LMFDB - Embedded newform 82.6.f.b.31.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(23,82)] 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([9])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.23"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	82.31
Dual form			82.6.f.b.45.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23607 + 2.35114i) q^{2} +4.64210i q^{3} +(4.94427 + 15.2169i) q^{4} +(-24.0870 - 74.1322i) q^{5} +(-10.9142 + 15.0221i) q^{6} +(17.3773 + 23.9177i) q^{7} +(-19.7771 + 60.8676i) q^{8} +221.451 q^{9} +(96.3480 - 296.529i) q^{10} +(580.229 + 188.528i) q^{11} +(-70.6384 + 22.9518i) q^{12} +(443.795 - 610.831i) q^{13} +118.256i q^{14} +(344.129 - 111.814i) q^{15} +(-207.108 + 150.473i) q^{16} +(-926.462 - 301.026i) q^{17} +(716.630 + 520.662i) q^{18} +(1554.27 + 2139.27i) q^{19} +(1008.97 - 733.059i) q^{20} +(-111.028 + 80.6669i) q^{21} +(1434.41 + 1974.29i) q^{22} +(-774.325 - 562.580i) q^{23} +(-282.553 - 91.8072i) q^{24} +(-2387.22 + 1734.41i) q^{25} +(2872.30 - 933.267i) q^{26} +2156.03i q^{27} +(-278.036 + 382.684i) q^{28} +(4943.50 - 1606.24i) q^{29} +(1376.52 + 447.257i) q^{30} +(2301.71 - 7083.94i) q^{31} -1024.00 q^{32} +(-875.165 + 2693.48i) q^{33} +(-2290.34 - 3152.38i) q^{34} +(1354.51 - 1864.32i) q^{35} +(1094.91 + 3369.80i) q^{36} +(-2341.77 - 7207.22i) q^{37} +10577.1i q^{38} +(2835.54 + 2060.14i) q^{39} +4988.62 q^{40} +(-10569.5 + 2035.24i) q^{41} -548.955 q^{42} +(9669.52 + 7025.31i) q^{43} +9761.42i q^{44} +(-5334.09 - 16416.6i) q^{45} +(-1183.06 - 3641.10i) q^{46} +(-16473.2 + 22673.4i) q^{47} +(-698.511 - 961.417i) q^{48} +(4923.56 - 15153.2i) q^{49} -11803.1 q^{50} +(1397.39 - 4300.73i) q^{51} +(11489.2 + 3733.07i) q^{52} +(3026.74 - 983.446i) q^{53} +(-5069.12 + 6977.05i) q^{54} -47554.7i q^{55} +(-1799.49 + 584.689i) q^{56} +(-9930.69 + 7215.07i) q^{57} +(19774.0 + 6424.96i) q^{58} +(-5413.36 - 3933.04i) q^{59} +(3402.93 + 4683.74i) q^{60} +(-2689.63 + 1954.13i) q^{61} +(24103.8 - 17512.5i) q^{62} +(3848.21 + 5296.60i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-55971.9 - 18186.4i) q^{65} +(-9164.85 + 6658.65i) q^{66} +(-40406.6 + 13128.9i) q^{67} -15586.2i q^{68} +(2611.55 - 3594.49i) q^{69} +(8766.56 - 2848.43i) q^{70} +(28032.4 + 9108.28i) q^{71} +(-4379.65 + 13479.2i) q^{72} -64369.9 q^{73} +(9367.07 - 28828.9i) q^{74} +(-8051.33 - 11081.7i) q^{75} +(-24868.3 + 34228.3i) q^{76} +(5573.63 + 17153.9i) q^{77} +(4332.32 + 13333.5i) q^{78} -14978.1i q^{79} +(16143.5 + 11728.9i) q^{80} +43804.1 q^{81} +(-38988.7 - 18264.2i) q^{82} -100202. q^{83} +(-1776.46 - 1290.67i) q^{84} +75931.5i q^{85} +(14773.7 + 45468.8i) q^{86} +(7456.32 + 22948.2i) q^{87} +(-22950.5 + 31588.6i) q^{88} +(14548.7 + 20024.6i) q^{89} +(21336.4 - 65666.6i) q^{90} +22321.6 q^{91} +(4732.25 - 14564.4i) q^{92} +(32884.3 + 10684.8i) q^{93} +(-106617. + 34641.9i) q^{94} +(121151. - 166750. i) q^{95} -4753.51i q^{96} +(143737. - 46702.9i) q^{97} +(51560.2 - 37460.7i) q^{98} +(128492. + 41749.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Character values

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

$n$	$47$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$			4.64210i			0.297791i	0.988853	+	0.148895i	$0.0475718\pi$
$3$			4.64210i			0.297791i	−0.988853	+	0.148895i	$0.952428\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−24.0870	−	74.1322i	−0.430881	−	1.32612i	−0.897249	−	0.441525i	$-0.854437\pi$
$5$	−24.0870	−	74.1322i	−0.430881	−	1.32612i	0.466367	−	0.884591i	$-0.345563\pi$
$6$	−10.9142	+	15.0221i	−0.123770	+	0.170355i
$7$	17.3773	+	23.9177i	0.134040	+	0.184491i	0.870761	−	0.491706i	$-0.163627\pi$
$7$	17.3773	+	23.9177i	0.134040	+	0.184491i	−0.736721	+	0.676197i	$0.763627\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	221.451			0.911321
$10$	96.3480	−	296.529i	0.304679	−	0.937706i
$11$	580.229	+	188.528i	1.44583	+	0.469779i	0.923710	−	0.383092i	$-0.125141\pi$
$11$	580.229	+	188.528i	1.44583	+	0.469779i	0.522122	+	0.852871i	$0.325141\pi$
$12$	−70.6384	+	22.9518i	−0.141608	+	0.0460112i
$13$	443.795	−	610.831i	0.728323	−	1.00245i	−0.270883	−	0.962612i	$-0.587316\pi$
$13$	443.795	−	610.831i	0.728323	−	1.00245i	0.999206	−	0.0398382i	$-0.0126842\pi$
$14$			118.256i			0.161251i
$15$	344.129	−	111.814i	0.394905	−	0.128313i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−926.462	−	301.026i	−0.777509	−	0.252628i	−0.106733	−	0.994288i	$-0.534039\pi$
$17$	−926.462	−	301.026i	−0.777509	−	0.252628i	−0.670776	+	0.741660i	$0.734039\pi$
$18$	716.630	+	520.662i	0.521331	+	0.378769i
$19$	1554.27	+	2139.27i	0.987739	+	1.35951i	0.932554	+	0.361030i	$0.117575\pi$
$19$	1554.27	+	2139.27i	0.987739	+	1.35951i	0.0551850	+	0.998476i	$0.482425\pi$
$20$	1008.97	−	733.059i	0.564031	−	0.409793i
$21$	−111.028	+	80.6669i	−0.0549397	+	0.0399160i
$22$	1434.41	+	1974.29i	0.631852	+	0.869669i
$23$	−774.325	−	562.580i	−0.305214	−	0.221751i	0.424626	−	0.905369i	$-0.360405\pi$
$23$	−774.325	−	562.580i	−0.305214	−	0.221751i	−0.729840	+	0.683618i	$0.760405\pi$
$24$	−282.553	−	91.8072i	−0.100132	−	0.0325348i
$25$	−2387.22	+	1734.41i	−0.763910	+	0.555013i
$26$	2872.30	−	933.267i	0.833291	−	0.270753i
$27$			2156.03i			0.569174i
$28$	−278.036	+	382.684i	−0.0670202	+	0.0922455i
$29$	4943.50	−	1606.24i	1.09154	−	0.354663i	0.292698	−	0.956205i	$-0.405447\pi$
$29$	4943.50	−	1606.24i	1.09154	−	0.354663i	0.798841	+	0.601542i	$0.205447\pi$
$30$	1376.52	+	447.257i	0.279240	+	0.0907306i
$31$	2301.71	−	7083.94i	0.430176	−	1.32395i	−0.467773	−	0.883849i	$-0.654944\pi$
$31$	2301.71	−	7083.94i	0.430176	−	1.32395i	0.897950	−	0.440098i	$-0.145056\pi$
$32$	−1024.00			−0.176777
$33$	−875.165	+	2693.48i	−0.139896	+	0.430555i
$34$	−2290.34	−	3152.38i	−0.339784	−	0.467672i
$35$	1354.51	−	1864.32i	0.186901	−	0.257247i
$36$	1094.91	+	3369.80i	0.140807	+	0.433359i
$37$	−2341.77	−	7207.22i	−0.281216	−	0.865493i	−0.987508	−	0.157572i	$-0.949633\pi$
$37$	−2341.77	−	7207.22i	−0.281216	−	0.865493i	0.706292	−	0.707921i	$-0.250367\pi$
$38$			10577.1i			1.18825i
$39$	2835.54	+	2060.14i	0.298520	+	0.216888i
$40$	4988.62			0.492981
$41$	−10569.5	+	2035.24i	−0.981961	+	0.189084i
$41$	−10569.5	+	2035.24i	−0.981961	+	0.189084i
$42$	−548.955			−0.0480190
$43$	9669.52	+	7025.31i	0.797505	+	0.579421i	0.910181	−	0.414210i	$-0.135942\pi$
$43$	9669.52	+	7025.31i	0.797505	+	0.579421i	−0.112676	+	0.993632i	$0.535942\pi$
$44$			9761.42i			0.760119i
$45$	−5334.09	−	16416.6i	−0.392671	−	1.20852i
$46$	−1183.06	−	3641.10i	−0.0824354	−	0.253710i
$47$	−16473.2	+	22673.4i	−1.08776	+	1.49717i	−0.237078	+	0.971491i	$0.576190\pi$
$47$	−16473.2	+	22673.4i	−1.08776	+	1.49717i	−0.850681	+	0.525682i	$0.823810\pi$
$48$	−698.511	−	961.417i	−0.0437593	−	0.0602295i
$49$	4923.56	−	15153.2i	0.292947	−	0.901598i
$50$	−11803.1			−0.667681
$51$	1397.39	−	4300.73i	0.0752303	−	0.231535i
$52$	11489.2	+	3733.07i	0.589226	+	0.191451i
$53$	3026.74	−	983.446i	0.148008	−	0.0480907i	−0.234076	−	0.972218i	$-0.575206\pi$
$53$	3026.74	−	983.446i	0.148008	−	0.0480907i	0.382084	+	0.924128i	$0.375206\pi$
$54$	−5069.12	+	6977.05i	−0.236564	+	0.325602i
$55$		−	47554.7i		−	2.11976i
$56$	−1799.49	+	584.689i	−0.0766794	+	0.0249146i
$57$	−9930.69	+	7215.07i	−0.404848	+	0.294140i
$58$	19774.0	+	6424.96i	0.771835	+	0.250784i
$59$	−5413.36	−	3933.04i	−0.202459	−	0.147095i	0.481936	−	0.876206i	$-0.339934\pi$
$59$	−5413.36	−	3933.04i	−0.202459	−	0.147095i	−0.684395	+	0.729111i	$0.739934\pi$
$60$	3402.93	+	4683.74i	0.122032	+	0.167963i
$61$	−2689.63	+	1954.13i	−0.0925482	+	0.0672402i	−0.633097	−	0.774072i	$-0.718217\pi$
$61$	−2689.63	+	1954.13i	−0.0925482	+	0.0672402i	0.540549	+	0.841313i	$0.318217\pi$
$62$	24103.8	−	17512.5i	0.796355	−	0.578586i
$63$	3848.21	+	5296.60i	0.122154	+	0.168130i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−55971.9	−	18186.4i	−1.64319	−	0.533904i
$66$	−9164.85	+	6658.65i	−0.258980	+	0.188160i
$67$	−40406.6	+	13128.9i	−1.09968	+	0.357307i	−0.801978	−	0.597353i	$-0.796219\pi$
$67$	−40406.6	+	13128.9i	−1.09968	+	0.357307i	−0.297699	+	0.954660i	$0.596219\pi$
$68$		−	15586.2i		−	0.408761i
$69$	2611.55	−	3594.49i	0.0660353	−	0.0908898i
$70$	8766.56	−	2848.43i	0.213838	−	0.0694800i
$71$	28032.4	+	9108.28i	0.659955	+	0.214432i	0.619798	−	0.784761i	$-0.287214\pi$
$71$	28032.4	+	9108.28i	0.659955	+	0.214432i	0.0401565	+	0.999193i	$0.487214\pi$
$72$	−4379.65	+	13479.2i	−0.0995654	+	0.306431i
$73$	−64369.9			−1.41376			−0.706880	−	0.707334i	$-0.749898\pi$
$73$	−64369.9			−1.41376			−0.706880	+	0.707334i	$0.749898\pi$
$74$	9367.07	−	28828.9i	0.198849	−	0.611996i
$75$	−8051.33	−	11081.7i	−0.165278	−	0.227485i
$76$	−24868.3	+	34228.3i	−0.493870	+	0.679753i
$77$	5573.63	+	17153.9i	0.107130	+	0.329712i
$78$	4332.32	+	13333.5i	0.0806276	+	0.248146i
$79$		−	14978.1i		−	0.270016i	−0.990845	−	0.135008i	$-0.956894\pi$
$79$		−	14978.1i		−	0.270016i	0.990845	−	0.135008i	$-0.0431060\pi$
$80$	16143.5	+	11728.9i	0.282016	+	0.204896i
$81$	43804.1			0.741826
$82$	−38988.7	−	18264.2i	−0.640330	−	0.299962i
$83$	−100202.			−1.59655			−0.798273	−	0.602296i	$-0.794253\pi$
$83$	−100202.			−1.59655			−0.798273	+	0.602296i	$0.794253\pi$
$84$	−1776.46	−	1290.67i	−0.0274698	−	0.0199580i
$85$			75931.5i			1.13992i
$86$	14773.7	+	45468.8i	0.215399	+	0.662929i
$87$	7456.32	+	22948.2i	0.105615	+	0.325050i
$88$	−22950.5	+	31588.6i	−0.315926	+	0.434835i
$89$	14548.7	+	20024.6i	0.194693	+	0.267972i	0.895191	−	0.445682i	$-0.147039\pi$
$89$	14548.7	+	20024.6i	0.194693	+	0.267972i	−0.700498	+	0.713654i	$0.747039\pi$
$90$	21336.4	−	65666.6i	0.277660	−	0.854551i
$91$	22321.6			0.282568
$92$	4732.25	−	14564.4i	0.0582906	−	0.179400i
$93$	32884.3	+	10684.8i	0.394259	+	0.128103i
$94$	−106617.	+	34641.9i	−1.24453	+	0.404372i
$95$	121151.	−	166750.i	1.37727	−	1.89564i
$96$		−	4753.51i		−	0.0526425i
$97$	143737.	−	46702.9i	1.55109	−	0.503981i	0.596683	−	0.802477i	$-0.296485\pi$
$97$	143737.	−	46702.9i	1.55109	−	0.503981i	0.954411	+	0.298496i	$0.0964850\pi$
$98$	51560.2	−	37460.7i	0.542312	−	0.394013i
$99$	128492.	+	41749.7i	1.31762	+	0.428120i
$100$	−38195.5	−	27750.6i	−0.381955	−	0.277506i
$101$	−28210.1	−	38827.8i	−0.275170	−	0.378739i	0.648957	−	0.760825i	$-0.275206\pi$
$101$	−28210.1	−	38827.8i	−0.275170	−	0.378739i	−0.924127	+	0.382087i	$0.875206\pi$
$102$	14633.7	−	10632.0i	0.139269	−	0.101185i
$103$	38173.8	−	27734.9i	0.354546	−	0.257593i	−0.396228	−	0.918152i	$-0.629681\pi$
$103$	38173.8	−	27734.9i	0.354546	−	0.257593i	0.750774	+	0.660559i	$0.229681\pi$
$104$	28402.9	+	39093.2i	0.257501	+	0.354420i
$105$	8654.36	+	6287.76i	0.0766058	+	0.0556574i
$106$	12106.9	+	3933.79i	0.104657	+	0.0340053i
$107$	−44217.3	+	32125.8i	−0.373364	+	0.271265i	−0.758605	−	0.651551i	$-0.774119\pi$
$107$	−44217.3	+	32125.8i	−0.373364	+	0.271265i	0.385240	+	0.922816i	$0.374119\pi$
$108$	−32808.1	+	10660.0i	−0.270658	+	0.0879422i
$109$			234449.i			1.89009i	0.326940	+	0.945045i	$0.393983\pi$
$109$			234449.i			1.89009i	−0.326940	+	0.945045i	$0.606017\pi$
$110$	111808.	−	153890.i	0.881030	−	1.21263i
$111$	33456.6	−	10870.7i	0.257736	−	0.0837434i
$112$	−7197.95	−	2338.76i	−0.0542205	−	0.0176173i
$113$	−65529.4	+	201679.i	−0.482770	+	1.48581i	0.352415	+	0.935844i	$0.385361\pi$
$113$	−65529.4	+	201679.i	−0.482770	+	1.48581i	−0.835185	+	0.549969i	$0.814639\pi$
$114$	−49100.1			−0.353851
$115$	−23054.1	+	70953.3i	−0.162556	+	0.500297i
$116$	48884.0	+	67283.0i	0.337304	+	0.464259i
$117$	98278.8	−	135269.i	0.663736	−	0.913554i
$118$	−8270.88	−	25455.2i	−0.0546823	−	0.168295i
$119$	−8899.51	−	27389.9i	−0.0576101	−	0.177306i
$120$			23157.7i			0.146805i
$121$	170830.	+	124115.i	1.06072	+	0.770659i
$122$	−13298.3			−0.0808901
$123$	−9447.76	−	49064.6i	−0.0563075	−	0.292419i
$124$	119176.			0.696040
$125$	−10987.5	−	7982.88i	−0.0628960	−	0.0456967i
$126$			26187.9i			0.146951i
$127$	21313.9	+	65597.4i	0.117261	+	0.360892i	0.992412	−	0.122958i	$-0.0392381\pi$
$127$	21313.9	+	65597.4i	0.117261	+	0.360892i	−0.875151	+	0.483850i	$0.839238\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	−32612.2	+	44886.8i	−0.172546	+	0.237490i
$130$	−138370.	−	190450.i	−0.718099	−	0.988379i
$131$	79062.9	−	243331.i	0.402526	−	1.23885i	−0.520417	−	0.853912i	$-0.674223\pi$
$131$	79062.9	−	243331.i	0.402526	−	1.23885i	0.922943	−	0.384937i	$-0.125777\pi$
$132$	−45313.5			−0.226356
$133$	−24157.5	+	74349.2i	−0.118420	+	0.364458i
$134$	−161626.	−	52515.6i	−0.777589	−	0.252654i
$135$	159831.	−	51932.2i	0.754791	−	0.245246i
$136$	36645.4	−	50438.1i	0.169892	−	0.233836i
$137$			244567.i			1.11326i	0.830760	+	0.556630i	$0.187906\pi$
$137$			244567.i			1.11326i	−0.830760	+	0.556630i	$0.812094\pi$
$138$	16902.3	−	5491.90i	0.0755525	−	0.0245485i
$139$	−185103.	+	134485.i	−0.812598	+	0.590387i	−0.914583	−	0.404399i	$-0.867481\pi$
$139$	−185103.	+	134485.i	−0.812598	+	0.590387i	0.101985	+	0.994786i	$0.467481\pi$
$140$	35066.2	+	11393.7i	0.151206	+	0.0491298i
$141$	−105252.	−	76470.1i	−0.445844	−	0.323925i
$142$	69299.9	+	95383.1i	0.288411	+	0.396964i
$143$	372661.	−	270754.i	1.52396	−	1.10722i
$144$	−45864.3	+	33322.4i	−0.184318	+	0.133915i
$145$	−238148.	−	327783.i	−0.940648	−	1.29469i
$146$	−208305.	−	151343.i	−0.808757	−	0.587597i
$147$	70342.5	+	22855.6i	0.268488	+	0.0872369i
$148$	98093.2	−	71268.9i	0.368116	−	0.267452i
$149$	−223185.	+	72517.1i	−0.823567	+	0.267593i	−0.690333	−	0.723491i	$-0.742536\pi$
$149$	−223185.	+	72517.1i	−0.823567	+	0.267593i	−0.133234	+	0.991085i	$0.542536\pi$
$150$		−	54790.9i		−	0.198829i
$151$	−166215.	+	228775.i	−0.593236	+	0.816519i	−0.995068	−	0.0991942i	$-0.968374\pi$
$151$	−166215.	+	228775.i	−0.593236	+	0.816519i	0.401832	+	0.915713i	$0.368374\pi$
$152$	−160951.	+	52296.2i	−0.565047	+	0.183595i
$153$	−205166.	−	66662.4i	−0.708560	−	0.230225i
$154$	−22294.5	+	68615.5i	−0.0757524	+	0.233142i
$155$	−580589.			−1.94106
$156$	−17329.3	+	53334.0i	−0.0570123	+	0.175466i
$157$	151173.	+	208071.i	0.489468	+	0.673695i	0.980290	−	0.197565i	$-0.0633034\pi$
$157$	151173.	+	208071.i	0.489468	+	0.673695i	−0.490822	+	0.871260i	$0.663303\pi$
$158$	35215.6	−	48470.2i	0.112226	−	0.154466i
$159$	4565.26	+	14050.4i	0.0143210	+	0.0440754i
$160$	24665.1	+	75911.3i	0.0761698	+	0.234427i
$161$		−	28296.2i		−	0.0860327i
$162$	141753.	+	102990.i	0.424370	+	0.308323i
$163$	180722.			0.532771			0.266386	−	0.963867i	$-0.414171\pi$
$163$	180722.			0.532771			0.266386	+	0.963867i	$0.414171\pi$
$164$	−83228.4	−	150772.i	−0.241636	−	0.437735i
$165$	220754.			0.631245
$166$	−324261.	−	235589.i	−0.913322	−	0.663567i
$167$		−	867.868i		−	0.00240803i	−0.999999	−	0.00120402i	$-0.999617\pi$
$167$		−	867.868i		−	0.00240803i	0.999999	−	0.00120402i	$-0.000383250\pi$
$168$	−2714.18	−	8353.40i	−0.00741935	−	0.0228344i
$169$	−61425.1	−	189047.i	−0.165436	−	0.509159i
$170$	−178526.	+	245719.i	−0.473782	+	0.652104i
$171$	344194.	+	473743.i	0.900147	+	1.23895i
$172$	−59094.8	+	181875.i	−0.152310	+	0.468762i
$173$	−597749.			−1.51846			−0.759230	−	0.650822i	$-0.774424\pi$
$173$	−597749.			−1.51846			−0.759230	+	0.650822i	$0.774424\pi$
$174$	−29825.3	+	91792.8i	−0.0746812	+	0.229845i
$175$	−82966.6	−	26957.5i	−0.204790	−	0.0665402i
$176$	−148539.	+	48263.1i	−0.361458	+	0.117445i
$177$	18257.6	−	25129.4i	0.0438036	−	0.0602904i
$178$			99007.1i			0.234216i
$179$	151629.	−	49267.4i	0.353713	−	0.114928i	−0.126771	−	0.991932i	$-0.540461\pi$
$179$	151629.	−	49267.4i	0.353713	−	0.114928i	0.480483	+	0.877004i	$0.340461\pi$
$180$	223437.	−	162337.i	0.514013	−	0.373452i
$181$	−494030.	−	160520.i	−1.12087	−	0.364194i	−0.310773	−	0.950484i	$-0.600588\pi$
$181$	−494030.	−	160520.i	−1.12087	−	0.364194i	−0.810101	+	0.586290i	$0.800588\pi$
$182$	72234.3	+	52481.3i	0.161646	+	0.117443i
$183$	−9071.27	−	12485.5i	−0.0200235	−	0.0275600i
$184$	49556.8	−	36005.1i	0.107909	−	0.0784007i
$185$	−477881.	+	347201.i	−1.02657	+	0.745849i
$186$	81294.6	+	111892.i	0.172298	+	0.237147i
$187$	−480809.	−	349328.i	−1.00547	−	0.730515i
$188$	−426467.	−	138567.i	−0.880016	−	0.285934i
$189$	−51567.3	+	37465.8i	−0.105007	+	0.0762923i
$190$	784105.	−	254771.i	1.57576	−	0.511996i
$191$		−	386007.i		−	0.765618i	−0.923828	−	0.382809i	$-0.874957\pi$
$191$		−	386007.i		−	0.765618i	0.923828	−	0.382809i	$-0.125043\pi$
$192$	11176.2	−	15382.7i	0.0218796	−	0.0301147i
$193$	608786.	−	197806.i	1.17644	−	0.382250i	0.345399	−	0.938456i	$-0.387743\pi$
$193$	608786.	−	197806.i	1.17644	−	0.382250i	0.831044	+	0.556206i	$0.187743\pi$
$194$	574946.	+	186811.i	1.09679	+	0.356368i
$195$	84423.0	−	259827.i	0.158992	−	0.489326i
$196$	254928.			0.473998
$197$	279362.	−	859789.i	0.512864	−	1.57843i	−0.274271	−	0.961653i	$-0.588436\pi$
$197$	279362.	−	859789.i	0.512864	−	1.57843i	0.787135	−	0.616781i	$-0.211564\pi$
$198$	317650.	+	437208.i	0.575820	+	0.792548i
$199$	449217.	−	618294.i	0.804125	−	1.10678i	−0.188079	−	0.982154i	$-0.560226\pi$
$199$	449217.	−	618294.i	0.804125	−	1.10678i	0.992203	−	0.124629i	$-0.0397739\pi$
$200$	−58357.5	−	179606.i	−0.103162	−	0.317501i
$201$	−60945.6	−	187571.i	−0.106403	−	0.327474i
$202$		−	191975.i		−	0.331030i
$203$	124322.	+	90325.2i	0.211742	+	0.153840i
$204$	72352.9			0.121725
$205$	405464.	+	734516.i	0.673856	+	1.22072i
$206$	188742.			0.309885
$207$	−171475.	−	124584.i	−0.278147	−	0.202086i
$208$			193287.i			0.309774i
$209$	498521.	+	1.53429e6i	0.789437	+	2.42964i
$210$	13222.7	+	40695.2i	0.0206905	+	0.0636789i
$211$	129134.	−	177737.i	0.199679	−	0.274835i	−0.697421	−	0.716661i	$-0.745669\pi$
$211$	129134.	−	177737.i	0.199679	−	0.274835i	0.897101	+	0.441826i	$0.145669\pi$
$212$	29930.0	+	41195.1i	0.0457370	+	0.0629515i
$213$	−42281.5	+	130129.i	−0.0638560	+	0.196528i
$214$	−218622.			−0.326332
$215$	287892.	−	886041.i	0.424750	−	1.30725i
$216$	−131232.	−	42639.9i	−0.191384	−	0.0621845i
$217$	209429.	−	68047.7i	0.301917	−	0.0980988i
$218$	−551223.	+	758694.i	−0.785573	+	1.08125i
$219$		−	298811.i		−	0.421005i
$220$	723636.	−	235123.i	1.00801	−	0.327521i
$221$	−595035.	+	432318.i	−0.819525	+	0.595419i
$222$	133826.	+	43482.9i	0.182247	+	0.0592155i
$223$	7921.14	+	5755.04i	0.0106666	+	0.00774973i	0.593106	−	0.805125i	$-0.297902\pi$
$223$	7921.14	+	5755.04i	0.0106666	+	0.00774973i	−0.582439	+	0.812874i	$0.697902\pi$
$224$	−17794.3	−	24491.8i	−0.0236952	−	0.0326137i
$225$	−528651.	+	384088.i	−0.696167	+	0.505795i
$226$	−686233.	+	498578.i	−0.893718	+	0.649324i
$227$	−495039.	−	681362.i	−0.637638	−	0.877634i	0.360849	−	0.932624i	$-0.382487\pi$
$227$	−495039.	−	681362.i	−0.637638	−	0.877634i	−0.998487	+	0.0549906i	$0.982487\pi$
$228$	−158891.	−	115441.i	−0.202424	−	0.147070i
$229$	−147544.	−	47939.9i	−0.185923	−	0.0604099i	0.214576	−	0.976707i	$-0.431163\pi$
$229$	−147544.	−	47939.9i	−0.185923	−	0.0604099i	−0.400499	+	0.916297i	$0.631163\pi$
$230$	−241426.	+	175406.i	−0.300929	+	0.218638i
$231$	−79629.9	+	25873.3i	−0.0981853	+	0.0319023i
$232$			332666.i			0.405777i
$233$	−213566.	+	293948.i	−0.257716	+	0.354716i	−0.918195	−	0.396129i	$-0.870353\pi$
$233$	−213566.	+	293948.i	−0.257716	+	0.354716i	0.660479	+	0.750845i	$0.270353\pi$
$234$	636074.	−	206673.i	0.759395	−	0.246742i
$235$	2.07762e6	+	675059.i	2.45412	+	0.797392i
$236$	33083.5	−	101821.i	0.0386662	−	0.119002i
$237$	69529.8			0.0804082
$238$	35598.0	−	109560.i	0.0407365	−	0.125374i
$239$	−375094.	−	516273.i	−0.424762	−	0.584635i	0.541979	−	0.840392i	$-0.317675\pi$
$239$	−375094.	−	516273.i	−0.424762	−	0.584635i	−0.966741	+	0.255757i	$0.917675\pi$
$240$	−54446.9	+	74939.8i	−0.0610162	+	0.0839816i
$241$	252659.	+	777604.i	0.280215	+	0.862414i	0.987792	+	0.155778i	$0.0497883\pi$
$241$	252659.	+	777604.i	0.280215	+	0.862414i	−0.707577	+	0.706636i	$0.750212\pi$
$242$	261005.	+	803291.i	0.286491	+	0.881728i
$243$			727257.i			0.790083i
$244$	−43034.1	−	31266.1i	−0.0462741	−	0.0336201i
$245$	−1.24193e6			−1.32185
$246$	84784.2	−	180989.i	0.0893258	−	0.190684i
$247$	1.99651e6			2.08223
$248$	385661.	+	280199.i	0.398178	+	0.289293i
$249$		−	465148.i		−	0.475437i
$250$	−16787.4	−	51666.3i	−0.0169876	−	0.0522826i
$251$	−192560.	−	592640.i	−0.192922	−	0.593754i	−0.999995	−	0.00330109i	$-0.998949\pi$
$251$	−192560.	−	592640.i	−0.192922	−	0.593754i	0.807072	−	0.590453i	$-0.201051\pi$
$252$	−61571.3	+	84745.7i	−0.0610769	+	0.0840652i
$253$	−343224.	−	472407.i	−0.337114	−	0.463997i
$254$	−85255.5	+	262389.i	−0.0829159	+	0.255189i
$255$	−352481.			−0.339458
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−675869.	−	219603.i	−0.638307	−	0.207399i	−0.0280559	−	0.999606i	$-0.508932\pi$
$257$	−675869.	−	219603.i	−0.638307	−	0.207399i	−0.610252	+	0.792208i	$0.708932\pi$
$258$	−211071.	+	68581.0i	−0.197414	+	0.0641438i
$259$	131687.	−	181251.i	0.121981	−	0.167893i
$260$		−	941638.i		−	0.863874i
$261$	1.09474e6	−	355703.i	0.994742	−	0.323211i
$262$	827957.	−	601546.i	0.745169	−	0.541397i
$263$	−1.11635e6	−	362723.i	−0.995199	−	0.323360i	−0.234253	−	0.972176i	$-0.575265\pi$
$263$	−1.11635e6	−	362723.i	−0.995199	−	0.323360i	−0.760945	+	0.648816i	$0.775265\pi$
$264$	−146638.	−	106538.i	−0.129490	−	0.0940798i
$265$	−145810.	−	200690.i	−0.127548	−	0.175554i
$266$	−252981.	+	183801.i	−0.219222	+	0.159274i
$267$	−92956.2	+	67536.7i	−0.0797995	+	0.0579778i
$268$	−399562.	−	549950.i	−0.339819	−	0.467721i
$269$	1.05689e6	+	767875.i	0.890530	+	0.647008i	0.936016	−	0.351957i	$-0.114484\pi$
$269$	1.05689e6	+	767875.i	0.890530	+	0.647008i	−0.0454859	+	0.998965i	$0.514484\pi$
$270$	639324.	+	207729.i	0.533718	+	0.173415i
$271$	−1.63558e6	+	1.18832e6i	−1.35285	+	0.982903i	−0.353986	+	0.935251i	$0.615174\pi$
$271$	−1.63558e6	+	1.18832e6i	−1.35285	+	0.982903i	−0.998864	+	0.0476528i	$0.984826\pi$
$272$	237174.	−	77062.6i	0.194377	−	0.0631570i
$273$			103619.i			0.0841461i
$274$	−575012.	+	791436.i	−0.462701	+	0.636853i
$275$	−1.71212e6	+	556301.i	−1.36522	+	0.443586i
$276$	67609.3	+	21967.6i	0.0534237	+	0.0173584i
$277$	59558.7	−	183303.i	0.0466386	−	0.143539i	−0.925025	−	0.379905i	$-0.875957\pi$
$277$	59558.7	−	183303.i	0.0466386	−	0.143539i	0.971664	+	0.236366i	$0.0759566\pi$
$278$	−915198.			−0.710236
$279$	509716.	−	1.56874e6i	0.392029	−	1.20654i
$280$	86688.5	+	119316.i	0.0660794	+	0.0909506i
$281$	806585.	−	1.11017e6i	0.609375	−	0.838733i	−0.387151	−	0.922016i	$-0.626541\pi$
$281$	806585.	−	1.11017e6i	0.609375	−	0.838733i	0.996526	+	0.0832837i	$0.0265408\pi$
$282$	−160811.	−	494925.i	−0.120418	−	0.370610i
$283$	140165.	+	431383.i	0.104033	+	0.320182i	0.989502	−	0.144517i	$-0.0461627\pi$
$283$	140165.	+	431383.i	0.104033	+	0.320182i	−0.885469	+	0.464699i	$0.846163\pi$
$284$			471600.i			0.346959i
$285$	774070.	+	562394.i	0.564505	+	0.410137i
$286$	1.84254e6			1.33199
$287$	−232347.	−	217431.i	−0.166507	−	0.155818i
$288$	−226766.			−0.161100
$289$	−380973.	−	276793.i	−0.268318	−	0.194944i
$290$		−	1.62065e6i		−	1.13160i
$291$	216799.	+	667239.i	0.150081	+	0.461901i
$292$	−318262.	−	979510.i	−0.218438	−	0.672283i
$293$	−63490.1	+	87386.6i	−0.0432053	+	0.0594669i	−0.830073	−	0.557655i	$-0.811701\pi$
$293$	−63490.1	+	87386.6i	−0.0432053	+	0.0594669i	0.786868	+	0.617122i	$0.211701\pi$
$294$	173896.	+	239347.i	0.117333	+	0.161496i
$295$	−161173.	+	496040.i	−0.107829	+	0.331865i
$296$	485000.			0.321745
$297$	−406471.	+	1.25099e6i	−0.267386	+	0.822929i
$298$	−892739.	−	290069.i	−0.582350	−	0.189217i
$299$	−687283.	+	223312.i	−0.444588	+	0.144455i
$300$	128821.	−	177307.i	0.0826388	−	0.113743i
$301$			353354.i			0.224798i
$302$	−1.07577e6	+	349537.i	−0.678735	+	0.220534i
$303$	180243.	−	130954.i	0.112785	−	0.0819430i
$304$	−643804.	−	209185.i	−0.399549	−	0.129821i
$305$	209649.	+	152319.i	0.129046	+	0.0937571i
$306$	−507198.	−	698098.i	−0.309652	−	0.426200i
$307$	1.12945e6	−	820594.i	0.683945	−	0.496915i	−0.190719	−	0.981645i	$-0.561082\pi$
$307$	1.12945e6	−	820594.i	0.683945	−	0.496915i	0.874664	+	0.484729i	$0.161082\pi$
$308$	−233471.	+	169627.i	−0.140235	+	0.101887i
$309$	128748.	+	177207.i	0.0767088	+	0.105581i
$310$	−1.87883e6	−	1.36505e6i	−1.11041	−	0.806758i
$311$	−914656.	−	297190.i	−0.536237	−	0.174234i	0.0283643	−	0.999598i	$-0.490970\pi$
$311$	−914656.	−	297190.i	−0.536237	−	0.174234i	−0.564602	+	0.825364i	$0.690970\pi$
$312$	−181475.	+	131849.i	−0.105543	+	0.0766814i
$313$	−1.58718e6	+	515706.i	−0.915725	+	0.297537i	−0.728712	−	0.684820i	$-0.759881\pi$
$313$	−1.58718e6	+	515706.i	−0.915725	+	0.297537i	−0.187013	+	0.982357i	$0.559881\pi$
$314$			1.02876e6i			0.588831i
$315$	299957.	−	412855.i	0.170327	−	0.234435i
$316$	227920.	−	74055.8i	0.128400	−	0.0417197i
$317$	−1.01709e6	−	330474.i	−0.568477	−	0.184709i	0.0106551	−	0.999943i	$-0.496608\pi$
$317$	−1.01709e6	−	330474.i	−0.568477	−	0.184709i	−0.579132	+	0.815234i	$0.696608\pi$
$318$	−18261.0	+	56201.7i	−0.0101265	+	0.0311660i
$319$	3.17118e6			1.74480
$320$	−98660.4	+	303645.i	−0.0538602	+	0.165765i
$321$	−149131.	−	205261.i	−0.0807802	−	0.111184i
$322$	66528.4	−	91568.4i	0.0357575	−	0.0492160i
$323$	−795997.	−	2.44983e6i	−0.424527	−	1.30656i
$324$	216579.	+	666563.i	0.114618	+	0.352759i
$325$			2.22791e6i			1.17001i
$326$	584827.	+	424902.i	0.304778	+	0.221434i
$327$	−1.08834e6			−0.562852
$328$	85153.7	−	683590.i	0.0437038	−	0.350842i
$329$	−828555.			−0.422018
$330$	714374.	+	519023.i	0.361111	+	0.262363i
$331$			1.91012e6i			0.958276i	0.877740	+	0.479138i	$0.159051\pi$
$331$			1.91012e6i			0.958276i	−0.877740	+	0.479138i	$0.840949\pi$
$332$	−495426.	−	1.52476e6i	−0.246680	−	0.759203i
$333$	−518586.	−	1.59605e6i	−0.256278	−	0.788741i
$334$	2040.48	−	2808.48i	0.00100084	−	0.00137754i
$335$	1.94655e6	+	2.67919e6i	0.947661	+	1.30434i
$336$	10856.7	−	33413.6i	0.00524627	−	0.0161464i
$337$	−364089.			−0.174636			−0.0873179	−	0.996180i	$-0.527830\pi$
$337$	−364089.			−0.174636			−0.0873179	+	0.996180i	$0.527830\pi$
$338$	245700.	−	756188.i	0.116981	−	0.360029i
$339$	−936213.	−	304194.i	−0.442462	−	0.143764i
$340$	−1.15544e6	+	375426.i	−0.542064	+	0.176127i
$341$	2.67104e6	−	3.67637e6i	1.24393	−	1.71212i
$342$			2.34231e6i			1.08288i
$343$	920549.	−	299105.i	0.422485	−	0.137274i
$344$	−618849.	+	449620.i	−0.281961	+	0.204856i
$345$	−329372.	−	107019.i	−0.148984	−	0.0484078i
$346$	−1.93436e6	−	1.40539e6i	−0.868653	−	0.631113i
$347$	−477035.	−	656583.i	−0.212680	−	0.292729i	0.689327	−	0.724450i	$-0.257906\pi$
$347$	−477035.	−	656583.i	−0.212680	−	0.292729i	−0.902007	+	0.431721i	$0.857906\pi$
$348$	−312334.	+	226924.i	−0.138252	+	0.100446i
$349$	134122.	−	97445.1i	0.0589434	−	0.0428249i	−0.557923	−	0.829892i	$-0.688402\pi$
$349$	134122.	−	97445.1i	0.0589434	−	0.0428249i	0.616867	+	0.787068i	$0.288402\pi$
$350$	−205105.	−	282302.i	−0.0894963	−	0.123181i
$351$	1.31697e6	+	956834.i	0.570568	+	0.414542i
$352$	−594155.	−	193053.i	−0.255589	−	0.0830460i
$353$	−12291.8	+	8930.50i	−0.00525023	+	0.00381451i	−0.590407	−	0.807105i	$-0.701033\pi$
$353$	−12291.8	+	8930.50i	−0.00525023	+	0.00381451i	0.585157	+	0.810920i	$0.301033\pi$
$354$	118165.	−	38394.3i	0.0501167	−	0.0162839i
$355$		−	2.29749e6i		−	0.967572i
$356$	−232780.	+	320394.i	−0.0973465	+	0.133986i
$357$	127147.	−	41312.4i	0.0528000	−	0.0171558i
$358$	606518.	+	197070.i	0.250113	+	0.0812666i
$359$	−644706.	+	1.98420e6i	−0.264013	+	0.812549i	0.727906	+	0.685677i	$0.240494\pi$
$359$	−644706.	+	1.98420e6i	−0.264013	+	0.812549i	−0.991919	+	0.126872i	$0.959506\pi$
$360$	1.10473e6			0.449264
$361$	−1.39556e6	+	4.29509e6i	−0.563612	+	1.73462i
$362$	−1.22131e6	−	1.68099e6i	−0.489840	−	0.674207i
$363$	−576156.	+	793010.i	−0.229495	+	0.315873i
$364$	110364.	+	339666.i	0.0436591	+	0.134369i
$365$	1.55048e6	+	4.77188e6i	0.609163	+	1.87481i
$366$		−	61731.8i		−	0.0240883i
$367$	3.36795e6	+	2.44696e6i	1.30527	+	0.948334i	0.999992	−	0.00392947i	$-0.00125079\pi$
$367$	3.36795e6	+	2.44696e6i	1.30527	+	0.948334i	0.305277	+	0.952263i	$0.401251\pi$
$368$	245022.			0.0943162
$369$	−2.34062e6	+	450705.i	−0.894881	+	0.172316i
$370$	−2.36277e6			−0.897258
$371$	76118.2	+	55303.1i	0.0287114	+	0.0208600i
$372$			553226.i			0.207274i
$373$	−399974.	−	1.23099e6i	−0.148854	−	0.458125i	0.848633	−	0.528983i	$-0.177426\pi$
$373$	−399974.	−	1.23099e6i	−0.148854	−	0.458125i	−0.997486	+	0.0708576i	$0.977426\pi$
$374$	−734610.	−	2.26090e6i	−0.271568	−	0.835799i
$375$	37057.3	−	51005.0i	0.0136080	−	0.0187299i
$376$	−1.05428e6	−	1.45110e6i	−0.384581	−	0.529330i
$377$	1.21276e6	−	3.73248e6i	0.439461	−	1.35252i
$378$	−254963.			−0.0917798
$379$	867956.	−	2.67130e6i	0.310384	−	0.955265i	−0.667228	−	0.744853i	$-0.732520\pi$
$379$	867956.	−	2.67130e6i	0.310384	−	0.955265i	0.977613	−	0.210412i	$-0.0674805\pi$
$380$	3.13642e6	+	1.01908e6i	1.11423	+	0.362036i
$381$	−304509.	+	98941.1i	−0.107470	+	0.0349192i
$382$	907557.	−	1.24915e6i	0.318211	−	0.437980i
$383$			3.15107e6i			1.09764i	0.835940	+	0.548821i	$0.184923\pi$
$383$			3.15107e6i			1.09764i	−0.835940	+	0.548821i	$0.815077\pi$
$384$	72333.7	−	23502.6i	0.0250330	−	0.00813371i
$385$	1.13740e6	−	826370.i	0.391077	−	0.284134i
$386$	2.43514e6	+	791226.i	0.831871	+	0.270291i
$387$	2.14132e6	+	1.55576e6i	0.726783	+	0.528039i
$388$	1.42135e6	+	1.95631e6i	0.479314	+	0.659720i
$389$	−1.45204e6	+	1.05497e6i	−0.486526	+	0.353482i	−0.803847	−	0.594837i	$-0.797217\pi$
$389$	−1.45204e6	+	1.05497e6i	−0.486526	+	0.353482i	0.317321	+	0.948318i	$0.397217\pi$
$390$	884089.	−	642328.i	0.294330	−	0.213843i
$391$	548032.	+	754301.i	0.181286	+	0.249519i
$392$	824963.	+	599371.i	0.271156	+	0.197006i
$393$	1.12956e6	+	367018.i	0.368918	+	0.119869i
$394$	2.92552e6	−	2.12552e6i	0.949429	−	0.689801i
$395$	−1.11036e6	+	360778.i	−0.358072	+	0.116345i
$396$			2.16168e6i			0.692712i
$397$	3.06359e6	−	4.21667e6i	0.975562	−	1.34275i	0.0363753	−	0.999338i	$-0.488419\pi$
$397$	3.06359e6	−	4.21667e6i	0.975562	−	1.34275i	0.939187	−	0.343407i	$-0.111581\pi$
$398$	2.90739e6	−	944669.i	0.920017	−	0.298932i
$399$	−345136.	−	112142.i	−0.108532	−	0.0352642i
$400$	233430.	−	718424.i	0.0729469	−	0.224507i
$401$	−3.78035e6			−1.17401			−0.587004	−	0.809584i	$-0.699693\pi$
$401$	−3.78035e6			−1.17401			−0.587004	+	0.809584i	$0.699693\pi$
$402$	243783.	−	750286.i	0.0752380	−	0.231559i
$403$	−3.30560e6	−	4.54977e6i	−1.01388	−	1.39549i
$404$	451361.	−	621245.i	0.137585	−	0.189369i
$405$	−1.05511e6	−	3.24729e6i	−0.319639	−	0.983748i
$406$	189947.	+	584597.i	0.0571897	+	0.176012i
$407$		−	4.62333e6i		−	1.38347i
$408$	234139.	+	170112.i	0.0696343	+	0.0505923i
$409$	5.76263e6			1.70338			0.851691	−	0.524044i	$-0.175577\pi$
$409$	5.76263e6			1.70338			0.851691	+	0.524044i	$0.175577\pi$
$410$	−414843.	+	3.33025e6i	−0.121878	+	0.978401i
$411$	−1.13530e6			−0.331519
$412$	610782.	+	443759.i	0.177273	+	0.128796i
$413$		−	197821.i		−	0.0570686i
$414$	−261991.	−	806324.i	−0.0751250	−	0.231211i
$415$	2.41357e6	+	7.42820e6i	0.687922	+	2.11721i
$416$	−454446.	+	625491.i	−0.128751	+	0.177210i
$417$	−624292.	−	859265.i	−0.175812	−	0.241984i
$418$	−1.99408e6	+	6.13716e6i	−0.558216	+	1.71801i
$419$	1.96476e6			0.546731			0.273366	−	0.961910i	$-0.411863\pi$
$419$	1.96476e6			0.546731			0.273366	+	0.961910i	$0.411863\pi$
$420$	−52890.7	+	162781.i	−0.0146304	+	0.0450278i
$421$	969015.	+	314852.i	0.266456	+	0.0865768i	0.439198	−	0.898390i	$-0.355263\pi$
$421$	969015.	+	314852.i	0.266456	+	0.0865768i	−0.172742	+	0.984967i	$0.555263\pi$
$422$	835770.	−	271558.i	0.228458	−	0.0742304i
$423$	−3.64800e6	+	5.02104e6i	−0.991298	+	1.36440i
$424$			203680.i			0.0550217i
$425$	2.73377e6	−	888256.i	0.734158	−	0.238543i
$426$	−442778.	+	321697.i	−0.118212	+	0.0858861i
$427$	−93476.8	−	30372.4i	−0.0248104	−	0.00806139i
$428$	−707477.	−	514012.i	−0.186682	−	0.135633i
$429$	1.25687e6	+	1.72993e6i	0.329721	+	0.453822i
$430$	3.01485e6	−	2.19041e6i	0.786310	−	0.571288i
$431$	−61253.0	+	44502.9i	−0.0158831	+	0.0115397i	−0.595698	−	0.803208i	$-0.703125\pi$
$431$	−61253.0	+	44502.9i	−0.0158831	+	0.0115397i	0.579815	+	0.814748i	$0.303125\pi$
$432$	−324424.	−	446531.i	−0.0836380	−	0.115118i
$433$	1.48843e6	+	1.08141e6i	0.381514	+	0.277186i	0.761969	−	0.647613i	$-0.224233\pi$
$433$	1.48843e6	+	1.08141e6i	0.381514	+	0.277186i	−0.380456	+	0.924799i	$0.624233\pi$
$434$	837717.	+	272191.i	0.213488	+	0.0693664i
$435$	1.52160e6	−	1.10551e6i	0.385547	−	0.280116i
$436$	−3.56759e6	+	1.15918e6i	−0.898791	+	0.292035i
$437$		−	2.53089e6i		−	0.633971i
$438$	702548.	−	966974.i	0.174981	−	0.240840i
$439$	−4.34633e6	+	1.41221e6i	−1.07637	+	0.349734i	−0.792965	−	0.609267i	$-0.791464\pi$
$439$	−4.34633e6	+	1.41221e6i	−1.07637	+	0.349734i	−0.283405	+	0.959000i	$0.591464\pi$
$440$	2.89454e6	+	940494.i	0.712768	+	0.231592i
$441$	1.09033e6	−	3.35568e6i	0.266969	−	0.821645i
$442$	−2.94202e6			−0.716291
$443$	−1.24283e6	+	3.82503e6i	−0.300885	+	0.926030i	0.680295	+	0.732938i	$0.261852\pi$
$443$	−1.24283e6	+	3.82503e6i	−0.300885	+	0.926030i	−0.981181	+	0.193092i	$0.938148\pi$
$444$	330837.	+	455358.i	0.0796447	+	0.109622i
$445$	1.13403e6	−	1.56086e6i	0.271472	−	0.373650i
$446$	12102.4	+	37247.4i	0.00288095	+	0.00886664i
$447$	−336632.	−	1.03605e6i	−0.0796868	−	0.245251i
$448$		−	121094.i		−	0.0285054i
$449$	696179.	+	505804.i	0.162969	+	0.118404i	0.666281	−	0.745701i	$-0.267885\pi$
$449$	696179.	+	505804.i	0.162969	+	0.118404i	−0.503312	+	0.864105i	$0.667885\pi$
$450$	−2.61380e6			−0.608472
$451$	−6.51642e6	−	811740.i	−1.50858	−	0.187921i
$452$	−3.39292e6			−0.781138
$453$	−1.06200e6	−	771586.i	−0.243152	−	0.176660i
$454$		−	3.36884e6i		−	0.767080i
$455$	−537661.	−	1.65475e6i	−0.121753	−	0.374718i
$456$	−242764.	−	747151.i	−0.0546729	−	0.168266i
$457$	4.44631e6	−	6.11982e6i	0.995885	−	1.37072i	0.0680684	−	0.997681i	$-0.478316\pi$
$457$	4.44631e6	−	6.11982e6i	0.995885	−	1.37072i	0.927816	−	0.373037i	$-0.121684\pi$
$458$	−364748.	−	502033.i	−0.0812511	−	0.111833i
$459$	649020.	−	1.99748e6i	0.143789	−	0.442538i
$460$	−1.19368e6			−0.263022
$461$	−627963.	+	1.93267e6i	−0.137620	+	0.423551i	−0.995988	−	0.0894830i	$-0.971479\pi$
$461$	−627963.	+	1.93267e6i	−0.137620	+	0.423551i	0.858368	+	0.513034i	$0.171479\pi$
$462$	−318520.	−	103493.i	−0.0694275	−	0.0225584i
$463$	−4.32824e6	+	1.40633e6i	−0.938337	+	0.304884i	−0.737967	−	0.674836i	$-0.764214\pi$
$463$	−4.32824e6	+	1.40633e6i	−0.938337	+	0.304884i	−0.200369	+	0.979720i	$0.564214\pi$
$464$	−782144.	+	1.07653e6i	−0.168652	+	0.232130i
$465$		−	2.69515e6i		−	0.578031i
$466$	−1.38223e6	+	449113.i	−0.294859	+	0.0958055i
$467$	−563168.	+	409165.i	−0.119494	+	0.0868174i	−0.645927	−	0.763399i	$-0.723529\pi$
$467$	−563168.	+	409165.i	−0.119494	+	0.0868174i	0.526433	+	0.850216i	$0.323529\pi$
$468$	2.54429e6	+	826691.i	0.536973	+	0.174473i
$469$	−1.01617e6	−	738290.i	−0.213321	−	0.154987i
$470$	5.13615e6	+	7.06931e6i	1.07249	+	1.47616i
$471$	−965888.	+	701759.i	−0.200620	+	0.145759i
$472$	346455.	−	251715.i	0.0715801	−	0.0520060i
$473$	4.28607e6	+	5.89926e6i	0.880858	+	1.21240i
$474$	225003.	+	163474.i	0.0459984	+	0.0334198i
$475$	−7.42076e6	−	2.41115e6i	−1.50909	−	0.490332i
$476$	372788.	−	270846.i	0.0754126	−	0.0547905i
$477$	670274.	−	217785.i	0.134883	−	0.0438260i
$478$		−	2.55259e6i		−	0.510989i
$479$	1.99331e6	−	2.74356e6i	0.396951	−	0.546356i	−0.563025	−	0.826440i	$-0.690362\pi$
$479$	1.99331e6	−	2.74356e6i	0.396951	−	0.546356i	0.959975	+	0.280084i	$0.0903624\pi$
$480$	−352388.	+	114498.i	−0.0698101	+	0.0226827i
$481$	−5.44166e6	−	1.76810e6i	−1.07243	−	0.348453i
$482$	−1.01064e6	+	3.11042e6i	−0.198142	+	0.609819i
$483$	131354.			0.0256197
$484$	−1.04402e6	+	3.21317e6i	−0.202580	+	0.623476i
$485$	−6.92437e6	−	9.53057e6i	−1.33667	−	1.83978i
$486$	−1.70988e6	+	2.35345e6i	−0.328380	+	0.451976i
$487$	1.49017e6	+	4.58627e6i	0.284717	+	0.876269i	0.986483	+	0.163862i	$0.0523952\pi$
$487$	1.49017e6	+	4.58627e6i	0.284717	+	0.876269i	−0.701766	+	0.712407i	$0.747605\pi$
$488$	−65750.2	−	202358.i	−0.0124982	−	0.0384655i
$489$			838927.i			0.158654i
$490$	−4.01897e6	−	2.91995e6i	−0.756179	−	0.549396i
$491$	−1.80931e6			−0.338695			−0.169347	−	0.985556i	$-0.554166\pi$
$491$	−1.80931e6			−0.338695			−0.169347	+	0.985556i	$0.554166\pi$
$492$	699899.	−	386354.i	0.130353	−	0.0719570i
$493$	−5.06348e6			−0.938279
$494$	6.46084e6	+	4.69407e6i	1.19116	+	0.865431i
$495$		−	1.05310e7i		−	1.93178i
$496$	589238.	+	1.81349e6i	0.107544	+	0.330987i
$497$	269277.	+	828748.i	0.0488999	+	0.150498i
$498$	1.09363e6	−	1.50525e6i	0.197604	−	0.271979i
$499$	1.68573e6	+	2.32021e6i	0.303066	+	0.417134i	0.933203	−	0.359349i	$-0.117001\pi$
$499$	1.68573e6	+	2.32021e6i	0.303066	+	0.417134i	−0.630137	+	0.776484i	$0.717001\pi$
$500$	67149.5	−	206665.i	0.0120121	−	0.0369694i
$501$	4028.73			0.000717090
$502$	770241.	−	2.37056e6i	0.136417	−	0.419847i
$503$	−4.80470e6	−	1.56114e6i	−0.846733	−	0.275120i	−0.146656	−	0.989188i	$-0.546851\pi$
$503$	−4.80470e6	−	1.56114e6i	−0.846733	−	0.275120i	−0.700077	+	0.714067i	$0.746851\pi$
$504$	−398498.	+	129480.i	−0.0698795	+	0.0227052i
$505$	−2.19890e6	+	3.02652e6i	−0.383686	+	0.528099i
$506$		−	2.33571e6i		−	0.405548i
$507$	877575.	−	285141.i	0.151623	−	0.0492652i
$508$	−892807.	+	648662.i	−0.153496	+	0.111522i
$509$	6.43443e6	+	2.09067e6i	1.10082	+	0.357678i	0.802418	−	0.596763i	$-0.203547\pi$
$509$	6.43443e6	+	2.09067e6i	1.10082	+	0.357678i	0.298401	+	0.954441i	$0.403547\pi$
$510$	−1.14065e6	−	828733.i	−0.194191	−	0.141088i
$511$	−1.11857e6	−	1.53958e6i	−0.189501	−	0.260826i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	−4.61232e6	+	3.35105e6i	−0.773795	+	0.562195i
$514$	−1.67084e6	−	2.29972e6i	−0.278951	−	0.383943i
$515$	−2.97554e6	−	2.16186e6i	−0.494366	−	0.359178i
$516$	−844282.	−	274324.i	−0.139593	−	0.0453565i
$517$	−1.38328e7	+	1.00501e7i	−2.27606	+	1.65365i
$518$	852295.	−	276928.i	0.139562	−	0.0453463i
$519$		−	2.77481e6i		−	0.452183i
$520$	2.21392e6	−	3.04720e6i	0.359050	−	0.494189i
$521$	8.66469e6	−	2.81533e6i	1.39849	−	0.454396i	0.489786	−	0.871843i	$-0.337075\pi$
$521$	8.66469e6	−	2.81533e6i	1.39849	−	0.454396i	0.908701	+	0.417447i	$0.137075\pi$
$522$	4.37897e6	+	1.42281e6i	0.703389	+	0.228545i
$523$	−1.42052e6	+	4.37191e6i	−0.227087	+	0.698903i	0.770986	+	0.636852i	$0.219764\pi$
$523$	−1.42052e6	+	4.37191e6i	−0.227087	+	0.698903i	−0.998073	+	0.0620505i	$0.980236\pi$
$524$	4.09365e6			0.651301
$525$	125139.	−	385139.i	0.0198151	−	0.0609845i
$526$	−2.75976e6	−	3.79849e6i	−0.434918	−	0.598613i
$527$	−4.26490e6	+	5.87013e6i	−0.668932	+	0.920706i
$528$	−224042.	−	689531.i	−0.0349740	−	0.107639i
$529$	−1.70586e6	−	5.25009e6i	−0.265035	−	0.815694i
$530$		−	992268.i		−	0.153440i
$531$	−1.19879e6	−	870975.i	−0.184505	−	0.134051i
$532$	−1.25081e6			−0.191607
$533$	−3.44750e6	+	7.35940e6i	−0.525637	+	1.12208i
$534$	−459601.			−0.0697473
$535$	3.44661e6	+	2.50411e6i	0.520605	+	0.378242i
$536$		−	2.71910e6i		−	0.408803i
$537$	228704.	+	703879.i	0.0342246	+	0.105332i
$538$	1.61478e6	+	4.96979e6i	0.240524	+	0.740257i
$539$	5.71359e6	−	7.86408e6i	0.847104	−	1.16594i
$540$	1.58050e6	+	2.17537e6i	0.233243	+	0.321032i
$541$	−2.12006e6	+	6.52488e6i	−0.311426	+	0.958472i	0.665774	+	0.746153i	$0.268101\pi$
$541$	−2.12006e6	+	6.52488e6i	−0.311426	+	0.958472i	−0.977201	+	0.212318i	$0.931899\pi$
$542$	−8.08677e6			−1.18243
$543$	745150.	−	2.29334e6i	0.108454	−	0.333786i
$544$	948697.	+	308250.i	0.137445	+	0.0446587i
$545$	1.73802e7	−	5.64718e6i	2.50648	−	0.814405i
$546$	−243623.	+	335319.i	−0.0349734	+	0.0481367i
$547$			9.29009e6i			1.32755i	0.747931	+	0.663776i	$0.231047\pi$
$547$			9.29009e6i			1.32755i	−0.747931	+	0.663776i	$0.768953\pi$
$548$	−3.72156e6	+	1.20921e6i	−0.529387	+	0.172008i
$549$	−595621.	+	432744.i	−0.0843411	+	0.0612774i
$550$	−6.84847e6	−	2.22520e6i	−0.965355	−	0.313663i
$551$	1.11197e7	+	8.07894e6i	1.56032	+	1.13364i
$552$	167139.	+	230048.i	0.0233470	+	0.0321344i
$553$	358242.	−	260278.i	0.0498155	−	0.0361930i
$554$	623707.	−	453150.i	0.0863388	−	0.0627288i
$555$	−1.61174e6	−	2.21837e6i	−0.222107	−	0.305704i
$556$	−2.96164e6	−	2.15176e6i	−0.406299	−	0.295193i
$557$	660459.	+	214596.i	0.0902002	+	0.0293078i	0.353769	−	0.935333i	$-0.384900\pi$
$557$	660459.	+	214596.i	0.0902002	+	0.0293078i	−0.263569	+	0.964640i	$0.584900\pi$
$558$	5.33782e6	−	3.87815e6i	0.725735	−	0.527277i
$559$	8.58256e6	−	2.78864e6i	1.16168	−	0.377454i
$560$			589933.i			0.0794937i
$561$	1.62161e6	−	2.23196e6i	0.217541	−	0.299419i
$562$	5.22033e6	−	1.69619e6i	0.697200	−	0.226534i
$563$	−9.96352e6	−	3.23734e6i	−1.32477	−	0.430445i	−0.440642	−	0.897683i	$-0.645249\pi$
$563$	−9.96352e6	−	3.23734e6i	−1.32477	−	0.430445i	−0.884132	+	0.467238i	$0.845249\pi$
$564$	643244.	−	1.97970e6i	0.0851486	−	0.262061i
$565$	1.65293e7			2.17838
$566$	−560659.	+	1.72553e6i	−0.0735627	+	0.226403i
$567$	761195.	+	1.04769e6i	0.0994347	+	0.136860i
$568$	−1.10880e6	+	1.52613e6i	−0.144205	+	0.198482i
$569$	−714043.	−	2.19760e6i	−0.0924579	−	0.284556i	0.894125	−	0.447818i	$-0.147799\pi$
$569$	−714043.	−	2.19760e6i	−0.0924579	−	0.284556i	−0.986583	+	0.163261i	$0.947799\pi$
$570$	1.18267e6	+	3.63989e6i	0.152468	+	0.469247i
$571$			6.45105e6i			0.828018i	0.910273	+	0.414009i	$0.135872\pi$
$571$			6.45105e6i			0.828018i	−0.910273	+	0.414009i	$0.864128\pi$
$572$	5.96258e6	+	4.33207e6i	0.761981	+	0.553612i
$573$	1.79188e6			0.227994
$574$	−240678.	−	1.24990e6i	−0.0304900	−	0.158342i
$575$	2.82423e6			0.356230
$576$	−733829.	−	533158.i	−0.0921592	−	0.0669576i
$577$		−	1.15111e7i		−	1.43939i	−0.694292	−	0.719693i	$-0.744282\pi$
$577$		−	1.15111e7i		−	1.43939i	0.694292	−	0.719693i	$-0.255718\pi$
$578$	−582075.	−	1.79144e6i	−0.0724701	−	0.223040i
$579$	918237.	+	2.82604e6i	0.113830	+	0.350334i
$580$	3.81037e6	−	5.24452e6i	0.470324	−	0.647345i
$581$	−1.74124e6	−	2.39661e6i	−0.214002	−	0.294548i
$582$	−867197.	+	2.66896e6i	−0.106123	+	0.326614i
$583$	1.94161e6			0.236587
$584$	1.27305e6	−	3.91804e6i	0.154459	−	0.475376i
$585$	−1.23950e7	−	4.02739e6i	−1.49747	−	0.486558i
$586$	−410916.	+	133515.i	−0.0494321	+	0.0160615i
$587$	−443979.	+	611084.i	−0.0531823	+	0.0731991i	−0.834780	−	0.550584i	$-0.814405\pi$
$587$	−443979.	+	611084.i	−0.0531823	+	0.0731991i	0.781598	+	0.623783i	$0.214405\pi$
$588$			1.18340e6i			0.141152i
$589$	1.87319e7	−	6.08637e6i	2.22482	−	0.722887i
$590$	−1.68783e6	+	1.22628e6i	−0.199617	+	0.145030i
$591$	3.99123e6	+	1.29683e6i	0.470043	+	0.152726i
$592$	1.56949e6	+	1.14030e6i	0.184058	+	0.133726i
$593$	2.50595e6	+	3.44914e6i	0.292641	+	0.402786i	0.929870	−	0.367889i	$-0.119919\pi$
$593$	2.50595e6	+	3.44914e6i	0.292641	+	0.402786i	−0.637229	+	0.770675i	$0.719919\pi$
$594$	−4.25662e6	+	3.09262e6i	−0.494993	+	0.359633i
$595$	−1.81611e6	+	1.31948e6i	−0.210305	+	0.152795i
$596$	−2.20697e6	−	3.03764e6i	−0.254496	−	0.350284i
$597$	2.87018e6	+	2.08531e6i	0.329590	+	0.239461i
$598$	−2.74913e6	−	893247.i	−0.314371	−	0.102145i
$599$	1.24587e7	−	9.05175e6i	1.41875	−	1.03078i	0.426768	−	0.904361i	$-0.359652\pi$
$599$	1.24587e7	−	9.05175e6i	1.41875	−	1.03078i	0.991977	−	0.126418i	$-0.0403479\pi$
$600$	833748.	−	270901.i	0.0945490	−	0.0307208i
$601$			3.10513e6i			0.350666i	0.984509	+	0.175333i	$0.0561003\pi$
$601$			3.10513e6i			0.350666i	−0.984509	+	0.175333i	$0.943900\pi$
$602$	−830784.	+	1.14348e6i	−0.0934323	+	0.128598i
$603$	−8.94808e6	+	2.90741e6i	−1.00216	+	0.325621i
$604$	−4.30306e6	−	1.39815e6i	−0.479938	−	0.155941i
$605$	5.08615e6	−	1.56536e7i	0.564938	−	1.73870i
$606$	891168.			0.0985776
$607$	−4.49287e6	+	1.38276e7i	−0.494939	+	1.52327i	0.322112	+	0.946701i	$0.395607\pi$
$607$	−4.49287e6	+	1.38276e7i	−0.494939	+	1.52327i	−0.817051	+	0.576565i	$0.804393\pi$
$608$	−1.59157e6	−	2.19061e6i	−0.174609	−	0.240329i
$609$	−419299.	+	577115.i	−0.0458121	+	0.0630549i
$610$	320315.	+	985829.i	0.0348540	+	0.107270i
$611$	6.53890e6	+	2.01247e7i	0.708601	+	2.18085i
$612$		−	3.45159e6i		−	0.372512i
$613$	−4.17030e6	−	3.02990e6i	−0.448246	−	0.325669i	0.340657	−	0.940188i	$-0.389350\pi$
$613$	−4.17030e6	−	3.02990e6i	−0.448246	−	0.325669i	−0.788903	+	0.614518i	$0.789350\pi$
$614$	5.58431e6			0.597790
$615$	−3.40970e6	+	1.88220e6i	−0.363520	+	0.200668i
$616$	−1.15434e6			−0.122570
$617$	6.04478e6	+	4.39179e6i	0.639246	+	0.464439i	0.859591	−	0.510983i	$-0.170718\pi$
$617$	6.04478e6	+	4.39179e6i	0.639246	+	0.464439i	−0.220345	+	0.975422i	$0.570718\pi$
$618$			876158.i			0.0922808i
$619$	4.24951e6	+	1.30786e7i	0.445771	+	1.37194i	0.881636	+	0.471931i	$0.156443\pi$
$619$	4.24951e6	+	1.30786e7i	0.445771	+	1.37194i	−0.435864	+	0.900012i	$0.643557\pi$
$620$	−2.87059e6	−	8.83477e6i	−0.299911	−	0.923030i
$621$	1.21294e6	−	1.66947e6i	0.126215	−	0.173720i
$622$	−2.26116e6	−	3.11221e6i	−0.234344	−	0.322547i
$623$	−226126.	+	695945.i	−0.0233416	+	0.0718381i
$624$	−897259.			−0.0922479
$625$	−3.17662e6	+	9.77663e6i	−0.325286	+	1.00113i
$626$	−6.34871e6	−	2.06282e6i	−0.647515	−	0.210390i
$627$	−7.12232e6	+	2.31418e6i	−0.723524	+	0.235087i
$628$	−2.41876e6	+	3.32914e6i	−0.244734	+	0.336848i
$629$			7.38215e6i			0.743971i
$630$	1.94136e6	−	630787.i	0.194875	−	0.0633186i
$631$	5.85465e6	−	4.25365e6i	0.585366	−	0.425293i	−0.255288	−	0.966865i	$-0.582170\pi$
$631$	5.85465e6	−	4.25365e6i	0.585366	−	0.425293i	0.840655	+	0.541571i	$0.182170\pi$
$632$	911682.	+	296223.i	0.0907926	+	0.0295003i
$633$	825073.	+	599451.i	0.0818433	+	0.0594626i
$634$	−2.51439e6	−	3.46076e6i	−0.248433	−	0.341939i
$635$	4.34949e6	−	3.16009e6i	0.428059	−	0.311003i
$636$	−191232.	+	138938.i	−0.0187464	+	0.0136200i
$637$	−7.07097e6	−	9.73236e6i	−0.690447	−	0.950319i
$638$	1.02622e7	+	7.45590e6i	0.998130	+	0.725184i
$639$	6.20780e6	+	2.01704e6i	0.601431	+	0.195417i
$640$	−1.03318e6	+	750653.i	−0.0997076	+	0.0724418i
$641$	−1.67172e7	+	5.43176e6i	−1.60701	+	0.522150i	−0.968828	−	0.247733i	$-0.920314\pi$
$641$	−1.67172e7	+	5.43176e6i	−1.60701	+	0.522150i	−0.638184	+	0.769884i	$0.720314\pi$
$642$		−	1.01487e6i		−	0.0971788i
$643$	475399.	−	654330.i	0.0453451	−	0.0624122i	−0.785742	−	0.618554i	$-0.787719\pi$
$643$	475399.	−	654330.i	0.0453451	−	0.0624122i	0.831087	+	0.556142i	$0.187719\pi$
$644$	430581.	−	139904.i	0.0409110	−	0.0132928i
$645$	4.11309e6	+	1.33642e6i	0.389286	+	0.126487i
$646$	3.18399e6	−	9.79931e6i	0.300186	−	0.923877i
$647$	1.20841e7			1.13489			0.567444	−	0.823412i	$-0.307932\pi$
$647$	1.20841e7			1.13489			0.567444	+	0.823412i	$0.307932\pi$
$648$	−866317.	+	2.66625e6i	−0.0810475	+	0.249438i
$649$	−2.39950e6	−	3.30263e6i	−0.223620	−	0.307786i
$650$	−5.23813e6	+	7.20967e6i	−0.486288	+	0.669318i
$651$	315884.	+	972191.i	0.0292129	+	0.0899082i
$652$	893536.	+	2.75002e6i	0.0823177	+	0.253348i
$653$			7.24647e6i			0.665034i	0.943097	+	0.332517i	$0.107898\pi$
$653$			7.24647e6i			0.665034i	−0.943097	+	0.332517i	$0.892102\pi$
$654$	−3.52193e6	−	2.55883e6i	−0.321986	−	0.233936i
$655$	−1.99430e7			−1.81630
$656$	1.88278e6	−	2.01194e6i	0.170821	−	0.182539i
$657$	−1.42548e7			−1.28839
$658$	−2.68126e6	−	1.94805e6i	−0.241420	−	0.175402i
$659$			8.03938e6i			0.721122i	0.932736	+	0.360561i	$0.117415\pi$
$659$			8.03938e6i			0.721122i	−0.932736	+	0.360561i	$0.882585\pi$
$660$	1.09147e6	+	3.35919e6i	0.0975328	+	0.300175i
$661$	−4.05345e6	−	1.24752e7i	−0.360845	−	1.11057i	−0.952542	−	0.304407i	$-0.901542\pi$
$661$	−4.05345e6	−	1.24752e7i	−0.360845	−	1.11057i	0.591697	−	0.806161i	$-0.298458\pi$
$662$	−4.49096e6	+	6.18128e6i	−0.398285	+	0.548193i
$663$	−2.00686e6	−	2.76221e6i	−0.177310	−	0.244047i
$664$	1.98170e6	−	6.09906e6i	0.174429	−	0.536837i
$665$	6.09355e6			0.534338
$666$	2.07435e6	−	6.38418e6i	0.181216	−	0.557724i
$667$	−4.73151e6	−	1.53736e6i	−0.411799	−	0.133802i
$668$	13206.3	−	4290.97i	0.00114509	−	0.000372062i
$669$	−26715.5	+	36770.7i	−0.00230780	+	0.00317641i
$670$			1.32467e7i			1.14004i
$671$	−1.92901e6	+	626773.i	−0.165397	+	0.0537408i
$672$	113693.	−	82602.9i	0.00971206	−	0.00705622i
$673$	−1.51779e7	−	4.93161e6i	−1.29174	−	0.419711i	−0.419039	−	0.907968i	$-0.637633\pi$
$673$	−1.51779e7	−	4.93161e6i	−1.29174	−	0.419711i	−0.872700	+	0.488257i	$0.837633\pi$
$674$	−1.17822e6	−	856025.i	−0.0999024	−	0.0725833i
$675$	−3.73945e6	−	5.14691e6i	−0.315899	−	0.434797i
$676$	2.57301e6	−	1.86940e6i	0.216558	−	0.157339i
$677$	−4.71302e6	+	3.42421e6i	−0.395210	+	0.287137i	−0.767587	−	0.640945i	$-0.778543\pi$
$677$	−4.71302e6	+	3.42421e6i	−0.395210	+	0.287137i	0.372377	+	0.928081i	$0.378543\pi$
$678$	−2.31445e6	−	3.18556e6i	−0.193363	−	0.266141i
$679$	3.61477e6	+	2.62629e6i	0.300889	+	0.218609i
$680$	−4.62177e6	−	1.50170e6i	−0.383297	−	0.124541i
$681$	3.16295e6	−	2.29802e6i	0.261351	−	0.189883i
$682$	1.72873e7	−	5.61699e6i	1.42320	−	0.462427i
$683$		−	1.68016e7i		−	1.37816i	−0.724686	−	0.689079i	$-0.758015\pi$
$683$		−	1.68016e7i		−	1.37816i	0.724686	−	0.689079i	$-0.241985\pi$
$684$	−5.50711e6	+	7.57989e6i	−0.450074	+	0.619473i
$685$	1.81303e7	−	5.89089e6i	1.47631	−	0.479683i
$686$	3.68220e6	+	1.19642e6i	0.298742	+	0.0970673i
$687$	222542.	−	684913.i	0.0179895	−	0.0553660i
$688$	−3.05976e6			−0.246443
$689$	742531.	−	2.28527e6i	0.0595890	−	0.183396i
$690$	−814253.	−	1.12072e6i	−0.0651083	−	0.0896139i
$691$	14369.3	−	19777.6i	0.00114483	−	0.00157572i	−0.808444	−	0.588573i	$-0.799690\pi$
$691$	14369.3	−	19777.6i	0.00114483	−	0.00157572i	0.809589	+	0.586997i	$0.199690\pi$
$692$	−2.95543e6	−	9.09589e6i	−0.234615	−	0.722071i
$693$	1.23429e6	+	3.79874e6i	0.0976298	+	0.300474i
$694$		−	3.24632e6i		−	0.255855i
$695$	1.44282e7	+	1.04827e7i	1.13305	+	0.823212i
$696$	−1.54427e6			−0.120837
$697$	1.04049e7	+	1.29612e6i	0.811251	+	0.101056i
$698$	663134.			0.0515185
$699$	−1.36454e6	−	991393.i	−0.105631	−	0.0767455i
$700$		−	1.39578e6i		−	0.107664i
$701$	−1.41841e6	−	4.36541e6i	−0.109020	−	0.335529i	0.881633	−	0.471936i	$-0.156445\pi$
$701$	−1.41841e6	−	4.36541e6i	−0.109020	−	0.335529i	−0.990653	+	0.136407i	$0.956445\pi$
$702$	2.01215e6	+	6.19276e6i	0.154105	+	0.474287i
$703$	1.17784e7	−	1.62116e7i	0.898875	−	1.23720i
$704$	−1.46883e6	−	2.02167e6i	−0.111697	−	0.153737i
$705$	−3.13369e6	+	9.64450e6i	−0.237456	+	0.730814i
$706$	−60773.9			−0.00458887
$707$	438460.	−	1.34944e6i	0.0329900	−	0.101533i
$708$	472662.	+	153577.i	0.0354378	+	0.0115144i
$709$	−1.50641e7	+	4.89464e6i	−1.12546	+	0.365683i	−0.811848	−	0.583869i	$-0.801538\pi$
$709$	−1.50641e7	+	4.89464e6i	−1.12546	+	0.365683i	−0.313609	+	0.949552i	$0.601538\pi$
$710$	5.40173e6	−	7.43484e6i	0.402149	−	0.553511i
$711$		−	3.31692e6i		−	0.246071i
$712$	−1.50658e6	+	489518.i	−0.111376	+	0.0361884i
$713$	−5.76756e6	+	4.19038e6i	−0.424882	+	0.308695i
$714$	508586.	+	165250.i	0.0373352	+	0.0121310i
$715$	−2.90479e7	−	2.11045e7i	−2.12496	−	1.54387i
$716$	1.49939e6	+	2.06374e6i	0.109303	+	0.150443i
$717$	2.39659e6	−	1.74122e6i	0.174099	−	0.126490i
$718$	−6.75145e6	+	4.90521e6i	−0.488749	+	0.355097i
$719$	−4.41079e6	−	6.07092e6i	−0.318195	−	0.437958i	0.619720	−	0.784823i	$-0.287246\pi$
$719$	−4.41079e6	−	6.07092e6i	−0.318195	−	0.437958i	−0.937915	+	0.346865i	$0.887246\pi$
$720$	3.57500e6	+	2.59739e6i	0.257007	+	0.186726i
$721$	1.32671e6	+	431075.i	0.0950471	+	0.0308827i
$722$	−1.46145e7	+	1.06180e7i	−1.04337	+	0.758056i
$723$	−3.60971e6	+	1.17287e6i	−0.256819	+	0.0834455i
$724$		−	8.31127e6i		−	0.589279i
$725$	−9.01532e6	+	1.24085e7i	−0.636995	+	0.876748i
$726$	−3.72896e6	+	1.21161e6i	−0.262570	+	0.0853143i
$727$	1.88166e7	+	6.11389e6i	1.32040	+	0.429024i	0.882632	−	0.470064i	$-0.155769\pi$
$727$	1.88166e7	+	6.11389e6i	1.32040	+	0.429024i	0.437768	+	0.899088i	$0.355769\pi$
$728$	−441457.	+	1.35866e6i	−0.0308717	+	0.0950132i
$729$	7.26839e6			0.506547
$730$	−6.20191e6	+	1.90875e7i	−0.430743	+	1.32569i
$731$	−6.84364e6	−	9.41946e6i	−0.473689	−	0.651978i
$732$	145140.	−	199768.i	0.0100118	−	0.0137800i
$733$	4.60439e6	+	1.41708e7i	0.316528	+	0.974173i	0.975121	+	0.221673i	$0.0711519\pi$
$733$	4.60439e6	+	1.41708e7i	0.316528	+	0.974173i	−0.658593	+	0.752499i	$0.728848\pi$
$734$	5.14577e6	+	1.58370e7i	0.352541	+	1.08501i
$735$		−	5.76516e6i		−	0.393635i
$736$	792909.	+	576082.i	0.0539546	+	0.0392003i
$737$	−2.59202e7			−1.75780
$738$	−8.63408e6	−	4.04462e6i	−0.583546	−	0.273361i
$739$	999491.			0.0673237			0.0336618	−	0.999433i	$-0.489283\pi$
$739$	999491.			0.0673237			0.0336618	+	0.999433i	$0.489283\pi$
$740$	−7.64609e6	−	5.55521e6i	−0.513287	−	0.372925i
$741$			9.26799e6i			0.620069i
$742$	116298.	+	357929.i	0.00775467	+	0.0238664i
$743$	−3.67339e6	−	1.13055e7i	−0.244115	−	0.751309i	−0.995781	−	0.0917645i	$-0.970749\pi$
$743$	−3.67339e6	−	1.13055e7i	−0.244115	−	0.751309i	0.751666	−	0.659544i	$-0.229251\pi$
$744$	−1.30071e6	+	1.79028e6i	−0.0861488	+	0.118574i
$745$	1.07517e7	+	1.47985e7i	0.709719	+	0.976845i
$746$	1.59990e6	−	4.92398e6i	0.105256	−	0.323943i
$747$	−2.21898e7			−1.45497
$748$	2.93844e6	−	9.04359e6i	0.192027	−	0.590999i
$749$	−1.53675e6	−	499320.i	−0.100092	−	0.0325218i
$750$	239840.	−	77928.7i	0.0155693	−	0.00505876i
$751$	1.71898e7	−	2.36598e7i	1.11217	−	1.53077i	0.293993	−	0.955808i	$-0.405016\pi$
$751$	1.71898e7	−	2.36598e7i	1.11217	−	1.53077i	0.818178	−	0.574965i	$-0.194984\pi$
$752$		−	7.17462e6i		−	0.462652i
$753$	2.75109e6	−	893884.i	0.176814	−	0.0574505i
$754$	1.27002e7	−	9.22721e6i	0.813544	−	0.591074i
$755$	2.09632e7	+	6.81136e6i	1.33841	+	0.434877i
$756$	−825077.	−	599453.i	−0.0525037	−	0.0381462i
$757$	−4.54044e6	−	6.24938e6i	−0.287977	−	0.396367i	0.640378	−	0.768060i	$-0.278778\pi$
$757$	−4.54044e6	−	6.24938e6i	−0.287977	−	0.396367i	−0.928356	+	0.371693i	$0.878778\pi$
$758$	9.08936e6	−	6.60381e6i	0.574593	−	0.417466i
$759$	2.19296e6	−	1.59328e6i	0.138174	−	0.100389i
$760$	7.75366e6	+	1.06720e7i	0.486937	+	0.670211i
$761$	−2.42369e7	−	1.76091e7i	−1.51710	−	1.10224i	−0.962900	−	0.269858i	$-0.913023\pi$
$761$	−2.42369e7	−	1.76091e7i	−1.51710	−	1.10224i	−0.554203	−	0.832381i	$-0.686977\pi$
$762$	−1.21804e6	−	395764.i	−0.0759929	−	0.0246916i
$763$	−5.60749e6	+	4.07408e6i	−0.348704	+	0.253349i
$764$	5.87384e6	−	1.90852e6i	0.364073	−	0.118294i
$765$			1.68151e7i			1.03883i
$766$	−7.40861e6	+	1.01971e7i	−0.456210	+	0.627919i
$767$	−4.80485e6	+	1.56119e6i	−0.294911	+	0.0958224i
$768$	289335.	+	94010.6i	0.0177010	+	0.00575140i
$769$	8.26077e6	−	2.54240e7i	0.503738	−	1.55035i	−0.299144	−	0.954208i	$-0.596701\pi$
$769$	8.26077e6	−	2.54240e7i	0.503738	−	1.55035i	0.802882	−	0.596138i	$-0.203299\pi$
$770$	5.62362e6			0.341814
$771$	1.01942e6	−	3.13745e6i	0.0617614	−	0.190082i
$772$	6.02000e6	+	8.28583e6i	0.363541	+	0.500371i
$773$	−7.06226e6	+	9.72036e6i	−0.425104	+	0.585105i	−0.966821	−	0.255456i	$-0.917774\pi$
$773$	−7.06226e6	+	9.72036e6i	−0.425104	+	0.585105i	0.541717	+	0.840561i	$0.317774\pi$
$774$	3.27165e6	+	1.00691e7i	0.196297	+	0.604141i
$775$	6.79180e6	+	2.09030e7i	0.406192	+	1.25013i
$776$			9.67255e6i			0.576616i
$777$	841387.	+	611303.i	0.0499969	+	0.0363249i
$778$	−7.17930e6			−0.425239
$779$	−2.07817e7	−	1.94477e7i	−1.22698	−	1.14822i
$780$	4.37118e6			0.257254
$781$	1.45480e7	+	1.05698e7i	0.853448	+	0.620066i
$782$			3.72947e6i			0.218087i
$783$	3.46310e6	+	1.06583e7i	0.201865	+	0.621275i
$784$	1.26043e6	+	3.87921e6i	0.0732367	+	0.225400i
$785$	1.17835e7	−	1.62186e7i	0.682495	−	0.939374i
$786$	2.79244e6	+	3.84346e6i	0.161223	+	0.221904i
$787$	3.41058e6	−	1.04967e7i	0.196287	−	0.604108i	−0.803672	−	0.595072i	$-0.797124\pi$
$787$	3.41058e6	−	1.04967e7i	0.196287	−	0.604108i	0.999959	−	0.00903648i	$-0.00287644\pi$
$788$	1.44646e7			0.829832
$789$	1.68380e6	−	5.18219e6i	0.0962935	−	0.296361i
$790$	−4.44144e6	−	1.44311e6i	−0.253195	−	0.0822682i
$791$	−5.96242e6	+	1.93731e6i	−0.338830	+	0.110092i
$792$	−5.08241e6	+	6.99533e6i	−0.287910	+	0.396274i
$793$			2.51014e6i			0.141748i
$794$	1.98280e7	−	6.44250e6i	1.11616	−	0.362663i
$795$	931624.	−	676865.i	0.0522785	−	0.0379825i
$796$	1.16296e7	+	3.77868e6i	0.650550	+	0.211377i
$797$	6.46677e6	+	4.69838e6i	0.360613	+	0.262001i	0.753308	−	0.657668i	$-0.228457\pi$
$797$	6.46677e6	+	4.69838e6i	0.360613	+	0.262001i	−0.392695	+	0.919669i	$0.628457\pi$
$798$	−853224.	−	1.17436e6i	−0.0474303	−	0.0652822i
$799$	2.20871e7	−	1.60472e7i	1.22397	−	0.889266i
$800$	2.44451e6	−	1.77604e6i	0.135041	−	0.0981133i
$801$	3.22183e6	+	4.43447e6i	0.177428	+	0.244208i
$802$	−1.22335e7	−	8.88813e6i	−0.671604	−	0.487949i
$803$	−3.73493e7	−	1.21355e7i	−2.04406	−	0.664155i
$804$	2.55292e6	−	1.85481e6i	0.139283	−	0.101195i
$805$	−2.09766e6	+	681571.i	−0.114089	+	0.0370699i
$806$		−	2.24953e7i		−	1.21970i
$807$	−3.56455e6	+	4.90618e6i	−0.192673	+	0.265192i
$808$	2.92127e6	−	949178.i	0.157414	−	0.0511469i
$809$	2.90156e7	+	9.42774e6i	1.55869	+	0.506450i	0.956458	−	0.291870i	$-0.0942776\pi$
$809$	2.90156e7	+	9.42774e6i	1.55869	+	0.506450i	0.602234	+	0.798320i	$0.294278\pi$
$810$	4.22044e6	−	1.29892e7i	0.226019	−	0.695615i
$811$	−2.87079e7			−1.53267			−0.766335	−	0.642441i	$-0.777922\pi$
$811$	−2.87079e7			−1.53267			−0.766335	+	0.642441i	$0.777922\pi$
$812$	−759788.	+	2.33839e6i	−0.0404392	+	0.124459i
$813$	−5.51631e6	−	7.59255e6i	−0.292700	−	0.402866i
$814$	1.08701e7	−	1.49614e7i	0.575006	−	0.791428i
$815$	−4.35304e6	−	1.33973e7i	−0.229561	−	0.706517i
$816$	357732.	+	1.10099e6i	0.0188076	+	0.0578838i
$817$			3.16049e7i			1.65653i
$818$	1.86483e7	+	1.35488e7i	0.974440	+	0.707972i
$819$	4.94315e6			0.257510
$820$	−9.17234e6	+	9.80155e6i	−0.476371	+	0.509050i
$821$	−3.11657e7			−1.61369			−0.806843	−	0.590766i	$-0.798826\pi$
$821$	−3.11657e7			−1.61369			−0.806843	+	0.590766i	$0.798826\pi$
$822$	−3.67392e6	−	2.66926e6i	−0.189649	−	0.137788i
$823$		−	1.14863e7i		−	0.591126i	−0.955323	−	0.295563i	$-0.904493\pi$
$823$		−	1.14863e7i		−	0.591126i	0.955323	−	0.295563i	$-0.0955072\pi$
$824$	933191.	+	2.87207e6i	0.0478798	+	0.147359i
$825$	−2.58240e6	−	7.94782e6i	−0.132096	−	0.406549i
$826$	465105.	−	640162.i	0.0237192	−	0.0326467i
$827$	9.25277e6	+	1.27353e7i	0.470444	+	0.647510i	0.976633	−	0.214912i	$-0.0689464\pi$
$827$	9.25277e6	+	1.27353e7i	0.470444	+	0.647510i	−0.506190	+	0.862422i	$0.668946\pi$
$828$	1.04796e6	−	3.22530e6i	0.0531214	−	0.163491i
$829$	5.40550e6			0.273180			0.136590	−	0.990628i	$-0.456386\pi$
$829$	5.40550e6			0.273180			0.136590	+	0.990628i	$0.456386\pi$
$830$	−9.65427e6	+	2.97128e7i	−0.486434	+	1.49709i
$831$	850910.	+	276477.i	0.0427446	+	0.0138886i
$832$	−2.94124e6	+	955666.i	−0.147306	+	0.0478627i
$833$	−9.12298e6	+	1.25567e7i	−0.455538	+	0.626994i
$834$		−	4.24844e6i		−	0.211502i
$835$	−64336.9	+	20904.3i	−0.00319333	+	0.00103758i
$836$	−2.08823e7	+	1.51719e7i	−1.03339	+	0.750799i
$837$	1.52732e7	+	4.96255e6i	0.753556	+	0.244845i
$838$	6.35809e6	+	4.61942e6i	0.312764	+	0.227236i
$839$	1.67633e7	+	2.30727e7i	0.822157	+	1.13160i	0.989333	+	0.145675i	$0.0465354\pi$
$839$	1.67633e7	+	2.30727e7i	0.822157	+	1.13160i	−0.167175	+	0.985927i	$0.553465\pi$
$840$	−553879.	+	402417.i	−0.0270842	+	0.0196779i
$841$	5.26429e6	−	3.82473e6i	0.256655	−	0.186471i
$842$	2.39554e6	+	3.29717e6i	0.116445	+	0.160273i
$843$	5.15352e6	+	3.74425e6i	0.249767	+	0.181466i
$844$	3.34308e6	+	1.08623e6i	0.161544	+	0.0524888i
$845$	−1.25349e7	+	9.10715e6i	−0.603920	+	0.438774i
$846$	−2.36104e7	+	7.67147e6i	−1.13417	+	0.368513i
$847$			6.24265e6i			0.298993i
$848$	−478880.	+	659122.i	−0.0228685	+	0.0314758i
$849$	−2.00252e6	+	650659.i	−0.0953472	+	0.0309802i
$850$	1.09351e7	+	3.55302e6i	0.519128	+	0.168675i
$851$	−2.24135e6	+	6.89816e6i	−0.106093	+	0.326520i
$852$	−2.18921e6			−0.103321
$853$	7.69217e6	−	2.36741e7i	0.361973	−	1.11404i	−0.589882	−	0.807490i	$-0.700826\pi$
$853$	7.69217e6	−	2.36741e7i	0.361973	−	1.11404i	0.951855	−	0.306549i	$-0.0991743\pi$
$854$	−231087.	−	318064.i	−0.0108425	−	0.0149235i
$855$	2.68290e7	−	3.69269e7i	1.25513	−	1.72754i
$856$	−1.08093e6	−	3.32676e6i	−0.0504211	−	0.155180i
$857$	3.06779e6	+	9.44169e6i	0.142684	+	0.439135i	0.996706	−	0.0811016i	$-0.0258438\pi$
$857$	3.06779e6	+	9.44169e6i	0.142684	+	0.439135i	−0.854022	+	0.520236i	$0.825844\pi$
$858$			8.55325e6i			0.396655i
$859$	−6.71172e6	−	4.87635e6i	−0.310349	−	0.225482i	0.421697	−	0.906737i	$-0.361435\pi$
$859$	−6.71172e6	−	4.87635e6i	−0.310349	−	0.225482i	−0.732046	+	0.681255i	$0.761435\pi$
$860$	1.49062e7			0.687260
$861$	1.00934e6	−	1.07858e6i	0.0464011	−	0.0495842i
$862$	−302852.			−0.0138823
$863$	1.11820e7	+	8.12420e6i	0.511084	+	0.371325i	0.813235	−	0.581936i	$-0.197704\pi$
$863$	1.11820e7	+	8.12420e6i	0.511084	+	0.371325i	−0.302150	+	0.953260i	$0.597704\pi$
$864$		−	2.20777e6i		−	0.100617i
$865$	1.43980e7	+	4.43124e7i	0.654276	+	2.01366i
$866$	2.27413e6	+	6.99904e6i	0.103043	+	0.317135i
$867$	1.28490e6	−	1.76851e6i	0.0580526	−	0.0799025i
$868$	2.07095e6	+	2.85042e6i	0.0932975	+	0.128413i
$869$	2.82379e6	−	8.69073e6i	0.126848	−	0.390397i
$870$	7.52320e6			0.336980
$871$	−9.91270e6	+	3.05081e7i	−0.442738	+	1.36261i
$872$	−1.42704e7	−	4.63672e6i	−0.635542	−	0.206500i
$873$	3.18306e7	−	1.03424e7i	1.41354	−	0.459288i
$874$	5.95048e6	−	8.19013e6i	0.263496	−	0.362671i
$875$		−	401516.i		−	0.0177290i
$876$	4.54698e6	−	1.47740e6i	0.200200	−	0.0650488i
$877$	9.22856e6	−	6.70494e6i	0.405168	−	0.294372i	−0.366475	−	0.930428i	$-0.619435\pi$
$877$	9.22856e6	−	6.70494e6i	0.405168	−	0.294372i	0.771643	+	0.636056i	$0.219435\pi$
$878$	−1.73853e7	−	5.64884e6i	−0.761109	−	0.247299i
$879$	−405657.	−	294727.i	−0.0177087	−	0.0128661i
$880$	7.15570e6	+	9.84898e6i	0.311491	+	0.428731i
$881$	2.07487e7	−	1.50748e7i	0.900639	−	0.654353i	−0.0379911	−	0.999278i	$-0.512096\pi$
$881$	2.07487e7	−	1.50748e7i	0.900639	−	0.654353i	0.938630	+	0.344926i	$0.112096\pi$
$882$	1.14181e7	−	8.29570e6i	0.494220	−	0.359072i
$883$	1.35469e6	+	1.86457e6i	0.0584707	+	0.0804780i	0.837251	−	0.546819i	$-0.184161\pi$
$883$	1.35469e6	+	1.86457e6i	0.0584707	+	0.0804780i	−0.778780	+	0.627297i	$0.784161\pi$
$884$	−9.52056e6	−	6.91709e6i	−0.409762	−	0.297710i
$885$	−2.30266e6	−	748181.i	−0.0988263	−	0.0321106i
$886$	−1.30150e7	+	9.45598e6i	−0.557008	+	0.404690i
$887$	3.46692e7	−	1.12647e7i	1.47957	−	0.480741i	0.545584	−	0.838056i	$-0.316308\pi$
$887$	3.46692e7	−	1.12647e7i	1.47957	−	0.480741i	0.933984	+	0.357316i	$0.116308\pi$
$888$			2.25142e6i			0.0958127i
$889$	−1.19856e6	+	1.64968e6i	−0.0508636	+	0.0700077i
$890$	7.33961e6	−	2.38479e6i	0.310598	−	0.100919i
$891$	2.54164e7	+	8.25829e6i	1.07256	+	0.348494i
$892$	−48409.7	+	148990.i	−0.00203714	+	0.00626966i
$893$	−7.41082e7			−3.10984
$894$	1.34653e6	−	4.14418e6i	0.0563471	−	0.173418i
$895$	−7.30460e6	−	1.00539e7i	−0.304817	−	0.419544i
$896$	284709.	−	391868.i	0.0118476	−	0.0163068i
$897$	−1.03664e6	−	3.19044e6i	−0.0430175	−	0.132394i
$898$	1.06367e6	+	3.27363e6i	0.0440164	+	0.135469i
$899$		−	3.87165e7i		−	1.59771i
$900$	−8.45842e6	−	6.14540e6i	−0.348083	−	0.252897i
$901$	−3.10020e6			−0.127227
$902$	−1.91791e7	−	1.79479e7i	−0.784894	−	0.734508i
$903$	−1.64030e6			−0.0669429
$904$	−1.09797e7	−	7.97724e6i	−0.446859	−	0.324662i
$905$			4.04900e7i			1.64334i
$906$	−1.62259e6	−	4.99381e6i	−0.0656731	−	0.202121i
$907$	−9.51329e6	−	2.92789e7i	−0.383983	−	1.18178i	−0.937215	−	0.348752i	$-0.886606\pi$
$907$	−9.51329e6	−	2.92789e7i	−0.383983	−	1.18178i	0.553232	−	0.833027i	$-0.313394\pi$
$908$	7.92062e6	−	1.09018e7i	0.318819	−	0.438817i
$909$	−6.24715e6	−	8.59846e6i	−0.250768	−	0.345152i
$910$	2.15065e6	−	6.61901e6i	0.0860925	−	0.264965i
$911$	1.33690e7			0.533709			0.266854	−	0.963737i	$-0.414016\pi$
$911$	1.33690e7			0.533709			0.266854	+	0.963737i	$0.414016\pi$
$912$	971056.	−	2.98860e6i	0.0386596	−	0.118982i
$913$	−5.81401e7	−	1.88909e7i	−2.30834	−	0.750024i
$914$	2.87771e7	−	9.35025e6i	1.13941	−	0.370218i
$915$	−707080.	+	973212.i	−0.0279200	+	0.0384286i
$916$		−	2.48219e6i		−	0.0977453i
$917$	7.19381e6	−	2.33741e6i	0.282511	−	0.0917935i
$918$	6.79662e6	−	4.93804e6i	0.266187	−	0.193396i
$919$	3.71894e7	+	1.20836e7i	1.45255	+	0.471961i	0.925784	−	0.378052i	$-0.123406\pi$
$919$	3.71894e7	+	1.20836e7i	1.45255	+	0.471961i	0.526762	+	0.850013i	$0.323406\pi$
$920$	−3.86281e6	−	2.80650e6i	−0.150465	−	0.109319i
$921$	3.80928e6	+	5.24302e6i	0.147977	+	0.203673i
$922$	−6.57611e6	+	4.77783e6i	−0.254766	+	0.185099i
$923$	1.80043e7	−	1.30809e7i	0.695618	−	0.505396i
$924$	−787424.	−	1.08380e6i	−0.0303409	−	0.0417607i
$925$	1.80906e7	+	1.31436e7i	0.695183	+	0.505080i
$926$	−1.73130e7	−	5.62532e6i	−0.663504	−	0.215586i
$927$	8.45363e6	−	6.14192e6i	0.323105	−	0.234750i
$928$	−5.06214e6	+	1.64479e6i	−0.192959	+	0.0626961i
$929$		−	3.66054e7i		−	1.39157i	−0.718248	−	0.695787i	$-0.755056\pi$
$929$		−	3.66054e7i		−	1.39157i	0.718248	−	0.695787i	$-0.244944\pi$
$930$	6.33668e6	−	8.72170e6i	0.240245	−	0.330669i
$931$	4.00692e7	−	1.30193e7i	1.51508	−	0.492280i
$932$	−5.52891e6	−	1.79645e6i	−0.208497	−	0.0677447i
$933$	1.37958e6	−	4.24593e6i	0.0518853	−	0.159687i
$934$	−2.78446e6			−0.104441
$935$	−1.43152e7	+	4.40577e7i	−0.535511	+	1.64813i
$936$	6.28984e6	+	8.65723e6i	0.234666	+	0.322990i
$937$	9.84833e6	−	1.35551e7i	0.366449	−	0.504374i	−0.585482	−	0.810685i	$-0.699095\pi$
$937$	9.84833e6	−	1.35551e7i	0.366449	−	0.504374i	0.951931	+	0.306311i	$0.0990949\pi$
$938$	−1.55257e6	−	4.77831e6i	−0.0576161	−	0.177324i
$939$	−2.39396e6	−	7.36784e6i	−0.0886038	−	0.272694i
$940$			3.49526e7i			1.29021i
$941$	2.28557e7	+	1.66056e7i	0.841433	+	0.611337i	0.922771	−	0.385350i	$-0.125919\pi$
$941$	2.28557e7	+	1.66056e7i	0.841433	+	0.611337i	−0.0813376	+	0.996687i	$0.525919\pi$
$942$	−4.77561e6			−0.175348
$943$	9.32920e6	+	4.37025e6i	0.341637	+	0.160039i
$944$	1.71297e6			0.0625633
$945$	4.01952e6	+	2.92036e6i	0.146418	+	0.106379i
$946$			2.91676e7i			1.05967i
$947$	6.62207e6	+	2.03806e7i	0.239949	+	0.738487i	0.996426	+	0.0844673i	$0.0269188\pi$
$947$	6.62207e6	+	2.03806e7i	0.239949	+	0.738487i	−0.756477	+	0.654020i	$0.773081\pi$
$948$	343774.	+	1.05803e6i	0.0124238	+	0.0382364i
$949$	−2.85670e7	+	3.93191e7i	−1.02967	+	1.41722i
$950$	−1.83451e7	−	2.52499e7i	−0.659495	−	0.907717i
$951$	1.53409e6	−	4.72145e6i	0.0550047	−	0.169287i
$952$	1.84316e6			0.0659131
$953$	−5.16453e6	+	1.58948e7i	−0.184204	+	0.566921i	−0.999934	−	0.0115121i	$-0.996336\pi$
$953$	−5.16453e6	+	1.58948e7i	−0.184204	+	0.566921i	0.815730	+	0.578433i	$0.196336\pi$
$954$	2.68109e6	+	871141.i	0.0953765	+	0.0309897i
$955$	−2.86156e7	+	9.29776e6i	−1.01530	+	0.329891i
$956$	6.00151e6	−	8.26037e6i	0.212381	−	0.292317i
$957$			1.47209e7i			0.519584i
$958$	1.29010e7	−	4.19178e6i	0.454160	−	0.147566i
$959$	−5.84949e6	+	4.24991e6i	−0.205386	+	0.149222i
$960$	−1.40955e6	−	457991.i	−0.0493632	−	0.0160391i
$961$	−2.17228e7	−	1.57826e7i	−0.758767	−	0.551276i
$962$	−1.34525e7	−	1.85158e7i	−0.468669	−	0.645067i
$963$	−9.79196e6	+	7.11428e6i	−0.340255	+	0.247209i
$964$	−1.05835e7	+	7.68937e6i	−0.366807	+	0.266501i
$965$	−2.93276e7	−	4.03660e7i	−1.01382	−	1.39540i
$966$	425070.	+	308831.i	0.0146561	+	0.0106483i
$967$	−3.90689e7	−	1.26942e7i	−1.34358	−	0.436557i	−0.453054	−	0.891483i	$-0.649666\pi$
$967$	−3.90689e7	−	1.26942e7i	−1.34358	−	0.436557i	−0.890529	+	0.454926i	$0.849666\pi$
$968$	−1.09331e7	+	7.94338e6i	−0.375021	+	0.272469i
$969$	1.13723e7	−	3.69510e6i	0.389081	−	0.126420i
$970$		−	4.71218e7i		−	1.60802i
$971$	−1.76507e7	+	2.42942e7i	−0.600779	+	0.826902i	−0.995779	−	0.0917793i	$-0.970745\pi$
$971$	−1.76507e7	+	2.42942e7i	−0.600779	+	0.826902i	0.395000	+	0.918681i	$0.370745\pi$
$972$	−1.10666e7	+	3.59576e6i	−0.375707	+	0.122074i
$973$	−6.43315e6	−	2.09026e6i	−0.217842	−	0.0707811i
$974$	−5.96068e6	+	1.83451e7i	−0.201325	+	0.619616i
$975$	−1.03422e7			−0.348418
$976$	263001.	−	809434.i	0.00883757	−	0.0271992i
$977$	6.36645e6	+	8.76266e6i	0.213383	+	0.293697i	0.902270	−	0.431173i	$-0.141900\pi$
$977$	6.36645e6	+	8.76266e6i	0.213383	+	0.293697i	−0.688886	+	0.724870i	$0.741900\pi$
$978$	−1.97244e6	+	2.71483e6i	−0.0659410	+	0.0907600i
$979$	4.66640e6	+	1.43617e7i	0.155606	+	0.478905i
$980$	−6.14044e6	−	1.88983e7i	−0.204237	−	0.628577i
$981$			5.19190e7i			1.72248i
$982$	−5.85504e6	−	4.25393e6i	−0.193754	−	0.140771i
$983$	−1.31263e7			−0.433271			−0.216636	−	0.976253i	$-0.569508\pi$
$983$	−1.31263e7			−0.433271			−0.216636	+	0.976253i	$0.569508\pi$
$984$	3.17329e6	+	395292.i	0.104477	+	0.0130146i
$985$	−7.04670e7			−2.31417
$986$	−1.63858e7	−	1.19050e7i	−0.536753	−	0.389974i
$987$		−	3.84623e6i		−	0.125673i
$988$	9.87128e6	+	3.03807e7i	0.321722	+	0.990159i
$989$	−3.53505e6	−	1.08798e7i	−0.114922	−	0.353695i
$990$	2.47600e7	−	3.40791e7i	0.802901	−	1.10510i
$991$	5.36998e6	+	7.39114e6i	0.173695	+	0.239071i	0.886985	−	0.461798i	$-0.152796\pi$
$991$	5.36998e6	+	7.39114e6i	0.173695	+	0.239071i	−0.713290	+	0.700869i	$0.752796\pi$
$992$	−2.35695e6	+	7.25395e6i	−0.0760452	+	0.234043i
$993$	−8.86696e6			−0.285366
$994$	−1.07711e6	+	3.31499e6i	−0.0345774	+	0.106418i
$995$	−5.66558e7	−	1.84086e7i	−1.81420	−	0.589471i
$996$	7.07811e6	−	2.29982e6i	0.226084	−	0.0734590i
$997$	−1.15548e7	+	1.59038e7i	−0.368149	+	0.506713i	−0.952397	−	0.304862i	$-0.901390\pi$
$997$	−1.15548e7	+	1.59038e7i	−0.368149	+	0.506713i	0.584248	+	0.811575i	$0.301390\pi$
$998$			1.14718e7i			0.364589i
$999$	1.55390e7	−	5.04891e6i	0.492616	−	0.160061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.f.b.31.7	✓	40
41.4	even	10	inner	82.6.f.b.45.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.f.b.31.7	✓	40	1.1	even	1	trivial
82.6.f.b.45.4	yes	40	41.4	even	10	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.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +4.64210i q^{3} +(4.94427 + 15.2169i) q^{4} +(-24.0870 - 74.1322i) q^{5} +(-10.9142 + 15.0221i) q^{6} +(17.3773 + 23.9177i) q^{7} +(-19.7771 + 60.8676i) q^{8} +221.451 q^{9} +(96.3480 - 296.529i) q^{10} +(580.229 + 188.528i) q^{11} +(-70.6384 + 22.9518i) q^{12} +(443.795 - 610.831i) q^{13} +118.256i q^{14} +(344.129 - 111.814i) q^{15} +(-207.108 + 150.473i) q^{16} +(-926.462 - 301.026i) q^{17} +(716.630 + 520.662i) q^{18} +(1554.27 + 2139.27i) q^{19} +(1008.97 - 733.059i) q^{20} +(-111.028 + 80.6669i) q^{21} +(1434.41 + 1974.29i) q^{22} +(-774.325 - 562.580i) q^{23} +(-282.553 - 91.8072i) q^{24} +(-2387.22 + 1734.41i) q^{25} +(2872.30 - 933.267i) q^{26} +2156.03i q^{27} +(-278.036 + 382.684i) q^{28} +(4943.50 - 1606.24i) q^{29} +(1376.52 + 447.257i) q^{30} +(2301.71 - 7083.94i) q^{31} -1024.00 q^{32} +(-875.165 + 2693.48i) q^{33} +(-2290.34 - 3152.38i) q^{34} +(1354.51 - 1864.32i) q^{35} +(1094.91 + 3369.80i) q^{36} +(-2341.77 - 7207.22i) q^{37} +10577.1i q^{38} +(2835.54 + 2060.14i) q^{39} +4988.62 q^{40} +(-10569.5 + 2035.24i) q^{41} -548.955 q^{42} +(9669.52 + 7025.31i) q^{43} +9761.42i q^{44} +(-5334.09 - 16416.6i) q^{45} +(-1183.06 - 3641.10i) q^{46} +(-16473.2 + 22673.4i) q^{47} +(-698.511 - 961.417i) q^{48} +(4923.56 - 15153.2i) q^{49} -11803.1 q^{50} +(1397.39 - 4300.73i) q^{51} +(11489.2 + 3733.07i) q^{52} +(3026.74 - 983.446i) q^{53} +(-5069.12 + 6977.05i) q^{54} -47554.7i q^{55} +(-1799.49 + 584.689i) q^{56} +(-9930.69 + 7215.07i) q^{57} +(19774.0 + 6424.96i) q^{58} +(-5413.36 - 3933.04i) q^{59} +(3402.93 + 4683.74i) q^{60} +(-2689.63 + 1954.13i) q^{61} +(24103.8 - 17512.5i) q^{62} +(3848.21 + 5296.60i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-55971.9 - 18186.4i) q^{65} +(-9164.85 + 6658.65i) q^{66} +(-40406.6 + 13128.9i) q^{67} -15586.2i q^{68} +(2611.55 - 3594.49i) q^{69} +(8766.56 - 2848.43i) q^{70} +(28032.4 + 9108.28i) q^{71} +(-4379.65 + 13479.2i) q^{72} -64369.9 q^{73} +(9367.07 - 28828.9i) q^{74} +(-8051.33 - 11081.7i) q^{75} +(-24868.3 + 34228.3i) q^{76} +(5573.63 + 17153.9i) q^{77} +(4332.32 + 13333.5i) q^{78} -14978.1i q^{79} +(16143.5 + 11728.9i) q^{80} +43804.1 q^{81} +(-38988.7 - 18264.2i) q^{82} -100202. q^{83} +(-1776.46 - 1290.67i) q^{84} +75931.5i q^{85} +(14773.7 + 45468.8i) q^{86} +(7456.32 + 22948.2i) q^{87} +(-22950.5 + 31588.6i) q^{88} +(14548.7 + 20024.6i) q^{89} +(21336.4 - 65666.6i) q^{90} +22321.6 q^{91} +(4732.25 - 14564.4i) q^{92} +(32884.3 + 10684.8i) q^{93} +(-106617. + 34641.9i) q^{94} +(121151. - 166750. i) q^{95} -4753.51i q^{96} +(143737. - 46702.9i) q^{97} +(51560.2 - 37460.7i) q^{98} +(128492. + 41749.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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