LMFDB - Embedded newform 260.2.j.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(31,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("260.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.j (of order $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41372 - 0.0374414i) q^{2} +1.74175i q^{3} +(1.99720 + 0.105863i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0652137 - 2.46234i) q^{6} +(-2.26642 + 2.26642i) q^{7} +(-2.81951 - 0.224439i) q^{8} -0.0336953 q^{9} +O(q^{10})$	\(q+(-1.41372 - 0.0374414i) q^{2} +1.74175i q^{3} +(1.99720 + 0.105863i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0652137 - 2.46234i) q^{6} +(-2.26642 + 2.26642i) q^{7} +(-2.81951 - 0.224439i) q^{8} -0.0336953 q^{9} +(1.02612 - 0.973174i) q^{10} +(-1.59814 + 1.59814i) q^{11} +(-0.184387 + 3.47862i) q^{12} +(-0.802125 - 3.51520i) q^{13} +(3.28893 - 3.11922i) q^{14} +(-1.23160 - 1.23160i) q^{15} +(3.97759 + 0.422860i) q^{16} +2.66821i q^{17} +(0.0476357 + 0.00126160i) q^{18} +(-1.15916 - 1.15916i) q^{19} +(-1.48709 + 1.33737i) q^{20} +(-3.94753 - 3.94753i) q^{21} +(2.31915 - 2.19948i) q^{22} -6.60293 q^{23} +(0.390916 - 4.91088i) q^{24} -1.00000i q^{25} +(1.00236 + 4.99953i) q^{26} +5.16656i q^{27} +(-4.76641 + 4.28655i) q^{28} -4.10480 q^{29} +(1.69503 + 1.78725i) q^{30} +(2.23464 + 2.23464i) q^{31} +(-5.60735 - 0.746731i) q^{32} +(-2.78355 - 2.78355i) q^{33} +(0.0999017 - 3.77210i) q^{34} -3.20520i q^{35} +(-0.0672962 - 0.00356710i) q^{36} +(1.73673 + 1.73673i) q^{37} +(1.59533 + 1.68213i) q^{38} +(6.12259 - 1.39710i) q^{39} +(2.15240 - 1.83499i) q^{40} +(-8.52565 + 8.52565i) q^{41} +(5.43289 + 5.72850i) q^{42} +8.27355 q^{43} +(-3.36098 + 3.02261i) q^{44} +(0.0238262 - 0.0238262i) q^{45} +(9.33467 + 0.247223i) q^{46} +(-0.0921897 + 0.0921897i) q^{47} +(-0.736516 + 6.92796i) q^{48} -3.27328i q^{49} +(-0.0374414 + 1.41372i) q^{50} -4.64736 q^{51} +(-1.22987 - 7.10545i) q^{52} +12.0006 q^{53} +(0.193444 - 7.30406i) q^{54} -2.26011i q^{55} +(6.89885 - 5.88151i) q^{56} +(2.01898 - 2.01898i) q^{57} +(5.80304 + 0.153690i) q^{58} +(8.17489 - 8.17489i) q^{59} +(-2.32937 - 2.59014i) q^{60} +0.324404 q^{61} +(-3.07548 - 3.24282i) q^{62} +(0.0763676 - 0.0763676i) q^{63} +(7.89925 + 1.26561i) q^{64} +(3.05281 + 1.91843i) q^{65} +(3.83094 + 4.03938i) q^{66} +(4.81749 + 4.81749i) q^{67} +(-0.282466 + 5.32894i) q^{68} -11.5007i q^{69} +(-0.120007 + 4.53124i) q^{70} +(-0.303597 - 0.303597i) q^{71} +(0.0950042 + 0.00756254i) q^{72} +(6.07038 + 6.07038i) q^{73} +(-2.39022 - 2.52027i) q^{74} +1.74175 q^{75} +(-2.19237 - 2.43779i) q^{76} -7.24408i q^{77} +(-8.70793 + 1.74587i) q^{78} +6.79738i q^{79} +(-3.11158 + 2.51357i) q^{80} -9.09995 q^{81} +(12.3721 - 11.7336i) q^{82} +(-6.51285 - 6.51285i) q^{83} +(-7.46610 - 8.30189i) q^{84} +(-1.88671 - 1.88671i) q^{85} +(-11.6965 - 0.309774i) q^{86} -7.14955i q^{87} +(4.86464 - 4.14727i) q^{88} +(11.7278 + 11.7278i) q^{89} +(-0.0345756 + 0.0327914i) q^{90} +(9.78484 + 6.14895i) q^{91} +(-13.1873 - 0.699007i) q^{92} +(-3.89218 + 3.89218i) q^{93} +(0.133782 - 0.126879i) q^{94} +1.63931 q^{95} +(1.30062 - 9.76661i) q^{96} +(-5.65621 + 5.65621i) q^{97} +(-0.122557 + 4.62750i) q^{98} +(0.0538497 - 0.0538497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.41372	−	0.0374414i	−0.999649	−	0.0264751i
$2$	−1.41372	−	0.0374414i	−0.999649	−	0.0264751i
$3$			1.74175i			1.00560i	0.864403	+	0.502800i	$0.167697\pi$
$3$			1.74175i			1.00560i	−0.864403	+	0.502800i	$0.832303\pi$
$4$	1.99720	+	0.105863i	0.998598	+	0.0529316i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.0652137	−	2.46234i	0.0266234	−	1.00525i
$7$	−2.26642	+	2.26642i	−0.856625	+	0.856625i	−0.990939	−	0.134314i	$-0.957117\pi$
$7$	−2.26642	+	2.26642i	−0.856625	+	0.856625i	0.134314	+	0.990939i	$0.457117\pi$
$8$	−2.81951	−	0.224439i	−0.996847	−	0.0793511i
$9$	−0.0336953			−0.0112318
$10$	1.02612	−	0.973174i	0.324489	−	0.307745i
$11$	−1.59814	+	1.59814i	−0.481856	+	0.481856i	−0.905724	−	0.423868i	$-0.860672\pi$
$11$	−1.59814	+	1.59814i	−0.481856	+	0.481856i	0.423868	+	0.905724i	$0.360672\pi$
$12$	−0.184387	+	3.47862i	−0.0532281	+	1.00419i
$13$	−0.802125	−	3.51520i	−0.222469	−	0.974940i
$13$	−0.802125	−	3.51520i	−0.222469	−	0.974940i
$14$	3.28893	−	3.11922i	0.879004	−	0.833645i
$15$	−1.23160	−	1.23160i	−0.317999	−	0.317999i
$16$	3.97759	+	0.422860i	0.994396	+	0.105715i
$17$			2.66821i			0.647136i	0.946205	+	0.323568i	$0.104883\pi$
$17$			2.66821i			0.647136i	−0.946205	+	0.323568i	$0.895117\pi$
$18$	0.0476357	+	0.00126160i	0.0112278	+	0.000297362i
$19$	−1.15916	−	1.15916i	−0.265931	−	0.265931i	0.561528	−	0.827458i	$-0.310214\pi$
$19$	−1.15916	−	1.15916i	−0.265931	−	0.265931i	−0.827458	+	0.561528i	$0.810214\pi$
$20$	−1.48709	+	1.33737i	−0.332523	+	0.299046i
$21$	−3.94753	−	3.94753i	−0.861422	−	0.861422i
$22$	2.31915	−	2.19948i	0.494444	−	0.468930i
$23$	−6.60293			−1.37681			−0.688403	−	0.725329i	$-0.741688\pi$
$23$	−6.60293			−1.37681			−0.688403	+	0.725329i	$0.741688\pi$
$24$	0.390916	−	4.91088i	0.0797955	−	1.00243i
$25$		−	1.00000i		−	0.200000i
$26$	1.00236	+	4.99953i	0.196580	+	0.980488i
$27$			5.16656i			0.994306i
$28$	−4.76641	+	4.28655i	−0.900766	+	0.810081i
$29$	−4.10480			−0.762243			−0.381122	−	0.924525i	$-0.624462\pi$
$29$	−4.10480			−0.762243			−0.381122	+	0.924525i	$0.624462\pi$
$30$	1.69503	+	1.78725i	0.309468	+	0.326306i
$31$	2.23464	+	2.23464i	0.401353	+	0.401353i	0.878710	−	0.477357i	$-0.158405\pi$
$31$	2.23464	+	2.23464i	0.401353	+	0.401353i	−0.477357	+	0.878710i	$0.658405\pi$
$32$	−5.60735	−	0.746731i	−0.991249	−	0.132005i
$33$	−2.78355	−	2.78355i	−0.484555	−	0.484555i
$34$	0.0999017	−	3.77210i	0.0171330	−	0.646910i
$35$		−	3.20520i		−	0.541777i
$36$	−0.0672962	−	0.00356710i	−0.0112160	−	0.000594516i
$37$	1.73673	+	1.73673i	0.285516	+	0.285516i	0.835304	−	0.549788i	$-0.185291\pi$
$37$	1.73673	+	1.73673i	0.285516	+	0.285516i	−0.549788	+	0.835304i	$0.685291\pi$
$38$	1.59533	+	1.68213i	0.258797	+	0.272878i
$39$	6.12259	−	1.39710i	0.980400	−	0.223715i
$40$	2.15240	−	1.83499i	0.340324	−	0.290138i
$41$	−8.52565	+	8.52565i	−1.33148	+	1.33148i	−0.427438	+	0.904045i	$0.640584\pi$
$41$	−8.52565	+	8.52565i	−1.33148	+	1.33148i	−0.904045	+	0.427438i	$0.859416\pi$
$42$	5.43289	+	5.72850i	0.838314	+	0.883926i
$43$	8.27355			1.26170			0.630852	−	0.775903i	$-0.282705\pi$
$43$	8.27355			1.26170			0.630852	+	0.775903i	$0.282705\pi$
$44$	−3.36098	+	3.02261i	−0.506686	+	0.455675i
$45$	0.0238262	−	0.0238262i	0.00355180	−	0.00355180i
$46$	9.33467	+	0.247223i	1.37632	+	0.0364511i
$47$	−0.0921897	+	0.0921897i	−0.0134472	+	0.0134472i	−0.713798	−	0.700351i	$-0.753027\pi$
$47$	−0.0921897	+	0.0921897i	−0.0134472	+	0.0134472i	0.700351	+	0.713798i	$0.253027\pi$
$48$	−0.736516	+	6.92796i	−0.106307	+	0.999965i
$49$		−	3.27328i		−	0.467612i
$50$	−0.0374414	+	1.41372i	−0.00529502	+	0.199930i
$51$	−4.64736			−0.650761
$52$	−1.22987	−	7.10545i	−0.170552	−	0.985349i
$53$	12.0006			1.64841			0.824206	−	0.566290i	$-0.191622\pi$
$53$	12.0006			1.64841			0.824206	+	0.566290i	$0.191622\pi$
$54$	0.193444	−	7.30406i	0.0263243	−	0.993957i
$55$		−	2.26011i		−	0.304753i
$56$	6.89885	−	5.88151i	0.921898	−	0.785950i
$57$	2.01898	−	2.01898i	0.267420	−	0.267420i
$58$	5.80304	+	0.153690i	0.761976	+	0.0201805i
$59$	8.17489	−	8.17489i	1.06428	−	1.06428i	0.0664931	−	0.997787i	$-0.478819\pi$
$59$	8.17489	−	8.17489i	1.06428	−	1.06428i	0.997787	−	0.0664931i	$-0.0211810\pi$
$60$	−2.32937	−	2.59014i	−0.300721	−	0.334385i
$61$	0.324404			0.0415356			0.0207678	−	0.999784i	$-0.493389\pi$
$61$	0.324404			0.0415356			0.0207678	+	0.999784i	$0.493389\pi$
$62$	−3.07548	−	3.24282i	−0.390586	−	0.411838i
$63$	0.0763676	−	0.0763676i	0.00962142	−	0.00962142i
$64$	7.89925	+	1.26561i	0.987407	+	0.158202i
$65$	3.05281	+	1.91843i	0.378654	+	0.237952i
$66$	3.83094	+	4.03938i	0.471556	+	0.497213i
$67$	4.81749	+	4.81749i	0.588550	+	0.588550i	0.937239	−	0.348689i	$-0.113373\pi$
$67$	4.81749	+	4.81749i	0.588550	+	0.588550i	−0.348689	+	0.937239i	$0.613373\pi$
$68$	−0.282466	+	5.32894i	−0.0342540	+	0.646229i
$69$		−	11.5007i		−	1.38452i
$70$	−0.120007	+	4.53124i	−0.0143436	+	0.541587i
$71$	−0.303597	−	0.303597i	−0.0360304	−	0.0360304i	0.688862	−	0.724892i	$-0.258111\pi$
$71$	−0.303597	−	0.303597i	−0.0360304	−	0.0360304i	−0.724892	+	0.688862i	$0.758111\pi$
$72$	0.0950042	+	0.00756254i	0.0111964	+	0.000891253i
$73$	6.07038	+	6.07038i	0.710485	+	0.710485i	0.966637	−	0.256152i	$-0.0824547\pi$
$73$	6.07038	+	6.07038i	0.710485	+	0.710485i	−0.256152	+	0.966637i	$0.582455\pi$
$74$	−2.39022	−	2.52027i	−0.277857	−	0.292975i
$75$	1.74175			0.201120
$76$	−2.19237	−	2.43779i	−0.251482	−	0.279634i
$77$		−	7.24408i		−	0.825540i
$78$	−8.70793	+	1.74587i	−0.985979	+	0.197681i
$79$			6.79738i			0.764765i	0.924004	+	0.382383i	$0.124896\pi$
$79$			6.79738i			0.764765i	−0.924004	+	0.382383i	$0.875104\pi$
$80$	−3.11158	+	2.51357i	−0.347886	+	0.281026i
$81$	−9.09995			−1.01111
$82$	12.3721	−	11.7336i	1.36627	−	1.29576i
$83$	−6.51285	−	6.51285i	−0.714878	−	0.714878i	0.252674	−	0.967552i	$-0.418690\pi$
$83$	−6.51285	−	6.51285i	−0.714878	−	0.714878i	−0.967552	+	0.252674i	$0.918690\pi$
$84$	−7.46610	−	8.30189i	−0.814618	−	0.905811i
$85$	−1.88671	−	1.88671i	−0.204643	−	0.204643i
$86$	−11.6965	−	0.309774i	−1.26126	−	0.0334037i
$87$		−	7.14955i		−	0.766512i
$88$	4.86464	−	4.14727i	0.518573	−	0.442101i
$89$	11.7278	+	11.7278i	1.24314	+	1.24314i	0.958692	+	0.284448i	$0.0918102\pi$
$89$	11.7278	+	11.7278i	1.24314	+	1.24314i	0.284448	+	0.958692i	$0.408190\pi$
$90$	−0.0345756	+	0.0327914i	−0.00364459	+	0.00345652i
$91$	9.78484	+	6.14895i	1.02573	+	0.644585i
$92$	−13.1873	−	0.699007i	−1.37488	−	0.0728766i
$93$	−3.89218	+	3.89218i	−0.403601	+	0.403601i
$94$	0.133782	−	0.126879i	0.0137986	−	0.0130865i
$95$	1.63931			0.168189
$96$	1.30062	−	9.76661i	0.132744	−	0.996800i
$97$	−5.65621	+	5.65621i	−0.574301	+	0.574301i	−0.933327	−	0.359027i	$-0.883109\pi$
$97$	−5.65621	+	5.65621i	−0.574301	+	0.574301i	0.359027	+	0.933327i	$0.383109\pi$
$98$	−0.122557	+	4.62750i	−0.0123801	+	0.467448i
$99$	0.0538497	−	0.0538497i	0.00541210	−	0.00541210i
$100$	0.105863	−	1.99720i	0.0105863	−	0.199720i
$101$			3.67474i			0.365651i	0.983145	+	0.182825i	$0.0585243\pi$
$101$			3.67474i			0.365651i	−0.983145	+	0.182825i	$0.941476\pi$
$102$	6.57006	+	0.174004i	0.650532	+	0.0172290i
$103$	−11.1740			−1.10101			−0.550503	−	0.834833i	$-0.685564\pi$
$103$	−11.1740			−1.10101			−0.550503	+	0.834833i	$0.685564\pi$
$104$	1.47265	+	10.0911i	0.144405	+	0.989519i
$105$	5.58265			0.544811
$106$	−16.9655	−	0.449321i	−1.64783	−	0.0436419i
$107$			4.97288i			0.480746i	0.970681	+	0.240373i	$0.0772698\pi$
$107$			4.97288i			0.480746i	−0.970681	+	0.240373i	$0.922730\pi$
$108$	−0.546949	+	10.3186i	−0.0526302	+	0.992912i
$109$	5.15389	−	5.15389i	0.493653	−	0.493653i	−0.415802	−	0.909455i	$-0.636499\pi$
$109$	5.15389	−	5.15389i	0.493653	−	0.493653i	0.909455	+	0.415802i	$0.136499\pi$
$110$	−0.0846216	+	3.19515i	−0.00806836	+	0.304646i
$111$	−3.02495	+	3.02495i	−0.287115	+	0.287115i
$112$	−9.97324	+	8.05649i	−0.942383	+	0.761267i
$113$	19.5213			1.83641			0.918204	−	0.396108i	$-0.129639\pi$
$113$	19.5213			1.83641			0.918204	+	0.396108i	$0.129639\pi$
$114$	−2.92985	+	2.77867i	−0.274406	+	0.260246i
$115$	4.66897	−	4.66897i	0.435384	−	0.435384i
$116$	−8.19810	−	0.434548i	−0.761175	−	0.0403468i
$117$	0.0270278	+	0.118446i	0.00249873	+	0.0109503i
$118$	−11.8631	+	11.2509i	−1.09208	+	1.03573i
$119$	−6.04728	−	6.04728i	−0.554353	−	0.554353i
$120$	3.19610	+	3.74894i	0.291762	+	0.342230i
$121$			5.89192i			0.535629i
$122$	−0.458615	−	0.0121461i	−0.0415211	−	0.00109966i
$123$	−14.8496	−	14.8496i	−1.33894	−	1.33894i
$124$	4.22645	+	4.69958i	0.379546	+	0.422035i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.110822	+	0.105103i	−0.00987277	+	0.00936332i
$127$	−5.90768			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$127$	−5.90768			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$128$	−11.1199	−	2.08498i	−0.982872	−	0.184288i
$129$			14.4105i			1.26877i
$130$	−4.24398	−	2.82642i	−0.372221	−	0.247894i
$131$			12.5382i			1.09547i	0.836651	+	0.547736i	$0.184510\pi$
$131$			12.5382i			1.09547i	−0.836651	+	0.547736i	$0.815490\pi$
$132$	−5.26463	−	5.85398i	−0.458227	−	0.509524i
$133$	5.25430			0.455605
$134$	−6.63019	−	6.99094i	−0.572762	−	0.603925i
$135$	−3.65331	−	3.65331i	−0.314427	−	0.314427i
$136$	0.598850	−	7.52305i	0.0513510	−	0.645096i
$137$	−5.79801	−	5.79801i	−0.495357	−	0.495357i	0.414632	−	0.909989i	$-0.363910\pi$
$137$	−5.79801	−	5.79801i	−0.495357	−	0.495357i	−0.909989	+	0.414632i	$0.863910\pi$
$138$	−0.430601	+	16.2587i	−0.0366552	+	1.38403i
$139$		−	17.2729i		−	1.46507i	−0.680731	−	0.732533i	$-0.738338\pi$
$139$		−	17.2729i		−	1.46507i	0.680731	−	0.732533i	$-0.261662\pi$
$140$	0.339313	−	6.40141i	0.0286772	−	0.541018i
$141$	−0.160571	−	0.160571i	−0.0135226	−	0.0135226i
$142$	0.417834	+	0.440568i	0.0350638	+	0.0369717i
$143$	6.89966	+	4.33586i	0.576979	+	0.362582i
$144$	−0.134026	−	0.0142484i	−0.0111688	−	0.00118737i
$145$	2.90254	−	2.90254i	0.241042	−	0.241042i
$146$	−8.35453	−	8.80909i	−0.691425	−	0.729046i
$147$	5.70125			0.470231
$148$	3.28473	+	3.65244i	0.270003	+	0.300229i
$149$	−11.1511	+	11.1511i	−0.913538	+	0.913538i	−0.996549	−	0.0830109i	$-0.973546\pi$
$149$	−11.1511	+	11.1511i	−0.913538	+	0.913538i	0.0830109	+	0.996549i	$0.473546\pi$
$150$	−2.46234	−	0.0652137i	−0.201050	−	0.00532467i
$151$	0.342003	−	0.342003i	0.0278318	−	0.0278318i	−0.693054	−	0.720886i	$-0.743735\pi$
$151$	0.342003	−	0.342003i	0.0278318	−	0.0278318i	0.720886	+	0.693054i	$0.243735\pi$
$152$	3.00811	+	3.52843i	0.243990	+	0.286194i
$153$		−	0.0899063i		−	0.00726849i
$154$	−0.271229	+	10.2411i	−0.0218563	+	0.825251i
$155$	−3.16026			−0.253838
$156$	12.3759	−	2.14213i	0.990867	−	0.171507i
$157$	−23.1929			−1.85100			−0.925498	−	0.378753i	$-0.876353\pi$
$157$	−23.1929			−1.85100			−0.925498	+	0.378753i	$0.876353\pi$
$158$	0.254504	−	9.60958i	0.0202472	−	0.764497i
$159$			20.9021i			1.65764i
$160$	4.49301	−	3.43698i	0.355204	−	0.271717i
$161$	14.9650	−	14.9650i	1.17941	−	1.17941i
$162$	12.8648	+	0.340715i	1.01075	+	0.0267691i
$163$	13.3797	−	13.3797i	1.04798	−	1.04798i	0.0491895	−	0.998789i	$-0.484336\pi$
$163$	13.3797	−	13.3797i	1.04798	−	1.04798i	0.998789	−	0.0491895i	$-0.0156638\pi$
$164$	−17.9299	+	16.1248i	−1.40009	+	1.25914i
$165$	3.93654			0.306459
$166$	8.96348	+	9.45118i	0.695701	+	0.733554i
$167$	14.2333	−	14.2333i	1.10141	−	1.10141i	0.107167	−	0.994241i	$-0.465822\pi$
$167$	14.2333	−	14.2333i	1.10141	−	1.10141i	0.994241	−	0.107167i	$-0.0341781\pi$
$168$	10.2441	+	12.0161i	0.790351	+	0.927061i
$169$	−11.7132	+	5.63925i	−0.901015	+	0.433788i
$170$	2.59664	+	2.73792i	0.199153	+	0.209989i
$171$	0.0390584	+	0.0390584i	0.00298687	+	0.00298687i
$172$	16.5239	+	0.875865i	1.25994	+	0.0667841i
$173$		−	0.148781i		−	0.0113116i	−0.999984	−	0.00565582i	$-0.998200\pi$
$173$		−	0.148781i		−	0.0113116i	0.999984	−	0.00565582i	$-0.00180031\pi$
$174$	−0.267689	+	10.1074i	−0.0202935	+	0.766243i
$175$	2.26642	+	2.26642i	0.171325	+	0.171325i
$176$	−7.03251	+	5.68094i	−0.530095	+	0.428217i
$177$	14.2386	+	14.2386i	1.07024	+	1.07024i
$178$	−16.1406	−	17.0188i	−1.20979	−	1.27562i
$179$	−10.0381			−0.750284			−0.375142	−	0.926967i	$-0.622406\pi$
$179$	−10.0381			−0.750284			−0.375142	+	0.926967i	$0.622406\pi$
$180$	0.0501079	−	0.0450633i	0.00373482	−	0.00335882i
$181$		−	12.5627i		−	0.933778i	−0.884316	−	0.466889i	$-0.845375\pi$
$181$		−	12.5627i		−	0.933778i	0.884316	−	0.466889i	$-0.154625\pi$
$182$	−13.6028	−	9.05923i	−1.00831	−	0.671515i
$183$			0.565030i			0.0417682i
$184$	18.6170	+	1.48195i	1.37246	+	0.109251i
$185$	−2.45610			−0.180576
$186$	5.64818	−	5.35672i	0.414144	−	0.392774i
$187$	−4.26417	−	4.26417i	−0.311827	−	0.311827i
$188$	−0.193880	+	0.174361i	−0.0141402	+	0.0127166i
$189$	−11.7096	−	11.7096i	−0.851747	−	0.851747i
$190$	−2.31752	−	0.0613780i	−0.168130	−	0.00445283i
$191$		−	2.49716i		−	0.180688i	−0.995911	−	0.0903439i	$-0.971203\pi$
$191$		−	2.49716i		−	0.180688i	0.995911	−	0.0903439i	$-0.0287966\pi$
$192$	−2.20438	+	13.7585i	−0.159088	+	0.992936i
$193$	−14.6915	−	14.6915i	−1.05752	−	1.05752i	−0.998242	−	0.0592746i	$-0.981121\pi$
$193$	−14.6915	−	14.6915i	−1.05752	−	1.05752i	−0.0592746	−	0.998242i	$-0.518879\pi$
$194$	8.20806	−	7.78450i	0.589304	−	0.558895i
$195$	−3.34143	+	5.31723i	−0.239285	+	0.380775i
$196$	0.346521	−	6.53739i	0.0247515	−	0.466957i
$197$	13.6209	−	13.6209i	0.970450	−	0.970450i	−0.0291254	−	0.999576i	$-0.509272\pi$
$197$	13.6209	−	13.6209i	0.970450	−	0.970450i	0.999576	+	0.0291254i	$0.00927222\pi$
$198$	−0.0781445	+	0.0741121i	−0.00555349	+	0.00526692i
$199$	−6.78411			−0.480913			−0.240456	−	0.970660i	$-0.577297\pi$
$199$	−6.78411			−0.480913			−0.240456	+	0.970660i	$0.577297\pi$
$200$	−0.224439	+	2.81951i	−0.0158702	+	0.199369i
$201$	−8.39086	+	8.39086i	−0.591846	+	0.591846i
$202$	0.137588	−	5.19505i	0.00968064	−	0.365522i
$203$	9.30320	−	9.30320i	0.652956	−	0.652956i
$204$	−9.28169	−	0.491985i	−0.649848	−	0.0344458i
$205$		−	12.0571i		−	0.842103i
$206$	15.7969	+	0.418371i	1.10062	+	0.0291493i
$207$	0.222488			0.0154640
$208$	−1.70409	−	14.3212i	−0.118157	−	0.992995i
$209$	3.70500			0.256281
$210$	−7.89230	−	0.209023i	−0.544620	−	0.0144239i
$211$			18.6094i			1.28112i	0.767907	+	0.640562i	$0.221298\pi$
$211$			18.6094i			1.28112i	−0.767907	+	0.640562i	$0.778702\pi$
$212$	23.9676	+	1.27043i	1.64610	+	0.0872532i
$213$	0.528791	−	0.528791i	0.0362322	−	0.0362322i
$214$	0.186192	−	7.03025i	0.0127278	−	0.480578i
$215$	−5.85028	+	5.85028i	−0.398986	+	0.398986i
$216$	1.15958	−	14.5672i	0.0788992	−	0.991170i
$217$	−10.1292			−0.687618
$218$	−7.47911	+	7.09317i	−0.506549	+	0.480410i
$219$	−10.5731	+	10.5731i	−0.714464	+	0.714464i
$220$	0.239262	−	4.51388i	0.0161311	−	0.304325i
$221$	9.37929	−	2.14024i	0.630919	−	0.143968i
$222$	4.38968	−	4.16316i	0.294616	−	0.279413i
$223$	10.2948	+	10.2948i	0.689390	+	0.689390i	0.962097	−	0.272707i	$-0.0879190\pi$
$223$	10.2948	+	10.2948i	0.689390	+	0.689390i	−0.272707	+	0.962097i	$0.587919\pi$
$224$	14.4010	−	11.0162i	0.962207	−	0.736050i
$225$			0.0336953i			0.00224635i
$226$	−27.5976	−	0.730905i	−1.83576	−	0.0486191i
$227$	8.79374	+	8.79374i	0.583661	+	0.583661i	0.935907	−	0.352246i	$-0.114582\pi$
$227$	8.79374	+	8.79374i	0.583661	+	0.583661i	−0.352246	+	0.935907i	$0.614582\pi$
$228$	4.24603	−	3.81855i	0.281200	−	0.252890i
$229$	7.70788	+	7.70788i	0.509351	+	0.509351i	0.914327	−	0.404976i	$-0.132720\pi$
$229$	7.70788	+	7.70788i	0.509351	+	0.509351i	−0.404976	+	0.914327i	$0.632720\pi$
$230$	−6.77543	+	6.42580i	−0.446758	+	0.423705i
$231$	12.6174			0.830163
$232$	11.5735	+	0.921277i	0.759840	+	0.0604848i
$233$		−	0.758703i		−	0.0497043i	−0.999691	−	0.0248521i	$-0.992089\pi$
$233$		−	0.758703i		−	0.0497043i	0.999691	−	0.0248521i	$-0.00791150\pi$
$234$	−0.0337750	−	0.168461i	−0.00220794	−	0.0110126i
$235$		−	0.130376i		−	0.00850479i
$236$	17.1923	−	15.4614i	1.11912	−	1.00645i
$237$	−11.8393			−0.769048
$238$	8.32273	+	8.77556i	0.539482	+	0.568835i
$239$	4.72028	+	4.72028i	0.305329	+	0.305329i	0.843095	−	0.537765i	$-0.180731\pi$
$239$	4.72028	+	4.72028i	0.305329	+	0.305329i	−0.537765	+	0.843095i	$0.680731\pi$
$240$	−4.37801	−	5.41960i	−0.282600	−	0.349834i
$241$	9.83574	+	9.83574i	0.633576	+	0.633576i	0.948963	−	0.315387i	$-0.102134\pi$
$241$	9.83574	+	9.83574i	0.633576	+	0.633576i	−0.315387	+	0.948963i	$0.602134\pi$
$242$	0.220602	−	8.32951i	0.0141808	−	0.535441i
$243$		−	0.350156i		−	0.0224625i
$244$	0.647898	+	0.0343424i	0.0414774	+	0.00219855i
$245$	2.31456	+	2.31456i	0.147872	+	0.147872i
$246$	20.4371	+	21.5491i	1.30302	+	1.37392i
$247$	−3.14489	+	5.00448i	−0.200105	+	0.318428i
$248$	−5.79904	−	6.80212i	−0.368240	−	0.431935i
$249$	11.3438	−	11.3438i	0.718881	−	0.718881i
$250$	−0.973174	−	1.02612i	−0.0615490	−	0.0648978i
$251$	5.95358			0.375787			0.187893	−	0.982189i	$-0.439834\pi$
$251$	5.95358			0.375787			0.187893	+	0.982189i	$0.439834\pi$
$252$	0.160606	−	0.144437i	0.0101172	−	0.00909865i
$253$	10.5524	−	10.5524i	0.663422	−	0.663422i
$254$	8.35179	+	0.221192i	0.524038	+	0.0138788i
$255$	3.28618	−	3.28618i	0.205789	−	0.205789i
$256$	15.6424	+	3.36392i	0.977649	+	0.210245i
$257$			16.3793i			1.02171i	0.859667	+	0.510855i	$0.170671\pi$
$257$			16.3793i			1.02171i	−0.859667	+	0.510855i	$0.829329\pi$
$258$	0.539548	−	20.3723i	0.0335908	−	1.26833i
$259$	−7.87230			−0.489161
$260$	5.89396	+	4.15466i	0.365528	+	0.257661i
$261$	0.138313			0.00856134
$262$	0.469450	−	17.7255i	0.0290027	−	1.09509i
$263$		−	6.44453i		−	0.397387i	−0.980062	−	0.198693i	$-0.936330\pi$
$263$		−	6.44453i		−	0.397387i	0.980062	−	0.198693i	$-0.0636698\pi$
$264$	7.22352	+	8.47299i	0.444577	+	0.521477i
$265$	−8.48572	+	8.48572i	−0.521274	+	0.521274i
$266$	−7.42809	−	0.196729i	−0.455446	−	0.0120622i
$267$	−20.4268	+	20.4268i	−1.25010	+	1.25010i
$268$	9.11147	+	10.1315i	0.556572	+	0.618878i
$269$	−16.8537			−1.02759			−0.513793	−	0.857914i	$-0.671760\pi$
$269$	−16.8537			−1.02759			−0.513793	+	0.857914i	$0.671760\pi$
$270$	5.02797	+	5.30154i	0.305992	+	0.322641i
$271$	4.89574	−	4.89574i	0.297395	−	0.297395i	−0.542598	−	0.839993i	$-0.682559\pi$
$271$	4.89574	−	4.89574i	0.297395	−	0.297395i	0.839993	+	0.542598i	$0.182559\pi$
$272$	−1.12828	+	10.6130i	−0.0684120	+	0.643510i
$273$	−10.7099	+	17.0428i	−0.648195	+	1.03147i
$274$	7.97966	+	8.41383i	0.482069	+	0.508298i
$275$	1.59814	+	1.59814i	0.0963712	+	0.0963712i
$276$	1.21750	−	22.9691i	0.0732847	−	1.38257i
$277$			13.3596i			0.802703i	0.915924	+	0.401351i	$0.131459\pi$
$277$			13.3596i			0.802703i	−0.915924	+	0.401351i	$0.868541\pi$
$278$	−0.646722	+	24.4190i	−0.0387878	+	1.46455i
$279$	−0.0752969	−	0.0752969i	−0.00450790	−	0.00450790i
$280$	−0.719370	+	9.03708i	−0.0429906	+	0.540069i
$281$	1.74676	+	1.74676i	0.104203	+	0.104203i	0.757286	−	0.653083i	$-0.226525\pi$
$281$	1.74676	+	1.74676i	0.104203	+	0.104203i	−0.653083	+	0.757286i	$0.726525\pi$
$282$	0.220991	+	0.233015i	0.0131598	+	0.0138758i
$283$	−3.58713			−0.213233			−0.106616	−	0.994300i	$-0.534002\pi$
$283$	−3.58713			−0.213233			−0.106616	+	0.994300i	$0.534002\pi$
$284$	−0.574204	−	0.638483i	−0.0340727	−	0.0378870i
$285$			2.85526i			0.169131i
$286$	−9.59184	−	6.38801i	−0.567177	−	0.377731i
$287$		−	38.6453i		−	2.28116i
$288$	0.188942	+	0.0251613i	0.0111335	+	0.00148265i
$289$	9.88065			0.581214
$290$	−4.21204	+	3.99469i	−0.247340	+	0.234576i
$291$	−9.85170	−	9.85170i	−0.577517	−	0.577517i
$292$	11.4811	+	12.7664i	0.671882	+	0.747096i
$293$	−17.0450	−	17.0450i	−0.995780	−	0.995780i	0.00421083	−	0.999991i	$-0.498660\pi$
$293$	−17.0450	−	17.0450i	−0.995780	−	0.995780i	−0.999991	+	0.00421083i	$0.998660\pi$
$294$	−8.05995	−	0.213463i	−0.470066	−	0.0124494i
$295$			11.5610i			0.673110i
$296$	−4.50693	−	5.28651i	−0.261960	−	0.307272i
$297$	−8.25687	−	8.25687i	−0.479112	−	0.479112i
$298$	16.1821	−	15.3471i	0.937403	−	0.889031i
$299$	5.29637	+	23.2106i	0.306297	+	1.34230i
$300$	3.47862	+	0.184387i	0.200838	+	0.0106456i
$301$	−18.7513	+	18.7513i	−1.08081	+	1.08081i
$302$	−0.496301	+	0.470690i	−0.0285589	+	0.0270852i
$303$	−6.40049			−0.367698
$304$	−4.12051	−	5.10084i	−0.236328	−	0.292553i
$305$	−0.229388	+	0.229388i	−0.0131347	+	0.0131347i
$306$	−0.00336622	+	0.127102i	−0.000192434	+	0.00726594i
$307$	−18.9386	+	18.9386i	−1.08089	+	1.08089i	−0.0844588	+	0.996427i	$0.526916\pi$
$307$	−18.9386	+	18.9386i	−1.08089	+	1.08089i	−0.996427	+	0.0844588i	$0.973084\pi$
$308$	0.766882	−	14.4679i	0.0436972	−	0.824383i
$309$		−	19.4623i		−	1.10717i
$310$	4.46771	+	0.118325i	0.253749	+	0.00672038i
$311$	3.93596			0.223188			0.111594	−	0.993754i	$-0.464404\pi$
$311$	3.93596			0.223188			0.111594	+	0.993754i	$0.464404\pi$
$312$	−17.5763	+	2.56499i	−0.995060	+	0.145214i
$313$	−3.48356			−0.196902			−0.0984511	−	0.995142i	$-0.531389\pi$
$313$	−3.48356			−0.196902			−0.0984511	+	0.995142i	$0.531389\pi$
$314$	32.7882	+	0.868376i	1.85035	+	0.0490053i
$315$			0.108000i			0.00608512i
$316$	−0.719593	+	13.5757i	−0.0404803	+	0.763693i
$317$	7.76202	−	7.76202i	0.435959	−	0.435959i	−0.454691	−	0.890649i	$-0.650250\pi$
$317$	7.76202	−	7.76202i	0.435959	−	0.435959i	0.890649	+	0.454691i	$0.150250\pi$
$318$	0.782605	−	29.5497i	0.0438863	−	1.65706i
$319$	6.56004	−	6.56004i	0.367292	−	0.367292i
$320$	−6.48054	+	4.69069i	−0.362273	+	0.262218i
$321$	−8.66151			−0.483438
$322$	−21.7166	+	20.5959i	−1.21022	+	1.14777i
$323$	3.09290	−	3.09290i	0.172093	−	0.172093i
$324$	−18.1744	−	0.963351i	−1.00969	−	0.0535195i
$325$	−3.51520	+	0.802125i	−0.194988	+	0.0444939i
$326$	−19.4161	+	18.4142i	−1.07536	+	1.01987i
$327$	8.97679	+	8.97679i	0.496417	+	0.496417i
$328$	25.9516	−	22.1246i	1.43294	−	1.22163i
$329$		−	0.417880i		−	0.0230385i
$330$	−5.56516	−	0.147390i	−0.306352	−	0.00811354i
$331$	−17.5261	−	17.5261i	−0.963320	−	0.963320i	0.0360307	−	0.999351i	$-0.488529\pi$
$331$	−17.5261	−	17.5261i	−0.963320	−	0.963320i	−0.999351	+	0.0360307i	$0.988529\pi$
$332$	−12.3180	−	13.6969i	−0.676036	−	0.751715i
$333$	−0.0585196	−	0.0585196i	−0.00320686	−	0.00320686i
$334$	−20.6548	+	19.5890i	−1.13018	+	1.07186i
$335$	−6.81296			−0.372232
$336$	−14.0324	−	17.3709i	−0.765530	−	0.947660i
$337$		−	23.9200i		−	1.30300i	−0.758647	−	0.651502i	$-0.774139\pi$
$337$		−	23.9200i		−	1.30300i	0.758647	−	0.651502i	$-0.225861\pi$
$338$	16.7703	−	7.53375i	0.912184	−	0.409782i
$339$			34.0012i			1.84669i
$340$	−3.56840	−	3.96786i	−0.193524	−	0.215188i
$341$	−7.14251			−0.386789
$342$	−0.0537552	−	0.0566800i	−0.00290675	−	0.00306490i
$343$	−8.44629	−	8.44629i	−0.456057	−	0.456057i
$344$	−23.3273	−	1.85690i	−1.25773	−	0.100118i
$345$	8.13219	+	8.13219i	0.437822	+	0.437822i
$346$	−0.00557059	+	0.210335i	−0.000299477	+	0.0113077i
$347$		−	34.5651i		−	1.85555i	−0.373140	−	0.927775i	$-0.621719\pi$
$347$		−	34.5651i		−	1.85555i	0.373140	−	0.927775i	$-0.378281\pi$
$348$	0.756874	−	14.2790i	0.0405727	−	0.765437i
$349$	2.27974	+	2.27974i	0.122032	+	0.122032i	0.765485	−	0.643453i	$-0.222499\pi$
$349$	2.27974	+	2.27974i	0.122032	+	0.122032i	−0.643453	+	0.765485i	$0.722499\pi$
$350$	−3.11922	−	3.28893i	−0.166729	−	0.175801i
$351$	18.1615	−	4.14423i	0.969388	−	0.221202i
$352$	10.1547	−	7.76793i	0.541247	−	0.414032i
$353$	−7.87362	+	7.87362i	−0.419070	+	0.419070i	−0.884883	−	0.465813i	$-0.845762\pi$
$353$	−7.87362	+	7.87362i	−0.419070	+	0.419070i	0.465813	+	0.884883i	$0.345762\pi$
$354$	−19.5963	−	20.6625i	−1.04153	−	1.09820i
$355$	0.429352			0.0227876
$356$	22.1811	+	24.6642i	1.17560	+	1.30720i
$357$	10.5329	−	10.5329i	0.557458	−	0.557458i
$358$	14.1911	+	0.375842i	0.750021	+	0.0198639i
$359$	23.1155	−	23.1155i	1.21999	−	1.21999i	0.252355	−	0.967635i	$-0.418795\pi$
$359$	23.1155	−	23.1155i	1.21999	−	1.21999i	0.967635	−	0.252355i	$-0.0812050\pi$
$360$	−0.0725257	+	0.0618306i	−0.00382244	+	0.00325876i
$361$		−	16.3127i		−	0.858562i
$362$	−0.470366	+	17.7601i	−0.0247219	+	0.933451i
$363$	−10.2623			−0.538629
$364$	18.8913	+	13.3165i	0.990173	+	0.697975i
$365$	−8.58482			−0.449350
$366$	0.0211556	−	0.798794i	0.00110582	−	0.0417536i
$367$			36.0866i			1.88371i	0.336026	+	0.941853i	$0.390917\pi$
$367$			36.0866i			1.88371i	−0.336026	+	0.941853i	$0.609083\pi$
$368$	−26.2637	−	2.79211i	−1.36909	−	0.145549i
$369$	0.287274	−	0.287274i	0.0149549	−	0.0149549i
$370$	3.47224	+	0.0919601i	0.180513	+	0.00478078i
$371$	−27.1984	+	27.1984i	−1.41207	+	1.41207i
$372$	−8.18549	+	7.36141i	−0.424398	+	0.381672i
$373$	27.3536			1.41631			0.708157	−	0.706055i	$-0.249527\pi$
$373$	27.3536			1.41631			0.708157	+	0.706055i	$0.249527\pi$
$374$	5.86867	+	6.18798i	0.303462	+	0.319973i
$375$	−1.23160	+	1.23160i	−0.0635997	+	0.0635997i
$376$	0.280621	−	0.239239i	0.0144719	−	0.0123378i
$377$	3.29256	+	14.4292i	0.169576	+	0.743141i
$378$	16.1156	+	16.9925i	0.828898	+	0.873998i
$379$	5.93611	+	5.93611i	0.304917	+	0.304917i	0.842934	−	0.538017i	$-0.180826\pi$
$379$	5.93611	+	5.93611i	0.304917	+	0.304917i	−0.538017	+	0.842934i	$0.680826\pi$
$380$	3.27402	+	0.173542i	0.167953	+	0.00890253i
$381$		−	10.2897i		−	0.527158i
$382$	−0.0934971	+	3.53027i	−0.00478373	+	0.180625i
$383$	16.3492	+	16.3492i	0.835403	+	0.835403i	0.988250	−	0.152847i	$-0.0488442\pi$
$383$	16.3492	+	16.3492i	0.835403	+	0.835403i	−0.152847	+	0.988250i	$0.548844\pi$
$384$	3.63152	−	19.3681i	0.185320	−	0.988377i
$385$	5.12234	+	5.12234i	0.261059	+	0.261059i
$386$	20.2195	+	21.3197i	1.02915	+	1.08514i
$387$	−0.278780			−0.0141712
$388$	−11.8953	+	10.6978i	−0.603894	+	0.543097i
$389$		−	35.4161i		−	1.79567i	−0.440335	−	0.897833i	$-0.645140\pi$
$389$		−	35.4161i		−	1.79567i	0.440335	−	0.897833i	$-0.354860\pi$
$390$	4.92292	−	7.39195i	0.249282	−	0.374306i
$391$		−	17.6180i		−	0.890981i
$392$	−0.734652	+	9.22905i	−0.0371055	+	0.466138i
$393$	−21.8385			−1.10161
$394$	−19.7661	+	18.7462i	−0.995803	+	0.944417i
$395$	−4.80648	−	4.80648i	−0.241840	−	0.241840i
$396$	0.113249	−	0.101848i	0.00569098	−	0.00511804i
$397$	13.4882	+	13.4882i	0.676952	+	0.676952i	0.959309	−	0.282358i	$-0.0911165\pi$
$397$	13.4882	+	13.4882i	0.676952	+	0.676952i	−0.282358	+	0.959309i	$0.591116\pi$
$398$	9.59082	+	0.254007i	0.480744	+	0.0127322i
$399$			9.15168i			0.458157i
$400$	0.422860	−	3.97759i	0.0211430	−	0.198879i
$401$	−5.86978	−	5.86978i	−0.293123	−	0.293123i	0.545190	−	0.838313i	$-0.316458\pi$
$401$	−5.86978	−	5.86978i	−0.293123	−	0.293123i	−0.838313	+	0.545190i	$0.816458\pi$
$402$	12.1765	−	11.5481i	0.607308	−	0.575969i
$403$	6.06273	−	9.64765i	0.302006	−	0.480584i
$404$	−0.389020	+	7.33918i	−0.0193545	+	0.365138i
$405$	6.43464	−	6.43464i	0.319740	−	0.319740i
$406$	−13.5004	+	12.8038i	−0.670015	+	0.635440i
$407$	−5.55106			−0.275156
$408$	13.1033	+	1.04305i	0.648709	+	0.0516385i
$409$	2.86259	−	2.86259i	0.141546	−	0.141546i	−0.632783	−	0.774329i	$-0.718088\pi$
$409$	2.86259	−	2.86259i	0.141546	−	0.141546i	0.774329	+	0.632783i	$0.218088\pi$
$410$	−0.451435	+	17.0453i	−0.0222948	+	0.841808i
$411$	10.0987	−	10.0987i	0.498131	−	0.498131i
$412$	−22.3167	−	1.18292i	−1.09946	−	0.0582781i
$413$			37.0554i			1.82338i
$414$	−0.314535	−	0.00833026i	−0.0154585	−	0.000409410i
$415$	9.21056			0.452129
$416$	1.87289	+	20.3099i	0.0918260	+	0.995775i
$417$	30.0851			1.47327
$418$	−5.23783	−	0.138721i	−0.256191	−	0.00678505i
$419$		−	18.2943i		−	0.893736i	−0.894600	−	0.446868i	$-0.852539\pi$
$419$		−	18.2943i		−	0.893736i	0.894600	−	0.446868i	$-0.147461\pi$
$420$	11.1497	+	0.590998i	0.544047	+	0.0288377i
$421$	7.42783	−	7.42783i	0.362010	−	0.362010i	−0.502542	−	0.864553i	$-0.667602\pi$
$421$	7.42783	−	7.42783i	0.362010	−	0.362010i	0.864553	+	0.502542i	$0.167602\pi$
$422$	0.696763	−	26.3084i	0.0339179	−	1.28067i
$423$	0.00310636	−	0.00310636i	0.000151036	−	0.000151036i
$424$	−33.8359	−	2.69341i	−1.64321	−	0.130803i
$425$	2.66821			0.129427
$426$	−0.767360	+	0.727762i	−0.0371787	+	0.0352602i
$427$	−0.735234	+	0.735234i	−0.0355805	+	0.0355805i
$428$	−0.526445	+	9.93181i	−0.0254467	+	0.480072i
$429$	−7.55198	+	12.0175i	−0.364613	+	0.580210i
$430$	8.48969	−	8.05160i	0.409409	−	0.388283i
$431$	−12.8147	−	12.8147i	−0.617262	−	0.617262i	0.327566	−	0.944828i	$-0.393772\pi$
$431$	−12.8147	−	12.8147i	−0.617262	−	0.617262i	−0.944828	+	0.327566i	$0.893772\pi$
$432$	−2.18473	+	20.5504i	−0.105113	+	0.988734i
$433$		−	5.75123i		−	0.276387i	−0.990405	−	0.138193i	$-0.955870\pi$
$433$		−	5.75123i		−	0.276387i	0.990405	−	0.138193i	$-0.0441295\pi$
$434$	14.3199	+	0.379253i	0.687377	+	0.0182047i
$435$	5.05549	+	5.05549i	0.242392	+	0.242392i
$436$	10.8389	−	9.74772i	0.519091	−	0.466831i
$437$	7.65388	+	7.65388i	0.366135	+	0.366135i
$438$	15.3432	−	14.5515i	0.733129	−	0.695298i
$439$	−34.4028			−1.64196			−0.820978	−	0.570959i	$-0.806571\pi$
$439$	−34.4028			−1.64196			−0.820978	+	0.570959i	$0.806571\pi$
$440$	−0.507255	+	6.37239i	−0.0241824	+	0.303792i
$441$			0.110294i			0.00525211i
$442$	−13.3398	+	2.67452i	−0.634509	+	0.127214i
$443$		−	7.48543i		−	0.355644i	−0.984063	−	0.177822i	$-0.943095\pi$
$443$		−	7.48543i		−	0.355644i	0.984063	−	0.177822i	$-0.0569051\pi$
$444$	−6.36165	+	5.72118i	−0.301910	+	0.271515i
$445$	−16.5855			−0.786230
$446$	−14.1685	−	14.9394i	−0.670897	−	0.707400i
$447$	−19.4225	−	19.4225i	−0.918654	−	0.918654i
$448$	−20.7714	+	15.0346i	−0.981357	+	0.710318i
$449$	18.7505	+	18.7505i	0.884892	+	0.884892i	0.994027	−	0.109135i	$-0.0348081\pi$
$449$	18.7505	+	18.7505i	0.884892	+	0.884892i	−0.109135	+	0.994027i	$0.534808\pi$
$450$	0.00126160	−	0.0476357i	5.94725e−5	−	0.00224557i
$451$		−	27.2503i		−	1.28317i
$452$	38.9878	+	2.06659i	1.83383	+	0.0972041i
$453$	0.595684	+	0.595684i	0.0279877	+	0.0279877i
$454$	−12.1026	−	12.7611i	−0.568004	−	0.598909i
$455$	−11.2669	+	2.57097i	−0.528200	+	0.120529i
$456$	−6.14565	+	5.23938i	−0.287797	+	0.245357i
$457$	−18.0533	+	18.0533i	−0.844497	+	0.844497i	−0.989440	−	0.144943i	$-0.953700\pi$
$457$	−18.0533	+	18.0533i	−0.844497	+	0.844497i	0.144943	+	0.989440i	$0.453700\pi$
$458$	−10.6082	−	11.1854i	−0.495687	−	0.522657i
$459$	−13.7855			−0.643451
$460$	9.81913	−	8.83058i	0.457819	−	0.411728i
$461$	0.192351	−	0.192351i	0.00895870	−	0.00895870i	−0.702613	−	0.711572i	$-0.747984\pi$
$461$	0.192351	−	0.192351i	0.00895870	−	0.00895870i	0.711572	+	0.702613i	$0.247984\pi$
$462$	−17.8374	−	0.472413i	−0.829872	−	0.0219787i
$463$	−7.40063	+	7.40063i	−0.343936	+	0.343936i	−0.857845	−	0.513909i	$-0.828197\pi$
$463$	−7.40063	+	7.40063i	−0.343936	+	0.343936i	0.513909	+	0.857845i	$0.328197\pi$
$464$	−16.3272	−	1.73576i	−0.757972	−	0.0805804i
$465$		−	5.50438i		−	0.255259i
$466$	−0.0284069	+	1.07259i	−0.00131593	+	0.0496869i
$467$	30.7576			1.42329			0.711646	−	0.702538i	$-0.247950\pi$
$467$	30.7576			1.42329			0.711646	+	0.702538i	$0.247950\pi$
$468$	0.0414409	+	0.239420i	0.00191560	+	0.0110672i
$469$	−21.8369			−1.00833
$470$	−0.00488146	+	0.184315i	−0.000225165	+	0.00850181i
$471$		−	40.3963i		−	1.86136i
$472$	−24.8839	+	21.2144i	−1.14538	+	0.976472i
$473$	−13.2223	+	13.2223i	−0.607960	+	0.607960i
$474$	16.7375	+	0.443282i	0.768779	+	0.0203606i
$475$	−1.15916	+	1.15916i	−0.0531861	+	0.0531861i
$476$	−11.4374	−	12.7178i	−0.524233	−	0.582919i
$477$	−0.404365			−0.0185146
$478$	−6.49641	−	6.84988i	−0.297139	−	0.313306i
$479$	14.6743	−	14.6743i	0.670485	−	0.670485i	−0.287343	−	0.957828i	$-0.592772\pi$
$479$	14.6743	−	14.6743i	0.670485	−	0.670485i	0.957828	+	0.287343i	$0.0927720\pi$
$480$	5.98636	+	7.82571i	0.273239	+	0.357193i
$481$	4.71187	−	7.49801i	0.214843	−	0.341880i
$482$	−13.5367	−	14.2732i	−0.616580	−	0.650128i
$483$	26.0653	+	26.0653i	1.18601	+	1.18601i
$484$	−0.623738	+	11.7673i	−0.0283517	+	0.534878i
$485$		−	7.99909i		−	0.363220i
$486$	−0.0131103	+	0.495021i	−0.000594697	+	0.0224546i
$487$	28.9284	+	28.9284i	1.31087	+	1.31087i	0.920772	+	0.390101i	$0.127560\pi$
$487$	28.9284	+	28.9284i	1.31087	+	1.31087i	0.390101	+	0.920772i	$0.372440\pi$
$488$	−0.914659	−	0.0728088i	−0.0414047	−	0.00329590i
$489$	23.3041	+	23.3041i	1.05385	+	1.05385i
$490$	−3.18548	−	3.35880i	−0.143905	−	0.151735i
$491$	23.8509			1.07638			0.538188	−	0.842825i	$-0.319109\pi$
$491$	23.8509			1.07638			0.538188	+	0.842825i	$0.319109\pi$
$492$	−28.0854	−	31.2295i	−1.26619	−	1.40793i
$493$		−	10.9525i		−	0.493275i
$494$	4.63337	−	6.95718i	0.208465	−	0.313018i
$495$			0.0761550i			0.00342291i
$496$	7.94353	+	9.83340i	0.356675	+	0.441533i
$497$	1.37616			0.0617290
$498$	−16.4616	+	15.6121i	−0.737662	+	0.699597i
$499$	0.393448	+	0.393448i	0.0176132	+	0.0176132i	0.715859	−	0.698245i	$-0.246036\pi$
$499$	0.393448	+	0.393448i	0.0176132	+	0.0176132i	−0.698245	+	0.715859i	$0.746036\pi$
$500$	1.33737	+	1.48709i	0.0598092	+	0.0665046i
$501$	24.7909	+	24.7909i	1.10758	+	1.10758i
$502$	−8.41668	−	0.222911i	−0.375655	−	0.00994899i
$503$			34.6269i			1.54394i	0.635661	+	0.771969i	$0.280728\pi$
$503$			34.6269i			1.54394i	−0.635661	+	0.771969i	$0.719272\pi$
$504$	−0.232459	+	0.198179i	−0.0103545	+	0.00882761i
$505$	−2.59844	−	2.59844i	−0.115629	−	0.115629i
$506$	−15.3132	+	14.5230i	−0.680754	+	0.645625i
$507$	−9.82217	−	20.4015i	−0.436218	−	0.906061i
$508$	−11.7988	−	0.625407i	−0.523487	−	0.0277479i
$509$	−6.20122	+	6.20122i	−0.274864	+	0.274864i	−0.831055	−	0.556191i	$-0.812262\pi$
$509$	−6.20122	+	6.20122i	−0.274864	+	0.274864i	0.556191	+	0.831055i	$0.312262\pi$
$510$	−4.76877	+	4.52269i	−0.211165	+	0.200268i
$511$	−27.5160			−1.21724
$512$	−21.9880	−	5.34131i	−0.971740	−	0.236055i
$513$	5.98890	−	5.98890i	0.264416	−	0.264416i
$514$	0.613264	−	23.1557i	0.0270499	−	1.02135i
$515$	7.90121	−	7.90121i	0.348169	−	0.348169i
$516$	−1.52554	+	28.7805i	−0.0671581	+	1.26699i
$517$		−	0.294663i		−	0.0129593i
$518$	11.1292	+	0.294750i	0.488989	+	0.0129506i
$519$	0.259140			0.0113750
$520$	−8.17684	−	6.09420i	−0.358578	−	0.267248i
$521$	2.74943			0.120455			0.0602275	−	0.998185i	$-0.480817\pi$
$521$	2.74943			0.120455			0.0602275	+	0.998185i	$0.480817\pi$
$522$	−0.195535	−	0.00517863i	−0.00855834	−	0.000226662i
$523$			16.1667i			0.706919i	0.935450	+	0.353460i	$0.114995\pi$
$523$			16.1667i			0.706919i	−0.935450	+	0.353460i	$0.885005\pi$
$524$	−1.32734	+	25.0413i	−0.0579851	+	1.09394i
$525$	−3.94753	+	3.94753i	−0.172284	+	0.172284i
$526$	−0.241293	+	9.11075i	−0.0105209	+	0.397248i
$527$	−5.96249	+	5.96249i	−0.259730	+	0.259730i
$528$	−9.89478	−	12.2489i	−0.430615	−	0.533064i
$529$	20.5986			0.895593
$530$	12.3141	−	11.6787i	0.534892	−	0.507290i
$531$	−0.275456	+	0.275456i	−0.0119538	+	0.0119538i
$532$	10.4939	+	0.556237i	0.454967	+	0.0241159i
$533$	36.8079	+	23.1307i	1.59433	+	1.00190i
$534$	29.6426	−	28.1129i	1.28276	−	1.21657i
$535$	−3.51636	−	3.51636i	−0.152025	−	0.152025i
$536$	−12.5017	−	14.6642i	−0.539992	−	0.633396i
$537$		−	17.4839i		−	0.754486i
$538$	23.8263	+	0.631026i	1.02723	+	0.0272055i
$539$	5.23115	+	5.23115i	0.225322	+	0.225322i
$540$	−6.90963	−	7.68313i	−0.297343	−	0.330629i
$541$	10.5714	+	10.5714i	0.454500	+	0.454500i	0.896845	−	0.442345i	$-0.145853\pi$
$541$	10.5714	+	10.5714i	0.454500	+	0.454500i	−0.442345	+	0.896845i	$0.645853\pi$
$542$	−7.10449	+	6.73789i	−0.305164	+	0.289417i
$543$	21.8811			0.939008
$544$	1.99244	−	14.9616i	0.0854250	−	0.641473i
$545$			7.28870i			0.312213i
$546$	15.7789	−	23.6927i	0.675276	−	1.01395i
$547$		−	26.4379i		−	1.13040i	−0.824953	−	0.565201i	$-0.808798\pi$
$547$		−	26.4379i		−	1.13040i	0.824953	−	0.565201i	$-0.191202\pi$
$548$	−10.9660	−	12.1936i	−0.468443	−	0.520883i
$549$	−0.0109309			−0.000466519
$550$	−2.19948	−	2.31915i	−0.0937860	−	0.0988889i
$551$	4.75814	+	4.75814i	0.202704	+	0.202704i
$552$	−2.58119	+	32.4262i	−0.109863	+	1.38015i
$553$	−15.4057	−	15.4057i	−0.655117	−	0.655117i
$554$	0.500204	−	18.8868i	0.0212516	−	0.802422i
$555$		−	4.27792i		−	0.181588i
$556$	1.82856	−	34.4973i	0.0775484	−	1.46301i
$557$	1.31630	+	1.31630i	0.0557736	+	0.0557736i	0.734443	−	0.678670i	$-0.237443\pi$
$557$	1.31630	+	1.31630i	0.0557736	+	0.0557736i	−0.678670	+	0.734443i	$0.737443\pi$
$558$	0.103629	+	0.109268i	0.00438698	+	0.00462567i
$559$	−6.63642	−	29.0831i	−0.280690	−	1.23009i
$560$	1.35535	−	12.7489i	0.0572739	−	0.538741i
$561$	7.42711	−	7.42711i	0.313573	−	0.313573i
$562$	−2.40403	−	2.53483i	−0.101408	−	0.106925i
$563$	29.6395			1.24916			0.624578	−	0.780963i	$-0.285271\pi$
$563$	29.6395			1.24916			0.624578	+	0.780963i	$0.285271\pi$
$564$	−0.303694	−	0.337691i	−0.0127878	−	0.0142194i
$565$	−13.8036	+	13.8036i	−0.580723	+	0.580723i
$566$	5.07120	+	0.134307i	0.213158	+	0.00564536i
$567$	20.6243	−	20.6243i	0.866138	−	0.866138i
$568$	0.787856	+	0.924134i	0.0330577	+	0.0387758i
$569$		−	0.251459i		−	0.0105417i	−0.999986	−	0.00527086i	$-0.998322\pi$
$569$		−	0.251459i		−	0.0105417i	0.999986	−	0.00527086i	$-0.00167777\pi$
$570$	0.106905	−	4.03654i	0.00447776	−	0.169072i
$571$	−18.1185			−0.758237			−0.379119	−	0.925348i	$-0.623773\pi$
$571$	−18.1185			−0.758237			−0.379119	+	0.925348i	$0.623773\pi$
$572$	13.3210	+	9.38998i	0.556978	+	0.392615i
$573$	4.34942			0.181700
$574$	−1.44694	+	54.6336i	−0.0603940	+	2.28036i
$575$			6.60293i			0.275361i
$576$	−0.266168	−	0.0426453i	−0.0110903	−	0.00177689i
$577$	11.6490	−	11.6490i	0.484956	−	0.484956i	−0.421754	−	0.906710i	$-0.638585\pi$
$577$	11.6490	−	11.6490i	0.484956	−	0.484956i	0.906710	+	0.421754i	$0.138585\pi$
$578$	−13.9684	−	0.369946i	−0.581011	−	0.0153877i
$579$	25.5889	−	25.5889i	1.06344	−	1.06344i
$580$	6.10420	−	5.48966i	0.253463	−	0.227946i
$581$	29.5217			1.22476
$582$	13.5587	+	14.2964i	0.562025	+	0.592604i
$583$	−19.1786	+	19.1786i	−0.794298	+	0.794298i
$584$	−15.7531	−	18.4779i	−0.651867	−	0.764622i
$585$	−0.102865	−	0.0646421i	−0.00425296	−	0.00267262i
$586$	23.4586	+	24.7350i	0.969068	+	1.02179i
$587$	−15.2424	−	15.2424i	−0.629120	−	0.629120i	0.318727	−	0.947847i	$-0.396745\pi$
$587$	−15.2424	−	15.2424i	−0.629120	−	0.629120i	−0.947847	+	0.318727i	$0.896745\pi$
$588$	11.3865	+	0.603553i	0.469572	+	0.0248901i
$589$		−	5.18063i		−	0.213464i
$590$	0.432862	−	16.3440i	0.0178206	−	0.672874i
$591$	23.7242	+	23.7242i	0.975885	+	0.975885i
$592$	6.17359	+	7.64238i	0.253733	+	0.314100i
$593$	−28.2874	−	28.2874i	−1.16162	−	1.16162i	−0.984120	−	0.177504i	$-0.943198\pi$
$593$	−28.2874	−	28.2874i	−1.16162	−	1.16162i	−0.177504	−	0.984120i	$-0.556802\pi$
$594$	11.3637	+	11.9820i	0.466260	+	0.491629i
$595$	8.55214			0.350604
$596$	−23.4515	+	21.0905i	−0.960612	+	0.863902i
$597$		−	11.8162i		−	0.483606i
$598$	−6.61853	−	33.0115i	−0.270652	−	1.34994i
$599$			8.15426i			0.333174i	0.986027	+	0.166587i	$0.0532746\pi$
$599$			8.15426i			0.333174i	−0.986027	+	0.166587i	$0.946725\pi$
$600$	−4.91088	−	0.390916i	−0.200486	−	0.0159591i
$601$	−14.8920			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$601$	−14.8920			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$602$	27.2111	−	25.8070i	1.10904	−	1.05181i
$603$	−0.162327	−	0.162327i	−0.00661046	−	0.00661046i
$604$	0.719252	−	0.646841i	0.0292660	−	0.0263196i
$605$	−4.16622	−	4.16622i	−0.169381	−	0.169381i
$606$	9.04848	+	0.239643i	0.367569	+	0.00973485i
$607$			27.0818i			1.09922i	0.835423	+	0.549608i	$0.185223\pi$
$607$			27.0818i			1.09922i	−0.835423	+	0.549608i	$0.814777\pi$
$608$	5.63426	+	7.36543i	0.228499	+	0.298707i
$609$	16.2038	+	16.2038i	0.656613	+	0.656613i
$610$	0.332879	−	0.315701i	0.0134779	−	0.0127824i
$611$	0.398012	+	0.250117i	0.0161019	+	0.0101187i
$612$	0.00951777	−	0.179560i	0.000384733	−	0.00725830i
$613$	−9.92420	+	9.92420i	−0.400835	+	0.400835i	−0.878527	−	0.477692i	$-0.841473\pi$
$613$	−9.92420	+	9.92420i	−0.400835	+	0.400835i	0.477692	+	0.878527i	$0.341473\pi$
$614$	27.4830	−	26.0648i	1.10912	−	1.05189i
$615$	21.0004			0.846819
$616$	−1.62585	+	20.4248i	−0.0655075	+	0.822937i
$617$	22.8112	−	22.8112i	0.918346	−	0.918346i	−0.0785635	−	0.996909i	$-0.525033\pi$
$617$	22.8112	−	22.8112i	0.918346	−	0.918346i	0.996909	+	0.0785635i	$0.0250333\pi$
$618$	−0.728697	+	27.5142i	−0.0293125	+	1.10678i
$619$	9.11360	−	9.11360i	0.366306	−	0.366306i	−0.499822	−	0.866128i	$-0.666601\pi$
$619$	9.11360	−	9.11360i	0.366306	−	0.366306i	0.866128	+	0.499822i	$0.166601\pi$
$620$	−6.31165	−	0.334555i	−0.253482	−	0.0134361i
$621$		−	34.1144i		−	1.36897i
$622$	−5.56433	−	0.147368i	−0.223109	−	0.00590891i
$623$	−53.1599			−2.12981
$624$	24.9439	−	2.96809i	0.998556	−	0.118819i
$625$	−1.00000			−0.0400000
$626$	4.92477	+	0.130429i	0.196833	+	0.00521301i
$627$			6.45319i			0.257716i
$628$	−46.3208	−	2.45528i	−1.84840	−	0.0979762i
$629$	−4.63396	+	4.63396i	−0.184768	+	0.184768i
$630$	0.00404368	−	0.152682i	0.000161104	−	0.00608298i
$631$	2.43988	−	2.43988i	0.0971301	−	0.0971301i	−0.656872	−	0.754002i	$-0.728121\pi$
$631$	2.43988	−	2.43988i	0.0971301	−	0.0971301i	0.754002	+	0.656872i	$0.228121\pi$
$632$	1.52560	−	19.1653i	0.0606849	−	0.762354i
$633$	−32.4129			−1.28830
$634$	−11.2639	+	10.6827i	−0.447348	+	0.424264i
$635$	4.17736	−	4.17736i	0.165774	−	0.165774i
$636$	−2.21276	+	41.7456i	−0.0877418	+	1.65532i
$637$	−11.5062	+	2.62558i	−0.455894	+	0.104029i
$638$	−9.51966	+	9.02842i	−0.376887	+	0.357439i
$639$	0.0102298	+	0.0102298i	0.000404685	+	0.000404685i
$640$	9.33728	−	6.38867i	0.369088	−	0.252535i
$641$			9.06432i			0.358019i	0.983847	+	0.179009i	$0.0572893\pi$
$641$			9.06432i			0.358019i	−0.983847	+	0.179009i	$0.942711\pi$
$642$	12.2449	+	0.324300i	0.483269	+	0.0127991i
$643$	2.58292	+	2.58292i	0.101860	+	0.101860i	0.756200	−	0.654340i	$-0.227053\pi$
$643$	2.58292	+	2.58292i	0.101860	+	0.101860i	−0.654340	+	0.756200i	$0.727053\pi$
$644$	31.4722	−	28.3038i	1.24018	−	1.11532i
$645$	−10.1897	−	10.1897i	−0.401220	−	0.401220i
$646$	−4.48828	+	4.25668i	−0.176589	+	0.167477i
$647$	11.0164			0.433101			0.216551	−	0.976271i	$-0.430519\pi$
$647$	11.0164			0.433101			0.216551	+	0.976271i	$0.430519\pi$
$648$	25.6574	+	2.04238i	1.00792	+	0.0802323i
$649$			26.1292i			1.02566i
$650$	4.99953	−	1.00236i	0.196098	−	0.0393159i
$651$		−	17.6426i		−	0.691468i
$652$	28.1383	−	25.3055i	1.10198	−	0.991039i
$653$	−16.6590			−0.651916			−0.325958	−	0.945384i	$-0.605687\pi$
$653$	−16.6590			−0.651916			−0.325958	+	0.945384i	$0.605687\pi$
$654$	−12.3545	−	13.0267i	−0.483101	−	0.509386i
$655$	−8.86588	−	8.86588i	−0.346419	−	0.346419i
$656$	−37.5166	+	30.3063i	−1.46478	+	1.18326i
$657$	−0.204544	−	0.204544i	−0.00798000	−	0.00798000i
$658$	−0.0156460	+	0.590765i	−0.000609946	+	0.0230304i
$659$		−	5.43051i		−	0.211543i	−0.994390	−	0.105771i	$-0.966269\pi$
$659$		−	5.43051i		−	0.211543i	0.994390	−	0.105771i	$-0.0337312\pi$
$660$	7.86204	+	0.416735i	0.306030	+	0.0162214i
$661$	26.9221	+	26.9221i	1.04715	+	1.04715i	0.998832	+	0.0483179i	$0.0153860\pi$
$661$	26.9221	+	26.9221i	1.04715	+	1.04715i	0.0483179	+	0.998832i	$0.484614\pi$
$662$	24.1207	+	25.4331i	0.937478	+	0.988486i
$663$	3.72776	+	16.3364i	0.144774	+	0.634452i
$664$	16.9013	+	19.8248i	0.655897	+	0.769350i
$665$	−3.71535	+	3.71535i	−0.144075	+	0.144075i
$666$	0.0805392	+	0.0849213i	0.00312083	+	0.00329063i
$667$	27.1037			1.04946
$668$	29.9335	−	26.9200i	1.15816	−	1.04157i
$669$	−17.9310	+	17.9310i	−0.693251	+	0.693251i
$670$	9.63160	+	0.255087i	0.372101	+	0.00985487i
$671$	−0.518441	+	0.518441i	−0.0200142	+	0.0200142i
$672$	19.1875	+	25.0829i	0.740172	+	0.967596i
$673$		−	5.34687i		−	0.206107i	−0.994676	−	0.103053i	$-0.967139\pi$
$673$		−	5.34687i		−	0.206107i	0.994676	−	0.103053i	$-0.0328613\pi$
$674$	−0.895599	+	33.8161i	−0.0344972	+	1.30255i
$675$	5.16656			0.198861
$676$	−23.9905	+	10.0227i	−0.922713	+	0.385488i
$677$	−3.14277			−0.120786			−0.0603932	−	0.998175i	$-0.519235\pi$
$677$	−3.14277			−0.120786			−0.0603932	+	0.998175i	$0.519235\pi$
$678$	1.27305	−	48.0681i	0.0488914	−	1.84604i
$679$		−	25.6386i		−	0.983921i
$680$	4.89615	+	5.74305i	0.187759	+	0.220236i
$681$	−15.3165	+	15.3165i	−0.586930	+	0.586930i
$682$	10.0975	+	0.267426i	0.386653	+	0.0102403i
$683$	−20.6483	+	20.6483i	−0.790084	+	0.790084i	−0.981508	−	0.191424i	$-0.938690\pi$
$683$	−20.6483	+	20.6483i	−0.790084	+	0.790084i	0.191424	+	0.981508i	$0.438690\pi$
$684$	0.0738725	+	0.0821422i	0.00282458	+	0.00314078i
$685$	8.19962			0.313291
$686$	11.6244	+	12.2569i	0.443823	+	0.467971i
$687$	−13.4252	+	13.4252i	−0.512203	+	0.512203i
$688$	32.9087	+	3.49855i	1.25463	+	0.133381i
$689$	−9.62600	−	42.1845i	−0.366721	−	1.60710i
$690$	−11.1921	−	11.8011i	−0.426077	−	0.449260i
$691$	1.36608	+	1.36608i	0.0519681	+	0.0519681i	0.732613	−	0.680645i	$-0.238300\pi$
$691$	1.36608	+	1.36608i	0.0519681	+	0.0519681i	−0.680645	+	0.732613i	$0.738300\pi$
$692$	0.0157505	−	0.297145i	0.000598743	−	0.0112958i
$693$			0.244092i			0.00927228i
$694$	−1.29417	+	48.8653i	−0.0491259	+	1.85490i
$695$	12.2138	+	12.2138i	0.463295	+	0.463295i
$696$	−1.60464	+	20.1582i	−0.0608235	+	0.764095i
$697$	−22.7482	−	22.7482i	−0.861651	−	0.861651i
$698$	−3.13756	−	3.30827i	−0.118758	−	0.125220i
$699$	1.32147			0.0499826
$700$	4.28655	+	4.76641i	0.162016	+	0.180153i
$701$			0.108679i			0.00410476i	0.999998	+	0.00205238i	$0.000653294\pi$
$701$			0.108679i			0.00410476i	−0.999998	+	0.00205238i	$0.999347\pi$
$702$	−25.8304	+	5.17878i	−0.974904	+	0.195460i
$703$		−	4.02631i		−	0.151855i
$704$	−14.6467	+	10.6015i	−0.552019	+	0.399558i
$705$	0.227082			0.00855242
$706$	11.4259	−	10.8363i	0.430018	−	0.407829i
$707$	−8.32850	−	8.32850i	−0.313225	−	0.313225i
$708$	26.9300	+	29.9447i	1.01209	+	1.12539i
$709$	−5.18698	−	5.18698i	−0.194801	−	0.194801i	0.602966	−	0.797767i	$-0.293986\pi$
$709$	−5.18698	−	5.18698i	−0.194801	−	0.194801i	−0.797767	+	0.602966i	$0.793986\pi$
$710$	−0.606982	−	0.0160755i	−0.0227796	−	0.000603304i
$711$		−	0.229040i		−	0.00858967i
$712$	−30.4343	−	35.6987i	−1.14057	−	1.33786i
$713$	−14.7552	−	14.7552i	−0.552585	−	0.552585i
$714$	−15.2848	+	14.4961i	−0.572021	+	0.542503i
$715$	−7.94471	+	1.81289i	−0.297115	+	0.0677981i
$716$	−20.0481	−	1.06267i	−0.749233	−	0.0397138i
$717$	−8.22155	+	8.22155i	−0.307039	+	0.307039i
$718$	−33.5443	+	31.8133i	−1.25186	+	1.18726i
$719$	−48.7697			−1.81880			−0.909402	−	0.415919i	$-0.863460\pi$
$719$	−48.7697			−1.81880			−0.909402	+	0.415919i	$0.863460\pi$
$720$	0.104846	−	0.0846956i	0.00390737	−	0.00315642i
$721$	25.3249	−	25.3249i	0.943150	−	0.943150i
$722$	−0.610770	+	23.0615i	−0.0227305	+	0.858261i
$723$	−17.1314	+	17.1314i	−0.637124	+	0.637124i
$724$	1.32993	−	25.0902i	0.0494264	−	0.932469i
$725$			4.10480i			0.152449i
$726$	14.5079	+	0.384234i	0.538440	+	0.0142603i
$727$	−6.38976			−0.236983			−0.118492	−	0.992955i	$-0.537806\pi$
$727$	−6.38976			−0.236983			−0.118492	+	0.992955i	$0.537806\pi$
$728$	−26.2084	−	19.5331i	−0.971347	−	0.723945i
$729$	−26.6900			−0.988517
$730$	12.1365	+	0.321428i	0.449192	+	0.0118966i
$731$			22.0756i			0.816495i
$732$	−0.0598160	+	1.12848i	−0.00221086	+	0.0417097i
$733$	−19.5916	+	19.5916i	−0.723633	+	0.723633i	−0.969343	−	0.245710i	$-0.920979\pi$
$733$	−19.5916	+	19.5916i	−0.723633	+	0.723633i	0.245710	+	0.969343i	$0.420979\pi$
$734$	1.35113	−	51.0163i	0.0498713	−	1.88305i
$735$	−4.03139	+	4.03139i	−0.148700	+	0.148700i
$736$	37.0249	+	4.93061i	1.36476	+	0.181745i
$737$	−15.3980			−0.567193
$738$	−0.416881	+	0.395369i	−0.0153456	+	0.0145537i
$739$	10.0163	−	10.0163i	0.368454	−	0.368454i	−0.498459	−	0.866913i	$-0.666101\pi$
$739$	10.0163	−	10.0163i	0.368454	−	0.368454i	0.866913	+	0.498459i	$0.166101\pi$
$740$	−4.90532	−	0.260011i	−0.180323	−	0.00955821i
$741$	−8.71656	−	5.47762i	−0.320211	−	0.201225i
$742$	39.4692	−	37.4325i	1.44896	−	1.37419i
$743$	13.9773	+	13.9773i	0.512776	+	0.512776i	0.915376	−	0.402600i	$-0.131893\pi$
$743$	13.9773	+	13.9773i	0.512776	+	0.512776i	−0.402600	+	0.915376i	$0.631893\pi$
$744$	11.8476	−	10.1005i	0.434354	−	0.370302i
$745$		−	15.7701i		−	0.577772i
$746$	−38.6702	−	1.02416i	−1.41582	−	0.0374971i
$747$	0.219453	+	0.219453i	0.00802935	+	0.00802935i
$748$	−8.06496	−	8.96779i	−0.294884	−	0.327895i
$749$	−11.2706	−	11.2706i	−0.411819	−	0.411819i
$750$	1.78725	−	1.69503i	0.0652613	−	0.0618936i
$751$	−9.35509			−0.341372			−0.170686	−	0.985325i	$-0.554598\pi$
$751$	−9.35509			−0.341372			−0.170686	+	0.985325i	$0.554598\pi$
$752$	−0.405676	+	0.327709i	−0.0147935	+	0.0119503i
$753$			10.3697i			0.377891i
$754$	−4.11451	−	20.5221i	−0.149842	−	0.747370i
$755$			0.483665i			0.0176024i
$756$	−22.1467	−	24.6259i	−0.805468	−	0.895637i
$757$	50.2995			1.82817			0.914083	−	0.405528i	$-0.132912\pi$
$757$	50.2995			1.82817			0.914083	+	0.405528i	$0.132912\pi$
$758$	−8.16972	−	8.61424i	−0.296738	−	0.312883i
$759$	18.3796	+	18.3796i	0.667137	+	0.667137i
$760$	−4.62204	−	0.367924i	−0.167659	−	0.0133460i
$761$	−6.26200	−	6.26200i	−0.226997	−	0.226997i	0.584440	−	0.811437i	$-0.301314\pi$
$761$	−6.26200	−	6.26200i	−0.226997	−	0.226997i	−0.811437	+	0.584440i	$0.801314\pi$
$762$	−0.385262	+	14.5467i	−0.0139566	+	0.526973i
$763$			23.3617i			0.845750i
$764$	0.264357	−	4.98731i	0.00956410	−	0.180435i
$765$	0.0635733	+	0.0635733i	0.00229850	+	0.00229850i
$766$	−22.5010	−	23.7252i	−0.812992	−	0.857227i
$767$	−35.2936	−	22.1791i	−1.27438	−	0.800839i
$768$	−5.85911	+	27.2451i	−0.211422	+	0.983124i
$769$	30.0666	−	30.0666i	1.08423	−	1.08423i	0.0881203	−	0.996110i	$-0.471914\pi$
$769$	30.0666	−	30.0666i	1.08423	−	1.08423i	0.996110	−	0.0881203i	$-0.0280860\pi$
$770$	−7.04976	−	7.43333i	−0.254056	−	0.267879i
$771$	−28.5286			−1.02743
$772$	−27.7865	−	30.8971i	−1.00006	−	1.11201i
$773$	−18.4121	+	18.4121i	−0.662239	+	0.662239i	−0.955907	−	0.293668i	$-0.905124\pi$
$773$	−18.4121	+	18.4121i	−0.662239	+	0.662239i	0.293668	+	0.955907i	$0.405124\pi$
$774$	0.394116	+	0.0104379i	0.0141662	+	0.000375183i
$775$	2.23464	−	2.23464i	0.0802706	−	0.0802706i
$776$	17.2172	−	14.6783i	0.618061	−	0.526919i
$777$		−	13.7116i		−	0.491900i
$778$	−1.32603	+	50.0683i	−0.0475405	+	1.79504i
$779$	19.7653			0.708164
$780$	−7.23639	+	10.2658i	−0.259104	+	0.367575i
$781$	0.970380			0.0347229
$782$	−0.659644	+	24.9069i	−0.0235888	+	0.890669i
$783$		−	21.2077i		−	0.757903i
$784$	1.38414	−	13.0198i	0.0494336	−	0.464992i
$785$	16.3999	−	16.3999i	0.585336	−	0.585336i
$786$	30.8735	+	0.817665i	1.10122	+	0.0291651i
$787$	−15.1960	+	15.1960i	−0.541677	+	0.541677i	−0.924020	−	0.382343i	$-0.875117\pi$
$787$	−15.1960	+	15.1960i	−0.541677	+	0.541677i	0.382343	+	0.924020i	$0.375117\pi$
$788$	28.6456	−	25.7617i	1.02046	−	0.917722i
$789$	11.2248			0.399612
$790$	6.61504	+	6.97496i	0.235353	+	0.248158i
$791$	−44.2434	+	44.2434i	−1.57311	+	1.57311i
$792$	−0.163916	+	0.139744i	−0.00582449	+	0.00496558i
$793$	−0.260212	−	1.14034i	−0.00924041	−	0.0404947i
$794$	−18.5634	−	19.5735i	−0.658792	−	0.694637i
$795$	−14.7800	−	14.7800i	−0.524193	−	0.524193i
$796$	−13.5492	−	0.718188i	−0.480239	−	0.0254555i
$797$			18.8382i			0.667285i	0.942700	+	0.333642i	$0.108278\pi$
$797$			18.8382i			0.667285i	−0.942700	+	0.333642i	$0.891722\pi$
$798$	0.342652	−	12.9379i	0.0121297	−	0.457996i
$799$	−0.245982	−	0.245982i	−0.00870221	−	0.00870221i
$800$	−0.746731	+	5.60735i	−0.0264009	+	0.198250i
$801$	−0.395170	−	0.395170i	−0.0139627	−	0.0139627i
$802$	8.07844	+	8.51799i	0.285260	+	0.300781i
$803$	−19.4026			−0.684703
$804$	−17.6465	+	15.8699i	−0.622344	+	0.559689i
$805$			21.1637i			0.745922i
$806$	−8.93221	+	13.4121i	−0.314624	+	0.472419i
$807$		−	29.3549i		−	1.03334i
$808$	0.824755	−	10.3610i	0.0290148	−	0.364498i
$809$	−11.7526			−0.413199			−0.206600	−	0.978426i	$-0.566240\pi$
$809$	−11.7526			−0.413199			−0.206600	+	0.978426i	$0.566240\pi$
$810$	−9.33768	+	8.85584i	−0.328093	+	0.311162i
$811$	34.0621	+	34.0621i	1.19608	+	1.19608i	0.975330	+	0.220752i	$0.0708511\pi$
$811$	34.0621	+	34.0621i	1.19608	+	1.19608i	0.220752	+	0.975330i	$0.429149\pi$
$812$	19.5652	−	17.5954i	0.686603	−	0.617479i
$813$	8.52715	+	8.52715i	0.299060	+	0.299060i
$814$	7.84763	+	0.207840i	0.275059	+	0.00728477i
$815$			18.9218i			0.662800i
$816$	−18.4853	−	1.96518i	−0.647114	−	0.0687951i
$817$	−9.59040	−	9.59040i	−0.335526	−	0.335526i
$818$	−4.15407	+	3.93971i	−0.145244	+	0.137749i
$819$	−0.329703	−	0.207191i	−0.0115208	−	0.00723983i
$820$	1.27640	−	24.0804i	0.0445739	−	0.840923i
$821$	−19.6398	+	19.6398i	−0.685434	+	0.685434i	−0.961219	−	0.275785i	$-0.911062\pi$
$821$	−19.6398	+	19.6398i	−0.685434	+	0.685434i	0.275785	+	0.961219i	$0.411062\pi$
$822$	−14.6548	+	13.8986i	−0.511145	+	0.484769i
$823$	−33.8837			−1.18111			−0.590555	−	0.806997i	$-0.701091\pi$
$823$	−33.8837			−1.18111			−0.590555	+	0.806997i	$0.701091\pi$
$824$	31.5052	+	2.50788i	1.09753	+	0.0873661i
$825$	−2.78355	+	2.78355i	−0.0969109	+	0.0969109i
$826$	1.38741	−	52.3859i	0.0482741	−	1.82274i
$827$	6.04452	−	6.04452i	0.210189	−	0.210189i	−0.594159	−	0.804348i	$-0.702515\pi$
$827$	6.04452	−	6.04452i	0.210189	−	0.210189i	0.804348	+	0.594159i	$0.202515\pi$
$828$	0.444352	+	0.0235533i	0.0154423	+	0.000818533i
$829$			8.49703i			0.295114i	0.989054	+	0.147557i	$0.0471410\pi$
$829$			8.49703i			0.295114i	−0.989054	+	0.147557i	$0.952859\pi$
$830$	−13.0211	−	0.344857i	−0.451970	−	0.0119701i
$831$	−23.2692			−0.807198
$832$	−1.88731	−	28.7826i	−0.0654306	−	0.997857i
$833$	8.73382			0.302609
$834$	−42.5318	−	1.12643i	−1.47276	−	0.0390050i
$835$			20.1290i			0.696592i
$836$	7.39962	+	0.392224i	0.255921	+	0.0135654i
$837$	−11.5454	+	11.5454i	−0.399067	+	0.399067i
$838$	−0.684966	+	25.8630i	−0.0236618	+	0.893423i
$839$	−17.7696	+	17.7696i	−0.613475	+	0.613475i	−0.943850	−	0.330375i	$-0.892825\pi$
$839$	−17.7696	+	17.7696i	−0.613475	+	0.613475i	0.330375	+	0.943850i	$0.392825\pi$
$840$	−15.7403	−	1.25296i	−0.543093	−	0.0432314i
$841$	−12.1506			−0.418985
$842$	−10.7790	+	10.2227i	−0.371468	+	0.352299i
$843$	−3.04242	+	3.04242i	−0.104787	+	0.104787i
$844$	−1.97005	+	37.1666i	−0.0678120	+	1.27933i
$845$	4.29493	−	12.2700i	0.147750	−	0.422102i
$846$	−0.00450783	+	0.00427521i	−0.000154982	+	0.000146985i
$847$	−13.3535	−	13.3535i	−0.458833	−	0.458833i
$848$	47.7335	+	5.07458i	1.63918	+	0.174262i
$849$		−	6.24789i		−	0.214427i
$850$	−3.77210	−	0.0999017i	−0.129382	−	0.00342660i
$851$	−11.4675	−	11.4675i	−0.393100	−	0.393100i
$852$	1.11208	−	1.00012i	0.0380992	−	0.0342635i
$853$	8.82745	+	8.82745i	0.302246	+	0.302246i	0.841892	−	0.539646i	$-0.181442\pi$
$853$	8.82745	+	8.82745i	0.302246	+	0.302246i	−0.539646	+	0.841892i	$0.681442\pi$
$854$	1.06694	−	1.01189i	0.0365100	−	0.0346260i
$855$	−0.0552369			−0.00188906
$856$	1.11611	−	14.0211i	0.0381477	−	0.479230i
$857$			40.4876i			1.38303i	0.722362	+	0.691515i	$0.243056\pi$
$857$			40.4876i			1.38303i	−0.722362	+	0.691515i	$0.756944\pi$
$858$	11.1263	−	16.7066i	0.379846	−	0.570354i
$859$			51.4191i			1.75440i	0.480127	+	0.877199i	$0.340590\pi$
$859$			51.4191i			1.75440i	−0.480127	+	0.877199i	$0.659410\pi$
$860$	−12.3035	+	11.0648i	−0.419546	+	0.377308i
$861$	67.3105			2.29394
$862$	17.6366	+	18.5962i	0.600704	+	0.633388i
$863$	38.5670	+	38.5670i	1.31283	+	1.31283i	0.919317	+	0.393517i	$0.128742\pi$
$863$	38.5670	+	38.5670i	1.31283	+	1.31283i	0.393517	+	0.919317i	$0.371258\pi$
$864$	3.85803	−	28.9707i	0.131253	−	0.985604i
$865$	0.105204	+	0.105204i	0.00357705	+	0.00357705i
$866$	−0.215335	+	8.13062i	−0.00731736	+	0.276290i
$867$			17.2096i			0.584469i
$868$	−20.2301	−	1.07231i	−0.686654	−	0.0363967i
$869$	−10.8631	−	10.8631i	−0.368507	−	0.368507i
$870$	−6.95775	−	7.33632i	−0.235890	−	0.248725i
$871$	13.0702	−	20.7986i	0.442866	−	0.704735i
$872$	−15.6882	+	13.3747i	−0.531268	+	0.452924i
$873$	0.190588	−	0.190588i	0.00645042	−	0.00645042i
$874$	−10.5339	−	11.1070i	−0.356313	−	0.375700i
$875$	−3.20520			−0.108355
$876$	−22.2358	+	19.9972i	−0.751280	+	0.675644i
$877$	−26.1011	+	26.1011i	−0.881371	+	0.881371i	−0.993674	−	0.112303i	$-0.964177\pi$
$877$	−26.1011	+	26.1011i	−0.881371	+	0.881371i	0.112303	+	0.993674i	$0.464177\pi$
$878$	48.6359	+	1.28809i	1.64138	+	0.0434710i
$879$	29.6882	−	29.6882i	1.00136	−	1.00136i
$880$	0.955707	−	8.98977i	0.0322169	−	0.303045i
$881$		−	21.4832i		−	0.723789i	−0.932219	−	0.361894i	$-0.882130\pi$
$881$		−	21.4832i		−	0.723789i	0.932219	−	0.361894i	$-0.117870\pi$
$882$	0.00412958	−	0.155925i	0.000139050	−	0.00525027i
$883$	3.38988			0.114079			0.0570393	−	0.998372i	$-0.481834\pi$
$883$	3.38988			0.114079			0.0570393	+	0.998372i	$0.481834\pi$
$884$	18.9588	−	3.28155i	0.637655	−	0.110371i
$885$	−20.1364			−0.676879
$886$	−0.280265	+	10.5823i	−0.00941570	+	0.355519i
$887$			22.4098i			0.752449i	0.926529	+	0.376224i	$0.122778\pi$
$887$			22.4098i			0.752449i	−0.926529	+	0.376224i	$0.877222\pi$
$888$	9.20778	−	7.84995i	0.308993	−	0.263427i
$889$	13.3893	−	13.3893i	0.449062	−	0.449062i
$890$	23.4473	+	0.620987i	0.785955	+	0.0208155i
$891$	14.5430	−	14.5430i	0.487208	−	0.487208i
$892$	19.4709	+	21.6505i	0.651933	+	0.724914i
$893$	0.213726			0.00715207
$894$	26.7308	+	28.1852i	0.894010	+	0.942653i
$895$	7.09802	−	7.09802i	0.237261	−	0.237261i
$896$	29.9278	−	20.4770i	0.999818	−	0.684087i
$897$	−40.4270	+	9.22496i	−1.34982	+	0.308012i
$898$	−25.8059	−	27.2100i	−0.861154	−	0.908009i
$899$	−9.17275	−	9.17275i	−0.305928	−	0.305928i
$900$	−0.00356710	+	0.0672962i	−0.000118903	+	0.00224321i
$901$			32.0202i			1.06675i
$902$	−1.02029	+	38.5242i	−0.0339720	+	1.28272i
$903$	−32.6601	−	32.6601i	−1.08686	−	1.08686i
$904$	−55.0404	−	4.38133i	−1.83062	−	0.145721i
$905$	8.88317	+	8.88317i	0.295287	+	0.295287i
$906$	−0.819825	−	0.864432i	−0.0272369	−	0.0287188i
$907$	−12.4767			−0.414282			−0.207141	−	0.978311i	$-0.566416\pi$
$907$	−12.4767			−0.414282			−0.207141	+	0.978311i	$0.566416\pi$
$908$	16.6319	+	18.4938i	0.551949	+	0.613737i
$909$		−	0.123822i		−	0.00410690i
$910$	16.0245	−	3.21277i	0.531206	−	0.106502i
$911$			0.958971i			0.0317721i	0.999874	+	0.0158861i	$0.00505690\pi$
$911$			0.958971i			0.0317721i	−0.999874	+	0.0158861i	$0.994943\pi$
$912$	8.88439	−	7.17690i	0.294192	−	0.237651i
$913$	20.8168			0.688937
$914$	26.1982	−	24.8463i	0.866559	−	0.821842i
$915$	−0.399537	−	0.399537i	−0.0132083	−	0.0132083i
$916$	14.5782	+	16.2101i	0.481676	+	0.535598i
$917$	−28.4169	−	28.4169i	−0.938408	−	0.938408i
$918$	19.4888	+	0.516149i	0.643226	+	0.0170354i
$919$		−	28.2468i		−	0.931775i	−0.884844	−	0.465888i	$-0.845735\pi$
$919$		−	28.2468i		−	0.931775i	0.884844	−	0.465888i	$-0.154265\pi$
$920$	−14.2121	+	12.1163i	−0.468559	+	0.399463i
$921$	−32.9864	−	32.9864i	−1.08694	−	1.08694i
$922$	−0.279133	+	0.264729i	−0.00919274	+	0.00871838i
$923$	−0.823681	+	1.31073i	−0.0271118	+	0.0431431i
$924$	25.1994	+	1.33572i	0.828999	+	0.0439419i
$925$	1.73673	−	1.73673i	0.0571033	−	0.0571033i
$926$	10.7395	−	10.1853i	0.352921	−	0.334710i
$927$	0.376511			0.0123663
$928$	23.0171	+	3.06518i	0.755573	+	0.100620i
$929$	−18.8354	+	18.8354i	−0.617970	+	0.617970i	−0.945010	−	0.327041i	$-0.893949\pi$
$929$	−18.8354	+	18.8354i	−0.617970	+	0.617970i	0.327041	+	0.945010i	$0.393949\pi$
$930$	−0.206092	+	7.78164i	−0.00675802	+	0.255170i
$931$	−3.79427	+	3.79427i	−0.124352	+	0.124352i
$932$	0.0803188	−	1.51528i	0.00263093	−	0.0496346i
$933$			6.85545i			0.224437i
$934$	−43.4826	−	1.15161i	−1.42279	−	0.0376818i
$935$	6.03044			0.197217
$936$	−0.0496214	−	0.340025i	−0.00162193	−	0.0111140i
$937$	6.12174			0.199989			0.0999943	−	0.994988i	$-0.468118\pi$
$937$	6.12174			0.199989			0.0999943	+	0.994988i	$0.468118\pi$
$938$	30.8712	+	0.817604i	1.00798	+	0.0266957i
$939$		−	6.06749i		−	0.198005i
$940$	0.0138020	−	0.260386i	0.000450172	−	0.00849286i
$941$	5.87583	−	5.87583i	0.191547	−	0.191547i	−0.604818	−	0.796364i	$-0.706754\pi$
$941$	5.87583	−	5.87583i	0.191547	−	0.191547i	0.796364	+	0.604818i	$0.206754\pi$
$942$	−1.51249	+	57.1089i	−0.0492797	+	1.86071i
$943$	56.2942	−	56.2942i	1.83319	−	1.83319i
$944$	35.9732	−	29.0595i	1.17083	−	0.945806i
$945$	16.5599			0.538692
$946$	19.1876	−	18.1975i	0.623843	−	0.591651i
$947$	−5.05346	+	5.05346i	−0.164215	+	0.164215i	−0.784431	−	0.620216i	$-0.787045\pi$
$947$	−5.05346	+	5.05346i	−0.164215	+	0.164215i	0.620216	+	0.784431i	$0.287045\pi$
$948$	−23.6455	−	1.25335i	−0.767970	−	0.0407070i
$949$	16.4694	−	26.2078i	0.534619	−	0.850741i
$950$	1.68213	−	1.59533i	0.0545756	−	0.0517594i
$951$	13.5195	+	13.5195i	0.438400	+	0.438400i
$952$	15.6931	+	18.4076i	0.508617	+	0.596594i
$953$		−	43.2043i		−	1.39952i	−0.714377	−	0.699762i	$-0.753290\pi$
$953$		−	43.2043i		−	1.39952i	0.714377	−	0.699762i	$-0.246710\pi$
$954$	0.571658	+	0.0151400i	0.0185081	+	0.000490176i
$955$	1.76576	+	1.76576i	0.0571385	+	0.0571385i
$956$	8.92762	+	9.92703i	0.288740	+	0.321063i
$957$	11.4259	+	11.4259i	0.369348	+	0.369348i
$958$	−21.2947	+	20.1959i	−0.688001	+	0.652499i
$959$	26.2814			0.848671
$960$	−8.17002	−	11.2875i	−0.263686	−	0.364302i
$961$		−	21.0128i		−	0.677832i
$962$	−6.94199	+	10.4237i	−0.223819	+	0.336072i
$963$		−	0.167563i		−	0.00539963i
$964$	18.6027	+	20.6851i	0.599151	+	0.666224i
$965$	20.7769			0.668832
$966$	−35.8730	−	37.8248i	−1.15420	−	1.21699i
$967$	27.7802	+	27.7802i	0.893350	+	0.893350i	0.994837	−	0.101487i	$-0.0323600\pi$
$967$	27.7802	+	27.7802i	0.893350	+	0.893350i	−0.101487	+	0.994837i	$0.532360\pi$
$968$	1.32238	−	16.6123i	0.0425028	−	0.533940i
$969$	5.38705	+	5.38705i	0.173057	+	0.173057i
$970$	−0.299497	+	11.3084i	−0.00961628	+	0.363092i
$971$			43.9442i			1.41024i	0.709089	+	0.705119i	$0.249106\pi$
$971$			43.9442i			1.41024i	−0.709089	+	0.705119i	$0.750894\pi$
$972$	0.0370686	−	0.699329i	0.00118898	−	0.0224310i
$973$	39.1475	+	39.1475i	1.25501	+	1.25501i
$974$	−39.8135	−	41.9798i	−1.27571	−	1.34512i
$975$	−1.39710	−	6.12259i	−0.0447430	−	0.196080i
$976$	1.29034	+	0.137177i	0.0413029	+	0.00439094i
$977$	−1.42510	+	1.42510i	−0.0455930	+	0.0455930i	−0.729536	−	0.683943i	$-0.760264\pi$
$977$	−1.42510	+	1.42510i	−0.0455930	+	0.0455930i	0.683943	+	0.729536i	$0.260264\pi$
$978$	−32.0729	−	33.8180i	−1.02558	−	1.08138i
$979$	−37.4851			−1.19803
$980$	4.37761	+	4.86766i	0.139838	+	0.155492i
$981$	−0.173662	+	0.173662i	−0.00554460	+	0.00554460i
$982$	−33.7184	−	0.893012i	−1.07600	−	0.0284972i
$983$	10.8561	−	10.8561i	0.346254	−	0.346254i	−0.512458	−	0.858712i	$-0.671265\pi$
$983$	10.8561	−	10.8561i	0.346254	−	0.346254i	0.858712	+	0.512458i	$0.171265\pi$
$984$	38.5356	+	45.2013i	1.22847	+	1.44096i
$985$			19.2629i			0.613767i
$986$	−0.410077	+	15.4837i	−0.0130595	+	0.493102i
$987$	0.727844			0.0231675
$988$	−6.81076	+	9.66201i	−0.216679	+	0.307389i
$989$	−54.6296			−1.73712
$990$	0.00285135	−	0.107662i	9.06220e−5	−	0.00342171i
$991$		−	23.6093i		−	0.749973i	−0.927030	−	0.374987i	$-0.877647\pi$
$991$		−	23.6093i		−	0.749973i	0.927030	−	0.374987i	$-0.122353\pi$
$992$	−10.8617	−	14.1991i	−0.344860	−	0.450821i
$993$	30.5260	−	30.5260i	0.968715	−	0.968715i
$994$	−1.94550	−	0.0515253i	−0.0617074	−	0.00163428i
$995$	4.79709	−	4.79709i	0.152078	−	0.152078i
$996$	23.8566	−	21.4548i	0.755925	−	0.679822i
$997$	1.47855			0.0468261			0.0234131	−	0.999726i	$-0.492547\pi$
$997$	1.47855			0.0468261			0.0234131	+	0.999726i	$0.492547\pi$
$998$	−0.541493	−	0.570956i	−0.0171407	−	0.0180733i
$999$	−8.97292	+	8.97292i	−0.283891	+	0.283891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.j.a.31.1	✓	56
4.3	odd	2	inner	260.2.j.a.31.14	yes	56
13.8	odd	4	inner	260.2.j.a.151.14	yes	56
52.47	even	4	inner	260.2.j.a.151.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.j.a.31.1	✓	56	1.1	even	1	trivial
260.2.j.a.31.14	yes	56	4.3	odd	2	inner
260.2.j.a.151.1	yes	56	52.47	even	4	inner
260.2.j.a.151.14	yes	56	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41372 - 0.0374414i) q^{2} +1.74175i q^{3} +(1.99720 + 0.105863i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0652137 - 2.46234i) q^{6} +(-2.26642 + 2.26642i) q^{7} +(-2.81951 - 0.224439i) q^{8} -0.0336953 q^{9} +O(q^{10})\)	\(q+(-1.41372 - 0.0374414i) q^{2} +1.74175i q^{3} +(1.99720 + 0.105863i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0652137 - 2.46234i) q^{6} +(-2.26642 + 2.26642i) q^{7} +(-2.81951 - 0.224439i) q^{8} -0.0336953 q^{9} +(1.02612 - 0.973174i) q^{10} +(-1.59814 + 1.59814i) q^{11} +(-0.184387 + 3.47862i) q^{12} +(-0.802125 - 3.51520i) q^{13} +(3.28893 - 3.11922i) q^{14} +(-1.23160 - 1.23160i) q^{15} +(3.97759 + 0.422860i) q^{16} +2.66821i q^{17} +(0.0476357 + 0.00126160i) q^{18} +(-1.15916 - 1.15916i) q^{19} +(-1.48709 + 1.33737i) q^{20} +(-3.94753 - 3.94753i) q^{21} +(2.31915 - 2.19948i) q^{22} -6.60293 q^{23} +(0.390916 - 4.91088i) q^{24} -1.00000i q^{25} +(1.00236 + 4.99953i) q^{26} +5.16656i q^{27} +(-4.76641 + 4.28655i) q^{28} -4.10480 q^{29} +(1.69503 + 1.78725i) q^{30} +(2.23464 + 2.23464i) q^{31} +(-5.60735 - 0.746731i) q^{32} +(-2.78355 - 2.78355i) q^{33} +(0.0999017 - 3.77210i) q^{34} -3.20520i q^{35} +(-0.0672962 - 0.00356710i) q^{36} +(1.73673 + 1.73673i) q^{37} +(1.59533 + 1.68213i) q^{38} +(6.12259 - 1.39710i) q^{39} +(2.15240 - 1.83499i) q^{40} +(-8.52565 + 8.52565i) q^{41} +(5.43289 + 5.72850i) q^{42} +8.27355 q^{43} +(-3.36098 + 3.02261i) q^{44} +(0.0238262 - 0.0238262i) q^{45} +(9.33467 + 0.247223i) q^{46} +(-0.0921897 + 0.0921897i) q^{47} +(-0.736516 + 6.92796i) q^{48} -3.27328i q^{49} +(-0.0374414 + 1.41372i) q^{50} -4.64736 q^{51} +(-1.22987 - 7.10545i) q^{52} +12.0006 q^{53} +(0.193444 - 7.30406i) q^{54} -2.26011i q^{55} +(6.89885 - 5.88151i) q^{56} +(2.01898 - 2.01898i) q^{57} +(5.80304 + 0.153690i) q^{58} +(8.17489 - 8.17489i) q^{59} +(-2.32937 - 2.59014i) q^{60} +0.324404 q^{61} +(-3.07548 - 3.24282i) q^{62} +(0.0763676 - 0.0763676i) q^{63} +(7.89925 + 1.26561i) q^{64} +(3.05281 + 1.91843i) q^{65} +(3.83094 + 4.03938i) q^{66} +(4.81749 + 4.81749i) q^{67} +(-0.282466 + 5.32894i) q^{68} -11.5007i q^{69} +(-0.120007 + 4.53124i) q^{70} +(-0.303597 - 0.303597i) q^{71} +(0.0950042 + 0.00756254i) q^{72} +(6.07038 + 6.07038i) q^{73} +(-2.39022 - 2.52027i) q^{74} +1.74175 q^{75} +(-2.19237 - 2.43779i) q^{76} -7.24408i q^{77} +(-8.70793 + 1.74587i) q^{78} +6.79738i q^{79} +(-3.11158 + 2.51357i) q^{80} -9.09995 q^{81} +(12.3721 - 11.7336i) q^{82} +(-6.51285 - 6.51285i) q^{83} +(-7.46610 - 8.30189i) q^{84} +(-1.88671 - 1.88671i) q^{85} +(-11.6965 - 0.309774i) q^{86} -7.14955i q^{87} +(4.86464 - 4.14727i) q^{88} +(11.7278 + 11.7278i) q^{89} +(-0.0345756 + 0.0327914i) q^{90} +(9.78484 + 6.14895i) q^{91} +(-13.1873 - 0.699007i) q^{92} +(-3.89218 + 3.89218i) q^{93} +(0.133782 - 0.126879i) q^{94} +1.63931 q^{95} +(1.30062 - 9.76661i) q^{96} +(-5.65621 + 5.65621i) q^{97} +(-0.122557 + 4.62750i) q^{98} +(0.0538497 - 0.0538497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

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