LMFDB - Embedded newform 833.2.o.g.557.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(30,833)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("833.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.8
Character	$\chi$	$=$	833.557
Dual form			833.2.o.g.667.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36164 - 0.786146i) q^{2} +(1.96499 - 0.526518i) q^{3} +(0.236050 - 0.408850i) q^{4} +(0.878646 - 3.27915i) q^{5} +(2.26170 - 2.26170i) q^{6} +2.40230i q^{8} +(0.985896 - 0.569207i) q^{9} +O(q^{10})$	\(q+(1.36164 - 0.786146i) q^{2} +(1.96499 - 0.526518i) q^{3} +(0.236050 - 0.408850i) q^{4} +(0.878646 - 3.27915i) q^{5} +(2.26170 - 2.26170i) q^{6} +2.40230i q^{8} +(0.985896 - 0.569207i) q^{9} +(-1.38149 - 5.15578i) q^{10} +(-1.20885 - 4.51148i) q^{11} +(0.248569 - 0.927672i) q^{12} +3.63777 q^{13} -6.90613i q^{15} +(2.36066 + 4.08878i) q^{16} +(2.39540 + 3.35590i) q^{17} +(0.894959 - 1.55012i) q^{18} +(-5.36723 + 3.09877i) q^{19} +(-1.13328 - 1.13328i) q^{20} +(-5.19270 - 5.19270i) q^{22} +(-0.649191 - 0.173950i) q^{23} +(1.26486 + 4.72051i) q^{24} +(-5.65069 - 3.26243i) q^{25} +(4.95335 - 2.85982i) q^{26} +(-2.67784 + 2.67784i) q^{27} +(-3.95461 - 3.95461i) q^{29} +(-5.42922 - 9.40369i) q^{30} +(7.39761 - 1.98218i) q^{31} +(2.26785 + 1.30934i) q^{32} +(-4.75075 - 8.22854i) q^{33} +(5.89991 + 2.68641i) q^{34} -0.537445i q^{36} +(-0.354204 + 1.32191i) q^{37} +(-4.87217 + 8.43884i) q^{38} +(7.14819 - 1.91535i) q^{39} +(7.87752 + 2.11077i) q^{40} +(0.492170 - 0.492170i) q^{41} +6.64216i q^{43} +(-2.12987 - 0.570696i) q^{44} +(-1.00026 - 3.73303i) q^{45} +(-1.02072 + 0.273500i) q^{46} +(-2.16296 - 3.74636i) q^{47} +(6.79150 + 6.79150i) q^{48} -10.2590 q^{50} +(6.47388 + 5.33310i) q^{51} +(0.858695 - 1.48730i) q^{52} +(3.53287 + 2.03970i) q^{53} +(-1.54109 + 5.75144i) q^{54} -15.8560 q^{55} +(-8.91500 + 8.91500i) q^{57} +(-8.49368 - 2.27587i) q^{58} +(2.36632 + 1.36620i) q^{59} +(-2.82357 - 1.63019i) q^{60} +(11.6857 + 3.13118i) q^{61} +(8.51463 - 8.51463i) q^{62} -5.32531 q^{64} +(3.19631 - 11.9288i) q^{65} +(-12.9377 - 7.46956i) q^{66} +(-6.27952 + 10.8764i) q^{67} +(1.93749 - 0.187200i) q^{68} -1.36724 q^{69} +(3.04461 + 3.04461i) q^{71} +(1.36741 + 2.36842i) q^{72} +(1.59488 - 0.427346i) q^{73} +(0.556911 + 2.07842i) q^{74} +(-12.8213 - 3.43545i) q^{75} +2.92586i q^{76} +(8.22754 - 8.22754i) q^{78} +(-9.66384 - 2.58942i) q^{79} +(15.4819 - 4.14837i) q^{80} +(-5.55963 + 9.62956i) q^{81} +(0.283243 - 1.05708i) q^{82} +4.69160i q^{83} +(13.1092 - 4.90623i) q^{85} +(5.22170 + 9.04425i) q^{86} +(-9.85296 - 5.68861i) q^{87} +(10.8379 - 2.90402i) q^{88} +(1.02353 + 1.77280i) q^{89} +(-4.29671 - 4.29671i) q^{90} +(-0.224361 + 0.224361i) q^{92} +(13.4926 - 7.78995i) q^{93} +(-5.89036 - 3.40080i) q^{94} +(5.44544 + 20.3227i) q^{95} +(5.14569 + 1.37878i) q^{96} +(-2.99116 - 2.99116i) q^{97} +(-3.75976 - 3.75976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6	$ 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 12 q^{12} - 16 q^{16} + 12 q^{17} + 8 q^{18} + 40 q^{20} - 40 q^{22} - 4 q^{24} + 16 q^{27} + 32 q^{29} + 36 q^{30} - 4 q^{31} + 16 q^{33} + 72 q^{34} + 28 q^{37} - 48 q^{38} - 20 q^{39} + 24 q^{40} - 48 q^{41} + 28 q^{44} - 36 q^{45} - 8 q^{46} - 40 q^{47} - 16 q^{48} - 56 q^{50} + 40 q^{51} + 28 q^{54} - 80 q^{55} + 72 q^{57} - 56 q^{58} + 16 q^{61} - 80 q^{62} + 64 q^{64} - 8 q^{65} + 32 q^{68} - 176 q^{69} - 16 q^{71} - 108 q^{72} - 8 q^{73} - 36 q^{74} - 8 q^{75} - 88 q^{78} + 4 q^{79} + 116 q^{80} - 4 q^{81} + 16 q^{82} + 32 q^{85} - 44 q^{86} - 72 q^{88} - 48 q^{89} + 112 q^{90} - 64 q^{92} - 44 q^{95} - 68 q^{96} - 48 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 12 * q^12 - 16 * q^16 + 12 * q^17 + 8 * q^18 + 40 * q^20 - 40 * q^22 - 4 * q^24 + 16 * q^27 + 32 * q^29 + 36 * q^30 - 4 * q^31 + 16 * q^33 + 72 * q^34 + 28 * q^37 - 48 * q^38 - 20 * q^39 + 24 * q^40 - 48 * q^41 + 28 * q^44 - 36 * q^45 - 8 * q^46 - 40 * q^47 - 16 * q^48 - 56 * q^50 + 40 * q^51 + 28 * q^54 - 80 * q^55 + 72 * q^57 - 56 * q^58 + 16 * q^61 - 80 * q^62 + 64 * q^64 - 8 * q^65 + 32 * q^68 - 176 * q^69 - 16 * q^71 - 108 * q^72 - 8 * q^73 - 36 * q^74 - 8 * q^75 - 88 * q^78 + 4 * q^79 + 116 * q^80 - 4 * q^81 + 16 * q^82 + 32 * q^85 - 44 * q^86 - 72 * q^88 - 48 * q^89 + 112 * q^90 - 64 * q^92 - 44 * q^95 - 68 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.36164	−	0.786146i	0.962828	−	0.555889i	0.0657856	−	0.997834i	$-0.479045\pi$
$2$	1.36164	−	0.786146i	0.962828	−	0.555889i	0.897042	+	0.441945i	$0.145711\pi$
$3$	1.96499	−	0.526518i	1.13449	−	0.303985i	0.357756	−	0.933815i	$-0.383542\pi$
$3$	1.96499	−	0.526518i	1.13449	−	0.303985i	0.776733	+	0.629830i	$0.216875\pi$
$4$	0.236050	−	0.408850i	0.118025	−	0.204425i
$5$	0.878646	−	3.27915i	0.392942	−	1.46648i	−0.432314	−	0.901723i	$-0.642303\pi$
$5$	0.878646	−	3.27915i	0.392942	−	1.46648i	0.825257	−	0.564758i	$-0.191030\pi$
$6$	2.26170	−	2.26170i	0.923335	−	0.923335i
$7$		0			0
$7$		0			0
$8$			2.40230i			0.849343i
$9$	0.985896	−	0.569207i	0.328632	−	0.189736i
$10$	−1.38149	−	5.15578i	−0.436865	−	1.63040i
$11$	−1.20885	−	4.51148i	−0.364481	−	1.36026i	−0.868123	−	0.496349i	$-0.834673\pi$
$11$	−1.20885	−	4.51148i	−0.364481	−	1.36026i	0.503642	−	0.863913i	$-0.331993\pi$
$12$	0.248569	−	0.927672i	0.0717557	−	0.267796i
$13$	3.63777			1.00894			0.504468	−	0.863430i	$-0.331689\pi$
$13$	3.63777			1.00894			0.504468	+	0.863430i	$0.331689\pi$
$14$		0			0
$15$		−	6.90613i		−	1.78315i
$16$	2.36066	+	4.08878i	0.590165	+	1.02220i
$17$	2.39540	+	3.35590i	0.580970	+	0.813925i
$17$	2.39540	+	3.35590i	0.580970	+	0.813925i
$18$	0.894959	−	1.55012i	0.210944	−	0.365366i
$19$	−5.36723	+	3.09877i	−1.23133	+	0.710906i	−0.967306	−	0.253611i	$-0.918382\pi$
$19$	−5.36723	+	3.09877i	−1.23133	+	0.710906i	−0.264020	+	0.964517i	$0.585048\pi$
$20$	−1.13328	−	1.13328i	−0.253409	−	0.253409i
$21$		0			0
$22$	−5.19270	−	5.19270i	−1.10709	−	1.10709i
$23$	−0.649191	−	0.173950i	−0.135366	−	0.0362711i	0.190500	−	0.981687i	$-0.438989\pi$
$23$	−0.649191	−	0.173950i	−0.135366	−	0.0362711i	−0.325866	+	0.945416i	$0.605656\pi$
$24$	1.26486	+	4.72051i	0.258188	+	0.963570i
$25$	−5.65069	−	3.26243i	−1.13014	−	0.652485i
$26$	4.95335	−	2.85982i	0.971431	−	0.560856i
$27$	−2.67784	+	2.67784i	−0.515351	+	0.515351i
$28$		0			0
$29$	−3.95461	−	3.95461i	−0.734353	−	0.734353i	0.237126	−	0.971479i	$-0.423795\pi$
$29$	−3.95461	−	3.95461i	−0.734353	−	0.734353i	−0.971479	+	0.237126i	$0.923795\pi$
$30$	−5.42922	−	9.40369i	−0.991236	−	1.71687i
$31$	7.39761	−	1.98218i	1.32865	−	0.356011i	0.476439	−	0.879208i	$-0.341927\pi$
$31$	7.39761	−	1.98218i	1.32865	−	0.356011i	0.852212	+	0.523197i	$0.175261\pi$
$32$	2.26785	+	1.30934i	0.400902	+	0.231461i
$33$	−4.75075	−	8.22854i	−0.826999	−	1.43240i
$34$	5.89991	+	2.68641i	1.01183	+	0.460715i
$35$		0			0
$36$		−	0.537445i		−	0.0895742i
$37$	−0.354204	+	1.32191i	−0.0582307	+	0.217320i	−0.988910	−	0.148516i	$-0.952550\pi$
$37$	−0.354204	+	1.32191i	−0.0582307	+	0.217320i	0.930679	+	0.365836i	$0.119217\pi$
$38$	−4.87217	+	8.43884i	−0.790370	+	1.36896i
$39$	7.14819	−	1.91535i	1.14463	−	0.306702i
$40$	7.87752	+	2.11077i	1.24555	+	0.333743i
$41$	0.492170	−	0.492170i	0.0768640	−	0.0768640i	−0.667630	−	0.744494i	$-0.732691\pi$
$41$	0.492170	−	0.492170i	0.0768640	−	0.0768640i	0.744494	+	0.667630i	$0.232691\pi$
$42$		0			0
$43$			6.64216i			1.01292i	0.862264	+	0.506460i	$0.169046\pi$
$43$			6.64216i			1.01292i	−0.862264	+	0.506460i	$0.830954\pi$
$44$	−2.12987	−	0.570696i	−0.321090	−	0.0860357i
$45$	−1.00026	−	3.73303i	−0.149110	−	0.556488i
$46$	−1.02072	+	0.273500i	−0.150496	+	0.0403254i
$47$	−2.16296	−	3.74636i	−0.315500	−	0.546462i	0.664043	−	0.747694i	$-0.268839\pi$
$47$	−2.16296	−	3.74636i	−0.315500	−	0.546462i	−0.979544	+	0.201232i	$0.935506\pi$
$48$	6.79150	+	6.79150i	0.980268	+	0.980268i
$49$		0			0
$50$	−10.2590			−1.45084
$51$	6.47388	+	5.33310i	0.906525	+	0.746783i
$52$	0.858695	−	1.48730i	0.119080	−	0.206252i
$53$	3.53287	+	2.03970i	0.485277	+	0.280175i	0.722613	−	0.691253i	$-0.242941\pi$
$53$	3.53287	+	2.03970i	0.485277	+	0.280175i	−0.237336	+	0.971428i	$0.576274\pi$
$54$	−1.54109	+	5.75144i	−0.209716	+	0.782672i
$55$	−15.8560			−2.13802
$56$		0			0
$57$	−8.91500	+	8.91500i	−1.18082	+	1.18082i
$58$	−8.49368	−	2.27587i	−1.11527	−	0.298837i
$59$	2.36632	+	1.36620i	0.308069	+	0.177864i	0.646062	−	0.763285i	$-0.276415\pi$
$59$	2.36632	+	1.36620i	0.308069	+	0.177864i	−0.337993	+	0.941149i	$0.609748\pi$
$60$	−2.82357	−	1.63019i	−0.364522	−	0.210457i
$61$	11.6857	+	3.13118i	1.49620	+	0.400907i	0.911827	−	0.410575i	$-0.134672\pi$
$61$	11.6857	+	3.13118i	1.49620	+	0.400907i	0.584378	+	0.811482i	$0.301339\pi$
$62$	8.51463	−	8.51463i	1.08136	−	1.08136i
$63$		0			0
$64$	−5.32531			−0.665664
$65$	3.19631	−	11.9288i	0.396454	−	1.47958i
$66$	−12.9377	−	7.46956i	−1.59252	−	0.919440i
$67$	−6.27952	+	10.8764i	−0.767165	+	1.32877i	0.171929	+	0.985109i	$0.445000\pi$
$67$	−6.27952	+	10.8764i	−0.767165	+	1.32877i	−0.939094	+	0.343659i	$0.888333\pi$
$68$	1.93749	−	0.187200i	0.234956	−	0.0227013i
$69$	−1.36724			−0.164597
$70$		0			0
$71$	3.04461	+	3.04461i	0.361328	+	0.361328i	0.864302	−	0.502973i	$-0.167761\pi$
$71$	3.04461	+	3.04461i	0.361328	+	0.361328i	−0.502973	+	0.864302i	$0.667761\pi$
$72$	1.36741	+	2.36842i	0.161151	+	0.279121i
$73$	1.59488	−	0.427346i	0.186666	−	0.0500170i	−0.164275	−	0.986415i	$-0.552528\pi$
$73$	1.59488	−	0.427346i	0.186666	−	0.0500170i	0.350941	+	0.936398i	$0.385862\pi$
$74$	0.556911	+	2.07842i	0.0647396	+	0.241612i
$75$	−12.8213	−	3.43545i	−1.48047	−	0.396692i
$76$			2.92586i			0.335619i
$77$		0			0
$78$	8.22754	−	8.22754i	0.931586	−	0.931586i
$79$	−9.66384	−	2.58942i	−1.08727	−	0.291332i	−0.329697	−	0.944087i	$-0.606947\pi$
$79$	−9.66384	−	2.58942i	−1.08727	−	0.291332i	−0.757570	+	0.652754i	$0.773613\pi$
$80$	15.4819	−	4.14837i	1.73093	−	0.463802i
$81$	−5.55963	+	9.62956i	−0.617736	+	1.06995i
$82$	0.283243	−	1.05708i	0.0312789	−	0.116735i
$83$			4.69160i			0.514970i	0.966282	+	0.257485i	$0.0828938\pi$
$83$			4.69160i			0.514970i	−0.966282	+	0.257485i	$0.917106\pi$
$84$		0			0
$85$	13.1092	−	4.90623i	1.42189	−	0.532155i
$86$	5.22170	+	9.04425i	0.563071	+	0.975267i
$87$	−9.85296	−	5.68861i	−1.05635	−	0.609883i
$88$	10.8379	−	2.90402i	1.15533	−	0.309569i
$89$	1.02353	+	1.77280i	0.108494	+	0.187917i	0.915160	−	0.403090i	$-0.132064\pi$
$89$	1.02353	+	1.77280i	0.108494	+	0.187917i	−0.806666	+	0.591007i	$0.798731\pi$
$90$	−4.29671	−	4.29671i	−0.452913	−	0.452913i
$91$		0			0
$92$	−0.224361	+	0.224361i	−0.0233912	+	0.0233912i
$93$	13.4926	−	7.78995i	1.39912	−	0.807780i
$94$	−5.89036	−	3.40080i	−0.607545	−	0.350766i
$95$	5.44544	+	20.3227i	0.558690	+	2.08506i
$96$	5.14569	+	1.37878i	0.525180	+	0.140722i
$97$	−2.99116	−	2.99116i	−0.303706	−	0.303706i	0.538756	−	0.842462i	$-0.318895\pi$
$97$	−2.99116	−	2.99116i	−0.303706	−	0.303706i	−0.842462	+	0.538756i	$0.818895\pi$
$98$		0			0
$99$	−3.75976	−	3.75976i	−0.377870	−	0.377870i
$100$	−2.66769	+	1.54019i	−0.266769	+	0.154019i
$101$	2.69264	−	4.66379i	0.267928	−	0.464065i	−0.700399	−	0.713752i	$-0.746994\pi$
$101$	2.69264	−	4.66379i	0.267928	−	0.464065i	0.968327	+	0.249687i	$0.0803277\pi$
$102$	13.0077	+	2.17236i	1.28796	+	0.215096i
$103$	1.98128	+	3.43167i	0.195221	+	0.338133i	0.946973	−	0.321313i	$-0.104124\pi$
$103$	1.98128	+	3.43167i	0.195221	+	0.338133i	−0.751752	+	0.659446i	$0.770791\pi$
$104$			8.73903i			0.856932i
$105$		0			0
$106$	6.41401			0.622984
$107$	2.94531	−	10.9920i	0.284734	−	1.06264i	−0.664300	−	0.747466i	$-0.731270\pi$
$107$	2.94531	−	10.9920i	0.284734	−	1.06264i	0.949034	−	0.315175i	$-0.102063\pi$
$108$	0.462733	+	1.72694i	0.0445265	+	0.166175i
$109$	−1.14030	−	4.25566i	−0.109221	−	0.407619i	0.889569	−	0.456801i	$-0.151005\pi$
$109$	−1.14030	−	4.25566i	−0.109221	−	0.407619i	−0.998790	+	0.0491827i	$0.984338\pi$
$110$	−21.5902	+	12.4651i	−2.05854	+	1.18850i
$111$			2.78403i			0.264248i
$112$		0			0
$113$	−8.20042	+	8.20042i	−0.771430	+	0.771430i	−0.978357	−	0.206926i	$-0.933654\pi$
$113$	−8.20042	+	8.20042i	−0.771430	+	0.771430i	0.206926	+	0.978357i	$0.433654\pi$
$114$	−5.13057	+	19.1475i	−0.480522	+	1.79333i
$115$	−1.14082	+	1.97595i	−0.106382	+	0.184259i
$116$	−2.55033	+	0.683359i	−0.236792	+	0.0634483i
$117$	3.58646	−	2.07064i	0.331568	−	0.191431i
$118$	4.29612			0.395490
$119$		0			0
$120$	16.5906			1.51451
$121$	−9.36585	+	5.40738i	−0.851441	+	0.491580i
$122$	18.3734	−	4.92313i	1.66345	−	0.445719i
$123$	0.707973	−	1.22625i	0.0638358	−	0.110567i
$124$	0.935789	−	3.49241i	0.0840363	−	0.313628i
$125$	−3.66041	+	3.66041i	−0.327397	+	0.327397i
$126$		0			0
$127$			5.12889i			0.455115i	0.973765	+	0.227558i	$0.0730740\pi$
$127$			5.12889i			0.455115i	−0.973765	+	0.227558i	$0.926926\pi$
$128$	−11.7869	+	6.80515i	−1.04182	+	0.601496i
$129$	3.49722	+	13.0518i	0.307913	+	1.14915i
$130$	−5.02553	−	18.7555i	−0.440768	−	1.64497i
$131$	2.16203	−	8.06881i	0.188898	−	0.704975i	−0.804865	−	0.593458i	$-0.797762\pi$
$131$	2.16203	−	8.06881i	0.188898	−	0.704975i	0.993762	−	0.111517i	$-0.0355710\pi$
$132$	−4.48566			−0.390426
$133$		0			0
$134$			19.7465i			1.70583i
$135$	6.42818	+	11.1339i	0.553249	+	0.958256i
$136$	−8.06189	+	5.75448i	−0.691302	+	0.493442i
$137$	10.0969	−	17.4884i	0.862639	−	1.49413i	−0.00673433	−	0.999977i	$-0.502144\pi$
$137$	10.0969	−	17.4884i	0.862639	−	1.49413i	0.869373	−	0.494157i	$-0.164523\pi$
$138$	−1.86170	+	1.07485i	−0.158478	+	0.0914974i
$139$	5.51905	+	5.51905i	0.468120	+	0.468120i	0.901305	−	0.433185i	$-0.142610\pi$
$139$	5.51905	+	5.51905i	0.468120	+	0.468120i	−0.433185	+	0.901305i	$0.642610\pi$
$140$		0			0
$141$	−6.22272	−	6.22272i	−0.524048	−	0.524048i
$142$	6.53918	+	1.75217i	0.548755	+	0.147039i
$143$	−4.39751	−	16.4117i	−0.367738	−	1.37242i
$144$	4.65473	+	2.68741i	0.387894	+	0.223951i
$145$	−16.4425	+	9.49307i	−1.36547	+	0.788356i
$146$	1.83570	−	1.83570i	0.151923	−	0.151923i
$147$		0			0
$148$	0.456852	+	0.456852i	0.0375530	+	0.0375530i
$149$	−0.335290	−	0.580739i	−0.0274680	−	0.0475760i	0.851965	−	0.523599i	$-0.175411\pi$
$149$	−0.335290	−	0.580739i	−0.0274680	−	0.0475760i	−0.879433	+	0.476023i	$0.842078\pi$
$150$	−20.1588	+	5.40153i	−1.64596	+	0.441033i
$151$	−9.89318	−	5.71183i	−0.805096	−	0.464822i	0.0401543	−	0.999193i	$-0.487215\pi$
$151$	−9.89318	−	5.71183i	−0.805096	−	0.464822i	−0.845250	+	0.534371i	$0.820548\pi$
$152$	−7.44419	−	12.8937i	−0.603803	−	1.04582i
$153$	4.27182	+	1.94509i	0.345356	+	0.157251i
$154$		0			0
$155$		−	25.9995i		−	2.08833i
$156$	0.904237	−	3.37466i	0.0723969	−	0.270189i
$157$	−11.6916	+	20.2504i	−0.933090	+	1.61616i	−0.155086	+	0.987901i	$0.549565\pi$
$157$	−11.6916	+	20.2504i	−0.933090	+	1.61616i	−0.778004	+	0.628259i	$0.783768\pi$
$158$	−15.1944	+	4.07132i	−1.20880	+	0.323897i
$159$	8.01600	+	2.14788i	0.635710	+	0.170338i
$160$	6.28617	−	6.28617i	0.496965	−	0.496965i
$161$		0			0
$162$			17.4827i			1.37357i
$163$	−11.6655	−	3.12576i	−0.913714	−	0.244829i	−0.228817	−	0.973469i	$-0.573486\pi$
$163$	−11.6655	−	3.12576i	−0.913714	−	0.244829i	−0.684896	+	0.728641i	$0.740152\pi$
$164$	−0.0850472	−	0.317400i	−0.00664107	−	0.0247848i
$165$	−31.1569	+	8.34845i	−2.42556	+	0.649926i
$166$	3.68828	+	6.38829i	0.286266	+	0.495827i
$167$	−17.3482	−	17.3482i	−1.34244	−	1.34244i	−0.893620	−	0.448823i	$-0.851843\pi$
$167$	−17.3482	−	17.3482i	−1.34244	−	1.34244i	−0.448823	−	0.893620i	$-0.648157\pi$
$168$		0			0
$169$	0.233365			0.0179511
$170$	13.9931	−	16.9863i	1.07322	−	1.30279i
$171$	−3.52768	+	6.11013i	−0.269769	+	0.467253i
$172$	2.71565	+	1.56788i	0.207066	+	0.119550i
$173$	0.922753	−	3.44376i	0.0701556	−	0.261824i	−0.921936	−	0.387343i	$-0.873393\pi$
$173$	0.922753	−	3.44376i	0.0701556	−	0.261824i	0.992091	+	0.125519i	$0.0400596\pi$
$174$	−17.8883			−1.35611
$175$		0			0
$176$	15.5928	−	15.5928i	1.17535	−	1.17535i
$177$	5.36913	+	1.43865i	0.403568	+	0.108136i
$178$	2.78736	+	1.60929i	0.208922	+	0.120621i
$179$	−3.43046	−	1.98058i	−0.256405	−	0.148035i	0.366289	−	0.930501i	$-0.380628\pi$
$179$	−3.43046	−	1.98058i	−0.256405	−	0.148035i	−0.622693	+	0.782466i	$0.713962\pi$
$180$	−1.76236	−	0.472224i	−0.131359	−	0.0351975i
$181$	−1.36267	+	1.36267i	−0.101287	+	0.101287i	−0.755934	−	0.654648i	$-0.772817\pi$
$181$	−1.36267	+	1.36267i	−0.101287	+	0.101287i	0.654648	+	0.755934i	$0.272817\pi$
$182$		0			0
$183$	24.6110			1.81930
$184$	0.417881	−	1.55955i	0.0308066	−	0.114972i
$185$	4.02351	+	2.32298i	0.295814	+	0.170789i
$186$	12.2481	−	21.2143i	0.898072	−	1.55551i
$187$	12.2444	−	14.8636i	0.895399	−	1.08693i
$188$	−2.04227			−0.148948
$189$		0			0
$190$	23.3913	+	23.3913i	1.69699	+	1.69699i
$191$	12.5863	+	21.8001i	0.910714	+	1.57740i	0.813058	+	0.582183i	$0.197801\pi$
$191$	12.5863	+	21.8001i	0.910714	+	1.57740i	0.0976558	+	0.995220i	$0.468866\pi$
$192$	−10.4642	+	2.80387i	−0.755188	+	0.202352i
$193$	2.91087	+	10.8635i	0.209529	+	0.781972i	0.988021	+	0.154318i	$0.0493180\pi$
$193$	2.91087	+	10.8635i	0.209529	+	0.781972i	−0.778493	+	0.627654i	$0.784015\pi$
$194$	−6.42438	−	1.72141i	−0.461243	−	0.123590i
$195$		−	25.1229i		−	1.79909i
$196$		0			0
$197$	−16.0035	+	16.0035i	−1.14020	+	1.14020i	−0.151789	+	0.988413i	$0.548503\pi$
$197$	−16.0035	+	16.0035i	−1.14020	+	1.14020i	−0.988413	+	0.151789i	$0.951497\pi$
$198$	−8.07518	−	2.16374i	−0.573878	−	0.153770i
$199$	5.07058	−	1.35866i	0.359444	−	0.0963127i	−0.0745776	−	0.997215i	$-0.523761\pi$
$199$	5.07058	−	1.35866i	0.359444	−	0.0963127i	0.434022	+	0.900903i	$0.357094\pi$
$200$	7.83734	−	13.5747i	0.554184	−	0.959874i
$201$	−6.61256	+	24.6784i	−0.466414	+	1.74068i
$202$		−	8.46724i		−	0.595753i
$203$		0			0
$204$	3.70860	−	1.38797i	0.259654	−	0.0971775i
$205$	−1.18146	−	2.04634i	−0.0825164	−	0.142923i
$206$	5.39559	+	3.11514i	0.375928	+	0.217042i
$207$	−0.739048	+	0.198027i	−0.0513674	+	0.0137638i
$208$	8.58754	+	14.8741i	0.595439	+	1.03133i
$209$	20.4682	+	20.4682i	1.41581	+	1.41581i
$210$		0			0
$211$	−6.87817	+	6.87817i	−0.473513	+	0.473513i	−0.903050	−	0.429536i	$-0.858677\pi$
$211$	−6.87817	+	6.87817i	−0.473513	+	0.473513i	0.429536	+	0.903050i	$0.358677\pi$
$212$	1.66787	−	0.962943i	0.114550	−	0.0661352i
$213$	7.58567	+	4.37959i	0.519761	+	0.300084i
$214$	−4.63088	−	17.2827i	−0.316561	−	1.18142i
$215$	21.7806	+	5.83610i	1.48543	+	0.398019i
$216$	−6.43299	−	6.43299i	−0.437710	−	0.437710i
$217$		0			0
$218$	−4.89826	−	4.89826i	−0.331752	−	0.331752i
$219$	2.90891	−	1.67946i	0.196566	−	0.113487i
$220$	−3.74280	+	6.48272i	−0.252340	+	0.437065i
$221$	8.71391	+	12.2080i	0.586161	+	0.821198i
$222$	2.18865	+	3.79086i	0.146893	+	0.254426i
$223$		−	17.5438i		−	1.17482i	−0.809289	−	0.587411i	$-0.800147\pi$
$223$		−	17.5438i		−	1.17482i	0.809289	−	0.587411i	$-0.199853\pi$
$224$		0			0
$225$	−7.42798			−0.495199
$226$	−4.71933	+	17.6128i	−0.313925	+	1.17158i
$227$	−2.15948	−	8.05931i	−0.143330	−	0.534915i	−0.999824	−	0.0187580i	$-0.994029\pi$
$227$	−2.15948	−	8.05931i	−0.143330	−	0.534915i	0.856494	−	0.516157i	$-0.172638\pi$
$228$	1.54052	+	5.74928i	0.102023	+	0.380756i
$229$	13.2886	−	7.67215i	0.878132	−	0.506990i	0.00809010	−	0.999967i	$-0.497425\pi$
$229$	13.2886	−	7.67215i	0.878132	−	0.506990i	0.870042	+	0.492977i	$0.164091\pi$
$230$			3.58739i			0.236546i
$231$		0			0
$232$	9.50018	−	9.50018i	0.623717	−	0.623717i
$233$	6.33522	−	23.6434i	0.415034	−	1.54893i	−0.369733	−	0.929138i	$-0.620551\pi$
$233$	6.33522	−	23.6434i	0.415034	−	1.54893i	0.784767	−	0.619790i	$-0.212782\pi$
$234$	3.25566	−	5.63896i	0.212829	−	0.368630i
$235$	−14.1853	+	3.80095i	−0.925350	+	0.247947i
$236$	1.11714	−	0.644981i	0.0727196	−	0.0419847i
$237$	−20.3527			−1.32205
$238$		0			0
$239$	14.5771			0.942916			0.471458	−	0.881889i	$-0.343728\pi$
$239$	14.5771			0.942916			0.471458	+	0.881889i	$0.343728\pi$
$240$	28.2377	−	16.3030i	1.82273	−	1.05236i
$241$	14.6969	−	3.93803i	0.946712	−	0.253671i	0.247745	−	0.968825i	$-0.420310\pi$
$241$	14.6969	−	3.93803i	0.946712	−	0.253671i	0.698966	+	0.715155i	$0.253644\pi$
$242$	−8.50197	+	14.7258i	−0.546527	+	0.946613i
$243$	−2.91401	+	10.8752i	−0.186934	+	0.697647i
$244$	4.03860	−	4.03860i	0.258545	−	0.258545i
$245$		0			0
$246$		−	2.22628i		−	0.141942i
$247$	−19.5247	+	11.2726i	−1.24233	+	0.717259i
$248$	4.76181	+	17.7713i	0.302375	+	1.12848i
$249$	2.47021	+	9.21896i	0.156543	+	0.584228i
$250$	−2.10656	+	7.86180i	−0.133231	+	0.497224i
$251$	1.54033			0.0972246			0.0486123	−	0.998818i	$-0.484520\pi$
$251$	1.54033			0.0972246			0.0486123	+	0.998818i	$0.484520\pi$
$252$		0			0
$253$			3.13909i			0.197353i
$254$	4.03206	+	6.98372i	0.252994	+	0.438198i
$255$	23.1763	−	16.5429i	1.45135	−	1.03596i
$256$	−5.37437	+	9.30869i	−0.335898	+	0.581793i
$257$	−3.48942	+	2.01462i	−0.217664	+	0.125668i	−0.604868	−	0.796326i	$-0.706774\pi$
$257$	−3.48942	+	2.01462i	−0.217664	+	0.125668i	0.387204	+	0.921994i	$0.373441\pi$
$258$	15.0226	+	15.0226i	0.935264	+	0.935264i
$259$		0			0
$260$	−4.12260	−	4.12260i	−0.255673	−	0.255673i
$261$	−6.14983	−	1.64784i	−0.380665	−	0.101999i
$262$	−3.39934	−	12.6865i	−0.210012	−	0.783776i
$263$	−15.5660	−	8.98703i	−0.959841	−	0.554164i	−0.0637166	−	0.997968i	$-0.520295\pi$
$263$	−15.5660	−	8.98703i	−0.959841	−	0.554164i	−0.896124	+	0.443804i	$0.853629\pi$
$264$	19.7675	−	11.4127i	1.21660	−	0.702406i
$265$	9.79263	−	9.79263i	0.601557	−	0.601557i
$266$		0			0
$267$	2.94464	+	2.94464i	0.180209	+	0.180209i
$268$	2.96456	+	5.13477i	0.181089	+	0.313656i
$269$	−17.4172	+	4.66693i	−1.06195	+	0.284548i	−0.747181	−	0.664621i	$-0.768593\pi$
$269$	−17.4172	+	4.66693i	−1.06195	+	0.284548i	−0.314767	+	0.949169i	$0.601926\pi$
$270$	17.5058	+	10.1070i	1.06537	+	0.615090i
$271$	−8.35400	−	14.4696i	−0.507469	−	0.878963i	−0.999963	−	0.00864660i	$-0.997248\pi$
$271$	−8.35400	−	14.4696i	−0.507469	−	0.878963i	0.492493	−	0.870316i	$-0.336086\pi$
$272$	−8.06683	+	17.7164i	−0.489123	+	1.07422i
$273$		0			0
$274$		−	31.7506i		−	1.91812i
$275$	−7.88755	+	29.4367i	−0.475637	+	1.77510i
$276$	−0.322737	+	0.558997i	−0.0194265	+	0.0336477i
$277$	1.00804	−	0.270103i	0.0605670	−	0.0162289i	−0.228408	−	0.973565i	$-0.573352\pi$
$277$	1.00804	−	0.270103i	0.0605670	−	0.0162289i	0.288975	+	0.957337i	$0.406685\pi$
$278$	11.8538	+	3.17620i	0.710941	+	0.190496i
$279$	6.16500	−	6.16500i	0.369089	−	0.369089i
$280$		0			0
$281$		−	3.53036i		−	0.210604i	−0.994440	−	0.105302i	$-0.966419\pi$
$281$		−	3.53036i		−	0.210604i	0.994440	−	0.105302i	$-0.0335809\pi$
$282$	−13.3651	−	3.58117i	−0.795880	−	0.213255i
$283$	−0.471949	−	1.76134i	−0.0280545	−	0.104701i	0.950479	−	0.310789i	$-0.100593\pi$
$283$	−0.471949	−	1.76134i	−0.0280545	−	0.104701i	−0.978533	+	0.206088i	$0.933927\pi$
$284$	1.96347	−	0.526110i	0.116510	−	0.0312189i
$285$	21.4005	+	37.0667i	1.26766	+	2.19564i
$286$	−18.8898	−	18.8898i	−1.11698	−	1.11698i
$287$		0			0
$288$	2.98115			0.175666
$289$	−5.52413	+	16.0774i	−0.324949	+	0.945732i
$290$	−14.9259	+	25.8524i	−0.876477	+	1.51810i
$291$	−7.45250	−	4.30270i	−0.436873	−	0.252229i
$292$	0.201750	−	0.752940i	0.0118065	−	0.0440625i
$293$	14.9585			0.873883			0.436942	−	0.899490i	$-0.356062\pi$
$293$	14.9585			0.873883			0.436942	+	0.899490i	$0.356062\pi$
$294$		0			0
$295$	6.55912	−	6.55912i	0.381887	−	0.381887i
$296$	−3.17562	−	0.850905i	−0.184579	−	0.0494579i
$297$	15.3181	+	8.84393i	0.888848	+	0.513177i
$298$	−0.913091	−	0.527174i	−0.0528940	−	0.0305383i
$299$	−2.36161	−	0.632790i	−0.136575	−	0.0365952i
$300$	−4.43105	+	4.43105i	−0.255827	+	0.255827i
$301$		0			0
$302$	−17.9613			−1.03356
$303$	2.83545	−	10.5820i	0.162892	−	0.607923i
$304$	−25.3404	−	14.6303i	−1.45337	−	0.839104i
$305$	20.5352	−	35.5681i	1.17584	−	2.03662i
$306$	7.34582	−	0.709750i	0.419932	−	0.0405737i
$307$	−7.16409			−0.408876			−0.204438	−	0.978879i	$-0.565537\pi$
$307$	−7.16409			−0.408876			−0.204438	+	0.978879i	$0.565537\pi$
$308$		0			0
$309$	5.70003	+	5.70003i	0.324263	+	0.324263i
$310$	−20.4394	−	35.4021i	−1.16088	−	2.01070i
$311$	6.08000	−	1.62913i	0.344765	−	0.0923796i	−0.0822815	−	0.996609i	$-0.526221\pi$
$311$	6.08000	−	1.62913i	0.344765	−	0.0923796i	0.427047	+	0.904230i	$0.359554\pi$
$312$	4.60126	+	17.1721i	0.260495	+	0.972180i
$313$	−30.3029	−	8.11965i	−1.71282	−	0.458950i	−0.736710	−	0.676209i	$-0.763622\pi$
$313$	−30.3029	−	8.11965i	−1.71282	−	0.458950i	−0.976114	+	0.217259i	$0.930288\pi$
$314$			36.7652i			2.07478i
$315$		0			0
$316$	−3.33983	+	3.33983i	−0.187880	+	0.187880i
$317$	−16.0010	−	4.28746i	−0.898708	−	0.240808i	−0.220247	−	0.975444i	$-0.570686\pi$
$317$	−16.0010	−	4.28746i	−0.898708	−	0.240808i	−0.678461	+	0.734636i	$0.737353\pi$
$318$	12.6035	−	3.37709i	0.706768	−	0.189378i
$319$	−13.0606	+	22.6217i	−0.731255	+	1.26657i
$320$	−4.67906	+	17.4625i	−0.261567	+	0.976183i
$321$		−	23.1500i		−	1.29211i
$322$		0			0
$323$	−23.2558	−	10.5891i	−1.29399	−	0.589192i
$324$	2.62470	+	4.54611i	0.145817	+	0.252562i
$325$	−20.5559	−	11.8680i	−1.14024	−	0.658316i
$326$	−18.3416	+	4.91461i	−1.01585	+	0.272195i
$327$	−4.48137	−	7.76196i	−0.247820	−	0.429237i
$328$	1.18234	+	1.18234i	0.0652839	+	0.0652839i
$329$		0			0
$330$	−35.8614	+	35.8614i	−1.97411	+	1.97411i
$331$	4.09885	−	2.36647i	0.225293	−	0.130073i	−0.383106	−	0.923704i	$-0.625146\pi$
$331$	4.09885	−	2.36647i	0.225293	−	0.130073i	0.608399	+	0.793632i	$0.291812\pi$
$332$	1.91816	+	1.10745i	0.105273	+	0.0607793i
$333$	0.403231	+	1.50488i	0.0220969	+	0.0824667i
$334$	−37.2603	−	9.98386i	−2.03879	−	0.546293i
$335$	30.1480	+	30.1480i	1.64716	+	1.64716i
$336$		0			0
$337$	17.0523	+	17.0523i	0.928898	+	0.928898i	0.997635	−	0.0687369i	$-0.0218969\pi$
$337$	17.0523	+	17.0523i	0.928898	+	0.928898i	−0.0687369	+	0.997635i	$0.521897\pi$
$338$	0.317760	−	0.183459i	0.0172838	−	0.00997883i
$339$	−11.7961	+	20.4314i	−0.640675	+	1.10968i
$340$	1.08851	−	6.51782i	0.0590330	−	0.353478i
$341$	−17.8852	−	30.9780i	−0.968536	−	1.67755i
$342$			11.0931i			0.599846i
$343$		0			0
$344$	−15.9565			−0.860316
$345$	−1.20132	+	4.48339i	−0.0646770	+	0.241378i
$346$	−1.45084	−	5.41459i	−0.0779974	−	0.291090i
$347$	−5.92855	−	22.1256i	−0.318261	−	1.18777i	−0.920915	−	0.389764i	$-0.872557\pi$
$347$	−5.92855	−	22.1256i	−0.318261	−	1.18777i	0.602654	−	0.798003i	$-0.294110\pi$
$348$	−4.65158	+	2.68559i	−0.249351	+	0.143963i
$349$		−	10.1897i		−	0.545442i	−0.962093	−	0.272721i	$-0.912076\pi$
$349$		−	10.1897i		−	0.545442i	0.962093	−	0.272721i	$-0.0879235\pi$
$350$		0			0
$351$	−9.74137	+	9.74137i	−0.519956	+	0.519956i
$352$	3.16559	−	11.8141i	0.168726	−	0.629696i
$353$	8.39994	−	14.5491i	0.447084	−	0.774372i	−0.551111	−	0.834432i	$-0.685796\pi$
$353$	8.39994	−	14.5491i	0.447084	−	0.774372i	0.998195	+	0.0600602i	$0.0191293\pi$
$354$	8.44183	−	2.26198i	0.448678	−	0.120223i
$355$	12.6589	−	7.30860i	0.671862	−	0.387900i
$356$	0.966416			0.0512199
$357$		0			0
$358$	−6.22809			−0.329165
$359$	24.4581	−	14.1209i	1.29085	−	0.745273i	0.312046	−	0.950067i	$-0.398986\pi$
$359$	24.4581	−	14.1209i	1.29085	−	0.745273i	0.978805	+	0.204794i	$0.0656523\pi$
$360$	8.96788	−	2.40294i	0.472649	−	0.126646i
$361$	9.70474	−	16.8091i	0.510776	−	0.884689i
$362$	−0.784216	+	2.92673i	−0.0412175	+	0.153826i
$363$	−15.5567	+	15.5567i	−0.816517	+	0.816517i
$364$		0			0
$365$		−	5.60532i		−	0.293396i
$366$	33.5114	−	19.3478i	1.75167	−	1.01133i
$367$	−4.86903	−	18.1715i	−0.254161	−	0.948543i	−0.968555	−	0.248799i	$-0.919964\pi$
$367$	−4.86903	−	18.1715i	−0.254161	−	0.948543i	0.714394	−	0.699744i	$-0.246703\pi$
$368$	−0.821274	−	3.06504i	−0.0428119	−	0.159776i
$369$	0.205081	−	0.765374i	0.0106761	−	0.0398438i
$370$	7.30479			0.379758
$371$		0			0
$372$		−	7.35527i		−	0.381353i
$373$	−15.4827	−	26.8169i	−0.801666	−	1.38853i	−0.918519	−	0.395377i	$-0.870614\pi$
$373$	−15.4827	−	26.8169i	−0.801666	−	1.38853i	0.116853	−	0.993149i	$-0.462719\pi$
$374$	4.98759	−	29.8648i	0.257902	−	1.54427i
$375$	−5.26541	+	9.11996i	−0.271905	+	0.470953i
$376$	8.99989	−	5.19609i	0.464134	−	0.267968i
$377$	−14.3860	−	14.3860i	−0.740915	−	0.740915i
$378$		0			0
$379$	−8.80375	−	8.80375i	−0.452218	−	0.452218i	0.443872	−	0.896090i	$-0.353604\pi$
$379$	−8.80375	−	8.80375i	−0.452218	−	0.452218i	−0.896090	+	0.443872i	$0.853604\pi$
$380$	9.59433	+	2.57079i	0.492179	+	0.131879i
$381$	2.70045	+	10.0782i	0.138348	+	0.516323i
$382$	34.2762	+	19.7894i	1.75372	+	1.01251i
$383$	−25.8472	+	14.9229i	−1.32073	+	0.762523i	−0.983845	−	0.179023i	$-0.942706\pi$
$383$	−25.8472	+	14.9229i	−1.32073	+	0.762523i	−0.336884	+	0.941546i	$0.609373\pi$
$384$	−19.5781	+	19.5781i	−0.999089	+	0.999089i
$385$		0			0
$386$	12.5039	+	12.5039i	0.636429	+	0.636429i
$387$	3.78076	+	6.54847i	0.192187	+	0.332878i
$388$	−1.92900	+	0.516874i	−0.0979300	+	0.0262403i
$389$	18.1350	+	10.4702i	0.919479	+	0.530861i	0.883469	−	0.468490i	$-0.155202\pi$
$389$	18.1350	+	10.4702i	0.919479	+	0.530861i	0.0360099	+	0.999351i	$0.488535\pi$
$390$	−19.7503	−	34.2085i	−1.00009	−	1.73221i
$391$	−0.971311	−	2.59530i	−0.0491213	−	0.131250i
$392$		0			0
$393$		−	16.9935i		−	0.857208i
$394$	−9.20999	+	34.3721i	−0.463992	+	1.73164i
$395$	−16.9822	+	29.4140i	−0.854467	+	1.47998i
$396$	−2.42467	+	0.649689i	−0.121844	+	0.0326481i
$397$	27.3943	+	7.34029i	1.37488	+	0.368399i	0.869260	−	0.494356i	$-0.164596\pi$
$397$	27.3943	+	7.34029i	1.37488	+	0.368399i	0.505623	+	0.862755i	$0.331263\pi$
$398$	5.83622	−	5.83622i	0.292543	−	0.292543i
$399$		0			0
$400$		−	30.8059i		−	1.54030i
$401$	−3.15744	−	0.846034i	−0.157675	−	0.0422489i	0.179118	−	0.983828i	$-0.442676\pi$
$401$	−3.15744	−	0.846034i	−0.157675	−	0.0422489i	−0.336793	+	0.941579i	$0.609342\pi$
$402$	10.3969	+	38.8016i	0.518548	+	1.93525i
$403$	26.9108	−	7.21073i	1.34052	−	0.359192i
$404$	−1.27120	−	2.20178i	−0.0632444	−	0.109542i
$405$	26.6918	+	26.6918i	1.32633	+	1.32633i
$406$		0			0
$407$	6.39193			0.316836
$408$	−12.8117	+	15.5522i	−0.634274	+	0.769950i
$409$	17.1932	−	29.7795i	0.850149	−	1.47250i	−0.0309240	−	0.999522i	$-0.509845\pi$
$409$	17.1932	−	29.7795i	0.850149	−	1.47250i	0.881073	−	0.472980i	$-0.156822\pi$
$410$	−3.21744	−	1.85759i	−0.158898	−	0.0917399i
$411$	10.6324	−	39.6808i	0.524459	−	1.95731i
$412$	1.87072			0.0921638
$413$		0			0
$414$	−0.850642	+	0.850642i	−0.0418068	+	0.0418068i
$415$	15.3845	+	4.12226i	0.755194	+	0.202354i
$416$	8.24990	+	4.76308i	0.404485	+	0.233529i
$417$	13.7508	+	7.93901i	0.673378	+	0.388775i
$418$	43.9614	+	11.7794i	2.15022	+	0.576150i
$419$	−12.3869	+	12.3869i	−0.605140	+	0.605140i	−0.941672	−	0.336532i	$-0.890746\pi$
$419$	−12.3869	+	12.3869i	−0.605140	+	0.605140i	0.336532	+	0.941672i	$0.390746\pi$
$420$		0			0
$421$	−13.1028			−0.638593			−0.319296	−	0.947655i	$-0.603447\pi$
$421$	−13.1028			−0.638593			−0.319296	+	0.947655i	$0.603447\pi$
$422$	−3.95838	+	14.7729i	−0.192691	+	0.719132i
$423$	−4.26491	−	2.46234i	−0.207367	−	0.119723i
$424$	−4.89998	+	8.48702i	−0.237964	+	0.412166i
$425$	−2.58728	−	26.7780i	−0.125501	−	1.29892i
$426$	13.7720			0.667254
$427$		0			0
$428$	−3.79886	−	3.79886i	−0.183625	−	0.183625i
$429$	−17.2821	−	29.9335i	−0.834389	−	1.44520i
$430$	34.2455	−	9.17606i	1.65147	−	0.442509i
$431$	6.80250	+	25.3873i	0.327665	+	1.22286i	0.911606	+	0.411066i	$0.134843\pi$
$431$	6.80250	+	25.3873i	0.327665	+	1.22286i	−0.583941	+	0.811796i	$0.698490\pi$
$432$	−17.2706	−	4.62764i	−0.830932	−	0.222648i
$433$			0.783681i			0.0376613i	0.999823	+	0.0188307i	$0.00599434\pi$
$433$			0.783681i			0.0376613i	−0.999823	+	0.0188307i	$0.994006\pi$
$434$		0			0
$435$	−27.3111	+	27.3111i	−1.30947	+	1.30947i
$436$	−2.00910	−	0.538336i	−0.0962184	−	0.0257816i
$437$	4.02338	−	1.07806i	0.192465	−	0.0515707i
$438$	2.64060	−	4.57366i	0.126173	−	0.218538i
$439$	6.51034	−	24.2969i	0.310722	−	1.15963i	−0.617185	−	0.786818i	$-0.711727\pi$
$439$	6.51034	−	24.2969i	0.310722	−	1.15963i	0.927907	−	0.372812i	$-0.121606\pi$
$440$		−	38.0909i		−	1.81591i
$441$		0			0
$442$	21.4625	+	9.77254i	1.02087	+	0.464832i
$443$	6.06586	+	10.5064i	0.288197	+	0.499173i	0.973380	−	0.229199i	$-0.0736107\pi$
$443$	6.06586	+	10.5064i	0.288197	+	0.499173i	−0.685182	+	0.728372i	$0.740277\pi$
$444$	1.13825	+	0.657170i	0.0540190	+	0.0311879i
$445$	6.71261	−	1.79864i	0.318208	−	0.0852637i
$446$	−13.7920	−	23.8885i	−0.653071	−	1.13115i
$447$	−0.964612	−	0.964612i	−0.0456246	−	0.0456246i
$448$		0			0
$449$	26.1661	−	26.1661i	1.23485	−	1.23485i	0.272777	−	0.962077i	$-0.412058\pi$
$449$	26.1661	−	26.1661i	1.23485	−	1.23485i	0.962077	−	0.272777i	$-0.0879421\pi$
$450$	−10.1143	+	5.83948i	−0.476791	+	0.275276i
$451$	−2.81537	−	1.62545i	−0.132571	−	0.0765397i
$452$	1.41704	+	5.28845i	0.0666518	+	0.248748i
$453$	−22.4474	−	6.01476i	−1.05467	−	0.282598i
$454$	−9.27624	−	9.27624i	−0.435355	−	0.435355i
$455$		0			0
$456$	−21.4165	−	21.4165i	−1.00292	−	1.00292i
$457$	11.0746	−	6.39394i	0.518050	−	0.299096i	−0.218087	−	0.975929i	$-0.569982\pi$
$457$	11.0746	−	6.39394i	0.518050	−	0.299096i	0.736136	+	0.676833i	$0.236648\pi$
$458$	12.0629	−	20.8935i	0.563660	−	0.976288i
$459$	−15.4011	−	2.57207i	−0.718860	−	0.120054i
$460$	0.538580	+	0.932847i	0.0251114	+	0.0434942i
$461$		−	4.58089i		−	0.213353i	−0.994294	−	0.106677i	$-0.965979\pi$
$461$		−	4.58089i		−	0.213353i	0.994294	−	0.106677i	$-0.0340210\pi$
$462$		0			0
$463$	−1.53844			−0.0714973			−0.0357486	−	0.999361i	$-0.511382\pi$
$463$	−1.53844			−0.0714973			−0.0357486	+	0.999361i	$0.511382\pi$
$464$	6.83406	−	25.5051i	0.317263	−	1.18404i
$465$	−13.6892	−	51.0889i	−0.634822	−	2.36919i
$466$	−9.96081	−	37.1743i	−0.461426	−	1.72206i
$467$	−9.52860	+	5.50134i	−0.440931	+	0.254572i	−0.703992	−	0.710207i	$-0.748601\pi$
$467$	−9.52860	+	5.50134i	−0.440931	+	0.254572i	0.263061	+	0.964779i	$0.415268\pi$
$468$		−	1.95510i		−	0.0903746i
$469$		0			0
$470$	−16.3273	+	16.3273i	−0.753122	+	0.753122i
$471$	−12.3117	+	45.9478i	−0.567291	+	2.11716i
$472$	−3.28202	+	5.68462i	−0.151067	+	0.261656i
$473$	29.9660	−	8.02935i	1.37784	−	0.369190i
$474$	−27.7132	+	16.0002i	−1.27291	+	0.734914i
$475$	40.4380			1.85542
$476$		0			0
$477$	4.64405			0.212637
$478$	19.8489	−	11.4597i	0.907866	−	0.524156i
$479$	−22.4693	+	6.02062i	−1.02665	+	0.275089i	−0.732570	−	0.680692i	$-0.761679\pi$
$479$	−22.4693	+	6.02062i	−1.02665	+	0.275089i	−0.294078	+	0.955781i	$0.595012\pi$
$480$	9.04248	−	15.6620i	0.412731	−	0.714871i
$481$	−1.28851	+	4.80879i	−0.0587511	+	0.219262i
$482$	16.9161	−	16.9161i	0.770508	−	0.770508i
$483$		0			0
$484$			5.10564i			0.232075i
$485$	−12.4366	+	7.18029i	−0.564718	+	0.326040i
$486$	4.58168	+	17.0991i	0.207829	+	0.775629i
$487$	5.70334	+	21.2851i	0.258443	+	0.964522i	0.966143	+	0.258009i	$0.0830663\pi$
$487$	5.70334	+	21.2851i	0.258443	+	0.964522i	−0.707700	+	0.706513i	$0.750267\pi$
$488$	−7.52205	+	28.0727i	−0.340507	+	1.27079i
$489$	−24.5684			−1.11102
$490$		0			0
$491$		−	19.2671i		−	0.869512i	−0.900548	−	0.434756i	$-0.856835\pi$
$491$		−	19.2671i		−	0.869512i	0.900548	−	0.434756i	$-0.143165\pi$
$492$	−0.334234	−	0.578910i	−0.0150684	−	0.0260993i
$493$	3.79841	−	22.7442i	0.171072	−	1.02435i
$494$	−17.7238	+	30.6986i	−0.797432	+	1.38119i
$495$	−15.6323	+	9.02533i	−0.702621	+	0.405658i
$496$	25.5680	+	25.5680i	1.14804	+	1.14804i
$497$		0			0
$498$	10.6110	+	10.6110i	0.475490	+	0.475490i
$499$	−40.9180	−	10.9640i	−1.83174	−	0.490814i	−0.833636	−	0.552314i	$-0.813745\pi$
$499$	−40.9180	−	10.9640i	−1.83174	−	0.490814i	−0.998107	+	0.0614998i	$0.980412\pi$
$500$	0.632522	+	2.36060i	0.0282872	+	0.105569i
$501$	−43.2232	−	24.9549i	−1.93107	−	1.11490i
$502$	2.09738	−	1.21092i	0.0936106	−	0.0540461i
$503$	−7.89613	+	7.89613i	−0.352071	+	0.352071i	−0.860880	−	0.508809i	$-0.830086\pi$
$503$	−7.89613	+	7.89613i	−0.352071	+	0.352071i	0.508809	+	0.860880i	$0.330086\pi$
$504$		0			0
$505$	−12.9274	−	12.9274i	−0.575262	−	0.575262i
$506$	2.46778	+	4.27432i	0.109706	+	0.190017i
$507$	0.458560	−	0.122871i	0.0203653	−	0.00545688i
$508$	2.09695	+	1.21067i	0.0930371	+	0.0537150i
$509$	16.8980	+	29.2682i	0.748991	+	1.29729i	0.948307	+	0.317356i	$0.102795\pi$
$509$	16.8980	+	29.2682i	0.748991	+	1.29729i	−0.199315	+	0.979935i	$0.563872\pi$
$510$	18.5527	−	40.7455i	0.821527	−	1.80424i
$511$		0			0
$512$		−	10.3205i		−	0.456104i
$513$	6.07457	−	22.6706i	0.268199	−	1.00093i
$514$	−3.16756	+	5.48638i	−0.139715	+	0.241994i
$515$	12.9938	−	3.48168i	0.572576	−	0.153421i
$516$	6.16175	+	1.65103i	0.271256	+	0.0726827i
$517$	−14.2869	+	14.2869i	−0.628338	+	0.628338i
$518$		0			0
$519$		−	7.25281i		−	0.318363i
$520$	28.6566	+	7.67851i	1.25667	+	0.336725i
$521$	3.83601	+	14.3162i	0.168059	+	0.627203i	0.997630	+	0.0688031i	$0.0219180\pi$
$521$	3.83601	+	14.3162i	0.168059	+	0.627203i	−0.829572	+	0.558400i	$0.811415\pi$
$522$	−9.66932	+	2.59089i	−0.423215	+	0.113400i
$523$	1.37970	+	2.38971i	0.0603300	+	0.104495i	0.894613	−	0.446842i	$-0.147451\pi$
$523$	1.37970	+	2.38971i	0.0603300	+	0.104495i	−0.834283	+	0.551337i	$0.814118\pi$
$524$	−2.78859	−	2.78859i	−0.121820	−	0.121820i
$525$		0			0
$526$	−28.2605			−1.23221
$527$	24.3722	+	20.0775i	1.06167	+	0.874591i
$528$	22.4298	−	38.8496i	0.976132	−	1.69071i
$529$	−19.5274	−	11.2741i	−0.849017	−	0.490180i
$530$	5.63565	−	21.0325i	0.244797	−	0.913594i
$531$	3.11059			0.134988
$532$		0			0
$533$	1.79040	−	1.79040i	0.0775508	−	0.0775508i
$534$	6.32447	+	1.69464i	0.273686	+	0.0733341i
$535$	−33.4567	−	19.3162i	−1.44646	−	0.835113i
$536$	−26.1285	−	15.0853i	−1.12858	−	0.651586i
$537$	−7.78364	−	2.08562i	−0.335889	−	0.0900011i
$538$	−20.0472	+	20.0472i	−0.864296	+	0.864296i
$539$		0			0
$540$	6.06948			0.261189
$541$	2.88703	−	10.7745i	0.124123	−	0.463233i	−0.875684	−	0.482885i	$-0.839589\pi$
$541$	2.88703	−	10.7745i	0.124123	−	0.463233i	0.999807	+	0.0196516i	$0.00625569\pi$
$542$	−22.7504	−	13.1349i	−0.977211	−	0.564193i
$543$	−1.96017	+	3.39511i	−0.0841189	+	0.145698i
$544$	1.03838	+	10.7471i	0.0445201	+	0.460777i
$545$	−14.9569			−0.640683
$546$		0			0
$547$	5.17129	+	5.17129i	0.221108	+	0.221108i	0.808965	−	0.587857i	$-0.200028\pi$
$547$	5.17129	+	5.17129i	0.221108	+	0.221108i	−0.587857	+	0.808965i	$0.700028\pi$
$548$	−4.76676	−	8.25627i	−0.203626	−	0.352690i
$549$	13.3032	−	3.56458i	0.567767	−	0.152133i
$550$	12.4015	+	46.2831i	0.528803	+	1.97352i
$551$	33.4797	+	8.97086i	1.42628	+	0.382172i
$552$		−	3.28453i		−	0.139799i
$553$		0			0
$554$	1.16025	−	1.16025i	0.0492942	−	0.0492942i
$555$	9.12925	+	2.44618i	0.387515	+	0.103834i
$556$	3.55924	−	0.953695i	0.150945	−	0.0404457i
$557$	−7.67715	+	13.2972i	−0.325291	+	0.563421i	−0.981571	−	0.191096i	$-0.938796\pi$
$557$	−7.67715	+	13.2972i	−0.325291	+	0.563421i	0.656280	+	0.754518i	$0.272129\pi$
$558$	3.54795	−	13.2411i	0.150197	−	0.560542i
$559$			24.1626i			1.02197i
$560$		0			0
$561$	16.2342	−	35.6537i	0.685409	−	1.50530i
$562$	−2.77538	−	4.80710i	−0.117072	−	0.202775i
$563$	5.73828	+	3.31299i	0.241839	+	0.139626i	0.616022	−	0.787729i	$-0.288743\pi$
$563$	5.73828	+	3.31299i	0.241839	+	0.139626i	−0.374182	+	0.927355i	$0.622077\pi$
$564$	−4.01304	+	1.07529i	−0.168979	+	0.0452779i
$565$	19.6851	+	34.0957i	0.828160	+	1.43442i
$566$	−2.02730	−	2.02730i	−0.0852136	−	0.0852136i
$567$		0			0
$568$	−7.31407	+	7.31407i	−0.306892	+	0.306892i
$569$	−32.0150	+	18.4838i	−1.34214	+	0.774883i	−0.987121	−	0.159977i	$-0.948858\pi$
$569$	−32.0150	+	18.4838i	−1.34214	+	0.774883i	−0.355016	+	0.934860i	$0.615525\pi$
$570$	58.2797	+	33.6478i	2.44107	+	1.40935i
$571$	−9.46916	−	35.3394i	−0.396272	−	1.47891i	−0.819603	−	0.572932i	$-0.805806\pi$
$571$	−9.46916	−	35.3394i	−0.396272	−	1.47891i	0.423331	−	0.905975i	$-0.360861\pi$
$572$	−7.74797	−	2.07606i	−0.323959	−	0.0868045i
$573$	36.2102	+	36.2102i	1.51270	+	1.51270i
$574$		0			0
$575$	3.10087	+	3.10087i	0.129315	+	0.129315i
$576$	−5.25020	+	3.03120i	−0.218758	+	0.126300i
$577$	−3.35458	+	5.81030i	−0.139653	+	0.241886i	−0.927365	−	0.374157i	$-0.877932\pi$
$577$	−3.35458	+	5.81030i	−0.139653	+	0.241886i	0.787712	+	0.616043i	$0.211265\pi$
$578$	5.11731	+	26.2345i	0.212852	+	1.09121i
$579$	11.4397	+	19.8141i	0.475416	+	0.823444i
$580$			8.96335i			0.372183i
$581$		0			0
$582$	−13.5302			−0.560845
$583$	4.93138	−	18.4041i	0.204237	−	0.762222i
$584$	1.02661	+	3.83138i	0.0424816	+	0.158543i
$585$	−3.63873	−	13.5799i	−0.150443	−	0.561460i
$586$	20.3681	−	11.7595i	0.841399	−	0.485782i
$587$		−	0.653601i		−	0.0269770i	−0.999909	−	0.0134885i	$-0.995706\pi$
$587$		−	0.653601i		−	0.0269770i	0.999909	−	0.0134885i	$-0.00429365\pi$
$588$		0			0
$589$	−33.5623	+	33.5623i	−1.38291	+	1.38291i
$590$	3.77477	−	14.0876i	0.155405	−	0.579978i
$591$	−23.0206	+	39.8729i	−0.946941	+	1.64015i
$592$	−6.24114	+	1.67231i	−0.256509	+	0.0687315i
$593$	23.9967	−	13.8545i	0.985428	−	0.568937i	0.0815231	−	0.996671i	$-0.474022\pi$
$593$	23.9967	−	13.8545i	0.985428	−	0.568937i	0.903904	+	0.427735i	$0.140688\pi$
$594$	27.8105			1.14108
$595$		0			0
$596$	−0.316581			−0.0129677
$597$	9.24829	−	5.33950i	0.378507	−	0.218531i
$598$	−3.71313	+	0.994931i	−0.151841	+	0.0406857i
$599$	3.77268	−	6.53448i	0.154148	−	0.266992i	−0.778601	−	0.627520i	$-0.784070\pi$
$599$	3.77268	−	6.53448i	0.154148	−	0.266992i	0.932748	+	0.360528i	$0.117404\pi$
$600$	8.25300	−	30.8006i	0.336927	−	1.25743i
$601$	12.8735	−	12.8735i	0.525119	−	0.525119i	−0.393994	−	0.919113i	$-0.628907\pi$
$601$	12.8735	−	12.8735i	0.525119	−	0.525119i	0.919113	+	0.393994i	$0.128907\pi$
$602$		0			0
$603$			14.2974i			0.582234i
$604$	−4.67057	+	2.69655i	−0.190043	+	0.109721i
$605$	9.50234	+	35.4632i	0.386325	+	1.44178i
$606$	−4.45815	−	16.6381i	−0.181100	−	0.675875i
$607$	−3.16518	+	11.8126i	−0.128470	+	0.479458i	−0.999940	−	0.0109920i	$-0.996501\pi$
$607$	−3.16518	+	11.8126i	−0.128470	+	0.479458i	0.871469	+	0.490450i	$0.163168\pi$
$608$	−16.2294			−0.658189
$609$		0			0
$610$		−	64.5748i		−	2.61456i
$611$	−7.86835	−	13.6284i	−0.318319	−	0.551345i
$612$	1.80361	−	1.28740i	0.0729067	−	0.0520399i
$613$	19.7050	−	34.1300i	0.795876	−	1.37850i	−0.126406	−	0.991979i	$-0.540344\pi$
$613$	19.7050	−	34.1300i	0.795876	−	1.37850i	0.922282	−	0.386519i	$-0.126322\pi$
$614$	−9.75495	+	5.63202i	−0.393678	+	0.227290i
$615$	−3.39899	−	3.39899i	−0.137060	−	0.137060i
$616$		0			0
$617$	10.4142	+	10.4142i	0.419260	+	0.419260i	0.884948	−	0.465689i	$-0.154193\pi$
$617$	10.4142	+	10.4142i	0.419260	+	0.419260i	−0.465689	+	0.884948i	$0.654193\pi$
$618$	12.2425	+	3.28036i	0.492464	+	0.131955i
$619$	9.57465	+	35.7331i	0.384838	+	1.43623i	0.838423	+	0.545021i	$0.183478\pi$
$619$	9.57465	+	35.7331i	0.384838	+	1.43623i	−0.453585	+	0.891213i	$0.649855\pi$
$620$	−10.6299	−	6.13719i	−0.426908	−	0.246475i
$621$	2.20424	−	1.27262i	0.0884531	−	0.0510684i
$622$	6.99806	−	6.99806i	0.280597	−	0.280597i
$623$		0			0
$624$	24.7059	+	24.7059i	0.989028	+	0.989028i
$625$	−7.52528	−	13.0342i	−0.301011	−	0.521367i
$626$	−47.6451	+	12.7665i	−1.90428	+	0.510250i
$627$	50.9967	+	29.4429i	2.03661	+	1.17584i
$628$	5.51960	+	9.56022i	0.220256	+	0.381494i
$629$	−5.28464	+	1.97782i	−0.210713	+	0.0788609i
$630$		0			0
$631$			31.7794i			1.26512i	0.774512	+	0.632559i	$0.217996\pi$
$631$			31.7794i			1.26512i	−0.774512	+	0.632559i	$0.782004\pi$
$632$	6.22057	−	23.2155i	0.247441	−	0.923462i
$633$	−9.89407	+	17.1370i	−0.393254	+	0.681136i
$634$	−25.1583	+	6.74114i	−0.999163	+	0.267725i
$635$	16.8184	+	4.50648i	0.667418	+	0.178834i
$636$	2.77034	−	2.77034i	0.109851	−	0.109851i
$637$		0			0
$638$			41.0702i			1.62599i
$639$	4.73468	+	1.26865i	0.187301	+	0.0501871i
$640$	11.9586	+	44.6302i	0.472707	+	1.76417i
$641$	18.3069	−	4.90532i	0.723080	−	0.193749i	0.121534	−	0.992587i	$-0.461219\pi$
$641$	18.3069	−	4.90532i	0.723080	−	0.193749i	0.601545	+	0.798839i	$0.294552\pi$
$642$	−18.1993	−	31.5221i	−0.718269	−	1.24408i
$643$	−19.0600	−	19.0600i	−0.751652	−	0.751652i	0.223135	−	0.974787i	$-0.428371\pi$
$643$	−19.0600	−	19.0600i	−0.751652	−	0.751652i	−0.974787	+	0.223135i	$0.928371\pi$
$644$		0			0
$645$	45.8716			1.80619
$646$	−39.9907	+	3.86389i	−1.57341	+	0.152023i
$647$	−0.408070	+	0.706798i	−0.0160429	+	0.0277871i	−0.873935	−	0.486042i	$-0.838440\pi$
$647$	−0.408070	+	0.706798i	−0.0160429	+	0.0277871i	0.857893	+	0.513829i	$0.171773\pi$
$648$	−23.1331	−	13.3559i	−0.908755	−	0.524670i
$649$	3.30304	−	12.3271i	0.129656	−	0.483882i
$650$	−37.3198			−1.46380
$651$		0			0
$652$	−4.03161	+	4.03161i	−0.157890	+	0.157890i
$653$	−25.6118	−	6.86267i	−1.00227	−	0.268557i	−0.279873	−	0.960037i	$-0.590292\pi$
$653$	−25.6118	−	6.86267i	−1.00227	−	0.268557i	−0.722396	+	0.691480i	$0.756959\pi$
$654$	−12.2041	−	7.04602i	−0.477216	−	0.275521i
$655$	−24.5592	−	14.1793i	−0.959607	−	0.554029i
$656$	3.17422	+	0.850530i	0.123932	+	0.0332076i
$657$	1.32913	−	1.32913i	0.0518544	−	0.0518544i
$658$		0			0
$659$	−15.6995			−0.611566			−0.305783	−	0.952101i	$-0.598918\pi$
$659$	−15.6995			−0.611566			−0.305783	+	0.952101i	$0.598918\pi$
$660$	−3.94130	+	14.7091i	−0.153415	+	0.572553i
$661$	13.4338	+	7.75601i	0.522515	+	0.301674i	0.737963	−	0.674841i	$-0.235788\pi$
$661$	13.4338	+	7.75601i	0.522515	+	0.301674i	−0.215448	+	0.976515i	$0.569121\pi$
$662$	3.72078	−	6.44458i	0.144612	−	0.250476i
$663$	23.5505	+	19.4006i	0.914625	+	0.753456i
$664$	−11.2707			−0.437386
$665$		0			0
$666$	1.73211	+	1.73211i	0.0671179	+	0.0671179i
$667$	1.87939	+	3.25520i	0.0727703	+	0.126042i
$668$	−11.1879	+	2.99778i	−0.432871	+	0.115988i
$669$	−9.23715	−	34.4735i	−0.357129	−	1.33282i
$670$	64.7516	+	17.3501i	2.50157	+	0.670295i
$671$		−	56.5050i		−	2.18135i
$672$		0			0
$673$	25.7151	−	25.7151i	0.991243	−	0.991243i	−0.00871919	−	0.999962i	$-0.502775\pi$
$673$	25.7151	−	25.7151i	0.991243	−	0.991243i	0.999962	+	0.00871919i	$0.00277544\pi$
$674$	36.6248	+	9.81357i	1.41073	+	0.378005i
$675$	23.8679	−	6.39539i	0.918676	−	0.246159i
$676$	0.0550857	−	0.0954112i	0.00211868	−	0.00366966i
$677$	−7.41857	+	27.6865i	−0.285119	+	1.06408i	0.663634	+	0.748058i	$0.269013\pi$
$677$	−7.41857	+	27.6865i	−0.285119	+	1.06408i	−0.948752	+	0.316020i	$0.897653\pi$
$678$			37.0938i			1.42458i
$679$		0			0
$680$	11.7863	+	31.4923i	0.451982	+	1.20768i
$681$	−8.48674	−	14.6995i	−0.325213	−	0.563285i
$682$	−48.7065	−	28.1207i	−1.86507	−	1.07680i
$683$	−19.1060	+	5.11944i	−0.731071	+	0.195890i	−0.605106	−	0.796145i	$-0.706869\pi$
$683$	−19.1060	+	5.11944i	−0.731071	+	0.195890i	−0.125965	+	0.992035i	$0.540203\pi$
$684$	1.66542	+	2.88459i	0.0636789	+	0.110295i
$685$	−48.4754	−	48.4754i	−1.85215	−	1.85215i
$686$		0			0
$687$	22.0724	−	22.0724i	0.842114	−	0.842114i
$688$	−27.1583	+	15.6799i	−1.03540	+	0.597790i
$689$	12.8518	+	7.41997i	0.489613	+	0.282678i
$690$	1.88883	+	7.04920i	0.0719064	+	0.268358i
$691$	−36.4110	−	9.75631i	−1.38514	−	0.371147i	−0.512155	−	0.858893i	$-0.671153\pi$
$691$	−36.4110	−	9.75631i	−1.38514	−	0.371147i	−0.872986	+	0.487745i	$0.837819\pi$
$692$	−1.19017	−	1.19017i	−0.0452434	−	0.0452434i
$693$		0			0
$694$	−25.4665	−	25.4665i	−0.966697	−	0.966697i
$695$	22.9471	−	13.2485i	0.870433	−	0.502544i
$696$	13.6658	−	23.6698i	0.517999	−	0.897201i
$697$	2.83061	+	0.472729i	0.107217	+	0.0179059i
$698$	−8.01058	−	13.8747i	−0.303205	−	0.525166i
$699$		−	49.7946i		−	1.88341i
$700$		0			0
$701$	12.4612			0.470652			0.235326	−	0.971916i	$-0.424384\pi$
$701$	12.4612			0.470652			0.235326	+	0.971916i	$0.424384\pi$
$702$	−5.60615	+	20.9224i	−0.211590	+	0.789666i
$703$	−2.19519	−	8.19256i	−0.0827932	−	0.308988i
$704$	6.43748	+	24.0250i	0.242622	+	0.905477i
$705$	−25.8728	+	14.9377i	−0.974427	+	0.562586i
$706$		−	26.4143i		−	0.994116i
$707$		0			0
$708$	1.85558	−	1.85558i	0.0697368	−	0.0697368i
$709$	−3.73707	+	13.9469i	−0.140349	+	0.523788i	0.859570	+	0.511018i	$0.170732\pi$
$709$	−3.73707	+	13.9469i	−0.140349	+	0.523788i	−0.999918	+	0.0127698i	$0.995935\pi$
$710$	11.4912	−	19.9034i	0.431259	−	0.746962i
$711$	−11.0015	+	2.94783i	−0.412587	+	0.110552i
$712$	−4.25882	+	2.45883i	−0.159606	+	0.0921485i
$713$	−5.14726			−0.192766
$714$		0			0
$715$	−57.6804			−2.15712
$716$	−1.61952	+	0.935030i	−0.0605243	+	0.0349437i
$717$	28.6439	−	7.67512i	1.06973	−	0.286633i
$718$	22.2022	−	38.4553i	0.828578	−	1.43514i
$719$	−2.39423	+	8.93538i	−0.0892896	+	0.333233i	−0.996092	−	0.0883228i	$-0.971849\pi$
$719$	−2.39423	+	8.93538i	−0.0892896	+	0.333233i	0.906802	+	0.421556i	$0.138516\pi$
$720$	12.9023	−	12.9023i	0.480840	−	0.480840i
$721$		0			0
$722$		−	30.5173i		−	1.13574i
$723$	26.8059	−	15.4764i	0.996922	−	0.575573i
$724$	0.235470	+	0.878788i	0.00875119	+	0.0326599i
$725$	9.44465	+	35.2479i	0.350765	+	1.30907i
$726$	−8.95288	+	33.4126i	−0.332273	+	1.24006i
$727$	33.0618			1.22619			0.613096	−	0.790008i	$-0.289924\pi$
$727$	33.0618			1.22619			0.613096	+	0.790008i	$0.289924\pi$
$728$		0			0
$729$		−	10.4537i		−	0.387175i
$730$	−4.40660	−	7.63246i	−0.163096	−	0.282490i
$731$	−22.2904	+	15.9106i	−0.824441	+	0.588475i
$732$	5.80942	−	10.0622i	0.214722	−	0.371910i
$733$	1.57407	−	0.908789i	0.0581396	−	0.0335669i	−0.470648	−	0.882321i	$-0.655980\pi$
$733$	1.57407	−	0.908789i	0.0581396	−	0.0335669i	0.528788	+	0.848754i	$0.322647\pi$
$734$	−20.9153	−	20.9153i	−0.771998	−	0.771998i
$735$		0			0
$736$	−1.24450	−	1.24450i	−0.0458730	−	0.0458730i
$737$	56.6598	+	15.1819i	2.08709	+	0.559234i
$738$	−0.322448	−	1.20339i	−0.0118695	−	0.0442974i
$739$	26.1195	+	15.0801i	0.960820	+	0.554730i	0.896425	−	0.443195i	$-0.146155\pi$
$739$	26.1195	+	15.0801i	0.960820	+	0.554730i	0.0643946	+	0.997925i	$0.479488\pi$
$740$	1.89950	−	1.09668i	0.0698270	−	0.0403146i
$741$	−32.4307	+	32.4307i	−1.19137	+	1.19137i
$742$		0			0
$743$	28.0426	+	28.0426i	1.02878	+	1.02878i	0.999573	+	0.0292082i	$0.00929860\pi$
$743$	28.0426	+	28.0426i	1.02878	+	1.02878i	0.0292082	+	0.999573i	$0.490701\pi$
$744$	18.7138	+	32.4133i	0.686082	+	1.18833i
$745$	−2.19893	+	0.589202i	−0.0805627	+	0.0215867i
$746$	−42.1640	−	24.3434i	−1.54373	−	0.891274i
$747$	2.67049	+	4.62543i	0.0977082	+	0.169236i
$748$	−3.18668	−	8.51467i	−0.116517	−	0.311327i
$749$		0			0
$750$			16.5575i			0.604595i
$751$	−10.8266	+	40.4055i	−0.395069	+	1.47442i	0.426594	+	0.904443i	$0.359713\pi$
$751$	−10.8266	+	40.4055i	−0.395069	+	1.47442i	−0.821663	+	0.569974i	$0.806953\pi$
$752$	10.2120	−	17.6878i	0.372394	−	0.645006i
$753$	3.02673	−	0.811010i	0.110300	−	0.0295549i
$754$	−30.8980	−	8.27910i	−1.12524	−	0.301507i
$755$	−27.4226	+	27.4226i	−0.998009	+	0.998009i
$756$		0			0
$757$			29.9024i			1.08682i	0.839467	+	0.543411i	$0.182867\pi$
$757$			29.9024i			1.08682i	−0.839467	+	0.543411i	$0.817133\pi$
$758$	−18.9086	−	5.06654i	−0.686791	−	0.184025i
$759$	1.65279	+	6.16828i	0.0599923	+	0.223894i
$760$	−48.8212	+	13.0816i	−1.77093	+	0.474520i
$761$	14.9404	+	25.8775i	0.541588	+	0.938058i	0.998813	+	0.0487070i	$0.0155101\pi$
$761$	14.9404	+	25.8775i	0.541588	+	0.938058i	−0.457225	+	0.889351i	$0.651157\pi$
$762$	11.6000	+	11.6000i	0.420224	+	0.420224i
$763$		0			0
$764$	11.8840			0.429948
$765$	10.1317	−	12.2989i	0.366311	−	0.444667i
$766$	−23.4631	+	40.6393i	−0.847756	+	1.46836i
$767$	8.60813	+	4.96991i	0.310822	+	0.179453i
$768$	−5.65941	+	21.1212i	−0.204216	+	0.762146i
$769$	35.8821			1.29394			0.646971	−	0.762514i	$-0.276035\pi$
$769$	35.8821			1.29394			0.646971	+	0.762514i	$0.276035\pi$
$770$		0			0
$771$	−5.79594	+	5.79594i	−0.208736	+	0.208736i
$772$	5.12866	+	1.37422i	0.184584	+	0.0494592i
$773$	−11.4284	−	6.59820i	−0.411052	−	0.237321i	0.280190	−	0.959945i	$-0.409603\pi$
$773$	−11.4284	−	6.59820i	−0.411052	−	0.237321i	−0.691241	+	0.722624i	$0.742936\pi$
$774$	10.2961	+	5.94446i	0.370086	+	0.213669i
$775$	−48.2683	−	12.9335i	−1.73385	−	0.464584i
$776$	7.18567	−	7.18567i	0.257950	−	0.257950i
$777$		0			0
$778$	32.9245			1.18040
$779$	−1.11647	+	4.16670i	−0.0400015	+	0.149288i
$780$	−10.2715	−	5.93026i	−0.367779	−	0.212337i
$781$	10.0552	−	17.4161i	0.359804	−	0.623199i
$782$	−3.36286	−	2.77028i	−0.120256	−	0.0990650i
$783$	21.1797			0.756899
$784$		0			0
$785$	56.1314	+	56.1314i	2.00342	+	2.00342i
$786$	−13.3594	−	23.1391i	−0.476513	−	0.825344i
$787$	−27.7189	+	7.42724i	−0.988070	+	0.264753i	−0.716440	−	0.697649i	$-0.754230\pi$
$787$	−27.7189	+	7.42724i	−0.988070	+	0.264753i	−0.271631	+	0.962402i	$0.587563\pi$
$788$	2.76541	+	10.3207i	0.0985137	+	0.367658i
$789$	−35.3189	−	9.46367i	−1.25739	−	0.336916i
$790$			53.4019i			1.89995i
$791$		0			0
$792$	9.03209	−	9.03209i	0.320941	−	0.320941i
$793$	42.5100	+	11.3905i	1.50957	+	0.404489i
$794$	43.0719	−	11.5411i	1.52856	−	0.409577i
$795$	14.0864	−	24.3984i	0.499595	−	0.865323i
$796$	0.641422	−	2.39382i	0.0227346	−	0.0848467i
$797$			10.8120i			0.382980i	0.981495	+	0.191490i	$0.0613320\pi$
$797$			10.8120i			0.382980i	−0.981495	+	0.191490i	$0.938668\pi$
$798$		0			0
$799$	7.39125	−	16.2327i	0.261484	−	0.574272i
$800$	−8.54326	−	14.7974i	−0.302050	−	0.523166i
$801$	2.01819	+	1.16520i	0.0713091	+	0.0411703i
$802$	−4.96442	+	1.33021i	−0.175300	+	0.0469714i
$803$	−3.85592	−	6.67865i	−0.136073	−	0.235684i
$804$	8.52888	+	8.52888i	0.300790	+	0.300790i
$805$		0			0
$806$	30.9743	−	30.9743i	1.09102	−	1.09102i
$807$	−31.7675	+	18.3410i	−1.11827	+	0.645633i
$808$	11.2039	+	6.46855i	0.394150	+	0.227563i
$809$	13.1968	+	49.2510i	0.463974	+	1.73157i	0.660269	+	0.751029i	$0.270442\pi$
$809$	13.1968	+	49.2510i	0.463974	+	1.73157i	−0.196295	+	0.980545i	$0.562891\pi$
$810$	57.3284	+	15.3611i	2.01432	+	0.539734i
$811$	10.8591	+	10.8591i	0.381315	+	0.381315i	0.871576	−	0.490261i	$-0.163098\pi$
$811$	10.8591	+	10.8591i	0.381315	+	0.381315i	−0.490261	+	0.871576i	$0.663098\pi$
$812$		0			0
$813$	−24.0340	−	24.0340i	−0.842910	−	0.842910i
$814$	8.70353	−	5.02499i	0.305059	−	0.176126i
$815$	−20.4997	+	35.5065i	−0.718074	+	1.24374i
$816$	−6.52324	+	39.0599i	−0.228359	+	1.36737i
$817$	−20.5825	−	35.6500i	−0.720091	−	1.24723i
$818$		−	54.0654i		−	1.89035i
$819$		0			0
$820$	−1.11553			−0.0389560
$821$	3.60669	−	13.4603i	0.125874	−	0.469769i	−0.873995	−	0.485935i	$-0.838479\pi$
$821$	3.60669	−	13.4603i	0.125874	−	0.469769i	0.999869	+	0.0161658i	$0.00514596\pi$
$822$	−16.7173	−	62.3897i	−0.583082	−	2.17609i
$823$	3.17686	+	11.8562i	0.110738	+	0.413281i	0.998933	−	0.0461864i	$-0.0147068\pi$
$823$	3.17686	+	11.8562i	0.110738	+	0.413281i	−0.888194	+	0.459468i	$0.848040\pi$
$824$	−8.24392	+	4.75963i	−0.287190	+	0.165810i
$825$			61.9959i			2.15842i
$826$		0			0
$827$	11.8528	−	11.8528i	0.412162	−	0.412162i	−0.470329	−	0.882491i	$-0.655865\pi$
$827$	11.8528	−	11.8528i	0.412162	−	0.412162i	0.882491	+	0.470329i	$0.155865\pi$
$828$	−0.0934886	+	0.348904i	−0.00324895	+	0.0121253i
$829$	21.7133	−	37.6085i	0.754134	−	1.30620i	−0.191670	−	0.981459i	$-0.561390\pi$
$829$	21.7133	−	37.6085i	0.754134	−	1.30620i	0.945804	−	0.324739i	$-0.105276\pi$
$830$	24.1889	−	6.48139i	0.839608	−	0.224972i
$831$	1.83857	−	1.06150i	0.0637793	−	0.0368230i
$832$	−19.3722			−0.671612
$833$		0			0
$834$	24.9649			0.864463
$835$	−72.1303	+	41.6444i	−2.49617	+	1.44117i
$836$	13.1999	−	3.53691i	0.456529	−	0.122327i
$837$	−14.5017	+	25.1176i	−0.501251	+	0.868192i
$838$	−7.12865	+	26.6045i	−0.246255	+	0.919036i
$839$	4.20215	−	4.20215i	0.145074	−	0.145074i	−0.630839	−	0.775914i	$-0.717289\pi$
$839$	4.20215	−	4.20215i	0.145074	−	0.145074i	0.775914	+	0.630839i	$0.217289\pi$
$840$		0			0
$841$			2.27792i			0.0785488i
$842$	−17.8414	+	10.3007i	−0.614855	+	0.354987i
$843$	−1.85880	−	6.93714i	−0.0640205	−	0.238928i
$844$	1.18855	+	4.43574i	0.0409117	+	0.152684i
$845$	0.205045	−	0.765238i	0.00705376	−	0.0263250i
$846$	−7.74305			−0.266211
$847$		0			0
$848$			19.2602i			0.661397i
$849$	−1.85475	−	3.21253i	−0.0636549	−	0.110254i
$850$	−24.5743	−	34.4281i	−0.842892	−	1.18087i
$851$	0.459891	−	0.796555i	0.0157649	−	0.0273056i
$852$	3.58119	−	2.06760i	0.122690	−	0.0708349i
$853$	−9.18348	−	9.18348i	−0.314436	−	0.314436i	0.532189	−	0.846625i	$-0.321370\pi$
$853$	−9.18348	−	9.18348i	−0.314436	−	0.314436i	−0.846625	+	0.532189i	$0.821370\pi$
$854$		0			0
$855$	16.9364	+	16.9364i	0.579214	+	0.579214i
$856$	26.4062	+	7.07553i	0.902546	+	0.241837i
$857$	−7.45226	−	27.8122i	−0.254564	−	0.950048i	−0.968332	−	0.249665i	$-0.919679\pi$
$857$	−7.45226	−	27.8122i	−0.254564	−	0.950048i	0.713768	−	0.700382i	$-0.246987\pi$
$858$	−47.0642	−	27.1725i	−1.60675	−	0.927655i
$859$	7.14240	−	4.12366i	0.243695	−	0.140698i	−0.373179	−	0.927760i	$-0.621732\pi$
$859$	7.14240	−	4.12366i	0.243695	−	0.140698i	0.616874	+	0.787062i	$0.288399\pi$
$860$	7.52741	−	7.52741i	0.256683	−	0.256683i
$861$		0			0
$862$	29.2207	+	29.2207i	0.995260	+	0.995260i
$863$	17.8414	+	30.9022i	0.607329	+	1.05192i	0.991679	+	0.128737i	$0.0410924\pi$
$863$	17.8414	+	30.9022i	0.607329	+	1.05192i	−0.384350	+	0.923188i	$0.625574\pi$
$864$	−9.57915	+	2.56673i	−0.325889	+	0.0873218i
$865$	−10.4818	−	6.05169i	−0.356393	−	0.205764i
$866$	0.616088	+	1.06710i	0.0209355	+	0.0362614i
$867$	−2.38981	+	34.5006i	−0.0811621	+	1.17170i
$868$		0			0
$869$			46.7284i			1.58515i
$870$	−15.7175	+	58.6584i	−0.532872	+	1.98871i
$871$	−22.8434	+	39.5660i	−0.774020	+	1.34064i
$872$	10.2234	−	2.73935i	0.346208	−	0.0927662i
$873$	−4.65156	−	1.24638i	−0.157431	−	0.0421836i
$874$	4.63090	−	4.63090i	0.156643	−	0.156643i
$875$		0			0
$876$		−	1.58575i		−	0.0535774i
$877$	13.5940	+	3.64250i	0.459036	+	0.122998i	0.480925	−	0.876762i	$-0.340301\pi$
$877$	13.5940	+	3.64250i	0.459036	+	0.122998i	−0.0218882	+	0.999760i	$0.506968\pi$
$878$	−10.2362	−	38.2019i	−0.345454	−	1.28925i
$879$	29.3933	−	7.87590i	0.991410	−	0.265648i
$880$	−37.4306	−	64.8316i	−1.26178	−	2.18547i
$881$	10.4454	+	10.4454i	0.351914	+	0.351914i	0.860821	−	0.508907i	$-0.169950\pi$
$881$	10.4454	+	10.4454i	0.351914	+	0.351914i	−0.508907	+	0.860821i	$0.669950\pi$
$882$		0			0
$883$	4.72305			0.158943			0.0794717	−	0.996837i	$-0.474677\pi$
$883$	4.72305			0.158943			0.0794717	+	0.996837i	$0.474677\pi$
$884$	7.04816	−	0.680991i	0.237055	−	0.0229042i
$885$	9.43513	−	16.3421i	0.317158	−	0.549334i
$886$	16.5191	+	9.53729i	0.554969	+	0.320412i
$887$	−11.6779	+	43.5827i	−0.392107	+	1.46336i	0.434545	+	0.900650i	$0.356909\pi$
$887$	−11.6779	+	43.5827i	−0.392107	+	1.46336i	−0.826652	+	0.562713i	$0.809758\pi$
$888$	−6.68809			−0.224437
$889$		0			0
$890$	7.72620	−	7.72620i	0.258983	−	0.258983i
$891$	50.1643	+	13.4415i	1.68057	+	0.450307i
$892$	−7.17281	−	4.14122i	−0.240163	−	0.138658i
$893$	23.2182	+	13.4050i	0.776967	+	0.448582i
$894$	−2.07178	−	0.555133i	−0.0692908	−	0.0185664i
$895$	−9.50877	+	9.50877i	−0.317843	+	0.317843i
$896$		0			0
$897$	−4.97371			−0.166067
$898$	15.0585	−	56.1993i	0.502510	−	1.87539i
$899$	−37.0935	−	21.4159i	−1.23714	−	0.714261i
$900$	−1.75337	+	3.03693i	−0.0584458	+	0.101231i
$901$	1.61759	+	16.7419i	0.0538898	+	0.557752i
$902$	−5.11138			−0.170190
$903$		0			0
$904$	−19.6999	−	19.6999i	−0.655209	−	0.655209i
$905$	3.27110	+	5.66571i	0.108735	+	0.188335i
$906$	−35.2938	+	9.45696i	−1.17256	+	0.314186i
$907$	8.76614	+	32.7157i	0.291075	+	1.08631i	0.944285	+	0.329129i	$0.106755\pi$
$907$	8.76614	+	32.7157i	0.291075	+	1.08631i	−0.653210	+	0.757177i	$0.726578\pi$
$908$	−3.80480	−	1.01949i	−0.126267	−	0.0338330i
$909$		−	6.13069i		−	0.203342i
$910$		0			0
$911$	7.16704	−	7.16704i	0.237455	−	0.237455i	−0.578341	−	0.815795i	$-0.696300\pi$
$911$	7.16704	−	7.16704i	0.237455	−	0.237455i	0.815795	+	0.578341i	$0.196300\pi$
$912$	−57.4968	−	15.4062i	−1.90391	−	0.510151i
$913$	21.1661	−	5.67143i	0.700494	−	0.187697i
$914$	10.0531	−	17.4126i	0.332528	−	0.575956i
$915$	21.6243	−	80.7032i	0.714879	−	2.66796i
$916$		−	7.24404i		−	0.239350i
$917$		0			0
$918$	−22.9928	+	8.60524i	−0.758876	+	0.284015i
$919$	3.95035	+	6.84221i	0.130310	+	0.225704i	0.923796	−	0.382885i	$-0.125069\pi$
$919$	3.95035	+	6.84221i	0.130310	+	0.225704i	−0.793486	+	0.608589i	$0.791736\pi$
$920$	−4.74684	−	2.74059i	−0.156499	−	0.0903546i
$921$	−14.0774	+	3.77202i	−0.463866	+	0.124292i
$922$	−3.60125	−	6.23754i	−0.118601	−	0.205423i
$923$	11.0756	+	11.0756i	0.364557	+	0.364557i
$924$		0			0
$925$	6.31412	−	6.31412i	0.207607	−	0.207607i
$926$	−2.09481	+	1.20944i	−0.0688396	+	0.0397446i
$927$	3.90666	+	2.25551i	0.128312	+	0.0740808i
$928$	−3.79052	−	14.1464i	−0.124430	−	0.464378i
$929$	8.84740	+	2.37065i	0.290274	+	0.0777786i	0.401018	−	0.916070i	$-0.368657\pi$
$929$	8.84740	+	2.37065i	0.290274	+	0.0777786i	−0.110744	+	0.993849i	$0.535323\pi$
$930$	−58.8031	−	58.8031i	−1.92823	−	1.92823i
$931$		0			0
$932$	−8.17117	−	8.17117i	−0.267656	−	0.267656i
$933$	11.0894	−	6.40246i	0.363050	−	0.209607i
$934$	−8.64971	+	14.9817i	−0.283027	+	0.490217i
$935$	−37.9814	−	53.2110i	−1.24212	−	1.74019i
$936$	4.97432	+	8.61577i	0.162591	+	0.281615i
$937$			53.4400i			1.74581i	0.487891	+	0.872905i	$0.337766\pi$
$937$			53.4400i			1.74581i	−0.487891	+	0.872905i	$0.662234\pi$
$938$		0			0
$939$	−63.8202			−2.08269
$940$	−1.79443	+	6.69690i	−0.0585278	+	0.218429i
$941$	12.9787	+	48.4370i	0.423092	+	1.57900i	0.768055	+	0.640384i	$0.221225\pi$
$941$	12.9787	+	48.4370i	0.423092	+	1.57900i	−0.344963	+	0.938616i	$0.612108\pi$
$942$	19.3575	+	72.2432i	0.630702	+	2.35381i
$943$	−0.405125	+	0.233899i	−0.0131927	+	0.00761679i
$944$			12.9005i			0.419876i
$945$		0			0
$946$	34.4907	−	34.4907i	1.12139	−	1.12139i
$947$	−3.79776	+	14.1735i	−0.123411	+	0.460575i	−0.999778	−	0.0210682i	$-0.993293\pi$
$947$	−3.79776	+	14.1735i	−0.123411	+	0.460575i	0.876367	+	0.481643i	$0.159960\pi$
$948$	−4.80426	+	8.32123i	−0.156035	+	0.270261i
$949$	5.80179	−	1.55458i	0.188334	−	0.0504640i
$950$	55.0622	−	31.7902i	1.78645	−	1.03141i
$951$	−33.6993			−1.09278
$952$		0			0
$953$	−4.66197			−0.151016			−0.0755080	−	0.997145i	$-0.524058\pi$
$953$	−4.66197			−0.151016			−0.0755080	+	0.997145i	$0.524058\pi$
$954$	6.32355	−	3.65090i	0.204732	−	0.118202i
$955$	82.5449	−	22.1178i	2.67109	−	0.715716i
$956$	3.44093	−	5.95986i	0.111288	−	0.192756i
$957$	−13.7533	+	51.3281i	−0.444581	+	1.65920i
$958$	−25.8621	+	25.8621i	−0.835566	+	0.835566i
$959$		0			0
$960$			36.7773i			1.18698i
$961$	23.9488	−	13.8269i	0.772543	−	0.446028i
$962$	2.02592	+	7.56082i	0.0653181	+	0.243771i
$963$	−3.35298	−	12.5135i	−0.108048	−	0.403242i
$964$	1.85914	−	6.93841i	0.0598789	−	0.223471i
$965$	38.1807			1.22908
$966$		0			0
$967$			15.2606i			0.490748i	0.969428	+	0.245374i	$0.0789108\pi$
$967$			15.2606i			0.490748i	−0.969428	+	0.245374i	$0.921089\pi$
$968$	−12.9902	−	22.4996i	−0.417520	−	0.723165i
$969$	−51.2728	−	8.56286i	−1.64712	−	0.275079i
$970$	−11.2895	+	19.5540i	−0.362484	+	0.627841i
$971$	−16.1056	+	9.29856i	−0.516852	+	0.298405i	−0.735646	−	0.677366i	$-0.763121\pi$
$971$	−16.1056	+	9.29856i	−0.516852	+	0.298405i	0.218793	+	0.975771i	$0.429788\pi$
$972$	3.75850	+	3.75850i	0.120554	+	0.120554i
$973$		0			0
$974$	24.4991	+	24.4991i	0.785003	+	0.785003i
$975$	−46.6409	−	12.4974i	−1.49370	−	0.400237i
$976$	14.7833	+	55.1721i	0.473202	+	1.76602i
$977$	−18.8317	−	10.8725i	−0.602479	−	0.347842i	0.167537	−	0.985866i	$-0.446419\pi$
$977$	−18.8317	−	10.8725i	−0.602479	−	0.347842i	−0.770016	+	0.638024i	$0.779752\pi$
$978$	−33.4534	+	19.3143i	−1.06972	+	0.617605i
$979$	6.76068	−	6.76068i	0.216072	−	0.216072i
$980$		0			0
$981$	−3.54657	−	3.54657i	−0.113233	−	0.113233i
$982$	−15.1467	−	26.2349i	−0.483352	−	0.837190i
$983$	3.44998	−	0.924420i	0.110037	−	0.0294844i	−0.203380	−	0.979100i	$-0.565193\pi$
$983$	3.44998	−	0.924420i	0.110037	−	0.0294844i	0.313418	+	0.949615i	$0.398526\pi$
$984$	2.94581	+	1.70077i	0.0939091	+	0.0542185i
$985$	38.4165	+	66.5393i	1.22405	+	2.12012i
$986$	−12.7081	−	33.9556i	−0.404710	−	1.08137i
$987$		0			0
$988$			10.6436i			0.338618i
$989$	1.15540	−	4.31203i	0.0367397	−	0.137114i
$990$	−14.1904	+	24.5786i	−0.451002	+	0.781159i
$991$	0.409880	−	0.109827i	0.0130203	−	0.00348877i	−0.252303	−	0.967648i	$-0.581188\pi$
$991$	0.409880	−	0.109827i	0.0130203	−	0.00348877i	0.265323	+	0.964160i	$0.414521\pi$
$992$	19.3720	+	5.19071i	0.615062	+	0.164805i
$993$	6.80821	−	6.80821i	0.216052	−	0.216052i
$994$		0			0
$995$		−	17.8210i		−	0.564963i
$996$	4.35227	+	1.16619i	0.137907	+	0.0369520i
$997$	−9.68988	−	36.1631i	−0.306882	−	1.14530i	−0.931314	−	0.364218i	$-0.881336\pi$
$997$	−9.68988	−	36.1631i	−0.306882	−	1.14530i	0.624432	−	0.781079i	$-0.285331\pi$
$998$	−64.3351	+	17.2385i	−2.03649	+	0.545676i
$999$	−2.59135	−	4.48836i	−0.0819868	−	0.142005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.o.g.557.8		40
7.2	even	3	inner	833.2.o.g.30.3		40
7.3	odd	6		833.2.g.h.540.8		20
7.4	even	3		119.2.g.a.64.8	✓	20
7.5	odd	6		833.2.o.f.30.3		40
7.6	odd	2		833.2.o.f.557.8		40
17.4	even	4	inner	833.2.o.g.361.3		40
21.11	odd	6		1071.2.n.c.64.3		20
119.4	even	12		119.2.g.a.106.3	yes	20
119.32	even	24		2023.2.a.n.1.3		10
119.38	odd	12		833.2.g.h.344.3		20
119.53	even	24		2023.2.a.m.1.3		10
119.55	odd	4		833.2.o.f.361.3		40
119.72	even	12	inner	833.2.o.g.667.8		40
119.89	odd	12		833.2.o.f.667.8		40
357.242	odd	12		1071.2.n.c.820.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.g.a.64.8	✓	20	7.4	even	3
119.2.g.a.106.3	yes	20	119.4	even	12
833.2.g.h.344.3		20	119.38	odd	12
833.2.g.h.540.8		20	7.3	odd	6
833.2.o.f.30.3		40	7.5	odd	6
833.2.o.f.361.3		40	119.55	odd	4
833.2.o.f.557.8		40	7.6	odd	2
833.2.o.f.667.8		40	119.89	odd	12
833.2.o.g.30.3		40	7.2	even	3	inner
833.2.o.g.361.3		40	17.4	even	4	inner
833.2.o.g.557.8		40	1.1	even	1	trivial
833.2.o.g.667.8		40	119.72	even	12	inner
1071.2.n.c.64.3		20	21.11	odd	6
1071.2.n.c.820.8		20	357.242	odd	12
2023.2.a.m.1.3		10	119.53	even	24
2023.2.a.n.1.3		10	119.32	even	24

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36164 - 0.786146i) q^{2} +(1.96499 - 0.526518i) q^{3} +(0.236050 - 0.408850i) q^{4} +(0.878646 - 3.27915i) q^{5} +(2.26170 - 2.26170i) q^{6} +2.40230i q^{8} +(0.985896 - 0.569207i) q^{9} +O(q^{10})\)	\(q+(1.36164 - 0.786146i) q^{2} +(1.96499 - 0.526518i) q^{3} +(0.236050 - 0.408850i) q^{4} +(0.878646 - 3.27915i) q^{5} +(2.26170 - 2.26170i) q^{6} +2.40230i q^{8} +(0.985896 - 0.569207i) q^{9} +(-1.38149 - 5.15578i) q^{10} +(-1.20885 - 4.51148i) q^{11} +(0.248569 - 0.927672i) q^{12} +3.63777 q^{13} -6.90613i q^{15} +(2.36066 + 4.08878i) q^{16} +(2.39540 + 3.35590i) q^{17} +(0.894959 - 1.55012i) q^{18} +(-5.36723 + 3.09877i) q^{19} +(-1.13328 - 1.13328i) q^{20} +(-5.19270 - 5.19270i) q^{22} +(-0.649191 - 0.173950i) q^{23} +(1.26486 + 4.72051i) q^{24} +(-5.65069 - 3.26243i) q^{25} +(4.95335 - 2.85982i) q^{26} +(-2.67784 + 2.67784i) q^{27} +(-3.95461 - 3.95461i) q^{29} +(-5.42922 - 9.40369i) q^{30} +(7.39761 - 1.98218i) q^{31} +(2.26785 + 1.30934i) q^{32} +(-4.75075 - 8.22854i) q^{33} +(5.89991 + 2.68641i) q^{34} -0.537445i q^{36} +(-0.354204 + 1.32191i) q^{37} +(-4.87217 + 8.43884i) q^{38} +(7.14819 - 1.91535i) q^{39} +(7.87752 + 2.11077i) q^{40} +(0.492170 - 0.492170i) q^{41} +6.64216i q^{43} +(-2.12987 - 0.570696i) q^{44} +(-1.00026 - 3.73303i) q^{45} +(-1.02072 + 0.273500i) q^{46} +(-2.16296 - 3.74636i) q^{47} +(6.79150 + 6.79150i) q^{48} -10.2590 q^{50} +(6.47388 + 5.33310i) q^{51} +(0.858695 - 1.48730i) q^{52} +(3.53287 + 2.03970i) q^{53} +(-1.54109 + 5.75144i) q^{54} -15.8560 q^{55} +(-8.91500 + 8.91500i) q^{57} +(-8.49368 - 2.27587i) q^{58} +(2.36632 + 1.36620i) q^{59} +(-2.82357 - 1.63019i) q^{60} +(11.6857 + 3.13118i) q^{61} +(8.51463 - 8.51463i) q^{62} -5.32531 q^{64} +(3.19631 - 11.9288i) q^{65} +(-12.9377 - 7.46956i) q^{66} +(-6.27952 + 10.8764i) q^{67} +(1.93749 - 0.187200i) q^{68} -1.36724 q^{69} +(3.04461 + 3.04461i) q^{71} +(1.36741 + 2.36842i) q^{72} +(1.59488 - 0.427346i) q^{73} +(0.556911 + 2.07842i) q^{74} +(-12.8213 - 3.43545i) q^{75} +2.92586i q^{76} +(8.22754 - 8.22754i) q^{78} +(-9.66384 - 2.58942i) q^{79} +(15.4819 - 4.14837i) q^{80} +(-5.55963 + 9.62956i) q^{81} +(0.283243 - 1.05708i) q^{82} +4.69160i q^{83} +(13.1092 - 4.90623i) q^{85} +(5.22170 + 9.04425i) q^{86} +(-9.85296 - 5.68861i) q^{87} +(10.8379 - 2.90402i) q^{88} +(1.02353 + 1.77280i) q^{89} +(-4.29671 - 4.29671i) q^{90} +(-0.224361 + 0.224361i) q^{92} +(13.4926 - 7.78995i) q^{93} +(-5.89036 - 3.40080i) q^{94} +(5.44544 + 20.3227i) q^{95} +(5.14569 + 1.37878i) q^{96} +(-2.99116 - 2.99116i) q^{97} +(-3.75976 - 3.75976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6	\( 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 12 q^{12} - 16 q^{16} + 12 q^{17} + 8 q^{18} + 40 q^{20} - 40 q^{22} - 4 q^{24} + 16 q^{27} + 32 q^{29} + 36 q^{30} - 4 q^{31} + 16 q^{33} + 72 q^{34} + 28 q^{37} - 48 q^{38} - 20 q^{39} + 24 q^{40} - 48 q^{41} + 28 q^{44} - 36 q^{45} - 8 q^{46} - 40 q^{47} - 16 q^{48} - 56 q^{50} + 40 q^{51} + 28 q^{54} - 80 q^{55} + 72 q^{57} - 56 q^{58} + 16 q^{61} - 80 q^{62} + 64 q^{64} - 8 q^{65} + 32 q^{68} - 176 q^{69} - 16 q^{71} - 108 q^{72} - 8 q^{73} - 36 q^{74} - 8 q^{75} - 88 q^{78} + 4 q^{79} + 116 q^{80} - 4 q^{81} + 16 q^{82} + 32 q^{85} - 44 q^{86} - 72 q^{88} - 48 q^{89} + 112 q^{90} - 64 q^{92} - 44 q^{95} - 68 q^{96} - 48 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 + 24 * q^4 + 8 * q^5 + 8 * q^6 - 4 * q^10 + 4 * q^11 - 12 * q^12 - 16 * q^16 + 12 * q^17 + 8 * q^18 + 40 * q^20 - 40 * q^22 - 4 * q^24 + 16 * q^27 + 32 * q^29 + 36 * q^30 - 4 * q^31 + 16 * q^33 + 72 * q^34 + 28 * q^37 - 48 * q^38 - 20 * q^39 + 24 * q^40 - 48 * q^41 + 28 * q^44 - 36 * q^45 - 8 * q^46 - 40 * q^47 - 16 * q^48 - 56 * q^50 + 40 * q^51 + 28 * q^54 - 80 * q^55 + 72 * q^57 - 56 * q^58 + 16 * q^61 - 80 * q^62 + 64 * q^64 - 8 * q^65 + 32 * q^68 - 176 * q^69 - 16 * q^71 - 108 * q^72 - 8 * q^73 - 36 * q^74 - 8 * q^75 - 88 * q^78 + 4 * q^79 + 116 * q^80 - 4 * q^81 + 16 * q^82 + 32 * q^85 - 44 * q^86 - 72 * q^88 - 48 * q^89 + 112 * q^90 - 64 * q^92 - 44 * q^95 - 68 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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