LMFDB - Embedded newform 105.3.r.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(19,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("105.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.r (of order $6$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	105.19
Dual form			105.3.r.a.94.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32532 - 0.765175i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.829016 - 1.43590i) q^{4} +(-3.72620 + 3.33398i) q^{5} -2.65064i q^{6} +(6.34933 + 2.94719i) q^{7} +8.65876i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.32532 - 0.765175i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.829016 - 1.43590i) q^{4} +(-3.72620 + 3.33398i) q^{5} -2.65064i q^{6} +(6.34933 + 2.94719i) q^{7} +8.65876i q^{8} +(-1.50000 + 2.59808i) q^{9} +(7.48949 - 1.56739i) q^{10} +(6.68282 + 11.5750i) q^{11} +(1.43590 - 2.48705i) q^{12} -15.5994 q^{13} +(-6.15979 - 8.76433i) q^{14} +(-8.22795 - 2.70200i) q^{15} +(3.30940 - 5.73206i) q^{16} +(10.4267 + 18.0595i) q^{17} +(3.97596 - 2.29552i) q^{18} +(23.3408 + 13.4758i) q^{19} +(7.87633 + 2.58653i) q^{20} +(1.07789 + 12.0763i) q^{21} -20.4541i q^{22} +(-20.1960 - 11.6602i) q^{23} +(-12.9881 + 7.49871i) q^{24} +(2.76920 - 24.8462i) q^{25} +(20.6743 + 11.9363i) q^{26} -5.19615 q^{27} +(-1.03183 - 11.5603i) q^{28} -43.9323 q^{29} +(8.83718 + 9.87684i) q^{30} +(27.3477 - 15.7892i) q^{31} +(21.2228 - 12.2530i) q^{32} +(-11.5750 + 20.0485i) q^{33} -31.9129i q^{34} +(-33.4848 + 10.1867i) q^{35} +4.97409 q^{36} +(-30.6172 - 17.6768i) q^{37} +(-20.6227 - 35.7196i) q^{38} +(-13.5095 - 23.3992i) q^{39} +(-28.8681 - 32.2643i) q^{40} -19.4847i q^{41} +(7.81196 - 16.8298i) q^{42} +18.7524i q^{43} +(11.0803 - 19.1917i) q^{44} +(-3.07262 - 14.6819i) q^{45} +(17.8441 + 30.9069i) q^{46} +(1.46083 - 2.53023i) q^{47} +11.4641 q^{48} +(31.6281 + 37.4254i) q^{49} +(-22.6817 + 30.8102i) q^{50} +(-18.0595 + 31.2800i) q^{51} +(12.9322 + 22.3992i) q^{52} +(51.8892 - 29.9582i) q^{53} +(6.88657 + 3.97596i) q^{54} +(-63.4923 - 20.8504i) q^{55} +(-25.5191 + 54.9774i) q^{56} +46.6816i q^{57} +(58.2244 + 33.6159i) q^{58} +(14.7210 - 8.49916i) q^{59} +(2.94131 + 14.0545i) q^{60} +(83.2155 + 48.0445i) q^{61} -48.3259 q^{62} +(-17.1810 + 12.0753i) q^{63} -63.9779 q^{64} +(58.1267 - 52.0082i) q^{65} +(30.6812 - 17.7138i) q^{66} +(-29.6807 + 17.1362i) q^{67} +(17.2877 - 29.9432i) q^{68} -40.3920i q^{69} +(52.1727 + 12.1211i) q^{70} +76.6463 q^{71} +(-22.4961 - 12.9881i) q^{72} +(23.9200 + 41.4306i) q^{73} +(27.0517 + 46.8550i) q^{74} +(39.6674 - 17.3636i) q^{75} -44.6866i q^{76} +(8.31774 + 93.1890i) q^{77} +41.3486i q^{78} +(-25.8537 + 44.7799i) q^{79} +(6.77903 + 32.3923i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-14.9092 + 25.8235i) q^{82} +13.1844 q^{83} +(16.4468 - 11.5592i) q^{84} +(-99.0619 - 32.5312i) q^{85} +(14.3488 - 24.8529i) q^{86} +(-38.0465 - 65.8984i) q^{87} +(-100.225 + 57.8650i) q^{88} +(-46.8569 - 27.0529i) q^{89} +(-7.16203 + 21.8094i) q^{90} +(-99.0461 - 45.9746i) q^{91} +38.6658i q^{92} +(47.3675 + 27.3477i) q^{93} +(-3.87214 + 2.23558i) q^{94} +(-131.901 + 27.6040i) q^{95} +(36.7590 + 21.2228i) q^{96} +95.2693 q^{97} +(-13.2804 - 73.8017i) q^{98} -40.0969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9	$ 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39} + 330 q^{40} + 320 q^{44} + 18 q^{45} - 60 q^{46} + 356 q^{49} + 12 q^{51} - 468 q^{56} - 804 q^{59} - 198 q^{60} + 336 q^{61} - 400 q^{64} - 46 q^{65} - 108 q^{66} - 438 q^{70} + 344 q^{71} + 900 q^{74} + 144 q^{75} - 20 q^{79} + 1140 q^{80} - 144 q^{81} + 780 q^{84} + 304 q^{85} + 144 q^{86} + 24 q^{89} - 224 q^{91} - 924 q^{94} - 342 q^{95} + 900 q^{96} + 168 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9 + 78 * q^10 - 28 * q^11 + 60 * q^14 - 24 * q^15 - 40 * q^16 - 60 * q^19 + 12 * q^21 - 34 * q^25 - 96 * q^26 - 88 * q^29 + 84 * q^31 - 170 * q^35 - 192 * q^36 + 36 * q^39 + 330 * q^40 + 320 * q^44 + 18 * q^45 - 60 * q^46 + 356 * q^49 + 12 * q^51 - 468 * q^56 - 804 * q^59 - 198 * q^60 + 336 * q^61 - 400 * q^64 - 46 * q^65 - 108 * q^66 - 438 * q^70 + 344 * q^71 + 900 * q^74 + 144 * q^75 - 20 * q^79 + 1140 * q^80 - 144 * q^81 + 780 * q^84 + 304 * q^85 + 144 * q^86 + 24 * q^89 - 224 * q^91 - 924 * q^94 - 342 * q^95 + 900 * q^96 + 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.32532	−	0.765175i	−0.662661	−	0.382587i	0.130629	−	0.991431i	$-0.458300\pi$
$2$	−1.32532	−	0.765175i	−0.662661	−	0.382587i	−0.793290	+	0.608844i	$0.791634\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	−0.829016	−	1.43590i	−0.207254	−	0.358974i
$5$	−3.72620	+	3.33398i	−0.745241	+	0.666795i
$5$	−3.72620	+	3.33398i	−0.745241	+	0.666795i
$6$		−	2.65064i		−	0.441774i
$7$	6.34933	+	2.94719i	0.907048	+	0.421028i
$7$	6.34933	+	2.94719i	0.907048	+	0.421028i
$8$			8.65876i			1.08235i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	7.48949	−	1.56739i	0.748949	−	0.156739i
$11$	6.68282	+	11.5750i	0.607529	+	1.05227i	0.991646	+	0.128987i	$0.0411726\pi$
$11$	6.68282	+	11.5750i	0.607529	+	1.05227i	−0.384117	+	0.923284i	$0.625494\pi$
$12$	1.43590	−	2.48705i	0.119658	−	0.207254i
$13$	−15.5994			−1.19996			−0.599979	−	0.800016i	$-0.704824\pi$
$13$	−15.5994			−1.19996			−0.599979	+	0.800016i	$0.704824\pi$
$14$	−6.15979	−	8.76433i	−0.439985	−	0.626023i
$15$	−8.22795	−	2.70200i	−0.548530	−	0.180133i
$16$	3.30940	−	5.73206i	0.206838	−	0.358253i
$17$	10.4267	+	18.0595i	0.613333	+	1.06232i	0.990674	+	0.136250i	$0.0435050\pi$
$17$	10.4267	+	18.0595i	0.613333	+	1.06232i	−0.377341	+	0.926074i	$0.623162\pi$
$18$	3.97596	−	2.29552i	0.220887	−	0.127529i
$19$	23.3408	+	13.4758i	1.22846	+	0.709253i	0.966708	−	0.255881i	$-0.0823655\pi$
$19$	23.3408	+	13.4758i	1.22846	+	0.709253i	0.261755	+	0.965134i	$0.415699\pi$
$20$	7.87633	+	2.58653i	0.393816	+	0.129326i
$21$	1.07789	+	12.0763i	0.0513283	+	0.575064i
$22$		−	20.4541i		−	0.929732i
$23$	−20.1960	−	11.6602i	−0.878086	−	0.506963i	−0.00805929	−	0.999968i	$-0.502565\pi$
$23$	−20.1960	−	11.6602i	−0.878086	−	0.506963i	−0.870027	+	0.493004i	$0.835899\pi$
$24$	−12.9881	+	7.49871i	−0.541173	+	0.312446i
$25$	2.76920	−	24.8462i	0.110768	−	0.993846i
$26$	20.6743	+	11.9363i	0.795165	+	0.459088i
$27$	−5.19615			−0.192450
$28$	−1.03183	−	11.5603i	−0.0368511	−	0.412866i
$29$	−43.9323			−1.51491			−0.757453	−	0.652890i	$-0.773557\pi$
$29$	−43.9323			−1.51491			−0.757453	+	0.652890i	$0.773557\pi$
$30$	8.83718	+	9.87684i	0.294573	+	0.329228i
$31$	27.3477	−	15.7892i	0.882183	−	0.509328i	0.0108052	−	0.999942i	$-0.496561\pi$
$31$	27.3477	−	15.7892i	0.882183	−	0.509328i	0.871377	+	0.490613i	$0.163227\pi$
$32$	21.2228	−	12.2530i	0.663212	−	0.382906i
$33$	−11.5750	+	20.0485i	−0.350757	+	0.607529i
$34$		−	31.9129i		−	0.938614i
$35$	−33.4848	+	10.1867i	−0.956708	+	0.291048i
$36$	4.97409			0.138169
$37$	−30.6172	−	17.6768i	−0.827491	−	0.477752i	0.0255017	−	0.999675i	$-0.491882\pi$
$37$	−30.6172	−	17.6768i	−0.827491	−	0.477752i	−0.852993	+	0.521923i	$0.825215\pi$
$38$	−20.6227	−	35.7196i	−0.542703	−	0.939989i
$39$	−13.5095	−	23.3992i	−0.346398	−	0.599979i
$40$	−28.8681	−	32.2643i	−0.721703	−	0.806608i
$41$		−	19.4847i		−	0.475237i	−0.971359	−	0.237618i	$-0.923633\pi$
$41$		−	19.4847i		−	0.475237i	0.971359	−	0.237618i	$-0.0763667\pi$
$42$	7.81196	−	16.8298i	0.185999	−	0.400710i
$43$			18.7524i			0.436102i	0.975937	+	0.218051i	$0.0699699\pi$
$43$			18.7524i			0.436102i	−0.975937	+	0.218051i	$0.930030\pi$
$44$	11.0803	−	19.1917i	0.251826	−	0.436175i
$45$	−3.07262	−	14.6819i	−0.0682804	−	0.326265i
$46$	17.8441	+	30.9069i	0.387915	+	0.671889i
$47$	1.46083	−	2.53023i	0.0310815	−	0.0538348i	−0.850066	−	0.526676i	$-0.823438\pi$
$47$	1.46083	−	2.53023i	0.0310815	−	0.0538348i	0.881148	+	0.472841i	$0.156772\pi$
$48$	11.4641			0.238836
$49$	31.6281	+	37.4254i	0.645471	+	0.763785i
$50$	−22.6817	+	30.8102i	−0.453634	+	0.616204i
$51$	−18.0595	+	31.2800i	−0.354108	+	0.613333i
$52$	12.9322	+	22.3992i	0.248696	+	0.430754i
$53$	51.8892	−	29.9582i	0.979041	−	0.565250i	0.0770605	−	0.997026i	$-0.475447\pi$
$53$	51.8892	−	29.9582i	0.979041	−	0.565250i	0.901980	+	0.431777i	$0.142113\pi$
$54$	6.88657	+	3.97596i	0.127529	+	0.0736290i
$55$	−63.4923	−	20.8504i	−1.15441	−	0.379098i
$56$	−25.5191	+	54.9774i	−0.455697	+	0.981739i
$57$			46.6816i			0.818975i
$58$	58.2244	+	33.6159i	1.00387	+	0.579584i
$59$	14.7210	−	8.49916i	0.249508	−	0.144054i	−0.370031	−	0.929019i	$-0.620653\pi$
$59$	14.7210	−	8.49916i	0.249508	−	0.144054i	0.619539	+	0.784966i	$0.287320\pi$
$60$	2.94131	+	14.0545i	0.0490218	+	0.234242i
$61$	83.2155	+	48.0445i	1.36419	+	0.787615i	0.990178	−	0.139810i	$-0.0446492\pi$
$61$	83.2155	+	48.0445i	1.36419	+	0.787615i	0.374010	+	0.927425i	$0.377983\pi$
$62$	−48.3259			−0.779450
$63$	−17.1810	+	12.0753i	−0.272715	+	0.191671i
$64$	−63.9779			−0.999655
$65$	58.1267	−	52.0082i	0.894257	−	0.800126i
$66$	30.6812	−	17.7138i	0.464866	−	0.268390i
$67$	−29.6807	+	17.1362i	−0.442996	+	0.255764i	−0.704867	−	0.709339i	$-0.748994\pi$
$67$	−29.6807	+	17.1362i	−0.442996	+	0.255764i	0.261872	+	0.965103i	$0.415660\pi$
$68$	17.2877	−	29.9432i	0.254231	−	0.440342i
$69$		−	40.3920i		−	0.585391i
$70$	52.1727	+	12.1211i	0.745324	+	0.173158i
$71$	76.6463			1.07953			0.539763	−	0.841817i	$-0.318514\pi$
$71$	76.6463			1.07953			0.539763	+	0.841817i	$0.318514\pi$
$72$	−22.4961	−	12.9881i	−0.312446	−	0.180391i
$73$	23.9200	+	41.4306i	0.327671	+	0.567543i	0.982049	−	0.188625i	$-0.0604029\pi$
$73$	23.9200	+	41.4306i	0.327671	+	0.567543i	−0.654378	+	0.756167i	$0.727070\pi$
$74$	27.0517	+	46.8550i	0.365564	+	0.633175i
$75$	39.6674	−	17.3636i	0.528899	−	0.231515i
$76$		−	44.6866i		−	0.587982i
$77$	8.31774	+	93.1890i	0.108023	+	1.21025i
$78$			41.3486i			0.530110i
$79$	−25.8537	+	44.7799i	−0.327262	+	0.566834i	−0.981968	−	0.189050i	$-0.939459\pi$
$79$	−25.8537	+	44.7799i	−0.327262	+	0.566834i	0.654706	+	0.755884i	$0.272793\pi$
$80$	6.77903	+	32.3923i	0.0847378	+	0.404904i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−14.9092	+	25.8235i	−0.181820	+	0.314921i
$83$	13.1844			0.158848			0.0794241	−	0.996841i	$-0.474692\pi$
$83$	13.1844			0.158848			0.0794241	+	0.996841i	$0.474692\pi$
$84$	16.4468	−	11.5592i	0.195795	−	0.137610i
$85$	−99.0619	−	32.5312i	−1.16543	−	0.382720i
$86$	14.3488	−	24.8529i	0.166847	−	0.288988i
$87$	−38.0465	−	65.8984i	−0.437316	−	0.757453i
$88$	−100.225	+	57.8650i	−1.13892	+	0.657556i
$89$	−46.8569	−	27.0529i	−0.526482	−	0.303965i	0.213100	−	0.977030i	$-0.431644\pi$
$89$	−46.8569	−	27.0529i	−0.526482	−	0.303965i	−0.739583	+	0.673066i	$0.764977\pi$
$90$	−7.16203	+	21.8094i	−0.0795781	+	0.242326i
$91$	−99.0461	−	45.9746i	−1.08842	−	0.505215i
$92$			38.6658i			0.420281i
$93$	47.3675	+	27.3477i	0.509328	+	0.294061i
$94$	−3.87214	+	2.23558i	−0.0411930	+	0.0237828i
$95$	−131.901	+	27.6040i	−1.38843	+	0.290569i
$96$	36.7590	+	21.2228i	0.382906	+	0.221071i
$97$	95.2693			0.982157			0.491079	−	0.871115i	$-0.336603\pi$
$97$	95.2693			0.982157			0.491079	+	0.871115i	$0.336603\pi$
$98$	−13.2804	−	73.8017i	−0.135514	−	0.753079i
$99$	−40.0969			−0.405019
$100$	−37.9722	+	16.6216i	−0.379722	+	0.166216i
$101$	20.9559	−	12.0989i	0.207485	−	0.119791i	−0.392657	−	0.919685i	$-0.628444\pi$
$101$	20.9559	−	12.0989i	0.207485	−	0.119791i	0.600142	+	0.799894i	$0.295111\pi$
$102$	47.8693	−	27.6374i	0.469307	−	0.270955i
$103$	59.7184	−	103.435i	0.579790	−	1.00423i	−0.415713	−	0.909496i	$-0.636468\pi$
$103$	59.7184	−	103.435i	0.579790	−	1.00423i	0.995503	−	0.0947303i	$-0.0301989\pi$
$104$		−	135.072i		−	1.29877i
$105$	−44.2787	−	41.4053i	−0.421702	−	0.394336i
$106$	−91.6931			−0.865029
$107$	−15.7438	−	9.08971i	−0.147139	−	0.0849506i	0.424623	−	0.905370i	$-0.360407\pi$
$107$	−15.7438	−	9.08971i	−0.147139	−	0.0849506i	−0.571762	+	0.820420i	$0.693740\pi$
$108$	4.30769	+	7.46114i	0.0398860	+	0.0690846i
$109$	55.8094	+	96.6646i	0.512012	+	0.886831i	0.999903	+	0.0139267i	$0.00443315\pi$
$109$	55.8094	+	96.6646i	0.512012	+	0.886831i	−0.487891	+	0.872905i	$0.662234\pi$
$110$	68.1935	+	76.2162i	0.619941	+	0.692874i
$111$		−	61.2343i		−	0.551661i
$112$	37.9060	−	26.6413i	0.338446	−	0.237869i
$113$		−	73.3681i		−	0.649275i	−0.945838	−	0.324638i	$-0.894758\pi$
$113$		−	73.3681i		−	0.649275i	0.945838	−	0.324638i	$-0.105242\pi$
$114$	35.7196	−	61.8681i	0.313330	−	0.542703i
$115$	114.129	−	23.8848i	0.992427	−	0.207694i
$116$	36.4206	+	63.0822i	0.313970	+	0.543812i
$117$	23.3992	−	40.5285i	0.199993	−	0.346398i
$118$	−26.0134			−0.220452
$119$	12.9775	+	145.395i	0.109055	+	1.22181i
$120$	23.3960	−	71.2439i	0.194966	−	0.593699i
$121$	−28.8202	+	49.9180i	−0.238183	+	0.412546i
$122$	−73.5248	−	127.349i	−0.602663	−	1.04384i
$123$	29.2271	−	16.8742i	0.237618	−	0.137189i
$124$	−45.3433	−	26.1790i	−0.365672	−	0.211121i
$125$	72.5179	+	101.814i	0.580143	+	0.814514i
$126$	32.0101	−	2.85711i	0.254048	−	0.0226755i
$127$		−	175.469i		−	1.38165i	−0.723022	−	0.690825i	$-0.757248\pi$
$127$		−	175.469i		−	1.38165i	0.723022	−	0.690825i	$-0.242752\pi$
$128$	−0.0998682	−	0.0576589i	−0.000780220	−	0.000450460i
$129$	−28.1286	+	16.2400i	−0.218051	+	0.125892i
$130$	−116.832	+	24.4505i	−0.898707	+	0.188081i
$131$	−145.101	−	83.7743i	−1.10764	−	0.639499i	−0.169426	−	0.985543i	$-0.554191\pi$
$131$	−145.101	−	83.7743i	−1.10764	−	0.639499i	−0.938218	+	0.346044i	$0.887525\pi$
$132$	38.3834			0.290783
$133$	108.483	+	154.352i	0.815659	+	1.16054i
$134$	52.4486			0.391408
$135$	19.3619	−	17.3239i	0.143422	−	0.128325i
$136$	−156.373	+	90.2820i	−1.14980	+	0.663838i
$137$	108.617	−	62.7101i	0.792825	−	0.457738i	−0.0481310	−	0.998841i	$-0.515326\pi$
$137$	108.617	−	62.7101i	0.792825	−	0.457738i	0.840956	+	0.541103i	$0.181993\pi$
$138$	−30.9069	+	53.5323i	−0.223963	+	0.387915i
$139$			148.923i			1.07139i	0.844411	+	0.535696i	$0.179951\pi$
$139$			148.923i			1.07139i	−0.844411	+	0.535696i	$0.820049\pi$
$140$	42.3865	+	39.6358i	0.302760	+	0.283113i
$141$	5.06047			0.0358899
$142$	−101.581	−	58.6478i	−0.715359	−	0.413013i
$143$	−104.248	−	180.563i	−0.729009	−	1.26268i
$144$	9.92821	+	17.1962i	0.0689459	+	0.119418i
$145$	163.701	−	146.469i	1.12897	−	1.01013i
$146$		−	73.2118i		−	0.501451i
$147$	−28.7474	+	79.8535i	−0.195561	+	0.543221i
$148$			58.6175i			0.396064i
$149$	64.8655	−	112.350i	0.435339	−	0.754030i	−0.561984	−	0.827148i	$-0.689962\pi$
$149$	64.8655	−	112.350i	0.435339	−	0.754030i	0.997323	+	0.0731184i	$0.0232951\pi$
$150$	−65.8583	−	7.34015i	−0.439055	−	0.0489343i
$151$	−44.9286	−	77.8185i	−0.297540	−	0.515355i	0.678032	−	0.735032i	$-0.262833\pi$
$151$	−44.9286	−	77.8185i	−0.297540	−	0.515355i	−0.975573	+	0.219677i	$0.929500\pi$
$152$	−116.684	+	202.102i	−0.767657	+	1.32962i
$153$	−62.5600			−0.408889
$154$	60.2822	−	129.870i	0.391443	−	0.843311i
$155$	−49.2622	+	150.010i	−0.317821	+	0.967808i
$156$	−22.3992	+	38.7966i	−0.143585	+	0.248696i
$157$	80.7569	+	139.875i	0.514375	+	0.890923i	0.999861	+	0.0166790i	$0.00530935\pi$
$157$	80.7569	+	139.875i	0.514375	+	0.890923i	−0.485486	+	0.874244i	$0.661357\pi$
$158$	68.5289	−	39.5652i	0.433727	−	0.250412i
$159$	89.8747	+	51.8892i	0.565250	+	0.326347i
$160$	−38.2293	+	116.413i	−0.238933	+	0.727584i
$161$	−93.8663	−	133.556i	−0.583021	−	0.829539i
$162$			13.7731i			0.0850194i
$163$	−91.5483	−	52.8555i	−0.561646	−	0.324267i	0.192160	−	0.981364i	$-0.438451\pi$
$163$	−91.5483	−	52.8555i	−0.561646	−	0.324267i	−0.753806	+	0.657097i	$0.771784\pi$
$164$	−27.9780	+	16.1531i	−0.170598	+	0.0984947i
$165$	−23.7104	−	113.295i	−0.143699	−	0.686639i
$166$	−17.4736	−	10.0884i	−0.105262	−	0.0607733i
$167$	90.4269			0.541478			0.270739	−	0.962653i	$-0.412732\pi$
$167$	90.4269			0.541478			0.270739	+	0.962653i	$0.412732\pi$
$168$	−104.566	+	9.33323i	−0.622418	+	0.0555549i
$169$	74.3427			0.439898
$170$	106.397	+	118.914i	0.625863	+	0.699493i
$171$	−70.0224	+	40.4274i	−0.409488	+	0.236418i
$172$	26.9265	−	15.5460i	0.156549	−	0.0903838i
$173$	26.5209	−	45.9355i	0.153300	−	0.265523i	−0.779139	−	0.626852i	$-0.784343\pi$
$173$	26.5209	−	45.9355i	0.153300	−	0.265523i	0.932439	+	0.361328i	$0.117677\pi$
$174$			116.449i			0.669246i
$175$	90.8090	−	149.595i	0.518909	−	0.854830i
$176$	88.4646			0.502640
$177$	25.4975	+	14.7210i	0.144054	+	0.0831694i
$178$	41.4003	+	71.7075i	0.232586	+	0.402851i
$179$	−19.0032	−	32.9145i	−0.106163	−	0.183880i	0.808050	−	0.589114i	$-0.200523\pi$
$179$	−19.0032	−	32.9145i	−0.106163	−	0.183880i	−0.914213	+	0.405234i	$0.867190\pi$
$180$	−18.5345	+	16.5835i	−0.102969	+	0.0921306i
$181$		−	195.548i		−	1.08037i	−0.841545	−	0.540187i	$-0.818354\pi$
$181$		−	195.548i		−	1.08037i	0.841545	−	0.540187i	$-0.181646\pi$
$182$	96.0893	+	136.719i	0.527963	+	0.751201i
$183$			166.431i			0.909459i
$184$	100.963	−	174.872i	0.548709	−	0.950393i
$185$	173.020	−	36.2095i	0.935243	−	0.195727i
$186$	−41.8515	−	72.4889i	−0.225008	−	0.389725i
$187$	−139.359	+	241.377i	−0.745236	+	1.29079i
$188$	−4.84421			−0.0257671
$189$	−32.9921	−	15.3141i	−0.174561	−	0.0810268i
$190$	195.933	+	64.3428i	1.03122	+	0.338646i
$191$	−142.750	+	247.250i	−0.747380	+	1.29450i	0.201694	+	0.979449i	$0.435355\pi$
$191$	−142.750	+	247.250i	−0.747380	+	1.29450i	−0.949074	+	0.315052i	$0.897978\pi$
$192$	−55.4065	−	95.9669i	−0.288576	−	0.499827i
$193$	−270.421	+	156.127i	−1.40114	+	0.808950i	−0.994510	−	0.104641i	$-0.966631\pi$
$193$	−270.421	+	156.127i	−1.40114	+	0.808950i	−0.406633	+	0.913592i	$0.633297\pi$
$194$	−126.262	−	72.8976i	−0.650837	−	0.375761i
$195$	128.352	+	42.1497i	0.658213	+	0.216152i
$196$	27.5189	−	76.4410i	0.140403	−	0.390005i
$197$			19.8534i			0.100779i	0.998730	+	0.0503894i	$0.0160462\pi$
$197$			19.8534i			0.100779i	−0.998730	+	0.0503894i	$0.983954\pi$
$198$	53.1413	+	30.6812i	0.268390	+	0.154955i
$199$	10.8150	−	6.24405i	0.0543468	−	0.0313771i	−0.472580	−	0.881288i	$-0.656677\pi$
$199$	10.8150	−	6.24405i	0.0543468	−	0.0313771i	0.526927	+	0.849910i	$0.323344\pi$
$200$	215.137	+	23.9778i	1.07569	+	0.119889i
$201$	−51.4085	−	29.6807i	−0.255764	−	0.147665i
$202$	−37.0311			−0.183322
$203$	−278.941	−	129.477i	−1.37409	−	0.637818i
$204$	59.8865			0.293561
$205$	64.9615	+	72.6040i	0.316886	+	0.354166i
$206$	−158.292	+	91.3900i	−0.768408	+	0.443641i
$207$	60.5879	−	34.9805i	0.292695	−	0.168988i
$208$	−51.6249	+	89.4169i	−0.248196	+	0.429889i
$209$			360.226i			1.72357i
$210$	27.0013	+	88.7562i	0.128577	+	0.422649i
$211$	248.958			1.17989			0.589947	−	0.807442i	$-0.299149\pi$
$211$	248.958			1.17989			0.589947	+	0.807442i	$0.299149\pi$
$212$	−86.0339	−	49.6717i	−0.405820	−	0.234300i
$213$	66.3777	+	114.969i	0.311632	+	0.539763i
$214$	13.9104	+	24.0936i	0.0650020	+	0.112587i
$215$	−62.5200	−	69.8752i	−0.290791	−	0.325001i
$216$		−	44.9923i		−	0.208297i
$217$	220.173	−	19.6519i	1.01462	−	0.0905618i
$218$		−	170.816i		−	0.783558i
$219$	−41.4306	+	71.7599i	−0.189181	+	0.327671i
$220$	22.6971	+	108.454i	0.103169	+	0.492971i
$221$	−162.650	−	281.718i	−0.735974	−	1.27474i
$222$	−46.8550	+	81.1552i	−0.211058	+	0.365564i
$223$	121.412			0.544449			0.272224	−	0.962234i	$-0.412241\pi$
$223$	121.412			0.544449			0.272224	+	0.962234i	$0.412241\pi$
$224$	170.863	−	15.2506i	0.762779	−	0.0680831i
$225$	60.3984	+	44.4638i	0.268437	+	0.197617i
$226$	−56.1394	+	97.2363i	−0.248405	+	0.430249i
$227$	1.27143	+	2.20218i	0.00560100	+	0.00970121i	0.868812	−	0.495142i	$-0.164884\pi$
$227$	1.27143	+	2.20218i	0.00560100	+	0.00970121i	−0.863211	+	0.504843i	$0.831550\pi$
$228$	67.0300	−	38.6998i	0.293991	−	0.169736i
$229$	−29.8283	−	17.2214i	−0.130255	−	0.0752026i	0.433457	−	0.901174i	$-0.357294\pi$
$229$	−29.8283	−	17.2214i	−0.130255	−	0.0752026i	−0.563711	+	0.825972i	$0.690627\pi$
$230$	−169.534	−	55.6736i	−0.737103	−	0.242059i
$231$	−132.580	+	93.1807i	−0.573940	+	0.403380i
$232$		−	380.399i		−	1.63965i
$233$	138.357	+	79.8804i	0.593807	+	0.342834i	0.766601	−	0.642123i	$-0.221946\pi$
$233$	138.357	+	79.8804i	0.593807	+	0.342834i	−0.172795	+	0.984958i	$0.555280\pi$
$234$	−62.0228	+	35.8089i	−0.265055	+	0.153029i
$235$	2.99239	+	14.2986i	0.0127336	+	0.0608449i
$236$	−24.4078	−	14.0919i	−0.103423	−	0.0597113i
$237$	−89.5598			−0.377889
$238$	94.0534	−	202.626i	0.395182	−	0.851368i
$239$	143.736			0.601405			0.300702	−	0.953718i	$-0.402779\pi$
$239$	143.736			0.601405			0.300702	+	0.953718i	$0.402779\pi$
$240$	−42.7176	+	38.2211i	−0.177990	+	0.159254i
$241$	360.060	−	207.880i	1.49402	−	0.862575i	0.494047	−	0.869435i	$-0.335517\pi$
$241$	360.060	−	207.880i	1.49402	−	0.862575i	0.999976	+	0.00686081i	$0.00218388\pi$
$242$	76.3920	−	44.1050i	0.315670	−	0.182252i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$		−	159.319i		−	0.652945i
$245$	−242.628	−	34.0075i	−0.990320	−	0.138806i
$246$	−51.6470			−0.209947
$247$	−364.103	−	210.215i	−1.47410	−	0.851074i
$248$	136.715	+	236.797i	0.551269	+	0.954826i
$249$	11.4180	+	19.7766i	0.0458555	+	0.0794241i
$250$	−18.2038	−	190.426i	−0.0728153	−	0.761702i
$251$			324.436i			1.29257i	0.763094	+	0.646287i	$0.223679\pi$
$251$			324.436i			1.29257i	−0.763094	+	0.646287i	$0.776321\pi$
$252$	31.5822	+	14.6596i	0.125326	+	0.0581731i
$253$		−	311.691i		−	1.23198i
$254$	−134.265	+	232.553i	−0.528602	+	0.915565i
$255$	−36.9933	−	176.766i	−0.145072	−	0.693199i
$256$	128.044	+	221.779i	0.500172	+	0.866324i
$257$	−106.413	+	184.312i	−0.414057	+	0.717168i	−0.995329	−	0.0965411i	$-0.969222\pi$
$257$	−106.413	+	184.312i	−0.414057	+	0.717168i	0.581272	+	0.813710i	$0.302555\pi$
$258$	49.7059			0.192658
$259$	−142.302	−	202.471i	−0.549427	−	0.781741i
$260$	−122.866	−	40.3484i	−0.472563	−	0.155186i
$261$	65.8984	−	114.139i	0.252484	−	0.437316i
$262$	128.204	+	222.056i	0.489328	+	0.847541i
$263$	75.5406	−	43.6134i	0.287227	−	0.165830i	−0.349464	−	0.936950i	$-0.613636\pi$
$263$	75.5406	−	43.6134i	0.287227	−	0.165830i	0.636690	+	0.771119i	$0.280303\pi$
$264$	−173.595	−	100.225i	−0.657556	−	0.379640i
$265$	−93.4696	+	284.628i	−0.352716	+	1.07407i
$266$	−25.6679	−	287.575i	−0.0964960	−	1.08111i
$267$		−	93.7139i		−	0.350988i
$268$	49.2115	+	28.4123i	0.183625	+	0.106016i
$269$	−91.3238	+	52.7258i	−0.339494	+	0.196007i	−0.660048	−	0.751223i	$-0.729464\pi$
$269$	−91.3238	+	52.7258i	−0.339494	+	0.196007i	0.320554	+	0.947230i	$0.396131\pi$
$270$	−38.9165	+	8.14442i	−0.144135	+	0.0301645i
$271$	−245.661	−	141.833i	−0.906500	−	0.523368i	−0.0271965	−	0.999630i	$-0.508658\pi$
$271$	−245.661	−	141.833i	−0.906500	−	0.523368i	−0.879303	+	0.476262i	$0.841991\pi$
$272$	138.024			0.507442
$273$	−16.8145	−	188.384i	−0.0615917	−	0.690052i
$274$	−191.937			−0.700499
$275$	306.100	−	133.989i	1.11309	−	0.487233i
$276$	−57.9987	+	33.4856i	−0.210140	+	0.121325i
$277$	31.7800	−	18.3482i	0.114729	−	0.0662389i	−0.441537	−	0.897243i	$-0.645567\pi$
$277$	31.7800	−	18.3482i	0.114729	−	0.0662389i	0.556266	+	0.831004i	$0.312233\pi$
$278$	113.952	−	197.371i	0.409901	−	0.709969i
$279$			94.7351i			0.339552i
$280$	−88.2041	−	289.937i	−0.315015	−	1.03549i
$281$	292.564			1.04115			0.520576	−	0.853815i	$-0.325717\pi$
$281$	292.564			1.04115			0.520576	+	0.853815i	$0.325717\pi$
$282$	−6.70675	−	3.87214i	−0.0237828	−	0.0137310i
$283$	46.0381	+	79.7403i	0.162679	+	0.281768i	0.935829	−	0.352456i	$-0.114653\pi$
$283$	46.0381	+	79.7403i	0.162679	+	0.281768i	−0.773150	+	0.634223i	$0.781320\pi$
$284$	−63.5410	−	110.056i	−0.223736	−	0.387522i
$285$	−155.635	−	173.945i	−0.546089	−	0.610334i
$286$			319.073i			1.11564i
$287$	57.4252	−	123.715i	0.200088	−	0.431062i
$288$			73.5179i			0.255271i
$289$	−72.9306	+	126.320i	−0.252355	+	0.437092i
$290$	−329.031	+	68.8592i	−1.13459	+	0.237445i
$291$	82.5056	+	142.904i	0.283524	+	0.491079i
$292$	39.6601	−	68.6933i	0.135822	−	0.235251i
$293$	−248.214			−0.847146			−0.423573	−	0.905862i	$-0.639224\pi$
$293$	−248.214			−0.847146			−0.423573	+	0.905862i	$0.639224\pi$
$294$	99.2015	−	83.8348i	0.337420	−	0.285152i
$295$	−26.5174	+	80.7490i	−0.0898894	+	0.273726i
$296$	153.060	−	265.107i	0.517093	−	0.895631i
$297$	−34.7250	−	60.1454i	−0.116919	−	0.202510i
$298$	−171.935	+	99.2669i	−0.576964	+	0.333111i
$299$	315.046	+	181.892i	1.05367	+	0.608334i
$300$	−57.8173	−	42.5637i	−0.192724	−	0.141879i
$301$	−55.2669	+	119.065i	−0.183611	+	0.395565i
$302$			137.513i			0.455340i
$303$	36.2968	+	20.9559i	0.119791	+	0.0691615i
$304$	154.488	−	89.1938i	0.508185	−	0.293401i
$305$	−470.257	+	98.4149i	−1.54183	+	0.322672i
$306$	82.9121	+	47.8693i	0.270955	+	0.156436i
$307$	−109.013			−0.355090			−0.177545	−	0.984113i	$-0.556816\pi$
$307$	−109.013			−0.355090			−0.177545	+	0.984113i	$0.556816\pi$
$308$	126.914	−	89.1986i	0.412060	−	0.289606i
$309$	206.871			0.669484
$310$	180.072	−	161.118i	0.580878	−	0.519734i
$311$	−179.504	+	103.637i	−0.577183	+	0.333237i	−0.760013	−	0.649908i	$-0.774807\pi$
$311$	−179.504	+	103.637i	−0.577183	+	0.333237i	0.182830	+	0.983144i	$0.441474\pi$
$312$	202.608	−	116.976i	0.649384	−	0.374922i
$313$	116.112	−	201.113i	0.370966	−	0.642532i	−0.618748	−	0.785589i	$-0.712360\pi$
$313$	116.112	−	201.113i	0.370966	−	0.642532i	0.989714	+	0.143057i	$0.0456932\pi$
$314$		−	247.172i		−	0.787173i
$315$	23.7614	−	102.276i	0.0754330	−	0.324686i
$316$	85.7324			0.271305
$317$	−336.182	−	194.095i	−1.06051	−	0.612287i	−0.134938	−	0.990854i	$-0.543084\pi$
$317$	−336.182	−	194.095i	−1.06051	−	0.612287i	−0.925574	+	0.378567i	$0.876417\pi$
$318$	−79.4086	−	137.540i	−0.249712	−	0.432515i
$319$	−293.592	−	508.516i	−0.920350	−	1.59409i
$320$	238.395	−	213.301i	0.744984	−	0.666565i
$321$		−	31.4877i		−	0.0980925i
$322$	22.2096	+	248.828i	0.0689738	+	0.772759i
$323$			562.031i			1.74003i
$324$	−7.46114	+	12.9231i	−0.0230282	+	0.0398860i
$325$	−43.1979	+	387.586i	−0.132917	+	1.19257i
$326$	80.8873	+	140.101i	0.248121	+	0.429757i
$327$	−96.6646	+	167.428i	−0.295610	+	0.512012i
$328$	168.713			0.514370
$329$	16.7324	−	11.7600i	0.0508584	−	0.0357445i
$330$	−55.2669	+	168.295i	−0.167476	+	0.509986i
$331$	−109.863	+	190.288i	−0.331912	+	0.574888i	−0.982887	−	0.184211i	$-0.941027\pi$
$331$	−109.863	+	190.288i	−0.331912	+	0.574888i	0.650975	+	0.759099i	$0.274360\pi$
$332$	−10.9301	−	18.9315i	−0.0329219	−	0.0570224i
$333$	91.8515	−	53.0305i	0.275830	−	0.159251i
$334$	−119.845	−	69.1924i	−0.358816	−	0.207163i
$335$	53.4648	−	162.808i	0.159596	−	0.485993i
$336$	72.7895	+	33.7870i	0.216635	+	0.100556i
$337$			86.9979i			0.258154i	0.991635	+	0.129077i	$0.0412015\pi$
$337$			86.9979i			0.258154i	−0.991635	+	0.129077i	$0.958799\pi$
$338$	−98.5280	−	56.8852i	−0.291503	−	0.168299i
$339$	110.052	−	63.5387i	0.324638	−	0.187430i
$340$	35.4124	+	169.212i	0.104154	+	0.497681i
$341$	365.519	+	211.033i	1.07190	+	0.618864i
$342$	123.736			0.361802
$343$	90.5173	+	330.841i	0.263899	+	0.964550i
$344$	−162.372			−0.472013
$345$	134.666	+	150.509i	0.390336	+	0.436257i
$346$	−70.2974	+	40.5862i	−0.203172	+	0.117301i
$347$	290.307	−	167.609i	0.836619	−	0.483022i	−0.0194948	−	0.999810i	$-0.506206\pi$
$347$	290.307	−	167.609i	0.836619	−	0.483022i	0.856113	+	0.516788i	$0.172872\pi$
$348$	−63.0822	+	109.262i	−0.181271	+	0.313970i
$349$			424.055i			1.21506i	0.794298	+	0.607528i	$0.207839\pi$
$349$			424.055i			1.21506i	−0.794298	+	0.607528i	$0.792161\pi$
$350$	−234.818	+	128.777i	−0.670907	+	0.367934i
$351$	81.0571			0.230932
$352$	283.656	+	163.769i	0.805842	+	0.465253i
$353$	78.6516	+	136.229i	0.222809	+	0.385917i	0.955660	−	0.294473i	$-0.0951440\pi$
$353$	78.6516	+	136.229i	0.222809	+	0.385917i	−0.732851	+	0.680389i	$0.761811\pi$
$354$	−22.5282	−	39.0201i	−0.0636391	−	0.110226i
$355$	−285.600	+	255.537i	−0.804507	+	0.719823i
$356$			89.7090i			0.251992i
$357$	−206.854	+	145.382i	−0.579423	+	0.407233i
$358$			58.1631i			0.162467i
$359$	−135.372	+	234.471i	−0.377080	+	0.653121i	−0.990636	−	0.136530i	$-0.956405\pi$
$359$	−135.372	+	234.471i	−0.377080	+	0.653121i	0.613556	+	0.789651i	$0.289738\pi$
$360$	127.127	−	26.6051i	0.353132	−	0.0739030i
$361$	182.695	+	316.437i	0.506081	+	0.876558i
$362$	−149.628	+	259.163i	−0.413337	+	0.715921i
$363$	−99.8361			−0.275031
$364$	16.0960	+	180.334i	0.0442197	+	0.495422i
$365$	−227.259	−	74.6303i	−0.622629	−	0.204467i
$366$	127.349	−	220.575i	0.347947	−	0.602663i
$367$	−241.128	−	417.646i	−0.657025	−	1.13800i	−0.981382	−	0.192066i	$-0.938481\pi$
$367$	−241.128	−	417.646i	−0.657025	−	1.13800i	0.324357	−	0.945935i	$-0.394852\pi$
$368$	−133.673	+	77.1763i	−0.363243	+	0.209718i
$369$	50.6227	+	29.2271i	0.137189	+	0.0792061i
$370$	−257.014	−	84.4013i	−0.694631	−	0.228112i
$371$	417.754	−	37.2873i	1.12602	−	0.100505i
$372$		−	90.6866i		−	0.243781i
$373$	332.295	+	191.850i	0.890870	+	0.514344i	0.874227	−	0.485517i	$-0.161369\pi$
$373$	332.295	+	191.850i	0.890870	+	0.514344i	0.0166433	+	0.999861i	$0.494702\pi$
$374$	369.391	−	213.268i	0.987677	−	0.570235i
$375$	−89.9191	+	196.951i	−0.239784	+	0.525202i
$376$	21.9087	+	12.6490i	0.0582678	+	0.0336410i
$377$	685.319			1.81782
$378$	32.0072	+	45.5408i	0.0846752	+	0.120478i
$379$	140.636			0.371072			0.185536	−	0.982637i	$-0.440598\pi$
$379$	140.636			0.371072			0.185536	+	0.982637i	$0.440598\pi$
$380$	148.984	+	166.512i	0.392064	+	0.438188i
$381$	263.204	−	151.961i	0.690825	−	0.398848i
$382$	378.378	−	218.457i	0.990519	−	0.571877i
$383$	10.7803	−	18.6720i	0.0281469	−	0.0487519i	−0.851609	−	0.524178i	$-0.824373\pi$
$383$	10.7803	−	18.6720i	0.0281469	−	0.0487519i	0.879756	+	0.475426i	$0.157706\pi$
$384$		−	0.199736i		−	0.000520147i
$385$	−341.684	−	319.510i	−0.887490	−	0.829897i
$386$	477.859			1.23798
$387$	−48.7201	−	28.1286i	−0.125892	−	0.0726837i
$388$	−78.9797	−	136.797i	−0.203556	−	0.352569i
$389$	−196.466	−	340.289i	−0.505054	−	0.874780i	−0.999983	−	0.00584625i	$-0.998139\pi$
$389$	−196.466	−	340.289i	−0.505054	−	0.874780i	0.494928	−	0.868934i	$-0.335194\pi$
$390$	−137.855	−	154.073i	−0.353475	−	0.395059i
$391$		−	486.306i		−	1.24375i
$392$	−324.058	+	273.860i	−0.826679	+	0.698623i
$393$		−	290.203i		−	0.738429i
$394$	15.1913	−	26.3122i	0.0385567	−	0.0667822i
$395$	−52.9590	−	253.055i	−0.134073	−	0.640645i
$396$	33.2410	+	57.5751i	0.0839419	+	0.145392i
$397$	−295.912	+	512.535i	−0.745372	+	1.29102i	0.204649	+	0.978835i	$0.434395\pi$
$397$	−295.912	+	512.535i	−0.745372	+	1.29102i	−0.950021	+	0.312186i	$0.898939\pi$
$398$	−19.1112			−0.0480180
$399$	−137.580	+	296.397i	−0.344811	+	0.742850i
$400$	−133.255	−	98.0991i	−0.333138	−	0.245248i
$401$	63.4311	−	109.866i	0.158182	−	0.273980i	−0.776031	−	0.630695i	$-0.782770\pi$
$401$	63.4311	−	109.866i	0.158182	−	0.273980i	0.934213	+	0.356715i	$0.116103\pi$
$402$	45.4218	+	78.6730i	0.112990	+	0.195704i
$403$	−426.608	+	246.302i	−1.05858	+	0.611172i
$404$	−34.7456	−	20.0604i	−0.0860040	−	0.0496544i
$405$	42.7537	+	14.0400i	0.105565	+	0.0346666i
$406$	270.614	+	385.037i	0.666536	+	0.948367i
$407$		−	472.524i		−	1.16099i
$408$	−270.846	−	156.373i	−0.663838	−	0.383267i
$409$	−492.397	+	284.286i	−1.20390	+	0.695075i	−0.961421	−	0.275081i	$-0.911295\pi$
$409$	−492.397	+	284.286i	−1.20390	+	0.695075i	−0.242483	+	0.970156i	$0.577962\pi$
$410$	−30.5402	−	145.931i	−0.0744883	−	0.355928i
$411$	188.130	+	108.617i	0.457738	+	0.264275i
$412$	−198.030			−0.480655
$413$	118.517	−	10.5784i	0.286966	−	0.0256136i
$414$	−107.065			−0.258610
$415$	−49.1278	+	43.9565i	−0.118380	+	0.105919i
$416$	−331.064	+	191.140i	−0.795826	+	0.459471i
$417$	−223.385	+	128.971i	−0.535696	+	0.309284i
$418$	275.636	−	477.415i	0.659415	−	1.14214i
$419$		−	600.904i		−	1.43414i	−0.697002	−	0.717069i	$-0.745483\pi$
$419$		−	600.904i		−	1.43414i	0.697002	−	0.717069i	$-0.254517\pi$
$420$	−22.7460	+	97.9053i	−0.0541570	+	0.233108i
$421$	−718.912			−1.70763			−0.853815	−	0.520577i	$-0.825717\pi$
$421$	−718.912			−1.70763			−0.853815	+	0.520577i	$0.825717\pi$
$422$	−329.949	−	190.496i	−0.781869	−	0.451413i
$423$	4.38250	+	7.59070i	0.0103605	+	0.0179449i
$424$	259.401	+	449.296i	0.611795	+	1.05966i
$425$	477.583	−	209.052i	1.12372	−	0.491888i
$426$		−	203.162i		−	0.476906i
$427$	386.767	+	550.303i	0.905776	+	1.28877i
$428$			30.1421i			0.0704254i
$429$	180.563	−	312.745i	0.420894	−	0.729009i
$430$	29.3924	+	140.446i	0.0683543	+	0.326618i
$431$	33.7279	+	58.4184i	0.0782549	+	0.135542i	0.902497	−	0.430696i	$-0.141732\pi$
$431$	33.7279	+	58.4184i	0.0782549	+	0.135542i	−0.824242	+	0.566237i	$0.808399\pi$
$432$	−17.1962	+	29.7846i	−0.0398059	+	0.0689459i
$433$	73.3677			0.169440			0.0847202	−	0.996405i	$-0.473000\pi$
$433$	73.3677			0.169440			0.0847202	+	0.996405i	$0.473000\pi$
$434$	−306.837	−	142.426i	−0.706999	−	0.328170i
$435$	361.473	+	118.705i	0.830972	+	0.272885i
$436$	92.5336	−	160.273i	0.212233	−	0.367599i
$437$	−314.260	−	544.315i	−0.719131	−	1.24557i
$438$	109.818	−	63.4033i	0.250725	−	0.144756i
$439$	91.2189	+	52.6653i	0.207788	+	0.119966i	0.600283	−	0.799788i	$-0.295055\pi$
$439$	91.2189	+	52.6653i	0.207788	+	0.119966i	−0.392495	+	0.919754i	$0.628388\pi$
$440$	180.539	−	549.765i	0.410315	−	1.24947i
$441$	−144.676	+	26.0340i	−0.328064	+	0.0590341i
$442$			497.823i			1.12630i
$443$	460.362	+	265.790i	1.03919	+	0.599978i	0.919605	−	0.392845i	$-0.128509\pi$
$443$	460.362	+	265.790i	1.03919	+	0.599978i	0.119588	+	0.992824i	$0.461843\pi$
$444$	−87.9262	+	50.7642i	−0.198032	+	0.114334i
$445$	264.792	−	55.4154i	0.595039	−	0.124529i
$446$	−160.910	−	92.9014i	−0.360785	−	0.208299i
$447$	224.701			0.502686
$448$	−406.217	−	188.555i	−0.906735	−	0.420882i
$449$	−692.156			−1.54155			−0.770775	−	0.637108i	$-0.780131\pi$
$449$	−692.156			−1.54155			−0.770775	+	0.637108i	$0.780131\pi$
$450$	−46.0247	−	105.144i	−0.102277	−	0.233654i
$451$	225.535	−	130.213i	0.500078	−	0.288720i
$452$	−105.349	+	60.8233i	−0.233073	+	0.134565i
$453$	77.8185	−	134.786i	0.171785	−	0.297540i
$454$		−	3.89145i		−	0.00857148i
$455$	522.344	−	158.907i	1.14801	−	0.349245i
$456$	−404.205			−0.886414
$457$	−784.892	−	453.158i	−1.71749	−	0.991592i	−0.923444	−	0.383732i	$-0.874638\pi$
$457$	−784.892	−	453.158i	−1.71749	−	0.991592i	−0.794044	−	0.607860i	$-0.792028\pi$
$458$	26.3547	+	45.6477i	0.0575431	+	0.0996676i
$459$	−54.1785	−	93.8400i	−0.118036	−	0.204444i
$460$	−128.911	−	144.077i	−0.280241	−	0.313210i
$461$			432.778i			0.938780i	0.882991	+	0.469390i	$0.155526\pi$
$461$			432.778i			0.938780i	−0.882991	+	0.469390i	$0.844474\pi$
$462$	247.011	−	22.0473i	0.534655	−	0.0477215i
$463$		−	521.261i		−	1.12583i	−0.826513	−	0.562917i	$-0.809679\pi$
$463$		−	521.261i		−	1.12583i	0.826513	−	0.562917i	$-0.190321\pi$
$464$	−145.390	+	251.822i	−0.313340	+	0.542720i
$465$	−267.678	+	56.0193i	−0.575651	+	0.120472i
$466$	−122.245	−	211.734i	−0.262328	−	0.454366i
$467$	181.357	−	314.119i	0.388344	−	0.672632i	−0.603883	−	0.797073i	$-0.706381\pi$
$467$	181.357	−	314.119i	0.388344	−	0.672632i	0.992227	+	0.124441i	$0.0397139\pi$
$468$	−77.5931			−0.165797
$469$	−238.956	+	21.3284i	−0.509502	+	0.0454764i
$470$	6.97501	−	21.2399i	0.0148405	−	0.0451912i
$471$	−139.875	+	242.271i	−0.296974	+	0.514375i
$472$	73.5922	+	127.466i	0.155916	+	0.270054i
$473$	−217.059	+	125.319i	−0.458898	+	0.264945i
$474$	118.696	+	68.5289i	0.250412	+	0.144576i
$475$	399.457	−	542.612i	0.840963	−	1.14234i
$476$	198.014	−	139.169i	0.415996	−	0.292372i
$477$			179.749i			0.376833i
$478$	−190.496	−	109.983i	−0.398527	−	0.230090i
$479$	545.762	−	315.096i	1.13938	−	0.657820i	0.193102	−	0.981179i	$-0.438145\pi$
$479$	545.762	−	315.096i	1.13938	−	0.657820i	0.946277	+	0.323359i	$0.104812\pi$
$480$	−207.728	+	43.4730i	−0.432766	+	0.0905688i
$481$	477.611	+	275.749i	0.992954	+	0.573282i
$482$	−636.259			−1.32004
$483$	119.043	−	256.462i	0.246466	−	0.530977i
$484$	95.5696			0.197458
$485$	−354.993	+	317.626i	−0.731944	+	0.654898i
$486$	−20.6597	+	11.9279i	−0.0425097	+	0.0245430i
$487$	707.623	−	408.546i	1.45302	−	0.838904i	0.454373	−	0.890812i	$-0.349863\pi$
$487$	707.623	−	408.546i	1.45302	−	0.838904i	0.998652	+	0.0519077i	$0.0165302\pi$
$488$	−416.006	+	720.543i	−0.852471	+	1.47652i
$489$		−	183.097i		−	0.374431i
$490$	295.539	+	230.724i	0.603140	+	0.470865i
$491$	−675.044			−1.37483			−0.687417	−	0.726263i	$-0.741256\pi$
$491$	−675.044			−1.37483			−0.687417	+	0.726263i	$0.741256\pi$
$492$	−48.4594	−	27.9780i	−0.0984947	−	0.0568659i
$493$	−458.067	−	793.396i	−0.929142	−	1.60932i
$494$	321.703	+	557.205i	0.651220	+	1.12795i
$495$	149.409	−	133.682i	0.301837	−	0.270065i
$496$		−	209.011i		−	0.421393i
$497$	486.653	+	225.892i	0.979181	+	0.454510i
$498$		−	34.9471i		−	0.0701750i
$499$	173.757	−	300.955i	0.348210	−	0.603117i	−0.637722	−	0.770267i	$-0.720123\pi$
$499$	173.757	−	300.955i	0.348210	−	0.603117i	0.985931	+	0.167150i	$0.0534564\pi$
$500$	86.0764	−	188.534i	0.172153	−	0.377068i
$501$	78.3120	+	135.640i	0.156311	+	0.270739i
$502$	248.250	−	429.982i	0.494522	−	0.856538i
$503$	−446.658			−0.887989			−0.443994	−	0.896030i	$-0.646439\pi$
$503$	−446.658			−0.887989			−0.443994	+	0.896030i	$0.646439\pi$
$504$	−104.557	−	148.767i	−0.207454	−	0.295172i
$505$	−37.7486	+	114.950i	−0.0747497	+	0.227623i
$506$	−238.498	+	413.091i	−0.471340	+	0.816385i
$507$	64.3827	+	111.514i	0.126988	+	0.219949i
$508$	−251.956	+	145.467i	−0.495977	+	0.286352i
$509$	238.227	+	137.540i	0.468029	+	0.270217i	0.715414	−	0.698700i	$-0.246238\pi$
$509$	238.227	+	137.540i	0.468029	+	0.270217i	−0.247385	+	0.968917i	$0.579571\pi$
$510$	−86.2285	+	262.578i	−0.169076	+	0.514858i
$511$	29.7719	+	333.554i	0.0582620	+	0.652747i
$512$		−	391.443i		−	0.764537i
$513$	−121.282	−	70.0224i	−0.236418	−	0.136496i
$514$	282.062	−	162.849i	0.548759	−	0.316826i
$515$	122.328	+	584.521i	0.237530	+	1.13499i
$516$	46.6381	+	26.9265i	0.0903838	+	0.0521831i
$517$	39.0499			0.0755317
$518$	33.6698	+	377.225i	0.0649996	+	0.728233i
$519$	91.8711			0.177016
$520$	450.327	+	503.306i	0.866013	+	0.967895i
$521$	622.018	−	359.122i	1.19389	−	0.689294i	0.234705	−	0.972067i	$-0.424588\pi$
$521$	622.018	−	359.122i	1.19389	−	0.689294i	0.959187	+	0.282773i	$0.0912543\pi$
$522$	−174.673	+	100.848i	−0.334623	+	0.193195i
$523$	45.2226	−	78.3278i	0.0864677	−	0.149766i	−0.819548	−	0.573011i	$-0.805775\pi$
$523$	45.2226	−	78.3278i	0.0864677	−	0.149766i	0.906016	+	0.423244i	$0.139109\pi$
$524$			277.801i			0.530154i
$525$	303.036	+	6.66026i	0.577211	+	0.0126862i
$526$	−133.487			−0.253778
$527$	570.290	+	329.257i	1.08214	+	0.624776i
$528$	76.6126	+	132.697i	0.145100	+	0.251320i
$529$	7.41849	+	12.8492i	0.0140236	+	0.0242896i
$530$	341.667	−	305.703i	0.644655	−	0.576797i
$531$			50.9950i			0.0960357i
$532$	131.700	−	283.730i	0.247557	−	0.533328i
$533$			303.951i			0.570264i
$534$	−71.7075	+	124.201i	−0.134284	+	0.232586i
$535$	88.9697	−	18.6195i	0.166298	−	0.0348028i
$536$	−148.378	−	256.998i	−0.276825	−	0.479474i
$537$	32.9145	−	57.0097i	0.0612934	−	0.106163i
$538$	161.378			0.299959
$539$	−221.834	+	616.202i	−0.411566	+	1.14323i
$540$	−40.9266	−	13.4400i	−0.0757900	−	0.0248889i
$541$	388.775	−	673.377i	0.718622	−	1.24469i	−0.242924	−	0.970045i	$-0.578106\pi$
$541$	388.775	−	673.377i	0.718622	−	1.24469i	0.961546	−	0.274645i	$-0.0885602\pi$
$542$	217.054	+	375.948i	0.400468	+	0.693631i
$543$	293.321	−	169.349i	0.540187	−	0.311877i
$544$	442.566	+	255.515i	0.813540	+	0.469698i
$545$	−530.235	−	174.125i	−0.972908	−	0.319496i
$546$	−121.862	+	262.536i	−0.223191	+	0.480835i
$547$			350.839i			0.641387i	0.947183	+	0.320694i	$0.103916\pi$
$547$			350.839i			0.641387i	−0.947183	+	0.320694i	$0.896084\pi$
$548$	−180.090	−	103.975i	−0.328632	−	0.189736i
$549$	−249.646	+	144.133i	−0.454729	+	0.262538i
$550$	−508.206	−	56.6414i	−0.924011	−	0.102984i
$551$	−1025.41	−	592.023i	−1.86101	−	1.07445i
$552$	349.744			0.633595
$553$	−296.129	+	208.127i	−0.535495	+	0.376359i
$554$	−56.1582			−0.101369
$555$	204.154	+	228.172i	0.367845	+	0.411120i
$556$	213.839	−	123.460i	0.384602	−	0.222050i
$557$	−216.647	+	125.081i	−0.388954	+	0.224563i	−0.681707	−	0.731625i	$-0.738762\pi$
$557$	−216.647	+	125.081i	−0.388954	+	0.224563i	0.292753	+	0.956188i	$0.405429\pi$
$558$	72.4889	−	125.554i	0.129908	−	0.225008i
$559$		−	292.527i		−	0.523304i
$560$	−52.4240	+	225.649i	−0.0936144	+	0.402944i
$561$	−482.754			−0.860524
$562$	−387.741	−	223.862i	−0.689930	−	0.398331i
$563$	468.524	+	811.508i	0.832192	+	1.44140i	0.896296	+	0.443456i	$0.146248\pi$
$563$	468.524	+	811.508i	0.832192	+	1.44140i	−0.0641039	+	0.997943i	$0.520419\pi$
$564$	−4.19521	−	7.26631i	−0.00743831	−	0.0128835i
$565$	244.608	+	273.385i	0.432934	+	0.483867i
$566$		−	140.909i		−	0.248955i
$567$	−5.60090	−	62.7505i	−0.00987813	−	0.110671i
$568$			663.662i			1.16842i
$569$	447.718	−	775.471i	0.786851	−	1.36287i	−0.141035	−	0.990005i	$-0.545043\pi$
$569$	447.718	−	775.471i	0.786851	−	1.36287i	0.927887	−	0.372862i	$-0.121624\pi$
$570$	73.1684	+	349.621i	0.128366	+	0.613371i
$571$	−396.998	−	687.621i	−0.695269	−	1.20424i	−0.970090	−	0.242745i	$-0.921952\pi$
$571$	−396.998	−	687.621i	−0.695269	−	1.20424i	0.274822	−	0.961495i	$-0.411381\pi$
$572$	−172.847	+	299.380i	−0.302180	+	0.523391i
$573$	−494.499			−0.863001
$574$	−170.770	+	120.022i	−0.297509	+	0.209097i
$575$	−345.637	+	469.503i	−0.601107	+	0.816528i
$576$	95.9669	−	166.220i	0.166609	−	0.288576i
$577$	117.778	+	203.998i	0.204122	+	0.353549i	0.949853	−	0.312698i	$-0.101233\pi$
$577$	117.778	+	203.998i	0.204122	+	0.353549i	−0.745731	+	0.666247i	$0.767899\pi$
$578$	193.313	−	111.609i	0.334452	−	0.193096i
$579$	−468.382	−	270.421i	−0.808950	−	0.467048i
$580$	−346.025	−	113.632i	−0.596595	−	0.195917i
$581$	83.7122	+	38.8570i	0.144083	+	0.0668795i
$582$		−	252.525i		−	0.433891i
$583$	693.532	+	400.411i	1.18959	+	0.686811i
$584$	−358.738	+	207.117i	−0.614277	+	0.354653i
$585$	47.9312	+	229.030i	0.0819336	+	0.391504i
$586$	328.963	+	189.927i	0.561370	+	0.324107i
$587$	−209.863			−0.357518			−0.178759	−	0.983893i	$-0.557208\pi$
$587$	−209.863			−0.357518			−0.178759	+	0.983893i	$0.557208\pi$
$588$	138.494	−	24.9215i	0.235533	−	0.0423834i
$589$	851.088			1.44497
$590$	96.9311	−	86.7280i	0.164290	−	0.146997i
$591$	−29.7801	+	17.1936i	−0.0503894	+	0.0290923i
$592$	−202.649	+	117.000i	−0.342313	+	0.197634i
$593$	−57.9723	+	100.411i	−0.0977610	+	0.169327i	−0.910758	−	0.412941i	$-0.864501\pi$
$593$	−57.9723	+	100.411i	−0.0977610	+	0.169327i	0.812997	+	0.582268i	$0.197835\pi$
$594$			106.283i			0.178927i
$595$	−533.101	−	498.506i	−0.895969	−	0.837825i
$596$	−215.098			−0.360903
$597$	18.7322	+	10.8150i	0.0313771	+	0.0181156i
$598$	−278.358	−	482.131i	−0.465482	−	0.806238i
$599$	179.638	+	311.142i	0.299896	+	0.519435i	0.976112	−	0.217268i	$-0.0697147\pi$
$599$	179.638	+	311.142i	0.299896	+	0.519435i	−0.676216	+	0.736703i	$0.736381\pi$
$600$	150.347	+	343.471i	0.250579	+	0.572452i
$601$		−	8.45971i		−	0.0140761i	−0.999975	−	0.00703803i	$-0.997760\pi$
$601$		−	8.45971i		−	0.0140761i	0.999975	−	0.00703803i	$-0.00224029\pi$
$602$	164.352	−	115.511i	0.273010	−	0.191878i
$603$		−	102.817i		−	0.170509i
$604$	−74.4930	+	129.026i	−0.123333	+	0.213619i
$605$	−59.0357	−	282.091i	−0.0975796	−	0.466266i
$606$	−32.0699	−	55.5467i	−0.0529206	−	0.0916612i
$607$	−463.572	+	802.929i	−0.763709	+	1.32278i	0.177217	+	0.984172i	$0.443291\pi$
$607$	−463.572	+	802.929i	−0.763709	+	1.32278i	−0.940926	+	0.338611i	$0.890043\pi$
$608$	660.476			1.08631
$609$	−47.3543	−	530.541i	−0.0777575	−	0.871168i
$610$	698.546	+	229.397i	1.14516	+	0.376061i
$611$	−22.7882	+	39.4703i	−0.0372965	+	0.0645994i
$612$	51.8632	+	89.8297i	0.0847438	+	0.146781i
$613$	891.498	−	514.707i	1.45432	−	0.839652i	0.455597	−	0.890186i	$-0.349426\pi$
$613$	891.498	−	514.707i	1.45432	−	0.839652i	0.998722	+	0.0505339i	$0.0160923\pi$
$614$	144.477	+	83.4137i	0.235304	+	0.135853i
$615$	−52.6476	+	160.319i	−0.0856059	+	0.260682i
$616$	−806.902	+	72.0213i	−1.30991	+	0.116918i
$617$		−	490.920i		−	0.795657i	−0.917460	−	0.397829i	$-0.869764\pi$
$617$		−	490.920i		−	0.795657i	0.917460	−	0.397829i	$-0.130236\pi$
$618$	−274.170	−	158.292i	−0.443641	−	0.256136i
$619$	519.641	−	300.015i	0.839485	−	0.484677i	−0.0176044	−	0.999845i	$-0.505604\pi$
$619$	519.641	−	300.015i	0.839485	−	0.484677i	0.857089	+	0.515168i	$0.172271\pi$
$620$	256.238	−	53.6253i	0.413288	−	0.0864924i
$621$	104.941	+	60.5879i	0.168988	+	0.0975651i
$622$	317.200			0.509968
$623$	−217.780	−	309.864i	−0.349567	−	0.497374i
$624$	−178.834			−0.286593
$625$	−609.663	−	137.608i	−0.975461	−	0.220172i
$626$	−307.773	+	177.693i	−0.491649	+	0.283854i
$627$	−540.339	+	311.965i	−0.861784	+	0.497551i
$628$	133.897	−	231.917i	0.213212	−	0.369295i
$629$		−	737.242i		−	1.17209i
$630$	−109.751	+	117.367i	−0.174207	+	0.186297i
$631$	−1026.40			−1.62662			−0.813309	−	0.581831i	$-0.802336\pi$
$631$	−1026.40			−1.62662			−0.813309	+	0.581831i	$0.802336\pi$
$632$	−387.739	−	223.861i	−0.613510	−	0.354210i
$633$	215.604	+	373.437i	0.340606	+	0.589947i
$634$	297.033	+	514.476i	0.468506	+	0.811477i
$635$	585.011	+	653.835i	0.921277	+	1.02966i
$636$		−	172.068i		−	0.270547i
$637$	−493.381	−	583.816i	−0.774538	−	0.916509i
$638$			898.595i			1.40846i
$639$	−114.969	+	199.133i	−0.179921	+	0.311632i
$640$	0.564363	−	0.118109i	0.000881817	−	0.000184546i
$641$	−172.759	−	299.227i	−0.269515	−	0.466813i	0.699222	−	0.714905i	$-0.253530\pi$
$641$	−172.759	−	299.227i	−0.269515	−	0.466813i	−0.968737	+	0.248092i	$0.920197\pi$
$642$	−24.0936	+	41.7313i	−0.0375289	+	0.0650020i
$643$	121.941			0.189644			0.0948219	−	0.995494i	$-0.469772\pi$
$643$	121.941			0.189644			0.0948219	+	0.995494i	$0.469772\pi$
$644$	−113.956	+	245.502i	−0.176950	+	0.381215i
$645$	50.6689	−	154.294i	0.0785564	−	0.239215i
$646$	430.052	−	744.872i	0.665715	−	1.15305i
$647$	216.429	+	374.866i	0.334511	+	0.579391i	0.983391	−	0.181500i	$-0.0580954\pi$
$647$	216.429	+	374.866i	0.334511	+	0.579391i	−0.648879	+	0.760891i	$0.724762\pi$
$648$	67.4884	−	38.9644i	0.104149	−	0.0601303i
$649$	196.755	+	113.597i	0.303167	+	0.175034i
$650$	353.822	−	480.622i	0.544342	−	0.739419i
$651$	220.153	+	313.241i	0.338177	+	0.481169i
$652$			175.272i			0.268822i
$653$	98.5453	+	56.8952i	0.150912	+	0.0871289i	0.573554	−	0.819167i	$-0.305564\pi$
$653$	98.5453	+	56.8952i	0.150912	+	0.0871289i	−0.422643	+	0.906296i	$0.638897\pi$
$654$	256.223	−	147.931i	0.391779	−	0.226194i
$655$	819.979	−	171.604i	1.25188	−	0.261991i
$656$	−111.687	−	64.4827i	−0.170255	−	0.0982969i
$657$	−143.520			−0.218447
$658$	−31.1742	+	2.78251i	−0.0473772	+	0.00422873i
$659$	448.120			0.680000			0.340000	−	0.940425i	$-0.389573\pi$
$659$	448.120			0.680000			0.340000	+	0.940425i	$0.389573\pi$
$660$	−143.024	+	127.969i	−0.216703	+	0.193893i
$661$	−917.434	+	529.681i	−1.38795	+	0.801332i	−0.993084	−	0.117407i	$-0.962542\pi$
$661$	−917.434	+	529.681i	−1.38795	+	0.801332i	−0.394865	+	0.918739i	$0.629209\pi$
$662$	291.207	−	168.128i	0.439890	−	0.253970i
$663$	281.718	−	487.951i	0.424915	−	0.735974i
$664$			114.161i			0.171929i
$665$	−918.836	−	213.470i	−1.38171	−	0.321007i
$666$	−162.310			−0.243709
$667$	887.256	+	512.257i	1.33022	+	0.768002i
$668$	−74.9653	−	129.844i	−0.112224	−	0.194377i
$669$	105.146	+	182.118i	0.157169	+	0.272224i
$670$	−195.434	+	174.863i	−0.291693	+	0.260989i
$671$			1284.29i			1.91400i
$672$	170.847	+	243.086i	0.254237	+	0.361736i
$673$			188.436i			0.279993i	0.990152	+	0.139997i	$0.0447092\pi$
$673$			188.436i			0.279993i	−0.990152	+	0.139997i	$0.955291\pi$
$674$	66.5686	−	115.300i	0.0987665	−	0.171069i
$675$	−14.3892	+	129.104i	−0.0213173	+	0.191266i
$676$	−61.6313	−	106.748i	−0.0911705	−	0.157912i
$677$	380.192	−	658.513i	0.561584	−	0.972692i	−0.435774	−	0.900056i	$-0.643525\pi$
$677$	380.192	−	658.513i	0.561584	−	0.972692i	0.997359	−	0.0726362i	$-0.0231412\pi$
$678$	−194.473			−0.286833
$679$	604.896	+	280.777i	0.890864	+	0.413515i
$680$	281.680	−	857.753i	0.414235	−	1.26140i
$681$	−2.20218	+	3.81428i	−0.00323374	+	0.00560100i
$682$	−322.953	−	559.372i	−0.473539	−	0.820193i
$683$	−37.0896	+	21.4137i	−0.0543040	+	0.0313524i	−0.526906	−	0.849923i	$-0.676648\pi$
$683$	−37.0896	+	21.4137i	−0.0543040	+	0.0313524i	0.472602	+	0.881276i	$0.343315\pi$
$684$	116.099	+	67.0300i	0.169736	+	0.0979970i
$685$	−195.655	+	595.797i	−0.285628	+	0.869777i
$686$	133.186	−	507.732i	0.194149	−	0.740134i
$687$		−	59.6566i		−	0.0868364i
$688$	107.490	+	62.0592i	0.156235	+	0.0902023i
$689$	−809.442	+	467.332i	−1.17481	+	0.678275i
$690$	−63.3101	−	302.515i	−0.0917538	−	0.438428i
$691$	−98.9013	−	57.1007i	−0.143128	−	0.0826348i	0.426726	−	0.904381i	$-0.359667\pi$
$691$	−98.9013	−	57.1007i	−0.143128	−	0.0826348i	−0.569854	+	0.821746i	$0.693000\pi$
$692$	−87.9450			−0.127088
$693$	−254.589	−	118.173i	−0.367372	−	0.170524i
$694$	−512.999			−0.739192
$695$	−496.507	−	554.919i	−0.714399	−	0.798444i
$696$	570.599	−	329.435i	0.819826	−	0.473327i
$697$	351.884	−	203.160i	0.504855	−	0.291478i
$698$	324.476	−	562.009i	0.464865	−	0.805170i
$699$			276.714i			0.395871i
$700$	−290.085	−	6.37563i	−0.414408	−	0.00910804i
$701$	1179.03			1.68192			0.840962	−	0.541094i	$-0.181990\pi$
$701$	1179.03			1.68192			0.840962	+	0.541094i	$0.181990\pi$
$702$	−107.427	−	62.0228i	−0.153029	−	0.0883516i
$703$	−476.419	−	825.183i	−0.677695	−	1.17380i
$704$	−427.553	−	740.543i	−0.607320	−	1.05191i
$705$	−18.8563	+	16.8715i	−0.0267466	+	0.0239312i
$706$		−	240.729i		−	0.340976i
$707$	168.714	−	15.0589i	0.238634	−	0.0212996i
$708$		−	48.8157i		−	0.0689487i
$709$	−522.247	+	904.558i	−0.736597	+	1.27582i	0.217423	+	0.976078i	$0.430235\pi$
$709$	−522.247	+	904.558i	−0.736597	+	1.27582i	−0.954019	+	0.299745i	$0.903098\pi$
$710$	574.042	−	120.135i	0.808510	−	0.169204i
$711$	−77.5611	−	134.340i	−0.109087	−	0.188945i
$712$	234.244	−	405.723i	0.328995	−	0.569836i
$713$	−736.417			−1.03284
$714$	385.391	−	34.3987i	0.539763	−	0.0481774i
$715$	990.445	+	325.255i	1.38524	+	0.454901i
$716$	−31.5079	+	54.5733i	−0.0440055	+	0.0762198i
$717$	124.479	+	215.604i	0.173611	+	0.300702i
$718$	358.822	−	207.166i	0.499752	−	0.288532i
$719$	−494.987	−	285.781i	−0.688437	−	0.397470i	0.114589	−	0.993413i	$-0.463445\pi$
$719$	−494.987	−	285.781i	−0.688437	−	0.397470i	−0.803026	+	0.595943i	$0.796778\pi$
$720$	−94.3262	−	30.9760i	−0.131009	−	0.0430222i
$721$	684.016	−	480.744i	0.948705	−	0.666773i
$722$		−	559.175i		−	0.774480i
$723$	623.641	+	360.060i	0.862575	+	0.498008i
$724$	−280.786	+	162.112i	−0.387826	+	0.223912i
$725$	−121.657	+	1091.55i	−0.167803	+	1.50558i
$726$	132.315	+	76.3920i	0.182252	+	0.105223i
$727$	−1086.28			−1.49420			−0.747099	−	0.664713i	$-0.768554\pi$
$727$	−1086.28			−1.49420			−0.747099	+	0.664713i	$0.768554\pi$
$728$	398.083	−	857.617i	0.546818	−	1.17805i
$729$	27.0000			0.0370370
$730$	244.087	+	272.802i	0.334365	+	0.373702i
$731$	−338.659	+	195.525i	−0.463282	+	0.267476i
$732$	238.978	−	137.974i	0.326472	−	0.188489i
$733$	−275.974	+	478.002i	−0.376500	+	0.652117i	−0.990550	−	0.137150i	$-0.956206\pi$
$733$	−275.974	+	478.002i	−0.376500	+	0.652117i	0.614050	+	0.789267i	$0.289539\pi$
$734$			738.020i			1.00548i
$735$	−159.111	−	393.394i	−0.216478	−	0.535230i
$736$	−571.487			−0.776477
$737$	−396.702	−	229.036i	−0.538266	−	0.310768i
$738$	−44.7276	−	77.4705i	−0.0606065	−	0.104974i
$739$	−419.089	−	725.883i	−0.567102	−	0.982250i	−0.996851	−	0.0793012i	$-0.974731\pi$
$739$	−419.089	−	725.883i	−0.567102	−	0.982250i	0.429748	−	0.902949i	$-0.358602\pi$
$740$	−195.429	−	218.421i	−0.264094	−	0.295163i
$741$		−	728.207i		−	0.982735i
$742$	−582.190	−	270.237i	−0.784623	−	0.364201i
$743$		−	1114.83i		−	1.50044i	−0.661186	−	0.750222i	$-0.729947\pi$
$743$		−	1114.83i		−	1.50044i	0.661186	−	0.750222i	$-0.270053\pi$
$744$	−236.797	+	410.144i	−0.318275	+	0.551269i
$745$	132.871	+	634.901i	0.178351	+	0.852216i
$746$	−293.598	−	508.527i	−0.393563	−	0.681671i
$747$	−19.7766	+	34.2541i	−0.0264747	+	0.0458555i
$748$	462.123			0.617812
$749$	−73.1738	−	104.114i	−0.0976953	−	0.139004i
$750$	269.873	−	192.219i	0.359831	−	0.256292i
$751$	−497.021	+	860.866i	−0.661812	+	1.14629i	0.318327	+	0.947981i	$0.396879\pi$
$751$	−497.021	+	860.866i	−0.661812	+	1.14629i	−0.980139	+	0.198312i	$0.936454\pi$
$752$	−9.66896	−	16.7471i	−0.0128577	−	0.0222701i
$753$	−486.654	+	280.970i	−0.646287	+	0.373134i
$754$	−908.268	−	524.389i	−1.20460	−	0.695476i
$755$	426.858	+	140.177i	0.565375	+	0.185665i
$756$	5.36154	+	60.0689i	0.00709199	+	0.0794562i
$757$			531.879i			0.702614i	0.936260	+	0.351307i	$0.114263\pi$
$757$			531.879i			0.702614i	−0.936260	+	0.351307i	$0.885737\pi$
$758$	−186.388	−	107.611i	−0.245895	−	0.141967i
$759$	467.536	−	269.932i	0.615990	−	0.355642i
$760$	−239.017	−	1142.10i	−0.314496	−	1.50276i
$761$	−1107.08	−	639.174i	−1.45477	−	0.839914i	−0.456027	−	0.889966i	$-0.650728\pi$
$761$	−1107.08	−	639.174i	−1.45477	−	0.839914i	−0.998747	+	0.0500522i	$0.984061\pi$
$762$	−465.107			−0.610376
$763$	69.4628	+	778.237i	0.0910391	+	1.01997i
$764$	473.367			0.619590
$765$	233.111	−	208.574i	0.304721	−	0.272645i
$766$	−28.5746	+	16.4976i	−0.0373037	+	0.0215373i
$767$	−229.639	+	132.582i	−0.299399	+	0.172858i
$768$	−221.779	+	384.132i	−0.288775	+	0.500172i
$769$		−	658.330i		−	0.856086i	−0.903758	−	0.428043i	$-0.859203\pi$
$769$		−	658.330i		−	0.856086i	0.903758	−	0.428043i	$-0.140797\pi$
$770$	208.360	+	684.901i	0.270597	+	0.889482i
$771$	−368.625			−0.478112
$772$	448.366	+	258.864i	0.580785	+	0.335316i
$773$	428.534	+	742.243i	0.554378	+	0.960211i	0.997952	+	0.0639731i	$0.0203772\pi$
$773$	428.534	+	742.243i	0.554378	+	0.960211i	−0.443573	+	0.896238i	$0.646289\pi$
$774$	43.0465	+	74.5588i	0.0556157	+	0.0963292i
$775$	−316.569	−	723.208i	−0.408477	−	0.933171i
$776$			824.914i			1.06303i
$777$	180.470	−	388.797i	0.232264	−	0.500383i
$778$			601.324i			0.772910i
$779$	262.572	−	454.788i	0.337063	−	0.583811i
$780$	−45.8828	−	219.242i	−0.0588241	−	0.281080i
$781$	512.214	+	887.180i	0.655843	+	1.13595i
$782$	−372.109	+	644.512i	−0.475843	+	0.824184i
$783$	228.279			0.291544
$784$	319.195	−	57.4381i	0.407136	−	0.0732629i
$785$	−767.257	−	251.961i	−0.977397	−	0.320970i
$786$	−222.056	+	384.612i	−0.282514	+	0.489328i
$787$	−82.3159	−	142.575i	−0.104595	−	0.181163i	0.808978	−	0.587839i	$-0.200021\pi$
$787$	−82.3159	−	142.575i	−0.104595	−	0.181163i	−0.913572	+	0.406676i	$0.866688\pi$
$788$	28.5075	−	16.4588i	0.0361770	−	0.0208868i
$789$	130.840	+	75.5406i	0.165830	+	0.0957422i
$790$	−123.443	+	375.902i	−0.156257	+	0.475825i
$791$	216.230	−	465.839i	0.273363	−	0.588924i
$792$		−	347.190i		−	0.438371i
$793$	−1298.12	−	749.467i	−1.63697	−	0.945104i
$794$	784.358	−	452.849i	0.987857	−	0.570339i
$795$	−507.889	+	106.290i	−0.638854	+	0.133699i
$796$	−17.9316	−	10.3528i	−0.0225272	−	0.0130061i
$797$	264.950			0.332434			0.166217	−	0.986089i	$-0.446845\pi$
$797$	264.950			0.332434			0.166217	+	0.986089i	$0.446845\pi$
$798$	409.133	−	287.549i	0.512698	−	0.360337i
$799$	60.9264			0.0762533
$800$	−245.669	−	561.236i	−0.307087	−	0.701545i
$801$	140.571	−	81.1586i	0.175494	−	0.101322i
$802$	−168.133	+	97.0717i	−0.209642	+	0.121037i
$803$	−319.706	+	553.747i	−0.398139	+	0.689598i
$804$			98.4231i			0.122417i
$805$	795.037	+	184.708i	0.987623	+	0.229451i
$806$	753.858			0.935307
$807$	−158.178	−	91.3238i	−0.196007	−	0.113165i
$808$	104.762	+	181.453i	0.129656	+	0.224570i
$809$	412.372	+	714.249i	0.509730	+	0.882879i	0.999936	+	0.0112723i	$0.00358816\pi$
$809$	412.372	+	714.249i	0.509730	+	0.882879i	−0.490206	+	0.871607i	$0.663079\pi$
$810$	−45.9193	−	51.3215i	−0.0566905	−	0.0633599i
$811$			1009.49i			1.24475i	0.782720	+	0.622375i	$0.213832\pi$
$811$			1009.49i			1.24475i	−0.782720	+	0.622375i	$0.786168\pi$
$812$	45.3306	+	507.869i	0.0558259	+	0.625454i
$813$		−	491.323i		−	0.604333i
$814$	−361.564	+	626.247i	−0.444181	+	0.769345i
$815$	517.347	−	108.270i	0.634781	−	0.132846i
$816$	119.532	+	207.036i	0.146486	+	0.253721i
$817$	−252.704	+	437.696i	−0.309307	+	0.535735i
$818$	870.112			1.06371
$819$	268.015	−	188.367i	0.327246	−	0.229997i
$820$	50.3977	−	153.468i	0.0614606	−	0.187156i
$821$	705.880	−	1222.62i	0.859781	−	1.48918i	−0.0123566	−	0.999924i	$-0.503933\pi$
$821$	705.880	−	1222.62i	0.859781	−	1.48918i	0.872138	−	0.489261i	$-0.162733\pi$
$822$	−166.222	−	287.905i	−0.202217	−	0.350249i
$823$	50.1505	−	28.9544i	0.0609362	−	0.0351815i	−0.469222	−	0.883080i	$-0.655466\pi$
$823$	50.1505	−	28.9544i	0.0609362	−	0.0351815i	0.530159	+	0.847899i	$0.322132\pi$
$824$	895.622	+	517.088i	1.08692	+	0.627533i
$825$	466.074	+	343.112i	0.564938	+	0.415893i
$826$	−165.168	−	76.6665i	−0.199961	−	0.0928165i
$827$			1305.86i			1.57904i	0.613726	+	0.789519i	$0.289670\pi$
$827$			1305.86i			1.57904i	−0.613726	+	0.789519i	$0.710330\pi$
$828$	−100.457	−	57.9987i	−0.121325	−	0.0700468i
$829$	−1071.49	+	618.622i	−1.29250	+	0.746227i	−0.979097	−	0.203392i	$-0.934803\pi$
$829$	−1071.49	+	618.622i	−1.29250	+	0.746227i	−0.313406	+	0.949619i	$0.601470\pi$
$830$	98.7445	−	20.6652i	0.118969	−	0.0248978i
$831$	55.0445	+	31.7800i	0.0662389	+	0.0382430i
$832$	998.020			1.19954
$833$	−346.110	+	961.410i	−0.415498	+	1.15415i
$834$	394.743			0.473312
$835$	−336.949	+	301.481i	−0.403532	+	0.361055i
$836$	517.247	−	298.633i	0.618717	−	0.357216i
$837$	−142.103	+	82.0430i	−0.169776	+	0.0980203i
$838$	−459.797	+	796.391i	−0.548683	+	0.950347i
$839$		−	937.212i		−	1.11706i	−0.829485	−	0.558529i	$-0.811366\pi$
$839$		−	937.212i		−	1.11706i	0.829485	−	0.558529i	$-0.188634\pi$
$840$	358.518	−	383.399i	0.426808	−	0.456427i
$841$	1089.05			1.29494
$842$	952.789	+	550.093i	1.13158	+	0.653317i
$843$	253.367	+	438.845i	0.300555	+	0.520576i
$844$	−206.390	−	357.478i	−0.244538	−	0.423552i
$845$	−277.016	+	247.857i	−0.327830	+	0.293322i
$846$		−	13.4135i		−	0.0158552i
$847$	−330.107	+	232.008i	−0.389737	+	0.273917i
$848$		−	396.575i		−	0.467660i
$849$	−79.7403	+	138.114i	−0.0939226	+	0.162679i
$850$	−792.912	−	88.3730i	−0.932838	−	0.103968i
$851$	412.229	+	714.002i	0.484406	+	0.839015i
$852$	110.056	−	190.623i	0.129174	−	0.223736i
$853$	981.087			1.15016			0.575080	−	0.818097i	$-0.304971\pi$
$853$	981.087			1.15016			0.575080	+	0.818097i	$0.304971\pi$
$854$	−91.5123	−	1025.27i	−0.107157	−	1.20055i
$855$	126.134	−	384.094i	0.147525	−	0.449233i
$856$	78.7057	−	136.322i	0.0919459	−	0.159255i
$857$	93.1575	+	161.353i	0.108702	+	0.188277i	0.915245	−	0.402899i	$-0.131997\pi$
$857$	93.1575	+	161.353i	0.108702	+	0.188277i	−0.806543	+	0.591176i	$0.798664\pi$
$858$	−478.609	+	276.325i	−0.557819	+	0.322057i
$859$	−446.411	−	257.735i	−0.519686	−	0.300041i	0.217120	−	0.976145i	$-0.430334\pi$
$859$	−446.411	−	257.735i	−0.519686	−	0.300041i	−0.736806	+	0.676104i	$0.763667\pi$
$860$	−48.5036	+	147.700i	−0.0563995	+	0.171744i
$861$	235.304	−	21.0024i	0.273292	−	0.0243931i
$862$		−	103.231i		−	0.119757i
$863$	−919.801	−	531.048i	−1.06582	−	0.615351i	−0.138782	−	0.990323i	$-0.544319\pi$
$863$	−919.801	−	531.048i	−1.06582	−	0.615351i	−0.927036	+	0.374972i	$0.877652\pi$
$864$	−110.277	+	63.6684i	−0.127635	+	0.0736902i
$865$	54.3258	+	259.585i	0.0628043	+	0.300099i
$866$	−97.2357	−	56.1391i	−0.112281	−	0.0648257i
$867$	−252.639			−0.291395
$868$	−210.745	−	299.854i	−0.242794	−	0.345454i
$869$	−691.102			−0.795284
$870$	−388.238	−	433.912i	−0.446250	−	0.498749i
$871$	463.003	−	267.315i	0.531576	−	0.306905i
$872$	−836.996	+	483.240i	−0.959858	+	0.554174i
$873$	−142.904	+	247.517i	−0.163693	+	0.283524i
$874$			961.856i			1.10052i
$875$	160.374	+	860.177i	0.183285	+	0.983060i
$876$	137.387			0.156834
$877$	846.866	+	488.938i	0.965639	+	0.557512i	0.897904	−	0.440191i	$-0.145089\pi$
$877$	846.866	+	488.938i	0.965639	+	0.557512i	0.0677352	+	0.997703i	$0.478423\pi$
$878$	−80.5962	−	139.597i	−0.0917953	−	0.158994i
$879$	−214.959	−	372.321i	−0.244550	−	0.423573i
$880$	−329.637	+	294.939i	−0.374588	+	0.335158i
$881$			1248.52i			1.41717i	0.705628	+	0.708583i	$0.250665\pi$
$881$			1248.52i			1.41717i	−0.705628	+	0.708583i	$0.749335\pi$
$882$	211.663	+	76.1992i	0.239981	+	0.0863936i
$883$		−	1022.49i		−	1.15797i	−0.815338	−	0.578985i	$-0.803449\pi$
$883$		−	1022.49i		−	1.15797i	0.815338	−	0.578985i	$-0.196551\pi$
$884$	−269.679	+	467.098i	−0.305067	+	0.528391i
$885$	−144.088	+	30.1547i	−0.162812	+	0.0340731i
$886$	−406.752	−	704.515i	−0.459088	−	0.795164i
$887$	305.093	−	528.436i	0.343960	−	0.595756i	−0.641204	−	0.767370i	$-0.721565\pi$
$887$	305.093	−	528.436i	0.343960	−	0.595756i	0.985164	+	0.171614i	$0.0548982\pi$
$888$	530.214			0.597088
$889$	517.143	−	1114.11i	0.581713	−	1.25322i
$890$	−393.337	−	129.169i	−0.441952	−	0.145134i
$891$	60.1454	−	104.175i	0.0675032	−	0.116919i
$892$	−100.653	−	174.335i	−0.112839	−	0.195443i
$893$	68.1940	−	39.3718i	0.0763650	−	0.0440894i
$894$	−297.801	−	171.935i	−0.333111	−	0.192321i
$895$	180.546	+	59.2900i	0.201728	+	0.0662458i
$896$	−0.464164	−	0.660426i	−0.000518041	−	0.000737083i
$897$			630.092i			0.702444i
$898$	917.329	+	529.620i	1.02152	+	0.589777i
$899$	−1201.45	+	693.655i	−1.33642	+	0.771585i
$900$	13.7742	−	123.587i	0.0153047	−	0.137319i
$901$	1082.06	+	624.729i	1.20096	+	0.693373i
$902$	−398.542			−0.441843
$903$	−226.460	+	20.2131i	−0.250787	+	0.0223844i
$904$	635.277			0.702740
$905$	651.951	+	728.650i	0.720388	+	0.805138i
$906$	−206.269	+	119.090i	−0.227670	+	0.131445i
$907$	−105.125	+	60.6938i	−0.115904	+	0.0669171i	−0.556831	−	0.830626i	$-0.687983\pi$
$907$	−105.125	+	60.6938i	−0.115904	+	0.0669171i	0.440927	+	0.897543i	$0.354650\pi$
$908$	2.10807	−	3.65128i	0.00232166	−	0.00402123i
$909$			72.5935i			0.0798608i
$910$	−813.865	−	189.082i	−0.894357	−	0.207783i
$911$	1512.29			1.66003			0.830016	−	0.557739i	$-0.188331\pi$
$911$	1512.29			1.66003			0.830016	+	0.557739i	$0.188331\pi$
$912$	267.581	+	154.488i	0.293401	+	0.169395i
$913$	88.1090	+	152.609i	0.0965050	+	0.167151i
$914$	693.490	+	1201.16i	0.758741	+	1.31418i
$915$	−554.877	−	620.156i	−0.606423	−	0.677766i
$916$			57.1072i			0.0623441i
$917$	−674.398	−	959.553i	−0.735439	−	1.04640i
$918$			165.824i			0.180636i
$919$	509.381	−	882.274i	0.554278	−	0.960037i	−0.443682	−	0.896185i	$-0.646328\pi$
$919$	509.381	−	882.274i	0.554278	−	0.960037i	0.997959	−	0.0638527i	$-0.0203388\pi$
$920$	206.813	+	988.216i	0.224797	+	1.07415i
$921$	−94.4077	−	163.519i	−0.102506	−	0.177545i
$922$	331.150	−	573.569i	0.359165	−	0.622092i
$923$	−1195.64			−1.29538
$924$	243.709	+	113.123i	0.263754	+	0.122428i
$925$	−523.986	+	711.769i	−0.566472	+	0.769479i
$926$	−398.856	+	690.839i	−0.430730	+	0.746046i
$927$	179.155	+	310.306i	0.193263	+	0.334742i
$928$	−932.366	+	538.302i	−1.00470	+	0.580066i
$929$	107.788	+	62.2316i	0.116026	+	0.0669878i	0.556890	−	0.830586i	$-0.311994\pi$
$929$	107.788	+	62.2316i	0.116026	+	0.0669878i	−0.440864	+	0.897574i	$0.645328\pi$
$930$	397.623	+	130.577i	0.427552	+	0.140405i
$931$	233.887	+	1299.75i	0.251221	+	1.39608i
$932$		−	264.888i		−	0.284215i
$933$	−310.910	−	179.504i	−0.333237	−	0.192394i
$934$	−480.712	+	277.539i	−0.514681	+	0.297151i
$935$	−285.465	−	1364.04i	−0.305310	−	1.45887i
$936$	350.927	+	202.608i	0.374922	+	0.216461i
$937$	1567.35			1.67273			0.836364	−	0.548174i	$-0.184677\pi$
$937$	1567.35			1.67273			0.836364	+	0.548174i	$0.184677\pi$
$938$	333.014	+	154.576i	0.355025	+	0.164793i
$939$	402.225			0.428355
$940$	18.0505	−	16.1505i	0.0192027	−	0.0171814i
$941$	−247.910	+	143.131i	−0.263454	+	0.152105i	−0.625909	−	0.779896i	$-0.715272\pi$
$941$	−247.910	+	143.131i	−0.263454	+	0.152105i	0.362455	+	0.932001i	$0.381939\pi$
$942$	370.759	−	214.058i	0.393587	−	0.227237i
$943$	−227.195	+	393.513i	−0.240928	+	0.417299i
$944$		−	112.509i		−	0.119183i
$945$	173.992	−	52.9316i	0.184119	−	0.0560123i
$946$	383.563			0.405458
$947$	−42.2155	−	24.3732i	−0.0445782	−	0.0257372i	0.477545	−	0.878607i	$-0.341527\pi$
$947$	−42.2155	−	24.3732i	−0.0445782	−	0.0257372i	−0.522123	+	0.852870i	$0.674860\pi$
$948$	74.2465	+	128.599i	0.0783191	+	0.135653i
$949$	−373.138	−	646.295i	−0.393191	−	0.681027i
$950$	−944.602	+	413.480i	−0.994318	+	0.435243i
$951$		−	672.364i		−	0.707008i
$952$	−1258.94	+	112.369i	−1.32242	+	0.118035i
$953$		−	1139.67i		−	1.19587i	−0.801543	−	0.597937i	$-0.795987\pi$
$953$		−	1139.67i		−	1.19587i	0.801543	−	0.597937i	$-0.204013\pi$
$954$	137.540	−	238.226i	0.144172	−	0.249712i
$955$	−292.410	−	1397.23i	−0.306189	−	1.46306i
$956$	−119.159	−	206.390i	−0.124643	−	0.215889i
$957$	508.516	−	880.775i	0.531364	−	0.920350i
$958$	−964.413			−1.00669
$959$	874.465	−	78.0518i	0.911851	−	0.0813887i
$960$	526.407	+	172.868i	0.548341	+	0.180071i
$961$	18.0965	−	31.3440i	0.0188309	−	0.0326160i
$962$	−421.992	−	730.912i	−0.438661	−	0.759783i
$963$	47.2315	−	27.2691i	0.0490462	−	0.0283169i
$964$	−596.990	−	344.672i	−0.619284	−	0.357544i
$965$	487.117	−	1483.34i	0.504785	−	1.53714i
$966$	−354.008	+	248.806i	−0.366468	+	0.257563i
$967$		−	1521.86i		−	1.57380i	−0.617084	−	0.786898i	$-0.711686\pi$
$967$		−	1521.86i		−	1.57380i	0.617084	−	0.786898i	$-0.288314\pi$
$968$	−432.229	−	249.547i	−0.446517	−	0.257797i
$969$	−843.047	+	486.733i	−0.870017	+	0.502305i
$970$	713.518	−	149.324i	0.735586	−	0.153943i
$971$	−1254.51	−	724.294i	−1.29198	−	0.745926i	−0.312977	−	0.949761i	$-0.601326\pi$
$971$	−1254.51	−	724.294i	−1.29198	−	0.745926i	−0.979005	+	0.203834i	$0.934660\pi$
$972$	−25.8461			−0.0265907
$973$	−438.906	+	945.564i	−0.451085	+	0.971803i
$974$	−1250.44			−1.28382
$975$	−618.790	+	270.863i	−0.634656	+	0.277808i
$976$	550.787	−	317.997i	0.564331	−	0.325817i
$977$	202.336	−	116.819i	0.207100	−	0.119569i	−0.392863	−	0.919597i	$-0.628515\pi$
$977$	202.336	−	116.819i	0.207100	−	0.119569i	0.599963	+	0.800028i	$0.295182\pi$
$978$	−140.101	+	242.662i	−0.143252	+	0.248121i
$979$		−	723.158i		−	0.738670i
$980$	152.311	+	376.582i	0.155420	+	0.384267i
$981$	−334.856			−0.341342
$982$	894.650	+	516.526i	0.911049	+	0.525994i
$983$	−851.171	−	1474.27i	−0.865891	−	1.49977i	−0.866160	−	0.499767i	$-0.833419\pi$
$983$	−851.171	−	1474.27i	−0.865891	−	1.49977i	0.000268965	−	1.00000i	$-0.499914\pi$
$984$	146.110	+	253.070i	0.148486	+	0.257185i
$985$	−66.1909	−	73.9779i	−0.0671989	−	0.0751045i
$986$			1402.01i			1.42191i
$987$	32.1306	+	14.9142i	0.0325538	+	0.0151106i
$988$			697.087i			0.705554i
$989$	218.656	−	378.723i	0.221088	−	0.382935i
$990$	−300.306	+	62.8477i	−0.303339	+	0.0634825i
$991$	148.878	+	257.865i	0.150230	+	0.260207i	0.931312	−	0.364222i	$-0.118665\pi$
$991$	148.878	+	257.865i	0.150230	+	0.260207i	−0.781082	+	0.624429i	$0.785332\pi$
$992$	386.929	−	670.181i	0.390050	−	0.675586i
$993$	−380.576			−0.383259
$994$	−472.125	−	671.754i	−0.474975	−	0.675808i
$995$	−19.4814	+	59.3236i	−0.0195793	+	0.0596217i
$996$	18.9315	−	32.7902i	0.0190075	−	0.0329219i
$997$	−363.607	−	629.786i	−0.364701	−	0.631681i	0.624027	−	0.781403i	$-0.285496\pi$
$997$	−363.607	−	629.786i	−0.364701	−	0.631681i	−0.988728	+	0.149722i	$0.952162\pi$
$998$	−460.567	+	265.908i	−0.461490	+	0.266441i
$999$	159.092	+	91.8515i	0.159251	+	0.0919435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.r.a.19.6	✓	32
3.2	odd	2		315.3.bi.e.19.11		32
5.2	odd	4		525.3.o.q.376.6		16
5.3	odd	4		525.3.o.p.376.3		16
5.4	even	2	inner	105.3.r.a.19.11	yes	32
7.2	even	3		735.3.e.a.244.10		32
7.3	odd	6	inner	105.3.r.a.94.11	yes	32
7.5	odd	6		735.3.e.a.244.30		32
15.14	odd	2		315.3.bi.e.19.6		32
21.17	even	6		315.3.bi.e.199.6		32
35.3	even	12		525.3.o.p.451.3		16
35.9	even	6		735.3.e.a.244.29		32
35.17	even	12		525.3.o.q.451.6		16
35.19	odd	6		735.3.e.a.244.9		32
35.24	odd	6	inner	105.3.r.a.94.6	yes	32
105.59	even	6		315.3.bi.e.199.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.6	✓	32	1.1	even	1	trivial
105.3.r.a.19.11	yes	32	5.4	even	2	inner
105.3.r.a.94.6	yes	32	35.24	odd	6	inner
105.3.r.a.94.11	yes	32	7.3	odd	6	inner
315.3.bi.e.19.6		32	15.14	odd	2
315.3.bi.e.19.11		32	3.2	odd	2
315.3.bi.e.199.6		32	21.17	even	6
315.3.bi.e.199.11		32	105.59	even	6
525.3.o.p.376.3		16	5.3	odd	4
525.3.o.p.451.3		16	35.3	even	12
525.3.o.q.376.6		16	5.2	odd	4
525.3.o.q.451.6		16	35.17	even	12
735.3.e.a.244.9		32	35.19	odd	6
735.3.e.a.244.10		32	7.2	even	3
735.3.e.a.244.29		32	35.9	even	6
735.3.e.a.244.30		32	7.5	odd	6

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32532 - 0.765175i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.829016 - 1.43590i) q^{4} +(-3.72620 + 3.33398i) q^{5} -2.65064i q^{6} +(6.34933 + 2.94719i) q^{7} +8.65876i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.32532 - 0.765175i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.829016 - 1.43590i) q^{4} +(-3.72620 + 3.33398i) q^{5} -2.65064i q^{6} +(6.34933 + 2.94719i) q^{7} +8.65876i q^{8} +(-1.50000 + 2.59808i) q^{9} +(7.48949 - 1.56739i) q^{10} +(6.68282 + 11.5750i) q^{11} +(1.43590 - 2.48705i) q^{12} -15.5994 q^{13} +(-6.15979 - 8.76433i) q^{14} +(-8.22795 - 2.70200i) q^{15} +(3.30940 - 5.73206i) q^{16} +(10.4267 + 18.0595i) q^{17} +(3.97596 - 2.29552i) q^{18} +(23.3408 + 13.4758i) q^{19} +(7.87633 + 2.58653i) q^{20} +(1.07789 + 12.0763i) q^{21} -20.4541i q^{22} +(-20.1960 - 11.6602i) q^{23} +(-12.9881 + 7.49871i) q^{24} +(2.76920 - 24.8462i) q^{25} +(20.6743 + 11.9363i) q^{26} -5.19615 q^{27} +(-1.03183 - 11.5603i) q^{28} -43.9323 q^{29} +(8.83718 + 9.87684i) q^{30} +(27.3477 - 15.7892i) q^{31} +(21.2228 - 12.2530i) q^{32} +(-11.5750 + 20.0485i) q^{33} -31.9129i q^{34} +(-33.4848 + 10.1867i) q^{35} +4.97409 q^{36} +(-30.6172 - 17.6768i) q^{37} +(-20.6227 - 35.7196i) q^{38} +(-13.5095 - 23.3992i) q^{39} +(-28.8681 - 32.2643i) q^{40} -19.4847i q^{41} +(7.81196 - 16.8298i) q^{42} +18.7524i q^{43} +(11.0803 - 19.1917i) q^{44} +(-3.07262 - 14.6819i) q^{45} +(17.8441 + 30.9069i) q^{46} +(1.46083 - 2.53023i) q^{47} +11.4641 q^{48} +(31.6281 + 37.4254i) q^{49} +(-22.6817 + 30.8102i) q^{50} +(-18.0595 + 31.2800i) q^{51} +(12.9322 + 22.3992i) q^{52} +(51.8892 - 29.9582i) q^{53} +(6.88657 + 3.97596i) q^{54} +(-63.4923 - 20.8504i) q^{55} +(-25.5191 + 54.9774i) q^{56} +46.6816i q^{57} +(58.2244 + 33.6159i) q^{58} +(14.7210 - 8.49916i) q^{59} +(2.94131 + 14.0545i) q^{60} +(83.2155 + 48.0445i) q^{61} -48.3259 q^{62} +(-17.1810 + 12.0753i) q^{63} -63.9779 q^{64} +(58.1267 - 52.0082i) q^{65} +(30.6812 - 17.7138i) q^{66} +(-29.6807 + 17.1362i) q^{67} +(17.2877 - 29.9432i) q^{68} -40.3920i q^{69} +(52.1727 + 12.1211i) q^{70} +76.6463 q^{71} +(-22.4961 - 12.9881i) q^{72} +(23.9200 + 41.4306i) q^{73} +(27.0517 + 46.8550i) q^{74} +(39.6674 - 17.3636i) q^{75} -44.6866i q^{76} +(8.31774 + 93.1890i) q^{77} +41.3486i q^{78} +(-25.8537 + 44.7799i) q^{79} +(6.77903 + 32.3923i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-14.9092 + 25.8235i) q^{82} +13.1844 q^{83} +(16.4468 - 11.5592i) q^{84} +(-99.0619 - 32.5312i) q^{85} +(14.3488 - 24.8529i) q^{86} +(-38.0465 - 65.8984i) q^{87} +(-100.225 + 57.8650i) q^{88} +(-46.8569 - 27.0529i) q^{89} +(-7.16203 + 21.8094i) q^{90} +(-99.0461 - 45.9746i) q^{91} +38.6658i q^{92} +(47.3675 + 27.3477i) q^{93} +(-3.87214 + 2.23558i) q^{94} +(-131.901 + 27.6040i) q^{95} +(36.7590 + 21.2228i) q^{96} +95.2693 q^{97} +(-13.2804 - 73.8017i) q^{98} -40.0969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39} + 330 q^{40} + 320 q^{44} + 18 q^{45} - 60 q^{46} + 356 q^{49} + 12 q^{51} - 468 q^{56} - 804 q^{59} - 198 q^{60} + 336 q^{61} - 400 q^{64} - 46 q^{65} - 108 q^{66} - 438 q^{70} + 344 q^{71} + 900 q^{74} + 144 q^{75} - 20 q^{79} + 1140 q^{80} - 144 q^{81} + 780 q^{84} + 304 q^{85} + 144 q^{86} + 24 q^{89} - 224 q^{91} - 924 q^{94} - 342 q^{95} + 900 q^{96} + 168 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9 + 78 * q^10 - 28 * q^11 + 60 * q^14 - 24 * q^15 - 40 * q^16 - 60 * q^19 + 12 * q^21 - 34 * q^25 - 96 * q^26 - 88 * q^29 + 84 * q^31 - 170 * q^35 - 192 * q^36 + 36 * q^39 + 330 * q^40 + 320 * q^44 + 18 * q^45 - 60 * q^46 + 356 * q^49 + 12 * q^51 - 468 * q^56 - 804 * q^59 - 198 * q^60 + 336 * q^61 - 400 * q^64 - 46 * q^65 - 108 * q^66 - 438 * q^70 + 344 * q^71 + 900 * q^74 + 144 * q^75 - 20 * q^79 + 1140 * q^80 - 144 * q^81 + 780 * q^84 + 304 * q^85 + 144 * q^86 + 24 * q^89 - 224 * q^91 - 924 * q^94 - 342 * q^95 + 900 * q^96 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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