LMFDB - Embedded newform 289.3.e.r.214.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,3,Mod(40,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([15]))

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

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

chi := DirichletCharacter("289.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			214.1
Character	$\chi$	$=$	289.214
Dual form			289.3.e.r.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43186 + 3.45680i) q^{2} +(-2.06607 - 1.38050i) q^{3} +(-7.07086 - 7.07086i) q^{4} +(-1.12265 + 0.223308i) q^{5} +(7.73043 - 5.16531i) q^{6} +(5.36760 + 1.06768i) q^{7} +(20.7398 - 8.59071i) q^{8} +(-1.08130 - 2.61050i) q^{9} +O(q^{10})$	\(q+(-1.43186 + 3.45680i) q^{2} +(-2.06607 - 1.38050i) q^{3} +(-7.07086 - 7.07086i) q^{4} +(-1.12265 + 0.223308i) q^{5} +(7.73043 - 5.16531i) q^{6} +(5.36760 + 1.06768i) q^{7} +(20.7398 - 8.59071i) q^{8} +(-1.08130 - 2.61050i) q^{9} +(0.835535 - 4.20052i) q^{10} +(7.66699 + 11.4745i) q^{11} +(4.84754 + 24.3702i) q^{12} +(-2.12584 + 2.12584i) q^{13} +(-11.3764 + 17.0260i) q^{14} +(2.62774 + 1.08845i) q^{15} +43.9953i q^{16} +10.5722 q^{18} +(7.91348 - 19.1048i) q^{19} +(9.51706 + 6.35910i) q^{20} +(-9.61588 - 9.61588i) q^{21} +(-50.6430 + 10.0735i) q^{22} +(-14.3414 + 9.58265i) q^{23} +(-54.7093 - 10.8824i) q^{24} +(-21.8865 + 9.06569i) q^{25} +(-4.30473 - 10.3925i) q^{26} +(-5.73266 + 28.8200i) q^{27} +(-30.4041 - 45.5030i) q^{28} +(4.78964 + 24.0792i) q^{29} +(-7.52509 + 7.52509i) q^{30} +(-2.89949 + 4.33939i) q^{31} +(-69.1239 - 28.6320i) q^{32} -34.2913i q^{33} -6.26434 q^{35} +(-10.8127 + 26.1042i) q^{36} +(-18.0163 - 12.0381i) q^{37} +(54.7107 + 54.7107i) q^{38} +(7.32687 - 1.45741i) q^{39} +(-21.3651 + 14.2757i) q^{40} +(68.3964 + 13.6049i) q^{41} +(47.0088 - 19.4717i) q^{42} +(23.2155 + 56.0473i) q^{43} +(26.9221 - 135.347i) q^{44} +(1.79687 + 2.68920i) q^{45} +(-12.5905 - 63.2965i) q^{46} +(-50.5516 + 50.5516i) q^{47} +(60.7356 - 90.8972i) q^{48} +(-17.5989 - 7.28972i) q^{49} -88.6382i q^{50} +30.0631 q^{52} +(-0.756385 + 1.82608i) q^{53} +(-91.4169 - 61.0828i) q^{54} +(-11.1697 - 11.1697i) q^{55} +(120.495 - 23.9680i) q^{56} +(-42.7241 + 28.5473i) q^{57} +(-90.0950 - 17.9210i) q^{58} +(21.6747 - 8.97796i) q^{59} +(-10.8841 - 26.2766i) q^{60} +(-20.5091 + 103.106i) q^{61} +(-10.8488 - 16.2363i) q^{62} +(-3.01682 - 15.1666i) q^{63} +(73.5133 - 73.5133i) q^{64} +(1.91185 - 2.86129i) q^{65} +(118.538 + 49.1002i) q^{66} +0.440407i q^{67} +42.8592 q^{69} +(8.96963 - 21.6546i) q^{70} +(50.1228 + 33.4910i) q^{71} +(-44.8521 - 44.8521i) q^{72} +(-34.6609 + 6.89449i) q^{73} +(67.4102 - 45.0420i) q^{74} +(57.7342 + 11.4840i) q^{75} +(-191.043 + 79.1325i) q^{76} +(28.9023 + 69.7762i) q^{77} +(-5.45305 + 27.4143i) q^{78} +(2.51112 + 3.75816i) q^{79} +(-9.82452 - 49.3912i) q^{80} +(33.6483 - 33.6483i) q^{81} +(-144.963 + 216.953i) q^{82} +(-27.8742 - 11.5459i) q^{83} +135.985i q^{84} -226.986 q^{86} +(23.3456 - 56.3613i) q^{87} +(257.586 + 172.113i) q^{88} +(17.0533 + 17.0533i) q^{89} +(-11.8689 + 2.36087i) q^{90} +(-13.6804 + 9.14095i) q^{91} +(169.164 + 33.6488i) q^{92} +(11.9811 - 4.96272i) q^{93} +(-102.364 - 247.129i) q^{94} +(-4.61778 + 23.2151i) q^{95} +(103.288 + 154.581i) q^{96} +(34.6193 + 174.043i) q^{97} +(50.3983 - 50.3983i) q^{98} +(21.6637 - 32.4220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q + 288 q^{18} + 384 q^{35} + 1920 q^{52} - 1152 q^{69} - 6240 q^{86}+O(q^{100}) $ 96 * q + 288 * q^18 + 384 * q^35 + 1920 * q^52 - 1152 * q^69 - 6240 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−1.43186	+	3.45680i	−0.715928	+	1.72840i	−0.0312990	+	0.999510i	$0.509964\pi$
$2$	−1.43186	+	3.45680i	−0.715928	+	1.72840i	−0.684629	+	0.728892i	$0.740036\pi$
$3$	−2.06607	−	1.38050i	−0.688689	−	0.460167i	0.161343	−	0.986898i	$-0.448417\pi$
$3$	−2.06607	−	1.38050i	−0.688689	−	0.460167i	−0.850032	+	0.526731i	$0.823417\pi$
$4$	−7.07086	−	7.07086i	−1.76771	−	1.76771i
$5$	−1.12265	+	0.223308i	−0.224529	+	0.0446617i	−0.306073	−	0.952008i	$-0.599015\pi$
$5$	−1.12265	+	0.223308i	−0.224529	+	0.0446617i	0.0815433	+	0.996670i	$0.474015\pi$
$6$	7.73043	−	5.16531i	1.28841	−	0.860885i
$7$	5.36760	+	1.06768i	0.766800	+	0.152526i	0.562966	−	0.826480i	$-0.309660\pi$
$7$	5.36760	+	1.06768i	0.766800	+	0.152526i	0.203833	+	0.979006i	$0.434660\pi$
$8$	20.7398	−	8.59071i	2.59248	−	1.07384i
$9$	−1.08130	−	2.61050i	−0.120145	−	0.290055i
$10$	0.835535	−	4.20052i	0.0835535	−	0.420052i
$11$	7.66699	+	11.4745i	0.696999	+	1.04313i	0.996041	+	0.0888931i	$0.0283330\pi$
$11$	7.66699	+	11.4745i	0.696999	+	1.04313i	−0.299042	+	0.954240i	$0.596667\pi$
$12$	4.84754	+	24.3702i	0.403961	+	2.03085i
$13$	−2.12584	+	2.12584i	−0.163527	+	0.163527i	−0.784127	−	0.620600i	$-0.786889\pi$
$13$	−2.12584	+	2.12584i	−0.163527	+	0.163527i	0.620600	+	0.784127i	$0.286889\pi$
$14$	−11.3764	+	17.0260i	−0.812599	+	1.21614i
$15$	2.62774	+	1.08845i	0.175183	+	0.0725631i
$16$			43.9953i			2.74971i
$17$		0			0
$17$		0			0
$18$	10.5722			0.587347
$19$	7.91348	−	19.1048i	0.416499	−	1.00552i	−0.566855	−	0.823818i	$-0.691840\pi$
$19$	7.91348	−	19.1048i	0.416499	−	1.00552i	0.983354	−	0.181700i	$-0.0581600\pi$
$20$	9.51706	+	6.35910i	0.475853	+	0.317955i
$21$	−9.61588	−	9.61588i	−0.457899	−	0.457899i
$22$	−50.6430	+	10.0735i	−2.30195	+	0.457887i
$23$	−14.3414	+	9.58265i	−0.623541	+	0.416637i	−0.826806	−	0.562487i	$-0.809845\pi$
$23$	−14.3414	+	9.58265i	−0.623541	+	0.416637i	0.203265	+	0.979124i	$0.434845\pi$
$24$	−54.7093	−	10.8824i	−2.27956	−	0.453432i
$25$	−21.8865	+	9.06569i	−0.875461	+	0.362628i
$26$	−4.30473	−	10.3925i	−0.165566	−	0.399713i
$27$	−5.73266	+	28.8200i	−0.212321	+	1.06741i
$28$	−30.4041	−	45.5030i	−1.08586	−	1.62511i
$29$	4.78964	+	24.0792i	0.165160	+	0.830316i	0.971165	+	0.238407i	$0.0766254\pi$
$29$	4.78964	+	24.0792i	0.165160	+	0.830316i	−0.806005	+	0.591909i	$0.798375\pi$
$30$	−7.52509	+	7.52509i	−0.250836	+	0.250836i
$31$	−2.89949	+	4.33939i	−0.0935319	+	0.139980i	−0.875285	−	0.483608i	$-0.839326\pi$
$31$	−2.89949	+	4.33939i	−0.0935319	+	0.139980i	0.781753	+	0.623589i	$0.214326\pi$
$32$	−69.1239	−	28.6320i	−2.16012	−	0.894752i
$33$		−	34.2913i		−	1.03913i
$34$		0			0
$35$	−6.26434			−0.178981
$36$	−10.8127	+	26.1042i	−0.300353	+	0.725117i
$37$	−18.0163	−	12.0381i	−0.486927	−	0.325355i	0.287756	−	0.957704i	$-0.407091\pi$
$37$	−18.0163	−	12.0381i	−0.486927	−	0.325355i	−0.774683	+	0.632349i	$0.782091\pi$
$38$	54.7107	+	54.7107i	1.43976	+	1.43976i
$39$	7.32687	−	1.45741i	0.187868	−	0.0373694i
$40$	−21.3651	+	14.2757i	−0.534128	+	0.356893i
$41$	68.3964	+	13.6049i	1.66820	+	0.331827i	0.936733	−	0.350045i	$-0.113834\pi$
$41$	68.3964	+	13.6049i	1.66820	+	0.331827i	0.731472	+	0.681872i	$0.238834\pi$
$42$	47.0088	−	19.4717i	1.11926	−	0.463611i
$43$	23.2155	+	56.0473i	0.539896	+	1.30343i	0.924795	+	0.380466i	$0.124236\pi$
$43$	23.2155	+	56.0473i	0.539896	+	1.30343i	−0.384898	+	0.922959i	$0.625764\pi$
$44$	26.9221	−	135.347i	0.611866	−	3.07606i
$45$	1.79687	+	2.68920i	0.0399304	+	0.0597601i
$46$	−12.5905	−	63.2965i	−0.273706	−	1.37601i
$47$	−50.5516	+	50.5516i	−1.07557	+	1.07557i	−0.0786640	+	0.996901i	$0.525065\pi$
$47$	−50.5516	+	50.5516i	−1.07557	+	1.07557i	−0.996901	+	0.0786640i	$0.974935\pi$
$48$	60.7356	−	90.8972i	1.26532	−	1.89369i
$49$	−17.5989	−	7.28972i	−0.359162	−	0.148770i
$50$		−	88.6382i		−	1.77276i
$51$		0			0
$52$	30.0631			0.578137
$53$	−0.756385	+	1.82608i	−0.0142714	+	0.0344543i	−0.930855	−	0.365390i	$-0.880936\pi$
$53$	−0.756385	+	1.82608i	−0.0142714	+	0.0344543i	0.916583	+	0.399844i	$0.130936\pi$
$54$	−91.4169	−	61.0828i	−1.69291	−	1.13116i
$55$	−11.1697	−	11.1697i	−0.203085	−	0.203085i
$56$	120.495	−	23.9680i	2.15170	−	0.427999i
$57$	−42.7241	+	28.5473i	−0.749545	+	0.500830i
$58$	−90.0950	−	17.9210i	−1.55336	−	0.308983i
$59$	21.6747	−	8.97796i	0.367368	−	0.152169i	−0.191360	−	0.981520i	$-0.561290\pi$
$59$	21.6747	−	8.97796i	0.367368	−	0.152169i	0.558728	+	0.829351i	$0.311290\pi$
$60$	−10.8841	−	26.2766i	−0.181402	−	0.437944i
$61$	−20.5091	+	103.106i	−0.336215	+	1.69026i	0.329579	+	0.944128i	$0.393093\pi$
$61$	−20.5091	+	103.106i	−0.336215	+	1.69026i	−0.665793	+	0.746136i	$0.731907\pi$
$62$	−10.8488	−	16.2363i	−0.174980	−	0.261877i
$63$	−3.01682	−	15.1666i	−0.0478861	−	0.240739i
$64$	73.5133	−	73.5133i	1.14865	−	1.14865i
$65$	1.91185	−	2.86129i	0.0294131	−	0.0440199i
$66$	118.538	+	49.1002i	1.79604	+	0.743942i
$67$			0.440407i			0.00657324i	0.999995	+	0.00328662i	$0.00104617\pi$
$67$			0.440407i			0.00657324i	−0.999995	+	0.00328662i	$0.998954\pi$
$68$		0			0
$69$	42.8592			0.621149
$70$	8.96963	−	21.6546i	0.128138	−	0.309351i
$71$	50.1228	+	33.4910i	0.705955	+	0.471704i	0.856001	−	0.516975i	$-0.172942\pi$
$71$	50.1228	+	33.4910i	0.705955	+	0.471704i	−0.150045	+	0.988679i	$0.547942\pi$
$72$	−44.8521	−	44.8521i	−0.622945	−	0.622945i
$73$	−34.6609	+	6.89449i	−0.474807	+	0.0944451i	−0.426693	−	0.904397i	$-0.640321\pi$
$73$	−34.6609	+	6.89449i	−0.474807	+	0.0944451i	−0.0481149	+	0.998842i	$0.515321\pi$
$74$	67.4102	−	45.0420i	0.910948	−	0.608676i
$75$	57.7342	+	11.4840i	0.769790	+	0.153121i
$76$	−191.043	+	79.1325i	−2.51372	+	1.04122i
$77$	28.9023	+	69.7762i	0.375354	+	0.906185i
$78$	−5.45305	+	27.4143i	−0.0699109	+	0.351466i
$79$	2.51112	+	3.75816i	0.0317863	+	0.0475716i	0.847022	−	0.531557i	$-0.178393\pi$
$79$	2.51112	+	3.75816i	0.0317863	+	0.0475716i	−0.815236	+	0.579129i	$0.803393\pi$
$80$	−9.82452	−	49.3912i	−0.122806	−	0.617390i
$81$	33.6483	−	33.6483i	0.415411	−	0.415411i
$82$	−144.963	+	216.953i	−1.76784	+	2.64576i
$83$	−27.8742	−	11.5459i	−0.335834	−	0.139107i	0.208393	−	0.978045i	$-0.433177\pi$
$83$	−27.8742	−	11.5459i	−0.335834	−	0.139107i	−0.544226	+	0.838938i	$0.683177\pi$
$84$			135.985i			1.61887i
$85$		0			0
$86$	−226.986			−2.63937
$87$	23.3456	−	56.3613i	0.268340	−	0.647831i
$88$	257.586	+	172.113i	2.92711	+	1.95583i
$89$	17.0533	+	17.0533i	0.191611	+	0.191611i	0.796392	−	0.604781i	$-0.206739\pi$
$89$	17.0533	+	17.0533i	0.191611	+	0.191611i	−0.604781	+	0.796392i	$0.706739\pi$
$90$	−11.8689	+	2.36087i	−0.131877	+	0.0262319i
$91$	−13.6804	+	9.14095i	−0.150334	+	0.100450i
$92$	169.164	+	33.6488i	1.83874	+	0.365748i
$93$	11.9811	−	4.96272i	0.128829	−	0.0533626i
$94$	−102.364	−	247.129i	−1.08898	−	2.62904i
$95$	−4.61778	+	23.2151i	−0.0486082	+	0.244370i
$96$	103.288	+	154.581i	1.07592	+	1.61022i
$97$	34.6193	+	174.043i	0.356900	+	1.79426i	0.574808	+	0.818289i	$0.305077\pi$
$97$	34.6193	+	174.043i	0.356900	+	1.79426i	−0.217908	+	0.975969i	$0.569923\pi$
$98$	50.3983	−	50.3983i	0.514268	−	0.514268i
$99$	21.6637	−	32.4220i	0.218825	−	0.327495i
$100$	218.859	+	90.6543i	2.18859	+	0.906543i
$101$		−	6.73359i		−	0.0666692i	−0.999444	−	0.0333346i	$-0.989387\pi$
$101$		−	6.73359i		−	0.0666692i	0.999444	−	0.0333346i	$-0.0106127\pi$
$102$		0			0
$103$	40.8498			0.396600			0.198300	−	0.980141i	$-0.436458\pi$
$103$	40.8498			0.396600			0.198300	+	0.980141i	$0.436458\pi$
$104$	−25.8271	+	62.3521i	−0.248337	+	0.599540i
$105$	12.9425	+	8.64793i	0.123262	+	0.0823613i
$106$	−5.22935	−	5.22935i	−0.0493335	−	0.0493335i
$107$	−56.2986	+	11.1985i	−0.526156	+	0.104659i	−0.451019	−	0.892514i	$-0.648939\pi$
$107$	−56.2986	+	11.1985i	−0.526156	+	0.104659i	−0.0751367	+	0.997173i	$0.523939\pi$
$108$	244.317	−	163.248i	2.26220	−	1.51155i
$109$	−90.2592	−	17.9537i	−0.828066	−	0.164713i	−0.237178	−	0.971466i	$-0.576222\pi$
$109$	−90.2592	−	17.9537i	−0.828066	−	0.164713i	−0.590888	+	0.806754i	$0.701222\pi$
$110$	54.6047	−	22.6180i	0.496407	−	0.205618i
$111$	20.6043	+	49.7431i	0.185624	+	0.448136i
$112$	−46.9730	+	236.149i	−0.419401	+	2.10847i
$113$	79.9851	+	119.706i	0.707832	+	1.05935i	0.994844	+	0.101419i	$0.0323383\pi$
$113$	79.9851	+	119.706i	0.707832	+	1.05935i	−0.287011	+	0.957927i	$0.592662\pi$
$114$	−37.5078	−	188.564i	−0.329016	−	1.65407i
$115$	13.9605	−	13.9605i	0.121396	−	0.121396i
$116$	136.394	−	204.127i	1.17581	−	1.75972i
$117$	7.84820	+	3.25083i	0.0670786	+	0.0277849i
$118$			87.7804i			0.743901i
$119$		0			0
$120$	63.8494			0.532078
$121$	−26.5759	+	64.1598i	−0.219635	+	0.530246i
$122$	−327.052	−	218.529i	−2.68075	−	1.79122i
$123$	−122.530	−	122.530i	−0.996179	−	0.996179i
$124$	51.1851	−	10.1813i	0.412783	−	0.0821077i
$125$	46.3398	−	30.9632i	0.370718	−	0.247706i
$126$	56.7476	+	11.2878i	0.450378	+	0.0895857i
$127$	−1.74397	+	0.722377i	−0.0137321	+	0.00568801i	−0.389539	−	0.921010i	$-0.627366\pi$
$127$	−1.74397	+	0.722377i	−0.0137321	+	0.00568801i	0.375807	+	0.926698i	$0.377366\pi$
$128$	34.3325	+	82.8860i	0.268223	+	0.647547i
$129$	29.4085	−	147.847i	0.227973	−	1.14610i
$130$	7.15343	+	10.7059i	0.0550264	+	0.0823528i
$131$	−29.4370	−	147.990i	−0.224710	−	1.12969i	−0.914158	−	0.405358i	$-0.867147\pi$
$131$	−29.4370	−	147.990i	−0.224710	−	1.12969i	0.689448	−	0.724335i	$-0.257853\pi$
$132$	−242.469	+	242.469i	−1.83689	+	1.83689i
$133$	62.8743	−	94.0980i	0.472739	−	0.707504i
$134$	−1.52240	−	0.630600i	−0.0113612	−	0.00470597i
$135$		−	33.6349i		−	0.249147i
$136$		0			0
$137$	125.667			0.917278			0.458639	−	0.888623i	$-0.348337\pi$
$137$	125.667			0.917278			0.458639	+	0.888623i	$0.348337\pi$
$138$	−61.3682	+	148.156i	−0.444697	+	1.07359i
$139$	107.093	+	71.5572i	0.770453	+	0.514800i	0.877571	−	0.479446i	$-0.159162\pi$
$139$	107.093	+	71.5572i	0.770453	+	0.514800i	−0.107119	+	0.994246i	$0.534162\pi$
$140$	44.2943	+	44.2943i	0.316388	+	0.316388i
$141$	174.229	−	34.6564i	1.23567	−	0.245790i
$142$	−187.540	+	125.311i	−1.32071	+	0.882468i
$143$	−40.6918	−	8.09410i	−0.284558	−	0.0566021i
$144$	114.850	−	47.5723i	0.797567	−	0.330363i
$145$	−10.7542	−	25.9628i	−0.0741666	−	0.179054i
$146$	25.7965	−	129.688i	0.176689	−	0.888274i
$147$	26.2971	+	39.3564i	0.178892	+	0.267731i
$148$	42.2710	+	212.511i	0.285615	+	1.43588i
$149$	101.552	−	101.552i	0.681560	−	0.681560i	−0.278792	−	0.960352i	$-0.589934\pi$
$149$	101.552	−	101.552i	0.681560	−	0.681560i	0.960352	+	0.278792i	$0.0899338\pi$
$150$	−122.365	+	183.132i	−0.815768	+	1.22088i
$151$	−207.540	−	85.9660i	−1.37444	−	0.569311i	−0.431450	−	0.902137i	$-0.641998\pi$
$151$	−207.540	−	85.9660i	−1.37444	−	0.569311i	−0.942988	+	0.332826i	$0.891998\pi$
$152$		−	464.213i		−	3.05403i
$153$		0			0
$154$	−282.587			−1.83498
$155$	2.28608	−	5.51909i	0.0147489	−	0.0356070i
$156$	−62.1124	−	41.5022i	−0.398156	−	0.266040i
$157$	144.008	+	144.008i	0.917249	+	0.917249i	0.996828	−	0.0795798i	$-0.0253579\pi$
$157$	144.008	+	144.008i	0.917249	+	0.917249i	−0.0795798	+	0.996828i	$0.525358\pi$
$158$	−16.5868	+	3.29931i	−0.104980	+	0.0208817i
$159$	4.08364	−	2.72860i	0.0256833	−	0.0171610i
$160$	83.9955	+	16.7077i	0.524972	+	0.104423i
$161$	−87.2103	+	36.1237i	−0.541679	+	0.224371i
$162$	68.1360	+	164.495i	0.420593	+	1.01540i
$163$	39.6705	−	199.437i	0.243378	−	1.22354i	−0.644912	−	0.764257i	$-0.723106\pi$
$163$	39.6705	−	199.437i	0.243378	−	1.22354i	0.888289	−	0.459284i	$-0.151894\pi$
$164$	−387.423	−	579.820i	−2.36234	−	3.53549i
$165$	7.65754	+	38.4970i	0.0464093	+	0.233315i
$166$	79.8236	−	79.8236i	0.480865	−	0.480865i
$167$	82.7098	−	123.784i	0.495268	−	0.741221i	−0.496671	−	0.867939i	$-0.665444\pi$
$167$	82.7098	−	123.784i	0.495268	−	0.741221i	0.991939	+	0.126718i	$0.0404443\pi$
$168$	−282.039	−	116.824i	−1.67880	−	0.695383i
$169$			159.962i			0.946518i
$170$		0			0
$171$	−58.4300			−0.341696
$172$	232.149	−	560.456i	1.34970	−	3.25847i
$173$	106.231	+	70.9811i	0.614051	+	0.410296i	0.823332	−	0.567560i	$-0.192112\pi$
$173$	106.231	+	70.9811i	0.614051	+	0.410296i	−0.209281	+	0.977855i	$0.567112\pi$
$174$	161.402	+	161.402i	0.927600	+	0.927600i
$175$	−127.157	+	25.2932i	−0.726613	+	0.144532i
$176$	−504.822	+	337.312i	−2.86831	+	1.91654i
$177$	−57.1755	−	11.3729i	−0.323025	−	0.0642537i
$178$	−83.3680	+	34.5321i	−0.468359	+	0.194001i
$179$	−20.8076	−	50.2339i	−0.116243	−	0.280636i	0.855040	−	0.518562i	$-0.173532\pi$
$179$	−20.8076	−	50.2339i	−0.116243	−	0.280636i	−0.971283	+	0.237926i	$0.923532\pi$
$180$	6.30958	−	31.7204i	0.0350532	−	0.176224i
$181$	−122.341	−	183.097i	−0.675919	−	1.01158i	−0.997896	−	0.0648366i	$-0.979347\pi$
$181$	−122.341	−	183.097i	−0.675919	−	1.01158i	0.321977	−	0.946747i	$-0.395653\pi$
$182$	−12.0101	−	60.3790i	−0.0659897	−	0.331753i
$183$	184.711	−	184.711i	1.00935	−	1.00935i
$184$	−215.117	+	321.945i	−1.16911	+	1.74970i
$185$	22.9142	+	9.49136i	0.123860	+	0.0513047i
$186$			48.5221i			0.260872i
$187$		0			0
$188$	714.886			3.80259
$189$	−61.5412	+	148.574i	−0.325615	+	0.786104i
$190$	−73.6382	−	49.2035i	−0.387570	−	0.258966i
$191$	−61.3483	−	61.3483i	−0.321195	−	0.321195i	0.528030	−	0.849226i	$-0.322931\pi$
$191$	−61.3483	−	61.3483i	−0.321195	−	0.321195i	−0.849226	+	0.528030i	$0.822931\pi$
$192$	−253.369	+	50.3982i	−1.31963	+	0.262490i
$193$	−55.5314	+	37.1049i	−0.287727	+	0.192253i	−0.691055	−	0.722803i	$-0.742854\pi$
$193$	−55.5314	+	37.1049i	−0.287727	+	0.192253i	0.403327	+	0.915056i	$0.367854\pi$
$194$	−651.203	−	129.532i	−3.35671	−	0.667692i
$195$	−7.90004	+	3.27230i	−0.0405130	+	0.0167810i
$196$	72.8951	+	175.984i	0.371914	+	0.897879i
$197$	−57.0948	+	287.035i	−0.289821	+	1.45703i	0.511751	+	0.859134i	$0.328997\pi$
$197$	−57.0948	+	287.035i	−0.289821	+	1.45703i	−0.801573	+	0.597897i	$0.796003\pi$
$198$	81.0574	+	121.311i	0.409381	+	0.612681i
$199$	−39.4890	−	198.525i	−0.198437	−	0.997611i	−0.943690	−	0.330830i	$-0.892671\pi$
$199$	−39.4890	−	198.525i	−0.198437	−	0.997611i	0.745253	−	0.666782i	$-0.232329\pi$
$200$	−376.041	+	376.041i	−1.88021	+	1.88021i
$201$	0.607983	−	0.909911i	0.00302479	−	0.00452692i
$202$	23.2767	+	9.64153i	0.115231	+	0.0477303i
$203$			134.361i			0.661877i
$204$		0			0
$205$	−79.8231			−0.389381
$206$	−58.4910	+	141.210i	−0.283937	+	0.685485i
$207$	40.5229	+	27.0766i	0.195763	+	0.130805i
$208$	−93.5272	−	93.5272i	−0.449650	−	0.449650i
$209$	279.890	−	55.6737i	1.33919	−	0.266381i
$210$	−48.4261	+	32.3573i	−0.230600	+	0.154082i
$211$	−119.867	−	23.8430i	−0.568090	−	0.113000i	−0.0973153	−	0.995254i	$-0.531026\pi$
$211$	−119.867	−	23.8430i	−0.568090	−	0.113000i	−0.470775	+	0.882253i	$0.656026\pi$
$212$	18.2602	−	7.56363i	0.0861331	−	0.0356775i
$213$	−57.3227	−	138.389i	−0.269121	−	0.649715i
$214$	41.9005	−	210.648i	0.195797	−	0.984337i
$215$	−38.5787	−	57.7371i	−0.179436	−	0.268545i
$216$	128.690	+	646.970i	0.595788	+	2.99523i
$217$	−20.1964	+	20.1964i	−0.0930708	+	0.0930708i
$218$	191.300	−	286.301i	0.877525	−	1.31331i
$219$	81.1297	+	33.6050i	0.370455	+	0.153448i
$220$			157.958i			0.717993i
$221$		0			0
$222$	−201.455			−0.907453
$223$	60.0048	−	144.864i	0.269080	−	0.649616i	−0.730361	−	0.683062i	$-0.760648\pi$
$223$	60.0048	−	144.864i	0.269080	−	0.649616i	0.999441	+	0.0334455i	$0.0106480\pi$
$224$	−340.459	−	227.488i	−1.51991	−	1.01557i
$225$	47.3319	+	47.3319i	0.210364	+	0.210364i
$226$	−528.328	+	105.091i	−2.33773	+	0.465004i
$227$	190.279	−	127.141i	0.838234	−	0.560090i	−0.0607087	−	0.998156i	$-0.519336\pi$
$227$	190.279	−	127.141i	0.838234	−	0.560090i	0.898943	+	0.438065i	$0.144336\pi$
$228$	503.950	+	100.242i	2.21031	+	0.439657i
$229$	359.396	−	148.867i	1.56942	−	0.650074i	0.582724	−	0.812670i	$-0.301987\pi$
$229$	359.396	−	148.867i	1.56942	−	0.650074i	0.986693	+	0.162596i	$0.0519869\pi$
$230$	28.2693	+	68.2481i	0.122910	+	0.296731i
$231$	36.6122	−	184.062i	0.158494	−	0.796805i
$232$	306.193	+	458.251i	1.31980	+	1.97522i
$233$	−3.94430	−	19.8293i	−0.0169283	−	0.0851044i	0.971398	−	0.237459i	$-0.0763145\pi$
$233$	−3.94430	−	19.8293i	−0.0169283	−	0.0851044i	−0.988326	+	0.152354i	$0.951314\pi$
$234$	−22.4750	+	22.4750i	−0.0960468	+	0.0960468i
$235$	45.4630	−	68.0402i	0.193460	−	0.289533i
$236$	−216.741	−	89.7769i	−0.918393	−	0.380411i
$237$		−	11.2312i		−	0.0473890i
$238$		0			0
$239$	−274.079			−1.14677			−0.573387	−	0.819285i	$-0.694371\pi$
$239$	−274.079			−1.14677			−0.573387	+	0.819285i	$0.694371\pi$
$240$	−47.8865	+	115.608i	−0.199527	+	0.481701i
$241$	−45.6516	−	30.5034i	−0.189426	−	0.126570i	0.457241	−	0.889343i	$-0.348838\pi$
$241$	−45.6516	−	30.5034i	−0.189426	−	0.126570i	−0.646667	+	0.762772i	$0.723838\pi$
$242$	−183.735	−	183.735i	−0.759236	−	0.759236i
$243$	143.409	−	28.5259i	0.590161	−	0.117390i
$244$	874.066	−	584.032i	3.58224	−	2.39357i
$245$	21.3853	+	4.25379i	0.0872868	+	0.0173624i
$246$	599.007	−	248.117i	2.43499	−	1.00861i
$247$	23.7911	+	57.4368i	0.0963202	+	0.232538i
$248$	−22.8564	+	114.907i	−0.0921628	+	0.463334i
$249$	41.6509	+	62.3349i	0.167273	+	0.250341i
$250$	40.6820	+	204.522i	0.162728	+	0.818089i
$251$	−93.1908	+	93.1908i	−0.371278	+	0.371278i	−0.867943	−	0.496664i	$-0.834558\pi$
$251$	−93.1908	+	93.1908i	−0.371278	+	0.371278i	0.496664	+	0.867943i	$0.334558\pi$
$252$	−85.9093	+	128.572i	−0.340910	+	0.510208i
$253$	−219.911	−	91.0903i	−0.869215	−	0.360041i
$254$		−	7.06291i		−	0.0278067i
$255$		0			0
$256$	80.1741			0.313180
$257$	−177.952	+	429.615i	−0.692422	+	1.67165i	0.0474212	+	0.998875i	$0.484900\pi$
$257$	−177.952	+	429.615i	−0.692422	+	1.67165i	−0.739843	+	0.672779i	$0.765100\pi$
$258$	468.968	+	313.354i	1.81770	+	1.21455i
$259$	−83.8515	−	83.8515i	−0.323751	−	0.323751i
$260$	−33.7503	+	6.71334i	−0.129809	+	0.0258206i
$261$	57.6795	−	38.5402i	0.220994	−	0.147664i
$262$	553.721	+	110.142i	2.11344	+	0.420389i
$263$	−184.994	+	76.6270i	−0.703399	+	0.291357i	−0.705570	−	0.708640i	$-0.749309\pi$
$263$	−184.994	+	76.6270i	−0.703399	+	0.291357i	0.00217119	+	0.999998i	$0.499309\pi$
$264$	−294.587	−	711.195i	−1.11586	−	2.69392i
$265$	0.441376	−	2.21895i	0.00166557	−	0.00837338i
$266$	235.252	+	352.079i	0.884404	+	1.32360i
$267$	−11.6912	−	58.7755i	−0.0437872	−	0.220133i
$268$	3.11406	−	3.11406i	0.0116196	−	0.0116196i
$269$	−157.735	+	236.067i	−0.586375	+	0.877572i	−0.999451	−	0.0331241i	$-0.989454\pi$
$269$	−157.735	+	236.067i	−0.586375	+	0.877572i	0.413076	+	0.910697i	$0.364454\pi$
$270$	116.269	+	48.1603i	0.430627	+	0.178371i
$271$			375.324i			1.38496i	0.721438	+	0.692479i	$0.243481\pi$
$271$			375.324i			1.38496i	−0.721438	+	0.692479i	$0.756519\pi$
$272$		0			0
$273$	40.8837			0.149757
$274$	−179.937	+	434.406i	−0.656704	+	1.58542i
$275$	−271.828	−	181.629i	−0.988464	−	0.660471i
$276$	−303.052	−	303.052i	−1.09801	−	1.09801i
$277$	10.4601	−	2.08064i	0.0377621	−	0.00751135i	−0.176173	−	0.984359i	$-0.556372\pi$
$277$	10.4601	−	2.08064i	0.0377621	−	0.00751135i	0.213935	+	0.976848i	$0.431372\pi$
$278$	−400.701	+	267.740i	−1.44137	+	0.963092i
$279$	14.4632	+	2.87691i	0.0518394	+	0.0103115i
$280$	−129.921	+	53.8151i	−0.464004	+	0.192197i
$281$	−32.9976	−	79.6633i	−0.117429	−	0.283499i	0.854226	−	0.519902i	$-0.174032\pi$
$281$	−32.9976	−	79.6633i	−0.117429	−	0.283499i	−0.971655	+	0.236403i	$0.924032\pi$
$282$	−129.671	+	651.900i	−0.459826	+	2.31170i
$283$	−51.0448	−	76.3940i	−0.180370	−	0.269943i	0.730256	−	0.683173i	$-0.239401\pi$
$283$	−51.0448	−	76.3940i	−0.180370	−	0.269943i	−0.910627	+	0.413230i	$0.864401\pi$
$284$	−117.601	−	591.222i	−0.414089	−	2.08177i
$285$	41.5892	−	41.5892i	0.145927	−	0.145927i
$286$	86.2444	−	129.074i	0.301554	−	0.451307i
$287$	352.599	+	146.051i	1.22857	+	0.508889i
$288$			211.408i			0.734054i
$289$		0			0
$290$	105.147			0.362575
$291$	168.741	−	407.377i	0.579866	−	1.39992i
$292$	293.833	+	196.333i	1.00628	+	0.672372i
$293$	41.5105	+	41.5105i	0.141674	+	0.141674i	0.774387	−	0.632713i	$-0.218059\pi$
$293$	41.5105	+	41.5105i	0.141674	+	0.141674i	−0.632713	+	0.774387i	$0.718059\pi$
$294$	−173.701	+	34.5513i	−0.590820	+	0.117521i
$295$	−22.3282	+	14.9192i	−0.0756888	+	0.0505736i
$296$	−477.071	−	94.8953i	−1.61173	−	0.320592i
$297$	−374.647	+	155.184i	−1.26144	+	0.522504i
$298$	205.639	+	496.455i	0.690062	+	1.66596i
$299$	10.1165	−	50.8589i	0.0338343	−	0.170097i
$300$	−327.028	−	489.433i	−1.09009	−	1.63144i
$301$	64.7710	+	325.626i	0.215186	+	1.08181i
$302$	594.335	−	594.335i	1.96800	−	1.96800i
$303$	−9.29573	+	13.9120i	−0.0306790	+	0.0459144i
$304$	840.523	+	348.156i	2.76488	+	1.14525i
$305$		−	120.332i		−	0.394530i
$306$		0			0
$307$	115.335			0.375683			0.187841	−	0.982199i	$-0.439851\pi$
$307$	115.335			0.375683			0.187841	+	0.982199i	$0.439851\pi$
$308$	289.014	−	697.742i	0.938357	−	2.26539i
$309$	−84.3984	−	56.3932i	−0.273134	−	0.182502i
$310$	15.8051	+	15.8051i	0.0509841	+	0.0509841i
$311$	−384.947	+	76.5706i	−1.23777	+	0.246208i	−0.770231	−	0.637765i	$-0.779859\pi$
$311$	−384.947	+	76.5706i	−1.23777	+	0.246208i	−0.467539	+	0.883972i	$0.654859\pi$
$312$	139.438	−	93.1693i	0.446916	−	0.298620i
$313$	−203.089	−	40.3969i	−0.648846	−	0.129063i	−0.140314	−	0.990107i	$-0.544811\pi$
$313$	−203.089	−	40.3969i	−0.648846	−	0.129063i	−0.508531	+	0.861044i	$0.669811\pi$
$314$	−704.006	+	291.609i	−2.24206	+	0.928691i
$315$	6.77365	+	16.3530i	0.0215037	+	0.0519144i
$316$	8.81762	−	44.3292i	0.0279039	−	0.140282i
$317$	47.9100	+	71.7024i	0.151136	+	0.226191i	0.899310	−	0.437312i	$-0.144069\pi$
$317$	47.9100	+	71.7024i	0.151136	+	0.226191i	−0.748174	+	0.663502i	$0.769069\pi$
$318$	3.58506	+	18.0233i	0.0112738	+	0.0566771i
$319$	−239.573	+	239.573i	−0.751014	+	0.751014i
$320$	−66.1134	+	98.9457i	−0.206604	+	0.309205i
$321$	131.776	+	54.5835i	0.410518	+	0.170042i
$322$		−	353.193i		−	1.09687i
$323$		0			0
$324$	−475.844			−1.46866
$325$	27.2551	−	65.7996i	0.0838618	−	0.202460i
$326$	632.613	+	422.699i	1.94053	+	1.29662i
$327$	161.696	+	161.696i	0.494484	+	0.494484i
$328$	1535.40	−	305.411i	4.68111	−	0.931131i
$329$	−325.313	+	217.367i	−0.988795	+	0.660691i
$330$	−144.041	−	28.6516i	−0.436489	−	0.0868230i
$331$	291.136	−	120.593i	0.879566	−	0.364328i	0.103237	−	0.994657i	$-0.467080\pi$
$331$	291.136	−	120.593i	0.879566	−	0.364328i	0.776328	+	0.630329i	$0.217080\pi$
$332$	115.455	+	278.734i	0.347757	+	0.839560i
$333$	−11.9444	+	60.0484i	−0.0358690	+	0.180326i
$334$	309.468	+	463.152i	0.926552	+	1.38668i
$335$	−0.0983467	−	0.494422i	−0.000293572	−	0.00147589i
$336$	423.053	−	423.053i	1.25909	−	1.25909i
$337$	−223.619	+	334.669i	−0.663557	+	0.993084i	0.335146	+	0.942166i	$0.391214\pi$
$337$	−223.619	+	334.669i	−0.663557	+	0.993084i	−0.998703	+	0.0509173i	$0.983786\pi$
$338$	−552.956	−	229.042i	−1.63596	−	0.677638i
$339$		−	357.740i		−	1.05528i
$340$		0			0
$341$	−72.0225			−0.211210
$342$	83.6633	−	201.981i	0.244630	−	0.590588i
$343$	−309.652	−	206.903i	−0.902775	−	0.603215i
$344$	962.972	+	962.972i	2.79934	+	2.79934i
$345$	−48.1158	+	9.57083i	−0.139466	+	0.0277415i
$346$	−397.475	+	265.584i	−1.14877	+	0.767585i
$347$	494.106	+	98.2837i	1.42394	+	0.283238i	0.846148	−	0.532949i	$-0.178916\pi$
$347$	494.106	+	98.2837i	1.42394	+	0.283238i	0.577788	+	0.816187i	$0.303916\pi$
$348$	−563.596	+	233.449i	−1.61953	+	0.670831i
$349$	−248.967	−	601.060i	−0.713373	−	1.72223i	−0.691397	−	0.722475i	$-0.743004\pi$
$349$	−248.967	−	601.060i	−0.713373	−	1.72223i	−0.0219760	−	0.999758i	$-0.506996\pi$
$350$	94.6373	−	475.774i	0.270392	−	1.35935i
$351$	−49.0802	−	73.4537i	−0.139830	−	0.209270i
$352$	−201.435	−	1012.68i	−0.572258	−	2.87694i
$353$	−323.389	+	323.389i	−0.916116	+	0.916116i	−0.996744	−	0.0806282i	$-0.974307\pi$
$353$	−323.389	+	323.389i	−0.916116	+	0.916116i	0.0806282	+	0.996744i	$0.474307\pi$
$354$	121.181	−	181.360i	0.342319	−	0.512317i
$355$	−63.7491	−	26.4057i	−0.179575	−	0.0743823i
$356$		−	241.164i		−	0.677426i
$357$		0			0
$358$	203.442			0.568274
$359$	196.968	−	475.522i	0.548657	−	1.32457i	−0.369821	−	0.929103i	$-0.620581\pi$
$359$	196.968	−	475.522i	0.548657	−	1.32457i	0.918478	−	0.395472i	$-0.129419\pi$
$360$	60.3689	+	40.3372i	0.167691	+	0.112048i
$361$	−47.1061	−	47.1061i	−0.130488	−	0.130488i
$362$	808.105	−	160.742i	2.23233	−	0.444039i
$363$	143.480	−	95.8705i	0.395262	−	0.264106i
$364$	161.367	+	32.0978i	0.443315	+	0.0881808i
$365$	37.3724	−	15.4802i	0.102390	−	0.0424114i
$366$	374.031	+	902.991i	1.02194	+	2.46719i
$367$	34.3773	−	172.827i	0.0936712	−	0.470917i	−0.905267	−	0.424843i	$-0.860329\pi$
$367$	34.3773	−	172.827i	0.0936712	−	0.470917i	0.998938	−	0.0460736i	$-0.0146709\pi$
$368$	−421.591	−	630.956i	−1.14563	−	1.71455i
$369$	−38.4417	−	193.260i	−0.104178	−	0.523739i
$370$	−65.6196	+	65.6196i	−0.177350	+	0.177350i
$371$	−6.00964	+	8.99406i	−0.0161985	+	0.0242427i
$372$	−119.807	−	49.6258i	−0.322062	−	0.133403i
$373$		−	704.841i		−	1.88965i	−0.327569	−	0.944827i	$-0.606229\pi$
$373$		−	704.841i		−	1.88965i	0.327569	−	0.944827i	$-0.393771\pi$
$374$		0			0
$375$	−138.486			−0.369296
$376$	−614.156	+	1482.70i	−1.63339	+	3.94336i
$377$	−61.3706	−	41.0065i	−0.162787	−	0.108771i
$378$	−425.472	−	425.472i	−1.12559	−	1.12559i
$379$	−483.583	+	96.1907i	−1.27595	+	0.253801i	−0.786150	−	0.618036i	$-0.787929\pi$
$379$	−483.583	+	96.1907i	−1.27595	+	0.253801i	−0.489796	+	0.871837i	$0.662929\pi$
$380$	196.803	−	131.499i	0.517902	−	0.346051i
$381$	4.60041	+	0.915078i	0.0120746	+	0.00240178i
$382$	299.911	−	124.227i	0.785108	−	0.325202i
$383$	141.953	+	342.706i	0.370636	+	0.894793i	0.993643	+	0.112577i	$0.0359106\pi$
$383$	141.953	+	342.706i	0.370636	+	0.894793i	−0.623007	+	0.782216i	$0.714089\pi$
$384$	43.4910	−	218.644i	0.113258	−	0.569386i
$385$	−48.0286	−	71.8799i	−0.124750	−	0.186701i
$386$	−48.7514	−	245.090i	−0.126299	−	0.634948i
$387$	121.208	−	121.208i	0.313200	−	0.313200i
$388$	985.846	−	1475.42i	2.54084	−	3.80263i
$389$	384.232	+	159.154i	0.987744	+	0.409137i	0.817289	−	0.576229i	$-0.195476\pi$
$389$	384.232	+	159.154i	0.987744	+	0.409137i	0.170455	+	0.985365i	$0.445476\pi$
$390$		−	31.9944i		−	0.0820368i
$391$		0			0
$392$	−427.623			−1.09087
$393$	−143.481	+	346.395i	−0.365092	+	0.881411i
$394$	−910.473	−	608.358i	−2.31084	−	1.54406i
$395$	−3.65833	−	3.65833i	−0.00926159	−	0.00926159i
$396$	−382.433	+	76.0706i	−0.965739	+	0.192098i
$397$	−143.866	+	96.1285i	−0.362384	+	0.242137i	−0.723410	−	0.690418i	$-0.757426\pi$
$397$	−143.866	+	96.1285i	−0.362384	+	0.242137i	0.361026	+	0.932556i	$0.382426\pi$
$398$	742.803	+	147.753i	1.86634	+	0.371238i
$399$	−259.805	+	107.615i	−0.651140	+	0.269711i
$400$	−398.848	−	962.904i	−0.997120	−	2.40726i
$401$	−43.1783	+	217.072i	−0.107677	+	0.541327i	0.888861	+	0.458178i	$0.151498\pi$
$401$	−43.1783	+	217.072i	−0.107677	+	0.541327i	−0.996537	+	0.0831488i	$0.973502\pi$
$402$	2.27484	+	3.40454i	0.00565881	+	0.00846900i
$403$	−3.06101	−	15.3887i	−0.00759556	−	0.0381854i
$404$	−47.6123	+	47.6123i	−0.117852	+	0.117852i
$405$	−30.2612	+	45.2891i	−0.0747190	+	0.111825i
$406$	−464.460	−	192.386i	−1.14399	−	0.473856i
$407$		−	299.024i		−	0.734702i
$408$		0			0
$409$	494.716			1.20958			0.604788	−	0.796387i	$-0.293258\pi$
$409$	494.716			1.20958			0.604788	+	0.796387i	$0.293258\pi$
$410$	114.295	−	275.933i	0.278769	−	0.673007i
$411$	−259.637	−	173.484i	−0.631719	−	0.422101i
$412$	−288.843	−	288.843i	−0.701076	−	0.701076i
$413$	125.927	−	25.0484i	0.304907	−	0.0606498i
$414$	−151.621	+	101.310i	−0.366235	+	0.244710i
$415$	33.8712	+	6.73740i	0.0816173	+	0.0162347i
$416$	207.814	−	86.0794i	0.499553	−	0.206922i
$417$	−122.476	−	295.684i	−0.293708	−	0.709074i
$418$	−208.310	+	1047.24i	−0.498348	+	2.50537i
$419$	−124.239	−	185.937i	−0.296514	−	0.443765i	0.653061	−	0.757306i	$-0.273485\pi$
$419$	−124.239	−	185.937i	−0.296514	−	0.443765i	−0.949575	+	0.313541i	$0.898485\pi$
$420$	−30.3666	−	152.663i	−0.0723015	−	0.363484i
$421$	−319.365	+	319.365i	−0.758587	+	0.758587i	−0.976065	−	0.217478i	$-0.930217\pi$
$421$	−319.365	+	319.365i	−0.758587	+	0.758587i	0.217478	+	0.976065i	$0.430217\pi$
$422$	254.053	−	380.217i	0.602021	−	0.900988i
$423$	186.626	+	77.3032i	0.441197	+	0.182750i
$424$			44.3703i			0.104647i
$425$		0			0
$426$	560.462			1.31564
$427$	−220.169	+	531.535i	−0.515618	+	1.24481i
$428$	477.263	+	318.897i	1.11510	+	0.745086i
$429$	72.8980	+	72.8980i	0.169925	+	0.169925i
$430$	254.825	−	50.6878i	0.592616	−	0.117879i
$431$	285.262	−	190.606i	0.661861	−	0.442241i	−0.178740	−	0.983896i	$-0.557202\pi$
$431$	285.262	−	190.606i	0.661861	−	0.442241i	0.840601	+	0.541655i	$0.182202\pi$
$432$	−1267.95	−	252.210i	−2.93506	−	0.583820i
$433$	382.612	−	158.483i	0.883630	−	0.366012i	0.105727	−	0.994395i	$-0.466283\pi$
$433$	382.612	−	158.483i	0.883630	−	0.366012i	0.777904	+	0.628384i	$0.216283\pi$
$434$	−40.8966	−	98.7332i	−0.0942319	−	0.227496i
$435$	−13.6229	+	68.4871i	−0.0313171	+	0.157442i
$436$	511.262	+	765.158i	1.17262	+	1.75495i
$437$	69.5842	+	349.823i	0.159231	+	0.800511i
$438$	−232.332	+	232.332i	−0.530438	+	0.530438i
$439$	−334.098	+	500.013i	−0.761043	+	1.13898i	0.225302	+	0.974289i	$0.427663\pi$
$439$	−334.098	+	500.013i	−0.761043	+	1.13898i	−0.986345	+	0.164693i	$0.947337\pi$
$440$	−327.612	−	135.701i	−0.744573	−	0.308412i
$441$			53.8244i			0.122051i
$442$		0			0
$443$	−451.079			−1.01824			−0.509119	−	0.860696i	$-0.670029\pi$
$443$	−451.079			−1.01824			−0.509119	+	0.860696i	$0.670029\pi$
$444$	206.037	−	497.416i	0.464047	−	1.12031i
$445$	−22.9530	−	15.3367i	−0.0515799	−	0.0344646i
$446$	414.850	+	414.850i	0.930156	+	0.930156i
$447$	−350.008	+	69.6208i	−0.783015	+	0.155751i
$448$	473.079	−	316.101i	1.05598	−	0.705583i
$449$	168.961	+	33.6084i	0.376305	+	0.0748517i	0.379619	−	0.925143i	$-0.376055\pi$
$449$	168.961	+	33.6084i	0.376305	+	0.0748517i	−0.00331441	+	0.999995i	$0.501055\pi$
$450$	−231.390	+	95.8448i	−0.514199	+	0.212988i
$451$	368.286	+	889.121i	0.816598	+	1.97144i
$452$	280.862	−	1411.99i	0.621376	−	3.12387i
$453$	310.116	+	464.121i	0.684582	+	1.02455i
$454$	167.048	+	839.805i	0.367946	+	1.84979i
$455$	13.3170	−	13.3170i	0.0292682	−	0.0292682i
$456$	−640.847	+	959.096i	−1.40537	+	2.10328i
$457$	−109.453	−	45.3370i	−0.239504	−	0.0992056i	0.259703	−	0.965688i	$-0.416375\pi$
$457$	−109.453	−	45.3370i	−0.239504	−	0.0992056i	−0.499207	+	0.866483i	$0.666375\pi$
$458$			1455.52i			3.17799i
$459$		0			0
$460$	−197.425			−0.429186
$461$	232.642	−	561.647i	0.504646	−	1.21832i	−0.442281	−	0.896876i	$-0.645831\pi$
$461$	232.642	−	561.647i	0.504646	−	1.21832i	0.946927	−	0.321447i	$-0.104169\pi$
$462$	583.843	+	390.111i	1.26373	+	0.844397i
$463$	−57.4903	−	57.4903i	−0.124169	−	0.124169i	0.642291	−	0.766460i	$-0.277984\pi$
$463$	−57.4903	−	57.4903i	−0.124169	−	0.124169i	−0.766460	+	0.642291i	$0.777984\pi$
$464$	−1059.37	+	210.722i	−2.28312	+	0.454142i
$465$	−12.3423	+	8.24686i	−0.0265426	+	0.0177352i
$466$	74.1938	+	14.7581i	0.159214	+	0.0316697i
$467$	65.0705	−	26.9531i	0.139337	−	0.0577154i	−0.311925	−	0.950107i	$-0.600974\pi$
$467$	65.0705	−	26.9531i	0.139337	−	0.0577154i	0.451262	+	0.892391i	$0.350974\pi$
$468$	−32.5073	−	78.4797i	−0.0694601	−	0.167692i
$469$	−0.470215	+	2.36393i	−0.00100259	+	0.00504036i
$470$	170.105	+	254.580i	0.361926	+	0.541660i
$471$	−98.7269	−	496.334i	−0.209611	−	1.05379i
$472$	372.402	−	372.402i	0.788988	−	0.788988i
$473$	−465.119	+	696.100i	−0.983339	+	1.47167i
$474$	38.8241	+	16.0815i	0.0819073	+	0.0339271i
$475$			489.880i			1.03133i
$476$		0			0
$477$	5.58485			0.0117083
$478$	392.442	−	947.438i	0.821007	−	1.98209i
$479$	438.319	+	292.875i	0.915070	+	0.611430i	0.921428	−	0.388549i	$-0.127024\pi$
$479$	438.319	+	292.875i	0.915070	+	0.611430i	−0.00635755	+	0.999980i	$0.502024\pi$
$480$	−150.475	−	150.475i	−0.313490	−	0.313490i
$481$	63.8911	−	12.7087i	0.132830	−	0.0264215i
$482$	170.811	−	114.132i	0.354380	−	0.236789i
$483$	230.051	+	45.7600i	0.476296	+	0.0947413i
$484$	641.579	−	265.751i	1.32558	−	0.549072i
$485$	−77.7305	−	187.658i	−0.160269	−	0.386924i
$486$	−106.733	+	536.582i	−0.219615	+	1.10408i
$487$	−424.322	−	635.043i	−0.871298	−	1.30399i	−0.951638	−	0.307222i	$-0.900601\pi$
$487$	−424.322	−	635.043i	−0.871298	−	1.30399i	0.0803402	−	0.996768i	$-0.474399\pi$
$488$	460.400	+	2314.59i	0.943443	+	4.74301i
$489$	−357.285	+	357.285i	−0.730645	+	0.730645i
$490$	−45.3251	+	67.8338i	−0.0925002	+	0.138436i
$491$	582.511	+	241.284i	1.18638	+	0.491413i	0.886573	−	0.462588i	$-0.153079\pi$
$491$	582.511	+	241.284i	1.18638	+	0.491413i	0.299803	+	0.954001i	$0.403079\pi$
$492$			1732.78i			3.52192i
$493$		0			0
$494$	−232.613			−0.470877
$495$	−17.0806	+	41.2362i	−0.0345063	+	0.0833055i
$496$	−190.913	−	127.564i	−0.384905	−	0.257185i
$497$	233.281	+	233.281i	0.469379	+	0.469379i
$498$	−275.118	+	54.7243i	−0.552445	+	0.109888i
$499$	197.228	−	131.784i	0.395247	−	0.264096i	−0.342026	−	0.939691i	$-0.611113\pi$
$499$	197.228	−	131.784i	0.395247	−	0.264096i	0.737273	+	0.675595i	$0.236113\pi$
$500$	−546.599	−	108.725i	−1.09320	−	0.217450i
$501$	−341.768	+	141.565i	−0.682171	+	0.282565i
$502$	−188.707	−	455.578i	−0.375910	−	0.907526i
$503$	−116.243	+	584.393i	−0.231099	+	1.16181i	0.674695	+	0.738097i	$0.264275\pi$
$503$	−116.243	+	584.393i	−0.231099	+	1.16181i	−0.905794	+	0.423718i	$0.860725\pi$
$504$	−192.860	−	288.635i	−0.382659	−	0.572689i
$505$	1.50367	+	7.55945i	0.00297756	+	0.0149692i
$506$	629.763	−	629.763i	1.24459	−	1.24459i
$507$	220.827	−	330.491i	0.435557	−	0.651857i
$508$	17.4392	+	7.22356i	0.0343292	+	0.0142196i
$509$		−	779.738i		−	1.53190i	−0.642899	−	0.765951i	$-0.722268\pi$
$509$		−	779.738i		−	1.53190i	0.642899	−	0.765951i	$-0.277732\pi$
$510$		0			0
$511$	−193.407			−0.378487
$512$	−252.128	+	608.690i	−0.492437	+	1.18885i
$513$	505.237	+	337.588i	0.984867	+	0.658067i
$514$	−1230.29	−	1230.29i	−2.39357	−	2.39357i
$515$	−45.8599	+	9.12211i	−0.0890484	+	0.0177128i
$516$	−1253.35	+	837.459i	−2.42896	+	1.62298i
$517$	−967.631	−	192.474i	−1.87163	−	0.372290i
$518$	409.921	−	169.795i	0.791354	−	0.327789i
$519$	−121.490	−	293.304i	−0.234085	−	0.565132i
$520$	15.0710	−	75.7669i	0.0289826	−	0.145705i
$521$	195.969	+	293.288i	0.376140	+	0.562933i	0.970450	−	0.241303i	$-0.0775747\pi$
$521$	195.969	+	293.288i	0.376140	+	0.562933i	−0.594310	+	0.804236i	$0.702575\pi$
$522$	50.6373	+	254.571i	0.0970063	+	0.487684i
$523$	−13.6010	+	13.6010i	−0.0260058	+	0.0260058i	−0.719990	−	0.693984i	$-0.755854\pi$
$523$	−13.6010	+	13.6010i	−0.0260058	+	0.0260058i	0.693984	+	0.719990i	$0.255854\pi$
$524$	−838.270	+	1254.56i	−1.59975	+	2.39420i
$525$	297.633	+	123.284i	0.566919	+	0.234826i
$526$		−	749.206i		−	1.42435i
$527$		0			0
$528$	1508.66			2.85730
$529$	−88.5896	+	213.874i	−0.167466	+	0.404299i
$530$	7.03848	+	4.70296i	0.0132801	+	0.00887351i
$531$	−46.8739	−	46.8739i	−0.0882747	−	0.0882747i
$532$	−1109.93	+	220.779i	−2.08633	+	0.414997i
$533$	−174.322	+	116.478i	−0.327058	+	0.218533i
$534$	219.916	+	43.7439i	0.411827	+	0.0819175i
$535$	60.7028	−	25.1439i	0.113463	−	0.0469980i
$536$	3.78341	+	9.13396i	0.00705860	+	0.0170410i
$537$	−26.3582	+	132.511i	−0.0490841	+	0.246762i
$538$	−590.184	−	883.273i	−1.09700	−	1.64177i
$539$	−51.2853	−	257.829i	−0.0951490	−	0.478346i
$540$	−237.828	+	237.828i	−0.440421	+	0.440421i
$541$	423.110	−	633.229i	0.782088	−	1.17048i	−0.199580	−	0.979882i	$-0.563958\pi$
$541$	423.110	−	633.229i	0.782088	−	1.17048i	0.981668	−	0.190597i	$-0.0610422\pi$
$542$	−1297.42	−	537.409i	−2.39376	−	0.991530i
$543$			547.182i			1.00770i
$544$		0			0
$545$	105.338			0.193281
$546$	−58.5396	+	141.327i	−0.107215	+	0.258841i
$547$	−588.189	−	393.016i	−1.07530	−	0.718493i	−0.113857	−	0.993497i	$-0.536321\pi$
$547$	−588.189	−	393.016i	−1.07530	−	0.718493i	−0.961443	+	0.275004i	$0.911321\pi$
$548$	−888.574	−	888.574i	−1.62149	−	1.62149i
$549$	291.335	−	57.9501i	0.530665	−	0.105556i
$550$	1017.08	−	679.588i	1.84923	−	1.23561i
$551$	497.931	+	99.0447i	0.903687	+	0.179754i
$552$	888.893	−	368.191i	1.61031	−	0.667013i
$553$	9.46616	+	22.8533i	0.0171178	+	0.0413261i
$554$	−7.78497	+	39.1377i	−0.0140523	+	0.0706457i
$555$	−34.2394	−	51.2429i	−0.0616926	−	0.0923295i
$556$	−251.268	−	1263.21i	−0.451921	−	2.27196i
$557$	383.046	−	383.046i	0.687695	−	0.687695i	−0.274027	−	0.961722i	$-0.588356\pi$
$557$	383.046	−	383.046i	0.687695	−	0.687695i	0.961722	+	0.274027i	$0.0883557\pi$
$558$	−30.6541	+	45.8771i	−0.0549357	+	0.0822171i
$559$	−168.500	−	69.7952i	−0.301432	−	0.124857i
$560$		−	275.601i		−	0.492146i
$561$		0			0
$562$	322.628			0.574072
$563$	7.89751	−	19.0663i	0.0140276	−	0.0338655i	−0.916711	−	0.399552i	$-0.869166\pi$
$563$	7.89751	−	19.0663i	0.0140276	−	0.0338655i	0.930738	+	0.365686i	$0.119166\pi$
$564$	−1477.00	−	986.901i	−2.61880	−	1.74983i
$565$	−116.526	−	116.526i	−0.206241	−	0.206241i
$566$	337.168	−	67.0669i	0.595703	−	0.118493i
$567$	216.536	−	144.685i	0.381898	−	0.255176i
$568$	1327.25	+	264.006i	2.33671	+	0.464800i
$569$	454.299	−	188.177i	0.798417	−	0.330715i	0.0540948	−	0.998536i	$-0.482773\pi$
$569$	454.299	−	188.177i	0.798417	−	0.330715i	0.744322	+	0.667821i	$0.232773\pi$
$570$	84.2160	+	203.315i	0.147747	+	0.356694i
$571$	212.624	−	1068.93i	0.372370	−	1.87203i	−0.106754	−	0.994286i	$-0.534046\pi$
$571$	212.624	−	1068.93i	0.372370	−	1.87203i	0.479124	−	0.877747i	$-0.340954\pi$
$572$	230.494	+	344.958i	0.402961	+	0.603073i
$573$	42.0583	+	211.441i	0.0734001	+	0.369007i
$574$	−1009.74	+	1009.74i	−1.75913	+	1.75913i
$575$	227.011	−	339.746i	0.394802	−	0.590862i
$576$	−271.397	−	112.416i	−0.471175	−	0.195167i
$577$			601.205i			1.04195i	0.853572	+	0.520975i	$0.174431\pi$
$577$			601.205i			1.04195i	−0.853572	+	0.520975i	$0.825569\pi$
$578$		0			0
$579$	165.955			0.286623
$580$	−107.538	+	259.621i	−0.185411	+	0.447622i
$581$	−137.290	−	91.7343i	−0.236300	−	0.157890i
$582$	1166.61	+	1166.61i	2.00448	+	2.00448i
$583$	−26.7524	+	5.32139i	−0.0458875	+	0.00912760i
$584$	−659.633	+	440.753i	−1.12951	+	0.754713i
$585$	−9.53669	−	1.89697i	−0.0163020	−	0.00324268i
$586$	−202.931	+	84.0567i	−0.346298	+	0.143442i
$587$	−17.4289	−	42.0771i	−0.0296915	−	0.0716816i	0.908338	−	0.418236i	$-0.137352\pi$
$587$	−17.4289	−	42.0771i	−0.0296915	−	0.0716816i	−0.938030	+	0.346555i	$0.887352\pi$
$588$	92.3405	−	464.227i	0.157042	−	0.789502i
$589$	59.9583	+	89.7340i	0.101797	+	0.152350i
$590$	−19.6021	−	98.5464i	−0.0332239	−	0.167028i
$591$	514.214	−	514.214i	0.870075	−	0.870075i
$592$	529.621	−	792.633i	0.894629	−	1.33891i
$593$	−316.725	−	131.192i	−0.534106	−	0.221234i	0.0992943	−	0.995058i	$-0.468341\pi$
$593$	−316.725	−	131.192i	−0.534106	−	0.221234i	−0.633401	+	0.773824i	$0.718341\pi$
$594$		−	1517.28i		−	2.55435i
$595$		0			0
$596$	−1436.13			−2.40961
$597$	−192.477	+	464.680i	−0.322407	+	0.778358i
$598$	161.324	+	107.793i	0.269773	+	0.180256i
$599$	184.459	+	184.459i	0.307944	+	0.307944i	0.844112	−	0.536167i	$-0.180128\pi$
$599$	184.459	+	184.459i	0.307944	+	0.307944i	−0.536167	+	0.844112i	$0.680128\pi$
$600$	1296.05	−	257.801i	2.16009	−	0.429668i
$601$	−4.55871	+	3.04603i	−0.00758521	+	0.00506828i	−0.559357	−	0.828927i	$-0.688952\pi$
$601$	−4.55871	+	3.04603i	−0.00758521	+	0.00506828i	0.551772	+	0.833995i	$0.313952\pi$
$602$	−1218.37	−	242.349i	−2.02387	−	0.402572i
$603$	1.14968	−	0.476214i	0.00190660	−	0.000789741i
$604$	859.634	+	2075.34i	1.42324	+	3.43600i
$605$	15.5079	−	77.9635i	0.0256329	−	0.128865i
$606$	−34.7811	−	52.0536i	−0.0573945	−	0.0858970i
$607$	142.989	+	718.857i	0.235567	+	1.18428i	0.899648	+	0.436616i	$0.143823\pi$
$607$	142.989	+	718.857i	0.235567	+	1.18428i	−0.664080	+	0.747661i	$0.731177\pi$
$608$	−1094.02	+	1094.02i	−1.79938	+	1.79938i
$609$	185.486	−	277.599i	0.304574	−	0.455828i
$610$	415.963	+	172.298i	0.681907	+	0.282455i
$611$		−	214.930i		−	0.351767i
$612$		0			0
$613$	−118.452			−0.193233			−0.0966163	−	0.995322i	$-0.530802\pi$
$613$	−118.452			−0.193233			−0.0966163	+	0.995322i	$0.530802\pi$
$614$	−165.143	+	398.689i	−0.268962	+	0.649331i
$615$	164.920	+	110.196i	0.268162	+	0.179180i
$616$	1198.85	+	1198.85i	1.94619	+	1.94619i
$617$	980.371	−	195.008i	1.58893	−	0.316058i	0.680068	−	0.733149i	$-0.261950\pi$
$617$	980.371	−	195.008i	1.58893	−	0.316058i	0.908865	+	0.417091i	$0.136950\pi$
$618$	315.787	−	211.002i	0.510982	−	0.341427i
$619$	−32.0409	−	6.37333i	−0.0517623	−	0.0102962i	0.169141	−	0.985592i	$-0.445901\pi$
$619$	−32.0409	−	6.37333i	−0.0517623	−	0.0102962i	−0.220904	+	0.975296i	$0.570901\pi$
$620$	−55.1892	+	22.8601i	−0.0890149	+	0.0368712i
$621$	−193.958	−	468.255i	−0.312331	−	0.754034i
$622$	286.498	−	1440.32i	0.460608	−	2.31563i
$623$	73.3279	+	109.743i	0.117701	+	0.176153i
$624$	64.1190	+	322.348i	0.102755	+	0.516583i
$625$	373.672	−	373.672i	0.597874	−	0.597874i
$626$	430.438	−	644.195i	0.687600	−	1.02907i
$627$	−655.130	−	271.364i	−1.04486	−	0.432797i
$628$		−	2036.52i		−	3.24287i
$629$		0			0
$630$	−66.2282			−0.105124
$631$	300.962	−	726.587i	0.476960	−	1.15148i	−0.484067	−	0.875031i	$-0.660841\pi$
$631$	300.962	−	726.587i	0.476960	−	1.15148i	0.961027	−	0.276453i	$-0.0891591\pi$
$632$	84.3654	+	56.3711i	0.133489	+	0.0891948i
$633$	214.738	+	214.738i	0.339238	+	0.339238i
$634$	−316.461	+	62.9481i	−0.499151	+	0.0992872i
$635$	1.79655	−	1.20042i	0.00282922	−	0.00189042i
$636$	−48.1684	−	9.58130i	−0.0757365	−	0.0150649i
$637$	52.9094	−	21.9158i	0.0830603	−	0.0344047i
$638$	−485.124	−	1171.19i	−0.760382	−	1.83573i
$639$	33.2302	−	167.059i	0.0520034	−	0.261439i
$640$	−57.0524	−	85.3850i	−0.0891444	−	0.133414i
$641$	−154.754	−	778.001i	−0.241426	−	1.21373i	−0.891203	−	0.453605i	$-0.850138\pi$
$641$	−154.754	−	778.001i	−0.241426	−	1.21373i	0.649777	−	0.760125i	$-0.274862\pi$
$642$	−377.369	+	377.369i	−0.587803	+	0.587803i
$643$	147.758	−	221.135i	0.229795	−	0.343912i	−0.698597	−	0.715515i	$-0.746192\pi$
$643$	147.758	−	221.135i	0.229795	−	0.343912i	0.928392	+	0.371604i	$0.121192\pi$
$644$	872.078	+	361.226i	1.35416	+	0.560910i
$645$			172.547i			0.267514i
$646$		0			0
$647$	724.922			1.12044			0.560218	−	0.828345i	$-0.310717\pi$
$647$	724.922			1.12044			0.560218	+	0.828345i	$0.310717\pi$
$648$	408.796	−	986.921i	0.630858	−	1.52303i
$649$	269.197	+	179.872i	0.414788	+	0.277152i
$650$	188.431	+	188.431i	0.289894	+	0.289894i
$651$	69.6082	−	13.8459i	0.106925	−	0.0212687i
$652$	−1690.70	+	1129.69i	−2.59309	+	1.73265i
$653$	−326.815	−	65.0075i	−0.500482	−	0.0995521i	−0.0616075	−	0.998100i	$-0.519623\pi$
$653$	−326.815	−	65.0075i	−0.500482	−	0.0995521i	−0.438874	+	0.898548i	$0.644623\pi$
$654$	−790.479	+	327.427i	−1.20868	+	0.500653i
$655$	66.0947	+	159.567i	0.100908	+	0.243613i
$656$	−598.551	+	3009.12i	−0.912425	+	4.58707i
$657$	55.4770	+	83.0273i	0.0844399	+	0.126373i
$658$	−285.595	−	1435.78i	−0.434035	−	2.18204i
$659$	−69.6644	+	69.6644i	−0.105712	+	0.105712i	−0.757985	−	0.652272i	$-0.773816\pi$
$659$	−69.6644	+	69.6644i	−0.105712	+	0.105712i	0.652272	+	0.757985i	$0.273816\pi$
$660$	218.062	−	326.353i	0.330397	−	0.494474i
$661$	−890.769	−	368.969i	−1.34761	−	0.558198i	−0.411983	−	0.911192i	$-0.635164\pi$
$661$	−890.769	−	368.969i	−1.34761	−	0.558198i	−0.935626	+	0.352994i	$0.885164\pi$
$662$			1179.07i			1.78108i
$663$		0			0
$664$	−677.293			−1.02002
$665$	−49.5728	+	119.679i	−0.0745455	+	0.179969i
$666$	−190.473	−	127.270i	−0.285995	−	0.191096i
$667$	−299.433	−	299.433i	−0.448924	−	0.448924i
$668$	−1460.09	+	290.430i	−2.18576	+	0.434775i
$669$	−323.960	+	216.463i	−0.484244	+	0.323562i
$670$	1.84994	+	0.367976i	0.00276110	+	0.000549217i
$671$	−1340.33	+	555.183i	−1.99751	+	0.827397i
$672$	389.365	+	940.009i	0.579412	+	1.39882i
$673$	55.5537	−	279.287i	0.0825464	−	0.414989i	−0.917312	−	0.398169i	$-0.869646\pi$
$673$	55.5537	−	279.287i	0.0825464	−	0.414989i	0.999859	−	0.0168199i	$-0.00535420\pi$
$674$	−836.696	−	1252.20i	−1.24139	−	1.85787i
$675$	−135.806	−	682.741i	−0.201193	−	1.01147i
$676$	1131.07	−	1131.07i	1.67317	−	1.67317i
$677$	6.53347	−	9.77803i	0.00965062	−	0.0144432i	−0.826613	−	0.562771i	$-0.809735\pi$
$677$	6.53347	−	9.77803i	0.00965062	−	0.0144432i	0.836264	+	0.548328i	$0.184735\pi$
$678$	1236.64	+	512.232i	1.82395	+	0.755505i
$679$			971.155i			1.43027i
$680$		0			0
$681$	−568.647			−0.835018
$682$	103.126	−	248.968i	0.151211	−	0.365055i
$683$	−197.909	−	132.239i	−0.289765	−	0.193615i	0.402189	−	0.915557i	$-0.368250\pi$
$683$	−197.909	−	132.239i	−0.289765	−	0.193615i	−0.691953	+	0.721942i	$0.743250\pi$
$684$	413.150	+	413.150i	0.604021	+	0.604021i
$685$	−141.080	+	28.0625i	−0.205956	+	0.0409672i
$686$	1158.60	−	774.151i	1.68892	−	1.12850i
$687$	−948.048	−	188.578i	−1.37998	−	0.274496i
$688$	−2465.82	+	1021.37i	−3.58404	+	1.48456i
$689$	−2.27400	−	5.48991i	−0.00330043	−	0.00796794i
$690$	35.8104	−	180.031i	0.0518991	−	0.260915i
$691$	56.2295	+	84.1535i	0.0813742	+	0.121785i	0.869924	−	0.493186i	$-0.164168\pi$
$691$	56.2295	+	84.1535i	0.0813742	+	0.121785i	−0.788550	+	0.614971i	$0.789168\pi$
$692$	−249.245	−	1253.04i	−0.360181	−	1.81075i
$693$	150.899	−	150.899i	0.217747	−	0.217747i
$694$	−1047.24	+	1567.30i	−1.50898	+	2.25835i
$695$	−136.207	−	56.4187i	−0.195981	−	0.0811780i
$696$		−	1369.48i		−	1.96764i
$697$		0			0
$698$	2434.23			3.48744
$699$	−19.2252	+	46.4138i	−0.0275039	+	0.0664003i
$700$	1077.96	+	720.267i	1.53994	+	1.02895i
$701$	−791.094	−	791.094i	−1.12852	−	1.12852i	−0.990418	−	0.138104i	$-0.955899\pi$
$701$	−791.094	−	791.094i	−1.12852	−	1.12852i	−0.138104	−	0.990418i	$-0.544101\pi$
$702$	324.191	−	64.4855i	0.461810	−	0.0918597i
$703$	−372.558	+	248.935i	−0.529955	+	0.354104i
$704$	1407.15	+	279.900i	1.99880	+	0.397585i
$705$	−187.859	+	77.8138i	−0.266467	+	0.110374i
$706$	−654.846	−	1580.94i	−0.927544	−	2.23929i
$707$	7.18933	−	36.1432i	0.0101688	−	0.0511219i
$708$	323.864	+	484.696i	0.457434	+	0.684599i
$709$	175.605	+	882.825i	0.247679	+	1.24517i	0.881684	+	0.471840i	$0.156410\pi$
$709$	175.605	+	882.825i	0.247679	+	1.24517i	−0.634005	+	0.773329i	$0.718590\pi$
$710$	182.559	−	182.559i	0.257125	−	0.257125i
$711$	7.09537	−	10.6190i	0.00997943	−	0.0149353i
$712$	500.183	+	207.183i	0.702505	+	0.290987i
$713$		−	90.0179i		−	0.126252i
$714$		0			0
$715$	47.4900			0.0664195
$716$	−208.069	+	502.324i	−0.290600	+	0.701570i
$717$	566.266	+	378.367i	0.789771	+	0.527708i
$718$	1361.76	+	1361.76i	1.89660	+	1.89660i
$719$	−78.5955	+	15.6336i	−0.109312	+	0.0217436i	−0.249443	−	0.968389i	$-0.580248\pi$
$719$	−78.5955	+	15.6336i	−0.109312	+	0.0217436i	0.140131	+	0.990133i	$0.455248\pi$
$720$	−118.312	+	79.0538i	−0.164323	+	0.109797i
$721$	219.265	+	43.6146i	0.304113	+	0.0604918i
$722$	230.286	−	95.3875i	0.318956	−	0.132116i
$723$	52.2093	+	126.044i	0.0722120	+	0.174335i
$724$	−429.593	+	2159.71i	−0.593360	+	2.98302i
$725$	−323.123	−	483.588i	−0.445687	−	0.667017i
$726$	125.962	+	633.256i	0.173502	+	0.872253i
$727$	775.207	−	775.207i	1.06631	−	1.06631i	0.0686703	−	0.997639i	$-0.478124\pi$
$727$	775.207	−	775.207i	1.06631	−	1.06631i	0.997639	−	0.0686703i	$-0.0218757\pi$
$728$	−205.202	+	307.106i	−0.281870	+	0.421849i
$729$	−731.345	−	302.933i	−1.00322	−	0.415546i
$730$			151.354i			0.207335i
$731$		0			0
$732$	−2612.14			−3.56849
$733$	−216.024	+	521.528i	−0.294712	+	0.711498i	0.705284	+	0.708924i	$0.250819\pi$
$733$	−216.024	+	521.528i	−0.294712	+	0.711498i	−0.999997	+	0.00257394i	$0.999181\pi$
$734$	548.204	+	366.298i	0.746872	+	0.499044i
$735$	−38.3110	−	38.3110i	−0.0521238	−	0.0521238i
$736$	1265.71	−	251.765i	1.71971	−	0.342072i
$737$	−5.05344	+	3.37660i	−0.00685677	+	0.00458155i
$738$	723.104	+	143.834i	0.979815	+	0.194897i
$739$	653.407	−	270.650i	0.884177	−	0.366238i	0.106061	−	0.994360i	$-0.466176\pi$
$739$	653.407	−	270.650i	0.884177	−	0.366238i	0.778115	+	0.628122i	$0.216176\pi$
$740$	−94.9108	−	229.135i	−0.128258	−	0.309642i
$741$	30.1376	−	151.512i	0.0406715	−	0.204469i
$742$	−22.4858	−	33.6523i	−0.0303043	−	0.0453536i
$743$	65.8407	+	331.004i	0.0886147	+	0.445496i	0.999463	+	0.0327557i	$0.0104283\pi$
$743$	65.8407	+	331.004i	0.0886147	+	0.445496i	−0.910849	+	0.412740i	$0.864572\pi$
$744$	205.852	−	205.852i	0.276683	−	0.276683i
$745$	−91.3301	+	136.685i	−0.122591	+	0.183470i
$746$	2436.50	+	1009.23i	3.26608	+	1.35286i
$747$			85.2501i			0.114123i
$748$		0			0
$749$	−314.145			−0.419419
$750$	198.292	−	478.718i	0.264389	−	0.638291i
$751$	456.607	+	305.095i	0.607999	+	0.406252i	0.821105	−	0.570777i	$-0.193358\pi$
$751$	456.607	+	305.095i	0.607999	+	0.406252i	−0.213106	+	0.977029i	$0.568358\pi$
$752$	−2224.03	−	2224.03i	−2.95749	−	2.95749i
$753$	321.189	−	63.8884i	0.426545	−	0.0848451i
$754$	229.625	−	153.431i	0.304543	−	0.203489i
$755$	252.191	+	50.1640i	0.334028	+	0.0664424i
$756$	1485.69	−	615.394i	1.96520	−	0.814014i
$757$	−202.019	−	487.716i	−0.266867	−	0.644275i	0.732465	−	0.680804i	$-0.238370\pi$
$757$	−202.019	−	487.716i	−0.266867	−	0.644275i	−0.999333	+	0.0365296i	$0.988370\pi$
$758$	359.909	−	1809.38i	0.474814	−	2.38705i
$759$	328.602	+	491.787i	0.432940	+	0.647941i
$760$	103.663	+	521.148i	0.136398	+	0.685721i
$761$	−60.9884	+	60.9884i	−0.0801425	+	0.0801425i	−0.746042	−	0.665899i	$-0.768048\pi$
$761$	−60.9884	+	60.9884i	−0.0801425	+	0.0801425i	0.665899	+	0.746042i	$0.268048\pi$
$762$	−9.75036	+	14.5924i	−0.0127958	+	0.0191502i
$763$	−465.306	−	192.736i	−0.609838	−	0.252603i
$764$			867.571i			1.13556i
$765$		0			0
$766$	−1387.92			−1.81191
$767$	−26.9913	+	65.1628i	−0.0351908	+	0.0849580i
$768$	−165.645	−	110.681i	−0.215684	−	0.144115i
$769$	407.656	+	407.656i	0.530112	+	0.530112i	0.920606	−	0.390494i	$-0.127696\pi$
$769$	407.656	+	407.656i	0.530112	+	0.530112i	−0.390494	+	0.920606i	$0.627696\pi$
$770$	317.245	−	63.1040i	0.412006	−	0.0819532i
$771$	960.746	−	641.950i	1.24610	−	0.832620i
$772$	655.018	+	130.291i	0.848469	+	0.168771i
$773$	349.275	−	144.674i	0.451843	−	0.187160i	−0.145144	−	0.989411i	$-0.546364\pi$
$773$	349.275	−	144.674i	0.451843	−	0.187160i	0.596987	+	0.802251i	$0.296364\pi$
$774$	245.441	+	592.546i	0.317107	+	0.765563i
$775$	24.1201	−	121.260i	0.0311227	−	0.156465i
$776$	2213.15	+	3312.21i	2.85200	+	4.26832i
$777$	57.4856	+	289.000i	0.0739841	+	0.371943i
$778$	−1100.33	+	1100.33i	−1.41431	+	1.41431i
$779$	801.173	−	1199.04i	1.02846	−	1.53920i
$780$	78.9981	+	32.7221i	0.101280	+	0.0419514i
$781$			831.908i			1.06518i
$782$		0			0
$783$	−721.420			−0.921353
$784$	320.713	−	774.271i	0.409073	−	0.987590i
$785$	−193.828	−	129.512i	−0.246915	−	0.164983i
$786$	−991.974	−	991.974i	−1.26205	−	1.26205i
$787$	819.045	−	162.918i	1.04072	−	0.207012i	0.354991	−	0.934870i	$-0.384484\pi$
$787$	819.045	−	162.918i	1.04072	−	0.207012i	0.685728	+	0.727858i	$0.259484\pi$
$788$	2433.29	−	1625.88i	3.08794	−	2.06329i
$789$	487.993	+	97.0679i	0.618496	+	0.123027i
$790$	17.8843	−	7.40793i	0.0226384	−	0.00937713i
$791$	301.520	+	727.933i	0.381188	+	0.920269i
$792$	170.773	−	858.534i	0.215622	−	1.08401i
$793$	−175.589	−	262.787i	−0.221423	−	0.331383i
$794$	−126.301	−	634.960i	−0.159070	−	0.799698i
$795$	−3.97517	+	3.97517i	−0.00500021	+	0.00500021i
$796$	−1124.52	+	1682.96i	−1.41271	+	2.11427i
$797$	561.050	+	232.394i	0.703952	+	0.291587i	0.705799	−	0.708412i	$-0.250588\pi$
$797$	561.050	+	232.394i	0.703952	+	0.291587i	−0.00184721	+	0.999998i	$0.500588\pi$
$798$		−	1052.18i		−	1.31853i
$799$		0			0
$800$	1772.45			2.21556
$801$	26.0779	−	62.9575i	0.0325566	−	0.0785987i
$802$	−688.550	−	460.075i	−0.858541	−	0.573659i
$803$	−344.856	−	344.856i	−0.429459	−	0.429459i
$804$	−10.7328	+	2.13489i	−0.0133493	+	0.00265534i
$805$	89.8397	−	60.0290i	0.111602	−	0.0745701i
$806$	57.5788	+	11.4531i	0.0714377	+	0.0142098i
$807$	651.782	−	269.977i	0.807660	−	0.334544i
$808$	−57.8463	−	139.653i	−0.0715920	−	0.172838i
$809$	−210.645	+	1058.99i	−0.260377	+	1.30901i	0.600267	+	0.799799i	$0.295061\pi$
$809$	−210.645	+	1058.99i	−0.260377	+	1.30901i	−0.860645	+	0.509206i	$0.829939\pi$
$810$	−113.226	−	169.454i	−0.139785	−	0.209203i
$811$	−25.7182	−	129.294i	−0.0317117	−	0.159426i	0.961685	−	0.274158i	$-0.0883991\pi$
$811$	−25.7182	−	129.294i	−0.0317117	−	0.159426i	−0.993396	+	0.114732i	$0.963399\pi$
$812$	950.048	−	950.048i	1.17001	−	1.17001i
$813$	518.135	−	775.444i	0.637312	−	0.953805i
$814$	1033.67	+	428.159i	1.26986	+	0.525993i
$815$			232.756i			0.285591i
$816$		0			0
$817$	1254.49			1.53548
$818$	−708.362	+	1710.14i	−0.865968	+	2.09063i
$819$	38.6551	+	25.8285i	0.0471979	+	0.0315366i
$820$	564.418	+	564.418i	0.688315	+	0.688315i
$821$	−691.585	+	137.565i	−0.842369	+	0.167558i	−0.597370	−	0.801966i	$-0.703788\pi$
$821$	−691.585	+	137.565i	−0.842369	+	0.167558i	−0.244999	+	0.969523i	$0.578788\pi$
$822$	971.461	−	649.109i	1.18183	−	0.789671i
$823$	−589.634	−	117.285i	−0.716444	−	0.142510i	−0.176610	−	0.984281i	$-0.556513\pi$
$823$	−589.634	−	117.285i	−0.716444	−	0.142510i	−0.539834	+	0.841771i	$0.681513\pi$
$824$	847.217	−	350.929i	1.02818	−	0.425885i
$825$	310.874	+	750.517i	0.376818	+	0.909718i
$826$	−93.7215	+	471.170i	−0.113464	+	0.570423i
$827$	506.704	+	758.335i	0.612701	+	0.916971i	0.999988	−	0.00498782i	$-0.00158768\pi$
$827$	506.704	+	758.335i	0.612701	+	0.916971i	−0.387287	+	0.921959i	$0.626588\pi$
$828$	−95.0774	−	477.987i	−0.114828	−	0.577278i
$829$	68.4251	−	68.4251i	0.0825393	−	0.0825393i	−0.664632	−	0.747171i	$-0.731412\pi$
$829$	68.4251	−	68.4251i	0.0825393	−	0.0825393i	0.747171	+	0.664632i	$0.231412\pi$
$830$	−71.7885	+	107.439i	−0.0864922	+	0.129445i
$831$	−24.4836	−	10.1414i	−0.0294628	−	0.0122039i
$832$			312.556i			0.375668i
$833$		0			0
$834$	1197.49			1.43584
$835$	−65.2119	+	157.435i	−0.0780981	+	0.188545i
$836$	−2372.73	−	1585.41i	−2.83819	−	1.89642i
$837$	−108.440	−	108.440i	−0.129557	−	0.129557i
$838$	820.642	−	163.236i	0.979287	−	0.194792i
$839$	−1156.84	+	772.973i	−1.37883	+	0.921302i	−0.999991	−	0.00416189i	$-0.998675\pi$
$839$	−1156.84	+	772.973i	−1.37883	+	0.921302i	−0.378835	+	0.925464i	$0.623675\pi$
$840$	342.718	+	68.1708i	0.407997	+	0.0811557i
$841$	220.117	−	91.1755i	0.261733	−	0.108413i
$842$	−646.698	−	1561.27i	−0.768050	−	1.85424i
$843$	−41.8000	+	210.143i	−0.0495849	+	0.249280i
$844$	678.972	+	1016.15i	0.804469	+	1.20397i
$845$	−35.7208	−	179.580i	−0.0422731	−	0.212521i
$846$	−534.444	+	534.444i	−0.631730	+	0.631730i
$847$	−211.151	+	316.010i	−0.249293	+	0.373093i
$848$	−80.3387	−	33.2774i	−0.0947391	−	0.0392422i
$849$			228.303i			0.268908i
$850$		0			0
$851$	373.737			0.439174
$852$	−573.210	+	1383.85i	−0.672782	+	1.62424i
$853$	747.071	+	499.177i	0.875816	+	0.585202i	0.910182	−	0.414207i	$-0.135941\pi$
$853$	747.071	+	499.177i	0.875816	+	0.585202i	−0.0343660	+	0.999409i	$0.510941\pi$
$854$	−1522.16	−	1522.16i	−1.78239	−	1.78239i
$855$	65.5963	−	13.0479i	0.0767208	−	0.0152607i
$856$	−1071.42	+	715.900i	−1.25166	+	0.836332i
$857$	191.638	+	38.1191i	0.223615	+	0.0444797i	0.305626	−	0.952152i	$-0.401134\pi$
$857$	191.638	+	38.1191i	0.223615	+	0.0444797i	−0.0820111	+	0.996631i	$0.526134\pi$
$858$	−356.373	+	147.615i	−0.415354	+	0.172045i
$859$	−226.402	−	546.583i	−0.263565	−	0.636302i	0.735589	−	0.677428i	$-0.236905\pi$
$859$	−226.402	−	546.583i	−0.263565	−	0.636302i	−0.999154	+	0.0411262i	$0.986905\pi$
$860$	−135.466	+	681.035i	−0.157519	+	0.791902i
$861$	−526.868	−	788.514i	−0.611926	−	0.915812i
$862$	250.434	+	1259.01i	0.290526	+	1.46057i
$863$	−742.830	+	742.830i	−0.860753	+	0.860753i	−0.991426	−	0.130672i	$-0.958286\pi$
$863$	−742.830	+	742.830i	−0.860753	+	0.860753i	0.130672	+	0.991426i	$0.458286\pi$
$864$	1221.44	−	1828.01i	1.41370	−	2.11576i
$865$	−135.110	−	55.9646i	−0.156197	−	0.0646989i
$866$			1549.54i			1.78931i
$867$		0			0
$868$	285.611			0.329045
$869$	−23.8701	+	57.6275i	−0.0274685	+	0.0663147i
$870$	−217.240	−	145.155i	−0.249702	−	0.166845i
$871$	−0.936238	−	0.936238i	−0.00107490	−	0.00107490i
$872$	−2026.19	+	403.035i	−2.32362	+	0.462196i
$873$	416.905	−	278.567i	0.477554	−	0.319092i
$874$	−1308.90	−	260.357i	−1.49760	−	0.297892i
$875$	281.792	−	116.722i	0.322048	−	0.133397i
$876$	−336.040	−	811.273i	−0.383608	−	0.926111i
$877$	−194.984	+	980.249i	−0.222330	+	1.11773i	0.694819	+	0.719185i	$0.255485\pi$
$877$	−194.984	+	980.249i	−0.222330	+	1.11773i	−0.917149	+	0.398544i	$0.869515\pi$
$878$	−1250.07	−	1870.86i	−1.42377	−	2.13082i
$879$	−28.4582	−	143.069i	−0.0323756	−	0.162763i
$880$	491.413	−	491.413i	0.558424	−	0.558424i
$881$	−334.226	+	500.204i	−0.379371	+	0.567769i	−0.971191	−	0.238301i	$-0.923410\pi$
$881$	−334.226	+	500.204i	−0.379371	+	0.567769i	0.591820	+	0.806070i	$0.298410\pi$
$882$	−186.060	−	77.0687i	−0.210953	−	0.0873795i
$883$		−	886.900i		−	1.00442i	−0.864747	−	0.502208i	$-0.832521\pi$
$883$		−	886.900i		−	1.00442i	0.864747	−	0.502208i	$-0.167479\pi$
$884$		0			0
$885$	66.7276			0.0753984
$886$	645.880	−	1559.29i	0.728985	−	1.75992i
$887$	571.959	+	382.171i	0.644824	+	0.430858i	0.834514	−	0.550986i	$-0.185748\pi$
$887$	571.959	+	382.171i	0.644824	+	0.430858i	−0.189690	+	0.981844i	$0.560748\pi$
$888$	854.657	+	854.657i	0.962452	+	0.962452i
$889$	−10.1322	+	2.01542i	−0.0113973	+	0.00226707i
$890$	85.8815	−	57.3842i	0.0964961	−	0.0644766i
$891$	644.077	+	128.115i	0.722870	+	0.143788i
$892$	−1448.60	+	600.030i	−1.62399	+	0.672680i
$893$	565.741	+	1365.82i	0.633528	+	1.52947i
$894$	260.495	−	1309.59i	0.291381	−	1.46487i
$895$	34.5772	+	51.7484i	0.0386337	+	0.0578195i
$896$	95.7872	+	481.555i	0.106905	+	0.537450i
$897$	−91.1121	+	91.1121i	−0.101574	+	0.101574i
$898$	−358.105	+	535.942i	−0.398781	+	0.596818i
$899$	−118.376	−	49.0331i	−0.131676	−	0.0545419i
$900$		−	669.355i		−	0.743728i
$901$		0			0
$902$	−3600.85			−3.99207
$903$	315.706	−	762.182i	0.349619	−	0.844055i
$904$	2687.24	+	1795.55i	2.97261	+	1.98623i
$905$	178.233	+	178.233i	0.196943	+	0.196943i
$906$	−2048.42	+	407.455i	−2.26095	+	0.449730i
$907$	−706.861	+	472.309i	−0.779339	+	0.520738i	−0.880451	−	0.474137i	$-0.842760\pi$
$907$	−706.861	+	472.309i	−0.779339	+	0.520738i	0.101112	+	0.994875i	$0.467760\pi$
$908$	−2244.43	−	446.445i	−2.47184	−	0.491680i
$909$	−17.5780	+	7.28106i	−0.0193378	+	0.00800996i
$910$	26.9663	+	65.1024i	0.0296333	+	0.0715410i
$911$	26.1489	−	131.459i	0.0287035	−	0.144302i	−0.963776	−	0.266713i	$-0.914062\pi$
$911$	26.1489	−	131.459i	0.0287035	−	0.144302i	0.992480	+	0.122411i	$0.0390625\pi$
$912$	−1255.95	−	1879.66i	−1.37713	−	2.06103i
$913$	−81.2286	−	408.364i	−0.0889689	−	0.447277i
$914$	313.442	−	313.442i	0.342934	−	0.342934i
$915$	−166.118	+	248.613i	−0.181550	+	0.271708i
$916$	−3593.86	−	1488.62i	−3.92343	−	1.62514i
$917$		−	825.779i		−	0.900522i
$918$		0			0
$919$	−141.545			−0.154021			−0.0770106	−	0.997030i	$-0.524538\pi$
$919$	−141.545			−0.154021			−0.0770106	+	0.997030i	$0.524538\pi$
$920$	169.607	−	409.469i	0.184356	−	0.445075i
$921$	−238.289	−	159.220i	−0.258729	−	0.172877i
$922$	1608.40	+	1608.40i	1.74446	+	1.74446i
$923$	−177.750	+	35.3567i	−0.192579	+	0.0383063i
$924$	−1560.36	+	1042.60i	−1.68870	+	1.12835i
$925$	503.448	+	100.142i	0.544268	+	0.108262i
$926$	281.050	−	116.415i	0.303510	−	0.125718i
$927$	−44.1710	−	106.638i	−0.0476495	−	0.115036i
$928$	358.357	−	1801.58i	0.386161	−	1.94136i
$929$	648.167	+	970.050i	0.697704	+	1.04419i	0.995968	+	0.0897043i	$0.0285922\pi$
$929$	648.167	+	970.050i	0.697704	+	1.04419i	−0.298265	+	0.954483i	$0.596408\pi$
$930$	−10.8354	−	54.4732i	−0.0116510	−	0.0585734i
$931$	−278.538	+	278.538i	−0.299181	+	0.299181i
$932$	−112.321	+	168.100i	−0.120516	+	0.180365i
$933$	901.031	+	373.219i	0.965736	+	0.400021i
$934$			263.529i			0.282151i
$935$		0			0
$936$	190.697			0.203736
$937$	270.033	−	651.918i	0.288189	−	0.695750i	−0.711789	−	0.702394i	$-0.752115\pi$
$937$	270.033	−	651.918i	0.288189	−	0.695750i	0.999978	+	0.00664341i	$0.00211468\pi$
$938$	−7.49836	−	5.01024i	−0.00799399	−	0.00534141i
$939$	363.827	+	363.827i	0.387462	+	0.387462i
$940$	−802.565	+	159.640i	−0.853792	+	0.169830i
$941$	37.8946	−	25.3204i	0.0402706	−	0.0269079i	−0.535272	−	0.844680i	$-0.679791\pi$
$941$	37.8946	−	25.3204i	0.0402706	−	0.0269079i	0.575543	+	0.817772i	$0.304791\pi$
$942$	1857.09	+	369.398i	1.97143	+	0.392143i
$943$	−1111.27	+	460.305i	−1.17845	+	0.488128i
$944$	394.988	+	953.585i	0.418419	+	1.01015i
$945$	35.9113	−	180.538i	0.0380014	−	0.191046i
$946$	−1740.30	−	2604.54i	−1.83964	−	2.75321i
$947$	125.745	+	632.161i	0.132782	+	0.667540i	0.988637	+	0.150324i	$0.0480317\pi$
$947$	125.745	+	632.161i	0.132782	+	0.667540i	−0.855855	+	0.517216i	$0.826968\pi$
$948$	−79.4143	+	79.4143i	−0.0837703	+	0.0837703i
$949$	59.0272	−	88.3404i	0.0621993	−	0.0930879i
$950$	−1693.42	−	701.437i	−1.78255	−	0.738354i
$951$		−	214.282i		−	0.225323i
$952$		0			0
$953$	522.396			0.548160			0.274080	−	0.961707i	$-0.411627\pi$
$953$	522.396			0.548160			0.274080	+	0.961707i	$0.411627\pi$
$954$	−7.99669	+	19.3057i	−0.00838228	+	0.0202366i
$955$	82.5721	+	55.1729i	0.0864630	+	0.0577727i
$956$	1937.97	+	1937.97i	2.02717	+	2.02717i
$957$	825.706	−	164.243i	0.862807	−	0.171623i
$958$	−1640.02	+	1095.83i	−1.71192	+	1.14387i
$959$	674.530	+	134.172i	0.703368	+	0.139909i
$960$	273.189	−	113.159i	0.284572	−	0.117874i
$961$	357.335	+	862.684i	0.371837	+	0.897694i
$962$	−47.5512	+	239.056i	−0.0494295	+	0.248499i
$963$	90.1096	+	134.859i	0.0935717	+	0.140040i
$964$	107.111	+	538.482i	0.111111	+	0.558591i
$965$	54.0563	−	54.0563i	0.0560169	−	0.0560169i
$966$	−487.583	+	729.720i	−0.504745	+	0.755404i
$967$	616.335	+	255.294i	0.637368	+	0.264006i	0.677880	−	0.735173i	$-0.262899\pi$
$967$	616.335	+	255.294i	0.637368	+	0.264006i	−0.0405121	+	0.999179i	$0.512899\pi$
$968$			1558.97i			1.61050i
$969$		0			0
$970$	759.996			0.783501
$971$	−126.591	+	305.617i	−0.130371	+	0.314744i	−0.975563	−	0.219719i	$-0.929486\pi$
$971$	−126.591	+	305.617i	−0.130371	+	0.314744i	0.845192	+	0.534463i	$0.179486\pi$
$972$	−1215.73	−	812.324i	−1.25075	−	0.835724i
$973$	498.431	+	498.431i	0.512262	+	0.512262i
$974$	2802.79	−	557.509i	2.87760	−	0.572391i
$975$	−147.147	+	98.3207i	−0.150920	+	0.100842i
$976$	−4536.18	−	902.303i	−4.64773	−	0.924491i
$977$	−1335.32	+	553.107i	−1.36675	+	0.566128i	−0.940906	−	0.338668i	$-0.890024\pi$
$977$	−1335.32	+	553.107i	−1.36675	+	0.566128i	−0.425847	+	0.904795i	$0.640024\pi$
$978$	−723.485	−	1746.65i	−0.739760	−	1.78594i
$979$	−64.9301	+	326.426i	−0.0663229	+	0.333428i
$980$	−121.134	−	181.290i	−0.123606	−	0.184990i
$981$	50.7296	+	255.035i	0.0517121	+	0.259974i
$982$	−1668.14	+	1668.14i	−1.69872	+	1.69872i
$983$	−952.831	+	1426.01i	−0.969309	+	1.45067i	−0.0781712	+	0.996940i	$0.524908\pi$
$983$	−952.831	+	1426.01i	−0.969309	+	1.45067i	−0.891138	+	0.453733i	$0.850092\pi$
$984$	−3593.87	−	1488.63i	−3.65230	−	1.51283i
$985$		−	334.989i		−	0.340090i
$986$		0			0
$987$	972.195			0.985000
$988$	237.904	−	574.351i	0.240793	−	0.581327i
$989$	−870.026	−	581.333i	−0.879703	−	0.587798i
$990$	−118.089	−	118.089i	−0.119281	−	0.119281i
$991$	−1539.10	+	306.146i	−1.55308	+	0.308926i	−0.895708	−	0.444643i	$-0.853331\pi$
$991$	−1539.10	+	306.146i	−1.55308	+	0.308926i	−0.657369	+	0.753569i	$0.728331\pi$
$992$	324.670	−	216.937i	0.327288	−	0.218687i
$993$	−767.985	−	152.762i	−0.773399	−	0.153839i
$994$	−1140.43	+	472.383i	−1.14732	+	0.475234i
$995$	88.6645	+	214.055i	0.0891100	+	0.215131i
$996$	146.254	−	735.269i	0.146841	−	0.738222i
$997$	328.333	+	491.385i	0.329321	+	0.492864i	0.958772	−	0.284176i	$-0.0917201\pi$
$997$	328.333	+	491.385i	0.329321	+	0.492864i	−0.629451	+	0.777040i	$0.716720\pi$
$998$	173.148	+	870.475i	0.173495	+	0.872220i
$999$	450.220	−	450.220i	0.450671	−	0.450671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.r.214.1	yes	96
17.2	even	8	inner	289.3.e.r.40.1	✓	96
17.3	odd	16	inner	289.3.e.r.158.11	yes	96
17.4	even	4	inner	289.3.e.r.75.11	yes	96
17.5	odd	16	inner	289.3.e.r.131.2	yes	96
17.6	odd	16	inner	289.3.e.r.224.1	yes	96
17.7	odd	16	inner	289.3.e.r.65.11	yes	96
17.8	even	8	inner	289.3.e.r.249.12	yes	96
17.9	even	8	inner	289.3.e.r.249.11	yes	96
17.10	odd	16	inner	289.3.e.r.65.12	yes	96
17.11	odd	16	inner	289.3.e.r.224.2	yes	96
17.12	odd	16	inner	289.3.e.r.131.1	yes	96
17.13	even	4	inner	289.3.e.r.75.12	yes	96
17.14	odd	16	inner	289.3.e.r.158.12	yes	96
17.15	even	8	inner	289.3.e.r.40.2	yes	96
17.16	even	2	inner	289.3.e.r.214.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.3.e.r.40.1	✓	96	17.2	even	8	inner
289.3.e.r.40.2	yes	96	17.15	even	8	inner
289.3.e.r.65.11	yes	96	17.7	odd	16	inner
289.3.e.r.65.12	yes	96	17.10	odd	16	inner
289.3.e.r.75.11	yes	96	17.4	even	4	inner
289.3.e.r.75.12	yes	96	17.13	even	4	inner
289.3.e.r.131.1	yes	96	17.12	odd	16	inner
289.3.e.r.131.2	yes	96	17.5	odd	16	inner
289.3.e.r.158.11	yes	96	17.3	odd	16	inner
289.3.e.r.158.12	yes	96	17.14	odd	16	inner
289.3.e.r.214.1	yes	96	1.1	even	1	trivial
289.3.e.r.214.2	yes	96	17.16	even	2	inner
289.3.e.r.224.1	yes	96	17.6	odd	16	inner
289.3.e.r.224.2	yes	96	17.11	odd	16	inner
289.3.e.r.249.11	yes	96	17.9	even	8	inner
289.3.e.r.249.12	yes	96	17.8	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43186 + 3.45680i) q^{2} +(-2.06607 - 1.38050i) q^{3} +(-7.07086 - 7.07086i) q^{4} +(-1.12265 + 0.223308i) q^{5} +(7.73043 - 5.16531i) q^{6} +(5.36760 + 1.06768i) q^{7} +(20.7398 - 8.59071i) q^{8} +(-1.08130 - 2.61050i) q^{9} +O(q^{10})\)	\(q+(-1.43186 + 3.45680i) q^{2} +(-2.06607 - 1.38050i) q^{3} +(-7.07086 - 7.07086i) q^{4} +(-1.12265 + 0.223308i) q^{5} +(7.73043 - 5.16531i) q^{6} +(5.36760 + 1.06768i) q^{7} +(20.7398 - 8.59071i) q^{8} +(-1.08130 - 2.61050i) q^{9} +(0.835535 - 4.20052i) q^{10} +(7.66699 + 11.4745i) q^{11} +(4.84754 + 24.3702i) q^{12} +(-2.12584 + 2.12584i) q^{13} +(-11.3764 + 17.0260i) q^{14} +(2.62774 + 1.08845i) q^{15} +43.9953i q^{16} +10.5722 q^{18} +(7.91348 - 19.1048i) q^{19} +(9.51706 + 6.35910i) q^{20} +(-9.61588 - 9.61588i) q^{21} +(-50.6430 + 10.0735i) q^{22} +(-14.3414 + 9.58265i) q^{23} +(-54.7093 - 10.8824i) q^{24} +(-21.8865 + 9.06569i) q^{25} +(-4.30473 - 10.3925i) q^{26} +(-5.73266 + 28.8200i) q^{27} +(-30.4041 - 45.5030i) q^{28} +(4.78964 + 24.0792i) q^{29} +(-7.52509 + 7.52509i) q^{30} +(-2.89949 + 4.33939i) q^{31} +(-69.1239 - 28.6320i) q^{32} -34.2913i q^{33} -6.26434 q^{35} +(-10.8127 + 26.1042i) q^{36} +(-18.0163 - 12.0381i) q^{37} +(54.7107 + 54.7107i) q^{38} +(7.32687 - 1.45741i) q^{39} +(-21.3651 + 14.2757i) q^{40} +(68.3964 + 13.6049i) q^{41} +(47.0088 - 19.4717i) q^{42} +(23.2155 + 56.0473i) q^{43} +(26.9221 - 135.347i) q^{44} +(1.79687 + 2.68920i) q^{45} +(-12.5905 - 63.2965i) q^{46} +(-50.5516 + 50.5516i) q^{47} +(60.7356 - 90.8972i) q^{48} +(-17.5989 - 7.28972i) q^{49} -88.6382i q^{50} +30.0631 q^{52} +(-0.756385 + 1.82608i) q^{53} +(-91.4169 - 61.0828i) q^{54} +(-11.1697 - 11.1697i) q^{55} +(120.495 - 23.9680i) q^{56} +(-42.7241 + 28.5473i) q^{57} +(-90.0950 - 17.9210i) q^{58} +(21.6747 - 8.97796i) q^{59} +(-10.8841 - 26.2766i) q^{60} +(-20.5091 + 103.106i) q^{61} +(-10.8488 - 16.2363i) q^{62} +(-3.01682 - 15.1666i) q^{63} +(73.5133 - 73.5133i) q^{64} +(1.91185 - 2.86129i) q^{65} +(118.538 + 49.1002i) q^{66} +0.440407i q^{67} +42.8592 q^{69} +(8.96963 - 21.6546i) q^{70} +(50.1228 + 33.4910i) q^{71} +(-44.8521 - 44.8521i) q^{72} +(-34.6609 + 6.89449i) q^{73} +(67.4102 - 45.0420i) q^{74} +(57.7342 + 11.4840i) q^{75} +(-191.043 + 79.1325i) q^{76} +(28.9023 + 69.7762i) q^{77} +(-5.45305 + 27.4143i) q^{78} +(2.51112 + 3.75816i) q^{79} +(-9.82452 - 49.3912i) q^{80} +(33.6483 - 33.6483i) q^{81} +(-144.963 + 216.953i) q^{82} +(-27.8742 - 11.5459i) q^{83} +135.985i q^{84} -226.986 q^{86} +(23.3456 - 56.3613i) q^{87} +(257.586 + 172.113i) q^{88} +(17.0533 + 17.0533i) q^{89} +(-11.8689 + 2.36087i) q^{90} +(-13.6804 + 9.14095i) q^{91} +(169.164 + 33.6488i) q^{92} +(11.9811 - 4.96272i) q^{93} +(-102.364 - 247.129i) q^{94} +(-4.61778 + 23.2151i) q^{95} +(103.288 + 154.581i) q^{96} +(34.6193 + 174.043i) q^{97} +(50.3983 - 50.3983i) q^{98} +(21.6637 - 32.4220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q + 288 q^{18} + 384 q^{35} + 1920 q^{52} - 1152 q^{69} - 6240 q^{86}+O(q^{100}) \) 96 * q + 288 * q^18 + 384 * q^35 + 1920 * q^52 - 1152 * q^69 - 6240 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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