LMFDB - Embedded newform 26.6.c.b.9.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,6,Mod(3,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.3"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] 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:	$4.16997931514$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 715x^{6} - 6060x^{5} + 441025x^{4} - 2166450x^{3} + 59373900x^{2} + 212706000x + 4928040000 $ x^8 + 715x^6 - 6060x^5 + 441025x^4 - 2166450x^3 + 59373900x^2 + 212706000x + 4928040000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.4
Root			$-13.5189 + 23.4153i$ of defining polynomial
Character	$\chi$	$=$	26.9
Dual form			26.6.c.b.3.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 - 3.46410i) q^{2} +(13.5189 - 23.4153i) q^{3} +(-8.00000 - 13.8564i) q^{4} -47.6248 q^{5} +(-54.0754 - 93.6614i) q^{6} +(112.612 + 195.050i) q^{7} -64.0000 q^{8} +(-244.019 - 422.653i) q^{9} +(-95.2496 + 164.977i) q^{10} +(233.725 - 404.824i) q^{11} -432.603 q^{12} +(577.516 - 194.339i) q^{13} +900.898 q^{14} +(-643.833 + 1115.15i) q^{15} +(-128.000 + 221.703i) q^{16} +(56.9452 + 98.6320i) q^{17} -1952.15 q^{18} +(477.522 + 827.093i) q^{19} +(380.999 + 659.909i) q^{20} +6089.55 q^{21} +(-934.901 - 1619.30i) q^{22} +(-946.464 + 1639.32i) q^{23} +(-865.207 + 1498.58i) q^{24} -856.877 q^{25} +(481.821 - 2389.25i) q^{26} -6625.26 q^{27} +(1801.80 - 3120.80i) q^{28} +(-1254.36 + 2172.61i) q^{29} +(2575.33 + 4460.61i) q^{30} +6294.02 q^{31} +(512.000 + 886.810i) q^{32} +(-6319.40 - 10945.5i) q^{33} +455.562 q^{34} +(-5363.14 - 9289.23i) q^{35} +(-3904.30 + 6762.45i) q^{36} +(-5423.18 + 9393.23i) q^{37} +3820.18 q^{38} +(3256.84 - 16150.0i) q^{39} +3047.99 q^{40} +(213.721 - 370.175i) q^{41} +(12179.1 - 21094.8i) q^{42} +(1755.13 + 3039.97i) q^{43} -7479.21 q^{44} +(11621.4 + 20128.8i) q^{45} +(3785.86 + 6557.29i) q^{46} -11051.7 q^{47} +(3460.83 + 5994.33i) q^{48} +(-16959.5 + 29374.8i) q^{49} +(-1713.75 + 2968.31i) q^{50} +3079.34 q^{51} +(-7312.98 - 6447.59i) q^{52} +20736.2 q^{53} +(-13250.5 + 22950.6i) q^{54} +(-11131.1 + 19279.7i) q^{55} +(-7207.18 - 12483.2i) q^{56} +25822.2 q^{57} +(5017.43 + 8690.44i) q^{58} +(267.804 + 463.851i) q^{59} +20602.7 q^{60} +(-12220.3 - 21166.2i) q^{61} +(12588.0 - 21803.1i) q^{62} +(54959.0 - 95191.8i) q^{63} +4096.00 q^{64} +(-27504.1 + 9255.38i) q^{65} -50555.2 q^{66} +(-2419.17 + 4190.12i) q^{67} +(911.123 - 1578.11i) q^{68} +(25590.2 + 44323.6i) q^{69} -42905.1 q^{70} +(-25647.1 - 44422.1i) q^{71} +(15617.2 + 27049.8i) q^{72} -47040.2 q^{73} +(21692.7 + 37572.9i) q^{74} +(-11584.0 + 20064.1i) q^{75} +(7640.36 - 13233.5i) q^{76} +105281. q^{77} +(-49431.5 - 43582.0i) q^{78} -62968.3 q^{79} +(6095.98 - 10558.5i) q^{80} +(-30269.4 + 52428.1i) q^{81} +(-854.884 - 1480.70i) q^{82} -30245.7 q^{83} +(-48716.4 - 84379.3i) q^{84} +(-2712.00 - 4697.33i) q^{85} +14041.0 q^{86} +(33914.9 + 58742.4i) q^{87} +(-14958.4 + 25908.7i) q^{88} +(46755.4 - 80982.8i) q^{89} +92970.9 q^{90} +(102941. + 90759.6i) q^{91} +30286.8 q^{92} +(85088.0 - 147377. i) q^{93} +(-22103.3 + 38284.1i) q^{94} +(-22741.9 - 39390.1i) q^{95} +27686.6 q^{96} +(75406.9 + 130609. i) q^{97} +(67838.1 + 117499. i) q^{98} -228134. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{2} - 64 q^{4} - 24 q^{5} + 126 q^{7} - 512 q^{8} - 458 q^{9} - 48 q^{10} + 446 q^{11} + 1384 q^{13} + 1008 q^{14} - 790 q^{15} - 1024 q^{16} - 500 q^{17} - 3664 q^{18} + 4048 q^{19} + 192 q^{20}+ \cdots - 533984 q^{99}+O(q^{100}) $ 8 * q + 16 * q^2 - 64 * q^4 - 24 * q^5 + 126 * q^7 - 512 * q^8 - 458 * q^9 - 48 * q^10 + 446 * q^11 + 1384 * q^13 + 1008 * q^14 - 790 * q^15 - 1024 * q^16 - 500 * q^17 - 3664 * q^18 + 4048 * q^19 + 192 * q^20 + 2300 * q^21 - 1784 * q^22 + 296 * q^23 + 19788 * q^25 + 1112 * q^26 - 18180 * q^27 + 2016 * q^28 - 4114 * q^29 + 3160 * q^30 - 25036 * q^31 + 4096 * q^32 - 9730 * q^33 - 4000 * q^34 + 2340 * q^35 - 7328 * q^36 + 16258 * q^37 + 32384 * q^38 + 2460 * q^39 + 1536 * q^40 - 6056 * q^41 + 4600 * q^42 + 4818 * q^43 - 14272 * q^44 + 24964 * q^45 - 1184 * q^46 - 43060 * q^47 - 95094 * q^49 + 39576 * q^50 + 129440 * q^51 - 17696 * q^52 - 30032 * q^53 - 36360 * q^54 - 3360 * q^55 - 8064 * q^56 + 37940 * q^57 + 16456 * q^58 - 6734 * q^59 + 25280 * q^60 + 6978 * q^61 - 50072 * q^62 + 175812 * q^63 + 32768 * q^64 - 149818 * q^65 - 77840 * q^66 + 24464 * q^67 - 8000 * q^68 + 115290 * q^69 + 18720 * q^70 - 18552 * q^71 + 29312 * q^72 - 84596 * q^73 - 65032 * q^74 - 218210 * q^75 + 64768 * q^76 + 358604 * q^77 - 202680 * q^78 - 529664 * q^79 + 3072 * q^80 + 64624 * q^81 + 24224 * q^82 + 139800 * q^83 - 18400 * q^84 + 171548 * q^85 + 38544 * q^86 - 39420 * q^87 - 28544 * q^88 + 154642 * q^89 + 199712 * q^90 - 65074 * q^91 - 9472 * q^92 + 331860 * q^93 - 86120 * q^94 + 284278 * q^95 + 206498 * q^97 + 380376 * q^98 - 533984 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	13.5189	−	23.4153i	0.867235	−	1.50210i	0.00242428	−	0.999997i	$-0.499228\pi$
$3$	13.5189	−	23.4153i	0.867235	−	1.50210i	0.864811	−	0.502098i	$-0.167438\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−47.6248			−0.851939			−0.425969	−	0.904738i	$-0.640067\pi$
$5$	−47.6248			−0.851939			−0.425969	+	0.904738i	$0.640067\pi$
$6$	−54.0754	−	93.6614i	−0.613228	−	1.06214i
$7$	112.612	+	195.050i	0.868641	+	1.50453i	0.863386	+	0.504545i	$0.168340\pi$
$7$	112.612	+	195.050i	0.868641	+	1.50453i	0.00525567	+	0.999986i	$0.498327\pi$
$8$	−64.0000			−0.353553
$9$	−244.019	−	422.653i	−1.00419	−	1.73931i
$10$	−95.2496	+	164.977i	−0.301206	+	0.521704i
$11$	233.725	−	404.824i	0.582404	−	1.00875i	−0.412790	−	0.910826i	$-0.635446\pi$
$11$	233.725	−	404.824i	0.582404	−	1.00875i	0.995194	−	0.0979266i	$-0.0312210\pi$
$12$	−432.603			−0.867235
$13$	577.516	−	194.339i	0.947776	−	0.318935i
$13$	577.516	−	194.339i	0.947776	−	0.318935i
$14$	900.898			1.22844
$15$	−643.833	+	1115.15i	−0.738831	+	1.27969i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	56.9452	+	98.6320i	0.0477898	+	0.0827743i	0.888931	−	0.458042i	$-0.151449\pi$
$17$	56.9452	+	98.6320i	0.0477898	+	0.0827743i	−0.841141	+	0.540816i	$0.818116\pi$
$18$	−1952.15			−1.42014
$19$	477.522	+	827.093i	0.303466	+	0.525618i	0.976919	−	0.213612i	$-0.0685229\pi$
$19$	477.522	+	827.093i	0.303466	+	0.525618i	−0.673453	+	0.739230i	$0.735190\pi$
$20$	380.999	+	659.909i	0.212985	+	0.368900i
$21$	6089.55			3.01326
$22$	−934.901	−	1619.30i	−0.411822	−	0.713296i
$23$	−946.464	+	1639.32i	−0.373065	+	0.646167i	−0.990035	−	0.140819i	$-0.955026\pi$
$23$	−946.464	+	1639.32i	−0.373065	+	0.646167i	0.616970	+	0.786986i	$0.288360\pi$
$24$	−865.207	+	1498.58i	−0.306614	+	0.531071i
$25$	−856.877			−0.274201
$26$	481.821	−	2389.25i	0.139782	−	0.693153i
$27$	−6625.26			−1.74902
$28$	1801.80	−	3120.80i	0.434321	−	0.752265i
$29$	−1254.36	+	2172.61i	−0.276966	+	0.479719i	−0.970629	−	0.240580i	$-0.922662\pi$
$29$	−1254.36	+	2172.61i	−0.276966	+	0.479719i	0.693663	+	0.720299i	$0.255996\pi$
$30$	2575.33	+	4460.61i	0.522432	+	0.904879i
$31$	6294.02			1.17632			0.588158	−	0.808746i	$-0.299853\pi$
$31$	6294.02			1.17632			0.588158	+	0.808746i	$0.299853\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	−6319.40	−	10945.5i	−1.01016	−	1.74965i
$34$	455.562			0.0675849
$35$	−5363.14	−	9289.23i	−0.740029	−	1.28177i
$36$	−3904.30	+	6762.45i	−0.502097	+	0.869657i
$37$	−5423.18	+	9393.23i	−0.651253	+	1.12800i	0.331566	+	0.943432i	$0.392423\pi$
$37$	−5423.18	+	9393.23i	−0.651253	+	1.12800i	−0.982819	+	0.184571i	$0.940910\pi$
$38$	3820.18			0.429165
$39$	3256.84	−	16150.0i	0.342874	−	1.70024i
$40$	3047.99			0.301206
$41$	213.721	−	370.175i	0.0198558	−	0.0343912i	−0.855927	−	0.517097i	$-0.827013\pi$
$41$	213.721	−	370.175i	0.0198558	−	0.0343912i	0.875783	+	0.482706i	$0.160346\pi$
$42$	12179.1	−	21094.8i	1.06535	−	1.84524i
$43$	1755.13	+	3039.97i	0.144756	+	0.250725i	0.929282	−	0.369371i	$-0.120427\pi$
$43$	1755.13	+	3039.97i	0.144756	+	0.250725i	−0.784526	+	0.620096i	$0.787093\pi$
$44$	−7479.21			−0.582404
$45$	11621.4	+	20128.8i	0.855511	+	1.48179i
$46$	3785.86	+	6557.29i	0.263797	+	0.456909i
$47$	−11051.7			−0.729765			−0.364883	−	0.931053i	$-0.618891\pi$
$47$	−11051.7			−0.729765			−0.364883	+	0.931053i	$0.618891\pi$
$48$	3460.83	+	5994.33i	0.216809	+	0.375524i
$49$	−16959.5	+	29374.8i	−1.00908	+	1.74777i
$50$	−1713.75	+	2968.31i	−0.0969445	+	0.167913i
$51$	3079.34			0.165780
$52$	−7312.98	−	6447.59i	−0.375047	−	0.330665i
$53$	20736.2			1.01401			0.507003	−	0.861944i	$-0.330753\pi$
$53$	20736.2			1.01401			0.507003	+	0.861944i	$0.330753\pi$
$54$	−13250.5	+	22950.6i	−0.618370	+	1.07105i
$55$	−11131.1	+	19279.7i	−0.496172	+	0.859396i
$56$	−7207.18	−	12483.2i	−0.307111	−	0.531932i
$57$	25822.2			1.05270
$58$	5017.43	+	8690.44i	0.195844	+	0.339213i
$59$	267.804	+	463.851i	0.0100158	+	0.0173480i	0.870990	−	0.491301i	$-0.163478\pi$
$59$	267.804	+	463.851i	0.0100158	+	0.0173480i	−0.860974	+	0.508649i	$0.830145\pi$
$60$	20602.7			0.738831
$61$	−12220.3	−	21166.2i	−0.420492	−	0.728313i	0.575496	−	0.817805i	$-0.304809\pi$
$61$	−12220.3	−	21166.2i	−0.420492	−	0.728313i	−0.995988	+	0.0894918i	$0.971476\pi$
$62$	12588.0	−	21803.1i	0.415891	−	0.720344i
$63$	54959.0	−	95191.8i	1.74457	−	3.02168i
$64$	4096.00			0.125000
$65$	−27504.1	+	9255.38i	−0.807447	+	0.271713i
$66$	−50555.2			−1.42858
$67$	−2419.17	+	4190.12i	−0.0658383	+	0.114035i	−0.897066	−	0.441897i	$-0.854305\pi$
$67$	−2419.17	+	4190.12i	−0.0658383	+	0.114035i	0.831227	+	0.555933i	$0.187639\pi$
$68$	911.123	−	1578.11i	0.0238949	−	0.0413871i
$69$	25590.2	+	44323.6i	0.647070	+	1.12076i
$70$	−42905.1			−1.04656
$71$	−25647.1	−	44422.1i	−0.603799	−	1.04581i	−0.992240	−	0.124337i	$-0.960320\pi$
$71$	−25647.1	−	44422.1i	−0.603799	−	1.04581i	0.388441	−	0.921473i	$-0.373014\pi$
$72$	15617.2	+	27049.8i	0.355036	+	0.614940i
$73$	−47040.2			−1.03315			−0.516573	−	0.856243i	$-0.672793\pi$
$73$	−47040.2			−1.03315			−0.516573	+	0.856243i	$0.672793\pi$
$74$	21692.7	+	37572.9i	0.460505	+	0.797619i
$75$	−11584.0	+	20064.1i	−0.237796	+	0.411875i
$76$	7640.36	−	13233.5i	0.151733	−	0.262809i
$77$	105281.			2.02360
$78$	−49431.5	−	43582.0i	−0.919957	−	0.811093i
$79$	−62968.3			−1.13515			−0.567576	−	0.823321i	$-0.692119\pi$
$79$	−62968.3			−1.13515			−0.567576	+	0.823321i	$0.692119\pi$
$80$	6095.98	−	10558.5i	0.106492	−	0.184450i
$81$	−30269.4	+	52428.1i	−0.512614	+	0.887874i
$82$	−854.884	−	1480.70i	−0.0140402	−	0.0243183i
$83$	−30245.7			−0.481913			−0.240957	−	0.970536i	$-0.577461\pi$
$83$	−30245.7			−0.481913			−0.240957	+	0.970536i	$0.577461\pi$
$84$	−48716.4	−	84379.3i	−0.753316	−	1.30478i
$85$	−2712.00	−	4697.33i	−0.0407139	−	0.0705186i
$86$	14041.0			0.204716
$87$	33914.9	+	58742.4i	0.480389	+	0.832058i
$88$	−14958.4	+	25908.7i	−0.205911	+	0.356648i
$89$	46755.4	−	80982.8i	0.625687	−	1.08372i	−0.362721	−	0.931898i	$-0.618152\pi$
$89$	46755.4	−	80982.8i	0.625687	−	1.08372i	0.988408	−	0.151824i	$-0.0485146\pi$
$90$	92970.9			1.20988
$91$	102941.	+	90759.6i	1.30313	+	1.14892i
$92$	30286.8			0.373065
$93$	85088.0	−	147377.i	1.02014	−	1.76694i
$94$	−22103.3	+	38284.1i	−0.258011	+	0.446888i
$95$	−22741.9	−	39390.1i	−0.258534	−	0.447794i
$96$	27686.6			0.306614
$97$	75406.9	+	130609.i	0.813732	+	1.40943i	0.910235	+	0.414093i	$0.135901\pi$
$97$	75406.9	+	130609.i	0.813732	+	1.40943i	−0.0965020	+	0.995333i	$0.530765\pi$
$98$	67838.1	+	117499.i	0.713524	+	1.23586i
$99$	−228134.			−2.33938
$100$	6855.01	+	11873.2i	0.0685501	+	0.118732i
$101$	−57390.4	+	99403.1i	−0.559804	+	0.969609i	0.437708	+	0.899117i	$0.355790\pi$
$101$	−57390.4	+	99403.1i	−0.559804	+	0.969609i	−0.997512	+	0.0704919i	$0.977543\pi$
$102$	6158.67	−	10667.1i	0.0586120	−	0.101519i
$103$	−122673.			−1.13935			−0.569673	−	0.821871i	$-0.692930\pi$
$103$	−122673.			−1.13935			−0.569673	+	0.821871i	$0.692930\pi$
$104$	−36961.0	+	12437.7i	−0.335090	+	0.112761i
$105$	−290014.			−2.56712
$106$	41472.5	−	71832.5i	0.358505	−	0.620949i
$107$	92302.4	−	159872.i	0.779388	−	1.34994i	−0.152907	−	0.988241i	$-0.548864\pi$
$107$	92302.4	−	159872.i	0.779388	−	1.34994i	0.932295	−	0.361699i	$-0.117803\pi$
$108$	53002.1	+	91802.3i	0.437254	+	0.757346i
$109$	184212.			1.48508			0.742542	−	0.669799i	$-0.233620\pi$
$109$	184212.			1.48508			0.742542	+	0.669799i	$0.233620\pi$
$110$	44524.5	+	77118.7i	0.350847	+	0.607684i
$111$	146630.	+	253971.i	1.12958	+	1.95649i
$112$	−57657.5			−0.434321
$113$	−28412.6	−	49212.1i	−0.209322	−	0.362556i	0.742179	−	0.670202i	$-0.233792\pi$
$113$	−28412.6	−	49212.1i	−0.209322	−	0.362556i	−0.951501	+	0.307645i	$0.900459\pi$
$114$	51644.4	−	89450.8i	0.372187	−	0.644647i
$115$	45075.2	−	78072.5i	0.317828	−	0.550495i
$116$	40139.4			0.276966
$117$	−223063.	−	196667.i	−1.50648	−	1.32821i
$118$	2142.44			0.0141646
$119$	−12825.5	+	22214.3i	−0.0830243	+	0.143802i
$120$	41205.3	−	71369.7i	0.261216	−	0.452440i
$121$	−28729.6	−	49761.1i	−0.178388	−	0.308977i
$122$	−97762.4			−0.594665
$123$	−5778.52	−	10008.7i	−0.0344393	−	0.0596506i
$124$	−50352.2	−	87212.6i	−0.294079	−	0.509360i
$125$	189636.			1.08554
$126$	−219836.	−	380767.i	−1.23360	−	2.13665i
$127$	18626.6	−	32262.2i	0.102476	−	0.177494i	−0.810228	−	0.586115i	$-0.800657\pi$
$127$	18626.6	−	32262.2i	0.102476	−	0.177494i	0.912704	+	0.408621i	$0.133990\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	94909.3			0.502151
$130$	−22946.6	+	113788.i	−0.119086	+	0.590524i
$131$	−112029.			−0.570363			−0.285182	−	0.958473i	$-0.592054\pi$
$131$	−112029.			−0.570363			−0.285182	+	0.958473i	$0.592054\pi$
$132$	−101110.	+	175128.i	−0.505081	+	0.874826i
$133$	−107550.	+	186282.i	−0.527206	+	0.913147i
$134$	9676.67	+	16760.5i	0.0465547	+	0.0806351i
$135$	315527.			1.49005
$136$	−3644.49	−	6312.45i	−0.0168962	−	0.0292651i
$137$	−40585.0	−	70295.3i	−0.184741	−	0.319982i	0.758748	−	0.651384i	$-0.225811\pi$
$137$	−40585.0	−	70295.3i	−0.184741	−	0.319982i	−0.943489	+	0.331403i	$0.892478\pi$
$138$	204722.			0.915095
$139$	−133239.	−	230777.i	−0.584917	−	1.01311i	−0.994886	−	0.101006i	$-0.967794\pi$
$139$	−133239.	−	230777.i	−0.584917	−	1.01311i	0.409969	−	0.912100i	$-0.365540\pi$
$140$	−85810.2	+	148628.i	−0.370015	+	0.640884i
$141$	−149406.	+	258779.i	−0.632878	+	1.09618i
$142$	−205177.			−0.853900
$143$	56306.9	−	279215.i	0.230262	−	1.14182i
$144$	124938.			0.502097
$145$	59738.5	−	103470.i	0.235958	−	0.408691i
$146$	−94080.4	+	162952.i	−0.365272	+	0.632670i
$147$	458547.	+	794226.i	1.75021	+	3.03145i
$148$	173542.			0.651253
$149$	−120469.	−	208658.i	−0.444539	−	0.769964i	0.553481	−	0.832862i	$-0.313299\pi$
$149$	−120469.	−	208658.i	−0.444539	−	0.769964i	−0.998020	+	0.0628980i	$0.979966\pi$
$150$	46336.0	+	80256.3i	0.168147	+	0.291240i
$151$	202422.			0.722463			0.361232	−	0.932476i	$-0.382356\pi$
$151$	202422.			0.722463			0.361232	+	0.932476i	$0.382356\pi$
$152$	−30561.4	−	52933.9i	−0.107291	−	0.185834i
$153$	27791.4	−	48136.1i	0.0959803	−	0.166243i
$154$	210563.	−	364705.i	0.715451	−	1.23920i
$155$	−299752.			−1.00215
$156$	−249836.	+	84071.9i	−0.821945	+	0.276592i
$157$	34209.8			0.110765			0.0553823	−	0.998465i	$-0.482362\pi$
$157$	34209.8			0.110765			0.0553823	+	0.998465i	$0.482362\pi$
$158$	−125937.	+	218128.i	−0.401337	+	0.695136i
$159$	280330.	−	485546.i	0.879381	−	1.52313i
$160$	−24383.9	−	42234.2i	−0.0753014	−	0.130426i
$161$	−426334.			−1.29624
$162$	121077.	+	209712.i	0.362473	+	0.627822i
$163$	181360.	+	314126.i	0.534655	+	0.926050i	0.999180	+	0.0404896i	$0.0128918\pi$
$163$	181360.	+	314126.i	0.534655	+	0.926050i	−0.464525	+	0.885560i	$0.653775\pi$
$164$	−6839.07			−0.0198558
$165$	300960.	+	521278.i	0.860596	+	1.49060i
$166$	−60491.5	+	104774.i	−0.170382	+	0.295110i
$167$	−315212.	+	545964.i	−0.874605	+	1.51486i	−0.0174229	+	0.999848i	$0.505546\pi$
$167$	−315212.	+	545964.i	−0.874605	+	1.51486i	−0.857183	+	0.515013i	$0.827787\pi$
$168$	−389731.			−1.06535
$169$	295757.	−	224468.i	0.796561	−	0.604559i
$170$	−21696.0			−0.0575782
$171$	233049.	−	403653.i	0.609476	−	1.05564i
$172$	28082.1	−	48639.6i	0.0723782	−	0.125363i
$173$	−64488.7	−	111698.i	−0.163821	−	0.283746i	0.772415	−	0.635118i	$-0.219048\pi$
$173$	−64488.7	−	111698.i	−0.163821	−	0.283746i	−0.936236	+	0.351372i	$0.885715\pi$
$174$	271320.			0.679373
$175$	−96494.8	−	167134.i	−0.238182	−	0.412543i
$176$	59833.7	+	103635.i	0.145601	+	0.252188i
$177$	14481.6			0.0347444
$178$	−187022.	−	323931.i	−0.442427	−	0.766307i
$179$	−352693.	+	610882.i	−0.822742	+	1.42503i	0.0808902	+	0.996723i	$0.474224\pi$
$179$	−352693.	+	610882.i	−0.822742	+	1.42503i	−0.903633	+	0.428309i	$0.859110\pi$
$180$	185942.	−	322060.i	0.427755	−	0.740894i
$181$	−46848.7			−0.106292			−0.0531461	−	0.998587i	$-0.516925\pi$
$181$	−46848.7			−0.106292			−0.0531461	+	0.998587i	$0.516925\pi$
$182$	520283.	−	175080.i	1.16429	−	0.391794i
$183$	−660818.			−1.45866
$184$	60573.7	−	104917.i	0.131898	−	0.228455i
$185$	258278.	−	447351.i	0.554828	−	0.960990i
$186$	−340352.	−	589507.i	−0.721350	−	1.24941i
$187$	53238.1			0.111332
$188$	88413.4	+	153136.i	0.182441	+	0.315998i
$189$	−746086.	−	1.29226e6i	−1.51927	−	2.63145i
$190$	−181935.			−0.365623
$191$	217190.	+	376185.i	0.430782	+	0.746136i	0.996941	−	0.0781601i	$-0.0249045\pi$
$191$	217190.	+	376185.i	0.430782	+	0.746136i	−0.566159	+	0.824296i	$0.691571\pi$
$192$	55373.2	−	95909.3i	0.108404	−	0.187762i
$193$	263979.	−	457226.i	0.510125	−	0.883563i	−0.489806	−	0.871831i	$-0.662932\pi$
$193$	263979.	−	457226.i	0.510125	−	0.883563i	0.999931	−	0.0117311i	$-0.00373422\pi$
$194$	603255.			1.15079
$195$	−155106.	+	769140.i	−0.292107	+	1.44850i
$196$	542705.			1.00908
$197$	78270.5	−	135568.i	0.143692	−	0.248882i	−0.785192	−	0.619252i	$-0.787436\pi$
$197$	78270.5	−	135568.i	0.143692	−	0.248882i	0.928884	+	0.370370i	$0.120769\pi$
$198$	−456267.	+	790278.i	−0.827097	+	1.43257i
$199$	−455460.	−	788879.i	−0.815299	−	1.41214i	−0.909113	−	0.416550i	$-0.863239\pi$
$199$	−455460.	−	788879.i	−0.815299	−	1.41214i	0.0938133	−	0.995590i	$-0.470094\pi$
$200$	54840.1			0.0969445
$201$	65408.7	+	113291.i	0.114195	+	0.197791i
$202$	229562.	+	397612.i	0.395841	+	0.685617i
$203$	−565024.			−0.962336
$204$	−24634.7	−	42668.5i	−0.0414449	−	0.0717848i
$205$	−10178.4	+	17629.5i	−0.0169159	+	0.0292992i
$206$	−245346.	+	424952.i	−0.402820	+	0.697704i
$207$	923820.			1.49852
$208$	−30836.6	+	152912.i	−0.0494205	+	0.245067i
$209$	446436.			0.706958
$210$	−580028.	+	1.00464e6i	−0.907613	+	1.57203i
$211$	−121117.	+	209781.i	−0.187283	+	0.324384i	−0.944344	−	0.328961i	$-0.893302\pi$
$211$	−121117.	+	209781.i	−0.187283	+	0.324384i	0.757060	+	0.653345i	$0.226635\pi$
$212$	−165890.	−	287330.i	−0.253501	−	0.439077i
$213$	−1.38688e6			−2.09454
$214$	−369210.	−	639490.i	−0.551110	−	0.954551i
$215$	−83587.7	−	144778.i	−0.123324	−	0.213603i
$216$	424017.			0.618370
$217$	708784.	+	1.22765e6i	1.02180	+	1.76980i
$218$	368424.	−	638129.i	0.525057	−	0.909425i
$219$	−635930.	+	1.10146e6i	−0.895981	+	1.55188i
$220$	356196.			0.496172
$221$	52054.9	+	45894.9i	0.0716936	+	0.0632097i
$222$	1.17304e6			1.59747
$223$	139655.	−	241889.i	0.188059	−	0.325727i	−0.756544	−	0.653943i	$-0.773114\pi$
$223$	139655.	−	241889.i	0.188059	−	0.325727i	0.944603	+	0.328215i	$0.106447\pi$
$224$	−115315.	+	199731.i	−0.153556	+	0.265966i
$225$	209094.	+	362162.i	0.275350	+	0.476921i
$226$	−227301.			−0.296026
$227$	286538.	+	496298.i	0.369077	+	0.639260i	0.989422	−	0.145069i	$-0.0463405\pi$
$227$	286538.	+	496298.i	0.369077	+	0.639260i	−0.620344	+	0.784330i	$0.713007\pi$
$228$	−206578.	−	357803.i	−0.263176	−	0.455834i
$229$	−348997.			−0.439777			−0.219889	−	0.975525i	$-0.570569\pi$
$229$	−348997.			−0.439777			−0.219889	+	0.975525i	$0.570569\pi$
$230$	−180301.	−	312290.i	−0.224739	−	0.389259i
$231$	1.42328e6	−	2.46520e6i	1.75494	−	3.03964i
$232$	80278.9	−	139047.i	0.0979222	−	0.169606i
$233$	901508.			1.08788			0.543938	−	0.839125i	$-0.316932\pi$
$233$	901508.			1.08788			0.543938	+	0.839125i	$0.316932\pi$
$234$	−1.12740e6	+	379380.i	−1.34598	+	0.452934i
$235$	526334.			0.621715
$236$	4284.87	−	7421.62i	0.00500792	−	0.00867398i
$237$	−851259.	+	1.47442e6i	−0.984444	+	1.70511i
$238$	51301.8	+	88857.3i	0.0587070	+	0.101684i
$239$	917562.			1.03906			0.519530	−	0.854452i	$-0.326107\pi$
$239$	917562.			1.03906			0.519530	+	0.854452i	$0.326107\pi$
$240$	−164821.	−	285479.i	−0.184708	−	0.319923i
$241$	112697.	+	195197.i	0.124989	+	0.216487i	0.921729	−	0.387836i	$-0.126777\pi$
$241$	112697.	+	195197.i	0.124989	+	0.216487i	−0.796740	+	0.604322i	$0.793444\pi$
$242$	−229837.			−0.252279
$243$	13445.1	+	23287.5i	0.0146065	+	0.0252993i
$244$	−195525.	+	338659.i	−0.210246	+	0.364156i
$245$	807694.	−	1.39897e6i	0.859670	−	1.48899i
$246$	−46228.2			−0.0487045
$247$	436514.	+	384858.i	0.455256	+	0.401382i
$248$	−402818.			−0.415891
$249$	−408888.	+	708214.i	−0.417932	+	0.723880i
$250$	379272.	−	656919.i	0.383797	−	0.664755i
$251$	−674858.	−	1.16889e6i	−0.676127	−	1.17109i	−0.976138	−	0.217150i	$-0.930324\pi$
$251$	−674858.	−	1.16889e6i	−0.676127	−	1.17109i	0.300012	−	0.953936i	$-0.403009\pi$
$252$	−1.75869e6			−1.74457
$253$	442425.	+	766303.i	0.434549	+	0.752661i
$254$	−74506.3	−	129049.i	−0.0724617	−	0.125507i
$255$	−146653.			−0.141234
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−900816.	+	1.56026e6i	−0.850753	+	1.47355i	0.0297775	+	0.999557i	$0.490520\pi$
$257$	−900816.	+	1.56026e6i	−0.850753	+	1.47355i	−0.880530	+	0.473990i	$0.842813\pi$
$258$	189819.	−	328776.i	0.177537	−	0.307504i
$259$	−2.44287e6			−2.26282
$260$	348279.	+	307065.i	0.319517	+	0.281707i
$261$	1.22435e6			1.11251
$262$	−224058.	+	388079.i	−0.201654	+	0.349275i
$263$	579521.	−	1.00376e6i	0.516630	−	0.894829i	−0.483184	−	0.875519i	$-0.660520\pi$
$263$	579521.	−	1.00376e6i	0.516630	−	0.894829i	0.999814	−	0.0193101i	$-0.00614699\pi$
$264$	404442.	+	700513.i	0.357146	+	0.618595i
$265$	−987560.			−0.863871
$266$	430199.	+	745126.i	0.372791	+	0.645692i
$267$	−1.26416e6	−	2.18959e6i	−1.08524	−	1.87968i
$268$	77413.3			0.0658383
$269$	629295.	+	1.08997e6i	0.530241	+	0.918405i	0.999378	+	0.0352791i	$0.0112320\pi$
$269$	629295.	+	1.08997e6i	0.530241	+	0.918405i	−0.469136	+	0.883126i	$0.655435\pi$
$270$	631054.	−	1.09302e6i	0.526814	−	0.912468i
$271$	−771752.	+	1.33671e6i	−0.638343	+	1.10564i	0.347453	+	0.937697i	$0.387047\pi$
$271$	−771752.	+	1.33671e6i	−0.638343	+	1.10564i	−0.985796	+	0.167946i	$0.946287\pi$
$272$	−29155.9			−0.0238949
$273$	3.51682e6	−	1.18344e6i	2.85590	−	0.961036i
$274$	−324680.			−0.261264
$275$	−200274.	+	346884.i	−0.159695	+	0.276601i
$276$	409443.	−	709177.i	0.323535	−	0.560379i
$277$	−553053.	−	957916.i	−0.433079	−	0.750116i	0.564057	−	0.825736i	$-0.309240\pi$
$277$	−553053.	−	957916.i	−0.433079	−	0.750116i	−0.997137	+	0.0756200i	$0.975906\pi$
$278$	−1.06591e6			−0.827197
$279$	−1.53586e6	−	2.66019e6i	−1.18125	−	2.04598i
$280$	343241.	+	594510.i	0.261640	+	0.453173i
$281$	−1.22166e6			−0.922963			−0.461482	−	0.887150i	$-0.652682\pi$
$281$	−1.22166e6			−0.922963			−0.461482	+	0.887150i	$0.652682\pi$
$282$	597624.	+	1.03511e6i	0.447512	+	0.775114i
$283$	644847.	−	1.11691e6i	0.478620	−	0.828994i	−0.521079	−	0.853508i	$-0.674470\pi$
$283$	644847.	−	1.11691e6i	0.478620	−	0.828994i	0.999699	+	0.0245140i	$0.00780383\pi$
$284$	−410353.	+	710753.i	−0.301899	+	0.522905i
$285$	−1.22978e6			−0.896839
$286$	−854614.	−	753482.i	−0.617810	−	0.544701i
$287$	96270.3			0.0689903
$288$	249875.	−	432797.i	0.177518	−	0.307470i
$289$	703443.	−	1.21840e6i	0.495432	−	0.858114i
$290$	−238954.	−	413881.i	−0.166847	−	0.288988i
$291$	4.07766e6			2.82279
$292$	376322.	+	651808.i	0.258287	+	0.447366i
$293$	−321159.	−	556264.i	−0.218550	−	0.378540i	0.735815	−	0.677183i	$-0.236799\pi$
$293$	−321159.	−	556264.i	−0.218550	−	0.378540i	−0.954365	+	0.298643i	$0.903466\pi$
$294$	3.66837e6			2.47517
$295$	−12754.1	−	22090.8i	−0.00853289	−	0.0147794i
$296$	347084.	−	601166.i	0.230253	−	0.398809i
$297$	−1.54849e6	+	2.68207e6i	−1.01863	+	1.76432i
$298$	−963752.			−0.628673
$299$	−228013.	+	1.13067e6i	−0.147497	+	0.731406i
$300$	370688.			0.237796
$301$	−395298.	+	684676.i	−0.251483	+	0.435581i
$302$	404844.	−	701211.i	0.255429	−	0.442416i
$303$	1.55171e6	+	2.68763e6i	0.970963	+	1.68176i
$304$	−244491.			−0.151733
$305$	581990.	+	1.00804e6i	0.358233	+	0.620478i
$306$	−111166.	−	192545.i	−0.0678683	−	0.117551i
$307$	−111936.			−0.0677833			−0.0338917	−	0.999426i	$-0.510790\pi$
$307$	−111936.			−0.0677833			−0.0338917	+	0.999426i	$0.510790\pi$
$308$	−842251.	−	1.45882e6i	−0.505900	−	0.876244i
$309$	−1.65840e6	+	2.87243e6i	−0.988081	+	1.71141i
$310$	−599504.	+	1.03837e6i	−0.354313	+	0.613689i
$311$	−1.86681e6			−1.09446			−0.547230	−	0.836983i	$-0.684318\pi$
$311$	−1.86681e6			−1.09446			−0.547230	+	0.836983i	$0.684318\pi$
$312$	−208437.	+	1.03360e6i	−0.121224	+	0.601126i
$313$	−217411.			−0.125435			−0.0627177	−	0.998031i	$-0.519977\pi$
$313$	−217411.			−0.125435			−0.0627177	+	0.998031i	$0.519977\pi$
$314$	68419.6	−	118506.i	0.0391612	−	0.0678292i
$315$	−2.61741e6	+	4.53349e6i	−1.48626	+	2.57428i
$316$	503746.	+	872514.i	0.283788	+	0.491535i
$317$	2.20907e6			1.23470			0.617349	−	0.786689i	$-0.288206\pi$
$317$	2.20907e6			1.23470			0.617349	+	0.786689i	$0.288206\pi$
$318$	−1.12132e6	−	1.94219e6i	−0.621817	−	1.07702i
$319$	586350.	+	1.01559e6i	0.322612	+	0.558780i
$320$	−195071.			−0.106492
$321$	−2.49565e6	−	4.32258e6i	−1.35182	−	2.34143i
$322$	−852667.	+	1.47686e6i	−0.458289	+	0.793781i
$323$	−54385.2	+	94197.9i	−0.0290051	+	0.0502383i
$324$	968620.			0.512614
$325$	−494860.	+	166525.i	−0.259881	+	0.0874522i
$326$	1.45088e6			0.756116
$327$	2.49033e6	−	4.31338e6i	1.28792	−	2.23074i
$328$	−13678.1	+	23691.2i	−0.00702008	+	0.0121591i
$329$	−1.24455e6	−	2.15563e6i	−0.633904	−	1.09795i
$330$	2.40768e6			1.21707
$331$	654797.	+	1.13414e6i	0.328501	+	0.568980i	0.982215	−	0.187762i	$-0.0601233\pi$
$331$	654797.	+	1.13414e6i	0.328501	+	0.568980i	−0.653714	+	0.756742i	$0.726790\pi$
$332$	241966.	+	419097.i	0.120478	+	0.208675i
$333$	5.29344e6			2.61594
$334$	1.26085e6	+	2.18386e6i	0.618439	+	1.07117i
$335$	115212.	−	199554.i	0.0560902	−	0.0971511i
$336$	−779463.	+	1.35007e6i	−0.376658	+	0.652391i
$337$	1.13935e6			0.546492			0.273246	−	0.961944i	$-0.411903\pi$
$337$	1.13935e6			0.546492			0.273246	+	0.961944i	$0.411903\pi$
$338$	−186067.	−	1.47347e6i	−0.0885884	−	0.701536i
$339$	−1.53642e6			−0.726126
$340$	−43392.1	+	75157.3i	−0.0203570	+	0.0352593i
$341$	1.47107e6	−	2.54797e6i	0.685091	−	1.18661i
$342$	−932196.	−	1.61461e6i	−0.430965	−	0.746453i
$343$	−3.85405e6			−1.76882
$344$	−112328.	−	194558.i	−0.0511791	−	0.0886448i
$345$	−1.21873e6	−	2.11090e6i	−0.551264	−	0.954817i
$346$	−515910.			−0.231677
$347$	−1.65211e6	−	2.86154e6i	−0.736572	−	1.27578i	−0.954030	−	0.299710i	$-0.903110\pi$
$347$	−1.65211e6	−	2.86154e6i	−0.736572	−	1.27578i	0.217458	−	0.976070i	$-0.430223\pi$
$348$	542639.	−	939879.i	0.240194	−	0.416029i
$349$	501148.	−	868014.i	0.220243	−	0.381473i	−0.734638	−	0.678459i	$-0.762648\pi$
$349$	501148.	−	868014.i	0.220243	−	0.381473i	0.954882	+	0.296986i	$0.0959815\pi$
$350$	−771958.			−0.336840
$351$	−3.82620e6	+	1.28755e6i	−1.65768	+	0.557823i
$352$	478670.			0.205911
$353$	−1.13940e6	+	1.97350e6i	−0.486676	+	0.842948i	−0.999883	−	0.0153175i	$-0.995124\pi$
$353$	−1.13940e6	+	1.97350e6i	−0.486676	+	0.842948i	0.513207	+	0.858265i	$0.328457\pi$
$354$	28963.3	−	50165.9i	0.0122840	−	0.0212765i
$355$	1.22144e6	+	2.11559e6i	0.514399	+	0.890966i
$356$	−1.49617e6			−0.625687
$357$	346771.	+	600625.i	0.144003	+	0.249421i
$358$	1.41077e6	+	2.44353e6i	0.581767	+	1.00765i
$359$	427622.			0.175115			0.0875575	−	0.996159i	$-0.472094\pi$
$359$	427622.			0.175115			0.0875575	+	0.996159i	$0.472094\pi$
$360$	−743767.	−	1.28824e6i	−0.302469	−	0.523891i
$361$	781995.	−	1.35445e6i	0.315817	−	0.547011i
$362$	−93697.4	+	162289.i	−0.0375799	+	0.0650904i
$363$	−1.55356e6			−0.618818
$364$	434072.	−	2.15247e6i	0.171715	−	0.851500i
$365$	2.24028e6			0.880177
$366$	−1.32164e6	+	2.28914e6i	−0.515714	+	0.893243i
$367$	2.34369e6	−	4.05939e6i	0.908312	−	1.57324i	0.0919041	−	0.995768i	$-0.470705\pi$
$367$	2.34369e6	−	4.05939e6i	0.908312	−	1.57324i	0.816408	−	0.577475i	$-0.195962\pi$
$368$	−242295.	−	419667.i	−0.0932662	−	0.161542i
$369$	−208608.			−0.0797562
$370$	−1.03311e6	−	1.78940e6i	−0.392322	−	0.679522i
$371$	2.33516e6	+	4.04461e6i	0.880807	+	1.52560i
$372$	−2.72282e6			−1.02014
$373$	1.67501e6	+	2.90120e6i	0.623369	+	1.07971i	0.988854	+	0.148889i	$0.0475698\pi$
$373$	1.67501e6	+	2.90120e6i	0.623369	+	1.07971i	−0.365485	+	0.930817i	$0.619097\pi$
$374$	106476.	−	184422.i	0.0393617	−	0.0681765i
$375$	2.56366e6	−	4.44040e6i	0.941419	−	1.63059i
$376$	707307.			0.258011
$377$	−302188.	+	1.49849e6i	−0.109502	+	0.543001i
$378$	−5.96868e6			−2.14857
$379$	−763823.	+	1.32298e6i	−0.273146	+	0.473103i	−0.969666	−	0.244435i	$-0.921398\pi$
$379$	−763823.	+	1.32298e6i	−0.273146	+	0.473103i	0.696520	+	0.717538i	$0.254731\pi$
$380$	−363871.	+	630242.i	−0.129267	+	0.223897i
$381$	−503620.	−	872295.i	−0.177742	−	0.307858i
$382$	1.73752e6			0.609217
$383$	1.04213e6	+	1.80503e6i	0.363017	+	0.628764i	0.988456	−	0.151509i	$-0.0484134\pi$
$383$	1.04213e6	+	1.80503e6i	0.363017	+	0.628764i	−0.625439	+	0.780273i	$0.715080\pi$
$384$	−221493.	−	383637.i	−0.0766535	−	0.132768i
$385$	−5.01400e6			−1.72398
$386$	−1.05592e6	−	1.82890e6i	−0.360713	−	0.624773i
$387$	856569.	−	1.48362e6i	0.290727	−	0.503554i
$388$	1.20651e6	−	2.08974e6i	0.406866	−	0.704713i
$389$	1.76752e6			0.592231			0.296115	−	0.955152i	$-0.404309\pi$
$389$	1.76752e6			0.592231			0.296115	+	0.955152i	$0.404309\pi$
$390$	2.35417e6	+	2.07558e6i	0.783747	+	0.691001i
$391$	−215586.			−0.0713147
$392$	1.08541e6	−	1.87999e6i	0.356762	−	0.617930i
$393$	−1.51450e6	+	2.62319e6i	−0.494639	+	0.856740i
$394$	−313082.	−	542274.i	−0.101606	−	0.175986i
$395$	2.99885e6			0.967080
$396$	1.82507e6	+	3.16111e6i	0.584846	+	1.01298i
$397$	506091.	+	876575.i	0.161158	+	0.279134i	0.935284	−	0.353897i	$-0.115144\pi$
$397$	506091.	+	876575.i	0.161158	+	0.279134i	−0.774126	+	0.633031i	$0.781810\pi$
$398$	−3.64368e6			−1.15301
$399$	2.90790e6	+	5.03663e6i	0.914422	+	1.58383i
$400$	109680.	−	189972.i	0.0342751	−	0.0593662i
$401$	−678402.	+	1.17503e6i	−0.210682	+	0.364911i	−0.951928	−	0.306322i	$-0.900902\pi$
$401$	−678402.	+	1.17503e6i	−0.210682	+	0.364911i	0.741246	+	0.671233i	$0.234235\pi$
$402$	523270.			0.161496
$403$	3.63490e6	−	1.22318e6i	1.11489	−	0.375169i
$404$	1.83649e6			0.559804
$405$	1.44157e6	−	2.49688e6i	0.436716	−	0.756414i
$406$	−1.13005e6	+	1.95730e6i	−0.340237	+	0.589308i
$407$	2.53507e6	+	4.39087e6i	0.758584	+	1.31391i
$408$	−197077.			−0.0586120
$409$	−2.16096e6	−	3.74289e6i	−0.638761	−	1.10637i	−0.985705	−	0.168481i	$-0.946114\pi$
$409$	−2.16096e6	−	3.74289e6i	−0.638761	−	1.10637i	0.346943	−	0.937886i	$-0.387220\pi$
$410$	40713.7	+	70518.1i	0.0119614	+	0.0207177i
$411$	−2.19465e6			−0.640857
$412$	981384.	+	1.69981e6i	0.284837	+	0.493351i
$413$	−60316.1	+	104471.i	−0.0174004	+	0.0301383i
$414$	1.84764e6	−	3.20021e6i	0.529806	−	0.917650i
$415$	1.44045e6			0.410561
$416$	468031.	+	412646.i	0.132599	+	0.116908i
$417$	−7.20495e6			−2.02904
$418$	892872.	−	1.54650e6i	0.249947	−	0.432922i
$419$	−1.02532e6	+	1.77591e6i	−0.285316	+	0.494181i	−0.972686	−	0.232126i	$-0.925432\pi$
$419$	−1.02532e6	+	1.77591e6i	−0.285316	+	0.494181i	0.687370	+	0.726307i	$0.258765\pi$
$420$	2.32011e6	+	4.01855e6i	0.641779	+	1.11159i
$421$	−5.29741e6			−1.45666			−0.728330	−	0.685226i	$-0.759703\pi$
$421$	−5.29741e6			−1.45666			−0.728330	+	0.685226i	$0.759703\pi$
$422$	484468.	+	839123.i	0.132429	+	0.229374i
$423$	2.69682e6	+	4.67102e6i	0.732825	+	1.26929i
$424$	−1.32712e6			−0.358505
$425$	−48795.0	−	84515.4i	−0.0131040	−	0.0226968i
$426$	−2.77375e6	+	4.80428e6i	−0.740532	+	1.28264i
$427$	2.75231e6	−	4.76714e6i	0.730513	−	1.26529i
$428$	−2.95368e6			−0.779388
$429$	−5.77670e6	−	5.09311e6i	−1.51543	−	1.33610i
$430$	−668701.			−0.174406
$431$	−721596.	+	1.24984e6i	−0.187112	+	0.324087i	−0.944286	−	0.329126i	$-0.893246\pi$
$431$	−721596.	+	1.24984e6i	−0.187112	+	0.324087i	0.757174	+	0.653213i	$0.226579\pi$
$432$	848034.	−	1.46884e6i	0.218627	−	0.378673i
$433$	−90229.8	−	156283.i	−0.0231276	−	0.0400581i	0.854230	−	0.519895i	$-0.174029\pi$
$433$	−90229.8	−	156283.i	−0.0231276	−	0.0400581i	−0.877358	+	0.479837i	$0.840696\pi$
$434$	5.67027e6			1.44504
$435$	−1.61519e6	−	2.79760e6i	−0.409262	−	0.708862i
$436$	−1.47369e6	−	2.55251e6i	−0.371271	−	0.643061i
$437$	−1.80783e6			−0.452850
$438$	2.54372e6	+	4.40585e6i	0.633554	+	1.09735i
$439$	2.22383e6	−	3.85179e6i	0.550732	−	0.953896i	−0.447490	−	0.894289i	$-0.647682\pi$
$439$	2.22383e6	−	3.85179e6i	0.550732	−	0.953896i	0.998222	−	0.0596072i	$-0.0189848\pi$
$440$	712392.	−	1.23390e6i	0.175423	−	0.303842i
$441$	1.65538e7			4.05323
$442$	263094.	−	88533.6i	0.0640554	−	0.0215552i
$443$	−2.70696e6			−0.655348			−0.327674	−	0.944791i	$-0.606265\pi$
$443$	−2.70696e6			−0.655348			−0.327674	+	0.944791i	$0.606265\pi$
$444$	2.34609e6	−	4.06354e6i	0.564789	−	0.978244i
$445$	−2.22672e6	+	3.85679e6i	−0.533047	+	0.923264i
$446$	−558619.	−	967556.i	−0.132978	−	0.230324i
$447$	−6.51441e6			−1.54208
$448$	461260.	+	798925.i	0.108580	+	0.188066i
$449$	297264.	+	514877.i	0.0695868	+	0.120528i	0.898719	−	0.438524i	$-0.144499\pi$
$449$	297264.	+	514877.i	0.0695868	+	0.120528i	−0.829133	+	0.559052i	$0.811165\pi$
$450$	1.67275e6			0.389404
$451$	−99904.0	−	173039.i	−0.0231282	−	0.0400592i
$452$	−454602.	+	787393.i	−0.104661	+	0.181278i
$453$	2.73652e6	−	4.73978e6i	0.626545	−	1.08521i
$454$	2.29230e6			0.521954
$455$	−4.90256e6	−	4.32241e6i	−1.11018	−	0.978808i
$456$	−1.65262e6			−0.372187
$457$	642091.	−	1.11213e6i	0.143816	−	0.249096i	−0.785115	−	0.619350i	$-0.787396\pi$
$457$	642091.	−	1.11213e6i	0.143816	−	0.249096i	0.928930	+	0.370254i	$0.120729\pi$
$458$	−697994.	+	1.20896e6i	−0.155485	+	0.269307i
$459$	−377277.	−	653463.i	−0.0835850	−	0.144773i
$460$	−1.44241e6			−0.317828
$461$	−285196.	−	493974.i	−0.0625016	−	0.108256i	0.833081	−	0.553150i	$-0.186575\pi$
$461$	−285196.	−	493974.i	−0.0625016	−	0.108256i	−0.895583	+	0.444894i	$0.853241\pi$
$462$	−5.69313e6	−	9.86080e6i	−1.24093	−	2.14935i
$463$	−756568.			−0.164020			−0.0820098	−	0.996632i	$-0.526134\pi$
$463$	−756568.			−0.164020			−0.0820098	+	0.996632i	$0.526134\pi$
$464$	−321115.	−	556188.i	−0.0692415	−	0.119930i
$465$	−4.05230e6	+	7.01879e6i	−0.869099	+	1.50532i
$466$	1.80302e6	−	3.12292e6i	0.384623	−	0.666186i
$467$	−2.94606e6			−0.625101			−0.312550	−	0.949901i	$-0.601183\pi$
$467$	−2.94606e6			−0.625101			−0.312550	+	0.949901i	$0.601183\pi$
$468$	−940588.	+	4.66419e6i	−0.198511	+	0.984377i
$469$	−1.08971e6			−0.228760
$470$	1.05267e6	−	1.82327e6i	0.219810	−	0.380721i
$471$	462477.	−	801034.i	0.0960590	−	0.166379i
$472$	−17139.5	−	29686.5i	−0.00354114	−	0.00613343i
$473$	1.64087e6			0.337227
$474$	3.40504e6	+	5.89769e6i	0.696107	+	1.20569i
$475$	−409178.	−	708717.i	−0.0832105	−	0.144125i
$476$	410414.			0.0830243
$477$	−5.06004e6	−	8.76424e6i	−1.01826	−	1.76367i
$478$	1.83512e6	−	3.17853e6i	0.367363	−	0.636292i
$479$	−3.64517e6	+	6.31362e6i	−0.725904	+	1.25730i	0.232697	+	0.972549i	$0.425245\pi$
$479$	−3.64517e6	+	6.31362e6i	−0.725904	+	1.25730i	−0.958601	+	0.284753i	$0.908088\pi$
$480$	−1.31857e6			−0.261216
$481$	−1.30650e6	+	6.47868e6i	−0.257482	+	1.27680i
$482$	901578.			0.176761
$483$	−5.76354e6	+	9.98275e6i	−1.12414	+	1.94707i
$484$	−459673.	+	796178.i	−0.0891941	+	0.154489i
$485$	−3.59124e6	−	6.22021e6i	−0.693250	−	1.20074i
$486$	107560.			0.0206568
$487$	2.50131e6	+	4.33240e6i	0.477910	+	0.827764i	0.999679	−	0.0253225i	$-0.00806126\pi$
$487$	2.50131e6	+	4.33240e6i	0.477910	+	0.827764i	−0.521770	+	0.853086i	$0.674728\pi$
$488$	782099.	+	1.35464e6i	0.148666	+	0.257497i
$489$	9.80714e6			1.85469
$490$	−3.23078e6	−	5.59587e6i	−0.607879	−	1.05288i
$491$	−3.44003e6	+	5.95830e6i	−0.643959	+	1.11537i	0.340582	+	0.940215i	$0.389376\pi$
$491$	−3.44003e6	+	5.95830e6i	−0.643959	+	1.11537i	−0.984541	+	0.175155i	$0.943957\pi$
$492$	−92456.4	+	160139.i	−0.0172196	+	0.0298253i
$493$	−285718.			−0.0529445
$494$	2.20622e6	−	742411.i	0.406753	−	0.136876i
$495$	1.08648e7			1.99301
$496$	−805635.	+	1.39540e6i	−0.147040	+	0.254680i
$497$	5.77635e6	−	1.00049e7i	1.04897	−	1.81687i
$498$	1.63555e6	+	2.83286e6i	0.295523	+	0.511860i
$499$	6.81040e6			1.22439			0.612197	−	0.790705i	$-0.290286\pi$
$499$	6.81040e6			1.22439			0.612197	+	0.790705i	$0.290286\pi$
$500$	−1.51709e6	−	2.62768e6i	−0.271385	−	0.470053i
$501$	8.52262e6	+	1.47616e7i	1.51698	+	2.62748i
$502$	−5.39886e6			−0.956187
$503$	49367.4	+	85506.8i	0.00870002	+	0.0150689i	0.870343	−	0.492447i	$-0.163897\pi$
$503$	49367.4	+	85506.8i	0.00870002	+	0.0150689i	−0.861643	+	0.507516i	$0.830564\pi$
$504$	−3.51738e6	+	6.09228e6i	−0.616798	+	1.06832i
$505$	2.73321e6	−	4.73406e6i	0.476919	−	0.826047i
$506$	3.53940e6			0.614545
$507$	−1.25770e6	−	9.95982e6i	−0.217300	−	1.72080i
$508$	−596050.			−0.102476
$509$	1.44582e6	−	2.50423e6i	0.247354	−	0.428430i	−0.715437	−	0.698677i	$-0.753772\pi$
$509$	1.44582e6	−	2.50423e6i	0.247354	−	0.428430i	0.962791	+	0.270248i	$0.0871056\pi$
$510$	−293306.	+	508020.i	−0.0499338	+	0.0864879i
$511$	−5.29730e6	−	9.17519e6i	−0.897434	−	1.55440i
$512$	−262144.			−0.0441942
$513$	−3.16371e6	−	5.47971e6i	−0.530766	−	0.919314i
$514$	3.60326e6	+	6.24104e6i	0.601573	+	1.04195i
$515$	5.84228e6			0.970653
$516$	−759275.	−	1.31510e6i	−0.125538	−	0.217438i
$517$	−2.58306e6	+	4.47398e6i	−0.425018	+	0.736153i
$518$	−4.88573e6	+	8.46234e6i	−0.800028	+	1.38569i
$519$	−3.48725e6			−0.568284
$520$	1.76026e6	−	592344.i	0.285476	−	0.0960652i
$521$	−5.59892e6			−0.903671			−0.451835	−	0.892101i	$-0.649231\pi$
$521$	−5.59892e6			−0.903671			−0.451835	+	0.892101i	$0.649231\pi$
$522$	2.44870e6	−	4.24126e6i	0.393331	−	0.681270i
$523$	4.16181e6	−	7.20846e6i	0.665316	−	1.15236i	−0.313884	−	0.949461i	$-0.601630\pi$
$523$	4.16181e6	−	7.20846e6i	0.665316	−	1.15236i	0.979200	−	0.202899i	$-0.0650364\pi$
$524$	896231.	+	1.55232e6i	0.142591	+	0.246975i
$525$	−5.21800e6			−0.826239
$526$	−2.31808e6	−	4.01504e6i	−0.365312	−	0.632740i
$527$	358414.	+	620792.i	0.0562159	+	0.0973687i
$528$	3.23553e6			0.505081
$529$	1.42658e6	+	2.47092e6i	0.221645	+	0.383901i
$530$	−1.97512e6	+	3.42101e6i	−0.305424	+	0.529011i
$531$	130699.	−	226377.i	0.0201157	−	0.0348414i
$532$	3.44159e6			0.527206
$533$	51487.6	−	255317.i	0.00785027	−	0.0389279i
$534$	−1.01133e7			−1.53475
$535$	−4.39588e6	+	7.61390e6i	−0.663990	+	1.15007i
$536$	154827.	−	268168.i	0.0232774	−	0.0403176i
$537$	9.53600e6	+	1.65168e7i	1.42702	+	2.47167i
$538$	5.03436e6			0.749874
$539$	7.92774e6	+	1.37313e7i	1.17538	+	2.03582i
$540$	−2.52422e6	−	4.37207e6i	−0.372513	−	0.645212i
$541$	1.01110e7			1.48525			0.742624	−	0.669709i	$-0.233581\pi$
$541$	1.01110e7			1.48525			0.742624	+	0.669709i	$0.233581\pi$
$542$	3.08701e6	+	5.34685e6i	0.451377	+	0.781808i
$543$	−633341.	+	1.09698e6i	−0.0921803	+	0.159661i
$544$	−58311.9	+	100999.i	−0.00844811	+	0.0146326i
$545$	−8.77306e6			−1.26520
$546$	2.93408e6	−	1.45495e7i	0.421201	−	2.08865i
$547$	7.16618e6			1.02405			0.512023	−	0.858972i	$-0.328896\pi$
$547$	7.16618e6			1.02405			0.512023	+	0.858972i	$0.328896\pi$
$548$	−649360.	+	1.12473e6i	−0.0923707	+	0.159991i
$549$	−5.96397e6	+	1.03299e7i	−0.844510	+	1.46273i
$550$	801095.	+	1.38754e6i	0.112922	+	0.195586i
$551$	−2.39593e6			−0.336199
$552$	−1.63777e6	−	2.83671e6i	−0.228774	−	0.396248i
$553$	−7.09100e6	−	1.22820e7i	−0.986040	−	1.70787i
$554$	−4.42443e6			−0.612467
$555$	−6.98325e6	−	1.20953e7i	−0.962332	−	1.66681i
$556$	−2.13182e6	+	3.69243e6i	−0.292458	+	0.506553i
$557$	−2.04544e6	+	3.54281e6i	−0.279350	+	0.483848i	−0.971223	−	0.238170i	$-0.923452\pi$
$557$	−2.04544e6	+	3.54281e6i	−0.279350	+	0.483848i	0.691873	+	0.722019i	$0.256786\pi$
$558$	−1.22869e7			−1.67054
$559$	1.60440e6	+	1.41454e6i	0.217162	+	0.191464i
$560$	2.74593e6			0.370015
$561$	719719.	−	1.24659e6i	0.0965508	−	0.167231i
$562$	−2.44332e6	+	4.23195e6i	−0.326317	+	0.565197i
$563$	317737.	+	550337.i	0.0422471	+	0.0731741i	0.886376	−	0.462967i	$-0.153215\pi$
$563$	317737.	+	550337.i	0.0422471	+	0.0731741i	−0.844129	+	0.536141i	$0.819882\pi$
$564$	4.78099e6			0.632878
$565$	1.35315e6	+	2.34372e6i	0.178330	+	0.308876i
$566$	−2.57939e6	−	4.46763e6i	−0.338435	−	0.586187i
$567$	−1.36348e7			−1.78111
$568$	1.64141e6	+	2.84301e6i	0.213475	+	0.369750i
$569$	7.42894e6	−	1.28673e7i	0.961936	−	1.66612i	0.244306	−	0.969698i	$-0.421440\pi$
$569$	7.42894e6	−	1.28673e7i	0.961936	−	1.66612i	0.717630	−	0.696425i	$-0.245227\pi$
$570$	−2.45956e6	+	4.26008e6i	−0.317081	+	0.549200i
$571$	1.19643e6			0.153567			0.0767834	−	0.997048i	$-0.475535\pi$
$571$	1.19643e6			0.153567			0.0767834	+	0.997048i	$0.475535\pi$
$572$	−4.31937e6	+	1.45351e6i	−0.551989	+	0.185749i
$573$	1.17447e7			1.49436
$574$	192541.	−	333490.i	0.0243917	−	0.0422477i
$575$	811003.	−	1.40470e6i	0.102295	−	0.177179i
$576$	−999501.	−	1.73119e6i	−0.125524	−	0.217414i
$577$	3.58855e6			0.448725			0.224362	−	0.974506i	$-0.427970\pi$
$577$	3.58855e6			0.448725			0.224362	+	0.974506i	$0.427970\pi$
$578$	−2.81377e6	−	4.87360e6i	−0.350324	−	0.606778i
$579$	−7.13740e6	−	1.23623e7i	−0.884797	−	1.53251i
$580$	−1.91163e6			−0.235958
$581$	−3.40604e6	−	5.89943e6i	−0.418610	−	0.725053i
$582$	8.15532e6	−	1.41254e7i	0.998007	−	1.72860i
$583$	4.84659e6	−	8.39454e6i	0.590561	−	1.02288i
$584$	3.01057e6			0.365272
$585$	1.06233e7	+	9.36621e6i	1.28343	+	1.13155i
$586$	−2.56927e6			−0.309077
$587$	8.00539e6	−	1.38657e7i	0.958931	−	1.66092i	0.233826	−	0.972278i	$-0.424875\pi$
$587$	8.00539e6	−	1.38657e7i	0.958931	−	1.66092i	0.725105	−	0.688639i	$-0.241791\pi$
$588$	7.33675e6	−	1.27076e7i	0.875105	−	1.51573i
$589$	3.00554e6	+	5.20574e6i	0.356972	+	0.618293i
$590$	−102033.			−0.0120673
$591$	−2.11625e6	−	3.66546e6i	−0.249229	−	0.431678i
$592$	−1.38833e6	−	2.40467e6i	−0.162813	−	0.282001i
$593$	1.08156e7			1.26303			0.631517	−	0.775362i	$-0.282433\pi$
$593$	1.08156e7			1.26303			0.631517	+	0.775362i	$0.282433\pi$
$594$	6.19397e6	+	1.07283e7i	0.720282	+	1.24757i
$595$	610810.	−	1.05795e6i	0.0707316	−	0.122511i
$596$	−1.92750e6	+	3.33853e6i	−0.222269	+	0.384982i
$597$	−2.46292e7			−2.82822
$598$	3.46073e6	+	3.05120e6i	0.395745	+	0.348914i
$599$	−1.60799e7			−1.83112			−0.915561	−	0.402179i	$-0.868253\pi$
$599$	−1.60799e7			−1.83112			−0.915561	+	0.402179i	$0.868253\pi$
$600$	741376.	−	1.28410e6i	0.0840737	−	0.145620i
$601$	−7.82074e6	+	1.35459e7i	−0.883205	+	1.52976i	−0.0354482	+	0.999372i	$0.511286\pi$
$601$	−7.82074e6	+	1.35459e7i	−0.883205	+	1.52976i	−0.847757	+	0.530385i	$0.822047\pi$
$602$	1.58119e6	+	2.73870e6i	0.177825	+	0.308002i
$603$	2.36129e6			0.264458
$604$	−1.61938e6	−	2.80484e6i	−0.180616	−	0.312836i
$605$	1.36824e6	+	2.36986e6i	0.151976	+	0.263230i
$606$	1.24136e7			1.37315
$607$	575901.	+	997489.i	0.0634418	+	0.109884i	0.896002	−	0.444051i	$-0.146459\pi$
$607$	575901.	+	997489.i	0.0634418	+	0.109884i	−0.832560	+	0.553935i	$0.813126\pi$
$608$	−488983.	+	846943.i	−0.0536457	+	0.0929170i
$609$	−7.63848e6	+	1.32302e7i	−0.834571	+	1.44552i
$610$	4.65592e6			0.506618
$611$	−6.38252e6	+	2.14778e6i	−0.691654	+	0.232748i
$612$	−889325.			−0.0959803
$613$	−2.63593e6	+	4.56557e6i	−0.283324	+	0.490731i	−0.972201	−	0.234147i	$-0.924770\pi$
$613$	−2.63593e6	+	4.56557e6i	−0.283324	+	0.490731i	0.688878	+	0.724878i	$0.258104\pi$
$614$	−223871.	+	387757.i	−0.0239650	+	0.0415086i
$615$	275201.	+	476662.i	0.0293402	+	0.0508186i
$616$	−6.73801e6			−0.715451
$617$	−4.56011e6	−	7.89834e6i	−0.482239	−	0.835263i	0.517553	−	0.855651i	$-0.326843\pi$
$617$	−4.56011e6	−	7.89834e6i	−0.482239	−	0.835263i	−0.999792	+	0.0203883i	$0.993510\pi$
$618$	6.63359e6	+	1.14897e7i	0.698679	+	1.21015i
$619$	−1.28556e7			−1.34855			−0.674274	−	0.738481i	$-0.735543\pi$
$619$	−1.28556e7			−1.34855			−0.674274	+	0.738481i	$0.735543\pi$
$620$	2.39801e6	+	4.15348e6i	0.250537	+	0.433943i
$621$	6.27057e6	−	1.08609e7i	0.652496	−	1.13016i
$622$	−3.73362e6	+	6.46683e6i	−0.386950	+	0.670217i
$623$	2.10609e7			2.17399
$624$	3.16362e6	+	2.78925e6i	0.325254	+	0.286765i
$625$	−6.35365e6			−0.650613
$626$	−434821.	+	753132.i	−0.0443481	+	0.0768131i
$627$	6.03531e6	−	1.04535e7i	0.613099	−	1.06192i
$628$	−273678.	−	474025.i	−0.0276912	−	0.0479625i
$629$	−1.23530e6			−0.124493
$630$	1.04697e7	+	1.81340e7i	1.05095	+	1.82029i
$631$	257892.	+	446682.i	0.0257848	+	0.0446606i	0.878630	−	0.477503i	$-0.158458\pi$
$631$	257892.	+	446682.i	0.0257848	+	0.0446606i	−0.852845	+	0.522164i	$0.825125\pi$
$632$	4.02997e6			0.401337
$633$	3.27472e6	+	5.67199e6i	0.324837	+	0.562634i
$634$	4.41814e6	−	7.65244e6i	0.436532	−	0.756096i
$635$	−887087.	+	1.53648e6i	−0.0873036	+	0.151214i
$636$	−8.97057e6			−0.879381
$637$	−4.08573e6	+	2.02603e7i	−0.398952	+	1.97832i
$638$	4.69080e6			0.456242
$639$	−1.25167e7	+	2.16796e7i	−1.21266	+	2.10039i
$640$	−390143.	+	675747.i	−0.0376507	+	0.0652130i
$641$	−7.15754e6	−	1.23972e7i	−0.688048	−	1.19173i	−0.972468	−	0.233035i	$-0.925134\pi$
$641$	−7.15754e6	−	1.23972e7i	−0.688048	−	1.19173i	0.284420	−	0.958700i	$-0.408199\pi$
$642$	−1.99652e7			−1.91177
$643$	−2.58903e6	−	4.48433e6i	−0.246950	−	0.427730i	0.715728	−	0.698379i	$-0.246095\pi$
$643$	−2.58903e6	−	4.48433e6i	−0.246950	−	0.427730i	−0.962678	+	0.270649i	$0.912762\pi$
$644$	3.41067e6	+	5.90745e6i	0.324060	+	0.561288i
$645$	−4.52004e6			−0.427802
$646$	217541.	+	376792.i	0.0205097	+	0.0355238i
$647$	1.48690e6	−	2.57539e6i	0.139644	−	0.241870i	−0.787718	−	0.616036i	$-0.788738\pi$
$647$	1.48690e6	−	2.57539e6i	0.139644	−	0.241870i	0.927362	+	0.374166i	$0.122071\pi$
$648$	1.93724e6	−	3.35540e6i	0.181237	−	0.313911i
$649$	250371.			0.0233331
$650$	−412861.	+	2.04730e6i	−0.0383284	+	0.190063i
$651$	3.83278e7			3.54455
$652$	2.90177e6	−	5.02601e6i	0.267328	−	0.463025i
$653$	−6.08249e6	+	1.05352e7i	−0.558211	+	0.966850i	0.439435	+	0.898274i	$0.355179\pi$
$653$	−6.08249e6	+	1.05352e7i	−0.558211	+	0.966850i	−0.997646	+	0.0685754i	$0.978155\pi$
$654$	−9.96133e6	−	1.72535e7i	−0.910695	−	1.57737i
$655$	5.33535e6			0.485914
$656$	54712.5	+	94764.9i	0.00496395	+	0.00859781i
$657$	1.14787e7	+	1.98817e7i	1.03748	+	1.79697i
$658$	−9.95643e6			−0.896476
$659$	−4.21884e6	−	7.30724e6i	−0.378425	−	0.655451i	0.612409	−	0.790541i	$-0.290201\pi$
$659$	−4.21884e6	−	7.30724e6i	−0.378425	−	0.655451i	−0.990833	+	0.135091i	$0.956867\pi$
$660$	4.81536e6	−	8.34045e6i	0.430298	−	0.745298i
$661$	5.59989e6	−	9.69930e6i	0.498513	−	0.863449i	−0.501486	−	0.865166i	$-0.667213\pi$
$661$	5.59989e6	−	9.69930e6i	0.498513	−	0.863449i	0.999999	+	0.00171662i	$0.000546419\pi$
$662$	5.23837e6			0.464570
$663$	1.77837e6	−	598436.i	0.157122	−	0.0528730i
$664$	1.93573e6			0.170382
$665$	5.12203e6	−	8.87162e6i	0.449147	−	0.777945i
$666$	1.05869e7	−	1.83370e7i	0.924873	−	1.60193i
$667$	−2.37441e6	−	4.11259e6i	−0.206652	−	0.357933i
$668$	1.00868e7			0.874605
$669$	−3.77594e6	−	6.54013e6i	−0.326182	−	0.564964i
$670$	−460849.	−	798215.i	−0.0396618	−	0.0686962i
$671$	−1.14248e7			−0.979583
$672$	3.11785e6	+	5.40028e6i	0.266337	+	0.461310i
$673$	−2.26972e6	+	3.93128e6i	−0.193168	+	0.334577i	−0.946298	−	0.323294i	$-0.895210\pi$
$673$	−2.26972e6	+	3.93128e6i	−0.193168	+	0.334577i	0.753130	+	0.657871i	$0.228543\pi$
$674$	2.27871e6	−	3.94684e6i	0.193214	−	0.334657i
$675$	5.67703e6			0.479581
$676$	−5.47638e6	−	2.30239e6i	−0.460922	−	0.193781i
$677$	1.89907e7			1.59247			0.796233	−	0.604990i	$-0.206823\pi$
$677$	1.89907e7			1.59247			0.796233	+	0.604990i	$0.206823\pi$
$678$	−3.07285e6	+	5.32233e6i	−0.256724	+	0.444659i
$679$	−1.69835e7	+	2.94162e7i	−1.41368	+	2.44857i
$680$	173568.	+	300629.i	0.0143946	+	0.0249321i
$681$	1.54946e7			1.28031
$682$	−5.88429e6	−	1.01919e7i	−0.484433	−	0.839062i
$683$	−9.40153e6	−	1.62839e7i	−0.771164	−	1.33570i	−0.936925	−	0.349529i	$-0.886342\pi$
$683$	−9.40153e6	−	1.62839e7i	−0.771164	−	1.33570i	0.165762	−	0.986166i	$-0.446992\pi$
$684$	−7.45757e6			−0.609476
$685$	1.93285e6	+	3.34780e6i	0.157388	+	0.272605i
$686$	−7.70811e6	+	1.33508e7i	−0.625371	+	1.08317i
$687$	−4.71804e6	+	8.17188e6i	−0.381390	+	0.660587i
$688$	−898626.			−0.0723782
$689$	1.19755e7	−	4.02987e6i	0.961051	−	0.323402i
$690$	−9.74983e6			−0.779605
$691$	−105554.	+	182826.i	−0.00840972	+	0.0145661i	−0.870200	−	0.492699i	$-0.836010\pi$
$691$	−105554.	+	182826.i	−0.00840972	+	0.0145661i	0.861790	+	0.507265i	$0.169344\pi$
$692$	−1.03182e6	+	1.78716e6i	−0.0819103	+	0.141873i
$693$	−2.56906e7	−	4.44975e7i	−2.03208	−	3.51967i
$694$	−1.32169e7			−1.04167
$695$	6.34548e6	+	1.09907e7i	0.498313	+	0.863104i
$696$	−2.17056e6	−	3.75951e6i	−0.169843	−	0.294177i
$697$	48681.5			0.00379561
$698$	−2.00459e6	−	3.47206e6i	−0.155736	−	0.269742i
$699$	1.21874e7	−	2.11091e7i	0.943445	−	1.63409i
$700$	−1.54392e6	+	2.67414e6i	−0.119091	+	0.206272i
$701$	−5.76834e6			−0.443359			−0.221679	−	0.975120i	$-0.571154\pi$
$701$	−5.76834e6			−0.443359			−0.221679	+	0.975120i	$0.571154\pi$
$702$	−3.19219e6	+	1.58294e7i	−0.244482	+	1.21234i
$703$	−1.03588e7			−0.790532
$704$	957339.	−	1.65816e6i	0.0728005	−	0.126094i
$705$	7.11543e6	−	1.23243e7i	0.539173	−	0.933876i
$706$	4.55760e6	+	7.89400e6i	0.344132	+	0.596054i
$707$	−2.58515e7			−1.94508
$708$	−115853.	−	200663.i	−0.00868610	−	0.0150448i
$709$	8.44542e6	+	1.46279e7i	0.630966	+	1.09286i	0.987355	+	0.158527i	$0.0506744\pi$
$709$	8.44542e6	+	1.46279e7i	0.630966	+	1.09286i	−0.356389	+	0.934338i	$0.615992\pi$
$710$	9.77150e6			0.727471
$711$	1.53654e7	+	2.66137e7i	1.13991	+	1.97439i
$712$	−2.99235e6	+	5.18290e6i	−0.221214	+	0.383153i
$713$	−5.95707e6	+	1.03179e7i	−0.438842	+	0.760097i
$714$	2.77417e6			0.203651
$715$	−2.68161e6	+	1.32975e7i	−0.196169	+	0.972762i
$716$	1.12862e7			0.822742
$717$	1.24044e7	−	2.14850e7i	0.901109	−	1.56077i
$718$	855243.	−	1.48132e6i	0.0619125	−	0.107236i
$719$	3.24084e6	+	5.61330e6i	0.233795	+	0.404945i	0.958922	−	0.283670i	$-0.0915522\pi$
$719$	3.24084e6	+	5.61330e6i	0.233795	+	0.404945i	−0.725127	+	0.688615i	$0.758219\pi$
$720$	−5.95013e6			−0.427755
$721$	−1.38145e7	−	2.39274e7i	−0.989683	−	1.71418i
$722$	−3.12798e6	−	5.41782e6i	−0.223316	−	0.386795i
$723$	6.09415e6			0.433578
$724$	374790.	+	649155.i	0.0265730	+	0.0460258i
$725$	1.07483e6	−	1.86166e6i	0.0759442	−	0.131539i
$726$	−3.10713e6	+	5.38171e6i	−0.218785	+	0.378947i
$727$	1.21057e7			0.849481			0.424741	−	0.905315i	$-0.360365\pi$
$727$	1.21057e7			0.849481			0.424741	+	0.905315i	$0.360365\pi$
$728$	−6.58825e6	−	5.80862e6i	−0.460725	−	0.406204i
$729$	−1.39839e7			−0.974560
$730$	4.48056e6	−	7.76056e6i	0.311190	−	0.538996i
$731$	−199892.	+	346224.i	−0.0138357	+	0.0239642i
$732$	5.28654e6	+	9.15656e6i	0.364665	+	0.631618i
$733$	−1.34135e6			−0.0922111			−0.0461055	−	0.998937i	$-0.514681\pi$
$733$	−1.34135e6			−0.0922111			−0.0461055	+	0.998937i	$0.514681\pi$
$734$	−9.37476e6	−	1.62376e7i	−0.642274	−	1.11245i
$735$	−2.18382e7	−	3.78249e7i	−1.49107	−	2.58261i
$736$	−1.93836e6			−0.131898
$737$	1.13084e6	+	1.95867e6i	0.0766890	+	0.132829i
$738$	−417216.	+	722638.i	−0.0281981	+	0.0488405i
$739$	−1.76280e6	+	3.05325e6i	−0.118738	+	0.205661i	−0.919268	−	0.393632i	$-0.871218\pi$
$739$	−1.76280e6	+	3.05325e6i	−0.118738	+	0.205661i	0.800530	+	0.599293i	$0.204552\pi$
$740$	−8.26490e6			−0.554828
$741$	1.49128e7	−	5.01828e6i	0.997728	−	0.335745i
$742$	1.86812e7			1.24565
$743$	−1.16894e7	+	2.02466e7i	−0.776817	+	1.34549i	0.156950	+	0.987606i	$0.449834\pi$
$743$	−1.16894e7	+	2.02466e7i	−0.776817	+	1.34549i	−0.933768	+	0.357880i	$0.883500\pi$
$744$	−5.44563e6	+	9.43211e6i	−0.360675	+	0.624707i
$745$	5.73731e6	+	9.93732e6i	0.378720	+	0.655962i
$746$	1.34001e7			0.881577
$747$	7.38053e6	+	1.27835e7i	0.483934	+	0.838198i
$748$	−425905.	−	737689.i	−0.0278329	−	0.0482080i
$749$	4.15775e7			2.70803
$750$	−1.02547e7	−	1.77616e7i	−0.665684	−	1.15300i
$751$	9.24454e6	−	1.60120e7i	0.598116	−	1.03597i	−0.394983	−	0.918689i	$-0.629249\pi$
$751$	9.24454e6	−	1.60120e7i	0.598116	−	1.03597i	0.993099	−	0.117279i	$-0.0374172\pi$
$752$	1.41461e6	−	2.45018e6i	0.0912207	−	0.157999i
$753$	−3.64932e7			−2.34544
$754$	4.58654e6	+	4.04379e6i	0.293804	+	0.259036i
$755$	−9.64032e6			−0.615494
$756$	−1.19374e7	+	2.06761e7i	−0.759634	+	1.31572i
$757$	7.73288e6	−	1.33937e7i	0.490458	−	0.849498i	−0.509482	−	0.860481i	$-0.670163\pi$
$757$	7.73288e6	−	1.33937e7i	0.490458	−	0.849498i	0.999940	+	0.0109836i	$0.00349626\pi$
$758$	3.05529e6	+	5.29192e6i	0.193143	+	0.334534i
$759$	2.39243e7			1.50742
$760$	1.45548e6	+	2.52097e6i	0.0914056	+	0.158319i
$761$	−1.07733e7	−	1.86600e7i	−0.674355	−	1.16802i	−0.976657	−	0.214805i	$-0.931088\pi$
$761$	−1.07733e7	−	1.86600e7i	−0.674355	−	1.16802i	0.302302	−	0.953212i	$-0.402245\pi$
$762$	−4.02896e6			−0.251365
$763$	2.07445e7	+	3.59305e7i	1.29001	+	2.23436i
$764$	3.47505e6	−	6.01896e6i	0.215391	−	0.373068i
$765$	−1.32356e6	+	2.29247e6i	−0.0817693	+	0.141629i
$766$	8.33708e6			0.513383
$767$	244806.	+	215837.i	0.0150257	+	0.0132476i
$768$	−1.77194e6			−0.108404
$769$	1.10972e7	−	1.92209e7i	0.676701	−	1.17208i	−0.299267	−	0.954169i	$-0.596742\pi$
$769$	1.10972e7	−	1.92209e7i	0.676701	−	1.17208i	0.975969	−	0.217911i	$-0.0699244\pi$
$770$	−1.00280e7	+	1.73690e7i	−0.609520	+	1.05572i
$771$	2.43560e7	+	4.21858e7i	1.47560	+	2.55582i
$772$	−8.44734e6			−0.510125
$773$	1.18858e7	+	2.05868e7i	0.715449	+	1.23919i	0.962786	+	0.270264i	$0.0871111\pi$
$773$	1.18858e7	+	2.05868e7i	0.715449	+	1.23919i	−0.247337	+	0.968929i	$0.579556\pi$
$774$	−3.42628e6	−	5.93449e6i	−0.205575	−	0.356066i
$775$	−5.39320e6			−0.322547
$776$	−4.82604e6	−	8.35895e6i	−0.287698	−	0.498307i
$777$	−3.30248e7	+	5.72006e7i	−1.96240	+	3.39897i
$778$	3.53504e6	−	6.12288e6i	0.209385	−	0.362666i
$779$	408226.			0.0241022
$780$	1.18984e7	−	4.00391e6i	0.700247	−	0.235639i
$781$	−2.39775e7			−1.40662
$782$	−431173.	+	746813.i	−0.0252136	+	0.0436712i
$783$	8.31045e6	−	1.43941e7i	0.484418	−	0.839036i
$784$	−4.34164e6	−	7.51994e6i	−0.252269	−	0.436942i
$785$	−1.62924e6			−0.0943647
$786$	6.05801e6	+	1.04928e7i	0.349763	+	0.605807i
$787$	−6.19098e6	−	1.07231e7i	−0.356306	−	0.617140i	0.631035	−	0.775755i	$-0.282631\pi$
$787$	−6.19098e6	−	1.07231e7i	−0.356306	−	0.617140i	−0.987341	+	0.158615i	$0.949297\pi$
$788$	−2.50466e6			−0.143692
$789$	−1.56689e7	−	2.71393e7i	−0.896079	−	1.55205i
$790$	5.99770e6	−	1.03883e7i	0.341914	−	0.592213i
$791$	6.39921e6	−	1.10838e7i	0.363652	−	0.629863i
$792$	1.46006e7			0.827097
$793$	−1.11708e7	−	9.84893e6i	−0.630817	−	0.556168i
$794$	4.04873e6			0.227912
$795$	−1.33507e7	+	2.31241e7i	−0.749179	+	1.29762i
$796$	−7.28735e6	+	1.26221e7i	−0.407650	+	0.706070i
$797$	9.10722e6	+	1.57742e7i	0.507856	+	0.879632i	0.999959	+	0.00909476i	$0.00289499\pi$
$797$	9.10722e6	+	1.57742e7i	0.507856	+	0.879632i	−0.492103	+	0.870537i	$0.663772\pi$
$798$	2.32632e7			1.29319
$799$	−629340.	−	1.09005e6i	−0.0348753	−	0.0604058i
$800$	−438721.	−	759887.i	−0.0242361	−	0.0419782i
$801$	−4.56368e7			−2.51324
$802$	2.71361e6	+	4.70011e6i	0.148974	+	0.258031i
$803$	−1.09945e7	+	1.90430e7i	−0.601708	+	1.04219i
$804$	1.04654e6	−	1.81266e6i	0.0570973	−	0.0988954i
$805$	2.03041e7			1.10432
$806$	3.03259e6	−	1.50380e7i	0.164428	−	0.815367i
$807$	3.40294e7			1.83938
$808$	3.67299e6	−	6.36180e6i	0.197921	−	0.342808i
$809$	1.44744e7	−	2.50705e7i	0.777554	−	1.34676i	−0.155793	−	0.987790i	$-0.549793\pi$
$809$	1.44744e7	−	2.50705e7i	0.777554	−	1.34676i	0.933348	−	0.358974i	$-0.116873\pi$
$810$	−5.76629e6	−	9.98751e6i	−0.308805	−	0.534866i
$811$	−2.56540e7			−1.36963			−0.684814	−	0.728718i	$-0.740117\pi$
$811$	−2.56540e7			−1.36963			−0.684814	+	0.728718i	$0.740117\pi$
$812$	4.52019e6	+	7.82920e6i	0.240584	+	0.416704i
$813$	2.08664e7	+	3.61417e7i	1.10719	+	1.91770i
$814$	2.02806e7			1.07280
$815$	−8.63726e6	−	1.49602e7i	−0.455493	−	0.788937i
$816$	−394155.	+	682696.i	−0.0207225	+	0.0358924i
$817$	−1.67623e6	+	2.90331e6i	−0.0878572	+	0.152173i
$818$	−1.72877e7			−0.903345
$819$	1.32402e7	−	6.56556e7i	0.689740	−	3.42028i
$820$	325709.			0.0169159
$821$	−1.19214e7	+	2.06485e7i	−0.617261	+	1.06913i	0.372722	+	0.927943i	$0.378424\pi$
$821$	−1.19214e7	+	2.06485e7i	−0.617261	+	1.06913i	−0.989983	+	0.141185i	$0.954909\pi$
$822$	−4.38930e6	+	7.60250e6i	−0.226577	+	0.392443i
$823$	−9.95359e6	−	1.72401e7i	−0.512248	−	0.887239i	−0.999899	−	0.0142005i	$-0.995480\pi$
$823$	−9.95359e6	−	1.72401e7i	−0.512248	−	0.887239i	0.487652	−	0.873038i	$-0.337854\pi$
$824$	7.85107e6			0.402820
$825$	5.41495e6	+	9.37896e6i	0.276987	+	0.479755i
$826$	241264.	+	417882.i	0.0123039	+	0.0213110i
$827$	2.82809e7			1.43790			0.718952	−	0.695060i	$-0.244622\pi$
$827$	2.82809e7			1.43790			0.718952	+	0.695060i	$0.244622\pi$
$828$	−7.39056e6	−	1.28008e7i	−0.374629	−	0.648877i
$829$	1.74077e7	−	3.01510e7i	0.879741	−	1.52376i	0.0281161	−	0.999605i	$-0.491049\pi$
$829$	1.74077e7	−	3.01510e7i	0.879741	−	1.52376i	0.851625	−	0.524152i	$-0.175617\pi$
$830$	2.88090e6	−	4.98986e6i	0.145155	−	0.251416i
$831$	−2.99066e7			−1.50233
$832$	2.36551e6	−	796014.i	0.118472	−	0.0398669i
$833$	−3.86305e6			−0.192894
$834$	−1.44099e7	+	2.49587e7i	−0.717375	+	1.24253i
$835$	1.50119e7	−	2.60014e7i	0.745110	−	1.29057i
$836$	−3.57149e6	−	6.18600e6i	−0.176740	−	0.306122i
$837$	−4.16996e7			−2.05740
$838$	4.10129e6	+	7.10364e6i	0.201749	+	0.349439i
$839$	−573636.	−	993566.i	−0.0281340	−	0.0487295i	0.851616	−	0.524167i	$-0.175623\pi$
$839$	−573636.	−	993566.i	−0.0281340	−	0.0487295i	−0.879750	+	0.475437i	$0.842290\pi$
$840$	1.85609e7			0.907613
$841$	7.10875e6	+	1.23127e7i	0.346580	+	0.600294i
$842$	−1.05948e7	+	1.83508e7i	−0.515007	+	0.892018i
$843$	−1.65154e7	+	2.86056e7i	−0.800426	+	1.38638i
$844$	3.87574e6			0.187283
$845$	−1.40854e7	+	1.06903e7i	−0.678621	+	0.515047i
$846$	2.15745e7			1.03637
$847$	6.47061e6	−	1.12074e7i	0.309911	−	0.536781i
$848$	−2.65424e6	+	4.59728e6i	−0.126751	+	0.219539i
$849$	−1.74352e7	−	3.01986e7i	−0.830152	−	1.43787i
$850$	−390360.			−0.0185318
$851$	−1.02657e7	−	1.77807e7i	−0.485919	−	0.841637i
$852$	1.10950e7	+	1.92171e7i	0.523635	+	0.906963i
$853$	4.15172e6			0.195369			0.0976845	−	0.995217i	$-0.468856\pi$
$853$	4.15172e6			0.195369			0.0976845	+	0.995217i	$0.468856\pi$
$854$	−1.10092e7	−	1.90686e7i	−0.516550	−	0.894692i
$855$	−1.10989e7	+	1.92239e7i	−0.519236	+	0.899344i
$856$	−5.90735e6	+	1.02318e7i	−0.275555	+	0.477276i
$857$	4.88464e6			0.227185			0.113593	−	0.993527i	$-0.463764\pi$
$857$	4.88464e6			0.227185			0.113593	+	0.993527i	$0.463764\pi$
$858$	−2.91965e7	+	9.82487e6i	−1.35398	+	0.455626i
$859$	−2.11300e7			−0.977049			−0.488524	−	0.872550i	$-0.662465\pi$
$859$	−2.11300e7			−0.977049			−0.488524	+	0.872550i	$0.662465\pi$
$860$	−1.33740e6	+	2.31645e6i	−0.0616618	+	0.106801i
$861$	1.30146e6	−	2.25420e6i	0.0598308	−	0.103630i
$862$	2.88638e6	+	4.99936e6i	0.132308	+	0.229164i
$863$	9.60289e6			0.438910			0.219455	−	0.975623i	$-0.429572\pi$
$863$	9.60289e6			0.438910			0.219455	+	0.975623i	$0.429572\pi$
$864$	−3.39213e6	−	5.87535e6i	−0.154593	−	0.267762i
$865$	3.07126e6	+	5.31958e6i	0.139565	+	0.241734i
$866$	−721838.			−0.0327073
$867$	−1.90195e7	−	3.29427e7i	−0.859312	−	1.48837i
$868$	1.13405e7	−	1.96424e7i	0.510899	−	0.884902i
$869$	−1.47173e7	+	2.54911e7i	−0.661117	+	1.14509i
$870$	−1.29215e7			−0.578784
$871$	−582803.	+	2.89000e6i	−0.0260301	+	0.129078i
$872$	−1.17896e7			−0.525057
$873$	3.68014e7	−	6.37419e7i	1.63429	−	2.83067i
$874$	−3.61566e6	+	6.26251e6i	−0.160107	+	0.277313i
$875$	2.13554e7	+	3.69886e7i	0.942945	+	1.63323i
$876$	2.03497e7			0.895981
$877$	4.58757e6	+	7.94590e6i	0.201411	+	0.348854i	0.948983	−	0.315326i	$-0.102114\pi$
$877$	4.58757e6	+	7.94590e6i	0.201411	+	0.348854i	−0.747572	+	0.664181i	$0.768781\pi$
$878$	−8.89533e6	−	1.54072e7i	−0.389427	−	0.674507i
$879$	−1.73668e7			−0.758138
$880$	−2.84957e6	−	4.93560e6i	−0.124043	−	0.214849i
$881$	−3.76611e6	+	6.52309e6i	−0.163476	+	0.283148i	−0.936113	−	0.351700i	$-0.885604\pi$
$881$	−3.76611e6	+	6.52309e6i	−0.163476	+	0.283148i	0.772637	+	0.634848i	$0.218937\pi$
$882$	3.31076e7	−	5.73440e7i	1.43303	−	2.48208i
$883$	3.85504e7			1.66390			0.831950	−	0.554851i	$-0.187225\pi$
$883$	3.85504e7			1.66390			0.831950	+	0.554851i	$0.187225\pi$
$884$	219499.	−	1.08845e6i	0.00944718	−	0.0468467i
$885$	−689685.			−0.0296001
$886$	−5.41392e6	+	9.37718e6i	−0.231701	+	0.401317i
$887$	−1.03221e7	+	1.78784e7i	−0.440514	+	0.762992i	−0.997728	−	0.0673768i	$-0.978537\pi$
$887$	−1.03221e7	+	1.78784e7i	−0.440514	+	0.762992i	0.557214	+	0.830369i	$0.311870\pi$
$888$	−9.38435e6	−	1.62542e7i	−0.399366	−	0.691723i
$889$	8.39032e6			0.356061
$890$	8.90688e6	+	1.54272e7i	0.376921	+	0.652846i
$891$	1.41494e7	+	2.45075e7i	0.597097	+	1.03420i
$892$	−4.46895e6			−0.188059
$893$	−5.27742e6	−	9.14076e6i	−0.221459	−	0.383578i
$894$	−1.30288e7	+	2.25666e7i	−0.545207	+	0.944326i
$895$	1.67969e7	−	2.90931e7i	0.700926	−	1.21404i
$896$	3.69008e6			0.153556
$897$	2.33926e7	+	2.06244e7i	0.970727	+	0.855855i
$898$	2.37812e6			0.0984107
$899$	−7.89495e6	+	1.36745e7i	−0.325799	+	0.564301i
$900$	3.34551e6	−	5.79459e6i	0.137675	−	0.238460i
$901$	1.18083e6	+	2.04526e6i	0.0484591	+	0.0839336i
$902$	−799232.			−0.0327082
$903$	1.06880e7	+	1.85121e7i	0.436189	+	0.755502i
$904$	1.81841e6	+	3.14957e6i	0.0740065	+	0.128183i
$905$	2.23116e6			0.0905544
$906$	−1.09461e7	−	1.89591e7i	−0.443034	−	0.767358i
$907$	9.27933e6	−	1.60723e7i	0.374540	−	0.648722i	−0.615718	−	0.787967i	$-0.711134\pi$
$907$	9.27933e6	−	1.60723e7i	0.374540	−	0.648722i	0.990258	+	0.139244i	$0.0444673\pi$
$908$	4.58460e6	−	7.94077e6i	0.184539	−	0.319630i
$909$	5.60174e7			2.24860
$910$	−2.47784e7	+	8.33815e6i	−0.991904	+	0.333785i
$911$	−3.13685e7			−1.25227			−0.626134	−	0.779715i	$-0.715364\pi$
$911$	−3.13685e7			−1.25227			−0.626134	+	0.779715i	$0.715364\pi$
$912$	−3.30524e6	+	5.72485e6i	−0.131588	+	0.227917i
$913$	−7.06920e6	+	1.22442e7i	−0.280668	+	0.486131i
$914$	−2.56836e6	−	4.44854e6i	−0.101693	−	0.176137i
$915$	3.14713e7			1.24269
$916$	2.79197e6	+	4.83584e6i	0.109944	+	0.190429i
$917$	−1.26158e7	−	2.18512e7i	−0.495441	−	0.858129i
$918$	−3.01821e6			−0.118207
$919$	1.62589e7	+	2.81612e7i	0.635040	+	1.09992i	0.986507	+	0.163721i	$0.0523498\pi$
$919$	1.62589e7	+	2.81612e7i	0.635040	+	1.09992i	−0.351466	+	0.936200i	$0.614317\pi$
$920$	−2.88481e6	+	4.99664e6i	−0.112369	+	0.194629i
$921$	−1.51324e6	+	2.62101e6i	−0.0587841	+	0.101817i
$922$	−2.28157e6			−0.0883906
$923$	−2.34446e7	−	2.06702e7i	−0.905812	−	0.798621i
$924$	−4.55451e7			−1.75494
$925$	4.64700e6	−	8.04884e6i	0.178574	−	0.309299i
$926$	−1.51314e6	+	2.62083e6i	−0.0579897	+	0.100441i
$927$	2.99345e7	+	5.18481e7i	1.14412	+	1.98168i
$928$	−2.56892e6			−0.0979222
$929$	−2.31106e6	−	4.00287e6i	−0.0878560	−	0.152171i	0.818749	−	0.574152i	$-0.194668\pi$
$929$	−2.31106e6	−	4.00287e6i	−0.0878560	−	0.152171i	−0.906605	+	0.421981i	$0.861335\pi$
$930$	1.62092e7	+	2.80752e7i	0.614546	+	1.06442i
$931$	−3.23942e7			−1.22488
$932$	−7.21206e6	−	1.24917e7i	−0.271969	−	0.471065i
$933$	−2.52372e7	+	4.37120e7i	−0.949153	+	1.64398i
$934$	−5.89213e6	+	1.02055e7i	−0.221006	+	0.382794i
$935$	−2.53546e6			−0.0948478
$936$	1.42760e7	+	1.25867e7i	0.532621	+	0.469592i
$937$	−698488.			−0.0259902			−0.0129951	−	0.999916i	$-0.504137\pi$
$937$	−698488.			−0.0259902			−0.0129951	+	0.999916i	$0.504137\pi$
$938$	−2.17942e6	+	3.77487e6i	−0.0808787	+	0.140086i
$939$	−2.93914e6	+	5.09074e6i	−0.108782	+	0.188416i
$940$	−4.21067e6	−	7.29309e6i	−0.155429	−	0.269211i
$941$	1.20398e7			0.443247			0.221623	−	0.975132i	$-0.428864\pi$
$941$	1.20398e7			0.443247			0.221623	+	0.975132i	$0.428864\pi$
$942$	−1.84991e6	−	3.20414e6i	−0.0679240	−	0.117648i
$943$	404558.	+	700715.i	0.0148150	+	0.0256603i
$944$	−137116.			−0.00500792
$945$	3.55322e7	+	6.15436e7i	1.29432	+	2.24183i
$946$	3.28174e6	−	5.68415e6i	0.119228	−	0.206508i
$947$	5.63462e6	−	9.75944e6i	0.204169	−	0.353631i	−0.745699	−	0.666283i	$-0.767884\pi$
$947$	5.63462e6	−	9.75944e6i	0.204169	−	0.353631i	0.949868	+	0.312652i	$0.101218\pi$
$948$	2.72403e7			0.984444
$949$	−2.71665e7	+	9.14176e6i	−0.979192	+	0.329507i
$950$	−3.27342e6			−0.117677
$951$	2.98641e7	−	5.17261e7i	1.07077	−	1.85464i
$952$	820829.	−	1.42172e6i	0.0293535	−	0.0508418i
$953$	−6.49614e6	−	1.12516e7i	−0.231698	−	0.401313i	0.726610	−	0.687050i	$-0.241095\pi$
$953$	−6.49614e6	−	1.12516e7i	−0.231698	−	0.401313i	−0.958308	+	0.285737i	$0.907762\pi$
$954$	−4.04803e7			−1.44003
$955$	−1.03437e7	−	1.79157e7i	−0.367000	−	0.635662i
$956$	−7.34050e6	−	1.27141e7i	−0.259765	−	0.449926i
$957$	3.17071e7			1.11912
$958$	1.45807e7	+	2.52545e7i	0.513292	+	0.889047i
$959$	9.14074e6	−	1.58322e7i	0.320948	−	0.555898i
$960$	−2.63714e6	+	4.56766e6i	−0.0923539	+	0.159962i
$961$	1.09856e7			0.383720
$962$	1.98298e7	+	1.74832e7i	0.690845	+	0.609093i
$963$	−9.00941e7			−3.13062
$964$	1.80316e6	−	3.12316e6i	0.0624943	−	0.108243i
$965$	−1.25720e7	+	2.17753e7i	−0.434595	+	0.752741i
$966$	2.30542e7	+	3.99310e7i	0.794889	+	1.37679i
$967$	2.53817e6			0.0872880			0.0436440	−	0.999047i	$-0.486103\pi$
$967$	2.53817e6			0.0872880			0.0436440	+	0.999047i	$0.486103\pi$
$968$	1.83869e6	+	3.18471e6i	0.0630697	+	0.109240i
$969$	1.47045e6	+	2.54690e6i	0.0503085	+	0.0871368i
$970$	−2.87299e7			−0.980404
$971$	2.78665e7	+	4.82662e7i	0.948493	+	1.64284i	0.748602	+	0.663019i	$0.230725\pi$
$971$	2.78665e7	+	4.82662e7i	0.948493	+	1.64284i	0.199891	+	0.979818i	$0.435941\pi$
$972$	215121.	−	372600.i	0.00730327	−	0.0126496i
$973$	3.00087e7	−	5.19765e7i	1.01617	−	1.76005i
$974$	2.00105e7			0.675866
$975$	−2.79071e6	+	1.38386e7i	−0.0940162	+	0.466207i
$976$	6.25679e6			0.210246
$977$	1.59934e7	−	2.77013e7i	0.536048	−	0.928462i	−0.463064	−	0.886325i	$-0.653250\pi$
$977$	1.59934e7	−	2.77013e7i	0.536048	−	0.928462i	0.999112	−	0.0421369i	$-0.0134166\pi$
$978$	1.96143e7	−	3.39729e7i	0.655731	−	1.13576i
$979$	−2.18559e7	−	3.78555e7i	−0.728805	−	1.26233i
$980$	−2.58462e7			−0.859670
$981$	−4.49512e7	−	7.78577e7i	−1.49131	−	2.58303i
$982$	1.37601e7	+	2.38332e7i	0.455348	+	0.788686i
$983$	−4.02352e7			−1.32807			−0.664037	−	0.747700i	$-0.731158\pi$
$983$	−4.02352e7			−1.32807			−0.664037	+	0.747700i	$0.731158\pi$
$984$	369826.	+	640557.i	0.0121761	+	0.0210897i
$985$	−3.72762e6	+	6.45642e6i	−0.122417	+	0.212032i
$986$	−571437.	+	989758.i	−0.0187187	+	0.0324218i
$987$	−6.72997e7			−2.19898
$988$	1.84064e6	−	9.12738e6i	0.0599898	−	0.297477i
$989$	−6.64466e6			−0.216014
$990$	2.17296e7	−	3.76369e7i	0.704636	−	1.22046i
$991$	−2.52965e6	+	4.38149e6i	−0.0818233	+	0.141722i	−0.904033	−	0.427462i	$-0.859408\pi$
$991$	−2.52965e6	+	4.38149e6i	−0.0818233	+	0.141722i	0.822210	+	0.569185i	$0.192741\pi$
$992$	3.22254e6	+	5.58160e6i	0.103973	+	0.180086i
$993$	3.54084e7			1.13955
$994$	−2.31054e7	−	4.00197e7i	−0.741733	−	1.28472i
$995$	2.16912e7	+	3.75702e7i	0.694585	+	1.20306i
$996$	1.30844e7			0.417932
$997$	−1.48662e7	−	2.57490e7i	−0.473654	−	0.820393i	0.525891	−	0.850552i	$-0.323732\pi$
$997$	−1.48662e7	−	2.57490e7i	−0.473654	−	0.820393i	−0.999545	+	0.0301589i	$0.990399\pi$
$998$	1.36208e7	−	2.35919e7i	0.432889	−	0.749786i
$999$	3.59300e7	−	6.22326e7i	1.13905	−	1.97290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.c.b.9.4	yes	8
3.2	odd	2		234.6.h.f.217.3		8
4.3	odd	2		208.6.i.c.113.1		8
13.3	even	3	inner	26.6.c.b.3.4	✓	8
13.4	even	6		338.6.a.k.1.1		4
13.6	odd	12		338.6.b.e.337.5		8
13.7	odd	12		338.6.b.e.337.1		8
13.9	even	3		338.6.a.j.1.1		4
39.29	odd	6		234.6.h.f.55.3		8
52.3	odd	6		208.6.i.c.81.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.c.b.3.4	✓	8	13.3	even	3	inner
26.6.c.b.9.4	yes	8	1.1	even	1	trivial
208.6.i.c.81.1		8	52.3	odd	6
208.6.i.c.113.1		8	4.3	odd	2
234.6.h.f.55.3		8	39.29	odd	6
234.6.h.f.217.3		8	3.2	odd	2
338.6.a.j.1.1		4	13.9	even	3
338.6.a.k.1.1		4	13.4	even	6
338.6.b.e.337.1		8	13.7	odd	12
338.6.b.e.337.5		8	13.6	odd	12

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(13.5189 - 23.4153i) q^{3} +(-8.00000 - 13.8564i) q^{4} -47.6248 q^{5} +(-54.0754 - 93.6614i) q^{6} +(112.612 + 195.050i) q^{7} -64.0000 q^{8} +(-244.019 - 422.653i) q^{9} +(-95.2496 + 164.977i) q^{10} +(233.725 - 404.824i) q^{11} -432.603 q^{12} +(577.516 - 194.339i) q^{13} +900.898 q^{14} +(-643.833 + 1115.15i) q^{15} +(-128.000 + 221.703i) q^{16} +(56.9452 + 98.6320i) q^{17} -1952.15 q^{18} +(477.522 + 827.093i) q^{19} +(380.999 + 659.909i) q^{20} +6089.55 q^{21} +(-934.901 - 1619.30i) q^{22} +(-946.464 + 1639.32i) q^{23} +(-865.207 + 1498.58i) q^{24} -856.877 q^{25} +(481.821 - 2389.25i) q^{26} -6625.26 q^{27} +(1801.80 - 3120.80i) q^{28} +(-1254.36 + 2172.61i) q^{29} +(2575.33 + 4460.61i) q^{30} +6294.02 q^{31} +(512.000 + 886.810i) q^{32} +(-6319.40 - 10945.5i) q^{33} +455.562 q^{34} +(-5363.14 - 9289.23i) q^{35} +(-3904.30 + 6762.45i) q^{36} +(-5423.18 + 9393.23i) q^{37} +3820.18 q^{38} +(3256.84 - 16150.0i) q^{39} +3047.99 q^{40} +(213.721 - 370.175i) q^{41} +(12179.1 - 21094.8i) q^{42} +(1755.13 + 3039.97i) q^{43} -7479.21 q^{44} +(11621.4 + 20128.8i) q^{45} +(3785.86 + 6557.29i) q^{46} -11051.7 q^{47} +(3460.83 + 5994.33i) q^{48} +(-16959.5 + 29374.8i) q^{49} +(-1713.75 + 2968.31i) q^{50} +3079.34 q^{51} +(-7312.98 - 6447.59i) q^{52} +20736.2 q^{53} +(-13250.5 + 22950.6i) q^{54} +(-11131.1 + 19279.7i) q^{55} +(-7207.18 - 12483.2i) q^{56} +25822.2 q^{57} +(5017.43 + 8690.44i) q^{58} +(267.804 + 463.851i) q^{59} +20602.7 q^{60} +(-12220.3 - 21166.2i) q^{61} +(12588.0 - 21803.1i) q^{62} +(54959.0 - 95191.8i) q^{63} +4096.00 q^{64} +(-27504.1 + 9255.38i) q^{65} -50555.2 q^{66} +(-2419.17 + 4190.12i) q^{67} +(911.123 - 1578.11i) q^{68} +(25590.2 + 44323.6i) q^{69} -42905.1 q^{70} +(-25647.1 - 44422.1i) q^{71} +(15617.2 + 27049.8i) q^{72} -47040.2 q^{73} +(21692.7 + 37572.9i) q^{74} +(-11584.0 + 20064.1i) q^{75} +(7640.36 - 13233.5i) q^{76} +105281. q^{77} +(-49431.5 - 43582.0i) q^{78} -62968.3 q^{79} +(6095.98 - 10558.5i) q^{80} +(-30269.4 + 52428.1i) q^{81} +(-854.884 - 1480.70i) q^{82} -30245.7 q^{83} +(-48716.4 - 84379.3i) q^{84} +(-2712.00 - 4697.33i) q^{85} +14041.0 q^{86} +(33914.9 + 58742.4i) q^{87} +(-14958.4 + 25908.7i) q^{88} +(46755.4 - 80982.8i) q^{89} +92970.9 q^{90} +(102941. + 90759.6i) q^{91} +30286.8 q^{92} +(85088.0 - 147377. i) q^{93} +(-22103.3 + 38284.1i) q^{94} +(-22741.9 - 39390.1i) q^{95} +27686.6 q^{96} +(75406.9 + 130609. i) q^{97} +(67838.1 + 117499. i) q^{98} -228134. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{2} - 64 q^{4} - 24 q^{5} + 126 q^{7} - 512 q^{8} - 458 q^{9} - 48 q^{10} + 446 q^{11} + 1384 q^{13} + 1008 q^{14} - 790 q^{15} - 1024 q^{16} - 500 q^{17} - 3664 q^{18} + 4048 q^{19} + 192 q^{20}+ \cdots - 533984 q^{99}+O(q^{100}) \) 8 * q + 16 * q^2 - 64 * q^4 - 24 * q^5 + 126 * q^7 - 512 * q^8 - 458 * q^9 - 48 * q^10 + 446 * q^11 + 1384 * q^13 + 1008 * q^14 - 790 * q^15 - 1024 * q^16 - 500 * q^17 - 3664 * q^18 + 4048 * q^19 + 192 * q^20 + 2300 * q^21 - 1784 * q^22 + 296 * q^23 + 19788 * q^25 + 1112 * q^26 - 18180 * q^27 + 2016 * q^28 - 4114 * q^29 + 3160 * q^30 - 25036 * q^31 + 4096 * q^32 - 9730 * q^33 - 4000 * q^34 + 2340 * q^35 - 7328 * q^36 + 16258 * q^37 + 32384 * q^38 + 2460 * q^39 + 1536 * q^40 - 6056 * q^41 + 4600 * q^42 + 4818 * q^43 - 14272 * q^44 + 24964 * q^45 - 1184 * q^46 - 43060 * q^47 - 95094 * q^49 + 39576 * q^50 + 129440 * q^51 - 17696 * q^52 - 30032 * q^53 - 36360 * q^54 - 3360 * q^55 - 8064 * q^56 + 37940 * q^57 + 16456 * q^58 - 6734 * q^59 + 25280 * q^60 + 6978 * q^61 - 50072 * q^62 + 175812 * q^63 + 32768 * q^64 - 149818 * q^65 - 77840 * q^66 + 24464 * q^67 - 8000 * q^68 + 115290 * q^69 + 18720 * q^70 - 18552 * q^71 + 29312 * q^72 - 84596 * q^73 - 65032 * q^74 - 218210 * q^75 + 64768 * q^76 + 358604 * q^77 - 202680 * q^78 - 529664 * q^79 + 3072 * q^80 + 64624 * q^81 + 24224 * q^82 + 139800 * q^83 - 18400 * q^84 + 171548 * q^85 + 38544 * q^86 - 39420 * q^87 - 28544 * q^88 + 154642 * q^89 + 199712 * q^90 - 65074 * q^91 - 9472 * q^92 + 331860 * q^93 - 86120 * q^94 + 284278 * q^95 + 206498 * q^97 + 380376 * q^98 - 533984 * q^99

Introduction

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