LMFDB - Embedded newform 82.6.d.b.37.8

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			37.8
Character	$\chi$	$=$	82.37
Dual form			82.6.d.b.51.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23607 - 2.35114i) q^{2} +24.2649 q^{3} +(4.94427 - 15.2169i) q^{4} +(13.8621 - 42.6631i) q^{5} +(78.5227 - 57.0501i) q^{6} +(-139.296 - 101.205i) q^{7} +(-19.7771 - 60.8676i) q^{8} +345.784 q^{9} +(-55.4484 - 170.653i) q^{10} +(-138.603 - 426.575i) q^{11} +(119.972 - 369.236i) q^{12} +(-170.340 + 123.759i) q^{13} -688.719 q^{14} +(336.362 - 1035.22i) q^{15} +(-207.108 - 150.473i) q^{16} +(718.605 + 2211.64i) q^{17} +(1118.98 - 812.986i) q^{18} +(2260.66 + 1642.46i) q^{19} +(-580.663 - 421.876i) q^{20} +(-3380.01 - 2455.72i) q^{21} +(-1451.46 - 1054.55i) q^{22} +(2761.45 - 2006.31i) q^{23} +(-479.888 - 1476.94i) q^{24} +(900.193 + 654.028i) q^{25} +(-260.256 + 800.987i) q^{26} +2494.03 q^{27} +(-2228.74 + 1619.28i) q^{28} +(-2014.52 + 6200.06i) q^{29} +(-1345.45 - 4140.86i) q^{30} +(-1651.46 - 5082.67i) q^{31} -1024.00 q^{32} +(-3363.17 - 10350.8i) q^{33} +(7525.33 + 5467.47i) q^{34} +(-6248.65 + 4539.91i) q^{35} +(1709.65 - 5261.76i) q^{36} +(2357.85 - 7256.73i) q^{37} +11177.3 q^{38} +(-4133.28 + 3003.00i) q^{39} -2870.95 q^{40} +(9806.08 - 4438.14i) q^{41} -16711.7 q^{42} +(1682.31 - 1222.27i) q^{43} -7176.43 q^{44} +(4793.28 - 14752.2i) q^{45} +(4219.12 - 12985.1i) q^{46} +(-8094.48 + 5880.98i) q^{47} +(-5025.46 - 3651.21i) q^{48} +(3967.43 + 12210.5i) q^{49} +4450.80 q^{50} +(17436.9 + 53665.1i) q^{51} +(1041.03 + 3203.95i) q^{52} +(-7355.29 + 22637.3i) q^{53} +(8070.85 - 5863.82i) q^{54} -20120.3 q^{55} +(-3405.21 + 10480.2i) q^{56} +(54854.5 + 39854.1i) q^{57} +(8058.09 + 24800.2i) q^{58} +(13891.5 - 10092.8i) q^{59} +(-14089.7 - 10236.8i) q^{60} +(-6381.51 - 4636.44i) q^{61} +(-17294.3 - 12565.1i) q^{62} +(-48166.4 - 34994.9i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(2918.69 + 8982.80i) q^{65} +(-35219.6 - 25588.5i) q^{66} +(-16340.1 + 50289.5i) q^{67} +37207.3 q^{68} +(67006.2 - 48682.9i) q^{69} +(-9547.09 + 29382.9i) q^{70} +(-3054.37 - 9400.38i) q^{71} +(-6838.59 - 21047.0i) q^{72} -32298.0 q^{73} +(-9431.42 - 29026.9i) q^{74} +(21843.1 + 15869.9i) q^{75} +(36170.5 - 26279.4i) q^{76} +(-23864.6 + 73447.5i) q^{77} +(-6315.09 + 19435.8i) q^{78} +24715.7 q^{79} +(-9290.61 + 6750.02i) q^{80} -23508.1 q^{81} +(21298.4 - 37417.6i) q^{82} -68840.9 q^{83} +(-54080.1 + 39291.5i) q^{84} +104317. q^{85} +(2570.34 - 7910.71i) q^{86} +(-48882.1 + 150444. i) q^{87} +(-23223.4 + 16872.8i) q^{88} +(-9868.43 - 7169.83i) q^{89} +(-19173.1 - 59008.8i) q^{90} +36252.8 q^{91} +(-16876.5 - 51940.5i) q^{92} +(-40072.5 - 123330. i) q^{93} +(-12367.3 + 38062.5i) q^{94} +(101410. - 73678.7i) q^{95} -24847.2 q^{96} +(31988.7 - 98451.0i) q^{97} +(41547.5 + 30186.0i) q^{98} +(-47926.5 - 147503. i) 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 $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$3$	24.2649			1.55659			0.778296	−	0.627898i	$-0.216084\pi$
$3$	24.2649			1.55659			0.778296	+	0.627898i	$0.216084\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	13.8621	−	42.6631i	0.247973	−	0.763181i	−0.747161	−	0.664643i	$-0.768583\pi$
$5$	13.8621	−	42.6631i	0.247973	−	0.763181i	0.995133	−	0.0985378i	$-0.0314165\pi$
$6$	78.5227	−	57.0501i	0.890466	−	0.646961i
$7$	−139.296	−	101.205i	−1.07447	−	0.780649i	−0.0977605	−	0.995210i	$-0.531168\pi$
$7$	−139.296	−	101.205i	−1.07447	−	0.780649i	−0.976711	+	0.214561i	$0.931168\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$	345.784			1.42298
$10$	−55.4484	−	170.653i	−0.175343	−	0.539651i
$11$	−138.603	−	426.575i	−0.345374	−	1.06295i	−0.961383	−	0.275213i	$-0.911252\pi$
$11$	−138.603	−	426.575i	−0.345374	−	1.06295i	0.616010	−	0.787739i	$-0.288748\pi$
$12$	119.972	−	369.236i	0.240507	−	0.740203i
$13$	−170.340	+	123.759i	−0.279549	+	0.203104i	−0.718721	−	0.695299i	$-0.755272\pi$
$13$	−170.340	+	123.759i	−0.279549	+	0.203104i	0.439171	+	0.898403i	$0.355272\pi$
$14$	−688.719			−0.939122
$15$	336.362	−	1035.22i	0.385992	−	1.18796i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	718.605	+	2211.64i	0.603071	+	1.85606i	0.509546	+	0.860444i	$0.329813\pi$
$17$	718.605	+	2211.64i	0.603071	+	1.85606i	0.0935248	+	0.995617i	$0.470187\pi$
$18$	1118.98	−	812.986i	0.814031	−	0.591428i
$19$	2260.66	+	1642.46i	1.43665	+	1.04379i	0.988730	+	0.149712i	$0.0478345\pi$
$19$	2260.66	+	1642.46i	1.43665	+	1.04379i	0.447919	+	0.894074i	$0.352165\pi$
$20$	−580.663	−	421.876i	−0.324600	−	0.235836i
$21$	−3380.01	−	2455.72i	−1.67251	−	1.21515i
$22$	−1451.46	−	1054.55i	−0.639366	−	0.464527i
$23$	2761.45	−	2006.31i	1.08847	−	0.790822i	0.109332	−	0.994005i	$-0.465129\pi$
$23$	2761.45	−	2006.31i	1.08847	−	0.790822i	0.979141	+	0.203184i	$0.0651288\pi$
$24$	−479.888	−	1476.94i	−0.170064	−	0.523403i
$25$	900.193	+	654.028i	0.288062	+	0.209289i
$26$	−260.256	+	800.987i	−0.0755037	+	0.232376i
$27$	2494.03			0.658404
$28$	−2228.74	+	1619.28i	−0.537236	+	0.390324i
$29$	−2014.52	+	6200.06i	−0.444813	+	1.36899i	0.437877	+	0.899035i	$0.355731\pi$
$29$	−2014.52	+	6200.06i	−0.444813	+	1.36899i	−0.882689	+	0.469957i	$0.844269\pi$
$30$	−1345.45	−	4140.86i	−0.272938	−	0.840016i
$31$	−1651.46	−	5082.67i	−0.308648	−	0.949922i	−0.978291	−	0.207238i	$-0.933553\pi$
$31$	−1651.46	−	5082.67i	−0.308648	−	0.949922i	0.669642	−	0.742684i	$-0.266447\pi$
$32$	−1024.00			−0.176777
$33$	−3363.17	−	10350.8i	−0.537606	−	1.65458i
$34$	7525.33	+	5467.47i	1.11642	+	0.811128i
$35$	−6248.65	+	4539.91i	−0.862216	+	0.626437i
$36$	1709.65	−	5261.76i	0.219862	−	0.676666i
$37$	2357.85	−	7256.73i	0.283147	−	0.871438i	−0.703800	−	0.710398i	$-0.748515\pi$
$37$	2357.85	−	7256.73i	0.283147	−	0.871438i	0.986948	−	0.161040i	$-0.0514849\pi$
$38$	11177.3			1.25568
$39$	−4133.28	+	3003.00i	−0.435144	+	0.316151i
$40$	−2870.95			−0.283711
$41$	9806.08	−	4438.14i	0.911036	−	0.412327i
$41$	9806.08	−	4438.14i	0.911036	−	0.412327i
$42$	−16711.7			−1.46183
$43$	1682.31	−	1222.27i	0.138751	−	0.100808i	−0.516245	−	0.856441i	$-0.672671\pi$
$43$	1682.31	−	1222.27i	0.138751	−	0.100808i	0.654996	+	0.755633i	$0.272671\pi$
$44$	−7176.43			−0.558827
$45$	4793.28	−	14752.2i	0.352860	−	1.08599i
$46$	4219.12	−	12985.1i	0.293986	−	0.904797i
$47$	−8094.48	+	5880.98i	−0.534496	+	0.388334i	−0.822037	−	0.569435i	$-0.807162\pi$
$47$	−8094.48	+	5880.98i	−0.534496	+	0.388334i	0.287541	+	0.957768i	$0.407162\pi$
$48$	−5025.46	−	3651.21i	−0.314827	−	0.228735i
$49$	3967.43	+	12210.5i	0.236058	+	0.726513i
$50$	4450.80			0.251775
$51$	17436.9	+	53665.1i	0.938735	+	2.88913i
$52$	1041.03	+	3203.95i	0.0533892	+	0.164315i
$53$	−7355.29	+	22637.3i	−0.359675	+	1.10697i	0.593574	+	0.804780i	$0.297716\pi$
$53$	−7355.29	+	22637.3i	−0.359675	+	1.10697i	−0.953249	+	0.302186i	$0.902284\pi$
$54$	8070.85	−	5863.82i	0.376647	−	0.273650i
$55$	−20120.3			−0.896868
$56$	−3405.21	+	10480.2i	−0.145102	+	0.446579i
$57$	54854.5	+	39854.1i	2.23627	+	1.62475i
$58$	8058.09	+	24800.2i	0.314530	+	0.968024i
$59$	13891.5	−	10092.8i	0.519540	−	0.377468i	−0.296890	−	0.954912i	$-0.595950\pi$
$59$	13891.5	−	10092.8i	0.519540	−	0.377468i	0.816431	+	0.577443i	$0.195950\pi$
$60$	−14089.7	−	10236.8i	−0.505270	−	0.367100i
$61$	−6381.51	−	4636.44i	−0.219583	−	0.159536i	0.472556	−	0.881301i	$-0.343331\pi$
$61$	−6381.51	−	4636.44i	−0.219583	−	0.159536i	−0.692139	+	0.721764i	$0.743331\pi$
$62$	−17294.3	−	12565.1i	−0.571379	−	0.415131i
$63$	−48166.4	−	34994.9i	−1.52895	−	1.11085i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	2918.69	+	8982.80i	0.0856850	+	0.263711i
$66$	−35219.6	−	25588.5i	−0.995232	−	0.723078i
$67$	−16340.1	+	50289.5i	−0.444700	+	1.36864i	0.438113	+	0.898920i	$0.355647\pi$
$67$	−16340.1	+	50289.5i	−0.444700	+	1.36864i	−0.882813	+	0.469725i	$0.844353\pi$
$68$	37207.3			0.975789
$69$	67006.2	−	48682.9i	1.69431	−	1.23099i
$70$	−9547.09	+	29382.9i	−0.232877	+	0.716720i
$71$	−3054.37	−	9400.38i	−0.0719077	−	0.221309i	0.908643	−	0.417573i	$-0.137119\pi$
$71$	−3054.37	−	9400.38i	−0.0719077	−	0.221309i	−0.980551	+	0.196264i	$0.937119\pi$
$72$	−6838.59	−	21047.0i	−0.155466	−	0.478475i
$73$	−32298.0			−0.709363			−0.354682	−	0.934987i	$-0.615411\pi$
$73$	−32298.0			−0.709363			−0.354682	+	0.934987i	$0.615411\pi$
$74$	−9431.42	−	29026.9i	−0.200215	−	0.616200i
$75$	21843.1	+	15869.9i	0.448395	+	0.325778i
$76$	36170.5	−	26279.4i	0.718324	−	0.521893i
$77$	−23864.6	+	73447.5i	−0.458698	+	1.41173i
$78$	−6315.09	+	19435.8i	−0.117528	+	0.361715i
$79$	24715.7			0.445559			0.222780	−	0.974869i	$-0.428487\pi$
$79$	24715.7			0.445559			0.222780	+	0.974869i	$0.428487\pi$
$80$	−9290.61	+	6750.02i	−0.162300	+	0.117918i
$81$	−23508.1			−0.398112
$82$	21298.4	−	37417.6i	0.349795	−	0.614527i
$83$	−68840.9			−1.09686			−0.548430	−	0.836196i	$-0.684774\pi$
$83$	−68840.9			−1.09686			−0.548430	+	0.836196i	$0.684774\pi$
$84$	−54080.1	+	39291.5i	−0.836256	+	0.607576i
$85$	104317.			1.56606
$86$	2570.34	−	7910.71i	0.0374753	−	0.115337i
$87$	−48882.1	+	150444.i	−0.692392	+	2.13096i
$88$	−23223.4	+	16872.8i	−0.319683	+	0.232263i
$89$	−9868.43	−	7169.83i	−0.132061	−	0.0959476i	0.519794	−	0.854292i	$-0.326009\pi$
$89$	−9868.43	−	7169.83i	−0.132061	−	0.0959476i	−0.651854	+	0.758344i	$0.726009\pi$
$90$	−19173.1	−	59008.8i	−0.249509	−	0.767911i
$91$	36252.8			0.458921
$92$	−16876.5	−	51940.5i	−0.207880	−	0.639788i
$93$	−40072.5	−	123330.i	−0.480440	−	1.47864i
$94$	−12367.3	+	38062.5i	−0.144362	+	0.444301i
$95$	101410.	−	73678.7i	1.15285	−	0.837593i
$96$	−24847.2			−0.275169
$97$	31988.7	−	98451.0i	0.345197	−	1.06241i	−0.616281	−	0.787526i	$-0.711362\pi$
$97$	31988.7	−	98451.0i	0.345197	−	1.06241i	0.961478	−	0.274881i	$-0.0886384\pi$
$98$	41547.5	+	30186.0i	0.436998	+	0.317498i
$99$	−47926.5	−	147503.i	−0.491459	−	1.51256i
$100$	14403.1	−	10464.5i	0.144031	−	0.104645i
$101$	2668.35	+	1938.67i	0.0260279	+	0.0189104i	0.600723	−	0.799457i	$-0.294879\pi$
$101$	2668.35	+	1938.67i	0.0260279	+	0.0189104i	−0.574695	+	0.818367i	$0.694879\pi$
$102$	182601.	+	132668.i	1.73781	+	1.26260i
$103$	62518.0	+	45422.0i	0.580647	+	0.421864i	0.838957	−	0.544198i	$-0.183166\pi$
$103$	62518.0	+	45422.0i	0.580647	+	0.421864i	−0.258311	+	0.966062i	$0.583166\pi$
$104$	10901.8	+	7920.60i	0.0988356	+	0.0718083i
$105$	−151623.	+	110160.i	−1.34212	+	0.975106i
$106$	29421.2	+	90549.1i	0.254329	+	0.782743i
$107$	−130644.	−	94918.2i	−1.10314	−	0.801475i	−0.121567	−	0.992583i	$-0.538792\pi$
$107$	−130644.	−	94918.2i	−1.10314	−	0.801475i	−0.981569	+	0.191108i	$0.938792\pi$
$108$	12331.2	−	37951.4i	0.101729	−	0.313090i
$109$	−180685.			−1.45665			−0.728327	−	0.685229i	$-0.759702\pi$
$109$	−180685.			−1.45665			−0.728327	+	0.685229i	$0.759702\pi$
$110$	−65110.8	+	47305.7i	−0.513063	+	0.372762i
$111$	57213.0	−	176084.i	0.440745	−	1.35647i
$112$	13620.9	+	41920.7i	0.102603	+	0.315779i
$113$	27814.0	+	85602.7i	0.204912	+	0.630654i	0.999717	+	0.0237893i	$0.00757308\pi$
$113$	27814.0	+	85602.7i	0.204912	+	0.630654i	−0.794805	+	0.606865i	$0.792427\pi$
$114$	271216.			1.95458
$115$	−47316.0	−	145624.i	−0.333629	−	1.02680i
$116$	84385.4	+	61309.6i	0.582267	+	0.423042i
$117$	−58900.8	+	42793.9i	−0.397793	+	0.289013i
$118$	21224.3	−	65321.8i	0.140323	−	0.431870i
$119$	123729.	−	380800.i	0.800950	−	2.46507i
$120$	−69663.3			−0.441622
$121$	−32462.3	+	23585.2i	−0.201565	+	0.146446i
$122$	−31551.9			−0.191923
$123$	237943.	−	107691.i	1.41811	−	0.641824i
$124$	−85507.8			−0.499404
$125$	153792.	−	111737.i	0.880358	−	0.639617i
$126$	−238148.			−1.33635
$127$	−37316.0	+	114847.i	−0.205298	+	0.631844i	0.794403	+	0.607392i	$0.207784\pi$
$127$	−37316.0	+	114847.i	−0.205298	+	0.631844i	−0.999701	+	0.0244520i	$0.992216\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$	40821.1	−	29658.2i	0.215978	−	0.156917i
$130$	30564.9	+	22206.7i	0.158623	+	0.115246i
$131$	77604.3	+	238842.i	0.395101	+	1.21599i	0.928883	+	0.370373i	$0.120770\pi$
$131$	77604.3	+	238842.i	0.395101	+	1.21599i	−0.533782	+	0.845622i	$0.679230\pi$
$132$	−174135.			−0.869865
$133$	−148676.	−	457578.i	−0.728806	−	2.24304i
$134$	65360.2	+	201158.i	0.314450	+	0.967778i
$135$	34572.5	−	106403.i	0.163266	−	0.502482i
$136$	120405.	−	87479.6i	0.558211	−	0.405564i
$137$	−355539.			−1.61840			−0.809200	−	0.587534i	$-0.800099\pi$
$137$	−355539.			−1.61840			−0.809200	+	0.587534i	$0.800099\pi$
$138$	102376.	−	315082.i	0.457617	−	1.40840i
$139$	66305.1	+	48173.5i	0.291078	+	0.211481i	0.723735	−	0.690078i	$-0.242424\pi$
$139$	66305.1	+	48173.5i	0.291078	+	0.211481i	−0.432657	+	0.901559i	$0.642424\pi$
$140$	38188.4	+	117532.i	0.164669	+	0.506798i
$141$	−196411.	+	142701.i	−0.831991	+	0.604477i
$142$	−31985.8	−	23239.0i	−0.133118	−	0.0967157i
$143$	76402.2	+	55509.4i	0.312439	+	0.227000i
$144$	−71614.7	−	52031.1i	−0.287803	−	0.209101i
$145$	236589.	+	171892.i	0.934488	+	0.678945i
$146$	−104519.	+	75937.2i	−0.405799	+	0.294830i
$147$	96269.2	+	296286.i	0.367446	+	1.13088i
$148$	−98767.1	−	71758.5i	−0.370645	−	0.269289i
$149$	35656.0	−	109738.i	0.131573	−	0.404940i	−0.863468	−	0.504403i	$-0.831713\pi$
$149$	35656.0	−	109738.i	0.131573	−	0.404940i	0.995041	+	0.0994630i	$0.0317125\pi$
$150$	107998.			0.391911
$151$	−152966.	+	111136.i	−0.545950	+	0.396656i	−0.826290	−	0.563245i	$-0.809553\pi$
$151$	−152966.	+	111136.i	−0.545950	+	0.396656i	0.280340	+	0.959901i	$0.409553\pi$
$152$	55263.6	−	170084.i	0.194013	−	0.597110i
$153$	248482.	+	764749.i	0.858156	+	2.64113i
$154$	95458.2	+	293790.i	0.324348	+	0.998241i
$155$	−239735.			−0.801499
$156$	25260.4	+	77743.4i	0.0831051	+	0.255771i
$157$	−11750.1	−	8536.97i	−0.0380446	−	0.0276410i	0.568600	−	0.822614i	$-0.307485\pi$
$157$	−11750.1	−	8536.97i	−0.0380446	−	0.0276410i	−0.606645	+	0.794973i	$0.707485\pi$
$158$	79981.7	−	58110.1i	0.254887	−	0.185186i
$159$	−178475.	+	549290.i	−0.559867	+	1.72309i
$160$	−14194.8	+	43687.0i	−0.0438358	+	0.134913i
$161$	−587708.			−1.78689
$162$	−76073.8	+	55270.9i	−0.227744	+	0.165466i
$163$	553600.			1.63203			0.816013	−	0.578033i	$-0.196179\pi$
$163$	553600.			1.63203			0.816013	+	0.578033i	$0.196179\pi$
$164$	−19050.8	−	171161.i	−0.0553101	−	0.496931i
$165$	−488217.			−1.39606
$166$	−222774.	+	161855.i	−0.627471	+	0.455885i
$167$	29587.1			0.0820941			0.0410470	−	0.999157i	$-0.486931\pi$
$167$	29587.1			0.0820941			0.0410470	+	0.999157i	$0.486931\pi$
$168$	−82627.1	+	254300.i	−0.225865	+	0.695141i
$169$	−101036.	+	310958.i	−0.272121	+	0.837501i
$170$	337576.	−	245264.i	0.895880	−	0.650895i
$171$	781698.	+	567937.i	2.04432	+	1.48528i
$172$	−10281.4	−	31642.8i	−0.0264990	−	0.0815557i
$173$	−375611.			−0.954163			−0.477082	−	0.878859i	$-0.658305\pi$
$173$	−375611.			−0.954163			−0.477082	+	0.878859i	$0.658305\pi$
$174$	195528.	+	601775.i	0.489595	+	1.50682i
$175$	−59202.8	−	182208.i	−0.146133	−	0.449750i
$176$	−35482.2	+	109203.i	−0.0863435	+	0.265738i
$177$	337075.	−	244900.i	0.808712	−	0.587564i
$178$	−48792.2			−0.115425
$179$	128202.	−	394564.i	0.299062	−	0.920419i	−0.682765	−	0.730638i	$-0.739223\pi$
$179$	128202.	−	394564.i	0.299062	−	0.920419i	0.981827	−	0.189780i	$-0.0607775\pi$
$180$	−200784.	−	145878.i	−0.461899	−	0.335589i
$181$	107241.	+	330054.i	0.243313	+	0.748839i	0.995909	+	0.0903575i	$0.0288010\pi$
$181$	107241.	+	330054.i	0.243313	+	0.748839i	−0.752597	+	0.658482i	$0.771199\pi$
$182$	117316.	−	85235.4i	0.262531	−	0.190740i
$183$	−154846.	−	112502.i	−0.341801	−	0.248333i
$184$	−176733.	−	128404.i	−0.384833	−	0.279598i
$185$	−276910.	−	201187.i	−0.594852	−	0.432186i
$186$	−419644.	−	304889.i	−0.889404	−	0.646190i
$187$	843829.	−	613078.i	1.76462	−	1.28207i
$188$	49469.0	+	152250.i	0.102080	+	0.314169i
$189$	−347409.	−	252408.i	−0.707436	−	0.513982i
$190$	154941.	−	476858.i	0.311373	−	0.958309i
$191$	47929.2			0.0950641			0.0475320	−	0.998870i	$-0.484864\pi$
$191$	47929.2			0.0950641			0.0475320	+	0.998870i	$0.484864\pi$
$192$	−80407.3	+	58419.3i	−0.157414	+	0.114368i
$193$	−109216.	+	336133.i	−0.211054	+	0.649557i	0.788356	+	0.615219i	$0.210932\pi$
$193$	−109216.	+	336133.i	−0.211054	+	0.649557i	−0.999410	+	0.0343382i	$0.989068\pi$
$194$	−127955.	−	393804.i	−0.244091	−	0.751235i
$195$	70821.6	+	217967.i	0.133376	+	0.410491i
$196$	205422.			0.381950
$197$	−255584.	−	786607.i	−0.469211	−	1.44408i	−0.853608	−	0.520916i	$-0.825591\pi$
$197$	−255584.	−	786607.i	−0.469211	−	1.44408i	0.384397	−	0.923168i	$-0.374409\pi$
$198$	−501893.	−	364646.i	−0.909804	−	0.661011i
$199$	−263623.	+	191534.i	−0.471901	+	0.342856i	−0.798182	−	0.602417i	$-0.794205\pi$
$199$	−263623.	+	191534.i	−0.471901	+	0.342856i	0.326281	+	0.945273i	$0.394205\pi$
$200$	22006.0	−	67727.4i	0.0389014	−	0.119726i
$201$	−396489.	+	1.22027e6i	−0.692216	+	2.13042i
$202$	13193.0			0.0227492
$203$	908091.	−	659767.i	1.54664	−	1.12370i
$204$	902830.			1.51890
$205$	−53412.2	−	479880.i	−0.0887678	−	0.797531i
$206$	309106.			0.507504
$207$	954864.	−	693749.i	1.54887	−	1.12532i
$208$	53901.3			0.0863855
$209$	387300.	−	1.19199e6i	0.613313	−	1.88758i
$210$	−231659.	+	712972.i	−0.362494	+	1.11564i
$211$	−10409.5	+	7562.93i	−0.0160962	+	0.0116946i	−0.595804	−	0.803130i	$-0.703167\pi$
$211$	−10409.5	+	7562.93i	−0.0160962	+	0.0116946i	0.579708	+	0.814824i	$0.303167\pi$
$212$	308103.	+	223850.i	0.470821	+	0.342071i
$213$	−74113.8	−	228099.i	−0.111931	−	0.344488i
$214$	−645938.			−0.964176
$215$	−28825.6	−	88715.9i	−0.0425286	−	0.130890i
$216$	−49324.7	−	151806.i	−0.0719333	−	0.221388i
$217$	−284348.	+	875134.i	−0.409922	+	1.26161i
$218$	−584710.	+	424817.i	−0.833296	+	0.605425i
$219$	−783707.			−1.10419
$220$	−99480.4	+	306169.i	−0.138574	+	0.426486i
$221$	−396118.	−	287797.i	−0.545562	−	0.396374i
$222$	−228852.	−	704334.i	−0.311654	−	0.959171i
$223$	328190.	−	238444.i	0.441940	−	0.321088i	−0.344465	−	0.938799i	$-0.611940\pi$
$223$	328190.	−	238444.i	0.441940	−	0.321088i	0.786405	+	0.617711i	$0.211940\pi$
$224$	142639.	+	103634.i	0.189941	+	0.138001i
$225$	311272.	+	226152.i	0.409905	+	0.297814i
$226$	291272.	+	211621.i	0.379339	+	0.275606i
$227$	−79267.2	−	57591.0i	−0.102101	−	0.0741806i	0.535563	−	0.844495i	$-0.320099\pi$
$227$	−79267.2	−	57591.0i	−0.102101	−	0.0741806i	−0.637664	+	0.770314i	$0.720099\pi$
$228$	877672.	−	637666.i	1.11814	−	0.812374i
$229$	79627.9	+	245069.i	0.100341	+	0.308816i	0.988609	−	0.150509i	$-0.0480912\pi$
$229$	79627.9	+	245069.i	0.100341	+	0.308816i	−0.888268	+	0.459325i	$0.848091\pi$
$230$	−495500.	−	360002.i	−0.617624	−	0.448730i
$231$	−579070.	+	1.78219e6i	−0.714005	+	2.19748i
$232$	417224.			0.508920
$233$	1.04077e6	−	756167.i	1.25593	−	0.912490i	0.257384	−	0.966309i	$-0.417140\pi$
$233$	1.04077e6	−	756167.i	1.25593	−	0.912490i	0.998551	+	0.0538195i	$0.0171396\pi$
$234$	−89992.4	+	276968.i	−0.107440	+	0.330667i
$235$	138695.	+	426858.i	0.163829	+	0.504213i
$236$	−84897.3	−	261287.i	−0.0992234	−	0.305378i
$237$	599724.			0.693554
$238$	−494917.	−	1.52320e6i	−0.566357	−	1.74307i
$239$	137228.	+	99702.3i	0.155399	+	0.112904i	0.662768	−	0.748825i	$-0.269382\pi$
$239$	137228.	+	99702.3i	0.155399	+	0.112904i	−0.507368	+	0.861729i	$0.669382\pi$
$240$	−225435.	+	163788.i	−0.252635	+	0.183550i
$241$	−360797.	+	1.11042e6i	−0.400148	+	1.23153i	0.524732	+	0.851267i	$0.324165\pi$
$241$	−360797.	+	1.11042e6i	−0.400148	+	1.23153i	−0.924880	+	0.380260i	$0.875835\pi$
$242$	−49598.0	+	152647.i	−0.0544409	+	0.167552i
$243$	−1.17647e6			−1.27810
$244$	−102104.	+	74183.0i	−0.109791	+	0.0797682i
$245$	575935.			0.612997
$246$	516804.	−	907933.i	0.544487	−	0.956568i
$247$	−588350.			−0.613612
$248$	−276709.	+	201041.i	−0.285690	+	0.207566i
$249$	−1.67041e6			−1.70736
$250$	234974.	−	723174.i	0.237776	−	0.731801i
$251$	339240.	−	1.04407e6i	0.339878	−	1.04604i	−0.624391	−	0.781112i	$-0.714653\pi$
$251$	339240.	−	1.04407e6i	0.339878	−	1.04604i	0.964269	−	0.264925i	$-0.0853471\pi$
$252$	−770662.	+	559919.i	−0.764474	+	0.555423i
$253$	−1.23859e6	−	899885.i	−1.21653	−	0.883864i
$254$	149264.	+	459387.i	0.145168	+	0.446781i
$255$	2.53123e6			2.43771
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−59890.1	−	184323.i	−0.0565616	−	0.174079i	0.918784	−	0.394760i	$-0.129172\pi$
$257$	−59890.1	−	184323.i	−0.0565616	−	0.174079i	−0.975346	+	0.220681i	$0.929172\pi$
$258$	62369.1	−	191952.i	0.0583337	−	0.179533i
$259$	−1.06286e6	+	772210.i	−0.984521	+	0.715296i
$260$	151121.			0.138641
$261$	−696589.	+	2.14388e6i	−0.632958	+	1.94805i
$262$	812683.	+	590449.i	0.731422	+	0.531409i
$263$	311256.	+	957946.i	0.277477	+	0.853988i	0.988553	+	0.150872i	$0.0482083\pi$
$263$	311256.	+	957946.i	0.277477	+	0.853988i	−0.711076	+	0.703115i	$0.751792\pi$
$264$	−563513.	+	409416.i	−0.497616	+	0.361539i
$265$	863817.	+	627600.i	0.755626	+	0.548995i
$266$	−1.55696e6	−	1.13120e6i	−1.34919	−	0.980243i
$267$	−239456.	−	173975.i	−0.205564	−	0.149351i
$268$	684461.	+	497290.i	0.582119	+	0.422934i
$269$	952613.	−	692114.i	0.802668	−	0.583172i	−0.109028	−	0.994039i	$-0.534774\pi$
$269$	952613.	−	692114.i	0.802668	−	0.583172i	0.911696	+	0.410866i	$0.134774\pi$
$270$	−138290.	−	425613.i	−0.115447	−	0.355308i
$271$	316124.	+	229677.i	0.261477	+	0.189974i	0.710798	−	0.703396i	$-0.248334\pi$
$271$	316124.	+	229677.i	0.261477	+	0.189974i	−0.449321	+	0.893371i	$0.648334\pi$
$272$	183963.	−	566180.i	0.150768	−	0.464015i
$273$	879669.			0.714353
$274$	−1.15055e6	+	835922.i	−0.925824	+	0.672650i
$275$	154223.	−	474649.i	0.122975	−	0.378479i
$276$	−409505.	−	1.26033e6i	−0.323584	−	0.995889i
$277$	628167.	+	1.93330e6i	0.491899	+	1.51391i	0.821735	+	0.569870i	$0.193006\pi$
$277$	628167.	+	1.93330e6i	0.491899	+	1.51391i	−0.329836	+	0.944038i	$0.606994\pi$
$278$	327831.			0.254412
$279$	−571048.	−	1.75751e6i	−0.439200	−	1.35172i
$280$	399914.	+	290554.i	0.304839	+	0.221479i
$281$	869073.	−	631419.i	0.656585	−	0.477037i	−0.208923	−	0.977932i	$-0.566996\pi$
$281$	869073.	−	631419.i	0.656585	−	0.477037i	0.865508	+	0.500895i	$0.166996\pi$
$282$	−300090.	+	923582.i	−0.224713	+	0.691596i
$283$	467118.	−	1.43764e6i	0.346705	−	1.06705i	−0.613960	−	0.789337i	$-0.710424\pi$
$283$	467118.	−	1.43764e6i	0.346705	−	1.06705i	0.960665	−	0.277711i	$-0.0895757\pi$
$284$	−158146.			−0.116349
$285$	2.46070e6	−	1.78780e6i	1.79451	−	1.30379i
$286$	377753.			0.273082
$287$	−1.81511e6	−	374205.i	−1.30076	−	0.268166i
$288$	−354082.			−0.251549
$289$	−3.22627e6	+	2.34402e6i	−2.27225	+	1.65089i
$290$	1.16976e6			0.816772
$291$	776201.	−	2.38890e6i	0.537331	−	1.65373i
$292$	−159690.	+	491476.i	−0.109603	+	0.337322i
$293$	1.17675e6	−	854962.i	0.800787	−	0.581805i	−0.110358	−	0.993892i	$-0.535200\pi$
$293$	1.17675e6	−	854962.i	0.800787	−	0.581805i	0.911145	+	0.412086i	$0.135200\pi$
$294$	1.00814e6	+	732460.i	0.680228	+	0.494214i
$295$	−238024.	−	732562.i	−0.159245	−	0.490105i
$296$	−488331.			−0.323955
$297$	−345679.	−	1.06389e6i	−0.227395	−	0.699851i
$298$	−142624.	−	438952.i	−0.0930362	−	0.286336i
$299$	−222086.	+	683510.i	−0.143662	+	0.442147i
$300$	349489.	−	253919.i	0.224197	−	0.162889i
$301$	−358040.			−0.227780
$302$	−233711.	+	719290.i	−0.147456	+	0.453823i
$303$	64747.1	+	47041.5i	0.0405148	+	0.0294357i
$304$	−221054.	−	680335.i	−0.137188	−	0.422220i
$305$	−286266.	+	207984.i	−0.176206	+	0.128021i
$306$	2.60214e6	+	1.89056e6i	1.58864	+	1.15422i
$307$	1.03460e6	+	751681.i	0.626508	+	0.455185i	0.855189	−	0.518317i	$-0.173441\pi$
$307$	1.03460e6	+	751681.i	0.626508	+	0.455185i	−0.228681	+	0.973502i	$0.573441\pi$
$308$	999651.	+	726289.i	0.600443	+	0.436247i
$309$	1.51699e6	+	1.10216e6i	0.903830	+	0.656671i
$310$	−775800.	+	563652.i	−0.458507	+	0.333125i
$311$	−736714.	−	2.26737e6i	−0.431915	−	1.32930i	−0.896216	−	0.443619i	$-0.853694\pi$
$311$	−736714.	−	2.26737e6i	−0.431915	−	1.32930i	0.464301	−	0.885677i	$-0.346306\pi$
$312$	264530.	+	192192.i	0.153847	+	0.111776i
$313$	−467331.	+	1.43830e6i	−0.269627	+	0.829826i	0.720964	+	0.692972i	$0.243699\pi$
$313$	−467331.	+	1.43830e6i	−0.269627	+	0.829826i	−0.990591	+	0.136854i	$0.956301\pi$
$314$	−58095.8			−0.0332522
$315$	−2.16068e6	+	1.56983e6i	−1.22691	+	0.891405i
$316$	122201.	−	376097.i	0.0688427	−	0.211876i
$317$	591898.	+	1.82167e6i	0.330825	+	1.01818i	0.968742	+	0.248070i	$0.0797964\pi$
$317$	591898.	+	1.82167e6i	0.330825	+	1.01818i	−0.637917	+	0.770105i	$0.720204\pi$
$318$	713901.	+	2.19716e6i	0.395886	+	1.21841i
$319$	2.92401e6			1.60880
$320$	56779.1	+	174748.i	0.0309966	+	0.0953977i
$321$	−3.17005e6	−	2.30318e6i	−1.71713	−	1.24757i
$322$	−1.90186e6	+	1.38178e6i	−1.02221	+	0.742678i
$323$	−2.00802e6	+	6.18004e6i	−1.07093	+	3.29598i
$324$	−116230.	+	357721.i	−0.0615117	+	0.189313i
$325$	−234281.			−0.123035
$326$	1.79149e6	−	1.30159e6i	0.933620	−	0.678314i
$327$	−4.38430e6			−2.26742
$328$	−464075.	−	509099.i	−0.238179	−	0.261287i
$329$	1.72271e6			0.877452
$330$	−1.57990e6	+	1.14787e6i	−0.798630	+	0.580239i
$331$	−2.44942e6			−1.22883			−0.614417	−	0.788982i	$-0.710609\pi$
$331$	−2.44942e6			−1.22883			−0.614417	+	0.788982i	$0.710609\pi$
$332$	−340368.	+	1.04755e6i	−0.169474	+	0.521588i
$333$	815307.	−	2.50926e6i	0.402912	−	1.24004i
$334$	95746.0	−	69563.5i	0.0469628	−	0.0341205i
$335$	1.91900e6	+	1.39424e6i	0.934251	+	0.678773i
$336$	330508.	+	1.01720e6i	0.159711	+	0.491539i
$337$	663612.			0.318302			0.159151	−	0.987254i	$-0.449124\pi$
$337$	663612.			0.318302			0.159151	+	0.987254i	$0.449124\pi$
$338$	404146.	+	1.24383e6i	0.192418	+	0.592203i
$339$	674903.	+	2.07714e6i	0.318964	+	0.981671i
$340$	515771.	−	1.58738e6i	0.241969	−	0.744704i
$341$	−1.93924e6	+	1.40894e6i	−0.903122	+	0.656156i
$342$	3.86493e6			1.78680
$343$	−211130.	+	649790.i	−0.0968978	+	0.298221i
$344$	−107668.	−	78225.4i	−0.0490558	−	0.0356411i
$345$	−1.14812e6	−	3.53354e6i	−0.519324	−	1.59831i
$346$	−1.21550e6	+	883114.i	−0.545840	+	0.396576i
$347$	727169.	+	528319.i	0.324199	+	0.235544i	0.737965	−	0.674839i	$-0.235787\pi$
$347$	727169.	+	528319.i	0.324199	+	0.235544i	−0.413766	+	0.910383i	$0.635787\pi$
$348$	2.04760e6	+	1.48767e6i	0.906352	+	0.658504i
$349$	−1.62851e6	−	1.18318e6i	−0.715694	−	0.519982i	0.169311	−	0.985563i	$-0.445846\pi$
$349$	−1.62851e6	−	1.18318e6i	−0.715694	−	0.519982i	−0.885006	+	0.465580i	$0.845846\pi$
$350$	−619980.	−	450442.i	−0.270525	−	0.196548i
$351$	−424833.	+	308660.i	−0.184056	+	0.133725i
$352$	141929.	+	436812.i	0.0610540	+	0.187905i
$353$	−3.74312e6	−	2.71954e6i	−1.59881	−	1.16160i	−0.889740	−	0.456468i	$-0.849114\pi$
$353$	−3.74312e6	−	2.71954e6i	−1.59881	−	1.16160i	−0.709071	−	0.705137i	$-0.750886\pi$
$354$	515005.	−	1.58502e6i	0.218426	−	0.672245i
$355$	−443389.			−0.186730
$356$	−157895.	+	114717.i	−0.0660303	+	0.0479738i
$357$	3.00228e6	−	9.24005e6i	1.24675	−	3.83711i
$358$	−512807.	−	1.57826e6i	−0.211469	−	0.650834i
$359$	−803098.	−	2.47168e6i	−0.328876	−	1.01218i	−0.969660	−	0.244456i	$-0.921391\pi$
$359$	−803098.	−	2.47168e6i	−0.328876	−	1.01218i	0.640784	−	0.767721i	$-0.278609\pi$
$360$	−992729.			−0.403715
$361$	1.64772e6	+	5.07118e6i	0.665452	+	2.04805i
$362$	1.12304e6	+	815938.i	0.450427	+	0.327255i
$363$	−787693.	+	572293.i	−0.313755	+	0.227956i
$364$	179244.	−	551655.i	0.0709072	−	0.218230i
$365$	−447718.	+	1.37793e6i	−0.175903	+	0.541373i
$366$	−765603.			−0.298745
$367$	1.70129e6	−	1.23606e6i	0.659347	−	0.479043i	−0.207096	−	0.978321i	$-0.566401\pi$
$367$	1.70129e6	−	1.23606e6i	0.659347	−	0.479043i	0.866442	+	0.499277i	$0.166401\pi$
$368$	−873815.			−0.336357
$369$	3.39078e6	−	1.53464e6i	1.29638	−	0.586732i
$370$	−1.36912e6			−0.519920
$371$	3.31556e6	−	2.40890e6i	1.25061	−	0.908623i
$372$	−2.07484e6			−0.777368
$373$	−89604.0	+	275773.i	−0.0333469	+	0.102631i	−0.966345	−	0.257251i	$-0.917183\pi$
$373$	−89604.0	+	275773.i	−0.0333469	+	0.102631i	0.932998	+	0.359882i	$0.117183\pi$
$374$	1.28926e6	−	3.96792e6i	0.476607	−	1.46684i
$375$	3.73175e6	−	2.71127e6i	1.37036	−	0.995623i
$376$	518046.	+	376383.i	0.188973	+	0.137297i
$377$	−424162.	−	1.30543e6i	−0.153701	−	0.473044i
$378$	−1.71769e6			−0.618322
$379$	272175.	+	837668.i	0.0973307	+	0.299553i	0.987854	−	0.155384i	$-0.0496616\pi$
$379$	272175.	+	837668.i	0.0973307	+	0.299553i	−0.890523	+	0.454938i	$0.849662\pi$
$380$	−619763.	−	1.90743e6i	−0.220174	−	0.677627i
$381$	−905467.	+	2.78674e6i	−0.319566	+	0.983522i
$382$	155102.	−	112688.i	0.0543825	−	0.0395112i
$383$	−1.40998e6			−0.491152			−0.245576	−	0.969377i	$-0.578977\pi$
$383$	−1.40998e6			−0.491152			−0.245576	+	0.969377i	$0.578977\pi$
$384$	−122851.	+	378098.i	−0.0425160	+	0.130851i
$385$	2.80269e6	+	2.03627e6i	0.963658	+	0.700139i
$386$	436864.	+	1.34453e6i	0.149238	+	0.459306i
$387$	581716.	−	422641.i	0.197439	−	0.143448i
$388$	−1.33996e6	−	973537.i	−0.451869	−	0.328302i
$389$	−3.85043e6	−	2.79750e6i	−1.29014	−	0.937338i	−0.290327	−	0.956927i	$-0.593764\pi$
$389$	−3.85043e6	−	2.79750e6i	−1.29014	−	0.937338i	−0.999808	+	0.0195891i	$0.993764\pi$
$390$	741654.	+	538843.i	0.246911	+	0.179391i
$391$	6.42163e6	+	4.66559e6i	2.12424	+	1.54335i
$392$	664760.	−	482976.i	0.218499	−	0.158749i
$393$	1.88306e6	+	5.79546e6i	0.615010	+	1.89281i
$394$	−2.67651e6	−	1.94460e6i	−0.868618	−	0.631088i
$395$	342612.	−	1.05445e6i	0.110487	−	0.340043i
$396$	−2.48149e6			−0.795198
$397$	956527.	−	694958.i	0.304594	−	0.221300i	−0.424979	−	0.905203i	$-0.639719\pi$
$397$	956527.	−	694958.i	0.304594	−	0.221300i	0.729573	+	0.683903i	$0.239719\pi$
$398$	−402781.	+	1.23963e6i	−0.127456	+	0.392270i
$399$	−3.60761e6	−	1.11031e7i	−1.13445	−	3.49149i
$400$	−88023.8	−	270910.i	−0.0275074	−	0.0846592i
$401$	−4.84346e6			−1.50416			−0.752082	−	0.659070i	$-0.770950\pi$
$401$	−4.84346e6			−1.50416			−0.752082	+	0.659070i	$0.770950\pi$
$402$	1.58596e6	+	4.88108e6i	0.489470	+	1.50643i
$403$	910338.	+	661399.i	0.279216	+	0.202862i
$404$	42693.5	−	31018.7i	0.0130139	−	0.00945518i
$405$	−325871.	+	1.00293e6i	−0.0987208	+	0.303831i
$406$	1.38744e6	−	4.27010e6i	0.417733	−	1.28565i
$407$	−3.42234e6			−1.02409
$408$	2.92162e6	−	2.12268e6i	0.868907	−	0.631298i
$409$	4.56690e6			1.34994			0.674968	−	0.737847i	$-0.264157\pi$
$409$	4.56690e6			1.34994			0.674968	+	0.737847i	$0.264157\pi$
$410$	−1.30111e6	−	1.42734e6i	−0.382256	−	0.419343i
$411$	−8.62710e6			−2.51919
$412$	1.00029e6	−	726751.i	0.290323	−	0.210932i
$413$	−2.95647e6			−0.852901
$414$	1.45890e6	−	4.49004e6i	0.418336	−	1.28751i
$415$	−954279.	+	2.93697e6i	−0.271991	+	0.837103i
$416$	174428.	−	126730.i	0.0494178	−	0.0359041i
$417$	1.60888e6	+	1.16892e6i	0.453090	+	0.329189i
$418$	−1.54920e6	−	4.76795e6i	−0.433678	−	1.33472i
$419$	2.66430e6			0.741393			0.370697	−	0.928754i	$-0.379119\pi$
$419$	2.66430e6			0.741393			0.370697	+	0.928754i	$0.379119\pi$
$420$	926635.	+	2.85189e6i	0.256322	+	0.788877i
$421$	−2.08315e6	−	6.41127e6i	−0.572815	−	1.76294i	−0.643500	−	0.765446i	$-0.722518\pi$
$421$	−2.08315e6	−	6.41127e6i	−0.572815	−	1.76294i	0.0706847	−	0.997499i	$-0.477482\pi$
$422$	−15904.3	+	48948.3i	−0.00434743	+	0.0133800i
$423$	−2.79894e6	+	2.03355e6i	−0.760575	+	0.552590i
$424$	1.52334e6			0.411512
$425$	−799592.	+	2.46089e6i	−0.214732	+	0.660876i
$426$	−776130.	−	563891.i	−0.207210	−	0.150547i
$427$	419691.	+	1.29168e6i	0.111394	+	0.342834i
$428$	−2.09030e6	+	1.51869e6i	−0.551568	+	0.400738i
$429$	1.85389e6	+	1.34693e6i	0.486340	+	0.353347i
$430$	−301865.	−	219318.i	−0.0787303	−	0.0572009i
$431$	5.22568e6	+	3.79668e6i	1.35503	+	0.984489i	0.998744	+	0.0501136i	$0.0159583\pi$
$431$	5.22568e6	+	3.79668e6i	1.35503	+	0.984489i	0.356290	+	0.934376i	$0.384042\pi$
$432$	−516535.	−	375284.i	−0.133165	−	0.0967500i
$433$	−450245.	+	327122.i	−0.115406	+	0.0838476i	−0.643991	−	0.765033i	$-0.722723\pi$
$433$	−450245.	+	327122.i	−0.115406	+	0.0838476i	0.528585	+	0.848880i	$0.322723\pi$
$434$	1.13739e6	+	3.50053e6i	0.289859	+	0.892093i
$435$	5.74079e6	+	4.17093e6i	1.45462	+	1.05684i
$436$	−893357.	+	2.74947e6i	−0.225065	+	0.692680i
$437$	9.53798e6			2.38920
$438$	−2.53613e6	+	1.84260e6i	−0.631664	+	0.458931i
$439$	1.60787e6	−	4.94850e6i	0.398188	−	1.22550i	−0.528262	−	0.849081i	$-0.677156\pi$
$439$	1.60787e6	−	4.94850e6i	0.398188	−	1.22550i	0.926451	−	0.376416i	$-0.122844\pi$
$440$	397922.	+	1.22468e6i	0.0979864	+	0.301571i
$441$	1.37187e6	+	4.22219e6i	0.335906	+	1.03381i
$442$	−1.95852e6			−0.476839
$443$	995882.	+	3.06501e6i	0.241101	+	0.742032i	0.996253	+	0.0864827i	$0.0275627\pi$
$443$	995882.	+	3.06501e6i	0.241101	+	0.742032i	−0.755153	+	0.655549i	$0.772437\pi$
$444$	−2.39657e6	−	1.74121e6i	−0.576943	−	0.419173i
$445$	−442685.	+	321629.i	−0.105973	+	0.0769937i
$446$	501430.	−	1.54324e6i	0.119364	−	0.367364i
$447$	865188.	−	2.66278e6i	0.204806	−	0.630327i
$448$	705248.			0.166015
$449$	−3.40857e6	+	2.47647e6i	−0.797915	+	0.579719i	−0.910302	−	0.413945i	$-0.864151\pi$
$449$	−3.40857e6	+	2.47647e6i	−0.797915	+	0.579719i	0.112386	+	0.993665i	$0.464151\pi$
$450$	1.53901e6			0.358271
$451$	−3.25234e6	−	3.56789e6i	−0.752931	−	0.825980i
$452$	1.44013e6			0.331554
$453$	−3.71170e6	+	2.69671e6i	−0.849822	+	0.617431i
$454$	−391919.			−0.0892394
$455$	502539.	−	1.54666e6i	0.113800	−	0.350240i
$456$	1.34096e6	−	4.12706e6i	0.301999	−	0.929456i
$457$	3.13513e6	−	2.27780e6i	0.702206	−	0.510183i	−0.178444	−	0.983950i	$-0.557106\pi$
$457$	3.13513e6	−	2.27780e6i	0.702206	−	0.510183i	0.880650	+	0.473768i	$0.157106\pi$
$458$	833874.	+	605845.i	0.185753	+	0.134958i
$459$	1.79222e6	+	5.51590e6i	0.397064	+	1.22204i
$460$	−2.44989e6			−0.539823
$461$	583941.	+	1.79719e6i	0.127973	+	0.393859i	0.994431	−	0.105390i	$-0.0336092\pi$
$461$	583941.	+	1.79719e6i	0.127973	+	0.393859i	−0.866458	+	0.499249i	$0.833609\pi$
$462$	2.31628e6	+	7.12878e6i	0.504878	+	1.55385i
$463$	692108.	−	2.13009e6i	0.150045	−	0.461791i	−0.847580	−	0.530667i	$-0.821941\pi$
$463$	692108.	−	2.13009e6i	0.150045	−	0.461791i	0.997625	+	0.0688764i	$0.0219414\pi$
$464$	1.35017e6	−	980953.i	0.291134	−	0.211521i
$465$	−5.81715e6			−1.24761
$466$	1.59016e6	−	4.89402e6i	0.339216	−	1.04400i
$467$	−2.09604e6	−	1.52287e6i	−0.444742	−	0.323124i	0.342774	−	0.939418i	$-0.388633\pi$
$467$	−2.09604e6	−	1.52287e6i	−0.444742	−	0.323124i	−0.787516	+	0.616294i	$0.788633\pi$
$468$	359970.	+	1.10787e6i	0.0759716	+	0.233817i
$469$	7.36565e6	−	5.35146e6i	1.54625	−	1.12341i
$470$	1.45243e6	+	1.05525e6i	0.303285	+	0.220349i
$471$	−285115.	−	207148.i	−0.0592200	−	0.0430258i
$472$	−889056.	−	645937.i	−0.183685	−	0.133455i
$473$	−754563.	−	548222.i	−0.155075	−	0.112669i
$474$	1.94075e6	−	1.41003e6i	0.396755	−	0.288260i
$475$	960809.	+	2.95707e6i	0.195390	+	0.601350i
$476$	−5.18284e6	−	3.76555e6i	−1.04846	−	0.761748i
$477$	−2.54334e6	+	7.82760e6i	−0.511810	+	1.57519i
$478$	678495.			0.135824
$479$	−3.25413e6	+	2.36426e6i	−0.648032	+	0.470823i	−0.862600	−	0.505886i	$-0.831166\pi$
$479$	−3.25413e6	+	2.36426e6i	−0.648032	+	0.470823i	0.214568	+	0.976709i	$0.431166\pi$
$480$	−344434.	+	1.06006e6i	−0.0682344	+	0.210004i
$481$	496451.	+	1.52792e6i	0.0978393	+	0.301118i
$482$	1.44319e6	+	4.44167e6i	0.282947	+	0.870821i
$483$	−1.42607e7			−2.78145
$484$	198392.	+	610588.i	0.0384956	+	0.118477i
$485$	−3.75680e6	−	2.72947e6i	−0.725210	−	0.526896i
$486$	−3.80714e6	+	2.76605e6i	−0.731153	+	0.531213i
$487$	2.16401e6	−	6.66015e6i	0.413464	−	1.27251i	−0.500154	−	0.865937i	$-0.666723\pi$
$487$	2.16401e6	−	6.66015e6i	0.413464	−	1.27251i	0.913618	−	0.406574i	$-0.133277\pi$
$488$	−156001.	+	480122.i	−0.0296537	+	0.0912646i
$489$	1.34330e7			2.54040
$490$	1.86377e6	−	1.35410e6i	0.350672	−	0.254778i
$491$	1.30023e6			0.243397			0.121699	−	0.992567i	$-0.461166\pi$
$491$	1.30023e6			0.243397			0.121699	+	0.992567i	$0.461166\pi$
$492$	−462266.	−	4.15321e6i	−0.0860952	−	0.773519i
$493$	−1.51600e7			−2.80919
$494$	−1.90394e6	+	1.38329e6i	−0.351024	+	0.255034i
$495$	−6.95728e6			−1.27622
$496$	−422774.	+	1.30116e6i	−0.0771621	+	0.237481i
$497$	−525900.	+	1.61856e6i	−0.0955020	+	0.293925i
$498$	−5.40558e6	+	3.92738e6i	−0.976717	+	0.709626i
$499$	4.20660e6	+	3.05627e6i	0.756274	+	0.549465i	0.897765	−	0.440474i	$-0.145190\pi$
$499$	4.20660e6	+	3.05627e6i	0.756274	+	0.549465i	−0.141491	+	0.989940i	$0.545190\pi$
$500$	−939894.	−	2.89270e6i	−0.168133	−	0.517461i
$501$	717928.			0.127787
$502$	−1.35696e6	−	4.17629e6i	−0.240330	−	0.739659i
$503$	1.38708e6	+	4.26898e6i	0.244445	+	0.752323i	0.995727	+	0.0923425i	$0.0294355\pi$
$503$	1.38708e6	+	4.26898e6i	0.244445	+	0.752323i	−0.751283	+	0.659980i	$0.770565\pi$
$504$	−1.17747e6	+	3.62387e6i	−0.206477	+	0.635472i
$505$	119698.	−	86966.0i	0.0208862	−	0.0151747i
$506$	−6.12390e6			−1.06329
$507$	−2.45164e6	+	7.54536e6i	−0.423581	+	1.30365i
$508$	1.56311e6	+	1.13567e6i	0.268739	+	0.195250i
$509$	2.32235e6	+	7.14747e6i	0.397314	+	1.22281i	0.927145	+	0.374703i	$0.122255\pi$
$509$	2.32235e6	+	7.14747e6i	0.397314	+	1.22281i	−0.529831	+	0.848103i	$0.677745\pi$
$510$	8.19125e6	−	5.95129e6i	1.39452	−	1.01318i
$511$	4.49899e6	+	3.26871e6i	0.762190	+	0.553763i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$	5.63815e6	+	4.09635e6i	0.945895	+	0.687233i
$514$	−627177.	−	455671.i	−0.104709	−	0.0760752i
$515$	2.80447e6	−	2.03757e6i	0.465943	−	0.338528i
$516$	−249476.	−	767809.i	−0.0412482	−	0.126949i
$517$	3.63059e6	+	2.63778e6i	0.597381	+	0.434022i
$518$	−1.62390e6	+	4.99785e6i	−0.265910	+	0.818387i
$519$	−9.11414e6			−1.48524
$520$	489039.	−	355307.i	0.0793113	−	0.0576230i
$521$	1.65378e6	−	5.08982e6i	0.266922	−	0.821500i	−0.724323	−	0.689461i	$-0.757847\pi$
$521$	1.65378e6	−	5.08982e6i	0.266922	−	0.821500i	0.991244	−	0.132039i	$-0.0421525\pi$
$522$	2.78636e6	+	8.57552e6i	0.447569	+	1.37748i
$523$	−1.36232e6	−	4.19279e6i	−0.217783	−	0.670268i	−0.998944	−	0.0459385i	$-0.985372\pi$
$523$	−1.36232e6	−	4.19279e6i	−0.217783	−	0.670268i	0.781161	−	0.624330i	$-0.214628\pi$
$524$	4.01813e6			0.639286
$525$	−1.43655e6	−	4.42124e6i	−0.227469	−	0.700077i
$526$	3.25951e6	+	2.36817e6i	0.513674	+	0.373206i
$527$	1.00543e7	−	7.30487e6i	1.57698	−	1.14574i
$528$	−860972.	+	2.64980e6i	−0.134402	+	0.413645i
$529$	1.61138e6	−	4.95933e6i	0.250357	−	0.770519i
$530$	4.27095e6			0.660441
$531$	4.80345e6	−	3.48991e6i	0.739294	−	0.537129i
$532$	−7.69802e6			−1.17923
$533$	−1.12111e6	+	1.96959e6i	−0.170934	+	0.300301i
$534$	−1.18394e6			−0.179670
$535$	−5.86050e6	+	4.25790e6i	−0.885218	+	0.643149i
$536$	3.38416e6			0.508791
$537$	3.11080e6	−	9.57405e6i	0.465518	−	1.43272i
$538$	1.45546e6	−	4.47945e6i	0.216793	−	0.667221i
$539$	4.65879e6	−	3.38481e6i	0.690719	−	0.501837i
$540$	−1.44819e6	−	1.05217e6i	−0.213718	−	0.155275i
$541$	3.93072e6	+	1.20975e7i	0.577403	+	1.77706i	0.627847	+	0.778337i	$0.283936\pi$
$541$	3.93072e6	+	1.20975e7i	0.577403	+	1.77706i	−0.0504439	+	0.998727i	$0.516064\pi$
$542$	1.56300e6			0.228540
$543$	2.60219e6	+	8.00871e6i	0.378738	+	1.16564i
$544$	−735852.	−	2.26472e6i	−0.106609	−	0.328108i
$545$	−2.50468e6	+	7.70860e6i	−0.361210	+	1.11169i
$546$	2.84667e6	−	2.06823e6i	0.408654	−	0.296904i
$547$	−2.75572e6			−0.393792			−0.196896	−	0.980424i	$-0.563086\pi$
$547$	−2.75572e6			−0.393792			−0.196896	+	0.980424i	$0.563086\pi$
$548$	−1.75788e6	+	5.41020e6i	−0.250056	+	0.769595i
$549$	−2.20662e6	−	1.60320e6i	−0.312462	−	0.227017i
$550$	−616892.	−	1.89860e6i	−0.0869566	−	0.267625i
$551$	−1.47375e7	+	1.07074e7i	−2.06797	+	1.50247i
$552$	−4.28840e6	−	3.11570e6i	−0.599028	−	0.435219i
$553$	−3.44281e6	−	2.50135e6i	−0.478741	−	0.347825i
$554$	6.57825e6	+	4.77938e6i	0.910617	+	0.661602i
$555$	−6.71918e6	−	4.88177e6i	−0.925942	−	0.672737i
$556$	1.06088e6	−	770776.i	0.145539	−	0.105740i
$557$	−2.14482e6	−	6.60107e6i	−0.292922	−	0.901522i	−0.983911	−	0.178657i	$-0.942825\pi$
$557$	−2.14482e6	−	6.60107e6i	−0.292922	−	0.901522i	0.690989	−	0.722865i	$-0.257175\pi$
$558$	−5.98009e6	−	4.34479e6i	−0.813060	−	0.590722i
$559$	−135298.	+	416404.i	−0.0183131	+	0.0563618i
$560$	1.97728e6			0.266439
$561$	2.04754e7	−	1.48762e7i	2.74679	−	1.99566i
$562$	1.32783e6	−	4.08663e6i	0.177337	−	0.545788i
$563$	2.08600e6	+	6.42005e6i	0.277360	+	0.853626i	0.988585	+	0.150662i	$0.0481404\pi$
$563$	2.08600e6	+	6.42005e6i	0.277360	+	0.853626i	−0.711226	+	0.702964i	$0.751860\pi$
$564$	1.20036e6	+	3.69433e6i	0.158896	+	0.489032i
$565$	4.03764e6			0.532116
$566$	−1.86847e6	−	5.75056e6i	−0.245157	−	0.754517i
$567$	3.27459e6	+	2.37913e6i	0.427760	+	0.310786i
$568$	−511772.	+	371824.i	−0.0665588	+	0.0483578i
$569$	3.07045e6	−	9.44989e6i	0.397578	−	1.22362i	−0.529358	−	0.848399i	$-0.677567\pi$
$569$	3.07045e6	−	9.44989e6i	0.397578	−	1.22362i	0.926936	−	0.375220i	$-0.122433\pi$
$570$	3.75962e6	−	1.15709e7i	0.484681	−	1.49170i
$571$	−6.42334e6			−0.824462			−0.412231	−	0.911079i	$-0.635250\pi$
$571$	−6.42334e6			−0.824462			−0.412231	+	0.911079i	$0.635250\pi$
$572$	1.22243e6	−	888151.i	0.156220	−	0.113500i
$573$	1.16299e6			0.147976
$574$	−6.75363e6	+	3.05663e6i	−0.855574	+	0.387225i
$575$	3.79802e6			0.479058
$576$	−1.14583e6	+	832498.i	−0.143902	+	0.104551i
$577$	−7.77693e6			−0.972453			−0.486226	−	0.873833i	$-0.661627\pi$
$577$	−7.77693e6			−0.972453			−0.486226	+	0.873833i	$0.661627\pi$
$578$	−4.92930e6	+	1.51708e7i	−0.613714	+	1.88882i
$579$	−2.65011e6	+	8.15621e6i	−0.328525	+	1.01110i
$580$	3.78542e6	−	2.75027e6i	0.467244	−	0.339473i
$581$	9.58929e6	+	6.96702e6i	1.17854	+	0.856263i
$582$	−3.10480e6	−	9.55560e6i	−0.379950	−	1.16937i
$583$	1.06759e7			1.30087
$584$	638760.	+	1.96590e6i	0.0775008	+	0.238523i
$585$	1.00924e6	+	3.10611e6i	0.121928	+	0.375255i
$586$	1.79792e6	−	5.53343e6i	0.216285	−	0.665657i
$587$	82787.1	−	60148.4i	0.00991671	−	0.00720491i	−0.582816	−	0.812604i	$-0.698049\pi$
$587$	82787.1	−	60148.4i	0.00991671	−	0.00720491i	0.592733	+	0.805399i	$0.298049\pi$
$588$	4.98454e6			0.594541
$589$	4.61472e6	−	1.42026e7i	0.548096	−	1.68687i
$590$	−2.49262e6	−	1.81099e6i	−0.294799	−	0.214184i
$591$	−6.20171e6	−	1.90869e7i	−0.730370	−	2.24785i
$592$	−1.58027e6	+	1.14814e6i	−0.185322	+	0.134645i
$593$	−6.32727e6	−	4.59703e6i	−0.738890	−	0.536835i	0.153474	−	0.988153i	$-0.450954\pi$
$593$	−6.32727e6	−	4.59703e6i	−0.738890	−	0.536835i	−0.892363	+	0.451318i	$0.850954\pi$
$594$	−3.62000e6	−	2.63008e6i	−0.420961	−	0.305846i
$595$	−1.45310e7	−	1.05574e7i	−1.68268	−	1.22254i
$596$	−1.49358e6	−	1.08515e6i	−0.172231	−	0.125133i
$597$	−6.39678e6	+	4.64754e6i	−0.734558	+	0.533687i
$598$	888344.	+	2.73404e6i	0.101585	+	0.312645i
$599$	−9.07932e6	−	6.59651e6i	−1.03392	−	0.751186i	−0.0648292	−	0.997896i	$-0.520650\pi$
$599$	−9.07932e6	−	6.59651e6i	−1.03392	−	0.751186i	−0.969089	+	0.246711i	$0.920650\pi$
$600$	533972.	−	1.64340e6i	0.0605536	−	0.186365i
$601$	−4.40321e6			−0.497259			−0.248630	−	0.968599i	$-0.579980\pi$
$601$	−4.40321e6			−0.497259			−0.248630	+	0.968599i	$0.579980\pi$
$602$	−1.15864e6	+	841802.i	−0.130304	+	0.0946713i
$603$	−5.65013e6	+	1.73893e7i	−0.632798	+	1.94755i
$604$	934846.	+	2.87716e6i	0.104267	+	0.320901i
$605$	556225.	+	1.71188e6i	0.0617820	+	0.190145i
$606$	320127.			0.0354112
$607$	−2.81278e6	−	8.65683e6i	−0.309858	−	0.953646i	−0.977819	−	0.209450i	$-0.932833\pi$
$607$	−2.81278e6	−	8.65683e6i	−0.309858	−	0.953646i	0.667961	−	0.744196i	$-0.267167\pi$
$608$	−2.31491e6	−	1.68188e6i	−0.253966	−	0.184517i
$609$	2.20347e7	−	1.60092e7i	2.40749	−	1.74914i
$610$	−437375.	+	1.34610e6i	−0.0475915	+	0.146472i
$611$	650988.	−	2.00353e6i	0.0705456	−	0.217117i
$612$	1.28657e7			1.38853
$613$	−1.46251e6	+	1.06258e6i	−0.157198	+	0.114211i	−0.663604	−	0.748084i	$-0.730974\pi$
$613$	−1.46251e6	+	1.06258e6i	−0.157198	+	0.114211i	0.506406	+	0.862295i	$0.330974\pi$
$614$	5.11535e6			0.547588
$615$	−1.29604e6	−	1.16442e7i	−0.138175	−	1.24143i
$616$	4.94255e6			0.524806
$617$	−1.37274e7	+	9.97352e6i	−1.45169	+	1.05472i	−0.466261	+	0.884647i	$0.654399\pi$
$617$	−1.37274e7	+	9.97352e6i	−1.45169	+	1.05472i	−0.985432	+	0.170069i	$0.945601\pi$
$618$	7.50041e6			0.789976
$619$	−2.20246e6	+	6.77846e6i	−0.231037	+	0.711057i	0.766586	+	0.642142i	$0.221954\pi$
$619$	−2.20246e6	+	6.77846e6i	−0.231037	+	0.711057i	−0.997622	+	0.0689157i	$0.978046\pi$
$620$	−1.18532e6	+	3.64803e6i	−0.123838	+	0.381135i
$621$	6.88714e6	−	5.00380e6i	0.716655	−	0.520680i
$622$	−7.71497e6	−	5.60525e6i	−0.799573	−	0.580924i
$623$	649015.	+	1.99746e6i	0.0669938	+	0.206186i
$624$	1.30791e6			0.134467
$625$	−1.56064e6	−	4.80316e6i	−0.159810	−	0.491843i
$626$	1.86932e6	+	5.75318e6i	0.190655	+	0.586776i
$627$	9.39779e6	−	2.89234e7i	0.954678	−	2.93820i
$628$	−188002.	+	136591.i	−0.0190223	+	0.0138205i
$629$	1.77436e7			1.78820
$630$	−3.30123e6	+	1.01601e7i	−0.331378	+	1.01988i
$631$	2.80751e6	+	2.03977e6i	0.280703	+	0.203943i	0.719224	−	0.694778i	$-0.244497\pi$
$631$	2.80751e6	+	2.03977e6i	0.280703	+	0.203943i	−0.438521	+	0.898721i	$0.644497\pi$
$632$	−488805.	−	1.50439e6i	−0.0486791	−	0.149819i
$633$	−252585.	+	183514.i	−0.0250552	+	0.0182037i
$634$	6.19844e6	+	4.50343e6i	0.612434	+	0.444959i
$635$	4.38245e6	+	3.18403e6i	0.431303	+	0.313360i
$636$	7.47607e6	+	5.43168e6i	0.732876	+	0.532465i
$637$	−2.18698e6	−	1.58893e6i	−0.213548	−	0.155152i
$638$	9.46229e6	−	6.87475e6i	0.920332	−	0.668660i
$639$	−1.05615e6	−	3.25050e6i	−0.102323	−	0.314918i
$640$	594599.	+	432001.i	0.0573818	+	0.0416903i
$641$	2.72153e6	−	8.37601e6i	0.261618	−	0.805179i	−0.730835	−	0.682554i	$-0.760869\pi$
$641$	2.72153e6	−	8.37601e6i	0.261618	−	0.805179i	0.992453	−	0.122624i	$-0.0391310\pi$
$642$	−1.56736e7			−1.50083
$643$	−6.34123e6	+	4.60717e6i	−0.604848	+	0.439448i	−0.847596	−	0.530642i	$-0.821951\pi$
$643$	−6.34123e6	+	4.60717e6i	−0.604848	+	0.439448i	0.242749	+	0.970089i	$0.421951\pi$
$644$	−2.90579e6	+	8.94310e6i	−0.276089	+	0.849715i
$645$	−699448.	−	2.15268e6i	−0.0661997	−	0.203742i
$646$	8.03207e6	+	2.47202e7i	0.757262	+	2.33061i
$647$	−1.94436e7			−1.82606			−0.913032	−	0.407889i	$-0.866265\pi$
$647$	−1.94436e7			−1.82606			−0.913032	+	0.407889i	$0.866265\pi$
$648$	464922.	+	1.43088e6i	0.0434953	+	0.133865i
$649$	−6.23072e6	−	4.52688e6i	−0.580666	−	0.421878i
$650$	−758149.	+	550828.i	−0.0703836	+	0.0511367i
$651$	−6.89967e6	+	2.12350e7i	−0.638081	+	1.96381i
$652$	2.73715e6	−	8.42408e6i	0.252162	−	0.776075i
$653$	2.55382e6			0.234373			0.117186	−	0.993110i	$-0.462613\pi$
$653$	2.55382e6			0.234373			0.117186	+	0.993110i	$0.462613\pi$
$654$	−1.41879e7	+	1.03081e7i	−1.29710	+	0.942399i
$655$	1.12655e7			1.02600
$656$	−2.69874e6	−	556374.i	−0.244851	−	0.0504786i
$657$	−1.11681e7			−1.00941
$658$	5.57482e6	−	4.05034e6i	0.501957	−	0.364693i
$659$	−1.86885e7			−1.67633			−0.838167	−	0.545414i	$-0.816373\pi$
$659$	−1.86885e7			−1.67633			−0.838167	+	0.545414i	$0.816373\pi$
$660$	−2.41388e6	+	7.42915e6i	−0.215703	+	0.663865i
$661$	258405.	−	795289.i	0.0230037	−	0.0707980i	−0.938896	−	0.344202i	$-0.888150\pi$
$661$	258405.	−	795289.i	0.0230037	−	0.0707980i	0.961899	+	0.273404i	$0.0881495\pi$
$662$	−7.92648e6	+	5.75893e6i	−0.702968	+	0.510736i
$663$	−9.61176e6	−	6.98335e6i	−0.849218	−	0.616993i
$664$	1.36147e6	+	4.19018e6i	0.119836	+	0.368818i
$665$	−2.15827e7			−1.89257
$666$	−3.26123e6	−	1.00370e7i	−0.284902	−	0.876839i
$667$	6.87625e6	+	2.11629e7i	0.598463	+	1.84188i
$668$	146287.	−	450225.i	0.0126842	−	0.0390380i
$669$	7.96349e6	−	5.78581e6i	0.687920	−	0.499803i
$670$	9.48807e6			0.816565
$671$	−1.09329e6	+	3.36481e6i	−0.0937412	+	0.288506i
$672$	3.46113e6	+	2.51466e6i	0.295661	+	0.214810i
$673$	4.44260e6	+	1.36729e7i	0.378093	+	1.16365i	0.941368	+	0.337382i	$0.109541\pi$
$673$	4.44260e6	+	1.36729e7i	0.378093	+	1.16365i	−0.563274	+	0.826270i	$0.690459\pi$
$674$	2.14749e6	−	1.56024e6i	0.182088	−	0.132295i
$675$	2.24511e6	+	1.63117e6i	0.189661	+	0.137797i
$676$	4.23227e6	+	3.07492e6i	0.356210	+	0.258802i
$677$	1.25631e6	+	912761.i	0.105348	+	0.0765395i	0.639212	−	0.769031i	$-0.279261\pi$
$677$	1.25631e6	+	912761.i	0.105348	+	0.0765395i	−0.533864	+	0.845570i	$0.679261\pi$
$678$	7.06767e6	+	5.13497e6i	0.590476	+	0.429006i
$679$	−1.44196e7	+	1.04765e7i	−1.20027	+	0.872048i
$680$	−2.06308e6	−	6.34952e6i	−0.171098	−	0.526585i
$681$	−1.92341e6	−	1.39744e6i	−0.158929	−	0.115469i
$682$	−2.96290e6	+	9.11887e6i	−0.243925	+	0.750723i
$683$	1.64996e7			1.35339			0.676695	−	0.736264i	$-0.263412\pi$
$683$	1.64996e7			1.35339			0.676695	+	0.736264i	$0.263412\pi$
$684$	1.25072e7	−	9.08699e6i	1.02216	−	0.742642i
$685$	−4.92851e6	+	1.51684e7i	−0.401319	+	1.23513i
$686$	844519.	+	2.59916e6i	0.0685171	+	0.210874i
$687$	1.93216e6	+	5.94658e6i	0.156189	+	0.480701i
$688$	−532340.			−0.0428763
$689$	−1.54867e6	−	4.76632e6i	−0.124283	−	0.382503i
$690$	−1.20232e7	−	8.73539e6i	−0.961388	−	0.698489i
$691$	1.24778e7	−	9.06568e6i	0.994133	−	0.722280i	0.0333105	−	0.999445i	$-0.489395\pi$
$691$	1.24778e7	−	9.06568e6i	0.994133	−	0.722280i	0.960822	+	0.277165i	$0.0893950\pi$
$692$	−1.85712e6	+	5.71563e6i	−0.147426	+	0.453732i
$693$	−8.25197e6	+	2.53970e7i	−0.652717	+	2.00885i
$694$	3.59532e6			0.283360
$695$	2.97436e6	−	2.16100e6i	0.233578	−	0.169704i
$696$	1.01239e7			0.792181
$697$	1.68623e7	+	1.84982e7i	1.31472	+	1.44228i
$698$	−8.05181e6			−0.625540
$699$	2.52543e7	−	1.83483e7i	1.95498	−	1.42037i
$700$	−3.06535e6			−0.236448
$701$	−3.28892e6	+	1.01223e7i	−0.252789	+	0.778005i	0.741468	+	0.670988i	$0.234130\pi$
$701$	−3.28892e6	+	1.01223e7i	−0.252789	+	0.778005i	−0.994257	+	0.107017i	$0.965870\pi$
$702$	−649088.	+	1.99769e6i	−0.0497119	+	0.152998i
$703$	1.72492e7	−	1.25323e7i	1.31638	−	0.956405i
$704$	1.48630e6	+	1.07986e6i	0.113025	+	0.0821175i
$705$	3.36541e6	+	1.03577e7i	0.255015	+	0.784854i
$706$	−1.85070e7			−1.39741
$707$	−175489.	−	540099.i	−0.0132039	−	0.0406373i
$708$	−2.06002e6	−	6.34010e6i	−0.154450	−	0.475349i
$709$	3.89935e6	−	1.20010e7i	0.291324	−	0.896603i	−0.693108	−	0.720834i	$-0.743759\pi$
$709$	3.89935e6	−	1.20010e7i	0.291324	−	0.896603i	0.984432	−	0.175769i	$-0.0562411\pi$
$710$	−1.43484e6	+	1.04247e6i	−0.106821	+	0.0776101i
$711$	8.54629e6			0.634021
$712$	−241242.	+	742466.i	−0.0178342	+	0.0548879i
$713$	−1.47578e7	−	1.07222e7i	−1.08717	−	0.789878i
$714$	−1.20091e7	−	3.69602e7i	−0.881587	−	2.71324i
$715$	3.42730e6	−	2.49008e6i	0.250719	−	0.182158i
$716$	−5.37018e6	−	3.90167e6i	−0.391477	−	0.284425i
$717$	3.32983e6	+	2.41926e6i	0.241893	+	0.175746i
$718$	−8.41015e6	−	6.11033e6i	−0.608825	−	0.442337i
$719$	5.27747e6	+	3.83431e6i	0.380718	+	0.276608i	0.761641	−	0.647999i	$-0.224394\pi$
$719$	5.27747e6	+	3.83431e6i	0.380718	+	0.276608i	−0.380923	+	0.924607i	$0.624394\pi$
$720$	−3.21254e6	+	2.33405e6i	−0.230950	+	0.167795i
$721$	−4.11161e6	−	1.26542e7i	−0.294560	−	0.906562i
$722$	1.72552e7	+	1.25366e7i	1.23190	+	0.895031i
$723$	−8.75469e6	+	2.69442e7i	−0.622866	+	1.91699i
$724$	5.55263e6			0.393688
$725$	−5.86848e6	+	4.26370e6i	−0.414649	+	0.301260i
$726$	−1.20349e6	+	3.70396e6i	−0.0847423	+	0.260810i
$727$	1.61157e6	+	4.95990e6i	0.113087	+	0.348046i	0.991543	−	0.129777i	$-0.0414261\pi$
$727$	1.61157e6	+	4.95990e6i	0.113087	+	0.348046i	−0.878456	+	0.477823i	$0.841426\pi$
$728$	−716975.	−	2.20662e6i	−0.0501390	−	0.154312i
$729$	−2.28344e7			−1.59137
$730$	1.79087e6	+	5.51174e6i	0.124382	+	0.382808i
$731$	3.91214e6	+	2.84234e6i	0.270783	+	0.196735i
$732$	−2.47754e6	+	1.80004e6i	−0.170900	+	0.124166i
$733$	−4.99821e6	+	1.53829e7i	−0.343601	+	1.05750i	0.618727	+	0.785606i	$0.287649\pi$
$733$	−4.99821e6	+	1.53829e7i	−0.343601	+	1.05750i	−0.962328	+	0.271889i	$0.912351\pi$
$734$	2.59934e6	−	7.99996e6i	0.178083	−	0.548084i
$735$	1.39750e7			0.954186
$736$	−2.82772e6	+	2.05446e6i	−0.192417	+	0.139799i
$737$	2.37170e7			1.60839
$738$	7.36465e6	−	1.29384e7i	0.497750	−	0.874459i
$739$	1.52720e7			1.02869			0.514345	−	0.857583i	$-0.328035\pi$
$739$	1.52720e7			1.02869			0.514345	+	0.857583i	$0.328035\pi$
$740$	−4.43056e6	+	3.21899e6i	−0.297426	+	0.216093i
$741$	−1.42762e7			−0.955143
$742$	5.06573e6	−	1.55907e7i	0.337779	−	1.03958i
$743$	6.24722e6	−	1.92270e7i	0.415159	−	1.27773i	−0.496950	−	0.867779i	$-0.665547\pi$
$743$	6.24722e6	−	1.92270e7i	0.415159	−	1.27773i	0.912109	−	0.409949i	$-0.134453\pi$
$744$	−6.71431e6	+	4.87823e6i	−0.444702	+	0.323095i
$745$	−4.18750e6	−	3.04239e6i	−0.276416	−	0.200828i
$746$	358416.	+	1.10309e6i	0.0235798	+	0.0725712i
$747$	−2.38041e7			−1.56081
$748$	−5.15702e6	−	1.58717e7i	−0.337012	−	1.03722i
$749$	8.59202e6	+	2.64435e7i	0.559617	+	1.72232i
$750$	5.70160e6	−	1.75477e7i	0.370121	−	1.13912i
$751$	−1.02072e7	+	7.41599e6i	−0.660402	+	0.479810i	−0.866799	−	0.498658i	$-0.833826\pi$
$751$	−1.02072e7	+	7.41599e6i	−0.660402	+	0.479810i	0.206397	+	0.978468i	$0.433826\pi$
$752$	2.56136e6			0.165168
$753$	8.23161e6	−	2.53343e7i	0.529051	−	1.62825i
$754$	−4.44188e6	−	3.22721e6i	−0.284537	−	0.206728i
$755$	2.62100e6	+	8.06660e6i	0.167340	+	0.515019i
$756$	−5.55855e6	+	4.03852e6i	−0.353718	+	0.256991i
$757$	−2.07037e7	−	1.50421e7i	−1.31313	−	0.954044i	−0.999991	−	0.00433679i	$-0.998620\pi$
$757$	−2.07037e7	−	1.50421e7i	−1.31313	−	0.954044i	−0.313139	−	0.949707i	$-0.601380\pi$
$758$	2.85025e6	+	2.07083e6i	0.180182	+	0.130910i
$759$	−3.00541e7	−	2.18356e7i	−1.89365	−	1.37582i
$760$	−6.49024e6	−	4.71544e6i	−0.407593	−	0.296134i
$761$	4.04579e6	−	2.93944e6i	0.253246	−	0.183994i	−0.453918	−	0.891043i	$-0.649974\pi$
$761$	4.04579e6	−	2.93944e6i	0.253246	−	0.183994i	0.707164	+	0.707049i	$0.249974\pi$
$762$	3.62187e6	+	1.11470e7i	0.225967	+	0.695455i
$763$	2.51688e7	+	1.82862e7i	1.56513	+	1.13714i
$764$	236975.	−	729334.i	0.0146882	−	0.0452057i
$765$	3.60711e7			2.22846
$766$	−4.56279e6	+	3.31506e6i	−0.280969	+	0.204136i
$767$	−1.11721e6	+	3.43841e6i	−0.0685717	+	0.211042i
$768$	491406.	+	1.51239e6i	0.0300633	+	0.0925254i
$769$	−6.74169e6	−	2.07488e7i	−0.411105	−	1.26525i	−0.915688	−	0.401889i	$-0.868354\pi$
$769$	−6.74169e6	−	2.07488e7i	−0.411105	−	1.26525i	0.504583	−	0.863363i	$-0.331646\pi$
$770$	1.38573e7			0.842268
$771$	−1.45322e6	−	4.47256e6i	−0.0880434	−	0.270970i
$772$	4.57490e6	+	3.32386e6i	0.276273	+	0.200724i
$773$	−7.74556e6	+	5.62748e6i	−0.466234	+	0.338739i	−0.795972	−	0.605334i	$-0.793040\pi$
$773$	−7.74556e6	+	5.62748e6i	−0.466234	+	0.338739i	0.329738	+	0.944073i	$0.393040\pi$
$774$	888783.	−	2.73539e6i	0.0533265	−	0.164122i
$775$	1.83758e6	−	5.65549e6i	0.109899	−	0.338233i
$776$	−6.62512e6			−0.394948
$777$	−2.57901e7	+	1.87376e7i	−1.53250	+	1.11342i
$778$	−1.90376e7			−1.12762
$779$	2.94576e7	+	6.07301e6i	1.73922	+	0.358559i
$780$	3.66694e6			0.215808
$781$	−3.58662e6	+	2.60583e6i	−0.210406	+	0.152869i
$782$	3.17503e7			1.85665
$783$	−5.02428e6	+	1.54631e7i	−0.292866	+	0.901350i
$784$	1.01566e6	−	3.12589e6i	0.0590146	−	0.181628i
$785$	−527095.	+	382957.i	−0.0305292	+	0.0221807i
$786$	1.97196e7	+	1.43272e7i	1.13853	+	0.827187i
$787$	54151.9	+	166662.i	0.00311657	+	0.00959181i	0.952603	−	0.304217i	$-0.0983948\pi$
$787$	54151.9	+	166662.i	0.00311657	+	0.00959181i	−0.949486	+	0.313809i	$0.898395\pi$
$788$	−1.32334e7			−0.759200
$789$	7.55257e6	+	2.32444e7i	0.431919	+	1.32931i
$790$	−1.37045e6	−	4.21780e6i	−0.0781258	−	0.240446i
$791$	4.78901e6	−	1.47391e7i	0.272147	−	0.837584i
$792$	−8.03028e6	+	5.83434e6i	−0.454902	+	0.330506i
$793$	1.66083e6			0.0937868
$794$	1.46144e6	−	4.49786e6i	0.0822680	−	0.253195i
$795$	2.09604e7	+	1.52286e7i	1.17620	+	0.854560i
$796$	1.61112e6	+	4.95852e6i	0.0901251	+	0.277377i
$797$	−1.32364e7	+	9.61679e6i	−0.738114	+	0.536271i	−0.892120	−	0.451799i	$-0.850783\pi$
$797$	−1.32364e7	+	9.61679e6i	−0.738114	+	0.536271i	0.154006	+	0.988070i	$0.450783\pi$
$798$	−3.77793e7	−	2.74483e7i	−2.10014	−	1.52584i
$799$	−1.88233e7	−	1.36760e7i	−1.04311	−	0.757863i
$800$	−921798.	−	669725.i	−0.0509226	−	0.0369974i
$801$	−3.41234e6	−	2.47921e6i	−0.187919	−	0.136531i
$802$	−1.56738e7	+	1.13877e7i	−0.860474	+	0.625171i
$803$	4.47658e6	+	1.37775e7i	0.244995	+	0.754018i
$804$	1.66084e7	+	1.20667e7i	0.906122	+	0.658336i
$805$	−8.14686e6	+	2.50735e7i	−0.443099	+	1.36372i
$806$	4.50096e6			0.244044
$807$	2.31150e7	−	1.67940e7i	1.24943	−	0.907761i
$808$	65229.9	−	200757.i	0.00351495	−	0.0108179i
$809$	1.51884e6	+	4.67450e6i	0.0815906	+	0.251110i	0.983528	−	0.180757i	$-0.0578549\pi$
$809$	1.51884e6	+	4.67450e6i	0.0815906	+	0.251110i	−0.901937	+	0.431867i	$0.857855\pi$
$810$	1.30349e6	+	4.01172e6i	0.0698062	+	0.214841i
$811$	−1.38015e7			−0.736839			−0.368420	−	0.929660i	$-0.620101\pi$
$811$	−1.38015e7			−0.736839			−0.368420	+	0.929660i	$0.620101\pi$
$812$	−5.54976e6	−	1.70804e7i	−0.295382	−	0.909093i
$813$	7.67070e6	+	5.57309e6i	0.407014	+	0.295713i
$814$	−1.10749e7	+	8.04641e6i	−0.585841	+	0.425639i
$815$	7.67406e6	−	2.36183e7i	0.404698	−	1.24553i
$816$	4.46384e6	−	1.37383e7i	0.234684	−	0.722282i
$817$	5.81066e6			0.304558
$818$	1.47788e7	−	1.07374e7i	0.772246	−	0.561070i
$819$	1.25356e7			0.653034
$820$	−7.56637e6	−	1.55989e6i	−0.392964	−	0.0810138i
$821$	−1.07969e6			−0.0559037			−0.0279519	−	0.999609i	$-0.508899\pi$
$821$	−1.07969e6			−0.0559037			−0.0279519	+	0.999609i	$0.508899\pi$
$822$	−2.79179e7	+	2.02835e7i	−1.44113	+	1.04704i
$823$	8.48111e6			0.436469			0.218234	−	0.975896i	$-0.429970\pi$
$823$	8.48111e6			0.436469			0.218234	+	0.975896i	$0.429970\pi$
$824$	1.52830e6	−	4.70363e6i	0.0784136	−	0.241332i
$825$	3.74220e6	−	1.15173e7i	0.191422	−	0.589137i
$826$	−9.56734e6	+	6.95108e6i	−0.487912	+	0.354489i
$827$	−1.66708e7	−	1.21121e7i	−0.847606	−	0.615822i	0.0768792	−	0.997040i	$-0.475504\pi$
$827$	−1.66708e7	−	1.21121e7i	−0.847606	−	0.615822i	−0.924485	+	0.381219i	$0.875504\pi$
$828$	−5.83561e6	−	1.79602e7i	−0.295808	−	0.910404i
$829$	−9.04839e6			−0.457283			−0.228642	−	0.973511i	$-0.573428\pi$
$829$	−9.04839e6			−0.457283			−0.228642	+	0.973511i	$0.573428\pi$
$830$	3.81712e6	+	1.17479e7i	0.192327	+	0.591921i
$831$	1.52424e7	+	4.69112e7i	0.765685	+	2.35654i
$832$	266503.	−	820211.i	0.0133473	−	0.0410787i
$833$	−2.41542e7	+	1.75491e7i	−1.20609	+	0.876277i
$834$	7.95476e6			0.396015
$835$	410140.	−	1.26228e6i	0.0203571	−	0.0626527i
$836$	−1.62234e7	−	1.17870e7i	−0.802837	−	0.583295i
$837$	−4.11879e6	−	1.26763e7i	−0.203215	−	0.625432i
$838$	8.62187e6	−	6.26415e6i	0.424123	−	0.308143i
$839$	−2.09410e7	−	1.52146e7i	−1.02705	−	0.746199i	−0.0593375	−	0.998238i	$-0.518899\pi$
$839$	−2.09410e7	−	1.52146e7i	−1.02705	−	0.746199i	−0.967717	+	0.252039i	$0.918899\pi$
$840$	9.70385e6	+	7.05026e6i	0.474511	+	0.344752i
$841$	−1.77886e7	−	1.29242e7i	−0.867265	−	0.630105i
$842$	−2.18150e7	−	1.58495e7i	−1.06041	−	0.770435i
$843$	2.10879e7	−	1.53213e7i	1.02203	−	0.742551i
$844$	63617.1	+	195793.i	0.00307410	+	0.00946110i
$845$	1.18659e7	+	8.62106e6i	0.571687	+	0.415355i
$846$	−4.27640e6	+	1.31614e7i	−0.205424	+	0.632231i
$847$	6.90882e6			0.330899
$848$	4.92964e6	−	3.58159e6i	0.235410	−	0.171036i
$849$	1.13345e7	−	3.48841e7i	0.539678	−	1.66096i
$850$	3.19837e6	+	9.84356e6i	0.151838	+	0.467310i
$851$	−8.04816e6	−	2.47697e7i	−0.380954	−	1.17246i
$852$	−3.83740e6			−0.181108
$853$	8.55741e6	+	2.63370e7i	0.402689	+	1.23935i	0.922810	+	0.385256i	$0.125887\pi$
$853$	8.55741e6	+	2.63370e7i	0.402689	+	1.23935i	−0.520121	+	0.854093i	$0.674113\pi$
$854$	4.39507e6	+	3.19320e6i	0.206215	+	0.149824i
$855$	3.50659e7	−	2.54769e7i	1.64048	−	1.19188i
$856$	−3.19369e6	+	9.82918e6i	−0.148973	+	0.458493i
$857$	4.63842e6	−	1.42756e7i	0.215734	−	0.663961i	−0.783367	−	0.621560i	$-0.786499\pi$
$857$	4.63842e6	−	1.42756e7i	0.215734	−	0.663961i	0.999101	−	0.0424010i	$-0.0135007\pi$
$858$	9.16613e6			0.425077
$859$	1.84725e7	−	1.34210e7i	0.854166	−	0.620588i	−0.0721258	−	0.997396i	$-0.522978\pi$
$859$	1.84725e7	−	1.34210e7i	0.854166	−	0.620588i	0.926291	+	0.376808i	$0.122978\pi$
$860$	−1.49250e6			−0.0688128
$861$	−4.40434e7	−	9.08003e6i	−2.02476	−	0.417426i
$862$	2.58372e7			1.18434
$863$	2.63307e7	−	1.91304e7i	1.20347	−	0.874372i	0.208849	−	0.977948i	$-0.433028\pi$
$863$	2.63307e7	−	1.91304e7i	1.20347	−	0.874372i	0.994622	+	0.103576i	$0.0330284\pi$
$864$	−2.55389e6			−0.116390
$865$	−5.20675e6	+	1.60247e7i	−0.236606	+	0.728200i
$866$	−687914.	+	2.11718e6i	−0.0311702	+	0.0959319i
$867$	−7.82850e7	+	5.68774e7i	−3.53696	+	2.56976i
$868$	1.19109e7	+	8.65380e6i	0.536595	+	0.389859i
$869$	−3.42566e6	−	1.05431e7i	−0.153885	−	0.473608i
$870$	2.83840e7			1.27138
$871$	−3.44043e6	−	1.05886e7i	−0.153662	−	0.472924i
$872$	3.57343e6	+	1.09979e7i	0.159145	+	0.489799i
$873$	1.10612e7	−	3.40427e7i	0.491208	−	1.51178i
$874$	3.08655e7	−	2.24251e7i	1.36677	−	0.993016i
$875$	−3.27310e7			−1.44524
$876$	−3.87486e6	+	1.19256e7i	−0.170607	+	0.525073i
$877$	−1.64627e7	−	1.19609e7i	−0.722775	−	0.525127i	0.164495	−	0.986378i	$-0.447401\pi$
$877$	−1.64627e7	−	1.19609e7i	−0.722775	−	0.525127i	−0.887270	+	0.461251i	$0.847401\pi$
$878$	−6.43146e6	−	1.97940e7i	−0.281562	−	0.866558i
$879$	2.85538e7	−	2.07455e7i	1.24650	−	0.905634i
$880$	4.16709e6	+	3.02757e6i	0.181395	+	0.131791i
$881$	1.00413e7	+	7.29543e6i	0.435863	+	0.316673i	0.783989	−	0.620775i	$-0.213182\pi$
$881$	1.00413e7	+	7.29543e6i	0.435863	+	0.316673i	−0.348126	+	0.937448i	$0.613182\pi$
$882$	1.43664e7	+	1.04378e7i	0.621839	+	0.451792i
$883$	2.16167e7	+	1.57054e7i	0.933013	+	0.677873i	0.946729	−	0.322033i	$-0.104366\pi$
$883$	2.16167e7	+	1.57054e7i	0.933013	+	0.677873i	−0.0137160	+	0.999906i	$0.504366\pi$
$884$	−6.33789e6	+	4.60475e6i	−0.272781	+	0.198187i
$885$	−5.77562e6	−	1.77755e7i	−0.247879	−	0.762894i
$886$	1.04290e7	+	7.57712e6i	0.446333	+	0.324280i
$887$	7.78381e6	−	2.39561e7i	0.332188	−	1.02237i	−0.635903	−	0.771769i	$-0.719372\pi$
$887$	7.78381e6	−	2.39561e7i	0.332188	−	1.02237i	0.968091	−	0.250599i	$-0.0806277\pi$
$888$	−1.18493e7			−0.504266
$889$	1.68210e7	−	1.22212e7i	0.713835	−	0.518632i
$890$	−676362.	+	2.08163e6i	−0.0286223	+	0.0880903i
$891$	3.25828e6	+	1.00280e7i	0.137497	+	0.423173i
$892$	−2.00572e6	−	6.17297e6i	−0.0844031	−	0.259766i
$893$	−2.79581e7			−1.17322
$894$	−3.46075e6	−	1.06511e7i	−0.144819	−	0.445708i
$895$	−1.50562e7	−	1.09390e7i	−0.628287	−	0.456477i
$896$	2.28223e6	−	1.65814e6i	0.0949707	−	0.0690003i
$897$	−5.38889e6	+	1.65853e7i	−0.223624	+	0.688243i
$898$	−5.20784e6	+	1.60281e7i	−0.215510	+	0.663270i
$899$	3.48398e7			1.43773
$900$	4.98035e6	−	3.61844e6i	0.204953	−	0.148907i
$901$	−5.53510e7			−2.27151
$902$	−1.89134e7	−	3.89920e6i	−0.774022	−	0.159573i
$903$	−8.68778e6			−0.354560
$904$	4.66035e6	−	3.38594e6i	0.189670	−	0.137803i
$905$	1.55677e7			0.631835
$906$	−5.67098e6	+	1.74535e7i	−0.229529	+	0.706417i
$907$	−2.68495e6	+	8.26342e6i	−0.108372	+	0.333535i	−0.990507	−	0.137462i	$-0.956106\pi$
$907$	−2.68495e6	+	8.26342e6i	−0.108372	+	0.333535i	0.882135	+	0.470997i	$0.156106\pi$
$908$	−1.26828e6	+	921456.i	−0.0510504	+	0.0370903i
$909$	922671.	+	670359.i	0.0370371	+	0.0269090i
$910$	−2.01016e6	−	6.18663e6i	−0.0804686	−	0.247657i
$911$	−774644.			−0.0309247			−0.0154624	−	0.999880i	$-0.504922\pi$
$911$	−774644.			−0.0309247			−0.0154624	+	0.999880i	$0.504922\pi$
$912$	−5.36385e6	−	1.65082e7i	−0.213545	−	0.657225i
$913$	9.54152e6	+	2.93658e7i	0.378827	+	1.16591i
$914$	4.79005e6	−	1.47422e7i	0.189659	−	0.583711i
$915$	−6.94620e6	+	5.04671e6i	−0.274280	+	0.199276i
$916$	4.12290e6			0.162354
$917$	1.33619e7	−	4.11237e7i	0.524741	−	1.61499i
$918$	1.87684e7	+	1.36360e7i	0.735057	+	0.534050i
$919$	−9.67593e6	−	2.97795e7i	−0.377924	−	1.16313i	−0.941485	−	0.337055i	$-0.890569\pi$
$919$	−9.67593e6	−	2.97795e7i	−0.377924	−	1.16313i	0.563561	−	0.826074i	$-0.309431\pi$
$920$	−7.92800e6	+	5.76003e6i	−0.308812	+	0.224365i
$921$	2.51044e7	+	1.82394e7i	0.975217	+	0.708537i
$922$	6.11511e6	+	4.44289e6i	0.236907	+	0.172123i
$923$	1.68367e6	+	1.22325e6i	0.0650506	+	0.0472621i
$924$	2.42564e7	+	1.76233e7i	0.934645	+	0.679059i
$925$	6.86863e6	−	4.99035e6i	0.263946	−	0.191768i
$926$	−2.76843e6	−	8.52036e6i	−0.106098	−	0.326535i
$927$	2.16177e7	+	1.57062e7i	0.826247	+	0.600304i
$928$	2.06287e6	−	6.34886e6i	0.0786325	−	0.242006i
$929$	8.73027e6			0.331885			0.165943	−	0.986135i	$-0.446933\pi$
$929$	8.73027e6			0.331885			0.165943	+	0.986135i	$0.446933\pi$
$930$	−1.88247e7	+	1.36769e7i	−0.713708	+	0.518539i
$931$	−1.10863e7	+	3.41201e7i	−0.419191	+	1.29014i
$932$	−6.36065e6	−	1.95761e7i	−0.239862	−	0.738220i
$933$	−1.78763e7	−	5.50175e7i	−0.672315	−	2.06917i
$934$	−1.03634e7			−0.388719
$935$	−1.44586e7	−	4.44989e7i	−0.540875	−	1.66464i
$936$	3.76965e6	+	2.73881e6i	0.140641	+	0.102182i
$937$	1.49836e6	−	1.08862e6i	0.0557530	−	0.0405069i	−0.559560	−	0.828790i	$-0.689030\pi$
$937$	1.49836e6	−	1.08862e6i	0.0557530	−	0.0405069i	0.615313	+	0.788283i	$0.289030\pi$
$938$	1.12537e7	−	3.46354e7i	0.417627	−	1.28532i
$939$	−1.13397e7	+	3.49000e7i	−0.419699	+	1.29170i
$940$	7.18121e6			0.265081
$941$	1.28479e6	−	933456.i	0.0472997	−	0.0343653i	−0.563884	−	0.825854i	$-0.690694\pi$
$941$	1.28479e6	−	933456.i	0.0472997	−	0.0343653i	0.611184	+	0.791489i	$0.290694\pi$
$942$	−1.40969e6			−0.0517602
$943$	1.81747e7	−	3.19297e7i	0.665561	−	1.16927i
$944$	−4.39574e6			−0.160547
$945$	−1.55843e7	+	1.13227e7i	−0.567686	+	0.412448i
$946$	−3.73076e6			−0.135541
$947$	−9.61180e6	+	2.95821e7i	−0.348281	+	1.07190i	0.611523	+	0.791227i	$0.290557\pi$
$947$	−9.61180e6	+	2.95821e7i	−0.348281	+	1.07190i	−0.959804	+	0.280672i	$0.909443\pi$
$948$	2.96520e6	−	9.12594e6i	0.107160	−	0.329805i
$949$	5.50164e6	−	3.99718e6i	0.198302	−	0.144075i
$950$	1.00617e7	+	7.31027e6i	0.361712	+	0.262799i
$951$	1.43623e7	+	4.42027e7i	0.514960	+	1.58488i
$952$	−2.56254e7			−0.916385
$953$	5.16756e6	+	1.59041e7i	0.184312	+	0.567254i	0.999936	−	0.0113285i	$-0.00360606\pi$
$953$	5.16756e6	+	1.59041e7i	0.184312	+	0.567254i	−0.815624	+	0.578583i	$0.803606\pi$
$954$	1.01734e7	+	3.13104e7i	0.361904	+	1.11383i
$955$	664399.	−	2.04481e6i	0.0235733	−	0.0725511i
$956$	2.19565e6	−	1.59524e6i	0.0776997	−	0.0564521i
$957$	7.09506e7			2.50424
$958$	−4.97187e6	+	1.53018e7i	−0.175027	+	0.538679i
$959$	4.95253e7	+	3.59822e7i	1.73892	+	1.26340i
$960$	1.37774e6	+	4.24024e6i	0.0482490	+	0.148495i
$961$	55221.9	−	40121.0i	0.00192887	−	0.00140141i
$962$	5.19890e6	+	3.77722e6i	0.181123	+	0.131594i
$963$	−4.51744e7	−	3.28212e7i	−1.56974	−	1.14048i
$964$	1.51133e7	+	1.09804e7i	0.523800	+	0.380563i
$965$	1.28265e7	+	9.31900e6i	0.443394	+	0.322145i
$966$	−4.61485e7	+	3.35288e7i	−1.59116	+	1.15605i
$967$	1.69334e7	+	5.21155e7i	0.582340	+	1.79226i	0.609698	+	0.792634i	$0.291291\pi$
$967$	1.69334e7	+	5.21155e7i	0.582340	+	1.79226i	−0.0273580	+	0.999626i	$0.508709\pi$
$968$	2.07759e6	+	1.50946e6i	0.0712641	+	0.0517764i
$969$	−4.87242e7	+	1.49958e8i	−1.66700	+	5.13050i
$970$	−1.85746e7			−0.633856
$971$	3.23302e7	−	2.34893e7i	1.10042	−	0.799505i	0.119295	−	0.992859i	$-0.461936\pi$
$971$	3.23302e7	−	2.34893e7i	1.10042	−	0.799505i	0.981129	+	0.193354i	$0.0619365\pi$
$972$	−5.81679e6	+	1.79022e7i	−0.197478	+	0.607773i
$973$	−4.36068e6	−	1.34208e7i	−0.147663	−	0.454460i
$974$	−8.65605e6	−	2.66406e7i	−0.292363	−	0.899801i
$975$	−5.68480e6			−0.191515
$976$	624005.	+	1.92049e6i	0.0209683	+	0.0645338i
$977$	−2.26254e7	−	1.64383e7i	−0.758334	−	0.550962i	0.140065	−	0.990142i	$-0.455269\pi$
$977$	−2.26254e7	−	1.64383e7i	−0.758334	−	0.550962i	−0.898399	+	0.439180i	$0.855269\pi$
$978$	4.34702e7	−	3.15830e7i	1.45326	−	1.05586i
$979$	−1.69068e6	+	5.20338e6i	−0.0563774	+	0.173512i
$980$	2.84758e6	−	8.76395e6i	0.0947132	−	0.291497i
$981$	−6.24780e7			−2.07279
$982$	4.20763e6	−	3.05702e6i	0.139238	−	0.101162i
$983$	−2.51517e7			−0.830203			−0.415101	−	0.909775i	$-0.636254\pi$
$983$	−2.51517e7			−0.830203			−0.415101	+	0.909775i	$0.636254\pi$
$984$	−1.12607e7	−	1.23532e7i	−0.370747	−	0.406717i
$985$	−3.71020e7			−1.21845
$986$	−4.90586e7	+	3.56432e7i	−1.60703	+	1.16757i
$987$	4.18014e7			1.36584
$988$	−2.90896e6	+	8.95287e6i	−0.0948082	+	0.291790i
$989$	2.19336e6	−	6.75048e6i	0.0713050	−	0.219454i
$990$	−2.25142e7	+	1.63575e7i	−0.730078	+	0.530433i
$991$	3.69600e6	+	2.68530e6i	0.119549	+	0.0868578i	0.645953	−	0.763377i	$-0.276460\pi$
$991$	3.69600e6	+	2.68530e6i	0.119549	+	0.0868578i	−0.526404	+	0.850235i	$0.676460\pi$
$992$	1.69110e6	+	5.20466e6i	0.0545618	+	0.167924i
$993$	−5.94348e7			−1.91279
$994$	2.10360e6	+	6.47422e6i	0.0675301	+	0.207836i
$995$	4.51705e6	+	1.39021e7i	0.144643	+	0.445165i
$996$	−8.25899e6	+	2.54185e7i	−0.263802	+	0.811900i
$997$	1.87458e7	−	1.36196e7i	0.597262	−	0.433937i	−0.247644	−	0.968851i	$-0.579656\pi$
$997$	1.87458e7	−	1.36196e7i	0.597262	−	0.433937i	0.844906	+	0.534915i	$0.179656\pi$
$998$	2.07986e7			0.661008
$999$	5.88056e6	−	1.80985e7i	0.186425	−	0.573758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.b.37.8	✓	36
41.10	even	5	inner	82.6.d.b.51.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.b.37.8	✓	36	1.1	even	1	trivial
82.6.d.b.51.8	yes	36	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} +24.2649 q^{3} +(4.94427 - 15.2169i) q^{4} +(13.8621 - 42.6631i) q^{5} +(78.5227 - 57.0501i) q^{6} +(-139.296 - 101.205i) q^{7} +(-19.7771 - 60.8676i) q^{8} +345.784 q^{9} +(-55.4484 - 170.653i) q^{10} +(-138.603 - 426.575i) q^{11} +(119.972 - 369.236i) q^{12} +(-170.340 + 123.759i) q^{13} -688.719 q^{14} +(336.362 - 1035.22i) q^{15} +(-207.108 - 150.473i) q^{16} +(718.605 + 2211.64i) q^{17} +(1118.98 - 812.986i) q^{18} +(2260.66 + 1642.46i) q^{19} +(-580.663 - 421.876i) q^{20} +(-3380.01 - 2455.72i) q^{21} +(-1451.46 - 1054.55i) q^{22} +(2761.45 - 2006.31i) q^{23} +(-479.888 - 1476.94i) q^{24} +(900.193 + 654.028i) q^{25} +(-260.256 + 800.987i) q^{26} +2494.03 q^{27} +(-2228.74 + 1619.28i) q^{28} +(-2014.52 + 6200.06i) q^{29} +(-1345.45 - 4140.86i) q^{30} +(-1651.46 - 5082.67i) q^{31} -1024.00 q^{32} +(-3363.17 - 10350.8i) q^{33} +(7525.33 + 5467.47i) q^{34} +(-6248.65 + 4539.91i) q^{35} +(1709.65 - 5261.76i) q^{36} +(2357.85 - 7256.73i) q^{37} +11177.3 q^{38} +(-4133.28 + 3003.00i) q^{39} -2870.95 q^{40} +(9806.08 - 4438.14i) q^{41} -16711.7 q^{42} +(1682.31 - 1222.27i) q^{43} -7176.43 q^{44} +(4793.28 - 14752.2i) q^{45} +(4219.12 - 12985.1i) q^{46} +(-8094.48 + 5880.98i) q^{47} +(-5025.46 - 3651.21i) q^{48} +(3967.43 + 12210.5i) q^{49} +4450.80 q^{50} +(17436.9 + 53665.1i) q^{51} +(1041.03 + 3203.95i) q^{52} +(-7355.29 + 22637.3i) q^{53} +(8070.85 - 5863.82i) q^{54} -20120.3 q^{55} +(-3405.21 + 10480.2i) q^{56} +(54854.5 + 39854.1i) q^{57} +(8058.09 + 24800.2i) q^{58} +(13891.5 - 10092.8i) q^{59} +(-14089.7 - 10236.8i) q^{60} +(-6381.51 - 4636.44i) q^{61} +(-17294.3 - 12565.1i) q^{62} +(-48166.4 - 34994.9i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(2918.69 + 8982.80i) q^{65} +(-35219.6 - 25588.5i) q^{66} +(-16340.1 + 50289.5i) q^{67} +37207.3 q^{68} +(67006.2 - 48682.9i) q^{69} +(-9547.09 + 29382.9i) q^{70} +(-3054.37 - 9400.38i) q^{71} +(-6838.59 - 21047.0i) q^{72} -32298.0 q^{73} +(-9431.42 - 29026.9i) q^{74} +(21843.1 + 15869.9i) q^{75} +(36170.5 - 26279.4i) q^{76} +(-23864.6 + 73447.5i) q^{77} +(-6315.09 + 19435.8i) q^{78} +24715.7 q^{79} +(-9290.61 + 6750.02i) q^{80} -23508.1 q^{81} +(21298.4 - 37417.6i) q^{82} -68840.9 q^{83} +(-54080.1 + 39291.5i) q^{84} +104317. q^{85} +(2570.34 - 7910.71i) q^{86} +(-48882.1 + 150444. i) q^{87} +(-23223.4 + 16872.8i) q^{88} +(-9868.43 - 7169.83i) q^{89} +(-19173.1 - 59008.8i) q^{90} +36252.8 q^{91} +(-16876.5 - 51940.5i) q^{92} +(-40072.5 - 123330. i) q^{93} +(-12367.3 + 38062.5i) q^{94} +(101410. - 73678.7i) q^{95} -24847.2 q^{96} +(31988.7 - 98451.0i) q^{97} +(41547.5 + 30186.0i) q^{98} +(-47926.5 - 147503. i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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