LMFDB - Embedded newform 275.3.bk.c.93.9

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			93.9
Character	$\chi$	$=$	275.93
Dual form			275.3.bk.c.207.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.326489 + 0.166354i) q^{2} +(0.147121 + 0.928883i) q^{3} +(-2.27222 - 3.12744i) q^{4} +(-0.106490 + 0.327744i) q^{6} +(-1.64794 + 10.4047i) q^{7} +(-0.450878 - 2.84673i) q^{8} +(7.71833 - 2.50784i) q^{9} +(-8.46786 + 7.02107i) q^{11} +(2.57074 - 2.57074i) q^{12} +(1.33395 - 2.61803i) q^{13} +(-2.26890 + 3.12287i) q^{14} +(-4.45195 + 13.7017i) q^{16} +(7.26994 + 14.2681i) q^{17} +(2.93714 + 0.465197i) q^{18} +(-8.60484 + 11.8435i) q^{19} -9.90719 q^{21} +(-3.93264 + 0.883634i) q^{22} +(28.3868 + 28.3868i) q^{23} +(2.57795 - 0.837625i) q^{24} +(0.871040 - 0.632848i) q^{26} +(7.30766 + 14.3421i) q^{27} +(36.2846 - 18.4879i) q^{28} +(-18.1268 - 24.9494i) q^{29} +(16.2065 + 49.8786i) q^{31} +(-11.8850 + 11.8850i) q^{32} +(-7.76755 - 6.83271i) q^{33} +5.86775i q^{34} +(-25.3809 - 18.4403i) q^{36} +(-2.86026 + 18.0590i) q^{37} +(-4.77961 + 2.43533i) q^{38} +(2.62809 + 0.853920i) q^{39} +(-27.3139 - 19.8447i) q^{41} +(-3.23459 - 1.64810i) q^{42} +(-47.0885 - 47.0885i) q^{43} +(41.1988 + 10.5293i) q^{44} +(4.54571 + 13.9903i) q^{46} +(30.7629 - 4.87237i) q^{47} +(-13.3822 - 2.11954i) q^{48} +(-58.9402 - 19.1508i) q^{49} +(-12.1838 + 8.85205i) q^{51} +(-11.2188 + 1.77688i) q^{52} +(-11.0563 + 21.6991i) q^{53} +5.89819i q^{54} +30.3624 q^{56} +(-12.2672 - 6.25046i) q^{57} +(-1.76775 - 11.1612i) q^{58} +(-2.90572 - 3.99938i) q^{59} +(21.4090 - 65.8900i) q^{61} +(-3.00627 + 18.9808i) q^{62} +(13.3739 + 84.4396i) q^{63} +(48.9493 - 15.9046i) q^{64} +(-1.39937 - 3.52297i) q^{66} +(31.7791 - 31.7791i) q^{67} +(28.1036 - 55.1565i) q^{68} +(-22.1918 + 30.5443i) q^{69} +(8.18581 - 25.1933i) q^{71} +(-10.6192 - 20.8413i) q^{72} +(12.7127 + 2.01349i) q^{73} +(-3.93804 + 5.42024i) q^{74} +56.5921 q^{76} +(-59.0975 - 99.6758i) q^{77} +(0.715990 + 0.715990i) q^{78} +(74.0458 - 24.0589i) q^{79} +(46.8434 - 34.0337i) q^{81} +(-5.61642 - 11.0228i) q^{82} +(-64.0530 + 32.6366i) q^{83} +(22.5113 + 30.9842i) q^{84} +(-7.54048 - 23.2072i) q^{86} +(20.5082 - 20.5082i) q^{87} +(23.8050 + 20.9401i) q^{88} +43.9843i q^{89} +(25.0415 + 18.1937i) q^{91} +(24.2771 - 153.279i) q^{92} +(-43.9471 + 22.3922i) q^{93} +(10.8543 + 3.52677i) q^{94} +(-12.7883 - 9.29123i) q^{96} +(111.980 + 57.0567i) 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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.326489	+	0.166354i	0.163244	+	0.0831771i	0.533704	−	0.845672i	$-0.320800\pi$
$2$	0.326489	+	0.166354i	0.163244	+	0.0831771i	−0.370459	+	0.928849i	$0.620800\pi$
$3$	0.147121	+	0.928883i	0.0490402	+	0.309628i	1.00000		0.000313023i	$9.96383e-5\pi$
$3$	0.147121	+	0.928883i	0.0490402	+	0.309628i	−0.950960	+	0.309315i	$0.899900\pi$
$4$	−2.27222	−	3.12744i	−0.568055	−	0.781861i
$5$		0			0
$5$		0			0
$6$	−0.106490	+	0.327744i	−0.0177484	+	0.0546240i
$7$	−1.64794	+	10.4047i	−0.235420	+	1.48638i	0.532823	+	0.846227i	$0.321131\pi$
$7$	−1.64794	+	10.4047i	−0.235420	+	1.48638i	−0.768243	+	0.640158i	$0.778869\pi$
$8$	−0.450878	−	2.84673i	−0.0563597	−	0.355841i
$9$	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
$13$	1.33395	−	2.61803i	0.102612	−	0.201387i	−0.833993	−	0.551776i	$-0.813951\pi$
$13$	1.33395	−	2.61803i	0.102612	−	0.201387i	0.936604	+	0.350389i	$0.113951\pi$
$14$	−2.26890	+	3.12287i	−0.162064	+	0.223062i
$15$		0			0
$16$	−4.45195	+	13.7017i	−0.278247	+	0.856355i
$17$	7.26994	+	14.2681i	0.427644	+	0.839298i	0.999816	+	0.0191647i	$0.00610068\pi$
$17$	7.26994	+	14.2681i	0.427644	+	0.839298i	−0.572173	+	0.820133i	$0.693899\pi$
$18$	2.93714	+	0.465197i	0.163174	+	0.0258443i
$19$	−8.60484	+	11.8435i	−0.452886	+	0.623344i	−0.973015	−	0.230744i	$-0.925884\pi$
$19$	−8.60484	+	11.8435i	−0.452886	+	0.623344i	0.520128	+	0.854088i	$0.325884\pi$
$20$		0			0
$21$	−9.90719			−0.471771
$22$	−3.93264	+	0.883634i	−0.178757	+	0.0401652i
$23$	28.3868	+	28.3868i	1.23421	+	1.23421i	0.962332	+	0.271878i	$0.0876448\pi$
$23$	28.3868	+	28.3868i	1.23421	+	1.23421i	0.271878	+	0.962332i	$0.412355\pi$
$24$	2.57795	−	0.837625i	0.107414	−	0.0349011i
$25$		0			0
$26$	0.871040	−	0.632848i	0.0335016	−	0.0243403i
$27$	7.30766	+	14.3421i	0.270654	+	0.531188i
$28$	36.2846	−	18.4879i	1.29588	−	0.660283i
$29$	−18.1268	−	24.9494i	−0.625062	−	0.860324i	0.372647	−	0.927973i	$-0.378450\pi$
$29$	−18.1268	−	24.9494i	−0.625062	−	0.860324i	−0.997709	+	0.0676492i	$0.978450\pi$
$30$		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
$33$	−7.76755	−	6.83271i	−0.235380	−	0.207052i
$34$			5.86775i			0.172581i
$35$		0			0
$36$	−25.3809	−	18.4403i	−0.705024	−	0.512230i
$37$	−2.86026	+	18.0590i	−0.0773045	+	0.488081i	0.918412	+	0.395625i	$0.129472\pi$
$37$	−2.86026	+	18.0590i	−0.0773045	+	0.488081i	−0.995717	+	0.0924564i	$0.970528\pi$
$38$	−4.77961	+	2.43533i	−0.125779	+	0.0640877i
$39$	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	$0.835075\pi$
$42$	−3.23459	−	1.64810i	−0.0770139	−	0.0392406i
$43$	−47.0885	−	47.0885i	−1.09508	−	1.09508i	−0.994977	−	0.100104i	$-0.968083\pi$
$43$	−47.0885	−	47.0885i	−1.09508	−	1.09508i	−0.100104	−	0.994977i	$-0.531917\pi$
$44$	41.1988	+	10.5293i	0.936337	+	0.239303i
$45$		0			0
$46$	4.54571	+	13.9903i	0.0988197	+	0.304136i
$47$	30.7629	−	4.87237i	0.654530	−	0.103667i	0.179668	−	0.983727i	$-0.442498\pi$
$47$	30.7629	−	4.87237i	0.654530	−	0.103667i	0.474863	+	0.880060i	$0.342498\pi$
$48$	−13.3822	−	2.11954i	−0.278797	−	0.0441570i
$49$	−58.9402	−	19.1508i	−1.20286	−	0.390833i
$50$		0			0
$51$	−12.1838	+	8.85205i	−0.238898	+	0.173570i
$52$	−11.2188	+	1.77688i	−0.215745	+	0.0341707i
$53$	−11.0563	+	21.6991i	−0.208609	+	0.409418i	−0.971476	−	0.237137i	$-0.923791\pi$
$53$	−11.0563	+	21.6991i	−0.208609	+	0.409418i	0.762867	+	0.646555i	$0.223791\pi$
$54$			5.89819i			0.109226i
$55$		0			0
$56$	30.3624			0.542185
$57$	−12.2672	−	6.25046i	−0.215214	−	0.109657i
$58$	−1.76775	−	11.1612i	−0.0304785	−	0.192434i
$59$	−2.90572	−	3.99938i	−0.0492495	−	0.0677862i	0.783682	−	0.621162i	$-0.213339\pi$
$59$	−2.90572	−	3.99938i	−0.0492495	−	0.0677862i	−0.832931	+	0.553376i	$0.813339\pi$
$60$		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	$-0.0922346\pi$
$62$	−3.00627	+	18.9808i	−0.0484882	+	0.306142i
$63$	13.3739	+	84.4396i	0.212284	+	1.34031i
$64$	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	$-0.641132\pi$
$67$	31.7791	−	31.7791i	0.474314	−	0.474314i	0.903308	+	0.428993i	$0.141132\pi$
$68$	28.1036	−	55.1565i	0.413289	−	0.811125i
$69$	−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	$0.0402700\pi$
$72$	−10.6192	−	20.8413i	−0.147488	−	0.289462i
$73$	12.7127	+	2.01349i	0.174147	+	0.0275821i	0.242899	−	0.970052i	$-0.421902\pi$
$73$	12.7127	+	2.01349i	0.174147	+	0.0275821i	−0.0687521	+	0.997634i	$0.521902\pi$
$74$	−3.93804	+	5.42024i	−0.0532167	+	0.0732465i
$75$		0			0
$76$	56.5921			0.744633
$77$	−59.0975	−	99.6758i	−0.767500	−	1.29449i
$78$	0.715990	+	0.715990i	0.00917936	+	0.00917936i
$79$	74.0458	−	24.0589i	0.937288	−	0.304543i	0.199748	−	0.979847i	$-0.435988\pi$
$79$	74.0458	−	24.0589i	0.937288	−	0.304543i	0.737540	+	0.675304i	$0.235988\pi$
$80$		0			0
$81$	46.8434	−	34.0337i	0.578314	−	0.420170i
$82$	−5.61642	−	11.0228i	−0.0684929	−	0.134425i
$83$	−64.0530	+	32.6366i	−0.771723	+	0.393212i	−0.795072	−	0.606515i	$-0.792567\pi$
$83$	−64.0530	+	32.6366i	−0.771723	+	0.393212i	0.0233493	+	0.999727i	$0.492567\pi$
$84$	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
$88$	23.8050	+	20.9401i	0.270512	+	0.237955i
$89$			43.9843i			0.494205i	0.968989	+	0.247103i	$0.0794785\pi$
$89$			43.9843i			0.494205i	−0.968989	+	0.247103i	$0.920522\pi$
$90$		0			0
$91$	25.0415	+	18.1937i	0.275181	+	0.199931i
$92$	24.2771	−	153.279i	0.263881	−	1.66608i
$93$	−43.9471	+	22.3922i	−0.472549	+	0.240776i
$94$	10.8543	+	3.52677i	0.115471	+	0.0375189i
$95$		0			0
$96$	−12.7883	−	9.29123i	−0.133211	−	0.0967837i
$97$	111.980	+	57.0567i	1.15443	+	0.588213i	0.923062	−	0.384652i	$-0.125679\pi$
$97$	111.980	+	57.0567i	1.15443	+	0.588213i	0.231372	+	0.972865i	$0.425679\pi$
$98$	−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	$-0.211990\pi$
$102$	−5.45045	+	0.863267i	−0.0534358	+	0.00846340i
$103$	−162.045	−	25.6654i	−1.57325	−	0.249178i	−0.692024	−	0.721875i	$-0.743281\pi$
$103$	−162.045	−	25.6654i	−1.57325	−	0.249178i	−0.881225	+	0.472696i	$0.843281\pi$
$104$	−8.05427	−	2.61699i	−0.0774449	−	0.0251634i
$105$		0			0
$106$	−7.21949	+	5.24527i	−0.0681084	+	0.0494836i
$107$	−121.810	+	19.2927i	−1.13841	+	0.180306i	−0.697048	−	0.717025i	$-0.745503\pi$
$107$	−121.810	+	19.2927i	−1.13841	+	0.180306i	−0.441359	+	0.897331i	$0.645503\pi$
$108$	28.2494	−	55.4427i	0.261569	−	0.513358i
$109$		−	79.0032i		−	0.724800i	−0.932023	−	0.362400i	$-0.881957\pi$
$109$		−	79.0032i		−	0.724800i	0.932023	−	0.362400i	$-0.118043\pi$
$110$		0			0
$111$	−17.1955			−0.154914
$112$	−135.225	−	68.9007i	−1.20737	−	0.615185i
$113$	14.5821	+	92.0678i	0.129045	+	0.814759i	0.964284	+	0.264872i	$0.0853296\pi$
$113$	14.5821	+	92.0678i	0.129045	+	0.814759i	−0.835238	+	0.549888i	$0.814670\pi$
$114$	−2.96532	−	4.08141i	−0.0260115	−	0.0358018i
$115$		0			0
$116$	−36.8397	+	113.381i	−0.317584	+	0.977422i
$117$	3.73029	−	23.5521i	0.0318828	−	0.201300i
$118$	−0.283371	−	1.78913i	−0.00240145	−	0.0151621i
$119$	−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
$123$	14.4150	−	28.2909i	0.117195	−	0.230008i
$124$	119.168	−	164.020i	0.961030	−	1.32274i
$125$		0			0
$126$	−9.68046	+	29.7934i	−0.0768290	+	0.236455i
$127$	34.0472	+	66.8213i	0.268088	+	0.526152i	0.985327	−	0.170675i	$-0.0545947\pi$
$127$	34.0472	+	66.8213i	0.268088	+	0.526152i	−0.717240	+	0.696827i	$0.754595\pi$
$128$	85.0311	+	13.4676i	0.664305	+	0.105216i
$129$	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	$0.0864639\pi$
$132$	−3.71933	+	39.8180i	−0.0281767	+	0.301651i
$133$	−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
$137$	55.9341	+	109.777i	0.408278	+	0.801291i	0.999988	−	0.00485985i	$-0.00154694\pi$
$137$	55.9341	+	109.777i	0.408278	+	0.801291i	−0.591710	+	0.806151i	$0.701547\pi$
$138$	−12.3265	+	6.28069i	−0.0893228	+	0.0455122i
$139$	−47.1210	−	64.8564i	−0.339000	−	0.466593i	0.605149	−	0.796112i	$-0.293113\pi$
$139$	−47.1210	−	64.8564i	−0.339000	−	0.466593i	−0.944149	+	0.329519i	$0.893113\pi$
$140$		0			0
$141$	9.05172	+	27.8583i	0.0641966	+	0.197577i
$142$	6.86359	−	6.86359i	0.0483352	−	0.0483352i
$143$	7.08563	+	31.5349i	0.0495499	+	0.220523i
$144$			116.919i			0.811937i
$145$		0			0
$146$	3.81560	+	2.77220i	0.0261342	+	0.0189876i
$147$	9.11756	−	57.5660i	0.0620242	−	0.391606i
$148$	62.9776	−	32.0887i	0.425525	−	0.216816i
$149$	19.5223	+	6.34317i	0.131022	+	0.0425716i	0.373794	−	0.927512i	$-0.378057\pi$
$149$	19.5223	+	6.34317i	0.131022	+	0.0425716i	−0.242772	+	0.970083i	$0.578057\pi$
$150$		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	$0.905742\pi$
$152$	37.5951	+	19.1557i	0.247336	+	0.126024i
$153$	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
$157$	−106.251	+	16.8286i	−0.676760	+	0.107188i	−0.485347	−	0.874321i	$-0.661307\pi$
$157$	−106.251	+	16.8286i	−0.676760	+	0.107188i	−0.191413	+	0.981510i	$0.561307\pi$
$158$	28.1774	+	4.46286i	0.178338	+	0.0282460i
$159$	−21.7826	−	7.07758i	−0.136997	−	0.0445131i
$160$		0			0
$161$	−342.136	+	248.576i	−2.12507	+	1.54395i
$162$	20.9555	−	3.31903i	0.129355	−	0.0204878i
$163$	96.2244	−	188.851i	0.590334	−	1.15860i	−0.381817	−	0.924238i	$-0.624701\pi$
$163$	96.2244	−	188.851i	0.590334	−	1.15860i	0.972151	−	0.234357i	$-0.0752986\pi$
$164$			130.514i			0.795817i
$165$		0			0
$166$	−26.3418			−0.158686
$167$	263.889	+	134.458i	1.58018	+	0.805140i	0.999957	−	0.00932044i	$-0.00296683\pi$
$167$	263.889	+	134.458i	1.58018	+	0.805140i	0.580219	+	0.814460i	$0.302967\pi$
$168$	4.46693	+	28.2031i	0.0265889	+	0.167876i
$169$	94.2611	+	129.739i	0.557758	+	0.767688i
$170$		0			0
$171$	−36.7133	+	112.992i	−0.214698	+	0.660771i
$172$	−40.2711	+	254.262i	−0.234134	+	1.47827i
$173$	32.0882	+	202.597i	0.185481	+	1.17108i	0.888147	+	0.459560i	$0.151993\pi$
$173$	32.0882	+	202.597i	0.185481	+	1.17108i	−0.702666	+	0.711520i	$0.748007\pi$
$174$	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
$178$	−7.31697	+	14.3604i	−0.0411066	+	0.0806762i
$179$	−94.6411	+	130.262i	−0.528721	+	0.727722i	−0.986935	−	0.161120i	$-0.948489\pi$
$179$	−94.6411	+	130.262i	−0.528721	+	0.727722i	0.458214	+	0.888842i	$0.348489\pi$
$180$		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	$0.942431\pi$
$182$	5.14917	+	10.1058i	0.0282921	+	0.0555264i
$183$	64.3538	+	10.1926i	0.351660	+	0.0556975i
$184$	68.0107	−	93.6086i	0.369623	−	0.508743i
$185$		0			0
$186$	−18.0733			−0.0971681
$187$	−161.738	−	69.7772i	−0.864908	−	0.373140i
$188$	−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	$0.261332\pi$
$192$	21.9750	+	43.1283i	0.114453	+	0.224627i
$193$	51.7834	−	26.3850i	0.268308	−	0.136710i	−0.314661	−	0.949204i	$-0.601891\pi$
$193$	51.7834	−	26.3850i	0.268308	−	0.136710i	0.582969	+	0.812494i	$0.301891\pi$
$194$	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	$-0.678080\pi$
$197$	62.4136	−	62.4136i	0.316820	−	0.316820i	0.847544	+	0.530724i	$0.178080\pi$
$198$	−28.1374	+	16.6826i	−0.142108	+	0.0842556i
$199$		−	235.857i		−	1.18521i	−0.805492	−	0.592606i	$-0.798099\pi$
$199$		−	235.857i		−	1.18521i	0.805492	−	0.592606i	$-0.201901\pi$
$200$		0			0
$201$	34.1944	+	24.8437i	0.170121	+	0.123600i
$202$	3.99026	−	25.1935i	0.0197538	−	0.124720i
$203$	289.463	−	147.489i	1.42592	−	0.726545i
$204$	55.3686	+	17.9903i	0.271415	+	0.0881879i
$205$		0			0
$206$	−48.6362	−	35.3363i	−0.236098	−	0.171535i
$207$	290.288	+	147.909i	1.40236	+	0.714538i
$208$	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	$0.884545\pi$
$212$	92.9850	−	14.7274i	0.438609	−	0.0694688i
$213$	24.6060	+	3.89720i	0.115521	+	0.0182967i
$214$	−42.9789	−	13.9647i	−0.200836	−	0.0652555i
$215$		0			0
$216$	37.5332	−	27.2695i	0.173765	−	0.126248i
$217$	−545.679	+	86.4271i	−2.51465	+	0.398282i
$218$	13.1425	−	25.7937i	0.0602868	−	0.118320i
$219$			12.1048i			0.0552732i
$220$		0			0
$221$	47.0519			0.212905
$222$	−5.61414	−	2.86055i	−0.0252889	−	0.0128853i
$223$	−24.2766	−	153.277i	−0.108864	−	0.687339i	−0.980401	−	0.197010i	$-0.936877\pi$
$223$	−24.2766	−	153.277i	−0.108864	−	0.687339i	0.871538	−	0.490329i	$-0.163123\pi$
$224$	−104.074	−	143.245i	−0.464615	−	0.639488i
$225$		0			0
$226$	−10.5550	+	32.4849i	−0.0467035	+	0.143738i
$227$	−52.1964	+	329.555i	−0.229940	+	1.45178i	0.554812	+	0.831975i	$0.312790\pi$
$227$	−52.1964	+	329.555i	−0.229940	+	1.45178i	−0.784753	+	0.619809i	$0.787210\pi$
$228$	8.32586	+	52.5674i	0.0365169	+	0.230559i
$229$	144.163	−	46.8414i	0.629533	−	0.204548i	0.0231646	−	0.999732i	$-0.492626\pi$
$229$	144.163	−	46.8414i	0.629533	−	0.204548i	0.606368	+	0.795184i	$0.292626\pi$
$230$		0			0
$231$	83.8927	−	69.5590i	0.363172	−	0.301121i
$232$	−62.8512	+	62.8512i	−0.270910	+	0.270910i
$233$	−147.905	+	290.281i	−0.634787	+	1.24584i	0.319680	+	0.947525i	$0.396424\pi$
$233$	−147.905	+	290.281i	−0.634787	+	1.24584i	−0.954468	+	0.298315i	$0.903576\pi$
$234$	5.13590	−	7.06896i	0.0219483	−	0.0302092i
$235$		0			0
$236$	−5.90540	+	18.1750i	−0.0250229	+	0.0770125i
$237$	33.2416	+	65.2403i	0.140260	+	0.275275i
$238$	−61.0521	−	9.66970i	−0.256521	−	0.0406290i
$239$	−4.37606	+	6.02313i	−0.0183099	+	0.0252014i	−0.818074	−	0.575113i	$-0.804958\pi$
$239$	−4.37606	+	6.02313i	−0.0183099	+	0.0252014i	0.799764	+	0.600315i	$0.204958\pi$
$240$		0			0
$241$	−79.0071			−0.327830			−0.163915	−	0.986474i	$-0.552412\pi$
$241$	−79.0071			−0.327830			−0.163915	+	0.986474i	$0.552412\pi$
$242$	27.0970	−	35.0938i	0.111971	−	0.145016i
$243$	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
$247$	19.5283	+	38.3264i	0.0790619	+	0.155168i
$248$	134.684	−	68.6248i	0.543080	−	0.276713i
$249$	−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
$253$	−439.681	−	41.0699i	−1.73787	−	0.162332i
$254$			27.4803i			0.108190i
$255$		0			0
$256$	−141.034	−	102.467i	−0.550913	−	0.400262i
$257$	63.8105	−	402.884i	0.248290	−	1.56764i	−0.476815	−	0.879004i	$-0.658209\pi$
$257$	63.8105	−	402.884i	0.248290	−	1.56764i	0.725105	−	0.688638i	$-0.241791\pi$
$258$	20.4474	−	10.4185i	0.0792536	−	0.0403817i
$259$	−183.185	−	59.5204i	−0.707277	−	0.229808i
$260$		0			0
$261$	−202.478	−	147.109i	−0.775776	−	0.563634i
$262$	82.4036	+	41.9867i	0.314518	+	0.160255i
$263$	−191.700	−	191.700i	−0.728899	−	0.728899i	0.241501	−	0.970400i	$-0.422360\pi$
$263$	−191.700	−	191.700i	−0.728899	−	0.728899i	−0.970400	+	0.241501i	$0.922360\pi$
$264$	−15.9487	+	25.1928i	−0.0604116	+	0.0954274i
$265$		0			0
$266$	−17.4624	−	53.7436i	−0.0656480	−	0.202044i
$267$	−40.8562	+	6.47099i	−0.153020	+	0.0242359i
$268$	−171.596	−	27.1782i	−0.640285	−	0.101411i
$269$	467.686	+	151.961i	1.73861	+	0.564909i	0.994649	−	0.103312i	$-0.0329441\pi$
$269$	467.686	+	151.961i	1.73861	+	0.564909i	0.743963	+	0.668221i	$0.232944\pi$
$270$		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	$0.338982\pi$
$272$	−227.862	+	36.0898i	−0.837728	+	0.132683i
$273$	−13.2157	+	25.9373i	−0.0484092	+	0.0950084i
$274$			45.1458i			0.164766i
$275$		0			0
$276$	145.950			0.528805
$277$	−194.311	−	99.0065i	−0.701485	−	0.357424i	0.0665937	−	0.997780i	$-0.478787\pi$
$277$	−194.311	−	99.0065i	−0.701485	−	0.357424i	−0.768078	+	0.640356i	$0.778787\pi$
$278$	−4.59531	−	29.0137i	−0.0165299	−	0.104366i
$279$	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	$-0.127697\pi$
$282$	−1.67907	+	10.6012i	−0.00595415	+	0.0375930i
$283$	−19.1620	−	120.984i	−0.0677103	−	0.427506i	−0.998136	−	0.0610260i	$-0.980563\pi$
$283$	−19.1620	−	120.984i	−0.0677103	−	0.427506i	0.930426	−	0.366480i	$-0.119437\pi$
$284$	−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
$288$	−61.9266	+	121.538i	−0.215023	+	0.422006i
$289$	19.1444	−	26.3500i	0.0662435	−	0.0911763i
$290$		0			0
$291$	−36.5244	+	112.411i	−0.125513	+	0.386291i
$292$	−22.5890	−	44.3333i	−0.0773595	−	0.151827i
$293$	521.815	+	82.6474i	1.78094	+	0.282073i	0.958149	−	0.286271i	$-0.0924156\pi$
$293$	521.815	+	82.6474i	1.78094	+	0.282073i	0.822791	+	0.568344i	$0.192416\pi$
$294$	12.5531	−	17.2779i	0.0426977	−	0.0587684i
$295$		0			0
$296$	52.6987			0.178036
$297$	−162.577	−	70.1392i	−0.547397	−	0.236159i
$298$	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
$302$	−30.2581	−	59.3849i	−0.100192	−	0.196639i
$303$	58.3316	−	29.7214i	0.192514	−	0.0980906i
$304$	−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	0.0324958	−	0.999472i	$-0.489654\pi$
$307$	316.814	−	316.814i	1.03197	−	1.03197i	0.999472	−	0.0324958i	$-0.0103456\pi$
$308$	−177.448	+	411.309i	−0.576129	+	1.33542i
$309$		−	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	$0.684426\pi$
$312$	1.24593	−	7.86649i	0.00399336	−	0.0252131i
$313$	173.059	−	88.1780i	0.552904	−	0.281719i	−0.155133	−	0.987894i	$-0.549581\pi$
$313$	173.059	−	88.1780i	0.552904	−	0.281719i	0.708038	+	0.706175i	$0.249581\pi$
$314$	−37.4894	−	12.1810i	−0.119393	−	0.0387931i
$315$		0			0
$316$	−243.491	−	176.907i	−0.770542	−	0.559831i
$317$	−197.819	−	100.794i	−0.624034	−	0.317961i	0.113227	−	0.993569i	$-0.463881\pi$
$317$	−197.819	−	100.794i	−0.624034	−	0.317961i	−0.737261	+	0.675608i	$0.763881\pi$
$318$	−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
$322$	−153.055	+	24.2416i	−0.475327	+	0.0752844i
$323$	−231.541	−	36.6725i	−0.716845	−	0.113537i
$324$	−212.877	−	69.1679i	−0.657028	−	0.213481i
$325$		0			0
$326$	62.8324	−	45.6504i	0.192737	−	0.140032i
$327$	73.3847	−	11.6230i	0.224418	−	0.0355443i
$328$	−44.1772	+	86.7027i	−0.134687	+	0.264337i
$329$			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	$0.149935\pi$
$332$	247.612	+	126.164i	0.745818	+	0.380013i
$333$	23.2126	+	146.558i	0.0697074	+	0.440115i
$334$	63.7892	+	87.7983i	0.190986	+	0.262869i
$335$		0			0
$336$	44.1063	−	135.745i	0.131269	−	0.404004i
$337$	−9.40843	+	59.4025i	−0.0279182	+	0.176269i	−0.997707	−	0.0676761i	$-0.978442\pi$
$337$	−9.40843	+	59.4025i	−0.0279182	+	0.176269i	0.969789	+	0.243945i	$0.0784415\pi$
$338$	9.19249	+	58.0391i	0.0271967	+	0.171713i
$339$	−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
$343$	62.0453	−	121.771i	0.180890	−	0.355017i
$344$	−112.817	+	155.279i	−0.327956	+	0.451393i
$345$		0			0
$346$	−23.2264	+	71.4836i	−0.0671284	+	0.206600i
$347$	−11.4973	−	22.5648i	−0.0331335	−	0.0650281i	0.873846	−	0.486202i	$-0.161618\pi$
$347$	−11.4973	−	22.5648i	−0.0331335	−	0.0650281i	−0.906980	+	0.421174i	$0.861618\pi$
$348$	−110.738	−	17.5391i	−0.318211	−	0.0503997i
$349$	204.827	−	281.920i	0.586898	−	0.807795i	−0.407533	−	0.913191i	$-0.633611\pi$
$349$	204.827	−	281.920i	0.586898	−	0.807795i	0.994430	+	0.105395i	$0.0336108\pi$
$350$		0			0
$351$	47.2961			0.134747
$352$	17.1951	−	184.086i	0.0488498	−	0.522970i
$353$	−313.352	−	313.352i	−0.887684	−	0.887684i	0.106617	−	0.994300i	$-0.465998\pi$
$353$	−313.352	−	313.352i	−0.887684	−	0.887684i	−0.994300	+	0.106617i	$0.965998\pi$
$354$	1.62021	−	0.526437i	0.00457685	−	0.00148711i
$355$		0			0
$356$	137.558	−	99.9419i	0.386399	−	0.280736i
$357$	−72.0247	−	141.356i	−0.201750	−	0.395956i
$358$	−52.5689	+	26.7852i	−0.146841	+	0.0748190i
$359$	110.962	+	152.726i	0.309086	+	0.425421i	0.935096	−	0.354394i	$-0.115313\pi$
$359$	110.962	+	152.726i	0.309086	+	0.425421i	−0.626010	+	0.779815i	$0.715313\pi$
$360$		0			0
$361$	45.3289	+	139.508i	0.125565	+	0.386449i
$362$	−44.5571	+	44.5571i	−0.123086	+	0.123086i
$363$	113.747	+	3.32196i	0.313354	+	0.00915141i
$364$		−	119.656i		−	0.328725i
$365$		0			0
$366$	19.3152	+	14.0333i	0.0527738	+	0.0383424i
$367$	68.9910	−	435.592i	0.187986	−	1.18690i	−0.695529	−	0.718498i	$-0.744830\pi$
$367$	68.9910	−	435.592i	0.187986	−	1.18690i	0.883516	−	0.468402i	$-0.155170\pi$
$368$	−515.324	+	262.571i	−1.40034	+	0.713507i
$369$	−260.585	−	84.6690i	−0.706191	−	0.229455i
$370$		0			0
$371$	−207.553	−	150.796i	−0.559441	−	0.406458i
$372$	169.888	+	86.5621i	0.456687	+	0.232694i
$373$	−315.552	−	315.552i	−0.845985	−	0.845985i	0.143645	−	0.989629i	$-0.454118\pi$
$373$	−315.552	−	315.552i	−0.845985	−	0.845985i	−0.989629	+	0.143645i	$0.954118\pi$
$374$	−41.1978	−	49.6873i	−0.110155	−	0.132854i
$375$		0			0
$376$	−27.7406	−	85.3769i	−0.0737783	−	0.227066i
$377$	−89.4985	+	14.1752i	−0.237396	+	0.0375999i
$378$	−61.3689	−	9.71987i	−0.162352	−	0.0257140i
$379$	−63.3937	−	20.5979i	−0.167266	−	0.0543480i	0.224187	−	0.974546i	$-0.428027\pi$
$379$	−63.3937	−	20.5979i	−0.167266	−	0.0543480i	−0.391453	+	0.920198i	$0.628027\pi$
$380$		0			0
$381$	−57.0602	+	41.4566i	−0.149764	+	0.108810i
$382$	16.7532	−	2.65345i	0.0438567	−	0.00694621i
$383$	88.0570	−	172.822i	0.229914	−	0.451231i	−0.747012	−	0.664811i	$-0.768512\pi$
$383$	88.0570	−	172.822i	0.229914	−	0.451231i	0.976926	+	0.213579i	$0.0685122\pi$
$384$			80.9653i			0.210847i
$385$		0			0
$386$	21.2960			0.0551709
$387$	−481.535	−	245.354i	−1.24428	−	0.633990i
$388$	−76.0018	−	479.857i	−0.195881	−	1.23674i
$389$	−225.724	−	310.683i	−0.580268	−	0.798671i	0.413456	−	0.910524i	$-0.364321\pi$
$389$	−225.724	−	310.683i	−0.580268	−	0.798671i	−0.993725	+	0.111853i	$0.964321\pi$
$390$		0			0
$391$	−198.654	+	611.396i	−0.508068	+	1.56367i
$392$	−27.9424	+	176.421i	−0.0712817	+	0.450055i
$393$	37.1323	+	234.444i	0.0944842	+	0.596550i
$394$	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	$-0.853065\pi$
$397$	−178.629	+	178.629i	−0.449946	+	0.449946i	0.445391	+	0.895336i	$0.353065\pi$
$398$	39.2359	−	77.0047i	0.0985826	−	0.193479i
$399$	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	$0.0539858\pi$
$402$	7.03123	+	13.7996i	0.0174906	+	0.0343273i
$403$	152.202	+	24.1065i	0.377673	+	0.0598176i
$404$	−158.173	+	217.706i	−0.391517	+	0.538877i
$405$		0			0
$406$	119.042			0.293206
$407$	−102.573	−	173.003i	−0.252022	−	0.425069i
$408$	30.6928	+	30.6928i	0.0752275	+	0.0752275i
$409$	291.234	−	94.6276i	0.712063	−	0.231363i	0.0694843	−	0.997583i	$-0.477865\pi$
$409$	291.234	−	94.6276i	0.712063	−	0.231363i	0.642579	+	0.766220i	$0.277865\pi$
$410$		0			0
$411$	−93.7408	+	68.1067i	−0.228080	+	0.165710i
$412$	287.934	+	565.103i	0.698869	+	1.37161i
$413$	46.4008	−	23.6424i	0.112351	−	0.0572455i
$414$	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
$418$	23.3744	−	54.1800i	0.0559196	−	0.129617i
$419$			209.142i			0.499147i	0.968356	+	0.249573i	$0.0802904\pi$
$419$			209.142i			0.499147i	−0.968356	+	0.249573i	$0.919710\pi$
$420$		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	$0.817912\pi$
$422$	−1.17405	+	7.41263i	−0.00278210	+	0.0175655i
$423$	225.219	−	114.755i	0.532433	−	0.271288i
$424$	66.7566	+	21.6905i	0.157445	+	0.0511569i
$425$		0			0
$426$	7.38525	+	5.36570i	0.0173363	+	0.0125955i
$427$	650.285	+	331.337i	1.52291	+	0.775964i
$428$	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	$0.760959\pi$
$432$	−229.044	+	36.2770i	−0.530195	+	0.0839746i
$433$	335.954	+	53.2099i	0.775876	+	0.122887i	0.531800	−	0.846870i	$-0.321516\pi$
$433$	335.954	+	53.2099i	0.775876	+	0.122887i	0.244075	+	0.969756i	$0.421516\pi$
$434$	−192.536	−	62.5586i	−0.443630	−	0.144144i
$435$		0			0
$436$	−247.078	+	179.513i	−0.566693	+	0.411726i
$437$	−580.465	+	91.9366i	−1.32829	+	0.210381i
$438$	−2.01369	+	3.95209i	−0.00459747	+	0.00902304i
$439$		−	745.582i		−	1.69836i	−0.528100	−	0.849182i	$-0.677096\pi$
$439$		−	745.582i		−	1.69836i	0.528100	−	0.849182i	$-0.322904\pi$
$440$		0			0
$441$	−502.947			−1.14047
$442$	15.3619	+	7.82729i	0.0347555	+	0.0177088i
$443$	62.2972	+	393.329i	0.140626	+	0.887876i	0.952609	+	0.304196i	$0.0983877\pi$
$443$	62.2972	+	393.329i	0.140626	+	0.887876i	−0.811984	+	0.583680i	$0.801612\pi$
$444$	39.0720	+	53.7780i	0.0879999	+	0.121122i
$445$		0			0
$446$	17.5722	−	54.0816i	0.0393995	−	0.121259i
$447$	−3.01993	+	19.0671i	−0.00675600	+	0.0426557i
$448$	84.8168	+	535.512i	0.189323	+	1.19534i
$449$	−497.787	+	161.741i	−1.10866	+	0.360224i	−0.805428	−	0.592694i	$-0.798065\pi$
$449$	−497.787	+	161.741i	−1.10866	+	0.360224i	−0.303228	+	0.952918i	$0.598065\pi$
$450$		0			0
$451$	370.621	−	23.7304i	0.821775	−	0.0526174i
$452$	254.803	−	254.803i	0.563724	−	0.563724i
$453$	77.6597	−	152.416i	0.171434	−	0.336459i
$454$	−71.8644	+	98.9129i	−0.158292	+	0.217870i
$455$		0			0
$456$	−12.2624	+	37.7396i	−0.0268911	+	0.0827624i
$457$	44.8205	+	87.9652i	0.0980755	+	0.192484i	0.934831	−	0.355092i	$-0.115551\pi$
$457$	44.8205	+	87.9652i	0.0980755	+	0.192484i	−0.836756	+	0.547576i	$0.815551\pi$
$458$	54.8599	+	8.68895i	0.119781	+	0.0189715i
$459$	−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	$0.418914\pi$
$462$	38.9615	−	8.75433i	0.0843322	−	0.0189488i
$463$	231.578	+	231.578i	0.500168	+	0.500168i	0.911490	−	0.411322i	$-0.134933\pi$
$463$	231.578	+	231.578i	0.500168	+	0.500168i	−0.411322	+	0.911490i	$0.634933\pi$
$464$	422.548	−	137.294i	0.910664	−	0.295893i
$465$		0			0
$466$	−96.5789	+	70.1687i	−0.207251	+	0.150577i
$467$	317.208	+	622.555i	0.679245	+	1.33309i	0.930899	+	0.365277i	$0.119026\pi$
$467$	317.208	+	622.555i	0.679245	+	1.33309i	−0.251654	+	0.967817i	$0.580974\pi$
$468$	−82.1340	+	41.8494i	−0.175500	+	0.0894217i
$469$	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
$473$	729.350	+	68.1273i	1.54197	+	0.144032i
$474$			26.8301i			0.0566036i
$475$		0			0
$476$	527.573	+	383.304i	1.10835	+	0.805261i
$477$	−30.9180	+	195.208i	−0.0648175	+	0.409242i
$478$	−2.43071	+	1.23851i	−0.00508516	+	0.00259102i
$479$	499.509	+	162.300i	1.04282	+	0.338832i	0.779846	−	0.625972i	$-0.215298\pi$
$479$	499.509	+	162.300i	1.04282	+	0.338832i	0.262971	+	0.964804i	$0.415298\pi$
$480$		0			0
$481$	43.4635	+	31.5781i	0.0903607	+	0.0656509i
$482$	−25.7949	−	13.1432i	−0.0535164	−	0.0272680i
$483$	−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
$487$	572.208	−	90.6289i	1.17497	−	0.186096i	0.461730	−	0.887020i	$-0.347229\pi$
$487$	572.208	−	90.6289i	1.17497	−	0.186096i	0.713236	+	0.700924i	$0.247229\pi$
$488$	−197.224	−	31.2372i	−0.404147	−	0.0640106i
$489$	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	$0.980853\pi$
$492$	−121.232	+	19.2013i	−0.246407	+	0.0390270i
$493$	224.199	−	440.015i	0.454764	−	0.892525i
$494$			15.7618i			0.0319064i
$495$		0			0
$496$	−755.572			−1.52333
$497$	248.639	+	126.688i	0.500280	+	0.254905i
$498$	−3.87543	−	24.4685i	−0.00778198	−	0.0491335i
$499$	−203.530	−	280.135i	−0.407876	−	0.561393i	0.554823	−	0.831968i	$-0.312786\pi$
$499$	−203.530	−	280.135i	−0.407876	−	0.561393i	−0.962699	+	0.270576i	$0.912786\pi$
$500$		0			0
$501$	−86.0725	+	264.904i	−0.171801	+	0.528750i
$502$	−24.0795	+	152.032i	−0.0479672	+	0.302853i
$503$	−46.9968	−	296.726i	−0.0934330	−	0.589913i	−0.989335	−	0.145660i	$-0.953469\pi$
$503$	−46.9968	−	296.726i	−0.0934330	−	0.589913i	0.895902	−	0.444252i	$-0.146531\pi$
$504$	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
$508$	131.617	−	258.313i	0.259089	−	0.508491i
$509$	63.4809	−	87.3740i	0.124717	−	0.171658i	−0.742093	−	0.670297i	$-0.766167\pi$
$509$	63.4809	−	87.3740i	0.124717	−	0.171658i	0.866810	+	0.498639i	$0.166167\pi$
$510$		0			0
$511$	−41.8996	+	128.954i	−0.0819953	+	0.252355i
$512$	−185.338	−	363.746i	−0.361988	−	0.710442i
$513$	−232.742	−	36.8628i	−0.453689	−	0.0718572i
$514$	87.8549	−	120.922i	0.170924	−	0.235257i
$515$		0			0
$516$	−242.104			−0.469194
$517$	−226.287	+	257.247i	−0.437692	+	0.497577i
$518$	−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	$0.377702\pi$
$522$	−41.6345	−	81.7123i	−0.0797596	−	0.156537i
$523$	−378.312	+	192.760i	−0.723350	+	0.368565i	−0.776581	−	0.630017i	$-0.783048\pi$
$523$	−378.312	+	192.760i	−0.723350	+	0.368565i	0.0532315	+	0.998582i	$0.483048\pi$
$524$	−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
$528$	128.200	−	76.0096i	0.242804	−	0.143958i
$529$			1082.62i			2.04655i
$530$		0			0
$531$	−32.4571	−	23.5815i	−0.0611245	−	0.0444096i
$532$	−93.2604	+	588.823i	−0.175302	+	1.10681i
$533$	−88.3893	+	45.0366i	−0.165834	+	0.0844964i
$534$	−14.4156	−	4.68390i	−0.0269955	−	0.00877136i
$535$		0			0
$536$	−104.795	−	76.1380i	−0.195513	−	0.142048i
$537$	−134.922	−	68.7463i	−0.251252	−	0.128019i
$538$	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	$0.833120\pi$
$542$	−23.9626	+	3.79531i	−0.0442115	+	0.00700242i
$543$	−159.737	−	25.2999i	−0.294175	−	0.0465927i
$544$	−255.979	−	83.1725i	−0.470549	−	0.152891i
$545$		0			0
$546$	−8.62956	+	6.26975i	−0.0158051	+	0.0114831i
$547$	831.270	−	131.660i	1.51969	−	0.240695i	0.659904	−	0.751350i	$-0.270597\pi$
$547$	831.270	−	131.660i	1.51969	−	0.240695i	0.859786	+	0.510655i	$0.170597\pi$
$548$	216.226	−	424.368i	0.394573	−	0.774394i
$549$		−	562.251i		−	1.02414i
$550$		0			0
$551$	451.467			0.819360
$552$	96.9572	+	49.4022i	0.175647	+	0.0894967i
$553$	128.303	+	810.071i	0.232012	+	1.46487i
$554$	−46.9703	−	64.6490i	−0.0847839	−	0.116695i
$555$		0			0
$556$	−95.7656	+	294.736i	−0.172240	+	0.530101i
$557$	−96.2519	+	607.711i	−0.172804	+	1.09104i	0.736966	+	0.675930i	$0.236258\pi$
$557$	−96.2519	+	607.711i	−0.172804	+	1.09104i	−0.909770	+	0.415113i	$0.863742\pi$
$558$	24.3975	+	154.040i	0.0437231	+	0.276057i
$559$	−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
$563$	114.729	−	225.168i	0.203781	−	0.399943i	−0.766386	−	0.642381i	$-0.777947\pi$
$563$	114.729	−	225.168i	0.203781	−	0.399943i	0.970167	+	0.242437i	$0.0779469\pi$
$564$	66.5578	−	91.6090i	0.118010	−	0.162427i
$565$		0			0
$566$	13.8701	−	42.6877i	0.0245054	−	0.0754199i
$567$	276.915	+	543.477i	0.488387	+	0.958513i
$568$	−75.4094	−	11.9437i	−0.132763	−	0.0210276i
$569$	168.013	−	231.250i	0.295278	−	0.406415i	−0.635442	−	0.772149i	$-0.719182\pi$
$569$	168.013	−	231.250i	0.295278	−	0.406415i	0.930719	+	0.365734i	$0.119182\pi$
$570$		0			0
$571$	496.264			0.869114			0.434557	−	0.900644i	$-0.356905\pi$
$571$	496.264			0.869114			0.434557	+	0.900644i	$0.356905\pi$
$572$	82.5233	−	93.8140i	0.144272	−	0.164011i
$573$	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
$577$	−426.012	−	836.096i	−0.738323	−	1.44904i	−0.887778	−	0.460272i	$-0.847752\pi$
$577$	−426.012	−	836.096i	−0.738323	−	1.44904i	0.149455	−	0.988769i	$-0.452248\pi$
$578$	10.6338	−	5.41822i	0.0183977	−	0.00937408i
$579$	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
$583$	−58.7282	−	261.372i	−0.100734	−	0.448322i
$584$		−	37.0975i		−	0.0635231i
$585$		0			0
$586$	156.618	+	113.790i	0.267266	+	0.194180i
$587$	8.34641	−	52.6972i	0.0142188	−	0.0897737i	−0.979558	−	0.201160i	$-0.935529\pi$
$587$	8.34641	−	52.6972i	0.0142188	−	0.0897737i	0.993777	+	0.111386i	$0.0355290\pi$
$588$	−200.752	+	102.288i	−0.341414	+	0.173959i
$589$	−730.194	−	237.254i	−1.23972	−	0.402809i
$590$		0			0
$591$	67.1572	+	48.7926i	0.113633	+	0.0825593i
$592$	−234.705	−	119.588i	−0.396461	−	0.202007i
$593$	−71.7371	−	71.7371i	−0.120973	−	0.120973i	0.644028	−	0.765002i	$-0.277262\pi$
$593$	−71.7371	−	71.7371i	−0.120973	−	0.120973i	−0.765002	+	0.644028i	$0.777262\pi$
$594$	−41.4116	−	49.9450i	−0.0697165	−	0.0840826i
$595$		0			0
$596$	−24.5210	−	75.4678i	−0.0411426	−	0.126624i
$597$	219.084	−	34.6995i	0.366975	−	0.0581231i
$598$	42.6906	+	6.76153i	0.0713890	+	0.0113069i
$599$	−488.511	−	158.727i	−0.815544	−	0.264986i	−0.128600	−	0.991697i	$-0.541048\pi$
$599$	−488.511	−	158.727i	−0.815544	−	0.264986i	−0.686944	+	0.726710i	$0.741048\pi$
$600$		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	$0.0185352\pi$
$602$	253.890	−	40.2123i	0.421745	−	0.0667978i
$603$	165.585	−	324.978i	0.274601	−	0.538935i
$604$			703.136i			1.16413i
$605$		0			0
$606$	23.9889			0.0395857
$607$	−579.149	−	295.091i	−0.954117	−	0.486147i	−0.0936234	−	0.995608i	$-0.529845\pi$
$607$	−579.149	−	295.091i	−0.954117	−	0.486147i	−0.860494	+	0.509461i	$0.829845\pi$
$608$	−38.4919	−	243.029i	−0.0633091	−	0.399718i
$609$	179.586	+	247.178i	0.294886	+	0.405876i
$610$		0			0
$611$	28.2803	−	87.0377i	0.0462852	−	0.142451i
$612$	78.5896	−	496.195i	0.128414	−	0.810777i
$613$	71.8222	+	453.468i	0.117165	+	0.739751i	0.974399	+	0.224825i	$0.0721809\pi$
$613$	71.8222	+	453.468i	0.117165	+	0.739751i	−0.857234	+	0.514927i	$0.827819\pi$
$614$	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	$-0.641015\pi$
$617$	292.953	−	292.953i	0.474803	−	0.474803i	0.903465	+	0.428662i	$0.141015\pi$
$618$	25.6679	−	50.3760i	0.0415338	−	0.0815146i
$619$	−178.737	+	246.011i	−0.288752	+	0.397433i	−0.928608	−	0.371062i	$-0.878994\pi$
$619$	−178.737	+	246.011i	−0.288752	+	0.397433i	0.639856	+	0.768495i	$0.278994\pi$
$620$		0			0
$621$	−199.685	+	614.568i	−0.321554	+	0.989642i
$622$	5.06047	+	9.93174i	0.00813581	+	0.0159674i
$623$	−457.643	−	72.4835i	−0.734579	−	0.116346i
$624$	−23.4003	+	32.2077i	−0.0375004	+	0.0516149i
$625$		0			0
$626$	71.1706			0.113691
$627$	147.762	−	33.2009i	0.235665	−	0.0529520i
$628$	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	$0.336953\pi$
$632$	−101.875	−	199.941i	−0.161194	−	0.316362i
$633$	−17.1628	+	8.74487i	−0.0271134	+	0.0138150i
$634$	−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
$638$	93.3324	+	82.0996i	0.146289	+	0.128683i
$639$		−	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	$0.936523\pi$
$642$	6.64848	−	41.9768i	0.0103559	−	0.0653845i
$643$	−239.840	+	122.204i	−0.373001	+	0.190054i	−0.630434	−	0.776243i	$-0.717123\pi$
$643$	−239.840	+	122.204i	−0.373001	+	0.190054i	0.257433	+	0.966296i	$0.417123\pi$
$644$	1554.82	+	505.191i	2.41431	+	0.784458i
$645$		0			0
$646$	−69.4949	−	50.4910i	−0.107577	−	0.0781595i
$647$	−409.189	−	208.492i	−0.632440	−	0.322244i	0.108217	−	0.994127i	$-0.465486\pi$
$647$	−409.189	−	208.492i	−0.632440	−	0.322244i	−0.740657	+	0.671883i	$0.765486\pi$
$648$	−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
$652$	−809.264	+	128.175i	−1.24120	+	0.196587i
$653$	−52.2225	−	8.27124i	−0.0799733	−	0.0126665i	0.116320	−	0.993212i	$-0.462890\pi$
$653$	−52.2225	−	8.27124i	−0.0799733	−	0.0126665i	−0.196293	+	0.980545i	$0.562890\pi$
$654$	25.8928	+	8.41309i	0.0395915	+	0.0128641i
$655$		0			0
$656$	393.505	−	285.898i	0.599856	−	0.435821i
$657$	103.170	−	16.3406i	0.157032	−	0.0248715i
$658$	−54.5822	+	107.124i	−0.0829517	+	0.162802i
$659$		−	164.064i		−	0.248960i	−0.992222	−	0.124480i	$-0.960274\pi$
$659$		−	164.064i		−	0.248960i	0.992222	−	0.124480i	$-0.0397262\pi$
$660$		0			0
$661$	−382.249			−0.578290			−0.289145	−	0.957285i	$-0.593371\pi$
$661$	−382.249			−0.578290			−0.289145	+	0.957285i	$0.593371\pi$
$662$	192.598	+	98.1337i	0.290934	+	0.148238i
$663$	6.92231	+	43.7058i	0.0104409	+	0.0659212i
$664$	121.788	+	167.626i	0.183415	+	0.252449i
$665$		0			0
$666$	−16.8020	+	51.7112i	−0.0252282	+	0.0776444i
$667$	193.672	−	1222.80i	0.290363	−	1.83328i
$668$	−179.104	−	1130.82i	−0.268120	−	1.69284i
$669$	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
$673$	−515.427	+	1011.58i	−0.765865	+	1.50309i	0.0956792	+	0.995412i	$0.469498\pi$
$673$	−515.427	+	1011.58i	−0.765865	+	1.50309i	−0.861544	+	0.507683i	$0.830502\pi$
$674$	−12.9536	+	17.8291i	−0.0192190	+	0.0264527i
$675$		0			0
$676$	191.570	−	589.592i	0.283388	−	0.872178i
$677$	−224.561	−	440.725i	−0.331700	−	0.650997i	0.663574	−	0.748111i	$-0.269039\pi$
$677$	−224.561	−	440.725i	−0.331700	−	0.650997i	−0.995273	+	0.0971137i	$0.969039\pi$
$678$	−31.7275	−	5.02515i	−0.0467958	−	0.00741172i
$679$	−778.194	+	1071.09i	−1.14609	+	1.57746i
$680$		0			0
$681$	−313.797			−0.460789
$682$	−107.809	−	181.834i	−0.158078	−	0.266619i
$683$	152.022	+	152.022i	0.222580	+	0.222580i	0.809584	−	0.587004i	$-0.199693\pi$
$683$	152.022	+	152.022i	0.222580	+	0.222580i	−0.587004	+	0.809584i	$0.699693\pi$
$684$	436.796	−	141.924i	0.638591	−	0.207491i
$685$		0			0
$686$	40.5142	−	29.4353i	0.0590586	−	0.0429086i
$687$	64.7195	+	127.019i	0.0942060	+	0.184890i
$688$	854.827	−	435.556i	1.24248	−	0.633076i
$689$	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
$693$	−706.105	−	621.124i	−1.01891	−	0.896282i
$694$		−	9.27977i		−	0.0133714i
$695$		0			0
$696$	−67.6281	−	49.1347i	−0.0971669	−	0.0705959i
$697$	84.5750	−	533.985i	0.121341	−	0.766120i
$698$	113.772	−	57.9700i	0.162998	−	0.0830515i
$699$	−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	$0.351985\pi$
$702$	15.4416	+	7.86790i	0.0219966	+	0.0112078i
$703$	−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
$707$	724.288	−	114.716i	1.02445	−	0.162257i
$708$	−17.7512	−	2.81152i	−0.0250723	−	0.00397107i
$709$	572.197	+	185.918i	0.807047	+	0.262226i	0.683347	−	0.730094i	$-0.260524\pi$
$709$	572.197	+	185.918i	0.807047	+	0.262226i	0.123701	+	0.992320i	$0.460524\pi$
$710$		0			0
$711$	511.174	−	371.389i	0.718950	−	0.522348i
$712$	125.211	−	19.8315i	0.175859	−	0.0278533i
$713$	−955.843	+	1875.95i	−1.34059	+	2.63106i
$714$		−	58.1329i		−	0.0814186i
$715$		0			0
$716$	622.433			0.869320
$717$	−6.23859	−	3.17872i	−0.00870096	−	0.00443336i
$718$	10.8212	+	68.3223i	0.0150713	+	0.0951565i
$719$	−367.141	−	505.327i	−0.510628	−	0.702819i	0.473397	−	0.880849i	$-0.343027\pi$
$719$	−367.141	−	505.327i	−0.510628	−	0.702819i	−0.984025	+	0.178030i	$0.943027\pi$
$720$		0			0
$721$	534.080	−	1643.73i	0.740749	−	2.27979i
$722$	−8.40838	+	53.0884i	−0.0116460	+	0.0735297i
$723$	−11.6236	−	73.3883i	−0.0160769	−	0.101505i
$724$	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	$-0.848326\pi$
$727$	−312.563	+	312.563i	−0.429936	+	0.429936i	0.458671	+	0.888606i	$0.348326\pi$
$728$	40.5020	−	79.4896i	0.0556346	−	0.109189i
$729$	196.120	−	269.936i	0.269026	−	0.370283i
$730$		0			0
$731$	329.531	−	1014.19i	0.450795	−	1.38740i
$732$	−114.349	−	224.423i	−0.156215	−	0.306588i
$733$	85.2930	+	13.5091i	0.116362	+	0.0184299i	0.214344	−	0.976758i	$-0.431239\pi$
$733$	85.2930	+	13.5091i	0.116362	+	0.0184299i	−0.0979821	+	0.995188i	$0.531239\pi$
$734$	94.9874	−	130.739i	0.129411	−	0.178118i
$735$		0			0
$736$	−674.754			−0.916785
$737$	−45.9778	+	492.224i	−0.0623850	+	0.667875i
$738$	−70.9928	−	70.9928i	−0.0961963	−	0.0961963i
$739$	−534.104	+	173.541i	−0.722738	+	0.234832i	−0.647210	−	0.762312i	$-0.724064\pi$
$739$	−534.104	+	173.541i	−0.722738	+	0.234832i	−0.0755282	+	0.997144i	$0.524064\pi$
$740$		0			0
$741$	−32.7278	+	23.7781i	−0.0441670	+	0.0320892i
$742$	−42.6781	−	83.7605i	−0.0575176	−	0.112885i
$743$	−380.846	+	194.051i	−0.512578	+	0.261172i	−0.691093	−	0.722766i	$-0.742871\pi$
$743$	−380.846	+	194.051i	−0.512578	+	0.261172i	0.178515	+	0.983937i	$0.442871\pi$
$744$	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
$748$	149.280	+	664.375i	0.199572	+	0.888202i
$749$		−	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	$0.677446\pi$
$752$	−70.1953	+	443.196i	−0.0933448	+	0.589356i
$753$	−352.006	+	179.356i	−0.467472	+	0.238189i
$754$	−31.5783	−	10.2604i	−0.0418811	−	0.0136080i
$755$		0			0
$756$	530.311	+	385.293i	0.701469	+	0.509647i
$757$	−199.406	−	101.603i	−0.263417	−	0.134217i	0.317295	−	0.948327i	$-0.397226\pi$
$757$	−199.406	−	101.603i	−0.263417	−	0.134217i	−0.580711	+	0.814110i	$0.697226\pi$
$758$	−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	$0.703150\pi$
$762$	−25.5260	+	4.04292i	−0.0334987	+	0.00530567i
$763$	822.004	+	130.193i	1.07733	+	0.170633i
$764$	−170.188	−	55.2975i	−0.222760	−	0.0723790i
$765$		0			0
$766$	57.4992	−	41.7756i	0.0750642	−	0.0545374i
$767$	−14.3466	+	2.27228i	−0.0187048	+	0.00296255i
$768$	74.4309	−	146.079i	0.0969153	−	0.190207i
$769$			892.786i			1.16097i	0.814271	+	0.580485i	$0.197137\pi$
$769$			892.786i			1.16097i	−0.814271	+	0.580485i	$0.802863\pi$
$770$		0			0
$771$	383.620			0.497562
$772$	−200.181	−	101.997i	−0.259302	−	0.132121i
$773$	−170.093	−	1073.93i	−0.220043	−	1.38929i	−0.812156	−	0.583440i	$-0.801706\pi$
$773$	−170.093	−	1073.93i	−0.220043	−	1.38929i	0.592113	−	0.805855i	$-0.298294\pi$
$774$	−116.400	−	160.211i	−0.150387	−	0.206991i
$775$		0			0
$776$	111.936	−	344.503i	0.144247	−	0.443947i
$777$	28.3372	−	178.914i	0.0364700	−	0.230263i
$778$	−22.0130	−	138.985i	−0.0282944	−	0.178644i
$779$	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
$783$	225.362	−	442.298i	0.287819	−	0.564876i
$784$	524.797	−	722.321i	0.669384	−	0.921328i
$785$		0			0
$786$	−26.8775	+	82.7204i	−0.0341953	+	0.105242i
$787$	250.303	+	491.248i	0.318047	+	0.624203i	0.993581	−	0.113127i	$-0.0360866\pi$
$787$	250.303	+	491.248i	0.318047	+	0.624203i	−0.675533	+	0.737329i	$0.736087\pi$
$788$	−337.012	−	53.3775i	−0.427680	−	0.0677379i
$789$	149.864	−	206.270i	0.189942	−	0.261433i
$790$		0			0
$791$	−981.968			−1.24143
$792$	236.249	+	101.923i	0.298295	+	0.128691i
$793$	−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
$797$	−531.605	−	1043.33i	−0.667007	−	1.30908i	−0.938047	−	0.346508i	$-0.887367\pi$
$797$	−531.605	−	1043.33i	−0.667007	−	1.30908i	0.271040	−	0.962568i	$-0.412633\pi$
$798$	47.3525	−	24.1273i	0.0593389	−	0.0302347i
$799$	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
$803$	−121.786	+	72.2067i	−0.151664	+	0.0899212i
$804$		−	163.391i		−	0.203223i
$805$		0			0
$806$	45.6821	+	33.1900i	0.0566776	+	0.0411787i
$807$	−72.3473	+	456.783i	−0.0896496	+	0.566026i
$808$	−178.768	+	91.0867i	−0.221247	+	0.112731i
$809$	−958.766	−	311.522i	−1.18512	−	0.385070i	−0.350856	−	0.936429i	$-0.614109\pi$
$809$	−958.766	−	311.522i	−1.18512	−	0.385070i	−0.834268	+	0.551359i	$0.814109\pi$
$810$		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	$0.810214\pi$
$812$	−1118.98	−	570.151i	−1.37806	−	0.702157i
$813$	−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
$817$	962.883	−	152.506i	1.17856	−	0.186665i
$818$	110.826	+	17.5531i	0.135484	+	0.0214586i
$819$	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	$0.326943\pi$
$822$	−41.9352	+	6.64188i	−0.0510160	+	0.00808014i
$823$	−639.367	+	1254.83i	−0.776873	+	1.52470i	0.0727737	+	0.997348i	$0.476815\pi$
$823$	−639.367	+	1254.83i	−0.776873	+	1.52470i	−0.849647	+	0.527352i	$0.823185\pi$
$824$			472.869i			0.573871i
$825$		0			0
$826$	19.0824			0.0231021
$827$	941.381	+	479.658i	1.13831	+	0.579997i	0.918451	−	0.395535i	$-0.129441\pi$
$827$	941.381	+	479.658i	1.13831	+	0.579997i	0.219858	+	0.975532i	$0.429441\pi$
$828$	−197.021	−	1243.94i	−0.237948	−	1.50235i
$829$	274.311	+	377.556i	0.330893	+	0.455436i	0.941754	−	0.336303i	$-0.109176\pi$
$829$	274.311	+	377.556i	0.330893	+	0.455436i	−0.610861	+	0.791738i	$0.709176\pi$
$830$		0			0
$831$	63.3783	−	195.058i	0.0762675	−	0.234727i
$832$	23.6574	−	149.367i	0.0284343	−	0.179527i
$833$	−155.246	−	980.188i	−0.186370	−	1.17670i
$834$	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
$838$	−34.7918	+	68.2827i	−0.0415176	+	0.0814829i
$839$	−826.244	+	1137.23i	−0.984796	+	1.35546i	−0.0505912	+	0.998719i	$0.516111\pi$
$839$	−826.244	+	1137.23i	−0.984796	+	1.35546i	−0.934205	+	0.356736i	$0.883889\pi$
$840$		0			0
$841$	−34.0082	+	104.666i	−0.0404378	+	0.124455i
$842$	−50.7077	−	99.5196i	−0.0602230	−	0.118194i
$843$	342.384	+	54.2284i	0.406150	+	0.0643278i
$844$	46.5388	−	64.0552i	0.0551408	−	0.0758948i
$845$		0			0
$846$	92.6215			0.109482
$847$	1200.26	+	429.113i	1.41707	+	0.506627i
$848$	−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
$852$	−43.7219	−	85.8090i	−0.0513168	−	0.100715i
$853$	−899.755	+	458.448i	−1.05481	+	0.537454i	−0.893320	−	0.449420i	$-0.851631\pi$
$853$	−899.755	+	458.448i	−1.05481	+	0.537454i	−0.161492	+	0.986874i	$0.551631\pi$
$854$	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	$-0.975119\pi$
$857$	−787.462	+	787.462i	−0.918859	+	0.918859i	0.0780872	+	0.996947i	$0.475119\pi$
$858$	−11.0899	−	1.03589i	−0.0129253	−	0.00120733i
$859$		−	333.892i		−	0.388699i	−0.980932	−	0.194349i	$-0.937740\pi$
$859$		−	333.892i		−	0.388699i	0.980932	−	0.194349i	$-0.0622595\pi$
$860$		0			0
$861$	270.604	+	196.605i	0.314290	+	0.228345i
$862$	−20.9036	+	131.980i	−0.0242501	+	0.153109i
$863$	1278.62	−	651.489i	1.48160	−	0.754912i	0.488541	−	0.872541i	$-0.337529\pi$
$863$	1278.62	−	651.489i	1.48160	−	0.754912i	0.993058	+	0.117628i	$0.0375292\pi$
$864$	−257.307	−	83.6041i	−0.297809	−	0.0967640i
$865$		0			0
$866$	100.834	+	73.2598i	0.116436	+	0.0845957i
$867$	27.2926	+	13.9063i	0.0314793	+	0.0160395i
$868$	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
$872$	−224.901	+	35.6208i	−0.257914	+	0.0408495i
$873$	1007.39	+	159.555i	1.15394	+	0.182766i
$874$	−204.809	−	66.5465i	−0.234335	−	0.0761402i
$875$		0			0
$876$	37.8572	−	27.5049i	0.0432160	−	0.0313982i
$877$	1257.22	−	199.124i	1.43355	−	0.227051i	0.609146	−	0.793058i	$-0.291512\pi$
$877$	1257.22	−	199.124i	1.43355	−	0.227051i	0.824401	+	0.566007i	$0.191512\pi$
$878$	124.031	−	243.424i	0.141265	−	0.277248i
$879$			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	$0.541031\pi$
$882$	−164.206	−	83.6674i	−0.186175	−	0.0948610i
$883$	144.643	+	913.239i	0.163808	+	1.03425i	0.923398	+	0.383843i	$0.125400\pi$
$883$	144.643	+	913.239i	0.163808	+	1.03425i	−0.759590	+	0.650402i	$0.774600\pi$
$884$	−106.912	−	147.152i	−0.120942	−	0.166462i
$885$		0			0
$886$	−45.0926	+	138.781i	−0.0508946	+	0.156638i
$887$	236.730	−	1494.65i	0.266888	−	1.68507i	−0.381985	−	0.924169i	$-0.624759\pi$
$887$	236.730	−	1494.65i	0.266888	−	1.68507i	0.648873	−	0.760897i	$-0.275241\pi$
$888$	7.75307	+	48.9510i	0.00873094	+	0.0551250i
$889$	−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
$893$	−207.004	+	406.268i	−0.231807	+	0.454947i
$894$	−4.15787	+	5.72282i	−0.00465086	+	0.00640136i
$895$		0			0
$896$	−280.252	+	862.528i	−0.312782	+	0.962643i
$897$	50.3632	+	98.8433i	0.0561463	+	0.110193i
$898$	−189.428	−	30.0024i	−0.210944	−	0.0334103i
$899$	950.668	−	1308.48i	1.05747	−	1.45549i
$900$		0			0
$901$	−389.983			−0.432833
$902$	124.951	+	53.9066i	0.138527	+	0.0597634i
$903$	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
$907$	−40.5260	−	79.5367i	−0.0446813	−	0.0876920i	0.867586	−	0.497286i	$-0.165670\pi$
$907$	−40.5260	−	79.5367i	−0.0446813	−	0.0876920i	−0.912268	+	0.409594i	$0.865670\pi$
$908$	1149.27	−	585.580i	1.26571	−	0.644912i
$909$	−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
$913$	313.248	−	726.083i	0.343097	−	0.795271i
$914$			36.1757i			0.0395796i
$915$		0			0
$916$	−474.064	−	344.428i	−0.517537	−	0.376013i
$917$	−415.930	+	2626.08i	−0.453576	+	2.86377i
$918$	−84.1558	+	42.8795i	−0.0916729	+	0.0467097i
$919$	−24.7032	−	8.02657i	−0.0268806	−	0.00873402i	0.295546	−	0.955329i	$-0.404498\pi$
$919$	−24.7032	−	8.02657i	−0.0268806	−	0.00873402i	−0.322426	+	0.946595i	$0.604498\pi$
$920$		0			0
$921$	340.893	+	247.673i	0.370134	+	0.268918i
$922$	75.8552	+	38.6502i	0.0822724	+	0.0419199i
$923$	−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
$927$	−1315.08	+	208.288i	−1.41864	+	0.224690i
$928$	511.960	+	81.0864i	0.551681	+	0.0873776i
$929$	853.382	+	277.281i	0.918603	+	0.298472i	0.729894	−	0.683561i	$-0.239570\pi$
$929$	853.382	+	277.281i	0.918603	+	0.298472i	0.188709	+	0.982033i	$0.439570\pi$
$930$		0			0
$931$	733.984	−	533.271i	0.788383	−	0.572794i
$932$	1243.91	−	197.016i	1.33467	−	0.211391i
$933$	−12.9881	+	25.4906i	−0.0139208	+	0.0273211i
$934$			256.026i			0.274118i
$935$		0			0
$936$	−68.7285			−0.0734279
$937$	1127.79	+	574.636i	1.20361	+	0.613272i	0.936593	−	0.350418i	$-0.113961\pi$
$937$	1127.79	+	574.636i	1.20361	+	0.613272i	0.267021	+	0.963691i	$0.413961\pi$
$938$	27.1385	+	171.346i	0.0289323	+	0.182671i
$939$	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	$0.889738\pi$
$942$	5.79930	−	36.6153i	0.00615636	−	0.0388698i
$943$	−212.026	−	1338.68i	−0.224842	−	1.41960i
$944$	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	−0.0142062	+	0.999899i	$0.504522\pi$
$947$	−960.358	+	960.358i	−1.01411	+	1.01411i	−0.999899	+	0.0142062i	$0.995478\pi$
$948$	128.503	−	252.201i	0.135552	−	0.266035i
$949$	22.2295	−	30.5963i	0.0234242	−	0.0322406i
$950$		0			0
$951$	64.5223	−	198.579i	0.0678468	−	0.208811i
$952$	220.733	+	433.212i	0.231862	+	0.455055i
$953$	1048.23	+	166.024i	1.09993	+	0.174212i	0.679905	−	0.733300i	$-0.262021\pi$
$953$	1048.23	+	166.024i	1.09993	+	0.174212i	0.420026	+	0.907512i	$0.362021\pi$
$954$	−42.5681	+	58.5900i	−0.0446207	+	0.0614151i
$955$		0			0
$956$	28.7803			0.0301050
$957$	−29.6712	+	317.651i	−0.0310044	+	0.331923i
$958$	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
$962$	8.93720	+	17.5402i	0.00929022	+	0.0182331i
$963$	−891.783	+	454.386i	−0.926047	+	0.471844i
$964$	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	$-0.807626\pi$
$967$	−246.228	+	246.228i	−0.254631	+	0.254631i	0.568235	+	0.822866i	$0.307626\pi$
$968$	−348.599	−	10.1808i	−0.360123	−	0.0105173i
$969$		−	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	$0.593873\pi$
$972$	120.537	−	761.042i	0.124009	−	0.782965i
$973$	752.464	−	383.400i	0.773344	−	0.394039i
$974$	201.896	+	65.6000i	0.207286	+	0.0673512i
$975$		0			0
$976$	807.493	+	586.678i	0.827349	+	0.601104i
$977$	4.00708	+	2.04171i	0.00410141	+	0.00208977i	0.456040	−	0.889959i	$-0.349267\pi$
$977$	4.00708	+	2.04171i	0.00410141	+	0.00208977i	−0.451939	+	0.892049i	$0.649267\pi$
$978$	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
$982$	−299.564	+	47.4462i	−0.305055	+	0.0483159i
$983$	−123.252	−	19.5212i	−0.125383	−	0.0198588i	0.0934273	−	0.995626i	$-0.470218\pi$
$983$	−123.252	−	19.5212i	−0.125383	−	0.0198588i	−0.218811	+	0.975767i	$0.570218\pi$
$984$	−87.0360	−	28.2797i	−0.0884513	−	0.0287396i
$985$		0			0
$986$	146.397	−	106.363i	0.148475	−	0.107874i
$987$	−304.774	+	48.2715i	−0.308788	+	0.0489073i
$988$	75.4911	−	148.160i	0.0764080	−	0.149959i
$989$		−	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	$0.762603\pi$
$992$	−785.421	−	400.192i	−0.791755	−	0.403419i
$993$	86.7876	+	547.955i	0.0873994	+	0.551818i
$994$	60.1028	+	82.7244i	0.0604656	+	0.0832237i
$995$		0			0
$996$	−80.7632	+	248.564i	−0.0810876	+	0.249562i
$997$	98.6185	−	622.653i	0.0989153	−	0.624526i	−0.887570	−	0.460674i	$-0.847608\pi$
$997$	98.6185	−	622.653i	0.0989153	−	0.624526i	0.986485	−	0.163853i	$-0.0523922\pi$
$998$	−19.8486	−	125.319i	−0.0198883	−	0.125570i
$999$	−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.93.9	yes	128
5.2	odd	4	inner	275.3.bk.c.82.8	✓	128
5.3	odd	4	inner	275.3.bk.c.82.9	yes	128
5.4	even	2	inner	275.3.bk.c.93.8	yes	128
11.9	even	5	inner	275.3.bk.c.218.8	yes	128
55.9	even	10	inner	275.3.bk.c.218.9	yes	128
55.42	odd	20	inner	275.3.bk.c.207.9	yes	128
55.53	odd	20	inner	275.3.bk.c.207.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.8	✓	128	5.2	odd	4	inner
275.3.bk.c.82.9	yes	128	5.3	odd	4	inner
275.3.bk.c.93.8	yes	128	5.4	even	2	inner
275.3.bk.c.93.9	yes	128	1.1	even	1	trivial
275.3.bk.c.207.8	yes	128	55.53	odd	20	inner
275.3.bk.c.207.9	yes	128	55.42	odd	20	inner
275.3.bk.c.218.8	yes	128	11.9	even	5	inner
275.3.bk.c.218.9	yes	128	55.9	even	10	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+(0.326489 + 0.166354i) q^{2} +(0.147121 + 0.928883i) q^{3} +(-2.27222 - 3.12744i) q^{4} +(-0.106490 + 0.327744i) q^{6} +(-1.64794 + 10.4047i) q^{7} +(-0.450878 - 2.84673i) q^{8} +(7.71833 - 2.50784i) q^{9} +(-8.46786 + 7.02107i) q^{11} +(2.57074 - 2.57074i) q^{12} +(1.33395 - 2.61803i) q^{13} +(-2.26890 + 3.12287i) q^{14} +(-4.45195 + 13.7017i) q^{16} +(7.26994 + 14.2681i) q^{17} +(2.93714 + 0.465197i) q^{18} +(-8.60484 + 11.8435i) q^{19} -9.90719 q^{21} +(-3.93264 + 0.883634i) q^{22} +(28.3868 + 28.3868i) q^{23} +(2.57795 - 0.837625i) q^{24} +(0.871040 - 0.632848i) q^{26} +(7.30766 + 14.3421i) q^{27} +(36.2846 - 18.4879i) q^{28} +(-18.1268 - 24.9494i) q^{29} +(16.2065 + 49.8786i) q^{31} +(-11.8850 + 11.8850i) q^{32} +(-7.76755 - 6.83271i) q^{33} +5.86775i q^{34} +(-25.3809 - 18.4403i) q^{36} +(-2.86026 + 18.0590i) q^{37} +(-4.77961 + 2.43533i) q^{38} +(2.62809 + 0.853920i) q^{39} +(-27.3139 - 19.8447i) q^{41} +(-3.23459 - 1.64810i) q^{42} +(-47.0885 - 47.0885i) q^{43} +(41.1988 + 10.5293i) q^{44} +(4.54571 + 13.9903i) q^{46} +(30.7629 - 4.87237i) q^{47} +(-13.3822 - 2.11954i) q^{48} +(-58.9402 - 19.1508i) q^{49} +(-12.1838 + 8.85205i) q^{51} +(-11.2188 + 1.77688i) q^{52} +(-11.0563 + 21.6991i) q^{53} +5.89819i q^{54} +30.3624 q^{56} +(-12.2672 - 6.25046i) q^{57} +(-1.76775 - 11.1612i) q^{58} +(-2.90572 - 3.99938i) q^{59} +(21.4090 - 65.8900i) q^{61} +(-3.00627 + 18.9808i) q^{62} +(13.3739 + 84.4396i) q^{63} +(48.9493 - 15.9046i) q^{64} +(-1.39937 - 3.52297i) q^{66} +(31.7791 - 31.7791i) q^{67} +(28.1036 - 55.1565i) q^{68} +(-22.1918 + 30.5443i) q^{69} +(8.18581 - 25.1933i) q^{71} +(-10.6192 - 20.8413i) q^{72} +(12.7127 + 2.01349i) q^{73} +(-3.93804 + 5.42024i) q^{74} +56.5921 q^{76} +(-59.0975 - 99.6758i) q^{77} +(0.715990 + 0.715990i) q^{78} +(74.0458 - 24.0589i) q^{79} +(46.8434 - 34.0337i) q^{81} +(-5.61642 - 11.0228i) q^{82} +(-64.0530 + 32.6366i) q^{83} +(22.5113 + 30.9842i) q^{84} +(-7.54048 - 23.2072i) q^{86} +(20.5082 - 20.5082i) q^{87} +(23.8050 + 20.9401i) q^{88} +43.9843i q^{89} +(25.0415 + 18.1937i) q^{91} +(24.2771 - 153.279i) q^{92} +(-43.9471 + 22.3922i) q^{93} +(10.8543 + 3.52677i) q^{94} +(-12.7883 - 9.29123i) q^{96} +(111.980 + 57.0567i) 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

Fields

Representations

Groups

Database

Properties

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