LMFDB - Embedded newform 220.3.i.a.87.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, degree $2$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			87.19
Character	$\chi$	$=$	220.87
Dual form			220.3.i.a.43.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33338 - 1.49067i) q^{2} +(3.87627 + 3.87627i) q^{3} +(-0.444207 + 3.97526i) q^{4} +(3.64792 - 3.41945i) q^{5} +(0.609714 - 10.9468i) q^{6} +(5.44609 + 5.44609i) q^{7} +(6.51810 - 4.63836i) q^{8} +21.0509i q^{9} +(-9.96134 - 0.878432i) q^{10} +(7.73363 - 7.82247i) q^{11} +(-17.1310 + 13.6873i) q^{12} +(-14.7946 - 14.7946i) q^{13} +(0.856637 - 15.3800i) q^{14} +(27.3951 + 0.885606i) q^{15} +(-15.6054 - 3.53167i) q^{16} +(-5.69580 + 5.69580i) q^{17} +(31.3800 - 28.0688i) q^{18} +21.1920i q^{19} +(11.9728 + 16.0204i) q^{20} +42.2210i q^{21} +(-21.9726 - 1.09800i) q^{22} +(7.64133 + 7.64133i) q^{23} +(43.2454 + 7.28640i) q^{24} +(1.61467 - 24.9478i) q^{25} +(-2.32710 + 41.7806i) q^{26} +(-46.7126 + 46.7126i) q^{27} +(-24.0688 + 19.2304i) q^{28} +2.11660 q^{29} +(-35.2078 - 42.0179i) q^{30} -23.3398i q^{31} +(15.5433 + 27.9715i) q^{32} +(60.2996 - 0.344346i) q^{33} +(16.0852 + 0.895915i) q^{34} +(38.4895 + 1.24426i) q^{35} +(-83.6829 - 9.35096i) q^{36} +(7.12170 + 7.12170i) q^{37} +(31.5904 - 28.2570i) q^{38} -114.695i q^{39} +(7.91689 - 39.2087i) q^{40} -13.4770i q^{41} +(62.9377 - 56.2965i) q^{42} +(-18.4300 + 18.4300i) q^{43} +(27.6610 + 34.2180i) q^{44} +(71.9827 + 76.7922i) q^{45} +(1.20194 - 21.5795i) q^{46} +(25.7009 - 25.7009i) q^{47} +(-46.8009 - 74.1803i) q^{48} +10.3197i q^{49} +(-39.3420 + 30.8579i) q^{50} -44.1569 q^{51} +(65.3840 - 52.2403i) q^{52} +(-10.8004 + 10.8004i) q^{53} +(131.919 + 7.34763i) q^{54} +(1.46313 - 54.9805i) q^{55} +(60.7590 + 10.2373i) q^{56} +(-82.1460 + 82.1460i) q^{57} +(-2.82223 - 3.15516i) q^{58} -84.0088 q^{59} +(-15.6896 + 108.509i) q^{60} -87.3519i q^{61} +(-34.7919 + 31.1207i) q^{62} +(-114.645 + 114.645i) q^{63} +(20.9713 - 60.4666i) q^{64} +(-104.559 - 3.38009i) q^{65} +(-80.9155 - 89.4278i) q^{66} +(-55.9563 + 55.9563i) q^{67} +(-20.1122 - 25.1724i) q^{68} +59.2397i q^{69} +(-49.4663 - 59.0344i) q^{70} +24.0536i q^{71} +(97.6417 + 137.212i) q^{72} +(69.0302 + 69.0302i) q^{73} +(1.12020 - 20.1120i) q^{74} +(102.963 - 90.4455i) q^{75} +(-84.2438 - 9.41364i) q^{76} +(84.7198 - 0.483800i) q^{77} +(-170.973 + 152.932i) q^{78} -47.8344i q^{79} +(-69.0035 + 40.4785i) q^{80} -172.683 q^{81} +(-20.0898 + 17.9699i) q^{82} +(11.0631 - 11.0631i) q^{83} +(-167.839 - 18.7548i) q^{84} +(-1.30131 + 40.2543i) q^{85} +(52.0472 + 2.89893i) q^{86} +(8.20451 + 8.20451i) q^{87} +(14.1252 - 86.8590i) q^{88} -90.4306i q^{89} +(18.4918 - 209.696i) q^{90} -161.145i q^{91} +(-33.7706 + 26.9819i) q^{92} +(90.4712 - 90.4712i) q^{93} +(-72.5807 - 4.04261i) q^{94} +(72.4652 + 77.3069i) q^{95} +(-48.1752 + 168.675i) q^{96} +(-88.2136 - 88.2136i) q^{97} +(15.3833 - 13.7601i) q^{98} +(164.670 + 162.800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.33338	−	1.49067i	−0.666689	−	0.745336i
$2$	−1.33338	−	1.49067i	−0.666689	−	0.745336i
$3$	3.87627	+	3.87627i	1.29209	+	1.29209i	0.933492	+	0.358598i	$0.116745\pi$
$3$	3.87627	+	3.87627i	1.29209	+	1.29209i	0.358598	+	0.933492i	$0.383255\pi$
$4$	−0.444207	+	3.97526i	−0.111052	+	0.993815i
$5$	3.64792	−	3.41945i	0.729584	−	0.683891i
$5$	3.64792	−	3.41945i	0.729584	−	0.683891i
$6$	0.609714	−	10.9468i	0.101619	−	1.82446i
$7$	5.44609	+	5.44609i	0.778012	+	0.778012i	0.979493	−	0.201480i	$-0.0645752\pi$
$7$	5.44609	+	5.44609i	0.778012	+	0.778012i	−0.201480	+	0.979493i	$0.564575\pi$
$8$	6.51810	−	4.63836i	0.814763	−	0.579794i
$9$			21.0509i			2.33899i
$10$	−9.96134	−	0.878432i	−0.996134	−	0.0878432i
$11$	7.73363	−	7.82247i	0.703057	−	0.711133i
$11$	7.73363	−	7.82247i	0.703057	−	0.711133i
$12$	−17.1310	+	13.6873i	−1.42759	+	1.14061i
$13$	−14.7946	−	14.7946i	−1.13804	−	1.13804i	−0.988801	−	0.149242i	$-0.952317\pi$
$13$	−14.7946	−	14.7946i	−1.13804	−	1.13804i	−0.149242	−	0.988801i	$-0.547683\pi$
$14$	0.856637	−	15.3800i	0.0611884	−	1.09857i
$15$	27.3951	+	0.885606i	1.82634	+	0.0590404i
$16$	−15.6054	−	3.53167i	−0.975335	−	0.220729i
$17$	−5.69580	+	5.69580i	−0.335047	+	0.335047i	−0.854499	−	0.519452i	$-0.826136\pi$
$17$	−5.69580	+	5.69580i	−0.335047	+	0.335047i	0.519452	+	0.854499i	$0.326136\pi$
$18$	31.3800	−	28.0688i	1.74334	−	1.55938i
$19$			21.1920i			1.11537i	0.830053	+	0.557685i	$0.188310\pi$
$19$			21.1920i			1.11537i	−0.830053	+	0.557685i	$0.811690\pi$
$20$	11.9728	+	16.0204i	0.598639	+	0.801019i
$21$			42.2210i			2.01052i
$22$	−21.9726	−	1.09800i	−0.998754	−	0.0499093i
$23$	7.64133	+	7.64133i	0.332232	+	0.332232i	0.853434	−	0.521202i	$-0.174516\pi$
$23$	7.64133	+	7.64133i	0.332232	+	0.332232i	−0.521202	+	0.853434i	$0.674516\pi$
$24$	43.2454	+	7.28640i	1.80189	+	0.303600i
$25$	1.61467	−	24.9478i	0.0645869	−	0.997912i
$26$	−2.32710	+	41.7806i	−0.0895037	+	1.60694i
$27$	−46.7126	+	46.7126i	−1.73010	+	1.73010i
$28$	−24.0688	+	19.2304i	−0.859600	+	0.686801i
$29$	2.11660			0.0729862			0.0364931	−	0.999334i	$-0.488381\pi$
$29$	2.11660			0.0729862			0.0364931	+	0.999334i	$0.488381\pi$
$30$	−35.2078	−	42.0179i	−1.17359	−	1.40060i
$31$		−	23.3398i		−	0.752896i	−0.926438	−	0.376448i	$-0.877145\pi$
$31$		−	23.3398i		−	0.752896i	0.926438	−	0.376448i	$-0.122855\pi$
$32$	15.5433	+	27.9715i	0.485728	+	0.874110i
$33$	60.2996	−	0.344346i	1.82726	−	0.0104347i
$34$	16.0852	+	0.895915i	0.473095	+	0.0263505i
$35$	38.4895	+	1.24426i	1.09970	+	0.0355503i
$36$	−83.6829	−	9.35096i	−2.32452	−	0.259749i
$37$	7.12170	+	7.12170i	0.192478	+	0.192478i	0.796766	−	0.604288i	$-0.206542\pi$
$37$	7.12170	+	7.12170i	0.192478	+	0.192478i	−0.604288	+	0.796766i	$0.706542\pi$
$38$	31.5904	−	28.2570i	0.831326	−	0.743605i
$39$		−	114.695i		−	2.94091i
$40$	7.91689	−	39.2087i	0.197922	−	0.980218i
$41$		−	13.4770i		−	0.328707i	−0.986401	−	0.164354i	$-0.947446\pi$
$41$		−	13.4770i		−	0.328707i	0.986401	−	0.164354i	$-0.0525538\pi$
$42$	62.9377	−	56.2965i	1.49852	−	1.34039i
$43$	−18.4300	+	18.4300i	−0.428604	+	0.428604i	−0.888153	−	0.459548i	$-0.848011\pi$
$43$	−18.4300	+	18.4300i	−0.428604	+	0.428604i	0.459548	+	0.888153i	$0.348011\pi$
$44$	27.6610	+	34.2180i	0.628659	+	0.777681i
$45$	71.9827	+	76.7922i	1.59962	+	1.70649i
$46$	1.20194	−	21.5795i	0.0261291	−	0.469120i
$47$	25.7009	−	25.7009i	0.546829	−	0.546829i	−0.378694	−	0.925522i	$-0.623627\pi$
$47$	25.7009	−	25.7009i	0.546829	−	0.546829i	0.925522	+	0.378694i	$0.123627\pi$
$48$	−46.8009	−	74.1803i	−0.975018	−	1.54542i
$49$			10.3197i			0.210606i
$50$	−39.3420	+	30.8579i	−0.786839	+	0.617158i
$51$	−44.1569			−0.865821
$52$	65.3840	−	52.2403i	1.25739	−	1.00462i
$53$	−10.8004	+	10.8004i	−0.203782	+	0.203782i	−0.801618	−	0.597836i	$-0.796027\pi$
$53$	−10.8004	+	10.8004i	−0.203782	+	0.203782i	0.597836	+	0.801618i	$0.296027\pi$
$54$	131.919	+	7.34763i	2.44294	+	0.136067i
$55$	1.46313	−	54.9805i	0.0266023	−	0.999646i
$56$	60.7590	+	10.2373i	1.08498	+	0.182808i
$57$	−82.1460	+	82.1460i	−1.44116	+	1.44116i
$58$	−2.82223	−	3.15516i	−0.0486591	−	0.0543992i
$59$	−84.0088			−1.42388			−0.711939	−	0.702242i	$-0.752183\pi$
$59$	−84.0088			−1.42388			−0.711939	+	0.702242i	$0.752183\pi$
$60$	−15.6896	+	108.509i	−0.261493	+	1.80848i
$61$		−	87.3519i		−	1.43200i	−0.698101	−	0.715999i	$-0.745971\pi$
$61$		−	87.3519i		−	1.43200i	0.698101	−	0.715999i	$-0.254029\pi$
$62$	−34.7919	+	31.1207i	−0.561160	+	0.501947i
$63$	−114.645	+	114.645i	−1.81976	+	1.81976i
$64$	20.9713	−	60.4666i	0.327677	−	0.944790i
$65$	−104.559	−	3.38009i	−1.60860	−	0.0520014i
$66$	−80.9155	−	89.4278i	−1.22599	−	1.35497i
$67$	−55.9563	+	55.9563i	−0.835169	+	0.835169i	−0.988218	−	0.153050i	$-0.951091\pi$
$67$	−55.9563	+	55.9563i	−0.835169	+	0.835169i	0.153050	+	0.988218i	$0.451091\pi$
$68$	−20.1122	−	25.1724i	−0.295767	−	0.370182i
$69$			59.2397i			0.858547i
$70$	−49.4663	−	59.0344i	−0.706662	−	0.843348i
$71$			24.0536i			0.338784i	0.985549	+	0.169392i	$0.0541804\pi$
$71$			24.0536i			0.338784i	−0.985549	+	0.169392i	$0.945820\pi$
$72$	97.6417	+	137.212i	1.35613	+	1.90572i
$73$	69.0302	+	69.0302i	0.945619	+	0.945619i	0.998596	−	0.0529764i	$-0.0168708\pi$
$73$	69.0302	+	69.0302i	0.945619	+	0.945619i	−0.0529764	+	0.998596i	$0.516871\pi$
$74$	1.12020	−	20.1120i	0.0151379	−	0.271784i
$75$	102.963	−	90.4455i	1.37284	−	1.20594i
$76$	−84.2438	−	9.41364i	−1.10847	−	0.123864i
$77$	84.7198	−	0.483800i	1.10026	−	0.00628312i
$78$	−170.973	+	152.932i	−2.19196	+	1.96067i
$79$		−	47.8344i		−	0.605499i	−0.953070	−	0.302749i	$-0.902095\pi$
$79$		−	47.8344i		−	0.605499i	0.953070	−	0.302749i	$-0.0979045\pi$
$80$	−69.0035	+	40.4785i	−0.862544	+	0.505982i
$81$	−172.683			−2.13189
$82$	−20.0898	+	17.9699i	−0.244997	+	0.219145i
$83$	11.0631	−	11.0631i	0.133290	−	0.133290i	−0.637314	−	0.770604i	$-0.719955\pi$
$83$	11.0631	−	11.0631i	0.133290	−	0.133290i	0.770604	+	0.637314i	$0.219955\pi$
$84$	−167.839	−	18.7548i	−1.99809	−	0.223272i
$85$	−1.30131	+	40.2543i	−0.0153095	+	0.473580i
$86$	52.0472	+	2.89893i	0.605200	+	0.0337085i
$87$	8.20451	+	8.20451i	0.0943047	+	0.0943047i
$88$	14.1252	−	86.8590i	0.160514	−	0.987034i
$89$		−	90.4306i		−	1.01607i	−0.861335	−	0.508037i	$-0.830371\pi$
$89$		−	90.4306i		−	1.01607i	0.861335	−	0.508037i	$-0.169629\pi$
$90$	18.4918	−	209.696i	0.205465	−	2.32995i
$91$		−	161.145i		−	1.77082i
$92$	−33.7706	+	26.9819i	−0.367072	+	0.293282i
$93$	90.4712	−	90.4712i	0.972809	−	0.972809i
$94$	−72.5807	−	4.04261i	−0.772136	−	0.0430065i
$95$	72.4652	+	77.3069i	0.762791	+	0.813757i
$96$	−48.1752	+	168.675i	−0.501825	+	1.75703i
$97$	−88.2136	−	88.2136i	−0.909418	−	0.909418i	0.0868070	−	0.996225i	$-0.472334\pi$
$97$	−88.2136	−	88.2136i	−0.909418	−	0.909418i	−0.996225	+	0.0868070i	$0.972334\pi$
$98$	15.3833	−	13.7601i	0.156973	−	0.140409i
$99$	164.670	+	162.800i	1.66333	+	1.64445i
$100$	98.4567	+	17.5007i	0.984567	+	0.175007i
$101$		−	52.6106i		−	0.520897i	−0.965488	−	0.260449i	$-0.916130\pi$
$101$		−	52.6106i		−	0.520897i	0.965488	−	0.260449i	$-0.0838704\pi$
$102$	58.8778	+	65.8234i	0.577234	+	0.645328i
$103$	53.2977	+	53.2977i	0.517453	+	0.517453i	0.916800	−	0.399347i	$-0.130763\pi$
$103$	53.2977	+	53.2977i	0.517453	+	0.517453i	−0.399347	+	0.916800i	$0.630763\pi$
$104$	−165.055	−	27.8100i	−1.58707	−	0.267404i
$105$	144.373	+	154.019i	1.37498	+	1.46685i
$106$	30.5010	+	1.69885i	0.287745	+	0.0160269i
$107$	−47.1165	−	47.1165i	−0.440341	−	0.440341i	0.451786	−	0.892127i	$-0.350787\pi$
$107$	−47.1165	−	47.1165i	−0.440341	−	0.440341i	−0.892127	+	0.451786i	$0.850787\pi$
$108$	−164.945	−	206.445i	−1.52727	−	1.91153i
$109$	−178.673			−1.63920			−0.819599	−	0.572938i	$-0.805804\pi$
$109$	−178.673			−1.63920			−0.819599	+	0.572938i	$0.805804\pi$
$110$	−83.9088	+	71.1288i	−0.762808	+	0.646625i
$111$			55.2113i			0.497399i
$112$	−65.7544	−	104.222i	−0.587092	−	0.930553i
$113$	−22.6903	+	22.6903i	−0.200799	+	0.200799i	−0.800342	−	0.599543i	$-0.795349\pi$
$113$	−22.6903	+	22.6903i	−0.200799	+	0.200799i	0.599543	+	0.800342i	$0.295349\pi$
$114$	231.985	+	12.9211i	2.03495	+	0.113343i
$115$	54.0042	+	1.74580i	0.469601	+	0.0151809i
$116$	−0.940207	+	8.41403i	−0.00810524	+	0.0725347i
$117$	311.439	−	311.439i	2.66187	−	2.66187i
$118$	112.015	+	125.230i	0.949283	+	1.06127i
$119$	−62.0396			−0.521341
$120$	182.672	−	121.296i	1.52226	−	1.01080i
$121$	−1.38192	−	120.992i	−0.0114208	−	0.999935i
$122$	−130.213	+	116.473i	−1.06732	+	0.954698i
$123$	52.2405	−	52.2405i	0.424719	−	0.424719i
$124$	92.7816	+	10.3677i	0.748239	+	0.0836103i
$125$	−79.4176	−	96.5289i	−0.635341	−	0.772232i
$126$	323.764	+	18.0330i	2.56955	+	0.143119i
$127$	0.187577	+	0.187577i	0.00147699	+	0.00147699i	0.707845	−	0.706368i	$-0.249668\pi$
$127$	0.187577	+	0.187577i	0.00147699	+	0.00147699i	−0.706368	+	0.707845i	$0.749668\pi$
$128$	−118.098	+	49.3634i	−0.922644	+	0.385652i
$129$	−142.879			−1.10759
$130$	134.378	+	160.370i	1.03367	+	1.23361i
$131$	106.461			0.812681			0.406340	−	0.913722i	$-0.366805\pi$
$131$	106.461			0.812681			0.406340	+	0.913722i	$0.366805\pi$
$132$	−25.4166	+	239.860i	−0.192550	+	1.81712i
$133$	−115.414	+	115.414i	−0.867772	+	0.867772i
$134$	158.023	+	8.80160i	1.17928	+	0.0656836i
$135$	−10.6724	+	330.136i	−0.0790546	+	2.44545i
$136$	−10.7067	+	63.5449i	−0.0787254	+	0.467242i
$137$	63.3415	+	63.3415i	0.462347	+	0.462347i	0.899424	−	0.437077i	$-0.143986\pi$
$137$	63.3415	+	63.3415i	0.462347	+	0.462347i	−0.437077	+	0.899424i	$0.643986\pi$
$138$	88.3070	−	78.9889i	0.639906	−	0.572384i
$139$		−	224.103i		−	1.61225i	−0.591746	−	0.806124i	$-0.701561\pi$
$139$		−	224.103i		−	1.61225i	0.591746	−	0.806124i	$-0.298439\pi$
$140$	−22.0436	+	152.453i	−0.157454	+	1.08895i
$141$	199.248			1.41310
$142$	35.8561	−	32.0726i	0.252508	−	0.225863i
$143$	−230.146	+	1.31427i	−1.60941	+	0.00919067i
$144$	74.3450	−	328.507i	0.516284	−	2.28130i
$145$	7.72119	−	7.23761i	0.0532496	−	0.0499146i
$146$	10.8580	−	194.945i	0.0743702	−	1.33524i
$147$	−40.0020	+	40.0020i	−0.272122	+	0.272122i
$148$	−31.4741	+	25.1471i	−0.212663	+	0.169913i
$149$	160.633			1.07807			0.539037	−	0.842282i	$-0.318788\pi$
$149$	160.633			1.07807			0.539037	+	0.842282i	$0.318788\pi$
$150$	−272.114	−	32.8865i	−1.81409	−	0.219243i
$151$	190.101			1.25895			0.629474	−	0.777022i	$-0.283271\pi$
$151$	190.101			1.25895			0.629474	+	0.777022i	$0.283271\pi$
$152$	98.2962	+	138.132i	0.646686	+	0.908762i
$153$	−119.902	−	119.902i	−0.783672	−	0.783672i
$154$	−113.685	−	125.644i	−0.738213	−	0.815873i
$155$	−79.8093	−	85.1417i	−0.514898	−	0.549301i
$156$	455.944	+	50.9484i	2.92272	+	0.326592i
$157$	−60.5266	−	60.5266i	−0.385520	−	0.385520i	0.487566	−	0.873086i	$-0.337885\pi$
$157$	−60.5266	−	60.5266i	−0.385520	−	0.385520i	−0.873086	+	0.487566i	$0.837885\pi$
$158$	−71.3054	+	63.7813i	−0.451300	+	0.403679i
$159$	−83.7309			−0.526609
$160$	152.348	+	48.8884i	0.952175	+	0.305553i
$161$			83.2307i			0.516961i
$162$	230.252	+	257.414i	1.42131	+	1.58898i
$163$	40.7392	+	40.7392i	0.249934	+	0.249934i	0.820943	−	0.571010i	$-0.193448\pi$
$163$	40.7392	+	40.7392i	0.249934	+	0.249934i	−0.571010	+	0.820943i	$0.693448\pi$
$164$	53.5745	+	5.98657i	0.326674	+	0.0365035i
$165$	218.791	−	207.448i	1.32601	−	1.25726i
$166$	−31.2428	−	1.74016i	−0.188209	−	0.0104829i
$167$	100.104	+	100.104i	0.599423	+	0.599423i	0.940159	−	0.340736i	$-0.110676\pi$
$167$	100.104	+	100.104i	0.599423	+	0.599423i	−0.340736	+	0.940159i	$0.610676\pi$
$168$	195.836	+	275.201i	1.16569	+	1.63810i
$169$			268.758i			1.59028i
$170$	61.7412	−	51.7344i	0.363183	−	0.304320i
$171$	−446.112			−2.60884
$172$	−65.0772	−	81.4507i	−0.378356	−	0.473551i
$173$	139.979	+	139.979i	0.809126	+	0.809126i	0.984502	−	0.175376i	$-0.0561141\pi$
$173$	139.979	+	139.979i	0.809126	+	0.809126i	−0.175376	+	0.984502i	$0.556114\pi$
$174$	1.29052	−	23.1699i	0.00741679	−	0.133161i
$175$	144.662	−	127.074i	0.826637	−	0.726138i
$176$	−148.312	+	94.7597i	−0.842685	+	0.538408i
$177$	−325.641	−	325.641i	−1.83978	−	1.83978i
$178$	−134.802	+	120.578i	−0.757316	+	0.677405i
$179$	−106.678			−0.595964			−0.297982	−	0.954571i	$-0.596314\pi$
$179$	−106.678			−0.595964			−0.297982	+	0.954571i	$0.596314\pi$
$180$	−337.244	+	252.038i	−1.87358	+	1.40021i
$181$	12.7141			0.0702438			0.0351219	−	0.999383i	$-0.488818\pi$
$181$	12.7141			0.0702438			0.0351219	+	0.999383i	$0.488818\pi$
$182$	−240.214	+	214.867i	−1.31986	+	1.18059i
$183$	338.600	−	338.600i	1.85027	−	1.85027i
$184$	85.2502	+	14.3638i	0.463316	+	0.0780639i
$185$	50.3318	+	1.62709i	0.272064	+	0.00879506i
$186$	−255.495	−	14.2306i	−1.37363	−	0.0765086i
$187$	0.505983	+	88.6044i	0.00270579	+	0.473820i
$188$	90.7514	+	113.584i	0.482720	+	0.604172i
$189$	−508.802			−2.69208
$190$	18.6158	−	211.101i	0.0979777	−	1.11106i
$191$		−	4.38351i		−	0.0229503i	−0.999934	−	0.0114751i	$-0.996347\pi$
$191$		−	4.38351i		−	0.0229503i	0.999934	−	0.0114751i	$-0.00365273\pi$
$192$	315.675	−	153.094i	1.64414	−	0.797366i
$193$	−194.296	−	194.296i	−1.00672	−	1.00672i	−0.999977	−	0.00673955i	$-0.997855\pi$
$193$	−194.296	−	194.296i	−1.00672	−	1.00672i	−0.00673955	−	0.999977i	$-0.502145\pi$
$194$	−13.8755	+	249.119i	−0.0715231	+	1.28412i
$195$	−392.195	−	418.400i	−2.01126	−	2.14564i
$196$	−41.0235	−	4.58408i	−0.209304	−	0.0233882i
$197$	−119.247	+	119.247i	−0.605314	+	0.605314i	−0.941718	−	0.336404i	$-0.890789\pi$
$197$	−119.247	+	119.247i	−0.605314	+	0.605314i	0.336404	+	0.941718i	$0.390789\pi$
$198$	23.1140	−	462.543i	0.116737	−	2.33608i
$199$	351.199			1.76482			0.882410	−	0.470482i	$-0.155920\pi$
$199$	351.199			1.76482			0.882410	+	0.470482i	$0.155920\pi$
$200$	−105.192	−	170.102i	−0.525961	−	0.850509i
$201$	−433.803			−2.15823
$202$	−78.4252	+	70.1498i	−0.388243	+	0.347276i
$203$	11.5272	+	11.5272i	0.0567842	+	0.0567842i
$204$	19.6148	−	175.535i	0.0961509	−	0.860466i
$205$	−46.0840	−	49.1630i	−0.224800	−	0.239820i
$206$	8.38341	−	150.515i	0.0406962	−	0.730657i
$207$	−160.857	+	160.857i	−0.777088	+	0.777088i
$208$	178.625	+	283.124i	0.858773	+	1.36117i
$209$	165.774	+	163.891i	0.793177	+	0.784169i
$210$	37.0883	−	420.578i	0.176611	−	2.00275i
$211$	−253.350			−1.20071			−0.600355	−	0.799734i	$-0.704974\pi$
$211$	−253.350			−1.20071			−0.600355	+	0.799734i	$0.704974\pi$
$212$	−38.1369	−	47.7322i	−0.179891	−	0.225152i
$213$	−93.2384	+	93.2384i	−0.437739	+	0.437739i
$214$	−7.41114	+	133.059i	−0.0346315	+	0.621772i
$215$	−4.21067	+	130.252i	−0.0195845	+	0.605822i
$216$	−87.8079	+	521.148i	−0.406518	+	2.41272i
$217$	127.110	−	127.110i	0.585762	−	0.585762i
$218$	238.238	+	266.342i	1.09283	+	1.22175i
$219$			535.159i			2.44365i
$220$	217.912	+	30.2390i	0.990509	+	0.137450i
$221$	168.534			0.762595
$222$	82.3019	−	73.6175i	0.370729	−	0.331610i
$223$	−77.2143	−	77.2143i	−0.346252	−	0.346252i	0.512459	−	0.858712i	$-0.328735\pi$
$223$	−77.2143	−	77.2143i	−0.346252	−	0.346252i	−0.858712	+	0.512459i	$0.828735\pi$
$224$	−67.6853	+	236.985i	−0.302167	+	1.05797i
$225$	525.174	+	33.9904i	2.33411	+	0.151068i
$226$	64.0785	+	3.56905i	0.283533	+	0.0157922i
$227$	219.293	+	219.293i	0.966048	+	0.966048i	0.999442	−	0.0333944i	$-0.0106317\pi$
$227$	219.293	+	219.293i	0.966048	+	0.966048i	−0.0333944	+	0.999442i	$0.510632\pi$
$228$	−290.062	−	363.042i	−1.27220	−	1.59229i
$229$			257.724i			1.12543i	0.826650	+	0.562717i	$0.190244\pi$
$229$			257.724i			1.12543i	−0.826650	+	0.562717i	$0.809756\pi$
$230$	−69.4055	−	82.8303i	−0.301763	−	0.360132i
$231$	330.272	+	326.522i	1.42975	+	1.41351i
$232$	13.7962	−	9.81754i	0.0594664	−	0.0423170i
$233$	153.796	+	153.796i	0.660067	+	0.660067i	0.955396	−	0.295328i	$-0.0954291\pi$
$233$	153.796	+	153.796i	0.660067	+	0.660067i	−0.295328	+	0.955396i	$0.595429\pi$
$234$	−879.520	−	48.9876i	−3.75863	−	0.209349i
$235$	5.87186	−	181.638i	0.0249866	−	0.772929i
$236$	37.3172	−	333.957i	0.158124	−	1.41507i
$237$	185.419	−	185.419i	0.782359	−	0.782359i
$238$	82.7222	+	92.4807i	0.347572	+	0.388574i
$239$			38.8269i			0.162456i	0.996696	+	0.0812279i	$0.0258842\pi$
$239$			38.8269i			0.162456i	−0.996696	+	0.0812279i	$0.974116\pi$
$240$	−424.382	−	110.571i	−1.76826	−	0.460711i
$241$		−	0.772619i		−	0.00320589i	−0.999999	−	0.00160294i	$-0.999490\pi$
$241$		−	0.772619i		−	0.00320589i	0.999999	−	0.00160294i	$-0.000510233\pi$
$242$	−178.517	+	163.388i	−0.737673	+	0.675158i
$243$	−248.953	−	248.953i	−1.02450	−	1.02450i
$244$	347.246	+	38.8023i	1.42314	+	0.159026i
$245$	35.2878	+	37.6455i	0.144032	+	0.153655i
$246$	−147.530	−	8.21712i	−0.599714	−	0.0334029i
$247$	313.527	−	313.527i	1.26934	−	1.26934i
$248$	−108.258	−	152.131i	−0.436525	−	0.613431i
$249$	85.7672			0.344446
$250$	−37.9993	+	247.095i	−0.151997	+	0.988381i
$251$		−	14.8441i		−	0.0591399i	−0.999563	−	0.0295699i	$-0.990586\pi$
$251$		−	14.8441i		−	0.0591399i	0.999563	−	0.0295699i	$-0.00941378\pi$
$252$	−404.818	−	506.670i	−1.60642	−	2.01060i
$253$	118.869	−	0.678814i	0.469839	−	0.00268306i
$254$	0.0295048	−	0.529727i	0.000116161	−	0.00208554i
$255$	−161.081	+	150.992i	−0.631690	+	0.592127i
$256$	231.055	+	110.226i	0.902557	+	0.430570i
$257$	−64.3743	−	64.3743i	−0.250484	−	0.250484i	0.570685	−	0.821169i	$-0.306678\pi$
$257$	−64.3743	−	64.3743i	−0.250484	−	0.250484i	−0.821169	+	0.570685i	$0.806678\pi$
$258$	190.512	+	212.986i	0.738418	+	0.825527i
$259$			77.5708i			0.299501i
$260$	59.8824	−	414.146i	0.230317	−	1.59287i
$261$			44.5564i			0.170714i
$262$	−141.953	−	158.699i	−0.541805	−	0.605720i
$263$	−67.4719	+	67.4719i	−0.256547	+	0.256547i	−0.823648	−	0.567101i	$-0.808065\pi$
$263$	−67.4719	+	67.4719i	−0.256547	+	0.256547i	0.567101	+	0.823648i	$0.308065\pi$
$264$	391.442	−	281.936i	1.48273	−	1.06794i
$265$	−2.46756	+	76.3308i	−0.00931156	+	0.288041i
$266$	325.934	+	18.1539i	1.22532	+	0.0682477i
$267$	350.533	−	350.533i	1.31286	−	1.31286i
$268$	−197.585	−	247.297i	−0.737256	−	0.922750i
$269$		−	261.542i		−	0.972275i	−0.873882	−	0.486137i	$-0.838405\pi$
$269$		−	261.542i		−	0.972275i	0.873882	−	0.486137i	$-0.161595\pi$
$270$	506.355	−	424.287i	1.87539	−	1.57143i
$271$	−383.025			−1.41338			−0.706689	−	0.707525i	$-0.749812\pi$
$271$	−383.025			−1.41338			−0.706689	+	0.707525i	$0.749812\pi$
$272$	109.001	−	68.7693i	0.400738	−	0.252828i
$273$	624.641	−	624.641i	2.28806	−	2.28806i
$274$	9.96325	−	178.880i	0.0363622	−	0.652845i
$275$	−182.666	−	205.568i	−0.664240	−	0.747519i
$276$	−235.493	−	26.3147i	−0.853236	−	0.0953430i
$277$	−105.551	+	105.551i	−0.381051	+	0.381051i	−0.871481	−	0.490430i	$-0.836840\pi$
$277$	−105.551	+	105.551i	−0.381051	+	0.381051i	0.490430	+	0.871481i	$0.336840\pi$
$278$	−334.063	+	298.813i	−1.20167	+	1.07487i
$279$	491.324			1.76102
$280$	256.650	−	170.418i	0.916607	−	0.608636i
$281$			198.947i			0.707998i	0.935246	+	0.353999i	$0.115178\pi$
$281$			198.947i			0.707998i	−0.935246	+	0.353999i	$0.884822\pi$
$282$	−265.672	−	297.013i	−0.942100	−	1.05324i
$283$	−169.428	+	169.428i	−0.598687	+	0.598687i	−0.939963	−	0.341276i	$-0.889141\pi$
$283$	−169.428	+	169.428i	−0.598687	+	0.598687i	0.341276	+	0.939963i	$0.389141\pi$
$284$	−95.6195	−	10.6848i	−0.336688	−	0.0376225i
$285$	−18.7678	+	580.557i	−0.0658519	+	2.03704i
$286$	308.830	+	341.319i	1.07983	+	1.19342i
$287$	73.3969	−	73.3969i	0.255738	−	0.255738i
$288$	−588.827	+	327.200i	−2.04454	+	1.13611i
$289$			224.116i			0.775487i
$290$	−21.0842	−	1.85929i	−0.0727041	−	0.00641134i
$291$		−	683.879i		−	2.35010i
$292$	−305.077	+	243.749i	−1.04478	+	0.834758i
$293$	118.377	+	118.377i	0.404016	+	0.404016i	0.879646	−	0.475629i	$-0.157780\pi$
$293$	118.377	+	118.377i	0.404016	+	0.404016i	−0.475629	+	0.879646i	$0.657780\pi$
$294$	112.968	+	6.29208i	0.384244	+	0.0214016i
$295$	−306.457	+	287.264i	−1.03884	+	0.973777i
$296$	79.4530	+	13.3870i	0.268422	+	0.0452263i
$297$	4.14969	+	726.666i	0.0139720	+	2.44669i
$298$	−214.185	−	239.451i	−0.718740	−	0.803528i
$299$		−	226.100i		−	0.756188i
$300$	313.807	+	449.482i	1.04602	+	1.49827i
$301$	−200.743			−0.666919
$302$	−253.477	−	283.378i	−0.839326	−	0.938339i
$303$	203.933	−	203.933i	0.673046	−	0.673046i
$304$	74.8433	−	330.709i	0.246195	−	1.08786i
$305$	−298.696	−	318.653i	−0.979331	−	1.04476i
$306$	−18.8599	+	338.609i	−0.0616335	+	1.10656i
$307$	195.242	+	195.242i	0.635966	+	0.635966i	0.949558	−	0.313592i	$-0.101532\pi$
$307$	195.242	+	195.242i	0.635966	+	0.635966i	−0.313592	+	0.949558i	$0.601532\pi$
$308$	−35.7099	+	336.998i	−0.115941	+	1.09415i
$309$			413.192i			1.33719i
$310$	−20.5024	+	232.495i	−0.0661368	+	0.749985i
$311$			522.926i			1.68144i	0.541474	+	0.840718i	$0.317867\pi$
$311$			522.926i			1.68144i	−0.541474	+	0.840718i	$0.682133\pi$
$312$	−531.998	−	747.596i	−1.70512	−	2.39614i
$313$	−242.759	+	242.759i	−0.775587	+	0.775587i	−0.979077	−	0.203490i	$-0.934772\pi$
$313$	−242.759	+	242.759i	−0.775587	+	0.775587i	0.203490	+	0.979077i	$0.434772\pi$
$314$	−9.52047	+	170.930i	−0.0303200	+	0.544363i
$315$	−26.1928	+	810.241i	−0.0831518	+	2.57219i
$316$	190.154	+	21.2484i	0.601753	+	0.0672416i
$317$	−33.9249	−	33.9249i	−0.107019	−	0.107019i	0.651570	−	0.758589i	$-0.274111\pi$
$317$	−33.9249	−	33.9249i	−0.107019	−	0.107019i	−0.758589	+	0.651570i	$0.774111\pi$
$318$	111.645	+	124.815i	0.351085	+	0.392501i
$319$	16.3690	−	16.5570i	0.0513135	−	0.0519029i
$320$	−130.261	−	292.288i	−0.407065	−	0.913399i
$321$		−	365.272i		−	1.13792i
$322$	124.070	−	110.978i	0.385310	−	0.344652i
$323$	−120.706	−	120.706i	−0.373701	−	0.373701i
$324$	76.7070	−	686.461i	0.236750	−	2.11871i
$325$	−392.980	+	345.203i	−1.20917	+	1.06216i
$326$	6.40803	−	115.049i	0.0196565	−	0.352912i
$327$	−692.583	−	692.583i	−2.11799	−	2.11799i
$328$	−62.5111	−	87.8444i	−0.190583	−	0.267818i
$329$	279.939			0.850879
$330$	−600.968	−	49.5389i	−1.82111	−	0.150118i
$331$			423.596i			1.27975i	0.768480	+	0.639873i	$0.221013\pi$
$331$			423.596i			1.27975i	−0.768480	+	0.639873i	$0.778987\pi$
$332$	39.0644	+	48.8930i	0.117664	+	0.147268i
$333$	−149.918	+	149.918i	−0.450206	+	0.450206i
$334$	15.7457	−	282.698i	0.0471429	−	0.846400i
$335$	−12.7843	+	395.464i	−0.0381620	+	1.18049i
$336$	149.111	−	658.874i	0.443782	−	1.96093i
$337$	−295.524	+	295.524i	−0.876926	+	0.876926i	−0.993215	−	0.116290i	$-0.962900\pi$
$337$	−295.524	+	295.524i	−0.876926	+	0.876926i	0.116290	+	0.993215i	$0.462900\pi$
$338$	400.630	−	358.356i	1.18529	−	1.06022i
$339$	−175.907			−0.518900
$340$	−159.443	−	23.0543i	−0.468951	−	0.0678067i
$341$	−182.575	−	180.501i	−0.535409	−	0.529329i
$342$	594.836	+	665.007i	1.73929	+	1.94446i
$343$	210.656	−	210.656i	0.614158	−	0.614158i
$344$	−34.6437	+	205.613i	−0.100708	+	0.597713i
$345$	202.567	+	216.102i	0.587152	+	0.626382i
$346$	22.0178	−	395.307i	0.0636354	−	1.14251i
$347$	−235.404	−	235.404i	−0.678398	−	0.678398i	0.281239	−	0.959638i	$-0.409255\pi$
$347$	−235.404	−	235.404i	−0.678398	−	0.678398i	−0.959638	+	0.281239i	$0.909255\pi$
$348$	−36.2595	+	28.9706i	−0.104194	+	0.0832487i
$349$	−487.495			−1.39683			−0.698416	−	0.715692i	$-0.746112\pi$
$349$	−487.495			−1.39683			−0.698416	+	0.715692i	$0.746112\pi$
$350$	−382.315	−	46.2049i	−1.09233	−	0.132014i
$351$	1382.19			3.93785
$352$	339.012	+	94.7347i	0.963103	+	0.269133i
$353$	292.174	−	292.174i	0.827689	−	0.827689i	−0.159508	−	0.987197i	$-0.550991\pi$
$353$	292.174	−	292.174i	0.827689	−	0.827689i	0.987197	+	0.159508i	$0.0509907\pi$
$354$	−51.2214	+	919.625i	−0.144693	+	2.59781i
$355$	82.2503	+	87.7458i	0.231691	+	0.247171i
$356$	359.485	+	40.1698i	1.00979	+	0.112837i
$357$	−240.482	−	240.482i	−0.673620	−	0.673620i
$358$	142.242	+	159.021i	0.397323	+	0.444194i
$359$			183.518i			0.511193i	0.966784	+	0.255596i	$0.0822718\pi$
$359$			183.518i			0.511193i	−0.966784	+	0.255596i	$0.917728\pi$
$360$	825.380	+	166.658i	2.29272	+	0.462938i
$361$	−88.1024			−0.244051
$362$	−16.9527	−	18.9526i	−0.0468308	−	0.0523553i
$363$	463.641	−	474.355i	1.27725	−	1.30676i
$364$	640.592	+	71.5816i	1.75987	+	0.196653i
$365$	487.862	+	15.7712i	1.33661	+	0.0432089i
$366$	−956.222	−	53.2597i	−2.61263	−	0.145518i
$367$	−309.683	+	309.683i	−0.843822	+	0.843822i	−0.989354	−	0.145532i	$-0.953511\pi$
$367$	−309.683	+	309.683i	−0.843822	+	0.843822i	0.145532	+	0.989354i	$0.453511\pi$
$368$	−92.2591	−	146.232i	−0.250704	−	0.397371i
$369$	283.703			0.768843
$370$	−64.6858	−	77.1977i	−0.174827	−	0.208642i
$371$	−117.640			−0.317090
$372$	319.459	+	399.834i	0.858760	+	1.07482i
$373$	−195.281	−	195.281i	−0.523542	−	0.523542i	0.395097	−	0.918639i	$-0.370711\pi$
$373$	−195.281	−	195.281i	−0.523542	−	0.523542i	−0.918639	+	0.395097i	$0.870711\pi$
$374$	131.405	−	118.897i	0.351351	−	0.317907i
$375$	66.3280	−	682.016i	0.176875	−	1.81871i
$376$	48.3112	−	286.731i	0.128487	−	0.762584i
$377$	−31.3142	−	31.3142i	−0.0830614	−	0.0830614i
$378$	678.426	+	758.457i	1.79478	+	2.00650i
$379$	−683.030			−1.80219			−0.901095	−	0.433621i	$-0.857236\pi$
$379$	−683.030			−1.80219			−0.901095	+	0.433621i	$0.857236\pi$
$380$	−339.504	+	253.728i	−0.893433	+	0.667704i
$381$			1.45420i			0.00381680i
$382$	−6.53437	+	5.84487i	−0.0171057	+	0.0153007i
$383$	283.380	+	283.380i	0.739895	+	0.739895i	0.972557	−	0.232663i	$-0.0747438\pi$
$383$	283.380	+	283.380i	0.739895	+	0.739895i	−0.232663	+	0.972557i	$0.574744\pi$
$384$	−649.127	−	266.436i	−1.69044	−	0.693843i
$385$	307.397	−	291.460i	0.798434	−	0.757040i
$386$	−30.5617	+	548.703i	−0.0791753	+	1.42151i
$387$	−387.968	−	387.968i	−1.00250	−	1.00250i
$388$	389.857	−	311.487i	1.00479	−	0.802801i
$389$		−	699.754i		−	1.79885i	−0.437072	−	0.899427i	$-0.643984\pi$
$389$		−	699.754i		−	1.79885i	0.437072	−	0.899427i	$-0.356016\pi$
$390$	−100.752	+	1142.52i	−0.258339	+	2.92954i
$391$	−87.0469			−0.222626
$392$	47.8665	+	67.2650i	0.122108	+	0.171594i
$393$	412.672	+	412.672i	1.05006	+	1.05006i
$394$	336.759	+	18.7568i	0.854718	+	0.0476062i
$395$	−163.568	−	174.496i	−0.414095	−	0.441762i
$396$	−720.320	+	582.290i	−1.81899	+	1.47043i
$397$	482.013	+	482.013i	1.21414	+	1.21414i	0.969653	+	0.244487i	$0.0786195\pi$
$397$	482.013	+	482.013i	1.21414	+	1.21414i	0.244487	+	0.969653i	$0.421380\pi$
$398$	−468.281	−	523.523i	−1.17659	−	1.31538i
$399$	−894.749			−2.24248
$400$	−113.305	+	383.617i	−0.283263	+	0.959042i
$401$	615.908			1.53593			0.767965	−	0.640492i	$-0.221270\pi$
$401$	615.908			1.53593			0.767965	+	0.640492i	$0.221270\pi$
$402$	578.424	+	646.659i	1.43887	+	1.60860i
$403$	−345.301	+	345.301i	−0.856828	+	0.856828i
$404$	209.141	+	23.3700i	0.517675	+	0.0578465i
$405$	−629.935	+	590.482i	−1.55540	+	1.45798i
$406$	1.81316	−	32.5533i	0.00446591	−	0.0801807i
$407$	110.786	−	0.632653i	0.272201	−	0.00155443i
$408$	−287.819	+	204.815i	−0.705439	+	0.501998i
$409$	330.071			0.807019			0.403509	−	0.914976i	$-0.367790\pi$
$409$	330.071			0.807019			0.403509	+	0.914976i	$0.367790\pi$
$410$	−11.8386	+	134.249i	−0.0288747	+	0.327436i
$411$			491.058i			1.19479i
$412$	−235.547	+	188.197i	−0.571717	+	0.456789i
$413$	−457.519	−	457.519i	−1.10779	−	1.10779i
$414$	454.269	+	25.3019i	1.09727	+	0.0611157i
$415$	2.52757	−	78.1871i	0.00609054	−	0.188403i
$416$	183.870	−	643.782i	0.441996	−	1.54755i
$417$	868.682	−	868.682i	2.08317	−	2.08317i
$418$	23.2690	−	465.644i	0.0556674	−	1.11398i
$419$	429.690			1.02551			0.512757	−	0.858534i	$-0.328624\pi$
$419$	429.690			1.02551			0.512757	+	0.858534i	$0.328624\pi$
$420$	−676.396	+	505.503i	−1.61047	+	1.20358i
$421$	261.974			0.622267			0.311134	−	0.950366i	$-0.399291\pi$
$421$	261.974			0.622267			0.311134	+	0.950366i	$0.399291\pi$
$422$	337.811	+	377.661i	0.800500	+	0.894932i
$423$	541.029	+	541.029i	1.27903	+	1.27903i
$424$	−20.3021	+	120.495i	−0.0478823	+	0.284186i
$425$	132.901	+	151.294i	0.312708	+	0.355987i
$426$	263.310	+	14.6659i	0.618098	+	0.0344269i
$427$	475.726	−	475.726i	1.11411	−	1.11411i
$428$	208.230	−	166.371i	0.486518	−	0.388717i
$429$	−897.201	−	887.012i	−2.09138	−	2.06763i
$430$	199.777	−	167.398i	0.464597	−	0.389298i
$431$	−425.806			−0.987949			−0.493974	−	0.869476i	$-0.664456\pi$
$431$	−425.806			−0.987949			−0.493974	+	0.869476i	$0.664456\pi$
$432$	893.941	−	563.994i	2.06931	−	1.30554i
$433$	−441.920	+	441.920i	−1.02060	+	1.02060i	−0.0208168	+	0.999783i	$0.506627\pi$
$433$	−441.920	+	441.920i	−1.02060	+	1.02060i	−0.999783	+	0.0208168i	$0.993373\pi$
$434$	−358.966	−	19.9937i	−0.827111	−	0.0460685i
$435$	57.9844	+	1.87447i	0.133297	+	0.00430913i
$436$	79.3675	−	710.270i	0.182036	−	1.62906i
$437$	−161.935	+	161.935i	−0.370561	+	0.370561i
$438$	797.747	−	713.570i	1.82134	−	1.62915i
$439$			39.1211i			0.0891140i	0.999007	+	0.0445570i	$0.0141876\pi$
$439$			39.1211i			0.0891140i	−0.999007	+	0.0445570i	$0.985812\pi$
$440$	−245.482	−	365.155i	−0.557915	−	0.829898i
$441$	−217.240			−0.492607
$442$	−224.719	−	251.228i	−0.508414	−	0.568390i
$443$	441.330	+	441.330i	0.996231	+	0.996231i	0.999993	−	0.00376227i	$-0.00119757\pi$
$443$	441.330	+	441.330i	0.996231	+	0.996231i	−0.00376227	+	0.999993i	$0.501198\pi$
$444$	−219.479	−	24.5252i	−0.494322	−	0.0552370i
$445$	−309.223	−	329.884i	−0.694883	−	0.741312i
$446$	−12.1454	+	218.057i	−0.0272317	+	0.488917i
$447$	622.657	+	622.657i	1.39297	+	1.39297i
$448$	443.518	−	215.095i	0.989995	−	0.480122i
$449$			553.397i			1.23251i	0.787547	+	0.616254i	$0.211351\pi$
$449$			553.397i			1.23251i	−0.787547	+	0.616254i	$0.788649\pi$
$450$	−649.587	−	828.185i	−1.44353	−	1.84041i
$451$	−105.423	−	104.226i	−0.233755	−	0.231100i
$452$	−80.1205	−	100.279i	−0.177258	−	0.221856i
$453$	736.883	+	736.883i	1.62667	+	1.62667i
$454$	34.4935	−	619.294i	0.0759768	−	1.36408i
$455$	−551.027	−	587.844i	−1.21105	−	1.29196i
$456$	−154.414	+	916.459i	−0.338627	+	2.00978i
$457$	154.432	−	154.432i	0.337925	−	0.337925i	−0.517661	−	0.855586i	$-0.673197\pi$
$457$	154.432	−	154.432i	0.337925	−	0.337925i	0.855586	+	0.517661i	$0.173197\pi$
$458$	384.182	−	343.644i	0.838826	−	0.750314i
$459$		−	532.132i		−	1.15933i
$460$	−30.9290	+	213.905i	−0.0672370	+	0.465011i
$461$		−	471.965i		−	1.02379i	−0.859049	−	0.511893i	$-0.828944\pi$
$461$		−	471.965i		−	1.02379i	0.859049	−	0.511893i	$-0.171056\pi$
$462$	46.3589	−	927.704i	0.100344	−	2.00802i
$463$	100.365	+	100.365i	0.216771	+	0.216771i	0.807136	−	0.590365i	$-0.201016\pi$
$463$	100.365	+	100.365i	0.216771	+	0.216771i	−0.590365	+	0.807136i	$0.701016\pi$
$464$	−33.0303	−	7.47513i	−0.0711860	−	0.0161102i
$465$	20.6698	−	639.394i	0.0444513	−	1.37504i
$466$	24.1912	−	434.327i	0.0519124	−	0.932032i
$467$	239.686	−	239.686i	0.513247	−	0.513247i	−0.402273	−	0.915520i	$-0.631780\pi$
$467$	239.686	−	239.686i	0.513247	−	0.513247i	0.915520	+	0.402273i	$0.131780\pi$
$468$	1099.71	+	1376.39i	2.34980	+	2.94101i
$469$	−609.486			−1.29954
$470$	−278.592	+	233.439i	−0.592750	+	0.496680i
$471$		−	469.235i		−	0.996252i
$472$	−547.578	+	389.663i	−1.16012	+	0.825556i
$473$	1.63722	+	286.699i	0.00346135	+	0.606128i
$474$	−523.633	−	29.1653i	−1.10471	−	0.0615302i
$475$	528.695	+	34.2182i	1.11304	+	0.0720384i
$476$	27.5584	−	246.623i	0.0578958	−	0.518117i
$477$	−227.359	−	227.359i	−0.476645	−	0.476645i
$478$	57.8782	−	51.7710i	0.121084	−	0.108307i
$479$		−	400.843i		−	0.836833i	−0.908255	−	0.418417i	$-0.862585\pi$
$479$		−	400.843i		−	0.836833i	0.908255	−	0.418417i	$-0.137415\pi$
$480$	401.037	+	780.047i	0.835494	+	1.62510i
$481$		−	210.725i		−	0.438098i
$482$	−1.15172	+	1.03019i	−0.00238946	+	0.00213733i
$483$	−322.625	+	322.625i	−0.667960	+	0.667960i
$484$	481.589	+	48.2520i	0.995018	+	0.0996942i
$485$	−623.438	−	20.1540i	−1.28544	−	0.0415547i
$486$	−39.1588	+	703.056i	−0.0805738	+	1.44662i
$487$	−24.4248	+	24.4248i	−0.0501536	+	0.0501536i	−0.731739	−	0.681585i	$-0.761291\pi$
$487$	−24.4248	+	24.4248i	−0.0501536	+	0.0501536i	0.681585	+	0.731739i	$0.261291\pi$
$488$	−405.169	−	569.369i	−0.830265	−	1.16674i
$489$			315.832i			0.645873i
$490$	9.06517	−	102.798i	0.0185003	−	0.209792i
$491$	311.219			0.633846			0.316923	−	0.948451i	$-0.397350\pi$
$491$	311.219			0.633846			0.316923	+	0.948451i	$0.397350\pi$
$492$	184.464	+	230.875i	0.374926	+	0.469258i
$493$	−12.0557	+	12.0557i	−0.0244538	+	0.0244538i
$494$	−885.415	−	49.3159i	−1.79234	−	0.0998298i
$495$	1157.39	+	30.8002i	2.33816	+	0.0622226i
$496$	−82.4284	+	364.226i	−0.166186	+	0.734326i
$497$	−130.998	+	130.998i	−0.263578	+	0.263578i
$498$	−114.360	−	127.851i	−0.229639	−	0.256728i
$499$	108.280			0.216994			0.108497	−	0.994097i	$-0.465396\pi$
$499$	108.280			0.216994			0.108497	+	0.994097i	$0.465396\pi$
$500$	419.005	−	272.827i	0.838011	−	0.545654i
$501$			776.057i			1.54902i
$502$	−22.1277	+	19.7928i	−0.0440791	+	0.0394279i
$503$	22.0758	−	22.0758i	0.0438882	−	0.0438882i	−0.684822	−	0.728710i	$-0.740120\pi$
$503$	22.0758	−	22.0758i	0.0438882	−	0.0438882i	0.728710	+	0.684822i	$0.240120\pi$
$504$	−215.504	+	1279.03i	−0.427587	+	2.53777i
$505$	−179.900	−	191.919i	−0.356237	−	0.380038i
$506$	−159.510	−	176.290i	−0.315236	−	0.348399i
$507$	−1041.78	+	1041.78i	−2.05479	+	2.05479i
$508$	−0.828991	+	0.662345i	−0.00163187	+	0.00130383i
$509$		−	417.953i		−	0.821125i	−0.911832	−	0.410562i	$-0.865332\pi$
$509$		−	417.953i		−	0.821125i	0.911832	−	0.410562i	$-0.134668\pi$
$510$	439.862	+	38.7888i	0.862474	+	0.0760565i
$511$			751.889i			1.47141i
$512$	−143.772	−	491.400i	−0.280805	−	0.959765i
$513$	−989.936	−	989.936i	−1.92970	−	1.92970i
$514$	−10.1257	+	181.796i	−0.0196998	+	0.353689i
$515$	376.675	+	12.1768i	0.731407	+	0.0236444i
$516$	63.4679	−	567.982i	0.123000	−	1.10074i
$517$	−2.28313	−	399.806i	−0.00441611	−	0.773320i
$518$	115.633	−	103.431i	0.223229	−	0.199674i
$519$			1085.19i			2.09093i
$520$	−697.202	+	462.949i	−1.34077	+	0.890286i
$521$	253.019			0.485640			0.242820	−	0.970071i	$-0.421927\pi$
$521$	253.019			0.485640			0.242820	+	0.970071i	$0.421927\pi$
$522$	66.4190	−	59.4105i	0.127239	−	0.113813i
$523$	−605.834	+	605.834i	−1.15838	+	1.15838i	−0.173559	+	0.984823i	$0.555527\pi$
$523$	−605.834	+	605.834i	−1.15838	+	1.15838i	−0.984823	+	0.173559i	$0.944473\pi$
$524$	−47.2907	+	423.211i	−0.0902495	+	0.807654i
$525$	1053.32	+	68.1731i	2.00633	+	0.129854i
$526$	190.544	+	10.6129i	0.362251	+	0.0201767i
$527$	132.939	+	132.939i	0.252255	+	0.252255i
$528$	−942.213	−	207.585i	−1.78450	−	0.393153i
$529$		−	412.220i		−	0.779244i
$530$	117.074	−	98.0995i	0.220895	−	0.185093i
$531$		−	1768.46i		−	3.33044i
$532$	−407.532	−	510.067i	−0.766037	−	0.958772i
$533$	−199.386	+	199.386i	−0.374083	+	0.374083i
$534$	−989.923	−	55.1368i	−1.85379	−	0.103252i
$535$	−332.990	−	10.7646i	−0.622411	−	0.0201208i
$536$	−105.184	+	624.274i	−0.196238	+	1.16469i
$537$	−413.511	−	413.511i	−0.770040	−	0.770040i
$538$	−389.873	+	348.734i	−0.724671	+	0.648205i
$539$	80.7256	+	79.8089i	0.149769	+	0.148068i
$540$	−1307.63	−	189.074i	−2.42155	−	0.350137i
$541$		−	391.623i		−	0.723887i	−0.932200	−	0.361944i	$-0.882113\pi$
$541$		−	391.623i		−	0.723887i	0.932200	−	0.361944i	$-0.117887\pi$
$542$	510.718	+	570.965i	0.942283	+	1.05344i
$543$	49.2834	+	49.2834i	0.0907613	+	0.0907613i
$544$	−247.852	−	70.7888i	−0.455609	−	0.130126i
$545$	−651.784	+	610.962i	−1.19593	+	1.12103i
$546$	−1764.02	−	98.2524i	−3.23080	−	0.179949i
$547$	−166.752	−	166.752i	−0.304847	−	0.304847i	0.538059	−	0.842907i	$-0.319158\pi$
$547$	−166.752	−	166.752i	−0.304847	−	0.304847i	−0.842907	+	0.538059i	$0.819158\pi$
$548$	−279.936	+	223.662i	−0.510832	+	0.408143i
$549$	1838.84			3.34943
$550$	−62.8714	+	546.395i	−0.114312	+	0.993445i
$551$			44.8551i			0.0814066i
$552$	274.775	+	386.131i	0.497781	+	0.699512i
$553$	260.510	−	260.510i	0.471085	−	0.471085i
$554$	298.082	+	16.6026i	0.538053	+	0.0299685i
$555$	188.792	+	201.406i	0.340167	+	0.362895i
$556$	890.866	+	99.5478i	1.60228	+	0.179043i
$557$	−355.499	+	355.499i	−0.638238	+	0.638238i	−0.950121	−	0.311883i	$-0.899040\pi$
$557$	−355.499	+	355.499i	−0.638238	+	0.638238i	0.311883	+	0.950121i	$0.399040\pi$
$558$	−655.120	−	732.403i	−1.17405	−	1.31255i
$559$	545.327			0.975540
$560$	−596.249	−	155.350i	−1.06473	−	0.277410i
$561$	−341.493	+	345.416i	−0.608722	+	0.615714i
$562$	296.565	−	265.272i	0.527696	−	0.472014i
$563$	−608.314	+	608.314i	−1.08049	+	1.08049i	−0.0840234	+	0.996464i	$0.526777\pi$
$563$	−608.314	+	608.314i	−1.08049	+	1.08049i	−0.996464	+	0.0840234i	$0.973223\pi$
$564$	−88.5071	+	792.060i	−0.156927	+	1.40436i
$565$	−5.18401	+	160.361i	−0.00917525	+	0.283824i
$566$	478.474	+	26.6501i	0.845361	+	0.0470850i
$567$	−940.448	−	940.448i	−1.65864	−	1.65864i
$568$	111.569	+	156.784i	0.196425	+	0.276028i
$569$	937.364			1.64739			0.823694	−	0.567035i	$-0.191909\pi$
$569$	937.364			1.64739			0.823694	+	0.567035i	$0.191909\pi$
$570$	890.445	−	746.125i	1.56218	−	1.30899i
$571$	703.275			1.23166			0.615828	−	0.787881i	$-0.288822\pi$
$571$	703.275			1.23166			0.615828	+	0.787881i	$0.288822\pi$
$572$	97.0076	−	915.472i	0.169594	−	1.60048i
$573$	16.9917	−	16.9917i	0.0296538	−	0.0296538i
$574$	−207.276	−	11.5449i	−0.361109	−	0.0201131i
$575$	202.973	−	178.296i	0.352996	−	0.310080i
$576$	1272.88	+	441.466i	2.20986	+	0.766433i
$577$	−123.821	−	123.821i	−0.214594	−	0.214594i	0.591621	−	0.806216i	$-0.298488\pi$
$577$	−123.821	−	123.821i	−0.214594	−	0.214594i	−0.806216	+	0.591621i	$0.798488\pi$
$578$	334.083	−	298.831i	0.577999	−	0.517009i
$579$		−	1506.29i		−	2.60154i
$580$	25.3416	+	33.9087i	0.0436924	+	0.0584633i
$581$	120.501			0.207403
$582$	−1019.44	+	911.869i	−1.75161	+	1.56679i
$583$	0.959452	+	168.013i	0.00164572	+	0.288187i
$584$	770.133	+	129.759i	1.31872	+	0.222191i
$585$	71.1541	−	2201.06i	0.121631	−	3.76249i
$586$	18.6200	−	334.302i	0.0317747	−	0.570481i
$587$	37.1908	−	37.1908i	0.0633573	−	0.0633573i	−0.674718	−	0.738075i	$-0.735735\pi$
$587$	37.1908	−	37.1908i	0.0633573	−	0.0633573i	0.738075	+	0.674718i	$0.235735\pi$
$588$	−141.249	−	176.787i	−0.240220	−	0.300659i
$589$	494.617			0.839758
$590$	836.840	+	73.7960i	1.41837	+	0.125078i
$591$	−924.465			−1.56424
$592$	−85.9852	−	136.288i	−0.145245	−	0.230217i
$593$	113.671	+	113.671i	0.191688	+	0.191688i	0.796425	−	0.604737i	$-0.206722\pi$
$593$	113.671	+	113.671i	0.191688	+	0.191688i	−0.604737	+	0.796425i	$0.706722\pi$
$594$	1077.69	−	975.107i	1.81429	−	1.64159i
$595$	−226.316	+	212.142i	−0.380362	+	0.356540i
$596$	−71.3543	+	638.558i	−0.119722	+	1.07141i
$597$	1361.34	+	1361.34i	2.28031	+	2.28031i
$598$	−337.041	+	301.477i	−0.563614	+	0.504142i
$599$	−811.770			−1.35521			−0.677605	−	0.735426i	$-0.736982\pi$
$599$	−811.770			−1.35521			−0.677605	+	0.735426i	$0.736982\pi$
$600$	251.607	−	1067.11i	0.419345	−	1.77852i
$601$			210.411i			0.350102i	0.984559	+	0.175051i	$0.0560091\pi$
$601$			210.411i			0.350102i	−0.984559	+	0.175051i	$0.943991\pi$
$602$	267.666	+	299.241i	0.444628	+	0.497079i
$603$	−1177.93	−	1177.93i	−1.95345	−	1.95345i
$604$	−84.4441	+	755.701i	−0.139808	+	1.25116i
$605$	−418.768	−	436.644i	−0.692179	−	0.721726i
$606$	−575.917	−	32.0774i	−0.950358	−	0.0529331i
$607$	14.5520	+	14.5520i	0.0239736	+	0.0239736i	0.718992	−	0.695018i	$-0.244604\pi$
$607$	14.5520	+	14.5520i	0.0239736	+	0.0239736i	−0.695018	+	0.718992i	$0.744604\pi$
$608$	−592.774	+	329.394i	−0.974957	+	0.541766i
$609$			89.3649i			0.146740i
$610$	−76.7327	+	870.142i	−0.125791	+	1.42646i
$611$	−760.468			−1.24463
$612$	529.902	−	423.380i	0.865853	−	0.691797i
$613$	−511.327	−	511.327i	−0.834139	−	0.834139i	0.153941	−	0.988080i	$-0.450803\pi$
$613$	−511.327	−	511.327i	−0.834139	−	0.834139i	−0.988080	+	0.153941i	$0.950803\pi$
$614$	30.7104	−	551.372i	0.0500169	−	0.898000i
$615$	11.9353	−	369.203i	0.0194070	−	0.600330i
$616$	549.969	−	396.114i	0.892806	−	0.643043i
$617$	−307.862	−	307.862i	−0.498965	−	0.498965i	0.412151	−	0.911116i	$-0.364778\pi$
$617$	−307.862	−	307.862i	−0.498965	−	0.498965i	−0.911116	+	0.412151i	$0.864778\pi$
$618$	615.934	−	550.942i	0.996657	−	0.891491i
$619$	149.498			0.241515			0.120758	−	0.992682i	$-0.461468\pi$
$619$	149.498			0.241515			0.120758	+	0.992682i	$0.461468\pi$
$620$	373.912	−	279.442i	0.603084	−	0.450713i
$621$	−713.894			−1.14959
$622$	779.512	−	697.259i	1.25323	−	1.12099i
$623$	492.493	−	492.493i	0.790518	−	0.790518i
$624$	−405.066	+	1789.86i	−0.649145	+	2.86837i
$625$	−619.786	−	80.5651i	−0.991657	−	0.128904i
$626$	685.563	+	38.1845i	1.09515	+	0.0609976i
$627$	7.29740	+	1277.87i	0.0116386	+	2.03807i
$628$	267.495	−	213.722i	0.425948	−	0.340322i
$629$	−81.1276			−0.128979
$630$	1242.73	−	1041.31i	1.97258	−	1.65288i
$631$		−	367.025i		−	0.581655i	−0.956775	−	0.290828i	$-0.906069\pi$
$631$		−	367.025i		−	0.581655i	0.956775	−	0.290828i	$-0.0939306\pi$
$632$	−221.873	−	311.789i	−0.351065	−	0.493338i
$633$	−982.052	−	982.052i	−1.55142	−	1.55142i
$634$	−5.33619	+	95.8057i	−0.00841671	+	0.151113i
$635$	1.32568	+	0.0428555i	0.00208768	+	6.74890e-5i
$636$	37.1938	−	332.852i	0.0584808	−	0.523352i
$637$	152.676	−	152.676i	0.239679	−	0.239679i
$638$	−46.5072	−	2.32404i	−0.0728952	−	0.00364269i
$639$	−506.352			−0.792413
$640$	−262.018	+	583.906i	−0.409403	+	0.912353i
$641$	−768.223			−1.19848			−0.599238	−	0.800571i	$-0.704530\pi$
$641$	−768.223			−1.19848			−0.599238	+	0.800571i	$0.704530\pi$
$642$	−544.501	+	487.046i	−0.848133	+	0.758639i
$643$	−440.590	−	440.590i	−0.685210	−	0.685210i	0.275959	−	0.961169i	$-0.411004\pi$
$643$	−440.590	−	440.590i	−0.685210	−	0.685210i	−0.961169	+	0.275959i	$0.911004\pi$
$644$	−330.864	−	36.9716i	−0.513763	−	0.0574093i
$645$	−521.212	+	488.569i	−0.808081	+	0.757471i
$646$	−18.9863	+	340.878i	−0.0293905	+	0.527676i
$647$	93.8740	−	93.8740i	0.145091	−	0.145091i	−0.630830	−	0.775921i	$-0.717285\pi$
$647$	93.8740	−	93.8740i	0.145091	−	0.145091i	0.775921	+	0.630830i	$0.217285\pi$
$648$	−1125.57	+	800.966i	−1.73699	+	1.23606i
$649$	−649.693	+	657.156i	−1.00107	+	1.01257i
$650$	1038.58	+	125.518i	1.59781	+	0.193105i
$651$	985.428			1.51371
$652$	−180.045	+	143.852i	−0.276143	+	0.220632i
$653$	539.451	−	539.451i	0.826112	−	0.826112i	−0.160864	−	0.986977i	$-0.551428\pi$
$653$	539.451	−	539.451i	0.826112	−	0.826112i	0.986977	+	0.160864i	$0.0514281\pi$
$654$	−108.939	+	1955.89i	−0.166574	+	2.99066i
$655$	388.362	−	364.039i	0.592919	−	0.555785i
$656$	−47.5963	+	210.313i	−0.0725554	+	0.320600i
$657$	−1453.15	+	1453.15i	−2.21180	+	2.21180i
$658$	−373.265	−	417.297i	−0.567271	−	0.634191i
$659$		−	232.233i		−	0.352402i	−0.984354	−	0.176201i	$-0.943619\pi$
$659$		−	232.233i		−	0.352402i	0.984354	−	0.176201i	$-0.0563809\pi$
$660$	727.471	+	961.900i	1.10223	+	1.45742i
$661$	579.441			0.876613			0.438306	−	0.898826i	$-0.355578\pi$
$661$	579.441			0.876613			0.438306	+	0.898826i	$0.355578\pi$
$662$	631.443	−	564.814i	0.953841	−	0.853193i
$663$	653.282	+	653.282i	0.985342	+	0.985342i
$664$	20.7958	−	123.425i	0.0313190	−	0.185881i
$665$	−26.3684	+	815.672i	−0.0396517	+	1.22657i
$666$	423.377	+	23.5813i	0.635702	+	0.0354074i
$667$	16.1736	+	16.1736i	0.0242483	+	0.0242483i
$668$	−442.405	+	353.471i	−0.662282	+	0.529148i
$669$		−	598.607i		−	0.894778i
$670$	606.554	−	508.246i	0.905304	−	0.758576i
$671$	−683.307	−	675.547i	−1.01834	−	1.00678i
$672$	−1180.99	+	656.253i	−1.75742	+	0.976567i
$673$	727.635	+	727.635i	1.08118	+	1.08118i	0.996400	+	0.0847817i	$0.0270193\pi$
$673$	727.635	+	727.635i	1.08118	+	1.08118i	0.0847817	+	0.996400i	$0.472981\pi$
$674$	834.574	+	46.4842i	1.23824	+	0.0689676i
$675$	1089.95	+	1240.80i	1.61474	+	1.83823i
$676$	−1068.38	−	119.384i	−1.58045	−	0.176603i
$677$	464.202	−	464.202i	0.685675	−	0.685675i	−0.275598	−	0.961273i	$-0.588876\pi$
$677$	464.202	−	464.202i	0.685675	−	0.685675i	0.961273	+	0.275598i	$0.0888757\pi$
$678$	234.551	+	262.220i	0.345945	+	0.386755i
$679$		−	960.837i		−	1.41508i
$680$	178.232	+	268.418i	0.262106	+	0.394732i
$681$			1700.08i			2.49644i
$682$	−25.6272	+	512.835i	−0.0375765	+	0.751957i
$683$	419.389	+	419.389i	0.614040	+	0.614040i	0.943996	−	0.329956i	$-0.107034\pi$
$683$	419.389	+	419.389i	0.614040	+	0.614040i	−0.329956	+	0.943996i	$0.607034\pi$
$684$	198.166	−	1773.41i	0.289716	−	2.59271i
$685$	447.658	+	14.4716i	0.653516	+	0.0211264i
$686$	−594.904	−	33.1350i	−0.867206	−	0.0483017i
$687$	−999.009	+	999.009i	−1.45416	+	1.45416i
$688$	352.695	−	222.518i	0.512638	−	0.323427i
$689$	319.576			0.463825
$690$	52.0380	−	590.107i	0.0754175	−	0.855228i
$691$			1091.80i			1.58003i	0.613085	+	0.790017i	$0.289928\pi$
$691$			1091.80i			1.58003i	−0.613085	+	0.790017i	$0.710072\pi$
$692$	−618.631	+	494.272i	−0.893976	+	0.714266i
$693$	10.1844	+	1783.43i	0.0146962	+	2.57349i
$694$	−37.0277	+	664.793i	−0.0533541	+	0.957916i
$695$	−766.308	−	817.509i	−1.10260	−	1.17627i
$696$	91.5333	+	15.4224i	0.131513	+	0.0221586i
$697$	76.7622	+	76.7622i	0.110132	+	0.110132i
$698$	650.015	+	726.695i	0.931253	+	1.04111i
$699$			1192.31i			1.70573i
$700$	440.893	+	631.514i	0.629848	+	0.902163i
$701$		−	1231.26i		−	1.75643i	−0.478262	−	0.878217i	$-0.658733\pi$
$701$		−	1231.26i		−	1.75643i	0.478262	−	0.878217i	$-0.341267\pi$
$702$	−1842.98	−	2060.39i	−2.62532	−	2.93502i
$703$	−150.923	+	150.923i	−0.214685	+	0.214685i
$704$	−310.813	−	631.673i	−0.441496	−	0.897263i
$705$	726.840	−	681.318i	1.03098	−	0.966408i
$706$	−825.115	−	45.9573i	−1.16872	−	0.0650953i
$707$	286.522	−	286.522i	0.405264	−	0.405264i
$708$	1439.16	−	1149.85i	2.03271	−	1.62409i
$709$		−	172.519i		−	0.243327i	−0.992571	−	0.121664i	$-0.961177\pi$
$709$		−	172.519i		−	0.243327i	0.992571	−	0.121664i	$-0.0388229\pi$
$710$	21.1295	−	239.607i	0.0297598	−	0.337474i
$711$	1006.96			1.41626
$712$	−419.449	−	589.436i	−0.589114	−	0.827859i
$713$	178.347	−	178.347i	0.250136	−	0.250136i
$714$	−37.8264	+	679.134i	−0.0529782	+	0.951168i
$715$	−835.059	+	791.766i	−1.16791	+	1.10737i
$716$	47.3869	−	424.071i	0.0661828	−	0.592278i
$717$	−150.504	+	150.504i	−0.209907	+	0.209907i
$718$	273.566	−	244.699i	0.381011	−	0.340807i
$719$	157.766			0.219424			0.109712	−	0.993963i	$-0.465007\pi$
$719$	157.766			0.219424			0.109712	+	0.993963i	$0.465007\pi$
$720$	−852.111	−	1452.59i	−1.18349	−	2.01748i
$721$			580.528i			0.805170i
$722$	117.474	+	131.332i	0.162706	+	0.181900i
$723$	2.99488	−	2.99488i	0.00414229	−	0.00414229i
$724$	−5.64770	+	50.5420i	−0.00780069	+	0.0698093i
$725$	3.41762	−	52.8045i	0.00471396	−	0.0728338i
$726$	−1325.32	−	58.6431i	−1.82550	−	0.0807756i
$727$	883.116	−	883.116i	1.21474	−	1.21474i	0.245290	−	0.969450i	$-0.421117\pi$
$727$	883.116	−	883.116i	1.21474	−	1.21474i	0.969450	−	0.245290i	$-0.0788833\pi$
$728$	−747.447	−	1050.36i	−1.02671	−	1.44280i
$729$		−	375.868i		−	0.515595i
$730$	−626.995	−	748.272i	−0.858898	−	1.02503i
$731$		−	209.947i		−	0.287205i
$732$	1195.61	+	1496.43i	1.63335	+	2.04430i
$733$	125.612	+	125.612i	0.171366	+	0.171366i	0.787580	−	0.616213i	$-0.211334\pi$
$733$	125.612	+	125.612i	0.171366	+	0.171366i	−0.616213	+	0.787580i	$0.711334\pi$
$734$	874.559	+	48.7112i	1.19150	+	0.0663641i
$735$	−9.13920	+	282.709i	−0.0124343	+	0.384638i
$736$	−94.9684	+	332.511i	−0.129033	+	0.451781i
$737$	4.97085	+	870.462i	0.00674471	+	1.18109i
$738$	−378.284	−	422.909i	−0.512579	−	0.573047i
$739$		−	47.4462i		−	0.0642033i	−0.999485	−	0.0321016i	$-0.989780\pi$
$739$		−	47.4462i		−	0.0642033i	0.999485	−	0.0321016i	$-0.0102200\pi$
$740$	−28.8258	+	199.359i	−0.0389538	+	0.269404i
$741$	2430.63			3.28020
$742$	156.859	+	175.363i	0.211400	+	0.236339i
$743$	735.075	−	735.075i	0.989334	−	0.989334i	−0.0106101	−	0.999944i	$-0.503377\pi$
$743$	735.075	−	735.075i	0.989334	−	0.989334i	0.999944	+	0.0106101i	$0.00337736\pi$
$744$	170.063	−	1009.34i	0.228579	−	1.35664i
$745$	585.977	−	549.277i	0.786546	−	0.737285i
$746$	−30.7166	+	551.484i	−0.0411751	+	0.739255i
$747$	232.889	+	232.889i	0.311765	+	0.311765i
$748$	−352.450	−	37.3472i	−0.471190	−	0.0499294i
$749$		−	513.201i		−	0.685181i
$750$	−1105.10	+	810.512i	−1.47347	+	1.08068i
$751$			1011.71i			1.34715i	0.739120	+	0.673573i	$0.235241\pi$
$751$			1011.71i			1.34715i	−0.739120	+	0.673573i	$0.764759\pi$
$752$	−491.840	+	310.305i	−0.654042	+	0.412640i
$753$	57.5398	−	57.5398i	0.0764140	−	0.0764140i
$754$	−4.92553	+	88.4327i	−0.00653254	+	0.117285i
$755$	693.474	−	650.042i	0.918509	−	0.860983i
$756$	226.013	−	2022.62i	0.298959	−	2.67542i
$757$	−788.218	−	788.218i	−1.04124	−	1.04124i	−0.999112	−	0.0421273i	$-0.986586\pi$
$757$	−788.218	−	788.218i	−1.04124	−	1.04124i	−0.0421273	−	0.999112i	$-0.513414\pi$
$758$	910.737	+	1018.17i	1.20150	+	1.34324i
$759$	463.401	+	458.138i	0.610541	+	0.603607i
$760$	830.912	+	167.775i	1.09331	+	0.220757i
$761$			1401.09i			1.84111i	0.390609	+	0.920557i	$0.372265\pi$
$761$			1401.09i			1.84111i	−0.390609	+	0.920557i	$0.627735\pi$
$762$	2.16774	−	1.93900i	0.00284480	−	0.00254462i
$763$	−973.066	−	973.066i	−1.27532	−	1.27532i
$764$	17.4256	+	1.94718i	0.0228083	+	0.00254867i
$765$	−847.391	−	27.3938i	−1.10770	−	0.0358089i
$766$	44.5740	−	800.279i	0.0581906	−	1.04475i
$767$	1242.87	+	1242.87i	1.62043	+	1.62043i
$768$	468.364	+	1322.90i	0.609849	+	1.72252i
$769$	392.963			0.511005			0.255502	−	0.966808i	$-0.417759\pi$
$769$	392.963			0.511005			0.255502	+	0.966808i	$0.417759\pi$
$770$	−844.348	−	69.6013i	−1.09656	−	0.0903913i
$771$		−	499.064i		−	0.647295i
$772$	858.686	−	686.071i	1.11229	−	0.888692i
$773$	−147.039	+	147.039i	−0.190219	+	0.190219i	−0.795791	−	0.605572i	$-0.792944\pi$
$773$	−147.039	+	147.039i	−0.190219	+	0.190219i	0.605572	+	0.795791i	$0.292944\pi$
$774$	−61.0251	+	1095.64i	−0.0788439	+	1.41556i
$775$	−582.276	−	37.6861i	−0.751324	−	0.0486272i
$776$	−984.151	−	165.819i	−1.26824	−	0.213684i
$777$	−300.685	+	300.685i	−0.386983	+	0.386983i
$778$	−1043.10	+	933.036i	−1.34075	+	1.19928i
$779$	285.605			0.366630
$780$	1837.46	−	1373.22i	2.35572	−	1.76054i
$781$	188.159	+	186.022i	0.240920	+	0.238184i
$782$	116.066	+	129.758i	0.148423	+	0.165932i
$783$	−98.8720	+	98.8720i	−0.126273	+	0.126273i
$784$	36.4458	−	161.043i	0.0464870	−	0.205412i
$785$	−427.764	−	13.8284i	−0.544922	−	0.0176158i
$786$	64.9109	−	1165.41i	0.0825839	−	1.48271i
$787$	69.9045	+	69.9045i	0.0888240	+	0.0888240i	0.750123	−	0.661299i	$-0.229994\pi$
$787$	69.9045	+	69.9045i	0.0888240	+	0.0888240i	−0.661299	+	0.750123i	$0.729994\pi$
$788$	−421.067	−	527.007i	−0.534349	−	0.668791i
$789$	−523.078			−0.662963
$790$	−42.0193	+	476.495i	−0.0531889	+	0.603158i
$791$	−247.146			−0.312448
$792$	1828.46	+	297.349i	2.30866	+	0.375441i
$793$	−1292.33	+	1292.33i	−1.62968	+	1.62968i
$794$	75.8179	−	1361.23i	0.0954885	−	1.71440i
$795$	−305.444	+	286.314i	−0.384206	+	0.360143i
$796$	−156.005	+	1396.11i	−0.195986	+	1.75390i
$797$	733.422	+	733.422i	0.920228	+	0.920228i	0.997045	−	0.0768168i	$-0.0244757\pi$
$797$	733.422	+	733.422i	0.920228	+	0.920228i	−0.0768168	+	0.997045i	$0.524476\pi$
$798$	1193.04	+	1333.78i	1.49504	+	1.67140i
$799$			292.775i			0.366426i
$800$	722.925	−	342.606i	0.903657	−	0.428257i
$801$	1903.65			2.37659
$802$	−821.238	−	918.116i	−1.02399	−	1.14478i
$803$	1073.84	−	6.13226i	1.33729	−	0.00763669i
$804$	192.698	−	1724.48i	0.239675	−	2.14488i
$805$	284.604	+	303.619i	0.353545	+	0.377167i
$806$	975.149	+	54.3139i	1.20986	+	0.0673870i
$807$	1013.81	−	1013.81i	1.25627	−	1.25627i
$808$	−244.027	−	342.921i	−0.302013	−	0.424408i
$809$	641.096			0.792455			0.396227	−	0.918152i	$-0.370319\pi$
$809$	641.096			0.792455			0.396227	+	0.918152i	$0.370319\pi$
$810$	1720.16	+	151.690i	2.12365	+	0.187272i
$811$	−1069.33			−1.31853			−0.659264	−	0.751911i	$-0.729132\pi$
$811$	−1069.33			−1.31853			−0.659264	+	0.751911i	$0.729132\pi$
$812$	−50.9440	+	40.7031i	−0.0627389	+	0.0501270i
$813$	−1484.71	−	1484.71i	−1.82621	−	1.82621i
$814$	−148.663	−	164.302i	−0.182632	−	0.201845i
$815$	287.919	+	9.30762i	0.353275	+	0.0114204i
$816$	689.084	+	155.948i	0.844466	+	0.191112i
$817$	−390.569	−	390.569i	−0.478053	−	0.478053i
$818$	−440.109	−	492.027i	−0.538030	−	0.601500i
$819$	3392.25			4.14194
$820$	215.907	−	161.357i	0.263301	−	0.196777i
$821$			20.6937i			0.0252055i	0.999921	+	0.0126028i	$0.00401169\pi$
$821$			20.6937i			0.0252055i	−0.999921	+	0.0126028i	$0.995988\pi$
$822$	732.006	−	654.765i	0.890518	−	0.796552i
$823$	210.860	+	210.860i	0.256209	+	0.256209i	0.823510	−	0.567301i	$-0.192012\pi$
$823$	210.860	+	210.860i	0.256209	+	0.256209i	−0.567301	+	0.823510i	$0.692012\pi$
$824$	594.613	+	100.186i	0.721618	+	0.121585i
$825$	88.7735	−	1504.90i	0.107604	−	1.82412i
$826$	−71.9651	+	1292.06i	−0.0871248	+	1.56423i
$827$	127.688	+	127.688i	0.154399	+	0.154399i	0.780080	−	0.625680i	$-0.215179\pi$
$827$	127.688	+	127.688i	0.154399	+	0.154399i	−0.625680	+	0.780080i	$0.715179\pi$
$828$	−567.995	−	710.902i	−0.685984	−	0.858578i
$829$			1285.31i			1.55044i	0.631693	+	0.775219i	$0.282360\pi$
$829$			1285.31i			1.55044i	−0.631693	+	0.775219i	$0.717640\pi$
$830$	−119.922	+	100.485i	−0.144484	+	0.121067i
$831$	−818.289			−0.984704
$832$	−1204.84	+	584.315i	−1.44812	+	0.702301i
$833$	−58.7790	−	58.7790i	−0.0705630	−	0.0705630i
$834$	−2453.20	−	136.639i	−2.94149	−	0.163835i
$835$	707.470	+	22.8705i	0.847270	+	0.0273899i
$836$	−725.149	+	586.193i	−0.867403	+	0.701188i
$837$	1090.26	+	1090.26i	1.30258	+	1.30258i
$838$	−572.939	−	640.527i	−0.683698	−	0.764352i
$839$	−723.511			−0.862350			−0.431175	−	0.902268i	$-0.641901\pi$
$839$	−723.511			−0.862350			−0.431175	+	0.902268i	$0.641901\pi$
$840$	1655.43	+	334.259i	1.97075	+	0.397927i
$841$	−836.520			−0.994673
$842$	−349.311	−	390.518i	−0.414859	−	0.463798i
$843$	−771.174	+	771.174i	−0.914797	+	0.914797i
$844$	112.540	−	1007.13i	0.133341	−	1.19328i
$845$	919.005	+	980.407i	1.08758	+	1.16025i
$846$	85.1006	−	1527.89i	0.100592	−	1.80602i
$847$	651.407	−	666.460i	0.769076	−	0.786847i
$848$	206.689	−	130.401i	0.243736	−	0.153775i
$849$	−1313.50			−1.54711
$850$	48.3235	−	399.844i	0.0568512	−	0.470405i
$851$			108.839i			0.127895i
$852$	−329.230	−	412.064i	−0.386420	−	0.483643i
$853$	−258.829	−	258.829i	−0.303434	−	0.303434i	0.538922	−	0.842356i	$-0.318832\pi$
$853$	−258.829	−	258.829i	−0.303434	−	0.303434i	−0.842356	+	0.538922i	$0.818832\pi$
$854$	−1343.47	−	74.8289i	−1.57315	−	0.0876217i
$855$	−1627.38	+	1525.46i	−1.90337	+	1.78416i
$856$	−525.653	−	88.5670i	−0.614081	−	0.103466i
$857$	−206.625	+	206.625i	−0.241102	+	0.241102i	−0.817306	−	0.576204i	$-0.804533\pi$
$857$	−206.625	+	206.625i	−0.241102	+	0.241102i	0.576204	+	0.817306i	$0.304533\pi$
$858$	−125.936	+	2520.15i	−0.146779	+	2.93724i
$859$	231.485			0.269482			0.134741	−	0.990881i	$-0.456980\pi$
$859$	231.485			0.269482			0.134741	+	0.990881i	$0.456980\pi$
$860$	−515.914	−	74.5971i	−0.599900	−	0.0867409i
$861$	569.012			0.660874
$862$	567.760	+	634.737i	0.658655	+	0.736354i
$863$	−638.441	−	638.441i	−0.739793	−	0.739793i	0.232745	−	0.972538i	$-0.425229\pi$
$863$	−638.441	−	638.441i	−0.739793	−	0.739793i	−0.972538	+	0.232745i	$0.925229\pi$
$864$	−2032.69	−	580.556i	−2.35265	−	0.671940i
$865$	989.282	+	31.9807i	1.14368	+	0.0369720i
$866$	1248.00	+	69.5114i	1.44111	+	0.0802672i
$867$	−868.733	+	868.733i	−1.00200	+	1.00200i
$868$	448.833	+	561.760i	0.517089	+	0.647189i
$869$	−374.183	−	369.934i	−0.430590	−	0.425700i
$870$	−74.5208	−	88.9350i	−0.0856561	−	0.102224i
$871$	1655.70			1.90092
$872$	−1164.61	+	828.747i	−1.33556	+	0.950398i
$873$	1856.98	−	1856.98i	2.12712	−	2.12712i
$874$	457.314	+	25.4715i	0.523242	+	0.0291436i
$875$	93.1896	−	958.220i	0.106502	−	1.09511i
$876$	−2127.40	−	237.721i	−2.42854	−	0.271371i
$877$	481.721	−	481.721i	0.549282	−	0.549282i	−0.376951	−	0.926233i	$-0.623027\pi$
$877$	481.721	−	481.721i	0.549282	−	0.549282i	0.926233	+	0.376951i	$0.123027\pi$
$878$	58.3167	−	52.1632i	0.0664199	−	0.0594113i
$879$			917.721i			1.04405i
$880$	−217.006	+	852.824i	−0.246598	+	0.969118i
$881$	−878.141			−0.996755			−0.498377	−	0.866960i	$-0.666071\pi$
$881$	−878.141			−0.996755			−0.498377	+	0.866960i	$0.666071\pi$
$882$	289.662	+	323.833i	0.328415	+	0.367158i
$883$	−792.572	−	792.572i	−0.897591	−	0.897591i	0.0976320	−	0.995223i	$-0.468873\pi$
$883$	−792.572	−	792.572i	−0.897591	−	0.897591i	−0.995223	+	0.0976320i	$0.968873\pi$
$884$	−74.8637	+	669.965i	−0.0846875	+	0.757878i
$885$	−2301.42	−	74.3987i	−2.60048	−	0.0840663i
$886$	69.4186	−	1246.34i	0.0783506	−	1.40670i
$887$	395.005	+	395.005i	0.445327	+	0.445327i	0.893798	−	0.448471i	$-0.148031\pi$
$887$	395.005	+	395.005i	0.445327	+	0.445327i	−0.448471	+	0.893798i	$0.648031\pi$
$888$	256.090	+	359.873i	0.288389	+	0.405262i
$889$			2.04312i			0.00229823i
$890$	−79.4371	+	900.810i	−0.0892551	+	1.01215i
$891$	−1335.47	+	1350.81i	−1.49884	+	1.51606i
$892$	341.246	−	272.648i	0.382563	−	0.305659i
$893$	544.655	+	544.655i	0.609916	+	0.609916i
$894$	97.9403	−	1758.41i	0.109553	−	1.96691i
$895$	−389.152	+	364.779i	−0.434806	+	0.407575i
$896$	−912.012	−	374.337i	−1.01787	−	0.417787i
$897$	876.425	−	876.425i	0.977063	−	0.977063i
$898$	824.933	−	737.887i	0.918633	−	0.821700i
$899$		−	49.4009i		−	0.0549510i
$900$	−368.406	+	2072.61i	−0.409340	+	2.30289i
$901$		−	123.034i		−	0.136553i
$902$	−14.7978	+	296.124i	−0.0164055	+	0.328298i
$903$	−778.132	−	778.132i	−0.861719	−	0.861719i
$904$	−42.6520	+	253.143i	−0.0471814	+	0.280025i
$905$	46.3802	−	43.4754i	0.0512488	−	0.0480391i
$906$	115.907	−	2080.99i	0.127933	−	2.29690i
$907$	948.453	−	948.453i	1.04570	−	1.04570i	0.0467987	−	0.998904i	$-0.485098\pi$
$907$	948.453	−	948.453i	1.04570	−	1.04570i	0.998904	−	0.0467987i	$-0.0149019\pi$
$908$	−969.157	+	774.335i	−1.06735	+	0.852791i
$909$	1107.50			1.21837
$910$	−141.555	+	1605.22i	−0.155555	+	1.76398i
$911$		−	190.484i		−	0.209093i	−0.994520	−	0.104546i	$-0.966661\pi$
$911$		−	190.484i		−	0.209093i	0.994520	−	0.104546i	$-0.0333391\pi$
$912$	1572.03	−	991.806i	1.72372	−	1.08751i
$913$	−0.982785	−	172.099i	−0.00107644	−	0.188498i
$914$	−436.123	−	24.2912i	−0.477159	−	0.0265768i
$915$	77.3594	−	2393.01i	0.0845458	−	2.61531i
$916$	−1024.52	−	114.483i	−1.11847	−	0.124981i
$917$	579.797	+	579.797i	0.632276	+	0.632276i
$918$	−793.234	+	709.532i	−0.864089	+	0.772911i
$919$			139.794i			0.152115i	0.997103	+	0.0760576i	$0.0242333\pi$
$919$			139.794i			0.152115i	−0.997103	+	0.0760576i	$0.975767\pi$
$920$	360.102	−	239.111i	0.391416	−	0.259903i
$921$			1513.62i			1.64345i
$922$	−703.546	+	629.308i	−0.763065	+	0.682547i
$923$	355.863	−	355.863i	0.385550	−	0.385550i
$924$	−1444.72	+	1167.87i	−1.56355	+	1.26393i
$925$	189.170	−	166.172i	0.204508	−	0.179645i
$926$	15.7868	−	283.436i	0.0170484	−	0.306086i
$927$	−1121.97	+	1121.97i	−1.21032	+	1.21032i
$928$	32.8989	+	59.2045i	0.0354514	+	0.0637980i
$929$		−	98.0946i		−	0.105592i	−0.998605	−	0.0527958i	$-0.983187\pi$
$929$		−	98.0946i		−	0.105592i	0.998605	−	0.0527958i	$-0.0168133\pi$
$930$	−980.688	+	821.742i	−1.05450	+	0.883594i
$931$	−218.696			−0.234904
$932$	−679.695	+	543.061i	−0.729286	+	0.582683i
$933$	−2027.00	+	2027.00i	−2.17257	+	2.17257i
$934$	−676.886	−	37.7013i	−0.724717	−	0.0403654i
$935$	304.824	+	321.492i	0.326015	+	0.343841i
$936$	585.427	−	3474.56i	0.625456	−	3.71213i
$937$	−1026.90	+	1026.90i	−1.09594	+	1.09594i	−0.101059	+	0.994880i	$0.532223\pi$
$937$	−1026.90	+	1026.90i	−1.09594	+	1.09594i	−0.994880	+	0.101059i	$0.967777\pi$
$938$	812.675	+	908.543i	0.866391	+	0.968596i
$939$	−1882.00			−2.00426
$940$	719.451	+	104.027i	0.765373	+	0.110667i
$941$			1528.72i			1.62457i	0.583262	+	0.812284i	$0.301776\pi$
$941$			1528.72i			1.62457i	−0.583262	+	0.812284i	$0.698224\pi$
$942$	−699.475	+	625.667i	−0.742542	+	0.664190i
$943$	102.982	−	102.982i	0.109207	−	0.109207i
$944$	1310.99	+	296.691i	1.38876	+	0.314292i
$945$	−1856.07	+	1739.83i	−1.96410	+	1.84109i
$946$	425.191	−	384.718i	0.449462	−	0.406679i
$947$	−118.985	+	118.985i	−0.125644	+	0.125644i	−0.767132	−	0.641489i	$-0.778317\pi$
$947$	−118.985	+	118.985i	−0.125644	+	0.125644i	0.641489	+	0.767132i	$0.278317\pi$
$948$	654.724	+	819.453i	0.690637	+	0.864402i
$949$		−	2042.54i		−	2.15231i
$950$	−653.942	−	833.736i	−0.688360	−	0.877617i
$951$		−	263.004i		−	0.276556i
$952$	−404.380	+	287.762i	−0.424769	+	0.302271i
$953$	204.792	+	204.792i	0.214892	+	0.214892i	0.806342	−	0.591450i	$-0.201444\pi$
$953$	204.792	+	204.792i	0.214892	+	0.214892i	−0.591450	+	0.806342i	$0.701444\pi$
$954$	−35.7623	+	642.075i	−0.0374867	+	0.673034i
$955$	−14.9892	−	15.9907i	−0.0156955	−	0.0167442i
$956$	−154.347	−	17.2472i	−0.161451	−	0.0180410i
$957$	127.630	−	0.728843i	0.133365	−	0.000761592i
$958$	−597.526	+	534.475i	−0.623722	+	0.557908i
$959$			689.927i			0.719423i
$960$	628.060	−	1637.91i	0.654229	−	1.70616i
$961$	416.255			0.433148
$962$	−314.122	+	280.976i	−0.326530	+	0.292075i
$963$	991.846	−	991.846i	1.02995	−	1.02995i
$964$	3.07136	+	0.343202i	0.00318606	+	0.000356019i
$965$	−1373.17	−	44.3906i	−1.42297	−	0.0460006i
$966$	911.108	+	50.7470i	0.943176	+	0.0525331i
$967$	−327.566	−	327.566i	−0.338745	−	0.338745i	0.517150	−	0.855895i	$-0.326993\pi$
$967$	−327.566	−	327.566i	−0.338745	−	0.338745i	−0.855895	+	0.517150i	$0.826993\pi$
$968$	−570.212	−	782.229i	−0.589062	−	0.808088i
$969$		−	935.774i		−	0.965711i
$970$	801.236	+	956.215i	0.826016	+	0.985789i
$971$		−	702.038i		−	0.723005i	−0.932371	−	0.361503i	$-0.882264\pi$
$971$		−	702.038i		−	0.723005i	0.932371	−	0.361503i	$-0.117736\pi$
$972$	1100.24	−	879.066i	1.13193	−	0.904389i
$973$	1220.48	−	1220.48i	1.25435	−	1.25435i
$974$	68.9769	+	3.84188i	0.0708181	+	0.00394443i
$975$	−2861.40	−	185.196i	−2.93477	−	0.189944i
$976$	−308.498	+	1363.16i	−0.316084	+	1.39668i
$977$	96.8366	+	96.8366i	0.0991163	+	0.0991163i	0.754926	−	0.655810i	$-0.227673\pi$
$977$	96.8366	+	96.8366i	0.0991163	+	0.0991163i	−0.655810	+	0.754926i	$0.727673\pi$
$978$	470.802	−	421.123i	0.481393	−	0.430597i
$979$	−707.390	−	699.357i	−0.722564	−	0.714358i
$980$	−165.326	+	123.556i	−0.168700	+	0.126077i
$981$		−	3761.22i		−	3.83407i
$982$	−414.972	−	463.925i	−0.422578	−	0.472429i
$983$	374.140	+	374.140i	0.380611	+	0.380611i	0.871322	−	0.490711i	$-0.163263\pi$
$983$	374.140	+	374.140i	0.380611	+	0.380611i	−0.490711	+	0.871322i	$0.663263\pi$
$984$	98.1988	−	582.818i	0.0997955	−	0.592295i
$985$	−27.2442	+	842.762i	−0.0276590	+	0.855596i
$986$	34.0460	+	1.89629i	0.0345294	+	0.00192322i
$987$	1085.12	+	1085.12i	1.09941	+	1.09941i
$988$	1107.08	+	1385.62i	1.12053	+	1.40245i
$989$	−281.659			−0.284792
$990$	−1497.33	−	1766.36i	−1.51245	−	1.78420i
$991$		−	905.275i		−	0.913496i	−0.889596	−	0.456748i	$-0.849014\pi$
$991$		−	905.275i		−	0.913496i	0.889596	−	0.456748i	$-0.150986\pi$
$992$	652.849	−	362.777i	0.658114	−	0.365702i
$993$	−1641.97	+	1641.97i	−1.65355	+	1.65355i
$994$	369.946	+	20.6053i	0.372179	+	0.0207296i
$995$	1281.15	−	1200.91i	1.28758	−	1.20694i
$996$	−38.0983	+	340.947i	−0.0382513	+	0.342316i
$997$	618.290	−	618.290i	0.620150	−	0.620150i	−0.325419	−	0.945570i	$-0.605505\pi$
$997$	618.290	−	618.290i	0.620150	−	0.620150i	0.945570	+	0.325419i	$0.105505\pi$
$998$	−144.378	−	161.410i	−0.144668	−	0.161734i
$999$	−665.347			−0.666013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.i.a.87.19	yes	136
4.3	odd	2	inner	220.3.i.a.87.53	yes	136
5.3	odd	4	inner	220.3.i.a.43.16	✓	136
11.10	odd	2	inner	220.3.i.a.87.50	yes	136
20.3	even	4	inner	220.3.i.a.43.50	yes	136
44.43	even	2	inner	220.3.i.a.87.16	yes	136
55.43	even	4	inner	220.3.i.a.43.53	yes	136
220.43	odd	4	inner	220.3.i.a.43.19	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.i.a.43.16	✓	136	5.3	odd	4	inner
220.3.i.a.43.19	yes	136	220.43	odd	4	inner
220.3.i.a.43.50	yes	136	20.3	even	4	inner
220.3.i.a.43.53	yes	136	55.43	even	4	inner
220.3.i.a.87.16	yes	136	44.43	even	2	inner
220.3.i.a.87.19	yes	136	1.1	even	1	trivial
220.3.i.a.87.50	yes	136	11.10	odd	2	inner
220.3.i.a.87.53	yes	136	4.3	odd	2	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33338 - 1.49067i) q^{2} +(3.87627 + 3.87627i) q^{3} +(-0.444207 + 3.97526i) q^{4} +(3.64792 - 3.41945i) q^{5} +(0.609714 - 10.9468i) q^{6} +(5.44609 + 5.44609i) q^{7} +(6.51810 - 4.63836i) q^{8} +21.0509i q^{9} +(-9.96134 - 0.878432i) q^{10} +(7.73363 - 7.82247i) q^{11} +(-17.1310 + 13.6873i) q^{12} +(-14.7946 - 14.7946i) q^{13} +(0.856637 - 15.3800i) q^{14} +(27.3951 + 0.885606i) q^{15} +(-15.6054 - 3.53167i) q^{16} +(-5.69580 + 5.69580i) q^{17} +(31.3800 - 28.0688i) q^{18} +21.1920i q^{19} +(11.9728 + 16.0204i) q^{20} +42.2210i q^{21} +(-21.9726 - 1.09800i) q^{22} +(7.64133 + 7.64133i) q^{23} +(43.2454 + 7.28640i) q^{24} +(1.61467 - 24.9478i) q^{25} +(-2.32710 + 41.7806i) q^{26} +(-46.7126 + 46.7126i) q^{27} +(-24.0688 + 19.2304i) q^{28} +2.11660 q^{29} +(-35.2078 - 42.0179i) q^{30} -23.3398i q^{31} +(15.5433 + 27.9715i) q^{32} +(60.2996 - 0.344346i) q^{33} +(16.0852 + 0.895915i) q^{34} +(38.4895 + 1.24426i) q^{35} +(-83.6829 - 9.35096i) q^{36} +(7.12170 + 7.12170i) q^{37} +(31.5904 - 28.2570i) q^{38} -114.695i q^{39} +(7.91689 - 39.2087i) q^{40} -13.4770i q^{41} +(62.9377 - 56.2965i) q^{42} +(-18.4300 + 18.4300i) q^{43} +(27.6610 + 34.2180i) q^{44} +(71.9827 + 76.7922i) q^{45} +(1.20194 - 21.5795i) q^{46} +(25.7009 - 25.7009i) q^{47} +(-46.8009 - 74.1803i) q^{48} +10.3197i q^{49} +(-39.3420 + 30.8579i) q^{50} -44.1569 q^{51} +(65.3840 - 52.2403i) q^{52} +(-10.8004 + 10.8004i) q^{53} +(131.919 + 7.34763i) q^{54} +(1.46313 - 54.9805i) q^{55} +(60.7590 + 10.2373i) q^{56} +(-82.1460 + 82.1460i) q^{57} +(-2.82223 - 3.15516i) q^{58} -84.0088 q^{59} +(-15.6896 + 108.509i) q^{60} -87.3519i q^{61} +(-34.7919 + 31.1207i) q^{62} +(-114.645 + 114.645i) q^{63} +(20.9713 - 60.4666i) q^{64} +(-104.559 - 3.38009i) q^{65} +(-80.9155 - 89.4278i) q^{66} +(-55.9563 + 55.9563i) q^{67} +(-20.1122 - 25.1724i) q^{68} +59.2397i q^{69} +(-49.4663 - 59.0344i) q^{70} +24.0536i q^{71} +(97.6417 + 137.212i) q^{72} +(69.0302 + 69.0302i) q^{73} +(1.12020 - 20.1120i) q^{74} +(102.963 - 90.4455i) q^{75} +(-84.2438 - 9.41364i) q^{76} +(84.7198 - 0.483800i) q^{77} +(-170.973 + 152.932i) q^{78} -47.8344i q^{79} +(-69.0035 + 40.4785i) q^{80} -172.683 q^{81} +(-20.0898 + 17.9699i) q^{82} +(11.0631 - 11.0631i) q^{83} +(-167.839 - 18.7548i) q^{84} +(-1.30131 + 40.2543i) q^{85} +(52.0472 + 2.89893i) q^{86} +(8.20451 + 8.20451i) q^{87} +(14.1252 - 86.8590i) q^{88} -90.4306i q^{89} +(18.4918 - 209.696i) q^{90} -161.145i q^{91} +(-33.7706 + 26.9819i) q^{92} +(90.4712 - 90.4712i) q^{93} +(-72.5807 - 4.04261i) q^{94} +(72.4652 + 77.3069i) q^{95} +(-48.1752 + 168.675i) q^{96} +(-88.2136 - 88.2136i) q^{97} +(15.3833 - 13.7601i) q^{98} +(164.670 + 162.800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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