LMFDB - Embedded newform 975.2.bn.d.257.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.20
Character	$\chi$	$=$	975.257
Dual form			975.2.bn.d.368.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.496187 - 1.85180i) q^{2} +(0.676428 - 1.59450i) q^{3} +(-1.45090 - 0.837676i) q^{4} +(-2.61706 - 2.04378i) q^{6} +(-0.527913 - 1.97020i) q^{7} +(0.440097 - 0.440097i) q^{8} +(-2.08489 - 2.15713i) q^{9} +(-0.0324046 - 0.0561264i) q^{11} +(-2.31710 + 1.74683i) q^{12} +(-3.39239 + 1.22133i) q^{13} -3.91035 q^{14} +(-2.27195 - 3.93513i) q^{16} +(1.31006 + 4.88919i) q^{17} +(-5.02907 + 2.79045i) q^{18} +(1.37598 - 2.38327i) q^{19} +(-3.49859 - 0.490937i) q^{21} +(-0.120014 + 0.0321575i) q^{22} +(1.36681 - 5.10100i) q^{23} +(-0.404043 - 0.999430i) q^{24} +(0.578399 + 6.88803i) q^{26} +(-4.84984 + 1.86522i) q^{27} +(-0.884440 + 3.30077i) q^{28} +(-1.40236 - 2.42895i) q^{29} +0.312918i q^{31} +(-7.21201 + 1.93245i) q^{32} +(-0.111413 + 0.0137038i) q^{33} +9.70382 q^{34} +(1.21798 + 4.87624i) q^{36} +(1.21737 + 0.326192i) q^{37} +(-3.73059 - 3.73059i) q^{38} +(-0.347286 + 6.23533i) q^{39} +(5.66614 + 9.81404i) q^{41} +(-2.64507 + 6.23507i) q^{42} +(-2.53152 - 9.44778i) q^{43} +0.108578i q^{44} +(-8.76782 - 5.06210i) q^{46} +(0.638524 + 0.638524i) q^{47} +(-7.81140 + 0.960802i) q^{48} +(2.45919 - 1.41981i) q^{49} +(8.68200 + 1.21830i) q^{51} +(5.94510 + 1.06970i) q^{52} +(5.43756 + 5.43756i) q^{53} +(1.04758 + 9.90641i) q^{54} +(-1.09941 - 0.634745i) q^{56} +(-2.86938 - 3.80612i) q^{57} +(-5.19376 + 1.39166i) q^{58} +(-5.86942 - 3.38871i) q^{59} +(-1.38357 + 2.39642i) q^{61} +(0.579461 + 0.155266i) q^{62} +(-3.14934 + 5.24643i) q^{63} +5.22623i q^{64} +(-0.0299051 + 0.213114i) q^{66} +(-10.5842 - 2.83602i) q^{67} +(2.19480 - 8.19111i) q^{68} +(-7.20902 - 5.62984i) q^{69} +(6.90717 - 11.9636i) q^{71} +(-1.86690 - 0.0317942i) q^{72} +(7.38949 + 7.38949i) q^{73} +(1.20808 - 2.09246i) q^{74} +(-3.99282 + 2.30525i) q^{76} +(-0.0934734 + 0.0934734i) q^{77} +(11.3742 + 3.73700i) q^{78} +5.34069i q^{79} +(-0.306459 + 8.99478i) q^{81} +(20.9851 - 5.62293i) q^{82} +(-2.60495 + 2.60495i) q^{83} +(4.66484 + 3.64298i) q^{84} -18.7515 q^{86} +(-4.82157 + 0.593053i) q^{87} +(-0.0389622 - 0.0104399i) q^{88} +(12.5211 - 7.22908i) q^{89} +(4.19716 + 6.03893i) q^{91} +(-6.25608 + 6.25608i) q^{92} +(0.498950 + 0.211667i) q^{93} +(1.49924 - 0.865588i) q^{94} +(-1.79710 + 12.8068i) q^{96} +(1.90959 + 7.12670i) q^{97} +(-1.40899 - 5.25841i) q^{98} +(-0.0535122 + 0.186919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.496187	−	1.85180i	0.350857	−	1.30942i	−0.534761	−	0.845004i	$-0.679598\pi$
$2$	0.496187	−	1.85180i	0.350857	−	1.30942i	0.885618	−	0.464414i	$-0.153735\pi$
$3$	0.676428	−	1.59450i	0.390536	−	0.920588i
$3$	0.676428	−	1.59450i	0.390536	−	0.920588i
$4$	−1.45090	−	0.837676i	−0.725448	−	0.418838i
$5$		0			0
$5$		0			0
$6$	−2.61706	−	2.04378i	−1.06841	−	0.834369i
$7$	−0.527913	−	1.97020i	−0.199532	−	0.744665i	−0.991047	−	0.133515i	$-0.957374\pi$
$7$	−0.527913	−	1.97020i	−0.199532	−	0.744665i	0.791514	−	0.611150i	$-0.209293\pi$
$8$	0.440097	−	0.440097i	0.155598	−	0.155598i
$9$	−2.08489	−	2.15713i	−0.694964	−	0.719045i
$10$		0			0
$11$	−0.0324046	−	0.0561264i	−0.00977036	−	0.0169228i	0.861099	−	0.508438i	$-0.169777\pi$
$11$	−0.0324046	−	0.0561264i	−0.00977036	−	0.0169228i	−0.870869	+	0.491515i	$0.836443\pi$
$12$	−2.31710	+	1.74683i	−0.668890	+	0.504268i
$13$	−3.39239	+	1.22133i	−0.940881	+	0.338737i
$13$	−3.39239	+	1.22133i	−0.940881	+	0.338737i
$14$	−3.91035			−1.04508
$15$		0			0
$16$	−2.27195	−	3.93513i	−0.567988	−	0.983783i
$17$	1.31006	+	4.88919i	0.317735	+	1.18580i	0.921416	+	0.388577i	$0.127033\pi$
$17$	1.31006	+	4.88919i	0.317735	+	1.18580i	−0.603681	+	0.797226i	$0.706300\pi$
$18$	−5.02907	+	2.79045i	−1.18536	+	0.657715i
$19$	1.37598	−	2.38327i	0.315672	−	0.546760i	−0.663908	−	0.747814i	$-0.731103\pi$
$19$	1.37598	−	2.38327i	0.315672	−	0.546760i	0.979580	+	0.201054i	$0.0644368\pi$
$20$		0			0
$21$	−3.49859	−	0.490937i	−0.763454	−	0.107131i
$22$	−0.120014	+	0.0321575i	−0.0255870	+	0.00685601i
$23$	1.36681	−	5.10100i	0.284999	−	1.06363i	−0.663840	−	0.747874i	$-0.731075\pi$
$23$	1.36681	−	5.10100i	0.284999	−	1.06363i	0.948840	−	0.315758i	$-0.102259\pi$
$24$	−0.404043	−	0.999430i	−0.0824749	−	0.204008i
$25$		0			0
$26$	0.578399	+	6.88803i	0.113433	+	1.35085i
$27$	−4.84984	+	1.86522i	−0.933352	+	0.358962i
$28$	−0.884440	+	3.30077i	−0.167143	+	0.623788i
$29$	−1.40236	−	2.42895i	−0.260411	−	0.451045i	0.705940	−	0.708271i	$-0.250525\pi$
$29$	−1.40236	−	2.42895i	−0.260411	−	0.451045i	−0.966351	+	0.257226i	$0.917191\pi$
$30$		0			0
$31$			0.312918i			0.0562018i	0.999605	+	0.0281009i	$0.00894597\pi$
$31$			0.312918i			0.0562018i	−0.999605	+	0.0281009i	$0.991054\pi$
$32$	−7.21201	+	1.93245i	−1.27492	+	0.341613i
$33$	−0.111413	+	0.0137038i	−0.0193946	+	0.00238553i
$34$	9.70382			1.66419
$35$		0			0
$36$	1.21798	+	4.87624i	0.202997	+	0.812707i
$37$	1.21737	+	0.326192i	0.200134	+	0.0536257i	0.357493	−	0.933916i	$-0.383631\pi$
$37$	1.21737	+	0.326192i	0.200134	+	0.0536257i	−0.157359	+	0.987541i	$0.550298\pi$
$38$	−3.73059	−	3.73059i	−0.605181	−	0.605181i
$39$	−0.347286	+	6.23533i	−0.0556103	+	0.998453i
$40$		0			0
$41$	5.66614	+	9.81404i	0.884903	+	1.53270i	0.845825	+	0.533460i	$0.179109\pi$
$41$	5.66614	+	9.81404i	0.884903	+	1.53270i	0.0390773	+	0.999236i	$0.487558\pi$
$42$	−2.64507	+	6.23507i	−0.408143	+	0.962092i
$43$	−2.53152	−	9.44778i	−0.386054	−	1.44077i	−0.836499	−	0.547968i	$-0.815401\pi$
$43$	−2.53152	−	9.44778i	−0.386054	−	1.44077i	0.450445	−	0.892804i	$-0.351265\pi$
$44$			0.108578i			0.0163688i
$45$		0			0
$46$	−8.76782	−	5.06210i	−1.29274	−	0.746366i
$47$	0.638524	+	0.638524i	0.0931382	+	0.0931382i	0.752141	−	0.659003i	$-0.229021\pi$
$47$	0.638524	+	0.638524i	0.0931382	+	0.0931382i	−0.659003	+	0.752141i	$0.729021\pi$
$48$	−7.81140	+	0.960802i	−1.12748	+	0.138680i
$49$	2.45919	−	1.41981i	0.351313	−	0.202830i
$50$		0			0
$51$	8.68200	+	1.21830i	1.21572	+	0.170596i
$52$	5.94510	+	1.06970i	0.824436	+	0.148340i
$53$	5.43756	+	5.43756i	0.746906	+	0.746906i	0.973897	−	0.226991i	$-0.0728887\pi$
$53$	5.43756	+	5.43756i	0.746906	+	0.746906i	−0.226991	+	0.973897i	$0.572889\pi$
$54$	1.04758	+	9.90641i	0.142558	+	1.34809i
$55$		0			0
$56$	−1.09941	−	0.634745i	−0.146915	−	0.0848214i
$57$	−2.86938	−	3.80612i	−0.380059	−	0.504133i
$58$	−5.19376	+	1.39166i	−0.681974	+	0.182734i
$59$	−5.86942	−	3.38871i	−0.764133	−	0.441172i	0.0666447	−	0.997777i	$-0.478771\pi$
$59$	−5.86942	−	3.38871i	−0.764133	−	0.441172i	−0.830778	+	0.556604i	$0.812104\pi$
$60$		0			0
$61$	−1.38357	+	2.39642i	−0.177149	+	0.306830i	−0.940903	−	0.338677i	$-0.890021\pi$
$61$	−1.38357	+	2.39642i	−0.177149	+	0.306830i	0.763754	+	0.645507i	$0.223354\pi$
$62$	0.579461	+	0.155266i	0.0735916	+	0.0197188i
$63$	−3.14934	+	5.24643i	−0.396780	+	0.660988i
$64$			5.22623i			0.653279i
$65$		0			0
$66$	−0.0299051	+	0.213114i	−0.00368107	+	0.0262326i
$67$	−10.5842	−	2.83602i	−1.29306	−	0.346475i	−0.454239	−	0.890880i	$-0.650089\pi$
$67$	−10.5842	−	2.83602i	−1.29306	−	0.346475i	−0.838823	+	0.544405i	$0.816756\pi$
$68$	2.19480	−	8.19111i	0.266159	−	0.993318i
$69$	−7.20902	−	5.62984i	−0.867864	−	0.677753i
$70$		0			0
$71$	6.90717	−	11.9636i	0.819730	−	1.41981i	−0.0861512	−	0.996282i	$-0.527457\pi$
$71$	6.90717	−	11.9636i	0.819730	−	1.41981i	0.905881	−	0.423532i	$-0.139210\pi$
$72$	−1.86690	−	0.0317942i	−0.220017	−	0.00374698i
$73$	7.38949	+	7.38949i	0.864874	+	0.864874i	0.991900	−	0.127025i	$-0.0405429\pi$
$73$	7.38949	+	7.38949i	0.864874	+	0.864874i	−0.127025	+	0.991900i	$0.540543\pi$
$74$	1.20808	−	2.09246i	0.140437	−	0.243244i
$75$		0			0
$76$	−3.99282	+	2.30525i	−0.458007	+	0.264431i
$77$	−0.0934734	+	0.0934734i	−0.0106523	+	0.0106523i
$78$	11.3742	+	3.73700i	1.28788	+	0.423132i
$79$			5.34069i			0.600875i	0.953802	+	0.300437i	$0.0971326\pi$
$79$			5.34069i			0.600875i	−0.953802	+	0.300437i	$0.902867\pi$
$80$		0			0
$81$	−0.306459	+	8.99478i	−0.0340510	+	0.999420i
$82$	20.9851	−	5.62293i	2.31741	−	0.620949i
$83$	−2.60495	+	2.60495i	−0.285931	+	0.285931i	−0.835469	−	0.549538i	$-0.814804\pi$
$83$	−2.60495	+	2.60495i	−0.285931	+	0.285931i	0.549538	+	0.835469i	$0.314804\pi$
$84$	4.66484	+	3.64298i	0.508976	+	0.397482i
$85$		0			0
$86$	−18.7515			−2.02202
$87$	−4.82157	+	0.593053i	−0.516926	+	0.0635820i
$88$	−0.0389622	−	0.0104399i	−0.00415339	−	0.00111290i
$89$	12.5211	−	7.22908i	1.32724	−	0.766281i	0.342366	−	0.939567i	$-0.388772\pi$
$89$	12.5211	−	7.22908i	1.32724	−	0.766281i	0.984872	+	0.173285i	$0.0554383\pi$
$90$		0			0
$91$	4.19716	+	6.03893i	0.439982	+	0.633052i
$92$	−6.25608	+	6.25608i	−0.652242	+	0.652242i
$93$	0.498950	+	0.211667i	0.0517387	+	0.0219488i
$94$	1.49924	−	0.865588i	0.154635	−	0.0892786i
$95$		0			0
$96$	−1.79710	+	12.8068i	−0.183416	+	1.30708i
$97$	1.90959	+	7.12670i	0.193890	+	0.723607i	0.992551	+	0.121827i	$0.0388752\pi$
$97$	1.90959	+	7.12670i	0.193890	+	0.723607i	−0.798661	+	0.601781i	$0.794458\pi$
$98$	−1.40899	−	5.25841i	−0.142329	−	0.531179i
$99$	−0.0535122	+	0.186919i	−0.00537818	+	0.0187860i
$100$		0			0
$101$	10.1123	−	5.83835i	1.00621	−	0.580938i	0.0961330	−	0.995368i	$-0.469353\pi$
$101$	10.1123	−	5.83835i	1.00621	−	0.580938i	0.910081	+	0.414431i	$0.136019\pi$
$102$	6.56393	−	15.4728i	0.649926	−	1.53203i
$103$	12.9298	−	12.9298i	1.27401	−	1.27401i	0.330042	−	0.943966i	$-0.392937\pi$
$103$	12.9298	−	12.9298i	1.27401	−	1.27401i	0.943966	−	0.330042i	$-0.107063\pi$
$104$	−0.955477	+	2.03049i	−0.0936922	+	0.199106i
$105$		0			0
$106$	12.7673	−	7.37120i	1.24007	−	0.715955i
$107$	14.4728	+	3.87796i	1.39913	+	0.374897i	0.878034	−	0.478598i	$-0.158855\pi$
$107$	14.4728	+	3.87796i	1.39913	+	0.374897i	0.521101	+	0.853495i	$0.325522\pi$
$108$	8.59907	+	1.35635i	0.827446	+	0.130514i
$109$	−16.1230			−1.54430			−0.772152	−	0.635437i	$-0.780820\pi$
$109$	−16.1230			−1.54430			−0.772152	+	0.635437i	$0.780820\pi$
$110$		0			0
$111$	1.34358	−	1.72045i	0.127527	−	0.163298i
$112$	−6.55360	+	6.55360i	−0.619257	+	0.619257i
$113$	10.3184	−	2.76481i	0.970675	−	0.260092i	0.261562	−	0.965187i	$-0.415762\pi$
$113$	10.3184	−	2.76481i	0.970675	−	0.260092i	0.709113	+	0.705095i	$0.249096\pi$
$114$	−8.47191	+	3.42497i	−0.793467	+	0.320777i
$115$		0			0
$116$			4.69888i			0.436280i
$117$	9.70736	+	4.77150i	0.897445	+	0.441126i
$118$	−9.18753	+	9.18753i	−0.845781	+	0.845781i
$119$	8.94108	−	5.16214i	0.819628	−	0.473212i
$120$		0			0
$121$	5.49790	−	9.52264i	0.499809	−	0.865695i
$122$	3.75117	+	3.75117i	0.339615	+	0.339615i
$123$	19.4813	−	2.39620i	1.75657	−	0.216058i
$124$	0.262124	−	0.454012i	0.0235394	−	0.0407715i
$125$		0			0
$126$	8.15265	+	8.43515i	0.726296	+	0.751463i
$127$	0.151301	−	0.564662i	0.0134258	−	0.0501056i	−0.958888	−	0.283785i	$-0.908410\pi$
$127$	0.151301	−	0.564662i	0.0134258	−	0.0501056i	0.972314	+	0.233679i	$0.0750765\pi$
$128$	−4.74611	−	1.27172i	−0.419500	−	0.112405i
$129$	−16.7769	−	2.35421i	−1.47713	−	0.207277i
$130$		0			0
$131$			5.77110i			0.504223i	0.967698	+	0.252112i	$0.0811250\pi$
$131$			5.77110i			0.504223i	−0.967698	+	0.252112i	$0.918875\pi$
$132$	0.173129	+	0.0734453i	0.0150689	+	0.00639260i
$133$	−5.42192	−	1.45280i	−0.470140	−	0.125974i
$134$	−10.5035	+	18.1925i	−0.907361	+	1.57159i
$135$		0			0
$136$	2.72827	+	1.57517i	0.233947	+	0.135069i
$137$	−7.02411	+	1.88211i	−0.600111	+	0.160799i	−0.546070	−	0.837740i	$-0.683877\pi$
$137$	−7.02411	+	1.88211i	−0.600111	+	0.160799i	−0.0540406	+	0.998539i	$0.517210\pi$
$138$	−14.0023	+	10.5562i	−1.19196	+	0.898602i
$139$	−1.85213	−	1.06933i	−0.157096	−	0.0906994i	0.419391	−	0.907806i	$-0.362244\pi$
$139$	−1.85213	−	1.06933i	−0.157096	−	0.0906994i	−0.576487	+	0.817106i	$0.695577\pi$
$140$		0			0
$141$	1.45004	−	0.586214i	0.122116	−	0.0493681i
$142$	−18.7268	−	18.7268i	−1.57152	−	1.57152i
$143$	0.178478	+	0.150826i	0.0149251	+	0.0126127i
$144$	−3.75184	+	13.1052i	−0.312654	+	1.09210i
$145$		0			0
$146$	17.3504	−	10.0173i	1.43593	−	0.829034i
$147$	−0.600435	−	4.88159i	−0.0495231	−	0.402627i
$148$	−1.49303	−	1.49303i	−0.122726	−	0.122726i
$149$	2.52248	+	1.45635i	0.206649	+	0.119309i	0.599753	−	0.800185i	$-0.295265\pi$
$149$	2.52248	+	1.45635i	0.206649	+	0.119309i	−0.393104	+	0.919494i	$0.628599\pi$
$150$		0			0
$151$		−	12.1330i		−	0.987367i	−0.869642	−	0.493683i	$-0.835650\pi$
$151$		−	12.1330i		−	0.987367i	0.869642	−	0.493683i	$-0.164350\pi$
$152$	−0.443305	−	1.65444i	−0.0359568	−	0.134192i
$153$	7.81532	−	13.0194i	0.631831	−	1.05256i
$154$	0.126713	+	0.219474i	0.0102109	+	0.0176857i
$155$		0			0
$156$	5.72706	−	8.75591i	0.458532	−	0.701034i
$157$	−0.818660	−	0.818660i	−0.0653362	−	0.0653362i	0.673684	−	0.739020i	$-0.264711\pi$
$157$	−0.818660	−	0.818660i	−0.0653362	−	0.0653362i	−0.739020	+	0.673684i	$0.764711\pi$
$158$	9.88987	+	2.64998i	0.786796	+	0.210821i
$159$	12.3483	−	4.99210i	0.979286	−	0.395899i
$160$		0			0
$161$	−10.7715			−0.848916
$162$	16.5044	+	5.03060i	1.29671	+	0.395241i
$163$	−17.5892	+	4.71302i	−1.37769	+	0.369152i	−0.870283	−	0.492552i	$-0.836064\pi$
$163$	−17.5892	+	4.71302i	−1.37769	+	0.369152i	−0.507411	+	0.861704i	$0.669397\pi$
$164$		−	18.9856i		−	1.48252i
$165$		0			0
$166$	3.53130	+	6.11638i	0.274082	+	0.474723i
$167$	−1.59456	+	5.95097i	−0.123391	+	0.460500i	−0.999777	−	0.0211085i	$-0.993280\pi$
$167$	−1.59456	+	5.95097i	−0.123391	+	0.460500i	0.876387	+	0.481608i	$0.159947\pi$
$168$	−1.75578	+	1.32366i	−0.135461	+	0.102122i
$169$	10.0167	−	8.28650i	0.770514	−	0.637423i
$170$		0			0
$171$	−8.00981	+	2.00068i	−0.612525	+	0.152996i
$172$	−4.24119	+	15.8283i	−0.323388	+	1.20690i
$173$	−3.24998	+	0.870829i	−0.247091	+	0.0662079i	−0.380239	−	0.924888i	$-0.624158\pi$
$173$	−3.24998	+	0.870829i	−0.247091	+	0.0662079i	0.133148	+	0.991096i	$0.457492\pi$
$174$	−1.29419	+	9.22283i	−0.0981121	+	0.699181i
$175$		0			0
$176$	−0.147243	+	0.255033i	−0.0110989	+	0.0192238i
$177$	−9.37355	+	7.06660i	−0.704559	+	0.531158i
$178$	−7.17396	−	26.7736i	−0.537711	−	2.00676i
$179$	−1.62397	−	2.81281i	−0.121382	−	0.210239i	0.798931	−	0.601422i	$-0.205399\pi$
$179$	−1.62397	−	2.81281i	−0.121382	−	0.210239i	−0.920313	+	0.391183i	$0.872066\pi$
$180$		0			0
$181$	−6.71234			−0.498925			−0.249462	−	0.968385i	$-0.580254\pi$
$181$	−6.71234			−0.498925			−0.249462	+	0.968385i	$0.580254\pi$
$182$	13.2655	−	4.77584i	0.983301	−	0.354009i
$183$	2.88522	+	3.82712i	0.213281	+	0.282909i
$184$	−1.64341	−	2.84646i	−0.121154	−	0.209844i
$185$		0			0
$186$	0.639536	−	0.818927i	0.0468931	−	0.0600466i
$187$	0.231961	−	0.231961i	0.0169627	−	0.0169627i
$188$	−0.391556	−	1.46131i	−0.0285572	−	0.106577i
$189$	6.23515	+	8.57047i	0.453541	+	0.623410i
$190$		0			0
$191$	−1.36065	−	0.785571i	−0.0984531	−	0.0568419i	0.449965	−	0.893046i	$-0.351436\pi$
$191$	−1.36065	−	0.785571i	−0.0984531	−	0.0568419i	−0.548418	+	0.836204i	$0.684770\pi$
$192$	8.33325	+	3.53517i	0.601401	+	0.255129i
$193$	−0.793102	+	2.95990i	−0.0570888	+	0.213058i	−0.988578	−	0.150711i	$-0.951844\pi$
$193$	−0.793102	+	2.95990i	−0.0570888	+	0.213058i	0.931489	+	0.363769i	$0.118510\pi$
$194$	14.1447			1.01553
$195$		0			0
$196$	−4.75737			−0.339812
$197$	1.92918	−	7.19978i	0.137448	−	0.512963i	−0.862528	−	0.506010i	$-0.831120\pi$
$197$	1.92918	−	7.19978i	0.137448	−	0.512963i	0.999976	−	0.00695355i	$-0.00221340\pi$
$198$	0.319583	+	0.191840i	0.0227118	+	0.0136335i
$199$	−4.35231	−	2.51281i	−0.308527	−	0.178128i	0.337740	−	0.941239i	$-0.390338\pi$
$199$	−4.35231	−	2.51281i	−0.308527	−	0.178128i	−0.646267	+	0.763111i	$0.723671\pi$
$200$		0			0
$201$	−11.6815	+	14.9581i	−0.823948	+	1.05507i
$202$	−5.79383	−	21.6229i	−0.407653	−	1.52138i
$203$	−4.04520	+	4.04520i	−0.283917	+	0.283917i
$204$	−11.5761	−	9.04032i	−0.810492	−	0.632949i
$205$		0			0
$206$	−17.5277	−	30.3589i	−1.22121	−	2.11520i
$207$	−13.8532	+	7.68664i	−0.962863	+	0.534258i
$208$	12.5135	+	10.5747i	0.867653	+	0.733225i
$209$	−0.178353			−0.0123369
$210$		0			0
$211$	−7.34656	−	12.7246i	−0.505758	−	0.875999i	−0.999978	−	0.00666177i	$-0.997879\pi$
$211$	−7.34656	−	12.7246i	−0.505758	−	0.875999i	0.494220	−	0.869337i	$-0.335454\pi$
$212$	−3.33443	−	12.4442i	−0.229009	−	0.854674i
$213$	−14.4038	−	19.1060i	−0.986930	−	1.30912i
$214$	14.3624	−	24.8764i	0.981793	−	1.70052i
$215$		0			0
$216$	−1.31352	+	2.95528i	−0.0893737	+	0.201081i
$217$	0.616511	−	0.165194i	0.0418515	−	0.0112141i
$218$	−8.00003	+	29.8565i	−0.541831	+	2.02214i
$219$	16.7810	−	6.78412i	1.13396	−	0.458428i
$220$		0			0
$221$	−10.4156	−	14.9861i	−0.700627	−	1.00807i
$222$	−2.51926	−	3.34170i	−0.169082	−	0.224280i
$223$	−1.08114	+	4.03489i	−0.0723988	+	0.270196i	−0.992631	−	0.121177i	$-0.961333\pi$
$223$	−1.08114	+	4.03489i	−0.0723988	+	0.270196i	0.920232	+	0.391373i	$0.128000\pi$
$224$	7.61463	+	13.1889i	0.508774	+	0.881222i
$225$		0			0
$226$		−	20.4795i		−	1.36227i
$227$	22.6915	−	6.08018i	1.50609	−	0.403556i	0.590956	−	0.806704i	$-0.298751\pi$
$227$	22.6915	−	6.08018i	1.50609	−	0.403556i	0.915135	+	0.403148i	$0.132084\pi$
$228$	0.974886	+	7.92590i	0.0645634	+	0.524906i
$229$	11.4151			0.754332			0.377166	−	0.926146i	$-0.376899\pi$
$229$	11.4151			0.754332			0.377166	+	0.926146i	$0.376899\pi$
$230$		0			0
$231$	0.0858158	+	0.212272i	0.00564626	+	0.0139665i
$232$	−1.68615	−	0.451802i	−0.110701	−	0.0296622i
$233$	8.68792	+	8.68792i	0.569164	+	0.569164i	0.931894	−	0.362730i	$-0.118155\pi$
$233$	8.68792	+	8.68792i	0.569164	+	0.569164i	−0.362730	+	0.931894i	$0.618155\pi$
$234$	13.6525	−	15.6085i	0.892493	−	1.02036i
$235$		0			0
$236$	5.67728	+	9.83333i	0.369559	+	0.640096i
$237$	8.51576	+	3.61259i	0.553158	+	0.234663i
$238$	−5.12277	−	19.1185i	−0.332060	−	1.23927i
$239$			8.54627i			0.552812i	0.961041	+	0.276406i	$0.0891435\pi$
$239$			8.54627i			0.552812i	−0.961041	+	0.276406i	$0.910856\pi$
$240$		0			0
$241$	−17.8914	−	10.3296i	−1.15249	−	0.665388i	−0.202995	−	0.979180i	$-0.565067\pi$
$241$	−17.8914	−	10.3296i	−1.15249	−	0.665388i	−0.949492	+	0.313792i	$0.898401\pi$
$242$	−14.9060	−	14.9060i	−0.958194	−	0.958194i
$243$	14.1349	+	6.57297i	0.906756	+	0.421656i
$244$	4.01485	−	2.31797i	0.257024	−	0.148393i
$245$		0			0
$246$	5.22909	−	37.2643i	0.333395	−	2.37589i
$247$	−1.75710	+	9.76553i	−0.111802	+	0.621366i
$248$	0.137714	+	0.137714i	0.00874487	+	0.00874487i
$249$	2.39155	+	5.91567i	0.151558	+	0.374890i
$250$		0			0
$251$	17.9829	+	10.3824i	1.13507	+	0.655333i	0.945205	−	0.326477i	$-0.105862\pi$
$251$	17.9829	+	10.3824i	1.13507	+	0.655333i	0.189865	+	0.981810i	$0.439195\pi$
$252$	8.96417	−	4.97390i	0.564690	−	0.313326i
$253$	−0.330592	+	0.0885818i	−0.0207841	+	0.00556909i
$254$	−0.970565	−	0.560356i	−0.0608987	−	0.0351599i
$255$		0			0
$256$	−9.93615	+	17.2099i	−0.621009	+	1.07562i
$257$	−22.4808	−	6.02371i	−1.40231	−	0.375749i	−0.523138	−	0.852248i	$-0.675239\pi$
$257$	−22.4808	−	6.02371i	−1.40231	−	0.375749i	−0.879175	+	0.476499i	$0.841905\pi$
$258$	−12.6840	+	29.8993i	−0.789672	+	1.86145i
$259$		−	2.57066i		−	0.159733i
$260$		0			0
$261$	−2.31582	+	8.08917i	−0.143345	+	0.500707i
$262$	10.6869	+	2.86355i	0.660239	+	0.176911i
$263$	−5.86610	+	21.8926i	−0.361719	+	1.34996i	0.510095	+	0.860118i	$0.329610\pi$
$263$	−5.86610	+	21.8926i	−0.361719	+	1.34996i	−0.871814	+	0.489837i	$0.837056\pi$
$264$	−0.0430016	+	0.0550637i	−0.00264657	+	0.00338893i
$265$		0			0
$266$	−5.38057	+	9.31942i	−0.329904	+	0.571410i
$267$	−3.05716	−	24.8550i	−0.187095	−	1.52110i
$268$	12.9809	+	12.9809i	0.792933	+	0.792933i
$269$	−4.58057	+	7.93378i	−0.279282	+	0.483731i	−0.971207	−	0.238239i	$-0.923430\pi$
$269$	−4.58057	+	7.93378i	−0.279282	+	0.483731i	0.691924	+	0.721970i	$0.256763\pi$
$270$		0			0
$271$	−7.38686	+	4.26480i	−0.448720	+	0.259068i	−0.707289	−	0.706924i	$-0.750082\pi$
$271$	−7.38686	+	4.26480i	−0.448720	+	0.259068i	0.258570	+	0.965993i	$0.416749\pi$
$272$	16.2632	−	16.2632i	0.986104	−	0.986104i
$273$	12.4682	−	2.60749i	0.754609	−	0.157813i
$274$			13.9411i			0.842213i
$275$		0			0
$276$	5.74356	+	14.2071i	0.345722	+	0.855169i
$277$	21.2717	−	5.69974i	1.27809	−	0.342464i	0.444967	−	0.895547i	$-0.353215\pi$
$277$	21.2717	−	5.69974i	1.27809	−	0.342464i	0.833126	+	0.553083i	$0.186549\pi$
$278$	−2.89919	+	2.89919i	−0.173882	+	0.173882i
$279$	0.675007	−	0.652401i	0.0404116	−	0.0390582i
$280$		0			0
$281$	−1.14521			−0.0683174			−0.0341587	−	0.999416i	$-0.510875\pi$
$281$	−1.14521			−0.0683174			−0.0341587	+	0.999416i	$0.510875\pi$
$282$	−0.366055	−	2.97606i	−0.0217983	−	0.177222i
$283$	9.42831	+	2.52631i	0.560455	+	0.150174i	0.527915	−	0.849297i	$-0.322974\pi$
$283$	9.42831	+	2.52631i	0.560455	+	0.150174i	0.0325397	+	0.999470i	$0.489640\pi$
$284$	−20.0432	+	11.5719i	−1.18934	+	0.686668i
$285$		0			0
$286$	0.367858	−	0.255668i	0.0217519	−	0.0151179i
$287$	16.3444	−	16.3444i	0.964779	−	0.964779i
$288$	19.2048	+	11.5283i	1.13165	+	0.679313i
$289$	−7.46552	+	4.31022i	−0.439148	+	0.253542i
$290$		0			0
$291$	12.6553	+	1.77584i	0.741865	+	0.104102i
$292$	−4.53139	−	16.9114i	−0.265180	−	0.989664i
$293$	−5.80825	−	21.6767i	−0.339321	−	1.26636i	−0.899108	−	0.437728i	$-0.855783\pi$
$293$	−5.80825	−	21.6767i	−0.339321	−	1.26636i	0.559786	−	0.828637i	$-0.310883\pi$
$294$	−9.33763	−	1.31030i	−0.544582	−	0.0764181i
$295$		0			0
$296$	0.679316	−	0.392203i	0.0394844	−	0.0227963i
$297$	0.261846	+	0.211762i	0.0151938	+	0.0122877i
$298$	3.94849	−	3.94849i	0.228730	−	0.228730i
$299$	1.59327	+	18.9739i	0.0921413	+	1.09729i
$300$		0			0
$301$	−17.2776	+	9.97521i	−0.995863	+	0.574962i
$302$	−22.4678	−	6.02022i	−1.29288	−	0.346425i
$303$	−2.46903	−	20.0734i	−0.141842	−	1.15319i
$304$	−12.5047			−0.717191
$305$		0			0
$306$	−20.2314	−	20.9324i	−1.15655	−	1.19663i
$307$	8.67444	−	8.67444i	0.495076	−	0.495076i	−0.414825	−	0.909901i	$-0.636157\pi$
$307$	8.67444	−	8.67444i	0.495076	−	0.495076i	0.909901	+	0.414825i	$0.136157\pi$
$308$	0.213921	−	0.0573199i	0.0121893	−	0.00326610i
$309$	−11.8705	−	29.3626i	−0.675291	−	1.67038i
$310$		0			0
$311$			3.86942i			0.219415i	0.993964	+	0.109707i	$0.0349913\pi$
$311$			3.86942i			0.219415i	−0.993964	+	0.109707i	$0.965009\pi$
$312$	2.59131	+	2.89699i	0.146704	+	0.164010i
$313$	−22.5004	+	22.5004i	−1.27180	+	1.27180i	−0.326658	+	0.945143i	$0.605922\pi$
$313$	−22.5004	+	22.5004i	−1.27180	+	1.27180i	−0.945143	+	0.326658i	$0.894078\pi$
$314$	−1.92220	+	1.10978i	−0.108476	+	0.0626287i
$315$		0			0
$316$	4.47377	−	7.74879i	0.251669	−	0.435903i
$317$	−1.27451	−	1.27451i	−0.0715836	−	0.0715836i	0.670409	−	0.741992i	$-0.266119\pi$
$317$	−1.27451	−	1.27451i	−0.0715836	−	0.0715836i	−0.741992	+	0.670409i	$0.766119\pi$
$318$	−3.11726	−	25.3436i	−0.174807	−	1.42120i
$319$	−0.0908856	+	0.157419i	−0.00508862	+	0.00881375i
$320$		0			0
$321$	15.9732	−	20.4537i	0.891538	−	1.14162i
$322$	−5.34470	+	19.9467i	−0.297849	+	1.11159i
$323$	13.4549	+	3.60522i	0.748650	+	0.200600i
$324$	7.97935	−	12.7938i	0.443297	−	0.710766i
$325$		0			0
$326$			34.9102i			1.93350i
$327$	−10.9061	+	25.7082i	−0.603106	+	1.42167i
$328$	6.81278	+	1.82548i	0.376173	+	0.100795i
$329$	0.920933	−	1.59510i	0.0507727	−	0.0879409i
$330$		0			0
$331$	2.71099	+	1.56519i	0.149009	+	0.0860307i	0.572651	−	0.819799i	$-0.305915\pi$
$331$	2.71099	+	1.56519i	0.149009	+	0.0860307i	−0.423642	+	0.905830i	$0.639248\pi$
$332$	5.96162	−	1.59741i	0.327186	−	0.0876693i
$333$	−1.83444	−	3.30610i	−0.100526	−	0.181173i
$334$	10.2288	+	5.90559i	0.559694	+	0.323139i
$335$		0			0
$336$	6.01671	+	14.8828i	0.328239	+	0.811923i
$337$	20.2542	+	20.2542i	1.10332	+	1.10332i	0.994008	+	0.109311i	$0.0348643\pi$
$337$	20.2542	+	20.2542i	1.10332	+	1.10332i	0.109311	+	0.994008i	$0.465136\pi$
$338$	−10.3748	−	22.6605i	−0.564312	−	1.23257i
$339$	2.57116	−	18.3230i	0.139646	−	0.995167i
$340$		0			0
$341$	0.0175630	−	0.0101400i	0.000951090	−	0.000549112i
$342$	−0.269511	+	15.8252i	−0.0145735	+	0.855731i
$343$	−14.1915	−	14.1915i	−0.766272	−	0.766272i
$344$	−5.27205	−	3.04382i	−0.284250	−	0.164112i
$345$		0			0
$346$			6.45039i			0.346775i
$347$	8.30799	+	31.0059i	0.445996	+	1.66448i	0.713292	+	0.700867i	$0.247203\pi$
$347$	8.30799	+	31.0059i	0.445996	+	1.66448i	−0.267296	+	0.963615i	$0.586130\pi$
$348$	7.49238	+	3.17845i	0.401634	+	0.170383i
$349$	9.95791	+	17.2476i	0.533035	+	0.923243i	0.999256	+	0.0385748i	$0.0122818\pi$
$349$	9.95791	+	17.2476i	0.533035	+	0.923243i	−0.466221	+	0.884668i	$0.654385\pi$
$350$		0			0
$351$	14.1745	−	12.2508i	0.756579	−	0.653902i
$352$	0.342164	+	0.342164i	0.0182374	+	0.0182374i
$353$	5.14341	+	1.37817i	0.273756	+	0.0733527i	0.393085	−	0.919502i	$-0.371408\pi$
$353$	5.14341	+	1.37817i	0.273756	+	0.0733527i	−0.119329	+	0.992855i	$0.538074\pi$
$354$	8.43486	+	20.8643i	0.448308	+	1.10892i
$355$		0			0
$356$	−24.2225			−1.28379
$357$	−2.18306	−	17.7484i	−0.115540	−	0.939346i
$358$	−6.01454	+	1.61159i	−0.317878	+	0.0851752i
$359$		−	18.4430i		−	0.973387i	−0.873573	−	0.486693i	$-0.838203\pi$
$359$		−	18.4430i		−	0.973387i	0.873573	−	0.486693i	$-0.161797\pi$
$360$		0			0
$361$	5.71335	+	9.89581i	0.300703	+	0.520832i
$362$	−3.33058	+	12.4299i	−0.175051	+	0.653301i
$363$	−11.4650	−	15.2078i	−0.601755	−	0.798203i
$364$	−1.03098	−	12.2777i	−0.0540380	−	0.643528i
$365$		0			0
$366$	8.51866	−	3.44386i	0.445277	−	0.180014i
$367$	7.94586	−	29.6544i	0.414770	−	1.54794i	−0.370524	−	0.928823i	$-0.620822\pi$
$367$	7.94586	−	29.6544i	0.414770	−	1.54794i	0.785295	−	0.619122i	$-0.212511\pi$
$368$	−23.1784	+	6.21064i	−1.20826	+	0.323752i
$369$	9.35693	−	32.6838i	0.487102	−	1.70145i
$370$		0			0
$371$	7.84251	−	13.5836i	0.407163	−	0.705227i
$372$	−0.546617	−	0.725065i	−0.0283408	−	0.0375928i
$373$	6.36353	+	23.7490i	0.329491	+	1.22968i	0.909719	+	0.415224i	$0.136297\pi$
$373$	6.36353	+	23.7490i	0.329491	+	1.22968i	−0.580228	+	0.814454i	$0.697037\pi$
$374$	−0.314449	−	0.544641i	−0.0162597	−	0.0281627i
$375$		0			0
$376$	0.562024			0.0289842
$377$	7.72391	+	6.52722i	0.397802	+	0.336169i
$378$	18.9646	−	7.29367i	0.975432	−	0.375146i
$379$	11.2914	+	19.5573i	0.580002	+	1.00459i	0.995478	+	0.0949885i	$0.0302814\pi$
$379$	11.2914	+	19.5573i	0.580002	+	1.00459i	−0.415477	+	0.909604i	$0.636385\pi$
$380$		0			0
$381$	−0.798012	−	0.623202i	−0.0408834	−	0.0319276i
$382$	−2.12985	+	2.12985i	−0.108973	+	0.108973i
$383$	−0.474622	−	1.77131i	−0.0242521	−	0.0905099i	0.952739	−	0.303790i	$-0.0982521\pi$
$383$	−0.474622	−	1.77131i	−0.0242521	−	0.0905099i	−0.976991	+	0.213280i	$0.931585\pi$
$384$	−5.23815	+	6.70746i	−0.267308	+	0.342289i
$385$		0			0
$386$	5.08760	+	2.93733i	0.258952	+	0.149506i
$387$	−15.1022	+	25.1584i	−0.767687	+	1.27887i
$388$	3.19924	−	11.9397i	0.162417	−	0.606148i
$389$	15.3065			0.776072			0.388036	−	0.921644i	$-0.373154\pi$
$389$	15.3065			0.776072			0.388036	+	0.921644i	$0.373154\pi$
$390$		0			0
$391$	26.7304			1.35181
$392$	0.457426	−	1.70714i	0.0231035	−	0.0862234i
$393$	9.20205	+	3.90373i	0.464182	+	0.196917i
$394$	−12.3753	−	7.14488i	−0.623459	−	0.359954i
$395$		0			0
$396$	0.234218	−	0.226374i	0.0117699	−	0.0113757i
$397$	2.07456	+	7.74235i	0.104119	+	0.388578i	0.998244	−	0.0592405i	$-0.0188679\pi$
$397$	2.07456	+	7.74235i	0.104119	+	0.388578i	−0.894125	+	0.447818i	$0.852201\pi$
$398$	−6.81277	+	6.81277i	−0.341493	+	0.341493i
$399$	−5.98403	+	7.66256i	−0.299576	+	0.383608i
$400$		0			0
$401$	−2.14596	−	3.71692i	−0.107164	−	0.185614i	0.807456	−	0.589928i	$-0.200844\pi$
$401$	−2.14596	−	3.71692i	−0.107164	−	0.185614i	−0.914620	+	0.404314i	$0.867510\pi$
$402$	21.9032	+	29.0537i	1.09243	+	1.44907i
$403$	−0.382178	−	1.06154i	−0.0190376	−	0.0528792i
$404$	−19.5626			−0.973275
$405$		0			0
$406$	5.48370	+	9.49805i	0.272152	+	0.471380i
$407$	−0.0211403	−	0.0788966i	−0.00104789	−	0.00391076i
$408$	4.35709	−	3.28475i	0.215708	−	0.162619i
$409$	−18.8150	+	32.5886i	−0.930343	+	1.61140i	−0.147607	+	0.989046i	$0.547157\pi$
$409$	−18.8150	+	32.5886i	−0.930343	+	1.61140i	−0.782735	+	0.622355i	$0.786176\pi$
$410$		0			0
$411$	−1.75028	+	12.4731i	−0.0863349	+	0.615252i
$412$	−29.5907	+	7.92881i	−1.45783	+	0.390624i
$413$	−3.57789	+	13.3529i	−0.176056	+	0.657051i
$414$	7.36031	+	29.4673i	0.361740	+	1.44824i
$415$		0			0
$416$	22.1058	−	15.3639i	1.08383	−	0.753278i
$417$	−2.95789	+	2.22991i	−0.144848	+	0.109199i
$418$	−0.0884963	+	0.330273i	−0.00432850	+	0.0161542i
$419$	−6.05083	−	10.4803i	−0.295602	−	0.511998i	0.679522	−	0.733655i	$-0.262187\pi$
$419$	−6.05083	−	10.4803i	−0.295602	−	0.511998i	−0.975125	+	0.221656i	$0.928854\pi$
$420$		0			0
$421$			22.2934i			1.08651i	0.839567	+	0.543256i	$0.182809\pi$
$421$			22.2934i			1.08651i	−0.839567	+	0.543256i	$0.817191\pi$
$422$	−27.2087	+	7.29054i	−1.32450	+	0.354898i
$423$	0.0461292	−	2.70863i	0.00224288	−	0.131698i
$424$	4.78611			0.232434
$425$		0			0
$426$	−42.5274	+	17.1927i	−2.06046	+	0.832988i
$427$	5.45183	+	1.46081i	0.263833	+	0.0706937i
$428$	−17.7500	−	17.7500i	−0.857979	−	0.857979i
$429$	0.361221	−	0.182562i	0.0174399	−	0.00881416i
$430$		0			0
$431$	0.197713	+	0.342449i	0.00952349	+	0.0164952i	0.870748	−	0.491730i	$-0.163635\pi$
$431$	0.197713	+	0.342449i	0.00952349	+	0.0164952i	−0.861224	+	0.508225i	$0.830302\pi$
$432$	18.3585	+	14.8471i	0.883274	+	0.714330i
$433$	−2.90501	−	10.8417i	−0.139606	−	0.521017i	−0.999936	−	0.0112798i	$-0.996409\pi$
$433$	−2.90501	−	10.8417i	−0.139606	−	0.521017i	0.860330	−	0.509737i	$-0.170257\pi$
$434$		−	1.22362i		−	0.0587357i
$435$		0			0
$436$	23.3928	+	13.5059i	1.12031	+	0.646813i
$437$	−10.2764	−	10.2764i	−0.491585	−	0.491585i
$438$	−4.23627	−	34.4413i	−0.202417	−	1.64567i
$439$	18.5828	−	10.7288i	0.886911	−	0.512058i	0.0139799	−	0.999902i	$-0.495550\pi$
$439$	18.5828	−	10.7288i	0.886911	−	0.512058i	0.872931	+	0.487844i	$0.162217\pi$
$440$		0			0
$441$	−8.18987	−	2.34464i	−0.389994	−	0.111650i
$442$	−32.9192	+	11.8516i	−1.56581	+	0.563724i
$443$	15.8402	+	15.8402i	0.752590	+	0.752590i	0.974962	−	0.222372i	$-0.0713799\pi$
$443$	15.8402	+	15.8402i	0.752590	+	0.752590i	−0.222372	+	0.974962i	$0.571380\pi$
$444$	−3.39057	+	1.37072i	−0.160909	+	0.0650513i
$445$		0			0
$446$	6.93533	+	4.00412i	0.328398	+	0.189600i
$447$	4.02843	−	3.03698i	0.190538	−	0.143644i
$448$	10.2967	−	2.75900i	0.486474	−	0.130350i
$449$	17.4060	+	10.0493i	0.821438	+	0.474257i	0.850912	−	0.525308i	$-0.176050\pi$
$449$	17.4060	+	10.0493i	0.821438	+	0.474257i	−0.0294742	+	0.999566i	$0.509383\pi$
$450$		0			0
$451$	0.367218	−	0.636041i	0.0172916	−	0.0299500i
$452$	−17.2870	−	4.63203i	−0.813111	−	0.217872i
$453$	−19.3461	−	8.20708i	−0.908958	−	0.385602i
$454$		−	45.0370i		−	2.11369i
$455$		0			0
$456$	−2.93787	−	0.412255i	−0.137578	−	0.0193056i
$457$	−22.6812	−	6.07741i	−1.06098	−	0.284289i	−0.314199	−	0.949357i	$-0.601736\pi$
$457$	−22.6812	−	6.07741i	−1.06098	−	0.284289i	−0.746783	+	0.665068i	$0.768402\pi$
$458$	5.66403	−	21.1385i	0.264663	−	0.987735i
$459$	−15.4730	−	21.2683i	−0.722217	−	0.992717i
$460$		0			0
$461$	2.45668	−	4.25509i	0.114419	−	0.198179i	−0.803128	−	0.595806i	$-0.796833\pi$
$461$	2.45668	−	4.25509i	0.114419	−	0.198179i	0.917547	+	0.397627i	$0.130166\pi$
$462$	0.435665	−	0.0535868i	0.0202690	−	0.00249308i
$463$	8.17642	+	8.17642i	0.379991	+	0.379991i	0.871099	−	0.491108i	$-0.163408\pi$
$463$	8.17642	+	8.17642i	0.379991	+	0.379991i	−0.491108	+	0.871099i	$0.663408\pi$
$464$	−6.37217	+	11.0369i	−0.295820	+	0.512376i
$465$		0			0
$466$	20.3991	−	11.7774i	0.944969	−	0.545578i
$467$	18.4859	−	18.4859i	0.855427	−	0.855427i	−0.135368	−	0.990795i	$-0.543222\pi$
$467$	18.4859	−	18.4859i	0.855427	−	0.855427i	0.990795	+	0.135368i	$0.0432217\pi$
$468$	−10.0874	−	15.0546i	−0.466290	−	0.695898i
$469$			22.3501i			1.03203i
$470$		0			0
$471$	−1.85912	+	0.751593i	−0.0856638	+	0.0346316i
$472$	−4.07447	+	1.09175i	−0.187543	+	0.0502519i
$473$	−0.448237	+	0.448237i	−0.0206100	+	0.0206100i
$474$	10.9152	−	13.9769i	0.501351	−	0.641981i
$475$		0			0
$476$	−17.2968			−0.792797
$477$	0.392829	−	23.0663i	0.0179864	−	1.05613i
$478$	15.8260	+	4.24055i	0.723862	+	0.193958i
$479$	−16.1211	+	9.30755i	−0.736594	+	0.425273i	−0.820830	−	0.571173i	$-0.806488\pi$
$479$	−16.1211	+	9.30755i	−0.736594	+	0.425273i	0.0842357	+	0.996446i	$0.473155\pi$
$480$		0			0
$481$	−4.52818	+	0.380238i	−0.206467	+	0.0173374i
$482$	−28.0058	+	28.0058i	−1.27563	+	1.27563i
$483$	−7.28617	+	17.1753i	−0.331532	+	0.781502i
$484$	−15.9538	+	9.21091i	−0.725171	+	0.418678i
$485$		0			0
$486$	19.1854	−	22.9136i	0.870266	−	1.03938i
$487$	8.68654	+	32.4186i	0.393625	+	1.46903i	0.824110	+	0.566430i	$0.191676\pi$
$487$	8.68654	+	32.4186i	0.393625	+	1.46903i	−0.430485	+	0.902598i	$0.641657\pi$
$488$	0.445751	+	1.66356i	0.0201782	+	0.0753060i
$489$	−4.38291	+	31.2341i	−0.198202	+	1.41245i
$490$		0			0
$491$	−26.7145	+	15.4236i	−1.20561	+	0.696059i	−0.961797	−	0.273764i	$-0.911731\pi$
$491$	−26.7145	+	15.4236i	−1.20561	+	0.696059i	−0.243812	+	0.969822i	$0.578398\pi$
$492$	−30.2726	−	12.8424i	−1.36479	−	0.578978i
$493$	10.0385	−	10.0385i	0.452109	−	0.452109i
$494$	17.2119	+	8.09933i	0.774401	+	0.364406i
$495$		0			0
$496$	1.23138	−	0.710935i	0.0552904	−	0.0319219i
$497$	−27.2170	−	7.29277i	−1.22085	−	0.327125i
$498$	12.1413	−	1.49338i	0.544063	−	0.0669198i
$499$	−10.3869			−0.464982			−0.232491	−	0.972598i	$-0.574688\pi$
$499$	−10.3869			−0.464982			−0.232491	+	0.972598i	$0.574688\pi$
$500$		0			0
$501$	8.41024	+	6.56793i	0.375742	+	0.293433i
$502$	28.1490	−	28.1490i	1.25635	−	1.25635i
$503$	−6.62041	+	1.77393i	−0.295189	+	0.0790957i	−0.403374	−	0.915035i	$-0.632163\pi$
$503$	−6.62041	+	1.77393i	−0.295189	+	0.0790957i	0.108185	+	0.994131i	$0.465496\pi$
$504$	0.922921	+	3.69495i	0.0411102	+	0.164586i
$505$		0			0
$506$			0.656142i			0.0291691i
$507$	−6.43729	−	21.5769i	−0.285890	−	0.958262i
$508$	−0.692525	+	0.692525i	−0.0307258	+	0.0307258i
$509$	−16.1412	+	9.31914i	−0.715447	+	0.413064i	−0.813075	−	0.582159i	$-0.802208\pi$
$509$	−16.1412	+	9.31914i	−0.715447	+	0.413064i	0.0976275	+	0.995223i	$0.468875\pi$
$510$		0			0
$511$	10.6578	−	18.4598i	0.471471	−	0.816612i
$512$	19.9903	+	19.9903i	0.883454	+	0.883454i
$513$	−2.22796	+	14.1250i	−0.0983668	+	0.623634i
$514$	−22.3094	+	38.6409i	−0.984024	+	1.70438i
$515$		0			0
$516$	22.3695	+	17.4693i	0.984763	+	0.769044i
$517$	0.0151469	−	0.0565292i	0.000666162	−	0.00248615i
$518$	−4.76033	−	1.27553i	−0.209157	−	0.0560434i
$519$	−0.809834	+	5.77116i	−0.0355478	+	0.253326i
$520$		0			0
$521$			15.0847i			0.660871i	0.943829	+	0.330435i	$0.107196\pi$
$521$			15.0847i			0.660871i	−0.943829	+	0.330435i	$0.892804\pi$
$522$	13.8304	+	8.30217i	0.605341	+	0.363376i
$523$	1.55097	+	0.415581i	0.0678191	+	0.0181721i	0.292569	−	0.956244i	$-0.405490\pi$
$523$	1.55097	+	0.415581i	0.0678191	+	0.0181721i	−0.224750	+	0.974416i	$0.572157\pi$
$524$	4.83431	−	8.37327i	0.211188	−	0.365788i
$525$		0			0
$526$	37.6299	+	21.7257i	1.64074	+	0.947283i
$527$	−1.52992	+	0.409940i	−0.0666443	+	0.0178573i
$528$	0.307052	+	0.407292i	0.0133627	+	0.0177251i
$529$	−4.23345	−	2.44419i	−0.184063	−	0.106269i
$530$		0			0
$531$	4.92719	+	19.7262i	0.213822	+	0.856045i
$532$	6.64967	+	6.64967i	0.288300	+	0.288300i
$533$	−31.2080	−	26.3729i	−1.35177	−	1.14234i
$534$	−47.5433	−	6.67148i	−2.05740	−	0.288703i
$535$		0			0
$536$	−5.90618	+	3.40994i	−0.255108	+	0.147287i
$537$	−5.58353	+	0.686775i	−0.240947	+	0.0296365i
$538$	12.4189	+	12.4189i	0.535418	+	0.535418i
$539$	−0.159378	−	0.0920170i	−0.00686490	−	0.00396345i
$540$		0			0
$541$			27.8477i			1.19727i	0.801023	+	0.598634i	$0.204290\pi$
$541$			27.8477i			1.19727i	−0.801023	+	0.598634i	$0.795710\pi$
$542$	4.23228	+	15.7951i	0.181792	+	0.678458i
$543$	−4.54041	+	10.7029i	−0.194848	+	0.459304i
$544$	−18.8963	−	32.7293i	−0.810171	−	1.40326i
$545$		0			0
$546$	1.35801	−	24.3823i	0.0581175	−	1.04347i
$547$	4.94438	+	4.94438i	0.211406	+	0.211406i	0.804865	−	0.593458i	$-0.202238\pi$
$547$	4.94438	+	4.94438i	0.211406	+	0.211406i	−0.593458	+	0.804865i	$0.702238\pi$
$548$	11.7679	+	3.15319i	0.502698	+	0.134697i
$549$	8.05400	−	2.01172i	0.343737	−	0.0858581i
$550$		0			0
$551$	−7.71847			−0.328818
$552$	−5.65034	+	0.694992i	−0.240495	+	0.0295808i
$553$	10.5222	−	2.81942i	0.447450	−	0.119894i
$554$		−	42.2190i		−	1.79371i
$555$		0			0
$556$	1.79150	+	3.10298i	0.0759767	+	0.131595i
$557$	−0.531756	+	1.98454i	−0.0225312	+	0.0840877i	−0.976276	−	0.216530i	$-0.930526\pi$
$557$	−0.531756	+	1.98454i	−0.0225312	+	0.0840877i	0.953745	+	0.300618i	$0.0971928\pi$
$558$	−0.873183	−	1.57369i	−0.0369648	−	0.0666195i
$559$	20.1268	+	28.9588i	0.851274	+	1.22482i
$560$		0			0
$561$	−0.212958	−	0.526768i	−0.00899110	−	0.0222402i
$562$	−0.568237	+	2.12069i	−0.0239697	+	0.0894560i
$563$	17.7814	−	4.76452i	0.749399	−	0.200801i	0.136147	−	0.990689i	$-0.456528\pi$
$563$	17.7814	−	4.76452i	0.749399	−	0.200801i	0.613251	+	0.789888i	$0.289861\pi$
$564$	−2.59492	−	0.364131i	−0.109266	−	0.0153327i
$565$		0			0
$566$	9.35642	−	16.2058i	0.393280	−	0.681180i
$567$	17.8833	−	4.14468i	0.751027	−	0.174060i
$568$	−2.22531	−	8.30495i	−0.0933717	−	0.348468i
$569$	2.39632	+	4.15054i	0.100459	+	0.174000i	0.911874	−	0.410471i	$-0.134636\pi$
$569$	2.39632	+	4.15054i	0.100459	+	0.174000i	−0.811415	+	0.584471i	$0.801302\pi$
$570$		0			0
$571$	−11.0204			−0.461190			−0.230595	−	0.973050i	$-0.574067\pi$
$571$	−11.0204			−0.461190			−0.230595	+	0.973050i	$0.574067\pi$
$572$	−0.132610	−	0.368340i	−0.00554472	−	0.0154011i
$573$	−2.17298	+	1.63818i	−0.0907774	+	0.0684359i
$574$	−22.1566	−	38.3763i	−0.924798	−	1.60180i
$575$		0			0
$576$	11.2737	−	10.8961i	0.469737	−	0.454005i
$577$	−20.8346	+	20.8346i	−0.867358	+	0.867358i	−0.992179	−	0.124822i	$-0.960164\pi$
$577$	−20.8346	+	20.8346i	−0.867358	+	0.867358i	0.124822	+	0.992179i	$0.460164\pi$
$578$	4.27735	+	15.9633i	0.177914	+	0.663986i
$579$	4.18310	+	3.26676i	0.173844	+	0.135762i
$580$		0			0
$581$	6.50746	+	3.75708i	0.269975	+	0.155870i
$582$	9.56788	−	22.5538i	0.396601	−	0.934886i
$583$	0.128989	−	0.481393i	0.00534217	−	0.0199373i
$584$	6.50418			0.269145
$585$		0			0
$586$	−43.0228			−1.77725
$587$	−7.06095	+	26.3518i	−0.291437	+	1.08766i	0.652569	+	0.757729i	$0.273691\pi$
$587$	−7.06095	+	26.3518i	−0.291437	+	1.08766i	−0.944006	+	0.329928i	$0.892976\pi$
$588$	−3.21802	+	7.58565i	−0.132709	+	0.312827i
$589$	0.745769	+	0.430570i	0.0307289	+	0.0177413i
$590$		0			0
$591$	−10.1751	−	7.94622i	−0.418549	−	0.326864i
$592$	−1.48219	−	5.53159i	−0.0609175	−	0.227347i
$593$	10.8114	−	10.8114i	0.443972	−	0.443972i	−0.449373	−	0.893344i	$-0.648352\pi$
$593$	10.8114	−	10.8114i	0.443972	−	0.443972i	0.893344	+	0.449373i	$0.148352\pi$
$594$	0.522065	−	0.379811i	0.0214206	−	0.0155838i
$595$		0			0
$596$	−2.43990	−	4.22603i	−0.0999422	−	0.173105i
$597$	−6.95071	+	5.24005i	−0.284474	+	0.214461i
$598$	35.9264	+	6.46421i	1.46914	+	0.264341i
$599$	19.7870			0.808476			0.404238	−	0.914654i	$-0.367537\pi$
$599$	19.7870			0.808476			0.404238	+	0.914654i	$0.367537\pi$
$600$		0			0
$601$	5.88386	+	10.1912i	0.240008	+	0.415706i	0.960716	−	0.277533i	$-0.0895167\pi$
$601$	5.88386	+	10.1912i	0.240008	+	0.415706i	−0.720708	+	0.693238i	$0.756183\pi$
$602$	9.89915	+	36.9441i	0.403459	+	1.50573i
$603$	15.9492	+	28.7443i	0.649500	+	1.17056i
$604$	−10.1635	+	17.6037i	−0.413547	+	0.716284i
$605$		0			0
$606$	−38.3969	−	5.38802i	−1.55977	−	0.218873i
$607$	37.4060	−	10.0229i	1.51826	−	0.406817i	0.599094	−	0.800679i	$-0.295528\pi$
$607$	37.4060	−	10.0229i	1.51826	−	0.406817i	0.919170	+	0.393861i	$0.128861\pi$
$608$	−5.31804	+	19.8472i	−0.215675	+	0.804910i
$609$	3.71380	+	9.18637i	0.150491	+	0.372250i
$610$		0			0
$611$	−2.94597	−	1.38627i	−0.119181	−	0.0560826i
$612$	−22.2453	+	12.3431i	−0.899211	+	0.498940i
$613$	1.57858	−	5.89134i	0.0637583	−	0.237949i	−0.926692	−	0.375823i	$-0.877360\pi$
$613$	1.57858	−	5.89134i	0.0637583	−	0.237949i	0.990450	+	0.137874i	$0.0440268\pi$
$614$	−11.7591	−	20.3674i	−0.474560	−	0.821963i
$615$		0			0
$616$			0.0822747i			0.00331494i
$617$	−40.3273	+	10.8057i	−1.62352	+	0.435020i	−0.952032	−	0.306000i	$-0.901009\pi$
$617$	−40.3273	+	10.8057i	−1.62352	+	0.435020i	−0.671484	+	0.741019i	$0.734343\pi$
$618$	−60.2636	+	7.41243i	−2.42416	+	0.298172i
$619$	−38.9070			−1.56380			−0.781902	−	0.623402i	$-0.785750\pi$
$619$	−38.9070			−1.56380			−0.781902	+	0.623402i	$0.785750\pi$
$620$		0			0
$621$	2.88570	+	27.2884i	0.115799	+	1.09505i
$622$	7.16537	+	1.91996i	0.287305	+	0.0769832i
$623$	−20.8528	−	20.8528i	−0.835450	−	0.835450i
$624$	25.3259	−	12.7998i	1.01385	−	0.512400i
$625$		0			0
$626$	30.5018	+	52.8307i	1.21910	+	2.11154i
$627$	−0.120643	+	0.284384i	−0.00481801	+	0.0113572i
$628$	0.502020	+	1.87356i	0.0200328	+	0.0747633i
$629$			6.37927i			0.254358i
$630$		0			0
$631$	6.37109	+	3.67835i	0.253629	+	0.146433i	0.621425	−	0.783474i	$-0.286554\pi$
$631$	6.37109	+	3.67835i	0.253629	+	0.146433i	−0.367796	+	0.929907i	$0.619887\pi$
$632$	2.35042	+	2.35042i	0.0934947	+	0.0934947i
$633$	−25.2589	+	3.10684i	−1.00395	+	0.123486i
$634$	−2.99253	+	1.72774i	−0.118849	+	0.0686172i
$635$		0			0
$636$	−22.0979	−	3.10088i	−0.876239	−	0.122958i
$637$	−6.60847	+	7.82006i	−0.261837	+	0.309842i
$638$	0.246411	+	0.246411i	0.00975550	+	0.00975550i
$639$	−40.2077	+	10.0430i	−1.59059	+	0.397297i
$640$		0			0
$641$	−27.5842	−	15.9257i	−1.08951	−	0.629029i	−0.156064	−	0.987747i	$-0.549881\pi$
$641$	−27.5842	−	15.9257i	−1.08951	−	0.629029i	−0.933446	+	0.358718i	$0.883214\pi$
$642$	−29.9504	−	39.7280i	−1.18205	−	1.56794i
$643$	−11.7226	+	3.14107i	−0.462295	+	0.123872i	−0.482447	−	0.875925i	$-0.660252\pi$
$643$	−11.7226	+	3.14107i	−0.462295	+	0.123872i	0.0201514	+	0.999797i	$0.493585\pi$
$644$	15.6284	+	9.02306i	0.615845	+	0.355558i
$645$		0			0
$646$	13.3523	−	23.1268i	0.525338	−	0.909913i
$647$	31.0824	+	8.32851i	1.22198	+	0.327427i	0.811450	−	0.584422i	$-0.198679\pi$
$647$	31.0824	+	8.32851i	1.22198	+	0.327427i	0.410526	+	0.911849i	$0.365345\pi$
$648$	3.82370	+	4.09345i	0.150209	+	0.160806i
$649$			0.439239i			0.0172417i
$650$		0			0
$651$	0.153623	−	1.09477i	0.00602097	−	0.0429075i
$652$	29.4681	+	7.89596i	1.15406	+	0.309230i
$653$	8.57665	−	32.0085i	0.335630	−	1.25259i	−0.567554	−	0.823336i	$-0.692110\pi$
$653$	8.57665	−	32.0085i	0.335630	−	1.25259i	0.903184	−	0.429253i	$-0.141223\pi$
$654$	42.1949	+	32.9519i	1.64995	+	1.28852i
$655$		0			0
$656$	25.7464	−	44.5940i	1.00523	−	1.74110i
$657$	0.533843	−	31.3464i	0.0208272	−	1.22294i
$658$	−2.49685	−	2.49685i	−0.0973374	−	0.0973374i
$659$	−17.7029	+	30.6623i	−0.689606	+	1.19443i	0.282359	+	0.959309i	$0.408883\pi$
$659$	−17.7029	+	30.6623i	−0.689606	+	1.19443i	−0.971965	+	0.235124i	$0.924450\pi$
$660$		0			0
$661$	9.03793	−	5.21805i	0.351535	−	0.202959i	−0.313826	−	0.949480i	$-0.601611\pi$
$661$	9.03793	−	5.21805i	0.351535	−	0.202959i	0.665361	+	0.746522i	$0.268278\pi$
$662$	4.24357	−	4.24357i	0.164931	−	0.164931i
$663$	−30.9407	+	6.47068i	−1.20164	+	0.251300i
$664$			2.29286i			0.0889803i
$665$		0			0
$666$	−7.03245	+	1.75656i	−0.272502	+	0.0680652i
$667$	−14.3068	+	3.83351i	−0.553963	+	0.148434i
$668$	7.29852	−	7.29852i	0.282388	−	0.282388i
$669$	5.70233	+	4.45320i	0.220465	+	0.172171i
$670$		0			0
$671$	0.179337			0.00692322
$672$	26.1806	−	3.22021i	1.00994	−	0.124222i
$673$	30.6699	+	8.21798i	1.18224	+	0.316780i	0.795814	−	0.605541i	$-0.207043\pi$
$673$	30.6699	+	8.21798i	1.18224	+	0.316780i	0.386425	+	0.922321i	$0.373710\pi$
$674$	47.5566	−	27.4568i	1.83181	−	1.05760i
$675$		0			0
$676$	−21.4746	+	3.63212i	−0.825945	+	0.139697i
$677$	10.8855	−	10.8855i	0.418365	−	0.418365i	−0.466275	−	0.884640i	$-0.654404\pi$
$677$	10.8855	−	10.8855i	0.418365	−	0.418365i	0.884640	+	0.466275i	$0.154404\pi$
$678$	−32.6546	−	13.8529i	−1.25409	−	0.532017i
$679$	13.0329	−	7.52456i	0.500158	−	0.288766i
$680$		0			0
$681$	5.65431	−	40.2946i	0.216674	−	1.54409i
$682$	−0.0100627	−	0.0375544i	−0.000385320	−	0.00143803i
$683$	5.64971	+	21.0850i	0.216180	+	0.806796i	0.985748	+	0.168230i	$0.0538052\pi$
$683$	5.64971	+	21.0850i	0.216180	+	0.806796i	−0.769567	+	0.638566i	$0.779528\pi$
$684$	13.2973	+	3.80684i	0.508436	+	0.145558i
$685$		0			0
$686$	−33.3215	+	19.2382i	−1.27222	+	0.734517i
$687$	7.72150	−	18.2014i	0.294593	−	0.694428i
$688$	−31.4268	+	31.4268i	−1.19813	+	1.19813i
$689$	−25.0874	−	11.8053i	−0.955755	−	0.449745i
$690$		0			0
$691$	−34.2377	+	19.7672i	−1.30246	+	0.751978i	−0.980826	−	0.194884i	$-0.937567\pi$
$691$	−34.2377	+	19.7672i	−1.30246	+	0.751978i	−0.321639	+	0.946863i	$0.604234\pi$
$692$	5.44485	+	1.45894i	0.206982	+	0.0554607i
$693$	0.396517	+	0.00675285i	0.0150624	+	0.000256520i
$694$	61.5388			2.33598
$695$		0			0
$696$	−1.86096	+	2.38296i	−0.0705394	+	0.0903258i
$697$	−40.5598	+	40.5598i	−1.53631	+	1.53631i
$698$	36.8800	−	9.88198i	1.39593	−	0.374038i
$699$	19.7297	−	7.97618i	0.746245	−	0.301687i
$700$		0			0
$701$			22.5069i			0.850074i	0.905176	+	0.425037i	$0.139739\pi$
$701$			22.5069i			0.850074i	−0.905176	+	0.425037i	$0.860261\pi$
$702$	−15.6529	−	32.3270i	−0.590779	−	1.22010i
$703$	2.45248	−	2.45248i	0.0924970	−	0.0924970i
$704$	0.293330	−	0.169354i	0.0110553	−	0.00638277i
$705$		0			0
$706$	5.10419	−	8.84072i	0.192099	−	0.332725i
$707$	−16.8411	−	16.8411i	−0.633376	−	0.633376i
$708$	19.5196	−	2.40091i	0.733590	−	0.0902316i
$709$	20.0553	−	34.7369i	0.753194	−	1.30457i	−0.193073	−	0.981184i	$-0.561846\pi$
$709$	20.0553	−	34.7369i	0.753194	−	1.30457i	0.946267	−	0.323386i	$-0.104821\pi$
$710$		0			0
$711$	11.5206	−	11.1348i	0.432056	−	0.417586i
$712$	2.32902	−	8.69201i	0.0872836	−	0.325747i
$713$	1.59620	+	0.427700i	0.0597780	+	0.0160175i
$714$	−33.9496	−	4.76396i	−1.27053	−	0.178287i
$715$		0			0
$716$			5.44145i			0.203357i
$717$	13.6271	+	5.78094i	0.508912	+	0.215893i
$718$	−34.1528	−	9.15120i	−1.27457	−	0.341520i
$719$	−5.00371	+	8.66669i	−0.186607	+	0.323213i	−0.944117	−	0.329611i	$-0.893082\pi$
$719$	−5.00371	+	8.66669i	−0.186607	+	0.323213i	0.757510	+	0.652824i	$0.226416\pi$
$720$		0			0
$721$	−32.3000	−	18.6484i	−1.20292	−	0.694503i
$722$	21.1599	−	5.66978i	0.787490	−	0.211007i
$723$	−28.5728	+	21.5407i	−1.06264	+	0.801107i
$724$	9.73892	+	5.62277i	0.361944	+	0.208968i
$725$		0			0
$726$	−33.8505	+	13.6849i	−1.25631	+	0.507893i
$727$	6.32057	+	6.32057i	0.234417	+	0.234417i	0.814534	−	0.580116i	$-0.196993\pi$
$727$	6.32057	+	6.32057i	0.234417	+	0.234417i	−0.580116	+	0.814534i	$0.696993\pi$
$728$	4.50487	+	0.810558i	0.166962	+	0.0300413i
$729$	20.0419	−	18.0921i	0.742292	−	0.670076i
$730$		0			0
$731$	42.8756	−	24.7542i	1.58581	−	0.915568i
$732$	−0.980265	−	7.96963i	−0.0362316	−	0.294566i
$733$	−23.4455	−	23.4455i	−0.865981	−	0.865981i	0.126044	−	0.992025i	$-0.459772\pi$
$733$	−23.4455	−	23.4455i	−0.865981	−	0.865981i	−0.992025	+	0.126044i	$0.959772\pi$
$734$	−50.9712	−	29.4282i	−1.88138	−	1.08622i
$735$		0			0
$736$			39.4298i			1.45340i
$737$	0.183800	+	0.685952i	0.00677037	+	0.0252674i
$738$	−55.8810	−	33.5444i	−2.05701	−	1.23479i
$739$	−3.41081	−	5.90770i	−0.125469	−	0.217318i	0.796447	−	0.604708i	$-0.206710\pi$
$739$	−3.41081	−	5.90770i	−0.125469	−	0.217318i	−0.921916	+	0.387390i	$0.873377\pi$
$740$		0			0
$741$	14.3826	+	9.40738i	0.528359	+	0.345589i
$742$	−21.2628	−	21.2628i	−0.780580	−	0.780580i
$743$	−18.6549	−	4.99856i	−0.684381	−	0.183379i	−0.100157	−	0.994972i	$-0.531935\pi$
$743$	−18.6549	−	4.99856i	−0.684381	−	0.183379i	−0.584224	+	0.811592i	$0.698601\pi$
$744$	0.312740	−	0.126432i	0.0114656	−	0.00463524i
$745$		0			0
$746$	47.1359			1.72577
$747$	11.0503	+	0.188191i	0.404308	+	0.00688555i
$748$	−0.530860	+	0.142243i	−0.0194102	+	0.00520094i
$749$		−	30.5614i		−	1.11669i
$750$		0			0
$751$	−19.9689	−	34.5872i	−0.728677	−	1.26211i	−0.957442	−	0.288624i	$-0.906802\pi$
$751$	−19.9689	−	34.5872i	−0.728677	−	1.26211i	0.228765	−	0.973482i	$-0.426531\pi$
$752$	1.06198	−	3.96337i	0.0387265	−	0.144529i
$753$	28.7190	−	21.6508i	1.04658	−	0.789001i
$754$	15.9196	−	11.0644i	0.579757	−	0.402941i
$755$		0			0
$756$	−1.86729	−	17.6579i	−0.0679126	−	0.642212i
$757$	10.8250	−	40.3994i	0.393440	−	1.46834i	−0.430980	−	0.902362i	$-0.641832\pi$
$757$	10.8250	−	40.3994i	0.393440	−	1.46834i	0.824420	−	0.565978i	$-0.191501\pi$
$758$	41.8188	−	11.2053i	1.51893	−	0.406996i
$759$	−0.0823774	+	0.587050i	−0.00299011	+	0.0213086i
$760$		0			0
$761$	0.0958031	−	0.165936i	0.00347286	−	0.00601517i	−0.864284	−	0.503005i	$-0.832228\pi$
$761$	0.0958031	−	0.165936i	0.00347286	−	0.00601517i	0.867757	+	0.496989i	$0.165561\pi$
$762$	−1.55001	+	1.16853i	−0.0561508	+	0.0423314i
$763$	8.51155	+	31.7655i	0.308139	+	1.14999i
$764$	1.31611	+	2.27956i	0.0476151	+	0.0824717i
$765$		0			0
$766$	−3.51561			−0.127024
$767$	24.0501	+	4.32732i	0.868400	+	0.156250i
$768$	20.7202	+	27.4845i	0.747676	+	0.991761i
$769$	4.49084	+	7.77836i	0.161944	+	0.280495i	0.935566	−	0.353153i	$-0.114890\pi$
$769$	4.49084	+	7.77836i	0.161944	+	0.280495i	−0.773622	+	0.633647i	$0.781557\pi$
$770$		0			0
$771$	−24.8115	+	31.7711i	−0.893563	+	1.14421i
$772$	3.63014	−	3.63014i	0.130652	−	0.130652i
$773$	−4.59533	−	17.1500i	−0.165282	−	0.616842i	−0.998004	−	0.0631504i	$-0.979885\pi$
$773$	−4.59533	−	17.1500i	−0.165282	−	0.616842i	0.832722	−	0.553692i	$-0.186781\pi$
$774$	39.0948	+	40.4494i	1.40523	+	1.45393i
$775$		0			0
$776$	3.97685	+	2.29603i	0.142761	+	0.0824228i
$777$	−4.09892	−	1.73886i	−0.147048	−	0.0623814i
$778$	7.59490	−	28.3446i	0.272290	−	1.01620i
$779$	31.1860			1.11736
$780$		0			0
$781$	−0.895297			−0.0320362
$782$	13.2633	−	49.4992i	0.474293	−	1.77009i
$783$	11.3317	+	9.16432i	0.404963	+	0.327506i
$784$	−11.1743	−	6.45149i	−0.399082	−	0.230410i
$785$		0			0
$786$	11.7949	−	15.1033i	0.420709	−	0.538718i
$787$	8.41390	+	31.4011i	0.299923	+	1.11933i	0.937228	+	0.348717i	$0.113382\pi$
$787$	8.41390	+	31.4011i	0.299923	+	1.11933i	−0.637305	+	0.770612i	$0.719951\pi$
$788$	−8.83012	+	8.83012i	−0.314560	+	0.314560i
$789$	30.9398	+	24.1623i	1.10149	+	0.860200i
$790$		0			0
$791$	−10.8945	−	18.8698i	−0.387362	−	0.670931i
$792$	0.0587118	+	0.105813i	0.00208623	+	0.00375990i
$793$	1.76680	−	9.81941i	0.0627409	−	0.348698i
$794$	15.3666			0.545341
$795$		0			0
$796$	4.20984	+	7.29165i	0.149214	+	0.258446i
$797$	−5.63774	−	21.0403i	−0.199699	−	0.745287i	−0.991000	−	0.133860i	$-0.957263\pi$
$797$	−5.63774	−	21.0403i	−0.199699	−	0.745287i	0.791301	−	0.611427i	$-0.209404\pi$
$798$	11.2203	+	14.8833i	0.397194	+	0.526862i
$799$	−2.28536	+	3.95837i	−0.0808503	+	0.140037i
$800$		0			0
$801$	−41.6993	−	11.9379i	−1.47337	−	0.421806i
$802$	−7.94777	+	2.12960i	−0.280645	+	0.0751987i
$803$	0.175292	−	0.654199i	0.00618593	−	0.0230862i
$804$	29.4787	−	11.9174i	1.03963	−	0.420296i
$805$		0			0
$806$	−2.15539	+	0.180992i	−0.0759205	+	0.00637516i
$807$	9.55203	+	12.6704i	0.336247	+	0.446018i
$808$	1.88096	−	7.01984i	0.0661720	−	0.246957i
$809$	−9.05040	−	15.6758i	−0.318195	−	0.551130i	0.661916	−	0.749578i	$-0.269743\pi$
$809$	−9.05040	−	15.6758i	−0.318195	−	0.551130i	−0.980112	+	0.198448i	$0.936410\pi$
$810$		0			0
$811$			23.9232i			0.840056i	0.907511	+	0.420028i	$0.137980\pi$
$811$			23.9232i			0.840056i	−0.907511	+	0.420028i	$0.862020\pi$
$812$	9.25772	−	2.48060i	0.324882	−	0.0870520i
$813$	1.80358	+	14.6632i	0.0632542	+	0.514261i
$814$	−0.156590			−0.00548848
$815$		0			0
$816$	−14.9309	−	36.9327i	−0.522686	−	1.29290i
$817$	−25.9999	−	6.96666i	−0.909623	−	0.243733i
$818$	51.0116	+	51.0116i	1.78358	+	1.78358i
$819$	4.27617	−	21.6444i	0.149421	−	0.756315i
$820$		0			0
$821$	−9.77979	−	16.9391i	−0.341317	−	0.591179i	0.643360	−	0.765563i	$-0.277540\pi$
$821$	−9.77979	−	16.9391i	−0.341317	−	0.591179i	−0.984678	+	0.174385i	$0.944206\pi$
$822$	22.2292	+	9.43015i	0.775331	+	0.328914i
$823$	1.15104	+	4.29575i	0.0401228	+	0.149740i	0.983081	−	0.183170i	$-0.0586360\pi$
$823$	1.15104	+	4.29575i	0.0401228	+	0.149740i	−0.942958	+	0.332911i	$0.891969\pi$
$824$		−	11.3807i		−	0.396466i
$825$		0			0
$826$	22.9515	+	13.2510i	0.798584	+	0.461063i
$827$	−0.374621	−	0.374621i	−0.0130268	−	0.0130268i	0.700563	−	0.713590i	$-0.252932\pi$
$827$	−0.374621	−	0.374621i	−0.0130268	−	0.0130268i	−0.713590	+	0.700563i	$0.752932\pi$
$828$	26.5385	+	0.451962i	0.922275	+	0.0157067i
$829$	−29.3227	+	16.9295i	−1.01842	+	0.587985i	−0.913646	−	0.406511i	$-0.866745\pi$
$829$	−29.3227	+	16.9295i	−1.01842	+	0.587985i	−0.104774	+	0.994496i	$0.533412\pi$
$830$		0			0
$831$	5.30052	−	37.7733i	0.183873	−	1.31034i
$832$	−6.38298	−	17.7294i	−0.221290	−	0.614658i
$833$	10.1634	+	10.1634i	0.352141	+	0.352141i
$834$	2.66168	+	6.58386i	0.0921664	+	0.227980i
$835$		0			0
$836$	0.258771	+	0.149402i	0.00894979	+	0.00516717i
$837$	−0.583663	−	1.51760i	−0.0201743	−	0.0524561i
$838$	−22.4098	+	6.00469i	−0.774134	+	0.207429i
$839$	−26.5275	−	15.3157i	−0.915831	−	0.528755i	−0.0335282	−	0.999438i	$-0.510674\pi$
$839$	−26.5275	−	15.3157i	−0.915831	−	0.528755i	−0.882303	+	0.470683i	$0.844008\pi$
$840$		0			0
$841$	10.5668	−	18.3022i	0.364372	−	0.631111i
$842$	41.2828	+	11.0617i	1.42270	+	0.381211i
$843$	−0.774650	+	1.82604i	−0.0266804	+	0.0628921i
$844$			24.6161i			0.847323i
$845$		0			0
$846$	−4.99295	−	1.42941i	−0.171661	−	0.0491442i
$847$	−21.6639	−	5.80483i	−0.744381	−	0.199456i
$848$	9.04366	−	33.7514i	0.310560	−	1.15903i
$849$	10.4058	−	13.3246i	0.357126	−	0.457300i
$850$		0			0
$851$	3.32782	−	5.76395i	0.114076	−	0.197586i
$852$	4.89374	+	39.7865i	0.167657	+	1.36306i
$853$	−5.73121	−	5.73121i	−0.196233	−	0.196233i	0.602150	−	0.798383i	$-0.294311\pi$
$853$	−5.73121	−	5.73121i	−0.196233	−	0.196233i	−0.798383	+	0.602150i	$0.794311\pi$
$854$	5.41026	−	9.37085i	0.185135	−	0.320664i
$855$		0			0
$856$	8.07610	−	4.66274i	0.276035	−	0.159369i
$857$	13.1772	−	13.1772i	0.450125	−	0.450125i	−0.445271	−	0.895396i	$-0.646893\pi$
$857$	13.1772	−	13.1772i	0.450125	−	0.450125i	0.895396	+	0.445271i	$0.146893\pi$
$858$	−0.158834	−	0.759492i	−0.00542250	−	0.0259286i
$859$		−	11.2173i		−	0.382729i	−0.981519	−	0.191365i	$-0.938709\pi$
$859$		−	11.2173i		−	0.382729i	0.981519	−	0.191365i	$-0.0612913\pi$
$860$		0			0
$861$	−15.0054	−	37.1170i	−0.511383	−	1.26494i
$862$	0.732248	−	0.196205i	0.0249405	−	0.00668278i
$863$	−9.74312	+	9.74312i	−0.331659	+	0.331659i	−0.853216	−	0.521557i	$-0.825351\pi$
$863$	−9.74312	+	9.74312i	−0.331659	+	0.331659i	0.521557	+	0.853216i	$0.325351\pi$
$864$	31.3726	−	22.8241i	1.06732	−	0.776491i
$865$		0			0
$866$	−21.5180			−0.731210
$867$	1.82278	+	14.8194i	0.0619049	+	0.503292i
$868$	−1.03287	−	0.276757i	−0.0350580	−	0.00939376i
$869$	0.299754	−	0.173063i	0.0101685	−	0.00587076i
$870$		0			0
$871$	39.3694	−	3.30591i	1.33398	−	0.112017i
$872$	−7.09569	+	7.09569i	−0.240290	+	0.240290i
$873$	11.3920	−	18.9777i	0.385560	−	0.642296i
$874$	−24.1287	+	13.9307i	−0.816166	+	0.471214i
$875$		0			0
$876$	−30.0304	−	4.21400i	−1.01463	−	0.142378i
$877$	−13.5555	−	50.5897i	−0.457736	−	1.70829i	−0.679919	−	0.733287i	$-0.737985\pi$
$877$	−13.5555	−	50.5897i	−0.457736	−	1.70829i	0.222183	−	0.975005i	$-0.428682\pi$
$878$	−10.6470	−	39.7351i	−0.359319	−	1.34100i
$879$	−38.4924	−	5.40142i	−1.29832	−	0.182186i
$880$		0			0
$881$	6.05038	−	3.49319i	0.203842	−	0.117688i	−0.394604	−	0.918851i	$-0.629118\pi$
$881$	6.05038	−	3.49319i	0.203842	−	0.117688i	0.598446	+	0.801163i	$0.295785\pi$
$882$	−8.40551	+	14.0026i	−0.283028	+	0.471491i
$883$	−40.5116	+	40.5116i	−1.36332	+	1.36332i	−0.493681	+	0.869643i	$0.664349\pi$
$883$	−40.5116	+	40.5116i	−1.36332	+	1.36332i	−0.869643	+	0.493681i	$0.835651\pi$
$884$	2.55845	+	30.4681i	0.0860501	+	1.02475i
$885$		0			0
$886$	37.1925	−	21.4731i	1.24951	−	0.721403i
$887$	−3.23586	−	0.867046i	−0.108650	−	0.0291126i	0.204085	−	0.978953i	$-0.434578\pi$
$887$	−3.23586	−	0.867046i	−0.108650	−	0.0291126i	−0.312734	+	0.949841i	$0.601245\pi$
$888$	−0.165862	−	1.34847i	−0.00556596	−	0.0452517i
$889$	−1.19237			−0.0399908
$890$		0			0
$891$	0.514776	−	0.274272i	0.0172456	−	0.00918846i
$892$	4.94855	−	4.94855i	0.165690	−	0.165690i
$893$	2.40037	−	0.643178i	0.0803254	−	0.0215231i
$894$	−3.62502	−	8.96675i	−0.121239	−	0.299893i
$895$		0			0
$896$			10.0221i			0.334816i
$897$	31.3318	+	10.2940i	1.04614	+	0.343707i
$898$	27.2459	−	27.2459i	0.909208	−	0.909208i
$899$	0.760064	−	0.438823i	0.0253495	−	0.0146356i
$900$		0			0
$901$	−19.4618	+	33.7088i	−0.648366	+	1.12300i
$902$	−0.995609	−	0.995609i	−0.0331501	−	0.0331501i
$903$	4.21849	+	34.2967i	0.140383	+	1.14132i
$904$	3.32432	−	5.75789i	0.110565	−	0.191505i
$905$		0			0
$906$	−24.7971	+	31.7527i	−0.823829	+	1.05491i
$907$	−0.640173	+	2.38916i	−0.0212566	+	0.0793307i	−0.975739	−	0.218935i	$-0.929742\pi$
$907$	−0.640173	+	2.38916i	−0.0212566	+	0.0793307i	0.954483	+	0.298266i	$0.0964083\pi$
$908$	−38.0163	−	10.1864i	−1.26162	−	0.338049i
$909$	−33.6772	−	9.64131i	−1.11700	−	0.319782i
$910$		0			0
$911$			38.3512i			1.27063i	0.772253	+	0.635316i	$0.219130\pi$
$911$			38.3512i			1.27063i	−0.772253	+	0.635316i	$0.780870\pi$
$912$	−8.45849	+	19.9387i	−0.280089	+	0.660237i
$913$	0.230619	+	0.0617942i	0.00763238	+	0.00204509i
$914$	−22.5082	+	38.9854i	−0.744506	+	1.28952i
$915$		0			0
$916$	−16.5621	−	9.56216i	−0.547229	−	0.315943i
$917$	11.3702	−	3.04664i	0.375478	−	0.100609i
$918$	−47.0620	+	18.0998i	−1.55328	+	0.597382i
$919$	−8.63426	−	4.98500i	−0.284818	−	0.164440i	0.350785	−	0.936456i	$-0.385915\pi$
$919$	−8.63426	−	4.98500i	−0.284818	−	0.164440i	−0.635603	+	0.772016i	$0.719248\pi$
$920$		0			0
$921$	−7.96380	−	19.6991i	−0.262416	−	0.649106i
$922$	−6.66059	−	6.66059i	−0.219355	−	0.219355i
$923$	−8.82033	+	49.0211i	−0.290325	+	1.61355i
$924$	0.0533051	−	0.379870i	0.00175361	−	0.0124968i
$925$		0			0
$926$	19.1981	−	11.0840i	0.630889	−	0.364244i
$927$	−54.8484	−	0.934092i	−1.80146	−	0.0306796i
$928$	14.8076	+	14.8076i	0.486085	+	0.486085i
$929$	34.8259	+	20.1067i	1.14260	+	0.659681i	0.947073	−	0.321017i	$-0.104025\pi$
$929$	34.8259	+	20.1067i	1.14260	+	0.659681i	0.195527	+	0.980698i	$0.437358\pi$
$930$		0			0
$931$		−	7.81455i		−	0.256111i
$932$	−5.32761	−	19.8829i	−0.174512	−	0.651287i
$933$	6.16980	+	2.61738i	0.201990	+	0.0856892i
$934$	−25.0597	−	43.4047i	−0.819979	−	1.42024i
$935$		0			0
$936$	6.37210	−	2.17225i	0.208279	−	0.0710023i
$937$	27.2652	+	27.2652i	0.890716	+	0.890716i	0.994590	−	0.103874i	$-0.0331239\pi$
$937$	27.2652	+	27.2652i	0.890716	+	0.890716i	−0.103874	+	0.994590i	$0.533124\pi$
$938$	41.3878	+	11.0898i	1.35136	+	0.362096i
$939$	20.6571	+	51.0970i	0.674120	+	1.66749i
$940$		0			0
$941$	−18.4961			−0.602957			−0.301479	−	0.953473i	$-0.597480\pi$
$941$	−18.4961			−0.602957			−0.301479	+	0.953473i	$0.597480\pi$
$942$	0.469324	+	3.81565i	0.0152914	+	0.124320i
$943$	57.8060	−	15.4891i	1.88242	−	0.504393i
$944$			30.7959i			1.00232i
$945$		0			0
$946$	0.607634	+	1.05245i	0.0197559	+	0.0342182i
$947$	7.58936	−	28.3239i	0.246621	−	0.920403i	−0.725941	−	0.687757i	$-0.758595\pi$
$947$	7.58936	−	28.3239i	0.246621	−	0.920403i	0.972562	−	0.232645i	$-0.0747381\pi$
$948$	−9.32930	−	12.3749i	−0.303002	−	0.401919i
$949$	−34.0931	−	16.0430i	−1.10671	−	0.520779i
$950$		0			0
$951$	−2.89433	+	1.17010i	−0.0938550	+	0.0379431i
$952$	1.66310	−	6.20678i	0.0539015	−	0.201163i
$953$	−6.32491	+	1.69476i	−0.204884	+	0.0548985i	−0.359801	−	0.933029i	$-0.617156\pi$
$953$	−6.32491	+	1.69476i	−0.204884	+	0.0548985i	0.154917	+	0.987927i	$0.450489\pi$
$954$	−42.5191	−	12.1726i	−1.37661	−	0.394103i
$955$		0			0
$956$	7.15900	−	12.3998i	0.231539	−	0.401037i
$957$	0.189527	+	0.251400i	0.00612654	+	0.00812660i
$958$	9.23657	+	34.4714i	0.298420	+	1.11372i
$959$	7.41624	+	12.8453i	0.239483	+	0.414797i
$960$		0			0
$961$	30.9021			0.996841
$962$	−1.54270	+	8.57393i	−0.0497387	+	0.276435i
$963$	−21.8088	−	39.3048i	−0.702780	−	1.26658i
$964$	17.3057	+	29.9744i	0.557380	+	0.965410i
$965$		0			0
$966$	28.1898	+	22.0147i	0.906992	+	0.708310i
$967$	28.2870	−	28.2870i	0.909648	−	0.909648i	−0.0865951	−	0.996244i	$-0.527599\pi$
$967$	28.2870	−	28.2870i	0.909648	−	0.909648i	0.996244	+	0.0865951i	$0.0275986\pi$
$968$	−1.77128	−	6.61049i	−0.0569310	−	0.212469i
$969$	14.8498	−	19.0152i	0.477044	−	0.610856i
$970$		0			0
$971$	−18.4125	−	10.6304i	−0.590884	−	0.341147i	0.174563	−	0.984646i	$-0.444149\pi$
$971$	−18.4125	−	10.6304i	−0.590884	−	0.341147i	−0.765447	+	0.643499i	$0.777482\pi$
$972$	−15.0023	−	21.3772i	−0.481199	−	0.685673i
$973$	−1.12903	+	4.21359i	−0.0361949	+	0.135081i
$974$	64.3428			2.06168
$975$		0			0
$976$	12.5736			0.402473
$977$	−7.09314	+	26.4720i	−0.226930	+	0.846913i	0.754692	+	0.656079i	$0.227786\pi$
$977$	−7.09314	+	26.4720i	−0.226930	+	0.846913i	−0.981622	+	0.190835i	$0.938881\pi$
$978$	55.6645	+	23.6142i	1.77995	+	0.755099i
$979$	−0.811485	−	0.468511i	−0.0259352	−	0.0149737i
$980$		0			0
$981$	33.6147	+	34.7795i	1.07324	+	1.11042i
$982$	15.3060	+	57.1228i	0.488435	+	1.82286i
$983$	−8.33022	+	8.33022i	−0.265693	+	0.265693i	−0.827362	−	0.561669i	$-0.810159\pi$
$983$	−8.33022	+	8.33022i	−0.265693	+	0.265693i	0.561669	+	0.827362i	$0.310159\pi$
$984$	7.51909	−	9.62821i	0.239700	−	0.306936i
$985$		0			0
$986$	−13.6082	−	23.5701i	−0.433374	−	0.750625i
$987$	−1.92045	−	2.54740i	−0.0611287	−	0.0810848i
$988$	10.7297	−	12.6969i	0.341358	−	0.403942i
$989$	−51.6532			−1.64248
$990$		0			0
$991$	−11.6131	−	20.1145i	−0.368903	−	0.638959i	0.620491	−	0.784213i	$-0.286933\pi$
$991$	−11.6131	−	20.1145i	−0.368903	−	0.638959i	−0.989394	+	0.145255i	$0.953600\pi$
$992$	−0.604700	−	2.25677i	−0.0191992	−	0.0716525i
$993$	4.32949	−	3.26395i	0.137392	−	0.103578i
$994$	−27.0094	+	46.7817i	−0.856688	+	1.48383i
$995$		0			0
$996$	1.48553	−	10.5864i	0.0470707	−	0.335442i
$997$	−16.0824	+	4.30927i	−0.509335	+	0.136476i	−0.504329	−	0.863512i	$-0.668260\pi$
$997$	−16.0824	+	4.30927i	−0.509335	+	0.136476i	−0.00500582	+	0.999987i	$0.501593\pi$
$998$	−5.15386	+	19.2345i	−0.163143	+	0.608856i
$999$	−6.51246	+	0.688680i	−0.206045	+	0.0217889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.257.20		96
3.2	odd	2	inner	975.2.bn.d.257.5		96
5.2	odd	4		195.2.bf.a.23.20	yes	96
5.3	odd	4	inner	975.2.bn.d.218.5		96
5.4	even	2		195.2.bf.a.62.5	yes	96
13.4	even	6	inner	975.2.bn.d.407.20		96
15.2	even	4		195.2.bf.a.23.5	yes	96
15.8	even	4	inner	975.2.bn.d.218.20		96
15.14	odd	2		195.2.bf.a.62.20	yes	96
39.17	odd	6	inner	975.2.bn.d.407.5		96
65.4	even	6		195.2.bf.a.17.5	✓	96
65.17	odd	12		195.2.bf.a.173.20	yes	96
65.43	odd	12	inner	975.2.bn.d.368.5		96
195.17	even	12		195.2.bf.a.173.5	yes	96
195.134	odd	6		195.2.bf.a.17.20	yes	96
195.173	even	12	inner	975.2.bn.d.368.20		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.5	✓	96	65.4	even	6
195.2.bf.a.17.20	yes	96	195.134	odd	6
195.2.bf.a.23.5	yes	96	15.2	even	4
195.2.bf.a.23.20	yes	96	5.2	odd	4
195.2.bf.a.62.5	yes	96	5.4	even	2
195.2.bf.a.62.20	yes	96	15.14	odd	2
195.2.bf.a.173.5	yes	96	195.17	even	12
195.2.bf.a.173.20	yes	96	65.17	odd	12
975.2.bn.d.218.5		96	5.3	odd	4	inner
975.2.bn.d.218.20		96	15.8	even	4	inner
975.2.bn.d.257.5		96	3.2	odd	2	inner
975.2.bn.d.257.20		96	1.1	even	1	trivial
975.2.bn.d.368.5		96	65.43	odd	12	inner
975.2.bn.d.368.20		96	195.173	even	12	inner
975.2.bn.d.407.5		96	39.17	odd	6	inner
975.2.bn.d.407.20		96	13.4	even	6	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.496187 - 1.85180i) q^{2} +(0.676428 - 1.59450i) q^{3} +(-1.45090 - 0.837676i) q^{4} +(-2.61706 - 2.04378i) q^{6} +(-0.527913 - 1.97020i) q^{7} +(0.440097 - 0.440097i) q^{8} +(-2.08489 - 2.15713i) q^{9} +(-0.0324046 - 0.0561264i) q^{11} +(-2.31710 + 1.74683i) q^{12} +(-3.39239 + 1.22133i) q^{13} -3.91035 q^{14} +(-2.27195 - 3.93513i) q^{16} +(1.31006 + 4.88919i) q^{17} +(-5.02907 + 2.79045i) q^{18} +(1.37598 - 2.38327i) q^{19} +(-3.49859 - 0.490937i) q^{21} +(-0.120014 + 0.0321575i) q^{22} +(1.36681 - 5.10100i) q^{23} +(-0.404043 - 0.999430i) q^{24} +(0.578399 + 6.88803i) q^{26} +(-4.84984 + 1.86522i) q^{27} +(-0.884440 + 3.30077i) q^{28} +(-1.40236 - 2.42895i) q^{29} +0.312918i q^{31} +(-7.21201 + 1.93245i) q^{32} +(-0.111413 + 0.0137038i) q^{33} +9.70382 q^{34} +(1.21798 + 4.87624i) q^{36} +(1.21737 + 0.326192i) q^{37} +(-3.73059 - 3.73059i) q^{38} +(-0.347286 + 6.23533i) q^{39} +(5.66614 + 9.81404i) q^{41} +(-2.64507 + 6.23507i) q^{42} +(-2.53152 - 9.44778i) q^{43} +0.108578i q^{44} +(-8.76782 - 5.06210i) q^{46} +(0.638524 + 0.638524i) q^{47} +(-7.81140 + 0.960802i) q^{48} +(2.45919 - 1.41981i) q^{49} +(8.68200 + 1.21830i) q^{51} +(5.94510 + 1.06970i) q^{52} +(5.43756 + 5.43756i) q^{53} +(1.04758 + 9.90641i) q^{54} +(-1.09941 - 0.634745i) q^{56} +(-2.86938 - 3.80612i) q^{57} +(-5.19376 + 1.39166i) q^{58} +(-5.86942 - 3.38871i) q^{59} +(-1.38357 + 2.39642i) q^{61} +(0.579461 + 0.155266i) q^{62} +(-3.14934 + 5.24643i) q^{63} +5.22623i q^{64} +(-0.0299051 + 0.213114i) q^{66} +(-10.5842 - 2.83602i) q^{67} +(2.19480 - 8.19111i) q^{68} +(-7.20902 - 5.62984i) q^{69} +(6.90717 - 11.9636i) q^{71} +(-1.86690 - 0.0317942i) q^{72} +(7.38949 + 7.38949i) q^{73} +(1.20808 - 2.09246i) q^{74} +(-3.99282 + 2.30525i) q^{76} +(-0.0934734 + 0.0934734i) q^{77} +(11.3742 + 3.73700i) q^{78} +5.34069i q^{79} +(-0.306459 + 8.99478i) q^{81} +(20.9851 - 5.62293i) q^{82} +(-2.60495 + 2.60495i) q^{83} +(4.66484 + 3.64298i) q^{84} -18.7515 q^{86} +(-4.82157 + 0.593053i) q^{87} +(-0.0389622 - 0.0104399i) q^{88} +(12.5211 - 7.22908i) q^{89} +(4.19716 + 6.03893i) q^{91} +(-6.25608 + 6.25608i) q^{92} +(0.498950 + 0.211667i) q^{93} +(1.49924 - 0.865588i) q^{94} +(-1.79710 + 12.8068i) q^{96} +(1.90959 + 7.12670i) q^{97} +(-1.40899 - 5.25841i) q^{98} +(-0.0535122 + 0.186919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more