LMFDB - Embedded newform 804.2.j.a.499.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.4
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35015 - 0.420832i) q^{2} -1.00000 q^{3} +(1.64580 + 1.13637i) q^{4} +2.13147i q^{5} +(1.35015 + 0.420832i) q^{6} +(-1.61812 + 2.80266i) q^{7} +(-1.74385 - 2.22688i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.35015 - 0.420832i) q^{2} -1.00000 q^{3} +(1.64580 + 1.13637i) q^{4} +2.13147i q^{5} +(1.35015 + 0.420832i) q^{6} +(-1.61812 + 2.80266i) q^{7} +(-1.74385 - 2.22688i) q^{8} +1.00000 q^{9} +(0.896992 - 2.87780i) q^{10} +(-2.69894 + 4.67470i) q^{11} +(-1.64580 - 1.13637i) q^{12} +(-1.11569 + 0.644144i) q^{13} +(3.36415 - 3.10305i) q^{14} -2.13147i q^{15} +(1.41732 + 3.74048i) q^{16} +(-1.68388 - 2.91657i) q^{17} +(-1.35015 - 0.420832i) q^{18} +(-0.0433640 + 0.0250362i) q^{19} +(-2.42214 + 3.50798i) q^{20} +(1.61812 - 2.80266i) q^{21} +(5.61124 - 5.17574i) q^{22} +(-5.65931 + 3.26740i) q^{23} +(1.74385 + 2.22688i) q^{24} +0.456822 q^{25} +(1.77742 - 0.400172i) q^{26} -1.00000 q^{27} +(-5.84796 + 2.77384i) q^{28} +(4.08277 - 7.07157i) q^{29} +(-0.896992 + 2.87780i) q^{30} +(4.07249 - 7.05376i) q^{31} +(-0.339481 - 5.64666i) q^{32} +(2.69894 - 4.67470i) q^{33} +(1.04610 + 4.64643i) q^{34} +(-5.97380 - 3.44897i) q^{35} +(1.64580 + 1.13637i) q^{36} +(0.830470 + 1.43842i) q^{37} +(0.0690839 - 0.0155537i) q^{38} +(1.11569 - 0.644144i) q^{39} +(4.74652 - 3.71698i) q^{40} +(-3.04104 - 1.75575i) q^{41} +(-3.36415 + 3.10305i) q^{42} +8.31453 q^{43} +(-9.75412 + 4.62663i) q^{44} +2.13147i q^{45} +(9.01593 - 2.02986i) q^{46} +(-5.22962 - 3.01932i) q^{47} +(-1.41732 - 3.74048i) q^{48} +(-1.73661 - 3.00789i) q^{49} +(-0.616777 - 0.192245i) q^{50} +(1.68388 + 2.91657i) q^{51} +(-2.56819 - 0.207705i) q^{52} +8.31744i q^{53} +(1.35015 + 0.420832i) q^{54} +(-9.96401 - 5.75272i) q^{55} +(9.06294 - 1.28409i) q^{56} +(0.0433640 - 0.0250362i) q^{57} +(-8.48829 + 7.82951i) q^{58} -7.42326i q^{59} +(2.42214 - 3.50798i) q^{60} +(-2.02872 + 1.17128i) q^{61} +(-8.46692 + 7.80979i) q^{62} +(-1.61812 + 2.80266i) q^{63} +(-1.91795 + 7.76669i) q^{64} +(-1.37298 - 2.37806i) q^{65} +(-5.61124 + 5.17574i) q^{66} +(-5.29310 - 6.24365i) q^{67} +(0.542969 - 6.71360i) q^{68} +(5.65931 - 3.26740i) q^{69} +(6.61408 + 7.17059i) q^{70} +(-0.526176 - 0.303788i) q^{71} +(-1.74385 - 2.22688i) q^{72} +(-1.17825 - 2.04079i) q^{73} +(-0.515926 - 2.29156i) q^{74} -0.456822 q^{75} +(-0.0998190 - 0.00807297i) q^{76} +(-8.73441 - 15.1284i) q^{77} +(-1.77742 + 0.400172i) q^{78} +(-4.08552 + 7.07632i) q^{79} +(-7.97274 + 3.02098i) q^{80} +1.00000 q^{81} +(3.36698 + 3.65028i) q^{82} +(-11.8514 + 6.84241i) q^{83} +(5.84796 - 2.77384i) q^{84} +(6.21658 - 3.58914i) q^{85} +(-11.2258 - 3.49902i) q^{86} +(-4.08277 + 7.07157i) q^{87} +(15.1165 - 2.14180i) q^{88} -7.96321 q^{89} +(0.896992 - 2.87780i) q^{90} -4.16920i q^{91} +(-13.0271 - 1.05358i) q^{92} +(-4.07249 + 7.05376i) q^{93} +(5.79014 + 6.27733i) q^{94} +(-0.0533641 - 0.0924293i) q^{95} +(0.339481 + 5.64666i) q^{96} +(-10.9547 + 6.32468i) q^{97} +(1.07886 + 4.79192i) q^{98} +(-2.69894 + 4.67470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.35015	−	0.420832i	−0.954699	−	0.297573i
$2$	−1.35015	−	0.420832i	−0.954699	−	0.297573i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.64580	+	1.13637i	0.822900	+	0.568186i
$5$			2.13147i			0.953224i	0.879114	+	0.476612i	$0.158135\pi$
$5$			2.13147i			0.953224i	−0.879114	+	0.476612i	$0.841865\pi$
$6$	1.35015	+	0.420832i	0.551196	+	0.171804i
$7$	−1.61812	+	2.80266i	−0.611591	+	1.05931i	0.379381	+	0.925240i	$0.376137\pi$
$7$	−1.61812	+	2.80266i	−0.611591	+	1.05931i	−0.990972	+	0.134066i	$0.957197\pi$
$8$	−1.74385	−	2.22688i	−0.616546	−	0.787319i
$9$	1.00000			0.333333
$10$	0.896992	−	2.87780i	0.283654	−	0.910042i
$11$	−2.69894	+	4.67470i	−0.813762	+	1.40948i	0.0964523	+	0.995338i	$0.469250\pi$
$11$	−2.69894	+	4.67470i	−0.813762	+	1.40948i	−0.910214	+	0.414139i	$0.864083\pi$
$12$	−1.64580	−	1.13637i	−0.475102	−	0.328042i
$13$	−1.11569	+	0.644144i	−0.309437	+	0.178653i	−0.646674	−	0.762766i	$-0.723841\pi$
$13$	−1.11569	+	0.644144i	−0.309437	+	0.178653i	0.337238	+	0.941420i	$0.390507\pi$
$14$	3.36415	−	3.10305i	0.899106	−	0.829326i
$15$		−	2.13147i		−	0.550344i
$16$	1.41732	+	3.74048i	0.354330	+	0.935120i
$17$	−1.68388	−	2.91657i	−0.408401	−	0.707371i	0.586310	−	0.810087i	$-0.300580\pi$
$17$	−1.68388	−	2.91657i	−0.408401	−	0.707371i	−0.994711	+	0.102716i	$0.967247\pi$
$18$	−1.35015	−	0.420832i	−0.318233	−	0.0991910i
$19$	−0.0433640	+	0.0250362i	−0.00994839	+	0.00574371i	−0.504966	−	0.863139i	$-0.668495\pi$
$19$	−0.0433640	+	0.0250362i	−0.00994839	+	0.00574371i	0.495018	+	0.868883i	$0.335162\pi$
$20$	−2.42214	+	3.50798i	−0.541608	+	0.784408i
$21$	1.61812	−	2.80266i	0.353102	−	0.611591i
$22$	5.61124	−	5.17574i	1.19632	−	1.10347i
$23$	−5.65931	+	3.26740i	−1.18005	+	0.681300i	−0.956025	−	0.293284i	$-0.905252\pi$
$23$	−5.65931	+	3.26740i	−1.18005	+	0.681300i	−0.224021	+	0.974584i	$0.571919\pi$
$24$	1.74385	+	2.22688i	0.355963	+	0.454559i
$25$	0.456822			0.0913644
$26$	1.77742	−	0.400172i	0.348581	−	0.0784802i
$27$	−1.00000			−0.192450
$28$	−5.84796	+	2.77384i	−1.10516	+	0.524207i
$29$	4.08277	−	7.07157i	0.758152	−	1.31316i	−0.185640	−	0.982618i	$-0.559436\pi$
$29$	4.08277	−	7.07157i	0.758152	−	1.31316i	0.943792	−	0.330540i	$-0.107231\pi$
$30$	−0.896992	+	2.87780i	−0.163768	+	0.525413i
$31$	4.07249	−	7.05376i	0.731441	−	1.26689i	−0.224826	−	0.974399i	$-0.572181\pi$
$31$	4.07249	−	7.05376i	0.731441	−	1.26689i	0.956267	−	0.292494i	$-0.0944852\pi$
$32$	−0.339481	−	5.64666i	−0.0600123	−	0.998198i
$33$	2.69894	−	4.67470i	0.469825	−	0.813762i
$34$	1.04610	+	4.64643i	0.179405	+	0.796856i
$35$	−5.97380	−	3.44897i	−1.00976	−	0.582983i
$36$	1.64580	+	1.13637i	0.274300	+	0.189395i
$37$	0.830470	+	1.43842i	0.136529	+	0.236474i	0.926180	−	0.377081i	$-0.123072\pi$
$37$	0.830470	+	1.43842i	0.136529	+	0.236474i	−0.789652	+	0.613555i	$0.789739\pi$
$38$	0.0690839	−	0.0155537i	0.0112069	−	0.00252314i
$39$	1.11569	−	0.644144i	0.178653	−	0.103146i
$40$	4.74652	−	3.71698i	0.750491	−	0.587706i
$41$	−3.04104	−	1.75575i	−0.474931	−	0.274201i	0.243371	−	0.969933i	$-0.421747\pi$
$41$	−3.04104	−	1.75575i	−0.474931	−	0.274201i	−0.718301	+	0.695732i	$0.755080\pi$
$42$	−3.36415	+	3.10305i	−0.519099	+	0.478812i
$43$	8.31453			1.26795			0.633977	−	0.773352i	$-0.281421\pi$
$43$	8.31453			1.26795			0.633977	+	0.773352i	$0.281421\pi$
$44$	−9.75412	+	4.62663i	−1.47049	+	0.697491i
$45$			2.13147i			0.317741i
$46$	9.01593	−	2.02986i	1.32933	−	0.299287i
$47$	−5.22962	−	3.01932i	−0.762819	−	0.440414i	0.0674880	−	0.997720i	$-0.478502\pi$
$47$	−5.22962	−	3.01932i	−0.762819	−	0.440414i	−0.830307	+	0.557306i	$0.811835\pi$
$48$	−1.41732	−	3.74048i	−0.204573	−	0.539892i
$49$	−1.73661	−	3.00789i	−0.248087	−	0.429699i
$50$	−0.616777	−	0.192245i	−0.0872255	−	0.0271876i
$51$	1.68388	+	2.91657i	0.235790	+	0.408401i
$52$	−2.56819	−	0.207705i	−0.356144	−	0.0288035i
$53$			8.31744i			1.14249i	0.820780	+	0.571244i	$0.193539\pi$
$53$			8.31744i			1.14249i	−0.820780	+	0.571244i	$0.806461\pi$
$54$	1.35015	+	0.420832i	0.183732	+	0.0572680i
$55$	−9.96401	−	5.75272i	−1.34355	−	0.775697i
$56$	9.06294	−	1.28409i	1.21109	−	0.171593i
$57$	0.0433640	−	0.0250362i	0.00574371	−	0.00331613i
$58$	−8.48829	+	7.82951i	−1.11457	+	1.02806i
$59$		−	7.42326i		−	0.966426i	−0.875503	−	0.483213i	$-0.839470\pi$
$59$		−	7.42326i		−	0.966426i	0.875503	−	0.483213i	$-0.160530\pi$
$60$	2.42214	−	3.50798i	0.312698	−	0.452878i
$61$	−2.02872	+	1.17128i	−0.259751	+	0.149968i	−0.624221	−	0.781248i	$-0.714584\pi$
$61$	−2.02872	+	1.17128i	−0.259751	+	0.149968i	0.364470	+	0.931215i	$0.381250\pi$
$62$	−8.46692	+	7.80979i	−1.07530	+	0.991844i
$63$	−1.61812	+	2.80266i	−0.203864	+	0.353102i
$64$	−1.91795	+	7.76669i	−0.239743	+	0.970836i
$65$	−1.37298	−	2.37806i	−0.170297	−	0.294962i
$66$	−5.61124	+	5.17574i	−0.690695	+	0.637090i
$67$	−5.29310	−	6.24365i	−0.646655	−	0.762783i
$67$	−5.29310	−	6.24365i	−0.646655	−	0.762783i
$68$	0.542969	−	6.71360i	0.0658447	−	0.814143i
$69$	5.65931	−	3.26740i	0.681300	−	0.393349i
$70$	6.61408	+	7.17059i	0.790533	+	0.857050i
$71$	−0.526176	−	0.303788i	−0.0624457	−	0.0360530i	0.468452	−	0.883489i	$-0.344812\pi$
$71$	−0.526176	−	0.303788i	−0.0624457	−	0.0360530i	−0.530898	+	0.847436i	$0.678145\pi$
$72$	−1.74385	−	2.22688i	−0.205515	−	0.262440i
$73$	−1.17825	−	2.04079i	−0.137904	−	0.238857i	0.788799	−	0.614651i	$-0.210703\pi$
$73$	−1.17825	−	2.04079i	−0.137904	−	0.238857i	−0.926703	+	0.375795i	$0.877370\pi$
$74$	−0.515926	−	2.29156i	−0.0599752	−	0.266389i
$75$	−0.456822			−0.0527493
$76$	−0.0998190	−	0.00807297i	−0.0114500	−	0.000926033i
$77$	−8.73441	−	15.1284i	−0.995378	−	1.72405i
$78$	−1.77742	+	0.400172i	−0.201254	+	0.0453105i
$79$	−4.08552	+	7.07632i	−0.459656	+	0.796148i	−0.998943	−	0.0459743i	$-0.985361\pi$
$79$	−4.08552	+	7.07632i	−0.459656	+	0.796148i	0.539286	+	0.842123i	$0.318694\pi$
$80$	−7.97274	+	3.02098i	−0.891379	+	0.337756i
$81$	1.00000			0.111111
$82$	3.36698	+	3.65028i	0.371821	+	0.403106i
$83$	−11.8514	+	6.84241i	−1.30086	+	0.751052i	−0.980552	−	0.196262i	$-0.937120\pi$
$83$	−11.8514	+	6.84241i	−1.30086	+	0.751052i	−0.320308	+	0.947313i	$0.603786\pi$
$84$	5.84796	−	2.77384i	0.638065	−	0.302651i
$85$	6.21658	−	3.58914i	0.674283	−	0.389297i
$86$	−11.2258	−	3.49902i	−1.21051	−	0.377309i
$87$	−4.08277	+	7.07157i	−0.437719	+	0.758152i
$88$	15.1165	−	2.14180i	1.61143	−	0.228316i
$89$	−7.96321			−0.844099			−0.422049	−	0.906573i	$-0.638689\pi$
$89$	−7.96321			−0.844099			−0.422049	+	0.906573i	$0.638689\pi$
$90$	0.896992	−	2.87780i	0.0945513	−	0.303347i
$91$		−	4.16920i		−	0.437051i
$92$	−13.0271	−	1.05358i	−1.35817	−	0.109843i
$93$	−4.07249	+	7.05376i	−0.422298	+	0.731441i
$94$	5.79014	+	6.27733i	0.597207	+	0.647457i
$95$	−0.0533641	−	0.0924293i	−0.00547504	−	0.00948305i
$96$	0.339481	+	5.64666i	0.0346481	+	0.576310i
$97$	−10.9547	+	6.32468i	−1.11228	+	0.642174i	−0.939418	−	0.342773i	$-0.888634\pi$
$97$	−10.9547	+	6.32468i	−1.11228	+	0.642174i	−0.172859	+	0.984947i	$0.555300\pi$
$98$	1.07886	+	4.79192i	0.108981	+	0.484057i
$99$	−2.69894	+	4.67470i	−0.271254	+	0.469825i
$100$	0.751838	+	0.519119i	0.0751838	+	0.0519119i
$101$	10.4593	+	6.03866i	1.04074	+	0.600869i	0.920042	−	0.391820i	$-0.128155\pi$
$101$	10.4593	+	6.03866i	1.04074	+	0.600869i	0.120694	+	0.992690i	$0.461488\pi$
$102$	−1.04610	−	4.64643i	−0.103580	−	0.460065i
$103$	−10.0101	−	5.77936i	−0.986329	−	0.569457i	−0.0821541	−	0.996620i	$-0.526180\pi$
$103$	−10.0101	−	5.77936i	−0.986329	−	0.569457i	−0.904175	+	0.427162i	$0.859513\pi$
$104$	3.38003	+	1.36121i	0.331439	+	0.133478i
$105$	5.97380	+	3.44897i	0.582983	+	0.336585i
$106$	3.50024	−	11.2298i	0.339974	−	1.09073i
$107$			1.17808i			0.113889i	0.998377	+	0.0569447i	$0.0181359\pi$
$107$			1.17808i			0.113889i	−0.998377	+	0.0569447i	$0.981864\pi$
$108$	−1.64580	−	1.13637i	−0.158367	−	0.109347i
$109$			4.44469i			0.425724i	0.977082	+	0.212862i	$0.0682785\pi$
$109$			4.44469i			0.425724i	−0.977082	+	0.212862i	$0.931722\pi$
$110$	11.0320	+	11.9602i	1.05186	+	1.14036i
$111$	−0.830470	−	1.43842i	−0.0788248	−	0.136529i
$112$	−12.7767	−	2.08026i	−1.20728	−	0.196567i
$113$	−5.19799	−	3.00106i	−0.488986	−	0.282316i	0.235168	−	0.971955i	$-0.424436\pi$
$113$	−5.19799	−	3.00106i	−0.488986	−	0.282316i	−0.724154	+	0.689639i	$0.757769\pi$
$114$	−0.0690839	+	0.0155537i	−0.00647030	+	0.00145673i
$115$	−6.96438	−	12.0627i	−0.649432	−	1.12485i
$116$	14.7554	−	6.99885i	1.37000	−	0.649827i
$117$	−1.11569	+	0.644144i	−0.103146	+	0.0595511i
$118$	−3.12394	+	10.0225i	−0.287582	+	0.922646i
$119$	10.8989			0.999097
$120$	−4.74652	+	3.71698i	−0.433296	+	0.339312i
$121$	−9.06857	−	15.7072i	−0.824416	−	1.42793i
$122$	3.23199	−	0.727655i	0.292611	−	0.0658788i
$123$	3.04104	+	1.75575i	0.274201	+	0.158310i
$124$	14.7182	−	6.98123i	1.32173	−	0.626933i
$125$			11.6311i			1.04031i
$126$	3.36415	−	3.10305i	0.299702	−	0.276442i
$127$	15.9663	+	9.21814i	1.41678	+	0.817978i	0.996014	−	0.0891922i	$-0.0284285\pi$
$127$	15.9663	+	9.21814i	1.41678	+	0.817978i	0.420765	+	0.907170i	$0.361762\pi$
$128$	5.85798	−	9.67905i	0.517777	−	0.855515i
$129$	−8.31453			−0.732053
$130$	0.852956	+	3.78853i	0.0748092	+	0.332276i
$131$		−	2.94657i		−	0.257443i	−0.991681	−	0.128721i	$-0.958913\pi$
$131$		−	2.94657i		−	0.257443i	0.991681	−	0.128721i	$-0.0410873\pi$
$132$	9.75412	−	4.62663i	0.848987	−	0.402697i
$133$		−	0.162046i		−	0.0140512i
$134$	4.51894	+	10.6574i	0.390377	+	0.920655i
$135$		−	2.13147i		−	0.183448i
$136$	−3.55839	+	8.83586i	−0.305129	+	0.757668i
$137$		−	18.0427i		−	1.54149i	−0.637145	−	0.770744i	$-0.719885\pi$
$137$		−	18.0427i		−	1.54149i	0.637145	−	0.770744i	$-0.280115\pi$
$138$	−9.01593	+	2.02986i	−0.767487	+	0.172793i
$139$	20.0223			1.69827			0.849134	−	0.528177i	$-0.177124\pi$
$139$	20.0223			1.69827			0.849134	+	0.528177i	$0.177124\pi$
$140$	−5.91237	−	12.4648i	−0.499686	−	1.05347i
$141$	5.22962	+	3.01932i	0.440414	+	0.254273i
$142$	0.582572	+	0.631591i	0.0488884	+	0.0530019i
$143$		−	6.95403i		−	0.581525i
$144$	1.41732	+	3.74048i	0.118110	+	0.311707i
$145$	15.0729	+	8.70232i	1.25173	+	0.722689i
$146$	0.731984	+	3.25122i	0.0605794	+	0.269073i
$147$	1.73661	+	3.00789i	0.143233	+	0.248087i
$148$	−0.267786	+	3.31107i	−0.0220119	+	0.272168i
$149$	−1.59423			−0.130604			−0.0653021	−	0.997866i	$-0.520801\pi$
$149$	−1.59423			−0.130604			−0.0653021	+	0.997866i	$0.520801\pi$
$150$	0.616777	+	0.192245i	0.0503597	+	0.0156968i
$151$	−5.65842	+	3.26689i	−0.460475	+	0.265856i	−0.712244	−	0.701932i	$-0.752321\pi$
$151$	−5.65842	+	3.26689i	−0.460475	+	0.265856i	0.251769	+	0.967787i	$0.418988\pi$
$152$	0.131373	+	0.0529068i	0.0106558	+	0.00429130i
$153$	−1.68388	−	2.91657i	−0.136134	−	0.235790i
$154$	5.42622	+	24.1014i	0.437257	+	1.94214i
$155$	15.0349	+	8.68041i	1.20763	+	0.697227i
$156$	2.56819	+	0.207705i	0.205620	+	0.0166297i
$157$	−5.32231	−	9.21850i	−0.424766	−	0.735717i	0.571632	−	0.820510i	$-0.306310\pi$
$157$	−5.32231	−	9.21850i	−0.424766	−	0.735717i	−0.996399	+	0.0847932i	$0.972977\pi$
$158$	8.49399	−	7.83477i	0.675746	−	0.623301i
$159$		−	8.31744i		−	0.659616i
$160$	12.0357	−	0.723594i	0.951506	−	0.0572051i
$161$		−	21.1482i		−	1.66671i
$162$	−1.35015	−	0.420832i	−0.106078	−	0.0330637i
$163$	−19.9770	−	11.5337i	−1.56472	−	0.903389i	−0.996769	−	0.0803246i	$-0.974404\pi$
$163$	−19.9770	−	11.5337i	−1.56472	−	0.903389i	−0.567947	−	0.823065i	$-0.692262\pi$
$164$	−3.00977	−	6.34536i	−0.235023	−	0.495489i
$165$	9.96401	+	5.75272i	0.775697	+	0.447849i
$166$	18.8806	−	4.25082i	1.46542	−	0.329927i
$167$	13.6835	+	7.90020i	1.05886	+	0.611335i	0.925118	−	0.379680i	$-0.123966\pi$
$167$	13.6835	+	7.90020i	1.05886	+	0.611335i	0.133746	+	0.991016i	$0.457299\pi$
$168$	−9.06294	+	1.28409i	−0.699221	+	0.0990695i
$169$	−5.67016	+	9.82100i	−0.436166	+	0.755462i
$170$	−9.90373	+	2.22974i	−0.759582	+	0.171013i
$171$	−0.0433640	+	0.0250362i	−0.00331613	+	0.00191457i
$172$	13.6841	+	9.44839i	1.04340	+	0.720433i
$173$	9.77747	+	16.9351i	0.743368	+	1.28755i	0.950954	+	0.309334i	$0.100106\pi$
$173$	9.77747	+	16.9351i	0.743368	+	1.28755i	−0.207586	+	0.978217i	$0.566561\pi$
$174$	8.48829	−	7.82951i	0.643496	−	0.593554i
$175$	−0.739192	+	1.28032i	−0.0558776	+	0.0967829i
$176$	−21.3109	−	3.46978i	−1.60637	−	0.261545i
$177$			7.42326i			0.557966i
$178$	10.7515	+	3.35117i	0.805860	+	0.251181i
$179$	0.0461232			0.00344741			0.00172371	−	0.999999i	$-0.499451\pi$
$179$	0.0461232			0.00344741			0.00172371	+	0.999999i	$0.499451\pi$
$180$	−2.42214	+	3.50798i	−0.180536	+	0.261469i
$181$	3.95910	−	6.85736i	0.294277	−	0.509703i	−0.680539	−	0.732712i	$-0.738254\pi$
$181$	3.95910	−	6.85736i	0.294277	−	0.509703i	0.974817	+	0.223008i	$0.0715877\pi$
$182$	−1.75453	+	5.62904i	−0.130055	+	0.417252i
$183$	2.02872	−	1.17128i	0.149968	−	0.0865838i
$184$	17.1451	+	6.90469i	1.26395	+	0.509021i
$185$	−3.06595	+	1.77013i	−0.225413	+	0.130142i
$186$	8.46692	−	7.80979i	0.620824	−	0.572642i
$187$	18.1788			1.32936
$188$	−5.17585	−	10.9120i	−0.377487	−	0.795839i
$189$	1.61812	−	2.80266i	0.117701	−	0.203864i
$190$	0.0331522	+	0.147251i	0.00240512	+	0.0106827i
$191$	8.76560	+	15.1825i	0.634257	+	1.09856i	0.986672	+	0.162721i	$0.0520271\pi$
$191$	8.76560	+	15.1825i	0.634257	+	1.09856i	−0.352415	+	0.935844i	$0.614640\pi$
$192$	1.91795	−	7.76669i	0.138416	−	0.560513i
$193$	−3.04757			−0.219369			−0.109684	−	0.993966i	$-0.534984\pi$
$193$	−3.04757			−0.219369			−0.109684	+	0.993966i	$0.534984\pi$
$194$	17.4520	−	3.92918i	1.25298	−	0.282099i
$195$	1.37298	+	2.37806i	0.0983208	+	0.170297i
$196$	0.559972	−	6.92383i	0.0399980	−	0.494559i
$197$	−10.3449	−	5.97264i	−0.737045	−	0.425533i	0.0839487	−	0.996470i	$-0.473247\pi$
$197$	−10.3449	−	5.97264i	−0.737045	−	0.425533i	−0.820994	+	0.570937i	$0.806580\pi$
$198$	5.61124	−	5.17574i	0.398773	−	0.367824i
$199$	−11.8484	+	6.84065i	−0.839908	+	0.484921i	−0.857233	−	0.514929i	$-0.827818\pi$
$199$	−11.8484	+	6.84065i	−0.839908	+	0.484921i	0.0173250	+	0.999850i	$0.494485\pi$
$200$	−0.796631	−	1.01729i	−0.0563303	−	0.0719329i
$201$	5.29310	+	6.24365i	0.373346	+	0.440393i
$202$	−11.5803	−	12.5547i	−0.814787	−	0.883344i
$203$	13.2128	+	22.8853i	0.927358	+	1.60623i
$204$	−0.542969	+	6.71360i	−0.0380155	+	0.470046i
$205$	3.74232	−	6.48190i	0.261375	−	0.452715i
$206$	11.0830	+	12.0156i	0.772192	+	0.837165i
$207$	−5.65931	+	3.26740i	−0.393349	+	0.227100i
$208$	−3.99070	−	3.26026i	−0.276705	−	0.226058i
$209$		−	0.270285i		−	0.0186960i
$210$	−6.61408	−	7.17059i	−0.456415	−	0.494818i
$211$	−3.91421	+	2.25987i	−0.269465	+	0.155576i	−0.628645	−	0.777693i	$-0.716390\pi$
$211$	−3.91421	+	2.25987i	−0.269465	+	0.155576i	0.359179	+	0.933269i	$0.383057\pi$
$212$	−9.45170	+	13.6889i	−0.649145	+	0.940154i
$213$	0.526176	+	0.303788i	0.0360530	+	0.0208152i
$214$	0.495775	−	1.59059i	0.0338904	−	0.108730i
$215$			17.7222i			1.20864i
$216$	1.74385	+	2.22688i	0.118654	+	0.151520i
$217$	13.1795	+	22.8276i	0.894685	+	1.54964i
$218$	1.87047	−	6.00099i	0.126684	−	0.406438i
$219$	1.17825	+	2.04079i	0.0796189	+	0.137904i
$220$	−9.86154	−	20.7906i	−0.664865	−	1.40170i
$221$	3.75738	+	2.16932i	0.252748	+	0.145924i
$222$	0.515926	+	2.29156i	0.0346267	+	0.153800i
$223$		−	13.5853i		−	0.909741i	−0.890558	−	0.454870i	$-0.849686\pi$
$223$		−	13.5853i		−	0.909741i	0.890558	−	0.454870i	$-0.150314\pi$
$224$	16.3750	+	8.18551i	1.09410	+	0.546917i
$225$	0.456822			0.0304548
$226$	5.75512	+	6.23936i	0.382825	+	0.415036i
$227$	20.7867	+	12.0012i	1.37966	+	0.796548i	0.992118	−	0.125304i	$-0.0399907\pi$
$227$	20.7867	+	12.0012i	1.37966	+	0.796548i	0.387542	+	0.921852i	$0.373324\pi$
$228$	0.0998190	+	0.00807297i	0.00661068	+	0.000534646i
$229$	−10.4273	+	6.02020i	−0.689055	+	0.397826i	−0.803258	−	0.595631i	$-0.796902\pi$
$229$	−10.4273	+	6.02020i	−0.689055	+	0.397826i	0.114203	+	0.993457i	$0.463569\pi$
$230$	4.32659	+	19.2172i	0.285287	+	1.26715i
$231$	8.73441	+	15.1284i	0.574682	+	0.995378i
$232$	−22.8673	+	3.23996i	−1.50131	+	0.212714i
$233$	−3.93359	−	2.27106i	−0.257698	−	0.148782i	0.365586	−	0.930778i	$-0.380869\pi$
$233$	−3.93359	−	2.27106i	−0.257698	−	0.148782i	−0.623284	+	0.781995i	$0.714202\pi$
$234$	1.77742	−	0.400172i	0.116194	−	0.0261601i
$235$	6.43561	−	11.1468i	0.419813	−	0.727137i
$236$	8.43558	−	12.2172i	0.549109	−	0.795272i
$237$	4.08552	−	7.07632i	0.265383	−	0.459656i
$238$	−14.7151	−	4.58659i	−0.953837	−	0.297304i
$239$	−8.30585	+	14.3862i	−0.537261	+	0.930563i	0.461790	+	0.886990i	$0.347208\pi$
$239$	−8.30585	+	14.3862i	−0.537261	+	0.930563i	−0.999050	+	0.0435733i	$0.986126\pi$
$240$	7.97274	−	3.02098i	0.514638	−	0.195004i
$241$	−4.39549			−0.283139			−0.141569	−	0.989928i	$-0.545215\pi$
$241$	−4.39549			−0.283139			−0.141569	+	0.989928i	$0.545215\pi$
$242$	5.63381	+	25.0234i	0.362155	+	1.60857i
$243$	−1.00000			−0.0641500
$244$	−4.66989	−	0.377682i	−0.298959	−	0.0241786i
$245$	6.41125	−	3.70153i	0.409599	−	0.236482i
$246$	−3.36698	−	3.65028i	−0.214671	−	0.232734i
$247$	0.0322539	−	0.0558654i	0.00205227	−	0.00355463i
$248$	−22.8097	+	3.23180i	−1.44842	+	0.205220i
$249$	11.8514	−	6.84241i	0.751052	−	0.433620i
$250$	4.89473	−	15.7037i	0.309570	−	0.993187i
$251$	−15.4661	−	26.7880i	−0.976210	−	1.69084i	−0.675884	−	0.737008i	$-0.736238\pi$
$251$	−15.4661	−	26.7880i	−0.976210	−	1.69084i	−0.300326	−	0.953837i	$-0.597096\pi$
$252$	−5.84796	+	2.77384i	−0.368387	+	0.174736i
$253$		−	35.2741i		−	2.21766i
$254$	−17.6776	−	19.1650i	−1.10919	−	1.20252i
$255$	−6.21658	+	3.58914i	−0.389297	+	0.224761i
$256$	−11.9824	+	10.6029i	−0.748900	+	0.662683i
$257$	−4.74529	+	8.21908i	−0.296003	+	0.512692i	−0.975218	−	0.221247i	$-0.928987\pi$
$257$	−4.74529	+	8.21908i	−0.296003	+	0.512692i	0.679215	+	0.733940i	$0.262320\pi$
$258$	11.2258	+	3.49902i	0.698891	+	0.217839i
$259$	−5.37520			−0.333998
$260$	0.442718	−	5.47403i	0.0274562	−	0.339485i
$261$	4.08277	−	7.07157i	0.252717	−	0.437719i
$262$	−1.24001	+	3.97830i	−0.0766081	+	0.245781i
$263$		−	22.0134i		−	1.35740i	−0.734414	−	0.678702i	$-0.762543\pi$
$263$		−	22.0134i		−	1.35740i	0.734414	−	0.678702i	$-0.237457\pi$
$264$	−15.1165	+	2.14180i	−0.930359	+	0.131818i
$265$	−17.7284			−1.08905
$266$	−0.0681943	+	0.218787i	−0.00418126	+	0.0134147i
$267$	7.96321			0.487341
$268$	−1.61628	−	16.2907i	−0.0987301	−	0.995114i
$269$	32.6641			1.99156			0.995782	−	0.0917516i	$-0.0292466\pi$
$269$	32.6641			1.99156			0.995782	+	0.0917516i	$0.0292466\pi$
$270$	−0.896992	+	2.87780i	−0.0545892	+	0.175138i
$271$	−4.32241			−0.262568			−0.131284	−	0.991345i	$-0.541910\pi$
$271$	−4.32241			−0.262568			−0.131284	+	0.991345i	$0.541910\pi$
$272$	8.52276	−	10.4322i	0.516768	−	0.632547i
$273$			4.16920i			0.252332i
$274$	−7.59293	+	24.3603i	−0.458706	+	1.47166i
$275$	−1.23294	+	2.13551i	−0.0743488	+	0.128776i
$276$	13.0271	+	1.05358i	0.784138	+	0.0634180i
$277$	−7.62539			−0.458165			−0.229083	−	0.973407i	$-0.573573\pi$
$277$	−7.62539			−0.458165			−0.229083	+	0.973407i	$0.573573\pi$
$278$	−27.0331	−	8.42602i	−1.62133	−	0.505359i
$279$	4.07249	−	7.05376i	0.243814	−	0.422298i
$280$	2.73700	+	19.3174i	0.163567	+	1.15444i
$281$	−13.3504	+	7.70788i	−0.796421	+	0.459814i	−0.842218	−	0.539137i	$-0.818751\pi$
$281$	−13.3504	+	7.70788i	−0.796421	+	0.459814i	0.0457973	+	0.998951i	$0.485417\pi$
$282$	−5.79014	−	6.27733i	−0.344798	−	0.373809i
$283$		−	13.0527i		−	0.775901i	−0.921680	−	0.387951i	$-0.873183\pi$
$283$		−	13.0527i		−	0.775901i	0.921680	−	0.387951i	$-0.126817\pi$
$284$	−0.520766	−	1.09791i	−0.0309018	−	0.0651488i
$285$	0.0533641	+	0.0924293i	0.00316102	+	0.00547504i
$286$	−2.92648	+	9.38897i	−0.173046	+	0.555181i
$287$	9.84152	−	5.68200i	0.580927	−	0.335398i
$288$	−0.339481	−	5.64666i	−0.0200041	−	0.332733i
$289$	2.82910	−	4.90014i	0.166417	−	0.288243i
$290$	−16.6884	−	18.0926i	−0.979976	−	1.06243i
$291$	10.9547	−	6.32468i	0.642174	−	0.370759i
$292$	0.379929	−	4.69767i	0.0222337	−	0.274910i
$293$	−5.54943			−0.324201			−0.162101	−	0.986774i	$-0.551827\pi$
$293$	−5.54943			−0.324201			−0.162101	+	0.986774i	$0.551827\pi$
$294$	−1.07886	−	4.79192i	−0.0629205	−	0.279471i
$295$	15.8225			0.921220
$296$	1.75496	−	4.35774i	0.102005	−	0.253289i
$297$	2.69894	−	4.67470i	0.156608	−	0.271254i
$298$	2.15244	+	0.670902i	0.124688	+	0.0388643i
$299$	4.20935	−	7.29081i	0.243433	−	0.421639i
$300$	−0.751838	−	0.519119i	−0.0434074	−	0.0299714i
$301$	−13.4539	+	23.3028i	−0.775469	+	1.34315i
$302$	9.01451	−	2.02954i	0.518727	−	0.116787i
$303$	−10.4593	−	6.03866i	−0.600869	−	0.346912i
$304$	−0.155108	−	0.126718i	−0.00889608	−	0.00726777i
$305$	−2.49656	−	4.32417i	−0.142953	−	0.247601i
$306$	1.04610	+	4.64643i	0.0598018	+	0.265619i
$307$	2.01720	−	1.16463i	0.115128	−	0.0664690i	−0.441330	−	0.897345i	$-0.645493\pi$
$307$	2.01720	−	1.16463i	0.115128	−	0.0664690i	0.556458	+	0.830876i	$0.312160\pi$
$308$	2.81642	−	34.8239i	0.160481	−	1.98428i
$309$	10.0101	+	5.77936i	0.569457	+	0.328776i
$310$	−16.6464	−	18.0470i	−0.945450	−	1.02500i
$311$	−2.40715			−0.136497			−0.0682484	−	0.997668i	$-0.521741\pi$
$311$	−2.40715			−0.136497			−0.0682484	+	0.997668i	$0.521741\pi$
$312$	−3.38003	−	1.36121i	−0.191356	−	0.0770633i
$313$			23.9029i			1.35107i	0.737328	+	0.675535i	$0.236087\pi$
$313$			23.9029i			1.35107i	−0.737328	+	0.675535i	$0.763913\pi$
$314$	3.30646	+	14.6861i	0.186594	+	0.828787i
$315$	−5.97380	−	3.44897i	−0.336585	−	0.194328i
$316$	−14.7653	+	7.00355i	−0.830611	+	0.393981i
$317$	7.28605	+	12.6198i	0.409225	+	0.708799i	0.994803	−	0.101817i	$-0.0324658\pi$
$317$	7.28605	+	12.6198i	0.409225	+	0.708799i	−0.585578	+	0.810616i	$0.699132\pi$
$318$	−3.50024	+	11.2298i	−0.196284	+	0.629735i
$319$	22.0383	+	38.1715i	1.23391	+	2.13719i
$320$	−16.5545	−	4.08805i	−0.925424	−	0.228529i
$321$		−	1.17808i		−	0.0657541i
$322$	−8.89982	+	28.5532i	−0.495968	+	1.59120i
$323$	0.146040	+	0.0843161i	0.00812587	+	0.00469147i
$324$	1.64580	+	1.13637i	0.0914334	+	0.0631317i
$325$	−0.509672	+	0.294259i	−0.0282715	+	0.0163226i
$326$	22.1181	+	23.9792i	1.22501	+	1.32808i
$327$		−	4.44469i		−	0.245792i
$328$	1.39331	+	9.83378i	0.0769324	+	0.542980i
$329$	16.9243	−	9.77124i	0.933066	−	0.538706i
$330$	−11.0320	−	11.9602i	−0.607289	−	0.658387i
$331$	−4.89465	+	8.47779i	−0.269034	+	0.465981i	−0.968613	−	0.248575i	$-0.920038\pi$
$331$	−4.89465	+	8.47779i	−0.269034	+	0.465981i	0.699578	+	0.714556i	$0.253371\pi$
$332$	−27.2806	−	2.20634i	−1.49721	−	0.121089i
$333$	0.830470	+	1.43842i	0.0455095	+	0.0788248i
$334$	−15.1502	−	16.4249i	−0.828980	−	0.898731i
$335$	13.3082	−	11.2821i	0.727103	−	0.616407i
$336$	12.7767	+	2.08026i	0.697026	+	0.113488i
$337$	−25.3699	+	14.6473i	−1.38199	+	0.797891i	−0.992395	−	0.123096i	$-0.960718\pi$
$337$	−25.3699	+	14.6473i	−1.38199	+	0.797891i	−0.389593	+	0.920987i	$0.627384\pi$
$338$	11.7885	−	10.8736i	0.641212	−	0.591447i
$339$	5.19799	+	3.00106i	0.282316	+	0.162995i
$340$	14.3099	+	1.15732i	0.776061	+	0.0627648i
$341$	21.9828	+	38.0754i	1.19044	+	2.06190i
$342$	0.0690839	−	0.0155537i	0.00373563	−	0.000841046i
$343$	−11.4135			−0.616271
$344$	−14.4993	−	18.5154i	−0.781751	−	0.998284i
$345$	6.96438	+	12.0627i	0.374950	+	0.649432i
$346$	−6.07422	−	26.9795i	−0.326552	−	1.45043i
$347$	−4.86935	+	8.43396i	−0.261400	+	0.452759i	−0.966614	−	0.256236i	$-0.917518\pi$
$347$	−4.86935	+	8.43396i	−0.261400	+	0.452759i	0.705214	+	0.708995i	$0.250851\pi$
$348$	−14.7554	+	6.99885i	−0.790971	+	0.375178i
$349$	−18.0287			−0.965057			−0.482528	−	0.875880i	$-0.660281\pi$
$349$	−18.0287			−0.965057			−0.482528	+	0.875880i	$0.660281\pi$
$350$	1.53682	−	1.41754i	0.0821463	−	0.0757709i
$351$	1.11569	−	0.644144i	0.0595511	−	0.0343819i
$352$	27.3127	+	13.6530i	1.45577	+	0.727709i
$353$	2.31204	−	1.33486i	0.123058	−	0.0710473i	−0.437208	−	0.899361i	$-0.644033\pi$
$353$	2.31204	−	1.33486i	0.123058	−	0.0710473i	0.560265	+	0.828313i	$0.310699\pi$
$354$	3.12394	−	10.0225i	0.166036	−	0.532690i
$355$	0.647516	−	1.12153i	0.0343666	−	0.0595247i
$356$	−13.1059	−	9.04916i	−0.694609	−	0.479605i
$357$	−10.8989			−0.576829
$358$	−0.0622732	−	0.0194101i	−0.00329124	−	0.00102586i
$359$		−	26.4720i		−	1.39714i	−0.715541	−	0.698570i	$-0.753820\pi$
$359$		−	26.4720i		−	1.39714i	0.715541	−	0.698570i	$-0.246180\pi$
$360$	4.74652	−	3.71698i	0.250164	−	0.195902i
$361$	−9.49875	+	16.4523i	−0.499934	+	0.865911i
$362$	−8.23116	+	7.59234i	−0.432620	+	0.399044i
$363$	9.06857	+	15.7072i	0.475977	+	0.824416i
$364$	4.73776	−	6.86168i	0.248326	−	0.359650i
$365$	4.34989	−	2.51141i	0.227684	−	0.131453i
$366$	−3.23199	+	0.727655i	−0.168939	+	0.0380352i
$367$	−0.154740	+	0.268017i	−0.00807736	+	0.0139904i	−0.870036	−	0.492988i	$-0.835904\pi$
$367$	−0.154740	+	0.268017i	−0.00807736	+	0.0139904i	0.861958	+	0.506979i	$0.169238\pi$
$368$	−20.2427	−	16.5376i	−1.05522	−	0.862080i
$369$	−3.04104	−	1.75575i	−0.158310	−	0.0914005i
$370$	4.88441	−	1.09968i	0.253928	−	0.0571698i
$371$	−23.3110	−	13.4586i	−1.21025	−	0.698736i
$372$	−14.7182	+	6.98123i	−0.763103	+	0.361960i
$373$	16.7176	+	9.65191i	0.865605	+	0.499757i	0.865885	−	0.500243i	$-0.166756\pi$
$373$	16.7176	+	9.65191i	0.865605	+	0.499757i	−0.000280536		1.00000i	$0.500089\pi$
$374$	−24.5440	−	7.65021i	−1.26914	−	0.395583i
$375$		−	11.6311i		−	0.600626i
$376$	2.39604	+	16.9110i	0.123566	+	0.872117i
$377$			10.5196i			0.541786i
$378$	−3.36415	+	3.10305i	−0.173033	+	0.159604i
$379$	−8.11710	−	14.0592i	−0.416947	−	0.722174i	0.578683	−	0.815552i	$-0.303567\pi$
$379$	−8.11710	−	14.0592i	−0.416947	−	0.722174i	−0.995631	+	0.0933783i	$0.970233\pi$
$380$	0.0172073	−	0.212762i	0.000882717	−	0.0109144i
$381$	−15.9663	−	9.21814i	−0.817978	−	0.472260i
$382$	−5.44560	−	24.1874i	−0.278621	−	1.23754i
$383$	−13.7088	−	23.7444i	−0.700489	−	1.21328i	−0.968295	−	0.249810i	$-0.919632\pi$
$383$	−13.7088	−	23.7444i	−0.700489	−	1.21328i	0.267806	−	0.963473i	$-0.413701\pi$
$384$	−5.85798	+	9.67905i	−0.298939	+	0.493932i
$385$	32.2459	−	18.6172i	1.64340	−	0.948818i
$386$	4.11467	+	1.28251i	0.209431	+	0.0652782i
$387$	8.31453			0.422651
$388$	−25.2164	−	2.03940i	−1.28017	−	0.103535i
$389$	−1.09502	−	1.89663i	−0.0555196	−	0.0961628i	0.836930	−	0.547310i	$-0.184348\pi$
$389$	−1.09502	−	1.89663i	−0.0555196	−	0.0961628i	−0.892449	+	0.451147i	$0.851015\pi$
$390$	−0.852956	−	3.78853i	−0.0431911	−	0.191840i
$391$	19.0592	+	11.0038i	0.963864	+	0.556487i
$392$	−3.66981	+	9.11254i	−0.185354	+	0.460253i
$393$			2.94657i			0.148635i
$394$	11.4537	+	12.4174i	0.577029	+	0.625581i
$395$	−15.0830	−	8.70817i	−0.758907	−	0.438155i
$396$	−9.75412	+	4.62663i	−0.490163	+	0.232497i
$397$	−17.4046			−0.873512			−0.436756	−	0.899580i	$-0.643873\pi$
$397$	−17.4046			−0.873512			−0.436756	+	0.899580i	$0.643873\pi$
$398$	18.8758	−	4.24973i	0.946159	−	0.213020i
$399$			0.162046i			0.00811246i
$400$	0.647464	+	1.70873i	0.0323732	+	0.0854367i
$401$			15.6797i			0.783006i	0.920177	+	0.391503i	$0.128045\pi$
$401$			15.6797i			0.783006i	−0.920177	+	0.391503i	$0.871955\pi$
$402$	−4.51894	−	10.6574i	−0.225384	−	0.531541i
$403$			10.4931i			0.522698i
$404$	10.3517	+	21.8240i	0.515017	+	1.08579i
$405$			2.13147i			0.105914i
$406$	−8.20841	−	36.4589i	−0.407377	−	1.80942i
$407$	−8.96557			−0.444407
$408$	3.55839	−	8.83586i	0.176166	−	0.437440i
$409$	−25.8324	−	14.9143i	−1.27733	−	0.737465i	−0.300971	−	0.953633i	$-0.597311\pi$
$409$	−25.8324	−	14.9143i	−1.27733	−	0.737465i	−0.976356	+	0.216168i	$0.930644\pi$
$410$	−7.78048	+	7.17663i	−0.384251	+	0.354429i
$411$			18.0427i			0.889979i
$412$	−9.90721	−	20.8869i	−0.488093	−	1.02902i
$413$	20.8049	+	12.0117i	1.02374	+	0.591057i
$414$	9.01593	−	2.02986i	0.443109	−	0.0997622i
$415$	−14.5844	−	25.2609i	−0.715920	−	1.24001i
$416$	4.01602	+	6.08125i	0.196901	+	0.298158i
$417$	−20.0223			−0.980495
$418$	−0.113745	+	0.364925i	−0.00556344	+	0.0178491i
$419$	−21.6368	+	12.4920i	−1.05703	+	0.610274i	−0.924608	−	0.380920i	$-0.875607\pi$
$419$	−21.6368	+	12.4920i	−1.05703	+	0.610274i	−0.132418	+	0.991194i	$0.542274\pi$
$420$	5.91237	+	12.4648i	0.288494	+	0.608219i
$421$	8.35441	+	14.4703i	0.407169	+	0.705238i	0.994571	−	0.104057i	$-0.0331826\pi$
$421$	8.35441	+	14.4703i	0.407169	+	0.705238i	−0.587402	+	0.809295i	$0.699849\pi$
$422$	6.23578	−	1.40393i	0.303553	−	0.0683424i
$423$	−5.22962	−	3.01932i	−0.254273	−	0.146805i
$424$	18.5219	−	14.5044i	0.899503	−	0.704396i
$425$	−0.769233	−	1.33235i	−0.0373133	−	0.0646285i
$426$	−0.582572	−	0.631591i	−0.0282257	−	0.0306007i
$427$		−	7.58110i		−	0.366875i
$428$	−1.33874	+	1.93889i	−0.0647104	+	0.0937197i
$429$			6.95403i			0.335744i
$430$	7.45807	−	23.9276i	0.359660	−	1.15389i
$431$	8.88516	+	5.12985i	0.427983	+	0.247096i	0.698487	−	0.715623i	$-0.253857\pi$
$431$	8.88516	+	5.12985i	0.427983	+	0.247096i	−0.270504	+	0.962719i	$0.587190\pi$
$432$	−1.41732	−	3.74048i	−0.0681909	−	0.179964i
$433$	−11.7913	−	6.80773i	−0.566655	−	0.327159i	0.189157	−	0.981947i	$-0.439424\pi$
$433$	−11.7913	−	6.80773i	−0.566655	−	0.327159i	−0.755812	+	0.654788i	$0.772758\pi$
$434$	−8.18774	−	36.3671i	−0.393024	−	1.74567i
$435$	−15.0729	−	8.70232i	−0.722689	−	0.417244i
$436$	−5.05082	+	7.31507i	−0.241890	+	0.350328i
$437$	0.163607	−	0.283376i	0.00782638	−	0.0135557i
$438$	−0.731984	−	3.25122i	−0.0349755	−	0.155349i
$439$	−4.36804	+	2.52189i	−0.208475	+	0.120363i	−0.600603	−	0.799548i	$-0.705073\pi$
$439$	−4.36804	+	2.52189i	−0.208475	+	0.120363i	0.392127	+	0.919911i	$0.371739\pi$
$440$	4.56518	+	32.2205i	0.217636	+	1.53605i
$441$	−1.73661	−	3.00789i	−0.0826956	−	0.143233i
$442$	−4.16009	−	4.51013i	−0.197876	−	0.214525i
$443$	−19.2730	+	33.3818i	−0.915687	+	1.58602i	−0.109795	+	0.993954i	$0.535019\pi$
$443$	−19.2730	+	33.3818i	−0.915687	+	1.58602i	−0.805892	+	0.592062i	$0.798314\pi$
$444$	0.267786	−	3.31107i	0.0127086	−	0.157136i
$445$		−	16.9734i		−	0.804615i
$446$	−5.71714	+	18.3422i	−0.270714	+	0.868529i
$447$	1.59423			0.0754044
$448$	−18.6639	−	17.9428i	−0.881789	−	0.847716i
$449$	1.48859	−	2.57832i	0.0702511	−	0.121678i	−0.828760	−	0.559604i	$-0.810953\pi$
$449$	1.48859	−	2.57832i	0.0702511	−	0.121678i	0.899011	+	0.437925i	$0.144287\pi$
$450$	−0.616777	−	0.192245i	−0.0290752	−	0.00906253i
$451$	16.4152	−	9.47731i	0.772961	−	0.446269i
$452$	−5.14454	−	10.8460i	−0.241979	−	0.510153i
$453$	5.65842	−	3.26689i	0.265856	−	0.153492i
$454$	−23.0146	−	24.9511i	−1.08013	−	1.17101i
$455$	8.88654			0.416608
$456$	−0.131373	−	0.0529068i	−0.00615211	−	0.00247759i
$457$	2.83779	−	4.91520i	0.132746	−	0.229923i	−0.791988	−	0.610537i	$-0.790954\pi$
$457$	2.83779	−	4.91520i	0.132746	−	0.229923i	0.924734	+	0.380613i	$0.124287\pi$
$458$	16.6119	−	3.74002i	0.776222	−	0.174760i
$459$	1.68388	+	2.91657i	0.0785968	+	0.136134i
$460$	2.24567	−	27.7669i	0.104705	−	1.29464i
$461$	39.9492			1.86062			0.930311	−	0.366772i	$-0.119537\pi$
$461$	39.9492			1.86062			0.930311	+	0.366772i	$0.119537\pi$
$462$	−5.42622	−	24.1014i	−0.252450	−	1.12130i
$463$	−17.5079	−	30.3246i	−0.813661	−	1.40930i	−0.910286	−	0.413981i	$-0.864138\pi$
$463$	−17.5079	−	30.3246i	−0.813661	−	1.40930i	0.0966247	−	0.995321i	$-0.469195\pi$
$464$	32.2377	+	5.24885i	1.49660	+	0.243672i
$465$	−15.0349	−	8.68041i	−0.697227	−	0.402544i
$466$	4.35520	+	4.72165i	0.201751	+	0.218726i
$467$	29.4366	−	16.9952i	1.36216	−	0.786445i	0.372251	−	0.928132i	$-0.378586\pi$
$467$	29.4366	−	16.9952i	1.36216	−	0.786445i	0.989911	+	0.141688i	$0.0452528\pi$
$468$	−2.56819	−	0.207705i	−0.118715	−	0.00960117i
$469$	26.0637	−	4.73180i	1.20351	−	0.218494i
$470$	−13.3800	+	12.3415i	−0.617171	+	0.569272i
$471$	5.32231	+	9.21850i	0.245239	+	0.424766i
$472$	−16.5307	+	12.9451i	−0.760886	+	0.595846i
$473$	−22.4404	+	38.8680i	−1.03181	+	1.78715i
$474$	−8.49399	+	7.83477i	−0.390142	+	0.359863i
$475$	−0.0198096	+	0.0114371i	−0.000908929	+	0.000524770i
$476$	17.9374	+	12.3852i	0.822157	+	0.567673i
$477$			8.31744i			0.380829i
$478$	17.2683	−	15.9281i	0.789833	−	0.728533i
$479$	12.1419	−	7.01014i	0.554778	−	0.320301i	−0.196269	−	0.980550i	$-0.562883\pi$
$479$	12.1419	−	7.01014i	0.554778	−	0.320301i	0.751047	+	0.660249i	$0.229549\pi$
$480$	−12.0357	+	0.723594i	−0.549352	+	0.0330274i
$481$	−1.85310	−	1.06989i	−0.0844939	−	0.0487826i
$482$	5.93457	+	1.84976i	0.270312	+	0.0842544i
$483$			21.1482i			0.962275i
$484$	2.92417	−	36.1562i	0.132917	−	1.64347i
$485$	−13.4809	−	23.3496i	−0.612135	−	1.06025i
$486$	1.35015	+	0.420832i	0.0612440	+	0.0190893i
$487$	−4.49994	−	7.79412i	−0.203912	−	0.353185i	0.745874	−	0.666087i	$-0.232032\pi$
$487$	−4.49994	−	7.79412i	−0.203912	−	0.353185i	−0.949785	+	0.312902i	$0.898699\pi$
$488$	6.14610	+	2.47516i	0.278221	+	0.112045i
$489$	19.9770	+	11.5337i	0.903389	+	0.521572i
$490$	−10.2139	+	2.29956i	−0.461415	+	0.103884i
$491$			24.2122i			1.09268i	0.837563	+	0.546341i	$0.183980\pi$
$491$			24.2122i			1.09268i	−0.837563	+	0.546341i	$0.816020\pi$
$492$	3.00977	+	6.34536i	0.135691	+	0.286071i
$493$	−27.4996			−1.23852
$494$	−0.0670575	+	0.0618531i	−0.00301706	+	0.00278290i
$495$	−9.96401	−	5.75272i	−0.447849	−	0.258566i
$496$	32.1565	+	5.23563i	1.44387	+	0.235087i
$497$	1.70283	−	0.983130i	0.0763824	−	0.0440994i
$498$	−18.8806	+	4.25082i	−0.846062	+	0.190484i
$499$	21.1993	+	36.7182i	0.949009	+	1.64373i	0.747517	+	0.664242i	$0.231246\pi$
$499$	21.1993	+	36.7182i	0.949009	+	1.64373i	0.201492	+	0.979490i	$0.435421\pi$
$500$	−13.2172	+	19.1424i	−0.591092	+	0.856075i
$501$	−13.6835	−	7.90020i	−0.611335	−	0.352955i
$502$	9.60824	+	42.6764i	0.428837	+	1.90474i
$503$	−15.6770	+	27.1533i	−0.699002	+	1.21071i	0.269811	+	0.962913i	$0.413039\pi$
$503$	−15.6770	+	27.1533i	−0.699002	+	1.21071i	−0.968813	+	0.247793i	$0.920295\pi$
$504$	9.06294	−	1.28409i	0.403695	−	0.0571978i
$505$	−12.8712	+	22.2936i	−0.572763	+	0.992054i
$506$	−14.8445	+	47.6253i	−0.659917	+	2.11720i
$507$	5.67016	−	9.82100i	0.251821	−	0.436166i
$508$	15.8021	+	33.3149i	0.701105	+	1.47811i
$509$	−13.4600			−0.596606			−0.298303	−	0.954471i	$-0.596421\pi$
$509$	−13.4600			−0.596606			−0.298303	+	0.954471i	$0.596421\pi$
$510$	9.90373	−	2.22974i	0.438545	−	0.0987346i
$511$	7.62620			0.337363
$512$	20.6401	−	9.27295i	0.912171	−	0.409810i
$513$	0.0433640	−	0.0250362i	0.00191457	−	0.00110538i
$514$	9.86569	−	9.10001i	0.435157	−	0.401384i
$515$	12.3186	−	21.3364i	0.542820	−	0.940192i
$516$	−13.6841	−	9.44839i	−0.602407	−	0.415942i
$517$	28.2289	−	16.2980i	1.24151	−	0.716783i
$518$	7.25731	+	2.26205i	0.318868	+	0.0993889i
$519$	−9.77747	−	16.9351i	−0.429183	−	0.743368i
$520$	−2.90138	+	7.20444i	−0.127234	+	0.315936i
$521$		−	22.6986i		−	0.994444i	−0.867623	−	0.497222i	$-0.834353\pi$
$521$		−	22.6986i		−	0.994444i	0.867623	−	0.497222i	$-0.165647\pi$
$522$	−8.48829	+	7.82951i	−0.371523	+	0.342688i
$523$	19.8545	−	11.4630i	0.868175	−	0.501241i	0.00143380	−	0.999999i	$-0.499544\pi$
$523$	19.8545	−	11.4630i	0.868175	−	0.501241i	0.866741	+	0.498758i	$0.166210\pi$
$524$	3.34840	−	4.84947i	0.146275	−	0.211850i
$525$	0.739192	−	1.28032i	0.0322610	−	0.0558776i
$526$	−9.26394	+	29.7213i	−0.403927	+	1.29591i
$527$	−27.4303			−1.19488
$528$	21.3109	+	3.46978i	0.927438	+	0.151003i
$529$	9.85183	−	17.0639i	0.428340	−	0.741907i
$530$	23.9360	+	7.46068i	1.03971	+	0.324071i
$531$		−	7.42326i		−	0.322142i
$532$	0.184145	−	0.266696i	0.00798369	−	0.0115627i
$533$	4.52381			0.195948
$534$	−10.7515	−	3.35117i	−0.465264	−	0.145019i
$535$	−2.51105			−0.108562
$536$	−4.67344	+	22.6751i	−0.201862	+	0.979414i
$537$	−0.0461232			−0.00199037
$538$	−44.1013	−	13.7461i	−1.90134	−	0.592636i
$539$	18.7480			0.807534
$540$	2.42214	−	3.50798i	0.104233	−	0.150959i
$541$			26.0846i			1.12146i	0.827997	+	0.560732i	$0.189480\pi$
$541$			26.0846i			1.12146i	−0.827997	+	0.560732i	$0.810520\pi$
$542$	5.83589	+	1.81901i	0.250673	+	0.0781331i
$543$	−3.95910	+	6.85736i	−0.169901	+	0.294277i
$544$	−15.8972	+	10.4984i	−0.681587	+	0.450116i
$545$	−9.47373			−0.405810
$546$	1.75453	−	5.62904i	0.0750871	−	0.240901i
$547$	19.6882	−	34.1010i	0.841807	−	1.45805i	−0.0465589	−	0.998916i	$-0.514826\pi$
$547$	19.6882	−	34.1010i	0.841807	−	1.45805i	0.888366	−	0.459137i	$-0.151841\pi$
$548$	20.5032	−	29.6946i	0.875852	−	1.26849i
$549$	−2.02872	+	1.17128i	−0.0865838	+	0.0499892i
$550$	2.56334	−	2.36439i	0.109301	−	0.100818i
$551$			0.408869i			0.0174184i
$552$	−17.1451	−	6.90469i	−0.729744	−	0.293883i
$553$	−13.2217	−	22.9006i	−0.562243	−	0.973834i
$554$	10.2954	+	3.20901i	0.437410	+	0.136338i
$555$	3.06595	−	1.77013i	0.130142	−	0.0751376i
$556$	32.9527	+	22.7527i	1.39751	+	0.964931i
$557$	−14.6001	+	25.2881i	−0.618626	+	1.07149i	0.371111	+	0.928589i	$0.378977\pi$
$557$	−14.6001	+	25.2881i	−0.618626	+	1.07149i	−0.989737	+	0.142903i	$0.954356\pi$
$558$	−8.46692	+	7.80979i	−0.358433	+	0.330615i
$559$	−9.27644	+	5.35575i	−0.392351	+	0.226524i
$560$	4.43403	−	27.2332i	0.187372	−	1.15081i
$561$	−18.1788			−0.767508
$562$	21.2688	−	4.78849i	0.897170	−	0.201990i
$563$	15.6869			0.661123			0.330561	−	0.943785i	$-0.392762\pi$
$563$	15.6869			0.661123			0.330561	+	0.943785i	$0.392762\pi$
$564$	5.17585	+	10.9120i	0.217942	+	0.459478i
$565$	6.39668	−	11.0794i	0.269111	−	0.466113i
$566$	−5.49299	+	17.6231i	−0.230887	+	0.740752i
$567$	−1.61812	+	2.80266i	−0.0679545	+	0.117701i
$568$	0.241077	+	1.70149i	0.0101154	+	0.0713930i
$569$	−16.6625	+	28.8603i	−0.698529	+	1.20989i	0.270447	+	0.962735i	$0.412828\pi$
$569$	−16.6625	+	28.8603i	−0.698529	+	1.20989i	−0.968976	+	0.247153i	$0.920505\pi$
$570$	−0.0331522	−	0.147251i	−0.00138859	−	0.00616765i
$571$	2.41504	+	1.39432i	0.101066	+	0.0583507i	0.549681	−	0.835374i	$-0.314749\pi$
$571$	2.41504	+	1.39432i	0.101066	+	0.0583507i	−0.448615	+	0.893725i	$0.648083\pi$
$572$	7.90236	−	11.4449i	0.330414	−	0.478537i
$573$	−8.76560	−	15.1825i	−0.366188	−	0.634257i
$574$	−15.6787	+	3.52992i	−0.654416	+	0.147336i
$575$	−2.58529	+	1.49262i	−0.107814	+	0.0622466i
$576$	−1.91795	+	7.76669i	−0.0799144	+	0.323612i
$577$	−8.45563	−	4.88186i	−0.352012	−	0.203234i	0.313559	−	0.949569i	$-0.398479\pi$
$577$	−8.45563	−	4.88186i	−0.352012	−	0.203234i	−0.665571	+	0.746334i	$0.731812\pi$
$578$	−5.88184	+	5.42534i	−0.244652	+	0.225664i
$579$	3.04757			0.126653
$580$	14.9179	+	31.4507i	0.619431	+	1.30592i
$581$		−	44.2873i		−	1.83735i
$582$	−17.4520	+	3.92918i	−0.723410	+	0.162870i
$583$	−38.8816	−	22.4483i	−1.61031	−	0.929713i
$584$	−2.48989	+	6.18266i	−0.103032	+	0.255840i
$585$	−1.37298	−	2.37806i	−0.0567656	−	0.0983208i
$586$	7.49255	+	2.33538i	0.309514	+	0.0964735i
$587$	15.2557	+	26.4236i	0.629669	+	1.09062i	0.987618	+	0.156877i	$0.0501427\pi$
$587$	15.2557	+	26.4236i	0.629669	+	1.09062i	−0.357949	+	0.933741i	$0.616524\pi$
$588$	−0.559972	+	6.92383i	−0.0230929	+	0.285534i
$589$			0.407840i			0.0168047i
$590$	−21.3627	−	6.65860i	−0.879488	−	0.274130i
$591$	10.3449	+	5.97264i	0.425533	+	0.245682i
$592$	−4.20333	+	5.14506i	−0.172756	+	0.211461i
$593$	−36.5700	+	21.1137i	−1.50175	+	0.867036i	−0.501752	+	0.865012i	$0.667311\pi$
$593$	−36.5700	+	21.1137i	−1.50175	+	0.867036i	−0.999998	+	0.00202385i	$0.999356\pi$
$594$	−5.61124	+	5.17574i	−0.230232	+	0.212363i
$595$			23.2306i			0.952363i
$596$	−2.62378	−	1.81163i	−0.107474	−	0.0742074i
$597$	11.8484	−	6.84065i	0.484921	−	0.279969i
$598$	−8.75146	+	8.07225i	−0.357874	+	0.330099i
$599$	11.2242	−	19.4408i	0.458607	−	0.794330i	−0.540281	−	0.841485i	$-0.681682\pi$
$599$	11.2242	−	19.4408i	0.458607	−	0.794330i	0.998888	+	0.0471544i	$0.0150153\pi$
$600$	0.796631	+	1.01729i	0.0325223	+	0.0415305i
$601$	−10.5983	−	18.3568i	−0.432314	−	0.748791i	0.564758	−	0.825257i	$-0.308970\pi$
$601$	−10.5983	−	18.3568i	−0.432314	−	0.748791i	−0.997072	+	0.0764662i	$0.975636\pi$
$602$	27.9713	−	25.8004i	1.14003	−	1.05155i
$603$	−5.29310	−	6.24365i	−0.215552	−	0.254261i
$604$	−13.0250	−	1.05341i	−0.529981	−	0.0428628i
$605$	33.4795	−	19.3294i	1.36114	−	0.785853i
$606$	11.5803	+	12.5547i	0.470418	+	0.509999i
$607$	6.29212	+	3.63276i	0.255389	+	0.147449i	0.622229	−	0.782835i	$-0.286227\pi$
$607$	6.29212	+	3.63276i	0.255389	+	0.147449i	−0.366840	+	0.930284i	$0.619560\pi$
$608$	0.156092	+	0.236363i	0.00633038	+	0.00958577i
$609$	−13.2128	−	22.8853i	−0.535410	−	0.927358i
$610$	1.55098	+	6.88890i	0.0627973	+	0.278923i
$611$	7.77952			0.314726
$612$	0.542969	−	6.71360i	0.0219482	−	0.271381i
$613$	6.89333	+	11.9396i	0.278419	+	0.482236i	0.970992	−	0.239112i	$-0.0768563\pi$
$613$	6.89333	+	11.9396i	0.278419	+	0.482236i	−0.692573	+	0.721348i	$0.743523\pi$
$614$	−3.21363	+	0.723522i	−0.129692	+	0.0291990i
$615$	−3.74232	+	6.48190i	−0.150905	+	0.261375i
$616$	−18.4576	+	45.8322i	−0.743678	+	1.84663i
$617$	42.8505			1.72510			0.862548	−	0.505975i	$-0.168867\pi$
$617$	42.8505			1.72510			0.862548	+	0.505975i	$0.168867\pi$
$618$	−11.0830	−	12.0156i	−0.445825	−	0.483338i
$619$	−15.8385	+	9.14437i	−0.636604	+	0.367543i	−0.783305	−	0.621638i	$-0.786468\pi$
$619$	−15.8385	+	9.14437i	−0.636604	+	0.367543i	0.146701	+	0.989181i	$0.453134\pi$
$620$	14.8803	+	31.3715i	0.597607	+	1.25991i
$621$	5.65931	−	3.26740i	0.227100	−	0.131116i
$622$	3.25001	+	1.01300i	0.130313	+	0.0406178i
$623$	12.8854	−	22.3182i	0.516243	−	0.894159i
$624$	3.99070	+	3.26026i	0.159756	+	0.130515i
$625$	−22.5072			−0.900288
$626$	10.0591	−	32.2724i	0.402042	−	1.28987i
$627$			0.270285i			0.0107942i
$628$	1.71619	−	21.2199i	0.0684832	−	0.846768i
$629$	2.79683	−	4.84424i	0.111517	−	0.193153i
$630$	6.61408	+	7.17059i	0.263511	+	0.285683i
$631$	3.71172	+	6.42888i	0.147761	+	0.255930i	0.930400	−	0.366547i	$-0.119460\pi$
$631$	3.71172	+	6.42888i	0.147761	+	0.255930i	−0.782639	+	0.622476i	$0.786127\pi$
$632$	22.8826	−	3.24214i	0.910222	−	0.128965i
$633$	3.91421	−	2.25987i	0.155576	−	0.0898217i
$634$	−4.52643	−	20.1048i	−0.179767	−	0.798464i
$635$	−19.6482	+	34.0317i	−0.779716	+	1.35051i
$636$	9.45170	−	13.6889i	0.374784	−	0.542798i
$637$	3.87503	+	2.23725i	0.153534	+	0.0886431i
$638$	−13.6912	−	60.8117i	−0.542041	−	2.40756i
$639$	−0.526176	−	0.303788i	−0.0208152	−	0.0120177i
$640$	20.6306	+	12.4861i	0.815498	+	0.493558i
$641$	−7.09000	−	4.09342i	−0.280038	−	0.161680i	0.353402	−	0.935471i	$-0.385025\pi$
$641$	−7.09000	−	4.09342i	−0.280038	−	0.161680i	−0.633441	+	0.773791i	$0.718358\pi$
$642$	−0.495775	+	1.59059i	−0.0195667	+	0.0627754i
$643$			14.1085i			0.556384i	0.960525	+	0.278192i	$0.0897352\pi$
$643$			14.1085i			0.556384i	−0.960525	+	0.278192i	$0.910265\pi$
$644$	24.0322	−	34.8057i	0.947000	−	1.37154i
$645$		−	17.7222i		−	0.697811i
$646$	−0.161692	−	0.175297i	−0.00636170	−	0.00689698i
$647$	11.4730	+	19.8718i	0.451050	+	0.781241i	0.998452	−	0.0556289i	$-0.0177164\pi$
$647$	11.4730	+	19.8718i	0.451050	+	0.781241i	−0.547402	+	0.836870i	$0.684383\pi$
$648$	−1.74385	−	2.22688i	−0.0685051	−	0.0874799i
$649$	34.7015	+	20.0349i	1.36215	+	0.786440i
$650$	0.811966	−	0.182807i	0.0318479	−	0.00717029i
$651$	−13.1795	−	22.8276i	−0.516547	−	0.894685i
$652$	−19.7715	−	41.6834i	−0.774313	−	1.63245i
$653$	−16.3700	+	9.45123i	−0.640608	+	0.369855i	−0.784849	−	0.619687i	$-0.787259\pi$
$653$	−16.3700	+	9.45123i	−0.640608	+	0.369855i	0.144241	+	0.989543i	$0.453926\pi$
$654$	−1.87047	+	6.00099i	−0.0731410	+	0.234657i
$655$	6.28053			0.245401
$656$	2.25720	−	13.8634i	0.0881289	−	0.541275i
$657$	−1.17825	−	2.04079i	−0.0459680	−	0.0796189i
$658$	−26.9624	+	6.07035i	−1.05110	+	0.236647i
$659$	−6.71226	−	3.87532i	−0.261472	−	0.150961i	0.363534	−	0.931581i	$-0.381570\pi$
$659$	−6.71226	−	3.87532i	−0.261472	−	0.150961i	−0.625006	+	0.780620i	$0.714903\pi$
$660$	9.86154	+	20.7906i	0.383860	+	0.809275i
$661$		−	43.9935i		−	1.71115i	−0.517680	−	0.855574i	$-0.673204\pi$
$661$		−	43.9935i		−	1.71115i	0.517680	−	0.855574i	$-0.326796\pi$
$662$	10.1762	−	9.38644i	0.395510	−	0.364815i
$663$	−3.75738	−	2.16932i	−0.145924	−	0.0842495i
$664$	35.9043	+	14.4594i	1.39336	+	0.561134i
$665$	0.345397			0.0133939
$666$	−0.515926	−	2.29156i	−0.0199917	−	0.0887963i
$667$			53.3603i			2.06612i
$668$	13.5428	+	28.5517i	0.523988	+	1.10470i
$669$			13.5853i			0.525239i
$670$	−22.7159	+	9.63199i	−0.877590	+	0.372116i
$671$		−	12.6449i		−	0.488151i
$672$	−16.3750	−	8.18551i	−0.631679	−	0.315763i
$673$			15.3709i			0.592506i	0.955110	+	0.296253i	$0.0957371\pi$
$673$			15.3709i			0.592506i	−0.955110	+	0.296253i	$0.904263\pi$
$674$	40.4172	−	9.09960i	1.55681	−	0.350503i
$675$	−0.456822			−0.0175831
$676$	−20.4923	+	9.72001i	−0.788163	+	0.373847i
$677$	41.1950	+	23.7839i	1.58325	+	0.914091i	0.994381	+	0.105863i	$0.0337606\pi$
$677$	41.1950	+	23.7839i	1.58325	+	0.914091i	0.588871	+	0.808227i	$0.299573\pi$
$678$	−5.75512	−	6.23936i	−0.221024	−	0.239621i
$679$		−	40.9363i		−	1.57099i
$680$	−18.8334	−	7.58460i	−0.722228	−	0.290856i
$681$	−20.7867	−	12.0012i	−0.796548	−	0.459887i
$682$	−13.6567	−	60.6585i	−0.522944	−	2.32273i
$683$	−15.0403	−	26.0506i	−0.575503	−	0.996800i	−0.995987	−	0.0895000i	$-0.971473\pi$
$683$	−15.0403	−	26.0506i	−0.575503	−	0.996800i	0.420484	−	0.907300i	$-0.361860\pi$
$684$	−0.0998190	−	0.00807297i	−0.00381668	−	0.000308678i
$685$	38.4575			1.46938
$686$	15.4099	+	4.80316i	0.588353	+	0.183386i
$687$	10.4273	−	6.02020i	0.397826	−	0.229685i
$688$	11.7844	+	31.1003i	0.449275	+	1.18569i
$689$	−5.35763	−	9.27969i	−0.204109	−	0.353528i
$690$	−4.32659	−	19.2172i	−0.164711	−	0.731587i
$691$	−4.54036	−	2.62138i	−0.172723	−	0.0997219i	0.411146	−	0.911570i	$-0.365129\pi$
$691$	−4.54036	−	2.62138i	−0.172723	−	0.0997219i	−0.583869	+	0.811848i	$0.698462\pi$
$692$	−3.15276	+	38.9826i	−0.119850	+	1.48190i
$693$	−8.73441	−	15.1284i	−0.331793	−	0.574682i
$694$	10.1236	−	9.33792i	0.384288	−	0.354463i
$695$			42.6770i			1.61883i
$696$	22.8673	−	3.23996i	0.866782	−	0.122810i
$697$			11.8259i			0.447936i
$698$	24.3415	+	7.58707i	0.921339	+	0.287175i
$699$	3.93359	+	2.27106i	0.148782	+	0.0858994i
$700$	−2.67148	+	1.26715i	−0.100972	+	0.0478938i
$701$	−41.5582	−	23.9936i	−1.56963	−	0.906226i	−0.996212	−	0.0869633i	$-0.972284\pi$
$701$	−41.5582	−	23.9936i	−1.56963	−	0.906226i	−0.573418	−	0.819263i	$-0.694383\pi$
$702$	−1.77742	+	0.400172i	−0.0670845	+	0.0151035i
$703$	−0.0720251	−	0.0415837i	−0.00271648	−	0.00156836i
$704$	−31.1306	−	29.9277i	−1.17328	−	1.12794i
$705$	−6.43561	+	11.1468i	−0.242379	+	0.419813i
$706$	−3.68335	+	0.829276i	−0.138625	+	0.0312102i
$707$	−33.8486	+	19.5425i	−1.27301	+	0.734972i
$708$	−8.43558	+	12.2172i	−0.317028	+	0.459151i
$709$	15.0795	+	26.1184i	0.566321	+	0.980896i	0.996925	+	0.0783556i	$0.0249669\pi$
$709$	15.0795	+	26.1184i	0.566321	+	0.980896i	−0.430605	+	0.902541i	$0.641700\pi$
$710$	−1.34622	+	1.24174i	−0.0505227	+	0.0466016i
$711$	−4.08552	+	7.07632i	−0.153219	+	0.265383i
$712$	13.8867	+	17.7331i	0.520425	+	0.664575i
$713$			53.2259i			1.99332i
$714$	14.7151	+	4.58659i	0.550698	+	0.171649i
$715$	14.8223			0.554323
$716$	0.0759097	+	0.0524131i	0.00283688	+	0.00195877i
$717$	8.30585	−	14.3862i	0.310188	−	0.537261i
$718$	−11.1403	+	35.7412i	−0.415751	+	1.33385i
$719$	18.1206	−	10.4619i	0.675785	−	0.390164i	−0.122480	−	0.992471i	$-0.539085\pi$
$719$	18.1206	−	10.4619i	0.675785	−	0.390164i	0.798265	+	0.602307i	$0.205751\pi$
$720$	−7.97274	+	3.02098i	−0.297126	+	0.112585i
$721$	32.3952	−	18.7034i	1.20646	−	0.696550i
$722$	19.7484	−	18.2157i	0.734958	−	0.677918i
$723$	4.39549			0.163470
$724$	14.3084	−	6.78684i	0.531767	−	0.252231i
$725$	1.86510	−	3.23045i	0.0692681	−	0.119976i
$726$	−5.63381	−	25.0234i	−0.209090	−	0.928707i
$727$	2.48072	+	4.29674i	0.0920049	+	0.159357i	0.908355	−	0.418201i	$-0.137339\pi$
$727$	2.48072	+	4.29674i	0.0920049	+	0.159357i	−0.816350	+	0.577558i	$0.804006\pi$
$728$	−9.28429	+	7.27048i	−0.344099	+	0.269462i
$729$	1.00000			0.0370370
$730$	−6.92988	+	1.56020i	−0.256486	+	0.0577458i
$731$	−14.0007	−	24.2499i	−0.517833	−	0.896914i
$732$	4.66989	+	0.377682i	0.172604	+	0.0139595i
$733$	26.6700	+	15.3979i	0.985079	+	0.568736i	0.903800	−	0.427955i	$-0.140766\pi$
$733$	26.6700	+	15.3979i	0.985079	+	0.568736i	0.0812796	+	0.996691i	$0.474099\pi$
$734$	0.321712	−	0.296744i	0.0118746	−	0.0109530i
$735$	−6.41125	+	3.70153i	−0.236482	+	0.136533i
$736$	20.3711	+	30.8469i	0.750890	+	1.13703i
$737$	43.4730	−	7.89241i	1.60135	−	0.290721i
$738$	3.36698	+	3.65028i	0.123940	+	0.134369i
$739$	−4.30085	−	7.44928i	−0.158209	−	0.274026i	0.776014	−	0.630716i	$-0.217239\pi$
$739$	−4.30085	−	7.44928i	−0.158209	−	0.274026i	−0.934223	+	0.356690i	$0.883905\pi$
$740$	−7.05746	−	0.570780i	−0.259437	−	0.0209823i
$741$	−0.0322539	+	0.0558654i	−0.00118488	+	0.00205227i
$742$	25.8095	+	27.9811i	0.947495	+	1.02722i
$743$	−7.84426	+	4.52888i	−0.287778	+	0.166149i	−0.636939	−	0.770914i	$-0.719800\pi$
$743$	−7.84426	+	4.52888i	−0.287778	+	0.166149i	0.349161	+	0.937063i	$0.386466\pi$
$744$	22.8097	−	3.23180i	0.836243	−	0.118484i
$745$		−	3.39805i		−	0.124495i
$746$	−18.5094	−	20.0668i	−0.677678	−	0.734698i
$747$	−11.8514	+	6.84241i	−0.433620	+	0.250351i
$748$	29.9186	+	20.6578i	1.09393	+	0.755325i
$749$	−3.30177	−	1.90628i	−0.120644	−	0.0696538i
$750$	−4.89473	+	15.7037i	−0.178730	+	0.573417i
$751$			24.3515i			0.888600i	0.895878	+	0.444300i	$0.146548\pi$
$751$			24.3515i			0.888600i	−0.895878	+	0.444300i	$0.853452\pi$
$752$	3.88167	−	23.8407i	0.141550	−	0.869379i
$753$	15.4661	+	26.7880i	0.563615	+	0.976210i
$754$	4.42697	−	14.2030i	0.161221	−	0.517242i
$755$	−6.96329	−	12.0608i	−0.253420	−	0.438936i
$756$	5.84796	−	2.77384i	0.212688	−	0.100884i
$757$	43.5684	+	25.1543i	1.58352	+	0.914247i	0.994340	+	0.106247i	$0.0338833\pi$
$757$	43.5684	+	25.1543i	1.58352	+	0.914247i	0.589182	+	0.808000i	$0.299450\pi$
$758$	5.04272	+	22.3980i	0.183160	+	0.813531i
$759$			35.2741i			1.28037i
$760$	−0.112769	+	0.280018i	−0.00409057	+	0.0101573i
$761$	−14.2398			−0.516194			−0.258097	−	0.966119i	$-0.583095\pi$
$761$	−14.2398			−0.516194			−0.258097	+	0.966119i	$0.583095\pi$
$762$	17.6776	+	19.1650i	0.640391	+	0.694274i
$763$	−12.4570	−	7.19203i	−0.450972	−	0.260369i
$764$	−2.82648	+	34.9483i	−0.102258	+	1.26438i
$765$	6.21658	−	3.58914i	0.224761	−	0.129766i
$766$	8.51656	+	37.8276i	0.307716	+	1.36677i
$767$	4.78165	+	8.28206i	0.172655	+	0.299048i
$768$	11.9824	−	10.6029i	0.432378	−	0.382600i
$769$	−17.0244	−	9.82903i	−0.613915	−	0.354444i	0.160581	−	0.987023i	$-0.448663\pi$
$769$	−17.0244	−	9.82903i	−0.613915	−	0.354444i	−0.774496	+	0.632579i	$0.781996\pi$
$770$	−51.3714	+	11.5658i	−1.85130	+	0.416804i
$771$	4.74529	−	8.21908i	0.170897	−	0.296003i
$772$	−5.01569	−	3.46317i	−0.180519	−	0.124642i
$773$	12.2504	−	21.2183i	0.440615	−	0.763167i	−0.557120	−	0.830432i	$-0.688094\pi$
$773$	12.2504	−	21.2183i	0.440615	−	0.763167i	0.997735	+	0.0672643i	$0.0214271\pi$
$774$	−11.2258	−	3.49902i	−0.403505	−	0.125770i
$775$	1.86040	−	3.22231i	0.0668277	−	0.115749i
$776$	33.1876	+	13.3653i	1.19137	+	0.479788i
$777$	5.37520			0.192834
$778$	0.680276	+	3.02155i	0.0243891	+	0.108328i
$779$	0.175829			0.00629973
$780$	−0.442718	+	5.47403i	−0.0158518	+	0.196002i
$781$	2.84024	−	1.63981i	0.101632	−	0.0586771i
$782$	−21.1020	−	22.8775i	−0.754605	−	0.818098i
$783$	−4.08277	+	7.07157i	−0.145906	+	0.252717i
$784$	8.78964	−	10.7589i	0.313916	−	0.384247i
$785$	19.6490	−	11.3444i	0.701303	−	0.404897i
$786$	1.24001	−	3.97830i	0.0442297	−	0.141901i
$787$	−17.2628	−	29.9000i	−0.615351	−	1.06582i	−0.990323	−	0.138783i	$-0.955681\pi$
$787$	−17.2628	−	29.9000i	−0.615351	−	1.06582i	0.374972	−	0.927036i	$-0.377652\pi$
$788$	−10.2385	−	21.5855i	−0.364733	−	0.768950i
$789$			22.0134i			0.783697i
$790$	16.6996	+	18.1047i	0.594145	+	0.644137i
$791$	16.8219	−	9.71214i	0.598119	−	0.345324i
$792$	15.1165	−	2.14180i	0.537143	−	0.0761054i
$793$	1.50895	−	2.61358i	0.0535844	−	0.0928109i
$794$	23.4988	+	7.32441i	0.833941	+	0.259934i
$795$	17.7284			0.628762
$796$	−27.2736	−	2.20578i	−0.966686	−	0.0781817i
$797$	8.48573	−	14.6977i	0.300580	−	0.520619i	−0.675688	−	0.737188i	$-0.736153\pi$
$797$	8.48573	−	14.6977i	0.300580	−	0.520619i	0.976267	+	0.216569i	$0.0694865\pi$
$798$	0.0681943	−	0.218787i	0.00241405	−	0.00774496i
$799$			20.3367i			0.719461i
$800$	−0.155082	−	2.57952i	−0.00548298	−	0.0911997i
$801$	−7.96321			−0.281366
$802$	6.59851	−	21.1699i	0.233001	−	0.747535i
$803$	12.7201			0.448884
$804$	1.61628	+	16.2907i	0.0570018	+	0.574529i
$805$	45.0767			1.58875
$806$	4.41582	−	14.1672i	0.155541	−	0.499019i
$807$	−32.6641			−1.14983
$808$	−4.79209	−	33.8220i	−0.168585	−	1.18985i
$809$		−	50.5254i		−	1.77638i	−0.459478	−	0.888189i	$-0.651964\pi$
$809$		−	50.5254i		−	1.77638i	0.459478	−	0.888189i	$-0.348036\pi$
$810$	0.896992	−	2.87780i	0.0315171	−	0.101116i
$811$	−6.11241	+	10.5870i	−0.214636	+	0.371760i	−0.953160	−	0.302467i	$-0.902190\pi$
$811$	−6.11241	+	10.5870i	−0.214636	+	0.371760i	0.738524	+	0.674227i	$0.235523\pi$
$812$	−4.26049	+	52.6793i	−0.149514	+	1.84868i
$813$	4.32241			0.151594
$814$	12.1048	+	3.77300i	0.424275	+	0.132243i
$815$	24.5838	−	42.5804i	0.861132	−	1.49152i
$816$	−8.52276	+	10.4322i	−0.298356	+	0.365201i
$817$	−0.360552	+	0.208165i	−0.0126141	+	0.00728276i
$818$	28.6011	+	31.0076i	1.00001	+	1.08416i
$819$		−	4.16920i		−	0.145684i
$820$	13.5250	−	6.41524i	0.472312	−	0.224030i
$821$	−22.1885	−	38.4315i	−0.774383	−	1.34127i	−0.935141	−	0.354276i	$-0.884727\pi$
$821$	−22.1885	−	38.4315i	−0.774383	−	1.34127i	0.160758	−	0.986994i	$-0.448606\pi$
$822$	7.59293	−	24.3603i	0.264834	−	0.849662i
$823$	−29.9846	+	17.3116i	−1.04520	+	0.603446i	−0.921301	−	0.388849i	$-0.872873\pi$
$823$	−29.9846	+	17.3116i	−1.04520	+	0.603446i	−0.123898	+	0.992295i	$0.539539\pi$
$824$	4.58632	+	32.3697i	0.159772	+	1.12765i
$825$	1.23294	−	2.13551i	0.0429253	−	0.0743488i
$826$	−23.0348	−	24.9729i	−0.801482	−	0.868920i
$827$	−34.5627	+	19.9548i	−1.20186	+	0.693897i	−0.960969	−	0.276655i	$-0.910774\pi$
$827$	−34.5627	+	19.9548i	−1.20186	+	0.693897i	−0.240895	+	0.970551i	$0.577441\pi$
$828$	−13.0271	−	1.05358i	−0.452722	−	0.0366144i
$829$	−29.7130			−1.03197			−0.515987	−	0.856596i	$-0.672575\pi$
$829$	−29.7130			−1.03197			−0.515987	+	0.856596i	$0.672575\pi$
$830$	9.06050	+	40.2436i	0.314495	+	1.39688i
$831$	7.62539			0.264522
$832$	−2.86303	−	9.90065i	−0.0992579	−	0.343243i
$833$	−5.84848	+	10.1299i	−0.202638	+	0.350979i
$834$	27.0331	+	8.42602i	0.936078	+	0.291769i
$835$	−16.8391	+	29.1661i	−0.582740	+	1.00933i
$836$	0.307145	−	0.444836i	0.0106228	−	0.0153850i
$837$	−4.07249	+	7.05376i	−0.140766	+	0.243814i
$838$	34.4699	−	7.76061i	1.19074	−	0.268086i
$839$	31.7681	+	18.3413i	1.09676	+	0.633213i	0.935368	−	0.353677i	$-0.115069\pi$
$839$	31.7681	+	18.3413i	1.09676	+	0.633213i	0.161390	+	0.986891i	$0.448402\pi$
$840$	−2.73700	−	19.3174i	−0.0944354	−	0.666514i
$841$	−18.8381	−	32.6285i	−0.649589	−	1.12512i
$842$	−5.19015	−	23.0528i	−0.178864	−	0.794452i
$843$	13.3504	−	7.70788i	0.459814	−	0.265474i
$844$	−9.01005	−	0.728698i	−0.310139	−	0.0250828i
$845$	−20.9332	−	12.0858i	−0.720124	−	0.415764i
$846$	5.79014	+	6.27733i	0.199069	+	0.215819i
$847$	58.6961			2.01682
$848$	−31.1112	+	11.7885i	−1.06836	+	0.404818i
$849$			13.0527i			0.447967i
$850$	0.477883	+	2.12259i	0.0163913	+	0.0728042i
$851$	−9.39977	−	5.42696i	−0.322220	−	0.186034i
$852$	0.520766	+	1.09791i	0.0178411	+	0.0376137i
$853$	−17.5288	−	30.3607i	−0.600173	−	1.03953i	−0.992794	−	0.119830i	$-0.961765\pi$
$853$	−17.5288	−	30.3607i	−0.600173	−	1.03953i	0.392621	−	0.919700i	$-0.371568\pi$
$854$	−3.19037	+	10.2356i	−0.109172	+	0.350255i
$855$	−0.0533641	−	0.0924293i	−0.00182501	−	0.00316102i
$856$	2.62344	−	2.05440i	0.0896674	−	0.0702181i
$857$			36.3304i			1.24102i	0.784198	+	0.620511i	$0.213075\pi$
$857$			36.3304i			1.24102i	−0.784198	+	0.620511i	$0.786925\pi$
$858$	2.92648	−	9.38897i	0.0999083	−	0.320534i
$859$	5.52213	+	3.18820i	0.188413	+	0.108780i	0.591239	−	0.806496i	$-0.298639\pi$
$859$	5.52213	+	3.18820i	0.188413	+	0.108780i	−0.402827	+	0.915276i	$0.631972\pi$
$860$	−20.1390	+	29.1672i	−0.686734	+	0.994593i
$861$	−9.84152	+	5.68200i	−0.335398	+	0.193642i
$862$	−9.83748	−	10.6652i	−0.335066	−	0.363259i
$863$		−	18.7073i		−	0.636805i	−0.947956	−	0.318402i	$-0.896854\pi$
$863$		−	18.7073i		−	0.636805i	0.947956	−	0.318402i	$-0.103146\pi$
$864$	0.339481	+	5.64666i	0.0115494	+	0.192103i
$865$	−36.0967	+	20.8404i	−1.22732	+	0.708596i
$866$	13.0551	+	14.1536i	0.443632	+	0.480959i
$867$	−2.82910	+	4.90014i	−0.0960812	+	0.166417i
$868$	−4.24976	+	52.5466i	−0.144246	+	1.78355i
$869$	−22.0531	−	38.1971i	−0.748101	−	1.29575i
$870$	16.6884	+	18.0926i	0.565789	+	0.613396i
$871$	9.92726	+	3.55646i	0.336372	+	0.120506i
$872$	9.89777	−	7.75089i	0.335181	−	0.262478i
$873$	−10.9547	+	6.32468i	−0.370759	+	0.214058i
$874$	−0.340147	+	0.313748i	−0.0115056	+	0.0106127i
$875$	−32.5980	−	18.8204i	−1.10201	−	0.636247i
$876$	−0.379929	+	4.69767i	−0.0128366	+	0.158719i
$877$	0.807183	+	1.39808i	0.0272566	+	0.0472098i	0.879332	−	0.476209i	$-0.157990\pi$
$877$	0.807183	+	1.39808i	0.0272566	+	0.0472098i	−0.852075	+	0.523419i	$0.824656\pi$
$878$	6.95880	−	1.56672i	0.234848	−	0.0528741i
$879$	5.54943			0.187178
$880$	7.39574	−	45.4236i	0.249311	−	1.53123i
$881$	−11.5953	−	20.0837i	−0.390656	−	0.676636i	0.601880	−	0.798586i	$-0.294419\pi$
$881$	−11.5953	−	20.0837i	−0.390656	−	0.676636i	−0.992536	+	0.121950i	$0.961085\pi$
$882$	1.07886	+	4.79192i	0.0363271	+	0.161352i
$883$	8.13346	−	14.0876i	0.273713	−	0.474084i	−0.696097	−	0.717948i	$-0.745082\pi$
$883$	8.13346	−	14.0876i	0.273713	−	0.474084i	0.969810	+	0.243864i	$0.0784149\pi$
$884$	3.71874	+	7.84005i	0.125075	+	0.263689i
$885$	−15.8225			−0.531867
$886$	40.0695	−	36.9597i	1.34616	−	1.24168i
$887$	7.49342	−	4.32633i	0.251604	−	0.145264i	−0.368894	−	0.929471i	$-0.620264\pi$
$887$	7.49342	−	4.32633i	0.251604	−	0.145264i	0.620499	+	0.784208i	$0.286930\pi$
$888$	−1.75496	+	4.35774i	−0.0588925	+	0.146236i
$889$	−51.6707	+	29.8321i	−1.73298	+	1.00054i
$890$	−7.14294	+	22.9166i	−0.239432	+	0.768165i
$891$	−2.69894	+	4.67470i	−0.0904179	+	0.156608i
$892$	15.4380	−	22.3587i	0.516902	−	0.748626i
$893$	0.302370			0.0101184
$894$	−2.15244	−	0.670902i	−0.0719885	−	0.0224383i
$895$			0.0983105i			0.00328616i
$896$	17.6482	+	32.0798i	0.589585	+	1.07171i
$897$	−4.20935	+	7.29081i	−0.140546	+	0.243433i
$898$	−3.09486	+	2.85467i	−0.103277	+	0.0952614i
$899$	−33.2541	−	57.5978i	−1.10909	−	1.92100i
$900$	0.751838	+	0.519119i	0.0250613	+	0.0173040i
$901$	24.2584	−	14.0056i	0.808163	−	0.466593i
$902$	−26.1513	+	5.88774i	−0.870742	+	0.196040i
$903$	13.4539	−	23.3028i	0.447717	−	0.775469i
$904$	2.38155	+	16.8087i	0.0792092	+	0.559049i
$905$	14.6163	+	8.43871i	0.485861	+	0.280512i
$906$	−9.01451	+	2.02954i	−0.299487	+	0.0674270i
$907$	−10.5436	−	6.08737i	−0.350095	−	0.202128i	0.314632	−	0.949214i	$-0.398119\pi$
$907$	−10.5436	−	6.08737i	−0.350095	−	0.202128i	−0.664727	+	0.747086i	$0.731452\pi$
$908$	20.5729	+	43.3730i	0.682737	+	1.43938i
$909$	10.4593	+	6.03866i	0.346912	+	0.200290i
$910$	−11.9982	−	3.73974i	−0.397735	−	0.123971i
$911$			54.2148i			1.79622i	0.439775	+	0.898108i	$0.355058\pi$
$911$			54.2148i			1.79622i	−0.439775	+	0.898108i	$0.644942\pi$
$912$	0.155108	+	0.126718i	0.00513615	+	0.00419605i
$913$		−	73.8690i		−	2.44471i
$914$	−5.89991	+	5.44202i	−0.195152	+	0.180006i
$915$	2.49656	+	4.32417i	0.0825337	+	0.142953i
$916$	−24.0024	−	1.94122i	−0.793062	−	0.0641398i
$917$	8.25824	+	4.76789i	0.272711	+	0.157450i
$918$	−1.04610	−	4.64643i	−0.0345266	−	0.153355i
$919$	27.4357	+	47.5201i	0.905021	+	1.56754i	0.820889	+	0.571087i	$0.193478\pi$
$919$	27.4357	+	47.5201i	0.905021	+	1.56754i	0.0841313	+	0.996455i	$0.473188\pi$
$920$	−14.7172	+	36.5443i	−0.485211	+	1.20483i
$921$	−2.01720	+	1.16463i	−0.0664690	+	0.0383759i
$922$	−53.9374	−	16.8119i	−1.77633	−	0.553671i
$923$	0.782733			0.0257640
$924$	−2.81642	+	34.8239i	−0.0926535	+	1.14562i
$925$	0.379377	+	0.657100i	0.0124738	+	0.0216053i
$926$	10.8767	+	48.3105i	0.357431	+	1.58758i
$927$	−10.0101	−	5.77936i	−0.328776	−	0.189819i
$928$	−41.3168	−	20.6534i	−1.35629	−	0.677980i
$929$		−	21.9453i		−	0.720001i	−0.932952	−	0.360001i	$-0.882776\pi$
$929$		−	21.9453i		−	0.720001i	0.932952	−	0.360001i	$-0.117224\pi$
$930$	16.6464	+	18.0470i	0.545856	+	0.591785i
$931$	0.150613	+	0.0869563i	0.00493613	+	0.00284988i
$932$	−3.89314	−	8.20774i	−0.127524	−	0.268853i
$933$	2.40715			0.0788064
$934$	−46.8959	+	10.5582i	−1.53448	+	0.345475i
$935$			38.7476i			1.26718i
$936$	3.38003	+	1.36121i	0.110480	+	0.0444925i
$937$			49.1198i			1.60468i	0.596871	+	0.802338i	$0.296411\pi$
$937$			49.1198i			1.60468i	−0.596871	+	0.802338i	$0.703589\pi$
$938$	−37.1811	−	4.57980i	−1.21401	−	0.149536i
$939$		−	23.9029i		−	0.780041i
$940$	23.2586	−	11.0322i	0.758613	−	0.359830i
$941$			4.50601i			0.146892i	0.997299	+	0.0734459i	$0.0233996\pi$
$941$			4.50601i			0.146892i	−0.997299	+	0.0734459i	$0.976600\pi$
$942$	−3.30646	−	14.6861i	−0.107730	−	0.478500i
$943$	22.9469			0.747254
$944$	27.7666	−	10.5211i	0.903725	−	0.342434i
$945$	5.97380	+	3.44897i	0.194328	+	0.112195i
$946$	46.6548	−	43.0339i	1.51688	−	1.39915i
$947$			15.2981i			0.497121i	0.968616	+	0.248560i	$0.0799574\pi$
$947$			15.2981i			0.497121i	−0.968616	+	0.248560i	$0.920043\pi$
$948$	14.7653	−	7.00355i	0.479554	−	0.227465i
$949$	2.62913	+	1.51793i	0.0853451	+	0.0492740i
$950$	0.0315591	−	0.00710526i	0.00102391	−	0.000230525i
$951$	−7.28605	−	12.6198i	−0.236266	−	0.409225i
$952$	−19.0060	−	24.2704i	−0.615989	−	0.786608i
$953$	−32.5720			−1.05511			−0.527556	−	0.849520i	$-0.676891\pi$
$953$	−32.5720			−1.05511			−0.527556	+	0.849520i	$0.676891\pi$
$954$	3.50024	−	11.2298i	0.113325	−	0.363578i
$955$	−32.3610	+	18.6836i	−1.04718	+	0.604589i
$956$	−30.0178	+	14.2382i	−0.970844	+	0.460497i
$957$	−22.0383	−	38.1715i	−0.712398	−	1.23391i
$958$	−19.3435	+	4.35502i	−0.624959	+	0.140704i
$959$	50.5675	+	29.1951i	1.63291	+	0.942760i
$960$	16.5545	+	4.08805i	0.534294	+	0.131941i
$961$	−17.6704	−	30.6060i	−0.570012	−	0.987290i
$962$	2.05171	+	2.22435i	0.0661498	+	0.0717158i
$963$			1.17808i			0.0379632i
$964$	−7.23411	−	4.99491i	−0.232995	−	0.160875i
$965$		−	6.49580i		−	0.209107i
$966$	8.89982	−	28.5532i	0.286347	−	0.918683i
$967$	−4.81457	−	2.77969i	−0.154826	−	0.0893889i	0.420585	−	0.907253i	$-0.361825\pi$
$967$	−4.81457	−	2.77969i	−0.154826	−	0.0893889i	−0.575411	+	0.817864i	$0.695158\pi$
$968$	−19.1638	+	47.5857i	−0.615947	+	1.52946i
$969$	−0.146040	−	0.0843161i	−0.00469147	−	0.00270862i
$970$	8.37494	+	37.1986i	0.268903	+	1.19437i
$971$	−44.9650	−	25.9605i	−1.44300	−	0.833114i	−0.444947	−	0.895557i	$-0.646777\pi$
$971$	−44.9650	−	25.9605i	−1.44300	−	0.833114i	−0.998048	+	0.0624436i	$0.980111\pi$
$972$	−1.64580	−	1.13637i	−0.0527891	−	0.0364491i
$973$	−32.3984	+	56.1157i	−1.03865	+	1.79899i
$974$	2.79557	+	12.4169i	0.0895758	+	0.397864i
$975$	0.509672	−	0.294259i	0.0163226	−	0.00942383i
$976$	−7.25652	−	5.92831i	−0.232275	−	0.189761i
$977$	−2.94231	−	5.09623i	−0.0941328	−	0.163043i	0.815114	−	0.579301i	$-0.196674\pi$
$977$	−2.94231	−	5.09623i	−0.0941328	−	0.163043i	−0.909246	+	0.416258i	$0.863341\pi$
$978$	−22.1181	−	23.9792i	−0.707259	−	0.766769i
$979$	21.4922	−	37.2256i	0.686895	−	1.18974i
$980$	14.7580	+	1.19357i	0.471425	+	0.0381270i
$981$			4.44469i			0.141908i
$982$	10.1893	−	32.6901i	0.325153	−	1.04318i
$983$	−17.0393			−0.543469			−0.271735	−	0.962372i	$-0.587597\pi$
$983$	−17.0393			−0.543469			−0.271735	+	0.962372i	$0.587597\pi$
$984$	−1.39331	−	9.83378i	−0.0444169	−	0.313489i
$985$	12.7305	−	22.0499i	0.405628	−	0.702569i
$986$	37.1285	+	11.5727i	1.18241	+	0.368550i
$987$	−16.9243	+	9.77124i	−0.538706	+	0.311022i
$988$	0.116567	−	0.0552909i	0.00370850	−	0.00175904i
$989$	−47.0545	+	27.1669i	−1.49624	+	0.863857i
$990$	11.0320	+	11.9602i	0.350619	+	0.380120i
$991$	4.57898			0.145456			0.0727281	−	0.997352i	$-0.476829\pi$
$991$	4.57898			0.145456			0.0727281	+	0.997352i	$0.476829\pi$
$992$	−41.2127	−	20.6014i	−1.30851	−	0.654094i
$993$	4.89465	−	8.47779i	0.155327	−	0.269034i
$994$	−2.71281	+	0.610765i	−0.0860450	+	0.0193723i
$995$	−14.5807	−	25.2545i	−0.462238	−	0.800620i
$996$	27.2806	+	2.20634i	0.864417	+	0.0699107i
$997$	33.3913			1.05751			0.528757	−	0.848773i	$-0.322658\pi$
$997$	33.3913			1.05751			0.528757	+	0.848773i	$0.322658\pi$
$998$	−13.1700	−	58.4963i	−0.416888	−	1.85167i
$999$	−0.830470	−	1.43842i	−0.0262749	−	0.0455095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.4	✓	68
4.3	odd	2		804.2.j.b.499.15	yes	68
67.38	odd	6		804.2.j.b.775.15	yes	68
268.239	even	6	inner	804.2.j.a.775.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.4	✓	68	1.1	even	1	trivial
804.2.j.a.775.4	yes	68	268.239	even	6	inner
804.2.j.b.499.15	yes	68	4.3	odd	2
804.2.j.b.775.15	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35015 - 0.420832i) q^{2} -1.00000 q^{3} +(1.64580 + 1.13637i) q^{4} +2.13147i q^{5} +(1.35015 + 0.420832i) q^{6} +(-1.61812 + 2.80266i) q^{7} +(-1.74385 - 2.22688i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.35015 - 0.420832i) q^{2} -1.00000 q^{3} +(1.64580 + 1.13637i) q^{4} +2.13147i q^{5} +(1.35015 + 0.420832i) q^{6} +(-1.61812 + 2.80266i) q^{7} +(-1.74385 - 2.22688i) q^{8} +1.00000 q^{9} +(0.896992 - 2.87780i) q^{10} +(-2.69894 + 4.67470i) q^{11} +(-1.64580 - 1.13637i) q^{12} +(-1.11569 + 0.644144i) q^{13} +(3.36415 - 3.10305i) q^{14} -2.13147i q^{15} +(1.41732 + 3.74048i) q^{16} +(-1.68388 - 2.91657i) q^{17} +(-1.35015 - 0.420832i) q^{18} +(-0.0433640 + 0.0250362i) q^{19} +(-2.42214 + 3.50798i) q^{20} +(1.61812 - 2.80266i) q^{21} +(5.61124 - 5.17574i) q^{22} +(-5.65931 + 3.26740i) q^{23} +(1.74385 + 2.22688i) q^{24} +0.456822 q^{25} +(1.77742 - 0.400172i) q^{26} -1.00000 q^{27} +(-5.84796 + 2.77384i) q^{28} +(4.08277 - 7.07157i) q^{29} +(-0.896992 + 2.87780i) q^{30} +(4.07249 - 7.05376i) q^{31} +(-0.339481 - 5.64666i) q^{32} +(2.69894 - 4.67470i) q^{33} +(1.04610 + 4.64643i) q^{34} +(-5.97380 - 3.44897i) q^{35} +(1.64580 + 1.13637i) q^{36} +(0.830470 + 1.43842i) q^{37} +(0.0690839 - 0.0155537i) q^{38} +(1.11569 - 0.644144i) q^{39} +(4.74652 - 3.71698i) q^{40} +(-3.04104 - 1.75575i) q^{41} +(-3.36415 + 3.10305i) q^{42} +8.31453 q^{43} +(-9.75412 + 4.62663i) q^{44} +2.13147i q^{45} +(9.01593 - 2.02986i) q^{46} +(-5.22962 - 3.01932i) q^{47} +(-1.41732 - 3.74048i) q^{48} +(-1.73661 - 3.00789i) q^{49} +(-0.616777 - 0.192245i) q^{50} +(1.68388 + 2.91657i) q^{51} +(-2.56819 - 0.207705i) q^{52} +8.31744i q^{53} +(1.35015 + 0.420832i) q^{54} +(-9.96401 - 5.75272i) q^{55} +(9.06294 - 1.28409i) q^{56} +(0.0433640 - 0.0250362i) q^{57} +(-8.48829 + 7.82951i) q^{58} -7.42326i q^{59} +(2.42214 - 3.50798i) q^{60} +(-2.02872 + 1.17128i) q^{61} +(-8.46692 + 7.80979i) q^{62} +(-1.61812 + 2.80266i) q^{63} +(-1.91795 + 7.76669i) q^{64} +(-1.37298 - 2.37806i) q^{65} +(-5.61124 + 5.17574i) q^{66} +(-5.29310 - 6.24365i) q^{67} +(0.542969 - 6.71360i) q^{68} +(5.65931 - 3.26740i) q^{69} +(6.61408 + 7.17059i) q^{70} +(-0.526176 - 0.303788i) q^{71} +(-1.74385 - 2.22688i) q^{72} +(-1.17825 - 2.04079i) q^{73} +(-0.515926 - 2.29156i) q^{74} -0.456822 q^{75} +(-0.0998190 - 0.00807297i) q^{76} +(-8.73441 - 15.1284i) q^{77} +(-1.77742 + 0.400172i) q^{78} +(-4.08552 + 7.07632i) q^{79} +(-7.97274 + 3.02098i) q^{80} +1.00000 q^{81} +(3.36698 + 3.65028i) q^{82} +(-11.8514 + 6.84241i) q^{83} +(5.84796 - 2.77384i) q^{84} +(6.21658 - 3.58914i) q^{85} +(-11.2258 - 3.49902i) q^{86} +(-4.08277 + 7.07157i) q^{87} +(15.1165 - 2.14180i) q^{88} -7.96321 q^{89} +(0.896992 - 2.87780i) q^{90} -4.16920i q^{91} +(-13.0271 - 1.05358i) q^{92} +(-4.07249 + 7.05376i) q^{93} +(5.79014 + 6.27733i) q^{94} +(-0.0533641 - 0.0924293i) q^{95} +(0.339481 + 5.64666i) q^{96} +(-10.9547 + 6.32468i) q^{97} +(1.07886 + 4.79192i) q^{98} +(-2.69894 + 4.67470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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