LMFDB - Embedded newform 833.2.bc.d.31.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(31,833)] 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("833.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([8, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.bc (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,0,8,0,8,-16,0,0,-24,0,-8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$9$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	833.31
Dual form			833.2.bc.d.215.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.20032 + 1.68837i) q^{2} +(1.15302 - 1.31477i) q^{3} +(1.47319 + 5.49804i) q^{4} +(-0.123911 + 0.251267i) q^{5} +(4.75684 - 0.946194i) q^{6} +(-3.91849 + 9.46008i) q^{8} +(-0.00758215 - 0.0575922i) q^{9} +(-0.696875 + 0.343660i) q^{10} +(1.16285 - 3.42565i) q^{11} +(8.92729 + 4.40245i) q^{12} +(3.56914 - 3.56914i) q^{13} +(0.187486 + 0.452632i) q^{15} +(-14.7352 + 8.50737i) q^{16} +(-3.16693 + 2.64018i) q^{17} +(0.0805535 - 0.139523i) q^{18} +(-1.82600 + 2.37968i) q^{19} +(-1.56402 - 0.311103i) q^{20} +(8.34238 - 5.57420i) q^{22} +(0.214773 - 0.188351i) q^{23} +(7.91973 + 16.0596i) q^{24} +(2.99603 + 3.90450i) q^{25} +(13.8792 - 1.82724i) q^{26} +(4.27761 + 2.85821i) q^{27} +(-2.91151 - 4.35739i) q^{29} +(-0.351678 + 1.31248i) q^{30} +(-7.71272 - 6.76387i) q^{31} +(-26.4819 - 3.48640i) q^{32} +(-3.16315 - 5.47873i) q^{33} +(-11.4258 + 0.462312i) q^{34} +(0.305474 - 0.126531i) q^{36} +(3.45899 - 1.17417i) q^{37} +(-8.03555 + 2.15312i) q^{38} +(-0.577300 - 8.80790i) q^{39} +(-1.89146 - 2.15680i) q^{40} +(2.98363 - 4.46532i) q^{41} +(-2.25647 - 0.934662i) q^{43} +(20.5474 + 1.34675i) q^{44} +(0.0154105 + 0.00523117i) q^{45} +(0.790575 - 0.0518171i) q^{46} +(-4.75298 - 1.27356i) q^{47} +(-5.80478 + 29.1826i) q^{48} +13.6495i q^{50} +(-0.180309 + 7.20798i) q^{51} +(24.8813 + 14.3652i) q^{52} +(0.956305 - 7.26386i) q^{53} +(4.58641 + 13.5111i) q^{54} +(0.716661 + 0.716661i) q^{55} +(1.02332 + 5.14460i) q^{57} +(0.950600 - 14.5034i) q^{58} +(0.853801 - 0.655145i) q^{59} +(-2.21238 + 1.69762i) q^{60} +(0.173394 - 2.64548i) q^{61} +(-5.55057 - 27.9046i) q^{62} +(-28.3198 - 28.3198i) q^{64} +(0.454550 + 1.33906i) q^{65} +(2.29016 - 17.3955i) q^{66} +(0.815594 + 0.470883i) q^{67} +(-19.1813 - 13.5224i) q^{68} -0.499551i q^{69} +(0.0645053 - 0.324290i) q^{71} +(0.574537 + 0.153947i) q^{72} +(0.762287 - 0.0499630i) q^{73} +(9.59332 + 3.25649i) q^{74} +(8.58801 + 0.562888i) q^{75} +(-15.7736 - 6.53366i) q^{76} +(13.6007 - 20.3549i) q^{78} +(8.87374 + 10.1186i) q^{79} +(-0.311766 - 4.75663i) q^{80} +(8.85840 - 2.37360i) q^{81} +(14.1040 - 4.78767i) q^{82} +(-3.27605 + 1.35698i) q^{83} +(-0.270973 - 1.12289i) q^{85} +(-3.38691 - 5.86631i) q^{86} +(-9.08602 - 1.19620i) q^{87} +(27.8503 + 24.4240i) q^{88} +(-2.00114 + 7.46835i) q^{89} +(0.0250760 + 0.0375288i) q^{90} +(1.35196 + 0.903354i) q^{92} +(-17.7859 + 2.34156i) q^{93} +(-8.30785 - 10.8270i) q^{94} +(-0.371675 - 0.753682i) q^{95} +(-35.1181 + 30.7977i) q^{96} +(1.13223 - 0.756532i) q^{97} +(-0.206107 - 0.0409973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 8 q^{5} - 16 q^{6} - 24 q^{9} - 8 q^{11} + 64 q^{13} + 40 q^{18} + 24 q^{19} + 48 q^{22} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 16 q^{27} + 80 q^{31} + 40 q^{32} - 80 q^{33} + 240 q^{36}+ \cdots + 80 q^{99}+O(q^{100}) $ 144 * q + 8 * q^3 + 8 * q^5 - 16 * q^6 - 24 * q^9 - 8 * q^11 + 64 * q^13 + 40 * q^18 + 24 * q^19 + 48 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 16 * q^27 + 80 * q^31 + 40 * q^32 - 80 * q^33 + 240 * q^36 - 48 * q^37 - 56 * q^38 + 16 * q^39 - 32 * q^40 - 48 * q^41 + 48 * q^43 - 32 * q^44 - 48 * q^45 - 40 * q^47 + 40 * q^51 + 24 * q^53 + 200 * q^54 - 96 * q^57 - 32 * q^58 + 8 * q^59 + 80 * q^60 - 256 * q^62 + 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 + 32 * q^74 + 128 * q^75 - 144 * q^76 - 96 * q^78 + 32 * q^79 + 256 * q^80 - 16 * q^81 - 152 * q^82 - 64 * q^85 + 80 * q^86 - 64 * q^87 - 56 * q^88 - 64 * q^89 + 752 * q^90 - 432 * q^92 + 32 * q^93 - 128 * q^94 - 32 * q^95 + 32 * q^96 + 16 * q^97 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	2.20032	+	1.68837i	1.55586	+	1.19385i	0.897381	+	0.441257i	$0.145467\pi$
$2$	2.20032	+	1.68837i	1.55586	+	1.19385i	0.658481	+	0.752598i	$0.271199\pi$
$3$	1.15302	−	1.31477i	0.665699	−	0.759084i	−0.316158	−	0.948706i	$-0.602393\pi$
$3$	1.15302	−	1.31477i	0.665699	−	0.759084i	0.981857	+	0.189623i	$0.0607264\pi$
$4$	1.47319	+	5.49804i	0.736597	+	2.74902i
$5$	−0.123911	+	0.251267i	−0.0554147	+	0.112370i	−0.922819	−	0.385235i	$-0.874120\pi$
$5$	−0.123911	+	0.251267i	−0.0554147	+	0.112370i	0.867404	+	0.497605i	$0.165787\pi$
$6$	4.75684	−	0.946194i	1.94197	−	0.386282i
$7$		0			0
$7$		0			0
$8$	−3.91849	+	9.46008i	−1.38540	+	3.34464i
$9$	−0.00758215	−	0.0575922i	−0.00252738	−	0.0191974i
$10$	−0.696875	+	0.343660i	−0.220371	+	0.108675i
$11$	1.16285	−	3.42565i	0.350612	−	1.03287i	−0.618401	−	0.785863i	$-0.712219\pi$
$11$	1.16285	−	3.42565i	0.350612	−	1.03287i	0.969013	−	0.247008i	$-0.0794475\pi$
$12$	8.92729	+	4.40245i	2.57709	+	1.27088i
$13$	3.56914	−	3.56914i	0.989900	−	0.989900i	−0.0100493	−	0.999950i	$-0.503199\pi$
$13$	3.56914	−	3.56914i	0.989900	−	0.989900i	0.999950	+	0.0100493i	$0.00319885\pi$
$14$		0			0
$15$	0.187486	+	0.452632i	0.0484087	+	0.116869i
$16$	−14.7352	+	8.50737i	−3.68380	+	2.12684i
$17$	−3.16693	+	2.64018i	−0.768093	+	0.640338i
$17$	−3.16693	+	2.64018i	−0.768093	+	0.640338i
$18$	0.0805535	−	0.139523i	0.0189866	−	0.0328858i
$19$	−1.82600	+	2.37968i	−0.418912	+	0.545937i	−0.954371	−	0.298625i	$-0.903472\pi$
$19$	−1.82600	+	2.37968i	−0.418912	+	0.545937i	0.535458	+	0.844562i	$0.320139\pi$
$20$	−1.56402	−	0.311103i	−0.349726	−	0.0695647i
$21$		0			0
$22$	8.34238	−	5.57420i	1.77860	−	1.18842i
$23$	0.214773	−	0.188351i	0.0447833	−	0.0392739i	−0.636662	−	0.771143i	$-0.719685\pi$
$23$	0.214773	−	0.188351i	0.0447833	−	0.0392739i	0.681445	+	0.731869i	$0.261352\pi$
$24$	7.91973	+	16.0596i	1.61661	+	3.27816i
$25$	2.99603	+	3.90450i	0.599205	+	0.780899i
$26$	13.8792	−	1.82724i	2.72194	−	0.358351i
$27$	4.27761	+	2.85821i	0.823226	+	0.550062i
$28$		0			0
$29$	−2.91151	−	4.35739i	−0.540655	−	0.809147i	0.456076	−	0.889941i	$-0.349254\pi$
$29$	−2.91151	−	4.35739i	−0.540655	−	0.809147i	−0.996731	+	0.0807939i	$0.974254\pi$
$30$	−0.351678	+	1.31248i	−0.0642073	+	0.239625i
$31$	−7.71272	−	6.76387i	−1.38525	−	1.21483i	−0.949109	−	0.314947i	$-0.898013\pi$
$31$	−7.71272	−	6.76387i	−1.38525	−	1.21483i	−0.436136	−	0.899881i	$-0.643653\pi$
$32$	−26.4819	−	3.48640i	−4.68138	−	0.616315i
$33$	−3.16315	−	5.47873i	−0.550633	−	0.953725i
$34$	−11.4258	+	0.462312i	−1.95952	+	0.0792859i
$35$		0			0
$36$	0.305474	−	0.126531i	0.0509123	−	0.0210886i
$37$	3.45899	−	1.17417i	0.568655	−	0.193032i	−0.0222798	−	0.999752i	$-0.507092\pi$
$37$	3.45899	−	1.17417i	0.568655	−	0.193032i	0.590935	+	0.806720i	$0.298759\pi$
$38$	−8.03555	+	2.15312i	−1.30354	+	0.349282i
$39$	−0.577300	−	8.80790i	−0.0924420	−	1.41039i
$40$	−1.89146	−	2.15680i	−0.299066	−	0.341020i
$41$	2.98363	−	4.46532i	0.465965	−	0.697365i	−0.521844	−	0.853041i	$-0.674756\pi$
$41$	2.98363	−	4.46532i	0.465965	−	0.697365i	0.987808	+	0.155676i	$0.0497555\pi$
$42$		0			0
$43$	−2.25647	−	0.934662i	−0.344109	−	0.142535i	0.203934	−	0.978985i	$-0.434627\pi$
$43$	−2.25647	−	0.934662i	−0.344109	−	0.142535i	−0.548043	+	0.836450i	$0.684627\pi$
$44$	20.5474	+	1.34675i	3.09764	+	0.203030i
$45$	0.0154105	+	0.00523117i	0.00229727	+	0.000779816i
$46$	0.790575	−	0.0518171i	0.116564	−	0.00764001i
$47$	−4.75298	−	1.27356i	−0.693294	−	0.185767i	−0.105069	−	0.994465i	$-0.533506\pi$
$47$	−4.75298	−	1.27356i	−0.693294	−	0.185767i	−0.588225	+	0.808697i	$0.700173\pi$
$48$	−5.80478	+	29.1826i	−0.837848	+	4.21215i
$49$		0			0
$50$			13.6495i			1.93034i
$51$	−0.180309	+	7.20798i	−0.0252483	+	1.00932i
$52$	24.8813	+	14.3652i	3.45041	+	1.99210i
$53$	0.956305	−	7.26386i	0.131359	−	0.997768i	−0.791104	−	0.611682i	$-0.790493\pi$
$53$	0.956305	−	7.26386i	0.131359	−	0.997768i	0.922463	−	0.386086i	$-0.126173\pi$
$54$	4.58641	+	13.5111i	0.624132	+	1.83863i
$55$	0.716661	+	0.716661i	0.0966346	+	0.0966346i
$56$		0			0
$57$	1.02332	+	5.14460i	0.135543	+	0.681419i
$58$	0.950600	−	14.5034i	0.124820	−	1.90438i
$59$	0.853801	−	0.655145i	0.111155	−	0.0852926i	−0.551688	−	0.834051i	$-0.686016\pi$
$59$	0.853801	−	0.655145i	0.111155	−	0.0852926i	0.662844	+	0.748758i	$0.269349\pi$
$60$	−2.21238	+	1.69762i	−0.285617	+	0.219162i
$61$	0.173394	−	2.64548i	0.0222008	−	0.338719i	−0.972281	−	0.233814i	$-0.924879\pi$
$61$	0.173394	−	2.64548i	0.0222008	−	0.338719i	0.994482	−	0.104905i	$-0.0334540\pi$
$62$	−5.55057	−	27.9046i	−0.704923	−	3.54388i
$63$		0			0
$64$	−28.3198	−	28.3198i	−3.53997	−	3.53997i
$65$	0.454550	+	1.33906i	0.0563800	+	0.166090i
$66$	2.29016	−	17.3955i	0.281900	−	2.14124i
$67$	0.815594	+	0.470883i	0.0996406	+	0.0575275i	0.548992	−	0.835827i	$-0.315012\pi$
$67$	0.815594	+	0.470883i	0.0996406	+	0.0575275i	−0.449352	+	0.893355i	$0.648345\pi$
$68$	−19.1813	−	13.5224i	−2.32608	−	1.63983i
$69$		−	0.499551i		−	0.0601389i
$70$		0			0
$71$	0.0645053	−	0.324290i	0.00765537	−	0.0384862i	−0.976769	−	0.214296i	$-0.931254\pi$
$71$	0.0645053	−	0.324290i	0.00765537	−	0.0384862i	0.984424	+	0.175810i	$0.0562543\pi$
$72$	0.574537	+	0.153947i	0.0677098	+	0.0181428i
$73$	0.762287	−	0.0499630i	0.0892190	−	0.00584772i	−0.0207282	−	0.999785i	$-0.506598\pi$
$73$	0.762287	−	0.0499630i	0.0892190	−	0.00584772i	0.109947	+	0.993937i	$0.464932\pi$
$74$	9.59332	+	3.25649i	1.11520	+	0.378560i
$75$	8.58801	+	0.562888i	0.991658	+	0.0649967i
$76$	−15.7736	−	6.53366i	−1.80936	−	0.749462i
$77$		0			0
$78$	13.6007	−	20.3549i	1.53998	−	2.30474i
$79$	8.87374	+	10.1186i	0.998374	+	1.13843i	0.990368	+	0.138459i	$0.0442150\pi$
$79$	8.87374	+	10.1186i	0.998374	+	1.13843i	0.00800558	+	0.999968i	$0.497452\pi$
$80$	−0.311766	−	4.75663i	−0.0348565	−	0.531807i
$81$	8.85840	−	2.37360i	0.984267	−	0.263734i
$82$	14.1040	−	4.78767i	1.55753	−	0.528710i
$83$	−3.27605	+	1.35698i	−0.359593	+	0.148948i	−0.555163	−	0.831741i	$-0.687344\pi$
$83$	−3.27605	+	1.35698i	−0.359593	+	0.148948i	0.195570	+	0.980690i	$0.437344\pi$
$84$		0			0
$85$	−0.270973	−	1.12289i	−0.0293911	−	0.121795i
$86$	−3.38691	−	5.86631i	−0.365220	−	0.632580i
$87$	−9.08602	−	1.19620i	−0.974123	−	0.128246i
$88$	27.8503	+	24.4240i	2.96885	+	2.60361i
$89$	−2.00114	+	7.46835i	−0.212120	+	0.791643i	0.775040	+	0.631912i	$0.217730\pi$
$89$	−2.00114	+	7.46835i	−0.212120	+	0.791643i	−0.987160	+	0.159732i	$0.948937\pi$
$90$	0.0250760	+	0.0375288i	0.00264324	+	0.00395589i
$91$		0			0
$92$	1.35196	+	0.903354i	0.140952	+	0.0941811i
$93$	−17.7859	+	2.34156i	−1.84431	+	0.242808i
$94$	−8.30785	−	10.8270i	−0.856890	−	1.11672i
$95$	−0.371675	−	0.753682i	−0.0381330	−	0.0773261i
$96$	−35.1181	+	30.7977i	−3.58422	+	3.14328i
$97$	1.13223	−	0.756532i	0.114961	−	0.0768142i	−0.496761	−	0.867888i	$-0.665477\pi$
$97$	1.13223	−	0.756532i	0.114961	−	0.0768142i	0.611721	+	0.791073i	$0.290477\pi$
$98$		0			0
$99$	−0.206107	−	0.0409973i	−0.0207146	−	0.00412038i
$100$	−17.0533	+	22.2243i	−1.70533	+	2.22243i
$101$	6.23947	−	10.8071i	0.620850	−	1.07534i	−0.368477	−	0.929637i	$-0.620121\pi$
$101$	6.23947	−	10.8071i	0.620850	−	1.07534i	0.989328	−	0.145708i	$-0.0465458\pi$
$102$	−12.5664	+	15.5554i	−1.24426	+	1.54022i
$103$	−5.19638	+	3.00013i	−0.512015	+	0.295612i	−0.733662	−	0.679515i	$-0.762190\pi$
$103$	−5.19638	+	3.00013i	−0.512015	+	0.295612i	0.221647	+	0.975127i	$0.428857\pi$
$104$	19.7787	+	47.7499i	1.93946	+	4.68227i
$105$		0			0
$106$	14.3682	−	14.3682i	1.39557	−	1.39557i
$107$	−1.88738	−	0.930751i	−0.182460	−	0.0899791i	0.348765	−	0.937210i	$-0.386601\pi$
$107$	−1.88738	−	0.930751i	−0.182460	−	0.0899791i	−0.531224	+	0.847231i	$0.678268\pi$
$108$	−9.41277	+	27.7291i	−0.905745	+	2.66824i
$109$	12.9352	−	6.37895i	1.23897	−	0.610993i	0.299656	−	0.954047i	$-0.403128\pi$
$109$	12.9352	−	6.37895i	1.23897	−	0.610993i	0.939315	+	0.343055i	$0.111462\pi$
$110$	0.366899	+	2.78687i	0.0349824	+	0.265718i
$111$	2.44454	−	5.90163i	0.232025	−	0.560158i
$112$		0			0
$113$	−15.5989	+	3.10282i	−1.46742	+	0.291889i	−0.863174	−	0.504906i	$-0.831527\pi$
$113$	−15.5989	+	3.10282i	−1.46742	+	0.291889i	−0.604250	+	0.796795i	$0.706527\pi$
$114$	−6.43432	+	13.0475i	−0.602630	+	1.22201i
$115$	0.0207136	+	0.0773042i	0.00193155	+	0.00720866i
$116$	19.6679	−	22.4269i	1.82611	−	2.08228i
$117$	−0.232616	−	0.178493i	−0.0215054	−	0.0165016i
$118$	2.98476			0.274769
$119$		0			0
$120$	−5.01659			−0.457950
$121$	−1.65594	−	1.27065i	−0.150540	−	0.115513i
$122$	4.84806	−	5.52816i	0.438923	−	0.500496i
$123$	−2.43068	−	9.07141i	−0.219167	−	0.817941i
$124$	25.8257	−	52.3693i	2.31922	−	4.70290i
$125$	−2.72619	+	0.542273i	−0.243838	+	0.0485024i
$126$		0			0
$127$	−5.10039	+	12.3134i	−0.452587	+	1.09264i	0.518748	+	0.854927i	$0.326398\pi$
$127$	−5.10039	+	12.3134i	−0.452587	+	1.09264i	−0.971335	+	0.237714i	$0.923602\pi$
$128$	−7.52566	−	57.1631i	−0.665181	−	5.05255i
$129$	−3.83063	+	1.88906i	−0.337269	+	0.166322i
$130$	−1.26067	+	3.71381i	−0.110568	+	0.325723i
$131$	−1.46744	−	0.723661i	−0.128211	−	0.0632265i	0.377052	−	0.926192i	$-0.376938\pi$
$131$	−1.46744	−	0.723661i	−0.128211	−	0.0632265i	−0.505263	+	0.862966i	$0.668604\pi$
$132$	25.4623	−	25.4623i	2.21621	−	2.21621i
$133$		0			0
$134$	0.999544	+	2.41311i	0.0863475	+	0.208461i
$135$	−1.24822	+	0.720658i	−0.107429	+	0.0620243i
$136$	−12.5667	−	40.3049i	−1.07759	−	3.45612i
$137$	−0.398044	+	0.689433i	−0.0340072	+	0.0589022i	−0.882528	−	0.470260i	$-0.844160\pi$
$137$	−0.398044	+	0.689433i	−0.0340072	+	0.0589022i	0.848521	+	0.529162i	$0.177494\pi$
$138$	0.843425	−	1.09917i	0.0717971	−	0.0935678i
$139$	−19.0957	−	3.79838i	−1.61968	−	0.322174i	−0.699789	−	0.714350i	$-0.746722\pi$
$139$	−19.0957	−	3.79838i	−1.61968	−	0.322174i	−0.919890	+	0.392176i	$0.871722\pi$
$140$		0			0
$141$	−7.15474	+	4.78064i	−0.602538	+	0.402603i
$142$	0.689453	−	0.604634i	0.0578576	−	0.0507397i
$143$	−8.07622	−	16.3770i	−0.675368	−	1.36951i
$144$	0.601682	+	0.784128i	0.0501402	+	0.0653440i
$145$	1.45564	−	0.191638i	0.120884	−	0.0159147i
$146$	1.76163	+	1.17708i	0.145794	+	0.0974162i
$147$		0			0
$148$	11.5514	+	17.2879i	0.949519	+	1.42106i
$149$	−0.207849	+	0.775705i	−0.0170277	+	0.0635482i	−0.973917	−	0.226905i	$-0.927139\pi$
$149$	−0.207849	+	0.775705i	−0.0170277	+	0.0635482i	0.956889	+	0.290453i	$0.0938060\pi$
$150$	17.9460	+	15.7382i	1.46529	+	1.28502i
$151$	−8.65457	−	1.13940i	−0.704299	−	0.0927227i	−0.230134	−	0.973159i	$-0.573916\pi$
$151$	−8.65457	−	1.13940i	−0.704299	−	0.0927227i	−0.474164	+	0.880436i	$0.657250\pi$
$152$	−15.3568	−	26.5988i	−1.24560	−	2.15745i
$153$	0.176066	+	0.162372i	0.0142341	+	0.0131270i
$154$		0			0
$155$	2.65523	−	1.09983i	0.213273	−	0.0883406i
$156$	47.5757	−	16.1498i	3.80910	−	1.29302i
$157$	15.2741	−	4.09268i	1.21901	−	0.326632i	0.408717	−	0.912661i	$-0.365976\pi$
$157$	15.2741	−	4.09268i	1.21901	−	0.326632i	0.810290	+	0.586030i	$0.199310\pi$
$158$	2.44124	+	37.2462i	0.194215	+	2.96315i
$159$	−8.44767	−	9.63273i	−0.669944	−	0.763925i
$160$	4.15742	−	6.22201i	0.328673	−	0.491893i
$161$		0			0
$162$	23.4988	+	9.73353i	1.84624	+	0.764739i
$163$	−2.00307	−	0.131288i	−0.156892	−	0.0102833i	−0.0132454	−	0.999912i	$-0.504216\pi$
$163$	−2.00307	−	0.131288i	−0.156892	−	0.0102833i	−0.143647	+	0.989629i	$0.545883\pi$
$164$	28.9459	+	9.82582i	2.26030	+	0.767268i
$165$	1.76857	−	0.115918i	0.137683	−	0.00902424i
$166$	−9.49945	−	2.54537i	−0.737300	−	0.197559i
$167$	−3.06874	+	15.4276i	−0.237466	+	1.19382i	0.659493	+	0.751711i	$0.270771\pi$
$167$	−3.06874	+	15.4276i	−0.237466	+	1.19382i	−0.896959	+	0.442114i	$0.854229\pi$
$168$		0			0
$169$		−	12.4775i		−	0.959805i
$170$	1.29963	−	2.92822i	0.0996768	−	0.224585i
$171$	0.150896	+	0.0871200i	0.0115393	+	0.00666223i
$172$	1.81458	−	13.7831i	0.138361	−	1.05095i
$173$	3.83726	+	11.3042i	0.291741	+	0.859442i	0.989681	+	0.143286i	$0.0457669\pi$
$173$	3.83726	+	11.3042i	0.291741	+	0.859442i	−0.697940	+	0.716156i	$0.745900\pi$
$174$	−17.9725	−	17.9725i	−1.36249	−	1.36249i
$175$		0			0
$176$	12.0084	+	60.3704i	0.905168	+	4.55059i
$177$	0.123087	−	1.87795i	0.00925182	−	0.141155i
$178$	−17.0124	+	13.0541i	−1.27514	+	0.978447i
$179$	12.4592	−	9.56027i	0.931243	−	0.714568i	−0.0272663	−	0.999628i	$-0.508680\pi$
$179$	12.4592	−	9.56027i	0.931243	−	0.714568i	0.958510	+	0.285060i	$0.0920135\pi$
$180$	−0.00605845	+	0.0924341i	−0.000451571	+	0.00688963i
$181$	1.86848	+	9.39351i	0.138883	+	0.698214i	0.985992	+	0.166794i	$0.0533414\pi$
$181$	1.86848	+	9.39351i	0.138883	+	0.698214i	−0.847108	+	0.531420i	$0.821659\pi$
$182$		0			0
$183$	−3.27828	−	3.27828i	−0.242337	−	0.242337i
$184$	0.940229	+	2.76982i	0.0693146	+	0.204194i
$185$	−0.133578	+	1.01462i	−0.00982082	+	0.0745966i
$186$	−43.0881	−	24.8769i	−3.15937	−	1.82406i
$187$	5.36166	+	13.9189i	0.392084	+	1.01785i
$188$		−	28.0083i		−	2.04271i
$189$		0			0
$190$	0.454687	−	2.28586i	0.0329864	−	0.165834i
$191$	6.15502	+	1.64923i	0.445361	+	0.119334i	0.474528	−	0.880240i	$-0.342619\pi$
$191$	6.15502	+	1.64923i	0.445361	+	0.119334i	−0.0291668	+	0.999575i	$0.509285\pi$
$192$	−69.8875	+	4.58067i	−5.04369	+	0.330581i
$193$	−14.7315	−	5.00066i	−1.06039	−	0.359955i	−0.263867	−	0.964559i	$-0.584998\pi$
$193$	−14.7315	−	5.00066i	−1.06039	−	0.359955i	−0.796526	+	0.604604i	$0.793331\pi$
$194$	3.76857	+	0.247005i	0.270568	+	0.0177339i
$195$	2.28467	+	0.946340i	0.163608	+	0.0677688i
$196$		0			0
$197$	2.58876	−	3.87435i	0.184441	−	0.276036i	−0.727714	−	0.685881i	$-0.759417\pi$
$197$	2.58876	−	3.87435i	0.184441	−	0.276036i	0.912155	+	0.409845i	$0.134417\pi$
$198$	−0.384284	−	0.438192i	−0.0273099	−	0.0311409i
$199$	1.65283	+	25.2173i	0.117166	+	1.78761i	0.502246	+	0.864725i	$0.332507\pi$
$199$	1.65283	+	25.2173i	0.117166	+	1.78761i	−0.385079	+	0.922883i	$0.625826\pi$
$200$	−48.6768	+	13.0429i	−3.44197	+	0.922272i
$201$	1.55950	−	0.529380i	0.109999	−	0.0373396i
$202$	31.9751	−	13.2445i	2.24976	−	0.931882i
$203$		0			0
$204$	−39.8954	+	9.62741i	−2.79324	+	0.674054i
$205$	0.752282	+	1.30299i	0.0525416	+	0.0910048i
$206$	−16.4990	−	2.17214i	−1.14954	−	0.151340i
$207$	−0.0124760	−	0.0109412i	−0.000867142	−	0.000760463i
$208$	−22.2280	+	82.9559i	−1.54123	+	5.75196i
$209$	6.02860	+	9.02243i	0.417007	+	0.624095i
$210$		0			0
$211$	2.28982	+	1.53001i	0.157638	+	0.105330i	0.631887	−	0.775060i	$-0.282281\pi$
$211$	2.28982	+	1.53001i	0.157638	+	0.105330i	−0.474249	+	0.880391i	$0.657281\pi$
$212$	41.3458	−	5.44328i	2.83964	−	0.373846i
$213$	−0.351991	−	0.458724i	−0.0241181	−	0.0314313i
$214$	−2.58139	−	5.23453i	−0.176460	−	0.357825i
$215$	0.514452	−	0.451162i	0.0350853	−	0.0307690i
$216$	−43.8006	+	29.2666i	−2.98026	+	1.99134i
$217$		0			0
$218$	39.2317	+	7.80366i	2.65710	+	0.528531i
$219$	0.813246	−	1.05984i	0.0549541	−	0.0716175i
$220$	−2.88445	+	4.99601i	−0.194470	+	0.336831i
$221$	−1.88003	+	20.7264i	−0.126465	+	1.39421i
$222$	15.3429	−	8.85821i	1.02975	−	0.594524i
$223$	−7.06322	−	17.0521i	−0.472988	−	1.14190i	−0.962836	−	0.270087i	$-0.912948\pi$
$223$	−7.06322	−	17.0521i	−0.472988	−	1.14190i	0.489847	−	0.871808i	$-0.337052\pi$
$224$		0			0
$225$	0.202152	−	0.202152i	0.0134768	−	0.0134768i
$226$	−39.5613	−	19.5095i	−2.63158	−	1.29775i
$227$	−3.11776	+	9.18463i	−0.206933	+	0.609605i	0.793067	+	0.609135i	$0.208483\pi$
$227$	−3.11776	+	9.18463i	−0.206933	+	0.609605i	−1.00000		0.000470476i	$0.999850\pi$
$228$	−26.7777	+	13.2053i	−1.77339	+	0.874541i
$229$	1.30149	+	9.88578i	0.0860047	+	0.653270i	0.979097	+	0.203396i	$0.0651979\pi$
$229$	1.30149	+	9.88578i	0.0860047	+	0.653270i	−0.893092	+	0.449874i	$0.851469\pi$
$230$	−0.0849412	+	0.205066i	−0.00560086	+	0.0135217i
$231$		0			0
$232$	52.6300	−	10.4688i	3.45533	−	0.687307i
$233$	8.63634	−	17.5128i	0.565785	−	1.14730i	−0.406532	−	0.913636i	$-0.633262\pi$
$233$	8.63634	−	17.5128i	0.565785	−	1.14730i	0.972318	−	0.233663i	$-0.0750712\pi$
$234$	−0.210469	−	0.785482i	−0.0137588	−	0.0513485i
$235$	0.908950	−	1.03646i	0.0592934	−	0.0676111i
$236$	4.85982	+	3.72907i	0.316348	+	0.242742i
$237$	23.5352			1.52878
$238$		0			0
$239$	−6.02802			−0.389921			−0.194960	−	0.980811i	$-0.562458\pi$
$239$	−6.02802			−0.389921			−0.194960	+	0.980811i	$0.562458\pi$
$240$	−6.61335	−	5.07460i	−0.426890	−	0.327564i
$241$	−17.7837	+	20.2785i	−1.14555	+	1.30625i	−0.200364	+	0.979722i	$0.564212\pi$
$241$	−17.7837	+	20.2785i	−1.14555	+	1.30625i	−0.945187	+	0.326529i	$0.894121\pi$
$242$	−1.49828	−	5.59167i	−0.0963132	−	0.359446i
$243$	0.266964	−	0.541348i	0.0171257	−	0.0347275i
$244$	14.8004	−	2.94398i	0.947499	−	0.188469i
$245$		0			0
$246$	9.96758	−	24.0639i	0.635510	−	1.53426i
$247$	1.97619	+	15.0106i	0.125742	+	0.955105i
$248$	94.2090	−	46.4587i	5.98228	−	2.95013i
$249$	−1.99324	+	5.87190i	−0.126316	+	0.372116i
$250$	−6.91405	−	3.40963i	−0.437283	−	0.215644i
$251$	−16.2694	+	16.2694i	−1.02692	+	1.02692i	−0.0272894	+	0.999628i	$0.508688\pi$
$251$	−16.2694	+	16.2694i	−1.02692	+	1.02692i	−0.999628	+	0.0272894i	$0.991312\pi$
$252$		0			0
$253$	−0.395475	−	0.954761i	−0.0248633	−	0.0600253i
$254$	−32.0121	+	18.4822i	−2.00862	+	1.15968i
$255$	−1.78879	−	0.938455i	−0.112018	−	0.0587683i
$256$	39.9030	−	69.1140i	2.49394	−	4.31963i
$257$	−2.41236	+	3.14384i	−0.150479	+	0.196108i	−0.862510	−	0.506040i	$-0.831109\pi$
$257$	−2.41236	+	3.14384i	−0.150479	+	0.196108i	0.712031	+	0.702148i	$0.247775\pi$
$258$	−11.6180	−	2.31097i	−0.723308	−	0.143875i
$259$		0			0
$260$	−6.69257	+	4.47183i	−0.415056	+	0.277331i
$261$	−0.228876	+	0.200719i	−0.0141671	+	0.0124242i
$262$	−2.00703	−	4.06986i	−0.123995	−	0.251437i
$263$	10.9004	+	14.2056i	0.672145	+	0.875957i	0.997574	−	0.0696099i	$-0.0221754\pi$
$263$	10.9004	+	14.2056i	0.672145	+	0.875957i	−0.325429	+	0.945566i	$0.605509\pi$
$264$	64.2240	−	8.45525i	3.95272	−	0.520385i
$265$	1.70667	+	1.14036i	0.104840	+	0.0700518i
$266$		0			0
$267$	7.51182	+	11.2422i	0.459716	+	0.688013i
$268$	−1.38741	+	5.17787i	−0.0847493	+	0.316289i
$269$	8.87546	+	7.78357i	0.541146	+	0.474573i	0.885742	−	0.464179i	$-0.153650\pi$
$269$	8.87546	+	7.78357i	0.541146	+	0.474573i	−0.344595	+	0.938751i	$0.611984\pi$
$270$	−3.96321	−	0.521766i	−0.241193	−	0.0317537i
$271$	−0.140981	−	0.244186i	−0.00856397	−	0.0148332i	0.861712	−	0.507398i	$-0.169393\pi$
$271$	−0.140981	−	0.244186i	−0.00856397	−	0.0148332i	−0.870276	+	0.492565i	$0.836059\pi$
$272$	24.2043	−	65.8458i	1.46760	−	3.99249i
$273$		0			0
$274$	−2.03984	+	0.844929i	−0.123231	+	0.0510440i
$275$	16.8594	−	5.72298i	1.01666	−	0.345109i
$276$	2.74655	−	0.735936i	0.165323	−	0.0442981i
$277$	0.583436	+	8.90151i	0.0350553	+	0.534840i	0.978885	+	0.204409i	$0.0655274\pi$
$277$	0.583436	+	8.90151i	0.0350553	+	0.534840i	−0.943830	+	0.330431i	$0.892806\pi$
$278$	−35.6037	−	40.5982i	−2.13537	−	2.43492i
$279$	−0.331067	+	0.495477i	−0.0198205	+	0.0296634i
$280$		0			0
$281$	−20.4858	−	8.48549i	−1.22208	−	0.506202i	−0.324009	−	0.946054i	$-0.605031\pi$
$281$	−20.4858	−	8.48549i	−1.22208	−	0.506202i	−0.898070	+	0.439852i	$0.855031\pi$
$282$	−23.8142	−	1.56086i	−1.41811	−	0.0929481i
$283$	−8.34627	−	2.83318i	−0.496134	−	0.168415i	0.0621464	−	0.998067i	$-0.480205\pi$
$283$	−8.34627	−	2.83318i	−0.496134	−	0.168415i	−0.558281	+	0.829652i	$0.688539\pi$
$284$	1.87799	−	0.123090i	0.111438	−	0.00730404i
$285$	−1.41947	−	0.380346i	−0.0840821	−	0.0225297i
$286$	9.88001	−	49.6702i	0.584217	−	2.93706i
$287$		0			0
$288$			1.55158i			0.0914279i
$289$	3.05888	−	16.7225i	0.179934	−	0.983679i
$290$	3.52642	+	2.03598i	0.207079	+	0.119557i
$291$	0.310822	−	2.36092i	0.0182207	−	0.138400i
$292$	1.39770	+	4.11748i	0.0817940	+	0.240957i
$293$	16.6001	+	16.6001i	0.969790	+	0.969790i	0.999557	−	0.0297673i	$-0.00947661\pi$
$293$	16.6001	+	16.6001i	0.969790	+	0.969790i	−0.0297673	+	0.999557i	$0.509477\pi$
$294$		0			0
$295$	0.0588207	+	0.295712i	0.00342467	+	0.0172170i
$296$	−2.44630	+	37.3233i	−0.142188	+	2.16937i
$297$	14.7654	−	11.3299i	0.856776	−	0.657428i
$298$	−1.76701	+	1.35587i	−0.102360	+	0.0785436i
$299$	0.0943043	−	1.43881i	0.00545376	−	0.0832083i
$300$	9.55703	+	48.0465i	0.551776	+	2.77396i
$301$		0			0
$302$	−17.1191	−	17.1191i	−0.985094	−	0.985094i
$303$	−7.01458	−	20.6643i	−0.402977	−	1.18713i
$304$	6.66156	−	50.5995i	0.382066	−	2.90208i
$305$	0.643237	+	0.371373i	0.0368316	+	0.0212647i
$306$	0.113258	+	0.654534i	0.00647453	+	0.0374172i
$307$			28.3065i			1.61554i	0.589498	+	0.807770i	$0.299326\pi$
$307$			28.3065i			1.61554i	−0.589498	+	0.807770i	$0.700674\pi$
$308$		0			0
$309$	−2.04706	+	10.2913i	−0.116453	+	0.585451i
$310$	7.69927	+	2.06301i	0.437289	+	0.117171i
$311$	1.98353	−	0.130007i	0.112476	−	0.00737204i	−0.00906141	−	0.999959i	$-0.502884\pi$
$311$	1.98353	−	0.130007i	0.112476	−	0.00737204i	0.121537	+	0.992587i	$0.461218\pi$
$312$	85.5856	+	29.0524i	4.84533	+	1.64477i
$313$	23.3098	+	1.52781i	1.31755	+	0.0863567i	0.707898	−	0.706314i	$-0.249643\pi$
$313$	23.3098	+	1.52781i	1.31755	+	0.0863567i	0.609650	+	0.792671i	$0.291310\pi$
$314$	40.5179	+	16.7831i	2.28656	+	0.947122i
$315$		0			0
$316$	−42.5595	+	63.6948i	−2.39416	+	3.58311i
$317$	−11.2919	−	12.8759i	−0.634215	−	0.723184i	0.342069	−	0.939675i	$-0.388872\pi$
$317$	−11.2919	−	12.8759i	−0.634215	−	0.723184i	−0.976285	+	0.216491i	$0.930539\pi$
$318$	−2.32403	−	35.4578i	−0.130325	−	1.98838i
$319$	−18.3125	+	4.90683i	−1.02530	+	0.274730i
$320$	10.6250	−	3.60669i	0.593954	−	0.201620i
$321$	−3.39992	+	1.40829i	−0.189765	+	0.0786032i
$322$		0			0
$323$	−0.499998	−	12.3573i	−0.0278207	−	0.687576i
$324$	26.1003	+	45.2070i	1.45002	+	2.51150i
$325$	24.6289	+	3.24246i	1.36617	+	0.179859i
$326$	−4.18573	−	3.67078i	−0.231826	−	0.203306i
$327$	6.52777	−	24.3620i	0.360987	−	1.34722i
$328$	30.5509	+	45.7227i	1.68689	+	2.52461i
$329$		0			0
$330$	4.08714	+	2.73094i	0.224990	+	0.150333i
$331$	3.24287	−	0.426932i	0.178244	−	0.0234663i	−0.0408757	−	0.999164i	$-0.513015\pi$
$331$	3.24287	−	0.426932i	0.178244	−	0.0234663i	0.219120	+	0.975698i	$0.429681\pi$
$332$	−12.2870	−	16.0127i	−0.674337	−	0.878814i
$333$	−0.0938496	−	0.190308i	−0.00514293	−	0.0104288i
$334$	−32.7997	+	28.7645i	−1.79472	+	1.57393i
$335$	−0.219379	+	0.146584i	−0.0119859	+	0.00800874i
$336$		0			0
$337$	−21.0741	−	4.19189i	−1.14798	−	0.228347i	−0.415797	−	0.909458i	$-0.636497\pi$
$337$	−21.0741	−	4.19189i	−1.14798	−	0.228347i	−0.732181	+	0.681111i	$0.761497\pi$
$338$	21.0665	−	27.4544i	1.14587	−	1.49332i
$339$	−13.9064	+	24.0867i	−0.755294	+	1.30821i
$340$	5.77451	−	3.14406i	0.313167	−	0.170510i
$341$	−32.1394	+	18.5557i	−1.74044	+	1.00485i
$342$	0.184930	+	0.446460i	0.00999985	+	0.0241418i
$343$		0			0
$344$	17.6839	−	17.6839i	0.953455	−	0.953455i
$345$	0.125521	+	0.0619000i	0.00675781	+	0.00333258i
$346$	−10.6424	+	31.3516i	−0.572140	+	1.68547i
$347$	20.0372	−	9.88126i	1.07565	−	0.530454i	0.183887	−	0.982947i	$-0.441132\pi$
$347$	20.0372	−	9.88126i	1.07565	−	0.530454i	0.891768	+	0.452493i	$0.149465\pi$
$348$	−6.80874	−	51.7175i	−0.364987	−	2.77235i
$349$	1.11310	−	2.68726i	0.0595828	−	0.143846i	−0.891284	−	0.453445i	$-0.850195\pi$
$349$	1.11310	−	2.68726i	0.0595828	−	0.143846i	0.950867	+	0.309599i	$0.100195\pi$
$350$		0			0
$351$	25.4687	−	5.06604i	1.35942	−	0.270405i
$352$	−42.7376	+	86.6633i	−2.27792	+	4.61917i
$353$	−6.02985	−	22.5037i	−0.320937	−	1.19775i	−0.918334	−	0.395807i	$-0.870465\pi$
$353$	−6.02985	−	22.5037i	−0.320937	−	1.19775i	0.597397	−	0.801945i	$-0.296202\pi$
$354$	3.44150	−	3.92428i	0.182914	−	0.208573i
$355$	0.0734905	+	0.0563912i	0.00390047	+	0.00299294i
$356$	−44.0093			−2.33249
$357$		0			0
$358$	43.5554			2.30198
$359$	12.0077	+	9.21381i	0.633740	+	0.486286i	0.874967	−	0.484183i	$-0.160883\pi$
$359$	12.0077	+	9.21381i	0.633740	+	0.486286i	−0.241226	+	0.970469i	$0.577550\pi$
$360$	−0.109873	+	0.125286i	−0.00579083	+	0.00660318i
$361$	2.58893	+	9.66200i	0.136259	+	0.508526i
$362$	−11.7484	+	23.8234i	−0.617482	+	1.25213i
$363$	−3.57995	+	0.712097i	−0.187899	+	0.0373754i
$364$		0			0
$365$	−0.0819019	+	0.197729i	−0.00428694	+	0.0103496i
$366$	−1.67833	−	12.7482i	−0.0877278	−	0.666359i
$367$	14.9548	−	7.37490i	0.780635	−	0.384966i	−0.00789053	−	0.999969i	$-0.502512\pi$
$367$	14.9548	−	7.37490i	0.780635	−	0.384966i	0.788525	+	0.615002i	$0.210845\pi$
$368$	−1.56235	+	4.60255i	−0.0814433	+	0.239924i
$369$	−0.279790	−	0.137977i	−0.0145653	−	0.00718279i
$370$	−2.00697	+	2.00697i	−0.104337	+	0.104337i
$371$		0			0
$372$	−39.0761	−	94.3380i	−2.02600	−	4.89120i
$373$	11.1951	−	6.46351i	0.579662	−	0.334668i	−0.181337	−	0.983421i	$-0.558043\pi$
$373$	11.1951	−	6.46351i	0.579662	−	0.334668i	0.760999	+	0.648753i	$0.224709\pi$
$374$	−11.7028	+	39.6785i	−0.605139	+	2.05173i
$375$	−2.43040	+	4.20957i	−0.125505	+	0.217381i
$376$	30.6725	−	39.9732i	1.58181	−	2.06146i
$377$	−25.9437	−	5.16052i	−1.33617	−	0.265780i
$378$		0			0
$379$	10.4024	−	6.95069i	0.534338	−	0.357033i	−0.258940	−	0.965893i	$-0.583373\pi$
$379$	10.4024	−	6.95069i	0.534338	−	0.357033i	0.793277	+	0.608861i	$0.208373\pi$
$380$	3.59622	−	3.15380i	0.184482	−	0.161787i
$381$	10.3085	+	20.9035i	0.528120	+	1.07092i
$382$	10.7585	+	14.0208i	0.550453	+	0.717364i
$383$	−20.9689	+	2.76061i	−1.07146	+	0.141060i	−0.645560	−	0.763710i	$-0.723376\pi$
$383$	−20.9689	+	2.76061i	−1.07146	+	0.141060i	−0.425900	+	0.904770i	$0.640043\pi$
$384$	−83.8336	−	56.0158i	−4.27812	−	2.85855i
$385$		0			0
$386$	−23.9710	−	35.8751i	−1.22009	−	1.82600i
$387$	−0.0367203	+	0.137042i	−0.00186660	+	0.00696623i
$388$	5.82744	+	5.11053i	0.295843	+	0.259448i
$389$	30.1917	+	3.97482i	1.53078	+	0.201531i	0.848357	−	0.529425i	$-0.177592\pi$
$389$	30.1917	+	3.97482i	1.53078	+	0.201531i	0.682424	+	0.730956i	$0.260926\pi$
$390$	3.42923	+	5.93960i	0.173646	+	0.300764i
$391$	−0.182891	+	1.16354i	−0.00924918	+	0.0588425i
$392$		0			0
$393$	−2.64344	+	1.09495i	−0.133344	+	0.0552329i
$394$	12.2374	−	4.15404i	0.616512	−	0.209278i
$395$	−3.64202	+	0.975875i	−0.183250	+	0.0491016i
$396$	−0.0782315	−	1.19358i	−0.00393128	−	0.0599798i
$397$	12.1613	+	13.8674i	0.610361	+	0.695983i	0.971637	−	0.236476i	$-0.0759924\pi$
$397$	12.1613	+	13.8674i	0.610361	+	0.695983i	−0.361277	+	0.932459i	$0.617659\pi$
$398$	−38.9393	+	58.2768i	−1.95185	+	2.92115i
$399$		0			0
$400$	−77.3640	−	32.0452i	−3.86820	−	1.60226i
$401$	−31.5365	−	2.06701i	−1.57486	−	0.103222i	−0.747256	−	0.664536i	$-0.768629\pi$
$401$	−31.5365	−	2.06701i	−1.57486	−	0.103222i	−0.827602	+	0.561315i	$0.810296\pi$
$402$	4.32519	+	1.46821i	0.215721	+	0.0732274i
$403$	−51.6689	+	3.38656i	−2.57381	+	0.168697i
$404$	68.6097	+	18.3839i	3.41346	+	0.914633i
$405$	−0.501247	+	2.51994i	−0.0249072	+	0.125217i
$406$		0			0
$407$		−	13.2147i		−	0.655026i
$408$	−67.4815	−	29.9502i	−3.34083	−	1.48275i
$409$	12.1976	+	7.04231i	0.603134	+	0.348220i	0.770274	−	0.637713i	$-0.220120\pi$
$409$	12.1976	+	7.04231i	0.603134	+	0.348220i	−0.167139	+	0.985933i	$0.553453\pi$
$410$	−0.544662	+	4.13712i	−0.0268990	+	0.204318i
$411$	0.447492	+	1.31827i	0.0220732	+	0.0650255i
$412$	−24.1501	−	24.1501i	−1.18979	−	1.18979i
$413$		0			0
$414$	−0.00897852	−	0.0451381i	−0.000441270	−	0.00221842i
$415$	0.0649738	−	0.991309i	0.00318944	−	0.0486614i
$416$	−106.961	+	82.0739i	−5.24419	+	4.02401i
$417$	−27.0118	+	20.7269i	−1.32278	+	1.01500i
$418$	−1.96832	+	30.0307i	−0.0962735	+	1.46885i
$419$	−4.64053	−	23.3295i	−0.226705	−	1.13972i	−0.911600	−	0.411079i	$-0.865152\pi$
$419$	−4.64053	−	23.3295i	−0.226705	−	1.13972i	0.684895	−	0.728642i	$-0.259848\pi$
$420$		0			0
$421$	19.1651	+	19.1651i	0.934051	+	0.934051i	0.997956	−	0.0639052i	$-0.0203555\pi$
$421$	19.1651	+	19.1651i	0.934051	+	0.934051i	−0.0639052	+	0.997956i	$0.520356\pi$
$422$	2.45513	+	7.23258i	0.119514	+	0.352076i
$423$	−0.0373091	+	0.283391i	−0.00181403	+	0.0137789i
$424$	64.9694	+	37.5101i	3.15519	+	1.82165i
$425$	−19.7968	−	4.45521i	−0.960285	−	0.216110i
$426$		−	1.60363i		−	0.0776961i
$427$		0			0
$428$	2.33683	−	11.7480i	0.112955	−	0.567863i
$429$	−30.8441	−	8.26464i	−1.48916	−	0.399021i
$430$	1.89369	−	0.124119i	0.0913216	−	0.00598553i
$431$	−32.7615	−	11.1210i	−1.57807	−	0.535682i	−0.611314	−	0.791388i	$-0.709359\pi$
$431$	−32.7615	−	11.1210i	−1.57807	−	0.535682i	−0.966755	+	0.255706i	$0.917692\pi$
$432$	−87.3472	−	5.72504i	−4.20249	−	0.275446i
$433$	24.8250	+	10.2828i	1.19301	+	0.494162i	0.888735	−	0.458421i	$-0.151585\pi$
$433$	24.8250	+	10.2828i	1.19301	+	0.494162i	0.304278	+	0.952583i	$0.401585\pi$
$434$		0			0
$435$	1.42642	−	2.13479i	0.0683918	−	0.102356i
$436$	54.1278	+	61.7210i	2.59225	+	2.95590i
$437$	0.0560410	+	0.855021i	0.00268081	+	0.0409012i
$438$	3.57880	−	0.958937i	0.171002	−	0.0458198i
$439$	−3.67346	+	1.24697i	−0.175325	+	0.0595148i	−0.407722	−	0.913106i	$-0.633677\pi$
$439$	−3.67346	+	1.24697i	−0.175325	+	0.0595148i	0.232397	+	0.972621i	$0.425343\pi$
$440$	−9.58791	+	3.97144i	−0.457085	+	0.189331i
$441$		0			0
$442$	−39.1304	+	42.4305i	−1.86124	+	2.01821i
$443$	−2.08183	−	3.60583i	−0.0989106	−	0.171318i	0.812323	−	0.583207i	$-0.198202\pi$
$443$	−2.08183	−	3.60583i	−0.0989106	−	0.171318i	−0.911234	+	0.411889i	$0.864869\pi$
$444$	36.0487	+	4.74590i	1.71079	+	0.225230i
$445$	−1.62859	−	1.42823i	−0.0772024	−	0.0677047i
$446$	13.2489	−	49.4455i	0.627352	−	2.34131i
$447$	0.780219	+	1.16768i	0.0369031	+	0.0552294i
$448$		0			0
$449$	20.1255	+	13.4475i	0.949783	+	0.634624i	0.930930	−	0.365198i	$-0.118999\pi$
$449$	20.1255	+	13.4475i	0.949783	+	0.634624i	0.0188527	+	0.999822i	$0.493999\pi$
$450$	0.786106	−	0.103493i	0.0370574	−	0.00487870i
$451$	−11.8271	−	15.4133i	−0.556915	−	0.725786i
$452$	−40.0397	−	81.1924i	−1.88331	−	3.81897i
$453$	−11.4770	+	10.0650i	−0.539235	+	0.472896i
$454$	−22.3671	+	14.9452i	−1.04974	+	0.701413i
$455$		0			0
$456$	−52.6782	−	10.4784i	−2.46688	−	0.490694i
$457$	8.22143	−	10.7144i	0.384582	−	0.501198i	−0.560444	−	0.828193i	$-0.689369\pi$
$457$	8.22143	−	10.7144i	0.384582	−	0.501198i	0.945026	+	0.326995i	$0.106036\pi$
$458$	−13.8271	+	23.9493i	−0.646098	+	1.11908i
$459$	−21.0931	+	2.24192i	−0.984540	+	0.104644i
$460$	−0.394506	+	0.227768i	−0.0183940	+	0.0106198i
$461$	−10.5562	−	25.4849i	−0.491651	−	1.18695i	−0.953879	−	0.300190i	$-0.902950\pi$
$461$	−10.5562	−	25.4849i	−0.491651	−	1.18695i	0.462228	−	0.886761i	$-0.347050\pi$
$462$		0			0
$463$	−21.5321	+	21.5321i	−1.00068	+	1.00068i	−0.000680151		1.00000i	$0.500216\pi$
$463$	−21.5321	+	21.5321i	−1.00068	+	1.00068i	−1.00000		0.000680151i	$0.999784\pi$
$464$	79.9717	+	39.4377i	3.71259	+	1.83085i
$465$	1.61552	−	4.75915i	0.0749177	−	0.220700i
$466$	48.5707	−	23.9524i	2.24999	−	1.10957i
$467$	−2.30670	−	17.5212i	−0.106741	−	0.810782i	−0.958148	−	0.286275i	$-0.907583\pi$
$467$	−2.30670	−	17.5212i	−0.106741	−	0.810782i	0.851406	−	0.524507i	$-0.175750\pi$
$468$	0.638670	−	1.54189i	0.0295225	−	0.0712737i
$469$		0			0
$470$	3.74990	−	0.745902i	0.172970	−	0.0344059i
$471$	12.2305	−	24.8009i	0.563550	−	1.14277i
$472$	2.85211	+	10.6442i	0.131279	+	0.489939i
$473$	−5.82576	+	6.64301i	−0.267869	+	0.305446i
$474$	51.7851	+	39.7361i	2.37857	+	1.82514i
$475$	−14.7622			−0.677336
$476$		0			0
$477$	−0.425592			−0.0194865
$478$	−13.2636	−	10.1775i	−0.606662	−	0.465508i
$479$	6.02172	−	6.86646i	0.275139	−	0.313736i	−0.597723	−	0.801703i	$-0.703928\pi$
$479$	6.02172	−	6.86646i	0.275139	−	0.313736i	0.872863	+	0.487966i	$0.162261\pi$
$480$	−3.38693	−	12.6402i	−0.154591	−	0.576943i
$481$	8.15484	−	16.5364i	0.371829	−	0.753994i
$482$	−73.3674	+	14.5937i	−3.34179	+	0.664724i
$483$		0			0
$484$	4.54655	−	10.9763i	0.206661	−	0.498924i
$485$	0.0497956	+	0.378235i	0.00226110	+	0.0171748i
$486$	1.50140	−	0.740408i	0.0681049	−	0.0335856i
$487$	8.84799	−	26.0653i	0.400941	−	1.18113i	−0.539737	−	0.841833i	$-0.681476\pi$
$487$	8.84799	−	26.0653i	0.400941	−	1.18113i	0.940678	−	0.339300i	$-0.110190\pi$
$488$	24.3470	+	12.0066i	1.10214	+	0.543514i
$489$	−2.48220	+	2.48220i	−0.112249	+	0.112249i
$490$		0			0
$491$	−1.36564	−	3.29695i	−0.0616305	−	0.148789i	0.890064	−	0.455835i	$-0.150659\pi$
$491$	−1.36564	−	3.29695i	−0.0616305	−	0.148789i	−0.951695	+	0.307046i	$0.900659\pi$
$492$	46.2941	−	26.7279i	2.08710	−	1.20499i
$493$	20.7249	+	6.11262i	0.933401	+	0.275298i
$494$	−20.9952	+	36.3648i	−0.944619	+	1.63613i
$495$	0.0358403	−	0.0467079i	0.00161090	−	0.00209937i
$496$	171.191	+	34.0521i	7.68671	+	1.52898i
$497$		0			0
$498$	−14.2997	+	9.55473i	−0.640784	+	0.428158i
$499$	−16.9616	+	14.8749i	−0.759305	+	0.665893i	−0.948760	−	0.315996i	$-0.897661\pi$
$499$	−16.9616	+	14.8749i	−0.759305	+	0.665893i	0.189455	+	0.981889i	$0.439328\pi$
$500$	−6.99765	−	14.1898i	−0.312944	−	0.634588i
$501$	16.7455	+	21.8231i	0.748132	+	0.974984i
$502$	−63.2667	+	8.32922i	−2.82373	+	0.371751i
$503$	1.63831	+	1.09468i	0.0730487	+	0.0488096i	0.591558	−	0.806262i	$-0.298513\pi$
$503$	1.63831	+	1.09468i	0.0730487	+	0.0488096i	−0.518510	+	0.855072i	$0.673513\pi$
$504$		0			0
$505$	1.94232	+	2.90689i	0.0864322	+	0.129355i
$506$	0.741814	−	2.76849i	0.0329776	−	0.123074i
$507$	−16.4050	−	14.3868i	−0.728572	−	0.638941i
$508$	−75.2136	−	9.90206i	−3.33707	−	0.439333i
$509$	−19.4968	−	33.7694i	−0.864179	−	1.49680i	−0.867860	−	0.496809i	$-0.834505\pi$
$509$	−19.4968	−	33.7694i	−0.864179	−	1.49680i	0.00368101	−	0.999993i	$-0.498828\pi$
$510$	−2.35145	−	5.08502i	−0.104124	−	0.225169i
$511$		0			0
$512$	97.9542	−	40.5739i	4.32900	−	1.79313i
$513$	−14.6125	+	4.96028i	−0.645159	+	0.219002i
$514$	−10.6159	+	2.84453i	−0.468248	+	0.125467i
$515$	−0.109945	−	1.67743i	−0.00484474	−	0.0739164i
$516$	−16.0294	−	18.2780i	−0.705655	−	0.804645i
$517$	−9.88976	+	14.8011i	−0.434951	+	0.650951i
$518$		0			0
$519$	19.2869	+	7.98889i	0.846601	+	0.350674i
$520$	−14.4488	−	0.947023i	−0.633621	−	0.0415297i
$521$	−0.617750	−	0.209698i	−0.0270641	−	0.00918704i	0.307875	−	0.951427i	$-0.400382\pi$
$521$	−0.617750	−	0.209698i	−0.0270641	−	0.00918704i	−0.334939	+	0.942240i	$0.608716\pi$
$522$	−0.842487	+	0.0552195i	−0.0368747	+	0.00241689i
$523$	27.9141	+	7.47956i	1.22060	+	0.327058i	0.810912	−	0.585168i	$-0.198971\pi$
$523$	27.9141	+	7.47956i	1.22060	+	0.327058i	0.409687	+	0.912226i	$0.365638\pi$
$524$	1.81689	−	9.13413i	0.0793713	−	0.399026i
$525$		0			0
$526$			49.6607i			2.16531i
$527$	42.2835	+	1.05773i	1.84190	+	0.0460754i
$528$	93.2192	+	53.8201i	4.05685	+	2.34222i
$529$	−2.99145	+	22.7223i	−0.130063	+	0.987927i
$530$	1.82988	+	5.39064i	0.0794848	+	0.234155i
$531$	−0.0442049	−	0.0442049i	−0.00191833	−	0.00191833i
$532$		0			0
$533$	−5.28834	−	26.5863i	−0.229064	−	1.15158i
$534$	−2.45258	+	37.4192i	−0.106134	+	1.61929i
$535$	0.467734	−	0.358905i	0.0202219	−	0.0155168i
$536$	−7.65049	+	5.87043i	−0.330451	+	0.253564i
$537$	1.79617	−	27.4042i	0.0775103	−	1.18258i
$538$	6.38735	+	32.1114i	0.275378	+	1.38442i
$539$		0			0
$540$	−5.80107	−	5.80107i	−0.249638	−	0.249638i
$541$	4.58338	+	13.5022i	0.197055	+	0.580505i	0.999877	−	0.0157142i	$-0.00500219\pi$
$541$	4.58338	+	13.5022i	0.197055	+	0.580505i	−0.802822	+	0.596219i	$0.796669\pi$
$542$	0.102072	−	0.775314i	0.00438437	−	0.0333026i
$543$	14.5047	+	8.37431i	0.622457	+	0.359376i
$544$	93.0710	−	58.8757i	3.99038	−	2.52428i
$545$			4.04062i			0.173081i
$546$		0			0
$547$	−0.348693	+	1.75300i	−0.0149090	+	0.0749528i	−0.987524	−	0.157471i	$-0.949666\pi$
$547$	−0.348693	+	1.75300i	−0.0149090	+	0.0749528i	0.972615	+	0.232424i	$0.0746658\pi$
$548$	−4.37693	−	1.17279i	−0.186973	−	0.0500993i
$549$	−0.153674	+	0.0100723i	−0.00655864	+	0.000429876i
$550$	46.7585	+	15.8724i	1.99379	+	0.676800i
$551$	15.6856	+	1.02809i	0.668230	+	0.0437981i
$552$	4.72579	+	1.95749i	0.201143	+	0.0833162i
$553$		0			0
$554$	−13.7453	+	20.5712i	−0.583980	+	0.873988i
$555$	1.17998	+	1.34551i	0.0500873	+	0.0571137i
$556$	−7.24811	−	110.585i	−0.307388	−	4.68984i
$557$	3.68929	−	0.988543i	0.156320	−	0.0418859i	−0.179810	−	0.983701i	$-0.557548\pi$
$557$	3.68929	−	0.988543i	0.156320	−	0.0418859i	0.336131	+	0.941815i	$0.390882\pi$
$558$	−1.56500	+	0.531246i	−0.0662517	+	0.0224894i
$559$	−11.3896	+	4.71772i	−0.481729	+	0.199538i
$560$		0			0
$561$	24.4823	+	8.99948i	1.03364	+	0.379958i
$562$	−30.7487	−	53.2583i	−1.29705	−	2.24657i
$563$	−1.81204	−	0.238560i	−0.0763685	−	0.0100541i	0.0922451	−	0.995736i	$-0.470596\pi$
$563$	−1.81204	−	0.238560i	−0.0763685	−	0.0100541i	−0.168614	+	0.985682i	$0.553929\pi$
$564$	−36.8245	−	32.2942i	−1.55059	−	1.35983i
$565$	1.15324	−	4.30397i	0.0485174	−	0.181069i
$566$	−13.5810	−	20.3254i	−0.570853	−	0.854342i
$567$		0			0
$568$	2.81505	+	1.88095i	0.118117	+	0.0789231i
$569$	−34.1854	+	4.50060i	−1.43313	+	0.188675i	−0.806772	−	0.590862i	$-0.798788\pi$
$569$	−34.1854	+	4.50060i	−1.43313	+	0.188675i	−0.626356	+	0.779537i	$0.715454\pi$
$570$	−2.48113	−	3.23347i	−0.103923	−	0.135435i
$571$	−5.39801	−	10.9461i	−0.225900	−	0.458080i	0.754184	−	0.656663i	$-0.228033\pi$
$571$	−5.39801	−	10.9461i	−0.225900	−	0.458080i	−0.980084	+	0.198583i	$0.936366\pi$
$572$	78.1433	−	68.5298i	3.26734	−	2.86538i
$573$	9.26524	−	6.19084i	0.387061	−	0.258626i
$574$		0			0
$575$	1.37888	+	0.274277i	0.0575034	+	0.0114381i
$576$	−1.41627	+	1.84572i	−0.0590114	+	0.0769052i
$577$	−0.162345	+	0.281189i	−0.00675850	+	0.0117061i	−0.869385	−	0.494136i	$-0.835485\pi$
$577$	−0.162345	+	0.281189i	−0.00675850	+	0.0117061i	0.862626	+	0.505842i	$0.168818\pi$
$578$	34.9643	−	31.6304i	1.45432	−	1.31565i
$579$	−23.5604	+	13.6026i	−0.979139	+	0.565306i
$580$	3.19807	+	7.72082i	0.132793	+	0.320590i
$581$		0			0
$582$	4.67001	−	4.67001i	0.193578	−	0.193578i
$583$	−23.7714	−	11.7227i	−0.984509	−	0.485506i
$584$	−2.51436	+	7.40708i	−0.104045	+	0.306507i
$585$	0.0736730	−	0.0363315i	0.00304600	−	0.00150212i
$586$	8.49852	+	64.5527i	0.351071	+	2.66665i
$587$	6.54464	−	15.8002i	0.270126	−	0.652142i	−0.729362	−	0.684128i	$-0.760183\pi$
$587$	6.54464	−	15.8002i	0.270126	−	0.652142i	0.999488	+	0.0319856i	$0.0101831\pi$
$588$		0			0
$589$	30.1793	−	6.00303i	1.24352	−	0.247351i
$590$	−0.369845	+	0.749971i	−0.0152263	+	0.0308758i
$591$	−2.10899	−	7.87084i	−0.0867521	−	0.323763i
$592$	−40.9798	+	46.7285i	−1.68426	+	1.92053i
$593$	15.9245	+	12.2193i	0.653941	+	0.501786i	0.881626	−	0.471948i	$-0.156449\pi$
$593$	15.9245	+	12.2193i	0.653941	+	0.501786i	−0.227686	+	0.973735i	$0.573116\pi$
$594$	51.6177			2.11790
$595$		0			0
$596$	−4.57106			−0.187238
$597$	35.0608	+	26.9031i	1.43494	+	1.10107i
$598$	2.63673	−	3.00661i	0.107824	−	0.122950i
$599$	−9.13817	−	34.1041i	−0.373375	−	1.39346i	−0.855704	−	0.517466i	$-0.826876\pi$
$599$	−9.13817	−	34.1041i	−0.373375	−	1.39346i	0.482329	−	0.875990i	$-0.339791\pi$
$600$	−38.9770	+	79.0376i	−1.59123	+	3.22670i
$601$	26.2764	−	5.22670i	1.07184	−	0.213201i	0.372527	−	0.928021i	$-0.378491\pi$
$601$	26.2764	−	5.22670i	1.07184	−	0.213201i	0.699309	+	0.714820i	$0.253491\pi$
$602$		0			0
$603$	0.0209352	−	0.0505421i	0.000852549	−	0.00205823i
$604$	−6.48542	−	49.2617i	−0.263888	−	2.00443i
$605$	0.524461	−	0.258636i	0.0213224	−	0.0105150i
$606$	19.4545	−	57.3112i	0.790287	−	2.32811i
$607$	−10.0229	−	4.94272i	−0.406815	−	0.200619i	0.227356	−	0.973812i	$-0.426992\pi$
$607$	−10.0229	−	4.94272i	−0.406815	−	0.200619i	−0.634171	+	0.773193i	$0.718659\pi$
$608$	56.6523	−	56.6523i	2.29756	−	2.29756i
$609$		0			0
$610$	0.788314	+	1.90316i	0.0319179	+	0.0770566i
$611$	−21.5095	+	12.4185i	−0.870183	+	0.502400i
$612$	−0.633348	+	1.20722i	−0.0256016	+	0.0487991i
$613$	−16.9255	+	29.3158i	−0.683613	+	1.18405i	0.290257	+	0.956949i	$0.406259\pi$
$613$	−16.9255	+	29.3158i	−0.683613	+	1.18405i	−0.973870	+	0.227104i	$0.927074\pi$
$614$	−47.7918	+	62.2834i	−1.92872	+	2.51356i
$615$	2.58053	+	0.513300i	0.104057	+	0.0206983i
$616$		0			0
$617$	−34.6692	+	23.1652i	−1.39573	+	0.932597i	−0.395832	+	0.918323i	$0.629544\pi$
$617$	−34.6692	+	23.1652i	−1.39573	+	0.932597i	−0.999898	+	0.0142739i	$0.995456\pi$
$618$	−21.8796	+	19.1879i	−0.880129	+	0.771852i
$619$	5.51403	+	11.1813i	0.221628	+	0.449416i	0.979080	−	0.203474i	$-0.0652231\pi$
$619$	5.51403	+	11.1813i	0.221628	+	0.449416i	−0.757453	+	0.652890i	$0.773556\pi$
$620$	9.95859	+	12.9783i	0.399947	+	0.521220i
$621$	1.45706	−	0.191826i	0.0584699	−	0.00769771i
$622$	4.58390	+	3.06286i	0.183797	+	0.122810i
$623$		0			0
$624$	83.4387	+	124.875i	3.34022	+	4.99899i
$625$	−6.16735	+	23.0169i	−0.246694	+	0.920675i
$626$	48.7095	+	42.7171i	1.94682	+	1.70732i
$627$	18.8136	+	2.47685i	0.751341	+	0.0989159i
$628$	45.0035	+	77.9483i	1.79583	+	3.11047i
$629$	−7.85436	+	12.8509i	−0.313174	+	0.512398i
$630$		0			0
$631$	−11.0788	+	4.58899i	−0.441040	+	0.182685i	−0.592142	−	0.805833i	$-0.701718\pi$
$631$	−11.0788	+	4.58899i	−0.441040	+	0.182685i	0.151103	+	0.988518i	$0.451718\pi$
$632$	−130.494	+	44.2968i	−5.19078	+	1.76203i
$633$	4.65184	−	1.24646i	0.184894	−	0.0495422i
$634$	−3.10650	−	47.3960i	−0.123375	−	1.88233i
$635$	−2.46197	−	2.80733i	−0.0977001	−	0.111406i
$636$	40.5160	−	60.6365i	1.60656	−	2.40439i
$637$		0			0
$638$	−48.5779	−	20.1216i	−1.92322	−	0.796623i
$639$	−0.0191657	−	0.00125618i	−0.000758182	−	4.96939e-5i
$640$	15.2957	+	5.19219i	0.604616	+	0.205239i
$641$	31.9679	−	2.09529i	1.26266	−	0.0827588i	0.580679	−	0.814133i	$-0.302787\pi$
$641$	31.9679	−	2.09529i	1.26266	−	0.0827588i	0.681977	+	0.731374i	$0.261120\pi$
$642$	−9.85862	−	2.64161i	−0.389089	−	0.104256i
$643$	9.28576	−	46.6826i	0.366194	−	1.84098i	−0.155480	−	0.987839i	$-0.549692\pi$
$643$	9.28576	−	46.6826i	0.366194	−	1.84098i	0.521674	−	0.853145i	$-0.325308\pi$
$644$		0			0
$645$		−	1.19659i		−	0.0471156i
$646$	19.7634	−	28.0341i	0.777581	−	1.10299i
$647$	8.50263	+	4.90900i	0.334273	+	0.192993i	0.657737	−	0.753248i	$-0.271514\pi$
$647$	8.50263	+	4.90900i	0.334273	+	0.192993i	−0.323464	+	0.946241i	$0.604847\pi$
$648$	−12.2571	+	93.1021i	−0.481505	+	3.65740i
$649$	−1.25145	−	3.68665i	−0.0491237	−	0.144714i
$650$	48.7170	+	48.7170i	1.91084	+	1.91084i
$651$		0			0
$652$	−2.22908	−	11.2063i	−0.0872975	−	0.438874i
$653$	0.531808	−	8.11383i	0.0208113	−	0.317519i	−0.974743	−	0.223329i	$-0.928307\pi$
$653$	0.531808	−	8.11383i	0.0208113	−	0.317519i	0.995554	−	0.0941893i	$-0.0300259\pi$
$654$	55.4951	−	42.5829i	2.17003	−	1.66512i
$655$	0.363664	−	0.279049i	0.0142095	−	0.0109034i
$656$	−5.97626	+	91.1802i	−0.233334	+	3.55999i
$657$	−0.00865726	−	0.0435230i	−0.000337752	−	0.00169799i
$658$		0			0
$659$	−25.1230	−	25.1230i	−0.978654	−	0.978654i	0.0211227	−	0.999777i	$-0.493276\pi$
$659$	−25.1230	−	25.1230i	−0.978654	−	0.978654i	−0.999777	+	0.0211227i	$0.993276\pi$
$660$	3.24278	+	9.55291i	0.126225	+	0.371847i
$661$	1.61017	−	12.2304i	0.0626282	−	0.475708i	−0.931177	−	0.364568i	$-0.881217\pi$
$661$	1.61017	−	12.2304i	0.0626282	−	0.475708i	0.993805	−	0.111140i	$-0.0354502\pi$
$662$	7.85617	+	4.53576i	0.305339	+	0.176287i
$663$	25.0827	+	26.3698i	0.974132	+	1.02412i
$664$		−	36.3090i		−	1.40906i
$665$		0			0
$666$	0.114810	−	0.577191i	0.00444882	−	0.0223657i
$667$	−1.44603	−	0.387464i	−0.0559907	−	0.0150027i
$668$	−89.3425	+	5.85581i	−3.45676	+	0.226568i
$669$	−30.5637	−	10.3750i	−1.18166	−	0.401120i
$670$	−0.730190	−	0.0478592i	−0.0282097	−	0.00184896i
$671$	−8.86085	−	3.67029i	−0.342069	−	0.141690i
$672$		0			0
$673$	16.0619	−	24.0383i	0.619140	−	0.926609i	−0.380858	−	0.924634i	$-0.624371\pi$
$673$	16.0619	−	24.0383i	0.619140	−	0.926609i	0.999998	−	0.00197520i	$-0.000628725\pi$
$674$	−39.2922	−	44.8042i	−1.51348	−	1.72579i
$675$	1.65597	+	25.2652i	0.0637382	+	0.972457i
$676$	68.6015	−	18.3817i	2.63852	−	0.706990i
$677$	−5.44084	+	1.84692i	−0.209109	+	0.0709828i	−0.424028	−	0.905649i	$-0.639384\pi$
$677$	−5.44084	+	1.84692i	−0.209109	+	0.0709828i	0.214920	+	0.976632i	$0.431051\pi$
$678$	−71.2657	+	29.5192i	−2.73694	+	1.13368i
$679$		0			0
$680$	11.6845	+	1.83663i	0.448078	+	0.0704314i
$681$	8.48084	+	14.6892i	0.324986	+	0.562893i
$682$	−102.046	−	13.4346i	−3.90753	−	0.514436i
$683$	6.66373	+	5.84393i	0.254980	+	0.223612i	0.777287	−	0.629146i	$-0.216595\pi$
$683$	6.66373	+	5.84393i	0.254980	+	0.223612i	−0.522307	+	0.852758i	$0.674928\pi$
$684$	−0.256689	+	0.957977i	−0.00981476	+	0.0366292i
$685$	−0.123910	−	0.185444i	−0.00473434	−	0.00708544i
$686$		0			0
$687$	14.4982	+	9.68738i	0.553140	+	0.369596i
$688$	41.2011	−	5.42423i	1.57078	−	0.206797i
$689$	−22.5125	−	29.3389i	−0.857659	−	1.11772i
$690$	0.171676	+	0.348125i	0.00653559	+	0.0132529i
$691$	32.1734	−	28.2153i	1.22393	−	1.07336i	0.228937	−	0.973441i	$-0.426475\pi$
$691$	32.1734	−	28.2153i	1.22393	−	1.07336i	0.994996	−	0.0999183i	$-0.0318582\pi$
$692$	−56.4979	+	37.7507i	−2.14773	+	1.43507i
$693$		0			0
$694$	60.7715	+	12.0882i	2.30685	+	0.458862i
$695$	3.32058	−	4.32746i	0.125957	−	0.164150i
$696$	46.9196	−	81.2672i	1.77848	−	3.08042i
$697$	2.34030	+	22.0187i	0.0886453	+	0.834016i
$698$	6.98624	−	4.03351i	0.264433	−	0.152671i
$699$	−13.0674	−	31.5475i	−0.494254	−	1.19323i
$700$		0			0
$701$	26.2787	−	26.2787i	0.992534	−	0.992534i	−0.00743832	−	0.999972i	$-0.502368\pi$
$701$	26.2787	−	26.2787i	0.992534	−	0.992534i	0.999972	+	0.00743832i	$0.00236771\pi$
$702$	64.5926	+	31.8535i	2.43789	+	1.20223i
$703$	−3.52195	+	10.3753i	−0.132833	+	0.391313i
$704$	−129.945	+	64.0819i	−4.89750	+	2.41518i
$705$	−0.314666	−	2.39012i	−0.0118510	−	0.0900173i
$706$	24.7269	−	59.6960i	0.930609	−	2.24669i
$707$		0			0
$708$	10.5064	−	2.08985i	0.394854	−	0.0785413i
$709$	−9.36914	+	18.9987i	−0.351865	+	0.713512i	−0.998797	−	0.0490356i	$-0.984385\pi$
$709$	−9.36914	+	18.9987i	−0.351865	+	0.713512i	0.646932	+	0.762548i	$0.276052\pi$
$710$	0.0664936	+	0.248158i	0.00249546	+	0.00931319i
$711$	0.515468	−	0.587778i	0.0193316	−	0.0220434i
$712$	−62.8097	−	48.1956i	−2.35389	−	1.80621i
$713$	−2.93047			−0.109747
$714$		0			0
$715$	5.11572			0.191317
$716$	70.9175	+	54.4169i	2.65031	+	2.03366i
$717$	−6.95046	+	7.92548i	−0.259570	+	0.295982i
$718$	10.8644	+	40.5467i	0.405457	+	1.51319i
$719$	−1.03905	+	2.10699i	−0.0387502	+	0.0785776i	−0.915387	−	0.402575i	$-0.868115\pi$
$719$	−1.03905	+	2.10699i	−0.0387502	+	0.0785776i	0.876637	+	0.481153i	$0.159782\pi$
$720$	−0.271581	+	0.0540207i	−0.0101212	+	0.00201323i
$721$		0			0
$722$	−10.6165	+	25.6305i	−0.395106	+	0.953870i
$723$	6.15648	+	46.7631i	0.228962	+	1.73914i
$724$	−48.8932	+	24.1115i	−1.81710	+	0.896095i
$725$	8.29044	−	24.4228i	0.307899	−	0.907042i
$726$	−9.07932	−	4.47742i	−0.336965	−	0.166173i
$727$	9.02527	−	9.02527i	0.334729	−	0.334729i	−0.519650	−	0.854379i	$-0.673938\pi$
$727$	9.02527	−	9.02527i	0.334729	−	0.334729i	0.854379	+	0.519650i	$0.173938\pi$
$728$		0			0
$729$	10.1247	+	24.4432i	0.374989	+	0.905304i
$730$	−0.514048	+	0.296786i	−0.0190258	+	0.0109845i
$731$	9.61377	−	2.99749i	0.355578	−	0.110866i
$732$	13.1946	−	22.8536i	0.487685	−	0.844695i
$733$	4.96859	−	6.47519i	0.183519	−	0.239167i	−0.692530	−	0.721389i	$-0.743504\pi$
$733$	4.96859	−	6.47519i	0.183519	−	0.239167i	0.876049	+	0.482223i	$0.160170\pi$
$734$	45.3569	+	9.02205i	1.67415	+	0.333010i
$735$		0			0
$736$	−6.34427	+	4.23910i	−0.233853	+	0.156255i
$737$	2.56149	−	2.24637i	0.0943538	−	0.0827460i
$738$	−0.382671	−	0.775981i	−0.0140863	−	0.0285642i
$739$	−21.3867	−	27.8717i	−0.786724	−	1.02528i	−0.998846	−	0.0480349i	$-0.984704\pi$
$739$	−21.3867	−	27.8717i	−0.786724	−	1.02528i	0.212122	−	0.977243i	$-0.431963\pi$
$740$	−5.77522	+	0.760322i	−0.212301	+	0.0279500i
$741$	22.0142	+	14.7094i	0.808711	+	0.540363i
$742$		0			0
$743$	−1.24411	−	1.86194i	−0.0456418	−	0.0683078i	0.807947	−	0.589255i	$-0.200579\pi$
$743$	−1.24411	−	1.86194i	−0.0456418	−	0.0683078i	−0.853589	+	0.520947i	$0.825579\pi$
$744$	47.5426	−	177.431i	1.74300	−	6.50495i
$745$	−0.169154	−	0.148344i	−0.00619733	−	0.00543491i
$746$	35.5456	+	4.67967i	1.30142	+	0.171335i
$747$	0.102991	+	0.178386i	0.00376825	+	0.00652680i
$748$	−68.6279	+	49.9839i	−2.50929	+	1.82759i
$749$		0			0
$750$	−12.4550	+	5.15901i	−0.454790	+	0.188380i
$751$	36.4452	−	12.3715i	1.32991	−	0.451442i	0.436101	−	0.899898i	$-0.356359\pi$
$751$	36.4452	−	12.3715i	1.32991	−	0.451442i	0.893805	+	0.448456i	$0.148026\pi$
$752$	80.8707	−	21.6693i	2.94905	−	0.790196i
$753$	2.63154	+	40.1496i	0.0958988	+	1.46313i
$754$	−48.3716	−	55.1573i	−1.76159	−	2.00871i
$755$	1.35869	−	2.03342i	0.0494478	−	0.0740038i
$756$		0			0
$757$	0.599790	+	0.248441i	0.0217997	+	0.00902975i	0.393557	−	0.919300i	$-0.371245\pi$
$757$	0.599790	+	0.248441i	0.0217997	+	0.00902975i	−0.371757	+	0.928330i	$0.621245\pi$
$758$	34.6240	+	2.26938i	1.25760	+	0.0824275i
$759$	−1.71129	−	0.580903i	−0.0621157	−	0.0210854i
$760$	8.58629	−	0.562775i	0.311458	−	0.0204140i
$761$	32.3932	+	8.67974i	1.17425	+	0.314640i	0.792645	−	0.609684i	$-0.208704\pi$
$761$	32.3932	+	8.67974i	1.17425	+	0.314640i	0.381608	+	0.924324i	$0.375370\pi$
$762$	−12.6108	+	63.3990i	−0.456843	+	2.29670i
$763$		0			0
$764$			36.2701i			1.31221i
$765$	−0.0626153	+	0.0241198i	−0.00226386	+	0.000872055i
$766$	−50.7992	−	29.3289i	−1.83545	−	1.05970i
$767$	0.709032	−	5.38563i	0.0256017	−	0.194464i
$768$	−44.8601	−	132.153i	−1.61875	−	4.76868i
$769$	1.44428	+	1.44428i	0.0520821	+	0.0520821i	0.732668	−	0.680586i	$-0.238275\pi$
$769$	1.44428	+	1.44428i	0.0520821	+	0.0520821i	−0.680586	+	0.732668i	$0.738275\pi$
$770$		0			0
$771$	1.35193	+	6.79663i	0.0486887	+	0.244775i
$772$	5.79149	−	88.3610i	0.208440	−	3.18018i
$773$	7.12978	−	5.47088i	0.256441	−	0.196774i	−0.472538	−	0.881310i	$-0.656662\pi$
$773$	7.12978	−	5.47088i	0.256441	−	0.196774i	0.728979	+	0.684537i	$0.239995\pi$
$774$	−0.312173	+	0.239539i	−0.0112208	+	0.00861005i
$775$	3.30202	−	50.3790i	0.118612	−	1.80967i
$776$	2.72022	+	13.6755i	0.0976501	+	0.490920i
$777$		0			0
$778$	59.7205	+	59.7205i	2.14108	+	2.14108i
$779$	5.17795	+	15.2537i	0.185519	+	0.546522i
$780$	−1.83725	+	13.9553i	−0.0657842	+	0.499681i
$781$	−1.03589	−	0.598073i	−0.0370672	−	0.0214007i
$782$	−2.36689	+	2.25136i	−0.0846398	+	0.0805086i
$783$		−	26.9609i		−	0.963504i
$784$		0			0
$785$	−0.864276	+	4.34501i	−0.0308473	+	0.155080i
$786$	−7.66509	−	2.05386i	−0.273405	−	0.0732586i
$787$	−3.34142	+	0.219008i	−0.119109	+	0.00780680i	−0.124841	−	0.992177i	$-0.539842\pi$
$787$	−3.34142	+	0.219008i	−0.119109	+	0.00780680i	0.00573215	+	0.999984i	$0.498175\pi$
$788$	25.1151	+	8.52541i	0.894687	+	0.303705i
$789$	31.2455	+	2.04794i	1.11237	+	0.0729086i
$790$	−9.66123	−	4.00181i	−0.343731	−	0.142378i
$791$		0			0
$792$	1.19547	−	1.78914i	0.0424791	−	0.0635744i
$793$	−8.82322	−	10.0610i	−0.313322	−	0.357275i
$794$	3.34569	+	51.0454i	0.118734	+	1.81153i
$795$	3.46715	−	0.929019i	0.122967	−	0.0329489i
$796$	−136.211	+	46.2373i	−4.82786	+	1.63884i
$797$	7.28127	−	3.01600i	0.257916	−	0.106832i	−0.249979	−	0.968251i	$-0.580424\pi$
$797$	7.28127	−	3.01600i	0.257916	−	0.106832i	0.507895	+	0.861419i	$0.330424\pi$
$798$		0			0
$799$	18.4148	−	8.51547i	0.651468	−	0.301256i
$800$	−65.7277	−	113.844i	−2.32383	−	4.02498i
$801$	0.445291	+	0.0586237i	0.0157336	+	0.00207137i
$802$	−65.9006	−	57.7932i	−2.32703	−	2.04075i
$803$	0.715270	−	2.66943i	0.0252413	−	0.0942020i
$804$	5.20800	+	7.79433i	0.183672	+	0.274885i
$805$		0			0
$806$	−119.406	−	79.7845i	−4.20590	−	2.81029i
$807$	20.4672	−	2.69456i	0.720481	−	0.0948531i
$808$	77.7865	+	101.373i	2.73652	+	3.56630i
$809$	7.13184	+	14.4620i	0.250742	+	0.508455i	0.985458	−	0.169920i	$-0.0543510\pi$
$809$	7.13184	+	14.4620i	0.250742	+	0.508455i	−0.734716	+	0.678375i	$0.762684\pi$
$810$	−5.35748	+	4.69839i	−0.188243	+	0.165084i
$811$	32.8354	−	21.9399i	1.15301	−	0.770415i	0.176162	−	0.984361i	$-0.443632\pi$
$811$	32.8354	−	21.9399i	1.15301	−	0.770415i	0.976845	+	0.213947i	$0.0686319\pi$
$812$		0			0
$813$	−0.483603	−	0.0961946i	−0.0169607	−	0.00337369i
$814$	22.3112	−	29.0765i	0.782006	−	1.01913i
$815$	0.281191	−	0.487036i	0.00984967	−	0.0170601i
$816$	−58.6641	−	107.745i	−2.05365	−	3.77183i
$817$	6.34451	−	3.66301i	0.221966	−	0.128152i
$818$	14.9487	+	36.0894i	0.522670	+	1.26184i
$819$		0			0
$820$	−6.05563	+	6.05563i	−0.211472	+	0.211472i
$821$	−8.37387	−	4.12953i	−0.292250	−	0.144122i	0.290254	−	0.956950i	$-0.406260\pi$
$821$	−8.37387	−	4.12953i	−0.292250	−	0.144122i	−0.582504	+	0.812828i	$0.697927\pi$
$822$	−1.24109	+	3.65615i	−0.0432882	+	0.127523i
$823$	37.4619	−	18.4742i	1.30584	−	0.643969i	0.349695	−	0.936863i	$-0.386285\pi$
$823$	37.4619	−	18.4742i	1.30584	−	0.643969i	0.956145	+	0.292894i	$0.0946184\pi$
$824$	−8.01951	−	60.9142i	−0.279373	−	2.12205i
$825$	11.9148	−	28.7649i	0.414821	−	1.00147i
$826$		0			0
$827$	−44.5575	+	8.86303i	−1.54942	+	0.308198i	−0.894348	−	0.447372i	$-0.852360\pi$
$827$	−44.5575	+	8.86303i	−1.54942	+	0.308198i	−0.655068	+	0.755570i	$0.727360\pi$
$828$	0.0417753	−	0.0847119i	0.00145179	−	0.00294394i
$829$	−2.08650	−	7.78693i	−0.0724672	−	0.270451i	0.920180	−	0.391496i	$-0.128042\pi$
$829$	−2.08650	−	7.78693i	−0.0724672	−	0.270451i	−0.992647	+	0.121045i	$0.961376\pi$
$830$	1.81665	−	2.07150i	0.0630570	−	0.0719027i
$831$	12.3762	+	9.49657i	0.429325	+	0.329432i
$832$	−202.154			−7.00844
$833$		0			0
$834$	−94.4293			−3.26982
$835$	−3.49620	−	2.68273i	−0.120991	−	0.0928396i
$836$	−40.7244	+	46.4372i	−1.40848	+	1.60607i
$837$	−13.6594	−	50.9777i	−0.472140	−	1.76205i
$838$	29.1781	−	59.1673i	1.00794	−	2.04390i
$839$	23.2517	−	4.62505i	0.802737	−	0.159674i	0.223362	−	0.974736i	$-0.428297\pi$
$839$	23.2517	−	4.62505i	0.802737	−	0.159674i	0.579375	+	0.815061i	$0.303297\pi$
$840$		0			0
$841$	0.587896	−	1.41931i	0.0202723	−	0.0489416i
$842$	9.81168	+	74.5271i	0.338133	+	2.56837i
$843$	−34.7771	+	17.1502i	−1.19779	+	0.590683i
$844$	−5.03870	+	14.8435i	−0.173439	+	0.510936i
$845$	3.13517	+	1.54610i	0.107853	+	0.0531873i
$846$	−0.560559	+	0.560559i	−0.0192724	+	0.0192724i
$847$		0			0
$848$	47.7050	+	115.170i	1.63820	+	3.95496i
$849$	−13.3484	+	7.70672i	−0.458117	+	0.264494i
$850$	−36.0372	−	43.2271i	−1.23607	−	1.48268i
$851$	0.521743	−	0.903685i	0.0178851	−	0.0309779i
$852$	2.00353	−	2.61105i	0.0686398	−	0.0894532i
$853$	−28.7674	−	5.72219i	−0.984977	−	0.195924i	−0.323777	−	0.946133i	$-0.604953\pi$
$853$	−28.7674	−	5.72219i	−0.984977	−	0.195924i	−0.661200	+	0.750209i	$0.729953\pi$
$854$		0			0
$855$	−0.0405881	+	0.0271201i	−0.00138808	+	0.000927488i
$856$	16.2007	−	14.2076i	0.553727	−	0.485606i
$857$	−14.5946	−	29.5949i	−0.498542	−	1.01094i	−0.990135	−	0.140118i	$-0.955252\pi$
$857$	−14.5946	−	29.5949i	−0.498542	−	1.01094i	0.491593	−	0.870825i	$-0.336415\pi$
$858$	−53.9131	−	70.2609i	−1.84056	−	2.39867i
$859$	−42.0674	+	5.53828i	−1.43532	+	0.188964i	−0.807718	−	0.589570i	$-0.799297\pi$
$859$	−42.0674	+	5.53828i	−1.43532	+	0.188964i	−0.627603	+	0.778533i	$0.715964\pi$
$860$	3.23839	+	2.16383i	0.110428	+	0.0737858i
$861$		0			0
$862$	−53.3095	−	79.7833i	−1.81573	−	2.71743i
$863$	6.85546	−	25.5849i	0.233363	−	0.870921i	−0.745517	−	0.666486i	$-0.767798\pi$
$863$	6.85546	−	25.5849i	0.233363	−	0.870921i	0.978880	−	0.204435i	$-0.0655358\pi$
$864$	−103.314	−	90.6041i	−3.51482	−	3.08241i
$865$	−3.31585	−	0.436540i	−0.112742	−	0.0148428i
$866$	37.2617	+	64.5392i	1.26621	+	2.19313i
$867$	−18.4594	−	23.3032i	−0.626913	−	0.791419i
$868$		0			0
$869$	44.9814	−	18.6319i	1.52589	−	0.632045i
$870$	6.74290	−	2.28891i	0.228606	−	0.0776012i
$871$	4.59161	−	1.23032i	0.155581	−	0.0416877i
$872$	9.65876	+	147.364i	0.327087	+	4.99038i
$873$	−0.0521551	−	0.0594715i	−0.00176518	−	0.00201280i
$874$	−1.32028	+	1.97594i	−0.0446591	+	0.0668371i
$875$		0			0
$876$	7.02512	+	2.90990i	0.237357	+	0.0983164i
$877$	26.2598	+	1.72116i	0.886731	+	0.0581194i	0.501958	−	0.864892i	$-0.332613\pi$
$877$	26.2598	+	1.72116i	0.886731	+	0.0581194i	0.384773	+	0.923011i	$0.374280\pi$
$878$	−10.1881	−	3.45841i	−0.343833	−	0.116716i
$879$	40.9657	−	2.68503i	1.38174	−	0.0905640i
$880$	−16.6570	−	4.46324i	−0.561509	−	0.150456i
$881$	−7.16565	+	36.0242i	−0.241417	+	1.21368i	0.649799	+	0.760106i	$0.274853\pi$
$881$	−7.16565	+	36.0242i	−0.241417	+	1.21368i	−0.891216	+	0.453579i	$0.850147\pi$
$882$		0			0
$883$		−	40.0516i		−	1.34784i	−0.738803	−	0.673922i	$-0.764608\pi$
$883$		−	40.0516i		−	1.34784i	0.738803	−	0.673922i	$-0.235392\pi$
$884$	−116.724	+	20.1975i	−3.92585	+	0.679315i
$885$	0.456615	+	0.263627i	0.0153489	+	0.00886172i
$886$	1.50727	−	11.4489i	0.0506378	−	0.384632i
$887$	−3.72500	−	10.9735i	−0.125073	−	0.368454i	0.866300	−	0.499524i	$-0.166492\pi$
$887$	−3.72500	−	10.9735i	−0.125073	−	0.368454i	−0.991373	+	0.131071i	$0.958159\pi$
$888$	46.2510	+	46.2510i	1.55208	+	1.55208i
$889$		0			0
$890$	−1.17203	−	5.89221i	−0.0392867	−	0.197507i
$891$	2.16987	−	33.1059i	0.0726935	−	1.10909i
$892$	83.3477	−	63.9550i	2.79069	−	2.14137i
$893$	11.7096	−	8.98509i	0.391847	−	0.300674i
$894$	−0.254739	+	3.88657i	−0.00851975	+	0.129986i
$895$	0.858348	+	4.31521i	0.0286914	+	0.144241i
$896$		0			0
$897$	−1.78297	−	1.78297i	−0.0595315	−	0.0595315i
$898$	21.5784	+	63.5680i	0.720081	+	2.12129i
$899$	−7.01714	+	53.3004i	−0.234035	+	1.77767i
$900$	1.40925	+	0.813631i	0.0469750	+	0.0271210i
$901$	16.1494	+	25.5289i	0.538013	+	0.850493i
$902$		−	53.8827i		−	1.79410i
$903$		0			0
$904$	31.7714	−	159.725i	1.05670	−	5.31239i
$905$	−2.59180	−	0.694472i	−0.0861545	−	0.0230850i
$906$	−42.2464	+	2.76898i	−1.40354	+	0.0919931i
$907$	−1.16512	−	0.395504i	−0.0386871	−	0.0131325i	0.302029	−	0.953299i	$-0.402336\pi$
$907$	−1.16512	−	0.395504i	−0.0386871	−	0.0131325i	−0.340716	+	0.940166i	$0.610669\pi$
$908$	−55.0905	−	3.61082i	−1.82824	−	0.119829i
$909$	−0.669712	−	0.277404i	−0.0222129	−	0.00920090i
$910$		0			0
$911$	26.5307	−	39.7060i	0.879002	−	1.31552i	−0.0691182	−	0.997608i	$-0.522019\pi$
$911$	26.5307	−	39.7060i	0.879002	−	1.31552i	0.948120	−	0.317911i	$-0.102981\pi$
$912$	−58.8459	−	67.1009i	−1.94858	−	2.22193i
$913$	0.838993	+	12.8006i	0.0277666	+	0.423637i
$914$	36.1796	−	9.69429i	1.19671	−	0.320659i
$915$	1.22994	−	0.417508i	0.0406605	−	0.0138024i
$916$	−52.4350	+	21.7193i	−1.73250	+	0.717626i
$917$		0			0
$918$	−50.1967	−	30.6798i	−1.65674	−	1.01259i
$919$	14.1996	+	24.5945i	0.468402	+	0.811296i	0.999348	−	0.0361096i	$-0.0114966\pi$
$919$	14.1996	+	24.5945i	0.468402	+	0.811296i	−0.530946	+	0.847406i	$0.678163\pi$
$920$	−0.812470	−	0.106964i	−0.0267863	−	0.00352649i
$921$	37.2166	+	32.6381i	1.22633	+	1.07546i
$922$	19.8008	−	73.8977i	0.652106	−	2.43369i
$923$	−0.927207	−	1.38766i	−0.0305194	−	0.0456755i
$924$		0			0
$925$	14.9478	+	9.98778i	0.491480	+	0.328396i
$926$	−83.7314	+	11.0235i	−2.75159	+	0.362253i
$927$	0.212184	+	0.276524i	0.00696904	+	0.00908223i
$928$	61.9107	+	125.543i	2.03232	+	4.12114i
$929$	−16.2305	+	14.2338i	−0.532507	+	0.466996i	−0.882870	−	0.469618i	$-0.844392\pi$
$929$	−16.2305	+	14.2338i	−0.532507	+	0.466996i	0.350363	+	0.936614i	$0.386058\pi$
$930$	11.5898	−	7.74408i	0.380046	−	0.253939i
$931$		0			0
$932$	109.009	+	21.6832i	3.57070	+	0.710257i
$933$	2.11612	−	2.75779i	0.0692788	−	0.0902859i
$934$	24.5066	−	42.4467i	0.801881	−	1.38890i
$935$	−4.16173	−	0.377500i	−0.136103	−	0.0123456i
$936$	2.60006	−	1.50114i	0.0849855	−	0.0490664i
$937$	−2.20027	−	5.31191i	−0.0718795	−	0.173533i	0.883856	−	0.467758i	$-0.154938\pi$
$937$	−2.20027	−	5.31191i	−0.0718795	−	0.173533i	−0.955736	+	0.294226i	$0.904938\pi$
$938$		0			0
$939$	28.8855	−	28.8855i	0.942642	−	0.942642i
$940$	7.03755	+	3.47054i	0.229540	+	0.113196i
$941$	12.5603	−	37.0014i	0.409453	−	1.20621i	−0.525301	−	0.850916i	$-0.676047\pi$
$941$	12.5603	−	37.0014i	0.409453	−	1.20621i	0.934754	−	0.355294i	$-0.115619\pi$
$942$	68.7840	−	33.9205i	2.24110	−	1.10519i
$943$	−0.200244	−	1.52100i	−0.00652083	−	0.0495306i
$944$	−7.00737	+	16.9173i	−0.228070	+	0.550611i
$945$		0			0
$946$	−24.0344	+	4.78073i	−0.781424	+	0.155435i
$947$	−16.5894	+	33.6399i	−0.539083	+	1.09315i	0.441539	+	0.897242i	$0.354433\pi$
$947$	−16.5894	+	33.6399i	−0.539083	+	1.09315i	−0.980622	+	0.195910i	$0.937234\pi$
$948$	34.6720	+	129.398i	1.12609	+	4.20264i
$949$	2.54238	−	2.89903i	0.0825292	−	0.0941066i
$950$	−32.4816	−	24.9240i	−1.05384	−	0.808641i
$951$	−29.9487			−0.971154
$952$		0			0
$953$	−15.8726			−0.514163			−0.257081	−	0.966390i	$-0.582761\pi$
$953$	−15.8726			−0.514163			−0.257081	+	0.966390i	$0.582761\pi$
$954$	−0.936439	−	0.718555i	−0.0303183	−	0.0232641i
$955$	−1.17707	+	1.34219i	−0.0380892	+	0.0434324i
$956$	−8.88045	−	33.1423i	−0.287214	−	1.07190i
$957$	−14.6634	+	29.7345i	−0.474001	+	0.961179i
$958$	24.8428	−	4.94154i	0.802635	−	0.159654i
$959$		0			0
$960$	7.50887	−	18.1280i	0.242348	−	0.585079i
$961$	9.68975	+	73.6009i	0.312573	+	2.37422i
$962$	45.8627	−	22.6170i	1.47867	−	0.729201i
$963$	−0.0392936	+	0.115755i	−0.00126622	+	0.00373016i
$964$	−137.691	−	67.9015i	−4.43472	−	2.18696i
$965$	3.08189	−	3.08189i	0.0992096	−	0.0992096i
$966$		0			0
$967$	9.85306	+	23.7874i	0.316853	+	0.764951i	0.999418	+	0.0341258i	$0.0108647\pi$
$967$	9.85306	+	23.7874i	0.316853	+	0.764951i	−0.682564	+	0.730826i	$0.739135\pi$
$968$	18.5092	−	10.6863i	0.594909	−	0.343471i
$969$	−16.8235	−	13.5908i	−0.540448	−	0.436600i
$970$	−0.529032	+	0.916311i	−0.0169862	+	0.0294210i
$971$	−13.4597	+	17.5410i	−0.431942	+	0.562918i	−0.957719	−	0.287705i	$-0.907108\pi$
$971$	−13.4597	+	17.5410i	−0.431942	+	0.562918i	0.525777	+	0.850622i	$0.323775\pi$
$972$	3.36964	+	0.670264i	0.108081	+	0.0214987i
$973$		0			0
$974$	63.4762	−	42.4135i	2.03391	−	1.35902i
$975$	32.6608	−	28.6428i	1.04598	−	0.917302i
$976$	19.9511	+	40.4568i	0.638619	+	1.29499i
$977$	11.3323	+	14.7686i	0.362553	+	0.472488i	0.938639	−	0.344901i	$-0.112087\pi$
$977$	11.3323	+	14.7686i	0.362553	+	0.472488i	−0.576086	+	0.817389i	$0.695421\pi$
$978$	−9.65248	+	1.27077i	−0.308652	+	0.0406349i
$979$	23.2569	+	15.5398i	0.743294	+	0.496653i
$980$		0			0
$981$	−0.465455	−	0.696602i	−0.0148608	−	0.0222408i
$982$	2.56160	−	9.56004i	0.0817441	−	0.305073i
$983$	−35.4068	−	31.0509i	−1.12930	−	0.990371i	−0.129302	−	0.991605i	$-0.541274\pi$
$983$	−35.4068	−	31.0509i	−1.12930	−	0.990371i	−0.999999	+	0.00123421i	$0.999607\pi$
$984$	95.3408	+	12.5519i	3.03935	+	0.400139i
$985$	0.652720	+	1.13054i	0.0207974	+	0.0360221i
$986$	35.2810	+	48.4408i	1.12358	+	1.54267i
$987$		0			0
$988$	−79.6178	+	32.9788i	−2.53298	+	1.04919i
$989$	−0.660675	+	0.224269i	−0.0210082	+	0.00713133i
$990$	0.157720	−	0.0422610i	0.00501267	−	0.00134314i
$991$	−1.35218	−	20.6303i	−0.0429534	−	0.655343i	−0.964002	−	0.265895i	$-0.914333\pi$
$991$	−1.35218	−	20.6303i	−0.0429534	−	0.655343i	0.921049	−	0.389448i	$-0.127334\pi$
$992$	180.666	+	206.010i	5.73614	+	6.54081i
$993$	3.17779	−	4.75590i	0.100844	−	0.150924i
$994$		0			0
$995$	−6.54108	−	2.70941i	−0.207366	−	0.0858939i
$996$	−35.2203	−	2.30846i	−1.11600	−	0.0731464i
$997$	27.5164	+	9.34055i	0.871452	+	0.295818i	0.721114	−	0.692816i	$-0.243630\pi$
$997$	27.5164	+	9.34055i	0.871452	+	0.295818i	0.150338	+	0.988635i	$0.451964\pi$
$998$	−62.4353	+	4.09222i	−1.97635	+	0.129537i
$999$	18.1522	+	4.86387i	0.574311	+	0.153886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.bc.d.31.9		144
7.2	even	3	inner	833.2.bc.d.558.9		144
7.3	odd	6		833.2.t.d.48.1	yes	72
7.4	even	3		833.2.t.a.48.1	✓	72
7.5	odd	6		833.2.bc.a.558.9		144
7.6	odd	2		833.2.bc.a.31.9		144
17.11	odd	16		833.2.bc.a.521.9		144
119.11	odd	48		833.2.t.d.538.1	yes	72
119.45	even	48		833.2.t.a.538.1	yes	72
119.62	even	16	inner	833.2.bc.d.521.9		144
119.79	odd	48		833.2.bc.a.215.9		144
119.96	even	48	inner	833.2.bc.d.215.9		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.t.a.48.1	✓	72	7.4	even	3
833.2.t.a.538.1	yes	72	119.45	even	48
833.2.t.d.48.1	yes	72	7.3	odd	6
833.2.t.d.538.1	yes	72	119.11	odd	48
833.2.bc.a.31.9		144	7.6	odd	2
833.2.bc.a.215.9		144	119.79	odd	48
833.2.bc.a.521.9		144	17.11	odd	16
833.2.bc.a.558.9		144	7.5	odd	6
833.2.bc.d.31.9		144	1.1	even	1	trivial
833.2.bc.d.215.9		144	119.96	even	48	inner
833.2.bc.d.521.9		144	119.62	even	16	inner
833.2.bc.d.558.9		144	7.2	even	3	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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.bc (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.20032 + 1.68837i) q^{2} +(1.15302 - 1.31477i) q^{3} +(1.47319 + 5.49804i) q^{4} +(-0.123911 + 0.251267i) q^{5} +(4.75684 - 0.946194i) q^{6} +(-3.91849 + 9.46008i) q^{8} +(-0.00758215 - 0.0575922i) q^{9} +(-0.696875 + 0.343660i) q^{10} +(1.16285 - 3.42565i) q^{11} +(8.92729 + 4.40245i) q^{12} +(3.56914 - 3.56914i) q^{13} +(0.187486 + 0.452632i) q^{15} +(-14.7352 + 8.50737i) q^{16} +(-3.16693 + 2.64018i) q^{17} +(0.0805535 - 0.139523i) q^{18} +(-1.82600 + 2.37968i) q^{19} +(-1.56402 - 0.311103i) q^{20} +(8.34238 - 5.57420i) q^{22} +(0.214773 - 0.188351i) q^{23} +(7.91973 + 16.0596i) q^{24} +(2.99603 + 3.90450i) q^{25} +(13.8792 - 1.82724i) q^{26} +(4.27761 + 2.85821i) q^{27} +(-2.91151 - 4.35739i) q^{29} +(-0.351678 + 1.31248i) q^{30} +(-7.71272 - 6.76387i) q^{31} +(-26.4819 - 3.48640i) q^{32} +(-3.16315 - 5.47873i) q^{33} +(-11.4258 + 0.462312i) q^{34} +(0.305474 - 0.126531i) q^{36} +(3.45899 - 1.17417i) q^{37} +(-8.03555 + 2.15312i) q^{38} +(-0.577300 - 8.80790i) q^{39} +(-1.89146 - 2.15680i) q^{40} +(2.98363 - 4.46532i) q^{41} +(-2.25647 - 0.934662i) q^{43} +(20.5474 + 1.34675i) q^{44} +(0.0154105 + 0.00523117i) q^{45} +(0.790575 - 0.0518171i) q^{46} +(-4.75298 - 1.27356i) q^{47} +(-5.80478 + 29.1826i) q^{48} +13.6495i q^{50} +(-0.180309 + 7.20798i) q^{51} +(24.8813 + 14.3652i) q^{52} +(0.956305 - 7.26386i) q^{53} +(4.58641 + 13.5111i) q^{54} +(0.716661 + 0.716661i) q^{55} +(1.02332 + 5.14460i) q^{57} +(0.950600 - 14.5034i) q^{58} +(0.853801 - 0.655145i) q^{59} +(-2.21238 + 1.69762i) q^{60} +(0.173394 - 2.64548i) q^{61} +(-5.55057 - 27.9046i) q^{62} +(-28.3198 - 28.3198i) q^{64} +(0.454550 + 1.33906i) q^{65} +(2.29016 - 17.3955i) q^{66} +(0.815594 + 0.470883i) q^{67} +(-19.1813 - 13.5224i) q^{68} -0.499551i q^{69} +(0.0645053 - 0.324290i) q^{71} +(0.574537 + 0.153947i) q^{72} +(0.762287 - 0.0499630i) q^{73} +(9.59332 + 3.25649i) q^{74} +(8.58801 + 0.562888i) q^{75} +(-15.7736 - 6.53366i) q^{76} +(13.6007 - 20.3549i) q^{78} +(8.87374 + 10.1186i) q^{79} +(-0.311766 - 4.75663i) q^{80} +(8.85840 - 2.37360i) q^{81} +(14.1040 - 4.78767i) q^{82} +(-3.27605 + 1.35698i) q^{83} +(-0.270973 - 1.12289i) q^{85} +(-3.38691 - 5.86631i) q^{86} +(-9.08602 - 1.19620i) q^{87} +(27.8503 + 24.4240i) q^{88} +(-2.00114 + 7.46835i) q^{89} +(0.0250760 + 0.0375288i) q^{90} +(1.35196 + 0.903354i) q^{92} +(-17.7859 + 2.34156i) q^{93} +(-8.30785 - 10.8270i) q^{94} +(-0.371675 - 0.753682i) q^{95} +(-35.1181 + 30.7977i) q^{96} +(1.13223 - 0.756532i) q^{97} +(-0.206107 - 0.0409973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 8 q^{5} - 16 q^{6} - 24 q^{9} - 8 q^{11} + 64 q^{13} + 40 q^{18} + 24 q^{19} + 48 q^{22} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 16 q^{27} + 80 q^{31} + 40 q^{32} - 80 q^{33} + 240 q^{36}+ \cdots + 80 q^{99}+O(q^{100}) \) 144 * q + 8 * q^3 + 8 * q^5 - 16 * q^6 - 24 * q^9 - 8 * q^11 + 64 * q^13 + 40 * q^18 + 24 * q^19 + 48 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 16 * q^27 + 80 * q^31 + 40 * q^32 - 80 * q^33 + 240 * q^36 - 48 * q^37 - 56 * q^38 + 16 * q^39 - 32 * q^40 - 48 * q^41 + 48 * q^43 - 32 * q^44 - 48 * q^45 - 40 * q^47 + 40 * q^51 + 24 * q^53 + 200 * q^54 - 96 * q^57 - 32 * q^58 + 8 * q^59 + 80 * q^60 - 256 * q^62 + 24 * q^65 - 8 * q^66 - 40 * q^68 - 48 * q^73 + 32 * q^74 + 128 * q^75 - 144 * q^76 - 96 * q^78 + 32 * q^79 + 256 * q^80 - 16 * q^81 - 152 * q^82 - 64 * q^85 + 80 * q^86 - 64 * q^87 - 56 * q^88 - 64 * q^89 + 752 * q^90 - 432 * q^92 + 32 * q^93 - 128 * q^94 - 32 * q^95 + 32 * q^96 + 16 * q^97 + 80 * q^99

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