LMFDB - Embedded newform 82.6.d.b.57.2

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			57.2
Character	$\chi$	$=$	82.57
Dual form			82.6.d.b.59.2

$q$-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} -20.2284 q^{3} +(-12.9443 - 9.40456i) q^{4} +(-77.2940 - 56.1574i) q^{5} +(25.0037 - 76.9535i) q^{6} +(-23.9851 - 73.8187i) q^{7} +(51.7771 - 37.6183i) q^{8} +166.189 q^{9} +(309.176 - 224.630i) q^{10} +(-303.319 + 220.374i) q^{11} +(261.842 + 190.239i) q^{12} +(63.8852 - 196.619i) q^{13} +310.470 q^{14} +(1563.54 + 1135.98i) q^{15} +(79.1084 + 243.470i) q^{16} +(-1341.61 + 974.739i) q^{17} +(-205.420 + 632.219i) q^{18} +(-562.495 - 1731.18i) q^{19} +(472.379 + 1453.83i) q^{20} +(485.181 + 1493.23i) q^{21} +(-463.430 - 1426.29i) q^{22} +(-34.4748 + 106.103i) q^{23} +(-1047.37 + 760.958i) q^{24} +(1855.04 + 5709.22i) q^{25} +(669.015 + 486.068i) q^{26} +1553.77 q^{27} +(-383.762 + 1181.10i) q^{28} +(1094.49 + 795.195i) q^{29} +(-6254.14 + 4543.90i) q^{30} +(1332.75 - 968.303i) q^{31} -1024.00 q^{32} +(6135.66 - 4457.82i) q^{33} +(-2049.80 - 6308.65i) q^{34} +(-2291.56 + 7052.69i) q^{35} +(-2151.19 - 1562.93i) q^{36} +(-2088.01 - 1517.03i) q^{37} +7281.08 q^{38} +(-1292.30 + 3977.28i) q^{39} -6114.60 q^{40} +(9359.89 + 5314.94i) q^{41} -6280.32 q^{42} +(-3460.89 + 10651.5i) q^{43} +5998.77 q^{44} +(-12845.4 - 9332.72i) q^{45} +(-361.025 - 262.300i) q^{46} +(7169.34 - 22065.0i) q^{47} +(-1600.24 - 4925.02i) q^{48} +(8723.24 - 6337.80i) q^{49} -24012.1 q^{50} +(27138.7 - 19717.4i) q^{51} +(-2676.06 + 1944.27i) q^{52} +(-5201.43 - 3779.06i) q^{53} +(-1920.57 + 5910.90i) q^{54} +35820.4 q^{55} +(-4018.81 - 2919.84i) q^{56} +(11378.4 + 35019.0i) q^{57} +(-4377.97 + 3180.78i) q^{58} +(-6393.13 + 19676.0i) q^{59} +(-9555.48 - 29408.7i) q^{60} +(-10040.4 - 30901.3i) q^{61} +(2036.27 + 6266.99i) q^{62} +(-3986.06 - 12267.8i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-15979.5 + 11609.8i) q^{65} +(9374.46 + 28851.6i) q^{66} +(-37624.7 - 27335.9i) q^{67} +26533.2 q^{68} +(697.371 - 2146.29i) q^{69} +(-23997.5 - 17435.2i) q^{70} +(21210.4 - 15410.3i) q^{71} +(8604.76 - 6251.73i) q^{72} +48037.9 q^{73} +(8352.03 - 6068.10i) q^{74} +(-37524.4 - 115488. i) q^{75} +(-8999.91 + 27698.9i) q^{76} +(23542.9 + 17104.9i) q^{77} +(-13533.1 - 9832.38i) q^{78} -103071. q^{79} +(7558.07 - 23261.3i) q^{80} -71814.2 q^{81} +(-31788.7 + 29037.5i) q^{82} -72366.1 q^{83} +(7762.90 - 23891.8i) q^{84} +158438. q^{85} +(-36242.9 - 26332.0i) q^{86} +(-22139.8 - 16085.5i) q^{87} +(-7414.88 + 22820.7i) q^{88} +(43775.0 + 134726. i) q^{89} +(51381.6 - 37330.9i) q^{90} -16046.4 q^{91} +(1444.10 - 1049.20i) q^{92} +(-26959.5 + 19587.2i) q^{93} +(75078.3 + 54547.6i) q^{94} +(-53741.1 + 165398. i) q^{95} +20713.9 q^{96} +(90218.3 + 65547.4i) q^{97} +(13327.9 + 41019.1i) q^{98} +(-50408.2 + 36623.7i) 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 $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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
$3$	−20.2284			−1.29765			−0.648827	−	0.760936i	$-0.724740\pi$
$3$	−20.2284			−1.29765			−0.648827	+	0.760936i	$0.724740\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−77.2940	−	56.1574i	−1.38268	−	1.00457i	−0.996624	−	0.0820980i	$-0.973838\pi$
$5$	−77.2940	−	56.1574i	−1.38268	−	1.00457i	−0.386054	−	0.922476i	$-0.626162\pi$
$6$	25.0037	−	76.9535i	0.283548	−	0.872670i
$7$	−23.9851	−	73.8187i	−0.185011	−	0.569405i	0.814938	−	0.579549i	$-0.196771\pi$
$7$	−23.9851	−	73.8187i	−0.185011	−	0.569405i	−0.999949	+	0.0101438i	$0.996771\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	166.189			0.683904
$10$	309.176	−	224.630i	0.977701	−	0.710341i
$11$	−303.319	+	220.374i	−0.755819	+	0.549135i	−0.897625	−	0.440760i	$-0.854709\pi$
$11$	−303.319	+	220.374i	−0.755819	+	0.549135i	0.141806	+	0.989894i	$0.454709\pi$
$12$	261.842	+	190.239i	0.524912	+	0.381371i
$13$	63.8852	−	196.619i	0.104844	−	0.322676i	−0.884850	−	0.465876i	$-0.845739\pi$
$13$	63.8852	−	196.619i	0.104844	−	0.322676i	0.989694	+	0.143200i	$0.0457393\pi$
$14$	310.470			0.423350
$15$	1563.54	+	1135.98i	1.79424	+	1.30359i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−1341.61	+	974.739i	−1.12591	+	0.818024i	−0.985095	−	0.172011i	$-0.944974\pi$
$17$	−1341.61	+	974.739i	−1.12591	+	0.818024i	−0.140819	+	0.990035i	$0.544974\pi$
$18$	−205.420	+	632.219i	−0.149438	+	0.459924i
$19$	−562.495	−	1731.18i	−0.357466	−	1.10017i	−0.954566	−	0.298000i	$-0.903681\pi$
$19$	−562.495	−	1731.18i	−0.357466	−	1.10017i	0.597100	−	0.802167i	$-0.296319\pi$
$20$	472.379	+	1453.83i	0.264068	+	0.812718i
$21$	485.181	+	1493.23i	0.240080	+	0.738890i
$22$	−463.430	−	1426.29i	−0.204140	−	0.628278i
$23$	−34.4748	+	106.103i	−0.0135888	+	0.0418221i	−0.957621	−	0.288031i	$-0.906999\pi$
$23$	−34.4748	+	106.103i	−0.0135888	+	0.0418221i	0.944032	+	0.329853i	$0.106999\pi$
$24$	−1047.37	+	760.958i	−0.371169	+	0.269670i
$25$	1855.04	+	5709.22i	0.593612	+	1.82695i
$26$	669.015	+	486.068i	0.194090	+	0.141014i
$27$	1553.77			0.410183
$28$	−383.762	+	1181.10i	−0.0925054	+	0.284702i
$29$	1094.49	+	795.195i	0.241667	+	0.175581i	0.702026	−	0.712152i	$-0.252279\pi$
$29$	1094.49	+	795.195i	0.241667	+	0.175581i	−0.460359	+	0.887733i	$0.652279\pi$
$30$	−6254.14	+	4543.90i	−1.26872	+	0.921777i
$31$	1332.75	−	968.303i	0.249084	−	0.180970i	−0.456237	−	0.889858i	$-0.650803\pi$
$31$	1332.75	−	968.303i	0.249084	−	0.180970i	0.705321	+	0.708888i	$0.250803\pi$
$32$	−1024.00			−0.176777
$33$	6135.66	−	4457.82i	0.980791	−	0.712587i
$34$	−2049.80	−	6308.65i	−0.304099	−	0.935920i
$35$	−2291.56	+	7052.69i	−0.316199	+	0.973161i
$36$	−2151.19	−	1562.93i	−0.276645	−	0.200994i
$37$	−2088.01	−	1517.03i	−0.250742	−	0.182175i	0.455313	−	0.890331i	$-0.349527\pi$
$37$	−2088.01	−	1517.03i	−0.250742	−	0.182175i	−0.706056	+	0.708156i	$0.749527\pi$
$38$	7281.08			0.817969
$39$	−1292.30	+	3977.28i	−0.136051	+	0.418721i
$40$	−6114.60			−0.604252
$41$	9359.89	+	5314.94i	0.869583	+	0.493786i
$41$	9359.89	+	5314.94i	0.869583	+	0.493786i
$42$	−6280.32			−0.549362
$43$	−3460.89	+	10651.5i	−0.285441	+	0.878498i	0.700825	+	0.713334i	$0.252816\pi$
$43$	−3460.89	+	10651.5i	−0.285441	+	0.878498i	−0.986266	+	0.165165i	$0.947184\pi$
$44$	5998.77			0.467122
$45$	−12845.4	−	9332.72i	−0.945619	−	0.687032i
$46$	−361.025	−	262.300i	−0.0251561	−	0.0182769i
$47$	7169.34	−	22065.0i	0.473407	−	1.45700i	−0.374687	−	0.927151i	$-0.622250\pi$
$47$	7169.34	−	22065.0i	0.473407	−	1.45700i	0.848094	−	0.529845i	$-0.177750\pi$
$48$	−1600.24	−	4925.02i	−0.100249	−	0.308535i
$49$	8723.24	−	6337.80i	0.519024	−	0.377093i
$50$	−24012.1			−1.35833
$51$	27138.7	−	19717.4i	1.46105	−	1.06151i
$52$	−2676.06	+	1944.27i	−0.137242	+	0.0997123i
$53$	−5201.43	−	3779.06i	−0.254351	−	0.184797i	0.453302	−	0.891357i	$-0.350246\pi$
$53$	−5201.43	−	3779.06i	−0.254351	−	0.184797i	−0.707653	+	0.706560i	$0.750246\pi$
$54$	−1920.57	+	5910.90i	−0.0896283	+	0.275848i
$55$	35820.4			1.59670
$56$	−4018.81	−	2919.84i	−0.171249	−	0.124420i
$57$	11378.4	+	35019.0i	0.463866	+	1.42763i
$58$	−4377.97	+	3180.78i	−0.170884	+	0.124155i
$59$	−6393.13	+	19676.0i	−0.239102	+	0.735881i	0.757449	+	0.652895i	$0.226446\pi$
$59$	−6393.13	+	19676.0i	−0.239102	+	0.735881i	−0.996551	+	0.0829859i	$0.973554\pi$
$60$	−9555.48	−	29408.7i	−0.342669	−	1.05463i
$61$	−10040.4	−	30901.3i	−0.345484	−	1.06329i	−0.961324	−	0.275419i	$-0.911183\pi$
$61$	−10040.4	−	30901.3i	−0.345484	−	1.06329i	0.615840	−	0.787871i	$-0.288817\pi$
$62$	2036.27	+	6266.99i	0.0672753	+	0.207052i
$63$	−3986.06	−	12267.8i	−0.126530	−	0.389418i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−15979.5	+	11609.8i	−0.469117	+	0.340833i
$66$	9374.46	+	28851.6i	0.264903	+	0.815287i
$67$	−37624.7	−	27335.9i	−1.02397	−	0.743956i	−0.0568747	−	0.998381i	$-0.518114\pi$
$67$	−37624.7	−	27335.9i	−1.02397	−	0.743956i	−0.967092	+	0.254426i	$0.918114\pi$
$68$	26533.2			0.695853
$69$	697.371	−	2146.29i	0.0176336	−	0.0542706i
$70$	−23997.5	−	17435.2i	−0.585357	−	0.425287i
$71$	21210.4	−	15410.3i	0.499348	−	0.362798i	−0.309420	−	0.950926i	$-0.600135\pi$
$71$	21210.4	−	15410.3i	0.499348	−	0.362798i	0.808768	+	0.588128i	$0.200135\pi$
$72$	8604.76	−	6251.73i	0.195618	−	0.142124i
$73$	48037.9			1.05506			0.527530	−	0.849536i	$-0.323118\pi$
$73$	48037.9			1.05506			0.527530	+	0.849536i	$0.323118\pi$
$74$	8352.03	−	6068.10i	0.177302	−	0.128817i
$75$	−37524.4	−	115488.i	−0.770302	−	2.37075i
$76$	−8999.91	+	27698.9i	−0.178733	+	0.550083i
$77$	23542.9	+	17104.9i	0.452515	+	0.328771i
$78$	−13533.1	−	9832.38i	−0.251861	−	0.182988i
$79$	−103071.			−1.85809			−0.929047	−	0.369962i	$-0.879371\pi$
$79$	−103071.			−1.85809			−0.929047	+	0.369962i	$0.879371\pi$
$80$	7558.07	−	23261.3i	0.132034	−	0.406359i
$81$	−71814.2			−1.21618
$82$	−31788.7	+	29037.5i	−0.522081	+	0.476897i
$83$	−72366.1			−1.15303			−0.576514	−	0.817087i	$-0.695587\pi$
$83$	−72366.1			−1.15303			−0.576514	+	0.817087i	$0.695587\pi$
$84$	7762.90	−	23891.8i	0.120040	−	0.369445i
$85$	158438.			2.37854
$86$	−36242.9	−	26332.0i	−0.528418	−	0.383918i
$87$	−22139.8	−	16085.5i	−0.313600	−	0.227844i
$88$	−7414.88	+	22820.7i	−0.102070	+	0.314139i
$89$	43775.0	+	134726.i	0.585803	+	1.80291i	0.596023	+	0.802967i	$0.296747\pi$
$89$	43775.0	+	134726.i	0.585803	+	1.80291i	−0.0102207	+	0.999948i	$0.503253\pi$
$90$	51381.6	−	37330.9i	0.668654	−	0.485805i
$91$	−16046.4			−0.203130
$92$	1444.10	−	1049.20i	0.0177880	−	0.0129238i
$93$	−26959.5	+	19587.2i	−0.323225	+	0.234836i
$94$	75078.3	+	54547.6i	0.876385	+	0.636731i
$95$	−53741.1	+	165398.i	−0.610939	+	1.88028i
$96$	20713.9			0.229395
$97$	90218.3	+	65547.4i	0.973566	+	0.707337i	0.956261	−	0.292513i	$-0.0944916\pi$
$97$	90218.3	+	65547.4i	0.973566	+	0.707337i	0.0173044	+	0.999850i	$0.494492\pi$
$98$	13327.9	+	41019.1i	0.140184	+	0.431441i
$99$	−50408.2	+	36623.7i	−0.516908	+	0.375555i
$100$	29680.6	−	91347.5i	0.296806	−	0.913475i
$101$	17730.9	+	54570.0i	0.172952	+	0.532292i	0.999534	−	0.0305243i	$-0.00971770\pi$
$101$	17730.9	+	54570.0i	0.172952	+	0.532292i	−0.826582	+	0.562817i	$0.809718\pi$
$102$	41464.3	+	127614.i	0.394615	+	1.21450i
$103$	13941.2	+	42906.5i	0.129481	+	0.398502i	0.994691	−	0.102908i	$-0.0328148\pi$
$103$	13941.2	+	42906.5i	0.129481	+	0.398502i	−0.865210	+	0.501410i	$0.832815\pi$
$104$	−4088.66	−	12583.6i	−0.0370678	−	0.114083i
$105$	46354.6	−	142665.i	0.410317	−	1.26282i
$106$	20805.7	−	15116.2i	0.179853	−	0.130671i
$107$	−27125.3	−	83483.2i	−0.229042	−	0.704920i	−0.997856	−	0.0654469i	$-0.979153\pi$
$107$	−27125.3	−	83483.2i	−0.229042	−	0.704920i	0.768814	−	0.639473i	$-0.220847\pi$
$108$	−20112.4	−	14612.5i	−0.165923	−	0.120550i
$109$	214215.			1.72697			0.863483	−	0.504378i	$-0.168278\pi$
$109$	214215.			1.72697			0.863483	+	0.504378i	$0.168278\pi$
$110$	−44276.5	+	136269.i	−0.348892	+	1.07378i
$111$	42237.1	+	30687.0i	0.325377	+	0.236400i
$112$	16075.2	−	11679.3i	0.121091	−	0.0879779i
$113$	−207272.	+	150592.i	−1.52702	+	1.10944i	−0.569148	+	0.822235i	$0.692727\pi$
$113$	−207272.	+	150592.i	−1.52702	+	1.10944i	−0.957869	+	0.287207i	$0.907273\pi$
$114$	−147285.			−1.06144
$115$	8623.14	−	6265.08i	0.0608024	−	0.0441756i
$116$	−6688.94	−	20586.4i	−0.0461543	−	0.142048i
$117$	10617.0	−	32675.8i	0.0717030	−	0.220679i
$118$	−66949.7	−	48641.8i	−0.442633	−	0.321592i
$119$	104133.	+	75656.9i	0.674093	+	0.489757i
$120$	123689.			0.784110
$121$	−6329.83	+	19481.2i	−0.0393033	+	0.120963i
$122$	129966.			0.790552
$123$	−189336.	−	107513.i	−1.12842	−	0.640763i
$124$	−26358.0			−0.153942
$125$	84969.9	−	261511.i	0.486396	−	1.49697i
$126$	51596.6			0.289531
$127$	183214.	+	133113.i	1.00797	+	0.732335i	0.963783	−	0.266688i	$-0.0859294\pi$
$127$	183214.	+	133113.i	1.00797	+	0.732335i	0.0441895	+	0.999023i	$0.485929\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	70008.4	−	215464.i	0.370404	−	1.13999i
$130$	−24414.6	−	75140.3i	−0.126704	−	0.389955i
$131$	39966.4	−	29037.3i	0.203478	−	0.147835i	−0.481380	−	0.876512i	$-0.659864\pi$
$131$	39966.4	−	29037.3i	0.203478	−	0.147835i	0.684858	+	0.728677i	$0.259864\pi$
$132$	−121346.			−0.606162
$133$	−114302.	+	83045.2i	−0.560305	+	0.407085i
$134$	150499.	−	109344.i	0.724054	−	0.526056i
$135$	−120097.	−	87255.8i	−0.567151	−	0.412059i
$136$	−32796.9	+	100938.i	−0.152049	+	0.467960i
$137$	−293769.			−1.33723			−0.668613	−	0.743610i	$-0.733112\pi$
$137$	−293769.			−1.33723			−0.668613	+	0.743610i	$0.733112\pi$
$138$	7302.96	+	5305.91i	0.0326438	+	0.0237171i
$139$	−109669.	−	337527.i	−0.481446	−	1.48174i	−0.837062	−	0.547107i	$-0.815729\pi$
$139$	−109669.	−	337527.i	−0.481446	−	1.48174i	0.355616	−	0.934632i	$-0.384271\pi$
$140$	95990.0	−	69740.8i	0.413910	−	0.300723i
$141$	−145024.	+	446339.i	−0.614318	+	1.89068i
$142$	32406.6	+	99737.4i	0.134869	+	0.415085i
$143$	23952.0	+	73716.8i	0.0979496	+	0.301458i
$144$	13146.9	+	40462.0i	0.0528345	+	0.162608i
$145$	−39941.6	−	122928.i	−0.157763	−	0.485545i
$146$	−59378.2	+	182747.i	−0.230539	+	0.709526i
$147$	−176457.	+	128204.i	−0.673513	+	0.489336i
$148$	12760.8	+	39273.6i	0.0478875	+	0.147383i
$149$	293752.	+	213423.i	1.08396	+	0.787547i	0.978370	−	0.206863i	$-0.0663253\pi$
$149$	293752.	+	213423.i	1.08396	+	0.787547i	0.105595	+	0.994409i	$0.466325\pi$
$150$	485727.			1.76264
$151$	46491.1	−	143085.i	0.165931	−	0.510683i	−0.833173	−	0.553013i	$-0.813478\pi$
$151$	46491.1	−	143085.i	0.165931	−	0.510683i	0.999104	+	0.0423296i	$0.0134780\pi$
$152$	−94248.3	−	68475.4i	−0.330876	−	0.240395i
$153$	−222961.	+	161991.i	−0.770017	+	0.559450i
$154$	−94171.5	+	68419.6i	−0.319976	+	0.232476i
$155$	−157391.			−0.526201
$156$	54132.4	−	39329.5i	0.178093	−	0.129392i
$157$	−170302.	−	524135.i	−0.551404	−	1.69705i	−0.705255	−	0.708953i	$-0.749168\pi$
$157$	−170302.	−	524135.i	−0.551404	−	1.69705i	0.153851	−	0.988094i	$-0.450832\pi$
$158$	127402.	−	392104.i	0.406008	−	1.24957i
$159$	105217.	+	76444.3i	0.330059	+	0.239802i
$160$	79149.1	+	57505.2i	0.244425	+	0.177585i
$161$	8659.23			0.0263278
$162$	88767.2	−	273197.i	0.265745	−	0.817879i
$163$	−322336.			−0.950254			−0.475127	−	0.879917i	$-0.657598\pi$
$163$	−322336.			−0.950254			−0.475127	+	0.879917i	$0.657598\pi$
$164$	−71172.3	−	156824.i	−0.206634	−	0.455305i
$165$	−724590.			−2.07196
$166$	89449.4	−	275297.i	0.251946	−	0.775409i
$167$	−394761.			−1.09533			−0.547663	−	0.836699i	$-0.684482\pi$
$167$	−394761.			−1.09533			−0.547663	+	0.836699i	$0.684482\pi$
$168$	81294.1	+	59063.7i	0.222222	+	0.161453i
$169$	265805.	+	193118.i	0.715890	+	0.520124i
$170$	−195840.	+	602732.i	−0.519731	+	1.59957i
$171$	−93480.2	−	287703.i	−0.244472	−	0.752408i
$172$	144972.	−	105328.i	0.373648	−	0.271471i
$173$	226102.			0.574367			0.287183	−	0.957876i	$-0.407281\pi$
$173$	226102.			0.574367			0.287183	+	0.957876i	$0.407281\pi$
$174$	88559.3	−	64342.1i	0.221749	−	0.161110i
$175$	376953.	−	273873.i	0.930449	−	0.676011i
$176$	−77649.7	−	56415.8i	−0.188955	−	0.137284i
$177$	129323.	−	398015.i	0.310272	−	0.954918i
$178$	−566636.			−1.34046
$179$	547922.	+	398089.i	1.27816	+	0.928640i	0.999496	−	0.0317484i	$-0.0101075\pi$
$179$	547922.	+	398089.i	1.27816	+	0.928640i	0.278667	+	0.960388i	$0.410108\pi$
$180$	78504.1	+	241611.i	0.180597	+	0.555821i
$181$	61104.7	−	44395.2i	0.138637	−	0.100725i	−0.516305	−	0.856405i	$-0.672693\pi$
$181$	61104.7	−	44395.2i	0.138637	−	0.100725i	0.654942	+	0.755679i	$0.272693\pi$
$182$	19834.5	−	61044.2i	0.0443856	−	0.136605i
$183$	203102.	+	625084.i	0.448318	+	1.37978i
$184$	2206.39	+	6790.56i	0.00480438	+	0.0147864i
$185$	76198.2	+	234514.i	0.163688	+	0.503778i
$186$	−41190.5	−	126771.i	−0.0873000	−	0.268682i
$187$	192130.	−	591314.i	0.401782	−	1.23656i
$188$	−300313.	+	218190.i	−0.619698	+	0.450237i
$189$	−37267.4	−	114697.i	−0.0758883	−	0.233560i
$190$	−562784.	−	408887.i	−1.13099	−	0.821711i
$191$	436141.			0.865055			0.432528	−	0.901621i	$-0.357622\pi$
$191$	436141.			0.865055			0.432528	+	0.901621i	$0.357622\pi$
$192$	−25603.8	+	78800.3i	−0.0501246	+	0.154268i
$193$	72190.2	+	52449.2i	0.139503	+	0.101355i	0.655348	−	0.755327i	$-0.272522\pi$
$193$	72190.2	+	52449.2i	0.139503	+	0.101355i	−0.515845	+	0.856682i	$0.672522\pi$
$194$	−360873.	+	262190.i	−0.688415	+	0.500163i
$195$	323241.	−	234848.i	0.608751	−	0.442283i
$196$	−172520.			−0.320775
$197$	305322.	−	221829.i	0.560521	−	0.407243i	−0.271128	−	0.962543i	$-0.587397\pi$
$197$	305322.	−	221829.i	0.560521	−	0.407243i	0.831650	+	0.555301i	$0.187397\pi$
$198$	−77016.9	−	237034.i	−0.139612	−	0.429682i
$199$	218390.	−	672134.i	0.390930	−	1.20316i	−0.541156	−	0.840922i	$-0.682013\pi$
$199$	218390.	−	672134.i	0.390930	−	1.20316i	0.932086	−	0.362237i	$-0.117987\pi$
$200$	310819.	+	225823.i	0.549456	+	0.399203i
$201$	761088.	+	552963.i	1.32875	+	0.965396i
$202$	−229513.			−0.395757
$203$	32448.7	−	99866.8i	0.0552659	−	0.170091i
$204$	−536725.			−0.902976
$205$	−424991.	−	936441.i	−0.706309	−	1.55631i
$206$	−180458.			−0.296284
$207$	−5729.32	+	17633.0i	−0.00929346	+	0.0286023i
$208$	52924.7			0.0848203
$209$	552123.	+	401141.i	0.874319	+	0.635230i
$210$	485431.	+	352686.i	0.759590	+	0.551875i
$211$	58604.3	−	180365.i	0.0906199	−	0.278899i	−0.895468	−	0.445127i	$-0.853159\pi$
$211$	58604.3	−	180365.i	0.0906199	−	0.278899i	0.986087	+	0.166228i	$0.0531586\pi$
$212$	31788.3	+	97834.3i	0.0485766	+	0.149504i
$213$	−429053.	+	311725.i	−0.647981	+	0.470785i
$214$	351118.			0.524105
$215$	865669.	−	628945.i	1.27719	−	0.927933i
$216$	80449.8	−	58450.2i	0.117325	−	0.0852416i
$217$	−103445.	−	75157.3i	−0.149128	−	0.108348i
$218$	−264784.	+	814922.i	−0.377356	+	1.16138i
$219$	−971731.			−1.36910
$220$	−463669.	−	336875.i	−0.645879	−	0.469259i
$221$	105943.	+	326058.i	0.145912	+	0.449070i
$222$	−168948.	+	122748.i	−0.230076	+	0.167160i
$223$	−341312.	+	1.05045e6i	−0.459610	+	1.41453i	0.406028	+	0.913861i	$0.366914\pi$
$223$	−341312.	+	1.05045e6i	−0.459610	+	1.41453i	−0.865637	+	0.500672i	$0.833086\pi$
$224$	24560.8	+	75590.3i	0.0327056	+	0.100657i
$225$	308286.	+	948807.i	0.405973	+	1.24946i
$226$	−316683.	−	974649.i	−0.412433	−	1.26934i
$227$	230248.	+	708629.i	0.296572	+	0.912755i	0.982689	+	0.185264i	$0.0593139\pi$
$227$	230248.	+	708629.i	0.296572	+	0.912755i	−0.686117	+	0.727492i	$0.740686\pi$
$228$	182054.	−	560304.i	0.231933	−	0.713817i
$229$	−325252.	+	236309.i	−0.409855	+	0.297777i	−0.773543	−	0.633744i	$-0.781517\pi$
$229$	−325252.	+	236309.i	−0.409855	+	0.297777i	0.363688	+	0.931521i	$0.381517\pi$
$230$	13175.0	+	40548.5i	0.0164222	+	0.0505423i
$231$	−476235.	−	346005.i	−0.587207	−	0.426631i
$232$	86583.4			0.105612
$233$	−309681.	+	953099.i	−0.373701	+	1.15013i	0.570650	+	0.821193i	$0.306691\pi$
$233$	−309681.	+	953099.i	−0.373701	+	1.15013i	−0.944351	+	0.328940i	$0.893309\pi$
$234$	111183.	+	80779.0i	0.132739	+	0.0964403i
$235$	−1.79326e6	+	1.30288e6i	−2.11823	+	1.53898i
$236$	267799.	−	194567.i	0.312989	−	0.227400i
$237$	2.08496e6			2.41116
$238$	−416531.	+	302628.i	−0.476656	+	0.346311i
$239$	−66633.4	−	205077.i	−0.0754566	−	0.232232i	0.906213	−	0.422821i	$-0.138960\pi$
$239$	−66633.4	−	205077.i	−0.0754566	−	0.232232i	−0.981670	+	0.190589i	$0.938960\pi$
$240$	−152888.	+	470540.i	−0.171334	+	0.527313i
$241$	1.41024e6	+	1.02460e6i	1.56405	+	1.13635i	0.932587	+	0.360945i	$0.117546\pi$
$241$	1.41024e6	+	1.02460e6i	1.56405	+	1.13635i	0.631464	+	0.775405i	$0.282454\pi$
$242$	−66286.8	−	48160.2i	−0.0727594	−	0.0528628i
$243$	1.07512e6			1.16800
$244$	−160647.	+	494420.i	−0.172742	+	0.531645i
$245$	−1.03017e6			−1.09646
$246$	643035.	−	587383.i	0.677481	−	0.618847i
$247$	−376317.			−0.392475
$248$	32580.3	−	100272.i	0.0336376	−	0.103526i
$249$	1.46385e6			1.49623
$250$	889817.	+	646490.i	0.900431	+	0.654202i
$251$	226332.	+	164440.i	0.226757	+	0.164749i	0.695363	−	0.718659i	$-0.255244\pi$
$251$	226332.	+	164440.i	0.226757	+	0.164749i	−0.468606	+	0.883407i	$0.655244\pi$
$252$	−63776.9	+	196285.i	−0.0632648	+	0.194709i
$253$	−12925.4	−	39780.3i	−0.0126953	−	0.0390721i
$254$	−732855.	+	532450.i	−0.712744	+	0.517839i
$255$	−3.20494e6			−3.08652
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	392810.	−	285393.i	0.370979	−	0.269532i	−0.386638	−	0.922232i	$-0.626364\pi$
$257$	392810.	−	285393.i	0.370979	−	0.269532i	0.757617	+	0.652700i	$0.226364\pi$
$258$	733137.	+	532655.i	0.685703	+	0.498192i
$259$	−61903.7	+	190520.i	−0.0573412	+	0.176478i
$260$	316029.			0.289930
$261$	181892.	+	132152.i	0.165277	+	0.120081i
$262$	61063.3	+	187933.i	0.0549575	+	0.169142i
$263$	−198750.	+	144401.i	−0.177182	+	0.128730i	−0.672841	−	0.739787i	$-0.734926\pi$
$263$	−198750.	+	144401.i	−0.177182	+	0.128730i	0.495660	+	0.868517i	$0.334926\pi$
$264$	149991.	−	461626.i	0.132451	−	0.407643i
$265$	189817.	+	584197.i	0.166043	+	0.511028i
$266$	−174638.	−	537480.i	−0.151333	−	0.465756i
$267$	−885499.	−	2.72529e6i	−0.760169	−	2.33956i
$268$	229942.	+	707688.i	0.195560	+	0.601873i
$269$	46466.9	−	143010.i	0.0391528	−	0.120500i	−0.929570	−	0.368646i	$-0.879821\pi$
$269$	46466.9	−	143010.i	0.0391528	−	0.120500i	0.968723	+	0.248146i	$0.0798214\pi$
$270$	480389.	−	349023.i	0.401036	−	0.291370i
$271$	484451.	+	1.49099e6i	0.400707	+	1.23325i	0.924427	+	0.381359i	$0.124544\pi$
$271$	484451.	+	1.49099e6i	0.400707	+	1.23325i	−0.523720	+	0.851890i	$0.675456\pi$
$272$	−343453.	−	249533.i	−0.281478	−	0.204506i
$273$	324594.			0.263593
$274$	363119.	−	1.11756e6i	0.292195	−	0.899283i
$275$	−1.82083e6	−	1.32291e6i	−1.45190	−	1.05487i
$276$	−29211.8	+	21223.6i	−0.0230827	+	0.0167706i
$277$	451021.	−	327686.i	0.353181	−	0.256601i	−0.397021	−	0.917809i	$-0.629956\pi$
$277$	451021.	−	327686.i	0.353181	−	0.256601i	0.750202	+	0.661208i	$0.229956\pi$
$278$	1.41959e6			1.10167
$279$	221489.	−	160921.i	0.170350	−	0.123766i
$280$	146660.	+	451372.i	0.111793	+	0.344064i
$281$	−81337.8	+	250332.i	−0.0614507	+	0.189126i	−0.977069	−	0.212923i	$-0.931702\pi$
$281$	−81337.8	+	250332.i	−0.0614507	+	0.189126i	0.915618	+	0.402049i	$0.131702\pi$
$282$	−1.51872e6	−	1.10341e6i	−1.13724	−	0.826256i
$283$	−1.20720e6	−	877079.i	−0.896007	−	0.650987i	0.0414303	−	0.999141i	$-0.486809\pi$
$283$	−1.20720e6	−	877079.i	−0.896007	−	0.650987i	−0.937437	+	0.348154i	$0.886809\pi$
$284$	−419480.			−0.308614
$285$	1.08710e6	−	3.34574e6i	0.792787	−	2.43995i
$286$	−310042.			−0.224133
$287$	167844.	−	818414.i	0.120282	−	0.586501i
$288$	−170177.			−0.120898
$289$	411051.	−	1.26508e6i	0.289501	−	0.890994i
$290$	517015.			0.361001
$291$	−1.82497e6	−	1.32592e6i	−1.26335	−	0.917878i
$292$	−621816.	−	451776.i	−0.426781	−	0.310074i
$293$	13603.3	−	41866.7i	0.00925711	−	0.0284905i	−0.946321	−	0.323228i	$-0.895232\pi$
$293$	13603.3	−	41866.7i	0.00925711	−	0.0284905i	0.955578	+	0.294737i	$0.0952321\pi$
$294$	−269603.	−	829752.i	−0.181910	−	0.559861i
$295$	1.59911e6	−	1.16182e6i	1.06985	−	0.777290i
$296$	−165179.			−0.109578
$297$	−471289.	+	342411.i	−0.310024	+	0.225246i
$298$	−1.17501e6	+	853693.i	−0.766479	+	0.556880i
$299$	18659.3	+	13556.8i	0.0120703	+	0.00876957i
$300$	−600391.	+	1.84781e6i	−0.385151	+	1.18537i
$301$	869292.			0.553031
$302$	486862.	+	353726.i	0.307177	+	0.223177i
$303$	−358667.	−	1.10386e6i	−0.224432	−	0.690731i
$304$	376993.	−	273902.i	0.233964	−	0.169985i
$305$	−959270.	+	2.95233e6i	−0.590461	+	1.81725i
$306$	−340654.	−	1.04843e6i	−0.207974	−	0.640080i
$307$	486959.	+	1.49870e6i	0.294881	+	0.907549i	0.983262	+	0.182200i	$0.0583218\pi$
$307$	486959.	+	1.49870e6i	0.294881	+	0.907549i	−0.688381	+	0.725349i	$0.741678\pi$
$308$	−143881.	−	442821.i	−0.0864226	−	0.265982i
$309$	−282008.	−	867931.i	−0.168022	−	0.517117i
$310$	194546.	−	598752.i	0.114979	−	0.353869i
$311$	2.63386e6	−	1.91361e6i	1.54416	−	1.12190i	0.596497	−	0.802615i	$-0.296559\pi$
$311$	2.63386e6	−	1.91361e6i	1.54416	−	1.12190i	0.947660	−	0.319281i	$-0.103441\pi$
$312$	82707.0	+	254546.i	0.0481012	+	0.148040i
$313$	−1.05568e6	−	766999.i	−0.609078	−	0.442521i	0.240012	−	0.970770i	$-0.422849\pi$
$313$	−1.05568e6	−	766999.i	−0.609078	−	0.442521i	−0.849089	+	0.528249i	$0.822849\pi$
$314$	2.20443e6			1.26175
$315$	−380831.	+	1.17208e6i	−0.216250	+	0.665548i
$316$	1.33418e6	+	969335.i	0.751615	+	0.546080i
$317$	−2.16441e6	+	1.57253e6i	−1.20974	+	0.878925i	−0.995207	−	0.0977929i	$-0.968822\pi$
$317$	−2.16441e6	+	1.57253e6i	−1.20974	+	0.878925i	−0.214529	+	0.976718i	$0.568822\pi$
$318$	−420866.	+	305777.i	−0.233387	+	0.169565i
$319$	−507221.			−0.279075
$320$	−316596.	+	230021.i	−0.172835	+	0.125572i
$321$	548702.	+	1.68873e6i	0.297217	+	0.914741i
$322$	−10703.4	+	32941.7i	−0.00575284	+	0.0177054i
$323$	2.44210e6	+	1.77429e6i	1.30244	+	0.946277i
$324$	929582.	+	675381.i	0.491955	+	0.357426i
$325$	1.24105e6			0.651748
$326$	398429.	−	1.22624e6i	0.207638	−	0.639045i
$327$	−4.33323e6			−2.24100
$328$	684567.	−	76910.7i	0.351343	−	0.0394732i
$329$	−1.80076e6			−0.917206
$330$	895642.	−	2.75650e6i	0.452741	−	1.39339i
$331$	648665.			0.325424			0.162712	−	0.986674i	$-0.447976\pi$
$331$	648665.			0.325424			0.162712	+	0.986674i	$0.447976\pi$
$332$	936726.	+	680571.i	0.466409	+	0.338866i
$333$	−347003.	−	252112.i	−0.171484	−	0.124590i
$334$	487951.	−	1.50176e6i	0.239337	−	0.736605i
$335$	1.37305e6	+	4.22581e6i	0.668458	+	2.05730i
$336$	−325177.	+	236255.i	−0.157134	+	0.114165i
$337$	492670.			0.236310			0.118155	−	0.992995i	$-0.462302\pi$
$337$	492670.			0.236310			0.118155	+	0.992995i	$0.462302\pi$
$338$	−1.06322e6	+	772474.i	−0.506210	+	0.367783i
$339$	4.19277e6	−	3.04623e6i	1.98154	−	1.43967i
$340$	−2.05086e6	−	1.49004e6i	−0.962141	−	0.699036i
$341$	−190861.	+	587409.i	−0.0888855	+	0.273561i
$342$	1.21003e6			0.559412
$343$	−1.73245e6	−	1.25870e6i	−0.795108	−	0.577680i
$344$	221497.	+	681698.i	0.100919	+	0.310596i
$345$	−174433.	+	126733.i	−0.0789005	+	0.0573246i
$346$	−279478.	+	860144.i	−0.125504	+	0.386261i
$347$	−581286.	−	1.78901e6i	−0.259159	−	0.797609i	−0.992982	−	0.118268i	$-0.962266\pi$
$347$	−581286.	−	1.78901e6i	−0.259159	−	0.797609i	0.733823	−	0.679341i	$-0.237734\pi$
$348$	135307.	+	416431.i	0.0598923	+	0.184329i
$349$	964541.	+	2.96855e6i	0.423894	+	1.30461i	0.904049	+	0.427428i	$0.140580\pi$
$349$	964541.	+	2.96855e6i	0.423894	+	1.30461i	−0.480156	+	0.877183i	$0.659420\pi$
$350$	575934.	+	1.77254e6i	0.251306	+	0.773439i
$351$	99263.1	−	305500.i	0.0430051	−	0.132356i
$352$	310599.	−	225663.i	0.133611	−	0.0970742i
$353$	−404154.	−	1.24386e6i	−0.172628	−	0.531293i	0.826890	−	0.562364i	$-0.190108\pi$
$353$	−404154.	−	1.24386e6i	−0.172628	−	0.531293i	−0.999517	+	0.0310712i	$0.990108\pi$
$354$	1.35429e6	+	983947.i	0.574384	+	0.417314i
$355$	−2.50484e6			−1.05489
$356$	700400.	−	2.15561e6i	0.292901	−	0.901457i
$357$	−2.10644e6	−	1.53042e6i	−0.874739	−	0.635535i
$358$	−2.19169e6	+	1.59235e6i	−0.903797	+	0.656647i
$359$	−2.07562e6	+	1.50802e6i	−0.849984	+	0.617549i	−0.925142	−	0.379622i	$-0.876054\pi$
$359$	−2.07562e6	+	1.50802e6i	−0.849984	+	0.617549i	0.0751577	+	0.997172i	$0.476054\pi$
$360$	−1.01618e6			−0.413251
$361$	−677379.	+	492145.i	−0.273567	+	0.198758i
$362$	93359.7	+	287332.i	0.0374445	+	0.115242i
$363$	128042.	−	394074.i	0.0510020	−	0.156968i
$364$	207709.	+	150910.i	0.0821679	+	0.0596985i
$365$	−3.71305e6	−	2.69769e6i	−1.45881	−	1.05989i
$366$	−2.62901e6			−1.02586
$367$	81618.1	−	251195.i	0.0316316	−	0.0973521i	−0.933994	−	0.357288i	$-0.883701\pi$
$367$	81618.1	−	251195.i	0.0316316	−	0.0973521i	0.965626	+	0.259936i	$0.0837015\pi$
$368$	−28560.1			−0.0109936
$369$	1.55551e6	+	883283.i	0.594712	+	0.337702i
$370$	−986331.			−0.374557
$371$	−154208.	+	474604.i	−0.0581664	+	0.179018i
$372$	533180.			0.199764
$373$	1.28071e6	+	930492.i	0.476628	+	0.346290i	0.800019	−	0.599975i	$-0.204823\pi$
$373$	1.28071e6	+	930492.i	0.476628	+	0.346290i	−0.323391	+	0.946265i	$0.604823\pi$
$374$	2.01201e6	+	1.46181e6i	0.743790	+	0.540395i
$375$	−1.71881e6	+	5.28994e6i	−0.631174	+	1.94255i
$376$	−458838.	−	1.41216e6i	−0.167375	−	0.515126i
$377$	226272.	−	164396.i	0.0819931	−	0.0595715i
$378$	482400.			0.173651
$379$	3.14086e6	−	2.28197e6i	1.12318	−	0.816040i	0.138494	−	0.990363i	$-0.455774\pi$
$379$	3.14086e6	−	2.28197e6i	1.12318	−	0.816040i	0.984688	+	0.174324i	$0.0557739\pi$
$380$	2.25114e6	−	1.63555e6i	0.799729	−	0.581037i
$381$	−3.70612e6	−	2.69266e6i	−1.30800	−	0.950317i
$382$	−539100.	+	1.65918e6i	−0.189021	+	0.581748i
$383$	−1.24107e6			−0.432314			−0.216157	−	0.976359i	$-0.569352\pi$
$383$	−1.24107e6			−0.432314			−0.216157	+	0.976359i	$0.569352\pi$
$384$	−268126.	−	194805.i	−0.0927922	−	0.0674175i
$385$	−859157.	−	2.64421e6i	−0.295407	−	0.909169i
$386$	−288761.	+	209797.i	−0.0986438	+	0.0716689i
$387$	−575161.	+	1.77016e6i	−0.195214	+	0.600808i
$388$	−551365.	−	1.69693e6i	−0.185935	−	0.572248i
$389$	−570896.	−	1.75704e6i	−0.191286	−	0.588717i	−1.00000		0.000515280i	$-0.999836\pi$
$389$	−570896.	−	1.75704e6i	−0.191286	−	0.588717i	0.808714	−	0.588202i	$-0.200164\pi$
$390$	493868.	+	1.51997e6i	0.164418	+	0.506026i
$391$	−57170.5	−	175953.i	−0.0189117	−	0.0582041i
$392$	213247.	−	656306.i	0.0700918	−	0.215720i
$393$	−808457.	+	587378.i	−0.264044	+	0.191839i
$394$	466490.	+	1.43571e6i	0.151392	+	0.465936i
$395$	7.96676e6	+	5.78819e6i	2.56915	+	1.86659i
$396$	996927.			0.319467
$397$	313744.	−	965606.i	0.0999079	−	0.307485i	−0.888594	−	0.458695i	$-0.848317\pi$
$397$	313744.	−	965606.i	0.0999079	−	0.307485i	0.988502	+	0.151210i	$0.0483170\pi$
$398$	2.28700e6	+	1.66161e6i	0.723701	+	0.525800i
$399$	2.31215e6	−	1.67987e6i	0.727081	−	0.528256i
$400$	−1.24328e6	+	903293.i	−0.388524	+	0.282279i
$401$	−4.10201e6			−1.27390			−0.636951	−	0.770904i	$-0.719805\pi$
$401$	−4.10201e6			−1.27390			−0.636951	+	0.770904i	$0.719805\pi$
$402$	−3.04435e6	+	2.21185e6i	−0.939571	+	0.682638i
$403$	−105243.	−	323904.i	−0.0322798	−	0.0993469i
$404$	283694.	−	873119.i	0.0864761	−	0.266146i
$405$	5.55081e6	+	4.03290e6i	1.68158	+	1.22174i
$406$	339807.	+	246884.i	0.102310	+	0.0743324i
$407$	967645.			0.289554
$408$	663428.	−	2.04182e6i	0.197307	−	0.607250i
$409$	2.56960e6			0.759553			0.379776	−	0.925078i	$-0.376001\pi$
$409$	2.56960e6			0.759553			0.379776	+	0.925078i	$0.376001\pi$
$410$	4.08775e6	−	459256.i	1.20095	−	0.134926i
$411$	5.94249e6			1.73526
$412$	223059.	−	686504.i	0.0647405	−	0.199251i
$413$	1.60580e6			0.463250
$414$	−59998.2	−	43591.3i	−0.0172043	−	0.0124997i
$415$	5.59347e6	+	4.06389e6i	1.59427	+	1.15830i
$416$	−65418.5	+	201337.i	−0.0185339	+	0.0570415i
$417$	2.21843e6	+	6.82764e6i	0.624750	+	1.92278i
$418$	−2.20849e6	+	1.60456e6i	−0.618237	+	0.449175i
$419$	3.63703e6			1.01207			0.506037	−	0.862512i	$-0.331110\pi$
$419$	3.63703e6			1.01207			0.506037	+	0.862512i	$0.331110\pi$
$420$	−1.94172e6	+	1.41075e6i	−0.537112	+	0.390234i
$421$	−5.30633e6	+	3.85528e6i	−1.45911	+	1.06011i	−0.475522	+	0.879704i	$0.657741\pi$
$421$	−5.30633e6	+	3.85528e6i	−1.45911	+	1.06011i	−0.983592	+	0.180405i	$0.942259\pi$
$422$	613712.	+	445888.i	0.167758	+	0.121883i
$423$	1.19146e6	−	3.66695e6i	0.323765	−	0.996446i
$424$	−411476.			−0.111155
$425$	−8.05374e6	−	5.85139e6i	−2.16284	−	1.57140i
$426$	−655535.	−	2.01753e6i	−0.175014	−	0.538636i
$427$	−2.04027e6	+	1.48234e6i	−0.541524	+	0.393440i
$428$	−434005.	+	1.33573e6i	−0.114521	+	0.352460i
$429$	−484512.	−	1.49117e6i	−0.127105	−	0.391188i
$430$	1.32262e6	+	4.07062e6i	0.344957	+	1.06167i
$431$	603037.	+	1.85596e6i	0.156369	+	0.481255i	0.998297	−	0.0583354i	$-0.0185793\pi$
$431$	603037.	+	1.85596e6i	0.156369	+	0.481255i	−0.841928	+	0.539590i	$0.818579\pi$
$432$	122916.	+	378297.i	0.0316884	+	0.0975268i
$433$	−440038.	+	1.35430e6i	−0.112790	+	0.347132i	−0.991480	−	0.130261i	$-0.958418\pi$
$433$	−440038.	+	1.35430e6i	−0.112790	+	0.347132i	0.878690	+	0.477393i	$0.158418\pi$
$434$	413780.	−	300629.i	0.105450	−	0.0766137i
$435$	807955.	+	2.48663e6i	0.204722	+	0.630069i
$436$	−2.77286e6	−	2.01460e6i	−0.698572	−	0.507542i
$437$	203075.			0.0508689
$438$	1.20113e6	−	3.69668e6i	0.299160	−	0.920719i
$439$	−2.21660e6	−	1.61046e6i	−0.548942	−	0.398830i	0.278453	−	0.960450i	$-0.410178\pi$
$439$	−2.21660e6	−	1.61046e6i	−0.548942	−	0.398830i	−0.827395	+	0.561620i	$0.810178\pi$
$440$	1.85468e6	−	1.34750e6i	0.456706	−	0.331816i
$441$	1.44970e6	−	1.05327e6i	0.354963	−	0.257895i
$442$	−1.37135e6			−0.333882
$443$	−4.21824e6	+	3.06473e6i	−1.02123	+	0.741965i	−0.966534	−	0.256538i	$-0.917418\pi$
$443$	−4.21824e6	+	3.06473e6i	−1.02123	+	0.741965i	−0.0546931	+	0.998503i	$0.517418\pi$
$444$	−258130.	−	794442.i	−0.0621414	−	0.191252i
$445$	4.18230e6	−	1.28718e7i	1.00119	−	3.08133i
$446$	−3.57426e6	−	2.59685e6i	−0.850843	−	0.618173i
$447$	−5.94214e6	−	4.31722e6i	−1.40661	−	1.02196i
$448$	−317921.			−0.0748385
$449$	−496468.	+	1.52797e6i	−0.116218	+	0.357684i	−0.992199	−	0.124662i	$-0.960215\pi$
$449$	−496468.	+	1.52797e6i	−0.116218	+	0.357684i	0.875981	+	0.482346i	$0.160215\pi$
$450$	−3.99054e6			−0.928967
$451$	−4.01031e6	+	450556.i	−0.928403	+	0.104306i
$452$	4.09923e6			0.943748
$453$	−940442.	+	2.89438e6i	−0.215321	+	0.662690i
$454$	−2.98039e6			−0.678630
$455$	1.24029e6	+	901125.i	0.280864	+	0.204059i
$456$	1.90649e6	+	1.38515e6i	0.429362	+	0.311950i
$457$	2.60667e6	−	8.02251e6i	0.583843	−	1.79688i	−0.0200272	−	0.999799i	$-0.506375\pi$
$457$	2.60667e6	−	8.02251e6i	0.583843	−	1.79688i	0.603870	−	0.797083i	$-0.293625\pi$
$458$	−496940.	−	1.52942e6i	−0.110698	−	0.340694i
$459$	−2.08456e6	+	1.51452e6i	−0.461831	+	0.335540i
$460$	−170541.			−0.0375780
$461$	−4.74328e6	+	3.44620e6i	−1.03951	+	0.755245i	−0.970189	−	0.242350i	$-0.922082\pi$
$461$	−4.74328e6	+	3.44620e6i	−1.03951	+	0.755245i	−0.0693162	+	0.997595i	$0.522082\pi$
$462$	1.90494e6	−	1.38402e6i	0.415218	−	0.301674i
$463$	4.76037e6	+	3.45861e6i	1.03202	+	0.749807i	0.968712	−	0.248187i	$-0.0798347\pi$
$463$	4.76037e6	+	3.45861e6i	1.03202	+	0.749807i	0.0633089	+	0.997994i	$0.479835\pi$
$464$	−107023.	+	329383.i	−0.0230772	+	0.0710242i
$465$	3.18378e6			0.682826
$466$	−3.24302e6	−	2.35619e6i	−0.691806	−	0.502627i
$467$	−681315.	−	2.09687e6i	−0.144563	−	0.444918i	0.852392	−	0.522903i	$-0.175151\pi$
$467$	−681315.	−	2.09687e6i	−0.144563	−	0.444918i	−0.996954	+	0.0779856i	$0.975151\pi$
$468$	−444731.	+	323116.i	−0.0938604	+	0.0681936i
$469$	−1.11547e6	+	3.43306e6i	−0.234167	+	0.720692i
$470$	−2.73986e6	−	8.43241e6i	−0.572115	−	1.76079i
$471$	3.44493e6	+	1.06024e7i	0.715531	+	2.20218i
$472$	409160.	+	1.25927e6i	0.0845354	+	0.260173i
$473$	−1.29757e6	−	3.99350e6i	−0.266672	−	0.820732i
$474$	−2.57715e6	+	7.93165e6i	−0.526858	+	1.62150i
$475$	8.84023e6	−	6.42281e6i	1.79775	−	1.30614i
$476$	−636403.	−	1.95865e6i	−0.128740	−	0.396222i
$477$	−864418.	−	628036.i	−0.173951	−	0.126383i
$478$	862521.			0.172663
$479$	2.92398e6	−	8.99907e6i	0.582284	−	1.79209i	−0.0276296	−	0.999618i	$-0.508796\pi$
$479$	2.92398e6	−	8.99907e6i	0.582284	−	1.79209i	0.609914	−	0.792468i	$-0.291204\pi$
$480$	−1.60106e6	−	1.16324e6i	−0.317179	−	0.230444i
$481$	−431668.	+	313625.i	−0.0850721	+	0.0618085i
$482$	−5.64097e6	+	4.09840e6i	−1.10595	+	0.803521i
$483$	−175163.			−0.0341644
$484$	265147.	−	192641.i	0.0514486	−	0.0373796i
$485$	−3.29236e6	−	1.01329e7i	−0.635555	−	1.95604i
$486$	−1.32892e6	+	4.09000e6i	−0.255216	+	0.785476i
$487$	3.51491e6	+	2.55373e6i	0.671571	+	0.487925i	0.870551	−	0.492079i	$-0.163763\pi$
$487$	3.51491e6	+	2.55373e6i	0.671571	+	0.487925i	−0.198980	+	0.980004i	$0.563763\pi$
$488$	−1.68232e6	−	1.22227e6i	−0.319785	−	0.232337i
$489$	6.52035e6			1.23310
$490$	1.27336e6	−	3.91900e6i	0.239586	−	0.737369i
$491$	−7.36882e6			−1.37941			−0.689706	−	0.724089i	$-0.742260\pi$
$491$	−7.36882e6			−1.37941			−0.689706	+	0.724089i	$0.742260\pi$
$492$	1.43970e6	+	3.17230e6i	0.268139	+	0.590828i
$493$	−2.24349e6			−0.415726
$494$	465154.	−	1.43160e6i	0.0857589	−	0.263939i
$495$	5.95294e6			1.09199
$496$	341185.	+	247885.i	0.0622710	+	0.0452425i
$497$	−1.64630e6	−	1.19611e6i	−0.298963	−	0.217210i
$498$	−1.80942e6	+	5.56882e6i	−0.326938	+	1.00621i
$499$	157080.	+	483441.i	0.0282402	+	0.0869145i	0.964183	−	0.265237i	$-0.0854502\pi$
$499$	157080.	+	483441.i	0.0282402	+	0.0869145i	−0.935943	+	0.352151i	$0.885450\pi$
$500$	−3.55927e6	+	2.58596e6i	−0.636701	+	0.462590i
$501$	7.98539e6			1.42135
$502$	−905327.	+	657758.i	−0.160342	+	0.116495i
$503$	−2.07709e6	+	1.50910e6i	−0.366047	+	0.265948i	−0.755570	−	0.655068i	$-0.772640\pi$
$503$	−2.07709e6	+	1.50910e6i	−0.366047	+	0.265948i	0.389523	+	0.921017i	$0.372640\pi$
$504$	−667881.	−	485244.i	−0.117118	−	0.0850910i
$505$	1.69402e6	−	5.21365e6i	0.295590	−	0.909732i
$506$	167310.			0.0290499
$507$	−5.37681e6	−	3.90648e6i	−0.928976	−	0.674941i
$508$	−1.11970e6	−	3.44609e6i	−0.192506	−	0.592471i
$509$	3.34716e6	−	2.43185e6i	0.572640	−	0.416047i	−0.263423	−	0.964680i	$-0.584852\pi$
$509$	3.34716e6	−	2.43185e6i	0.572640	−	0.416047i	0.836063	+	0.548633i	$0.184852\pi$
$510$	3.96153e6	−	1.21923e7i	0.674430	−	2.07568i
$511$	−1.15220e6	−	3.54610e6i	−0.195198	−	0.600756i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−873988.	−	2.68986e6i	−0.146626	−	0.451270i
$514$	600160.	+	1.84710e6i	0.100198	+	0.308378i
$515$	1.33195e6	−	4.09932e6i	0.221294	−	0.681073i
$516$	−2.93255e6	+	2.13062e6i	−0.484865	+	0.352275i
$517$	2.68795e6	+	8.27266e6i	0.442278	+	1.36119i
$518$	−648264.	−	470991.i	−0.106152	−	0.0771238i
$519$	−4.57369e6			−0.745329
$520$	−390633.	+	1.20224e6i	−0.0633520	+	0.194978i
$521$	7.13801e6	+	5.18607e6i	1.15208	+	0.837035i	0.988756	−	0.149537i	$-0.0477783\pi$
$521$	7.13801e6	+	5.18607e6i	1.15208	+	0.837035i	0.163324	+	0.986572i	$0.447778\pi$
$522$	−727568.	+	528609.i	−0.116869	+	0.0849100i
$523$	−1.50510e6	+	1.09352e6i	−0.240608	+	0.174812i	−0.701554	−	0.712616i	$-0.747510\pi$
$523$	−1.50510e6	+	1.09352e6i	−0.240608	+	0.174812i	0.460946	+	0.887428i	$0.347510\pi$
$524$	−790419.			−0.125756
$525$	−7.62517e6	+	5.54001e6i	−1.20740	+	0.877227i
$526$	−303664.	−	934580.i	−0.0478551	−	0.147283i
$527$	−844199.	+	2.59818e6i	−0.132409	+	0.407514i
$528$	1.57073e6	+	1.14120e6i	0.245198	+	0.178147i
$529$	5.19704e6	+	3.77587e6i	0.807453	+	0.586649i
$530$	−2.45705e6			−0.379947
$531$	−1.06247e6	+	3.26993e6i	−0.163523	+	0.503272i
$532$	2.26056e6			0.346287
$533$	1.64298e6	−	1.50078e6i	0.250503	−	0.228823i
$534$	1.14621e7			1.73945
$535$	−2.59157e6	+	7.97604e6i	−0.391452	+	1.20477i
$536$	−2.97643e6			−0.447490
$537$	−1.10836e7	−	8.05270e6i	−1.65861	−	1.20505i
$538$	486608.	+	353541.i	0.0724809	+	0.0526604i
$539$	−1.24924e6	+	3.84475e6i	−0.185214	+	0.570029i
$540$	733969.	+	2.25893e6i	0.108316	+	0.333363i
$541$	−8.38441e6	+	6.09163e6i	−1.23163	+	0.894829i	−0.997011	−	0.0772587i	$-0.975383\pi$
$541$	−8.38441e6	+	6.09163e6i	−1.23163	+	0.894829i	−0.234616	+	0.972088i	$0.575383\pi$
$542$	−6.27087e6			−0.916916
$543$	−1.23605e6	+	898044.i	−0.179902	+	0.130707i
$544$	1.37381e6	−	998133.i	0.199035	−	0.144608i
$545$	−1.65575e7	−	1.20298e7i	−2.38784	−	1.73487i
$546$	−401220.	+	1.23483e6i	−0.0575971	+	0.177266i
$547$	6.43341e6			0.919333			0.459666	−	0.888092i	$-0.347969\pi$
$547$	6.43341e6			0.919333			0.459666	+	0.888092i	$0.347969\pi$
$548$	3.80263e6	+	2.76277e6i	0.540920	+	0.393001i
$549$	−1.66861e6	−	5.13544e6i	−0.236278	−	0.727188i
$550$	7.28333e6	−	5.29165e6i	1.02665	−	0.745906i
$551$	760980.	−	2.34206e6i	0.106781	−	0.328638i
$552$	−44631.7	−	137362.i	−0.00623442	−	0.0191876i
$553$	2.47217e6	+	7.60855e6i	0.343768	+	1.05801i
$554$	689098.	+	2.12083e6i	0.0953909	+	0.293583i
$555$	−1.54137e6	−	4.74385e6i	−0.212410	−	0.653730i
$556$	−1.75471e6	+	5.40044e6i	−0.240723	+	0.740870i
$557$	4.17853e6	−	3.03588e6i	0.570671	−	0.414616i	−0.264678	−	0.964337i	$-0.585266\pi$
$557$	4.17853e6	−	3.03588e6i	0.570671	−	0.414616i	0.835349	+	0.549720i	$0.185266\pi$
$558$	338405.	+	1.04150e6i	0.0460098	+	0.141604i
$559$	1.87319e6	+	1.36095e6i	0.253543	+	0.184210i
$560$	−1.89840e6			−0.255810
$561$	−3.88648e6	+	1.19613e7i	−0.521373	+	1.60462i
$562$	−851781.	−	618855.i	−0.113759	−	0.0826510i
$563$	2.81659e6	−	2.04637e6i	0.374500	−	0.272090i	−0.384574	−	0.923094i	$-0.625652\pi$
$563$	2.81659e6	−	2.04637e6i	0.374500	−	0.272090i	0.759075	+	0.651004i	$0.225652\pi$
$564$	6.07486e6	−	4.41364e6i	0.804153	−	0.584251i
$565$	2.44777e7			3.22589
$566$	4.82878e6	−	3.50831e6i	0.633573	−	0.460317i
$567$	1.72247e6	+	5.30123e6i	0.225006	+	0.692498i
$568$	518506.	−	1.59580e6i	0.0674346	−	0.207542i
$569$	−3.03187e6	−	2.20278e6i	−0.392581	−	0.285227i	0.373931	−	0.927456i	$-0.378010\pi$
$569$	−3.03187e6	−	2.20278e6i	−0.392581	−	0.285227i	−0.766512	+	0.642230i	$0.778010\pi$
$570$	1.13842e7	+	8.27113e6i	1.46763	+	1.06630i
$571$	8.09825e6			1.03944			0.519721	−	0.854336i	$-0.326036\pi$
$571$	8.09825e6			1.03944			0.519721	+	0.854336i	$0.326036\pi$
$572$	383233.	−	1.17947e6i	0.0489748	−	0.150729i
$573$	−8.82245e6			−1.12254
$574$	2.90597e6	+	1.65013e6i	0.368138	+	0.209044i
$575$	−669715.			−0.0844734
$576$	210351.	−	647392.i	0.0264172	−	0.0813039i
$577$	1.77622e6			0.222105			0.111052	−	0.993815i	$-0.464578\pi$
$577$	1.77622e6			0.222105			0.111052	+	0.993815i	$0.464578\pi$
$578$	4.30458e6	+	3.12746e6i	0.535934	+	0.389379i
$579$	−1.46029e6	−	1.06096e6i	−0.181027	−	0.131524i
$580$	−639066.	+	1.96684e6i	−0.0788816	+	0.242773i
$581$	1.73571e6	+	5.34197e6i	0.213323	+	0.656539i
$582$	7.29989e6	−	5.30368e6i	0.893324	−	0.649038i
$583$	2.41050e6			0.293721
$584$	2.48726e6	−	1.80710e6i	0.301780	−	0.219256i
$585$	−2.65562e6	+	1.92942e6i	−0.320831	+	0.233097i
$586$	142456.	+	103500.i	0.0171370	+	0.0124508i
$587$	586340.	−	1.80457e6i	0.0702351	−	0.216161i	−0.909778	−	0.415096i	$-0.863748\pi$
$587$	586340.	−	1.80457e6i	0.0702351	−	0.216161i	0.980013	+	0.198934i	$0.0637480\pi$
$588$	3.48981e6			0.416254
$589$	−2.42597e6	−	1.76257e6i	−0.288136	−	0.209343i
$590$	2.44322e6	+	7.51945e6i	0.288956	+	0.889315i
$591$	−6.17617e6	+	4.48725e6i	−0.727362	+	0.528460i
$592$	204172.	−	628377.i	0.0239438	−	0.0736913i
$593$	−1.98031e6	−	6.09478e6i	−0.231258	−	0.711740i	−0.997596	−	0.0693015i	$-0.977923\pi$
$593$	−1.98031e6	−	6.09478e6i	−0.231258	−	0.711740i	0.766338	−	0.642438i	$-0.222077\pi$
$594$	−720065.	−	2.21613e6i	−0.0837347	−	0.257709i
$595$	−3.80015e6	−	1.16957e7i	−0.440056	−	1.35435i
$596$	−1.79525e6	−	5.52522e6i	−0.207019	−	0.637139i
$597$	−4.41767e6	+	1.35962e7i	−0.507292	+	1.56128i
$598$	−74637.2	+	54227.1i	−0.00853498	+	0.00620103i
$599$	1.77914e6	+	5.47562e6i	0.202601	+	0.623543i	0.999803	+	0.0198303i	$0.00631260\pi$
$599$	1.77914e6	+	5.47562e6i	0.202601	+	0.623543i	−0.797202	+	0.603713i	$0.793687\pi$
$600$	−6.28738e6	−	4.56805e6i	−0.713003	−	0.518027i
$601$	−8.61261e6			−0.972632			−0.486316	−	0.873783i	$-0.661660\pi$
$601$	−8.61261e6			−0.972632			−0.486316	+	0.873783i	$0.661660\pi$
$602$	−1.07450e6	+	3.30698e6i	−0.120842	+	0.371912i
$603$	−6.25280e6	−	4.54292e6i	−0.700295	−	0.508794i
$604$	−1.94745e6	+	1.41490e6i	−0.217207	+	0.157810i
$605$	1.58327e6	−	1.15032e6i	0.175860	−	0.127770i
$606$	4.64268e6			0.513556
$607$	−7.38894e6	+	5.36838e6i	−0.813974	+	0.591387i	−0.914980	−	0.403499i	$-0.867794\pi$
$607$	−7.38894e6	+	5.36838e6i	−0.813974	+	0.591387i	0.101006	+	0.994886i	$0.467794\pi$
$608$	575994.	+	1.77273e6i	0.0631916	+	0.194484i
$609$	−656385.	+	2.02015e6i	−0.0717159	+	0.220719i
$610$	−1.00456e7	−	7.29856e6i	−1.09308	−	0.794168i
$611$	−3.88037e6	−	2.81925e6i	−0.420504	−	0.305514i
$612$	4.40952e6			0.475897
$613$	−3.01234e6	+	9.27103e6i	−0.323782	+	0.996498i	0.648205	+	0.761465i	$0.275520\pi$
$613$	−3.01234e6	+	9.27103e6i	−0.323782	+	0.996498i	−0.971987	+	0.235033i	$0.924480\pi$
$614$	−6.30333e6			−0.674759
$615$	8.59689e6	+	1.89427e7i	0.916544	+	2.01955i
$616$	1.86244e6			0.197756
$617$	1.94470e6	−	5.98516e6i	0.205655	−	0.632941i	−0.794031	−	0.607877i	$-0.792021\pi$
$617$	1.94470e6	−	5.98516e6i	0.205655	−	0.632941i	0.999686	−	0.0250634i	$-0.00797878\pi$
$618$	3.65039e6			0.384475
$619$	1.12364e7	+	8.16369e6i	1.17869	+	0.856367i	0.992023	−	0.126057i	$-0.0402321\pi$
$619$	1.12364e7	+	8.16369e6i	1.17869	+	0.856367i	0.186665	+	0.982424i	$0.440232\pi$
$620$	2.03732e6	+	1.48020e6i	0.212853	+	0.154647i
$621$	−53566.0	+	164859.i	−0.00557391	+	0.0171547i
$622$	4.02418e6	+	1.23851e7i	0.417063	+	1.28359i
$623$	8.89532e6	−	6.46283e6i	0.918209	−	0.667118i
$624$	−1.07058e6			−0.110067
$625$	−6.07671e6	+	4.41499e6i	−0.622255	+	0.452095i
$626$	4.22273e6	−	3.06800e6i	0.430683	−	0.312910i
$627$	−1.11686e7	−	8.11444e6i	−1.13456	−	0.824308i
$628$	−2.72483e6	+	8.38616e6i	−0.275702	+	0.848524i
$629$	4.28000e6			0.431338
$630$	−3.98811e6	−	2.89753e6i	−0.400328	−	0.290855i
$631$	934309.	+	2.87551e6i	0.0934151	+	0.287502i	0.986837	−	0.161716i	$-0.0517027\pi$
$631$	934309.	+	2.87551e6i	0.0934151	+	0.287502i	−0.893422	+	0.449218i	$0.851703\pi$
$632$	−5.33670e6	+	3.87734e6i	−0.531472	+	0.386137i
$633$	−1.18547e6	+	3.64851e6i	−0.117593	+	0.361914i
$634$	−3.30692e6	−	1.01776e7i	−0.326739	−	1.00560i
$635$	−6.68607e6	−	2.05776e7i	−0.658016	−	2.02517i
$636$	−643027.	−	1.97903e6i	−0.0630356	−	0.194004i
$637$	−688844.	−	2.12004e6i	−0.0672624	−	0.207012i
$638$	626959.	−	1.92958e6i	0.0609800	−	0.187677i
$639$	3.52493e6	−	2.56101e6i	0.341506	−	0.248119i
$640$	−483716.	−	1.48873e6i	−0.0466811	−	0.143670i
$641$	−504112.	−	366259.i	−0.0484598	−	0.0352081i	0.563292	−	0.826258i	$-0.309535\pi$
$641$	−504112.	−	366259.i	−0.0484598	−	0.0352081i	−0.611751	+	0.791050i	$0.709535\pi$
$642$	−7.10255e6			−0.680106
$643$	305209.	−	939338.i	0.0291119	−	0.0895972i	−0.935445	−	0.353473i	$-0.885001\pi$
$643$	305209.	−	939338.i	0.0291119	−	0.0895972i	0.964557	+	0.263875i	$0.0850008\pi$
$644$	−112087.	−	81436.3i	−0.0106498	−	0.00773755i
$645$	−1.75111e7	+	1.27226e7i	−1.65735	+	1.20414i
$646$	−9.76840e6	+	7.09716e6i	−0.920963	+	0.669119i
$647$	8.93971e6			0.839581			0.419791	−	0.907621i	$-0.362104\pi$
$647$	8.93971e6			0.839581			0.419791	+	0.907621i	$0.362104\pi$
$648$	−3.71833e6	+	2.70152e6i	−0.347865	+	0.252738i
$649$	−2.39693e6	−	7.37700e6i	−0.223380	−	0.687492i
$650$	−1.53402e6	+	4.72122e6i	−0.142412	+	0.438300i
$651$	2.09253e6	+	1.52031e6i	0.193517	+	0.140598i
$652$	4.17241e6	+	3.03143e6i	0.384386	+	0.279273i
$653$	4.71483e6			0.432696			0.216348	−	0.976316i	$-0.430585\pi$
$653$	4.71483e6			0.432696			0.216348	+	0.976316i	$0.430585\pi$
$654$	5.35617e6	−	1.64846e7i	0.489677	−	1.50707i
$655$	−4.71983e6			−0.429856
$656$	−553585.	+	2.69931e6i	−0.0502256	+	0.244903i
$657$	7.98336e6			0.721560
$658$	2.22587e6	−	6.85051e6i	0.200417	−	0.616820i
$659$	2.80692e6			0.251778			0.125889	−	0.992044i	$-0.459822\pi$
$659$	2.80692e6			0.251778			0.125889	+	0.992044i	$0.459822\pi$
$660$	9.37929e6	+	6.81445e6i	0.838127	+	0.608935i
$661$	−5.80863e6	−	4.22022e6i	−0.517095	−	0.375692i	0.298413	−	0.954437i	$-0.403543\pi$
$661$	−5.80863e6	−	4.22022e6i	−0.517095	−	0.375692i	−0.815508	+	0.578745i	$0.803543\pi$
$662$	−801793.	+	2.46767e6i	−0.0711079	+	0.218847i
$663$	−2.14305e6	−	6.59563e6i	−0.189343	−	0.582737i
$664$	−3.74690e6	+	2.72228e6i	−0.329801	+	0.239615i
$665$	1.34985e7			1.18367
$666$	1.38801e6	−	1.00845e6i	0.121257	−	0.0880985i
$667$	−122105.	+	88714.2i	−0.0106272	+	0.00772109i
$668$	5.10989e6	+	3.71256e6i	0.443068	+	0.321908i
$669$	6.90419e6	−	2.12489e7i	0.596414	−	1.83557i
$670$	−1.77731e7			−1.52960
$671$	9.85530e6	+	7.16029e6i	0.845013	+	0.613938i
$672$	−496826.	−	1.52907e6i	−0.0424405	−	0.130619i
$673$	−4.30838e6	+	3.13022e6i	−0.366671	+	0.266402i	−0.755829	−	0.654769i	$-0.772766\pi$
$673$	−4.30838e6	+	3.13022e6i	−0.366671	+	0.266402i	0.389158	+	0.921171i	$0.372766\pi$
$674$	−608974.	+	1.87423e6i	−0.0516356	+	0.158918i
$675$	2.88230e6	+	8.87082e6i	0.243490	+	0.749384i
$676$	−1.62445e6	−	4.99956e6i	−0.136723	−	0.420789i
$677$	3.36182e6	+	1.03466e7i	0.281905	+	0.867615i	0.987309	+	0.158809i	$0.0507655\pi$
$677$	3.36182e6	+	1.03466e7i	0.281905	+	0.867615i	−0.705404	+	0.708805i	$0.749235\pi$
$678$	6.40599e6	+	1.97156e7i	0.535195	+	1.64716i
$679$	2.67473e6	−	8.23196e6i	0.222641	−	0.685218i
$680$	8.20344e6	−	5.96015e6i	0.680336	−	0.494293i
$681$	−4.65754e6	−	1.43344e7i	−0.384848	−	1.18444i
$682$	−1.99872e6	−	1.45216e6i	−0.164547	−	0.119551i
$683$	−1.69288e7			−1.38860			−0.694298	−	0.719688i	$-0.744285\pi$
$683$	−1.69288e7			−1.38860			−0.694298	+	0.719688i	$0.744285\pi$
$684$	−1.49568e6	+	4.60324e6i	−0.122236	+	0.376204i
$685$	2.27066e7	+	1.64973e7i	1.84895	+	1.34334i
$686$	6.92981e6	−	5.03481e6i	0.562227	−	0.408481i
$687$	6.57932e6	−	4.78016e6i	0.531850	−	0.386412i
$688$	−2.86712e6			−0.230927
$689$	−1.07533e6	+	781271.i	−0.0862964	+	0.0626980i
$690$	−266509.	−	820231.i	−0.0213103	−	0.0655863i
$691$	−6.88018e6	+	2.11750e7i	−0.548157	+	1.68705i	0.165206	+	0.986259i	$0.447171\pi$
$691$	−6.88018e6	+	2.11750e7i	−0.548157	+	1.68705i	−0.713363	+	0.700795i	$0.752829\pi$
$692$	−2.92673e6	−	2.12639e6i	−0.232336	−	0.168802i
$693$	3.91256e6	+	2.84264e6i	0.309477	+	0.224848i
$694$	7.52432e6			0.593019
$695$	−1.04779e7	+	3.22476e7i	−0.822832	+	2.53242i
$696$	−1.75145e6			−0.137048
$697$	−1.77380e7	+	1.99286e6i	−1.38301	+	0.155380i
$698$	−1.24853e7			−0.969973
$699$	6.26435e6	−	1.92797e7i	0.484934	−	1.49247i
$700$	−7.45504e6			−0.575049
$701$	−3.93845e6	−	2.86145e6i	−0.302712	−	0.219933i	0.426051	−	0.904699i	$-0.359905\pi$
$701$	−3.93845e6	−	2.86145e6i	−0.302712	−	0.219933i	−0.728763	+	0.684766i	$0.759905\pi$
$702$	1.03950e6	+	755238.i	0.0796123	+	0.0578417i
$703$	−1.45175e6	+	4.46803e6i	−0.110791	+	0.340979i
$704$	474553.	+	1.46052e6i	0.0360872	+	0.111065i
$705$	3.62748e7	−	2.63552e7i	2.74873	−	1.99707i
$706$	5.23148e6			0.395014
$707$	3.60300e6	−	2.61774e6i	0.271092	−	0.196960i
$708$	−5.41715e6	+	3.93579e6i	−0.406151	+	0.295086i
$709$	−1.24877e7	−	9.07284e6i	−0.932967	−	0.677840i	0.0137502	−	0.999905i	$-0.495623\pi$
$709$	−1.24877e7	−	9.07284e6i	−0.932967	−	0.677840i	−0.946718	+	0.322065i	$0.895623\pi$
$710$	3.09615e6	−	9.52898e6i	0.230503	−	0.709415i
$711$	−1.71292e7			−1.27076
$712$	7.33469e6	+	5.32896e6i	0.542228	+	0.393951i
$713$	56792.9	+	174791.i	0.00418380	+	0.0128764i
$714$	8.42576e6	−	6.12167e6i	0.618534	−	0.449391i
$715$	2.28840e6	−	7.04296e6i	0.167404	−	0.515217i
$716$	−3.34860e6	−	1.03059e7i	−0.244107	−	0.751285i
$717$	1.34789e6	+	4.14837e6i	0.0979166	+	0.301356i
$718$	−3.17126e6	−	9.76013e6i	−0.229573	−	0.706552i
$719$	−6.18628e6	−	1.90394e7i	−0.446280	−	1.37351i	−0.881074	−	0.472979i	$-0.843179\pi$
$719$	−6.18628e6	−	1.90394e7i	−0.446280	−	1.37351i	0.434794	−	0.900530i	$-0.356821\pi$
$720$	1.25606e6	−	3.86577e6i	0.0902986	−	0.277910i
$721$	2.83292e6	−	2.05824e6i	0.202953	−	0.147454i
$722$	−1.03494e6	−	3.18523e6i	−0.0738879	−	0.227404i
$723$	−2.85270e7	−	2.07260e7i	−2.02960	−	1.47459i
$724$	−1.20847e6			−0.0856822
$725$	−2.50962e6	+	7.72381e6i	−0.177322	+	0.545741i
$726$	1.34088e6	+	974205.i	0.0944164	+	0.0685976i
$727$	1.56568e6	−	1.13753e6i	0.109867	−	0.0798229i	−0.531495	−	0.847061i	$-0.678370\pi$
$727$	1.56568e6	−	1.13753e6i	0.109867	−	0.0798229i	0.641362	+	0.767238i	$0.278370\pi$
$728$	−830837.	+	603638.i	−0.0581015	+	0.0422132i
$729$	−4.29713e6			−0.299474
$730$	1.48522e7	−	1.07907e7i	1.03153	−	0.749453i
$731$	−5.73929e6	−	1.76637e7i	−0.397251	−	1.22261i
$732$	3.24963e6	−	1.00013e7i	0.224159	−	0.689891i
$733$	−2.50585e6	−	1.82061e6i	−0.172264	−	0.125157i	0.498312	−	0.866998i	$-0.333953\pi$
$733$	−2.50585e6	−	1.82061e6i	−0.172264	−	0.125157i	−0.670577	+	0.741840i	$0.733953\pi$
$734$	854716.	+	620987.i	0.0585574	+	0.0425444i
$735$	2.08387e7			1.42283
$736$	35302.2	−	108649.i	0.00240219	−	0.00739318i
$737$	1.74364e7			1.18247
$738$	−5.28292e6	+	4.82571e6i	−0.357053	+	0.326152i
$739$	−1.08358e7			−0.729875			−0.364937	−	0.931032i	$-0.618910\pi$
$739$	−1.08358e7			−0.729875			−0.364937	+	0.931032i	$0.618910\pi$
$740$	1.21917e6	−	3.75223e6i	0.0818438	−	0.251889i
$741$	7.61230e6			0.509296
$742$	−1.61489e6	−	1.17328e6i	−0.107679	−	0.0782337i
$743$	1.64930e7	+	1.19829e7i	1.09604	+	0.796322i	0.980410	−	0.196970i	$-0.0631101\pi$
$743$	1.64930e7	+	1.19829e7i	1.09604	+	0.796322i	0.115634	+	0.993292i	$0.463110\pi$
$744$	−659047.	+	2.02834e6i	−0.0436500	+	0.134341i
$745$	−1.07200e7	−	3.29927e7i	−0.707625	−	2.17785i
$746$	−5.12285e6	+	3.72197e6i	−0.337027	+	0.244864i
$747$	−1.20264e7			−0.788560
$748$	−8.04803e6	+	5.84724e6i	−0.525939	+	0.382117i
$749$	−5.51201e6	+	4.00471e6i	−0.359009	+	0.260836i
$750$	−1.79996e7	−	1.30775e7i	−1.16845	−	0.848927i
$751$	3.50040e6	−	1.07731e7i	0.226474	−	0.697014i	−0.771665	−	0.636029i	$-0.780576\pi$
$751$	3.50040e6	−	1.07731e7i	0.226474	−	0.697014i	0.998139	−	0.0609850i	$-0.0194242\pi$
$752$	5.93932e6			0.382994
$753$	−4.57833e6	−	3.32635e6i	−0.294252	−	0.213787i
$754$	345713.	+	1.06399e6i	0.0221456	+	0.0681571i
$755$	−1.16288e7	+	8.44880e6i	−0.742449	+	0.539421i
$756$	−596279.	+	1.83516e6i	−0.0379442	+	0.116780i
$757$	2.31463e6	+	7.12370e6i	0.146805	+	0.451820i	0.997239	−	0.0742624i	$-0.0236602\pi$
$757$	2.31463e6	+	7.12370e6i	0.146805	+	0.451820i	−0.850433	+	0.526083i	$0.823660\pi$
$758$	4.79880e6	+	1.47692e7i	0.303361	+	0.933650i
$759$	261460.	+	804692.i	0.0164741	+	0.0507020i
$760$	3.43943e6	+	1.05855e7i	0.216000	+	0.664778i
$761$	−1.02474e6	+	3.15384e6i	−0.0641436	+	0.197414i	−0.977992	−	0.208641i	$-0.933096\pi$
$761$	−1.02474e6	+	3.15384e6i	−0.0641436	+	0.197414i	0.913849	+	0.406055i	$0.133096\pi$
$762$	1.48245e7	−	1.07706e7i	0.924895	−	0.671975i
$763$	−5.13798e6	−	1.58131e7i	−0.319507	−	0.983343i
$764$	−5.64553e6	−	4.10172e6i	−0.349922	−	0.254233i
$765$	2.63305e7			1.62669
$766$	1.53405e6	−	4.72131e6i	0.0944640	−	0.290730i
$767$	3.46025e6	+	2.51402e6i	0.212382	+	0.154305i
$768$	1.07251e6	−	779221.i	0.0656140	−	0.0476713i
$769$	−7.63782e6	+	5.54920e6i	−0.465750	+	0.338388i	−0.795783	−	0.605582i	$-0.792940\pi$
$769$	−7.63782e6	+	5.54920e6i	−0.465750	+	0.338388i	0.330032	+	0.943970i	$0.392940\pi$
$770$	1.11212e7			0.675964
$771$	−7.94591e6	+	5.77304e6i	−0.481402	+	0.349759i
$772$	−441187.	−	1.35783e6i	−0.0266428	−	0.0819981i
$773$	294056.	−	905013.i	0.0177004	−	0.0544761i	−0.941816	−	0.336128i	$-0.890882\pi$
$773$	294056.	−	905013.i	0.0177004	−	0.0544761i	0.959517	+	0.281652i	$0.0908824\pi$
$774$	−6.02316e6	−	4.37609e6i	−0.361387	−	0.262563i
$775$	8.00056e6	+	5.81274e6i	0.478482	+	0.347638i
$776$	7.13702e6			0.425464
$777$	1.25221e6	−	3.85392e6i	0.0744090	−	0.229007i
$778$	7.38983e6			0.437709
$779$	3.93623e6	−	1.91933e7i	0.232400	−	1.13320i
$780$	−6.39276e6			−0.376229
$781$	−3.03750e6	+	9.34846e6i	−0.178192	+	0.548419i
$782$	740030.			0.0432745
$783$	1.70059e6	+	1.23555e6i	0.0991278	+	0.0720205i
$784$	2.23315e6	+	1.62248e6i	0.129756	+	0.0942733i
$785$	−1.62707e7	+	5.00762e7i	−0.942396	+	2.90040i
$786$	−1.23521e6	−	3.80159e6i	−0.0713157	−	0.219487i
$787$	1.62937e7	−	1.18380e7i	0.937739	−	0.681307i	−0.0101362	−	0.999949i	$-0.503227\pi$
$787$	1.62937e7	−	1.18380e7i	0.937739	−	0.681307i	0.947875	+	0.318641i	$0.103227\pi$
$788$	−6.03837e6			−0.346421
$789$	4.02040e6	−	2.92099e6i	0.229920	−	0.167047i
$790$	−3.18670e7	+	2.31527e7i	−1.81666	+	1.31988i
$791$	1.60879e7	+	1.16886e7i	0.914236	+	0.664231i
$792$	−1.23227e6	+	3.79254e6i	−0.0698060	+	0.214841i
$793$	−6.71720e6			−0.379320
$794$	3.28557e6	+	2.38711e6i	0.184952	+	0.134376i
$795$	−3.83970e6	−	1.18174e7i	−0.215466	−	0.663137i
$796$	−9.14802e6	+	6.64642e6i	−0.511734	+	0.371797i
$797$	−5.24686e6	+	1.61482e7i	−0.292586	+	0.900487i	0.691436	+	0.722438i	$0.256979\pi$
$797$	−5.24686e6	+	1.61482e7i	−0.292586	+	0.900487i	−0.984022	+	0.178049i	$0.943021\pi$
$798$	3.53265e6	+	1.08724e7i	0.196378	+	0.604389i
$799$	1.18891e7	+	3.65909e7i	0.658843	+	2.02771i
$800$	−1.89956e6	−	5.84624e6i	−0.104937	−	0.322962i
$801$	7.27491e6	+	2.23899e7i	0.400633	+	1.23302i
$802$	5.07036e6	−	1.56050e7i	0.278358	−	0.856697i
$803$	−1.45708e7	+	1.05863e7i	−0.797435	+	0.579370i
$804$	−4.65135e6	−	1.43154e7i	−0.253769	−	0.781022i
$805$	−669307.	−	486280.i	−0.0364029	−	0.0264482i
$806$	1.36229e6			0.0738640
$807$	−939952.	+	2.89287e6i	−0.0508068	+	0.156367i
$808$	2.97088e6	+	2.15847e6i	0.160087	+	0.116310i
$809$	1.30834e7	−	9.50568e6i	0.702831	−	0.510636i	−0.178022	−	0.984026i	$-0.556970\pi$
$809$	1.30834e7	−	9.50568e6i	0.702831	−	0.510636i	0.880853	+	0.473390i	$0.156970\pi$
$810$	−2.22032e7	+	1.61316e7i	−1.18906	+	0.863902i
$811$	1.31507e6			0.0702097			0.0351048	−	0.999384i	$-0.488823\pi$
$811$	1.31507e6			0.0702097			0.0351048	+	0.999384i	$0.488823\pi$
$812$	−1.35923e6	+	987537.i	−0.0723440	+	0.0525610i
$813$	−9.79968e6	−	3.01603e7i	−0.519979	−	1.60033i
$814$	−1.19608e6	+	3.68114e6i	−0.0632700	+	0.194725i
$815$	2.49147e7	+	1.81016e7i	1.31390	+	0.954601i
$816$	6.94751e6	+	5.04766e6i	0.365261	+	0.265378i
$817$	2.03865e7			1.06853
$818$	−3.17620e6	+	9.77535e6i	−0.165968	+	0.510798i
$819$	−2.66673e6			−0.138922
$820$	−3.30562e6	+	1.61184e7i	−0.171680	+	0.837119i
$821$	1.33031e7			0.688802			0.344401	−	0.938823i	$-0.388082\pi$
$821$	1.33031e7			0.688802			0.344401	+	0.938823i	$0.388082\pi$
$822$	−7.34532e6	+	2.26066e7i	−0.379167	+	1.16696i
$823$	−1.93833e7			−0.997536			−0.498768	−	0.866735i	$-0.666214\pi$
$823$	−1.93833e7			−0.997536			−0.498768	+	0.866735i	$0.666214\pi$
$824$	2.33590e6	+	1.69713e6i	0.119850	+	0.0870758i
$825$	3.68325e7	+	2.67604e7i	1.88407	+	1.36886i
$826$	−1.98488e6	+	6.10882e6i	−0.101224	+	0.311535i
$827$	−9.44218e6	−	2.90600e7i	−0.480074	−	1.47752i	−0.838990	−	0.544147i	$-0.816853\pi$
$827$	−9.44218e6	−	2.90600e7i	−0.480074	−	1.47752i	0.358915	−	0.933370i	$-0.383147\pi$
$828$	239993.	−	174365.i	0.0121653	−	0.00883861i
$829$	1.14370e7			0.577997			0.288998	−	0.957330i	$-0.406678\pi$
$829$	1.14370e7			0.577997			0.288998	+	0.957330i	$0.406678\pi$
$830$	−2.23739e7	+	1.62556e7i	−1.12732	+	0.819043i
$831$	−9.12343e6	+	6.62856e6i	−0.458306	+	0.332979i
$832$	−685071.	−	497733.i	−0.0343105	−	0.0249281i
$833$	−5.52551e6	+	1.70058e7i	−0.275905	+	0.849149i
$834$	−2.87160e7			−1.42958
$835$	3.05127e7	+	2.21688e7i	1.51448	+	1.10034i
$836$	−3.37427e6	−	1.03849e7i	−0.166980	−	0.513912i
$837$	2.07080e6	−	1.50452e6i	0.102170	−	0.0742309i
$838$	−4.49562e6	+	1.38361e7i	−0.221146	+	0.680618i
$839$	−1.50046e6	−	4.61795e6i	−0.0735902	−	0.226487i	0.907495	−	0.420062i	$-0.137992\pi$
$839$	−1.50046e6	−	4.61795e6i	−0.0735902	−	0.226487i	−0.981086	+	0.193575i	$0.937992\pi$
$840$	−2.96669e6	−	9.13054e6i	−0.145069	−	0.446476i
$841$	−5.77272e6	−	1.77666e7i	−0.281443	−	0.866192i
$842$	−8.10736e6	−	2.49519e7i	−0.394093	−	1.21289i
$843$	1.64533e6	−	5.06382e6i	0.0797417	−	0.245420i
$844$	−2.45485e6	+	1.78355e6i	−0.118623	+	0.0861846i
$845$	−9.70009e6	−	2.98538e7i	−0.467341	−	1.43833i
$846$	1.24772e7	+	9.06519e6i	0.599363	+	0.435463i
$847$	1.58990e6			0.0761485
$848$	508613.	−	1.56535e6i	0.0242883	−	0.0747518i
$849$	2.44196e7	+	1.77419e7i	1.16271	+	0.844756i
$850$	3.22150e7	−	2.34055e7i	1.52936	−	1.11115i
$851$	232944.	−	169244.i	0.0110262	−	0.00801103i
$852$	8.48542e6			0.400474
$853$	−8.22874e6	+	5.97853e6i	−0.387223	+	0.281334i	−0.764316	−	0.644841i	$-0.776923\pi$
$853$	−8.22874e6	+	5.97853e6i	−0.387223	+	0.281334i	0.377094	+	0.926175i	$0.376923\pi$
$854$	−3.11725e6	−	9.59392e6i	−0.146261	−	0.450144i
$855$	−8.93117e6	+	2.74873e7i	−0.417823	+	1.28593i
$856$	−4.54496e6	−	3.30211e6i	−0.212005	−	0.154031i
$857$	−2.69792e6	−	1.96016e6i	−0.125481	−	0.0911672i	0.523275	−	0.852164i	$-0.324710\pi$
$857$	−2.69792e6	−	1.96016e6i	−0.125481	−	0.0911672i	−0.648755	+	0.760997i	$0.724710\pi$
$858$	6.27165e6			0.290846
$859$	8.48443e6	−	2.61124e7i	0.392320	−	1.20744i	−0.538710	−	0.842491i	$-0.681088\pi$
$859$	8.48443e6	−	2.61124e7i	0.392320	−	1.20744i	0.931029	−	0.364944i	$-0.118912\pi$
$860$	−1.71204e7			−0.789347
$861$	−3.39521e6	+	1.65552e7i	−0.156084	+	0.761075i
$862$	−7.80588e6			−0.357811
$863$	−4.73439e6	+	1.45710e7i	−0.216390	+	0.665980i	0.782662	+	0.622447i	$0.213861\pi$
$863$	−4.73439e6	+	1.45710e7i	−0.216390	+	0.665980i	−0.999052	+	0.0435331i	$0.986139\pi$
$864$	−1.59106e6			−0.0725108
$865$	−1.74764e7	−	1.26973e7i	−0.794165	−	0.576994i
$866$	−4.60814e6	−	3.34801e6i	−0.208800	−	0.151702i
$867$	−8.31490e6	+	2.55906e7i	−0.375672	+	1.15620i
$868$	632200.	+	1.94571e6i	0.0284810	+	0.0876555i
$869$	3.12633e7	−	2.27141e7i	1.40438	−	1.02034i
$870$	−1.04584e7			−0.468454
$871$	−7.77842e6	+	5.65135e6i	−0.347413	+	0.252410i
$872$	1.10914e7	−	8.05840e6i	0.493965	−	0.358887i
$873$	1.49933e7	+	1.08932e7i	0.665825	+	0.483751i
$874$	−251014.	+	772542.i	−0.0111153	+	0.0342092i
$875$	−2.13424e7			−0.942373
$876$	1.25784e7	+	9.13871e6i	0.553813	+	0.402369i
$877$	1.26436e7	+	3.89130e7i	0.555100	+	1.70842i	0.695678	+	0.718354i	$0.255104\pi$
$877$	1.26436e7	+	3.89130e7i	0.555100	+	1.70842i	−0.140577	+	0.990070i	$0.544896\pi$
$878$	8.86641e6	−	6.44182e6i	0.388161	−	0.282015i
$879$	−275173.	+	846897.i	−0.0120125	+	0.0369707i
$880$	2.83369e6	+	8.72121e6i	0.123352	+	0.379638i
$881$	−8.93885e6	−	2.75109e7i	−0.388009	−	1.19417i	−0.934274	−	0.356556i	$-0.883951\pi$
$881$	−8.93885e6	−	2.75109e7i	−0.388009	−	1.19417i	0.546265	−	0.837613i	$-0.316049\pi$
$882$	2.21495e6	+	6.81691e6i	0.0958721	+	0.295064i
$883$	2.07491e6	+	6.38592e6i	0.0895566	+	0.275627i	0.985797	−	0.167942i	$-0.0537121\pi$
$883$	2.07491e6	+	6.38592e6i	0.0895566	+	0.275627i	−0.896240	+	0.443569i	$0.853712\pi$
$884$	1.69508e6	−	5.21692e6i	0.0729558	−	0.224535i
$885$	−3.23474e7	+	2.35017e7i	−1.38829	+	1.00865i
$886$	−6.44490e6	−	1.98354e7i	−0.275824	−	0.848899i
$887$	−2.45485e6	−	1.78355e6i	−0.104765	−	0.0761161i	0.534169	−	0.845377i	$-0.320624\pi$
$887$	−2.45485e6	−	1.78355e6i	−0.104765	−	0.0761161i	−0.638934	+	0.769261i	$0.720624\pi$
$888$	3.34130e6			0.142195
$889$	5.43178e6	−	1.67173e7i	0.230509	−	0.709434i
$890$	4.37976e7	+	3.18208e7i	1.85342	+	1.34659i
$891$	2.17826e7	−	1.58260e7i	0.919212	−	0.667846i
$892$	1.42970e7	−	1.03874e7i	0.601637	−	0.437115i
$893$	−4.22311e7			−1.77217
$894$	2.37685e7	−	1.72689e7i	0.994624	−	0.722636i
$895$	−1.99955e7	−	6.15398e7i	−0.834400	−	2.56802i
$896$	392973.	−	1.20945e6i	0.0163528	−	0.0503287i
$897$	−377448.	−	274232.i	−0.0156630	−	0.0113799i
$898$	−5.19908e6	−	3.77735e6i	−0.215147	−	0.156314i
$899$	2.22868e6			0.0919704
$900$	4.93258e6	−	1.51809e7i	0.202987	−	0.624729i
$901$	1.06619e7			0.437545
$902$	3.24300e6	−	1.58130e7i	0.132718	−	0.647141i
$903$	−1.75844e7			−0.717642
$904$	−5.06692e6	+	1.55944e7i	−0.206216	+	0.634669i
$905$	−7.21615e6			−0.292876
$906$	−9.84844e6	−	7.15531e6i	−0.398609	−	0.289606i
$907$	2.28795e7	+	1.66229e7i	0.923482	+	0.670949i	0.944388	−	0.328833i	$-0.106655\pi$
$907$	2.28795e7	+	1.66229e7i	0.923482	+	0.670949i	−0.0209064	+	0.999781i	$0.506655\pi$
$908$	3.68396e6	−	1.13381e7i	0.148286	−	0.456378i
$909$	2.94667e6	+	9.06891e6i	0.118283	+	0.364037i
$910$	−4.96117e6	+	3.60450e6i	−0.198601	+	0.144292i
$911$	6.26985e6			0.250300			0.125150	−	0.992138i	$-0.460059\pi$
$911$	6.26985e6			0.250300			0.125150	+	0.992138i	$0.460059\pi$
$912$	−7.62598e6	+	5.54060e6i	−0.303605	+	0.220582i
$913$	2.19500e7	−	1.59476e7i	0.871480	−	0.633168i
$914$	2.72974e7	+	1.98327e7i	1.08083	+	0.785266i
$915$	1.94045e7	−	5.97209e7i	0.766214	−	2.35816i
$916$	6.43253e6			0.253305
$917$	−3.10209e6	−	2.25380e6i	−0.121824	−	0.0885101i
$918$	−3.18493e6	−	9.80220e6i	−0.124736	−	0.383899i
$919$	−1.39677e7	+	1.01481e7i	−0.545550	+	0.396366i	−0.826142	−	0.563462i	$-0.809469\pi$
$919$	−1.39677e7	+	1.01481e7i	−0.545550	+	0.396366i	0.280592	+	0.959827i	$0.409469\pi$
$920$	210800.	−	648775.i	0.00821109	−	0.0252711i
$921$	−9.85040e6	−	3.03164e7i	−0.382653	−	1.17768i
$922$	−7.24709e6	−	2.23042e7i	−0.280761	−	0.864093i
$923$	−1.67491e6	−	5.15485e6i	−0.0647125	−	0.199164i
$924$	2.91049e6	+	8.95757e6i	0.112147	+	0.345152i
$925$	4.78770e6	−	1.47350e7i	0.183981	−	0.566235i
$926$	−1.90415e7	+	1.38345e7i	−0.729749	+	0.530194i
$927$	2.31686e6	+	7.13058e6i	0.0885526	+	0.272537i
$928$	−1.12076e6	−	814279.i	−0.0427211	−	0.0310387i
$929$	9.71844e6			0.369452			0.184726	−	0.982790i	$-0.440860\pi$
$929$	9.71844e6			0.369452			0.184726	+	0.982790i	$0.440860\pi$
$930$	−3.93536e6	+	1.21118e7i	−0.149203	+	0.459200i
$931$	−1.58787e7	−	1.15365e7i	−0.600398	−	0.436215i
$932$	1.29721e7	−	9.42476e6i	0.489181	−	0.355411i
$933$	−5.32788e7	+	3.87093e7i	−2.00378	+	1.45583i
$934$	8.81913e6			0.330795
$935$	−4.80571e7	+	3.49156e7i	−1.79775	+	1.30614i
$936$	−679488.	−	2.09125e6i	−0.0253508	−	0.0780219i
$937$	−1.14344e7	+	3.51916e7i	−0.425467	+	1.30945i	0.477079	+	0.878860i	$0.341695\pi$
$937$	−1.14344e7	+	3.51916e7i	−0.425467	+	1.30945i	−0.902546	+	0.430593i	$0.858305\pi$
$938$	−1.16813e7	−	8.48699e6i	−0.433497	−	0.314954i
$939$	2.13548e7	+	1.55152e7i	0.790372	+	0.574239i
$940$	3.54654e7			1.30914
$941$	1.93260e6	−	5.94794e6i	0.0711489	−	0.218974i	−0.909159	−	0.416449i	$-0.863274\pi$
$941$	1.93260e6	−	5.94794e6i	0.0711489	−	0.218974i	0.980308	+	0.197476i	$0.0632743\pi$
$942$	−4.45922e7			−1.63731
$943$	−886609.	+	809877.i	−0.0324678	+	0.0296579i
$944$	−5.29628e6			−0.193438
$945$	−3.56056e6	+	1.09583e7i	−0.129699	+	0.399174i
$946$	1.67961e7			0.610211
$947$	4.18835e7	+	3.04301e7i	1.51764	+	1.10263i	0.962643	+	0.270773i	$0.0872794\pi$
$947$	4.18835e7	+	3.04301e7i	1.51764	+	1.10263i	0.554994	+	0.831854i	$0.312721\pi$
$948$	−2.69883e7	−	1.96081e7i	−0.975335	−	0.708623i
$949$	3.06892e6	−	9.44515e6i	0.110616	−	0.340442i
$950$	1.35067e7	+	4.15693e7i	0.485556	+	1.49439i
$951$	4.37825e7	−	3.18098e7i	1.56982	−	1.14054i
$952$	8.23777e6			0.294590
$953$	3.89174e7	−	2.82751e7i	1.38807	−	1.00849i	0.391995	−	0.919967i	$-0.371785\pi$
$953$	3.89174e7	−	2.82751e7i	1.38807	−	1.00849i	0.996074	−	0.0885244i	$-0.0282151\pi$
$954$	3.45767e6	−	2.51215e6i	0.123002	−	0.0893663i
$955$	−3.37111e7	−	2.44926e7i	−1.19609	−	0.869012i
$956$	−1.06614e6	+	3.28123e6i	−0.0377283	+	0.116116i
$957$	1.02603e7			0.362142
$958$	3.06203e7	+	2.22469e7i	1.07794	+	0.783170i
$959$	7.04610e6	+	2.16857e7i	0.247401	+	0.761423i
$960$	6.40424e6	−	4.65295e6i	0.224280	−	0.162949i
$961$	−8.00827e6	+	2.46469e7i	−0.279724	+	0.860903i
$962$	−659530.	−	2.02983e6i	−0.0229772	−	0.0707165i
$963$	−4.50792e6	−	1.38740e7i	−0.156643	−	0.482097i
$964$	−8.61863e6	−	2.65254e7i	−0.298707	−	0.919326i
$965$	−2.63446e6	−	8.10803e6i	−0.0910695	−	0.280283i
$966$	216513.	−	666358.i	0.00746519	−	0.0229755i
$967$	8.67204e6	−	6.30061e6i	0.298233	−	0.216679i	−0.428598	−	0.903495i	$-0.640992\pi$
$967$	8.67204e6	−	6.30061e6i	0.298233	−	0.216679i	0.726831	+	0.686817i	$0.240992\pi$
$968$	405109.	+	1.24680e6i	0.0138958	+	0.0427669i
$969$	−4.93998e7	−	3.58911e7i	−1.69011	−	1.22794i
$970$	4.26172e7			1.45431
$971$	5.21625e6	−	1.60540e7i	0.177546	−	0.546430i	−0.822195	−	0.569206i	$-0.807251\pi$
$971$	5.21625e6	−	1.60540e7i	0.177546	−	0.546430i	0.999741	+	0.0227763i	$0.00725055\pi$
$972$	−1.39166e7	−	1.01110e7i	−0.472464	−	0.343265i
$973$	−2.22854e7	+	1.61913e7i	−0.754637	+	0.548276i
$974$	−1.40596e7	+	1.02149e7i	−0.474872	+	0.345015i
$975$	−2.51044e7			−0.845743
$976$	6.72927e6	−	4.88910e6i	0.226122	−	0.164287i
$977$	2.38043e6	+	7.32620e6i	0.0797844	+	0.245551i	0.982991	−	0.183656i	$-0.0587931\pi$
$977$	2.38043e6	+	7.32620e6i	0.0797844	+	0.245551i	−0.903206	+	0.429207i	$0.858793\pi$
$978$	−8.05959e6	+	2.48049e7i	−0.269442	+	0.829258i
$979$	−4.29678e7	−	3.12180e7i	−1.43280	−	1.04099i
$980$	1.33348e7	+	9.68829e6i	0.443528	+	0.322242i
$981$	3.56001e7			1.18108
$982$	9.10836e6	−	2.80326e7i	0.301413	−	0.927653i
$983$	−2.72498e7			−0.899457			−0.449728	−	0.893165i	$-0.648479\pi$
$983$	−2.72498e7			−0.899457			−0.449728	+	0.893165i	$0.648479\pi$
$984$	−1.38477e7	+	1.55578e6i	−0.455921	+	0.0512225i
$985$	−3.60569e7			−1.18413
$986$	2.77311e6	−	8.53475e6i	0.0908395	−	0.279575i
$987$	3.64266e7			1.19022
$988$	4.87115e6	+	3.53910e6i	0.158759	+	0.115345i
$989$	−1.01084e6	−	734419.i	−0.0328619	−	0.0238755i
$990$	−7.35824e6	+	2.26463e7i	−0.238609	+	0.734362i
$991$	−1.20739e7	−	3.71598e7i	−0.390540	−	1.20196i	−0.932381	−	0.361477i	$-0.882273\pi$
$991$	−1.20739e7	−	3.71598e7i	−0.390540	−	1.20196i	0.541841	−	0.840481i	$-0.317727\pi$
$992$	−1.36474e6	+	991542.i	−0.0440322	+	0.0319913i
$993$	−1.31215e7			−0.422288
$994$	6.58520e6	−	4.78443e6i	0.211399	−	0.153590i
$995$	−5.46255e7	+	3.96878e7i	−1.74919	+	1.27086i
$996$	−1.89485e7	−	1.37669e7i	−0.605238	−	0.439731i
$997$	1.06956e7	−	3.29177e7i	0.340775	−	1.04880i	−0.623032	−	0.782196i	$-0.714099\pi$
$997$	1.06956e7	−	3.29177e7i	0.340775	−	1.04880i	0.963807	−	0.266601i	$-0.0859005\pi$
$998$	−2.03328e6			−0.0646206
$999$	−3.24429e6	−	2.35711e6i	−0.102850	−	0.0747251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.b.57.2	✓	36
41.18	even	5	inner	82.6.d.b.59.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.b.57.2	✓	36	1.1	even	1	trivial
82.6.d.b.59.2	yes	36	41.18	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+(-1.23607 + 3.80423i) q^{2} -20.2284 q^{3} +(-12.9443 - 9.40456i) q^{4} +(-77.2940 - 56.1574i) q^{5} +(25.0037 - 76.9535i) q^{6} +(-23.9851 - 73.8187i) q^{7} +(51.7771 - 37.6183i) q^{8} +166.189 q^{9} +(309.176 - 224.630i) q^{10} +(-303.319 + 220.374i) q^{11} +(261.842 + 190.239i) q^{12} +(63.8852 - 196.619i) q^{13} +310.470 q^{14} +(1563.54 + 1135.98i) q^{15} +(79.1084 + 243.470i) q^{16} +(-1341.61 + 974.739i) q^{17} +(-205.420 + 632.219i) q^{18} +(-562.495 - 1731.18i) q^{19} +(472.379 + 1453.83i) q^{20} +(485.181 + 1493.23i) q^{21} +(-463.430 - 1426.29i) q^{22} +(-34.4748 + 106.103i) q^{23} +(-1047.37 + 760.958i) q^{24} +(1855.04 + 5709.22i) q^{25} +(669.015 + 486.068i) q^{26} +1553.77 q^{27} +(-383.762 + 1181.10i) q^{28} +(1094.49 + 795.195i) q^{29} +(-6254.14 + 4543.90i) q^{30} +(1332.75 - 968.303i) q^{31} -1024.00 q^{32} +(6135.66 - 4457.82i) q^{33} +(-2049.80 - 6308.65i) q^{34} +(-2291.56 + 7052.69i) q^{35} +(-2151.19 - 1562.93i) q^{36} +(-2088.01 - 1517.03i) q^{37} +7281.08 q^{38} +(-1292.30 + 3977.28i) q^{39} -6114.60 q^{40} +(9359.89 + 5314.94i) q^{41} -6280.32 q^{42} +(-3460.89 + 10651.5i) q^{43} +5998.77 q^{44} +(-12845.4 - 9332.72i) q^{45} +(-361.025 - 262.300i) q^{46} +(7169.34 - 22065.0i) q^{47} +(-1600.24 - 4925.02i) q^{48} +(8723.24 - 6337.80i) q^{49} -24012.1 q^{50} +(27138.7 - 19717.4i) q^{51} +(-2676.06 + 1944.27i) q^{52} +(-5201.43 - 3779.06i) q^{53} +(-1920.57 + 5910.90i) q^{54} +35820.4 q^{55} +(-4018.81 - 2919.84i) q^{56} +(11378.4 + 35019.0i) q^{57} +(-4377.97 + 3180.78i) q^{58} +(-6393.13 + 19676.0i) q^{59} +(-9555.48 - 29408.7i) q^{60} +(-10040.4 - 30901.3i) q^{61} +(2036.27 + 6266.99i) q^{62} +(-3986.06 - 12267.8i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-15979.5 + 11609.8i) q^{65} +(9374.46 + 28851.6i) q^{66} +(-37624.7 - 27335.9i) q^{67} +26533.2 q^{68} +(697.371 - 2146.29i) q^{69} +(-23997.5 - 17435.2i) q^{70} +(21210.4 - 15410.3i) q^{71} +(8604.76 - 6251.73i) q^{72} +48037.9 q^{73} +(8352.03 - 6068.10i) q^{74} +(-37524.4 - 115488. i) q^{75} +(-8999.91 + 27698.9i) q^{76} +(23542.9 + 17104.9i) q^{77} +(-13533.1 - 9832.38i) q^{78} -103071. q^{79} +(7558.07 - 23261.3i) q^{80} -71814.2 q^{81} +(-31788.7 + 29037.5i) q^{82} -72366.1 q^{83} +(7762.90 - 23891.8i) q^{84} +158438. q^{85} +(-36242.9 - 26332.0i) q^{86} +(-22139.8 - 16085.5i) q^{87} +(-7414.88 + 22820.7i) q^{88} +(43775.0 + 134726. i) q^{89} +(51381.6 - 37330.9i) q^{90} -16046.4 q^{91} +(1444.10 - 1049.20i) q^{92} +(-26959.5 + 19587.2i) q^{93} +(75078.3 + 54547.6i) q^{94} +(-53741.1 + 165398. i) q^{95} +20713.9 q^{96} +(90218.3 + 65547.4i) q^{97} +(13327.9 + 41019.1i) q^{98} +(-50408.2 + 36623.7i) 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

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Database

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