LMFDB - Embedded newform 833.2.o.g.361.3

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			361.3
Character	$\chi$	$=$	833.361
Dual form			833.2.o.g.30.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36164 + 0.786146i) q^{2} +(-0.526518 - 1.96499i) q^{3} +(0.236050 - 0.408850i) q^{4} +(-3.27915 - 0.878646i) q^{5} +(2.26170 + 2.26170i) q^{6} -2.40230i q^{8} +(-0.985896 + 0.569207i) q^{9} +O(q^{10})$	\(q+(-1.36164 + 0.786146i) q^{2} +(-0.526518 - 1.96499i) q^{3} +(0.236050 - 0.408850i) q^{4} +(-3.27915 - 0.878646i) q^{5} +(2.26170 + 2.26170i) q^{6} -2.40230i q^{8} +(-0.985896 + 0.569207i) q^{9} +(5.15578 - 1.38149i) q^{10} +(4.51148 - 1.20885i) q^{11} +(-0.927672 - 0.248569i) q^{12} +3.63777 q^{13} +6.90613i q^{15} +(2.36066 + 4.08878i) q^{16} +(-4.10399 - 0.396526i) 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} +(0.173950 - 0.649191i) q^{23} +(-4.72051 + 1.26486i) 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} +(-1.98218 - 7.39761i) q^{31} +(-2.26785 - 1.30934i) q^{32} +(-4.75075 - 8.22854i) q^{33} +(5.89991 - 2.68641i) q^{34} +0.537445i q^{36} +(1.32191 + 0.354204i) q^{37} +(-4.87217 + 8.43884i) q^{38} +(-1.91535 - 7.14819i) q^{39} +(-2.11077 + 7.87752i) q^{40} +(0.492170 + 0.492170i) q^{41} -6.64216i q^{43} +(0.570696 - 2.12987i) q^{44} +(3.73303 - 1.00026i) q^{45} +(0.273500 + 1.02072i) q^{46} +(-2.16296 - 3.74636i) q^{47} +(6.79150 - 6.79150i) q^{48} -10.2590 q^{50} +(1.38166 + 8.27309i) q^{51} +(0.858695 - 1.48730i) q^{52} +(-3.53287 - 2.03970i) q^{53} +(5.75144 + 1.54109i) q^{54} -15.8560 q^{55} +(-8.91500 - 8.91500i) q^{57} +(2.27587 - 8.49368i) q^{58} +(-2.36632 - 1.36620i) q^{59} +(2.82357 + 1.63019i) q^{60} +(-3.13118 + 11.6857i) q^{61} +(8.51463 + 8.51463i) q^{62} -5.32531 q^{64} +(-11.9288 - 3.19631i) q^{65} +(12.9377 + 7.46956i) q^{66} +(-6.27952 + 10.8764i) q^{67} +(-1.13087 + 1.58432i) q^{68} -1.36724 q^{69} +(3.04461 - 3.04461i) q^{71} +(1.36741 + 2.36842i) q^{72} +(-0.427346 - 1.59488i) q^{73} +(-2.07842 + 0.556911i) q^{74} +(3.43545 - 12.8213i) q^{75} -2.92586i q^{76} +(8.22754 + 8.22754i) q^{78} +(2.58942 - 9.66384i) q^{79} +(-4.14837 - 15.4819i) q^{80} +(-5.55963 + 9.62956i) q^{81} +(-1.05708 - 0.283243i) q^{82} -4.69160i q^{83} +(13.1092 + 4.90623i) q^{85} +(5.22170 + 9.04425i) q^{86} +(9.85296 + 5.68861i) q^{87} +(-2.90402 - 10.8379i) 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} +(-20.3227 + 5.44544i) q^{95} +(-1.37878 + 5.14569i) 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 $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.36164	+	0.786146i	−0.962828	+	0.555889i	−0.897042	−	0.441945i	$-0.854289\pi$
$2$	−1.36164	+	0.786146i	−0.962828	+	0.555889i	−0.0657856	+	0.997834i	$0.520955\pi$
$3$	−0.526518	−	1.96499i	−0.303985	−	1.13449i	−0.933815	−	0.357756i	$-0.883542\pi$
$3$	−0.526518	−	1.96499i	−0.303985	−	1.13449i	0.629830	−	0.776733i	$-0.283125\pi$
$4$	0.236050	−	0.408850i	0.118025	−	0.204425i
$5$	−3.27915	−	0.878646i	−1.46648	−	0.392942i	−0.564758	−	0.825257i	$-0.691030\pi$
$5$	−3.27915	−	0.878646i	−1.46648	−	0.392942i	−0.901723	+	0.432314i	$0.857697\pi$
$6$	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
$10$	5.15578	−	1.38149i	1.63040	−	0.436865i
$11$	4.51148	−	1.20885i	1.36026	−	0.364481i	0.496349	−	0.868123i	$-0.334673\pi$
$11$	4.51148	−	1.20885i	1.36026	−	0.364481i	0.863913	+	0.503642i	$0.168007\pi$
$12$	−0.927672	−	0.248569i	−0.267796	−	0.0717557i
$13$	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
$17$	−4.10399	−	0.396526i	−0.995365	−	0.0961718i
$17$	−4.10399	−	0.396526i	−0.995365	−	0.0961718i
$18$	0.894959	−	1.55012i	0.210944	−	0.365366i
$19$	5.36723	−	3.09877i	1.23133	−	0.710906i	0.264020	−	0.964517i	$-0.414952\pi$
$19$	5.36723	−	3.09877i	1.23133	−	0.710906i	0.967306	+	0.253611i	$0.0816183\pi$
$20$	−1.13328	+	1.13328i	−0.253409	+	0.253409i
$21$		0			0
$22$	−5.19270	+	5.19270i	−1.10709	+	1.10709i
$23$	0.173950	−	0.649191i	0.0362711	−	0.135366i	−0.945416	−	0.325866i	$-0.894344\pi$
$23$	0.173950	−	0.649191i	0.0362711	−	0.135366i	0.981687	+	0.190500i	$0.0610109\pi$
$24$	−4.72051	+	1.26486i	−0.963570	+	0.258188i
$25$	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	−0.971479	−	0.237126i	$-0.923795\pi$
$29$	−3.95461	+	3.95461i	−0.734353	+	0.734353i	0.237126	+	0.971479i	$0.423795\pi$
$30$	−5.42922	−	9.40369i	−0.991236	−	1.71687i
$31$	−1.98218	−	7.39761i	−0.356011	−	1.32865i	−0.879208	−	0.476439i	$-0.841927\pi$
$31$	−1.98218	−	7.39761i	−0.356011	−	1.32865i	0.523197	−	0.852212i	$-0.324739\pi$
$32$	−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
$37$	1.32191	+	0.354204i	0.217320	+	0.0582307i	0.365836	−	0.930679i	$-0.380783\pi$
$37$	1.32191	+	0.354204i	0.217320	+	0.0582307i	−0.148516	+	0.988910i	$0.547450\pi$
$38$	−4.87217	+	8.43884i	−0.790370	+	1.36896i
$39$	−1.91535	−	7.14819i	−0.306702	−	1.14463i
$40$	−2.11077	+	7.87752i	−0.333743	+	1.24555i
$41$	0.492170	+	0.492170i	0.0768640	+	0.0768640i	0.744494	−	0.667630i	$-0.232691\pi$
$41$	0.492170	+	0.492170i	0.0768640	+	0.0768640i	−0.667630	+	0.744494i	$0.732691\pi$
$42$		0			0
$43$		−	6.64216i		−	1.01292i	−0.862264	−	0.506460i	$-0.830954\pi$
$43$		−	6.64216i		−	1.01292i	0.862264	−	0.506460i	$-0.169046\pi$
$44$	0.570696	−	2.12987i	0.0860357	−	0.321090i
$45$	3.73303	−	1.00026i	0.556488	−	0.149110i
$46$	0.273500	+	1.02072i	0.0403254	+	0.150496i
$47$	−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
$51$	1.38166	+	8.27309i	0.193470	+	1.15846i
$52$	0.858695	−	1.48730i	0.119080	−	0.206252i
$53$	−3.53287	−	2.03970i	−0.485277	−	0.280175i	0.237336	−	0.971428i	$-0.423726\pi$
$53$	−3.53287	−	2.03970i	−0.485277	−	0.280175i	−0.722613	+	0.691253i	$0.757059\pi$
$54$	5.75144	+	1.54109i	0.782672	+	0.209716i
$55$	−15.8560			−2.13802
$56$		0			0
$57$	−8.91500	−	8.91500i	−1.18082	−	1.18082i
$58$	2.27587	−	8.49368i	0.298837	−	1.11527i
$59$	−2.36632	−	1.36620i	−0.308069	−	0.177864i	0.337993	−	0.941149i	$-0.390252\pi$
$59$	−2.36632	−	1.36620i	−0.308069	−	0.177864i	−0.646062	+	0.763285i	$0.723585\pi$
$60$	2.82357	+	1.63019i	0.364522	+	0.210457i
$61$	−3.13118	+	11.6857i	−0.400907	+	1.49620i	0.410575	+	0.911827i	$0.365328\pi$
$61$	−3.13118	+	11.6857i	−0.400907	+	1.49620i	−0.811482	+	0.584378i	$0.801339\pi$
$62$	8.51463	+	8.51463i	1.08136	+	1.08136i
$63$		0			0
$64$	−5.32531			−0.665664
$65$	−11.9288	−	3.19631i	−1.47958	−	0.396454i
$66$	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	$0.888333\pi$
$68$	−1.13087	+	1.58432i	−0.137138	+	0.192127i
$69$	−1.36724			−0.164597
$70$		0			0
$71$	3.04461	−	3.04461i	0.361328	−	0.361328i	−0.502973	−	0.864302i	$-0.667761\pi$
$71$	3.04461	−	3.04461i	0.361328	−	0.361328i	0.864302	+	0.502973i	$0.167761\pi$
$72$	1.36741	+	2.36842i	0.161151	+	0.279121i
$73$	−0.427346	−	1.59488i	−0.0500170	−	0.186666i	0.936398	−	0.350941i	$-0.114138\pi$
$73$	−0.427346	−	1.59488i	−0.0500170	−	0.186666i	−0.986415	+	0.164275i	$0.947472\pi$
$74$	−2.07842	+	0.556911i	−0.241612	+	0.0647396i
$75$	3.43545	−	12.8213i	0.396692	−	1.48047i
$76$		−	2.92586i		−	0.335619i
$77$		0			0
$78$	8.22754	+	8.22754i	0.931586	+	0.931586i
$79$	2.58942	−	9.66384i	0.291332	−	1.08727i	−0.652754	−	0.757570i	$-0.726387\pi$
$79$	2.58942	−	9.66384i	0.291332	−	1.08727i	0.944087	−	0.329697i	$-0.106947\pi$
$80$	−4.14837	−	15.4819i	−0.463802	−	1.73093i
$81$	−5.55963	+	9.62956i	−0.617736	+	1.06995i
$82$	−1.05708	−	0.283243i	−0.116735	−	0.0312789i
$83$		−	4.69160i		−	0.514970i	−0.966282	−	0.257485i	$-0.917106\pi$
$83$		−	4.69160i		−	0.514970i	0.966282	−	0.257485i	$-0.0828938\pi$
$84$		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
$88$	−2.90402	−	10.8379i	−0.309569	−	1.15533i
$89$	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
$95$	−20.3227	+	5.44544i	−2.08506	+	0.558690i
$96$	−1.37878	+	5.14569i	−0.140722	+	0.525180i
$97$	−2.99116	+	2.99116i	−0.303706	+	0.303706i	−0.842462	−	0.538756i	$-0.818895\pi$
$97$	−2.99116	+	2.99116i	−0.303706	+	0.303706i	0.538756	+	0.842462i	$0.318895\pi$
$98$		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	$0.0803277\pi$
$102$	−8.38518	−	10.1788i	−0.830256	−	1.00785i
$103$	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
$107$	−10.9920	−	2.94531i	−1.06264	−	0.284734i	−0.315175	−	0.949034i	$-0.602063\pi$
$107$	−10.9920	−	2.94531i	−1.06264	−	0.284734i	−0.747466	+	0.664300i	$0.768730\pi$
$108$	−1.72694	+	0.462733i	−0.166175	+	0.0445265i
$109$	4.25566	−	1.14030i	0.407619	−	0.109221i	−0.0491827	−	0.998790i	$-0.515662\pi$
$109$	4.25566	−	1.14030i	0.407619	−	0.109221i	0.456801	+	0.889569i	$0.348995\pi$
$110$	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	0.206926	−	0.978357i	$-0.433654\pi$
$113$	−8.20042	−	8.20042i	−0.771430	−	0.771430i	−0.978357	+	0.206926i	$0.933654\pi$
$114$	19.1475	+	5.13057i	1.79333	+	0.480522i
$115$	−1.14082	+	1.97595i	−0.106382	+	0.184259i
$116$	0.683359	+	2.55033i	0.0634483	+	0.236792i
$117$	−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
$122$	−4.92313	−	18.3734i	−0.445719	−	1.66345i
$123$	0.707973	−	1.22625i	0.0638358	−	0.110567i
$124$	−3.49241	−	0.935789i	−0.313628	−	0.0840363i
$125$	−3.66041	−	3.66041i	−0.327397	−	0.327397i
$126$		0			0
$127$		−	5.12889i		−	0.455115i	−0.973765	−	0.227558i	$-0.926926\pi$
$127$		−	5.12889i		−	0.455115i	0.973765	−	0.227558i	$-0.0730740\pi$
$128$	11.7869	−	6.80515i	1.04182	−	0.601496i
$129$	−13.0518	+	3.49722i	−1.14915	+	0.307913i
$130$	18.7555	−	5.02553i	1.64497	−	0.440768i
$131$	−8.06881	−	2.16203i	−0.704975	−	0.188898i	−0.111517	−	0.993762i	$-0.535571\pi$
$131$	−8.06881	−	2.16203i	−0.704975	−	0.188898i	−0.593458	+	0.804865i	$0.702238\pi$
$132$	−4.48566			−0.390426
$133$		0			0
$134$		−	19.7465i		−	1.70583i
$135$	6.42818	+	11.1339i	0.553249	+	0.958256i
$136$	−0.952577	+	9.85904i	−0.0816828	+	0.845406i
$137$	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	−0.433185	−	0.901305i	$-0.642610\pi$
$139$	5.51905	−	5.51905i	0.468120	−	0.468120i	0.901305	+	0.433185i	$0.142610\pi$
$140$		0			0
$141$	−6.22272	+	6.22272i	−0.524048	+	0.524048i
$142$	−1.75217	+	6.53918i	−0.147039	+	0.548755i
$143$	16.4117	−	4.39751i	1.37242	−	0.367738i
$144$	−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	$0.842078\pi$
$150$	5.40153	+	20.1588i	0.441033	+	1.64596i
$151$	9.89318	+	5.71183i	0.805096	+	0.464822i	0.845250	−	0.534371i	$-0.179452\pi$
$151$	9.89318	+	5.71183i	0.805096	+	0.464822i	−0.0401543	+	0.999193i	$0.512785\pi$
$152$	−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
$156$	−3.37466	−	0.904237i	−0.270189	−	0.0723969i
$157$	−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	$0.783768\pi$
$158$	4.07132	+	15.1944i	0.323897	+	1.20880i
$159$	−2.14788	+	8.01600i	−0.170338	+	0.635710i
$160$	6.28617	+	6.28617i	0.496965	+	0.496965i
$161$		0			0
$162$		−	17.4827i		−	1.37357i
$163$	3.12576	−	11.6655i	0.244829	−	0.913714i	−0.728641	−	0.684896i	$-0.759848\pi$
$163$	3.12576	−	11.6655i	0.244829	−	0.913714i	0.973469	−	0.228817i	$-0.0734858\pi$
$164$	0.317400	−	0.0850472i	0.0247848	−	0.00664107i
$165$	8.34845	+	31.1569i	0.649926	+	2.42556i
$166$	3.68828	+	6.38829i	0.286266	+	0.495827i
$167$	−17.3482	+	17.3482i	−1.34244	+	1.34244i	−0.448823	+	0.893620i	$0.648157\pi$
$167$	−17.3482	+	17.3482i	−1.34244	+	1.34244i	−0.893620	+	0.448823i	$0.851843\pi$
$168$		0			0
$169$	0.233365			0.0179511
$170$	−21.7071	+	3.62521i	−1.66486	+	0.278041i
$171$	−3.52768	+	6.11013i	−0.269769	+	0.467253i
$172$	−2.71565	−	1.56788i	−0.207066	−	0.119550i
$173$	−3.44376	−	0.922753i	−0.261824	−	0.0701556i	0.125519	−	0.992091i	$-0.459940\pi$
$173$	−3.44376	−	0.922753i	−0.261824	−	0.0701556i	−0.387343	+	0.921936i	$0.626607\pi$
$174$	−17.8883			−1.35611
$175$		0			0
$176$	15.5928	+	15.5928i	1.17535	+	1.17535i
$177$	−1.43865	+	5.36913i	−0.108136	+	0.403568i
$178$	−2.78736	−	1.60929i	−0.208922	−	0.120621i
$179$	3.43046	+	1.98058i	0.256405	+	0.148035i	0.622693	−	0.782466i	$-0.286038\pi$
$179$	3.43046	+	1.98058i	0.256405	+	0.148035i	−0.366289	+	0.930501i	$0.619372\pi$
$180$	0.472224	−	1.76236i	0.0351975	−	0.131359i
$181$	−1.36267	−	1.36267i	−0.101287	−	0.101287i	0.654648	−	0.755934i	$-0.272817\pi$
$181$	−1.36267	−	1.36267i	−0.101287	−	0.101287i	−0.755934	+	0.654648i	$0.772817\pi$
$182$		0			0
$183$	24.6110			1.81930
$184$	−1.55955	−	0.417881i	−0.114972	−	0.0308066i
$185$	−4.02351	−	2.32298i	−0.295814	−	0.170789i
$186$	12.2481	−	21.2143i	0.898072	−	1.55551i
$187$	−18.9944	+	3.17218i	−1.38901	+	0.231973i
$188$	−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	$0.468866\pi$
$192$	2.80387	+	10.4642i	0.202352	+	0.755188i
$193$	−10.8635	+	2.91087i	−0.781972	+	0.209529i	−0.627654	−	0.778493i	$-0.715985\pi$
$193$	−10.8635	+	2.91087i	−0.781972	+	0.209529i	−0.154318	+	0.988021i	$0.549318\pi$
$194$	1.72141	−	6.42438i	0.123590	−	0.461243i
$195$			25.1229i			1.79909i
$196$		0			0
$197$	−16.0035	−	16.0035i	−1.14020	−	1.14020i	−0.988413	−	0.151789i	$-0.951497\pi$
$197$	−16.0035	−	16.0035i	−1.14020	−	1.14020i	−0.151789	−	0.988413i	$-0.548503\pi$
$198$	2.16374	−	8.07518i	0.153770	−	0.573878i
$199$	−1.35866	−	5.07058i	−0.0963127	−	0.359444i	0.900903	−	0.434022i	$-0.142906\pi$
$199$	−1.35866	−	5.07058i	−0.0963127	−	0.359444i	−0.997215	+	0.0745776i	$0.976239\pi$
$200$	7.83734	−	13.5747i	0.554184	−	0.959874i
$201$	24.6784	+	6.61256i	1.74068	+	0.466414i
$202$			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
$207$	0.198027	+	0.739048i	0.0137638	+	0.0513674i
$208$	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	0.429536	−	0.903050i	$-0.358677\pi$
$211$	−6.87817	−	6.87817i	−0.473513	−	0.473513i	−0.903050	+	0.429536i	$0.858677\pi$
$212$	−1.66787	+	0.962943i	−0.114550	+	0.0661352i
$213$	−7.58567	−	4.37959i	−0.519761	−	0.300084i
$214$	17.2827	−	4.63088i	1.18142	−	0.316561i
$215$	−5.83610	+	21.7806i	−0.398019	+	1.48543i
$216$	−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
$221$	−14.9294	−	1.44247i	−1.00426	−	0.0970311i
$222$	2.18865	+	3.79086i	0.146893	+	0.254426i
$223$			17.5438i			1.17482i	0.809289	+	0.587411i	$0.199853\pi$
$223$			17.5438i			1.17482i	−0.809289	+	0.587411i	$0.800147\pi$
$224$		0			0
$225$	−7.42798			−0.495199
$226$	17.6128	+	4.71933i	1.17158	+	0.313925i
$227$	8.05931	−	2.15948i	0.534915	−	0.143330i	0.0187580	−	0.999824i	$-0.494029\pi$
$227$	8.05931	−	2.15948i	0.534915	−	0.143330i	0.516157	+	0.856494i	$0.327362\pi$
$228$	−5.74928	+	1.54052i	−0.380756	+	0.102023i
$229$	−13.2886	+	7.67215i	−0.878132	+	0.506990i	−0.870042	−	0.492977i	$-0.835909\pi$
$229$	−13.2886	+	7.67215i	−0.878132	+	0.506990i	−0.00809010	+	0.999967i	$0.502575\pi$
$230$		−	3.58739i		−	0.236546i
$231$		0			0
$232$	9.50018	+	9.50018i	0.623717	+	0.623717i
$233$	−23.6434	−	6.33522i	−1.54893	−	0.415034i	−0.619790	−	0.784767i	$-0.712782\pi$
$233$	−23.6434	−	6.33522i	−1.54893	−	0.415034i	−0.929138	+	0.369733i	$0.879449\pi$
$234$	3.25566	−	5.63896i	0.212829	−	0.368630i
$235$	3.80095	+	14.1853i	0.247947	+	0.925350i
$236$	−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
$241$	−3.93803	−	14.6969i	−0.253671	−	0.946712i	−0.968825	−	0.247745i	$-0.920310\pi$
$241$	−3.93803	−	14.6969i	−0.253671	−	0.946712i	0.715155	−	0.698966i	$-0.246356\pi$
$242$	−8.50197	+	14.7258i	−0.546527	+	0.946613i
$243$	10.8752	+	2.91401i	0.697647	+	0.186934i
$244$	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
$248$	−17.7713	+	4.76181i	−1.12848	+	0.302375i
$249$	−9.21896	+	2.47021i	−0.584228	+	0.156543i
$250$	7.86180	+	2.10656i	0.497224	+	0.133231i
$251$	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
$255$	2.73846	−	28.3427i	0.171489	−	1.77489i
$256$	−5.37437	+	9.30869i	−0.335898	+	0.581793i
$257$	3.48942	−	2.01462i	0.217664	−	0.125668i	−0.387204	−	0.921994i	$-0.626559\pi$
$257$	3.48942	−	2.01462i	0.217664	−	0.125668i	0.604868	+	0.796326i	$0.293226\pi$
$258$	15.0226	−	15.0226i	0.935264	−	0.935264i
$259$		0			0
$260$	−4.12260	+	4.12260i	−0.255673	+	0.255673i
$261$	1.64784	−	6.14983i	0.101999	−	0.380665i
$262$	12.6865	−	3.39934i	0.783776	−	0.210012i
$263$	15.5660	+	8.98703i	0.959841	+	0.554164i	0.896124	−	0.443804i	$-0.146371\pi$
$263$	15.5660	+	8.98703i	0.959841	+	0.554164i	0.0637166	+	0.997968i	$0.479705\pi$
$264$	−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
$269$	4.66693	+	17.4172i	0.284548	+	1.06195i	0.949169	+	0.314767i	$0.101926\pi$
$269$	4.66693	+	17.4172i	0.284548	+	1.06195i	−0.664621	+	0.747181i	$0.731407\pi$
$270$	−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
$275$	29.4367	+	7.88755i	1.77510	+	0.475637i
$276$	−0.322737	+	0.558997i	−0.0194265	+	0.0336477i
$277$	−0.270103	−	1.00804i	−0.0162289	−	0.0605670i	0.957337	−	0.288975i	$-0.0933146\pi$
$277$	−0.270103	−	1.00804i	−0.0162289	−	0.0605670i	−0.973565	+	0.228408i	$0.926648\pi$
$278$	−3.17620	+	11.8538i	−0.190496	+	0.710941i
$279$	6.16500	+	6.16500i	0.369089	+	0.369089i
$280$		0			0
$281$			3.53036i			0.210604i	0.994440	+	0.105302i	$0.0335809\pi$
$281$			3.53036i			0.210604i	−0.994440	+	0.105302i	$0.966419\pi$
$282$	3.58117	−	13.3651i	0.213255	−	0.795880i
$283$	1.76134	−	0.471949i	0.104701	−	0.0280545i	−0.206088	−	0.978533i	$-0.566073\pi$
$283$	1.76134	−	0.471949i	0.104701	−	0.0280545i	0.310789	+	0.950479i	$0.399407\pi$
$284$	−0.526110	−	1.96347i	−0.0312189	−	0.116510i
$285$	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
$289$	16.6855	+	3.25468i	0.981502	+	0.191452i
$290$	−14.9259	+	25.8524i	−0.876477	+	1.51810i
$291$	7.45250	+	4.30270i	0.436873	+	0.252229i
$292$	−0.752940	−	0.201750i	−0.0440625	−	0.0118065i
$293$	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
$296$	0.850905	−	3.17562i	0.0494579	−	0.184579i
$297$	−15.3181	−	8.84393i	−0.888848	−	0.513177i
$298$	0.913091	+	0.527174i	0.0528940	+	0.0305383i
$299$	0.632790	−	2.36161i	0.0365952	−	0.136575i
$300$	−4.43105	−	4.43105i	−0.255827	−	0.255827i
$301$		0			0
$302$	−17.9613			−1.03356
$303$	−10.5820	−	2.83545i	−0.607923	−	0.162892i
$304$	25.3404	+	14.6303i	1.45337	+	0.839104i
$305$	20.5352	−	35.5681i	1.17584	−	2.03662i
$306$	−4.28757	+	6.00679i	−0.245104	+	0.343385i
$307$	−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
$311$	−1.62913	−	6.08000i	−0.0923796	−	0.344765i	0.904230	−	0.427047i	$-0.140446\pi$
$311$	−1.62913	−	6.08000i	−0.0923796	−	0.344765i	−0.996609	+	0.0822815i	$0.973779\pi$
$312$	−17.1721	+	4.60126i	−0.972180	+	0.260495i
$313$	8.11965	−	30.3029i	0.458950	−	1.71282i	−0.217259	−	0.976114i	$-0.569712\pi$
$313$	8.11965	−	30.3029i	0.458950	−	1.71282i	0.676209	−	0.736710i	$-0.263622\pi$
$314$		−	36.7652i		−	2.07478i
$315$		0			0
$316$	−3.33983	−	3.33983i	−0.187880	−	0.187880i
$317$	4.28746	−	16.0010i	0.240808	−	0.898708i	−0.734636	−	0.678461i	$-0.762647\pi$
$317$	4.28746	−	16.0010i	0.240808	−	0.898708i	0.975444	−	0.220247i	$-0.0706862\pi$
$318$	−3.37709	−	12.6035i	−0.189378	−	0.706768i
$319$	−13.0606	+	22.6217i	−0.731255	+	1.26657i
$320$	17.4625	+	4.67906i	0.976183	+	0.261567i
$321$			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
$326$	4.91461	+	18.3416i	0.272195	+	1.01585i
$327$	−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	−0.608399	−	0.793632i	$-0.708188\pi$
$331$	−4.09885	+	2.36647i	−0.225293	+	0.130073i	0.383106	+	0.923704i	$0.374854\pi$
$332$	−1.91816	−	1.10745i	−0.105273	−	0.0607793i
$333$	−1.50488	+	0.403231i	−0.0824667	+	0.0220969i
$334$	9.98386	−	37.2603i	0.546293	−	2.03879i
$335$	30.1480	−	30.1480i	1.64716	−	1.64716i
$336$		0			0
$337$	17.0523	−	17.0523i	0.928898	−	0.928898i	−0.0687369	−	0.997635i	$-0.521897\pi$
$337$	17.0523	−	17.0523i	0.928898	−	0.928898i	0.997635	+	0.0687369i	$0.0218969\pi$
$338$	−0.317760	+	0.183459i	−0.0172838	+	0.00997883i
$339$	−11.7961	+	20.4314i	−0.640675	+	1.10968i
$340$	5.10034	−	4.20159i	0.276605	−	0.227863i
$341$	−17.8852	−	30.9780i	−0.968536	−	1.67755i
$342$		−	11.0931i		−	0.599846i
$343$		0			0
$344$	−15.9565			−0.860316
$345$	4.48339	+	1.20132i	0.241378	+	0.0646770i
$346$	5.41459	−	1.45084i	0.291090	−	0.0779974i
$347$	22.1256	−	5.92855i	1.18777	−	0.318261i	0.389764	−	0.920915i	$-0.372557\pi$
$347$	22.1256	−	5.92855i	1.18777	−	0.318261i	0.798003	+	0.602654i	$0.205890\pi$
$348$	4.65158	−	2.68559i	0.249351	−	0.143963i
$349$			10.1897i			0.545442i	0.962093	+	0.272721i	$0.0879235\pi$
$349$			10.1897i			0.545442i	−0.962093	+	0.272721i	$0.912076\pi$
$350$		0			0
$351$	−9.74137	−	9.74137i	−0.519956	−	0.519956i
$352$	−11.8141	−	3.16559i	−0.629696	−	0.168726i
$353$	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	$0.0191293\pi$
$354$	−2.26198	−	8.44183i	−0.120223	−	0.448678i
$355$	−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	−0.978805	−	0.204794i	$-0.934348\pi$
$359$	−24.4581	+	14.1209i	−1.29085	+	0.745273i	−0.312046	+	0.950067i	$0.601014\pi$
$360$	−2.40294	−	8.96788i	−0.126646	−	0.472649i
$361$	9.70474	−	16.8091i	0.510776	−	0.884689i
$362$	2.92673	+	0.784216i	0.153826	+	0.0412175i
$363$	−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
$367$	18.1715	−	4.86903i	0.948543	−	0.254161i	0.248799	−	0.968555i	$-0.419964\pi$
$367$	18.1715	−	4.86903i	0.948543	−	0.254161i	0.699744	+	0.714394i	$0.253297\pi$
$368$	3.06504	−	0.821274i	0.159776	−	0.0428119i
$369$	−0.765374	−	0.205081i	−0.0398438	−	0.0106761i
$370$	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	$-0.462719\pi$
$374$	23.3698	−	19.2518i	1.20843	−	0.995485i
$375$	−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	−0.896090	−	0.443872i	$-0.853604\pi$
$379$	−8.80375	+	8.80375i	−0.452218	+	0.452218i	0.443872	+	0.896090i	$0.353604\pi$
$380$	−2.57079	+	9.59433i	−0.131879	+	0.492179i
$381$	−10.0782	+	2.70045i	−0.516323	+	0.138348i
$382$	−34.2762	−	19.7894i	−1.75372	−	1.01251i
$383$	25.8472	−	14.9229i	1.32073	−	0.762523i	0.336884	−	0.941546i	$-0.390627\pi$
$383$	25.8472	−	14.9229i	1.32073	−	0.762523i	0.983845	+	0.179023i	$0.0572937\pi$
$384$	−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
$388$	0.516874	+	1.92900i	0.0262403	+	0.0979300i
$389$	−18.1350	−	10.4702i	−0.919479	−	0.530861i	−0.0360099	−	0.999351i	$-0.511465\pi$
$389$	−18.1350	−	10.4702i	−0.919479	−	0.530861i	−0.883469	+	0.468490i	$0.844798\pi$
$390$	−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
$394$	34.3721	+	9.20999i	1.73164	+	0.463992i
$395$	−16.9822	+	29.4140i	−0.854467	+	1.47998i
$396$	0.649689	+	2.42467i	0.0326481	+	0.121844i
$397$	−7.34029	+	27.3943i	−0.368399	+	1.37488i	0.494356	+	0.869260i	$0.335404\pi$
$397$	−7.34029	+	27.3943i	−0.368399	+	1.37488i	−0.862755	+	0.505623i	$0.831263\pi$
$398$	5.83622	+	5.83622i	0.292543	+	0.292543i
$399$		0			0
$400$			30.8059i			1.54030i
$401$	0.846034	−	3.15744i	0.0422489	−	0.157675i	−0.941579	−	0.336793i	$-0.890658\pi$
$401$	0.846034	−	3.15744i	0.0422489	−	0.157675i	0.983828	+	0.179118i	$0.0573244\pi$
$402$	−38.8016	+	10.3969i	−1.93525	+	0.518548i
$403$	−7.21073	−	26.9108i	−0.359192	−	1.34052i
$404$	−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
$408$	19.8745	−	3.31916i	0.983934	−	0.164323i
$409$	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
$411$	−39.6808	−	10.6324i	−1.95731	−	0.524459i
$412$	1.87072			0.0921638
$413$		0			0
$414$	−0.850642	−	0.850642i	−0.0418068	−	0.0418068i
$415$	−4.12226	+	15.3845i	−0.202354	+	0.755194i
$416$	−8.24990	−	4.76308i	−0.404485	−	0.233529i
$417$	−13.7508	−	7.93901i	−0.673378	−	0.388775i
$418$	−11.7794	+	43.9614i	−0.576150	+	2.15022i
$419$	−12.3869	−	12.3869i	−0.605140	−	0.605140i	0.336532	−	0.941672i	$-0.390746\pi$
$419$	−12.3869	−	12.3869i	−0.605140	−	0.605140i	−0.941672	+	0.336532i	$0.890746\pi$
$420$		0			0
$421$	−13.1028			−0.638593			−0.319296	−	0.947655i	$-0.603447\pi$
$421$	−13.1028			−0.638593			−0.319296	+	0.947655i	$0.603447\pi$
$422$	14.7729	+	3.95838i	0.719132	+	0.192691i
$423$	4.26491	+	2.46234i	0.207367	+	0.119723i
$424$	−4.89998	+	8.48702i	−0.237964	+	0.412166i
$425$	−21.8967	−	15.6296i	−1.06215	−	0.758148i
$426$	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
$430$	−9.17606	−	34.2455i	−0.442509	−	1.65147i
$431$	−25.3873	+	6.80250i	−1.22286	+	0.327665i	−0.811796	−	0.583941i	$-0.801510\pi$
$431$	−25.3873	+	6.80250i	−1.22286	+	0.327665i	−0.411066	+	0.911606i	$0.634843\pi$
$432$	4.62764	−	17.2706i	0.222648	−	0.830932i
$433$		−	0.783681i		−	0.0376613i	−0.999823	−	0.0188307i	$-0.994006\pi$
$433$		−	0.783681i		−	0.0376613i	0.999823	−	0.0188307i	$-0.00599434\pi$
$434$		0			0
$435$	−27.3111	−	27.3111i	−1.30947	−	1.30947i
$436$	0.538336	−	2.00910i	0.0257816	−	0.0962184i
$437$	−1.07806	−	4.02338i	−0.0515707	−	0.192465i
$438$	2.64060	−	4.57366i	0.126173	−	0.218538i
$439$	−24.2969	−	6.51034i	−1.15963	−	0.310722i	−0.372812	−	0.927907i	$-0.621606\pi$
$439$	−24.2969	−	6.51034i	−1.15963	−	0.310722i	−0.786818	+	0.617185i	$0.788273\pi$
$440$			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
$445$	−1.79864	−	6.71261i	−0.0852637	−	0.318208i
$446$	−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	0.962077	+	0.272777i	$0.0879421\pi$
$449$	26.1661	+	26.1661i	1.23485	+	1.23485i	0.272777	+	0.962077i	$0.412058\pi$
$450$	10.1143	−	5.83948i	0.476791	−	0.275276i
$451$	2.81537	+	1.62545i	0.132571	+	0.0765397i
$452$	−5.28845	+	1.41704i	−0.248748	+	0.0666518i
$453$	6.01476	−	22.4474i	0.282598	−	1.05467i
$454$	−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	−0.736136	−	0.676833i	$-0.763352\pi$
$457$	−11.0746	+	6.39394i	−0.518050	+	0.299096i	0.218087	+	0.975929i	$0.430018\pi$
$458$	12.0629	−	20.8935i	0.563660	−	0.976288i
$459$	9.92801	+	12.0517i	0.463400	+	0.562524i
$460$	0.538580	+	0.932847i	0.0251114	+	0.0434942i
$461$			4.58089i			0.213353i	0.994294	+	0.106677i	$0.0340210\pi$
$461$			4.58089i			0.213353i	−0.994294	+	0.106677i	$0.965979\pi$
$462$		0			0
$463$	−1.53844			−0.0714973			−0.0357486	−	0.999361i	$-0.511382\pi$
$463$	−1.53844			−0.0714973			−0.0357486	+	0.999361i	$0.511382\pi$
$464$	−25.5051	−	6.83406i	−1.18404	−	0.317263i
$465$	51.0889	−	13.6892i	2.36919	−	0.634822i
$466$	37.1743	−	9.96081i	1.72206	−	0.461426i
$467$	9.52860	−	5.50134i	0.440931	−	0.254572i	−0.263061	−	0.964779i	$-0.584732\pi$
$467$	9.52860	−	5.50134i	0.440931	−	0.254572i	0.703992	+	0.710207i	$0.251399\pi$
$468$			1.95510i			0.0903746i
$469$		0			0
$470$	−16.3273	−	16.3273i	−0.753122	−	0.753122i
$471$	45.9478	+	12.3117i	2.11716	+	0.567291i
$472$	−3.28202	+	5.68462i	−0.151067	+	0.261656i
$473$	−8.02935	−	29.9660i	−0.369190	−	1.37784i
$474$	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
$479$	6.02062	+	22.4693i	0.275089	+	1.02665i	0.955781	+	0.294078i	$0.0950125\pi$
$479$	6.02062	+	22.4693i	0.275089	+	1.02665i	−0.680692	+	0.732570i	$0.738321\pi$
$480$	9.04248	−	15.6620i	0.412731	−	0.714871i
$481$	4.80879	+	1.28851i	0.219262	+	0.0587511i
$482$	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
$486$	−17.0991	+	4.58168i	−0.775629	+	0.207829i
$487$	−21.2851	+	5.70334i	−0.964522	+	0.258443i	−0.706513	−	0.707700i	$-0.749733\pi$
$487$	−21.2851	+	5.70334i	−0.964522	+	0.258443i	−0.258009	+	0.966143i	$0.583066\pi$
$488$	28.0727	+	7.52205i	1.27079	+	0.340507i
$489$	−24.5684			−1.11102
$490$		0			0
$491$			19.2671i			0.869512i	0.900548	+	0.434756i	$0.143165\pi$
$491$			19.2671i			0.869512i	−0.900548	+	0.434756i	$0.856835\pi$
$492$	−0.334234	−	0.578910i	−0.0150684	−	0.0260993i
$493$	17.7978	−	14.6616i	0.801573	−	0.660325i
$494$	−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
$499$	10.9640	−	40.9180i	0.490814	−	1.83174i	−0.0614998	−	0.998107i	$-0.519588\pi$
$499$	10.9640	−	40.9180i	0.490814	−	1.83174i	0.552314	−	0.833636i	$-0.313745\pi$
$500$	−2.36060	+	0.632522i	−0.105569	+	0.0282872i
$501$	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	0.508809	−	0.860880i	$-0.330086\pi$
$503$	−7.89613	−	7.89613i	−0.352071	−	0.352071i	−0.860880	+	0.508809i	$0.830086\pi$
$504$		0			0
$505$	−12.9274	+	12.9274i	−0.575262	+	0.575262i
$506$	2.46778	+	4.27432i	0.109706	+	0.190017i
$507$	−0.122871	−	0.458560i	−0.00545688	−	0.0203653i
$508$	−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
$513$	−22.6706	−	6.07457i	−1.00093	−	0.268199i
$514$	−3.16756	+	5.48638i	−0.139715	+	0.241994i
$515$	−3.48168	−	12.9938i	−0.153421	−	0.572576i
$516$	−1.65103	+	6.16175i	−0.0726827	+	0.271256i
$517$	−14.2869	−	14.2869i	−0.628338	−	0.628338i
$518$		0			0
$519$			7.25281i			0.318363i
$520$	−7.67851	+	28.6566i	−0.336725	+	1.25667i
$521$	−14.3162	+	3.83601i	−0.627203	+	0.168059i	−0.558400	−	0.829572i	$-0.688585\pi$
$521$	−14.3162	+	3.83601i	−0.627203	+	0.168059i	−0.0688031	+	0.997630i	$0.521918\pi$
$522$	2.59089	+	9.66932i	0.113400	+	0.423215i
$523$	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
$527$	5.20152	+	31.1457i	0.226582	+	1.35673i
$528$	22.4298	−	38.8496i	0.976132	−	1.69071i
$529$	19.5274	+	11.2741i	0.849017	+	0.490180i
$530$	−21.0325	−	5.63565i	−0.913594	−	0.244797i
$531$	3.11059			0.134988
$532$		0			0
$533$	1.79040	+	1.79040i	0.0775508	+	0.0775508i
$534$	−1.69464	+	6.32447i	−0.0733341	+	0.273686i
$535$	33.4567	+	19.3162i	1.44646	+	0.835113i
$536$	26.1285	+	15.0853i	1.12858	+	0.651586i
$537$	2.08562	−	7.78364i	0.0900011	−	0.335889i
$538$	−20.0472	−	20.0472i	−0.864296	−	0.864296i
$539$		0			0
$540$	6.06948			0.261189
$541$	−10.7745	−	2.88703i	−0.463233	−	0.124123i	0.0196516	−	0.999807i	$-0.493744\pi$
$541$	−10.7745	−	2.88703i	−0.463233	−	0.124123i	−0.482885	+	0.875684i	$0.660411\pi$
$542$	22.7504	+	13.1349i	0.977211	+	0.564193i
$543$	−1.96017	+	3.39511i	−0.0841189	+	0.145698i
$544$	8.78804	+	6.27279i	0.376784	+	0.268944i
$545$	−14.9569			−0.640683
$546$		0			0
$547$	5.17129	−	5.17129i	0.221108	−	0.221108i	−0.587857	−	0.808965i	$-0.700028\pi$
$547$	5.17129	−	5.17129i	0.221108	−	0.221108i	0.808965	+	0.587857i	$0.200028\pi$
$548$	−4.76676	−	8.25627i	−0.203626	−	0.352690i
$549$	−3.56458	−	13.3032i	−0.152133	−	0.567767i
$550$	−46.2831	+	12.4015i	−1.97352	+	0.528803i
$551$	−8.97086	+	33.4797i	−0.382172	+	1.42628i
$552$			3.28453i			0.139799i
$553$		0			0
$554$	1.16025	+	1.16025i	0.0492942	+	0.0492942i
$555$	−2.44618	+	9.12925i	−0.103834	+	0.387515i
$556$	−0.953695	−	3.55924i	−0.0404457	−	0.150945i
$557$	−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	$0.272129\pi$
$558$	−13.2411	−	3.54795i	−0.560542	−	0.150197i
$559$		−	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	0.374182	−	0.927355i	$-0.377923\pi$
$563$	−5.73828	−	3.31299i	−0.241839	−	0.139626i	−0.616022	+	0.787729i	$0.711257\pi$
$564$	1.07529	+	4.01304i	0.0452779	+	0.168979i
$565$	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	0.355016	−	0.934860i	$-0.384475\pi$
$569$	32.0150	−	18.4838i	1.34214	−	0.774883i	0.987121	+	0.159977i	$0.0511420\pi$
$570$	−58.2797	−	33.6478i	−2.44107	−	1.40935i
$571$	35.3394	−	9.46916i	1.47891	−	0.396272i	0.572932	−	0.819603i	$-0.305806\pi$
$571$	35.3394	−	9.46916i	1.47891	−	0.396272i	0.905975	+	0.423331i	$0.139139\pi$
$572$	2.07606	−	7.74797i	0.0868045	−	0.323959i
$573$	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	$0.211265\pi$
$578$	−25.2784	+	8.68554i	−1.05144	+	0.361271i
$579$	11.4397	+	19.8141i	0.475416	+	0.823444i
$580$		−	8.96335i		−	0.372183i
$581$		0			0
$582$	−13.5302			−0.560845
$583$	−18.4041	−	4.93138i	−0.762222	−	0.204237i
$584$	−3.83138	+	1.02661i	−0.158543	+	0.0424816i
$585$	13.5799	−	3.63873i	0.561460	−	0.150443i
$586$	−20.3681	+	11.7595i	−0.841399	+	0.485782i
$587$			0.653601i			0.0269770i	0.999909	+	0.0134885i	$0.00429365\pi$
$587$			0.653601i			0.0269770i	−0.999909	+	0.0134885i	$0.995706\pi$
$588$		0			0
$589$	−33.5623	−	33.5623i	−1.38291	−	1.38291i
$590$	−14.0876	−	3.77477i	−0.579978	−	0.155405i
$591$	−23.0206	+	39.8729i	−0.946941	+	1.64015i
$592$	1.67231	+	6.24114i	0.0687315	+	0.256509i
$593$	−23.9967	+	13.8545i	−0.985428	+	0.568937i	−0.903904	−	0.427735i	$-0.859312\pi$
$593$	−23.9967	+	13.8545i	−0.985428	+	0.568937i	−0.0815231	+	0.996671i	$0.525978\pi$
$594$	27.8105			1.14108
$595$		0			0
$596$	−0.316581			−0.0129677
$597$	−9.24829	+	5.33950i	−0.378507	+	0.218531i
$598$	0.994931	+	3.71313i	0.0406857	+	0.151841i
$599$	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	$0.117404\pi$
$600$	−30.8006	−	8.25300i	−1.25743	−	0.336927i
$601$	12.8735	+	12.8735i	0.525119	+	0.525119i	0.919113	−	0.393994i	$-0.128907\pi$
$601$	12.8735	+	12.8735i	0.525119	+	0.525119i	−0.393994	+	0.919113i	$0.628907\pi$
$602$		0			0
$603$		−	14.2974i		−	0.582234i
$604$	4.67057	−	2.69655i	0.190043	−	0.109721i
$605$	−35.4632	+	9.50234i	−1.44178	+	0.386325i
$606$	16.6381	−	4.45815i	0.675875	−	0.181100i
$607$	11.8126	+	3.16518i	0.479458	+	0.128470i	0.490450	−	0.871469i	$-0.336832\pi$
$607$	11.8126	+	3.16518i	0.479458	+	0.128470i	−0.0109920	+	0.999940i	$0.503499\pi$
$608$	−16.2294			−0.658189
$609$		0			0
$610$			64.5748i			2.61456i
$611$	−7.86835	−	13.6284i	−0.318319	−	0.551345i
$612$	0.213111	−	2.20567i	0.00861451	−	0.0891590i
$613$	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	−0.465689	−	0.884948i	$-0.654193\pi$
$617$	10.4142	−	10.4142i	0.419260	−	0.419260i	0.884948	+	0.465689i	$0.154193\pi$
$618$	−3.28036	+	12.2425i	−0.131955	+	0.492464i
$619$	−35.7331	+	9.57465i	−1.43623	+	0.384838i	−0.891213	−	0.453585i	$-0.850145\pi$
$619$	−35.7331	+	9.57465i	−1.43623	+	0.384838i	−0.545021	+	0.838423i	$0.683478\pi$
$620$	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
$626$	12.7665	+	47.6451i	0.510250	+	1.90428i
$627$	−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	$-0.782004\pi$
$631$		−	31.7794i		−	1.26512i	0.774512	−	0.632559i	$-0.217996\pi$
$632$	−23.2155	−	6.22057i	−0.923462	−	0.247441i
$633$	−9.89407	+	17.1370i	−0.393254	+	0.681136i
$634$	6.74114	+	25.1583i	0.267725	+	0.999163i
$635$	−4.50648	+	16.8184i	−0.178834	+	0.667418i
$636$	2.77034	+	2.77034i	0.109851	+	0.109851i
$637$		0			0
$638$		−	41.0702i		−	1.62599i
$639$	−1.26865	+	4.73468i	−0.0501871	+	0.187301i
$640$	−44.6302	+	11.9586i	−1.76417	+	0.472707i
$641$	−4.90532	−	18.3069i	−0.193749	−	0.723080i	−0.992587	−	0.121534i	$-0.961219\pi$
$641$	−4.90532	−	18.3069i	−0.193749	−	0.723080i	0.798839	−	0.601545i	$-0.205448\pi$
$642$	−18.1993	−	31.5221i	−0.718269	−	1.24408i
$643$	−19.0600	+	19.0600i	−0.751652	+	0.751652i	−0.974787	−	0.223135i	$-0.928371\pi$
$643$	−19.0600	+	19.0600i	−0.751652	+	0.751652i	0.223135	+	0.974787i	$0.428371\pi$
$644$		0			0
$645$	45.8716			1.80619
$646$	23.3416	−	32.7010i	0.918362	−	1.28660i
$647$	−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
$649$	−12.3271	−	3.30304i	−0.483882	−	0.129656i
$650$	−37.3198			−1.46380
$651$		0			0
$652$	−4.03161	−	4.03161i	−0.157890	−	0.157890i
$653$	6.86267	−	25.6118i	0.268557	−	1.00227i	−0.691480	−	0.722396i	$-0.743041\pi$
$653$	6.86267	−	25.6118i	0.268557	−	1.00227i	0.960037	−	0.279873i	$-0.0902924\pi$
$654$	12.2041	+	7.04602i	0.477216	+	0.275521i
$655$	24.5592	+	14.1793i	0.959607	+	0.554029i
$656$	−0.850530	+	3.17422i	−0.0332076	+	0.123932i
$657$	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	$0.598918\pi$
$660$	14.7091	+	3.94130i	0.572553	+	0.153415i
$661$	−13.4338	−	7.75601i	−0.522515	−	0.301674i	0.215448	−	0.976515i	$-0.430879\pi$
$661$	−13.4338	−	7.75601i	−0.522515	−	0.301674i	−0.737963	+	0.674841i	$0.764212\pi$
$662$	3.72078	−	6.44458i	0.144612	−	0.250476i
$663$	5.02614	+	30.0956i	0.195199	+	1.16882i
$664$	−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
$668$	2.99778	+	11.1879i	0.115988	+	0.432871i
$669$	34.4735	−	9.23715i	1.33282	−	0.357129i
$670$	−17.3501	+	64.7516i	−0.670295	+	2.50157i
$671$			56.5050i			2.18135i
$672$		0			0
$673$	25.7151	+	25.7151i	0.991243	+	0.991243i	0.999962	−	0.00871919i	$-0.00277544\pi$
$673$	25.7151	+	25.7151i	0.991243	+	0.991243i	−0.00871919	+	0.999962i	$0.502775\pi$
$674$	−9.81357	+	36.6248i	−0.378005	+	1.41073i
$675$	−6.39539	−	23.8679i	−0.246159	−	0.918676i
$676$	0.0550857	−	0.0954112i	0.00211868	−	0.00366966i
$677$	27.6865	+	7.41857i	1.06408	+	0.285119i	0.748058	−	0.663634i	$-0.230987\pi$
$677$	27.6865	+	7.41857i	1.06408	+	0.285119i	0.316020	+	0.948752i	$0.397653\pi$
$678$		−	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
$683$	5.11944	+	19.1060i	0.195890	+	0.731071i	0.992035	+	0.125965i	$0.0402026\pi$
$683$	5.11944	+	19.1060i	0.195890	+	0.731071i	−0.796145	+	0.605106i	$0.793131\pi$
$684$	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
$690$	−7.04920	+	1.88883i	−0.268358	+	0.0719064i
$691$	9.75631	−	36.4110i	0.371147	−	1.38514i	−0.487745	−	0.872986i	$-0.662181\pi$
$691$	9.75631	−	36.4110i	0.371147	−	1.38514i	0.858893	−	0.512155i	$-0.171153\pi$
$692$	−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
$697$	−1.82470	−	2.21502i	−0.0691155	−	0.0838998i
$698$	−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	$0.424384\pi$
$702$	20.9224	+	5.60615i	0.789666	+	0.211590i
$703$	8.19256	−	2.19519i	0.308988	−	0.0827932i
$704$	−24.0250	+	6.43748i	−0.905477	+	0.242622i
$705$	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
$709$	13.9469	+	3.73707i	0.523788	+	0.140349i	0.511018	−	0.859570i	$-0.329268\pi$
$709$	13.9469	+	3.73707i	0.523788	+	0.140349i	0.0127698	+	0.999918i	$0.495935\pi$
$710$	11.4912	−	19.9034i	0.431259	−	0.746962i
$711$	2.94783	+	11.0015i	0.110552	+	0.412587i
$712$	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
$717$	−7.67512	−	28.6439i	−0.286633	−	1.06973i
$718$	22.2022	−	38.4553i	0.828578	−	1.43514i
$719$	8.93538	+	2.39423i	0.333233	+	0.0892896i	0.421556	−	0.906802i	$-0.361484\pi$
$719$	8.93538	+	2.39423i	0.333233	+	0.0892896i	−0.0883228	+	0.996092i	$0.528151\pi$
$720$	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
$724$	−0.878788	+	0.235470i	−0.0326599	+	0.00875119i
$725$	−35.2479	+	9.44465i	−1.30907	+	0.350765i
$726$	33.4126	+	8.95288i	1.24006	+	0.332273i
$727$	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
$731$	−2.63379	+	27.2594i	−0.0974143	+	1.00822i
$732$	5.80942	−	10.0622i	0.214722	−	0.371910i
$733$	−1.57407	+	0.908789i	−0.0581396	+	0.0335669i	−0.528788	−	0.848754i	$-0.677353\pi$
$733$	−1.57407	+	0.908789i	−0.0581396	+	0.0335669i	0.470648	+	0.882321i	$0.344020\pi$
$734$	−20.9153	+	20.9153i	−0.771998	+	0.771998i
$735$		0			0
$736$	−1.24450	+	1.24450i	−0.0458730	+	0.0458730i
$737$	−15.1819	+	56.6598i	−0.559234	+	2.08709i
$738$	1.20339	−	0.322448i	0.0442974	−	0.0118695i
$739$	−26.1195	−	15.0801i	−0.960820	−	0.554730i	−0.0643946	−	0.997925i	$-0.520512\pi$
$739$	−26.1195	−	15.0801i	−0.960820	−	0.554730i	−0.896425	+	0.443195i	$0.853845\pi$
$740$	−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	0.0292082	−	0.999573i	$-0.490701\pi$
$743$	28.0426	−	28.0426i	1.02878	−	1.02878i	0.999573	−	0.0292082i	$-0.00929860\pi$
$744$	18.7138	+	32.4133i	0.686082	+	1.18833i
$745$	0.589202	+	2.19893i	0.0215867	+	0.0805627i
$746$	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
$751$	40.4055	+	10.8266i	1.47442	+	0.395069i	0.904443	−	0.426594i	$-0.140287\pi$
$751$	40.4055	+	10.8266i	1.47442	+	0.395069i	0.569974	+	0.821663i	$0.306953\pi$
$752$	10.2120	−	17.6878i	0.372394	−	0.645006i
$753$	−0.811010	−	3.02673i	−0.0295549	−	0.110300i
$754$	8.27910	−	30.8980i	0.301507	−	1.12524i
$755$	−27.4226	−	27.4226i	−0.998009	−	0.998009i
$756$		0			0
$757$		−	29.9024i		−	1.08682i	−0.839467	−	0.543411i	$-0.817133\pi$
$757$		−	29.9024i		−	1.08682i	0.839467	−	0.543411i	$-0.182867\pi$
$758$	5.06654	−	18.9086i	0.184025	−	0.686791i
$759$	−6.16828	+	1.65279i	−0.223894	+	0.0599923i
$760$	13.0816	+	48.8212i	0.474520	+	1.77093i
$761$	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
$765$	−15.7170	+	2.62483i	−0.568248	+	0.0949008i
$766$	−23.4631	+	40.6393i	−0.847756	+	1.46836i
$767$	−8.60813	−	4.96991i	−0.310822	−	0.179453i
$768$	21.1212	+	5.65941i	0.762146	+	0.204216i
$769$	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
$772$	−1.37422	+	5.12866i	−0.0494592	+	0.184584i
$773$	11.4284	+	6.59820i	0.411052	+	0.237321i	0.691241	−	0.722624i	$-0.257064\pi$
$773$	11.4284	+	6.59820i	0.411052	+	0.237321i	−0.280190	+	0.959945i	$0.590397\pi$
$774$	−10.2961	−	5.94446i	−0.370086	−	0.213669i
$775$	12.9335	−	48.2683i	0.464584	−	1.73385i
$776$	7.18567	+	7.18567i	0.257950	+	0.257950i
$777$		0			0
$778$	32.9245			1.18040
$779$	4.16670	+	1.11647i	0.149288	+	0.0400015i
$780$	10.2715	+	5.93026i	0.367779	+	0.212337i
$781$	10.0552	−	17.4161i	0.359804	−	0.623199i
$782$	−0.717702	−	4.29746i	−0.0256650	−	0.153677i
$783$	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
$787$	7.42724	+	27.7189i	0.264753	+	0.988070i	0.962402	+	0.271631i	$0.0875629\pi$
$787$	7.42724	+	27.7189i	0.264753	+	0.988070i	−0.697649	+	0.716440i	$0.745770\pi$
$788$	−10.3207	+	2.76541i	−0.367658	+	0.0985137i
$789$	9.46367	−	35.3189i	0.336916	−	1.25739i
$790$		−	53.4019i		−	1.89995i
$791$		0			0
$792$	9.03209	+	9.03209i	0.320941	+	0.320941i
$793$	−11.3905	+	42.5100i	−0.404489	+	1.50957i
$794$	−11.5411	−	43.0719i	−0.409577	−	1.52856i
$795$	14.0864	−	24.3984i	0.499595	−	0.865323i
$796$	−2.39382	−	0.641422i	−0.0848467	−	0.0227346i
$797$		−	10.8120i		−	0.382980i	−0.981495	−	0.191490i	$-0.938668\pi$
$797$		−	10.8120i		−	0.382980i	0.981495	−	0.191490i	$-0.0613320\pi$
$798$		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
$802$	1.33021	+	4.96442i	0.0469714	+	0.175300i
$803$	−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
$809$	−49.2510	+	13.1968i	−1.73157	+	0.463974i	−0.980545	−	0.196295i	$-0.937109\pi$
$809$	−49.2510	+	13.1968i	−1.73157	+	0.463974i	−0.751029	+	0.660269i	$0.770442\pi$
$810$	−15.3611	+	57.3284i	−0.539734	+	2.01432i
$811$	10.8591	−	10.8591i	0.381315	−	0.381315i	−0.490261	−	0.871576i	$-0.663098\pi$
$811$	10.8591	−	10.8591i	0.381315	−	0.381315i	0.871576	+	0.490261i	$0.163098\pi$
$812$		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
$816$	−30.5653	+	25.1793i	−1.07000	+	0.881450i
$817$	−20.5825	−	35.6500i	−0.720091	−	1.24723i
$818$			54.0654i			1.89035i
$819$		0			0
$820$	−1.11553			−0.0389560
$821$	−13.4603	−	3.60669i	−0.469769	−	0.125874i	0.0161658	−	0.999869i	$-0.494854\pi$
$821$	−13.4603	−	3.60669i	−0.469769	−	0.125874i	−0.485935	+	0.873995i	$0.661521\pi$
$822$	62.3897	−	16.7173i	2.17609	−	0.583082i
$823$	−11.8562	+	3.17686i	−0.413281	+	0.110738i	−0.459468	−	0.888194i	$-0.651960\pi$
$823$	−11.8562	+	3.17686i	−0.413281	+	0.110738i	0.0461864	+	0.998933i	$0.485293\pi$
$824$	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	0.882491	−	0.470329i	$-0.155865\pi$
$827$	11.8528	+	11.8528i	0.412162	+	0.412162i	−0.470329	+	0.882491i	$0.655865\pi$
$828$	0.348904	+	0.0934886i	0.0121253	+	0.00324895i
$829$	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	$-0.105276\pi$
$830$	−6.48139	−	24.1889i	−0.224972	−	0.839608i
$831$	−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
$836$	−3.53691	−	13.1999i	−0.122327	−	0.456529i
$837$	−14.5017	+	25.1176i	−0.501251	+	0.868192i
$838$	26.6045	+	7.12865i	0.919036	+	0.246255i
$839$	4.20215	+	4.20215i	0.145074	+	0.145074i	0.775914	−	0.630839i	$-0.217289\pi$
$839$	4.20215	+	4.20215i	0.145074	+	0.145074i	−0.630839	+	0.775914i	$0.717289\pi$
$840$		0			0
$841$		−	2.27792i		−	0.0785488i
$842$	17.8414	−	10.3007i	0.614855	−	0.354987i
$843$	6.93714	−	1.85880i	0.238928	−	0.0640205i
$844$	−4.43574	+	1.18855i	−0.152684	+	0.0409117i
$845$	−0.765238	−	0.205045i	−0.0263250	−	0.00705376i
$846$	−7.74305			−0.266211
$847$		0			0
$848$		−	19.2602i		−	0.661397i
$849$	−1.85475	−	3.21253i	−0.0636549	−	0.110254i
$850$	42.1027	+	4.06795i	1.44411	+	0.139530i
$851$	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	−0.846625	−	0.532189i	$-0.821370\pi$
$853$	−9.18348	+	9.18348i	−0.314436	+	0.314436i	0.532189	+	0.846625i	$0.321370\pi$
$854$		0			0
$855$	16.9364	−	16.9364i	0.579214	−	0.579214i
$856$	−7.07553	+	26.4062i	−0.241837	+	0.902546i
$857$	27.8122	−	7.45226i	0.950048	−	0.254564i	0.249665	−	0.968332i	$-0.419679\pi$
$857$	27.8122	−	7.45226i	0.950048	−	0.254564i	0.700382	+	0.713768i	$0.253013\pi$
$858$	47.0642	+	27.1725i	1.60675	+	0.927655i
$859$	−7.14240	+	4.12366i	−0.243695	+	0.140698i	−0.616874	−	0.787062i	$-0.711601\pi$
$859$	−7.14240	+	4.12366i	−0.243695	+	0.140698i	0.373179	+	0.927760i	$0.378268\pi$
$860$	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	$0.625574\pi$
$864$	2.56673	+	9.57915i	0.0873218	+	0.325889i
$865$	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
$870$	58.6584	+	15.7175i	1.98871	+	0.532872i
$871$	−22.8434	+	39.5660i	−0.774020	+	1.34064i
$872$	−2.73935	−	10.2234i	−0.0927662	−	0.346208i
$873$	1.24638	−	4.65156i	0.0421836	−	0.157431i
$874$	4.63090	+	4.63090i	0.156643	+	0.156643i
$875$		0			0
$876$			1.58575i			0.0535774i
$877$	−3.64250	+	13.5940i	−0.122998	+	0.459036i	−0.999760	−	0.0218882i	$-0.993032\pi$
$877$	−3.64250	+	13.5940i	−0.122998	+	0.459036i	0.876762	+	0.480925i	$0.159699\pi$
$878$	38.2019	−	10.2362i	1.28925	−	0.345454i
$879$	−7.87590	−	29.3933i	−0.265648	−	0.991410i
$880$	−37.4306	−	64.8316i	−1.26178	−	2.18547i
$881$	10.4454	−	10.4454i	0.351914	−	0.351914i	−0.508907	−	0.860821i	$-0.669950\pi$
$881$	10.4454	−	10.4454i	0.351914	−	0.351914i	0.860821	+	0.508907i	$0.169950\pi$
$882$		0			0
$883$	4.72305			0.158943			0.0794717	−	0.996837i	$-0.474677\pi$
$883$	4.72305			0.158943			0.0794717	+	0.996837i	$0.474677\pi$
$884$	−4.11383	+	5.76339i	−0.138363	+	0.193844i
$885$	9.43513	−	16.3421i	0.317158	−	0.549334i
$886$	−16.5191	−	9.53729i	−0.554969	−	0.320412i
$887$	43.5827	+	11.6779i	1.46336	+	0.392107i	0.900650	−	0.434545i	$-0.143091\pi$
$887$	43.5827	+	11.6779i	1.46336	+	0.392107i	0.562713	+	0.826652i	$0.309758\pi$
$888$	−6.68809			−0.224437
$889$		0			0
$890$	7.72620	+	7.72620i	0.258983	+	0.258983i
$891$	−13.4415	+	50.1643i	−0.450307	+	1.68057i
$892$	7.17281	+	4.14122i	0.240163	+	0.138658i
$893$	−23.2182	−	13.4050i	−0.776967	−	0.448582i
$894$	0.555133	−	2.07178i	0.0185664	−	0.0692908i
$895$	−9.50877	−	9.50877i	−0.317843	−	0.317843i
$896$		0			0
$897$	−4.97371			−0.166067
$898$	−56.1993	−	15.0585i	−1.87539	−	0.502510i
$899$	37.0935	+	21.4159i	1.23714	+	0.714261i
$900$	−1.75337	+	3.03693i	−0.0584458	+	0.101231i
$901$	13.6901	+	9.77180i	0.456082	+	0.325546i
$902$	−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
$906$	9.45696	+	35.2938i	0.314186	+	1.17256i
$907$	−32.7157	+	8.76614i	−1.08631	+	0.291075i	−0.757177	−	0.653210i	$-0.773422\pi$
$907$	−32.7157	+	8.76614i	−1.08631	+	0.291075i	−0.329129	+	0.944285i	$0.606755\pi$
$908$	1.01949	−	3.80480i	0.0338330	−	0.126267i
$909$			6.13069i			0.203342i
$910$		0			0
$911$	7.16704	+	7.16704i	0.237455	+	0.237455i	0.815795	−	0.578341i	$-0.196300\pi$
$911$	7.16704	+	7.16704i	0.237455	+	0.237455i	−0.578341	+	0.815795i	$0.696300\pi$
$912$	15.4062	−	57.4968i	0.510151	−	1.90391i
$913$	−5.67143	−	21.1661i	−0.187697	−	0.700494i
$914$	10.0531	−	17.4126i	0.332528	−	0.575956i
$915$	−80.7032	−	21.6243i	−2.66796	−	0.714879i
$916$			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
$921$	3.77202	+	14.0774i	0.124292	+	0.463866i
$922$	−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
$928$	14.1464	−	3.79052i	0.464378	−	0.124430i
$929$	−2.37065	+	8.84740i	−0.0777786	+	0.290274i	−0.993849	−	0.110744i	$-0.964677\pi$
$929$	−2.37065	+	8.84740i	−0.0777786	+	0.290274i	0.916070	+	0.401018i	$0.131343\pi$
$930$	−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
$935$	65.0728	+	6.28731i	2.12811	+	0.205617i
$936$	4.97432	+	8.61577i	0.162591	+	0.281615i
$937$		−	53.4400i		−	1.74581i	−0.487891	−	0.872905i	$-0.662234\pi$
$937$		−	53.4400i		−	1.74581i	0.487891	−	0.872905i	$-0.337766\pi$
$938$		0			0
$939$	−63.8202			−2.08269
$940$	6.69690	+	1.79443i	0.218429	+	0.0585278i
$941$	−48.4370	+	12.9787i	−1.57900	+	0.423092i	−0.938616	−	0.344963i	$-0.887892\pi$
$941$	−48.4370	+	12.9787i	−1.57900	+	0.423092i	−0.640384	+	0.768055i	$0.721225\pi$
$942$	−72.2432	+	19.3575i	−2.35381	+	0.630702i
$943$	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
$947$	14.1735	+	3.79776i	0.460575	+	0.123411i	0.481643	−	0.876367i	$-0.340040\pi$
$947$	14.1735	+	3.79776i	0.460575	+	0.123411i	−0.0210682	+	0.999778i	$0.506707\pi$
$948$	−4.80426	+	8.32123i	−0.156035	+	0.270261i
$949$	−1.55458	−	5.80179i	−0.0504640	−	0.188334i
$950$	−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
$955$	−22.1178	−	82.5449i	−0.715716	−	2.67109i
$956$	3.44093	−	5.95986i	0.111288	−	0.192756i
$957$	51.3281	+	13.7533i	1.65920	+	0.444581i
$958$	−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
$962$	−7.56082	+	2.02592i	−0.243771	+	0.0653181i
$963$	12.5135	−	3.35298i	0.403242	−	0.108048i
$964$	−6.93841	−	1.85914i	−0.223471	−	0.0598789i
$965$	38.1807			1.22908
$966$		0			0
$967$		−	15.2606i		−	0.490748i	−0.969428	−	0.245374i	$-0.921089\pi$
$967$		−	15.2606i		−	0.490748i	0.969428	−	0.245374i	$-0.0789108\pi$
$968$	−12.9902	−	22.4996i	−0.417520	−	0.723165i
$969$	33.0521	+	40.1221i	1.06179	+	1.28891i
$970$	−11.2895	+	19.5540i	−0.362484	+	0.627841i
$971$	16.1056	−	9.29856i	0.516852	−	0.298405i	−0.218793	−	0.975771i	$-0.570212\pi$
$971$	16.1056	−	9.29856i	0.516852	−	0.298405i	0.735646	+	0.677366i	$0.236879\pi$
$972$	3.75850	−	3.75850i	0.120554	−	0.120554i
$973$		0			0
$974$	24.4991	−	24.4991i	0.785003	−	0.785003i
$975$	12.4974	−	46.6409i	0.400237	−	1.49370i
$976$	−55.1721	+	14.7833i	−1.76602	+	0.473202i
$977$	18.8317	+	10.8725i	0.602479	+	0.347842i	0.770016	−	0.638024i	$-0.220248\pi$
$977$	18.8317	+	10.8725i	0.602479	+	0.347842i	−0.167537	+	0.985866i	$0.553581\pi$
$978$	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
$983$	−0.924420	−	3.44998i	−0.0294844	−	0.110037i	0.949615	−	0.313418i	$-0.101474\pi$
$983$	−0.924420	−	3.44998i	−0.0294844	−	0.110037i	−0.979100	+	0.203380i	$0.934807\pi$
$984$	−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
$989$	−4.31203	−	1.15540i	−0.137114	−	0.0367397i
$990$	−14.1904	+	24.5786i	−0.451002	+	0.781159i
$991$	−0.109827	−	0.409880i	−0.00348877	−	0.0130203i	0.964160	−	0.265323i	$-0.0854787\pi$
$991$	−0.109827	−	0.409880i	−0.00348877	−	0.0130203i	−0.967648	+	0.252303i	$0.918812\pi$
$992$	−5.19071	+	19.3720i	−0.164805	+	0.615062i
$993$	6.80821	+	6.80821i	0.216052	+	0.216052i
$994$		0			0
$995$			17.8210i			0.564963i
$996$	−1.16619	+	4.35227i	−0.0369520	+	0.137907i
$997$	36.1631	−	9.68988i	1.14530	−	0.306882i	0.364218	−	0.931314i	$-0.381336\pi$
$997$	36.1631	−	9.68988i	1.14530	−	0.306882i	0.781079	+	0.624432i	$0.214669\pi$
$998$	17.2385	+	64.3351i	0.545676	+	2.03649i
$999$	−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.361.3		40
7.2	even	3	inner	833.2.o.g.667.8		40
7.3	odd	6		833.2.g.h.344.3		20
7.4	even	3		119.2.g.a.106.3	yes	20
7.5	odd	6		833.2.o.f.667.8		40
7.6	odd	2		833.2.o.f.361.3		40
17.13	even	4	inner	833.2.o.g.557.8		40
21.11	odd	6		1071.2.n.c.820.8		20
119.13	odd	4		833.2.o.f.557.8		40
119.25	even	24		2023.2.a.n.1.3		10
119.30	even	12	inner	833.2.o.g.30.3		40
119.47	odd	12		833.2.o.f.30.3		40
119.60	even	24		2023.2.a.m.1.3		10
119.81	even	12		119.2.g.a.64.8	✓	20
119.115	odd	12		833.2.g.h.540.8		20
357.200	odd	12		1071.2.n.c.64.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.g.a.64.8	✓	20	119.81	even	12
119.2.g.a.106.3	yes	20	7.4	even	3
833.2.g.h.344.3		20	7.3	odd	6
833.2.g.h.540.8		20	119.115	odd	12
833.2.o.f.30.3		40	119.47	odd	12
833.2.o.f.361.3		40	7.6	odd	2
833.2.o.f.557.8		40	119.13	odd	4
833.2.o.f.667.8		40	7.5	odd	6
833.2.o.g.30.3		40	119.30	even	12	inner
833.2.o.g.361.3		40	1.1	even	1	trivial
833.2.o.g.557.8		40	17.13	even	4	inner
833.2.o.g.667.8		40	7.2	even	3	inner
1071.2.n.c.64.3		20	357.200	odd	12
1071.2.n.c.820.8		20	21.11	odd	6
2023.2.a.m.1.3		10	119.60	even	24
2023.2.a.n.1.3		10	119.25	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)

\(f(q)\)	\(=\)	\(q+(-1.36164 + 0.786146i) q^{2} +(-0.526518 - 1.96499i) q^{3} +(0.236050 - 0.408850i) q^{4} +(-3.27915 - 0.878646i) q^{5} +(2.26170 + 2.26170i) q^{6} -2.40230i q^{8} +(-0.985896 + 0.569207i) q^{9} +O(q^{10})\)	\(q+(-1.36164 + 0.786146i) q^{2} +(-0.526518 - 1.96499i) q^{3} +(0.236050 - 0.408850i) q^{4} +(-3.27915 - 0.878646i) q^{5} +(2.26170 + 2.26170i) q^{6} -2.40230i q^{8} +(-0.985896 + 0.569207i) q^{9} +(5.15578 - 1.38149i) q^{10} +(4.51148 - 1.20885i) q^{11} +(-0.927672 - 0.248569i) q^{12} +3.63777 q^{13} +6.90613i q^{15} +(2.36066 + 4.08878i) q^{16} +(-4.10399 - 0.396526i) 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} +(0.173950 - 0.649191i) q^{23} +(-4.72051 + 1.26486i) 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} +(-1.98218 - 7.39761i) q^{31} +(-2.26785 - 1.30934i) q^{32} +(-4.75075 - 8.22854i) q^{33} +(5.89991 - 2.68641i) q^{34} +0.537445i q^{36} +(1.32191 + 0.354204i) q^{37} +(-4.87217 + 8.43884i) q^{38} +(-1.91535 - 7.14819i) q^{39} +(-2.11077 + 7.87752i) q^{40} +(0.492170 + 0.492170i) q^{41} -6.64216i q^{43} +(0.570696 - 2.12987i) q^{44} +(3.73303 - 1.00026i) q^{45} +(0.273500 + 1.02072i) q^{46} +(-2.16296 - 3.74636i) q^{47} +(6.79150 - 6.79150i) q^{48} -10.2590 q^{50} +(1.38166 + 8.27309i) q^{51} +(0.858695 - 1.48730i) q^{52} +(-3.53287 - 2.03970i) q^{53} +(5.75144 + 1.54109i) q^{54} -15.8560 q^{55} +(-8.91500 - 8.91500i) q^{57} +(2.27587 - 8.49368i) q^{58} +(-2.36632 - 1.36620i) q^{59} +(2.82357 + 1.63019i) q^{60} +(-3.13118 + 11.6857i) q^{61} +(8.51463 + 8.51463i) q^{62} -5.32531 q^{64} +(-11.9288 - 3.19631i) q^{65} +(12.9377 + 7.46956i) q^{66} +(-6.27952 + 10.8764i) q^{67} +(-1.13087 + 1.58432i) q^{68} -1.36724 q^{69} +(3.04461 - 3.04461i) q^{71} +(1.36741 + 2.36842i) q^{72} +(-0.427346 - 1.59488i) q^{73} +(-2.07842 + 0.556911i) q^{74} +(3.43545 - 12.8213i) q^{75} -2.92586i q^{76} +(8.22754 + 8.22754i) q^{78} +(2.58942 - 9.66384i) q^{79} +(-4.14837 - 15.4819i) q^{80} +(-5.55963 + 9.62956i) q^{81} +(-1.05708 - 0.283243i) q^{82} -4.69160i q^{83} +(13.1092 + 4.90623i) q^{85} +(5.22170 + 9.04425i) q^{86} +(9.85296 + 5.68861i) q^{87} +(-2.90402 - 10.8379i) 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} +(-20.3227 + 5.44544i) q^{95} +(-1.37878 + 5.14569i) 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

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Database

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