LMFDB - Embedded newform 975.2.bn.d.218.20

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)

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")

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);

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			218.20
Character	$\chi$	$=$	975.218
Dual form			975.2.bn.d.407.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.85180 + 0.496187i) q^{2} +(-1.71910 - 0.211449i) q^{3} +(1.45090 + 0.837676i) q^{4} +(-3.07850 - 1.24455i) q^{6} +(-1.97020 + 0.527913i) q^{7} +(-0.440097 - 0.440097i) q^{8} +(2.91058 + 0.727001i) q^{9} +(0.0324046 + 0.0561264i) q^{11} +(-2.31710 - 1.74683i) q^{12} +(-1.22133 - 3.39239i) q^{13} -3.91035 q^{14} +(-2.27195 - 3.93513i) q^{16} +(-4.88919 + 1.31006i) q^{17} +(5.02907 + 2.79045i) q^{18} +(-1.37598 + 2.38327i) q^{19} +(3.49859 - 0.490937i) q^{21} +(0.0321575 + 0.120014i) q^{22} +(-5.10100 - 1.36681i) q^{23} +(0.663511 + 0.849627i) q^{24} +(-0.578399 - 6.88803i) q^{26} +(-4.84984 - 1.86522i) q^{27} +(-3.30077 - 0.884440i) q^{28} +(-1.40236 - 2.42895i) q^{29} +0.312918i q^{31} +(-1.93245 - 7.21201i) q^{32} +(-0.0438388 - 0.103339i) q^{33} -9.70382 q^{34} +(3.61396 + 3.49292i) q^{36} +(0.326192 - 1.21737i) q^{37} +(-3.73059 + 3.73059i) q^{38} +(1.38227 + 6.09010i) q^{39} +(-5.66614 - 9.81404i) q^{41} +(6.72227 + 0.826839i) q^{42} +(9.44778 - 2.53152i) q^{43} +0.108578i q^{44} +(-8.76782 - 5.06210i) q^{46} +(-0.638524 + 0.638524i) q^{47} +(3.07362 + 7.24527i) q^{48} +(-2.45919 + 1.41981i) q^{49} +(8.68200 - 1.21830i) q^{51} +(1.06970 - 5.94510i) q^{52} +(5.43756 - 5.43756i) q^{53} +(-8.05541 - 5.86044i) q^{54} +(1.09941 + 0.634745i) q^{56} +(2.86938 - 3.80612i) q^{57} +(-1.39166 - 5.19376i) q^{58} +(-5.86942 - 3.38871i) q^{59} +(-1.38357 + 2.39642i) q^{61} +(-0.155266 + 0.579461i) q^{62} +(-6.11821 + 0.104196i) q^{63} -5.22623i q^{64} +(-0.0299051 - 0.213114i) q^{66} +(-2.83602 + 10.5842i) q^{67} +(-8.19111 - 2.19480i) q^{68} +(8.48010 + 3.42828i) q^{69} +(-6.90717 + 11.9636i) q^{71} +(-0.960986 - 1.60089i) 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} +(-0.462143 + 11.9635i) q^{78} -5.34069i q^{79} +(7.94294 + 4.23199i) q^{81} +(-5.62293 - 20.9851i) q^{82} +(2.60495 + 2.60495i) q^{83} +(5.48733 + 2.21838i) q^{84} +18.7515 q^{86} +(1.89719 + 4.47213i) q^{87} +(0.0104399 - 0.0389622i) q^{88} +(12.5211 - 7.22908i) q^{89} +(4.19716 + 6.03893i) q^{91} +(-6.25608 - 6.25608i) q^{92} +(0.0661662 - 0.537937i) q^{93} +(-1.49924 + 0.865588i) q^{94} +(1.79710 + 12.8068i) q^{96} +(7.12670 - 1.90959i) q^{97} +(-5.25841 + 1.40899i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.85180	+	0.496187i	1.30942	+	0.350857i	0.845004	−	0.534761i	$-0.179598\pi$
$2$	1.85180	+	0.496187i	1.30942	+	0.350857i	0.464414	+	0.885618i	$0.346265\pi$
$3$	−1.71910	−	0.211449i	−0.992520	−	0.122080i
$3$	−1.71910	−	0.211449i	−0.992520	−	0.122080i
$4$	1.45090	+	0.837676i	0.725448	+	0.418838i
$5$		0			0
$5$		0			0
$6$	−3.07850	−	1.24455i	−1.25679	−	0.508087i
$7$	−1.97020	+	0.527913i	−0.744665	+	0.199532i	−0.611150	−	0.791514i	$-0.709293\pi$
$7$	−1.97020	+	0.527913i	−0.744665	+	0.199532i	−0.133515	+	0.991047i	$0.542626\pi$
$8$	−0.440097	−	0.440097i	−0.155598	−	0.155598i
$9$	2.91058	+	0.727001i	0.970193	+	0.242334i
$10$		0			0
$11$	0.0324046	+	0.0561264i	0.00977036	+	0.0169228i	0.870869	−	0.491515i	$-0.163557\pi$
$11$	0.0324046	+	0.0561264i	0.00977036	+	0.0169228i	−0.861099	+	0.508438i	$0.830223\pi$
$12$	−2.31710	−	1.74683i	−0.668890	−	0.504268i
$13$	−1.22133	−	3.39239i	−0.338737	−	0.940881i
$13$	−1.22133	−	3.39239i	−0.338737	−	0.940881i
$14$	−3.91035			−1.04508
$15$		0			0
$16$	−2.27195	−	3.93513i	−0.567988	−	0.983783i
$17$	−4.88919	+	1.31006i	−1.18580	+	0.317735i	−0.797226	−	0.603681i	$-0.793700\pi$
$17$	−4.88919	+	1.31006i	−1.18580	+	0.317735i	−0.388577	+	0.921416i	$0.627033\pi$
$18$	5.02907	+	2.79045i	1.18536	+	0.657715i
$19$	−1.37598	+	2.38327i	−0.315672	+	0.546760i	−0.979580	−	0.201054i	$-0.935563\pi$
$19$	−1.37598	+	2.38327i	−0.315672	+	0.546760i	0.663908	+	0.747814i	$0.268897\pi$
$20$		0			0
$21$	3.49859	−	0.490937i	0.763454	−	0.107131i
$22$	0.0321575	+	0.120014i	0.00685601	+	0.0255870i
$23$	−5.10100	−	1.36681i	−1.06363	−	0.284999i	−0.315758	−	0.948840i	$-0.602259\pi$
$23$	−5.10100	−	1.36681i	−1.06363	−	0.284999i	−0.747874	+	0.663840i	$0.768925\pi$
$24$	0.663511	+	0.849627i	0.135439	+	0.173429i
$25$		0			0
$26$	−0.578399	−	6.88803i	−0.113433	−	1.35085i
$27$	−4.84984	−	1.86522i	−0.933352	−	0.358962i
$28$	−3.30077	−	0.884440i	−0.623788	−	0.167143i
$29$	−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	$0.991054\pi$
$32$	−1.93245	−	7.21201i	−0.341613	−	1.27492i
$33$	−0.0438388	−	0.103339i	−0.00763135	−	0.0179889i
$34$	−9.70382			−1.66419
$35$		0			0
$36$	3.61396	+	3.49292i	0.602326	+	0.582154i
$37$	0.326192	−	1.21737i	0.0536257	−	0.200134i	−0.933916	−	0.357493i	$-0.883631\pi$
$37$	0.326192	−	1.21737i	0.0536257	−	0.200134i	0.987541	+	0.157359i	$0.0502981\pi$
$38$	−3.73059	+	3.73059i	−0.605181	+	0.605181i
$39$	1.38227	+	6.09010i	0.221341	+	0.975197i
$40$		0			0
$41$	−5.66614	−	9.81404i	−0.884903	−	1.53270i	−0.845825	−	0.533460i	$-0.820891\pi$
$41$	−5.66614	−	9.81404i	−0.884903	−	1.53270i	−0.0390773	−	0.999236i	$-0.512442\pi$
$42$	6.72227	+	0.826839i	1.03727	+	0.127584i
$43$	9.44778	−	2.53152i	1.44077	−	0.386054i	0.547968	−	0.836499i	$-0.315401\pi$
$43$	9.44778	−	2.53152i	1.44077	−	0.386054i	0.892804	+	0.450445i	$0.148735\pi$
$44$			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	$-0.770979\pi$
$47$	−0.638524	+	0.638524i	−0.0931382	+	0.0931382i	0.659003	+	0.752141i	$0.270979\pi$
$48$	3.07362	+	7.24527i	0.443639	+	1.04576i
$49$	−2.45919	+	1.41981i	−0.351313	+	0.202830i
$50$		0			0
$51$	8.68200	−	1.21830i	1.21572	−	0.170596i
$52$	1.06970	−	5.94510i	0.148340	−	0.824436i
$53$	5.43756	−	5.43756i	0.746906	−	0.746906i	−0.226991	−	0.973897i	$-0.572889\pi$
$53$	5.43756	−	5.43756i	0.746906	−	0.746906i	0.973897	+	0.226991i	$0.0728887\pi$
$54$	−8.05541	−	5.86044i	−1.09620	−	0.797505i
$55$		0			0
$56$	1.09941	+	0.634745i	0.146915	+	0.0848214i
$57$	2.86938	−	3.80612i	0.380059	−	0.504133i
$58$	−1.39166	−	5.19376i	−0.182734	−	0.681974i
$59$	−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	$0.223354\pi$
$62$	−0.155266	+	0.579461i	−0.0197188	+	0.0735916i
$63$	−6.11821	+	0.104196i	−0.770822	+	0.0131274i
$64$		−	5.22623i		−	0.653279i
$65$		0			0
$66$	−0.0299051	−	0.213114i	−0.00368107	−	0.0262326i
$67$	−2.83602	+	10.5842i	−0.346475	+	1.29306i	0.544405	+	0.838823i	$0.316756\pi$
$67$	−2.83602	+	10.5842i	−0.346475	+	1.29306i	−0.890880	+	0.454239i	$0.849911\pi$
$68$	−8.19111	−	2.19480i	−0.993318	−	0.266159i
$69$	8.48010	+	3.42828i	1.02088	+	0.412716i
$70$		0			0
$71$	−6.90717	+	11.9636i	−0.819730	+	1.41981i	0.0861512	+	0.996282i	$0.472543\pi$
$71$	−6.90717	+	11.9636i	−0.819730	+	1.41981i	−0.905881	+	0.423532i	$0.860790\pi$
$72$	−0.960986	−	1.60089i	−0.113253	−	0.188666i
$73$	−7.38949	+	7.38949i	−0.864874	+	0.864874i	−0.991900	−	0.127025i	$-0.959457\pi$
$73$	−7.38949	+	7.38949i	−0.864874	+	0.864874i	0.127025	+	0.991900i	$0.459457\pi$
$74$	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
$78$	−0.462143	+	11.9635i	−0.0523274	+	1.35460i
$79$		−	5.34069i		−	0.600875i	−0.953802	−	0.300437i	$-0.902867\pi$
$79$		−	5.34069i		−	0.600875i	0.953802	−	0.300437i	$-0.0971326\pi$
$80$		0			0
$81$	7.94294	+	4.23199i	0.882549	+	0.470221i
$82$	−5.62293	−	20.9851i	−0.620949	−	2.31741i
$83$	2.60495	+	2.60495i	0.285931	+	0.285931i	0.835469	−	0.549538i	$-0.185196\pi$
$83$	2.60495	+	2.60495i	0.285931	+	0.285931i	−0.549538	+	0.835469i	$0.685196\pi$
$84$	5.48733	+	2.21838i	0.598717	+	0.242045i
$85$		0			0
$86$	18.7515			2.02202
$87$	1.89719	+	4.47213i	0.203400	+	0.479462i
$88$	0.0104399	−	0.0389622i	0.00111290	−	0.00415339i
$89$	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
$93$	0.0661662	−	0.537937i	0.00686112	−	0.0557814i
$94$	−1.49924	+	0.865588i	−0.154635	+	0.0892786i
$95$		0			0
$96$	1.79710	+	12.8068i	0.183416	+	1.30708i
$97$	7.12670	−	1.90959i	0.723607	−	0.193890i	0.121827	−	0.992551i	$-0.461125\pi$
$97$	7.12670	−	1.90959i	0.723607	−	0.193890i	0.601781	+	0.798661i	$0.294458\pi$
$98$	−5.25841	+	1.40899i	−0.531179	+	0.142329i
$99$	0.0535122	+	0.186919i	0.00537818	+	0.0187860i
$100$		0			0
$101$	−10.1123	+	5.83835i	−1.00621	+	0.580938i	−0.910081	−	0.414431i	$-0.863981\pi$
$101$	−10.1123	+	5.83835i	−1.00621	+	0.580938i	−0.0961330	+	0.995368i	$0.530647\pi$
$102$	16.6818	+	2.05186i	1.65174	+	0.203165i
$103$	12.9298	+	12.9298i	1.27401	+	1.27401i	0.943966	+	0.330042i	$0.107063\pi$
$103$	12.9298	+	12.9298i	1.27401	+	1.27401i	0.330042	+	0.943966i	$0.392937\pi$
$104$	−0.955477	+	2.03049i	−0.0936922	+	0.199106i
$105$		0			0
$106$	12.7673	−	7.37120i	1.24007	−	0.715955i
$107$	−3.87796	+	14.4728i	−0.374897	+	1.39913i	0.478598	+	0.878034i	$0.341145\pi$
$107$	−3.87796	+	14.4728i	−0.374897	+	1.39913i	−0.853495	+	0.521101i	$0.825522\pi$
$108$	−5.47416	−	6.76884i	−0.526752	−	0.651332i
$109$	16.1230			1.54430			0.772152	−	0.635437i	$-0.219180\pi$
$109$	16.1230			1.54430			0.772152	+	0.635437i	$0.219180\pi$
$110$		0			0
$111$	−0.818167	+	2.02380i	−0.0776570	+	0.192090i
$112$	6.55360	+	6.55360i	0.619257	+	0.619257i
$113$	−2.76481	−	10.3184i	−0.260092	−	0.970675i	−0.965187	−	0.261562i	$-0.915762\pi$
$113$	−2.76481	−	10.3184i	−0.260092	−	0.970675i	0.705095	−	0.709113i	$-0.250904\pi$
$114$	7.20206	−	5.62441i	0.674535	−	0.526774i
$115$		0			0
$116$		−	4.69888i		−	0.436280i
$117$	−1.08851	−	10.7617i	−0.100633	−	0.994924i
$118$	−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
$123$	7.66547	+	18.0694i	0.691172	+	1.62926i
$124$	−0.262124	+	0.454012i	−0.0235394	+	0.0407715i
$125$		0			0
$126$	−11.3814	−	2.84283i	−1.01393	−	0.253259i
$127$	−0.564662	−	0.151301i	−0.0501056	−	0.0134258i	0.233679	−	0.972314i	$-0.424923\pi$
$127$	−0.564662	−	0.151301i	−0.0501056	−	0.0134258i	−0.283785	+	0.958888i	$0.591590\pi$
$128$	−1.27172	+	4.74611i	−0.112405	+	0.419500i
$129$	−16.7769	+	2.35421i	−1.47713	+	0.207277i
$130$		0			0
$131$		−	5.77110i		−	0.504223i	−0.967698	−	0.252112i	$-0.918875\pi$
$131$		−	5.77110i		−	0.504223i	0.967698	−	0.252112i	$-0.0811250\pi$
$132$	0.0229587	−	0.186656i	0.00199830	−	0.0162463i
$133$	1.45280	−	5.42192i	0.125974	−	0.470140i
$134$	−10.5035	+	18.1925i	−0.907361	+	1.57159i
$135$		0			0
$136$	2.72827	+	1.57517i	0.233947	+	0.135069i
$137$	−1.88211	−	7.02411i	−0.160799	−	0.600111i	−0.998539	−	0.0540406i	$-0.982790\pi$
$137$	−1.88211	−	7.02411i	−0.160799	−	0.600111i	0.837740	−	0.546070i	$-0.183877\pi$
$138$	14.0023	+	10.5562i	1.19196	+	0.898602i
$139$	1.85213	+	1.06933i	0.157096	+	0.0906994i	0.576487	−	0.817106i	$-0.304423\pi$
$139$	1.85213	+	1.06933i	0.157096	+	0.0906994i	−0.419391	+	0.907806i	$0.637756\pi$
$140$		0			0
$141$	1.23270	−	0.962668i	0.103812	−	0.0810713i
$142$	−18.7268	+	18.7268i	−1.57152	+	1.57152i
$143$	0.150826	−	0.178478i	0.0126127	−	0.0149251i
$144$	−3.75184	−	13.1052i	−0.312654	−	1.09210i
$145$		0			0
$146$	−17.3504	+	10.0173i	−1.43593	+	0.829034i
$147$	4.52780	−	1.92080i	0.373446	−	0.158425i
$148$	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	$-0.164350\pi$
$152$	1.65444	−	0.443305i	0.134192	−	0.0359568i
$153$	−15.1828	+	0.258570i	−1.22746	+	0.0209041i
$154$	−0.126713	−	0.219474i	−0.0102109	−	0.0176857i
$155$		0			0
$156$	−3.09599	+	9.99400i	−0.247878	+	0.800161i
$157$	−0.818660	+	0.818660i	−0.0653362	+	0.0653362i	−0.739020	−	0.673684i	$-0.764711\pi$
$157$	−0.818660	+	0.818660i	−0.0653362	+	0.0653362i	0.673684	+	0.739020i	$0.264711\pi$
$158$	2.64998	−	9.88987i	0.210821	−	0.786796i
$159$	−10.4974	+	8.19792i	−0.832502	+	0.650137i
$160$		0			0
$161$	10.7715			0.848916
$162$	12.6088	+	11.7780i	0.990644	+	0.925364i
$163$	−4.71302	−	17.5892i	−0.369152	−	1.37769i	−0.861704	−	0.507411i	$-0.830603\pi$
$163$	−4.71302	−	17.5892i	−0.369152	−	1.37769i	0.492552	−	0.870283i	$-0.336064\pi$
$164$		−	18.9856i		−	1.48252i
$165$		0			0
$166$	3.53130	+	6.11638i	0.274082	+	0.474723i
$167$	−5.95097	−	1.59456i	−0.460500	−	0.123391i	0.0211085	−	0.999777i	$-0.493280\pi$
$167$	−5.95097	−	1.59456i	−0.460500	−	0.123391i	−0.481608	+	0.876387i	$0.659947\pi$
$168$	−1.75578	−	1.32366i	−0.135461	−	0.102122i
$169$	−10.0167	+	8.28650i	−0.770514	+	0.637423i
$170$		0			0
$171$	−5.73754	+	5.93636i	−0.438761	+	0.453965i
$172$	15.8283	+	4.24119i	1.20690	+	0.323388i
$173$	0.870829	+	3.24998i	0.0662079	+	0.247091i	0.991096	−	0.133148i	$-0.0425085\pi$
$173$	0.870829	+	3.24998i	0.0662079	+	0.247091i	−0.924888	+	0.380239i	$0.875842\pi$
$174$	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
$178$	26.7736	−	7.17396i	2.00676	−	0.537711i
$179$	−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	$0.580254\pi$
$182$	4.77584	+	13.2655i	0.354009	+	0.983301i
$183$	2.88522	−	3.82712i	0.213281	−	0.282909i
$184$	1.64341	+	2.84646i	0.121154	+	0.209844i
$185$		0			0
$186$	0.389444	−	0.963318i	0.0285554	−	0.0706339i
$187$	−0.231961	−	0.231961i	−0.0169627	−	0.0169627i
$188$	−1.46131	+	0.391556i	−0.106577	+	0.0285572i
$189$	10.5398	+	1.11457i	0.766659	+	0.0810727i
$190$		0			0
$191$	1.36065	+	0.785571i	0.0984531	+	0.0568419i	0.548418	−	0.836204i	$-0.315230\pi$
$191$	1.36065	+	0.785571i	0.0984531	+	0.0568419i	−0.449965	+	0.893046i	$0.648564\pi$
$192$	−1.10508	+	8.98439i	−0.0797523	+	0.648393i
$193$	−2.95990	−	0.793102i	−0.213058	−	0.0570888i	0.150711	−	0.988578i	$-0.451844\pi$
$193$	−2.95990	−	0.793102i	−0.213058	−	0.0570888i	−0.363769	+	0.931489i	$0.618510\pi$
$194$	14.1447			1.01553
$195$		0			0
$196$	−4.75737			−0.339812
$197$	7.19978	+	1.92918i	0.512963	+	0.137448i	0.506010	−	0.862528i	$-0.331120\pi$
$197$	7.19978	+	1.92918i	0.512963	+	0.137448i	0.00695355	+	0.999976i	$0.497787\pi$
$198$	0.00634703	+	0.372687i	0.000451064	+	0.0264857i
$199$	4.35231	+	2.51281i	0.308527	+	0.178128i	0.646267	−	0.763111i	$-0.276329\pi$
$199$	4.35231	+	2.51281i	0.308527	+	0.178128i	−0.337740	+	0.941239i	$0.609662\pi$
$200$		0			0
$201$	7.11340	−	17.5955i	0.501740	−	1.24109i
$202$	−21.6229	+	5.79383i	−1.52138	+	0.407653i
$203$	4.04520	+	4.04520i	0.283917	+	0.283917i
$204$	13.6172	+	5.50508i	0.953396	+	0.385432i
$205$		0			0
$206$	17.5277	+	30.3589i	1.22121	+	2.11520i
$207$	−13.8532	−	7.68664i	−0.962863	−	0.534258i
$208$	−10.5747	+	12.5135i	−0.733225	+	0.867653i
$209$	−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	$-0.335454\pi$
$212$	12.4442	−	3.33443i	0.854674	−	0.229009i
$213$	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
$217$	−0.165194	−	0.616511i	−0.0112141	−	0.0418515i
$218$	29.8565	+	8.00003i	2.02214	+	0.541831i
$219$	14.2657	−	11.1407i	0.963989	−	0.752822i
$220$		0			0
$221$	10.4156	+	14.9861i	0.700627	+	1.00807i
$222$	−2.51926	+	3.34170i	−0.169082	+	0.224280i
$223$	−4.03489	−	1.08114i	−0.270196	−	0.0723988i	0.121177	−	0.992631i	$-0.461333\pi$
$223$	−4.03489	−	1.08114i	−0.270196	−	0.0723988i	−0.391373	+	0.920232i	$0.628000\pi$
$224$	7.61463	+	13.1889i	0.508774	+	0.881222i
$225$		0			0
$226$		−	20.4795i		−	1.36227i
$227$	6.08018	+	22.6915i	0.403556	+	1.50609i	0.806704	+	0.590956i	$0.201249\pi$
$227$	6.08018	+	22.6915i	0.403556	+	1.50609i	−0.403148	+	0.915135i	$0.632084\pi$
$228$	7.35147	−	3.11867i	0.486863	−	0.206539i
$229$	−11.4151			−0.754332			−0.377166	−	0.926146i	$-0.623101\pi$
$229$	−11.4151			−0.754332			−0.377166	+	0.926146i	$0.623101\pi$
$230$		0			0
$231$	0.140925	+	0.180455i	0.00927218	+	0.0118730i
$232$	−0.451802	+	1.68615i	−0.0296622	+	0.110701i
$233$	8.68792	−	8.68792i	0.569164	−	0.569164i	−0.362730	−	0.931894i	$-0.618155\pi$
$233$	8.68792	−	8.68792i	0.569164	−	0.569164i	0.931894	+	0.362730i	$0.118155\pi$
$234$	3.32413	−	20.4687i	0.217305	−	1.33808i
$235$		0			0
$236$	−5.67728	−	9.83333i	−0.369559	−	0.640096i
$237$	−1.12928	+	9.18116i	−0.0733548	+	0.596380i
$238$	19.1185	−	5.12277i	1.23927	−	0.332060i
$239$			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
$243$	−12.7598	−	8.95472i	−0.818543	−	0.574445i
$244$	−4.01485	+	2.31797i	−0.257024	+	0.148393i
$245$		0			0
$246$	5.22909	+	37.2643i	0.333395	+	2.37589i
$247$	9.76553	+	1.75710i	0.621366	+	0.111802i
$248$	0.137714	−	0.137714i	0.00874487	−	0.00874487i
$249$	−3.92735	−	5.02897i	−0.248885	−	0.318698i
$250$		0			0
$251$	−17.9829	−	10.3824i	−1.13507	−	0.655333i	−0.189865	−	0.981810i	$-0.560805\pi$
$251$	−17.9829	−	10.3824i	−1.13507	−	0.655333i	−0.945205	+	0.326477i	$0.894138\pi$
$252$	−8.96417	−	4.97390i	−0.564690	−	0.313326i
$253$	−0.0885818	−	0.330592i	−0.00556909	−	0.0207841i
$254$	−0.970565	−	0.560356i	−0.0608987	−	0.0351599i
$255$		0			0
$256$	−9.93615	+	17.2099i	−0.621009	+	1.07562i
$257$	6.02371	−	22.4808i	0.375749	−	1.40231i	−0.476499	−	0.879175i	$-0.658095\pi$
$257$	6.02371	−	22.4808i	0.375749	−	1.40231i	0.852248	−	0.523138i	$-0.175239\pi$
$258$	−32.2356	−	3.96498i	−2.00690	−	0.246849i
$259$			2.57066i			0.159733i
$260$		0			0
$261$	−2.31582	−	8.08917i	−0.143345	−	0.500707i
$262$	2.86355	−	10.6869i	0.176911	−	0.660239i
$263$	21.8926	+	5.86610i	1.34996	+	0.361719i	0.860118	−	0.510095i	$-0.170390\pi$
$263$	21.8926	+	5.86610i	1.34996	+	0.361719i	0.489837	+	0.871814i	$0.337056\pi$
$264$	−0.0261857	+	0.0647723i	−0.00161162	+	0.00398646i
$265$		0			0
$266$	5.38057	−	9.31942i	0.329904	−	0.571410i
$267$	−23.0536	+	9.77990i	−1.41086	+	0.598520i
$268$	−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
$273$	−5.93840	−	11.2690i	−0.359408	−	0.682030i
$274$		−	13.9411i		−	0.842213i
$275$		0			0
$276$	9.43196	+	12.0776i	0.567737	+	0.726989i
$277$	−5.69974	−	21.2717i	−0.342464	−	1.27809i	−0.895547	−	0.444967i	$-0.853215\pi$
$277$	−5.69974	−	21.2717i	−0.342464	−	1.27809i	0.553083	−	0.833126i	$-0.313451\pi$
$278$	2.89919	+	2.89919i	0.173882	+	0.173882i
$279$	−0.227492	+	0.910774i	−0.0136196	+	0.0545266i
$280$		0			0
$281$	1.14521			0.0683174			0.0341587	−	0.999416i	$-0.489125\pi$
$281$	1.14521			0.0683174			0.0341587	+	0.999416i	$0.489125\pi$
$282$	2.76037	−	1.17102i	0.164378	−	0.0697330i
$283$	−2.52631	+	9.42831i	−0.150174	+	0.560455i	0.849297	+	0.527915i	$0.177026\pi$
$283$	−2.52631	+	9.42831i	−0.150174	+	0.560455i	−0.999470	+	0.0325397i	$0.989640\pi$
$284$	−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
$288$	−0.381414	−	22.3960i	−0.0224750	−	1.31970i
$289$	7.46552	−	4.31022i	0.439148	−	0.253542i
$290$		0			0
$291$	−12.6553	+	1.77584i	−0.741865	+	0.104102i
$292$	−16.9114	+	4.53139i	−0.989664	+	0.265180i
$293$	−21.6767	+	5.80825i	−1.26636	+	0.339321i	−0.828637	−	0.559786i	$-0.810883\pi$
$293$	−21.6767	+	5.80825i	−1.26636	+	0.339321i	−0.437728	+	0.899108i	$0.644217\pi$
$294$	9.33763	−	1.31030i	0.544582	−	0.0764181i
$295$		0			0
$296$	−0.679316	+	0.392203i	−0.0394844	+	0.0227963i
$297$	−0.0524689	−	0.332646i	−0.00304455	−	0.0193021i
$298$	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
$302$	6.02022	−	22.4678i	0.346425	−	1.29288i
$303$	18.6186	−	7.89845i	1.06961	−	0.453754i
$304$	12.5047			0.717191
$305$		0			0
$306$	−28.2437	−	7.05469i	−1.61459	−	0.403290i
$307$	−8.67444	−	8.67444i	−0.495076	−	0.495076i	0.414825	−	0.909901i	$-0.363843\pi$
$307$	−8.67444	−	8.67444i	−0.495076	−	0.495076i	−0.909901	+	0.414825i	$0.863843\pi$
$308$	−0.0573199	−	0.213921i	−0.00326610	−	0.0121893i
$309$	−19.4935	−	24.9615i	−1.10895	−	1.42001i
$310$		0			0
$311$		−	3.86942i		−	0.219415i	−0.993964	−	0.109707i	$-0.965009\pi$
$311$		−	3.86942i		−	0.219415i	0.993964	−	0.109707i	$-0.0349913\pi$
$312$	2.07190	−	3.28857i	0.117298	−	0.186179i
$313$	−22.5004	−	22.5004i	−1.27180	−	1.27180i	−0.945143	−	0.326658i	$-0.894078\pi$
$313$	−22.5004	−	22.5004i	−1.27180	−	1.27180i	−0.326658	−	0.945143i	$-0.605922\pi$
$314$	−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	$-0.733881\pi$
$317$	1.27451	−	1.27451i	0.0715836	−	0.0715836i	0.741992	+	0.670409i	$0.233881\pi$
$318$	−23.5068	+	9.97217i	−1.31820	+	0.559212i
$319$	0.0908856	−	0.157419i	0.00508862	−	0.00881375i
$320$		0			0
$321$	9.72684	−	24.0601i	0.542899	−	1.34290i
$322$	19.9467	+	5.34470i	1.11159	+	0.297849i
$323$	3.60522	−	13.4549i	0.200600	−	0.748650i
$324$	7.97935	+	12.7938i	0.443297	+	0.710766i
$325$		0			0
$326$		−	34.9102i		−	1.93350i
$327$	−27.7170	−	3.40919i	−1.53275	−	0.188529i
$328$	−1.82548	+	6.81278i	−0.100795	+	0.376173i
$329$	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	$0.639248\pi$
$332$	1.59741	+	5.96162i	0.0876693	+	0.327186i
$333$	1.83444	−	3.30610i	0.100526	−	0.181173i
$334$	−10.2288	−	5.90559i	−0.559694	−	0.323139i
$335$		0			0
$336$	−9.88052	−	12.6520i	−0.539026	−	0.690224i
$337$	20.2542	−	20.2542i	1.10332	−	1.10332i	0.109311	−	0.994008i	$-0.465136\pi$
$337$	20.2542	−	20.2542i	1.10332	−	1.10332i	0.994008	−	0.109311i	$-0.0348643\pi$
$338$	−22.6605	+	10.3748i	−1.23257	+	0.564312i
$339$	2.57116	+	18.3230i	0.139646	+	0.995167i
$340$		0			0
$341$	−0.0175630	+	0.0101400i	−0.000951090	+	0.000549112i
$342$	−13.5703	+	8.14603i	−0.733798	+	0.440487i
$343$	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
$347$	−31.0059	+	8.30799i	−1.66448	+	0.445996i	−0.963615	−	0.267296i	$-0.913870\pi$
$347$	−31.0059	+	8.30799i	−1.66448	+	0.445996i	−0.700867	+	0.713292i	$0.747203\pi$
$348$	−0.993572	+	8.07782i	−0.0532611	+	0.433017i
$349$	−9.95791	−	17.2476i	−0.533035	−	0.923243i	−0.999256	−	0.0385748i	$-0.987718\pi$
$349$	−9.95791	−	17.2476i	−0.533035	−	0.923243i	0.466221	−	0.884668i	$-0.345615\pi$
$350$		0			0
$351$	−0.404297	+	18.7306i	−0.0215798	+	0.999767i
$352$	0.342164	−	0.342164i	0.0182374	−	0.0182374i
$353$	1.37817	−	5.14341i	0.0733527	−	0.273756i	−0.919502	−	0.393085i	$-0.871408\pi$
$353$	1.37817	−	5.14341i	0.0733527	−	0.273756i	0.992855	+	0.119329i	$0.0380744\pi$
$354$	13.8515	+	17.7369i	0.736202	+	0.942707i
$355$		0			0
$356$	24.2225			1.28379
$357$	−16.4621	+	6.98363i	−0.871267	+	0.369613i
$358$	−1.61159	−	6.01454i	−0.0851752	−	0.317878i
$359$		−	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
$362$	−12.4299	−	3.33058i	−0.653301	−	0.175051i
$363$	−11.4650	+	15.2078i	−0.601755	+	0.798203i
$364$	1.03098	+	12.2777i	0.0540380	+	0.643528i
$365$		0			0
$366$	7.24180	−	5.65544i	0.378535	−	0.295615i
$367$	−29.6544	−	7.94586i	−1.54794	−	0.414770i	−0.619122	−	0.785295i	$-0.712511\pi$
$367$	−29.6544	−	7.94586i	−1.54794	−	0.414770i	−0.928823	+	0.370524i	$0.879178\pi$
$368$	6.21064	+	23.1784i	0.323752	+	1.20826i
$369$	−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
$373$	−23.7490	+	6.36353i	−1.22968	+	0.329491i	−0.814454	−	0.580228i	$-0.802963\pi$
$373$	−23.7490	+	6.36353i	−1.22968	+	0.329491i	−0.415224	+	0.909719i	$0.636297\pi$
$374$	−0.314449	−	0.544641i	−0.0162597	−	0.0281627i
$375$		0			0
$376$	0.562024			0.0289842
$377$	−6.52722	+	7.72391i	−0.336169	+	0.397802i
$378$	18.9646	+	7.29367i	0.975432	+	0.375146i
$379$	−11.2914	−	19.5573i	−0.580002	−	1.00459i	−0.995478	−	0.0949885i	$-0.969719\pi$
$379$	−11.2914	−	19.5573i	−0.580002	−	1.00459i	0.415477	−	0.909604i	$-0.363615\pi$
$380$		0			0
$381$	0.938715	+	0.379497i	0.0480918	+	0.0194422i
$382$	2.12985	+	2.12985i	0.108973	+	0.108973i
$383$	−1.77131	+	0.474622i	−0.0905099	+	0.0242521i	−0.303790	−	0.952739i	$-0.598252\pi$
$383$	−1.77131	+	0.474622i	−0.0905099	+	0.0242521i	0.213280	+	0.976991i	$0.431585\pi$
$384$	3.18976	−	7.89011i	0.162777	−	0.402640i
$385$		0			0
$386$	−5.08760	−	2.93733i	−0.258952	−	0.149506i
$387$	29.3389	−	0.499655i	1.49138	−	0.0253989i
$388$	11.9397	+	3.19924i	0.606148	+	0.162417i
$389$	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
$392$	1.70714	+	0.457426i	0.0862234	+	0.0231035i
$393$	−1.22029	+	9.92107i	−0.0615556	+	0.500452i
$394$	12.3753	+	7.14488i	0.623459	+	0.359954i
$395$		0			0
$396$	−0.0789365	+	0.316025i	−0.00396671	+	0.0158809i
$397$	7.74235	−	2.07456i	0.388578	−	0.104119i	−0.0592405	−	0.998244i	$-0.518868\pi$
$397$	7.74235	−	2.07456i	0.388578	−	0.104119i	0.447818	+	0.894125i	$0.352201\pi$
$398$	6.81277	+	6.81277i	0.341493	+	0.341493i
$399$	−3.64396	+	9.01360i	−0.182426	+	0.451244i
$400$		0			0
$401$	2.14596	+	3.71692i	0.107164	+	0.185614i	0.914620	−	0.404314i	$-0.132490\pi$
$401$	2.14596	+	3.71692i	0.107164	+	0.185614i	−0.807456	+	0.589928i	$0.799156\pi$
$402$	21.9032	−	29.0537i	1.09243	−	1.44907i
$403$	1.06154	−	0.382178i	0.0528792	−	0.0190376i
$404$	−19.5626			−0.973275
$405$		0			0
$406$	5.48370	+	9.49805i	0.272152	+	0.471380i
$407$	0.0788966	−	0.0211403i	0.00391076	−	0.00104789i
$408$	−4.35709	−	3.28475i	−0.215708	−	0.162619i
$409$	18.8150	−	32.5886i	0.930343	−	1.61140i	0.147607	−	0.989046i	$-0.452843\pi$
$409$	18.8150	−	32.5886i	0.930343	−	1.61140i	0.782735	−	0.622355i	$-0.213824\pi$
$410$		0			0
$411$	1.75028	+	12.4731i	0.0863349	+	0.615252i
$412$	7.92881	+	29.5907i	0.390624	+	1.45783i
$413$	13.3529	+	3.57789i	0.657051	+	0.176056i
$414$	−21.8393	−	21.1079i	−1.07334	−	1.03740i
$415$		0			0
$416$	−22.1058	+	15.3639i	−1.08383	+	0.753278i
$417$	−2.95789	−	2.22991i	−0.144848	−	0.109199i
$418$	−0.330273	−	0.0884963i	−0.0161542	−	0.00432850i
$419$	−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	$0.817191\pi$
$422$	−7.29054	−	27.2087i	−0.354898	−	1.32450i
$423$	−2.32268	+	1.39427i	−0.112933	+	0.0677915i
$424$	−4.78611			−0.232434
$425$		0			0
$426$	36.1530	−	28.2335i	1.75162	−	1.36792i
$427$	1.46081	−	5.45183i	0.0706937	−	0.263833i
$428$	−17.7500	+	17.7500i	−0.857979	+	0.857979i
$429$	−0.297024	+	0.274929i	−0.0143404	+	0.0132737i
$430$		0			0
$431$	−0.197713	−	0.342449i	−0.00952349	−	0.0164952i	0.861224	−	0.508225i	$-0.169698\pi$
$431$	−0.197713	−	0.342449i	−0.00952349	−	0.0164952i	−0.870748	+	0.491730i	$0.836365\pi$
$432$	3.67869	+	23.3225i	0.176991	+	1.12210i
$433$	10.8417	−	2.90501i	0.521017	−	0.139606i	0.0112798	−	0.999936i	$-0.496409\pi$
$433$	10.8417	−	2.90501i	0.521017	−	0.139606i	0.509737	+	0.860330i	$0.329743\pi$
$434$		−	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
$438$	31.9451	−	13.5519i	1.52640	−	0.647535i
$439$	−18.5828	+	10.7288i	−0.886911	+	0.512058i	−0.872931	−	0.487844i	$-0.837783\pi$
$439$	−18.5828	+	10.7288i	−0.886911	+	0.512058i	−0.0139799	+	0.999902i	$0.504450\pi$
$440$		0			0
$441$	−8.18987	+	2.34464i	−0.389994	+	0.111650i
$442$	11.8516	+	32.9192i	0.563724	+	1.56581i
$443$	15.8402	−	15.8402i	0.752590	−	0.752590i	−0.222372	−	0.974962i	$-0.571380\pi$
$443$	15.8402	−	15.8402i	0.752590	−	0.752590i	0.974962	+	0.222372i	$0.0713799\pi$
$444$	−2.88236	+	2.25096i	−0.136791	+	0.106826i
$445$		0			0
$446$	−6.93533	−	4.00412i	−0.328398	−	0.189600i
$447$	−4.02843	−	3.03698i	−0.190538	−	0.143644i
$448$	2.75900	+	10.2967i	0.130350	+	0.486474i
$449$	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
$452$	4.63203	−	17.2870i	0.217872	−	0.813111i
$453$	−2.56550	+	20.8577i	−0.120538	+	0.979982i
$454$			45.0370i			2.11369i
$455$		0			0
$456$	−2.93787	+	0.412255i	−0.137578	+	0.0193056i
$457$	−6.07741	+	22.6812i	−0.284289	+	1.06098i	0.665068	+	0.746783i	$0.268402\pi$
$457$	−6.07741	+	22.6812i	−0.284289	+	1.06098i	−0.949357	+	0.314199i	$0.898264\pi$
$458$	−21.1385	−	5.66403i	−0.987735	−	0.264663i
$459$	26.1553	+	2.76588i	1.22083	+	0.129100i
$460$		0			0
$461$	−2.45668	+	4.25509i	−0.114419	+	0.198179i	−0.917547	−	0.397627i	$-0.869834\pi$
$461$	−2.45668	+	4.25509i	−0.114419	+	0.198179i	0.803128	+	0.595806i	$0.203167\pi$
$462$	0.171425	+	0.404090i	0.00797541	+	0.0188000i
$463$	−8.17642	+	8.17642i	−0.379991	+	0.379991i	−0.871099	−	0.491108i	$-0.836592\pi$
$463$	−8.17642	+	8.17642i	−0.379991	+	0.379991i	0.491108	+	0.871099i	$0.336592\pi$
$464$	−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	0.990795	−	0.135368i	$-0.0432217\pi$
$467$	18.4859	+	18.4859i	0.855427	+	0.855427i	−0.135368	+	0.990795i	$0.543222\pi$
$468$	7.43553	−	16.5260i	0.343707	−	0.763915i
$469$		−	22.3501i		−	1.03203i
$470$		0			0
$471$	1.58046	−	1.23425i	0.0728237	−	0.0568712i
$472$	1.09175	+	4.07447i	0.0502519	+	0.187543i
$473$	0.448237	+	0.448237i	0.0206100	+	0.0206100i
$474$	−6.64677	+	16.4413i	−0.305296	+	0.755174i
$475$		0			0
$476$	17.2968			0.792797
$477$	19.7796	−	11.8733i	0.905644	−	0.543643i
$478$	−4.24055	+	15.8260i	−0.193958	+	0.723862i
$479$	−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
$483$	−18.5173	−	2.27763i	−0.842567	−	0.103636i
$484$	15.9538	−	9.21091i	0.725171	−	0.418678i
$485$		0			0
$486$	−19.1854	−	22.9136i	−0.870266	−	1.03938i
$487$	32.4186	−	8.68654i	1.46903	−	0.393625i	0.566430	−	0.824110i	$-0.308324\pi$
$487$	32.4186	−	8.68654i	1.46903	−	0.393625i	0.902598	+	0.430485i	$0.141657\pi$
$488$	1.66356	−	0.445751i	0.0753060	−	0.0201782i
$489$	4.38291	+	31.2341i	0.198202	+	1.41245i
$490$		0			0
$491$	26.7145	−	15.4236i	1.20561	−	0.696059i	0.243812	−	0.969822i	$-0.421602\pi$
$491$	26.7145	−	15.4236i	1.20561	−	0.696059i	0.961797	+	0.273764i	$0.0882687\pi$
$492$	−4.01447	+	32.6380i	−0.180986	+	1.47143i
$493$	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
$497$	7.29277	−	27.2170i	0.327125	−	1.22085i
$498$	−4.77733	−	11.2613i	−0.214077	−	0.504632i
$499$	10.3869			0.464982			0.232491	−	0.972598i	$-0.425312\pi$
$499$	10.3869			0.464982			0.232491	+	0.972598i	$0.425312\pi$
$500$		0			0
$501$	9.89311	+	3.99952i	0.441992	+	0.178685i
$502$	−28.1490	−	28.1490i	−1.25635	−	1.25635i
$503$	1.77393	+	6.62041i	0.0790957	+	0.295189i	0.994131	−	0.108185i	$-0.0345039\pi$
$503$	1.77393	+	6.62041i	0.0790957	+	0.295189i	−0.915035	+	0.403374i	$0.867837\pi$
$504$	2.73846	+	2.64675i	0.121981	+	0.117896i
$505$		0			0
$506$		−	0.656142i		−	0.0291691i
$507$	18.9718	−	12.1273i	0.842568	−	0.538591i
$508$	−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
$513$	11.1186	−	8.99197i	0.490899	−	0.397005i
$514$	22.3094	−	38.6409i	0.984024	−	1.70438i
$515$		0			0
$516$	−26.3136	−	10.6379i	−1.15839	−	0.468307i
$517$	−0.0565292	−	0.0151469i	−0.00248615	−	0.000666162i
$518$	−1.27553	+	4.76033i	−0.0560434	+	0.209157i
$519$	−0.809834	−	5.77116i	−0.0355478	−	0.253326i
$520$		0			0
$521$		−	15.0847i		−	0.660871i	−0.943829	−	0.330435i	$-0.892804\pi$
$521$		−	15.0847i		−	0.660871i	0.943829	−	0.330435i	$-0.107196\pi$
$522$	−0.274677	−	16.1286i	−0.0120223	−	0.705929i
$523$	−0.415581	+	1.55097i	−0.0181721	+	0.0678191i	−0.974416	−	0.224750i	$-0.927843\pi$
$523$	−0.415581	+	1.55097i	−0.0181721	+	0.0678191i	0.956244	+	0.292569i	$0.0945101\pi$
$524$	4.83431	−	8.37327i	0.211188	−	0.365788i
$525$		0			0
$526$	37.6299	+	21.7257i	1.64074	+	0.947283i
$527$	−0.409940	−	1.52992i	−0.0178573	−	0.0666443i
$528$	−0.307052	+	0.407292i	−0.0133627	+	0.0177251i
$529$	4.23345	+	2.44419i	0.184063	+	0.106269i
$530$		0			0
$531$	−14.6198	−	14.1302i	−0.634446	−	0.613198i
$532$	6.64967	−	6.64967i	0.288300	−	0.288300i
$533$	−26.3729	+	31.2080i	−1.14234	+	1.35177i
$534$	−47.5433	+	6.67148i	−2.05740	+	0.288703i
$535$		0			0
$536$	5.90618	−	3.40994i	0.255108	−	0.147287i
$537$	2.19700	+	5.17887i	0.0948077	+	0.223485i
$538$	−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	$0.795710\pi$
$542$	−15.7951	+	4.23228i	−0.678458	+	0.181792i
$543$	11.5392	+	1.41932i	0.495193	+	0.0609087i
$544$	18.8963	+	32.7293i	0.810171	+	1.40326i
$545$		0			0
$546$	−5.40517	−	23.8144i	−0.231320	−	1.01916i
$547$	4.94438	−	4.94438i	0.211406	−	0.211406i	−0.593458	−	0.804865i	$-0.702238\pi$
$547$	4.94438	−	4.94438i	0.211406	−	0.211406i	0.804865	+	0.593458i	$0.202238\pi$
$548$	3.15319	−	11.7679i	0.134697	−	0.502698i
$549$	−5.76920	+	5.96911i	−0.246224	+	0.254755i
$550$		0			0
$551$	7.71847			0.328818
$552$	−2.22329	−	5.24084i	−0.0946295	−	0.223065i
$553$	2.81942	+	10.5222i	0.119894	+	0.447450i
$554$		−	42.2190i		−	1.79371i
$555$		0			0
$556$	1.79150	+	3.10298i	0.0759767	+	0.131595i
$557$	−1.98454	−	0.531756i	−0.0840877	−	0.0225312i	0.216530	−	0.976276i	$-0.430526\pi$
$557$	−1.98454	−	0.531756i	−0.0840877	−	0.0225312i	−0.300618	+	0.953745i	$0.597193\pi$
$558$	−0.873183	+	1.57369i	−0.0369648	+	0.0666195i
$559$	−20.1268	−	28.9588i	−0.851274	−	1.22482i
$560$		0			0
$561$	0.349715	+	0.447811i	0.0147650	+	0.0189066i
$562$	2.12069	+	0.568237i	0.0894560	+	0.0239697i
$563$	−4.76452	−	17.7814i	−0.200801	−	0.749399i	−0.990689	−	0.136147i	$-0.956528\pi$
$563$	−4.76452	−	17.7814i	−0.200801	−	0.749399i	0.789888	−	0.613251i	$-0.210139\pi$
$564$	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
$568$	8.30495	−	2.22531i	0.348468	−	0.0933717i
$569$	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	$0.574067\pi$
$572$	0.368340	−	0.132610i	0.0154011	−	0.00554472i
$573$	−2.17298	−	1.63818i	−0.0907774	−	0.0684359i
$574$	22.1566	+	38.3763i	0.924798	+	1.60180i
$575$		0			0
$576$	3.79948	−	15.2114i	0.158312	−	0.633807i
$577$	20.8346	+	20.8346i	0.867358	+	0.867358i	0.992179	−	0.124822i	$-0.0398358\pi$
$577$	20.8346	+	20.8346i	0.867358	+	0.867358i	−0.124822	+	0.992179i	$0.539836\pi$
$578$	15.9633	−	4.27735i	0.663986	−	0.177914i
$579$	4.92065	+	1.98929i	0.204495	+	0.0826719i
$580$		0			0
$581$	−6.50746	−	3.75708i	−0.269975	−	0.155870i
$582$	−24.3161	−	2.99088i	−1.00794	−	0.123976i
$583$	0.481393	+	0.128989i	0.0199373	+	0.00534217i
$584$	6.50418			0.269145
$585$		0			0
$586$	−43.0228			−1.77725
$587$	−26.3518	−	7.06095i	−1.08766	−	0.291437i	−0.329928	−	0.944006i	$-0.607024\pi$
$587$	−26.3518	−	7.06095i	−1.08766	−	0.291437i	−0.757729	+	0.652569i	$0.773691\pi$
$588$	8.17837	+	1.00594i	0.337270	+	0.0414843i
$589$	−0.745769	−	0.430570i	−0.0307289	−	0.0177413i
$590$		0			0
$591$	−11.9692	−	4.83882i	−0.492347	−	0.199043i
$592$	−5.53159	+	1.48219i	−0.227347	+	0.0609175i
$593$	−10.8114	−	10.8114i	−0.443972	−	0.443972i	0.449373	−	0.893344i	$-0.351648\pi$
$593$	−10.8114	−	10.8114i	−0.443972	−	0.443972i	−0.893344	+	0.449373i	$0.851648\pi$
$594$	0.0678931	−	0.642027i	0.00278569	−	0.0263427i
$595$		0			0
$596$	2.43990	+	4.22603i	0.0999422	+	0.173105i
$597$	−6.95071	−	5.24005i	−0.284474	−	0.214461i
$598$	−6.46421	+	35.9264i	−0.264341	+	1.46914i
$599$	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	$0.756183\pi$
$602$	−36.9441	+	9.89915i	−1.50573	+	0.403459i
$603$	−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
$607$	−10.0229	−	37.4060i	−0.406817	−	1.51826i	−0.800679	−	0.599094i	$-0.795528\pi$
$607$	−10.0229	−	37.4060i	−0.406817	−	1.51826i	0.393861	−	0.919170i	$-0.371139\pi$
$608$	19.8472	+	5.31804i	0.804910	+	0.215675i
$609$	−6.09873	−	7.80943i	−0.247133	−	0.316454i
$610$		0			0
$611$	2.94597	+	1.38627i	0.119181	+	0.0560826i
$612$	−22.2453	−	12.3431i	−0.899211	−	0.498940i
$613$	5.89134	+	1.57858i	0.237949	+	0.0637583i	0.375823	−	0.926692i	$-0.377360\pi$
$613$	5.89134	+	1.57858i	0.237949	+	0.0637583i	−0.137874	+	0.990450i	$0.544027\pi$
$614$	−11.7591	−	20.3674i	−0.474560	−	0.821963i
$615$		0			0
$616$			0.0822747i			0.00331494i
$617$	−10.8057	−	40.3273i	−0.435020	−	1.62352i	−0.741019	−	0.671484i	$-0.765657\pi$
$617$	−10.8057	−	40.3273i	−0.435020	−	1.62352i	0.306000	−	0.952032i	$-0.401009\pi$
$618$	−23.7125	−	55.8960i	−0.953855	−	2.24847i
$619$	38.9070			1.56380			0.781902	−	0.623402i	$-0.214250\pi$
$619$	38.9070			1.56380			0.781902	+	0.623402i	$0.214250\pi$
$620$		0			0
$621$	22.1896	+	16.1433i	0.890439	+	0.647809i
$622$	1.91996	−	7.16537i	0.0769832	−	0.287305i
$623$	−20.8528	+	20.8528i	−0.835450	+	0.835450i
$624$	20.8249	−	19.2758i	0.833663	−	0.771651i
$625$		0			0
$626$	−30.5018	−	52.8307i	−1.21910	−	2.11154i
$627$	0.306605	+	0.0377125i	0.0122446	+	0.00150609i
$628$	−1.87356	+	0.502020i	−0.0747633	+	0.0200328i
$629$			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
$633$	9.93884	+	23.4283i	0.395033	+	0.931190i
$634$	2.99253	−	1.72774i	0.118849	−	0.0686172i
$635$		0			0
$636$	−22.0979	+	3.10088i	−0.876239	+	0.122958i
$637$	7.82006	+	6.60847i	0.309842	+	0.261837i
$638$	0.246411	−	0.246411i	0.00975550	−	0.00975550i
$639$	−28.8014	+	29.7994i	−1.13937	+	1.17885i
$640$		0			0
$641$	27.5842	+	15.9257i	1.08951	+	0.629029i	0.933446	−	0.358718i	$-0.116786\pi$
$641$	27.5842	+	15.9257i	1.08951	+	0.629029i	0.156064	+	0.987747i	$0.450119\pi$
$642$	29.9504	−	39.7280i	1.18205	−	1.56794i
$643$	−3.14107	−	11.7226i	−0.123872	−	0.462295i	0.875925	−	0.482447i	$-0.160252\pi$
$643$	−3.14107	−	11.7226i	−0.123872	−	0.462295i	−0.999797	+	0.0201514i	$0.993585\pi$
$644$	15.6284	+	9.02306i	0.615845	+	0.355558i
$645$		0			0
$646$	13.3523	−	23.1268i	0.525338	−	0.909913i
$647$	−8.32851	+	31.0824i	−0.327427	+	1.22198i	0.584422	+	0.811450i	$0.301321\pi$
$647$	−8.32851	+	31.0824i	−0.327427	+	1.22198i	−0.911849	+	0.410526i	$0.865345\pi$
$648$	−1.63318	−	5.35815i	−0.0641573	−	0.210488i
$649$		−	0.439239i		−	0.0172417i
$650$		0			0
$651$	0.153623	+	1.09477i	0.00602097	+	0.0429075i
$652$	7.89596	−	29.4681i	0.309230	−	1.15406i
$653$	−32.0085	−	8.57665i	−1.25259	−	0.335630i	−0.429253	−	0.903184i	$-0.641223\pi$
$653$	−32.0085	−	8.57665i	−1.25259	−	0.335630i	−0.823336	+	0.567554i	$0.807890\pi$
$654$	−49.6346	−	20.0660i	−1.94087	−	0.784641i
$655$		0			0
$656$	−25.7464	+	44.5940i	−1.00523	+	1.74110i
$657$	−26.8799	+	16.1355i	−1.04868	+	0.629507i
$658$	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
$663$	−14.7366	−	27.9648i	−0.572321	−	1.08606i
$664$		−	2.29286i		−	0.0889803i
$665$		0			0
$666$	5.03745	−	5.21200i	0.195197	−	0.201961i
$667$	3.83351	+	14.3068i	0.148434	+	0.553963i
$668$	−7.29852	−	7.29852i	−0.282388	−	0.282388i
$669$	6.70775	+	2.71176i	0.259336	+	0.104843i
$670$		0			0
$671$	−0.179337			−0.00692322
$672$	−10.3015	−	24.2831i	−0.397389	−	0.936742i
$673$	−8.21798	+	30.6699i	−0.316780	+	1.18224i	0.605541	+	0.795814i	$0.292957\pi$
$673$	−8.21798	+	30.6699i	−0.316780	+	1.18224i	−0.922321	+	0.386425i	$0.873710\pi$
$674$	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	0.884640	−	0.466275i	$-0.154404\pi$
$677$	10.8855	+	10.8855i	0.418365	+	0.418365i	−0.466275	+	0.884640i	$0.654404\pi$
$678$	−4.33036	+	35.2062i	−0.166306	+	1.35209i
$679$	−13.0329	+	7.52456i	−0.500158	+	0.288766i
$680$		0			0
$681$	−5.65431	−	40.2946i	−0.216674	−	1.54409i
$682$	−0.0375544	+	0.0100627i	−0.00143803	+	0.000385320i
$683$	21.0850	−	5.64971i	0.806796	−	0.216180i	0.168230	−	0.985748i	$-0.446195\pi$
$683$	21.0850	−	5.64971i	0.806796	−	0.216180i	0.638566	+	0.769567i	$0.279528\pi$
$684$	−13.2973	+	3.80684i	−0.508436	+	0.145558i
$685$		0			0
$686$	33.3215	−	19.2382i	1.27222	−	0.734517i
$687$	19.6237	+	2.41371i	0.748689	+	0.0920888i
$688$	−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	$0.604234\pi$
$692$	−1.45894	+	5.44485i	−0.0554607	+	0.206982i
$693$	−0.204106	−	0.340017i	−0.00775336	−	0.0129162i
$694$	−61.5388			−2.33598
$695$		0			0
$696$	1.13322	−	2.80311i	0.0429547	−	0.106252i
$697$	40.5598	+	40.5598i	1.53631	+	1.53631i
$698$	−9.88198	−	36.8800i	−0.374038	−	1.39593i
$699$	−16.7724	+	13.0983i	−0.634391	+	0.495424i
$700$		0			0
$701$		−	22.5069i		−	0.850074i	−0.905176	−	0.425037i	$-0.860261\pi$
$701$		−	22.5069i		−	0.850074i	0.905176	−	0.425037i	$-0.139739\pi$
$702$	−10.0426	+	34.4847i	−0.379033	+	1.30154i
$703$	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
$708$	7.68054	+	18.1049i	0.288652	+	0.680424i
$709$	−20.0553	+	34.7369i	−0.753194	+	1.30457i	0.193073	+	0.981184i	$0.438154\pi$
$709$	−20.0553	+	34.7369i	−0.753194	+	1.30457i	−0.946267	+	0.323386i	$0.895179\pi$
$710$		0			0
$711$	3.88269	−	15.5445i	0.145612	−	0.582964i
$712$	−8.69201	−	2.32902i	−0.325747	−	0.0872836i
$713$	0.427700	−	1.59620i	0.0160175	−	0.0597780i
$714$	−33.9496	+	4.76396i	−1.27053	+	0.178287i
$715$		0			0
$716$		−	5.44145i		−	0.203357i
$717$	1.80710	−	14.6919i	0.0674873	−	0.548678i
$718$	9.15120	−	34.1528i	0.341520	−	1.27457i
$719$	−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
$722$	5.66978	+	21.1599i	0.211007	+	0.787490i
$723$	28.5728	+	21.5407i	1.06264	+	0.801107i
$724$	−9.73892	−	5.62277i	−0.361944	−	0.208968i
$725$		0			0
$726$	−28.7767	+	22.4730i	−1.06800	+	0.834051i
$727$	6.32057	−	6.32057i	0.234417	−	0.234417i	−0.580116	−	0.814534i	$-0.696993\pi$
$727$	6.32057	−	6.32057i	0.234417	−	0.234417i	0.814534	+	0.580116i	$0.196993\pi$
$728$	0.810558	−	4.50487i	0.0300413	−	0.166962i
$729$	20.0419	+	18.0921i	0.742292	+	0.670076i
$730$		0			0
$731$	−42.8756	+	24.7542i	−1.58581	+	0.915568i
$732$	7.39204	−	3.13588i	0.273218	−	0.115906i
$733$	23.4455	−	23.4455i	0.865981	−	0.865981i	−0.126044	−	0.992025i	$-0.540228\pi$
$733$	23.4455	−	23.4455i	0.865981	−	0.865981i	0.992025	+	0.126044i	$0.0402280\pi$
$734$	−50.9712	−	29.4282i	−1.88138	−	1.08622i
$735$		0			0
$736$			39.4298i			1.45340i
$737$	−0.685952	+	0.183800i	−0.0252674	+	0.00677037i
$738$	−1.10982	−	65.1666i	−0.0408529	−	2.39882i
$739$	3.41081	+	5.90770i	0.125469	+	0.217318i	0.921916	−	0.387390i	$-0.126623\pi$
$739$	3.41081	+	5.90770i	0.125469	+	0.217318i	−0.796447	+	0.604708i	$0.793290\pi$
$740$		0			0
$741$	−16.4163	−	5.08554i	−0.603069	−	0.186822i
$742$	−21.2628	+	21.2628i	−0.780580	+	0.780580i
$743$	−4.99856	+	18.6549i	−0.183379	+	0.684381i	0.811592	+	0.584224i	$0.198601\pi$
$743$	−4.99856	+	18.6549i	−0.183379	+	0.684381i	−0.994972	+	0.100157i	$0.968065\pi$
$744$	−0.265864	+	0.207625i	−0.00974704	+	0.00761189i
$745$		0			0
$746$	−47.1359			−1.72577
$747$	5.68811	+	9.47572i	0.208117	+	0.346698i
$748$	−0.142243	−	0.530860i	−0.00520094	−	0.0194102i
$749$		−	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	$-0.426531\pi$
$752$	3.96337	+	1.06198i	0.144529	+	0.0387265i
$753$	28.7190	+	21.6508i	1.04658	+	0.789001i
$754$	−15.9196	+	11.0644i	−0.579757	+	0.402941i
$755$		0			0
$756$	14.3585	+	10.4461i	0.522215	+	0.379920i
$757$	−40.3994	−	10.8250i	−1.46834	−	0.393440i	−0.565978	−	0.824420i	$-0.691501\pi$
$757$	−40.3994	−	10.8250i	−1.46834	−	0.393440i	−0.902362	+	0.430980i	$0.858168\pi$
$758$	−11.2053	−	41.8188i	−0.406996	−	1.51893i
$759$	0.0823774	+	0.587050i	0.00299011	+	0.0213086i
$760$		0			0
$761$	−0.0958031	+	0.165936i	−0.00347286	+	0.00601517i	−0.867757	−	0.496989i	$-0.834439\pi$
$761$	−0.0958031	+	0.165936i	−0.00347286	+	0.00601517i	0.864284	+	0.503005i	$0.167772\pi$
$762$	1.55001	+	1.16853i	0.0561508	+	0.0423314i
$763$	−31.7655	+	8.51155i	−1.14999	+	0.308139i
$764$	1.31611	+	2.27956i	0.0476151	+	0.0824717i
$765$		0			0
$766$	−3.51561			−0.127024
$767$	−4.32732	+	24.0501i	−0.156250	+	0.868400i
$768$	20.7202	−	27.4845i	0.747676	−	0.991761i
$769$	−4.49084	−	7.77836i	−0.161944	−	0.280495i	0.773622	−	0.633647i	$-0.218443\pi$
$769$	−4.49084	−	7.77836i	−0.161944	−	0.280495i	−0.935566	+	0.353153i	$0.885110\pi$
$770$		0			0
$771$	−15.1089	+	37.3729i	−0.544132	+	1.34595i
$772$	−3.63014	−	3.63014i	−0.130652	−	0.130652i
$773$	−17.1500	+	4.59533i	−0.616842	+	0.165282i	−0.553692	−	0.832722i	$-0.686781\pi$
$773$	−17.1500	+	4.59533i	−0.616842	+	0.165282i	−0.0631504	+	0.998004i	$0.520115\pi$
$774$	54.5776	+	13.6323i	1.96175	+	0.490004i
$775$		0			0
$776$	−3.97685	−	2.29603i	−0.142761	−	0.0824228i
$777$	0.543562	−	4.41920i	0.0195002	−	0.158538i
$778$	28.3446	+	7.59490i	1.01620	+	0.272290i
$779$	31.1860			1.11736
$780$		0			0
$781$	−0.895297			−0.0320362
$782$	49.4992	+	13.2633i	1.77009	+	0.474293i
$783$	2.27067	+	14.3957i	0.0811469	+	0.514462i
$784$	11.1743	+	6.45149i	0.399082	+	0.230410i
$785$		0			0
$786$	−7.18244	+	17.7663i	−0.256189	+	0.633703i
$787$	31.4011	−	8.41390i	1.11933	−	0.299923i	0.348717	−	0.937228i	$-0.386618\pi$
$787$	31.4011	−	8.41390i	1.11933	−	0.299923i	0.770612	+	0.637305i	$0.219951\pi$
$788$	8.83012	+	8.83012i	0.314560	+	0.314560i
$789$	−36.3951	−	14.7136i	−1.29570	−	0.523816i
$790$		0			0
$791$	10.8945	+	18.8698i	0.387362	+	0.670931i
$792$	0.0587118	−	0.105813i	0.00208623	−	0.00375990i
$793$	9.81941	+	1.76680i	0.348698	+	0.0627409i
$794$	15.3666			0.545341
$795$		0			0
$796$	4.20984	+	7.29165i	0.149214	+	0.258446i
$797$	21.0403	−	5.63774i	0.745287	−	0.199699i	0.133860	−	0.991000i	$-0.457263\pi$
$797$	21.0403	−	5.63774i	0.745287	−	0.199699i	0.611427	+	0.791301i	$0.290596\pi$
$798$	−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
$802$	2.12960	+	7.94777i	0.0751987	+	0.280645i
$803$	−0.654199	−	0.175292i	−0.0230862	−	0.00618593i
$804$	25.0601	−	19.5706i	0.883803	−	0.690201i
$805$		0			0
$806$	2.15539	−	0.180992i	0.0759205	−	0.00637516i
$807$	9.55203	−	12.6704i	0.336247	−	0.446018i
$808$	7.01984	+	1.88096i	0.246957	+	0.0661720i
$809$	−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	$0.862020\pi$
$812$	2.48060	+	9.25772i	0.0870520	+	0.324882i
$813$	13.6005	−	5.76966i	0.476990	−	0.202351i
$814$	0.156590			0.00548848
$815$		0			0
$816$	−24.5192	−	31.3969i	−0.858345	−	1.09911i
$817$	−6.96666	+	25.9999i	−0.243733	+	0.909623i
$818$	51.0116	−	51.0116i	1.78358	−	1.78358i
$819$	7.82586	+	20.6281i	0.273458	+	0.720805i
$820$		0			0
$821$	9.77979	+	16.9391i	0.341317	+	0.591179i	0.984678	−	0.174385i	$-0.0557937\pi$
$821$	9.77979	+	16.9391i	0.341317	+	0.591179i	−0.643360	+	0.765563i	$0.722460\pi$
$822$	−2.94783	+	23.9661i	−0.102817	+	0.835913i
$823$	−4.29575	+	1.15104i	−0.149740	+	0.0401228i	−0.332911	−	0.942958i	$-0.608031\pi$
$823$	−4.29575	+	1.15104i	−0.149740	+	0.0401228i	0.183170	+	0.983081i	$0.441364\pi$
$824$		−	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	$-0.747068\pi$
$827$	0.374621	−	0.374621i	0.0130268	−	0.0130268i	0.713590	+	0.700563i	$0.247068\pi$
$828$	−13.6606	−	22.7570i	−0.474740	−	0.790860i
$829$	29.3227	−	16.9295i	1.01842	−	0.587985i	0.104774	−	0.994496i	$-0.466588\pi$
$829$	29.3227	−	16.9295i	1.01842	−	0.587985i	0.913646	+	0.406511i	$0.133255\pi$
$830$		0			0
$831$	5.30052	+	37.7733i	0.183873	+	1.31034i
$832$	−17.7294	+	6.38298i	−0.614658	+	0.221290i
$833$	10.1634	−	10.1634i	0.352141	−	0.352141i
$834$	−4.37095	−	5.59701i	−0.151354	−	0.193809i
$835$		0			0
$836$	−0.258771	−	0.149402i	−0.00894979	−	0.00516717i
$837$	0.583663	−	1.51760i	0.0201743	−	0.0524561i
$838$	−6.00469	−	22.4098i	−0.207429	−	0.774134i
$839$	−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
$842$	−11.0617	+	41.2828i	−0.381211	+	1.42270i
$843$	−1.96872	−	0.242153i	−0.0678064	−	0.00834018i
$844$		−	24.6161i		−	0.847323i
$845$		0			0
$846$	−4.99295	+	1.42941i	−0.171661	+	0.0491442i
$847$	−5.80483	+	21.6639i	−0.199456	+	0.744381i
$848$	−33.7514	−	9.04366i	−1.15903	−	0.310560i
$849$	6.33657	−	15.6740i	0.217471	−	0.537930i
$850$		0			0
$851$	−3.32782	+	5.76395i	−0.114076	+	0.197586i
$852$	36.9030	−	15.6552i	1.26428	−	0.536337i
$853$	5.73121	−	5.73121i	0.196233	−	0.196233i	−0.602150	−	0.798383i	$-0.705689\pi$
$853$	5.73121	−	5.73121i	0.196233	−	0.196233i	0.798383	+	0.602150i	$0.205689\pi$
$854$	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	0.895396	−	0.445271i	$-0.146893\pi$
$857$	13.1772	+	13.1772i	0.450125	+	0.450125i	−0.445271	+	0.895396i	$0.646893\pi$
$858$	−0.686444	+	0.361734i	−0.0234348	+	0.0123494i
$859$			11.2173i			0.382729i	0.981519	+	0.191365i	$0.0612913\pi$
$859$			11.2173i			0.382729i	−0.981519	+	0.191365i	$0.938709\pi$
$860$		0			0
$861$	−24.6416	−	31.5536i	−0.839782	−	1.07534i
$862$	−0.196205	−	0.732248i	−0.00668278	−	0.0249405i
$863$	9.74312	+	9.74312i	0.331659	+	0.331659i	0.853216	−	0.521557i	$-0.174649\pi$
$863$	9.74312	+	9.74312i	0.331659	+	0.331659i	−0.521557	+	0.853216i	$0.674649\pi$
$864$	−4.07992	+	38.5816i	−0.138802	+	1.31257i
$865$		0			0
$866$	21.5180			0.731210
$867$	−13.7453	+	5.83111i	−0.466816	+	0.198035i
$868$	0.276757	−	1.03287i	0.00939376	−	0.0350580i
$869$	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
$873$	22.1311	−	0.376903i	0.749025	−	0.0127562i
$874$	24.1287	−	13.9307i	0.816166	−	0.471214i
$875$		0			0
$876$	30.0304	−	4.21400i	1.01463	−	0.142378i
$877$	−50.5897	+	13.5555i	−1.70829	+	0.457736i	−0.975005	−	0.222183i	$-0.928682\pi$
$877$	−50.5897	+	13.5555i	−1.70829	+	0.457736i	−0.733287	+	0.679919i	$0.762015\pi$
$878$	−39.7351	+	10.6470i	−1.34100	+	0.359319i
$879$	38.4924	−	5.40142i	1.29832	−	0.182186i
$880$		0			0
$881$	−6.05038	+	3.49319i	−0.203842	+	0.117688i	−0.598446	−	0.801163i	$-0.704215\pi$
$881$	−6.05038	+	3.49319i	−0.203842	+	0.117688i	0.394604	+	0.918851i	$0.370882\pi$
$882$	−16.3293	+	0.278096i	−0.549838	+	0.00936397i
$883$	−40.5116	−	40.5116i	−1.36332	−	1.36332i	−0.869643	−	0.493681i	$-0.835651\pi$
$883$	−40.5116	−	40.5116i	−1.36332	−	1.36332i	−0.493681	−	0.869643i	$-0.664349\pi$
$884$	2.55845	+	30.4681i	0.0860501	+	1.02475i
$885$		0			0
$886$	37.1925	−	21.4731i	1.24951	−	0.721403i
$887$	0.867046	−	3.23586i	0.0291126	−	0.108650i	−0.949841	−	0.312734i	$-0.898755\pi$
$887$	0.867046	−	3.23586i	0.0291126	−	0.108650i	0.978953	+	0.204085i	$0.0654218\pi$
$888$	1.25074	−	0.530594i	0.0419721	−	0.0178056i
$889$	1.19237			0.0399908
$890$		0			0
$891$	0.0198614	+	0.582945i	0.000665381	+	0.0195294i
$892$	−4.94855	−	4.94855i	−0.165690	−	0.165690i
$893$	−0.643178	−	2.40037i	−0.0215231	−	0.0803254i
$894$	−5.95292	−	7.62273i	−0.199096	−	0.254942i
$895$		0			0
$896$		−	10.0221i		−	0.334816i
$897$	1.27303	−	32.9549i	0.0425052	−	1.10033i
$898$	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
$903$	31.8110	−	13.4950i	1.05861	−	0.449086i
$904$	−3.32432	+	5.75789i	−0.110565	+	0.191505i
$905$		0			0
$906$	−15.1001	+	37.3513i	−0.501668	+	1.24091i
$907$	2.38916	+	0.640173i	0.0793307	+	0.0212566i	0.298266	−	0.954483i	$-0.403592\pi$
$907$	2.38916	+	0.640173i	0.0793307	+	0.0212566i	−0.218935	+	0.975739i	$0.570258\pi$
$908$	−10.1864	+	38.0163i	−0.338049	+	1.26162i
$909$	−33.6772	+	9.64131i	−1.11700	+	0.319782i
$910$		0			0
$911$		−	38.3512i		−	1.27063i	−0.772253	−	0.635316i	$-0.780870\pi$
$911$		−	38.3512i		−	1.27063i	0.772253	−	0.635316i	$-0.219130\pi$
$912$	−21.4967	−	2.64409i	−0.711827	−	0.0875547i
$913$	−0.0617942	+	0.230619i	−0.00204509	+	0.00763238i
$914$	−22.5082	+	38.9854i	−0.744506	+	1.28952i
$915$		0			0
$916$	−16.5621	−	9.56216i	−0.547229	−	0.315943i
$917$	3.04664	+	11.3702i	0.100609	+	0.375478i
$918$	47.0620	+	18.0998i	1.55328	+	0.597382i
$919$	8.63426	+	4.98500i	0.284818	+	0.164440i	0.635603	−	0.772016i	$-0.280752\pi$
$919$	8.63426	+	4.98500i	0.284818	+	0.164440i	−0.350785	+	0.936456i	$0.614085\pi$
$920$		0			0
$921$	13.0780	+	16.7464i	0.430934	+	0.551812i
$922$	−6.66059	+	6.66059i	−0.219355	+	0.219355i
$923$	49.0211	+	8.82033i	1.61355	+	0.290325i
$924$	0.0533051	+	0.379870i	0.00175361	+	0.0124968i
$925$		0			0
$926$	−19.1981	+	11.0840i	−0.630889	+	0.364244i
$927$	28.2332	+	47.0331i	0.927299	+	1.54477i
$928$	−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
$932$	19.8829	−	5.32761i	0.651287	−	0.174512i
$933$	−0.818183	+	6.65190i	−0.0267861	+	0.217773i
$934$	25.0597	+	43.4047i	0.819979	+	1.42024i
$935$		0			0
$936$	−4.25716	+	5.21526i	−0.139150	+	0.170466i
$937$	27.2652	−	27.2652i	0.890716	−	0.890716i	−0.103874	−	0.994590i	$-0.533124\pi$
$937$	27.2652	−	27.2652i	0.890716	−	0.890716i	0.994590	+	0.103874i	$0.0331239\pi$
$938$	11.0898	−	41.3878i	0.362096	−	1.35136i
$939$	33.9227	+	43.4381i	1.10703	+	1.41755i
$940$		0			0
$941$	18.4961			0.602957			0.301479	−	0.953473i	$-0.402520\pi$
$941$	18.4961			0.602957			0.301479	+	0.953473i	$0.402520\pi$
$942$	3.53911	−	1.50138i	0.115310	−	0.0489175i
$943$	15.4891	+	57.8060i	0.504393	+	1.88242i
$944$			30.7959i			1.00232i
$945$		0			0
$946$	0.607634	+	1.05245i	0.0197559	+	0.0342182i
$947$	28.3239	+	7.58936i	0.920403	+	0.246621i	0.687757	−	0.725941i	$-0.258595\pi$
$947$	28.3239	+	7.58936i	0.920403	+	0.246621i	0.232645	+	0.972562i	$0.425262\pi$
$948$	−9.32930	+	12.3749i	−0.303002	+	0.401919i
$949$	34.0931	+	16.0430i	1.10671	+	0.520779i
$950$		0			0
$951$	−2.46050	+	1.92151i	−0.0797871	+	0.0623093i
$952$	−6.20678	−	1.66310i	−0.201163	−	0.0539015i
$953$	1.69476	+	6.32491i	0.0548985	+	0.204884i	0.987927	−	0.154917i	$-0.0495111\pi$
$953$	1.69476	+	6.32491i	0.0548985	+	0.204884i	−0.933029	+	0.359801i	$0.882844\pi$
$954$	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
$958$	−34.4714	+	9.23657i	−1.11372	+	0.298420i
$959$	7.41624	+	12.8453i	0.239483	+	0.414797i
$960$		0			0
$961$	30.9021			0.996841
$962$	−8.57393	−	1.54270i	−0.276435	−	0.0497387i
$963$	−21.8088	+	39.3048i	−0.702780	+	1.26658i
$964$	−17.3057	−	29.9744i	−0.557380	−	0.965410i
$965$		0			0
$966$	−33.1601	−	13.4058i	−1.06691	−	0.431323i
$967$	−28.2870	−	28.2870i	−0.909648	−	0.909648i	0.0865951	−	0.996244i	$-0.472401\pi$
$967$	−28.2870	−	28.2870i	−0.909648	−	0.909648i	−0.996244	+	0.0865951i	$0.972401\pi$
$968$	−6.61049	+	1.77128i	−0.212469	+	0.0569310i
$969$	−9.04274	+	22.3679i	−0.290495	+	0.718561i
$970$		0			0
$971$	18.4125	+	10.6304i	0.590884	+	0.341147i	0.765447	−	0.643499i	$-0.222518\pi$
$971$	18.4125	+	10.6304i	0.590884	+	0.341147i	−0.174563	+	0.984646i	$0.555851\pi$
$972$	−11.0120	−	23.6810i	−0.353211	−	0.759567i
$973$	−4.21359	−	1.12903i	−0.135081	−	0.0361949i
$974$	64.3428			2.06168
$975$		0			0
$976$	12.5736			0.402473
$977$	−26.4720	−	7.09314i	−0.846913	−	0.226930i	−0.190835	−	0.981622i	$-0.561119\pi$
$977$	−26.4720	−	7.09314i	−0.846913	−	0.226930i	−0.656079	+	0.754692i	$0.727786\pi$
$978$	−7.38172	+	60.0139i	−0.236041	+	1.91903i
$979$	0.811485	+	0.468511i	0.0259352	+	0.0149737i
$980$		0			0
$981$	46.9273	+	11.7215i	1.49827	+	0.374237i
$982$	57.1228	−	15.3060i	1.82286	−	0.488435i
$983$	8.33022	+	8.33022i	0.265693	+	0.265693i	0.827362	−	0.561669i	$-0.189841\pi$
$983$	8.33022	+	8.33022i	0.265693	+	0.265693i	−0.561669	+	0.827362i	$0.689841\pi$
$984$	4.57873	−	11.3258i	0.145965	−	0.361054i
$985$		0			0
$986$	13.6082	+	23.5701i	0.433374	+	0.750625i
$987$	−1.92045	+	2.54740i	−0.0611287	+	0.0810848i
$988$	12.6969	+	10.7297i	0.403942	+	0.341358i
$989$	−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	$0.953600\pi$
$992$	2.25677	−	0.604700i	0.0716525	−	0.0191992i
$993$	−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
$997$	4.30927	+	16.0824i	0.136476	+	0.509335i	0.999987	+	0.00500582i	$0.00159341\pi$
$997$	4.30927	+	16.0824i	0.136476	+	0.509335i	−0.863512	+	0.504329i	$0.831740\pi$
$998$	19.2345	+	5.15386i	0.608856	+	0.163143i
$999$	−3.85264	+	5.29561i	−0.121892	+	0.167546i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.5	✓	96	195.173	even	12
195.2.bf.a.17.20	yes	96	65.43	odd	12
195.2.bf.a.23.5	yes	96	5.4	even	2
195.2.bf.a.23.20	yes	96	15.14	odd	2
195.2.bf.a.62.5	yes	96	15.8	even	4
195.2.bf.a.62.20	yes	96	5.3	odd	4
195.2.bf.a.173.5	yes	96	65.4	even	6
195.2.bf.a.173.20	yes	96	195.134	odd	6
975.2.bn.d.218.5		96	3.2	odd	2	inner
975.2.bn.d.218.20		96	1.1	even	1	trivial
975.2.bn.d.257.5		96	5.2	odd	4	inner
975.2.bn.d.257.20		96	15.2	even	4	inner
975.2.bn.d.368.5		96	39.17	odd	6	inner
975.2.bn.d.368.20		96	13.4	even	6	inner
975.2.bn.d.407.5		96	65.17	odd	12	inner
975.2.bn.d.407.20		96	195.17	even	12	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+(1.85180 + 0.496187i) q^{2} +(-1.71910 - 0.211449i) q^{3} +(1.45090 + 0.837676i) q^{4} +(-3.07850 - 1.24455i) q^{6} +(-1.97020 + 0.527913i) q^{7} +(-0.440097 - 0.440097i) q^{8} +(2.91058 + 0.727001i) q^{9} +(0.0324046 + 0.0561264i) q^{11} +(-2.31710 - 1.74683i) q^{12} +(-1.22133 - 3.39239i) q^{13} -3.91035 q^{14} +(-2.27195 - 3.93513i) q^{16} +(-4.88919 + 1.31006i) q^{17} +(5.02907 + 2.79045i) q^{18} +(-1.37598 + 2.38327i) q^{19} +(3.49859 - 0.490937i) q^{21} +(0.0321575 + 0.120014i) q^{22} +(-5.10100 - 1.36681i) q^{23} +(0.663511 + 0.849627i) q^{24} +(-0.578399 - 6.88803i) q^{26} +(-4.84984 - 1.86522i) q^{27} +(-3.30077 - 0.884440i) q^{28} +(-1.40236 - 2.42895i) q^{29} +0.312918i q^{31} +(-1.93245 - 7.21201i) q^{32} +(-0.0438388 - 0.103339i) q^{33} -9.70382 q^{34} +(3.61396 + 3.49292i) q^{36} +(0.326192 - 1.21737i) q^{37} +(-3.73059 + 3.73059i) q^{38} +(1.38227 + 6.09010i) q^{39} +(-5.66614 - 9.81404i) q^{41} +(6.72227 + 0.826839i) q^{42} +(9.44778 - 2.53152i) q^{43} +0.108578i q^{44} +(-8.76782 - 5.06210i) q^{46} +(-0.638524 + 0.638524i) q^{47} +(3.07362 + 7.24527i) q^{48} +(-2.45919 + 1.41981i) q^{49} +(8.68200 - 1.21830i) q^{51} +(1.06970 - 5.94510i) q^{52} +(5.43756 - 5.43756i) q^{53} +(-8.05541 - 5.86044i) q^{54} +(1.09941 + 0.634745i) q^{56} +(2.86938 - 3.80612i) q^{57} +(-1.39166 - 5.19376i) q^{58} +(-5.86942 - 3.38871i) q^{59} +(-1.38357 + 2.39642i) q^{61} +(-0.155266 + 0.579461i) q^{62} +(-6.11821 + 0.104196i) q^{63} -5.22623i q^{64} +(-0.0299051 - 0.213114i) q^{66} +(-2.83602 + 10.5842i) q^{67} +(-8.19111 - 2.19480i) q^{68} +(8.48010 + 3.42828i) q^{69} +(-6.90717 + 11.9636i) q^{71} +(-0.960986 - 1.60089i) 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} +(-0.462143 + 11.9635i) q^{78} -5.34069i q^{79} +(7.94294 + 4.23199i) q^{81} +(-5.62293 - 20.9851i) q^{82} +(2.60495 + 2.60495i) q^{83} +(5.48733 + 2.21838i) q^{84} +18.7515 q^{86} +(1.89719 + 4.47213i) q^{87} +(0.0104399 - 0.0389622i) q^{88} +(12.5211 - 7.22908i) q^{89} +(4.19716 + 6.03893i) q^{91} +(-6.25608 - 6.25608i) q^{92} +(0.0661662 - 0.537937i) q^{93} +(-1.49924 + 0.865588i) q^{94} +(1.79710 + 12.8068i) q^{96} +(7.12670 - 1.90959i) q^{97} +(-5.25841 + 1.40899i) 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

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