LMFDB - Embedded newform 82.6.d.b.59.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(37,82)] 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([8])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.37"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			59.9
Character	$\chi$	$=$	82.59
Dual form			82.6.d.b.57.9

$q$-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} +28.4547 q^{3} +(-12.9443 + 9.40456i) q^{4} +(-21.6635 + 15.7394i) q^{5} +(-35.1720 - 108.248i) q^{6} +(-76.2234 + 234.592i) q^{7} +(51.7771 + 37.6183i) q^{8} +566.670 q^{9} +(86.6539 + 62.9578i) q^{10} +(80.1959 + 58.2657i) q^{11} +(-368.325 + 267.604i) q^{12} +(293.601 + 903.610i) q^{13} +986.657 q^{14} +(-616.428 + 447.861i) q^{15} +(79.1084 - 243.470i) q^{16} +(-914.033 - 664.084i) q^{17} +(-700.443 - 2155.74i) q^{18} +(277.934 - 855.392i) q^{19} +(132.395 - 407.471i) q^{20} +(-2168.91 + 6675.23i) q^{21} +(122.528 - 377.104i) q^{22} +(-587.860 - 1809.25i) q^{23} +(1473.30 + 1070.42i) q^{24} +(-744.102 + 2290.11i) q^{25} +(3074.63 - 2233.85i) q^{26} +9209.94 q^{27} +(-1219.57 - 3753.46i) q^{28} +(4773.51 - 3468.16i) q^{29} +(2465.71 + 1791.44i) q^{30} +(1554.42 + 1129.35i) q^{31} -1024.00 q^{32} +(2281.95 + 1657.93i) q^{33} +(-1396.52 + 4298.04i) q^{34} +(-2041.08 - 6281.78i) q^{35} +(-7335.13 + 5329.29i) q^{36} +(10992.6 - 7986.63i) q^{37} -3597.65 q^{38} +(8354.32 + 25712.0i) q^{39} -1713.76 q^{40} +(-7235.69 - 7968.75i) q^{41} +28075.0 q^{42} +(4208.11 + 12951.2i) q^{43} -1586.04 q^{44} +(-12276.1 + 8919.07i) q^{45} +(-6156.15 + 4472.71i) q^{46} +(1038.60 + 3196.48i) q^{47} +(2251.00 - 6927.88i) q^{48} +(-35626.0 - 25883.8i) q^{49} +9631.85 q^{50} +(-26008.5 - 18896.3i) q^{51} +(-12298.5 - 8935.39i) q^{52} +(-3236.89 + 2351.74i) q^{53} +(-11384.1 - 35036.7i) q^{54} -2654.39 q^{55} +(-12771.6 + 9279.07i) q^{56} +(7908.53 - 24339.9i) q^{57} +(-19094.1 - 13872.6i) q^{58} +(-3067.38 - 9440.42i) q^{59} +(3767.27 - 11594.5i) q^{60} +(-8661.87 + 26658.5i) q^{61} +(2374.94 - 7309.30i) q^{62} +(-43193.5 + 132936. i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-20582.7 - 14954.2i) q^{65} +(3486.51 - 10730.4i) q^{66} +(52111.3 - 37861.1i) q^{67} +18076.9 q^{68} +(-16727.4 - 51481.6i) q^{69} +(-21374.4 + 15529.4i) q^{70} +(22583.0 + 16407.5i) q^{71} +(29340.5 + 21317.1i) q^{72} +27223.9 q^{73} +(-43970.6 - 31946.5i) q^{74} +(-21173.2 + 65164.4i) q^{75} +(4446.94 + 13686.3i) q^{76} +(-19781.5 + 14372.1i) q^{77} +(87487.6 - 63563.5i) q^{78} -43968.1 q^{79} +(2118.33 + 6519.54i) q^{80} +124365. q^{81} +(-21371.1 + 37376.1i) q^{82} -10881.0 q^{83} +(-34702.6 - 106804. i) q^{84} +30253.4 q^{85} +(44067.9 - 32017.2i) q^{86} +(135829. - 98685.5i) q^{87} +(1960.45 + 6033.66i) q^{88} +(9891.28 - 30442.2i) q^{89} +(49104.2 + 35676.3i) q^{90} -234359. q^{91} +(24624.6 + 17890.8i) q^{92} +(44230.4 + 32135.3i) q^{93} +(10876.3 - 7902.12i) q^{94} +(7442.38 + 22905.3i) q^{95} -29137.6 q^{96} +(-58413.8 + 42440.1i) q^{97} +(-54431.7 + 167524. i) q^{98} +(45444.6 + 33017.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) $ 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Character values

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

$n$	$47$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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
$3$	28.4547			1.82537			0.912685	−	0.408664i	$-0.134005\pi$
$3$	28.4547			1.82537			0.912685	+	0.408664i	$0.134005\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−21.6635	+	15.7394i	−0.387528	+	0.281556i	−0.764442	−	0.644693i	$-0.776985\pi$
$5$	−21.6635	+	15.7394i	−0.387528	+	0.281556i	0.376914	+	0.926248i	$0.376985\pi$
$6$	−35.1720	−	108.248i	−0.398858	−	1.22756i
$7$	−76.2234	+	234.592i	−0.587954	+	1.80954i	−0.000884354		1.00000i	$0.500281\pi$
$7$	−76.2234	+	234.592i	−0.587954	+	1.80954i	−0.587070	+	0.809536i	$0.699719\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$	566.670			2.33198
$10$	86.6539	+	62.9578i	0.274024	+	0.199090i
$11$	80.1959	+	58.2657i	0.199834	+	0.145188i	0.683202	−	0.730229i	$-0.260587\pi$
$11$	80.1959	+	58.2657i	0.199834	+	0.145188i	−0.483368	+	0.875417i	$0.660587\pi$
$12$	−368.325	+	267.604i	−0.738378	+	0.536463i
$13$	293.601	+	903.610i	0.481836	+	1.48294i	0.836512	+	0.547948i	$0.184591\pi$
$13$	293.601	+	903.610i	0.481836	+	1.48294i	−0.354677	+	0.934989i	$0.615409\pi$
$14$	986.657			1.34538
$15$	−616.428	+	447.861i	−0.707382	+	0.513943i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−914.033	−	664.084i	−0.767078	−	0.557315i	0.133995	−	0.990982i	$-0.457219\pi$
$17$	−914.033	−	664.084i	−0.767078	−	0.557315i	−0.901073	+	0.433667i	$0.857219\pi$
$18$	−700.443	−	2155.74i	−0.509556	−	1.56825i
$19$	277.934	−	855.392i	0.176627	−	0.543602i	−0.823077	−	0.567930i	$-0.807744\pi$
$19$	277.934	−	855.392i	0.176627	−	0.543602i	0.999704	+	0.0243275i	$0.00774444\pi$
$20$	132.395	−	407.471i	0.0740113	−	0.227783i
$21$	−2168.91	+	6675.23i	−1.07323	+	3.30307i
$22$	122.528	−	377.104i	0.0539734	−	0.166113i
$23$	−587.860	−	1809.25i	−0.231715	−	0.713146i	−0.997540	−	0.0700970i	$-0.977669\pi$
$23$	−587.860	−	1809.25i	−0.231715	−	0.713146i	0.765825	−	0.643049i	$-0.222331\pi$
$24$	1473.30	+	1070.42i	0.522112	+	0.379337i
$25$	−744.102	+	2290.11i	−0.238113	+	0.732835i
$26$	3074.63	−	2233.85i	0.891988	−	0.648067i
$27$	9209.94			2.43135
$28$	−1219.57	−	3753.46i	−0.293977	−	0.904768i
$29$	4773.51	−	3468.16i	1.05401	−	0.765781i	0.0810363	−	0.996711i	$-0.474177\pi$
$29$	4773.51	−	3468.16i	1.05401	−	0.765781i	0.972970	+	0.230931i	$0.0741770\pi$
$30$	2465.71	+	1791.44i	0.500195	+	0.363413i
$31$	1554.42	+	1129.35i	0.290511	+	0.211069i	0.723489	−	0.690336i	$-0.242537\pi$
$31$	1554.42	+	1129.35i	0.290511	+	0.211069i	−0.432978	+	0.901405i	$0.642537\pi$
$32$	−1024.00			−0.176777
$33$	2281.95	+	1657.93i	0.364772	+	0.265022i
$34$	−1396.52	+	4298.04i	−0.207181	+	0.637636i
$35$	−2041.08	−	6281.78i	−0.281636	−	0.866788i
$36$	−7335.13	+	5329.29i	−0.943304	+	0.685351i
$37$	10992.6	−	7986.63i	1.32007	−	0.959089i	0.320142	−	0.947370i	$-0.396269\pi$
$37$	10992.6	−	7986.63i	1.32007	−	0.959089i	0.999931	−	0.0117199i	$-0.00373063\pi$
$38$	−3597.65			−0.404166
$39$	8354.32	+	25712.0i	0.879528	+	2.70691i
$40$	−1713.76			−0.169356
$41$	−7235.69	−	7968.75i	−0.672233	−	0.740339i
$41$	−7235.69	−	7968.75i	−0.672233	−	0.740339i
$42$	28075.0			2.45582
$43$	4208.11	+	12951.2i	0.347069	+	1.06817i	0.960467	+	0.278395i	$0.0898025\pi$
$43$	4208.11	+	12951.2i	0.347069	+	1.06817i	−0.613397	+	0.789775i	$0.710198\pi$
$44$	−1586.04			−0.123505
$45$	−12276.1	+	8919.07i	−0.903706	+	0.656581i
$46$	−6156.15	+	4472.71i	−0.428958	+	0.311656i
$47$	1038.60	+	3196.48i	0.0685809	+	0.211070i	0.979473	−	0.201573i	$-0.0646055\pi$
$47$	1038.60	+	3196.48i	0.0685809	+	0.211070i	−0.910893	+	0.412644i	$0.864605\pi$
$48$	2251.00	−	6927.88i	0.141018	−	0.434008i
$49$	−35626.0	−	25883.8i	−2.11971	−	1.54006i
$50$	9631.85			0.544860
$51$	−26008.5	−	18896.3i	−1.40020	−	1.01731i
$52$	−12298.5	−	8935.39i	−0.630731	−	0.458253i
$53$	−3236.89	+	2351.74i	−0.158285	+	0.115000i	−0.664108	−	0.747636i	$-0.731189\pi$
$53$	−3236.89	+	2351.74i	−0.158285	+	0.115000i	0.505824	+	0.862637i	$0.331189\pi$
$54$	−11384.1	−	35036.7i	−0.531270	−	1.63508i
$55$	−2654.39			−0.118320
$56$	−12771.6	+	9279.07i	−0.544219	+	0.395398i
$57$	7908.53	−	24339.9i	0.322410	−	0.992276i
$58$	−19094.1	−	13872.6i	−0.745295	−	0.541489i
$59$	−3067.38	−	9440.42i	−0.114719	−	0.353070i	0.877169	−	0.480182i	$-0.159429\pi$
$59$	−3067.38	−	9440.42i	−0.114719	−	0.353070i	−0.991888	+	0.127112i	$0.959429\pi$
$60$	3767.27	−	11594.5i	0.135098	−	0.415789i
$61$	−8661.87	+	26658.5i	−0.298049	+	0.917300i	0.684132	+	0.729359i	$0.260181\pi$
$61$	−8661.87	+	26658.5i	−0.298049	+	0.917300i	−0.982180	+	0.187941i	$0.939819\pi$
$62$	2374.94	−	7309.30i	0.0784644	−	0.241489i
$63$	−43193.5	+	132936.i	−1.37109	+	4.21980i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−20582.7	−	14954.2i	−0.604254	−	0.439016i
$66$	3486.51	−	10730.4i	0.0985215	−	0.303218i
$67$	52111.3	−	37861.1i	1.41822	−	1.03040i	0.426163	−	0.904647i	$-0.359865\pi$
$67$	52111.3	−	37861.1i	1.41822	−	1.03040i	0.992061	−	0.125754i	$-0.0401349\pi$
$68$	18076.9			0.474080
$69$	−16727.4	−	51481.6i	−0.422966	−	1.30176i
$70$	−21374.4	+	15529.4i	−0.521374	+	0.378800i
$71$	22583.0	+	16407.5i	0.531662	+	0.386275i	0.820979	−	0.570958i	$-0.193428\pi$
$71$	22583.0	+	16407.5i	0.531662	+	0.386275i	−0.289317	+	0.957233i	$0.593428\pi$
$72$	29340.5	+	21317.1i	0.667017	+	0.484616i
$73$	27223.9			0.597921			0.298960	−	0.954266i	$-0.403360\pi$
$73$	27223.9			0.597921			0.298960	+	0.954266i	$0.403360\pi$
$74$	−43970.6	−	31946.5i	−0.933433	−	0.678179i
$75$	−21173.2	+	65164.4i	−0.434644	+	1.33770i
$76$	4446.94	+	13686.3i	0.0883136	+	0.271801i
$77$	−19781.5	+	14372.1i	−0.380217	+	0.276244i
$78$	87487.6	−	63563.5i	1.62821	−	1.18296i
$79$	−43968.1			−0.792628			−0.396314	−	0.918115i	$-0.629711\pi$
$79$	−43968.1			−0.792628			−0.396314	+	0.918115i	$0.629711\pi$
$80$	2118.33	+	6519.54i	0.0370056	+	0.113892i
$81$	124365.			2.10614
$82$	−21371.1	+	37376.1i	−0.350989	+	0.613846i
$83$	−10881.0			−0.173370			−0.0866851	−	0.996236i	$-0.527627\pi$
$83$	−10881.0			−0.173370			−0.0866851	+	0.996236i	$0.527627\pi$
$84$	−34702.6	−	106804.i	−0.536617	−	1.65154i
$85$	30253.4			0.454179
$86$	44067.9	−	32017.2i	0.642505	−	0.466807i
$87$	135829.	−	98685.5i	1.92395	−	1.39783i
$88$	1960.45	+	6033.66i	0.0269867	+	0.0830566i
$89$	9891.28	−	30442.2i	0.132366	−	0.407382i	−0.862805	−	0.505537i	$-0.831294\pi$
$89$	9891.28	−	30442.2i	0.132366	−	0.407382i	0.995171	+	0.0981557i	$0.0312943\pi$
$90$	49104.2	+	35676.3i	0.639017	+	0.464273i
$91$	−234359.			−2.96673
$92$	24624.6	+	17890.8i	0.303319	+	0.220374i
$93$	44230.4	+	32135.3i	0.530291	+	0.385279i
$94$	10876.3	−	7902.12i	0.126959	−	0.0922411i
$95$	7442.38	+	22905.3i	0.0846064	+	0.260392i
$96$	−29137.6			−0.322683
$97$	−58413.8	+	42440.1i	−0.630357	+	0.457981i	−0.856524	−	0.516108i	$-0.827380\pi$
$97$	−58413.8	+	42440.1i	−0.630357	+	0.457981i	0.226167	+	0.974089i	$0.427380\pi$
$98$	−54431.7	+	167524.i	−0.572515	+	1.76202i
$99$	45444.6	+	33017.5i	0.466009	+	0.338576i
$100$	−11905.6	−	36641.8i	−0.119056	−	0.366418i
$101$	−40641.1	+	125081.i	−0.396426	+	1.22007i	0.531419	+	0.847109i	$0.321659\pi$
$101$	−40641.1	+	125081.i	−0.396426	+	1.22007i	−0.927845	+	0.372965i	$0.878341\pi$
$102$	−39737.5	+	122299.i	−0.378181	+	1.16392i
$103$	20339.1	−	62597.4i	0.188903	−	0.581385i	−0.811090	−	0.584921i	$-0.801126\pi$
$103$	20339.1	−	62597.4i	0.188903	−	0.581385i	0.999994	+	0.00353621i	$0.00112561\pi$
$104$	−18790.5	+	57831.1i	−0.170355	+	0.524298i
$105$	−58078.2	−	178746.i	−0.514091	−	1.58221i
$106$	12947.6	+	9406.96i	0.111924	+	0.0813176i
$107$	49923.9	−	153650.i	0.421550	−	1.29740i	−0.484710	−	0.874675i	$-0.661075\pi$
$107$	49923.9	−	153650.i	0.421550	−	1.29740i	0.906260	−	0.422721i	$-0.138925\pi$
$108$	−119216.	+	86615.5i	−0.983502	+	0.714556i
$109$	−55532.4			−0.447693			−0.223846	−	0.974624i	$-0.571861\pi$
$109$	−55532.4			−0.447693			−0.223846	+	0.974624i	$0.571861\pi$
$110$	3281.01	+	10097.9i	0.0258539	+	0.0795701i
$111$	312793.	−	227257.i	2.40962	−	1.75069i
$112$	51086.2	+	37116.3i	0.384821	+	0.279589i
$113$	−114746.	−	83367.6i	−0.845357	−	0.614188i	0.0785048	−	0.996914i	$-0.474985\pi$
$113$	−114746.	−	83367.6i	−0.845357	−	0.614188i	−0.923862	+	0.382726i	$0.874985\pi$
$114$	−102370.			−0.737753
$115$	41211.6	+	29942.0i	0.290586	+	0.211123i
$116$	−29173.1	+	89785.7i	−0.201297	+	0.619529i
$117$	166375.	+	512049.i	1.12363	+	3.45818i
$118$	−32122.0	+	23338.0i	−0.212372	+	0.154297i
$119$	225459.	−	163806.i	1.45949	−	1.06038i
$120$	−48764.6			−0.309137
$121$	−46731.0	−	143823.i	−0.290163	−	0.893029i
$122$	112122.			0.682009
$123$	−205889.	−	226749.i	−1.22707	−	1.35139i
$124$	−30741.8			−0.179546
$125$	−45783.7	−	140908.i	−0.262081	−	0.806603i
$126$	559109.			3.13740
$127$	−120718.	+	87706.5i	−0.664143	+	0.482528i	−0.868059	−	0.496460i	$-0.834633\pi$
$127$	−120718.	+	87706.5i	−0.664143	+	0.482528i	0.203917	+	0.978988i	$0.434633\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$	119741.	+	368524.i	0.633530	+	1.94981i
$130$	−31447.6	+	96785.8i	−0.163203	+	0.502289i
$131$	266549.	+	193659.i	1.35706	+	0.985961i	0.998626	+	0.0524052i	$0.0166887\pi$
$131$	266549.	+	193659.i	1.35706	+	0.985961i	0.358433	+	0.933556i	$0.383311\pi$
$132$	−45130.3			−0.225441
$133$	179483.	+	130402.i	0.879820	+	0.639226i
$134$	−208445.	−	151444.i	−1.00284	−	0.728603i
$135$	−199519.	+	144959.i	−0.942217	+	0.684560i
$136$	−22344.3	−	68768.6i	−0.103590	−	0.318818i
$137$	119505.			0.543981			0.271991	−	0.962300i	$-0.412318\pi$
$137$	119505.			0.543981			0.271991	+	0.962300i	$0.412318\pi$
$138$	−175172.	+	127270.i	−0.783007	+	0.568888i
$139$	−20588.6	+	63365.3i	−0.0903837	+	0.278173i	−0.986023	−	0.166608i	$-0.946718\pi$
$139$	−20588.6	+	63365.3i	−0.0903837	+	0.278173i	0.895639	+	0.444781i	$0.146718\pi$
$140$	85497.7	+	62117.7i	0.368667	+	0.267852i
$141$	29553.0	+	90954.8i	0.125185	+	0.385281i
$142$	34503.7	−	106192.i	0.143597	−	0.441946i
$143$	−29103.9	+	89572.7i	−0.119018	+	0.366299i
$144$	44828.4	−	137967.i	0.180155	−	0.554460i
$145$	−48824.0	+	150265.i	−0.192847	+	0.593523i
$146$	−33650.6	−	103566.i	−0.130651	−	0.402101i
$147$	−1.01373e6	−	736517.i	−3.86926	−	2.81118i
$148$	−67181.1	+	206762.i	−0.252112	+	0.775920i
$149$	408757.	−	296980.i	1.50834	−	1.09587i	0.541437	−	0.840742i	$-0.317881\pi$
$149$	408757.	−	296980.i	1.50834	−	1.09587i	0.966906	−	0.255133i	$-0.0821194\pi$
$150$	274072.			0.994571
$151$	−40153.3	−	123579.i	−0.143311	−	0.441065i	0.853479	−	0.521127i	$-0.174488\pi$
$151$	−40153.3	−	123579.i	−0.143311	−	0.441065i	−0.996790	+	0.0800618i	$0.974488\pi$
$152$	46569.0	−	33834.3i	0.163489	−	0.118781i
$153$	−517955.	−	376316.i	−1.78881	−	1.29964i
$154$	79125.8	+	57488.3i	0.268854	+	0.195334i
$155$	−51449.4			−0.172009
$156$	−349950.	−	254254.i	−1.15132	−	0.836481i
$157$	30562.5	−	94061.6i	0.0989553	−	0.304553i	−0.889309	−	0.457307i	$-0.848814\pi$
$157$	30562.5	−	94061.6i	0.0989553	−	0.304553i	0.988264	+	0.152754i	$0.0488141\pi$
$158$	54347.5	+	167264.i	0.173196	+	0.533041i
$159$	−92104.8	+	66918.1i	−0.288928	+	0.209918i
$160$	22183.4	−	16117.2i	0.0685059	−	0.0497725i
$161$	469243.			1.42670
$162$	−153724.	−	473114.i	−0.460208	−	1.41637i
$163$	479156.			1.41256			0.706282	−	0.707931i	$-0.250371\pi$
$163$	479156.			1.41256			0.706282	+	0.707931i	$0.250371\pi$
$164$	168603.	+	35101.3i	0.489504	+	0.101909i
$165$	−75529.9			−0.215978
$166$	13449.7	+	41393.9i	0.0378828	+	0.116591i
$167$	60276.4			0.167246			0.0836230	−	0.996497i	$-0.473351\pi$
$167$	60276.4			0.167246			0.0836230	+	0.996497i	$0.473351\pi$
$168$	−363411.	+	264033.i	−0.993401	+	0.721748i
$169$	−429928.	+	312361.i	−1.15792	+	0.841279i
$170$	−37395.3	−	115091.i	−0.0992418	−	0.305435i
$171$	157497.	−	484725.i	0.411890	−	1.26767i
$172$	−176272.	−	128069.i	−0.454320	−	0.330083i
$173$	29117.2			0.0739663			0.0369832	−	0.999316i	$-0.488225\pi$
$173$	29117.2			0.0739663			0.0369832	+	0.999316i	$0.488225\pi$
$174$	−543316.	−	394742.i	−1.36044	−	0.988417i
$175$	−480522.	−	349120.i	−1.18609	−	0.861746i
$176$	20530.1	−	14916.0i	0.0499586	−	0.0362971i
$177$	−87281.3	−	268624.i	−0.209406	−	0.644484i
$178$	−128035.			−0.302887
$179$	56435.7	−	41002.9i	0.131650	−	0.0956494i	−0.520011	−	0.854159i	$-0.674072\pi$
$179$	56435.7	−	41002.9i	0.131650	−	0.0956494i	0.651661	+	0.758510i	$0.274072\pi$
$180$	75024.5	−	230902.i	0.172593	−	0.531185i
$181$	133464.	+	96967.0i	0.302807	+	0.220002i	0.728804	−	0.684722i	$-0.240077\pi$
$181$	133464.	+	96967.0i	0.302807	+	0.220002i	−0.425997	+	0.904725i	$0.640077\pi$
$182$	289683.	+	891553.i	0.648253	+	1.99512i
$183$	−246471.	+	758560.i	−0.544049	+	1.67441i
$184$	37623.1	−	115792.i	0.0819237	−	0.252135i
$185$	−112434.	+	346036.i	−0.241528	+	0.743348i
$186$	67578.1	−	207984.i	0.143227	−	0.440806i
$187$	−34608.4	−	106514.i	−0.0723731	−	0.222741i
$188$	−43505.4	−	31608.5i	−0.0897735	−	0.0652243i
$189$	−702013.	+	2.16057e6i	−1.42952	+	4.39962i
$190$	77937.7	−	56625.0i	0.156626	−	0.113795i
$191$	58999.3			0.117021			0.0585105	−	0.998287i	$-0.481365\pi$
$191$	58999.3			0.117021			0.0585105	+	0.998287i	$0.481365\pi$
$192$	36016.1	+	110846.i	0.0705088	+	0.217004i
$193$	−100623.	+	73106.9i	−0.194448	+	0.141275i	−0.680750	−	0.732516i	$-0.738346\pi$
$193$	−100623.	+	73106.9i	−0.194448	+	0.141275i	0.486301	+	0.873791i	$0.338346\pi$
$194$	233655.	+	169761.i	0.445729	+	0.323841i
$195$	−585676.	−	425518.i	−1.10299	−	0.801367i
$196$	704579.			1.31006
$197$	754053.	+	547852.i	1.38432	+	1.00577i	0.996462	+	0.0840482i	$0.0267850\pi$
$197$	754053.	+	547852.i	1.38432	+	1.00577i	0.387858	+	0.921719i	$0.373215\pi$
$198$	69433.2	−	213693.i	0.125865	−	0.387372i
$199$	−216093.	−	665064.i	−0.386818	−	1.19050i	−0.935153	−	0.354245i	$-0.884738\pi$
$199$	−216093.	−	665064.i	−0.386818	−	1.19050i	0.548334	−	0.836259i	$-0.315262\pi$
$200$	−124677.	+	90583.4i	−0.220400	+	0.160130i
$201$	1.48281e6	−	1.07733e6i	2.58878	−	1.88086i
$202$	526070.			0.907120
$203$	449748.	+	1.38418e6i	0.766000	+	2.35751i
$204$	514373.			0.865372
$205$	282174.	+	58745.3i	0.468956	+	0.0976312i
$206$	−263275.			−0.432257
$207$	−333123.	−	1.02525e6i	−0.540354	−	1.66304i
$208$	243229.			0.389813
$209$	72129.2	−	52404.9i	0.114221	−	0.0829863i
$210$	−608203.	+	441885.i	−0.951700	+	0.691451i
$211$	−298619.	−	919056.i	−0.461755	−	1.42114i	−0.863018	−	0.505173i	$-0.831429\pi$
$211$	−298619.	−	919056.i	−0.461755	−	1.42114i	0.401263	−	0.915963i	$-0.368571\pi$
$212$	19782.1	−	60883.1i	0.0302297	−	0.0930373i
$213$	642592.	+	466871.i	0.970480	+	0.705095i
$214$	−646228.			−0.964609
$215$	−295008.	−	214336.i	−0.435248	−	0.316226i
$216$	476864.	+	346462.i	0.695441	+	0.505267i
$217$	−383419.	+	278570.i	−0.552744	+	0.401592i
$218$	68641.8	+	211258.i	0.0978245	+	0.301073i
$219$	774649.			1.09143
$220$	34359.2	−	24963.4i	0.0478615	−	0.0347734i
$221$	331712.	−	1.02090e6i	0.456857	−	1.40606i
$222$	−1.25117e6	−	909029.i	−1.70386	−	1.23793i
$223$	−199064.	−	612655.i	−0.268058	−	0.824999i	−0.990973	−	0.134062i	$-0.957198\pi$
$223$	−199064.	−	612655.i	−0.268058	−	0.824999i	0.722914	−	0.690938i	$-0.242802\pi$
$224$	78052.8	−	240222.i	0.103937	−	0.319884i
$225$	−421660.	+	1.29774e6i	−0.555273	+	1.70895i
$226$	−175316.	+	539567.i	−0.228323	+	0.702706i
$227$	47374.6	−	145804.i	0.0610213	−	0.187804i	−0.915899	−	0.401409i	$-0.868521\pi$
$227$	47374.6	−	145804.i	0.0610213	−	0.187804i	0.976920	+	0.213605i	$0.0685206\pi$
$228$	126536.	+	389439.i	0.161205	+	0.496138i
$229$	491169.	+	356855.i	0.618931	+	0.449679i	0.852548	−	0.522649i	$-0.175056\pi$
$229$	491169.	+	356855.i	0.618931	+	0.449679i	−0.233617	+	0.972329i	$0.575056\pi$
$230$	62965.8	−	193789.i	0.0784847	−	0.241551i
$231$	−562875.	+	408953.i	−0.694037	+	0.504247i
$232$	377625.			0.460618
$233$	294570.	+	906593.i	0.355466	+	1.09401i	0.955739	+	0.294217i	$0.0950589\pi$
$233$	294570.	+	906593.i	0.355466	+	1.09401i	−0.600272	+	0.799796i	$0.704941\pi$
$234$	1.74230e6	−	1.26586e6i	2.08010	−	1.51128i
$235$	−72810.4	−	52899.9i	−0.0860050	−	0.0624863i
$236$	128488.	+	93352.0i	0.150170	+	0.109105i
$237$	−1.25110e6			−1.44684
$238$	−901836.	−	655222.i	−1.03201	−	0.749802i
$239$	−301456.	+	927788.i	−0.341374	+	1.05064i	0.622123	+	0.782919i	$0.286270\pi$
$239$	−301456.	+	927788.i	−0.341374	+	1.05064i	−0.963497	+	0.267720i	$0.913730\pi$
$240$	60276.4	+	185512.i	0.0675490	+	0.207894i
$241$	−274551.	+	199473.i	−0.304496	+	0.221229i	−0.729531	−	0.683948i	$-0.760262\pi$
$241$	−274551.	+	199473.i	−0.304496	+	0.221229i	0.425035	+	0.905177i	$0.360262\pi$
$242$	−489373.	+	355551.i	−0.537158	+	0.390268i
$243$	1.30076e6			1.41313
$244$	−138590.	−	426536.i	−0.149024	−	0.458650i
$245$	1.17918e6			1.25506
$246$	−608110.	+	1.06353e6i	−0.640684	+	1.12050i
$247$	854543.			0.891234
$248$	37999.0	+	116949.i	0.0392322	+	0.120744i
$249$	−309616.			−0.316465
$250$	−479453.	+	348343.i	−0.485172	+	0.352498i
$251$	−859896.	+	624751.i	−0.861512	+	0.625925i	−0.928296	−	0.371842i	$-0.878726\pi$
$251$	−859896.	+	624751.i	−0.861512	+	0.625925i	0.0667836	+	0.997767i	$0.478726\pi$
$252$	−691097.	−	2.12698e6i	−0.685547	−	2.10990i
$253$	58273.2	−	179346.i	0.0572357	−	0.176154i
$254$	482871.	+	350826.i	0.469620	+	0.341199i
$255$	860853.			0.829045
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−1.03883e6	−	754756.i	−0.981099	−	0.712810i	−0.0231450	−	0.999732i	$-0.507368\pi$
$257$	−1.03883e6	−	754756.i	−0.981099	−	0.712810i	−0.957954	+	0.286922i	$0.907368\pi$
$258$	1.25394e6	−	911041.i	1.17281	−	0.852096i
$259$	1.03570e6	+	3.18755e6i	0.959365	+	2.95262i
$260$	407067.			0.373450
$261$	2.70501e6	−	1.96530e6i	2.45792	−	1.78578i
$262$	407250.	−	1.25339e6i	0.366529	−	1.12806i
$263$	−1.44895e6	−	1.05273e6i	−1.29171	−	0.938482i	−0.291871	−	0.956458i	$-0.594278\pi$
$263$	−1.44895e6	−	1.05273e6i	−1.29171	−	0.938482i	−0.999838	+	0.0179759i	$0.994278\pi$
$264$	55784.2	+	171686.i	0.0492608	+	0.151609i
$265$	33107.3	−	101894.i	0.0289607	−	0.0891318i
$266$	274225.	−	843979.i	0.237631	−	0.731353i
$267$	281453.	−	866224.i	0.241617	−	0.743622i
$268$	−318476.	+	980168.i	−0.270857	+	0.833611i
$269$	557977.	+	1.71728e6i	0.470149	+	1.44697i	0.852390	+	0.522907i	$0.175153\pi$
$269$	557977.	+	1.71728e6i	0.470149	+	1.44697i	−0.382241	+	0.924063i	$0.624847\pi$
$270$	798078.	+	579837.i	0.666248	+	0.484057i
$271$	110750.	−	340855.i	0.0916056	−	0.281933i	−0.894749	−	0.446570i	$-0.852645\pi$
$271$	110750.	−	340855.i	0.0916056	−	0.281933i	0.986354	+	0.164637i	$0.0526453\pi$
$272$	−233992.	+	170005.i	−0.191769	+	0.139329i
$273$	−6.66861e6			−5.41537
$274$	−147716.	−	454623.i	−0.118864	−	0.365827i
$275$	−193109.	+	140302.i	−0.153982	+	0.111875i
$276$	700686.	+	509078.i	0.553670	+	0.402265i
$277$	514216.	+	373600.i	0.402667	+	0.292555i	0.770626	−	0.637287i	$-0.219943\pi$
$277$	514216.	+	373600.i	0.402667	+	0.292555i	−0.367959	+	0.929842i	$0.619943\pi$
$278$	266505.			0.206820
$279$	880841.	+	639969.i	0.677465	+	0.492207i
$280$	130629.	−	402034.i	0.0995735	−	0.306456i
$281$	−95214.2	−	293039.i	−0.0719343	−	0.221391i	0.908625	−	0.417612i	$-0.137133\pi$
$281$	−95214.2	−	293039.i	−0.0719343	−	0.221391i	−0.980560	+	0.196221i	$0.937133\pi$
$282$	309483.	−	224853.i	0.231747	−	0.168374i
$283$	1.08244e6	−	786441.i	0.803414	−	0.583714i	−0.108500	−	0.994096i	$-0.534605\pi$
$283$	1.08244e6	−	786441.i	0.803414	−	0.583714i	0.911914	+	0.410382i	$0.134605\pi$
$284$	−446626.			−0.328585
$285$	211771.	+	651764.i	0.154438	+	0.475311i
$286$	376729.			0.272342
$287$	2.42093e6	−	1.09003e6i	1.73491	−	0.781145i
$288$	−580270.			−0.412239
$289$	−44311.2	−	136376.i	−0.0312082	−	0.0960491i
$290$	631991.			0.441282
$291$	−1.66215e6	+	1.20762e6i	−1.15063	+	0.835985i
$292$	−352394.	+	256029.i	−0.241864	+	0.175725i
$293$	−604098.	−	1.85922e6i	−0.411091	−	1.26521i	−0.915701	−	0.401861i	$-0.868364\pi$
$293$	−604098.	−	1.85922e6i	−0.411091	−	1.26521i	0.504610	−	0.863348i	$-0.331636\pi$
$294$	−1.54884e6	+	4.76684e6i	−1.04505	+	3.21634i
$295$	215037.	+	156233.i	0.143866	+	0.104525i
$296$	869610.			0.576893
$297$	738600.	+	536624.i	0.485868	+	0.353004i
$298$	−1.63503e6	−	1.18792e6i	−1.06656	−	0.774901i
$299$	1.46226e6	−	1.06239e6i	0.945902	−	0.687238i
$300$	−338771.	−	1.04263e6i	−0.217322	−	0.668848i
$301$	−3.35901e6			−2.13695
$302$	−420491.	+	305505.i	−0.265301	+	0.192753i
$303$	−1.15643e6	+	3.55913e6i	−0.723624	+	2.22709i
$304$	−186276.	−	135337.i	−0.115604	−	0.0839912i
$305$	−231944.	−	713849.i	−0.142769	−	0.439397i
$306$	−791365.	+	2.43557e6i	−0.483140	+	1.48695i
$307$	350446.	−	1.07856e6i	0.212215	−	0.653130i	−0.787125	−	0.616794i	$-0.788431\pi$
$307$	350446.	−	1.07856e6i	0.212215	−	0.653130i	0.999340	−	0.0363364i	$-0.0115688\pi$
$308$	120893.	−	372072.i	0.0726150	−	0.223486i
$309$	578744.	−	1.78119e6i	0.344818	−	1.06124i
$310$	63594.9	+	195725.i	0.0375853	+	0.115676i
$311$	−2.32117e6	−	1.68643e6i	−1.36084	−	0.988707i	−0.998391	−	0.0567026i	$-0.981941\pi$
$311$	−2.32117e6	−	1.68643e6i	−1.36084	−	0.988707i	−0.362447	−	0.932004i	$-0.618059\pi$
$312$	−534677.	+	1.64557e6i	−0.310960	+	0.957037i
$313$	−1.37068e6	+	995859.i	−0.790817	+	0.574562i	−0.908206	−	0.418524i	$-0.862548\pi$
$313$	−1.37068e6	+	995859.i	−0.790817	+	0.574562i	0.117389	+	0.993086i	$0.462548\pi$
$314$	−395609.			−0.226434
$315$	−1.15662e6	−	3.55970e6i	−0.656770	−	2.02133i
$316$	569135.	−	413500.i	0.320625	−	0.232948i
$317$	1.34818e6	+	979512.i	0.753530	+	0.547472i	0.896919	−	0.442195i	$-0.145800\pi$
$317$	1.34818e6	+	979512.i	0.753530	+	0.547472i	−0.143389	+	0.989666i	$0.545800\pi$
$318$	368419.	+	267672.i	0.204303	+	0.148435i
$319$	584891.			0.321809
$320$	−88733.6	−	64468.7i	−0.0484410	−	0.0351945i
$321$	1.42057e6	−	4.37206e6i	0.769484	−	2.36823i
$322$	−580016.	−	1.78511e6i	−0.311746	−	0.959455i
$323$	−822093.	+	597285.i	−0.438444	+	0.318548i
$324$	−1.60982e6	+	1.16960e6i	−0.851951	+	0.618978i
$325$	−2.28784e6			−1.20148
$326$	−592269.	−	1.82282e6i	−0.308656	−	0.949947i
$327$	−1.58016e6			−0.817205
$328$	−74872.1	−	684793.i	−0.0384269	−	0.351459i
$329$	−829032.			−0.422261
$330$	93360.2	+	287333.i	0.0471929	+	0.145245i
$331$	−2.50055e6			−1.25448			−0.627242	−	0.778825i	$-0.715816\pi$
$331$	−2.50055e6			−1.25448			−0.627242	+	0.778825i	$0.715816\pi$
$332$	140847.	−	102331.i	0.0701297	−	0.0509522i
$333$	6.22921e6	−	4.52578e6i	3.07838	−	2.23657i
$334$	−74505.7	−	229305.i	−0.0365446	−	0.112473i
$335$	−533000.	+	1.64041e6i	−0.259487	+	0.798618i
$336$	1.45364e6	+	1.05613e6i	0.702441	+	0.510353i
$337$	1.42127e6			0.681716			0.340858	−	0.940115i	$-0.389282\pi$
$337$	1.42127e6			0.681716			0.340858	+	0.940115i	$0.389282\pi$
$338$	1.71971e6	+	1.24944e6i	0.818774	+	0.594874i
$339$	−3.26505e6	−	2.37220e6i	−1.54309	−	1.12112i
$340$	−391609.	+	284520.i	−0.183719	+	0.133480i
$341$	58855.4	+	181138.i	0.0274095	+	0.0843576i
$342$	−2.03868e6			−0.942506
$343$	5.43374e6	−	3.94784e6i	2.49381	−	1.81186i
$344$	−269319.	+	828879.i	−0.122708	+	0.377655i
$345$	1.17267e6	+	851991.i	0.530428	+	0.385378i
$346$	−35990.8	−	110768.i	−0.0161622	−	0.0497422i
$347$	−429727.	+	1.32256e6i	−0.191588	+	0.589648i	0.808411	+	0.588618i	$0.200328\pi$
$347$	−429727.	+	1.32256e6i	−0.191588	+	0.589648i	−0.999999	+	0.00102963i	$0.999672\pi$
$348$	−830113.	+	2.55482e6i	−0.367442	+	1.13087i
$349$	−779015.	+	2.39756e6i	−0.342359	+	1.05367i	0.620623	+	0.784109i	$0.286880\pi$
$349$	−779015.	+	2.39756e6i	−0.342359	+	1.05367i	−0.962982	+	0.269564i	$0.913120\pi$
$350$	−734173.	+	2.25955e6i	−0.320353	+	0.985944i
$351$	2.70405e6	+	8.32220e6i	1.17151	+	3.60554i
$352$	−82120.6	−	59664.1i	−0.0353261	−	0.0256659i
$353$	−427571.	+	1.31593e6i	−0.182630	+	0.562077i	−0.999899	−	0.0141786i	$-0.995487\pi$
$353$	−427571.	+	1.31593e6i	−0.182630	+	0.562077i	0.817270	+	0.576255i	$0.195487\pi$
$354$	−914022.	+	664076.i	−0.387658	+	0.281650i
$355$	−747471.			−0.314792
$356$	158260.	+	487076.i	0.0661831	+	0.203691i
$357$	6.41537e6	−	4.66104e6i	2.66410	−	1.93559i
$358$	−225743.	−	164012.i	−0.0930906	−	0.0676343i
$359$	403114.	+	292879.i	0.165079	+	0.119937i	0.667258	−	0.744827i	$-0.267468\pi$
$359$	403114.	+	292879.i	0.165079	+	0.119937i	−0.502179	+	0.864764i	$0.667468\pi$
$360$	−971138.			−0.394934
$361$	1.34876e6	+	979929.i	0.544711	+	0.395755i
$362$	203914.	−	627583.i	0.0817855	−	0.251710i
$363$	−1.32972e6	−	4.09245e6i	−0.529655	−	1.63011i
$364$	3.03360e6	−	2.20404e6i	1.20007	−	0.871899i
$365$	−589765.	+	428489.i	−0.231711	+	0.168348i
$366$	3.19039e6			1.24492
$367$	−321572.	−	989697.i	−0.124627	−	0.383563i	0.869206	−	0.494451i	$-0.164631\pi$
$367$	−321572.	−	989697.i	−0.124627	−	0.383563i	−0.993833	+	0.110887i	$0.964631\pi$
$368$	−487003.			−0.187462
$369$	−4.10025e6	−	4.51566e6i	−1.56763	−	1.72645i
$370$	1.45538e6			0.552676
$371$	−304971.	−	938605.i	−0.115033	−	0.354037i
$372$	−874749.			−0.327738
$373$	−3.94169e6	+	2.86381e6i	−1.46693	+	1.06579i	−0.485446	+	0.874267i	$0.661343\pi$
$373$	−3.94169e6	+	2.86381e6i	−1.46693	+	1.06579i	−0.981488	+	0.191523i	$0.938657\pi$
$374$	−362423.	+	263316.i	−0.133979	+	0.0973415i
$375$	−1.30276e6	−	4.00949e6i	−0.478395	−	1.47235i
$376$	−66470.3	+	204574.i	−0.0242470	+	0.0746246i
$377$	4.53537e6	+	3.29514e6i	1.64346	+	1.19405i
$378$	9.08705e6			3.27110
$379$	−265749.	−	193078.i	−0.0950329	−	0.0690454i	0.539254	−	0.842143i	$-0.318706\pi$
$379$	−265749.	−	193078.i	−0.0950329	−	0.0690454i	−0.634287	+	0.773098i	$0.718706\pi$
$380$	−311751.	−	226500.i	−0.110751	−	0.0804654i
$381$	−3.43499e6	+	2.49566e6i	−1.21231	+	0.880792i
$382$	−72927.2	−	224447.i	−0.0255700	−	0.0786964i
$383$	399486.			0.139157			0.0695784	−	0.997576i	$-0.477835\pi$
$383$	399486.			0.139157			0.0695784	+	0.997576i	$0.477835\pi$
$384$	377165.	−	274027.i	0.130528	−	0.0948341i
$385$	202327.	−	622698.i	0.0695667	−	0.214104i
$386$	402492.	+	292428.i	0.137496	+	0.0998965i
$387$	2.38461e6	+	7.33908e6i	0.809358	+	2.49095i
$388$	356994.	−	1.09871e6i	0.120387	−	0.370514i
$389$	574205.	−	1.76722e6i	0.192395	−	0.592130i	−0.807602	−	0.589727i	$-0.799235\pi$
$389$	574205.	−	1.76722e6i	0.192395	−	0.592130i	0.999997	−	0.00240274i	$-0.000764815\pi$
$390$	−894833.	+	2.75401e6i	−0.297907	+	0.916863i
$391$	−664168.	+	2.04410e6i	−0.219703	+	0.676177i
$392$	−870908.	−	2.68038e6i	−0.286258	−	0.881010i
$393$	7.58457e6	+	5.51051e6i	2.47713	+	1.79974i
$394$	1.15209e6	−	3.54577e6i	0.373892	−	1.15072i
$395$	952501.	−	692033.i	0.307166	−	0.223169i
$396$	−898762.			−0.288010
$397$	882413.	+	2.71579e6i	0.280993	+	0.864808i	0.987571	+	0.157173i	$0.0502380\pi$
$397$	882413.	+	2.71579e6i	0.280993	+	0.864808i	−0.706578	+	0.707635i	$0.749762\pi$
$398$	−2.26295e6	+	1.64413e6i	−0.716090	+	0.520270i
$399$	5.10713e6	+	3.71055e6i	1.60600	+	1.16682i
$400$	498709.	+	362334.i	0.155847	+	0.113229i
$401$	−1.01244e6			−0.314418			−0.157209	−	0.987565i	$-0.550250\pi$
$401$	−1.01244e6			−0.314418			−0.157209	+	0.987565i	$0.550250\pi$
$402$	−5.93125e6	−	4.30930e6i	−1.83055	−	1.32997i
$403$	−564114.	+	1.73616e6i	−0.173023	+	0.532510i
$404$	−650258.	−	2.00129e6i	−0.198213	−	0.610037i
$405$	−2.69419e6	+	1.95744e6i	−0.816188	+	0.592995i
$406$	4.70982e6	−	3.42188e6i	1.41804	−	1.03027i
$407$	1.34691e6			0.403045
$408$	−635800.	−	1.95679e6i	−0.189091	−	0.581961i
$409$	−3.81359e6			−1.12726			−0.563631	−	0.826026i	$-0.690596\pi$
$409$	−3.81359e6			−1.12726			−0.563631	+	0.826026i	$0.690596\pi$
$410$	−125306.	−	1.14607e6i	−0.0368138	−	0.336705i
$411$	3.40047e6			0.992967
$412$	325426.	+	1.00156e6i	0.0944516	+	0.290692i
$413$	2.44845e6			0.706343
$414$	−3.48851e6	+	2.53455e6i	−1.00032	+	0.726775i
$415$	235721.	−	171261.i	0.0671858	−	0.0488133i
$416$	−300647.	−	925297.i	−0.0851773	−	0.262149i
$417$	−585843.	+	1.80304e6i	−0.164984	+	0.507768i
$418$	−288517.	−	209620.i	−0.0807664	−	0.0586802i
$419$	−5.21670e6			−1.45165			−0.725824	−	0.687881i	$-0.758541\pi$
$419$	−5.21670e6			−1.45165			−0.725824	+	0.687881i	$0.758541\pi$
$420$	2.43281e6	+	1.76754e6i	0.672954	+	0.488929i
$421$	3.38005e6	+	2.45575e6i	0.929432	+	0.675272i	0.945854	−	0.324593i	$-0.105227\pi$
$421$	3.38005e6	+	2.45575e6i	0.929432	+	0.675272i	−0.0164213	+	0.999865i	$0.505227\pi$
$422$	−3.12718e6	+	2.27203e6i	−0.854815	+	0.621059i
$423$	588543.	+	1.81135e6i	0.159929	+	0.492211i
$424$	−256065.			−0.0691729
$425$	2.20096e6	−	1.59909e6i	0.591071	−	0.429438i
$426$	981794.	−	3.02165e6i	0.262118	−	0.806715i
$427$	−5.59362e6	−	4.06400e6i	−1.48465	−	1.07866i
$428$	798782.	+	2.45840e6i	0.210775	+	0.648698i
$429$	−828144.	+	2.54877e6i	−0.217251	+	0.668631i
$430$	−450732.	+	1.38721e6i	−0.117557	+	0.361802i
$431$	−840487.	+	2.58675e6i	−0.217940	+	0.670752i	0.780991	+	0.624542i	$0.214714\pi$
$431$	−840487.	+	2.58675e6i	−0.217940	+	0.670752i	−0.998932	+	0.0462099i	$0.985286\pi$
$432$	728583.	−	2.24235e6i	0.187832	−	0.578088i
$433$	−1.52902e6	−	4.70583e6i	−0.391915	−	1.20619i	−0.931338	−	0.364156i	$-0.881358\pi$
$433$	−1.52902e6	−	4.70583e6i	−0.391915	−	1.20619i	0.539423	−	0.842035i	$-0.318642\pi$
$434$	1.53367e6	+	1.11428e6i	0.390849	+	0.283968i
$435$	−1.38927e6	+	4.27574e6i	−0.352018	+	1.08340i
$436$	718826.	−	522258.i	0.181096	−	0.131574i
$437$	−1.71100e6			−0.428595
$438$	−957519.	−	2.94694e6i	−0.238486	−	0.733983i
$439$	−4.91136e6	+	3.56832e6i	−1.21630	+	0.883694i	−0.995788	−	0.0916901i	$-0.970773\pi$
$439$	−4.91136e6	+	3.56832e6i	−1.21630	+	0.883694i	−0.220513	+	0.975384i	$0.570773\pi$
$440$	−137437.	−	99853.6i	−0.0338432	−	0.0245885i
$441$	−2.01882e7	−	1.46676e7i	−4.94312	−	3.59139i
$442$	−4.29377e6			−1.04540
$443$	4.85710e6	+	3.52889e6i	1.17589	+	0.854336i	0.991702	−	0.128555i	$-0.0410338\pi$
$443$	4.85710e6	+	3.52889e6i	1.17589	+	0.854336i	0.184190	+	0.982891i	$0.441034\pi$
$444$	−1.91162e6	+	5.88336e6i	−0.460197	+	1.41634i
$445$	264864.	+	815168.i	0.0634049	+	0.195140i
$446$	−2.08462e6	+	1.51457e6i	−0.496238	+	0.360538i
$447$	1.16311e7	−	8.45047e6i	2.75328	−	2.00038i
$448$	−1.01034e6			−0.237832
$449$	−817530.	−	2.51610e6i	−0.191376	−	0.588995i	−1.00000		0.000668865i	$-0.999787\pi$
$449$	−817530.	−	2.51610e6i	−0.191376	−	0.588995i	0.808624	−	0.588326i	$-0.200213\pi$
$450$	5.45809e6			1.27060
$451$	−115967.	−	1.06065e6i	−0.0268468	−	0.245546i
$452$	2.26934e6			0.522460
$453$	−1.14255e6	−	3.51641e6i	−0.261595	−	0.805107i
$454$	−613230.			−0.139632
$455$	5.07702e6	−	3.68867e6i	1.14969	−	0.835298i
$456$	1.32511e6	−	962746.i	0.298427	−	0.216820i
$457$	1.29362e6	+	3.98136e6i	0.289746	+	0.891746i	0.984936	+	0.172920i	$0.0553202\pi$
$457$	1.29362e6	+	3.98136e6i	0.289746	+	0.891746i	−0.695190	+	0.718826i	$0.744680\pi$
$458$	750439.	−	2.30961e6i	0.167167	−	0.514488i
$459$	−8.41819e6	−	6.11617e6i	−1.86503	−	1.35503i
$460$	−815046.			−0.179592
$461$	−2.64036e6	−	1.91833e6i	−0.578643	−	0.420409i	0.259591	−	0.965719i	$-0.416412\pi$
$461$	−2.64036e6	−	1.91833e6i	−0.578643	−	0.420409i	−0.838235	+	0.545310i	$0.816412\pi$
$462$	2.25150e6	+	1.63581e6i	0.490758	+	0.356557i
$463$	−312579.	+	227102.i	−0.0677653	+	0.0492344i	−0.621152	−	0.783690i	$-0.713335\pi$
$463$	−312579.	+	227102.i	−0.0677653	+	0.0492344i	0.553387	+	0.832924i	$0.313335\pi$
$464$	−466770.	−	1.43657e6i	−0.100649	−	0.309765i
$465$	−1.46398e6			−0.313980
$466$	3.08478e6	−	2.24122e6i	0.658050	−	0.478101i
$467$	−665674.	+	2.04873e6i	−0.141244	+	0.434703i	−0.996509	−	0.0834872i	$-0.973394\pi$
$467$	−665674.	+	2.04873e6i	−0.141244	+	0.434703i	0.855265	+	0.518191i	$0.173394\pi$
$468$	−6.96920e6	−	5.06342e6i	−1.47085	−	1.06863i
$469$	4.90979e6	+	1.51108e7i	1.03070	+	3.17216i
$470$	−111244.	+	342375.i	−0.0232292	+	0.0714920i
$471$	869646.	−	2.67650e6i	0.180630	−	0.555922i
$472$	196312.	−	604187.i	0.0405595	−	0.124829i
$473$	−417140.	+	1.28383e6i	−0.0857293	+	0.263848i
$474$	1.54644e6	+	4.75946e6i	0.316146	+	0.972998i
$475$	1.75213e6	+	1.27300e6i	0.356314	+	0.258877i
$476$	−1.37788e6	+	4.24069e6i	−0.278737	+	0.857865i
$477$	−1.83425e6	+	1.33266e6i	−0.369116	+	0.268178i
$478$	3.90213e6			0.781146
$479$	−2.76311e6	−	8.50397e6i	−0.550249	−	1.69349i	−0.708172	−	0.706040i	$-0.750480\pi$
$479$	−2.76311e6	−	8.50397e6i	−0.550249	−	1.69349i	0.157923	−	0.987451i	$-0.449520\pi$
$480$	631222.	−	458610.i	0.125049	−	0.0908532i
$481$	1.04442e7	+	7.58819e6i	2.05833	+	1.49546i
$482$	1.09821e6	+	797893.i	0.215311	+	0.156433i
$483$	1.33522e7			2.60426
$484$	1.95749e6	+	1.42220e6i	0.379828	+	0.275961i
$485$	597463.	−	1.83880e6i	0.115334	−	0.354961i
$486$	−1.60783e6	−	4.94840e6i	−0.308781	−	0.950329i
$487$	−1.50889e6	+	1.09627e6i	−0.288293	+	0.209457i	−0.722526	−	0.691343i	$-0.757019\pi$
$487$	−1.50889e6	+	1.09627e6i	−0.288293	+	0.209457i	0.434234	+	0.900800i	$0.357019\pi$
$488$	−1.45133e6	+	1.05446e6i	−0.275878	+	0.200437i
$489$	1.36342e7			2.57845
$490$	−1.45755e6	−	4.48587e6i	−0.274241	−	0.844027i
$491$	−2.18212e6			−0.408485			−0.204242	−	0.978920i	$-0.565473\pi$
$491$	−2.18212e6			−0.408485			−0.204242	+	0.978920i	$0.565473\pi$
$492$	4.79756e6	+	998796.i	0.893527	+	0.186022i
$493$	−6.66630e6			−1.23529
$494$	−1.05627e6	−	3.25087e6i	−0.194742	−	0.599353i
$495$	−1.50417e6			−0.275920
$496$	397930.	−	289113.i	0.0726278	−	0.0527672i
$497$	−5.57041e6	+	4.04714e6i	−1.01157	+	0.734950i
$498$	382707.	+	1.17785e6i	0.0691501	+	0.212822i
$499$	582748.	−	1.79351e6i	0.104768	−	0.322443i	−0.884908	−	0.465766i	$-0.845779\pi$
$499$	582748.	−	1.79351e6i	0.104768	−	0.322443i	0.989676	+	0.143323i	$0.0457788\pi$
$500$	1.91781e6	+	1.39337e6i	0.343069	+	0.249254i
$501$	1.71515e6			0.305286
$502$	3.43958e6	+	2.49900e6i	0.609181	+	0.442596i
$503$	−5.48562e6	−	3.98554e6i	−0.966732	−	0.702372i	−0.0120276	−	0.999928i	$-0.503829\pi$
$503$	−5.48562e6	−	3.98554e6i	−0.966732	−	0.702372i	−0.954704	+	0.297556i	$0.903829\pi$
$504$	−7.23726e6	+	5.25818e6i	−1.26911	+	0.922059i
$505$	−1.08827e6	−	3.34935e6i	−0.189892	−	0.584429i
$506$	−754304.			−0.130969
$507$	−1.22335e7	+	8.88814e6i	−2.11363	+	1.53565i
$508$	737761.	−	2.27059e6i	0.126840	−	0.390373i
$509$	−1.27847e6	−	928863.i	−0.218724	−	0.158912i	0.473028	−	0.881047i	$-0.343161\pi$
$509$	−1.27847e6	−	928863.i	−0.218724	−	0.158912i	−0.691752	+	0.722135i	$0.743161\pi$
$510$	−1.06407e6	−	3.27488e6i	−0.181153	−	0.557532i
$511$	−2.07510e6	+	6.38650e6i	−0.351550	+	1.08196i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$	2.55975e6	−	7.87812e6i	0.429442	−	1.32169i
$514$	−1.58720e6	+	4.88488e6i	−0.264986	+	0.815542i
$515$	544632.	+	1.67620e6i	0.0904868	+	0.278490i
$516$	−5.01576e6	−	3.64416e6i	−0.829302	−	0.602523i
$517$	−102954.	+	316859.i	−0.0169401	+	0.0521362i
$518$	1.08460e7	−	7.88006e6i	1.77600	−	1.29034i
$519$	828521.			0.135016
$520$	−503162.	−	1.54857e6i	−0.0816017	−	0.251144i
$521$	−1.43028e6	+	1.03916e6i	−0.230849	+	0.167721i	−0.697197	−	0.716880i	$-0.745570\pi$
$521$	−1.43028e6	+	1.03916e6i	−0.230849	+	0.167721i	0.466348	+	0.884601i	$0.345570\pi$
$522$	−1.08200e7	−	7.86122e6i	−1.73801	−	1.26274i
$523$	4.37109e6	+	3.17578e6i	0.698772	+	0.507687i	0.879532	−	0.475840i	$-0.157856\pi$
$523$	4.37109e6	+	3.17578e6i	0.698772	+	0.507687i	−0.180760	+	0.983527i	$0.557856\pi$
$524$	−5.27156e6			−0.838708
$525$	−1.36731e7	−	9.93410e6i	−2.16506	−	1.57301i
$526$	−2.21380e6	+	6.81338e6i	−0.348879	+	1.07374i
$527$	−670804.	−	2.06452e6i	−0.105213	−	0.323812i
$528$	584179.	−	424431.i	0.0911930	−	0.0662556i
$529$	2.27931e6	−	1.65602e6i	0.354132	−	0.257292i
$530$	−428550.			−0.0662692
$531$	−1.73819e6	−	5.34960e6i	−0.267523	−	0.823352i
$532$	−3.54965e6			−0.543758
$533$	5.07625e6	−	8.87787e6i	0.773971	−	1.35360i
$534$	−3.64321e6			−0.552880
$535$	1.33684e6	+	4.11436e6i	0.201927	+	0.621467i
$536$	4.12244e6			0.619787
$537$	1.60586e6	−	1.16673e6i	0.240310	−	0.174595i
$538$	5.84321e6	−	4.24534e6i	0.870354	−	0.632349i
$539$	−1.34892e6	−	4.15155e6i	−0.199993	−	0.615515i
$540$	1.21935e6	−	3.75279e6i	0.179947	−	0.553821i
$541$	1.86655e6	+	1.35613e6i	0.274187	+	0.199208i	0.716378	−	0.697712i	$-0.245799\pi$
$541$	1.86655e6	+	1.35613e6i	0.274187	+	0.199208i	−0.442191	+	0.896921i	$0.645799\pi$
$542$	−1.43358e6			−0.209616
$543$	3.79767e6	+	2.75917e6i	0.552735	+	0.401586i
$544$	935969.	+	680022.i	0.135601	+	0.0985202i
$545$	1.20303e6	−	874049.i	0.173494	−	0.126050i
$546$	8.24285e6	+	2.53689e7i	1.18330	+	3.64183i
$547$	3.10399e6			0.443559			0.221780	−	0.975097i	$-0.428813\pi$
$547$	3.10399e6			0.443559			0.221780	+	0.975097i	$0.428813\pi$
$548$	−1.54690e6	+	1.12389e6i	−0.220045	+	0.159872i
$549$	−4.90843e6	+	1.51066e7i	−0.695043	+	2.13912i
$550$	772435.	+	561207.i	0.108882	+	0.0791073i
$551$	−1.63992e6	−	5.04715e6i	−0.230114	−	0.708218i
$552$	1.07055e6	−	3.29482e6i	0.149541	−	0.460240i
$553$	3.35140e6	−	1.03145e7i	0.466029	−	1.43429i
$554$	785652.	−	2.41799e6i	0.108757	−	0.334718i
$555$	−3.19928e6	+	9.84636e6i	−0.440879	+	1.35689i
$556$	−329418.	−	1.01384e6i	−0.0451919	−	0.139086i
$557$	−8.41294e6	−	6.11236e6i	−1.14897	−	0.834777i	−0.160629	−	0.987015i	$-0.551352\pi$
$557$	−8.41294e6	−	6.11236e6i	−1.14897	−	0.834777i	−0.988344	+	0.152237i	$0.951352\pi$
$558$	1.34581e6	−	4.14196e6i	0.182977	−	0.563146i
$559$	−1.04674e7	+	7.60499e6i	−1.41680	+	1.02936i
$560$	−1.69089e6			−0.227849
$561$	−984771.	−	3.03081e6i	−0.132108	−	0.406585i
$562$	−997096.	+	724433.i	−0.133167	+	0.0967514i
$563$	2.16681e6	+	1.57428e6i	0.288104	+	0.209320i	0.722444	−	0.691429i	$-0.243019\pi$
$563$	2.16681e6	+	1.57428e6i	0.288104	+	0.209320i	−0.434340	+	0.900749i	$0.643019\pi$
$564$	−1.23793e6	−	899411.i	−0.163870	−	0.119058i
$565$	3.79795e6			0.500528
$566$	−4.32978e6	−	3.14577e6i	−0.568099	−	0.412748i
$567$	−9.47955e6	+	2.91751e7i	−1.23831	+	3.81113i
$568$	552060.	+	1.69907e6i	0.0717985	+	0.220973i
$569$	6.29024e6	−	4.57013e6i	0.814492	−	0.591763i	−0.100637	−	0.994923i	$-0.532088\pi$
$569$	6.29024e6	−	4.57013e6i	0.814492	−	0.591763i	0.915130	+	0.403160i	$0.132088\pi$
$570$	2.21769e6	−	1.61125e6i	0.285900	−	0.207719i
$571$	1.80496e6			0.231674			0.115837	−	0.993268i	$-0.463045\pi$
$571$	1.80496e6			0.231674			0.115837	+	0.993268i	$0.463045\pi$
$572$	−465663.	−	1.43316e6i	−0.0595089	−	0.183149i
$573$	1.67881e6			0.213607
$574$	−7.13914e6	−	7.86242e6i	−0.904411	−	0.996040i
$575$	4.58080e6			0.577793
$576$	717254.	+	2.20748e6i	0.0900775	+	0.277230i
$577$	9.77880e6			1.22277			0.611387	−	0.791332i	$-0.290612\pi$
$577$	9.77880e6			1.22277			0.611387	+	0.791332i	$0.290612\pi$
$578$	−464033.	+	337140.i	−0.0577736	+	0.0419750i
$579$	−2.86320e6	+	2.08024e6i	−0.354940	+	0.257879i
$580$	−781184.	−	2.40424e6i	−0.0964237	−	0.296761i
$581$	829388.	−	2.55259e6i	0.101934	−	0.313720i
$582$	6.64859e6	+	4.83049e6i	0.813621	+	0.591130i
$583$	−396611.			−0.0483274
$584$	1.40958e6	+	1.02412e6i	0.171024	+	0.124256i
$585$	−1.16636e7	−	8.47412e6i	−1.40911	−	1.02378i
$586$	−6.32619e6	+	4.59625e6i	−0.761024	+	0.552916i
$587$	−4.52766e6	−	1.39347e7i	−0.542348	−	1.66918i	−0.727213	−	0.686412i	$-0.759185\pi$
$587$	−4.52766e6	−	1.39347e7i	−0.542348	−	1.66918i	0.184864	−	0.982764i	$-0.440815\pi$
$588$	2.00486e7			2.39134
$589$	1.39806e6	−	1.01575e6i	0.166050	−	0.120642i
$590$	328547.	−	1.01116e6i	0.0388569	−	0.119589i
$591$	2.14564e7	+	1.55890e7i	2.52690	+	1.83590i
$592$	−1.07490e6	−	3.30819e6i	−0.126056	−	0.387960i
$593$	−3.53264e6	+	1.08724e7i	−0.412537	+	1.26966i	0.501898	+	0.864927i	$0.332635\pi$
$593$	−3.53264e6	+	1.08724e7i	−0.412537	+	1.26966i	−0.914435	+	0.404732i	$0.867365\pi$
$594$	1.12848e6	−	3.47310e6i	0.131228	−	0.403879i
$595$	−2.30602e6	+	7.09720e6i	−0.267037	+	0.821854i
$596$	−2.49810e6	+	7.68837e6i	−0.288068	+	0.886581i
$597$	−6.14885e6	−	1.89242e7i	−0.706087	−	2.17311i
$598$	−5.84904e6	−	4.24957e6i	−0.668854	−	0.485951i
$599$	−1.22390e6	+	3.76678e6i	−0.139373	+	0.428947i	−0.996245	−	0.0865834i	$-0.972405\pi$
$599$	−1.22390e6	+	3.76678e6i	−0.139373	+	0.428947i	0.856871	+	0.515530i	$0.172405\pi$
$600$	−3.54766e6	+	2.57752e6i	−0.402312	+	0.292297i
$601$	6.45363e6			0.728816			0.364408	−	0.931239i	$-0.381271\pi$
$601$	6.45363e6			0.728816			0.364408	+	0.931239i	$0.381271\pi$
$602$	4.15196e6	+	1.27784e7i	0.466941	+	1.43710i
$603$	2.95299e7	−	2.14547e7i	3.30727	−	2.40287i
$604$	1.68196e6	+	1.22202e6i	0.187596	+	0.136297i
$605$	3.27605e6	+	2.38019e6i	0.363884	+	0.264377i
$606$	1.49692e7			1.65583
$607$	3.04895e6	+	2.21519e6i	0.335876	+	0.244028i	0.742920	−	0.669381i	$-0.233440\pi$
$607$	3.04895e6	+	2.21519e6i	0.335876	+	0.244028i	−0.407044	+	0.913409i	$0.633440\pi$
$608$	−284604.	+	875922.i	−0.0312236	+	0.0960962i
$609$	1.27974e7	+	3.93865e7i	1.39823	+	4.30332i
$610$	−2.42895e6	+	1.76473e6i	−0.264298	+	0.192023i
$611$	−2.58344e6	+	1.87698e6i	−0.279959	+	0.203402i
$612$	1.02436e7			1.10554
$613$	2.69719e6	+	8.30111e6i	0.289909	+	0.892247i	0.984884	+	0.173214i	$0.0554151\pi$
$613$	2.69719e6	+	8.30111e6i	0.289909	+	0.892247i	−0.694976	+	0.719033i	$0.744585\pi$
$614$	−4.53627e6			−0.485600
$615$	8.02917e6	+	1.67158e6i	0.856018	+	0.178213i
$616$	−1.56488e6			−0.166161
$617$	318938.	+	981591.i	0.0337282	+	0.103805i	0.966503	−	0.256654i	$-0.0826201\pi$
$617$	318938.	+	981591.i	0.0337282	+	0.103805i	−0.932775	+	0.360459i	$0.882620\pi$
$618$	−7.49142e6			−0.789029
$619$	7.85789e6	−	5.70909e6i	0.824288	−	0.598881i	−0.0936492	−	0.995605i	$-0.529853\pi$
$619$	7.85789e6	−	5.70909e6i	0.824288	−	0.598881i	0.917938	+	0.396725i	$0.129853\pi$
$620$	665975.	−	483859.i	0.0695790	−	0.0505521i
$621$	−5.41416e6	−	1.66631e7i	−0.563381	−	1.73391i
$622$	−3.54644e6	+	1.09148e7i	−0.367550	+	1.13120i
$623$	6.38754e6	+	4.64082e6i	0.659346	+	0.479043i
$624$	6.92100e6			0.711553
$625$	−2.87812e6	−	2.09108e6i	−0.294719	−	0.214126i
$626$	5.48273e6	+	3.98343e6i	0.559192	+	0.406277i
$627$	2.05242e6	−	1.49117e6i	0.208495	−	0.151481i
$628$	488999.	+	1.50499e6i	0.0494777	+	0.152277i
$629$	−1.53514e7			−1.54711
$630$	−1.21122e7	+	8.80006e6i	−1.21583	+	0.883353i
$631$	−1.78998e6	+	5.50900e6i	−0.178968	+	0.550807i	−0.999792	−	0.0203737i	$-0.993514\pi$
$631$	−1.78998e6	+	5.50900e6i	−0.178968	+	0.550807i	0.820824	+	0.571181i	$0.193514\pi$
$632$	−2.27654e6	−	1.65400e6i	−0.226716	−	0.164719i
$633$	−8.49712e6	−	2.61515e7i	−0.842874	−	2.59410i
$634$	2.05984e6	−	6.33954e6i	0.203522	−	0.626375i
$635$	1.23471e6	−	3.80006e6i	0.121516	−	0.373986i
$636$	562894.	−	1.73241e6i	0.0551803	−	0.169828i
$637$	1.29291e7	−	3.97916e7i	1.26246	−	3.88546i
$638$	−722965.	−	2.22506e6i	−0.0703179	−	0.216416i
$639$	1.27971e7	+	9.29764e6i	1.23982	+	0.900784i
$640$	−135573.	+	417250.i	−0.0130835	+	0.0402668i
$641$	−3.74926e6	+	2.72399e6i	−0.360413	+	0.261855i	−0.753224	−	0.657764i	$-0.771502\pi$
$641$	−3.74926e6	+	2.72399e6i	−0.360413	+	0.261855i	0.392812	+	0.919619i	$0.371502\pi$
$642$	−1.83882e7			−1.76077
$643$	−437566.	−	1.34669e6i	−0.0417365	−	0.128452i	0.928017	−	0.372537i	$-0.121512\pi$
$643$	−437566.	−	1.34669e6i	−0.0417365	−	0.128452i	−0.969754	+	0.244086i	$0.921512\pi$
$644$	−6.07401e6	+	4.41303e6i	−0.577113	+	0.419297i
$645$	−8.39436e6	−	6.09886e6i	−0.794489	−	0.577230i
$646$	3.28837e6	+	2.38914e6i	0.310027	+	0.225248i
$647$	−53751.4			−0.00504812			−0.00252406	−	0.999997i	$-0.500803\pi$
$647$	−53751.4			−0.00504812			−0.00252406	+	0.999997i	$0.500803\pi$
$648$	6.43928e6	+	4.67841e6i	0.602420	+	0.437684i
$649$	304062.	−	935806.i	0.0283367	−	0.0872115i
$650$	2.82792e6	+	8.70344e6i	0.262533	+	0.807993i
$651$	−1.09101e7	+	7.92662e6i	−1.00896	+	0.733054i
$652$	−6.20232e6	+	4.50625e6i	−0.571394	+	0.415142i
$653$	−1.11988e7			−1.02776			−0.513878	−	0.857863i	$-0.671792\pi$
$653$	−1.11988e7			−1.02776			−0.513878	+	0.857863i	$0.671792\pi$
$654$	1.95318e6	+	6.01128e6i	0.178566	+	0.549569i
$655$	−8.82246e6			−0.803501
$656$	−2.51256e6	+	1.13128e6i	−0.227959	+	0.102639i
$657$	1.54270e7			1.39434
$658$	1.02474e6	+	3.15382e6i	0.0922675	+	0.283970i
$659$	5.82637e6			0.522618			0.261309	−	0.965255i	$-0.415846\pi$
$659$	5.82637e6			0.522618			0.261309	+	0.965255i	$0.415846\pi$
$660$	977680.	−	710326.i	0.0873649	−	0.0634743i
$661$	4.28807e6	−	3.11547e6i	0.381732	−	0.277345i	−0.380327	−	0.924852i	$-0.624189\pi$
$661$	4.28807e6	−	3.11547e6i	0.381732	−	0.277345i	0.762059	+	0.647508i	$0.224189\pi$
$662$	3.09085e6	+	9.51265e6i	0.274115	+	0.843638i
$663$	9.43877e6	−	2.90495e7i	0.833934	−	2.56658i
$664$	−563387.	−	409325.i	−0.0495892	−	0.0360286i
$665$	−5.94067e6			−0.520933
$666$	−2.49168e7	−	1.81031e7i	−2.17674	−	1.58150i
$667$	−9.08092e6	−	6.59768e6i	−0.790343	−	0.574218i
$668$	−780233.	+	566873.i	−0.0676524	+	0.0491524i
$669$	−5.66429e6	−	1.74329e7i	−0.489306	−	1.50593i
$670$	6.89930e6			0.593769
$671$	−2.24792e6	+	1.63321e6i	−0.192742	+	0.140035i
$672$	2.22097e6	−	6.83544e6i	0.189723	−	0.583906i
$673$	2.51988e6	+	1.83080e6i	0.214458	+	0.155813i	0.689829	−	0.723973i	$-0.257686\pi$
$673$	2.51988e6	+	1.83080e6i	0.214458	+	0.155813i	−0.475370	+	0.879786i	$0.657686\pi$
$674$	−1.75679e6	−	5.40685e6i	−0.148960	−	0.458453i
$675$	−6.85313e6	+	2.10918e7i	−0.578935	+	1.78178i
$676$	2.62749e6	−	8.08657e6i	0.221143	−	0.680609i
$677$	−720806.	+	2.21841e6i	−0.0604431	+	0.186025i	−0.976719	−	0.214523i	$-0.931180\pi$
$677$	−720806.	+	2.21841e6i	−0.0604431	+	0.186025i	0.916276	+	0.400548i	$0.131180\pi$
$678$	−4.98856e6	+	1.53532e7i	−0.416774	+	1.28270i
$679$	−5.50359e6	−	1.69383e7i	−0.458112	−	1.40992i
$680$	1.56643e6	+	1.13808e6i	0.129909	+	0.0943846i
$681$	1.34803e6	−	4.14881e6i	0.111386	−	0.342812i
$682$	616342.	−	447799.i	0.0507412	−	0.0368656i
$683$	−1.12447e7			−0.922354			−0.461177	−	0.887308i	$-0.652573\pi$
$683$	−1.12447e7			−0.922354			−0.461177	+	0.887308i	$0.652573\pi$
$684$	2.51995e6	+	7.75561e6i	0.205945	+	0.633834i
$685$	−2.58889e6	+	1.88094e6i	−0.210808	+	0.153161i
$686$	−2.17349e7	−	1.57914e7i	−1.76339	−	1.28118i
$687$	1.39761e7	+	1.01542e7i	1.12978	+	0.820831i
$688$	3.48614e6			0.280785
$689$	−3.07541e6	−	2.23442e6i	−0.246806	−	0.179315i
$690$	1.79167e6	−	5.51420e6i	0.143264	−	0.440920i
$691$	−1.97365e6	−	6.07427e6i	−0.157244	−	0.483949i	0.841137	−	0.540822i	$-0.181887\pi$
$691$	−1.97365e6	−	6.07427e6i	−0.157244	−	0.483949i	−0.998381	+	0.0568736i	$0.981887\pi$
$692$	−376901.	+	273834.i	−0.0299200	+	0.0217382i
$693$	−1.12096e7	+	8.14422e6i	−0.886657	+	0.644194i
$694$	5.56250e6			0.438401
$695$	−551313.	−	1.69677e6i	−0.0432948	−	0.133248i
$696$	1.07452e7			0.840798
$697$	1.32173e6	+	1.20888e7i	0.103053	+	0.942543i
$698$	1.00838e7			0.783402
$699$	8.38190e6	+	2.57968e7i	0.648858	+	1.99698i
$700$	9.50333e6			0.733045
$701$	−9.00898e6	+	6.54541e6i	−0.692438	+	0.503085i	−0.877461	−	0.479649i	$-0.840764\pi$
$701$	−9.00898e6	+	6.54541e6i	−0.692438	+	0.503085i	0.185023	+	0.982734i	$0.440764\pi$
$702$	2.83171e7	−	2.05736e7i	2.16874	−	1.57568i
$703$	−3.77647e6	−	1.16228e7i	−0.288203	−	0.886996i
$704$	−125469.	+	386154.i	−0.00954125	+	0.0293649i
$705$	−2.07180e6	−	1.50525e6i	−0.156991	−	0.114061i
$706$	5.53460e6			0.417902
$707$	−2.62450e7	−	1.90681e7i	−1.97469	−	1.43469i
$708$	3.65609e6	+	2.65630e6i	0.274115	+	0.199157i
$709$	−1.47292e7	+	1.07014e7i	−1.10043	+	0.799511i	−0.981131	−	0.193347i	$-0.938066\pi$
$709$	−1.47292e7	+	1.07014e7i	−1.10043	+	0.799511i	−0.119302	+	0.992858i	$0.538066\pi$
$710$	923925.	+	2.84355e6i	0.0687845	+	0.211697i
$711$	−2.49154e7			−1.84839
$712$	1.65732e6	−	1.20412e6i	0.122520	−	0.0890161i
$713$	1.12949e6	−	3.47622e6i	0.0832070	−	0.256085i
$714$	−2.56615e7	−	1.86442e7i	−1.88381	−	1.36867i
$715$	−779332.	−	2.39854e6i	−0.0570108	−	0.175461i
$716$	−344904.	+	1.06151e6i	−0.0251429	+	0.0773820i
$717$	−8.57785e6	+	2.63999e7i	−0.623133	+	1.91781i
$718$	615903.	−	1.89556e6i	0.0445863	−	0.137222i
$719$	−2.11788e6	+	6.51817e6i	−0.152785	+	0.470223i	−0.997930	−	0.0643143i	$-0.979514\pi$
$719$	−2.11788e6	+	6.51817e6i	−0.152785	+	0.470223i	0.845145	+	0.534537i	$0.179514\pi$
$720$	1.20039e6	+	3.69443e6i	0.0862963	+	0.265593i
$721$	1.31345e7	+	9.54278e6i	0.940970	+	0.683655i
$722$	2.06072e6	−	6.34224e6i	0.147121	−	0.452793i
$723$	−7.81228e6	+	5.67595e6i	−0.555817	+	0.403825i
$724$	−2.63952e6			−0.187145
$725$	4.39049e6	+	1.35125e7i	0.310219	+	0.954755i
$726$	−1.39250e7	+	1.01171e7i	−0.980512	+	0.712384i
$727$	−1.52652e7	−	1.10908e7i	−1.07119	−	0.778267i	−0.0950662	−	0.995471i	$-0.530306\pi$
$727$	−1.52652e7	−	1.10908e7i	−1.07119	−	0.778267i	−0.976126	+	0.217204i	$0.930306\pi$
$728$	−1.21344e7	−	8.81616e6i	−0.848575	−	0.616526i
$729$	6.79205e6			0.473350
$730$	2.35906e6	+	1.71396e6i	0.163845	+	0.119040i
$731$	4.75435e6	−	1.46324e7i	0.329077	−	1.01280i
$732$	−3.94354e6	−	1.21370e7i	−0.272025	−	0.837206i
$733$	5.42404e6	−	3.94079e6i	0.372875	−	0.270909i	−0.385527	−	0.922696i	$-0.625980\pi$
$733$	5.42404e6	−	3.94079e6i	0.372875	−	0.270909i	0.758402	+	0.651787i	$0.225980\pi$
$734$	−3.36755e6	+	2.44667e6i	−0.230714	+	0.167623i
$735$	3.35532e7			2.29095
$736$	601969.	+	1.85267e6i	0.0409618	+	0.126068i
$737$	6.38512e6			0.433012
$738$	−1.21104e7	+	2.11799e7i	−0.818497	+	1.43147i
$739$	−1.71468e7			−1.15498			−0.577488	−	0.816399i	$-0.695967\pi$
$739$	−1.71468e7			−1.15498			−0.577488	+	0.816399i	$0.695967\pi$
$740$	−1.79894e6	−	5.53658e6i	−0.120764	−	0.371674i
$741$	2.43158e7			1.62683
$742$	−3.19370e6	+	2.32036e6i	−0.212953	+	0.154720i
$743$	3.06258e6	−	2.22509e6i	0.203524	−	0.147869i	−0.481355	−	0.876526i	$-0.659855\pi$
$743$	3.06258e6	−	2.22509e6i	0.203524	−	0.147869i	0.684879	+	0.728657i	$0.259855\pi$
$744$	1.08125e6	+	3.32774e6i	0.0716133	+	0.220403i
$745$	−4.18082e6	+	1.28672e7i	−0.275975	+	0.849365i
$746$	1.57668e7	+	1.14552e7i	1.03728	+	0.753627i
$747$	−6.16595e6			−0.404295
$748$	1.44969e6	+	1.05326e6i	0.0947376	+	0.0688309i
$749$	3.22396e7	+	2.34234e7i	2.09983	+	1.52562i
$750$	−1.36427e7	+	9.91200e6i	−0.885619	+	0.643440i
$751$	720184.	+	2.21650e6i	0.0465955	+	0.143406i	0.971647	−	0.236434i	$-0.0759789\pi$
$751$	720184.	+	2.21650e6i	0.0465955	+	0.143406i	−0.925052	+	0.379841i	$0.875979\pi$
$752$	860409.			0.0554831
$753$	−2.44681e7	+	1.77771e7i	−1.57258	+	1.14255i
$754$	6.92944e6	−	2.13266e7i	0.443884	−	1.36613i
$755$	2.81493e6	+	2.04516e6i	0.179721	+	0.130575i
$756$	−1.12322e7	−	3.45692e7i	−0.714761	−	2.19981i
$757$	−5.57741e6	+	1.71655e7i	−0.353747	+	1.08872i	0.602986	+	0.797752i	$0.293978\pi$
$757$	−5.57741e6	+	1.71655e7i	−0.353747	+	1.08872i	−0.956733	+	0.290969i	$0.906022\pi$
$758$	−406029.	+	1.24963e6i	−0.0256675	+	0.0789965i
$759$	1.65815e6	−	5.10325e6i	0.104476	−	0.321545i
$760$	−476313.	+	1.46594e6i	−0.0299129	+	0.0920623i
$761$	1.38319e6	+	4.25702e6i	0.0865805	+	0.266467i	0.984968	−	0.172736i	$-0.0552607\pi$
$761$	1.38319e6	+	4.25702e6i	0.0865805	+	0.266467i	−0.898388	+	0.439203i	$0.855261\pi$
$762$	1.37399e7	+	9.98265e6i	0.857230	+	0.622814i
$763$	4.23287e6	−	1.30274e7i	0.263223	−	0.810116i
$764$	−763704.	+	554863.i	−0.0473360	+	0.0343916i
$765$	1.71437e7			1.05914
$766$	−493792.	−	1.51973e6i	−0.0304069	−	0.0935828i
$767$	7.62987e6	−	5.54343e6i	0.468305	−	0.340244i
$768$	−1.50866e6	−	1.09611e6i	−0.0922972	−	0.0670579i
$769$	1.25333e7	+	9.10596e6i	0.764273	+	0.555277i	0.900218	−	0.435439i	$-0.143407\pi$
$769$	1.25333e7	+	9.10596e6i	0.764273	+	0.555277i	−0.135945	+	0.990716i	$0.543407\pi$
$770$	−2.61897e6			−0.159186
$771$	−2.95597e7	−	2.14764e7i	−1.79087	−	1.30114i
$772$	614953.	−	1.89263e6i	0.0371363	−	0.114294i
$773$	−8.26754e6	−	2.54449e7i	−0.497654	−	1.53162i	−0.812779	−	0.582572i	$-0.802046\pi$
$773$	−8.26754e6	−	2.54449e7i	−0.497654	−	1.53162i	0.315125	−	0.949050i	$-0.397954\pi$
$774$	2.49720e7	−	1.81432e7i	1.49831	−	1.08858i
$775$	−3.74298e6	+	2.71943e6i	−0.223853	+	0.162639i
$776$	−4.62102e6			−0.275476
$777$	2.94705e7	+	9.07008e7i	1.75120	+	5.38963i
$778$	−7.43267e6			−0.440246
$779$	−8.82745e6	+	3.97456e6i	−0.521185	+	0.234664i
$780$	1.15830e7			0.681684
$781$	855068.	+	2.63163e6i	0.0501618	+	0.154382i
$782$	8.59718e6			0.502735
$783$	4.39638e7	−	3.19416e7i	2.56266	−	1.86188i
$784$	−9.12026e6	+	6.62626e6i	−0.529929	+	0.385016i
$785$	818387.	+	2.51874e6i	0.0474007	+	0.145884i
$786$	1.15882e7	−	3.56648e7i	0.669051	−	2.05913i
$787$	−4.66652e6	−	3.39043e6i	−0.268569	−	0.195127i	0.445347	−	0.895358i	$-0.353080\pi$
$787$	−4.66652e6	−	3.39043e6i	−0.268569	−	0.195127i	−0.713916	+	0.700231i	$0.753080\pi$
$788$	−1.49130e7			−0.855557
$789$	−4.12295e7	−	2.99550e7i	−2.35785	−	1.71308i
$790$	−3.81000e6	−	2.76813e6i	−0.217199	−	0.157804i
$791$	2.83036e7	−	2.05638e7i	1.60843	−	1.16859i
$792$	1.11093e6	+	3.41910e6i	0.0629324	+	0.193686i
$793$	−2.66320e7			−1.50391
$794$	9.24075e6	−	6.71380e6i	0.520183	−	0.377935i
$795$	942058.	−	2.89936e6i	0.0528640	−	0.162699i
$796$	9.05180e6	+	6.57652e6i	0.506352	+	0.367886i
$797$	−7.34346e6	−	2.26008e7i	−0.409501	−	1.26031i	−0.917078	−	0.398708i	$-0.869459\pi$
$797$	−7.34346e6	−	2.26008e7i	−0.409501	−	1.26031i	0.507577	−	0.861606i	$-0.330541\pi$
$798$	7.80300e6	−	2.40152e7i	0.433765	−	1.33499i
$799$	1.17342e6	−	3.61140e6i	0.0650256	−	0.200128i
$800$	761960.	−	2.34507e6i	0.0420927	−	0.129548i
$801$	5.60509e6	−	1.72507e7i	0.308675	−	0.950004i
$802$	1.25144e6	+	3.85154e6i	0.0687029	+	0.211446i
$803$	2.18325e6	+	1.58622e6i	0.119485	+	0.0868111i
$804$	−9.06214e6	+	2.78904e7i	−0.494414	+	1.52165i
$805$	−1.01654e7	+	7.38562e6i	−0.552887	+	0.401696i
$806$	7.30204e6			0.395919
$807$	1.58771e7	+	4.88646e7i	0.858196	+	2.64126i
$808$	−6.80959e6	+	4.94746e6i	−0.366938	+	0.266596i
$809$	−395473.	−	287328.i	−0.0212445	−	0.0154350i	0.577112	−	0.816665i	$-0.304179\pi$
$809$	−395473.	−	287328.i	−0.0212445	−	0.0154350i	−0.598357	+	0.801230i	$0.704179\pi$
$810$	1.07767e7	+	7.82976e6i	0.577132	+	0.419311i
$811$	3.08480e7			1.64693			0.823464	−	0.567369i	$-0.192039\pi$
$811$	3.08480e7			1.64693			0.823464	+	0.567369i	$0.192039\pi$
$812$	−1.88393e7	−	1.36875e7i	−1.00271	−	0.728510i
$813$	3.15137e6	−	9.69892e6i	0.167214	−	0.514632i
$814$	−1.66487e6	−	5.12396e6i	−0.0880685	−	0.271047i
$815$	−1.03802e7	+	7.54165e6i	−0.547408	+	0.397715i
$816$	−6.65818e6	+	4.83745e6i	−0.350050	+	0.254326i
$817$	1.22480e7			0.641962
$818$	4.71385e6	+	1.45077e7i	0.246316	+	0.758083i
$819$	−1.32804e8			−6.91834
$820$	−4.20501e6	+	1.89331e6i	−0.218390	+	0.0983301i
$821$	3.32253e7			1.72032			0.860162	−	0.510020i	$-0.170362\pi$
$821$	3.32253e7			1.72032			0.860162	+	0.510020i	$0.170362\pi$
$822$	−4.20322e6	−	1.29362e7i	−0.216971	−	0.667769i
$823$	−3.36384e7			−1.73116			−0.865578	−	0.500774i	$-0.833049\pi$
$823$	−3.36384e7			−1.73116			−0.865578	+	0.500774i	$0.833049\pi$
$824$	3.40791e6	−	2.47599e6i	0.174852	−	0.127037i
$825$	−5.49485e6	+	3.99225e6i	−0.281074	+	0.204213i
$826$	−3.02645e6	−	9.31445e6i	−0.154342	−	0.475015i
$827$	7.65993e6	−	2.35748e7i	0.389458	−	1.19863i	−0.543736	−	0.839257i	$-0.682991\pi$
$827$	7.65993e6	−	2.35748e7i	0.389458	−	1.19863i	0.933194	−	0.359373i	$-0.117009\pi$
$828$	1.39540e7	+	1.01382e7i	0.707333	+	0.513908i
$829$	−2.36577e7			−1.19560			−0.597800	−	0.801645i	$-0.703958\pi$
$829$	−2.36577e7			−1.19560			−0.597800	+	0.801645i	$0.703958\pi$
$830$	−942883.	−	685044.i	−0.0475075	−	0.0345162i
$831$	1.46319e7	+	1.06307e7i	0.735016	+	0.534021i
$832$	−3.14842e6	+	2.28746e6i	−0.157683	+	0.114563i
$833$	1.53743e7	+	4.73173e7i	0.767686	+	2.36270i
$834$	7.58331e6			0.377523
$835$	−1.30580e6	+	948716.i	−0.0648125	+	0.0470891i
$836$	−440815.	+	1.35669e6i	−0.0218142	+	0.0671374i
$837$	1.43161e7	+	1.04012e7i	0.706335	+	0.513182i
$838$	6.44820e6	+	1.98455e7i	0.317197	+	0.976230i
$839$	−1.11715e7	+	3.43823e7i	−0.547906	+	1.68628i	0.166073	+	0.986114i	$0.446891\pi$
$839$	−1.11715e7	+	3.43823e7i	−0.547906	+	1.68628i	−0.713979	+	0.700167i	$0.753109\pi$
$840$	3.71700e6	−	1.14398e7i	0.181759	−	0.559395i
$841$	4.42001e6	−	1.36034e7i	0.215493	−	0.663219i
$842$	5.16426e6	−	1.58939e7i	0.251031	−	0.772594i
$843$	−2.70929e6	−	8.33834e6i	−0.131307	−	0.404120i
$844$	1.25087e7	+	9.08812e6i	0.604445	+	0.439155i
$845$	4.39735e6	−	1.35336e7i	0.211860	−	0.652038i
$846$	6.16330e6	−	4.47790e6i	0.296065	−	0.215104i
$847$	3.73017e7			1.78657
$848$	316514.	+	974130.i	0.0151148	+	0.0465187i
$849$	3.08006e7	−	2.23780e7i	1.46653	−	1.06549i
$850$	−8.80383e6	−	6.39636e6i	−0.417950	−	0.303658i
$851$	−2.09119e7	−	1.51934e7i	−0.989852	−	0.719170i
$852$	−1.27086e7			−0.599790
$853$	1.99437e7	+	1.44900e7i	0.938500	+	0.681860i	0.948059	−	0.318095i	$-0.103043\pi$
$853$	1.99437e7	+	1.44900e7i	0.938500	+	0.681860i	−0.00955950	+	0.999954i	$0.503043\pi$
$854$	−8.54629e6	+	2.63028e7i	−0.400990	+	1.23412i
$855$	4.21738e6	+	1.29798e7i	0.197300	+	0.607227i
$856$	8.36495e6	−	6.07749e6i	0.390193	−	0.283491i
$857$	−1.12737e6	+	819083.i	−0.0524342	+	0.0380957i	−0.613694	−	0.789544i	$-0.710317\pi$
$857$	−1.12737e6	+	819083.i	−0.0524342	+	0.0380957i	0.561259	+	0.827640i	$0.310317\pi$
$858$	1.07197e7			0.497125
$859$	−9.76195e6	−	3.00442e7i	−0.451392	−	1.38924i	−0.875320	−	0.483545i	$-0.839349\pi$
$859$	−9.76195e6	−	3.00442e7i	−0.451392	−	1.38924i	0.423928	−	0.905696i	$-0.360651\pi$
$860$	5.83439e6			0.268998
$861$	6.88869e7	−	3.10163e7i	3.16686	−	1.42588i
$862$	1.08795e7			0.498701
$863$	9.81394e6	+	3.02042e7i	0.448556	+	1.38051i	0.878537	+	0.477675i	$0.158520\pi$
$863$	9.81394e6	+	3.02042e7i	0.448556	+	1.38051i	−0.429981	+	0.902838i	$0.641480\pi$
$864$	−9.43098e6			−0.429806
$865$	−630779.	+	458288.i	−0.0286640	+	0.0208256i
$866$	−1.60121e7	+	1.16334e7i	−0.725525	+	0.527125i
$867$	−1.26086e6	−	3.88054e6i	−0.0569666	−	0.175325i
$868$	2.34325e6	−	7.21177e6i	0.105565	−	0.324895i
$869$	−3.52606e6	−	2.56183e6i	−0.158394	−	0.115080i
$870$	1.79831e7			0.805503
$871$	4.95116e7	+	3.59723e7i	2.21137	+	1.60665i
$872$	−2.87531e6	−	2.08903e6i	−0.128054	−	0.0930366i
$873$	−3.31014e7	+	2.40496e7i	−1.46998	+	1.06800i
$874$	2.11492e6	+	6.50904e6i	0.0936515	+	0.288230i
$875$	3.65455e7			1.61367
$876$	−1.00273e7	+	7.28524e6i	−0.441492	+	0.320762i
$877$	−1.48588e6	+	4.57306e6i	−0.0652355	+	0.200774i	−0.978361	−	0.206904i	$-0.933661\pi$
$877$	−1.48588e6	+	4.57306e6i	−0.0652355	+	0.200774i	0.913126	+	0.407678i	$0.133661\pi$
$878$	1.96455e7	+	1.42733e7i	0.860054	+	0.624866i
$879$	−1.71894e7	−	5.29036e7i	−0.750394	−	2.30947i
$880$	−209985.	+	646266.i	−0.00914073	+	0.0281323i
$881$	−3.01099e6	+	9.26687e6i	−0.130698	+	0.402248i	−0.994896	−	0.100904i	$-0.967826\pi$
$881$	−3.01099e6	+	9.26687e6i	−0.130698	+	0.402248i	0.864198	+	0.503152i	$0.167826\pi$
$882$	−3.08448e7	+	9.49307e7i	−1.33509	+	4.10899i
$883$	9.08180e6	−	2.79509e7i	0.391986	−	1.20641i	−0.539299	−	0.842114i	$-0.681311\pi$
$883$	9.08180e6	−	2.79509e7i	0.391986	−	1.20641i	0.931284	−	0.364293i	$-0.118689\pi$
$884$	5.30739e6	+	1.63345e7i	0.228429	+	0.703031i
$885$	6.11881e6	+	4.44558e6i	0.262609	+	0.190796i
$886$	7.42099e6	−	2.28394e7i	0.317598	−	0.977465i
$887$	1.84682e7	−	1.34179e7i	0.788162	−	0.572633i	−0.119256	−	0.992864i	$-0.538051\pi$
$887$	1.84682e7	−	1.34179e7i	0.788162	−	0.572633i	0.907417	+	0.420231i	$0.138051\pi$
$888$	2.47445e7			1.05304
$889$	−1.13737e7	−	3.50046e7i	−0.482666	−	1.48549i
$890$	2.77369e6	−	2.01521e6i	0.117377	−	0.0852794i
$891$	9.97359e6	+	7.24624e6i	0.420879	+	0.305786i
$892$	8.33848e6	+	6.05826e6i	0.350893	+	0.254939i
$893$	3.02290e6			0.126852
$894$	−4.65243e7	−	3.38019e7i	−1.94687	−	1.41448i
$895$	−577230.	+	1.77653e6i	−0.0240875	+	0.0741336i
$896$	1.24884e6	+	3.84355e6i	0.0519683	+	0.159942i
$897$	4.16081e7	−	3.02301e7i	1.72662	−	1.25446i
$898$	−8.56128e6	+	6.22014e6i	−0.354281	+	0.257400i
$899$	1.13368e7			0.467833
$900$	−6.74657e6	−	2.07638e7i	−0.277636	−	0.854477i
$901$	4.52038e6			0.185508
$902$	−3.89162e6	+	1.75221e6i	−0.159263	+	0.0717082i
$903$	−9.55796e7			−3.90073
$904$	−2.80505e6	−	8.63307e6i	−0.114162	−	0.351353i
$905$	−4.41749e6			−0.179289
$906$	−1.19649e7	+	8.69304e6i	−0.484273	+	0.351845i
$907$	3.46900e7	−	2.52037e7i	1.40019	−	1.01729i	0.405526	−	0.914083i	$-0.367088\pi$
$907$	3.46900e7	−	2.52037e7i	1.40019	−	1.01729i	0.994659	−	0.103211i	$-0.0329117\pi$
$908$	757994.	+	2.33287e6i	0.0305106	+	0.0939021i
$909$	−2.30301e7	+	7.08794e7i	−0.924456	+	2.84518i
$910$	−2.03081e7	−	1.47547e7i	−0.812953	−	0.590645i
$911$	1.95004e6			0.0778479			0.0389240	−	0.999242i	$-0.487607\pi$
$911$	1.95004e6			0.0778479			0.0389240	+	0.999242i	$0.487607\pi$
$912$	−5.30043e6	−	3.85099e6i	−0.211020	−	0.153315i
$913$	−872613.	−	633990.i	−0.0346453	−	0.0251713i
$914$	1.35470e7	−	9.84247e6i	0.536386	−	0.389707i
$915$	−6.59989e6	−	2.03124e7i	−0.260606	−	0.802062i
$916$	−9.71388e6			−0.382520
$917$	−6.57480e7	+	4.77688e7i	−2.58202	+	1.87595i
$918$	−1.28618e7	+	3.95847e7i	−0.503729	+	1.55032i
$919$	1.67595e7	+	1.21765e7i	0.654593	+	0.475590i	0.864833	−	0.502060i	$-0.167424\pi$
$919$	1.67595e7	+	1.21765e7i	0.654593	+	0.475590i	−0.210240	+	0.977650i	$0.567424\pi$
$920$	1.00745e6	+	3.10062e6i	0.0392424	+	0.120776i
$921$	9.97185e6	−	3.06902e7i	0.387371	−	1.19220i
$922$	−4.03411e6	+	1.24157e7i	−0.156286	+	0.481000i
$923$	−8.19561e6	+	2.52235e7i	−0.316648	+	0.974542i
$924$	3.43999e6	−	1.05872e7i	0.132549	−	0.407944i
$925$	1.01106e7	+	3.11172e7i	0.388528	+	1.19577i
$926$	1.25032e6	+	908408.i	0.0479173	+	0.0348140i
$927$	1.15256e7	−	3.54721e7i	0.440518	−	1.35578i
$928$	−4.88808e6	+	3.55140e6i	−0.186324	+	0.135372i
$929$	8.58335e6			0.326300			0.163150	−	0.986601i	$-0.447834\pi$
$929$	8.58335e6			0.326300			0.163150	+	0.986601i	$0.447834\pi$
$930$	1.80957e6	+	5.56930e6i	0.0686071	+	0.211151i
$931$	−3.20425e7	+	2.32802e7i	−1.21158	+	0.880265i
$932$	−1.23391e7	−	8.96488e6i	−0.465311	−	0.338069i
$933$	−6.60483e7	−	4.79869e7i	−2.48403	−	1.80476i
$934$	8.61666e6			0.323200
$935$	2.42620e6	+	1.76274e6i	0.0907607	+	0.0659415i
$936$	−1.06480e7	+	3.27711e7i	−0.397263	+	1.22265i
$937$	5.41728e6	+	1.66727e7i	0.201573	+	0.620378i	0.999837	+	0.0180696i	$0.00575205\pi$
$937$	5.41728e6	+	1.66727e7i	0.201573	+	0.620378i	−0.798264	+	0.602308i	$0.794248\pi$
$938$	5.14160e7	−	3.73559e7i	1.90805	−	1.38628i
$939$	−3.90024e7	+	2.83369e7i	−1.44353	+	1.04879i
$940$	1.43998e6			0.0531540
$941$	8.45781e6	+	2.60305e7i	0.311375	+	0.958314i	0.977221	+	0.212224i	$0.0680708\pi$
$941$	8.45781e6	+	2.60305e7i	0.311375	+	0.958314i	−0.665846	+	0.746089i	$0.731929\pi$
$942$	−1.12569e7			−0.413326
$943$	−1.01639e7	+	1.77757e7i	−0.372203	+	0.650948i
$944$	−2.54112e6			−0.0928100
$945$	−1.87982e7	−	5.78549e7i	−0.684757	−	2.10746i
$946$	5.39957e6			0.196170
$947$	2.96221e7	−	2.15217e7i	1.07335	−	0.779834i	0.0968378	−	0.995300i	$-0.469127\pi$
$947$	2.96221e7	−	2.15217e7i	1.07335	−	0.779834i	0.976511	+	0.215466i	$0.0691272\pi$
$948$	1.61946e7	−	1.17660e7i	0.585259	−	0.425216i
$949$	7.99297e6	+	2.45998e7i	0.288100	+	0.886679i
$950$	2.67702e6	−	8.23902e6i	0.0962371	−	0.296187i
$951$	3.83621e7	+	2.78717e7i	1.37547	+	0.999338i
$952$	1.78357e7			0.637819
$953$	4.07426e7	+	2.96012e7i	1.45317	+	1.05579i	0.985078	+	0.172111i	$0.0550588\pi$
$953$	4.07426e7	+	2.96012e7i	1.45317	+	1.05579i	0.468093	+	0.883679i	$0.344941\pi$
$954$	7.33700e6	+	5.33064e6i	0.261004	+	0.189631i
$955$	−1.27813e6	+	928617.i	−0.0453489	+	0.0329479i
$956$	−4.82330e6	−	1.48446e7i	−0.170687	−	0.525320i
$957$	1.66429e7			0.587421
$958$	−2.89356e7	+	2.10230e7i	−1.01864	+	0.740083i
$959$	−9.10906e6	+	2.80348e7i	−0.319836	+	0.984354i
$960$	−2.52489e6	−	1.83444e6i	−0.0884228	−	0.0642429i
$961$	−7.70612e6	−	2.37170e7i	−0.269170	−	0.828421i
$962$	1.59574e7	−	4.91118e7i	0.555935	−	1.71099i
$963$	2.82904e7	−	8.70688e7i	0.983044	−	3.02550i
$964$	1.67791e6	−	5.16407e6i	0.0581535	−	0.178978i
$965$	1.02918e6	−	3.16750e6i	0.0355774	−	0.109496i
$966$	−1.65042e7	−	5.07947e7i	−0.569051	−	1.75136i
$967$	−3.77740e7	−	2.74444e7i	−1.29905	−	0.943818i	−0.299108	−	0.954219i	$-0.596689\pi$
$967$	−3.77740e7	−	2.74444e7i	−1.29905	−	0.943818i	−0.999946	+	0.0104012i	$0.996689\pi$
$968$	2.99078e6	−	9.20469e6i	0.102588	−	0.315734i
$969$	−2.33924e7	+	1.69956e7i	−0.800323	+	0.581469i
$970$	−7.73372e6			−0.263912
$971$	−7.66677e6	−	2.35959e7i	−0.260954	−	0.803135i	−0.992598	−	0.121447i	$-0.961246\pi$
$971$	−7.66677e6	−	2.35959e7i	−0.260954	−	0.803135i	0.731644	−	0.681687i	$-0.238754\pi$
$972$	−1.68374e7	+	1.22331e7i	−0.571624	+	0.415309i
$973$	−1.32956e7	−	9.65983e6i	−0.450222	−	0.327105i
$974$	6.03554e6	+	4.38508e6i	0.203854	+	0.148109i
$975$	−6.50997e7			−2.19315
$976$	5.80533e6	+	4.21782e6i	0.195075	+	0.141731i
$977$	−3.39165e6	+	1.04384e7i	−0.113678	+	0.349864i	−0.991669	−	0.128813i	$-0.958883\pi$
$977$	−3.39165e6	+	1.04384e7i	−0.113678	+	0.349864i	0.877991	+	0.478677i	$0.158883\pi$
$978$	−1.68528e7	−	5.18677e7i	−0.563412	−	1.73400i
$979$	2.56698e6	−	1.86502e6i	0.0855984	−	0.0621908i
$980$	−1.52636e7	+	1.10897e7i	−0.507683	+	0.368853i
$981$	−3.14686e7			−1.04401
$982$	2.69725e6	+	8.30129e6i	0.0892572	+	0.274705i
$983$	−3.79222e7			−1.25173			−0.625864	−	0.779932i	$-0.715253\pi$
$983$	−3.79222e7			−1.25173			−0.625864	+	0.779932i	$0.715253\pi$
$984$	−2.13046e6	−	1.94856e7i	−0.0701433	−	0.641543i
$985$	−2.49583e7			−0.819642
$986$	8.24000e6	+	2.53601e7i	0.269920	+	0.830728i
$987$	−2.35899e7			−0.770784
$988$	−1.10614e7	+	8.03660e6i	−0.360512	+	0.261927i
$989$	2.09582e7	−	1.52270e7i	0.681340	−	0.495022i
$990$	1.85925e6	+	5.72218e6i	0.0602906	+	0.185556i
$991$	4.56486e6	−	1.40492e7i	0.147653	−	0.454430i	−0.849689	−	0.527284i	$-0.823211\pi$
$991$	4.56486e6	−	1.40492e7i	0.147653	−	0.454430i	0.997343	+	0.0728534i	$0.0232105\pi$
$992$	−1.59172e6	−	1.15645e6i	−0.0513556	−	0.0373120i
$993$	−7.11523e7			−2.28990
$994$	2.22817e7	+	1.61886e7i	0.715289	+	0.519688i
$995$	1.51491e7	+	1.10064e7i	0.485096	+	0.352443i
$996$	4.00776e6	−	2.91180e6i	0.128013	−	0.0930066i
$997$	4.52924e6	+	1.39396e7i	0.144307	+	0.444131i	0.996921	−	0.0784097i	$-0.0249842\pi$
$997$	4.52924e6	+	1.39396e7i	0.144307	+	0.444131i	−0.852614	+	0.522541i	$0.824984\pi$
$998$	−7.54325e6			−0.239735
$999$	1.01242e8	−	7.35564e7i	3.20956	−	2.33188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.b.59.9	yes	36
41.16	even	5	inner	82.6.d.b.57.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.b.57.9	✓	36	41.16	even	5	inner
82.6.d.b.59.9	yes	36	1.1	even	1	trivial

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.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +28.4547 q^{3} +(-12.9443 + 9.40456i) q^{4} +(-21.6635 + 15.7394i) q^{5} +(-35.1720 - 108.248i) q^{6} +(-76.2234 + 234.592i) q^{7} +(51.7771 + 37.6183i) q^{8} +566.670 q^{9} +(86.6539 + 62.9578i) q^{10} +(80.1959 + 58.2657i) q^{11} +(-368.325 + 267.604i) q^{12} +(293.601 + 903.610i) q^{13} +986.657 q^{14} +(-616.428 + 447.861i) q^{15} +(79.1084 - 243.470i) q^{16} +(-914.033 - 664.084i) q^{17} +(-700.443 - 2155.74i) q^{18} +(277.934 - 855.392i) q^{19} +(132.395 - 407.471i) q^{20} +(-2168.91 + 6675.23i) q^{21} +(122.528 - 377.104i) q^{22} +(-587.860 - 1809.25i) q^{23} +(1473.30 + 1070.42i) q^{24} +(-744.102 + 2290.11i) q^{25} +(3074.63 - 2233.85i) q^{26} +9209.94 q^{27} +(-1219.57 - 3753.46i) q^{28} +(4773.51 - 3468.16i) q^{29} +(2465.71 + 1791.44i) q^{30} +(1554.42 + 1129.35i) q^{31} -1024.00 q^{32} +(2281.95 + 1657.93i) q^{33} +(-1396.52 + 4298.04i) q^{34} +(-2041.08 - 6281.78i) q^{35} +(-7335.13 + 5329.29i) q^{36} +(10992.6 - 7986.63i) q^{37} -3597.65 q^{38} +(8354.32 + 25712.0i) q^{39} -1713.76 q^{40} +(-7235.69 - 7968.75i) q^{41} +28075.0 q^{42} +(4208.11 + 12951.2i) q^{43} -1586.04 q^{44} +(-12276.1 + 8919.07i) q^{45} +(-6156.15 + 4472.71i) q^{46} +(1038.60 + 3196.48i) q^{47} +(2251.00 - 6927.88i) q^{48} +(-35626.0 - 25883.8i) q^{49} +9631.85 q^{50} +(-26008.5 - 18896.3i) q^{51} +(-12298.5 - 8935.39i) q^{52} +(-3236.89 + 2351.74i) q^{53} +(-11384.1 - 35036.7i) q^{54} -2654.39 q^{55} +(-12771.6 + 9279.07i) q^{56} +(7908.53 - 24339.9i) q^{57} +(-19094.1 - 13872.6i) q^{58} +(-3067.38 - 9440.42i) q^{59} +(3767.27 - 11594.5i) q^{60} +(-8661.87 + 26658.5i) q^{61} +(2374.94 - 7309.30i) q^{62} +(-43193.5 + 132936. i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-20582.7 - 14954.2i) q^{65} +(3486.51 - 10730.4i) q^{66} +(52111.3 - 37861.1i) q^{67} +18076.9 q^{68} +(-16727.4 - 51481.6i) q^{69} +(-21374.4 + 15529.4i) q^{70} +(22583.0 + 16407.5i) q^{71} +(29340.5 + 21317.1i) q^{72} +27223.9 q^{73} +(-43970.6 - 31946.5i) q^{74} +(-21173.2 + 65164.4i) q^{75} +(4446.94 + 13686.3i) q^{76} +(-19781.5 + 14372.1i) q^{77} +(87487.6 - 63563.5i) q^{78} -43968.1 q^{79} +(2118.33 + 6519.54i) q^{80} +124365. q^{81} +(-21371.1 + 37376.1i) q^{82} -10881.0 q^{83} +(-34702.6 - 106804. i) q^{84} +30253.4 q^{85} +(44067.9 - 32017.2i) q^{86} +(135829. - 98685.5i) q^{87} +(1960.45 + 6033.66i) q^{88} +(9891.28 - 30442.2i) q^{89} +(49104.2 + 35676.3i) q^{90} -234359. q^{91} +(24624.6 + 17890.8i) q^{92} +(44230.4 + 32135.3i) q^{93} +(10876.3 - 7902.12i) q^{94} +(7442.38 + 22905.3i) q^{95} -29137.6 q^{96} +(-58413.8 + 42440.1i) q^{97} +(-54431.7 + 167524. i) q^{98} +(45444.6 + 33017.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) \) 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Introduction

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