LMFDB - Embedded newform 82.6.d.b.57.1

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			57.1
Character	$\chi$	$=$	82.57
Dual form			82.6.d.b.59.1

$q$-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} -29.2964 q^{3} +(-12.9443 - 9.40456i) q^{4} +(72.0590 + 52.3539i) q^{5} +(36.2123 - 111.450i) q^{6} +(-58.7271 - 180.743i) q^{7} +(51.7771 - 37.6183i) q^{8} +615.279 q^{9} +(-288.236 + 209.416i) q^{10} +(102.025 - 74.1256i) q^{11} +(379.220 + 275.520i) q^{12} +(9.10492 - 28.0220i) q^{13} +760.179 q^{14} +(-2111.07 - 1533.78i) q^{15} +(79.1084 + 243.470i) q^{16} +(-1175.14 + 853.791i) q^{17} +(-760.526 + 2340.66i) q^{18} +(806.718 + 2482.82i) q^{19} +(-440.385 - 1355.37i) q^{20} +(1720.49 + 5295.13i) q^{21} +(155.881 + 479.751i) q^{22} +(708.701 - 2181.16i) q^{23} +(-1516.88 + 1102.08i) q^{24} +(1485.89 + 4573.09i) q^{25} +(95.3479 + 69.2743i) q^{26} -10906.4 q^{27} +(-939.633 + 2891.89i) q^{28} +(-1635.36 - 1188.16i) q^{29} +(8444.28 - 6135.13i) q^{30} +(-424.822 + 308.651i) q^{31} -1024.00 q^{32} +(-2988.97 + 2171.61i) q^{33} +(-1795.46 - 5525.85i) q^{34} +(5230.81 - 16098.8i) q^{35} +(-7964.33 - 5786.43i) q^{36} +(7997.91 + 5810.83i) q^{37} -10442.4 q^{38} +(-266.741 + 820.945i) q^{39} +5700.47 q^{40} +(10496.6 - 2382.59i) q^{41} -22270.5 q^{42} +(-2430.88 + 7481.49i) q^{43} -2017.76 q^{44} +(44336.4 + 32212.3i) q^{45} +(7421.61 + 5392.12i) q^{46} +(-7706.28 + 23717.5i) q^{47} +(-2317.59 - 7132.81i) q^{48} +(-15622.1 + 11350.1i) q^{49} -19233.7 q^{50} +(34427.4 - 25013.0i) q^{51} +(-381.392 + 277.097i) q^{52} +(2529.15 + 1837.53i) q^{53} +(13481.1 - 41490.5i) q^{54} +11232.6 q^{55} +(-9839.96 - 7149.15i) q^{56} +(-23633.9 - 72737.7i) q^{57} +(6541.45 - 4752.64i) q^{58} +(-9979.99 + 30715.3i) q^{59} +(12901.7 + 39707.4i) q^{60} +(15920.3 + 48997.6i) q^{61} +(-649.070 - 1997.63i) q^{62} +(-36133.5 - 111207. i) q^{63} +(1265.73 - 3895.53i) q^{64} +(2123.16 - 1542.56i) q^{65} +(-4566.74 - 14055.0i) q^{66} +(16635.2 + 12086.2i) q^{67} +23240.9 q^{68} +(-20762.4 + 63900.0i) q^{69} +(54777.7 + 39798.4i) q^{70} +(4821.76 - 3503.22i) q^{71} +(31857.3 - 23145.7i) q^{72} -42766.5 q^{73} +(-31991.7 + 23243.3i) q^{74} +(-43531.2 - 133975. i) q^{75} +(12907.5 - 39725.1i) q^{76} +(-19389.3 - 14087.2i) q^{77} +(-2793.35 - 2029.49i) q^{78} +18322.5 q^{79} +(-7046.17 + 21685.9i) q^{80} +170006. q^{81} +(-3910.65 + 42876.6i) q^{82} +71723.3 q^{83} +(27527.9 - 84722.0i) q^{84} -129379. q^{85} +(-25456.5 - 18495.3i) q^{86} +(47910.2 + 34808.8i) q^{87} +(2494.09 - 7676.01i) q^{88} +(5947.91 + 18305.8i) q^{89} +(-177345. + 128849. i) q^{90} -5599.50 q^{91} +(-29686.5 + 21568.5i) q^{92} +(12445.8 - 9042.37i) q^{93} +(-80701.2 - 58632.9i) q^{94} +(-71854.2 + 221144. i) q^{95} +29999.5 q^{96} +(-100420. - 72959.3i) q^{97} +(-23868.5 - 73459.6i) q^{98} +(62773.9 - 45607.9i) 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
$3$	−29.2964			−1.87936			−0.939682	−	0.342049i	$-0.888879\pi$
$3$	−29.2964			−1.87936			−0.939682	+	0.342049i	$0.888879\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	72.0590	+	52.3539i	1.28903	+	0.936536i	0.999785	−	0.0207194i	$-0.00659566\pi$
$5$	72.0590	+	52.3539i	1.28903	+	0.936536i	0.289245	+	0.957255i	$0.406596\pi$
$6$	36.2123	−	111.450i	0.410656	−	1.26387i
$7$	−58.7271	−	180.743i	−0.452995	−	1.39417i	−0.873473	−	0.486872i	$-0.838138\pi$
$7$	−58.7271	−	180.743i	−0.452995	−	1.39417i	0.420479	−	0.907302i	$-0.361862\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	615.279			2.53201
$10$	−288.236	+	209.416i	−0.911482	+	0.662231i
$11$	102.025	−	74.1256i	0.254229	−	0.184708i	−0.453370	−	0.891322i	$-0.649778\pi$
$11$	102.025	−	74.1256i	0.254229	−	0.184708i	0.707599	+	0.706614i	$0.249778\pi$
$12$	379.220	+	275.520i	0.760219	+	0.552331i
$13$	9.10492	−	28.0220i	0.0149423	−	0.0459877i	−0.943307	−	0.331921i	$-0.892303\pi$
$13$	9.10492	−	28.0220i	0.0149423	−	0.0459877i	0.958250	+	0.285933i	$0.0923034\pi$
$14$	760.179			1.03656
$15$	−2111.07	−	1533.78i	−2.42256	−	1.76009i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−1175.14	+	853.791i	−0.986207	+	0.716521i	−0.959087	−	0.283111i	$-0.908634\pi$
$17$	−1175.14	+	853.791i	−0.986207	+	0.716521i	−0.0271200	+	0.999632i	$0.508634\pi$
$18$	−760.526	+	2340.66i	−0.553265	+	1.70277i
$19$	806.718	+	2482.82i	0.512670	+	1.57783i	0.787483	+	0.616337i	$0.211384\pi$
$19$	806.718	+	2482.82i	0.512670	+	1.57783i	−0.274813	+	0.961498i	$0.588616\pi$
$20$	−440.385	−	1355.37i	−0.246183	−	0.757673i
$21$	1720.49	+	5295.13i	0.851342	+	2.62016i
$22$	155.881	+	479.751i	0.0686650	+	0.211329i
$23$	708.701	−	2181.16i	0.279347	−	0.859741i	−0.708690	−	0.705520i	$-0.750713\pi$
$23$	708.701	−	2181.16i	0.279347	−	0.859741i	0.988036	−	0.154220i	$-0.0492866\pi$
$24$	−1516.88	+	1102.08i	−0.537556	+	0.390557i
$25$	1485.89	+	4573.09i	0.475484	+	1.46339i
$26$	95.3479	+	69.2743i	0.0276616	+	0.0200974i
$27$	−10906.4			−2.87921
$28$	−939.633	+	2891.89i	−0.226497	+	0.697087i
$29$	−1635.36	−	1188.16i	−0.361093	−	0.262349i	0.392415	−	0.919788i	$-0.371640\pi$
$29$	−1635.36	−	1188.16i	−0.361093	−	0.262349i	−0.753508	+	0.657439i	$0.771640\pi$
$30$	8444.28	−	6135.13i	1.71301	−	1.24457i
$31$	−424.822	+	308.651i	−0.0793968	+	0.0576851i	−0.626776	−	0.779200i	$-0.715626\pi$
$31$	−424.822	+	308.651i	−0.0793968	+	0.0576851i	0.547379	+	0.836885i	$0.315626\pi$
$32$	−1024.00			−0.176777
$33$	−2988.97	+	2171.61i	−0.477789	+	0.347134i
$34$	−1795.46	−	5525.85i	−0.266365	−	0.819789i
$35$	5230.81	−	16098.8i	0.721770	−	2.22138i
$36$	−7964.33	−	5786.43i	−1.02422	−	0.744139i
$37$	7997.91	+	5810.83i	0.960445	+	0.697804i	0.953254	−	0.302170i	$-0.0977110\pi$
$37$	7997.91	+	5810.83i	0.960445	+	0.697804i	0.00719089	+	0.999974i	$0.497711\pi$
$38$	−10442.4			−1.17311
$39$	−266.741	+	820.945i	−0.0280820	+	0.0864276i
$40$	5700.47			0.563327
$41$	10496.6	−	2382.59i	0.975193	−	0.221355i
$41$	10496.6	−	2382.59i	0.975193	−	0.221355i
$42$	−22270.5			−1.94808
$43$	−2430.88	+	7481.49i	−0.200490	+	0.617045i	0.799378	+	0.600828i	$0.205162\pi$
$43$	−2430.88	+	7481.49i	−0.200490	+	0.617045i	−0.999868	+	0.0162172i	$0.994838\pi$
$44$	−2017.76			−0.157122
$45$	44336.4	+	32212.3i	3.26384	+	2.37132i
$46$	7421.61	+	5392.12i	0.517135	+	0.375720i
$47$	−7706.28	+	23717.5i	−0.508862	+	1.56612i	0.285317	+	0.958433i	$0.407901\pi$
$47$	−7706.28	+	23717.5i	−0.508862	+	1.56612i	−0.794179	+	0.607684i	$0.792099\pi$
$48$	−2317.59	−	7132.81i	−0.145189	−	0.446845i
$49$	−15622.1	+	11350.1i	−0.929501	+	0.675322i
$50$	−19233.7			−1.08802
$51$	34427.4	−	25013.0i	1.85344	−	1.34661i
$52$	−381.392	+	277.097i	−0.0195597	+	0.0142110i
$53$	2529.15	+	1837.53i	0.123676	+	0.0898557i	0.647904	−	0.761722i	$-0.275646\pi$
$53$	2529.15	+	1837.53i	0.123676	+	0.0898557i	−0.524228	+	0.851578i	$0.675646\pi$
$54$	13481.1	−	41490.5i	0.629130	−	1.93626i
$55$	11232.6			0.500695
$56$	−9839.96	−	7149.15i	−0.419299	−	0.304638i
$57$	−23633.9	−	72737.7i	−0.963493	−	2.96533i
$58$	6541.45	−	4752.64i	0.255331	−	0.185509i
$59$	−9979.99	+	30715.3i	−0.373250	+	1.14875i	0.571401	+	0.820671i	$0.306400\pi$
$59$	−9979.99	+	30715.3i	−0.373250	+	1.14875i	−0.944652	+	0.328075i	$0.893600\pi$
$60$	12901.7	+	39707.4i	0.462667	+	1.42394i
$61$	15920.3	+	48997.6i	0.547805	+	1.68597i	0.714225	+	0.699916i	$0.246779\pi$
$61$	15920.3	+	48997.6i	0.547805	+	1.68597i	−0.166420	+	0.986055i	$0.553221\pi$
$62$	−649.070	−	1997.63i	−0.0214443	−	0.0659989i
$63$	−36133.5	−	111207.i	−1.14699	−	3.53006i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	2123.16	−	1542.56i	0.0623302	−	0.0452855i
$66$	−4566.74	−	14055.0i	−0.129046	−	0.397164i
$67$	16635.2	+	12086.2i	0.452731	+	0.328928i	0.790673	−	0.612239i	$-0.209731\pi$
$67$	16635.2	+	12086.2i	0.452731	+	0.328928i	−0.337942	+	0.941167i	$0.609731\pi$
$68$	23240.9			0.609510
$69$	−20762.4	+	63900.0i	−0.524994	+	1.61577i
$70$	54777.7	+	39798.4i	1.33616	+	0.970778i
$71$	4821.76	−	3503.22i	0.113517	−	0.0824747i	−0.529579	−	0.848261i	$-0.677650\pi$
$71$	4821.76	−	3503.22i	0.113517	−	0.0824747i	0.643095	+	0.765786i	$0.277650\pi$
$72$	31857.3	−	23145.7i	0.724233	−	0.526186i
$73$	−42766.5			−0.939282			−0.469641	−	0.882857i	$-0.655617\pi$
$73$	−42766.5			−0.939282			−0.469641	+	0.882857i	$0.655617\pi$
$74$	−31991.7	+	23243.3i	−0.679137	+	0.493422i
$75$	−43531.2	−	133975.i	−0.893608	−	2.75024i
$76$	12907.5	−	39725.1i	0.256335	−	0.788917i
$77$	−19389.3	−	14087.2i	−0.372680	−	0.270768i
$78$	−2793.35	−	2029.49i	−0.0519863	−	0.0377703i
$79$	18322.5			0.330306			0.165153	−	0.986268i	$-0.447188\pi$
$79$	18322.5			0.330306			0.165153	+	0.986268i	$0.447188\pi$
$80$	−7046.17	+	21685.9i	−0.123091	+	0.378837i
$81$	170006.			2.87907
$82$	−3910.65	+	42876.6i	−0.0642265	+	0.704184i
$83$	71723.3			1.14279			0.571393	−	0.820677i	$-0.306403\pi$
$83$	71723.3			1.14279			0.571393	+	0.820677i	$0.306403\pi$
$84$	27527.9	−	84722.0i	0.425671	−	1.31008i
$85$	−129379.			−1.94230
$86$	−25456.5	−	18495.3i	−0.371153	−	0.269659i
$87$	47910.2	+	34808.8i	0.678625	+	0.493050i
$88$	2494.09	−	7676.01i	0.0343325	−	0.105665i
$89$	5947.91	+	18305.8i	0.0795956	+	0.244970i	0.982934	−	0.183958i	$-0.0588912\pi$
$89$	5947.91	+	18305.8i	0.0795956	+	0.244970i	−0.903338	+	0.428929i	$0.858891\pi$
$90$	−177345.	+	128849.i	−2.30788	+	1.67678i
$91$	−5599.50			−0.0708836
$92$	−29686.5	+	21568.5i	−0.365670	+	0.265674i
$93$	12445.8	−	9042.37i	0.149215	−	0.108411i
$94$	−80701.2	−	58632.9i	−0.942021	−	0.684418i
$95$	−71854.2	+	221144.i	−0.816852	+	2.51401i
$96$	29999.5			0.332228
$97$	−100420.	−	72959.3i	−1.08365	−	0.787320i	−0.105336	−	0.994437i	$-0.533592\pi$
$97$	−100420.	−	72959.3i	−1.08365	−	0.787320i	−0.978316	+	0.207117i	$0.933592\pi$
$98$	−23868.5	−	73459.6i	−0.251050	−	0.772651i
$99$	62773.9	−	45607.9i	0.643711	−	0.467683i
$100$	23774.2	−	73169.5i	0.237742	−	0.731695i
$101$	−642.833	−	1978.44i	−0.00627039	−	0.0192983i	0.947872	−	0.318650i	$-0.103230\pi$
$101$	−642.833	−	1978.44i	−0.00627039	−	0.0192983i	−0.954143	+	0.299352i	$0.903230\pi$
$102$	52600.4	+	161887.i	0.500598	+	1.54068i
$103$	−10813.4	−	33280.1i	−0.100431	−	0.309094i	0.888200	−	0.459457i	$-0.151956\pi$
$103$	−10813.4	−	33280.1i	−0.100431	−	0.309094i	−0.988631	+	0.150362i	$0.951956\pi$
$104$	−582.715	−	1793.41i	−0.00528290	−	0.0162591i
$105$	−153244.	+	471636.i	−1.35647	+	4.17478i
$106$	−10116.6	+	7350.13i	−0.0874520	+	0.0635376i
$107$	−28546.6	−	87857.5i	−0.241044	−	0.741856i	−0.996262	−	0.0863827i	$-0.972469\pi$
$107$	−28546.6	−	87857.5i	−0.241044	−	0.741856i	0.755218	−	0.655473i	$-0.227531\pi$
$108$	141176.	+	102570.i	1.16466	+	0.846178i
$109$	165138.			1.33131			0.665655	−	0.746259i	$-0.268152\pi$
$109$	165138.			1.33131			0.665655	+	0.746259i	$0.268152\pi$
$110$	−13884.3	+	42731.3i	−0.109406	+	0.336717i
$111$	−234310.	−	170236.i	−1.80503	−	1.31143i
$112$	39359.9	−	28596.6i	0.296489	−	0.215412i
$113$	−27895.6	+	20267.3i	−0.205513	+	0.149314i	−0.685781	−	0.727808i	$-0.740539\pi$
$113$	−27895.6	+	20267.3i	−0.205513	+	0.149314i	0.480268	+	0.877122i	$0.340539\pi$
$114$	305924.			2.20471
$115$	165260.	−	120069.i	1.16526	−	0.846614i
$116$	9994.44	+	30759.7i	0.0689626	+	0.212245i
$117$	5602.06	−	17241.4i	0.0378341	−	0.116441i
$118$	−104512.	−	75932.3i	−0.690972	−	0.502020i
$119$	223330.	+	162258.i	1.44570	+	1.05036i
$120$	−167003.			−1.05870
$121$	−44853.0	+	138043.i	−0.278502	+	0.857140i
$122$	−206076.			−1.25351
$123$	−307514.	+	69801.3i	−1.83274	+	0.416007i
$124$	8401.74			0.0490699
$125$	−46335.0	+	142604.i	−0.265237	+	0.816316i
$126$	467722.			2.62459
$127$	241964.	+	175797.i	1.33119	+	0.967169i	0.999719	+	0.0237044i	$0.00754604\pi$
$127$	241964.	+	175797.i	1.33119	+	0.967169i	0.331474	+	0.943464i	$0.392454\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	71216.1	−	219181.i	0.376794	−	1.15965i
$130$	3243.89	+	9983.68i	0.0168348	+	0.0518122i
$131$	−161365.	+	117239.i	−0.821546	+	0.596888i	−0.917155	−	0.398531i	$-0.869520\pi$
$131$	−161365.	+	117239.i	−0.821546	+	0.596888i	0.0956087	+	0.995419i	$0.469520\pi$
$132$	59113.1			0.295290
$133$	401377.	−	291618.i	1.96754	−	1.42950i
$134$	−66540.7	+	48344.6i	−0.320129	+	0.232587i
$135$	−785906.	−	570994.i	−3.71139	−	2.69648i
$136$	−28727.3	+	88413.6i	−0.133183	+	0.409894i
$137$	195154.			0.888331			0.444166	−	0.895945i	$-0.353500\pi$
$137$	195154.			0.888331			0.444166	+	0.895945i	$0.353500\pi$
$138$	−217426.	−	157970.i	−0.971885	−	0.706116i
$139$	60401.9	+	185898.i	0.265163	+	0.816089i	0.991656	+	0.128914i	$0.0411492\pi$
$139$	60401.9	+	185898.i	0.265163	+	0.816089i	−0.726493	+	0.687174i	$0.758851\pi$
$140$	−219111.	+	159193.i	−0.944809	+	0.686444i
$141$	225766.	−	694837.i	0.956337	−	2.94330i
$142$	7367.00	+	22673.3i	0.0306598	+	0.0943612i
$143$	−1148.22	−	3533.86i	−0.00469554	−	0.0144514i
$144$	48673.7	+	149802.i	0.195609	+	0.602021i
$145$	−55637.7	−	171235.i	−0.219760	−	0.676352i
$146$	52862.2	−	162693.i	0.205241	−	0.631666i
$147$	457672.	−	332518.i	1.74687	−	1.26918i
$148$	−48878.9	−	150434.i	−0.183429	−	0.564535i
$149$	−194233.	−	141119.i	−0.716733	−	0.520737i	0.168606	−	0.985684i	$-0.446074\pi$
$149$	−194233.	−	141119.i	−0.716733	−	0.520737i	−0.885339	+	0.464946i	$0.846074\pi$
$150$	563479.			2.04479
$151$	−45680.6	+	140590.i	−0.163038	+	0.501780i	−0.998886	−	0.0471808i	$-0.984976\pi$
$151$	−45680.6	+	140590.i	−0.163038	+	0.501780i	0.835848	+	0.548961i	$0.184976\pi$
$152$	135169.	+	98206.0i	0.474535	+	0.344770i
$153$	−723040.	+	525319.i	−2.49709	+	1.81424i
$154$	77557.4	−	56348.7i	0.263525	−	0.191462i
$155$	−46771.4			−0.156369
$156$	11173.4	−	8117.95i	0.0367599	−	0.0267076i
$157$	−34600.1	−	106488.i	−0.112028	−	0.344788i	0.879287	−	0.476292i	$-0.158019\pi$
$157$	−34600.1	−	106488.i	−0.112028	−	0.344788i	−0.991316	+	0.131504i	$0.958019\pi$
$158$	−22647.8	+	69702.8i	−0.0721744	+	0.222130i
$159$	−74094.9	−	53833.1i	−0.232432	−	0.168872i
$160$	−73788.4	−	53610.4i	−0.227871	−	0.165558i
$161$	−435850.			−1.32517
$162$	−210139.	+	646742.i	−0.629099	+	1.93617i
$163$	−205038.			−0.604457			−0.302229	−	0.953235i	$-0.597731\pi$
$163$	−205038.			−0.604457			−0.302229	+	0.953235i	$0.597731\pi$
$164$	−158279.	−	67875.4i	−0.459529	−	0.197062i
$165$	−329075.			−0.940989
$166$	−88654.8	+	272852.i	−0.249708	+	0.768522i
$167$	380920.			1.05692			0.528461	−	0.848958i	$-0.322769\pi$
$167$	380920.			1.05692			0.528461	+	0.848958i	$0.322769\pi$
$168$	288275.	+	209444.i	0.788015	+	0.572526i
$169$	299680.	+	217730.i	0.807125	+	0.586411i
$170$	159921.	−	492187.i	0.424408	−	1.30619i
$171$	496356.	+	1.52763e6i	1.29808	+	3.99509i
$172$	101826.	−	73981.0i	0.262445	−	0.190677i
$173$	−132215.			−0.335865			−0.167932	−	0.985799i	$-0.553709\pi$
$173$	−132215.			−0.335865			−0.167932	+	0.985799i	$0.553709\pi$
$174$	−191641.	+	139235.i	−0.479860	+	0.348639i
$175$	739294.	−	537129.i	1.82483	−	1.32582i
$176$	26118.4	+	18976.2i	0.0635573	+	0.0461771i
$177$	292378.	−	899846.i	0.701473	−	2.15891i
$178$	−76991.3			−0.182134
$179$	−209684.	−	152344.i	−0.489139	−	0.355381i	0.315714	−	0.948854i	$-0.397756\pi$
$179$	−209684.	−	152344.i	−0.489139	−	0.355381i	−0.804853	+	0.593474i	$0.797756\pi$
$180$	−270960.	−	833928.i	−0.623338	−	1.91844i
$181$	505225.	−	367068.i	1.14627	−	0.832817i	0.158294	−	0.987392i	$-0.449401\pi$
$181$	505225.	−	367068.i	1.14627	−	0.832817i	0.987981	+	0.154575i	$0.0494007\pi$
$182$	6921.37	−	21301.8i	0.0154886	−	0.0476691i
$183$	−466407.	−	1.43545e6i	−1.02953	−	3.16855i
$184$	−45356.9	−	139594.i	−0.0987640	−	0.303964i
$185$	272102.	+	837445.i	0.584525	+	1.79898i
$186$	19015.4	+	58523.4i	0.0403017	+	0.124036i
$187$	−56606.3	+	174216.i	−0.118375	+	0.364321i
$188$	322805.	−	234531.i	0.666109	−	0.483957i
$189$	640502.	+	1.97126e6i	1.30427	+	4.01412i
$190$	−752467.	−	546699.i	−1.51218	−	1.09866i
$191$	−426687.			−0.846303			−0.423151	−	0.906059i	$-0.639076\pi$
$191$	−426687.			−0.846303			−0.423151	+	0.906059i	$0.639076\pi$
$192$	−37081.4	+	114125.i	−0.0725944	+	0.223423i
$193$	−449642.	−	326684.i	−0.868909	−	0.631299i	0.0613853	−	0.998114i	$-0.480448\pi$
$193$	−449642.	−	326684.i	−0.868909	−	0.631299i	−0.930294	+	0.366815i	$0.880448\pi$
$194$	401679.	−	291837.i	0.766258	−	0.556719i
$195$	−62200.8	+	45191.5i	−0.117141	+	0.0851080i
$196$	308960.			0.574463
$197$	499091.	−	362611.i	0.916250	−	0.665695i	−0.0263375	−	0.999653i	$-0.508384\pi$
$197$	499091.	−	362611.i	0.916250	−	0.665695i	0.942588	+	0.333958i	$0.108384\pi$
$198$	95910.0	+	295180.i	0.173860	+	0.535087i
$199$	61760.1	−	190078.i	0.110554	−	0.340251i	−0.880440	−	0.474158i	$-0.842752\pi$
$199$	61760.1	−	190078.i	0.110554	−	0.340251i	0.990994	+	0.133907i	$0.0427524\pi$
$200$	248967.	+	180885.i	0.440115	+	0.319762i
$201$	−487350.	−	354081.i	−0.850847	−	0.618176i
$202$	8321.01			0.0143482
$203$	−118712.	+	365358.i	−0.202187	+	0.622269i
$204$	−680874.			−1.14549
$205$	881115.	+	377853.i	1.46436	+	0.627970i
$206$	139971.			0.229811
$207$	436049.	−	1.34202e6i	0.707309	−	2.17687i
$208$	7542.82			0.0120886
$209$	266346.	+	193512.i	0.421775	+	0.306437i
$210$	−1.60479e6	−	1.16595e6i	−2.51113	−	1.82445i
$211$	101860.	−	313493.i	0.157506	−	0.484754i	−0.840900	−	0.541190i	$-0.817974\pi$
$211$	101860.	−	313493.i	0.157506	−	0.484754i	0.998406	+	0.0564366i	$0.0179739\pi$
$212$	−15456.8	−	47571.1i	−0.0236200	−	0.0726948i
$213$	−141260.	+	102632.i	−0.213339	+	0.155000i
$214$	369515.			0.551567
$215$	−566852.	+	411842.i	−0.836323	+	0.607624i
$216$	−564703.	+	410281.i	−0.823541	+	0.598338i
$217$	80735.2	+	58657.6i	0.116389	+	0.0845619i
$218$	−204121.	+	628220.i	−0.290902	+	0.895305i
$219$	1.25290e6			1.76525
$220$	−145398.	−	105638.i	−0.202535	−	0.147151i
$221$	13225.4	+	40703.6i	0.0182150	+	0.0560599i
$222$	937240.	−	680945.i	1.27635	−	0.927320i
$223$	−164841.	+	507330.i	−0.221975	+	0.683169i	0.776610	+	0.629982i	$0.216938\pi$
$223$	−164841.	+	507330.i	−0.221975	+	0.683169i	−0.998585	+	0.0531866i	$0.983062\pi$
$224$	60136.5	+	185081.i	0.0800789	+	0.246458i
$225$	914235.	+	2.81373e6i	1.20393	+	3.70532i
$226$	−42620.6	−	131173.i	−0.0555072	−	0.170833i
$227$	−110784.	−	340958.i	−0.142696	−	0.439173i	0.854011	−	0.520254i	$-0.174163\pi$
$227$	−110784.	−	340958.i	−0.142696	−	0.439173i	−0.996708	+	0.0810808i	$0.974163\pi$
$228$	−378143.	+	1.16380e6i	−0.481746	+	1.48266i
$229$	−619867.	+	450360.i	−0.781106	+	0.567506i	−0.905311	−	0.424750i	$-0.860362\pi$
$229$	−619867.	+	450360.i	−0.781106	+	0.567506i	0.124205	+	0.992257i	$0.460362\pi$
$230$	252496.	+	777101.i	0.314727	+	0.968630i
$231$	568038.	+	412704.i	0.700402	+	0.508872i
$232$	−129371.			−0.157803
$233$	−219469.	+	675455.i	−0.264840	+	0.815092i	0.726891	+	0.686753i	$0.240965\pi$
$233$	−219469.	+	675455.i	−0.264840	+	0.815092i	−0.991730	+	0.128339i	$0.959035\pi$
$234$	58665.5	+	42623.0i	0.0700396	+	0.0508867i
$235$	−1.79701e6	+	1.30560e6i	−2.12266	+	1.54220i
$236$	418047.	−	303729.i	0.488591	−	0.354982i
$237$	−536782.			−0.620765
$238$	−893319.	+	649034.i	−1.02227	+	0.742720i
$239$	−115377.	−	355093.i	−0.130654	−	0.402112i	0.864235	−	0.503089i	$-0.167803\pi$
$239$	−115377.	−	355093.i	−0.130654	−	0.402112i	−0.994889	+	0.100977i	$0.967803\pi$
$240$	206427.	−	635318.i	0.231334	−	0.711972i
$241$	1.04231e6	+	757282.i	1.15599	+	0.839875i	0.989266	−	0.146128i	$-0.0466812\pi$
$241$	1.04231e6	+	757282.i	1.15599	+	0.839875i	0.166724	+	0.986004i	$0.446681\pi$
$242$	−469706.	−	341262.i	−0.515571	−	0.374584i
$243$	−2.33030e6			−2.53161
$244$	254724.	−	783961.i	0.273903	−	0.842985i
$245$	−1.71994e6			−1.83062
$246$	114568.	−	1.25613e6i	0.120705	−	1.32342i
$247$	76918.8			0.0802214
$248$	−10385.1	+	31962.1i	−0.0107222	+	0.0329994i
$249$	−2.10123e6			−2.14771
$250$	−485226.	−	352538.i	−0.491015	−	0.356743i
$251$	244681.	+	177771.i	0.245141	+	0.178105i	0.703570	−	0.710626i	$-0.251588\pi$
$251$	244681.	+	177771.i	0.245141	+	0.178105i	−0.458430	+	0.888731i	$0.651588\pi$
$252$	−578136.	+	1.77932e6i	−0.573494	+	1.76503i
$253$	−89374.3	−	275066.i	−0.0877832	−	0.270169i
$254$	−967855.	+	703188.i	−0.941296	+	0.683891i
$255$	3.79034e6			3.65029
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	950738.	−	690752.i	0.897900	−	0.652363i	−0.0400255	−	0.999199i	$-0.512744\pi$
$257$	950738.	−	690752.i	0.897900	−	0.652363i	0.937926	+	0.346836i	$0.112744\pi$
$258$	745785.	+	541844.i	0.697532	+	0.506787i
$259$	580574.	−	1.78682e6i	0.537784	−	1.65513i
$260$	−41989.8			−0.0385222
$261$	−1.00620e6	−	731049.i	−0.914291	−	0.664271i
$262$	−246544.	−	758785.i	−0.221892	−	0.682914i
$263$	−545822.	+	396563.i	−0.486588	+	0.353527i	−0.803871	−	0.594804i	$-0.797230\pi$
$263$	−545822.	+	396563.i	−0.486588	+	0.353527i	0.317283	+	0.948331i	$0.397230\pi$
$264$	−73067.8	+	224880.i	−0.0645232	+	0.198582i
$265$	86045.8	+	264822.i	0.0752688	+	0.231654i
$266$	613250.	+	1.88739e6i	0.531414	+	1.63553i
$267$	−174252.	−	536293.i	−0.149589	−	0.460388i
$268$	−101665.	−	312893.i	−0.0864639	−	0.266109i
$269$	578851.	−	1.78152e6i	0.487737	−	1.50110i	−0.340240	−	0.940339i	$-0.610508\pi$
$269$	578851.	−	1.78152e6i	0.487737	−	1.50110i	0.827977	−	0.560762i	$-0.189492\pi$
$270$	3.14362e6	−	2.28398e6i	2.62435	−	1.90670i
$271$	−239558.	−	737285.i	−0.198147	−	0.609834i	−0.999925	−	0.0122127i	$-0.996112\pi$
$271$	−239558.	−	737285.i	−0.198147	−	0.609834i	0.801778	−	0.597622i	$-0.203888\pi$
$272$	−300836.	−	218570.i	−0.246552	−	0.179130i
$273$	164045.			0.133216
$274$	−241223.	+	742408.i	−0.194108	+	0.597402i
$275$	490581.	+	356428.i	0.391182	+	0.284211i
$276$	869706.	−	631878.i	0.687226	−	0.499299i
$277$	1.23999e6	−	900908.i	0.971001	−	0.705474i	0.0153219	−	0.999883i	$-0.495123\pi$
$277$	1.23999e6	−	900908.i	0.971001	−	0.705474i	0.955680	+	0.294409i	$0.0951227\pi$
$278$	−781858.			−0.606759
$279$	−261384.	+	189907.i	−0.201033	+	0.146059i
$280$	−334772.	−	1.03032e6i	−0.255184	−	0.785376i
$281$	−528277.	+	1.62587e6i	−0.399113	+	1.22834i	0.526599	+	0.850114i	$0.323467\pi$
$281$	−528277.	+	1.62587e6i	−0.399113	+	1.22834i	−0.925712	+	0.378230i	$0.876533\pi$
$282$	2.36425e6	+	1.71773e6i	1.77040	+	1.28627i
$283$	−1.93564e6	−	1.40632e6i	−1.43667	−	1.04380i	−0.988725	−	0.149746i	$-0.952155\pi$
$283$	−1.93564e6	−	1.40632e6i	−1.43667	−	1.04380i	−0.447949	−	0.894059i	$-0.647845\pi$
$284$	−95360.4			−0.0701572
$285$	2.10507e6	−	6.47874e6i	1.53516	−	4.72474i
$286$	14862.9			0.0107445
$287$	−1.04707e6	−	1.75728e6i	−0.750365	−	1.25932i
$288$	−630045.			−0.447600
$289$	213241.	−	656287.i	0.150185	−	0.462221i
$290$	720189.			0.502865
$291$	2.94194e6	+	2.13744e6i	2.03658	+	1.47966i
$292$	553581.	+	402200.i	0.379948	+	0.276048i
$293$	−572889.	+	1.76317e6i	−0.389854	+	1.19985i	0.543044	+	0.839704i	$0.317272\pi$
$293$	−572889.	+	1.76317e6i	−0.389854	+	1.19985i	−0.932897	+	0.360142i	$0.882728\pi$
$294$	699260.	+	2.15210e6i	0.471814	+	1.45209i
$295$	−2.32721e6	+	1.69082e6i	−1.55697	+	1.13121i
$296$	632702.			0.419730
$297$	−1.11273e6	+	808445.i	−0.731978	+	0.531813i
$298$	776932.	−	564474.i	0.506807	−	0.368217i
$299$	−54667.8	−	39718.5i	−0.0353634	−	0.0256930i
$300$	−696499.	+	2.14360e6i	−0.446804	+	1.37512i
$301$	1.49499e6			0.951089
$302$	−478373.	−	347558.i	−0.301821	−	0.219286i
$303$	18832.7	+	57961.1i	0.0117844	+	0.0362685i
$304$	−540676.	+	392824.i	−0.335547	+	0.243789i
$305$	−1.41802e6	+	4.36421e6i	−0.872834	+	2.68631i
$306$	−1.10471e6	−	3.39994e6i	−0.674440	−	2.07571i
$307$	294271.	+	905672.i	0.178197	+	0.548435i	0.999765	−	0.0216760i	$-0.00690023\pi$
$307$	294271.	+	905672.i	0.178197	+	0.548435i	−0.821568	+	0.570111i	$0.806900\pi$
$308$	118497.	+	364697.i	0.0711756	+	0.219056i
$309$	316792.	+	974986.i	0.188746	+	0.580901i
$310$	57812.6	−	177929.i	0.0341679	−	0.105158i
$311$	549581.	−	399294.i	0.322204	−	0.234095i	−0.414911	−	0.909862i	$-0.636187\pi$
$311$	549581.	−	399294.i	0.322204	−	0.234095i	0.737115	+	0.675767i	$0.236187\pi$
$312$	17071.4	+	52540.5i	0.00992850	+	0.0305568i
$313$	−588940.	−	427890.i	−0.339790	−	0.246872i	0.404783	−	0.914413i	$-0.367347\pi$
$313$	−588940.	−	427890.i	−0.339790	−	0.246872i	−0.744573	+	0.667541i	$0.767347\pi$
$314$	447873.			0.256348
$315$	3.21841e6	−	9.90523e6i	1.82753	−	5.62456i
$316$	−237171.	−	172315.i	−0.133611	−	0.0970744i
$317$	−981333.	+	712980.i	−0.548489	+	0.398501i	−0.827228	−	0.561866i	$-0.810084\pi$
$317$	−981333.	+	712980.i	−0.548489	+	0.398501i	0.278739	+	0.960367i	$0.410084\pi$
$318$	296380.	−	215332.i	0.164354	−	0.119410i
$319$	−254921.			−0.140258
$320$	295154.	−	214442.i	0.161129	−	0.117067i
$321$	836314.	+	2.57391e6i	0.453009	+	1.39422i
$322$	538740.	−	1.65807e6i	0.289560	−	0.891175i
$323$	−3.06782e6	−	2.22890e6i	−1.63615	−	1.18873i
$324$	−2.20060e6	−	1.59883e6i	−1.16461	−	0.846137i
$325$	141676.			0.0744027
$326$	253441.	−	780011.i	0.132079	−	0.406497i
$327$	−4.83793e6			−2.50202
$328$	453857.	−	518229.i	0.232935	−	0.265973i
$329$	4.73935e6			2.41395
$330$	406758.	−	1.25187e6i	0.205614	−	0.632813i
$331$	712648.			0.357524			0.178762	−	0.983892i	$-0.442791\pi$
$331$	712648.			0.357524			0.178762	+	0.983892i	$0.442791\pi$
$332$	−928405.	−	674526.i	−0.462267	−	0.335856i
$333$	4.92095e6	+	3.57528e6i	2.43186	+	1.76685i
$334$	−470843.	+	1.44911e6i	−0.230946	+	0.710778i
$335$	565956.	+	1.74183e6i	0.275531	+	0.847997i
$336$	−1.15310e6	+	837777.i	−0.557211	+	0.404837i
$337$	899703.			0.431543			0.215772	−	0.976444i	$-0.430773\pi$
$337$	899703.			0.431543			0.215772	+	0.976444i	$0.430773\pi$
$338$	−1.19872e6	+	870921.i	−0.570724	+	0.414655i
$339$	817240.	−	593759.i	0.386234	−	0.280615i
$340$	1.67472e6	+	1.21675e6i	0.785677	+	0.570827i
$341$	−20463.6	+	62980.4i	−0.00953005	+	0.0293305i
$342$	−6.42497e6			−2.97034
$343$	384836.	+	279600.i	0.176620	+	0.128322i
$344$	155577.	+	478815.i	0.0708840	+	0.218158i
$345$	−4.84154e6	+	3.51758e6i	−2.18996	+	1.59110i
$346$	163426.	−	502974.i	0.0733891	−	0.225868i
$347$	641373.	+	1.97394e6i	0.285948	+	0.880057i	0.986113	+	0.166076i	$0.0531097\pi$
$347$	641373.	+	1.97394e6i	0.285948	+	0.880057i	−0.700165	+	0.713981i	$0.746890\pi$
$348$	−292801.	−	901149.i	−0.129606	−	0.398886i
$349$	29004.7	+	89267.2i	0.0127469	+	0.0392309i	0.957228	−	0.289336i	$-0.0934344\pi$
$349$	29004.7	+	89267.2i	0.0127469	+	0.0392309i	−0.944481	+	0.328567i	$0.893434\pi$
$350$	1.12954e6	+	3.47637e6i	0.492869	+	1.51690i
$351$	−99302.0	+	305620.i	−0.0430220	+	0.132408i
$352$	−104474.	+	75904.6i	−0.0449418	+	0.0326521i
$353$	105538.	+	324814.i	0.0450789	+	0.138739i	0.971063	−	0.238825i	$-0.0767621\pi$
$353$	105538.	+	324814.i	0.0450789	+	0.138739i	−0.925984	+	0.377563i	$0.876762\pi$
$354$	3.06182e6	+	2.22454e6i	1.29859	+	0.943479i
$355$	530859.			0.223567
$356$	95166.5	−	292892.i	0.0397978	−	0.122485i
$357$	−6.54275e6	−	4.75359e6i	−2.71700	−	1.97402i
$358$	838736.	−	609377.i	0.345874	−	0.251292i
$359$	426766.	−	310063.i	0.174765	−	0.126974i	−0.496964	−	0.867771i	$-0.665552\pi$
$359$	426766.	−	310063.i	0.174765	−	0.126974i	0.671729	+	0.740797i	$0.265552\pi$
$360$	3.50738e6			1.42635
$361$	−3.51040e6	+	2.55046e6i	−1.41772	+	1.03003i
$362$	771916.	+	2.37571e6i	0.309598	+	0.952845i
$363$	1.31403e6	−	4.04417e6i	0.523406	−	1.61088i
$364$	72481.5	+	52660.9i	0.0286730	+	0.0208322i
$365$	−3.08171e6	−	2.23899e6i	−1.21076	−	0.879671i
$366$	6.03730e6			2.35581
$367$	−1.27094e6	+	3.91154e6i	−0.492559	+	1.51594i	0.328168	+	0.944620i	$0.393569\pi$
$367$	−1.27094e6	+	3.91154e6i	−0.492559	+	1.51594i	−0.820727	+	0.571321i	$0.806431\pi$
$368$	587112.			0.225996
$369$	6.45836e6	−	1.46596e6i	2.46920	−	0.560474i
$370$	−3.52217e6			−1.33754
$371$	183592.	−	565040.i	0.0692501	−	0.213130i
$372$	−246141.			−0.0922202
$373$	−3.59191e6	−	2.60968e6i	−1.33676	−	0.971214i	−0.999556	−	0.0297826i	$-0.990518\pi$
$373$	−3.59191e6	−	2.60968e6i	−1.33676	−	0.971214i	−0.337205	−	0.941431i	$-0.609482\pi$
$374$	−592789.	−	430686.i	−0.219140	−	0.159214i
$375$	1.35745e6	−	4.17780e6i	0.498477	−	1.53415i
$376$	493202.	+	1.51792e6i	0.179910	+	0.553706i
$377$	−48184.5	+	35008.1i	−0.0174604	+	0.0126857i
$378$	−8.29083e6			−2.98448
$379$	1.70525e6	−	1.23894e6i	0.609803	−	0.443048i	−0.239542	−	0.970886i	$-0.576997\pi$
$379$	1.70525e6	−	1.23894e6i	0.609803	−	0.443048i	0.849345	+	0.527838i	$0.176997\pi$
$380$	3.00987e6	−	2.18680e6i	1.06927	−	0.776872i
$381$	−7.08867e6	−	5.15022e6i	−2.50180	−	1.81766i
$382$	527414.	−	1.62321e6i	0.184924	−	0.569137i
$383$	3.50078e6			1.21946			0.609730	−	0.792609i	$-0.291278\pi$
$383$	3.50078e6			1.21946			0.609730	+	0.792609i	$0.291278\pi$
$384$	−388322.	−	282132.i	−0.134389	−	0.0976393i
$385$	−659657.	−	2.03022e6i	−0.226812	−	0.698056i
$386$	1.79857e6	−	1.30674e6i	0.614411	−	0.446396i
$387$	−1.49567e6	+	4.60320e6i	−0.507643	+	1.56236i
$388$	613711.	+	1.88881e6i	0.206959	+	0.636955i
$389$	−164339.	−	505783.i	−0.0550638	−	0.169469i	0.919742	−	0.392522i	$-0.128397\pi$
$389$	−164339.	−	505783.i	−0.0550638	−	0.169469i	−0.974806	+	0.223054i	$0.928397\pi$
$390$	−95034.4	−	292486.i	−0.0316387	−	0.0973740i
$391$	1.02943e6	+	3.16825e6i	0.340529	+	1.04804i
$392$	−381896.	+	1.17535e6i	−0.125525	+	0.386326i
$393$	4.72742e6	−	3.43467e6i	1.54398	−	1.12177i
$394$	762543.	+	2.34687e6i	0.247471	+	0.761637i
$395$	1.32030e6	+	959252.i	0.425774	+	0.309343i
$396$	−1.24148e6			−0.397835
$397$	−480327.	+	1.47830e6i	−0.152954	+	0.470744i	−0.997948	−	0.0640320i	$-0.979604\pi$
$397$	−480327.	+	1.47830e6i	−0.152954	+	0.470744i	0.844994	+	0.534776i	$0.179604\pi$
$398$	646760.	+	469899.i	0.204661	+	0.148695i
$399$	−1.17589e7	+	8.54334e6i	−3.69773	+	2.68655i
$400$	−995867.	+	723540.i	−0.311208	+	0.226106i
$401$	−2.77185e6			−0.860814			−0.430407	−	0.902635i	$-0.641630\pi$
$401$	−2.77185e6			−0.860814			−0.430407	+	0.902635i	$0.641630\pi$
$402$	1.94940e6	−	1.41632e6i	0.601639	−	0.437117i
$403$	4781.07	+	14714.6i	0.00146643	+	0.00451322i
$404$	−10285.3	+	31655.0i	−0.00313520	+	0.00964914i
$405$	1.22505e7	+	8.90049e6i	3.71121	+	2.69635i
$406$	−1.24317e6	−	903214.i	−0.374295	−	0.271942i
$407$	1.24672e6			0.373063
$408$	841607.	−	2.59020e6i	0.250299	−	0.770341i
$409$	−1.04703e6			−0.309494			−0.154747	−	0.987954i	$-0.549456\pi$
$409$	−1.04703e6			−0.309494			−0.154747	+	0.987954i	$0.549456\pi$
$410$	−2.52656e6	+	2.88491e6i	−0.742283	+	0.847564i
$411$	−5.71730e6			−1.66950
$412$	−173014.	+	532481.i	−0.0502154	+	0.154547i
$413$	6.13767e6			1.77063
$414$	4.56636e6	+	3.31765e6i	1.30939	+	0.951328i
$415$	5.16831e6	+	3.75500e6i	1.47309	+	1.07026i
$416$	−9323.43	+	28694.6i	−0.00264145	+	0.00812955i
$417$	−1.76956e6	−	5.44614e6i	−0.498338	−	1.53373i
$418$	−1.06538e6	+	774047.i	−0.298240	+	0.216684i
$419$	−6.62680e6			−1.84403			−0.922016	−	0.387151i	$-0.873459\pi$
$419$	−6.62680e6			−1.84403			−0.922016	+	0.387151i	$0.873459\pi$
$420$	6.41916e6	−	4.66379e6i	1.77564	−	1.29008i
$421$	1.17268e6	−	852002.i	0.322459	−	0.234280i	−0.414765	−	0.909929i	$-0.636136\pi$
$421$	1.17268e6	−	852002.i	0.322459	−	0.234280i	0.737224	+	0.675648i	$0.236136\pi$
$422$	1.06669e6	+	774996.i	0.291580	+	0.211845i
$423$	−4.74151e6	+	1.45929e7i	−1.28844	+	3.96542i
$424$	200077.			0.0540483
$425$	−5.65060e6	−	4.10540e6i	−1.51748	−	1.10251i
$426$	−215826.	−	664246.i	−0.0576210	−	0.177339i
$427$	7.92103e6	−	5.75497e6i	2.10238	−	1.52747i
$428$	−456746.	+	1.40572e6i	−0.120522	+	0.370928i
$429$	33638.7	+	103529.i	0.00882463	+	0.0271594i
$430$	−866073.	−	2.66550e6i	−0.225883	−	0.695196i
$431$	−1.53012e6	−	4.70923e6i	−0.396764	−	1.22111i	−0.927579	−	0.373627i	$-0.878114\pi$
$431$	−1.53012e6	−	4.70923e6i	−0.396764	−	1.22111i	0.530815	−	0.847488i	$-0.321886\pi$
$432$	−862789.	−	2.65539e6i	−0.222431	−	0.684572i
$433$	881893.	−	2.71419e6i	0.226046	−	0.695697i	−0.772138	−	0.635455i	$-0.780813\pi$
$433$	881893.	−	2.71419e6i	0.226046	−	0.695697i	0.998184	−	0.0602421i	$-0.0191873\pi$
$434$	−322941.	+	234630.i	−0.0822998	+	0.0597943i
$435$	1.62998e6	+	5.01657e6i	0.413010	+	1.27111i
$436$	−2.13758e6	−	1.55305e6i	−0.538527	−	0.391262i
$437$	5.98715e6			1.49974
$438$	−1.54867e6	+	4.76633e6i	−0.385722	+	1.18713i
$439$	5.29151e6	+	3.84451e6i	1.31044	+	0.952093i	0.999999	+	0.00150113i	$0.000477825\pi$
$439$	5.29151e6	+	3.84451e6i	1.31044	+	0.952093i	0.310444	+	0.950592i	$0.399522\pi$
$440$	581591.	−	422551.i	0.143214	−	0.104051i
$441$	−9.61196e6	+	6.98350e6i	−2.35351	+	1.70992i
$442$	−171193.			−0.0416803
$443$	−6.01154e6	+	4.36764e6i	−1.45538	+	1.05739i	−0.470842	+	0.882217i	$0.656050\pi$
$443$	−6.01154e6	+	4.36764e6i	−1.45538	+	1.05739i	−0.984537	+	0.175177i	$0.943950\pi$
$444$	1.43198e6	+	4.40717e6i	0.344729	+	1.06097i
$445$	−529779.	+	1.63049e6i	−0.126822	+	0.390318i
$446$	−1.72624e6	−	1.25419e6i	−0.410927	−	0.298556i
$447$	5.69033e6	+	4.13427e6i	1.34700	+	0.978655i
$448$	−778423.			−0.183240
$449$	2.49598e6	−	7.68185e6i	0.584287	−	1.79825i	−0.0178290	−	0.999841i	$-0.505675\pi$
$449$	2.49598e6	−	7.68185e6i	0.584287	−	1.79825i	0.602116	−	0.798409i	$-0.294325\pi$
$450$	−1.18341e7			−2.75489
$451$	894310.	−	1.02115e6i	0.207036	−	0.236401i
$452$	551693.			0.127014
$453$	1.33828e6	−	4.11879e6i	0.306408	−	0.943027i
$454$	1.43402e6			0.326524
$455$	−403495.	−	293156.i	−0.0913712	−	0.0663850i
$456$	−3.95996e6	−	2.87708e6i	−0.891823	−	0.647948i
$457$	291614.	−	897496.i	0.0653158	−	0.201021i	−0.913073	−	0.407797i	$-0.866297\pi$
$457$	291614.	−	897496.i	0.0653158	−	0.201021i	0.978388	+	0.206776i	$0.0662971\pi$
$458$	−947072.	−	2.91479e6i	−0.210969	−	0.649297i
$459$	1.28166e7	−	9.31180e6i	2.83949	−	2.06301i
$460$	−3.26837e6			−0.720173
$461$	3.58847e6	−	2.60717e6i	0.786423	−	0.571370i	−0.120477	−	0.992716i	$-0.538442\pi$
$461$	3.58847e6	−	2.60717e6i	0.786423	−	0.571370i	0.906900	+	0.421346i	$0.138442\pi$
$462$	−2.27215e6	+	1.65081e6i	−0.495259	+	0.359827i
$463$	−1.73687e6	−	1.26191e6i	−0.376543	−	0.273574i	0.383376	−	0.923592i	$-0.374761\pi$
$463$	−1.73687e6	−	1.26191e6i	−0.376543	−	0.273574i	−0.759919	+	0.650018i	$0.774761\pi$
$464$	159911.	−	492156.i	0.0344813	−	0.106122i
$465$	1.37023e6			0.293874
$466$	−2.29831e6	−	1.66982e6i	−0.490279	−	0.356208i
$467$	−1.99056e6	−	6.12631e6i	−0.422360	−	1.29989i	−0.905500	−	0.424347i	$-0.860504\pi$
$467$	−1.99056e6	−	6.12631e6i	−0.422360	−	1.29989i	0.483139	−	0.875543i	$-0.339496\pi$
$468$	−234662.	+	170492.i	−0.0495254	+	0.0359823i
$469$	1.20756e6	−	3.71648e6i	0.253499	−	0.780189i
$470$	−2.74559e6	−	8.45005e6i	−0.573312	−	1.76447i
$471$	1.01366e6	+	3.11972e6i	0.210542	+	0.647982i
$472$	638719.	+	1.96578e6i	0.131964	+	0.406143i
$473$	306559.	+	943490.i	0.0630029	+	0.193903i
$474$	663499.	−	2.04204e6i	0.135642	−	0.417463i
$475$	−1.01555e7	+	7.37839e6i	−2.06522	+	1.50047i
$476$	−1.36487e6	−	4.20064e6i	−0.276105	−	0.849763i
$477$	1.55613e6	+	1.13060e6i	0.313148	+	0.227516i
$478$	1.49347e6			0.298969
$479$	−1.67015e6	+	5.14019e6i	−0.332596	+	1.02362i	0.635299	+	0.772267i	$0.280877\pi$
$479$	−1.67015e6	+	5.14019e6i	−0.332596	+	1.02362i	−0.967894	+	0.251358i	$0.919123\pi$
$480$	2.16173e6	+	1.57059e6i	0.428252	+	0.311143i
$481$	235652.	−	171211.i	0.0464416	−	0.0337418i
$482$	−4.16924e6	+	3.02913e6i	−0.817408	+	0.593882i
$483$	1.27688e7			2.49048
$484$	1.87883e6	−	1.36505e6i	0.364563	−	0.264871i
$485$	−3.41645e6	−	1.05147e7i	−0.659508	−	2.02976i
$486$	2.88041e6	−	8.86501e6i	0.553177	−	1.70250i
$487$	4.83320e6	+	3.51152e6i	0.923447	+	0.670924i	0.944380	−	0.328857i	$-0.106664\pi$
$487$	4.83320e6	+	3.51152e6i	0.923447	+	0.670924i	−0.0209325	+	0.999781i	$0.506664\pi$
$488$	2.66751e6	+	1.93806e6i	0.507057	+	0.368398i
$489$	6.00688e6			1.13600
$490$	2.12596e6	−	6.54304e6i	0.400005	−	1.23109i
$491$	3.70157e6			0.692918			0.346459	−	0.938065i	$-0.387384\pi$
$491$	3.70157e6			0.692918			0.346459	+	0.938065i	$0.387384\pi$
$492$	4.63699e6	+	1.98851e6i	0.863622	+	0.370351i
$493$	2.93622e6			0.544091
$494$	−95076.9	+	292617.i	−0.0175290	+	0.0539488i
$495$	6.91118e6			1.26777
$496$	−108754.	−	79014.7i	−0.0198492	−	0.0144213i
$497$	−916351.	−	665768.i	−0.166407	−	0.120902i
$498$	2.59727e6	−	7.99357e6i	0.469292	−	1.44433i
$499$	1.08597e6	+	3.34226e6i	0.195238	+	0.600882i	0.999974	+	0.00724839i	$0.00230725\pi$
$499$	1.08597e6	+	3.34226e6i	0.195238	+	0.600882i	−0.804735	+	0.593634i	$0.797693\pi$
$500$	1.94091e6	−	1.41015e6i	0.347200	−	0.252255i
$501$	−1.11596e7			−1.98634
$502$	−978722.	+	711083.i	−0.173341	+	0.125939i
$503$	281537.	−	204549.i	0.0496153	−	0.0360477i	−0.562701	−	0.826660i	$-0.690238\pi$
$503$	281537.	−	204549.i	0.0496153	−	0.0360477i	0.612317	+	0.790613i	$0.290238\pi$
$504$	−6.05432e6	−	4.39872e6i	−1.06167	−	0.771347i
$505$	57257.0	−	176219.i	0.00999080	−	0.0307485i
$506$	1.15688e6			0.200869
$507$	−8.77954e6	−	6.37871e6i	−1.51688	−	1.10208i
$508$	−1.47875e6	−	4.55113e6i	−0.254235	−	0.782456i
$509$	2.58606e6	−	1.87888e6i	0.442429	−	0.321444i	−0.344170	−	0.938907i	$-0.611840\pi$
$509$	2.58606e6	−	1.87888e6i	0.442429	−	0.321444i	0.786600	+	0.617464i	$0.211840\pi$
$510$	−4.68511e6	+	1.44193e7i	−0.797617	+	2.45481i
$511$	2.51155e6	+	7.72975e6i	0.425490	+	1.30952i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−8.79840e6	−	2.70787e7i	−1.47608	−	4.54291i
$514$	1.45260e6	+	4.47064e6i	0.242515	+	0.746383i
$515$	963143.	−	2.96425e6i	0.160019	−	0.492489i
$516$	−2.98314e6	+	2.16738e6i	−0.493230	+	0.358352i
$517$	971839.	+	2.99101e6i	0.159907	+	0.492144i
$518$	6.07985e6	+	4.41727e6i	0.995562	+	0.723318i
$519$	3.87341e6			0.631212
$520$	51902.3	−	159739.i	0.00841740	−	0.0259061i
$521$	−7.29087e6	−	5.29713e6i	−1.17675	−	0.854960i	−0.184951	−	0.982748i	$-0.559212\pi$
$521$	−7.29087e6	−	5.29713e6i	−1.17675	−	0.854960i	−0.991802	+	0.127787i	$0.959212\pi$
$522$	4.02481e6	−	2.92420e6i	0.646501	−	0.469711i
$523$	5.85358e6	−	4.25287e6i	0.935766	−	0.679874i	−0.0116319	−	0.999932i	$-0.503703\pi$
$523$	5.85358e6	−	4.25287e6i	0.935766	−	0.679874i	0.947398	+	0.320059i	$0.103703\pi$
$524$	3.19134e6			0.507744
$525$	−2.16587e7	+	1.57359e7i	−3.42952	+	2.49169i
$526$	−833941.	−	2.56661e6i	−0.131423	−	0.404478i
$527$	235703.	−	725418.i	0.0369690	−	0.113779i
$528$	−765176.	−	555933.i	−0.119447	−	0.0867836i
$529$	951920.	+	691611.i	0.147898	+	0.107454i
$530$	−1.11380e6			−0.172233
$531$	−6.14047e6	+	1.88984e7i	−0.945074	+	2.90864i
$532$	−7.93807e6			−1.21601
$533$	28806.0	−	315831.i	0.00439202	−	0.0481544i
$534$	2.25557e6			0.342297
$535$	2.54264e6	−	7.82546e6i	0.384062	−	1.18202i
$536$	1.31598e6			0.197851
$537$	6.14298e6	+	4.46314e6i	0.919271	+	0.667890i
$538$	6.06180e6	+	4.40416e6i	0.902913	+	0.656005i
$539$	−752514.	+	2.31600e6i	−0.111569	+	0.343373i
$540$	4.80303e6	+	1.47822e7i	0.708812	+	2.18150i
$541$	−6.70757e6	+	4.87333e6i	−0.985308	+	0.715868i	−0.958889	−	0.283783i	$-0.908410\pi$
$541$	−6.70757e6	+	4.87333e6i	−0.985308	+	0.715868i	−0.0264191	+	0.999651i	$0.508410\pi$
$542$	3.10091e6			0.453409
$543$	−1.48013e7	+	1.07538e7i	−2.15427	+	1.56517i
$544$	1.20335e6	−	874282.i	0.174338	−	0.126664i
$545$	1.18996e7	+	8.64560e6i	1.71610	+	1.24682i
$546$	−202771.	+	624065.i	−0.0291088	+	0.0895877i
$547$	−6.06401e6			−0.866546			−0.433273	−	0.901263i	$-0.642641\pi$
$547$	−6.06401e6			−0.866546			−0.433273	+	0.901263i	$0.642641\pi$
$548$	−2.52612e6	−	1.83533e6i	−0.359338	−	0.261074i
$549$	9.79541e6	+	3.01472e7i	1.38705	+	4.26890i
$550$	−1.96232e6	+	1.42571e6i	−0.276608	+	0.200967i
$551$	1.63071e6	−	5.01882e6i	0.228822	−	0.704243i
$552$	1.32879e6	+	4.08960e6i	0.185613	+	0.571260i
$553$	−1.07602e6	−	3.31166e6i	−0.149627	−	0.460504i
$554$	1.89454e6	+	5.83080e6i	0.262259	+	0.807149i
$555$	−7.97161e6	−	2.45341e7i	−1.09853	−	3.38094i
$556$	966430.	−	2.97437e6i	0.132582	−	0.408044i
$557$	5.56640e6	−	4.04423e6i	0.760215	−	0.552329i	−0.138761	−	0.990326i	$-0.544312\pi$
$557$	5.56640e6	−	4.04423e6i	0.760215	−	0.552329i	0.898976	+	0.437997i	$0.144312\pi$
$558$	−399359.	−	1.22910e6i	−0.0542973	−	0.167110i
$559$	187514.	+	136237.i	0.0253807	+	0.0184401i
$560$	4.33338e6			0.583924
$561$	1.65836e6	−	5.10391e6i	0.222470	−	0.684693i
$562$	−5.53219e6	−	4.01937e6i	−0.738850	−	0.536806i
$563$	−7.84265e6	+	5.69802e6i	−1.04278	+	0.757622i	−0.970826	−	0.239786i	$-0.922923\pi$
$563$	−7.84265e6	+	5.69802e6i	−1.04278	+	0.757622i	−0.0719518	+	0.997408i	$0.522923\pi$
$564$	−9.45702e6	+	6.87093e6i	−1.25186	+	0.909531i
$565$	−3.07120e6			−0.404750
$566$	7.74255e6	−	5.62529e6i	1.01588	−	0.738081i
$567$	−9.98396e6	−	3.07275e7i	−1.30420	−	4.01392i
$568$	117872.	−	362773.i	0.0153299	−	0.0471806i
$569$	−6.93068e6	−	5.03544e6i	−0.897419	−	0.652013i	0.0403826	−	0.999184i	$-0.487142\pi$
$569$	−6.93068e6	−	5.03544e6i	−0.897419	−	0.652013i	−0.937802	+	0.347171i	$0.887142\pi$
$570$	2.20446e7	+	1.60163e7i	2.84194	+	2.06479i
$571$	1.05770e7			1.35760			0.678800	−	0.734323i	$-0.262500\pi$
$571$	1.05770e7			1.35760			0.678800	+	0.734323i	$0.262500\pi$
$572$	−18371.5	+	56541.8i	−0.00234777	+	0.00722569i
$573$	1.25004e7			1.59051
$574$	7.97933e6	−	1.81119e6i	1.01085	−	0.229449i
$575$	1.10277e7			1.39096
$576$	778779.	−	2.39683e6i	0.0978043	−	0.301011i
$577$	2.66648e6			0.333425			0.166713	−	0.986006i	$-0.446685\pi$
$577$	2.66648e6			0.333425			0.166713	+	0.986006i	$0.446685\pi$
$578$	2.23309e6	+	1.62243e6i	0.278026	+	0.201998i
$579$	1.31729e7	+	9.57067e6i	1.63300	+	1.18644i
$580$	−890203.	+	2.73976e6i	−0.109880	+	0.338176i
$581$	−4.21210e6	−	1.29635e7i	−0.517676	−	1.59324i
$582$	−1.17678e7	+	8.54977e6i	−1.44008	+	1.04628i
$583$	394245.			0.0480391
$584$	−2.21432e6	+	1.60880e6i	−0.268664	+	0.195195i
$585$	1.30633e6	−	949106.i	0.157821	−	0.114663i
$586$	−5.99938e6	−	4.35880e6i	−0.721709	−	0.524352i
$587$	2.86001e6	−	8.80221e6i	0.342588	−	1.05438i	−0.620274	−	0.784385i	$-0.712978\pi$
$587$	2.86001e6	−	8.80221e6i	0.342588	−	1.05438i	0.962862	−	0.269993i	$-0.0870215\pi$
$588$	−9.05142e6			−1.07963
$589$	−1.10904e6	−	805763.i	−0.131722	−	0.0957016i
$590$	−3.55566e6	−	1.09432e7i	−0.420524	−	1.29424i
$591$	−1.46216e7	+	1.06232e7i	−1.72197	+	1.25108i
$592$	−782062.	+	2.40694e6i	−0.0917143	+	0.282268i
$593$	1.94435e6	+	5.98409e6i	0.227058	+	0.698813i	0.998076	+	0.0620000i	$0.0197479\pi$
$593$	1.94435e6	+	5.98409e6i	0.227058	+	0.698813i	−0.771018	+	0.636813i	$0.780252\pi$
$594$	−1.70010e6	−	5.23237e6i	−0.197701	−	0.608460i
$595$	7.59804e6	+	2.33844e7i	0.879851	+	2.70790i
$596$	1.18705e6	+	3.65336e6i	0.136884	+	0.421285i
$597$	−1.80935e6	+	5.56860e6i	−0.207772	+	0.639456i
$598$	218671.	−	158874.i	0.0250057	−	0.0181677i
$599$	−4.17314e6	−	1.28436e7i	−0.475222	−	1.46258i	−0.845659	−	0.533724i	$-0.820792\pi$
$599$	−4.17314e6	−	1.28436e7i	−0.475222	−	1.46258i	0.370437	−	0.928858i	$-0.379208\pi$
$600$	−7.29383e6	−	5.29928e6i	−0.827137	−	0.600950i
$601$	3.07044e6			0.346748			0.173374	−	0.984856i	$-0.444533\pi$
$601$	3.07044e6			0.346748			0.173374	+	0.984856i	$0.444533\pi$
$602$	−1.84791e6	+	5.68727e6i	−0.207821	+	0.639606i
$603$	1.02353e7	+	7.43635e6i	1.14632	+	0.832850i
$604$	1.91349e6	−	1.39023e6i	0.213420	−	0.155058i
$605$	−1.04592e7	+	7.59903e6i	−1.16174	+	0.844053i
$606$	−243775.			−0.0269655
$607$	5.99955e6	−	4.35893e6i	0.660917	−	0.480184i	−0.206056	−	0.978540i	$-0.566063\pi$
$607$	5.99955e6	−	4.35893e6i	0.660917	−	0.480184i	0.866972	+	0.498356i	$0.166063\pi$
$608$	−826079.	−	2.54241e6i	−0.0906280	−	0.278924i
$609$	3.47783e6	−	1.07037e7i	0.379984	−	1.16947i
$610$	−1.48497e7	−	1.07889e7i	−1.61582	−	1.17396i
$611$	594448.	+	431892.i	0.0644185	+	0.0468028i
$612$	1.42996e7			1.54328
$613$	3.64093e6	−	1.12056e7i	0.391347	−	1.20444i	−0.540424	−	0.841393i	$-0.681736\pi$
$613$	3.64093e6	−	1.12056e7i	0.391347	−	1.20444i	0.931770	−	0.363048i	$-0.118264\pi$
$614$	−3.80912e6			−0.407759
$615$	−2.58135e7	−	1.10697e7i	−2.75207	−	1.18018i
$616$	−1.53386e6			−0.162867
$617$	−2.11014e6	+	6.49433e6i	−0.223150	+	0.686786i	0.775324	+	0.631564i	$0.217587\pi$
$617$	−2.11014e6	+	6.49433e6i	−0.223150	+	0.686786i	−0.998474	+	0.0552223i	$0.982413\pi$
$618$	−4.10064e6			−0.431898
$619$	−8.80671e6	−	6.39845e6i	−0.923819	−	0.671194i	0.0206524	−	0.999787i	$-0.493426\pi$
$619$	−8.80671e6	−	6.39845e6i	−0.923819	−	0.671194i	−0.944472	+	0.328593i	$0.893426\pi$
$620$	605421.	+	439864.i	0.0632526	+	0.0459557i
$621$	−7.72939e6	+	2.37886e7i	−0.804297	+	2.47537i
$622$	839686.	+	2.58429e6i	0.0870243	+	0.267833i
$623$	2.95934e6	−	2.15009e6i	0.305475	−	0.221940i
$624$	−220977.			−0.0227188
$625$	1.35182e6	−	982154.i	0.138426	−	0.100573i
$626$	2.35576e6	−	1.71156e6i	0.240268	−	0.174565i
$627$	−7.80298e6	−	5.66920e6i	−0.792669	−	0.575907i
$628$	−553601.	+	1.70381e6i	−0.0560142	+	0.172394i
$629$	−1.43599e7			−1.44719
$630$	3.37036e7	+	2.44871e7i	3.38318	+	2.45802i
$631$	−2.24394e6	−	6.90615e6i	−0.224356	−	0.690498i	−0.998356	−	0.0573122i	$-0.981747\pi$
$631$	−2.24394e6	−	6.90615e6i	−0.224356	−	0.690498i	0.774000	−	0.633186i	$-0.218253\pi$
$632$	948683.	−	689259.i	0.0944775	−	0.0686419i
$633$	−2.98413e6	+	9.18420e6i	−0.296011	+	0.911029i
$634$	−1.49934e6	−	4.61450e6i	−0.148142	−	0.455934i
$635$	8.23201e6	+	2.53355e7i	0.810161	+	2.49342i
$636$	452828.	+	1.39366e6i	0.0443905	+	0.136620i
$637$	175816.	+	541106.i	0.0171676	+	0.0528365i
$638$	315100.	−	969777.i	0.0306476	−	0.0943236i
$639$	2.96673e6	−	2.15545e6i	0.287426	−	0.208827i
$640$	450955.	+	1.38790e6i	0.0435194	+	0.133939i
$641$	−3.68175e6	−	2.67494e6i	−0.353923	−	0.257140i	0.396590	−	0.917996i	$-0.370193\pi$
$641$	−3.68175e6	−	2.67494e6i	−0.353923	−	0.257140i	−0.750513	+	0.660856i	$0.770193\pi$
$642$	−1.08255e7			−1.03660
$643$	−1.85797e6	+	5.71823e6i	−0.177219	+	0.545424i	−0.999728	−	0.0233283i	$-0.992574\pi$
$643$	−1.85797e6	+	5.71823e6i	−0.177219	+	0.545424i	0.822509	+	0.568752i	$0.192574\pi$
$644$	5.64175e6	+	4.09897e6i	0.536043	+	0.389458i
$645$	1.66067e7	−	1.20655e7i	1.57175	−	1.14195i
$646$	1.22713e7	−	8.91560e6i	1.15693	−	0.840561i
$647$	−3.59021e6			−0.337178			−0.168589	−	0.985686i	$-0.553921\pi$
$647$	−3.59021e6			−0.337178			−0.168589	+	0.985686i	$0.553921\pi$
$648$	8.80242e6	−	6.39533e6i	0.823502	−	0.598309i
$649$	1.25858e6	+	3.87350e6i	0.117292	+	0.360987i
$650$	−175122.	+	538969.i	−0.0162576	+	0.0500357i
$651$	−2.36525e6	−	1.71845e6i	−0.218738	−	0.158923i
$652$	2.65407e6	+	1.92829e6i	0.244508	+	0.177646i
$653$	−2.27134e6			−0.208449			−0.104225	−	0.994554i	$-0.533236\pi$
$653$	−2.27134e6			−0.208449			−0.104225	+	0.994554i	$0.533236\pi$
$654$	5.98001e6	−	1.84046e7i	0.546711	−	1.68260i
$655$	−1.77657e7			−1.61801
$656$	1.41046e6	+	2.36714e6i	0.127968	+	0.214765i
$657$	−2.63133e7			−2.37827
$658$	−5.85815e6	+	1.80295e7i	−0.527468	+	1.62338i
$659$	5.59475e6			0.501842			0.250921	−	0.968008i	$-0.419267\pi$
$659$	5.59475e6			0.501842			0.250921	+	0.968008i	$0.419267\pi$
$660$	4.25963e6	+	3.09480e6i	0.380638	+	0.276550i
$661$	9.12041e6	+	6.62636e6i	0.811915	+	0.589891i	0.914385	−	0.404845i	$-0.132675\pi$
$661$	9.12041e6	+	6.62636e6i	0.811915	+	0.589891i	−0.102470	+	0.994736i	$0.532675\pi$
$662$	−880881.	+	2.71107e6i	−0.0781218	+	0.240434i
$663$	−387456.	−	1.19247e6i	−0.0342325	−	0.105357i
$664$	3.71362e6	−	2.69810e6i	0.326872	−	0.237486i
$665$	4.41902e7			3.87500
$666$	−1.96838e7	+	1.43011e7i	−1.71958	+	1.24935i
$667$	−3.75055e6	+	2.72493e6i	−0.326422	+	0.237160i
$668$	−4.93073e6	−	3.58239e6i	−0.427534	−	0.310621i
$669$	4.82926e6	−	1.48629e7i	0.417172	−	1.28392i
$670$	−7.32589e6			−0.630483
$671$	5.25624e6	+	3.81888e6i	0.450681	+	0.327439i
$672$	−1.76178e6	−	5.42221e6i	−0.150497	−	0.463184i
$673$	−1.60300e7	+	1.16465e7i	−1.36426	+	0.991190i	−0.366095	+	0.930577i	$0.619306\pi$
$673$	−1.60300e7	+	1.16465e7i	−1.36426	+	0.991190i	−0.998161	+	0.0606130i	$0.980694\pi$
$674$	−1.11209e6	+	3.42267e6i	−0.0942956	+	0.290212i
$675$	−1.62057e7	−	4.98761e7i	−1.36902	−	4.21340i
$676$	−1.83148e6	−	5.63672e6i	−0.154147	−	0.474416i
$677$	1.02612e6	+	3.15807e6i	0.0860451	+	0.264820i	0.984817	−	0.173598i	$-0.0555392\pi$
$677$	1.02612e6	+	3.15807e6i	0.0860451	+	0.264820i	−0.898772	+	0.438417i	$0.855539\pi$
$678$	1.24863e6	+	3.84289e6i	0.104318	+	0.321058i
$679$	−7.28954e6	+	2.24349e7i	−0.606772	+	1.86745i
$680$	−6.69886e6	+	4.86701e6i	−0.555557	+	0.403636i
$681$	3.24557e6	+	9.98883e6i	0.268178	+	0.825367i
$682$	−214297.	−	155696.i	−0.0176423	−	0.0128179i
$683$	1.03186e7			0.846391			0.423195	−	0.906038i	$-0.360908\pi$
$683$	1.03186e7			0.846391			0.423195	+	0.906038i	$0.360908\pi$
$684$	7.94170e6	−	2.44420e7i	0.649042	−	1.99755i
$685$	1.40626e7	+	1.02171e7i	1.14509	+	0.831954i
$686$	−1.53935e6	+	1.11840e6i	−0.124889	+	0.0907375i
$687$	1.81599e7	−	1.31939e7i	1.46798	−	1.06655i
$688$	−2.01382e6			−0.162200
$689$	74519.1	−	54141.3i	0.00598026	−	0.00434491i
$690$	−7.39721e6	−	2.27663e7i	−0.591487	−	1.82041i
$691$	−1.42204e6	+	4.37659e6i	−0.113297	+	0.348691i	−0.991588	−	0.129435i	$-0.958684\pi$
$691$	−1.42204e6	+	4.37659e6i	−0.113297	+	0.348691i	0.878291	+	0.478126i	$0.158684\pi$
$692$	1.71142e6	+	1.24342e6i	0.135860	+	0.0987081i
$693$	−1.19298e7	−	8.66754e6i	−0.943630	−	0.685587i
$694$	−8.30210e6			−0.654319
$695$	−5.37998e6	+	1.65579e7i	−0.422492	+	1.30030i
$696$	3.79010e6			0.296570
$697$	−1.03008e7	+	1.17618e7i	−0.803137	+	0.917049i
$698$	−375444.			−0.0291680
$699$	6.42964e6	−	1.97884e7i	0.497730	−	1.53186i
$700$	−1.46211e7			−1.12781
$701$	−1.43018e7	−	1.03908e7i	−1.09924	−	0.798648i	−0.118308	−	0.992977i	$-0.537747\pi$
$701$	−1.43018e7	−	1.03908e7i	−1.09924	−	0.798648i	−0.980936	+	0.194329i	$0.937747\pi$
$702$	−1.03990e6	−	755535.i	−0.0796436	−	0.0578644i
$703$	−7.97518e6	+	2.45451e7i	−0.608629	+	1.87317i
$704$	−159622.	−	491265.i	−0.0121384	−	0.0373580i
$705$	5.26459e7	−	3.82495e7i	3.98926	−	2.89837i
$706$	−1.36612e6			−0.103152
$707$	−319838.	+	232376.i	−0.0240647	+	0.0174840i
$708$	−1.22473e7	+	8.89817e6i	−0.918240	+	0.667141i
$709$	−1.05174e7	−	7.64133e6i	−0.785765	−	0.570892i	0.120939	−	0.992660i	$-0.461410\pi$
$709$	−1.05174e7	−	7.64133e6i	−0.785765	−	0.570892i	−0.906704	+	0.421768i	$0.861410\pi$
$710$	−656177.	+	2.01951e6i	−0.0488512	+	0.150349i
$711$	1.12734e7			0.836337
$712$	996596.	+	724070.i	0.0736749	+	0.0535279i
$713$	372145.	+	1.14535e6i	0.0274150	+	0.0843748i
$714$	2.61710e7	−	1.90144e7i	1.92121	−	1.39584i
$715$	102272.	−	314760.i	0.00748154	−	0.0230258i
$716$	1.28147e6	+	3.94397e6i	0.0934173	+	0.287509i
$717$	3.38012e6	+	1.04029e7i	0.245547	+	0.755715i
$718$	652040.	+	2.00677e6i	0.0472023	+	0.145274i
$719$	1.84881e6	+	5.69005e6i	0.133374	+	0.410482i	0.995333	−	0.0964948i	$-0.0307631\pi$
$719$	1.84881e6	+	5.69005e6i	0.133374	+	0.410482i	−0.861960	+	0.506976i	$0.830763\pi$
$720$	−4.33536e6	+	1.33429e7i	−0.311669	+	0.959218i
$721$	−5.38011e6	+	3.90888e6i	−0.385437	+	0.280036i
$722$	−5.36342e6	−	1.65069e7i	−0.382912	−	1.17848i
$723$	−3.05359e7	−	2.21856e7i	−2.17253	−	1.57843i
$724$	−9.99189e6			−0.708437
$725$	3.00360e6	−	9.24413e6i	0.212225	−	0.653162i
$726$	1.37607e7	+	9.99774e6i	0.968945	+	0.703980i
$727$	−3.69658e6	+	2.68572e6i	−0.259396	+	0.188463i	−0.709881	−	0.704322i	$-0.751251\pi$
$727$	−3.69658e6	+	2.68572e6i	−0.259396	+	0.188463i	0.450484	+	0.892784i	$0.351251\pi$
$728$	−289926.	+	210644.i	−0.0202749	+	0.0147306i
$729$	2.69580e7			1.87875
$730$	1.23268e7	−	8.95597e6i	0.856139	−	0.622021i
$731$	−3.53099e6	−	1.08673e7i	−0.244401	−	0.752190i
$732$	−7.46251e6	+	2.29672e7i	−0.514763	+	1.58428i
$733$	2.29061e7	+	1.66422e7i	1.57467	+	1.14407i	0.922499	+	0.386000i	$0.126144\pi$
$733$	2.29061e7	+	1.66422e7i	1.57467	+	1.14407i	0.652176	+	0.758068i	$0.273856\pi$
$734$	−1.33094e7	−	9.66985e6i	−0.911840	−	0.662490i
$735$	5.03880e7			3.44040
$736$	−725710.	+	2.23351e6i	−0.0493820	+	0.151982i
$737$	2.59310e6			0.175853
$738$	−2.40614e6	+	2.63811e7i	−0.162622	+	1.78300i
$739$	2.20350e7			1.48424			0.742118	−	0.670269i	$-0.233821\pi$
$739$	2.20350e7			1.48424			0.742118	+	0.670269i	$0.233821\pi$
$740$	4.35364e6	−	1.33991e7i	0.292262	−	0.899491i
$741$	−2.25344e6			−0.150765
$742$	1.92261e6	+	1.39685e6i	0.128198	+	0.0931411i
$743$	−2.38297e7	−	1.73133e7i	−1.58361	−	1.15056i	−0.912411	−	0.409276i	$-0.865781\pi$
$743$	−2.38297e7	−	1.73133e7i	−1.58361	−	1.15056i	−0.671195	−	0.741281i	$-0.734219\pi$
$744$	304247.	−	936375.i	0.0201509	−	0.0620180i
$745$	−6.60813e6	−	2.03377e7i	−0.436202	−	1.34249i
$746$	1.43677e7	−	1.04387e7i	0.945233	−	0.686752i
$747$	4.41298e7			2.89355
$748$	2.37116e6	−	1.72275e6i	0.154955	−	0.112581i
$749$	−1.42032e7	+	1.03192e7i	−0.925085	+	0.672114i
$750$	1.42154e7	+	1.03281e7i	0.922796	+	0.670450i
$751$	7.86198e6	−	2.41967e7i	0.508665	−	1.56551i	−0.285855	−	0.958273i	$-0.592278\pi$
$751$	7.86198e6	−	2.41967e7i	0.508665	−	1.56551i	0.794520	−	0.607238i	$-0.207722\pi$
$752$	−6.38414e6			−0.411678
$753$	−7.16826e6	−	5.20804e6i	−0.460708	−	0.334724i
$754$	−73619.4	−	226577.i	−0.00471589	−	0.0145140i
$755$	−1.06522e7	+	7.73924e6i	−0.680096	+	0.494118i
$756$	1.02480e7	−	3.15402e7i	0.652133	−	2.00706i
$757$	6.99729e6	+	2.15354e7i	0.443803	+	1.36588i	0.883792	+	0.467881i	$0.154982\pi$
$757$	6.99729e6	+	2.15354e7i	0.443803	+	1.36588i	−0.439989	+	0.898003i	$0.645018\pi$
$758$	2.60539e6	+	8.01856e6i	0.164702	+	0.506901i
$759$	2.61834e6	+	8.05843e6i	0.164977	+	0.507746i
$760$	4.59867e6	+	1.41532e7i	0.288801	+	0.888837i
$761$	5.07818e6	−	1.56290e7i	0.317868	−	0.978297i	−0.656690	−	0.754161i	$-0.728044\pi$
$761$	5.07818e6	−	1.56290e7i	0.317868	−	0.978297i	0.974558	−	0.224136i	$-0.0719560\pi$
$762$	2.83547e7	−	2.06009e7i	1.76904	−	1.28528i
$763$	−9.69804e6	−	2.98475e7i	−0.603077	−	1.85608i
$764$	5.52315e6	+	4.01280e6i	0.342337	+	0.248722i
$765$	−7.96041e7			−4.91792
$766$	−4.32720e6	+	1.33178e7i	−0.266462	+	0.820085i
$767$	769837.	+	559320.i	0.0472510	+	0.0343298i
$768$	1.55329e6	−	1.12853e6i	0.0950274	−	0.0690414i
$769$	2.70796e6	−	1.96744e6i	0.165130	−	0.119974i	−0.502151	−	0.864780i	$-0.667458\pi$
$769$	2.70796e6	−	1.96744e6i	0.165130	−	0.119974i	0.667281	+	0.744806i	$0.267458\pi$
$770$	8.53878e6			0.519002
$771$	−2.78532e7	+	2.02365e7i	−1.68748	+	1.22603i
$772$	2.74797e6	+	8.45738e6i	0.165947	+	0.510732i
$773$	2.57708e6	−	7.93143e6i	0.155124	−	0.477423i	−0.843049	−	0.537836i	$-0.819242\pi$
$773$	2.57708e6	−	7.93143e6i	0.155124	−	0.477423i	0.998173	+	0.0604135i	$0.0192419\pi$
$774$	−1.56629e7	−	1.13797e7i	−0.939764	−	0.682778i
$775$	−2.04273e6	−	1.48413e6i	−0.122168	−	0.0887601i
$776$	−7.94405e6			−0.473574
$777$	−1.70087e7	+	5.23474e7i	−1.01069	+	3.11059i
$778$	2.12724e6			0.125999
$779$	1.43834e7	+	2.41392e7i	0.849214	+	1.42521i
$780$	1.23015e6			0.0723972
$781$	232263.	−	714832.i	0.0136255	−	0.0419350i
$782$	−1.33252e7			−0.779214
$783$	1.78359e7	+	1.29586e7i	1.03966	+	0.755358i
$784$	−3.99926e6	−	2.90564e6i	−0.232375	−	0.168831i
$785$	3.08182e6	−	9.48487e6i	0.178498	−	0.549360i
$786$	7.22286e6	+	2.22297e7i	0.417016	+	1.28344i
$787$	6.57040e6	−	4.77368e6i	0.378142	−	0.274736i	−0.382437	−	0.923982i	$-0.624915\pi$
$787$	6.57040e6	−	4.77368e6i	0.378142	−	0.274736i	0.760579	+	0.649245i	$0.224915\pi$
$788$	−9.87057e6			−0.566274
$789$	1.59906e7	−	1.16179e7i	0.914476	−	0.664406i
$790$	−5.28119e6	+	3.83701e6i	−0.301068	+	0.218738i
$791$	5.30141e6	+	3.85170e6i	0.301266	+	0.218883i
$792$	1.53456e6	−	4.72289e6i	0.0869302	−	0.267544i
$793$	1.51797e6			0.0857194
$794$	−5.03005e6	−	3.65455e6i	−0.283153	−	0.205723i
$795$	−2.52083e6	−	7.75832e6i	−0.141457	−	0.435361i
$796$	−2.58704e6	+	1.87960e6i	−0.144717	+	0.105143i
$797$	−2.72137e6	+	8.37550e6i	−0.151754	+	0.467052i	−0.997818	−	0.0660307i	$-0.978966\pi$
$797$	−2.72137e6	+	8.37550e6i	−0.151754	+	0.467052i	0.846063	+	0.533083i	$0.178966\pi$
$798$	−1.79660e7	−	5.52937e7i	−0.998721	−	3.07375i
$799$	−1.11938e7	−	3.44510e7i	−0.620313	−	1.90913i
$800$	−1.52155e6	−	4.68285e6i	−0.0840545	−	0.258693i
$801$	3.65962e6	+	1.12631e7i	0.201537	+	0.620267i
$802$	3.42620e6	−	1.05448e7i	0.188095	−	0.578896i
$803$	−4.36325e6	+	3.17009e6i	−0.238793	+	0.173493i
$804$	2.97842e6	+	9.16664e6i	0.162497	+	0.500115i
$805$	−3.14069e7	−	2.28184e7i	−1.70819	−	1.24107i
$806$	−61887.5			−0.00335556
$807$	−1.69582e7	+	5.21921e7i	−0.916636	+	2.82112i
$808$	−107709.	−	78255.4i	−0.00580397	−	0.00421683i
$809$	−3.19610e6	+	2.32210e6i	−0.171691	+	0.124741i	−0.670313	−	0.742079i	$-0.733840\pi$
$809$	−3.19610e6	+	2.32210e6i	−0.171691	+	0.124741i	0.498621	+	0.866820i	$0.333840\pi$
$810$	−4.90019e7	+	3.56019e7i	−2.62422	+	1.90661i
$811$	1.69462e7			0.904734			0.452367	−	0.891832i	$-0.350580\pi$
$811$	1.69462e7			0.904734			0.452367	+	0.891832i	$0.350580\pi$
$812$	4.97267e6	−	3.61286e6i	0.264667	−	0.192292i
$813$	7.01819e6	+	2.15998e7i	0.372391	+	1.14610i
$814$	−1.54103e6	+	4.74280e6i	−0.0815173	+	0.250885i
$815$	−1.47748e7	−	1.07346e7i	−0.779164	−	0.566096i
$816$	8.81342e6	+	6.40333e6i	0.463361	+	0.336651i
$817$	−2.05362e7			−1.07638
$818$	1.29420e6	−	3.98315e6i	0.0676268	−	0.208134i
$819$	−3.44525e6			−0.179478
$820$	−7.85185e6	−	1.31775e7i	−0.407791	−	0.684384i
$821$	−2.28647e6			−0.118388			−0.0591940	−	0.998246i	$-0.518853\pi$
$821$	−2.28647e6			−0.118388			−0.0591940	+	0.998246i	$0.518853\pi$
$822$	7.06697e6	−	2.17499e7i	0.364799	−	1.12274i
$823$	−3.12208e6			−0.160673			−0.0803367	−	0.996768i	$-0.525600\pi$
$823$	−3.12208e6			−0.160673			−0.0803367	+	0.996768i	$0.525600\pi$
$824$	−1.81182e6	−	1.31637e6i	−0.0929603	−	0.0675396i
$825$	−1.43723e7	−	1.04421e7i	−0.735174	−	0.534135i
$826$	−7.58658e6	+	2.33491e7i	−0.386897	+	1.19075i
$827$	6.96835e6	+	2.14464e7i	0.354296	+	1.09041i	0.956417	+	0.292005i	$0.0943225\pi$
$827$	6.96835e6	+	2.14464e7i	0.354296	+	1.09041i	−0.602121	+	0.798405i	$0.705678\pi$
$828$	−1.82654e7	+	1.32706e7i	−0.925879	+	0.672691i
$829$	3.25567e6			0.164533			0.0822666	−	0.996610i	$-0.473784\pi$
$829$	3.25567e6			0.164533			0.0822666	+	0.996610i	$0.473784\pi$
$830$	−2.06732e7	+	1.50200e7i	−1.04163	+	0.756788i
$831$	−3.63273e7	+	2.63933e7i	−1.82487	+	1.32584i
$832$	−97636.3	−	70936.9i	−0.00488993	−	0.00355274i
$833$	8.66758e6	−	2.66761e7i	0.432798	−	1.33202i
$834$	2.29056e7			1.14032
$835$	2.74487e7	+	1.99427e7i	1.36240	+	0.989845i
$836$	−1.62776e6	−	5.00974e6i	−0.0805518	−	0.247913i
$837$	4.63329e6	−	3.36628e6i	0.228600	−	0.166087i
$838$	8.19117e6	−	2.52098e7i	0.402936	−	1.24011i
$839$	7.87929e6	+	2.42500e7i	0.386440	+	1.18934i	0.935430	+	0.353511i	$0.115012\pi$
$839$	7.87929e6	+	2.42500e7i	0.386440	+	1.18934i	−0.548990	+	0.835829i	$0.684988\pi$
$840$	9.80761e6	+	3.01847e7i	0.479584	+	1.47601i
$841$	−5.07561e6	−	1.56211e7i	−0.247456	−	0.761592i
$842$	1.79170e6	+	5.51427e6i	0.0870931	+	0.268045i
$843$	1.54766e7	−	4.76321e7i	0.750079	−	2.30851i
$844$	−4.26676e6	+	3.09998e6i	−0.206178	+	0.149797i
$845$	1.01956e7	+	3.13789e7i	0.491215	+	1.51180i
$846$	−4.96537e7	−	3.60755e7i	−2.38521	−	1.73295i
$847$	2.75845e7			1.32116
$848$	−247308.	+	761137.i	−0.0118100	+	0.0363474i
$849$	5.67072e7	+	4.12002e7i	2.70003	+	1.96169i
$850$	2.26024e7	−	1.64216e7i	1.07302	−	0.779593i
$851$	1.83425e7	−	1.33266e7i	0.868228	−	0.630804i
$852$	2.79372e6			0.131851
$853$	884549.	−	642663.i	0.0416245	−	0.0302420i	−0.566778	−	0.823870i	$-0.691810\pi$
$853$	884549.	−	642663.i	0.0416245	−	0.0302420i	0.608403	+	0.793628i	$0.291810\pi$
$854$	1.21023e7	+	3.72469e7i	0.567835	+	1.74762i
$855$	−4.42104e7	+	1.36065e8i	−2.06828	+	6.36550i
$856$	−4.78311e6	−	3.47513e6i	−0.223114	−	0.162101i
$857$	−3.21860e6	−	2.33845e6i	−0.149698	−	0.108762i	0.510415	−	0.859928i	$-0.329492\pi$
$857$	−3.21860e6	−	2.33845e6i	−0.149698	−	0.108762i	−0.660113	+	0.751166i	$0.729492\pi$
$858$	−435429.			−0.0201929
$859$	−5.88555e6	+	1.81139e7i	−0.272147	+	0.837584i	0.717813	+	0.696236i	$0.245143\pi$
$859$	−5.88555e6	+	1.81139e7i	−0.272147	+	0.837584i	−0.989960	+	0.141347i	$0.954857\pi$
$860$	1.12107e7			0.516876
$861$	3.06755e7	+	5.14818e7i	1.41021	+	2.36672i
$862$	1.98063e7			0.907894
$863$	−7.80831e6	+	2.40315e7i	−0.356886	+	1.09838i	0.598021	+	0.801480i	$0.295954\pi$
$863$	−7.80831e6	+	2.40315e7i	−0.356886	+	1.09838i	−0.954908	+	0.296903i	$0.904046\pi$
$864$	1.11682e7			0.508977
$865$	−9.52726e6	−	6.92196e6i	−0.432940	−	0.314549i
$866$	9.23530e6	+	6.70984e6i	0.418462	+	0.304031i
$867$	−6.24718e6	+	1.92269e7i	−0.282252	+	0.868681i
$868$	−493410.	−	1.51856e6i	−0.0222284	−	0.0684120i
$869$	1.86935e6	−	1.35816e6i	0.0839733	−	0.0610102i
$870$	−2.10990e7			−0.945067
$871$	490141.	−	356108.i	0.0218915	−	0.0159051i
$872$	8.55034e6	−	6.21219e6i	0.380796	−	0.276664i
$873$	−6.17862e7	−	4.48903e7i	−2.74382	−	1.99350i
$874$	−7.40052e6	+	2.27765e7i	−0.327705	+	1.00857i
$875$	2.84959e7			1.25824
$876$	−1.62179e7	−	1.17830e7i	−0.714060	−	0.518795i
$877$	−476754.	−	1.46730e6i	−0.0209313	−	0.0644198i	0.940045	−	0.341050i	$-0.110782\pi$
$877$	−476754.	−	1.46730e6i	−0.0209313	−	0.0644198i	−0.960977	+	0.276630i	$0.910782\pi$
$878$	−2.11660e7	+	1.53780e7i	−0.926623	+	0.673231i
$879$	1.67836e7	−	5.16546e7i	0.732677	−	2.25495i
$880$	888592.	+	2.73481e6i	0.0386808	+	0.119047i
$881$	−6.86047e6	−	2.11143e7i	−0.297793	−	0.916511i	−0.982269	−	0.187476i	$-0.939969\pi$
$881$	−6.86047e6	−	2.11143e7i	−0.297793	−	0.916511i	0.684476	−	0.729035i	$-0.260031\pi$
$882$	−1.46858e7	−	4.51981e7i	−0.635660	−	1.95636i
$883$	−9.42209e6	−	2.89982e7i	−0.406673	−	1.25161i	−0.919490	−	0.393113i	$-0.871398\pi$
$883$	−9.42209e6	−	2.89982e7i	−0.406673	−	1.25161i	0.512817	−	0.858498i	$-0.328602\pi$
$884$	211606.	−	651257.i	0.00910748	−	0.0280299i
$885$	6.81789e7	−	4.95349e7i	2.92612	−	2.12595i
$886$	−9.18481e6	−	2.82679e7i	−0.393084	−	1.20979i
$887$	1.73856e7	+	1.26314e7i	0.741959	+	0.539065i	0.893324	−	0.449413i	$-0.148367\pi$
$887$	1.73856e7	+	1.26314e7i	0.741959	+	0.539065i	−0.151365	+	0.988478i	$0.548367\pi$
$888$	−1.85359e7			−0.788825
$889$	1.75643e7	−	5.40574e7i	0.745378	−	2.29404i
$890$	−5.54792e6	−	4.03080e6i	−0.234777	−	0.170575i
$891$	1.73449e7	−	1.26018e7i	0.731943	−	0.531788i
$892$	6.90496e6	−	5.01675e6i	0.290569	−	0.211111i
$893$	−6.51031e7			−2.73195
$894$	−2.27613e7	+	1.65371e7i	−0.952475	+	0.692014i
$895$	−7.13379e6	−	2.19556e7i	−0.297689	−	0.916193i
$896$	962184.	−	2.96130e6i	0.0400395	−	0.123229i
$897$	1.60157e6	+	1.16361e6i	0.0664607	+	0.0482865i
$898$	2.61383e7	+	1.89906e7i	1.08165	+	0.785864i
$899$	1.06146e6			0.0438032
$900$	1.46278e7	−	4.50196e7i	0.601966	−	1.85266i
$901$	−4.54098e6			−0.186353
$902$	2.77927e6	+	4.66437e6i	0.113740	+	0.190887i
$903$	−4.37977e7			−1.78744
$904$	−681930.	+	2.09877e6i	−0.0277536	+	0.0854167i
$905$	5.56235e7			2.25755
$906$	1.40146e7	+	1.01822e7i	0.567232	+	0.412118i
$907$	6.42761e6	+	4.66993e6i	0.259437	+	0.188492i	0.709899	−	0.704304i	$-0.248741\pi$
$907$	6.42761e6	+	4.66993e6i	0.259437	+	0.188492i	−0.450462	+	0.892796i	$0.648741\pi$
$908$	−1.77254e6	+	5.45533e6i	−0.0713480	+	0.219587i
$909$	−395521.	−	1.21729e6i	−0.0158767	−	0.0488635i
$910$	1.61398e6	−	1.17262e6i	0.0646092	−	0.0469413i
$911$	−9.09838e6			−0.363219			−0.181609	−	0.983371i	$-0.558131\pi$
$911$	−9.09838e6			−0.363219			−0.181609	+	0.983371i	$0.558131\pi$
$912$	1.58398e7	−	1.15083e7i	0.630614	−	0.458168i
$913$	7.31758e6	−	5.31653e6i	0.290530	−	0.211082i
$914$	3.05382e6	+	2.21873e6i	0.120915	+	0.0878495i
$915$	4.15428e7	−	1.27856e8i	1.64037	−	5.04855i
$916$	1.22592e7			0.482750
$917$	3.06666e7	+	2.22806e7i	1.20432	+	0.874992i
$918$	1.95820e7	+	6.02673e7i	0.766921	+	2.36034i
$919$	−1.33369e7	+	9.68981e6i	−0.520913	+	0.378466i	−0.816948	−	0.576712i	$-0.804336\pi$
$919$	−1.33369e7	+	9.68981e6i	−0.520913	+	0.378466i	0.296035	+	0.955177i	$0.404336\pi$
$920$	4.03993e6	−	1.24336e7i	0.157364	−	0.484315i
$921$	−8.62107e6	−	2.65329e7i	−0.334898	−	1.03071i
$922$	5.48269e6	+	1.68740e7i	0.212406	+	0.653717i
$923$	−54265.5	−	167012.i	−0.00209662	−	0.00645273i
$924$	−3.47154e6	−	1.06843e7i	−0.133765	−	0.411686i
$925$	−1.46894e7	+	4.52094e7i	−0.564483	+	1.73730i
$926$	6.94747e6	−	5.04764e6i	0.266256	−	0.193446i
$927$	−6.65322e6	−	2.04765e7i	−0.254292	−	0.782630i
$928$	1.67461e6	+	1.21668e6i	0.0638328	+	0.0463772i
$929$	−3.16574e7			−1.20347			−0.601736	−	0.798695i	$-0.705524\pi$
$929$	−3.16574e7			−1.20347			−0.601736	+	0.798695i	$0.705524\pi$
$930$	−1.69370e6	+	5.21267e6i	−0.0642139	+	0.197630i
$931$	−4.07830e7	−	2.96306e7i	−1.54207	−	1.12038i
$932$	9.19323e6	−	6.67927e6i	0.346680	−	0.251877i
$933$	−1.61008e7	+	1.16979e7i	−0.605539	+	0.439950i
$934$	2.57663e7			0.966464
$935$	−1.31999e7	+	9.59029e6i	−0.493789	+	0.358759i
$936$	−358532.	−	1.10345e6i	−0.0133764	−	0.0411682i
$937$	−93222.2	+	286908.i	−0.00346873	+	0.0106756i	−0.952776	−	0.303674i	$-0.901787\pi$
$937$	−93222.2	+	286908.i	−0.00346873	+	0.0106756i	0.949307	+	0.314350i	$0.101787\pi$
$938$	1.26457e7	+	9.18764e6i	0.469284	+	0.340955i
$939$	1.72538e7	+	1.25356e7i	0.638589	+	0.463962i
$940$	3.55396e7			1.31188
$941$	4.63284e6	−	1.42584e7i	0.170558	−	0.524925i	−0.828844	−	0.559479i	$-0.811001\pi$
$941$	4.63284e6	−	1.42584e7i	0.170558	−	0.524925i	0.999403	+	0.0345544i	$0.0110012\pi$
$942$	−1.31211e7			−0.481772
$943$	2.24218e6	−	2.45834e7i	0.0821090	−	0.900248i
$944$	−8.26776e6			−0.301966
$945$	−5.70494e7	+	1.75580e8i	−2.07812	+	6.39581i
$946$	−3.96818e6			−0.144166
$947$	1.89453e7	+	1.37645e7i	0.686477	+	0.498755i	0.875500	−	0.483218i	$-0.160532\pi$
$947$	1.89453e7	+	1.37645e7i	0.686477	+	0.498755i	−0.189023	+	0.981973i	$0.560532\pi$
$948$	6.94825e6	+	5.04820e6i	0.251105	+	0.182438i
$949$	−389385.	+	1.19840e6i	−0.0140350	+	0.0431954i
$950$	−1.55162e7	−	4.77539e7i	−0.557797	−	1.71672i
$951$	2.87495e7	−	2.08877e7i	1.03081	−	0.748928i
$952$	1.76672e7			0.631795
$953$	−3.84897e7	+	2.79644e7i	−1.37282	+	0.997409i	−0.375305	+	0.926901i	$0.622462\pi$
$953$	−3.84897e7	+	2.79644e7i	−1.37282	+	0.997409i	−0.997511	+	0.0705081i	$0.977538\pi$
$954$	−6.22452e6	+	4.52238e6i	−0.221429	+	0.160878i
$955$	−3.07466e7	−	2.23387e7i	−1.09091	−	0.792593i
$956$	−1.84603e6	+	5.68148e6i	−0.0653270	+	0.201056i
$957$	7.46827e6			0.263597
$958$	−1.74900e7	−	1.27073e7i	−0.615711	−	0.447340i
$959$	−1.14608e7	−	3.52727e7i	−0.402409	−	1.23849i
$960$	−8.64694e6	+	6.28237e6i	−0.302820	+	0.220011i
$961$	−8.76169e6	+	2.69657e7i	−0.306041	+	0.941896i
$962$	360044.	+	1.10810e6i	0.0125435	+	0.0386048i
$963$	−1.75641e7	−	5.40569e7i	−0.610325	−	1.87839i
$964$	−6.37003e6	−	1.96049e7i	−0.220774	−	0.679474i
$965$	−1.52976e7	−	4.70811e7i	−0.528816	−	1.62753i
$966$	−1.57831e7	+	4.85755e7i	−0.544190	+	1.67484i
$967$	1.00617e7	−	7.31024e6i	0.346022	−	0.251400i	−0.401176	−	0.916001i	$-0.631398\pi$
$967$	1.00617e7	−	7.31024e6i	0.346022	−	0.251400i	0.747198	+	0.664601i	$0.231398\pi$
$968$	2.87059e6	+	8.83477e6i	0.0984652	+	0.303045i
$969$	8.98760e7	+	6.52987e7i	3.07492	+	2.23406i
$970$	4.42234e7			1.50912
$971$	−8.24650e6	+	2.53801e7i	−0.280687	+	0.863864i	0.706972	+	0.707242i	$0.250061\pi$
$971$	−8.24650e6	+	2.53801e7i	−0.280687	+	0.863864i	−0.987658	+	0.156623i	$0.949939\pi$
$972$	3.01641e7	+	2.19155e7i	1.02406	+	0.744022i
$973$	3.00526e7	−	2.18345e7i	1.01765	−	0.739368i
$974$	−1.93328e7	+	1.40461e7i	−0.652976	+	0.474415i
$975$	−4.15061e6			−0.139830
$976$	−1.06700e7	+	7.75224e6i	−0.358543	+	0.260497i
$977$	−8.07932e6	−	2.48656e7i	−0.270794	−	0.833417i	−0.990302	−	0.138933i	$-0.955633\pi$
$977$	−8.07932e6	−	2.48656e7i	−0.270794	−	0.833417i	0.719508	−	0.694484i	$-0.244367\pi$
$978$	−7.42491e6	+	2.28515e7i	−0.248224	+	0.763955i
$979$	1.96376e6	+	1.42676e6i	0.0654835	+	0.0475766i
$980$	2.22634e7	+	1.61753e7i	0.740501	+	0.538005i
$981$	1.01606e8			3.37089
$982$	−4.57539e6	+	1.40816e7i	−0.151408	+	0.465986i
$983$	4.22662e6			0.139511			0.0697557	−	0.997564i	$-0.477778\pi$
$983$	4.22662e6			0.139511			0.0697557	+	0.997564i	$0.477778\pi$
$984$	−1.32964e7	+	1.51822e7i	−0.437769	+	0.499860i
$985$	5.49481e7			1.80452
$986$	−3.62937e6	+	1.11701e7i	−0.118888	+	0.365900i
$987$	−1.38846e8			−4.53670
$988$	−995658.	−	723388.i	−0.0324502	−	0.0235765i
$989$	1.45955e7	+	1.06043e7i	0.474492	+	0.344739i
$990$	−8.54268e6	+	2.62917e7i	−0.277017	+	0.852570i
$991$	−1.21142e7	−	3.72837e7i	−0.391842	−	1.20597i	−0.931394	−	0.364014i	$-0.881406\pi$
$991$	−1.21142e7	−	3.72837e7i	−0.391842	−	1.20597i	0.539551	−	0.841953i	$-0.318594\pi$
$992$	435018.	−	316059.i	0.0140355	−	0.0101974i
$993$	−2.08780e7			−0.671918
$994$	3.66540e6	−	2.66307e6i	0.117667	−	0.0854903i
$995$	1.44017e7	−	1.04635e7i	0.461165	−	0.335056i
$996$	2.71989e7	+	1.97612e7i	0.868767	+	0.631196i
$997$	−3.12354e6	+	9.61328e6i	−0.0995199	+	0.306291i	−0.988405	−	0.151839i	$-0.951480\pi$
$997$	−3.12354e6	+	9.61328e6i	−0.0995199	+	0.306291i	0.888885	+	0.458130i	$0.151480\pi$
$998$	−1.40571e7			−0.446754
$999$	−8.72286e7	−	6.33753e7i	−2.76532	−	2.00912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.b.57.1	✓	36
41.18	even	5	inner	82.6.d.b.59.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.b.57.1	✓	36	1.1	even	1	trivial
82.6.d.b.59.1	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} -29.2964 q^{3} +(-12.9443 - 9.40456i) q^{4} +(72.0590 + 52.3539i) q^{5} +(36.2123 - 111.450i) q^{6} +(-58.7271 - 180.743i) q^{7} +(51.7771 - 37.6183i) q^{8} +615.279 q^{9} +(-288.236 + 209.416i) q^{10} +(102.025 - 74.1256i) q^{11} +(379.220 + 275.520i) q^{12} +(9.10492 - 28.0220i) q^{13} +760.179 q^{14} +(-2111.07 - 1533.78i) q^{15} +(79.1084 + 243.470i) q^{16} +(-1175.14 + 853.791i) q^{17} +(-760.526 + 2340.66i) q^{18} +(806.718 + 2482.82i) q^{19} +(-440.385 - 1355.37i) q^{20} +(1720.49 + 5295.13i) q^{21} +(155.881 + 479.751i) q^{22} +(708.701 - 2181.16i) q^{23} +(-1516.88 + 1102.08i) q^{24} +(1485.89 + 4573.09i) q^{25} +(95.3479 + 69.2743i) q^{26} -10906.4 q^{27} +(-939.633 + 2891.89i) q^{28} +(-1635.36 - 1188.16i) q^{29} +(8444.28 - 6135.13i) q^{30} +(-424.822 + 308.651i) q^{31} -1024.00 q^{32} +(-2988.97 + 2171.61i) q^{33} +(-1795.46 - 5525.85i) q^{34} +(5230.81 - 16098.8i) q^{35} +(-7964.33 - 5786.43i) q^{36} +(7997.91 + 5810.83i) q^{37} -10442.4 q^{38} +(-266.741 + 820.945i) q^{39} +5700.47 q^{40} +(10496.6 - 2382.59i) q^{41} -22270.5 q^{42} +(-2430.88 + 7481.49i) q^{43} -2017.76 q^{44} +(44336.4 + 32212.3i) q^{45} +(7421.61 + 5392.12i) q^{46} +(-7706.28 + 23717.5i) q^{47} +(-2317.59 - 7132.81i) q^{48} +(-15622.1 + 11350.1i) q^{49} -19233.7 q^{50} +(34427.4 - 25013.0i) q^{51} +(-381.392 + 277.097i) q^{52} +(2529.15 + 1837.53i) q^{53} +(13481.1 - 41490.5i) q^{54} +11232.6 q^{55} +(-9839.96 - 7149.15i) q^{56} +(-23633.9 - 72737.7i) q^{57} +(6541.45 - 4752.64i) q^{58} +(-9979.99 + 30715.3i) q^{59} +(12901.7 + 39707.4i) q^{60} +(15920.3 + 48997.6i) q^{61} +(-649.070 - 1997.63i) q^{62} +(-36133.5 - 111207. i) q^{63} +(1265.73 - 3895.53i) q^{64} +(2123.16 - 1542.56i) q^{65} +(-4566.74 - 14055.0i) q^{66} +(16635.2 + 12086.2i) q^{67} +23240.9 q^{68} +(-20762.4 + 63900.0i) q^{69} +(54777.7 + 39798.4i) q^{70} +(4821.76 - 3503.22i) q^{71} +(31857.3 - 23145.7i) q^{72} -42766.5 q^{73} +(-31991.7 + 23243.3i) q^{74} +(-43531.2 - 133975. i) q^{75} +(12907.5 - 39725.1i) q^{76} +(-19389.3 - 14087.2i) q^{77} +(-2793.35 - 2029.49i) q^{78} +18322.5 q^{79} +(-7046.17 + 21685.9i) q^{80} +170006. q^{81} +(-3910.65 + 42876.6i) q^{82} +71723.3 q^{83} +(27527.9 - 84722.0i) q^{84} -129379. q^{85} +(-25456.5 - 18495.3i) q^{86} +(47910.2 + 34808.8i) q^{87} +(2494.09 - 7676.01i) q^{88} +(5947.91 + 18305.8i) q^{89} +(-177345. + 128849. i) q^{90} -5599.50 q^{91} +(-29686.5 + 21568.5i) q^{92} +(12445.8 - 9042.37i) q^{93} +(-80701.2 - 58632.9i) q^{94} +(-71854.2 + 221144. i) q^{95} +29999.5 q^{96} +(-100420. - 72959.3i) q^{97} +(-23868.5 - 73459.6i) q^{98} +(62773.9 - 45607.9i) 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

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Representations

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Database

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