LMFDB - Embedded newform 160.4.z.a.29.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(29,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("160.29");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.z (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.18
Character	$\chi$	$=$	160.29
Dual form			160.4.z.a.149.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89989 + 2.09533i) q^{2} +(3.43485 - 8.29247i) q^{3} +(-0.780855 - 7.96180i) q^{4} +(-9.81187 - 5.35978i) q^{5} +(10.8497 + 22.9519i) q^{6} +(-3.51241 - 3.51241i) q^{7} +(18.1662 + 13.4904i) q^{8} +(-37.8750 - 37.8750i) q^{9} +(29.8720 - 10.3762i) q^{10} +(57.2938 - 23.7319i) q^{11} +(-68.7051 - 20.8724i) q^{12} +(6.77573 + 2.80660i) q^{13} +(14.0328 - 0.686491i) q^{14} +(-78.1482 + 62.9546i) q^{15} +(-62.7805 + 12.4340i) q^{16} -115.914 q^{17} +(151.319 - 7.40257i) q^{18} +(8.39272 - 20.2618i) q^{19} +(-35.0118 + 82.3054i) q^{20} +(-41.1912 + 17.0619i) q^{21} +(-59.1256 + 165.138i) q^{22} +(-135.801 + 135.801i) q^{23} +(174.267 - 104.305i) q^{24} +(67.5456 + 105.179i) q^{25} +(-18.7539 + 8.86520i) q^{26} +(-220.276 + 91.2412i) q^{27} +(-25.2224 + 30.7078i) q^{28} +(-143.380 - 59.3899i) q^{29} +(16.5617 - 283.353i) q^{30} -8.07804 q^{31} +(93.2225 - 155.169i) q^{32} -556.623i q^{33} +(220.224 - 242.879i) q^{34} +(15.6376 + 53.2890i) q^{35} +(-271.978 + 331.128i) q^{36} +(88.3608 - 36.6002i) q^{37} +(26.5101 + 56.0807i) q^{38} +(46.5473 - 46.5473i) q^{39} +(-105.939 - 229.732i) q^{40} +(121.999 + 121.999i) q^{41} +(42.5081 - 118.725i) q^{42} +(-106.239 - 256.484i) q^{43} +(-233.687 - 437.631i) q^{44} +(168.623 + 574.626i) q^{45} +(-26.5420 - 542.557i) q^{46} +369.471 q^{47} +(-112.533 + 563.315i) q^{48} -318.326i q^{49} +(-348.714 - 58.2975i) q^{50} +(-398.148 + 961.215i) q^{51} +(17.0547 - 56.1385i) q^{52} +(51.6579 + 124.713i) q^{53} +(227.318 - 634.899i) q^{54} +(-689.357 - 74.2281i) q^{55} +(-16.4233 - 111.191i) q^{56} +(-139.193 - 139.193i) q^{57} +(396.847 - 187.595i) q^{58} +(99.4186 + 240.018i) q^{59} +(562.254 + 573.042i) q^{60} +(15.8197 + 6.55272i) q^{61} +(15.3474 - 16.9262i) q^{62} +266.065i q^{63} +(148.020 + 490.137i) q^{64} +(-51.4398 - 63.8544i) q^{65} +(1166.31 + 1057.52i) q^{66} +(328.782 - 793.751i) q^{67} +(90.5122 + 922.885i) q^{68} +(659.671 + 1592.59i) q^{69} +(-141.368 - 68.4772i) q^{70} +(-172.016 + 172.016i) q^{71} +(-177.096 - 1198.99i) q^{72} +(395.478 - 395.478i) q^{73} +(-91.1858 + 254.682i) q^{74} +(1104.20 - 198.846i) q^{75} +(-167.874 - 50.9996i) q^{76} +(-284.595 - 117.883i) q^{77} +(9.09754 + 185.967i) q^{78} -1115.82i q^{79} +(682.638 + 214.489i) q^{80} +693.821i q^{81} +(-487.414 + 23.8444i) q^{82} +(-1018.10 - 421.713i) q^{83} +(168.008 + 314.633i) q^{84} +(1137.33 + 621.274i) q^{85} +(739.262 + 264.684i) q^{86} +(-984.978 + 984.978i) q^{87} +(1360.96 + 341.798i) q^{88} +(546.196 - 546.196i) q^{89} +(-1524.40 - 738.403i) q^{90} +(-13.9412 - 33.6570i) q^{91} +(1187.27 + 975.182i) q^{92} +(-27.7469 + 66.9869i) q^{93} +(-701.954 + 774.166i) q^{94} +(-190.947 + 153.823i) q^{95} +(-966.533 - 1306.03i) q^{96} +135.082i q^{97} +(666.999 + 604.784i) q^{98} +(-3068.85 - 1271.16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) $ 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−1.89989	+	2.09533i	−0.671712	+	0.740813i
$2$	−1.89989	+	2.09533i	−0.671712	+	0.740813i
$3$	3.43485	−	8.29247i	0.661038	−	1.59589i	−0.135141	−	0.990826i	$-0.543149\pi$
$3$	3.43485	−	8.29247i	0.661038	−	1.59589i	0.796179	−	0.605061i	$-0.206851\pi$
$4$	−0.780855	−	7.96180i	−0.0976069	−	0.995225i
$5$	−9.81187	−	5.35978i	−0.877600	−	0.479393i
$5$	−9.81187	−	5.35978i	−0.877600	−	0.479393i
$6$	10.8497	+	22.9519i	0.738227	+	1.56168i
$7$	−3.51241	−	3.51241i	−0.189652	−	0.189652i	0.605894	−	0.795546i	$-0.292816\pi$
$7$	−3.51241	−	3.51241i	−0.189652	−	0.189652i	−0.795546	+	0.605894i	$0.792816\pi$
$8$	18.1662	+	13.4904i	0.802839	+	0.596196i
$9$	−37.8750	−	37.8750i	−1.40278	−	1.40278i
$10$	29.8720	−	10.3762i	0.944635	−	0.328124i
$11$	57.2938	−	23.7319i	1.57043	−	0.650494i	0.583570	−	0.812063i	$-0.301656\pi$
$11$	57.2938	−	23.7319i	1.57043	−	0.650494i	0.986861	+	0.161569i	$0.0516556\pi$
$12$	−68.7051	−	20.8724i	−1.65279	−	0.502112i
$13$	6.77573	+	2.80660i	0.144558	+	0.0598777i	0.453789	−	0.891109i	$-0.350072\pi$
$13$	6.77573	+	2.80660i	0.144558	+	0.0598777i	−0.309232	+	0.950987i	$0.600072\pi$
$14$	14.0328	−	0.686491i	0.267888	−	0.0131052i
$15$	−78.1482	+	62.9546i	−1.34518	+	1.08365i
$16$	−62.7805	+	12.4340i	−0.980946	+	0.194282i
$17$	−115.914			−1.65372			−0.826862	−	0.562405i	$-0.809876\pi$
$17$	−115.914			−1.65372			−0.826862	+	0.562405i	$0.809876\pi$
$18$	151.319	−	7.40257i	1.98146	−	0.0969334i
$19$	8.39272	−	20.2618i	0.101338	−	0.244652i	−0.865076	−	0.501640i	$-0.832730\pi$
$19$	8.39272	−	20.2618i	0.101338	−	0.244652i	0.966414	+	0.256988i	$0.0827302\pi$
$20$	−35.0118	+	82.3054i	−0.391444	+	0.920202i
$21$	−41.1912	+	17.0619i	−0.428031	+	0.177296i
$22$	−59.1256	+	165.138i	−0.572983	+	1.60034i
$23$	−135.801	+	135.801i	−1.23115	+	1.23115i	−0.267634	+	0.963521i	$0.586242\pi$
$23$	−135.801	+	135.801i	−1.23115	+	1.23115i	−0.963521	+	0.267634i	$0.913758\pi$
$24$	174.267	−	104.305i	1.48217	−	0.887132i
$25$	67.5456	+	105.179i	0.540364	+	0.841431i
$26$	−18.7539	+	8.86520i	−0.141459	+	0.0668695i
$27$	−220.276	+	91.2412i	−1.57008	+	0.650347i
$28$	−25.2224	+	30.7078i	−0.170235	+	0.207258i
$29$	−143.380	−	59.3899i	−0.918102	−	0.380290i	−0.126949	−	0.991909i	$-0.540519\pi$
$29$	−143.380	−	59.3899i	−0.918102	−	0.380290i	−0.791153	+	0.611619i	$0.790519\pi$
$30$	16.5617	−	283.353i	0.100792	−	1.72443i
$31$	−8.07804			−0.0468019			−0.0234010	−	0.999726i	$-0.507449\pi$
$31$	−8.07804			−0.0468019			−0.0234010	+	0.999726i	$0.507449\pi$
$32$	93.2225	−	155.169i	0.514986	−	0.857198i
$33$		−	556.623i		−	2.93623i
$34$	220.224	−	242.879i	1.11083	−	1.22510i
$35$	15.6376	+	53.2890i	0.0755209	+	0.257357i
$36$	−271.978	+	331.128i	−1.25916	+	1.53300i
$37$	88.3608	−	36.6002i	0.392606	−	0.162623i	−0.177642	−	0.984095i	$-0.556847\pi$
$37$	88.3608	−	36.6002i	0.392606	−	0.162623i	0.570248	+	0.821472i	$0.306847\pi$
$38$	26.5101	+	56.0807i	0.113171	+	0.239408i
$39$	46.5473	−	46.5473i	0.191116	−	0.191116i
$40$	−105.939	−	229.732i	−0.418760	−	0.908097i
$41$	121.999	+	121.999i	0.464710	+	0.464710i	0.900196	−	0.435486i	$-0.143423\pi$
$41$	121.999	+	121.999i	0.464710	+	0.464710i	−0.435486	+	0.900196i	$0.643423\pi$
$42$	42.5081	−	118.725i	0.156170	−	0.436183i
$43$	−106.239	−	256.484i	−0.376775	−	0.909615i	−0.992566	−	0.121705i	$-0.961164\pi$
$43$	−106.239	−	256.484i	−0.376775	−	0.909615i	0.615792	−	0.787909i	$-0.288836\pi$
$44$	−233.687	−	437.631i	−0.800673	−	1.49944i
$45$	168.623	+	574.626i	0.558596	+	1.90356i
$46$	−26.5420	−	542.557i	−0.0850741	−	1.73904i
$47$	369.471			1.14666			0.573329	−	0.819325i	$-0.305652\pi$
$47$	369.471			1.14666			0.573329	+	0.819325i	$0.305652\pi$
$48$	−112.533	+	563.315i	−0.338391	+	1.69391i
$49$		−	318.326i		−	0.928064i
$50$	−348.714	−	58.2975i	−0.986312	−	0.164890i
$51$	−398.148	+	961.215i	−1.09317	+	2.63916i
$52$	17.0547	−	56.1385i	0.0454820	−	0.149712i
$53$	51.6579	+	124.713i	0.133882	+	0.323221i	0.976576	−	0.215173i	$-0.0690315\pi$
$53$	51.6579	+	124.713i	0.133882	+	0.323221i	−0.842694	+	0.538393i	$0.819031\pi$
$54$	227.318	−	634.899i	0.572854	−	1.59998i
$55$	−689.357	−	74.2281i	−1.69005	−	0.181980i
$56$	−16.4233	−	111.191i	−0.0391904	−	0.265330i
$57$	−139.193	−	139.193i	−0.323448	−	0.323448i
$58$	396.847	−	187.595i	0.898424	−	0.424696i
$59$	99.4186	+	240.018i	0.219376	+	0.529621i	0.994803	−	0.101816i	$-0.0324654\pi$
$59$	99.4186	+	240.018i	0.219376	+	0.529621i	−0.775427	+	0.631437i	$0.782465\pi$
$60$	562.254	+	573.042i	1.20978	+	1.23299i
$61$	15.8197	+	6.55272i	0.0332049	+	0.0137539i	0.399224	−	0.916853i	$-0.369280\pi$
$61$	15.8197	+	6.55272i	0.0332049	+	0.0137539i	−0.366019	+	0.930607i	$0.619280\pi$
$62$	15.3474	−	16.9262i	0.0314374	−	0.0346714i
$63$			266.065i			0.532080i
$64$	148.020	+	490.137i	0.289101	+	0.957299i
$65$	−51.4398	−	63.8544i	−0.0981588	−	0.121849i
$66$	1166.31	+	1057.52i	2.17520	+	1.97230i
$67$	328.782	−	793.751i	0.599510	−	1.44735i	−0.274572	−	0.961567i	$-0.588536\pi$
$67$	328.782	−	793.751i	0.599510	−	1.44735i	0.874082	−	0.485778i	$-0.161464\pi$
$68$	90.5122	+	922.885i	0.161415	+	1.64583i
$69$	659.671	+	1592.59i	1.15094	+	2.77862i
$70$	−141.368	−	68.4772i	−0.241381	−	0.116923i
$71$	−172.016	+	172.016i	−0.287529	+	0.287529i	−0.836102	−	0.548573i	$-0.815171\pi$
$71$	−172.016	+	172.016i	−0.287529	+	0.287529i	0.548573	+	0.836102i	$0.315171\pi$
$72$	−177.096	−	1198.99i	−0.289875	−	1.96253i
$73$	395.478	−	395.478i	0.634071	−	0.634071i	−0.315015	−	0.949087i	$-0.602010\pi$
$73$	395.478	−	395.478i	0.634071	−	0.634071i	0.949087	+	0.315015i	$0.102010\pi$
$74$	−91.1858	+	254.682i	−0.143245	+	0.400083i
$75$	1104.20	−	198.846i	1.70003	−	0.306143i
$76$	−167.874	−	50.9996i	−0.253375	−	0.0769744i
$77$	−284.595	−	117.883i	−0.421203	−	0.174468i
$78$	9.09754	+	185.967i	0.0132063	+	0.269956i
$79$		−	1115.82i		−	1.58911i	−0.607194	−	0.794553i	$-0.707705\pi$
$79$		−	1115.82i		−	1.58911i	0.607194	−	0.794553i	$-0.292295\pi$
$80$	682.638	+	214.489i	0.954016	+	0.299757i
$81$			693.821i			0.951743i
$82$	−487.414	+	23.8444i	−0.656414	+	0.0321119i
$83$	−1018.10	−	421.713i	−1.34640	−	0.557699i	−0.411115	−	0.911583i	$-0.634861\pi$
$83$	−1018.10	−	421.713i	−1.34640	−	0.557699i	−0.935289	+	0.353885i	$0.884861\pi$
$84$	168.008	+	314.633i	0.218228	+	0.408682i
$85$	1137.33	+	621.274i	1.45131	+	0.792784i
$86$	739.262	+	264.684i	0.926938	+	0.331879i
$87$	−984.978	+	984.978i	−1.21380	+	1.21380i
$88$	1360.96	+	341.798i	1.64862	+	0.414042i
$89$	546.196	−	546.196i	0.650524	−	0.650524i	−0.302595	−	0.953119i	$-0.597853\pi$
$89$	546.196	−	546.196i	0.650524	−	0.650524i	0.953119	+	0.302595i	$0.0978529\pi$
$90$	−1524.40	−	738.403i	−1.78540	−	0.864828i
$91$	−13.9412	−	33.6570i	−0.0160597	−	0.0387716i
$92$	1187.27	+	975.182i	1.34544	+	1.10511i
$93$	−27.7469	+	66.9869i	−0.0309378	+	0.0746906i
$94$	−701.954	+	774.166i	−0.770224	+	0.849459i
$95$	−190.947	+	153.823i	−0.206219	+	0.166126i
$96$	−966.533	−	1306.03i	−1.02757	−	1.38850i
$97$			135.082i			0.141397i	0.997498	+	0.0706986i	$0.0225229\pi$
$97$			135.082i			0.141397i	−0.997498	+	0.0706986i	$0.977477\pi$
$98$	666.999	+	604.784i	0.687522	+	0.623391i
$99$	−3068.85	−	1271.16i	−3.11546	−	1.29047i
$100$	784.670	−	619.914i	0.784670	−	0.619914i
$101$	−60.6648	−	146.458i	−0.0597661	−	0.144288i	0.891175	−	0.453659i	$-0.149882\pi$
$101$	−60.6648	−	146.458i	−0.0597661	−	0.144288i	−0.950941	+	0.309371i	$0.899882\pi$
$102$	−1257.63	−	2660.45i	−1.22082	−	2.58259i
$103$	−1114.62	−	1114.62i	−1.06628	−	1.06628i	−0.997641	−	0.0686427i	$-0.978133\pi$
$103$	−1114.62	−	1114.62i	−1.06628	−	1.06628i	−0.0686427	−	0.997641i	$-0.521867\pi$
$104$	85.2270	+	142.392i	0.0803576	+	0.134257i
$105$	495.610	+	53.3660i	0.460635	+	0.0495999i
$106$	−359.460	−	128.701i	−0.329376	−	0.117929i
$107$	−10.7450	−	25.9406i	−0.00970798	−	0.0234371i	0.918951	−	0.394371i	$-0.129038\pi$
$107$	−10.7450	−	25.9406i	−0.00970798	−	0.0234371i	−0.928659	+	0.370934i	$0.879038\pi$
$108$	898.448	+	1682.55i	0.800492	+	1.49910i
$109$	−669.250	+	1615.71i	−0.588097	+	1.41979i	0.297223	+	0.954808i	$0.403939\pi$
$109$	−669.250	+	1615.71i	−0.588097	+	1.41979i	−0.885320	+	0.464983i	$0.846061\pi$
$110$	1465.23	−	1303.41i	1.27004	−	1.12977i
$111$		−	858.446i		−	0.734055i
$112$	264.184	+	176.837i	0.222884	+	0.149193i
$113$	−339.512			−0.282642			−0.141321	−	0.989964i	$-0.545135\pi$
$113$	−339.512			−0.282642			−0.141321	+	0.989964i	$0.545135\pi$
$114$	556.106	−	27.2049i	0.456878	−	0.0223506i
$115$	2060.33	−	604.600i	1.67067	−	0.490255i
$116$	−360.891	+	1187.94i	−0.288861	+	0.950837i
$117$	−150.331	−	362.931i	−0.118787	−	0.286777i
$118$	−691.801	−	247.691i	−0.539707	−	0.193236i
$119$	407.138	+	407.138i	0.313632	+	0.313632i
$120$	−2268.93	+	89.3967i	−1.72604	+	0.0680063i
$121$	1778.22	−	1778.22i	1.33600	−	1.33600i
$122$	−43.7857	+	20.6981i	−0.0324932	+	0.0153600i
$123$	1430.73	−	592.626i	1.04881	−	0.434433i
$124$	6.30778	+	64.3157i	0.00456819	+	0.0465784i
$125$	−99.0128	−	1394.03i	−0.0708478	−	0.997487i
$126$	−557.495	−	505.493i	−0.394171	−	0.357404i
$127$			394.238i			0.275456i	0.990470	+	0.137728i	$0.0439800\pi$
$127$			394.238i			0.275456i	−0.990470	+	0.137728i	$0.956020\pi$
$128$	−1308.22	−	621.054i	−0.903372	−	0.428859i
$129$	−2491.80			−1.70070
$130$	231.526	+	13.5325i	0.156201	+	0.00912983i
$131$	−310.007	−	128.409i	−0.206759	−	0.0856425i	0.276900	−	0.960899i	$-0.410693\pi$
$131$	−310.007	−	128.409i	−0.206759	−	0.0856425i	−0.483660	+	0.875256i	$0.660693\pi$
$132$	−4431.72	+	434.642i	−2.92221	+	0.286597i
$133$	−100.646	+	41.6891i	−0.0656177	+	0.0271797i
$134$	1038.52	+	2196.95i	0.669514	+	1.41632i
$135$	2650.35	+	285.382i	1.68967	+	0.181939i
$136$	−2105.72	−	1563.72i	−1.32767	−	0.985943i
$137$	154.632	−	154.632i	0.0964314	−	0.0964314i	−0.657245	−	0.753677i	$-0.728278\pi$
$137$	154.632	−	154.632i	0.0964314	−	0.0964314i	0.753677	+	0.657245i	$0.228278\pi$
$138$	−4590.31	−	1643.50i	−2.83154	−	1.01380i
$139$	810.281	−	335.629i	0.494440	−	0.204804i	−0.121508	−	0.992590i	$-0.538773\pi$
$139$	810.281	−	335.629i	0.494440	−	0.204804i	0.615948	+	0.787787i	$0.288773\pi$
$140$	412.066	−	166.114i	0.248757	−	0.100280i
$141$	1269.08	−	3063.83i	0.757985	−	1.82994i
$142$	−33.6201	−	687.243i	−0.0198686	−	0.406142i
$143$	454.813			0.265968
$144$	2848.75	+	1906.87i	1.64858	+	1.10351i
$145$	1088.51	+	1351.21i	0.623418	+	0.773875i
$146$	77.2951	+	1580.02i	0.0438150	+	0.895641i
$147$	−2639.71	−	1093.40i	−1.48109	−	0.613486i
$148$	−360.401	−	674.932i	−0.200167	−	0.374858i
$149$	−1472.77	+	610.042i	−0.809760	+	0.335414i	−0.748858	−	0.662730i	$-0.769398\pi$
$149$	−1472.77	+	610.042i	−0.809760	+	0.335414i	−0.0609017	+	0.998144i	$0.519398\pi$
$150$	−1681.21	+	2691.46i	−0.915136	+	1.46504i
$151$	1042.51	+	1042.51i	0.561844	+	0.561844i	0.929831	−	0.367987i	$-0.119953\pi$
$151$	1042.51	+	1042.51i	0.561844	+	0.561844i	−0.367987	+	0.929831i	$0.619953\pi$
$152$	425.803	−	254.859i	0.227218	−	0.135999i
$153$	4390.25	+	4390.25i	2.31981	+	2.31981i
$154$	787.704	−	372.358i	0.412175	−	0.194840i
$155$	79.2607	+	43.2965i	0.0410734	+	0.0224365i
$156$	−406.947	−	334.253i	−0.208858	−	0.171549i
$157$	841.052	−	2030.48i	0.427537	−	1.03216i	−0.552530	−	0.833493i	$-0.686337\pi$
$157$	841.052	−	2030.48i	0.427537	−	1.03216i	0.980066	−	0.198671i	$-0.0636626\pi$
$158$	2338.01	+	2119.93i	1.17723	+	1.06742i
$159$	1211.62			0.604325
$160$	−1746.36	+	1022.85i	−0.862887	+	0.505397i
$161$	953.980			0.466982
$162$	−1453.79	−	1318.18i	−0.705064	−	0.639297i
$163$	−610.064	+	1472.82i	−0.293153	+	0.707733i	0.706847	+	0.707366i	$0.250117\pi$
$163$	−610.064	+	1472.82i	−0.293153	+	0.707733i	−1.00000		0.000366913i	$0.999883\pi$
$164$	876.070	−	1066.60i	0.417132	−	0.507849i
$165$	−2983.38	+	5461.51i	−1.40761	+	2.57684i
$166$	2817.91	−	1332.06i	1.31755	−	0.622820i
$167$	−7.45625	−	7.45625i	−0.00345498	−	0.00345498i	0.705377	−	0.708832i	$-0.250778\pi$
$167$	−7.45625	−	7.45625i	−0.00345498	−	0.00345498i	−0.708832	+	0.705377i	$0.750778\pi$
$168$	−978.458	−	245.734i	−0.449343	−	0.112850i
$169$	−1515.48	−	1515.48i	−0.689795	−	0.689795i
$170$	−3462.58	+	1202.75i	−1.56217	+	0.542626i
$171$	−1085.29	+	449.542i	−0.485346	+	0.201037i
$172$	−1959.12	+	1046.13i	−0.868495	+	0.463760i
$173$	−149.514	−	61.9307i	−0.0657071	−	0.0272168i	0.349588	−	0.936904i	$-0.386322\pi$
$173$	−149.514	−	61.9307i	−0.0657071	−	0.0272168i	−0.415295	+	0.909687i	$0.636322\pi$
$174$	−192.511	−	3935.20i	−0.0838749	−	1.71452i
$175$	132.184	−	606.679i	0.0570979	−	0.262061i
$176$	−3301.85	+	2202.29i	−1.41413	+	0.943205i
$177$	2331.83			0.990231
$178$	106.753	+	2182.18i	0.0449519	+	0.918882i
$179$	−1704.48	+	4114.97i	−0.711725	+	1.71825i	−0.0160779	+	0.999871i	$0.505118\pi$
$179$	−1704.48	+	4114.97i	−0.711725	+	1.71825i	−0.695647	+	0.718384i	$0.744882\pi$
$180$	4443.39	−	1791.24i	1.83995	−	0.741730i
$181$	3813.39	−	1579.56i	1.56601	−	0.648662i	0.579888	−	0.814696i	$-0.303096\pi$
$181$	3813.39	−	1579.56i	1.56601	−	0.648662i	0.986120	+	0.166035i	$0.0530965\pi$
$182$	97.0095	+	34.7331i	0.0395100	+	0.0141461i
$183$	108.677	−	108.677i	0.0438994	−	0.0438994i
$184$	−4299.00	+	634.981i	−1.72243	+	0.254410i
$185$	−1063.15	−	114.477i	−0.422512	−	0.0454949i
$186$	−87.6441	−	185.407i	−0.0345504	−	0.0730897i
$187$	−6641.16	+	2750.86i	−2.59706	+	1.07574i
$188$	−288.504	−	2941.66i	−0.111922	−	1.14118i
$189$	1094.17	+	453.222i	0.421108	+	0.174429i
$190$	40.4669	−	692.345i	0.0154515	−	0.264358i
$191$	2245.65			0.850732			0.425366	−	0.905021i	$-0.360145\pi$
$191$	2245.65			0.850732			0.425366	+	0.905021i	$0.360145\pi$
$192$	4572.87	+	456.099i	1.71885	+	0.171438i
$193$		−	4384.49i		−	1.63525i	−0.575753	−	0.817624i	$-0.695291\pi$
$193$		−	4384.49i		−	1.63525i	0.575753	−	0.817624i	$-0.304709\pi$
$194$	−283.043	−	256.641i	−0.104749	−	0.0949782i
$195$	−706.199	+	207.233i	−0.259343	+	0.0761038i
$196$	−2534.45	+	248.567i	−0.923633	+	0.0905855i
$197$	2533.57	−	1049.44i	0.916293	−	0.379541i	0.125831	−	0.992052i	$-0.459840\pi$
$197$	2533.57	−	1049.44i	0.916293	−	0.379541i	0.790462	+	0.612511i	$0.209840\pi$
$198$	8493.97	−	4015.21i	3.04869	−	1.44115i
$199$	1270.49	−	1270.49i	0.452578	−	0.452578i	−0.443632	−	0.896209i	$-0.646310\pi$
$199$	1270.49	−	1270.49i	0.452578	−	0.452578i	0.896209	+	0.443632i	$0.146310\pi$
$200$	−191.858	+	2821.91i	−0.0678319	+	0.997697i
$201$	−5452.84	−	5452.84i	−1.91350	−	1.91350i
$202$	422.134	+	151.140i	0.147036	+	0.0526445i
$203$	295.007	+	712.210i	0.101997	+	0.246243i
$204$	7963.90	+	2419.41i	2.73326	+	0.830355i
$205$	−543.152	−	1850.93i	−0.185051	−	0.630608i
$206$	4453.17	−	217.850i	1.50615	−	0.0736814i
$207$	10287.0			3.45407
$208$	−460.281	−	91.9501i	−0.153436	−	0.0306519i
$209$		−	1360.05i		−	0.450128i
$210$	−1053.42	+	937.080i	−0.346158	+	0.307927i
$211$	−867.411	+	2094.11i	−0.283009	+	0.683245i	−0.999903	−	0.0139375i	$-0.995563\pi$
$211$	−867.411	+	2094.11i	−0.283009	+	0.683245i	0.716893	+	0.697183i	$0.245563\pi$
$212$	952.605	−	508.673i	0.308609	−	0.164792i
$213$	835.589	+	2017.29i	0.268796	+	0.648932i
$214$	74.7685	+	26.7700i	0.0238835	+	0.00855121i
$215$	−332.292	+	3086.00i	−0.105405	+	0.978901i
$216$	−5232.45	−	1314.10i	−1.64825	−	0.413949i
$217$	28.3734	+	28.3734i	0.00887608	+	0.00887608i
$218$	−2113.96	−	4471.98i	−0.656768	−	1.38936i
$219$	−1921.08	−	4637.90i	−0.592761	−	1.43105i
$220$	−52.7008	+	5546.49i	−0.0161504	+	1.69975i
$221$	−785.403	−	325.324i	−0.239058	−	0.0990212i
$222$	1798.73	+	1630.95i	0.543797	+	0.493073i
$223$			1822.89i			0.547397i	0.961816	+	0.273699i	$0.0882471\pi$
$223$			1822.89i			0.547397i	−0.961816	+	0.273699i	$0.911753\pi$
$224$	−872.454	+	217.583i	−0.260238	+	0.0649013i
$225$	1425.36	−	6541.94i	0.422329	−	1.93835i
$226$	645.034	−	711.391i	0.189854	−	0.209385i
$227$	1218.96	−	2942.82i	0.356410	−	0.860449i	−0.639389	−	0.768883i	$-0.720813\pi$
$227$	1218.96	−	2942.82i	0.356410	−	0.860449i	0.995799	−	0.0915658i	$-0.0291872\pi$
$228$	−999.536	+	1216.91i	−0.290333	+	0.353474i
$229$	−963.796	−	2326.81i	−0.278120	−	0.671441i	0.721664	−	0.692244i	$-0.243378\pi$
$229$	−963.796	−	2326.81i	−0.278120	−	0.671441i	−0.999784	+	0.0208032i	$0.993378\pi$
$230$	−2647.56	+	5465.76i	−0.759021	+	1.56696i
$231$	−1955.09	+	1955.09i	−0.556863	+	0.556863i
$232$	−1803.47	−	3013.13i	−0.510361	−	0.852680i
$233$	390.710	−	390.710i	0.109855	−	0.109855i	−0.650043	−	0.759898i	$-0.725249\pi$
$233$	390.710	−	390.710i	0.109855	−	0.109855i	0.759898	+	0.650043i	$0.225249\pi$
$234$	1046.07	+	374.534i	0.292239	+	0.104633i
$235$	−3625.21	−	1980.28i	−1.00631	−	0.549700i
$236$	1833.34	−	978.970i	0.505679	−	0.270023i
$237$	−9252.90	−	3832.68i	−2.53603	−	1.05046i
$238$	−1626.61	+	79.5740i	−0.443013	+	0.0216723i
$239$		−	450.792i		−	0.122005i	−0.998138	−	0.0610027i	$-0.980570\pi$
$239$		−	450.792i		−	0.122005i	0.998138	−	0.0610027i	$-0.0194298\pi$
$240$	4123.40	−	4924.02i	1.10902	−	1.32435i
$241$		−	797.569i		−	0.213178i	−0.994303	−	0.106589i	$-0.966007\pi$
$241$		−	797.569i		−	0.213178i	0.994303	−	0.106589i	$-0.0339929\pi$
$242$	347.549	+	7104.39i	0.0923193	+	1.88714i
$243$	−193.954	−	80.3385i	−0.0512024	−	0.0212087i
$244$	39.8186	−	131.070i	0.0104472	−	0.0343889i
$245$	−1706.16	+	3123.37i	−0.444908	+	0.814469i
$246$	−1476.47	+	4123.77i	−0.382667	+	1.06879i
$247$	113.734	−	113.734i	0.0292984	−	0.0292984i
$248$	−146.747	−	108.976i	−0.0375744	−	0.0279031i
$249$	−6994.09	+	6994.09i	−1.78005	+	1.78005i
$250$	3109.07	+	2441.04i	0.786540	+	0.617539i
$251$	2068.66	+	4994.19i	0.520210	+	1.25590i	0.937773	+	0.347250i	$0.112885\pi$
$251$	2068.66	+	4994.19i	0.520210	+	1.25590i	−0.417562	+	0.908648i	$0.637115\pi$
$252$	2118.36	−	207.758i	0.529539	−	0.0519347i
$253$	−4557.76	+	11003.4i	−1.13258	+	2.73430i
$254$	−826.060	−	749.007i	−0.204061	−	0.185027i
$255$	9058.48	−	7297.33i	2.22456	−	1.79206i
$256$	3786.79	−	1561.23i	0.924509	−	0.381160i
$257$			5117.81i			1.24218i	0.783740	+	0.621090i	$0.213310\pi$
$257$			5117.81i			1.24218i	−0.783740	+	0.621090i	$0.786690\pi$
$258$	4734.14	−	5221.16i	1.14238	−	1.25990i
$259$	−438.914	−	181.804i	−0.105300	−	0.0436169i
$260$	−468.229	+	459.415i	−0.111686	+	0.109583i
$261$	3181.12	+	7679.90i	0.754430	+	1.82136i
$262$	858.039	−	405.606i	0.202328	−	0.0956428i
$263$	−1579.13	−	1579.13i	−0.370240	−	0.370240i	0.497324	−	0.867565i	$-0.334316\pi$
$263$	−1579.13	−	1579.13i	−0.370240	−	0.370240i	−0.867565	+	0.497324i	$0.834316\pi$
$264$	7509.05	−	10111.7i	1.75057	−	2.35732i
$265$	161.575	−	1500.55i	0.0374545	−	0.347841i
$266$	103.864	−	290.093i	0.0239411	−	0.0668674i
$267$	−2653.21	−	6405.42i	−0.608142	−	1.46819i
$268$	−6576.42	−	1997.90i	−1.49895	−	0.455376i
$269$	2082.47	−	5027.53i	0.472009	−	1.13953i	−0.491264	−	0.871010i	$-0.663465\pi$
$269$	2082.47	−	5027.53i	0.472009	−	1.13953i	0.963274	−	0.268521i	$-0.0865349\pi$
$270$	−5633.34	+	5011.17i	−1.26976	+	1.12952i
$271$			6321.77i			1.41705i	0.705686	+	0.708525i	$0.250639\pi$
$271$			6321.77i			1.41705i	−0.705686	+	0.708525i	$0.749361\pi$
$272$	7277.15	−	1441.28i	1.62221	−	0.321288i
$273$	−326.986			−0.0724912
$274$	30.2224	+	617.789i	0.00666352	+	0.136212i
$275$	6366.04	+	4423.12i	1.39595	+	0.969906i
$276$	12164.8	−	6495.75i	2.65302	−	1.41666i
$277$	−1406.82	−	3396.37i	−0.305155	−	0.736708i	−0.999849	−	0.0174030i	$-0.994460\pi$
$277$	−1406.82	−	3396.37i	−0.305155	−	0.736708i	0.694694	−	0.719305i	$-0.255540\pi$
$278$	−836.187	+	2335.47i	−0.180400	+	0.503856i
$279$	305.956	+	305.956i	0.0656527	+	0.0656527i
$280$	−434.814	+	1179.01i	−0.0928039	+	0.251641i
$281$	−1023.74	+	1023.74i	−0.217334	+	0.217334i	−0.807374	−	0.590040i	$-0.799112\pi$
$281$	−1023.74	+	1023.74i	−0.217334	+	0.217334i	0.590040	+	0.807374i	$0.299112\pi$
$282$	4008.64	+	8480.08i	0.846494	+	1.79072i
$283$	2570.86	−	1064.89i	0.540007	−	0.223678i	−0.0959728	−	0.995384i	$-0.530596\pi$
$283$	2570.86	−	1064.89i	0.540007	−	0.223678i	0.635980	+	0.771706i	$0.280596\pi$
$284$	1503.88	+	1235.24i	0.314221	+	0.258091i
$285$	619.699	+	2111.78i	0.128799	+	0.438917i
$286$	−864.094	+	952.986i	−0.178654	+	0.197032i
$287$		−	857.023i		−	0.176266i
$288$	−9407.85	+	2346.24i	−1.92487	+	0.480047i
$289$	8523.09			1.73480
$290$	−4899.28	−	286.358i	−0.992053	−	0.0579846i
$291$	1120.17	+	463.988i	0.225654	+	0.0934690i
$292$	−3457.53	−	2839.91i	−0.692933	−	0.569154i
$293$	4420.88	−	1831.19i	0.881470	−	0.365117i	0.104403	−	0.994535i	$-0.466707\pi$
$293$	4420.88	−	1831.19i	0.881470	−	0.365117i	0.777067	+	0.629418i	$0.216707\pi$
$294$	7306.20	−	3453.73i	1.44934	−	0.685122i
$295$	310.959	−	2887.88i	0.0613720	−	0.569963i
$296$	2098.93	+	527.134i	0.412155	+	0.103510i
$297$	−10455.1	+	10455.1i	−2.04265	+	2.04265i
$298$	1519.86	−	4244.96i	0.295447	−	0.825182i
$299$	−1301.29	+	539.013i	−0.251691	+	0.104254i
$300$	−2445.39	−	8636.17i	−0.470616	−	1.66203i
$301$	−527.721	+	1274.03i	−0.101054	+	0.243967i
$302$	−4165.06	+	203.756i	−0.793618	+	0.0388240i
$303$	−1422.87			−0.269775
$304$	−274.963	+	1376.40i	−0.0518758	+	0.259678i
$305$	−120.099	−	149.084i	−0.0225471	−	0.0279887i
$306$	−17540.0	+	858.062i	−3.27678	+	0.160301i
$307$	3473.70	+	1438.85i	0.645780	+	0.267491i	0.681441	−	0.731873i	$-0.261354\pi$
$307$	3473.70	+	1438.85i	0.645780	+	0.267491i	−0.0356611	+	0.999364i	$0.511354\pi$
$308$	−716.335	+	2357.94i	−0.132523	+	0.436221i
$309$	−13071.6	+	5414.42i	−2.40652	+	0.996815i
$310$	−241.307	+	83.8192i	−0.0442107	+	0.0153568i
$311$	−6628.08	−	6628.08i	−1.20850	−	1.20850i	−0.971512	−	0.236989i	$-0.923839\pi$
$311$	−6628.08	−	6628.08i	−1.20850	−	1.20850i	−0.236989	−	0.971512i	$-0.576161\pi$
$312$	1473.53	−	217.646i	0.267378	−	0.0394929i
$313$	2243.48	+	2243.48i	0.405140	+	0.405140i	0.880040	−	0.474900i	$-0.157516\pi$
$313$	2243.48	+	2243.48i	0.405140	+	0.405140i	−0.474900	+	0.880040i	$0.657516\pi$
$314$	2656.63	+	5619.97i	0.477459	+	1.01004i
$315$	1426.05	−	2610.59i	0.255075	−	0.466953i
$316$	−8883.93	+	871.293i	−1.58152	+	0.155108i
$317$	375.236	−	905.900i	0.0664838	−	0.160506i	−0.887145	−	0.461490i	$-0.847315\pi$
$317$	375.236	−	905.900i	0.0664838	−	0.160506i	0.953629	+	0.300984i	$0.0973150\pi$
$318$	−2301.94	+	2538.75i	−0.405932	+	0.447692i
$319$	−9624.21			−1.68919
$320$	1174.67	−	5602.51i	0.205207	−	0.978719i
$321$	−252.019			−0.0438204
$322$	−1812.45	+	1998.91i	−0.313677	+	0.345946i
$323$	−972.835	+	2348.63i	−0.167585	+	0.404586i
$324$	5524.06	−	541.774i	0.947199	−	0.0928967i
$325$	162.475	+	902.237i	0.0277308	+	0.153991i
$326$	−1927.01	−	4076.49i	−0.327384	−	0.692564i
$327$	11099.5	+	11099.5i	1.87707	+	1.87707i
$328$	570.445	+	3862.08i	0.0960291	+	0.650145i
$329$	−1297.73	−	1297.73i	−0.217466	−	0.217466i
$330$	−5775.62	−	16627.4i	−0.963447	−	2.77367i
$331$	6011.52	−	2490.05i	0.998257	−	0.413492i	0.177099	−	0.984193i	$-0.443329\pi$
$331$	6011.52	−	2490.05i	0.998257	−	0.413492i	0.821158	+	0.570701i	$0.193329\pi$
$332$	−2562.60	+	8435.25i	−0.423617	+	1.39441i
$333$	−4732.90	−	1960.43i	−0.778863	−	0.322616i
$334$	29.7894	−	1.45731i	0.00488025	−	0.000238743i
$335$	−7480.30	+	6025.98i	−1.21998	+	0.982789i
$336$	2373.85	−	1583.33i	0.385430	−	0.257077i
$337$	−3775.58			−0.610294			−0.305147	−	0.952305i	$-0.598706\pi$
$337$	−3775.58			−0.610294			−0.305147	+	0.952305i	$0.598706\pi$
$338$	6054.68	−	296.197i	0.974353	−	0.0476656i
$339$	−1166.17	+	2815.39i	−0.186837	+	0.451065i
$340$	4058.37	−	9540.35i	0.647341	−	1.52176i
$341$	−462.822	+	191.707i	−0.0734992	+	0.0304443i
$342$	1119.99	−	3128.13i	0.177082	−	0.494590i
$343$	−2322.85	+	2322.85i	−0.365662	+	0.365662i
$344$	1530.10	−	6092.54i	0.239819	−	0.954906i
$345$	2063.31	−	19162.0i	0.321985	−	2.99028i
$346$	413.825	−	195.620i	0.0642988	−	0.0303948i
$347$	10698.5	−	4431.45i	1.65511	−	0.685570i	0.657424	−	0.753521i	$-0.271646\pi$
$347$	10698.5	−	4431.45i	1.65511	−	0.685570i	0.997689	+	0.0679511i	$0.0216462\pi$
$348$	8611.32	+	7073.07i	1.32648	+	1.08953i
$349$	3945.56	+	1634.30i	0.605160	+	0.250665i	0.664157	−	0.747593i	$-0.268790\pi$
$349$	3945.56	+	1634.30i	0.605160	+	0.250665i	−0.0589976	+	0.998258i	$0.518790\pi$
$350$	1020.06	+	1429.59i	0.155784	+	0.218328i
$351$	−1748.61			−0.265908
$352$	1658.61	−	11102.6i	0.251148	−	1.68117i
$353$		−	113.851i		−	0.0171662i	−0.999963	−	0.00858311i	$-0.997268\pi$
$353$		−	113.851i		−	0.0171662i	0.999963	−	0.00858311i	$-0.00273212\pi$
$354$	−4430.21	+	4885.96i	−0.665150	+	0.733576i
$355$	2609.77	−	765.832i	0.390175	−	0.114496i
$356$	−4775.21	−	3922.20i	−0.710914	−	0.583923i
$357$	4774.64	−	1977.72i	0.707845	−	0.293199i
$358$	−5383.93	−	11389.4i	−0.794831	−	1.68143i
$359$	−6292.68	+	6292.68i	−0.925111	+	0.925111i	−0.997385	−	0.0722740i	$-0.976974\pi$
$359$	−6292.68	+	6292.68i	−0.925111	+	0.925111i	0.0722740	+	0.997385i	$0.476974\pi$
$360$	−4688.69	+	12713.5i	−0.686432	+	1.86129i
$361$	4509.94	+	4509.94i	0.657522	+	0.657522i
$362$	−3935.31	+	10991.3i	−0.571369	+	1.59583i
$363$	−8637.92	−	20853.8i	−1.24896	−	3.01526i
$364$	−257.085	+	137.278i	−0.0370189	+	0.0197674i
$365$	−6000.05	+	1760.70i	−0.860431	+	0.252492i
$366$	21.2405	+	434.187i	0.00303350	+	0.0620090i
$367$	−627.921			−0.0893112			−0.0446556	−	0.999002i	$-0.514219\pi$
$367$	−627.921			−0.0893112			−0.0446556	+	0.999002i	$0.514219\pi$
$368$	6837.13	−	10214.2i	0.968505	−	1.44689i
$369$		−	9241.45i		−	1.30377i
$370$	2259.74	−	2010.17i	0.317509	−	0.282442i
$371$	256.600	−	619.488i	0.0359084	−	0.0866906i
$372$	555.003	+	168.608i	0.0773537	+	0.0234998i
$373$	3795.16	+	9162.32i	0.526825	+	1.27187i	0.933592	+	0.358337i	$0.116656\pi$
$373$	3795.16	+	9162.32i	0.526825	+	1.27187i	−0.406767	+	0.913532i	$0.633344\pi$
$374$	6853.49	−	19141.8i	0.947555	−	2.64652i
$375$	−11900.1	−	3967.23i	−1.63871	−	0.546312i
$376$	6711.88	+	4984.31i	0.920582	+	0.683633i
$377$	−804.819	−	804.819i	−0.109948	−	0.109948i
$378$	−3028.46	+	1431.59i	−0.412082	+	0.194797i
$379$	3119.70	+	7531.62i	0.422818	+	1.02077i	0.981512	+	0.191400i	$0.0613027\pi$
$379$	3119.70	+	7531.62i	0.422818	+	1.02077i	−0.558694	+	0.829374i	$0.688697\pi$
$380$	1373.81	+	1400.17i	0.185461	+	0.189019i
$381$	3269.21	+	1354.15i	0.439597	+	0.182087i
$382$	−4266.49	+	4705.40i	−0.571447	+	0.630233i
$383$		−	4423.22i		−	0.590120i	−0.955479	−	0.295060i	$-0.904660\pi$
$383$		−	4423.22i		−	0.590120i	0.955479	−	0.295060i	$-0.0953397\pi$
$384$	−9643.62	+	8715.16i	−1.28157	+	1.15819i
$385$	2160.58	+	2682.02i	0.286009	+	0.355035i
$386$	9186.98	+	8330.04i	1.21141	+	1.09841i
$387$	−5690.52	+	13738.1i	−0.747456	+	1.80452i
$388$	1075.50	−	105.480i	0.140722	−	0.0138014i
$389$	−3799.30	−	9172.32i	−0.495198	−	1.19551i	−0.952042	−	0.305967i	$-0.901020\pi$
$389$	−3799.30	−	9172.32i	−0.495198	−	1.19551i	0.456844	−	0.889547i	$-0.348980\pi$
$390$	907.477	−	1873.44i	0.117825	−	0.243245i
$391$	15741.3	−	15741.3i	2.03599	−	2.03599i
$392$	4294.34	−	5782.77i	0.553308	−	0.745086i
$393$	−2129.66	+	2129.66i	−0.273351	+	0.273351i
$394$	−2614.58	+	7302.50i	−0.334316	+	0.933743i
$395$	−5980.54	+	10948.3i	−0.761807	+	1.39460i
$396$	−7724.38	+	25426.2i	−0.980215	+	3.22655i
$397$	8403.16	+	3480.70i	1.06232	+	0.440029i	0.844276	−	0.535909i	$-0.180031\pi$
$397$	8403.16	+	3480.70i	1.06232	+	0.440029i	0.218048	+	0.975938i	$0.430031\pi$
$398$	248.315	+	5075.91i	0.0312736	+	0.639277i
$399$			977.804i			0.122685i
$400$	−5548.34	−	5763.32i	−0.693543	−	0.720415i
$401$		−	3566.21i		−	0.444110i	−0.975034	−	0.222055i	$-0.928724\pi$
$401$		−	3566.21i		−	0.444110i	0.975034	−	0.222055i	$-0.0712764\pi$
$402$	21785.3	−	1065.74i	2.70287	−	0.132225i
$403$	−54.7346	−	22.6718i	−0.00676557	−	0.00280239i
$404$	−1118.70	+	597.363i	−0.137765	+	0.0735642i
$405$	3718.73	−	6807.68i	0.456259	−	0.835250i
$406$	−2052.80	−	734.980i	−0.250933	−	0.0898435i
$407$	4193.94	−	4193.94i	0.510776	−	0.510776i
$408$	−20200.0	+	12090.4i	−2.45110	+	1.46707i
$409$	−6400.22	+	6400.22i	−0.773767	+	0.773767i	−0.978763	−	0.204996i	$-0.934282\pi$
$409$	−6400.22	+	6400.22i	−0.773767	+	0.773767i	0.204996	+	0.978763i	$0.434282\pi$
$410$	4910.25	+	2378.47i	0.591463	+	0.286499i
$411$	−751.144	−	1813.42i	−0.0901489	−	0.217639i
$412$	−8004.06	+	9744.78i	−0.957116	+	1.16527i
$413$	493.841	−	1192.24i	0.0588386	−	0.142049i
$414$	−19544.1	+	21554.6i	−2.32014	+	2.55882i
$415$	7729.23	+	9594.61i	0.914248	+	1.13489i
$416$	1067.15	−	789.748i	0.125772	−	0.0930783i
$417$		−	7872.07i		−	0.924453i
$418$	2849.76	+	2583.95i	0.333461	+	0.302356i
$419$	−2331.36	−	965.681i	−0.271824	−	0.112593i	0.242608	−	0.970124i	$-0.421997\pi$
$419$	−2331.36	−	965.681i	−0.271824	−	0.112593i	−0.514432	+	0.857531i	$0.671997\pi$
$420$	37.8890	−	3987.62i	0.00440189	−	0.463276i
$421$	−3782.75	−	9132.38i	−0.437910	−	1.05721i	−0.976669	−	0.214749i	$-0.931107\pi$
$421$	−3782.75	−	9132.38i	−0.437910	−	1.05721i	0.538759	−	0.842460i	$-0.318893\pi$
$422$	−2739.89	−	5796.10i	−0.316056	−	0.668601i
$423$	−13993.7	−	13993.7i	−1.60851	−	1.60851i
$424$	−744.002	+	2962.45i	−0.0852168	+	0.339314i
$425$	−7829.49	−	12191.7i	−0.893614	−	1.39149i
$426$	−5814.42	−	2081.79i	−0.661291	−	0.236767i
$427$	−32.5493	−	78.5809i	−0.00368892	−	0.00890585i
$428$	−198.144	+	105.805i	−0.0223777	+	0.0119493i
$429$	1562.22	−	3771.53i	0.175815	−	0.424455i
$430$	−5834.89	−	6559.33i	−0.654380	−	0.735625i
$431$			6728.05i			0.751923i	0.926635	+	0.375961i	$0.122687\pi$
$431$			6728.05i			0.751923i	−0.926635	+	0.375961i	$0.877313\pi$
$432$	12694.5	−	8467.09i	1.41381	−	0.942993i
$433$	16521.9			1.83370			0.916848	−	0.399236i	$-0.130725\pi$
$433$	16521.9			1.83370			0.916848	+	0.399236i	$0.130725\pi$
$434$	−113.358	+	5.54550i	−0.0125377	+	0.000613347i
$435$	14943.7	−	4385.21i	1.64712	−	0.483344i
$436$	13386.6	+	4066.80i	1.47041	+	0.446707i
$437$	1611.84	+	3891.33i	0.176441	+	0.425967i
$438$	13367.8	+	4786.18i	1.45831	+	0.522129i
$439$	776.773	+	776.773i	0.0844496	+	0.0844496i	0.748070	−	0.663620i	$-0.230981\pi$
$439$	776.773	+	776.773i	0.0844496	+	0.0844496i	−0.663620	+	0.748070i	$0.730981\pi$
$440$	−11521.6	−	10648.1i	−1.24834	−	1.15370i
$441$	−12056.6	+	12056.6i	−1.30187	+	1.30187i
$442$	2173.84	−	1027.60i	0.233934	−	0.110584i
$443$	1193.96	−	494.555i	0.128051	−	0.0530406i	−0.317738	−	0.948179i	$-0.602923\pi$
$443$	1193.96	−	494.555i	0.128051	−	0.0530406i	0.445789	+	0.895138i	$0.352923\pi$
$444$	−6834.78	+	670.322i	−0.730550	+	0.0716489i
$445$	−8286.70	+	2431.72i	−0.882757	+	0.259044i
$446$	−3819.56	−	3463.28i	−0.405519	−	0.367693i
$447$			14308.3i			1.51401i
$448$	1201.65	−	2241.47i	0.126725	−	0.236382i
$449$	5762.50			0.605677			0.302838	−	0.953042i	$-0.402066\pi$
$449$	5762.50			0.605677			0.302838	+	0.953042i	$0.402066\pi$
$450$	10999.5	+	15415.6i	1.15227	+	1.61488i
$451$	9885.08	+	4094.53i	1.03208	+	0.427504i
$452$	265.110	+	2703.13i	0.0275879	+	0.281293i
$453$	12225.9	−	5064.12i	1.26804	−	0.525239i
$454$	3850.32	+	8145.15i	0.398027	+	0.842006i
$455$	−43.6050	+	404.960i	−0.00449282	+	0.0417249i
$456$	−650.838	−	4406.36i	−0.0668384	−	0.452515i
$457$	−1021.92	+	1021.92i	−0.104603	+	0.104603i	−0.757471	−	0.652868i	$-0.773565\pi$
$457$	−1021.92	+	1021.92i	−0.104603	+	0.104603i	0.652868	+	0.757471i	$0.273565\pi$
$458$	6706.55	+	2401.20i	0.684228	+	0.244980i
$459$	25533.1	−	10576.1i	2.59647	−	1.07549i
$460$	−6422.53	−	15931.8i	−0.650982	−	1.61484i
$461$	−1061.11	+	2561.74i	−0.107203	+	0.258812i	−0.968374	−	0.249505i	$-0.919732\pi$
$461$	−1061.11	+	2561.74i	−0.107203	+	0.258812i	0.861170	+	0.508317i	$0.169732\pi$
$462$	−382.117	−	7811.01i	−0.0384798	−	0.786582i
$463$	−7329.77			−0.735731			−0.367865	−	0.929879i	$-0.619911\pi$
$463$	−7329.77			−0.735731			−0.367865	+	0.929879i	$0.619911\pi$
$464$	9739.91	+	1945.74i	0.974492	+	0.194674i
$465$	631.284	−	508.550i	0.0629572	−	0.0507171i
$466$	76.3633	+	1560.97i	0.00759112	+	0.155173i
$467$	214.807	+	88.9760i	0.0212850	+	0.00881653i	0.393301	−	0.919410i	$-0.371333\pi$
$467$	214.807	+	88.9760i	0.0212850	+	0.00881653i	−0.372016	+	0.928226i	$0.621333\pi$
$468$	−2772.19	+	1480.30i	−0.273814	+	0.146211i
$469$	−3942.80	+	1633.16i	−0.388191	+	0.160794i
$470$	11036.8	−	3833.70i	1.08317	−	0.376246i
$471$	−13948.8	−	13948.8i	−1.36460	−	1.36460i
$472$	−1431.87	+	5701.40i	−0.139634	+	0.555992i
$473$	−12173.7	−	12173.7i	−1.18340	−	1.18340i
$474$	25610.2	−	12106.3i	2.48168	−	1.17312i
$475$	2698.01	−	485.859i	0.260617	−	0.0469321i
$476$	2923.63	−	3559.46i	0.281522	−	0.342747i
$477$	2766.97	−	6680.06i	0.265599	−	0.641214i
$478$	944.559	+	856.453i	0.0903831	+	0.0819524i
$479$	4994.51			0.476420			0.238210	−	0.971214i	$-0.423439\pi$
$479$	4994.51			0.476420			0.238210	+	0.971214i	$0.423439\pi$
$480$	2483.47	+	17995.0i	0.236155	+	1.71116i
$481$	701.431			0.0664917
$482$	1671.17	+	1515.29i	0.157925	+	0.143194i
$483$	3276.78	−	7910.85i	0.308693	−	0.745251i
$484$	−15546.4	−	12769.3i	−1.46003	−	1.19922i
$485$	724.011	−	1325.41i	0.0677849	−	0.124090i
$486$	536.828	−	253.765i	0.0501049	−	0.0236852i
$487$	−671.290	−	671.290i	−0.0624621	−	0.0624621i	0.675186	−	0.737648i	$-0.264063\pi$
$487$	−671.290	−	671.290i	−0.0624621	−	0.0624621i	−0.737648	+	0.675186i	$0.764063\pi$
$488$	198.984	+	332.451i	0.0184582	+	0.0308388i
$489$	10117.9	+	10117.9i	0.935677	+	0.935677i
$490$	−3303.01	−	9509.03i	−0.304520	−	0.876682i
$491$	1271.83	−	526.809i	0.116898	−	0.0484207i	−0.323468	−	0.946239i	$-0.604849\pi$
$491$	1271.83	−	526.809i	0.116898	−	0.0484207i	0.440366	+	0.897818i	$0.354849\pi$
$492$	−5835.56	−	10928.4i	−0.534730	−	1.00140i
$493$	16619.7	+	6884.12i	1.51829	+	0.628895i
$494$	22.2289	+	454.391i	0.00202455	+	0.0413846i
$495$	23298.0	+	28920.8i	2.11549	+	2.62605i
$496$	507.144	−	100.443i	0.0459101	−	0.00909275i
$497$	1208.38			0.109061
$498$	−1366.98	−	27942.9i	−0.123003	−	2.51436i
$499$	−5151.31	+	12436.4i	−0.462132	+	1.11569i	0.505388	+	0.862892i	$0.331350\pi$
$499$	−5151.31	+	12436.4i	−0.462132	+	1.11569i	−0.967520	+	0.252794i	$0.918650\pi$
$500$	−11021.7	+	1876.86i	−0.985809	+	0.167871i
$501$	−87.4419	+	36.2196i	−0.00779764	+	0.00322989i
$502$	−14394.7	−	5153.86i	−1.27982	−	0.458223i
$503$	−9822.57	+	9822.57i	−0.870709	+	0.870709i	−0.992550	−	0.121840i	$-0.961120\pi$
$503$	−9822.57	+	9822.57i	−0.870709	+	0.870709i	0.121840	+	0.992550i	$0.461120\pi$
$504$	−3589.31	+	4833.38i	−0.317224	+	0.427174i
$505$	−189.746	+	1762.17i	−0.0167200	+	0.155279i
$506$	−14396.6	−	30455.3i	−1.26483	−	2.67570i
$507$	−17772.5	+	7361.62i	−1.55682	+	0.644854i
$508$	3138.84	−	307.843i	0.274141	−	0.0268864i
$509$	17428.0	+	7218.91i	1.51765	+	0.628630i	0.977118	−	0.212696i	$-0.0682244\pi$
$509$	17428.0	+	7218.91i	1.51765	+	0.628630i	0.540528	+	0.841326i	$0.318224\pi$
$510$	−1919.74	+	32844.6i	−0.166681	+	2.85174i
$511$	−2778.16			−0.240506
$512$	−3923.17	+	10900.8i	−0.338636	+	0.940918i
$513$			5228.95i			0.450027i
$514$	−10723.5	−	9723.26i	−0.920222	−	0.834386i
$515$	4962.41	+	16910.7i	0.424602	+	1.44694i
$516$	1945.74	+	19839.2i	0.166001	+	1.69258i
$517$	21168.4	−	8768.25i	1.80075	−	0.745894i
$518$	1214.83	−	574.265i	0.103043	−	0.0487099i
$519$	−1027.12	+	1027.12i	−0.0868698	+	0.0868698i
$520$	−73.0455	−	1853.93i	−0.00616011	−	0.156347i
$521$	6519.18	+	6519.18i	0.548197	+	0.548197i	0.925919	−	0.377722i	$-0.123293\pi$
$521$	6519.18	+	6519.18i	0.548197	+	0.548197i	−0.377722	+	0.925919i	$0.623293\pi$
$522$	−22135.7	−	7925.44i	−1.85604	−	0.664534i
$523$	3221.41	+	7777.18i	0.269336	+	0.650234i	0.999452	−	0.0330887i	$-0.0105344\pi$
$523$	3221.41	+	7777.18i	0.269336	+	0.650234i	−0.730117	+	0.683322i	$0.760534\pi$
$524$	−780.297	+	2568.48i	−0.0650524	+	0.214131i
$525$	−4576.84	−	3179.98i	−0.380475	−	0.264354i
$526$	6308.96	−	308.636i	0.522973	−	0.0255840i
$527$	936.359			0.0773974
$528$	6921.07	+	34945.1i	0.570456	+	2.88028i
$529$		−	24717.0i		−	2.03148i
$530$	2837.17	+	3189.42i	0.232526	+	0.261395i
$531$	5325.19	−	12856.1i	0.435204	−	1.05068i
$532$	410.511	+	768.774i	0.0334547	+	0.0626514i
$533$	484.231	+	1169.04i	0.0393515	+	0.0950030i
$534$	18462.3	+	6610.21i	1.49615	+	0.535678i
$535$	−33.6079	+	312.117i	−0.00271588	+	0.0252224i
$536$	16680.7	−	9984.02i	1.34421	−	0.804560i
$537$	28268.7	+	28268.7i	2.27166	+	2.27166i
$538$	6577.90	+	13915.2i	0.527125	+	1.11511i
$539$	−7554.47	−	18238.1i	−0.603700	−	1.45746i
$540$	202.617	−	21324.4i	0.0161468	−	1.69936i
$541$	−18621.0	−	7713.06i	−1.47981	−	0.612958i	−0.510739	−	0.859736i	$-0.670628\pi$
$541$	−18621.0	−	7713.06i	−1.47981	−	0.612958i	−0.969072	+	0.246778i	$0.920628\pi$
$542$	−13246.2	−	12010.7i	−1.04977	−	0.951848i
$543$		−	37048.0i		−	2.92796i
$544$	−10805.8	+	17986.3i	−0.851645	+	1.41757i
$545$	15226.5	−	12266.1i	1.19675	−	0.964079i
$546$	621.237	−	685.145i	0.0486932	−	0.0537024i
$547$	−5487.38	+	13247.7i	−0.428927	+	1.03552i	0.550701	+	0.834703i	$0.314360\pi$
$547$	−5487.38	+	13247.7i	−0.428927	+	1.03552i	−0.979628	+	0.200819i	$0.935640\pi$
$548$	−1351.89	−	1110.40i	−0.105383	−	0.0865586i
$549$	−350.986	−	847.354i	−0.0272854	−	0.0658728i
$550$	−21362.7	+	4935.55i	−1.65619	+	0.382641i
$551$	−2406.69	+	2406.69i	−0.186077	+	0.186077i
$552$	−9500.89	+	37830.4i	−0.732581	+	2.91698i
$553$	−3919.21	+	3919.21i	−0.301378	+	0.301378i
$554$	9789.34	+	3504.96i	0.750739	+	0.268793i
$555$	−4601.08	+	8422.96i	−0.351901	+	0.644207i
$556$	−3304.93	−	6189.22i	−0.252087	−	0.472089i
$557$	−19618.6	−	8126.31i	−1.49240	−	0.618174i	−0.520565	−	0.853822i	$-0.674279\pi$
$557$	−19618.6	−	8126.31i	−1.49240	−	0.618174i	−0.971838	+	0.235648i	$0.924279\pi$
$558$	−1222.36	+	59.7982i	−0.0927360	+	0.00453667i
$559$		−	2036.04i		−	0.154052i
$560$	−1644.33	−	3151.07i	−0.124082	−	0.237781i
$561$			64520.5i			4.85572i
$562$	−200.087	−	4090.05i	−0.0150180	−	0.306990i
$563$	16885.6	+	6994.25i	1.26402	+	0.523575i	0.911141	−	0.412094i	$-0.135202\pi$
$563$	16885.6	+	6994.25i	1.26402	+	0.523575i	0.352880	+	0.935669i	$0.385202\pi$
$564$	−25384.6	−	7711.76i	−1.89518	−	0.575751i
$565$	3331.25	+	1819.71i	0.248047	+	0.135497i
$566$	−2653.06	+	7409.98i	−0.197025	+	0.550291i
$567$	2436.98	−	2436.98i	0.180500	−	0.180500i
$568$	−5445.44	+	804.314i	−0.402263	+	0.0594160i
$569$	6529.27	−	6529.27i	0.481057	−	0.481057i	−0.424412	−	0.905469i	$-0.639519\pi$
$569$	6529.27	−	6529.27i	0.481057	−	0.481057i	0.905469	+	0.424412i	$0.139519\pi$
$570$	−5602.25	−	2713.68i	−0.411671	−	0.199409i
$571$	−3730.01	−	9005.05i	−0.273373	−	0.659982i	0.726250	−	0.687431i	$-0.241262\pi$
$571$	−3730.01	−	9005.05i	−0.273373	−	0.659982i	−0.999623	+	0.0274492i	$0.991262\pi$
$572$	−355.143	−	3621.13i	−0.0259603	−	0.264698i
$573$	7713.50	−	18622.0i	0.562367	−	1.35767i
$574$	1795.75	+	1628.25i	0.130580	+	0.118400i
$575$	−23456.2	−	5110.66i	−1.70120	−	0.370659i
$576$	12957.7	−	24170.2i	0.937332	−	1.74842i
$577$		−	12185.2i		−	0.879161i	−0.898203	−	0.439580i	$-0.855127\pi$
$577$		−	12185.2i		−	0.879161i	0.898203	−	0.439580i	$-0.144873\pi$
$578$	−16192.9	+	17858.7i	−1.16529	+	1.28516i
$579$	−36358.3	−	15060.1i	−2.60967	−	1.08096i
$580$	9908.09	−	9721.58i	0.709330	−	0.695977i
$581$	2094.77	+	5057.23i	0.149580	+	0.361117i
$582$	−3100.40	+	1465.60i	−0.220817	+	0.104383i
$583$	5919.36	+	5919.36i	0.420506	+	0.420506i
$584$	12519.5	−	1849.18i	0.887088	−	0.131027i
$585$	−470.201	+	4366.77i	−0.0332315	+	0.308622i
$586$	−4562.22	+	12742.3i	−0.321610	+	0.898257i
$587$	−4790.89	−	11566.2i	−0.336868	−	0.813270i	−0.998013	−	0.0630123i	$-0.979929\pi$
$587$	−4790.89	−	11566.2i	−0.336868	−	0.813270i	0.661145	−	0.750258i	$-0.270071\pi$
$588$	−6644.23	+	21870.6i	−0.465992	+	1.53389i
$589$	−67.7967	+	163.676i	−0.00474281	+	0.0114502i
$590$	5460.29	+	6138.22i	0.381011	+	0.428316i
$591$		−	24614.3i		−	1.71319i
$592$	−5092.25	+	3396.46i	−0.353531	+	0.235800i
$593$	−6248.85			−0.432731			−0.216365	−	0.976312i	$-0.569420\pi$
$593$	−6248.85			−0.432731			−0.216365	+	0.976312i	$0.569420\pi$
$594$	−2043.42	−	41770.5i	−0.141149	−	2.88529i
$595$	−1812.61	−	6176.95i	−0.124891	−	0.425597i
$596$	6007.06	+	11249.6i	0.412850	+	0.773155i
$597$	−6171.57	−	14899.5i	−0.423092	−	1.02143i
$598$	1342.90	−	3750.71i	0.0918314	−	0.256485i
$599$	11410.8	+	11410.8i	0.778355	+	0.778355i	0.979551	−	0.201196i	$-0.0644829\pi$
$599$	11410.8	+	11410.8i	0.778355	+	0.778355i	−0.201196	+	0.979551i	$0.564483\pi$
$600$	22741.6	+	11283.8i	1.54737	+	0.767768i
$601$	−10026.8	+	10026.8i	−0.680538	+	0.680538i	−0.960121	−	0.279583i	$-0.909804\pi$
$601$	−10026.8	+	10026.8i	−0.680538	+	0.680538i	0.279583	+	0.960121i	$0.409804\pi$
$602$	−1666.91	−	3526.27i	−0.112854	−	0.238737i
$603$	−42515.9	+	17610.7i	−2.87128	+	1.18932i
$604$	7486.22	−	9114.32i	0.504321	−	0.614001i
$605$	−26978.6	+	7916.81i	−1.81295	+	0.532007i
$606$	2703.30	−	2981.39i	0.181211	−	0.199853i
$607$		−	18615.3i		−	1.24477i	−0.782713	−	0.622383i	$-0.786165\pi$
$607$		−	18615.3i		−	1.24477i	0.782713	−	0.622383i	$-0.213835\pi$
$608$	−2361.63	−	3191.15i	−0.157527	−	0.212859i
$609$	6919.29			0.460400
$610$	540.557	+	31.5951i	0.0358795	+	0.00209713i
$611$	2503.44	+	1036.96i	0.165758	+	0.0686593i
$612$	31526.1	−	38382.4i	2.08230	−	2.53516i
$613$	−15281.3	+	6329.72i	−1.00686	+	0.417056i	−0.824309	−	0.566140i	$-0.808436\pi$
$613$	−15281.3	+	6329.72i	−1.00686	+	0.417056i	−0.182553	+	0.983196i	$0.558436\pi$
$614$	−9614.51	+	4544.90i	−0.631938	+	0.298725i
$615$	−17214.4	−	1853.60i	−1.12870	−	0.121536i
$616$	−3579.72	−	5980.78i	−0.234141	−	0.391189i
$617$	−7294.81	+	7294.81i	−0.475977	+	0.475977i	−0.903843	−	0.427865i	$-0.859266\pi$
$617$	−7294.81	+	7294.81i	−0.475977	+	0.475977i	0.427865	+	0.903843i	$0.359266\pi$
$618$	13489.5	−	37676.1i	0.878037	−	2.45235i
$619$	20383.5	−	8443.10i	1.32355	−	0.548234i	0.394745	−	0.918791i	$-0.370833\pi$
$619$	20383.5	−	8443.10i	1.32355	−	0.548234i	0.928810	+	0.370557i	$0.120833\pi$
$620$	282.827	−	664.866i	0.0183203	−	0.0430672i
$621$	17523.1	−	42304.4i	1.13233	−	2.73369i
$622$	26480.7	−	1295.44i	1.70704	−	0.0835087i
$623$	−3836.93			−0.246747
$624$	−2343.49	+	3501.03i	−0.150344	+	0.224605i
$625$	−6500.19	+	14208.7i	−0.416012	+	0.909359i
$626$	−8963.19	+	438.482i	−0.572270	+	0.0279956i
$627$	−11278.2	−	4671.58i	−0.718354	−	0.297552i
$628$	−16823.0	−	5110.78i	−1.06897	−	0.324749i
$629$	−10242.3	+	4242.49i	−0.649262	+	0.268933i
$630$	2760.74	+	7947.88i	0.174588	+	0.502621i
$631$	−18008.8	−	18008.8i	−1.13616	−	1.13616i	−0.989132	−	0.147031i	$-0.953028\pi$
$631$	−18008.8	−	18008.8i	−1.13616	−	1.13616i	−0.147031	−	0.989132i	$-0.546972\pi$
$632$	15052.8	−	20270.2i	0.947419	−	1.27580i
$633$	14386.0	+	14386.0i	0.903302	+	0.903302i
$634$	1185.26	+	2507.35i	0.0742470	+	0.157066i
$635$	2113.03	−	3868.21i	0.132052	−	0.241740i
$636$	−946.100	−	9646.67i	−0.0589863	−	0.601439i
$637$	893.413	−	2156.89i	0.0555704	−	0.134159i
$638$	18284.9	−	20165.9i	1.13465	−	1.25138i
$639$	13030.2			0.806679
$640$	9507.39	+	13105.5i	0.587207	+	0.809437i
$641$	−1234.77			−0.0760853			−0.0380426	−	0.999276i	$-0.512112\pi$
$641$	−1234.77			−0.0760853			−0.0380426	+	0.999276i	$0.512112\pi$
$642$	478.808	−	528.065i	0.0294347	−	0.0324627i
$643$	−4805.84	+	11602.3i	−0.294749	+	0.711587i	0.705247	+	0.708961i	$0.250836\pi$
$643$	−4805.84	+	11602.3i	−0.294749	+	0.711587i	−0.999997	+	0.00262605i	$0.999164\pi$
$644$	−744.920	−	7595.40i	−0.0455807	−	0.464752i
$645$	24449.2	+	13355.5i	1.49254	+	0.815306i
$646$	−3072.89	−	6500.55i	−0.187154	−	0.395914i
$647$	−5445.02	−	5445.02i	−0.330859	−	0.330859i	0.522053	−	0.852913i	$-0.325166\pi$
$647$	−5445.02	−	5445.02i	−0.330859	−	0.330859i	−0.852913	+	0.522053i	$0.825166\pi$
$648$	−9359.90	+	12604.1i	−0.567425	+	0.764097i
$649$	11392.1	+	11392.1i	0.689030	+	0.689030i
$650$	−2199.17	−	1373.71i	−0.132706	−	0.0828942i
$651$	332.744	−	137.827i	0.0200327	−	0.00829780i
$652$	12202.7	+	3707.14i	0.732967	+	0.222673i
$653$	−10825.0	−	4483.85i	−0.648720	−	0.268709i	0.0339633	−	0.999423i	$-0.489187\pi$
$653$	−10825.0	−	4483.85i	−0.648720	−	0.268709i	−0.682683	+	0.730715i	$0.739187\pi$
$654$	−44344.9	+	2169.36i	−2.65141	+	0.129708i
$655$	2353.51	+	2921.50i	0.140396	+	0.174279i
$656$	−9176.12	−	6142.24i	−0.546139	−	0.365570i
$657$	−29957.5			−1.77892
$658$	5184.74	−	253.639i	0.307176	−	0.0150272i
$659$	−7010.88	+	16925.8i	−0.414423	+	1.00051i	0.569512	+	0.821983i	$0.307132\pi$
$659$	−7010.88	+	16925.8i	−0.414423	+	1.00051i	−0.983936	+	0.178524i	$0.942868\pi$
$660$	45813.1	+	19488.4i	2.70193	+	1.14937i
$661$	25600.5	−	10604.1i	1.50642	−	0.623979i	0.531604	−	0.846993i	$-0.321589\pi$
$661$	25600.5	−	10604.1i	1.50642	−	0.623979i	0.974815	+	0.223014i	$0.0715894\pi$
$662$	−6203.72	+	17327.0i	−0.364221	+	1.01727i
$663$	−5395.49	+	5395.49i	−0.316053	+	0.316053i
$664$	−12806.0	−	21395.5i	−0.748448	−	1.25046i
$665$	1210.97	+	130.394i	0.0706159	+	0.00760372i
$666$	13099.7	−	6192.41i	0.762169	−	0.360287i
$667$	27536.4	−	11406.0i	1.59852	−	0.662129i
$668$	−53.5430	+	65.1875i	−0.00310126	+	0.00377572i
$669$	15116.2	+	6261.35i	0.873584	+	0.361850i
$670$	1585.28	−	27122.4i	0.0914100	−	1.56393i
$671$	1061.88			0.0610929
$672$	−1192.45	+	7982.17i	−0.0684520	+	0.458212i
$673$			23814.2i			1.36400i	0.731352	+	0.682000i	$0.238890\pi$
$673$			23814.2i			1.36400i	−0.731352	+	0.682000i	$0.761110\pi$
$674$	7173.19	−	7911.11i	0.409942	−	0.452114i
$675$	−24475.3	−	17005.4i	−1.39564	−	0.969687i
$676$	−10882.6	+	13249.3i	−0.619173	+	0.753830i
$677$	−22041.1	+	9129.71i	−1.25127	+	0.518291i	−0.907218	−	0.420661i	$-0.861798\pi$
$677$	−22041.1	+	9129.71i	−1.25127	+	0.518291i	−0.344048	+	0.938952i	$0.611798\pi$
$678$	−3683.59	−	7792.45i	−0.208654	−	0.441397i
$679$	474.464	−	474.464i	0.0268163	−	0.0268163i
$680$	12279.8	+	26629.2i	0.692513	+	1.50174i
$681$	−20216.3	−	20216.3i	−1.13758	−	1.13758i
$682$	477.619	−	1333.99i	0.0268167	−	0.0748989i
$683$	−1710.44	−	4129.38i	−0.0958247	−	0.231341i	0.868698	−	0.495343i	$-0.164958\pi$
$683$	−1710.44	−	4129.38i	−0.0958247	−	0.231341i	−0.964522	+	0.264002i	$0.914958\pi$
$684$	4426.62	+	8289.84i	0.247450	+	0.463406i
$685$	−2346.02	+	688.436i	−0.130857	+	0.0383997i
$686$	−453.994	−	9280.29i	−0.0252676	−	0.516506i
$687$	−22605.5			−1.25539
$688$	9858.88	+	14781.2i	0.546317	+	0.819082i
$689$			990.007i			0.0547406i
$690$	36230.7	+	40728.9i	1.99895	+	2.24713i
$691$	1961.30	−	4735.01i	0.107976	−	0.260678i	−0.860651	−	0.509195i	$-0.829943\pi$
$691$	1961.30	−	4735.01i	0.107976	−	0.260678i	0.968627	+	0.248517i	$0.0799433\pi$
$692$	−376.331	+	1238.76i	−0.0206733	+	0.0680499i
$693$	6314.22	+	15243.9i	0.346115	+	0.835594i
$694$	−11040.5	+	30836.1i	−0.603879	+	1.68663i
$695$	−9749.27	−	1049.77i	−0.532102	−	0.0572953i
$696$	−31181.0	+	4605.56i	−1.69815	+	0.250824i
$697$	−14141.4	−	14141.4i	−0.768501	−	0.768501i
$698$	−10920.5	+	5162.27i	−0.592189	+	0.279935i
$699$	−1897.92	−	4581.99i	−0.102698	−	0.247935i
$700$	−4933.47	−	578.691i	−0.266382	−	0.0312464i
$701$	4186.34	+	1734.04i	0.225558	+	0.0934290i	0.492600	−	0.870256i	$-0.336046\pi$
$701$	4186.34	+	1734.04i	0.225558	+	0.0934290i	−0.267043	+	0.963685i	$0.586046\pi$
$702$	3322.15	−	3663.91i	0.178613	−	0.196988i
$703$		−	2097.53i		−	0.112532i
$704$	20112.5	+	24569.0i	1.07673	+	1.31531i
$705$	−28873.5	+	23259.9i	−1.54247	+	1.24258i
$706$	238.556	+	216.304i	0.0127170	+	0.0115307i
$707$	−301.340	+	727.499i	−0.0160298	+	0.0386993i
$708$	−1820.82	−	18565.6i	−0.0966534	−	0.985503i
$709$	10751.6	+	25956.6i	0.569511	+	1.37492i	0.901968	+	0.431803i	$0.142122\pi$
$709$	10751.6	+	25956.6i	0.569511	+	1.37492i	−0.332457	+	0.943118i	$0.607878\pi$
$710$	−3353.59	+	6923.34i	−0.177265	+	0.365955i
$711$	−42261.6	+	42261.6i	−2.22916	+	2.22916i
$712$	17290.7	−	2553.91i	0.910106	−	0.134427i
$713$	1097.01	−	1097.01i	0.0576204	−	0.0576204i
$714$	−4927.29	+	13761.9i	−0.258262	+	0.721326i
$715$	−4462.57	−	2437.70i	−0.233413	−	0.127503i
$716$	34093.6	+	10357.5i	1.77952	+	0.540612i
$717$	−3738.18	−	1548.40i	−0.194707	−	0.0806502i
$718$	−1229.89	−	25140.6i	−0.0639261	−	1.30674i
$719$		−	25997.0i		−	1.34843i	−0.738534	−	0.674217i	$-0.764481\pi$
$719$		−	25997.0i		−	1.34843i	0.738534	−	0.674217i	$-0.235519\pi$
$720$	−17731.2	−	33978.7i	−0.917779	−	1.75876i
$721$			7830.03i			0.404446i
$722$	−18018.2	+	881.456i	−0.928766	+	0.0454355i
$723$	−6613.82	−	2739.53i	−0.340208	−	0.140919i
$724$	−15553.8	−	29128.1i	−0.798417	−	1.49522i
$725$	−3438.11	−	19092.0i	−0.176122	−	0.978015i
$726$	60106.8	+	21520.5i	3.07269	+	1.10014i
$727$	10667.4	−	10667.4i	0.544199	−	0.544199i	−0.380558	−	0.924757i	$-0.624268\pi$
$727$	10667.4	−	10667.4i	0.544199	−	0.544199i	0.924757	+	0.380558i	$0.124268\pi$
$728$	200.788	−	799.492i	0.0102221	−	0.0407021i
$729$	−14578.8	+	14578.8i	−0.740678	+	0.740678i
$730$	7710.16	−	15917.3i	0.390912	−	0.807020i
$731$	12314.6	+	29730.1i	0.623081	+	1.50425i
$732$	−950.121	−	780.400i	−0.0479747	−	0.0394049i
$733$	4063.54	−	9810.25i	0.204761	−	0.494338i	−0.787822	−	0.615903i	$-0.788791\pi$
$733$	4063.54	−	9810.25i	0.204761	−	0.494338i	0.992583	+	0.121565i	$0.0387913\pi$
$734$	1192.98	−	1315.70i	0.0599913	−	0.0661628i
$735$	20040.1	+	24876.6i	1.00570	+	1.24842i
$736$	8412.49	+	33732.0i	0.421316	+	1.68937i
$737$		−	53279.7i		−	2.66293i
$738$	19363.9	+	17557.7i	0.965848	+	0.875756i
$739$	12755.4	+	5283.46i	0.634932	+	0.262997i	0.676847	−	0.736124i	$-0.263346\pi$
$739$	12755.4	+	5283.46i	0.634932	+	0.262997i	−0.0419149	+	0.999121i	$0.513346\pi$
$740$	−81.2773	+	8554.01i	−0.00403758	+	0.424935i
$741$	−552.474	−	1333.79i	−0.0273895	−	0.0661242i
$742$	810.523	+	1714.62i	0.0401014	+	0.0848325i
$743$	6110.98	+	6110.98i	0.301736	+	0.301736i	0.841693	−	0.539957i	$-0.181559\pi$
$743$	6110.98	+	6110.98i	0.301736	+	0.301736i	−0.539957	+	0.841693i	$0.681559\pi$
$744$	−1407.73	+	842.580i	−0.0693683	+	0.0415195i
$745$	17720.3	+	1908.08i	0.871441	+	0.0938343i
$746$	−26408.5	−	9455.25i	−1.29609	−	0.464050i
$747$	22588.3	+	54533.1i	1.10638	+	2.67103i
$748$	27087.6	+	50727.6i	1.32409	+	2.47966i
$749$	−53.3734	+	128.855i	−0.00260377	+	0.00628605i
$750$	30921.4	−	17397.3i	1.50546	−	0.847013i
$751$		−	3046.08i		−	0.148006i	−0.997258	−	0.0740032i	$-0.976422\pi$
$751$		−	3046.08i		−	0.148006i	0.997258	−	0.0740032i	$-0.0235775\pi$
$752$	−23195.6	+	4594.02i	−1.12481	+	0.222775i
$753$	48519.7			2.34815
$754$	3215.43	−	157.300i	0.155304	−	0.00759750i
$755$	−4641.36	−	15816.6i	−0.223730	−	0.762418i
$756$	2754.07	−	9065.50i	0.132493	−	0.436123i
$757$	8570.85	+	20691.9i	0.411510	+	0.993472i	0.984733	+	0.174073i	$0.0556928\pi$
$757$	8570.85	+	20691.9i	0.411510	+	0.993472i	−0.573223	+	0.819399i	$0.694307\pi$
$758$	−21708.3	−	7772.42i	−1.04021	−	0.372436i
$759$	75590.2	+	75590.2i	3.61495	+	3.61495i
$760$	−5543.91	+	218.432i	−0.264604	+	0.0104255i
$761$	17031.4	−	17031.4i	0.811286	−	0.811286i	−0.173541	−	0.984827i	$-0.555521\pi$
$761$	17031.4	−	17031.4i	0.811286	−	0.811286i	0.984827	+	0.173541i	$0.0555209\pi$
$762$	−9048.52	+	4277.35i	−0.430175	+	0.203349i
$763$	8025.72	−	3324.36i	0.380800	−	0.157733i
$764$	−1753.53	−	17879.5i	−0.0830374	−	0.846670i
$765$	−19545.8	−	66607.3i	−0.923764	−	3.14796i
$766$	9268.13	+	8403.62i	0.437168	+	0.396391i
$767$			1905.32i			0.0896965i
$768$	60.6143	−	36764.5i	0.00284796	−	1.72737i
$769$	17619.7			0.826247			0.413123	−	0.910675i	$-0.364438\pi$
$769$	17619.7			0.826247			0.413123	+	0.910675i	$0.364438\pi$
$770$	−9724.60	−	568.394i	−0.455130	−	0.0266020i
$771$	42439.3	+	17578.9i	1.98238	+	0.821128i
$772$	−34908.5	+	3423.66i	−1.62744	+	0.159611i
$773$	3704.59	−	1534.49i	0.172374	−	0.0713995i	−0.294828	−	0.955550i	$-0.595262\pi$
$773$	3704.59	−	1534.49i	0.172374	−	0.0713995i	0.467201	+	0.884151i	$0.345262\pi$
$774$	−17974.6	−	38024.5i	−0.834735	−	1.76584i
$775$	−545.636	−	849.639i	−0.0252901	−	0.0393806i
$776$	−1822.31	+	2453.93i	−0.0843005	+	0.113519i
$777$	−3015.21	+	3015.21i	−0.139215	+	0.139215i
$778$	26437.3	+	9465.57i	1.21828	+	0.436192i
$779$	3495.83	−	1448.02i	0.160785	−	0.0665992i
$780$	2201.39	+	5460.80i	0.101054	+	0.250677i
$781$	−5773.20	+	13937.7i	−0.264509	+	0.638581i
$782$	3076.60	+	62890.0i	0.140689	+	2.87588i
$783$	37001.9			1.68881
$784$	3958.08	+	19984.7i	0.180306	+	0.910381i
$785$	−19135.2	+	15414.9i	−0.870019	+	0.700870i
$786$	−416.236	−	8508.46i	−0.0188889	−	0.386116i
$787$	−3855.29	−	1596.91i	−0.174620	−	0.0723301i	0.293661	−	0.955910i	$-0.405126\pi$
$787$	−3855.29	−	1596.91i	−0.174620	−	0.0723301i	−0.468281	+	0.883580i	$0.655126\pi$
$788$	−10333.8	−	19352.3i	−0.467165	−	0.874872i
$789$	−18518.9	+	7670.80i	−0.835604	+	0.346119i
$790$	−11577.9	−	33331.7i	−0.521423	−	1.50113i
$791$	1192.50	+	1192.50i	0.0536038	+	0.0536038i
$792$	−38600.8	−	64492.0i	−1.73184	−	2.89346i
$793$	88.7989	+	88.7989i	0.00397647	+	0.00397647i
$794$	−23258.3	+	10994.5i	−1.03955	+	0.491410i
$795$	−11888.3	−	6494.01i	−0.530356	−	0.289709i
$796$	−11107.5	−	9123.35i	−0.494591	−	0.406242i
$797$	−2688.96	+	6491.73i	−0.119508	+	0.288518i	−0.972301	−	0.233731i	$-0.924907\pi$
$797$	−2688.96	+	6491.73i	−0.119508	+	0.288518i	0.852793	+	0.522248i	$0.174907\pi$
$798$	−2048.83	−	1857.72i	−0.0908868	−	0.0824091i
$799$	−42827.0			−1.89626
$800$	22617.3	−	675.974i	0.999554	−	0.0298741i
$801$	−41374.4			−1.82508
$802$	7472.41	+	6775.40i	0.329002	+	0.298314i
$803$	13273.0	−	32043.9i	0.583306	−	1.40822i
$804$	−39156.5	+	47672.3i	−1.71759	+	2.09113i
$805$	−9360.33	−	5113.12i	−0.409824	−	0.223868i
$806$	151.495	−	71.6134i	0.00662056	−	0.00312962i
$807$	−34537.7	−	34537.7i	−1.50655	−	1.50655i
$808$	873.722	−	3478.97i	0.0380414	−	0.151472i
$809$	−7494.08	−	7494.08i	−0.325683	−	0.325683i	0.525259	−	0.850942i	$-0.323968\pi$
$809$	−7494.08	−	7494.08i	−0.325683	−	0.325683i	−0.850942	+	0.525259i	$0.823968\pi$
$810$	7199.21	+	20725.8i	0.312289	+	0.899050i
$811$	7817.94	−	3238.30i	0.338502	−	0.140212i	−0.206956	−	0.978350i	$-0.566356\pi$
$811$	7817.94	−	3238.30i	0.338502	−	0.140212i	0.545458	+	0.838138i	$0.316356\pi$
$812$	5440.11	−	2904.92i	0.235112	−	0.125545i
$813$	52423.1	+	21714.4i	2.26145	+	0.936724i
$814$	819.694	+	16755.7i	0.0352951	+	0.721483i
$815$	13879.9	−	11181.4i	0.596553	−	0.480571i
$816$	13044.2	−	65296.2i	0.559605	−	2.80125i
$817$	−6088.47			−0.260720
$818$	−1250.91	−	25570.3i	−0.0534681	−	1.09296i
$819$	−746.737	+	1802.78i	−0.0318597	+	0.0769162i
$820$	−14312.6	+	5769.78i	−0.609534	+	0.245719i
$821$	−15296.2	+	6335.88i	−0.650231	+	0.269335i	−0.683321	−	0.730118i	$-0.739465\pi$
$821$	−15296.2	+	6335.88i	−0.650231	+	0.269335i	0.0330901	+	0.999452i	$0.489465\pi$
$822$	5226.81	+	1871.40i	0.221783	+	0.0794070i
$823$	−13223.2	+	13223.2i	−0.560062	+	0.560062i	−0.929325	−	0.369263i	$-0.879610\pi$
$823$	−13223.2	+	13223.2i	−0.560062	+	0.560062i	0.369263	+	0.929325i	$0.379610\pi$
$824$	−5211.77	−	35285.2i	−0.220340	−	1.49177i
$825$	58545.0	−	37597.4i	2.47064	−	1.58664i
$826$	1559.90	+	3299.88i	0.0657091	+	0.139004i
$827$	41513.9	−	17195.6i	1.74556	−	0.723036i	0.747278	−	0.664512i	$-0.231361\pi$
$827$	41513.9	−	17195.6i	1.74556	−	0.723036i	0.998286	−	0.0585241i	$-0.0186394\pi$
$828$	−8032.63	−	81902.7i	−0.337141	−	3.43758i
$829$	−9225.73	−	3821.42i	−0.386517	−	0.160101i	0.180959	−	0.983491i	$-0.442080\pi$
$829$	−9225.73	−	3821.42i	−0.386517	−	0.160101i	−0.567476	+	0.823390i	$0.692080\pi$
$830$	−34788.6	−	2033.36i	−1.45485	−	0.0850349i
$831$	−32996.6			−1.37742
$832$	−372.675	+	3736.47i	−0.0155291	+	0.155695i
$833$			36898.5i			1.53476i
$834$	16494.6	+	14956.1i	0.684847	+	0.620966i
$835$	33.1959	+	113.124i	0.00137580	+	0.00468839i
$836$	−10828.5	+	1062.00i	−0.447979	+	0.0439356i
$837$	1779.40	−	737.050i	0.0734826	−	0.0304375i
$838$	6452.75	−	3050.29i	0.265998	−	0.125741i
$839$	13798.6	−	13798.6i	0.567796	−	0.567796i	−0.363714	−	0.931511i	$-0.618492\pi$
$839$	13798.6	−	13798.6i	0.567796	−	0.567796i	0.931511	+	0.363714i	$0.118492\pi$
$840$	8283.42	+	7655.42i	0.340244	+	0.314449i
$841$	−215.017	−	215.017i	−0.00881616	−	0.00881616i
$842$	26322.2	+	9424.35i	1.07734	+	0.385730i
$843$	4972.92	+	12005.7i	0.203175	+	0.490508i
$844$	17350.2	+	5270.95i	0.707607	+	0.214969i
$845$	6747.06	+	22992.3i	0.274681	+	0.936048i
$846$	55908.1	−	2735.04i	2.27206	−	0.111150i
$847$	−12491.7			−0.506752
$848$	−4793.80	−	7187.25i	−0.194127	−	0.291051i
$849$		−	24976.5i		−	1.00965i
$850$	40420.9	+	6757.50i	1.63109	+	0.272683i
$851$	−7029.16	+	16969.9i	−0.283145	+	0.683573i
$852$	15408.8	−	8228.01i	0.619597	−	0.330853i
$853$	4259.10	+	10282.4i	0.170960	+	0.412734i	0.986017	−	0.166648i	$-0.0532942\pi$
$853$	4259.10	+	10282.4i	0.170960	+	0.412734i	−0.815057	+	0.579381i	$0.803294\pi$
$854$	226.493	+	81.0933i	0.00907546	+	0.00324936i
$855$	13058.2	+	1406.07i	0.522316	+	0.0562415i
$856$	154.754	−	616.195i	0.00617918	−	0.0246041i
$857$	−18546.8	−	18546.8i	−0.739259	−	0.739259i	0.233175	−	0.972435i	$-0.425088\pi$
$857$	−18546.8	−	18546.8i	−0.739259	−	0.739259i	−0.972435	+	0.233175i	$0.925088\pi$
$858$	4934.57	+	10438.8i	0.196344	+	0.415357i
$859$	11373.4	+	27457.8i	0.451752	+	1.09063i	0.971656	+	0.236401i	$0.0759678\pi$
$859$	11373.4	+	27457.8i	0.451752	+	1.09063i	−0.519904	+	0.854225i	$0.674032\pi$
$860$	24829.6	+	235.923i	0.984515	+	0.00935453i
$861$	−7106.84	−	2943.75i	−0.281301	−	0.116519i
$862$	−14097.5	−	12782.5i	−0.557034	−	0.505075i
$863$			20079.0i			0.792002i	0.918250	+	0.396001i	$0.129602\pi$
$863$			20079.0i			0.792002i	−0.918250	+	0.396001i	$0.870398\pi$
$864$	−6376.80	+	42685.8i	−0.251092	+	1.68079i
$865$	1135.08	+	1409.02i	0.0446170	+	0.0553850i
$866$	−31389.7	+	34618.8i	−1.23172	+	1.35843i
$867$	29275.6	−	70677.5i	1.14677	−	2.76855i
$868$	203.748	−	248.059i	0.00796733	−	0.00970007i
$869$	−26480.5	−	63929.5i	−1.03370	−	2.49558i
$870$	−19202.9	+	39643.5i	−0.748322	+	1.54488i
$871$	4455.48	−	4455.48i	0.173327	−	0.173327i
$872$	−33954.3	+	20322.9i	−1.31862	+	0.789243i
$873$	5116.24	−	5116.24i	0.198349	−	0.198349i
$874$	−11215.9	−	4015.74i	−0.434079	−	0.155417i
$875$	−4548.63	+	5244.18i	−0.175739	+	0.202612i
$876$	−35426.0	+	18916.8i	−1.36636	+	0.729611i
$877$	−7698.55	−	3188.84i	−0.296421	−	0.122782i	0.229516	−	0.973305i	$-0.426286\pi$
$877$	−7698.55	−	3188.84i	−0.296421	−	0.122782i	−0.525938	+	0.850523i	$0.676286\pi$
$878$	−3103.38	+	151.818i	−0.119287	+	0.00583555i
$879$		−	42949.9i		−	1.64808i
$880$	44201.2	−	3911.41i	1.69321	−	0.149834i
$881$		−	12341.2i		−	0.471947i	−0.971759	−	0.235973i	$-0.924172\pi$
$881$		−	12341.2i		−	0.471947i	0.971759	−	0.235973i	$-0.0758279\pi$
$882$	−2356.43	−	48168.8i	−0.0899604	−	1.83892i
$883$	−11027.5	−	4567.74i	−0.420277	−	0.174084i	0.162515	−	0.986706i	$-0.448040\pi$
$883$	−11027.5	−	4567.74i	−0.420277	−	0.174084i	−0.582791	+	0.812622i	$0.698040\pi$
$884$	−1976.88	+	6507.25i	−0.0752146	+	0.247582i
$885$	−22879.6	−	12498.1i	−0.869027	−	0.474710i
$886$	−1232.13	+	3441.34i	−0.0467204	+	0.130490i
$887$	−10885.4	+	10885.4i	−0.412058	+	0.412058i	−0.882455	−	0.470397i	$-0.844111\pi$
$887$	−10885.4	+	10885.4i	−0.412058	+	0.412058i	0.470397	+	0.882455i	$0.344111\pi$
$888$	11580.8	−	15594.7i	0.437641	−	0.589328i
$889$	1384.72	−	1384.72i	0.0522409	−	0.0522409i
$890$	10648.5	−	21983.4i	0.401056	−	0.827960i
$891$	16465.7	+	39751.7i	0.619103	+	1.49465i
$892$	14513.5	−	1423.41i	0.544783	−	0.0534298i
$893$	3100.87	−	7486.16i	0.116200	−	0.280532i
$894$	−29980.8	−	27184.2i	−1.12160	−	1.01698i
$895$	38779.5	−	31240.0i	1.44833	−	1.16675i
$896$	2413.61	+	6776.40i	0.0899924	+	0.252660i
$897$			12642.4i			0.470587i
$898$	−10948.1	+	12074.4i	−0.406840	+	0.448693i
$899$	1158.23	+	479.754i	0.0429689	+	0.0177983i
$900$	−53198.6	−	6240.14i	−1.97032	−	0.231116i
$901$	−5987.89	−	14456.0i	−0.221404	−	0.534518i
$902$	−27360.0	+	12933.4i	−1.00996	+	0.477422i
$903$	8752.22	+	8752.22i	0.322542	+	0.322542i
$904$	−6167.63	−	4580.14i	−0.226916	−	0.168510i
$905$	−45882.6	−	4940.51i	−1.68529	−	0.181468i
$906$	−12616.8	+	35238.6i	−0.462653	+	1.29219i
$907$	12945.8	+	31254.0i	0.473935	+	1.14418i	0.962410	+	0.271602i	$0.0875533\pi$
$907$	12945.8	+	31254.0i	0.473935	+	1.14418i	−0.488475	+	0.872578i	$0.662447\pi$
$908$	−24382.0	−	7407.17i	−0.891128	−	0.270722i
$909$	−3249.41	+	7844.76i	−0.118566	+	0.286242i
$910$	−765.683	−	860.746i	−0.0278925	−	0.0313554i
$911$			32506.1i			1.18219i	0.806602	+	0.591095i	$0.201304\pi$
$911$			32506.1i			1.18219i	−0.806602	+	0.591095i	$0.798696\pi$
$912$	10469.3	+	7007.87i	0.380125	+	0.254445i
$913$	−68339.2			−2.47721
$914$	−199.732	−	4082.81i	−0.00722817	−	0.147754i
$915$	−1648.80	+	483.838i	−0.0595713	+	0.0174811i
$916$	−17773.0	+	9490.45i	−0.641088	+	0.342329i
$917$	637.846	+	1539.90i	0.0229701	+	0.0554546i
$918$	−26349.4	+	73593.8i	−0.947342	+	2.64592i
$919$	−32014.2	−	32014.2i	−1.14913	−	1.14913i	−0.986724	−	0.162405i	$-0.948075\pi$
$919$	−32014.2	−	32014.2i	−1.14913	−	1.14913i	−0.162405	−	0.986724i	$-0.551925\pi$
$920$	45584.6	+	16811.4i	1.63357	+	0.602450i
$921$	23863.3	−	23863.3i	0.853770	−	0.853770i
$922$	−3351.72	−	7090.40i	−0.119721	−	0.253264i
$923$	−1648.32	+	682.755i	−0.0587811	+	0.0243479i
$924$	17092.7	+	14039.4i	0.608557	+	0.499850i
$925$	9817.95	+	6821.51i	0.348986	+	0.242475i
$926$	13925.7	−	15358.3i	0.494199	−	0.545039i
$927$			84432.8i			2.99152i
$928$	−22581.7	+	16711.7i	−0.798794	+	0.591151i
$929$	52409.8			1.85093			0.925463	−	0.378837i	$-0.123676\pi$
$929$	52409.8			1.85093			0.925463	+	0.378837i	$0.123676\pi$
$930$	−133.786	+	2288.94i	−0.00471724	+	0.0807067i
$931$	−6449.86	−	2671.62i	−0.227052	−	0.0940482i
$932$	−3415.85	−	2805.67i	−0.120053	−	0.0986081i
$933$	−77729.7	+	32196.7i	−2.72750	+	1.12977i
$934$	−594.544	+	281.048i	−0.0208288	+	0.00984602i
$935$	79906.2	+	8604.08i	2.79488	+	0.300945i
$936$	2165.13	−	8621.08i	0.0756085	−	0.301056i
$937$	38875.2	−	38875.2i	1.35539	−	1.35539i	0.475875	−	0.879513i	$-0.342131\pi$
$937$	38875.2	−	38875.2i	1.35539	−	1.35539i	0.879513	−	0.475875i	$-0.157869\pi$
$938$	4068.85	−	11364.3i	0.141634	−	0.395584i
$939$	26310.0	−	10898.0i	0.914371	−	0.378745i
$940$	−12935.9	+	30409.5i	−0.448853	+	1.05516i
$941$	11474.5	−	27701.9i	0.397512	−	0.959679i	−0.590742	−	0.806860i	$-0.701165\pi$
$941$	11474.5	−	27701.9i	0.397512	−	0.959679i	0.988254	−	0.152818i	$-0.0488350\pi$
$942$	55728.5	−	2726.26i	1.92753	−	0.0942953i
$943$	−33135.4			−1.14426
$944$	−9225.94	−	13832.3i	−0.318092	−	0.476909i
$945$	−8306.73	−	10311.5i	−0.285945	−	0.354955i
$946$	48636.6	−	2379.32i	1.67158	−	0.0817740i
$947$	7094.47	+	2938.63i	0.243442	+	0.100837i	0.501068	−	0.865408i	$-0.332940\pi$
$947$	7094.47	+	2938.63i	0.243442	+	0.100837i	−0.257627	+	0.966245i	$0.582940\pi$
$948$	−23289.8	+	76662.5i	−0.797910	+	2.62646i
$949$	3789.60	−	1569.70i	0.129627	−	0.0536931i
$950$	−4107.87	+	6576.30i	−0.140292	+	0.224593i
$951$	−6223.27	−	6223.27i	−0.212201	−	0.212201i
$952$	1903.70	+	12888.6i	0.0648100	+	0.438783i
$953$	−16493.5	−	16493.5i	−0.560626	−	0.560626i	0.368859	−	0.929485i	$-0.379748\pi$
$953$	−16493.5	−	16493.5i	−0.560626	−	0.560626i	−0.929485	+	0.368859i	$0.879748\pi$
$954$	8740.03	+	18489.1i	0.296613	+	0.627470i
$955$	−22034.1	−	12036.2i	−0.746603	−	0.407835i
$956$	−3589.11	+	352.003i	−0.121423	+	0.0119086i
$957$	−33057.8	+	79808.5i	−1.11662	+	2.69576i
$958$	−9489.01	+	10465.2i	−0.320017	+	0.352938i
$959$	−1086.26			−0.0365769
$960$	−42423.8	−	28984.8i	−1.42627	−	0.974458i
$961$	−29725.7			−0.997810
$962$	−1332.64	+	1469.73i	−0.0446632	+	0.0492579i
$963$	−575.536	+	1389.47i	−0.0192590	+	0.0464952i
$964$	−6350.09	+	622.786i	−0.212160	+	0.0208077i
$965$	−23499.9	+	43020.1i	−0.783926	+	1.43509i
$966$	10350.4	+	21895.7i	0.344739	+	0.729278i
$967$	−15017.3	−	15017.3i	−0.499404	−	0.499404i	0.411848	−	0.911253i	$-0.364883\pi$
$967$	−15017.3	−	15017.3i	−0.499404	−	0.499404i	−0.911253	+	0.411848i	$0.864883\pi$
$968$	56292.4	−	8314.62i	1.86912	−	0.276076i
$969$	16134.4	+	16134.4i	0.534894	+	0.534894i
$970$	1401.64	+	4035.18i	0.0463958	+	0.133569i
$971$	−32342.1	+	13396.5i	−1.06890	+	0.442755i	−0.846604	−	0.532224i	$-0.821357\pi$
$971$	−32342.1	+	13396.5i	−1.06890	+	0.442755i	−0.222300	+	0.974978i	$0.571357\pi$
$972$	−488.189	+	1606.96i	−0.0161097	+	0.0530280i
$973$	−4024.91	−	1667.17i	−0.132613	−	0.0549301i
$974$	2681.95	−	131.202i	0.0882293	−	0.00431620i
$975$	8039.85	+	1751.73i	0.264083	+	0.0575387i
$976$	−1074.64	−	214.681i	−0.0352444	−	0.00704075i
$977$	29024.7			0.950442			0.475221	−	0.879866i	$-0.342368\pi$
$977$	29024.7			0.950442			0.475221	+	0.879866i	$0.342368\pi$
$978$	−40423.2	+	1977.51i	−1.32167	+	0.0646563i
$979$	18331.4	−	44255.9i	0.598442	−	1.44477i
$980$	26199.9	+	11145.2i	0.854006	+	0.363285i
$981$	86543.0	−	35847.3i	2.81662	−	1.16668i
$982$	−1312.49	+	3665.79i	−0.0426510	+	0.119124i
$983$	36145.0	−	36145.0i	1.17278	−	1.17278i	0.191239	−	0.981543i	$-0.438749\pi$
$983$	36145.0	−	36145.0i	1.17278	−	1.17278i	0.981543	−	0.191239i	$-0.0612507\pi$
$984$	33985.6	+	8535.27i	1.10104	+	0.276519i
$985$	−30483.9	−	3282.42i	−0.986088	−	0.106179i
$986$	−46000.2	+	21744.9i	−1.48574	+	0.702330i
$987$	−15219.0	+	6303.90i	−0.490805	+	0.203298i
$988$	−994.334	−	816.715i	−0.0320182	−	0.0262987i
$989$	49258.3	+	20403.5i	1.58374	+	0.656008i
$990$	−104862.	−	6129.11i	−3.36641	−	0.196764i
$991$	−27516.2			−0.882019			−0.441010	−	0.897502i	$-0.645380\pi$
$991$	−27516.2			−0.882019			−0.441010	+	0.897502i	$0.645380\pi$
$992$	−753.055	+	1253.47i	−0.0241023	+	0.0401185i
$993$		−	58403.3i		−	1.86644i
$994$	−2295.79	+	2531.97i	−0.0732576	+	0.0807938i
$995$	−19275.5	+	5656.36i	−0.614145	+	0.180220i
$996$	61146.9	+	50224.1i	1.94529	+	1.59780i
$997$	21738.6	−	9004.43i	0.690540	−	0.286031i	−0.00968496	−	0.999953i	$-0.503083\pi$
$997$	21738.6	−	9004.43i	0.690540	−	0.286031i	0.700225	+	0.713922i	$0.253083\pi$
$998$	−16271.4	−	34421.4i	−0.516095	−	1.09177i
$999$	−16124.3	+	16124.3i	−0.510661	+	0.510661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.z.a.29.18	✓	280
5.4	even	2	inner	160.4.z.a.29.53	yes	280
32.21	even	8	inner	160.4.z.a.149.53	yes	280
160.149	even	8	inner	160.4.z.a.149.18	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.z.a.29.18	✓	280	1.1	even	1	trivial
160.4.z.a.29.53	yes	280	5.4	even	2	inner
160.4.z.a.149.18	yes	280	160.149	even	8	inner
160.4.z.a.149.53	yes	280	32.21	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89989 + 2.09533i) q^{2} +(3.43485 - 8.29247i) q^{3} +(-0.780855 - 7.96180i) q^{4} +(-9.81187 - 5.35978i) q^{5} +(10.8497 + 22.9519i) q^{6} +(-3.51241 - 3.51241i) q^{7} +(18.1662 + 13.4904i) q^{8} +(-37.8750 - 37.8750i) q^{9} +(29.8720 - 10.3762i) q^{10} +(57.2938 - 23.7319i) q^{11} +(-68.7051 - 20.8724i) q^{12} +(6.77573 + 2.80660i) q^{13} +(14.0328 - 0.686491i) q^{14} +(-78.1482 + 62.9546i) q^{15} +(-62.7805 + 12.4340i) q^{16} -115.914 q^{17} +(151.319 - 7.40257i) q^{18} +(8.39272 - 20.2618i) q^{19} +(-35.0118 + 82.3054i) q^{20} +(-41.1912 + 17.0619i) q^{21} +(-59.1256 + 165.138i) q^{22} +(-135.801 + 135.801i) q^{23} +(174.267 - 104.305i) q^{24} +(67.5456 + 105.179i) q^{25} +(-18.7539 + 8.86520i) q^{26} +(-220.276 + 91.2412i) q^{27} +(-25.2224 + 30.7078i) q^{28} +(-143.380 - 59.3899i) q^{29} +(16.5617 - 283.353i) q^{30} -8.07804 q^{31} +(93.2225 - 155.169i) q^{32} -556.623i q^{33} +(220.224 - 242.879i) q^{34} +(15.6376 + 53.2890i) q^{35} +(-271.978 + 331.128i) q^{36} +(88.3608 - 36.6002i) q^{37} +(26.5101 + 56.0807i) q^{38} +(46.5473 - 46.5473i) q^{39} +(-105.939 - 229.732i) q^{40} +(121.999 + 121.999i) q^{41} +(42.5081 - 118.725i) q^{42} +(-106.239 - 256.484i) q^{43} +(-233.687 - 437.631i) q^{44} +(168.623 + 574.626i) q^{45} +(-26.5420 - 542.557i) q^{46} +369.471 q^{47} +(-112.533 + 563.315i) q^{48} -318.326i q^{49} +(-348.714 - 58.2975i) q^{50} +(-398.148 + 961.215i) q^{51} +(17.0547 - 56.1385i) q^{52} +(51.6579 + 124.713i) q^{53} +(227.318 - 634.899i) q^{54} +(-689.357 - 74.2281i) q^{55} +(-16.4233 - 111.191i) q^{56} +(-139.193 - 139.193i) q^{57} +(396.847 - 187.595i) q^{58} +(99.4186 + 240.018i) q^{59} +(562.254 + 573.042i) q^{60} +(15.8197 + 6.55272i) q^{61} +(15.3474 - 16.9262i) q^{62} +266.065i q^{63} +(148.020 + 490.137i) q^{64} +(-51.4398 - 63.8544i) q^{65} +(1166.31 + 1057.52i) q^{66} +(328.782 - 793.751i) q^{67} +(90.5122 + 922.885i) q^{68} +(659.671 + 1592.59i) q^{69} +(-141.368 - 68.4772i) q^{70} +(-172.016 + 172.016i) q^{71} +(-177.096 - 1198.99i) q^{72} +(395.478 - 395.478i) q^{73} +(-91.1858 + 254.682i) q^{74} +(1104.20 - 198.846i) q^{75} +(-167.874 - 50.9996i) q^{76} +(-284.595 - 117.883i) q^{77} +(9.09754 + 185.967i) q^{78} -1115.82i q^{79} +(682.638 + 214.489i) q^{80} +693.821i q^{81} +(-487.414 + 23.8444i) q^{82} +(-1018.10 - 421.713i) q^{83} +(168.008 + 314.633i) q^{84} +(1137.33 + 621.274i) q^{85} +(739.262 + 264.684i) q^{86} +(-984.978 + 984.978i) q^{87} +(1360.96 + 341.798i) q^{88} +(546.196 - 546.196i) q^{89} +(-1524.40 - 738.403i) q^{90} +(-13.9412 - 33.6570i) q^{91} +(1187.27 + 975.182i) q^{92} +(-27.7469 + 66.9869i) q^{93} +(-701.954 + 774.166i) q^{94} +(-190.947 + 153.823i) q^{95} +(-966.533 - 1306.03i) q^{96} +135.082i q^{97} +(666.999 + 604.784i) q^{98} +(-3068.85 - 1271.16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) \) 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

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