.162022\pi$
$463$	7897.43	+	5075.37i	0.792710	+	0.509444i	−0.0805196	+	0.996753i	$0.525658\pi$
$464$	−5594.90	+	1167.57i	−0.559777	+	0.116817i
$465$	6612.47	−	14479.3i	0.659454	−	1.44400i
$466$	2541.84	+	10859.2i	0.252679	+	1.07949i
$467$	−1865.45	+	6353.16i	−0.184846	+	0.629527i	0.813972	+	0.580905i	$0.197301\pi$
$467$	−1865.45	+	6353.16i	−0.184846	+	0.629527i	−0.998817	+	0.0486220i	$0.984517\pi$
$468$	11486.4	+	12442.5i	1.13453	+	1.22896i
$469$	9446.15	−	4313.91i	0.930027	−	0.424729i
$470$	−3777.92	−	9661.97i	−0.370772	−	0.948241i
$471$	−2535.35	+	2925.95i	−0.248031	+	0.286243i
$472$	−10019.0	−	4871.90i	−0.977039	−	0.475100i
$473$	−561.244	+	164.796i	−0.0545582	+	0.0160197i
$474$	21475.0	−	12168.7i	2.08097	−	1.17917i
$475$	−13436.9	−	20908.2i	−1.29795	−	2.01965i
$476$	−5106.58	−	570.893i	−0.491722	−	0.0549723i
$477$	15928.8	−	2290.21i	1.52899	−	0.219836i
$478$	−3714.97	+	10459.9i	−0.355478	+	1.00089i
$479$	−136.493	+	949.331i	−0.0130199	+	0.0905554i	−0.995295	−	0.0968882i	$-0.969111\pi$
$479$	−136.493	+	949.331i	−0.0130199	+	0.0905554i	0.982275	+	0.187444i	$0.0600202\pi$
$480$	−25550.1	−	3484.25i	−2.42958	−	0.331320i
$481$	693.711	+	800.585i	0.0657599	+	0.0758910i
$482$	6503.14	−	568.077i	0.614544	−	0.0536830i
$483$	3011.75	−	9887.53i	0.283725	−	0.931467i
$484$	−19178.4	+	3376.40i	−1.80113	+	0.317092i
$485$	−7160.67	+	6204.76i	−0.670411	+	0.580915i
$486$	−6080.58	+	11564.7i	−0.567532	+	1.07939i
$487$	−352.775	+	2453.60i	−0.0328250	+	0.228303i	−0.999630	−	0.0272139i	$-0.991336\pi$
$487$	−352.775	+	2453.60i	−0.0328250	+	0.228303i	0.966805	+	0.255517i	$0.0822456\pi$
$488$	−1088.79	−	183.538i	−0.100999	−	0.0170254i
$489$	−4010.78	−	27895.6i	−0.370907	−	2.57972i
$490$	2056.25	−	10224.3i	0.189575	−	0.942626i
$491$	−7065.32	−	10993.9i	−0.649396	−	1.01048i	−0.997335	−	0.0729625i	$-0.976755\pi$
$491$	−7065.32	−	10993.9i	−0.649396	−	1.01048i	0.347939	−	0.937517i	$-0.386882\pi$
$492$	−3842.89	+	2644.13i	−0.352136	+	0.242290i
$493$	1409.49	+	4800.28i	0.128763	+	0.438527i
$494$	−12267.1	+	16936.0i	−1.11726	+	1.54248i
$495$	27873.4	−	32167.6i	2.53094	−	2.92086i
$496$	5761.10	−	4237.07i	0.521534	−	0.383569i
$497$	−3401.76	−	7448.81i	−0.307022	−	0.672283i
$498$	22603.2	−	17482.1i	2.03389	−	1.57308i
$499$	2092.25	−	7125.54i	0.187699	−	0.639244i	−0.810843	−	0.585264i	$-0.800991\pi$
$499$	2092.25	−	7125.54i	0.187699	−	0.639244i	0.998542	−	0.0539804i	$-0.0171908\pi$
$500$	7126.35	−	2338.41i	0.637400	−	0.209154i
$501$	−7704.93	−	3518.72i	−0.687088	−	0.313782i
$502$	−9735.40	−	542.498i	−0.865562	−	0.0482328i
$503$	−17979.7	−	11554.8i	−1.59379	−	1.02426i	−0.970136	−	0.242561i	$-0.922013\pi$
$503$	−17979.7	−	11554.8i	−1.59379	−	1.02426i	−0.623650	−	0.781704i	$-0.714351\pi$
$504$	−8548.09	−	5790.50i	−0.755481	−	0.511765i
$505$	2829.65			0.249343
$506$	11559.0	+	15260.3i	1.01554	+	1.34071i
$507$			5163.74i			0.452327i
$508$	−1469.30	−	1194.33i	−0.128326	−	0.104311i
$509$	−9204.21	+	14322.0i	−0.801511	+	1.24718i	0.163908	+	0.986476i	$0.447590\pi$
$509$	−9204.21	+	14322.0i	−0.801511	+	1.24718i	−0.965420	+	0.260700i	$0.916047\pi$
$510$	−1255.86	+	22537.0i	−0.109040	+	1.95678i
$511$	851.685	−	1864.93i	0.0737306	−	0.161447i
$512$	−9266.12	−	6953.91i	−0.799821	−	0.600238i
$513$	13951.4	+	4096.50i	1.20072	+	0.352563i
$514$	−5588.49	+	4322.34i	−0.479568	+	0.370915i
$515$	−29634.4	+	13533.6i	−2.53563	+	1.15798i
$516$	558.537	−	276.633i	0.0476516	−	0.0236009i
$517$	9758.84	+	8456.08i	0.830161	+	0.719339i
$518$	−523.082	−	378.881i	−0.0443685	−	0.0321372i
$519$	14614.1	−	4291.10i	1.23601	−	0.362926i
$520$	−13348.7	−	16180.4i	−1.12573	−	1.36453i
$521$	−15046.0	+	9669.50i	−1.26522	+	0.813106i	−0.988989	−	0.147986i	$-0.952721\pi$
$521$	−15046.0	+	9669.50i	−1.26522	+	0.813106i	−0.276229	+	0.961092i	$0.589085\pi$
$522$	−1982.02	+	9855.21i	−0.166189	+	0.826343i
$523$	8134.23	−	1169.53i	0.680086	−	0.0977816i	0.206390	−	0.978470i	$-0.433829\pi$
$523$	8134.23	−	1169.53i	0.680086	−	0.0977816i	0.473696	+	0.880688i	$0.342919\pi$
$524$	10834.8	+	2814.33i	0.903285	+	0.234627i
$525$	16582.9	+	2384.27i	1.37855	+	0.198206i
$526$	−13244.0	−	6963.54i	−1.09784	−	0.577233i
$527$	−4099.39	−	4730.94i	−0.338846	−	0.391050i
$528$	30166.5	−	10961.5i	2.48642	−	0.903479i
$529$	5276.27	−	10963.4i	0.433655	−	0.901079i
$530$	−19858.4	+	1734.71i	−1.62753	+	0.142172i
$531$	−14808.8	+	12831.9i	−1.21026	+	1.04869i
$532$	4929.14	−	11758.9i	0.401702	−	0.958299i
$533$	−3755.85	−	540.010i	−0.305223	−	0.0438845i
$534$	27769.0	+	9862.48i	2.25034	+	0.799235i
$535$	735.789	+	5117.52i	0.0594597	+	0.413551i
$536$	495.929	−	20488.8i	0.0399643	−	1.65108i
$537$	−4996.52	+	3211.07i	−0.401519	+	0.258041i
$538$	4343.51	−	2461.23i	0.348071	−	0.197232i
$539$	3657.14	+	12455.1i	0.292253	+	0.995322i
$540$	−7495.28	+	12511.6i	−0.597307	+	0.997064i
$541$	12533.0	+	10859.9i	0.995997	+	0.863036i	0.990578	−	0.136949i	$-0.0437298\pi$
$541$	12533.0	+	10859.9i	0.995997	+	0.863036i	0.00541853	+	0.999985i	$0.498275\pi$
$542$	18995.7	−	7427.49i	1.50541	−	0.588631i
$543$	−2656.35	−	5816.60i	−0.209936	−	0.459695i
$544$	−5420.51	+	8570.78i	−0.427211	+	0.675495i
$545$	20577.7	+	6042.16i	1.61734	+	0.474895i
$546$	−3212.75	−	13725.4i	−0.251818	−	1.07581i
$547$	−4249.11	−	1940.51i	−0.332137	−	0.151682i	0.242365	−	0.970185i	$-0.422077\pi$
$547$	−4249.11	−	1940.51i	−0.332137	−	0.151682i	−0.574502	+	0.818503i	$0.694804\pi$
$548$	363.335	+	11542.9i	0.0283228	+	0.899799i
$549$	−1049.94	+	1633.75i	−0.0816221	+	0.127007i
$550$	−21593.5	+	22283.9i	−1.67409	+	1.72761i
$551$	−12414.1			−0.959820
$552$	−14949.7	−	13878.9i	−1.15272	−	1.07016i
$553$	−12242.0			−0.941378
$554$	−8297.44	+	8562.73i	−0.636326	+	0.656670i
$555$	−1533.93	+	2386.84i	−0.117318	+	0.182551i
$556$	−4413.26	+	138.915i	−0.336626	+	0.0105959i
$557$	2122.16	+	969.156i	0.161434	+	0.0737243i	0.494493	−	0.869182i	$-0.335354\pi$
$557$	2122.16	+	969.156i	0.161434	+	0.0737243i	−0.333059	+	0.942906i	$0.608081\pi$
$558$	−2866.74	−	12247.2i	−0.217489	−	0.929151i
$559$	486.475	+	142.842i	0.0368080	+	0.0108078i
$560$	10173.1	+	7750.76i	0.767665	+	0.584874i
$561$	−11671.1	−	25556.2i	−0.878352	−	1.92332i
$562$	1227.16	−	479.832i	0.0921079	−	0.0360151i
$563$	−3821.48	−	3311.33i	−0.286068	−	0.247879i	0.499991	−	0.866030i	$-0.333337\pi$
$563$	−3821.48	−	3311.33i	−0.286068	−	0.247879i	−0.786059	+	0.618151i	$0.787882\pi$
$564$	−11803.5	−	7071.05i	−0.881233	−	0.527917i
$565$	5334.56	+	18167.9i	0.397216	+	1.35279i
$566$	16991.6	−	9628.16i	1.26185	−	0.715021i
$567$	2118.64	−	1361.57i	0.156922	−	0.100848i
$568$	−16156.5	−	391.068i	−1.19351	−	0.0288888i
$569$	−622.925	−	4332.54i	−0.0458952	−	0.319208i	−0.999817	−	0.0191516i	$-0.993903\pi$
$569$	−622.925	−	4332.54i	−0.0458952	−	0.319208i	0.953921	−	0.300057i	$-0.0970056\pi$
$570$	−52779.5	−	18745.3i	−3.87841	−	1.37746i
$571$	1979.94	+	284.673i	0.145110	+	0.0208637i	0.214487	−	0.976727i	$-0.431192\pi$
$571$	1979.94	+	284.673i	0.145110	+	0.0208637i	−0.0693768	+	0.997591i	$0.522101\pi$
$572$	24078.7	+	10093.4i	1.76011	+	0.737805i
$573$	12842.0	−	11127.7i	0.936270	−	0.811283i
$574$	2304.76	−	201.330i	0.167594	−	0.0146400i
$575$	18865.4	+	5746.42i	1.36825	+	0.416769i
$576$	−17654.8	+	10174.2i	−1.27711	+	0.735980i
$577$	−5254.23	−	6063.71i	−0.379093	−	0.437496i	0.533853	−	0.845577i	$-0.320744\pi$
$577$	−5254.23	−	6063.71i	−0.379093	−	0.437496i	−0.912946	+	0.408081i	$0.866198\pi$
$578$	−4442.57	−	2335.86i	−0.319700	−	0.168095i
$579$	28422.9	+	4086.59i	2.04009	+	0.293321i
$580$	3130.55	−	12052.2i	0.224119	−	0.862830i
$581$	−14028.0	+	2016.93i	−1.00169	+	0.144021i
$582$	−2477.70	+	12319.9i	−0.176467	+	0.877450i
$583$	20872.9	−	13414.2i	1.48279	−	0.952931i
$584$	−2574.95	−	3121.16i	−0.182452	−	0.221155i
$585$	−35399.1	+	10394.1i	−2.50183	+	0.734604i
$586$	−11034.1	−	7992.25i	−0.777839	−	0.563408i
$587$	10147.4	+	8792.79i	0.713507	+	0.618258i	0.934059	−	0.357118i	$-0.116240\pi$
$587$	10147.4	+	8792.79i	0.713507	+	0.618258i	−0.220552	+	0.975375i	$0.570786\pi$
$588$	−6139.01	−	12395.0i	−0.430559	−	0.869322i
$589$	14129.5	−	6452.74i	0.988450	−	0.451410i
$590$	19199.7	−	14849.7i	1.33973	−	1.03619i
$591$	36983.2	+	10859.2i	2.57408	+	0.755819i
$592$	−1123.91	+	601.405i	−0.0780278	+	0.0417527i
$593$	385.320	−	843.733i	0.0266833	−	0.0584282i	−0.895821	−	0.444415i	$-0.853412\pi$
$593$	385.320	−	843.733i	0.0266833	−	0.0584282i	0.922504	+	0.385987i	$0.126139\pi$
$594$	1010.03	−	18125.6i	0.0697680	−	1.25202i
$595$	6052.47	−	9417.82i	0.417020	−	0.648896i
$596$	11852.3	−	14581.0i	0.814576	−	1.00211i
$597$			9473.26i			0.649438i
$598$	−1277.43	−	16544.3i	−0.0873548	−	1.13135i
$599$	4470.57			0.304946			0.152473	−	0.988308i	$-0.451276\pi$
$599$	4470.57			0.304946			0.152473	+	0.988308i	$0.451276\pi$
$600$	18543.7	−	27374.7i	1.26174	−	1.86261i
$601$	−8477.90	−	5448.42i	−0.575409	−	0.369793i	0.220337	−	0.975424i	$-0.429284\pi$
$601$	−8477.90	−	5448.42i	−0.575409	−	0.369793i	−0.795746	+	0.605631i	$0.792921\pi$
$602$	−308.653	−	17.1994i	−0.0208966	−	0.00116444i
$603$	−32789.6	−	14974.5i	−2.21442	−	1.01129i
$604$	−265.105	−	807.911i	−0.0178592	−	0.0544262i
$605$	11952.9	−	40708.0i	0.803233	−	2.73556i
$606$	2968.65	−	2296.05i	0.198998	−	0.153912i
$607$	5088.88	+	11143.1i	0.340282	+	0.745115i	0.999979	−	0.00641706i	$-0.00204263\pi$
$607$	5088.88	+	11143.1i	0.340282	+	0.745115i	−0.659697	+	0.751532i	$0.729315\pi$
$608$	−16616.4	−	18897.2i	−1.10836	−	1.26050i
$609$	5480.00	−	6324.25i	0.364632	−	0.420807i
$610$	1411.16	−	1948.24i	0.0936657	−	0.129315i
$611$	−3153.31	−	10739.2i	−0.208788	−	0.711065i
$612$	10110.4	+	14694.2i	0.667794	+	0.970551i
$613$	944.048	+	1468.97i	0.0622018	+	0.0967880i	0.870961	−	0.491352i	$-0.163497\pi$
$613$	944.048	+	1468.97i	0.0622018	+	0.0967880i	−0.808760	+	0.588139i	$0.799861\pi$
$614$	3212.37	−	15972.9i	0.211141	−	1.04986i
$615$	−1446.33	−	10059.5i	−0.0948322	−	0.659572i
$616$	−15697.3	−	2646.08i	−1.02672	−	0.173074i
$617$	−2891.40	+	20110.1i	−0.188660	+	1.31216i	0.646822	+	0.762641i	$0.276098\pi$
$617$	−2891.40	+	20110.1i	−0.188660	+	1.31216i	−0.835482	+	0.549518i	$0.814811\pi$
$618$	−20108.5	+	38244.4i	−1.30887	+	2.48935i
$619$	−18881.2	+	16360.6i	−1.22601	+	1.06234i	−0.229989	+	0.973193i	$0.573869\pi$
$619$	−18881.2	+	16360.6i	−1.22601	+	1.06234i	−0.996018	+	0.0891482i	$0.971586\pi$
$620$	2701.48	+	15344.8i	0.174991	+	0.993972i
$621$	−10542.8	+	4686.98i	−0.681270	+	0.302870i
$622$	6464.95	−	564.741i	0.416754	−	0.0364052i
$623$	−9571.03	−	11045.6i	−0.615498	−	0.710323i
$624$	−27133.6	−	6143.61i	−1.74073	−	0.394137i
$625$	855.031	−	5946.87i	0.0547220	−	0.380600i
$626$	−9636.61	+	27133.0i	−0.615266	+	1.73235i
$627$	69004.9	−	9921.40i	4.39520	−	0.631934i
$628$	421.040	−	3766.17i	0.0267537	−	0.239310i
$629$	603.245	+	938.667i	0.0382400	+	0.0595026i
$630$	19570.8	−	11089.7i	1.23765	−	0.701308i
$631$	15930.8	−	4677.72i	1.00507	−	0.295114i	0.262533	−	0.964923i	$-0.415442\pi$
$631$	15930.8	−	4677.72i	1.00507	−	0.295114i	0.742533	+	0.669809i	$0.233624\pi$
$632$	−10565.5	+	21727.9i	−0.664988	+	1.36754i
$633$	8862.66	−	10228.1i	0.556492	−	0.642226i
$634$	−120.387	−	307.888i	−0.00754131	−	0.0192867i
$635$	3752.52	−	1713.72i	0.234510	−	0.107097i
$636$	−19426.2	+	17933.5i	−1.21116	+	1.11810i
$637$	3169.94	−	10795.8i	0.197170	−	0.671501i
$638$	3532.43	+	15091.2i	0.219201	+	0.936466i
$639$	−11808.2	+	25856.4i	−0.731027	+	1.60073i
$640$	22536.5	−	11366.6i	1.39193	−	0.702036i
$641$	6194.62	+	3981.04i	0.381705	+	0.245307i	0.717397	−	0.696665i	$-0.245334\pi$
$641$	6194.62	+	3981.04i	0.381705	+	0.245307i	−0.335691	+	0.941972i	$0.608970\pi$
$642$	4924.42	+	4771.85i	0.302728	+	0.293349i
$643$			2308.49i			0.141583i	0.997491	+	0.0707915i	$0.0225525\pi$
$643$			2308.49i			0.141583i	−0.997491	+	0.0707915i	$0.977447\pi$
$644$	3057.37	+	9644.24i	0.187076	+	0.590118i
$645$			1357.96i			0.0828984i
$646$	−15328.3	+	15818.4i	−0.933565	+	0.963413i
$647$	−24589.9	−	15803.0i	−1.49417	−	0.960244i	−0.995631	−	0.0933769i	$-0.970234\pi$
$647$	−24589.9	−	15803.0i	−1.49417	−	0.960244i	−0.498539	−	0.866868i	$-0.666130\pi$
$648$	−588.098	−	4935.42i	−0.0356523	−	0.299200i
$649$	−12550.3	+	27481.3i	−0.759078	+	1.66215i
$650$	26188.2	−	6129.93i	1.58028	−	0.369901i
$651$	−2949.94	+	10046.6i	−0.177600	+	0.604848i
$652$	18711.8	+	20269.3i	1.12395	+	1.21750i
$653$	−26730.9	+	12207.6i	−1.60193	+	0.731579i	−0.997862	−	0.0653517i	$-0.979183\pi$
$653$	−26730.9	+	12207.6i	−1.60193	+	0.731579i	−0.604071	+	0.796930i	$0.706456\pi$
$654$	26491.2	−	10358.3i	1.58393	−	0.619332i
$655$	−15971.5	+	18432.1i	−0.952758	+	1.09954i
$656$	1631.80	−	4264.39i	0.0971203	−	0.253806i
$657$	−6828.42	+	2005.00i	−0.405482	+	0.119060i
$658$	3364.33	+	5937.29i	0.199324	+	0.351762i
$659$	16058.7	+	24987.8i	0.949252	+	1.47707i	0.877462	+	0.479645i	$0.159235\pi$
$659$	16058.7	+	24987.8i	0.949252	+	1.47707i	0.0717898	+	0.997420i	$0.477129\pi$
$660$	−7769.23	+	69495.0i	−0.458207	+	4.09862i
$661$	16461.2	−	2366.76i	0.968632	−	0.139268i	0.360201	−	0.932875i	$-0.382708\pi$
$661$	16461.2	−	2366.76i	0.968632	−	0.139268i	0.608431	+	0.793606i	$0.291799\pi$
$662$	−15864.2	−	5634.37i	−0.931391	−	0.330795i
$663$	−3465.69	+	24104.4i	−0.203011	+	1.41197i
$664$	−8527.18	+	26638.6i	−0.498372	+	1.55689i
$665$	18191.3	+	20993.9i	1.06080	+	1.22422i
$666$	195.105	+	2233.50i	0.0113516	+	0.129949i
$667$	7509.14	−	6375.42i	0.435915	−	0.370101i
$668$	8165.50	−	1437.55i	0.472953	−	0.0832643i
$669$	37960.0	−	32892.5i	2.19375	−	1.90090i
$670$	39521.8	+	20780.1i	2.27890	+	1.19822i
$671$	−426.126	+	2963.77i	−0.0245163	+	0.170514i
$672$	16962.0	−	123.252i	0.973694	−	0.00707521i
$673$	184.386	+	1282.43i	0.0105610	+	0.0734532i	0.994420	−	0.105490i	$-0.0336412\pi$
$673$	184.386	+	1282.43i	0.0105610	+	0.0734532i	−0.983859	+	0.178943i	$0.942732\pi$
$674$	−3668.75	−	737.837i	−0.209666	−	0.0421668i
$675$	−10110.6	−	15732.5i	−0.576531	−	0.897100i
$676$	−2865.05	−	4163.98i	−0.163009	−	0.236913i
$677$	−807.041	−	2748.53i	−0.0458155	−	0.156033i	0.933408	−	0.358816i	$-0.116820\pi$
$677$	−807.041	−	2748.53i	−0.0458155	−	0.156033i	−0.979224	+	0.202783i	$0.935001\pi$
$678$	20338.5	+	14731.6i	1.15206	+	0.834463i
$679$	4081.50	−	4710.30i	0.230683	−	0.266222i
$680$	−11491.8	−	18870.4i	−0.648071	−	1.06419i
$681$	5651.25	+	12374.5i	0.317998	+	0.696318i
$682$	−11864.8	−	15340.3i	−0.666166	−	0.861308i
$683$	5855.25	−	19941.2i	0.328031	−	1.11717i	−0.616119	−	0.787653i	$-0.711296\pi$
$683$	5855.25	−	19941.2i	0.328031	−	1.11717i	0.944150	−	0.329517i	$-0.106886\pi$
$684$	−42052.8	+	13799.0i	−2.35077	+	0.771374i
$685$	−22887.2	−	10452.3i	−1.27661	−	0.583007i
$686$	−1000.55	+	17955.3i	−0.0556866	+	0.999325i
$687$	−4877.93	−	3134.86i	−0.270895	−	0.174093i
$688$	−296.910	+	532.972i	−0.0164529	+	0.0295340i
$689$	−21506.2			−1.18915
$690$	41552.4	−	15766.8i	2.29257	−	0.869899i
$691$		−	945.464i		−	0.0520508i	−0.999661	−	0.0260254i	$-0.991715\pi$
$691$		−	945.464i		−	0.0520508i	0.999661	−	0.0260254i	$-0.00828509\pi$
$692$	−9403.81	+	11568.8i	−0.516588	+	0.635521i
$693$	−15137.2	+	23553.9i	−0.829745	+	1.29111i
$694$	17229.8	+	960.117i	0.942413	+	0.0525152i
$695$	3996.25	−	8750.57i	0.218110	−	0.477595i
$696$	−6495.16	−	15184.4i	−0.353733	−	0.826960i
$697$	−3834.85	−	1126.01i	−0.208401	−	0.0611919i
$698$	9181.50	+	11871.1i	0.497887	+	0.643734i
$699$	−29314.6	+	13387.5i	−1.58624	+	0.724411i
$700$	−14695.2	+	7278.25i	−0.793465	+	0.392988i
$701$	−14969.0	−	12970.7i	−0.806521	−	0.698855i	0.150583	−	0.988597i	$-0.451885\pi$
$701$	−14969.0	−	12970.7i	−0.806521	−	0.698855i	−0.957105	+	0.289743i	$0.906430\pi$
$702$	−9230.45	+	12743.5i	−0.496269	+	0.685147i
$703$	−2656.55	+	780.034i	−0.142523	+	0.0418486i
$704$	−18244.0	+	25576.8i	−0.976701	+	1.36926i
$705$	25218.7	−	16207.1i	1.34722	−	0.865808i
$706$	−3143.71	−	632.243i	−0.167585	−	0.0337037i
$707$	−1842.40	+	264.898i	−0.0980067	+	0.0140912i
$708$	8093.33	−	31158.3i	0.429613	−	1.65395i
$709$	−15908.9	−	2287.35i	−0.842695	−	0.121161i	−0.292570	−	0.956244i	$-0.594511\pi$
$709$	−15908.9	−	2287.35i	−0.842695	−	0.121161i	−0.550124	+	0.835083i	$0.685420\pi$
$710$	16386.3	−	31165.1i	0.866150	−	1.64733i
$711$	27828.0	+	32115.2i	1.46784	+	1.69397i
$712$	−27864.7	+	7454.37i	−1.46668	+	0.392366i
$713$	−5232.88	+	11159.5i	−0.274857	+	0.586154i
$714$	−1292.10	−	14791.5i	−0.0677252	−	0.775294i
$715$	−42989.1	+	37250.2i	−2.24853	+	1.94836i
$716$	2247.51	−	5361.64i	0.117309	−	0.279852i
$717$	−31748.2	−	4564.70i	−1.65364	−	0.237757i
$718$	−7674.77	+	21609.2i	−0.398913	+	1.12319i
$719$	−1728.72	−	12023.5i	−0.0896665	−	0.623645i	−0.984255	−	0.176754i	$-0.943440\pi$
$719$	−1728.72	−	12023.5i	−0.0896665	−	0.623645i	0.894589	−	0.446891i	$-0.147469\pi$
$720$	−2792.03	−	44306.6i	−0.144518	−	2.29334i
$721$	18028.2	−	11586.0i	0.931213	−	0.598454i
$722$	−17381.3	−	30674.1i	−0.895934	−	1.58112i
$723$	5314.33	+	18098.9i	0.273364	+	0.930991i
$724$	5369.34	+	3216.59i	0.275622	+	0.165115i
$725$	12066.7	+	10455.8i	0.618132	+	0.535614i
$726$	−20491.4	−	52406.4i	−1.04753	−	2.67904i
$727$	8548.04	+	18717.6i	0.436079	+	0.954879i	0.992301	+	0.123846i	$0.0395229\pi$
$727$	8548.04	+	18717.6i	0.436079	+	0.954879i	−0.556223	+	0.831033i	$0.687750\pi$
$728$	10206.2	+	9285.48i	0.519595	+	0.472723i
$729$	−30534.9	−	8965.87i	−1.55134	−	0.455513i
$730$	8583.50	−	2009.16i	0.435191	−	0.101866i
$731$	485.780	+	221.848i	0.0245789	+	0.0112248i
$732$	−100.379	−	3188.98i	−0.00506847	−	0.161022i
$733$	−6087.24	+	9471.93i	−0.306736	+	0.477290i	−0.960062	−	0.279786i	$-0.909737\pi$
$733$	−6087.24	+	9471.93i	−0.306736	+	0.477290i	0.653327	+	0.757076i	$0.273373\pi$
$734$	4061.72	+	3935.88i	0.204252	+	0.197924i
$735$	30135.7			1.51234
$736$	19755.9	+	2897.08i	0.989418	+	0.145092i
$737$	−55577.7			−2.77779
$738$	−5767.25	−	5588.57i	−0.287663	−	0.278751i
$739$	−52.1505	+	81.1478i	−0.00259592	+	0.00403934i	−0.842549	−	0.538620i	$-0.818946\pi$
$739$	−52.1505	+	81.1478i	−0.00259592	+	0.00403934i	0.839953	+	0.542659i	$0.182582\pi$
$740$	−87.3736	−	2775.81i	−0.00434043	−	0.137893i
$741$	−54966.4	−	25102.3i	−2.72502	−	1.24448i
$742$	12767.5	−	2988.52i	0.631685	−	0.147860i
$743$	22844.7	+	6707.82i	1.12798	+	0.331206i	0.791915	−	0.610631i	$-0.209084\pi$
$743$	22844.7	+	6707.82i	1.12798	+	0.331206i	0.336069	+	0.941837i	$0.390902\pi$
$744$	15285.4	+	13906.5i	0.753210	+	0.685264i
$745$	17006.5	+	37239.1i	0.836337	+	1.83132i
$746$	4629.46	+	11839.7i	0.227207	+	0.581078i
$747$	37179.2	+	32215.9i	1.82104	+	1.57794i
$748$	23591.1	+	14132.6i	1.15318	+	0.690829i
$749$	−958.152	−	3263.17i	−0.0467425	−	0.159190i
$750$	10684.5	+	18855.8i	0.520191	+	0.918021i
$751$	−12462.3	+	8009.05i	−0.605535	+	0.389154i	−0.807180	−	0.590305i	$-0.799007\pi$
$751$	−12462.3	+	8009.05i	−0.605535	+	0.389154i	0.201646	+	0.979459i	$0.435371\pi$
$752$	13441.5	−	847.030i	0.651809	−	0.0410745i
$753$	−4009.72	−	27888.2i	−0.194054	−	1.34967i
$754$	4496.19	−	12659.6i	0.217164	−	0.611451i
$755$	1833.68	+	263.643i	0.0883898	+	0.0127085i
$756$	3708.95	−	8848.05i	0.178430	−	0.425662i
$757$	12990.2	−	11256.1i	0.623694	−	0.540434i	−0.284664	−	0.958627i	$-0.591882\pi$
$757$	12990.2	−	11256.1i	0.623694	−	0.540434i	0.908358	+	0.418193i	$0.137337\pi$
$758$	3314.23	+	37940.1i	0.158810	+	1.81800i
$759$	−36644.8	+	41439.5i	−1.75247	+	1.98176i
$760$	52961.5	−	14168.3i	2.52778	−	0.676233i
$761$	−26553.9	−	30644.8i	−1.26489	−	1.45976i	−0.828492	−	0.560001i	$-0.810801\pi$
$761$	−26553.9	−	30644.8i	−1.26489	−	1.45976i	−0.436395	−	0.899755i	$-0.643745\pi$
$762$	2546.28	−	4842.78i	0.121053	−	0.230230i
$763$	−13963.9	−	2007.70i	−0.662552	−	0.0952605i
$764$	−4181.57	+	16098.5i	−0.198016	+	0.762334i
$765$	−38464.7	+	5530.38i	−1.81790	+	0.261374i
$766$	−19985.3	−	4019.31i	−0.942686	−	0.189587i
$767$	22029.6	−	14157.6i	1.03708	−	0.666494i
$768$	14420.3	−	30211.6i	0.677538	−	1.41949i
$769$	13577.9	−	3986.83i	0.636711	−	0.186955i	0.0525829	−	0.998617i	$-0.483255\pi$
$769$	13577.9	−	3986.83i	0.636711	−	0.186955i	0.584128	+	0.811661i	$0.301436\pi$
$770$	20344.8	−	28087.9i	0.952176	−	1.31457i
$771$	−15428.6	−	13368.9i	−0.720682	−	0.624475i
$772$	−25187.3	+	12474.8i	−1.17424	+	0.581577i
$773$	268.983	−	122.841i	0.0125157	−	0.00571574i	−0.409147	−	0.912468i	$-0.634174\pi$
$773$	268.983	−	122.841i	0.0125157	−	0.00571574i	0.421663	+	0.906753i	$0.361447\pi$
$774$	656.497	+	848.807i	0.0304875	+	0.0394182i
$775$	−19168.9	−	5628.49i	−0.888473	−	0.260879i
$776$	−4837.59	−	11309.3i	−0.223788	−	0.523172i
$777$	775.307	−	1697.68i	0.0357966	−	0.0783836i
$778$	−8624.80	−	480.610i	−0.397447	−	0.0221474i
$779$	5361.76	−	8343.06i	0.246604	−	0.383724i
$780$	38231.7	−	47033.7i	1.75502	−	2.15907i
$781$			43826.1i			2.00797i
$782$	1148.17	−	17440.3i	0.0525044	−	0.797524i
$783$	−9341.06			−0.426338
$784$	11827.7	+	6589.02i	0.538798	+	0.300156i
$785$	6945.76	+	4463.77i	0.315802	+	0.202954i
$786$	−1799.73	+	32297.1i	−0.0816720	+	1.46565i
$787$	28841.1	+	13171.3i	1.30632	+	0.596576i	0.942286	−	0.334810i	$-0.108672\pi$
$787$	28841.1	+	13171.3i	1.30632	+	0.596576i	0.364034	+	0.931386i	$0.381399\pi$
$788$	−35847.9	+	11763.0i	−1.62060	+	0.531776i
$789$	12181.3	−	41485.8i	0.549641	−	1.87191i
$790$	−32204.0	−	41637.7i	−1.45034	−	1.87519i
$791$	−5174.15	−	11329.8i	−0.232581	−	0.509281i
$792$	28740.8	+	47194.7i	1.28947	+	2.11741i
$793$	1699.60	−	1961.44i	0.0761090	−	0.0878344i
$794$	16416.0	+	11890.5i	0.733730	+	0.531458i
$795$	−16228.1	−	55268.0i	−0.723966	−	2.46560i
$796$	−5256.15	−	7639.13i	−0.234044	−	0.340153i
$797$	4832.18	+	7519.02i	0.214761	+	0.334175i	0.931874	−	0.362782i	$-0.118173\pi$
$797$	4832.18	+	7519.02i	0.214761	+	0.334175i	−0.717113	+	0.696957i	$0.754537\pi$
$798$	36119.9	+	7264.21i	1.60229	+	0.322243i
$799$	−1677.78	−	11669.2i	−0.0742873	−	0.516679i
$800$	235.165	+	32363.5i	0.0103929	+	1.43028i
$801$	−7220.07	+	50216.7i	−0.318488	+	2.21513i
$802$	−18002.8	−	9465.68i	−0.792645	−	0.416764i
$803$	−8292.51	+	7185.50i	−0.364429	+	0.315779i
$804$	58324.6	−	10268.2i	2.55840	−	0.450411i
$805$	−21785.3	−	3356.57i	−0.953829	−	0.146961i
$806$	1462.83	+	16745.9i	0.0639279	+	0.731824i
$807$	9446.97	+	10902.4i	0.412081	+	0.475566i
$808$	−1119.94	+	3498.64i	−0.0487614	+	0.152329i
$809$	−1952.07	+	13577.0i	−0.0848346	+	0.590038i	0.902416	+	0.430865i	$0.141792\pi$
$809$	−1952.07	+	13577.0i	−0.0848346	+	0.590038i	−0.987251	+	0.159172i	$0.949117\pi$
$810$	10204.4	+	3624.20i	0.442647	+	0.157211i
$811$	8283.02	−	1190.92i	0.358639	−	0.0515645i	0.0393594	−	0.999225i	$-0.487468\pi$
$811$	8283.02	−	1190.92i	0.358639	−	0.0515645i	0.319279	+	0.947661i	$0.396559\pi$
$812$	−910.053	+	8140.33i	−0.0393308	+	0.351810i
$813$	31863.5	+	49580.6i	1.37454	+	2.13883i
$814$	1704.16	+	3007.46i	0.0733794	+	0.129498i
$815$	−57666.6	+	16932.4i	−2.47849	+	0.727751i
$816$	−27368.2	−	10472.6i	−1.17411	−	0.449282i
$817$	−867.790	+	1001.48i	−0.0371605	+	0.0428855i
$818$	−20325.5	+	7947.48i	−0.868784	+	0.339703i
$819$	22075.5	−	10081.5i	0.941856	−	0.430131i
$820$	6747.71	+	7309.36i	0.287366	+	0.311285i
$821$	7379.64	−	25132.7i	0.313704	−	1.06838i	−0.640185	−	0.768220i	$-0.721142\pi$
$821$	7379.64	−	25132.7i	0.313704	−	1.06838i	0.953890	−	0.300158i	$-0.0970393\pi$
$822$	−32492.7	+	7605.64i	−1.37873	+	0.322722i
$823$	6743.59	−	14766.4i	0.285622	−	0.625425i	−0.711379	−	0.702808i	$-0.751929\pi$
$823$	6743.59	−	14766.4i	0.285622	−	0.625425i	0.997001	+	0.0773832i	$0.0246565\pi$
$824$	−5004.30	−	41996.9i	−0.211569	−	1.77552i
$825$	−75429.8	−	48475.8i	−3.18319	−	2.04571i
$826$	−11110.9	+	11466.1i	−0.468035	+	0.482999i
$827$			3168.40i			0.133224i	0.997779	+	0.0666120i	$0.0212190\pi$
$827$			3168.40i			0.133224i	−0.997779	+	0.0666120i	$0.978781\pi$
$828$	18350.5	−	29943.5i	0.770198	−	1.25677i
$829$		−	45377.9i		−	1.90113i	−0.310521	−	0.950567i	$-0.600503\pi$
$829$		−	45377.9i		−	1.90113i	0.310521	−	0.950567i	$-0.399497\pi$
$830$	−43762.5	−	42406.7i	−1.83014	−	1.77344i
$831$	−28984.4	−	18627.2i	−1.20994	−	0.777580i
$832$	25288.9	−	10100.7i	1.05377	−	0.420887i
$833$	4923.24	−	10780.4i	0.204778	−	0.448401i
$834$	−2907.90	−	12423.1i	−0.120734	−	0.515798i
$835$	−5089.14	+	17332.0i	−0.210918	+	0.718322i
$836$	−50139.9	+	46287.2i	−2.07431	+	1.91492i
$837$	10631.8	−	4855.38i	0.439055	−	0.200510i
$838$	4605.36	+	11778.1i	0.189844	+	0.485523i
$839$	7890.97	−	9106.67i	0.324704	−	0.374728i	−0.569804	−	0.821781i	$-0.692981\pi$
$839$	7890.97	−	9106.67i	0.324704	−	0.374728i	0.894508	+	0.447052i	$0.147526\pi$
$840$	−16161.0	+	33235.0i	−0.663818	+	1.36514i
$841$	−15749.0	+	4624.33i	−0.645742	+	0.189607i
$842$	12422.4	−	7039.06i	0.508436	−	0.288102i
$843$	2058.45	+	3203.02i	0.0841007	+	0.130863i
$844$	−1471.81	+	13165.2i	−0.0600257	+	0.536924i
$845$	10900.0	−	1567.18i	0.443752	−	0.0638019i
$846$	7928.03	−	22322.3i	0.322188	−	0.907159i
$847$	−3971.75	+	27624.1i	−0.161123	+	1.12063i
$848$	5714.83	−	25239.9i	0.231425	−	1.02210i
$849$	36956.0	+	42649.5i	1.49391	+	1.72406i
$850$	28222.3	−	2465.34i	1.13884	−	0.0994828i
$851$	1206.32	−	1836.13i	0.0485922	−	0.0739622i
$852$	−8097.02	−	45992.2i	−0.325586	−	1.84937i
$853$	15938.9	−	13811.2i	0.639787	−	0.554379i	−0.273409	−	0.961898i	$-0.588151\pi$
$853$	15938.9	−	13811.2i	0.639787	−	0.554379i	0.913197	+	0.407519i	$0.133606\pi$
$854$	−736.428	+	1400.61i	−0.0295083	+	0.0561218i
$855$	13722.9	−	95445.2i	0.548906	−	3.81773i
$856$	−6618.62	−	1115.70i	−0.264275	−	0.0445489i
$857$	4511.16	+	31375.8i	0.179811	+	1.25061i	0.857198	+	0.514987i	$0.172203\pi$
$857$	4511.16	+	31375.8i	0.179811	+	1.25061i	−0.677387	+	0.735627i	$0.736888\pi$
$858$	−14874.9	+	73962.4i	−0.591864	+	2.94293i
$859$	−2311.72	−	3597.10i	−0.0918216	−	0.142877i	0.792304	−	0.610127i	$-0.208881\pi$
$859$	−2311.72	−	3597.10i	−0.0918216	−	0.142877i	−0.884126	+	0.467249i	$0.845245\pi$
$860$	−753.449	−	1095.04i	−0.0298749	−	0.0434192i
$861$	1883.43	+	6414.38i	0.0745496	+	0.253893i
$862$	902.294	−	1245.70i	0.0356523	−	0.0492214i
$863$	−21710.9	+	25055.7i	−0.856369	+	0.988303i	−0.999999	−	0.00132880i	$-0.999577\pi$
$863$	−21710.9	+	25055.7i	−0.856369	+	0.988303i	0.143630	+	0.989631i	$0.454122\pi$
$864$	−12503.1	−	14219.2i	−0.492319	−	0.559893i
$865$	−13493.3	−	29546.2i	−0.530388	−	1.16139i
$866$	−9628.06	+	7446.68i	−0.377800	+	0.292204i
$867$	4086.12	−	13916.1i	0.160060	−	0.545114i
$868$	−3195.45	−	9738.19i	−0.124955	−	0.380802i
$869$	59597.6	+	27217.3i	2.32648	+	1.06247i
$870$	35926.0	+	2001.95i	1.40001	+	0.0780142i
$871$	40526.3	+	26044.6i	1.57656	+	1.01319i
$872$	−15615.0	+	23051.3i	−0.606411	+	0.895200i
$873$	−21634.8			−0.838746
$874$	40720.2	+	14925.9i	1.57595	+	0.577660i
$875$		−	10748.9i		−	0.415290i
$876$	7374.83	−	9072.72i	0.284443	−	0.349930i
$877$	−195.514	+	304.226i	−0.00752799	+	0.0117138i	−0.844997	−	0.534771i	$-0.820398\pi$
$877$	−195.514	+	304.226i	−0.00752799	+	0.0117138i	0.837469	+	0.546485i	$0.184034\pi$
$878$	1300.32	−	23335.0i	0.0499816	−	0.896946i
$879$	16354.6	−	35811.6i	0.627562	−	1.37417i
$880$	−32293.7	−	60350.7i	−1.23707	−	2.31184i
$881$	30114.2	+	8842.34i	1.15162	+	0.338145i	0.801170	−	0.598437i	$-0.204211\pi$
$881$	30114.2	+	8842.34i	1.15162	+	0.338145i	0.350447	+	0.936582i	$0.386030\pi$
$882$	18836.7	−	14568.9i	0.719119	−	0.556192i
$883$	8292.14	−	3786.90i	0.316028	−	0.144325i	−0.251085	−	0.967965i	$-0.580787\pi$
$883$	8292.14	−	3786.90i	0.316028	−	0.144325i	0.567113	+	0.823640i	$0.308060\pi$
$884$	−10579.4	−	21360.4i	−0.402516	−	0.812703i
$885$	53006.0	+	45930.0i	2.01331	+	1.74454i
$886$	−33176.0	−	24030.2i	−1.25798	−	0.911184i
$887$	19057.3	−	5595.74i	0.721401	−	0.211822i	0.0996334	−	0.995024i	$-0.468233\pi$
$887$	19057.3	−	5595.74i	0.721401	−	0.211822i	0.621768	+	0.783202i	$0.286415\pi$
$888$	−2344.03	−	2841.26i	−0.0885816	−	0.107372i
$889$	−2282.86	+	1467.10i	−0.0861243	+	0.0553487i
$890$	12390.6	−	61609.9i	0.466667	−	2.32041i
$891$	−13341.3	+	1918.20i	−0.501630	+	0.0721234i
$892$	−12360.4	+	47585.9i	−0.463965	+	1.78621i
$893$	28955.6	+	4163.19i	1.08507	+	0.156009i
$894$	48058.7	+	25268.7i	1.79790	+	0.945316i
$895$	8294.57	+	9572.45i	0.309784	+	0.357510i
$896$	−13609.6	+	9510.59i	−0.507437	+	0.354605i
$897$	46140.0	−	13044.6i	1.71747	−	0.485558i
$898$	5189.96	−	453.365i	0.192863	−	0.0168474i
$899$	−7541.54	+	6534.78i	−0.279782	+	0.242433i
$900$	52498.1	+	22006.3i	1.94437	+	0.815046i
$901$	−22422.1	−	3223.81i	−0.829066	−	0.119202i
$902$	−11667.9	−	4143.98i	−0.430706	−	0.152970i
$903$	−127.125	−	884.172i	−0.00468488	−	0.0325841i
$904$	−24574.4	−	594.822i	−0.904130	−	0.0218844i
$905$	−11471.9	+	7372.53i	−0.421368	+	0.270797i
$906$	2137.67	−	1211.30i	0.0783879	−	0.0444180i
$907$	−12445.0	−	42383.9i	−0.455601	−	1.55164i	−0.792366	−	0.610046i	$-0.791151\pi$
$907$	−12445.0	−	42383.9i	−0.455601	−	1.55164i	0.336765	−	0.941589i	$-0.390667\pi$
$908$	−11423.0	−	6843.12i	−0.417495	−	0.250107i
$909$	4883.01	+	4231.15i	0.178173	+	0.154388i
$910$	−27997.5	+	10947.3i	−1.01990	+	0.398791i
$911$	−5531.03	−	12111.3i	−0.201154	−	0.440465i	0.781992	−	0.623288i	$-0.214204\pi$
$911$	−5531.03	−	12111.3i	−0.201154	−	0.440465i	−0.983146	+	0.182823i	$0.941476\pi$
$912$	44066.4	−	57838.5i	1.59998	−	2.10003i
$913$	72776.9	+	21369.2i	2.63808	+	0.774609i
$914$	−5362.24	−	22908.5i	−0.194056	−	0.829043i
$915$	6323.09	+	2887.66i	0.228453	+	0.104331i
$916$	5672.85	−	178.563i	0.204625	−	0.00644094i
$917$	8673.60	−	13496.4i	0.312353	−	0.486030i
$918$	−11533.8	+	11902.6i	−0.414676	+	0.427934i
$919$	16534.0			0.593477			0.296739	−	0.954959i	$-0.404101\pi$
$919$	16534.0			0.593477			0.296739	+	0.954959i	$0.404101\pi$
$920$	−24759.4	+	35769.1i	−0.887274	+	1.28182i
$921$	47079.3			1.68438
$922$	−14455.8	+	14918.0i	−0.516353	+	0.532862i
$923$	20537.6	−	31957.2i	0.732400	−	1.13964i
$924$	−1447.17	−	45975.9i	−0.0515244	−	1.63690i
$925$	3239.19	+	1479.29i	0.115139	+	0.0525823i
$926$	−6051.61	−	25853.6i	−0.214761	−	0.917496i
$927$	−71375.3	−	20957.7i	−2.52888	−	0.742547i
$928$	13662.6	+	8640.77i	0.483293	+	0.305654i
$929$	7460.63	+	16336.5i	0.263483	+	0.576946i	0.994419	−	0.105499i	$-0.0336439\pi$
$929$	7460.63	+	16336.5i	0.263483	+	0.576946i	−0.730937	+	0.682445i	$0.760917\pi$
$930$	−41930.8	+	16395.4i	−1.47846	+	0.578091i
$931$	22224.8	+	19257.9i	0.782374	+	0.677931i
$932$	16211.0	−	27060.5i	0.569753	−	0.951069i
$933$	5283.11	+	17992.6i	0.185382	+	0.631353i
$934$	16294.0	−	9232.89i	0.570830	−	0.323458i
$935$	−50403.7	+	32392.5i	−1.76297	+	1.13299i
$936$	1158.98	−	47881.9i	0.0404726	−	1.67208i
$937$	−4200.15	−	29212.7i	−0.146439	−	1.01850i	−0.921989	−	0.387216i	$-0.873437\pi$
$937$	−4200.15	−	29212.7i	−0.146439	−	1.01850i	0.775550	−	0.631286i	$-0.217472\pi$
$938$	−27678.2	−	9830.24i	−0.963460	−	0.342184i
$939$	−82354.7	−	11840.8i	−2.86213	−	0.411513i
$940$	−11343.7	+	27061.6i	−0.393608	+	0.938991i
$941$	1824.86	−	1581.25i	0.0632186	−	0.0547792i	−0.622678	−	0.782478i	$-0.713956\pi$
$941$	1824.86	−	1581.25i	0.0632186	−	0.0547792i	0.685897	+	0.727699i	$0.259410\pi$
$942$	10908.9	−	952.943i	0.377317	−	0.0329602i
$943$	1041.42	+	7800.19i	0.0359631	+	0.269363i
$944$	10761.5	+	29616.2i	0.371035	+	1.02111i
$945$	13688.1	+	15796.9i	0.471190	+	0.543782i
$946$	1464.37	+	769.952i	0.0503286	+	0.0264623i
$947$	−25995.2	−	3737.54i	−0.892006	−	0.128251i	−0.318954	−	0.947770i	$-0.603332\pi$
$947$	−25995.2	−	3737.54i	−0.892006	−	0.128251i	−0.573052	+	0.819519i	$0.694241\pi$
$948$	−67571.7	−	17551.7i	−2.31501	−	0.601321i
$949$	9414.00	−	1353.53i	0.322014	−	0.0462986i
$950$	−13860.1	+	68916.8i	−0.473349	+	2.35364i
$951$	803.619	−	516.455i	0.0274018	−	0.0176101i
$952$	9248.89	+	11210.8i	0.314872	+	0.381665i
$953$	33967.7	−	9973.80i	1.15459	−	0.339017i	0.352259	−	0.935902i	$-0.385413\pi$
$953$	33967.7	−	9973.80i	1.15459	−	0.339017i	0.802326	+	0.596885i	$0.203595\pi$
$954$	−36862.6	−	26700.5i	−1.25102	−	0.906143i
$955$	−27386.6	−	23730.6i	−0.927967	−	0.804088i
$956$	28134.0	−	13934.3i	0.951799	−	0.471408i
$957$	−40738.8	+	18604.8i	−1.37607	+	0.628431i
$958$	2145.80	−	1659.64i	0.0723672	−	0.0559713i
$959$	15880.5	+	4662.93i	0.534732	+	0.157011i
$960$	45039.8	+	57367.2i	1.51422	+	1.92866i
$961$	−7188.72	+	15741.1i	−0.241305	+	0.528384i
$962$	166.704	−	2991.59i	0.00558705	−	0.100263i
$963$	−6382.46	+	9931.30i	−0.213574	+	0.332328i
$964$	−14327.4	−	11646.2i	−0.478688	−	0.389106i
$965$		−	61237.2i		−	2.04279i
$966$	−25579.0	+	14155.7i	−0.851958	+	0.471484i
$967$	−29837.7			−0.992259			−0.496130	−	0.868248i	$-0.665246\pi$
$967$	−29837.7			−0.992259			−0.496130	+	0.868248i	$0.665246\pi$
$968$	45601.3	+	30890.5i	1.51413	+	1.02568i
$969$	−53544.4	−	34410.9i	−1.77512	−	1.14080i
$970$	26757.6	+	1491.05i	0.885707	+	0.0493553i
$971$	15040.5	+	6868.76i	0.497088	+	0.227012i	0.648151	−	0.761512i	$-0.275542\pi$
$971$	15040.5	+	6868.76i	0.497088	+	0.227012i	−0.151063	+	0.988524i	$0.548270\pi$
$972$	35113.6	−	11522.0i	1.15871	−	0.380215i
$973$	−1782.80	+	6071.66i	−0.0587399	+	0.200050i
$974$	5545.96	−	4289.44i	0.182448	−	0.141111i
$975$	32285.5	+	70695.4i	1.06048	+	2.32212i
$976$	1850.32	+	2515.87i	0.0606838	+	0.0825112i
$977$	9157.85	−	10568.7i	0.299883	−	0.346083i	−0.585731	−	0.810505i	$-0.699193\pi$
$977$	9157.85	−	10568.7i	0.299883	−	0.346083i	0.885614	+	0.464422i	$0.153738\pi$
$978$	−46759.7	+	64556.3i	−1.52885	+	2.11072i
$979$	22037.3	+	75052.2i	0.719423	+	2.45013i
$980$	−24301.1	+	16720.5i	−0.792111	+	0.545017i
$981$	26475.2	+	41196.3i	0.861661	+	1.34077i
$982$	−7287.86	+	36237.5i	−0.236828	+	1.17758i
$983$	−235.777	−	1639.86i	−0.00765016	−	0.0532080i	0.985639	−	0.168867i	$-0.0540110\pi$
$983$	−235.777	−	1639.86i	−0.00765016	−	0.0532080i	−0.993289	+	0.115659i	$0.963102\pi$
$984$	13010.2	+	2193.12i	0.421493	+	0.0710510i
$985$	11698.1	−	81362.3i	0.378410	−	2.63190i
$986$	6585.35	−	12524.7i	0.212698	−	0.404531i
$987$	−14902.8	+	12913.4i	−0.480610	+	0.416451i
$988$	58252.1	−	10255.4i	1.87576	−	0.330230i
$989$	10.5914	−	1051.45i	0.000340531	−	0.0338059i
$990$	−119932.	+	10476.6i	−3.85019	+	0.336331i
$991$	−10917.1	−	12599.0i	−0.349942	−	0.403855i	0.553303	−	0.832980i	$-0.313367\pi$
$991$	−10917.1	−	12599.0i	−0.349942	−	0.403855i	−0.903245	+	0.429125i	$0.858822\pi$
$992$	−20041.8	−	2733.09i	−0.641460	−	0.0874756i
$993$	6923.13	−	48151.4i	0.221248	−	1.53881i
$994$	−7751.69	+	21825.8i	−0.247353	+	0.696451i
$995$	19996.8	−	2875.11i	0.637127	−	0.0916050i
$996$	−80321.9	−	8979.63i	−2.55532	−	0.285673i
$997$	16343.3	+	25430.6i	0.519154	+	0.807820i	0.997523	−	0.0703391i	$-0.0224081\pi$
$997$	16343.3	+	25430.6i	0.519154	+	0.807820i	−0.478369	+	0.878159i	$0.658772\pi$
$998$	−18274.9	+	10355.4i	−0.579641	+	0.328450i
$999$	−1998.93	+	586.939i	−0.0633067	+	0.0185885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.p.a.13.17	✓	700
8.5	even	2	inner	184.4.p.a.13.24	yes	700
23.16	even	11	inner	184.4.p.a.85.24	yes	700
184.85	even	22	inner	184.4.p.a.85.17	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.p.a.13.17	✓	700	1.1	even	1	trivial
184.4.p.a.13.24	yes	700	8.5	even	2	inner
184.4.p.a.85.17	yes	700	184.85	even	22	inner
184.4.p.a.85.24	yes	700	23.16	even	11	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.p (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03122 - 1.96829i) q^{2} +(4.41866 - 6.87557i) q^{3} +(0.251690 + 7.99604i) q^{4} +(-15.8545 - 7.24050i) q^{5} +(-22.5084 + 5.26859i) q^{6} +(11.0008 + 3.23011i) q^{7} +(15.2273 - 16.7371i) q^{8} +(-16.5327 - 36.2016i) q^{9} +(17.9525 + 45.9132i) q^{10} +(-46.3735 - 40.1829i) q^{11} +(56.0895 + 33.6013i) q^{12} +(14.9844 + 51.0321i) q^{13} +(-15.9871 - 28.2137i) q^{14} +(-119.838 + 77.0153i) q^{15} +(-63.8733 + 4.02504i) q^{16} +(7.97272 + 55.4515i) q^{17} +(-37.6736 + 106.075i) q^{18} +(-137.596 - 19.7833i) q^{19} +(53.9049 - 128.595i) q^{20} +(70.8175 - 61.3637i) q^{21} +(15.1033 + 172.897i) q^{22} +(93.3897 - 58.6972i) q^{23} +(-47.7930 - 178.652i) q^{24} +(117.082 + 135.120i) q^{25} +(70.0093 - 133.151i) q^{26} +(-103.534 - 14.8860i) q^{27} +(-23.0593 + 88.7755i) q^{28} +(88.3945 - 12.7092i) q^{29} +(395.006 + 79.4411i) q^{30} +(-94.0027 + 60.4119i) q^{31} +(137.663 + 117.545i) q^{32} +(-481.190 + 141.290i) q^{33} +(92.9501 - 128.327i) q^{34} +(-151.024 - 130.863i) q^{35} +(285.309 - 141.308i) q^{36} +(18.1173 - 8.27390i) q^{37} +(240.548 + 311.012i) q^{38} +(417.086 + 122.467i) q^{39} +(-362.605 + 155.105i) q^{40} +(-29.6369 + 64.8957i) q^{41} +(-264.627 - 14.7461i) q^{42} +(5.15378 - 8.01944i) q^{43} +(309.632 - 380.918i) q^{44} +693.663i q^{45} +(-305.228 - 64.5910i) q^{46} -210.440 q^{47} +(-254.560 + 456.951i) q^{48} +(-177.967 - 114.372i) q^{49} +(28.1357 - 504.909i) q^{50} +(416.490 + 190.204i) q^{51} +(-404.283 + 132.660i) q^{52} +(-113.920 + 387.976i) q^{53} +(181.001 + 234.022i) q^{54} +(444.284 + 972.847i) q^{55} +(221.574 - 134.935i) q^{56} +(-744.011 + 858.635i) q^{57} +(-204.564 - 148.171i) q^{58} +(-138.713 - 472.412i) q^{59} +(-645.980 - 938.847i) q^{60} +(-26.3818 - 41.0509i) q^{61} +(309.848 + 62.3147i) q^{62} +(-64.9372 - 451.648i) q^{63} +(-48.2607 - 509.720i) q^{64} +(131.928 - 917.581i) q^{65} +(1255.50 + 660.129i) q^{66} +(684.520 - 593.140i) q^{67} +(-441.386 + 77.7068i) q^{68} +(9.08064 - 901.471i) q^{69} +(49.1864 + 563.069i) q^{70} +(-467.724 - 539.782i) q^{71} +(-857.658 - 274.542i) q^{72} +(25.4487 - 177.000i) q^{73} +(-53.0857 - 18.8540i) q^{74} +(1446.37 - 207.957i) q^{75} +(123.557 - 1105.20i) q^{76} +(-380.349 - 591.834i) q^{77} +(-606.141 - 1069.70i) q^{78} +(-1024.50 + 300.821i) q^{79} +(1041.82 + 398.660i) q^{80} +(143.847 - 166.008i) q^{81} +(187.932 - 73.4834i) q^{82} +(-1124.41 + 513.501i) q^{83} +(508.491 + 550.815i) q^{84} +(275.093 - 936.881i) q^{85} +(-26.2530 + 6.14511i) q^{86} +(303.203 - 663.921i) q^{87} +(-1378.69 + 164.283i) q^{88} +(-1072.40 - 689.188i) q^{89} +(1365.33 - 1408.98i) q^{90} +609.793i q^{91} +(492.850 + 731.974i) q^{92} +913.262i q^{93} +(427.449 + 414.206i) q^{94} +(2038.27 + 1309.92i) q^{95} +(1416.48 - 427.119i) q^{96} +(225.825 - 494.488i) q^{97} +(136.372 + 582.605i) q^{98} +(-688.005 + 2343.13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 700 q - 7 q^{2} + 13 q^{4} - 52 q^{6} + 10 q^{7} - 46 q^{8} + 576 q^{9} + 35 q^{10} - 24 q^{12} + 77 q^{14} - 246 q^{15} - 27 q^{16} - 18 q^{17} - 230 q^{18} + 53 q^{20} + 182 q^{22} + 144 q^{23} + 154 q^{24}+ \cdots - 7727 q^{98}+O(q^{100}) \) 700 * q - 7 * q^2 + 13 * q^4 - 52 * q^6 + 10 * q^7 - 46 * q^8 + 576 * q^9 + 35 * q^10 - 24 * q^12 + 77 * q^14 - 246 * q^15 - 27 * q^16 - 18 * q^17 - 230 * q^18 + 53 * q^20 + 182 * q^22 + 144 * q^23 + 154 * q^24 + 1532 * q^25 + 50 * q^26 + 151 * q^28 + 39 * q^30 - 546 * q^31 + 53 * q^32 - 126 * q^33 - 1175 * q^34 + 2613 * q^36 + 60 * q^38 + 174 * q^39 - 1565 * q^40 - 18 * q^41 + 2983 * q^42 - 2596 * q^44 + 3645 * q^46 - 40 * q^47 - 3908 * q^48 - 2860 * q^49 + 1858 * q^50 - 1154 * q^52 - 432 * q^54 - 518 * q^55 + 4562 * q^56 - 126 * q^57 - 4499 * q^58 + 2651 * q^60 - 1540 * q^62 - 14 * q^63 - 158 * q^64 - 518 * q^65 + 2368 * q^66 - 1270 * q^68 - 2006 * q^70 - 1498 * q^71 + 2103 * q^72 - 18 * q^73 + 2216 * q^74 + 6852 * q^76 + 7956 * q^78 + 1834 * q^79 + 2362 * q^80 - 3268 * q^81 + 1098 * q^82 - 7971 * q^84 - 8759 * q^86 - 2154 * q^87 - 4495 * q^88 - 866 * q^89 - 13676 * q^90 - 10844 * q^92 - 12229 * q^94 + 722 * q^95 - 12211 * q^96 - 18 * q^97 - 7727 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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