LMFDB - Embedded newform 82.6.f.b.23.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(23,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.23"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.8
Character	$\chi$	$=$	82.23
Dual form			82.6.f.b.25.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23607 - 3.80423i) q^{2} +18.1311i q^{3} +(-12.9443 + 9.40456i) q^{4} +(-14.5751 + 10.5894i) q^{5} +(68.9748 - 22.4113i) q^{6} +(-225.745 - 73.3489i) q^{7} +(51.7771 + 37.6183i) q^{8} -85.7366 q^{9} +(58.3003 + 42.3577i) q^{10} +(161.762 - 222.646i) q^{11} +(-170.515 - 234.694i) q^{12} +(547.828 - 178.000i) q^{13} +949.448i q^{14} +(-191.998 - 264.262i) q^{15} +(79.1084 - 243.470i) q^{16} +(861.681 - 1186.00i) q^{17} +(105.976 + 326.161i) q^{18} +(2284.25 + 742.196i) q^{19} +(89.0750 - 274.145i) q^{20} +(1329.90 - 4093.00i) q^{21} +(-1046.95 - 340.173i) q^{22} +(-838.752 - 2581.41i) q^{23} +(-682.060 + 938.775i) q^{24} +(-865.381 + 2663.37i) q^{25} +(-1354.30 - 1864.04i) q^{26} +2851.36i q^{27} +(3611.92 - 1173.58i) q^{28} +(-4730.31 - 6510.72i) q^{29} +(-767.991 + 1057.05i) q^{30} +(-4585.42 - 3331.51i) q^{31} -1024.00 q^{32} +(4036.82 + 2932.92i) q^{33} +(-5576.92 - 1812.05i) q^{34} +(4066.97 - 1321.44i) q^{35} +(1109.80 - 806.315i) q^{36} +(-782.073 + 568.209i) q^{37} -9607.19i q^{38} +(3227.33 + 9932.71i) q^{39} -1153.01 q^{40} +(8977.21 - 5938.52i) q^{41} -17214.5 q^{42} +(-7187.24 - 22120.1i) q^{43} +4403.30i q^{44} +(1249.62 - 907.900i) q^{45} +(-8783.52 + 6381.60i) q^{46} +(-9570.68 + 3109.70i) q^{47} +(4414.39 + 1434.32i) q^{48} +(31983.5 + 23237.3i) q^{49} +11201.7 q^{50} +(21503.5 + 15623.2i) q^{51} +(-5417.22 + 7456.16i) q^{52} +(10756.5 + 14805.0i) q^{53} +(10847.2 - 3524.47i) q^{54} +4958.05i q^{55} +(-8929.15 - 12289.9i) q^{56} +(-13456.8 + 41415.9i) q^{57} +(-18921.2 + 26042.9i) q^{58} +(-789.447 - 2429.67i) q^{59} +(4970.54 + 1615.03i) q^{60} +(11131.2 - 34258.3i) q^{61} +(-7005.91 + 21562.0i) q^{62} +(19354.6 + 6288.68i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-6099.71 + 8395.54i) q^{65} +(6167.71 - 18982.3i) q^{66} +(-21548.6 - 29659.0i) q^{67} +23455.7i q^{68} +(46803.8 - 15207.5i) q^{69} +(-10054.1 - 13838.3i) q^{70} +(-19597.4 + 26973.5i) q^{71} +(-4439.19 - 3225.26i) q^{72} -13053.5 q^{73} +(3128.29 + 2272.84i) q^{74} +(-48289.8 - 15690.3i) q^{75} +(-36547.9 + 11875.1i) q^{76} +(-52847.8 + 38396.2i) q^{77} +(33797.1 - 24555.0i) q^{78} -34524.1i q^{79} +(1425.20 + 4386.31i) q^{80} -72532.2 q^{81} +(-33687.9 - 26810.9i) q^{82} +15282.1 q^{83} +(21278.3 + 65488.0i) q^{84} +26410.8i q^{85} +(-75265.8 + 54683.8i) q^{86} +(118046. - 85765.7i) q^{87} +(16751.1 - 5442.77i) q^{88} +(97987.9 + 31838.2i) q^{89} +(-4998.47 - 3631.60i) q^{90} -136725. q^{91} +(35134.1 + 25526.4i) q^{92} +(60403.9 - 83138.8i) q^{93} +(23660.0 + 32565.2i) q^{94} +(-41152.5 + 13371.3i) q^{95} -18566.2i q^{96} +(-34839.0 - 47951.8i) q^{97} +(48866.4 - 150395. i) q^{98} +(-13868.9 + 19088.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$3$			18.1311i			1.16311i	0.813507	+	0.581555i	$0.197556\pi$
$3$			18.1311i			1.16311i	−0.813507	+	0.581555i	$0.802444\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−14.5751	+	10.5894i	−0.260727	+	0.189429i	−0.710467	−	0.703730i	$-0.751516\pi$
$5$	−14.5751	+	10.5894i	−0.260727	+	0.189429i	0.449741	+	0.893159i	$0.351516\pi$
$6$	68.9748	−	22.4113i	0.782190	−	0.254149i
$7$	−225.745	−	73.3489i	−1.74130	−	0.565781i	−0.746292	−	0.665619i	$-0.768168\pi$
$7$	−225.745	−	73.3489i	−1.74130	−	0.565781i	−0.995004	+	0.0998378i	$0.968168\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$	−85.7366			−0.352825
$10$	58.3003	+	42.3577i	0.184362	+	0.133947i
$11$	161.762	−	222.646i	0.403083	−	0.554797i	−0.558431	−	0.829551i	$-0.688597\pi$
$11$	161.762	−	222.646i	0.403083	−	0.554797i	0.961514	+	0.274754i	$0.0885965\pi$
$12$	−170.515	−	234.694i	−0.341830	−	0.470488i
$13$	547.828	−	178.000i	0.899053	−	0.292120i	0.177207	−	0.984174i	$-0.443294\pi$
$13$	547.828	−	178.000i	0.899053	−	0.292120i	0.721846	+	0.692053i	$0.243294\pi$
$14$			949.448i			1.29465i
$15$	−191.998	−	264.262i	−0.220327	−	0.303254i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	861.681	−	1186.00i	0.723143	−	0.995322i	−0.276270	−	0.961080i	$-0.589098\pi$
$17$	861.681	−	1186.00i	0.723143	−	0.995322i	0.999414	−	0.0342415i	$-0.0109015\pi$
$18$	105.976	+	326.161i	0.0770952	+	0.237275i
$19$	2284.25	+	742.196i	1.45164	+	0.471666i	0.925505	−	0.378735i	$-0.123641\pi$
$19$	2284.25	+	742.196i	1.45164	+	0.471666i	0.526134	+	0.850401i	$0.323641\pi$
$20$	89.0750	−	274.145i	0.0497944	−	0.153251i
$21$	1329.90	−	4093.00i	0.658066	−	2.02532i
$22$	−1046.95	−	340.173i	−0.461177	−	0.149845i
$23$	−838.752	−	2581.41i	−0.330608	−	1.01751i	−0.968845	−	0.247668i	$-0.920336\pi$
$23$	−838.752	−	2581.41i	−0.330608	−	1.01751i	0.638237	−	0.769840i	$-0.279664\pi$
$24$	−682.060	+	938.775i	−0.241710	+	0.332685i
$25$	−865.381	+	2663.37i	−0.276922	+	0.852278i
$26$	−1354.30	−	1864.04i	−0.392901	−	0.540781i
$27$			2851.36i			0.752735i
$28$	3611.92	−	1173.58i	0.870648	−	0.282891i
$29$	−4730.31	−	6510.72i	−1.04447	−	1.43759i	−0.893509	−	0.449046i	$-0.851764\pi$
$29$	−4730.31	−	6510.72i	−1.04447	−	1.43759i	−0.150958	−	0.988540i	$-0.548236\pi$
$30$	−767.991	+	1057.05i	−0.155795	+	0.214433i
$31$	−4585.42	−	3331.51i	−0.856989	−	0.622639i	0.0700750	−	0.997542i	$-0.477676\pi$
$31$	−4585.42	−	3331.51i	−0.856989	−	0.622639i	−0.927064	+	0.374903i	$0.877676\pi$
$32$	−1024.00			−0.176777
$33$	4036.82	+	2932.92i	0.645289	+	0.468830i
$34$	−5576.92	−	1812.05i	−0.827365	−	0.268827i
$35$	4066.97	−	1321.44i	0.561178	−	0.182338i
$36$	1109.80	−	806.315i	0.142721	−	0.103693i
$37$	−782.073	+	568.209i	−0.0939168	+	0.0682345i	−0.633753	−	0.773536i	$-0.718486\pi$
$37$	−782.073	+	568.209i	−0.0939168	+	0.0682345i	0.539836	+	0.841770i	$0.318486\pi$
$38$		−	9607.19i		−	1.07929i
$39$	3227.33	+	9932.71i	0.339768	+	1.04570i
$40$	−1153.01			−0.113942
$41$	8977.21	−	5938.52i	0.834030	−	0.551720i
$41$	8977.21	−	5938.52i	0.834030	−	0.551720i
$42$	−17214.5			−1.50582
$43$	−7187.24	−	22120.1i	−0.592777	−	1.82438i	−0.565496	−	0.824751i	$-0.691315\pi$
$43$	−7187.24	−	22120.1i	−0.592777	−	1.82438i	−0.0272806	−	0.999628i	$-0.508685\pi$
$44$			4403.30i			0.342883i
$45$	1249.62	−	907.900i	0.0919911	−	0.0668354i
$46$	−8783.52	+	6381.60i	−0.612032	+	0.444667i
$47$	−9570.68	+	3109.70i	−0.631973	+	0.205340i	−0.607449	−	0.794359i	$-0.707807\pi$
$47$	−9570.68	+	3109.70i	−0.631973	+	0.205340i	−0.0245240	+	0.999699i	$0.507807\pi$
$48$	4414.39	+	1434.32i	0.276546	+	0.0898552i
$49$	31983.5	+	23237.3i	1.90298	+	1.38260i
$50$	11201.7			0.633665
$51$	21503.5	+	15623.2i	1.15767	+	0.841095i
$52$	−5417.22	+	7456.16i	−0.277823	+	0.382390i
$53$	10756.5	+	14805.0i	0.525993	+	0.723968i	0.986513	−	0.163682i	$-0.0523369\pi$
$53$	10756.5	+	14805.0i	0.525993	+	0.723968i	−0.460520	+	0.887649i	$0.652337\pi$
$54$	10847.2	−	3524.47i	0.506213	−	0.164479i
$55$			4958.05i			0.221006i
$56$	−8929.15	−	12289.9i	−0.380487	−	0.523695i
$57$	−13456.8	+	41415.9i	−0.548600	+	1.68842i
$58$	−18921.2	+	26042.9i	−0.738550	+	1.01653i
$59$	−789.447	−	2429.67i	−0.0295252	−	0.0908692i	0.935208	−	0.354099i	$-0.115212\pi$
$59$	−789.447	−	2429.67i	−0.0295252	−	0.0908692i	−0.964733	+	0.263230i	$0.915212\pi$
$60$	4970.54	+	1615.03i	0.178248	+	0.0579164i
$61$	11131.2	−	34258.3i	0.383016	−	1.17880i	−0.554893	−	0.831922i	$-0.687241\pi$
$61$	11131.2	−	34258.3i	0.383016	−	1.17880i	0.937909	−	0.346881i	$-0.112759\pi$
$62$	−7005.91	+	21562.0i	−0.231465	+	0.712376i
$63$	19354.6	+	6288.68i	0.614373	+	0.199622i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−6099.71	+	8395.54i	−0.179071	+	0.246471i
$66$	6167.71	−	18982.3i	0.174287	−	0.536399i
$67$	−21548.6	−	29659.0i	−0.586450	−	0.807179i	0.407934	−	0.913011i	$-0.366249\pi$
$67$	−21548.6	−	29659.0i	−0.586450	−	0.807179i	−0.994384	+	0.105832i	$0.966249\pi$
$68$			23455.7i			0.615143i
$69$	46803.8	−	15207.5i	1.18347	−	0.384534i
$70$	−10054.1	−	13838.3i	−0.245244	−	0.337549i
$71$	−19597.4	+	26973.5i	−0.461374	+	0.635027i	−0.974793	−	0.223111i	$-0.928379\pi$
$71$	−19597.4	+	26973.5i	−0.461374	+	0.635027i	0.513419	+	0.858138i	$0.328379\pi$
$72$	−4439.19	−	3225.26i	−0.100919	−	0.0733219i
$73$	−13053.5			−0.286696			−0.143348	−	0.989672i	$-0.545787\pi$
$73$	−13053.5			−0.286696			−0.143348	+	0.989672i	$0.545787\pi$
$74$	3128.29	+	2272.84i	0.0664092	+	0.0482491i
$75$	−48289.8	−	15690.3i	−0.991293	−	0.322091i
$76$	−36547.9	+	11875.1i	−0.725820	+	0.235833i
$77$	−52847.8	+	38396.2i	−1.01578	+	0.738008i
$78$	33797.1	−	24555.0i	0.628988	−	0.456987i
$79$		−	34524.1i		−	0.622379i	−0.950348	−	0.311190i	$-0.899273\pi$
$79$		−	34524.1i		−	0.622379i	0.950348	−	0.311190i	$-0.100727\pi$
$80$	1425.20	+	4386.31i	0.0248972	+	0.0766257i
$81$	−72532.2			−1.22834
$82$	−33687.9	−	26810.9i	−0.553273	−	0.440329i
$83$	15282.1			0.243494			0.121747	−	0.992561i	$-0.461150\pi$
$83$	15282.1			0.243494			0.121747	+	0.992561i	$0.461150\pi$
$84$	21278.3	+	65488.0i	0.329033	+	1.01266i
$85$			26410.8i			0.396492i
$86$	−75265.8	+	54683.8i	−1.09737	+	0.797283i
$87$	118046.	−	85765.7i	1.67207	−	1.21483i
$88$	16751.1	−	5442.77i	0.230588	−	0.0749227i
$89$	97987.9	+	31838.2i	1.31129	+	0.426063i	0.879494	−	0.475910i	$-0.157881\pi$
$89$	97987.9	+	31838.2i	1.31129	+	0.426063i	0.431792	+	0.901973i	$0.357881\pi$
$90$	−4998.47	−	3631.60i	−0.0650475	−	0.0472598i
$91$	−136725.			−1.73079
$92$	35134.1	+	25526.4i	0.432772	+	0.314427i
$93$	60403.9	−	83138.8i	0.724198	−	0.996773i
$94$	23660.0	+	32565.2i	0.276182	+	0.380132i
$95$	−41152.5	+	13371.3i	−0.467829	+	0.152007i
$96$		−	18566.2i		−	0.205611i
$97$	−34839.0	−	47951.8i	−0.375955	−	0.517458i	0.578552	−	0.815645i	$-0.303618\pi$
$97$	−34839.0	−	47951.8i	−0.375955	−	0.517458i	−0.954507	+	0.298187i	$0.903618\pi$
$98$	48866.4	−	150395.i	0.513979	−	1.58186i
$99$	−13868.9	+	19088.9i	−0.142218	+	0.195746i
$100$	−13846.1	−	42613.9i	−0.138461	−	0.426139i
$101$	99724.4	+	32402.4i	0.972742	+	0.316063i	0.751923	−	0.659251i	$-0.229127\pi$
$101$	99724.4	+	32402.4i	0.972742	+	0.316063i	0.220820	+	0.975315i	$0.429127\pi$
$102$	32854.5	−	101116.i	0.312676	−	0.962317i
$103$	−3390.46	+	10434.7i	−0.0314894	+	0.0969145i	−0.965566	−	0.260158i	$-0.916225\pi$
$103$	−3390.46	+	10434.7i	−0.0314894	+	0.0969145i	0.934077	+	0.357073i	$0.116225\pi$
$104$	35061.0	+	11392.0i	0.317863	+	0.103280i
$105$	23959.1	+	73738.6i	0.212079	+	0.652712i
$106$	43025.9	−	59220.1i	0.371934	−	0.511923i
$107$	19928.4	−	61333.4i	0.168273	−	0.517890i	−0.830990	−	0.556287i	$-0.812225\pi$
$107$	19928.4	−	61333.4i	0.168273	−	0.517890i	0.999263	+	0.0383976i	$0.0122253\pi$
$108$	−26815.8	−	36908.8i	−0.221223	−	0.304488i
$109$		−	166098.i		−	1.33906i	−0.742787	−	0.669528i	$-0.766497\pi$
$109$		−	166098.i		−	1.33906i	0.742787	−	0.669528i	$-0.233503\pi$
$110$	18861.5	−	6128.49i	0.148626	−	0.0482916i
$111$	−10302.3	−	14179.8i	−0.0793643	−	0.109236i
$112$	−35716.6	+	49159.7i	−0.269045	+	0.370309i
$113$	3192.40	+	2319.41i	0.0235191	+	0.0170876i	0.599483	−	0.800388i	$-0.295373\pi$
$113$	3192.40	+	2319.41i	0.0235191	+	0.0170876i	−0.575964	+	0.817475i	$0.695373\pi$
$114$	174189.			1.25533
$115$	39560.5	+	28742.4i	0.278944	+	0.202665i
$116$	122461.	+	39790.0i	0.844992	+	0.274554i
$117$	−46968.8	+	15261.1i	−0.317209	+	0.103067i
$118$	−8267.20	+	6006.47i	−0.0546579	+	0.0397113i
$119$	−281512.	+	204530.i	−1.82234	+	1.32401i
$120$		−	20905.3i		−	0.132527i
$121$	26363.1	+	81137.2i	0.163694	+	0.503798i
$122$	−144085.			−0.876435
$123$	107672.	+	162767.i	0.641711	+	0.970068i
$124$	90686.3			0.529648
$125$	−32988.0	−	101527.i	−0.188834	−	0.581172i
$126$		−	81402.4i		−	0.456784i
$127$	−207705.	+	150907.i	−1.14271	+	0.830230i	−0.987495	−	0.157650i	$-0.949608\pi$
$127$	−207705.	+	150907.i	−1.14271	+	0.830230i	−0.155219	+	0.987880i	$0.549608\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$	401061.	−	130313.i	2.12195	−	0.689465i
$130$	39478.2	+	12827.2i	0.204880	+	0.0665694i
$131$	54665.6	+	39716.9i	0.278315	+	0.202207i	0.718182	−	0.695855i	$-0.244975\pi$
$131$	54665.6	+	39716.9i	0.278315	+	0.202207i	−0.439867	+	0.898063i	$0.644975\pi$
$132$	−79836.6			−0.398811
$133$	−461217.	−	335094.i	−2.26087	−	1.64262i
$134$	−86194.2	+	118636.i	−0.414683	+	0.570762i
$135$	−30194.2	−	41558.8i	−0.142590	−	0.196258i
$136$	89230.7	−	28992.8i	0.413682	−	0.134414i
$137$		−	264652.i		−	1.20469i	−0.798237	−	0.602343i	$-0.794234\pi$
$137$		−	264652.i		−	1.20469i	0.798237	−	0.602343i	$-0.205766\pi$
$138$	−115705.	−	159255.i	−0.517197	−	0.711861i
$139$	2782.50	−	8563.67i	0.0122151	−	0.0375944i	−0.944763	−	0.327754i	$-0.893708\pi$
$139$	2782.50	−	8563.67i	0.0122151	−	0.0375944i	0.956978	+	0.290159i	$0.0937083\pi$
$140$	−40216.4	+	55353.1i	−0.173414	+	0.238683i
$141$	−56382.3	−	173527.i	−0.238834	−	0.735054i
$142$	126837.	+	41211.9i	0.527868	+	0.171515i
$143$	48986.6	−	150765.i	0.200326	−	0.616540i
$144$	−6782.48	+	20874.3i	−0.0272573	+	0.0838892i
$145$	137889.	+	44803.0i	0.544641	+	0.176965i
$146$	16135.1	+	49658.6i	0.0626453	+	0.192803i
$147$	−421318.	+	579895.i	−1.60812	+	2.21338i
$148$	4779.61	−	14710.1i	0.0179365	−	0.0552029i
$149$	−71994.0	−	99091.2i	−0.265663	−	0.365653i	0.655257	−	0.755406i	$-0.272560\pi$
$149$	−71994.0	−	99091.2i	−0.265663	−	0.365653i	−0.920919	+	0.389753i	$0.872560\pi$
$150$			203100.i			0.737023i
$151$	126139.	−	40985.1i	0.450202	−	0.146279i	−0.0751359	−	0.997173i	$-0.523939\pi$
$151$	126139.	−	40985.1i	0.450202	−	0.146279i	0.525338	+	0.850894i	$0.323939\pi$
$152$	90351.5	+	124358.i	0.317195	+	0.436581i
$153$	−73877.6	+	101684.i	−0.255143	+	0.351175i
$154$	211391.	+	153585.i	0.718265	+	0.521850i
$155$	102112.			0.341386
$156$	−135188.	−	98220.1i	−0.444762	−	0.323139i
$157$	72775.9	+	23646.3i	0.235634	+	0.0765622i	0.424454	−	0.905450i	$-0.360466\pi$
$157$	72775.9	+	23646.3i	0.235634	+	0.0765622i	−0.188820	+	0.982012i	$0.560466\pi$
$158$	−131338.	+	42674.2i	−0.418549	+	0.135995i
$159$	−268431.	+	195027.i	−0.842054	+	0.611788i
$160$	14924.9	−	10843.6i	0.0460904	−	0.0334867i
$161$			644262.i			1.95883i
$162$	89654.8	+	275929.i	0.268402	+	0.826057i
$163$	242236.			0.714118			0.357059	−	0.934082i	$-0.383779\pi$
$163$	242236.			0.714118			0.357059	+	0.934082i	$0.383779\pi$
$164$	−60354.2	+	161296.i	−0.175226	+	0.468290i
$165$	−89894.9			−0.257054
$166$	−18889.8	−	58136.7i	−0.0532055	−	0.163750i
$167$			214753.i			0.595867i	0.954587	+	0.297933i	$0.0962973\pi$
$167$			214753.i			0.595867i	−0.954587	+	0.297933i	$0.903703\pi$
$168$	222830.	−	161895.i	0.609116	−	0.442548i
$169$	−31951.3	+	23214.0i	−0.0860542	+	0.0625220i
$170$	100473.	−	32645.5i	0.266640	−	0.0866366i
$171$	−195843.	−	63633.4i	−0.512175	−	0.166416i
$172$	301063.	+	218735.i	0.775955	+	0.563764i
$173$	180746.			0.459148			0.229574	−	0.973291i	$-0.426267\pi$
$173$	180746.			0.459148			0.229574	+	0.973291i	$0.426267\pi$
$174$	−472186.	−	343063.i	−1.18233	−	0.859015i
$175$	390710.	−	537767.i	0.964406	−	1.32739i
$176$	−41411.1	−	56997.4i	−0.100771	−	0.138699i
$177$	44052.5	−	14313.5i	0.105691	−	0.0343411i
$178$		−	412122.i		−	0.974936i
$179$	−6789.56	−	9345.03i	−0.0158383	−	0.0217996i	0.801024	−	0.598632i	$-0.204289\pi$
$179$	−6789.56	−	9345.03i	−0.0158383	−	0.0217996i	−0.816863	+	0.576832i	$0.804289\pi$
$180$	−7636.98	+	23504.2i	−0.0175687	+	0.0540710i
$181$	−455129.	+	626431.i	−1.03261	+	1.42127i	−0.129648	+	0.991560i	$0.541385\pi$
$181$	−455129.	+	626431.i	−1.03261	+	1.42127i	−0.902966	+	0.429711i	$0.858615\pi$
$182$	169002.	+	520134.i	0.378192	+	1.16396i
$183$	621140.	+	201821.i	1.37108	+	0.445490i
$184$	53680.1	−	165210.i	0.116888	−	0.359743i
$185$	5381.77	−	16563.4i	0.0115610	−	0.0355812i
$186$	−390942.	−	127025.i	−0.828571	−	0.269219i
$187$	−124672.	−	383700.i	−0.260714	−	0.802395i
$188$	94640.1	−	130261.i	0.195290	−	0.268794i
$189$	209144.	−	643679.i	0.425884	−	1.31073i
$190$	101735.	+	140026.i	0.204449	+	0.281400i
$191$			404440.i			0.802177i	0.916039	+	0.401089i	$0.131368\pi$
$191$			404440.i			0.802177i	−0.916039	+	0.401089i	$0.868632\pi$
$192$	−70630.2	+	22949.1i	−0.138273	+	0.0449276i
$193$	−529778.	−	729177.i	−1.02377	−	1.40909i	−0.909530	−	0.415638i	$-0.863558\pi$
$193$	−529778.	−	729177.i	−1.02377	−	1.40909i	−0.114235	−	0.993454i	$-0.536442\pi$
$194$	−139356.	+	191807.i	−0.265841	+	0.365898i
$195$	−152220.	−	110594.i	−0.286672	−	0.208280i
$196$	−632540.			−1.17611
$197$	248594.	+	180614.i	0.456378	+	0.331578i	0.792109	−	0.610380i	$-0.208983\pi$
$197$	248594.	+	180614.i	0.456378	+	0.331578i	−0.335731	+	0.941958i	$0.608983\pi$
$198$	89761.5	+	29165.3i	0.162715	+	0.0528693i
$199$	154053.	−	50054.7i	0.275763	−	0.0896009i	−0.167871	−	0.985809i	$-0.553689\pi$
$199$	154053.	−	50054.7i	0.275763	−	0.0896009i	0.443634	+	0.896208i	$0.353689\pi$
$200$	−144998.	+	105347.i	−0.256323	+	0.186230i
$201$	537751.	−	390699.i	0.938839	−	0.682106i
$202$		−	419426.i		−	0.723230i
$203$	590289.	+	1.81672e6i	1.00537	+	3.09420i
$204$	−425277.			−0.715479
$205$	−67958.0	+	181618.i	−0.112942	+	0.301838i
$206$	43887.0			0.0720556
$207$	71911.7	+	221321.i	0.116647	+	0.359003i
$208$		−	147461.i		−	0.236330i
$209$	534751.	−	388520.i	0.846810	−	0.615244i
$210$	250903.	−	182292.i	0.392607	−	0.285246i
$211$	−165347.	+	53724.4i	−0.255675	+	0.0830740i	−0.434050	−	0.900889i	$-0.642916\pi$
$211$	−165347.	+	53724.4i	−0.255675	+	0.0830740i	0.178375	+	0.983963i	$0.442916\pi$
$212$	−278470.	−	90480.2i	−0.425538	−	0.138266i
$213$	−489060.	−	355323.i	−0.738606	−	0.536629i
$214$	−257959.			−0.385049
$215$	338993.	+	246293.i	0.500143	+	0.363375i
$216$	−107263.	+	147635.i	−0.156429	+	0.215305i
$217$	790773.	+	1.08841e6i	1.13999	+	1.56907i
$218$	−631875.	+	205309.i	−0.900513	+	0.292594i
$219$		−	236675.i		−	0.333459i
$220$	−46628.3	−	64178.4i	−0.0649521	−	0.0893989i
$221$	260944.	−	803104.i	0.359391	−	1.10609i
$222$	−41209.0	+	56719.4i	−0.0561190	+	0.0772412i
$223$	−279567.	−	860418.i	−0.376464	−	1.15864i	−0.942486	−	0.334247i	$-0.891518\pi$
$223$	−279567.	−	860418.i	−0.376464	−	1.15864i	0.566021	−	0.824391i	$-0.308482\pi$
$224$	231163.	+	75109.3i	0.307820	+	0.100017i
$225$	74194.8	−	228348.i	0.0977051	−	0.300705i
$226$	4877.55	−	15011.6i	0.00635229	−	0.0195503i
$227$	−1.40468e6	−	456407.i	−1.80930	−	0.587878i	−1.00000		0.000486500i	$-0.999845\pi$
$227$	−1.40468e6	−	456407.i	−1.80930	−	0.587878i	−0.809303	−	0.587392i	$-0.800155\pi$
$228$	−215309.	−	662654.i	−0.274300	−	0.844208i
$229$	87381.8	−	120271.i	0.110111	−	0.151555i	−0.750405	−	0.660979i	$-0.770141\pi$
$229$	87381.8	−	120271.i	0.110111	−	0.151555i	0.860516	+	0.509423i	$0.170141\pi$
$230$	60443.1	−	186025.i	0.0753403	−	0.231873i
$231$	−696164.	−	958188.i	−0.858384	−	1.18146i
$232$		−	515052.i		−	0.628248i
$233$	1.08852e6	−	353680.i	1.31354	−	0.426796i	0.433271	−	0.901264i	$-0.357359\pi$
$233$	1.08852e6	−	353680.i	1.31354	−	0.426796i	0.880273	+	0.474467i	$0.157359\pi$
$234$	116113.	+	159816.i	0.138625	+	0.190801i
$235$	106564.	−	146672.i	0.125875	−	0.173252i
$236$	33068.8	+	24025.9i	0.0386490	+	0.0280801i
$237$	625960.			0.723896
$238$	1.12605e6	+	818122.i	1.28859	+	0.936215i
$239$	−792221.	−	257408.i	−0.897122	−	0.291493i	−0.176073	−	0.984377i	$-0.556340\pi$
$239$	−792221.	−	257408.i	−0.897122	−	0.291493i	−0.721049	+	0.692885i	$0.756340\pi$
$240$	−79528.6	+	25840.4i	−0.0891242	+	0.0289582i
$241$	1.28867e6	−	936276.i	1.42922	−	1.03839i	0.439062	−	0.898457i	$-0.355311\pi$
$241$	1.28867e6	−	936276.i	1.42922	−	1.03839i	0.990161	−	0.139935i	$-0.0446893\pi$
$242$	276078.	−	200582.i	0.303035	−	0.220168i
$243$		−	622209.i		−	0.675959i
$244$	178099.	+	548132.i	0.191508	+	0.589401i
$245$	−712231.			−0.758064
$246$	486111.	−	610798.i	0.512151	−	0.643517i
$247$	1.38348e6			1.44288
$248$	−112094.	−	344991.i	−0.115732	−	0.356188i
$249$			277082.i			0.283211i
$250$	−345455.	+	250987.i	−0.349575	+	0.253981i
$251$	−775134.	+	563168.i	−0.776591	+	0.564227i	−0.903954	−	0.427630i	$-0.859349\pi$
$251$	−775134.	+	563168.i	−0.776591	+	0.564227i	0.127363	+	0.991856i	$0.459349\pi$
$252$	−309673.	+	100619.i	−0.307187	+	0.0998110i
$253$	−710420.	−	230829.i	−0.697773	−	0.226720i
$254$	830820.	+	603626.i	0.808021	+	0.587062i
$255$	−478856.			−0.461163
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	245808.	−	338326.i	0.232147	−	0.319523i	−0.677012	−	0.735972i	$-0.736726\pi$
$257$	245808.	−	338326.i	0.232147	−	0.319523i	0.909159	+	0.416449i	$0.136726\pi$
$258$	−991477.	−	1.36465e6i	−0.927328	−	1.27636i
$259$	218226.	−	70906.1i	0.202143	−	0.0656801i
$260$		−	166039.i		−	0.152327i
$261$	405561.	+	558206.i	0.368514	+	0.507217i
$262$	83521.7	−	257053.i	0.0751702	−	0.231350i
$263$	−785918.	+	1.08172e6i	−0.700629	+	0.964332i	0.299320	+	0.954153i	$0.403240\pi$
$263$	−785918.	+	1.08172e6i	−0.700629	+	0.964332i	−0.999948	+	0.0101796i	$0.996760\pi$
$264$	98683.4	+	303716.i	0.0871434	+	0.268200i
$265$	−313553.	−	101880.i	−0.274281	−	0.0891194i
$266$	−704677.	+	2.16877e6i	−0.610641	+	1.87936i
$267$	−577261.	+	1.77663e6i	−0.495558	+	1.52517i
$268$	557861.	+	181260.i	0.474448	+	0.154158i
$269$	143400.	+	441340.i	0.120828	+	0.371871i	0.993118	−	0.117118i	$-0.0373657\pi$
$269$	143400.	+	441340.i	0.120828	+	0.371871i	−0.872290	+	0.488989i	$0.837366\pi$
$270$	−120777.	+	166235.i	−0.100826	+	0.138776i
$271$	197573.	−	608068.i	0.163420	−	0.502955i	−0.835496	−	0.549496i	$-0.814820\pi$
$271$	197573.	−	608068.i	0.163420	−	0.502955i	0.998916	+	0.0465409i	$0.0148198\pi$
$272$	−220590.	−	303617.i	−0.180786	−	0.248830i
$273$		−	2.47898e6i		−	2.01310i
$274$	−1.00680e6	+	327128.i	−0.810150	+	0.263234i
$275$	453003.	+	623506.i	0.361218	+	0.497174i
$276$	−462822.	+	637019.i	−0.365714	+	0.503361i
$277$	2912.41	+	2115.99i	0.00228062	+	0.00165697i	0.588925	−	0.808188i	$-0.299551\pi$
$277$	2912.41	+	2115.99i	0.00228062	+	0.00165697i	−0.586644	+	0.809845i	$0.699551\pi$
$278$	−36017.5			−0.0279513
$279$	393139.	+	285632.i	0.302368	+	0.219683i
$280$	260286.	+	84572.0i	0.198406	+	0.0644662i
$281$	−285526.	+	92773.0i	−0.215715	+	0.0700900i	−0.414881	−	0.909876i	$-0.636177\pi$
$281$	−285526.	+	92773.0i	−0.215715	+	0.0700900i	0.199166	+	0.979966i	$0.436177\pi$
$282$	−590443.	+	428982.i	−0.442136	+	0.321230i
$283$	−270651.	+	196639.i	−0.200883	+	0.145950i	−0.683679	−	0.729783i	$-0.739621\pi$
$283$	−270651.	+	196639.i	−0.200883	+	0.145950i	0.482796	+	0.875733i	$0.339621\pi$
$284$		−	533458.i		−	0.392468i
$285$	−242435.	−	746140.i	−0.176801	−	0.544137i
$286$	−634096.			−0.458395
$287$	−2.46214e6	+	682121.i	−1.76444	+	0.488829i
$288$	87794.2			0.0623713
$289$	−225348.	−	693549.i	−0.158712	−	0.488464i
$290$		−	579942.i		−	0.404939i
$291$	869418.	−	631669.i	0.601861	−	0.437277i
$292$	168969.	−	122763.i	0.115971	−	0.0842578i
$293$	2.08369e6	−	677031.i	1.41796	−	0.460723i	0.503006	−	0.864283i	$-0.332227\pi$
$293$	2.08369e6	−	677031.i	1.41796	−	0.460723i	0.914953	+	0.403560i	$0.132227\pi$
$294$	2.72683e6	+	886001.i	1.83988	+	0.597814i
$295$	37235.0	+	27052.8i	0.0249113	+	0.0180991i
$296$	−61868.5			−0.0410431
$297$	634844.	+	461241.i	0.417615	+	0.303415i
$298$	−287976.	+	396365.i	−0.187852	+	0.258556i
$299$	−918983.	−	1.26487e6i	−0.594469	−	0.818217i
$300$	772637.	−	251045.i	0.495647	−	0.161045i
$301$			5.52066e6i			3.51216i
$302$	−311833.	−	429201.i	−0.196745	−	0.270797i
$303$	−587491.	+	1.80811e6i	−0.367616	+	1.13141i
$304$	361406.	−	497432.i	0.224291	−	0.308710i
$305$	200537.	+	617190.i	0.123437	+	0.379900i
$306$	478146.	+	155359.i	0.291915	+	0.0948490i
$307$	−331572.	+	1.02047e6i	−0.200785	+	0.617953i	0.799075	+	0.601231i	$0.205323\pi$
$307$	−331572.	+	1.02047e6i	−0.200785	+	0.617953i	−0.999860	+	0.0167216i	$0.994677\pi$
$308$	322977.	−	994021.i	0.193997	−	0.597061i
$309$	−189193.	−	61472.7i	−0.112722	−	0.0366257i
$310$	−126217.	−	388456.i	−0.0745956	−	0.229582i
$311$	−555974.	+	765233.i	−0.325952	+	0.448635i	−0.940273	−	0.340422i	$-0.889430\pi$
$311$	−555974.	+	765233.i	−0.325952	+	0.448635i	0.614321	+	0.789056i	$0.289430\pi$
$312$	−206549.	+	635694.i	−0.120126	+	0.369710i
$313$	−346943.	−	477526.i	−0.200169	−	0.275509i	0.697118	−	0.716956i	$-0.254465\pi$
$313$	−346943.	−	477526.i	−0.200169	−	0.275509i	−0.897287	+	0.441447i	$0.854465\pi$
$314$		−	306084.i		−	0.175193i
$315$	−348688.	+	113296.i	−0.197998	+	0.0643334i
$316$	324685.	+	446890.i	0.182913	+	0.251758i
$317$	−1.94328e6	+	2.67470e6i	−1.08615	+	1.49495i	−0.233575	+	0.972339i	$0.575042\pi$
$317$	−1.94328e6	+	2.67470e6i	−1.08615	+	1.49495i	−0.852571	+	0.522612i	$0.824958\pi$
$318$	1.07372e6	+	780107.i	0.595422	+	0.432600i
$319$	−2.21477e6			−1.21857
$320$	−59699.5	−	43374.2i	−0.0325909	−	0.0236786i
$321$	1.11204e6	+	361324.i	0.602363	+	0.195720i
$322$	2.45092e6	−	796351.i	1.31731	−	0.428021i
$323$	2.84854e6	−	2.06958e6i	1.51920	−	1.10377i
$324$	938877.	−	682134.i	0.496874	−	0.361000i
$325$			1.61310e6i			0.847138i
$326$	−299420.	−	921521.i	−0.156041	−	0.480243i
$327$	3.01154e6			1.55747
$328$	688210.	+	30227.7i	0.353213	+	0.0155139i
$329$	2.38862e6			1.21663
$330$	111116.	+	341981.i	0.0561685	+	0.172869i
$331$		−	24618.6i		−	0.0123507i	−0.999981	−	0.00617536i	$-0.998034\pi$
$331$		−	24618.6i		−	0.0123507i	0.999981	−	0.00617536i	$-0.00196569\pi$
$332$	−197816.	+	143722.i	−0.0984956	+	0.0715612i
$333$	67052.3	−	48716.3i	0.0331362	−	0.0240749i
$334$	816971.	−	265450.i	0.400719	−	0.130202i
$335$	628144.	+	204096.i	0.305807	+	0.0993626i
$336$	−891318.	−	647581.i	−0.430710	−	0.312929i
$337$	−3.69737e6			−1.77344			−0.886722	−	0.462302i	$-0.847023\pi$
$337$	−3.69737e6			−1.77344			−0.886722	+	0.462302i	$0.847023\pi$
$338$	127805.	+	92856.0i	0.0608495	+	0.0442098i
$339$	−42053.5	+	57881.6i	−0.0198748	+	0.0273553i
$340$	−248382.	−	341868.i	−0.116526	−	0.160384i
$341$	−1.48349e6	+	482017.i	−0.690876	+	0.224479i
$342$			823688.i			0.380800i
$343$	−3.17079e6	−	4.36421e6i	−1.45523	−	2.00295i
$344$	459983.	−	1.41568e6i	0.209578	−	0.645015i
$345$	−521131.	+	717275.i	−0.235722	+	0.324443i
$346$	−223414.	−	687597.i	−0.100327	−	0.308776i
$347$	−704739.	−	228983.i	−0.314199	−	0.102089i	0.147673	−	0.989036i	$-0.452822\pi$
$347$	−704739.	−	228983.i	−0.314199	−	0.102089i	−0.461871	+	0.886947i	$0.652822\pi$
$348$	−721435.	+	2.22035e6i	−0.319337	+	0.982818i
$349$	244911.	−	753758.i	0.107633	−	0.331259i	−0.882707	−	0.469924i	$-0.844281\pi$
$349$	244911.	−	753758.i	0.107633	−	0.331259i	0.990339	+	0.138665i	$0.0442811\pi$
$350$	−2.52873e6	−	821634.i	−1.10340	−	0.358516i
$351$	507542.	+	1.56205e6i	0.219889	+	0.676749i
$352$	−165644.	+	227990.i	−0.0712557	+	0.0980751i
$353$	−1.11690e6	+	3.43746e6i	−0.477065	+	1.46825i	0.366088	+	0.930580i	$0.380697\pi$
$353$	−1.11690e6	+	3.43746e6i	−0.477065	+	1.46825i	−0.843153	+	0.537674i	$0.819303\pi$
$354$	−108904.	−	149893.i	−0.0461886	−	0.0635732i
$355$		−	600667.i		−	0.252966i
$356$	−1.56781e6	+	509411.i	−0.655643	+	0.213031i
$357$	−3.70836e6	−	5.10412e6i	−1.53997	−	2.11958i
$358$	−27158.2	+	37380.1i	−0.0111994	+	0.0154146i
$359$	1.67453e6	+	1.21662e6i	0.685737	+	0.498217i	0.875256	−	0.483660i	$-0.160693\pi$
$359$	1.67453e6	+	1.21662e6i	0.685737	+	0.498217i	−0.189519	+	0.981877i	$0.560693\pi$
$360$	98855.1			0.0402016
$361$	2.66372e6	+	1.93530e6i	1.07577	+	0.781594i
$362$	2.94566e6	+	957102.i	1.18144	+	0.383872i
$363$	−1.47111e6	+	477991.i	−0.585973	+	0.190394i
$364$	1.76981e6	−	1.28584e6i	0.700121	−	0.508667i
$365$	190256.	−	138229.i	0.0747493	−	0.0543086i
$366$		−	2.61242e6i		−	1.01939i
$367$	−1.01835e6	−	3.13417e6i	−0.394669	−	1.21467i	−0.929219	−	0.369530i	$-0.879519\pi$
$367$	−1.01835e6	−	3.13417e6i	−0.394669	−	1.21467i	0.534549	−	0.845137i	$-0.320481\pi$
$368$	−694850.			−0.267468
$369$	−769675.	+	509148.i	−0.294267	+	0.194661i
$370$	−69663.1			−0.0264544
$371$	−1.34229e6	−	4.13113e6i	−0.506303	−	1.55824i
$372$			1.64424e6i			0.616040i
$373$	3.29848e6	−	2.39649e6i	1.22756	−	0.891873i	0.230854	−	0.972988i	$-0.425848\pi$
$373$	3.29848e6	−	2.39649e6i	1.22756	−	0.891873i	0.996705	+	0.0811150i	$0.0258481\pi$
$374$	−1.30558e6	+	948559.i	−0.482641	+	0.350659i
$375$	1.84079e6	−	598108.i	0.675967	−	0.219635i
$376$	−612524.	−	199021.i	−0.223436	−	0.0725988i
$377$	−3.75030e6	−	2.72475e6i	−1.35898	−	0.987356i
$378$	−2.70722e6			−0.974526
$379$	4.39985e6	+	3.19668e6i	1.57340	+	1.14314i	0.923805	+	0.382863i	$0.125062\pi$
$379$	4.39985e6	+	3.19668e6i	1.57340	+	1.14314i	0.649596	+	0.760279i	$0.274938\pi$
$380$	406938.	−	560102.i	0.144567	−	0.198980i
$381$	−2.73610e6	−	3.76592e6i	−0.965650	−	1.32910i
$382$	1.53858e6	−	499915.i	0.539463	−	0.175282i
$383$			1.87973e6i			0.654786i	0.944888	+	0.327393i	$0.106170\pi$
$383$			1.87973e6i			0.654786i	−0.944888	+	0.327393i	$0.893830\pi$
$384$	174607.	+	240326.i	0.0604275	+	0.0831713i
$385$	363668.	−	1.11925e6i	0.125041	−	0.384837i
$386$	−2.11911e6	+	2.91671e6i	−0.723911	+	0.996379i
$387$	616209.	+	1.89650e6i	0.209147	+	0.643687i
$388$	901931.	+	293055.i	0.304154	+	0.0988257i
$389$	−495404.	+	1.52470e6i	−0.165991	+	0.510869i	−0.999108	−	0.0422285i	$-0.986554\pi$
$389$	−495404.	+	1.52470e6i	−0.165991	+	0.510869i	0.833117	+	0.553097i	$0.186554\pi$
$390$	−232572.	+	715783.i	−0.0774276	+	0.238298i
$391$	−3.78430e6	−	1.22959e6i	−1.25182	−	0.406743i
$392$	781862.	+	2.40632e6i	0.256989	+	0.790932i
$393$	−720111.	+	991148.i	−0.235190	+	0.323711i
$394$	379817.	−	1.16896e6i	0.123263	−	0.379366i
$395$	365590.	+	503192.i	0.117897	+	0.162271i
$396$		−	377523.i		−	0.120978i
$397$	−3.79858e6	+	1.23423e6i	−1.20961	+	0.393026i	−0.843288	−	0.537462i	$-0.819383\pi$
$397$	−3.79858e6	+	1.23423e6i	−1.20961	+	0.393026i	−0.366322	+	0.930488i	$0.619383\pi$
$398$	−380839.	−	524180.i	−0.120513	−	0.165872i
$399$	6.07562e6	−	8.36237e6i	1.91055	−	2.62965i
$400$	579993.	+	421389.i	0.181248	+	0.131684i
$401$	5.22286e6			1.62199			0.810993	−	0.585056i	$-0.198927\pi$
$401$	5.22286e6			1.62199			0.810993	+	0.585056i	$0.198927\pi$
$402$	−2.15100e6	−	1.56280e6i	−0.663859	−	0.482322i
$403$	−3.10503e6	−	1.00889e6i	−0.952364	−	0.309442i
$404$	−1.59559e6	+	518439.i	−0.486371	+	0.158032i
$405$	1.05716e6	−	768074.i	0.320261	−	0.232683i
$406$	6.18159e6	−	4.49119e6i	1.86117	−	1.35222i
$407$			266040.i			0.0796089i
$408$	525671.	+	1.61785e6i	0.156338	+	0.481158i
$409$	1.46085e6			0.431814			0.215907	−	0.976414i	$-0.430729\pi$
$409$	1.46085e6			0.431814			0.215907	+	0.976414i	$0.430729\pi$
$410$	774916.	+	34035.9i	0.227664	+	0.00999950i
$411$	4.79843e6			1.40118
$412$	−54247.3	−	166956.i	−0.0157447	−	0.0484573i
$413$			606390.i			0.174935i
$414$	753069.	−	547137.i	0.215940	−	0.156890i
$415$	−222738.	+	161829.i	−0.0634856	+	0.0461250i
$416$	−560975.	+	182272.i	−0.158932	+	0.0516400i
$417$	155269.	+	50449.8i	0.0437264	+	0.0142076i
$418$	−2.13901e6	−	1.55408e6i	−0.598785	−	0.435043i
$419$	1.21007e6			0.336725			0.168362	−	0.985725i	$-0.446152\pi$
$419$	1.21007e6			0.336725			0.168362	+	0.985725i	$0.446152\pi$
$420$	−1.00361e6	−	729167.i	−0.277615	−	0.201699i
$421$	1.24458e6	−	1.71302e6i	0.342231	−	0.471041i	−0.602860	−	0.797847i	$-0.705972\pi$
$421$	1.24458e6	−	1.71302e6i	0.342231	−	0.471041i	0.945091	+	0.326806i	$0.105972\pi$
$422$	408759.	+	562609.i	0.111734	+	0.153789i
$423$	820558.	−	266615.i	0.222976	−	0.0724493i
$424$			1.17120e6i			0.316386i
$425$	2.41308e6	+	3.32132e6i	0.648036	+	0.891945i
$426$	−747217.	+	2.29970e6i	−0.199491	+	0.613969i
$427$	−5.02561e6	+	6.91716e6i	−1.33389	+	1.83594i
$428$	318855.	+	981334.i	0.0841363	+	0.258945i
$429$	2.73354e6	+	888181.i	0.717104	+	0.233001i
$430$	517935.	−	1.59404e6i	0.135084	−	0.415746i
$431$	1.19237e6	−	3.66974e6i	0.309184	−	0.951572i	−0.668898	−	0.743354i	$-0.733234\pi$
$431$	1.19237e6	−	3.66974e6i	0.309184	−	0.951572i	0.978083	−	0.208218i	$-0.0667663\pi$
$432$	694222.	+	225566.i	0.178973	+	0.0581520i
$433$	−1.89839e6	−	5.84265e6i	−0.486593	−	1.49758i	−0.829660	−	0.558269i	$-0.811466\pi$
$433$	−1.89839e6	−	5.84265e6i	−0.486593	−	1.49758i	0.343066	−	0.939311i	$-0.388534\pi$
$434$	3.16309e6	−	4.35362e6i	0.806097	−	1.10950i
$435$	−812327.	+	2.50008e6i	−0.205829	+	0.633478i
$436$	1.56208e6	+	2.15002e6i	0.393538	+	0.541659i
$437$		−	6.51910e6i		−	1.63299i
$438$	−900365.	+	292546.i	−0.224251	+	0.0728634i
$439$	3.68755e6	+	5.07547e6i	0.913221	+	1.25694i	0.966055	+	0.258338i	$0.0831748\pi$
$439$	3.68755e6	+	5.07547e6i	0.913221	+	1.25694i	−0.0528332	+	0.998603i	$0.516825\pi$
$440$	−186513.	+	256713.i	−0.0459281	+	0.0632145i
$441$	−2.74215e6	−	1.99229e6i	−0.671421	−	0.487816i
$442$	−3.37773e6			−0.822375
$443$	4.56437e6	+	3.31621e6i	1.10502	+	0.802846i	0.981873	−	0.189542i	$-0.0607004\pi$
$443$	4.56437e6	+	3.31621e6i	1.10502	+	0.802846i	0.123150	+	0.992388i	$0.460700\pi$
$444$	266710.	+	86659.5i	0.0642070	+	0.0208621i
$445$	−1.76533e6	+	573590.i	−0.422596	+	0.137310i
$446$	−2.92766e6	+	2.12707e6i	−0.696922	+	0.506343i
$447$	1.79663e6	−	1.30533e6i	0.425295	−	0.308995i
$448$		−	972235.i		−	0.228863i
$449$	1.74310e6	+	5.36472e6i	0.408044	+	1.25583i	0.918327	+	0.395824i	$0.129541\pi$
$449$	1.74310e6	+	5.36472e6i	0.408044	+	1.25583i	−0.510282	+	0.860007i	$0.670459\pi$
$450$	−960397.			−0.223573
$451$	129982.	−	2.95937e6i	0.0300913	−	0.685106i
$452$	−63136.3			−0.0145356
$453$	743104.	+	2.28704e6i	0.170139	+	0.523634i
$454$			5.90785e6i			1.34521i
$455$	1.99278e6	−	1.44784e6i	0.451265	−	0.327863i
$456$	−2.25475e6	+	1.63817e6i	−0.507792	+	0.368933i
$457$	−3.12653e6	+	1.01587e6i	−0.700281	+	0.227535i	−0.637453	−	0.770489i	$-0.720012\pi$
$457$	−3.12653e6	+	1.01587e6i	−0.700281	+	0.227535i	−0.0628282	+	0.998024i	$0.520012\pi$
$458$	−565547.	−	183757.i	−0.125981	−	0.0409337i
$459$	3.38172e6	+	2.45696e6i	0.749214	+	0.544336i
$460$	−782392.			−0.172397
$461$	−3.00605e6	−	2.18402e6i	−0.658785	−	0.478635i	0.207467	−	0.978242i	$-0.433478\pi$
$461$	−3.00605e6	−	2.18402e6i	−0.658785	−	0.478635i	−0.866252	+	0.499607i	$0.833478\pi$
$462$	−2.78466e6	+	3.83275e6i	−0.606969	+	0.835422i
$463$	3.12713e6	+	4.30413e6i	0.677944	+	0.933110i	0.999907	−	0.0136423i	$-0.00434260\pi$
$463$	3.12713e6	+	4.30413e6i	0.677944	+	0.933110i	−0.321963	+	0.946752i	$0.604343\pi$
$464$	−1.95937e6	+	636639.i	−0.422496	+	0.137277i
$465$			1.85140e6i			0.397070i
$466$	−2.69096e6	−	3.70379e6i	−0.574040	−	0.790098i
$467$	1.38108e6	−	4.25052e6i	0.293039	−	0.901881i	−0.690834	−	0.723013i	$-0.742756\pi$
$467$	1.38108e6	−	4.25052e6i	0.293039	−	0.901881i	0.983873	−	0.178868i	$-0.0572435\pi$
$468$	464453.	−	639265.i	0.0980229	−	0.134917i
$469$	2.68901e6	+	8.27593e6i	0.564496	+	1.73734i
$470$	−689694.	−	224095.i	−0.144016	−	0.0467937i
$471$	−428734.	+	1.31951e6i	−0.0890503	+	0.274069i
$472$	50524.6	−	155499.i	0.0104387	−	0.0321271i
$473$	−6.08757e6	−	1.97797e6i	−1.25110	−	0.406506i
$474$	−773730.	−	2.38130e6i	−0.158177	−	0.486819i
$475$	−3.95349e6	+	5.44151e6i	−0.803982	+	1.10659i
$476$	1.72045e6	−	5.29500e6i	0.348036	−	1.07114i
$477$	−922223.	−	1.26933e6i	−0.185584	−	0.255434i
$478$			3.33196e6i			0.667007i
$479$	−968526.	+	314693.i	−0.192873	+	0.0626684i	−0.403861	−	0.914820i	$-0.632332\pi$
$479$	−968526.	+	314693.i	−0.192873	+	0.0626684i	0.210988	+	0.977489i	$0.432332\pi$
$480$	196606.	+	270604.i	0.0389487	+	0.0536083i
$481$	−327300.	+	450490.i	−0.0645035	+	0.0887815i
$482$	−5.15469e6	−	3.74510e6i	−1.01061	−	0.734254i
$483$	−1.16812e7			−2.27834
$484$	−1.10431e6	−	802329.i	−0.214278	−	0.155682i
$485$	1.01556e6	+	329976.i	0.196043	+	0.0636983i
$486$	−2.36702e6	+	769092.i	−0.454581	+	0.147702i
$487$	5.50854e6	−	4.00219e6i	1.05248	−	0.764672i	0.0797977	−	0.996811i	$-0.474573\pi$
$487$	5.50854e6	−	4.00219e6i	1.05248	−	0.764672i	0.972683	+	0.232139i	$0.0745726\pi$
$488$	1.86508e6	−	1.35506e6i	0.354525	−	0.257578i
$489$			4.39201e6i			0.830598i
$490$	880366.	+	2.70949e6i	0.165643	+	0.509797i
$491$	9.31099e6			1.74298			0.871489	−	0.490414i	$-0.163155\pi$
$491$	9.31099e6			1.74298			0.871489	+	0.490414i	$0.163155\pi$
$492$	−2.92448e6	−	1.09429e6i	−0.544673	−	0.203807i
$493$	−1.17977e7			−2.18616
$494$	−1.71008e6	−	5.26308e6i	−0.315282	−	0.970338i
$495$		−	425086.i		−	0.0779766i
$496$	−1.17387e6	+	852866.i	−0.214247	+	0.155660i
$497$	6.40249e6	−	4.65168e6i	1.16267	−	0.844732i
$498$	1.05408e6	−	342492.i	0.190459	−	0.0618839i
$499$	−1.27375e6	−	413866.i	−0.228998	−	0.0744061i	0.192270	−	0.981342i	$-0.438415\pi$
$499$	−1.27375e6	−	413866.i	−0.228998	−	0.0744061i	−0.421269	+	0.906936i	$0.638415\pi$
$500$	1.38182e6	+	1.00395e6i	0.247187	+	0.179592i
$501$	−3.89372e6			−0.693058
$502$	3.10054e6	+	2.25267e6i	0.549133	+	0.398968i
$503$	1.85095e6	−	2.54762e6i	0.326194	−	0.448967i	−0.614152	−	0.789188i	$-0.710502\pi$
$503$	1.85095e6	−	2.54762e6i	0.326194	−	0.448967i	0.940346	+	0.340221i	$0.110502\pi$
$504$	765554.	+	1.05369e6i	0.134245	+	0.184773i
$505$	−1.79661e6	+	583755.i	−0.313492	+	0.101860i
$506$			2.98792e6i			0.518791i
$507$	−420895.	−	579312.i	−0.0727200	−	0.100091i
$508$	1.26938e6	−	3.90675e6i	0.218239	−	0.671671i
$509$	2.01751e6	−	2.77686e6i	0.345160	−	0.475072i	−0.600780	−	0.799415i	$-0.705143\pi$
$509$	2.01751e6	−	2.77686e6i	0.345160	−	0.475072i	0.945940	+	0.324343i	$0.105143\pi$
$510$	591899.	+	1.82168e6i	0.100768	+	0.310132i
$511$	2.94677e6	+	957463.i	0.499222	+	0.162207i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$	−2.11627e6	+	6.51320e6i	−0.355040	+	1.09270i
$514$	−1.59090e6	−	516916.i	−0.265605	−	0.0863002i
$515$	−61081.7	−	187990.i	−0.0101483	−	0.0312332i
$516$	−3.96591e6	+	5.45860e6i	−0.655720	+	0.902521i
$517$	−855809.	+	2.63391e6i	−0.140816	+	0.433386i
$518$	−539485.	−	742538.i	−0.0883396	−	0.121589i
$519$			3.27711e6i			0.534039i
$520$	−631651.	+	205236.i	−0.102440	+	0.0332847i
$521$	2.97370e6	+	4.09294e6i	0.479957	+	0.660604i	0.978497	−	0.206263i	$-0.0661301\pi$
$521$	2.97370e6	+	4.09294e6i	0.479957	+	0.660604i	−0.498539	+	0.866867i	$0.666130\pi$
$522$	1.62224e6	−	2.23283e6i	0.260579	−	0.358656i
$523$	−3.02386e6	−	2.19697e6i	−0.483402	−	0.351212i	0.319240	−	0.947674i	$-0.396573\pi$
$523$	−3.02386e6	−	2.19697e6i	−0.483402	−	0.351212i	−0.802641	+	0.596462i	$0.796573\pi$
$524$	−1.08113e6			−0.172008
$525$	9.75030e6	+	7.08401e6i	1.54390	+	1.12171i
$526$	5.08657e6	+	1.65273e6i	0.801605	+	0.260457i
$527$	−7.90235e6	+	2.56763e6i	−1.23945	+	0.402722i
$528$	1.03343e6	−	750828.i	0.161322	−	0.117208i
$529$	−753074.	+	547140.i	−0.117003	+	0.0850079i
$530$			1.31876e6i			0.203927i
$531$	67684.5	+	208311.i	0.0104172	+	0.0320610i
$532$	9.12153e6			1.39730
$533$	3.86090e6	−	4.85123e6i	0.588669	−	0.739662i
$534$	7.47223e6			1.13396
$535$	359026.	+	1.10497e6i	0.0542303	+	0.166904i
$536$		−	2.34628e6i		−	0.352750i
$537$	169436.	−	123102.i	0.0253553	−	0.0184217i
$538$	1.50170e6	−	1.09105e6i	0.223681	−	0.162514i
$539$	1.03474e7	−	3.36208e6i	1.53412	−	0.498467i
$540$	781684.	+	253985.i	0.115358	+	0.0374820i
$541$	3.69055e6	+	2.68134e6i	0.542123	+	0.393875i	0.824873	−	0.565318i	$-0.191247\pi$
$541$	3.69055e6	+	2.68134e6i	0.542123	+	0.393875i	−0.282750	+	0.959194i	$0.591247\pi$
$542$	−2.55744e6			−0.373945
$543$	−1.13579e7	−	8.25199e6i	−1.65310	−	1.20104i
$544$	−882362.	+	1.21447e6i	−0.127835	+	0.175950i
$545$	1.75888e6	+	2.42089e6i	0.253656	+	0.349128i
$546$	−9.43060e6	+	3.06419e6i	−1.35381	+	0.439879i
$547$			1.89098e6i			0.270221i	0.990831	+	0.135110i	$0.0431389\pi$
$547$			1.89098e6i			0.270221i	−0.990831	+	0.135110i	$0.956861\pi$
$548$	2.48894e6	+	3.42573e6i	0.354048	+	0.487306i
$549$	−954350.	+	2.93719e6i	−0.135138	+	0.415911i
$550$	1.81201e6	−	2.49402e6i	0.255420	−	0.351555i
$551$	−5.97296e6	−	1.83829e7i	−0.838129	−	2.57950i
$552$	2.99544e6	+	973279.i	0.418421	+	0.135953i
$553$	−2.53231e6	+	7.79364e6i	−0.352131	+	1.08375i
$554$	4449.77	−	13695.0i	0.000615976	−	0.00189578i
$555$	300312.	+	97577.4i	0.0413848	+	0.0134467i
$556$	44520.1	+	137019.i	0.00610757	+	0.0187972i
$557$	3.36066e6	−	4.62555e6i	0.458972	−	0.631721i	−0.515323	−	0.856996i	$-0.672328\pi$
$557$	3.36066e6	−	4.62555e6i	0.458972	−	0.631721i	0.974295	+	0.225275i	$0.0723281\pi$
$558$	600662.	−	1.84865e6i	0.0816667	−	0.251344i
$559$	−7.87474e6	−	1.08386e7i	−1.06588	−	1.46705i
$560$		−	1.09472e6i		−	0.147514i
$561$	6.95691e6	−	2.26044e6i	0.933274	−	0.303239i
$562$	705859.	+	971532.i	0.0942708	+	0.129753i
$563$	−6.17261e6	+	8.49586e6i	−0.820725	+	1.12963i	0.168854	+	0.985641i	$0.445993\pi$
$563$	−6.17261e6	+	8.49586e6i	−0.820725	+	1.12963i	−0.989579	+	0.143990i	$0.954007\pi$
$564$	2.36177e6	+	1.71593e6i	0.312637	+	0.227144i
$565$	−71090.7			−0.00936896
$566$	1.08260e6	+	786557.i	0.142046	+	0.103202i
$567$	1.63738e7	+	5.32016e6i	2.13890	+	0.694971i
$568$	−2.02939e6	+	659390.i	−0.263934	+	0.0857574i
$569$	−2.86189e6	+	2.07928e6i	−0.370571	+	0.269236i	−0.757448	−	0.652896i	$-0.773554\pi$
$569$	−2.86189e6	+	2.07928e6i	−0.370571	+	0.269236i	0.386876	+	0.922132i	$0.373554\pi$
$570$	−2.53882e6	+	1.84456e6i	−0.327299	+	0.237796i
$571$		−	9.79015e6i		−	1.25661i	−0.777969	−	0.628303i	$-0.783750\pi$
$571$		−	9.79015e6i		−	1.25661i	0.777969	−	0.628303i	$-0.216250\pi$
$572$	783786.	+	2.41225e6i	0.100163	+	0.308270i
$573$	−7.33293e6			−0.933021
$574$	5.63831e6	+	8.52339e6i	0.714282	+	1.07977i
$575$	7.60109e6			0.958752
$576$	−108520.	−	333989.i	−0.0136286	−	0.0419446i
$577$			719551.i			0.0899750i	0.998988	+	0.0449875i	$0.0143248\pi$
$577$			719551.i			0.0899750i	−0.998988	+	0.0449875i	$0.985675\pi$
$578$	−2.35987e6	+	1.71455e6i	−0.293811	+	0.213467i
$579$	1.32208e7	−	9.60545e6i	1.63893	−	1.19075i
$580$	−2.20623e6	+	716847.i	−0.272321	+	0.0884824i
$581$	−3.44986e6	−	1.12093e6i	−0.423996	−	0.137765i
$582$	−3.47767e6	−	2.52668e6i	−0.425580	−	0.309202i
$583$	5.03627e6			0.613674
$584$	−675875.	−	491052.i	−0.0820038	−	0.0595793i
$585$	522968.	−	719804.i	0.0631809	−	0.0869611i
$586$	−5.15116e6	−	7.08996e6i	−0.619671	−	0.852904i
$587$	3.96337e6	−	1.28778e6i	0.474755	−	0.154257i	−0.0618595	−	0.998085i	$-0.519703\pi$
$587$	3.96337e6	−	1.28778e6i	0.474755	−	0.154257i	0.536614	+	0.843828i	$0.319703\pi$
$588$		−	1.14686e7i		−	1.36794i
$589$	−8.00160e6	−	1.10133e7i	−0.950362	−	1.30806i
$590$	56890.0	−	175090.i	0.00672831	−	0.0207076i
$591$	−3.27473e6	+	4.50728e6i	−0.385662	+	0.530818i
$592$	76473.7	+	235362.i	0.00896825	+	0.0276014i
$593$	−6.82267e6	−	2.21682e6i	−0.796742	−	0.258877i	−0.117769	−	0.993041i	$-0.537574\pi$
$593$	−6.82267e6	−	2.21682e6i	−0.796742	−	0.258877i	−0.678972	+	0.734164i	$0.737574\pi$
$594$	969956.	−	2.98522e6i	0.112794	−	0.347144i
$595$	1.93720e6	−	5.96209e6i	0.224327	−	0.690409i
$596$	1.86382e6	+	605592.i	0.214926	+	0.0698336i
$597$	907547.	+	2.79314e6i	0.104216	+	0.320743i
$598$	−3.67593e6	+	5.05948e6i	−0.420353	+	0.578566i
$599$	178514.	−	549411.i	0.0203285	−	0.0625648i	−0.940378	−	0.340132i	$-0.889528\pi$
$599$	178514.	−	549411.i	0.0203285	−	0.0625648i	0.960706	+	0.277567i	$0.0895282\pi$
$600$	−1.91006e6	−	2.62898e6i	−0.216605	−	0.298132i
$601$			3.29675e6i			0.372306i	0.982521	+	0.186153i	$0.0596020\pi$
$601$			3.29675e6i			0.372306i	−0.982521	+	0.186153i	$0.940398\pi$
$602$	2.10018e7	−	6.82391e6i	2.36193	−	0.767436i
$603$	1.84750e6	+	2.54286e6i	0.206914	+	0.284793i
$604$	−1.24733e6	+	1.71680e6i	−0.139120	+	0.191482i
$605$	−1.24344e6	−	903411.i	−0.138113	−	0.100345i
$606$	7.60465e6			0.841196
$607$	−6.79781e6	−	4.93890e6i	−0.748854	−	0.544074i	0.146618	−	0.989193i	$-0.453161\pi$
$607$	−6.79781e6	−	4.93890e6i	−0.748854	−	0.544074i	−0.895471	+	0.445119i	$0.853161\pi$
$608$	−2.33907e6	−	760009.i	−0.256616	−	0.0833796i
$609$	−3.29392e7	+	1.07026e7i	−3.59890	+	1.16935i
$610$	2.10005e6	−	1.52578e6i	0.228510	−	0.166022i
$611$	−4.68956e6	+	3.40716e6i	−0.508193	+	0.369224i
$612$		−	2.01101e6i		−	0.217038i
$613$	2.49063e6	+	7.66538e6i	0.267706	+	0.823915i	0.991058	+	0.133435i	$0.0426007\pi$
$613$	2.49063e6	+	7.66538e6i	0.267706	+	0.823915i	−0.723351	+	0.690480i	$0.757399\pi$
$614$	4.29195e6			0.459445
$615$	−3.29293e6	−	1.23215e6i	−0.351071	−	0.131364i
$616$	−4.18070e6			−0.443912
$617$	−3.67706e6	−	1.13168e7i	−0.388855	−	1.19677i	−0.933645	−	0.358200i	$-0.883391\pi$
$617$	−3.67706e6	−	1.13168e7i	−0.388855	−	1.19677i	0.544790	−	0.838572i	$-0.316609\pi$
$618$			795719.i			0.0838086i
$619$	−747700.	+	543236.i	−0.0784334	+	0.0569852i	−0.626311	−	0.779573i	$-0.715436\pi$
$619$	−747700.	+	543236.i	−0.0784334	+	0.0569852i	0.547878	+	0.836559i	$0.315436\pi$
$620$	−1.32176e6	+	960315.i	−0.138094	+	0.100331i
$621$	7.36053e6	−	2.39158e6i	0.765914	−	0.248861i
$622$	3.59834e6	+	1.16917e6i	0.372929	+	0.121172i
$623$	−1.97850e7	−	1.43746e7i	−2.04228	−	1.48380i
$624$	2.67363e6			0.274878
$625$	−5.52408e6	−	4.01348e6i	−0.565666	−	0.410980i
$626$	−1.38777e6	+	1.91010e6i	−0.141541	+	0.194815i
$627$	7.04429e6	+	9.69563e6i	0.715596	+	0.984934i
$628$	−1.16441e6	+	378341.i	−0.117817	+	0.0382811i
$629$			1.41716e6i			0.142821i
$630$	862004.	+	1.18645e6i	0.0865282	+	0.119096i
$631$	2.28916e6	−	7.04531e6i	0.228877	−	0.704412i	−0.768998	−	0.639252i	$-0.779244\pi$
$631$	2.28916e6	−	7.04531e6i	0.228877	−	0.704412i	0.997875	−	0.0651600i	$-0.0207558\pi$
$632$	1.29874e6	−	1.78756e6i	0.129339	−	0.178020i
$633$	−974081.	−	2.99791e6i	−0.0966242	−	0.297379i
$634$	1.25772e7	+	4.08658e6i	1.24268	+	0.403772i
$635$	1.42930e6	−	4.39895e6i	0.140666	−	0.432927i
$636$	1.64051e6	−	5.04896e6i	0.160818	−	0.494947i
$637$	2.16577e7	+	7.03700e6i	2.11477	+	0.687130i
$638$	2.73761e6	+	8.42549e6i	0.266268	+	0.819490i
$639$	1.68022e6	−	2.31262e6i	0.162784	−	0.224054i
$640$	−91212.8	+	280724.i	−0.00880249	+	0.0270913i
$641$	379665.	+	522564.i	0.0364968	+	0.0502336i	0.826875	−	0.562385i	$-0.190116\pi$
$641$	379665.	+	522564.i	0.0364968	+	0.0502336i	−0.790379	+	0.612619i	$0.790116\pi$
$642$		−	4.67708e6i		−	0.447855i
$643$	1.15186e6	−	374263.i	0.109868	−	0.0356984i	−0.253567	−	0.967318i	$-0.581604\pi$
$643$	1.15186e6	−	374263.i	0.109868	−	0.0356984i	0.363435	+	0.931619i	$0.381604\pi$
$644$	−6.05900e6	−	8.33950e6i	−0.575687	−	0.792365i
$645$	−4.46556e6	+	6.14631e6i	−0.422646	+	0.581722i
$646$	−1.13942e7	−	8.27834e6i	−1.07424	−	0.780480i
$647$	−1.25783e6			−0.118130			−0.0590650	−	0.998254i	$-0.518812\pi$
$647$	−1.25783e6			−0.118130			−0.0590650	+	0.998254i	$0.518812\pi$
$648$	−3.75551e6	−	2.72854e6i	−0.351343	−	0.255266i
$649$	−668659.	−	217260.i	−0.0623151	−	0.0202474i
$650$	6.13661e6	−	1.99391e6i	0.569699	−	0.185106i
$651$	−1.97340e7	+	1.43376e7i	−1.82500	+	1.32594i
$652$	−3.13557e6	+	2.27813e6i	−0.288867	+	0.209874i
$653$			4.35362e6i			0.399547i	0.979842	+	0.199773i	$0.0640206\pi$
$653$			4.35362e6i			0.399547i	−0.979842	+	0.199773i	$0.935979\pi$
$654$	−3.72247e6	−	1.14566e7i	−0.340319	−	1.04740i
$655$	−1.21733e6			−0.110868
$656$	−735682.	−	2.65547e6i	−0.0667468	−	0.240925i
$657$	1.11917e6			0.101154
$658$	−2.95250e6	−	9.08687e6i	−0.265843	−	0.818181i
$659$			1.03586e7i			0.929154i	0.885533	+	0.464577i	$0.153794\pi$
$659$			1.03586e7i			0.929154i	−0.885533	+	0.464577i	$0.846206\pi$
$660$	1.16362e6	−	845422.i	0.103981	−	0.0755464i
$661$	5.15907e6	−	3.74828e6i	0.459269	−	0.333679i	−0.333975	−	0.942582i	$-0.608390\pi$
$661$	5.15907e6	−	3.74828e6i	0.459269	−	0.333679i	0.793245	+	0.608903i	$0.208390\pi$
$662$	−93654.6	+	30430.2i	−0.00830585	+	0.00269873i
$663$	1.45612e7	+	4.73121e6i	1.28651	+	0.418011i
$664$	791265.	+	574888.i	0.0696469	+	0.0506014i
$665$	1.02707e7			0.900631
$666$	−268209.	−	194865.i	−0.0234308	−	0.0170235i
$667$	−1.28393e7	+	1.76718e7i	−1.11745	+	1.53803i
$668$	−2.01966e6	−	2.77983e6i	−0.175121	−	0.241033i
$669$	1.56003e7	−	5.06885e6i	1.34762	−	0.437869i
$670$		−	2.64188e6i		−	0.227366i
$671$	−5.82687e6	−	8.02000e6i	−0.499608	−	0.687651i
$672$	−1.36181e6	+	4.19123e6i	−0.116331	+	0.358029i
$673$	−6.80346e6	+	9.36416e6i	−0.579018	+	0.796950i	−0.993587	−	0.113068i	$-0.963932\pi$
$673$	−6.80346e6	+	9.36416e6i	−0.579018	+	0.796950i	0.414569	+	0.910018i	$0.363932\pi$
$674$	4.57020e6	+	1.40656e7i	0.387512	+	1.19264i
$675$	−7.59422e6	−	2.46751e6i	−0.641540	−	0.208449i
$676$	195269.	−	600977.i	0.0164349	−	0.0505814i
$677$	−2.63985e6	+	8.12461e6i	−0.221364	+	0.681288i	0.777276	+	0.629159i	$0.216601\pi$
$677$	−2.63985e6	+	8.12461e6i	−0.221364	+	0.681288i	−0.998640	+	0.0521289i	$0.983399\pi$
$678$	272176.	+	88435.3i	0.0227392	+	0.00738842i
$679$	4.34751e6	+	1.33803e7i	0.361881	+	1.11376i
$680$	−993528.	+	1.36747e6i	−0.0823963	+	0.113409i
$681$	8.27515e6	−	2.54683e7i	0.683767	−	2.10442i
$682$	3.66740e6	+	5.04774e6i	0.301924	+	0.415563i
$683$			7.83161e6i			0.642391i	0.947013	+	0.321195i	$0.104085\pi$
$683$			7.83161e6i			0.642391i	−0.947013	+	0.321195i	$0.895915\pi$
$684$	3.13349e6	−	1.01813e6i	0.256088	−	0.0832079i
$685$	2.80251e6	+	3.85733e6i	0.228203	+	0.314094i
$686$	−1.26831e7	+	1.74569e7i	−1.02900	+	1.41630i
$687$	2.18064e6	+	1.58433e6i	0.176276	+	0.128072i
$688$	−5.95415e6			−0.479566
$689$	8.52799e6	+	6.19595e6i	0.684382	+	0.497233i
$690$	3.37283e6	+	1.09590e6i	0.269694	+	0.0876290i
$691$	−5.24182e6	+	1.70317e6i	−0.417625	+	0.135695i	−0.510289	−	0.860003i	$-0.670462\pi$
$691$	−5.24182e6	+	1.70317e6i	−0.417625	+	0.135695i	0.0926642	+	0.995697i	$0.470462\pi$
$692$	−2.33962e6	+	1.69983e6i	−0.185729	+	0.134940i
$693$	4.53099e6	−	3.29195e6i	0.358393	−	0.260388i
$694$			2.96402e6i			0.233606i
$695$	50129.0	+	154281.i	0.00393665	+	0.0121158i
$696$	9.33846e6			0.730722
$697$	692393.	−	1.57641e7i	0.0539847	−	1.22910i
$698$	−3.17019e6			−0.246290
$699$	6.41261e6	+	1.97360e7i	0.496411	+	1.52780i
$700$			1.06355e7i			0.820372i
$701$	2.83515e6	−	2.05986e6i	0.217912	−	0.158323i	−0.473474	−	0.880808i	$-0.657000\pi$
$701$	2.83515e6	−	2.05986e6i	0.217912	−	0.158323i	0.691386	+	0.722485i	$0.257000\pi$
$702$	5.31505e6	−	3.86161e6i	0.407065	−	0.295750i
$703$	−2.20817e6	+	717478.i	−0.168517	+	0.0547546i
$704$	1.07207e6	+	348337.i	0.0815253	+	0.0264892i
$705$	2.65933e6	+	1.93211e6i	0.201511	+	0.146406i
$706$	1.44574e7			1.09164
$707$	−2.01356e7	−	1.46293e7i	−1.51501	−	1.10072i
$708$	−435615.	+	599573.i	−0.0326603	+	0.0449530i
$709$	5.81418e6	+	8.00254e6i	0.434383	+	0.597877i	0.968952	−	0.247247i	$-0.0795260\pi$
$709$	5.81418e6	+	8.00254e6i	0.434383	+	0.597877i	−0.534569	+	0.845125i	$0.679526\pi$
$710$	−2.28507e6	+	742465.i	−0.170119	+	0.0552752i
$711$			2.95998e6i			0.219591i
$712$	3.87583e6	+	5.33462e6i	0.286527	+	0.394370i
$713$	−4.75396e6	+	1.46312e7i	−0.350212	+	1.07784i
$714$	−1.48334e7	+	2.04165e7i	−1.08892	+	1.49877i
$715$	882533.	+	2.71616e6i	0.0645603	+	0.198696i
$716$	175772.	+	57111.7i	0.0128135	+	0.00416335i
$717$	4.66709e6	−	1.43638e7i	0.339038	−	1.04345i
$718$	2.55846e6	−	7.87413e6i	0.185211	−	0.570022i
$719$	7.58034e6	+	2.46300e6i	0.546848	+	0.177682i	0.569395	−	0.822064i	$-0.307178\pi$
$719$	7.58034e6	+	2.46300e6i	0.546848	+	0.177682i	−0.0225470	+	0.999746i	$0.507178\pi$
$720$	−122192.	−	376067.i	−0.00878437	−	0.0270355i
$721$	1.53075e6	−	2.10690e6i	0.109665	−	0.150941i
$722$	4.06980e6	−	1.25255e7i	0.290556	−	0.894239i
$723$	1.69757e7	+	2.33650e7i	1.20776	+	1.66234i
$724$		−	1.23890e7i		−	0.878394i
$725$	2.14340e7	−	6.96432e6i	1.51446	−	0.492077i
$726$	3.63677e6	+	5.00559e6i	0.256079	+	0.352463i
$727$	8.68254e6	−	1.19505e7i	0.609271	−	0.838590i	−0.387246	−	0.921976i	$-0.626574\pi$
$727$	8.68254e6	−	1.19505e7i	0.609271	−	0.838590i	0.996517	+	0.0833867i	$0.0265737\pi$
$728$	−7.07924e6	−	5.14337e6i	−0.495060	−	0.359682i
$729$	−6.34401e6			−0.442125
$730$	−761026.	−	552918.i	−0.0528557	−	0.0384019i
$731$	−3.24276e7	−	1.05364e7i	−2.24451	−	0.729284i
$732$	−9.93824e6	+	3.22913e6i	−0.685538	+	0.222745i
$733$	4.03511e6	−	2.93168e6i	0.277393	−	0.201538i	−0.440386	−	0.897808i	$-0.645159\pi$
$733$	4.03511e6	−	2.93168e6i	0.277393	−	0.201538i	0.717780	+	0.696270i	$0.245159\pi$
$734$	−1.06643e7	+	7.74810e6i	−0.730624	+	0.530829i
$735$		−	1.29135e7i		−	0.881712i
$736$	858882.	+	2.64337e6i	0.0584439	+	0.179872i
$737$	−1.00892e7			−0.684209
$738$	2.88828e6	+	2.29867e6i	0.195209	+	0.155359i
$739$	1.68038e6			0.113187			0.0565936	−	0.998397i	$-0.481976\pi$
$739$	1.68038e6			0.113187			0.0565936	+	0.998397i	$0.481976\pi$
$740$	86108.4	+	265014.i	0.00578051	+	0.0177906i
$741$			2.50841e7i			1.67823i
$742$	−1.40566e7	+	1.02127e7i	−0.937282	+	0.680976i
$743$	1.37113e7	−	9.96186e6i	0.911187	−	0.662016i	−0.0301278	−	0.999546i	$-0.509591\pi$
$743$	1.37113e7	−	9.96186e6i	0.911187	−	0.662016i	0.941315	+	0.337530i	$0.109591\pi$
$744$	6.25507e6	−	2.03240e6i	0.414286	−	0.134610i
$745$	2.09864e6	+	681888.i	0.138531	+	0.0450114i
$746$	−1.31939e7	−	9.58595e6i	−0.868015	−	0.630650i
$747$	−1.31024e6			−0.0859110
$748$	5.22232e6	+	3.79424e6i	0.341279	+	0.247954i
$749$	−8.99747e6	+	1.23840e7i	−0.586025	+	0.806594i
$750$	−4.55068e6	−	6.26347e6i	−0.295408	−	0.406595i
$751$	−1.58512e6	+	515038.i	−0.102556	+	0.0333226i	−0.359846	−	0.933012i	$-0.617171\pi$
$751$	−1.58512e6	+	515038.i	−0.102556	+	0.0333226i	0.257289	+	0.966334i	$0.417171\pi$
$752$			2.57618e6i			0.166124i
$753$	−1.02108e7	−	1.40540e7i	−0.656258	−	0.903261i
$754$	−5.72995e6	+	1.76350e7i	−0.367048	+	1.12966i
$755$	−1.40448e6	+	1.93310e6i	−0.0896701	+	0.123420i
$756$	3.34630e6	+	1.02989e7i	0.212942	+	0.655367i
$757$	−2.20899e7	−	7.17743e6i	−1.40105	−	0.455228i	−0.491519	−	0.870867i	$-0.663558\pi$
$757$	−2.20899e7	−	7.17743e6i	−1.40105	−	0.455228i	−0.909530	+	0.415638i	$0.863558\pi$
$758$	6.72237e6	−	2.06893e7i	0.424961	−	1.30790i
$759$	4.18519e6	−	1.28807e7i	0.263700	−	0.811586i
$760$	−2.63376e6	−	855760.i	−0.165402	−	0.0537425i
$761$	−2.65111e6	−	8.15928e6i	−0.165946	−	0.510729i	0.833159	−	0.553034i	$-0.186530\pi$
$761$	−2.65111e6	−	8.15928e6i	−0.165946	−	0.510729i	−0.999105	+	0.0423049i	$0.986530\pi$
$762$	−1.09444e7	+	1.50637e7i	−0.682817	+	0.939817i
$763$	−1.21831e7	+	3.74958e7i	−0.757612	+	2.33169i
$764$	−3.80358e6	−	5.23518e6i	−0.235754	−	0.324488i
$765$		−	2.26437e6i		−	0.139892i
$766$	7.15093e6	−	2.32348e6i	0.440342	−	0.143076i
$767$	−864962.	−	1.19052e6i	−0.0530895	−	0.0730714i
$768$	698430.	−	961306.i	0.0427287	−	0.0588110i
$769$	−4.09966e6	−	2.97858e6i	−0.249995	−	0.181632i	0.455729	−	0.890118i	$-0.349378\pi$
$769$	−4.09966e6	−	2.97858e6i	−0.249995	−	0.181632i	−0.705725	+	0.708486i	$0.749378\pi$
$770$	−4.70741e6			−0.286125
$771$	6.13421e6	+	4.45677e6i	0.371640	+	0.270013i
$772$	1.37152e7	+	4.45633e6i	0.828244	+	0.269113i
$773$	−6.47551e6	+	2.10402e6i	−0.389785	+	0.126649i	−0.497352	−	0.867549i	$-0.665694\pi$
$773$	−6.47551e6	+	2.10402e6i	−0.389785	+	0.126649i	0.107567	+	0.994198i	$0.465694\pi$
$774$	6.45303e6	−	4.68840e6i	0.387178	−	0.281302i
$775$	1.28412e7	−	9.32965e6i	0.767981	−	0.557971i
$776$		−	3.79338e6i		−	0.226137i
$777$	1.28560e6	+	3.95668e6i	0.0763932	+	0.235114i
$778$	6.41264e6			0.379829
$779$	2.49137e7	−	6.90218e6i	1.47094	−	0.407514i
$780$	3.01047e6			0.177173
$781$	2.83544e6	+	8.72659e6i	0.166339	+	0.511937i
$782$			1.59162e7i			0.930727i
$783$	1.85644e7	−	1.34878e7i	1.08212	−	0.786207i
$784$	8.18777e6	−	5.94876e6i	0.475746	−	0.345650i
$785$	−1.31111e6	+	426007.i	−0.0759393	+	0.0246742i
$786$	4.66066e6	+	1.51434e6i	0.269086	+	0.0874313i
$787$	2.39489e7	+	1.73999e7i	1.37831	+	1.00140i	0.997035	+	0.0769435i	$0.0245161\pi$
$787$	2.39489e7	+	1.73999e7i	1.37831	+	1.00140i	0.381279	+	0.924460i	$0.375484\pi$
$788$	−4.91646e6			−0.282057
$789$	−1.96128e7	−	1.42496e7i	−1.12162	−	0.814908i
$790$	1.46236e6	−	2.01277e6i	0.0833656	−	0.114743i
$791$	−550540.	−	757754.i	−0.0312858	−	0.0430613i
$792$	−1.43618e6	+	466645.i	−0.0813574	+	0.0264346i
$793$		−	2.07490e7i		−	1.17169i
$794$	9.39061e6	+	1.29251e7i	0.528619	+	0.727582i
$795$	1.84719e6	−	5.68506e6i	0.103656	−	0.319019i
$796$	−1.52336e6	+	2.09672e6i	−0.0852155	+	0.117289i
$797$	8.03185e6	+	2.47195e7i	0.447889	+	1.37846i	0.879285	+	0.476297i	$0.158021\pi$
$797$	8.03185e6	+	2.47195e7i	0.447889	+	1.37846i	−0.431396	+	0.902163i	$0.641979\pi$
$798$	−3.93222e7	−	1.27766e7i	−2.18590	−	0.710243i
$799$	−4.55876e6	+	1.40304e7i	−0.252627	+	0.777507i
$800$	886150.	−	2.72729e6i	0.0489533	−	0.150663i
$801$	−8.40115e6	−	2.72970e6i	−0.462655	−	0.150326i
$802$	−6.45581e6	−	1.98689e7i	−0.354417	−	1.09078i
$803$	−2.11157e6	+	2.90632e6i	−0.115562	+	0.159058i
$804$	−3.28644e6	+	1.01146e7i	−0.179302	+	0.551835i
$805$	−6.82235e6	−	9.39016e6i	−0.371060	−	0.510721i
$806$			1.30593e7i			0.708079i
$807$	−8.00197e6	+	2.60000e6i	−0.432527	+	0.140537i
$808$	3.94452e6	+	5.42916e6i	0.212552	+	0.292553i
$809$	1.62083e7	−	2.23088e7i	0.870696	−	1.19841i	−0.108216	−	0.994127i	$-0.534514\pi$
$809$	1.62083e7	−	2.23088e7i	0.870696	−	1.19841i	0.978912	−	0.204283i	$-0.0654862\pi$
$810$	−4.22865e6	−	3.07230e6i	−0.226459	−	0.164532i
$811$	−1.00467e7			−0.536376			−0.268188	−	0.963367i	$-0.586425\pi$
$811$	−1.00467e7			−0.536376			−0.268188	+	0.963367i	$0.586425\pi$
$812$	−2.47263e7	−	1.79647e7i	−1.31604	−	0.956161i
$813$	1.10249e7	+	3.58222e6i	0.584992	+	0.190076i
$814$	1.01208e6	−	328844.i	0.0535369	−	0.0173952i
$815$	−3.53061e6	+	2.56514e6i	−0.186190	+	0.135275i
$816$	5.50490e6	−	3.99955e6i	0.289417	−	0.210274i
$817$		−	5.58620e7i		−	2.92793i
$818$	−1.80571e6	−	5.55739e6i	−0.0943548	−	0.290394i
$819$	1.17224e7			0.610668
$820$	−828368.	−	2.99002e6i	−0.0430218	−	0.155289i
$821$	2.11109e7			1.09307			0.546537	−	0.837435i	$-0.315946\pi$
$821$	2.11109e7			1.09307			0.546537	+	0.837435i	$0.315946\pi$
$822$	−5.93119e6	−	1.82543e7i	−0.306170	−	0.942294i
$823$			8.37473e6i			0.430994i	0.976504	+	0.215497i	$0.0691372\pi$
$823$			8.37473e6i			0.430994i	−0.976504	+	0.215497i	$0.930863\pi$
$824$	−568085.	+	412738.i	−0.0291471	+	0.0211766i
$825$	−1.13048e7	+	8.21345e6i	−0.578268	+	0.420137i
$826$	2.30684e6	−	749539.i	0.117644	−	0.0382247i
$827$	−1.37952e7	−	4.48233e6i	−0.701397	−	0.227898i	−0.0634579	−	0.997985i	$-0.520213\pi$
$827$	−1.37952e7	−	4.48233e6i	−0.701397	−	0.227898i	−0.637939	+	0.770087i	$0.720213\pi$
$828$	−3.01228e6	−	2.18855e6i	−0.152693	−	0.110938i
$829$	2.74306e7			1.38627			0.693137	−	0.720806i	$-0.256228\pi$
$829$	2.74306e7			1.38627			0.693137	+	0.720806i	$0.256228\pi$
$830$	890954.	+	647316.i	0.0448911	+	0.0326153i
$831$	−38365.3	+	52805.3i	−0.00192724	+	0.00265262i
$832$	1.38681e6	+	1.90878e6i	0.0694557	+	0.0955976i
$833$	5.51191e7	−	1.79093e7i	2.75226	−	0.894264i
$834$		−	653036.i		−	0.0325104i
$835$	−2.27411e6	−	3.13005e6i	−0.112875	−	0.155358i
$836$	−3.26811e6	+	1.00582e7i	−0.161726	+	0.497743i
$837$	9.49932e6	−	1.30747e7i	0.468683	−	0.645086i
$838$	−1.49573e6	−	4.60338e6i	−0.0735771	−	0.226447i
$839$	653446.	+	212318.i	0.0320483	+	0.0104131i	0.324997	−	0.945715i	$-0.394637\pi$
$839$	653446.	+	212318.i	0.0320483	+	0.0104131i	−0.292949	+	0.956128i	$0.594637\pi$
$840$	−1.53338e6	+	4.71927e6i	−0.0749812	+	0.230769i
$841$	−1.36753e7	+	4.20882e7i	−0.666724	+	2.05197i
$842$	−8.05512e6	−	2.61727e6i	−0.391554	−	0.127224i
$843$	−1.68208e6	−	5.17690e6i	−0.0815224	−	0.250900i
$844$	1.63504e6	−	2.25044e6i	0.0790081	−	0.108745i
$845$	219870.	−	676692.i	0.0105931	−	0.0326024i
$846$	−2.02853e6	−	2.79203e6i	−0.0974441	−	0.134120i
$847$		−	2.02500e7i		−	0.969876i
$848$	4.45551e6	−	1.44768e6i	0.212769	−	0.0691328i
$849$	−3.56528e6	−	4.90719e6i	−0.169756	−	0.233649i
$850$	9.65232e6	−	1.32853e7i	0.458231	−	0.630701i
$851$	2.12275e6	+	1.54227e6i	0.100479	+	0.0730021i
$852$	9.67218e6			0.456484
$853$	6.38350e6	+	4.63788e6i	0.300390	+	0.218246i	0.727762	−	0.685830i	$-0.240560\pi$
$853$	6.38350e6	+	4.63788e6i	0.300390	+	0.218246i	−0.427372	+	0.904076i	$0.640560\pi$
$854$	3.25265e7	+	1.05685e7i	1.52613	+	0.495870i
$855$	3.52827e6	−	1.14641e6i	0.165062	−	0.0536319i
$856$	3.33909e6	−	2.42599e6i	0.155756	−	0.113163i
$857$	−3.27429e7	+	2.37891e7i	−1.52288	+	1.10643i	−0.562838	+	0.826567i	$0.690291\pi$
$857$	−3.27429e7	+	2.37891e7i	−1.52288	+	1.10643i	−0.960039	+	0.279868i	$0.909709\pi$
$858$		−	1.14969e7i		−	0.533164i
$859$	−1.29584e7	−	3.98818e7i	−0.599195	−	1.84413i	−0.532625	−	0.846351i	$-0.678795\pi$
$859$	−1.29584e7	−	3.98818e7i	−0.599195	−	1.84413i	−0.0665697	−	0.997782i	$-0.521205\pi$
$860$	−6.70429e6			−0.309106
$861$	−1.23676e7	−	4.46413e7i	−0.568561	−	2.05224i
$862$	−1.54344e7			−0.707490
$863$	−5.73517e6	−	1.76510e7i	−0.262131	−	0.806757i	−0.992340	−	0.123534i	$-0.960577\pi$
$863$	−5.73517e6	−	1.76510e7i	−0.262131	−	0.806757i	0.730209	−	0.683224i	$-0.239423\pi$
$864$		−	2.91979e6i		−	0.133066i
$865$	−2.63438e6	+	1.91399e6i	−0.119712	+	0.0869760i
$866$	−1.98802e7	+	1.44438e7i	−0.900796	+	0.654467i
$867$	1.25748e7	−	4.08580e6i	0.568137	−	0.184599i
$868$	−2.04720e7	−	6.65174e6i	−0.922274	−	0.299665i
$869$	−7.68667e6	−	5.58469e6i	−0.345294	−	0.250871i
$870$	1.05150e7			0.470988
$871$	−1.70842e7	−	1.24124e7i	−0.763043	−	0.554383i
$872$	6.24832e6	−	8.60008e6i	0.278274	−	0.383011i
$873$	2.98697e6	+	4.11122e6i	0.132647	+	0.182572i
$874$	−2.48001e7	+	8.05805e6i	−1.09818	+	0.356822i
$875$			2.53387e7i			1.11883i
$876$	2.22583e6	+	3.06359e6i	0.0980011	+	0.134887i
$877$	−1.27993e7	+	3.93922e7i	−0.561937	+	1.72946i	0.114946	+	0.993372i	$0.463331\pi$
$877$	−1.27993e7	+	3.93922e7i	−0.561937	+	1.72946i	−0.676882	+	0.736091i	$0.736669\pi$
$878$	1.47502e7	−	2.03019e7i	0.645745	−	0.888792i
$879$	1.22753e7	+	3.77795e7i	0.535871	+	1.64924i
$880$	1.20714e6	+	392223.i	0.0525473	+	0.0170737i
$881$	−6.17216e6	+	1.89959e7i	−0.267915	+	0.824558i	0.723092	+	0.690751i	$0.242720\pi$
$881$	−6.17216e6	+	1.89959e7i	−0.267915	+	0.824558i	−0.991007	+	0.133806i	$0.957280\pi$
$882$	−4.18964e6	+	1.28944e7i	−0.181345	+	0.558121i
$883$	−2.06037e7	−	6.69455e6i	−0.889291	−	0.288948i	−0.171481	−	0.985187i	$-0.554855\pi$
$883$	−2.06037e7	−	6.69455e6i	−0.889291	−	0.288948i	−0.717810	+	0.696239i	$0.754855\pi$
$884$	4.17511e6	+	1.28497e7i	0.179696	+	0.553046i
$885$	−490497.	+	675111.i	−0.0210513	+	0.0289746i
$886$	6.97373e6	−	2.14629e7i	0.298456	−	0.918554i
$887$	2.37822e7	+	3.27334e7i	1.01495	+	1.39695i	0.915687	+	0.401892i	$0.131647\pi$
$887$	2.37822e7	+	3.27334e7i	1.01495	+	1.39695i	0.0992593	+	0.995062i	$0.468353\pi$
$888$		−	1.12174e6i		−	0.0477377i
$889$	5.79571e7	−	1.88314e7i	2.45953	−	0.799150i
$890$	4.36413e6	+	6.00672e6i	0.184681	+	0.254192i
$891$	−1.17330e7	+	1.61490e7i	−0.495123	+	0.681479i
$892$	1.17107e7	+	8.50829e6i	0.492798	+	0.358039i
$893$	−2.41698e7			−1.01425
$894$	−7.18653e6	−	5.22132e6i	−0.300729	−	0.218492i
$895$	197917.	+	64307.0i	0.00825895	+	0.00268350i
$896$	−3.69860e6	+	1.20175e6i	−0.153910	+	0.0500085i
$897$	2.29335e7	−	1.66622e7i	0.951676	−	0.691433i
$898$	1.82540e7	−	1.32623e7i	0.755383	−	0.548818i
$899$			4.56135e7i			1.88232i
$900$	1.18712e6	+	3.65357e6i	0.0488525	+	0.150353i
$901$	2.68275e7			1.10095
$902$	−1.14188e7	+	3.16350e6i	−0.467308	+	0.129465i
$903$	−1.00096e8			−4.08503
$904$	78040.8	+	240185.i	0.00317615	+	0.00977517i
$905$		−	1.39498e7i		−	0.566171i
$906$	7.78188e6	−	5.65387e6i	0.314966	−	0.228837i
$907$	2.67271e6	−	1.94184e6i	0.107878	−	0.0783781i	−0.532538	−	0.846406i	$-0.678762\pi$
$907$	2.67271e6	−	1.94184e6i	0.107878	−	0.0783781i	0.640416	+	0.768028i	$0.278762\pi$
$908$	2.24748e7	−	7.30251e6i	0.904651	−	0.293939i
$909$	−8.55002e6	−	2.77807e6i	−0.343208	−	0.111515i
$910$	−7.97113e6	−	5.79136e6i	−0.319092	−	0.231834i
$911$	9.81495e6			0.391825			0.195912	−	0.980621i	$-0.437233\pi$
$911$	9.81495e6			0.391825			0.195912	+	0.980621i	$0.437233\pi$
$912$	9.01899e6	+	6.55268e6i	0.359063	+	0.260875i
$913$	2.47207e6	−	3.40251e6i	0.0981486	−	0.135090i
$914$	7.72921e6	+	1.06384e7i	0.306034	+	0.421220i
$915$	−1.11903e7	+	3.63596e6i	−0.441865	+	0.143571i
$916$			2.37861e6i			0.0936664i
$917$	−9.42729e6	−	1.29755e7i	−0.370223	−	0.509568i
$918$	5.16681e6	−	1.59018e7i	0.202356	−	0.622787i
$919$	1.68438e7	−	2.31834e7i	0.657885	−	0.905501i	−0.341524	−	0.939873i	$-0.610943\pi$
$919$	1.68438e7	−	2.31834e7i	0.657885	−	0.905501i	0.999409	+	0.0343718i	$0.0109430\pi$
$920$	967089.	+	2.97640e6i	0.0376701	+	0.115937i
$921$	−1.85023e7	−	6.01175e6i	−0.718747	−	0.233535i
$922$	−4.59283e6	+	1.41353e7i	−0.177932	+	0.547618i
$923$	−5.93472e6	+	1.82652e7i	−0.229296	+	0.705700i
$924$	1.80227e7	+	5.85592e6i	0.694448	+	0.225640i
$925$	−836560.	−	2.57467e6i	−0.0321472	−	0.0989388i
$926$	1.25085e7	−	1.72165e7i	0.479379	−	0.659808i
$927$	290686.	−	894639.i	0.0111103	−	0.0341939i
$928$	4.84384e6	+	6.66697e6i	0.184637	+	0.254132i
$929$		−	1.93922e7i		−	0.737204i	−0.929587	−	0.368602i	$-0.879837\pi$
$929$		−	1.93922e7i		−	0.737204i	0.929587	−	0.368602i	$-0.120163\pi$
$930$	7.04313e6	−	2.28845e6i	0.267029	−	0.0867629i
$931$	5.58114e7	+	7.68178e7i	2.11032	+	2.90461i
$932$	−1.07638e7	+	1.48151e7i	−0.405908	+	0.558684i
$933$	−1.38745e7	−	1.00804e7i	−0.521812	−	0.379118i
$934$	−1.78770e7			−0.670545
$935$	5.88026e6	+	4.27226e6i	0.219972	+	0.159819i
$936$	−3.00601e6	−	976711.i	−0.112150	−	0.0364398i
$937$	−2.46089e7	+	7.99593e6i	−0.915681	+	0.297523i	−0.728694	−	0.684840i	$-0.759872\pi$
$937$	−2.46089e7	+	7.99593e6i	−0.915681	+	0.297523i	−0.186987	+	0.982362i	$0.559872\pi$
$938$	2.81597e7	−	2.04592e7i	1.04501	−	0.759246i
$939$	8.65807e6	−	6.29046e6i	0.320448	−	0.232819i
$940$			2.90075e6i			0.107076i
$941$	−7.26222e6	−	2.23508e7i	−0.267359	−	0.822848i	−0.991140	−	0.132818i	$-0.957597\pi$
$941$	−7.26222e6	−	2.23508e7i	−0.267359	−	0.822848i	0.723781	−	0.690030i	$-0.242403\pi$
$942$	5.54964e6			0.203769
$943$	−2.28594e7	−	1.81929e7i	−0.837116	−	0.666229i
$944$	−654004.			−0.0238864
$945$	3.76789e6	+	1.15964e7i	0.137252	+	0.422419i
$946$			2.56034e7i			0.930186i
$947$	3.03608e7	−	2.20584e7i	1.10011	−	0.799280i	0.119036	−	0.992890i	$-0.462020\pi$
$947$	3.03608e7	−	2.20584e7i	1.10011	−	0.799280i	0.981079	+	0.193610i	$0.0620195\pi$
$948$	−8.10260e6	+	5.88689e6i	−0.292822	+	0.212748i
$949$	−7.15109e6	+	2.32353e6i	−0.257755	+	0.0837496i
$950$	2.55875e7	+	8.31388e6i	0.919854	+	0.298879i
$951$	−4.84952e7	−	3.52339e7i	−1.73879	−	1.26331i
$952$	−2.22700e7			−0.796392
$953$	1.50563e6	+	1.09390e6i	0.0537013	+	0.0390163i	0.614312	−	0.789063i	$-0.289434\pi$
$953$	1.50563e6	+	1.09390e6i	0.0537013	+	0.0390163i	−0.560611	+	0.828079i	$0.689434\pi$
$954$	−3.68889e6	+	5.07733e6i	−0.131228	+	0.180619i
$955$	−4.28278e6	−	5.89474e6i	−0.151956	−	0.209149i
$956$	1.26755e7	−	4.11853e6i	0.448561	−	0.145746i
$957$		−	4.01562e7i		−	1.41734i
$958$	2.39433e6	+	3.29551e6i	0.0842888	+	0.116014i
$959$	−1.94119e7	+	5.97438e7i	−0.681589	+	2.09772i
$960$	786422.	−	1.08242e6i	0.0275409	−	0.0379068i
$961$	1.08029e6	+	3.32480e6i	0.0377340	+	0.116133i
$962$	2.11833e6	+	688287.i	0.0737999	+	0.0239790i
$963$	−1.70859e6	+	5.25851e6i	−0.0593708	+	0.182725i
$964$	−7.87567e6	+	2.42388e7i	−0.272957	+	0.840076i
$965$	1.54431e7	+	5.01777e6i	0.533846	+	0.173457i
$966$	1.44387e7	+	4.44378e7i	0.497835	+	1.53218i
$967$	2.18515e7	−	3.00761e7i	0.751477	−	1.03432i	−0.246398	−	0.969169i	$-0.579247\pi$
$967$	2.18515e7	−	3.00761e7i	0.751477	−	1.03432i	0.997875	−	0.0651508i	$-0.0207528\pi$
$968$	−1.68724e6	+	5.19278e6i	−0.0578745	+	0.178120i
$969$	3.75238e7	+	5.16471e7i	1.28380	+	1.76700i
$970$		−	4.27130e6i		−	0.145757i
$971$	−3.04408e7	+	9.89080e6i	−1.03611	+	0.336654i	−0.777205	−	0.629248i	$-0.783363\pi$
$971$	−3.04408e7	+	9.89080e6i	−1.03611	+	0.336654i	−0.258909	+	0.965902i	$0.583363\pi$
$972$	5.85160e6	+	8.05404e6i	0.198659	+	0.273431i
$973$	−1.25627e6	+	1.72911e6i	−0.0425404	+	0.0585518i
$974$	−2.20342e7	−	1.60087e7i	−0.744216	−	0.540705i
$975$	−2.92473e7			−0.985315
$976$	−7.46031e6	−	5.42023e6i	−0.250687	−	0.182135i
$977$	4.00305e7	+	1.30067e7i	1.34170	+	0.435944i	0.889892	−	0.456172i	$-0.150780\pi$
$977$	4.00305e7	+	1.30067e7i	1.34170	+	0.435944i	0.451806	+	0.892116i	$0.350780\pi$
$978$	1.67082e7	−	5.42882e6i	0.558576	−	0.181492i
$979$	2.29394e7	−	1.66664e7i	0.764936	−	0.555758i
$980$	9.21932e6	−	6.69823e6i	0.306643	−	0.222789i
$981$			1.42407e7i			0.472453i
$982$	−1.15090e7	−	3.54211e7i	−0.380855	−	1.17215i
$983$	3.53672e7			1.16739			0.583696	−	0.811972i	$-0.301606\pi$
$983$	3.53672e7			1.16739			0.583696	+	0.811972i	$0.301606\pi$
$984$	−548060.	+	1.24780e7i	−0.0180443	+	0.410825i
$985$	−5.53587e6			−0.181801
$986$	1.45828e7	+	4.48813e7i	0.477693	+	1.47019i
$987$			4.33084e7i			1.41507i
$988$	−1.79082e7	+	1.30111e7i	−0.583659	+	0.424053i
$989$	−5.10727e7	+	3.71065e7i	−1.66034	+	1.20631i
$990$	−1.61712e6	+	525436.i	−0.0524391	+	0.0170385i
$991$	2.10633e6	+	684387.i	0.0681305	+	0.0221369i	0.342884	−	0.939378i	$-0.388596\pi$
$991$	2.10633e6	+	684387.i	0.0681305	+	0.0221369i	−0.274753	+	0.961515i	$0.588596\pi$
$992$	4.69548e6	+	3.41146e6i	0.151496	+	0.110068i
$993$	446361.			0.0143653
$994$	−2.56100e7	−	1.86067e7i	−0.822135	−	0.597316i
$995$	−1.71528e6	+	2.36088e6i	−0.0549259	+	0.0755990i
$996$	−2.60584e6	−	3.58663e6i	−0.0832336	−	0.114561i
$997$	2.64219e7	−	8.58499e6i	0.841833	−	0.273528i	0.143812	−	0.989605i	$-0.454064\pi$
$997$	2.64219e7	−	8.58499e6i	0.841833	−	0.273528i	0.698021	+	0.716077i	$0.254064\pi$
$998$			5.35720e6i			0.170259i
$999$	−1.62017e6	−	2.22997e6i	−0.0513625	−	0.0706945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.f.b.23.8	✓	40
41.25	even	10	inner	82.6.f.b.25.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.f.b.23.8	✓	40	1.1	even	1	trivial
82.6.f.b.25.3	yes	40	41.25	even	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +18.1311i q^{3} +(-12.9443 + 9.40456i) q^{4} +(-14.5751 + 10.5894i) q^{5} +(68.9748 - 22.4113i) q^{6} +(-225.745 - 73.3489i) q^{7} +(51.7771 + 37.6183i) q^{8} -85.7366 q^{9} +(58.3003 + 42.3577i) q^{10} +(161.762 - 222.646i) q^{11} +(-170.515 - 234.694i) q^{12} +(547.828 - 178.000i) q^{13} +949.448i q^{14} +(-191.998 - 264.262i) q^{15} +(79.1084 - 243.470i) q^{16} +(861.681 - 1186.00i) q^{17} +(105.976 + 326.161i) q^{18} +(2284.25 + 742.196i) q^{19} +(89.0750 - 274.145i) q^{20} +(1329.90 - 4093.00i) q^{21} +(-1046.95 - 340.173i) q^{22} +(-838.752 - 2581.41i) q^{23} +(-682.060 + 938.775i) q^{24} +(-865.381 + 2663.37i) q^{25} +(-1354.30 - 1864.04i) q^{26} +2851.36i q^{27} +(3611.92 - 1173.58i) q^{28} +(-4730.31 - 6510.72i) q^{29} +(-767.991 + 1057.05i) q^{30} +(-4585.42 - 3331.51i) q^{31} -1024.00 q^{32} +(4036.82 + 2932.92i) q^{33} +(-5576.92 - 1812.05i) q^{34} +(4066.97 - 1321.44i) q^{35} +(1109.80 - 806.315i) q^{36} +(-782.073 + 568.209i) q^{37} -9607.19i q^{38} +(3227.33 + 9932.71i) q^{39} -1153.01 q^{40} +(8977.21 - 5938.52i) q^{41} -17214.5 q^{42} +(-7187.24 - 22120.1i) q^{43} +4403.30i q^{44} +(1249.62 - 907.900i) q^{45} +(-8783.52 + 6381.60i) q^{46} +(-9570.68 + 3109.70i) q^{47} +(4414.39 + 1434.32i) q^{48} +(31983.5 + 23237.3i) q^{49} +11201.7 q^{50} +(21503.5 + 15623.2i) q^{51} +(-5417.22 + 7456.16i) q^{52} +(10756.5 + 14805.0i) q^{53} +(10847.2 - 3524.47i) q^{54} +4958.05i q^{55} +(-8929.15 - 12289.9i) q^{56} +(-13456.8 + 41415.9i) q^{57} +(-18921.2 + 26042.9i) q^{58} +(-789.447 - 2429.67i) q^{59} +(4970.54 + 1615.03i) q^{60} +(11131.2 - 34258.3i) q^{61} +(-7005.91 + 21562.0i) q^{62} +(19354.6 + 6288.68i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-6099.71 + 8395.54i) q^{65} +(6167.71 - 18982.3i) q^{66} +(-21548.6 - 29659.0i) q^{67} +23455.7i q^{68} +(46803.8 - 15207.5i) q^{69} +(-10054.1 - 13838.3i) q^{70} +(-19597.4 + 26973.5i) q^{71} +(-4439.19 - 3225.26i) q^{72} -13053.5 q^{73} +(3128.29 + 2272.84i) q^{74} +(-48289.8 - 15690.3i) q^{75} +(-36547.9 + 11875.1i) q^{76} +(-52847.8 + 38396.2i) q^{77} +(33797.1 - 24555.0i) q^{78} -34524.1i q^{79} +(1425.20 + 4386.31i) q^{80} -72532.2 q^{81} +(-33687.9 - 26810.9i) q^{82} +15282.1 q^{83} +(21278.3 + 65488.0i) q^{84} +26410.8i q^{85} +(-75265.8 + 54683.8i) q^{86} +(118046. - 85765.7i) q^{87} +(16751.1 - 5442.77i) q^{88} +(97987.9 + 31838.2i) q^{89} +(-4998.47 - 3631.60i) q^{90} -136725. q^{91} +(35134.1 + 25526.4i) q^{92} +(60403.9 - 83138.8i) q^{93} +(23660.0 + 32565.2i) q^{94} +(-41152.5 + 13371.3i) q^{95} -18566.2i q^{96} +(-34839.0 - 47951.8i) q^{97} +(48866.4 - 150395. i) q^{98} +(-13868.9 + 19088.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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