LMFDB - Embedded newform 833.2.l.e.638.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(246,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("833.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.l (of order $8$, degree $4$, 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 $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			638.7
Character	$\chi$	$=$	833.638
Dual form			833.2.l.e.393.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.751304 - 0.751304i) q^{2} +(1.42979 + 0.592240i) q^{3} +0.871085i q^{4} +(1.27926 - 3.08842i) q^{5} +(1.51916 - 0.629258i) q^{6} +(2.15706 + 2.15706i) q^{8} +(-0.427757 - 0.427757i) q^{9} +(-1.35922 - 3.28146i) q^{10} +(1.09126 - 0.452013i) q^{11} +(-0.515892 + 1.24547i) q^{12} +5.97297i q^{13} +(3.65817 - 3.65817i) q^{15} +1.49904 q^{16} +(2.28653 - 3.43100i) q^{17} -0.642752 q^{18} +(4.06266 - 4.06266i) q^{19} +(2.69028 + 1.11435i) q^{20} +(0.480265 - 1.15946i) q^{22} +(-2.85627 + 1.18311i) q^{23} +(1.80665 + 4.36164i) q^{24} +(-4.36627 - 4.36627i) q^{25} +(4.48751 + 4.48751i) q^{26} +(-2.13499 - 5.15432i) q^{27} +(-0.715430 + 1.72720i) q^{29} -5.49679i q^{30} +(6.73059 + 2.78790i) q^{31} +(-3.18788 + 3.18788i) q^{32} +1.82797 q^{33} +(-0.859841 - 4.29561i) q^{34} +(0.372613 - 0.372613i) q^{36} +(-4.57472 - 1.89491i) q^{37} -6.10458i q^{38} +(-3.53743 + 8.54011i) q^{39} +(9.42134 - 3.90245i) q^{40} +(0.272762 + 0.658506i) q^{41} +(-7.40098 - 7.40098i) q^{43} +(0.393742 + 0.950576i) q^{44} +(-1.86831 + 0.773879i) q^{45} +(-1.25705 + 3.03480i) q^{46} +8.39144i q^{47} +(2.14332 + 0.887792i) q^{48} -6.56080 q^{50} +(5.30125 - 3.55145i) q^{51} -5.20296 q^{52} +(-6.01946 + 6.01946i) q^{53} +(-5.47649 - 2.26844i) q^{54} -3.94850i q^{55} +(8.21484 - 3.40270i) q^{57} +(0.760147 + 1.83516i) q^{58} +(0.465487 + 0.465487i) q^{59} +(3.18658 + 3.18658i) q^{60} +(-3.79500 - 9.16194i) q^{61} +(7.15128 - 2.96216i) q^{62} +7.78821i q^{64} +(18.4470 + 7.64100i) q^{65} +(1.37336 - 1.37336i) q^{66} -0.217748 q^{67} +(2.98869 + 1.99177i) q^{68} -4.78456 q^{69} +(10.0504 + 4.16299i) q^{71} -1.84539i q^{72} +(-1.83750 + 4.43612i) q^{73} +(-4.86065 + 2.01335i) q^{74} +(-3.65699 - 8.82876i) q^{75} +(3.53892 + 3.53892i) q^{76} +(3.75853 + 9.07390i) q^{78} +(1.35759 - 0.562333i) q^{79} +(1.91767 - 4.62966i) q^{80} -6.81923i q^{81} +(0.699665 + 0.289811i) q^{82} +(-3.20583 + 3.20583i) q^{83} +(-7.67128 - 11.4509i) q^{85} -11.1208 q^{86} +(-2.04584 + 2.04584i) q^{87} +(3.32892 + 1.37888i) q^{88} +5.20556i q^{89} +(-0.822249 + 1.98509i) q^{90} +(-1.03059 - 2.48806i) q^{92} +(7.97225 + 7.97225i) q^{93} +(6.30452 + 6.30452i) q^{94} +(-7.34998 - 17.7444i) q^{95} +(-6.44600 + 2.67002i) q^{96} +(5.46707 - 13.1987i) q^{97} +(-0.660144 - 0.273441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} + 8 q^{5} + 12 q^{6} + 20 q^{10} - 12 q^{12} - 8 q^{15} - 64 q^{16} - 16 q^{17} + 24 q^{18} - 8 q^{19} - 20 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{27} + 8 q^{29} + 36 q^{31} + 72 q^{33} - 8 q^{34}+ \cdots - 16 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 + 8 * q^5 + 12 * q^6 + 20 * q^10 - 12 * q^12 - 8 * q^15 - 64 * q^16 - 16 * q^17 + 24 * q^18 - 8 * q^19 - 20 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^27 + 8 * q^29 + 36 * q^31 + 72 * q^33 - 8 * q^34 - 16 * q^37 + 8 * q^39 - 80 * q^40 + 16 * q^41 - 32 * q^43 + 32 * q^44 + 36 * q^45 + 64 * q^46 - 112 * q^48 - 96 * q^50 + 8 * q^51 - 112 * q^52 + 100 * q^54 - 16 * q^57 + 80 * q^58 - 72 * q^60 - 96 * q^61 + 80 * q^62 - 8 * q^65 - 32 * q^67 + 116 * q^68 + 48 * q^69 - 16 * q^71 - 16 * q^73 - 80 * q^74 + 48 * q^75 + 16 * q^76 - 32 * q^78 - 16 * q^79 + 84 * q^80 + 40 * q^82 + 8 * q^83 + 16 * q^85 + 120 * q^86 + 48 * q^87 + 48 * q^88 + 72 * q^90 + 136 * q^92 - 16 * q^93 - 16 * q^94 + 16 * q^95 - 220 * q^96 - 8 * q^97 - 16 * q^99

Character values

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

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	0.751304	−	0.751304i	0.531252	−	0.531252i	−0.389693	−	0.920945i	$-0.627419\pi$
$2$	0.751304	−	0.751304i	0.531252	−	0.531252i	0.920945	+	0.389693i	$0.127419\pi$
$3$	1.42979	+	0.592240i	0.825492	+	0.341930i	0.755117	−	0.655591i	$-0.227580\pi$
$3$	1.42979	+	0.592240i	0.825492	+	0.341930i	0.0703755	+	0.997521i	$0.477580\pi$
$4$			0.871085i			0.435543i
$5$	1.27926	−	3.08842i	0.572105	−	1.38118i	−0.327655	−	0.944797i	$-0.606259\pi$
$5$	1.27926	−	3.08842i	0.572105	−	1.38118i	0.899760	−	0.436385i	$-0.143741\pi$
$6$	1.51916	−	0.629258i	0.620195	−	0.256893i
$7$		0			0
$7$		0			0
$8$	2.15706	+	2.15706i	0.762635	+	0.762635i
$9$	−0.427757	−	0.427757i	−0.142586	−	0.142586i
$10$	−1.35922	−	3.28146i	−0.429824	−	1.03769i
$11$	1.09126	−	0.452013i	0.329026	−	0.136287i	−0.212055	−	0.977258i	$-0.568015\pi$
$11$	1.09126	−	0.452013i	0.329026	−	0.136287i	0.541080	+	0.840971i	$0.318015\pi$
$12$	−0.515892	+	1.24547i	−0.148925	+	0.359537i
$13$			5.97297i			1.65660i	0.560283	+	0.828301i	$0.310692\pi$
$13$			5.97297i			1.65660i	−0.560283	+	0.828301i	$0.689308\pi$
$14$		0			0
$15$	3.65817	−	3.65817i	0.944535	−	0.944535i
$16$	1.49904			0.374760
$17$	2.28653	−	3.43100i	0.554566	−	0.832140i
$17$	2.28653	−	3.43100i	0.554566	−	0.832140i
$18$	−0.642752			−0.151498
$19$	4.06266	−	4.06266i	0.932038	−	0.932038i	−0.0657950	−	0.997833i	$-0.520958\pi$
$19$	4.06266	−	4.06266i	0.932038	−	0.932038i	0.997833	+	0.0657950i	$0.0209583\pi$
$20$	2.69028	+	1.11435i	0.601564	+	0.249176i
$21$		0			0
$22$	0.480265	−	1.15946i	0.102393	−	0.247198i
$23$	−2.85627	+	1.18311i	−0.595574	+	0.246695i	−0.660046	−	0.751225i	$-0.729463\pi$
$23$	−2.85627	+	1.18311i	−0.595574	+	0.246695i	0.0644729	+	0.997919i	$0.479463\pi$
$24$	1.80665	+	4.36164i	0.368781	+	0.890317i
$25$	−4.36627	−	4.36627i	−0.873255	−	0.873255i
$26$	4.48751	+	4.48751i	0.880073	+	0.880073i
$27$	−2.13499	−	5.15432i	−0.410879	−	0.991950i
$28$		0			0
$29$	−0.715430	+	1.72720i	−0.132852	+	0.320733i	−0.976281	−	0.216508i	$-0.930533\pi$
$29$	−0.715430	+	1.72720i	−0.132852	+	0.320733i	0.843429	+	0.537241i	$0.180533\pi$
$30$		−	5.49679i		−	1.00357i
$31$	6.73059	+	2.78790i	1.20885	+	0.500722i	0.893848	−	0.448369i	$-0.147995\pi$
$31$	6.73059	+	2.78790i	1.20885	+	0.500722i	0.315001	+	0.949091i	$0.397995\pi$
$32$	−3.18788	+	3.18788i	−0.563543	+	0.563543i
$33$	1.82797			0.318209
$34$	−0.859841	−	4.29561i	−0.147462	−	0.736690i
$35$		0			0
$36$	0.372613	−	0.372613i	0.0621022	−	0.0621022i
$37$	−4.57472	−	1.89491i	−0.752079	−	0.311521i	−0.0264893	−	0.999649i	$-0.508433\pi$
$37$	−4.57472	−	1.89491i	−0.752079	−	0.311521i	−0.725589	+	0.688128i	$0.758433\pi$
$38$		−	6.10458i		−	0.990294i
$39$	−3.53743	+	8.54011i	−0.566442	+	1.36751i
$40$	9.42134	−	3.90245i	1.48964	−	0.617031i
$41$	0.272762	+	0.658506i	0.0425983	+	0.102841i	0.943747	−	0.330670i	$-0.107275\pi$
$41$	0.272762	+	0.658506i	0.0425983	+	0.102841i	−0.901148	+	0.433511i	$0.857275\pi$
$42$		0			0
$43$	−7.40098	−	7.40098i	−1.12864	−	1.12864i	−0.990399	−	0.138240i	$-0.955855\pi$
$43$	−7.40098	−	7.40098i	−1.12864	−	1.12864i	−0.138240	−	0.990399i	$-0.544145\pi$
$44$	0.393742	+	0.950576i	0.0593588	+	0.143305i
$45$	−1.86831	+	0.773879i	−0.278511	+	0.115363i
$46$	−1.25705	+	3.03480i	−0.185343	+	0.447457i
$47$			8.39144i			1.22402i	0.790851	+	0.612009i	$0.209638\pi$
$47$			8.39144i			1.22402i	−0.790851	+	0.612009i	$0.790362\pi$
$48$	2.14332	+	0.887792i	0.309361	+	0.128142i
$49$		0			0
$50$	−6.56080			−0.927837
$51$	5.30125	−	3.55145i	0.742323	−	0.497302i
$52$	−5.20296			−0.721521
$53$	−6.01946	+	6.01946i	−0.826837	+	0.826837i	−0.987078	−	0.160241i	$-0.948773\pi$
$53$	−6.01946	+	6.01946i	−0.826837	+	0.826837i	0.160241	+	0.987078i	$0.448773\pi$
$54$	−5.47649	−	2.26844i	−0.745256	−	0.308695i
$55$		−	3.94850i		−	0.532415i
$56$		0			0
$57$	8.21484	−	3.40270i	1.08808	−	0.450698i
$58$	0.760147	+	1.83516i	0.0998122	+	0.240968i
$59$	0.465487	+	0.465487i	0.0606012	+	0.0606012i	0.736758	−	0.676157i	$-0.236356\pi$
$59$	0.465487	+	0.465487i	0.0606012	+	0.0606012i	−0.676157	+	0.736758i	$0.736356\pi$
$60$	3.18658	+	3.18658i	0.411385	+	0.411385i
$61$	−3.79500	−	9.16194i	−0.485900	−	1.17307i	−0.956765	−	0.290861i	$-0.906058\pi$
$61$	−3.79500	−	9.16194i	−0.485900	−	1.17307i	0.470866	−	0.882205i	$-0.343942\pi$
$62$	7.15128	−	2.96216i	0.908213	−	0.376194i
$63$		0			0
$64$			7.78821i			0.973527i
$65$	18.4470	+	7.64100i	2.28807	+	0.947750i
$66$	1.37336	−	1.37336i	0.169049	−	0.169049i
$67$	−0.217748			−0.0266021			−0.0133011	−	0.999912i	$-0.504234\pi$
$67$	−0.217748			−0.0266021			−0.0133011	+	0.999912i	$0.504234\pi$
$68$	2.98869	+	1.99177i	0.362432	+	0.241537i
$69$	−4.78456			−0.575994
$70$		0			0
$71$	10.0504	+	4.16299i	1.19276	+	0.494056i	0.888652	−	0.458582i	$-0.151642\pi$
$71$	10.0504	+	4.16299i	1.19276	+	0.494056i	0.304106	+	0.952638i	$0.401642\pi$
$72$		−	1.84539i		−	0.217482i
$73$	−1.83750	+	4.43612i	−0.215063	+	0.519209i	−0.994188	−	0.107661i	$-0.965664\pi$
$73$	−1.83750	+	4.43612i	−0.215063	+	0.519209i	0.779124	+	0.626869i	$0.215664\pi$
$74$	−4.86065	+	2.01335i	−0.565040	+	0.234047i
$75$	−3.65699	−	8.82876i	−0.422273	−	1.01946i
$76$	3.53892	+	3.53892i	0.405942	+	0.405942i
$77$		0			0
$78$	3.75853	+	9.07390i	0.425570	+	1.02742i
$79$	1.35759	−	0.562333i	0.152741	−	0.0632674i	−0.305003	−	0.952351i	$-0.598658\pi$
$79$	1.35759	−	0.562333i	0.152741	−	0.0632674i	0.457744	+	0.889084i	$0.348658\pi$
$80$	1.91767	−	4.62966i	0.214402	−	0.517612i
$81$		−	6.81923i		−	0.757692i
$82$	0.699665	+	0.289811i	0.0772651	+	0.0320043i
$83$	−3.20583	+	3.20583i	−0.351885	+	0.351885i	−0.860811	−	0.508925i	$-0.830043\pi$
$83$	−3.20583	+	3.20583i	−0.351885	+	0.351885i	0.508925	+	0.860811i	$0.330043\pi$
$84$		0			0
$85$	−7.67128	−	11.4509i	−0.832067	−	1.24203i
$86$	−11.1208			−1.19918
$87$	−2.04584	+	2.04584i	−0.219337	+	0.219337i
$88$	3.32892	+	1.37888i	0.354864	+	0.146989i
$89$			5.20556i			0.551789i	0.961188	+	0.275894i	$0.0889740\pi$
$89$			5.20556i			0.551789i	−0.961188	+	0.275894i	$0.911026\pi$
$90$	−0.822249	+	1.98509i	−0.0866727	+	0.209246i
$91$		0			0
$92$	−1.03059	−	2.48806i	−0.107446	−	0.259398i
$93$	7.97225	+	7.97225i	0.826684	+	0.826684i
$94$	6.30452	+	6.30452i	0.650262	+	0.650262i
$95$	−7.34998	−	17.7444i	−0.754092	−	1.82054i
$96$	−6.44600	+	2.67002i	−0.657892	+	0.272508i
$97$	5.46707	−	13.1987i	0.555096	−	1.34012i	−0.358511	−	0.933525i	$-0.616716\pi$
$97$	5.46707	−	13.1987i	0.555096	−	1.34012i	0.913608	−	0.406596i	$-0.133284\pi$
$98$		0			0
$99$	−0.660144	−	0.273441i	−0.0663470	−	0.0274818i
$100$	3.80340	−	3.80340i	0.380340	−	0.380340i
$101$	−6.97315			−0.693854			−0.346927	−	0.937892i	$-0.612775\pi$
$101$	−6.97315			−0.693854			−0.346927	+	0.937892i	$0.612775\pi$
$102$	1.31463	−	6.65106i	0.130168	−	0.658553i
$103$	−14.4526			−1.42406			−0.712029	−	0.702150i	$-0.752223\pi$
$103$	−14.4526			−1.42406			−0.712029	+	0.702150i	$0.752223\pi$
$104$	−12.8840	+	12.8840i	−1.26338	+	1.26338i
$105$		0			0
$106$			9.04489i			0.878517i
$107$	−1.53269	+	3.70024i	−0.148171	+	0.357716i	−0.980487	−	0.196586i	$-0.937015\pi$
$107$	−1.53269	+	3.70024i	−0.148171	+	0.357716i	0.832316	+	0.554302i	$0.187015\pi$
$108$	4.48985	−	1.85976i	0.432036	−	0.178955i
$109$	3.68959	+	8.90746i	0.353399	+	0.853180i	0.996196	+	0.0871437i	$0.0277739\pi$
$109$	3.68959	+	8.90746i	0.353399	+	0.853180i	−0.642797	+	0.766037i	$0.722226\pi$
$110$	−2.96652	−	2.96652i	−0.282847	−	0.282847i
$111$	−5.41866	−	5.41866i	−0.514317	−	0.514317i
$112$		0			0
$113$	−16.6375	+	6.89147i	−1.56512	+	0.648295i	−0.985970	−	0.166925i	$-0.946616\pi$
$113$	−16.6375	+	6.89147i	−1.56512	+	0.648295i	−0.579152	+	0.815220i	$0.696616\pi$
$114$	3.61538	−	8.72830i	0.338611	−	0.817480i
$115$			10.3349i			0.963731i
$116$	−1.50454	−	0.623201i	−0.139693	−	0.0578627i
$117$	2.55498	−	2.55498i	0.236208	−	0.236208i
$118$	0.699444			0.0643890
$119$		0			0
$120$	15.7818			1.44067
$121$	−6.79165	+	6.79165i	−0.617423	+	0.617423i
$122$	−9.73459	−	4.03220i	−0.881329	−	0.365058i
$123$			1.10307i			0.0994604i
$124$	−2.42850	+	5.86292i	−0.218086	+	0.526506i
$125$	−3.62841	+	1.50294i	−0.324535	+	0.134427i
$126$		0			0
$127$	−8.00675	−	8.00675i	−0.710484	−	0.710484i	0.256153	−	0.966636i	$-0.417545\pi$
$127$	−8.00675	−	8.00675i	−0.710484	−	0.710484i	−0.966636	+	0.256153i	$0.917545\pi$
$128$	−0.524446	−	0.524446i	−0.0463549	−	0.0463549i
$129$	−6.19872	−	14.9650i	−0.545767	−	1.31760i
$130$	19.6000	−	8.11860i	1.71904	−	0.712048i
$131$	−0.640977	+	1.54745i	−0.0560024	+	0.135202i	−0.949404	−	0.314057i	$-0.898312\pi$
$131$	−0.640977	+	1.54745i	−0.0560024	+	0.135202i	0.893402	+	0.449258i	$0.148312\pi$
$132$			1.59232i			0.138593i
$133$		0			0
$134$	−0.163595	+	0.163595i	−0.0141324	+	0.0141324i
$135$	−18.6499			−1.60513
$136$	12.3330	−	2.46868i	1.05755	−	0.211687i
$137$	18.5730			1.58680			0.793401	−	0.608700i	$-0.208309\pi$
$137$	18.5730			1.58680			0.793401	+	0.608700i	$0.208309\pi$
$138$	−3.59466	+	3.59466i	−0.305998	+	0.305998i
$139$	−10.3660	−	4.29373i	−0.879232	−	0.364190i	−0.103033	−	0.994678i	$-0.532855\pi$
$139$	−10.3660	−	4.29373i	−0.879232	−	0.364190i	−0.776199	+	0.630488i	$0.782855\pi$
$140$		0			0
$141$	−4.96975	+	11.9980i	−0.418528	+	1.01042i
$142$	10.6785	−	4.42320i	0.896123	−	0.371186i
$143$	2.69986	+	6.51803i	0.225773	+	0.545065i
$144$	−0.641226	−	0.641226i	−0.0534355	−	0.0534355i
$145$	4.41909	+	4.41909i	0.366986	+	0.366986i
$146$	1.95235	+	4.71340i	0.161578	+	0.390083i
$147$		0			0
$148$	1.65063	−	3.98497i	0.135681	−	0.327562i
$149$			12.8513i			1.05282i	0.850232	+	0.526408i	$0.176461\pi$
$149$			12.8513i			1.05282i	−0.850232	+	0.526408i	$0.823539\pi$
$150$	−9.38059	−	3.88557i	−0.765922	−	0.317255i
$151$	−10.8601	+	10.8601i	−0.883785	+	0.883785i	−0.993917	−	0.110132i	$-0.964873\pi$
$151$	−10.8601	+	10.8601i	−0.883785	+	0.883785i	0.110132	+	0.993917i	$0.464873\pi$
$152$	17.5268			1.42161
$153$	−2.44572	+	0.489554i	−0.197725	+	0.0395781i
$154$		0			0
$155$	17.2204	−	17.2204i	1.38318	−	1.38318i
$156$	−7.43916	−	3.08140i	−0.595610	−	0.246710i
$157$		−	10.1110i		−	0.806950i	−0.914991	−	0.403475i	$-0.867802\pi$
$157$		−	10.1110i		−	0.806950i	0.914991	−	0.403475i	$-0.132198\pi$
$158$	0.597481	−	1.44245i	0.0475330	−	0.114755i
$159$	−12.1716	+	5.04163i	−0.965268	+	0.399827i
$160$	5.76736	+	13.9236i	0.455950	+	1.10076i
$161$		0			0
$162$	−5.12331	−	5.12331i	−0.402525	−	0.402525i
$163$	−2.29605	−	5.54316i	−0.179841	−	0.434174i	0.808092	−	0.589056i	$-0.200500\pi$
$163$	−2.29605	−	5.54316i	−0.179841	−	0.434174i	−0.987933	+	0.154882i	$0.950500\pi$
$164$	−0.573615	+	0.237599i	−0.0447918	+	0.0185534i
$165$	2.33846	−	5.64554i	0.182049	−	0.439504i
$166$			4.81710i			0.373880i
$167$	−14.7839	−	6.12370i	−1.14401	−	0.473866i	−0.271491	−	0.962441i	$-0.587517\pi$
$167$	−14.7839	−	6.12370i	−1.14401	−	0.473866i	−0.872522	+	0.488575i	$0.837517\pi$
$168$		0			0
$169$	−22.6763			−1.74433
$170$	−14.3666	−	2.83967i	−1.10187	−	0.217792i
$171$	−3.47567			−0.265791
$172$	6.44688	−	6.44688i	0.491570	−	0.491570i
$173$	12.2192	+	5.06135i	0.929007	+	0.384807i	0.795302	−	0.606214i	$-0.207312\pi$
$173$	12.2192	+	5.06135i	0.929007	+	0.384807i	0.133705	+	0.991021i	$0.457312\pi$
$174$			3.07409i			0.233046i
$175$		0			0
$176$	1.63584	−	0.677585i	0.123306	−	0.0510749i
$177$	0.389870	+	0.941230i	0.0293044	+	0.0707472i
$178$	3.91096	+	3.91096i	0.293139	+	0.293139i
$179$	−13.9304	−	13.9304i	−1.04121	−	1.04121i	−0.999114	−	0.0420963i	$-0.986596\pi$
$179$	−13.9304	−	13.9304i	−1.04121	−	1.04121i	−0.0420963	−	0.999114i	$-0.513404\pi$
$180$	−0.674114	−	1.62746i	−0.0502455	−	0.121303i
$181$	10.9296	−	4.52719i	0.812391	−	0.336504i	0.0624837	−	0.998046i	$-0.480098\pi$
$181$	10.9296	−	4.52719i	0.812391	−	0.336504i	0.749908	+	0.661542i	$0.230098\pi$
$182$		0			0
$183$		−	15.3472i		−	1.13450i
$184$	−8.71317	−	3.60911i	−0.642343	−	0.266067i
$185$	−11.7045	+	11.7045i	−0.860535	+	0.860535i
$186$	11.9792			0.878355
$187$	0.944337	−	4.77764i	0.0690568	−	0.349376i
$188$	−7.30966			−0.533112
$189$		0			0
$190$	−18.8535	−	7.80938i	−1.36778	−	0.566552i
$191$		−	3.46239i		−	0.250530i	−0.992123	−	0.125265i	$-0.960022\pi$
$191$		−	3.46239i		−	0.250530i	0.992123	−	0.125265i	$-0.0399781\pi$
$192$	−4.61249	+	11.1355i	−0.332878	+	0.803638i
$193$	18.1768	−	7.52909i	1.30840	−	0.541956i	0.383981	−	0.923341i	$-0.374553\pi$
$193$	18.1768	−	7.52909i	1.30840	−	0.541956i	0.924416	+	0.381385i	$0.124553\pi$
$194$	−5.80878	−	14.0236i	−0.417046	−	1.00684i
$195$	21.8501	+	21.8501i	1.56472	+	1.56472i
$196$		0			0
$197$	7.76714	+	18.7515i	0.553386	+	1.33599i	0.914921	+	0.403633i	$0.132253\pi$
$197$	7.76714	+	18.7515i	0.553386	+	1.33599i	−0.361535	+	0.932359i	$0.617747\pi$
$198$	−0.701406	+	0.290532i	−0.0498467	+	0.0206472i
$199$	4.70819	−	11.3666i	0.333755	−	0.805756i	−0.664533	−	0.747259i	$-0.731369\pi$
$199$	4.70819	−	11.3666i	0.333755	−	0.805756i	0.998288	−	0.0584964i	$-0.0186306\pi$
$200$		−	18.8366i		−	1.33195i
$201$	−0.311334	−	0.128959i	−0.0219598	−	0.00909606i
$202$	−5.23895	+	5.23895i	−0.368611	+	0.368611i
$203$		0			0
$204$	3.09361	+	4.61784i	0.216596	+	0.323313i
$205$	2.38268			0.166413
$206$	−10.8583	+	10.8583i	−0.756533	+	0.756533i
$207$	1.72787	+	0.715709i	0.120095	+	0.0497452i
$208$			8.95371i			0.620828i
$209$	2.59702	−	6.26977i	0.179640	−	0.433689i
$210$		0			0
$211$	6.58994	+	15.9095i	0.453670	+	1.09526i	0.970916	+	0.239419i	$0.0769571\pi$
$211$	6.58994	+	15.9095i	0.453670	+	1.09526i	−0.517246	+	0.855837i	$0.673043\pi$
$212$	−5.24347	−	5.24347i	−0.360123	−	0.360123i
$213$	11.9044	+	11.9044i	0.815679	+	0.815679i
$214$	1.62849	+	3.93152i	0.111321	+	0.268753i
$215$	−32.3251	+	13.3895i	−2.20456	+	0.913157i
$216$	6.51287	−	15.7235i	0.443145	−	1.06985i
$217$		0			0
$218$	9.46422	+	3.92021i	0.640998	+	0.265510i
$219$	−5.25450	+	5.25450i	−0.355066	+	0.355066i
$220$	3.43948			0.231889
$221$	20.4932	+	13.6574i	1.37852	+	0.918696i
$222$	−8.14212			−0.546463
$223$	12.0117	−	12.0117i	0.804361	−	0.804361i	−0.179413	−	0.983774i	$-0.557420\pi$
$223$	12.0117	−	12.0117i	0.804361	−	0.804361i	0.983774	+	0.179413i	$0.0574197\pi$
$224$		0			0
$225$			3.73541i			0.249027i
$226$	−7.32221	+	17.6774i	−0.487066	+	1.17588i
$227$	−16.6270	+	6.88712i	−1.10357	+	0.457114i	−0.858719	−	0.512446i	$-0.828739\pi$
$227$	−16.6270	+	6.88712i	−1.10357	+	0.457114i	−0.244852	+	0.969560i	$0.578739\pi$
$228$	2.96404	+	7.15582i	0.196298	+	0.473906i
$229$	8.42737	+	8.42737i	0.556896	+	0.556896i	0.928422	−	0.371526i	$-0.121165\pi$
$229$	8.42737	+	8.42737i	0.556896	+	0.556896i	−0.371526	+	0.928422i	$0.621165\pi$
$230$	7.76462	+	7.76462i	0.511984	+	0.511984i
$231$		0			0
$232$	−5.26890	+	2.18245i	−0.345920	+	0.143285i
$233$	−2.53575	+	6.12184i	−0.166122	+	0.401055i	−0.984916	−	0.173033i	$-0.944643\pi$
$233$	−2.53575	+	6.12184i	−0.166122	+	0.401055i	0.818794	+	0.574088i	$0.194643\pi$
$234$		−	3.83913i		−	0.250972i
$235$	25.9163	+	10.7349i	1.69059	+	0.700266i
$236$	−0.405479	+	0.405479i	−0.0263944	+	0.0263944i
$237$	2.27411			0.147719
$238$		0			0
$239$	11.4690			0.741869			0.370935	−	0.928659i	$-0.379037\pi$
$239$	11.4690			0.741869			0.370935	+	0.928659i	$0.379037\pi$
$240$	5.48374	−	5.48374i	0.353974	−	0.353974i
$241$	−4.90377	−	2.03121i	−0.315880	−	0.130842i	0.219110	−	0.975700i	$-0.429685\pi$
$241$	−4.90377	−	2.03121i	−0.315880	−	0.130842i	−0.534990	+	0.844858i	$0.679685\pi$
$242$			10.2052i			0.656014i
$243$	−2.36635	+	5.71288i	−0.151802	+	0.366481i
$244$	7.98083	−	3.30577i	0.510920	−	0.211630i
$245$		0			0
$246$	0.828740	+	0.828740i	0.0528385	+	0.0528385i
$247$	24.2661	+	24.2661i	1.54402	+	1.54402i
$248$	8.50460	+	20.5319i	0.540043	+	1.30378i
$249$	−6.48230	+	2.68506i	−0.410799	+	0.170158i
$250$	−1.59688	+	3.85520i	−0.100995	+	0.243824i
$251$		−	3.65040i		−	0.230411i	−0.993342	−	0.115206i	$-0.963247\pi$
$251$		−	3.65040i		−	0.230411i	0.993342	−	0.115206i	$-0.0367527\pi$
$252$		0			0
$253$	−2.58214	+	2.58214i	−0.162338	+	0.162338i
$254$	−12.0310			−0.754892
$255$	−4.18665	−	20.9157i	−0.262178	−	1.30979i
$256$	−16.3645			−1.02278
$257$	0.00449160	−	0.00449160i	0.000280178	−	0.000280178i	−0.706967	−	0.707247i	$-0.749937\pi$
$257$	0.00449160	−	0.00449160i	0.000280178	−	0.000280178i	0.707247	+	0.706967i	$0.249937\pi$
$258$	−15.9004	−	6.58616i	−0.989916	−	0.410037i
$259$		0			0
$260$	−6.65597	+	16.0689i	−0.412785	+	0.996552i
$261$	1.04485	−	0.432793i	0.0646748	−	0.0267892i
$262$	0.681040	+	1.64418i	0.0420748	+	0.101578i
$263$	−16.6225	−	16.6225i	−1.02499	−	1.02499i	−0.999680	−	0.0253059i	$-0.991944\pi$
$263$	−16.6225	−	16.6225i	−1.02499	−	1.02499i	−0.0253059	−	0.999680i	$-0.508056\pi$
$264$	3.94304	+	3.94304i	0.242677	+	0.242677i
$265$	10.8901	+	26.2911i	0.668975	+	1.61505i
$266$		0			0
$267$	−3.08294	+	7.44289i	−0.188673	+	0.455497i
$268$		−	0.189677i		−	0.0115864i
$269$	18.7163	+	7.75254i	1.14115	+	0.472681i	0.871558	−	0.490293i	$-0.163110\pi$
$269$	18.7163	+	7.75254i	1.14115	+	0.472681i	0.269595	+	0.962974i	$0.413110\pi$
$270$	−14.0118	+	14.0118i	−0.852728	+	0.852728i
$271$	11.9320			0.724815			0.362408	−	0.932020i	$-0.381955\pi$
$271$	11.9320			0.724815			0.362408	+	0.932020i	$0.381955\pi$
$272$	3.42761	−	5.14321i	0.207829	−	0.311853i
$273$		0			0
$274$	13.9540	−	13.9540i	0.842991	−	0.842991i
$275$	−6.73833	−	2.79111i	−0.406337	−	0.168310i
$276$		−	4.16776i		−	0.250870i
$277$	1.27670	−	3.08222i	0.0767092	−	0.185193i	−0.880873	−	0.473353i	$-0.843044\pi$
$277$	1.27670	−	3.08222i	0.0767092	−	0.185193i	0.957582	+	0.288160i	$0.0930436\pi$
$278$	−11.0139	+	4.56211i	−0.660570	+	0.273617i
$279$	−1.68651	−	4.07161i	−0.100969	−	0.243761i
$280$		0			0
$281$	13.4269	+	13.4269i	0.800984	+	0.800984i	0.983249	−	0.182265i	$-0.0583429\pi$
$281$	13.4269	+	13.4269i	0.800984	+	0.800984i	−0.182265	+	0.983249i	$0.558343\pi$
$282$	5.28038	+	12.7480i	0.314442	+	0.759130i
$283$	−11.9191	+	4.93704i	−0.708516	+	0.293477i	−0.707690	−	0.706523i	$-0.750263\pi$
$283$	−11.9191	+	4.93704i	−0.708516	+	0.293477i	−0.000825368		1.00000i	$0.500263\pi$
$284$	−3.62632	+	8.75472i	−0.215183	+	0.519497i
$285$		−	29.7238i		−	1.76069i
$286$	6.92543	+	2.86861i	0.409509	+	0.169624i
$287$		0			0
$288$	2.72728			0.160706
$289$	−6.54352	−	15.6902i	−0.384913	−	0.922953i
$290$	6.64017			0.389924
$291$	15.6336	−	15.6336i	0.916455	−	0.916455i
$292$	−3.86424	−	1.60062i	−0.226137	−	0.0936692i
$293$		−	18.3192i		−	1.07022i	−0.844783	−	0.535108i	$-0.820271\pi$
$293$		−	18.3192i		−	1.07022i	0.844783	−	0.535108i	$-0.179729\pi$
$294$		0			0
$295$	2.03310	−	0.842137i	0.118372	−	0.0490311i
$296$	−5.78050	−	13.9554i	−0.335985	−	0.811138i
$297$	−4.65964	−	4.65964i	−0.270380	−	0.270380i
$298$	9.65520	+	9.65520i	0.559310	+	0.559310i
$299$	−7.06665	−	17.0604i	−0.408675	−	0.986629i
$300$	7.69060	−	3.18555i	0.444017	−	0.183918i
$301$		0			0
$302$			16.3185i			0.939025i
$303$	−9.97017	−	4.12978i	−0.572771	−	0.237250i
$304$	6.09009	−	6.09009i	0.349291	−	0.349291i
$305$	−33.1507			−1.89820
$306$	−1.46967	+	2.20528i	−0.0840156	+	0.126067i
$307$	−12.0656			−0.688619			−0.344309	−	0.938856i	$-0.611887\pi$
$307$	−12.0656			−0.688619			−0.344309	+	0.938856i	$0.611887\pi$
$308$		0			0
$309$	−20.6642	−	8.55941i	−1.17555	−	0.486928i
$310$		−	25.8755i		−	1.46963i
$311$	0.964500	−	2.32851i	0.0546918	−	0.132038i	−0.894172	−	0.447724i	$-0.852235\pi$
$311$	0.964500	−	2.32851i	0.0546918	−	0.132038i	0.948864	+	0.315686i	$0.102235\pi$
$312$	−26.0519	+	10.7911i	−1.47490	+	0.610924i
$313$	−6.19660	−	14.9599i	−0.350253	−	0.845585i	−0.996588	−	0.0825316i	$-0.973699\pi$
$313$	−6.19660	−	14.9599i	−0.350253	−	0.845585i	0.646336	−	0.763053i	$-0.276301\pi$
$314$	−7.59647	−	7.59647i	−0.428694	−	0.428694i
$315$		0			0
$316$	0.489840	+	1.18258i	0.0275556	+	0.0665252i
$317$	26.1662	−	10.8384i	1.46964	−	0.608746i	0.502864	−	0.864365i	$-0.332280\pi$
$317$	26.1662	−	10.8384i	1.46964	−	0.608746i	0.966777	+	0.255620i	$0.0822795\pi$
$318$	−5.35675	+	12.9323i	−0.300391	+	0.725209i
$319$			2.20820i			0.123635i
$320$	24.0533	+	9.96318i	1.34462	+	0.556959i
$321$	−4.38286	+	4.38286i	−0.244627	+	0.244627i
$322$		0			0
$323$	−4.64957	−	23.2284i	−0.258709	−	1.29246i
$324$	5.94013			0.330007
$325$	26.0796	−	26.0796i	1.44664	−	1.44664i
$326$	−5.88963	−	2.43957i	−0.326197	−	0.135115i
$327$			14.9210i			0.825131i
$328$	−0.832072	+	2.00880i	−0.0459435	+	0.110917i
$329$		0			0
$330$	−2.48462	−	5.99840i	−0.136774	−	0.330201i
$331$	0.842520	+	0.842520i	0.0463091	+	0.0463091i	0.729882	−	0.683573i	$-0.239575\pi$
$331$	0.842520	+	0.842520i	0.0463091	+	0.0463091i	−0.683573	+	0.729882i	$0.739575\pi$
$332$	−2.79255	−	2.79255i	−0.153261	−	0.153261i
$333$	1.14631	+	2.76743i	0.0628172	+	0.151654i
$334$	−15.7080	+	6.50645i	−0.859501	+	0.356017i
$335$	−0.278557	+	0.672496i	−0.0152192	+	0.0367424i
$336$		0			0
$337$	−18.9313	−	7.84160i	−1.03125	−	0.427159i	−0.198089	−	0.980184i	$-0.563473\pi$
$337$	−18.9313	−	7.84160i	−1.03125	−	0.427159i	−0.833165	+	0.553025i	$0.813473\pi$
$338$	−17.0368	+	17.0368i	−0.926680	+	0.926680i
$339$	−27.8696			−1.51367
$340$	9.97474	−	6.68234i	0.540956	−	0.362401i
$341$	8.60496			0.465985
$342$	−2.61128	+	2.61128i	−0.141202	+	0.141202i
$343$		0			0
$344$		−	31.9287i		−	1.72148i
$345$	−6.12072	+	14.7767i	−0.329529	+	0.795552i
$346$	12.9829	−	5.37771i	0.697967	−	0.289107i
$347$	−0.644277	−	1.55542i	−0.0345866	−	0.0834995i	0.905642	−	0.424042i	$-0.139389\pi$
$347$	−0.644277	−	1.55542i	−0.0345866	−	0.0834995i	−0.940229	+	0.340543i	$0.889389\pi$
$348$	−1.78210	−	1.78210i	−0.0955304	−	0.0955304i
$349$	−15.1598	−	15.1598i	−0.811488	−	0.811488i	0.173369	−	0.984857i	$-0.444535\pi$
$349$	−15.1598	−	15.1598i	−0.811488	−	0.811488i	−0.984857	+	0.173369i	$0.944535\pi$
$350$		0			0
$351$	30.7866	−	12.7522i	1.64327	−	0.680663i
$352$	−2.03783	+	4.91975i	−0.108617	+	0.262224i
$353$		−	8.56862i		−	0.456061i	−0.973654	−	0.228031i	$-0.926771\pi$
$353$		−	8.56862i		−	0.456061i	0.973654	−	0.228031i	$-0.0732287\pi$
$354$	1.00006	+	0.414239i	0.0531526	+	0.0220165i
$355$	25.7141	−	25.7141i	1.36476	−	1.36476i
$356$	−4.53449			−0.240327
$357$		0			0
$358$	−20.9320			−1.10629
$359$	16.6473	−	16.6473i	0.878610	−	0.878610i	−0.114781	−	0.993391i	$-0.536617\pi$
$359$	16.6473	−	16.6473i	0.878610	−	0.878610i	0.993391	+	0.114781i	$0.0366166\pi$
$360$	−5.69935	−	2.36075i	−0.300382	−	0.124422i
$361$		−	14.0104i		−	0.737390i
$362$	4.81016	−	11.6128i	0.252816	−	0.610353i
$363$	−13.7330	+	5.68838i	−0.720793	+	0.298562i
$364$		0			0
$365$	11.3499	+	11.3499i	0.594083	+	0.594083i
$366$	−11.5304	−	11.5304i	−0.602705	−	0.602705i
$367$	2.66309	+	6.42926i	0.139012	+	0.335604i	0.978019	−	0.208516i	$-0.0668634\pi$
$367$	2.66309	+	6.42926i	0.139012	+	0.335604i	−0.839007	+	0.544121i	$0.816863\pi$
$368$	−4.28166	+	1.77352i	−0.223197	+	0.0924513i
$369$	0.165005	−	0.398357i	0.00858981	−	0.0207376i
$370$			17.5873i			0.914322i
$371$		0			0
$372$	−6.94451	+	6.94451i	−0.360056	+	0.360056i
$373$	20.3560			1.05399			0.526997	−	0.849867i	$-0.323318\pi$
$373$	20.3560			1.05399			0.526997	+	0.849867i	$0.323318\pi$
$374$	−2.87997	−	4.29894i	−0.148920	−	0.222293i
$375$	−6.07798			−0.313865
$376$	−18.1008	+	18.1008i	−0.933479	+	0.933479i
$377$	−10.3165	−	4.27324i	−0.531327	−	0.220083i
$378$		0			0
$379$	−8.93729	+	21.5765i	−0.459078	+	1.10831i	0.509693	+	0.860356i	$0.329759\pi$
$379$	−8.93729	+	21.5765i	−0.459078	+	1.10831i	−0.968771	+	0.247956i	$0.920241\pi$
$380$	15.4569	−	6.40246i	0.792922	−	0.328439i
$381$	−6.70608	−	16.1899i	−0.343563	−	0.829434i
$382$	−2.60131	−	2.60131i	−0.133094	−	0.133094i
$383$	25.2521	+	25.2521i	1.29032	+	1.29032i	0.934586	+	0.355739i	$0.115771\pi$
$383$	25.2521	+	25.2521i	1.29032	+	1.29032i	0.355739	+	0.934586i	$0.384229\pi$
$384$	−0.439252	−	1.06045i	−0.0224155	−	0.0541158i
$385$		0			0
$386$	7.99969	−	19.3130i	0.407174	−	0.983004i
$387$			6.33165i			0.321856i
$388$	11.4972	+	4.76228i	0.583680	+	0.241768i
$389$	6.78956	−	6.78956i	0.344244	−	0.344244i	−0.513716	−	0.857960i	$-0.671732\pi$
$389$	6.78956	−	6.78956i	0.344244	−	0.344244i	0.857960	+	0.513716i	$0.171732\pi$
$390$	32.8322			1.66252
$391$	−2.47172	+	12.5051i	−0.125000	+	0.632409i
$392$		0			0
$393$	−1.83293	+	1.83293i	−0.0924591	+	0.0924591i
$394$	19.9236	+	8.25262i	1.00374	+	0.415761i
$395$		−	4.91218i		−	0.247159i
$396$	0.238190	−	0.575042i	0.0119695	−	0.0288969i
$397$	24.4139	−	10.1126i	1.22530	−	0.507535i	0.326208	−	0.945298i	$-0.394229\pi$
$397$	24.4139	−	10.1126i	1.22530	−	0.507535i	0.899091	+	0.437762i	$0.144229\pi$
$398$	−5.00247	−	12.0770i	−0.250751	−	0.605367i
$399$		0			0
$400$	−6.54522	−	6.54522i	−0.327261	−	0.327261i
$401$	−4.05059	−	9.77900i	−0.202277	−	0.488340i	0.789892	−	0.613247i	$-0.210137\pi$
$401$	−4.05059	−	9.77900i	−0.202277	−	0.488340i	−0.992168	+	0.124907i	$0.960137\pi$
$402$	−0.330794	+	0.137019i	−0.0164985	+	0.00683391i
$403$	−16.6520	+	40.2016i	−0.829497	+	2.00258i
$404$		−	6.07421i		−	0.302203i
$405$	−21.0606	−	8.72359i	−1.04651	−	0.433479i
$406$		0			0
$407$	−5.84871			−0.289910
$408$	19.0958	+	3.77443i	0.945382	+	0.186862i
$409$	34.3416			1.69809			0.849043	−	0.528324i	$-0.177180\pi$
$409$	34.3416			1.69809			0.849043	+	0.528324i	$0.177180\pi$
$410$	1.79011	−	1.79011i	0.0884074	−	0.0884074i
$411$	26.5556	+	10.9997i	1.30989	+	0.542575i
$412$		−	12.5895i		−	0.620238i
$413$		0			0
$414$	1.83587	−	0.760443i	0.0902282	−	0.0373737i
$415$	5.79984	+	14.0020i	0.284703	+	0.687333i
$416$	−19.0411	−	19.0411i	−0.933567	−	0.933567i
$417$	−12.2783	−	12.2783i	−0.601272	−	0.601272i
$418$	−2.75935	−	6.66166i	−0.134964	−	0.325832i
$419$	11.4115	−	4.72680i	0.557488	−	0.230919i	−0.0861061	−	0.996286i	$-0.527442\pi$
$419$	11.4115	−	4.72680i	0.557488	−	0.230919i	0.643594	+	0.765367i	$0.277442\pi$
$420$		0			0
$421$			7.76019i			0.378208i	0.981957	+	0.189104i	$0.0605584\pi$
$421$			7.76019i			0.378208i	−0.981957	+	0.189104i	$0.939442\pi$
$422$	16.9039	+	7.00183i	0.822870	+	0.340844i
$423$	3.58950	−	3.58950i	0.174528	−	0.174528i
$424$	−25.9687			−1.26115
$425$	−24.9643	+	4.99705i	−1.21095	+	0.242393i
$426$	17.8877			0.866663
$427$		0			0
$428$	−3.22322	−	1.33510i	−0.155800	−	0.0645346i
$429$			10.9184i			0.527145i
$430$	−14.2264	+	34.3456i	−0.686058	+	1.65629i
$431$	19.3785	−	8.02683i	0.933429	−	0.386639i	0.136451	−	0.990647i	$-0.456430\pi$
$431$	19.3785	−	8.02683i	0.933429	−	0.386639i	0.796978	+	0.604008i	$0.206430\pi$
$432$	−3.20044	−	7.72654i	−0.153981	−	0.371743i
$433$	24.3129	+	24.3129i	1.16840	+	1.16840i	0.982584	+	0.185821i	$0.0594944\pi$
$433$	24.3129	+	24.3129i	1.16840	+	1.16840i	0.185821	+	0.982584i	$0.440506\pi$
$434$		0			0
$435$	3.70123	+	8.93556i	0.177460	+	0.428427i
$436$	−7.75916	+	3.21395i	−0.371596	+	0.153920i
$437$	−6.79750	+	16.4106i	−0.325168	+	0.785026i
$438$			7.89545i			0.377259i
$439$	5.34646	+	2.21458i	0.255173	+	0.105696i	0.506603	−	0.862179i	$-0.330901\pi$
$439$	5.34646	+	2.21458i	0.255173	+	0.105696i	−0.251430	+	0.967875i	$0.580901\pi$
$440$	8.51713	−	8.51713i	0.406038	−	0.406038i
$441$		0			0
$442$	25.6575	−	5.13580i	1.22040	−	0.244285i
$443$	16.4947			0.783688			0.391844	−	0.920032i	$-0.371837\pi$
$443$	16.4947			0.783688			0.391844	+	0.920032i	$0.371837\pi$
$444$	4.72012	−	4.72012i	0.224007	−	0.224007i
$445$	16.0770	+	6.65929i	0.762121	+	0.315681i
$446$		−	18.0488i		−	0.854637i
$447$	−7.61103	+	18.3746i	−0.359989	+	0.869091i
$448$		0			0
$449$	−3.21268	−	7.75610i	−0.151616	−	0.366033i	0.829763	−	0.558116i	$-0.188476\pi$
$449$	−3.21268	−	7.75610i	−0.151616	−	0.366033i	−0.981379	+	0.192083i	$0.938476\pi$
$450$	2.80643	+	2.80643i	0.132296	+	0.132296i
$451$	0.595306	+	0.595306i	0.0280319	+	0.0280319i
$452$	−6.00305	−	14.4927i	−0.282360	−	0.681677i
$453$	−21.9596	+	9.09595i	−1.03175	+	0.427365i
$454$	−7.31759	+	17.6662i	−0.343432	+	0.829117i
$455$		0			0
$456$	25.0597	+	10.3801i	1.17353	+	0.486091i
$457$	21.9015	−	21.9015i	1.02451	−	1.02451i	0.0248176	−	0.999692i	$-0.492100\pi$
$457$	21.9015	−	21.9015i	1.02451	−	1.02451i	0.999692	−	0.0248176i	$-0.00790049\pi$
$458$	12.6630			0.591704
$459$	−22.5662	−	4.46038i	−1.05330	−	0.208193i
$460$	−9.00255			−0.419746
$461$	9.54950	−	9.54950i	0.444765	−	0.444765i	−0.448845	−	0.893610i	$-0.648164\pi$
$461$	9.54950	−	9.54950i	0.444765	−	0.444765i	0.893610	+	0.448845i	$0.148164\pi$
$462$		0			0
$463$		−	40.2240i		−	1.86937i	−0.355483	−	0.934683i	$-0.615683\pi$
$463$		−	40.2240i		−	1.86937i	0.355483	−	0.934683i	$-0.384317\pi$
$464$	−1.07246	+	2.58914i	−0.0497876	+	0.120198i
$465$	34.8203	−	14.4230i	1.61475	−	0.668852i
$466$	2.69424	+	6.50448i	0.124808	+	0.301314i
$467$	−29.2264	−	29.2264i	−1.35243	−	1.35243i	−0.882930	−	0.469505i	$-0.844432\pi$
$467$	−29.2264	−	29.2264i	−1.35243	−	1.35243i	−0.469505	−	0.882930i	$-0.655568\pi$
$468$	2.22561	+	2.22561i	0.102879	+	0.102879i
$469$		0			0
$470$	27.5362	−	11.4058i	1.27015	−	0.526113i
$471$	5.98817	−	14.4567i	0.275920	−	0.666130i
$472$			2.00816i			0.0924332i
$473$	−11.4217	−	4.73102i	−0.525170	−	0.217533i
$474$	1.70855	−	1.70855i	0.0784763	−	0.0784763i
$475$	−35.4774			−1.62781
$476$		0			0
$477$	5.14974			0.235790
$478$	8.61672	−	8.61672i	0.394120	−	0.394120i
$479$	15.4187	+	6.38663i	0.704498	+	0.291812i	0.706026	−	0.708186i	$-0.250486\pi$
$479$	15.4187	+	6.38663i	0.704498	+	0.291812i	−0.00152798	+	0.999999i	$0.500486\pi$
$480$			23.3236i			1.06457i
$481$	11.3182	−	27.3246i	0.516067	−	1.24590i
$482$	−5.21028	+	2.15817i	−0.237322	+	0.0983018i
$483$		0			0
$484$	−5.91611	−	5.91611i	−0.268914	−	0.268914i
$485$	−33.7692	−	33.7692i	−1.53338	−	1.53338i
$486$	2.51426	+	6.06996i	0.114049	+	0.275339i
$487$	−11.3931	+	4.71920i	−0.516273	+	0.213847i	−0.625579	−	0.780161i	$-0.715137\pi$
$487$	−11.3931	+	4.71920i	−0.516273	+	0.213847i	0.109306	+	0.994008i	$0.465137\pi$
$488$	11.5768	−	27.9488i	0.524057	−	1.26518i
$489$		−	9.28540i		−	0.419900i
$490$		0			0
$491$	1.78951	−	1.78951i	0.0807596	−	0.0807596i	−0.665573	−	0.746333i	$-0.731813\pi$
$491$	1.78951	−	1.78951i	0.0807596	−	0.0807596i	0.746333	+	0.665573i	$0.231813\pi$
$492$	−0.960867			−0.0433192
$493$	4.29017	+	6.40395i	0.193220	+	0.288419i
$494$	36.4625			1.64052
$495$	−1.68900	+	1.68900i	−0.0759148	+	0.0759148i
$496$	10.0894	+	4.17918i	0.453028	+	0.187651i
$497$		0			0
$498$	−2.85288	+	6.88747i	−0.127841	+	0.308635i
$499$	−5.05279	+	2.09293i	−0.226194	+	0.0936926i	−0.492902	−	0.870085i	$-0.664064\pi$
$499$	−5.05279	+	2.09293i	−0.226194	+	0.0936926i	0.266708	+	0.963777i	$0.414064\pi$
$500$	−1.30919	−	3.16065i	−0.0585485	−	0.141349i
$501$	−17.5112	−	17.5112i	−0.782345	−	0.782345i
$502$	−2.74256	−	2.74256i	−0.122406	−	0.122406i
$503$	13.6811	+	33.0291i	0.610010	+	1.47269i	0.862989	+	0.505222i	$0.168590\pi$
$503$	13.6811	+	33.0291i	0.610010	+	1.47269i	−0.252979	+	0.967472i	$0.581410\pi$
$504$		0			0
$505$	−8.92050	+	21.5360i	−0.396957	+	0.958339i
$506$			3.87994i			0.172485i
$507$	−32.4225	−	13.4298i	−1.43993	−	0.596440i
$508$	6.97456	−	6.97456i	0.309446	−	0.309446i
$509$	−13.8568			−0.614191			−0.307095	−	0.951679i	$-0.599357\pi$
$509$	−13.8568			−0.614191			−0.307095	+	0.951679i	$0.599357\pi$
$510$	−18.8595	−	12.5686i	−0.835113	−	0.556547i
$511$		0			0
$512$	−11.2458	+	11.2458i	−0.496998	+	0.496998i
$513$	−29.6140	−	12.2665i	−1.30749	−	0.541580i
$514$		−	0.00674911i		−	0.000297690i
$515$	−18.4887	+	44.6357i	−0.814710	+	1.96688i
$516$	13.0358	−	5.39961i	0.573870	−	0.237705i
$517$	3.79304	+	9.15720i	0.166818	+	0.402733i
$518$		0			0
$519$	14.4734	+	14.4734i	0.635311	+	0.635311i
$520$	23.3092	+	56.2733i	1.02218	+	2.46775i
$521$	25.2750	−	10.4692i	1.10732	−	0.458665i	0.247303	−	0.968938i	$-0.420456\pi$
$521$	25.2750	−	10.4692i	1.10732	−	0.458665i	0.860013	+	0.510273i	$0.170456\pi$
$522$	0.459844	−	1.11016i	0.0201268	−	0.0485904i
$523$			0.249143i			0.0108943i	0.999985	+	0.00544713i	$0.00173388\pi$
$523$			0.249143i			0.0108943i	−0.999985	+	0.00544713i	$0.998266\pi$
$524$	−1.34796	−	0.558345i	−0.0588861	−	0.0243914i
$525$		0			0
$526$	−24.9771			−1.08905
$527$	24.9550	−	16.7180i	1.08706	−	0.728248i
$528$	2.74020			0.119252
$529$	−9.50491	+	9.50491i	−0.413257	+	0.413257i
$530$	27.9344	+	11.5708i	1.21339	+	0.502604i
$531$		−	0.398231i		−	0.0172817i
$532$		0			0
$533$	−3.93323	+	1.62920i	−0.170367	+	0.0705684i
$534$	3.27564	+	7.90810i	0.141751	+	0.342217i
$535$	9.46717	+	9.46717i	0.409302	+	0.409302i
$536$	−0.469694	−	0.469694i	−0.0202877	−	0.0202877i
$537$	−11.6675	−	28.1678i	−0.503490	−	1.21553i
$538$	19.8861	−	8.23711i	0.857352	−	0.355127i
$539$		0			0
$540$		−	16.2457i		−	0.699102i
$541$	−38.2921	−	15.8611i	−1.64631	−	0.681922i	−0.649394	−	0.760452i	$-0.724977\pi$
$541$	−38.2921	−	15.8611i	−1.64631	−	0.681922i	−0.996912	+	0.0785296i	$0.974977\pi$
$542$	8.96453	−	8.96453i	0.385060	−	0.385060i
$543$	18.3083			0.785683
$544$	3.64842	+	18.2268i	0.156425	+	0.781468i
$545$	32.2299			1.38058
$546$		0			0
$547$	5.21042	+	2.15822i	0.222781	+	0.0922790i	0.491282	−	0.871000i	$-0.336528\pi$
$547$	5.21042	+	2.15822i	0.222781	+	0.0922790i	−0.268501	+	0.963279i	$0.586528\pi$
$548$			16.1787i			0.691120i
$549$	−2.29575	+	5.54243i	−0.0979801	+	0.236545i
$550$	−7.15950	+	2.96556i	−0.305282	+	0.126452i
$551$	4.11048	+	9.92358i	0.175112	+	0.422759i
$552$	−10.3206	−	10.3206i	−0.439273	−	0.439273i
$553$		0			0
$554$	−1.35649	−	3.27487i	−0.0576319	−	0.139136i
$555$	−23.6670	+	9.80319i	−1.00461	+	0.416122i
$556$	3.74021	−	9.02966i	0.158620	−	0.382943i
$557$			1.10102i			0.0466518i	0.999728	+	0.0233259i	$0.00742554\pi$
$557$			1.10102i			0.0466518i	−0.999728	+	0.0233259i	$0.992574\pi$
$558$	−4.32610	−	1.79193i	−0.183138	−	0.0758584i
$559$	44.2058	−	44.2058i	1.86971	−	1.86971i
$560$		0			0
$561$	4.17972	−	6.27177i	0.176468	−	0.264794i
$562$	20.1754			0.851049
$563$	25.9637	−	25.9637i	1.09424	−	1.09424i	0.0991671	−	0.995071i	$-0.468382\pi$
$563$	25.9637	−	25.9637i	1.09424	−	1.09424i	0.995071	−	0.0991671i	$-0.0316178\pi$
$564$	−10.4513	−	4.32907i	−0.440080	−	0.182287i
$565$			60.1995i			2.53261i
$566$	−5.24563	+	12.6641i	−0.220490	+	0.532310i
$567$		0			0
$568$	12.6994	+	30.6590i	0.532854	+	1.28642i
$569$	4.93826	+	4.93826i	0.207023	+	0.207023i	0.803001	−	0.595978i	$-0.203236\pi$
$569$	4.93826	+	4.93826i	0.207023	+	0.207023i	−0.595978	+	0.803001i	$0.703236\pi$
$570$	−22.3316	−	22.3316i	−0.935368	−	0.935368i
$571$	11.2022	+	27.0445i	0.468798	+	1.13178i	0.964689	+	0.263393i	$0.0848417\pi$
$571$	11.2022	+	27.0445i	0.468798	+	1.13178i	−0.495891	+	0.868385i	$0.665158\pi$
$572$	−5.67776	+	2.35180i	−0.237399	+	0.0983339i
$573$	2.05057	−	4.95051i	0.0856637	−	0.206810i
$574$		0			0
$575$	17.6370	+	7.30549i	0.735515	+	0.304660i
$576$	3.33147	−	3.33147i	0.138811	−	0.138811i
$577$	−27.1610			−1.13073			−0.565363	−	0.824842i	$-0.691264\pi$
$577$	−27.1610			−1.13073			−0.565363	+	0.824842i	$0.691264\pi$
$578$	−16.7043	−	6.87193i	−0.694806	−	0.285835i
$579$	30.4482			1.26538
$580$	−3.84941	+	3.84941i	−0.159838	+	0.159838i
$581$		0			0
$582$		−	23.4911i		−	0.973738i
$583$	−3.84790	+	9.28964i	−0.159364	+	0.384738i
$584$	−13.5326	+	5.60537i	−0.559981	+	0.231952i
$585$	−4.62235	−	11.1593i	−0.191111	−	0.461382i
$586$	−13.7633	−	13.7633i	−0.568555	−	0.568555i
$587$	−13.6303	−	13.6303i	−0.562583	−	0.562583i	0.367457	−	0.930040i	$-0.380228\pi$
$587$	−13.6303	−	13.6303i	−0.562583	−	0.562583i	−0.930040	+	0.367457i	$0.880228\pi$
$588$		0			0
$589$	38.6704	−	16.0178i	1.59339	−	0.660002i
$590$	0.894774	−	2.16018i	0.0368373	−	0.0889330i
$591$			31.4109i			1.29207i
$592$	−6.85768	−	2.84055i	−0.281849	−	0.116746i
$593$	8.95712	−	8.95712i	0.367825	−	0.367825i	−0.498859	−	0.866683i	$-0.666247\pi$
$593$	8.95712	−	8.95712i	0.367825	−	0.367825i	0.866683	+	0.498859i	$0.166247\pi$
$594$	−7.00161			−0.287279
$595$		0			0
$596$	−11.1945			−0.458546
$597$	13.4635	−	13.4635i	0.551024	−	0.551024i
$598$	−18.1267	−	7.50835i	−0.741258	−	0.307039i
$599$		−	3.65708i		−	0.149424i	−0.997205	−	0.0747121i	$-0.976196\pi$
$599$		−	3.65708i		−	0.149424i	0.997205	−	0.0747121i	$-0.0238038\pi$
$600$	11.1558	−	26.9325i	0.455433	−	1.09951i
$601$	32.0376	−	13.2704i	1.30684	−	0.541311i	0.382879	−	0.923798i	$-0.374933\pi$
$601$	32.0376	−	13.2704i	1.30684	−	0.541311i	0.923961	+	0.382488i	$0.124933\pi$
$602$		0			0
$603$	0.0931432	+	0.0931432i	0.00379309	+	0.00379309i
$604$	−9.46010	−	9.46010i	−0.384926	−	0.384926i
$605$	12.2871	+	29.6638i	0.499543	+	1.20600i
$606$	−10.5933	+	4.38791i	−0.430325	+	0.178246i
$607$	−18.0206	+	43.5056i	−0.731434	+	1.76584i	−0.0936744	+	0.995603i	$0.529861\pi$
$607$	−18.0206	+	43.5056i	−0.731434	+	1.76584i	−0.637760	+	0.770235i	$0.720139\pi$
$608$			25.9025i			1.05049i
$609$		0			0
$610$	−24.9062	+	24.9062i	−1.00842	+	1.00842i
$611$	−50.1218			−2.02771
$612$	−0.426443	−	2.13043i	−0.0172379	−	0.0861175i
$613$	10.7713			0.435050			0.217525	−	0.976055i	$-0.430202\pi$
$613$	10.7713			0.435050			0.217525	+	0.976055i	$0.430202\pi$
$614$	−9.06491	+	9.06491i	−0.365830	+	0.365830i
$615$	3.40674	+	1.41112i	0.137373	+	0.0569017i
$616$		0			0
$617$	−12.3579	+	29.8345i	−0.497509	+	1.20109i	0.453312	+	0.891352i	$0.350242\pi$
$617$	−12.3579	+	29.8345i	−0.497509	+	1.20109i	−0.950821	+	0.309741i	$0.899758\pi$
$618$	−21.9558	+	9.09441i	−0.883194	+	0.365831i
$619$	8.21258	+	19.8269i	0.330091	+	0.796911i	0.998584	+	0.0531927i	$0.0169397\pi$
$619$	8.21258	+	19.8269i	0.330091	+	0.796911i	−0.668493	+	0.743719i	$0.733060\pi$
$620$	15.0004	+	15.0004i	0.602432	+	0.602432i
$621$	12.1962	+	12.1962i	0.489417	+	0.489417i
$622$	−1.02478	−	2.47405i	−0.0410901	−	0.0992003i
$623$		0			0
$624$	−5.30275	+	12.8020i	−0.212280	+	0.512489i
$625$		−	17.7455i		−	0.709821i
$626$	−15.8950	−	6.58391i	−0.635291	−	0.263146i
$627$	7.42642	−	7.42642i	0.296583	−	0.296583i
$628$	8.80759			0.351461
$629$	−16.9617	+	11.3631i	−0.676306	+	0.453075i
$630$		0			0
$631$	−0.150152	+	0.150152i	−0.00597747	+	0.00597747i	−0.710089	−	0.704112i	$-0.751345\pi$
$631$	−0.150152	+	0.150152i	−0.00597747	+	0.00597747i	0.704112	+	0.710089i	$0.251345\pi$
$632$	4.14139	+	1.71542i	0.164736	+	0.0682357i
$633$			26.6502i			1.05925i
$634$	11.5159	−	27.8017i	0.457353	−	1.10415i
$635$	−34.9709	+	14.4854i	−1.38778	+	0.574837i
$636$	−4.39169	−	10.6025i	−0.174142	−	0.420415i
$637$		0			0
$638$	1.65903	+	1.65903i	0.0656816	+	0.0656816i
$639$	−2.51836	−	6.07987i	−0.0996249	−	0.240516i
$640$	−2.29061	+	0.948804i	−0.0905445	+	0.0375048i
$641$	−2.65088	+	6.39979i	−0.104703	+	0.252776i	−0.967545	−	0.252697i	$-0.918682\pi$
$641$	−2.65088	+	6.39979i	−0.104703	+	0.252776i	0.862842	+	0.505474i	$0.168682\pi$
$642$			6.58572i			0.259918i
$643$	15.3394	+	6.35378i	0.604926	+	0.250569i	0.664058	−	0.747681i	$-0.268833\pi$
$643$	15.3394	+	6.35378i	0.604926	+	0.250569i	−0.0591311	+	0.998250i	$0.518833\pi$
$644$		0			0
$645$	−54.1481			−2.13208
$646$	−20.9448	−	13.9583i	−0.824063	−	0.549184i
$647$	−34.7700			−1.36695			−0.683474	−	0.729975i	$-0.739532\pi$
$647$	−34.7700			−1.36695			−0.683474	+	0.729975i	$0.739532\pi$
$648$	14.7095	−	14.7095i	0.577842	−	0.577842i
$649$	0.718371	+	0.297559i	0.0281985	+	0.0116802i
$650$		−	39.1874i		−	1.53706i
$651$		0			0
$652$	4.82857	−	2.00006i	0.189101	−	0.0783283i
$653$	10.8461	+	26.1849i	0.424442	+	1.02469i	0.981021	+	0.193900i	$0.0621137\pi$
$653$	10.8461	+	26.1849i	0.424442	+	1.02469i	−0.556579	+	0.830795i	$0.687886\pi$
$654$	11.2102	+	11.2102i	0.438353	+	0.438353i
$655$	3.95921	+	3.95921i	0.154699	+	0.154699i
$656$	0.408881	+	0.987127i	0.0159641	+	0.0385408i
$657$	2.68359	−	1.11158i	0.104697	−	0.0433668i
$658$		0			0
$659$			32.9709i			1.28436i	0.766553	+	0.642181i	$0.221970\pi$
$659$			32.9709i			1.28436i	−0.766553	+	0.642181i	$0.778030\pi$
$660$	4.91774	+	2.03700i	0.191423	+	0.0792900i
$661$	6.78323	−	6.78323i	0.263837	−	0.263837i	−0.562774	−	0.826611i	$-0.690266\pi$
$661$	6.78323	−	6.78323i	0.263837	−	0.263837i	0.826611	+	0.562774i	$0.190266\pi$
$662$	1.26598			0.0492036
$663$	21.2127	+	31.6642i	0.823832	+	1.22973i
$664$	−13.8303			−0.536720
$665$		0			0
$666$	2.94041	+	1.21796i	0.113938	+	0.0471948i
$667$		−	5.77978i		−	0.223794i
$668$	5.33426	−	12.8780i	0.206389	−	0.498267i
$669$	24.2880	−	10.0604i	0.939029	−	0.388959i
$670$	0.295968	+	0.714530i	0.0114342	+	0.0276047i
$671$	−8.28262	−	8.28262i	−0.319747	−	0.319747i
$672$		0			0
$673$	−14.7065	−	35.5046i	−0.566893	−	1.36860i	−0.904161	−	0.427192i	$-0.859503\pi$
$673$	−14.7065	−	35.5046i	−0.566893	−	1.36860i	0.337268	−	0.941409i	$-0.390497\pi$
$674$	−20.1146	+	8.33173i	−0.774785	+	0.320926i
$675$	−13.1832	+	31.8271i	−0.507423	+	1.22503i
$676$		−	19.7530i		−	0.759731i
$677$	−14.5836	−	6.04073i	−0.560493	−	0.232164i	0.0844060	−	0.996431i	$-0.473101\pi$
$677$	−14.5836	−	6.04073i	−0.560493	−	0.232164i	−0.644899	+	0.764267i	$0.723101\pi$
$678$	−20.9385	+	20.9385i	−0.804138	+	0.804138i
$679$		0			0
$680$	8.15292	−	41.2477i	0.312650	−	1.58178i
$681$	−27.8520			−1.06729
$682$	6.46494	−	6.46494i	0.247555	−	0.247555i
$683$	6.58471	+	2.72747i	0.251957	+	0.104364i	0.505087	−	0.863068i	$-0.331460\pi$
$683$	6.58471	+	2.72747i	0.251957	+	0.104364i	−0.253131	+	0.967432i	$0.581460\pi$
$684$		−	3.02760i		−	0.115763i
$685$	23.7598	−	57.3613i	0.907816	−	2.19166i
$686$		0			0
$687$	7.05837	+	17.0404i	0.269294	+	0.650133i
$688$	−11.0944	−	11.0944i	−0.422969	−	0.422969i
$689$	−35.9540	−	35.9540i	−1.36974	−	1.36974i
$690$	6.50329	+	15.7003i	0.247576	+	0.597701i
$691$	11.8920	−	4.92584i	0.452394	−	0.187388i	−0.144839	−	0.989455i	$-0.546267\pi$
$691$	11.8920	−	4.92584i	0.452394	−	0.187388i	0.597233	+	0.802067i	$0.296267\pi$
$692$	−4.40887	+	10.6439i	−0.167600	+	0.404622i
$693$		0			0
$694$	−1.65264	−	0.684547i	−0.0627335	−	0.0259851i
$695$	−26.5217	+	26.5217i	−1.00603	+	1.00603i
$696$	−8.82597			−0.334547
$697$	2.88301	+	0.569850i	0.109202	+	0.0215846i
$698$	−22.7793			−0.862209
$699$	−7.25119	+	7.25119i	−0.274265	+	0.274265i
$700$		0			0
$701$			19.9283i			0.752681i	0.926481	+	0.376341i	$0.122818\pi$
$701$			19.9283i			0.752681i	−0.926481	+	0.376341i	$0.877182\pi$
$702$	13.5493	−	32.7109i	0.511385	−	1.23459i
$703$	−26.2839	+	10.8871i	−0.991316	+	0.410616i
$704$	3.52037	+	8.49893i	0.132679	+	0.320315i
$705$	30.6973	+	30.6973i	1.15613	+	1.15613i
$706$	−6.43763	−	6.43763i	−0.242284	−	0.242284i
$707$		0			0
$708$	−0.819892	+	0.339610i	−0.0308134	+	0.0127633i
$709$	5.27752	−	12.7411i	0.198201	−	0.478500i	−0.793263	−	0.608879i	$-0.791619\pi$
$709$	5.27752	−	12.7411i	0.198201	−	0.478500i	0.991464	+	0.130379i	$0.0416194\pi$
$710$		−	38.6382i		−	1.45007i
$711$	−0.821262	−	0.340178i	−0.0307997	−	0.0127577i
$712$	−11.2287	+	11.2287i	−0.420813	+	0.420813i
$713$	−22.5228			−0.843484
$714$		0			0
$715$	23.5842			0.882000
$716$	12.1346	−	12.1346i	0.453491	−	0.453491i
$717$	16.3983	+	6.79242i	0.612407	+	0.253667i
$718$		−	25.0143i		−	0.933526i
$719$	9.72891	−	23.4877i	0.362827	−	0.875942i	−0.632057	−	0.774922i	$-0.717789\pi$
$719$	9.72891	−	23.4877i	0.362827	−	0.875942i	0.994884	−	0.101020i	$-0.0322107\pi$
$720$	−2.80067	+	1.16008i	−0.104375	+	0.0432335i
$721$		0			0
$722$	−10.5261	−	10.5261i	−0.391740	−	0.391740i
$723$	−5.80842	−	5.80842i	−0.216018	−	0.216018i
$724$	3.94357	+	9.52062i	0.146562	+	0.353831i
$725$	10.6652	−	4.41767i	0.396095	−	0.164068i
$726$	−6.04392	+	14.5913i	−0.224311	+	0.541535i
$727$			14.9272i			0.553620i	0.960925	+	0.276810i	$0.0892773\pi$
$727$			14.9272i			0.553620i	−0.960925	+	0.276810i	$0.910723\pi$
$728$		0			0
$729$	−21.2326	+	21.2326i	−0.786391	+	0.786391i
$730$	17.0545			0.631216
$731$	−42.3154	+	8.47017i	−1.56509	+	0.313280i
$732$	13.3687			0.494123
$733$	8.49036	−	8.49036i	0.313598	−	0.313598i	−0.532704	−	0.846302i	$-0.678824\pi$
$733$	8.49036	−	8.49036i	0.313598	−	0.313598i	0.846302	+	0.532704i	$0.178824\pi$
$734$	6.83111	+	2.82954i	0.252141	+	0.104440i
$735$		0			0
$736$	5.33385	−	12.8770i	0.196608	−	0.474654i
$737$	−0.237618	+	0.0984248i	−0.00875279	+	0.00362552i
$738$	−0.175318	−	0.423256i	−0.00645356	−	0.0155803i
$739$	−0.248006	−	0.248006i	−0.00912306	−	0.00912306i	0.702531	−	0.711654i	$-0.252053\pi$
$739$	−0.248006	−	0.248006i	−0.00912306	−	0.00912306i	−0.711654	+	0.702531i	$0.752053\pi$
$740$	−10.1957	−	10.1957i	−0.374800	−	0.374800i
$741$	20.3242	+	49.0669i	0.746628	+	1.80252i
$742$		0			0
$743$	16.4359	−	39.6797i	0.602974	−	1.45571i	−0.267532	−	0.963549i	$-0.586208\pi$
$743$	16.4359	−	39.6797i	0.602974	−	1.45571i	0.870505	−	0.492159i	$-0.163792\pi$
$744$			34.3932i			1.26092i
$745$	39.6900	+	16.4402i	1.45413	+	0.602321i
$746$	15.2936	−	15.2936i	0.559937	−	0.559937i
$747$	2.74263			0.100348
$748$	4.16173	+	0.822598i	0.152168	+	0.0300772i
$749$		0			0
$750$	−4.56641	+	4.56641i	−0.166742	+	0.166742i
$751$	−23.8166	−	9.86515i	−0.869079	−	0.359984i	−0.0968275	−	0.995301i	$-0.530870\pi$
$751$	−23.8166	−	9.86515i	−0.869079	−	0.359984i	−0.772252	+	0.635317i	$0.780870\pi$
$752$			12.5791i			0.458713i
$753$	2.16191	−	5.21932i	0.0787844	−	0.190202i
$754$	−10.9613	+	4.54033i	−0.399188	+	0.165349i
$755$	19.6476	+	47.4336i	0.715051	+	1.72629i
$756$		0			0
$757$	−14.8435	−	14.8435i	−0.539496	−	0.539496i	0.383885	−	0.923381i	$-0.374586\pi$
$757$	−14.8435	−	14.8435i	−0.539496	−	0.539496i	−0.923381	+	0.383885i	$0.874586\pi$
$758$	9.49591	+	22.9252i	0.344907	+	0.832679i
$759$	−5.22118	+	2.16268i	−0.189517	+	0.0785004i
$760$	22.4214	−	54.1300i	0.813309	−	1.96350i
$761$			1.80316i			0.0653645i	0.999466	+	0.0326823i	$0.0104049\pi$
$761$			1.80316i			0.0653645i	−0.999466	+	0.0326823i	$0.989595\pi$
$762$	−17.2018	−	7.12524i	−0.623157	−	0.258120i
$763$		0			0
$764$	3.01604			0.109116
$765$	−1.61677	+	8.17967i	−0.0584546	+	0.295736i
$766$	37.9441			1.37097
$767$	−2.78034	+	2.78034i	−0.100392	+	0.100392i
$768$	−23.3978	−	9.69169i	−0.844296	−	0.349719i
$769$			40.8880i			1.47446i	0.675642	+	0.737229i	$0.263866\pi$
$769$			40.8880i			1.47446i	−0.675642	+	0.737229i	$0.736134\pi$
$770$		0			0
$771$	0.00908216	−	0.00376196i	0.000327086	−	0.000135484i
$772$	6.55848	+	15.8336i	0.236045	+	0.569863i
$773$	−6.89146	−	6.89146i	−0.247869	−	0.247869i	0.572227	−	0.820095i	$-0.306080\pi$
$773$	−6.89146	−	6.89146i	−0.247869	−	0.247869i	−0.820095	+	0.572227i	$0.806080\pi$
$774$	4.75699	+	4.75699i	0.170987	+	0.170987i
$775$	−17.2149	−	41.5603i	−0.618376	−	1.49289i
$776$	40.2631	−	16.6775i	1.44536	−	0.598687i
$777$		0			0
$778$		−	10.2020i		−	0.365761i
$779$	3.78343	+	1.56715i	0.135555	+	0.0561489i
$780$	−19.0333	+	19.0333i	−0.681502	+	0.681502i
$781$	12.8492			0.459782
$782$	7.53810	+	11.2521i	0.269562	+	0.402375i
$783$	10.4300			0.372737
$784$		0			0
$785$	−31.2271	−	12.9347i	−1.11454	−	0.461659i
$786$			2.75417i			0.0982381i
$787$	13.6326	−	32.9121i	0.485951	−	1.17319i	−0.470790	−	0.882245i	$-0.656031\pi$
$787$	13.6326	−	32.9121i	0.485951	−	1.17319i	0.956740	−	0.290943i	$-0.0939691\pi$
$788$	−16.3342	+	6.76584i	−0.581881	+	0.241023i
$789$	−13.9222	−	33.6112i	−0.495644	−	1.19659i
$790$	−3.69054	−	3.69054i	−0.131304	−	0.131304i
$791$		0			0
$792$	−0.834142	−	2.01380i	−0.0296399	−	0.0715571i
$793$	54.7239	−	22.6674i	1.94330	−	0.804943i
$794$	10.7446	−	25.9399i	0.381313	−	0.920572i
$795$			44.0404i			1.56195i
$796$	9.90126	+	4.10124i	0.350941	+	0.145364i
$797$	−26.8604	+	26.8604i	−0.951444	+	0.951444i	−0.998875	−	0.0474303i	$-0.984897\pi$
$797$	−26.8604	+	26.8604i	−0.951444	+	0.951444i	0.0474303	+	0.998875i	$0.484897\pi$
$798$		0			0
$799$	28.7910	+	19.1873i	1.01855	+	0.678799i
$800$	27.8383			0.984233
$801$	2.22672	−	2.22672i	0.0786772	−	0.0786772i
$802$	−10.3902	−	4.30377i	−0.366892	−	0.151971i
$803$			5.67151i			0.200143i
$804$	0.112334	−	0.271199i	0.00396172	−	0.00956445i
$805$		0			0
$806$	17.6929	+	42.7143i	0.623204	+	1.50455i
$807$	22.1691	+	22.1691i	0.780388	+	0.780388i
$808$	−15.0415	−	15.0415i	−0.529157	−	0.529157i
$809$	15.9979	+	38.6223i	0.562455	+	1.35789i	0.907797	+	0.419410i	$0.137763\pi$
$809$	15.9979	+	38.6223i	0.562455	+	1.35789i	−0.345341	+	0.938477i	$0.612237\pi$
$810$	−22.3770	+	9.26885i	−0.786247	+	0.325674i
$811$	−4.06581	+	9.81573i	−0.142770	+	0.344677i	−0.979048	−	0.203628i	$-0.934727\pi$
$811$	−4.06581	+	9.81573i	−0.142770	+	0.344677i	0.836278	+	0.548305i	$0.184727\pi$
$812$		0			0
$813$	17.0603	+	7.06659i	0.598329	+	0.247836i
$814$	−4.39415	+	4.39415i	−0.154015	+	0.154015i
$815$	−20.0569			−0.702561
$816$	7.94679	−	5.32376i	0.278193	−	0.186369i
$817$	−60.1353			−2.10387
$818$	25.8010	−	25.8010i	0.902111	−	0.902111i
$819$		0			0
$820$			2.07551i			0.0724801i
$821$	−2.47092	+	5.96533i	−0.0862357	+	0.208191i	−0.961114	−	0.276151i	$-0.910941\pi$
$821$	−2.47092	+	5.96533i	−0.0862357	+	0.208191i	0.874879	+	0.484342i	$0.160941\pi$
$822$	28.2154	−	11.6872i	0.984127	−	0.407639i
$823$	−12.5241	−	30.2359i	−0.436564	−	1.05396i	−0.977127	−	0.212655i	$-0.931789\pi$
$823$	−12.5241	−	30.2359i	−0.436564	−	1.05396i	0.540563	−	0.841303i	$-0.318211\pi$
$824$	−31.1751	−	31.1751i	−1.08604	−	1.08604i
$825$	−7.98142	−	7.98142i	−0.277877	−	0.277877i
$826$		0			0
$827$	−9.49557	+	3.93319i	−0.330193	+	0.136771i	−0.541620	−	0.840623i	$-0.682189\pi$
$827$	−9.49557	+	3.93319i	−0.330193	+	0.136771i	0.211427	+	0.977394i	$0.432189\pi$
$828$	−0.623443	+	1.50512i	−0.0216661	+	0.0523067i
$829$			3.85523i			0.133898i	0.997756	+	0.0669488i	$0.0213264\pi$
$829$			3.85523i			0.133898i	−0.997756	+	0.0669488i	$0.978674\pi$
$830$	14.8772	+	6.16235i	0.516396	+	0.213898i
$831$	3.65083	−	3.65083i	0.126646	−	0.126646i
$832$	−46.5187			−1.61275
$833$		0			0
$834$	−18.4495			−0.638853
$835$	−37.8251	+	37.8251i	−1.30899	+	1.30899i
$836$	5.46151	+	2.26223i	0.188890	+	0.0782409i
$837$		−	40.6438i		−	1.40485i
$838$	5.02224	−	12.1248i	0.173490	−	0.418843i
$839$	−39.4592	+	16.3445i	−1.36228	+	0.564275i	−0.939685	−	0.342042i	$-0.888881\pi$
$839$	−39.4592	+	16.3445i	−1.36228	+	0.564275i	−0.422597	+	0.906318i	$0.638881\pi$
$840$		0			0
$841$	18.0347	+	18.0347i	0.621887	+	0.621887i
$842$	5.83026	+	5.83026i	0.200924	+	0.200924i
$843$	11.2458	+	27.1497i	0.387326	+	0.935087i
$844$	−13.8585	+	5.74040i	−0.477031	+	0.197593i
$845$	−29.0090	+	70.0340i	−0.997940	+	2.40924i
$846$		−	5.39361i		−	0.185436i
$847$		0			0
$848$	−9.02342	+	9.02342i	−0.309865	+	0.309865i
$849$	−19.9657			−0.685222
$850$	−15.0015	+	22.5101i	−0.514547	+	0.772090i
$851$	15.3085			0.524769
$852$	−10.3698	+	10.3698i	−0.355263	+	0.355263i
$853$	−17.8998	−	7.41435i	−0.612878	−	0.253862i	0.0545805	−	0.998509i	$-0.482618\pi$
$853$	−17.8998	−	7.41435i	−0.612878	−	0.253862i	−0.667458	+	0.744647i	$0.732618\pi$
$854$		0			0
$855$	−4.44630	+	10.7343i	−0.152060	+	0.367106i
$856$	−11.2877	+	4.67553i	−0.385807	+	0.159806i
$857$	9.18093	+	22.1647i	0.313615	+	0.757133i	0.999565	+	0.0294846i	$0.00938659\pi$
$857$	9.18093	+	22.1647i	0.313615	+	0.757133i	−0.685951	+	0.727648i	$0.740613\pi$
$858$	8.20304	+	8.20304i	0.280047	+	0.280047i
$859$	−24.9778	−	24.9778i	−0.852232	−	0.852232i	0.138175	−	0.990408i	$-0.455876\pi$
$859$	−24.9778	−	24.9778i	−0.852232	−	0.852232i	−0.990408	+	0.138175i	$0.955876\pi$
$860$	−11.6634	−	28.1579i	−0.397719	−	0.960178i
$861$		0			0
$862$	8.52854	−	20.5897i	0.290483	−	0.701289i
$863$		−	7.21550i		−	0.245619i	−0.992430	−	0.122809i	$-0.960810\pi$
$863$		−	7.21550i		−	0.245619i	0.992430	−	0.122809i	$-0.0391903\pi$
$864$	23.2375	+	9.62527i	0.790554	+	0.327458i
$865$	31.2631	−	31.2631i	1.06298	−	1.06298i
$866$	36.5328			1.24143
$867$	−0.0635230	−	26.3091i	−0.00215735	−	0.893504i
$868$		0			0
$869$	1.22730	−	1.22730i	0.0416332	−	0.0416332i
$870$	9.49407	+	3.93257i	0.321879	+	0.133327i
$871$		−	1.30060i		−	0.0440691i
$872$	−11.2552	+	27.1726i	−0.381151	+	0.920179i
$873$	−7.98441	+	3.30725i	−0.270231	+	0.111933i
$874$	7.22237	+	17.4363i	0.244300	+	0.589793i
$875$		0			0
$876$	−4.57711	−	4.57711i	−0.154646	−	0.154646i
$877$	−2.41316	−	5.82588i	−0.0814866	−	0.196726i	0.877885	−	0.478871i	$-0.158954\pi$
$877$	−2.41316	−	5.82588i	−0.0814866	−	0.196726i	−0.959372	+	0.282145i	$0.908954\pi$
$878$	5.68064	−	2.35300i	0.191712	−	0.0794098i
$879$	10.8493	−	26.1926i	0.365939	−	0.883455i
$880$		−	5.91895i		−	0.199528i
$881$	11.7401	+	4.86291i	0.395534	+	0.163836i	0.571580	−	0.820546i	$-0.306331\pi$
$881$	11.7401	+	4.86291i	0.395534	+	0.163836i	−0.176046	+	0.984382i	$0.556331\pi$
$882$		0			0
$883$	−18.0560			−0.607631			−0.303816	−	0.952731i	$-0.598261\pi$
$883$	−18.0560			−0.607631			−0.303816	+	0.952731i	$0.598261\pi$
$884$	−11.8968	+	17.8514i	−0.400131	+	0.600406i
$885$	3.40566			0.114480
$886$	12.3925	−	12.3925i	0.416336	−	0.416336i
$887$	10.8090	+	4.47725i	0.362932	+	0.150331i	0.556695	−	0.830717i	$-0.312069\pi$
$887$	10.8090	+	4.47725i	0.362932	+	0.150331i	−0.193763	+	0.981048i	$0.562069\pi$
$888$		−	23.3767i		−	0.784471i
$889$		0			0
$890$	17.0818	−	7.07553i	0.572584	−	0.237172i
$891$	−3.08238	−	7.44152i	−0.103264	−	0.249300i
$892$	10.4632	+	10.4632i	0.350334	+	0.350334i
$893$	34.0916	+	34.0916i	1.14083	+	1.14083i
$894$	8.08675	+	19.5231i	0.270461	+	0.652951i
$895$	−60.8437	+	25.2023i	−2.03378	+	0.842420i
$896$		0			0
$897$		−	28.5780i		−	0.954192i
$898$	−8.24089	−	3.41349i	−0.275002	−	0.113910i
$899$	−9.63053	+	9.63053i	−0.321196	+	0.321196i
$900$	−3.25386			−0.108462
$901$	6.88907	+	34.4165i	0.229508	+	1.14658i
$902$	0.894512			0.0297840
$903$		0			0
$904$	−50.7533	−	21.0227i	−1.68803	−	0.699204i
$905$		−	39.5467i		−	1.31458i
$906$	−9.66448	+	23.3321i	−0.321081	+	0.775158i
$907$	6.34566	−	2.62846i	0.210704	−	0.0872765i	−0.274835	−	0.961491i	$-0.588623\pi$
$907$	6.34566	−	2.62846i	0.210704	−	0.0872765i	0.485539	+	0.874215i	$0.338623\pi$
$908$	−5.99927	−	14.4835i	−0.199093	−	0.480652i
$909$	2.98282	+	2.98282i	0.0989338	+	0.0989338i
$910$		0			0
$911$	0.598738	+	1.44548i	0.0198371	+	0.0478909i	0.933488	−	0.358609i	$-0.116749\pi$
$911$	0.598738	+	1.44548i	0.0198371	+	0.0478909i	−0.913651	+	0.406500i	$0.866749\pi$
$912$	12.3144	−	5.10078i	0.407770	−	0.168904i
$913$	−2.04930	+	4.94745i	−0.0678220	+	0.163737i
$914$		−	32.9094i		−	1.08855i
$915$	−47.3987	−	19.6332i	−1.56695	−	0.649053i
$916$	−7.34095	+	7.34095i	−0.242552	+	0.242552i
$917$		0			0
$918$	−20.3052	+	13.6030i	−0.670171	+	0.448965i
$919$	34.4075			1.13500			0.567500	−	0.823373i	$-0.307911\pi$
$919$	34.4075			1.13500			0.567500	+	0.823373i	$0.307911\pi$
$920$	−22.2929	+	22.2929i	−0.734975	+	0.734975i
$921$	−17.2513	−	7.14572i	−0.568449	−	0.235459i
$922$		−	14.3492i		−	0.472564i
$923$	−24.8654	+	60.0304i	−0.818455	+	1.97593i
$924$		0			0
$925$	11.7008	+	28.2482i	0.384719	+	0.928794i
$926$	−30.2204	−	30.2204i	−0.993104	−	0.993104i
$927$	6.18221	+	6.18221i	0.203050	+	0.203050i
$928$	−3.22540	−	7.78682i	−0.105879	−	0.255615i
$929$	15.3249	−	6.34779i	0.502794	−	0.208264i	−0.116846	−	0.993150i	$-0.537278\pi$
$929$	15.3249	−	6.34779i	0.502794	−	0.208264i	0.619640	+	0.784886i	$0.287278\pi$
$930$	15.3245	−	36.9967i	0.502511	−	1.21317i
$931$		0			0
$932$	−5.33264	−	2.20885i	−0.174676	−	0.0723534i
$933$	2.75807	−	2.75807i	0.0902952	−	0.0902952i
$934$	−43.9158			−1.43697
$935$	−13.5473	−	9.02837i	−0.443044	−	0.295259i
$936$	11.0225			0.360281
$937$	−1.46176	+	1.46176i	−0.0477536	+	0.0477536i	−0.730580	−	0.682827i	$-0.760750\pi$
$937$	−1.46176	+	1.46176i	−0.0477536	+	0.0477536i	0.682827	+	0.730580i	$0.260750\pi$
$938$		0			0
$939$		−	25.0595i		−	0.817785i
$940$	−9.35099	+	22.5753i	−0.304996	+	0.736325i
$941$	24.2662	−	10.0514i	0.791055	−	0.327666i	0.0496872	−	0.998765i	$-0.484178\pi$
$941$	24.2662	−	10.0514i	0.791055	−	0.327666i	0.741368	+	0.671099i	$0.234178\pi$
$942$	−6.36245	−	15.3603i	−0.207300	−	0.500466i
$943$	−1.55816	−	1.55816i	−0.0507408	−	0.0507408i
$944$	0.697783	+	0.697783i	0.0227109	+	0.0227109i
$945$		0			0
$946$	−12.1356	+	5.02673i	−0.394562	+	0.163433i
$947$	−15.6097	+	37.6851i	−0.507246	+	1.22460i	0.438216	+	0.898870i	$0.355610\pi$
$947$	−15.6097	+	37.6851i	−0.507246	+	1.22460i	−0.945462	+	0.325731i	$0.894390\pi$
$948$			1.98095i			0.0643381i
$949$	−26.4968	−	10.9753i	−0.860122	−	0.356274i
$950$	−26.6543	+	26.6543i	−0.864779	+	0.864779i
$951$	43.8313			1.42133
$952$		0			0
$953$	21.4906			0.696149			0.348075	−	0.937467i	$-0.386836\pi$
$953$	21.4906			0.696149			0.348075	+	0.937467i	$0.386836\pi$
$954$	3.86902	−	3.86902i	0.125264	−	0.125264i
$955$	−10.6933	−	4.42931i	−0.346027	−	0.143329i
$956$			9.99050i			0.323116i
$957$	−1.30778	+	3.15727i	−0.0422747	+	0.102060i
$958$	16.3824	−	6.78582i	0.529292	−	0.219240i
$959$		0			0
$960$	28.4906	+	28.4906i	0.919530	+	0.919530i
$961$	15.6081	+	15.6081i	0.503488	+	0.503488i
$962$	−12.0257	−	29.0325i	−0.387723	−	0.936046i
$963$	2.23842	−	0.927186i	0.0721322	−	0.0298781i
$964$	1.76936	−	4.27160i	0.0569871	−	0.137579i
$965$		−	65.7694i		−	2.11719i
$966$		0			0
$967$	12.9847	−	12.9847i	0.417561	−	0.417561i	−0.466801	−	0.884362i	$-0.654594\pi$
$967$	12.9847	−	12.9847i	0.417561	−	0.417561i	0.884362	+	0.466801i	$0.154594\pi$
$968$	−29.3000			−0.941737
$969$	7.10886	−	35.9655i	0.228369	−	1.15538i
$970$	−50.7418			−1.62922
$971$	11.1517	−	11.1517i	0.357874	−	0.357874i	−0.505155	−	0.863029i	$-0.668565\pi$
$971$	11.1517	−	11.1517i	0.357874	−	0.357874i	0.863029	+	0.505155i	$0.168565\pi$
$972$	−4.97640	−	2.06129i	−0.159618	−	0.0661160i
$973$		0			0
$974$	−5.01416	+	12.1053i	−0.160664	+	0.387878i
$975$	52.7339	−	21.8431i	1.68883	−	0.699538i
$976$	−5.68885	−	13.7341i	−0.182096	−	0.439618i
$977$	12.0422	+	12.0422i	0.385263	+	0.385263i	0.872994	−	0.487731i	$-0.162175\pi$
$977$	12.0422	+	12.0422i	0.385263	+	0.385263i	−0.487731	+	0.872994i	$0.662175\pi$
$978$	−6.97615	−	6.97615i	−0.223073	−	0.223073i
$979$	2.35298	+	5.68060i	0.0752016	+	0.181553i
$980$		0			0
$981$	2.23198	−	5.38848i	0.0712617	−	0.172041i
$982$		−	2.68894i		−	0.0858074i
$983$	−42.0109	−	17.4015i	−1.33994	−	0.555022i	−0.406467	−	0.913666i	$-0.633239\pi$
$983$	−42.0109	−	17.4015i	−1.33994	−	0.555022i	−0.933474	+	0.358644i	$0.883239\pi$
$984$	−2.37938	+	2.37938i	−0.0758519	+	0.0758519i
$985$	67.8488			2.16184
$986$	8.03453	+	1.58809i	0.255872	+	0.0505750i
$987$		0			0
$988$	−21.1379	+	21.1379i	−0.672485	+	0.672485i
$989$	29.8953	+	12.3831i	0.950617	+	0.393758i
$990$			2.53790i			0.0806598i
$991$	6.48321	−	15.6518i	0.205946	−	0.497197i	−0.786832	−	0.617168i	$-0.788280\pi$
$991$	6.48321	−	15.6518i	0.205946	−	0.497197i	0.992777	+	0.119970i	$0.0382800\pi$
$992$	−30.3438	+	12.5688i	−0.963417	+	0.399060i
$993$	0.705656	+	1.70360i	0.0223933	+	0.0540622i
$994$		0			0
$995$	−29.0817	−	29.0817i	−0.921953	−	0.921953i
$996$	−2.33891	−	5.64663i	−0.0741113	−	0.178920i
$997$	14.2656	−	5.90900i	0.451796	−	0.187140i	−0.145170	−	0.989407i	$-0.546373\pi$
$997$	14.2656	−	5.90900i	0.451796	−	0.187140i	0.596966	+	0.802267i	$0.296373\pi$
$998$	−2.22375	+	5.36861i	−0.0703916	+	0.169940i
$999$			27.6252i			0.874022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.l.e.638.7	yes	40
7.2	even	3		833.2.v.g.655.4		80
7.3	odd	6		833.2.v.h.128.7		80
7.4	even	3		833.2.v.g.128.7		80
7.5	odd	6		833.2.v.h.655.4		80
7.6	odd	2		833.2.l.d.638.7	yes	40
17.2	even	8	inner	833.2.l.e.393.7	yes	40
119.2	even	24		833.2.v.g.410.7		80
119.19	odd	24		833.2.v.h.410.7		80
119.53	even	24		833.2.v.g.716.4		80
119.87	odd	24		833.2.v.h.716.4		80
119.104	odd	8		833.2.l.d.393.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.l.d.393.7	✓	40	119.104	odd	8
833.2.l.d.638.7	yes	40	7.6	odd	2
833.2.l.e.393.7	yes	40	17.2	even	8	inner
833.2.l.e.638.7	yes	40	1.1	even	1	trivial
833.2.v.g.128.7		80	7.4	even	3
833.2.v.g.410.7		80	119.2	even	24
833.2.v.g.655.4		80	7.2	even	3
833.2.v.g.716.4		80	119.53	even	24
833.2.v.h.128.7		80	7.3	odd	6
833.2.v.h.410.7		80	119.19	odd	24
833.2.v.h.655.4		80	7.5	odd	6
833.2.v.h.716.4		80	119.87	odd	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.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.751304 - 0.751304i) q^{2} +(1.42979 + 0.592240i) q^{3} +0.871085i q^{4} +(1.27926 - 3.08842i) q^{5} +(1.51916 - 0.629258i) q^{6} +(2.15706 + 2.15706i) q^{8} +(-0.427757 - 0.427757i) q^{9} +(-1.35922 - 3.28146i) q^{10} +(1.09126 - 0.452013i) q^{11} +(-0.515892 + 1.24547i) q^{12} +5.97297i q^{13} +(3.65817 - 3.65817i) q^{15} +1.49904 q^{16} +(2.28653 - 3.43100i) q^{17} -0.642752 q^{18} +(4.06266 - 4.06266i) q^{19} +(2.69028 + 1.11435i) q^{20} +(0.480265 - 1.15946i) q^{22} +(-2.85627 + 1.18311i) q^{23} +(1.80665 + 4.36164i) q^{24} +(-4.36627 - 4.36627i) q^{25} +(4.48751 + 4.48751i) q^{26} +(-2.13499 - 5.15432i) q^{27} +(-0.715430 + 1.72720i) q^{29} -5.49679i q^{30} +(6.73059 + 2.78790i) q^{31} +(-3.18788 + 3.18788i) q^{32} +1.82797 q^{33} +(-0.859841 - 4.29561i) q^{34} +(0.372613 - 0.372613i) q^{36} +(-4.57472 - 1.89491i) q^{37} -6.10458i q^{38} +(-3.53743 + 8.54011i) q^{39} +(9.42134 - 3.90245i) q^{40} +(0.272762 + 0.658506i) q^{41} +(-7.40098 - 7.40098i) q^{43} +(0.393742 + 0.950576i) q^{44} +(-1.86831 + 0.773879i) q^{45} +(-1.25705 + 3.03480i) q^{46} +8.39144i q^{47} +(2.14332 + 0.887792i) q^{48} -6.56080 q^{50} +(5.30125 - 3.55145i) q^{51} -5.20296 q^{52} +(-6.01946 + 6.01946i) q^{53} +(-5.47649 - 2.26844i) q^{54} -3.94850i q^{55} +(8.21484 - 3.40270i) q^{57} +(0.760147 + 1.83516i) q^{58} +(0.465487 + 0.465487i) q^{59} +(3.18658 + 3.18658i) q^{60} +(-3.79500 - 9.16194i) q^{61} +(7.15128 - 2.96216i) q^{62} +7.78821i q^{64} +(18.4470 + 7.64100i) q^{65} +(1.37336 - 1.37336i) q^{66} -0.217748 q^{67} +(2.98869 + 1.99177i) q^{68} -4.78456 q^{69} +(10.0504 + 4.16299i) q^{71} -1.84539i q^{72} +(-1.83750 + 4.43612i) q^{73} +(-4.86065 + 2.01335i) q^{74} +(-3.65699 - 8.82876i) q^{75} +(3.53892 + 3.53892i) q^{76} +(3.75853 + 9.07390i) q^{78} +(1.35759 - 0.562333i) q^{79} +(1.91767 - 4.62966i) q^{80} -6.81923i q^{81} +(0.699665 + 0.289811i) q^{82} +(-3.20583 + 3.20583i) q^{83} +(-7.67128 - 11.4509i) q^{85} -11.1208 q^{86} +(-2.04584 + 2.04584i) q^{87} +(3.32892 + 1.37888i) q^{88} +5.20556i q^{89} +(-0.822249 + 1.98509i) q^{90} +(-1.03059 - 2.48806i) q^{92} +(7.97225 + 7.97225i) q^{93} +(6.30452 + 6.30452i) q^{94} +(-7.34998 - 17.7444i) q^{95} +(-6.44600 + 2.67002i) q^{96} +(5.46707 - 13.1987i) q^{97} +(-0.660144 - 0.273441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} + 8 q^{5} + 12 q^{6} + 20 q^{10} - 12 q^{12} - 8 q^{15} - 64 q^{16} - 16 q^{17} + 24 q^{18} - 8 q^{19} - 20 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{27} + 8 q^{29} + 36 q^{31} + 72 q^{33} - 8 q^{34}+ \cdots - 16 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 + 8 * q^5 + 12 * q^6 + 20 * q^10 - 12 * q^12 - 8 * q^15 - 64 * q^16 - 16 * q^17 + 24 * q^18 - 8 * q^19 - 20 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^27 + 8 * q^29 + 36 * q^31 + 72 * q^33 - 8 * q^34 - 16 * q^37 + 8 * q^39 - 80 * q^40 + 16 * q^41 - 32 * q^43 + 32 * q^44 + 36 * q^45 + 64 * q^46 - 112 * q^48 - 96 * q^50 + 8 * q^51 - 112 * q^52 + 100 * q^54 - 16 * q^57 + 80 * q^58 - 72 * q^60 - 96 * q^61 + 80 * q^62 - 8 * q^65 - 32 * q^67 + 116 * q^68 + 48 * q^69 - 16 * q^71 - 16 * q^73 - 80 * q^74 + 48 * q^75 + 16 * q^76 - 32 * q^78 - 16 * q^79 + 84 * q^80 + 40 * q^82 + 8 * q^83 + 16 * q^85 + 120 * q^86 + 48 * q^87 + 48 * q^88 + 72 * q^90 + 136 * q^92 - 16 * q^93 - 16 * q^94 + 16 * q^95 - 220 * q^96 - 8 * q^97 - 16 * q^99

Introduction

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