LMFDB - Embedded newform 184.4.p.a.13.16

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			13.16
Character	$\chi$	$=$	184.13
Dual form			184.4.p.a.85.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14354 + 1.84532i) q^{2} +(0.182132 - 0.283403i) q^{3} +(1.18957 - 7.91106i) q^{4} +(2.56171 + 1.16989i) q^{5} +(0.132562 + 0.943579i) q^{6} +(-29.8765 - 8.77253i) q^{7} +(12.0486 + 19.1529i) q^{8} +(11.1691 + 24.4568i) q^{9} +(-7.64996 + 2.21946i) q^{10} +(41.7643 + 36.1890i) q^{11} +(-2.02536 - 1.77798i) q^{12} +(-23.4293 - 79.7928i) q^{13} +(80.2297 - 36.3275i) q^{14} +(0.798120 - 0.512921i) q^{15} +(-61.1699 - 18.8215i) q^{16} +(-10.9004 - 75.8137i) q^{17} +(-69.0721 - 31.8138i) q^{18} +(64.8138 + 9.31882i) q^{19} +(12.3024 - 18.8742i) q^{20} +(-7.92763 + 6.86933i) q^{21} +(-156.304 - 0.504056i) q^{22} +(107.156 - 26.1627i) q^{23} +(7.62241 + 0.0737452i) q^{24} +(-76.6639 - 88.4748i) q^{25} +(197.465 + 127.805i) q^{26} +(17.9686 + 2.58350i) q^{27} +(-104.940 + 225.919i) q^{28} +(101.769 - 14.6322i) q^{29} +(-0.764302 + 2.57226i) q^{30} +(161.236 - 103.620i) q^{31} +(165.852 - 72.5335i) q^{32} +(17.8627 - 5.24495i) q^{33} +(163.266 + 142.395i) q^{34} +(-66.2719 - 57.4250i) q^{35} +(206.766 - 59.2661i) q^{36} +(252.908 - 115.499i) q^{37} +(-156.128 + 99.6271i) q^{38} +(-26.8807 - 7.89289i) q^{39} +(8.45815 + 63.1596i) q^{40} +(96.1331 - 210.502i) q^{41} +(4.31709 - 29.3537i) q^{42} +(-42.6036 + 66.2924i) q^{43} +(335.975 - 287.351i) q^{44} +75.7179i q^{45} +(-181.416 + 253.819i) q^{46} -69.9143 q^{47} +(-16.4750 + 13.9077i) q^{48} +(527.098 + 338.745i) q^{49} +(327.597 + 48.1801i) q^{50} +(-23.4711 - 10.7189i) q^{51} +(-659.117 + 90.4317i) q^{52} +(-109.691 + 373.572i) q^{53} +(-43.2839 + 27.6200i) q^{54} +(64.6507 + 141.565i) q^{55} +(-191.950 - 677.917i) q^{56} +(14.4457 - 16.6712i) q^{57} +(-191.145 + 219.161i) q^{58} +(94.6186 + 322.241i) q^{59} +(-3.10833 - 6.92413i) q^{60} +(-338.361 - 526.499i) q^{61} +(-154.404 + 519.646i) q^{62} +(-119.144 - 828.665i) q^{63} +(-221.664 + 461.529i) q^{64} +(33.3300 - 231.816i) q^{65} +(-28.6108 + 44.2052i) q^{66} +(-79.1191 + 68.5571i) q^{67} +(-612.733 - 3.95198i) q^{68} +(12.1020 - 35.1335i) q^{69} +(248.024 + 0.799839i) q^{70} +(-183.655 - 211.949i) q^{71} +(-333.847 + 508.589i) q^{72} +(118.848 - 826.608i) q^{73} +(-328.987 + 714.276i) q^{74} +(-39.0370 + 5.61267i) q^{75} +(150.822 - 501.661i) q^{76} +(-930.302 - 1447.58i) q^{77} +(72.1850 - 32.6849i) q^{78} +(744.902 - 218.723i) q^{79} +(-134.680 - 119.777i) q^{80} +(-471.382 + 544.004i) q^{81} +(182.379 + 628.617i) q^{82} +(304.731 - 139.166i) q^{83} +(44.9132 + 70.8875i) q^{84} +(60.7703 - 206.965i) q^{85} +(-31.0083 - 220.718i) q^{86} +(14.3886 - 31.5066i) q^{87} +(-189.922 + 1235.93i) q^{88} +(-931.941 - 598.922i) q^{89} +(-139.724 - 162.305i) q^{90} +2589.46i q^{91} +(-79.5049 - 878.844i) q^{92} -64.5672i q^{93} +(149.865 - 129.015i) q^{94} +(155.132 + 99.6973i) q^{95} +(9.65076 - 60.2136i) q^{96} +(221.979 - 486.066i) q^{97} +(-1754.95 + 246.550i) q^{98} +(-418.600 + 1425.62i) 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 $

$2$	−2.14354	+	1.84532i	−0.757857	+	0.652420i
$2$	−2.14354	+	1.84532i	−0.757857	+	0.652420i
$3$	0.182132	−	0.283403i	0.0350513	−	0.0545409i	−0.823286	−	0.567627i	$-0.807862\pi$
$3$	0.182132	−	0.283403i	0.0350513	−	0.0545409i	0.858337	+	0.513086i	$0.171498\pi$
$4$	1.18957	−	7.91106i	0.148696	−	0.988883i
$5$	2.56171	+	1.16989i	0.229126	+	0.104638i	0.526670	−	0.850070i	$-0.323440\pi$
$5$	2.56171	+	1.16989i	0.229126	+	0.104638i	−0.297544	+	0.954708i	$0.596168\pi$
$6$	0.132562	+	0.943579i	0.00901969	+	0.0642024i
$7$	−29.8765	−	8.77253i	−1.61318	−	0.473672i	−0.654005	−	0.756490i	$-0.726913\pi$
$7$	−29.8765	−	8.77253i	−1.61318	−	0.473672i	−0.959174	+	0.282818i	$0.908731\pi$
$8$	12.0486	+	19.1529i	0.532477	+	0.846445i
$9$	11.1691	+	24.4568i	0.413669	+	0.905809i
$10$	−7.64996	+	2.21946i	−0.241913	+	0.0701855i
$11$	41.7643	+	36.1890i	1.14476	+	0.991944i	0.999997	+	0.00247846i	$0.000788919\pi$
$11$	41.7643	+	36.1890i	1.14476	+	0.991944i	0.144768	+	0.989466i	$0.453757\pi$
$12$	−2.02536	−	1.77798i	−0.0487226	−	0.0427717i
$13$	−23.4293	−	79.7928i	−0.499855	−	1.70235i	−0.692792	−	0.721138i	$-0.743619\pi$
$13$	−23.4293	−	79.7928i	−0.499855	−	1.70235i	0.192937	−	0.981211i	$-0.438199\pi$
$14$	80.2297	−	36.3275i	1.53159	−	0.693495i
$15$	0.798120	−	0.512921i	0.0137382	−	0.00882903i
$16$	−61.1699	−	18.8215i	−0.955779	−	0.294086i
$17$	−10.9004	−	75.8137i	−0.155513	−	1.08162i	−0.906775	−	0.421614i	$-0.861464\pi$
$17$	−10.9004	−	75.8137i	−0.155513	−	1.08162i	0.751262	−	0.660004i	$-0.229445\pi$
$18$	−69.0721	−	31.8138i	−0.904470	−	0.416588i
$19$	64.8138	+	9.31882i	0.782595	+	0.112520i	0.522020	−	0.852933i	$-0.325179\pi$
$19$	64.8138	+	9.31882i	0.782595	+	0.112520i	0.260575	+	0.965454i	$0.416088\pi$
$20$	12.3024	−	18.8742i	0.137545	−	0.211020i
$21$	−7.92763	+	6.86933i	−0.0823786	+	0.0713814i
$22$	−156.304	−	0.504056i	−1.51473	−	0.00488477i
$23$	107.156	−	26.1627i	0.971464	−	0.237187i
$23$	107.156	−	26.1627i	0.971464	−	0.237187i
$24$	7.62241	+	0.0737452i	0.0648299	+	0.000627216i
$25$	−76.6639	−	88.4748i	−0.613311	−	0.707799i
$26$	197.465	+	127.805i	1.48947	+	0.964023i
$27$	17.9686	+	2.58350i	0.128076	+	0.0184146i
$28$	−104.940	+	225.919i	−0.708279	+	1.52481i
$29$	101.769	−	14.6322i	0.651655	−	0.0936939i	0.191444	−	0.981503i	$-0.438683\pi$
$29$	101.769	−	14.6322i	0.651655	−	0.0936939i	0.460211	+	0.887810i	$0.347774\pi$
$30$	−0.764302	+	2.57226i	−0.00465139	+	0.0156543i
$31$	161.236	−	103.620i	0.934155	−	0.600345i	0.0174233	−	0.999848i	$-0.494454\pi$
$31$	161.236	−	103.620i	0.934155	−	0.600345i	0.916732	+	0.399503i	$0.130817\pi$
$32$	165.852	−	72.5335i	0.916212	−	0.400695i
$33$	17.8627	−	5.24495i	0.0942270	−	0.0276676i
$34$	163.266	+	142.395i	0.823527	+	0.718253i
$35$	−66.2719	−	57.4250i	−0.320057	−	0.277331i
$36$	206.766	−	59.2661i	0.957249	−	0.274380i
$37$	252.908	−	115.499i	1.12373	−	0.513189i	0.235169	−	0.971954i	$-0.424436\pi$
$37$	252.908	−	115.499i	1.12373	−	0.513189i	0.888557	+	0.458766i	$0.151708\pi$
$38$	−156.128	+	99.6271i	−0.666506	+	0.425307i
$39$	−26.8807	−	7.89289i	−0.110368	−	0.0324070i
$40$	8.45815	+	63.1596i	0.0334338	+	0.249660i
$41$	96.1331	−	210.502i	0.366182	−	0.801827i	−0.633425	−	0.773804i	$-0.718352\pi$
$41$	96.1331	−	210.502i	0.366182	−	0.801827i	0.999607	−	0.0280231i	$-0.00892118\pi$
$42$	4.31709	−	29.3537i	0.0158605	−	0.107842i
$43$	−42.6036	+	66.2924i	−0.151093	+	0.235105i	−0.908546	−	0.417784i	$-0.862807\pi$
$43$	−42.6036	+	66.2924i	−0.151093	+	0.235105i	0.757454	+	0.652889i	$0.226443\pi$
$44$	335.975	−	287.351i	1.15114	−	0.984540i
$45$			75.7179i			0.250830i
$46$	−181.416	+	253.819i	−0.581486	+	0.813557i
$47$	−69.9143			−0.216980			−0.108490	−	0.994098i	$-0.534602\pi$
$47$	−69.9143			−0.216980			−0.108490	+	0.994098i	$0.534602\pi$
$48$	−16.4750	+	13.9077i	−0.0495410	+	0.0418210i
$49$	527.098	+	338.745i	1.53673	+	0.987595i
$50$	327.597	+	48.1801i	0.926585	+	0.136274i
$51$	−23.4711	−	10.7189i	−0.0644434	−	0.0294303i
$52$	−659.117	+	90.4317i	−1.75775	+	0.241166i
$53$	−109.691	+	373.572i	−0.284286	+	0.968191i	0.686276	+	0.727341i	$0.259244\pi$
$53$	−109.691	+	373.572i	−0.284286	+	0.968191i	−0.970562	+	0.240850i	$0.922574\pi$
$54$	−43.2839	+	27.6200i	−0.109078	+	0.0696039i
$55$	64.6507	+	141.565i	0.158500	+	0.347067i
$56$	−191.950	−	677.917i	−0.458043	−	1.61769i
$57$	14.4457	−	16.6712i	0.0335679	−	0.0387395i
$58$	−191.145	+	219.161i	−0.432734	+	0.496160i
$59$	94.6186	+	322.241i	0.208785	+	0.711055i	0.995586	+	0.0938495i	$0.0299172\pi$
$59$	94.6186	+	322.241i	0.208785	+	0.711055i	−0.786802	+	0.617206i	$0.788265\pi$
$60$	−3.10833	−	6.92413i	−0.00668806	−	0.0148984i
$61$	−338.361	−	526.499i	−0.710207	−	1.10510i	−0.989449	−	0.144883i	$-0.953719\pi$
$61$	−338.361	−	526.499i	−0.710207	−	1.10510i	0.279242	−	0.960221i	$-0.409917\pi$
$62$	−154.404	+	519.646i	−0.316279	+	1.06444i
$63$	−119.144	−	828.665i	−0.238266	−	1.65717i
$64$	−221.664	+	461.529i	−0.432937	+	0.901424i
$65$	33.3300	−	231.816i	0.0636013	−	0.442357i
$66$	−28.6108	+	44.2052i	−0.0533598	+	0.0824437i
$67$	−79.1191	+	68.5571i	−0.144268	+	0.125009i	−0.724005	−	0.689795i	$-0.757701\pi$
$67$	−79.1191	+	68.5571i	−0.144268	+	0.125009i	0.579737	+	0.814804i	$0.303155\pi$
$68$	−612.733	−	3.95198i	−1.09272	−	0.00704776i
$69$	12.1020	−	35.1335i	0.0211147	−	0.0612982i
$70$	248.024	+	0.799839i	0.423494	+	0.00136570i
$71$	−183.655	−	211.949i	−0.306984	−	0.354278i	0.581205	−	0.813757i	$-0.302582\pi$
$71$	−183.655	−	211.949i	−0.306984	−	0.354278i	−0.888189	+	0.459479i	$0.848036\pi$
$72$	−333.847	+	508.589i	−0.546448	+	0.832470i
$73$	118.848	−	826.608i	0.190550	−	1.32530i	−0.640007	−	0.768369i	$-0.721068\pi$
$73$	118.848	−	826.608i	0.190550	−	1.32530i	0.830557	−	0.556934i	$-0.188022\pi$
$74$	−328.987	+	714.276i	−0.516810	+	1.12207i
$75$	−39.0370	+	5.61267i	−0.0601014	+	0.00864127i
$76$	150.822	−	501.661i	0.227638	−	0.757164i
$77$	−930.302	−	1447.58i	−1.37685	−	2.14243i
$78$	72.1850	−	32.6849i	0.104786	−	0.0474465i
$79$	744.902	−	218.723i	1.06086	−	0.311497i	0.295664	−	0.955292i	$-0.404459\pi$
$79$	744.902	−	218.723i	1.06086	−	0.311497i	0.765198	+	0.643795i	$0.222641\pi$
$80$	−134.680	−	119.777i	−0.188221	−	0.167394i
$81$	−471.382	+	544.004i	−0.646615	+	0.746233i
$82$	182.379	+	628.617i	0.245614	+	0.846575i
$83$	304.731	−	139.166i	0.402994	−	0.184041i	−0.203598	−	0.979055i	$-0.565263\pi$
$83$	304.731	−	139.166i	0.402994	−	0.184041i	0.606592	+	0.795013i	$0.292536\pi$
$84$	44.9132	+	70.8875i	0.0583385	+	0.0920769i
$85$	60.7703	−	206.965i	0.0775467	−	0.264100i
$86$	−31.0083	−	220.718i	−0.0388804	−	0.276752i
$87$	14.3886	−	31.5066i	0.0177312	−	0.0388260i
$88$	−189.922	+	1235.93i	−0.230065	+	1.49717i
$89$	−931.941	−	598.922i	−1.10995	−	0.713322i	−0.148668	−	0.988887i	$-0.547499\pi$
$89$	−931.941	−	598.922i	−1.10995	−	0.713322i	−0.961282	+	0.275565i	$0.911135\pi$
$90$	−139.724	−	162.305i	−0.163647	−	0.190093i
$91$			2589.46i			2.98296i
$92$	−79.5049	−	878.844i	−0.0900974	−	0.995933i
$93$		−	64.5672i		−	0.0719926i
$94$	149.865	−	129.015i	0.164440	−	0.141562i
$95$	155.132	+	99.6973i	0.167539	+	0.107671i
$96$	9.65076	−	60.2136i	0.0102602	−	0.0640159i
$97$	221.979	−	486.066i	0.232356	−	0.508789i	−0.757157	−	0.653233i	$-0.773412\pi$
$97$	221.979	−	486.066i	0.232356	−	0.508789i	0.989513	+	0.144444i	$0.0461394\pi$
$98$	−1754.95	+	246.550i	−1.80895	+	0.254136i
$99$	−418.600	+	1425.62i	−0.424958	+	1.44727i
$100$	−791.127	+	501.246i	−0.791127	+	0.501246i
$101$	−1161.42	+	530.401i	−1.14421	+	0.522544i	−0.895071	−	0.445924i	$-0.852875\pi$
$101$	−1161.42	+	530.401i	−1.14421	+	0.522544i	−0.249140	+	0.968467i	$0.580148\pi$
$102$	70.0912	−	20.3353i	0.0680398	−	0.0197402i
$103$	−497.361	+	573.985i	−0.475791	+	0.549092i	−0.942013	−	0.335576i	$-0.891069\pi$
$103$	−497.361	+	573.985i	−0.475791	+	0.549092i	0.466223	+	0.884667i	$0.345615\pi$
$104$	1245.97	−	1410.13i	1.17478	−	1.32956i
$105$	−28.3446	+	8.32274i	−0.0263443	+	0.00773539i
$106$	−454.235	−	1003.18i	−0.416219	−	0.919225i
$107$	−242.685	−	377.626i	−0.219264	−	0.341182i	0.714143	−	0.699999i	$-0.246816\pi$
$107$	−242.685	−	377.626i	−0.219264	−	0.341182i	−0.933408	+	0.358818i	$0.883180\pi$
$108$	41.8130	−	139.078i	0.0372543	−	0.123914i
$109$	837.724	−	120.447i	0.736142	−	0.105841i	0.235961	−	0.971762i	$-0.424176\pi$
$109$	837.724	−	120.447i	0.736142	−	0.105841i	0.500180	+	0.865921i	$0.333267\pi$
$110$	−399.815	−	184.150i	−0.346554	−	0.159618i
$111$	13.3298	−	92.7111i	0.0113983	−	0.0792770i
$112$	1662.43	+	1098.93i	1.40254	+	0.927139i
$113$	815.034	+	940.599i	0.678513	+	0.783045i	0.985683	−	0.168609i	$-0.0539276\pi$
$113$	815.034	+	940.599i	0.678513	+	0.783045i	−0.307170	+	0.951655i	$0.599382\pi$
$114$	−0.201205	+	62.3923i	−0.000165303	+	0.0512594i
$115$	305.111	+	58.3404i	0.247407	+	0.0473067i
$116$	5.30496	−	822.506i	0.00424615	−	0.658343i
$117$	1689.80	−	1464.22i	1.33523	−	1.15698i
$118$	−797.459	−	516.137i	−0.622136	−	0.402663i
$119$	−339.413	+	2360.67i	−0.261462	+	1.81851i
$120$	19.4401	+	9.10631i	0.0147886	+	0.00692741i
$121$	245.194	+	1705.36i	0.184218	+	1.28126i
$122$	1696.85	+	504.190i	1.25923	+	0.374158i
$123$	−42.1480	−	65.5836i	−0.0308972	−	0.0480770i
$124$	−627.943	−	1398.81i	−0.454766	−	1.01304i
$125$	−192.061	−	654.101i	−0.137428	−	0.468037i
$126$	1784.55	+	1556.42i	1.26175	+	1.10045i
$127$	−552.502	+	637.622i	−0.386037	+	0.445510i	−0.915194	−	0.403014i	$-0.867963\pi$
$127$	−552.502	+	637.622i	−0.386037	+	0.445510i	0.529157	+	0.848524i	$0.322508\pi$
$128$	−376.525	−	1398.35i	−0.260003	−	0.965608i
$129$	11.0280	+	24.1479i	0.00752683	+	0.0164815i
$130$	356.330	+	558.412i	0.240402	+	0.376738i
$131$	654.638	−	2229.49i	0.436611	−	1.48696i	−0.388213	−	0.921570i	$-0.626907\pi$
$131$	654.638	−	2229.49i	0.436611	−	1.48696i	0.824824	−	0.565390i	$-0.191274\pi$
$132$	−20.2443	−	147.552i	−0.0133488	−	0.0972936i
$133$	−1854.66	−	846.995i	−1.20917	−	0.552209i
$134$	43.0854	−	292.956i	0.0277762	−	0.188862i
$135$	43.0079	+	27.6395i	0.0274187	+	0.0176210i
$136$	1320.71	−	1122.22i	0.832723	−	0.707570i
$137$	676.489			0.421871			0.210936	−	0.977500i	$-0.432349\pi$
$137$	676.489			0.421871			0.210936	+	0.977500i	$0.432349\pi$
$138$	38.8914	+	97.6424i	0.0239903	+	0.0602310i
$139$			853.135i			0.520590i	0.965529	+	0.260295i	$0.0838197\pi$
$139$			853.135i			0.520590i	−0.965529	+	0.260295i	$0.916180\pi$
$140$	−533.127	+	455.971i	−0.321839	+	0.275261i
$141$	−12.7336	+	19.8139i	−0.00760543	+	0.0118343i
$142$	784.788	+	115.420i	0.463788	+	0.0682099i
$143$	1909.11	−	4180.37i	1.11642	−	2.44462i
$144$	−222.896	−	1706.24i	−0.128991	−	0.987407i
$145$	277.820	+	81.5754i	0.159115	+	0.0467205i
$146$	1270.60	+	1991.18i	0.720245	+	1.12871i
$147$	192.003	−	87.6847i	0.107729	−	0.0491980i
$148$	−612.872	−	2138.17i	−0.340390	−	1.18754i
$149$	556.964	+	482.612i	0.306230	+	0.265350i	0.794395	−	0.607402i	$-0.207788\pi$
$149$	556.964	+	482.612i	0.306230	+	0.265350i	−0.488165	+	0.872751i	$0.662334\pi$
$150$	73.3203	−	84.0668i	0.0399105	−	0.0457602i
$151$	−2719.03	+	798.380i	−1.46537	+	0.430273i	−0.914593	−	0.404376i	$-0.867489\pi$
$151$	−2719.03	+	798.380i	−1.46537	+	0.430273i	−0.550782	+	0.834649i	$0.685670\pi$
$152$	602.432	+	1353.65i	0.321472	+	0.722338i
$153$	1732.42	−	1113.36i	0.915408	−	0.588297i
$154$	4665.39	+	1386.24i	2.44122	+	0.725367i
$155$	534.263	−	76.8155i	0.276858	−	0.0398062i
$156$	−94.4176	+	203.266i	−0.0484581	+	0.104322i
$157$	2650.45	+	381.077i	1.34732	+	0.193715i	0.777928	−	0.628353i	$-0.216271\pi$
$157$	2650.45	+	381.077i	1.34732	+	0.193715i	0.569389	+	0.822068i	$0.307180\pi$
$158$	−1193.12	+	1843.43i	−0.600755	+	0.928198i
$159$	85.8933	+	99.1262i	0.0428414	+	0.0494416i
$160$	509.721	+	8.21953i	0.251856	+	0.00406132i
$161$	−3430.97	−	158.384i	−1.67949	−	0.0775306i
$162$	6.56561	−	2035.95i	0.00318422	−	0.987403i
$163$	−1573.04	+	1363.05i	−0.755891	+	0.654983i	−0.945036	−	0.326966i	$-0.893974\pi$
$163$	−1573.04	+	1363.05i	−0.755891	+	0.654983i	0.189145	+	0.981949i	$0.439428\pi$
$164$	−1550.94	−	1010.92i	−0.738463	−	0.481340i
$165$	51.8950	+	7.46137i	0.0244850	+	0.00352041i
$166$	−396.398	+	860.635i	−0.185340	+	0.402399i
$167$	241.073	+	1676.70i	0.111706	+	0.776929i	0.966260	+	0.257568i	$0.0829210\pi$
$167$	241.073	+	1676.70i	0.111706	+	0.776929i	−0.854555	+	0.519361i	$0.826170\pi$
$168$	−227.084	−	69.0710i	−0.104285	−	0.0317199i
$169$	−3969.72	+	2551.19i	−1.80688	+	1.16121i
$170$	251.653	+	555.779i	0.113535	+	0.250743i
$171$	496.001	+	1689.22i	0.221814	+	0.755428i
$172$	473.764	+	415.899i	0.210024	+	0.184372i
$173$	401.317	+	347.743i	0.176367	+	0.152823i	0.738571	−	0.674176i	$-0.235501\pi$
$173$	401.317	+	347.743i	0.176367	+	0.152823i	−0.562204	+	0.826999i	$0.690046\pi$
$174$	27.2973	+	94.0873i	0.0118931	+	0.0409928i
$175$	1514.30	+	3315.85i	0.654116	+	1.43231i
$176$	−1873.59	−	2999.74i	−0.802426	−	1.28474i
$177$	108.557	+	31.8753i	0.0460998	+	0.0135361i
$178$	3102.86	−	435.916i	1.30657	−	0.183558i
$179$	2921.02	+	1333.98i	1.21971	+	0.557021i	0.918076	−	0.396405i	$-0.129742\pi$
$179$	2921.02	+	1333.98i	1.21971	+	0.557021i	0.301629	+	0.953425i	$0.402470\pi$
$180$	599.009	+	90.0714i	0.248042	+	0.0372974i
$181$	−31.3409	+	48.7673i	−0.0128704	+	0.0200268i	−0.847629	−	0.530589i	$-0.821971\pi$
$181$	−31.3409	+	48.7673i	−0.0128704	+	0.0200268i	0.834759	+	0.550616i	$0.185607\pi$
$182$	−4778.39	−	5550.63i	−1.94614	−	2.26066i
$183$	−210.838			−0.0851671
$184$	1792.17	+	1737.13i	0.718048	+	0.695994i
$185$	782.999			0.311174
$186$	119.147	+	138.403i	0.0469694	+	0.0545601i
$187$	2288.37	−	3560.78i	0.894879	−	1.39246i
$188$	−83.1678	+	553.097i	−0.0322640	+	0.214568i
$189$	−514.175	−	234.816i	−0.197887	−	0.0903722i
$190$	−516.506	+	72.5631i	−0.197217	+	0.0277067i
$191$	−2694.62	−	791.211i	−1.02082	−	0.299738i	−0.271844	−	0.962341i	$-0.587634\pi$
$191$	−2694.62	−	791.211i	−1.02082	−	0.299738i	−0.748971	+	0.662603i	$0.769452\pi$
$192$	90.4267	+	146.879i	0.0339895	+	0.0552089i
$193$	−412.505	−	903.260i	−0.153849	−	0.336881i	0.816976	−	0.576671i	$-0.195649\pi$
$193$	−412.505	−	903.260i	−0.153849	−	0.336881i	−0.970825	+	0.239790i	$0.922921\pi$
$194$	421.127	+	1451.53i	0.155851	+	0.537183i
$195$	−59.6267	−	51.6669i	−0.0218972	−	0.0189741i
$196$	3306.85	−	3766.94i	1.20512	−	1.37279i
$197$	−881.308	−	3001.46i	−0.318734	−	1.08551i	−0.950597	−	0.310428i	$-0.899528\pi$
$197$	−881.308	−	3001.46i	−0.318734	−	1.08551i	0.631863	−	0.775080i	$-0.282290\pi$
$198$	−1733.44	−	3828.33i	−0.622173	−	1.37408i
$199$	−174.165	+	111.929i	−0.0620414	+	0.0398716i	−0.571294	−	0.820746i	$-0.693558\pi$
$199$	−174.165	+	111.929i	−0.0620414	+	0.0398716i	0.509252	+	0.860617i	$0.329922\pi$
$200$	770.855	−	2534.33i	0.272538	−	0.896020i
$201$	5.01916	+	34.9090i	0.00176131	+	0.0122502i
$202$	1510.79	−	3280.13i	0.526231	−	1.14252i
$203$	−3168.86	−	455.613i	−1.09562	−	0.157526i
$204$	−112.718	+	172.931i	−0.0386856	+	0.0593508i
$205$	492.530	−	426.780i	0.167804	−	0.145403i
$206$	6.92746	−	2148.15i	0.00234300	−	0.726549i
$207$	1836.69	+	2328.50i	0.616710	+	0.781844i
$208$	−68.6525	+	5321.89i	−0.0228856	+	1.77407i
$209$	2369.67	+	2734.74i	0.784274	+	0.905100i
$210$	45.3999	−	70.1452i	0.0149185	−	0.0230499i
$211$	1619.80	+	232.892i	0.528492	+	0.0759857i	0.401396	−	0.915905i	$-0.368525\pi$
$211$	1619.80	+	232.892i	0.528492	+	0.0759857i	0.127096	+	0.991890i	$0.459434\pi$
$212$	2824.87	+	1312.16i	0.915155	+	0.425092i
$213$	−93.5165	+	13.4456i	−0.0300828	+	0.00432526i
$214$	1217.05	+	361.625i	0.388765	+	0.115515i
$215$	−186.693	+	119.980i	−0.0592202	+	0.0380585i
$216$	167.015	+	375.277i	0.0526107	+	0.118215i
$217$	−5726.17	+	1681.36i	−1.79133	+	0.525981i
$218$	−1573.44	+	1804.05i	−0.488838	+	0.560486i
$219$	−212.617	−	184.234i	−0.0656042	−	0.0568464i
$220$	1196.84	−	343.055i	0.366777	−	0.105131i
$221$	−5794.00	+	2646.03i	−1.76356	+	0.805390i
$222$	142.509	+	223.328i	0.0430836	+	0.0675172i
$223$	−4408.69	−	1294.51i	−1.32389	−	0.388729i	−0.457996	−	0.888954i	$-0.651432\pi$
$223$	−4408.69	−	1294.51i	−1.32389	−	0.388729i	−0.865895	+	0.500225i	$0.833251\pi$
$224$	−5591.38	+	712.104i	−1.66781	+	0.212408i
$225$	1307.55	−	2863.14i	0.387422	−	0.848337i
$226$	−3482.77	−	512.216i	−1.02509	−	0.150761i
$227$	−2663.10	+	4143.87i	−0.778662	+	1.21162i	0.194364	+	0.980929i	$0.437736\pi$
$227$	−2663.10	+	4143.87i	−0.778662	+	1.21162i	−0.973027	+	0.230693i	$0.925901\pi$
$228$	−114.703	−	134.112i	−0.0333174	−	0.0389552i
$229$		−	3486.74i		−	1.00616i	−0.864240	−	0.503079i	$-0.832200\pi$
$229$		−	3486.74i		−	1.00616i	0.864240	−	0.503079i	$-0.167800\pi$
$230$	−761.676	+	437.973i	−0.218363	+	0.125561i
$231$	−579.686			−0.165110
$232$	1506.42	+	1772.87i	0.426298	+	0.501700i
$233$	5626.64	+	3616.02i	1.58203	+	1.01671i	0.975048	+	0.221995i	$0.0712570\pi$
$233$	5626.64	+	3616.02i	1.58203	+	1.01671i	0.606983	+	0.794714i	$0.292379\pi$
$234$	−920.201	+	6256.83i	−0.257074	+	1.74796i
$235$	−179.100	−	81.7923i	−0.0497158	−	0.0227044i
$236$	2661.83	−	365.206i	0.734196	−	0.100733i
$237$	73.6838	−	250.944i	0.0201953	−	0.0687787i
$238$	−3628.65	−	5686.53i	−0.988279	−	1.54875i
$239$	172.665	+	378.083i	0.0467312	+	0.102327i	0.931558	−	0.363594i	$-0.118450\pi$
$239$	172.665	+	378.083i	0.0467312	+	0.102327i	−0.884826	+	0.465921i	$0.845723\pi$
$240$	−58.4748	+	16.3535i	−0.0157272	+	0.00439839i
$241$	1220.36	−	1408.37i	0.326183	−	0.376435i	−0.568845	−	0.822445i	$-0.692610\pi$
$241$	1220.36	−	1408.37i	0.326183	−	0.376435i	0.895028	+	0.446009i	$0.147155\pi$
$242$	−3672.53	−	3203.06i	−0.975533	−	0.850828i
$243$	206.407	+	702.959i	0.0544898	+	0.185575i
$244$	−4567.67	+	2050.49i	−1.19842	+	0.537987i
$245$	953.975	+	1484.41i	0.248764	+	0.387084i
$246$	211.369	+	62.8046i	0.0547821	+	0.0162775i
$247$	−774.966	−	5390.01i	−0.199635	−	1.38849i
$248$	3927.28	+	1839.65i	1.00557	+	0.471041i
$249$	16.0612	−	111.708i	0.00408770	−	0.0284306i
$250$	1618.72	+	1047.68i	0.409507	+	0.265044i
$251$	2239.63	−	1940.65i	0.563203	−	0.488018i	−0.326101	−	0.945335i	$-0.605735\pi$
$251$	2239.63	−	1940.65i	0.563203	−	0.488018i	0.889304	+	0.457317i	$0.151189\pi$
$252$	−6697.35	−	43.1963i	−1.67418	−	0.0107980i
$253$	5422.12	+	2785.22i	1.34737	+	0.692115i
$254$	7.69549	−	2386.32i	0.00190102	−	0.589491i
$255$	−47.5862	−	54.9174i	−0.0116861	−	0.0134865i
$256$	3387.50	+	2302.61i	0.827027	+	0.562162i
$257$	857.138	−	5961.53i	0.208042	−	1.44696i	−0.571493	−	0.820607i	$-0.693636\pi$
$257$	857.138	−	5961.53i	0.208042	−	1.44696i	0.779536	−	0.626358i	$-0.215455\pi$
$258$	−68.1998	−	31.4120i	−0.0164571	−	0.00757994i
$259$	−8569.24	+	1232.07i	−2.05585	+	0.295587i
$260$	−1794.26	−	539.436i	−0.427982	−	0.128671i
$261$	1494.52	+	2325.52i	0.354438	+	0.551517i
$262$	2710.89	+	5987.04i	0.639234	+	1.41176i
$263$	7485.30	−	2197.88i	1.75499	−	0.515313i	0.763540	−	0.645761i	$-0.223460\pi$
$263$	7485.30	−	2197.88i	1.75499	−	0.515313i	0.991455	+	0.130448i	$0.0416415\pi$
$264$	315.676	+	278.927i	0.0735928	+	0.0650256i
$265$	−718.035	+	828.657i	−0.166447	+	0.192091i
$266$	5538.53	−	1606.88i	1.27665	−	0.370390i
$267$	−339.473	+	155.032i	−0.0778105	+	0.0355348i
$268$	448.242	+	707.470i	0.102167	+	0.161252i
$269$	−1058.72	+	3605.67i	−0.239968	+	0.817255i	0.748146	+	0.663534i	$0.230944\pi$
$269$	−1058.72	+	3605.67i	−0.239968	+	0.817255i	−0.988114	+	0.153721i	$0.950874\pi$
$270$	−143.193	+	20.1170i	−0.0322758	+	0.00453437i
$271$	2563.86	−	5614.06i	0.574698	−	1.25841i	−0.369560	−	0.929207i	$-0.620492\pi$
$271$	2563.86	−	5614.06i	0.574698	−	1.25841i	0.944258	−	0.329206i	$-0.106781\pi$
$272$	−760.152	+	4842.67i	−0.169452	+	1.07952i
$273$	733.861	+	471.624i	0.162693	+	0.104557i
$274$	−1450.08	+	1248.34i	−0.319718	+	0.275237i
$275$		−	6469.48i		−	1.41863i
$276$	−263.547	−	137.534i	−0.0574771	−	0.0299948i
$277$			5214.42i			1.13106i	0.824727	+	0.565531i	$0.191329\pi$
$277$			5214.42i			1.13106i	−0.824727	+	0.565531i	$0.808671\pi$
$278$	−1574.31	−	1828.73i	−0.339643	−	0.394533i
$279$	4335.07	+	2785.98i	0.930229	+	0.597822i
$280$	301.369	−	1961.19i	0.0643223	−	0.418583i
$281$	90.0992	−	197.290i	0.0191276	−	0.0418837i	−0.899827	−	0.436247i	$-0.856307\pi$
$281$	90.0992	−	197.290i	0.0191276	−	0.0418837i	0.918955	+	0.394363i	$0.129035\pi$
$282$	−9.26797	−	65.9697i	−0.00195709	−	0.0139306i
$283$	1690.10	−	5755.94i	0.355003	−	1.20903i	−0.567609	−	0.823298i	$-0.692131\pi$
$283$	1690.10	−	5755.94i	0.355003	−	1.20903i	0.922612	−	0.385730i	$-0.126050\pi$
$284$	−1895.21	+	1200.78i	−0.395987	+	0.250891i
$285$	56.5090	−	25.8068i	0.0117449	−	0.00536373i
$286$	3621.87	+	12483.7i	0.748831	+	2.58105i
$287$	−4718.76	+	5445.73i	−0.970520	+	1.12004i
$288$	3626.35	+	3246.08i	0.741961	+	0.664157i
$289$	−914.904	+	268.640i	−0.186221	+	0.0546794i
$290$	−746.053	+	337.808i	−0.151068	+	0.0684026i
$291$	−97.3231	−	151.438i	−0.0196054	−	0.0305066i
$292$	−6397.97	−	1923.52i	−1.28224	−	0.385499i
$293$	−7648.80	+	1099.73i	−1.52508	+	0.219273i	−0.853276	−	0.521459i	$-0.825388\pi$
$293$	−7648.80	+	1099.73i	−1.52508	+	0.219273i	−0.671800	+	0.740732i	$0.734479\pi$
$294$	−249.760	+	542.263i	−0.0495452	+	0.107569i
$295$	−134.603	+	936.182i	−0.0265657	+	0.184768i
$296$	5259.33	+	3452.31i	1.03274	+	0.677911i
$297$	656.952	+	758.163i	0.128351	+	0.148125i
$298$	−2084.45	−	6.72202i	−0.405198	−	0.00130670i
$299$	−4598.19	−	7937.34i	−0.889366	−	1.53521i
$300$	−2.03490	+	315.501i	−0.000391617	+	0.0607181i
$301$	1854.40	−	1606.84i	0.355102	−	0.307698i
$302$	4355.10	−	6728.85i	0.829827	−	1.28213i
$303$	−61.2139	+	425.752i	−0.0116061	+	0.0807222i
$304$	−3789.26	−	1789.92i	−0.714898	−	0.337694i
$305$	−250.833	−	1744.58i	−0.0470907	−	0.327523i
$306$	−1659.01	+	5583.39i	−0.309932	+	1.04308i
$307$	3534.40	+	5499.64i	0.657065	+	1.02241i	0.996646	+	0.0818364i	$0.0260785\pi$
$307$	3534.40	+	5499.64i	0.657065	+	1.02241i	−0.339581	+	0.940577i	$0.610285\pi$
$308$	−12558.5	+	5637.69i	−2.32334	+	1.04298i
$309$	72.0837	+	245.495i	0.0132709	+	0.0451964i
$310$	−1003.47	+	1150.55i	−0.183849	+	0.210796i
$311$	1237.70	−	1428.39i	0.225671	−	0.260439i	−0.631611	−	0.775286i	$-0.717606\pi$
$311$	1237.70	−	1428.39i	0.225671	−	0.260439i	0.857282	+	0.514847i	$0.172151\pi$
$312$	−172.703	−	609.941i	−0.0313378	−	0.110677i
$313$	−2568.57	−	5624.38i	−0.463847	−	1.01568i	−0.986594	−	0.163195i	$-0.947820\pi$
$313$	−2568.57	−	5624.38i	−0.463847	−	1.01568i	0.522747	−	0.852488i	$-0.324907\pi$
$314$	−6384.56	+	4074.08i	−1.14746	+	0.732208i
$315$	664.237	−	2262.18i	0.118811	−	0.404634i
$316$	−844.221	−	6153.15i	−0.150288	−	1.09539i
$317$	−1876.74	−	857.076i	−0.332517	−	0.151856i	0.242159	−	0.970237i	$-0.422145\pi$
$317$	−1876.74	−	857.076i	−0.332517	−	0.151856i	−0.574676	+	0.818381i	$0.694872\pi$
$318$	−367.036	−	53.9805i	−0.0647244	−	0.00951910i
$319$	4779.83	+	3071.81i	0.838931	+	0.539148i
$320$	−1107.78	+	922.981i	−0.193521	+	0.161238i
$321$	−151.221			−0.0262939
$322$	7646.71	−	5991.75i	1.32340	−	1.03698i
$323$		−	5015.35i		−	0.863968i
$324$	3742.91	+	4376.26i	0.641788	+	0.750388i
$325$	−5263.48	+	8190.13i	−0.898354	+	1.39787i
$326$	856.621	−	5824.53i	0.145533	−	0.989542i
$327$	118.442	−	259.351i	0.0200301	−	0.0438597i
$328$	5189.98	−	695.028i	0.873686	−	0.117002i
$329$	2088.80	+	613.326i	0.350027	+	0.102777i
$330$	−125.008	+	79.7692i	−0.0208529	+	0.0133065i
$331$	2888.10	−	1318.95i	0.479589	−	0.219021i	−0.160926	−	0.986966i	$-0.551448\pi$
$331$	2888.10	−	1318.95i	0.479589	−	0.219021i	0.640515	+	0.767945i	$0.278721\pi$
$332$	−738.452	−	2576.29i	−0.122072	−	0.425881i
$333$	5649.50	+	4895.32i	0.929701	+	0.805591i
$334$	−3610.81	−	3149.23i	−0.591541	−	0.515922i
$335$	−282.885	+	83.0624i	−0.0461362	+	0.0135468i
$336$	614.223	−	270.986i	0.0997279	−	0.0439985i
$337$	4803.64	−	3087.11i	0.776471	−	0.499008i	−0.0913895	−	0.995815i	$-0.529131\pi$
$337$	4803.64	−	3087.11i	0.776471	−	0.499008i	0.867861	+	0.496807i	$0.165494\pi$
$338$	3801.52	−	12794.0i	0.611761	−	2.05888i
$339$	415.012	−	59.6697i	0.0664908	−	0.00955993i
$340$	−1565.02	−	726.956i	−0.249633	−	0.115955i
$341$	10483.8	+	1507.34i	1.66490	+	0.239376i
$342$	−4180.36	−	2705.64i	−0.660959	−	0.427791i
$343$	−5782.09	−	6672.89i	−0.910215	−	1.05044i
$344$	−1783.00	−	17.2502i	−0.279456	−	0.00270368i
$345$	72.1044	−	75.8437i	0.0112521	−	0.0118356i
$346$	−1501.94	−	4.84351i	−0.233366	−	0.000752569i
$347$	−4567.51	+	3957.77i	−0.706619	+	0.612289i	−0.932204	−	0.361935i	$-0.882116\pi$
$347$	−4567.51	+	3957.77i	−0.706619	+	0.612289i	0.225584	+	0.974224i	$0.427571\pi$
$348$	−232.134	−	151.308i	−0.0357578	−	0.0233074i
$349$	−3699.67	−	531.932i	−0.567446	−	0.0815865i	−0.147380	−	0.989080i	$-0.547084\pi$
$349$	−3699.67	−	531.932i	−0.567446	−	0.0815865i	−0.420066	+	0.907493i	$0.637993\pi$
$350$	−9364.79	−	4313.31i	−1.43020	−	0.658732i
$351$	−214.847	−	1494.29i	−0.0326715	−	0.227235i
$352$	9551.61	+	2972.70i	1.44631	+	0.450130i
$353$	−3557.50	+	2286.27i	−0.536393	+	0.344719i	−0.780627	−	0.624998i	$-0.785100\pi$
$353$	−3557.50	+	2286.27i	−0.536393	+	0.344719i	0.244234	+	0.969716i	$0.421464\pi$
$354$	−291.517	+	131.997i	−0.0437683	+	0.0198180i
$355$	−222.513	−	757.809i	−0.0332669	−	0.113297i
$356$	−5846.72	+	6660.19i	−0.870437	+	0.991543i
$357$	607.203	+	526.144i	0.0900184	+	0.0780014i
$358$	−8722.97	+	2530.77i	−1.28777	+	0.373618i
$359$	−2750.56	−	6022.89i	−0.404371	−	0.885448i	−0.996808	−	0.0798320i	$-0.974562\pi$
$359$	−2750.56	−	6022.89i	−0.404371	−	0.885448i	0.592438	−	0.805616i	$-0.298166\pi$
$360$	−1450.21	+	912.293i	−0.212314	+	0.133561i
$361$	−2467.17	−	724.427i	−0.359698	−	0.105617i
$362$	−22.8109	−	162.369i	−0.00331192	−	0.0235744i
$363$	527.962	+	241.112i	0.0763384	+	0.0348626i
$364$	20485.4	+	3080.34i	2.94980	+	0.443554i
$365$	1271.50	−	1978.49i	0.182338	−	0.283723i
$366$	451.940	−	389.064i	0.0645445	−	0.0555647i
$367$	−1557.46			−0.221522			−0.110761	−	0.993847i	$-0.535329\pi$
$367$	−1557.46			−0.221522			−0.110761	+	0.993847i	$0.535329\pi$
$368$	−7047.17	−	416.476i	−0.998258	−	0.0589953i
$369$	6221.93			0.877780
$370$	−1678.39	+	1444.89i	−0.235826	+	0.203016i
$371$	6554.35	−	10198.8i	0.917210	−	1.42721i
$372$	−510.795	−	76.8070i	−0.0711922	−	0.0107050i
$373$	5453.74	+	2490.64i	0.757062	+	0.345738i	0.756269	−	0.654261i	$-0.227020\pi$
$373$	5453.74	+	2490.64i	0.757062	+	0.345738i	0.000792993		1.00000i	$0.499748\pi$
$374$	1665.56	+	11855.5i	0.230278	+	1.63912i
$375$	−220.355	−	64.7020i	−0.0303442	−	0.00890985i
$376$	−842.368	−	1339.06i	−0.115537	−	0.183661i
$377$	−3551.91	−	7777.60i	−0.485233	−	1.06251i
$378$	1535.47	−	445.481i	0.208931	−	0.0606165i
$379$	2410.31	+	2088.55i	0.326674	+	0.283065i	0.802721	−	0.596355i	$-0.203385\pi$
$379$	2410.31	+	2088.55i	0.326674	+	0.283065i	−0.476046	+	0.879420i	$0.657931\pi$
$380$	973.252	−	1108.66i	0.131386	−	0.149666i
$381$	80.0755	+	272.712i	0.0107674	+	0.0366705i
$382$	7236.07	−	3276.44i	0.969188	−	0.438841i
$383$	−484.878	+	311.612i	−0.0646896	+	0.0415735i	−0.572586	−	0.819845i	$-0.694060\pi$
$383$	−484.878	+	311.612i	−0.0646896	+	0.0415735i	0.507896	+	0.861418i	$0.330423\pi$
$384$	−464.873	−	147.976i	−0.0617786	−	0.0196650i
$385$	−689.651	−	4796.63i	−0.0912931	−	0.634958i
$386$	2551.03	+	1174.97i	0.336383	+	0.154934i
$387$	−2097.14	−	301.524i	−0.275462	−	0.0396055i
$388$	−3581.24	−	2334.30i	−0.468582	−	0.305428i
$389$	4858.64	−	4210.04i	0.633273	−	0.548734i	−0.277977	−	0.960588i	$-0.589664\pi$
$389$	4858.64	−	4210.04i	0.633273	−	0.548734i	0.911250	+	0.411854i	$0.135119\pi$
$390$	223.155	+	0.719638i	0.0289740	+	9.34367e-5i
$391$	−3151.53	−	7838.74i	−0.407621	−	1.01387i
$392$	−137.158	+	14176.8i	−0.0176722	+	1.82663i
$393$	−512.614	−	591.588i	−0.0657964	−	0.0759331i
$394$	7427.78	+	4807.46i	0.949762	+	0.614712i
$395$	2164.10	+	311.151i	0.275666	+	0.0396347i
$396$	10780.2	+	5007.44i	1.36800	+	0.635437i
$397$	−2555.95	+	367.490i	−0.323122	+	0.0464580i	−0.301967	−	0.953318i	$-0.597643\pi$
$397$	−2555.95	+	367.490i	−0.323122	+	0.0464580i	−0.0211549	+	0.999776i	$0.506734\pi$
$398$	166.785	−	561.316i	0.0210055	−	0.0706940i
$399$	−577.834	+	371.351i	−0.0725009	+	0.0465935i
$400$	3024.29	+	6854.92i	0.378037	+	0.856865i
$401$	10406.4	−	3055.60i	1.29594	−	0.380523i	0.440188	−	0.897906i	$-0.354912\pi$
$401$	10406.4	−	3055.60i	1.29594	−	0.380523i	0.855754	+	0.517383i	$0.173094\pi$
$402$	−75.1772	−	65.5671i	−0.00932711	−	0.00813480i
$403$	−12045.8	−	10437.7i	−1.48894	−	1.29017i
$404$	2814.46	+	9818.99i	0.346595	+	1.20919i
$405$	−1843.97	+	842.113i	−0.226241	+	0.103321i
$406$	7633.34	−	4870.94i	0.933095	−	0.595420i
$407$	14742.3	+	4328.74i	1.79546	+	0.527194i
$408$	−77.4961	−	578.686i	−0.00940350	−	0.0702187i
$409$	−2868.82	+	6281.85i	−0.346832	+	0.759456i	0.653166	+	0.757215i	$0.273441\pi$
$409$	−2868.82	+	6281.85i	−0.346832	+	0.759456i	−0.999997	+	0.00224072i	$0.999287\pi$
$410$	−268.214	+	1823.70i	−0.0323076	+	0.219673i
$411$	123.210	−	191.719i	0.0147871	−	0.0230092i
$412$	3949.19	+	4617.45i	0.472239	+	0.552149i
$413$		−	10457.5i		−	1.24595i
$414$	−8233.86	−	1601.94i	−0.977469	−	0.190172i
$415$	943.440			0.111594
$416$	−9673.44	−	11534.4i	−1.14009	−	1.35942i
$417$	241.781	+	155.383i	0.0283934	+	0.0182474i
$418$	−10126.0	−	1489.24i	−1.18487	−	0.174261i
$419$	7925.16	+	3619.30i	0.924032	+	0.421991i	0.819858	−	0.572568i	$-0.194053\pi$
$419$	7925.16	+	3619.30i	0.924032	+	0.421991i	0.104175	+	0.994559i	$0.466780\pi$
$420$	32.1239	+	234.137i	0.00373210	+	0.0272017i
$421$	−2122.57	+	7228.82i	−0.245719	+	0.836843i	0.740593	+	0.671954i	$0.234545\pi$
$421$	−2122.57	+	7228.82i	−0.245719	+	0.836843i	−0.986312	+	0.164889i	$0.947273\pi$
$422$	−3901.88	+	2489.84i	−0.450096	+	0.287213i
$423$	−780.877	−	1709.88i	−0.0897578	−	0.196542i
$424$	−8476.59	+	2400.13i	−0.970896	+	0.274907i
$425$	−5871.94	+	6776.58i	−0.670190	+	0.773441i
$426$	175.645	−	201.389i	0.0199766	−	0.0229046i
$427$	5490.30	+	18698.2i	0.622234	+	2.11914i
$428$	−3276.11	+	1470.69i	−0.369993	+	0.166094i
$429$	−837.019	−	1302.43i	−0.0941997	−	0.146578i
$430$	178.782	−	601.692i	0.0200503	−	0.0674794i
$431$	1846.26	+	12841.0i	0.206337	+	1.43511i	0.784978	+	0.619524i	$0.212674\pi$
$431$	1846.26	+	12841.0i	0.206337	+	1.43511i	−0.578641	+	0.815582i	$0.696417\pi$
$432$	−1050.51	−	496.228i	−0.116997	−	0.0552657i
$433$	−435.429	+	3028.48i	−0.0483265	+	0.336118i	0.951287	+	0.308308i	$0.0997626\pi$
$433$	−435.429	+	3028.48i	−0.0483265	+	0.336118i	−0.999613	+	0.0278107i	$0.991146\pi$
$434$	9171.66	−	14170.7i	1.01441	−	1.56732i
$435$	73.7186	−	63.8776i	0.00812537	−	0.00704068i
$436$	43.6685	−	6770.57i	0.00479665	−	0.743696i
$437$	7189.03	−	697.132i	0.786951	−	0.0763120i
$438$	795.725	+	2.56609i	0.0868064	+	0.000279937i
$439$	−1935.84	−	2234.07i	−0.210461	−	0.242885i	0.640698	−	0.767793i	$-0.278645\pi$
$439$	−1935.84	−	2234.07i	−0.210461	−	0.242885i	−0.851159	+	0.524908i	$0.824100\pi$
$440$	−1932.43	+	2943.91i	−0.209375	+	0.318966i
$441$	−2397.45	+	16674.6i	−0.258875	+	1.80052i
$442$	7536.91	−	16363.7i	0.811073	−	1.76095i
$443$	−4092.04	+	588.346i	−0.438868	+	0.0630997i	−0.358208	−	0.933642i	$-0.616612\pi$
$443$	−4092.04	+	588.346i	−0.438868	+	0.0630997i	−0.0806605	+	0.996742i	$0.525703\pi$
$444$	−717.587	−	215.739i	−0.0767008	−	0.0230598i
$445$	−1686.69	−	2624.54i	−0.179678	−	0.279584i
$446$	11839.0	−	5360.62i	1.25694	−	0.569132i
$447$	238.214	−	69.9461i	0.0252062	−	0.00740120i
$448$	10671.3	−	11844.3i	1.12538	−	1.24909i
$449$	3052.56	−	3522.84i	0.320844	−	0.370274i	−0.572300	−	0.820044i	$-0.693949\pi$
$449$	3052.56	−	3522.84i	0.320844	−	0.370274i	0.893144	+	0.449770i	$0.148494\pi$
$450$	2480.62	+	8550.11i	0.259861	+	0.895681i
$451$	11632.8	−	5312.52i	1.21456	−	0.554671i
$452$	8410.68	−	5328.88i	0.875232	−	0.554534i
$453$	−268.959	+	915.992i	−0.0278958	+	0.0950045i
$454$	−1938.30	−	13796.9i	−0.200372	−	1.42625i
$455$	−3029.39	+	6633.45i	−0.312132	+	0.683474i
$456$	493.350	+	75.8115i	0.0506650	+	0.00778553i
$457$	12273.0	+	7887.41i	1.25626	+	0.807347i	0.987767	−	0.155936i	$-0.0498395\pi$
$457$	12273.0	+	7887.41i	1.25626	+	0.807347i	0.268489	+	0.963283i	$0.413476\pi$
$458$	6434.16	+	7473.99i	0.656438	+	0.762525i
$459$		−	1390.43i		−	0.141393i
$460$	824.485	−	2344.35i	0.0835692	−	0.237622i
$461$			9900.81i			1.00027i	0.865946	+	0.500137i	$0.166717\pi$
$461$			9900.81i			1.00027i	−0.865946	+	0.500137i	$0.833283\pi$
$462$	1242.58	−	1069.71i	0.125130	−	0.107721i
$463$	−3566.12	−	2291.81i	−0.357952	−	0.230042i	0.349288	−	0.937015i	$-0.386424\pi$
$463$	−3566.12	−	2291.81i	−0.357952	−	0.230042i	−0.707240	+	0.706974i	$0.750060\pi$
$464$	−6500.59	−	1020.39i	−0.650393	−	0.102092i
$465$	75.5367	−	165.402i	0.00753319	−	0.0164954i
$466$	−18733.7	+	2631.86i	−1.86228	+	0.261628i
$467$	−1327.98	+	4522.69i	−0.131588	+	0.448148i	−0.998756	−	0.0498684i	$-0.984120\pi$
$467$	−1327.98	+	4522.69i	−0.131588	+	0.448148i	0.867168	+	0.498016i	$0.165938\pi$
$468$	−9573.38	−	15109.9i	−0.945577	−	1.49242i
$469$	2965.22	−	1354.17i	0.291943	−	0.133326i
$470$	534.842	−	155.172i	0.0524903	−	0.0152288i
$471$	590.730	−	681.738i	0.0577906	−	0.0666939i
$472$	−5031.82	+	5694.77i	−0.490696	+	0.555345i
$473$	−4178.36	+	1226.88i	−0.406176	+	0.119264i
$474$	305.128	+	673.880i	0.0295675	+	0.0653003i
$475$	−4144.40	−	6448.81i	−0.400333	−	0.622930i
$476$	18271.7	+	5493.29i	1.75941	+	0.528959i
$477$	−10361.5	+	1489.76i	−0.994596	+	0.143001i
$478$	−1067.80	−	491.816i	−0.102176	−	0.0470610i
$479$	484.914	−	3372.65i	0.0462553	−	0.321713i	−0.953536	−	0.301279i	$-0.902586\pi$
$479$	484.914	−	3372.65i	0.0462553	−	0.321713i	0.999791	−	0.0204334i	$-0.00650461\pi$
$480$	95.1659	−	142.959i	0.00904939	−	0.0135941i
$481$	−15141.5	−	17474.2i	−1.43533	−	1.65645i
$482$	−16.9977	+	5270.85i	−0.00160627	+	0.498093i
$483$	−669.776	+	943.501i	−0.0630971	+	0.0888836i
$484$	13782.9	+	88.8963i	1.29441	+	0.00834863i
$485$	1137.29	−	985.468i	0.106478	−	0.0922635i
$486$	−1739.63	−	1125.93i	−0.162369	−	0.105089i
$487$	−810.449	+	5636.80i	−0.0754106	+	0.524492i	0.916744	+	0.399475i	$0.130808\pi$
$487$	−810.449	+	5636.80i	−0.0754106	+	0.524492i	−0.992155	+	0.125017i	$0.960101\pi$
$488$	6007.20	−	12824.1i	0.557240	−	1.18959i
$489$	99.7907	+	694.060i	0.00922841	+	0.0641850i
$490$	−4784.11	−	1421.52i	−0.441069	−	0.131056i
$491$	−8088.32	−	12585.7i	−0.743423	−	1.15679i	−0.982586	−	0.185809i	$-0.940509\pi$
$491$	−8088.32	−	12585.7i	−0.743423	−	1.15679i	0.239163	−	0.970980i	$-0.423127\pi$
$492$	−568.974	+	255.419i	−0.0521368	+	0.0234049i
$493$	−2218.63	−	7555.97i	−0.202682	−	0.690272i
$494$	11607.5	+	10123.7i	1.05718	+	0.922034i
$495$	−2740.15	+	3162.30i	−0.248809	+	0.287141i
$496$	−11813.1	+	3303.72i	−1.06940	+	0.299076i
$497$	3627.64	+	7943.42i	0.327408	+	0.716924i
$498$	171.710	+	269.089i	0.0154508	+	0.0242132i
$499$	3026.68	−	10307.9i	0.271528	−	0.924740i	−0.704974	−	0.709233i	$-0.749041\pi$
$499$	3026.68	−	10307.9i	0.271528	−	0.924740i	0.976502	−	0.215507i	$-0.0691405\pi$
$500$	−5403.11	+	741.313i	−0.483268	+	0.0663051i
$501$	519.089	+	237.060i	0.0462898	+	0.0211399i
$502$	−1219.62	+	8292.70i	−0.108435	+	0.737293i
$503$	2554.84	+	1641.90i	0.226471	+	0.145544i	0.648956	−	0.760826i	$-0.275206\pi$
$503$	2554.84	+	1641.90i	0.226471	+	0.145544i	−0.422485	+	0.906370i	$0.638842\pi$
$504$	14435.8	−	12266.2i	1.27584	−	1.08409i
$505$	−3595.72			−0.316847
$506$	−16762.2	+	4035.32i	−1.47267	+	0.354529i
$507$			1589.68i			0.139251i
$508$	4387.03	+	5129.38i	0.383155	+	0.447991i
$509$	−5949.32	+	9257.32i	−0.518072	+	0.806136i	−0.997442	−	0.0714766i	$-0.977229\pi$
$509$	−5949.32	+	9257.32i	−0.518072	+	0.806136i	0.479370	+	0.877613i	$0.340865\pi$
$510$	203.343	+	29.9060i	0.0176553	+	0.00259659i
$511$	−10802.2	+	23653.6i	−0.935150	+	2.04769i
$512$	−11510.3	+	1315.28i	−0.993534	+	0.113531i
$513$	1140.54	+	334.892i	0.0981599	+	0.0288223i
$514$	9163.63	+	14360.5i	0.786363	+	1.23232i
$515$	−1945.59	+	888.523i	−0.166472	+	0.0760253i
$516$	204.154	−	58.5176i	0.0174174	−	0.00499243i
$517$	−2919.92	−	2530.13i	−0.248391	−	0.215232i
$518$	16095.0	−	18454.0i	1.36520	−	1.56529i
$519$	171.644	−	50.3992i	0.0145170	−	0.00426258i
$520$	4841.51	−	2154.68i	0.408297	−	0.181710i
$521$	−9820.97	+	6311.55i	−0.825844	+	0.530737i	−0.883955	−	0.467573i	$-0.845129\pi$
$521$	−9820.97	+	6311.55i	−0.825844	+	0.530737i	0.0581111	+	0.998310i	$0.481492\pi$
$522$	−7494.90	−	2226.98i	−0.628434	−	0.186728i
$523$	−14393.8	+	2069.52i	−1.20344	+	0.173029i	−0.714719	−	0.699412i	$-0.753445\pi$
$523$	−14393.8	+	2069.52i	−1.20344	+	0.173029i	−0.488721	+	0.872440i	$0.662536\pi$
$524$	−16858.9	−	7831.02i	−1.40551	−	0.652862i
$525$	1215.53	+	174.766i	0.101047	+	0.0145284i
$526$	−11989.3	+	18524.1i	−0.993835	+	1.53553i
$527$	−9613.34	−	11094.4i	−0.794618	−	0.917038i
$528$	−1191.38	−	15.3688i	−0.0981969	−	0.00126674i
$529$	10798.0	−	5607.00i	0.887485	−	0.460837i
$530$	10.0011	−	3101.27i	0.000819661	−	0.254171i
$531$	−6824.20	+	5913.21i	−0.557712	+	0.483260i
$532$	−8906.87	+	13664.8i	−0.725868	+	1.11362i
$533$	−19048.9	−	2738.82i	−1.54803	−	0.222573i
$534$	441.591	−	958.755i	0.0357856	−	0.0776955i
$535$	−179.907	−	1251.28i	−0.0145384	−	0.101117i
$536$	−2266.34	−	689.341i	−0.182632	−	0.0555504i
$537$	910.066	−	584.864i	0.0731327	−	0.0469995i
$538$	−4384.21	−	9682.60i	−0.351332	−	0.775923i
$539$	9755.03	+	33222.6i	0.779552	+	2.65491i
$540$	269.819	−	307.359i	0.0215021	−	0.0244938i
$541$	8957.81	+	7761.99i	0.711879	+	0.616847i	0.933622	−	0.358258i	$-0.116629\pi$
$541$	8957.81	+	7761.99i	0.711879	+	0.616847i	−0.221743	+	0.975105i	$0.571175\pi$
$542$	4864.02	+	16765.1i	0.385475	+	1.32864i
$543$	8.11263	+	17.7642i	0.000641153	+	0.00140393i
$544$	−7306.87	−	11783.2i	−0.575882	−	0.928678i
$545$	2286.92	+	671.499i	0.179744	+	0.0527777i
$546$	−2443.36	+	343.264i	−0.191513	+	0.0269054i
$547$	−17721.3	−	8093.04i	−1.38521	−	0.632602i	−0.423301	−	0.905989i	$-0.639129\pi$
$547$	−17721.3	−	8093.04i	−1.38521	−	0.632602i	−0.961904	+	0.273387i	$0.911856\pi$
$548$	804.729	−	5351.75i	0.0627305	−	0.417181i
$549$	9097.33	−	14155.7i	0.707222	−	1.10046i
$550$	11938.3	+	13867.6i	0.925545	+	1.07512i
$551$	6732.38			0.520525
$552$	818.720	−	191.520i	0.0631287	−	0.0147675i
$553$	−24173.8			−1.85891
$554$	−9622.29	−	11177.3i	−0.737927	−	0.857183i
$555$	142.609	−	221.904i	0.0109071	−	0.0169717i
$556$	6749.20	+	1014.86i	0.514802	+	0.0774095i
$557$	4231.95	+	1932.67i	0.321927	+	0.147019i	0.569823	−	0.821768i	$-0.307012\pi$
$557$	4231.95	+	1932.67i	0.321927	+	0.147019i	−0.247896	+	0.968787i	$0.579739\pi$
$558$	−14433.4	+	2027.73i	−1.09501	+	0.153836i
$559$	6287.83	+	1846.27i	0.475755	+	0.139694i
$560$	2973.02	+	4760.01i	0.224345	+	0.359191i
$561$	−592.349	−	1297.06i	−0.0445793	−	0.0976150i
$562$	170.932	+	589.161i	0.0128297	+	0.0442211i
$563$	11033.4	+	9560.49i	0.825936	+	0.715678i	0.961415	−	0.275102i	$-0.0887117\pi$
$563$	11033.4	+	9560.49i	0.825936	+	0.715678i	−0.135479	+	0.990780i	$0.543257\pi$
$564$	141.602	+	124.307i	0.0105718	+	0.00928059i
$565$	987.478	+	3363.04i	0.0735283	+	0.250415i
$566$	6998.77	+	15456.9i	0.519753	+	1.14788i
$567$	18855.5	−	12117.7i	1.39657	−	0.897524i
$568$	1846.65	−	6071.20i	0.136415	−	0.448490i
$569$	427.357	+	2972.33i	0.0314864	+	0.218993i	0.999490	−	0.0319451i	$-0.0101702\pi$
$569$	427.357	+	2972.33i	0.0314864	+	0.218993i	−0.968003	+	0.250938i	$0.919261\pi$
$570$	−73.5077	+	159.595i	−0.00540158	+	0.0117276i
$571$	11538.0	+	1658.91i	0.845620	+	0.121582i	0.551488	−	0.834183i	$-0.314060\pi$
$571$	11538.0	+	1658.91i	0.845620	+	0.121582i	0.294132	+	0.955765i	$0.404969\pi$
$572$	−30800.2	−	20075.9i	−2.25143	−	1.46751i
$573$	−715.008	+	619.558i	−0.0521289	+	0.0451700i
$574$	65.7249	−	20380.8i	0.00477927	−	1.48202i
$575$	−10529.8	−	7474.92i	−0.763690	−	0.542132i
$576$	−13763.3	−	266.339i	−0.995610	−	0.0192664i
$577$	4156.21	+	4796.53i	0.299871	+	0.346069i	0.885610	−	0.464431i	$-0.153741\pi$
$577$	4156.21	+	4796.53i	0.299871	+	0.346069i	−0.585739	+	0.810500i	$0.699196\pi$
$578$	1465.41	−	2264.13i	0.105455	−	0.162934i
$579$	−331.117	−	47.6074i	−0.0237664	−	0.00341709i
$580$	975.834	−	2100.81i	0.0698608	−	0.150399i
$581$	−10325.1	+	1484.53i	−0.737277	+	0.106004i
$582$	488.068	+	145.021i	0.0347613	+	0.0103287i
$583$	−18100.4	+	11632.4i	−1.28583	+	0.826354i
$584$	17263.9	−	7683.17i	1.22326	−	0.544404i
$585$	6041.74	−	1774.01i	0.427000	−	0.125379i
$586$	14366.2	−	16471.8i	1.01273	−	1.16117i
$587$	4738.28	+	4105.74i	0.333168	+	0.288692i	0.805338	−	0.592816i	$-0.201984\pi$
$587$	4738.28	+	4105.74i	0.333168	+	0.288692i	−0.472170	+	0.881508i	$0.656529\pi$
$588$	−465.279	−	1623.25i	−0.0326323	−	0.113847i
$589$	11415.9	−	5213.48i	0.798616	−	0.364716i
$590$	−1439.03	−	2255.13i	−0.100414	−	0.157360i
$591$	−1011.14	−	296.896i	−0.0703766	−	0.0206644i
$592$	−17644.2	+	2304.97i	−1.22496	+	0.160023i
$593$	−4594.43	+	10060.4i	−0.318163	+	0.696679i	−0.999373	−	0.0354087i	$-0.988727\pi$
$593$	−4594.43	+	10060.4i	−0.318163	+	0.696679i	0.681210	+	0.732088i	$0.261454\pi$
$594$	−2807.26	−	412.868i	−0.193911	−	0.0285188i
$595$	−3631.21	+	5650.27i	−0.250193	+	0.389308i
$596$	4480.52	−	3832.08i	0.307935	−	0.263369i
$597$			69.7447i			0.00478134i
$598$	24503.4	+	8528.90i	1.67562	+	0.583232i
$599$	−5591.12			−0.381381			−0.190690	−	0.981650i	$-0.561073\pi$
$599$	−5591.12			−0.381381			−0.190690	+	0.981650i	$0.561073\pi$
$600$	−577.839	−	680.045i	−0.0393169	−	0.0462712i
$601$	−6345.63	−	4078.09i	−0.430688	−	0.276787i	0.307284	−	0.951618i	$-0.400580\pi$
$601$	−6345.63	−	4078.09i	−0.430688	−	0.276787i	−0.737972	+	0.674831i	$0.764216\pi$
$602$	−1009.84	+	6866.30i	−0.0683685	+	0.464867i
$603$	−2560.38	−	1169.28i	−0.172913	−	0.0789667i
$604$	3081.56	+	22460.2i	0.207594	+	1.51306i
$605$	−1366.98	+	4655.49i	−0.0918602	+	0.312847i
$606$	−654.435	−	1025.58i	−0.0438690	−	0.0687480i
$607$	−2857.29	−	6256.60i	−0.191061	−	0.418365i	0.789723	−	0.613464i	$-0.210224\pi$
$607$	−2857.29	−	6256.60i	−0.191061	−	0.418365i	−0.980784	+	0.195099i	$0.937497\pi$
$608$	11425.4	−	3155.63i	0.762109	−	0.210489i
$609$	−706.272	+	815.082i	−0.0469944	+	0.0542345i
$610$	3756.99	+	3276.72i	0.249371	+	0.217493i
$611$	1638.04	+	5578.66i	0.108458	+	0.369375i
$612$	−6747.00	−	15029.7i	−0.445640	−	0.992709i
$613$	−13198.4	−	20537.0i	−0.869619	−	1.35315i	−0.934761	−	0.355278i	$-0.884386\pi$
$613$	−13198.4	−	20537.0i	−0.869619	−	1.35315i	0.0651412	−	0.997876i	$-0.479250\pi$
$614$	−17724.8	−	5266.60i	−1.16500	−	0.346161i
$615$	−31.2451	−	217.315i	−0.00204866	−	0.0142487i
$616$	16516.4	−	35259.2i	1.08030	−	2.30622i
$617$	528.887	−	3678.49i	0.0345092	−	0.240017i	−0.965265	−	0.261273i	$-0.915858\pi$
$617$	528.887	−	3678.49i	0.0345092	−	0.240017i	0.999774	+	0.0212565i	$0.00676666\pi$
$618$	−607.532	−	393.211i	−0.0395445	−	0.0255943i
$619$	−799.929	+	693.142i	−0.0519416	+	0.0450077i	−0.680445	−	0.732799i	$-0.738213\pi$
$619$	−799.929	+	693.142i	−0.0519416	+	0.0450077i	0.628503	+	0.777807i	$0.283668\pi$
$620$	27.8498	−	4317.97i	0.00180399	−	0.279700i
$621$	1993.04	−	193.269i	0.128789	−	0.0124889i
$622$	−17.2393	+	5345.78i	−0.00111131	+	0.344608i
$623$	22589.1	+	26069.2i	1.45267	+	1.67647i
$624$	1495.73	+	988.742i	0.0959572	+	0.0634317i
$625$	−1809.36	+	12584.4i	−0.115799	+	0.805400i
$626$	15884.6	+	7316.27i	1.01418	+	0.467120i
$627$	1206.62	−	173.486i	0.0768548	−	0.0110501i
$628$	6167.61	−	20514.5i	0.391902	−	1.30353i
$629$	−11513.2	−	17914.9i	−0.729829	−	1.13564i
$630$	2750.64	+	6074.82i	0.173949	+	0.384170i
$631$	−25455.4	+	7474.37i	−1.60596	+	0.471553i	−0.957197	−	0.289436i	$-0.906532\pi$
$631$	−25455.4	+	7474.37i	−1.60596	+	0.471553i	−0.648764	+	0.760989i	$0.724714\pi$
$632$	13164.2	+	11631.7i	0.828549	+	0.732095i
$633$	361.020	−	416.640i	0.0226687	−	0.0261610i
$634$	5604.45	−	1626.00i	0.351074	−	0.101856i
$635$	−2161.30	+	987.032i	−0.135069	+	0.0616837i
$636$	886.369	−	561.590i	0.0552623	−	0.0350134i
$637$	14679.9	−	49995.1i	0.913091	−	3.10970i
$638$	−15914.3	+	2235.77i	−0.987541	+	0.138738i
$639$	3132.35	−	6858.89i	0.193919	−	0.424622i
$640$	671.372	−	4022.66i	0.0414661	−	0.248452i
$641$	6158.99	+	3958.14i	0.379510	+	0.243896i	0.716463	−	0.697625i	$-0.245760\pi$
$641$	6158.99	+	3958.14i	0.379510	+	0.243896i	−0.336953	+	0.941521i	$0.609396\pi$
$642$	324.149	−	279.052i	0.0199270	−	0.0171547i
$643$			24858.2i			1.52459i	0.647231	+	0.762294i	$0.275927\pi$
$643$			24858.2i			1.52459i	−0.647231	+	0.762294i	$0.724073\pi$
$644$	−5334.36	+	26954.2i	−0.326402	+	1.64929i
$645$			74.7616i			0.00456393i
$646$	9254.94	+	10750.6i	0.563670	+	0.654764i
$647$	11229.9	+	7217.02i	0.682370	+	0.438532i	0.835366	−	0.549694i	$-0.185256\pi$
$647$	11229.9	+	7217.02i	0.682370	+	0.438532i	−0.152996	+	0.988227i	$0.548892\pi$
$648$	−16098.7	−	2473.84i	−0.975952	−	0.149971i
$649$	−7709.91	+	16882.3i	−0.466318	+	1.02109i
$650$	−3830.94	−	27268.7i	−0.231172	−	1.64549i
$651$	−566.418	+	1929.04i	−0.0341009	+	0.116137i
$652$	8911.93	+	14065.9i	0.535304	+	0.844881i
$653$	−20859.4	+	9526.16i	−1.25006	+	0.570885i	−0.926846	−	0.375441i	$-0.877491\pi$
$653$	−20859.4	+	9526.16i	−1.25006	+	0.570885i	−0.323216	+	0.946325i	$0.604764\pi$
$654$	224.701	+	774.493i	0.0134350	+	0.0463074i
$655$	4285.26	−	4945.45i	0.255632	−	0.295015i
$656$	−9842.41	+	11067.0i	−0.585795	+	0.658681i
$657$	21543.6	−	6325.78i	1.27930	−	0.375635i
$658$	−5609.21	+	2539.81i	−0.332325	+	0.150474i
$659$	1916.93	+	2982.80i	0.113312	+	0.176318i	0.893278	−	0.449505i	$-0.148400\pi$
$659$	1916.93	+	2982.80i	0.113312	+	0.176318i	−0.779965	+	0.625823i	$0.784763\pi$
$660$	120.760	−	401.669i	0.00712208	−	0.0236893i
$661$	−2501.60	+	359.676i	−0.147203	+	0.0211645i	−0.215522	−	0.976499i	$-0.569145\pi$
$661$	−2501.60	+	359.676i	−0.147203	+	0.0211645i	0.0683195	+	0.997663i	$0.478236\pi$
$662$	−3756.88	+	8156.70i	−0.220567	+	0.478881i
$663$	−305.380	+	2123.96i	−0.0178883	+	0.124416i
$664$	6336.99	+	4159.71i	0.370366	+	0.243115i
$665$	−3760.20	−	4339.51i	−0.219270	−	0.253051i
$666$	−21143.4	−	68.1841i	−1.23016	−	0.00396709i
$667$	10522.4	−	4230.48i	0.610837	−	0.245584i
$668$	13551.3	+	87.4023i	0.784902	+	0.00506242i
$669$	−1169.83	+	1013.66i	−0.0676058	+	0.0585807i
$670$	453.099	−	700.061i	0.0261265	−	0.0403668i
$671$	4922.08	−	34233.8i	0.283181	−	1.96957i
$672$	−816.557	+	1714.31i	−0.0468740	+	0.0984091i
$673$	−3814.51	−	26530.5i	−0.218483	−	1.51958i	−0.743643	−	0.668576i	$-0.766904\pi$
$673$	−3814.51	−	26530.5i	−0.218483	−	1.51958i	0.525161	−	0.851003i	$-0.324005\pi$
$674$	−4600.10	+	15481.6i	−0.262892	+	0.884762i
$675$	−1148.97	−	1787.83i	−0.0655168	−	0.101946i
$676$	15460.3	+	34439.5i	0.879628	+	1.95946i
$677$	2192.64	+	7467.43i	0.124475	+	0.423924i	0.998026	−	0.0628099i	$-0.0200062\pi$
$677$	2192.64	+	7467.43i	0.124475	+	0.423924i	−0.873550	+	0.486734i	$0.838188\pi$
$678$	−779.487	+	893.736i	−0.0441534	+	0.0506250i
$679$	−10896.0	+	12574.6i	−0.615831	+	0.710707i
$680$	4696.16	−	1329.71i	0.264838	−	0.0749880i
$681$	689.348	+	1509.46i	0.0387898	+	0.0849379i
$682$	−25254.0	+	16114.9i	−1.41793	+	0.904799i
$683$	2669.04	−	9089.93i	0.149529	−	0.509248i	−0.850327	−	0.526255i	$-0.823596\pi$
$683$	2669.04	−	9089.93i	0.149529	−	0.509248i	0.999855	+	0.0170073i	$0.00541385\pi$
$684$	13953.6	−	1914.45i	0.780012	−	0.107019i
$685$	1732.97	+	791.420i	0.0966617	+	0.0441439i
$686$	24707.8	+	3633.81i	1.37514	+	0.202244i
$687$	−988.153	−	635.047i	−0.0548768	−	0.0352672i
$688$	3853.78	−	3253.24i	0.213552	−	0.180274i
$689$	32378.4			1.79030
$690$	−14.6027	+	295.630i	−0.000805676	+	0.0163108i
$691$			33601.8i			1.84989i	0.380104	+	0.924944i	$0.375888\pi$
$691$			33601.8i			1.84989i	−0.380104	+	0.924944i	$0.624112\pi$
$692$	3228.41	−	2761.18i	0.177349	−	0.151682i
$693$	25012.6	−	38920.3i	1.37107	−	2.13342i
$694$	2487.30	−	16912.2i	0.136047	−	0.925041i
$695$	−998.076	+	2185.48i	−0.0544737	+	0.119281i
$696$	776.803	−	104.027i	0.0423055	−	0.00566544i
$697$	−17006.8	−	4993.65i	−0.924217	−	0.271375i
$698$	8911.99	−	5686.86i	0.483272	−	0.308382i
$699$	2049.58	−	936.012i	0.110905	−	0.0506484i
$700$	28033.3	−	8035.29i	1.51366	−	0.433865i
$701$	5130.03	+	4445.19i	0.276403	+	0.239505i	0.782020	−	0.623254i	$-0.214190\pi$
$701$	5130.03	+	4445.19i	0.276403	+	0.239505i	−0.505617	+	0.862758i	$0.668735\pi$
$702$	3217.99	+	2806.62i	0.173013	+	0.150896i
$703$	17468.3	−	5129.15i	0.937167	−	0.275177i
$704$	−25959.9	+	11253.7i	−1.38977	+	0.602470i
$705$	−55.8000	+	35.8605i	−0.00298092	+	0.00191572i
$706$	3406.76	−	11465.5i	0.181608	−	0.611201i
$707$	39352.0	−	5657.97i	2.09333	−	0.300976i
$708$	381.303	−	820.885i	0.0202405	−	0.0435745i
$709$	28563.1	+	4106.75i	1.51299	+	0.217535i	0.848272	−	0.529560i	$-0.177643\pi$
$709$	28563.1	+	4106.75i	1.51299	+	0.217535i	0.664717	+	0.747095i	$0.268552\pi$
$710$	1875.37	+	1213.79i	0.0991286	+	0.0641587i
$711$	13669.1	+	15775.0i	0.721002	+	0.832081i
$712$	242.504	−	25065.5i	0.0127643	−	1.31934i
$713$	14566.5	−	15321.9i	0.765104	−	0.804783i
$714$	−2272.47	−	7.32836i	−0.119111	−	0.000384113i
$715$	9781.17	−	8475.43i	0.511602	−	0.443305i
$716$	14028.0	−	21521.5i	0.732193	−	1.12332i
$717$	138.598	+	19.9273i	0.00721900	+	0.00103794i
$718$	17010.1	+	7834.66i	0.884140	+	0.407224i
$719$	−3435.35	−	23893.4i	−0.178188	−	1.23932i	−0.860953	−	0.508685i	$-0.830132\pi$
$719$	−3435.35	−	23893.4i	−0.178188	−	1.23932i	0.682765	−	0.730638i	$-0.260777\pi$
$720$	1425.12	−	4631.65i	0.0737655	−	0.239738i
$721$	19894.7	−	12785.6i	1.02762	−	0.660414i
$722$	6625.29	−	2999.89i	0.341507	−	0.154632i
$723$	−176.869	−	602.362i	−0.00909798	−	0.0309849i
$724$	348.519	+	305.952i	0.0178904	+	0.0157052i
$725$	−9096.58	−	7882.23i	−0.465984	−	0.403777i
$726$	−1576.64	+	457.426i	−0.0805986	+	0.0233838i
$727$	137.645	+	301.402i	0.00702199	+	0.0153760i	0.913111	−	0.407712i	$-0.133673\pi$
$727$	137.645	+	301.402i	0.00702199	+	0.0153760i	−0.906089	+	0.423088i	$0.860946\pi$
$728$	−49595.6	+	31199.3i	−2.52491	+	1.58836i
$729$	−18411.1	−	5405.98i	−0.935379	−	0.274652i
$730$	925.439	+	6587.30i	0.0469206	+	0.333982i
$731$	5490.27	+	2507.32i	0.277790	+	0.126863i
$732$	−250.806	+	1667.95i	−0.0126640	+	0.0842203i
$733$	−13841.1	+	21537.1i	−0.697451	+	1.08525i	0.294130	+	0.955765i	$0.404970\pi$
$733$	−13841.1	+	21537.1i	−0.697451	+	1.08525i	−0.991581	+	0.129489i	$0.958666\pi$
$734$	3338.48	−	2874.01i	0.167882	−	0.144526i
$735$	594.436			0.0298315
$736$	15874.5	−	12111.6i	0.795027	−	0.606574i
$737$	−5785.37			−0.289154
$738$	−13337.0	+	11481.5i	−0.665232	+	0.572681i
$739$	−8649.30	+	13458.6i	−0.430541	+	0.669935i	−0.986960	−	0.160967i	$-0.948539\pi$
$739$	−8649.30	+	13458.6i	−0.430541	+	0.669935i	0.556419	+	0.830902i	$0.312175\pi$
$740$	931.430	−	6194.36i	0.0462703	−	0.307715i
$741$	−1668.69	−	762.065i	−0.0827272	−	0.0377803i
$742$	4770.48	+	33956.4i	0.236024	+	1.68003i
$743$	1492.48	+	438.232i	0.0736929	+	0.0216382i	0.318371	−	0.947966i	$-0.396864\pi$
$743$	1492.48	+	438.232i	0.0736929	+	0.0216382i	−0.244678	+	0.969604i	$0.578682\pi$
$744$	1236.65	−	777.943i	0.0609377	−	0.0383344i
$745$	862.174	+	1887.90i	0.0423995	+	0.0928419i
$746$	−16286.4	+	4725.11i	−0.799312	+	0.231902i
$747$	6807.11	+	5898.40i	0.333413	+	0.288904i
$748$	−25447.4	−	22339.2i	−1.24391	−	1.09198i
$749$	3937.85	+	13411.1i	0.192104	+	0.654247i
$750$	591.736	−	267.934i	0.0288095	−	0.0130448i
$751$	10529.5	−	6766.87i	0.511619	−	0.328797i	−0.259230	−	0.965816i	$-0.583469\pi$
$751$	10529.5	−	6766.87i	0.511619	−	0.328797i	0.770849	+	0.637018i	$0.219832\pi$
$752$	4276.65	+	1315.89i	0.207385	+	0.0638107i
$753$	−142.077	−	988.170i	−0.00687595	−	0.0478233i
$754$	21965.9	+	10117.2i	1.06094	+	0.488657i
$755$	−7899.38	−	1135.76i	−0.380779	−	0.0547477i
$756$	−2469.29	+	3788.34i	−0.118793	+	0.182250i
$757$	−8623.95	+	7472.69i	−0.414059	+	0.358784i	−0.836840	−	0.547448i	$-0.815599\pi$
$757$	−8623.95	+	7472.69i	−0.414059	+	0.358784i	0.422781	+	0.906232i	$0.361054\pi$
$758$	−9020.67	−	29.0902i	−0.432250	−	0.00139394i
$759$	1776.88	−	1029.37i	0.0849758	−	0.0492275i
$760$	−40.3674	+	4172.43i	−0.00192668	+	0.199145i
$761$	182.722	+	210.873i	0.00870392	+	0.0100449i	0.760085	−	0.649824i	$-0.225157\pi$
$761$	182.722	+	210.873i	0.00870392	+	0.0100449i	−0.751381	+	0.659869i	$0.770612\pi$
$762$	−674.887	−	436.805i	−0.0320848	−	0.0207661i
$763$	−26084.9	−	3750.44i	−1.23766	−	0.177949i
$764$	−9464.75	+	20376.1i	−0.448197	+	0.964897i
$765$	5740.45	−	825.352i	0.271302	−	0.0390074i
$766$	464.333	−	1562.71i	0.0219021	−	0.0737116i
$767$	23495.7	−	15099.8i	1.10610	−	0.710849i
$768$	1269.54	−	540.649i	0.0596492	−	0.0254023i
$769$	11933.2	−	3503.90i	0.559586	−	0.164309i	0.0103048	−	0.999947i	$-0.496720\pi$
$769$	11933.2	−	3503.90i	0.559586	−	0.164309i	0.549281	+	0.835638i	$0.314902\pi$
$770$	10329.6	+	9009.15i	0.483446	+	0.421646i
$771$	−1533.40	−	1328.70i	−0.0716266	−	0.0620648i
$772$	−7636.45	+	2188.87i	−0.356013	+	0.102045i
$773$	−11362.0	+	5188.85i	−0.528671	+	0.241436i	−0.661823	−	0.749660i	$-0.730217\pi$
$773$	−11362.0	+	5188.85i	−0.528671	+	0.241436i	0.133153	+	0.991096i	$0.457490\pi$
$774$	5051.73	−	3223.58i	0.234600	−	0.149702i
$775$	−21528.7	−	6321.40i	−0.997851	−	0.292996i
$776$	11984.1	−	1604.88i	0.554386	−	0.0742418i
$777$	−1211.56	+	2652.95i	−0.0559388	+	0.122489i
$778$	−2645.84	+	17990.2i	−0.121925	+	0.829022i
$779$	8192.38	−	12747.6i	0.376794	−	0.586303i
$780$	−479.670	+	410.250i	−0.0220191	+	0.0188324i
$781$		−	15498.2i		−	0.710076i
$782$	21220.5	+	10987.1i	0.970386	+	0.502427i
$783$	1866.45			0.0851869
$784$	−25866.8	−	30641.7i	−1.17833	−	1.39585i
$785$	6343.85	+	4076.95i	0.288436	+	0.185366i
$786$	2190.48	+	322.157i	0.0994045	+	0.0146196i
$787$	−9592.25	−	4380.64i	−0.434469	−	0.198415i	0.186161	−	0.982519i	$-0.440396\pi$
$787$	−9592.25	−	4380.64i	−0.434469	−	0.198415i	−0.620629	+	0.784104i	$0.713123\pi$
$788$	−24793.1	+	3401.65i	−1.12083	+	0.153780i
$789$	740.427	−	2521.66i	0.0334092	−	0.113781i
$790$	−5213.03	+	3326.50i	−0.234774	+	0.149812i
$791$	−16098.9	−	35251.7i	−0.723655	−	1.58458i
$792$	−32348.2	+	9159.31i	−1.45132	+	0.410937i
$793$	−34083.3	+	39334.2i	−1.52627	+	1.76141i
$794$	4800.66	−	5504.29i	0.214571	−	0.246020i
$795$	104.067	+	354.418i	0.00464259	+	0.0158112i
$796$	678.297	+	1510.98i	0.0302030	+	0.0672804i
$797$	15490.8	+	24104.2i	0.688474	+	1.07129i	0.992923	+	0.118758i	$0.0378912\pi$
$797$	15490.8	+	24104.2i	0.688474	+	1.07129i	−0.304449	+	0.952529i	$0.598472\pi$
$798$	553.349	−	1862.30i	0.0245468	−	0.0826123i
$799$	762.091	+	5300.46i	0.0337432	+	0.234689i
$800$	−19132.3	−	9113.04i	−0.845534	−	0.402743i
$801$	4238.83	−	29481.7i	0.186981	−	1.30048i
$802$	−16668.1	+	25753.1i	−0.733878	+	1.13388i
$803$	34877.7	−	30221.7i	1.53276	−	1.32815i
$804$	282.138	+	1.81972i	0.0123759	+	7.98216e-5i
$805$	−8603.86	−	4419.60i	−0.376703	−	0.193504i
$806$	45081.6	+	145.381i	1.97014	+	0.00635338i
$807$	829.031	+	956.752i	0.0361627	+	0.0417339i
$808$	−24152.1	−	15853.9i	−1.05157	−	0.690269i
$809$	1187.20	−	8257.19i	0.0515944	−	0.358847i	−0.947626	−	0.319381i	$-0.896525\pi$
$809$	1187.20	−	8257.19i	0.0515944	−	0.358847i	0.999221	−	0.0394663i	$-0.0125658\pi$
$810$	2398.66	−	5207.82i	0.104050	−	0.225907i
$811$	−8093.48	+	1163.67i	−0.350432	+	0.0503845i	−0.315283	−	0.948998i	$-0.602100\pi$
$811$	−8093.48	+	1163.67i	−0.350432	+	0.0503845i	−0.0351487	+	0.999382i	$0.511190\pi$
$812$	−7373.95	+	24527.1i	−0.318688	+	1.06001i
$813$	−1124.08	−	1749.10i	−0.0484911	−	0.0754536i
$814$	−39588.8	+	17925.5i	−1.70465	+	0.771854i
$815$	−5624.30	+	1651.44i	−0.241731	+	0.0709786i
$816$	1233.98	+	1097.43i	0.0529386	+	0.0470808i
$817$	−3379.07	+	3899.65i	−0.144698	+	0.166991i
$818$	−5442.59	−	18759.3i	−0.232635	−	0.801839i
$819$	−63330.0	+	28921.9i	−2.70199	+	1.23396i
$820$	−2790.38	−	4404.12i	−0.118835	−	0.187559i
$821$	−4013.61	+	13669.1i	−0.170616	+	0.581065i	0.829141	+	0.559039i	$0.188830\pi$
$821$	−4013.61	+	13669.1i	−0.170616	+	0.581065i	−0.999757	+	0.0220261i	$0.992988\pi$
$822$	89.6766	+	638.321i	0.00380515	+	0.0270852i
$823$	−8477.84	+	18563.9i	−0.359075	+	0.786265i	0.640753	+	0.767747i	$0.278622\pi$
$823$	−8477.84	+	18563.9i	−0.359075	+	0.786265i	−0.999829	+	0.0185182i	$0.994105\pi$
$824$	−16985.9	−	2610.18i	−0.718123	−	0.110352i
$825$	−1833.47	−	1178.30i	−0.0773736	−	0.0497250i
$826$	19297.4	+	22416.1i	0.812886	+	0.944256i
$827$		−	45550.4i		−	1.91529i	−0.287957	−	0.957643i	$-0.592976\pi$
$827$		−	45550.4i		−	1.91529i	0.287957	−	0.957643i	$-0.407024\pi$
$828$	20605.7	−	11760.3i	0.864854	−	0.493597i
$829$		−	22400.5i		−	0.938484i	−0.883070	−	0.469242i	$-0.844527\pi$
$829$		−	22400.5i		−	0.938484i	0.883070	−	0.469242i	$-0.155473\pi$
$830$	−2022.31	+	1740.95i	−0.0845726	+	0.0728064i
$831$	1477.78	+	949.712i	0.0616891	+	0.0396452i
$832$	42020.1	+	6873.85i	1.75094	+	0.286428i
$833$	19935.9	−	43653.6i	0.829219	−	1.81574i
$834$	−805.000	+	113.093i	−0.0334231	+	0.00469556i
$835$	−1344.00	+	4577.25i	−0.0557019	+	0.189703i
$836$	24453.6	−	15493.4i	1.01166	−	0.640970i
$837$	3164.88	−	1445.35i	0.130698	−	0.0596879i
$838$	−23666.7	+	6866.35i	−0.975600	+	0.283048i
$839$	−8415.10	+	9711.54i	−0.346271	+	0.399618i	−0.901993	−	0.431750i	$-0.857896\pi$
$839$	−8415.10	+	9711.54i	−0.346271	+	0.399618i	0.555722	+	0.831368i	$0.312442\pi$
$840$	−500.917	−	442.604i	−0.0205753	−	0.0181801i
$841$	−13258.3	+	3892.98i	−0.543617	+	0.159620i
$842$	−8789.67	−	19412.1i	−0.359753	−	0.794520i
$843$	−39.5025	−	61.4671i	−0.00161393	−	0.00251132i
$844$	3769.29	−	12537.3i	0.153726	−	0.511318i
$845$	−13153.9	+	1891.24i	−0.535512	+	0.0769950i
$846$	4829.13	+	2224.24i	0.196252	+	0.0903912i
$847$	7634.80	−	53101.2i	0.309722	−	2.15417i
$848$	13741.0	−	20786.8i	0.556446	−	0.841772i
$849$	−1323.43	−	1527.32i	−0.0534982	−	0.0617402i
$850$	81.7869	−	25361.5i	0.00330031	−	1.02340i
$851$	24079.0	−	18993.3i	0.969938	−	0.765077i
$852$	−4.87478	+	755.809i	−0.000196018	+	0.0303916i
$853$	1969.45	−	1706.54i	0.0790536	−	0.0685003i	−0.614438	−	0.788965i	$-0.710617\pi$
$853$	1969.45	−	1706.54i	0.0790536	−	0.0685003i	0.693491	+	0.720465i	$0.256072\pi$
$854$	−46273.0	−	29949.1i	−1.85413	−	1.20004i
$855$	−705.601	+	4907.56i	−0.0282234	+	0.196298i
$856$	4308.60	−	9197.97i	0.172038	−	0.367266i
$857$	5335.12	+	37106.6i	0.212654	+	1.47904i	0.764245	+	0.644926i	$0.223112\pi$
$857$	5335.12	+	37106.6i	0.212654	+	1.47904i	−0.551591	+	0.834114i	$0.685979\pi$
$858$	4197.59	+	1247.24i	0.167020	+	0.0496271i
$859$	12602.9	+	19610.4i	0.500587	+	0.778928i	0.995964	−	0.0897494i	$-0.0286066\pi$
$859$	12602.9	+	19610.4i	0.500587	+	0.778928i	−0.495377	+	0.868678i	$0.664970\pi$
$860$	727.088	+	1619.66i	0.0288296	+	0.0642210i
$861$	683.901	+	2329.15i	0.0270700	+	0.0921920i
$862$	−27653.4	−	24118.4i	−1.09267	−	0.952987i
$863$	−24637.3	+	28433.0i	−0.971802	+	1.12152i	0.0207610	+	0.999784i	$0.493391\pi$
$863$	−24637.3	+	28433.0i	−0.971802	+	1.12152i	−0.992563	+	0.121735i	$0.961154\pi$
$864$	3167.52	−	874.847i	0.124724	−	0.0344478i
$865$	621.234	+	1360.31i	0.0244192	+	0.0534706i
$866$	−4655.15	−	7295.18i	−0.182666	−	0.286259i
$867$	−90.4999	+	308.214i	−0.00354503	+	0.0120733i
$868$	6489.65	+	47300.2i	0.253771	+	1.84962i
$869$	39025.7	+	17822.4i	1.52342	+	0.695725i
$870$	−40.1445	+	272.959i	−0.00156440	+	0.0106370i
$871$	7324.07	+	4706.89i	0.284921	+	0.183108i
$872$	12400.3	+	14593.6i	0.481567	+	0.566745i
$873$	14366.9			0.556984
$874$	−14123.6	+	14760.4i	−0.546610	+	0.571257i
$875$			21227.1i			0.820123i
$876$	−1710.41	+	1462.87i	−0.0659695	+	0.0564221i
$877$	5494.10	−	8548.98i	0.211542	−	0.329166i	−0.719226	−	0.694776i	$-0.755503\pi$
$877$	5494.10	−	8548.98i	0.211542	−	0.329166i	0.930768	+	0.365610i	$0.119140\pi$
$878$	8272.14	+	1216.59i	0.317963	+	0.0467632i
$879$	−1081.42	+	2367.99i	−0.0414966	+	0.0908649i
$880$	−1290.21	−	9876.35i	−0.0494237	−	0.378332i
$881$	−23816.8	−	6993.24i	−0.910792	−	0.267433i	−0.207418	−	0.978252i	$-0.566506\pi$
$881$	−23816.8	−	6993.24i	−0.910792	−	0.267433i	−0.703374	+	0.710820i	$0.748324\pi$
$882$	−25631.0	−	40166.8i	−0.978504	−	1.53343i
$883$	−45052.4	+	20574.7i	−1.71703	+	0.784140i	−0.721214	+	0.692712i	$0.756416\pi$
$883$	−45052.4	+	20574.7i	−1.71703	+	0.784140i	−0.995812	+	0.0914278i	$0.970857\pi$
$884$	14040.6	+	48984.3i	0.534203	+	1.86371i
$885$	240.801	+	208.655i	0.00914627	+	0.00792529i
$886$	7685.78	−	8812.28i	0.291432	−	0.334147i
$887$	1288.03	−	378.199i	0.0487573	−	0.0143164i	−0.257263	−	0.966341i	$-0.582821\pi$
$887$	1288.03	−	378.199i	0.0487573	−	0.0143164i	0.306020	+	0.952025i	$0.401002\pi$
$888$	1936.29	−	861.732i	0.0731729	−	0.0325651i
$889$	22100.4	−	14203.1i	0.833772	−	0.535833i
$890$	8458.60	+	2513.33i	0.318576	+	0.0946595i
$891$	−39373.9	+	5661.11i	−1.48044	+	0.212856i
$892$	−15485.4	+	33337.5i	−0.581265	+	1.25137i
$893$	−4531.42	−	651.519i	−0.169807	−	0.0244146i
$894$	−381.550	+	589.515i	−0.0142740	+	0.0220541i
$895$	5922.18	+	6834.56i	0.221181	+	0.255256i
$896$	−1017.82	+	45080.9i	−0.0379497	+	1.68085i
$897$	−3086.94	−	142.503i	−0.114905	−	0.00530438i
$898$	−42.5174	+	13184.3i	−0.00157998	+	0.489940i
$899$	14892.6	−	12904.5i	0.552499	−	0.478743i
$900$	−21095.0	−	13750.0i	−0.781298	−	0.509260i
$901$	29517.6	+	4243.98i	1.09142	+	0.156923i
$902$	−15132.1	+	32853.9i	−0.558585	+	1.21276i
$903$	−117.639	−	818.199i	−0.00433532	−	0.0301528i
$904$	−8195.16	+	26943.1i	−0.301512	+	0.991277i
$905$	−137.339	+	88.2622i	−0.00504452	+	0.00324192i
$906$	−1113.77	−	2459.79i	−0.0408418	−	0.0901997i
$907$	−5852.91	−	19933.2i	−0.214270	−	0.729736i	−0.994546	−	0.104300i	$-0.966740\pi$
$907$	−5852.91	−	19933.2i	−0.214270	−	0.729736i	0.780276	−	0.625435i	$-0.215079\pi$
$908$	29614.5	+	25997.4i	1.08237	+	0.950169i
$909$	−25943.9	−	22480.5i	−0.946649	−	0.820276i
$910$	−5747.21	−	19809.3i	−0.209361	−	0.721617i
$911$	19014.0	+	41634.9i	0.691507	+	1.51419i	0.849974	+	0.526825i	$0.176618\pi$
$911$	19014.0	+	41634.9i	0.691507	+	1.51419i	−0.158466	+	0.987364i	$0.550655\pi$
$912$	−1197.41	+	747.885i	−0.0434763	+	0.0271545i
$913$	17763.1	+	5215.73i	0.643893	+	0.189064i
$914$	−40862.6	+	5740.72i	−1.47879	+	0.207753i
$915$	−540.105	−	246.658i	−0.0195140	−	0.00891174i
$916$	−27583.8	−	4147.71i	−0.994973	−	0.149612i
$917$	−39116.6	+	60866.6i	−1.40866	+	2.19192i
$918$	2565.79	+	2980.44i	0.0922479	+	0.107156i
$919$	54145.6			1.94353			0.971763	−	0.235960i	$-0.0758234\pi$
$919$	54145.6			1.94353			0.971763	+	0.235960i	$0.0758234\pi$
$920$	2558.77	+	6546.67i	0.0916958	+	0.234606i
$921$	2202.34			0.0787944
$922$	−18270.2	−	21222.8i	−0.652599	−	0.758066i
$923$	−12609.1	+	19620.2i	−0.449658	+	0.699681i
$924$	−689.575	+	4585.93i	−0.0245512	+	0.163275i
$925$	−29607.7	−	13521.4i	−1.05243	−	0.480628i
$926$	11873.3	−	1668.05i	0.421360	−	0.0591962i
$927$	−19592.9	−	5753.00i	−0.694192	−	0.203833i
$928$	15817.3	−	9808.42i	0.559512	−	0.346958i
$929$	−12300.7	−	26934.8i	−0.434417	−	0.951241i	−0.992590	−	0.121516i	$-0.961225\pi$
$929$	−12300.7	−	26934.8i	−0.434417	−	0.951241i	0.558172	−	0.829725i	$-0.311503\pi$
$930$	143.304	+	493.937i	0.00505283	+	0.0174159i
$931$	31006.5	+	26867.3i	1.09151	+	0.945800i
$932$	35299.8	−	40211.2i	1.24065	−	1.41326i
$933$	−179.383	−	610.924i	−0.00629448	−	0.0214370i
$934$	−5499.23	−	12145.1i	−0.192656	−	0.425483i
$935$	10027.9	−	6444.52i	0.350745	−	0.225410i
$936$	48403.6	+	14722.7i	1.69030	+	0.514130i
$937$	4612.00	+	32077.1i	0.160798	+	1.11837i	0.897135	+	0.441757i	$0.145645\pi$
$937$	4612.00	+	32077.1i	0.160798	+	1.11837i	−0.736337	+	0.676615i	$0.763446\pi$
$938$	−3857.20	+	8374.52i	−0.134267	+	0.291511i
$939$	−2061.78	−	296.440i	−0.0716547	−	0.0103024i
$940$	−860.115	+	1319.58i	−0.0298445	+	0.0457870i
$941$	1247.11	−	1080.63i	0.0432037	−	0.0374362i	−0.632991	−	0.774159i	$-0.718173\pi$
$941$	1247.11	−	1080.63i	0.0432037	−	0.0374362i	0.676195	+	0.736723i	$0.263628\pi$
$942$	−8.22794	+	2551.42i	−0.000284587	+	0.0882483i
$943$	4793.98	−	25071.8i	0.165550	−	0.865800i
$944$	277.252	−	21492.3i	0.00955909	−	0.741012i
$945$	−1042.46	−	1203.06i	−0.0358848	−	0.0414133i
$946$	6692.52	−	10340.3i	0.230013	−	0.355383i
$947$	41361.1	+	5946.83i	1.41928	+	0.204061i	0.808852	−	0.588013i	$-0.200090\pi$
$947$	41361.1	+	5946.83i	1.41928	+	0.204061i	0.610425	+	0.792074i	$0.290999\pi$
$948$	−1897.58	−	881.432i	−0.0650112	−	0.0301979i
$949$	−68741.9	+	9883.59i	−2.35138	+	0.338077i
$950$	20783.8	+	6175.56i	0.709807	+	0.210907i
$951$	−584.712	+	375.771i	−0.0199375	+	0.0128131i
$952$	−49303.0	+	21942.0i	−1.67849	+	0.747000i
$953$	748.055	−	219.649i	0.0254269	−	0.00746603i	−0.268994	−	0.963142i	$-0.586691\pi$
$953$	748.055	−	219.649i	0.0254269	−	0.00746603i	0.294421	+	0.955676i	$0.404873\pi$
$954$	19461.3	−	22313.8i	0.660465	−	0.757269i
$955$	−5977.19	−	5179.27i	−0.202531	−	0.175494i
$956$	3196.44	−	916.207i	0.108138	−	0.0309961i
$957$	1741.12	−	795.143i	0.0588113	−	0.0268582i
$958$	5184.20	+	8124.26i	0.174837	+	0.273990i
$959$	−20211.1	−	5934.52i	−0.680554	−	0.199829i
$960$	59.8138	+	482.052i	0.00201092	+	0.0162064i
$961$	2884.26	−	6315.65i	0.0968166	−	0.211999i
$962$	64702.0	+	9515.80i	2.16848	+	0.318921i
$963$	6524.96	−	10153.0i	0.218343	−	0.339748i
$964$	−9689.99	−	11329.7i	−0.323749	−	0.378531i
$965$		−	2796.48i		−	0.0932868i
$966$	−305.368	−	3258.39i	−0.0101709	−	0.108527i
$967$	677.835			0.0225416			0.0112708	−	0.999936i	$-0.496412\pi$
$967$	677.835			0.0225416			0.0112708	+	0.999936i	$0.496412\pi$
$968$	−29708.3	+	25243.3i	−0.986427	+	0.838174i
$969$	−1421.37	−	913.456i	−0.0471216	−	0.0302832i
$970$	−619.326	+	4211.06i	−0.0205004	+	0.139391i
$971$	14421.9	+	6586.27i	0.476644	+	0.217676i	0.639226	−	0.769019i	$-0.279255\pi$
$971$	14421.9	+	6586.27i	0.476644	+	0.217676i	−0.162582	+	0.986695i	$0.551982\pi$
$972$	5806.69	−	796.685i	0.191615	−	0.0262898i
$973$	7484.15	−	25488.7i	0.246589	−	0.839804i
$974$	−8664.48	−	13578.3i	−0.285039	−	0.446690i
$975$	1362.46	+	2983.37i	0.0447524	+	0.0979941i
$976$	10788.0	+	38574.3i	0.353806	+	1.26510i
$977$	38168.1	−	44048.4i	1.24985	−	1.44241i	0.399046	−	0.916931i	$-0.369341\pi$
$977$	38168.1	−	44048.4i	1.24985	−	1.44241i	0.850808	−	0.525477i	$-0.176113\pi$
$978$	−1494.67	−	1303.60i	−0.0488694	−	0.0426223i
$979$	−17247.5	−	58739.6i	−0.563057	−	1.91759i
$980$	12878.1	−	5781.15i	0.419771	−	0.188441i
$981$	12302.3	+	19142.8i	0.400391	+	0.623020i
$982$	40562.3	+	12052.4i	1.31812	+	0.391657i
$983$	1664.01	+	11573.5i	0.0539917	+	0.375520i	0.998846	+	0.0480292i	$0.0152941\pi$
$983$	1664.01	+	11573.5i	0.0539917	+	0.375520i	−0.944854	+	0.327491i	$0.893797\pi$
$984$	748.289	−	1597.44i	0.0242425	−	0.0517527i
$985$	1253.73	−	8719.89i	0.0405555	−	0.282070i
$986$	18699.0	+	12102.5i	0.603951	+	0.390894i
$987$	554.255	−	480.264i	0.0178745	−	0.0154883i
$988$	−43562.6	−	280.968i	−1.40274	−	0.00904734i
$989$	−2830.86	+	8218.29i	−0.0910173	+	0.264233i
$990$	38.1660	−	11835.0i	0.00122525	−	0.379940i
$991$	−2261.54	−	2609.96i	−0.0724927	−	0.0836610i	0.718345	−	0.695687i	$-0.244900\pi$
$991$	−2261.54	−	2609.96i	−0.0724927	−	0.0836610i	−0.790837	+	0.612026i	$0.790355\pi$
$992$	19225.4	−	28880.6i	0.615329	−	0.924354i
$993$	152.221	−	1058.72i	0.00486463	−	0.0338342i
$994$	−22434.2	−	10332.9i	−0.715864	−	0.329718i
$995$	−577.105	+	82.9752i	−0.0183874	+	0.00264371i
$996$	−864.624	−	259.945i	−0.0275067	−	0.00826977i
$997$	31274.7	+	48664.4i	0.993460	+	1.54585i	0.828832	+	0.559498i	$0.189006\pi$
$997$	31274.7	+	48664.4i	0.993460	+	1.54585i	0.164628	+	0.986356i	$0.447357\pi$
$998$	12533.6	+	27680.7i	0.397540	+	0.877972i
$999$	4842.80	−	1421.97i	0.153373	−	0.0450343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.p.a.13.16	✓	700
8.5	even	2	inner	184.4.p.a.13.56	yes	700
23.16	even	11	inner	184.4.p.a.85.56	yes	700
184.85	even	22	inner	184.4.p.a.85.16	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.p.a.13.16	✓	700	1.1	even	1	trivial
184.4.p.a.13.56	yes	700	8.5	even	2	inner
184.4.p.a.85.16	yes	700	184.85	even	22	inner
184.4.p.a.85.56	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+(-2.14354 + 1.84532i) q^{2} +(0.182132 - 0.283403i) q^{3} +(1.18957 - 7.91106i) q^{4} +(2.56171 + 1.16989i) q^{5} +(0.132562 + 0.943579i) q^{6} +(-29.8765 - 8.77253i) q^{7} +(12.0486 + 19.1529i) q^{8} +(11.1691 + 24.4568i) q^{9} +(-7.64996 + 2.21946i) q^{10} +(41.7643 + 36.1890i) q^{11} +(-2.02536 - 1.77798i) q^{12} +(-23.4293 - 79.7928i) q^{13} +(80.2297 - 36.3275i) q^{14} +(0.798120 - 0.512921i) q^{15} +(-61.1699 - 18.8215i) q^{16} +(-10.9004 - 75.8137i) q^{17} +(-69.0721 - 31.8138i) q^{18} +(64.8138 + 9.31882i) q^{19} +(12.3024 - 18.8742i) q^{20} +(-7.92763 + 6.86933i) q^{21} +(-156.304 - 0.504056i) q^{22} +(107.156 - 26.1627i) q^{23} +(7.62241 + 0.0737452i) q^{24} +(-76.6639 - 88.4748i) q^{25} +(197.465 + 127.805i) q^{26} +(17.9686 + 2.58350i) q^{27} +(-104.940 + 225.919i) q^{28} +(101.769 - 14.6322i) q^{29} +(-0.764302 + 2.57226i) q^{30} +(161.236 - 103.620i) q^{31} +(165.852 - 72.5335i) q^{32} +(17.8627 - 5.24495i) q^{33} +(163.266 + 142.395i) q^{34} +(-66.2719 - 57.4250i) q^{35} +(206.766 - 59.2661i) q^{36} +(252.908 - 115.499i) q^{37} +(-156.128 + 99.6271i) q^{38} +(-26.8807 - 7.89289i) q^{39} +(8.45815 + 63.1596i) q^{40} +(96.1331 - 210.502i) q^{41} +(4.31709 - 29.3537i) q^{42} +(-42.6036 + 66.2924i) q^{43} +(335.975 - 287.351i) q^{44} +75.7179i q^{45} +(-181.416 + 253.819i) q^{46} -69.9143 q^{47} +(-16.4750 + 13.9077i) q^{48} +(527.098 + 338.745i) q^{49} +(327.597 + 48.1801i) q^{50} +(-23.4711 - 10.7189i) q^{51} +(-659.117 + 90.4317i) q^{52} +(-109.691 + 373.572i) q^{53} +(-43.2839 + 27.6200i) q^{54} +(64.6507 + 141.565i) q^{55} +(-191.950 - 677.917i) q^{56} +(14.4457 - 16.6712i) q^{57} +(-191.145 + 219.161i) q^{58} +(94.6186 + 322.241i) q^{59} +(-3.10833 - 6.92413i) q^{60} +(-338.361 - 526.499i) q^{61} +(-154.404 + 519.646i) q^{62} +(-119.144 - 828.665i) q^{63} +(-221.664 + 461.529i) q^{64} +(33.3300 - 231.816i) q^{65} +(-28.6108 + 44.2052i) q^{66} +(-79.1191 + 68.5571i) q^{67} +(-612.733 - 3.95198i) q^{68} +(12.1020 - 35.1335i) q^{69} +(248.024 + 0.799839i) q^{70} +(-183.655 - 211.949i) q^{71} +(-333.847 + 508.589i) q^{72} +(118.848 - 826.608i) q^{73} +(-328.987 + 714.276i) q^{74} +(-39.0370 + 5.61267i) q^{75} +(150.822 - 501.661i) q^{76} +(-930.302 - 1447.58i) q^{77} +(72.1850 - 32.6849i) q^{78} +(744.902 - 218.723i) q^{79} +(-134.680 - 119.777i) q^{80} +(-471.382 + 544.004i) q^{81} +(182.379 + 628.617i) q^{82} +(304.731 - 139.166i) q^{83} +(44.9132 + 70.8875i) q^{84} +(60.7703 - 206.965i) q^{85} +(-31.0083 - 220.718i) q^{86} +(14.3886 - 31.5066i) q^{87} +(-189.922 + 1235.93i) q^{88} +(-931.941 - 598.922i) q^{89} +(-139.724 - 162.305i) q^{90} +2589.46i q^{91} +(-79.5049 - 878.844i) q^{92} -64.5672i q^{93} +(149.865 - 129.015i) q^{94} +(155.132 + 99.6973i) q^{95} +(9.65076 - 60.2136i) q^{96} +(221.979 - 486.066i) q^{97} +(-1754.95 + 246.550i) q^{98} +(-418.600 + 1425.62i) 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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