LMFDB - Embedded newform 275.3.bk.c.82.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(82,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			82.9
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.166354 - 0.326489i) q^{2} +(-0.928883 + 0.147121i) q^{3} +(2.27222 + 3.12744i) q^{4} +(-0.106490 + 0.327744i) q^{6} +(10.4047 + 1.64794i) q^{7} +(2.84673 - 0.450878i) q^{8} +(-7.71833 + 2.50784i) q^{9} +(-8.46786 + 7.02107i) q^{11} +(-2.57074 - 2.57074i) q^{12} +(2.61803 + 1.33395i) q^{13} +(2.26890 - 3.12287i) q^{14} +(-4.45195 + 13.7017i) q^{16} +(14.2681 - 7.26994i) q^{17} +(-0.465197 + 2.93714i) q^{18} +(8.60484 - 11.8435i) q^{19} -9.90719 q^{21} +(0.883634 + 3.93264i) q^{22} +(-28.3868 + 28.3868i) q^{23} +(-2.57795 + 0.837625i) q^{24} +(0.871040 - 0.632848i) q^{26} +(14.3421 - 7.30766i) q^{27} +(18.4879 + 36.2846i) q^{28} +(18.1268 + 24.9494i) q^{29} +(16.2065 + 49.8786i) q^{31} +(11.8850 + 11.8850i) q^{32} +(6.83271 - 7.76755i) q^{33} -5.86775i q^{34} +(-25.3809 - 18.4403i) q^{36} +(18.0590 + 2.86026i) q^{37} +(-2.43533 - 4.77961i) q^{38} +(-2.62809 - 0.853920i) q^{39} +(-27.3139 - 19.8447i) q^{41} +(-1.64810 + 3.23459i) q^{42} +(47.0885 - 47.0885i) q^{43} +(-41.1988 - 10.5293i) q^{44} +(4.54571 + 13.9903i) q^{46} +(-4.87237 - 30.7629i) q^{47} +(2.11954 - 13.3822i) q^{48} +(58.9402 + 19.1508i) q^{49} +(-12.1838 + 8.85205i) q^{51} +(1.77688 + 11.2188i) q^{52} +(-21.6991 - 11.0563i) q^{53} -5.89819i q^{54} +30.3624 q^{56} +(-6.25046 + 12.2672i) q^{57} +(11.1612 - 1.76775i) q^{58} +(2.90572 + 3.99938i) q^{59} +(21.4090 - 65.8900i) q^{61} +(18.9808 + 3.00627i) q^{62} +(-84.4396 + 13.3739i) q^{63} +(-48.9493 + 15.9046i) q^{64} +(-1.39937 - 3.52297i) q^{66} +(-31.7791 - 31.7791i) q^{67} +(55.1565 + 28.1036i) q^{68} +(22.1918 - 30.5443i) q^{69} +(8.18581 - 25.1933i) q^{71} +(-20.8413 + 10.6192i) q^{72} +(-2.01349 + 12.7127i) q^{73} +(3.93804 - 5.42024i) q^{74} +56.5921 q^{76} +(-99.6758 + 59.0975i) q^{77} +(-0.715990 + 0.715990i) q^{78} +(-74.0458 + 24.0589i) q^{79} +(46.8434 - 34.0337i) q^{81} +(-11.0228 + 5.61642i) q^{82} +(-32.6366 - 64.0530i) q^{83} +(-22.5113 - 30.9842i) q^{84} +(-7.54048 - 23.2072i) q^{86} +(-20.5082 - 20.5082i) q^{87} +(-20.9401 + 23.8050i) q^{88} -43.9843i q^{89} +(25.0415 + 18.1937i) q^{91} +(-153.279 - 24.2771i) q^{92} +(-22.3922 - 43.9471i) q^{93} +(-10.8543 - 3.52677i) q^{94} +(-12.7883 - 9.29123i) q^{96} +(57.0567 - 111.980i) q^{97} +(16.0575 - 16.0575i) q^{98} +(47.7500 - 75.4269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) $ 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.166354	−	0.326489i	0.0831771	−	0.163244i	−0.845672	−	0.533704i	$-0.820800\pi$
$2$	0.166354	−	0.326489i	0.0831771	−	0.163244i	0.928849	+	0.370459i	$0.120800\pi$
$3$	−0.928883	+	0.147121i	−0.309628	+	0.0490402i	−0.309315	−	0.950960i	$-0.600100\pi$
$3$	−0.928883	+	0.147121i	−0.309628	+	0.0490402i	−0.000313023		1.00000i	$0.500100\pi$
$4$	2.27222	+	3.12744i	0.568055	+	0.781861i
$5$		0			0
$5$		0			0
$6$	−0.106490	+	0.327744i	−0.0177484	+	0.0546240i
$7$	10.4047	+	1.64794i	1.48638	+	0.235420i	0.846227	−	0.532823i	$-0.178869\pi$
$7$	10.4047	+	1.64794i	1.48638	+	0.235420i	0.640158	+	0.768243i	$0.278869\pi$
$8$	2.84673	−	0.450878i	0.355841	−	0.0563597i
$9$	−7.71833	+	2.50784i	−0.857592	+	0.278649i
$10$		0			0
$11$	−8.46786	+	7.02107i	−0.769805	+	0.638279i
$11$	−8.46786	+	7.02107i	−0.769805	+	0.638279i
$12$	−2.57074	−	2.57074i	−0.214228	−	0.214228i
$13$	2.61803	+	1.33395i	0.201387	+	0.102612i	0.551776	−	0.833993i	$-0.313951\pi$
$13$	2.61803	+	1.33395i	0.201387	+	0.102612i	−0.350389	+	0.936604i	$0.613951\pi$
$14$	2.26890	−	3.12287i	0.162064	−	0.223062i
$15$		0			0
$16$	−4.45195	+	13.7017i	−0.278247	+	0.856355i
$17$	14.2681	−	7.26994i	0.839298	−	0.427644i	0.0191647	−	0.999816i	$-0.493899\pi$
$17$	14.2681	−	7.26994i	0.839298	−	0.427644i	0.820133	+	0.572173i	$0.193899\pi$
$18$	−0.465197	+	2.93714i	−0.0258443	+	0.163174i
$19$	8.60484	−	11.8435i	0.452886	−	0.623344i	−0.520128	−	0.854088i	$-0.674116\pi$
$19$	8.60484	−	11.8435i	0.452886	−	0.623344i	0.973015	+	0.230744i	$0.0741159\pi$
$20$		0			0
$21$	−9.90719			−0.471771
$22$	0.883634	+	3.93264i	0.0401652	+	0.178757i
$23$	−28.3868	+	28.3868i	−1.23421	+	1.23421i	−0.271878	+	0.962332i	$0.587645\pi$
$23$	−28.3868	+	28.3868i	−1.23421	+	1.23421i	−0.962332	+	0.271878i	$0.912355\pi$
$24$	−2.57795	+	0.837625i	−0.107414	+	0.0349011i
$25$		0			0
$26$	0.871040	−	0.632848i	0.0335016	−	0.0243403i
$27$	14.3421	−	7.30766i	0.531188	−	0.270654i
$28$	18.4879	+	36.2846i	0.660283	+	1.29588i
$29$	18.1268	+	24.9494i	0.625062	+	0.860324i	0.997709	−	0.0676492i	$-0.0215499\pi$
$29$	18.1268	+	24.9494i	0.625062	+	0.860324i	−0.372647	+	0.927973i	$0.621550\pi$
$30$		0			0
$31$	16.2065	+	49.8786i	0.522792	+	1.60899i	0.768642	+	0.639680i	$0.220933\pi$
$31$	16.2065	+	49.8786i	0.522792	+	1.60899i	−0.245850	+	0.969308i	$0.579067\pi$
$32$	11.8850	+	11.8850i	0.371406	+	0.371406i
$33$	6.83271	−	7.76755i	0.207052	−	0.235380i
$34$		−	5.86775i		−	0.172581i
$35$		0			0
$36$	−25.3809	−	18.4403i	−0.705024	−	0.512230i
$37$	18.0590	+	2.86026i	0.488081	+	0.0773045i	0.395625	−	0.918412i	$-0.370528\pi$
$37$	18.0590	+	2.86026i	0.488081	+	0.0773045i	0.0924564	+	0.995717i	$0.470528\pi$
$38$	−2.43533	−	4.77961i	−0.0640877	−	0.125779i
$39$	−2.62809	−	0.853920i	−0.0673870	−	0.0218954i
$40$		0			0
$41$	−27.3139	−	19.8447i	−0.666192	−	0.484016i	0.202557	−	0.979271i	$-0.435075\pi$
$41$	−27.3139	−	19.8447i	−0.666192	−	0.484016i	−0.868748	+	0.495254i	$0.835075\pi$
$42$	−1.64810	+	3.23459i	−0.0392406	+	0.0770139i
$43$	47.0885	−	47.0885i	1.09508	−	1.09508i	0.100104	−	0.994977i	$-0.468083\pi$
$43$	47.0885	−	47.0885i	1.09508	−	1.09508i	0.994977	−	0.100104i	$-0.0319175\pi$
$44$	−41.1988	−	10.5293i	−0.936337	−	0.239303i
$45$		0			0
$46$	4.54571	+	13.9903i	0.0988197	+	0.304136i
$47$	−4.87237	−	30.7629i	−0.103667	−	0.654530i	−0.983727	−	0.179668i	$-0.942498\pi$
$47$	−4.87237	−	30.7629i	−0.103667	−	0.654530i	0.880060	−	0.474863i	$-0.157502\pi$
$48$	2.11954	−	13.3822i	0.0441570	−	0.278797i
$49$	58.9402	+	19.1508i	1.20286	+	0.390833i
$50$		0			0
$51$	−12.1838	+	8.85205i	−0.238898	+	0.173570i
$52$	1.77688	+	11.2188i	0.0341707	+	0.215745i
$53$	−21.6991	−	11.0563i	−0.409418	−	0.208609i	0.237137	−	0.971476i	$-0.423791\pi$
$53$	−21.6991	−	11.0563i	−0.409418	−	0.208609i	−0.646555	+	0.762867i	$0.723791\pi$
$54$		−	5.89819i		−	0.109226i
$55$		0			0
$56$	30.3624			0.542185
$57$	−6.25046	+	12.2672i	−0.109657	+	0.215214i
$58$	11.1612	−	1.76775i	0.192434	−	0.0304785i
$59$	2.90572	+	3.99938i	0.0492495	+	0.0677862i	0.832931	−	0.553376i	$-0.186661\pi$
$59$	2.90572	+	3.99938i	0.0492495	+	0.0677862i	−0.783682	+	0.621162i	$0.786661\pi$
$60$		0			0
$61$	21.4090	−	65.8900i	0.350967	−	1.08016i	−0.607345	−	0.794438i	$-0.707765\pi$
$61$	21.4090	−	65.8900i	0.350967	−	1.08016i	0.958311	−	0.285726i	$-0.0922346\pi$
$62$	18.9808	+	3.00627i	0.306142	+	0.0484882i
$63$	−84.4396	+	13.3739i	−1.34031	+	0.212284i
$64$	−48.9493	+	15.9046i	−0.764833	+	0.248509i
$65$		0			0
$66$	−1.39937	−	3.52297i	−0.0212025	−	0.0533783i
$67$	−31.7791	−	31.7791i	−0.474314	−	0.474314i	0.428993	−	0.903308i	$-0.358868\pi$
$67$	−31.7791	−	31.7791i	−0.474314	−	0.474314i	−0.903308	+	0.428993i	$0.858868\pi$
$68$	55.1565	+	28.1036i	0.811125	+	0.413289i
$69$	22.1918	−	30.5443i	0.321620	−	0.442672i
$70$		0			0
$71$	8.18581	−	25.1933i	0.115293	−	0.354836i	−0.876715	−	0.481010i	$-0.840270\pi$
$71$	8.18581	−	25.1933i	0.115293	−	0.354836i	0.992008	+	0.126175i	$0.0402700\pi$
$72$	−20.8413	+	10.6192i	−0.289462	+	0.147488i
$73$	−2.01349	+	12.7127i	−0.0275821	+	0.174147i	−0.997634	−	0.0687521i	$-0.978098\pi$
$73$	−2.01349	+	12.7127i	−0.0275821	+	0.174147i	0.970052	+	0.242899i	$0.0780983\pi$
$74$	3.93804	−	5.42024i	0.0532167	−	0.0732465i
$75$		0			0
$76$	56.5921			0.744633
$77$	−99.6758	+	59.0975i	−1.29449	+	0.767500i
$78$	−0.715990	+	0.715990i	−0.00917936	+	0.00917936i
$79$	−74.0458	+	24.0589i	−0.937288	+	0.304543i	−0.737540	−	0.675304i	$-0.764012\pi$
$79$	−74.0458	+	24.0589i	−0.937288	+	0.304543i	−0.199748	+	0.979847i	$0.564012\pi$
$80$		0			0
$81$	46.8434	−	34.0337i	0.578314	−	0.420170i
$82$	−11.0228	+	5.61642i	−0.134425	+	0.0684929i
$83$	−32.6366	−	64.0530i	−0.393212	−	0.771723i	0.606515	−	0.795072i	$-0.292567\pi$
$83$	−32.6366	−	64.0530i	−0.393212	−	0.771723i	−0.999727	+	0.0233493i	$0.992567\pi$
$84$	−22.5113	−	30.9842i	−0.267992	−	0.368859i
$85$		0			0
$86$	−7.54048	−	23.2072i	−0.0876800	−	0.269851i
$87$	−20.5082	−	20.5082i	−0.235727	−	0.235727i
$88$	−20.9401	+	23.8050i	−0.237955	+	0.270512i
$89$		−	43.9843i		−	0.494205i	−0.968989	−	0.247103i	$-0.920522\pi$
$89$		−	43.9843i		−	0.494205i	0.968989	−	0.247103i	$-0.0794785\pi$
$90$		0			0
$91$	25.0415	+	18.1937i	0.275181	+	0.199931i
$92$	−153.279	−	24.2771i	−1.66608	−	0.263881i
$93$	−22.3922	−	43.9471i	−0.240776	−	0.472549i
$94$	−10.8543	−	3.52677i	−0.115471	−	0.0375189i
$95$		0			0
$96$	−12.7883	−	9.29123i	−0.133211	−	0.0967837i
$97$	57.0567	−	111.980i	0.588213	−	1.15443i	−0.384652	−	0.923062i	$-0.625679\pi$
$97$	57.0567	−	111.980i	0.588213	−	1.15443i	0.972865	−	0.231372i	$-0.0743214\pi$
$98$	16.0575	−	16.0575i	0.163852	−	0.163852i
$99$	47.7500	−	75.4269i	0.482324	−	0.761888i
$100$		0			0
$101$	−21.5112	−	66.2046i	−0.212982	−	0.655491i	−0.999291	−	0.0376575i	$-0.988010\pi$
$101$	−21.5112	−	66.2046i	−0.212982	−	0.655491i	0.786309	−	0.617834i	$-0.211990\pi$
$102$	0.863267	+	5.45045i	0.00846340	+	0.0534358i
$103$	25.6654	−	162.045i	0.249178	−	1.57325i	−0.472696	−	0.881225i	$-0.656719\pi$
$103$	25.6654	−	162.045i	0.249178	−	1.57325i	0.721875	−	0.692024i	$-0.243281\pi$
$104$	8.05427	+	2.61699i	0.0774449	+	0.0251634i
$105$		0			0
$106$	−7.21949	+	5.24527i	−0.0681084	+	0.0494836i
$107$	19.2927	+	121.810i	0.180306	+	1.13841i	0.897331	+	0.441359i	$0.145503\pi$
$107$	19.2927	+	121.810i	0.180306	+	1.13841i	−0.717025	+	0.697048i	$0.754497\pi$
$108$	55.4427	+	28.2494i	0.513358	+	0.261569i
$109$			79.0032i			0.724800i	0.932023	+	0.362400i	$0.118043\pi$
$109$			79.0032i			0.724800i	−0.932023	+	0.362400i	$0.881957\pi$
$110$		0			0
$111$	−17.1955			−0.154914
$112$	−68.9007	+	135.225i	−0.615185	+	1.20737i
$113$	−92.0678	+	14.5821i	−0.814759	+	0.129045i	−0.549888	−	0.835238i	$-0.685330\pi$
$113$	−92.0678	+	14.5821i	−0.814759	+	0.129045i	−0.264872	+	0.964284i	$0.585330\pi$
$114$	2.96532	+	4.08141i	0.0260115	+	0.0358018i
$115$		0			0
$116$	−36.8397	+	113.381i	−0.317584	+	0.977422i
$117$	−23.5521	−	3.73029i	−0.201300	−	0.0318828i
$118$	1.78913	−	0.283371i	0.0151621	−	0.00240145i
$119$	160.435	−	52.1286i	1.34820	−	0.438055i
$120$		0			0
$121$	22.4093	−	118.907i	0.185201	−	0.982701i
$122$	−17.9509	−	17.9509i	−0.147138	−	0.147138i
$123$	28.2909	+	14.4150i	0.230008	+	0.117195i
$124$	−119.168	+	164.020i	−0.961030	+	1.32274i
$125$		0			0
$126$	−9.68046	+	29.7934i	−0.0768290	+	0.236455i
$127$	66.8213	−	34.0472i	0.526152	−	0.268088i	−0.170675	−	0.985327i	$-0.554595\pi$
$127$	66.8213	−	34.0472i	0.526152	−	0.268088i	0.696827	+	0.717240i	$0.254595\pi$
$128$	−13.4676	+	85.0311i	−0.105216	+	0.664305i
$129$	−36.8120	+	50.6674i	−0.285364	+	0.392770i
$130$		0			0
$131$	252.393			1.92667			0.963334	−	0.268306i	$-0.0864639\pi$
$131$	252.393			1.92667			0.963334	+	0.268306i	$0.0864639\pi$
$132$	39.8180	+	3.71933i	0.301651	+	0.0281767i
$133$	109.048	−	109.048i	0.819911	−	0.819911i
$134$	−15.6621	+	5.08892i	−0.116881	+	0.0379770i
$135$		0			0
$136$	37.3395	−	27.1287i	0.274555	−	0.199476i
$137$	109.777	−	55.9341i	0.801291	−	0.408278i	−0.00485985	−	0.999988i	$-0.501547\pi$
$137$	109.777	−	55.9341i	0.801291	−	0.408278i	0.806151	+	0.591710i	$0.201547\pi$
$138$	−6.28069	−	12.3265i	−0.0455122	−	0.0893228i
$139$	47.1210	+	64.8564i	0.339000	+	0.466593i	0.944149	−	0.329519i	$-0.106887\pi$
$139$	47.1210	+	64.8564i	0.339000	+	0.466593i	−0.605149	+	0.796112i	$0.706887\pi$
$140$		0			0
$141$	9.05172	+	27.8583i	0.0641966	+	0.197577i
$142$	−6.86359	−	6.86359i	−0.0483352	−	0.0483352i
$143$	−31.5349	+	7.08563i	−0.220523	+	0.0495499i
$144$		−	116.919i		−	0.811937i
$145$		0			0
$146$	3.81560	+	2.77220i	0.0261342	+	0.0189876i
$147$	−57.5660	−	9.11756i	−0.391606	−	0.0620242i
$148$	32.0887	+	62.9776i	0.216816	+	0.425525i
$149$	−19.5223	−	6.34317i	−0.131022	−	0.0425716i	0.242772	−	0.970083i	$-0.421943\pi$
$149$	−19.5223	−	6.34317i	−0.131022	−	0.0425716i	−0.373794	+	0.927512i	$0.621943\pi$
$150$		0			0
$151$	−147.152	−	106.912i	−0.974515	−	0.708026i	−0.0180387	−	0.999837i	$-0.505742\pi$
$151$	−147.152	−	106.912i	−0.974515	−	0.708026i	−0.956476	+	0.291811i	$0.905742\pi$
$152$	19.1557	−	37.5951i	0.126024	−	0.247336i
$153$	−91.8938	+	91.8938i	−0.600613	+	0.600613i
$154$	2.71317	+	42.3741i	0.0176180	+	0.275157i
$155$		0			0
$156$	−3.30102	−	10.1595i	−0.0211604	−	0.0651250i
$157$	16.8286	+	106.251i	0.107188	+	0.676760i	0.981510	+	0.191413i	$0.0613069\pi$
$157$	16.8286	+	106.251i	0.107188	+	0.676760i	−0.874321	+	0.485347i	$0.838693\pi$
$158$	−4.46286	+	28.1774i	−0.0282460	+	0.178338i
$159$	21.7826	+	7.07758i	0.136997	+	0.0445131i
$160$		0			0
$161$	−342.136	+	248.576i	−2.12507	+	1.54395i
$162$	−3.31903	−	20.9555i	−0.0204878	−	0.129355i
$163$	188.851	+	96.2244i	1.15860	+	0.590334i	0.924238	−	0.381817i	$-0.124701\pi$
$163$	188.851	+	96.2244i	1.15860	+	0.590334i	0.234357	+	0.972151i	$0.424701\pi$
$164$		−	130.514i		−	0.795817i
$165$		0			0
$166$	−26.3418			−0.158686
$167$	134.458	−	263.889i	0.805140	−	1.58018i	−0.00932044	−	0.999957i	$-0.502967\pi$
$167$	134.458	−	263.889i	0.805140	−	1.58018i	0.814460	−	0.580219i	$-0.197033\pi$
$168$	−28.2031	+	4.46693i	−0.167876	+	0.0265889i
$169$	−94.2611	−	129.739i	−0.557758	−	0.767688i
$170$		0			0
$171$	−36.7133	+	112.992i	−0.214698	+	0.660771i
$172$	254.262	+	40.2711i	1.47827	+	0.234134i
$173$	−202.597	+	32.0882i	−1.17108	+	0.185481i	−0.711520	−	0.702666i	$-0.751993\pi$
$173$	−202.597	+	32.0882i	−1.17108	+	0.185481i	−0.459560	+	0.888147i	$0.651993\pi$
$174$	−10.1073	+	3.28407i	−0.0580882	+	0.0188740i
$175$		0			0
$176$	−58.5020	−	147.281i	−0.332398	−	0.836826i
$177$	−3.28747	−	3.28747i	−0.0185733	−	0.0185733i
$178$	−14.3604	−	7.31697i	−0.0806762	−	0.0411066i
$179$	94.6411	−	130.262i	0.528721	−	0.727722i	−0.458214	−	0.888842i	$-0.651511\pi$
$179$	94.6411	−	130.262i	0.528721	−	0.727722i	0.986935	+	0.161120i	$0.0515105\pi$
$180$		0			0
$181$	−53.1406	+	163.550i	−0.293595	+	0.903592i	0.690095	+	0.723719i	$0.257569\pi$
$181$	−53.1406	+	163.550i	−0.293595	+	0.903592i	−0.983690	+	0.179873i	$0.942431\pi$
$182$	10.1058	−	5.14917i	0.0555264	−	0.0282921i
$183$	−10.1926	+	64.3538i	−0.0556975	+	0.351660i
$184$	−68.0107	+	93.6086i	−0.369623	+	0.508743i
$185$		0			0
$186$	−18.0733			−0.0971681
$187$	−69.7772	+	161.738i	−0.373140	+	0.864908i
$188$	85.1382	−	85.1382i	0.452863	−	0.452863i
$189$	161.268	−	52.3990i	0.853268	−	0.277244i
$190$		0			0
$191$	37.4498	−	27.2089i	0.196072	−	0.142455i	−0.485418	−	0.874282i	$-0.661332\pi$
$191$	37.4498	−	27.2089i	0.196072	−	0.142455i	0.681490	+	0.731828i	$0.261332\pi$
$192$	43.1283	−	21.9750i	0.224627	−	0.114453i
$193$	26.3850	+	51.7834i	0.136710	+	0.268308i	0.949204	−	0.314661i	$-0.101891\pi$
$193$	26.3850	+	51.7834i	0.136710	+	0.268308i	−0.812494	+	0.582969i	$0.801891\pi$
$194$	−27.0686	−	37.2567i	−0.139529	−	0.192045i
$195$		0			0
$196$	74.0319	+	227.847i	0.377714	+	1.16248i
$197$	−62.4136	−	62.4136i	−0.316820	−	0.316820i	0.530724	−	0.847544i	$-0.321920\pi$
$197$	−62.4136	−	62.4136i	−0.316820	−	0.316820i	−0.847544	+	0.530724i	$0.821920\pi$
$198$	−16.6826	−	28.1374i	−0.0842556	−	0.142108i
$199$			235.857i			1.18521i	0.805492	+	0.592606i	$0.201901\pi$
$199$			235.857i			1.18521i	−0.805492	+	0.592606i	$0.798099\pi$
$200$		0			0
$201$	34.1944	+	24.8437i	0.170121	+	0.123600i
$202$	−25.1935	−	3.99026i	−0.124720	−	0.0197538i
$203$	147.489	+	289.463i	0.726545	+	1.42592i
$204$	−55.3686	−	17.9903i	−0.271415	−	0.0881879i
$205$		0			0
$206$	−48.6362	−	35.3363i	−0.236098	−	0.171535i
$207$	147.909	−	290.288i	0.714538	−	1.40236i
$208$	−29.9327	+	29.9327i	−0.143907	+	0.143907i
$209$	10.2897	+	160.705i	0.0492332	+	0.768921i
$210$		0			0
$211$	6.32918	+	19.4792i	0.0299961	+	0.0923186i	0.964934	−	0.262494i	$-0.0845448\pi$
$211$	6.32918	+	19.4792i	0.0299961	+	0.0923186i	−0.934938	+	0.354812i	$0.884545\pi$
$212$	−14.7274	−	92.9850i	−0.0694688	−	0.438609i
$213$	−3.89720	+	24.6060i	−0.0182967	+	0.115521i
$214$	42.9789	+	13.9647i	0.200836	+	0.0652555i
$215$		0			0
$216$	37.5332	−	27.2695i	0.173765	−	0.126248i
$217$	86.4271	+	545.679i	0.398282	+	2.51465i
$218$	25.7937	+	13.1425i	0.118320	+	0.0602868i
$219$		−	12.1048i		−	0.0552732i
$220$		0			0
$221$	47.0519			0.212905
$222$	−2.86055	+	5.61414i	−0.0128853	+	0.0252889i
$223$	153.277	−	24.2766i	0.687339	−	0.108864i	0.197010	−	0.980401i	$-0.436877\pi$
$223$	153.277	−	24.2766i	0.687339	−	0.108864i	0.490329	+	0.871538i	$0.336877\pi$
$224$	104.074	+	143.245i	0.464615	+	0.639488i
$225$		0			0
$226$	−10.5550	+	32.4849i	−0.0467035	+	0.143738i
$227$	329.555	+	52.1964i	1.45178	+	0.229940i	0.831975	−	0.554812i	$-0.187210\pi$
$227$	329.555	+	52.1964i	1.45178	+	0.229940i	0.619809	+	0.784753i	$0.287210\pi$
$228$	−52.5674	+	8.32586i	−0.230559	+	0.0365169i
$229$	−144.163	+	46.8414i	−0.629533	+	0.204548i	−0.606368	−	0.795184i	$-0.707374\pi$
$229$	−144.163	+	46.8414i	−0.629533	+	0.204548i	−0.0231646	+	0.999732i	$0.507374\pi$
$230$		0			0
$231$	83.8927	−	69.5590i	0.363172	−	0.301121i
$232$	62.8512	+	62.8512i	0.270910	+	0.270910i
$233$	−290.281	−	147.905i	−1.24584	−	0.634787i	−0.298315	−	0.954468i	$-0.596424\pi$
$233$	−290.281	−	147.905i	−1.24584	−	0.634787i	−0.947525	+	0.319680i	$0.896424\pi$
$234$	−5.13590	+	7.06896i	−0.0219483	+	0.0302092i
$235$		0			0
$236$	−5.90540	+	18.1750i	−0.0250229	+	0.0770125i
$237$	65.2403	−	33.2416i	0.275275	−	0.140260i
$238$	9.66970	−	61.0521i	0.0406290	−	0.256521i
$239$	4.37606	−	6.02313i	0.0183099	−	0.0252014i	−0.799764	−	0.600315i	$-0.795042\pi$
$239$	4.37606	−	6.02313i	0.0183099	−	0.0252014i	0.818074	+	0.575113i	$0.195042\pi$
$240$		0			0
$241$	−79.0071			−0.327830			−0.163915	−	0.986474i	$-0.552412\pi$
$241$	−79.0071			−0.327830			−0.163915	+	0.986474i	$0.552412\pi$
$242$	−35.0938	−	27.0970i	−0.145016	−	0.111971i
$243$	−140.943	+	140.943i	−0.580010	+	0.580010i
$244$	254.713	−	82.7613i	1.04391	−	0.339186i
$245$		0			0
$246$	9.41264	−	6.83868i	0.0382628	−	0.0277995i
$247$	38.3264	−	19.5283i	0.155168	−	0.0790619i
$248$	68.6248	+	134.684i	0.276713	+	0.543080i
$249$	39.7391	+	54.6962i	0.159595	+	0.219664i
$250$		0			0
$251$	129.811	+	399.517i	0.517174	+	1.59170i	0.779290	+	0.626663i	$0.215580\pi$
$251$	129.811	+	399.517i	0.517174	+	1.59170i	−0.262116	+	0.965036i	$0.584420\pi$
$252$	−233.692	−	233.692i	−0.927348	−	0.927348i
$253$	41.0699	−	439.681i	0.162332	−	1.73787i
$254$		−	27.4803i		−	0.108190i
$255$		0			0
$256$	−141.034	−	102.467i	−0.550913	−	0.400262i
$257$	−402.884	−	63.8105i	−1.56764	−	0.248290i	−0.688638	−	0.725105i	$-0.741791\pi$
$257$	−402.884	−	63.8105i	−1.56764	−	0.248290i	−0.879004	+	0.476815i	$0.841791\pi$
$258$	10.4185	+	20.4474i	0.0403817	+	0.0792536i
$259$	183.185	+	59.5204i	0.707277	+	0.229808i
$260$		0			0
$261$	−202.478	−	147.109i	−0.775776	−	0.563634i
$262$	41.9867	−	82.4036i	0.160255	−	0.314518i
$263$	191.700	−	191.700i	0.728899	−	0.728899i	−0.241501	−	0.970400i	$-0.577640\pi$
$263$	191.700	−	191.700i	0.728899	−	0.728899i	0.970400	+	0.241501i	$0.0776398\pi$
$264$	15.9487	−	25.1928i	0.0604116	−	0.0954274i
$265$		0			0
$266$	−17.4624	−	53.7436i	−0.0656480	−	0.202044i
$267$	6.47099	+	40.8562i	0.0242359	+	0.153020i
$268$	27.1782	−	171.596i	0.101411	−	0.640285i
$269$	−467.686	−	151.961i	−1.73861	−	0.564909i	−0.743963	−	0.668221i	$-0.767056\pi$
$269$	−467.686	−	151.961i	−1.73861	−	0.564909i	−0.994649	+	0.103312i	$0.967056\pi$
$270$		0			0
$271$	−53.5655	+	38.9176i	−0.197659	+	0.143607i	−0.682212	−	0.731154i	$-0.738982\pi$
$271$	−53.5655	+	38.9176i	−0.197659	+	0.143607i	0.484554	+	0.874762i	$0.338982\pi$
$272$	36.0898	+	227.862i	0.132683	+	0.837728i
$273$	−25.9373	−	13.2157i	−0.0950084	−	0.0484092i
$274$		−	45.1458i		−	0.164766i
$275$		0			0
$276$	145.950			0.528805
$277$	−99.0065	+	194.311i	−0.357424	+	0.701485i	−0.997780	−	0.0665937i	$-0.978787\pi$
$277$	−99.0065	+	194.311i	−0.357424	+	0.701485i	0.640356	+	0.768078i	$0.278787\pi$
$278$	29.0137	−	4.59531i	0.104366	−	0.0165299i
$279$	−250.175	−	344.336i	−0.896684	−	1.23418i
$280$		0			0
$281$	113.903	−	350.558i	0.405349	−	1.24754i	−0.515255	−	0.857037i	$-0.672303\pi$
$281$	113.903	−	350.558i	0.405349	−	1.24754i	0.920604	−	0.390499i	$-0.127697\pi$
$282$	10.6012	+	1.67907i	0.0375930	+	0.00595415i
$283$	120.984	−	19.1620i	0.427506	−	0.0677103i	0.0610260	−	0.998136i	$-0.480563\pi$
$283$	120.984	−	19.1620i	0.427506	−	0.0677103i	0.366480	+	0.930426i	$0.380563\pi$
$284$	97.3907	−	31.6441i	0.342925	−	0.111423i
$285$		0			0
$286$	−2.93258	+	11.4745i	−0.0102538	+	0.0401206i
$287$	−251.489	−	251.489i	−0.876270	−	0.876270i
$288$	−121.538	−	61.9266i	−0.422006	−	0.215023i
$289$	−19.1444	+	26.3500i	−0.0662435	+	0.0911763i
$290$		0			0
$291$	−36.5244	+	112.411i	−0.125513	+	0.386291i
$292$	−44.3333	+	22.5890i	−0.151827	+	0.0773595i
$293$	−82.6474	+	521.815i	−0.282073	+	1.78094i	0.286271	+	0.958149i	$0.407584\pi$
$293$	−82.6474	+	521.815i	−0.282073	+	1.78094i	−0.568344	+	0.822791i	$0.692416\pi$
$294$	−12.5531	+	17.2779i	−0.0426977	+	0.0587684i
$295$		0			0
$296$	52.6987			0.178036
$297$	−70.1392	+	162.577i	−0.236159	+	0.547397i
$298$	−5.31858	+	5.31858i	−0.0178476	+	0.0178476i
$299$	−112.184	+	36.4509i	−0.375198	+	0.121909i
$300$		0			0
$301$	567.540	−	412.342i	1.88552	−	1.36991i
$302$	−59.3849	+	30.2581i	−0.196639	+	0.100192i
$303$	29.7214	+	58.3316i	0.0980906	+	0.192514i
$304$	123.968	+	170.628i	0.407790	+	0.561275i
$305$		0			0
$306$	14.7154	+	45.2892i	0.0480894	+	0.148004i
$307$	−316.814	−	316.814i	−1.03197	−	1.03197i	−0.999472	−	0.0324958i	$-0.989654\pi$
$307$	−316.814	−	316.814i	−1.03197	−	1.03197i	−0.0324958	−	0.999472i	$-0.510346\pi$
$308$	−411.309	−	177.448i	−1.33542	−	0.576129i
$309$			154.296i			0.499341i
$310$		0			0
$311$	24.6102	+	17.8803i	0.0791324	+	0.0574931i	0.626648	−	0.779302i	$-0.284426\pi$
$311$	24.6102	+	17.8803i	0.0791324	+	0.0574931i	−0.547516	+	0.836795i	$0.684426\pi$
$312$	−7.86649	−	1.24593i	−0.0252131	−	0.00399336i
$313$	88.1780	+	173.059i	0.281719	+	0.552904i	0.987894	−	0.155133i	$-0.0495807\pi$
$313$	88.1780	+	173.059i	0.281719	+	0.552904i	−0.706175	+	0.708038i	$0.749581\pi$
$314$	37.4894	+	12.1810i	0.119393	+	0.0387931i
$315$		0			0
$316$	−243.491	−	176.907i	−0.770542	−	0.559831i
$317$	−100.794	+	197.819i	−0.317961	+	0.624034i	−0.993569	−	0.113227i	$-0.963881\pi$
$317$	−100.794	+	197.819i	−0.317961	+	0.624034i	0.675608	+	0.737261i	$0.263881\pi$
$318$	5.93437	−	5.93437i	0.0186616	−	0.0186616i
$319$	−328.666	−	83.9985i	−1.03030	−	0.263318i
$320$		0			0
$321$	−35.8414	−	110.308i	−0.111655	−	0.343640i
$322$	24.2416	+	153.055i	0.0752844	+	0.475327i
$323$	36.6725	−	231.541i	0.113537	−	0.716845i
$324$	212.877	+	69.1679i	0.657028	+	0.213481i
$325$		0			0
$326$	62.8324	−	45.6504i	0.192737	−	0.140032i
$327$	−11.6230	−	73.3847i	−0.0355443	−	0.224418i
$328$	−86.7027	−	44.1772i	−0.264337	−	0.134687i
$329$		−	328.108i		−	0.997290i
$330$		0			0
$331$	589.908			1.78220			0.891099	−	0.453809i	$-0.149935\pi$
$331$	589.908			1.78220			0.891099	+	0.453809i	$0.149935\pi$
$332$	126.164	−	247.612i	0.380013	−	0.745818i
$333$	−146.558	+	23.2126i	−0.440115	+	0.0697074i
$334$	−63.7892	−	87.7983i	−0.190986	−	0.262869i
$335$		0			0
$336$	44.1063	−	135.745i	0.131269	−	0.404004i
$337$	59.4025	+	9.40843i	0.176269	+	0.0279182i	0.243945	−	0.969789i	$-0.421558\pi$
$337$	59.4025	+	9.40843i	0.176269	+	0.0279182i	−0.0676761	+	0.997707i	$0.521558\pi$
$338$	−58.0391	+	9.19249i	−0.171713	+	0.0271967i
$339$	83.3749	−	27.0902i	0.245944	−	0.0799120i
$340$		0			0
$341$	−487.436	−	308.578i	−1.42943	−	0.904920i
$342$	30.7832	+	30.7832i	0.0900092	+	0.0900092i
$343$	121.771	+	62.0453i	0.355017	+	0.180890i
$344$	112.817	−	155.279i	0.327956	−	0.451393i
$345$		0			0
$346$	−23.2264	+	71.4836i	−0.0671284	+	0.206600i
$347$	−22.5648	+	11.4973i	−0.0650281	+	0.0331335i	−0.486202	−	0.873846i	$-0.661618\pi$
$347$	−22.5648	+	11.4973i	−0.0650281	+	0.0331335i	0.421174	+	0.906980i	$0.361618\pi$
$348$	17.5391	−	110.738i	0.0503997	−	0.318211i
$349$	−204.827	+	281.920i	−0.586898	+	0.807795i	−0.994430	−	0.105395i	$-0.966389\pi$
$349$	−204.827	+	281.920i	−0.586898	+	0.807795i	0.407533	+	0.913191i	$0.366389\pi$
$350$		0			0
$351$	47.2961			0.134747
$352$	−184.086	−	17.1951i	−0.522970	−	0.0488498i
$353$	313.352	−	313.352i	0.887684	−	0.887684i	−0.106617	−	0.994300i	$-0.534002\pi$
$353$	313.352	−	313.352i	0.887684	−	0.887684i	0.994300	+	0.106617i	$0.0340017\pi$
$354$	−1.62021	+	0.526437i	−0.00457685	+	0.00148711i
$355$		0			0
$356$	137.558	−	99.9419i	0.386399	−	0.280736i
$357$	−141.356	+	72.0247i	−0.395956	+	0.201750i
$358$	−26.7852	−	52.5689i	−0.0748190	−	0.146841i
$359$	−110.962	−	152.726i	−0.309086	−	0.425421i	0.626010	−	0.779815i	$-0.284687\pi$
$359$	−110.962	−	152.726i	−0.309086	−	0.425421i	−0.935096	+	0.354394i	$0.884687\pi$
$360$		0			0
$361$	45.3289	+	139.508i	0.125565	+	0.386449i
$362$	44.5571	+	44.5571i	0.123086	+	0.123086i
$363$	−3.32196	+	113.747i	−0.00915141	+	0.313354i
$364$			119.656i			0.328725i
$365$		0			0
$366$	19.3152	+	14.0333i	0.0527738	+	0.0383424i
$367$	−435.592	−	68.9910i	−1.18690	−	0.187986i	−0.468402	−	0.883516i	$-0.655170\pi$
$367$	−435.592	−	68.9910i	−1.18690	−	0.187986i	−0.718498	+	0.695529i	$0.755170\pi$
$368$	−262.571	−	515.324i	−0.713507	−	1.40034i
$369$	260.585	+	84.6690i	0.706191	+	0.229455i
$370$		0			0
$371$	−207.553	−	150.796i	−0.559441	−	0.406458i
$372$	86.5621	−	169.888i	0.232694	−	0.456687i
$373$	315.552	−	315.552i	0.845985	−	0.845985i	−0.143645	−	0.989629i	$-0.545882\pi$
$373$	315.552	−	315.552i	0.845985	−	0.845985i	0.989629	+	0.143645i	$0.0458822\pi$
$374$	41.1978	+	49.6873i	0.110155	+	0.132854i
$375$		0			0
$376$	−27.7406	−	85.3769i	−0.0737783	−	0.227066i
$377$	14.1752	+	89.4985i	0.0375999	+	0.237396i
$378$	9.71987	−	61.3689i	0.0257140	−	0.162352i
$379$	63.3937	+	20.5979i	0.167266	+	0.0543480i	0.391453	−	0.920198i	$-0.371973\pi$
$379$	63.3937	+	20.5979i	0.167266	+	0.0543480i	−0.224187	+	0.974546i	$0.571973\pi$
$380$		0			0
$381$	−57.0602	+	41.4566i	−0.149764	+	0.108810i
$382$	−2.65345	−	16.7532i	−0.00694621	−	0.0438567i
$383$	172.822	+	88.0570i	0.451231	+	0.229914i	0.664811	−	0.747012i	$-0.268512\pi$
$383$	172.822	+	88.0570i	0.451231	+	0.229914i	−0.213579	+	0.976926i	$0.568512\pi$
$384$		−	80.9653i		−	0.210847i
$385$		0			0
$386$	21.2960			0.0551709
$387$	−245.354	+	481.535i	−0.633990	+	1.24428i
$388$	479.857	−	76.0018i	1.23674	−	0.195881i
$389$	225.724	+	310.683i	0.580268	+	0.798671i	0.993725	−	0.111853i	$-0.0356786\pi$
$389$	225.724	+	310.683i	0.580268	+	0.798671i	−0.413456	+	0.910524i	$0.635679\pi$
$390$		0			0
$391$	−198.654	+	611.396i	−0.508068	+	1.56367i
$392$	176.421	+	27.9424i	0.450055	+	0.0712817i
$393$	−234.444	+	37.1323i	−0.596550	+	0.0944842i
$394$	−30.7601	+	9.99456i	−0.0780713	+	0.0253669i
$395$		0			0
$396$	344.392	−	22.0510i	0.869676	−	0.0556844i
$397$	178.629	+	178.629i	0.449946	+	0.449946i	0.895336	−	0.445391i	$-0.146935\pi$
$397$	178.629	+	178.629i	0.449946	+	0.449946i	−0.445391	+	0.895336i	$0.646935\pi$
$398$	77.0047	+	39.2359i	0.193479	+	0.0985826i
$399$	−85.2498	+	117.336i	−0.213659	+	0.294076i
$400$		0			0
$401$	35.7014	−	109.877i	0.0890308	−	0.274009i	−0.896621	−	0.442798i	$-0.853986\pi$
$401$	35.7014	−	109.877i	0.0890308	−	0.274009i	0.985652	+	0.168789i	$0.0539858\pi$
$402$	13.7996	−	7.03123i	0.0343273	−	0.0174906i
$403$	−24.1065	+	152.202i	−0.0598176	+	0.377673i
$404$	158.173	−	217.706i	0.391517	−	0.538877i
$405$		0			0
$406$	119.042			0.293206
$407$	−173.003	+	102.573i	−0.425069	+	0.252022i
$408$	−30.6928	+	30.6928i	−0.0752275	+	0.0752275i
$409$	−291.234	+	94.6276i	−0.712063	+	0.231363i	−0.642579	−	0.766220i	$-0.722135\pi$
$409$	−291.234	+	94.6276i	−0.712063	+	0.231363i	−0.0694843	+	0.997583i	$0.522135\pi$
$410$		0			0
$411$	−93.7408	+	68.1067i	−0.228080	+	0.165710i
$412$	565.103	−	287.934i	1.37161	−	0.698869i
$413$	23.6424	+	46.4008i	0.0572455	+	0.112351i
$414$	−70.1705	−	96.5815i	−0.169494	−	0.233289i
$415$		0			0
$416$	15.2612	+	46.9692i	0.0366856	+	0.112907i
$417$	−53.3116	−	53.3116i	−0.127846	−	0.127846i
$418$	54.1800	+	23.3744i	0.129617	+	0.0559196i
$419$		−	209.142i		−	0.499147i	−0.968356	−	0.249573i	$-0.919710\pi$
$419$		−	209.142i		−	0.499147i	0.968356	−	0.249573i	$-0.0802904\pi$
$420$		0			0
$421$	−246.603	−	179.167i	−0.585755	−	0.425576i	0.255039	−	0.966931i	$-0.417912\pi$
$421$	−246.603	−	179.167i	−0.585755	−	0.425576i	−0.840794	+	0.541355i	$0.817912\pi$
$422$	7.41263	+	1.17405i	0.0175655	+	0.00278210i
$423$	114.755	+	225.219i	0.271288	+	0.532433i
$424$	−66.7566	−	21.6905i	−0.157445	−	0.0511569i
$425$		0			0
$426$	7.38525	+	5.36570i	0.0173363	+	0.0125955i
$427$	331.337	−	650.285i	0.775964	−	1.52291i
$428$	−337.115	+	337.115i	−0.787652	+	0.787652i
$429$	28.2498	−	11.2212i	0.0658502	−	0.0261565i
$430$		0			0
$431$	112.689	+	346.822i	0.261460	+	0.804692i	0.992488	+	0.122344i	$0.0390411\pi$
$431$	112.689	+	346.822i	0.261460	+	0.804692i	−0.731028	+	0.682348i	$0.760959\pi$
$432$	36.2770	+	229.044i	0.0839746	+	0.530195i
$433$	−53.2099	+	335.954i	−0.122887	+	0.775876i	0.846870	+	0.531800i	$0.178484\pi$
$433$	−53.2099	+	335.954i	−0.122887	+	0.775876i	−0.969756	+	0.244075i	$0.921516\pi$
$434$	192.536	+	62.5586i	0.443630	+	0.144144i
$435$		0			0
$436$	−247.078	+	179.513i	−0.566693	+	0.411726i
$437$	91.9366	+	580.465i	0.210381	+	1.32829i
$438$	−3.95209	−	2.01369i	−0.00902304	−	0.00459747i
$439$			745.582i			1.69836i	0.528100	+	0.849182i	$0.322904\pi$
$439$			745.582i			1.69836i	−0.528100	+	0.849182i	$0.677096\pi$
$440$		0			0
$441$	−502.947			−1.14047
$442$	7.82729	−	15.3619i	0.0177088	−	0.0347555i
$443$	−393.329	+	62.2972i	−0.887876	+	0.140626i	−0.583680	−	0.811984i	$-0.698388\pi$
$443$	−393.329	+	62.2972i	−0.887876	+	0.140626i	−0.304196	+	0.952609i	$0.598388\pi$
$444$	−39.0720	−	53.7780i	−0.0879999	−	0.121122i
$445$		0			0
$446$	17.5722	−	54.0816i	0.0393995	−	0.121259i
$447$	19.0671	+	3.01993i	0.0426557	+	0.00675600i
$448$	−535.512	+	84.8168i	−1.19534	+	0.189323i
$449$	497.787	−	161.741i	1.10866	−	0.360224i	0.303228	−	0.952918i	$-0.401935\pi$
$449$	497.787	−	161.741i	1.10866	−	0.360224i	0.805428	+	0.592694i	$0.201935\pi$
$450$		0			0
$451$	370.621	−	23.7304i	0.821775	−	0.0526174i
$452$	−254.803	−	254.803i	−0.563724	−	0.563724i
$453$	152.416	+	77.6597i	0.336459	+	0.171434i
$454$	71.8644	−	98.9129i	0.158292	−	0.217870i
$455$		0			0
$456$	−12.2624	+	37.7396i	−0.0268911	+	0.0827624i
$457$	87.9652	−	44.8205i	0.192484	−	0.0980755i	−0.355092	−	0.934831i	$-0.615551\pi$
$457$	87.9652	−	44.8205i	0.192484	−	0.0980755i	0.547576	+	0.836756i	$0.315551\pi$
$458$	−8.68895	+	54.8599i	−0.0189715	+	0.119781i
$459$	151.508	−	208.532i	0.330082	−	0.454319i
$460$		0			0
$461$	232.336			0.503983			0.251992	−	0.967729i	$-0.418914\pi$
$461$	232.336			0.503983			0.251992	+	0.967729i	$0.418914\pi$
$462$	−8.75433	−	38.9615i	−0.0189488	−	0.0843322i
$463$	−231.578	+	231.578i	−0.500168	+	0.500168i	−0.911490	−	0.411322i	$-0.865067\pi$
$463$	−231.578	+	231.578i	−0.500168	+	0.500168i	0.411322	+	0.911490i	$0.365067\pi$
$464$	−422.548	+	137.294i	−0.910664	+	0.295893i
$465$		0			0
$466$	−96.5789	+	70.1687i	−0.207251	+	0.150577i
$467$	622.555	−	317.208i	1.33309	−	0.679245i	0.365277	−	0.930899i	$-0.380974\pi$
$467$	622.555	−	317.208i	1.33309	−	0.679245i	0.967817	+	0.251654i	$0.0809743\pi$
$468$	−41.8494	−	82.1340i	−0.0894217	−	0.175500i
$469$	−278.281	−	383.022i	−0.593351	−	0.816677i
$470$		0			0
$471$	−31.2635	−	96.2192i	−0.0663769	−	0.204287i
$472$	10.0750	+	10.0750i	0.0213454	+	0.0213454i
$473$	−68.1273	+	729.350i	−0.144032	+	1.54197i
$474$		−	26.8301i		−	0.0566036i
$475$		0			0
$476$	527.573	+	383.304i	1.10835	+	0.805261i
$477$	195.208	+	30.9180i	0.409242	+	0.0648175i
$478$	−1.23851	−	2.43071i	−0.00259102	−	0.00508516i
$479$	−499.509	−	162.300i	−1.04282	−	0.338832i	−0.262971	−	0.964804i	$-0.584702\pi$
$479$	−499.509	−	162.300i	−1.04282	−	0.338832i	−0.779846	+	0.625972i	$0.784702\pi$
$480$		0			0
$481$	43.4635	+	31.5781i	0.0903607	+	0.0656509i
$482$	−13.1432	+	25.7949i	−0.0272680	+	0.0535164i
$483$	281.234	−	281.234i	0.582264	−	0.582264i
$484$	422.793	−	200.099i	0.873539	−	0.413427i
$485$		0			0
$486$	22.5697	+	69.4625i	0.0464398	+	0.142927i
$487$	−90.6289	−	572.208i	−0.186096	−	1.17497i	−0.887020	−	0.461730i	$-0.847229\pi$
$487$	−90.6289	−	572.208i	−0.186096	−	1.17497i	0.700924	−	0.713236i	$-0.252771\pi$
$488$	31.2372	−	197.224i	0.0640106	−	0.404147i
$489$	−189.577	−	61.5974i	−0.387683	−	0.125966i
$490$		0			0
$491$	−669.637	+	486.520i	−1.36382	+	0.990876i	−0.365632	+	0.930759i	$0.619147\pi$
$491$	−669.637	+	486.520i	−1.36382	+	0.990876i	−0.998191	+	0.0601162i	$0.980853\pi$
$492$	19.2013	+	121.232i	0.0390270	+	0.246407i
$493$	440.015	+	224.199i	0.892525	+	0.454764i
$494$		−	15.7618i		−	0.0319064i
$495$		0			0
$496$	−755.572			−1.52333
$497$	126.688	−	248.639i	0.254905	−	0.500280i
$498$	24.4685	−	3.87543i	0.0491335	−	0.00778198i
$499$	203.530	+	280.135i	0.407876	+	0.561393i	0.962699	−	0.270576i	$-0.0872141\pi$
$499$	203.530	+	280.135i	0.407876	+	0.561393i	−0.554823	+	0.831968i	$0.687214\pi$
$500$		0			0
$501$	−86.0725	+	264.904i	−0.171801	+	0.528750i
$502$	152.032	+	24.0795i	0.302853	+	0.0479672i
$503$	296.726	−	46.9968i	0.589913	−	0.0934330i	0.145660	−	0.989335i	$-0.453469\pi$
$503$	296.726	−	46.9968i	0.589913	−	0.0934330i	0.444252	+	0.895902i	$0.353469\pi$
$504$	−234.347	+	76.1439i	−0.464974	+	0.151079i
$505$		0			0
$506$	−136.719	−	86.5518i	−0.270195	−	0.171051i
$507$	106.645	+	106.645i	0.210345	+	0.210345i
$508$	258.313	+	131.617i	0.508491	+	0.259089i
$509$	−63.4809	+	87.3740i	−0.124717	+	0.171658i	−0.866810	−	0.498639i	$-0.833833\pi$
$509$	−63.4809	+	87.3740i	−0.124717	+	0.171658i	0.742093	+	0.670297i	$0.233833\pi$
$510$		0			0
$511$	−41.8996	+	128.954i	−0.0819953	+	0.252355i
$512$	−363.746	+	185.338i	−0.710442	+	0.361988i
$513$	36.8628	−	232.742i	0.0718572	−	0.453689i
$514$	−87.8549	+	120.922i	−0.170924	+	0.235257i
$515$		0			0
$516$	−242.104			−0.469194
$517$	257.247	+	226.287i	0.497577	+	0.437692i
$518$	49.9063	−	49.9063i	0.0963442	−	0.0963442i
$519$	183.468	−	59.6123i	0.353503	−	0.114860i
$520$		0			0
$521$	−203.745	+	148.030i	−0.391066	+	0.284126i	−0.765892	−	0.642969i	$-0.777702\pi$
$521$	−203.745	+	148.030i	−0.391066	+	0.284126i	0.374826	+	0.927095i	$0.377702\pi$
$522$	−81.7123	+	41.6345i	−0.156537	+	0.0797596i
$523$	−192.760	−	378.312i	−0.368565	−	0.723350i	0.630017	−	0.776581i	$-0.283048\pi$
$523$	−192.760	−	378.312i	−0.368565	−	0.723350i	−0.998582	+	0.0532315i	$0.983048\pi$
$524$	573.493	+	789.346i	1.09445	+	1.50639i
$525$		0			0
$526$	−30.6978	−	94.4782i	−0.0583609	−	0.179616i
$527$	593.851	+	593.851i	1.12685	+	1.12685i
$528$	76.0096	+	128.200i	0.143958	+	0.242804i
$529$		−	1082.62i		−	2.04655i
$530$		0			0
$531$	−32.4571	−	23.5815i	−0.0611245	−	0.0444096i
$532$	588.823	+	93.2604i	1.10681	+	0.175302i
$533$	−45.0366	−	88.3893i	−0.0844964	−	0.165834i
$534$	14.4156	+	4.68390i	0.0269955	+	0.00877136i
$535$		0			0
$536$	−104.795	−	76.1380i	−0.195513	−	0.142048i
$537$	−68.7463	+	134.922i	−0.128019	+	0.251252i
$538$	−127.415	+	127.415i	−0.236831	+	0.236831i
$539$	−633.556	+	251.656i	−1.17543	+	0.466895i
$540$		0			0
$541$	69.7357	+	214.624i	0.128901	+	0.396718i	0.994592	−	0.103862i	$-0.0331201\pi$
$541$	69.7357	+	214.624i	0.128901	+	0.396718i	−0.865690	+	0.500580i	$0.833120\pi$
$542$	3.79531	+	23.9626i	0.00700242	+	0.0442115i
$543$	25.2999	−	159.737i	0.0465927	−	0.294175i
$544$	255.979	+	83.1725i	0.470549	+	0.152891i
$545$		0			0
$546$	−8.62956	+	6.26975i	−0.0158051	+	0.0114831i
$547$	−131.660	−	831.270i	−0.240695	−	1.51969i	−0.751350	−	0.659904i	$-0.770597\pi$
$547$	−131.660	−	831.270i	−0.240695	−	1.51969i	0.510655	−	0.859786i	$-0.329403\pi$
$548$	424.368	+	216.226i	0.774394	+	0.394573i
$549$			562.251i			1.02414i
$550$		0			0
$551$	451.467			0.819360
$552$	49.4022	−	96.9572i	0.0894967	−	0.175647i
$553$	−810.071	+	128.303i	−1.46487	+	0.232012i
$554$	46.9703	+	64.6490i	0.0847839	+	0.116695i
$555$		0			0
$556$	−95.7656	+	294.736i	−0.172240	+	0.530101i
$557$	607.711	+	96.2519i	1.09104	+	0.172804i	0.675930	−	0.736966i	$-0.263742\pi$
$557$	607.711	+	96.2519i	1.09104	+	0.172804i	0.415113	+	0.909770i	$0.363742\pi$
$558$	−154.040	+	24.3975i	−0.276057	+	0.0437231i
$559$	186.093	−	60.4652i	0.332903	−	0.108167i
$560$		0			0
$561$	41.0199	−	160.501i	0.0731193	−	0.286098i
$562$	−95.5048	−	95.5048i	−0.169937	−	0.169937i
$563$	225.168	+	114.729i	0.399943	+	0.203781i	0.642381	−	0.766386i	$-0.277947\pi$
$563$	225.168	+	114.729i	0.399943	+	0.203781i	−0.242437	+	0.970167i	$0.577947\pi$
$564$	−66.5578	+	91.6090i	−0.118010	+	0.162427i
$565$		0			0
$566$	13.8701	−	42.6877i	0.0245054	−	0.0754199i
$567$	543.477	−	276.915i	0.958513	−	0.488387i
$568$	11.9437	−	75.4094i	0.0210276	−	0.132763i
$569$	−168.013	+	231.250i	−0.295278	+	0.406415i	−0.930719	−	0.365734i	$-0.880818\pi$
$569$	−168.013	+	231.250i	−0.295278	+	0.406415i	0.635442	+	0.772149i	$0.280818\pi$
$570$		0			0
$571$	496.264			0.869114			0.434557	−	0.900644i	$-0.356905\pi$
$571$	496.264			0.869114			0.434557	+	0.900644i	$0.356905\pi$
$572$	−93.8140	−	82.5233i	−0.164011	−	0.144272i
$573$	−30.7835	+	30.7835i	−0.0537234	+	0.0537234i
$574$	−123.945	+	40.2721i	−0.215932	+	0.0701605i
$575$		0			0
$576$	337.921	−	245.514i	0.586668	−	0.426239i
$577$	−836.096	+	426.012i	−1.44904	+	0.738323i	−0.988769	−	0.149455i	$-0.952248\pi$
$577$	−836.096	+	426.012i	−1.44904	+	0.738323i	−0.460272	+	0.887778i	$0.652248\pi$
$578$	5.41822	+	10.6338i	0.00937408	+	0.0183977i
$579$	−32.1270	−	44.2190i	−0.0554870	−	0.0763713i
$580$		0			0
$581$	−234.019	−	720.235i	−0.402786	−	1.23965i
$582$	30.6248	+	30.6248i	0.0526199	+	0.0526199i
$583$	261.372	−	58.7282i	0.448322	−	0.100734i
$584$			37.0975i			0.0635231i
$585$		0			0
$586$	156.618	+	113.790i	0.267266	+	0.194180i
$587$	−52.6972	−	8.34641i	−0.0897737	−	0.0142188i	0.111386	−	0.993777i	$-0.464471\pi$
$587$	−52.6972	−	8.34641i	−0.0897737	−	0.0142188i	−0.201160	+	0.979558i	$0.564471\pi$
$588$	−102.288	−	200.752i	−0.173959	−	0.341414i
$589$	730.194	+	237.254i	1.23972	+	0.402809i
$590$		0			0
$591$	67.1572	+	48.7926i	0.113633	+	0.0825593i
$592$	−119.588	+	234.705i	−0.202007	+	0.396461i
$593$	71.7371	−	71.7371i	0.120973	−	0.120973i	−0.644028	−	0.765002i	$-0.722738\pi$
$593$	71.7371	−	71.7371i	0.120973	−	0.120973i	0.765002	+	0.644028i	$0.222738\pi$
$594$	41.4116	+	49.9450i	0.0697165	+	0.0840826i
$595$		0			0
$596$	−24.5210	−	75.4678i	−0.0411426	−	0.126624i
$597$	−34.6995	−	219.084i	−0.0581231	−	0.366975i
$598$	−6.76153	+	42.6906i	−0.0113069	+	0.0713890i
$599$	488.511	+	158.727i	0.815544	+	0.264986i	0.686944	−	0.726710i	$-0.258952\pi$
$599$	488.511	+	158.727i	0.815544	+	0.264986i	0.128600	+	0.991697i	$0.458952\pi$
$600$		0			0
$601$	752.121	−	546.448i	1.25145	−	0.909231i	0.253144	−	0.967429i	$-0.418535\pi$
$601$	752.121	−	546.448i	1.25145	−	0.909231i	0.998305	+	0.0581972i	$0.0185352\pi$
$602$	−40.2123	−	253.890i	−0.0667978	−	0.421745i
$603$	324.978	+	165.585i	0.538935	+	0.274601i
$604$		−	703.136i		−	1.16413i
$605$		0			0
$606$	23.9889			0.0395857
$607$	−295.091	+	579.149i	−0.486147	+	0.954117i	0.509461	+	0.860494i	$0.329845\pi$
$607$	−295.091	+	579.149i	−0.486147	+	0.954117i	−0.995608	+	0.0936234i	$0.970155\pi$
$608$	243.029	−	38.4919i	0.399718	−	0.0633091i
$609$	−179.586	−	247.178i	−0.294886	−	0.405876i
$610$		0			0
$611$	28.2803	−	87.0377i	0.0462852	−	0.142451i
$612$	−496.195	−	78.5896i	−0.810777	−	0.128414i
$613$	−453.468	+	71.8222i	−0.739751	+	0.117165i	−0.514927	−	0.857234i	$-0.672181\pi$
$613$	−453.468	+	71.8222i	−0.739751	+	0.117165i	−0.224825	+	0.974399i	$0.572181\pi$
$614$	−156.140	+	50.7328i	−0.254299	+	0.0826268i
$615$		0			0
$616$	−257.104	+	213.176i	−0.417377	+	0.346065i
$617$	−292.953	−	292.953i	−0.474803	−	0.474803i	0.428662	−	0.903465i	$-0.358985\pi$
$617$	−292.953	−	292.953i	−0.474803	−	0.474803i	−0.903465	+	0.428662i	$0.858985\pi$
$618$	50.3760	+	25.6679i	0.0815146	+	0.0415338i
$619$	178.737	−	246.011i	0.288752	−	0.397433i	−0.639856	−	0.768495i	$-0.721006\pi$
$619$	178.737	−	246.011i	0.288752	−	0.397433i	0.928608	+	0.371062i	$0.121006\pi$
$620$		0			0
$621$	−199.685	+	614.568i	−0.321554	+	0.989642i
$622$	9.93174	−	5.06047i	0.0159674	−	0.00813581i
$623$	72.4835	−	457.643i	0.116346	−	0.734579i
$624$	23.4003	−	32.2077i	0.0375004	−	0.0516149i
$625$		0			0
$626$	71.1706			0.113691
$627$	−33.2009	−	147.762i	−0.0529520	−	0.235665i
$628$	−294.057	+	294.057i	−0.468243	+	0.468243i
$629$	278.461	−	90.4774i	0.442704	−	0.143843i
$630$		0			0
$631$	−118.262	+	85.9222i	−0.187420	+	0.136168i	−0.677539	−	0.735487i	$-0.736953\pi$
$631$	−118.262	+	85.9222i	−0.187420	+	0.136168i	0.490119	+	0.871656i	$0.336953\pi$
$632$	−199.941	+	101.875i	−0.316362	+	0.161194i
$633$	−8.74487	−	17.1628i	−0.0138150	−	0.0271134i
$634$	47.8181	+	65.8160i	0.0754229	+	0.103811i
$635$		0			0
$636$	27.3600	+	84.2055i	0.0430189	+	0.132399i
$637$	128.761	+	128.761i	0.202136	+	0.202136i
$638$	−82.0996	+	93.3324i	−0.128683	+	0.146289i
$639$			214.979i			0.336431i
$640$		0			0
$641$	−701.684	−	509.804i	−1.09467	−	0.795325i	−0.114489	−	0.993424i	$-0.536523\pi$
$641$	−701.684	−	509.804i	−1.09467	−	0.795325i	−0.980182	+	0.198099i	$0.936523\pi$
$642$	−41.9768	−	6.64848i	−0.0653845	−	0.0103559i
$643$	−122.204	−	239.840i	−0.190054	−	0.373001i	0.776243	−	0.630434i	$-0.217123\pi$
$643$	−122.204	−	239.840i	−0.190054	−	0.373001i	−0.966296	+	0.257433i	$0.917123\pi$
$644$	−1554.82	−	505.191i	−2.41431	−	0.784458i
$645$		0			0
$646$	−69.4949	−	50.4910i	−0.107577	−	0.0781595i
$647$	−208.492	+	409.189i	−0.322244	+	0.632440i	−0.994127	−	0.108217i	$-0.965486\pi$
$647$	−208.492	+	409.189i	−0.322244	+	0.632440i	0.671883	+	0.740657i	$0.265486\pi$
$648$	118.005	−	118.005i	0.182107	−	0.182107i
$649$	−52.6852	−	13.4649i	−0.0811790	−	0.0207472i
$650$		0			0
$651$	−160.561	−	494.157i	−0.246638	−	0.759074i
$652$	128.175	+	809.264i	0.196587	+	1.24120i
$653$	8.27124	−	52.2225i	0.0126665	−	0.0799733i	−0.980545	−	0.196293i	$-0.937110\pi$
$653$	8.27124	−	52.2225i	0.0126665	−	0.0799733i	0.993212	+	0.116320i	$0.0371097\pi$
$654$	−25.8928	−	8.41309i	−0.0395915	−	0.0128641i
$655$		0			0
$656$	393.505	−	285.898i	0.599856	−	0.435821i
$657$	−16.3406	−	103.170i	−0.0248715	−	0.157032i
$658$	−107.124	−	54.5822i	−0.162802	−	0.0829517i
$659$			164.064i			0.248960i	0.992222	+	0.124480i	$0.0397262\pi$
$659$			164.064i			0.248960i	−0.992222	+	0.124480i	$0.960274\pi$
$660$		0			0
$661$	−382.249			−0.578290			−0.289145	−	0.957285i	$-0.593371\pi$
$661$	−382.249			−0.578290			−0.289145	+	0.957285i	$0.593371\pi$
$662$	98.1337	−	192.598i	0.148238	−	0.290934i
$663$	−43.7058	+	6.92231i	−0.0659212	+	0.0104409i
$664$	−121.788	−	167.626i	−0.183415	−	0.252449i
$665$		0			0
$666$	−16.8020	+	51.7112i	−0.0252282	+	0.0776444i
$667$	−1222.80	−	193.672i	−1.83328	−	0.290363i
$668$	1130.82	−	179.104i	1.69284	−	0.268120i
$669$	−138.804	+	45.1003i	−0.207480	+	0.0674145i
$670$		0			0
$671$	281.330	+	708.261i	0.419270	+	1.05553i
$672$	−117.747	−	117.747i	−0.175218	−	0.175218i
$673$	−1011.58	−	515.427i	−1.50309	−	0.765865i	−0.507683	−	0.861544i	$-0.669498\pi$
$673$	−1011.58	−	515.427i	−1.50309	−	0.765865i	−0.995412	+	0.0956792i	$0.969498\pi$
$674$	12.9536	−	17.8291i	0.0192190	−	0.0264527i
$675$		0			0
$676$	191.570	−	589.592i	0.283388	−	0.872178i
$677$	−440.725	+	224.561i	−0.650997	+	0.331700i	−0.748111	−	0.663574i	$-0.769039\pi$
$677$	−440.725	+	224.561i	−0.650997	+	0.331700i	0.0971137	+	0.995273i	$0.469039\pi$
$678$	5.02515	−	31.7275i	0.00741172	−	0.0467958i
$679$	778.194	−	1071.09i	1.14609	−	1.57746i
$680$		0			0
$681$	−313.797			−0.460789
$682$	−181.834	+	107.809i	−0.266619	+	0.158078i
$683$	−152.022	+	152.022i	−0.222580	+	0.222580i	−0.809584	−	0.587004i	$-0.800307\pi$
$683$	−152.022	+	152.022i	−0.222580	+	0.222580i	0.587004	+	0.809584i	$0.300307\pi$
$684$	−436.796	+	141.924i	−0.638591	+	0.207491i
$685$		0			0
$686$	40.5142	−	29.4353i	0.0590586	−	0.0429086i
$687$	127.019	−	64.7195i	0.184890	−	0.0942060i
$688$	435.556	+	854.827i	0.633076	+	1.24248i
$689$	−42.0604	−	57.8912i	−0.0610456	−	0.0840221i
$690$		0			0
$691$	−47.8360	−	147.224i	−0.0692272	−	0.213059i	0.910458	−	0.413602i	$-0.135729\pi$
$691$	−47.8360	−	147.224i	−0.0692272	−	0.213059i	−0.979685	+	0.200543i	$0.935729\pi$
$692$	−560.698	−	560.698i	−0.810258	−	0.810258i
$693$	621.124	−	706.105i	0.896282	−	1.01891i
$694$			9.27977i			0.0133714i
$695$		0			0
$696$	−67.6281	−	49.1347i	−0.0971669	−	0.0705959i
$697$	−533.985	−	84.5750i	−0.766120	−	0.121341i
$698$	57.9700	+	113.772i	0.0830515	+	0.162998i
$699$	291.397	+	94.6806i	0.416877	+	0.135451i
$700$		0			0
$701$	1007.39	+	731.909i	1.43707	+	1.04409i	0.988645	+	0.150272i	$0.0480148\pi$
$701$	1007.39	+	731.909i	1.43707	+	1.04409i	0.448425	+	0.893821i	$0.351985\pi$
$702$	7.86790	−	15.4416i	0.0112078	−	0.0219966i
$703$	189.270	−	189.270i	0.269232	−	0.269232i
$704$	302.829	−	478.354i	0.430154	−	0.679480i
$705$		0			0
$706$	−50.1785	−	154.434i	−0.0710743	−	0.218744i
$707$	−114.716	−	724.288i	−0.162257	−	1.02445i
$708$	2.81152	−	17.7512i	0.00397107	−	0.0250723i
$709$	−572.197	−	185.918i	−0.807047	−	0.262226i	−0.123701	−	0.992320i	$-0.539476\pi$
$709$	−572.197	−	185.918i	−0.807047	−	0.262226i	−0.683347	+	0.730094i	$0.739476\pi$
$710$		0			0
$711$	511.174	−	371.389i	0.718950	−	0.522348i
$712$	−19.8315	−	125.211i	−0.0278533	−	0.175859i
$713$	−1875.95	−	955.843i	−2.63106	−	1.34059i
$714$			58.1329i			0.0814186i
$715$		0			0
$716$	622.433			0.869320
$717$	−3.17872	+	6.23859i	−0.00443336	+	0.00870096i
$718$	−68.3223	+	10.8212i	−0.0951565	+	0.0150713i
$719$	367.141	+	505.327i	0.510628	+	0.702819i	0.984025	−	0.178030i	$-0.0569725\pi$
$719$	367.141	+	505.327i	0.510628	+	0.702819i	−0.473397	+	0.880849i	$0.656973\pi$
$720$		0			0
$721$	534.080	−	1643.73i	0.740749	−	2.27979i
$722$	53.0884	+	8.40838i	0.0735297	+	0.0116460i
$723$	73.3883	−	11.6236i	0.101505	−	0.0160769i
$724$	−632.241	+	205.427i	−0.873261	+	0.283740i
$725$		0			0
$726$	36.5846	+	20.0069i	0.0503920	+	0.0275578i
$727$	312.563	+	312.563i	0.429936	+	0.429936i	0.888606	−	0.458671i	$-0.151674\pi$
$727$	312.563	+	312.563i	0.429936	+	0.429936i	−0.458671	+	0.888606i	$0.651674\pi$
$728$	79.4896	+	40.5020i	0.109189	+	0.0556346i
$729$	−196.120	+	269.936i	−0.269026	+	0.370283i
$730$		0			0
$731$	329.531	−	1014.19i	0.450795	−	1.38740i
$732$	−224.423	+	114.349i	−0.306588	+	0.156215i
$733$	−13.5091	+	85.2930i	−0.0184299	+	0.116362i	−0.995188	−	0.0979821i	$-0.968761\pi$
$733$	−13.5091	+	85.2930i	−0.0184299	+	0.116362i	0.976758	+	0.214344i	$0.0687612\pi$
$734$	−94.9874	+	130.739i	−0.129411	+	0.178118i
$735$		0			0
$736$	−674.754			−0.916785
$737$	492.224	+	45.9778i	0.667875	+	0.0623850i
$738$	70.9928	−	70.9928i	0.0961963	−	0.0961963i
$739$	534.104	−	173.541i	0.722738	−	0.234832i	0.0755282	−	0.997144i	$-0.475936\pi$
$739$	534.104	−	173.541i	0.722738	−	0.234832i	0.647210	+	0.762312i	$0.275936\pi$
$740$		0			0
$741$	−32.7278	+	23.7781i	−0.0441670	+	0.0320892i
$742$	−83.7605	+	42.6781i	−0.112885	+	0.0575176i
$743$	−194.051	−	380.846i	−0.261172	−	0.512578i	0.722766	−	0.691093i	$-0.242871\pi$
$743$	−194.051	−	380.846i	−0.261172	−	0.512578i	−0.983937	+	0.178515i	$0.942871\pi$
$744$	−83.5592	−	115.009i	−0.112311	−	0.154582i
$745$		0			0
$746$	−50.5308	−	155.518i	−0.0677356	−	0.208469i
$747$	412.535	+	412.535i	0.552255	+	0.552255i
$748$	−664.375	+	149.280i	−0.888202	+	0.199572i
$749$			1299.18i			1.73456i
$750$		0			0
$751$	86.0258	+	62.5014i	0.114548	+	0.0832242i	0.643585	−	0.765375i	$-0.277446\pi$
$751$	86.0258	+	62.5014i	0.114548	+	0.0832242i	−0.529036	+	0.848599i	$0.677446\pi$
$752$	443.196	+	70.1953i	0.589356	+	0.0933448i
$753$	−179.356	−	352.006i	−0.238189	−	0.467472i
$754$	31.5783	+	10.2604i	0.0418811	+	0.0136080i
$755$		0			0
$756$	530.311	+	385.293i	0.701469	+	0.509647i
$757$	−101.603	+	199.406i	−0.134217	+	0.263417i	−0.948327	−	0.317295i	$-0.897226\pi$
$757$	−101.603	+	199.406i	−0.134217	+	0.263417i	0.814110	+	0.580711i	$0.197226\pi$
$758$	17.2708	−	17.2708i	0.0227847	−	0.0227847i
$759$	26.5371	+	414.455i	0.0349632	+	0.546054i
$760$		0			0
$761$	272.671	+	839.195i	0.358306	+	1.10275i	0.954068	+	0.299591i	$0.0968503\pi$
$761$	272.671	+	839.195i	0.358306	+	1.10275i	−0.595762	+	0.803161i	$0.703150\pi$
$762$	4.04292	+	25.5260i	0.00530567	+	0.0334987i
$763$	−130.193	+	822.004i	−0.170633	+	1.07733i
$764$	170.188	+	55.2975i	0.222760	+	0.0723790i
$765$		0			0
$766$	57.4992	−	41.7756i	0.0750642	−	0.0545374i
$767$	2.27228	+	14.3466i	0.00296255	+	0.0187048i
$768$	146.079	+	74.4309i	0.190207	+	0.0969153i
$769$		−	892.786i		−	1.16097i	−0.814271	−	0.580485i	$-0.802863\pi$
$769$		−	892.786i		−	1.16097i	0.814271	−	0.580485i	$-0.197137\pi$
$770$		0			0
$771$	383.620			0.497562
$772$	−101.997	+	200.181i	−0.132121	+	0.259302i
$773$	1073.93	−	170.093i	1.38929	−	0.220043i	0.583440	−	0.812156i	$-0.301706\pi$
$773$	1073.93	−	170.093i	1.38929	−	0.220043i	0.805855	+	0.592113i	$0.201706\pi$
$774$	116.400	+	160.211i	0.150387	+	0.206991i
$775$		0			0
$776$	111.936	−	344.503i	0.144247	−	0.443947i
$777$	−178.914	−	28.3372i	−0.230263	−	0.0364700i
$778$	138.985	−	22.0130i	0.178644	−	0.0282944i
$779$	−470.062	+	152.733i	−0.603418	+	0.196062i
$780$		0			0
$781$	107.568	+	270.807i	0.137731	+	0.346744i
$782$	166.567	+	166.567i	0.213001	+	0.213001i
$783$	442.298	+	225.362i	0.564876	+	0.287819i
$784$	−524.797	+	722.321i	−0.669384	+	0.921328i
$785$		0			0
$786$	−26.8775	+	82.7204i	−0.0341953	+	0.105242i
$787$	491.248	−	250.303i	0.624203	−	0.318047i	−0.113127	−	0.993581i	$-0.536087\pi$
$787$	491.248	−	250.303i	0.624203	−	0.318047i	0.737329	+	0.675533i	$0.236087\pi$
$788$	53.3775	−	337.012i	0.0677379	−	0.427680i
$789$	−149.864	+	206.270i	−0.189942	+	0.261433i
$790$		0			0
$791$	−981.968			−1.24143
$792$	101.923	−	236.249i	0.128691	−	0.298295i
$793$	143.943	−	143.943i	0.181517	−	0.181517i
$794$	88.0358	−	28.6046i	0.110876	−	0.0360259i
$795$		0			0
$796$	−737.630	+	535.920i	−0.926671	+	0.673266i
$797$	−1043.33	+	531.605i	−1.30908	+	0.667007i	−0.962568	−	0.271040i	$-0.912633\pi$
$797$	−1043.33	+	531.605i	−1.30908	+	0.667007i	−0.346508	+	0.938047i	$0.612633\pi$
$798$	24.1273	+	47.3525i	0.0302347	+	0.0593389i
$799$	−293.164	−	403.506i	−0.366914	−	0.505013i
$800$		0			0
$801$	110.305	+	339.485i	0.137710	+	0.423826i
$802$	−29.9347	−	29.9347i	−0.0373250	−	0.0373250i
$803$	−72.2067	−	121.786i	−0.0899212	−	0.151664i
$804$			163.391i			0.203223i
$805$		0			0
$806$	45.6821	+	33.1900i	0.0566776	+	0.0411787i
$807$	456.783	+	72.3473i	0.566026	+	0.0896496i
$808$	−91.0867	−	178.768i	−0.112731	−	0.221247i
$809$	958.766	+	311.522i	1.18512	+	0.385070i	0.834268	−	0.551359i	$-0.185891\pi$
$809$	958.766	+	311.522i	1.18512	+	0.385070i	0.350856	+	0.936429i	$0.385891\pi$
$810$		0			0
$811$	−445.331	−	323.552i	−0.549114	−	0.398954i	0.278345	−	0.960481i	$-0.410214\pi$
$811$	−445.331	−	323.552i	−0.549114	−	0.398954i	−0.827459	+	0.561527i	$0.810214\pi$
$812$	−570.151	+	1118.98i	−0.702157	+	1.37806i
$813$	44.0305	−	44.0305i	0.0541581	−	0.0541581i
$814$	4.70914	+	73.5471i	0.00578518	+	0.0903527i
$815$		0			0
$816$	−67.0464	−	206.348i	−0.0821647	−	0.252877i
$817$	−152.506	−	962.883i	−0.186665	−	1.17856i
$818$	−17.5531	+	110.826i	−0.0214586	+	0.135484i
$819$	−238.905	−	77.6251i	−0.291704	−	0.0947803i
$820$		0			0
$821$	−112.308	+	81.5964i	−0.136794	+	0.0993866i	−0.654078	−	0.756427i	$-0.726943\pi$
$821$	−112.308	+	81.5964i	−0.136794	+	0.0993866i	0.517284	+	0.855814i	$0.326943\pi$
$822$	6.64188	+	41.9352i	0.00808014	+	0.0510160i
$823$	−1254.83	−	639.367i	−1.52470	−	0.776873i	−0.527352	−	0.849647i	$-0.676815\pi$
$823$	−1254.83	−	639.367i	−1.52470	−	0.776873i	−0.997348	+	0.0727737i	$0.976815\pi$
$824$		−	472.869i		−	0.573871i
$825$		0			0
$826$	19.0824			0.0231021
$827$	479.658	−	941.381i	0.579997	−	1.13831i	−0.395535	−	0.918451i	$-0.629441\pi$
$827$	479.658	−	941.381i	0.579997	−	1.13831i	0.975532	−	0.219858i	$-0.0705593\pi$
$828$	1243.94	−	197.021i	1.50235	−	0.237948i
$829$	−274.311	−	377.556i	−0.330893	−	0.455436i	0.610861	−	0.791738i	$-0.290824\pi$
$829$	−274.311	−	377.556i	−0.330893	−	0.455436i	−0.941754	+	0.336303i	$0.890824\pi$
$830$		0			0
$831$	63.3783	−	195.058i	0.0762675	−	0.234727i
$832$	−149.367	−	23.6574i	−0.179527	−	0.0284343i
$833$	980.188	−	155.246i	1.17670	−	0.186370i
$834$	−26.2742	+	8.53702i	−0.0315039	+	0.0102362i
$835$		0			0
$836$	−479.214	+	397.337i	−0.573222	+	0.475283i
$837$	596.932	+	596.932i	0.713180	+	0.713180i
$838$	−68.2827	−	34.7918i	−0.0814829	−	0.0415176i
$839$	826.244	−	1137.23i	0.984796	−	1.35546i	0.0505912	−	0.998719i	$-0.483889\pi$
$839$	826.244	−	1137.23i	0.984796	−	1.35546i	0.934205	−	0.356736i	$-0.116111\pi$
$840$		0			0
$841$	−34.0082	+	104.666i	−0.0404378	+	0.124455i
$842$	−99.5196	+	50.7077i	−0.118194	+	0.0602230i
$843$	−54.2284	+	342.384i	−0.0643278	+	0.406150i
$844$	−46.5388	+	64.0552i	−0.0551408	+	0.0758948i
$845$		0			0
$846$	92.6215			0.109482
$847$	429.113	−	1200.26i	0.506627	−	1.41707i
$848$	248.093	−	248.093i	0.292562	−	0.292562i
$849$	−109.561	+	35.5986i	−0.129047	+	0.0419300i
$850$		0			0
$851$	−593.832	+	431.444i	−0.697805	+	0.506985i
$852$	−85.8090	+	43.7219i	−0.100715	+	0.0513168i
$853$	−458.448	−	899.755i	−0.537454	−	1.05481i	−0.986874	−	0.161492i	$-0.948369\pi$
$853$	−458.448	−	899.755i	−0.537454	−	1.05481i	0.449420	−	0.893320i	$-0.351631\pi$
$854$	−157.191	−	216.355i	−0.184065	−	0.253343i
$855$		0			0
$856$	109.842	+	338.060i	0.128321	+	0.394930i
$857$	787.462	+	787.462i	0.918859	+	0.918859i	0.996947	−	0.0780872i	$-0.0248812\pi$
$857$	787.462	+	787.462i	0.918859	+	0.918859i	−0.0780872	+	0.996947i	$0.524881\pi$
$858$	1.03589	−	11.0899i	0.00120733	−	0.0129253i
$859$			333.892i			0.388699i	0.980932	+	0.194349i	$0.0622595\pi$
$859$			333.892i			0.388699i	−0.980932	+	0.194349i	$0.937740\pi$
$860$		0			0
$861$	270.604	+	196.605i	0.314290	+	0.228345i
$862$	131.980	+	20.9036i	0.153109	+	0.0242501i
$863$	651.489	+	1278.62i	0.754912	+	1.48160i	0.872541	+	0.488541i	$0.162471\pi$
$863$	651.489	+	1278.62i	0.754912	+	1.48160i	−0.117628	+	0.993058i	$0.537529\pi$
$864$	257.307	+	83.6041i	0.297809	+	0.0967640i
$865$		0			0
$866$	100.834	+	73.2598i	0.116436	+	0.0845957i
$867$	13.9063	−	27.2926i	0.0160395	−	0.0314793i
$868$	−1510.20	+	1510.20i	−1.73986	+	1.73986i
$869$	458.090	−	723.608i	0.527146	−	0.832690i
$870$		0			0
$871$	−40.8067	−	125.590i	−0.0468505	−	0.144191i
$872$	35.6208	+	224.901i	0.0408495	+	0.257914i
$873$	−159.555	+	1007.39i	−0.182766	+	1.15394i
$874$	204.809	+	66.5465i	0.234335	+	0.0761402i
$875$		0			0
$876$	37.8572	−	27.5049i	0.0432160	−	0.0313982i
$877$	−199.124	−	1257.22i	−0.227051	−	1.43355i	−0.793058	−	0.609146i	$-0.791512\pi$
$877$	−199.124	−	1257.22i	−0.227051	−	1.43355i	0.566007	−	0.824401i	$-0.308488\pi$
$878$	243.424	+	124.031i	0.277248	+	0.141265i
$879$		−	496.865i		−	0.565261i
$880$		0			0
$881$	−226.497			−0.257091			−0.128545	−	0.991704i	$-0.541031\pi$
$881$	−226.497			−0.257091			−0.128545	+	0.991704i	$0.541031\pi$
$882$	−83.6674	+	164.206i	−0.0948610	+	0.186175i
$883$	−913.239	+	144.643i	−1.03425	+	0.163808i	−0.650402	−	0.759590i	$-0.725400\pi$
$883$	−913.239	+	144.643i	−1.03425	+	0.163808i	−0.383843	+	0.923398i	$0.625400\pi$
$884$	106.912	+	147.152i	0.120942	+	0.166462i
$885$		0			0
$886$	−45.0926	+	138.781i	−0.0508946	+	0.156638i
$887$	−1494.65	−	236.730i	−1.68507	−	0.266888i	−0.760897	−	0.648873i	$-0.775241\pi$
$887$	−1494.65	−	236.730i	−1.68507	−	0.266888i	−0.924169	+	0.381985i	$0.875241\pi$
$888$	−48.9510	+	7.75307i	−0.0551250	+	0.00873094i
$889$	751.363	−	244.133i	0.845178	−	0.274615i
$890$		0			0
$891$	−157.710	+	617.083i	−0.177004	+	0.692574i
$892$	424.202	+	424.202i	0.475563	+	0.475563i
$893$	−406.268	−	207.004i	−0.454947	−	0.231807i
$894$	4.15787	−	5.72282i	0.00465086	−	0.00640136i
$895$		0			0
$896$	−280.252	+	862.528i	−0.312782	+	0.962643i
$897$	98.8433	−	50.3632i	0.110193	−	0.0561463i
$898$	30.0024	−	189.428i	0.0334103	−	0.210944i
$899$	−950.668	+	1308.48i	−1.05747	+	1.45549i
$900$		0			0
$901$	−389.983			−0.432833
$902$	53.9066	−	124.951i	0.0597634	−	0.138527i
$903$	−466.514	+	466.514i	−0.516627	+	0.516627i
$904$	−255.517	+	83.0227i	−0.282652	+	0.0918392i
$905$		0			0
$906$	50.7100	−	36.8430i	0.0559713	−	0.0406655i
$907$	−79.5367	+	40.5260i	−0.0876920	+	0.0446813i	−0.497286	−	0.867586i	$-0.665670\pi$
$907$	−79.5367	+	40.5260i	−0.0876920	+	0.0446813i	0.409594	+	0.912268i	$0.365670\pi$
$908$	585.580	+	1149.27i	0.644912	+	1.26571i
$909$	332.061	+	457.043i	0.365303	+	0.502797i
$910$		0			0
$911$	−254.545	−	783.408i	−0.279412	−	0.859943i	−0.988018	−	0.154338i	$-0.950676\pi$
$911$	−254.545	−	783.408i	−0.279412	−	0.859943i	0.708606	−	0.705605i	$-0.249324\pi$
$912$	−140.255	−	140.255i	−0.153788	−	0.153788i
$913$	726.083	+	313.248i	0.795271	+	0.343097i
$914$		−	36.1757i		−	0.0395796i
$915$		0			0
$916$	−474.064	−	344.428i	−0.517537	−	0.376013i
$917$	2626.08	+	415.930i	2.86377	+	0.453576i
$918$	−42.8795	−	84.1558i	−0.0467097	−	0.0916729i
$919$	24.7032	+	8.02657i	0.0268806	+	0.00873402i	0.322426	−	0.946595i	$-0.395502\pi$
$919$	24.7032	+	8.02657i	0.0268806	+	0.00873402i	−0.295546	+	0.955329i	$0.595502\pi$
$920$		0			0
$921$	340.893	+	247.673i	0.370134	+	0.268918i
$922$	38.6502	−	75.8552i	0.0419199	−	0.0822724i
$923$	55.0374	−	55.0374i	0.0596288	−	0.0596288i
$924$	408.165	+	104.316i	0.441737	+	0.112896i
$925$		0			0
$926$	37.0836	+	114.131i	0.0400470	+	0.123252i
$927$	208.288	+	1315.08i	0.224690	+	1.41864i
$928$	−81.0864	+	511.960i	−0.0873776	+	0.551681i
$929$	−853.382	−	277.281i	−0.918603	−	0.298472i	−0.188709	−	0.982033i	$-0.560430\pi$
$929$	−853.382	−	277.281i	−0.918603	−	0.298472i	−0.729894	+	0.683561i	$0.760430\pi$
$930$		0			0
$931$	733.984	−	533.271i	0.788383	−	0.572794i
$932$	−197.016	−	1243.91i	−0.211391	−	1.33467i
$933$	−25.4906	−	12.9881i	−0.0273211	−	0.0139208i
$934$		−	256.026i		−	0.274118i
$935$		0			0
$936$	−68.7285			−0.0734279
$937$	574.636	−	1127.79i	0.613272	−	1.20361i	−0.350418	−	0.936593i	$-0.613961\pi$
$937$	574.636	−	1127.79i	0.613272	−	1.20361i	0.963691	−	0.267021i	$-0.0860394\pi$
$938$	−171.346	+	27.1385i	−0.182671	+	0.0289323i
$939$	−107.368	−	147.779i	−0.114343	−	0.157379i
$940$		0			0
$941$	−356.827	+	1098.20i	−0.379199	+	1.16706i	0.561402	+	0.827543i	$0.310262\pi$
$941$	−356.827	+	1098.20i	−0.379199	+	1.16706i	−0.940602	+	0.339513i	$0.889738\pi$
$942$	−36.6153	−	5.79930i	−0.0388698	−	0.00615636i
$943$	1338.68	−	212.026i	1.41960	−	0.224842i
$944$	−67.7344	+	22.0082i	−0.0717525	+	0.0233138i
$945$		0			0
$946$	226.791	+	143.573i	0.239737	+	0.151769i
$947$	960.358	+	960.358i	1.01411	+	1.01411i	0.999899	+	0.0142062i	$0.00452214\pi$
$947$	960.358	+	960.358i	1.01411	+	1.01411i	0.0142062	+	0.999899i	$0.495478\pi$
$948$	252.201	+	128.503i	0.266035	+	0.135552i
$949$	−22.2295	+	30.5963i	−0.0234242	+	0.0322406i
$950$		0			0
$951$	64.5223	−	198.579i	0.0678468	−	0.208811i
$952$	433.212	−	220.733i	0.455055	−	0.231862i
$953$	−166.024	+	1048.23i	−0.174212	+	1.09993i	0.733300	+	0.679905i	$0.237979\pi$
$953$	−166.024	+	1048.23i	−0.174212	+	1.09993i	−0.907512	+	0.420026i	$0.862021\pi$
$954$	42.5681	−	58.5900i	0.0446207	−	0.0614151i
$955$		0			0
$956$	28.7803			0.0301050
$957$	317.651	+	29.6712i	0.331923	+	0.0310044i
$958$	−136.085	+	136.085i	−0.142051	+	0.142051i
$959$	1234.37	−	401.071i	1.28714	−	0.418218i
$960$		0			0
$961$	−1447.76	+	1051.86i	−1.50651	+	1.09455i
$962$	17.5402	−	8.93720i	0.0182331	−	0.00929022i
$963$	−454.386	−	891.783i	−0.471844	−	0.926047i
$964$	−179.521	−	247.090i	−0.186226	−	0.256318i
$965$		0			0
$966$	−45.0352	−	138.604i	−0.0466203	−	0.143482i
$967$	246.228	+	246.228i	0.254631	+	0.254631i	0.822866	−	0.568235i	$-0.192374\pi$
$967$	246.228	+	246.228i	0.254631	+	0.254631i	−0.568235	+	0.822866i	$0.692374\pi$
$968$	10.1808	−	348.599i	0.0105173	−	0.360123i
$969$			220.470i			0.227523i
$970$		0			0
$971$	514.171	+	373.567i	0.529527	+	0.384724i	0.820181	−	0.572104i	$-0.193873\pi$
$971$	514.171	+	373.567i	0.529527	+	0.384724i	−0.290654	+	0.956828i	$0.593873\pi$
$972$	−761.042	−	120.537i	−0.782965	−	0.124009i
$973$	383.400	+	752.464i	0.394039	+	0.773344i
$974$	−201.896	−	65.6000i	−0.207286	−	0.0673512i
$975$		0			0
$976$	807.493	+	586.678i	0.827349	+	0.601104i
$977$	2.04171	−	4.00708i	0.00208977	−	0.00410141i	−0.889959	−	0.456040i	$-0.849267\pi$
$977$	2.04171	−	4.00708i	0.00208977	−	0.00410141i	0.892049	+	0.451939i	$0.149267\pi$
$978$	−51.6478	+	51.6478i	−0.0528096	+	0.0528096i
$979$	308.816	+	372.452i	0.315441	+	0.380442i
$980$		0			0
$981$	−198.127	−	609.773i	−0.201965	−	0.621583i
$982$	47.4462	+	299.564i	0.0483159	+	0.305055i
$983$	19.5212	−	123.252i	0.0198588	−	0.125383i	−0.975767	−	0.218811i	$-0.929782\pi$
$983$	19.5212	−	123.252i	0.0198588	−	0.125383i	0.995626	+	0.0934273i	$0.0297823\pi$
$984$	87.0360	+	28.2797i	0.0884513	+	0.0287396i
$985$		0			0
$986$	146.397	−	106.363i	0.148475	−	0.107874i
$987$	48.2715	+	304.774i	0.0489073	+	0.308788i
$988$	148.160	+	75.4911i	0.149959	+	0.0764080i
$989$			2673.38i			2.70312i
$990$		0			0
$991$	−1455.86			−1.46908			−0.734542	−	0.678564i	$-0.762603\pi$
$991$	−1455.86			−1.46908			−0.734542	+	0.678564i	$0.762603\pi$
$992$	−400.192	+	785.421i	−0.403419	+	0.791755i
$993$	−547.955	+	86.7876i	−0.551818	+	0.0873994i
$994$	−60.1028	−	82.7244i	−0.0604656	−	0.0832237i
$995$		0			0
$996$	−80.7632	+	248.564i	−0.0810876	+	0.249562i
$997$	−622.653	−	98.6185i	−0.624526	−	0.0989153i	−0.163853	−	0.986485i	$-0.552392\pi$
$997$	−622.653	−	98.6185i	−0.624526	−	0.0989153i	−0.460674	+	0.887570i	$0.652392\pi$
$998$	125.319	−	19.8486i	0.125570	−	0.0198883i
$999$	279.906	−	90.9469i	0.280186	−	0.0910379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.82.9	yes	128
5.2	odd	4	inner	275.3.bk.c.93.9	yes	128
5.3	odd	4	inner	275.3.bk.c.93.8	yes	128
5.4	even	2	inner	275.3.bk.c.82.8	✓	128
11.9	even	5	inner	275.3.bk.c.207.8	yes	128
55.9	even	10	inner	275.3.bk.c.207.9	yes	128
55.42	odd	20	inner	275.3.bk.c.218.8	yes	128
55.53	odd	20	inner	275.3.bk.c.218.9	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.8	✓	128	5.4	even	2	inner
275.3.bk.c.82.9	yes	128	1.1	even	1	trivial
275.3.bk.c.93.8	yes	128	5.3	odd	4	inner
275.3.bk.c.93.9	yes	128	5.2	odd	4	inner
275.3.bk.c.207.8	yes	128	11.9	even	5	inner
275.3.bk.c.207.9	yes	128	55.9	even	10	inner
275.3.bk.c.218.8	yes	128	55.42	odd	20	inner
275.3.bk.c.218.9	yes	128	55.53	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.166354 - 0.326489i) q^{2} +(-0.928883 + 0.147121i) q^{3} +(2.27222 + 3.12744i) q^{4} +(-0.106490 + 0.327744i) q^{6} +(10.4047 + 1.64794i) q^{7} +(2.84673 - 0.450878i) q^{8} +(-7.71833 + 2.50784i) q^{9} +(-8.46786 + 7.02107i) q^{11} +(-2.57074 - 2.57074i) q^{12} +(2.61803 + 1.33395i) q^{13} +(2.26890 - 3.12287i) q^{14} +(-4.45195 + 13.7017i) q^{16} +(14.2681 - 7.26994i) q^{17} +(-0.465197 + 2.93714i) q^{18} +(8.60484 - 11.8435i) q^{19} -9.90719 q^{21} +(0.883634 + 3.93264i) q^{22} +(-28.3868 + 28.3868i) q^{23} +(-2.57795 + 0.837625i) q^{24} +(0.871040 - 0.632848i) q^{26} +(14.3421 - 7.30766i) q^{27} +(18.4879 + 36.2846i) q^{28} +(18.1268 + 24.9494i) q^{29} +(16.2065 + 49.8786i) q^{31} +(11.8850 + 11.8850i) q^{32} +(6.83271 - 7.76755i) q^{33} -5.86775i q^{34} +(-25.3809 - 18.4403i) q^{36} +(18.0590 + 2.86026i) q^{37} +(-2.43533 - 4.77961i) q^{38} +(-2.62809 - 0.853920i) q^{39} +(-27.3139 - 19.8447i) q^{41} +(-1.64810 + 3.23459i) q^{42} +(47.0885 - 47.0885i) q^{43} +(-41.1988 - 10.5293i) q^{44} +(4.54571 + 13.9903i) q^{46} +(-4.87237 - 30.7629i) q^{47} +(2.11954 - 13.3822i) q^{48} +(58.9402 + 19.1508i) q^{49} +(-12.1838 + 8.85205i) q^{51} +(1.77688 + 11.2188i) q^{52} +(-21.6991 - 11.0563i) q^{53} -5.89819i q^{54} +30.3624 q^{56} +(-6.25046 + 12.2672i) q^{57} +(11.1612 - 1.76775i) q^{58} +(2.90572 + 3.99938i) q^{59} +(21.4090 - 65.8900i) q^{61} +(18.9808 + 3.00627i) q^{62} +(-84.4396 + 13.3739i) q^{63} +(-48.9493 + 15.9046i) q^{64} +(-1.39937 - 3.52297i) q^{66} +(-31.7791 - 31.7791i) q^{67} +(55.1565 + 28.1036i) q^{68} +(22.1918 - 30.5443i) q^{69} +(8.18581 - 25.1933i) q^{71} +(-20.8413 + 10.6192i) q^{72} +(-2.01349 + 12.7127i) q^{73} +(3.93804 - 5.42024i) q^{74} +56.5921 q^{76} +(-99.6758 + 59.0975i) q^{77} +(-0.715990 + 0.715990i) q^{78} +(-74.0458 + 24.0589i) q^{79} +(46.8434 - 34.0337i) q^{81} +(-11.0228 + 5.61642i) q^{82} +(-32.6366 - 64.0530i) q^{83} +(-22.5113 - 30.9842i) q^{84} +(-7.54048 - 23.2072i) q^{86} +(-20.5082 - 20.5082i) q^{87} +(-20.9401 + 23.8050i) q^{88} -43.9843i q^{89} +(25.0415 + 18.1937i) q^{91} +(-153.279 - 24.2771i) q^{92} +(-22.3922 - 43.9471i) q^{93} +(-10.8543 - 3.52677i) q^{94} +(-12.7883 - 9.29123i) q^{96} +(57.0567 - 111.980i) q^{97} +(16.0575 - 16.0575i) q^{98} +(47.7500 - 75.4269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) \) 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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